LMFDB - Embedded newform 637.2.h.m.165.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(165,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-8,0,24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	16.0.468066644398978174550016.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.8
Root			$0.756863 + 1.31093i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.m.471.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.43210 q^{2} +(0.376796 + 0.652630i) q^{3} +3.91511 q^{4} +(0.170769 + 0.295780i) q^{5} +(0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 - 2.10626i) q^{9} +(0.415326 + 0.719366i) q^{10} +(1.21605 + 2.10626i) q^{11} +(1.47520 + 2.55511i) q^{12} +(-2.50139 - 2.59674i) q^{13} +(-0.128690 + 0.222897i) q^{15} +3.49784 q^{16} +1.94823 q^{17} +(2.95755 - 5.12263i) q^{18} +(-3.14519 + 5.44764i) q^{19} +(0.668577 + 1.15801i) q^{20} +(2.95755 + 5.12263i) q^{22} -3.68948 q^{23} +(1.75501 + 3.03977i) q^{24} +(2.44168 - 4.22911i) q^{25} +(-6.08362 - 6.31553i) q^{26} +4.09359 q^{27} +(-2.22068 + 3.84632i) q^{29} +(-0.312986 + 0.542108i) q^{30} +(-0.987661 + 1.71068i) q^{31} -0.808361 q^{32} +(-0.916405 + 1.58726i) q^{33} +4.73830 q^{34} +(4.76096 - 8.24623i) q^{36} -9.62867 q^{37} +(-7.64942 + 13.2492i) q^{38} +(0.752198 - 2.61092i) q^{39} +(0.795393 + 1.37766i) q^{40} +(6.26793 - 10.8564i) q^{41} +(4.20368 + 7.28099i) q^{43} +(4.76096 + 8.24623i) q^{44} +0.830652 q^{45} -8.97318 q^{46} +(-4.50265 - 7.79882i) q^{47} +(1.31797 + 2.28279i) q^{48} +(5.93840 - 10.2856i) q^{50} +(0.734087 + 1.27148i) q^{51} +(-9.79320 - 10.1665i) q^{52} +(-0.746129 + 1.29233i) q^{53} +9.95601 q^{54} +(-0.415326 + 0.719366i) q^{55} -4.74039 q^{57} +(-5.40090 + 9.35464i) q^{58} -0.626991 q^{59} +(-0.503834 + 0.872666i) q^{60} +(-0.571597 + 0.990035i) q^{61} +(-2.40209 + 4.16054i) q^{62} -8.96169 q^{64} +(0.340905 - 1.18330i) q^{65} +(-2.22879 + 3.86037i) q^{66} +(2.79599 + 4.84280i) q^{67} +7.62754 q^{68} +(-1.39018 - 2.40786i) q^{69} +(-4.74859 - 8.22481i) q^{71} +(5.66402 - 9.81038i) q^{72} +(5.95934 - 10.3219i) q^{73} -23.4179 q^{74} +3.68006 q^{75} +(-12.3138 + 21.3281i) q^{76} +(1.82942 - 6.35002i) q^{78} +(-2.23583 - 3.87258i) q^{79} +(0.597321 + 1.03459i) q^{80} +(-2.10570 - 3.64718i) q^{81} +(15.2442 - 26.4038i) q^{82} -1.41231 q^{83} +(0.332697 + 0.576248i) q^{85} +(10.2238 + 17.7081i) q^{86} -3.34697 q^{87} +(5.66402 + 9.81038i) q^{88} -12.4444 q^{89} +2.02023 q^{90} -14.4447 q^{92} -1.48859 q^{93} +(-10.9509 - 18.9675i) q^{94} -2.14840 q^{95} +(-0.304587 - 0.527560i) q^{96} +(5.13850 + 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 24 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 + 8 * q^16 + 28 * q^18 + 28 * q^22 - 24 * q^23 + 12 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 + 16 * q^37 + 20 * q^39 + 32 * q^43 + 4 * q^44 + 8 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 - 48 * q^58 - 64 * q^60 - 64 * q^64 - 68 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 - 152 * q^74 + 28 * q^78 + 4 * q^79 + 56 * q^81 + 36 * q^85 - 4 * q^86 + 28 * q^88 - 160 * q^92 - 16 * q^93 - 104 * q^95 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.43210			1.71975			0.859877	−	0.510502i	$-0.170540\pi$
$2$	2.43210			1.71975			0.859877	+	0.510502i	$0.170540\pi$
$3$	0.376796	+	0.652630i	0.217543	+	0.376796i	0.954056	−	0.299627i	$-0.0968623\pi$
$3$	0.376796	+	0.652630i	0.217543	+	0.376796i	−0.736513	+	0.676423i	$0.763529\pi$
$4$	3.91511			1.95755
$5$	0.170769	+	0.295780i	0.0763700	+	0.132277i	0.901681	−	0.432401i	$-0.142334\pi$
$5$	0.170769	+	0.295780i	0.0763700	+	0.132277i	−0.825311	+	0.564678i	$0.809000\pi$
$6$	0.916405	+	1.58726i	0.374121	+	0.647996i
$7$		0			0
$7$		0			0
$8$	4.65773			1.64675
$9$	1.21605	−	2.10626i	0.405350	−	0.702086i
$10$	0.415326	+	0.719366i	0.131338	+	0.227483i
$11$	1.21605	+	2.10626i	0.366653	+	0.635061i	0.989040	−	0.147648i	$-0.0471704\pi$
$11$	1.21605	+	2.10626i	0.366653	+	0.635061i	−0.622387	+	0.782710i	$0.713837\pi$
$12$	1.47520	+	2.55511i	0.425852	+	0.737598i
$13$	−2.50139	−	2.59674i	−0.693760	−	0.720206i
$13$	−2.50139	−	2.59674i	−0.693760	−	0.720206i
$14$		0			0
$15$	−0.128690	+	0.222897i	−0.0332276	+	0.0575518i
$16$	3.49784			0.874460
$17$	1.94823			0.472516			0.236258	−	0.971690i	$-0.424079\pi$
$17$	1.94823			0.472516			0.236258	+	0.971690i	$0.424079\pi$
$18$	2.95755	−	5.12263i	0.697102	−	1.20742i
$19$	−3.14519	+	5.44764i	−0.721557	+	1.24977i	0.238819	+	0.971064i	$0.423240\pi$
$19$	−3.14519	+	5.44764i	−0.721557	+	1.24977i	−0.960376	+	0.278709i	$0.910093\pi$
$20$	0.668577	+	1.15801i	0.149498	+	0.258939i
$21$		0			0
$22$	2.95755	+	5.12263i	0.630552	+	1.09215i
$23$	−3.68948			−0.769309			−0.384655	−	0.923061i	$-0.625679\pi$
$23$	−3.68948			−0.769309			−0.384655	+	0.923061i	$0.625679\pi$
$24$	1.75501	+	3.03977i	0.358240	+	0.620491i
$25$	2.44168	−	4.22911i	0.488335	−	0.845821i
$26$	−6.08362	−	6.31553i	−1.19310	−	1.23858i
$27$	4.09359			0.787811
$28$		0			0
$29$	−2.22068	+	3.84632i	−0.412369	+	0.714244i	−0.995148	−	0.0983864i	$-0.968632\pi$
$29$	−2.22068	+	3.84632i	−0.412369	+	0.714244i	0.582779	+	0.812631i	$0.301965\pi$
$30$	−0.312986	+	0.542108i	−0.0571432	+	0.0989750i
$31$	−0.987661	+	1.71068i	−0.177389	+	0.307247i	−0.940986	−	0.338447i	$-0.890098\pi$
$31$	−0.987661	+	1.71068i	−0.177389	+	0.307247i	0.763596	+	0.645694i	$0.223432\pi$
$32$	−0.808361			−0.142899
$33$	−0.916405	+	1.58726i	−0.159526	+	0.276307i
$34$	4.73830			0.812611
$35$		0			0
$36$	4.76096	−	8.24623i	0.793494	−	1.37437i
$37$	−9.62867			−1.58294			−0.791472	−	0.611206i	$-0.790685\pi$
$37$	−9.62867			−1.58294			−0.791472	+	0.611206i	$0.790685\pi$
$38$	−7.64942	+	13.2492i	−1.24090	+	2.14930i
$39$	0.752198	−	2.61092i	0.120448	−	0.418082i
$40$	0.795393	+	1.37766i	0.125763	+	0.217827i
$41$	6.26793	−	10.8564i	0.978887	−	1.69548i	0.312426	−	0.949942i	$-0.398859\pi$
$41$	6.26793	−	10.8564i	0.978887	−	1.69548i	0.666461	−	0.745540i	$-0.267808\pi$
$42$		0			0
$43$	4.20368	+	7.28099i	0.641055	+	1.11034i	0.985198	+	0.171423i	$0.0548365\pi$
$43$	4.20368	+	7.28099i	0.641055	+	1.11034i	−0.344142	+	0.938918i	$0.611830\pi$
$44$	4.76096	+	8.24623i	0.717742	+	1.24317i
$45$	0.830652			0.123826
$46$	−8.97318			−1.32302
$47$	−4.50265	−	7.79882i	−0.656779	−	1.13757i	−0.981445	−	0.191745i	$-0.938585\pi$
$47$	−4.50265	−	7.79882i	−0.656779	−	1.13757i	0.324666	−	0.945829i	$-0.394748\pi$
$48$	1.31797	+	2.28279i	0.190233	+	0.329493i
$49$		0			0
$50$	5.93840	−	10.2856i	0.839816	−	1.45460i
$51$	0.734087	+	1.27148i	0.102793	+	0.178042i
$52$	−9.79320	−	10.1665i	−1.35807	−	1.40984i
$53$	−0.746129	+	1.29233i	−0.102489	+	0.177516i	−0.912709	−	0.408609i	$-0.866014\pi$
$53$	−0.746129	+	1.29233i	−0.102489	+	0.177516i	0.810221	+	0.586125i	$0.199347\pi$
$54$	9.95601			1.35484
$55$	−0.415326	+	0.719366i	−0.0560025	+	0.0969993i
$56$		0			0
$57$	−4.74039			−0.627879
$58$	−5.40090	+	9.35464i	−0.709173	+	1.22832i
$59$	−0.626991			−0.0816273			−0.0408136	−	0.999167i	$-0.512995\pi$
$59$	−0.626991			−0.0816273			−0.0408136	+	0.999167i	$0.512995\pi$
$60$	−0.503834	+	0.872666i	−0.0650447	+	0.112661i
$61$	−0.571597	+	0.990035i	−0.0731855	+	0.126761i	−0.900296	−	0.435279i	$-0.856650\pi$
$61$	−0.571597	+	0.990035i	−0.0731855	+	0.126761i	0.827110	+	0.562040i	$0.189983\pi$
$62$	−2.40209	+	4.16054i	−0.305066	+	0.528389i
$63$		0			0
$64$	−8.96169			−1.12021
$65$	0.340905	−	1.18330i	0.0422841	−	0.146770i
$66$	−2.22879	+	3.86037i	−0.274345	+	0.475179i
$67$	2.79599	+	4.84280i	0.341585	+	0.591642i	0.984727	−	0.174104i	$-0.0557030\pi$
$67$	2.79599	+	4.84280i	0.341585	+	0.591642i	−0.643142	+	0.765747i	$0.722370\pi$
$68$	7.62754			0.924975
$69$	−1.39018	−	2.40786i	−0.167358	−	0.289873i
$70$		0			0
$71$	−4.74859	−	8.22481i	−0.563554	−	0.976105i	−0.997183	−	0.0750130i	$-0.976100\pi$
$71$	−4.74859	−	8.22481i	−0.563554	−	0.976105i	0.433628	−	0.901092i	$-0.357233\pi$
$72$	5.66402	−	9.81038i	0.667512	−	1.15616i
