LMFDB - Embedded newform 150.2.l.a.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	150.47
Dual form			150.2.l.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(1.32853 - 1.11131i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.92065 + 1.14503i) q^{5} +(-1.59332 - 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(0.987688 + 0.156434i) q^{8} +(0.529988 - 2.95281i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(1.32853 - 1.11131i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.92065 + 1.14503i) q^{5} +(-1.59332 - 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(0.987688 + 0.156434i) q^{8} +(0.529988 - 2.95281i) q^{9} +(0.148273 - 2.23115i) q^{10} +(-2.60836 - 0.847507i) q^{11} +(0.118176 + 1.72801i) q^{12} +(-5.27002 - 2.68521i) q^{13} +(0.891173 - 2.74275i) q^{14} +(3.82413 - 0.613226i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.936136 + 5.91053i) q^{17} +(-2.87159 + 0.868327i) q^{18} +(-3.04743 - 4.19443i) q^{19} +(-2.05528 + 0.880807i) q^{20} +(4.97538 + 0.442965i) q^{21} +(0.429036 + 2.70883i) q^{22} +(1.01194 - 0.515607i) q^{23} +(1.48602 - 0.889798i) q^{24} +(2.37780 + 4.39841i) q^{25} +5.91469i q^{26} +(-2.57738 - 4.51188i) q^{27} +(-2.84839 + 0.451141i) q^{28} +(2.34612 + 1.70456i) q^{29} +(-2.28251 - 3.12892i) q^{30} +(4.56563 - 3.31712i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.40713 + 1.77275i) q^{33} +(5.69132 - 1.84922i) q^{34} +(1.58166 + 6.25161i) q^{35} +(2.07736 + 2.16439i) q^{36} +(-3.66336 + 7.18975i) q^{37} +(-2.35376 + 4.61952i) q^{38} +(-9.98549 + 2.28924i) q^{39} +(1.71788 + 1.43139i) q^{40} +(-5.02666 + 1.63326i) q^{41} +(-1.86409 - 4.63420i) q^{42} +(-3.10789 + 3.10789i) q^{43} +(2.21880 - 1.61205i) q^{44} +(4.39899 - 5.06447i) q^{45} +(-0.918819 - 0.667561i) q^{46} +(4.58484 - 0.726167i) q^{47} +(-1.46746 - 0.920095i) q^{48} +1.31687i q^{49} +(2.83952 - 4.11548i) q^{50} +(5.32473 + 8.89266i) q^{51} +(5.27002 - 2.68521i) q^{52} +(-0.837944 - 5.29057i) q^{53} +(-2.85001 + 4.34482i) q^{54} +(-4.03933 - 4.61442i) q^{55} +(1.69511 + 2.33312i) q^{56} +(-8.70992 - 2.18579i) q^{57} +(0.453655 - 2.86426i) q^{58} +(-0.912145 - 2.80729i) q^{59} +(-1.75166 + 3.45423i) q^{60} +(-1.41844 + 4.36552i) q^{61} +(-5.02833 - 2.56206i) q^{62} +(7.10221 - 4.94069i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-7.04723 - 11.1917i) q^{65} +(3.58033 + 3.12197i) q^{66} +(-0.455818 - 0.0721944i) q^{67} +(-4.23147 - 4.23147i) q^{68} +(0.771390 - 1.80957i) q^{69} +(4.85217 - 4.24744i) q^{70} +(3.36294 - 4.62869i) q^{71} +(0.985385 - 2.83355i) q^{72} +(4.12620 + 8.09812i) q^{73} +8.06924 q^{74} +(8.04698 + 3.20096i) q^{75} +5.18460 q^{76} +(-3.59077 - 7.04728i) q^{77} +(6.57304 + 7.85784i) q^{78} +(6.90557 - 9.50470i) q^{79} +(0.495476 - 2.18048i) q^{80} +(-8.43823 - 3.12991i) q^{81} +(3.73730 + 3.73730i) q^{82} +(11.9275 + 1.88912i) q^{83} +(-3.28282 + 3.76480i) q^{84} +(-8.56574 + 10.2802i) q^{85} +(4.18011 + 1.35820i) q^{86} +(5.01118 - 0.342708i) q^{87} +(-2.44367 - 1.24511i) q^{88} +(0.402182 - 1.23779i) q^{89} +(-6.50958 - 1.62030i) q^{90} +(-5.27101 - 16.2225i) q^{91} +(-0.177666 + 1.12174i) q^{92} +(2.37923 - 9.48072i) q^{93} +(-2.72849 - 3.75545i) q^{94} +(-1.05030 - 11.5455i) q^{95} +(-0.153600 + 1.72523i) q^{96} +(1.03381 + 6.52722i) q^{97} +(1.17334 - 0.597845i) q^{98} +(-3.88493 + 7.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	1.32853	−	1.11131i	0.767028	−	0.641614i
$3$	1.32853	−	1.11131i	0.767028	−	0.641614i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	1.92065	+	1.14503i	0.858941	+	0.512074i
$5$	1.92065	+	1.14503i	0.858941	+	0.512074i
$6$	−1.59332	−	0.679206i	−0.650471	−	0.277285i
$7$	2.03922	+	2.03922i	0.770754	+	0.770754i	0.978238	−	0.207484i	$-0.0665276\pi$
$7$	2.03922	+	2.03922i	0.770754	+	0.770754i	−0.207484	+	0.978238i	$0.566528\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	0.529988	−	2.95281i	0.176663	−	0.984271i
$10$	0.148273	−	2.23115i	0.0468882	−	0.705550i
$11$	−2.60836	−	0.847507i	−0.786450	−	0.255533i	−0.111858	−	0.993724i	$-0.535680\pi$
$11$	−2.60836	−	0.847507i	−0.786450	−	0.255533i	−0.674592	+	0.738191i	$0.735680\pi$
$12$	0.118176	+	1.72801i	0.0341146	+	0.498835i
$13$	−5.27002	−	2.68521i	−1.46164	−	0.744744i	−0.471116	−	0.882071i	$-0.656149\pi$
$13$	−5.27002	−	2.68521i	−1.46164	−	0.744744i	−0.990526	+	0.137328i	$0.956149\pi$
$14$	0.891173	−	2.74275i	0.238176	−	0.733031i
$15$	3.82413	−	0.613226i	0.987386	−	0.158334i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.936136	+	5.91053i	−0.227046	+	1.43351i	0.566026	+	0.824387i	$0.308480\pi$
$17$	−0.936136	+	5.91053i	−0.227046	+	1.43351i	−0.793073	+	0.609127i	$0.791520\pi$
$18$	−2.87159	+	0.868327i	−0.676839	+	0.204667i
$19$	−3.04743	−	4.19443i	−0.699129	−	0.962269i	−0.999963	−	0.00859233i	$-0.997265\pi$
$19$	−3.04743	−	4.19443i	−0.699129	−	0.962269i	0.300834	−	0.953677i	$-0.402735\pi$
$20$	−2.05528	+	0.880807i	−0.459575	+	0.196954i
$21$	4.97538	+	0.442965i	1.08572	+	0.0966630i
$22$	0.429036	+	2.70883i	0.0914707	+	0.577523i
$23$	1.01194	−	0.515607i	0.211003	−	0.107512i	−0.345295	−	0.938494i	$-0.612221\pi$
$23$	1.01194	−	0.515607i	0.211003	−	0.107512i	0.556298	+	0.830983i	$0.312221\pi$
$24$	1.48602	−	0.889798i	0.303333	−	0.181629i
$25$	2.37780	+	4.39841i	0.475561	+	0.879683i
$26$			5.91469i			1.15997i
$27$	−2.57738	−	4.51188i	−0.496017	−	0.868313i
$28$	−2.84839	+	0.451141i	−0.538296	+	0.0852576i
$29$	2.34612	+	1.70456i	0.435664	+	0.316528i	0.783910	−	0.620875i	$-0.213223\pi$
$29$	2.34612	+	1.70456i	0.435664	+	0.316528i	−0.348246	+	0.937403i	$0.613223\pi$
$30$	−2.28251	−	3.12892i	−0.416727	−	0.571261i
$31$	4.56563	−	3.31712i	0.820011	−	0.595773i	−0.0967046	−	0.995313i	$-0.530830\pi$
$31$	4.56563	−	3.31712i	0.820011	−	0.595773i	0.916716	+	0.399540i	$0.130830\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−4.40713	+	1.77275i	−0.767182	+	0.308596i
$34$	5.69132	−	1.84922i	0.976053	−	0.317139i
$35$	1.58166	+	6.25161i	0.267350	+	1.05672i
$36$	2.07736	+	2.16439i	0.346226	+	0.360732i
$37$	−3.66336	+	7.18975i	−0.602253	+	1.18199i	0.365671	+	0.930744i	$0.380839\pi$
$37$	−3.66336	+	7.18975i	−0.602253	+	1.18199i	−0.967924	+	0.251243i	$0.919161\pi$
$38$	−2.35376	+	4.61952i	−0.381830	+	0.749384i
$39$	−9.98549	+	2.28924i	−1.59896	+	0.366571i
$40$	1.71788	+	1.43139i	0.271621	+	0.226323i
$41$	−5.02666	+	1.63326i	−0.785033	+	0.255073i	−0.673988	−	0.738743i	$-0.735420\pi$
$41$	−5.02666	+	1.63326i	−0.785033	+	0.255073i	−0.111045	+	0.993815i	$0.535420\pi$
$42$	−1.86409	−	4.63420i	−0.287635	−	0.715072i
$43$	−3.10789	+	3.10789i	−0.473950	+	0.473950i	−0.903190	−	0.429241i	$-0.858781\pi$
$43$	−3.10789	+	3.10789i	−0.473950	+	0.473950i	0.429241	+	0.903190i	$0.358781\pi$
$44$	2.21880	−	1.61205i	0.334497	−	0.243026i
$45$	4.39899	−	5.06447i	0.655763	−	0.754967i
$46$	−0.918819	−	0.667561i	−0.135473	−	0.0984265i
$47$	4.58484	−	0.726167i	0.668768	−	0.105922i	0.187187	−	0.982324i	$-0.440063\pi$
$47$	4.58484	−	0.726167i	0.668768	−	0.105922i	0.481581	+	0.876402i	$0.340063\pi$
$48$	−1.46746	−	0.920095i	−0.211809	−	0.132804i
$49$			1.31687i			0.188124i
$50$	2.83952	−	4.11548i	0.401568	−	0.582016i
$51$	5.32473	+	8.89266i	0.745612	+	1.24522i
$52$	5.27002	−	2.68521i	0.730821	−	0.372372i
$53$	−0.837944	−	5.29057i	−0.115100	−	0.726715i	−0.975972	−	0.217894i	$-0.930081\pi$
$53$	−0.837944	−	5.29057i	−0.115100	−	0.726715i	0.860872	−	0.508821i	$-0.169919\pi$
$54$	−2.85001	+	4.34482i	−0.387837	+	0.591255i
$55$	−4.03933	−	4.61442i	−0.544663	−	0.622208i
$56$	1.69511	+	2.33312i	0.226519	+	0.311777i
$57$	−8.70992	−	2.18579i	−1.15366	−	0.289516i
$58$	0.453655	−	2.86426i	0.0595678	−	0.376096i
$59$	−0.912145	−	2.80729i	−0.118751	−	0.365478i	0.873960	−	0.485998i	$-0.161544\pi$
$59$	−0.912145	−	2.80729i	−0.118751	−	0.365478i	−0.992711	+	0.120520i	$0.961544\pi$
$60$	−1.75166	+	3.45423i	−0.226138	+	0.445939i
$61$	−1.41844	+	4.36552i	−0.181613	+	0.558947i	−0.999874	−	0.0159002i	$-0.994939\pi$
$61$	−1.41844	+	4.36552i	−0.181613	+	0.558947i	0.818261	+	0.574847i	$0.194939\pi$
$62$	−5.02833	−	2.56206i	−0.638599	−	0.325382i
$63$	7.10221	−	4.94069i	0.894795	−	0.622468i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−7.04723	−	11.1917i	−0.874101	−	1.38816i
$66$	3.58033	+	3.12197i	0.440708	+	0.384287i
$67$	−0.455818	−	0.0721944i	−0.0556870	−	0.00881995i	0.128529	−	0.991706i	$-0.458975\pi$
$67$	−0.455818	−	0.0721944i	−0.0556870	−	0.00881995i	−0.184216	+	0.982886i	$0.558975\pi$
$68$	−4.23147	−	4.23147i	−0.513141	−	0.513141i
$69$	0.771390	−	1.80957i	0.0928645	−	0.217847i
$70$	4.85217	−	4.24744i	0.579945	−	0.507667i
$71$	3.36294	−	4.62869i	0.399107	−	0.549324i	−0.561412	−	0.827536i	$-0.689742\pi$
$71$	3.36294	−	4.62869i	0.399107	−	0.549324i	0.960520	+	0.278212i	$0.0897418\pi$
$72$	0.985385	−	2.83355i	0.116129	−	0.333937i
$73$	4.12620	+	8.09812i	0.482935	+	0.947814i	0.995991	+	0.0894583i	$0.0285136\pi$
$73$	4.12620	+	8.09812i	0.482935	+	0.947814i	−0.513055	+	0.858356i	$0.671486\pi$
$74$	8.06924			0.938031
$75$	8.04698	+	3.20096i	0.929185	+	0.369615i
$76$	5.18460			0.594715
$77$	−3.59077	−	7.04728i	−0.409206	−	0.803113i
$78$	6.57304	+	7.85784i	0.744250	+	0.889725i
$79$	6.90557	−	9.50470i	0.776937	−	1.06936i	−0.218676	−	0.975798i	$-0.570174\pi$
$79$	6.90557	−	9.50470i	0.776937	−	1.06936i	0.995613	−	0.0935650i	$-0.0298263\pi$
