LMFDB - Embedded newform 756.2.bs.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(11,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13, 12]))

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

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

chi := DirichletCharacter("756.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bs (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	756.11
Dual form			756.2.bs.a.275.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32375 - 0.497675i) q^{2} +(-0.154673 - 1.72513i) q^{3} +(1.50464 + 1.31760i) q^{4} +(3.70389 - 0.653095i) q^{5} +(-0.653807 + 2.36062i) q^{6} +(2.38269 + 1.15013i) q^{7} +(-1.33603 - 2.49299i) q^{8} +(-2.95215 + 0.533661i) q^{9} +O(q^{10})$	\(q+(-1.32375 - 0.497675i) q^{2} +(-0.154673 - 1.72513i) q^{3} +(1.50464 + 1.31760i) q^{4} +(3.70389 - 0.653095i) q^{5} +(-0.653807 + 2.36062i) q^{6} +(2.38269 + 1.15013i) q^{7} +(-1.33603 - 2.49299i) q^{8} +(-2.95215 + 0.533661i) q^{9} +(-5.22806 - 0.978797i) q^{10} +(-0.518126 + 2.93844i) q^{11} +(2.04030 - 2.79949i) q^{12} +(3.90281 - 3.27484i) q^{13} +(-2.58170 - 2.70829i) q^{14} +(-1.69956 - 6.28867i) q^{15} +(0.527874 + 3.96502i) q^{16} -5.14410i q^{17} +(4.17351 + 0.762779i) q^{18} +5.48072i q^{19} +(6.43353 + 3.89756i) q^{20} +(1.61558 - 4.28835i) q^{21} +(2.14826 - 3.63191i) q^{22} +(2.08467 - 1.74925i) q^{23} +(-4.09409 + 2.69043i) q^{24} +(8.59377 - 3.12788i) q^{25} +(-6.79616 + 2.39275i) q^{26} +(1.37725 + 5.01031i) q^{27} +(2.06969 + 4.86995i) q^{28} +(-2.48873 + 2.96595i) q^{29} +(-0.879916 + 9.17047i) q^{30} +(-1.76191 + 4.84079i) q^{31} +(1.27452 - 5.51141i) q^{32} +(5.14933 + 0.439339i) q^{33} +(-2.56009 + 6.80951i) q^{34} +(9.57635 + 2.70381i) q^{35} +(-5.14507 - 3.08678i) q^{36} +(-0.868980 + 1.50512i) q^{37} +(2.72762 - 7.25512i) q^{38} +(-6.25319 - 6.22633i) q^{39} +(-6.57667 - 8.36121i) q^{40} +(3.26572 + 3.89193i) q^{41} +(-4.27283 + 4.87267i) q^{42} +(-0.808573 - 2.22154i) q^{43} +(-4.65128 + 3.73861i) q^{44} +(-10.5859 + 3.90466i) q^{45} +(-3.63015 + 1.27808i) q^{46} +(5.29209 - 1.92616i) q^{47} +(6.75852 - 1.52393i) q^{48} +(4.35442 + 5.48078i) q^{49} +(-12.9327 - 0.136375i) q^{50} +(-8.87424 + 0.795651i) q^{51} +(10.1872 + 0.214873i) q^{52} +(-11.2037 - 6.46848i) q^{53} +(0.670366 - 7.31783i) q^{54} +11.2220i q^{55} +(-0.316097 - 7.47664i) q^{56} +(9.45496 - 0.847718i) q^{57} +(4.77055 - 2.68761i) q^{58} +(6.39905 - 5.36944i) q^{59} +(5.72871 - 11.7015i) q^{60} +(4.55711 - 1.65865i) q^{61} +(4.74147 - 5.53115i) q^{62} +(-7.64784 - 2.12380i) q^{63} +(-4.43004 + 6.66144i) q^{64} +(12.3168 - 14.6786i) q^{65} +(-6.59779 - 3.14427i) q^{66} +(-2.40925 + 0.424815i) q^{67} +(6.77785 - 7.74001i) q^{68} +(-3.34013 - 3.32577i) q^{69} +(-11.3311 - 8.34509i) q^{70} +(-6.64299 - 11.5060i) q^{71} +(5.27459 + 6.64671i) q^{72} +(0.209032 + 0.362053i) q^{73} +(1.89937 - 1.55993i) q^{74} +(-6.72522 - 14.3416i) q^{75} +(-7.22139 + 8.24651i) q^{76} +(-4.61411 + 6.40548i) q^{77} +(5.17899 + 11.3542i) q^{78} +(-12.4166 - 2.18938i) q^{79} +(4.54472 + 14.3412i) q^{80} +(8.43041 - 3.15090i) q^{81} +(-2.38608 - 6.77722i) q^{82} +(-10.0481 - 8.43136i) q^{83} +(8.08118 - 4.32373i) q^{84} +(-3.35958 - 19.0532i) q^{85} +(-0.0352537 + 3.34317i) q^{86} +(5.50160 + 3.83463i) q^{87} +(8.01775 - 2.63417i) q^{88} +2.12681i q^{89} +(15.9564 + 0.0995487i) q^{90} +(13.0657 - 3.31422i) q^{91} +(5.44149 + 0.114774i) q^{92} +(8.62352 + 2.29078i) q^{93} +(-7.96401 - 0.0839804i) q^{94} +(3.57943 + 20.3000i) q^{95} +(-9.70503 - 1.34624i) q^{96} +(-12.7654 + 4.64622i) q^{97} +(-3.03653 - 9.42229i) q^{98} +(-0.0385431 - 8.95123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.32375	−	0.497675i	−0.936034	−	0.351910i
$2$	−1.32375	−	0.497675i	−0.936034	−	0.351910i
$3$	−0.154673	−	1.72513i	−0.0893003	−	0.996005i
$3$	−0.154673	−	1.72513i	−0.0893003	−	0.996005i
$4$	1.50464	+	1.31760i	0.752319	+	0.658799i
$5$	3.70389	−	0.653095i	1.65643	−	0.292073i	0.734262	−	0.678867i	$-0.237529\pi$
$5$	3.70389	−	0.653095i	1.65643	−	0.292073i	0.922166	+	0.386794i	$0.126417\pi$
$6$	−0.653807	+	2.36062i	−0.266916	+	0.963720i
$7$	2.38269	+	1.15013i	0.900572	+	0.434706i
$7$	2.38269	+	1.15013i	0.900572	+	0.434706i
$8$	−1.33603	−	2.49299i	−0.472359	−	0.881406i
$9$	−2.95215	+	0.533661i	−0.984051	+	0.177887i
$10$	−5.22806	−	0.978797i	−1.65326	−	0.309523i
$11$	−0.518126	+	2.93844i	−0.156221	+	0.885973i	0.801440	+	0.598075i	$0.204068\pi$
$11$	−0.518126	+	2.93844i	−0.156221	+	0.885973i	−0.957661	+	0.287898i	$0.907044\pi$
$12$	2.04030	−	2.79949i	0.588984	−	0.808144i
$13$	3.90281	−	3.27484i	1.08244	−	0.908279i	0.0863228	−	0.996267i	$-0.472488\pi$
$13$	3.90281	−	3.27484i	1.08244	−	0.908279i	0.996121	+	0.0879887i	$0.0280439\pi$
$14$	−2.58170	−	2.70829i	−0.689989	−	0.723820i
$15$	−1.69956	−	6.28867i	−0.438826	−	1.62373i
$16$	0.527874	+	3.96502i	0.131968	+	0.991254i
$17$		−	5.14410i		−	1.24763i	−0.781573	−	0.623814i	$-0.785582\pi$
$17$		−	5.14410i		−	1.24763i	0.781573	−	0.623814i	$-0.214418\pi$
$18$	4.17351	+	0.762779i	0.983705	+	0.179789i
$19$			5.48072i			1.25736i	0.777662	+	0.628682i	$0.216405\pi$
$19$			5.48072i			1.25736i	−0.777662	+	0.628682i	$0.783595\pi$
$20$	6.43353	+	3.89756i	1.43858	+	0.871521i
$21$	1.61558	−	4.28835i	0.352548	−	0.935794i
$22$	2.14826	−	3.63191i	0.458011	−	0.774325i
$23$	2.08467	−	1.74925i	0.434685	−	0.364744i	−0.399031	−	0.916937i	$-0.630654\pi$
$23$	2.08467	−	1.74925i	0.434685	−	0.364744i	0.833716	+	0.552194i	$0.186209\pi$
$24$	−4.09409	+	2.69043i	−0.835703	+	0.549181i
$25$	8.59377	−	3.12788i	1.71875	−	0.625575i
$26$	−6.79616	+	2.39275i	−1.33284	+	0.469257i
$27$	1.37725	+	5.01031i	0.265052	+	0.964234i
$28$	2.06969	+	4.86995i	0.391134	+	0.920334i
$29$	−2.48873	+	2.96595i	−0.462146	+	0.550764i	−0.945908	−	0.324436i	$-0.894826\pi$
$29$	−2.48873	+	2.96595i	−0.462146	+	0.550764i	0.483762	+	0.875200i	$0.339270\pi$
$30$	−0.879916	+	9.17047i	−0.160650	+	1.67429i
$31$	−1.76191	+	4.84079i	−0.316447	+	0.869432i	0.674869	+	0.737937i	$0.264200\pi$
$31$	−1.76191	+	4.84079i	−0.316447	+	0.869432i	−0.991317	+	0.131495i	$0.958022\pi$
$32$	1.27452	−	5.51141i	0.225305	−	0.974288i
$33$	5.14933	+	0.439339i	0.896384	+	0.0764792i
$34$	−2.56009	+	6.80951i	−0.439052	+	1.16782i
$35$	9.57635	+	2.70381i	1.61870	+	0.457027i
$36$	−5.14507	−	3.08678i	−0.857512	−	0.514464i
$37$	−0.868980	+	1.50512i	−0.142859	+	0.247440i	−0.928572	−	0.371152i	$-0.878963\pi$
$37$	−0.868980	+	1.50512i	−0.142859	+	0.247440i	0.785713	+	0.618591i	$0.212296\pi$
$38$	2.72762	−	7.25512i	0.442479	−	1.17694i
$39$	−6.25319	−	6.22633i	−1.00131	−	0.997010i
$40$	−6.57667	−	8.36121i	−1.03986	−	1.32202i
$41$	3.26572	+	3.89193i	0.510020	+	0.607818i	0.958191	−	0.286130i	$-0.0923689\pi$
$41$	3.26572	+	3.89193i	0.510020	+	0.607818i	−0.448171	+	0.893948i	$0.647924\pi$
$42$	−4.27283	+	4.87267i	−0.659312	+	0.751869i
$43$	−0.808573	−	2.22154i	−0.123306	−	0.338781i	0.862646	−	0.505808i	$-0.168806\pi$
$43$	−0.808573	−	2.22154i	−0.123306	−	0.338781i	−0.985952	+	0.167027i	$0.946583\pi$
$44$	−4.65128	+	3.73861i	−0.701206	+	0.563617i
$45$	−10.5859	+	3.90466i	−1.57805	+	0.582072i
$46$	−3.63015	+	1.27808i	−0.535236	+	0.188443i
$47$	5.29209	−	1.92616i	0.771930	−	0.280960i	0.0741267	−	0.997249i	$-0.476383\pi$
$47$	5.29209	−	1.92616i	0.771930	−	0.280960i	0.697804	+	0.716289i	$0.254161\pi$
$48$	6.75852	−	1.52393i	0.975509	−	0.219960i
$49$	4.35442	+	5.48078i	0.622061	+	0.782969i
$50$	−12.9327	−	0.136375i	−1.82896	−	0.0192863i
$51$	−8.87424	+	0.795651i	−1.24264	+	0.111413i
$52$	10.1872	+	0.214873i	1.41272	+	0.0297975i
$53$	−11.2037	−	6.46848i	−1.53895	−	0.888515i	−0.998900	−	0.0468832i	$-0.985071\pi$
$53$	−11.2037	−	6.46848i	−1.53895	−	0.888515i	−0.540052	−	0.841632i	$-0.681596\pi$
$54$	0.670366	−	7.31783i	0.0912252	−	0.995830i
$55$			11.2220i			1.51318i
$56$	−0.316097	−	7.47664i	−0.0422402	−	0.999107i
$57$	9.45496	−	0.847718i	1.25234	−	0.112283i
$58$	4.77055	−	2.68761i	0.626403	−	0.352900i
$59$	6.39905	−	5.36944i	0.833086	−	0.699042i	−0.122911	−	0.992418i	$-0.539223\pi$
$59$	6.39905	−	5.36944i	0.833086	−	0.699042i	0.955997	+	0.293376i	$0.0947786\pi$
$60$	5.72871	−	11.7015i	0.739573	−	1.51066i
$61$	4.55711	−	1.65865i	0.583479	−	0.212369i	−0.0333801	−	0.999443i	$-0.510627\pi$
$61$	4.55711	−	1.65865i	0.583479	−	0.212369i	0.616859	+	0.787074i	$0.288405\pi$
$62$	4.74147	−	5.53115i	0.602167	−	0.702457i
$63$	−7.64784	−	2.12380i	−0.963538	−	0.267573i
$64$	−4.43004	+	6.66144i	−0.553754	+	0.832680i
$65$	12.3168	−	14.6786i	1.52771	−	1.82065i
$66$	−6.59779	−	3.14427i	−0.812132	−	0.387033i
$67$	−2.40925	+	0.424815i	−0.294336	+	0.0518994i	−0.318866	−	0.947800i	$-0.603302\pi$
$67$	−2.40925	+	0.424815i	−0.294336	+	0.0518994i	0.0245301	+	0.999699i	$0.492191\pi$
$68$	6.77785	−	7.74001i	0.821935	−	0.938614i
$69$	−3.34013	−	3.32577i	−0.402104	−	0.400376i
$70$	−11.3311	−	8.34509i	−1.35433	−	0.997429i
$71$	−6.64299	−	11.5060i	−0.788378	−	1.36551i	−0.926960	−	0.375160i	$-0.877588\pi$
$71$	−6.64299	−	11.5060i	−0.788378	−	1.36551i	0.138582	−	0.990351i	$-0.455745\pi$
$72$	5.27459	+	6.64671i	0.621616	+	0.783322i
$73$	0.209032	+	0.362053i	0.0244653	+	0.0423751i	0.877999	−	0.478663i	$-0.158878\pi$
$73$	0.209032	+	0.362053i	0.0244653	+	0.0423751i	−0.853534	+	0.521038i	$0.825545\pi$
$74$	1.89937	−	1.55993i	0.220798	−	0.181338i