$73$	5.95934	−	10.3219i	0.697488	−	1.20808i	−0.271847	−	0.962340i	$-0.587634\pi$
$73$	5.95934	−	10.3219i	0.697488	−	1.20808i	0.969335	−	0.245744i	$-0.0790322\pi$
$74$	−23.4179			−2.72227
$75$	3.68006			0.424936
$76$	−12.3138	+	21.3281i	−1.41249	+	2.44650i
$77$		0			0
$78$	1.82942	−	6.35002i	0.207141	−	0.718998i
$79$	−2.23583	−	3.87258i	−0.251551	−	0.435699i	0.712402	−	0.701772i	$-0.247607\pi$
$79$	−2.23583	−	3.87258i	−0.251551	−	0.435699i	−0.963953	+	0.266073i	$0.914274\pi$
$80$	0.597321	+	1.03459i	0.0667825	+	0.115671i
$81$	−2.10570	−	3.64718i	−0.233967	−	0.405242i
$82$	15.2442	−	26.4038i	1.68344	−	2.91581i
$83$	−1.41231			−0.155021			−0.0775104	−	0.996992i	$-0.524697\pi$
$83$	−1.41231			−0.155021			−0.0775104	+	0.996992i	$0.524697\pi$
$84$		0			0
$85$	0.332697	+	0.576248i	0.0360861	+	0.0625029i
$86$	10.2238	+	17.7081i	1.10246	+	1.90951i
$87$	−3.34697			−0.358833
$88$	5.66402	+	9.81038i	0.603787	+	1.04579i
$89$	−12.4444			−1.31910			−0.659551	−	0.751660i	$-0.729253\pi$
$89$	−12.4444			−1.31910			−0.659551	+	0.751660i	$0.729253\pi$
$90$	2.02023			0.212951
$91$		0			0
$92$	−14.4447			−1.50596
$93$	−1.48859			−0.154359
$94$	−10.9509	−	18.9675i	−1.12950	−	1.95635i
$95$	−2.14840			−0.220421
$96$	−0.304587	−	0.527560i	−0.0310868	−	0.0538439i
$97$	5.13850	+	8.90014i	0.521736	+	0.903673i	0.999680	+	0.0252826i	$0.00804857\pi$
$97$	5.13850	+	8.90014i	0.521736	+	0.903673i	−0.477945	+	0.878390i	$0.658618\pi$
$98$		0			0
$99$	5.91511			0.594490
$100$	9.55942	−	16.5574i	0.955942	−	1.65574i
$101$	7.52683	+	13.0369i	0.748948	+	1.29722i	0.948328	+	0.317293i	$0.102774\pi$
$101$	7.52683	+	13.0369i	0.748948	+	1.29722i	−0.199380	+	0.979922i	$0.563893\pi$
$102$	1.78537	+	3.09235i	0.176778	+	0.306189i
$103$	8.80880	+	15.2573i	0.867957	+	1.50335i	0.864080	+	0.503354i	$0.167901\pi$
$103$	8.80880	+	15.2573i	0.867957	+	1.50335i	0.00387687	+	0.999992i	$0.498766\pi$
$104$	−11.6508	−	12.0949i	−1.14245	−	1.18600i
$105$		0			0
$106$	−1.81466	+	3.14308i	−0.176255	+	0.305283i
$107$	6.38454			0.617217			0.308608	−	0.951189i	$-0.400137\pi$
$107$	6.38454			0.617217			0.308608	+	0.951189i	$0.400137\pi$
$108$	16.0268			1.54218
$109$	4.08736	−	7.07951i	0.391498	−	0.678095i	−0.601149	−	0.799137i	$-0.705290\pi$
$109$	4.08736	−	7.07951i	0.391498	−	0.678095i	0.992647	+	0.121042i	$0.0386236\pi$
$110$	−1.01011	+	1.74957i	−0.0963106	+	0.166815i
$111$	−3.62804	−	6.28396i	−0.344359	−	0.596447i
$112$		0			0
$113$	4.81083	+	8.33259i	0.452564	+	0.783865i	0.998545	−	0.0539336i	$-0.0171759\pi$
$113$	4.81083	+	8.33259i	0.452564	+	0.783865i	−0.545980	+	0.837798i	$0.683843\pi$
$114$	−11.5291			−1.07980
$115$	−0.630047	−	1.09127i	−0.0587522	−	0.101762i
$116$	−8.69418	+	15.0588i	−0.807234	+	1.39817i
$117$	−8.51122	+	2.11081i	−0.786863	+	0.195144i
$118$	−1.52490			−0.140379
$119$		0			0
$120$	−0.599402	+	1.03819i	−0.0547177	+	0.0947738i
$121$	2.54245	−	4.40365i	0.231132	−	0.400332i
$122$	−1.39018	+	2.40786i	−0.125861	+	0.217998i
$123$	9.44693			0.851801
$124$	−3.86680	+	6.69749i	−0.347249	+	0.601452i
$125$	3.37553			0.301917
$126$		0			0
$127$	−4.50988	+	7.81134i	−0.400187	+	0.693145i	−0.993748	−	0.111644i	$-0.964388\pi$
$127$	−4.50988	+	7.81134i	−0.400187	+	0.693145i	0.593561	+	0.804789i	$0.297722\pi$
$128$	−20.1790			−1.78359
$129$	−3.16786	+	5.48690i	−0.278915	+	0.483094i
$130$	0.829115	−	2.87791i	0.0727182	−	0.252409i
$131$	−0.0962416	−	0.166695i	−0.00840867	−	0.0145642i	0.861790	−	0.507264i	$-0.169343\pi$
$131$	−0.0962416	−	0.166695i	−0.00840867	−	0.0145642i	−0.870199	+	0.492700i	$0.836010\pi$
$132$	−3.58782	+	6.21429i	−0.312280	+	0.540885i
$133$		0			0
$134$	6.80013	+	11.7782i	0.587442	+	1.01748i
$135$	0.699056	+	1.21080i	0.0601651	+	0.104209i
$136$	9.07434			0.778118
$137$	4.87680			0.416653			0.208326	−	0.978059i	$-0.433198\pi$
$137$	4.87680			0.416653			0.208326	+	0.978059i	$0.433198\pi$
$138$	−3.38106	−	5.85616i	−0.287815	−	0.498510i
$139$	−5.53701	−	9.59038i	−0.469643	−	0.813446i	0.529755	−	0.848151i	$-0.322284\pi$
$139$	−5.53701	−	9.59038i	−0.469643	−	0.813446i	−0.999398	+	0.0347054i	$0.988951\pi$
$140$		0			0
$141$	3.39316	−	5.87713i	0.285756	−	0.494943i
$142$	−11.5491	−	20.0035i	−0.969175	−	1.67866i
$143$	2.42760	−	8.42634i	0.203006	−	0.704646i
$144$	4.25355	−	7.36736i	0.354462	−	0.613946i
$145$	−1.51689			−0.125971
$146$	14.4937	−	25.1038i	1.19951	−	2.07761i
$147$		0			0
$148$	−37.6973			−3.09869
$149$	−7.95435	+	13.7773i	−0.651646	+	1.12868i	0.331078	+	0.943603i	$0.392588\pi$
$149$	−7.95435	+	13.7773i	−0.651646	+	1.12868i	−0.982723	+	0.185080i	$0.940746\pi$
$150$	8.95026			0.730786
$151$	5.29518	−	9.17152i	0.430916	−	0.746368i	−0.566037	−	0.824380i	$-0.691524\pi$
$151$	5.29518	−	9.17152i	0.430916	−	0.746368i	0.996952	+	0.0780122i	$0.0248573\pi$
$152$	−14.6494	+	25.3736i	−1.18823	+	2.05807i
$153$	2.36915	−	4.10349i	0.191534	−	0.331747i
$154$		0			0
$155$	−0.674646			−0.0541889
$156$	2.94493	−	10.2220i	0.235783	−	0.818418i
$157$	4.56194	−	7.90151i	0.364082	−	0.630609i	−0.624546	−	0.780988i	$-0.714716\pi$
$157$	4.56194	−	7.90151i	0.364082	−	0.630609i	0.988628	+	0.150379i	$0.0480493\pi$
$158$	−5.43777	−	9.41849i	−0.432606	−	0.749295i
$159$	−1.12455			−0.0891829
$160$	−0.138043	−	0.239097i	−0.0109132	−	0.0189023i
$161$		0			0
$162$	−5.12127	−	8.87031i	−0.402365	−	0.696917i
$163$	5.48196	−	9.49504i	0.429380	−	0.743709i	−0.567438	−	0.823416i	$-0.692065\pi$
$163$	5.48196	−	9.49504i	0.429380	−	0.743709i	0.996818	+	0.0797075i	$0.0253986\pi$
$164$	24.5396	−	42.5039i	1.91622	−	3.31900i
$165$	−0.625973			−0.0487319
$166$	−3.43487			−0.266598
$167$	−9.13884	+	15.8289i	−0.707185	+	1.22488i	0.258713	+	0.965954i	$0.416702\pi$
$167$	−9.13884	+	15.8289i	−0.707185	+	1.22488i	−0.965897	+	0.258925i	$0.916632\pi$
$168$		0			0
$169$	−0.486122	+	12.9909i	−0.0373940	+	0.999301i
$170$	0.809152	+	1.40149i	0.0620591	+	0.107490i
$171$	7.64942	+	13.2492i	0.584966	+	1.01319i
$172$	16.4579	+	28.5058i	1.25490	+	2.17355i
$173$	−4.09918	+	7.09998i	−0.311655	+	0.539802i	−0.978721	−	0.205197i	$-0.934217\pi$
$173$	−4.09918	+	7.09998i	−0.311655	+	0.539802i	0.667066	+	0.744999i	$0.267550\pi$
$174$	−8.14015			−0.617104
$175$		0			0
$176$	4.25355	+	7.36736i	0.320623	+	0.555335i
$177$	−0.236248	−	0.409193i	−0.0177575	−	0.0307568i
$178$	−30.2659			−2.26853
$179$	7.77684	+	13.4699i	0.581268	+	1.00679i	0.995329	+	0.0965370i	$0.0307766\pi$
$179$	7.77684	+	13.4699i	0.581268	+	1.00679i	−0.414061	+	0.910249i	$0.635890\pi$
$180$	3.25209			0.242396
$181$	6.67302			0.496001			0.248001	−	0.968760i	$-0.420226\pi$
$181$	6.67302			0.496001			0.248001	+	0.968760i	$0.420226\pi$
$182$		0			0
$183$	−0.861502			−0.0636841
$184$	−17.1846			−1.26686
$185$	−1.64427	−	2.84797i	−0.120889	−	0.209387i
$186$	−3.62039			−0.265460
$187$	2.36915	+	4.10349i	0.173249	+	0.300077i
$188$	−17.6283	−	30.5332i	−1.28568	−	2.22686i
$189$		0			0
$190$	−5.22512			−0.379070
$191$	9.37296	−	16.2344i	0.678204	−	1.17468i	−0.297318	−	0.954779i	$-0.596092\pi$
$191$	9.37296	−	16.2344i	0.678204	−	1.17468i	0.975521	−	0.219905i	$-0.0705746\pi$
$192$	−3.37673	−	5.84867i	−0.243694	−	0.422091i
$193$	4.08655	+	7.07811i	0.294156	+	0.509493i	0.974788	−	0.223132i	$-0.0716281\pi$
$193$	4.08655	+	7.07811i	0.294156	+	0.509493i	−0.680632	+	0.732625i	$0.738295\pi$
$194$	12.4973	+	21.6460i	0.897257	+	1.55409i
$195$	0.900710	−	0.223378i	0.0645012	−	0.0159965i
$196$		0			0
$197$	−4.36006	+	7.55184i	−0.310641	+	0.538047i	−0.978501	−	0.206240i	$-0.933877\pi$
$197$	−4.36006	+	7.55184i	−0.310641	+	0.538047i	0.667860	+	0.744287i	$0.267210\pi$
$198$	14.3861			1.02238
$199$	17.4666			1.23818			0.619089	−	0.785321i	$-0.287502\pi$
$199$	17.4666			1.23818			0.619089	+	0.785321i	$0.287502\pi$
$200$	11.3727	−	19.6980i	0.804168	−	1.39286i
$201$	−2.10704	+	3.64950i	−0.148619	+	0.257416i
$202$	18.3060	+	31.7069i	1.28801	+	2.23089i
$203$		0			0
$204$	2.87403	+	4.97796i	0.201222	+	0.348527i
$205$	4.28146			0.299030
$206$	21.4239	+	37.1073i	1.49267	+	2.58539i