$80$	0.495476	−	2.18048i	0.0553959	−	0.243785i
$81$	−8.43823	−	3.12991i	−0.937581	−	0.347768i
$82$	3.73730	+	3.73730i	0.412716	+	0.412716i
$83$	11.9275	+	1.88912i	1.30921	+	0.207358i	0.771747	−	0.635930i	$-0.219383\pi$
$83$	11.9275	+	1.88912i	1.30921	+	0.207358i	0.537462	+	0.843288i	$0.319383\pi$
$84$	−3.28282	+	3.76480i	−0.358185	+	0.410773i
$85$	−8.56574	+	10.2802i	−0.929084	+	1.11504i
$86$	4.18011	+	1.35820i	0.450753	+	0.146458i
$87$	5.01118	−	0.342708i	0.537255	−	0.0367421i
$88$	−2.44367	−	1.24511i	−0.260496	−	0.132729i
$89$	0.402182	−	1.23779i	0.0426312	−	0.131205i	−0.927476	−	0.373884i	$-0.878026\pi$
$89$	0.402182	−	1.23779i	0.0426312	−	0.131205i	0.970107	+	0.242678i	$0.0780260\pi$
$90$	−6.50958	−	1.62030i	−0.686170	−	0.170795i
$91$	−5.27101	−	16.2225i	−0.552552	−	1.70058i
$92$	−0.177666	+	1.12174i	−0.0185230	+	0.116950i
$93$	2.37923	−	9.48072i	0.246715	−	0.983105i
$94$	−2.72849	−	3.75545i	−0.281423	−	0.387345i
$95$	−1.05030	−	11.5455i	−0.107758	−	1.18454i
$96$	−0.153600	+	1.72523i	−0.0156767	+	0.176080i
$97$	1.03381	+	6.52722i	0.104967	+	0.662738i	0.982926	+	0.184002i	$0.0589052\pi$
$97$	1.03381	+	6.52722i	0.104967	+	0.662738i	−0.877959	+	0.478737i	$0.841095\pi$
$98$	1.17334	−	0.597845i	0.118525	−	0.0603915i
$99$	−3.88493	+	7.25283i	−0.390450	+	0.728937i
$100$	−4.95603	−	0.661639i	−0.495603	−	0.0661639i
$101$		−	3.52971i		−	0.351219i	−0.984460	−	0.175610i	$-0.943810\pi$
$101$		−	3.52971i		−	0.351219i	0.984460	−	0.175610i	$-0.0561896\pi$
$102$	5.50604	−	8.78155i	0.545179	−	0.869503i
$103$	−6.37316	+	1.00941i	−0.627966	+	0.0994601i	−0.462303	−	0.886722i	$-0.652977\pi$
$103$	−6.37316	+	1.00941i	−0.627966	+	0.0994601i	−0.165664	+	0.986182i	$0.552977\pi$
$104$	−4.78508	−	3.47657i	−0.469216	−	0.340905i
$105$	9.04876	+	6.54775i	0.883068	+	0.638995i
$106$	−4.33351	+	3.14848i	−0.420908	+	0.305807i
$107$	−8.76915	+	8.76915i	−0.847745	+	0.847745i	−0.989851	−	0.142106i	$-0.954613\pi$
$107$	−8.76915	+	8.76915i	−0.847745	+	0.847745i	0.142106	+	0.989851i	$0.454613\pi$
$108$	5.16514	+	0.566874i	0.497016	+	0.0545474i
$109$	2.65577	−	0.862912i	0.254377	−	0.0826520i	−0.179053	−	0.983839i	$-0.557303\pi$
$109$	2.65577	−	0.862912i	0.254377	−	0.0826520i	0.433430	+	0.901187i	$0.357303\pi$
$110$	−2.27766	+	5.69397i	−0.217167	+	0.542899i
$111$	3.12314	+	13.6229i	0.296435	+	1.29303i
$112$	1.30926	−	2.56957i	0.123714	−	0.242802i
$113$	2.09855	−	4.11863i	0.197415	−	0.387449i	−0.770984	−	0.636854i	$-0.780235\pi$
$113$	2.09855	−	4.11863i	0.197415	−	0.387449i	0.968399	+	0.249406i	$0.0802353\pi$
$114$	2.00666	+	8.75292i	0.187941	+	0.819786i
$115$	2.53396	+	0.168398i	0.236293	+	0.0157032i
$116$	−2.75803	+	0.896139i	−0.256077	+	0.0832044i
$117$	−10.7220	+	14.1383i	−0.991247	+	1.30708i
$118$	−2.08721	+	2.08721i	−0.192143	+	0.192143i
$119$	−13.9619	+	10.1439i	−1.27988	+	0.929890i
$120$	3.87298	−	0.00745040i	0.353553	−	0.000680125i
$121$	−2.81392	−	2.04443i	−0.255811	−	0.185857i
$122$	4.53366	−	0.718062i	0.410459	−	0.0650103i
$123$	−4.86302	+	7.75601i	−0.438484	+	0.699336i
$124$			5.64343i			0.506795i
$125$	−0.469393	+	11.1705i	−0.0419838	+	0.999118i
$126$	−7.62652	−	4.08509i	−0.679424	−	0.363929i
$127$	11.1643	−	5.68850i	0.990672	−	0.504773i	0.117966	−	0.993018i	$-0.462363\pi$
$127$	11.1643	−	5.68850i	0.990672	−	0.504773i	0.872707	+	0.488245i	$0.162363\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	−0.675105	+	7.58276i	−0.0594397	+	0.667625i
$130$	−6.77250	+	11.3600i	−0.593988	+	0.996342i
$131$	−7.00579	−	9.64264i	−0.612099	−	0.842482i	0.384649	−	0.923063i	$-0.374322\pi$
$131$	−7.00579	−	9.64264i	−0.612099	−	0.842482i	−0.996748	+	0.0805811i	$0.974322\pi$
$132$	1.15626	−	4.60744i	0.100639	−	0.401026i
$133$	2.33899	−	14.7678i	0.202816	−	1.28053i
$134$	0.142611	+	0.438912i	0.0123197	+	0.0379162i
$135$	0.216000	−	11.6169i	0.0185903	−	0.999827i
$136$	−1.84922	+	5.69132i	−0.158569	+	0.488026i
$137$	17.7044	+	9.02083i	1.51259	+	0.770702i	0.996319	−	0.0857255i	$-0.0273208\pi$
$137$	17.7044	+	9.02083i	1.51259	+	0.770702i	0.516268	+	0.856427i	$0.327321\pi$
$138$	−1.96255	+	0.134216i	−0.167063	+	0.0114252i
$139$	9.07922	+	2.95002i	0.770090	+	0.250217i	0.667603	−	0.744517i	$-0.267320\pi$
$139$	9.07922	+	2.95002i	0.770090	+	0.250217i	0.102486	+	0.994734i	$0.467320\pi$
$140$	−5.98734	−	2.39502i	−0.506023	−	0.202416i
$141$	5.28411	−	6.05991i	0.445002	−	0.510336i
$142$	−5.65093	−	0.895020i	−0.474216	−	0.0751084i
$143$	11.4704	+	11.4704i	0.959201	+	0.959201i
$144$	−2.97207	+	0.408421i	−0.247672	+	0.0340351i
$145$	2.55431	+	5.96025i	0.212124	+	0.494971i
$146$	5.34223	−	7.35294i	0.442126	−	0.608534i
$147$	1.46344	+	1.74950i	0.120703	+	0.144296i
$148$	−3.66336	−	7.18975i	−0.301126	−	0.590994i
$149$	−12.0089			−0.983807			−0.491903	−	0.870650i	$-0.663699\pi$
$149$	−12.0089			−0.983807			−0.491903	+	0.870650i	$0.663699\pi$
$150$	−0.801180	−	8.62311i	−0.0654161	−	0.704074i
$151$	−11.1277			−0.905558			−0.452779	−	0.891623i	$-0.649567\pi$
$151$	−11.1277			−0.905558			−0.452779	+	0.891623i	$0.649567\pi$
$152$	−2.35376	−	4.61952i	−0.190915	−	0.374692i
$153$	16.9566	+	5.89674i	1.37086	+	0.476724i
$154$	−4.64900	+	6.39880i	−0.374627	+	0.515630i
$155$	12.5672	−	1.14325i	1.00942	−	0.0918278i
$156$	4.01729	−	9.42401i	0.321641	−	0.754524i
$157$	−11.6119	−	11.6119i	−0.926732	−	0.926732i	0.0707617	−	0.997493i	$-0.477457\pi$
$157$	−11.6119	−	11.6119i	−0.926732	−	0.926732i	−0.997493	+	0.0707617i	$0.977457\pi$
$158$	−11.6038	−	1.83786i	−0.923150	−	0.146213i
$159$	−6.99269	−	6.09747i	−0.554556	−	0.483561i
$160$	−2.16777	+	0.548446i	−0.171377	+	0.0433584i
$161$	3.11500	+	1.01213i	0.245497	+	0.0797667i
$162$	1.04210	+	8.93946i	0.0818753	+	0.702351i
$163$	5.83680	+	2.97400i	0.457173	+	0.232941i	0.667383	−	0.744715i	$-0.267415\pi$
$163$	5.83680	+	2.97400i	0.457173	+	0.232941i	−0.210209	+	0.977656i	$0.567415\pi$
$164$	1.63326	−	5.02666i	0.127536	−	0.392516i
$165$	−10.4944	−	1.64146i	−0.816989	−	0.127788i
$166$	−3.73173	−	11.4851i	−0.289639	−	0.891416i
$167$	2.65903	−	16.7884i	0.205762	−	1.29913i	−0.641159	−	0.767408i	$-0.721546\pi$
$167$	2.65903	−	16.7884i	0.205762	−	1.29913i	0.846920	−	0.531720i	$-0.178454\pi$
$168$	4.84483	+	1.21583i	0.373787	+	0.0938035i
$169$	12.9216	+	17.7850i	0.993968	+	1.36808i
$170$	13.0485	+	2.96503i	1.00077	+	0.227407i
$171$	−14.0005	+	6.77551i	−1.07064	+	0.518136i
$172$	−0.687565	−	4.34111i	−0.0524263	−	0.331007i
$173$	−6.04954	+	3.08240i	−0.459938	+	0.234350i	−0.668578	−	0.743642i	$-0.733097\pi$
$173$	−6.04954	+	3.08240i	−0.459938	+	0.234350i	0.208639	+	0.977993i	$0.433097\pi$
$174$	−2.58038	−	4.30941i	−0.195618	−	0.326696i
$175$	−4.12048	+	13.8182i	−0.311479	+	1.04456i
$176$			2.74259i			0.206731i
$177$	−4.33158	−	2.71590i	−0.325581	−	0.204140i
$178$	−1.28546	+	0.203597i	−0.0963496	+	0.0152603i
$179$	7.59016	+	5.51457i	0.567315	+	0.412179i	0.834129	−	0.551569i	$-0.185971\pi$
$179$	7.59016	+	5.51457i	0.567315	+	0.412179i	−0.266814	+	0.963748i	$0.585971\pi$
$180$	1.51158	+	6.53568i	0.112667	+	0.487141i
$181$	12.3025	−	8.93831i	0.914440	−	0.664379i	−0.0276940	−	0.999616i	$-0.508816\pi$
$181$	12.3025	−	8.93831i	0.914440	−	0.664379i	0.942134	+	0.335237i	$0.108816\pi$
$182$	−12.0614	+	12.0614i	−0.894048	+	0.894048i
$183$	2.96699	+	7.37605i	0.219326	+	0.545253i
$184$	1.08014	−	0.350958i	0.0796287	−	0.0258729i
$185$	−15.2685	+	9.61434i	−1.12256	+	0.706860i
$186$	−9.52753	+	2.18425i	−0.698593	+	0.160157i
$187$	7.45099	−	14.6234i	0.544871	−	1.06937i
$188$	−2.10742	+	4.13604i	−0.153699	+	0.301652i
$189$	3.94488	−	14.4566i	0.286948	−	1.05156i
$190$	−9.81025	+	6.17735i	−0.711710	+	0.448152i
$191$	−12.2756	+	3.98859i	−0.888232	+	0.288604i	−0.717371	−	0.696691i	$-0.754655\pi$
$191$	−12.2756	+	3.98859i	−0.888232	+	0.288604i	−0.170861	+	0.985295i	$0.554655\pi$
$192$	1.60692	−	0.646378i	0.115970	−	0.0466483i
$193$	3.91447	−	3.91447i	0.281770	−	0.281770i	−0.552045	−	0.833815i	$-0.686152\pi$
$193$	3.91447	−	3.91447i	0.281770	−	0.281770i	0.833815	+	0.552045i	$0.186152\pi$
$194$	5.34645	−	3.88442i	0.383853	−	0.278885i
$195$	−21.7999	−	7.03688i	−1.56112	−	0.503921i
$196$	−1.06537	−	0.774035i	−0.0760977	−	0.0552882i
$197$	25.2645	−	4.00150i	1.80002	−	0.285095i	0.835574	−	0.549378i	$-0.185135\pi$
$197$	25.2645	−	4.00150i	1.80002	−	0.285095i	0.964445	+	0.264282i	$0.0851351\pi$
$198$	8.22604	+	0.168782i	0.584599	+	0.0119948i
$199$			0.0768328i			0.00544653i	0.999996	+	0.00272327i	$0.000866844\pi$
$199$			0.0768328i			0.00544653i	−0.999996	+	0.00272327i	$0.999133\pi$
$200$	1.66047	+	4.71623i	0.117413	+	0.333488i
$201$	−0.685798	+	0.410641i	−0.0483725	+	0.0289644i
$202$	−3.14499	+	1.60245i	−0.221281	+	0.112748i
$203$	1.30829	+	8.26024i	0.0918242	+	0.579755i
$204$	−10.3241	−	0.919171i	−0.722832	−	0.0643548i
$205$	−11.5246	−	2.61876i	−0.804913	−	0.182902i
$206$	3.79275	+	5.22027i	0.264253	+	0.363713i
$207$	−0.986179	−	3.26133i	−0.0685442	−	0.226678i
$208$	−0.925261	+	5.84187i	−0.0641553	+	0.405061i
$209$	4.39399	+	13.5233i	0.303939	+	0.935427i
$210$	1.72604	−	11.0351i	0.119108	−	0.761495i
$211$	1.99342	−	6.13511i	0.137232	−	0.422358i	−0.858698	−	0.512482i	$-0.828726\pi$
$211$	1.99342	−	6.13511i	0.137232	−	0.422358i	0.995931	+	0.0901236i	$0.0287262\pi$
$212$	4.77269	+	2.43181i	0.327790	+	0.167017i
$213$	−0.676131	−	9.88661i	−0.0463278	−	0.677420i
$214$	11.7945	+	3.83226i	0.806254	+	0.261968i