$75$	−6.72522	−	14.3416i	−0.776561	−	1.65602i
$76$	−7.22139	+	8.24651i	−0.828350	+	0.945939i
$77$	−4.61411	+	6.40548i	−0.525827	+	0.729973i
$78$	5.17899	+	11.3542i	0.586405	+	1.28561i
$79$	−12.4166	−	2.18938i	−1.39697	−	0.246324i	−0.576075	−	0.817397i	$-0.695416\pi$
$79$	−12.4166	−	2.18938i	−1.39697	−	0.246324i	−0.820900	+	0.571073i	$0.806527\pi$
$80$	4.54472	+	14.3412i	0.508115	+	1.60340i
$81$	8.43041	−	3.15090i	0.936712	−	0.350100i
$82$	−2.38608	−	6.77722i	−0.263499	−	0.748419i
$83$	−10.0481	−	8.43136i	−1.10292	−	0.925462i	−0.105305	−	0.994440i	$-0.533582\pi$
$83$	−10.0481	−	8.43136i	−1.10292	−	0.925462i	−0.997618	+	0.0689777i	$0.978026\pi$
$84$	8.08118	−	4.32373i	0.881729	−	0.471757i
$85$	−3.35958	−	19.0532i	−0.364398	−	2.06660i
$86$	−0.0352537	+	3.34317i	−0.00380150	+	0.360503i
$87$	5.50160	+	3.83463i	0.589833	+	0.411116i
$88$	8.01775	−	2.63417i	0.854695	−	0.280803i
$89$			2.12681i			0.225442i	0.993627	+	0.112721i	$0.0359566\pi$
$89$			2.12681i			0.225442i	−0.993627	+	0.112721i	$0.964043\pi$
$90$	15.9564	+	0.0995487i	1.68195	+	0.0104934i
$91$	13.0657	−	3.31422i	1.36965	−	0.347425i
$92$	5.44149	+	0.114774i	0.567314	+	0.0119660i
$93$	8.62352	+	2.29078i	0.894218	+	0.237543i
$94$	−7.96401	−	0.0839804i	−0.821425	−	0.00866192i
$95$	3.57943	+	20.3000i	0.367242	+	2.08273i
$96$	−9.70503	−	1.34624i	−0.990516	−	0.137400i
$97$	−12.7654	+	4.64622i	−1.29613	+	0.471752i	−0.895734	−	0.444590i	$-0.853349\pi$
$97$	−12.7654	+	4.64622i	−1.29613	+	0.471752i	−0.400395	+	0.916343i	$0.631127\pi$
$98$	−3.03653	−	9.42229i	−0.306736	−	0.951795i
$99$	−0.0385431	−	8.95123i	−0.00387372	−	0.899632i
$100$	17.0518	+	6.61681i	1.70518	+	0.661681i
$101$	6.29192	−	7.49842i	0.626070	−	0.746121i	−0.356032	−	0.934474i	$-0.615871\pi$
$101$	6.29192	−	7.49842i	0.626070	−	0.746121i	0.982101	+	0.188353i	$0.0603150\pi$
$102$	12.1433	+	3.36325i	1.20236	+	0.333011i
$103$	−11.3503	+	2.00136i	−1.11838	+	0.197200i	−0.702128	−	0.712051i	$-0.747766\pi$
$103$	−11.3503	+	2.00136i	−1.11838	+	0.197200i	−0.416248	+	0.909251i	$0.636655\pi$
$104$	−13.3784	−	5.35438i	−1.31186	−	0.525040i
$105$	3.18322	−	16.9387i	0.310651	−	1.65304i
$106$	11.6118	+	14.1385i	1.12784	+	1.37325i
$107$	0.463569	+	0.802925i	0.0448149	+	0.0776217i	0.887563	−	0.460687i	$-0.152397\pi$
$107$	0.463569	+	0.802925i	0.0448149	+	0.0776217i	−0.842748	+	0.538309i	$0.819064\pi$
$108$	−4.52930	+	9.35336i	−0.435832	+	0.900028i
$109$	−1.00466	+	1.74013i	−0.0962292	+	0.166674i	−0.910121	−	0.414343i	$-0.864012\pi$
$109$	−1.00466	+	1.74013i	−0.0962292	+	0.166674i	0.813892	+	0.581017i	$0.197345\pi$
$110$	5.58493	−	14.8552i	0.532502	−	1.41639i
$111$	2.73093	+	1.26630i	0.259209	+	0.120192i
$112$	−3.30250	+	10.0545i	−0.312057	+	0.950063i
$113$	−6.72765	+	18.4841i	−0.632884	+	1.73883i	0.0401203	+	0.999195i	$0.487226\pi$
$113$	−6.72765	+	18.4841i	−0.632884	+	1.73883i	−0.673004	+	0.739639i	$0.734996\pi$
$114$	−12.9379	−	3.58333i	−1.21175	−	0.335610i
$115$	6.57897	−	7.84051i	0.613492	−	0.731131i
$116$	−7.65257	+	1.18354i	−0.710524	+	0.109889i
$117$	−9.77403	+	11.7506i	−0.903609	+	1.08635i
$118$	−11.1430	+	3.92316i	−1.02580	+	0.361156i
$119$	5.91636	−	12.2568i	0.542351	−	1.12358i
$120$	−13.4069	+	12.6389i	−1.22388	+	1.15377i
$121$	1.97064	+	0.717254i	0.179149	+	0.0652049i
$122$	−6.85796	−	0.0723171i	−0.620891	−	0.00654728i
$123$	6.20898	−	6.23577i	0.559845	−	0.562260i
$124$	−9.02925	+	4.96216i	−0.810850	+	0.445615i
$125$	13.5018	−	7.79529i	1.20764	−	0.697232i
$126$	9.06689	+	6.61752i	0.807742	+	0.589536i
$127$	−7.53215	−	4.34869i	−0.668371	−	0.385884i	0.127088	−	0.991891i	$-0.459437\pi$
$127$	−7.53215	−	4.34869i	−0.668371	−	0.385884i	−0.795459	+	0.606007i	$0.792770\pi$
$128$	9.17950	−	6.61338i	0.811361	−	0.584545i
$129$	−3.70738	+	1.73850i	−0.326416	+	0.153067i
$130$	−23.6095	+	13.3010i	−2.07069	+	1.16658i
$131$	−6.10623	+	5.12374i	−0.533504	+	0.447663i	−0.869309	−	0.494268i	$-0.835436\pi$
$131$	−6.10623	+	5.12374i	−0.533504	+	0.447663i	0.335805	+	0.941931i	$0.390992\pi$
$132$	7.16901	+	7.44580i	0.623983	+	0.648074i
$133$	−6.30352	+	13.0589i	−0.546584	+	1.13235i
$134$	3.40067	+	0.636673i	0.293773	+	0.0550002i
$135$	8.37339	+	17.6581i	0.720667	+	1.51977i
$136$	−12.8242	+	6.87268i	−1.09967	+	0.589328i
$137$	−1.57029	−	4.31433i	−0.134159	−	0.368598i	0.854363	−	0.519677i	$-0.173948\pi$
$137$	−1.57029	−	4.31433i	−0.134159	−	0.368598i	−0.988522	+	0.151079i	$0.951725\pi$
$138$	2.76634	+	6.06480i	0.235487	+	0.516270i
$139$	−1.19992	+	0.211578i	−0.101776	+	0.0179458i	−0.224304	−	0.974519i	$-0.572011\pi$
$139$	−1.19992	+	0.211578i	−0.101776	+	0.0179458i	0.122528	+	0.992465i	$0.460900\pi$
$140$	10.8464	+	16.6860i	0.916690	+	1.41023i
$141$	−4.14142	−	8.83162i	−0.348771	−	0.743756i
$142$	3.06742	+	18.5371i	0.257412	+	1.55560i
$143$	7.60079	+	13.1650i	0.635610	+	1.10091i
$144$	−3.67434	−	11.4236i	−0.306195	−	0.951969i
$145$	−7.28093	+	12.6109i	−0.604648	+	1.04728i
$146$	−0.0965209	−	0.583299i	−0.00798813	−	0.0482741i
$147$	8.78156	−	8.35968i	0.724291	−	0.689495i
$148$	−3.29064	+	1.11969i	−0.270489	+	0.0920381i
$149$	−2.58533	+	7.10313i	−0.211798	+	0.581911i	−0.999413	−	0.0342569i	$-0.989094\pi$
$149$	−2.58533	+	7.10313i	−0.211798	+	0.581911i	0.787615	+	0.616168i	$0.211316\pi$
$150$	1.76507	+	22.3317i	0.144117	+	1.82337i
$151$	15.6059	+	2.75173i	1.26999	+	0.223933i	0.767723	−	0.640782i	$-0.221390\pi$
$151$	15.6059	+	2.75173i	1.26999	+	0.223933i	0.502263	+	0.864715i	$0.332501\pi$
$152$	13.6634	−	7.32242i	1.10825	−	0.593927i
$153$	2.74520	+	15.1862i	0.221937	+	1.22773i
$154$	9.29579	−	6.18294i	0.749076	−	0.498236i
$155$	−3.36440	+	19.0804i	−0.270235	+	1.53258i
$156$	−1.20500	−	17.6076i	−0.0964776	−	1.40973i
$157$	10.0995	−	8.47449i	0.806028	−	0.676338i	−0.143628	−	0.989632i	$-0.545877\pi$
$157$	10.0995	−	8.47449i	0.806028	−	0.676338i	0.949656	+	0.313294i	$0.101432\pi$
$158$	15.3469	+	9.07762i	1.22093	+	0.722177i
$159$	−9.42607	+	20.3284i	−0.747536	+	1.61215i
$160$	1.12119	−	21.2460i	0.0886380	−	1.67964i
$161$	6.97899	−	1.77028i	0.550021	−	0.139518i
$162$	−12.7279	−	0.0246013i	−0.999998	−	0.00193286i
$163$	16.2289	−	9.36977i	1.27115	−	0.733897i	0.295944	−	0.955205i	$-0.404366\pi$
$163$	16.2289	−	9.36977i	1.27115	−	0.733897i	0.975204	+	0.221308i	$0.0710326\pi$
$164$	−0.214274	+	10.1589i	−0.0167320	+	0.793273i
$165$	19.3595	−	1.73574i	1.50713	−	0.135127i
$166$	9.10512	+	16.1617i	0.706694	+	1.25439i
$167$	−6.84881	−	2.49276i	−0.529976	−	0.192896i	0.0631513	−	0.998004i	$-0.479885\pi$
$167$	−6.84881	−	2.49276i	−0.529976	−	0.192896i	−0.593128	+	0.805108i	$0.702107\pi$
$168$	−12.8493	+	1.70174i	−0.991344	+	0.131292i
$169$	2.24988	−	12.7597i	0.173067	−	0.981514i
$170$	−5.03503	+	26.8936i	−0.386169	+	2.06265i
$171$	−2.92485	−	16.1799i	−0.223669	−	1.23731i
$172$	1.71048	−	4.40798i	0.130423	−	0.336105i
$173$	4.42844	−	5.27761i	0.336688	−	0.401249i	−0.570962	−	0.820976i	$-0.693430\pi$
$173$	4.42844	−	5.27761i	0.336688	−	0.401249i	0.907650	+	0.419727i	$0.137874\pi$
$174$	−5.37435	−	7.81412i	−0.407428	−	0.592387i
$175$	24.0737	+	2.43115i	1.81980	+	0.183778i
$176$	−11.9245	−	0.503253i	−0.898841	−	0.0379341i
$177$	−10.2528	−	10.2087i	−0.770644	−	0.767333i
$178$	1.05846	−	2.81537i	0.0793351	−	0.211021i
$179$	−18.1522			−1.35676			−0.678378	−	0.734713i	$-0.737317\pi$
$179$	−18.1522			−1.35676			−0.678378	+	0.734713i	$0.737317\pi$
$180$	−21.0727	−	8.07287i	−1.57067	−	0.601716i
$181$	−1.11736	+	1.93532i	−0.0830525	+	0.143851i	−0.904560	−	0.426347i	$-0.859800\pi$
$181$	−1.11736	+	1.93532i	−0.0830525	+	0.143851i	0.821507	+	0.570198i	$0.193134\pi$
$182$	−18.9451	−	2.11525i	−1.40430	−	0.156793i
$183$	−3.56626	−	7.60507i	−0.263625	−	0.562183i
$184$	−7.14606	−	2.86003i	−0.526814	−	0.210844i
$185$	−2.23562	+	6.14231i	−0.164366	+	0.451592i
$186$	−10.2753	−	7.32414i	−0.753425	−	0.537032i
$187$	15.1156	+	2.66529i	1.10536	+	0.194906i
$188$	10.5006	+	4.07466i	0.765834	+	0.297175i
$189$	−2.48091	+	13.5220i	−0.180460	+	0.983582i
$190$	5.36451	−	28.6535i	0.389183	−	2.07875i
$191$	−2.85755	+	16.2060i	−0.206765	+	1.17262i	0.687872	+	0.725832i	$0.258545\pi$
$191$	−2.85755	+	16.2060i	−0.206765	+	1.17262i	−0.894638	+	0.446793i	$0.852566\pi$
$192$	12.1771	+	6.61205i	0.878804	+	0.477183i
$193$	8.64629	+	3.14699i	0.622374	+	0.226525i	0.633909	−	0.773408i	$-0.281450\pi$
$193$	8.64629	+	3.14699i	0.622374	+	0.226525i	−0.0115350	+	0.999933i	$0.503672\pi$
$194$	19.2105	+	0.202575i	1.37923	+	0.0145440i
$195$	−27.2275	−	18.9777i	−1.94980	−	1.35902i
$196$	−0.669631	+	13.9840i	−0.0478308	+	0.998855i
$197$	7.50535	+	4.33322i	0.534734	+	0.308729i	0.742942	−	0.669356i	$-0.233430\pi$
$197$	7.50535	+	4.33322i	0.534734	+	0.308729i	−0.208208	+	0.978085i	$0.566763\pi$
$198$	−4.40379	+	11.8684i	−0.312963	+	0.843450i
$199$		−	8.05611i		−	0.571082i	−0.958366	−	0.285541i	$-0.907827\pi$
$199$		−	8.05611i		−	0.571082i	0.958366	−	0.285541i	$-0.0921733\pi$
$200$	−19.2793	−	17.2453i	−1.36325	−	1.21943i
$201$	1.10551	+	4.09056i	0.0779764	+	0.288526i
$202$	−12.0607	+	6.79471i	−0.848589	+	0.478074i
$203$	−9.34109	+	4.20460i	−0.655616	+	0.295105i
$204$	−14.4009	−	10.4955i	−1.00826	−	0.734833i
$205$	14.6377	+	12.2824i	1.02234	+	0.857843i
$206$	16.0210	+	2.99945i	1.11623	+	0.208981i
$207$	−5.22077	+	6.27656i	−0.362869	+	0.436251i
$208$	15.0450	+	13.7460i	1.04318	+	0.953113i
$209$	−16.1048	−	2.83971i	−1.11399	−	0.196427i