$207$	−4.48659	+	7.77100i	−0.311839	+	0.540122i
$208$	−8.74945	−	9.08298i	−0.606665	−	0.629791i
$209$	−15.2988			−1.05824
$210$		0			0
$211$	11.6284	−	20.1410i	0.800535	−	1.38657i	−0.118730	−	0.992927i	$-0.537882\pi$
$211$	11.6284	−	20.1410i	0.800535	−	1.38657i	0.919265	−	0.393640i	$-0.128784\pi$
$212$	−2.92117	+	5.05962i	−0.200627	+	0.347496i
$213$	3.57850	−	6.19815i	0.245195	−	0.424690i
$214$	15.5278			1.06146
$215$	−1.43571	+	2.48673i	−0.0979148	+	0.169593i
$216$	19.0668			1.29733
$217$		0			0
$218$	9.94086	−	17.2181i	0.673280	−	1.16616i
$219$	8.98182			0.606935
$220$	−1.62605	+	2.81639i	−0.109628	+	0.189881i
$221$	−4.87329	−	5.05906i	−0.327813	−	0.340309i
$222$	−8.82376	−	15.2832i	−0.592212	−	1.02574i
$223$	−14.6364	+	25.3510i	−0.980128	+	1.69763i	−0.318272	+	0.947999i	$0.603103\pi$
$223$	−14.6364	+	25.3510i	−0.980128	+	1.69763i	−0.661855	+	0.749632i	$0.730231\pi$
$224$		0			0
$225$	−5.93840	−	10.2856i	−0.395893	−	0.685707i
$226$	11.7004	+	20.2657i	0.778299	+	1.34805i
$227$	−19.8110			−1.31490			−0.657452	−	0.753496i	$-0.728366\pi$
$227$	−19.8110			−1.31490			−0.657452	+	0.753496i	$0.728366\pi$
$228$	−18.5591			−1.22911
$229$	−0.664107	−	1.15027i	−0.0438855	−	0.0760118i	0.843248	−	0.537524i	$-0.180640\pi$
$229$	−0.664107	−	1.15027i	−0.0438855	−	0.0760118i	−0.887134	+	0.461512i	$0.847307\pi$
$230$	−1.53234	−	2.65408i	−0.101039	−	0.175005i
$231$		0			0
$232$	−10.3433	+	17.9151i	−0.679071	+	1.17618i
$233$	−0.758171	−	1.31319i	−0.0496695	−	0.0860300i	0.840122	−	0.542398i	$-0.182483\pi$
$233$	−0.758171	−	1.31319i	−0.0496695	−	0.0860300i	−0.889791	+	0.456368i	$0.849150\pi$
$234$	−20.7001	+	5.13369i	−1.35321	+	0.335600i
$235$	1.53782	−	2.66358i	0.100316	−	0.173753i
$236$	−2.45474			−0.159790
$237$	1.68491	−	2.91834i	0.109446	−	0.189567i
$238$		0			0
$239$	22.4793			1.45406			0.727032	−	0.686603i	$-0.240899\pi$
$239$	22.4793			1.45406			0.727032	+	0.686603i	$0.240899\pi$
$240$	−0.450136	+	0.779659i	−0.0290562	+	0.0503268i
$241$	−13.3106			−0.857409			−0.428704	−	0.903445i	$-0.641030\pi$
$241$	−13.3106			−0.857409			−0.428704	+	0.903445i	$0.641030\pi$
$242$	6.18348	−	10.7101i	0.397489	−	0.688472i
$243$	7.72722	−	13.3839i	0.495701	−	0.858580i
$244$	−2.23786	+	3.87609i	−0.143265	+	0.248141i
$245$		0			0
$246$	22.9759			1.46489
$247$	22.0134	−	5.45939i	1.40068	−	0.347373i
$248$	−4.60026	+	7.96788i	−0.292116	+	0.505961i
$249$	−0.532152	−	0.921714i	−0.0337238	−	0.0584113i
$250$	8.20963			0.519222
$251$	7.95169	+	13.7727i	0.501906	+	0.869327i	0.999998	+	0.00220260i	$0.000701110\pi$
$251$	7.95169	+	13.7727i	0.501906	+	0.869327i	−0.498091	+	0.867125i	$0.665966\pi$
$252$		0			0
$253$	−4.48659	−	7.77100i	−0.282069	−	0.488559i
$254$	−10.9685	+	18.9980i	−0.688224	+	1.19204i
$255$	−0.250718	+	0.434256i	−0.0157006	+	0.0271942i
$256$	−31.1539			−1.94712
$257$	29.2397			1.82392			0.911960	−	0.410280i	$-0.134569\pi$
$257$	29.2397			1.82392			0.911960	+	0.410280i	$0.134569\pi$
$258$	−7.70455	+	13.3447i	−0.479664	+	0.830803i
$259$		0			0
$260$	1.33468	−	4.63275i	0.0827733	−	0.287311i
$261$	5.40090	+	9.35464i	0.334307	+	0.579037i
$262$	−0.234069	−	0.405420i	−0.0144608	−	0.0250469i
$263$	0.852177	+	1.47601i	0.0525475	+	0.0910149i	0.891103	−	0.453802i	$-0.149933\pi$
$263$	0.852177	+	1.47601i	0.0525475	+	0.0910149i	−0.838555	+	0.544817i	$0.816599\pi$
$264$	−4.26836	+	7.39302i	−0.262700	+	0.455009i
$265$	−0.509661			−0.0313083
$266$		0			0
$267$	−4.68899	−	8.12157i	−0.286962	−	0.497032i
$268$	10.9466	+	18.9601i	0.668670	+	1.15817i
$269$	−8.37874			−0.510861			−0.255430	−	0.966827i	$-0.582217\pi$
$269$	−8.37874			−0.510861			−0.255430	+	0.966827i	$0.582217\pi$
$270$	1.70017	+	2.94479i	0.103469	+	0.179214i
$271$	12.1575			0.738518			0.369259	−	0.929327i	$-0.379612\pi$
$271$	12.1575			0.738518			0.369259	+	0.929327i	$0.379612\pi$
$272$	6.81461			0.413196
$273$		0			0
$274$	11.8609			0.716540
$275$	11.8768			0.716198
$276$	−5.44270	−	9.42704i	−0.327612	−	0.567441i
$277$	10.3181			0.619957			0.309979	−	0.950744i	$-0.399678\pi$
$277$	10.3181			0.619957			0.309979	+	0.950744i	$0.399678\pi$
$278$	−13.4666	−	23.3248i	−0.807670	−	1.39893i
$279$	2.40209	+	4.16054i	0.143809	+	0.249085i
$280$		0			0
$281$	−2.59677			−0.154910			−0.0774551	−	0.996996i	$-0.524679\pi$
$281$	−2.59677			−0.154910			−0.0774551	+	0.996996i	$0.524679\pi$
$282$	8.25250	−	14.2938i	0.491429	−	0.851181i
$283$	2.30184	+	3.98690i	0.136830	+	0.236997i	0.926295	−	0.376799i	$-0.122975\pi$
$283$	2.30184	+	3.98690i	0.136830	+	0.236997i	−0.789465	+	0.613796i	$0.789642\pi$
$284$	−18.5912	−	32.2010i	−1.10319	−	1.91078i
$285$	−0.809509	−	1.40211i	−0.0479512	−	0.0830539i
$286$	5.90416	−	20.4937i	0.349120	−	1.21182i
$287$		0			0
$288$	−0.983006	+	1.70262i	−0.0579242	+	0.100328i
$289$	−13.2044			−0.776729
$290$	−3.68922			−0.216638
$291$	−3.87233	+	6.70708i	−0.227000	+	0.393176i
$292$	23.3314	−	40.4112i	1.36537	−	2.36489i
$293$	−0.980596	−	1.69844i	−0.0572870	−	0.0992241i	0.835960	−	0.548791i	$-0.184912\pi$
$293$	−0.980596	−	1.69844i	−0.0572870	−	0.0992241i	−0.893247	+	0.449567i	$0.851578\pi$
$294$		0			0
$295$	−0.107070	−	0.185451i	−0.00623388	−	0.0107974i
$296$	−44.8477			−2.60672
$297$	4.97800	+	8.62216i	0.288853	+	0.500308i
$298$	−19.3458	+	33.5078i	−1.12067	+	1.94106i
$299$	9.22882	+	9.58062i	0.533716	+	0.554061i
$300$	14.4078			0.831835
$301$		0			0
$302$	12.8784	−	22.3060i	0.741069	−	1.28357i
$303$	−5.67216	+	9.82447i	−0.325857	+	0.564401i
$304$	−11.0014	+	19.0550i	−0.630972	+	1.09288i
$305$	−0.390443			−0.0223567
$306$	5.76200	−	9.98008i	0.329392	−	0.570523i
$307$	−7.37658			−0.421004			−0.210502	−	0.977593i	$-0.567510\pi$
$307$	−7.37658			−0.421004			−0.210502	+	0.977593i	$0.567510\pi$
$308$		0			0
$309$	−6.63825	+	11.4978i	−0.377637	+	0.654086i
$310$	−1.64081			−0.0931915
$311$	7.08088	−	12.2644i	0.401520	−	0.695453i	−0.592390	−	0.805652i	$-0.701815\pi$
$311$	7.08088	−	12.2644i	0.401520	−	0.695453i	0.993910	+	0.110199i	$0.0351487\pi$
$312$	3.50353	−	12.1610i	0.198348	−	0.688479i
$313$	−13.3576	−	23.1361i	−0.755017	−	1.30773i	−0.945366	−	0.326011i	$-0.894295\pi$
$313$	−13.3576	−	23.1361i	−0.755017	−	1.30773i	0.190349	−	0.981716i	$-0.439038\pi$
$314$	11.0951	−	19.2173i	0.626132	−	1.08449i
$315$		0			0
$316$	−8.75352	−	15.1615i	−0.492424	−	0.852904i
$317$	−10.7181	−	18.5643i	−0.601989	−	1.04268i	−0.992520	−	0.122086i	$-0.961042\pi$
$317$	−10.7181	−	18.5643i	−0.601989	−	1.04268i	0.390530	−	0.920590i	$-0.372292\pi$
$318$	−2.73503			−0.153373
$319$	−10.8018			−0.604785
$320$	−1.53037	−	2.65069i	−0.0855506	−	0.148178i
$321$	2.40567	+	4.16674i	0.134271	+	0.232565i
$322$		0			0
$323$	−6.12757	+	10.6133i	−0.340947	+	0.590538i
$324$	−8.24404	−	14.2791i	−0.458002	−	0.793283i
$325$	−17.0895	+	4.23824i	−0.947953	+	0.235095i
$326$	13.3327	−	23.0929i	0.738429	−	1.27900i
$327$	6.16040			0.340671
$328$	29.1943	−	50.5660i	1.61199	−	2.79204i
$329$		0			0
$330$	−1.52243			−0.0838069
$331$	−5.30692	+	9.19185i	−0.291695	+	0.505230i	−0.974211	−	0.225641i	$-0.927552\pi$
$331$	−5.30692	+	9.19185i	−0.291695	+	0.505230i	0.682516	+	0.730871i	$0.260886\pi$
$332$	−5.52933			−0.303462
$333$	−11.7089	+	20.2805i	−0.641646	+	1.11136i
$334$	−22.2266	+	38.4975i	−1.21618	+	2.10649i
$335$	−0.954935	+	1.65400i	−0.0521737	+	0.0903675i
$336$		0			0
$337$	6.75587			0.368016			0.184008	−	0.982925i	$-0.441093\pi$
$337$	6.75587			0.368016			0.184008	+	0.982925i	$0.441093\pi$
$338$	−1.18230	+	31.5952i	−0.0643085	+	1.71855i
$339$	−3.62540	+	6.27938i	−0.196905	+	0.341049i
$340$	1.30254	+	2.25607i	0.0706404	+	0.122353i
$341$	−4.80418			−0.260161
$342$	18.6042	+	32.2233i	1.00600	+	1.74244i
$343$		0			0
$344$	19.5796	+	33.9129i	1.05566	+	1.82846i
$345$	0.474798	−	0.822375i	0.0255623	−	0.0442752i
$346$	−9.96960	+	17.2679i	−0.535969	+	0.928326i
$347$	−16.0204			−0.860021			−0.430010	−	0.902824i	$-0.641490\pi$
$347$	−16.0204			−0.860021			−0.430010	+	0.902824i	$0.641490\pi$
$348$	−13.1037			−0.702434
