LMFDB - Embedded newform 150.2.l.a.83.4

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			83.4
Character	$\chi$	$=$	150.83
Dual form			150.2.l.a.47.4

$q$-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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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	−0.207484	−	0.978238i	$-0.566528\pi$
$7$	2.03922	−	2.03922i	0.770754	−	0.770754i	0.978238	+	0.207484i	$0.0665276\pi$
$8$	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	−0.674592	−	0.738191i	$-0.735680\pi$
$11$	−2.60836	+	0.847507i	−0.786450	+	0.255533i	−0.111858	+	0.993724i	$0.535680\pi$
$12$	0.118176	−	1.72801i	0.0341146	−	0.498835i
$13$	−5.27002	+	2.68521i	−1.46164	+	0.744744i	−0.990526	−	0.137328i	$-0.956149\pi$
$13$	−5.27002	+	2.68521i	−1.46164	+	0.744744i	−0.471116	+	0.882071i	$0.656149\pi$
$14$	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	−0.793073	−	0.609127i	$-0.791520\pi$
$17$	−0.936136	−	5.91053i	−0.227046	−	1.43351i	0.566026	−	0.824387i	$-0.308480\pi$
$18$	−2.87159	−	0.868327i	−0.676839	−	0.204667i
$19$	−3.04743	+	4.19443i	−0.699129	+	0.962269i	0.300834	+	0.953677i	$0.402735\pi$
$19$	−3.04743	+	4.19443i	−0.699129	+	0.962269i	−0.999963	+	0.00859233i	$0.997265\pi$
$20$	−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	0.556298	−	0.830983i	$-0.312221\pi$
$23$	1.01194	+	0.515607i	0.211003	+	0.107512i	−0.345295	+	0.938494i	$0.612221\pi$
$24$	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	−0.348246	−	0.937403i	$-0.613223\pi$
$29$	2.34612	−	1.70456i	0.435664	−	0.316528i	0.783910	+	0.620875i	$0.213223\pi$
$30$	−2.28251	+	3.12892i	−0.416727	+	0.571261i
$31$	4.56563	+	3.31712i	0.820011	+	0.595773i	0.916716	−	0.399540i	$-0.130830\pi$
$31$	4.56563	+	3.31712i	0.820011	+	0.595773i	−0.0967046	+	0.995313i	$0.530830\pi$
$32$	−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	−0.967924	−	0.251243i	$-0.919161\pi$
$37$	−3.66336	−	7.18975i	−0.602253	−	1.18199i	0.365671	−	0.930744i	$-0.380839\pi$
$38$	−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	−0.111045	−	0.993815i	$-0.535420\pi$
$41$	−5.02666	−	1.63326i	−0.785033	−	0.255073i	−0.673988	+	0.738743i	$0.735420\pi$
$42$	−1.86409	+	4.63420i	−0.287635	+	0.715072i
$43$	−3.10789	−	3.10789i	−0.473950	−	0.473950i	0.429241	−	0.903190i	$-0.358781\pi$
$43$	−3.10789	−	3.10789i	−0.473950	−	0.473950i	−0.903190	+	0.429241i	$0.858781\pi$
$44$	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	0.481581	−	0.876402i	$-0.340063\pi$
$47$	4.58484	+	0.726167i	0.668768	+	0.105922i	0.187187	+	0.982324i	$0.440063\pi$
$48$	−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	0.860872	+	0.508821i	$0.169919\pi$
$53$	−0.837944	+	5.29057i	−0.115100	+	0.726715i	−0.975972	+	0.217894i	$0.930081\pi$
$54$	−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	−0.992711	−	0.120520i	$-0.961544\pi$
$59$	−0.912145	+	2.80729i	−0.118751	+	0.365478i	0.873960	+	0.485998i	$0.161544\pi$
$60$	−1.75166	−	3.45423i	−0.226138	−	0.445939i
$61$	−1.41844	−	4.36552i	−0.181613	−	0.558947i	0.818261	−	0.574847i	$-0.194939\pi$
$61$	−1.41844	−	4.36552i	−0.181613	−	0.558947i	−0.999874	+	0.0159002i	$0.994939\pi$
$62$	−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	−0.184216	−	0.982886i	$-0.558975\pi$
$67$	−0.455818	+	0.0721944i	−0.0556870	+	0.00881995i	0.128529	+	0.991706i	$0.458975\pi$
$68$	−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	0.960520	−	0.278212i	$-0.0897418\pi$
$71$	3.36294	+	4.62869i	0.399107	+	0.549324i	−0.561412	+	0.827536i	$0.689742\pi$
$72$	0.985385	+	2.83355i	0.116129	+	0.333937i
$73$	4.12620	−	8.09812i	0.482935	−	0.947814i	−0.513055	−	0.858356i	$-0.671486\pi$
$73$	4.12620	−	8.09812i	0.482935	−	0.947814i	0.995991	−	0.0894583i	$-0.0285136\pi$
$74$	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	0.995613	+	0.0935650i	$0.0298263\pi$
$79$	6.90557	+	9.50470i	0.776937	+	1.06936i	−0.218676	+	0.975798i	$0.570174\pi$
