LMFDB - Embedded newform 378.2.w.a.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	378.121
Dual form			378.2.w.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-1.58205 + 0.705062i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.56427 - 0.569347i) q^{5} +(1.72779 - 0.121449i) q^{6} +(0.319985 + 2.62633i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00577 - 2.23089i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.58205 + 0.705062i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.56427 - 0.569347i) q^{5} +(1.72779 - 0.121449i) q^{6} +(0.319985 + 2.62633i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00577 - 2.23089i) q^{9} -1.66466 q^{10} +(-2.55453 - 0.929774i) q^{11} +(-1.66513 - 0.476814i) q^{12} +(-0.391548 + 2.22058i) q^{13} +(0.597570 - 2.57738i) q^{14} +(-2.07333 + 2.00364i) q^{15} +(0.173648 + 0.984808i) q^{16} +7.12702 q^{17} +(-2.64782 + 1.41034i) q^{18} -3.53203 q^{19} +(1.56427 + 0.569347i) q^{20} +(-2.35796 - 3.92938i) q^{21} +(2.08247 + 1.74740i) q^{22} +(-0.455505 + 2.58330i) q^{23} +(1.40163 + 1.01757i) q^{24} +(-1.70744 + 1.43271i) q^{25} +(1.12742 - 1.95275i) q^{26} +(-1.60032 + 4.94358i) q^{27} +(-1.44305 + 2.21757i) q^{28} +(1.52100 + 8.62604i) q^{29} +(2.63358 - 1.17369i) q^{30} +(6.70932 + 5.62979i) q^{31} +(0.173648 - 0.984808i) q^{32} +(4.69695 - 0.330155i) q^{33} +(-6.69721 - 2.43759i) q^{34} +(1.99584 + 3.92610i) q^{35} +(2.97050 - 0.419674i) q^{36} +(4.94878 + 8.57154i) q^{37} +(3.31903 + 1.20803i) q^{38} +(-0.946199 - 3.78914i) q^{39} +(-1.27520 - 1.07002i) q^{40} +(0.959980 - 5.44432i) q^{41} +(0.871830 + 4.49888i) q^{42} +(-0.952500 + 0.799242i) q^{43} +(-1.35924 - 2.35427i) q^{44} +(1.86742 - 4.63169i) q^{45} +(1.31158 - 2.27172i) q^{46} +(0.462175 - 0.387811i) q^{47} +(-0.969071 - 1.43558i) q^{48} +(-6.79522 + 1.68077i) q^{49} +(2.09449 - 0.762331i) q^{50} +(-11.2753 + 5.02500i) q^{51} +(-1.72731 + 1.44938i) q^{52} +(-2.22157 - 3.84788i) q^{53} +(3.19461 - 4.09810i) q^{54} -4.52534 q^{55} +(2.11448 - 1.59028i) q^{56} +(5.58786 - 2.49030i) q^{57} +(1.52100 - 8.62604i) q^{58} +(1.88446 - 10.6873i) q^{59} +(-2.87618 + 0.202170i) q^{60} +(-7.23297 + 6.06918i) q^{61} +(-4.37920 - 7.58500i) q^{62} +(6.50087 + 4.55397i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.651795 + 3.69651i) q^{65} +(-4.52661 - 1.29621i) q^{66} +(0.977175 - 0.355662i) q^{67} +(5.45962 + 4.58116i) q^{68} +(-1.10075 - 4.40807i) q^{69} +(-0.532666 - 4.37195i) q^{70} +(-0.486389 + 0.842451i) q^{71} +(-2.93489 - 0.621606i) q^{72} +(3.95827 - 6.85593i) q^{73} +(-1.71869 - 9.74720i) q^{74} +(1.69111 - 3.47048i) q^{75} +(-2.70569 - 2.27035i) q^{76} +(1.62448 - 7.00656i) q^{77} +(-0.406826 + 3.88425i) q^{78} +(-0.744351 - 0.270922i) q^{79} +(0.832330 + 1.44164i) q^{80} +(-0.953742 - 8.94932i) q^{81} +(-2.76415 + 4.78765i) q^{82} +(1.53575 + 8.70965i) q^{83} +(0.719455 - 4.52575i) q^{84} +(11.1486 - 4.05775i) q^{85} +(1.16841 - 0.425268i) q^{86} +(-8.48820 - 12.5744i) q^{87} +(0.472059 + 2.67718i) q^{88} -6.88195 q^{89} +(-3.33893 + 3.71367i) q^{90} +(-5.95727 - 0.317783i) q^{91} +(-2.00945 + 1.68613i) q^{92} +(-14.5839 - 4.17613i) q^{93} +(-0.566941 + 0.206350i) q^{94} +(-5.52505 + 2.01095i) q^{95} +(0.419631 + 1.68045i) q^{96} +(13.0432 - 10.9446i) q^{97} +(6.96028 + 0.744693i) q^{98} +(-7.19804 + 3.83397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−1.58205	+	0.705062i	−0.913398	+	0.407068i
$3$	−1.58205	+	0.705062i	−0.913398	+	0.407068i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	1.56427	−	0.569347i	0.699562	−	0.254620i	0.0323383	−	0.999477i	$-0.489705\pi$
$5$	1.56427	−	0.569347i	0.699562	−	0.254620i	0.667224	+	0.744857i	$0.267482\pi$
$6$	1.72779	−	0.121449i	0.705366	−	0.0495811i
$7$	0.319985	+	2.62633i	0.120943	+	0.992659i
$7$	0.319985	+	2.62633i	0.120943	+	0.992659i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.00577	−	2.23089i	0.668591	−	0.743630i
$10$	−1.66466			−0.526412
$11$	−2.55453	−	0.929774i	−0.770221	−	0.280337i	−0.0731319	−	0.997322i	$-0.523299\pi$
$11$	−2.55453	−	0.929774i	−0.770221	−	0.280337i	−0.697089	+	0.716985i	$0.745522\pi$
$12$	−1.66513	−	0.476814i	−0.480681	−	0.137644i
$13$	−0.391548	+	2.22058i	−0.108596	+	0.615878i	0.881127	+	0.472880i	$0.156786\pi$
$13$	−0.391548	+	2.22058i	−0.108596	+	0.615878i	−0.989723	+	0.142999i	$0.954326\pi$
$14$	0.597570	−	2.57738i	0.159707	−	0.688835i
$15$	−2.07333	+	2.00364i	−0.535331	+	0.517339i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	7.12702			1.72856			0.864279	−	0.503014i	$-0.167775\pi$
$17$	7.12702			1.72856			0.864279	+	0.503014i	$0.167775\pi$
$18$	−2.64782	+	1.41034i	−0.624097	+	0.332419i
$19$	−3.53203			−0.810304			−0.405152	−	0.914249i	$-0.632781\pi$
$19$	−3.53203			−0.810304			−0.405152	+	0.914249i	$0.632781\pi$
$20$	1.56427	+	0.569347i	0.349781	+	0.127310i
$21$	−2.35796	−	3.92938i	−0.514549	−	0.857461i
$22$	2.08247	+	1.74740i	0.443985	+	0.372548i
$23$	−0.455505	+	2.58330i	−0.0949794	+	0.538655i	0.899774	+	0.436356i	$0.143731\pi$
$23$	−0.455505	+	2.58330i	−0.0949794	+	0.538655i	−0.994754	+	0.102299i	$0.967380\pi$
$24$	1.40163	+	1.01757i	0.286106	+	0.207710i
$25$	−1.70744	+	1.43271i	−0.341488	+	0.286543i
$26$	1.12742	−	1.95275i	0.221105	−	0.382965i
$27$	−1.60032	+	4.94358i	−0.307982	+	0.951392i
$28$	−1.44305	+	2.21757i	−0.272711	+	0.419081i
$29$	1.52100	+	8.62604i	0.282443	+	1.60182i	0.714278	+	0.699862i	$0.246755\pi$
$29$	1.52100	+	8.62604i	0.282443	+	1.60182i	−0.431835	+	0.901953i	$0.642134\pi$
$30$	2.63358	−	1.17369i	0.480823	−	0.214285i
$31$	6.70932	+	5.62979i	1.20503	+	1.01114i	0.999472	+	0.0324957i	$0.0103455\pi$
$31$	6.70932	+	5.62979i	1.20503	+	1.01114i	0.205558	+	0.978645i	$0.434099\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	4.69695	−	0.330155i	0.817634	−	0.0574726i
$34$	−6.69721	−	2.43759i	−1.14856	−	0.418042i
$35$	1.99584	+	3.92610i	0.337358	+	0.663633i
$36$	2.97050	−	0.419674i	0.495083	−	0.0699457i
$37$	4.94878	+	8.57154i	0.813575	+	1.40915i	0.910347	+	0.413846i	$0.135815\pi$
$37$	4.94878	+	8.57154i	0.813575	+	1.40915i	−0.0967722	+	0.995307i	$0.530852\pi$
$38$	3.31903	+	1.20803i	0.538417	+	0.195968i
$39$	−0.946199	−	3.78914i	−0.151513	−	0.606748i
$40$	−1.27520	−	1.07002i	−0.201627	−	0.169185i
$41$	0.959980	−	5.44432i	0.149924	−	0.850260i	−0.813357	−	0.581765i	$-0.802363\pi$
$41$	0.959980	−	5.44432i	0.149924	−	0.850260i	0.963281	−	0.268495i	$-0.0865264\pi$
$42$	0.871830	+	4.49888i	0.134526	+	0.694192i
$43$	−0.952500	+	0.799242i	−0.145255	+	0.121883i	−0.712520	−	0.701652i	$-0.752446\pi$
$43$	−0.952500	+	0.799242i	−0.145255	+	0.121883i	0.567265	+	0.823535i	$0.308002\pi$
$44$	−1.35924	−	2.35427i	−0.204913	−	0.354920i
$45$	1.86742	−	4.63169i	0.278378	−	0.690452i
$46$	1.31158	−	2.27172i	0.193381	−	0.334946i
$47$	0.462175	−	0.387811i	0.0674151	−	0.0565680i	−0.608457	−	0.793586i	$-0.708211\pi$
$47$	0.462175	−	0.387811i	0.0674151	−	0.0565680i	0.675873	+	0.737018i	$0.263767\pi$
$48$	−0.969071	−	1.43558i	−0.139873	−	0.207209i
$49$	−6.79522	+	1.68077i	−0.970746	+	0.240110i
$50$	2.09449	−	0.762331i	0.296205	−	0.107810i
$51$	−11.2753	+	5.02500i	−1.57886	+	0.703640i
$52$	−1.72731	+	1.44938i	−0.239534	+	0.200993i
$53$	−2.22157	−	3.84788i	−0.305157	−	0.528547i	0.672139	−	0.740425i	$-0.265376\pi$
$53$	−2.22157	−	3.84788i	−0.305157	−	0.528547i	−0.977296	+	0.211878i	$0.932042\pi$
$54$	3.19461	−	4.09810i	0.434732	−	0.557681i
$55$	−4.52534			−0.610197
$56$	2.11448	−	1.59028i	0.282559	−	0.212510i
$57$	5.58786	−	2.49030i	0.740130	−	0.329849i
$58$	1.52100	−	8.62604i	0.199718	−	1.13265i
$59$	1.88446	−	10.6873i	0.245336	−	1.39137i	−0.574376	−	0.818592i	$-0.694755\pi$
$59$	1.88446	−	10.6873i	0.245336	−	1.39137i	0.819712	−	0.572776i	$-0.194134\pi$
$60$	−2.87618	+	0.202170i	−0.371313	+	0.0261001i
$61$	−7.23297	+	6.06918i	−0.926087	+	0.777079i	−0.975111	−	0.221718i	$-0.928833\pi$
$61$	−7.23297	+	6.06918i	−0.926087	+	0.777079i	0.0490236	+	0.998798i	$0.484389\pi$
$62$	−4.37920	−	7.58500i	−0.556159	−	0.963296i
$63$	6.50087	+	4.55397i	0.819033	+	0.573747i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.651795	+	3.69651i	0.0808452	+	0.458496i
$66$	−4.52661	−	1.29621i	−0.557187	−	0.159552i
$67$	0.977175	−	0.355662i	0.119381	−	0.0434511i	−0.281639	−	0.959520i	$-0.590878\pi$
$67$	0.977175	−	0.355662i	0.119381	−	0.0434511i	0.401020	+	0.916069i	$0.368656\pi$
$68$	5.45962	+	4.58116i	0.662076	+	0.555548i