$349$	8.01922	−	13.8897i	0.429259	−	0.743498i	−0.567549	−	0.823340i	$-0.692108\pi$
$349$	8.01922	−	13.8897i	0.429259	−	0.743498i	0.996808	+	0.0798418i	$0.0254415\pi$
$350$		0			0
$351$	−10.2396	−	10.6300i	−0.546552	−	0.567386i
$352$	−0.983006	−	1.70262i	−0.0523944	−	0.0907498i
$353$	1.92156	+	3.32823i	0.102274	+	0.177144i	0.912621	−	0.408806i	$-0.134055\pi$
$353$	1.92156	+	3.32823i	0.102274	+	0.177144i	−0.810347	+	0.585950i	$0.800721\pi$
$354$	−0.574578	−	0.995198i	−0.0305385	−	0.0528942i
$355$	1.62182	−	2.80908i	0.0860773	−	0.149090i
$356$	−48.7210			−2.58221
$357$		0			0
$358$	18.9140	+	32.7601i	0.999638	+	1.73142i
$359$	10.5668	+	18.3022i	0.557692	+	0.965952i	0.997689	+	0.0679519i	$0.0216465\pi$
$359$	10.5668	+	18.3022i	0.557692	+	0.965952i	−0.439996	+	0.898000i	$0.645020\pi$
$360$	3.86895			0.203912
$361$	−10.2845	−	17.8133i	−0.541289	−	0.937540i
$362$	16.2294			0.853000
$363$	3.83194			0.201125
$364$		0			0
$365$	4.07067			0.213069
$366$	−2.09526			−0.109521
$367$	−7.36961	−	12.7645i	−0.384690	−	0.666303i	0.607036	−	0.794674i	$-0.292358\pi$
$367$	−7.36961	−	12.7645i	−0.384690	−	0.666303i	−0.991726	+	0.128371i	$0.959025\pi$
$368$	−12.9052			−0.672730
$369$	−15.2442	−	26.4038i	−0.793583	−	1.37453i
$370$	−3.99904	−	6.92653i	−0.207900	−	0.360093i
$371$		0			0
$372$	−5.82798			−0.302166
$373$	−6.46330	+	11.1948i	−0.334657	+	0.579643i	−0.983419	−	0.181349i	$-0.941954\pi$
$373$	−6.46330	+	11.1948i	−0.334657	+	0.579643i	0.648762	+	0.760991i	$0.275287\pi$
$374$	5.76200	+	9.98008i	0.297946	+	0.516058i
$375$	1.27189	+	2.20297i	0.0656800	+	0.113761i
$376$	−20.9721	−	36.3247i	−1.08155	−	1.87331i
$377$	15.5427	−	3.85463i	0.800488	−	0.198523i
$378$		0			0
$379$	13.4179	−	23.2405i	0.689231	−	1.19378i	−0.282856	−	0.959162i	$-0.591282\pi$
$379$	13.4179	−	23.2405i	0.689231	−	1.19378i	0.972087	−	0.234621i	$-0.0753848\pi$
$380$	−8.41121			−0.431486
$381$	−6.79722			−0.348232
$382$	22.7960	−	39.4838i	1.16634	−	2.02017i
$383$	−1.45391	+	2.51825i	−0.0742914	+	0.128677i	−0.900778	−	0.434280i	$-0.857003\pi$
$383$	−1.45391	+	2.51825i	−0.0742914	+	0.128677i	0.826487	+	0.562957i	$0.190336\pi$
$384$	−7.60337	−	13.1694i	−0.388008	−	0.672049i
$385$		0			0
$386$	9.93889	+	17.2147i	0.505876	+	0.876203i
$387$	20.4475			1.03941
$388$	20.1178	+	34.8450i	1.02132	+	1.76899i
$389$	8.35048	−	14.4635i	0.423386	−	0.733327i	−0.572882	−	0.819638i	$-0.694175\pi$
$389$	8.35048	−	14.4635i	0.423386	−	0.733327i	0.996268	+	0.0863114i	$0.0275080\pi$
$390$	2.19061	−	0.543278i	0.110926	−	0.0275100i
$391$	−7.18797			−0.363511
$392$		0			0
$393$	0.0725269	−	0.125620i	0.00365850	−	0.00633671i
$394$	−10.6041	+	18.3668i	−0.534227	+	0.925308i
$395$	0.763620	−	1.32263i	0.0384219	−	0.0665487i
$396$	23.1583			1.16375
$397$	−12.0492	+	20.8699i	−0.604733	+	1.04743i	0.387360	+	0.921928i	$0.373387\pi$
$397$	−12.0492	+	20.8699i	−0.604733	+	1.04743i	−0.992094	+	0.125500i	$0.959946\pi$
$398$	42.4806			2.12936
$399$		0			0
$400$	8.54059	−	14.7927i	0.427030	−	0.739637i
$401$	1.84490			0.0921297			0.0460649	−	0.998938i	$-0.485332\pi$
$401$	1.84490			0.0921297			0.0460649	+	0.998938i	$0.485332\pi$
$402$	−5.12453	+	8.87594i	−0.255588	+	0.442692i
$403$	6.91271	−	1.71437i	0.344347	−	0.0853990i
$404$	29.4683	+	51.0406i	1.46610	+	2.53937i
$405$	0.719175	−	1.24565i	0.0357361	−	0.0618967i
$406$		0			0
$407$	−11.7089	−	20.2805i	−0.580390	−	1.00527i
$408$	3.41918	+	5.92218i	0.169274	+	0.293192i
$409$	25.6703			1.26931			0.634657	−	0.772794i	$-0.281141\pi$
$409$	25.6703			1.26931			0.634657	+	0.772794i	$0.281141\pi$
$410$	10.4129			0.514259
$411$	1.83756	+	3.18274i	0.0906400	+	0.156993i
$412$	34.4874	+	59.7339i	1.69907	+	2.94288i
$413$		0			0
$414$	−10.9118	+	18.8998i	−0.536287	+	0.928876i
$415$	−0.241178	−	0.417732i	−0.0118389	−	0.0205057i
$416$	2.02202	+	2.09910i	0.0991378	+	0.102917i
$417$	4.17265	−	7.22724i	0.204335	−	0.353919i
$418$	−37.2083			−1.81992
$419$	−13.1199	+	22.7244i	−0.640950	+	1.11016i	0.344271	+	0.938870i	$0.388126\pi$
$419$	−13.1199	+	22.7244i	−0.640950	+	1.11016i	−0.985221	+	0.171288i	$0.945207\pi$
$420$		0			0
$421$	23.6637			1.15330			0.576650	−	0.816992i	$-0.304360\pi$
$421$	23.6637			1.15330			0.576650	+	0.816992i	$0.304360\pi$
$422$	28.2815	−	48.9850i	1.37672	−	2.38455i
$423$	−21.9018			−1.06490
$424$	−3.47526	+	6.01933i	−0.168774	+	0.292325i
$425$	4.75696	−	8.23929i	0.230746	−	0.399664i
$426$	8.70327	−	15.0745i	0.421675	−	0.730362i
$427$		0			0
$428$	24.9961			1.20823
$429$	6.41399	−	1.59069i	0.309670	−	0.0767991i
$430$	−3.49180	+	6.04797i	−0.168389	+	0.291659i
$431$	11.5088	+	19.9339i	0.554361	+	0.960182i	0.997953	+	0.0639528i	$0.0203707\pi$
$431$	11.5088	+	19.9339i	0.554361	+	0.960182i	−0.443592	+	0.896229i	$0.646296\pi$
$432$	14.3187			0.688909
$433$	−12.9304	−	22.3961i	−0.621394	−	1.07629i	−0.989226	−	0.146394i	$-0.953233\pi$
$433$	−12.9304	−	22.3961i	−0.621394	−	1.07629i	0.367832	−	0.929892i	$-0.380100\pi$
$434$		0			0
$435$	−0.571557	−	0.989965i	−0.0274040	−	0.0474652i
$436$	16.0024	−	27.7170i	0.766378	−	1.32741i
$437$	11.6041	−	20.0989i	0.555101	−	0.961462i
$438$	21.8447			1.04378
$439$	35.6771			1.70277			0.851387	−	0.524537i	$-0.175762\pi$
$439$	35.6771			1.70277			0.851387	+	0.524537i	$0.175762\pi$
$440$	−1.93447	+	3.35061i	−0.0922225	+	0.159734i
$441$		0			0
$442$	−11.8523	−	12.3041i	−0.563757	−	0.585248i
$443$	3.42940	+	5.93990i	0.162936	+	0.282213i	0.935920	−	0.352212i	$-0.114570\pi$
$443$	3.42940	+	5.93990i	0.162936	+	0.282213i	−0.772984	+	0.634425i	$0.781237\pi$
$444$	−14.2042	−	24.6024i	−0.674100	−	1.16758i
$445$	−2.12511	−	3.68079i	−0.100740	−	0.174486i
$446$	−35.5972	+	61.6562i	−1.68558	+	2.91951i
$447$	−11.9887			−0.567045
$448$		0			0
$449$	4.99075	+	8.64423i	0.235528	+	0.407946i	0.959426	−	0.281961i	$-0.0909847\pi$
$449$	4.99075	+	8.64423i	0.235528	+	0.407946i	−0.723898	+	0.689907i	$0.757651\pi$
$450$	−14.4428	−	25.0156i	−0.680839	−	1.17925i
$451$	30.4885			1.43565
$452$	18.8349	+	32.6230i	0.885919	+	1.53446i
$453$	7.98081			0.374971
$454$	−48.1824			−2.26131
$455$		0			0
$456$	−22.0794			−1.03396
$457$	−8.77311			−0.410389			−0.205194	−	0.978721i	$-0.565783\pi$
$457$	−8.77311			−0.410389			−0.205194	+	0.978721i	$0.565783\pi$
$458$	−1.61518	−	2.79757i	−0.0754722	−	0.130722i
$459$	7.97526			0.372253
$460$	−2.46670	−	4.27245i	−0.115010	−	0.199204i
$461$	3.44272	+	5.96296i	0.160343	+	0.277723i	0.934992	−	0.354669i	$-0.115407\pi$
$461$	3.44272	+	5.96296i	0.160343	+	0.277723i	−0.774649	+	0.632392i	$0.782073\pi$
$462$		0			0
$463$	−13.9526			−0.648432			−0.324216	−	0.945983i	$-0.605100\pi$
$463$	−13.9526			−0.648432			−0.324216	+	0.945983i	$0.605100\pi$
$464$	−7.76757	+	13.4538i	−0.360600	+	0.624578i
$465$	−0.254204	−	0.440294i	−0.0117884	−	0.0204181i
$466$	−1.84395	−	3.19381i	−0.0854192	−	0.147950i
$467$	−14.4056	−	24.9513i	−0.666613	−	1.15461i	−0.978845	−	0.204602i	$-0.934410\pi$
$467$	−14.4056	−	24.9513i	−0.666613	−	1.15461i	0.312232	−	0.950006i	$-0.398923\pi$
$468$	−33.3223	+	8.26403i	−1.54032	+	0.382005i
$469$		0			0
$470$	3.74013	−	6.47810i	0.172520	−	0.298813i
$471$	6.87568			0.316815
$472$	−2.92035			−0.134420
$473$	−10.2238	+	17.7081i	−0.470089	+	0.814219i
$474$	4.09786	−	7.09770i	0.188221	−	0.326008i
$475$	15.3591	+	26.6027i	0.704723	+	1.22062i
$476$		0			0
$477$	1.81466	+	3.14308i	0.0830876	+	0.143912i
$478$	54.6719			2.50063
$479$	−12.2936	−	21.2931i	−0.561707	−	0.972906i	−0.997348	−	0.0727849i	$-0.976811\pi$
$479$	−12.2936	−	21.2931i	−0.561707	−	0.972906i	0.435640	−	0.900121i	$-0.356522\pi$
$480$	0.104028	−	0.180181i	0.00474820	−	0.00822412i
$481$	24.0850	+	25.0032i	1.09818	+	1.14005i
$482$	−32.3726			−1.47453
$483$		0			0
$484$	9.95395	−	17.2407i	0.452452	−	0.783670i
$485$	−1.75499	+	3.03973i	−0.0796899	+	0.138027i
$486$	18.7934	−	32.5511i	0.852484	−	1.47655i
$487$	−2.57316			−0.116601			−0.0583004	−	0.998299i	$-0.518568\pi$
$487$	−2.57316			−0.116601			−0.0583004	+	0.998299i	$0.518568\pi$
$488$	−2.66234	+	4.61131i	−0.120519	+	0.208744i