$215$	−9.52782	+	2.41054i	−0.649792	+	0.164398i
$216$	−1.83984	−	4.85953i	−0.125185	−	0.330649i
$217$	16.0747	+	2.54598i	1.09122	+	0.172832i
$218$	−1.97456	−	1.97456i	−0.133734	−	0.133734i
$219$	14.4813	+	6.17313i	0.978555	+	0.417141i
$220$	6.10740	−	0.555595i	0.411761	−	0.0374582i
$221$	20.8045	−	28.6349i	1.39946	−	1.92619i
$222$	10.7202	−	8.96742i	0.719495	−	0.601854i
$223$	−2.46937	−	4.84642i	−0.165362	−	0.324540i	0.793425	−	0.608668i	$-0.208296\pi$
$223$	−2.46937	−	4.84642i	−0.165362	−	0.324540i	−0.958786	+	0.284128i	$0.908296\pi$
$224$	−2.88390			−0.192689
$225$	14.2479	−	4.69011i	0.949861	−	0.312674i
$226$	−4.62245			−0.307481
$227$	−8.90823	−	17.4834i	−0.591260	−	1.16041i	−0.971835	−	0.235662i	$-0.924274\pi$
$227$	−8.90823	−	17.4834i	−0.591260	−	1.16041i	0.380575	−	0.924750i	$-0.375726\pi$
$228$	6.88791	−	5.76169i	0.456163	−	0.381577i
$229$	10.2833	−	14.1538i	0.679543	−	0.935310i	−0.320385	−	0.947287i	$-0.603812\pi$
$229$	10.2833	−	14.1538i	0.679543	−	0.935310i	0.999928	+	0.0119768i	$0.00381244\pi$
$230$	−1.00035	−	2.33423i	−0.0659613	−	0.153915i
$231$	−12.6022	−	5.37208i	−0.829161	−	0.353457i
$232$	2.05059	+	2.05059i	0.134628	+	0.134628i
$233$	−28.6649	−	4.54007i	−1.87790	−	0.297430i	−0.890416	−	0.455148i	$-0.849586\pi$
$233$	−28.6649	−	4.54007i	−1.87790	−	0.297430i	−0.987484	+	0.157718i	$0.949586\pi$
$234$	17.4650	+	3.13471i	1.14172	+	0.204923i
$235$	9.63737	+	3.85507i	0.628672	+	0.251477i
$236$	2.80729	+	0.912145i	0.182739	+	0.0593756i
$237$	−1.38839	−	20.3015i	−0.0901857	−	1.31872i
$238$	15.3768	+	7.83489i	0.996733	+	0.507861i
$239$	−1.74681	+	5.37613i	−0.112992	+	0.347753i	−0.991523	−	0.129932i	$-0.958524\pi$
$239$	−1.74681	+	5.37613i	−0.112992	+	0.347753i	0.878531	+	0.477685i	$0.158524\pi$
$240$	−1.76493	−	3.44746i	−0.113926	−	0.222533i
$241$	4.35617	+	13.4069i	0.280605	+	0.863614i	0.987682	+	0.156477i	$0.0500137\pi$
$241$	4.35617	+	13.4069i	0.280605	+	0.863614i	−0.707076	+	0.707137i	$0.749986\pi$
$242$	−0.544110	+	3.43537i	−0.0349767	+	0.220834i
$243$	−14.6887	+	5.21929i	−0.942283	+	0.334817i
$244$	−2.69804	−	3.71353i	−0.172724	−	0.237734i
$245$	−1.50785	+	2.52924i	−0.0963333	+	0.161587i
$246$	9.11842	+	0.811827i	0.581369	+	0.0517602i
$247$	4.79711	+	30.2878i	0.305233	+	1.92716i
$248$	5.02833	−	2.56206i	0.319299	−	0.162691i
$249$	17.9454	−	10.7453i	1.13724	−	0.680957i
$250$	10.1661	−	4.65306i	0.642959	−	0.294285i
$251$			17.3182i			1.09311i	0.837422	+	0.546557i	$0.184062\pi$
$251$			17.3182i			1.09311i	−0.837422	+	0.546557i	$0.815938\pi$
$252$	−0.177478	+	8.64987i	−0.0111801	+	0.544891i
$253$	−3.07648	+	0.487266i	−0.193416	+	0.0306341i
$254$	−10.1370	−	7.36495i	−0.636051	−	0.462118i
$255$	0.0445847	+	23.1767i	0.00279200	+	1.45138i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	4.28914	−	4.28914i	0.267549	−	0.267549i	−0.560563	−	0.828112i	$-0.689415\pi$
$257$	4.28914	−	4.28914i	0.267549	−	0.267549i	0.828112	+	0.560563i	$0.189415\pi$
$258$	7.06278	−	2.84098i	0.439710	−	0.176872i
$259$	−22.1319	+	7.19110i	−1.37521	+	0.446833i
$260$	13.1965	+	0.876991i	0.818414	+	0.0543887i
$261$	6.27666	−	6.02427i	0.388515	−	0.372893i
$262$	−5.41110	+	10.6199i	−0.334299	+	0.656098i
$263$	−10.8405	+	21.2757i	−0.668454	+	1.31191i	0.268777	+	0.963203i	$0.413381\pi$
$263$	−10.8405	+	21.2757i	−0.668454	+	1.31191i	−0.937230	+	0.348711i	$0.886619\pi$
$264$	−4.63019	+	1.06150i	−0.284968	+	0.0653308i
$265$	4.44847	−	11.1208i	0.273267	−	0.683146i
$266$	−14.2201	+	4.62038i	−0.871889	+	0.283294i
$267$	−0.841253	−	2.09139i	−0.0514839	−	0.127991i
$268$	0.326329	−	0.326329i	0.0199337	−	0.0199337i
$269$	11.2436	−	8.16896i	0.685535	−	0.498070i	−0.189654	−	0.981851i	$-0.560737\pi$
$269$	11.2436	−	8.16896i	0.685535	−	0.498070i	0.875189	+	0.483781i	$0.160737\pi$
$270$	−10.4488	+	5.08152i	−0.635896	+	0.309252i
$271$	12.1633	+	8.83716i	0.738868	+	0.536819i	0.892357	−	0.451331i	$-0.149051\pi$
$271$	12.1633	+	8.83716i	0.738868	+	0.536819i	−0.153488	+	0.988151i	$0.549051\pi$
$272$	5.91053	−	0.936136i	0.358378	−	0.0567616i
$273$	−25.0309	−	15.6944i	−1.51494	−	0.949867i
$274$		−	19.8701i		−	1.20040i
$275$	−2.47448	−	13.4878i	−0.149217	−	0.813348i
$276$	1.01056	+	1.68771i	0.0608288	+	0.101588i
$277$	−1.61620	+	0.823495i	−0.0971080	+	0.0494790i	−0.501870	−	0.864943i	$-0.667354\pi$
$277$	−1.61620	+	0.823495i	−0.0971080	+	0.0494790i	0.404762	+	0.914422i	$0.367354\pi$
$278$	−1.49340	−	9.42893i	−0.0895679	−	0.565509i
$279$	−7.37512	−	15.2395i	−0.441537	−	0.912364i
$280$	0.584221	+	6.42207i	0.0349139	+	0.383792i
$281$	13.4707	+	18.5409i	0.803597	+	1.10606i	0.992280	+	0.124018i	$0.0395782\pi$
$281$	13.4707	+	18.5409i	0.803597	+	1.10606i	−0.188683	+	0.982038i	$0.560422\pi$
$282$	−7.79835	−	1.95703i	−0.464385	−	0.116540i
$283$	−0.445062	+	2.81001i	−0.0264562	+	0.167038i	−0.997379	−	0.0723553i	$-0.976948\pi$
$283$	−0.445062	+	2.81001i	−0.0264562	+	0.167038i	0.970923	+	0.239393i	$0.0769484\pi$
$284$	1.76800	+	5.44135i	0.104912	+	0.322885i
$285$	−14.2259	−	14.1713i	−0.842670	−	0.839434i
$286$	5.01274	−	15.4276i	0.296409	−	0.912255i
$287$	−13.5811	−	6.91991i	−0.801666	−	0.408469i
$288$	1.71320	+	2.46271i	0.100951	+	0.145117i
$289$	−17.8900	−	5.81283i	−1.05236	−	0.341931i
$290$	4.15099	−	4.98180i	0.243754	−	0.292541i
$291$	8.62720	+	7.52273i	0.505735	+	0.440990i
$292$	−8.97684	−	1.42179i	−0.525330	−	0.0832041i
$293$	9.44461	+	9.44461i	0.551760	+	0.551760i	0.926948	−	0.375189i	$-0.122422\pi$
$293$	9.44461	+	9.44461i	0.551760	+	0.551760i	−0.375189	+	0.926948i	$0.622422\pi$
$294$	0.894424	−	2.09819i	0.0521639	−	0.122369i
$295$	1.46253	−	6.43626i	0.0851516	−	0.374734i
$296$	−4.74298	+	6.52816i	−0.275680	+	0.379441i
$297$	2.89888	+	13.9530i	0.168210	+	0.809633i
$298$	5.45192	+	10.7000i	0.315821	+	0.619834i
$299$	−6.71745			−0.388480
$300$	−7.31952	+	4.62867i	−0.422593	+	0.267236i
$301$	−12.6754			−0.730597
$302$	5.05186	+	9.91484i	0.290702	+	0.570535i
$303$	−3.92259	−	4.68933i	−0.225347	−	0.269395i
$304$	−3.04743	+	4.19443i	−0.174782	+	0.240567i
$305$	−7.72299	+	6.76047i	−0.442217	+	0.387104i
$306$	−2.44408	−	17.7855i	−0.139719	−	1.01673i
$307$	−23.1889	−	23.1889i	−1.32346	−	1.32346i	−0.910955	−	0.412506i	$-0.864654\pi$
$307$	−23.1889	−	23.1889i	−1.32346	−	1.32346i	−0.412506	−	0.910955i	$-0.635346\pi$
$308$	7.81197	+	1.23730i	0.445129	+	0.0705014i
$309$	−7.34518	+	8.42358i	−0.417852	+	0.479201i
$310$	−6.72403	−	10.6784i	−0.381899	−	0.606494i
$311$	9.84506	+	3.19885i	0.558262	+	0.181390i	0.574539	−	0.818477i	$-0.305181\pi$
$311$	9.84506	+	3.19885i	0.558262	+	0.181390i	−0.0162770	+	0.999868i	$0.505181\pi$
$312$	−10.2207	+	0.698977i	−0.578631	+	0.0395718i
$313$	−12.2235	−	6.22820i	−0.690915	−	0.352039i	0.0730212	−	0.997330i	$-0.476736\pi$
$313$	−12.2235	−	6.22820i	−0.690915	−	0.352039i	−0.763936	+	0.645292i	$0.776736\pi$
$314$	−5.07459	+	15.6180i	−0.286376	+	0.881374i
$315$	19.2981	−	1.35707i	1.08733	−	0.0764624i
$316$	3.63047	+	11.1734i	0.204230	+	0.628556i
$317$	−2.95253	+	18.6415i	−0.165830	+	1.04701i	0.754623	+	0.656159i	$0.227820\pi$
$317$	−2.95253	+	18.6415i	−0.165830	+	1.04701i	−0.920453	+	0.390853i	$0.872180\pi$
$318$	−2.25827	+	8.99872i	−0.126638	+	0.504623i
$319$	−4.67490	−	6.43445i	−0.261744	−	0.360260i
$320$	1.47281	+	1.68250i	0.0823328	+	0.0940548i
$321$	−1.90486	+	21.3953i	−0.106319	+	1.19417i
$322$	−0.512371	−	3.23498i	−0.0285533	−	0.180279i
$323$	27.6441	−	14.0854i	1.53816	−	0.783732i
$324$	7.49202	−	4.98695i	0.416223	−	0.277053i
$325$	−0.720411	−	29.5647i	−0.0399612	−	1.63995i
$326$		−	6.55079i		−	0.362815i
$327$	2.56931	−	4.09779i	0.142083	−	0.226608i
$328$	−5.22028	+	0.826810i	−0.288241	+	0.0456530i
$329$	10.8303	+	7.86870i	0.597096	+	0.433815i
$330$	3.30181	+	10.0958i	0.181759	+	0.555755i
$331$	−25.6753	+	18.6542i	−1.41124	+	1.02533i	−0.418100	+	0.908401i	$0.637304\pi$
$331$	−25.6753	+	18.6542i	−1.41124	+	1.02533i	−0.993141	+	0.116926i	$0.962696\pi$
$332$	−8.53912	+	8.53912i	−0.468645	+	0.468645i
$333$	19.2885	+	14.6277i	1.05700	+	0.801593i
$334$	−16.1658	+	5.25258i	−0.884552	+	0.287408i
$335$	−0.792802	−	0.660586i	−0.0433154	−	0.0360917i
$336$	−1.11619	−	4.86875i	−0.0608932	−	0.265612i
$337$	−7.31518	+	14.3569i	−0.398483	+	0.782068i	−0.999857	−	0.0169001i	$-0.994620\pi$
$337$	−7.31518	+	14.3569i	−0.398483	+	0.782068i	0.601374	+	0.798968i	$0.294620\pi$
$338$	9.98030	−	19.5874i	0.542857	−	1.06542i
$339$	−1.78909	−	7.80387i	−0.0971698	−	0.423848i
$340$	−3.28201	−	12.9724i	−0.177992	−	0.703525i
$341$	−14.7201	+	4.78284i	−0.797137	+	0.259006i
$342$	12.3931	+	9.39851i	0.670143	+	0.508213i
$343$	11.5892	−	11.5892i	0.625757	−	0.625757i
$344$	−3.55581	+	2.58345i	−0.191717	+	0.139290i
$345$	3.55359	−	2.59229i	0.191319	−	0.139564i
$346$	5.49287	+	3.99080i	0.295299	+	0.214547i
$347$	−23.6313	+	3.74283i	−1.26859	+	0.200925i	−0.754209	−	0.656634i	$-0.771980\pi$
$347$	−23.6313	+	3.74283i	−1.26859	+	0.200925i	−0.514384	+	0.857560i	$0.671980\pi$
$348$	−2.66824	+	4.25557i	−0.143033	+	0.228123i
$349$			24.8956i			1.33263i	0.745670	+	0.666315i	$0.232129\pi$
$349$			24.8956i			1.33263i	−0.745670	+	0.666315i	$0.767871\pi$
$350$	14.1828	−	2.60197i	0.758102	−	0.139081i
$351$	1.46750	+	30.6986i	0.0783293	+	1.63857i
$352$	2.44367	−	1.24511i	0.130248	−	0.0663646i
$353$	−2.64576	−	16.7047i	−0.140820	−	0.889101i	−0.952398	−	0.304857i	$-0.901391\pi$