$210$	−12.6438	+	20.8384i	−0.872502	+	1.43798i
$211$	−0.0787090	+	0.216251i	−0.00541855	+	0.0148873i	−0.942372	−	0.334566i	$-0.891410\pi$
$211$	−0.0787090	+	0.216251i	−0.00541855	+	0.0148873i	0.936954	+	0.349453i	$0.113633\pi$
$212$	−8.33473	−	24.4948i	−0.572431	−	1.68231i
$213$	−18.8219	+	13.2397i	−1.28965	+	0.907169i
$214$	−0.214054	−	1.29358i	−0.0146325	−	0.0884274i
$215$	−4.44574	−	7.70024i	−0.303197	−	0.525152i
$216$	10.6506	−	10.1274i	0.724682	−	0.689083i
$217$	−9.76559	+	9.50770i	−0.662932	+	0.645425i
$218$	2.19594	−	1.80350i	0.148728	−	0.122148i
$219$	0.592258	−	0.416607i	0.0400211	−	0.0281517i
$220$	−14.7861	+	16.8851i	−0.996880	+	1.13839i
$221$	−16.8461	−	20.0764i	−1.13319	−	1.35049i
$222$	−2.98487	−	3.03539i	−0.200331	−	0.203722i
$223$	−0.345802	−	0.0609742i	−0.0231566	−	0.00408313i	0.162058	−	0.986781i	$-0.448187\pi$
$223$	−0.345802	−	0.0609742i	−0.0231566	−	0.00408313i	−0.185214	+	0.982698i	$0.559298\pi$
$224$	9.37559	−	11.6661i	0.626433	−	0.779476i
$225$	−23.7009	+	13.8201i	−1.58006	+	0.921342i
$226$	18.1048	−	21.1201i	1.20431	−	1.40489i
$227$	−1.27602	+	7.23668i	−0.0846925	+	0.480315i	0.912730	+	0.408563i	$0.133970\pi$
$227$	−1.27602	+	7.23668i	−0.0846925	+	0.480315i	−0.997423	+	0.0717518i	$0.977141\pi$
$228$	15.3433	+	11.1823i	1.01613	+	0.740568i
$229$	−15.9799	−	5.81620i	−1.05598	−	0.384346i	−0.245064	−	0.969507i	$-0.578809\pi$
$229$	−15.9799	−	5.81620i	−1.05598	−	0.384346i	−0.810917	+	0.585161i	$0.801031\pi$
$230$	−12.6109	+	7.10470i	−0.831541	+	0.468470i
$231$	11.7640	+	6.96919i	0.774013	+	0.458539i
$232$	10.7191	+	2.24178i	0.703745	+	0.147180i
$233$	−14.7622	−	8.52297i	−0.967105	−	0.558358i	−0.0687526	−	0.997634i	$-0.521902\pi$
$233$	−14.7622	−	8.52297i	−0.967105	−	0.558358i	−0.898352	+	0.439275i	$0.855235\pi$
$234$	18.7864	−	10.6906i	1.22810	−	0.698867i
$235$	18.3433	−	10.5905i	1.19659	−	0.690849i
$236$	16.7030	+	0.352306i	1.08727	+	0.0229331i
$237$	−1.85646	+	21.7589i	−0.120590	+	1.41339i
$238$	−13.9317	+	13.2805i	−0.903057	+	0.860849i
$239$	−0.183703	−	1.04183i	−0.0118827	−	0.0673904i	0.978290	−	0.207242i	$-0.0664487\pi$
$239$	−0.183703	−	1.04183i	−0.0118827	−	0.0673904i	−0.990173	+	0.139851i	$0.955338\pi$
$240$	24.0375	−	10.0584i	1.55162	−	0.649268i
$241$	13.0848	−	4.76247i	0.842864	−	0.306778i	0.115737	−	0.993280i	$-0.463077\pi$
$241$	13.0848	−	4.76247i	0.842864	−	0.306778i	0.727128	+	0.686502i	$0.240855\pi$
$242$	−2.25168	−	1.93021i	−0.144743	−	0.124078i
$243$	−6.73966	−	14.0562i	−0.432350	−	0.901706i
$244$	9.04225	+	3.50877i	0.578871	+	0.224626i
$245$	19.7078	+	17.4563i	1.25908	+	1.11524i
$246$	−11.3225	+	5.16456i	−0.721898	+	0.329280i
$247$	17.9485	+	21.3902i	1.14204	+	1.36103i
$248$	14.4220	−	2.07504i	0.915800	−	0.131765i
$249$	−12.9910	+	18.6384i	−0.823274	+	1.18116i
$250$	−21.7526	+	3.59950i	−1.37576	+	0.227652i
$251$	−13.6845	+	23.7023i	−0.863759	+	1.49607i	0.00451560	+	0.999990i	$0.498563\pi$
$251$	−13.6845	+	23.7023i	−0.863759	+	1.49607i	−0.868274	+	0.496084i	$0.834771\pi$
$252$	−8.70893	−	13.2723i	−0.548611	−	0.836078i
$253$	4.05994	+	7.03202i	0.255246	+	0.442099i
$254$	7.80647	+	9.50516i	0.489821	+	0.596407i
$255$	−32.3495	+	8.74272i	−2.02581	+	0.547491i
$256$	−15.4427	+	4.18606i	−0.965169	+	0.261628i
$257$	−8.29386	+	22.7872i	−0.517357	+	1.42143i	0.356065	+	0.934461i	$0.384118\pi$
$257$	−8.29386	+	22.7872i	−0.517357	+	1.42143i	−0.873421	+	0.486965i	$0.838104\pi$
$258$	5.77286	−	0.456280i	0.359402	−	0.0284067i
$259$	−3.80158	+	2.58679i	−0.236219	+	0.160736i
$260$	37.8727	−	5.85737i	2.34877	−	0.363259i
$261$	5.76430	−	10.0841i	0.356801	−	0.624189i
$262$	10.6331	−	3.74364i	0.656915	−	0.231283i
$263$	17.0539	+	14.3099i	1.05159	+	0.882386i	0.993260	−	0.115911i	$-0.0369789\pi$
$263$	17.0539	+	14.3099i	1.05159	+	0.882386i	0.0583273	+	0.998298i	$0.481423\pi$
$264$	−5.78441	−	13.4242i	−0.356006	−	0.826204i
$265$	−45.7219	−	16.6414i	−2.80868	−	1.02227i
$266$	14.8434	−	14.1496i	0.910105	−	0.867567i
$267$	3.66903	−	0.328960i	0.224541	−	0.0201320i
$268$	−4.18478	−	2.53522i	−0.255626	−	0.154863i
$269$	9.66070	+	5.57761i	0.589023	+	0.340073i	0.764711	−	0.644373i	$-0.222882\pi$
$269$	9.66070	+	5.57761i	0.589023	+	0.340073i	−0.175688	+	0.984446i	$0.556215\pi$
$270$	−2.29628	−	27.5422i	−0.139747	−	1.67617i
$271$	5.50779	−	3.17992i	0.334574	−	0.193167i	−0.323296	−	0.946298i	$-0.604791\pi$
$271$	5.50779	−	3.17992i	0.334574	−	0.193167i	0.657870	+	0.753131i	$0.271458\pi$
$272$	20.3964	−	2.71543i	1.23672	−	0.164647i
$273$	−7.73837	−	22.0274i	−0.468347	−	1.33316i
$274$	−0.0684643	+	6.49260i	−0.00413608	+	0.392232i
$275$	4.73842	+	26.8729i	0.285738	+	1.62050i
$276$	−0.643650	−	9.40503i	−0.0387432	−	0.566116i
$277$	−6.07632	−	5.09864i	−0.365091	−	0.306348i	0.441725	−	0.897150i	$-0.354367\pi$
$277$	−6.07632	−	5.09864i	−0.365091	−	0.306348i	−0.806816	+	0.590803i	$0.798811\pi$
$278$	1.69369	+	0.317093i	0.101581	+	0.0190180i
$279$	2.61807	−	15.2310i	0.156740	−	0.911858i
$280$	−6.05374	−	27.4862i	−0.361780	−	1.64261i
$281$	−1.96522	−	5.39939i	−0.117235	−	0.322100i	0.867171	−	0.498010i	$-0.165936\pi$
$281$	−1.96522	−	5.39939i	−0.117235	−	0.322100i	−0.984406	+	0.175909i	$0.943713\pi$
$282$	1.08694	+	13.7520i	0.0647262	+	0.818917i
$283$	19.3972	−	3.42024i	1.15304	−	0.203312i	0.435739	−	0.900073i	$-0.356487\pi$
$283$	19.3972	−	3.42024i	1.15304	−	0.203312i	0.717304	+	0.696761i	$0.245376\pi$
$284$	5.16497	−	26.0652i	0.306485	−	1.54668i
$285$	34.4665	−	9.31484i	2.04162	−	0.551763i
$286$	−3.50969	−	21.2099i	−0.207532	−	1.25417i
$287$	3.30499	+	13.0293i	0.195087	+	0.769093i
$288$	−0.821345	+	16.9507i	−0.0483982	+	0.998828i
$289$	−9.46175			−0.556573
$290$	15.9143	−	13.0702i	0.934519	−	0.767509i
$291$	9.98979	+	21.3033i	0.585612	+	1.24882i
$292$	−0.162524	+	0.820179i	−0.00951097	+	0.0479973i
$293$	−19.9733	+	3.52182i	−1.16685	+	0.205747i	−0.723320	−	0.690512i	$-0.757385\pi$
$293$	−19.9733	+	3.52182i	−1.16685	+	0.205747i	−0.443530	+	0.896260i	$0.646274\pi$
$294$	−15.7850	+	6.69578i	−0.920601	+	0.390506i
$295$	20.1946	−	24.0670i	1.17578	−	1.40123i
$296$	4.91323	+	0.155476i	0.285576	+	0.00903686i
$297$	−15.4361	+	1.45100i	−0.895692	+	0.0841957i
$298$	6.95739	−	8.11613i	0.403031	−	0.470155i
$299$	2.40756	−	13.6540i	0.139233	−	0.789629i
$300$	8.77741	−	30.4400i	0.506764	−	1.75746i
$301$	0.628465	−	6.22319i	0.0362241	−	0.358699i
$302$	−19.2888	−	11.4093i	−1.10995	−	0.656529i
$303$	−13.9089	−	9.69459i	−0.799048	−	0.556939i
$304$	−21.7312	+	2.89313i	−1.24637	+	0.165932i
$305$	15.7958	−	9.11969i	0.904463	−	0.522192i
$306$	3.92381	−	21.4689i	0.224309	−	1.22730i
$307$	−6.94842	+	4.01167i	−0.396567	+	0.228958i	−0.685002	−	0.728542i	$-0.740199\pi$
$307$	−6.94842	+	4.01167i	−0.396567	+	0.228958i	0.288435	+	0.957500i	$0.406865\pi$
$308$	−15.3824	+	3.55840i	−0.876494	+	0.202759i
$309$	5.20818	+	19.2712i	0.296283	+	1.09630i
$310$	13.9495	−	23.5834i	0.792278	−	1.33945i
$311$	−2.73080	−	15.4872i	−0.154850	−	0.878196i	−0.958923	−	0.283666i	$-0.908449\pi$
$311$	−2.73080	−	15.4872i	−0.154850	−	0.878196i	0.804074	−	0.594530i	$-0.202662\pi$
$312$	−7.16772	+	23.9077i	−0.405792	+	1.35351i
$313$	0.0561642	+	0.0471274i	0.00317459	+	0.00266380i	0.644374	−	0.764711i	$-0.277118\pi$
$313$	0.0561642	+	0.0471274i	0.00317459	+	0.00266380i	−0.641199	+	0.767375i	$0.721563\pi$
$314$	−17.5868	+	6.19185i	−0.992480	+	0.349426i
$315$	−29.7138	−	2.87153i	−1.67418	−	0.161792i
$316$	−15.7977	−	19.6543i	−0.888693	−	1.10564i
$317$	10.6673	+	29.3083i	0.599137	+	1.64612i	0.752998	+	0.658023i	$0.228607\pi$
$317$	10.6673	+	29.3083i	0.599137	+	1.64612i	−0.153861	+	0.988093i	$0.549171\pi$
$318$	22.5947	−	22.2187i	1.26705	−	1.24596i
$319$	−7.42580	−	8.84973i	−0.415765	−	0.495490i
$320$	−12.0578	+	27.5664i	−0.674051	+	1.54101i
$321$	1.31345	−	0.923908i	0.0733096	−	0.0515675i
$322$	−10.1195	−	1.12985i	−0.563936	−	0.0629643i
$323$	28.1934			1.56872
$324$	16.8363	+	6.36693i	0.935352	+	0.353718i
$325$	23.2965	−	40.3508i	1.29226	−	2.23826i
$326$	−26.1462	+	4.32652i	−1.44810	+	0.239624i
$327$	3.15734	+	1.46402i	0.174601	+	0.0809607i
$328$	5.33946	−	13.3412i	0.294822	−	0.736643i
$329$	14.8247	+	1.49711i	0.817314	+	0.0825386i
$330$	−26.4910	−	7.33704i	−1.45828	−	0.403891i
$331$	2.21374	+	6.08219i	0.121678	+	0.334307i	0.985545	−	0.169412i	$-0.0541868\pi$
$331$	2.21374	+	6.08219i	0.121678	+	0.334307i	−0.863867	+	0.503719i	$0.831965\pi$
$332$	−4.00963	−	25.9255i	−0.220057	−	1.42285i
$333$	1.76214	−	4.90708i	0.0965646	−	0.268906i
$334$	7.82553	+	6.70828i	0.428194	+	0.367061i
$335$	−8.64613	+	3.14693i	−0.472389	+	0.171935i
$336$	17.8562	+	4.14209i	0.974134	+	0.225970i
$337$	−4.55810	+	3.82470i	−0.248296	+	0.208345i	−0.758438	−	0.651745i	$-0.774037\pi$
$337$	−4.55810	+	3.82470i	−0.248296	+	0.208345i	0.510142	+	0.860090i	$0.329593\pi$
$338$	−9.32846	+	15.7709i	−0.507401	+	0.857826i
$339$	32.9280	+	8.74709i	1.78840	+	0.475077i
$340$	20.0494	−	33.0947i	1.08733	−	1.79481i
$341$	−13.3115	−	7.68540i	−0.720858	−	0.416188i
$342$	−4.18058	+	22.8738i	−0.226060	+	1.23688i
$343$	4.07166	+	18.0671i	0.219849	+	0.975534i
$344$	−4.45800	+	4.98381i	−0.240359	+	0.268709i
$345$	−14.5435	−	10.1369i	−0.782995	−	0.545751i
$346$	−8.48870	+	4.78232i	−0.456355	+	0.257099i
$347$	14.4168	+	5.24729i	0.773935	+	0.281689i	0.698641	−	0.715472i	$-0.253788\pi$
$347$	14.4168	+	5.24729i	0.773935	+	0.281689i	0.0752939	+	0.997161i	$0.476011\pi$
