LMFDB - Embedded newform 288.2.bf.a.11.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(11,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 15, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.24
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.182710 + 1.40236i) q^{2} +(1.71563 + 0.237910i) q^{3} +(-1.93323 - 0.512452i) q^{4} +(-0.526650 - 4.00030i) q^{5} +(-0.647100 + 2.36247i) q^{6} +(-0.622598 - 2.32357i) q^{7} +(1.07187 - 2.61746i) q^{8} +(2.88680 + 0.816334i) q^{9} +(5.70609 - 0.00765608i) q^{10} +(-0.0232888 + 0.0178701i) q^{11} +(-3.19480 - 1.33912i) q^{12} +(-0.407445 + 0.530993i) q^{13} +(3.37223 - 0.448567i) q^{14} +(0.0481750 - 6.98835i) q^{15} +(3.47479 + 1.98138i) q^{16} +7.10921 q^{17} +(-1.67224 + 3.89918i) q^{18} +(-4.43809 + 1.83832i) q^{19} +(-1.03183 + 8.00340i) q^{20} +(-0.515349 - 4.13451i) q^{21} +(-0.0208053 - 0.0359244i) q^{22} +(-2.73212 - 0.732071i) q^{23} +(2.46165 - 4.23560i) q^{24} +(-10.8954 + 2.91942i) q^{25} +(-0.670199 - 0.668403i) q^{26} +(4.75847 + 2.08733i) q^{27} +(0.0129104 + 4.81105i) q^{28} +(2.24558 + 0.295636i) q^{29} +(9.79139 + 1.34440i) q^{30} +(-0.933304 + 0.538843i) q^{31} +(-3.41349 + 4.51089i) q^{32} +(-0.0442066 + 0.0251180i) q^{33} +(-1.29893 + 9.96968i) q^{34} +(-8.96708 + 3.71429i) q^{35} +(-5.16252 - 3.05751i) q^{36} +(-2.70652 + 6.53412i) q^{37} +(-1.76710 - 6.55969i) q^{38} +(-0.825355 + 0.814054i) q^{39} +(-11.0351 - 2.90930i) q^{40} +(2.78780 - 10.4042i) q^{41} +(5.89224 + 0.0327127i) q^{42} +(5.61822 + 7.32180i) q^{43} +(0.0541803 - 0.0226128i) q^{44} +(1.74525 - 11.9780i) q^{45} +(1.52582 - 3.69767i) q^{46} +(8.79455 + 5.07754i) q^{47} +(5.49007 + 4.22601i) q^{48} +(1.05084 - 0.606706i) q^{49} +(-2.10337 - 15.8127i) q^{50} +(12.1968 + 1.69135i) q^{51} +(1.05979 - 0.817737i) q^{52} +(-0.361368 + 0.872419i) q^{53} +(-3.79661 + 6.29172i) q^{54} +(0.0837510 + 0.0837510i) q^{55} +(-6.74919 - 0.860924i) q^{56} +(-8.05150 + 2.09801i) q^{57} +(-0.824880 + 3.09510i) q^{58} +(-1.09061 + 0.143582i) q^{59} +(-3.67433 + 13.4854i) q^{60} +(0.453300 - 3.44315i) q^{61} +(-0.585129 - 1.40728i) q^{62} +(0.0994923 - 7.21591i) q^{63} +(-5.70221 - 5.61113i) q^{64} +(2.33871 + 1.35026i) q^{65} +(-0.0271475 - 0.0665829i) q^{66} +(-0.783679 + 1.02131i) q^{67} +(-13.7438 - 3.64313i) q^{68} +(-4.51316 - 1.90597i) q^{69} +(-3.57039 - 13.2537i) q^{70} +(5.54582 + 5.54582i) q^{71} +(5.23098 - 6.68108i) q^{72} +(-1.91778 + 1.91778i) q^{73} +(-8.66868 - 4.98937i) q^{74} +(-19.3871 + 2.41652i) q^{75} +(9.52193 - 1.27959i) q^{76} +(0.0560220 + 0.0429872i) q^{77} +(-0.990796 - 1.30618i) q^{78} +(-4.14646 + 7.18188i) q^{79} +(6.09612 - 14.9437i) q^{80} +(7.66720 + 4.71318i) q^{81} +(14.0811 + 5.81047i) q^{82} +(-14.6061 - 1.92292i) q^{83} +(-1.12245 + 8.25707i) q^{84} +(-3.74406 - 28.4390i) q^{85} +(-11.2943 + 6.54100i) q^{86} +(3.78226 + 1.04145i) q^{87} +(0.0218119 + 0.0801120i) q^{88} +(-4.61864 + 4.61864i) q^{89} +(16.4786 + 4.63598i) q^{90} +(1.48747 + 0.616131i) q^{91} +(4.90668 + 2.81535i) q^{92} +(-1.72940 + 0.702415i) q^{93} +(-8.72739 + 11.4054i) q^{94} +(9.69115 + 16.7856i) q^{95} +(-6.92948 + 6.92692i) q^{96} +(6.69755 - 11.6005i) q^{97} +(0.658820 + 1.58452i) q^{98} +(-0.0818181 + 0.0325760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.182710	+	1.40236i	−0.129196	+	0.991619i
$2$	−0.182710	+	1.40236i	−0.129196	+	0.991619i
$3$	1.71563	+	0.237910i	0.990522	+	0.137358i
$3$	1.71563	+	0.237910i	0.990522	+	0.137358i
$4$	−1.93323	−	0.512452i	−0.966617	−	0.256226i
$5$	−0.526650	−	4.00030i	−0.235525	−	1.78899i	−0.545363	−	0.838200i	$-0.683608\pi$
$5$	−0.526650	−	4.00030i	−0.235525	−	1.78899i	0.309838	−	0.950789i	$-0.399725\pi$
$6$	−0.647100	+	2.36247i	−0.264178	+	0.964474i
$7$	−0.622598	−	2.32357i	−0.235320	−	0.878226i	−0.978004	−	0.208584i	$-0.933114\pi$
$7$	−0.622598	−	2.32357i	−0.235320	−	0.878226i	0.742685	−	0.669641i	$-0.233552\pi$
$8$	1.07187	−	2.61746i	0.378962	−	0.925412i
$9$	2.88680	+	0.816334i	0.962266	+	0.272111i
$10$	5.70609	−	0.00765608i	1.80443	−	0.00242107i
$11$	−0.0232888	+	0.0178701i	−0.00702184	+	0.00538805i	−0.612266	−	0.790652i	$-0.709742\pi$
$11$	−0.0232888	+	0.0178701i	−0.00702184	+	0.00538805i	0.605245	+	0.796040i	$0.293075\pi$
$12$	−3.19480	−	1.33912i	−0.922260	−	0.386570i
$13$	−0.407445	+	0.530993i	−0.113005	+	0.147271i	−0.846431	−	0.532498i	$-0.821253\pi$
$13$	−0.407445	+	0.530993i	−0.113005	+	0.147271i	0.733426	+	0.679769i	$0.237920\pi$
$14$	3.37223	−	0.448567i	0.901268	−	0.119885i
$15$	0.0481750	−	6.98835i	0.0124387	−	1.80438i
$16$	3.47479	+	1.98138i	0.868696	+	0.495345i
$17$	7.10921			1.72424			0.862118	−	0.506708i	$-0.169138\pi$
$17$	7.10921			1.72424			0.862118	+	0.506708i	$0.169138\pi$
$18$	−1.67224	+	3.89918i	−0.394151	+	0.919046i
$19$	−4.43809	+	1.83832i	−1.01817	+	0.421739i	−0.828428	−	0.560095i	$-0.810765\pi$
$19$	−4.43809	+	1.83832i	−1.01817	+	0.421739i	−0.189740	+	0.981834i	$0.560765\pi$
$20$	−1.03183	+	8.00340i	−0.230723	+	1.78962i
$21$	−0.515349	−	4.13451i	−0.112458	−	0.902224i
$22$	−0.0208053	−	0.0359244i	−0.00443570	−	0.00765911i
$23$	−2.73212	−	0.732071i	−0.569687	−	0.152647i	−0.0375341	−	0.999295i	$-0.511950\pi$
$23$	−2.73212	−	0.732071i	−0.569687	−	0.152647i	−0.532153	+	0.846648i	$0.678617\pi$
$24$	2.46165	−	4.23560i	0.502482	−	0.864588i
$25$	−10.8954	+	2.91942i	−2.17909	+	0.583884i
$26$	−0.670199	−	0.668403i	−0.131437	−	0.131085i
$27$	4.75847	+	2.08733i	0.915768	+	0.401707i
$28$	0.0129104	+	4.81105i	0.00243983	+	0.909203i
$29$	2.24558	+	0.295636i	0.416994	+	0.0548983i	0.336104	−	0.941825i	$-0.390891\pi$
$29$	2.24558	+	0.295636i	0.416994	+	0.0548983i	0.0808896	+	0.996723i	$0.474224\pi$
$30$	9.79139	+	1.34440i	1.78765	+	0.245453i
$31$	−0.933304	+	0.538843i	−0.167626	+	0.0967791i	−0.581466	−	0.813571i	$-0.697521\pi$
$31$	−0.933304	+	0.538843i	−0.167626	+	0.0967791i	0.413840	+	0.910350i	$0.364187\pi$
$32$	−3.41349	+	4.51089i	−0.603425	+	0.797419i
$33$	−0.0442066	+	0.0251180i	−0.00769538	+	0.00437248i
$34$	−1.29893	+	9.96968i	−0.222764	+	1.70979i
$35$	−8.96708	+	3.71429i	−1.51571	+	0.627829i
$36$	−5.16252	−	3.05751i	−0.860420	−	0.509585i
$37$	−2.70652	+	6.53412i	−0.444949	+	1.07420i	0.529241	+	0.848472i	$0.322477\pi$
$37$	−2.70652	+	6.53412i	−0.444949	+	1.07420i	−0.974190	+	0.225730i	$0.927523\pi$
$38$	−1.76710	−	6.55969i	−0.286662	−	1.06412i
$39$	−0.825355	+	0.814054i	−0.132163	+	0.130353i
$40$	−11.0351	−	2.90930i	−1.74481	−	0.460001i
$41$	2.78780	−	10.4042i	0.435382	−	1.62487i	−0.304769	−	0.952426i	$-0.598579\pi$
$41$	2.78780	−	10.4042i	0.435382	−	1.62487i	0.740151	−	0.672441i	$-0.234754\pi$
$42$	5.89224	+	0.0327127i	0.909192	+	0.00504768i
$43$	5.61822	+	7.32180i	0.856770	+	1.11656i	0.992061	+	0.125758i	$0.0401364\pi$
$43$	5.61822	+	7.32180i	0.856770	+	1.11656i	−0.135291	+	0.990806i	$0.543197\pi$
$44$	0.0541803	−	0.0226128i	0.00816799	−	0.00340900i
$45$	1.74525	−	11.9780i	0.260167	−	1.78557i
$46$	1.52582	−	3.69767i	0.224969	−	0.545191i
$47$	8.79455	+	5.07754i	1.28282	+	0.740635i	0.977362	−	0.211572i	$-0.0678583\pi$
$47$	8.79455	+	5.07754i	1.28282	+	0.740635i	0.305454	+	0.952207i	$0.401192\pi$
$48$	5.49007	+	4.22601i	0.792423	+	0.609972i
$49$	1.05084	−	0.606706i	0.150121	−	0.0866722i
$50$	−2.10337	−	15.8127i	−0.297462	−	2.23626i
$51$	12.1968	+	1.69135i	1.70789	+	0.236837i
$52$	1.05979	−	0.817737i	0.146967	−	0.113400i
$53$	−0.361368	+	0.872419i	−0.0496377	+	0.119836i	−0.946753	−	0.321960i	$-0.895658\pi$
$53$	−0.361368	+	0.872419i	−0.0496377	+	0.119836i	0.897116	+	0.441796i	$0.145658\pi$
$54$	−3.79661	+	6.29172i	−0.516653	+	0.856195i
$55$	0.0837510	+	0.0837510i	0.0112930	+	0.0112930i
$56$	−6.74919	−	0.860924i	−0.901898	−	0.115046i
$57$	−8.05150	+	2.09801i	−1.06645	+	0.277889i
$58$	−0.824880	+	3.09510i	−0.108312	+	0.406406i
$59$	−1.09061	+	0.143582i	−0.141986	+	0.0186928i	−0.201184	−	0.979553i	$-0.564479\pi$
$59$	−1.09061	+	0.143582i	−0.141986	+	0.0186928i	0.0591982	+	0.998246i	$0.481146\pi$
$60$	−3.67433	+	13.4854i	−0.474354	+	1.74096i
$61$	0.453300	−	3.44315i	0.0580391	−	0.440851i	−0.937611	−	0.347685i	$-0.886968\pi$
$61$	0.453300	−	3.44315i	0.0580391	−	0.440851i	0.995651	−	0.0931660i	$-0.0296987\pi$
$62$	−0.585129	−	1.40728i	−0.0743114	−	0.178725i
$63$	0.0994923	−	7.21591i	0.0125348	−	0.909120i
$64$	−5.70221	−	5.61113i	−0.712776	−	0.701391i
$65$	2.33871	+	1.35026i	0.290082	+	0.167479i
$66$	−0.0271475	−	0.0665829i	−0.00334162	−	0.00819579i
$67$	−0.783679	+	1.02131i	−0.0957416	+	0.124773i	−0.838767	−	0.544490i	$-0.816723\pi$
$67$	−0.783679	+	1.02131i	−0.0957416	+	0.124773i	0.743026	+	0.669263i	$0.233390\pi$
$68$	−13.7438	−	3.64313i	−1.66668	−	0.441794i
$69$	−4.51316	−	1.90597i	−0.543320	−	0.229451i
$70$	−3.57039	−	13.2537i	−0.426743	−	1.58412i
$71$	5.54582	+	5.54582i	0.658167	+	0.658167i	0.954946	−	0.296779i	$-0.0959124\pi$
$71$	5.54582	+	5.54582i	0.658167	+	0.658167i	−0.296779	+	0.954946i	$0.595912\pi$
$72$	5.23098	−	6.68108i	0.616477	−	0.787373i
$73$	−1.91778	+	1.91778i	−0.224459	+	0.224459i	−0.810373	−	0.585914i	$-0.800736\pi$
$73$	−1.91778	+	1.91778i	−0.224459	+	0.224459i	0.585914	+	0.810373i	$0.300736\pi$
$74$	−8.66868	−	4.98937i	−1.00771	−	0.580002i
$75$	−19.3871	+	2.41652i	−2.23863	+	0.279036i
$76$	9.52193	−	1.27959i	1.09224	−	0.146779i
$77$	0.0560220	+	0.0429872i	0.00638430	+	0.00489885i
$78$	−0.990796	−	1.30618i	−0.112186	−	0.147896i
