LMFDB - Embedded newform 372.2.ba.a.55.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(43,372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("372.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 0, 19])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.ba (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			55.4
Character	$\chi$	$=$	372.55
Dual form			372.2.ba.a.115.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03878 + 0.959657i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.158117 - 1.99374i) q^{4} +(0.276419 - 0.478772i) q^{5} +(-0.816554 + 1.15466i) q^{6} +(-1.75660 + 3.94539i) q^{7} +(1.74906 + 2.22279i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.172319 + 0.762605i) q^{10} +(-0.0305488 - 0.290652i) q^{11} +(-0.259860 - 1.98305i) q^{12} +(-3.37405 + 3.03801i) q^{13} +(-1.96151 - 5.78412i) q^{14} +(0.170836 - 0.525780i) q^{15} +(-3.95000 - 0.630487i) q^{16} +(7.17664 + 0.754296i) q^{17} +(-0.558643 + 1.29920i) q^{18} +(5.40660 + 4.86812i) q^{19} +(-0.910840 - 0.626810i) q^{20} +(-0.897923 + 4.22439i) q^{21} +(0.310660 + 0.272606i) q^{22} +(-0.250567 - 0.182047i) q^{23} +(2.17298 + 1.81057i) q^{24} +(2.34719 + 4.06544i) q^{25} +(0.589441 - 6.39375i) q^{26} +(0.809017 - 0.587785i) q^{27} +(7.58834 + 4.12604i) q^{28} +(2.76073 - 0.897015i) q^{29} +(0.327108 + 0.710113i) q^{30} +(-0.709676 - 5.52235i) q^{31} +(4.70822 - 3.13571i) q^{32} +(-0.0903111 - 0.277949i) q^{33} +(-8.17880 + 6.10357i) q^{34} +(1.40338 + 1.93159i) q^{35} +(-0.666480 - 1.88568i) q^{36} +(-8.23631 + 4.75524i) q^{37} +(-10.2880 + 0.131585i) q^{38} +(-2.66868 + 3.67313i) q^{39} +(1.54768 - 0.222979i) q^{40} +(-9.08746 - 1.93160i) q^{41} +(-3.12123 - 5.24990i) q^{42} +(1.38092 - 1.53367i) q^{43} +(-0.584315 + 0.0149494i) q^{44} +(0.0577873 - 0.549810i) q^{45} +(0.434986 - 0.0513514i) q^{46} +(4.80305 + 1.56060i) q^{47} +(-3.99477 + 0.204542i) q^{48} +(-7.79656 - 8.65896i) q^{49} +(-6.33963 - 1.97060i) q^{50} +(7.17664 - 0.754296i) q^{51} +(5.52351 + 7.20734i) q^{52} +(-1.35967 - 3.05386i) q^{53} +(-0.276316 + 1.38696i) q^{54} +(-0.147600 - 0.0657159i) q^{55} +(-11.8422 + 2.99617i) q^{56} +(6.30059 + 3.63765i) q^{57} +(-2.00696 + 3.58115i) q^{58} +(1.17380 + 5.52230i) q^{59} +(-1.02126 - 0.423738i) q^{60} -4.08713i q^{61} +(6.03676 + 5.05545i) q^{62} +4.31877i q^{63} +(-1.88159 + 7.77558i) q^{64} +(0.521861 + 2.45516i) q^{65} +(0.360549 + 0.202060i) q^{66} +(9.16547 + 5.29168i) q^{67} +(2.63862 - 14.1891i) q^{68} +(-0.282941 - 0.125973i) q^{69} +(-3.31147 - 0.659727i) q^{70} +(-6.00423 - 13.4857i) q^{71} +(2.50193 + 1.31921i) q^{72} +(-3.36081 + 0.353235i) q^{73} +(3.99230 - 12.8437i) q^{74} +(3.14115 + 3.48860i) q^{75} +(10.5606 - 10.0096i) q^{76} +(1.20040 + 0.390033i) q^{77} +(-0.752775 - 6.37658i) q^{78} +(1.10761 - 10.5382i) q^{79} +(-1.39371 + 1.71687i) q^{80} +(0.669131 - 0.743145i) q^{81} +(11.2935 - 6.71434i) q^{82} +(-0.659561 - 0.140194i) q^{83} +(8.28037 + 2.45817i) q^{84} +(2.34490 - 3.22747i) q^{85} +(0.0373261 + 2.91835i) q^{86} +(2.51390 - 1.45140i) q^{87} +(0.592627 - 0.576271i) q^{88} +(-2.80552 - 3.86147i) q^{89} +(0.467601 + 0.626586i) q^{90} +(-6.05927 - 18.6485i) q^{91} +(-0.402574 + 0.470780i) q^{92} +(-1.84233 - 5.25412i) q^{93} +(-6.48694 + 2.98816i) q^{94} +(3.82521 - 1.24288i) q^{95} +(3.95338 - 4.04608i) q^{96} +(-2.80929 + 2.04107i) q^{97} +(16.4085 + 1.51270i) q^{98} +(-0.146127 - 0.253099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) $ 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{30}\right)$

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 $

$2$	−1.03878	+	0.959657i	−0.734526	+	0.678580i
$2$	−1.03878	+	0.959657i	−0.734526	+	0.678580i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$3$	0.978148	−	0.207912i	0.564734	−	0.120038i
$4$	0.158117	−	1.99374i	0.0790583	−	0.996870i
$5$	0.276419	−	0.478772i	0.123618	−	0.214113i	−0.797574	−	0.603222i	$-0.793883\pi$
$5$	0.276419	−	0.478772i	0.123618	−	0.214113i	0.921192	+	0.389108i	$0.127217\pi$
$6$	−0.816554	+	1.15466i	−0.333357	+	0.471388i
$7$	−1.75660	+	3.94539i	−0.663933	+	1.49122i	0.195890	+	0.980626i	$0.437241\pi$
$7$	−1.75660	+	3.94539i	−0.663933	+	1.49122i	−0.859823	+	0.510592i	$0.829426\pi$
$8$	1.74906	+	2.22279i	0.618386	+	0.785875i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	0.172319	+	0.762605i	0.0544920	+	0.241157i
$11$	−0.0305488	−	0.290652i	−0.00921080	−	0.0876349i	0.988951	−	0.148244i	$-0.0473622\pi$
$11$	−0.0305488	−	0.290652i	−0.00921080	−	0.0876349i	−0.998162	+	0.0606095i	$0.980696\pi$
$12$	−0.259860	−	1.98305i	−0.0750153	−	0.572456i
$13$	−3.37405	+	3.03801i	−0.935793	+	0.842592i	−0.987748	−	0.156057i	$-0.950122\pi$
$13$	−3.37405	+	3.03801i	−0.935793	+	0.842592i	0.0519547	+	0.998649i	$0.483455\pi$
$14$	−1.96151	−	5.78412i	−0.524235	−	1.54587i
$15$	0.170836	−	0.525780i	0.0441098	−	0.135756i
$16$	−3.95000	−	0.630487i	−0.987500	−	0.157622i
$17$	7.17664	+	0.754296i	1.74059	+	0.182944i	0.920883	−	0.389838i	$-0.127469\pi$
$17$	7.17664	+	0.754296i	1.74059	+	0.182944i	0.819708	+	0.572782i	$0.194136\pi$
$18$	−0.558643	+	1.29920i	−0.131673	+	0.306224i
$19$	5.40660	+	4.86812i	1.24036	+	1.11682i	0.988842	+	0.148971i	$0.0475960\pi$
$19$	5.40660	+	4.86812i	1.24036	+	1.11682i	0.251517	+	0.967853i	$0.419071\pi$
$20$	−0.910840	−	0.626810i	−0.203670	−	0.140159i
$21$	−0.897923	+	4.22439i	−0.195943	+	0.921839i
$22$	0.310660	+	0.272606i	0.0662329	+	0.0581199i
$23$	−0.250567	−	0.182047i	−0.0522467	−	0.0379595i	0.561355	−	0.827575i	$-0.310280\pi$
$23$	−0.250567	−	0.182047i	−0.0522467	−	0.0379595i	−0.613602	+	0.789615i	$0.710280\pi$
$24$	2.17298	+	1.81057i	0.443558	+	0.369580i
$25$	2.34719	+	4.06544i	0.469437	+	0.813089i
$26$	0.589441	−	6.39375i	0.115599	−	1.25392i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	7.58834	+	4.12604i	1.43406	+	0.779748i
$29$	2.76073	−	0.897015i	0.512654	−	0.166572i	−0.0412547	−	0.999149i	$-0.513136\pi$
$29$	2.76073	−	0.897015i	0.512654	−	0.166572i	0.553909	+	0.832577i	$0.313136\pi$
$30$	0.327108	+	0.710113i	0.0597214	+	0.129648i
$31$	−0.709676	−	5.52235i	−0.127462	−	0.991844i
$31$	−0.709676	−	5.52235i	−0.127462	−	0.991844i
$32$	4.70822	−	3.13571i	0.832304	−	0.554320i
$33$	−0.0903111	−	0.277949i	−0.0157212	−	0.0483847i
$34$	−8.17880	+	6.10357i	−1.40265	+	1.04675i
$35$	1.40338	+	1.93159i	0.237215	+	0.326499i
$36$	−0.666480	−	1.88568i	−0.111080	−	0.314281i
$37$	−8.23631	+	4.75524i	−1.35404	+	0.781756i	−0.988813	−	0.149161i	$-0.952343\pi$
$37$	−8.23631	+	4.75524i	−1.35404	+	0.781756i	−0.365229	+	0.930918i	$0.619009\pi$
$38$	−10.2880	+	0.131585i	−1.66893	+	0.0213458i
$39$	−2.66868	+	3.67313i	−0.427331	+	0.588171i
$40$	1.54768	−	0.222979i	0.244710	−	0.0352560i
$41$	−9.08746	−	1.93160i	−1.41922	−	0.301665i	−0.566514	−	0.824052i	$-0.691708\pi$
$41$	−9.08746	−	1.93160i	−1.41922	−	0.301665i	−0.852709	+	0.522387i	$0.825042\pi$
$42$	−3.12123	−	5.24990i	−0.481616	−	0.810078i
$43$	1.38092	−	1.53367i	0.210589	−	0.233882i	−0.628592	−	0.777735i	$-0.716368\pi$
$43$	1.38092	−	1.53367i	0.210589	−	0.233882i	0.839181	+	0.543853i	$0.183035\pi$
$44$	−0.584315	+	0.0149494i	−0.0880888	+	0.00225370i
$45$	0.0577873	−	0.549810i	0.00861442	−	0.0819608i
$46$	0.434986	−	0.0513514i	0.0641352	−	0.00757135i
$47$	4.80305	+	1.56060i	0.700597	+	0.227638i	0.637590	−	0.770376i	$-0.279931\pi$
$47$	4.80305	+	1.56060i	0.700597	+	0.227638i	0.0630061	+	0.998013i	$0.479931\pi$
$48$	−3.99477	+	0.204542i	−0.576595	+	0.0295231i
$49$	−7.79656	−	8.65896i	−1.11379	−	1.23699i
$50$	−6.33963	−	1.97060i	−0.896560	−	0.278685i
$51$	7.17664	−	0.754296i	1.00493	−	0.105622i
$52$	5.52351	+	7.20734i	0.765973	+	0.999478i
$53$	−1.35967	−	3.05386i	−0.186765	−	0.419481i	0.795760	−	0.605612i	$-0.207072\pi$
$53$	−1.35967	−	3.05386i	−0.186765	−	0.419481i	−0.982525	+	0.186131i	$0.940405\pi$
$54$	−0.276316	+	1.38696i	−0.0376019	+	0.188741i
$55$	−0.147600	−	0.0657159i	−0.0199024	−	0.00886113i
$56$	−11.8422	+	2.99617i	−1.58248	+	0.400380i
$57$	6.30059	+	3.63765i	0.834533	+	0.481818i
$58$	−2.00696	+	3.58115i	−0.263526	+	0.470228i
$59$	1.17380	+	5.52230i	0.152816	+	0.718942i	0.986108	+	0.166108i	$0.0531201\pi$
$59$	1.17380	+	5.52230i	0.152816	+	0.718942i	−0.833292	+	0.552834i	$0.813547\pi$
$60$	−1.02126	−	0.423738i	−0.131844	−	0.0547043i
$61$		−	4.08713i		−	0.523304i	−0.965162	−	0.261652i	$-0.915733\pi$
$61$		−	4.08713i		−	0.523304i	0.965162	−	0.261652i	$-0.0842673\pi$
$62$	6.03676	+	5.05545i	0.766669	+	0.642042i
$63$			4.31877i			0.544114i
$64$	−1.88159	+	7.77558i	−0.235198	+	0.971947i
$65$	0.521861	+	2.45516i	0.0647289	+	0.304526i
$66$	0.360549	+	0.202060i	0.0443805	+	0.0248718i
$67$	9.16547	+	5.29168i	1.11974	+	0.646482i	0.941335	−	0.337475i	$-0.109573\pi$
$67$	9.16547	+	5.29168i	1.11974	+	0.646482i	0.178405	+	0.983957i	$0.442906\pi$
$68$	2.63862	−	14.1891i	0.319979	−	1.72068i
$69$	−0.282941	−	0.125973i	−0.0340621	−	0.0151654i
$70$	−3.31147	−	0.659727i	−0.395797	−	0.0788525i
$71$	−6.00423	−	13.4857i	−0.712571	−	1.60046i	−0.796963	−	0.604028i	$-0.793561\pi$
$71$	−6.00423	−	13.4857i	−0.712571	−	1.60046i	0.0843919	−	0.996433i	$-0.473105\pi$
$72$	2.50193	+	1.31921i	0.294856	+	0.155471i
$73$	−3.36081	+	0.353235i	−0.393353	+	0.0413431i	−0.299141	−	0.954209i	$-0.596700\pi$
$73$	−3.36081	+	0.353235i	−0.393353	+	0.0413431i	−0.0942124	+	0.995552i	$0.530033\pi$
$74$	3.99230	−	12.8437i	0.464095	−	1.49305i
