LMFDB - Embedded newform 140.2.w.b.23.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(23,140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("140.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.10
Character	$\chi$	$=$	140.23
Dual form			140.2.w.b.67.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0450897 - 1.41349i) q^{2} +(-2.02821 - 0.543458i) q^{3} +(-1.99593 + 0.127468i) q^{4} +(-0.518800 + 2.17505i) q^{5} +(-0.676724 + 2.89137i) q^{6} +(-2.64471 + 0.0742486i) q^{7} +(0.270171 + 2.81549i) q^{8} +(1.22023 + 0.704499i) q^{9} +(3.09782 + 0.635249i) q^{10} +(0.366133 - 0.211387i) q^{11} +(4.11745 + 0.826174i) q^{12} +(-1.56422 - 1.56422i) q^{13} +(0.224199 + 3.73493i) q^{14} +(2.23429 - 4.12952i) q^{15} +(3.96750 - 0.508836i) q^{16} +(-4.41198 - 1.18219i) q^{17} +(0.940785 - 1.75655i) q^{18} +(-3.66683 + 6.35114i) q^{19} +(0.758241 - 4.40739i) q^{20} +(5.40439 + 1.28670i) q^{21} +(-0.315303 - 0.507996i) q^{22} +(-1.72616 - 6.44210i) q^{23} +(0.982138 - 5.85725i) q^{24} +(-4.46169 - 2.25683i) q^{25} +(-2.14049 + 2.28155i) q^{26} +(2.36225 + 2.36225i) q^{27} +(5.26920 - 0.485311i) q^{28} -4.72835i q^{29} +(-5.93780 - 2.97195i) q^{30} +(1.70170 - 0.982474i) q^{31} +(-0.898130 - 5.58510i) q^{32} +(-0.857477 + 0.229760i) q^{33} +(-1.47208 + 6.28961i) q^{34} +(1.21058 - 5.79090i) q^{35} +(-2.52529 - 1.25059i) q^{36} +(1.92971 + 7.20177i) q^{37} +(9.14263 + 4.89667i) q^{38} +(2.32248 + 4.02266i) q^{39} +(-6.26401 - 0.873042i) q^{40} -4.01882 q^{41} +(1.57506 - 7.69709i) q^{42} +(-1.88664 + 1.88664i) q^{43} +(-0.703833 + 0.468585i) q^{44} +(-2.16537 + 2.28856i) q^{45} +(-9.02804 + 2.73038i) q^{46} +(6.35786 - 1.70358i) q^{47} +(-8.32348 - 1.12414i) q^{48} +(6.98897 - 0.392732i) q^{49} +(-2.98885 + 6.40834i) q^{50} +(8.30597 + 4.79545i) q^{51} +(3.32147 + 2.92269i) q^{52} +(-0.209015 + 0.780053i) q^{53} +(3.23251 - 3.44554i) q^{54} +(0.269828 + 0.906026i) q^{55} +(-0.923572 - 7.42610i) q^{56} +(10.8887 - 10.8887i) q^{57} +(-6.68350 + 0.213200i) q^{58} +(-1.35717 - 2.35069i) q^{59} +(-3.93311 + 8.52705i) q^{60} +(0.925760 - 1.60346i) q^{61} +(-1.46545 - 2.36104i) q^{62} +(-3.27945 - 1.77259i) q^{63} +(-7.85401 + 1.52133i) q^{64} +(4.21378 - 2.59074i) q^{65} +(0.363428 + 1.20168i) q^{66} +(-2.33152 + 8.70137i) q^{67} +(8.95671 + 1.79718i) q^{68} +14.0041i q^{69} +(-8.23999 - 1.45004i) q^{70} +3.16317i q^{71} +(-1.65384 + 3.62588i) q^{72} +(-1.78752 + 6.67113i) q^{73} +(10.0927 - 3.05236i) q^{74} +(7.82277 + 7.00208i) q^{75} +(6.50918 - 13.1438i) q^{76} +(-0.952621 + 0.586243i) q^{77} +(5.58129 - 3.46420i) q^{78} +(-1.77995 + 3.08296i) q^{79} +(-0.951598 + 8.89351i) q^{80} +(-5.62086 - 9.73561i) q^{81} +(0.181207 + 5.68058i) q^{82} +(-4.71846 + 4.71846i) q^{83} +(-10.9508 - 1.87928i) q^{84} +(4.86025 - 8.98296i) q^{85} +(2.75182 + 2.58169i) q^{86} +(-2.56966 + 9.59011i) q^{87} +(0.694078 + 0.973735i) q^{88} +(-10.0333 - 5.79271i) q^{89} +(3.33251 + 2.95755i) q^{90} +(4.25305 + 4.02077i) q^{91} +(4.26646 + 12.6380i) q^{92} +(-3.98534 + 1.06787i) q^{93} +(-2.69468 - 8.90999i) q^{94} +(-11.9117 - 11.2705i) q^{95} +(-1.21367 + 11.8159i) q^{96} +(-4.64008 + 4.64008i) q^{97} +(-0.870255 - 9.86117i) q^{98} +0.595688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100}) $ 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.0450897	−	1.41349i	−0.0318832	−	0.999492i
$2$	−0.0450897	−	1.41349i	−0.0318832	−	0.999492i
$3$	−2.02821	−	0.543458i	−1.17099	−	0.313766i	−0.379643	−	0.925133i	$-0.623953\pi$
$3$	−2.02821	−	0.543458i	−1.17099	−	0.313766i	−0.791347	+	0.611367i	$0.790620\pi$
$4$	−1.99593	+	0.127468i	−0.997967	+	0.0637340i
$5$	−0.518800	+	2.17505i	−0.232014	+	0.972712i
$5$	−0.518800	+	2.17505i	−0.232014	+	0.972712i
$6$	−0.676724	+	2.89137i	−0.276271	+	1.18040i
$7$	−2.64471	+	0.0742486i	−0.999606	+	0.0280633i
$7$	−2.64471	+	0.0742486i	−0.999606	+	0.0280633i
$8$	0.270171	+	2.81549i	0.0955200	+	0.995428i
$9$	1.22023	+	0.704499i	0.406742	+	0.234833i
$10$	3.09782	+	0.635249i	0.979615	+	0.200883i
$11$	0.366133	−	0.211387i	0.110393	−	0.0637356i	−0.443787	−	0.896132i	$-0.646365\pi$
$11$	0.366133	−	0.211387i	0.110393	−	0.0637356i	0.554180	+	0.832397i	$0.313032\pi$
$12$	4.11745	+	0.826174i	1.18861	+	0.238496i
$13$	−1.56422	−	1.56422i	−0.433837	−	0.433837i	0.456095	−	0.889931i	$-0.349248\pi$
$13$	−1.56422	−	1.56422i	−0.433837	−	0.433837i	−0.889931	+	0.456095i	$0.849248\pi$
$14$	0.224199	+	3.73493i	0.0599197	+	0.998203i
$15$	2.23429	−	4.12952i	0.576890	−	1.06624i
$16$	3.96750	−	0.508836i	0.991876	−	0.127209i
$17$	−4.41198	−	1.18219i	−1.07006	−	0.286722i	−0.319544	−	0.947572i	$-0.603530\pi$
$17$	−4.41198	−	1.18219i	−1.07006	−	0.286722i	−0.750519	+	0.660849i	$0.770196\pi$
$18$	0.940785	−	1.75655i	0.221745	−	0.414023i
$19$	−3.66683	+	6.35114i	−0.841228	+	1.45705i	0.0476283	+	0.998865i	$0.484834\pi$
$19$	−3.66683	+	6.35114i	−0.841228	+	1.45705i	−0.888857	+	0.458185i	$0.848500\pi$
$20$	0.758241	−	4.40739i	0.169548	−	0.985522i
$21$	5.40439	+	1.28670i	1.17933	+	0.280780i
$22$	−0.315303	−	0.507996i	−0.0672229	−	0.108305i
$23$	−1.72616	−	6.44210i	−0.359928	−	1.34327i	−0.874168	−	0.485624i	$-0.838592\pi$
$23$	−1.72616	−	6.44210i	−0.359928	−	1.34327i	0.514239	−	0.857647i	$-0.328074\pi$
$24$	0.982138	−	5.85725i	0.200478	−	1.19561i
$25$	−4.46169	−	2.25683i	−0.892339	−	0.451367i
$26$	−2.14049	+	2.28155i	−0.419784	+	0.447448i
$27$	2.36225	+	2.36225i	0.454615	+	0.454615i
$28$	5.26920	−	0.485311i	0.995785	−	0.0917152i
$29$		−	4.72835i		−	0.878033i	−0.898479	−	0.439016i	$-0.855327\pi$
$29$		−	4.72835i		−	0.878033i	0.898479	−	0.439016i	$-0.144673\pi$
$30$	−5.93780	−	2.97195i	−1.08409	−	0.542602i
$31$	1.70170	−	0.982474i	0.305634	−	0.176458i	−0.339337	−	0.940665i	$-0.610203\pi$
$31$	1.70170	−	0.982474i	0.305634	−	0.176458i	0.644971	+	0.764207i	$0.276869\pi$
$32$	−0.898130	−	5.58510i	−0.158768	−	0.987316i
$33$	−0.857477	+	0.229760i	−0.149268	+	0.0399961i
$34$	−1.47208	+	6.28961i	−0.252459	+	1.07866i
$35$	1.21058	−	5.79090i	0.204626	−	0.978840i
$36$	−2.52529	−	1.25059i	−0.420882	−	0.208432i
$37$	1.92971	+	7.20177i	0.317242	+	1.18396i	0.921884	+	0.387467i	$0.126650\pi$
$37$	1.92971	+	7.20177i	0.317242	+	1.18396i	−0.604641	+	0.796498i	$0.706684\pi$
$38$	9.14263	+	4.89667i	1.48313	+	0.794345i
$39$	2.32248	+	4.02266i	0.371895	+	0.644141i
$40$	−6.26401	−	0.873042i	−0.990427	−	0.138040i
$41$	−4.01882			−0.627634			−0.313817	−	0.949483i	$-0.601608\pi$
$41$	−4.01882			−0.627634			−0.313817	+	0.949483i	$0.601608\pi$
$42$	1.57506	−	7.69709i	0.243037	−	1.18769i
$43$	−1.88664	+	1.88664i	−0.287710	+	0.287710i	−0.836174	−	0.548464i	$-0.815213\pi$
$43$	−1.88664	+	1.88664i	−0.287710	+	0.287710i	0.548464	+	0.836174i	$0.315213\pi$
$44$	−0.703833	+	0.468585i	−0.106107	+	0.0706419i
$45$	−2.16537	+	2.28856i	−0.322795	+	0.341159i
$46$	−9.02804	+	2.73038i	−1.33111	+	0.402573i
$47$	6.35786	−	1.70358i	0.927389	−	0.248493i	0.236648	−	0.971595i	$-0.423951\pi$
$47$	6.35786	−	1.70358i	0.927389	−	0.248493i	0.690741	+	0.723102i	$0.257284\pi$
$48$	−8.32348	−	1.12414i	−1.20139	−	0.162256i
$49$	6.98897	−	0.392732i	0.998425	−	0.0561046i
$50$	−2.98885	+	6.40834i	−0.422687	+	0.906276i
$51$	8.30597	+	4.79545i	1.16307	+	0.671498i
$52$	3.32147	+	2.92269i	0.460605	+	0.405304i
$53$	−0.209015	+	0.780053i	−0.0287104	+	0.107149i	−0.978794	−	0.204846i	$-0.934331\pi$
$53$	−0.209015	+	0.780053i	−0.0287104	+	0.107149i	0.950084	+	0.311995i	$0.100997\pi$
$54$	3.23251	−	3.44554i	0.439889	−	0.468879i
$55$	0.269828	+	0.906026i	0.0363836	+	0.122169i
$56$	−0.923572	−	7.42610i	−0.123417	−	0.992355i
$57$	10.8887	−	10.8887i	1.44224	−	1.44224i
$58$	−6.68350	+	0.213200i	−0.877586	+	0.0279945i
$59$	−1.35717	−	2.35069i	−0.176689	−	0.306034i	0.764056	−	0.645151i	$-0.223205\pi$
$59$	−1.35717	−	2.35069i	−0.176689	−	0.306034i	−0.940744	+	0.339116i	$0.889872\pi$
$60$	−3.93311	+	8.52705i	−0.507762	+	1.10084i
$61$	0.925760	−	1.60346i	0.118531	−	0.205302i	−0.800654	−	0.599126i	$-0.795515\pi$
$61$	0.925760	−	1.60346i	0.118531	−	0.205302i	0.919186	+	0.393824i	$0.128848\pi$
$62$	−1.46545	−	2.36104i	−0.186112	−	0.299852i
$63$	−3.27945	−	1.77259i	−0.413172	−	0.223326i
$64$	−7.85401	+	1.52133i	−0.981752	+	0.190167i
$65$	4.21378	−	2.59074i	0.522655	−	0.321342i
$66$	0.363428	+	1.20168i	0.0447349	+	0.147916i
$67$	−2.33152	+	8.70137i	−0.284841	+	1.06304i	0.664114	+	0.747631i	$0.268809\pi$
$67$	−2.33152	+	8.70137i	−0.284841	+	1.06304i	−0.948955	+	0.315410i	$0.897858\pi$
$68$	8.95671	+	1.79718i	1.08616	+	0.217940i
$69$			14.0041i			1.68589i
$70$	−8.23999	−	1.45004i	−0.984867	−	0.173313i
$71$			3.16317i			0.375400i	0.982226	+	0.187700i	$0.0601032\pi$
$71$			3.16317i			0.375400i	−0.982226	+	0.187700i	$0.939897\pi$
$72$	−1.65384	+	3.62588i	−0.194907	+	0.427314i
$73$	−1.78752	+	6.67113i	−0.209214	+	0.780797i	0.778910	+	0.627136i	$0.215773\pi$
$73$	−1.78752	+	6.67113i	−0.209214	+	0.780797i	−0.988124	+	0.153661i	$0.950894\pi$
$74$	10.0927	−	3.05236i	1.17325	−	0.354830i
$75$	7.82277	+	7.00208i	0.903296	+	0.808531i
$76$	6.50918	−	13.1438i	0.746654	−	1.50770i
$77$	−0.952621	+	0.586243i	−0.108561	+	0.0668085i
$78$	5.58129	−	3.46420i	0.631957	−	0.392243i
$79$	−1.77995	+	3.08296i	−0.200260	+	0.346860i	−0.948612	−	0.316441i	$-0.897512\pi$
$79$	−1.77995	+	3.08296i	−0.200260	+	0.346860i	0.748352	+	0.663301i	$0.230845\pi$
$80$	−0.951598	+	8.89351i	−0.106392	+	0.994324i
$81$	−5.62086	−	9.73561i	−0.624540	−	1.08173i
$82$	0.181207	+	5.68058i	0.0200110	+	0.627315i