$79$	−4.14646	+	7.18188i	−0.466513	+	0.808024i	−0.999268	−	0.0382451i	$-0.987823\pi$
$79$	−4.14646	+	7.18188i	−0.466513	+	0.808024i	0.532755	+	0.846269i	$0.321157\pi$
$80$	6.09612	−	14.9437i	0.681567	−	1.67075i
$81$	7.66720	+	4.71318i	0.851911	+	0.523687i
$82$	14.0811	+	5.81047i	1.55500	+	0.641659i
$83$	−14.6061	−	1.92292i	−1.60322	−	0.211068i	−0.724802	−	0.688957i	$-0.758069\pi$
$83$	−14.6061	−	1.92292i	−1.60322	−	0.211068i	−0.878420	+	0.477889i	$0.841402\pi$
$84$	−1.12245	+	8.25707i	−0.122469	+	0.900920i
$85$	−3.74406	−	28.4390i	−0.406101	−	3.08464i
$86$	−11.2943	+	6.54100i	−1.21790	+	0.705334i
$87$	3.78226	+	1.04145i	0.405501	+	0.111655i
$88$	0.0218119	+	0.0801120i	0.00232516	+	0.00853997i
$89$	−4.61864	+	4.61864i	−0.489574	+	0.489574i	−0.908172	−	0.418597i	$-0.862522\pi$
$89$	−4.61864	+	4.61864i	−0.489574	+	0.489574i	0.418597	+	0.908172i	$0.362522\pi$
$90$	16.4786	+	4.63598i	1.73700	+	0.488675i
$91$	1.48747	+	0.616131i	0.155929	+	0.0645880i
$92$	4.90668	+	2.81535i	0.511557	+	0.293520i
$93$	−1.72940	+	0.702415i	−0.179331	+	0.0728371i
$94$	−8.72739	+	11.4054i	−0.900162	+	1.17638i
$95$	9.69115	+	16.7856i	0.994291	+	1.72216i
$96$	−6.92948	+	6.92692i	−0.707237	+	0.706976i
$97$	6.69755	−	11.6005i	0.680034	−	1.17785i	−0.294937	−	0.955517i	$-0.595299\pi$
$97$	6.69755	−	11.6005i	0.680034	−	1.17785i	0.974970	−	0.222336i	$-0.0713682\pi$
$98$	0.658820	+	1.58452i	0.0665509	+	0.160060i
$99$	−0.0818181	+	0.0325760i	−0.00822303	+	0.00327401i
$100$	22.5595	−	0.0605379i	2.25595	−	0.00605379i
$101$	4.91336	−	3.77016i	0.488898	−	0.375144i	−0.334695	−	0.942327i	$-0.608633\pi$
$101$	4.91336	−	3.77016i	0.488898	−	0.375144i	0.823592	+	0.567182i	$0.191966\pi$
$102$	−4.60037	+	16.7953i	−0.455505	+	1.66298i
$103$	4.02021	+	1.07721i	0.396123	+	0.106141i	0.451381	−	0.892331i	$-0.350932\pi$
$103$	4.02021	+	1.07721i	0.396123	+	0.106141i	−0.0552582	+	0.998472i	$0.517598\pi$
$104$	0.953127	+	1.63562i	0.0934618	+	0.160386i
$105$	−16.2679	+	4.23899i	−1.58758	+	0.413683i
$106$	−1.15742	−	0.666169i	−0.112419	−	0.0647040i
$107$	−15.3286	−	6.34933i	−1.48188	−	0.613813i	−0.512344	−	0.858780i	$-0.671223\pi$
$107$	−15.3286	−	6.34933i	−1.48188	−	0.613813i	−0.969531	+	0.244967i	$0.921223\pi$
$108$	−8.12958	−	6.47378i	−0.782270	−	0.622940i
$109$	−0.274825	−	0.663485i	−0.0263234	−	0.0635503i	0.910171	−	0.414232i	$-0.135950\pi$
$109$	−0.274825	−	0.663485i	−0.0263234	−	0.0635503i	−0.936495	+	0.350682i	$0.885950\pi$
$110$	−0.132751	+	0.102147i	−0.0126573	+	0.00973933i
$111$	−6.19793	+	10.5662i	−0.588281	+	1.00290i
$112$	2.44047	−	9.30750i	0.230603	−	0.879476i
$113$	0.165657	+	0.286926i	0.0155837	+	0.0269917i	0.873712	−	0.486443i	$-0.161706\pi$
$113$	0.165657	+	0.286926i	0.0155837	+	0.0269917i	−0.858128	+	0.513435i	$0.828373\pi$
$114$	−1.47108	−	11.6744i	−0.137779	−	1.09341i
$115$	−1.48963	+	11.3149i	−0.138909	+	1.05512i
$116$	−4.18973	−	1.72229i	−0.389007	−	0.159910i
$117$	−1.60968	+	1.20026i	−0.148815	+	0.110964i
$118$	−0.00208730	−	1.55567i	−0.000192152	−	0.143211i
$119$	−4.42618	−	16.5187i	−0.405747	−	1.51427i
$120$	−18.2401	−	7.61666i	−1.66509	−	0.695303i
$121$	−2.84679	+	10.6244i	−0.258799	+	0.965850i
$122$	4.74572	+	1.26479i	0.429658	+	0.114509i
$123$	7.25812	−	17.1866i	0.654443	−	1.54966i
$124$	2.08043	−	0.563437i	0.186828	−	0.0505981i
$125$	9.69635	+	23.4091i	0.867268	+	2.09377i
$126$	10.1011	+	1.45795i	0.899881	+	0.129884i
$127$			4.17344i			0.370333i	0.982707	+	0.185167i	$0.0592824\pi$
$127$			4.17344i			0.370333i	−0.982707	+	0.185167i	$0.940718\pi$
$128$	8.91069	−	6.97135i	0.787601	−	0.616186i
$129$	7.89687	+	13.8982i	0.695281	+	1.22366i
$130$	−2.32085	+	3.03301i	−0.203552	+	0.266013i
$131$	13.7741	+	10.5693i	1.20345	+	0.923440i	0.998468	−	0.0553259i	$-0.0176198\pi$
$131$	13.7741	+	10.5693i	1.20345	+	0.923440i	0.204982	+	0.978766i	$0.434286\pi$
$132$	0.0983334	−	0.0259051i	0.00855882	−	0.00225475i
$133$	7.03460	+	9.16768i	0.609978	+	0.794938i
$134$	−1.28906	−	1.28560i	−0.111358	−	0.111059i
$135$	5.84390	−	20.1346i	0.502963	−	1.73291i
$136$	7.62011	−	18.6081i	0.653419	−	1.59563i
$137$	10.5790	−	2.83464i	0.903826	−	0.242180i	0.223168	−	0.974780i	$-0.428360\pi$
$137$	10.5790	−	2.83464i	0.903826	−	0.242180i	0.680659	+	0.732601i	$0.261694\pi$
$138$	3.49745	−	5.98084i	0.297723	−	0.509123i
$139$	−6.82369	+	0.898356i	−0.578778	+	0.0761976i	−0.414231	−	0.910172i	$-0.635950\pi$
$139$	−6.82369	+	0.898356i	−0.578778	+	0.0761976i	−0.164547	+	0.986369i	$0.552616\pi$
$140$	19.2389	−	2.58538i	1.62598	−	0.218505i
$141$	13.8802	+	10.8035i	1.16893	+	0.909819i
$142$	−8.79052	+	6.76396i	−0.737684	+	0.567619i
$143$		−	0.0196473i		−	0.00164299i
$144$	8.41353	+	8.55643i	0.701128	+	0.713036i
$145$		−	9.13870i		−	0.758927i
$146$	−2.33902	−	3.03982i	−0.193579	−	0.251577i
$147$	1.94721	−	0.790878i	0.160603	−	0.0652305i
$148$	8.58076	−	11.2450i	0.705334	−	0.924334i
$149$	−7.96237	+	1.04827i	−0.652303	+	0.0858773i	−0.449413	−	0.893324i	$-0.648367\pi$
$149$	−7.96237	+	1.04827i	−0.652303	+	0.0858773i	−0.202890	+	0.979202i	$0.565033\pi$
$150$	0.153393	−	27.6293i	0.0125245	−	2.25592i
$151$	9.11039	−	2.44112i	0.741393	−	0.198656i	0.131696	−	0.991290i	$-0.457958\pi$
$151$	9.11039	−	2.44112i	0.741393	−	0.198656i	0.609697	+	0.792635i	$0.291291\pi$
$152$	0.0546908	+	13.5870i	0.00443601	+	1.10205i
$153$	20.5228	+	5.80349i	1.65917	+	0.469184i
$154$	−0.0705194	+	0.0707089i	−0.00568262	+	0.00569789i
$155$	2.64706	+	3.44972i	0.212617	+	0.277088i
$156$	2.01277	−	1.15080i	0.161150	−	0.0921378i
$157$	−13.4602	−	10.3284i	−1.07424	−	0.824297i	−0.0890998	−	0.996023i	$-0.528399\pi$
$157$	−13.4602	−	10.3284i	−1.07424	−	0.824297i	−0.985145	+	0.171726i	$0.945066\pi$
$158$	−9.31398	−	7.12704i	−0.740981	−	0.566996i
$159$	−0.827533	+	1.41078i	−0.0656276	+	0.111882i
$160$	19.8426	+	11.2793i	1.56870	+	0.891710i
$161$			6.80406i			0.536235i
$162$	−8.01046	+	9.89103i	−0.629361	+	0.777113i
$163$	−4.20303	−	10.1470i	−0.329207	−	0.794776i	−0.998652	−	0.0519141i	$-0.983468\pi$
$163$	−4.20303	−	10.1470i	−0.329207	−	0.794776i	0.669445	−	0.742862i	$-0.266532\pi$
$164$	−10.7211	+	18.6852i	−0.837181	+	1.45907i
$165$	0.123761	+	0.163611i	0.00963477	+	0.0127371i
$166$	5.36531	−	20.1316i	0.416429	−	1.56252i
$167$	−0.287986	+	1.07478i	−0.0222850	+	0.0831689i	−0.976173	−	0.216995i	$-0.930375\pi$
$167$	−0.287986	+	1.07478i	−0.0222850	+	0.0831689i	0.953888	+	0.300164i	$0.0970413\pi$
$168$	−11.3743	−	3.08273i	−0.877547	−	0.237838i
$169$	3.24871	+	12.1243i	0.249900	+	0.932641i
$170$	40.5658	−	0.0544287i	3.11125	−	0.00417449i
$171$	−14.3126	+	1.68389i	−1.09451	+	0.128770i
$172$	−7.10925	−	17.0338i	−0.542075	−	1.29882i
$173$	−1.14014	+	8.66025i	−0.0866836	+	0.658427i	0.891849	+	0.452334i	$0.149408\pi$
$173$	−1.14014	+	8.66025i	−0.0866836	+	0.658427i	−0.978532	+	0.206093i	$0.933925\pi$
$174$	−2.15155	+	5.11381i	−0.163108	+	0.387677i
$175$	13.5669	+	23.4986i	1.02556	+	1.77633i
$176$	−0.116331	+	0.0159509i	−0.00876879	+	0.00120235i
$177$	−1.90526	−	0.0131341i	−0.143208	−	0.000987220i
$178$	−5.63312	−	7.32087i	−0.422220	−	0.548722i
$179$	1.03794	+	2.50582i	0.0775795	+	0.187293i	0.957911	−	0.287066i	$-0.0926798\pi$
$179$	1.03794	+	2.50582i	0.0775795	+	0.187293i	−0.880331	+	0.474359i	$0.842680\pi$
$180$	−9.51212	+	22.2619i	−0.708992	+	1.65930i
$181$	8.80197	+	3.64590i	0.654245	+	0.270997i	0.685015	−	0.728529i	$-0.259796\pi$
$181$	8.80197	+	3.64590i	0.654245	+	0.270997i	−0.0307694	+	0.999527i	$0.509796\pi$
$182$	−1.13581	+	1.97340i	−0.0841922	+	0.146278i
$183$	1.59686	−	5.79935i	0.118043	−	0.428700i
$184$	−4.84464	+	6.36655i	−0.357151	+	0.469348i
$185$	27.5638	+	7.38571i	2.02653	+	0.543008i
$186$	−0.669060	−	2.55359i	−0.0490578	−	0.187238i
$187$	−0.165565	+	0.127043i	−0.0121073	+	0.00929027i
$188$	−14.3999	−	14.3228i	−1.05022	−	1.04460i
$189$	1.88743	−	12.3562i	0.137290	−	0.898781i
$190$	−25.3101	+	10.5236i	−1.83619	+	0.763462i
$191$	0.999615	−	1.73138i	0.0723296	−	0.125279i	−0.827592	−	0.561330i	$-0.810290\pi$
$191$	0.999615	−	1.73138i	0.0723296	−	0.125279i	0.899922	+	0.436051i	$0.143623\pi$
$192$	−8.44796	−	10.9833i	−0.609679	−	0.792649i
$193$	0.229439	+	0.397400i	0.0165154	+	0.0286055i	0.874165	−	0.485629i	$-0.161409\pi$
$193$	0.229439	+	0.397400i	0.0165154	+	0.0286055i	−0.857650	+	0.514235i	$0.828076\pi$
$194$	15.0444	+	11.5119i	1.08012	+	0.826508i
$195$	3.69113	+	2.87295i	0.264328	+	0.205736i
$196$	−2.34244	+	0.634396i	−0.167317	+	0.0453140i
$197$	−18.5148	−	7.66907i	−1.31912	−	0.546399i	−0.391590	−	0.920140i	$-0.628075\pi$
$197$	−18.5148	−	7.66907i	−1.31912	−	0.546399i	−0.927533	+	0.373741i	$0.878075\pi$
$198$	−0.0307343	−	0.120691i	−0.00218419	−	0.00857710i
$199$	−2.98114	+	2.98114i	−0.211327	+	0.211327i	−0.804831	−	0.593504i	$-0.797744\pi$
$199$	−2.98114	+	2.98114i	−0.211327	+	0.211327i	0.593504	+	0.804831i	$0.297744\pi$
$200$	−4.03696	+	31.6476i	−0.285456	+	2.23782i
$201$	−1.58749	+	1.56575i	−0.111973	+	0.110439i
$202$	4.38940	+	7.57916i	0.308837	+	0.533268i
$203$	−0.711163	−	5.40182i	−0.0499138	−	0.379133i
$204$	−22.7125	−	9.52006i	−1.59019	−	0.666537i
$205$	−43.0882	−	5.67267i	−3.00941	−	0.396197i
$206$	−2.24517	+	5.44097i	−0.156429	+	0.379090i
$207$	−7.28948	−	4.34366i	−0.506654	−	0.301906i
$208$	−2.46788	+	1.03778i	−0.171117	+	0.0719573i
$209$	0.0705070	−	0.122122i	0.00487707	−	0.00844733i
$210$	−2.97228	−	23.5880i	−0.205107	−	1.62772i
$211$	7.86561	+	6.03550i	0.541491	+	0.415501i	0.842961	−	0.537975i	$-0.180811\pi$