$75$	3.14115	+	3.48860i	0.362708	+	0.402828i
$76$	10.5606	−	10.0096i	1.21139	−	1.14818i
$77$	1.20040	+	0.390033i	0.136798	+	0.0444484i
$78$	−0.752775	−	6.37658i	−0.0852350	−	0.722005i
$79$	1.10761	−	10.5382i	0.124616	−	1.18564i	−0.736215	−	0.676747i	$-0.763389\pi$
$79$	1.10761	−	10.5382i	0.124616	−	1.18564i	0.860831	−	0.508891i	$-0.169944\pi$
$80$	−1.39371	+	1.71687i	−0.155822	+	0.191952i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	11.2935	−	6.71434i	1.24716	−	0.741475i
$83$	−0.659561	−	0.140194i	−0.0723962	−	0.0153883i	0.171571	−	0.985172i	$-0.445116\pi$
$83$	−0.659561	−	0.140194i	−0.0723962	−	0.0153883i	−0.243967	+	0.969783i	$0.578449\pi$
$84$	8.28037	+	2.45817i	0.903462	+	0.268209i
$85$	2.34490	−	3.22747i	0.254340	−	0.350069i
$86$	0.0373261	+	2.91835i	0.00402498	+	0.314694i
$87$	2.51390	−	1.45140i	0.269518	−	0.155607i
$88$	0.592627	−	0.576271i	0.0631742	−	0.0614307i
$89$	−2.80552	−	3.86147i	−0.297385	−	0.409315i	0.634011	−	0.773324i	$-0.281408\pi$
$89$	−2.80552	−	3.86147i	−0.297385	−	0.409315i	−0.931395	+	0.364009i	$0.881408\pi$
$90$	0.467601	+	0.626586i	0.0492894	+	0.0660479i
$91$	−6.05927	−	18.6485i	−0.635185	−	1.95490i
$92$	−0.402574	+	0.470780i	−0.0419712	+	0.0490822i
$93$	−1.84233	−	5.25412i	−0.191041	−	0.544827i
$94$	−6.48694	+	2.98816i	−0.669077	+	0.308205i
$95$	3.82521	−	1.24288i	0.392458	−	0.127517i
$96$	3.95338	−	4.04608i	0.403490	−	0.412951i
$97$	−2.80929	+	2.04107i	−0.285240	+	0.207239i	−0.721200	−	0.692727i	$-0.756409\pi$
$97$	−2.80929	+	2.04107i	−0.285240	+	0.207239i	0.435960	+	0.899966i	$0.356409\pi$
$98$	16.4085	+	1.51270i	1.65751	+	0.152806i
$99$	−0.146127	−	0.253099i	−0.0146863	−	0.0254374i
$100$	8.47657	−	4.03686i	0.847657	−	0.403686i
$101$	14.3839	+	10.4505i	1.43125	+	1.03986i	0.989782	+	0.142586i	$0.0455419\pi$
$101$	14.3839	+	10.4505i	1.43125	+	1.03986i	0.441467	+	0.897277i	$0.354458\pi$
$102$	−6.73107	+	7.67066i	−0.666475	+	0.759509i
$103$	0.422384	−	1.98716i	0.0416187	−	0.195801i	−0.952427	−	0.304768i	$-0.901421\pi$
$103$	0.422384	−	1.98716i	0.0416187	−	0.195801i	0.994045	+	0.108967i	$0.0347544\pi$
$104$	−12.6543	−	2.18615i	−1.24085	−	0.214370i
$105$	1.77432	+	1.59760i	0.173156	+	0.155910i
$106$	4.34306	+	1.86747i	0.421835	+	0.181385i
$107$	−10.1512	−	1.06693i	−0.981349	−	0.103144i	−0.399754	−	0.916622i	$-0.630905\pi$
$107$	−10.1512	−	1.06693i	−0.981349	−	0.103144i	−0.581595	+	0.813478i	$0.697571\pi$
$108$	−1.04397	−	1.70591i	−0.100456	−	0.164151i
$109$	0.797413	−	2.45419i	0.0763783	−	0.235068i	−0.905577	−	0.424182i	$-0.860562\pi$
$109$	0.797413	−	2.45419i	0.0763783	−	0.235068i	0.981955	+	0.189114i	$0.0605616\pi$
$110$	0.216389	−	0.0733815i	0.0206318	−	0.00699665i
$111$	−7.06766	+	6.36375i	−0.670833	+	0.604020i
$112$	9.42609	−	14.4768i	0.890682	−	1.36793i
$113$	−0.909953	−	8.65762i	−0.0856012	−	0.814441i	−0.950129	−	0.311856i	$-0.899049\pi$
$113$	−0.909953	−	8.65762i	−0.0856012	−	0.814441i	0.864528	−	0.502584i	$-0.167617\pi$
$114$	−10.0358	+	2.26770i	−0.939939	+	0.212390i
$115$	−0.156420	+	0.0696429i	−0.0145863	+	0.00649423i
$116$	−1.35190	−	5.64601i	−0.125521	−	0.524219i
$117$	−1.84668	+	4.14771i	−0.170726	+	0.383456i
$118$	−6.51883	−	4.60999i	−0.600107	−	0.424384i
$119$	−15.5825	+	26.9897i	−1.42845	+	2.47414i
$120$	1.46750	−	0.539887i	0.133964	−	0.0492847i
$121$	10.6761	−	2.26927i	0.970553	−	0.206297i
$122$	3.92225	+	4.24562i	0.355104	+	0.384381i
$123$	−9.29048			−0.837694
$124$	−11.1223	+	0.541734i	−0.998816	+	0.0486492i
$125$	5.35942			0.479361
$126$	−4.14454	−	4.48624i	−0.369225	−	0.399666i
$127$	10.9402	−	2.32540i	0.970783	−	0.206346i	0.304885	−	0.952389i	$-0.401382\pi$
$127$	10.9402	−	2.32540i	0.970783	−	0.206346i	0.665898	+	0.746043i	$0.268049\pi$
$128$	−5.50734	−	9.88277i	−0.486785	−	0.873522i
$129$	1.03188	−	1.78726i	0.0908518	−	0.157360i
$130$	−2.89821	−	2.04956i	−0.254190	−	0.179758i
$131$	3.50165	−	7.86483i	0.305940	−	0.687153i	−0.693505	−	0.720452i	$-0.743935\pi$
$131$	3.50165	−	7.86483i	0.305940	−	0.687153i	0.999445	+	0.0332984i	$0.0106012\pi$
$132$	−0.568438	+	0.136109i	−0.0494762	+	0.0118467i
$133$	−28.7039	+	12.7798i	−2.48894	+	1.10815i
$134$	−14.5991	+	3.29882i	−1.26117	+	0.284975i
$135$	−0.0577873	−	0.549810i	−0.00497354	−	0.0473201i
$136$	10.8757	+	17.2715i	0.932586	+	1.48102i
$137$	13.9532	−	12.5635i	1.19210	−	1.07337i	0.196422	−	0.980519i	$-0.437068\pi$
$137$	13.9532	−	12.5635i	1.19210	−	1.07337i	0.995680	−	0.0928539i	$-0.0295990\pi$
$138$	0.414804	−	0.140668i	0.0353104	−	0.0119744i
$139$	2.11342	−	6.50445i	0.179258	−	0.551700i	−0.820544	−	0.571583i	$-0.806329\pi$
$139$	2.11342	−	6.50445i	0.179258	−	0.551700i	0.999802	+	0.0198830i	$0.00632936\pi$
$140$	4.07299	−	2.49257i	0.344231	−	0.210660i
$141$	5.02256	+	0.527892i	0.422976	+	0.0444565i
$142$	19.1787	+	8.24666i	1.60944	+	0.692044i
$143$	0.986076	+	0.887867i	0.0824599	+	0.0742472i
$144$	−3.86495	+	1.03063i	−0.322079	+	0.0858859i
$145$	0.333652	−	1.56971i	0.0277083	−	0.130357i
$146$	3.15215	−	3.59216i	0.260874	−	0.297289i
$147$	−9.42649	−	6.84874i	−0.777483	−	0.564875i
$148$	8.17841	+	17.1730i	0.672261	+	1.41161i
$149$	3.93109	+	6.80884i	0.322047	+	0.557802i	0.980910	−	0.194461i	$-0.0622957\pi$
$149$	3.93109	+	6.80884i	0.322047	+	0.557802i	−0.658863	+	0.752263i	$0.728962\pi$
$150$	−6.61081	−	0.609452i	−0.539770	−	0.0497615i
$151$	−13.2419	+	9.62079i	−1.07761	+	0.782929i	−0.977265	−	0.212024i	$-0.931995\pi$
$151$	−13.2419	+	9.62079i	−1.07761	+	0.782929i	−0.100345	+	0.994953i	$0.531995\pi$
$152$	−1.36435	+	20.5324i	−0.110664	+	1.66539i
$153$	6.86299	−	2.22992i	0.554840	−	0.180278i
$154$	−1.62124	+	0.746813i	−0.130644	+	0.0601799i
$155$	−2.84011	−	1.18671i	−0.228123	−	0.0953189i
$156$	6.90129	+	5.90144i	0.552546	+	0.472493i
$157$	−4.44574	−	13.6826i	−0.354809	−	1.09199i	−0.956120	−	0.292974i	$-0.905355\pi$
$157$	−4.44574	−	13.6826i	−0.354809	−	1.09199i	0.601312	−	0.799014i	$-0.294645\pi$
$158$	8.96249	+	12.0098i	0.713017	+	0.955445i
$159$	−1.96489	−	2.70444i	−0.155826	−	0.214476i
$160$	−0.199847	−	3.12093i	−0.0157993	−	0.246731i
$161$	1.15839	−	0.668799i	0.0912942	−	0.0527087i
$162$	0.0180865	+	1.41410i	0.00142101	+	0.111102i
$163$	−4.94074	+	6.80034i	−0.386989	+	0.532644i	−0.957419	−	0.288702i	$-0.906776\pi$
$163$	−4.94074	+	6.80034i	−0.386989	+	0.532644i	0.570431	+	0.821346i	$0.306776\pi$
$164$	−5.28799	+	17.8126i	−0.412922	+	1.39093i
$165$	−0.158038	−	0.0335920i	−0.0123032	−	0.00261513i
$166$	0.819675	−	0.487322i	0.0636191	−	0.0378235i
$167$	12.7323	−	14.1407i	0.985256	−	1.09424i	−0.0102884	−	0.999947i	$-0.503275\pi$
$167$	12.7323	−	14.1407i	0.985256	−	1.09424i	0.995545	−	0.0942909i	$-0.0300584\pi$
$168$	−10.9605	+	5.39282i	−0.845618	+	0.416065i
$169$	0.795850	−	7.57201i	0.0612192	−	0.582462i
$170$	0.661442	+	5.60292i	0.0507303	+	0.429724i
$171$	6.91922	+	2.24819i	0.529126	+	0.171923i
$172$	−2.83939	−	2.99570i	−0.216501	−	0.228420i
$173$	4.13165	+	4.58866i	0.314123	+	0.348869i	0.879444	−	0.476002i	$-0.157914\pi$
$173$	4.13165	+	4.58866i	0.314123	+	0.348869i	−0.565321	+	0.824871i	$0.691248\pi$
$174$	−1.21854	+	3.92016i	−0.0923769	+	0.297187i
$175$	−20.1628	+	2.11920i	−1.52417	+	0.160196i
$176$	−0.0625847	+	1.16734i	−0.00471750	+	0.0879912i
$177$	2.29630	+	5.15757i	0.172600	+	0.387667i
$178$	6.62000	+	1.31887i	0.496190	+	0.0988533i
$179$	−18.0905	−	8.05441i	−1.35215	−	0.602015i	−0.402524	−	0.915409i	$-0.631867\pi$
$179$	−18.0905	−	8.05441i	−1.35215	−	0.602015i	−0.949623	+	0.313394i	$0.898534\pi$
$180$	−1.08704	−	0.202147i	−0.0810232	−	0.0150671i
$181$	−9.66290	−	5.57888i	−0.718238	−	0.414675i	0.0958658	−	0.995394i	$-0.469438\pi$
$181$	−9.66290	−	5.57888i	−0.718238	−	0.414675i	−0.814104	+	0.580719i	$0.802771\pi$
$182$	24.1904	+	13.5568i	1.79311	+	1.00490i
$183$	−0.849763	−	3.99782i	−0.0628163	−	0.295527i
$184$	−0.0336029	−	0.875368i	−0.00247724	−	0.0645330i
$185$			5.25775i			0.386558i
$186$	6.95593	+	3.68986i	0.510033	+	0.270554i
$187$		−	2.10895i		−	0.154222i
$188$	3.87088	−	9.32927i	0.282313	−	0.680407i
$189$	0.897923	+	4.22439i	0.0653143	+	0.307280i
$190$	−2.78079	+	4.96197i	−0.201740	+	0.359979i
$191$	11.4876	+	6.63237i	0.831213	+	0.479901i	0.854268	−	0.519833i	$-0.174006\pi$
$191$	11.4876	+	6.63237i	0.831213	+	0.479901i	−0.0230545	+	0.999734i	$0.507339\pi$
$192$	−0.223836	+	7.99687i	−0.0161540	+	0.577124i
$193$	−1.94548	−	0.866185i	−0.140039	−	0.0623493i	0.335521	−	0.942033i	$-0.391088\pi$
$193$	−1.94548	−	0.866185i	−0.140039	−	0.0623493i	−0.475560	+	0.879683i	$0.657754\pi$
$194$	0.959499	−	4.81616i	0.0688880	−	0.345780i
$195$	1.02091	+	2.29301i	0.0731092	+	0.164206i
$196$	−18.4965	+	14.1752i	−1.32118	+	1.01251i
$197$	−15.0585	+	1.58272i	−1.07288	+	0.112764i	−0.624457	−	0.781059i	$-0.714680\pi$
$197$	−15.0585	+	1.58272i	−1.07288	+	0.112764i	−0.448420	+	0.893823i	$0.648013\pi$
$198$	0.394681	+	0.122682i	0.0280487	+	0.00871861i
$199$	7.21967	+	8.01825i	0.511789	+	0.568399i	0.942549	−	0.334067i	$-0.108421\pi$
$199$	7.21967	+	8.01825i	0.511789	+	0.568399i	−0.430761	+	0.902466i	$0.641755\pi$
$200$	−4.93126	+	12.3280i	−0.348693	+	0.871721i
$201$	10.0654	+	3.27044i	0.709957	+	0.230679i
$202$	−24.9705	+	2.94785i	−1.75692	+	0.207410i
$203$	−1.31042	+	12.4679i	−0.0919738	+	0.875072i
$204$	−0.369123	−	14.4276i	−0.0258438	−	1.01014i
$205$	−3.43674	+	3.81689i	−0.240033	+	0.266583i
$206$	1.46823	+	2.46956i	0.102296	+	0.172062i