$80$	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	0.537462	−	0.843288i	$-0.319383\pi$
$83$	11.9275	−	1.88912i	1.30921	−	0.207358i	0.771747	+	0.635930i	$0.219383\pi$
$84$	−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	0.970107	−	0.242678i	$-0.0780260\pi$
$89$	0.402182	+	1.23779i	0.0426312	+	0.131205i	−0.927476	+	0.373884i	$0.878026\pi$
$90$	−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	−0.877959	−	0.478737i	$-0.841095\pi$
$97$	1.03381	−	6.52722i	0.104967	−	0.662738i	0.982926	−	0.184002i	$-0.0589052\pi$
$98$	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	$0.0561896\pi$
$101$			3.52971i			0.351219i	−0.984460	+	0.175610i	$0.943810\pi$
$102$	5.50604	+	8.78155i	0.545179	+	0.869503i
$103$	−6.37316	−	1.00941i	−0.627966	−	0.0994601i	−0.165664	−	0.986182i	$-0.552977\pi$
$103$	−6.37316	−	1.00941i	−0.627966	−	0.0994601i	−0.462303	+	0.886722i	$0.652977\pi$
$104$	−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	0.142106	−	0.989851i	$-0.454613\pi$
$107$	−8.76915	−	8.76915i	−0.847745	−	0.847745i	−0.989851	+	0.142106i	$0.954613\pi$
$108$	5.16514	−	0.566874i	0.497016	−	0.0545474i
$109$	2.65577	+	0.862912i	0.254377	+	0.0826520i	0.433430	−	0.901187i	$-0.357303\pi$
$109$	2.65577	+	0.862912i	0.254377	+	0.0826520i	−0.179053	+	0.983839i	$0.557303\pi$
$110$	−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	0.968399	−	0.249406i	$-0.0802353\pi$
$113$	2.09855	+	4.11863i	0.197415	+	0.387449i	−0.770984	+	0.636854i	$0.780235\pi$
$114$	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	0.872707	−	0.488245i	$-0.162363\pi$
$127$	11.1643	+	5.68850i	0.990672	+	0.504773i	0.117966	+	0.993018i	$0.462363\pi$
$128$	−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	−0.996748	−	0.0805811i	$-0.974322\pi$
$131$	−7.00579	+	9.64264i	−0.612099	+	0.842482i	0.384649	+	0.923063i	$0.374322\pi$
$132$	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	0.516268	−	0.856427i	$-0.327321\pi$
$137$	17.7044	−	9.02083i	1.51259	−	0.770702i	0.996319	+	0.0857255i	$0.0273208\pi$
$138$	−1.96255	−	0.134216i	−0.167063	−	0.0114252i
$139$	9.07922	−	2.95002i	0.770090	−	0.250217i	0.102486	−	0.994734i	$-0.467320\pi$
$139$	9.07922	−	2.95002i	0.770090	−	0.250217i	0.667603	+	0.744517i	$0.267320\pi$
$140$	−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	−0.997493	−	0.0707617i	$-0.977457\pi$
$157$	−11.6119	+	11.6119i	−0.926732	+	0.926732i	0.0707617	+	0.997493i	$0.477457\pi$
$158$	−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	−0.210209	−	0.977656i	$-0.567415\pi$
$163$	5.83680	−	2.97400i	0.457173	−	0.232941i	0.667383	+	0.744715i	$0.267415\pi$
$164$	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	0.846920	+	0.531720i	$0.178454\pi$
$167$	2.65903	+	16.7884i	0.205762	+	1.29913i	−0.641159	+	0.767408i	$0.721546\pi$
$168$	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	0.208639	−	0.977993i	$-0.433097\pi$
$173$	−6.04954	−	3.08240i	−0.459938	−	0.234350i	−0.668578	+	0.743642i	$0.733097\pi$
$174$	−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	−0.266814	−	0.963748i	$-0.585971\pi$
$179$	7.59016	−	5.51457i	0.567315	−	0.412179i	0.834129	+	0.551569i	$0.185971\pi$
$180$	1.51158	−	6.53568i	0.112667	−	0.487141i
$181$	12.3025	+	8.93831i	0.914440	+	0.664379i	0.942134	−	0.335237i	$-0.108816\pi$
$181$	12.3025	+	8.93831i	0.914440	+	0.664379i	−0.0276940	+	0.999616i	$0.508816\pi$
$182$	−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	−0.170861	−	0.985295i	$-0.554655\pi$
$191$	−12.2756	−	3.98859i	−0.888232	−	0.288604i	−0.717371	+	0.696691i	$0.754655\pi$
$192$	1.60692	+	0.646378i	0.115970	+	0.0466483i
$193$	3.91447	+	3.91447i	0.281770	+	0.281770i	0.833815	−	0.552045i	$-0.186152\pi$
$193$	3.91447	+	3.91447i	0.281770	+	0.281770i	−0.552045	+	0.833815i	$0.686152\pi$
$194$	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	0.964445	−	0.264282i	$-0.0851351\pi$
$197$	25.2645	+	4.00150i	1.80002	+	0.285095i	0.835574	+	0.549378i	$0.185135\pi$