$211$	7.86561	+	6.03550i	0.541491	+	0.415501i	−0.301470	+	0.953476i	$0.597477\pi$
$212$	1.14568	−	1.50141i	0.0786858	−	0.103117i
$213$	8.19518	+	10.8340i	0.561525	+	0.742333i
$214$	11.7048	−	20.3362i	0.800121	−	1.39015i
$215$	26.3306	−	26.3306i	1.79573	−	1.79573i
$216$	10.5639	−	10.2178i	0.718785	−	0.695232i
$217$	1.83311	+	1.83311i	0.124440	+	0.124440i
$218$	0.980659	−	0.264178i	0.0664186	−	0.0178924i
$219$	−3.74647	+	2.83395i	−0.253163	+	0.191500i
$220$	−0.118992	−	0.204829i	−0.00802243	−	0.0138095i
$221$	−2.89661	+	3.77494i	−0.194847	+	0.253930i
$222$	−13.6853	−	10.6223i	−0.918494	−	0.712922i
$223$	−6.73338	−	3.88752i	−0.450900	−	0.260327i	0.257310	−	0.966329i	$-0.417164\pi$
$223$	−6.73338	−	3.88752i	−0.450900	−	0.260327i	−0.708210	+	0.706001i	$0.750497\pi$
$224$	12.6066	+	5.12300i	0.842312	+	0.342295i
$225$	−33.8361	−	0.466529i	−2.25574	−	0.0311019i
$226$	−0.432641	+	0.179886i	−0.0287789	+	0.0119659i
$227$	2.78400	−	21.1466i	0.184781	−	1.40355i	−0.607950	−	0.793976i	$-0.708008\pi$
$227$	2.78400	−	21.1466i	0.184781	−	1.40355i	0.792730	−	0.609573i	$-0.208659\pi$
$228$	16.6406	+	0.0700578i	1.10205	+	0.00463969i
$229$	−24.1239	+	3.17597i	−1.59415	+	0.209874i	−0.874699	−	0.484667i	$-0.838941\pi$
$229$	−24.1239	+	3.17597i	−1.59415	+	0.209874i	−0.719453	+	0.694541i	$0.755607\pi$
$230$	−15.5954	−	4.15635i	−1.02833	−	0.274061i
$231$	0.0858862	+	0.0870785i	0.00565090	+	0.00572935i
$232$	3.18078	−	5.56084i	0.208828	−	0.365087i
$233$	−14.1779	−	14.1779i	−0.928826	−	0.928826i	0.0688041	−	0.997630i	$-0.478082\pi$
$233$	−14.1779	−	14.1779i	−0.928826	−	0.928826i	−0.997630	+	0.0688041i	$0.978082\pi$
$234$	−1.38909	−	2.47665i	−0.0908076	−	0.161904i
$235$	15.6800	−	37.8549i	1.02285	−	2.46938i
$236$	2.18199	+	0.281310i	0.142036	+	0.0183117i
$237$	−8.82244	+	11.3350i	−0.573079	+	0.736286i
$238$	23.9739	−	3.18896i	1.55400	−	0.206709i
$239$	−13.7410	+	7.93337i	−0.888831	+	0.513167i	−0.873560	−	0.486717i	$-0.838194\pi$
$239$	−13.7410	+	7.93337i	−0.888831	+	0.513167i	−0.0152710	+	0.999883i	$0.504861\pi$
$240$	14.0140	−	24.1876i	0.904598	−	1.56130i
$241$	12.1765	+	7.03013i	0.784360	+	0.452850i	0.837973	−	0.545711i	$-0.183740\pi$
$241$	12.1765	+	7.03013i	0.784360	+	0.452850i	−0.0536132	+	0.998562i	$0.517074\pi$
$242$	−14.3790	−	5.93340i	−0.924320	−	0.381414i
$243$	12.0328	+	9.91020i	0.771904	+	0.635739i
$244$	−2.64079	+	6.42413i	−0.169059	+	0.411263i
$245$	−2.98043	−	3.88418i	−0.190413	−	0.248151i
$246$	22.7757	+	13.3187i	1.45212	+	0.849168i
$247$	0.832146	−	3.10561i	0.0529482	−	0.197605i
$248$	0.410026	+	3.02046i	0.0260367	+	0.191799i
$249$	−24.6012	−	6.77396i	−1.55903	−	0.429282i
$250$	−34.5996	+	9.32070i	−2.18827	+	0.589493i
$251$	−6.65731	+	16.0722i	−0.420205	+	1.01447i	0.562081	+	0.827082i	$0.310001\pi$
$251$	−6.65731	+	16.0722i	−0.420205	+	1.01447i	−0.982287	+	0.187384i	$0.939999\pi$
$252$	−3.89015	+	13.8991i	−0.245057	+	0.875559i
$253$	0.0767102	−	0.0317744i	0.00482273	−	0.00199764i
$254$	−5.85267	−	0.762531i	−0.367229	−	0.0478455i
$255$	0.342486	−	49.6816i	0.0214473	−	3.11118i
$256$	8.14827	+	13.7697i	0.509267	+	0.860609i
$257$	0.923715	−	0.533307i	0.0576198	−	0.0332668i	−0.470913	−	0.882179i	$-0.656076\pi$
$257$	0.923715	−	0.533307i	0.0576198	−	0.0332668i	0.528533	+	0.848913i	$0.322742\pi$
$258$	−20.9331	+	8.53492i	−1.30324	+	0.531361i
$259$	16.8675	+	2.22065i	1.04810	+	0.137985i
$260$	−3.82934	−	3.80884i	−0.237485	−	0.236214i
$261$	6.24120	+	2.68659i	0.386320	+	0.166295i
$262$	−17.3386	+	17.3852i	−1.07118	+	1.07406i
$263$	−19.5849	+	5.24775i	−1.20765	+	0.323590i	−0.805841	−	0.592132i	$-0.798287\pi$
$263$	−19.5849	+	5.24775i	−1.20765	+	0.323590i	−0.401813	+	0.915722i	$0.631620\pi$
$264$	0.0183618	+	0.142632i	0.00113009	+	0.00877840i
$265$	3.68026	+	0.986122i	0.226076	+	0.0605770i
$266$	−14.1417	+	8.19003i	−0.867082	+	0.502163i
$267$	−9.02271	+	6.82507i	−0.552181	+	0.417687i
$268$	2.03841	−	1.57283i	0.124515	−	0.0960761i
$269$	23.0590	−	9.55137i	1.40593	−	0.582357i	0.454650	−	0.890670i	$-0.349764\pi$
$269$	23.0590	−	9.55137i	1.40593	−	0.582357i	0.951285	+	0.308313i	$0.0997644\pi$
$270$	27.1683	+	11.8741i	1.65341	+	0.722632i
$271$	−7.36251			−0.447241			−0.223620	−	0.974676i	$-0.571788\pi$
$271$	−7.36251			−0.447241			−0.223620	+	0.974676i	$0.571788\pi$
$272$	24.7030	+	14.0860i	1.49784	+	0.854092i
$273$	2.40537	+	1.41094i	0.145580	+	0.0853939i
$274$	2.04229	+	15.3535i	0.123379	+	0.927540i
$275$	0.201571	−	0.262693i	0.0121552	−	0.0158410i
$276$	7.74827	+	5.99745i	0.466391	+	0.361004i
$277$	0.00203659	−	0.00156273i	0.000122367	−	9.38952e-5i	−0.608700	−	0.793400i	$-0.708309\pi$
$277$	0.00203659	−	0.00156273i	0.000122367	−	9.38952e-5i	0.608823	+	0.793306i	$0.291642\pi$
$278$	−0.0130597	−	9.73342i	−0.000783269	−	0.583772i
$279$	−3.13414	+	0.793644i	−0.187636	+	0.0475142i
$280$	0.110502	+	27.4522i	0.00660373	+	1.64058i
$281$	−4.85492	−	18.1188i	−0.289620	−	1.08088i	−0.945397	−	0.325922i	$-0.894325\pi$
$281$	−4.85492	−	18.1188i	−0.289620	−	1.08088i	0.655777	−	0.754955i	$-0.272341\pi$
$282$	−17.6865	+	17.4912i	−1.05321	+	1.04158i
$283$	−0.647987	−	4.92195i	−0.0385189	−	0.292580i	−0.999852	−	0.0171924i	$-0.994527\pi$
$283$	−0.647987	−	4.92195i	−0.0385189	−	0.292580i	0.961333	−	0.275387i	$-0.0888061\pi$
$284$	−7.87939	−	13.5633i	−0.467556	−	0.804835i
$285$	12.6330	+	31.1035i	0.748315	+	1.84241i
$286$	0.0275526	+	0.00358977i	0.00162922	+	0.000212267i
$287$	−25.9106			−1.52945
$288$	−13.5364	+	10.2355i	−0.797642	+	0.603131i
$289$	33.5408			1.97299
$290$	12.8158	+	1.66974i	0.752567	+	0.0980503i
$291$	14.2504	−	18.3088i	0.835375	−	1.07328i
$292$	4.69029	−	2.72475i	0.274478	−	0.159454i
$293$	2.99462	+	22.7464i	0.174948	+	1.32886i	0.823338	+	0.567551i	$0.192109\pi$
$293$	2.99462	+	22.7464i	0.174948	+	1.32886i	−0.648390	+	0.761308i	$0.724558\pi$
$294$	0.753321	+	2.87519i	0.0439346	+	0.167684i
$295$	1.14874	+	4.28717i	0.0668825	+	0.249609i
$296$	14.2018	+	14.0879i	0.825461	+	0.818843i
$297$	−0.148120	+	0.0364232i	−0.00859480	+	0.00211349i
$298$	−0.0152390	−	11.3576i	−0.000882771	−	0.657931i
$299$	1.50191	−	1.15246i	0.0868580	−	0.0666485i
$300$	38.7182	+	5.26327i	2.23540	+	0.303875i
$301$	13.5148	−	17.6128i	0.778980	−	1.01519i
$302$	1.75877	+	13.2221i	0.101206	+	0.760845i
$303$	9.32649	−	5.29927i	0.535793	−	0.304435i
$304$	−19.0638	−	2.40579i	−1.09339	−	0.137981i
$305$	−14.0124			−0.802347
$306$	−11.8883	+	27.7201i	−0.679610	+	1.58465i
$307$	12.7843	−	5.29544i	0.729640	−	0.302227i	0.0132358	−	0.999912i	$-0.495787\pi$
$307$	12.7843	−	5.29544i	0.729640	−	0.302227i	0.716404	+	0.697686i	$0.245787\pi$
$308$	−0.0862748	−	0.111813i	−0.00491596	−	0.00637113i
$309$	6.64092	+	2.80455i	0.377789	+	0.159545i
$310$	−5.32140	+	3.08184i	−0.302235	+	0.175037i
$311$	14.1064	+	3.77980i	0.799900	+	0.214333i	0.635540	−	0.772068i	$-0.280777\pi$
$311$	14.1064	+	3.77980i	0.799900	+	0.214333i	0.164360	+	0.986400i	$0.447444\pi$
$312$	1.24608	+	3.03289i	0.0705457	+	0.171704i
$313$	4.08906	−	1.09566i	0.231128	−	0.0619305i	−0.141396	−	0.989953i	$-0.545159\pi$
$313$	4.08906	−	1.09566i	0.231128	−	0.0619305i	0.372524	+	0.928023i	$0.378492\pi$
$314$	16.9435	−	16.9890i	0.956176	−	0.958746i
$315$	−28.9182	+	3.40226i	−1.62936	+	0.191696i
$316$	11.6964	−	11.7594i	0.657976	−	0.661517i
$317$	8.88400	+	1.16960i	0.498975	+	0.0656913i	0.375813	−	0.926695i	$-0.377363\pi$
$317$	8.88400	+	1.16960i	0.498975	+	0.0656913i	0.123162	+	0.992387i	$0.460697\pi$
$318$	−1.82722	−	1.41826i	−0.102466	−	0.0795323i
$319$	−0.0575800	+	0.0332438i	−0.00322386	+	0.00186130i
$320$	−19.4432	+	25.7657i	−1.08691	+	1.44034i
$321$	−24.7878	−	14.5400i	−1.38352	−	0.811542i
$322$	−9.54175	−	1.24317i	−0.531741	−	0.0692793i
$323$	−31.5513	+	13.0690i	−1.75556	+	0.727178i
$324$	−12.4072	−	13.0408i	−0.689289	−	0.724486i
$325$	2.88910	−	6.97490i	0.160258	−	0.386898i
$326$	14.9977	−	4.04020i	0.830647	−	0.223766i
$327$	−0.313648	−	1.20368i	−0.0173448	−	0.0665637i
$328$	−24.2445	−	18.4489i	−1.33868	−	1.01867i
$329$	6.32252	−	23.5960i	0.348572	−	1.30089i
$330$	−0.252055	+	0.143664i	−0.0138751	+	0.00790844i
$331$	−3.25661	−	4.24410i	−0.178999	−	0.233277i	0.695233	−	0.718785i	$-0.255301\pi$
$331$	−3.25661	−	4.24410i	−0.178999	−	0.233277i	−0.874232	+	0.485508i	$0.838635\pi$
$332$	27.2515	+	11.2024i	1.49562	+	0.614810i
$333$	−13.1472	+	16.6532i	−0.720462	+	0.912592i
$334$	−1.45461	−	0.600234i	−0.0795928	−	0.0328434i
$335$	4.49827	+	2.59708i	0.245767	+	0.141894i
$336$	6.40131	−	15.3876i	0.349220	−	0.839465i
$337$	0.951714	−	0.549472i	0.0518432	−	0.0299317i	−0.473854	−	0.880603i	$-0.657138\pi$
$337$	0.951714	−	0.549472i	0.0518432	−	0.0299317i	0.525698	+	0.850672i	$0.323804\pi$
$338$	−17.5963	+	2.34062i	−0.957111	+	0.127313i
$339$	0.215944	+	0.531672i	0.0117285	+	0.0288764i
$340$	−7.33547	+	56.8978i	−0.397822	+	3.08572i
$341$	0.0121063	−	0.0292273i	0.000655596	−	0.00158275i
$342$	0.253636	−	20.3790i	0.0137151	−	1.10197i
$343$	−13.9708	−	13.9708i	−0.754350	−	0.754350i
$344$	25.1865	−	6.85748i	1.35797	−	0.369731i
$345$	−5.24758	+	19.0578i	−0.282520	+	1.02604i
$346$	−11.9365	−	3.18121i	−0.641710	−	0.171023i
$347$	−17.0755	+	2.24803i	−0.916662	+	0.120681i	−0.574073	−	0.818804i	$-0.694637\pi$
$347$	−17.0755	+	2.24803i	−0.916662	+	0.120681i	−0.342589	+	0.939485i	$0.611304\pi$
$348$	−6.77830	−	3.95159i	−0.363355	−	0.211828i
$349$	1.41485	−	10.7469i	0.0757352	−	0.575266i	−0.910937	−	0.412545i	$-0.864640\pi$