$207$	−0.302949	−	0.0643938i	−0.0210564	−	0.00447568i
$208$	15.2429	−	9.87284i	1.05691	−	0.684558i
$209$	1.24976	−	1.72015i	0.0864480	−	0.118985i
$210$	−3.37627	+	0.0431830i	−0.232985	+	0.00297991i
$211$	−3.28089	+	1.89422i	−0.225866	+	0.130404i	−0.608663	−	0.793429i	$-0.708294\pi$
$211$	−3.28089	+	1.89422i	−0.225866	+	0.130404i	0.382798	+	0.923832i	$0.374961\pi$
$212$	−6.30360	+	2.22796i	−0.432933	+	0.153017i
$213$	−8.67686	−	11.9427i	−0.594529	−	0.818299i
$214$	11.5687	−	8.63333i	0.790818	−	0.590162i
$215$	−0.352564	−	1.08508i	−0.0240447	−	0.0740020i
$216$	2.72154	+	0.770204i	0.185177	+	0.0524057i
$217$	23.0345	+	6.90062i	1.56368	+	0.468445i
$218$	1.52684	+	3.31460i	0.103411	+	0.224493i
$219$	−3.21393	+	1.04427i	−0.217177	+	0.0705651i
$220$	−0.154358	+	0.283886i	−0.0104068	+	0.0191396i
$221$	−26.5059	+	19.2577i	−1.78298	+	1.29541i
$222$	1.23471	−	13.3931i	0.0828682	−	0.898883i
$223$	7.75561	+	13.4331i	0.519354	+	0.899548i	0.999747	+	0.0224946i	$0.00716084\pi$
$223$	7.75561	+	13.4331i	0.519354	+	0.899548i	−0.480393	+	0.877054i	$0.659506\pi$
$224$	4.10113	+	24.0840i	0.274019	+	1.60918i
$225$	3.79783	+	2.75928i	0.253188	+	0.183952i
$226$	9.25359	+	8.12010i	0.615539	+	0.540141i
$227$	−1.96392	+	9.23951i	−0.130350	+	0.613248i	0.863671	+	0.504056i	$0.168160\pi$
$227$	−1.96392	+	9.23951i	−0.130350	+	0.613248i	−0.994021	+	0.109192i	$0.965174\pi$
$228$	8.24875	−	11.9866i	0.546287	−	0.793830i
$229$	9.75256	+	8.78124i	0.644467	+	0.580281i	0.925188	−	0.379509i	$-0.123907\pi$
$229$	9.75256	+	8.78124i	0.644467	+	0.580281i	−0.280721	+	0.959789i	$0.590574\pi$
$230$	0.0956528	−	0.222453i	0.00630716	−	0.0146681i
$231$	1.25526	+	0.131933i	0.0825900	+	0.00868056i
$232$	6.82255	+	4.56759i	0.447923	+	0.299877i
$233$	−3.60665	+	11.1001i	−0.236280	+	0.727194i	0.760669	+	0.649139i	$0.224871\pi$
$233$	−3.60665	+	11.1001i	−0.236280	+	0.727194i	−0.996949	+	0.0780546i	$0.975129\pi$
$234$	−2.06209	−	6.08072i	−0.134803	−	0.397509i
$235$	2.07483	−	1.86818i	0.135347	−	0.121867i
$236$	11.1956	−	1.46709i	0.728773	−	0.0954992i
$237$	−1.10761	−	10.5382i	−0.0719469	−	0.684529i
$238$	−9.71409	−	42.9901i	−0.629671	−	2.78664i
$239$	10.1148	−	4.50339i	0.654270	−	0.291300i	−0.0526291	−	0.998614i	$-0.516760\pi$
$239$	10.1148	−	4.50339i	0.654270	−	0.291300i	0.706899	+	0.707314i	$0.250093\pi$
$240$	−1.00630	+	1.96912i	−0.0649564	+	0.127106i
$241$	2.29162	−	5.14706i	0.147616	−	0.331551i	−0.824570	−	0.565759i	$-0.808583\pi$
$241$	2.29162	−	5.14706i	0.147616	−	0.331551i	0.972186	+	0.234208i	$0.0752498\pi$
$242$	−8.91235	+	12.6026i	−0.572907	+	0.810128i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−8.14868	−	0.646244i	−0.521666	−	0.0413715i
$245$	−6.30078	+	1.33927i	−0.402542	+	0.0855630i
$246$	9.65074	−	8.91567i	0.615309	−	0.568443i
$247$	−33.0315			−2.10175
$248$	11.0338	−	11.2364i	0.700644	−	0.713511i
$249$	−0.674296			−0.0427317
$250$	−5.56724	+	5.14320i	−0.352103	+	0.325285i
$251$	−13.0324	+	2.77012i	−0.822596	+	0.174848i	−0.599936	−	0.800048i	$-0.704807\pi$
$251$	−13.0324	+	2.77012i	−0.822596	+	0.174848i	−0.222660	+	0.974896i	$0.571474\pi$
$252$	8.61051	+	0.682869i	0.542411	+	0.0430167i
$253$	−0.0452579	+	0.0783890i	−0.00284534	+	0.00492827i
$254$	−9.13281	+	12.9144i	−0.573043	+	0.810321i
$255$	1.62263	−	3.64448i	0.101613	−	0.228226i
$256$	15.2050	+	4.98084i	0.950311	+	0.311303i
$257$	21.8762	−	9.73990i	1.36460	−	0.607558i	0.411831	−	0.911260i	$-0.364889\pi$
$257$	21.8762	−	9.73990i	1.36460	−	0.607558i	0.952767	+	0.303702i	$0.0982226\pi$
$258$	0.643270	+	2.84682i	0.0400482	+	0.177235i
$259$	−4.29336	−	40.8486i	−0.266776	−	2.53821i
$260$	4.97747	−	0.652253i	0.308690	−	0.0404510i
$261$	2.15720	−	1.94235i	0.133527	−	0.120229i
$262$	3.91011	+	11.5302i	0.241567	+	0.712337i
$263$	−2.93078	+	9.02003i	−0.180720	+	0.556199i	−0.999848	−	0.0174114i	$-0.994458\pi$
$263$	−2.93078	+	9.02003i	−0.180720	+	0.556199i	0.819129	+	0.573610i	$0.194458\pi$
$264$	0.459863	−	0.686892i	0.0283026	−	0.0422753i
$265$	−1.83794	−	0.193176i	−0.112904	−	0.0118667i
$266$	17.5527	−	40.8213i	1.07623	−	2.50291i
$267$	−3.54706	−	3.19379i	−0.217076	−	0.195457i
$268$	11.9995	−	17.4369i	0.732983	−	1.06513i
$269$	−1.56411	+	7.35857i	−0.0953656	+	0.448660i	0.904393	+	0.426700i	$0.140324\pi$
$269$	−1.56411	+	7.35857i	−0.0953656	+	0.448660i	−0.999759	+	0.0219599i	$0.993009\pi$
$270$	0.587657	+	0.515674i	0.0357637	+	0.0313829i
$271$	5.09238	+	3.69983i	0.309340	+	0.224749i	0.731613	−	0.681720i	$-0.238768\pi$
$271$	5.09238	+	3.69983i	0.309340	+	0.224749i	−0.422273	+	0.906469i	$0.638768\pi$
$272$	−27.8722	−	7.50424i	−1.69000	−	0.455012i
$273$	−9.80411	−	16.9812i	−0.593372	−	1.02775i
$274$	−2.43760	+	26.4410i	−0.147261	+	1.59736i
$275$	1.10993	−	0.806408i	0.0669310	−	0.0486282i
$276$	−0.295896	+	0.544192i	−0.0178108	+	0.0327565i
$277$	11.4271	−	3.71288i	0.686586	−	0.223085i	0.0551095	−	0.998480i	$-0.482449\pi$
$277$	11.4271	−	3.71288i	0.686586	−	0.223085i	0.631476	+	0.775395i	$0.282449\pi$
$278$	4.04667	+	8.78484i	0.242703	+	0.526880i
$279$	−2.89446	−	4.75627i	−0.173287	−	0.284750i
$280$	−1.83892	+	6.49790i	−0.109897	+	0.388324i
$281$	−5.70975	−	17.5728i	−0.340615	−	1.04831i	−0.963890	−	0.266302i	$-0.914198\pi$
$281$	−5.70975	−	17.5728i	−0.340615	−	1.04831i	0.623274	−	0.782003i	$-0.285802\pi$
$282$	−5.72391	+	4.27157i	−0.340854	+	0.254368i
$283$	2.27582	+	3.13240i	0.135284	+	0.186202i	0.871284	−	0.490779i	$-0.163288\pi$
$283$	2.27582	+	3.13240i	0.135284	+	0.186202i	−0.736000	+	0.676981i	$0.763288\pi$
$284$	−27.8364	+	9.83856i	−1.65179	+	0.583811i
$285$	3.48321	−	2.01103i	0.206327	−	0.119123i
$286$	−1.87636	+	0.0239989i	−0.110952	+	0.00141909i
$287$	23.5840	−	32.4606i	1.39212	−	1.91609i
$288$	3.02577	−	4.77962i	0.178295	−	0.281642i
$289$	34.3067	+	7.29212i	2.01804	+	0.428948i
$290$	1.15979	+	1.95077i	0.0681054	+	0.114553i
$291$	−2.32354	+	2.58055i	−0.136208	+	0.151274i
$292$	0.172860	+	6.75643i	0.0101158	+	0.395390i
$293$	0.958979	−	9.12407i	0.0560241	−	0.533034i	−0.930133	−	0.367222i	$-0.880309\pi$
$293$	0.958979	−	9.12407i	0.0560241	−	0.533034i	0.986157	−	0.165812i	$-0.0530245\pi$
$294$	16.3645	−	1.93188i	0.954395	−	0.112669i
$295$	2.96838	+	0.964485i	0.172826	+	0.0561545i
$296$	−24.9757	−	9.99040i	−1.45168	−	0.580680i
$297$	−0.195555	−	0.217186i	−0.0113473	−	0.0126024i
$298$	−10.6177	−	3.30038i	−0.615066	−	0.191186i
$299$	1.39849	−	0.146987i	0.0808765	−	0.00850046i
$300$	7.45202	−	5.71102i	0.430243	−	0.329726i
$301$	3.62520	+	8.14232i	0.208953	+	0.469316i
$302$	4.52271	−	22.7015i	0.260253	−	1.30633i
$303$	16.2423	+	7.23156i	0.933098	+	0.415442i
$304$	−18.2868	−	22.6379i	−1.04882	−	1.29837i
$305$	−1.95680	−	1.12976i	−0.112046	−	0.0646900i
$306$	−4.98916	+	8.90251i	−0.285211	+	0.508922i
$307$	3.47913	+	16.3680i	0.198564	+	0.934171i	0.958703	+	0.284410i	$0.0917978\pi$
$307$	3.47913	+	16.3680i	0.198564	+	0.934171i	−0.760138	+	0.649761i	$0.774869\pi$
$308$	0.967427	−	2.33161i	0.0551243	−	0.132856i
$309$		−	2.03155i		−	0.115571i
$310$	4.08908	−	1.49281i	0.232244	−	0.0847858i
$311$		−	8.80712i		−	0.499406i	−0.968322	−	0.249703i	$-0.919667\pi$
$311$		−	8.80712i		−	0.499406i	0.968322	−	0.249703i	$-0.0803330\pi$
$312$	−12.8323	+	0.492594i	−0.726484	+	0.0278876i
$313$	−6.46077	−	30.3955i	−0.365184	−	1.71806i	−0.650398	−	0.759594i	$-0.725398\pi$
$313$	−6.46077	−	30.3955i	−0.365184	−	1.71806i	0.285214	−	0.958464i	$-0.407935\pi$
$314$	17.7487	+	9.94677i	1.00162	+	0.561328i
$315$	2.06771	+	1.19379i	0.116502	+	0.0672625i
$316$	−20.8353	−	3.87454i	−1.17208	−	0.217960i
$317$	−9.19087	−	4.09204i	−0.516210	−	0.229832i	0.132060	−	0.991242i	$-0.457841\pi$
$317$	−9.19087	−	4.09204i	−0.516210	−	0.229832i	−0.648271	+	0.761410i	$0.724507\pi$
$318$	4.63642	+	0.923690i	0.259997	+	0.0517979i
$319$	−0.345056	−	0.775009i	−0.0193194	−	0.0433922i
$320$	3.20262	+	3.05017i	0.179032	+	0.170510i
$321$	−10.1512	+	1.06693i	−0.566582	+	0.0595502i
$322$	−0.561496	+	1.80639i	−0.0312909	+	0.100666i
$323$	35.1292	+	39.0149i	1.95464	+	2.17085i
$324$	−1.37584	−	1.45158i	−0.0764354	−	0.0806431i
$325$	−20.2704	−	6.58624i	−1.12440	−	0.365339i
$326$	−1.39367	−	11.8055i	−0.0771883	−	0.653844i
$327$	0.269734	−	2.56635i	0.0149163	−	0.141919i
$328$	−11.6010	−	23.5780i	−0.640556	−	1.30188i
$329$	−14.5942	+	16.2086i	−0.804607	+	0.893606i
$330$	0.196403	−	0.116768i	0.0108116	−	0.00642785i
$331$	6.26389	+	1.33143i	0.344295	+	0.0731821i	0.376814	−	0.926289i	$-0.377020\pi$
$331$	6.26389	+	1.33143i	0.344295	+	0.0731821i	−0.0325192	+	0.999471i	$0.510353\pi$
$332$	−0.383798	+	1.29283i	−0.0210636	+	0.0709530i
$333$	−5.59012	+	7.69414i	−0.306337	+	0.421636i
$334$	0.344153	+	26.9077i	0.0188312	+	1.47232i
$335$	5.06702	−	2.92544i	0.276841	−	0.159834i
$336$	6.21022	−	16.1202i	0.338795	−	0.879430i
$337$	−6.69789	−	9.21885i	−0.364857	−	0.502183i	0.586637	−	0.809850i	$-0.300452\pi$
$337$	−6.69789	−	9.21885i	−0.364857	−	0.502183i	−0.951494	+	0.307667i	$0.900452\pi$
$338$	6.43982	+	8.62937i	0.350280	+	0.469376i
$339$	−2.69009	−	8.27924i	−0.146106	−	0.449667i
$340$	−6.06397	−	5.18543i	−0.328865	−	0.281219i
$341$	−1.58340	+	0.374970i	−0.0857461	+	0.0203057i
$342$	−9.34501	+	4.30471i	−0.505321	+	0.232772i
$343$	19.1067	−	6.20814i	1.03166	−	0.335208i
$344$	5.82434	+	0.387021i	0.314027	+	0.0208668i
$345$	−0.138523	+	0.100643i	−0.00745781	+	0.00541842i
$346$	−8.69540	−	0.801630i	−0.467468	−	0.0430959i