$353$	−2.64576	−	16.7047i	−0.140820	−	0.889101i	0.811578	−	0.584244i	$-0.198609\pi$
$354$	−0.453389	+	5.09246i	−0.0240974	+	0.270661i
$355$	11.7590	−	5.03942i	0.624104	−	0.267465i
$356$	0.764995	+	1.05293i	0.0405447	+	0.0558049i
$357$	−7.27579	+	28.9924i	−0.385076	+	1.53444i
$358$	1.46766	−	9.26645i	0.0775683	−	0.489747i
$359$	−1.67961	−	5.16932i	−0.0886466	−	0.272826i	0.896899	−	0.442235i	$-0.145814\pi$
$359$	−1.67961	−	5.16932i	−0.0886466	−	0.272826i	−0.985546	+	0.169409i	$0.945814\pi$
$360$	5.13709	−	4.31397i	0.270748	−	0.227366i
$361$	−2.43509	+	7.49444i	−0.128163	+	0.394444i
$362$	−13.5493	−	6.90373i	−0.712137	−	0.362852i
$363$	−6.01037	+	0.411041i	−0.315463	+	0.0215740i
$364$	16.2225	+	5.27101i	0.850290	+	0.276276i
$365$	−1.34762	+	20.2783i	−0.0705376	+	1.06142i
$366$	5.22512	−	5.99226i	0.273122	−	0.313221i
$367$	17.7079	+	2.80465i	0.924343	+	0.146401i	0.600422	−	0.799683i	$-0.294999\pi$
$367$	17.7079	+	2.80465i	0.924343	+	0.146401i	0.323920	+	0.946084i	$0.394999\pi$
$368$	−0.803077	−	0.803077i	−0.0418633	−	0.0418633i
$369$	2.15865	+	15.7084i	0.112375	+	0.817747i
$370$	15.4982	+	9.23954i	0.805713	+	0.480341i
$371$	9.07990	−	12.4974i	0.471405	−	0.648833i
$372$	6.27159	+	7.49747i	0.325167	+	0.388726i
$373$	11.6182	+	22.8020i	0.601568	+	1.18064i	0.968176	+	0.250269i	$0.0805190\pi$
$373$	11.6182	+	22.8020i	0.601568	+	1.18064i	−0.366608	+	0.930376i	$0.619481\pi$
$374$	−16.4122			−0.848656
$375$	11.7902	+	15.3620i	0.608846	+	0.793289i
$376$	4.64199			0.239392
$377$	−7.78702	−	15.2829i	−0.401052	−	0.787109i
$378$	−14.6719	+	3.04824i	−0.754639	+	0.156785i
$379$	5.71732	−	7.86922i	0.293679	−	0.404215i	−0.636526	−	0.771255i	$-0.719629\pi$
$379$	5.71732	−	7.86922i	0.293679	−	0.404215i	0.930205	+	0.367041i	$0.119629\pi$
$380$	9.95782	+	5.93654i	0.510825	+	0.304538i
$381$	8.51045	−	19.9643i	0.436004	−	1.02280i
$382$	9.12687	+	9.12687i	0.466971	+	0.466971i
$383$	−24.0895	−	3.81540i	−1.23092	−	0.194958i	−0.493108	−	0.869968i	$-0.664139\pi$
$383$	−24.0895	−	3.81540i	−1.23092	−	0.194958i	−0.737808	+	0.675010i	$0.764139\pi$
$384$	−1.30545	−	1.13833i	−0.0666187	−	0.0580900i
$385$	1.17275	−	17.6469i	0.0597687	−	0.899370i
$386$	−5.26495	−	1.71069i	−0.267979	−	0.0870717i
$387$	7.52989	+	10.8242i	0.382766	+	0.550224i
$388$	−5.88829	−	3.00023i	−0.298932	−	0.152314i
$389$	5.49358	−	16.9075i	0.278536	−	0.857245i	−0.709726	−	0.704477i	$-0.751181\pi$
$389$	5.49358	−	16.9075i	0.278536	−	0.857245i	0.988262	−	0.152767i	$-0.0488186\pi$
$390$	3.62704	+	22.6185i	0.183662	+	1.14533i
$391$	2.10020	+	6.46376i	0.106212	+	0.326886i
$392$	−0.206003	+	1.30065i	−0.0104047	+	0.0656929i
$393$	−20.0234	−	5.02496i	−1.01004	−	0.253475i
$394$	−15.0352	−	20.6942i	−0.757462	−	1.04256i
$395$	24.1464	−	10.3481i	1.21494	−	0.520670i
$396$	−3.58416	−	7.40608i	−0.180111	−	0.372170i
$397$	−3.00987	−	19.0036i	−0.151061	−	0.953762i	−0.940466	−	0.339889i	$-0.889611\pi$
$397$	−3.00987	−	19.0036i	−0.151061	−	0.953762i	0.789405	−	0.613873i	$-0.210389\pi$
$398$	0.0684585	−	0.0348814i	0.00343152	−	0.00174845i
$399$	−13.3041	−	22.2188i	−0.666040	−	1.11233i
$400$	3.44836	−	3.62061i	0.172418	−	0.181031i
$401$		−	31.1439i		−	1.55525i	−0.628726	−	0.777627i	$-0.716423\pi$
$401$		−	31.1439i		−	1.55525i	0.628726	−	0.777627i	$-0.283577\pi$
$402$	0.677230	+	0.424623i	0.0337772	+	0.0211783i
$403$	−32.9681	+	5.22164i	−1.64226	+	0.260108i
$404$	2.85559	+	2.07471i	0.142071	+	0.103221i
$405$	−12.6230	−	15.6735i	−0.627244	−	0.778823i
$406$	6.76598	−	4.91577i	0.335790	−	0.243966i
$407$	15.6487	−	15.6487i	0.775678	−	0.775678i
$408$	3.86806	+	9.61614i	0.191498	+	0.476070i
$409$	−14.9223	+	4.84855i	−0.737860	+	0.239745i	−0.653749	−	0.756711i	$-0.726805\pi$
$409$	−14.9223	+	4.84855i	−0.737860	+	0.239745i	−0.0841106	+	0.996456i	$0.526805\pi$
$410$	2.89873	+	11.4574i	0.143158	+	0.565840i
$411$	33.5457	−	7.69057i	1.65469	−	0.379348i
$412$	2.92942	−	5.74931i	0.144322	−	0.283248i
$413$	3.86463	−	7.58476i	0.190166	−	0.373222i
$414$	−2.45815	+	2.35930i	−0.120811	+	0.115953i
$415$	20.7454	+	17.2857i	1.01835	+	0.848520i
$416$	5.62520	−	1.82774i	0.275798	−	0.0896122i
$417$	15.3404	−	6.17063i	0.751223	−	0.302177i
$418$	10.0545	−	10.0545i	0.491783	−	0.491783i
$419$	2.78733	−	2.02511i	0.136170	−	0.0989333i	−0.517615	−	0.855614i	$-0.673180\pi$
$419$	2.78733	−	2.02511i	0.136170	−	0.0989333i	0.653785	+	0.756680i	$0.273180\pi$
$420$	−10.6160	+	3.47193i	−0.518006	+	0.169413i
$421$	10.9206	+	7.93429i	0.532238	+	0.386694i	0.821194	−	0.570649i	$-0.193308\pi$
$421$	10.9206	+	7.93429i	0.532238	+	0.386694i	−0.288956	+	0.957342i	$0.593308\pi$
$422$	−6.37141	+	1.00913i	−0.310156	+	0.0491238i
$423$	0.285673	−	13.9230i	0.0138899	−	0.676962i
$424$		−	5.35652i		−	0.260135i
$425$	−28.2229	+	9.93657i	−1.36901	+	0.481994i
$426$	−8.50208	+	5.09087i	−0.411927	+	0.246653i
$427$	−11.7948	+	6.00974i	−0.570790	+	0.290832i
$428$	−1.94001	−	12.2488i	−0.0937741	−	0.592066i
$429$	27.9859	+	2.49162i	1.35117	+	0.120297i
$430$	6.47335	+	7.39499i	0.312173	+	0.356618i
$431$	16.4092	+	22.5853i	0.790401	+	1.08789i	0.994058	+	0.108852i	$0.0347173\pi$
$431$	16.4092	+	22.5853i	0.790401	+	1.08789i	−0.203657	+	0.979042i	$0.565283\pi$
$432$	−3.49460	+	3.84548i	−0.168134	+	0.185016i
$433$	−0.408546	+	2.57946i	−0.0196335	+	0.123961i	−0.995558	−	0.0941457i	$-0.969988\pi$
$433$	−0.408546	+	2.57946i	−0.0196335	+	0.123961i	0.975925	+	0.218107i	$0.0699881\pi$
$434$	−5.02927	−	15.4785i	−0.241413	−	0.742992i
$435$	10.0171	+	5.07974i	0.480286	+	0.243555i
$436$	−0.862912	+	2.65577i	−0.0413260	+	0.127188i
$437$	−5.24649	−	2.67322i	−0.250974	−	0.127877i
$438$	−1.07407	−	15.7055i	−0.0513213	−	0.750436i
$439$	−10.4899	−	3.40836i	−0.500653	−	0.162672i	0.0477940	−	0.998857i	$-0.484781\pi$
$439$	−10.4899	−	3.40836i	−0.500653	−	0.162672i	−0.548447	+	0.836185i	$0.684781\pi$
$440$	−3.26774	−	5.18950i	−0.155783	−	0.247400i
$441$	3.88846	+	0.697923i	0.185165	+	0.0332344i
$442$	−34.9589	−	5.53695i	−1.66283	−	0.263366i
$443$	1.32181	+	1.32181i	0.0628009	+	0.0628009i	0.737810	−	0.675009i	$-0.235860\pi$
$443$	1.32181	+	1.32181i	0.0628009	+	0.0628009i	−0.675009	+	0.737810i	$0.735860\pi$
$444$	−12.8569	−	5.48068i	−0.610162	−	0.260102i
$445$	2.18976	−	1.91685i	0.103804	−	0.0908673i
$446$	−3.19712	+	4.40046i	−0.151388	+	0.208368i
$447$	−15.9542	+	13.3456i	−0.754607	+	0.631224i
$448$	1.30926	+	2.56957i	0.0618568	+	0.121401i
$449$	20.5238			0.968579			0.484289	−	0.874908i	$-0.339078\pi$
$449$	20.5238			0.968579			0.484289	+	0.874908i	$0.339078\pi$
$450$	−10.6473	−	10.5657i	−0.501920	−	0.498073i
$451$	14.4955			0.682569
$452$	2.09855	+	4.11863i	0.0987075	+	0.193724i
$453$	−14.7835	+	12.3663i	−0.694588	+	0.581019i
$454$	−11.5336	+	15.8746i	−0.541296	+	0.745031i
$455$	8.45151	−	37.1933i	0.396213	−	1.74365i
$456$	−8.26075	−	3.52142i	−0.386845	−	0.164905i
$457$	11.0498	+	11.0498i	0.516886	+	0.516886i	0.916628	−	0.399742i	$-0.130900\pi$
$457$	11.0498	+	11.0498i	0.516886	+	0.516886i	−0.399742	+	0.916628i	$0.630900\pi$
$458$	−17.2797	−	2.73683i	−0.807427	−	0.127884i
$459$	29.0804	−	11.0100i	1.35736	−	0.513901i
$460$	−1.62566	+	1.95104i	−0.0757970	+	0.0909677i
$461$	−13.2689	−	4.31131i	−0.617992	−	0.200798i	−0.0167435	−	0.999860i	$-0.505330\pi$
$461$	−13.2689	−	4.31131i	−0.617992	−	0.200798i	−0.601249	+	0.799062i	$0.705330\pi$
$462$	0.934699	+	13.6675i	0.0434861	+	0.635868i
$463$	29.3718	+	14.9657i	1.36502	+	0.695515i	0.974355	−	0.225017i	$-0.0722436\pi$
$463$	29.3718	+	14.9657i	1.36502	+	0.695515i	0.390669	+	0.920531i	$0.372244\pi$
$464$	0.896139	−	2.75803i	0.0416022	−	0.128038i
$465$	15.4254	−	15.4849i	0.715336	−	0.718093i
$466$	8.96836	+	27.6018i	0.415451	+	1.27863i
$467$	−0.578507	+	3.65255i	−0.0267701	+	0.169020i	−0.997451	−	0.0713509i	$-0.977269\pi$
$467$	−0.578507	+	3.65255i	−0.0267701	+	0.169020i	0.970681	+	0.240371i	$0.0772690\pi$
$468$	−5.13588	−	16.9845i	−0.237406	−	0.785110i
$469$	−0.782294	−	1.07673i	−0.0361230	−	0.0497190i
$470$	−0.940376	−	10.3371i	−0.0433763	−	0.476816i
$471$	−28.3312	−	2.52237i	−1.30543	−	0.116225i
$472$	−0.461757	−	2.91542i	−0.0212541	−	0.134193i
$473$	10.7405	−	5.47254i	0.493847	−	0.251628i
$474$	−17.4585	+	10.4538i	−0.801894	+	0.480157i
$475$	11.2027	−	23.3774i	0.514013	−	1.07263i
$476$		−	17.2578i		−	0.791012i
$477$	−16.0662	−	0.329645i	−0.735619	−	0.0150934i
$478$	5.58321	−	0.884293i	0.255370	−	0.0404466i
$479$	4.35190	+	3.16184i	0.198844	+	0.144468i	0.682752	−	0.730651i	$-0.260783\pi$
$479$	4.35190	+	3.16184i	0.198844	+	0.144468i	−0.483908	+	0.875119i	$0.660783\pi$
$480$	−2.27045	+	3.13768i	−0.103631	+	0.143215i
$481$	38.6120	−	28.0533i	1.76056	−	1.27912i
$482$	9.96798	−	9.96798i	0.454029	−	0.454029i
$483$	5.26316	−	2.11709i	0.239482	−	0.0963309i
$484$	3.30796	−	1.07482i	0.150362	−	0.0488555i
$485$	−5.48828	+	13.7203i	−0.249210	+	0.623004i
$486$	11.3190	+	10.7183i	0.513439	+	0.486190i
$487$	−1.90512	+	3.73900i	−0.0863291	+	0.169430i	−0.930135	−	0.367219i	$-0.880310\pi$
$487$	−1.90512	+	3.73900i	−0.0863291	+	0.169430i	0.843806	+	0.536649i	$0.180310\pi$
$488$	−2.08390	+	4.08988i	−0.0943336	+	0.185140i
$489$	11.0594	−	2.53544i	0.500123	−	0.114656i
$490$	2.93812	+	0.195256i	0.132731	+	0.00882078i
$491$	−30.0362	+	9.75934i	−1.35551	+	0.440433i	−0.894543	−	0.446983i	$-0.852499\pi$
$491$	−30.0362	+	9.75934i	−1.35551	+	0.440433i	−0.460970	+	0.887416i	$0.652499\pi$