$349$	1.41485	−	10.7469i	0.0757352	−	0.575266i	0.986672	−	0.162720i	$-0.0520269\pi$
$350$	−35.4324	+	14.7323i	−1.89394	+	0.787475i
$351$	−3.04717	+	1.67624i	−0.162646	+	0.0894712i
$352$	−0.00111401	−	0.166053i	−5.93771e−5	−	0.00885064i
$353$	9.62174	+	5.55512i	0.512114	+	0.295669i	0.733702	−	0.679471i	$-0.237791\pi$
$353$	9.62174	+	5.55512i	0.512114	+	0.295669i	−0.221588	+	0.975140i	$0.571124\pi$
$354$	0.366529	−	2.66946i	0.0194808	−	0.141880i
$355$	19.2642	−	25.1056i	1.02244	−	1.33247i
$356$	11.2957	−	6.56207i	0.598673	−	0.347789i
$357$	−3.66372	−	29.3931i	−0.193905	−	1.55565i
$358$	−3.70370	+	0.997732i	−0.195747	+	0.0527318i
$359$	4.94376	+	4.94376i	0.260922	+	0.260922i	0.825429	−	0.564507i	$-0.190934\pi$
$359$	4.94376	+	4.94376i	0.260922	+	0.260922i	−0.564507	+	0.825429i	$0.690934\pi$
$360$	−29.4812	−	17.4069i	−1.55380	−	0.917425i
$361$	2.88224	−	2.88224i	0.151697	−	0.151697i
$362$	−6.72107	+	11.6774i	−0.353252	+	0.613750i
$363$	−7.41169	+	17.5502i	−0.389013	+	0.921147i
$364$	−2.55989	−	1.95338i	−0.134175	−	0.102385i
$365$	8.68170	+	6.66170i	0.454421	+	0.348689i
$366$	7.84102	+	3.29897i	0.409856	+	0.172440i
$367$	17.2455	−	29.8701i	0.900210	−	1.55921i	0.0729879	−	0.997333i	$-0.476747\pi$
$367$	17.2455	−	29.8701i	0.900210	−	1.55921i	0.827222	−	0.561876i	$-0.189920\pi$
$368$	−8.04304	−	7.95716i	−0.419272	−	0.414796i
$369$	16.5411	−	27.7591i	0.861098	−	1.44508i
$370$	−15.3936	+	37.3050i	−0.800277	+	1.93939i
$371$	2.25211	+	0.296496i	0.116924	+	0.0153933i
$372$	3.70330	−	0.471696i	0.192007	−	0.0244563i
$373$	−0.291241	−	2.21220i	−0.0150799	−	0.114543i	0.982249	−	0.187580i	$-0.0600643\pi$
$373$	−0.291241	−	2.21220i	−0.0150799	−	0.114543i	−0.997329	+	0.0730367i	$0.976731\pi$
$374$	−0.147909	−	0.255394i	−0.00764820	−	0.0132061i
$375$	11.0661	+	42.4682i	0.571452	+	2.19305i
$376$	22.7168	−	17.5770i	1.17153	−	0.906463i
$377$	−1.07193	+	1.07193i	−0.0552073	+	0.0552073i
$378$	16.9830	+	4.90447i	0.873511	+	0.252259i
$379$	−9.65470	−	3.99911i	−0.495928	−	0.205420i	0.120678	−	0.992692i	$-0.461493\pi$
$379$	−9.65470	−	3.99911i	−0.495928	−	0.205420i	−0.616607	+	0.787271i	$0.711493\pi$
$380$	−10.1335	−	37.4167i	−0.519836	−	1.91944i
$381$	−0.992905	+	7.16010i	−0.0508680	+	0.366823i
$382$	2.24538	+	1.71816i	0.114884	+	0.0879089i
$383$	−16.3573	−	28.3316i	−0.835817	−	1.44768i	−0.893364	−	0.449334i	$-0.851661\pi$
$383$	−16.3573	−	28.3316i	−0.835817	−	1.44768i	0.0575467	−	0.998343i	$-0.481672\pi$
$384$	16.9460	−	9.84033i	0.864773	−	0.502162i
$385$	0.142458	−	0.246744i	0.00726033	−	0.0125753i
$386$	−0.599219	+	0.249147i	−0.0304995	+	0.0126813i
$387$	10.2416	+	25.7229i	0.520611	+	1.30757i
$388$	−18.8926	+	18.9943i	−0.959129	+	0.964290i
$389$	17.5400	−	13.4589i	0.889311	−	0.682392i	−0.0595030	−	0.998228i	$-0.518952\pi$
$389$	17.5400	−	13.4589i	0.889311	−	0.682392i	0.948814	+	0.315836i	$0.102285\pi$
$390$	−4.70332	+	4.65138i	−0.238162	+	0.235532i
$391$	−19.4232	−	5.20444i	−0.982275	−	0.263200i
$392$	−0.461665	−	3.40085i	−0.0233176	−	0.171769i
$393$	21.1168	+	21.4100i	1.06520	+	1.07999i
$394$	14.1377	−	24.5632i	0.712245	−	1.23748i
$395$	30.9134	+	12.8048i	1.55542	+	0.644277i
$396$	0.174867	−	0.0210492i	0.00878741	−	0.00105776i
$397$	9.34212	+	22.5539i	0.468867	+	1.13195i	0.964658	+	0.263504i	$0.0848783\pi$
$397$	9.34212	+	22.5539i	0.468867	+	1.13195i	−0.495791	+	0.868442i	$0.665122\pi$
$398$	−3.63594	−	4.72531i	−0.182253	−	0.236859i
$399$	9.88772	+	17.4020i	0.495005	+	0.871188i
$400$	−43.6438	−	11.4436i	−2.18219	−	0.572181i
$401$	−5.01523	−	8.68663i	−0.250448	−	0.433789i	0.713201	−	0.700960i	$-0.247245\pi$
$401$	−5.01523	−	8.68663i	−0.250448	−	0.433789i	−0.963649	+	0.267170i	$0.913911\pi$
$402$	−1.90569	−	2.51231i	−0.0950474	−	0.125302i
$403$	0.0941482	−	0.715127i	0.00468986	−	0.0356230i
$404$	−11.4307	+	4.77073i	−0.568699	+	0.237353i
$405$	14.8162	−	33.1533i	0.736224	−	1.64740i
$406$	7.70524	−	0.0103384i	0.382404	−	0.000513087i
$407$	−0.0537339	−	0.200538i	−0.00266349	−	0.00994029i
$408$	17.5004	−	30.1117i	0.866398	−	1.49075i
$409$	−5.61115	+	20.9411i	−0.277454	+	1.03547i	0.676725	+	0.736235i	$0.263398\pi$
$409$	−5.61115	+	20.9411i	−0.277454	+	1.03547i	−0.954179	+	0.299236i	$0.903268\pi$
$410$	15.8278	−	59.3888i	0.781680	−	2.93300i
$411$	18.8241	−	2.34634i	0.928525	−	0.115737i
$412$	−7.21998	−	4.14267i	−0.355703	−	0.204094i
$413$	1.01264	+	2.44472i	0.0498286	+	0.120297i
$414$	7.42325	−	9.42884i	0.364833	−	0.463402i
$415$			59.4413i			2.91786i
$416$	−1.00444	−	3.65048i	−0.0492466	−	0.178979i
$417$	−11.9207	−	0.0821767i	−0.583759	−	0.00402421i
$418$	0.158376	+	0.121189i	0.00774644	+	0.00592756i
$419$	0.0449277	+	0.0344742i	0.00219486	+	0.00168418i	0.609858	−	0.792510i	$-0.291226\pi$
$419$	0.0449277	+	0.0344742i	0.00219486	+	0.00168418i	−0.607663	+	0.794195i	$0.707893\pi$
$420$	33.6219	+	0.141550i	1.64058	+	0.00690695i
$421$	1.94585	+	2.53588i	0.0948348	+	0.123591i	0.838360	−	0.545116i	$-0.183515\pi$
$421$	1.94585	+	2.53588i	0.0948348	+	0.123591i	−0.743526	+	0.668707i	$0.766848\pi$
$422$	−9.90107	+	9.92768i	−0.481977	+	0.483272i
$423$	21.2431	+	21.8371i	1.03288	+	1.06176i
$424$	1.89619	+	1.88098i	0.0920870	+	0.0913486i
$425$	−77.4579	+	20.7548i	−3.75726	+	1.00675i
$426$	−16.6905	+	9.51312i	−0.808658	+	0.460912i
$427$	−8.28262	+	1.09043i	−0.400824	+	0.0527695i
$428$	26.3801	+	20.1299i	1.27513	+	0.973017i
$429$	0.00467429	−	0.0337076i	0.000225677	−	0.00162742i
$430$	32.1141	+	41.7359i	1.54868	+	2.01268i
$431$		−	12.7755i		−	0.615376i	−0.951487	−	0.307688i	$-0.900445\pi$
$431$		−	12.7755i		−	0.615376i	0.951487	−	0.307688i	$-0.0995552\pi$
$432$	12.3989	+	16.6814i	0.596541	+	0.802582i
$433$			33.4527i			1.60763i	0.594877	+	0.803817i	$0.297201\pi$
$433$			33.4527i			1.60763i	−0.594877	+	0.803817i	$0.702799\pi$
$434$	−2.90561	+	2.23576i	−0.139474	+	0.107320i
$435$	2.17419	−	15.6787i	0.104244	−	0.751734i
$436$	0.191296	+	1.42351i	0.00916140	+	0.0681736i
$437$	13.4712	−	1.77352i	0.644415	−	0.0848389i
$438$	−3.28970	−	5.77169i	−0.157188	−	0.275782i
$439$	−33.2794	+	8.91720i	−1.58834	+	0.425595i	−0.941495	−	0.337026i	$-0.890579\pi$
$439$	−33.2794	+	8.91720i	−1.58834	+	0.425595i	−0.646846	+	0.762621i	$0.723912\pi$
$440$	0.308985	−	0.129445i	0.0147303	−	0.00617106i
$441$	3.52885	−	0.893596i	0.168040	−	0.0425522i
$442$	−4.76458	−	4.75182i	−0.226628	−	0.226021i
$443$	−9.93145	−	12.9429i	−0.471857	−	0.614936i	0.495421	−	0.868653i	$-0.335014\pi$
$443$	−9.93145	−	12.9429i	−0.471857	−	0.614936i	−0.967279	+	0.253716i	$0.918347\pi$
$444$	17.3967	−	17.2509i	0.825613	−	0.818690i
$445$	20.9083	+	16.0435i	0.991151	+	0.760537i
$446$	6.68196	−	8.73234i	0.316400	−	0.413488i
$447$	−13.9099	−	0.0958896i	−0.657916	−	0.00453542i
$448$	−9.48765	+	16.7429i	−0.448249	+	0.791030i
$449$		−	18.4415i		−	0.870309i	−0.900356	−	0.435154i	$-0.856694\pi$
$449$		−	18.4415i		−	0.870309i	0.900356	−	0.435154i	$-0.143306\pi$
$450$	6.83646	−	47.3652i	0.322274	−	2.23282i
$451$	0.121000	+	0.292121i	0.00569768	+	0.0137554i
$452$	−0.173218	−	0.639586i	−0.00814747	−	0.0300836i
$453$	16.2109	−	2.02061i	0.761652	−	0.0949367i
$454$	29.1465	+	7.76788i	1.36791	+	0.364565i
$455$	1.68133	−	6.27482i	0.0788221	−	0.294168i
$456$	−3.13865	+	23.3233i	−0.146981	+	1.09221i
$457$	−5.68341	−	21.2108i	−0.265859	−	0.992198i	−0.961723	−	0.274025i	$-0.911645\pi$
$457$	−5.68341	−	21.2108i	−0.265859	−	0.992198i	0.695864	−	0.718174i	$-0.255022\pi$
$458$	−0.0461701	−	34.4107i	−0.00215739	−	1.60791i
$459$	33.8290	+	14.8393i	1.57900	+	0.692637i
$460$	8.67813	−	21.1109i	0.404620	−	0.984302i
$461$	5.35925	−	40.7075i	0.249605	−	1.89594i	−0.165572	−	0.986198i	$-0.552947\pi$
$461$	5.35925	−	40.7075i	0.249605	−	1.89594i	0.415177	−	0.909741i	$-0.363720\pi$
$462$	−0.137808	+	0.104533i	−0.00641140	+	0.00486333i
$463$	2.55376	+	4.42324i	0.118683	+	0.205566i	0.919246	−	0.393683i	$-0.128799\pi$
$463$	2.55376	+	4.42324i	0.118683	+	0.205566i	−0.800563	+	0.599249i	$0.795466\pi$
$464$	7.21714	+	5.47662i	0.335047	+	0.254246i
$465$	3.72066	+	6.54821i	0.172542	+	0.303666i
$466$	22.4730	−	17.2921i	1.04104	−	0.801041i
$467$	−8.45429	−	20.4105i	−0.391218	−	0.944484i	−0.989675	−	0.143329i	$-0.954219\pi$
$467$	−8.45429	−	20.4105i	−0.391218	−	0.944484i	0.598457	−	0.801155i	$-0.295781\pi$
$468$	3.72696	−	1.49549i	0.172279	−	0.0691293i
$469$	2.86100	+	1.18506i	0.132109	+	0.0547212i
$470$	50.2214	+	28.9056i	2.31654	+	1.33331i
$471$	−20.6356	−	20.9221i	−0.950839	−	0.964039i
$472$	−0.793171	+	3.00854i	−0.0365087	+	0.138479i
$473$	−0.261683	−	0.0701178i	−0.0120322	−	0.00322402i
$474$	−14.2838	−	14.4433i	−0.656076	−	0.663402i
$475$	42.9881	−	32.9859i	1.97243	−	1.51350i
$476$	0.0917824	+	34.2027i	0.00420684	+	1.56768i
$477$	−1.75538	+	2.22350i	−0.0803734	+	0.101807i
$478$	−8.61482	−	20.7193i	−0.394033	−	0.947681i
$479$	−17.2770	+	29.9247i	−0.789407	+	1.36729i	0.136924	+	0.990582i	$0.456278\pi$
$479$	−17.2770	+	29.9247i	−0.789407	+	1.36729i	−0.926331	+	0.376711i	$0.877055\pi$
$480$	31.3592	+	24.0720i	1.43134	+	1.09873i
$481$	−2.36681	−	4.09944i	−0.107917	−	0.186918i
$482$	−12.0836	+	15.7914i	−0.550391	+	0.719280i
$483$	−1.61876	+	11.6733i	−0.0736559	+	0.531152i
$484$	10.9480	−	19.0805i	0.497635	−	0.867296i
$485$	−49.9328	−	20.6828i	−2.26733	−	0.939159i
$486$	−16.0962	+	15.0636i	−0.730138	+	0.683300i
$487$	9.54616	−	9.54616i	0.432578	−	0.432578i	−0.456927	−	0.889504i	$-0.651050\pi$