$347$	2.48178	+	4.29857i	0.133229	+	0.230760i	0.924920	−	0.380163i	$-0.124132\pi$
$347$	2.48178	+	4.29857i	0.133229	+	0.230760i	−0.791690	+	0.610922i	$0.790799\pi$
$348$	−2.49623	−	5.24155i	−0.133812	−	0.280977i
$349$	1.00273	+	0.728527i	0.0536750	+	0.0389971i	0.614299	−	0.789073i	$-0.289439\pi$
$349$	1.00273	+	0.728527i	0.0536750	+	0.0389971i	−0.560624	+	0.828070i	$0.689439\pi$
$350$	18.9110	−	21.5508i	1.01084	−	1.15194i
$351$	−0.943968	+	4.44102i	−0.0503853	+	0.237044i
$352$	−1.05523	−	1.27266i	−0.0562440	−	0.0678331i
$353$	2.16014	+	1.94500i	0.114972	+	0.103522i	0.724612	−	0.689157i	$-0.242019\pi$
$353$	2.16014	+	1.94500i	0.114972	+	0.103522i	−0.609639	+	0.792679i	$0.708686\pi$
$354$	−7.33485	−	3.15391i	−0.389843	−	0.167628i
$355$	−8.11627	−	0.853054i	−0.430767	−	0.0452754i
$356$	−8.14237	+	4.98292i	−0.431545	+	0.264094i
$357$	−9.63051	+	29.6397i	−0.509701	+	1.56870i
$358$	26.5215	−	8.99394i	1.40170	−	0.475344i
$359$	9.61922	−	8.66118i	0.507683	−	0.457120i	−0.375043	−	0.927007i	$-0.622372\pi$
$359$	9.61922	−	8.66118i	0.507683	−	0.457120i	0.882726	+	0.469888i	$0.155706\pi$
$360$	1.32318	−	0.833200i	0.0697379	−	0.0439135i
$361$	3.54664	+	33.7440i	0.186665	+	1.77600i
$362$	15.3914	−	3.47786i	0.808955	−	0.182792i
$363$	9.97097	−	4.43936i	0.523340	−	0.233006i
$364$	−38.1384	+	9.13198i	−1.99899	+	0.478646i
$365$	−0.759873	+	1.70670i	−0.0397736	+	0.0893329i
$366$	4.71925	+	3.33736i	0.246679	+	0.174447i
$367$	−0.252646	+	0.437596i	−0.0131880	+	0.0228423i	−0.872544	−	0.488535i	$-0.837531\pi$
$367$	−0.252646	+	0.437596i	−0.0131880	+	0.0228423i	0.859356	+	0.511378i	$0.170865\pi$
$368$	0.874959	+	0.877065i	0.0456104	+	0.0457202i
$369$	−9.08746	+	1.93160i	−0.473074	+	0.100555i
$370$	−5.04564	−	5.46164i	−0.262310	−	0.283937i
$371$	14.4371			0.749537
$372$	−10.7667	+	2.84236i	−0.558225	+	0.147370i
$373$	25.9885			1.34563			0.672816	−	0.739810i	$-0.265084\pi$
$373$	25.9885			1.34563			0.672816	+	0.739810i	$0.265084\pi$
$374$	2.02387	+	2.19073i	0.104652	+	0.113280i
$375$	5.24230	−	1.11429i	0.270711	−	0.0575415i
$376$	4.93192	+	13.4058i	0.254344	+	0.691349i
$377$	−6.58970	+	11.4137i	−0.339387	+	0.587835i
$378$	−4.98671	−	3.52651i	−0.256489	−	0.181384i
$379$	−3.47607	+	7.80738i	−0.178554	+	0.401038i	−0.980544	−	0.196299i	$-0.937108\pi$
$379$	−3.47607	+	7.80738i	−0.178554	+	0.401038i	0.801990	+	0.597337i	$0.203774\pi$
$380$	−1.87316	−	7.82299i	−0.0960911	−	0.401311i
$381$	10.2176	−	4.54918i	0.523465	−	0.233061i
$382$	−18.2979	+	4.13460i	−0.936200	+	0.211545i
$383$	−0.397647	−	3.78336i	−0.0203188	−	0.193321i	0.979654	−	0.200694i	$-0.0643197\pi$
$383$	−0.397647	−	3.78336i	−0.0203188	−	0.193321i	−0.999973	+	0.00737329i	$0.997653\pi$
$384$	−7.44174	−	8.52177i	−0.379759	−	0.434875i
$385$	0.518550	−	0.466904i	0.0264277	−	0.0237957i
$386$	2.85216	−	0.967223i	0.145171	−	0.0492304i
$387$	0.637735	−	1.96275i	0.0324179	−	0.0997721i
$388$	3.62516	+	5.92371i	0.184040	+	0.300731i
$389$	−12.8946	−	1.35528i	−0.653784	−	0.0687155i	−0.228172	−	0.973621i	$-0.573275\pi$
$389$	−12.8946	−	1.35528i	−0.653784	−	0.0687155i	−0.425613	+	0.904905i	$0.639941\pi$
$390$	−3.26101	−	1.40220i	−0.165128	−	0.0710032i
$391$	−1.66091	−	1.49549i	−0.0839958	−	0.0756301i
$392$	5.61040	−	32.4751i	0.283368	−	1.64024i
$393$	1.78994	−	8.42100i	0.0902904	−	0.424783i
$394$	14.1236	−	16.0951i	0.711537	−	0.810861i
$395$	−4.73922	−	3.44325i	−0.238456	−	0.173249i
$396$	−0.527718	+	0.251319i	−0.0265188	+	0.0126293i
$397$	−2.51090	−	4.34901i	−0.126018	−	0.218270i	0.796112	−	0.605149i	$-0.206887\pi$
$397$	−2.51090	−	4.34901i	−0.126018	−	0.218270i	−0.922131	+	0.386879i	$0.873553\pi$
$398$	−15.1944	−	1.40077i	−0.761626	−	0.0702145i
$399$	−25.4196	+	18.4684i	−1.27257	+	0.924577i
$400$	−6.70817	−	17.5384i	−0.335408	−	0.876918i
$401$	20.5921	−	6.69077i	1.02832	−	0.334121i	0.254194	−	0.967153i	$-0.418190\pi$
$401$	20.5921	−	6.69077i	1.02832	−	0.334121i	0.774126	+	0.633032i	$0.218190\pi$
$402$	−13.5942	+	6.26205i	−0.678017	+	0.312323i
$403$	19.1714	+	16.4767i	0.954997	+	0.820762i
$404$	23.1099	−	27.0253i	1.14976	−	1.34456i
$405$	−0.170836	−	0.525780i	−0.00848893	−	0.0261262i
$406$	−10.6036	−	14.2089i	−0.526249	−	0.705175i
$407$	1.63373	+	2.24863i	0.0809809	+	0.111461i
$408$	14.2290	+	14.6329i	0.704441	+	0.724434i
$409$	−27.2300	+	15.7213i	−1.34644	+	0.777367i	−0.987743	−	0.156088i	$-0.950112\pi$
$409$	−27.2300	+	15.7213i	−1.34644	+	0.777367i	−0.358696	+	0.933455i	$0.616778\pi$
$410$	−0.0928946	−	7.26299i	−0.00458774	−	0.358694i
$411$	11.0362	−	15.1900i	0.544375	−	0.749268i
$412$	−3.89510	−	1.15633i	−0.191898	−	0.0569681i
$413$	−23.8495	−	5.06937i	−1.17356	−	0.249448i
$414$	0.376493	−	0.223837i	0.0185036	−	0.0110010i
$415$	−0.249436	+	0.277027i	−0.0122443	+	0.0135987i
$416$	−6.35946	+	24.8837i	−0.311798	+	1.22002i
$417$	0.714890	−	6.80172i	0.0350083	−	0.333082i
$418$	0.352530	+	2.98620i	0.0172428	+	0.146060i
$419$	−2.91296	−	0.946476i	−0.142307	−	0.0462384i	0.236997	−	0.971510i	$-0.423837\pi$
$419$	−2.91296	−	0.946476i	−0.142307	−	0.0462384i	−0.379305	+	0.925272i	$0.623837\pi$
$420$	3.46576	−	3.28492i	0.169112	−	0.160288i
$421$	22.7442	+	25.2600i	1.10848	+	1.23110i	0.970613	+	0.240647i	$0.0773596\pi$
$421$	22.7442	+	25.2600i	1.10848	+	1.23110i	0.137872	+	0.990450i	$0.455974\pi$
$422$	1.59031	−	5.11620i	0.0774150	−	0.249053i
$423$	5.02256	−	0.527892i	0.244205	−	0.0256670i
$424$	4.40996	−	8.36365i	0.214167	−	0.406175i
$425$	13.7784	+	30.9467i	0.668349	+	1.50114i
$426$	20.4742	+	4.07897i	0.991978	+	0.197627i
$427$	16.1254	+	7.17947i	0.780360	+	0.347439i
$428$	−3.73225	+	20.0701i	−0.180405	+	0.970123i
$429$	1.14913	+	0.663448i	0.0554803	+	0.0320316i
$430$	1.40754	+	0.788817i	0.0678777	+	0.0380402i
$431$	−2.83885	−	13.3557i	−0.136743	−	0.643324i	−0.992117	−	0.125314i	$-0.960006\pi$
$431$	−2.83885	−	13.3557i	−0.136743	−	0.643324i	0.855375	−	0.518010i	$-0.173327\pi$
$432$	−3.56621	+	1.81168i	−0.171579	+	0.0871643i
$433$			14.2387i			0.684271i	0.939651	+	0.342135i	$0.111150\pi$
$433$			14.2387i			0.684271i	−0.939651	+	0.342135i	$0.888850\pi$
$434$	−30.5499	+	14.9370i	−1.46644	+	0.716998i
$435$		−	1.60478i		−	0.0769433i
$436$	−4.76692	−	1.97788i	−0.228294	−	0.0947234i
$437$	−0.468484	−	2.20404i	−0.0224106	−	0.105434i
$438$	2.33641	−	4.16903i	0.111638	−	0.199204i
$439$	3.92477	+	2.26597i	0.187319	+	0.108149i	0.590727	−	0.806872i	$-0.298841\pi$
$439$	3.92477	+	2.26597i	0.187319	+	0.108149i	−0.403408	+	0.915020i	$0.632174\pi$
$440$	−0.112089	−	0.443025i	−0.00534363	−	0.0211204i
$441$	−10.6444	−	4.73920i	−0.506878	−	0.225676i
$442$	9.05298	−	45.4410i	0.430606	−	2.16141i
$443$	−0.107095	−	0.240539i	−0.00508823	−	0.0114284i	0.910983	−	0.412443i	$-0.135324\pi$
$443$	−0.107095	−	0.240539i	−0.00508823	−	0.0114284i	−0.916072	+	0.401015i	$0.868658\pi$
$444$	11.5701	+	15.0973i	0.549095	+	0.716486i
$445$	−2.62426	+	0.275821i	−0.124402	+	0.0130752i
$446$	−20.9475	−	6.51129i	−0.991895	−	0.308318i
$447$	5.26082	+	5.84274i	0.248828	+	0.276352i
$448$	−27.3725	−	21.0822i	−1.29323	−	0.996040i
$449$	−15.7919	−	5.13110i	−0.745266	−	0.242152i	−0.0883229	−	0.996092i	$-0.528151\pi$
$449$	−15.7919	−	5.13110i	−0.745266	−	0.242152i	−0.656943	+	0.753940i	$0.728151\pi$
$450$	−6.59306	+	0.778331i	−0.310800	+	0.0366909i
$451$	−0.283813	+	2.70030i	−0.0133642	+	0.127152i
$452$	−17.4049	+	0.445296i	−0.818659	+	0.0209449i
$453$	−10.9522	+	12.1637i	−0.514581	+	0.571500i
$454$	−6.82669	−	11.4825i	−0.320392	−	0.538899i
$455$	−10.6033	−	2.25380i	−0.497090	−	0.105660i
$456$	2.93438	+	20.3673i	0.137415	+	0.953788i
$457$	9.45831	−	13.0182i	0.442441	−	0.608968i	−0.528311	−	0.849051i	$-0.677175\pi$
$457$	9.45831	−	13.0182i	0.442441	−	0.608968i	0.970752	+	0.240083i	$0.0771746\pi$
$458$	−18.5577	+	0.237356i	−0.867145	+	0.0110909i
$459$	6.24939	−	3.60809i	0.291697	−	0.168411i
$460$	0.114117	+	0.322873i	0.00532074	+	0.0150541i
$461$	−10.2140	−	14.0584i	−0.475713	−	0.654763i	0.501961	−	0.864890i	$-0.332612\pi$
$461$	−10.2140	−	14.0584i	−0.475713	−	0.654763i	−0.977674	+	0.210128i	$0.932612\pi$
$462$	−1.43055	+	1.06757i	−0.0665550	+	0.0496678i
$463$	7.79770	+	23.9989i	0.362390	+	1.11532i	0.951599	+	0.307341i	$0.0994393\pi$
$463$	7.79770	+	23.9989i	0.362390	+	1.11532i	−0.589209	+	0.807980i	$0.700561\pi$
$464$	−11.4704	+	1.80261i	−0.532501	+	0.0836839i
$465$	−3.02478	−	0.570285i	−0.140271	−	0.0264463i
$466$	−6.90582	−	14.9917i	−0.319906	−	0.694478i
$467$	−14.3457	+	4.66122i	−0.663842	+	0.215695i	−0.621508	−	0.783408i	$-0.713479\pi$
$467$	−14.3457	+	4.66122i	−0.663842	+	0.215695i	−0.0423344	+	0.999103i	$0.513479\pi$
$468$	7.97746	+	4.33762i	0.368758	+	0.200507i
$469$	−36.9779	+	26.8660i	−1.70748	+	1.24056i
$470$	−0.362469	+	3.93175i	−0.0167194	+	0.181358i
$471$	−7.19336	−	12.4593i	−0.331452	−	0.574092i
$472$	−10.2219	+	12.2679i	−0.470499	+	0.564677i
$473$	−0.487949	−	0.354516i	−0.0224359	−	0.0163007i
$474$	11.2636	+	9.88390i	0.517354	+	0.453983i
$475$	−7.10079	+	33.4066i	−0.325807	+	1.53280i
$476$	51.3465	+	35.3350i	2.35347	+	1.61958i
$477$	−2.48424	−	2.23682i	−0.113745	−	0.102417i
$478$	−6.18529	+	14.3847i	−0.282908	+	0.657942i
$479$	−23.4187	−	2.46141i	−1.07003	−	0.112464i	−0.446900	−	0.894584i	$-0.647472\pi$
$479$	−23.4187	−	2.46141i	−1.07003	−	0.112464i	−0.623128	+	0.782120i	$0.714139\pi$
$480$	−0.844359	−	3.01118i	−0.0385395	−	0.137441i
$481$	13.3433	−	41.0664i	0.608401	−	1.87247i
$482$	2.55893	+	7.54581i	0.116556	+	0.343702i