$83$	−4.71846	+	4.71846i	−0.517919	+	0.517919i	−0.916941	−	0.399022i	$-0.869350\pi$
$83$	−4.71846	+	4.71846i	−0.517919	+	0.517919i	0.399022	+	0.916941i	$0.369350\pi$
$84$	−10.9508	−	1.87928i	−1.19483	−	0.205046i
$85$	4.86025	−	8.98296i	0.527168	−	0.974339i
$86$	2.75182	+	2.58169i	0.296737	+	0.278391i
$87$	−2.56966	+	9.59011i	−0.275497	+	1.02817i
$88$	0.694078	+	0.973735i	0.0739890	+	0.103801i
$89$	−10.0333	−	5.79271i	−1.06352	−	0.614026i	−0.137119	−	0.990555i	$-0.543784\pi$
$89$	−10.0333	−	5.79271i	−1.06352	−	0.614026i	−0.926405	+	0.376529i	$0.877118\pi$
$90$	3.33251	+	2.95755i	0.351277	+	0.311754i
$91$	4.25305	+	4.02077i	0.445841	+	0.421491i
$92$	4.26646	+	12.6380i	0.444809	+	1.31760i
$93$	−3.98534	+	1.06787i	−0.413260	+	0.110733i
$94$	−2.69468	−	8.90999i	−0.277935	−	0.918995i
$95$	−11.9117	−	11.2705i	−1.22211	−	1.15633i
$96$	−1.21367	+	11.8159i	−0.123870	+	1.20595i
$97$	−4.64008	+	4.64008i	−0.471128	+	0.471128i	−0.902280	−	0.431151i	$-0.858108\pi$
$97$	−4.64008	+	4.64008i	−0.471128	+	0.471128i	0.431151	+	0.902280i	$0.358108\pi$
$98$	−0.870255	−	9.86117i	−0.0879090	−	0.996129i
$99$	0.595688			0.0598689
$100$	9.19292	+	3.93577i	0.919292	+	0.393577i
$101$	−2.12019	−	3.67228i	−0.210967	−	0.365406i	0.741050	−	0.671449i	$-0.234328\pi$
$101$	−2.12019	−	3.67228i	−0.210967	−	0.365406i	−0.952017	+	0.306044i	$0.900995\pi$
$102$	6.40383	−	11.9567i	0.634074	−	1.18389i
$103$	−4.06958	−	15.1879i	−0.400987	−	1.49651i	−0.811338	−	0.584577i	$-0.801260\pi$
$103$	−4.06958	−	15.1879i	−0.400987	−	1.49651i	0.410351	−	0.911928i	$-0.365406\pi$
$104$	3.98145	−	4.82666i	0.390413	−	0.473293i
$105$	−5.60243	+	11.0873i	−0.546741	+	1.08201i
$106$	1.11203	+	0.260269i	0.108009	+	0.0252795i
$107$	0.542724	−	0.145422i	0.0524671	−	0.0140585i	−0.232490	−	0.972599i	$-0.574687\pi$
$107$	0.542724	−	0.145422i	0.0524671	−	0.0140585i	0.284957	+	0.958540i	$0.408021\pi$
$108$	−5.01601	−	4.41378i	−0.482665	−	0.424716i
$109$	−4.52802	+	2.61425i	−0.433706	+	0.250400i	−0.700924	−	0.713236i	$-0.747229\pi$
$109$	−4.52802	+	2.61425i	−0.433706	+	0.250400i	0.267218	+	0.963636i	$0.413895\pi$
$110$	1.26850	−	0.422253i	0.120946	−	0.0402602i
$111$		−	15.6555i		−	1.48595i
$112$	−10.4551	+	1.64030i	−0.987915	+	0.154994i
$113$	9.46096	+	9.46096i	0.890012	+	0.890012i	0.994524	−	0.104511i	$-0.0333278\pi$
$113$	9.46096	+	9.46096i	0.890012	+	0.890012i	−0.104511	+	0.994524i	$0.533328\pi$
$114$	−15.8821	−	14.9001i	−1.48749	−	1.39553i
$115$	14.9074	−	0.412314i	1.39012	−	0.0384485i
$116$	0.602714	+	9.43748i	0.0559606	+	0.876248i
$117$	−0.806713	−	3.01070i	−0.0745807	−	0.278339i
$118$	−3.26150	+	2.02435i	−0.300245	+	0.186357i
$119$	11.7562	+	2.79896i	1.07769	+	0.256580i
$120$	12.2303	+	5.17494i	1.11647	+	0.472405i
$121$	−5.41063	+	9.37149i	−0.491876	+	0.851953i
$122$	−2.30823	−	1.23626i	−0.208977	−	0.111925i
$123$	8.15103	+	2.18406i	0.734953	+	0.196930i
$124$	−3.27124	+	2.17787i	−0.293766	+	0.195578i
$125$	7.22345	−	8.53356i	0.646085	−	0.763265i
$126$	−2.35768	+	4.71542i	−0.210039	+	0.420083i
$127$	−15.7173	−	15.7173i	−1.39469	−	1.39469i	−0.814439	−	0.580249i	$-0.802955\pi$
$127$	−15.7173	−	15.7173i	−1.39469	−	1.39469i	−0.580249	−	0.814439i	$-0.697045\pi$
$128$	2.50453	+	11.0330i	0.221371	+	0.975190i
$129$	4.85182	−	2.80120i	0.427179	−	0.246632i
$130$	−3.85200	−	5.83933i	−0.337842	−	0.512143i
$131$	−15.5632	−	8.98542i	−1.35976	−	0.785060i	−0.370171	−	0.928963i	$-0.620701\pi$
$131$	−15.5632	−	8.98542i	−1.35976	−	0.785060i	−0.989592	+	0.143904i	$0.954034\pi$
$132$	1.68218	−	0.567887i	0.146415	−	0.0494282i
$133$	9.22614	−	17.0692i	0.800007	−	1.48008i
$134$	12.4045	+	2.90326i	1.07158	+	0.250803i
$135$	−6.36355	+	3.91248i	−0.547687	+	0.336733i
$136$	2.13645	−	12.7413i	0.183199	−	1.09256i
$137$	12.9822	+	3.47858i	1.10915	+	0.297195i	0.766485	−	0.642263i	$-0.222004\pi$
$137$	12.9822	+	3.47858i	1.10915	+	0.297195i	0.342664	+	0.939458i	$0.388671\pi$
$138$	19.7947	−	0.631438i	1.68503	−	0.0537516i
$139$	6.16658			0.523043			0.261521	−	0.965198i	$-0.415776\pi$
$139$	6.16658			0.523043			0.261521	+	0.965198i	$0.415776\pi$
$140$	−1.67809	+	11.7126i	−0.141824	+	0.989892i
$141$	−13.8209			−1.16393
$142$	4.47113	−	0.142627i	0.375209	−	0.0119690i
$143$	−0.903369	−	0.242057i	−0.0755435	−	0.0202418i
$144$	5.19973	+	2.17421i	0.433311	+	0.181184i
$145$	10.2844	+	2.45307i	0.854073	+	0.203716i
$146$	9.51021	+	2.22586i	0.787070	+	0.184213i
$147$	−14.3886	−	3.00167i	−1.18675	−	0.247574i
$148$	−4.76957	−	14.1283i	−0.392056	−	1.16134i
$149$	4.22837	+	2.44125i	0.346401	+	0.199995i	0.663099	−	0.748532i	$-0.269241\pi$
$149$	4.22837	+	2.44125i	0.346401	+	0.199995i	−0.316698	+	0.948526i	$0.602574\pi$
$150$	9.54468	−	11.3732i	0.779320	−	0.928615i
$151$	3.04218	−	1.75640i	0.247569	−	0.142934i	−0.371082	−	0.928600i	$-0.621013\pi$
$151$	3.04218	−	1.75640i	0.247569	−	0.142934i	0.618651	+	0.785666i	$0.287680\pi$
$152$	−18.8723	−	8.60804i	−1.53074	−	0.698204i
$153$	−4.55077	−	4.55077i	−0.367908	−	0.367908i
$154$	0.871604	+	1.32009i	0.0702359	+	0.106376i
$155$	1.25409	+	4.21098i	0.100731	+	0.338234i
$156$	−5.14829	−	7.73292i	−0.412193	−	0.619129i
$157$	−13.0349	−	3.49270i	−1.04030	−	0.278748i	−0.302062	−	0.953288i	$-0.597675\pi$
$157$	−13.0349	−	3.49270i	−1.04030	−	0.278748i	−0.738238	+	0.674541i	$0.764342\pi$
$158$	4.43801	+	2.37694i	0.353069	+	0.189099i
$159$	0.847853	−	1.46852i	0.0672391	−	0.116462i
$160$	12.6138	+	0.944073i	0.997211	+	0.0746355i
$161$	5.04350	+	16.9093i	0.397483	+	1.33264i
$162$	−13.5078	+	8.38403i	−1.06127	+	0.658712i
$163$	1.49311	+	5.57237i	0.116950	+	0.436462i	0.999425	−	0.0338961i	$-0.0107915\pi$
$163$	1.49311	+	5.57237i	0.116950	+	0.436462i	−0.882476	+	0.470358i	$0.844125\pi$
$164$	8.02130	−	0.512271i	0.626358	−	0.0400017i
$165$	−0.0548811	−	1.98426i	−0.00427249	−	0.154474i
$166$	6.88228	+	6.45677i	0.534168	+	0.501143i
$167$	6.11518	+	6.11518i	0.473207	+	0.473207i	0.902951	−	0.429744i	$-0.141396\pi$
$167$	6.11518	+	6.11518i	0.473207	+	0.473207i	−0.429744	+	0.902951i	$0.641396\pi$
$168$	−2.16258	+	15.5636i	−0.166846	+	1.20076i
$169$		−	8.10643i		−	0.623572i
$170$	−12.9165	−	6.46490i	−0.990651	−	0.495835i
$171$	−8.94873	+	5.16655i	−0.684327	+	0.395096i
$172$	3.52512	−	4.00610i	0.268788	−	0.305462i
$173$	−4.22300	+	1.13155i	−0.321069	+	0.0860302i	−0.415754	−	0.909477i	$-0.636482\pi$
$173$	−4.22300	+	1.13155i	−0.321069	+	0.0860302i	0.0946850	+	0.995507i	$0.469816\pi$
$174$	13.6714	+	3.19979i	1.03643	+	0.242575i
$175$	11.9674	+	5.63739i	0.904654	+	0.426147i
$176$	1.34507	−	1.02498i	0.101389	−	0.0772609i
$177$	1.47513	+	5.50528i	0.110878	+	0.413802i
$178$	−7.73556	+	14.4432i	−0.579805	+	1.08256i
$179$	−9.00305	−	15.5937i	−0.672920	−	1.16553i	−0.977072	−	0.212908i	$-0.931707\pi$
$179$	−9.00305	−	15.5937i	−0.672920	−	1.16553i	0.304152	−	0.952623i	$-0.401627\pi$
$180$	4.03023	−	4.84384i	0.300395	−	0.361038i
$181$	14.5671			1.08276			0.541382	−	0.840777i	$-0.317901\pi$
$181$	14.5671			1.08276			0.541382	+	0.840777i	$0.317901\pi$
$182$	5.49156	−	6.19296i	0.407062	−	0.459052i
$183$	−2.74905	+	2.74905i	−0.203216	+	0.203216i
$184$	17.6713	−	6.60045i	1.30275	−	0.486592i
$185$	−16.6654	+	0.460935i	−1.22526	+	0.0338886i
$186$	1.68912	+	5.58510i	0.123852	+	0.409519i
$187$	−1.86527	+	0.499798i	−0.136402	+	0.0365489i
$188$	−12.4727	+	4.21066i	−0.909666	+	0.307094i
$189$	−6.42286	−	6.07207i	−0.467194	−	0.441678i
$190$	−15.3937	+	17.3453i	−1.11678	+	1.25836i
$191$	−8.77337	−	5.06530i	−0.634818	−	0.366513i	0.147797	−	0.989018i	$-0.452782\pi$
$191$	−8.77337	−	5.06530i	−0.634818	−	0.366513i	−0.782616	+	0.622505i	$0.786115\pi$
$192$	16.7564	+	1.18274i	1.20929	+	0.0853570i
$193$	−5.49463	+	20.5062i	−0.395512	+	1.47607i	0.425395	+	0.905008i	$0.360135\pi$
$193$	−5.49463	+	20.5062i	−0.395512	+	1.47607i	−0.820907	+	0.571063i	$0.806531\pi$
$194$	6.76794	+	6.34950i	0.485910	+	0.455868i
$195$	−9.95440	+	2.96456i	−0.712849	+	0.212297i
$196$	−13.8995	+	1.67474i	−0.992819	+	0.119624i
$197$	−14.1612	+	14.1612i	−1.00895	+	1.00895i	−0.00898613	+	0.999960i	$0.502860\pi$
$197$	−14.1612	+	14.1612i	−1.00895	+	1.00895i	−0.999960	+	0.00898613i	$0.997140\pi$
$198$	−0.0268594	−	0.842002i	−0.00190881	−	0.0598385i
$199$	3.64221	+	6.30849i	0.258189	+	0.447197i	0.965757	−	0.259449i	$-0.0835408\pi$
$199$	3.64221	+	6.30849i	0.258189	+	0.447197i	−0.707568	+	0.706646i	$0.750207\pi$
$200$	5.14868	−	13.1716i	0.364067	−	0.931373i
$201$	9.45766	−	16.3811i	0.667092	−	1.15544i
$202$	−5.09515	+	3.16246i	−0.358494	+	0.222510i
$203$	0.351073	+	12.5051i	0.0246405	+	0.877687i
$204$	−17.1894	−	8.51266i	−1.20350	−	0.596005i
$205$	2.08496	−	8.74114i	0.145620	−	0.610508i
$206$	−21.2845	+	6.43714i	−1.48296	+	0.448497i
$207$	2.43215	−	9.07690i	0.169046	−	0.630888i
$208$	−7.00198	−	5.41012i	−0.485500	−	0.375124i
$209$			3.10048i			0.214465i
$210$	15.9244	+	7.41908i	1.09889	+	0.511965i
$211$			17.4066i			1.19832i	0.800630	+	0.599159i	$0.204498\pi$
$211$			17.4066i			1.19832i	−0.800630	+	0.599159i	$0.795502\pi$
$212$	0.317747	−	1.58358i	0.0218230	−	0.108761i
$213$	1.71905	−	6.41559i	0.117788	−	0.439589i
$214$	−0.230025	−	0.760580i	−0.0157242	−	0.0519922i
$215$	−3.12475	−	5.08233i	−0.213106	−	0.346612i
$216$	−6.01269	+	7.28911i	−0.409112	+	0.495961i
$217$	−4.42754	+	2.72471i	−0.300561	+	0.184965i
$218$	3.89940	+	6.28245i	0.264101	+	0.425502i
$219$	7.25096	−	12.5590i	0.489975	−	0.848661i
$220$	−0.654048	−	1.77397i	−0.0440959	−	0.119601i
$221$	5.05211	+	8.75051i	0.339842	+	0.588623i
$222$	−22.1289	+	0.705900i	−1.48519	+	0.0473769i