$492$	−3.41633	−	8.49313i	−0.154020	−	0.382900i
$493$	−12.2711	+	12.2711i	−0.552664	+	0.552664i
$494$	24.8088	−	18.0246i	1.11620	−	0.810966i
$495$	−15.7663	+	9.48179i	−0.708643	+	0.426175i
$496$	−4.56563	−	3.31712i	−0.205003	−	0.148943i
$497$	16.2967	−	2.58115i	0.731007	−	0.115780i
$498$	−17.7212	−	11.1112i	−0.794106	−	0.497904i
$499$		−	10.2536i		−	0.459015i	−0.973307	−	0.229508i	$-0.926288\pi$
$499$		−	10.2536i		−	0.459015i	0.973307	−	0.229508i	$-0.0737116\pi$
$500$	−8.76121	−	6.94559i	−0.391813	−	0.310616i
$501$	−15.1245	−	25.2590i	−0.675714	−	1.12849i
$502$	15.4306	−	7.86229i	0.688702	−	0.350911i
$503$	−0.104371	−	0.658974i	−0.00465369	−	0.0293822i	0.985252	−	0.171108i	$-0.0547348\pi$
$503$	−0.104371	−	0.658974i	−0.00465369	−	0.0293822i	−0.989906	+	0.141726i	$0.954735\pi$
$504$	7.78767	−	3.76883i	0.346890	−	0.167877i
$505$	4.04163	−	6.77934i	0.179850	−	0.301677i
$506$	1.83085	+	2.51995i	0.0813911	+	0.112025i
$507$	36.9314	+	9.26810i	1.64018	+	0.411611i
$508$	−1.96012	+	12.3757i	−0.0869664	+	0.549084i
$509$	−8.01814	−	24.6773i	−0.355398	−	1.09380i	−0.955779	−	0.294087i	$-0.904984\pi$
$509$	−8.01814	−	24.6773i	−0.355398	−	1.09380i	0.600381	−	0.799714i	$-0.295016\pi$
$510$	20.6303	−	10.5617i	0.913527	−	0.467681i
$511$	−8.09964	+	24.9281i	−0.358307	+	1.10276i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−11.0704	+	24.5603i	−0.488770	+	1.08436i
$514$	−5.76888	−	1.87442i	−0.254454	−	0.0826772i
$515$	−13.3964	−	5.35875i	−0.590317	−	0.236135i
$516$	−5.73777	−	5.00321i	−0.252591	−	0.220254i
$517$	−12.5743	−	1.99158i	−0.553019	−	0.0875896i
$518$	16.4550	+	16.4550i	0.722991	+	0.722991i
$519$	−4.61151	+	10.8180i	−0.202423	+	0.474856i
$520$	−5.20970	−	12.1563i	−0.228460	−	0.533091i
$521$	−24.0053	+	33.0404i	−1.05169	+	1.44753i	−0.164357	+	0.986401i	$0.552555\pi$
$521$	−24.0053	+	33.0404i	−1.05169	+	1.44753i	−0.887334	+	0.461127i	$0.847445\pi$
$522$	−8.21721	−	2.85758i	−0.359657	−	0.125073i
$523$	−12.3663	−	24.2703i	−0.540741	−	1.06126i	−0.986137	−	0.165931i	$-0.946937\pi$
$523$	−12.3663	−	24.2703i	−0.540741	−	1.06126i	0.445396	−	0.895334i	$-0.353063\pi$
$524$	11.9190			0.520682
$525$	9.88213	+	22.9371i	0.431291	+	1.00106i
$526$	23.8782			1.04114
$527$	15.3319	+	30.0906i	0.667868	+	1.31077i
$528$	3.04786	+	3.64362i	0.132641	+	0.158568i
$529$	−12.7609	+	17.5639i	−0.554822	+	0.763646i
$530$	−11.9283	+	1.08512i	−0.518131	+	0.0471348i
$531$	−8.77284	+	1.20556i	−0.380709	+	0.0523170i
$532$	10.5726	+	10.5726i	0.458379	+	0.458379i
$533$	30.8763	+	4.89032i	1.33740	+	0.211823i
$534$	−1.48152	+	1.69903i	−0.0641116	+	0.0735243i
$535$	−26.8834	+	6.80152i	−1.16227	+	0.294055i
$536$	−0.438912	−	0.142611i	−0.0189581	−	0.00615987i
$537$	16.2122	−	1.10873i	0.699606	−	0.0478451i
$538$	−12.3831	−	6.30950i	−0.533873	−	0.272022i
$539$	1.11605	−	3.43486i	0.0480718	−	0.147950i
$540$	9.27134	+	7.00302i	0.398975	+	0.301362i
$541$	4.75771	+	14.6427i	0.204550	+	0.629540i	0.999732	+	0.0231685i	$0.00737544\pi$
$541$	4.75771	+	14.6427i	0.204550	+	0.629540i	−0.795182	+	0.606371i	$0.792625\pi$
$542$	2.35194	−	14.8496i	0.101025	−	0.637844i
$543$	6.41107	−	25.5467i	0.275125	−	1.09631i
$544$	−3.51743	−	4.84132i	−0.150808	−	0.207570i
$545$	6.08887	+	1.38359i	0.260819	+	0.0592664i
$546$	−2.62000	+	29.4278i	−0.112126	+	1.25939i
$547$	−3.51301	−	22.1803i	−0.150205	−	0.948360i	−0.941522	−	0.336953i	$-0.890604\pi$
$547$	−3.51301	−	22.1803i	−0.150205	−	0.948360i	0.791316	−	0.611407i	$-0.209396\pi$
$548$	−17.7044	+	9.02083i	−0.756293	+	0.385351i
$549$	12.1388	+	6.50207i	0.518072	+	0.277502i
$550$	−10.8944	+	8.32813i	−0.464538	+	0.355113i
$551$		−	15.0352i		−	0.640520i
$552$	1.04497	−	1.66662i	0.0444770	−	0.0709362i
$553$	33.4642	−	5.30021i	1.42304	−	0.225388i
$554$	1.46748	+	1.06619i	0.0623472	+	0.0452979i
$555$	−9.60022	+	29.7410i	−0.407507	+	1.26243i
$556$	−7.72325	+	5.61127i	−0.327539	+	0.237971i
$557$	−1.66485	+	1.66485i	−0.0705420	+	0.0705420i	−0.741498	−	0.670956i	$-0.765884\pi$
$557$	−1.66485	+	1.66485i	−0.0705420	+	0.0705420i	0.670956	+	0.741498i	$0.265884\pi$
$558$	−10.2302	+	13.4899i	−0.433081	+	0.571071i
$559$	24.7240	−	8.03333i	1.04572	−	0.339773i
$560$	5.45688	−	3.43610i	0.230595	−	0.145202i
$561$	−6.35223	−	27.7080i	−0.268191	−	1.16983i
$562$	10.4045	−	20.4199i	0.438886	−	0.861362i
$563$	−21.4512	+	42.1004i	−0.904062	+	1.77432i	−0.369332	+	0.929297i	$0.620414\pi$
$563$	−21.4512	+	42.1004i	−0.904062	+	1.77432i	−0.534729	+	0.845023i	$0.679586\pi$
$564$	1.79665	+	7.83686i	0.0756525	+	0.329991i
$565$	8.74655	−	5.50756i	0.367970	−	0.231705i
$566$	2.70579	−	0.879165i	0.113733	−	0.0369541i
$567$	−10.8248	−	23.5900i	−0.454600	−	0.990688i
$568$	4.04562	−	4.04562i	0.169750	−	0.169750i
$569$	−19.9798	+	14.5162i	−0.837599	+	0.608551i	−0.921699	−	0.387906i	$-0.873198\pi$
$569$	−19.9798	+	14.5162i	−0.837599	+	0.608551i	0.0841003	+	0.996457i	$0.473198\pi$
$570$	−6.16828	+	19.1090i	−0.258361	+	0.800388i
$571$	4.83866	+	3.51549i	0.202491	+	0.147119i	0.684410	−	0.729097i	$-0.260060\pi$
$571$	4.83866	+	3.51549i	0.202491	+	0.147119i	−0.481919	+	0.876216i	$0.660060\pi$
$572$	−16.0218	+	2.53761i	−0.669907	+	0.106103i
$573$	−11.8760	+	18.9409i	−0.496126	+	0.791269i
$574$			15.2424i			0.636206i
$575$	4.67404	+	3.22490i	0.194921	+	0.134488i
$576$	1.41652	−	2.64452i	0.0590216	−	0.110188i
$577$	−28.0783	+	14.3066i	−1.16891	+	0.595591i	−0.927130	−	0.374739i	$-0.877732\pi$
$577$	−28.0783	+	14.3066i	−1.16891	+	0.595591i	−0.241783	+	0.970330i	$0.577732\pi$
$578$	2.94264	+	18.5791i	0.122398	+	0.772789i
$579$	0.850312	−	9.55068i	0.0353377	−	0.396913i
$580$	−6.32333	−	1.43686i	−0.262562	−	0.0596625i
$581$	20.4704	+	28.1751i	0.849256	+	1.16890i
$582$	2.78613	−	11.1021i	0.115489	−	0.460198i
$583$	−2.29814	+	14.5099i	−0.0951791	+	0.600937i
$584$	2.80857	+	8.64390i	0.116220	+	0.357687i
$585$	−36.7820	+	14.8777i	−1.52075	+	0.615117i
$586$	4.12744	−	12.7030i	0.170503	−	0.524755i
$587$	10.0374	+	5.11433i	0.414289	+	0.211091i	0.648696	−	0.761048i	$-0.275315\pi$
$587$	10.0374	+	5.11433i	0.414289	+	0.211091i	−0.234407	+	0.972139i	$0.575315\pi$
$588$	−2.27556	+	0.155623i	−0.0938427	+	0.00641777i
$589$	−27.8269	−	9.04151i	−1.14659	−	0.372549i
$590$	−6.39873	+	1.61888i	−0.263431	+	0.0666483i
$591$	29.1177	−	33.3927i	1.19774	−	1.37359i
$592$	7.96990	+	1.26231i	0.327561	+	0.0518805i
$593$	−17.4049	−	17.4049i	−0.714734	−	0.714734i	0.252788	−	0.967522i	$-0.418653\pi$
$593$	−17.4049	−	17.4049i	−0.714734	−	0.714734i	−0.967522	+	0.252788i	$0.918653\pi$
$594$	11.1161	−	8.91744i	0.456100	−	0.365887i
$595$	−38.4310	+	3.49610i	−1.57552	+	0.143326i
$596$	7.05865	−	9.71540i	0.289134	−	0.397958i
$597$	0.0853849	+	0.102075i	0.00349457	+	0.00417764i
$598$	3.04966	+	5.98529i	0.124710	+	0.244757i
$599$	25.8531			1.05633			0.528165	−	0.849142i	$-0.322880\pi$
$599$	25.8531			1.05633			0.528165	+	0.849142i	$0.322880\pi$
$600$	7.44717	+	4.42037i	0.304029	+	0.180461i
$601$	−36.7027			−1.49714			−0.748568	−	0.663058i	$-0.769258\pi$
$601$	−36.7027			−1.49714			−0.748568	+	0.663058i	$0.769258\pi$
$602$	5.75450	+	11.2939i	0.234536	+	0.460303i
$603$	−0.454755	+	1.30768i	−0.0185190	+	0.0532530i
$604$	6.54069	−	9.00249i	0.266137	−	0.366306i
$605$	−3.06362	−	7.14867i	−0.124554	−	0.290635i
$606$	−2.39740	+	5.62397i	−0.0973877	+	0.228458i
$607$	−23.2173	−	23.2173i	−0.942362	−	0.942362i	0.0560654	−	0.998427i	$-0.482144\pi$
$607$	−23.2173	−	23.2173i	−0.942362	−	0.942362i	−0.998427	+	0.0560654i	$0.982144\pi$
$608$	5.12077	+	0.811051i	0.207675	+	0.0328925i
$609$	10.9178	+	9.52007i	0.442411	+	0.385773i
$610$	9.52979	+	3.81204i	0.385850	+	0.154345i
$611$	−26.1121	−	8.48435i	−1.05638	−	0.343240i
$612$	−14.7374	+	10.2521i	−0.595723	+	0.414417i
$613$	19.5715	+	9.97216i	0.790484	+	0.402772i	0.802122	−	0.597161i	$-0.203705\pi$
$613$	19.5715	+	9.97216i	0.790484	+	0.402772i	−0.0116379	+	0.999932i	$0.503705\pi$
$614$	−10.1339	+	31.1890i	−0.408972	+	1.25869i
$615$	−18.2210	+	9.32828i	−0.734744	+	0.376153i
$616$	−2.44412	−	7.52224i	−0.0984766	−	0.303080i
$617$	−1.00125	+	6.32162i	−0.0403086	+	0.254499i	−0.999611	−	0.0278814i	$-0.991124\pi$
$617$	−1.00125	+	6.32162i	−0.0403086	+	0.254499i	0.959303	+	0.282380i	$0.0911239\pi$
$618$	10.8401	+	2.72038i	0.436053	+	0.109430i
$619$	14.0949	+	19.4000i	0.566524	+	0.779753i	0.992138	−	0.125152i	$-0.0399418\pi$
$619$	14.0949	+	19.4000i	0.566524	+	0.779753i	−0.425614	+	0.904905i	$0.639942\pi$
$620$	−6.46190	+	10.8391i	−0.259516	+	0.435307i
$621$	−4.93451	−	3.23682i	−0.198015	−	0.129889i
$622$	−1.61936	−	10.2243i	−0.0649306	−	0.409956i
$623$	3.34426	−	1.70399i	0.133985	−	0.0682688i
$624$	5.26288	+	8.78935i	0.210684	+	0.351856i
$625$	−13.6921	+	20.9171i	−0.547684	+	0.836685i
$626$			13.7188i			0.548313i
$627$	20.8661	+	13.0831i	0.833312	+	0.522487i
$628$	16.2195	−	2.56892i	0.647230	−	0.102511i
$629$	−39.0658	−	28.3830i	−1.55766	−	1.13170i
$630$	−9.97032	−	16.5787i	−0.397227	−	0.660509i
$631$	−23.7895	+	17.2841i	−0.947046	+	0.688069i	−0.950106	−	0.311926i	$-0.899026\pi$
$631$	−23.7895	+	17.2841i	−0.947046	+	0.688069i	0.00306072	+	0.999995i	$0.499026\pi$
$632$	8.30741	−	8.30741i	0.330451	−	0.330451i
$633$	−4.16968	−	10.3660i	−0.165730	−	0.412011i
$634$	17.9501	−	5.83235i	0.712891	−	0.231632i
$635$	27.9563	+	1.85787i	1.10941	+	0.0737271i
$636$	9.04315	−	2.07320i	0.358584	−	0.0822077i