$483$	0.994029	−	0.895028i	0.0452299	−	0.0407252i
$484$	−2.83627	−	21.6441i	−0.128921	−	0.983824i
$485$	0.200665	+	1.90920i	0.00911171	+	0.0866922i
$486$	0.311699	+	1.37944i	0.0141389	+	0.0625725i
$487$	14.4759	−	6.44510i	0.655967	−	0.292055i	−0.0516358	−	0.998666i	$-0.516443\pi$
$487$	14.4759	−	6.44510i	0.655967	−	0.292055i	0.707602	+	0.706611i	$0.249777\pi$
$488$	9.08484	−	7.14864i	0.411251	−	0.323604i
$489$	−3.41890	+	7.67898i	−0.154608	+	0.347255i
$490$	5.25987	−	7.43780i	0.237617	−	0.336005i
$491$	−0.130262	+	0.225620i	−0.00587863	+	0.0101821i	−0.868950	−	0.494900i	$-0.835205\pi$
$491$	−0.130262	+	0.225620i	−0.00587863	+	0.0101821i	0.863071	+	0.505082i	$0.168538\pi$
$492$	−1.46898	+	18.5228i	−0.0662267	+	0.835072i
$493$	20.4894	−	4.35515i	0.922795	−	0.196146i
$494$	34.3124	−	31.6989i	1.54379	−	1.42620i
$495$	−0.161569			−0.00726197
$496$	−0.678550	+	22.2607i	−0.0304678	+	0.999536i
$497$	63.7535			2.85974
$498$	0.700443	−	0.647093i	0.0313876	−	0.0289969i
$499$	−4.51186	+	0.959025i	−0.201978	+	0.0429318i	−0.307790	−	0.951454i	$-0.599589\pi$
$499$	−4.51186	+	0.959025i	−0.201978	+	0.0429318i	0.105811	+	0.994386i	$0.466256\pi$
$500$	0.847413	−	10.6853i	0.0378975	−	0.477860i
$501$	9.51407	−	16.4789i	0.425057	−	0.736221i
$502$	10.8794	−	15.3841i	0.485570	−	0.686628i
$503$	−16.3176	+	36.6500i	−0.727567	+	1.63414i	0.0448240	+	0.998995i	$0.485727\pi$
$503$	−16.3176	+	36.6500i	−0.727567	+	1.63414i	−0.772391	+	0.635147i	$0.780939\pi$
$504$	−9.59972	+	7.55378i	−0.427605	+	0.336472i
$505$	8.97938	−	3.99788i	0.399577	−	0.177903i
$506$	−0.0282137	−	0.124861i	−0.00125425	−	0.00555074i
$507$	−0.795850	−	7.57201i	−0.0353449	−	0.336285i
$508$	−2.90643	−	22.1795i	−0.128952	−	0.984058i
$509$	−4.29897	+	3.87081i	−0.190549	+	0.171571i	−0.758883	−	0.651227i	$-0.774255\pi$
$509$	−4.29897	+	3.87081i	−0.190549	+	0.171571i	0.568335	+	0.822798i	$0.307588\pi$
$510$	1.81190	+	5.34296i	0.0802323	+	0.236590i
$511$	4.50995	−	13.8802i	0.199509	−	0.614024i
$512$	−20.5745	+	9.41757i	−0.909272	+	0.416202i
$513$	7.23544	+	0.760475i	0.319452	+	0.0335758i
$514$	−13.3775	+	31.1112i	−0.590057	+	1.37226i
$515$	−0.834642	−	0.751515i	−0.0367787	−	0.0331157i
$516$	−3.40018	−	2.33989i	−0.149685	−	0.103008i
$517$	0.306866	−	1.44369i	0.0134959	−	0.0634934i
$518$	43.6604	+	38.3124i	1.91833	+	1.68335i
$519$	4.99540	+	3.62937i	0.219274	+	0.159312i
$520$	−4.54455	+	5.45421i	−0.199292	+	0.239183i
$521$	−18.7233	−	32.4298i	−0.820285	−	1.42077i	−0.905470	−	0.424409i	$-0.860482\pi$
$521$	−18.7233	−	32.4298i	−0.820285	−	1.42077i	0.0851859	−	0.996365i	$-0.472852\pi$
$522$	−0.376859	+	4.08785i	−0.0164947	+	0.178920i
$523$	31.3807	−	22.7994i	1.37218	−	0.996949i	0.374619	−	0.927179i	$-0.377773\pi$
$523$	31.3807	−	22.7994i	1.37218	−	0.996949i	0.997563	−	0.0697699i	$-0.0222265\pi$
$524$	−15.1268	−	8.22493i	−0.660815	−	0.359308i
$525$	−19.2816	+	6.26498i	−0.841519	+	0.273426i
$526$	−5.61170	−	12.1823i	−0.244682	−	0.531176i
$527$	−0.927606	−	40.1672i	−0.0404072	−	1.74971i
$528$	0.181486	+	1.15484i	0.00789815	+	0.0502579i
$529$	−7.07775	−	21.7831i	−0.307728	−	0.947090i
$530$	2.09460	−	1.56313i	0.0909834	−	0.0678980i
$531$	3.31844	+	4.56744i	0.144008	+	0.198210i
$532$	20.9410	+	59.2488i	0.907909	+	2.56876i
$533$	36.5298	−	21.0905i	1.58228	−	0.913530i
$534$	6.74954	−	0.0863276i	0.292081	−	0.00373576i
$535$	−3.31679	+	4.56517i	−0.143397	+	0.197369i
$536$	4.26864	+	29.6284i	0.184377	+	1.27975i
$537$	−19.3698	−	4.11717i	−0.835868	−	0.177669i
$538$	−5.43694	−	9.14493i	−0.234403	−	0.394266i
$539$	−2.27857	+	2.53061i	−0.0981449	+	0.109001i
$540$	−1.10531	+	0.0282789i	−0.0475652	+	0.00121693i
$541$	−3.62144	+	34.4557i	−0.155698	+	1.48137i	0.585823	+	0.810439i	$0.300771\pi$
$541$	−3.62144	+	34.4557i	−0.155698	+	1.48137i	−0.741521	+	0.670929i	$0.765895\pi$
$542$	−8.84042	+	1.04364i	−0.379729	+	0.0448281i
$543$	−10.6117	−	3.44794i	−0.455390	−	0.147965i
$544$	36.1545	−	18.9525i	1.55011	−	0.812580i
$545$	−0.954575	−	1.06016i	−0.0408895	−	0.0454124i
$546$	26.4804	+	8.23112i	1.13326	+	0.352259i
$547$	−21.2945	+	2.23814i	−0.910488	+	0.0956961i	−0.548178	−	0.836362i	$-0.684678\pi$
$547$	−21.2945	+	2.23814i	−0.910488	+	0.0956961i	−0.362310	+	0.932058i	$0.618012\pi$
$548$	−22.8421	−	29.8055i	−0.975768	−	1.27323i
$549$	−1.66239	−	3.73378i	−0.0709490	−	0.159354i
$550$	−0.379090	+	1.90283i	−0.0161645	+	0.0811368i
$551$	19.2929	+	8.58976i	0.821906	+	0.365936i
$552$	−0.214868	−	0.849253i	−0.00914538	−	0.0361466i
$553$	39.6317	+	22.8813i	1.68531	+	0.973014i
$554$	−8.30709	+	14.8229i	−0.352934	+	0.629766i
$555$	1.09315	+	5.14286i	0.0464016	+	0.218302i
$556$	−12.6340	−	5.24208i	−0.535802	−	0.222314i
$557$		−	6.51171i		−	0.275910i	−0.990438	−	0.137955i	$-0.955947\pi$
$557$		−	6.51171i		−	0.275910i	0.990438	−	0.137955i	$-0.0440529\pi$
$558$	7.57109	+	2.16301i	0.320510	+	0.0915675i
$559$			9.36993i			0.396306i
$560$	−4.32552	−	8.51461i	−0.182787	−	0.359808i
$561$	−0.438475	−	2.06286i	−0.0185124	−	0.0870941i
$562$	22.7950	+	12.7748i	0.961550	+	0.538874i
$563$	−31.5913	−	18.2393i	−1.33142	−	0.768693i	−0.345899	−	0.938272i	$-0.612426\pi$
$563$	−31.5913	−	18.2393i	−1.33142	−	0.768693i	−0.985517	+	0.169578i	$0.945759\pi$
$564$	1.84663	−	9.93021i	0.0777571	−	0.418137i
$565$	−4.39655	−	1.95747i	−0.184964	−	0.0823515i
$566$	−5.37010	−	1.06986i	−0.225722	−	0.0449695i
$567$	1.75660	+	3.94539i	0.0737704	+	0.165691i
$568$	19.4742	−	36.9335i	0.817118	−	1.54969i
$569$	2.36955	−	0.249050i	0.0993368	−	0.0104407i	−0.0547296	−	0.998501i	$-0.517430\pi$
$569$	2.36955	−	0.249050i	0.0993368	−	0.0104407i	0.154066	+	0.988060i	$0.450763\pi$
$570$	−1.68838	+	5.43170i	−0.0707183	+	0.227509i
$571$	−3.62881	−	4.03020i	−0.151861	−	0.168659i	0.662414	−	0.749138i	$-0.269532\pi$
$571$	−3.62881	−	4.03020i	−0.151861	−	0.168659i	−0.814275	+	0.580479i	$0.802865\pi$
$572$	1.92609	−	1.82559i	0.0805339	−	0.0763319i
$573$	12.6155	+	4.09903i	0.527021	+	0.171239i
$574$	6.65250	+	56.3518i	0.277670	+	2.35208i
$575$	0.151977	−	1.44596i	0.00633787	−	0.0603008i
$576$	1.44370	+	7.86866i	0.0601541	+	0.327861i
$577$	−1.46489	+	1.62692i	−0.0609840	+	0.0677296i	−0.772865	−	0.634571i	$-0.781177\pi$
$577$	−1.46489	+	1.62692i	−0.0609840	+	0.0677296i	0.711881	+	0.702300i	$0.247844\pi$
$578$	−42.6350	+	25.3478i	−1.77338	+	1.05433i
$579$	−2.08306	−	0.442768i	−0.0865690	−	0.0184008i
$580$	−3.07684	−	0.913414i	−0.127759	−	0.0379274i
$581$	1.71171	−	2.35596i	0.0710135	−	0.0977417i
$582$	−0.0628048	−	4.91041i	−0.00260334	−	0.203543i
$583$	−0.846076	+	0.488482i	−0.0350409	+	0.0202309i
$584$	−6.66342	−	6.85254i	−0.275734	−	0.283560i
$585$	1.47535	+	2.03064i	0.0609982	+	0.0839568i
$586$	7.75982	+	10.3982i	0.320555	+	0.429545i
$587$	−9.78247	−	30.1074i	−0.403766	−	1.24266i	−0.921921	−	0.387377i	$-0.873381\pi$
$587$	−9.78247	−	30.1074i	−0.403766	−	1.24266i	0.518156	−	0.855286i	$-0.326619\pi$
$588$	−15.1451	+	17.7111i	−0.624573	+	0.730392i
$589$	23.0465	−	33.3119i	0.949616	−	1.37259i
$590$	−4.00906	+	1.84674i	−0.165050	+	0.0760292i
$591$	−14.4004	+	4.67898i	−0.592354	+	0.192467i
$592$	35.5315	−	13.5903i	1.46034	−	0.558558i
$593$	−4.34961	+	3.16018i	−0.178617	+	0.129773i	−0.673501	−	0.739186i	$-0.735210\pi$
$593$	−4.34961	+	3.16018i	−0.178617	+	0.129773i	0.494884	+	0.868959i	$0.335210\pi$
$594$	0.411563	+	0.0379421i	0.0168866	+	0.00155678i
$595$	8.61460	+	14.9209i	0.353164	+	0.611698i
$596$	14.1966	−	6.76098i	0.581517	−	0.276940i
$597$	8.72899	+	6.34198i	0.357254	+	0.259560i
$598$	−1.31166	+	1.49475i	−0.0536377	+	0.0611250i
$599$	−2.68188	+	12.6172i	−0.109579	+	0.515526i	0.888784	+	0.458326i	$0.151551\pi$
$599$	−2.68188	+	12.6172i	−0.109579	+	0.515526i	−0.998363	+	0.0572005i	$0.981783\pi$
$600$	−2.26037	+	13.0839i	−0.0922791	+	0.534147i
$601$	8.13255	+	7.32258i	0.331734	+	0.298694i	0.818118	−	0.575051i	$-0.195018\pi$
$601$	8.13255	+	7.32258i	0.331734	+	0.298694i	−0.486384	+	0.873745i	$0.661684\pi$
$602$	−11.5796	−	4.97912i	−0.471950	−	0.202934i
$603$	10.5254	+	1.10626i	0.428627	+	0.0450505i
$604$	17.0876	+	27.9221i	0.695285	+	1.13613i
$605$	1.86461	−	5.73868i	0.0758071	−	0.233310i
$606$	−23.8120	+	8.07510i	−0.967296	+	0.328029i
$607$	−4.28589	+	3.85903i	−0.173959	+	0.156633i	−0.751511	−	0.659720i	$-0.770675\pi$
$607$	−4.28589	+	3.85903i	−0.173959	+	0.156633i	0.577552	+	0.816354i	$0.304008\pi$
$608$	40.7205	+	5.96667i	1.65143	+	0.241981i
$609$	1.31042	+	12.4679i	0.0531011	+	0.505223i
$610$	3.11687	−	0.704291i	0.126198	−	0.0285159i
$611$	−20.9469	+	9.32614i	−0.847419	+	0.377295i
$612$	−3.36073	−	14.0356i	−0.135849	−	0.567356i
$613$	−5.40949	+	12.1499i	−0.218487	+	0.490730i	−0.989222	−	0.146426i	$-0.953223\pi$
$613$	−5.40949	+	12.1499i	−0.218487	+	0.490730i	0.770734	+	0.637156i	$0.219889\pi$
$614$	−19.3217	−	13.6639i	−0.779761	−	0.551432i
$615$	−2.56807	+	4.44802i	−0.103554	+	0.179361i
$616$	1.23261	+	3.35042i	0.0496631	+	0.134992i
$617$	−36.5996	+	7.77948i	−1.47344	+	0.313190i	−0.873489	−	0.486844i	$-0.838148\pi$
$617$	−36.5996	+	7.77948i	−1.47344	+	0.313190i	−0.599954	+	0.800034i	$0.704815\pi$
$618$	1.94960	+	2.11033i	0.0784243	+	0.0848900i
$619$	−21.2869			−0.855594			−0.427797	−	0.903875i	$-0.640710\pi$
$619$	−21.2869			−0.855594			−0.427797	+	0.903875i	$0.640710\pi$
$620$	−2.81506	+	5.47481i	−0.113056	+	0.219874i
$621$	−0.309717			−0.0124285
$622$	8.45181	+	9.14864i	0.338887	+	0.366827i
$623$	20.1632	−	4.28582i	0.807822	−	0.171708i