$223$	−1.68218	+	1.68218i	−0.112647	+	0.112647i	−0.761183	−	0.648537i	$-0.775381\pi$
$223$	−1.68218	+	1.68218i	−0.112647	+	0.112647i	0.648537	+	0.761183i	$0.275381\pi$
$224$	2.78998	+	14.7043i	0.186413	+	0.982471i
$225$	−3.85434	−	5.89711i	−0.256956	−	0.393140i
$226$	12.9464	−	13.7996i	0.861183	−	0.917936i
$227$	4.05161	−	15.1208i	0.268915	−	1.00360i	−0.690895	−	0.722955i	$-0.742783\pi$
$227$	4.05161	−	15.1208i	0.268915	−	1.00360i	0.959810	−	0.280650i	$-0.0905499\pi$
$228$	−20.3451	+	23.1211i	−1.34739	+	1.53123i
$229$	−14.7843	−	8.53574i	−0.976976	−	0.564057i	−0.0756201	−	0.997137i	$-0.524094\pi$
$229$	−14.7843	−	8.53574i	−0.976976	−	0.564057i	−0.901356	+	0.433079i	$0.857427\pi$
$230$	−1.25497	−	21.0530i	−0.0827506	−	1.38819i
$231$	2.25072	−	0.671315i	0.148086	−	0.0441693i
$232$	13.3126	−	1.27747i	0.874018	−	0.0838697i
$233$	13.4441	−	3.60234i	0.880753	−	0.235997i	0.210021	−	0.977697i	$-0.432647\pi$
$233$	13.4441	−	3.60234i	0.880753	−	0.235997i	0.670732	+	0.741700i	$0.265980\pi$
$234$	−4.21923	+	1.27604i	−0.275820	+	0.0834171i
$235$	0.406922	+	14.7125i	0.0265447	+	0.959737i
$236$	3.00847	+	4.51883i	0.195835	+	0.294151i
$237$	5.28558	−	5.28558i	0.343335	−	0.343335i
$238$	3.42623	−	16.7435i	0.222089	−	1.08532i
$239$	−7.51141			−0.485873			−0.242936	−	0.970042i	$-0.578111\pi$
$239$	−7.51141			−0.485873			−0.242936	+	0.970042i	$0.578111\pi$
$240$	6.76329	−	17.5208i	0.436569	−	1.13096i
$241$	3.62580	+	6.28008i	0.233559	+	0.404535i	0.958853	−	0.283904i	$-0.0916296\pi$
$241$	3.62580	+	6.28008i	0.233559	+	0.404535i	−0.725294	+	0.688439i	$0.758296\pi$
$242$	13.4905	+	7.22534i	0.867203	+	0.464462i
$243$	3.51547	+	13.1199i	0.225518	+	0.841644i
$244$	−1.64336	+	3.31841i	−0.105206	+	0.212439i
$245$	−2.77167	+	15.4051i	−0.177075	+	0.984197i
$246$	2.71963	−	11.6199i	0.173397	−	0.740858i
$247$	15.6703	−	4.19885i	0.997078	−	0.267166i
$248$	3.22590	+	4.52568i	0.204845	+	0.287381i
$249$	12.1343	−	7.00577i	0.768983	−	0.443972i
$250$	−12.3878	−	9.82554i	−0.783476	−	0.621422i
$251$			3.63825i			0.229644i	0.993386	+	0.114822i	$0.0366298\pi$
$251$			3.63825i			0.229644i	−0.993386	+	0.114822i	$0.963370\pi$
$252$	6.77152	+	3.11995i	0.426566	+	0.196539i
$253$	−1.99378	−	1.99378i	−0.125348	−	0.125348i
$254$	−21.5077	+	22.9251i	−1.34951	+	1.43845i
$255$	−14.7395	+	15.5780i	−0.923023	+	0.975534i
$256$	15.4822	−	4.03762i	0.967636	−	0.252351i
$257$	−1.80480	−	6.73562i	−0.112581	−	0.420156i	0.886514	−	0.462702i	$-0.153120\pi$
$257$	−1.80480	−	6.73562i	−0.112581	−	0.420156i	−0.999095	+	0.0425454i	$0.986453\pi$
$258$	−4.17825	−	6.73171i	−0.260126	−	0.419098i
$259$	−5.63824	−	18.9033i	−0.350343	−	1.17460i
$260$	−8.08018	+	5.70807i	−0.501112	+	0.353999i
$261$	3.33112	−	5.76966i	0.206191	−	0.357133i
$262$	−11.9991	+	22.4036i	−0.741307	+	1.38410i
$263$	24.5021	+	6.56533i	1.51087	+	0.404836i	0.916723	−	0.399523i	$-0.130824\pi$
$263$	24.5021	+	6.56533i	1.51087	+	0.404836i	0.594144	+	0.804359i	$0.297491\pi$
$264$	−0.878554	−	2.35215i	−0.0540713	−	0.144765i
$265$	−1.58822	−	0.859309i	−0.0975635	−	0.0527869i
$266$	−24.5432	−	12.2714i	−1.50484	−	0.752411i
$267$	17.2015	+	17.2015i	1.05271	+	1.05271i
$268$	3.54442	−	17.6646i	0.216510	−	1.07903i
$269$	16.4868	−	9.51864i	1.00522	−	0.580361i	0.0954283	−	0.995436i	$-0.469578\pi$
$269$	16.4868	−	9.51864i	1.00522	−	0.580361i	0.909787	+	0.415075i	$0.136245\pi$
$270$	5.81720	+	8.81843i	0.354023	+	0.536673i
$271$	18.2717	+	10.5492i	1.10993	+	0.640817i	0.938811	−	0.344434i	$-0.111929\pi$
$271$	18.2717	+	10.5492i	1.10993	+	0.640817i	0.171117	+	0.985251i	$0.445262\pi$
$272$	−18.1061	−	2.44536i	−1.09784	−	0.148271i
$273$	−6.44097	−	10.4663i	−0.389825	−	0.633451i
$274$	4.33159	−	18.5072i	0.261681	−	1.11806i
$275$	−2.11064	+	0.116843i	−0.127276	+	0.00704588i
$276$	−1.78507	−	27.9512i	−0.107449	−	1.68246i
$277$	15.5701	+	4.17199i	0.935515	+	0.250670i	0.694205	−	0.719778i	$-0.255756\pi$
$277$	15.5701	+	4.17199i	0.935515	+	0.250670i	0.241310	+	0.970448i	$0.422423\pi$
$278$	−0.278049	−	8.71643i	−0.0166763	−	0.522777i
$279$	2.76861			0.165752
$280$	16.6313	+	1.84385i	0.993910	+	0.110191i
$281$	−6.00749			−0.358377			−0.179189	−	0.983815i	$-0.557347\pi$
$281$	−6.00749			−0.358377			−0.179189	+	0.983815i	$0.557347\pi$
$282$	0.623181	+	19.5358i	0.0371099	+	1.16334i
$283$	1.60792	+	0.430842i	0.0955812	+	0.0256109i	0.306293	−	0.951937i	$-0.400911\pi$
$283$	1.60792	+	0.430842i	0.0955812	+	0.0256109i	−0.210711	+	0.977548i	$0.567578\pi$
$284$	−0.403204	−	6.31349i	−0.0239257	−	0.374636i
$285$	18.0344	+	29.3325i	1.06827	+	1.73751i
$286$	−0.301414	+	1.28782i	−0.0178230	+	0.0761505i
$287$	10.6286	−	0.298392i	0.627387	−	0.0176135i
$288$	2.83877	−	7.44783i	0.167276	−	0.438867i
$289$	3.34556	+	1.93156i	0.196798	+	0.113621i
$290$	3.00368	−	14.6476i	0.176382	−	0.860134i
$291$	11.9328	−	6.88938i	0.699510	−	0.403863i
$292$	2.71742	−	13.5430i	0.159025	−	0.792543i
$293$	−14.2453	−	14.2453i	−0.832220	−	0.832220i	0.155600	−	0.987820i	$-0.450269\pi$
$293$	−14.2453	−	14.2453i	−0.832220	−	0.832220i	−0.987820	+	0.155600i	$0.950269\pi$
$294$	−3.59407	+	20.4735i	−0.209610	+	1.19404i
$295$	5.81698	−	1.73238i	0.338678	−	0.100863i
$296$	−19.7552	+	7.37880i	−1.14825	+	0.428884i
$297$	1.36425	+	0.365549i	0.0791617	+	0.0212113i
$298$	3.26004	−	6.08685i	0.188849	−	0.352602i
$299$	−7.37678	+	12.7770i	−0.426610	+	0.738910i
$300$	−16.5063	−	12.9785i	−0.952990	−	0.749316i
$301$	4.84953	−	5.12969i	0.279523	−	0.295671i
$302$	−2.61984	−	4.22091i	−0.150755	−	0.242886i
$303$	2.30447	+	8.60041i	0.132388	+	0.494081i
$304$	−11.3165	+	27.0640i	−0.649044	+	1.55222i
$305$	3.00733	+	2.84545i	0.172199	+	0.162930i
$306$	−6.22730	+	6.63768i	−0.355991	+	0.379451i
$307$	−3.60252	−	3.60252i	−0.205607	−	0.205607i	0.596790	−	0.802397i	$-0.296442\pi$
$307$	−3.60252	−	3.60252i	−0.205607	−	0.205607i	−0.802397	+	0.596790i	$0.796442\pi$
$308$	1.82664	−	1.29153i	0.104083	−	0.0735918i
$309$			33.0159i			1.87821i
$310$	5.89565	−	1.96252i	0.334851	−	0.111464i
$311$	0.374701	−	0.216334i	0.0212473	−	0.0122672i	−0.489339	−	0.872094i	$-0.662762\pi$
$311$	0.374701	−	0.216334i	0.0212473	−	0.0122672i	0.510586	+	0.859827i	$0.329428\pi$
$312$	−10.6983	+	7.62575i	−0.605673	+	0.431723i
$313$	−0.994998	+	0.266609i	−0.0562406	+	0.0150696i	−0.286830	−	0.957982i	$-0.592601\pi$
$313$	−0.994998	+	0.266609i	−0.0562406	+	0.0150696i	0.230589	+	0.973051i	$0.425935\pi$
$314$	−4.34917	+	18.5823i	−0.245438	+	1.04866i
$315$	5.55686	−	6.21336i	0.313094	−	0.350083i
$316$	3.15968	−	6.38027i	0.177746	−	0.358918i
$317$	−7.29750	−	27.2346i	−0.409868	−	1.52965i	−0.794897	−	0.606744i	$-0.792475\pi$
$317$	−7.29750	−	27.2346i	−0.409868	−	1.52965i	0.385029	−	0.922905i	$-0.374192\pi$
$318$	−2.11398	−	1.13222i	−0.118546	−	0.0634917i
$319$	−0.999513	−	1.73121i	−0.0559620	−	0.0969290i
$320$	0.765688	−	17.8721i	0.0428033	−	0.999084i
$321$	−1.17979			−0.0658495
$322$	23.6738	−	7.89139i	1.31929	−	0.439770i
$323$	23.6862	−	23.6862i	1.31794	−	1.31794i
$324$	12.4598	+	18.7152i	0.692214	+	1.03973i
$325$	3.44889	+	10.5093i	0.191310	+	0.582949i
$326$	7.80919	−	2.36176i	0.432511	−	0.130806i
$327$	10.6045	−	2.84147i	0.586432	−	0.157134i
$328$	−1.08577	−	11.3150i	−0.0599517	−	0.624765i
$329$	−16.6882	+	4.97754i	−0.920050	+	0.274421i
$330$	−2.80226	+	0.167044i	−0.154259	+	0.00919545i
$331$	−22.3187	−	12.8857i	−1.22675	−	0.708262i	−0.260398	−	0.965501i	$-0.583854\pi$
$331$	−22.3187	−	12.8857i	−1.22675	−	0.708262i	−0.966348	+	0.257239i	$0.917187\pi$
$332$	8.81629	−	10.0192i	0.483857	−	0.549875i
$333$	−2.71896	+	10.1473i	−0.148998	+	0.556068i
$334$	8.36805	−	8.91951i	0.457879	−	0.488054i
$335$	−17.7163	−	9.58546i	−0.967946	−	0.523709i
$336$	22.0966	+	2.35503i	1.20547	+	0.128477i
$337$	10.4788	−	10.4788i	0.570816	−	0.570816i	−0.361540	−	0.932356i	$-0.617749\pi$
$337$	10.4788	−	10.4788i	0.570816	−	0.570816i	0.932356	+	0.361540i	$0.117749\pi$
$338$	−11.4584	+	0.365516i	−0.623255	+	0.0198815i
$339$	−14.0472	−	24.3305i	−0.762940	−	1.32145i
$340$	−8.55570	+	18.5489i	−0.463998	+	1.00596i
$341$	0.415365	−	0.719433i	0.0224933	−	0.0389595i
$342$	7.70639	+	12.4160i	0.416714	+	0.671382i
$343$	−18.4546	+	1.55758i	−0.996457	+	0.0841016i
$344$	−5.82154	−	4.80211i	−0.313876	−	0.258912i
$345$	−30.4595	−	7.26530i	−1.63989	−	0.391151i
$346$	1.78985	+	5.91817i	0.0962231	+	0.318163i
$347$	−4.86030	+	18.1389i	−0.260914	+	0.973746i	0.703789	+	0.710409i	$0.251490\pi$
$347$	−4.86030	+	18.1389i	−0.260914	+	0.973746i	−0.964704	+	0.263337i	$0.915177\pi$
$348$	3.90644	−	19.4688i	0.209407	−	1.04364i
$349$			7.53504i			0.403341i	0.979453	+	0.201671i	$0.0646371\pi$
$349$			7.53504i			0.403341i	−0.979453	+	0.201671i	$0.935363\pi$
$350$	7.42882	−	17.1701i	0.397087	−	0.917781i
$351$		−	7.39016i		−	0.394457i
$352$	−1.50945	−	1.85504i	−0.0804542	−	0.0988739i
$353$	9.54063	−	35.6061i	0.507796	−	1.89512i	0.0664384	−	0.997791i	$-0.478836\pi$
$353$	9.54063	−	35.6061i	0.507796	−	1.89512i	0.441358	−	0.897331i	$-0.354497\pi$
$354$	7.71517	−	2.33333i	0.410056	−	0.124015i
$355$	−6.88006	−	1.64106i	−0.365156	−	0.0870982i
$356$	20.7641	+	10.2829i	1.10050	+	0.544995i
$357$	−22.3229	−	12.0659i	−1.18145	−	0.638594i
$358$	−21.6357	+	13.4289i	−1.14348	+	0.709739i
$359$	−9.04771	+	15.6711i	−0.477520	+	0.827089i	−0.999668	−	0.0257661i	$-0.991797\pi$
$359$	−9.04771	+	15.6711i	−0.477520	+	0.827089i	0.522148	+	0.852855i	$0.325131\pi$
$360$	−7.02846	−	5.47830i	−0.370432	−	0.288731i
$361$	−17.3913	−	30.1226i	−0.915331	−	1.58540i
$362$	−0.656826	−	20.5905i	−0.0345220	−	1.08221i