$489$	8.26233			0.373635
$490$		0			0
$491$	−7.01897	+	12.1572i	−0.316762	+	0.548647i	−0.979810	−	0.199929i	$-0.935929\pi$
$491$	−7.01897	+	12.1572i	−0.316762	+	0.548647i	0.663049	+	0.748576i	$0.269262\pi$
$492$	36.9857			1.66745
$493$	−4.32639	+	7.49354i	−0.194851	+	0.337492i
$494$	53.5389	−	13.2778i	2.40883	−	0.597396i
$495$	1.01011	+	1.74957i	0.0454012	+	0.0786373i
$496$	−3.45468	+	5.98368i	−0.155120	+	0.268675i
$497$		0			0
$498$	−1.29425	−	2.24170i	−0.0579965	−	0.100453i
$499$	−6.76726	−	11.7212i	−0.302944	−	0.524715i	0.673857	−	0.738862i	$-0.264636\pi$
$499$	−6.76726	−	11.7212i	−0.302944	−	0.524715i	−0.976801	+	0.214147i	$0.931303\pi$
$500$	13.2156			0.591018
$501$	−13.7739			−0.615373
$502$	19.3393	+	33.4966i	0.863155	+	1.49503i
$503$	−4.13877	−	7.16856i	−0.184539	−	0.319630i	0.758882	−	0.651228i	$-0.225746\pi$
$503$	−4.13877	−	7.16856i	−0.184539	−	0.319630i	−0.943421	+	0.331597i	$0.892412\pi$
$504$		0			0
$505$	−2.57069	+	4.45257i	−0.114394	+	0.198137i
$506$	−10.9118	−	18.8998i	−0.485090	−	0.840200i
$507$	−8.66142	+	4.57766i	−0.384667	+	0.203301i
$508$	−17.6567	+	30.5822i	−0.783388	+	1.35687i
$509$	0.166218			0.00736750			0.00368375	−	0.999993i	$-0.498827\pi$
$509$	0.166218			0.00736750			0.00368375	+	0.999993i	$0.498827\pi$
$510$	−0.609771	+	1.05615i	−0.0270011	+	0.0467673i
$511$		0			0
$512$	−35.4115			−1.56498
$513$	−12.8751	+	22.3004i	−0.568451	+	0.984585i
$514$	71.1137			3.13669
$515$	−3.00853	+	5.21093i	−0.132572	+	0.229621i
$516$	−12.4025	+	21.4818i	−0.545990	+	0.945683i
$517$	10.9509	−	18.9675i	0.481619	−	0.834189i
$518$		0			0
$519$	−6.17821			−0.271193
$520$	1.58784	−	5.51149i	0.0696315	−	0.241695i
$521$	−3.53090	+	6.11569i	−0.154691	+	0.267933i	−0.932947	−	0.360015i	$-0.882772\pi$
$521$	−3.53090	+	6.11569i	−0.154691	+	0.267933i	0.778255	+	0.627948i	$0.216105\pi$
$522$	13.1355	+	22.7514i	0.574926	+	0.995802i
$523$	−23.3912			−1.02283			−0.511414	−	0.859335i	$-0.670878\pi$
$523$	−23.3912			−1.02283			−0.511414	+	0.859335i	$0.670878\pi$
$524$	−0.376796	−	0.652630i	−0.0164604	−	0.0285103i
$525$		0			0
$526$	2.07258	+	3.58981i	0.0903687	+	0.156523i
$527$	−1.92420	+	3.33280i	−0.0838193	+	0.145179i
$528$	−3.20544	+	5.55198i	−0.139499	+	0.241619i
$529$	−9.38775			−0.408163
$530$	−1.23955			−0.0538425
$531$	−0.762452	+	1.32061i	−0.0330876	+	0.0573094i
$532$		0			0
$533$	−43.8697	+	10.8798i	−1.90021	+	0.471257i
$534$	−11.4041	−	19.7525i	−0.493503	−	0.854773i
$535$	1.09028	+	1.88842i	0.0471368	+	0.0816434i
$536$	13.0230	+	22.5564i	0.562507	+	0.974290i
$537$	−5.86056	+	10.1508i	−0.252902	+	0.438039i
$538$	−20.3779			−0.878554
$539$		0			0
$540$	2.73688	+	4.74041i	0.117776	+	0.203995i
$541$	−13.1540	−	22.7833i	−0.565533	−	0.979532i	−0.997000	−	0.0774030i	$-0.975337\pi$
$541$	−13.1540	−	22.7833i	−0.565533	−	0.979532i	0.431467	−	0.902129i	$-0.357996\pi$
$542$	29.5683			1.27007
$543$	2.51437	+	4.35501i	0.107902	+	0.186891i
$544$	−1.57488			−0.0675222
$545$	2.79197			0.119595
$546$		0			0
$547$	41.7636			1.78568			0.892841	−	0.450371i	$-0.148708\pi$
$547$	41.7636			1.78568			0.892841	+	0.450371i	$0.148708\pi$
$548$	19.0932			0.815620
$549$	1.39018	+	2.40786i	0.0593315	+	0.102765i
$550$	28.8855			1.23168
$551$	−13.9689	−	24.1949i	−0.595095	−	1.03074i
$552$	−6.47508	−	11.2152i	−0.275598	−	0.477349i
$553$		0			0
$554$	25.0948			1.06617
$555$	1.23911	−	2.14620i	0.0525974	−	0.0911013i
$556$	−21.6780	−	37.5474i	−0.919351	−	1.59236i
$557$	−3.65494	−	6.33053i	−0.154865	−	0.268233i	0.778145	−	0.628085i	$-0.216161\pi$
$557$	−3.65494	−	6.33053i	−0.154865	−	0.268233i	−0.933010	+	0.359851i	$0.882827\pi$
$558$	5.84212	+	10.1188i	0.247317	+	0.428365i
$559$	8.39181	−	29.1284i	0.354936	−	1.23200i
$560$		0			0
$561$	−1.78537	+	3.09235i	−0.0753785	+	0.130559i
$562$	−6.31560			−0.266407
$563$	−44.7737			−1.88699			−0.943493	−	0.331393i	$-0.892481\pi$
$563$	−44.7737			−1.88699			−0.943493	+	0.331393i	$0.892481\pi$
$564$	13.2846	−	23.0096i	0.559382	−	0.968878i
$565$	−1.64308	+	2.84589i	−0.0691247	+	0.119727i
$566$	5.59830	+	9.69654i	0.235314	+	0.407576i
$567$		0			0
$568$	−22.1176	−	38.3089i	−0.928036	−	1.60741i
$569$	−42.5127			−1.78222			−0.891112	−	0.453784i	$-0.850074\pi$
$569$	−42.5127			−1.78222			−0.891112	+	0.453784i	$0.850074\pi$
$570$	−1.96881	−	3.41007i	−0.0824642	−	0.142832i
$571$	20.4324	−	35.3899i	0.855069	−	1.48102i	−0.0215128	−	0.999769i	$-0.506848\pi$
$571$	20.4324	−	35.3899i	0.855069	−	1.48102i	0.876581	−	0.481254i	$-0.159818\pi$
$572$	9.50430	−	32.9900i	0.397395	−	1.37938i
$573$	14.1268			0.590155
$574$		0			0
$575$	−9.00851	+	15.6032i	−0.375681	+	0.650698i
$576$	−10.8979	+	18.8756i	−0.454077	+	0.786485i
$577$	−10.8640	+	18.8170i	−0.452275	+	0.783363i	−0.998527	−	0.0542578i	$-0.982721\pi$
$577$	−10.8640	+	18.8170i	−0.452275	+	0.783363i	0.546252	+	0.837621i	$0.316054\pi$
$578$	−32.1144			−1.33578
$579$	−3.07959	+	5.33400i	−0.127983	+	0.221674i
$580$	−5.93877			−0.246594
$581$		0			0
$582$	−9.41790	+	16.3123i	−0.390384	+	0.676166i
$583$	−3.62932			−0.150311
$584$	27.7570	−	48.0765i	1.14859	−	1.98942i
$585$	−2.07778	−	2.15699i	−0.0859057	−	0.0891805i
$586$	−2.38491	−	4.13078i	−0.0985196	−	0.170641i
$587$	10.2408	−	17.7376i	0.422683	−	0.732108i	−0.573518	−	0.819193i	$-0.694422\pi$
$587$	10.2408	−	17.7376i	0.422683	−	0.732108i	0.996201	+	0.0870851i	$0.0277552\pi$
$588$		0			0
$589$	−6.21277	−	10.7608i	−0.255993	−	0.443393i
$590$	−0.260406	−	0.451036i	−0.0107207	−	0.0185688i
$591$	−6.57141			−0.270312
$592$	−33.6795			−1.38422
$593$	−2.81930	−	4.88318i	−0.115775	−	0.200528i	0.802314	−	0.596902i	$-0.203602\pi$
$593$	−2.81930	−	4.88318i	−0.115775	−	0.200528i	−0.918089	+	0.396374i	$0.870268\pi$
$594$	12.1070	+	20.9699i	0.496756	+	0.860407i
$595$		0			0
$596$	−31.1421	+	53.9397i	−1.27563	+	2.20946i
$597$	6.58136	+	11.3993i	0.269357	+	0.466541i
$598$	22.4454	+	23.3010i	0.917860	+	0.952849i
$599$	−19.8359	+	34.3568i	−0.810474	+	1.40378i	0.102058	+	0.994778i	$0.467457\pi$
$599$	−19.8359	+	34.3568i	−0.810474	+	1.40378i	−0.912533	+	0.409004i	$0.865876\pi$
$600$	17.1407			0.699766
$601$	8.41334	−	14.5723i	0.343187	−	0.594418i	−0.641836	−	0.766842i	$-0.721827\pi$
$601$	8.41334	−	14.5723i	0.343187	−	0.594418i	0.985023	+	0.172425i	$0.0551602\pi$
$602$		0			0
$603$	13.6003			0.553845
$604$	20.7312	−	35.9075i	0.843540	−	1.46105i
$605$	1.73668			0.0706061
$606$	−13.7953	+	23.8941i	−0.560394	+	0.970631i
$607$	11.2490	−	19.4838i	0.456582	−	0.790823i	−0.542196	−	0.840252i	$-0.682407\pi$
$607$	11.2490	−	19.4838i	0.456582	−	0.790823i	0.998778	+	0.0494290i	$0.0157402\pi$
$608$	2.54245	−	4.40365i	0.103110	−	0.178592i
$609$		0			0
$610$	−0.949597			−0.0384480
$611$	−8.98863	+	31.2001i	−0.363641	+	1.26222i
$612$	9.27547	−	16.0656i	0.374939	−	0.649413i
$613$	−13.7135	−	23.7524i	−0.553882	−	0.959351i	−0.997990	−	0.0633780i	$-0.979813\pi$
$613$	−13.7135	−	23.7524i	−0.553882	−	0.959351i	0.444108	−	0.895973i	$-0.353521\pi$
$614$	−17.9406			−0.724022
$615$	1.61324	+	2.79421i	0.0650521	+	0.112673i
$616$		0			0
$617$	−5.31896	−	9.21271i	−0.214133	−	0.370890i	0.738871	−	0.673847i	$-0.235359\pi$
$617$	−5.31896	−	9.21271i	−0.214133	−	0.370890i	−0.953004	+	0.302957i	$0.902026\pi$
$618$	−16.1449	+	27.9637i	−0.649442	+	1.12487i
$619$	−22.7339	+	39.3762i	−0.913751	+	1.58266i	−0.105032	+	0.994469i	$0.533495\pi$
$619$	−22.7339	+	39.3762i	−0.913751	+	1.58266i	−0.808719	+	0.588195i	$0.799839\pi$
$620$	−2.64131			−0.106078
$621$	−15.1032			−0.606071
$622$	17.2214	−	29.8283i	0.690515	−	1.19601i
$623$		0			0
$624$	2.63107	−	9.13258i	0.105327	−	0.365596i
$625$	−11.6319	−	20.1471i	−0.465278	−	0.805885i
$626$	−32.4870	−	56.2692i	−1.29844	−	2.24897i
$627$	−5.76454	−	9.98448i	−0.230214	−	0.398742i
$628$	17.8605	−	30.9353i	0.712711	−	1.23445i
$629$	−18.7589			−0.747966
$630$		0			0
$631$	−14.7992	−	25.6329i	−0.589146	−	1.02043i	−0.994345	−	0.106202i	$-0.966131\pi$
$631$	−14.7992	−	25.6329i	−0.589146	−	1.02043i	0.405199	−	0.914229i	$-0.367202\pi$