$637$	3.53606	−	6.93992i	0.140104	−	0.274970i
$638$	−3.61078	+	7.08655i	−0.142952	+	0.280559i
$639$	−11.8853	−	12.3833i	−0.470177	−	0.489875i
$640$	0.830479	−	2.07613i	0.0328275	−	0.0820661i
$641$	18.3395	−	5.95888i	0.724368	−	0.235362i	0.0764522	−	0.997073i	$-0.475641\pi$
$641$	18.3395	−	5.95888i	0.724368	−	0.235362i	0.647916	+	0.761712i	$0.275641\pi$
$642$	19.9281	−	8.01603i	0.786501	−	0.316367i
$643$	−2.50826	+	2.50826i	−0.0989163	+	0.0989163i	−0.754833	−	0.655917i	$-0.772282\pi$
$643$	−2.50826	+	2.50826i	−0.0989163	+	0.0989163i	0.655917	+	0.754833i	$0.272282\pi$
$644$	−2.64978	+	1.92518i	−0.104416	+	0.0758627i
$645$	−9.97915	+	13.7908i	−0.392929	+	0.543013i
$646$	−25.1003	−	18.2365i	−0.987560	−	0.717504i
$647$	−36.9778	+	5.85671i	−1.45375	+	0.230251i	−0.832789	−	0.553591i	$-0.813257\pi$
$647$	−36.9778	+	5.85671i	−1.45375	+	0.230251i	−0.620960	+	0.783842i	$0.713257\pi$
$648$	−7.84471	−	4.41141i	−0.308169	−	0.173296i
$649$			8.09547i			0.317775i
$650$	−26.0152	+	14.0640i	−1.02040	+	0.551634i
$651$	24.1851	−	14.4815i	0.947889	−	0.567576i
$652$	−5.83680	+	2.97400i	−0.228587	+	0.116471i
$653$	0.348209	+	2.19851i	0.0136265	+	0.0860342i	0.993564	−	0.113269i	$-0.0361322\pi$
$653$	0.348209	+	2.19851i	0.0136265	+	0.0860342i	−0.979938	+	0.199303i	$0.936132\pi$
$654$	−4.81760	−	0.428918i	−0.188383	−	0.0167720i
$655$	−2.41455	−	26.5420i	−0.0943442	−	1.03708i
$656$	3.10665	+	4.27594i	0.121294	+	0.166947i
$657$	26.0991	−	7.89200i	1.01822	−	0.307896i
$658$	2.09419	−	13.2222i	0.0816401	−	0.515456i
$659$	4.81311	+	14.8132i	0.187492	+	0.577041i	0.999982	−	0.00593344i	$-0.00188868\pi$
$659$	4.81311	+	14.8132i	0.187492	+	0.577041i	−0.812490	+	0.582975i	$0.801889\pi$
$660$	7.49643	−	7.52533i	0.291798	−	0.292923i
$661$	−0.225919	+	0.695307i	−0.00878723	+	0.0270443i	−0.955354	−	0.295464i	$-0.904526\pi$
$661$	−0.225919	+	0.695307i	−0.00878723	+	0.0270443i	0.946567	+	0.322508i	$0.104526\pi$
$662$	28.2773	+	14.4080i	1.09903	+	0.559984i
$663$	−4.18282	−	61.1625i	−0.162447	−	2.37536i
$664$	11.4851	+	3.73173i	0.445708	+	0.144819i
$665$	21.4020	−	25.6856i	0.829933	−	0.996043i
$666$	4.27660	−	23.8270i	0.165715	−	0.923277i
$667$	3.25301	+	0.515226i	0.125957	+	0.0199496i
$668$	12.0192	+	12.0192i	0.465037	+	0.465037i
$669$	−8.66651	−	3.69438i	−0.335067	−	0.142833i
$670$	−0.228662	+	1.00629i	−0.00883398	+	0.0388764i
$671$	7.39961	−	10.1847i	0.285659	−	0.393176i
$672$	−3.83135	+	3.20490i	−0.147797	+	0.123632i
$673$	−6.83769	−	13.4197i	−0.263574	−	0.517292i	0.720853	−	0.693088i	$-0.243750\pi$
$673$	−6.83769	−	13.4197i	−0.263574	−	0.517292i	−0.984427	+	0.175796i	$0.943750\pi$
$674$	16.1131			0.620652
$675$	13.7166	−	22.0648i	0.527953	−	0.849273i
$676$	−21.9835			−0.845520
$677$	10.5178	+	20.6424i	0.404233	+	0.793351i	0.999952	−	0.00984177i	$-0.00313278\pi$
$677$	10.5178	+	20.6424i	0.404233	+	0.793351i	−0.595719	+	0.803193i	$0.703133\pi$
$678$	−6.14107	+	5.13697i	−0.235846	+	0.197284i
$679$	−11.2023	+	15.4186i	−0.429904	+	0.591712i
$680$	−10.0684	+	8.81362i	−0.386107	+	0.337987i
$681$	−31.2643	−	13.3274i	−1.19805	−	0.510708i
$682$	10.9443	+	10.9443i	0.419080	+	0.419080i
$683$	4.28854	+	0.679239i	0.164097	+	0.0259903i	0.237942	−	0.971279i	$-0.423527\pi$
$683$	4.28854	+	0.679239i	0.164097	+	0.0259903i	−0.0738455	+	0.997270i	$0.523527\pi$
$684$	2.74778	−	15.3092i	0.105064	−	0.585361i
$685$	23.6748	+	37.5979i	0.904567	+	1.43654i
$686$	−15.5874	−	5.06466i	−0.595130	−	0.193370i
$687$	−2.06751	−	30.2317i	−0.0788803	−	1.15341i
$688$	3.91618	+	1.99539i	0.149303	+	0.0760736i
$689$	−9.79031	+	30.1315i	−0.372981	+	1.14792i
$690$	−3.92305	−	1.98940i	−0.149348	−	0.0757350i
$691$	−9.14266	−	28.1382i	−0.347803	−	1.07043i	−0.960066	−	0.279774i	$-0.909741\pi$
$691$	−9.14266	−	28.1382i	−0.347803	−	1.07043i	0.612263	−	0.790654i	$-0.290259\pi$
$692$	1.06212	−	6.70597i	0.0403758	−	0.254923i
$693$	−22.7124	+	6.86790i	−0.862772	+	0.260890i
$694$	14.0633	+	19.3564i	0.533834	+	0.734759i
$695$	14.0602	+	16.0620i	0.533332	+	0.609265i
$696$	5.00310	+	0.445433i	0.189642	+	0.0168841i
$697$	−4.94780	−	31.2392i	−0.187411	−	1.18327i
$698$	22.1821	−	11.3024i	0.839606	−	0.427801i
$699$	−43.1276	+	25.8239i	−1.63124	+	0.976750i
$700$	−8.75722	−	11.4557i	−0.330992	−	0.432984i
$701$		−	19.5558i		−	0.738612i	−0.929308	−	0.369306i	$-0.879595\pi$
$701$		−	19.5558i		−	0.738612i	0.929308	−	0.369306i	$-0.120405\pi$
$702$	26.6864	−	15.2444i	1.00721	−	0.575363i
$703$	41.3208	−	6.54457i	1.55844	−	0.246833i
$704$	−2.21880	−	1.61205i	−0.0836243	−	0.0607566i
$705$	17.0877	−	5.58850i	0.643561	−	0.210475i
$706$	−13.6828	+	9.94116i	−0.514960	+	0.374140i
$707$	7.19787	−	7.19787i	0.270704	−	0.270704i
$708$	4.74325	−	1.90795i	0.178262	−	0.0717053i
$709$	21.2009	−	6.88858i	0.796216	−	0.258706i	0.117467	−	0.993077i	$-0.462523\pi$
$709$	21.2009	−	6.88858i	0.796216	−	0.258706i	0.678749	+	0.734371i	$0.262523\pi$
$710$	−9.82864	−	8.18952i	−0.368862	−	0.307347i
$711$	−24.4058	−	25.4282i	−0.915287	−	0.953634i
$712$	0.590863	−	1.15963i	0.0221435	−	0.0434591i
$713$	2.90979	−	5.71079i	0.108973	−	0.213871i
$714$	29.1356	−	6.67952i	1.09037	−	0.249975i
$715$	8.89665	+	35.1645i	0.332716	+	1.31508i
$716$	−8.92277	+	2.89918i	−0.333460	+	0.108348i
$717$	3.65385	+	9.08361i	0.136455	+	0.339233i
$718$	−3.84337	+	3.84337i	−0.143433	+	0.143433i
$719$	−2.20624	+	1.60292i	−0.0822787	+	0.0597790i	−0.628164	−	0.778081i	$-0.716193\pi$
$719$	−2.20624	+	1.60292i	−0.0822787	+	0.0597790i	0.545885	+	0.837860i	$0.316193\pi$
$720$	−6.17596	−	2.61868i	−0.230165	−	0.0975924i
$721$	−15.0547	−	10.9379i	−0.560667	−	0.407348i
$722$	7.78310	−	1.23272i	0.289657	−	0.0458772i
$723$	20.6865	+	12.9704i	0.769339	+	0.482376i
$724$			15.2068i			0.565155i
$725$	−1.91873	+	14.3723i	−0.0712599	+	0.533775i
$726$	3.09489	+	5.16867i	0.114862	+	0.191827i
$727$	17.3015	−	8.81556i	0.641677	−	0.326951i	−0.102698	−	0.994713i	$-0.532747\pi$
$727$	17.3015	−	8.81556i	0.641677	−	0.326951i	0.744375	+	0.667762i	$0.232747\pi$
$728$	−2.66836	−	16.8473i	−0.0988959	−	0.624404i
$729$	−13.7142	+	23.2577i	−0.507934	+	0.861396i
$730$	18.6799	−	8.00542i	0.691374	−	0.296294i
$731$	−15.4599	−	21.2787i	−0.571805	−	0.787022i
$732$	−7.71130	−	1.93519i	−0.285018	−	0.0715266i
$733$	3.79691	−	23.9728i	0.140242	−	0.885454i	−0.812784	−	0.582566i	$-0.802049\pi$
$733$	3.79691	−	23.9728i	0.140242	−	0.885454i	0.953026	−	0.302889i	$-0.0979511\pi$
$734$	−5.54024	−	17.0511i	−0.204494	−	0.629368i
$735$	0.807536	+	5.03587i	0.0297864	+	0.185751i
$736$	−0.350958	+	1.08014i	−0.0129365	+	0.0398144i
$737$	1.12775	+	0.574618i	0.0415412	+	0.0211663i
$738$	13.0163	−	9.05484i	0.479136	−	0.333313i
$739$	6.13821	+	1.99443i	0.225798	+	0.0733662i	0.419731	−	0.907649i	$-0.362124\pi$
$739$	6.13821	+	1.99443i	0.225798	+	0.0733662i	−0.193933	+	0.981015i	$0.562124\pi$
$740$	1.19645	−	18.0037i	0.0439825	−	0.661828i
$741$	40.0322	+	34.9072i	1.47062	+	1.28235i
$742$	−15.2575	−	2.41654i	−0.560119	−	0.0887141i
$743$	23.0403	+	23.0403i	0.845265	+	0.845265i	0.989538	−	0.144273i	$-0.0460842\pi$
$743$	23.0403	+	23.0403i	0.845265	+	0.845265i	−0.144273	+	0.989538i	$0.546084\pi$
$744$	3.83305	−	8.99180i	0.140526	−	0.329656i
$745$	−23.0649	−	13.7506i	−0.845032	−	0.503782i
$746$	15.0422	−	20.7038i	0.550734	−	0.758020i
$747$	11.8996	−	34.2184i	0.435385	−	1.25198i
$748$	7.45099	+	14.6234i	0.272435	+	0.534684i
$749$	−35.7645			−1.30681
$750$	8.33495	−	17.4794i	0.304350	−	0.638257i
$751$	31.4069			1.14606			0.573028	−	0.819536i	$-0.305769\pi$
$751$	31.4069			1.14606			0.573028	+	0.819536i	$0.305769\pi$
$752$	−2.10742	−	4.13604i	−0.0768497	−	0.150826i
$753$	19.2458	+	23.0077i	0.701357	+	0.838449i
$754$	−10.0819	+	13.8766i	−0.367162	+	0.505355i
$755$	−21.3724	−	12.7416i	−0.777821	−	0.463713i
$756$	9.37689	+	11.6889i	0.341034	+	0.425120i
$757$	6.35882	+	6.35882i	0.231115	+	0.231115i	0.813158	−	0.582043i	$-0.197746\pi$
$757$	6.35882	+	6.35882i	0.231115	+	0.231115i	−0.582043	+	0.813158i	$0.697746\pi$
$758$	−9.60713	−	1.52162i	−0.348947	−	0.0552678i
$759$	−3.54569	+	4.06626i	−0.128700	+	0.147596i
$760$	0.768739	−	11.5676i	0.0278851	−	0.419601i
$761$	8.94031	+	2.90488i	0.324086	+	0.105302i	0.466541	−	0.884499i	$-0.345500\pi$
$761$	8.94031	+	2.90488i	0.324086	+	0.105302i	−0.142456	+	0.989801i	$0.545500\pi$
$762$	−21.6520	+	1.48075i	−0.784370	+	0.0536419i
$763$	7.17538	+	3.65604i	0.259766	+	0.132358i
$764$	3.98859	−	12.2756i	0.144302	−	0.444116i
$765$	25.8157	+	30.7414i	0.933368	+	1.11146i
$766$	7.53686	+	23.1961i	0.272318	+	0.838108i
$767$	−2.73115	+	17.2438i	−0.0986161	+	0.622637i
$768$	−0.421593	+	1.67996i	−0.0152129	+	0.0606203i
$769$	−15.8011	−	21.7484i	−0.569803	−	0.784266i	0.422728	−	0.906256i	$-0.361072\pi$
$769$	−15.8011	−	21.7484i	−0.569803	−	0.784266i	−0.992531	+	0.121990i	$0.961072\pi$
$770$	−16.2559	+	6.96661i	−0.585823	+	0.251059i
$771$	0.931697	−	10.4648i	0.0335543	−	0.376881i
$772$	0.866006	+	5.46774i	0.0311682	+	0.196788i
$773$	19.3692	−	9.86911i	0.696662	−	0.354967i	−0.0695289	−	0.997580i	$-0.522150\pi$
$773$	19.3692	−	9.86911i	0.696662	−	0.354967i	0.766191	+	0.642613i	$0.222150\pi$
$774$	6.22592	−	11.6233i	0.223786	−	0.417789i
$775$	25.4463	+	12.1941i	0.914056	+	0.438023i
$776$			6.60858i			0.237234i
$777$	−21.4114	+	34.1490i	−0.768130	+	1.22509i
$778$	−17.5587	+	2.78103i	−0.629511	+	0.0997048i
$779$	22.1690	+	16.1067i	0.794288	+	0.577084i