$348$	3.22541	+	13.0186i	0.172900	+	0.697872i
$349$	16.4235	+	13.7809i	0.879128	+	0.737676i	0.966000	−	0.258543i	$-0.0832425\pi$
$349$	16.4235	+	13.7809i	0.879128	+	0.737676i	−0.0868715	+	0.996220i	$0.527687\pi$
$350$	−30.6577	−	15.1992i	−1.63873	−	0.812429i
$351$	21.7831	+	15.0440i	1.16270	+	0.802988i
$352$	15.5346	+	6.60070i	0.827996	+	0.351818i
$353$	−0.709540	−	1.94945i	−0.0377650	−	0.103759i	0.919377	−	0.393378i	$-0.128694\pi$
$353$	−0.709540	−	1.94945i	−0.0377650	−	0.103759i	−0.957142	+	0.289619i	$0.906471\pi$
$354$	8.49148	+	18.6163i	0.451317	+	0.989447i
$355$	−32.1194	−	38.2784i	−1.70472	−	2.03161i
$356$	−2.80228	+	3.20009i	−0.148521	+	0.169604i
$357$	−22.0597	−	8.31070i	−1.16752	−	0.439849i
$358$	24.0290	+	9.03389i	1.26997	+	0.477456i
$359$	8.85908			0.467564			0.233782	−	0.972289i	$-0.424890\pi$
$359$	8.85908			0.467564			0.233782	+	0.972289i	$0.424890\pi$
$360$	23.8774	+	21.1738i	1.25845	+	1.11596i
$361$	−11.0383			−0.580965
$362$	2.44226	−	2.00580i	0.128362	−	0.105423i
$363$	0.932553	−	3.51055i	0.0489463	−	0.184256i
$364$	24.0259	+	12.2286i	1.25930	+	0.640952i
$365$	1.01068	+	1.20449i	0.0529016	+	0.0630457i
$366$	0.935982	+	11.8421i	0.0489246	+	0.618995i
$367$	−30.1975	−	5.32464i	−1.57630	−	0.277944i	−0.684031	−	0.729453i	$-0.739775\pi$
$367$	−30.1975	−	5.32464i	−1.57630	−	0.277944i	−0.892266	+	0.451509i	$0.850886\pi$
$368$	8.03624	+	7.34238i	0.418918	+	0.382748i
$369$	−11.7179	−	9.74679i	−0.610008	−	0.507398i
$370$	6.01628	−	7.01828i	0.312772	−	0.364863i
$371$	−19.2555	−	28.2981i	−0.999695	−	1.46916i
$372$	9.95696	+	14.8091i	0.516244	+	0.767817i
$373$	−5.29384	−	30.0228i	−0.274105	−	1.55452i	−0.741792	−	0.670630i	$-0.766024\pi$
$373$	−5.29384	−	30.0228i	−0.274105	−	1.55452i	0.467687	−	0.883894i	$-0.345087\pi$
$374$	−18.6829	−	11.0509i	−0.966069	−	0.571427i
$375$	−15.5363	−	22.0867i	−0.802289	−	1.14055i
$376$	−11.8723	−	10.6197i	−0.612268	−	0.547670i
$377$			19.7258i			1.01593i
$378$	10.0137	−	16.6651i	0.515049	−	0.857161i
$379$			13.3196i			0.684184i	0.939666	+	0.342092i	$0.111135\pi$
$379$			13.3196i			0.684184i	−0.939666	+	0.342092i	$0.888865\pi$
$380$	−21.3614	+	35.2604i	−1.09582	+	1.80882i
$381$	−6.33704	+	13.6666i	−0.324657	+	0.700160i
$382$	11.8480	−	20.0306i	0.606197	−	1.02485i
$383$	0.976734	+	5.53933i	0.0499088	+	0.283047i	0.999540	−	0.0303225i	$-0.00965342\pi$
$383$	0.976734	+	5.53933i	0.0499088	+	0.283047i	−0.949631	+	0.313369i	$0.898542\pi$
$384$	−12.8288	−	14.8129i	−0.654665	−	0.755919i
$385$	−12.9067	+	26.7386i	−0.657789	+	1.36273i
$386$	−9.87936	−	8.46888i	−0.502846	−	0.431055i
$387$	3.57258	+	6.12681i	0.181604	+	0.311443i
$388$	−25.3291	−	9.82876i	−1.28589	−	0.498980i
$389$	−2.10556	−	0.371266i	−0.106756	−	0.0188240i	0.120015	−	0.992772i	$-0.461706\pi$
$389$	−2.10556	−	0.371266i	−0.106756	−	0.0188240i	−0.226771	+	0.973948i	$0.572817\pi$
$390$	26.5977	+	38.6722i	1.34683	+	1.95824i
$391$	−8.99831	−	10.7238i	−0.455064	−	0.542324i
$392$	7.84591	−	18.1781i	0.396278	−	0.918131i
$393$	9.78358	+	9.74155i	0.493516	+	0.491396i
$394$	−7.77869	−	9.47134i	−0.391885	−	0.477159i
$395$	−47.4195			−2.38593
$396$	11.7361	−	13.5191i	0.589762	−	0.679363i
$397$	6.57561			0.330021			0.165010	−	0.986292i	$-0.447234\pi$
$397$	6.57561			0.330021			0.165010	+	0.986292i	$0.447234\pi$
$398$	−4.00933	+	10.6643i	−0.200969	+	0.534552i
$399$	23.5032	+	8.85454i	1.17663	+	0.443282i
$400$	16.9385	+	32.4233i	0.846926	+	1.62117i
$401$	11.0261	+	13.1404i	0.550616	+	0.656199i	0.967533	−	0.252746i	$-0.0813337\pi$
$401$	11.0261	+	13.1404i	0.550616	+	0.656199i	−0.416917	+	0.908945i	$0.636889\pi$
$402$	0.572354	−	5.96507i	0.0285464	−	0.297511i
$403$	8.97647	+	24.6627i	0.447150	+	1.22853i
$404$	19.3470	−	2.99219i	0.962547	−	0.148867i
$405$	29.1674	−	17.1764i	1.44934	−	0.853503i
$406$	14.4578	−	0.917013i	0.717529	−	0.0455106i
$407$	−3.97246	−	3.33329i	−0.196907	−	0.165225i
$408$	13.8398	+	21.0604i	0.685174	+	1.04265i
$409$	22.9438	+	8.35087i	1.13450	+	0.412924i	0.839924	−	0.542704i	$-0.182600\pi$
$409$	22.9438	+	8.35087i	1.13450	+	0.412924i	0.294576	+	0.955628i	$0.404822\pi$
$410$	−13.2639	−	23.5437i	−0.655060	−	1.16274i
$411$	−7.19990	+	3.37626i	−0.355145	+	0.166539i
$412$	−19.7150	−	11.9438i	−0.971291	−	0.588427i
$413$	21.4225	−	5.43401i	1.05413	−	0.267390i
$414$	10.0347	−	5.71036i	0.493178	−	0.280649i
$415$	−42.7235	−	24.6664i	−2.09722	−	1.21083i
$416$	−13.0748	−	25.6838i	−0.641045	−	1.25925i
$417$	0.550594	+	2.03729i	0.0269627	+	0.0997664i
$418$	19.9055	+	11.7740i	0.973609	+	0.575886i
$419$	1.88352	−	1.58046i	0.0920158	−	0.0772104i	−0.595619	−	0.803267i	$-0.703093\pi$
$419$	1.88352	−	1.58046i	0.0920158	−	0.0772104i	0.687635	+	0.726056i	$0.258649\pi$
$420$	27.1079	−	21.2924i	1.32273	−	1.03896i
$421$	−0.0753066	+	0.0274094i	−0.00367022	+	0.00133585i	−0.343855	−	0.939023i	$-0.611733\pi$
$421$	−0.0753066	+	0.0274094i	−0.00367022	+	0.00133585i	0.340184	+	0.940359i	$0.389511\pi$
$422$	0.211814	−	0.247091i	0.0103109	−	0.0120282i
$423$	−14.5951	+	8.51050i	−0.709640	+	0.413795i
$424$	−1.15733	+	36.5730i	−0.0562048	+	1.77614i
$425$	−16.0901	−	44.2072i	−0.780485	−	2.14436i
$426$	31.5045	−	8.15889i	1.52640	−	0.395299i
$427$	12.7659	+	1.28919i	0.617783	+	0.0623884i
$428$	−0.360428	+	1.81891i	−0.0174220	+	0.0879203i
$429$	21.5356	−	15.1486i	1.03975	−	0.731382i
$430$	2.05283	+	12.4057i	0.0989963	+	0.598258i
$431$	9.27197	−	16.0595i	0.446615	−	0.773560i	−0.551548	−	0.834143i	$-0.685963\pi$
$431$	9.27197	−	16.0595i	0.446615	−	0.773560i	0.998163	+	0.0605833i	$0.0192961\pi$
$432$	−19.1389	+	8.10564i	−0.920822	+	0.389983i
$433$	7.29733			0.350687			0.175344	−	0.984507i	$-0.443896\pi$
$433$	7.29733			0.350687			0.175344	+	0.984507i	$0.443896\pi$
$434$	17.6590	−	7.72574i	0.847658	−	0.370848i
$435$	22.8817	+	10.6100i	1.09709	+	0.508710i
$436$	−3.80444	+	1.29452i	−0.182200	+	0.0619963i
$437$	9.58715	+	11.4255i	0.458616	+	0.546557i
$438$	−0.991337	+	0.256732i	−0.0473679	+	0.0122671i
$439$	−7.60588	−	20.8970i	−0.363009	−	0.997358i	−0.977960	−	0.208793i	$-0.933046\pi$
$439$	−7.60588	−	20.8970i	−0.363009	−	0.997358i	0.614951	−	0.788565i	$-0.289176\pi$
$440$	27.9765	−	14.9930i	1.33373	−	0.714763i
$441$	−15.7798	−	13.8563i	−0.751419	−	0.659825i
$442$	12.3085	+	34.9601i	0.585458	+	1.66288i
$443$	−22.7533	−	19.0923i	−1.08104	−	0.907101i	−0.0850345	−	0.996378i	$-0.527100\pi$
$443$	−22.7533	−	19.0923i	−1.08104	−	0.907101i	−0.996007	+	0.0892766i	$0.971544\pi$
$444$	2.44059	+	5.50360i	0.115825	+	0.261189i
$445$	1.38901	+	7.87748i	0.0658455	+	0.373428i
$446$	0.427410	+	0.252812i	0.0202385	+	0.0119710i
$447$	12.6537	+	3.36137i	0.598500	+	0.158987i
$448$	−18.2169	+	10.7771i	−0.860667	+	0.509168i
$449$	−11.8439	+	6.83809i	−0.558949	+	0.322710i	−0.752724	−	0.658337i	$-0.771260\pi$
$449$	−11.8439	+	6.83809i	−0.558949	+	0.322710i	0.193774	+	0.981046i	$0.437927\pi$
$450$	38.2521	−	6.49907i	1.80322	−	0.306369i
$451$	−13.1283	+	7.57961i	−0.618186	+	0.356910i
$452$	−34.4772	+	18.9475i	−1.62167	+	0.891215i
$453$	2.33330	−	27.3478i	0.109628	−	1.28491i
$454$	5.29065	−	8.94452i	0.248303	−	0.419787i
$455$	46.2292	−	20.8086i	2.16726	−	0.975523i
$456$	−14.7455	−	22.4386i	−0.690521	−	1.05078i
$457$	−3.31654	+	18.8090i	−0.155141	+	0.879849i	0.803515	+	0.595284i	$0.202960\pi$
$457$	−3.31654	+	18.8090i	−0.155141	+	0.879849i	−0.958657	+	0.284565i	$0.908151\pi$
$458$	18.2588	+	15.6520i	0.853179	+	0.731370i
$459$	25.7735	−	7.08472i	1.20300	−	0.330686i
$460$	20.2296	−	3.12870i	0.943210	−	0.145876i
$461$	11.7459	−	13.9983i	0.547063	−	0.651964i	−0.419693	−	0.907666i	$-0.637862\pi$
$461$	11.7459	−	13.9983i	0.547063	−	0.651964i	0.966756	+	0.255702i	$0.0823066\pi$
$462$	−12.1042	−	15.0801i	−0.563138	−	0.701591i
$463$	−8.38217	+	1.47800i	−0.389552	+	0.0686886i	−0.364994	−	0.931010i	$-0.618929\pi$
$463$	−8.38217	+	1.47800i	−0.389552	+	0.0686886i	−0.0245582	+	0.999698i	$0.507818\pi$
$464$	−13.0738	−	8.30221i	−0.606936	−	0.385420i
$465$	33.4366	+	2.85280i	1.55059	+	0.132296i
$466$	15.2998	+	18.6291i	0.708752	+	0.862976i
$467$	−3.74605			−0.173347			−0.0866733	−	0.996237i	$-0.527624\pi$
$467$	−3.74605			−0.173347			−0.0866733	+	0.996237i	$0.527624\pi$
$468$	−30.1890	+	4.80220i	−1.39549	+	0.221982i
$469$	−6.22908	−	1.75873i	−0.287632	−	0.0812107i
$470$	−29.5526	+	4.89020i	−1.36316	+	0.225568i
$471$	−16.1817	−	16.1122i	−0.745614	−	0.742411i
$472$	−21.9353	−	8.77905i	−1.00966	−	0.404089i
$473$	6.94680	−	1.22491i	0.319414	−	0.0563213i
$474$	13.2863	−	27.8794i	0.610262	−	1.28054i
$475$	17.1430	+	47.1001i	0.786576	+	2.16110i
$476$	25.0515	−	10.6467i	1.14823	−	0.487989i
$477$	36.5271	+	13.1170i	1.67246	+	0.600584i
$478$	−0.275316	+	1.47055i	−0.0125927	+	0.0672614i
$479$	30.4668	+	25.5646i	1.39206	+	1.16808i	0.964497	+	0.264094i	$0.0850728\pi$
$479$	30.4668	+	25.5646i	1.39206	+	1.16808i	0.427565	+	0.903985i	$0.359372\pi$
$480$	−36.8256	+	1.35197i	−1.68085	+	0.0617088i
$481$	1.53756	+	8.71996i	0.0701069	+	0.397596i
$482$	−19.6912	−	0.207643i	−0.896908	−	0.00945788i
$483$	−4.13343	−	11.7659i	−0.188077	−	0.535365i
$484$	2.02005	+	3.67572i	0.0918203	+	0.167078i
$485$	−44.2471	+	25.5461i	−2.00916	+	1.15999i
$486$	1.92622	+	21.9611i	0.0873750	+	0.996175i
$487$	3.11687	+	1.79952i	0.141239	+	0.0815442i	0.568954	−	0.822369i	$-0.307348\pi$