$487$	9.54616	−	9.54616i	0.432578	−	0.432578i	0.889504	+	0.456927i	$0.151050\pi$
$488$	−8.52645	−	4.87709i	−0.385974	−	0.220776i
$489$	−4.79679	−	18.4085i	−0.216918	−	0.832462i
$490$	5.99157	−	3.46996i	0.270672	−	0.156757i
$491$	−1.96330	−	14.9128i	−0.0886026	−	0.673004i	−0.976894	−	0.213724i	$-0.931441\pi$
$491$	−1.96330	−	14.9128i	−0.0886026	−	0.673004i	0.888292	−	0.459280i	$-0.151893\pi$
$492$	−22.8390	+	29.5063i	−1.02966	+	1.33024i
$493$	15.9643	+	2.10174i	0.718996	+	0.0946576i
$494$	4.20315	+	1.73440i	0.189108	+	0.0780342i
$495$	0.173403	+	0.310141i	0.00779391	+	0.0139398i
$496$	−4.31069	+	0.0231355i	−0.193555	+	0.00103881i
$497$	9.43326	−	16.3389i	0.423140	−	0.732899i
$498$	13.9944	−	33.2620i	0.627105	−	1.49051i
$499$	27.3534	+	20.9890i	1.22451	+	0.939598i	0.999397	−	0.0347347i	$-0.0110586\pi$
$499$	27.3534	+	20.9890i	1.22451	+	0.939598i	0.225112	+	0.974333i	$0.427725\pi$
$500$	−6.74929	−	50.2241i	−0.301837	−	2.24609i
$501$	−0.749780	+	1.77541i	−0.0334977	+	0.0793196i
$502$	−21.3226	−	12.2725i	−0.951675	−	0.547748i
$503$	8.40559	−	8.40559i	0.374787	−	0.374787i	−0.494431	−	0.869217i	$-0.664623\pi$
$503$	8.40559	−	8.40559i	0.374787	−	0.374787i	0.869217	+	0.494431i	$0.164623\pi$
$504$	−18.7807	−	7.99490i	−0.836560	−	0.356121i
$505$	−17.6694	−	17.6694i	−0.786277	−	0.786277i
$506$	0.0305434	+	0.113381i	0.00135782	+	0.00504039i
$507$	2.68908	+	21.5738i	0.119426	+	0.958127i
$508$	2.13869	−	8.06824i	0.0948890	−	0.357970i
$509$	−20.6777	+	26.9477i	−0.916524	+	1.19444i	0.0639831	+	0.997951i	$0.479620\pi$
$509$	−20.6777	+	26.9477i	−0.916524	+	1.19444i	−0.980507	+	0.196486i	$0.937047\pi$
$510$	69.6090	+	9.55764i	3.08234	+	0.423219i
$511$	5.65009	+	3.26208i	0.249945	+	0.144306i
$512$	−20.7989	+	8.91094i	−0.919191	+	0.393812i
$513$	−24.9557	−	0.516171i	−1.10182	−	0.0227895i
$514$	0.579117	+	1.39282i	0.0255437	+	0.0614348i
$515$	2.19193	−	16.6494i	0.0965880	−	0.733658i
$516$	−8.14435	−	30.9152i	−0.358535	−	1.36096i
$517$	−0.295551	+	0.0389100i	−0.0129983	+	0.00171126i
$518$	−6.19603	+	23.2486i	−0.272238	+	1.02149i
$519$	−4.01643	+	14.5866i	−0.176302	+	0.640279i
$520$	6.04103	−	4.67420i	0.264917	−	0.204977i
$521$	17.2744	+	17.2744i	0.756804	+	0.756804i	0.975739	−	0.218935i	$-0.0702584\pi$
$521$	17.2744	+	17.2744i	0.756804	+	0.756804i	−0.218935	+	0.975739i	$0.570258\pi$
$522$	−4.90789	+	8.26155i	−0.214813	+	0.361598i
$523$	−6.07147	+	14.6578i	−0.265487	+	0.640942i	−0.999260	−	0.0384519i	$-0.987757\pi$
$523$	−6.07147	+	14.6578i	−0.265487	+	0.640942i	0.733773	+	0.679394i	$0.237757\pi$
$524$	−21.2124	−	27.4914i	−0.926666	−	1.20097i
$525$	17.6853	+	43.5428i	0.771851	+	1.90036i
$526$	−3.78088	−	28.4239i	−0.164854	−	1.23934i
$527$	−6.63505	+	3.83075i	−0.289027	+	0.166870i
$528$	−0.203377		0.000310467i	−0.00885083		1.35113e-5i
$529$	−12.9900	−	7.49978i	−0.564783	−	0.326078i
$530$	−2.05532	+	4.98087i	−0.0892774	+	0.216355i
$531$	−3.26559	−	0.475813i	−0.141715	−	0.0206485i
$532$	−8.90154	−	21.3282i	−0.385931	−	0.924693i
$533$	4.38869	+	5.71945i	0.190095	+	0.247737i
$534$	−7.92266	−	13.9001i	−0.342847	−	0.601516i
$535$	−17.3264	+	64.6631i	−0.749086	+	2.79563i
$536$	1.83324	+	3.14595i	0.0791840	+	0.135885i
$537$	1.18457	+	4.54600i	0.0511180	+	0.196174i
$538$	9.18134	+	34.0822i	0.395836	+	1.46939i
$539$	−0.0136310	+	0.0329082i	−0.000587130	+	0.00141746i
$540$	−21.6156	+	35.9302i	−0.930189	+	1.54619i
$541$	−9.21880	+	3.81855i	−0.396347	+	0.164172i	−0.571949	−	0.820289i	$-0.693813\pi$
$541$	−9.21880	+	3.81855i	−0.396347	+	0.164172i	0.175602	+	0.984461i	$0.443813\pi$
$542$	1.34521	−	10.3249i	0.0577817	−	0.443493i
$543$	14.2336	+	8.34910i	0.610821	+	0.358294i
$544$	−24.2672	+	32.0688i	−1.04045	+	1.37494i
$545$	−2.50940	+	1.44881i	−0.107491	+	0.0620600i
$546$	−2.41813	+	3.11541i	−0.103487	+	0.133327i
$547$	−3.47812	−	0.457904i	−0.148714	−	0.0195785i	0.0558017	−	0.998442i	$-0.482229\pi$
$547$	−3.47812	−	0.457904i	−0.148714	−	0.0195785i	−0.204516	+	0.978863i	$0.565562\pi$
$548$	−21.9043	+	0.0587799i	−0.935707	+	0.00251095i
$549$	4.11935	−	9.56965i	0.175809	−	0.408422i
$550$	0.331561	+	0.330672i	0.0141378	+	0.0140999i
$551$	−10.5096	+	2.81603i	−0.447723	+	0.119967i
$552$	−9.82629	+	9.77008i	−0.418235	+	0.415842i
$553$	19.2691	+	5.16315i	0.819407	+	0.219559i
$554$	0.00181940	+	0.00314156i	7.72990e−5	+	0.000133472i
$555$	45.5323	+	19.2289i	1.93274	+	0.816221i
$556$	13.6522	+	1.76008i	0.578981	+	0.0746442i
$557$	−17.9461	+	7.43352i	−0.760401	+	0.314969i	−0.728978	−	0.684538i	$-0.760004\pi$
$557$	−17.9461	+	7.43352i	−0.760401	+	0.314969i	−0.0314237	+	0.999506i	$0.510004\pi$
$558$	−0.540336	−	4.54020i	−0.0228743	−	0.192202i
$559$	−6.17694			−0.261257
$560$	−38.5181	−	4.86084i	−1.62769	−	0.205408i
$561$	−0.314274	+	0.178569i	−0.0132686	+	0.00753918i
$562$	26.2961	−	3.49785i	1.10924	−	0.147548i
$563$	16.7996	−	21.8937i	0.708020	−	0.922710i	−0.291405	−	0.956600i	$-0.594123\pi$
$563$	16.7996	−	21.8937i	0.708020	−	0.922710i	0.999426	+	0.0338897i	$0.0107895\pi$
$564$	−21.2974	−	27.9987i	−0.896784	−	1.17896i
$565$	1.06055	−	0.813787i	0.0446176	−	0.0342363i
$566$	7.02075	−	0.00942001i	0.295104	−	0.000395953i
$567$	6.17781	−	20.7497i	0.259444	−	0.871404i
$568$	20.4603	−	8.57160i	0.858496	−	0.359656i
$569$	−9.18899	−	34.2938i	−0.385223	−	1.43767i	−0.837816	−	0.545953i	$-0.816168\pi$
$569$	−9.18899	−	34.2938i	−0.385223	−	1.43767i	0.452593	−	0.891717i	$-0.350499\pi$
$570$	−45.9265	+	12.0331i	−1.92365	+	0.504011i
$571$	1.33663	+	10.1527i	0.0559362	+	0.424877i	0.996386	+	0.0849441i	$0.0270712\pi$
$571$	1.33663	+	10.1527i	0.0559362	+	0.424877i	−0.940450	+	0.339933i	$0.889595\pi$
$572$	−0.0100683	+	0.0379828i	−0.000420977	+	0.00158814i
$573$	2.12689	−	2.73260i	0.0888520	−	0.114156i
$574$	4.73414	−	36.3360i	0.197599	−	1.51664i
$575$	31.9049			1.33053
$576$	−11.8806	−	20.8531i	−0.495024	−	0.868879i
$577$	−0.100738			−0.00419377			−0.00209688	−	0.999998i	$-0.500667\pi$
$577$	−0.100738			−0.00419377			−0.00209688	+	0.999998i	$0.500667\pi$
$578$	−6.12826	+	47.0364i	−0.254902	+	1.95645i
$579$	0.299088	+	0.736379i	0.0124297	+	0.0306029i
$580$	−4.68314	+	17.6672i	−0.194457	+	0.733592i
$581$	4.62566	+	35.1353i	0.191905	+	1.45766i
$582$	23.0718	+	23.3295i	0.956359	+	0.967037i
$583$	−0.00717443	−	0.0267753i	−0.000297134	−	0.00110892i
$584$	2.96411	+	7.07531i	0.122656	+	0.292779i
$585$	5.64913	+	5.80709i	0.233563	+	0.240093i
$586$	−32.4458	+	0.0435338i	−1.34032	+	0.00179837i
$587$	−9.23230	+	7.08419i	−0.381058	+	0.292396i	−0.781474	−	0.623937i	$-0.785532\pi$
$587$	−9.23230	+	7.08419i	−0.381058	+	0.292396i	0.400417	+	0.916333i	$0.368865\pi$
$588$	−4.16969	+	0.531101i	−0.171955	+	0.0219022i
$589$	3.15153	−	4.10715i	0.129856	−	0.169232i
$590$	−6.22205	+	0.827643i	−0.256158	+	0.0340735i
$591$	−29.9400	−	17.5622i	−1.23157	−	0.722411i
$592$	−22.3511	+	17.3420i	−0.918626	+	0.712752i
$593$	4.85470			0.199359			0.0996793	−	0.995020i	$-0.468218\pi$
$593$	4.85470			0.199359			0.0996793	+	0.995020i	$0.468218\pi$
$594$	−0.0240153	−	0.214373i	−0.000985361	−	0.00879582i
$595$	−63.7488	+	26.4056i	−2.61345	+	1.08252i
$596$	15.9303	+	2.05379i	0.652531	+	0.0841265i
$597$	−5.82378	+	4.40529i	−0.238351	+	0.180297i
$598$	1.34175	+	2.31679i	0.0548682	+	0.0947407i
$599$	42.5012	+	11.3882i	1.73655	+	0.465307i	0.981675	−	0.190561i	$-0.0610306\pi$
$599$	42.5012	+	11.3882i	1.73655	+	0.465307i	0.754876	+	0.655868i	$0.227697\pi$
$600$	−14.4552	+	53.3352i	−0.590132	+	2.17740i
$601$	−30.0522	+	8.05246i	−1.22586	+	0.328467i	−0.812964	−	0.582314i	$-0.802148\pi$
$601$	−30.0522	+	8.05246i	−1.22586	+	0.328467i	−0.412891	+	0.910781i	$0.635481\pi$
$602$	22.2303	+	22.1707i	0.906038	+	0.903610i
$603$	−3.09605	+	2.30857i	−0.126081	+	0.0940123i
$604$	−18.8635	+	0.0506198i	−0.767543	+	0.00205969i
$605$	43.9999	+	5.79269i	1.78885	+	0.235507i
$606$	5.72744	+	14.0473i	0.232661	+	0.570634i
$607$	−21.9441	+	12.6694i	−0.890683	+	0.514236i	−0.874166	−	0.485628i	$-0.838591\pi$
$607$	−21.9441	+	12.6694i	−0.890683	+	0.514236i	−0.0165172	+	0.999864i	$0.505258\pi$
$608$	6.85694	−	26.2948i	0.278086	−	1.06640i
$609$	0.0650533	−	9.43673i	0.00263609	−	0.382396i
$610$	2.56021	−	19.6504i	0.103660	−	0.795623i
$611$	−6.27943	+	2.60102i	−0.254039	+	0.105226i
$612$	−36.7014	−	21.7365i	−1.48357	−	0.878645i
$613$	−5.22440	+	12.6128i	−0.211012	+	0.509427i	−0.993579	−	0.113138i	$-0.963910\pi$
$613$	−5.22440	+	12.6128i	−0.211012	+	0.509427i	0.782568	+	0.622566i	$0.213910\pi$
$614$	5.09029	+	18.8958i	0.205427	+	0.762571i
$615$	−72.5741	−	19.9834i	−2.92647	−	0.805807i
$616$	0.172565	−	0.100559i	0.00695286	−	0.00405164i
$617$	−3.13322	+	11.6933i	−0.126139	+	0.470756i	−0.999878	−	0.0156389i	$-0.995022\pi$
$617$	−3.13322	+	11.6933i	−0.126139	+	0.470756i	0.873739	+	0.486395i	$0.161688\pi$
$618$	−5.14636	+	8.80055i	−0.207017	+	0.354010i
$619$	−17.5553	−	22.8785i	−0.705608	−	0.919566i	0.293733	−	0.955888i	$-0.405102\pi$
$619$	−17.5553	−	22.8785i	−0.705608	−	0.919566i	−0.999340	+	0.0363219i	$0.988436\pi$
$620$	−3.34957	−	8.02560i	−0.134522	−	0.322316i
$621$	−11.4727	−	9.18638i	−0.460382	−	0.368637i
$622$	−7.87803	+	19.0917i	−0.315880	+	0.765506i
$623$	13.6073	+	7.85616i	0.545163	+	0.314750i
$624$	−4.48088	+	1.19332i	−0.179379	+	0.0477710i
$625$	39.6939	−	22.9173i	1.58775	−	0.916690i
$626$	0.789398	+	5.93453i	0.0315507	+	0.237192i
$627$	0.150018	−	0.192742i	0.00599115	−	0.00769736i