$198$	8.22604	−	0.168782i	0.584599	−	0.0119948i
$199$		−	0.0768328i		−	0.00544653i	−0.999996	−	0.00272327i	$-0.999133\pi$
$199$		−	0.0768328i		−	0.00544653i	0.999996	−	0.00272327i	$-0.000866844\pi$
$200$	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	0.995931	−	0.0901236i	$-0.0287262\pi$
$211$	1.99342	+	6.13511i	0.137232	+	0.422358i	−0.858698	+	0.512482i	$0.828726\pi$
$212$	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	−0.958786	−	0.284128i	$-0.908296\pi$
$223$	−2.46937	+	4.84642i	−0.165362	+	0.324540i	0.793425	+	0.608668i	$0.208296\pi$
$224$	−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	0.380575	+	0.924750i	$0.375726\pi$
$227$	−8.90823	+	17.4834i	−0.591260	+	1.16041i	−0.971835	+	0.235662i	$0.924274\pi$
$228$	6.88791	+	5.76169i	0.456163	+	0.381577i
$229$	10.2833	+	14.1538i	0.679543	+	0.935310i	0.999928	−	0.0119768i	$-0.00381244\pi$
$229$	10.2833	+	14.1538i	0.679543	+	0.935310i	−0.320385	+	0.947287i	$0.603812\pi$
$230$	−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	−0.987484	−	0.157718i	$-0.949586\pi$
$233$	−28.6649	+	4.54007i	−1.87790	+	0.297430i	−0.890416	+	0.455148i	$0.849586\pi$
$234$	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	0.878531	−	0.477685i	$-0.158524\pi$
$239$	−1.74681	−	5.37613i	−0.112992	−	0.347753i	−0.991523	+	0.129932i	$0.958524\pi$
$240$	−1.76493	+	3.44746i	−0.113926	+	0.222533i
$241$	4.35617	−	13.4069i	0.280605	−	0.863614i	−0.707076	−	0.707137i	$-0.749986\pi$
$241$	4.35617	−	13.4069i	0.280605	−	0.863614i	0.987682	−	0.156477i	$-0.0500137\pi$
$242$	−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	$-0.815938\pi$
$251$		−	17.3182i		−	1.09311i	0.837422	−	0.546557i	$-0.184062\pi$
$252$	−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	0.828112	−	0.560563i	$-0.189415\pi$
$257$	4.28914	+	4.28914i	0.267549	+	0.267549i	−0.560563	+	0.828112i	$0.689415\pi$
$258$	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	−0.937230	−	0.348711i	$-0.886619\pi$
$263$	−10.8405	−	21.2757i	−0.668454	−	1.31191i	0.268777	−	0.963203i	$-0.413381\pi$
$264$	−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	0.875189	−	0.483781i	$-0.160737\pi$
$269$	11.2436	+	8.16896i	0.685535	+	0.498070i	−0.189654	+	0.981851i	$0.560737\pi$
$270$	−10.4488	−	5.08152i	−0.635896	−	0.309252i
$271$	12.1633	−	8.83716i	0.738868	−	0.536819i	−0.153488	−	0.988151i	$-0.549051\pi$
$271$	12.1633	−	8.83716i	0.738868	−	0.536819i	0.892357	+	0.451331i	$0.149051\pi$
$272$	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	0.404762	−	0.914422i	$-0.367354\pi$
$277$	−1.61620	−	0.823495i	−0.0971080	−	0.0494790i	−0.501870	+	0.864943i	$0.667354\pi$
$278$	−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	−0.188683	−	0.982038i	$-0.560422\pi$
$281$	13.4707	−	18.5409i	0.803597	−	1.10606i	0.992280	−	0.124018i	$-0.0395782\pi$
$282$	−7.79835	+	1.95703i	−0.464385	+	0.116540i
$283$	−0.445062	−	2.81001i	−0.0264562	−	0.167038i	0.970923	−	0.239393i	$-0.0769484\pi$
$283$	−0.445062	−	2.81001i	−0.0264562	−	0.167038i	−0.997379	+	0.0723553i	$0.976948\pi$
$284$	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	−0.375189	−	0.926948i	$-0.622422\pi$
$293$	9.44461	−	9.44461i	0.551760	−	0.551760i	0.926948	+	0.375189i	$0.122422\pi$
$294$	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	−0.412506	+	0.910955i	$0.635346\pi$
$307$	−23.1889	+	23.1889i	−1.32346	+	1.32346i	−0.910955	+	0.412506i	$0.864654\pi$
$308$	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	−0.0162770	−	0.999868i	$-0.505181\pi$
$311$	9.84506	−	3.19885i	0.558262	−	0.181390i	0.574539	+	0.818477i	$0.305181\pi$
$312$	−10.2207	−	0.698977i	−0.578631	−	0.0395718i
$313$	−12.2235	+	6.22820i	−0.690915	+	0.352039i	−0.763936	−	0.645292i	$-0.776736\pi$
$313$	−12.2235	+	6.22820i	−0.690915	+	0.352039i	0.0730212	+	0.997330i	$0.476736\pi$
$314$	−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	−0.920453	−	0.390853i	$-0.872180\pi$