$69$	−1.10075	−	4.40807i	−0.132515	−	0.530669i
$70$	−0.532666	−	4.37195i	−0.0636658	−	0.522548i
$71$	−0.486389	+	0.842451i	−0.0577238	+	0.0999805i	−0.893443	−	0.449176i	$-0.851718\pi$
$71$	−0.486389	+	0.842451i	−0.0577238	+	0.0999805i	0.835719	+	0.549157i	$0.185051\pi$
$72$	−2.93489	−	0.621606i	−0.345881	−	0.0732570i
$73$	3.95827	−	6.85593i	0.463281	−	0.802425i	−0.535842	−	0.844319i	$-0.680006\pi$
$73$	3.95827	−	6.85593i	0.463281	−	0.802425i	0.999122	+	0.0418931i	$0.0133389\pi$
$74$	−1.71869	−	9.74720i	−0.199794	−	1.13309i
$75$	1.69111	−	3.47048i	0.195272	−	0.400736i
$76$	−2.70569	−	2.27035i	−0.310364	−	0.260427i
$77$	1.62448	−	7.00656i	0.185127	−	0.798472i
$78$	−0.406826	+	3.88425i	−0.0460640	+	0.439804i
$79$	−0.744351	−	0.270922i	−0.0837461	−	0.0304811i	0.299807	−	0.954000i	$-0.403078\pi$
$79$	−0.744351	−	0.270922i	−0.0837461	−	0.0304811i	−0.383553	+	0.923519i	$0.625300\pi$
$80$	0.832330	+	1.44164i	0.0930573	+	0.161180i
$81$	−0.953742	−	8.94932i	−0.105971	−	0.994369i
$82$	−2.76415	+	4.78765i	−0.305250	+	0.528708i
$83$	1.53575	+	8.70965i	0.168570	+	0.956008i	0.945307	+	0.326183i	$0.105763\pi$
$83$	1.53575	+	8.70965i	0.168570	+	0.956008i	−0.776737	+	0.629826i	$0.783126\pi$
$84$	0.719455	−	4.52575i	0.0784990	−	0.493799i
$85$	11.1486	−	4.05775i	1.20923	−	0.440125i
$86$	1.16841	−	0.425268i	0.125993	−	0.0458578i
$87$	−8.48820	−	12.5744i	−0.910031	−	1.34812i
$88$	0.472059	+	2.67718i	0.0503216	+	0.285388i
$89$	−6.88195			−0.729486			−0.364743	−	0.931108i	$-0.618843\pi$
$89$	−6.88195			−0.729486			−0.364743	+	0.931108i	$0.618843\pi$
$90$	−3.33893	+	3.71367i	−0.351954	+	0.391456i
$91$	−5.95727	−	0.317783i	−0.624491	−	0.0333127i
$92$	−2.00945	+	1.68613i	−0.209500	+	0.175791i
$93$	−14.5839	−	4.17613i	−1.51228	−	0.433044i
$94$	−0.566941	+	0.206350i	−0.0584755	+	0.0212834i
$95$	−5.52505	+	2.01095i	−0.566858	+	0.206320i
$96$	0.419631	+	1.68045i	0.0428284	+	0.171510i
$97$	13.0432	−	10.9446i	1.32434	−	1.11125i	0.338976	−	0.940795i	$-0.389920\pi$
$97$	13.0432	−	10.9446i	1.32434	−	1.11125i	0.985365	−	0.170458i	$-0.0545248\pi$
$98$	6.96028	+	0.744693i	0.703094	+	0.0752254i
$99$	−7.19804	+	3.83397i	−0.723430	+	0.385328i
$100$	−2.22891			−0.222891
$101$	−0.823926	−	4.67272i	−0.0819837	−	0.464953i	−0.997967	−	0.0637358i	$-0.979699\pi$
$101$	−0.823926	−	4.67272i	−0.0819837	−	0.464953i	0.915983	−	0.401217i	$-0.131413\pi$
$102$	12.3140	−	0.865566i	1.21927	−	0.0857038i
$103$	13.2148	−	4.80978i	1.30209	−	0.473922i	0.404413	−	0.914576i	$-0.367476\pi$
$103$	13.2148	−	4.80978i	1.30209	−	0.473922i	0.897677	+	0.440654i	$0.145253\pi$
$104$	2.11885	−	0.771200i	0.207771	−	0.0756224i
$105$	−5.92566	−	4.80411i	−0.578286	−	0.468833i
$106$	0.771545	+	4.37565i	0.0749391	+	0.425001i
$107$	−6.02453	+	10.4348i	−0.582413	+	1.00877i	0.412779	+	0.910831i	$0.364558\pi$
$107$	−6.02453	+	10.4348i	−0.582413	+	1.00877i	−0.995193	+	0.0979380i	$0.968775\pi$
$108$	−4.40359	+	2.75833i	−0.423735	+	0.265421i
$109$	−0.493499	−	0.854765i	−0.0472686	−	0.0818717i	0.841423	−	0.540377i	$-0.181718\pi$
$109$	−0.493499	−	0.854765i	−0.0472686	−	0.0818717i	−0.888692	+	0.458505i	$0.848385\pi$
$110$	4.25243	+	1.54776i	0.405453	+	0.147573i
$111$	−13.8727	−	10.0714i	−1.31674	−	0.955937i
$112$	−2.53087	+	0.771181i	−0.239144	+	0.0728698i
$113$	−5.24150	−	4.39814i	−0.493079	−	0.413742i	0.362049	−	0.932159i	$-0.382077\pi$
$113$	−5.24150	−	4.39814i	−0.493079	−	0.413742i	−0.855128	+	0.518417i	$0.826522\pi$
$114$	−6.10260	+	0.428960i	−0.571561	+	0.0401758i
$115$	0.758262	+	4.30032i	0.0707083	+	0.401006i
$116$	−4.37955	+	7.58561i	−0.406631	+	0.704306i
$117$	4.16852	+	5.32749i	0.385379	+	0.492526i
$118$	−5.42608	+	9.39825i	−0.499512	+	0.865179i
$119$	2.28054	+	18.7179i	0.209057	+	1.71587i
$120$	2.77187	+	0.793733i	0.253036	+	0.0724576i
$121$	−2.76533	−	2.32039i	−0.251394	−	0.210944i
$122$	8.87255	−	3.22935i	0.803283	−	0.292371i
$123$	2.31985	+	9.29004i	0.209174	+	0.837655i
$124$	1.52088	+	8.62534i	0.136579	+	0.774579i
$125$	−6.01684	+	10.4215i	−0.538162	+	0.932124i
$126$	−4.55127	−	6.50276i	−0.405459	−	0.579312i
$127$	4.91915	+	8.52021i	0.436504	+	0.756047i	0.997417	−	0.0718278i	$-0.0228832\pi$
$127$	4.91915	+	8.52021i	0.436504	+	0.756047i	−0.560913	+	0.827875i	$0.689550\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	0.943388	−	1.93601i	0.0830607	−	0.170457i
$130$	0.651795	−	3.69651i	0.0571662	−	0.324206i
$131$	3.83924	−	21.7734i	0.335436	−	1.90235i	−0.0874499	−	0.996169i	$-0.527872\pi$
$131$	3.83924	−	21.7734i	0.335436	−	1.90235i	0.422886	−	0.906183i	$-0.361017\pi$
$132$	3.81029	+	2.76623i	0.331643	+	0.240769i
$133$	−1.13020	−	9.27628i	−0.0980005	−	0.804356i
$134$	−1.03989			−0.0898326
$135$	0.311282	+	8.64423i	0.0267909	+	0.743977i
$136$	−3.56351	−	6.17218i	−0.305569	−	0.529260i
$137$	−3.48667	+	2.92566i	−0.297886	+	0.249956i	−0.779464	−	0.626447i	$-0.784508\pi$
$137$	−3.48667	+	2.92566i	−0.297886	+	0.249956i	0.481578	+	0.876403i	$0.340064\pi$
$138$	−0.473279	+	4.51871i	−0.0402882	+	0.384658i
$139$	9.92396	−	3.61203i	0.841739	−	0.306368i	0.115072	−	0.993357i	$-0.463290\pi$
$139$	9.92396	−	3.61203i	0.841739	−	0.306368i	0.726668	+	0.686989i	$0.241068\pi$
$140$	−0.994752	+	4.29047i	−0.0840719	+	0.362611i
$141$	−0.457754	+	0.939399i	−0.0385498	+	0.0791116i
$142$	0.745192	−	0.625290i	0.0625351	−	0.0524732i
$143$	3.06486	−	5.30850i	0.256297	−	0.443919i
$144$	2.54530	+	1.58791i	0.212108	+	0.132326i
$145$	7.29047	+	12.6275i	0.605441	+	1.04865i
$146$	−6.06442	+	5.08865i	−0.501895	+	0.421140i
$147$	9.56534	−	7.45012i	0.788936	−	0.614476i
$148$	−1.71869	+	9.74720i	−0.141276	+	0.801215i
$149$	−5.97358	−	5.01242i	−0.489374	−	0.410634i	0.364428	−	0.931232i	$-0.381265\pi$
$149$	−5.97358	−	5.01242i	−0.489374	−	0.410634i	−0.853802	+	0.520598i	$0.825709\pi$
$150$	−2.77609	+	2.68279i	−0.226667	+	0.219049i
$151$	−15.7890	−	5.74674i	−1.28489	−	0.467663i	−0.392846	−	0.919604i	$-0.628510\pi$
$151$	−15.7890	−	5.74674i	−1.28489	−	0.467663i	−0.892048	+	0.451941i	$0.850732\pi$
$152$	1.76602	+	3.05883i	0.143243	+	0.248104i
$153$	14.2952	−	15.8996i	1.15570	−	1.28541i
$154$	−3.92290	+	6.02841i	−0.316116	+	0.485783i
$155$	13.7005	+	4.98657i	1.10045	+	0.400531i
$156$	1.71078	−	3.51085i	0.136972	−	0.281093i
$157$	1.77460	−	10.0643i	0.141629	−	0.803217i	−0.828383	−	0.560161i	$-0.810739\pi$
$157$	1.77460	−	10.0643i	0.141629	−	0.803217i	0.970012	−	0.243056i	$-0.0781498\pi$
$158$	0.606801	+	0.509166i	0.0482745	+	0.0405071i
$159$	6.22764	+	4.52120i	0.493884	+	0.358554i
$160$	−0.289065	−	1.63937i	−0.0228526	−	0.129604i
$161$	−6.93035	−	0.369691i	−0.546188	−	0.0291357i
$162$	−2.16462	+	8.73581i	−0.170069	+	0.686350i
$163$	9.74051	−	16.8711i	0.762936	−	1.32144i	−0.178395	−	0.983959i	$-0.557090\pi$
$163$	9.74051	−	16.8711i	0.762936	−	1.32144i	0.941331	−	0.337485i	$-0.109576\pi$
$164$	4.23493	−	3.55353i	0.330692	−	0.277484i
$165$	7.15932	−	3.19065i	0.557352	−	0.248392i
$166$	1.53575	−	8.70965i	0.119197	−	0.676000i
$167$	13.6941	+	11.4907i	1.05968	+	0.889179i	0.994078	−	0.108667i	$-0.0346583\pi$
$167$	13.6941	+	11.4907i	1.05968	+	0.889179i	0.0656035	+	0.997846i	$0.479103\pi$
$168$	−2.22396	+	4.00674i	−0.171583	+	0.309127i
$169$	7.43833	+	2.70733i	0.572179	+	0.208256i
$170$	−11.8641			−0.909933
$171$	−7.08446	+	7.87958i	−0.541762	+	0.602566i
$172$	−1.24340			−0.0948084
$173$	0.235749	+	1.33700i	0.0179237	+	0.101650i	0.992457	−	0.122592i	$-0.0391205\pi$
$173$	0.235749	+	1.33700i	0.0179237	+	0.101650i	−0.974534	+	0.224242i	$0.928009\pi$
$174$	3.67559	+	14.7192i	0.278646	+	1.11586i
$175$	−4.30913	−	4.02586i	−0.325740	−	0.304326i
$176$	0.472059	−	2.67718i	0.0355828	−	0.201800i
$177$	4.55390	+	18.2365i	0.342292	+	1.37074i
$178$	6.46692	+	2.35377i	0.484716	+	0.176422i
$179$	9.60898			0.718209			0.359104	−	0.933297i	$-0.383082\pi$
$179$	9.60898			0.718209			0.359104	+	0.933297i	$0.383082\pi$
$180$	4.40772	−	2.34773i	0.328532	−	0.174989i
$181$	−2.78085	−	4.81657i	−0.206699	−	0.358013i	0.743974	−	0.668209i	$-0.232939\pi$
$181$	−2.78085	−	4.81657i	−0.206699	−	0.358013i	−0.950673	+	0.310196i	$0.899605\pi$
$182$	5.48931	+	2.33612i	0.406895	+	0.173165i
$183$	7.16378	−	14.7015i	0.529562	−	1.08676i
$184$	2.46496	−	0.897170i	0.181719	−	0.0661403i
$185$	12.6214	+	10.5906i	0.927944	+	0.778638i
$186$	12.2760	+	8.91225i	0.900121	+	0.653478i
$187$	−18.2062	−	6.62652i	−1.33137	−	0.484579i
$188$	0.603326			0.0440021