$632$	−10.4139	−	18.0374i	−0.414243	−	0.717489i
$633$	17.5262			0.696604
$634$	−26.0675	−	45.1503i	−1.03527	−	1.79315i
$635$	−3.08058			−0.122249
$636$	−4.40275			−0.174580
$637$		0			0
$638$	−26.2711			−1.04008
$639$	−23.0981			−0.913747
$640$	−3.44594	−	5.96854i	−0.136213	−	0.235927i
$641$	−42.5646			−1.68120			−0.840601	−	0.541654i	$-0.817798\pi$
$641$	−42.5646			−1.68120			−0.840601	+	0.541654i	$0.817798\pi$
$642$	5.85082	+	10.1339i	0.230914	+	0.399954i
$643$	10.9980	+	19.0492i	0.433721	+	0.751226i	0.997190	−	0.0749106i	$-0.0238671\pi$
$643$	10.9980	+	19.0492i	0.433721	+	0.751226i	−0.563470	+	0.826137i	$0.690534\pi$
$644$		0			0
$645$	−2.16388			−0.0852029
$646$	−14.9029	+	25.8125i	−0.586345	+	1.01558i
$647$	17.4026	+	30.1421i	0.684166	+	1.18501i	0.973698	+	0.227841i	$0.0731668\pi$
$647$	17.4026	+	30.1421i	0.684166	+	1.18501i	−0.289533	+	0.957168i	$0.593500\pi$
$648$	−9.80778	−	16.9876i	−0.385286	−	0.667335i
$649$	−0.762452	−	1.32061i	−0.0299289	−	0.0518383i
$650$	−41.5633	+	10.3078i	−1.63025	+	0.404306i
$651$		0			0
$652$	21.4625	−	37.1741i	0.840535	−	1.45585i
$653$	−50.8167			−1.98861			−0.994306	−	0.106559i	$-0.966017\pi$
$653$	−50.8167			−1.98861			−0.994306	+	0.106559i	$0.966017\pi$
$654$	14.9827			0.585870
$655$	0.0328701	−	0.0569326i	0.00128434	−	0.00222454i
$656$	21.9242	−	37.9739i	0.855997	−	1.48263i
$657$	−14.4937	−	25.1038i	−0.565453	−	0.979394i
$658$		0			0
$659$	7.37203	+	12.7687i	0.287173	+	0.497399i	0.973134	−	0.230240i	$-0.0739511\pi$
$659$	7.37203	+	12.7687i	0.287173	+	0.497399i	−0.685960	+	0.727639i	$0.740618\pi$
$660$	−2.45075			−0.0953953
$661$	−9.06227	−	15.6963i	−0.352481	−	0.610516i	0.634202	−	0.773167i	$-0.281329\pi$
$661$	−9.06227	−	15.6963i	−0.352481	−	0.610516i	−0.986684	+	0.162651i	$0.947995\pi$
$662$	−12.9069	+	22.3555i	−0.501643	+	0.868871i
$663$	1.46546	−	5.08669i	0.0569136	−	0.197551i
$664$	−6.57814			−0.255281
$665$		0			0
$666$	−28.4773	+	49.3241i	−1.10347	+	1.91127i
$667$	8.19313	−	14.1909i	0.317239	−	0.549475i
$668$	−35.7795	+	61.9719i	−1.38435	+	2.39777i
$669$	−22.0598			−0.852881
$670$	−2.32250	+	4.02268i	−0.0897259	+	0.155410i
$671$	−2.78036			−0.107335
$672$		0			0
$673$	−10.4574	+	18.1127i	−0.403102	+	0.698193i	−0.994099	−	0.108481i	$-0.965401\pi$
$673$	−10.4574	+	18.1127i	−0.403102	+	0.698193i	0.590997	+	0.806674i	$0.298735\pi$
$674$	16.4309			0.632896
$675$	9.99521	−	17.3122i	0.384716	−	0.666348i
$676$	−1.90322	+	50.8608i	−0.0732008	+	1.95618i
$677$	−19.1089	−	33.0976i	−0.734416	−	1.27205i	−0.954979	−	0.296673i	$-0.904123\pi$
$677$	−19.1089	−	33.0976i	−0.734416	−	1.27205i	0.220563	−	0.975373i	$-0.429210\pi$
$678$	−8.81733	+	15.2721i	−0.338628	+	0.586520i
$679$		0			0
$680$	1.54961	+	2.68401i	0.0594249	+	0.102927i
$681$	−7.46472	−	12.9293i	−0.286049	−	0.495451i
$682$	−11.6842			−0.447413
$683$	−23.8253			−0.911649			−0.455825	−	0.890070i	$-0.650656\pi$
$683$	−23.8253			−0.911649			−0.455825	+	0.890070i	$0.650656\pi$
$684$	29.9483	+	51.8720i	1.14510	+	1.98337i
$685$	0.832803	+	1.44246i	0.0318198	+	0.0551135i
$686$		0			0
$687$	0.500466	−	0.866833i	0.0190940	−	0.0330717i
$688$	14.7038	+	25.4677i	0.560577	+	0.970948i
$689$	5.22221	−	1.29512i	0.198950	−	0.0493403i
$690$	1.15476	−	2.00010i	0.0439608	−	0.0761424i
$691$	19.1413			0.728168			0.364084	−	0.931366i	$-0.381382\pi$
$691$	19.1413			0.728168			0.364084	+	0.931366i	$0.381382\pi$
$692$	−16.0487	+	27.7972i	−0.610080	+	1.05669i
$693$		0			0
$694$	−38.9632			−1.47902
$695$	1.89109	−	3.27547i	0.0717333	−	0.124246i
$696$	−15.5893			−0.590909
$697$	12.2114	−	21.1508i	0.462540	−	0.801143i
$698$	19.5035	−	33.7811i	0.738219	−	1.27863i
$699$	0.571352	−	0.989611i	0.0216105	−	0.0374305i
$700$		0			0
$701$	−27.2956			−1.03094			−0.515471	−	0.856907i	$-0.672383\pi$
$701$	−27.2956			−1.03094			−0.515471	+	0.856907i	$0.672383\pi$
$702$	−24.9038	−	25.8532i	−0.939935	−	0.975765i
$703$	30.2840	−	52.4535i	1.14218	−	1.97832i
$704$	−10.8979	−	18.8756i	−0.410729	−	0.711403i
$705$	2.31778			0.0872927
$706$	4.67342	+	8.09460i	0.175886	+	0.304644i
$707$		0			0
$708$	−0.924935	−	1.60203i	−0.0347612	−	0.0602081i
$709$	−3.08583	+	5.34481i	−0.115891	+	0.200729i	−0.918135	−	0.396267i	$-0.870306\pi$
$709$	−3.08583	+	5.34481i	−0.115891	+	0.200729i	0.802245	+	0.596995i	$0.203639\pi$
$710$	3.94443	−	6.83195i	0.148032	−	0.256399i
$711$	−10.8755			−0.407865
$712$	−57.9625			−2.17224
$713$	3.64395	−	6.31152i	0.136467	−	0.236368i
$714$		0			0
$715$	2.90690	−	0.720919i	0.108712	−	0.0269608i
$716$	30.4471	+	52.7360i	1.13786	+	1.97084i
$717$	8.47011	+	14.6707i	0.316322	+	0.547886i
$718$	25.6994	+	44.5127i	0.959094	+	1.66120i
$719$	1.36066	−	2.35674i	0.0507442	−	0.0878915i	−0.839538	−	0.543302i	$-0.817174\pi$
$719$	1.36066	−	2.35674i	0.0507442	−	0.0878915i	0.890282	+	0.455410i	$0.150507\pi$
$720$	2.90549			0.108281
$721$		0			0
$722$	−25.0129	−	43.3236i	−0.930883	−	1.61234i
$723$	−5.01537	−	8.68687i	−0.186524	−	0.323068i
$724$	26.1256			0.970949
$725$	10.8443	+	18.7829i	0.402749	+	0.697581i
$726$	9.31965			0.345885
$727$	9.47153			0.351280			0.175640	−	0.984455i	$-0.443801\pi$
$727$	9.47153			0.351280			0.175640	+	0.984455i	$0.443801\pi$
$728$		0			0
$729$	−0.987863			−0.0365875
$730$	9.90027			0.366426
$731$	8.18976	+	14.1851i	0.302909	+	0.524654i
$732$	−3.37287			−0.124665
$733$	1.74853	+	3.02855i	0.0645836	+	0.111862i	0.896509	−	0.443025i	$-0.146095\pi$
$733$	1.74853	+	3.02855i	0.0645836	+	0.111862i	−0.831926	+	0.554887i	$0.812761\pi$
$734$	−17.9236	−	31.0446i	−0.661573	−	1.14588i
$735$		0			0
$736$	2.98243			0.109934
$737$	−6.80013	+	11.7782i	−0.250486	+	0.433855i
$738$	−37.0755	−	64.2166i	−1.36477	−	2.36385i
$739$	−16.0151	−	27.7390i	−0.589126	−	1.02040i	−0.994347	−	0.106178i	$-0.966139\pi$
$739$	−16.0151	−	27.7390i	−0.589126	−	1.02040i	0.405221	−	0.914219i	$-0.367195\pi$
$740$	−6.43750	−	11.1501i	−0.236647	−	0.409885i
$741$	11.8575	+	12.3096i	0.435598	+	0.452203i
$742$		0			0
$743$	−17.4593	+	30.2404i	−0.640519	+	1.10941i	0.344798	+	0.938677i	$0.387947\pi$
$743$	−17.4593	+	30.2404i	−0.640519	+	1.10941i	−0.985317	+	0.170734i	$0.945386\pi$
$744$	−6.93343			−0.254192
$745$	−5.43341			−0.199065
$746$	−15.7194	+	27.2268i	−0.575527	+	0.996842i
$747$	−1.71744	+	2.97469i	−0.0628377	+	0.108838i
$748$	9.27547	+	16.0656i	0.339145	+	0.587416i
$749$		0			0
$750$	3.09335	+	5.35785i	0.112953	+	0.195641i
$751$	26.9972			0.985143			0.492571	−	0.870272i	$-0.336057\pi$
$751$	26.9972			0.985143			0.492571	+	0.870272i	$0.336057\pi$
$752$	−15.7495	−	27.2790i	−0.574327	−	0.994763i
$753$	−5.99233	+	10.3790i	−0.218373	+	0.378233i
$754$	37.8013	−	9.37483i	1.37664	−	0.341411i
$755$	3.61700			0.131636
$756$		0			0
$757$	26.2950	−	45.5442i	0.955707	−	1.65533i	0.222965	−	0.974826i	$-0.428426\pi$
$757$	26.2950	−	45.5442i	0.955707	−	1.65533i	0.732742	−	0.680507i	$-0.238240\pi$
$758$	32.6337	−	56.5231i	1.18531	−	2.05301i
$759$	3.38106	−	5.85616i	0.122725	−	0.212565i
$760$	−10.0067			−0.362980
$761$	6.96431	−	12.0625i	0.252456	−	0.437267i	−0.711745	−	0.702437i	$-0.752095\pi$
$761$	6.96431	−	12.0625i	0.252456	−	0.437267i	0.964201	+	0.265171i	$0.0854284\pi$
$762$	−16.5315			−0.598874
$763$		0			0
$764$	36.6961	−	63.5596i	1.32762	−	2.29950i
$765$	1.61830			0.0585099
$766$	−3.53606	+	6.12463i	−0.127763	+	0.221292i
$767$	1.56835	+	1.62813i	0.0566297	+	0.0587885i
$768$	−11.7387	−	20.3320i	−0.423583	−	0.733668i
$769$	6.89545	−	11.9433i	0.248656	−	0.430685i	−0.714497	−	0.699639i	$-0.753344\pi$
$769$	6.89545	−	11.9433i	0.248656	−	0.430685i	0.963153	+	0.268953i	$0.0866777\pi$
$770$		0			0
$771$	11.0174	+	19.0827i	0.396781	+	0.687246i
$772$	15.9993	+	27.7115i	0.575826	+	0.997360i
$773$	−50.4870			−1.81589			−0.907946	−	0.419087i	$-0.862350\pi$
$773$	−50.4870			−1.81589			−0.907946	+	0.419087i	$0.862350\pi$
$774$	49.7304			1.78752
$775$	4.82310	+	8.35385i	0.173251	+	0.300079i
$776$	23.9337	+	41.4544i	0.859170	+	1.48813i
$777$		0			0
$778$	20.3092	−	35.1766i	0.728120	−	1.26114i