$363$	16.0669	−	16.0669i	0.843295	−	0.843295i
$364$	−9.00132	−	7.48306i	−0.471798	−	0.392219i
$365$	−13.5827	−	7.34894i	−0.710950	−	0.384661i
$366$	4.00973	+	3.76182i	0.209592	+	0.196633i
$367$	6.06169	−	22.6225i	0.316417	−	1.18089i	−0.606245	−	0.795278i	$-0.707325\pi$
$367$	6.06169	−	22.6225i	0.316417	−	1.18089i	0.922663	−	0.385608i	$-0.126008\pi$
$368$	−10.1265	−	24.6807i	−0.527880	−	1.28657i
$369$	−4.90388	−	2.83125i	−0.255286	−	0.147389i
$370$	1.40297	+	23.5356i	0.0729367	+	1.22356i
$371$	0.494865	−	2.07853i	0.0256921	−	0.107912i
$372$	7.81835	−	2.63940i	0.405362	−	0.136846i
$373$	−5.60369	+	1.50150i	−0.290148	+	0.0777450i	−0.400957	−	0.916097i	$-0.631322\pi$
$373$	−5.60369	+	1.50150i	−0.290148	+	0.0777450i	0.110809	+	0.993842i	$0.464656\pi$
$374$	0.790566	+	2.61402i	0.0408792	+	0.135168i
$375$	−19.2883	+	13.3822i	−0.996046	+	0.691056i
$376$	6.51414	+	17.4403i	0.335941	+	0.899412i
$377$	−7.39618	+	7.39618i	−0.380923	+	0.380923i
$378$	−8.29323	+	9.35246i	−0.426558	+	0.481039i
$379$	20.3909			1.04741			0.523706	−	0.851899i	$-0.324549\pi$
$379$	20.3909			1.04741			0.523706	+	0.851899i	$0.324549\pi$
$380$	25.2116	+	20.9768i	1.29333	+	1.07609i
$381$	23.3364	+	40.4198i	1.19556	+	2.07077i
$382$	−6.76419	+	12.6295i	−0.346086	+	0.646181i
$383$	2.73132	+	10.1934i	0.139564	+	0.520860i	0.999937	+	0.0111957i	$0.00356377\pi$
$383$	2.73132	+	10.1934i	0.139564	+	0.520860i	−0.860373	+	0.509664i	$0.829770\pi$
$384$	0.916257	−	23.7384i	0.0467576	−	1.21140i
$385$	−0.780887	−	2.37614i	−0.0397977	−	0.121099i
$386$	29.2332	+	6.84201i	1.48793	+	0.348249i
$387$	−3.63127	+	0.972995i	−0.184588	+	0.0494601i
$388$	8.66982	−	9.85275i	0.440144	−	0.500197i
$389$	−1.96021	+	1.13173i	−0.0993866	+	0.0573809i	−0.548869	−	0.835908i	$-0.684942\pi$
$389$	−1.96021	+	1.13173i	−0.0993866	+	0.0573809i	0.449483	+	0.893289i	$0.351608\pi$
$390$	4.63924	+	13.9368i	0.234917	+	0.705718i
$391$			30.4631i			1.54058i
$392$	2.99396	+	19.5713i	0.151218	+	0.988500i
$393$	26.6823	+	26.6823i	1.34594	+	1.34594i
$394$	20.6553	+	19.3783i	1.04060	+	0.976264i
$395$	−5.78216	−	5.47092i	−0.290932	−	0.275272i
$396$	−1.18895	+	0.0759312i	−0.0597472	+	0.00381569i
$397$	4.47408	+	16.6975i	0.224548	+	0.838024i	0.982585	+	0.185813i	$0.0594918\pi$
$397$	4.47408	+	16.6975i	0.224548	+	0.838024i	−0.758037	+	0.652211i	$0.773842\pi$
$398$	8.75279	−	5.43269i	0.438738	−	0.272316i
$399$	−27.9890	+	29.6059i	−1.40120	+	1.48215i
$400$	−18.8501	−	6.68373i	−0.942507	−	0.334186i
$401$	−2.49166	+	4.31568i	−0.124428	+	0.215515i	−0.921509	−	0.388357i	$-0.873043\pi$
$401$	−2.49166	+	4.31568i	−0.124428	+	0.215515i	0.797081	+	0.603872i	$0.206376\pi$
$402$	−23.5811	−	12.6297i	−1.17612	−	0.629914i
$403$	−4.19863	−	1.12502i	−0.209149	−	0.0560413i
$404$	4.69986	+	7.05937i	0.233827	+	0.351217i
$405$	24.0916	−	7.17482i	1.19712	−	0.356520i
$406$	17.6601	−	1.06009i	0.876455	−	0.0526115i
$407$	2.22889	+	2.22889i	0.110482	+	0.110482i
$408$	−11.2575	+	24.6810i	−0.557331	+	1.22189i
$409$	−1.80679	+	1.04315i	−0.0893400	+	0.0515805i	−0.544004	−	0.839082i	$-0.683093\pi$
$409$	−1.80679	+	1.04315i	−0.0893400	+	0.0515805i	0.454664	+	0.890663i	$0.349759\pi$
$410$	−12.4496	−	2.55295i	−0.614840	−	0.126081i
$411$	−24.4403	−	14.1106i	−1.20555	−	0.696025i
$412$	10.0586	+	29.7952i	0.495550	+	1.46791i
$413$	3.76387	+	6.11613i	0.185208	+	0.300955i
$414$	−12.9398	−	3.02855i	−0.635957	−	0.148845i
$415$	−7.81496	−	12.7108i	−0.383621	−	0.623951i
$416$	−7.33146	+	10.1412i	−0.359454	+	0.497213i
$417$	−12.5071	−	3.35128i	−0.612477	−	0.164113i
$418$	4.38252	−	0.139800i	0.214356	−	0.00683783i
$419$	−3.19769			−0.156217			−0.0781086	−	0.996945i	$-0.524888\pi$
$419$	−3.19769			−0.156217			−0.0781086	+	0.996945i	$0.524888\pi$
$420$	9.76880	−	22.8436i	0.476669	−	1.11465i
$421$	−39.6161			−1.93077			−0.965386	−	0.260824i	$-0.916006\pi$
$421$	−39.6161			−1.93077			−0.965386	+	0.260824i	$0.916006\pi$
$422$	24.6041	−	0.784857i	1.19771	−	0.0382062i
$423$	8.95821	+	2.40034i	0.435563	+	0.116709i
$424$	−2.25270	−	0.377731i	−0.109401	−	0.0183443i
$425$	17.0169	+	15.2317i	0.825441	+	0.738844i
$426$	−9.14592	−	2.14059i	−0.443121	−	0.103712i
$427$	−2.32931	+	4.30943i	−0.112723	+	0.208548i
$428$	−1.06470	+	0.359433i	−0.0514644	+	0.0173739i
$429$	1.70068	+	0.981887i	0.0821095	+	0.0474059i
$430$	−7.04295	+	4.64598i	−0.339641	+	0.224049i
$431$	−12.7288	+	7.34896i	−0.613123	+	0.353987i	−0.774187	−	0.632957i	$-0.781841\pi$
$431$	−12.7288	+	7.34896i	−0.613123	+	0.353987i	0.161064	+	0.986944i	$0.448508\pi$
$432$	10.5742	+	8.17024i	0.508753	+	0.393091i
$433$	6.03281	+	6.03281i	0.289919	+	0.289919i	0.837048	−	0.547129i	$-0.184279\pi$
$433$	6.03281	+	6.03281i	0.289919	+	0.289919i	−0.547129	+	0.837048i	$0.684279\pi$
$434$	4.05100	+	6.13545i	0.194454	+	0.294511i
$435$	−19.5258	−	10.5645i	−0.936192	−	0.506529i
$436$	8.70439	−	5.79505i	0.416865	−	0.277533i
$437$	47.2442	+	12.6590i	2.26000	+	0.605564i
$438$	−18.0791	−	9.68291i	−0.863851	−	0.462667i
$439$	3.31217	−	5.73685i	0.158081	−	0.273805i	−0.776095	−	0.630616i	$-0.782802\pi$
$439$	3.31217	−	5.73685i	0.158081	−	0.273805i	0.934177	+	0.356810i	$0.116136\pi$
$440$	−2.47801	+	1.00448i	−0.118135	+	0.0478868i
$441$	8.80482	+	4.44450i	0.419277	+	0.211643i
$442$	12.1410	−	7.53568i	0.577488	−	0.358436i
$443$	2.52589	+	9.42675i	0.120009	+	0.447879i	0.999613	−	0.0278280i	$-0.00885907\pi$
$443$	2.52589	+	9.42675i	0.120009	+	0.447879i	−0.879604	+	0.475707i	$0.842192\pi$
$444$	1.99557	+	31.2473i	0.0947056	+	1.48293i
$445$	17.8047	−	18.8176i	0.844023	−	0.892040i
$446$	2.45360	+	2.30190i	0.116181	+	0.108998i
$447$	−7.24931	−	7.24931i	−0.342881	−	0.342881i
$448$	20.6586	−	4.60663i	0.976028	−	0.217643i
$449$			18.0135i			0.850109i	0.905168	+	0.425055i	$0.139745\pi$
$449$			18.0135i			0.850109i	−0.905168	+	0.425055i	$0.860255\pi$
$450$	−8.16174	+	5.71399i	−0.384748	+	0.269360i
$451$	−1.47142	+	0.849527i	−0.0692867	+	0.0400027i
$452$	−20.0894	−	17.6775i	−0.944927	−	0.831479i
$453$	−7.12472	+	1.90906i	−0.334749	+	0.0896956i
$454$	−21.5559	−	5.04514i	−1.01167	−	0.236780i
$455$	−10.9519	+	7.16462i	−0.513431	+	0.335883i
$456$	33.5989	+	27.7152i	1.57341	+	1.29788i
$457$	0.328686	+	1.22667i	0.0153753	+	0.0573813i	0.973187	−	0.230014i	$-0.0738773\pi$
$457$	0.328686	+	1.22667i	0.0153753	+	0.0573813i	−0.957812	+	0.287396i	$0.907211\pi$
$458$	−11.3986	+	21.2824i	−0.532621	+	0.994463i
$459$	−7.62958	−	13.2148i	−0.356118	−	0.616815i
$460$	−29.7017	+	2.72317i	−1.38485	+	0.126969i
$461$	−17.6021			−0.819811			−0.409906	−	0.912128i	$-0.634438\pi$
$461$	−17.6021			−0.819811			−0.409906	+	0.912128i	$0.634438\pi$
$462$	−1.05038	−	3.15111i	−0.0488683	−	0.146603i
$463$	−13.7264	+	13.7264i	−0.637919	+	0.637919i	−0.950042	−	0.312123i	$-0.898960\pi$
$463$	−13.7264	+	13.7264i	−0.637919	+	0.637919i	0.312123	+	0.950042i	$0.398960\pi$
$464$	−2.40595	−	18.7597i	−0.111694	−	0.870900i
$465$	−0.255073	−	9.22232i	−0.0118287	−	0.427675i
$466$	−5.69808	−	18.8408i	−0.263958	−	0.872781i
$467$	−12.3923	+	3.32051i	−0.573447	+	0.153655i	−0.533877	−	0.845562i	$-0.679266\pi$
$467$	−12.3923	+	3.32051i	−0.573447	+	0.153655i	−0.0395701	+	0.999217i	$0.512599\pi$
$468$	1.99391	+	5.90632i	0.0921687	+	0.273020i
$469$	5.52014	−	23.1857i	0.254896	−	1.07062i
$470$	20.7777	−	1.23856i	0.958403	−	0.0571307i
$471$	24.5395	+	14.1679i	1.13072	+	0.652821i
$472$	6.25170	−	4.45621i	0.287758	−	0.205113i
$473$	−0.291950	+	1.08957i	−0.0134239	+	0.0500986i
$474$	−7.70946	−	7.23281i	−0.354107	−	0.332214i
$475$	30.6937	−	20.0614i	1.40832	−	0.920480i
$476$	−23.8213	−	4.08799i	−1.09185	−	0.187373i
$477$	−0.804592	+	0.804592i	−0.0368397	+	0.0368397i
$478$	0.338687	+	10.6173i	0.0154912	+	0.485626i
$479$	7.41948	+	12.8509i	0.339005	+	0.587173i	0.984246	−	0.176806i	$-0.0565764\pi$
$479$	7.41948	+	12.8509i	0.339005	+	0.587173i	−0.645241	+	0.763979i	$0.723243\pi$
$480$	−25.0705	−	8.76987i	−1.14431	−	0.400288i
$481$	8.24667	−	14.2837i	0.376016	−	0.651279i
$482$	8.71337	−	5.40822i	0.396883	−	0.246338i
$483$	−1.03978	−	37.0366i	−0.0473117	−	1.68523i
$484$	9.60470	−	19.3946i	0.436577	−	0.881571i
$485$	−7.68513	−	12.4997i	−0.348964	−	0.567581i
$486$	18.3864	−	5.56068i	0.834026	−	0.252237i
$487$	9.04342	−	33.7505i	0.409796	−	1.52938i	−0.385239	−	0.922817i	$-0.625881\pi$
$487$	9.04342	−	33.7505i	0.409796	−	1.52938i	0.795035	−	0.606564i	$-0.207452\pi$
$488$	4.76465	+	2.17326i	0.215686	+	0.0983789i
$489$		−	12.1134i		−	0.547787i
$490$	21.9000	+	3.22313i	0.989343	+	0.145606i
$491$		−	5.19048i		−	0.234243i	−0.993118	−	0.117122i	$-0.962633\pi$
$491$		−	5.19048i		−	0.234243i	0.993118	−	0.117122i	$-0.0373667\pi$
$492$	−16.5473	−	3.32025i	−0.746010	−	0.149688i
$493$	−5.58979	+	20.8614i	−0.251752	+	0.939550i
$494$	−6.64161	−	21.9606i	−0.298820	−	0.988053i
$495$	−0.309043	+	1.29565i	−0.0138904	+	0.0582352i
$496$	6.25157	−	4.76385i	0.280704	−	0.213903i
$497$	−0.234861	−	8.36568i	−0.0105350	−	0.375252i
$498$	−10.4497	−	16.8359i	−0.468264	−	0.754436i
$499$	5.42096	−	9.38938i	0.242675	−	0.420326i	−0.718800	−	0.695217i	$-0.755308\pi$
$499$	5.42096	−	9.38938i	0.242675	−	0.420326i	0.961475	+	0.274891i	$0.0886417\pi$
$500$	−13.3298	+	17.9532i	−0.596126	+	0.802891i
$501$	−9.07955	−	15.7262i	−0.405644	−	0.702597i
$502$	5.14265	−	0.164048i	0.229528	−	0.00732180i
$503$	−2.03813	+	2.03813i	−0.0908758	+	0.0908758i	−0.751083	−	0.660207i	$-0.770468\pi$
$503$	−2.03813	+	2.03813i	−0.0908758	+	0.0908758i	0.660207	+	0.751083i	$0.270468\pi$
$504$	4.10471	−	9.71219i	0.182838	−	0.432615i