$487$	3.11687	+	1.79952i	0.141239	+	0.0815442i	−0.427716	+	0.903913i	$0.640681\pi$
$488$	−10.2235	−	9.14484i	−0.462795	−	0.413968i
$489$	−18.6743	−	26.5478i	−0.844479	−	1.20053i
$490$	−17.4006	−	32.9159i	−0.786079	−	1.48699i
$491$	2.21138	+	0.804876i	0.0997981	+	0.0363235i	0.391437	−	0.920205i	$-0.371978\pi$
$491$	2.21138	+	0.804876i	0.0997981	+	0.0363235i	−0.291639	+	0.956529i	$0.594200\pi$
$492$	17.5585	−	1.20165i	0.791598	−	0.0541744i
$493$	15.2572	+	12.8023i	0.687148	+	0.576586i
$494$	−13.1140	−	37.2479i	−0.590027	−	1.67586i
$495$	−5.98876	−	33.1292i	−0.269175	−	1.48905i
$496$	−20.1239	−	4.43065i	−0.903589	−	0.198942i
$497$	−2.59485	−	35.0555i	−0.116395	−	1.57245i
$498$	26.4728	−	18.2073i	1.18627	−	0.815889i
$499$	−8.22163	+	22.5887i	−0.368051	+	1.01121i	0.608051	+	0.793898i	$0.291951\pi$
$499$	−8.22163	+	22.5887i	−0.368051	+	1.01121i	−0.976102	+	0.217313i	$0.930271\pi$
$500$	30.5864	+	6.06089i	1.36787	+	0.271051i
$501$	−3.24102	+	12.2006i	−0.144798	+	0.545085i
$502$	29.9109	−	24.5655i	1.33499	−	1.09641i
$503$	7.26166	+	12.5776i	0.323781	+	0.560806i	0.981265	−	0.192663i	$-0.0617124\pi$
$503$	7.26166	+	12.5776i	0.323781	+	0.560806i	−0.657484	+	0.753469i	$0.728379\pi$
$504$	4.92315	+	21.9035i	0.219295	+	0.975659i
$505$	18.4074	−	31.8825i	0.819117	−	1.41875i
$506$	−1.87469	−	11.3292i	−0.0833401	−	0.503644i
$507$	−22.3601	−	1.90776i	−0.993048	−	0.0847265i
$508$	−5.60334	−	16.4676i	−0.248608	−	0.730630i
$509$	−3.01323	−	3.59103i	−0.133559	−	0.159170i	0.695120	−	0.718894i	$-0.255351\pi$
$509$	−3.01323	−	3.59103i	−0.133559	−	0.159170i	−0.828679	+	0.559725i	$0.810907\pi$
$510$	47.1738	+	4.52637i	2.08889	+	0.200431i
$511$	0.0816509	+	1.10307i	0.00361202	+	0.0487971i
$512$	22.5256	+	2.14415i	0.995500	+	0.0947590i
$513$	−27.4601	+	7.54834i	−1.21239	+	0.333267i
$514$	22.3196	−	26.0369i	0.984477	−	1.14844i
$515$	−40.7330	+	14.8256i	−1.79491	+	0.653295i
$516$	−7.86891	−	2.26901i	−0.346409	−	0.0998875i
$517$	2.91794	+	16.5485i	0.128331	+	0.727801i
$518$	6.31974	−	1.53232i	0.277673	−	0.0673262i
$519$	−9.78953	−	6.82334i	−0.429713	−	0.299511i
$520$	−53.0492	−	11.0946i	−2.32636	−	0.486531i
$521$	−23.3322	+	13.4708i	−1.02220	+	0.590168i	−0.914741	−	0.404041i	$-0.867605\pi$
$521$	−23.3322	+	13.4708i	−1.02220	+	0.590168i	−0.107460	+	0.994209i	$0.534272\pi$
$522$	−12.6491	+	10.4801i	−0.553636	+	0.458701i
$523$	0.145780	+	0.0841664i	0.00637453	+	0.00368034i	0.503184	−	0.864179i	$-0.332162\pi$
$523$	0.145780	+	0.0841664i	0.00637453	+	0.00368034i	−0.496809	+	0.867860i	$0.665495\pi$
$524$	−15.9387	−	0.336184i	−0.696285	−	0.0146863i
$525$	0.470502	−	41.9064i	0.0205344	−	1.82895i
$526$	−15.4534	−	27.4300i	−0.673801	−	1.19601i
$527$	24.9015	+	9.06341i	1.08473	+	0.394808i
$528$	0.976211	+	20.6491i	0.0424841	+	0.898637i
$529$	−2.70792	+	15.3574i	−0.117735	+	0.667711i
$530$	52.2425	+	44.7838i	2.26927	+	1.94528i
$531$	−16.0255	+	19.2663i	−0.695448	+	0.836088i
$532$	−26.6908	+	11.3434i	−1.15719	+	0.491798i
$533$	25.4910	+	4.49474i	1.10414	+	0.194689i
$534$	−5.02060	−	1.39053i	−0.217263	−	0.0601739i
$535$	2.24139	+	2.67119i	0.0969039	+	0.115486i
$536$	4.27789	+	5.43867i	0.184777	+	0.234915i
$537$	2.80764	+	31.3149i	0.121159	+	1.35134i
$538$	−10.0125	−	12.1913i	−0.431671	−	0.525603i
$539$	−18.3611	+	9.95548i	−0.790869	+	0.428813i
$540$	−10.6674	+	37.6019i	−0.459051	+	1.61813i
$541$	−2.33451	−	4.04349i	−0.100369	−	0.173843i	0.811468	−	0.584397i	$-0.198669\pi$
$541$	−2.33451	−	4.04349i	−0.100369	−	0.173843i	−0.911837	+	0.410553i	$0.865336\pi$
$542$	−8.87352	+	1.46834i	−0.381150	+	0.0630706i
$543$	3.51150	+	1.62825i	0.150693	+	0.0698747i
$544$	−28.3512	−	6.55624i	−1.21555	−	0.281096i
$545$	−2.58469	+	7.10137i	−0.110716	+	0.304189i
$546$	−0.718793	+	33.0100i	−0.0307615	+	1.41270i
$547$	20.7427	+	3.65749i	0.886893	+	0.156383i	0.598494	−	0.801127i	$-0.295766\pi$
$547$	20.7427	+	3.65749i	0.886893	+	0.156383i	0.288399	+	0.957510i	$0.406877\pi$
$548$	3.32184	−	8.56051i	0.141902	−	0.365687i
$549$	−12.5681	+	7.32855i	−0.536395	+	0.312775i
$550$	7.10150	−	37.9313i	0.302809	−	1.61740i
$551$	−16.2556	−	13.6400i	−0.692511	−	0.581086i
$552$	−3.82862	+	12.7703i	−0.162957	+	0.543538i
$553$	−27.0668	−	19.4972i	−1.15100	−	0.829107i
$554$	5.50608	+	9.77337i	0.233931	+	0.415231i
$555$	10.9421	+	2.90669i	0.464465	+	0.123382i
$556$	−2.08422	−	1.26266i	−0.0883904	−	0.0535487i
$557$			0.433599i			0.0183722i	0.999958	+	0.00918609i	$0.00292407\pi$
$557$			0.433599i			0.0183722i	−0.999958	+	0.00918609i	$0.997076\pi$
$558$	−11.0458	+	18.8591i	−0.467605	+	0.798371i
$559$	−10.4309	−	6.02228i	−0.441180	−	0.254715i
$560$	−5.66554	+	39.3977i	−0.239413	+	1.66485i
$561$	2.26001	−	26.4887i	0.0954175	−	1.11835i
$562$	−0.0856832	+	8.12549i	−0.00361433	+	0.342753i
$563$	−40.0488	−	14.5766i	−1.68785	−	0.614329i	−0.693502	−	0.720455i	$-0.743933\pi$
$563$	−40.0488	−	14.5766i	−1.68785	−	0.614329i	−0.994353	+	0.106126i	$0.966155\pi$
$564$	5.40517	−	18.7451i	0.227599	−	0.789312i
$565$	−12.8466	+	72.8566i	−0.540460	+	3.06510i
$566$	−27.3792	−	5.12594i	−1.15083	−	0.215459i
$567$	23.7110	+	2.18841i	0.995768	+	0.0919048i
$568$	−19.8091	+	31.9333i	−0.831173	+	1.33989i
$569$	18.0403	+	3.18100i	0.756290	+	0.133354i	0.538482	−	0.842637i	$-0.318998\pi$
$569$	18.0403	+	3.18100i	0.756290	+	0.133354i	0.217808	+	0.975992i	$0.430109\pi$
$570$	−50.2608	−	4.82257i	−2.10519	−	0.201995i
$571$	−2.13014	+	5.85252i	−0.0891437	+	0.244920i	−0.976251	−	0.216643i	$-0.930489\pi$
$571$	−2.13014	+	5.85252i	−0.0891437	+	0.244920i	0.887107	+	0.461564i	$0.152711\pi$
$572$	−5.90967	+	29.8233i	−0.247096	+	1.24697i
$573$	28.3994	+	2.42303i	1.18640	+	0.101224i
$574$	2.10936	−	18.8923i	0.0880428	−	0.788550i
$575$	12.4438	−	21.5533i	0.518941	−	0.898833i
$576$	9.52319	−	22.0297i	0.396800	−	0.917905i
$577$	−35.0390			−1.45869			−0.729347	−	0.684144i	$-0.760176\pi$
$577$	−35.0390			−1.45869			−0.729347	+	0.684144i	$0.760176\pi$
$578$	12.5250	+	4.70888i	0.520972	+	0.195864i
$579$	4.09163	−	15.4027i	0.170042	−	0.640116i
$580$	−27.5713	+	9.38157i	−1.14484	+	0.389548i
$581$	−14.2444	−	31.6459i	−0.590957	−	1.31289i
$582$	−2.62187	−	33.1720i	−0.108680	−	1.37502i
$583$	24.8122	−	29.5700i	1.02762	−	1.22467i
$584$	0.623324	−	1.00483i	0.0257933	−	0.0415801i
$585$	−28.5276	+	49.9063i	−1.17947	+	2.06337i
$586$	28.1924	+	5.27818i	1.16462	+	0.218039i
$587$	−0.0492207	+	0.279144i	−0.00203156	+	0.0115215i	−0.985807	−	0.167884i	$-0.946306\pi$
$587$	−0.0492207	+	0.279144i	−0.00203156	+	0.0115215i	0.983775	+	0.179406i	$0.0574176\pi$
$588$	24.2278	−	1.00774i	0.999136	−	0.0415584i
$589$	−26.5311	−	9.65651i	−1.09319	−	0.397890i
$590$	−38.7102	+	21.8084i	−1.59367	+	0.897837i
$591$	6.31450	−	13.6179i	0.259744	−	0.560168i
$592$	−6.42653	−	2.65101i	−0.264129	−	0.108956i
$593$	−19.5575	+	11.2915i	−0.803131	+	0.463688i	−0.844565	−	0.535453i	$-0.820141\pi$
$593$	−19.5575	+	11.2915i	−0.803131	+	0.463688i	0.0414336	+	0.999141i	$0.486807\pi$
$594$	21.1557	+	5.76139i	0.868028	+	0.236393i
$595$	13.9087	−	49.2617i	0.570199	−	2.01953i
$596$	−13.2491	+	7.28122i	−0.542702	+	0.298250i
$597$	−13.8978	+	1.24606i	−0.568801	+	0.0509978i
$598$	−9.98226	+	16.8763i	−0.408205	+	0.690122i
$599$	−25.1815	+	21.1298i	−1.02889	+	0.863340i	−0.990718	−	0.135931i	$-0.956598\pi$
$599$	−25.1815	+	21.1298i	−1.02889	+	0.863340i	−0.0381707	+	0.999271i	$0.512153\pi$
$600$	−26.7684	+	35.9268i	−1.09281	+	1.46670i
$601$	−0.0617213	+	0.350039i	−0.00251766	+	0.0142784i	−0.986041	−	0.166504i	$-0.946752\pi$
$601$	−0.0617213	+	0.350039i	−0.00251766	+	0.0142784i	0.983523	+	0.180783i	$0.0578631\pi$
$602$	−3.92906	+	7.92519i	−0.160137	+	0.323007i
$603$	6.88576	−	2.53984i	0.280410	−	0.103430i
$604$	19.8555	+	24.7026i	0.807908	+	1.00513i
$605$	7.76746	+	1.36961i	0.315792	+	0.0556827i
$606$	13.5872	+	19.7554i	0.551944	+	0.802507i
$607$	−7.55846	+	20.7667i	−0.306788	+	0.842894i	0.686490	+	0.727140i	$0.259151\pi$
$607$	−7.55846	+	20.7667i	−0.306788	+	0.842894i	−0.993278	+	0.115754i	$0.963071\pi$
$608$	30.2065	+	6.98527i	1.22504	+	0.283290i
$609$	8.69829	+	15.4643i	0.352473	+	0.626644i
$610$	−25.4483	+	4.21104i	−1.03037	+	0.170500i
$611$	14.3461	−	24.8482i	0.580382	−	1.00525i
$612$	−15.8787	+	26.4668i	−0.641859	+	1.06986i
$613$	−10.7146	−	18.5582i	−0.432758	−	0.749559i	0.564352	−	0.825534i	$-0.309126\pi$
$613$	−10.7146	−	18.5582i	−0.432758	−	0.749559i	−0.997110	+	0.0759758i	$0.975793\pi$
$614$	11.1945	−	1.85240i	0.451773	−	0.0747568i
$615$	18.9248	−	27.1516i	0.763121	−	1.09486i
$616$	22.1334	+	2.94501i	0.891781	+	0.118658i
$617$	11.6531	−	2.05476i	0.469138	−	0.0827217i	0.0659185	−	0.997825i	$-0.479002\pi$
$617$	11.6531	−	2.05476i	0.469138	−	0.0827217i	0.403219	+	0.915103i	$0.367891\pi$
$618$	2.69643	−	28.1022i	0.108467	−	1.13044i
$619$	−11.1031	−	30.5056i	−0.446273	−	1.22612i	−0.935300	−	0.353856i	$-0.884870\pi$
$619$	−11.1031	−	30.5056i	−0.446273	−	1.22612i	0.489027	−	0.872269i	$-0.337352\pi$
$620$	−30.2025	+	24.2762i	−1.21296	+	0.974957i
$621$	11.6354	+	8.03570i	0.466912	+	0.322461i
$622$	−4.09267	+	21.8602i	−0.164101	+	0.876514i
$623$	−2.44610	+	5.06754i	−0.0980010	+	0.203027i
$624$	21.3866	−	28.0807i	0.856149	−	1.12413i
$625$	9.88966	−	8.29841i	0.395586	−	0.331936i
$626$	−0.0508934	−	0.0903365i	−0.00203411	−	0.00361057i
$627$	−2.40790	+	28.2221i	−0.0961622	+	1.12708i
$628$	26.3621	+	0.556037i	1.05196	+	0.0221883i
$629$	7.74247	+	4.47012i	0.308713	+	0.178235i