$628$	20.7290	+	26.8650i	0.827177	+	1.07203i
$629$	−19.2412	+	46.4524i	−0.767197	+	1.85218i
$630$	0.512467	−	41.1754i	0.0204172	−	1.64047i
$631$	−5.44377	−	5.44377i	−0.216713	−	0.216713i	0.590399	−	0.807112i	$-0.298971\pi$
$631$	−5.44377	−	5.44377i	−0.216713	−	0.216713i	−0.807112	+	0.590399i	$0.798971\pi$
$632$	14.3538	+	18.5512i	0.570965	+	0.737927i
$633$	12.0586	+	12.2260i	0.479286	+	0.485940i
$634$	−3.26340	+	12.2449i	−0.129606	+	0.486306i
$635$	16.6950	−	2.19794i	0.662522	−	0.0872227i
$636$	2.32277	−	2.30329i	0.0921038	−	0.0913316i
$637$	−0.106005	+	0.805190i	−0.00420008	+	0.0319028i
$638$	−0.0360994	−	0.0868219i	−0.00142919	−	0.00343731i
$639$	11.4824	+	20.5369i	0.454237	+	0.812427i
$640$	−32.5803	−	31.9740i	−1.28785	−	1.26388i
$641$	13.4648	+	7.77393i	0.531829	+	0.307052i	0.741761	−	0.670664i	$-0.233991\pi$
$641$	13.4648	+	7.77393i	0.531829	+	0.307052i	−0.209932	+	0.977716i	$0.567324\pi$
$642$	24.9193	−	32.1048i	0.983485	−	1.26707i
$643$	−4.96355	+	6.46862i	−0.195743	+	0.255098i	−0.880905	−	0.473294i	$-0.843065\pi$
$643$	−4.96355	+	6.46862i	−0.195743	+	0.255098i	0.685161	+	0.728391i	$0.259732\pi$
$644$	3.48675	−	13.1538i	0.137397	−	0.518334i
$645$	51.4380	−	38.9093i	2.02537	−	1.53205i
$646$	−12.5627	−	46.6342i	−0.494272	−	1.83480i
$647$	27.9651	+	27.9651i	1.09942	+	1.09942i	0.994478	+	0.104944i	$0.0334663\pi$
$647$	27.9651	+	27.9651i	1.09942	+	1.09942i	0.104944	+	0.994478i	$0.466534\pi$
$648$	20.5548	−	15.0167i	0.807468	−	0.589912i
$649$	0.0228333	−	0.0228333i	0.000896285	−	0.000896285i
$650$	9.25346	+	5.32594i	0.362950	+	0.208901i
$651$	2.70883	+	3.58106i	0.106167	+	0.140353i
$652$	2.92558	+	21.7704i	0.114575	+	0.852595i
$653$	−37.7523	−	28.9683i	−1.47736	−	1.13362i	−0.960756	−	0.277393i	$-0.910529\pi$
$653$	−37.7523	−	28.9683i	−1.47736	−	1.13362i	−0.516603	−	0.856225i	$-0.672804\pi$
$654$	1.74530	−	0.219923i	0.0682467	−	0.00859967i
$655$	35.0261	−	60.6669i	1.36858	−	2.37045i
$656$	30.3017	−	30.6288i	1.18308	−	1.19585i
$657$	−7.10179	+	3.97069i	−0.277067	+	0.154911i
$658$	31.9349	+	13.1777i	1.24495	+	0.513720i
$659$	0.317602	+	0.0418131i	0.0123720	+	0.00162881i	0.136710	−	0.990611i	$-0.456347\pi$
$659$	0.317602	+	0.0418131i	0.0123720	+	0.00162881i	−0.124338	+	0.992240i	$0.539681\pi$
$660$	−0.155416	−	0.379720i	−0.00604955	−	0.0147806i
$661$	4.61212	+	35.0326i	0.179391	+	1.36261i	0.809964	+	0.586479i	$0.199486\pi$
$661$	4.61212	+	35.0326i	0.179391	+	1.36261i	−0.630573	+	0.776130i	$0.717180\pi$
$662$	6.54677	−	3.79150i	0.254448	−	0.147361i
$663$	−5.86762	+	5.78728i	−0.227879	+	0.224759i
$664$	−20.6889	+	36.1697i	−0.802885	+	1.40366i
$665$	32.9687	−	32.9687i	1.27847	−	1.27847i
$666$	−20.9517	−	21.4798i	−0.811863	−	0.832327i
$667$	−5.91878	−	2.45164i	−0.229176	−	0.0949278i
$668$	1.10752	−	1.93022i	0.0428512	−	0.0746825i
$669$	−10.6271	−	8.27150i	−0.410869	−	0.319795i
$670$	−4.46392	+	5.83369i	−0.172456	+	0.225375i
$671$	0.0509728	+	0.0882875i	0.00196778	+	0.00340830i
$672$	20.4094	+	11.7884i	0.787311	+	0.454749i
$673$	−16.1528	+	27.9774i	−0.622643	+	1.07845i	0.366349	+	0.930478i	$0.380608\pi$
$673$	−16.1528	+	27.9774i	−0.622643	+	1.07845i	−0.988992	+	0.147972i	$0.952726\pi$
$674$	0.596671	+	1.43504i	0.0229829	+	0.0552757i
$675$	−57.9394	−	8.85035i	−2.23009	−	0.340650i
$676$	−0.0673661	−	25.1040i	−0.00259100	−	0.965538i
$677$	−28.6706	+	21.9997i	−1.10190	+	0.845518i	−0.988975	−	0.148085i	$-0.952689\pi$
$677$	−28.6706	+	21.9997i	−1.10190	+	0.845518i	−0.112926	+	0.993603i	$0.536022\pi$
$678$	−0.785051	+	0.205689i	−0.0301497	+	0.00789945i
$679$	−31.1244	−	8.33976i	−1.19445	−	0.320051i
$680$	−78.4511	−	20.6828i	−3.00846	−	0.793149i
$681$	9.80732	−	35.6175i	0.375817	−	1.36486i
$682$	0.0387753	+	0.0223176i	0.00148478	+	0.000854585i
$683$	8.61033	+	3.56652i	0.329465	+	0.136469i	0.541284	−	0.840840i	$-0.317939\pi$
$683$	8.61033	+	3.56652i	0.329465	+	0.136469i	−0.211818	+	0.977309i	$0.567939\pi$
$684$	28.5324	+	4.07915i	1.09097	+	0.155970i
$685$	−16.9109	−	40.8264i	−0.646130	−	1.55990i
$686$	22.1446	−	17.0394i	0.845487	−	0.650569i
$687$	−42.1434	−	0.290520i	−1.60787	−	0.0110840i
$688$	5.01483	+	36.5735i	0.191189	+	1.39435i
$689$	−0.316011	−	0.547347i	−0.0120391	−	0.0208522i
$690$	−25.7671	−	10.8411i	−0.980936	−	0.412712i
$691$	−1.99649	+	15.1648i	−0.0759500	+	0.576898i	0.910582	+	0.413329i	$0.135634\pi$
$691$	−1.99649	+	15.1648i	−0.0759500	+	0.576898i	−0.986532	+	0.163569i	$0.947699\pi$
$692$	6.64213	−	16.1580i	0.252496	−	0.614236i
$693$	0.126632	+	0.169828i	0.00481036	+	0.00645123i
$694$	−0.0326804	−	24.3568i	−0.00124053	−	0.924571i
$695$	7.18739	+	26.8237i	0.272633	+	1.01748i
$696$	6.78003	−	8.78362i	0.256996	−	0.332942i
$697$	19.8191	−	73.9658i	0.750701	−	2.80165i
$698$	14.8125	+	3.94769i	0.560660	+	0.149422i
$699$	−20.9510	−	27.6972i	−0.792441	−	1.04760i
$700$	−14.1861	−	52.3808i	−0.536186	−	1.97981i
$701$	−4.97726	−	12.0162i	−0.187989	−	0.453845i	0.801584	−	0.597883i	$-0.203991\pi$
$701$	−4.97726	−	12.0162i	−0.187989	−	0.453845i	−0.989572	+	0.144038i	$0.953991\pi$
$702$	−1.79395	−	4.57950i	−0.0677082	−	0.172842i
$703$		−	33.9745i		−	1.28137i
$704$	0.233069	+	0.0287773i	0.00878414	+	0.00108459i
$705$	35.9073	−	61.2148i	1.35235	−	2.30548i
$706$	−9.54827	+	12.4782i	−0.359354	+	0.469623i
$707$	−11.8193	−	9.06923i	−0.444509	−	0.341084i
$708$	3.67657	+	1.00174i	0.138174	+	0.0376478i
$709$	21.7479	+	28.3424i	0.816758	+	1.06442i	0.996735	+	0.0807486i	$0.0257311\pi$
$709$	21.7479	+	28.3424i	0.816758	+	1.06442i	−0.179977	+	0.983671i	$0.557602\pi$
$710$	31.6874	+	31.6025i	1.18921	+	1.18602i
$711$	−17.8328	+	17.3477i	−0.668782	+	0.650591i
$712$	7.13855	+	17.0397i	0.267528	+	0.638588i
$713$	2.94437	−	0.788943i	0.110268	−	0.0295461i
$714$	41.8891	+	0.232561i	1.56766	+	0.00870339i
$715$	−0.0785951	+	0.0103472i	−0.00293929	+	0.000386965i
$716$	−0.722475	−	5.37622i	−0.0270002	−	0.200919i
$717$	−25.4619	+	10.3416i	−0.950894	+	0.386215i
$718$	−7.83622	+	6.02967i	−0.292445	+	0.225025i
$719$			25.6407i			0.956237i	0.878295	+	0.478119i	$0.158681\pi$
$719$			25.6407i			0.956237i	−0.878295	+	0.478119i	$0.841319\pi$
$720$	29.7973	−	38.1629i	1.11048	−	1.42225i
$721$		−	10.0119i		−	0.372862i
$722$	3.51533	+	4.56856i	0.130827	+	0.170024i
$723$	19.2179	+	14.9581i	0.714723	+	0.556296i
$724$	−15.1479	−	11.5590i	−0.562968	−	0.429585i
$725$	−25.3296	+	3.33471i	−0.940720	+	0.123848i
$726$	−23.2575	−	13.6005i	−0.863169	−	0.504761i
$727$	−25.5813	+	6.85449i	−0.948758	+	0.254219i	−0.699835	−	0.714304i	$-0.746743\pi$
$727$	−25.5813	+	6.85449i	−0.948758	+	0.254219i	−0.248923	+	0.968523i	$0.580077\pi$
$728$	3.20707	−	3.23299i	0.118862	−	0.119823i
$729$	18.2861	+	19.8650i	0.677264	+	0.735740i
$730$	−10.9283	+	10.9577i	−0.404476	+	0.405563i
$731$	39.9411	+	52.0522i	1.47727	+	1.92522i
$732$	−6.05899	+	10.3932i	−0.223947	+	0.384143i
$733$	−2.03830	−	1.56404i	−0.0752862	−	0.0577692i	0.570433	−	0.821344i	$-0.306776\pi$
$733$	−2.03830	−	1.56404i	−0.0752862	−	0.0577692i	−0.645719	+	0.763575i	$0.723442\pi$
$734$	38.7378	+	29.6421i	1.42984	+	1.09411i
$735$	−4.18925	−	7.37290i	−0.154523	−	0.271953i
$736$	12.6284	−	9.82539i	0.465488	−	0.362169i
$737$		−	0.0377896i		−	0.00139200i
$738$	35.9061	+	28.2685i	1.32172	+	1.04058i
$739$	10.2651	+	24.7822i	0.377609	+	0.911630i	0.992413	+	0.122949i	$0.0392353\pi$
$739$	10.2651	+	24.7822i	0.377609	+	0.911630i	−0.614804	+	0.788680i	$0.710765\pi$
$740$	−49.5025	−	28.4034i	−1.81975	−	1.04413i
$741$	2.16651	−	5.13011i	0.0795889	−	0.188459i
$742$	−0.827279	+	3.10410i	−0.0303704	+	0.113955i
$743$	10.3552	−	38.6460i	0.379895	−	1.41779i	−0.466165	−	0.884698i	$-0.654365\pi$
$743$	10.3552	−	38.6460i	0.379895	−	1.41779i	0.846060	−	0.533088i	$-0.178969\pi$
$744$	−0.0151434	+	5.27954i	−0.000555182	+	0.193557i
$745$	8.38676	+	31.2998i	0.307267	+	1.14674i
$746$	3.15551	−	0.00423387i	0.115531	−	0.000155013i
$747$	−40.5950	−	17.4745i	−1.48529	−	0.639359i
$748$	0.385179	−	0.160759i	0.0140835	−	0.00587792i
$749$	−5.20952	+	39.5702i	−0.190352	+	1.44586i
$750$	−61.5777	+	7.75932i	−2.24850	+	0.283330i
$751$	−11.9982	−	20.7815i	−0.437822	−	0.758329i	0.559700	−	0.828696i	$-0.310917\pi$
$751$	−11.9982	−	20.7815i	−0.437822	−	0.758329i	−0.997521	+	0.0703662i	$0.977583\pi$
$752$	20.4986	+	35.0687i	0.747509	+	1.27882i
$753$	−15.2452	+	25.9901i	−0.555567	+	0.947132i
$754$	−1.30738	−	1.69909i	−0.0476120	−	0.0618771i
$755$	−14.5632	−	35.1587i	−0.530009	−	1.27956i
$756$	−9.98081	+	22.9202i	−0.362998	+	0.833599i
$757$	0.259402	+	0.107448i	0.00942812	+	0.00390525i	0.387393	−	0.921915i	$-0.373376\pi$
$757$	0.259402	+	0.107448i	0.00942812	+	0.00390525i	−0.377964	+	0.925820i	$0.623376\pi$
$758$	7.37221	−	12.8087i	0.267771	−	0.465233i
$759$	0.139166	−	0.0362631i	0.00505141	−	0.00131627i
$760$	54.3232	−	7.37436i	1.97051	−	0.267496i
$761$	0.236036	+	0.0632458i	0.00855632	+	0.00229266i	0.263095	−	0.964770i	$-0.415257\pi$
$761$	0.236036	+	0.0632458i	0.00855632	+	0.00229266i	−0.254538	+	0.967063i	$0.581924\pi$
$762$	−9.85963	−	2.70064i	−0.357177	−	0.0978337i
$763$	−1.37055	+	1.05166i	−0.0496171	+	0.0380726i
$764$	−2.81974	+	2.83491i	−0.102015	+	0.102564i
$765$	12.4073	−	85.1540i	0.448589	−	3.07875i
$766$	42.7198	−	17.7623i	1.54353	−	0.641778i
$767$	0.368124	−	0.637610i	0.0132922	−	0.0230228i
$768$	10.7035	+	25.5624i	0.386229	+	0.922403i
$769$	−1.04493	−	1.80987i	−0.0376811	−	0.0652656i	0.846570	−	0.532278i	$-0.178664\pi$