$317$	−2.95253	−	18.6415i	−0.165830	−	1.04701i	0.754623	−	0.656159i	$-0.227820\pi$
$318$	−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	−0.993141	−	0.116926i	$-0.962696\pi$
$331$	−25.6753	−	18.6542i	−1.41124	−	1.02533i	−0.418100	−	0.908401i	$-0.637304\pi$
$332$	−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	0.601374	−	0.798968i	$-0.294620\pi$
$337$	−7.31518	−	14.3569i	−0.398483	−	0.782068i	−0.999857	+	0.0169001i	$0.994620\pi$
$338$	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	−0.514384	−	0.857560i	$-0.671980\pi$
$347$	−23.6313	−	3.74283i	−1.26859	−	0.200925i	−0.754209	+	0.656634i	$0.771980\pi$
$348$	−2.66824	−	4.25557i	−0.143033	−	0.228123i
$349$		−	24.8956i		−	1.33263i	−0.745670	−	0.666315i	$-0.767871\pi$
$349$		−	24.8956i		−	1.33263i	0.745670	−	0.666315i	$-0.232129\pi$
$350$	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	0.811578	+	0.584244i	$0.198609\pi$
$353$	−2.64576	+	16.7047i	−0.140820	+	0.889101i	−0.952398	+	0.304857i	$0.901391\pi$
$354$	−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	−0.985546	−	0.169409i	$-0.945814\pi$
$359$	−1.67961	+	5.16932i	−0.0886466	+	0.272826i	0.896899	+	0.442235i	$0.145814\pi$
$360$	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	0.323920	−	0.946084i	$-0.394999\pi$
$367$	17.7079	−	2.80465i	0.924343	−	0.146401i	0.600422	+	0.799683i	$0.294999\pi$
$368$	−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	−0.366608	−	0.930376i	$-0.619481\pi$
$373$	11.6182	−	22.8020i	0.601568	−	1.18064i	0.968176	−	0.250269i	$-0.0805190\pi$
$374$	−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	0.930205	−	0.367041i	$-0.119629\pi$
$379$	5.71732	+	7.86922i	0.293679	+	0.404215i	−0.636526	+	0.771255i	$0.719629\pi$
$380$	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	−0.737808	−	0.675010i	$-0.764139\pi$
$383$	−24.0895	+	3.81540i	−1.23092	+	0.194958i	−0.493108	+	0.869968i	$0.664139\pi$
$384$	−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	0.988262	+	0.152767i	$0.0488186\pi$
$389$	5.49358	+	16.9075i	0.278536	+	0.857245i	−0.709726	+	0.704477i	$0.751181\pi$
$390$	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	0.789405	+	0.613873i	$0.210389\pi$
$397$	−3.00987	+	19.0036i	−0.151061	+	0.953762i	−0.940466	+	0.339889i	$0.889611\pi$
$398$	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	$0.283577\pi$
$401$			31.1439i			1.55525i	−0.628726	+	0.777627i	$0.716423\pi$
$402$	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	−0.0841106	−	0.996456i	$-0.526805\pi$
$409$	−14.9223	−	4.84855i	−0.737860	−	0.239745i	−0.653749	+	0.756711i	$0.726805\pi$
$410$	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	0.653785	−	0.756680i	$-0.273180\pi$
$419$	2.78733	+	2.02511i	0.136170	+	0.0989333i	−0.517615	+	0.855614i	$0.673180\pi$
$420$	−10.6160	−	3.47193i	−0.518006	−	0.169413i
$421$	10.9206	−	7.93429i	0.532238	−	0.386694i	−0.288956	−	0.957342i	$-0.593308\pi$
$421$	10.9206	−	7.93429i	0.532238	−	0.386694i	0.821194	+	0.570649i	$0.193308\pi$
$422$	−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	−0.203657	−	0.979042i	$-0.565283\pi$
$431$	16.4092	−	22.5853i	0.790401	−	1.08789i	0.994058	−	0.108852i	$-0.0347173\pi$
$432$	−3.49460	−	3.84548i	−0.168134	−	0.185016i
$433$	−0.408546	−	2.57946i	−0.0196335	−	0.123961i	0.975925	−	0.218107i	$-0.0699881\pi$
$433$	−0.408546	−	2.57946i	−0.0196335	−	0.123961i	−0.995558	+	0.0941457i	$0.969988\pi$
$434$	−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	−0.548447	−	0.836185i	$-0.684781\pi$
$439$	−10.4899	+	3.40836i	−0.500653	+	0.162672i	0.0477940	+	0.998857i	$0.484781\pi$
$440$	−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	−0.675009	−	0.737810i	$-0.735860\pi$
$443$	1.32181	−	1.32181i	0.0628009	−	0.0628009i	0.737810	+	0.675009i	$0.235860\pi$
$444$	−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	−0.399742	−	0.916628i	$-0.630900\pi$
$457$	11.0498	−	11.0498i	0.516886	−	0.516886i	0.916628	+	0.399742i	$0.130900\pi$