$505$	9.08736	−	2.70635i	0.404382	−	0.120431i
$506$	−2.72830	+	2.90810i	−0.121288	+	0.129281i
$507$	−4.40551	+	16.4416i	−0.195655	+	0.730196i
$508$	33.3742	+	29.3673i	1.48074	+	1.30296i
$509$	10.5939	+	6.11641i	0.469568	+	0.271105i	0.716059	−	0.698040i	$-0.245944\pi$
$509$	10.5939	+	6.11641i	0.469568	+	0.271105i	−0.246491	+	0.969145i	$0.579278\pi$
$510$	22.6840	+	20.1318i	1.00447	+	0.891450i
$511$	4.23216	−	17.7759i	0.187220	−	0.786361i
$512$	−6.40523	−	21.7019i	−0.283074	−	0.959098i
$513$	−23.6649	+	6.34100i	−1.04483	+	0.279962i
$514$	−9.43939	+	2.85479i	−0.416353	+	0.125919i
$515$	35.1457	−	0.972069i	1.54870	−	0.0428345i
$516$	−9.32685	+	6.20946i	−0.410592	+	0.273356i
$517$	1.96771	−	1.96771i	0.0865397	−	0.0865397i
$518$	−26.4655	+	8.82197i	−1.16283	+	0.387615i
$519$	9.18010			0.402962
$520$	8.43266	+	11.1639i	0.369797	+	0.489570i
$521$	−1.56024	−	2.70242i	−0.0683554	−	0.118395i	0.829822	−	0.558028i	$-0.188442\pi$
$521$	−1.56024	−	2.70242i	−0.0683554	−	0.118395i	−0.898178	+	0.439633i	$0.855109\pi$
$522$	−8.30559	−	4.44836i	−0.363526	−	0.194700i
$523$	1.80211	+	6.72558i	0.0788010	+	0.294089i	0.994068	−	0.108758i	$-0.0346873\pi$
$523$	1.80211	+	6.72558i	0.0788010	+	0.294089i	−0.915267	+	0.402847i	$0.868021\pi$
$524$	32.2085	+	15.9505i	1.40703	+	0.696800i
$525$	−21.2089	−	17.9376i	−0.925630	−	0.782863i
$526$	8.17527	−	34.9297i	0.356459	−	1.52301i
$527$	−8.66931	+	2.32294i	−0.377641	+	0.101189i
$528$	−3.28513	+	1.34789i	−0.142967	+	0.0586593i
$529$	−18.6025	+	10.7401i	−0.808803	+	0.466963i
$530$	−1.14302	+	2.28368i	−0.0496495	+	0.0991969i
$531$		−	3.82451i		−	0.165970i
$532$	−16.2390	+	35.2450i	−0.704049	+	1.52806i
$533$	6.28632	+	6.28632i	0.272291	+	0.272291i
$534$	23.5386	−	25.0898i	1.01862	−	1.08574i
$535$	0.0347359	+	1.25590i	0.00150177	+	0.0542971i
$536$	−25.1286	−	4.21353i	−1.08539	−	0.181997i
$537$	9.78557	+	36.5202i	0.422278	+	1.57596i
$538$	−14.1979	−	22.8748i	−0.612116	−	0.986201i
$539$	2.47588	−	1.62117i	0.106644	−	0.0698288i
$540$	12.2025	−	8.62020i	0.525112	−	0.370954i
$541$	1.93050	−	3.34372i	0.0829986	−	0.143758i	−0.821538	−	0.570154i	$-0.806884\pi$
$541$	1.93050	−	3.34372i	0.0829986	−	0.143758i	0.904537	+	0.426396i	$0.140217\pi$
$542$	14.0873	−	26.3026i	0.605103	−	1.12979i
$543$	−29.5452	−	7.91661i	−1.26791	−	0.339734i
$544$	−2.64010	+	25.7031i	−0.113193	+	1.10201i
$545$	−3.33700	−	11.2049i	−0.142941	−	0.479967i
$546$	−14.5037	+	9.57620i	−0.620700	+	0.409824i
$547$	−25.7583	−	25.7583i	−1.10135	−	1.10135i	−0.994249	−	0.107098i	$-0.965844\pi$
$547$	−25.7583	−	25.7583i	−1.10135	−	1.10135i	−0.107098	−	0.994249i	$-0.534156\pi$
$548$	−26.3551	−	5.28820i	−1.12583	−	0.225901i
$549$	2.25928	−	1.30439i	0.0964235	−	0.0556701i
$550$	0.260325	+	2.97811i	0.0111003	+	0.126987i
$551$	30.0304	+	17.3381i	1.27934	+	0.738626i
$552$	−39.4283	+	3.78350i	−1.67818	+	0.161036i
$553$	4.47854	−	8.28569i	0.190447	−	0.352344i
$554$	5.19503	−	22.1963i	0.220716	−	0.943032i
$555$	34.0514	+	8.12205i	1.44540	+	0.344762i
$556$	−12.3081	+	0.786042i	−0.521979	+	0.0333356i
$557$	−16.2233	−	4.34701i	−0.687402	−	0.184189i	−0.101821	−	0.994803i	$-0.532467\pi$
$557$	−16.2233	−	4.34701i	−0.687402	−	0.184189i	−0.585581	+	0.810614i	$0.699134\pi$
$558$	−0.124836	−	3.91341i	−0.00528472	−	0.165668i
$559$	5.90224			0.249638
$560$	1.85637	−	23.5914i	0.0784459	−	0.996918i
$561$	4.05479			0.171193
$562$	0.270876	+	8.49156i	0.0114262	+	0.358195i
$563$	10.8007	+	2.89404i	0.455195	+	0.121969i	0.479129	−	0.877744i	$-0.340953\pi$
$563$	10.8007	+	2.89404i	0.455195	+	0.121969i	−0.0239343	+	0.999714i	$0.507619\pi$
$564$	27.5856	−	1.76173i	1.16157	−	0.0741821i
$565$	−25.4864	+	15.6697i	−1.07222	+	0.659230i
$566$	0.536492	−	2.29222i	0.0225504	−	0.0963491i
$567$	15.5884	+	25.3305i	0.654651	+	1.06378i
$568$	−8.90590	+	0.854600i	−0.373683	+	0.0358582i
$569$	14.1920	+	8.19376i	0.594960	+	0.343500i	0.767056	−	0.641580i	$-0.221721\pi$
$569$	14.1920	+	8.19376i	0.594960	+	0.343500i	−0.172096	+	0.985080i	$0.555054\pi$
$570$	40.6482	−	26.8141i	1.70256	−	1.12312i
$571$	−39.2390	+	22.6547i	−1.64210	+	0.948068i	−0.662018	+	0.749488i	$0.730300\pi$
$571$	−39.2390	+	22.6547i	−1.64210	+	0.948068i	−0.980085	+	0.198580i	$0.936367\pi$
$572$	1.83392	+	0.367979i	0.0766800	+	0.0153860i
$573$	15.0415	+	15.0415i	0.628367	+	0.628367i
$574$	−0.901016	−	15.0100i	−0.0376077	−	0.626507i
$575$	−6.83717	+	32.6383i	−0.285130	+	1.36111i
$576$	−10.6555	−	3.67677i	−0.443978	−	0.153199i
$577$	−30.7727	−	8.24552i	−1.28108	−	0.343265i	−0.446817	−	0.894626i	$-0.647442\pi$
$577$	−30.7727	−	8.24552i	−1.28108	−	0.343265i	−0.834267	+	0.551360i	$0.814109\pi$
$578$	2.57940	−	4.81603i	0.107289	−	0.200320i
$579$	22.2886	−	38.6049i	0.926281	−	1.60437i
$580$	−20.8397	−	3.58523i	−0.865321	−	0.148869i
$581$	12.1286	−	12.8293i	0.503180	−	0.532249i
$582$	−10.2761	−	16.5562i	−0.425960	−	0.686278i
$583$	0.0883660	+	0.329786i	0.00365975	+	0.0136584i
$584$	−19.2655	−	3.23041i	−0.797211	−	0.133675i
$585$	6.96694	−	0.192694i	0.288047	−	0.00796690i
$586$	−19.4934	+	20.7780i	−0.805263	+	0.858331i
$587$	14.5087	+	14.5087i	0.598837	+	0.598837i	0.940003	−	0.341166i	$-0.110822\pi$
$587$	14.5087	+	14.5087i	0.598837	+	0.598837i	−0.341166	+	0.940003i	$0.610822\pi$
$588$	29.1012	+	4.15705i	1.20012	+	0.171434i
$589$			14.4103i			0.593765i
$590$	−2.71100	−	8.14416i	−0.111610	−	0.335290i
$591$	36.4180	−	21.0260i	1.49804	−	0.864892i
$592$	11.3207	+	27.5912i	0.465276	+	1.13399i
$593$	−42.6687	+	11.4330i	−1.75219	+	0.469498i	−0.985092	−	0.172029i	$-0.944968\pi$
$593$	−42.6687	+	11.4330i	−1.75219	+	0.469498i	−0.767100	+	0.641527i	$0.778301\pi$
$594$	0.455188	−	1.94484i	0.0186766	−	0.0797977i
$595$	−12.1870	+	24.1182i	−0.499617	+	0.988749i
$596$	−8.75072	−	4.33359i	−0.358443	−	0.177511i
$597$	−3.95878	−	14.7744i	−0.162022	−	0.604674i
$598$	18.3928	+	9.85093i	0.752136	+	0.402834i
$599$	20.0977	+	34.8103i	0.821170	+	1.42231i	0.904811	+	0.425813i	$0.140012\pi$
$599$	20.0977	+	34.8103i	0.821170	+	1.42231i	−0.0836409	+	0.996496i	$0.526655\pi$
$600$	−17.6008	+	23.9167i	−0.718551	+	0.976396i
$601$	17.3374			0.707207			0.353604	−	0.935395i	$-0.384956\pi$
$601$	17.3374			0.707207			0.353604	+	0.935395i	$0.384956\pi$
$602$	−7.46946	−	6.62349i	−0.304432	−	0.269953i
$603$	−8.97509	+	8.97509i	−0.365494	+	0.365494i
$604$	−5.84810	+	3.89344i	−0.237956	+	0.158422i
$605$	−17.5764	−	16.6303i	−0.714583	−	0.676119i
$606$	12.0527	−	3.64515i	0.489608	−	0.148074i
$607$	−1.27852	+	0.342579i	−0.0518936	+	0.0139048i	−0.284672	−	0.958625i	$-0.591885\pi$
$607$	−1.27852	+	0.342579i	−0.0518936	+	0.0139048i	0.232779	+	0.972530i	$0.425218\pi$
$608$	38.7650	+	14.7755i	1.57213	+	0.599225i
$609$	6.08395	−	25.5538i	0.246534	−	1.03549i
$610$	3.88643	−	4.37914i	0.157357	−	0.177306i
$611$	−12.6099	−	7.28031i	−0.510141	−	0.294530i
$612$	9.66311	+	8.50296i	0.390608	+	0.343712i
$613$	3.75107	−	13.9992i	0.151504	−	0.565422i	−0.847875	−	0.530196i	$-0.822118\pi$
$613$	3.75107	−	13.9992i	0.151504	−	0.565422i	0.999379	−	0.0352258i	$-0.0112150\pi$
$614$	−4.92970	+	5.25458i	−0.198947	+	0.212057i
$615$	−8.97920	+	16.5958i	−0.362076	+	0.669208i
$616$	−1.90793	−	2.52371i	−0.0768728	−	0.101683i
$617$	11.3496	−	11.3496i	0.456918	−	0.456918i	−0.440725	−	0.897642i	$-0.645278\pi$
$617$	11.3496	−	11.3496i	0.456918	−	0.456918i	0.897642	+	0.440725i	$0.145278\pi$
$618$	46.6678	−	1.48868i	1.87725	−	0.0598833i
$619$	10.7582	+	18.6337i	0.432407	+	0.748951i	0.997080	−	0.0763640i	$-0.0243311\pi$
$619$	10.7582	+	18.6337i	0.432407	+	0.748951i	−0.564673	+	0.825315i	$0.690998\pi$
$620$	−3.03985	−	8.24498i	−0.122083	−	0.331127i
$621$	11.1402	−	19.2955i	0.447043	−	0.774300i
$622$	−0.322681	−	0.519883i	−0.0129383	−	0.0208454i
$623$	26.9652	+	14.5751i	1.08034	+	0.583938i
$624$	11.2613	+	14.7782i	0.450814	+	0.591600i
$625$	14.8134	+	20.1386i	0.592536	+	0.805544i
$626$	0.421714	+	1.39440i	0.0168551	+	0.0557316i
$627$	1.68498	−	6.28844i	0.0672917	−	0.251136i
$628$	26.4620	+	5.30966i	1.05595	+	0.211878i
$629$		−	34.0554i		−	1.35788i
$630$	−9.03311	−	7.57444i	−0.359888	−	0.301773i
$631$		−	7.18172i		−	0.285900i	−0.989730	−	0.142950i	$-0.954341\pi$
$631$		−	7.18172i		−	0.285900i	0.989730	−	0.142950i	$-0.0456588\pi$
$632$	−9.16095	−	4.17851i	−0.364403	−	0.166212i
$633$	9.45974	−	35.3042i	0.375991	−	1.40322i
$634$	−38.1670	+	11.5430i	−1.51580	+	0.458430i
$635$	42.3402	−	26.0319i	1.68022	−	1.03304i
$636$	−1.50507	+	3.03915i	−0.0596798	+	0.120510i
$637$	−11.5466	−	10.3180i	−0.457494	−	0.408813i
$638$	−2.40198	+	1.49087i	−0.0950955	+	0.0590239i
$639$	−2.22845	+	3.85979i	−0.0881562	+	0.152691i
$640$	−25.2967	−	0.276446i	−0.999940	−	0.0109275i
$641$	13.1001	+	22.6901i	0.517425	+	0.896206i	0.999795	+	0.0202384i	$0.00644252\pi$
$641$	13.1001	+	22.6901i	0.517425	+	0.896206i	−0.482371	+	0.875967i	$0.660224\pi$
$642$	0.0531964	+	1.66763i	0.00209949	+	0.0658160i
$643$	−30.8400	+	30.8400i	−1.21621	+	1.21621i	−0.247263	+	0.968948i	$0.579531\pi$
$643$	−30.8400	+	30.8400i	−1.21621	+	1.21621i	−0.968948	+	0.247263i	$0.920469\pi$
$644$	−12.2219	−	33.1070i	−0.481610	−	1.30460i
$645$	3.57563	+	12.0062i	0.140790	+	0.472744i
$646$	−34.5483	−	32.4123i	−1.35929	−	1.27525i
$647$	−3.74467	+	13.9753i	−0.147218	+	0.549425i	0.852429	+	0.522844i	$0.175129\pi$
$647$	−3.74467	+	13.9753i	−0.147218	+	0.549425i	−0.999647	+	0.0265817i	$0.991538\pi$
$648$	25.8920	−	18.4558i	1.01713	−	0.725012i
$649$	−0.993813	−	0.573778i	−0.0390106	−	0.0225228i
$650$	14.6993	−	5.34884i	0.576553	−	0.209799i
$651$	10.4608	−	3.12010i	0.409990	−	0.122287i