$769$	−1.04493	−	1.80987i	−0.0376811	−	0.0652656i	−0.884251	+	0.467012i	$0.845330\pi$
$770$	0.319996	+	0.244860i	0.0115319	+	0.00882415i
$771$	1.71164	−	0.695198i	0.0616431	−	0.0250370i
$772$	−0.239911	−	0.885844i	−0.00863458	−	0.0318822i
$773$	5.65867	+	2.34390i	0.203528	+	0.0843041i	0.482119	−	0.876106i	$-0.339867\pi$
$773$	5.65867	+	2.34390i	0.203528	+	0.0843041i	−0.278591	+	0.960410i	$0.589867\pi$
$774$	−37.9440	+	9.66260i	−1.36387	+	0.347315i
$775$	8.59564	−	8.59564i	0.308765	−	0.308765i
$776$	−23.1850	−	29.9648i	−0.832293	−	1.07567i
$777$	28.4102	+	7.82278i	1.01921	+	0.280641i
$778$	15.6695	+	27.0564i	0.561778	+	0.970020i
$779$	6.75375	+	51.2998i	0.241978	+	1.83801i
$780$	−5.66357	−	7.44561i	−0.202789	−	0.266596i
$781$	−0.228260	−	0.0300510i	−0.00816779	−	0.00107531i
$782$	10.8473	−	26.2875i	0.387900	−	0.940039i
$783$	10.0684	+	6.09404i	0.359817	+	0.217783i
$784$	4.85357	−	0.0260491i	0.173342	−	0.000930327i
$785$	−34.2279	+	59.2845i	−1.22165	+	2.11595i
$786$	−33.8828	+	25.7016i	−1.20856	+	0.916744i
$787$	10.1384	+	7.77945i	0.361394	+	0.277308i	0.773458	−	0.633847i	$-0.218525\pi$
$787$	10.1384	+	7.77945i	0.361394	+	0.277308i	−0.412064	+	0.911155i	$0.635192\pi$
$788$	31.8634	+	24.3140i	1.13509	+	0.866152i
$789$	−34.8489	+	4.34377i	−1.24066	+	0.154642i
$790$	−23.6051	+	41.0122i	−0.839831	+	1.45915i
$791$	0.563554	−	0.563554i	0.0200377	−	0.0200377i
$792$	−0.00243148	+	0.249073i	−8.63989e−5	+	0.00885042i
$793$	1.64360	+	1.64360i	0.0583658	+	0.0583658i
$794$	−33.3356	+	8.98020i	−1.18304	+	0.318695i
$795$	6.07936	+	2.56739i	0.215613	+	0.0910561i
$796$	7.29092	−	4.23554i	0.258420	−	0.150125i
$797$	5.58443	−	7.27777i	0.197811	−	0.257792i	−0.683907	−	0.729569i	$-0.739721\pi$
$797$	5.58443	−	7.27777i	0.197811	−	0.257792i	0.881718	+	0.471777i	$0.156387\pi$
$798$	−26.2104	+	10.6866i	−0.927840	+	0.378303i
$799$	62.5223	+	36.0973i	2.21188	+	1.27703i
$800$	24.0223	−	59.1135i	0.849315	−	2.08998i
$801$	−17.1034	+	9.56272i	−0.604319	+	0.337882i
$802$	13.0981	−	5.44602i	0.462511	−	0.192306i
$803$	0.0103918	−	0.0789338i	0.000366720	−	0.00278551i
$804$	3.87135	−	2.21345i	0.136532	−	0.0780623i
$805$	27.2183	−	3.58336i	0.959319	−	0.126297i
$806$	0.985664	+	0.262691i	0.0347185	+	0.00925290i
$807$	41.8332	−	10.9007i	1.47260	−	0.383722i
$808$	−4.60178	−	16.9016i	−0.161890	−	0.594597i
$809$	14.8091	+	14.8091i	0.520660	+	0.520660i	0.917771	−	0.397110i	$-0.129987\pi$
$809$	14.8091	+	14.8091i	0.520660	+	0.520660i	−0.397110	+	0.917771i	$0.629987\pi$
$810$	43.7858	+	26.8351i	1.53848	+	0.942891i
$811$	18.9307	−	45.7027i	0.664746	−	1.60484i	−0.125531	−	0.992090i	$-0.540063\pi$
$811$	18.9307	−	45.7027i	0.664746	−	1.60484i	0.790277	−	0.612749i	$-0.209937\pi$
$812$	−1.39333	+	10.8074i	−0.0488963	+	0.379266i
$813$	−12.6314	−	1.75162i	−0.443002	−	0.0614319i
$814$	0.291044	−	0.0387140i	0.0102011	−	0.00135693i
$815$	−38.3776	+	22.1573i	−1.34431	+	0.776138i
$816$	39.0300	+	30.0436i	1.36632	+	1.05174i
$817$	−38.3940	−	22.1668i	−1.34324	−	0.775517i
$818$	−28.3418	−	11.6950i	−0.990947	−	0.408907i
$819$	3.79106	+	2.99292i	0.132470	+	0.104581i
$820$	80.3927	+	33.0473i	2.80743	+	1.15406i
$821$	17.7053	+	23.0740i	0.617919	+	0.805288i	0.992544	−	0.121889i	$-0.0388951\pi$
$821$	17.7053	+	23.0740i	0.617919	+	0.805288i	−0.374625	+	0.927176i	$0.622228\pi$
$822$	−0.148938	+	26.8269i	−0.00519482	+	0.935696i
$823$	12.2713	−	45.7970i	0.427749	−	1.59638i	−0.330096	−	0.943947i	$-0.607081\pi$
$823$	12.2713	−	45.7970i	0.427749	−	1.59638i	0.757845	−	0.652435i	$-0.226252\pi$
$824$	7.12868	−	9.36811i	0.248339	−	0.326354i
$825$	0.408320	−	0.402729i	0.0142159	−	0.0140212i
$826$	−3.61340	+	0.973407i	−0.125726	+	0.0338691i
$827$	−4.62464	+	11.1649i	−0.160815	+	0.388241i	−0.983663	−	0.180020i	$-0.942384\pi$
$827$	−4.62464	+	11.1649i	−0.160815	+	0.388241i	0.822848	+	0.568261i	$0.192384\pi$
$828$	11.8663	+	12.1328i	0.412384	+	0.421645i
$829$	−2.97227	+	1.23116i	−0.103231	+	0.0427598i	−0.433701	−	0.901057i	$-0.642793\pi$
$829$	−2.97227	+	1.23116i	−0.103231	+	0.0427598i	0.330470	+	0.943816i	$0.392793\pi$
$830$	−83.3582	−	10.8606i	−2.89341	−	0.376975i
$831$	0.00386582	−	0.00219654i	0.000134104	−	7.61972e-5i
$832$	5.30281	−	0.741605i	0.183842	−	0.0257105i
$833$	7.47067	−	4.31320i	0.258844	−	0.149443i
$834$	2.29328	−	16.7021i	0.0794096	−	0.578346i
$835$	4.45111	+	0.586000i	0.154037	+	0.0202794i
$836$	−0.198888	+	0.199958i	−0.00687869	+	0.00691570i
$837$	−5.56585	+	0.615959i	−0.192384	+	0.0212907i
$838$	−0.0565541	+	0.0567061i	−0.00195363	+	0.00195888i
$839$	52.2403	−	13.9978i	1.80354	−	0.483256i	0.809015	−	0.587788i	$-0.200001\pi$
$839$	52.2403	−	13.9978i	1.80354	−	0.483256i	0.994522	+	0.104532i	$0.0333344\pi$
$840$	−6.34158	+	47.1242i	−0.218805	+	1.62594i
$841$	−23.0566	−	6.17800i	−0.795056	−	0.213035i
$842$	−3.91174	+	2.26545i	−0.134808	+	0.0780725i
$843$	−4.01861	−	32.2403i	−0.138408	−	1.11041i
$844$	−12.1132	−	15.6988i	−0.416952	−	0.540374i
$845$	46.7901	−	19.3811i	1.60963	−	0.666730i
$846$	−34.5048	+	25.8007i	−1.18630	+	0.887045i
$847$	26.4588			0.909135
$848$	−2.98427	+	2.31546i	−0.102480	+	0.0795133i
$849$	0.0592743	−	8.59843i	0.00203429	−	0.295097i
$850$	−14.9533	−	112.416i	−0.512895	−	3.85584i
$851$	12.1780	−	15.8707i	0.417456	−	0.544039i
$852$	−10.2913	−	25.1443i	−0.352574	−	0.861429i
$853$	−21.5241	+	16.5160i	−0.736971	+	0.565498i	−0.907599	−	0.419838i	$-0.862087\pi$
$853$	−21.5241	+	16.5160i	−0.736971	+	0.565498i	0.170628	+	0.985335i	$0.445420\pi$
$854$	−0.0158519	−	11.8145i	−0.000542441	−	0.404282i
$855$	14.2738	+	56.3678i	0.488153	+	1.92774i
$856$	−33.0494	+	33.3165i	−1.12960	+	1.13873i
$857$	−9.04281	−	33.7482i	−0.308896	−	1.15282i	−0.929539	−	0.368724i	$-0.879795\pi$
$857$	−9.04281	−	33.7482i	−0.308896	−	1.15282i	0.620643	−	0.784094i	$-0.286872\pi$
$858$	0.0464161	+	0.0127138i	0.00158462	+	0.000434041i
$859$	1.72198	+	13.0797i	0.0587532	+	0.446275i	0.995385	+	0.0959601i	$0.0305921\pi$
$859$	1.72198	+	13.0797i	0.0587532	+	0.446275i	−0.936632	+	0.350315i	$0.886075\pi$
$860$	−64.3964	+	37.4100i	−2.19590	+	1.27567i
$861$	−44.4531	−	6.16440i	−1.51496	−	0.210082i
$862$	17.9159	+	2.33422i	0.610218	+	0.0795039i
$863$	5.30766			0.180675			0.0903375	−	0.995911i	$-0.471205\pi$
$863$	5.30766			0.180675			0.0903375	+	0.995911i	$0.471205\pi$
$864$	−25.6587	+	14.3399i	−0.872927	+	0.487852i
$865$	35.2441			1.19834
$866$	−46.9127	−	6.11215i	−1.59416	−	0.207699i
$867$	57.5438	+	7.97971i	1.95429	+	0.271005i
$868$	−2.60445	−	4.48322i	−0.0884008	−	0.152170i
$869$	−0.0317750	−	0.241355i	−0.00107789	−	0.00818742i
$870$	21.5899	+	5.91365i	0.731966	+	0.200492i
$871$	−0.223002	−	0.832255i	−0.00755614	−	0.0281999i
$872$	−2.03122	+	0.00817614i	−0.0687858	+	0.000276879i
$873$	28.8044	−	28.0209i	0.974880	−	0.948363i
$874$	0.0257822	+	19.2155i	0.000872097	+	0.649975i
$875$	48.3556	−	37.1045i	1.63472	−	1.25436i
$876$	8.69506	−	3.55880i	0.293779	−	0.120241i
$877$	10.2982	−	13.4209i	0.347747	−	0.453193i	−0.586432	−	0.809999i	$-0.699468\pi$
$877$	10.2982	−	13.4209i	0.347747	−	0.453193i	0.934178	+	0.356806i	$0.116134\pi$
$878$	−6.42463	−	48.2991i	−0.216821	−	1.63001i
$879$	−0.273932	+	39.7370i	−0.00923948	+	1.34029i
$880$	0.125074	+	0.456959i	0.00421625	+	0.0154041i
$881$	20.3432			0.685381			0.342691	−	0.939448i	$-0.388662\pi$
$881$	20.3432			0.685381			0.342691	+	0.939448i	$0.388662\pi$
$882$	0.608386	+	5.11199i	0.0204854	+	0.172130i
$883$	−37.1650	+	15.3943i	−1.25070	+	0.518058i	−0.907044	−	0.421037i	$-0.861666\pi$
$883$	−37.1650	+	15.3943i	−1.25070	+	0.518058i	−0.343659	+	0.939095i	$0.611666\pi$
$884$	7.53430	−	5.81346i	0.253406	−	0.195528i
$885$	0.950862	+	7.62851i	0.0319629	+	0.256430i
$886$	19.9652	−	11.5627i	0.670745	−	0.388456i
$887$	−42.7401	−	11.4522i	−1.43507	−	0.384527i	−0.544268	−	0.838911i	$-0.683192\pi$
$887$	−42.7401	−	11.4522i	−1.43507	−	0.384527i	−0.890806	+	0.454385i	$0.849859\pi$
$888$	21.0134	+	27.5484i	0.705163	+	0.924465i
$889$	9.69727	−	2.59838i	0.325236	−	0.0871467i
$890$	−26.3190	+	26.3897i	−0.882215	+	0.884586i
$891$	−0.262785	+	0.0272495i	−0.00880364	+	0.000912892i
$892$	11.0250	+	10.9660i	0.369145	+	0.367169i
$893$	−48.3652	−	6.36740i	−1.61848	−	0.213077i
$894$	2.67596	−	19.4892i	0.0894974	−	0.651816i
$895$	9.47739	−	5.47177i	0.316794	−	0.182901i
$896$	−21.7462	−	16.3642i	−0.726488	−	0.546690i
$897$	2.85092	−	1.61988i	0.0951894	−	0.0540861i
$898$	25.8617	+	3.36946i	0.863015	+	0.112440i
$899$	−2.25511	+	0.934098i	−0.0752122	+	0.0311539i
$900$	65.1741	+	18.2413i	2.17247	+	0.608043i
$901$	−2.56904	+	6.20221i	−0.0855871	+	0.206626i
$902$	−0.431767	+	0.116313i	−0.0143763	+	0.00387279i
$903$	27.3767	−	27.0019i	0.911040	−	0.898566i
$904$	0.928580	−	0.126054i	0.0308841	−	0.00419251i
$905$	9.94913	−	37.1307i	0.330720	−	1.23426i
$906$	−0.128262	+	23.1027i	−0.00426122	+	0.767534i
$907$	−17.5134	−	22.8238i	−0.581521	−	0.757853i	0.406250	−	0.913762i	$-0.366836\pi$
$907$	−17.5134	−	22.8238i	−0.581521	−	0.757853i	−0.987771	+	0.155909i	$0.950169\pi$
$908$	−16.2187	+	39.4546i	−0.538238	+	1.30935i
$909$	17.2616	−	6.87273i	0.572531	−	0.227954i
$910$	8.49237	+	3.50431i	0.281519	+	0.116167i
$911$	20.3253	+	11.7348i	0.673406	+	0.388791i	0.797366	−	0.603496i	$-0.206226\pi$
$911$	20.3253	+	11.7348i	0.673406	+	0.388791i	−0.123960	+	0.992287i	$0.539560\pi$
$912$	−32.1342	−	8.66293i	−1.06407	−	0.286858i
$913$	0.374521	−	0.216230i	0.0123948	−	0.00715616i