$458$	−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	−0.601249	−	0.799062i	$-0.705330\pi$
$461$	−13.2689	+	4.31131i	−0.617992	+	0.200798i	−0.0167435	+	0.999860i	$0.505330\pi$
$462$	0.934699	−	13.6675i	0.0434861	−	0.635868i
$463$	29.3718	−	14.9657i	1.36502	−	0.695515i	0.390669	−	0.920531i	$-0.372244\pi$
$463$	29.3718	−	14.9657i	1.36502	−	0.695515i	0.974355	+	0.225017i	$0.0722436\pi$
$464$	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	0.970681	−	0.240371i	$-0.0772690\pi$
$467$	−0.578507	−	3.65255i	−0.0267701	−	0.169020i	−0.997451	+	0.0713509i	$0.977269\pi$
$468$	−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	−0.483908	−	0.875119i	$-0.660783\pi$
$479$	4.35190	−	3.16184i	0.198844	−	0.144468i	0.682752	+	0.730651i	$0.260783\pi$
$480$	−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	0.843806	−	0.536649i	$-0.180310\pi$
$487$	−1.90512	−	3.73900i	−0.0863291	−	0.169430i	−0.930135	+	0.367219i	$0.880310\pi$
$488$	−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	−0.460970	−	0.887416i	$-0.652499\pi$
$491$	−30.0362	−	9.75934i	−1.35551	−	0.440433i	−0.894543	+	0.446983i	$0.852499\pi$
$492$	−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	$0.0737116\pi$
$499$			10.2536i			0.459015i	−0.973307	+	0.229508i	$0.926288\pi$
$500$	−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	−0.989906	−	0.141726i	$-0.954735\pi$
$503$	−0.104371	+	0.658974i	−0.00465369	+	0.0293822i	0.985252	+	0.171108i	$0.0547348\pi$
$504$	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	0.600381	+	0.799714i	$0.295016\pi$
$509$	−8.01814	+	24.6773i	−0.355398	+	1.09380i	−0.955779	+	0.294087i	$0.904984\pi$
$510$	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	−0.887334	−	0.461127i	$-0.847445\pi$
$521$	−24.0053	−	33.0404i	−1.05169	−	1.44753i	−0.164357	−	0.986401i	$-0.552555\pi$
$522$	−8.21721	+	2.85758i	−0.359657	+	0.125073i
$523$	−12.3663	+	24.2703i	−0.540741	+	1.06126i	0.445396	+	0.895334i	$0.353063\pi$
$523$	−12.3663	+	24.2703i	−0.540741	+	1.06126i	−0.986137	+	0.165931i	$0.946937\pi$
$524$	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	−0.795182	−	0.606371i	$-0.792625\pi$
$541$	4.75771	−	14.6427i	0.204550	−	0.629540i	0.999732	−	0.0231685i	$-0.00737544\pi$
$542$	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	0.791316	+	0.611407i	$0.209396\pi$
$547$	−3.51301	+	22.1803i	−0.150205	+	0.948360i	−0.941522	+	0.336953i	$0.890604\pi$
$548$	−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	0.670956	−	0.741498i	$-0.265884\pi$
$557$	−1.66485	−	1.66485i	−0.0705420	−	0.0705420i	−0.741498	+	0.670956i	$0.765884\pi$
$558$	−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	−0.534729	−	0.845023i	$-0.679586\pi$
$563$	−21.4512	−	42.1004i	−0.904062	−	1.77432i	−0.369332	−	0.929297i	$-0.620414\pi$
$564$	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	0.0841003	−	0.996457i	$-0.473198\pi$
$569$	−19.9798	−	14.5162i	−0.837599	−	0.608551i	−0.921699	+	0.387906i	$0.873198\pi$
$570$	−6.16828	−	19.1090i	−0.258361	−	0.800388i
$571$	4.83866	−	3.51549i	0.202491	−	0.147119i	−0.481919	−	0.876216i	$-0.660060\pi$
$571$	4.83866	−	3.51549i	0.202491	−	0.147119i	0.684410	+	0.729097i	$0.260060\pi$
$572$	−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	−0.241783	−	0.970330i	$-0.577732\pi$
$577$	−28.0783	−	14.3066i	−1.16891	−	0.595591i	−0.927130	+	0.374739i	$0.877732\pi$
$578$	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	−0.234407	−	0.972139i	$-0.575315\pi$
$587$	10.0374	−	5.11433i	0.414289	−	0.211091i	0.648696	+	0.761048i	$0.275315\pi$
$588$	−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	−0.967522	−	0.252788i	$-0.918653\pi$
$593$	−17.4049	+	17.4049i	−0.714734	+	0.714734i	0.252788	+	0.967522i	$0.418653\pi$
$594$	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	−0.998427	−	0.0560654i	$-0.982144\pi$
$607$	−23.2173	+	23.2173i	−0.942362	+	0.942362i	0.0560654	+	0.998427i	$0.482144\pi$