$189$	−13.4955	−	2.62110i	−0.981657	−	0.190657i
$190$	5.87964			0.426554
$191$	−15.9589	−	5.80857i	−1.15475	−	0.420294i	−0.307529	−	0.951539i	$-0.599502\pi$
$191$	−15.9589	−	5.80857i	−1.15475	−	0.420294i	−0.847218	+	0.531245i	$0.821724\pi$
$192$	0.180424	−	1.72263i	0.0130210	−	0.124320i
$193$	17.0542	+	14.3102i	1.22759	+	1.03007i	0.998392	+	0.0566875i	$0.0180539\pi$
$193$	17.0542	+	14.3102i	1.22759	+	1.03007i	0.229195	+	0.973380i	$0.426391\pi$
$194$	−15.9999	+	5.82349i	−1.14873	+	0.418102i
$195$	−3.63745	−	5.38852i	−0.260483	−	0.385880i
$196$	−6.28582	−	3.08034i	−0.448987	−	0.220024i
$197$	−0.401069	−	0.694672i	−0.0285750	−	0.0494934i	0.851384	−	0.524543i	$-0.175764\pi$
$197$	−0.401069	−	0.694672i	−0.0285750	−	0.0494934i	−0.879959	+	0.475049i	$0.842430\pi$
$198$	8.07524	−	1.14088i	0.573882	−	0.0810785i
$199$	−2.38942			−0.169382			−0.0846908	−	0.996407i	$-0.526990\pi$
$199$	−2.38942			−0.169382			−0.0846908	+	0.996407i	$0.526990\pi$
$200$	2.09449	+	0.762331i	0.148103	+	0.0539049i
$201$	−1.29518	+	1.25165i	−0.0913547	+	0.0882843i
$202$	−0.823926	+	4.67272i	−0.0579712	+	0.328771i
$203$	−22.1681	+	6.75486i	−1.55590	+	0.474098i
$204$	−11.8674	−	3.39826i	−0.830884	−	0.237926i
$205$	−1.59804	−	9.06294i	−0.111612	−	0.632983i
$206$	−14.0629			−0.979806
$207$	4.84942	+	6.19770i	0.337058	+	0.430770i
$208$	−2.25484			−0.156345
$209$	9.02269	+	3.28399i	0.624113	+	0.227158i
$210$	3.92520	+	6.54108i	0.270865	+	0.451378i
$211$	7.96237	+	6.68122i	0.548152	+	0.459954i	0.874315	−	0.485360i	$-0.161311\pi$
$211$	7.96237	+	6.68122i	0.548152	+	0.459954i	−0.326163	+	0.945314i	$0.605756\pi$
$212$	0.771545	−	4.37565i	0.0529899	−	0.300521i
$213$	0.175512	−	1.67574i	0.0120259	−	0.114820i
$214$	9.23011	−	7.74498i	0.630957	−	0.529436i
$215$	−1.03492	+	1.79253i	−0.0705809	+	0.122250i
$216$	5.08143	−	1.08587i	0.345747	−	0.0738842i
$217$	−12.6388	+	19.4223i	−0.857978	+	1.31848i
$218$	0.171390	+	0.972003i	0.0116080	+	0.0658324i
$219$	−1.42833	+	13.6373i	−0.0965177	+	0.921520i
$220$	−3.46661	−	2.90883i	−0.233719	−	0.196113i
$221$	−2.79057	+	15.8261i	−0.187714	+	1.06458i
$222$	9.59144	+	14.2088i	0.643736	+	0.953631i
$223$	−2.39329	−	0.871087i	−0.160267	−	0.0583323i	0.260641	−	0.965436i	$-0.416066\pi$
$223$	−2.39329	−	0.871087i	−0.160267	−	0.0583323i	−0.420908	+	0.907103i	$0.638288\pi$
$224$	2.64200	+	0.140934i	0.176526	+	0.00941654i
$225$	−0.228515	+	6.68281i	−0.0152343	+	0.445521i
$226$	3.42114	+	5.92560i	0.227571	+	0.394165i
$227$	6.72701	+	2.44843i	0.446487	+	0.162508i	0.555472	−	0.831535i	$-0.312538\pi$
$227$	6.72701	+	2.44843i	0.446487	+	0.162508i	−0.108985	+	0.994043i	$0.534760\pi$
$228$	5.88128	+	1.68412i	0.389498	+	0.111534i
$229$	9.98441	+	8.37792i	0.659789	+	0.553628i	0.910023	−	0.414557i	$-0.136063\pi$
$229$	9.98441	+	8.37792i	0.659789	+	0.553628i	−0.250235	+	0.968185i	$0.580508\pi$
$230$	0.758262	−	4.30032i	0.0499983	−	0.283554i
$231$	2.37005	+	12.2301i	0.155938	+	0.804681i
$232$	6.70987	−	5.63025i	0.440524	−	0.369644i
$233$	−8.78382	−	15.2140i	−0.575447	−	0.996704i	−0.995993	−	0.0894324i	$-0.971495\pi$
$233$	−8.78382	−	15.2140i	−0.575447	−	0.996704i	0.420546	−	0.907271i	$-0.361839\pi$
$234$	−2.09502	−	6.43191i	−0.136955	−	0.420467i
$235$	0.502167	−	0.869778i	0.0327577	−	0.0567381i
$236$	8.31324	−	6.97564i	0.541146	−	0.454075i
$237$	1.36862	−	0.0962020i	0.0889013	−	0.00624899i
$238$	4.25890	−	18.3691i	0.276063	−	1.19069i
$239$	−0.201785	+	0.0734437i	−0.0130524	+	0.00475068i	−0.348538	−	0.937295i	$-0.613322\pi$
$239$	−0.201785	+	0.0734437i	−0.0130524	+	0.00475068i	0.335486	+	0.942045i	$0.391100\pi$
$240$	−2.33323	−	1.69390i	−0.150610	−	0.109341i
$241$	−4.92102	+	4.12923i	−0.316991	+	0.265987i	−0.787374	−	0.616475i	$-0.788560\pi$
$241$	−4.92102	+	4.12923i	−0.316991	+	0.265987i	0.470383	+	0.882462i	$0.344116\pi$
$242$	1.80494	+	3.12625i	0.116026	+	0.200963i
$243$	7.81870	+	13.4858i	0.501570	+	0.865117i
$244$	−9.44197			−0.604460
$245$	−9.67261	+	6.49802i	−0.617960	+	0.415143i
$246$	0.997438	−	9.52322i	0.0635943	−	0.607178i
$247$	1.38296	−	7.84317i	0.0879958	−	0.499049i
$248$	1.52088	−	8.62534i	0.0965760	−	0.547710i
$249$	−8.57048	−	12.6963i	−0.543132	−	0.804597i
$250$	9.21833	−	7.73510i	0.583018	−	0.489210i
$251$	−8.78817	−	15.2216i	−0.554704	−	0.960776i	−0.997926	−	0.0643640i	$-0.979498\pi$
$251$	−8.78817	−	15.2216i	−0.554704	−	0.960776i	0.443222	−	0.896412i	$-0.353835\pi$
$252$	2.05272	+	7.66723i	0.129309	+	0.482990i
$253$	3.56549	−	6.17561i	0.224160	−	0.388257i
$254$	−1.70840	−	9.68883i	−0.107195	−	0.607931i
$255$	−14.7767	+	14.2800i	−0.925350	+	0.894249i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−12.5753	−	10.5520i	−0.784428	−	0.658213i	0.159932	−	0.987128i	$-0.448873\pi$
$257$	−12.5753	−	10.5520i	−0.784428	−	0.658213i	−0.944360	+	0.328915i	$0.893317\pi$
$258$	−1.54865	+	1.49660i	−0.0964148	+	0.0931743i
$259$	−20.9282	+	15.7399i	−1.30041	+	0.978030i
$260$	−1.87677	+	3.25066i	−0.116392	+	0.201597i
$261$	22.2945	+	13.9087i	1.38000	+	0.860926i
$262$	−11.0547	+	19.1472i	−0.682959	+	1.18292i
$263$	−3.66178	−	20.7670i	−0.225795	−	1.28055i	−0.861159	−	0.508335i	$-0.830261\pi$
$263$	−3.66178	−	20.7670i	−0.225795	−	1.28055i	0.635364	−	0.772213i	$-0.280850\pi$
$264$	−2.63440	−	3.90260i	−0.162136	−	0.240189i
$265$	−5.66592	−	4.75427i	−0.348055	−	0.292053i
$266$	−2.11064	+	9.10341i	−0.129412	+	0.558166i
$267$	10.8876	−	4.85221i	0.666311	−	0.296950i
$268$	0.977175	+	0.355662i	0.0596904	+	0.0217255i
$269$	4.06583	+	7.04222i	0.247898	+	0.429371i	0.962942	−	0.269707i	$-0.0869270\pi$
$269$	4.06583	+	7.04222i	0.247898	+	0.429371i	−0.715045	+	0.699079i	$0.753594\pi$
$270$	2.66399	−	8.22938i	0.162125	−	0.500824i
$271$	0.278589	−	0.482530i	0.0169231	−	0.0293116i	−0.857440	−	0.514584i	$-0.827946\pi$
$271$	0.278589	−	0.482530i	0.0169231	−	0.0293116i	0.874363	+	0.485273i	$0.161280\pi$
$272$	1.23759	+	7.01875i	0.0750402	+	0.425574i
$273$	9.64876	−	3.69750i	0.583970	−	0.223783i
$274$	4.27703	−	1.55671i	0.258385	−	0.0940444i
$275$	5.69381	−	2.07238i	0.343350	−	0.124969i
$276$	1.99023	−	4.08433i	0.119798	−	0.245848i
$277$	−4.99848	−	28.3478i	−0.300330	−	1.70325i	−0.644713	−	0.764424i	$-0.723023\pi$
$277$	−4.99848	−	28.3478i	−0.300330	−	1.70325i	0.344384	−	0.938829i	$-0.388088\pi$
$278$	−10.5609			−0.633398
$279$	26.0168	−	3.67568i	1.55759	−	0.220057i
$280$	2.40219	−	3.69150i	0.143558	−	0.220609i
$281$	−1.88720	+	1.58355i	−0.112581	+	0.0944664i	−0.697340	−	0.716740i	$-0.745633\pi$
$281$	−1.88720	+	1.58355i	−0.112581	+	0.0944664i	0.584760	+	0.811207i	$0.301189\pi$
$282$	0.751441	−	0.726185i	0.0447477	−	0.0432437i
$283$	−20.9002	+	7.60705i	−1.24239	+	0.452192i	−0.877823	−	0.478985i	$-0.841005\pi$
$283$	−20.9002	+	7.60705i	−1.24239	+	0.452192i	−0.364565	+	0.931178i	$0.618782\pi$
$284$	−0.914113	+	0.332710i	−0.0542426	+	0.0197427i
$285$	7.32307	−	7.07694i	0.433781	−	0.419202i
$286$	−4.69564	+	3.94011i	−0.277659	+	0.232984i
$287$	14.6058	+	0.779126i	0.862151	+	0.0459903i
$288$	−1.84870	−	2.36269i	−0.108936	−	0.139223i
$289$	33.7945			1.98791
$290$	−2.53195	−	14.3594i	−0.148681	−	0.843214i
$291$	−12.9185	+	26.5112i	−0.757294	+	1.55411i
$292$	7.43912	−	2.70762i	0.435341	−	0.158451i
$293$	−12.9815	+	4.72489i	−0.758389	+	0.276031i	−0.692131	−	0.721772i	$-0.743328\pi$
$293$	−12.9815	+	4.72489i	−0.758389	+	0.276031i	−0.0662575	+	0.997803i	$0.521106\pi$
$294$	−11.5366	+	3.72929i	−0.672826	+	0.217496i
$295$	−3.13698	−	17.7907i	−0.182642	−	1.03582i
$296$	4.94878	−	8.57154i	0.287642	−	0.498211i
$297$	8.68448	−	11.1406i	0.503925	−	0.646443i
$298$	3.89897	+	6.75322i	0.225862	+	0.391204i
$299$	−5.55807	−	2.02297i	−0.321432	−	0.116992i
$300$	3.52624	−	1.57152i	0.203588	−	0.0907316i
$301$	−2.40386	−	2.24583i	−0.138556	−	0.129448i
$302$	12.8713	+	10.8003i	0.740663	+	0.621490i
$303$	4.59805	+	6.81156i	0.264151	+	0.391314i
$304$	−0.613331	−	3.47837i	−0.0351770	−	0.199498i
$305$	−7.85884	+	13.6119i	−0.449996	+	0.779416i
$306$	−18.8711	+	10.0515i	−1.07879	+	0.574606i
$307$	−2.51120	+	4.34952i	−0.143322	+	0.248240i	−0.928746	−	0.370718i	$-0.879112\pi$
$307$	−2.51120	+	4.34952i	−0.143322	+	0.248240i	0.785424	+	0.618958i	$0.212445\pi$
$308$	5.74815	−	4.32314i	0.327532	−	0.246334i
$309$	−17.5153	+	16.9266i	−0.996408	+	0.962919i
$310$	−11.1687	−	9.37169i	−0.634342	−	0.532276i
$311$	18.3110	−	6.66466i	1.03832	−	0.377918i	0.234078	−	0.972218i	$-0.424793\pi$
$311$	18.3110	−	6.66466i	1.03832	−	0.377918i	0.804244	+	0.594299i	$0.202571\pi$