$624$	12.8571	−	12.8263i	0.514698	−	0.513462i
$625$	−10.2545	+	17.7613i	−0.410179	+	0.710451i
$626$	35.8806	+	25.3741i	1.43408	+	1.01415i
$627$	0.864814	−	1.94240i	0.0345374	−	0.0775722i
$628$	−27.9824	+	6.70020i	−1.11662	+	0.267367i
$629$	−62.6959	+	27.9140i	−2.49985	+	1.11301i
$630$	−3.29352	+	0.744206i	−0.131217	+	0.0296499i
$631$	−0.112226	−	1.06776i	−0.00446765	−	0.0425069i	0.992061	−	0.125758i	$-0.0401363\pi$
$631$	−0.112226	−	1.06776i	−0.00446765	−	0.0425069i	−0.996529	+	0.0832511i	$0.973470\pi$
$632$	25.3614	−	15.9699i	1.00882	−	0.635250i
$633$	−2.81536	+	2.53496i	−0.111901	+	0.100756i
$634$	13.4742	−	4.56936i	0.535129	−	0.181473i
$635$	1.91073	−	5.88063i	0.0758251	−	0.233366i
$636$	−5.70263	+	3.48986i	−0.226124	+	0.138382i
$637$	52.6120	+	5.52974i	2.08456	+	0.219096i
$638$	1.10218	+	0.473926i	0.0436357	+	0.0187629i
$639$	−10.9703	−	9.87768i	−0.433977	−	0.390755i
$640$	−6.25393	−	0.0950276i	−0.247208	−	0.00375630i
$641$	6.92794	−	32.5934i	0.273637	−	1.28736i	−0.599692	−	0.800231i	$-0.704710\pi$
$641$	6.92794	−	32.5934i	0.273637	−	1.28736i	0.873329	−	0.487131i	$-0.161956\pi$
$642$	9.52090	−	10.8499i	0.375760	−	0.428213i
$643$	−24.0988	−	17.5088i	−0.950364	−	0.690480i	0.000529114	−	1.00000i	$-0.499832\pi$
$643$	−24.0988	−	17.5088i	−0.950364	−	0.690480i	−0.950893	+	0.309520i	$0.899832\pi$
$644$	−1.15025	−	2.41528i	−0.0453262	−	0.0951755i
$645$	−0.570461	−	0.988068i	−0.0224619	−	0.0389051i
$646$	−73.9324	−	6.81584i	−2.90883	−	0.268166i
$647$	32.8267	−	23.8500i	1.29055	−	0.937639i	0.290733	−	0.956804i	$-0.406101\pi$
$647$	32.8267	−	23.8500i	1.29055	−	0.937639i	0.999816	+	0.0191656i	$0.00610098\pi$
$648$	2.82220	+	0.187533i	0.110867	+	0.00736697i
$649$	1.56921	−	0.509867i	0.0615968	−	0.0200140i
$650$	27.3769	−	12.6110i	1.07381	−	0.494643i
$651$	23.9658	+	1.96069i	0.939295	+	0.0768456i
$652$	12.7769	+	10.9258i	0.500382	+	0.427887i
$653$	−13.0816	−	40.2610i	−0.511923	−	1.57554i	−0.788812	−	0.614634i	$-0.789304\pi$
$653$	−13.0816	−	40.2610i	−0.511923	−	1.57554i	0.276889	−	0.960902i	$-0.410696\pi$
$654$	2.18262	+	2.92472i	0.0853472	+	0.114365i
$655$	−2.79754	−	3.85048i	−0.109309	−	0.150451i
$656$	34.6776	+	13.3593i	1.35393	+	0.521595i
$657$	−2.92658	+	1.68966i	−0.114177	+	0.0659199i
$658$	−0.394480	−	30.8425i	−0.0153784	−	1.20237i
$659$	−26.0639	+	35.8738i	−1.01530	+	1.39745i	−0.0998599	+	0.995002i	$0.531839\pi$
$659$	−26.0639	+	35.8738i	−1.01530	+	1.39745i	−0.915444	+	0.402445i	$0.868161\pi$
$660$	−0.0919621	+	0.309775i	−0.00357962	+	0.0120580i
$661$	13.1498	+	2.79507i	0.511467	+	0.108716i	0.456414	−	0.889768i	$-0.349134\pi$
$661$	13.1498	+	2.79507i	0.511467	+	0.108716i	0.0550534	+	0.998483i	$0.482467\pi$
$662$	−7.78451	+	4.62813i	−0.302553	+	0.179877i
$663$	−21.9228	+	24.3477i	−0.851411	+	0.945588i
$664$	−0.841989	−	1.71127i	−0.0326755	−	0.0664102i
$665$	−1.81570	+	17.2752i	−0.0704097	+	0.669903i
$666$	−1.57685	−	13.3571i	−0.0611015	−	0.517577i
$667$	−0.855045	−	0.277821i	−0.0331075	−	0.0107573i
$668$	−26.1796	−	27.6208i	−1.01292	−	1.06868i
$669$	10.3790	+	11.5271i	0.401277	+	0.445663i
$670$	−2.45608	+	7.90149i	−0.0948867	+	0.305261i
$671$	−1.18793	+	0.124857i	−0.0458597	+	0.00482005i
$672$	9.01885	+	22.7050i	0.347910	+	0.875865i
$673$	−2.27452	−	5.10867i	−0.0876765	−	0.196925i	0.864386	−	0.502830i	$-0.167708\pi$
$673$	−2.27452	−	5.10867i	−0.0876765	−	0.196925i	−0.952062	+	0.305905i	$0.901041\pi$
$674$	15.8045	+	3.14866i	0.608768	+	0.121282i
$675$	4.28852	+	1.90937i	0.165065	+	0.0734918i
$676$	−14.9708	−	2.78398i	−0.575799	−	0.107076i
$677$	31.1930	+	18.0093i	1.19884	+	0.692153i	0.960297	−	0.278979i	$-0.0899959\pi$
$677$	31.1930	+	18.0093i	1.19884	+	0.692153i	0.238546	+	0.971131i	$0.423329\pi$
$678$	10.7396	+	6.01873i	0.412453	+	0.231148i
$679$	−3.11801	−	14.6691i	−0.119658	−	0.562948i
$680$	11.2754	−	0.432829i	0.432390	−	0.0165982i
$681$			9.44592i			0.361969i
$682$	1.28496	−	1.90903i	0.0492037	−	0.0731007i
$683$			13.7501i			0.526132i	0.964778	+	0.263066i	$0.0847338\pi$
$683$			13.7501i			0.526132i	−0.964778	+	0.263066i	$0.915266\pi$
$684$	5.57635	−	13.4396i	0.213217	−	0.513877i
$685$	−2.15813	−	10.1532i	−0.0824578	−	0.387934i
$686$	−13.8899	+	24.7847i	−0.530319	+	0.946286i
$687$	11.3652	+	6.56168i	0.433608	+	0.250344i
$688$	−6.42160	+	5.18734i	−0.244821	+	0.197765i
$689$	13.8653	+	6.17321i	0.528224	+	0.235181i
$690$	0.0473118	−	0.237480i	0.00180113	−	0.00904070i
$691$	1.10832	+	2.48933i	0.0421625	+	0.0946985i	0.933399	−	0.358841i	$-0.116828\pi$
$691$	1.10832	+	2.48933i	0.0421625	+	0.0946985i	−0.891236	+	0.453539i	$0.850161\pi$
$692$	9.80187	−	7.51189i	0.372611	−	0.285559i
$693$	1.25526	−	0.131933i	0.0476834	−	0.00501172i
$694$	−6.70318	−	2.08360i	−0.254449	−	0.0790924i
$695$	−2.52996	−	2.80980i	−0.0959668	−	0.106582i
$696$	7.62312	+	3.04929i	0.288954	+	0.115583i
$697$	−63.7605	−	20.7170i	−2.41510	−	0.784713i
$698$	−1.74075	+	0.205501i	−0.0658884	+	0.00777832i
$699$	−1.21999	+	11.6074i	−0.0461443	+	0.439034i
$700$	1.03705	+	40.5345i	0.0391970	+	1.53206i
$701$	−6.77040	+	7.51929i	−0.255714	+	0.284000i	−0.857309	−	0.514802i	$-0.827866\pi$
$701$	−6.77040	+	7.51929i	−0.255714	+	0.284000i	0.601595	+	0.798801i	$0.294532\pi$
$702$	−3.28128	−	5.51911i	−0.123844	−	0.208306i
$703$	−67.6795	−	14.3857i	−2.55258	−	0.542568i
$704$	2.31747	+	0.309353i	0.0873429	+	0.0116592i
$705$	1.64107	−	2.25874i	0.0618063	−	0.0850691i
$706$	−4.11043	+	0.0525729i	−0.154698	+	0.00197861i
$707$	−66.4981	+	38.3927i	−2.50092	+	1.44391i
$708$	10.6459	−	3.76273i	0.400099	−	0.141412i
$709$	5.81839	+	8.00833i	0.218514	+	0.300759i	0.904175	−	0.427162i	$-0.140487\pi$
$709$	5.81839	+	8.00833i	0.218514	+	0.300759i	−0.685661	+	0.727921i	$0.740487\pi$
$710$	9.24963	−	6.90270i	0.347133	−	0.259054i
$711$	−3.27442	−	10.0776i	−0.122800	−	0.377940i
$712$	3.67621	−	12.9900i	0.137772	−	0.486822i
$713$	−0.827508	+	1.51291i	−0.0309904	+	0.0566590i
$714$	−18.4400	−	40.0310i	−0.690098	−	1.49812i
$715$	0.697656	−	0.226682i	0.0260909	−	0.00847743i
$716$	−18.9188	+	34.7942i	−0.707029	+	1.30032i
$717$	8.95743	−	6.50796i	0.334521	−	0.243044i
$718$	−1.68046	+	18.2282i	−0.0627142	+	0.680270i
$719$	−12.8877	−	22.3222i	−0.480631	−	0.832478i	0.519122	−	0.854700i	$-0.326259\pi$
$719$	−12.8877	−	22.3222i	−0.480631	−	0.832478i	−0.999753	+	0.0222224i	$0.992926\pi$
$720$	−0.574907	+	2.13531i	−0.0214255	+	0.0795784i
$721$	7.09817	+	5.15712i	0.264350	+	0.192061i
$722$	−36.0669	−	31.6490i	−1.34227	−	1.17785i
$723$	1.17141	−	5.51103i	0.0435651	−	0.204958i
$724$	−12.6507	+	18.3832i	−0.470160	+	0.683206i
$725$	10.1267	+	9.11813i	0.376096	+	0.338639i
$726$	−6.09735	+	14.1802i	−0.226294	+	0.526277i
$727$	−5.78090	−	0.607597i	−0.214402	−	0.0225345i	−0.00328134	−	0.999995i	$-0.501044\pi$
$727$	−5.78090	−	0.607597i	−0.214402	−	0.0225345i	−0.211120	+	0.977460i	$0.567711\pi$
$728$	30.8537	−	46.0859i	1.14352	−	1.70806i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.848510	−	2.50210i	−0.0314048	−	0.0926069i
$731$	11.0672	−	9.96497i	0.409336	−	0.368568i
$732$	−8.10498	+	1.06208i	−0.299569	+	0.0392558i
$733$	−3.88498	−	36.9631i	−0.143495	−	1.36526i	−0.794995	−	0.606616i	$-0.792527\pi$
$733$	−3.88498	−	36.9631i	−0.143495	−	1.36526i	0.651500	−	0.758649i	$-0.274140\pi$
$734$	−0.157499	−	0.697019i	−0.00581340	−	0.0257274i
$735$	−5.88465	+	2.62001i	−0.217058	+	0.0966406i
$736$	−1.75057	−	0.0714148i	−0.0645269	−	0.00263238i
$737$	1.25805	−	2.82562i	0.0463407	−	0.104083i
$738$	7.58617	−	10.7273i	0.279251	−	0.394879i
$739$	13.8940	−	24.0650i	0.511097	−	0.885247i	−0.488820	−	0.872385i	$-0.662573\pi$
$739$	13.8940	−	24.0650i	0.511097	−	0.885247i	0.999917	−	0.0128618i	$-0.00409416\pi$
$740$	10.4826	+	0.831338i	0.385348	+	0.0305606i
$741$	−32.3097	+	6.86764i	−1.18693	+	0.252289i
$742$	−14.9969	+	13.8547i	−0.550554	+	0.508621i
$743$	39.8512			1.46200			0.730999	−	0.682378i	$-0.239054\pi$
$743$	39.8512			1.46200			0.730999	+	0.682378i	$0.239054\pi$
$744$	8.45647	−	13.2849i	0.310029	−	0.487047i
$745$	4.34651			0.159244
$746$	−26.9962	+	24.9400i	−0.988403	+	0.913119i
$747$	−0.659561	+	0.140194i	−0.0241321	+	0.00512943i
$748$	−4.20469	−	0.333460i	−0.153739	−	0.0121925i
$749$	22.0410	−	38.1761i	0.805361	−	1.39493i
$750$	−4.37625	+	6.18831i	−0.159798	+	0.225965i
$751$	2.77786	−	6.23919i	0.101366	−	0.227671i	−0.855742	−	0.517402i	$-0.826899\pi$
$751$	2.77786	−	6.23919i	0.101366	−	0.227671i	0.957108	+	0.289731i	$0.0935658\pi$
$752$	−17.9881	−	9.19265i	−0.655958	−	0.335221i
$753$	−12.1716	+	5.41917i	−0.443559	+	0.197485i
$754$	−4.10800	−	18.1801i	−0.149605	−	0.662081i
$755$	0.945856	+	8.99921i	0.0344232	+	0.327515i
$756$	8.56432	−	1.12228i	0.311481	−	0.0408168i
$757$	−19.6437	+	17.6873i	−0.713963	+	0.642855i	−0.943855	−	0.330361i	$-0.892829\pi$
$757$	−19.6437	+	17.6873i	−0.713963	+	0.642855i	0.229892	+	0.973216i	$0.426163\pi$
$758$	−3.88154	−	11.4460i	−0.140984	−	0.415736i
$759$	−0.0279709	+	0.0860857i	−0.00101528	+	0.00312471i
$760$	9.45318	+	6.32875i	0.342903	+	0.229568i
$761$	46.7956	+	4.91842i	1.69634	+	0.178293i	0.902752	−	0.430162i	$-0.141543\pi$
$761$	46.7956	+	4.91842i	1.69634	+	0.178293i	0.793589	+	0.608454i	$0.208210\pi$
$762$	−6.24818	+	14.5310i	−0.226348	+	0.526402i
$763$	8.28199	+	7.45714i	0.299828	+	0.269966i
$764$	15.0396	−	21.8546i	0.544114	−	0.790672i
$765$	0.829438	−	3.90220i	0.0299884	−	0.141084i
$766$	4.04379	+	3.54846i	0.146108	+	0.128211i