$608$	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	−0.0116379	−	0.999932i	$-0.503705\pi$
$613$	19.5715	−	9.97216i	0.790484	−	0.402772i	0.802122	+	0.597161i	$0.203705\pi$
$614$	−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	0.959303	−	0.282380i	$-0.0911239\pi$
$617$	−1.00125	−	6.32162i	−0.0403086	−	0.254499i	−0.999611	+	0.0278814i	$0.991124\pi$
$618$	10.8401	−	2.72038i	0.436053	−	0.109430i
$619$	14.0949	−	19.4000i	0.566524	−	0.779753i	−0.425614	−	0.904905i	$-0.639942\pi$
$619$	14.0949	−	19.4000i	0.566524	−	0.779753i	0.992138	+	0.125152i	$0.0399418\pi$
$620$	−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	0.00306072	−	0.999995i	$-0.499026\pi$
$631$	−23.7895	−	17.2841i	−0.947046	−	0.688069i	−0.950106	+	0.311926i	$0.899026\pi$
$632$	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	0.647916	−	0.761712i	$-0.275641\pi$
$641$	18.3395	+	5.95888i	0.724368	+	0.235362i	0.0764522	+	0.997073i	$0.475641\pi$
$642$	19.9281	+	8.01603i	0.786501	+	0.316367i
$643$	−2.50826	−	2.50826i	−0.0989163	−	0.0989163i	0.655917	−	0.754833i	$-0.272282\pi$
$643$	−2.50826	−	2.50826i	−0.0989163	−	0.0989163i	−0.754833	+	0.655917i	$0.772282\pi$
$644$	−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	−0.620960	−	0.783842i	$-0.713257\pi$
$647$	−36.9778	−	5.85671i	−1.45375	−	0.230251i	−0.832789	+	0.553591i	$0.813257\pi$
$648$	−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	−0.979938	−	0.199303i	$-0.936132\pi$
$653$	0.348209	−	2.19851i	0.0136265	−	0.0860342i	0.993564	+	0.113269i	$0.0361322\pi$
$654$	−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	−0.812490	−	0.582975i	$-0.801889\pi$
$659$	4.81311	−	14.8132i	0.187492	−	0.577041i	0.999982	+	0.00593344i	$0.00188868\pi$
$660$	7.49643	+	7.52533i	0.291798	+	0.292923i
$661$	−0.225919	−	0.695307i	−0.00878723	−	0.0270443i	0.946567	−	0.322508i	$-0.104526\pi$
$661$	−0.225919	−	0.695307i	−0.00878723	−	0.0270443i	−0.955354	+	0.295464i	$0.904526\pi$
$662$	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	−0.984427	−	0.175796i	$-0.943750\pi$
$673$	−6.83769	+	13.4197i	−0.263574	+	0.517292i	0.720853	+	0.693088i	$0.243750\pi$
$674$	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	−0.595719	−	0.803193i	$-0.703133\pi$
$677$	10.5178	−	20.6424i	0.404233	−	0.793351i	0.999952	+	0.00984177i	$0.00313278\pi$
$678$	−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	−0.0738455	−	0.997270i	$-0.523527\pi$
$683$	4.28854	−	0.679239i	0.164097	−	0.0259903i	0.237942	+	0.971279i	$0.423527\pi$
$684$	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	0.612263	+	0.790654i	$0.290259\pi$
$691$	−9.14266	+	28.1382i	−0.347803	+	1.07043i	−0.960066	+	0.279774i	$0.909741\pi$
$692$	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	$0.120405\pi$
$701$			19.5558i			0.738612i	−0.929308	+	0.369306i	$0.879595\pi$
$702$	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	0.678749	−	0.734371i	$-0.262523\pi$
$709$	21.2009	+	6.88858i	0.796216	+	0.258706i	0.117467	+	0.993077i	$0.462523\pi$
$710$	−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	0.545885	−	0.837860i	$-0.316193\pi$
$719$	−2.20624	−	1.60292i	−0.0822787	−	0.0597790i	−0.628164	+	0.778081i	$0.716193\pi$
$720$	−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	0.744375	−	0.667762i	$-0.232747\pi$
$727$	17.3015	+	8.81556i	0.641677	+	0.326951i	−0.102698	+	0.994713i	$0.532747\pi$
$728$	−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	0.953026	+	0.302889i	$0.0979511\pi$
$733$	3.79691	+	23.9728i	0.140242	+	0.885454i	−0.812784	+	0.582566i	$0.802049\pi$
$734$	−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	−0.193933	−	0.981015i	$-0.562124\pi$
$739$	6.13821	−	1.99443i	0.225798	−	0.0733662i	0.419731	+	0.907649i	$0.362124\pi$
$740$	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	−0.144273	−	0.989538i	$-0.546084\pi$
$743$	23.0403	−	23.0403i	0.845265	−	0.845265i	0.989538	+	0.144273i	$0.0460842\pi$