$312$	−2.80839	+	2.71400i	−0.158994	+	0.153650i
$313$	−0.629073	−	3.56765i	−0.0355573	−	0.201656i	0.961854	−	0.273563i	$-0.0882024\pi$
$313$	−0.629073	−	3.56765i	−0.0355573	−	0.201656i	−0.997411	+	0.0719079i	$0.977091\pi$
$314$	−5.10977	+	8.85038i	−0.288361	+	0.499456i
$315$	12.7619	+	3.42239i	0.719052	+	0.192830i
$316$	−0.396061	−	0.685998i	−0.0222802	−	0.0385904i
$317$	−25.5479	+	21.4373i	−1.43492	+	1.20404i	−0.492180	+	0.870493i	$0.663800\pi$
$317$	−25.5479	+	21.4373i	−1.43492	+	1.20404i	−0.942735	+	0.333543i	$0.891756\pi$
$318$	−4.30573	−	6.37851i	−0.241453	−	0.357689i
$319$	4.13481	−	23.4497i	0.231505	−	1.31293i
$320$	−0.289065	+	1.63937i	−0.0161592	+	0.0916436i
$321$	2.17394	−	20.7560i	0.121337	−	1.15849i
$322$	6.38596	+	2.71772i	0.355876	+	0.151452i
$323$	−25.1729			−1.40066
$324$	5.02190	−	7.46863i	0.278995	−	0.414924i
$325$	−2.51291	−	4.35249i	−0.139391	−	0.241433i
$326$	−14.9233	+	12.5222i	−0.826527	+	0.693538i
$327$	1.38340	+	1.00434i	0.0765024	+	0.0555399i
$328$	−5.19491	+	1.89079i	−0.286841	+	0.104402i
$329$	1.16641	+	1.08973i	0.0643062	+	0.0600788i
$330$	−7.81883	+	0.549596i	−0.430412	+	0.0302543i
$331$	−2.72406	+	2.28575i	−0.149728	+	0.125636i	−0.714575	−	0.699559i	$-0.753380\pi$
$331$	−2.72406	+	2.28575i	−0.149728	+	0.125636i	0.564847	+	0.825196i	$0.308935\pi$
$332$	−4.42201	+	7.65914i	−0.242689	+	0.420350i
$333$	29.0483	+	6.15238i	1.59184	+	0.337149i
$334$	−8.93819	−	15.4814i	−0.489076	−	0.847105i
$335$	1.32607	−	1.11270i	0.0724509	−	0.0607935i
$336$	3.46023	−	3.00447i	0.188771	−	0.163907i
$337$	−6.23333	+	35.3510i	−0.339551	+	1.92569i	0.0370447	+	0.999314i	$0.488206\pi$
$337$	−6.23333	+	35.3510i	−0.339551	+	1.92569i	−0.376596	+	0.926378i	$0.622906\pi$
$338$	−6.06379	−	5.08812i	−0.329826	−	0.276757i
$339$	11.3933	+	3.26250i	0.618798	+	0.177195i
$340$	11.1486	+	4.05775i	0.604617	+	0.220062i
$341$	−11.9048	−	20.6196i	−0.644679	−	1.11662i
$342$	9.35219	−	4.98135i	0.505708	−	0.269361i
$343$	−6.58863	−	17.3087i	−0.355753	−	0.934580i
$344$	1.16841	+	0.425268i	0.0629966	+	0.0229289i
$345$	−4.23160	−	6.26870i	−0.227822	−	0.337495i
$346$	0.235749	−	1.33700i	0.0126740	−	0.0718776i
$347$	−11.8007	−	9.90200i	−0.633497	−	0.531567i	0.268516	−	0.963275i	$-0.413467\pi$
$347$	−11.8007	−	9.90200i	−0.633497	−	0.531567i	−0.902013	+	0.431708i	$0.857911\pi$
$348$	1.58035	−	15.0887i	0.0847157	−	0.808838i
$349$	−3.89158	−	22.0703i	−0.208312	−	1.18139i	−0.892143	−	0.451753i	$-0.850799\pi$
$349$	−3.89158	−	22.0703i	−0.208312	−	1.18139i	0.683831	−	0.729640i	$-0.260312\pi$
$350$	2.67234	+	5.25688i	0.142842	+	0.280992i
$351$	−10.3510	−	5.48929i	−0.552496	−	0.292997i
$352$	−1.35924	+	2.35427i	−0.0724477	+	0.125483i
$353$	3.93425	−	3.30123i	0.209399	−	0.175707i	−0.532056	−	0.846709i	$-0.678580\pi$
$353$	3.93425	−	3.30123i	0.209399	−	0.175707i	0.741455	+	0.671003i	$0.234136\pi$
$354$	1.95799	−	18.6942i	0.104066	−	0.993588i
$355$	−0.281196	+	1.59474i	−0.0149244	+	0.0846403i
$356$	−5.27188	−	4.42363i	−0.279409	−	0.234452i
$357$	−16.8052	−	28.0048i	−0.889427	−	1.48217i
$358$	−9.02949	−	3.28646i	−0.477223	−	0.173695i
$359$	33.6761			1.77736			0.888679	−	0.458531i	$-0.151624\pi$
$359$	33.6761			1.77736			0.888679	+	0.458531i	$0.151624\pi$
$360$	−4.94487	+	0.698615i	−0.260618	+	0.0368203i
$361$	−6.52474			−0.343407
$362$	0.965778	+	5.47720i	0.0507602	+	0.287875i
$363$	6.01091	+	1.72124i	0.315491	+	0.0903418i
$364$	−4.35927	−	4.07269i	−0.228488	−	0.213467i
$365$	2.28840	−	12.9781i	0.119780	−	0.679307i
$366$	−11.7599	+	11.3647i	−0.614702	+	0.594042i
$367$	6.72236	+	2.44674i	0.350904	+	0.127719i	0.511458	−	0.859308i	$-0.329106\pi$
$367$	6.72236	+	2.44674i	0.350904	+	0.127719i	−0.160553	+	0.987027i	$0.551328\pi$
$368$	−2.62315			−0.136741
$369$	−10.2202	−	13.0617i	−0.532041	−	0.679964i
$370$	−8.23804	−	14.2687i	−0.428275	−	0.741795i
$371$	9.39493	−	7.06585i	0.487761	−	0.366841i
$372$	−8.48752	−	12.5734i	−0.440057	−	0.651901i
$373$	−14.4455	+	5.25773i	−0.747959	+	0.272235i	−0.687747	−	0.725951i	$-0.741400\pi$
$373$	−14.4455	+	5.25773i	−0.747959	+	0.272235i	−0.0602123	+	0.998186i	$0.519178\pi$
$374$	14.8418	+	12.4538i	0.767453	+	0.643970i
$375$	2.17116	−	20.7295i	0.112118	−	1.07047i
$376$	−0.566941	−	0.206350i	−0.0292378	−	0.0106417i
$377$	−19.7504			−1.01720
$378$	11.7852	+	7.07878i	0.606165	+	0.364093i
$379$	−0.586331			−0.0301178			−0.0150589	−	0.999887i	$-0.504794\pi$
$379$	−0.586331			−0.0301178			−0.0150589	+	0.999887i	$0.504794\pi$
$380$	−5.52505	−	2.01095i	−0.283429	−	0.103160i
$381$	−13.7896	−	10.0111i	−0.706464	−	0.512885i
$382$	13.0098	+	10.9165i	0.665641	+	0.558539i
$383$	5.76529	−	2.09839i	0.294593	−	0.107223i	−0.190496	−	0.981688i	$-0.561010\pi$
$383$	5.76529	−	2.09839i	0.294593	−	0.107223i	0.485088	+	0.874465i	$0.338787\pi$
$384$	−0.758716	+	1.55703i	−0.0387181	+	0.0794570i
$385$	−1.44804	−	11.8850i	−0.0737990	−	0.605718i
$386$	−11.1313	−	19.2800i	−0.566570	−	0.981328i
$387$	−0.127478	+	3.72802i	−0.00648005	+	0.189506i
$388$	17.0267			0.864402
$389$	21.1620	+	7.70234i	1.07296	+	0.390524i	0.817282	−	0.576238i	$-0.195480\pi$
$389$	21.1620	+	7.70234i	1.07296	+	0.390524i	0.255675	+	0.966763i	$0.417702\pi$
$390$	1.57510	+	6.30763i	0.0797583	+	0.319399i
$391$	−3.24640	+	18.4112i	−0.164177	+	0.931096i
$392$	4.85320	+	5.04445i	0.245124	+	0.254783i
$393$	9.27774	+	37.1536i	0.468000	+	1.87415i
$394$	0.139290	+	0.789952i	0.00701732	+	0.0397972i
$395$	−1.31861			−0.0663467
$396$	−7.97844	−	1.68982i	−0.400932	−	0.0849167i
$397$	18.8572			0.946417			0.473209	−	0.880950i	$-0.343096\pi$
$397$	18.8572			0.946417			0.473209	+	0.880950i	$0.343096\pi$
$398$	2.24532	+	0.817231i	0.112548	+	0.0409641i
$399$	8.32839	+	13.8787i	0.416941	+	0.694804i
$400$	−1.70744	−	1.43271i	−0.0853721	−	0.0716357i
$401$	4.16253	−	23.6069i	0.207867	−	1.17887i	−0.684998	−	0.728545i	$-0.740197\pi$
$401$	4.16253	−	23.6069i	0.207867	−	1.17887i	0.892865	−	0.450325i	$-0.148692\pi$
$402$	1.64516	−	0.733186i	0.0820529	−	0.0365680i
$403$	−15.1284	+	12.6943i	−0.753601	+	0.632346i
$404$	2.37240	−	4.10912i	0.118031	−	0.204436i
$405$	−6.58718	−	13.4561i	−0.327320	−	0.668641i
$406$	23.1415	+	1.23446i	1.14849	+	0.0612650i
$407$	−4.67223	−	26.4975i	−0.231594	−	1.31343i
$408$	9.98943	+	7.25221i	0.494551	+	0.359038i
$409$	16.8224	+	14.1157i	0.831815	+	0.697975i	0.955707	−	0.294320i	$-0.0950933\pi$
$409$	16.8224	+	14.1157i	0.831815	+	0.697975i	−0.123892	+	0.992296i	$0.539538\pi$
$410$	−1.59804	+	9.06294i	−0.0789216	+	0.447587i
$411$	3.45331	−	7.08686i	0.170339	−	0.349569i
$412$	13.2148	+	4.80978i	0.651045	+	0.236961i
$413$	28.6714	+	1.52944i	1.41083	+	0.0752587i
$414$	−2.43722	−	7.48253i	−0.119783	−	0.367746i
$415$	7.36114	+	12.7499i	0.361344	+	0.625866i
$416$	2.11885	+	0.771200i	0.103885	+	0.0378112i
$417$	−13.1535	+	12.7114i	−0.644130	+	0.622481i
$418$	−7.35537	−	6.17189i	−0.359763	−	0.301877i
$419$	−1.76140	+	9.98941i	−0.0860501	+	0.488014i	0.911075	+	0.412241i	$0.135254\pi$
$419$	−1.76140	+	9.98941i	−0.0860501	+	0.488014i	−0.997125	+	0.0757736i	$0.975857\pi$
$420$	−1.45130	−	7.48911i	−0.0708162	−	0.365431i
$421$	−12.2553	+	10.2834i	−0.597289	+	0.501185i	−0.890573	−	0.454841i	$-0.849696\pi$
$421$	−12.2553	+	10.2834i	−0.597289	+	0.501185i	0.293284	+	0.956025i	$0.405252\pi$
$422$	−5.19707	−	9.00158i	−0.252989	−	0.438190i
$423$	0.0618551	−	1.80892i	0.00300750	−	0.0879528i
$424$	−2.22157	+	3.84788i	−0.107889	+	0.186870i
$425$	−12.1690	+	10.2110i	−0.590282	+	0.495305i
$426$	−0.738063	+	1.51465i	−0.0357593	+	0.0733849i
$427$	−18.2541	−	17.0541i	−0.883379	−	0.825307i
$428$	−11.3224	+	4.12102i	−0.547289	+	0.199197i
$429$	−1.10595	+	10.5592i	−0.0533957	+	0.509805i
$430$	1.58559	−	1.33047i	0.0764639	−	0.0641608i
$431$	10.1894	+	17.6486i	0.490809	+	0.850105i	0.999944	−	0.0105811i	$-0.00336812\pi$
$431$	10.1894	+	17.6486i	0.490809	+	0.850105i	−0.509135	+	0.860686i	$0.670035\pi$
$432$	−5.14637	−	0.717565i	−0.247605	−	0.0345238i
$433$	9.41053			0.452241			0.226121	−	0.974099i	$-0.427396\pi$
$433$	9.41053			0.452241			0.226121	+	0.974099i	$0.427396\pi$
$434$	18.5194	−	13.9283i	0.888961	−	0.668580i
$435$	−20.4371	−	14.8371i	−0.979882	−	0.711383i
$436$	0.171390	−	0.972003i	0.00820811	−	0.0465505i
$437$	1.60886	−	9.12430i	0.0769622	−	0.436474i
$438$	6.00641	−	12.3263i	0.286997	−	0.588974i
$439$	5.99346	−	5.02911i	0.286052	−	0.240026i	−0.488459	−	0.872587i	$-0.662441\pi$