$630$	37.9046	+	18.5890i	1.51015	+	0.740604i
$631$	−24.6382	+	14.2249i	−0.980833	+	0.566284i	−0.902521	−	0.430645i	$-0.858286\pi$
$631$	−24.6382	+	14.2249i	−0.980833	+	0.566284i	−0.0783113	+	0.996929i	$0.524953\pi$
$632$	11.1308	+	33.8795i	0.442761	+	1.34766i
$633$	0.385236	+	0.102335i	0.0153117	+	0.00406746i
$634$	0.465094	−	44.1057i	0.0184713	−	1.75166i
$635$	−30.7383	−	11.1878i	−1.21981	−	0.443976i
$636$	−40.9675	+	18.1672i	−1.62447	+	0.720375i
$637$	34.9432	+	7.13038i	1.38450	+	0.282516i
$638$	5.42563	+	15.4105i	0.214803	+	0.610107i
$639$	25.7514	+	30.4224i	1.01871	+	1.20349i
$640$	29.6807	−	30.4903i	1.17323	−	1.20523i
$641$	21.8187	−	26.0026i	0.861788	−	1.02704i	−0.137544	−	0.990496i	$-0.543921\pi$
$641$	21.8187	−	26.0026i	0.861788	−	1.02704i	0.999332	−	0.0365434i	$-0.0116347\pi$
$642$	−2.19849	+	0.569353i	−0.0867674	+	0.0224706i
$643$	13.7090	−	37.6652i	0.540631	−	1.48537i	−0.305393	−	0.952226i	$-0.598788\pi$
$643$	13.7090	−	37.6652i	0.540631	−	1.48537i	0.846024	−	0.533145i	$-0.178990\pi$
$644$	12.8334	+	6.53186i	0.505706	+	0.257391i
$645$	−12.5963	+	8.86049i	−0.495978	+	0.348882i
$646$	−37.3210	−	14.0311i	−1.46838	−	0.552048i
$647$	10.1005	−	17.4945i	0.397091	−	0.687781i	−0.596275	−	0.802780i	$-0.703353\pi$
$647$	10.1005	−	17.4945i	0.397091	−	0.687781i	0.993366	+	0.114999i	$0.0366866\pi$
$648$	−19.1185	−	16.8073i	−0.751044	−	0.660252i
$649$	12.4623	+	21.5853i	0.489187	+	0.847297i
$650$	−50.9204	+	41.8203i	−1.99726	+	1.64033i
$651$	17.9125	+	15.3763i	0.702046	+	0.602646i
$652$	36.7643	+	7.28507i	1.43980	+	0.285305i
$653$	20.4783	−	3.61088i	0.801378	−	0.141305i	0.242064	−	0.970260i	$-0.422176\pi$
$653$	20.4783	−	3.61088i	0.801378	−	0.141305i	0.559314	+	0.828956i	$0.311065\pi$
$654$	−3.45092	−	3.50933i	−0.134942	−	0.137226i
$655$	−19.2705	+	22.9657i	−0.752961	+	0.897343i
$656$	−13.7077	+	15.0031i	−0.535195	+	0.585772i
$657$	−0.810307	−	0.957285i	−0.0316131	−	0.0373472i
$658$	−18.8792	−	9.35971i	−0.735987	−	0.364880i
$659$	25.1313	−	9.14704i	0.978976	−	0.356318i	0.197534	−	0.980296i	$-0.436707\pi$
$659$	25.1313	−	9.14704i	0.978976	−	0.356318i	0.781442	+	0.623978i	$0.214484\pi$
$660$	31.4160	+	22.8963i	1.22287	+	0.891239i
$661$	0.649098	+	3.68122i	0.0252470	+	0.143183i	0.994826	−	0.101597i	$-0.0323953\pi$
$661$	0.649098	+	3.68122i	0.0252470	+	0.143183i	−0.969579	+	0.244780i	$0.921284\pi$
$662$	0.0965186	−	9.15304i	0.00375130	−	0.355743i
$663$	−32.0288	+	32.1670i	−1.24390	+	1.24926i
$664$	−7.59474	+	36.3144i	−0.294733	+	1.40927i
$665$	−14.8188	+	52.4853i	−0.574649	+	2.03529i
$666$	−4.77477	+	5.61878i	−0.185018	+	0.217723i
$667$			10.5365i			0.407973i
$668$	−7.02052	−	12.7747i	−0.271632	−	0.494267i
$669$	−0.0517024	+	0.605984i	−0.00199893	+	0.0234287i
$670$	13.0115	+	0.137206i	0.502677	+	0.00530073i
$671$	2.51270	+	14.2502i	0.0970015	+	0.550123i
$672$	−21.5757	−	14.3697i	−0.832302	−	0.554323i
$673$	−27.4887	−	23.0658i	−1.05961	−	0.889121i	−0.0655419	−	0.997850i	$-0.520878\pi$
$673$	−27.4887	−	23.0658i	−1.05961	−	0.889121i	−0.994071	+	0.108729i	$0.965322\pi$
$674$	7.93726	−	2.79450i	0.305732	−	0.107640i
$675$	27.5074	+	38.7496i	1.05876	+	1.49147i
$676$	20.1974	−	16.2343i	0.776822	−	0.624395i
$677$	19.1817	+	3.38226i	0.737214	+	0.129991i	0.529633	−	0.848227i	$-0.322330\pi$
$677$	19.1817	+	3.38226i	0.737214	+	0.129991i	0.207581	+	0.978218i	$0.433441\pi$
$678$	−39.2353	−	27.9664i	−1.50682	−	1.07404i
$679$	−35.7597	−	3.61129i	−1.37233	−	0.138588i
$680$	−43.0109	+	33.8311i	−1.64939	+	1.29736i
$681$	12.6816	+	1.08199i	0.485959	+	0.0414619i
$682$	13.7963	+	16.7984i	0.528287	+	0.643243i
$683$	5.79976	+	10.0455i	0.221922	+	0.384379i	0.955391	−	0.295343i	$-0.0954338\pi$
$683$	5.79976	+	10.0455i	0.221922	+	0.384379i	−0.733470	+	0.679722i	$0.762100\pi$
$684$	16.9178	−	28.1987i	0.646868	−	1.07821i
$685$	−8.63383	−	14.9542i	−0.329882	−	0.571372i
$686$	3.60170	−	25.9428i	0.137514	−	0.990500i
$687$	−7.56206	+	28.4670i	−0.288511	+	1.08608i
$688$	8.38160	−	4.37870i	0.319546	−	0.166936i
$689$	−64.9093	+	11.4453i	−2.47285	+	0.436030i
$690$	14.2071	+	20.6566i	0.540855	+	0.786385i
$691$	26.4869	−	31.5658i	1.00761	−	1.20082i	0.0280599	−	0.999606i	$-0.491067\pi$
$691$	26.4869	−	31.5658i	1.00761	−	1.20082i	0.979547	−	0.201213i	$-0.0644885\pi$
$692$	13.6170	−	2.10599i	0.517640	−	0.0800579i
$693$	10.2032	−	21.3723i	0.387587	−	0.811868i
$694$	−16.4728	−	14.1210i	−0.625301	−	0.536026i
$695$	−4.30617	+	1.56732i	−0.163343	+	0.0594518i
$696$	2.20941	−	18.8386i	0.0837474	−	0.714077i
$697$	20.0205	−	16.7992i	0.758330	−	0.636314i
$698$	−14.8822	−	26.4161i	−0.563299	−	0.999864i
$699$	−12.4199	+	26.7850i	−0.469765	+	1.01310i
$700$	33.0190	+	35.3775i	1.24800	+	1.33714i
$701$		−	32.4603i		−	1.22601i	−0.790079	−	0.613005i	$-0.789960\pi$
$701$		−	32.4603i		−	1.22601i	0.790079	−	0.613005i	$-0.210040\pi$
$702$	−21.3484	−	30.7554i	−0.805745	−	1.16079i
$703$	−8.24913	−	4.76264i	−0.311122	−	0.179626i
$704$	−17.2789	−	16.4689i	−0.651224	−	0.620694i
$705$	−21.1072	−	30.0066i	−0.794945	−	1.13011i
$706$	−0.0309359	+	2.93370i	−0.00116429	+	0.110411i
$707$	23.6158	−	10.6299i	0.888164	−	0.399779i
$708$	−1.97573	−	28.8694i	−0.0742524	−	1.08498i
$709$	28.4729	−	10.3633i	1.06932	−	0.389201i	0.253399	−	0.967362i	$-0.418452\pi$
$709$	28.4729	−	10.3633i	1.06932	−	0.389201i	0.815923	+	0.578161i	$0.196229\pi$
$710$	23.4679	+	66.6561i	0.880734	+	2.50156i
$711$	37.8240	−	0.162866i	1.41851	−	0.00610796i
$712$	5.30213	−	2.84149i	0.198706	−	0.106489i
$713$	4.79476	+	13.1735i	0.179565	+	0.493351i
$714$	25.0655	+	21.9799i	0.938053	+	0.822575i
$715$	36.7504	+	43.7974i	1.37439	+	1.63793i
$716$	−27.3124	−	23.9172i	−1.02071	−	0.893829i
$717$	−1.76888	+	0.478054i	−0.0660600	+	0.0178533i
$718$	−11.7272	−	4.40895i	−0.437656	−	0.164540i
$719$	−12.2143	+	21.1558i	−0.455516	+	0.788978i	−0.998718	−	0.0506248i	$-0.983879\pi$
$719$	−12.2143	+	21.1558i	−0.455516	+	0.788978i	0.543201	+	0.839603i	$0.317212\pi$
$720$	−21.0700	−	39.9121i	−0.785234	−	1.48744i
$721$	−29.3460	−	8.28562i	−1.09290	−	0.308572i
$722$	14.6120	+	5.49350i	0.543803	+	0.204447i
$723$	−10.2397	−	21.8363i	−0.380820	−	0.812102i
$724$	−4.23119	+	1.43973i	−0.157251	+	0.0535071i
$725$	−12.1104	+	33.2732i	−0.449771	+	1.23573i
$726$	−2.98158	+	4.18299i	−0.110657	+	0.155245i
$727$	−33.7172	+	40.1826i	−1.25050	+	1.49029i	−0.447536	+	0.894266i	$0.647698\pi$
$727$	−33.7172	+	40.1826i	−1.25050	+	1.49029i	−0.802966	+	0.596024i	$0.796746\pi$
$728$	−25.7185	−	28.1447i	−0.953191	−	1.04311i
$729$	−23.2064	+	13.8009i	−0.859495	+	0.511145i
$730$	−0.738452	−	2.09743i	−0.0273313	−	0.0776295i
$731$	−11.4278	+	4.15938i	−0.422672	+	0.153840i
$732$	4.65449	−	16.1418i	0.172035	−	0.596617i
$733$	12.3410	−	10.3553i	0.455824	−	0.382482i	−0.385768	−	0.922596i	$-0.626063\pi$
$733$	12.3410	−	10.3553i	0.455824	−	0.382482i	0.841592	+	0.540114i	$0.181619\pi$
$734$	37.3241	+	22.0771i	1.37766	+	0.814879i
$735$	27.0662	−	36.6985i	0.998353	−	1.35364i
$736$	−6.98387	−	13.7189i	−0.257429	−	0.505687i
$737$		−	7.29954i		−	0.268882i
$738$	10.6608	+	18.7340i	0.392430	+	0.689609i
$739$		−	3.07670i		−	0.113178i	−0.998398	−	0.0565891i	$-0.981978\pi$
$739$		−	3.07670i		−	0.113178i	0.998398	−	0.0565891i	$-0.0180225\pi$
$740$	−11.4569	+	6.29631i	−0.421164	+	0.231457i
$741$	34.1248	−	34.2720i	1.25360	−	1.25901i
$742$	11.4062	+	47.0426i	0.418735	+	1.72699i
$743$	−4.17544	+	3.50361i	−0.153182	+	0.128535i	−0.716158	−	0.697938i	$-0.754101\pi$
$743$	−4.17544	+	3.50361i	−0.153182	+	0.128535i	0.562976	+	0.826473i	$0.309656\pi$
$744$	−5.81041	−	24.5589i	−0.213020	−	0.900374i
$745$	−4.93674	+	27.9976i	−0.180868	+	1.02575i
$746$	−7.93390	+	42.3774i	−0.290481	+	1.55155i
$747$	34.1630	+	19.5284i	1.24996	+	0.714506i
$748$	19.2318	+	23.9266i	0.703183	+	0.874844i
$749$	0.181077	+	2.44628i	0.00661641	+	0.0893853i
$750$	9.57414	+	36.9694i	0.349598	+	1.34993i
$751$	12.9509	−	2.28359i	0.472585	−	0.0833294i	0.0677167	−	0.997705i	$-0.478429\pi$
$751$	12.9509	−	2.28359i	0.472585	−	0.0833294i	0.404868	+	0.914375i	$0.367317\pi$
$752$	10.4308	+	19.9664i	0.380373	+	0.728101i
$753$	43.0061	+	19.9415i	1.56723	+	0.726708i
$754$	9.81702	−	26.1120i	0.357515	−	0.950943i
$755$	59.5994			2.16905
$756$	−21.5495	+	17.0769i	−0.783746	+	0.621081i
$757$	−51.5901			−1.87507			−0.937537	−	0.347886i	$-0.886900\pi$
$757$	−51.5901			−1.87507			−0.937537	+	0.347886i	$0.886900\pi$
$758$	6.62886	−	17.6319i	0.240771	−	0.640420i
$759$	11.5032	−	8.09159i	0.417540	−	0.293706i
$760$	45.8255	−	36.0449i	1.66226	−	1.30749i
$761$	−17.9780	+	3.17000i	−0.651701	+	0.114912i	−0.489718	−	0.871881i	$-0.662900\pi$
$761$	−17.9780	+	3.17000i	−0.651701	+	0.114912i	−0.161983	+	0.986793i	$0.551789\pi$
$762$	15.1902	−	14.9374i	0.550283	−	0.541124i
$763$	−4.39516	+	2.99069i	−0.159116	+	0.108270i
$764$	−25.6526	+	20.6191i	−0.928077	+	0.745971i
$765$	20.0859	+	54.4549i	0.726208	+	1.96882i
$766$	1.46384	−	7.81880i	0.0528905	−	0.282505i
$767$	7.39018	−	41.9118i	0.266844	−	1.51335i
$768$	9.61006	+	25.9932i	0.346773	+	0.937949i
$769$	−19.3471	+	16.2341i	−0.697673	+	0.585417i	−0.921111	−	0.389301i	$-0.872717\pi$
$769$	−19.3471	+	16.2341i	−0.697673	+	0.585417i	0.223437	+	0.974718i	$0.428272\pi$
$770$	30.3925	−	28.9719i	1.09527	−	1.04408i
$771$	40.5937	+	10.7834i	1.46195	+	0.388356i
$772$	8.86307	+	16.1274i	0.318989	+	0.580438i