$744$	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	−0.582043	−	0.813158i	$-0.697746\pi$
$757$	6.35882	−	6.35882i	0.231115	−	0.231115i	0.813158	+	0.582043i	$0.197746\pi$
$758$	−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	−0.142456	−	0.989801i	$-0.545500\pi$
$761$	8.94031	−	2.90488i	0.324086	−	0.105302i	0.466541	+	0.884499i	$0.345500\pi$
$762$	−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	−0.992531	−	0.121990i	$-0.961072\pi$
$769$	−15.8011	+	21.7484i	−0.569803	+	0.784266i	0.422728	+	0.906256i	$0.361072\pi$
$770$	−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	0.766191	−	0.642613i	$-0.222150\pi$
$773$	19.3692	+	9.86911i	0.696662	+	0.354967i	−0.0695289	+	0.997580i	$0.522150\pi$
$774$	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	0.688205	−	0.725516i	$-0.258399\pi$
$787$	−8.50770	−	16.6973i	−0.303267	−	0.595194i	−0.991472	+	0.130322i	$0.958399\pi$
$788$	−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	−0.759398	−	0.650627i	$-0.774506\pi$
$797$	−47.5041	−	7.52391i	−1.68268	−	0.266511i	−0.923285	+	0.384116i	$0.874506\pi$
$798$	−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	−0.999855	−	0.0170329i	$-0.994578\pi$
$809$	−5.14657	+	15.8395i	−0.180944	+	0.556887i	0.818911	+	0.573920i	$0.194578\pi$
$810$	−8.23446	−	18.3628i	−0.289329	−	0.645204i
$811$	6.03759	+	18.5818i	0.212008	+	0.652495i	0.999352	+	0.0359809i	$0.0114556\pi$
$811$	6.03759	+	18.5818i	0.212008	+	0.652495i	−0.787344	+	0.616514i	$0.788544\pi$
$812$	−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	0.924954	−	0.380080i	$-0.124104\pi$
$821$	7.95552	+	10.9498i	0.277650	+	0.382152i	−0.647304	+	0.762232i	$0.724104\pi$
$822$	−22.0818	+	26.3980i	−0.770191	+	0.920737i
$823$	4.76071	−	9.34343i	0.165948	−	0.325691i	−0.793025	−	0.609189i	$-0.791495\pi$
$823$	4.76071	−	9.34343i	0.165948	−	0.325691i	0.958973	+	0.283498i	$0.0914949\pi$
$824$	−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	−0.687504	−	0.726180i	$-0.741294\pi$
$827$	8.74498	−	17.1630i	0.304093	−	0.596815i	0.991597	+	0.129365i	$0.0412938\pi$
$828$	3.21813	−	1.11912i	0.111838	−	0.0388923i
$829$	18.5685	+	25.5573i	0.644909	+	0.887641i	0.998865	−	0.0476205i	$-0.0151638\pi$
$829$	18.5685	+	25.5573i	0.644909	+	0.887641i	−0.353956	+	0.935262i	$0.615164\pi$
$830$	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	0.888032	+	0.459782i	$0.152073\pi$
$839$	12.7405	+	39.2113i	0.439852	+	1.35373i	−0.448179	+	0.893944i	$0.647927\pi$
$840$	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	−0.168285	−	0.985738i	$-0.553823\pi$
$853$	−18.4859	−	2.92787i	−0.632944	−	0.100248i	−0.464659	+	0.885490i	$0.653823\pi$
$854$	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	0.959338	−	0.282260i	$-0.0910842\pi$
$857$	19.8211	+	19.8211i	0.677078	+	0.677078i	−0.282260	+	0.959338i	$0.591084\pi$
$858$	−10.4853	+	26.0668i	−0.357961	+	0.889905i
$859$	−35.8942	−	11.6627i	−1.22469	−	0.397927i	−0.375904	−	0.926659i	$-0.622668\pi$
$859$	−35.8942	−	11.6627i	−1.22469	−	0.397927i	−0.848789	+	0.528732i	$0.822668\pi$
$860$	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	0.999730	−	0.0232522i	$-0.00740208\pi$
$863$	11.5537	+	22.6754i	0.393292	+	0.771879i	−0.606438	+	0.795131i	$0.707402\pi$
$864$	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	0.883368	−	0.468679i	$-0.155270\pi$
$877$	30.3080	+	15.4427i	1.02343	+	0.521463i	0.140061	+	0.990143i	$0.455270\pi$
$878$	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	−0.0490965	−	0.998794i	$-0.515634\pi$
$881$	27.1879	−	37.4210i	0.915985	−	1.26074i	0.965081	−	0.261951i	$-0.0843658\pi$
$882$	−1.14347	+	3.78150i	−0.0385027	+	0.127330i
$883$	−4.58634	−	28.9570i	−0.154343	−	0.974480i	−0.936313	−	0.351165i	$-0.885785\pi$
$883$	−4.58634	−	28.9570i	−0.154343	−	0.974480i	0.781971	−	0.623315i	$-0.214215\pi$
$884$	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	−0.0356241	−	0.999365i	$-0.511342\pi$