$439$	5.99346	−	5.02911i	0.286052	−	0.240026i	0.774511	+	0.632561i	$0.217996\pi$
$440$	2.26267	+	3.91906i	0.107869	+	0.186834i
$441$	−9.88006	+	18.5306i	−0.470479	+	0.882411i
$442$	8.03514	−	13.9173i	0.382193	−	0.661977i
$443$	2.97748	+	16.8861i	0.141464	+	0.802284i	0.970138	+	0.242552i	$0.0779847\pi$
$443$	2.97748	+	16.8861i	0.141464	+	0.802284i	−0.828674	+	0.559732i	$0.810904\pi$
$444$	−4.15332	−	16.6324i	−0.197108	−	0.789337i
$445$	−10.7652	+	3.91822i	−0.510321	+	0.185742i
$446$	1.95103	+	1.63711i	0.0923840	+	0.0775194i
$447$	12.9846	+	3.71817i	0.614149	+	0.175863i
$448$	−2.43446	−	1.03605i	−0.115017	−	0.0489488i
$449$	9.98223	−	17.2897i	0.471091	−	0.815953i	−0.528363	−	0.849019i	$-0.677194\pi$
$449$	9.98223	−	17.2897i	0.471091	−	0.815953i	0.999453	+	0.0330660i	$0.0105272\pi$
$450$	2.50039	−	6.20163i	0.117870	−	0.292348i
$451$	−7.51429	+	13.0151i	−0.353834	+	0.612858i
$452$	−1.18815	−	6.73834i	−0.0558859	−	0.316945i
$453$	29.0309	−	2.04062i	1.36399	−	0.0958767i
$454$	−5.48391	−	4.60154i	−0.257373	−	0.215961i
$455$	−9.49970	+	2.89466i	−0.445353	+	0.135704i
$456$	−4.95060	−	3.59408i	−0.231833	−	0.168308i
$457$	31.3648	+	11.4159i	1.46719	+	0.534012i	0.947335	−	0.320245i	$-0.103765\pi$
$457$	31.3648	+	11.4159i	1.46719	+	0.534012i	0.519851	+	0.854257i	$0.325987\pi$
$458$	−6.51686	−	11.2875i	−0.304513	−	0.527432i
$459$	−11.4055	+	35.2330i	−0.532364	+	1.64454i
$460$	−2.18333	+	3.78163i	−0.101798	+	0.176320i
$461$	4.49969	+	25.5190i	0.209571	+	1.18854i	0.890082	+	0.455800i	$0.150647\pi$
$461$	4.49969	+	25.5190i	0.209571	+	1.18854i	−0.680511	+	0.732738i	$0.738242\pi$
$462$	1.95582	−	12.3031i	0.0909931	−	0.572394i
$463$	4.50746	−	1.64058i	0.209480	−	0.0762443i	−0.235149	−	0.971959i	$-0.575558\pi$
$463$	4.50746	−	1.64058i	0.209480	−	0.0762443i	0.444629	+	0.895715i	$0.353336\pi$
$464$	−8.23087	+	2.99579i	−0.382109	+	0.139076i
$465$	−25.1907	+	1.77069i	−1.16819	+	0.0821138i
$466$	3.05059	+	17.3007i	0.141316	+	0.801442i
$467$	10.0205			0.463696			0.231848	−	0.972752i	$-0.425523\pi$
$467$	10.0205			0.463696			0.231848	+	0.972752i	$0.425523\pi$
$468$	−0.231173	+	6.76056i	−0.0106860	+	0.312507i
$469$	1.24677	+	2.45258i	0.0575704	+	0.113249i
$470$	−0.769364	+	0.645573i	−0.0354881	+	0.0297781i
$471$	4.28843	+	17.1734i	0.197601	+	0.791309i
$472$	−10.1977	+	3.71166i	−0.469387	+	0.170843i
$473$	3.17631	−	1.15608i	0.146047	−	0.0531567i
$474$	−1.31898	−	0.377695i	−0.0605829	−	0.0173481i
$475$	6.03074	−	5.06039i	0.276709	−	0.232187i
$476$	−10.2846	+	15.8047i	−0.471396	+	0.724405i
$477$	−13.0402	−	2.76189i	−0.597069	−	0.126458i
$478$	0.214735			0.00982176
$479$	1.89014	+	10.7195i	0.0863626	+	0.489787i	0.997054	+	0.0766998i	$0.0244383\pi$
$479$	1.89014	+	10.7195i	0.0863626	+	0.489787i	−0.910692	+	0.413087i	$0.864451\pi$
$480$	1.61317	+	2.38976i	0.0736310	+	0.109077i
$481$	−20.9715	+	7.63300i	−0.956218	+	0.348035i
$482$	6.03653	−	2.19712i	0.274956	−	0.100076i
$483$	11.2248	−	4.30146i	0.510747	−	0.195723i
$484$	−0.626850	−	3.55504i	−0.0284932	−	0.161593i
$485$	14.1719	−	24.5464i	0.643511	−	1.11459i
$486$	−2.73475	−	15.3467i	−0.124051	−	0.696140i
$487$	−6.78837	−	11.7578i	−0.307611	−	0.532797i	0.670229	−	0.742155i	$-0.266196\pi$
$487$	−6.78837	−	11.7578i	−0.307611	−	0.532797i	−0.977839	+	0.209358i	$0.932863\pi$
$488$	8.87255	+	3.22935i	0.401642	+	0.146186i
$489$	−3.51484	+	33.5586i	−0.158947	+	1.51757i
$490$	11.3117	−	2.79791i	0.511012	−	0.126397i
$491$	−14.8751	−	12.4817i	−0.671305	−	0.563292i	0.242146	−	0.970240i	$-0.422149\pi$
$491$	−14.8751	−	12.4817i	−0.671305	−	0.563292i	−0.913451	+	0.406948i	$0.866593\pi$
$492$	−4.19442	+	8.60775i	−0.189099	+	0.388067i
$493$	10.8402	+	61.4780i	0.488219	+	2.76883i
$494$	−3.98208	+	6.89716i	−0.179162	+	0.310318i
$495$	−9.07681	+	10.0955i	−0.407972	+	0.453761i
$496$	−4.37920	+	7.58500i	−0.196632	+	0.340576i
$497$	−2.36819	−	1.00785i	−0.106228	−	0.0452081i
$498$	3.71122	+	14.8619i	0.166304	+	0.665978i
$499$	−11.7524	−	9.86146i	−0.526111	−	0.441460i	0.340645	−	0.940192i	$-0.389355\pi$
$499$	−11.7524	−	9.86146i	−0.526111	−	0.441460i	−0.866756	+	0.498732i	$0.833799\pi$
$500$	−11.3080	+	4.11576i	−0.505707	+	0.184062i
$501$	−29.7665	−	8.52371i	−1.32987	−	0.380811i
$502$	3.05210	+	17.3093i	0.136222	+	0.772552i
$503$	−10.3416	+	17.9122i	−0.461111	+	0.798668i	−0.999017	−	0.0443375i	$-0.985882\pi$
$503$	−10.3416	+	17.9122i	−0.461111	+	0.798668i	0.537906	+	0.843005i	$0.319216\pi$
$504$	0.693421	−	7.90691i	0.0308874	−	0.352202i
$505$	−3.94924	−	6.84028i	−0.175739	−	0.304389i
$506$	−5.46264	+	4.58370i	−0.242844	+	0.203770i
$507$	−13.6767	+	0.961351i	−0.607402	+	0.0426951i
$508$	−1.70840	+	9.68883i	−0.0757981	+	0.429872i
$509$	−0.552492	+	3.13334i	−0.0244888	+	0.138883i	−0.994601	−	0.103775i	$-0.966908\pi$
$509$	−0.552492	+	3.13334i	−0.0244888	+	0.138883i	0.970112	+	0.242657i	$0.0780191\pi$
$510$	18.7696	−	8.36491i	0.831131	−	0.370405i
$511$	19.2725	+	8.20193i	0.852566	+	0.362832i
$512$	1.00000			0.0441942
$513$	5.65239	−	17.4609i	0.249559	−	0.770917i
$514$	8.20797	+	14.2166i	0.362038	+	0.627068i
$515$	17.9330	−	15.0476i	0.790223	−	0.663076i
$516$	1.96712	−	0.876675i	0.0865977	−	0.0385934i
$517$	−1.54122	+	0.560957i	−0.0677827	+	0.0246709i
$518$	25.0494	−	7.63281i	1.10061	−	0.335367i
$519$	−1.31564	−	1.94899i	−0.0577500	−	0.0855510i
$520$	2.87538	−	2.41273i	0.126094	−	0.105805i
$521$	15.0979	−	26.1503i	0.661449	−	1.14566i	−0.318786	−	0.947827i	$-0.603275\pi$
$521$	15.0979	−	26.1503i	0.661449	−	1.14566i	0.980235	−	0.197837i	$-0.0633916\pi$
$522$	−16.1930	−	20.6951i	−0.708746	−	0.905799i
$523$	−16.5375	−	28.6437i	−0.723133	−	1.25250i	−0.959738	−	0.280897i	$-0.909368\pi$
$523$	−16.5375	−	28.6437i	−0.723133	−	1.25250i	0.236605	−	0.971606i	$-0.423965\pi$
$524$	16.9367	−	14.2116i	0.739884	−	0.620836i
$525$	9.65575	+	3.33091i	0.421412	+	0.145373i
$526$	−3.66178	+	20.7670i	−0.159661	+	0.905484i
$527$	47.8175	+	40.1237i	2.08296	+	1.74781i
$528$	1.14076	+	4.56826i	0.0496450	+	0.198808i
$529$	15.1470	+	5.51305i	0.658564	+	0.239698i
$530$	3.69817	+	6.40541i	0.160638	+	0.278233i
$531$	−20.0624	−	25.6403i	−0.870634	−	1.11270i
$532$	5.09690	−	7.83252i	0.220979	−	0.339583i
$533$	11.7137	+	4.26343i	0.507376	+	0.184670i
$534$	−11.8906	+	0.835803i	−0.514555	+	0.0361687i
$535$	−3.48296	+	19.7529i	−0.150582	+	0.853991i
$536$	−0.796600	−	0.668427i	−0.0344079	−	0.0288716i
$537$	−15.2019	+	6.77493i	−0.656011	+	0.292360i
$538$	−1.41205	−	8.00811i	−0.0608776	−	0.345254i
$539$	18.9213	+	2.02443i	0.815000	+	0.0871984i
$540$	−5.31795	+	6.82195i	−0.228848	+	0.293570i
$541$	16.1933	−	28.0475i	0.696202	−	1.20586i	−0.273571	−	0.961852i	$-0.588205\pi$
$541$	16.1933	−	28.0475i	0.696202	−	1.20586i	0.969774	−	0.244006i	$-0.0784617\pi$
$542$	−0.426823	+	0.358147i	−0.0183336	+	0.0153837i
$543$	7.79543	+	5.65939i	0.334534	+	0.242868i
$544$	1.23759	−	7.01875i	0.0530614	−	0.300926i
$545$	−1.25862	−	1.05611i	−0.0539135	−	0.0452388i
$546$	−10.3315	+	0.174440i	−0.442147	+	0.00746534i
$547$	−12.8922	−	4.69236i	−0.551229	−	0.200631i	0.0513635	−	0.998680i	$-0.483643\pi$
$547$	−12.8922	−	4.69236i	−0.551229	−	0.200631i	−0.602592	+	0.798049i	$0.705866\pi$
$548$	−4.55152			−0.194431
$549$	−0.968023	+	28.3094i	−0.0413142	+	1.20821i
$550$	−6.05923			−0.258366
$551$	−5.37223	−	30.4675i	−0.228865	−	1.29796i
$552$	−3.26713	+	3.15732i	−0.139058	+	0.134384i
$553$	0.473349	−	2.04160i	0.0201288	−	0.0868178i
$554$	−4.99848	+	28.3478i	−0.212365	+	1.20438i
$555$	−27.4348	−	7.85602i	−1.16454	−	0.333470i
$556$	9.92396	+	3.61203i	0.420870	+	0.153184i
$557$	15.0898			0.639377			0.319689	−	0.947523i	$-0.396422\pi$
$557$	15.0898			0.639377			0.319689	+	0.947523i	$0.396422\pi$
$558$	−25.7050	−	5.44428i	−1.08818	−	0.230475i
$559$	−1.40183	−	2.42804i	−0.0592912	−	0.102695i
$560$	−3.51988	+	2.64728i	−0.148742	+	0.111868i
$561$	33.4753	−	2.35302i	1.41333	−	0.0993447i
$562$	2.31499	−	0.842587i	0.0976519	−	0.0355424i
$563$	25.3342	+	21.2579i	1.06771	+	0.895913i	0.994843	−	0.101428i	$-0.0323413\pi$
$563$	25.3342	+	21.2579i	1.06771	+	0.895913i	0.0728652	+	0.997342i	$0.476786\pi$
$564$	−0.954493	+	0.425383i	−0.0401914	+	0.0179118i
$565$	−10.7032	−	3.89564i	−0.450286	−	0.163891i
$566$	22.2415			0.934881
$567$	23.1987	−	5.36849i	0.974253	−	0.225455i
$568$	0.972779			0.0408169
$569$	−21.7809	−	7.92759i	−0.913102	−	0.332342i	−0.157611	−	0.987501i	$-0.550379\pi$