$767$	−20.7372	−	15.0665i	−0.748779	−	0.544020i
$768$	15.9083	+	1.71071i	0.574041	+	0.0617299i
$769$	−3.19360	−	5.53148i	−0.115164	−	0.199470i	0.802681	−	0.596408i	$-0.203406\pi$
$769$	−3.19360	−	5.53148i	−0.115164	−	0.199470i	−0.917845	+	0.396938i	$0.870073\pi$
$770$	−0.0905897	+	0.982640i	−0.00326463	+	0.0354119i
$771$	19.3731	−	14.0754i	0.697705	−	0.506912i
$772$	−2.03456	+	3.74183i	−0.0732254	+	0.134671i
$773$	−16.0360	+	5.21040i	−0.576773	+	0.187405i	−0.582855	−	0.812577i	$-0.698064\pi$
$773$	−16.0360	+	5.21040i	−0.576773	+	0.187405i	0.00608129	+	0.999982i	$0.498064\pi$
$774$	1.22110	+	2.65087i	0.0438915	+	0.0952834i
$775$	20.7851	−	15.8471i	0.746622	−	0.569246i
$776$	−9.45047	−	2.67451i	−0.339252	−	0.0960092i
$777$	−12.6924	−	39.0633i	−0.455338	−	1.40139i
$778$	14.6953	−	10.9666i	0.526851	−	0.393172i
$779$	−39.7290	−	54.6822i	−1.42344	−	1.95919i
$780$	4.73309	−	1.67288i	0.169472	−	0.0598985i
$781$	−3.73623	+	2.15711i	−0.133693	+	0.0771876i
$782$	3.16047	−	0.0404229i	0.113018	−	0.00144552i
$783$	1.70622	−	2.34842i	0.0609755	−	0.0839255i
$784$	25.3370	+	39.1185i	0.904894	+	1.39709i
$785$	−7.77972	−	1.65363i	−0.277670	−	0.0590206i
$786$	6.22192	+	10.4653i	0.221929	+	0.373284i
$787$	29.2706	−	32.5083i	1.04338	−	1.15879i	0.0563278	−	0.998412i	$-0.482061\pi$
$787$	29.2706	−	32.5083i	1.04338	−	1.15879i	0.987055	−	0.160382i	$-0.0512725\pi$
$788$	0.774520	+	30.2731i	0.0275911	+	1.07843i
$789$	−0.991371	+	9.43226i	−0.0352937	+	0.335797i
$790$	8.22733	−	0.971262i	0.292715	−	0.0345560i
$791$	35.7561	+	11.6179i	1.27134	+	0.413084i
$792$	0.307001	−	0.767493i	0.0109088	−	0.0272717i
$793$	12.4167	+	13.7902i	0.440932	+	0.489704i
$794$	6.78182	+	2.10805i	0.240678	+	0.0748118i
$795$	−1.83794	+	0.193176i	−0.0651851	+	0.00685123i
$796$	17.1279	−	13.1263i	0.607081	−	0.465250i
$797$	−18.6264	−	41.8356i	−0.659782	−	1.48189i	−0.864271	−	0.503026i	$-0.832220\pi$
$797$	−18.6264	−	41.8356i	−0.659782	−	1.48189i	0.204489	−	0.978869i	$-0.434447\pi$
$798$	8.68194	−	43.5786i	0.307338	−	1.54267i
$799$	33.2926	+	14.8228i	1.17781	+	0.524394i
$800$	23.7991	+	11.7809i	0.841426	+	0.416518i
$801$	−4.13357	−	2.38652i	−0.146053	−	0.0843235i
$802$	−14.9697	+	26.7116i	−0.528600	+	0.943218i
$803$	0.205337	+	0.966035i	0.00724619	+	0.0340906i
$804$	8.11191	−	19.5506i	0.286085	−	0.689498i
$805$		−	0.739475i		−	0.0260631i
$806$	−35.7268	+	1.28239i	−1.25842	+	0.0451703i
$807$			7.52296i			0.264821i
$808$	1.92899	+	50.2509i	0.0678616	+	1.76782i
$809$	7.49203	+	35.2472i	0.263406	+	1.23923i	0.888573	+	0.458736i	$0.151697\pi$
$809$	7.49203	+	35.2472i	0.263406	+	1.23923i	−0.625167	+	0.780491i	$0.714969\pi$
$810$	0.682030	+	0.382224i	0.0239641	+	0.0134300i
$811$	−30.2792	−	17.4817i	−1.06325	−	0.613866i	−0.136918	−	0.990582i	$-0.543720\pi$
$811$	−30.2792	−	17.4817i	−1.06325	−	0.613866i	−0.926328	+	0.376717i	$0.877053\pi$
$812$	24.6505	+	4.58402i	0.865062	+	0.160868i
$813$	5.75034	+	2.56022i	0.201673	+	0.0897907i
$814$	−3.85500	−	0.768011i	−0.135118	−	0.0269188i
$815$	1.89010	+	4.24523i	0.0662073	+	0.148704i
$816$	−28.8233	−	1.54531i	−1.00902	−	0.0540967i
$817$	14.9322	−	1.56943i	0.522411	−	0.0549076i
$818$	13.1989	−	42.4624i	0.461489	−	1.48466i
$819$	−13.1205	−	14.5717i	−0.458466	−	0.509178i
$820$	7.06648	+	7.45549i	0.246772	+	0.260357i
$821$	9.82346	+	3.19184i	0.342841	+	0.111396i	0.475377	−	0.879782i	$-0.342312\pi$
$821$	9.82346	+	3.19184i	0.342841	+	0.111396i	−0.132535	+	0.991178i	$0.542312\pi$
$822$	3.11306	+	26.3700i	0.108580	+	0.919759i
$823$	−5.88187	+	55.9623i	−0.205029	+	1.95072i	0.0917630	+	0.995781i	$0.470750\pi$
$823$	−5.88187	+	55.9623i	−0.205029	+	1.95072i	−0.296792	+	0.954942i	$0.595917\pi$
$824$	5.15581	−	2.53679i	0.179611	−	0.0883733i
$825$	0.918010	−	1.01955i	0.0319610	−	0.0354963i
$826$	29.6392	−	17.6214i	1.03128	−	0.613128i
$827$	25.7182	+	5.46658i	0.894310	+	0.190092i	0.632070	−	0.774911i	$-0.282205\pi$
$827$	25.7182	+	5.46658i	0.894310	+	0.190092i	0.262240	+	0.965003i	$0.415539\pi$
$828$	−0.176286	+	0.593820i	−0.00612636	+	0.0206367i
$829$	27.8515	−	38.3343i	0.967322	−	1.33140i	0.0239333	−	0.999714i	$-0.492381\pi$
$829$	27.8515	−	38.3343i	0.967322	−	1.33140i	0.943388	−	0.331690i	$-0.107619\pi$
$830$	−0.00674222	−	0.527142i	−0.000234026	−	0.0182974i
$831$	10.4054	−	6.00757i	0.360960	−	0.208400i
$832$	−17.2737	−	31.9515i	−0.598858	−	1.10772i
$833$	−49.4217	−	68.0232i	−1.71236	−	2.35686i
$834$	5.78471	+	7.75152i	0.200308	+	0.268413i
$835$	−3.25070	−	10.0046i	−0.112495	−	0.346224i
$836$	−3.23193	−	2.76369i	−0.111779	−	0.0955842i
$837$	−3.82010	−	4.05054i	−0.132042	−	0.140007i
$838$	3.93420	−	1.81226i	0.135905	−	0.0626035i
$839$	27.9900	−	9.09449i	0.966321	−	0.313977i	0.216991	−	0.976174i	$-0.430376\pi$
$839$	27.9900	−	9.09449i	0.966321	−	0.313977i	0.749330	+	0.662197i	$0.230376\pi$
$840$	−0.447749	+	6.73824i	−0.0154488	+	0.232491i
$841$	−16.6445	+	12.0929i	−0.573949	+	0.416998i
$842$	−47.8671	−	4.41288i	−1.64961	−	0.152078i
$843$	−9.23857	−	16.0017i	−0.318193	−	0.551127i
$844$	3.25782	+	6.84075i	0.112139	+	0.235468i
$845$	−3.40528	−	2.47408i	−0.117145	−	0.0851109i
$846$	−4.71072	+	5.36830i	−0.161958	+	0.184566i
$847$	−9.80046	+	46.1075i	−0.336748	+	1.58427i
$848$	3.44527	+	12.9200i	0.118311	+	0.443675i
$849$	2.87735	+	2.59078i	0.0987505	+	0.0889153i
$850$	−44.0109	−	18.9242i	−1.50956	−	0.649096i
$851$	2.92942	+	0.307895i	0.100419	+	0.0105545i
$852$	−25.1825	+	15.4111i	−0.862740	+	0.527975i
$853$	3.72874	−	11.4759i	0.127670	−	0.392927i	−0.866708	−	0.498815i	$-0.833769\pi$
$853$	3.72874	−	11.4759i	0.127670	−	0.392927i	0.994378	+	0.105888i	$0.0337686\pi$
$854$	−23.6405	+	8.01694i	−0.808960	+	0.274334i
$855$	2.98897	−	2.69128i	0.102221	−	0.0920399i
$856$	−15.3834	−	24.4300i	−0.525794	−	0.835000i
$857$	5.16423	+	49.1344i	0.176407	+	1.67840i	0.621887	+	0.783107i	$0.286366\pi$
$857$	5.16423	+	49.1344i	0.176407	+	1.67840i	−0.445480	+	0.895292i	$0.646967\pi$
$858$	−1.83037	+	0.413592i	−0.0624878	+	0.0141198i
$859$	21.7693	−	9.69230i	0.742758	−	0.330697i	−0.000231998	−	1.00000i	$-0.500074\pi$
$859$	21.7693	−	9.69230i	0.742758	−	0.330697i	0.742990	+	0.669303i	$0.233407\pi$
$860$	−2.21912	+	0.531352i	−0.0756713	+	0.0181190i
$861$	16.3197	−	36.6546i	0.556173	−	1.24919i
$862$	15.7659	+	11.1493i	0.536988	+	0.379747i
$863$	9.77602	−	16.9326i	0.332779	−	0.576391i	−0.650276	−	0.759698i	$-0.725347\pi$
$863$	9.77602	−	16.9326i	0.332779	−	0.576391i	0.983056	+	0.183307i	$0.0586802\pi$
$864$	1.96591	−	5.30426i	0.0668815	−	0.180455i
$865$	3.33899	−	0.709723i	0.113529	−	0.0241313i
$866$	−13.6643	−	14.7909i	−0.464332	−	0.502615i
$867$	35.0732			1.19115
$868$	17.4002	−	44.8336i	0.590601	−	1.52175i
$869$	−3.09678			−0.105051
$870$	1.54004	+	1.66701i	0.0522122	+	0.0565169i
$871$	−47.0009	+	9.99036i	−1.59257	+	0.338510i
$872$	6.84986	−	2.52003i	0.231966	−	0.0853391i
$873$	−1.73623	+	3.00725i	−0.0587626	+	0.101780i
$874$	2.60178	+	1.83993i	0.0880064	+	0.0622365i
$875$	−9.41436	+	21.1450i	−0.318264	+	0.714832i
$876$	1.57382	+	6.57285i	0.0531746	+	0.222076i
$877$	−38.5321	+	17.1556i	−1.30114	+	0.579303i	−0.936114	−	0.351696i	$-0.885605\pi$
$877$	−38.5321	+	17.1556i	−1.30114	+	0.579303i	−0.365022	+	0.930999i	$0.618938\pi$
$878$	−6.25151	+	1.41260i	−0.210978	+	0.0476729i
$879$	−0.958979	−	9.12407i	−0.0323456	−	0.307747i
$880$	0.541588	+	0.352638i	0.0182569	+	0.0118874i
$881$	18.1063	−	16.3030i	0.610017	−	0.549262i	−0.305167	−	0.952299i	$-0.598712\pi$
$881$	18.1063	−	16.3030i	0.610017	−	0.549262i	0.915184	+	0.403037i	$0.132046\pi$
$882$	15.6052	−	5.29202i	0.525454	−	0.178192i
$883$	−9.23395	+	28.4192i	−0.310747	+	0.956382i	0.666723	+	0.745306i	$0.267697\pi$
$883$	−9.23395	+	28.4192i	−0.310747	+	0.956382i	−0.977470	+	0.211076i	$0.932303\pi$
$884$	34.2038	+	55.8909i	1.15040	+	1.87981i
$885$	3.10404	+	0.326248i	0.104341	+	0.0109667i
$886$	0.342083	+	0.147092i	0.0114925	+	0.00494166i
$887$	−29.5424	−	26.6001i	−0.991938	−	0.893145i	0.00233734	−	0.999997i	$-0.499256\pi$
$887$	−29.5424	−	26.6001i	−0.991938	−	0.893145i	−0.994275	+	0.106853i	$0.965923\pi$
$888$	−26.5070	−	4.57935i	−0.889518	−	0.153673i
$889$	−10.0429	+	47.2481i	−0.336828	+	1.58465i
$890$	2.46133	−	2.80491i	0.0825040	−	0.0940208i
$891$	−0.236438	−	0.171782i	−0.00792096	−	0.00575491i
$892$	28.0084	−	13.3387i	0.937792	−	0.446612i
$893$	18.3709	+	31.8194i	0.614760	+	1.06480i
$894$	−11.0718	−	1.02072i	−0.370298	−	0.0341378i
$895$	−8.85678	+	6.43483i	−0.296050	+	0.215093i
$896$	48.6656	−	4.36852i	1.62580	−	0.145942i
$897$	1.33736	−	0.434536i	0.0446533	−	0.0145087i
$898$	21.3284	−	9.82474i	0.711737	−	0.327856i
$899$	−6.91286	−	14.6091i	−0.230557	−	0.487242i
$900$	6.10179	−	7.13559i	0.203393	−	0.237853i
$901$	−7.45434	−	22.9421i	−0.248340	−	0.764312i
$902$	−2.29654	−	3.07737i	−0.0764664	−	0.102465i
$903$	5.23886	+	7.21067i	0.174338	+	0.239956i
$904$	17.6525	−	17.1653i	0.587114	−	0.570910i
$905$	−5.34202	+	3.08422i	−0.177575	+	0.102523i
$906$	−0.296038	−	23.1458i	−0.00983519	−	0.768967i
$907$	−14.9054	+	20.5155i	−0.494925	+	0.681205i	−0.981287	−	0.192552i	$-0.938324\pi$
$907$	−14.9054	+	20.5155i	−0.494925	+	0.681205i	0.486362	+	0.873757i	$0.338324\pi$
$908$	18.1106	+	5.37646i	0.601023	+	0.178424i
$909$	17.3909	+	3.69656i	0.576821	+	0.122607i
$910$	13.1773	−	7.83433i	0.436824	−	0.259705i
$911$	3.04036	−	3.37666i	0.100731	−	0.111874i	−0.690671	−	0.723169i	$-0.742685\pi$