$887$	22.3947	−	11.4107i	0.751940	−	0.383133i	0.787564	+	0.616233i	$0.211342\pi$
$888$	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	0.327952	−	0.944694i	$-0.393642\pi$
$907$	38.3276	−	38.3276i	1.27265	−	1.27265i	0.944694	−	0.327952i	$-0.106358\pi$
$908$	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	−0.738683	−	0.674053i	$-0.764552\pi$
$911$	−28.3746	+	9.21947i	−0.940093	+	0.305455i	−0.201409	+	0.979507i	$0.564552\pi$
$912$	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	−0.921628	−	0.388075i	$-0.873140\pi$
$919$	−8.11678	+	11.1718i	−0.267748	+	0.368523i	0.653880	+	0.756598i	$0.273140\pi$
$920$	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	−0.598188	−	0.801356i	$-0.704112\pi$
$929$	−0.637117	+	0.462892i	−0.0209031	+	0.0151870i	0.577285	+	0.816543i	$0.304112\pi$
$930$	−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	0.919950	−	0.392035i	$-0.128229\pi$
$937$	1.89949	+	3.72797i	0.0620538	+	0.121787i	−0.857896	+	0.513823i	$0.828229\pi$
$938$	−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	0.104734	−	0.994500i	$-0.466601\pi$
$941$	−12.1196	−	3.93788i	−0.395086	−	0.128371i	−0.499821	+	0.866129i	$0.666601\pi$
$942$	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	−0.519980	−	0.854179i	$-0.674060\pi$
$947$	−39.3427	−	6.23127i	−1.27847	−	0.202489i	−0.758486	+	0.651690i	$0.774060\pi$
$948$	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	0.833590	+	0.552384i	$0.186282\pi$
$953$	−4.01002	+	25.3183i	−0.129897	+	0.820139i	−0.963487	+	0.267755i	$0.913718\pi$
$954$	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	−0.0958486	−	0.995396i	$-0.530556\pi$
$967$	3.74989	−	0.593924i	0.120588	−	0.0190993i	0.216437	+	0.976297i	$0.430556\pi$
$968$	−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	0.833316	−	0.552797i	$-0.186440\pi$
$971$	1.56008	+	2.14727i	0.0500655	+	0.0689092i	−0.783250	+	0.621707i	$0.786440\pi$
$972$	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	−0.723107	−	0.690736i	$-0.757287\pi$
$977$	8.15001	−	15.9953i	0.260742	−	0.511735i	0.983849	+	0.179001i	$0.0572867\pi$
$978$	−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	−0.750254	−	0.661150i	$-0.770069\pi$
$983$	−39.4883	+	6.25433i	−1.25948	+	0.199482i	−0.509227	+	0.860632i	$0.670069\pi$
$984$	−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	0.526831	+	0.849970i	$0.323380\pi$
$991$	−12.5601	+	38.6560i	−0.398984	+	1.22795i	−0.925815	+	0.377977i	$0.876620\pi$
$992$	−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	0.943342	+	0.331823i	$0.107664\pi$
$997$	−1.77985	+	11.2375i	−0.0563684	+	0.355896i	−0.999710	+	0.0240735i	$0.992336\pi$
$998$	−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.83.4	yes	80
3.2	odd	2	inner	150.2.l.a.83.9	yes	80
5.2	odd	4		750.2.l.c.107.4		80
5.3	odd	4		750.2.l.a.107.7		80
5.4	even	2		750.2.l.b.143.7		80
15.2	even	4		750.2.l.c.107.7		80
15.8	even	4		750.2.l.a.107.4		80
15.14	odd	2		750.2.l.b.143.2		80
25.3	odd	20		750.2.l.b.257.2		80
25.4	even	10		750.2.l.a.743.4		80
25.21	even	5		750.2.l.c.743.7		80
25.22	odd	20	inner	150.2.l.a.47.9	yes	80
75.29	odd	10		750.2.l.a.743.7		80
75.47	even	20	inner	150.2.l.a.47.4	✓	80
75.53	even	20		750.2.l.b.257.7		80
75.71	odd	10		750.2.l.c.743.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.4	✓	80	75.47	even	20	inner
150.2.l.a.47.9	yes	80	25.22	odd	20	inner
150.2.l.a.83.4	yes	80	1.1	even	1	trivial
150.2.l.a.83.9	yes	80	3.2	odd	2	inner
750.2.l.a.107.4		80	15.8	even	4
750.2.l.a.107.7		80	5.3	odd	4
750.2.l.a.743.4		80	25.4	even	10
750.2.l.a.743.7		80	75.29	odd	10
750.2.l.b.143.2		80	15.14	odd	2
750.2.l.b.143.7		80	5.4	even	2
750.2.l.b.257.2		80	25.3	odd	20
750.2.l.b.257.7		80	75.53	even	20
750.2.l.c.107.4		80	5.2	odd	4
750.2.l.c.107.7		80	15.2	even	4
750.2.l.c.743.4		80	75.71	odd	10
750.2.l.c.743.7		80	25.21	even	5

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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