$569$	−21.7809	−	7.92759i	−0.913102	−	0.332342i	−0.755491	+	0.655159i	$0.772601\pi$
$570$	−9.30189	+	4.14551i	−0.389613	+	0.173636i
$571$	−19.0717	−	16.0031i	−0.798126	−	0.669708i	0.149616	−	0.988744i	$-0.452196\pi$
$571$	−19.0717	−	16.0031i	−0.798126	−	0.669708i	−0.947742	+	0.319037i	$0.896641\pi$
$572$	5.76006	−	2.09649i	0.240840	−	0.0876586i
$573$	29.3432	−	2.06258i	1.22583	−	0.0861653i
$574$	−13.4584	−	5.72760i	−0.561745	−	0.239066i
$575$	−2.92338	−	5.06344i	−0.121913	−	0.211160i
$576$	0.929121	+	2.85250i	0.0387134	+	0.118854i
$577$	−10.3590			−0.431251			−0.215625	−	0.976476i	$-0.569179\pi$
$577$	−10.3590			−0.431251			−0.215625	+	0.976476i	$0.569179\pi$
$578$	−31.7564	−	11.5584i	−1.32089	−	0.480765i
$579$	−37.0702	−	10.6151i	−1.54058	−	0.441150i
$580$	−2.53195	+	14.3594i	−0.105134	+	0.596243i
$581$	−22.3830	+	6.82033i	−0.928603	+	0.282955i
$582$	21.2067	−	20.4940i	0.879048	−	0.849503i
$583$	2.09743	+	11.8951i	0.0868665	+	0.492645i
$584$	−7.91654			−0.327589
$585$	9.55387	+	5.96029i	0.395004	+	0.246428i
$586$	13.8147			0.570678
$587$	−9.95343	−	3.62275i	−0.410822	−	0.149527i	0.128338	−	0.991731i	$-0.459036\pi$
$587$	−9.95343	−	3.62275i	−0.410822	−	0.149527i	−0.539160	+	0.842203i	$0.681258\pi$
$588$	12.1163	+	0.441357i	0.499669	+	0.0182012i
$589$	−23.6976	−	19.8846i	−0.976441	−	0.819331i
$590$	−3.13698	+	17.7907i	−0.129148	+	0.732433i
$591$	1.12430	+	0.816229i	0.0462475	+	0.0335752i
$592$	−7.58197	+	6.36203i	−0.311617	+	0.261478i
$593$	−18.5963	+	32.2097i	−0.763659	+	1.32270i	0.177294	+	0.984158i	$0.443266\pi$
$593$	−18.5963	+	32.2097i	−0.763659	+	1.32270i	−0.940953	+	0.338538i	$0.890068\pi$
$594$	−11.9711	+	7.49847i	−0.491178	+	0.307666i
$595$	14.2244	+	27.9814i	0.583142	+	1.14713i
$596$	−1.35410	−	7.67948i	−0.0554661	−	0.314564i
$597$	3.78019	−	1.68469i	0.154713	−	0.0689499i
$598$	4.53098	+	3.80195i	0.185286	+	0.155473i
$599$	−0.116253	+	0.659303i	−0.00474996	+	0.0269384i	−0.987091	−	0.160163i	$-0.948798\pi$
$599$	−0.116253	+	0.659303i	−0.00474996	+	0.0269384i	0.982341	+	0.187101i	$0.0599092\pi$
$600$	−3.85108	+	0.270697i	−0.157220	+	0.0110512i
$601$	13.9237	+	5.06783i	0.567962	+	0.206721i	0.610009	−	0.792395i	$-0.291166\pi$
$601$	13.9237	+	5.06783i	0.567962	+	0.206721i	−0.0420474	+	0.999116i	$0.513388\pi$
$602$	1.49077	+	2.93256i	0.0607592	+	0.119522i
$603$	1.16655	−	2.89335i	0.0475055	−	0.117826i
$604$	−8.40117	−	14.5513i	−0.341839	−	0.592082i
$605$	−5.64683	−	2.05528i	−0.229576	−	0.0835589i
$606$	−1.99106	−	7.97340i	−0.0808814	−	0.323897i
$607$	22.3242	+	18.7323i	0.906113	+	0.760319i	0.971375	−	0.237549i	$-0.0763441\pi$
$607$	22.3242	+	18.7323i	0.906113	+	0.760319i	−0.0652628	+	0.997868i	$0.520789\pi$
$608$	−0.613331	+	3.47837i	−0.0248739	+	0.141067i
$609$	30.3085	−	26.3164i	1.22816	−	1.06640i
$610$	12.0404	−	10.1031i	0.487503	−	0.409064i
$611$	0.680201	+	1.17814i	0.0275180	+	0.0476626i
$612$	21.1708	−	2.99103i	0.855780	−	0.120905i
$613$	−21.1099	+	36.5635i	−0.852622	+	1.47679i	0.0262110	+	0.999656i	$0.491656\pi$
$613$	−21.1099	+	36.5635i	−0.852622	+	1.47679i	−0.878833	+	0.477129i	$0.841678\pi$
$614$	3.84738	−	3.22833i	0.155268	−	0.130285i
$615$	8.91812	+	13.2113i	0.359613	+	0.532732i
$616$	−6.88010	+	2.09644i	−0.277207	+	0.0844679i
$617$	−18.0926	+	6.58518i	−0.728382	+	0.265109i	−0.679480	−	0.733694i	$-0.737795\pi$
$617$	−18.0926	+	6.58518i	−0.728382	+	0.265109i	−0.0489024	+	0.998804i	$0.515572\pi$
$618$	22.2482	−	9.91520i	0.894953	−	0.398848i
$619$	−17.8850	+	15.0073i	−0.718858	+	0.603193i	−0.927069	−	0.374891i	$-0.877680\pi$
$619$	−17.8850	+	15.0073i	−0.718858	+	0.603193i	0.208211	+	0.978084i	$0.433236\pi$
$620$	7.28988	+	12.6264i	0.292769	+	0.507090i
$621$	−12.0418	−	6.38593i	−0.483220	−	0.256259i
$622$	−19.4862			−0.781324
$623$	−2.20212	−	18.0743i	−0.0882261	−	0.724131i
$624$	3.56727	−	1.58980i	0.142805	−	0.0636430i
$625$	−1.54329	+	8.75243i	−0.0617316	+	0.350097i
$626$	−0.629073	+	3.56765i	−0.0251428	+	0.142592i
$627$	−16.5898	+	1.16612i	−0.662532	+	0.0465703i
$628$	7.82862	−	6.56899i	0.312396	−	0.262131i
$629$	35.2701	+	61.0896i	1.40631	+	2.43580i
$630$	−10.8217	−	7.58082i	−0.431149	−	0.302027i
$631$	22.7548	−	39.4125i	0.905854	−	1.56898i	0.0860870	−	0.996288i	$-0.472564\pi$
$631$	22.7548	−	39.4125i	0.905854	−	1.56898i	0.819767	−	0.572697i	$-0.194103\pi$
$632$	0.137551	+	0.780088i	0.00547147	+	0.0310302i
$633$	−17.3075	−	4.95607i	−0.687913	−	0.196986i
$634$	31.3392	−	11.4065i	1.24464	−	0.453011i
$635$	12.5458	+	10.5272i	0.497866	+	0.417759i
$636$	1.86448	+	7.46649i	0.0739315	+	0.296066i
$637$	−1.07163	−	15.7474i	−0.0424596	−	0.623936i
$638$	−11.9057	+	20.6213i	−0.471352	+	0.816405i
$639$	0.903829	+	2.77485i	0.0357549	+	0.109771i
$640$	0.832330	−	1.44164i	0.0329007	−	0.0569858i
$641$	−3.99011	−	22.6290i	−0.157600	−	0.893793i	−0.956370	−	0.292157i	$-0.905627\pi$
$641$	−3.99011	−	22.6290i	−0.157600	−	0.893793i	0.798770	−	0.601636i	$-0.205484\pi$
$642$	−9.14182	+	18.7608i	−0.360799	+	0.740428i
$643$	−18.5835	−	15.5934i	−0.732862	−	0.614944i	0.198048	−	0.980192i	$-0.436540\pi$
$643$	−18.5835	−	15.5934i	−0.732862	−	0.614944i	−0.930910	+	0.365248i	$0.880984\pi$
$644$	−5.07132	−	4.73794i	−0.199838	−	0.186701i
$645$	0.373448	−	3.56556i	0.0147045	−	0.140394i
$646$	23.6548	+	8.60963i	0.930685	+	0.338741i
$647$	−12.9724	−	22.4688i	−0.509996	−	0.883339i	−0.999933	−	0.0115809i	$-0.996314\pi$
$647$	−12.9724	−	22.4688i	−0.509996	−	0.883339i	0.489937	−	0.871758i	$-0.337020\pi$
$648$	−7.27347	+	5.30063i	−0.285729	+	0.208228i
$649$	−14.7507	+	25.5489i	−0.579015	+	1.00288i
$650$	0.872725	+	4.94947i	0.0342311	+	0.194134i
$651$	6.30128	−	39.6383i	0.246967	−	1.55355i
$652$	18.3062	−	6.66290i	0.716925	−	0.260939i
$653$	−33.1582	+	12.0686i	−1.29758	+	0.472281i	−0.896208	−	0.443634i	$-0.853689\pi$
$653$	−33.1582	+	12.0686i	−1.29758	+	0.472281i	−0.401372	+	0.915915i	$0.631467\pi$
$654$	−0.956471	−	1.41692i	−0.0374010	−	0.0554059i
$655$	−6.39103	−	36.2453i	−0.249718	−	1.41622i
$656$	5.52831			0.215844
$657$	−7.35542	−	22.5819i	−0.286962	−	0.881004i
$658$	−0.723355	−	1.42295i	−0.0281993	−	0.0554722i
$659$	35.1799	−	29.5194i	1.37041	−	1.14991i	0.397803	−	0.917471i	$-0.369773\pi$
$659$	35.1799	−	29.5194i	1.37041	−	1.14991i	0.972610	−	0.232442i	$-0.0746716\pi$
$660$	7.53527	+	2.15775i	0.293310	+	0.0839901i
$661$	−8.01271	+	2.91639i	−0.311658	+	0.113434i	−0.493114	−	0.869965i	$-0.664141\pi$
$661$	−8.01271	+	2.91639i	−0.311658	+	0.113434i	0.181455	+	0.983399i	$0.441919\pi$
$662$	3.34155	−	1.21622i	0.129873	−	0.0472699i
$663$	−6.74358	−	27.0053i	−0.261899	−	1.04880i
$664$	6.77491	−	5.68482i	0.262917	−	0.220614i
$665$	−7.04936	−	13.8671i	−0.273362	−	0.537744i
$666$	−25.1922	−	15.7165i	−0.976179	−	0.609000i
$667$	−22.9765			−0.889652
$668$	3.10420	+	17.6048i	0.120105	+	0.681150i
$669$	4.40048	−	0.309316i	0.170133	−	0.0119588i
$670$	−1.62666	+	0.592057i	−0.0628435	+	0.0228732i
$671$	24.1198	−	8.77890i	0.931136	−	0.338906i
$672$	−4.27914	+	1.63981i	−0.165071	+	0.0632569i
$673$	7.67594	+	43.5324i	0.295886	+	1.67805i	0.663580	+	0.748105i	$0.269036\pi$
$673$	7.67594	+	43.5324i	0.295886	+	1.67805i	−0.367695	+	0.929947i	$0.619853\pi$
$674$	17.9482	−	31.0871i	0.691338	−	1.19743i
$675$	−4.35028	−	10.7337i	−0.167442	−	0.413139i
$676$	3.95785	+	6.85521i	0.152225	+	0.263662i
$677$	21.9242	+	7.97975i	0.842615	+	0.306687i	0.727026	−	0.686610i	$-0.240902\pi$
$677$	21.9242	+	7.97975i	0.842615	+	0.306687i	0.115589	+	0.993297i	$0.463124\pi$
$678$	−9.59034	−	6.96248i	−0.368315	−	0.267392i
$679$	32.9177	+	30.7538i	1.26327	+	1.18022i
$680$	−9.08841	−	7.62608i	−0.348525	−	0.292447i
$681$	−12.3688	+	0.869417i	−0.473972	+	0.0333161i
$682$	4.13448	+	23.4478i	0.158317	+	0.897862i
$683$	11.4740	−	19.8735i	0.439040	−	0.760439i	−0.558576	−	0.829453i	$-0.688652\pi$
$683$	11.4740	−	19.8735i	0.439040	−	0.760439i	0.997616	+	0.0690144i	$0.0219854\pi$
$684$	−10.4919	+	1.48230i	−0.401168	+	0.0566773i
$685$	−3.78837	+	6.56164i	−0.144746	+	0.250708i
$686$	0.271373	+	18.5183i	0.0103611	+	0.707031i
$687$	−21.7028	−	6.21466i	−0.828014	−	0.237104i
$688$	−0.952500	−	0.799242i	−0.0363137	−	0.0304708i
$689$	9.41439	−	3.42656i	0.358660	−	0.130541i
$690$	1.83238	+	7.33794i	0.0697576	+	0.279351i
$691$	−2.98381	−	16.9220i	−0.113509	−	0.643743i	−0.987477	−	0.157760i	$-0.949573\pi$
$691$	−2.98381	−	16.9220i	−0.113509	−	0.643743i	0.873968	−	0.485983i	$-0.161538\pi$
$692$	−0.678813	+	1.17574i	−0.0258046	+	0.0446949i