$773$		−	34.8249i		−	1.25256i	−0.779597	−	0.626282i	$-0.784576\pi$
$773$		−	34.8249i		−	1.25256i	0.779597	−	0.626282i	$-0.215424\pi$
$774$	−1.68005	−	9.88836i	−0.0603880	−	0.355430i
$775$			47.1117i			1.69230i
$776$	28.6380	+	25.6165i	1.02804	+	0.919580i
$777$	5.05056	+	6.15812i	0.181188	+	0.220921i
$778$	2.60246	+	1.53935i	0.0933029	+	0.0551883i
$779$	−21.3306	+	17.8985i	−0.764248	+	0.641280i
$780$	−15.9626	−	64.4294i	−0.571553	−	2.30694i
$781$	37.2516	−	13.5585i	1.33297	−	0.485160i
$782$	6.57457	+	18.6738i	0.235106	+	0.667775i
$783$	−18.2880	−	8.38444i	−0.653558	−	0.299635i
$784$	−19.4328	+	20.1585i	−0.694029	+	0.719947i
$785$	31.8728	−	37.9845i	1.13759	−	1.35572i
$786$	−8.10291	−	17.7644i	−0.289021	−	0.633637i
$787$	12.5476	−	34.4743i	0.447275	−	1.22888i	−0.487339	−	0.873213i	$-0.662032\pi$
$787$	12.5476	−	34.4743i	0.447275	−	1.22888i	0.934614	−	0.355664i	$-0.115745\pi$
$788$	5.58341	+	16.4090i	0.198901	+	0.584545i
$789$	22.0487	−	31.6335i	0.784954	−	1.12618i
$790$	62.7716	+	23.5995i	2.23331	+	0.839633i
$791$	−37.2889	+	36.3041i	−1.32584	+	1.29083i
$792$	−22.2639	+	12.0552i	−0.791112	+	0.428364i
$793$	12.3537	−	21.3972i	0.438693	−	0.759839i
$794$	−8.70448	−	3.27252i	−0.308910	−	0.116137i
$795$	−21.6367	+	81.4503i	−0.767374	+	2.88874i
$796$	10.6147	−	12.1215i	0.376228	−	0.429636i
$797$	25.7988	+	30.7458i	0.913840	+	1.08907i	0.995719	+	0.0924293i	$0.0294632\pi$
$797$	25.7988	+	30.7458i	0.913840	+	1.08907i	−0.0818797	+	0.996642i	$0.526092\pi$
$798$	−26.7058	−	23.4182i	−0.945374	−	0.828995i
$799$	−9.90837	−	27.2230i	−0.350533	−	0.963081i
$800$	−6.28610	−	51.3503i	−0.222247	−	1.81551i
$801$	−1.13500	−	6.27868i	−0.0401032	−	0.221846i
$802$	−8.05615	−	22.8820i	−0.284473	−	0.807991i
$803$	−1.17218	+	0.426638i	−0.0413652	+	0.0150557i
$804$	−3.72632	+	7.61142i	−0.131417	+	0.268434i
$805$	24.6932	−	11.1149i	0.870321	−	0.391748i
$806$	0.391373	−	37.1146i	0.0137855	−	1.30731i
$807$	8.12786	−	17.5287i	0.286114	−	0.617038i
$808$	−27.0997	−	5.66759i	−0.953365	−	0.199385i
$809$	−14.0220	−	8.09559i	−0.492986	−	0.284626i	0.232826	−	0.972518i	$-0.425203\pi$
$809$	−14.0220	−	8.09559i	−0.492986	−	0.284626i	−0.725812	+	0.687893i	$0.758536\pi$
$810$	−47.1587	+	8.22141i	−1.65699	+	0.288871i
$811$		−	18.5069i		−	0.649866i	−0.945737	−	0.324933i	$-0.894658\pi$
$811$		−	18.5069i		−	0.649866i	0.945737	−	0.324933i	$-0.105342\pi$
$812$	−19.5949	−	5.98140i	−0.687647	−	0.209906i
$813$	−6.33769	−	9.00981i	−0.222272	−	0.315988i
$814$	3.59965	+	6.38944i	0.126168	+	0.223950i
$815$	53.9907	−	45.3036i	1.89121	−	1.58692i
$816$	−7.83925	−	34.7665i	−0.274429	−	1.21707i
$817$	12.1756	−	4.43156i	0.425971	−	0.155041i
$818$	−26.2159	−	22.4731i	−0.916618	−	0.785752i
$819$	−36.8032	+	16.7567i	−1.28601	+	0.585528i
$820$	5.84105	+	37.7672i	0.203978	+	1.31889i
$821$	−5.46368	+	6.51136i	−0.190684	+	0.227248i	−0.852913	−	0.522053i	$-0.825166\pi$
$821$	−5.46368	+	6.51136i	−0.190684	+	0.227248i	0.662229	+	0.749302i	$0.269611\pi$
$822$	11.2112	−	0.886117i	0.391034	−	0.0309069i
$823$	−34.4138	+	6.06808i	−1.19959	+	0.211520i	−0.737521	−	0.675324i	$-0.764004\pi$
$823$	−34.4138	+	6.06808i	−1.19959	+	0.211520i	−0.462069	+	0.886844i	$0.652893\pi$
$824$	20.1537	+	25.6223i	0.702088	+	0.892595i
$825$	45.6264	−	12.3309i	1.58851	−	0.429307i
$826$	−31.0624	−	3.46817i	−1.08080	−	0.120673i
$827$	−10.8487	−	18.7906i	−0.377248	−	0.653412i	0.613413	−	0.789762i	$-0.289796\pi$
$827$	−10.8487	−	18.7906i	−0.377248	−	0.653412i	−0.990661	+	0.136350i	$0.956463\pi$
$828$	−16.1253	+	2.56508i	−0.560395	+	0.0891427i
$829$	9.23075	+	15.9881i	0.320597	+	0.555290i	0.980611	−	0.195963i	$-0.0627831\pi$
$829$	9.23075	+	15.9881i	0.320597	+	0.555290i	−0.660014	+	0.751253i	$0.729450\pi$
$830$	44.2795	+	53.9147i	1.53696	+	1.87141i
$831$	−7.85598	+	11.2711i	−0.272521	+	0.390989i
$832$	4.52561	+	40.5060i	0.156897	+	1.40429i
$833$	28.1937	−	22.3996i	0.976853	−	0.776100i
$834$	0.285059	−	2.97088i	0.00987078	−	0.102873i
$835$	−26.9952	−	4.75998i	−0.934208	−	0.164726i
$836$	−20.4903	−	25.4924i	−0.708671	−	0.881671i
$837$	−26.6805	−	2.16069i	−0.922211	−	0.0746844i
$838$	−3.27986	+	1.15475i	−0.113301	+	0.0398903i
$839$	−0.531760	−	0.446199i	−0.0183584	−	0.0154045i	0.633562	−	0.773692i	$-0.281592\pi$
$839$	−0.531760	−	0.446199i	−0.0183584	−	0.0154045i	−0.651921	+	0.758287i	$0.726036\pi$
$840$	−46.4809	+	14.6948i	−1.60374	+	0.507020i
$841$	2.43270	+	13.7965i	0.0838860	+	0.475741i
$842$	0.113328	+	0.00119505i	0.00390555	+	4.11840e-5i
$843$	−9.01068	+	4.22539i	−0.310344	+	0.145530i
$844$	−0.403360	+	0.221673i	−0.0138842	+	0.00763030i
$845$		−	48.7298i		−	1.67636i
$846$	23.5558	−	4.00216i	0.809865	−	0.137597i
$847$	3.87049	+	3.97548i	0.132992	+	0.136599i
$848$	19.7335	−	47.8376i	0.677650	−	1.64275i
$849$	−8.90058	−	32.9336i	−0.305467	−	1.13028i
$850$	−0.701527	+	66.5270i	−0.0240622	+	2.28186i
$851$	0.821286	+	4.65774i	0.0281533	+	0.159665i
$852$	−45.7647	−	4.87869i	−1.56787	−	0.167141i
$853$	45.3598	−	16.5096i	1.55309	−	0.565279i	0.583951	−	0.811789i	$-0.301506\pi$
$853$	45.3598	−	16.5096i	1.55309	−	0.565279i	0.969140	+	0.246510i	$0.0792839\pi$
$854$	−16.2572	−	8.05982i	−0.556311	−	0.275801i
$855$	−21.4003	−	58.0184i	−0.731876	−	1.98419i
$856$	1.38234	−	2.22841i	0.0472476	−	0.0761655i
$857$	−16.7606	+	19.9745i	−0.572530	+	0.682315i	−0.972148	−	0.234367i	$-0.924698\pi$
$857$	−16.7606	+	19.9745i	−0.572530	+	0.682315i	0.399618	+	0.916682i	$0.369143\pi$
$858$	−36.0469	+	9.33525i	−1.23062	+	0.318700i
$859$	45.9626	−	8.10445i	1.56822	−	0.276520i	0.679051	−	0.734091i	$-0.262391\pi$
$859$	45.9626	−	8.10445i	1.56822	−	0.276520i	0.889173	+	0.457570i	$0.151280\pi$
$860$	3.45659	−	17.4438i	0.117869	−	0.594828i
$861$	21.9660	−	7.71681i	0.748599	−	0.262988i
$862$	−20.2662	+	16.6444i	−0.690270	+	0.566910i
$863$	−13.3173	−	23.0662i	−0.453325	−	0.785181i	0.545266	−	0.838263i	$-0.316429\pi$
$863$	−13.3173	−	23.0662i	−0.453325	−	0.785181i	−0.998590	+	0.0530822i	$0.983095\pi$
$864$	29.3692	−	1.20488i	0.999160	−	0.0409908i
$865$	12.9557	−	22.4399i	0.440506	−	0.762978i
$866$	−9.65985	−	3.63170i	−0.328255	−	0.123410i
$867$	1.46347	+	16.3228i	0.0497022	+	0.554350i
$868$	−27.2210	+	1.43853i	−0.923941	+	0.0488270i
$869$	12.8667	−	35.3510i	0.436473	−	1.19920i
$870$	−25.0093	−	25.4326i	−0.847896	−	0.862247i
$871$	−8.01162	+	9.54788i	−0.271464	+	0.323518i
$872$	5.68038	+	0.179752i	0.192362	+	0.00608717i
$873$	35.2059	−	20.5287i	1.19154	−	0.694793i
$874$	−7.00481	−	19.8958i	−0.236941	−	0.672987i
$875$	41.1363	−	3.04496i	1.39066	−	0.102938i
$876$	1.44005	+	0.153515i	0.0486549	+	0.00518680i
$877$	40.2193	+	14.6386i	1.35811	+	0.494311i	0.915469	−	0.402389i	$-0.131820\pi$
$877$	40.2193	+	14.6386i	1.35811	+	0.494311i	0.442639	+	0.896700i	$0.354042\pi$
$878$	−0.331615	+	31.4477i	−0.0111915	+	1.06131i
$879$	9.16492	+	33.9118i	0.309125	+	1.14382i
$880$	−44.4955	+	5.92382i	−1.49994	+	0.199692i
$881$	−17.9299	+	10.3518i	−0.604072	+	0.348761i	−0.770642	−	0.637268i	$-0.780064\pi$
$881$	−17.9299	+	10.3518i	−0.604072	+	0.348761i	0.166570	+	0.986030i	$0.446731\pi$
$882$	13.9926	+	26.1956i	0.471155	+	0.882050i
$883$	−19.8282	−	11.4478i	−0.667273	−	0.385250i	0.127770	−	0.991804i	$-0.459218\pi$
$883$	−19.8282	−	11.4478i	−0.667273	−	0.385250i	−0.795042	+	0.606554i	$0.792551\pi$
$884$	1.10533	−	52.4042i	0.0371761	−	1.76254i
$885$	−44.6423	−	31.1158i	−1.50063	−	1.04595i
$886$	20.6180	+	36.5972i	0.692674	+	1.22951i
$887$	−33.6595	+	28.2437i	−1.13017	+	0.948329i	−0.999073	−	0.0430399i	$-0.986296\pi$
$887$	−33.6595	+	28.2437i	−1.13017	+	0.948329i	−0.131101	+	0.991369i	$0.541851\pi$
$888$	−0.491726	−	8.50002i	−0.0165013	−	0.285242i
$889$	−12.9453	−	19.0245i	−0.434170	−	0.638061i
$890$	2.08172	−	11.1191i	0.0697794	−	0.372713i
$891$	4.89071	+	26.4048i	0.163845	+	0.884595i
$892$	−0.439967	−	0.547372i	−0.0147312	−	0.0183274i
$893$	10.5568	+	29.0045i	0.353269	+	0.970597i
$894$	−15.0775	−	10.7471i	−0.504267	−	0.359435i
$895$	−67.2335	+	11.8551i	−2.24737	+	0.396272i
$896$	29.4781	−	5.20005i	0.984795	−	0.173721i
$897$	−23.9273	−	2.04147i	−0.798908	−	0.0681626i
$898$	19.0816	−	3.15751i	0.636760	−	0.105367i
$899$	−9.97267	−	17.2732i	−0.332607	−	0.576092i
$900$	−53.8707	−	10.4339i	−1.79569	−	0.347798i
$901$	−33.2745	+	57.6332i	−1.10854	+	1.92004i
$902$	21.1508	−	3.49991i	0.704243	−	0.116534i
$903$	−10.8330	−	0.121627i	−0.360501	−	0.00404751i
$904$	55.0690	−	7.92332i	1.83157	−	0.263526i
$905$	−2.87461	+	7.89794i	−0.0955554	+	0.262536i
$906$	−16.6990	+	35.0404i	−0.554788	+	1.16414i
$907$	13.6057	+	2.39905i	0.451769	+	0.0796590i	0.394903	−	0.918723i	$-0.370778\pi$
$907$	13.6057	+	2.39905i	0.451769	+	0.0796590i	0.0568658	+	0.998382i	$0.481889\pi$
$908$	−11.4550	+	9.20730i	−0.380147	+	0.305555i
$909$	−14.5731	+	25.4942i	−0.483359	+	0.845590i
$910$	−71.5520	+	4.53831i	−2.37192	+	0.150444i
$911$	−1.92264	+	10.9038i	−0.0636999	+	0.361260i	0.936251	+	0.351332i	$0.114271\pi$
$911$	−1.92264	+	10.9038i	−0.0636999	+	0.361260i	−0.999951	+	0.00992774i	$0.996840\pi$
$912$	8.35224	+	37.0416i	0.276570	+	1.22657i
$913$	29.9813	−	25.1573i	0.992235	−	0.832584i
$914$	13.7511	−	23.2479i	0.454845	−	0.768973i
$915$	−18.1758	−	25.8392i	−0.600875	−	0.854218i
$916$	−16.3805	−	29.8064i	−0.541228	−	0.984830i
$917$	−20.4422	+	5.18535i	−0.675061	+	0.171235i
$918$	−37.6436	−	3.44843i	−1.24242	−	0.113815i