$652$	−3.69045	−	10.9318i	−0.144529	−	0.428121i
$653$	36.4766	−	9.77388i	1.42744	−	0.382481i	0.539323	−	0.842099i	$-0.318680\pi$
$653$	36.4766	−	9.77388i	1.42744	−	0.382481i	0.888117	+	0.459618i	$0.152014\pi$
$654$	−4.49456	−	14.8613i	−0.175751	−	0.581124i
$655$	27.6179	−	29.1891i	1.07912	−	1.14051i
$656$	−15.9447	+	2.04492i	−0.622535	+	0.0798407i
$657$	−6.88099	+	6.88099i	−0.268453	+	0.268453i
$658$	7.78820	+	23.3642i	0.303616	+	0.910833i
$659$	−5.66966			−0.220859			−0.110429	−	0.993884i	$-0.535223\pi$
$659$	−5.66966			−0.220859			−0.110429	+	0.993884i	$0.535223\pi$
$660$	0.362468	+	3.95345i	0.0141091	+	0.153888i
$661$	14.4408	+	25.0122i	0.561682	+	0.972861i	0.997350	+	0.0727540i	$0.0231788\pi$
$661$	14.4408	+	25.0122i	0.561682	+	0.972861i	−0.435668	+	0.900107i	$0.643488\pi$
$662$	−17.2075	+	32.1284i	−0.668790	+	1.24870i
$663$	−5.49122	−	20.4935i	−0.213261	−	0.795902i
$664$	−14.5596	−	12.0100i	−0.565022	−	0.466079i
$665$	32.3398	+	28.9228i	1.25408	+	1.12158i
$666$	14.4657	+	3.38569i	0.560535	+	0.131193i
$667$	−30.4605	+	8.16187i	−1.17944	+	0.316029i
$668$	−12.9850	−	11.4260i	−0.502404	−	0.442086i
$669$	4.32600	−	2.49762i	0.167253	−	0.0965636i
$670$	−12.7502	+	25.4741i	−0.492582	+	0.984152i
$671$		−	0.782775i		−	0.0302187i
$672$	2.33249	−	31.3397i	0.0899778	−	1.20895i
$673$	−6.90378	−	6.90378i	−0.266121	−	0.266121i	0.561414	−	0.827535i	$-0.310258\pi$
$673$	−6.90378	−	6.90378i	−0.266121	−	0.266121i	−0.827535	+	0.561414i	$0.810258\pi$
$674$	−15.2842	−	14.3392i	−0.588725	−	0.552326i
$675$	−5.20843	−	15.8708i	−0.200473	−	0.610869i
$676$	1.03331	+	16.1799i	0.0397427	+	0.622304i
$677$	3.63810	+	13.5776i	0.139824	+	0.521829i	0.999931	+	0.0117165i	$0.00372956\pi$
$677$	3.63810	+	13.5776i	0.139824	+	0.521829i	−0.860108	+	0.510112i	$0.829604\pi$
$678$	−33.7576	+	20.9527i	−1.29645	+	0.804684i
$679$	11.9271	−	12.6162i	0.457721	−	0.484164i
$680$	26.6046	+	11.2571i	1.02024	+	0.431689i
$681$	−16.4351	+	28.4664i	−0.629794	+	1.09083i
$682$	−1.03564	−	0.554677i	−0.0396568	−	0.0212397i
$683$	−31.3572	−	8.40215i	−1.19985	−	0.321499i	−0.397079	−	0.917784i	$-0.629976\pi$
$683$	−31.3572	−	8.40215i	−1.19985	−	0.321499i	−0.802773	+	0.596285i	$0.796643\pi$
$684$	17.2025	−	11.4528i	0.657754	−	0.437908i
$685$	−14.3013	+	26.4324i	−0.546424	+	1.00993i
$686$	3.03375	+	26.0153i	0.115829	+	0.993269i
$687$	25.3470	+	25.3470i	0.967047	+	0.967047i
$688$	−6.52526	+	8.44524i	−0.248773	+	0.321972i
$689$	1.54712	−	0.893230i	0.0589406	−	0.0340294i
$690$	−8.89606	+	43.3820i	−0.338667	+	1.65152i
$691$	−3.27810	−	1.89261i	−0.124705	−	0.0719984i	0.436350	−	0.899777i	$-0.356271\pi$
$691$	−3.27810	−	1.89261i	−0.124705	−	0.0719984i	−0.561055	+	0.827779i	$0.689604\pi$
$692$	8.28460	−	2.79680i	0.314933	−	0.106318i
$693$	−1.57542	+	0.0442290i	−0.0598453	+	0.00168012i
$694$	25.8583	+	6.05213i	0.981570	+	0.229736i
$695$	−3.19922	+	13.4126i	−0.121353	+	0.508770i
$696$	−27.6951	−	4.64389i	−1.04978	−	0.176026i
$697$	17.7310	+	4.75099i	0.671608	+	0.179957i
$698$	10.6507	−	0.339753i	0.403136	−	0.0128598i
$699$	−29.2253			−1.10540
$700$	−24.6048	−	9.72640i	−0.929975	−	0.367623i
$701$	−5.66595			−0.214000			−0.107000	−	0.994259i	$-0.534124\pi$
$701$	−5.66595			−0.214000			−0.107000	+	0.994259i	$0.534124\pi$
$702$	−10.4459	+	0.333220i	−0.394257	+	0.0125766i
$703$	−52.8154	−	14.1518i	−1.99197	−	0.533747i
$704$	−2.55403	+	2.21725i	−0.0962585	+	0.0835657i
$705$	7.17030	−	30.0612i	0.270049	−	1.13217i
$706$	−50.7592	−	11.8802i	−1.91035	−	0.447116i
$707$	5.87996	+	9.55470i	0.221138	+	0.359341i
$708$	−3.64602	−	10.8001i	−0.137026	−	0.405894i
$709$	−10.3830	−	5.99462i	−0.389941	−	0.225133i	0.292193	−	0.956359i	$-0.405615\pi$
$709$	−10.3830	−	5.99462i	−0.389941	−	0.225133i	−0.682135	+	0.731227i	$0.738948\pi$
$710$	−2.00940	+	9.79893i	−0.0754115	+	0.367747i
$711$	−4.34388	+	2.50794i	−0.162908	+	0.0940552i
$712$	13.5986	−	29.8136i	0.509630	−	1.11731i
$713$	−9.26659	−	9.26659i	−0.347037	−	0.347037i
$714$	−16.0485	+	32.0974i	−0.600600	+	1.20121i
$715$	0.995155	−	1.83929i	0.0372167	−	0.0687857i
$716$	19.9572	+	29.9765i	0.745836	+	1.12027i
$717$	15.2348	+	4.08214i	0.568952	+	0.152450i
$718$	22.5590	+	12.0823i	0.841893	+	0.450907i
$719$	−12.5797	+	21.7886i	−0.469142	+	0.812578i	−0.999378	−	0.0352721i	$-0.988770\pi$
$719$	−12.5797	+	21.7886i	−0.469142	+	0.812578i	0.530235	+	0.847850i	$0.322104\pi$
$720$	−7.42663	+	10.1817i	−0.276774	+	0.379450i
$721$	11.8905	+	39.8653i	0.442826	+	1.48466i
$722$	−41.7939	+	25.9407i	−1.55541	+	0.965413i
$723$	−3.94095	−	14.7078i	−0.146565	−	0.546989i
$724$	−29.0750	+	1.85684i	−1.08056	+	0.0690089i
$725$	−10.6711	+	21.0964i	−0.396315	+	0.783502i
$726$	−23.4350	−	21.9861i	−0.869753	−	0.815979i
$727$	−20.9986	−	20.9986i	−0.778795	−	0.778795i	0.200831	−	0.979626i	$-0.435636\pi$
$727$	−20.9986	−	20.9986i	−0.778795	−	0.778795i	−0.979626	+	0.200831i	$0.935636\pi$
$728$	−10.1714	+	13.0607i	−0.376977	+	0.484063i
$729$			5.20463i			0.192764i
$730$	−9.77525	+	19.5304i	−0.361798	+	0.722853i
$731$	10.5542	−	6.09346i	0.390360	−	0.225375i
$732$	5.13651	−	5.83735i	0.189851	−	0.215755i
$733$	18.0645	−	4.84038i	0.667229	−	0.178783i	0.0907227	−	0.995876i	$-0.471082\pi$
$733$	18.0645	−	4.84038i	0.667229	−	0.178783i	0.576506	+	0.817093i	$0.304416\pi$
$734$	−32.2501	−	7.54812i	−1.19037	−	0.278606i
$735$	13.9936	−	29.7386i	0.516161	−	1.09692i
$736$	−34.4295	+	15.4266i	−1.26909	+	0.568632i
$737$	0.985709	+	3.67872i	0.0363091	+	0.135507i
$738$	−3.78085	+	7.05926i	−0.139175	+	0.259855i
$739$	8.20856	+	14.2176i	0.301957	+	0.523004i	0.976579	−	0.215159i	$-0.0690269\pi$
$739$	8.20856	+	14.2176i	0.301957	+	0.523004i	−0.674622	+	0.738163i	$0.735694\pi$
$740$	33.2042	−	3.04430i	1.22061	−	0.111911i
$741$	−34.0646			−1.25140
$742$	−2.96031	−	0.605769i	−0.108676	−	0.0222385i
$743$	11.1710	−	11.1710i	0.409825	−	0.409825i	−0.471852	−	0.881678i	$-0.656414\pi$
$743$	11.1710	−	11.1710i	0.409825	−	0.409825i	0.881678	+	0.471852i	$0.156414\pi$
$744$	−4.08330	−	10.9322i	−0.149701	−	0.400793i
$745$	−7.50352	+	7.93039i	−0.274908	+	0.290547i
$746$	2.37504	+	7.85309i	0.0869563	+	0.287522i
$747$	−9.08175	+	2.43345i	−0.332284	+	0.0890352i
$748$	3.65925	−	1.23533i	0.133795	−	0.0451680i
$749$	−1.42455	+	0.424896i	−0.0520519	+	0.0155254i
$750$	19.7854	+	26.6606i	0.722462	+	0.973506i
$751$	24.0345	+	13.8763i	0.877032	+	0.506355i	0.869679	−	0.493618i	$-0.164326\pi$
$751$	24.0345	+	13.8763i	0.877032	+	0.506355i	0.00735334	+	0.999973i	$0.497659\pi$
$752$	24.3580	−	9.99408i	0.888244	−	0.364447i
$753$	1.97724	−	7.37915i	0.0720545	−	0.268911i
$754$	10.7880	+	10.1210i	0.392874	+	0.368584i
$755$	2.24198	+	7.52812i	0.0815941	+	0.273976i
$756$	13.5936	+	11.3007i	0.494394	+	0.411004i
$757$	−4.34481	+	4.34481i	−0.157915	+	0.157915i	−0.781642	−	0.623727i	$-0.785618\pi$
$757$	−4.34481	+	4.34481i	−0.157915	+	0.157915i	0.623727	+	0.781642i	$0.285618\pi$
$758$	−0.919421	−	28.8225i	−0.0333949	−	1.04688i
$759$	2.96028	+	5.12735i	0.107451	+	0.186111i
$760$	28.5139	−	36.5823i	1.03431	−	1.32698i
$761$	11.7897	−	20.4203i	0.427376	−	0.740236i	−0.569263	−	0.822155i	$-0.692772\pi$
$761$	11.7897	−	20.4203i	0.427376	−	0.740236i	0.996639	+	0.0819190i	$0.0261049\pi$
$762$	56.0810	−	34.8084i	2.03160	−	1.26098i
$763$	11.7812	−	7.25014i	0.426508	−	0.262473i
$764$	18.1567	+	8.99169i	0.656887	+	0.325308i
$765$	12.2591	−	7.53722i	0.443229	−	0.272509i
$766$	14.2852	−	4.32033i	0.516145	−	0.156100i
$767$	−1.55408	+	5.79992i	−0.0561147	+	0.209423i
$768$	−33.5954	−	0.224767i	−1.21227	−	0.00811059i
$769$			11.6924i			0.421638i	0.977525	+	0.210819i	$0.0676131\pi$
$769$			11.6924i			0.421638i	−0.977525	+	0.210819i	$0.932387\pi$
$770$	−3.32345	+	1.21092i	−0.119769	+	0.0436385i
$771$			14.6421i			0.527323i
$772$	8.35302	−	41.6295i	0.300632	−	1.49828i
$773$	−4.86514	+	18.1569i	−0.174987	+	0.653060i	0.821567	+	0.570112i	$0.193100\pi$
$773$	−4.86514	+	18.1569i	−0.174987	+	0.653060i	−0.996554	+	0.0829479i	$0.973566\pi$
$774$	1.53906	+	5.08890i	0.0553202	+	0.182917i
$775$	−9.80972	+	0.543056i	−0.352376	+	0.0195071i
$776$	−14.3177	−	11.8105i	−0.513976	−	0.423972i
$777$	1.16240	+	41.4041i	0.0417007	+	1.48536i
$778$	1.68808	+	2.71972i	0.0605205	+	0.0975066i
$779$	14.7363	−	25.5241i	0.527984	−	0.914495i
$780$	19.4904	−	7.18594i	0.697869	−	0.257298i
$781$	0.668654	+	1.15814i	0.0239263	+	0.0414416i
$782$	43.0594	−	1.37357i	1.53980	−	0.0491188i
$783$	11.1695	−	11.1695i	0.399167	−	0.399167i
$784$	27.5289	−	5.11440i	0.983177	−	0.182657i
$785$	14.3593	−	26.5396i	0.512506	−	0.947239i
$786$	36.5122	−	38.9184i	1.30235	−	1.38817i
$787$	−13.2968	+	49.6245i	−0.473982	+	1.76892i	0.151262	+	0.988494i	$0.451666\pi$
$787$	−13.2968	+	49.6245i	−0.473982	+	1.76892i	−0.625244	+	0.780429i	$0.715001\pi$
$788$	26.4598	−	30.0700i	0.942590	−	1.07120i
$789$	−46.1276	−	26.6318i	−1.64219	−	0.948117i
$790$	−7.47240	+	8.41973i	−0.265856	+	0.299561i
$791$	−25.7240	−	24.3190i	−0.914639	−	0.864685i
$792$	0.160938	+	1.67716i	0.00571868	+	0.0595951i
$793$	−3.95626	+	1.06008i	−0.140491	+	0.0376444i
$794$	23.4001	−	7.07698i	0.830439	−	0.251153i
$795$	2.75425	+	2.60599i	0.0976831	+	0.0924250i
$796$	−8.07374	−	12.1271i	−0.286166	−	0.429832i
$797$	1.34897	−	1.34897i	0.0477829	−	0.0477829i	−0.682812	−	0.730594i	$-0.739243\pi$
$797$	1.34897	−	1.34897i	0.0477829	−	0.0477829i	0.730594	+	0.682812i	$0.239243\pi$
$798$	43.1098	+	38.2273i	1.52607	+	1.35323i
$799$	−30.0647			−1.06361
$800$	−8.59746	+	26.9459i	−0.303966	+	0.952683i