$914$	30.7836	−	4.09476i	1.01823	−	0.135443i
$915$	−24.0401	−	3.33369i	−0.794742	−	0.110208i
$916$	48.2647	+	6.22245i	1.59471	+	0.205595i
$917$	15.9826	−	38.5855i	0.527793	−	1.27420i
$918$	−26.9909	+	44.7291i	−0.890832	+	1.47628i
$919$	−19.6882	−	19.6882i	−0.649455	−	0.649455i	0.303406	−	0.952861i	$-0.401876\pi$
$919$	−19.6882	−	19.6882i	−0.649455	−	0.649455i	−0.952861	+	0.303406i	$0.901876\pi$
$920$	28.0196	+	16.0271i	0.923777	+	0.528397i
$921$	23.1931	−	6.04351i	0.764237	−	0.199140i
$922$	56.1075	+	14.9533i	1.84780	+	0.492460i
$923$	−5.20440	+	0.685173i	−0.171305	+	0.0225527i
$924$	−0.121414	−	0.212356i	−0.00399424	−	0.00698599i
$925$	10.4129	−	79.0935i	0.342373	−	2.60058i
$926$	−6.66958	+	2.77312i	−0.219176	+	0.0911304i
$927$	10.7262	+	6.39152i	0.352293	+	0.209925i
$928$	−8.99885	+	9.12040i	−0.295402	+	0.299392i
$929$	−11.5434	−	6.66461i	−0.378728	−	0.218659i	0.298537	−	0.954398i	$-0.403502\pi$
$929$	−11.5434	−	6.66461i	−0.378728	−	0.218659i	−0.677265	+	0.735739i	$0.736835\pi$
$930$	−9.86277	+	4.02129i	−0.323413	+	0.131863i
$931$	−3.54843	+	4.62441i	−0.116295	+	0.151559i
$932$	20.1437	+	34.6747i	0.659829	+	1.13581i
$933$	23.3022	+	9.84081i	0.762878	+	0.322174i
$934$	30.1675	−	8.12676i	0.987112	−	0.265916i
$935$	0.595403	+	0.595403i	0.0194718	+	0.0194718i
$936$	1.41627	+	5.49979i	0.0462922	+	0.179766i
$937$	−12.4737	+	12.4737i	−0.407497	+	0.407497i	−0.880865	−	0.473368i	$-0.843038\pi$
$937$	−12.4737	+	12.4737i	−0.407497	+	0.407497i	0.473368	+	0.880865i	$0.343038\pi$
$938$	−2.18462	+	3.79563i	−0.0713304	+	0.123932i
$939$	7.27601	−	0.906923i	0.237443	−	0.0295963i
$940$	−49.7120	+	65.1472i	−1.62143	+	2.12487i
$941$	24.4820	+	18.7857i	0.798089	+	0.612395i	0.925194	−	0.379494i	$-0.123902\pi$
$941$	24.4820	+	18.7857i	0.798089	+	0.612395i	−0.127105	+	0.991889i	$0.540569\pi$
$942$	33.1107	−	25.1159i	1.07880	−	0.818320i
$943$	−15.2333	+	26.3848i	−0.496063	+	0.859206i
$944$	−4.07414	−	1.66200i	−0.132602	−	0.0540936i
$945$	−50.4225	−	1.04291i	−1.64024	−	0.0339260i
$946$	0.146143	−	0.354163i	0.00475151	−	0.0115148i
$947$	−2.48344	−	0.326951i	−0.0807008	−	0.0106245i	0.0900676	−	0.995936i	$-0.471292\pi$
$947$	−2.48344	−	0.326951i	−0.0807008	−	0.0106245i	−0.170768	+	0.985311i	$0.554625\pi$
$948$	22.8645	−	17.3921i	0.742604	−	0.564869i
$949$	−0.236937	−	1.79972i	−0.00769131	−	0.0584213i
$950$	38.4038	+	66.3118i	1.24598	+	2.15144i
$951$	14.9634	+	4.12020i	0.485222	+	0.133607i
$952$	−47.9814	−	6.12049i	−1.55509	−	0.198366i
$953$	5.62522	−	5.62522i	0.182219	−	0.182219i	−0.610103	−	0.792322i	$-0.708872\pi$
$953$	5.62522	−	5.62522i	0.182219	−	0.182219i	0.792322	+	0.610103i	$0.208872\pi$
$954$	−2.79743	−	2.86794i	−0.0905700	−	0.0928529i
$955$	−7.45250	−	3.08693i	−0.241157	−	0.0998907i
$956$	30.6300	−	8.29545i	0.990646	−	0.268294i
$957$	−0.106695	+	0.0433353i	−0.00344897	+	0.00140083i
$958$	−38.8085	−	29.6962i	−1.25385	−	0.959439i
$959$	−13.1729	−	22.8162i	−0.425377	−	0.736774i
$960$	−39.4872	+	39.5787i	−1.27445	+	1.27740i
$961$	−14.9193	+	25.8410i	−0.481268	+	0.833580i
$962$	6.18133	−	2.57011i	0.199294	−	0.0828638i
$963$	−39.0675	−	30.8425i	−1.25893	−	0.993886i
$964$	−19.9375	−	19.8308i	−0.642144	−	0.638706i
$965$	1.46889	−	1.12712i	0.0472851	−	0.0362831i
$966$	−16.0744	−	4.40291i	−0.517185	−	0.141661i
$967$	−12.2618	−	3.28553i	−0.394312	−	0.105656i	0.0562141	−	0.998419i	$-0.482097\pi$
$967$	−12.2618	−	3.28553i	−0.394312	−	0.105656i	−0.450526	+	0.892763i	$0.648764\pi$
$968$	24.7575	+	18.8392i	0.795735	+	0.605516i
$969$	−57.2398	+	14.9152i	−1.83881	+	0.479146i
$970$	38.1281	−	66.2448i	1.22422	−	2.12699i
$971$	2.97541	+	1.23245i	0.0954854	+	0.0395513i	0.429915	−	0.902869i	$-0.358544\pi$
$971$	2.97541	+	1.23245i	0.0954854	+	0.0395513i	−0.334429	+	0.942421i	$0.608544\pi$
$972$	−18.1837	−	25.3250i	−0.583242	−	0.812298i
$973$	6.33581	+	15.2960i	0.203117	+	0.490367i
$974$	11.6430	+	15.1313i	0.373065	+	0.484840i
$975$	6.61603	−	11.2790i	0.211883	−	0.361218i
$976$	8.39732	−	11.0661i	0.268792	−	0.354216i
$977$	−14.7846	−	25.6076i	−0.473001	−	0.819261i	0.526522	−	0.850162i	$-0.323496\pi$
$977$	−14.7846	−	25.6076i	−0.473001	−	0.819261i	−0.999522	+	0.0309006i	$0.990162\pi$
$978$	26.6918	−	3.36340i	0.853510	−	0.107550i
$979$	0.0250269	−	0.190098i	0.000799864	−	0.00607557i
$980$	3.77142	+	9.03635i	0.120474	+	0.288656i
$981$	−0.251737	−	2.13970i	−0.00803736	−	0.0683152i
$982$	21.2718	−	0.0285412i	0.678811	−	0.000910786i
$983$	0.505873	+	1.88794i	0.0161348	+	0.0602160i	0.973524	−	0.228585i	$-0.0734100\pi$
$983$	0.505873	+	1.88794i	0.0161348	+	0.0602160i	−0.957389	+	0.288801i	$0.906743\pi$
$984$	−37.2055	−	37.4196i	−1.18607	−	1.19289i
$985$	−20.9278	+	78.1036i	−0.666815	+	2.48859i
$986$	−5.86424	+	22.0037i	−0.186756	+	0.700741i
$987$	16.4609	−	38.9779i	0.523955	−	1.24068i
$988$	−3.20021	+	5.57744i	−0.101812	+	0.177442i
$989$	−9.98959	−	24.1170i	−0.317650	−	0.766876i
$990$	−0.466612	+	0.186508i	−0.0148299	+	0.00592762i
$991$		−	49.7375i		−	1.57996i	−0.613131	−	0.789982i	$-0.710090\pi$
$991$		−	49.7375i		−	1.57996i	0.613131	−	0.789982i	$-0.289910\pi$
$992$	0.755163	−	6.04937i	0.0239765	−	0.192068i
$993$	−4.57744	−	8.05610i	−0.145261	−	0.255652i
$994$	21.1895	+	16.2141i	0.672089	+	0.514281i
$995$	13.4955	+	10.3554i	0.427835	+	0.328289i
$996$	44.0885	+	25.7026i	1.39700	+	0.814417i
$997$	34.3308	+	44.7408i	1.08727	+	1.41695i	0.900662	+	0.434520i	$0.143082\pi$
$997$	34.3308	+	44.7408i	1.08727	+	1.41695i	0.186605	+	0.982435i	$0.440251\pi$
$998$	−34.4320	+	34.5245i	−1.08992	+	1.09285i
$999$	−26.5177	+	25.4430i	−0.838984	+	0.804981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.24	✓	368
3.2	odd	2		864.2.bn.a.683.23		368
9.4	even	3		864.2.bn.a.395.9		368
9.5	odd	6	inner	288.2.bf.a.203.38	yes	368
32.3	odd	8	inner	288.2.bf.a.227.38	yes	368
96.35	even	8		864.2.bn.a.35.9		368
288.67	odd	24		864.2.bn.a.611.23		368
288.131	even	24	inner	288.2.bf.a.131.24	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.24	✓	368	1.1	even	1	trivial
288.2.bf.a.131.24	yes	368	288.131	even	24	inner
288.2.bf.a.203.38	yes	368	9.5	odd	6	inner
288.2.bf.a.227.38	yes	368	32.3	odd	8	inner
864.2.bn.a.35.9		368	96.35	even	8
864.2.bn.a.395.9		368	9.4	even	3
864.2.bn.a.611.23		368	288.67	odd	24
864.2.bn.a.683.23		368	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.182710 + 1.40236i) q^{2} +(1.71563 + 0.237910i) q^{3} +(-1.93323 - 0.512452i) q^{4} +(-0.526650 - 4.00030i) q^{5} +(-0.647100 + 2.36247i) q^{6} +(-0.622598 - 2.32357i) q^{7} +(1.07187 - 2.61746i) q^{8} +(2.88680 + 0.816334i) q^{9} +(5.70609 - 0.00765608i) q^{10} +(-0.0232888 + 0.0178701i) q^{11} +(-3.19480 - 1.33912i) q^{12} +(-0.407445 + 0.530993i) q^{13} +(3.37223 - 0.448567i) q^{14} +(0.0481750 - 6.98835i) q^{15} +(3.47479 + 1.98138i) q^{16} +7.10921 q^{17} +(-1.67224 + 3.89918i) q^{18} +(-4.43809 + 1.83832i) q^{19} +(-1.03183 + 8.00340i) q^{20} +(-0.515349 - 4.13451i) q^{21} +(-0.0208053 - 0.0359244i) q^{22} +(-2.73212 - 0.732071i) q^{23} +(2.46165 - 4.23560i) q^{24} +(-10.8954 + 2.91942i) q^{25} +(-0.670199 - 0.668403i) q^{26} +(4.75847 + 2.08733i) q^{27} +(0.0129104 + 4.81105i) q^{28} +(2.24558 + 0.295636i) q^{29} +(9.79139 + 1.34440i) q^{30} +(-0.933304 + 0.538843i) q^{31} +(-3.41349 + 4.51089i) q^{32} +(-0.0442066 + 0.0251180i) q^{33} +(-1.29893 + 9.96968i) q^{34} +(-8.96708 + 3.71429i) q^{35} +(-5.16252 - 3.05751i) q^{36} +(-2.70652 + 6.53412i) q^{37} +(-1.76710 - 6.55969i) q^{38} +(-0.825355 + 0.814054i) q^{39} +(-11.0351 - 2.90930i) q^{40} +(2.78780 - 10.4042i) q^{41} +(5.89224 + 0.0327127i) q^{42} +(5.61822 + 7.32180i) q^{43} +(0.0541803 - 0.0226128i) q^{44} +(1.74525 - 11.9780i) q^{45} +(1.52582 - 3.69767i) q^{46} +(8.79455 + 5.07754i) q^{47} +(5.49007 + 4.22601i) q^{48} +(1.05084 - 0.606706i) q^{49} +(-2.10337 - 15.8127i) q^{50} +(12.1968 + 1.69135i) q^{51} +(1.05979 - 0.817737i) q^{52} +(-0.361368 + 0.872419i) q^{53} +(-3.79661 + 6.29172i) q^{54} +(0.0837510 + 0.0837510i) q^{55} +(-6.74919 - 0.860924i) q^{56} +(-8.05150 + 2.09801i) q^{57} +(-0.824880 + 3.09510i) q^{58} +(-1.09061 + 0.143582i) q^{59} +(-3.67433 + 13.4854i) q^{60} +(0.453300 - 3.44315i) q^{61} +(-0.585129 - 1.40728i) q^{62} +(0.0994923 - 7.21591i) q^{63} +(-5.70221 - 5.61113i) q^{64} +(2.33871 + 1.35026i) q^{65} +(-0.0271475 - 0.0665829i) q^{66} +(-0.783679 + 1.02131i) q^{67} +(-13.7438 - 3.64313i) q^{68} +(-4.51316 - 1.90597i) q^{69} +(-3.57039 - 13.2537i) q^{70} +(5.54582 + 5.54582i) q^{71} +(5.23098 - 6.68108i) q^{72} +(-1.91778 + 1.91778i) q^{73} +(-8.66868 - 4.98937i) q^{74} +(-19.3871 + 2.41652i) q^{75} +(9.52193 - 1.27959i) q^{76} +(0.0560220 + 0.0429872i) q^{77} +(-0.990796 - 1.30618i) q^{78} +(-4.14646 + 7.18188i) q^{79} +(6.09612 - 14.9437i) q^{80} +(7.66720 + 4.71318i) q^{81} +(14.0811 + 5.81047i) q^{82} +(-14.6061 - 1.92292i) q^{83} +(-1.12245 + 8.25707i) q^{84} +(-3.74406 - 28.4390i) q^{85} +(-11.2943 + 6.54100i) q^{86} +(3.78226 + 1.04145i) q^{87} +(0.0218119 + 0.0801120i) q^{88} +(-4.61864 + 4.61864i) q^{89} +(16.4786 + 4.63598i) q^{90} +(1.48747 + 0.616131i) q^{91} +(4.90668 + 2.81535i) q^{92} +(-1.72940 + 0.702415i) q^{93} +(-8.72739 + 11.4054i) q^{94} +(9.69115 + 16.7856i) q^{95} +(-6.92948 + 6.92692i) q^{96} +(6.69755 - 11.6005i) q^{97} +(0.658820 + 1.58452i) q^{98} +(-0.0818181 + 0.0325760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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