$693$	−12.3725	−	17.6776i	−0.469993	−	0.671517i
$694$	7.70239	+	13.3409i	0.292379	+	0.506415i
$695$	13.4672	−	11.3004i	0.510842	−	0.428647i
$696$	−6.64568	+	13.6382i	−0.251904	+	0.516955i
$697$	6.84180	−	38.8018i	0.259152	−	1.46972i
$698$	−3.89158	+	22.0703i	−0.147299	+	0.835372i
$699$	24.6233	+	17.8762i	0.931338	+	0.676141i
$700$	−0.713216	−	5.85384i	−0.0269570	−	0.221254i
$701$	24.0297			0.907588			0.453794	−	0.891107i	$-0.350070\pi$
$701$	24.0297			0.907588			0.453794	+	0.891107i	$0.350070\pi$
$702$	7.84932	+	8.69850i	0.296254	+	0.328304i
$703$	−17.4793	−	30.2750i	−0.659243	−	1.14184i
$704$	2.08247	−	1.74740i	0.0784862	−	0.0658577i
$705$	−0.181206	+	1.73009i	−0.00682460	+	0.0651591i
$706$	−4.82607	+	1.75655i	−0.181632	+	0.0661085i
$707$	12.0084	−	3.65910i	0.451624	−	0.137615i
$708$	−8.23372	+	16.8972i	−0.309442	+	0.635035i
$709$	5.97148	−	5.01067i	0.224264	−	0.188179i	−0.523732	−	0.851883i	$-0.675461\pi$
$709$	5.97148	−	5.01067i	0.224264	−	0.188179i	0.747996	+	0.663703i	$0.231016\pi$
$710$	0.809673	−	1.40239i	0.0303865	−	0.0526309i
$711$	−2.09740	+	1.11716i	−0.0786585	+	0.0418967i
$712$	3.44098	+	5.95995i	0.128956	+	0.223358i
$713$	−17.5996	+	14.7678i	−0.659109	+	0.553058i
$714$	6.21355	+	32.0636i	0.232536	+	1.19995i
$715$	1.77189	−	10.0489i	0.0662649	−	0.375807i
$716$	7.36091	+	6.17653i	0.275090	+	0.230828i
$717$	0.267452	−	0.258463i	0.00998817	−	0.00965247i
$718$	−31.6452	−	11.5179i	−1.18099	−	0.429845i
$719$	0.526726	+	0.912316i	0.0196436	+	0.0340237i	0.875680	−	0.482892i	$-0.160414\pi$
$719$	0.526726	+	0.912316i	0.0196436	+	0.0340237i	−0.856037	+	0.516915i	$0.827080\pi$
$720$	4.88560	+	1.03476i	0.182076	+	0.0385633i
$721$	16.8606	+	33.1673i	0.627922	+	1.23521i
$722$	6.13125	+	2.23159i	0.228182	+	0.0830513i
$723$	4.87395	−	10.0023i	0.181264	−	0.371989i
$724$	0.965778	−	5.47720i	0.0358929	−	0.203559i
$725$	−14.9557	−	12.5493i	−0.555439	−	0.466069i
$726$	−5.05971	−	3.67329i	−0.187784	−	0.136329i
$727$	3.77605	+	21.4150i	0.140046	+	0.794239i	0.971212	+	0.238216i	$0.0765625\pi$
$727$	3.77605	+	21.4150i	0.140046	+	0.794239i	−0.831166	+	0.556024i	$0.812326\pi$
$728$	2.70343	+	5.31804i	0.100196	+	0.197100i
$729$	−21.8779	−	15.8226i	−0.810294	−	0.586023i
$730$	−6.58918	+	11.4128i	−0.243876	+	0.422406i
$731$	−6.78849	+	5.69622i	−0.251081	+	0.210682i
$732$	14.9377	−	6.65718i	0.552113	−	0.246057i
$733$	−8.85859	+	50.2395i	−0.327199	+	1.85564i	0.166547	+	0.986034i	$0.446738\pi$
$733$	−8.85859	+	50.2395i	−0.327199	+	1.85564i	−0.493746	+	0.869606i	$0.664373\pi$
$734$	−5.48012	−	4.59836i	−0.202275	−	0.169729i
$735$	10.7211	−	17.1000i	0.395452	−	0.630743i
$736$	2.46496	+	0.897170i	0.0908595	+	0.0330701i
$737$	−2.82691			−0.104131
$738$	5.13646	+	15.7695i	0.189076	+	0.580482i
$739$	38.5670			1.41871			0.709355	−	0.704851i	$-0.248986\pi$
$739$	38.5670			1.41871			0.709355	+	0.704851i	$0.248986\pi$
$740$	2.86104	+	16.2258i	0.105174	+	0.596471i
$741$	3.34201	+	13.3834i	0.122772	+	0.491650i
$742$	−11.2450	+	3.42647i	−0.412817	+	0.125790i
$743$	1.59146	−	9.02561i	0.0583849	−	0.331117i	−0.941599	−	0.336735i	$-0.890677\pi$
$743$	1.59146	−	9.02561i	0.0583849	−	0.331117i	0.999984	+	0.00561810i	$0.00178831\pi$
$744$	3.67529	+	14.7181i	0.134743	+	0.539590i
$745$	−12.1981	−	4.43974i	−0.446903	−	0.162660i
$746$	15.3726			0.562830
$747$	22.5106	+	14.0435i	0.823621	+	0.513825i
$748$	−9.68732	−	16.7789i	−0.354204	−	0.613499i
$749$	−29.3330	−	12.4834i	−1.07180	−	0.456134i
$750$	−9.13014	+	18.7368i	−0.333386	+	0.684172i
$751$	−4.43913	+	1.61571i	−0.161986	+	0.0589581i	−0.421740	−	0.906717i	$-0.638581\pi$
$751$	−4.43913	+	1.61571i	−0.161986	+	0.0589581i	0.259754	+	0.965675i	$0.416358\pi$
$752$	0.462175	+	0.387811i	0.0168538	+	0.0141420i
$753$	24.6355	+	17.8851i	0.897767	+	0.651768i
$754$	18.5593	+	6.75502i	0.675889	+	0.246003i
$755$	−27.9702			−1.01794
$756$	−8.65338	−	10.6827i	−0.314720	−	0.388524i
$757$	−7.23189			−0.262848			−0.131424	−	0.991326i	$-0.541955\pi$
$757$	−7.23189			−0.262848			−0.131424	+	0.991326i	$0.541955\pi$
$758$	0.550971	+	0.200537i	0.0200122	+	0.00728383i
$759$	−1.28660	+	12.2840i	−0.0467005	+	0.445882i
$760$	4.50406	+	3.77936i	0.163380	+	0.137092i
$761$	−17.2962	+	6.29531i	−0.626988	+	0.228205i	−0.635920	−	0.771755i	$-0.719379\pi$
$761$	−17.2962	+	6.29531i	−0.626988	+	0.228205i	0.00893183	+	0.999960i	$0.497157\pi$
$762$	9.53401	+	14.1237i	0.345381	+	0.511648i
$763$	2.08698	−	1.56960i	0.0755539	−	0.0568234i
$764$	−8.49157	−	14.7078i	−0.307214	−	0.532110i
$765$	13.3091	−	33.0102i	0.481193	−	1.19349i
$766$	−6.13529			−0.221677
$767$	22.9942	+	8.36919i	0.830271	+	0.302194i
$768$	1.24550	−	1.20364i	0.0449430	−	0.0434325i
$769$	−0.489316	+	2.77505i	−0.0176452	+	0.100071i	−0.992358	−	0.123388i	$-0.960624\pi$
$769$	−0.489316	+	2.77505i	−0.0176452	+	0.100071i	0.974713	+	0.223459i	$0.0717350\pi$
$770$	−2.70421	+	11.6635i	−0.0974530	+	0.420325i
$771$	27.3346	+	7.82735i	0.984432	+	0.281895i
$772$	3.86587	+	21.9244i	0.139136	+	0.789078i
$773$	16.6703			0.599589			0.299795	−	0.954004i	$-0.403082\pi$
$773$	16.6703			0.599589			0.299795	+	0.954004i	$0.403082\pi$
$774$	1.39485	−	3.45959i	0.0501368	−	0.124353i
$775$	−19.5217			−0.701239
$776$	−15.9999	−	5.82349i	−0.574363	−	0.209051i
$777$	22.0118	−	39.6570i	0.789670	−	1.42269i
$778$	−17.2514	−	14.4757i	−0.618494	−	0.518978i
$779$	−3.39068	+	19.2295i	−0.121484	+	0.688969i
$780$	0.677227	−	6.46595i	0.0242486	−	0.231518i
$781$	2.02579	−	1.69984i	0.0724883	−	0.0608249i
$782$	9.34763	−	16.1906i	0.334270	−	0.578973i
$783$	−45.0776	−	6.28523i	−1.61094	−	0.224616i
$784$	−2.83521	−	6.40012i	−0.101258	−	0.228576i
$785$	−2.95411	−	16.7536i	−0.105437	−	0.597962i
$786$	3.98904	−	38.0861i	0.142284	−	1.35849i
$787$	26.2083	+	21.9913i	0.934223	+	0.783907i	0.976571	−	0.215196i	$-0.0690392\pi$
$787$	26.2083	+	21.9913i	0.934223	+	0.783907i	−0.0423474	+	0.999103i	$0.513484\pi$
$788$	0.139290	−	0.789952i	0.00496200	−	0.0281409i
$789$	20.4352	+	30.2727i	0.727511	+	1.07774i
$790$	1.23909	+	0.450993i	0.0440849	+	0.0160456i
$791$	9.87376	−	15.1732i	0.351071	−	0.539498i
$792$	6.91933	+	4.31670i	0.245868	+	0.153387i
$793$	−10.6451	−	18.4378i	−0.378017	−	0.654745i
$794$	−17.7200	−	6.44955i	−0.628859	−	0.228886i
$795$	12.3158	+	3.52668i	0.436798	+	0.125078i
$796$	−1.83040	−	1.53589i	−0.0648770	−	0.0544382i
$797$	7.85355	−	44.5397i	0.278187	−	1.57768i	−0.450466	−	0.892794i	$-0.648742\pi$
$797$	7.85355	−	44.5397i	0.278187	−	1.57768i	0.728653	−	0.684883i	$-0.240147\pi$
$798$	−3.07933	−	15.8902i	−0.109007	−	0.562507i
$799$	3.29393	−	2.76394i	0.116531	−	0.0977810i
$800$	1.11445	+	1.93029i	0.0394019	+	0.0682460i
$801$	−13.8036	+	15.3529i	−0.487728	+	0.542467i
$802$	−11.9855	+	20.7595i	−0.423223	+	0.733044i
$803$	−16.4860	+	13.8334i	−0.581778	+	0.488170i
$804$	−1.79670	+	0.126293i	−0.0633649	+	0.00445400i
$805$	−11.0514	+	3.36748i	−0.389511	+	0.118688i
$806$	18.5578	−	6.75448i	0.653670	−	0.237916i
$807$	−11.3975	−	8.27449i	−0.401213	−	0.291276i
$808$	−3.63473	+	3.04990i	−0.127869	+	0.107295i
$809$	−1.08096	−	1.87227i	−0.0380044	−	0.0658255i	0.846398	−	0.532552i	$-0.178767\pi$
$809$	−1.08096	−	1.87227i	−0.0380044	−	0.0658255i	−0.884402	+	0.466726i	$0.845433\pi$
$810$	1.58766	+	14.8976i	0.0557846	+	0.523448i
$811$	−18.4044			−0.646264			−0.323132	−	0.946354i	$-0.604736\pi$
$811$	−18.4044			−0.646264			−0.323132	+	0.946354i	$0.604736\pi$
$812$	−21.3237	−	9.07487i	−0.748315	−	0.318466i
$813$	−0.100528	+	0.959810i	−0.00352567	+	0.0336620i
$814$	−4.67223	+	26.4975i	−0.163762	+	0.928738i
$815$	5.63129	−	31.9366i	0.197255	−	1.11869i
$816$	−6.90659	−	10.2314i	−0.241779	−	0.358172i
$817$	3.36426	−	2.82295i	0.117701	−	0.0987625i
$818$	−10.9800	−	19.0180i	−0.383908	−	0.664949i
$819$	−12.6579	+	12.6526i	−0.442302	+	0.442118i
$820$	4.60138	−	7.96982i	0.160687	−	0.278318i
$821$	−4.38936	−	24.8933i	−0.153190	−	0.868783i	−0.960422	−	0.278549i	$-0.910147\pi$
$821$	−4.38936	−	24.8933i	−0.153190	−	0.868783i	0.807232	−	0.590234i	$-0.200965\pi$
$822$	−5.66890	+	5.47837i	−0.197726	+	0.191080i
$823$	−21.0695	+	7.66866i	−0.734436	+	0.267313i	−0.682041	−	0.731314i	$-0.738908\pi$
$823$	−21.0695	+	7.66866i	−0.734436	+	0.267313i	−0.0523944	+	0.998626i	$0.516685\pi$
$824$	−10.7728	−	9.03944i	−0.375288	−	0.314904i
$825$	−7.54675	+	7.29310i	−0.262744	+	0.253913i
$826$	−26.4192	−	11.2434i	−0.919241	−	0.391208i