$911$	3.04036	−	3.37666i	0.100731	−	0.111874i	0.791402	+	0.611296i	$0.209351\pi$
$912$	−22.5938	−	18.3411i	−0.748156	−	0.607336i
$913$	−0.0205989	+	0.195985i	−0.000681724	+	0.00648617i
$914$	2.66797	+	22.5998i	0.0882488	+	0.747535i
$915$	−2.14893	−	0.698231i	−0.0710416	−	0.0230828i
$916$	19.0496	−	18.0556i	0.629415	−	0.596574i
$917$	24.8788	+	27.6308i	0.821572	+	0.912448i
$918$	−3.02920	+	9.74527i	−0.0999784	+	0.321642i
$919$	7.23268	−	0.760186i	0.238584	−	0.0250762i	0.0155183	−	0.999880i	$-0.495060\pi$
$919$	7.23268	−	0.760186i	0.238584	−	0.0250762i	0.223066	+	0.974803i	$0.428394\pi$
$920$	−0.428390	−	0.225880i	−0.0141236	−	0.00744705i
$921$	6.80620	+	15.2870i	0.224272	+	0.503723i
$922$	24.1013	+	4.80157i	0.793733	+	0.158131i
$923$	61.2283	+	27.2606i	2.01535	+	0.897294i
$924$	0.461518	−	2.48180i	0.0151828	−	0.0816452i
$925$	−38.6643	−	22.3228i	−1.27127	−	0.733971i
$926$	−31.1308	−	17.4464i	−1.02302	−	0.573323i
$927$	−0.422384	−	1.98716i	−0.0138729	−	0.0652669i
$928$	10.1853	−	12.8802i	0.334350	−	0.422813i
$929$		−	52.6725i		−	1.72813i	−0.503383	−	0.864064i	$-0.667911\pi$
$929$		−	52.6725i		−	1.72813i	0.503383	−	0.864064i	$-0.332089\pi$
$930$	3.68935	−	2.31035i	0.120979	−	0.0757595i
$931$		−	84.7701i		−	2.77823i
$932$	21.5605	+	8.94584i	0.706238	+	0.293031i
$933$	−1.83110	−	8.61466i	−0.0599476	−	0.282031i
$934$	10.4289	−	18.6090i	0.341243	−	0.608904i
$935$	−1.00971	−	0.582954i	−0.0330209	−	0.0190646i
$936$	−12.4494	+	3.14981i	−0.406923	+	0.102955i
$937$	−34.1136	−	15.1883i	−1.11444	−	0.496182i	−0.234908	−	0.972018i	$-0.575479\pi$
$937$	−34.1136	−	15.1883i	−1.11444	−	0.496182i	−0.879534	+	0.475836i	$0.842146\pi$
$938$	12.6296	−	63.3938i	0.412372	−	2.06988i
$939$	−12.6392	−	28.3881i	−0.412464	−	0.926409i
$940$	−3.39661	−	4.43206i	−0.110785	−	0.144558i
$941$	39.0429	−	4.10357i	1.27276	−	0.133773i	0.556053	−	0.831147i	$-0.312315\pi$
$941$	39.0429	−	4.10357i	1.27276	−	0.133773i	0.716707	+	0.697374i	$0.245648\pi$
$942$	19.4289	+	6.03924i	0.633028	+	0.196769i
$943$	1.92537	+	2.13834i	0.0626987	+	0.0696340i
$944$	−1.15477	−	22.5531i	−0.0375847	−	0.734042i
$945$	2.27072	+	0.737803i	0.0738667	+	0.0240007i
$946$	0.847085	−	0.100001i	0.0275411	−	0.00325131i
$947$	−0.904078	+	8.60173i	−0.0293786	+	0.279519i	0.969963	+	0.243251i	$0.0782137\pi$
$947$	−0.904078	+	8.60173i	−0.0293786	+	0.279519i	−0.999342	+	0.0362682i	$0.988453\pi$
$948$	−21.1855	+	0.542020i	−0.688074	+	0.0176040i
$949$	10.2664	−	11.4020i	0.333262	−	0.370125i
$950$	−24.6827	−	41.5163i	−0.800814	−	1.34697i
$951$	−9.84081	−	2.09173i	−0.319110	−	0.0678289i
$952$	−87.2471	+	12.5699i	−2.82769	+	0.407393i
$953$	−23.6718	+	32.5814i	−0.766804	+	1.05542i	0.229813	+	0.973235i	$0.426188\pi$
$953$	−23.6718	+	32.5814i	−0.766804	+	1.05542i	−0.996617	+	0.0821806i	$0.973812\pi$
$954$	4.72715	−	0.0604608i	0.153047	−	0.00195749i
$955$	6.35078	−	3.66663i	0.205506	−	0.118649i
$956$	−7.37927	−	20.8783i	−0.238663	−	0.675252i
$957$	−0.498649	−	0.686332i	−0.0161190	−	0.0221860i
$958$	26.6889	−	19.9171i	0.862280	−	0.643492i
$959$	25.0578	+	77.1199i	0.809158	+	2.49033i
$960$	3.76680	+	2.31765i	0.121573	+	0.0748019i
$961$	−29.9927	+	7.83816i	−0.967507	+	0.252844i
$962$	25.5490	+	55.4638i	0.823732	+	1.78823i
$963$	−9.70750	+	3.15416i	−0.312820	+	0.101641i
$964$	−9.89955	−	5.38272i	−0.318843	−	0.173366i
$965$	−0.952473	+	0.692013i	−0.0306612	+	0.0222767i
$966$	−0.173655	+	1.88366i	−0.00558726	+	0.0606058i
$967$	−4.78984	−	8.29625i	−0.154031	−	0.266789i	0.778675	−	0.627428i	$-0.215892\pi$
$967$	−4.78984	−	8.29625i	−0.154031	−	0.266789i	−0.932706	+	0.360638i	$0.882559\pi$
$968$	23.7172	+	19.7616i	0.762300	+	0.635161i
$969$	42.4732	+	30.8586i	1.36444	+	0.991321i
$970$	−2.04062	−	1.79066i	−0.0655204	−	0.0574947i
$971$	8.58615	−	40.3947i	0.275543	−	1.29633i	−0.594798	−	0.803876i	$-0.702768\pi$
$971$	8.58615	−	40.3947i	0.275543	−	1.29633i	0.870340	−	0.492451i	$-0.163899\pi$
$972$	−1.64757	−	1.13380i	−0.0528459	−	0.0363667i
$973$	21.9502	+	19.7640i	0.703690	+	0.633606i
$974$	−8.85218	+	20.5869i	−0.283642	+	0.659648i
$975$	−21.1968	−	2.22787i	−0.678840	−	0.0713490i
$976$	−2.57688	+	16.1442i	−0.0824840	+	0.516762i
$977$	−16.2618	+	50.0488i	−0.520262	+	1.60120i	0.253236	+	0.967405i	$0.418505\pi$
$977$	−16.2618	+	50.0488i	−0.520262	+	1.60120i	−0.773498	+	0.633798i	$0.781495\pi$
$978$	−3.81771	−	11.2577i	−0.122077	−	0.359982i
$979$	−1.03664	+	0.933394i	−0.0331311	+	0.0298314i
$980$	1.67390	+	12.7739i	0.0534709	+	0.408047i
$981$	−0.269734	−	2.56635i	−0.00861194	−	0.0819372i
$982$	−0.0812048	−	0.359375i	−0.00259135	−	0.0114681i
$983$	12.5994	−	5.60964i	0.401860	−	0.178920i	−0.195847	−	0.980635i	$-0.562745\pi$
$983$	12.5994	−	5.60964i	0.401860	−	0.178920i	0.597707	+	0.801715i	$0.296079\pi$
$984$	−16.2496	−	20.6508i	−0.518018	−	0.658323i
$985$	−3.40471	+	7.64710i	−0.108483	+	0.243657i
$986$	−17.1044	+	24.1868i	−0.544717	+	0.770265i
$987$	−10.9054	+	18.8887i	−0.347122	+	0.601233i
$988$	−5.22283	+	65.8563i	−0.166160	+	2.09517i
$989$	−0.625213	+	0.132893i	−0.0198806	+	0.00422576i
$990$	0.167834	−	0.155050i	0.00533411	−	0.00492783i
$991$	26.0175			0.826474			0.413237	−	0.910624i	$-0.364398\pi$
$991$	26.0175			0.826474			0.413237	+	0.910624i	$0.364398\pi$
$992$	−20.6578	−	23.7751i	−0.655886	−	0.754860i
$993$	6.40383			0.203219
$994$	−66.2257	+	61.1815i	−2.10055	+	1.94056i
$995$	5.83457	−	1.24018i	0.184968	−	0.0393162i
$996$	−0.106617	+	1.34437i	−0.00337830	+	0.0425980i
$997$	−13.2116	+	22.8832i	−0.418417	+	0.724719i	−0.995780	−	0.0917681i	$-0.970748\pi$
$997$	−13.2116	+	22.8832i	−0.418417	+	0.724719i	0.577364	+	0.816487i	$0.304081\pi$
$998$	3.76648	−	5.32605i	0.119226	−	0.168593i
$999$	−3.86826	+	8.68825i	−0.122386	+	0.274884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.ba.a.55.4	✓	128
4.3	odd	2		372.2.ba.b.55.16	yes	128
31.22	odd	30		372.2.ba.b.115.16	yes	128
124.115	even	30	inner	372.2.ba.a.115.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.ba.a.55.4	✓	128	1.1	even	1	trivial
372.2.ba.a.115.4	yes	128	124.115	even	30	inner
372.2.ba.b.55.16	yes	128	4.3	odd	2
372.2.ba.b.115.16	yes	128	31.22	odd	30

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:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03878 + 0.959657i) q^{2} +(0.978148 - 0.207912i) q^{3} +(0.158117 - 1.99374i) q^{4} +(0.276419 - 0.478772i) q^{5} +(-0.816554 + 1.15466i) q^{6} +(-1.75660 + 3.94539i) q^{7} +(1.74906 + 2.22279i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.172319 + 0.762605i) q^{10} +(-0.0305488 - 0.290652i) q^{11} +(-0.259860 - 1.98305i) q^{12} +(-3.37405 + 3.03801i) q^{13} +(-1.96151 - 5.78412i) q^{14} +(0.170836 - 0.525780i) q^{15} +(-3.95000 - 0.630487i) q^{16} +(7.17664 + 0.754296i) q^{17} +(-0.558643 + 1.29920i) q^{18} +(5.40660 + 4.86812i) q^{19} +(-0.910840 - 0.626810i) q^{20} +(-0.897923 + 4.22439i) q^{21} +(0.310660 + 0.272606i) q^{22} +(-0.250567 - 0.182047i) q^{23} +(2.17298 + 1.81057i) q^{24} +(2.34719 + 4.06544i) q^{25} +(0.589441 - 6.39375i) q^{26} +(0.809017 - 0.587785i) q^{27} +(7.58834 + 4.12604i) q^{28} +(2.76073 - 0.897015i) q^{29} +(0.327108 + 0.710113i) q^{30} +(-0.709676 - 5.52235i) q^{31} +(4.70822 - 3.13571i) q^{32} +(-0.0903111 - 0.277949i) q^{33} +(-8.17880 + 6.10357i) q^{34} +(1.40338 + 1.93159i) q^{35} +(-0.666480 - 1.88568i) q^{36} +(-8.23631 + 4.75524i) q^{37} +(-10.2880 + 0.131585i) q^{38} +(-2.66868 + 3.67313i) q^{39} +(1.54768 - 0.222979i) q^{40} +(-9.08746 - 1.93160i) q^{41} +(-3.12123 - 5.24990i) q^{42} +(1.38092 - 1.53367i) q^{43} +(-0.584315 + 0.0149494i) q^{44} +(0.0577873 - 0.549810i) q^{45} +(0.434986 - 0.0513514i) q^{46} +(4.80305 + 1.56060i) q^{47} +(-3.99477 + 0.204542i) q^{48} +(-7.79656 - 8.65896i) q^{49} +(-6.33963 - 1.97060i) q^{50} +(7.17664 - 0.754296i) q^{51} +(5.52351 + 7.20734i) q^{52} +(-1.35967 - 3.05386i) q^{53} +(-0.276316 + 1.38696i) q^{54} +(-0.147600 - 0.0657159i) q^{55} +(-11.8422 + 2.99617i) q^{56} +(6.30059 + 3.63765i) q^{57} +(-2.00696 + 3.58115i) q^{58} +(1.17380 + 5.52230i) q^{59} +(-1.02126 - 0.423738i) q^{60} -4.08713i q^{61} +(6.03676 + 5.05545i) q^{62} +4.31877i q^{63} +(-1.88159 + 7.77558i) q^{64} +(0.521861 + 2.45516i) q^{65} +(0.360549 + 0.202060i) q^{66} +(9.16547 + 5.29168i) q^{67} +(2.63862 - 14.1891i) q^{68} +(-0.282941 - 0.125973i) q^{69} +(-3.31147 - 0.659727i) q^{70} +(-6.00423 - 13.4857i) q^{71} +(2.50193 + 1.31921i) q^{72} +(-3.36081 + 0.353235i) q^{73} +(3.99230 - 12.8437i) q^{74} +(3.14115 + 3.48860i) q^{75} +(10.5606 - 10.0096i) q^{76} +(1.20040 + 0.390033i) q^{77} +(-0.752775 - 6.37658i) q^{78} +(1.10761 - 10.5382i) q^{79} +(-1.39371 + 1.71687i) q^{80} +(0.669131 - 0.743145i) q^{81} +(11.2935 - 6.71434i) q^{82} +(-0.659561 - 0.140194i) q^{83} +(8.28037 + 2.45817i) q^{84} +(2.34490 - 3.22747i) q^{85} +(0.0373261 + 2.91835i) q^{86} +(2.51390 - 1.45140i) q^{87} +(0.592627 - 0.576271i) q^{88} +(-2.80552 - 3.86147i) q^{89} +(0.467601 + 0.626586i) q^{90} +(-6.05927 - 18.6485i) q^{91} +(-0.402574 + 0.470780i) q^{92} +(-1.84233 - 5.25412i) q^{93} +(-6.48694 + 2.98816i) q^{94} +(3.82521 - 1.24288i) q^{95} +(3.95338 - 4.04608i) q^{96} +(-2.80929 + 2.04107i) q^{97} +(16.4085 + 1.51270i) q^{98} +(-0.146127 - 0.253099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) \) 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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