$801$	−8.16191	−	14.1368i	−0.288387	−	0.499501i
$802$	6.21254	+	3.32736i	0.219372	+	0.117493i
$803$	0.755719	+	2.82038i	0.0266688	+	0.0995292i
$804$	−16.7888	+	33.9012i	−0.592095	+	1.19560i
$805$	−39.3952	+	2.19731i	−1.38850	+	0.0774449i
$806$	−1.40089	+	5.98547i	−0.0493444	+	0.210829i
$807$	−38.6117	+	10.3460i	−1.35919	+	0.364195i
$808$	9.76647	−	6.96154i	0.343583	−	0.244906i
$809$	−3.46174	+	1.99864i	−0.121708	+	0.0702684i	−0.559618	−	0.828750i	$-0.689052\pi$
$809$	−3.46174	+	1.99864i	−0.121708	+	0.0702684i	0.437910	+	0.899019i	$0.355719\pi$
$810$	−11.2278	−	33.7298i	−0.394506	−	1.18514i
$811$		−	41.2999i		−	1.45024i	−0.688625	−	0.725118i	$-0.741785\pi$
$811$		−	41.2999i		−	1.45024i	0.688625	−	0.725118i	$-0.258215\pi$
$812$	−2.29472	−	24.9146i	−0.0805290	−	0.874332i
$813$	−31.3259	−	31.3259i	−1.09865	−	1.09865i
$814$	3.05003	−	3.25103i	0.106903	−	0.113949i
$815$	−12.8948	+	0.356648i	−0.451686	+	0.0124928i
$816$	35.3941	+	14.7996i	1.23904	+	0.518090i
$817$	−5.06432	−	18.9003i	−0.177178	−	0.661238i
$818$	1.55596	+	2.50685i	0.0544027	+	0.0876501i
$819$	2.35706	+	7.90252i	0.0823624	+	0.276136i
$820$	−3.04724	+	17.7125i	−0.106414	+	0.618547i
$821$	26.7751	−	46.3758i	0.934457	−	1.61853i	0.158857	−	0.987302i	$-0.449219\pi$
$821$	26.7751	−	46.3758i	0.934457	−	1.61853i	0.775600	−	0.631225i	$-0.217448\pi$
$822$	−18.8433	+	35.1825i	−0.657235	+	1.22713i
$823$	0.366523	+	0.0982095i	0.0127762	+	0.00342337i	0.265201	−	0.964193i	$-0.414562\pi$
$823$	0.366523	+	0.0982095i	0.0127762	+	0.00342337i	−0.252425	+	0.967616i	$0.581228\pi$
$824$	41.6619	−	15.5612i	1.45136	−	0.542100i
$825$	4.34433	+	0.910063i	0.151250	+	0.0316843i
$826$	8.47541	−	5.59598i	0.294897	−	0.194709i
$827$	−2.07441	−	2.07441i	−0.0721345	−	0.0721345i	0.670119	−	0.742254i	$-0.266243\pi$
$827$	−2.07441	−	2.07441i	−0.0721345	−	0.0721345i	−0.742254	+	0.670119i	$0.766243\pi$
$828$	−3.69739	+	18.4269i	−0.128493	+	0.640380i
$829$	23.1175	−	13.3469i	0.802903	−	0.463556i	−0.0415820	−	0.999135i	$-0.513240\pi$
$829$	23.1175	−	13.3469i	0.802903	−	0.463556i	0.844485	+	0.535579i	$0.179906\pi$
$830$	−17.6143	+	11.6195i	−0.611402	+	0.403320i
$831$	−29.3121	−	16.9234i	−1.01683	−	0.587065i
$832$	14.6651	+	9.90571i	0.508421	+	0.343419i
$833$	−31.2995	−	6.52954i	−1.08446	−	0.226235i
$834$	−4.17307	+	17.8299i	−0.144502	+	0.617398i
$835$	−16.4734	+	10.1283i	−0.570085	+	0.350503i
$836$	−0.395213	−	6.18836i	−0.0136687	−	0.214029i
$837$	6.34068	+	1.69898i	0.219166	+	0.0587253i
$838$	0.144183	+	4.51991i	0.00498071	+	0.156138i
$839$	23.5830			0.814175			0.407087	−	0.913389i	$-0.366544\pi$
$839$	23.5830			0.814175			0.407087	+	0.913389i	$0.366544\pi$
$840$	−32.7298	−	12.7781i	−1.12928	−	0.440888i
$841$	6.64270			0.229059
$842$	1.78628	+	55.9972i	0.0615593	+	1.92979i
$843$	12.1845	+	3.26482i	0.419656	+	0.112446i
$844$	−2.21878	−	34.7424i	−0.0763736	−	1.19588i
$845$	17.6319	+	4.20562i	0.606556	+	0.144678i
$846$	2.98895	−	12.7706i	0.102762	−	0.439063i
$847$	13.6137	−	25.1866i	0.467773	−	0.865422i
$848$	−0.432347	+	3.20122i	−0.0148469	+	0.109930i
$849$	−3.02707	−	1.74768i	−0.103889	−	0.0599802i
$850$	20.7626	−	24.7401i	0.712150	−	0.848578i
$851$	43.0636	−	24.8628i	1.47620	−	0.852285i
$852$	−2.61333	+	13.0242i	−0.0895313	+	0.446203i
$853$	35.4043	+	35.4043i	1.21222	+	1.21222i	0.970295	+	0.241926i	$0.0777791\pi$
$853$	35.4043	+	35.4043i	1.21222	+	1.21222i	0.241926	+	0.970295i	$0.422221\pi$
$854$	6.19638	+	3.09816i	0.212036	+	0.106017i
$855$	−6.59491	−	22.1444i	−0.225541	−	0.757321i
$856$	0.556064	+	1.48875i	0.0190059	+	0.0508843i
$857$	−38.0169	−	10.1866i	−1.29863	−	0.347967i	−0.457699	−	0.889107i	$-0.651326\pi$
$857$	−38.0169	−	10.1866i	−1.29863	−	0.347967i	−0.840932	+	0.541140i	$0.817993\pi$
$858$	1.31121	−	2.44817i	0.0447639	−	0.0835792i
$859$	−15.9154	+	27.5663i	−0.543026	+	0.940549i	0.455702	+	0.890132i	$0.349388\pi$
$859$	−15.9154	+	27.5663i	−0.543026	+	0.940549i	−0.998728	+	0.0504166i	$0.983945\pi$
$860$	6.88463	+	9.74568i	0.234764	+	0.332325i
$861$	−21.7193	−	5.17100i	−0.740190	−	0.176227i
$862$	10.9616	+	17.6607i	0.373355	+	0.601525i
$863$	−10.0303	−	37.4334i	−0.341434	−	1.27425i	−0.896723	−	0.442592i	$-0.854059\pi$
$863$	−10.0303	−	37.4334i	−0.341434	−	1.27425i	0.555289	−	0.831657i	$-0.312608\pi$
$864$	11.0718	−	15.3150i	0.376670	−	0.521027i
$865$	−0.270285	−	9.77229i	−0.00918996	−	0.332268i
$866$	8.25533	−	8.79937i	0.280528	−	0.299015i
$867$	−5.73580	−	5.73580i	−0.194798	−	0.194798i
$868$	8.48977	−	6.00271i	0.288162	−	0.203745i
$869$			1.50503i			0.0510547i
$870$	−14.0524	+	28.0760i	−0.476422	+	0.951866i
$871$	17.2579	−	9.96384i	0.584761	−	0.337612i
$872$	−8.58376	−	12.0423i	−0.290683	−	0.407804i
$873$	−8.93088	+	2.39302i	−0.302264	+	0.0809915i
$874$	15.7633	−	67.3502i	0.533200	−	2.27815i
$875$	−18.4703	+	23.1051i	−0.624411	+	0.781096i
$876$	−12.8716	+	25.9913i	−0.434890	+	0.878164i
$877$	0.720839	+	2.69021i	0.0243410	+	0.0908419i	0.977028	−	0.213112i	$-0.0683599\pi$
$877$	0.720839	+	2.69021i	0.0243410	+	0.0908419i	−0.952687	+	0.303954i	$0.901693\pi$
$878$	−8.25836	−	4.42307i	−0.278706	−	0.149271i
$879$	21.1508	+	36.6343i	0.713399	+	1.23564i
$880$	1.53156	+	3.45736i	0.0516289	+	0.116548i
$881$	−40.5035			−1.36460			−0.682299	−	0.731074i	$-0.739020\pi$
$881$	−40.5035			−1.36460			−0.682299	+	0.731074i	$0.739020\pi$
$882$	5.88527	−	12.6460i	0.198167	−	0.425812i
$883$	17.0113	−	17.0113i	0.572477	−	0.572477i	−0.360343	−	0.932820i	$-0.617340\pi$
$883$	17.0113	−	17.0113i	0.572477	−	0.572477i	0.932820	+	0.360343i	$0.117340\pi$
$884$	−11.1991	−	16.8215i	−0.376666	−	0.565767i
$885$	−12.7396	+	0.352354i	−0.428236	+	0.0118443i
$886$	13.2108	−	3.99538i	0.443825	−	0.134228i
$887$	−37.6278	+	10.0823i	−1.26342	+	0.338532i	−0.827505	−	0.561458i	$-0.810241\pi$
$887$	−37.6278	+	10.0823i	−1.26342	+	0.338532i	−0.435912	+	0.899989i	$0.643574\pi$
$888$	44.0778	−	4.22966i	1.47916	−	0.141938i
$889$	42.7348	+	40.4008i	1.43328	+	1.35500i
$890$	−27.4014	−	24.3184i	−0.918496	−	0.815153i
$891$	−4.11597	−	2.37636i	−0.137890	−	0.0796109i
$892$	3.14309	−	3.57194i	0.105238	−	0.119597i
$893$	−12.4935	+	46.6264i	−0.418079	+	1.56029i
$894$	−9.92000	+	10.5737i	−0.331774	+	0.353639i
$895$	38.5880	−	11.4921i	1.28985	−	0.384137i
$896$	−7.44294	−	28.9931i	−0.248651	−	0.968593i
$897$	21.9054	−	21.9054i	0.731401	−	0.731401i
$898$	25.4620	−	0.812223i	0.849677	−	0.0271042i
$899$	−4.64548	−	8.04621i	−0.154936	−	0.268356i
$900$	8.44471	+	11.2789i	0.281490	+	0.375964i
$901$	1.84434	−	3.19448i	0.0614438	−	0.106424i
$902$	1.26715	+	2.04155i	0.0421914	+	0.0679760i
$903$	−12.6237	+	7.76860i	−0.420089	+	0.258523i
$904$	−24.0812	+	29.1934i	−0.800929	+	0.970957i
$905$	−7.55741	+	31.6842i	−0.251217	+	1.05322i
$906$	3.01970	+	9.98467i	0.100323	+	0.331719i
$907$	5.92604	−	22.1163i	0.196771	−	0.734359i	−0.795030	−	0.606569i	$-0.792545\pi$
$907$	5.92604	−	22.1163i	0.196771	−	0.734359i	0.991801	−	0.127789i	$-0.0407881\pi$
$908$	−6.15933	+	30.6966i	−0.204405	+	1.01870i
$909$		−	5.97469i		−	0.198168i
$910$	10.6210	+	15.1573i	0.352082	+	0.502461i
$911$		−	43.8022i		−	1.45123i	−0.688100	−	0.725616i	$-0.741555\pi$
$911$		−	43.8022i		−	1.45123i	0.688100	−	0.725616i	$-0.258445\pi$
$912$	37.6604	−	48.7415i	1.24706	−	1.61399i
$913$	−0.730164	+	2.72501i	−0.0241649	+	0.0901847i
$914$	1.71907	−	0.519906i	0.0568619	−	0.0171970i
$915$	−4.55312	−	7.40554i	−0.150522	−	0.244820i
$916$	30.5966	+	15.1522i	1.01094	+	0.500644i
$917$	41.8273	+	22.6083i	1.38126	+	0.746591i
$918$	−18.3351	+	11.3802i	−0.605147	+	0.375603i
$919$	16.0826	−	27.8558i	0.530515	−	0.918879i	−0.468851	−	0.883277i	$-0.655332\pi$
$919$	16.0826	−	27.8558i	0.530515	−	0.918879i	0.999366	−	0.0356018i	$-0.0113348\pi$
$920$	5.18843	+	41.8604i	0.171057	+	1.38010i
$921$	5.34886	+	9.26450i	0.176251	+	0.305276i
$922$	0.793673	+	24.8805i	0.0261382	+	0.819395i
$923$	4.94790	−	4.94790i	0.162862	−	0.162862i
$924$	−4.40671	+	1.62680i	−0.144970	+	0.0535176i
$925$	7.64343	−	36.4871i	0.251315	−	1.19969i
$926$	20.0211	+	18.7832i	0.657934	+	0.617256i
$927$	5.73402	−	21.3997i	0.188330	−	0.702857i
$928$	−26.4083	+	4.24667i	−0.866896	+	0.139404i
$929$	35.6942	+	20.6080i	1.17109	+	0.676128i	0.953936	−	0.300010i	$-0.0969900\pi$
$929$	35.6942	+	20.6080i	1.17109	+	0.676128i	0.217152	+	0.976138i	$0.430323\pi$
$930$	−13.0242	+	0.776376i	−0.427080	+	0.0254584i
$931$	−23.1331	+	45.8280i	−0.758156	+	1.50195i
$932$	−26.3744	+	8.90373i	−0.863921	+	0.291651i
$933$	−0.877541	+	0.235137i	−0.0287294	+	0.00769802i
$934$	5.25228	+	17.3667i	0.171860	+	0.568257i
$935$	−0.119383	−	4.31636i	−0.00390424	−	0.141160i
$936$	8.25864	−	3.08470i	0.269942	−	0.100827i
$937$	25.3650	−	25.3650i	0.828637	−	0.828637i	−0.158691	−	0.987328i	$-0.550727\pi$
$937$	25.3650	−	25.3650i	0.828637	−	0.828637i	0.987328	+	0.158691i	$0.0507274\pi$
$938$	−33.0218	−	6.75725i	−1.07820	−	0.220632i
$939$	2.16296			0.0705855
$940$	−2.68756	−	29.3133i	−0.0876586	−	0.956094i
$941$	−11.4729	−	19.8717i	−0.374007	−	0.647799i	0.616171	−	0.787612i	$-0.288683\pi$
$941$	−11.4729	−	19.8717i	−0.374007	−	0.647799i	−0.990178	+	0.139814i	$0.955350\pi$
$942$	18.9197	−	35.3252i	0.616438	−	1.15096i
$943$	6.93711	+	25.8897i	0.225903	+	0.843083i
$944$	−6.58071	−	8.63581i	−0.214184	−	0.281072i
$945$	16.5392	−	10.8199i	0.538022	−	0.351970i
$946$	1.55327	+	0.363542i	0.0505012	+	0.0118198i
$947$	29.3070	−	7.85278i	0.952348	−	0.255181i	0.250990	−	0.967990i	$-0.419244\pi$
$947$	29.3070	−	7.85278i	0.952348	−	0.255181i	0.701359	+	0.712809i	$0.252577\pi$