$779$	39.4277	+	68.2908i	1.41265	+	2.44677i
$780$	3.52637	−	0.874550i	0.126264	−	0.0313139i
$781$	11.5491	−	20.0035i	0.413258	−	0.715783i
$782$	−17.4818			−0.625150
$783$	−9.09053	+	15.7453i	−0.324869	+	0.562690i
$784$		0			0
$785$	3.11614			0.111220
$786$	0.176393	−	0.305521i	0.00629172	−	0.0108976i
$787$	−10.8638			−0.387252			−0.193626	−	0.981075i	$-0.562025\pi$
$787$	−10.8638			−0.387252			−0.193626	+	0.981075i	$0.562025\pi$
$788$	−17.0701	+	29.5663i	−0.608097	+	1.05325i
$789$	−0.642194	+	1.11231i	−0.0228627	+	0.0395994i
$790$	1.85720	−	3.21676i	0.0660762	−	0.114447i
$791$		0			0
$792$	27.5509			0.978980
$793$	4.00065	−	0.992172i	0.142067	−	0.0352331i
$794$	−29.3049	+	50.7576i	−1.03999	+	1.80132i
$795$	−0.192038	−	0.332620i	−0.00681090	−	0.0117968i
$796$	68.3838			2.42380
$797$	−3.95840	−	6.85616i	−0.140214	−	0.242858i	0.787363	−	0.616489i	$-0.211446\pi$
$797$	−3.95840	−	6.85616i	−0.140214	−	0.242858i	−0.927577	+	0.373632i	$0.878112\pi$
$798$		0			0
$799$	−8.77221	−	15.1939i	−0.310339	−	0.537522i
$800$	−1.97375	+	3.41864i	−0.0697828	+	0.120867i
$801$	−15.1330	+	26.2111i	−0.534697	+	0.926123i
$802$	4.48697			0.158440
$803$	28.9874			1.02294
$804$	−8.24928	+	14.2882i	−0.290930	+	0.503905i
$805$		0			0
$806$	16.8124	−	4.16952i	0.592192	−	0.146865i
$807$	−3.15707	−	5.46821i	−0.111134	−	0.192490i
$808$	35.0579	+	60.7221i	1.23333	+	2.13620i
$809$	14.8194	+	25.6680i	0.521023	+	0.902439i	0.999701	+	0.0244482i	$0.00778287\pi$
$809$	14.8194	+	25.6680i	0.521023	+	0.902439i	−0.478678	+	0.877991i	$0.658884\pi$
$810$	1.74910	−	3.02954i	0.0614573	−	0.106447i
$811$	−15.8344			−0.556022			−0.278011	−	0.960578i	$-0.589675\pi$
$811$	−15.8344			−0.556022			−0.278011	+	0.960578i	$0.589675\pi$
$812$		0			0
$813$	4.58091	+	7.93438i	0.160660	+	0.278271i
$814$	−28.4773	−	49.3241i	−0.998129	−	1.72881i
$815$	3.74459			0.131167
$816$	2.56772	+	4.44742i	0.0898881	+	0.155691i
$817$	−52.8856			−1.85023
$818$	62.4327			2.18291
$819$		0			0
$820$	16.7624			0.585368
$821$	17.7394			0.619110			0.309555	−	0.950882i	$-0.399820\pi$
$821$	17.7394			0.619110			0.309555	+	0.950882i	$0.399820\pi$
$822$	4.46912	+	7.74075i	0.155879	+	0.269990i
$823$	−8.68200			−0.302635			−0.151318	−	0.988485i	$-0.548352\pi$
$823$	−8.68200			−0.302635			−0.151318	+	0.988485i	$0.548352\pi$
$824$	41.0290	+	71.0643i	1.42931	+	2.47564i
$825$	4.47513	+	7.75115i	0.155804	+	0.269860i
$826$		0			0
$827$	14.3121			0.497681			0.248840	−	0.968545i	$-0.419951\pi$
$827$	14.3121			0.497681			0.248840	+	0.968545i	$0.419951\pi$
$828$	−17.5655	+	30.4243i	−0.610442	+	1.05732i
$829$	12.6533	+	21.9161i	0.439467	+	0.761179i	0.997648	−	0.0685401i	$-0.0218341\pi$
$829$	12.6533	+	21.9161i	0.439467	+	0.761179i	−0.558182	+	0.829719i	$0.688501\pi$
$830$	−0.586568	−	1.01597i	−0.0203601	−	0.0352647i
$831$	3.88784	+	6.73393i	0.134868	+	0.233597i
$832$	22.4167	+	23.2712i	0.777158	+	0.806783i
$833$		0			0
$834$	10.1483	−	17.5774i	0.351407	−	0.608654i
$835$	−6.24250			−0.216031
$836$	−59.8966			−2.07157
$837$	−4.04308	+	7.00281i	−0.139749	+	0.242053i
$838$	−31.9090	+	55.2679i	−1.10228	+	1.90920i
$839$	6.52129	+	11.2952i	0.225140	+	0.389954i	0.956361	−	0.292186i	$-0.0943827\pi$
$839$	6.52129	+	11.2952i	0.225140	+	0.389954i	−0.731222	+	0.682140i	$0.761049\pi$
$840$		0			0
$841$	4.63720	+	8.03187i	0.159904	+	0.276961i
$842$	57.5525			1.98339
$843$	−0.978452	−	1.69473i	−0.0336997	−	0.0583696i
$844$	45.5266	−	78.8543i	1.56709	−	2.71428i
$845$	−3.92546	+	2.07465i	−0.135040	+	0.0713702i
$846$	−53.2673			−1.83137
$847$		0			0
$848$	−2.60984	+	4.52037i	−0.0896223	+	0.155230i
$849$	−1.73465	+	3.00450i	−0.0595330	+	0.103114i
$850$	11.5694	−	20.0388i	0.396827	−	0.687324i
$851$	35.5248			1.21777
$852$	14.0102	−	24.2664i	0.479982	−	0.831353i
$853$	−18.8926			−0.646869			−0.323435	−	0.946251i	$-0.604838\pi$
$853$	−18.8926			−0.646869			−0.323435	+	0.946251i	$0.604838\pi$
$854$		0			0
$855$	−2.61256	+	4.52509i	−0.0893477	+	0.154755i
$856$	29.7374			1.01640
$857$	12.3219	−	21.3422i	0.420909	−	0.729036i	−0.575119	−	0.818069i	$-0.695044\pi$
$857$	12.3219	−	21.3422i	0.420909	−	0.729036i	0.996029	+	0.0890333i	$0.0283777\pi$
$858$	15.5995	−	3.86871i	0.532557	−	0.132075i
$859$	1.28571	+	2.22691i	0.0438677	+	0.0759811i	0.887126	−	0.461528i	$-0.152699\pi$
$859$	1.28571	+	2.22691i	0.0438677	+	0.0759811i	−0.843258	+	0.537509i	$0.819365\pi$
$860$	−5.62097	+	9.73580i	−0.191673	+	0.331988i
$861$		0			0
$862$	27.9906	+	48.4812i	0.953365	+	1.65128i
$863$	−19.7704	−	34.2433i	−0.672991	−	1.16565i	−0.977052	−	0.213002i	$-0.931676\pi$
$863$	−19.7704	−	34.2433i	−0.672991	−	1.16565i	0.304061	−	0.952653i	$-0.401657\pi$
$864$	−3.30909			−0.112578
$865$	−2.80004			−0.0952043
$866$	−31.4479	−	54.4694i	−1.06864	−	1.85095i
$867$	−4.97536	−	8.61758i	−0.168972	−	0.292668i
$868$		0			0
$869$	5.43777	−	9.41849i	0.184464	−	0.319500i
$870$	−1.39008	−	2.40769i	−0.0471282	−	0.0816284i
$871$	5.58164	−	19.3742i	0.189127	−	0.656469i
$872$	19.0378	−	32.9744i	0.644701	−	1.11666i
$873$	24.9947			0.845942
$874$	28.2224	−	48.8826i	0.954636	−	1.65348i
$875$		0			0
$876$	35.1648			1.18811
$877$	−10.5227	+	18.2259i	−0.355328	+	0.615445i	−0.987174	−	0.159648i	$-0.948964\pi$
$877$	−10.5227	+	18.2259i	−0.355328	+	0.615445i	0.631846	+	0.775094i	$0.282297\pi$
$878$	86.7702			2.92835
$879$	0.738970	−	1.27993i	0.0249248	−	0.0431711i
$880$	−1.45274	+	2.51623i	−0.0489720	+	0.0848219i
$881$	−2.50592	+	4.34038i	−0.0844266	+	0.146231i	−0.905147	−	0.425099i	$-0.860239\pi$
$881$	−2.50592	+	4.34038i	−0.0844266	+	0.146231i	0.820720	+	0.571330i	$0.193573\pi$
$882$		0			0
$883$	−7.13079			−0.239970			−0.119985	−	0.992776i	$-0.538285\pi$
$883$	−7.13079			−0.239970			−0.119985	+	0.992776i	$0.538285\pi$
$884$	−19.0794	−	19.8067i	−0.641711	−	0.666173i
$885$	0.0806874	−	0.139755i	0.00271228	−	0.00469780i
$886$	8.34065	+	14.4464i	0.280210	+	0.485337i
$887$	−6.72602			−0.225838			−0.112919	−	0.993604i	$-0.536020\pi$
$887$	−6.72602			−0.225838			−0.112919	+	0.993604i	$0.536020\pi$
$888$	−16.8984	−	29.2689i	−0.567074	−	0.982202i
$889$		0			0
$890$	−5.16847	−	8.95206i	−0.173248	−	0.300074i
$891$	5.12127	−	8.87031i	0.171569	−	0.297166i
$892$	−57.3032	+	99.2520i	−1.91865	+	3.32320i
$893$	56.6468			1.89561
$894$	−29.1576			−0.975177
$895$	−2.65608	+	4.60046i	−0.0887829	+	0.153777i
$896$		0			0
$897$	−2.77522	+	9.63294i	−0.0926618	+	0.321635i
$898$	12.1380	+	21.0236i	0.405050	+	0.701567i
$899$	−4.38655	−	7.59773i	−0.146300	−	0.253398i
$900$	−23.2495	−	40.2692i	−0.774982	−	1.34231i
$901$	−1.45363	+	2.51777i	−0.0484276	+	0.0838790i
$902$	74.1510			2.46896
$903$		0			0
$904$	22.4075	+	38.8109i	0.745263	+	1.29083i
$905$	1.13954	+	1.97374i	0.0378796	+	0.0656095i
$906$	19.4101			0.644858
$907$	−14.7862	−	25.6105i	−0.490969	−	0.850383i	0.508977	−	0.860780i	$-0.330024\pi$
$907$	−14.7862	−	25.6105i	−0.490969	−	0.850383i	−0.999946	+	0.0103972i	$0.996690\pi$
$908$	−77.5623			−2.57399
$909$	36.6120			1.21434
$910$		0			0
$911$	−20.6132			−0.682947			−0.341473	−	0.939891i	$-0.610926\pi$
$911$	−20.6132			−0.682947			−0.341473	+	0.939891i	$0.610926\pi$
$912$	−16.5811			−0.549055
$913$	−1.71744	−	2.97469i	−0.0568388	−	0.0984477i
$914$	−21.3371			−0.705768
$915$	−0.147117	−	0.254815i	−0.00486355	−	0.00842392i
$916$	−2.60005	−	4.50342i	−0.0859081	−	0.148797i
$917$		0			0
$918$	19.3966			0.640184
$919$	2.08952	−	3.61916i	0.0689269	−	0.119385i	−0.829502	−	0.558503i	$-0.811376\pi$
$919$	2.08952	−	3.61916i	0.0689269	−	0.119385i	0.898429	+	0.439118i	$0.144709\pi$
$920$	−2.93459	−	5.08285i	−0.0967504	−	0.167577i
$921$	−2.77947	−	4.81418i	−0.0915865	−	0.158632i
$922$	8.37303	+	14.5025i	0.275751	+	0.477615i
$923$	−9.47961	+	32.9043i	−0.312025	+	1.08306i
$924$		0			0
$925$	−23.5101	+	40.7207i	−0.773007	+	1.33889i
$926$	−33.9341			−1.11514
$927$	42.8478			1.40731
$928$	1.79511	−	3.10922i	0.0589273	−	0.102065i
$929$	−24.0456	+	41.6482i	−0.788910	+	1.36643i	0.137725	+	0.990470i	$0.456021\pi$