$780$	18.5066	−	13.5003i	0.662643	−	0.483388i
$781$	−12.6946	+	9.22316i	−0.454248	+	0.330031i
$782$	4.80578	−	4.80578i	0.171854	−	0.171854i
$783$	1.64391	−	14.9787i	0.0587487	−	0.535296i
$784$	1.25241	−	0.406934i	0.0447291	−	0.0145334i
$785$	−9.00643	−	35.5984i	−0.321453	−	1.27056i
$786$	4.61315	+	20.1222i	0.164545	+	0.717736i
$787$	−8.50770	+	16.6973i	−0.303267	+	0.595194i	−0.991472	−	0.130322i	$-0.958399\pi$
$787$	−8.50770	+	16.6973i	−0.303267	+	0.595194i	0.688205	+	0.725516i	$0.258399\pi$
$788$	−11.6128	+	22.7914i	−0.413689	+	0.811911i
$789$	9.24190	+	40.3125i	0.329020	+	1.43516i
$790$	−20.1825	−	16.8166i	−0.718060	−	0.598309i
$791$	12.6782	−	4.11941i	0.450786	−	0.146469i
$792$	−4.97169	+	6.55580i	−0.176661	+	0.232950i
$793$	19.1976	−	19.1976i	0.681725	−	0.681725i
$794$	−15.5659	+	11.3093i	−0.552412	+	0.401351i
$795$	−6.44872	−	19.7180i	−0.228712	−	0.699324i
$796$	−0.0621591	−	0.0451612i	−0.00220317	−	0.00160070i
$797$	−47.5041	+	7.52391i	−1.68268	+	0.266511i	−0.923285	−	0.384116i	$-0.874506\pi$
$797$	−47.5041	+	7.52391i	−1.68268	+	0.266511i	−0.759398	+	0.650627i	$0.774506\pi$
$798$	−13.7571	+	21.9412i	−0.486997	+	0.776710i
$799$			27.7786i			0.982737i
$800$	−4.79151	−	1.42879i	−0.169405	−	0.0505153i
$801$	−3.44181	−	1.84358i	−0.121610	−	0.0651397i
$802$	−27.7494	+	14.1390i	−0.979867	+	0.499267i
$803$	−3.89939	−	24.6198i	−0.137607	−	0.868814i
$804$	0.0708861	−	0.796191i	0.00249996	−	0.0280795i
$805$	4.82392	+	5.51072i	0.170021	+	0.194227i
$806$	19.6197	+	27.0043i	0.691076	+	0.951184i
$807$	5.85925	−	23.3478i	0.206255	−	0.821883i
$808$	0.552168	−	3.48625i	0.0194252	−	0.122646i
$809$	−5.14657	−	15.8395i	−0.180944	−	0.556887i	0.818911	−	0.573920i	$-0.194578\pi$
$809$	−5.14657	−	15.8395i	−0.180944	−	0.556887i	−0.999855	+	0.0170329i	$0.994578\pi$
$810$	−8.23446	+	18.3628i	−0.289329	+	0.645204i
$811$	6.03759	−	18.5818i	0.212008	−	0.652495i	−0.787344	−	0.616514i	$-0.788544\pi$
$811$	6.03759	−	18.5818i	0.212008	−	0.652495i	0.999352	−	0.0359809i	$-0.0114556\pi$
$812$	−7.45167	−	3.79682i	−0.261502	−	0.133242i
$813$	25.9801	−	1.77675i	0.911163	−	0.0623132i
$814$	−21.0475	−	6.83874i	−0.737714	−	0.239698i
$815$	7.80513	+	12.3953i	0.273402	+	0.434190i
$816$	6.81198	−	7.81211i	0.238467	−	0.273478i
$817$	22.5070	+	3.56475i	0.787419	+	0.124715i
$818$	11.0947	+	11.0947i	0.387916	+	0.387916i
$819$	−50.6956	+	6.96659i	−1.77145	+	0.243432i
$820$	8.89262	−	7.78433i	0.310544	−	0.271841i
$821$	7.95552	−	10.9498i	0.277650	−	0.382152i	−0.647304	−	0.762232i	$-0.724104\pi$
$821$	7.95552	−	10.9498i	0.277650	−	0.382152i	0.924954	+	0.380080i	$0.124104\pi$
$822$	−22.0818	−	26.3980i	−0.770191	−	0.920737i
$823$	4.76071	+	9.34343i	0.165948	+	0.325691i	0.958973	−	0.283498i	$-0.0914949\pi$
$823$	4.76071	+	9.34343i	0.165948	+	0.325691i	−0.793025	+	0.609189i	$0.791495\pi$
$824$	−6.45260			−0.224787
$825$	−18.2766	−	15.1691i	−0.636309	−	0.528121i
$826$	−8.51258			−0.296191
$827$	8.74498	+	17.1630i	0.304093	+	0.596815i	0.991597	−	0.129365i	$-0.0412938\pi$
$827$	8.74498	+	17.1630i	0.304093	+	0.596815i	−0.687504	+	0.726180i	$0.741294\pi$
$828$	3.21813	+	1.11912i	0.111838	+	0.0388923i
$829$	18.5685	−	25.5573i	0.644909	−	0.887641i	−0.353956	−	0.935262i	$-0.615164\pi$
$829$	18.5685	−	25.5573i	0.644909	−	0.887641i	0.998865	+	0.0476205i	$0.0151638\pi$
$830$	5.98344	−	26.3318i	0.207688	−	0.913990i
$831$	−1.23201	+	2.89013i	−0.0427381	+	0.100258i
$832$	−4.18231	−	4.18231i	−0.144996	−	0.144996i
$833$	−7.78338	−	1.23277i	−0.269678	−	0.0427128i
$834$	−12.4625	−	10.8670i	−0.431540	−	0.376293i
$835$	24.3304	−	29.2001i	0.841987	−	1.01051i
$836$	−13.5233	−	4.39399i	−0.467713	−	0.151969i
$837$	−26.7338	−	12.0501i	−0.924057	−	0.416512i
$838$	−3.06981	−	1.56415i	−0.106045	−	0.0540325i
$839$	12.7405	−	39.2113i	0.439852	−	1.35373i	−0.448179	−	0.893944i	$-0.647927\pi$
$839$	12.7405	−	39.2113i	0.439852	−	1.35373i	0.888032	−	0.459782i	$-0.152073\pi$
$840$	7.91306	+	7.88267i	0.273026	+	0.271978i
$841$	−6.36272	−	19.5824i	−0.219404	−	0.675256i
$842$	2.11165	−	13.3324i	0.0727722	−	0.459466i
$843$	38.5009	+	9.66199i	1.32604	+	0.332777i
$844$	3.79170	+	5.21883i	0.130516	+	0.179640i
$845$	4.45343	+	48.9545i	0.153202	+	1.68409i
$846$	−12.5352	+	6.06639i	−0.430970	+	0.208567i
$847$	−1.56916	−	9.90726i	−0.0539169	−	0.340418i
$848$	−4.77269	+	2.43181i	−0.163895	+	0.0835086i
$849$	2.53151	+	4.22779i	0.0868812	+	0.145097i
$850$	21.6665	+	20.6357i	0.743154	+	0.707798i
$851$			9.16443i			0.314153i
$852$	8.39586	+	5.26420i	0.287637	+	0.180349i
$853$	−18.4859	+	2.92787i	−0.632944	+	0.100248i	−0.464659	−	0.885490i	$-0.653823\pi$
$853$	−18.4859	+	2.92787i	−0.632944	+	0.100248i	−0.168285	+	0.985738i	$0.553823\pi$
$854$	10.7094	+	7.78087i	0.366470	+	0.266256i
$855$	−34.6482	−	3.01761i	−1.18494	−	0.103200i
$856$	−10.0330	+	7.28939i	−0.342920	+	0.249146i
$857$	19.8211	−	19.8211i	0.677078	−	0.677078i	−0.282260	−	0.959338i	$-0.591084\pi$
$857$	19.8211	−	19.8211i	0.677078	−	0.677078i	0.959338	+	0.282260i	$0.0910842\pi$
$858$	−10.4853	−	26.0668i	−0.357961	−	0.889905i
$859$	−35.8942	+	11.6627i	−1.22469	+	0.397927i	−0.848789	−	0.528732i	$-0.822668\pi$
$859$	−35.8942	+	11.6627i	−1.22469	+	0.397927i	−0.375904	+	0.926659i	$0.622668\pi$
$860$	3.65014	−	9.12505i	0.124469	−	0.311162i
$861$	−25.7330	+	5.89946i	−0.876979	+	0.201053i
$862$	12.6740	−	24.8742i	0.431679	−	0.847217i
$863$	11.5537	−	22.6754i	0.393292	−	0.771879i	−0.606438	−	0.795131i	$-0.707402\pi$
$863$	11.5537	−	22.6754i	0.393292	−	0.771879i	0.999730	+	0.0232522i	$0.00740208\pi$
$864$	5.01287	+	1.36790i	0.170541	+	0.0465369i
$865$	−15.1485	−	1.00671i	−0.515065	−	0.0342292i
$866$	2.48379	−	0.807033i	0.0844027	−	0.0274241i
$867$	−30.2273	+	12.1588i	−1.02657	+	0.412936i
$868$	−11.5082	+	11.5082i	−0.390614	+	0.390614i
$869$	−26.0675	+	18.9392i	−0.884280	+	0.642467i
$870$	−0.0216059	−	11.2315i	−0.000732509	−	0.380784i
$871$	2.20831	+	1.60443i	0.0748258	+	0.0543641i
$872$	2.75806	−	0.436834i	0.0933998	−	0.0147931i
$873$	19.8216	+	0.406698i	0.670858	+	0.0137647i
$874$			5.88827i			0.199174i
$875$	−23.7363	+	21.8219i	−0.802434	+	0.737715i
$876$	−13.5061	+	8.08714i	−0.456327	+	0.273239i
$877$	30.3080	−	15.4427i	1.02343	−	0.521463i	0.140061	−	0.990143i	$-0.455270\pi$
$877$	30.3080	−	15.4427i	1.02343	−	0.521463i	0.883368	+	0.468679i	$0.155270\pi$
$878$	1.72542	+	10.8939i	0.0582302	+	0.367651i
$879$	23.0433	+	2.05158i	0.777232	+	0.0691981i
$880$	−3.14035	+	5.26756i	−0.105861	+	0.177569i
$881$	27.1879	+	37.4210i	0.915985	+	1.26074i	0.965081	+	0.261951i	$0.0843658\pi$
$881$	27.1879	+	37.4210i	0.915985	+	1.26074i	−0.0490965	+	0.998794i	$0.515634\pi$
$882$	−1.14347	−	3.78150i	−0.0385027	−	0.127330i
$883$	−4.58634	+	28.9570i	−0.154343	+	0.974480i	0.781971	+	0.623315i	$0.214215\pi$
$883$	−4.58634	+	28.9570i	−0.154343	+	0.974480i	−0.936313	+	0.351165i	$0.885785\pi$
$884$	10.9376	+	33.6624i	0.367870	+	1.13219i
$885$	−5.20966	−	10.1761i	−0.175121	−	0.342066i
$886$	0.577651	−	1.77783i	0.0194065	−	0.0597272i
$887$	22.3947	+	11.4107i	0.751940	+	0.383133i	0.787564	−	0.616233i	$-0.211342\pi$
$887$	22.3947	+	11.4107i	0.751940	+	0.383133i	−0.0356241	+	0.999365i	$0.511342\pi$
$888$	0.953595	+	13.9438i	0.0320005	+	0.467922i
$889$	34.3666	+	11.1664i	1.15262	+	0.374509i
$890$	−2.70205	−	1.08086i	−0.0905730	−	0.0362304i
$891$	19.3573	+	15.3154i	0.648494	+	0.513085i
$892$	5.37230	+	0.850889i	0.179878	+	0.0284899i
$893$	−17.0179	−	17.0179i	−0.569481	−	0.569481i
$894$	19.1340	+	8.15651i	0.639938	+	0.272795i
$895$	8.26369	+	19.2826i	0.276225	+	0.644545i
$896$	1.69511	−	2.33312i	0.0566297	−	0.0779441i
$897$	−8.92433	+	7.46515i	−0.297975	+	0.249254i
$898$	−9.31762	−	18.2869i	−0.310933	−	0.610240i
$899$	16.3657			0.545828
$900$	−4.58033	+	14.2836i	−0.152678	+	0.476119i
$901$	32.0545			1.06789
$902$	−6.58084	−	12.9156i	−0.219118	−	0.430043i
$903$	−16.8396	+	14.0863i	−0.560388	+	0.468761i
$904$	2.71701	−	3.73964i	0.0903664	−	0.124379i
$905$	33.8635	−	3.08059i	1.12566	−	0.102402i
$906$	17.7300	+	7.55799i	0.589040	+	0.251097i
$907$	38.3276	+	38.3276i	1.27265	+	1.27265i	0.944694	+	0.327952i	$0.106358\pi$
$907$	38.3276	+	38.3276i	1.27265	+	1.27265i	0.327952	+	0.944694i	$0.393642\pi$
$908$	19.3805	+	3.06957i	0.643164	+	0.101867i
$909$	−10.4226	−	1.87070i	−0.345695	−	0.0620473i
$910$	−36.9763	+	9.35503i	−1.22575	+	0.310116i
$911$	−28.3746	−	9.21947i	−0.940093	−	0.305455i	−0.201409	−	0.979507i	$-0.564552\pi$
$911$	−28.3746	−	9.21947i	−0.940093	−	0.305455i	−0.738683	+	0.674053i	$0.764552\pi$
$912$	0.612698	+	8.95907i	0.0202885	+	0.296665i
$913$	−29.5101	−	15.0361i	−0.976640	−	0.497623i
$914$	4.82892	−	14.8619i	0.159727	−	0.491588i
$915$	−2.74726	+	17.5641i	−0.0908216	+	0.580652i
$916$	5.40628	+	16.6388i	0.178628	+	0.549762i
$917$	5.37713	−	33.9499i	0.177569	−	1.12112i
$918$	−23.0122	−	20.9124i	−0.759515	−	0.690213i
$919$	−8.11678	−	11.1718i	−0.267748	−	0.368523i	0.653880	−	0.756598i	$-0.273140\pi$
$919$	−8.11678	−	11.1718i	−0.267748	−	0.368523i	−0.921628	+	0.388075i	$0.873140\pi$
$920$	2.47642	+	0.562724i	0.0816453	+	0.0185525i
$921$	−56.5772	−	5.03715i	−1.86428	−	0.165980i
$922$	2.18253	+	13.7799i	0.0718777	+	0.453818i
$923$	−30.1518	+	15.3631i	−0.992457	+	0.505682i
$924$	11.7535	−	7.03773i	0.386661	−	0.231524i
$925$	−40.3342	+	0.982837i	−1.32618	+	0.0323155i
$926$		−	32.9648i		−	1.08329i