$948$	−9.87592	+	11.2234i	−0.320755	+	0.364519i
$949$	13.2312	−	7.63904i	0.429503	−	0.247974i
$950$	−29.7406	−	42.4808i	−0.964914	−	1.37826i
$951$			59.2035i			1.91981i
$952$	−4.70426	+	33.8556i	−0.152466	+	1.09727i
$953$	−1.41682	−	1.41682i	−0.0458953	−	0.0458953i	0.683787	−	0.729682i	$-0.260332\pi$
$953$	−1.41682	−	1.41682i	−0.0458953	−	0.0458953i	−0.729682	+	0.683787i	$0.760332\pi$
$954$	1.17356	+	1.10101i	0.0379956	+	0.0356464i
$955$	15.5689	−	16.4546i	0.503798	−	0.532459i
$956$	14.9923	−	0.957466i	0.484885	−	0.0309666i
$957$	1.08639	+	4.05445i	0.0351179	+	0.131062i
$958$	17.8302	−	11.0668i	0.576066	−	0.357553i
$959$	−34.5926	−	8.23593i	−1.11705	−	0.265952i
$960$	−11.2657	+	35.8324i	−0.363600	+	1.15649i
$961$	−13.5695	+	23.5030i	−0.437725	+	0.758163i
$962$	−20.5617	−	11.0126i	−0.662936	−	0.355060i
$963$	0.764696	+	0.204900i	0.0246420	+	0.00660280i
$964$	−8.03737	−	12.0724i	−0.258866	−	0.388827i
$965$	−41.7515	−	22.5897i	−1.34403	−	0.727189i
$966$	−52.3042	+	3.13970i	−1.68286	+	0.101018i
$967$	30.6644	+	30.6644i	0.986102	+	0.986102i	0.999905	−	0.0138026i	$-0.00439363\pi$
$967$	30.6644	+	30.6644i	0.986102	+	0.986102i	−0.0138026	+	0.999905i	$0.504394\pi$
$968$	−27.8472	−	12.7017i	−0.895042	−	0.408248i
$969$	−60.9131	+	35.1682i	−1.95681	+	1.12977i
$970$	−17.3217	+	11.4265i	−0.556166	+	0.366883i
$971$	24.2994	+	14.0293i	0.779806	+	0.450221i	0.836362	−	0.548178i	$-0.184678\pi$
$971$	24.2994	+	14.0293i	0.779806	+	0.450221i	−0.0565554	+	0.998399i	$0.518012\pi$
$972$	−8.68902	−	25.7384i	−0.278701	−	0.825559i
$973$	−16.3088	+	0.457860i	−0.522837	+	0.0146783i
$974$	−48.1139	−	11.2610i	−1.54167	−	0.360826i
$975$	−1.28374	−	23.1893i	−0.0411125	−	0.742653i
$976$	2.85706	−	6.83281i	0.0914521	−	0.218713i
$977$	−26.6150	−	7.13146i	−0.851488	−	0.228156i	−0.193422	−	0.981116i	$-0.561959\pi$
$977$	−26.6150	−	7.13146i	−0.851488	−	0.228156i	−0.658066	+	0.752960i	$0.728625\pi$
$978$	−17.1222	+	0.546190i	−0.547508	+	0.0174652i
$979$	−4.89802			−0.156541
$980$	3.56841	−	31.1009i	0.113989	−	0.993482i
$981$	−7.36695			−0.235209
$982$	−7.33671	+	0.234037i	−0.234124	+	0.00746842i
$983$	−32.6601	−	8.75124i	−1.04169	−	0.279121i	−0.302879	−	0.953029i	$-0.597948\pi$
$983$	−32.6601	−	8.75124i	−1.04169	−	0.279121i	−0.738815	+	0.673908i	$0.764614\pi$
$984$	−3.94704	+	23.5392i	−0.125827	+	0.750404i
$985$	−23.4545	−	38.1482i	−0.747324	−	1.21550i
$986$	29.7395	+	6.96051i	0.947099	+	0.221668i
$987$	36.5523	−	1.02618i	1.16347	−	0.0326638i
$988$	−30.7417	+	10.3781i	−0.978023	+	0.330171i
$989$	15.4106	+	8.89729i	0.490027	+	0.282917i
$990$	1.84533	+	0.378410i	0.0586485	+	0.0120267i
$991$	−38.7625	+	22.3796i	−1.23133	+	0.710910i	−0.967308	−	0.253605i	$-0.918384\pi$
$991$	−38.7625	+	22.3796i	−1.23133	+	0.710910i	−0.264025	+	0.964516i	$0.585050\pi$
$992$	−7.01556	−	8.62175i	−0.222744	−	0.273741i
$993$	38.2642	+	38.2642i	1.21428	+	1.21428i
$994$	−11.8142	+	0.709181i	−0.374725	+	0.0224939i
$995$	−15.6109	+	4.64914i	−0.494898	+	0.147388i
$996$	−23.3263	+	15.5298i	−0.739123	+	0.492080i
$997$	−8.01061	−	2.14644i	−0.253699	−	0.0679784i	0.129728	−	0.991550i	$-0.458590\pi$
$997$	−8.01061	−	2.14644i	−0.253699	−	0.0679784i	−0.383427	+	0.923571i	$0.625256\pi$
$998$	−13.5163	−	7.23913i	−0.427850	−	0.229151i
$999$	−12.4539	+	21.5708i	−0.394025	+	0.682471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.w.b.23.10	yes	72
4.3	odd	2	inner	140.2.w.b.23.8	✓	72
5.2	odd	4	inner	140.2.w.b.107.18	yes	72
5.3	odd	4		700.2.be.e.107.1		72
5.4	even	2		700.2.be.e.443.9		72
7.2	even	3		980.2.k.k.883.5		36
7.3	odd	6		980.2.x.m.263.16		72
7.4	even	3	inner	140.2.w.b.123.16	yes	72
7.5	odd	6		980.2.k.j.883.5		36
7.6	odd	2		980.2.x.m.863.10		72
20.3	even	4		700.2.be.e.107.3		72
20.7	even	4	inner	140.2.w.b.107.16	yes	72
20.19	odd	2		700.2.be.e.443.11		72
28.3	even	6		980.2.x.m.263.18		72
28.11	odd	6	inner	140.2.w.b.123.18	yes	72
28.19	even	6		980.2.k.j.883.6		36
28.23	odd	6		980.2.k.k.883.6		36
28.27	even	2		980.2.x.m.863.8		72
35.2	odd	12		980.2.k.k.687.6		36
35.4	even	6		700.2.be.e.543.3		72
35.12	even	12		980.2.k.j.687.6		36
35.17	even	12		980.2.x.m.67.8		72
35.18	odd	12		700.2.be.e.207.11		72
35.27	even	4		980.2.x.m.667.18		72
35.32	odd	12	inner	140.2.w.b.67.8	yes	72
140.27	odd	4		980.2.x.m.667.16		72
140.39	odd	6		700.2.be.e.543.1		72
140.47	odd	12		980.2.k.j.687.5		36
140.67	even	12	inner	140.2.w.b.67.10	yes	72
140.87	odd	12		980.2.x.m.67.10		72
140.107	even	12		980.2.k.k.687.5		36
140.123	even	12		700.2.be.e.207.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.8	✓	72	4.3	odd	2	inner
140.2.w.b.23.10	yes	72	1.1	even	1	trivial
140.2.w.b.67.8	yes	72	35.32	odd	12	inner
140.2.w.b.67.10	yes	72	140.67	even	12	inner
140.2.w.b.107.16	yes	72	20.7	even	4	inner
140.2.w.b.107.18	yes	72	5.2	odd	4	inner
140.2.w.b.123.16	yes	72	7.4	even	3	inner
140.2.w.b.123.18	yes	72	28.11	odd	6	inner
700.2.be.e.107.1		72	5.3	odd	4
700.2.be.e.107.3		72	20.3	even	4
700.2.be.e.207.9		72	140.123	even	12
700.2.be.e.207.11		72	35.18	odd	12
700.2.be.e.443.9		72	5.4	even	2
700.2.be.e.443.11		72	20.19	odd	2
700.2.be.e.543.1		72	140.39	odd	6
700.2.be.e.543.3		72	35.4	even	6
980.2.k.j.687.5		36	140.47	odd	12
980.2.k.j.687.6		36	35.12	even	12
980.2.k.j.883.5		36	7.5	odd	6
980.2.k.j.883.6		36	28.19	even	6
980.2.k.k.687.5		36	140.107	even	12
980.2.k.k.687.6		36	35.2	odd	12
980.2.k.k.883.5		36	7.2	even	3
980.2.k.k.883.6		36	28.23	odd	6
980.2.x.m.67.8		72	35.17	even	12
980.2.x.m.67.10		72	140.87	odd	12
980.2.x.m.263.16		72	7.3	odd	6
980.2.x.m.263.18		72	28.3	even	6
980.2.x.m.667.16		72	140.27	odd	4
980.2.x.m.667.18		72	35.27	even	4
980.2.x.m.863.8		72	28.27	even	2
980.2.x.m.863.10		72	7.6	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0450897 - 1.41349i) q^{2} +(-2.02821 - 0.543458i) q^{3} +(-1.99593 + 0.127468i) q^{4} +(-0.518800 + 2.17505i) q^{5} +(-0.676724 + 2.89137i) q^{6} +(-2.64471 + 0.0742486i) q^{7} +(0.270171 + 2.81549i) q^{8} +(1.22023 + 0.704499i) q^{9} +(3.09782 + 0.635249i) q^{10} +(0.366133 - 0.211387i) q^{11} +(4.11745 + 0.826174i) q^{12} +(-1.56422 - 1.56422i) q^{13} +(0.224199 + 3.73493i) q^{14} +(2.23429 - 4.12952i) q^{15} +(3.96750 - 0.508836i) q^{16} +(-4.41198 - 1.18219i) q^{17} +(0.940785 - 1.75655i) q^{18} +(-3.66683 + 6.35114i) q^{19} +(0.758241 - 4.40739i) q^{20} +(5.40439 + 1.28670i) q^{21} +(-0.315303 - 0.507996i) q^{22} +(-1.72616 - 6.44210i) q^{23} +(0.982138 - 5.85725i) q^{24} +(-4.46169 - 2.25683i) q^{25} +(-2.14049 + 2.28155i) q^{26} +(2.36225 + 2.36225i) q^{27} +(5.26920 - 0.485311i) q^{28} -4.72835i q^{29} +(-5.93780 - 2.97195i) q^{30} +(1.70170 - 0.982474i) q^{31} +(-0.898130 - 5.58510i) q^{32} +(-0.857477 + 0.229760i) q^{33} +(-1.47208 + 6.28961i) q^{34} +(1.21058 - 5.79090i) q^{35} +(-2.52529 - 1.25059i) q^{36} +(1.92971 + 7.20177i) q^{37} +(9.14263 + 4.89667i) q^{38} +(2.32248 + 4.02266i) q^{39} +(-6.26401 - 0.873042i) q^{40} -4.01882 q^{41} +(1.57506 - 7.69709i) q^{42} +(-1.88664 + 1.88664i) q^{43} +(-0.703833 + 0.468585i) q^{44} +(-2.16537 + 2.28856i) q^{45} +(-9.02804 + 2.73038i) q^{46} +(6.35786 - 1.70358i) q^{47} +(-8.32348 - 1.12414i) q^{48} +(6.98897 - 0.392732i) q^{49} +(-2.98885 + 6.40834i) q^{50} +(8.30597 + 4.79545i) q^{51} +(3.32147 + 2.92269i) q^{52} +(-0.209015 + 0.780053i) q^{53} +(3.23251 - 3.44554i) q^{54} +(0.269828 + 0.906026i) q^{55} +(-0.923572 - 7.42610i) q^{56} +(10.8887 - 10.8887i) q^{57} +(-6.68350 + 0.213200i) q^{58} +(-1.35717 - 2.35069i) q^{59} +(-3.93311 + 8.52705i) q^{60} +(0.925760 - 1.60346i) q^{61} +(-1.46545 - 2.36104i) q^{62} +(-3.27945 - 1.77259i) q^{63} +(-7.85401 + 1.52133i) q^{64} +(4.21378 - 2.59074i) q^{65} +(0.363428 + 1.20168i) q^{66} +(-2.33152 + 8.70137i) q^{67} +(8.95671 + 1.79718i) q^{68} +14.0041i q^{69} +(-8.23999 - 1.45004i) q^{70} +3.16317i q^{71} +(-1.65384 + 3.62588i) q^{72} +(-1.78752 + 6.67113i) q^{73} +(10.0927 - 3.05236i) q^{74} +(7.82277 + 7.00208i) q^{75} +(6.50918 - 13.1438i) q^{76} +(-0.952621 + 0.586243i) q^{77} +(5.58129 - 3.46420i) q^{78} +(-1.77995 + 3.08296i) q^{79} +(-0.951598 + 8.89351i) q^{80} +(-5.62086 - 9.73561i) q^{81} +(0.181207 + 5.68058i) q^{82} +(-4.71846 + 4.71846i) q^{83} +(-10.9508 - 1.87928i) q^{84} +(4.86025 - 8.98296i) q^{85} +(2.75182 + 2.58169i) q^{86} +(-2.56966 + 9.59011i) q^{87} +(0.694078 + 0.973735i) q^{88} +(-10.0333 - 5.79271i) q^{89} +(3.33251 + 2.95755i) q^{90} +(4.25305 + 4.02077i) q^{91} +(4.26646 + 12.6380i) q^{92} +(-3.98534 + 1.06787i) q^{93} +(-2.69468 - 8.90999i) q^{94} +(-11.9117 - 11.2705i) q^{95} +(-1.21367 + 11.8159i) q^{96} +(-4.64008 + 4.64008i) q^{97} +(-0.870255 - 9.86117i) q^{98} +0.595688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33}+ \cdots - 90 q^{98}+O(q^{100}) \) 72 * q + 2 * q^2 - 8 * q^5 - 16 * q^6 - 4 * q^8 + 2 * q^10 + 10 * q^12 - 28 * q^16 + 4 * q^17 - 20 * q^18 - 56 * q^20 + 4 * q^21 - 16 * q^22 - 16 * q^25 - 4 * q^26 + 42 * q^28 - 32 * q^30 - 38 * q^32 - 64 * q^33 + 16 * q^36 - 4 * q^37 + 12 * q^38 + 2 * q^40 - 40 * q^41 + 78 * q^42 - 12 * q^45 - 28 * q^46 + 12 * q^48 - 28 * q^50 + 48 * q^52 - 24 * q^53 + 36 * q^56 - 16 * q^57 + 30 * q^58 - 10 * q^60 - 20 * q^61 + 56 * q^62 + 4 * q^65 + 44 * q^66 - 12 * q^68 + 84 * q^70 + 44 * q^72 - 12 * q^73 + 112 * q^76 + 16 * q^77 + 64 * q^78 + 52 * q^80 - 52 * q^81 - 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 - 32 * q^90 + 44 * q^92 + 12 * q^93 - 48 * q^96 - 24 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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