$929$	−24.0456	+	41.6482i	−0.788910	+	1.36643i	−0.926635	+	0.375962i	$0.877312\pi$
$930$	−0.618249	−	1.07084i	−0.0202732	−	0.0351142i
$931$		0			0
$932$	−2.96832	−	5.14128i	−0.0972306	−	0.168408i
$933$	10.6722			0.349392
$934$	−35.0359	−	60.6840i	−1.14641	−	1.98564i
$935$	−0.809152	+	1.40149i	−0.0264621	+	0.0458337i
$936$	−39.6429	+	9.83156i	−1.29577	+	0.321354i
$937$	−12.5441			−0.409798			−0.204899	−	0.978783i	$-0.565687\pi$
$937$	−12.5441			−0.409798			−0.204899	+	0.978783i	$0.565687\pi$
$938$		0			0
$939$	10.0662	−	17.4352i	0.328498	−	0.568975i
$940$	6.02073	−	10.4282i	0.196375	−	0.340131i
$941$	−15.2944	+	26.4907i	−0.498583	+	0.863572i	−0.999999	−	0.00163503i	$-0.999480\pi$
$941$	−15.2944	+	26.4907i	−0.498583	+	0.863572i	0.501415	+	0.865207i	$0.332813\pi$
$942$	16.7223			0.544843
$943$	−23.1254	+	40.0544i	−0.753067	+	1.30435i
$944$	−2.19311			−0.0713798
$945$		0			0
$946$	−24.8652	+	43.0678i	−0.808438	+	1.40026i
$947$	−7.78348			−0.252929			−0.126465	−	0.991971i	$-0.540363\pi$
$947$	−7.78348			−0.252929			−0.126465	+	0.991971i	$0.540363\pi$
$948$	6.59659	−	11.4256i	0.214247	−	0.371087i
$949$	−41.7098	+	10.3442i	−1.35396	+	0.335786i
$950$	37.3548	+	64.7005i	1.21195	+	2.09916i
$951$	8.07709	−	13.9899i	0.261917	−	0.453654i
$952$		0			0
$953$	19.2152	+	33.2817i	0.622442	+	1.07810i	0.989030	+	0.147717i	$0.0471926\pi$
$953$	19.2152	+	33.2817i	0.622442	+	1.07810i	−0.366588	+	0.930383i	$0.619474\pi$
$954$	4.41343	+	7.64429i	0.142890	+	0.247493i
$955$	6.40243			0.207178
$956$	88.0088			2.84641
$957$	−4.07008	−	7.04958i	−0.131567	−	0.227881i
$958$	−29.8992	−	51.7869i	−0.965998	−	1.67316i
$959$		0			0
$960$	1.15328	−	1.99754i	0.0372219	−	0.0644702i
$961$	13.5491	+	23.4676i	0.437066	+	0.757021i
$962$	58.5772	+	60.8101i	1.88860	+	1.96060i
$963$	7.76391	−	13.4475i	0.250189	−	0.433339i
$964$	−52.1123			−1.67842
$965$	−1.39571	+	2.41744i	−0.0449294	+	0.0778200i
$966$		0			0
$967$	7.80008			0.250834			0.125417	−	0.992104i	$-0.459973\pi$
$967$	7.80008			0.250834			0.125417	+	0.992104i	$0.459973\pi$
$968$	11.8420	−	20.5110i	0.380617	−	0.659248i
$969$	−9.23538			−0.296683
$970$	−4.26830	+	7.39292i	−0.137047	+	0.237372i
$971$	28.8957	−	50.0489i	0.927308	−	1.60614i	0.139501	−	0.990222i	$-0.455450\pi$
$971$	28.8957	−	50.0489i	0.927308	−	1.60614i	0.787807	−	0.615922i	$-0.211216\pi$
$972$	30.2529	−	52.3995i	0.970362	−	1.68072i
$973$		0			0
$974$	−6.25817			−0.200525
$975$	−9.20525	−	9.55615i	−0.294804	−	0.306042i
$976$	−1.99936	+	3.46298i	−0.0639978	+	0.110847i
$977$	−4.33707	−	7.51203i	−0.138755	−	0.240331i	0.788270	−	0.615329i	$-0.210977\pi$
$977$	−4.33707	−	7.51203i	−0.138755	−	0.240331i	−0.927026	+	0.374998i	$0.877643\pi$
$978$	20.0948			0.642561
$979$	−15.1330	−	26.2111i	−0.483652	−	0.837710i
$980$		0			0
$981$	−9.94086	−	17.2181i	−0.317387	−	0.549731i
$982$	−17.0708	+	29.5675i	−0.544752	+	0.943538i
$983$	18.5560	−	32.1400i	0.591846	−	1.02511i	−0.402138	−	0.915579i	$-0.631733\pi$
$983$	18.5560	−	32.1400i	0.591846	−	1.02511i	0.993984	−	0.109528i	$-0.0349339\pi$
$984$	44.0012			1.40271
$985$	−2.97824			−0.0948947
$986$	−10.5222	+	18.2250i	−0.335096	+	0.580403i
$987$		0			0
$988$	86.1849	−	21.3741i	2.74191	−	0.680001i
$989$	−15.5094	−	26.8631i	−0.493170	−	0.854196i
$990$	2.45670	+	4.25512i	0.0780790	+	0.135237i
$991$	22.6318	+	39.1995i	0.718924	+	1.24521i	0.961426	+	0.275062i	$0.0886984\pi$
$991$	22.6318	+	39.1995i	0.718924	+	1.24521i	−0.242502	+	0.970151i	$0.577968\pi$
$992$	0.798386	−	1.38285i	0.0253488	−	0.0439054i
$993$	−7.99850			−0.253825
$994$		0			0
$995$	2.98275	+	5.16628i	0.0945597	+	0.163782i
$996$	−2.08343	−	3.60861i	−0.0660160	−	0.114343i
$997$	44.2554			1.40158			0.700791	−	0.713367i	$-0.252831\pi$
$997$	44.2554			1.40158			0.700791	+	0.713367i	$0.252831\pi$
$998$	−16.4586	−	28.5072i	−0.520989	−	0.902380i
$999$	−39.4158			−1.24706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.m.165.8		16
7.2	even	3		637.2.g.m.373.1		16
7.3	odd	6		637.2.f.l.295.1	✓	16
7.4	even	3		637.2.f.l.295.2	yes	16
7.5	odd	6		637.2.g.m.373.2		16
7.6	odd	2	inner	637.2.h.m.165.7		16
13.3	even	3		637.2.g.m.263.1		16
91.3	odd	6		637.2.f.l.393.1	yes	16
91.4	even	6		8281.2.a.cl.1.1		8
91.16	even	3	inner	637.2.h.m.471.8		16
91.17	odd	6		8281.2.a.cl.1.2		8
91.55	odd	6		637.2.g.m.263.2		16
91.68	odd	6	inner	637.2.h.m.471.7		16
91.74	even	3		8281.2.a.ci.1.7		8
91.81	even	3		637.2.f.l.393.2	yes	16
91.87	odd	6		8281.2.a.ci.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.1	✓	16	7.3	odd	6
637.2.f.l.295.2	yes	16	7.4	even	3
637.2.f.l.393.1	yes	16	91.3	odd	6
637.2.f.l.393.2	yes	16	91.81	even	3
637.2.g.m.263.1		16	13.3	even	3
637.2.g.m.263.2		16	91.55	odd	6
637.2.g.m.373.1		16	7.2	even	3
637.2.g.m.373.2		16	7.5	odd	6
637.2.h.m.165.7		16	7.6	odd	2	inner
637.2.h.m.165.8		16	1.1	even	1	trivial
637.2.h.m.471.7		16	91.68	odd	6	inner
637.2.h.m.471.8		16	91.16	even	3	inner
8281.2.a.ci.1.7		8	91.74	even	3
8281.2.a.ci.1.8		8	91.87	odd	6
8281.2.a.cl.1.1		8	91.4	even	6
8281.2.a.cl.1.2		8	91.17	odd	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.43210 q^{2} +(0.376796 + 0.652630i) q^{3} +3.91511 q^{4} +(0.170769 + 0.295780i) q^{5} +(0.916405 + 1.58726i) q^{6} +4.65773 q^{8} +(1.21605 - 2.10626i) q^{9} +(0.415326 + 0.719366i) q^{10} +(1.21605 + 2.10626i) q^{11} +(1.47520 + 2.55511i) q^{12} +(-2.50139 - 2.59674i) q^{13} +(-0.128690 + 0.222897i) q^{15} +3.49784 q^{16} +1.94823 q^{17} +(2.95755 - 5.12263i) q^{18} +(-3.14519 + 5.44764i) q^{19} +(0.668577 + 1.15801i) q^{20} +(2.95755 + 5.12263i) q^{22} -3.68948 q^{23} +(1.75501 + 3.03977i) q^{24} +(2.44168 - 4.22911i) q^{25} +(-6.08362 - 6.31553i) q^{26} +4.09359 q^{27} +(-2.22068 + 3.84632i) q^{29} +(-0.312986 + 0.542108i) q^{30} +(-0.987661 + 1.71068i) q^{31} -0.808361 q^{32} +(-0.916405 + 1.58726i) q^{33} +4.73830 q^{34} +(4.76096 - 8.24623i) q^{36} -9.62867 q^{37} +(-7.64942 + 13.2492i) q^{38} +(0.752198 - 2.61092i) q^{39} +(0.795393 + 1.37766i) q^{40} +(6.26793 - 10.8564i) q^{41} +(4.20368 + 7.28099i) q^{43} +(4.76096 + 8.24623i) q^{44} +0.830652 q^{45} -8.97318 q^{46} +(-4.50265 - 7.79882i) q^{47} +(1.31797 + 2.28279i) q^{48} +(5.93840 - 10.2856i) q^{50} +(0.734087 + 1.27148i) q^{51} +(-9.79320 - 10.1665i) q^{52} +(-0.746129 + 1.29233i) q^{53} +9.95601 q^{54} +(-0.415326 + 0.719366i) q^{55} -4.74039 q^{57} +(-5.40090 + 9.35464i) q^{58} -0.626991 q^{59} +(-0.503834 + 0.872666i) q^{60} +(-0.571597 + 0.990035i) q^{61} +(-2.40209 + 4.16054i) q^{62} -8.96169 q^{64} +(0.340905 - 1.18330i) q^{65} +(-2.22879 + 3.86037i) q^{66} +(2.79599 + 4.84280i) q^{67} +7.62754 q^{68} +(-1.39018 - 2.40786i) q^{69} +(-4.74859 - 8.22481i) q^{71} +(5.66402 - 9.81038i) q^{72} +(5.95934 - 10.3219i) q^{73} -23.4179 q^{74} +3.68006 q^{75} +(-12.3138 + 21.3281i) q^{76} +(1.82942 - 6.35002i) q^{78} +(-2.23583 - 3.87258i) q^{79} +(0.597321 + 1.03459i) q^{80} +(-2.10570 - 3.64718i) q^{81} +(15.2442 - 26.4038i) q^{82} -1.41231 q^{83} +(0.332697 + 0.576248i) q^{85} +(10.2238 + 17.7081i) q^{86} -3.34697 q^{87} +(5.66402 + 9.81038i) q^{88} -12.4444 q^{89} +2.02023 q^{90} -14.4447 q^{92} -1.48859 q^{93} +(-10.9509 - 18.9675i) q^{94} -2.14840 q^{95} +(-0.304587 - 0.527560i) q^{96} +(5.13850 + 8.90014i) q^{97} +5.91511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44}+ \cdots + 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 24 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 + 8 * q^16 + 28 * q^18 + 28 * q^22 - 24 * q^23 + 12 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 + 16 * q^37 + 20 * q^39 + 32 * q^43 + 4 * q^44 + 8 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 - 48 * q^58 - 64 * q^60 - 64 * q^64 - 68 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 - 152 * q^74 + 28 * q^78 + 4 * q^79 + 56 * q^81 + 36 * q^85 - 4 * q^86 + 28 * q^88 - 160 * q^92 - 16 * q^93 - 104 * q^95 + 56 * q^99

Introduction

L-functions

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