$927$	−0.397100	+	19.3537i	−0.0130425	+	0.635660i
$928$	−2.86426	+	0.453655i	−0.0940240	+	0.0148919i
$929$	−0.637117	−	0.462892i	−0.0209031	−	0.0151870i	0.577285	−	0.816543i	$-0.304112\pi$
$929$	−0.637117	−	0.462892i	−0.0209031	−	0.0151870i	−0.598188	+	0.801356i	$0.704112\pi$
$930$	−20.8001	−	6.71415i	−0.682062	−	0.220166i
$931$	5.52351	−	4.01306i	0.181026	−	0.131523i
$932$	20.5218	−	20.5218i	0.672214	−	0.672214i
$933$	16.6344	−	6.69112i	0.544585	−	0.219057i
$934$	3.51708	−	1.14277i	0.115082	−	0.0373925i
$935$	31.0550	−	19.5548i	1.01561	−	0.639511i
$936$	−12.8017	+	12.2869i	−0.418436	+	0.401611i
$937$	1.89949	−	3.72797i	0.0620538	−	0.121787i	−0.857896	−	0.513823i	$-0.828229\pi$
$937$	1.89949	−	3.72797i	0.0620538	−	0.121787i	0.919950	+	0.392035i	$0.128229\pi$
$938$	−0.604224	+	1.18586i	−0.0197286	+	0.0387196i
$939$	−23.1608	+	5.30976i	−0.755824	+	0.173277i
$940$	−8.78352	+	5.53084i	−0.286487	+	0.180396i
$941$	−12.1196	+	3.93788i	−0.395086	+	0.128371i	−0.499821	−	0.866129i	$-0.666601\pi$
$941$	−12.1196	+	3.93788i	−0.395086	+	0.128371i	0.104734	+	0.994500i	$0.466601\pi$
$942$	10.6146	+	26.3884i	0.345844	+	0.859781i
$943$	−4.24454	+	4.24454i	−0.138221	+	0.138221i
$944$	−2.38803	+	1.73500i	−0.0777236	+	0.0564695i
$945$	24.1300	−	23.2491i	0.784949	−	0.756292i
$946$	−9.75214	−	7.08535i	−0.317069	−	0.230364i
$947$	−39.3427	+	6.23127i	−1.27847	+	0.202489i	−0.758486	−	0.651690i	$-0.774060\pi$
$947$	−39.3427	+	6.23127i	−1.27847	+	0.202489i	−0.519980	+	0.854179i	$0.674060\pi$
$948$	17.2403	+	10.8097i	0.559940	+	0.351083i
$949$		−	53.7570i		−	1.74503i
$950$	−25.9153	+	0.631486i	−0.840804	+	0.0204881i
$951$	16.7940	+	28.0470i	0.544581	+	0.909486i
$952$	−15.3768	+	7.83489i	−0.498366	+	0.253930i
$953$	−4.01002	−	25.3183i	−0.129897	−	0.820139i	−0.963487	−	0.267755i	$-0.913718\pi$
$953$	−4.01002	−	25.3183i	−0.129897	−	0.820139i	0.833590	−	0.552384i	$-0.186282\pi$
$954$	7.00017	+	14.4647i	0.226639	+	0.468312i
$955$	−28.1442	−	6.39528i	−0.910726	−	0.206946i
$956$	−3.32263	−	4.57321i	−0.107462	−	0.147908i
$957$	−13.3614	−	3.35311i	−0.431913	−	0.108391i
$958$	0.841500	−	5.31302i	0.0271876	−	0.171656i
$959$	17.7077	+	54.4987i	0.571811	+	1.75985i
$960$	3.82646	+	0.598508i	0.123498	+	0.0193168i
$961$	0.262130	−	0.806752i	0.00845579	−	0.0260243i
$962$	−42.5251	−	21.6676i	−1.37106	−	0.698592i
$963$	21.2461	+	30.5412i	0.684647	+	0.984177i
$964$	−13.4069	−	4.35617i	−0.431807	−	0.140303i
$965$	12.0005	−	3.03614i	0.386311	−	0.0977368i
$966$	−4.27577	−	3.72837i	−0.137571	−	0.119958i
$967$	3.74989	+	0.593924i	0.120588	+	0.0190993i	0.216437	−	0.976297i	$-0.430556\pi$
$967$	3.74989	+	0.593924i	0.120588	+	0.0190993i	−0.0958486	+	0.995396i	$0.530556\pi$
$968$	−2.45946	−	2.45946i	−0.0790499	−	0.0790499i
$969$	21.0729	−	49.4340i	0.676958	−	1.58805i
$970$	14.7165	−	1.33877i	0.472517	−	0.0429852i
$971$	1.56008	−	2.14727i	0.0500655	−	0.0689092i	−0.783250	−	0.621707i	$-0.786440\pi$
$971$	1.56008	−	2.14727i	0.0500655	−	0.0689092i	0.833316	+	0.552797i	$0.186440\pi$
$972$	4.41133	−	14.9513i	0.141494	−	0.479562i
$973$	12.4988	+	24.5303i	0.400694	+	0.786406i
$974$	4.19638			0.134461
$975$	−33.8125	−	38.4770i	−1.08287	−	1.23225i
$976$	4.59018			0.146928
$977$	8.15001	+	15.9953i	0.260742	+	0.511735i	0.983849	−	0.179001i	$-0.0572867\pi$
$977$	8.15001	+	15.9953i	0.260742	+	0.511735i	−0.723107	+	0.690736i	$0.757287\pi$
$978$	−7.27995	−	8.70293i	−0.232787	−	0.278289i
$979$	−2.09807	+	2.88774i	−0.0670546	+	0.0922927i
$980$	−1.15991	−	2.70653i	−0.0370518	−	0.0864570i
$981$	−1.14049	−	8.29933i	−0.0364131	−	0.264977i
$982$	22.3318	+	22.3318i	0.712635	+	0.712635i
$983$	−39.4883	−	6.25433i	−1.25948	−	0.199482i	−0.509227	−	0.860632i	$-0.670069\pi$
$983$	−39.4883	−	6.25433i	−1.25948	−	0.199482i	−0.750254	+	0.661150i	$0.770069\pi$
$984$	−6.01646	+	6.89978i	−0.191798	+	0.219957i
$985$	53.1061	+	21.2431i	1.69210	+	0.676863i
$986$	16.5046	+	5.36268i	0.525614	+	0.170782i
$987$	23.1330	−	1.58203i	0.736331	−	0.0503566i
$988$	−27.3230	−	13.9218i	−0.869260	−	0.442910i
$989$	−1.54254	+	4.74745i	−0.0490499	+	0.150960i
$990$	15.6061	+	9.74325i	0.495994	+	0.309661i
$991$	−12.5601	−	38.6560i	−0.398984	−	1.22795i	−0.925815	−	0.377977i	$-0.876620\pi$
$991$	−12.5601	−	38.6560i	−0.398984	−	1.22795i	0.526831	−	0.849970i	$-0.323380\pi$
$992$	−0.882826	+	5.57395i	−0.0280298	+	0.176973i
$993$	−13.3799	+	53.3158i	−0.424597	+	1.69193i
$994$	−9.69837	−	13.3487i	−0.307614	−	0.423394i
$995$	−0.0879760	+	0.147569i	−0.00278903	+	0.00467825i
$996$	−1.85489	+	20.8341i	−0.0587744	+	0.660153i
$997$	−1.77985	−	11.2375i	−0.0563684	−	0.355896i	−0.999710	−	0.0240735i	$-0.992336\pi$
$997$	−1.77985	−	11.2375i	−0.0563684	−	0.355896i	0.943342	−	0.331823i	$-0.107664\pi$
$998$	−9.13605	+	4.65505i	−0.289197	+	0.147353i
$999$	41.8812	−	2.00207i	1.32506	−	0.0633427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.47.4	✓	80
3.2	odd	2	inner	150.2.l.a.47.9	yes	80
5.2	odd	4		750.2.l.a.743.7		80
5.3	odd	4		750.2.l.c.743.4		80
5.4	even	2		750.2.l.b.257.7		80
15.2	even	4		750.2.l.a.743.4		80
15.8	even	4		750.2.l.c.743.7		80
15.14	odd	2		750.2.l.b.257.2		80
25.6	even	5		750.2.l.c.107.7		80
25.8	odd	20	inner	150.2.l.a.83.9	yes	80
25.17	odd	20		750.2.l.b.143.2		80
25.19	even	10		750.2.l.a.107.4		80
75.8	even	20	inner	150.2.l.a.83.4	yes	80
75.17	even	20		750.2.l.b.143.7		80
75.44	odd	10		750.2.l.a.107.7		80
75.56	odd	10		750.2.l.c.107.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.4	✓	80	1.1	even	1	trivial
150.2.l.a.47.9	yes	80	3.2	odd	2	inner
150.2.l.a.83.4	yes	80	75.8	even	20	inner
150.2.l.a.83.9	yes	80	25.8	odd	20	inner
750.2.l.a.107.4		80	25.19	even	10
750.2.l.a.107.7		80	75.44	odd	10
750.2.l.a.743.4		80	15.2	even	4
750.2.l.a.743.7		80	5.2	odd	4
750.2.l.b.143.2		80	25.17	odd	20
750.2.l.b.143.7		80	75.17	even	20
750.2.l.b.257.2		80	15.14	odd	2
750.2.l.b.257.7		80	5.4	even	2
750.2.l.c.107.4		80	75.56	odd	10
750.2.l.c.107.7		80	25.6	even	5
750.2.l.c.743.4		80	5.3	odd	4
750.2.l.c.743.7		80	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.32853 - 1.11131i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.92065 + 1.14503i) q^{5} +(-1.59332 - 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(0.987688 + 0.156434i) q^{8} +(0.529988 - 2.95281i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.32853 - 1.11131i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.92065 + 1.14503i) q^{5} +(-1.59332 - 0.679206i) q^{6} +(2.03922 + 2.03922i) q^{7} +(0.987688 + 0.156434i) q^{8} +(0.529988 - 2.95281i) q^{9} +(0.148273 - 2.23115i) q^{10} +(-2.60836 - 0.847507i) q^{11} +(0.118176 + 1.72801i) q^{12} +(-5.27002 - 2.68521i) q^{13} +(0.891173 - 2.74275i) q^{14} +(3.82413 - 0.613226i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.936136 + 5.91053i) q^{17} +(-2.87159 + 0.868327i) q^{18} +(-3.04743 - 4.19443i) q^{19} +(-2.05528 + 0.880807i) q^{20} +(4.97538 + 0.442965i) q^{21} +(0.429036 + 2.70883i) q^{22} +(1.01194 - 0.515607i) q^{23} +(1.48602 - 0.889798i) q^{24} +(2.37780 + 4.39841i) q^{25} +5.91469i q^{26} +(-2.57738 - 4.51188i) q^{27} +(-2.84839 + 0.451141i) q^{28} +(2.34612 + 1.70456i) q^{29} +(-2.28251 - 3.12892i) q^{30} +(4.56563 - 3.31712i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.40713 + 1.77275i) q^{33} +(5.69132 - 1.84922i) q^{34} +(1.58166 + 6.25161i) q^{35} +(2.07736 + 2.16439i) q^{36} +(-3.66336 + 7.18975i) q^{37} +(-2.35376 + 4.61952i) q^{38} +(-9.98549 + 2.28924i) q^{39} +(1.71788 + 1.43139i) q^{40} +(-5.02666 + 1.63326i) q^{41} +(-1.86409 - 4.63420i) q^{42} +(-3.10789 + 3.10789i) q^{43} +(2.21880 - 1.61205i) q^{44} +(4.39899 - 5.06447i) q^{45} +(-0.918819 - 0.667561i) q^{46} +(4.58484 - 0.726167i) q^{47} +(-1.46746 - 0.920095i) q^{48} +1.31687i q^{49} +(2.83952 - 4.11548i) q^{50} +(5.32473 + 8.89266i) q^{51} +(5.27002 - 2.68521i) q^{52} +(-0.837944 - 5.29057i) q^{53} +(-2.85001 + 4.34482i) q^{54} +(-4.03933 - 4.61442i) q^{55} +(1.69511 + 2.33312i) q^{56} +(-8.70992 - 2.18579i) q^{57} +(0.453655 - 2.86426i) q^{58} +(-0.912145 - 2.80729i) q^{59} +(-1.75166 + 3.45423i) q^{60} +(-1.41844 + 4.36552i) q^{61} +(-5.02833 - 2.56206i) q^{62} +(7.10221 - 4.94069i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-7.04723 - 11.1917i) q^{65} +(3.58033 + 3.12197i) q^{66} +(-0.455818 - 0.0721944i) q^{67} +(-4.23147 - 4.23147i) q^{68} +(0.771390 - 1.80957i) q^{69} +(4.85217 - 4.24744i) q^{70} +(3.36294 - 4.62869i) q^{71} +(0.985385 - 2.83355i) q^{72} +(4.12620 + 8.09812i) q^{73} +8.06924 q^{74} +(8.04698 + 3.20096i) q^{75} +5.18460 q^{76} +(-3.59077 - 7.04728i) q^{77} +(6.57304 + 7.85784i) q^{78} +(6.90557 - 9.50470i) q^{79} +(0.495476 - 2.18048i) q^{80} +(-8.43823 - 3.12991i) q^{81} +(3.73730 + 3.73730i) q^{82} +(11.9275 + 1.88912i) q^{83} +(-3.28282 + 3.76480i) q^{84} +(-8.56574 + 10.2802i) q^{85} +(4.18011 + 1.35820i) q^{86} +(5.01118 - 0.342708i) q^{87} +(-2.44367 - 1.24511i) q^{88} +(0.402182 - 1.23779i) q^{89} +(-6.50958 - 1.62030i) q^{90} +(-5.27101 - 16.2225i) q^{91} +(-0.177666 + 1.12174i) q^{92} +(2.37923 - 9.48072i) q^{93} +(-2.72849 - 3.75545i) q^{94} +(-1.05030 - 11.5455i) q^{95} +(-0.153600 + 1.72523i) q^{96} +(1.03381 + 6.52722i) q^{97} +(1.17334 - 0.597845i) q^{98} +(-3.88493 + 7.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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