$919$	35.4473	−	20.4655i	1.16930	−	0.675094i	0.215783	−	0.976441i	$-0.430770\pi$
$919$	35.4473	−	20.4655i	1.16930	−	0.675094i	0.953514	+	0.301347i	$0.0974364\pi$
$920$	−28.3361	−	5.92615i	−0.934212	−	0.195379i
$921$	7.99538	+	11.3664i	0.263457	+	0.374537i
$922$	−22.5153	+	12.6846i	−0.741502	+	0.417744i
$923$	−63.6067	−	23.1509i	−2.09364	−	0.762022i
$924$	8.51794	+	25.9863i	0.280220	+	0.854886i
$925$	−2.75999	+	15.6527i	−0.0907480	+	0.514658i
$926$	11.8315	+	2.21509i	0.388806	+	0.0727924i
$927$	32.4397	−	11.9655i	1.06546	−	0.392999i
$928$	13.1747	+	17.4966i	0.432479	+	0.574353i
$929$	1.92650	−	2.29591i	0.0632063	−	0.0753264i	−0.733515	−	0.679673i	$-0.762122\pi$
$929$	1.92650	−	2.29591i	0.0632063	−	0.0753264i	0.796721	+	0.604347i	$0.206566\pi$
$930$	−42.8420	−	20.4170i	−1.40485	−	0.669500i
$931$	−30.0387	+	23.8654i	−0.984477	+	0.782157i
$932$	−10.9820	−	32.2747i	−0.359726	−	1.05719i
$933$	−26.2950	+	7.10643i	−0.860859	+	0.232654i
$934$	4.95884	+	1.86432i	0.162258	+	0.0610023i
$935$	57.7272			1.88788
$936$	42.3526	+	8.66739i	1.38434	+	0.283302i
$937$	17.0388	−	29.5120i	0.556632	−	0.964115i	−0.441143	−	0.897437i	$-0.645427\pi$
$937$	17.0388	−	29.5120i	0.556632	−	0.964115i	0.997775	−	0.0666777i	$-0.0212399\pi$
$938$	7.37048	+	5.42818i	0.240655	+	0.177237i
$939$	0.0726138	−	0.104180i	0.00236966	−	0.00339978i
$940$	41.5541	+	8.23421i	1.35535	+	0.268570i
$941$	−1.23720	+	3.39917i	−0.0403314	+	0.110810i	−0.958224	−	0.286020i	$-0.907668\pi$
$941$	−1.23720	+	3.39917i	−0.0403314	+	0.110810i	0.917892	+	0.396830i	$0.129890\pi$
$942$	13.4019	+	29.3818i	0.436659	+	0.957311i
$943$	13.6159	+	2.40085i	0.443395	+	0.0781826i
$944$	24.6678	+	22.5380i	0.802869	+	0.733548i
$945$	−0.357857	+	51.7043i	−0.0116411	+	1.68194i
$946$	−9.80544	−	1.83578i	−0.318802	−	0.0596862i
$947$	6.84291	−	38.8081i	0.222365	−	1.26109i	−0.645295	−	0.763934i	$-0.723265\pi$
$947$	6.84291	−	38.8081i	0.222365	−	1.26109i	0.867659	−	0.497159i	$-0.165624\pi$
$948$	−31.4627	+	30.2932i	−1.02186	+	0.983876i
$949$	2.00148	+	0.728479i	0.0649707	+	0.0236474i
$950$	0.747434	−	70.8805i	0.0242500	−	2.29967i
$951$	48.9106	−	22.9357i	1.58604	−	0.743742i
$952$	−38.4605	+	1.62603i	−1.24651	+	0.0527000i
$953$	20.9270	+	12.0822i	0.677893	+	0.391382i	0.799061	−	0.601250i	$-0.205331\pi$
$953$	20.9270	+	12.0822i	0.677893	+	0.391382i	−0.121168	+	0.992632i	$0.538664\pi$
$954$	−41.8249	−	35.5423i	−1.35413	−	1.15072i
$955$			61.8914i			2.00276i
$956$	1.09631	−	1.80962i	0.0354571	−	0.0585274i
$957$	−14.1184	+	14.1793i	−0.456382	+	0.458351i
$958$	−27.6075	−	49.0038i	−0.891959	−	1.58324i
$959$	1.22051	−	12.0857i	0.0394123	−	0.390269i
$960$	49.4207	+	16.5375i	1.59505	+	0.533745i
$961$	3.41840	+	2.86838i	0.110271	+	0.0925282i
$962$	2.30436	−	12.3083i	0.0742954	−	0.396835i
$963$	−1.79702	−	2.12297i	−0.0579081	−	0.0684117i
$964$	25.9629	+	10.0747i	0.836208	+	0.324483i
$965$	34.0802	+	6.00925i	1.09708	+	0.193445i
$966$	−0.383941	+	17.6322i	−0.0123531	+	0.567306i
$967$	5.54956	−	15.2473i	0.178462	−	0.490320i	−0.817918	−	0.575335i	$-0.804872\pi$
$967$	5.54956	−	15.2473i	0.178462	−	0.490320i	0.996380	+	0.0850154i	$0.0270939\pi$
$968$	−0.844728	−	5.87107i	−0.0271506	−	0.188703i
$969$	−4.36074	−	48.6373i	−0.140087	−	1.56245i
$970$	71.2859	−	11.7960i	2.28885	−	0.378746i
$971$	7.53845	+	13.0570i	0.241920	+	0.419018i	0.961261	−	0.275639i	$-0.0888894\pi$
$971$	7.53845	+	13.0570i	0.241920	+	0.419018i	−0.719341	+	0.694657i	$0.755556\pi$
$972$	8.37966	−	30.0297i	0.268778	−	0.963202i
$973$	−3.10237	−	0.875930i	−0.0994575	−	0.0280810i
$974$	−3.23038	−	3.93331i	−0.103508	−	0.126031i
$975$	−73.2137	−	33.9484i	−2.34472	−	1.08722i
$976$	8.98217	+	17.1935i	0.287512	+	0.550350i
$977$	−25.2854	−	30.1340i	−0.808953	−	0.964072i	0.190894	−	0.981611i	$-0.438861\pi$
$977$	−25.2854	−	30.1340i	−0.808953	−	0.964072i	−0.999846	+	0.0175385i	$0.994417\pi$
$978$	11.5079	+	44.4364i	0.367982	+	1.42092i
$979$	−6.24952	−	1.10196i	−0.199735	−	0.0352187i
$980$	6.65263	+	52.2324i	0.212510	+	1.66850i
$981$	2.03728	−	5.67327i	0.0650453	−	0.181133i
$982$	−2.52675	−	2.16600i	−0.0806318	−	0.0691200i
$983$	−1.17486	+	6.66293i	−0.0374721	+	0.212515i	−0.997795	−	0.0663771i	$-0.978856\pi$
$983$	−1.17486	+	6.66293i	−0.0374721	+	0.212515i	0.960323	+	0.278892i	$0.0899671\pi$
$984$	−23.8411	−	7.14775i	−0.760027	−	0.227862i
$985$	30.6290	+	11.1480i	0.975920	+	0.355206i
$986$	−13.8253	−	24.5402i	−0.440288	−	0.781518i
$987$	0.289738	−	25.8062i	0.00922245	−	0.821419i
$988$	−1.17766	+	55.8335i	−0.0374663	+	1.77630i
$989$	−5.57163	−	3.21678i	−0.177168	−	0.102288i
$990$	−8.55993	+	46.8353i	−0.272052	+	1.48852i
$991$	−24.7891	+	14.3120i	−0.787451	+	0.454635i	−0.839064	−	0.544032i	$-0.816897\pi$
$991$	−24.7891	+	14.3120i	−0.787451	+	0.454635i	0.0516136	+	0.998667i	$0.483564\pi$
$992$	24.4340	+	15.8802i	0.775781	+	0.504198i
$993$	10.1502	−	4.75973i	0.322106	−	0.151046i
$994$	−14.0113	+	47.6962i	−0.444412	+	1.51283i
$995$	−5.26140	−	29.8389i	−0.166798	−	0.945957i
$996$	−44.1047	+	10.9271i	−1.39751	+	0.346238i
$997$	−7.92695	+	2.88517i	−0.251049	+	0.0913744i	−0.464479	−	0.885584i	$-0.653759\pi$
$997$	−7.92695	+	2.88517i	−0.251049	+	0.0913744i	0.213430	+	0.976958i	$0.431536\pi$
$998$	22.1253	−	25.8102i	0.700363	−	0.817007i
$999$	−8.73791	−	2.28093i	−0.276455	−	0.0721654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bs.a.11.15	yes	840
4.3	odd	2	inner	756.2.bs.a.11.1	✓	840
7.2	even	3		756.2.ci.a.443.79	yes	840
27.5	odd	18		756.2.ci.a.599.93	yes	840
28.23	odd	6		756.2.ci.a.443.93	yes	840
108.59	even	18		756.2.ci.a.599.79	yes	840
189.86	odd	18	inner	756.2.bs.a.275.1	yes	840
756.275	even	18	inner	756.2.bs.a.275.15	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.11.1	✓	840	4.3	odd	2	inner
756.2.bs.a.11.15	yes	840	1.1	even	1	trivial
756.2.bs.a.275.1	yes	840	189.86	odd	18	inner
756.2.bs.a.275.15	yes	840	756.275	even	18	inner
756.2.ci.a.443.79	yes	840	7.2	even	3
756.2.ci.a.443.93	yes	840	28.23	odd	6
756.2.ci.a.599.79	yes	840	108.59	even	18
756.2.ci.a.599.93	yes	840	27.5	odd	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32375 - 0.497675i) q^{2} +(-0.154673 - 1.72513i) q^{3} +(1.50464 + 1.31760i) q^{4} +(3.70389 - 0.653095i) q^{5} +(-0.653807 + 2.36062i) q^{6} +(2.38269 + 1.15013i) q^{7} +(-1.33603 - 2.49299i) q^{8} +(-2.95215 + 0.533661i) q^{9} +O(q^{10})\)	\(q+(-1.32375 - 0.497675i) q^{2} +(-0.154673 - 1.72513i) q^{3} +(1.50464 + 1.31760i) q^{4} +(3.70389 - 0.653095i) q^{5} +(-0.653807 + 2.36062i) q^{6} +(2.38269 + 1.15013i) q^{7} +(-1.33603 - 2.49299i) q^{8} +(-2.95215 + 0.533661i) q^{9} +(-5.22806 - 0.978797i) q^{10} +(-0.518126 + 2.93844i) q^{11} +(2.04030 - 2.79949i) q^{12} +(3.90281 - 3.27484i) q^{13} +(-2.58170 - 2.70829i) q^{14} +(-1.69956 - 6.28867i) q^{15} +(0.527874 + 3.96502i) q^{16} -5.14410i q^{17} +(4.17351 + 0.762779i) q^{18} +5.48072i q^{19} +(6.43353 + 3.89756i) q^{20} +(1.61558 - 4.28835i) q^{21} +(2.14826 - 3.63191i) q^{22} +(2.08467 - 1.74925i) q^{23} +(-4.09409 + 2.69043i) q^{24} +(8.59377 - 3.12788i) q^{25} +(-6.79616 + 2.39275i) q^{26} +(1.37725 + 5.01031i) q^{27} +(2.06969 + 4.86995i) q^{28} +(-2.48873 + 2.96595i) q^{29} +(-0.879916 + 9.17047i) q^{30} +(-1.76191 + 4.84079i) q^{31} +(1.27452 - 5.51141i) q^{32} +(5.14933 + 0.439339i) q^{33} +(-2.56009 + 6.80951i) q^{34} +(9.57635 + 2.70381i) q^{35} +(-5.14507 - 3.08678i) q^{36} +(-0.868980 + 1.50512i) q^{37} +(2.72762 - 7.25512i) q^{38} +(-6.25319 - 6.22633i) q^{39} +(-6.57667 - 8.36121i) q^{40} +(3.26572 + 3.89193i) q^{41} +(-4.27283 + 4.87267i) q^{42} +(-0.808573 - 2.22154i) q^{43} +(-4.65128 + 3.73861i) q^{44} +(-10.5859 + 3.90466i) q^{45} +(-3.63015 + 1.27808i) q^{46} +(5.29209 - 1.92616i) q^{47} +(6.75852 - 1.52393i) q^{48} +(4.35442 + 5.48078i) q^{49} +(-12.9327 - 0.136375i) q^{50} +(-8.87424 + 0.795651i) q^{51} +(10.1872 + 0.214873i) q^{52} +(-11.2037 - 6.46848i) q^{53} +(0.670366 - 7.31783i) q^{54} +11.2220i q^{55} +(-0.316097 - 7.47664i) q^{56} +(9.45496 - 0.847718i) q^{57} +(4.77055 - 2.68761i) q^{58} +(6.39905 - 5.36944i) q^{59} +(5.72871 - 11.7015i) q^{60} +(4.55711 - 1.65865i) q^{61} +(4.74147 - 5.53115i) q^{62} +(-7.64784 - 2.12380i) q^{63} +(-4.43004 + 6.66144i) q^{64} +(12.3168 - 14.6786i) q^{65} +(-6.59779 - 3.14427i) q^{66} +(-2.40925 + 0.424815i) q^{67} +(6.77785 - 7.74001i) q^{68} +(-3.34013 - 3.32577i) q^{69} +(-11.3311 - 8.34509i) q^{70} +(-6.64299 - 11.5060i) q^{71} +(5.27459 + 6.64671i) q^{72} +(0.209032 + 0.362053i) q^{73} +(1.89937 - 1.55993i) q^{74} +(-6.72522 - 14.3416i) q^{75} +(-7.22139 + 8.24651i) q^{76} +(-4.61411 + 6.40548i) q^{77} +(5.17899 + 11.3542i) q^{78} +(-12.4166 - 2.18938i) q^{79} +(4.54472 + 14.3412i) q^{80} +(8.43041 - 3.15090i) q^{81} +(-2.38608 - 6.77722i) q^{82} +(-10.0481 - 8.43136i) q^{83} +(8.08118 - 4.32373i) q^{84} +(-3.35958 - 19.0532i) q^{85} +(-0.0352537 + 3.34317i) q^{86} +(5.50160 + 3.83463i) q^{87} +(8.01775 - 2.63417i) q^{88} +2.12681i q^{89} +(15.9564 + 0.0995487i) q^{90} +(13.0657 - 3.31422i) q^{91} +(5.44149 + 0.114774i) q^{92} +(8.62352 + 2.29078i) q^{93} +(-7.96401 - 0.0839804i) q^{94} +(3.57943 + 20.3000i) q^{95} +(-9.70503 - 1.34624i) q^{96} +(-12.7654 + 4.64622i) q^{97} +(-3.03653 - 9.42229i) q^{98} +(-0.0385431 - 8.95123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

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