$827$	27.1071	−	46.9508i	0.942605	−	1.63264i	0.182128	−	0.983275i	$-0.441701\pi$
$827$	27.1071	−	46.9508i	0.942605	−	1.63264i	0.760477	−	0.649365i	$-0.224965\pi$
$828$	−0.268934	+	7.86486i	−0.00934611	+	0.273323i
$829$	23.4220	−	40.5680i	0.813478	−	1.40899i	−0.0969369	−	0.995291i	$-0.530905\pi$
$829$	23.4220	−	40.5680i	0.813478	−	1.40899i	0.910415	−	0.413695i	$-0.135762\pi$
$830$	−2.55650	−	14.4986i	−0.0887373	−	0.503254i
$831$	27.8948	+	41.3234i	0.967660	+	1.43349i
$832$	−1.72731	−	1.44938i	−0.0598835	−	0.0502483i
$833$	−48.4297	+	11.9789i	−1.67799	+	0.415044i
$834$	16.7078	−	7.44607i	0.578545	−	0.257836i
$835$	27.9635	+	10.1779i	0.967716	+	0.352220i
$836$	4.80088	+	8.31536i	0.166042	+	0.287593i
$837$	−38.5684	+	24.1586i	−1.33312	+	0.835044i
$838$	5.07175	−	8.78454i	0.175201	−	0.303457i
$839$	−2.54980	−	14.4606i	−0.0880289	−	0.499237i	−0.996662	−	0.0816409i	$-0.973984\pi$
$839$	−2.54980	−	14.4606i	−0.0880289	−	0.499237i	0.908633	−	0.417596i	$-0.137127\pi$
$840$	−1.19765	+	7.53383i	−0.0413228	+	0.259942i
$841$	−44.8440	+	16.3219i	−1.54634	+	0.562823i
$842$	15.0334	−	5.47171i	0.518085	−	0.188568i
$843$	1.86914	−	3.83584i	0.0643767	−	0.132113i
$844$	1.80492	+	10.2362i	0.0621280	+	0.352345i
$845$	13.1770			0.453301
$846$	−0.676813	+	1.67868i	−0.0232693	+	0.0577140i
$847$	5.20924	−	8.00516i	0.178992	−	0.275061i
$848$	3.40365	−	2.85600i	0.116882	−	0.0980755i
$849$	27.7018	−	26.7707i	0.950722	−	0.918768i
$850$	14.9275	−	5.43315i	0.512007	−	0.186355i
$851$	−24.3971	+	8.87980i	−0.836320	+	0.304396i
$852$	1.21159	−	1.17087i	0.0415085	−	0.0401134i
$853$	24.2543	−	20.3518i	0.830453	−	0.696833i	−0.124942	−	0.992164i	$-0.539874\pi$
$853$	24.2543	−	20.3518i	0.830453	−	0.696833i	0.955395	+	0.295331i	$0.0954300\pi$
$854$	11.3204	+	22.2689i	0.387376	+	0.762027i
$855$	−6.59578	+	16.3593i	−0.225571	+	0.559476i
$856$	12.0491			0.411828
$857$	1.41747	+	8.03885i	0.0484197	+	0.274602i	0.999399	−	0.0346513i	$-0.0110321\pi$
$857$	1.41747	+	8.03885i	0.0484197	+	0.274602i	−0.950980	+	0.309253i	$0.899921\pi$
$858$	4.65072	−	9.54418i	0.158773	−	0.325833i
$859$	20.6121	−	7.50220i	0.703277	−	0.255972i	0.0344674	−	0.999406i	$-0.489027\pi$
$859$	20.6121	−	7.50220i	0.703277	−	0.255972i	0.668809	+	0.743434i	$0.266804\pi$
$860$	−1.94501	+	0.707926i	−0.0663244	+	0.0241401i
$861$	−23.6564	+	9.06536i	−0.806208	+	0.308947i
$862$	−3.53876	−	20.0693i	−0.120531	−	0.683563i
$863$	11.5793	−	20.0560i	0.394165	−	0.682714i	−0.598829	−	0.800877i	$-0.704367\pi$
$863$	11.5793	−	20.0560i	0.394165	−	0.682714i	0.992994	+	0.118163i	$0.0377004\pi$
$864$	4.59058	+	2.43445i	0.156175	+	0.0828217i
$865$	1.12999	+	1.95720i	0.0384209	+	0.0665470i
$866$	−8.84300	−	3.21859i	−0.300498	−	0.109372i
$867$	−53.4646	+	23.8272i	−1.81575	+	0.809214i
$868$	−22.1663	+	6.75431i	−0.752374	+	0.229256i
$869$	1.64957	+	1.38416i	0.0559580	+	0.0469543i
$870$	14.1300	+	20.9322i	0.479051	+	0.709667i
$871$	0.407166	+	2.30915i	0.0137963	+	0.0782427i
$872$	−0.493499	+	0.854765i	−0.0167120	+	0.0289460i
$873$	1.74564	−	51.0504i	0.0590809	−	1.72779i
$874$	−4.63253	+	8.02377i	−0.156698	+	0.271408i
$875$	−29.2955	−	12.4675i	−0.990369	−	0.421478i
$876$	−9.86003	+	9.52863i	−0.333139	+	0.321943i
$877$	−19.7885	−	16.6045i	−0.668211	−	0.560696i	0.244324	−	0.969694i	$-0.421434\pi$
$877$	−19.7885	−	16.6045i	−0.668211	−	0.560696i	−0.912535	+	0.408998i	$0.865878\pi$
$878$	−7.35206	+	2.67593i	−0.248120	+	0.0903083i
$879$	17.2061	−	16.6278i	0.580347	−	0.560842i
$880$	−0.785817	−	4.45659i	−0.0264899	−	0.150232i
$881$	−2.02126	+	3.50093i	−0.0680981	+	0.117949i	−0.898064	−	0.439865i	$-0.855026\pi$
$881$	−2.02126	+	3.50093i	−0.0680981	+	0.117949i	0.829966	+	0.557814i	$0.188360\pi$
$882$	15.6221	−	14.0339i	0.526022	−	0.472547i
$883$	−22.8257	−	39.5352i	−0.768145	−	1.33047i	−0.938568	−	0.345095i	$-0.887847\pi$
$883$	−22.8257	−	39.5352i	−0.768145	−	1.33047i	0.170423	−	0.985371i	$-0.445487\pi$
$884$	−12.3105	+	10.3298i	−0.414048	+	0.347428i
$885$	17.5064	+	25.9341i	0.588473	+	0.871764i
$886$	2.97748	−	16.8861i	0.100030	−	0.567301i
$887$	−3.13730	+	17.7925i	−0.105340	+	0.597414i	0.885744	+	0.464175i	$0.153649\pi$
$887$	−3.13730	+	17.7925i	−0.105340	+	0.597414i	−0.991084	+	0.133239i	$0.957462\pi$
$888$	−1.78576	+	17.0498i	−0.0599260	+	0.572154i
$889$	−20.8028	+	15.6456i	−0.697705	+	0.524738i
$890$	11.4561			0.384010
$891$	−5.88448	+	23.7481i	−0.197138	+	0.795591i
$892$	−1.27344	−	2.20567i	−0.0426381	−	0.0738513i
$893$	−1.63242	+	1.36976i	−0.0546268	+	0.0458373i
$894$	−10.9298	−	7.93492i	−0.365548	−	0.265384i
$895$	15.0310	−	5.47085i	0.502432	−	0.182870i
$896$	1.93330	+	1.80620i	0.0645869	+	0.0603410i
$897$	10.2195	−	0.718341i	0.341219	−	0.0239847i
$898$	−15.2937	+	12.8329i	−0.510356	+	0.428240i
$899$	−38.3579	+	66.4378i	−1.27931	+	2.21583i
$900$	−4.47068	+	4.97244i	−0.149023	+	0.165748i
$901$	−15.8332	−	27.4239i	−0.527481	−	0.913624i
$902$	11.5126	−	9.66018i	0.383326	−	0.321649i
$903$	5.38648	+	1.85815i	0.179251	+	0.0618355i
$904$	−1.18815	+	6.73834i	−0.0395173	+	0.224114i
$905$	−7.09230	−	5.95114i	−0.235756	−	0.197823i
$906$	−27.9780	−	8.01159i	−0.929508	−	0.266167i
$907$	−5.59732	−	2.03726i	−0.185856	−	0.0676461i	0.247416	−	0.968909i	$-0.420419\pi$
$907$	−5.59732	−	2.03726i	−0.185856	−	0.0676461i	−0.433272	+	0.901263i	$0.642641\pi$
$908$	3.57937	+	6.19964i	0.118785	+	0.205742i
$909$	−12.0769	−	7.53432i	−0.400566	−	0.249898i
$910$	9.91683	+	0.529001i	0.328740	+	0.0175362i
$911$	24.8008	+	9.02675i	0.821687	+	0.299070i	0.718442	−	0.695586i	$-0.244855\pi$
$911$	24.8008	+	9.02675i	0.821687	+	0.299070i	0.103244	+	0.994656i	$0.467078\pi$
$912$	3.42279	+	5.07053i	0.113340	+	0.167902i
$913$	4.17489	−	23.6770i	0.138169	−	0.783594i
$914$	−25.5689	−	21.4548i	−0.845743	−	0.709662i
$915$	2.83584	−	27.0757i	0.0937501	−	0.895096i
$916$	2.26328	+	12.8357i	0.0747810	+	0.424104i
$917$	58.4127	+	3.11595i	1.92896	+	0.102898i
$918$	22.7681	−	29.2073i	0.751459	−	0.963984i
$919$	23.9771	−	41.5296i	0.790932	−	1.36993i	−0.134459	−	0.990919i	$-0.542930\pi$
$919$	23.9771	−	41.5296i	0.790932	−	1.36993i	0.925391	−	0.379015i	$-0.123737\pi$
$920$	3.34505	−	2.80683i	0.110283	−	0.0925385i
$921$	0.906160	−	8.65172i	0.0298590	−	0.285084i
$922$	4.49969	−	25.5190i	0.148189	−	0.840423i
$923$	−1.68029	−	1.40993i	−0.0553073	−	0.0464083i
$924$	−6.04579	+	10.8922i	−0.198892	+	0.358328i
$925$	−20.7303	−	7.54522i	−0.681608	−	0.248085i
$926$	−4.79674			−0.157631
$927$	15.7757	−	39.1280i	0.518144	−	1.28513i
$928$	8.75911			0.287532
$929$	−8.45277	−	47.9381i	−0.277326	−	1.57280i	−0.731474	−	0.681870i	$-0.761167\pi$
$929$	−8.45277	−	47.9381i	−0.277326	−	1.57280i	0.454147	−	0.890927i	$-0.349944\pi$
$930$	24.2772	+	6.95183i	0.796079	+	0.227960i
$931$	24.0009	−	5.93654i	0.786599	−	0.194562i
$932$	3.05059	−	17.3007i	0.0999254	−	0.566705i
$933$	−24.2700	+	23.4542i	−0.794563	+	0.767858i
$934$	−9.41624	−	3.42723i	−0.308109	−	0.112142i
$935$	−32.2522			−1.05476
$936$	2.52948	−	6.27378i	0.0826786	−	0.205065i
$937$	−28.4947	−	49.3543i	−0.930882	−	1.61233i	−0.781818	−	0.623507i	$-0.785707\pi$
$937$	−28.4947	−	49.3543i	−0.930882	−	1.61233i	−0.149064	−	0.988828i	$-0.547626\pi$
$938$	−0.332748	−	2.73109i	−0.0108646	−	0.0891732i
$939$	3.51064	+	5.20067i	0.114566	+	0.169718i
$940$	0.943765	−	0.343502i	0.0307822	−	0.0112038i
$941$	−13.1477	−	11.0322i	−0.428603	−	0.359641i	0.402821	−	0.915279i	$-0.368030\pi$
$941$	−13.1477	−	11.0322i	−0.428603	−	0.359641i	−0.831424	+	0.555638i	$0.812474\pi$
$942$	1.84385	−	17.6045i	0.0600758	−	0.573585i
$943$	13.6270	+	4.95983i	0.443757	+	0.161514i
$944$	10.8522			0.353208
$945$	−22.6030	+	3.58355i	−0.735275	+	0.116573i
$946$	−3.38015			−0.109898
$947$	−30.3973	−	11.0637i	−0.987780	−	0.359523i	−0.202920	−	0.979195i	$-0.565043\pi$
$947$	−30.3973	−	11.0637i	−0.987780	−	0.359523i	−0.784860	+	0.619673i	$0.787265\pi$
$948$	1.11026	+	0.806036i	0.0360596	+	0.0261788i
$949$	13.6743	+	11.4741i	0.443886	+	0.372465i
$950$	−7.39780	+	2.69258i	−0.240016	+	0.0873588i
$951$	25.3035	−	51.9277i	0.820524	−	1.68387i
$952$	15.0699	−	11.3340i	0.488419	−	0.367336i
$953$	5.02190	+	8.69819i	0.162675	+	0.281762i	0.935827	−	0.352459i	$-0.114654\pi$
$953$	5.02190	+	8.69819i	0.162675	+	0.281762i	−0.773152	+	0.634221i	$0.781321\pi$
$954$	11.3091	+	7.05533i	0.366147	+	0.228425i
$955$	−28.2711			−0.914833
$956$	−0.201785	−	0.0734437i	−0.00652619	−	0.00237534i
$957$	9.99201	+	40.0139i	0.322996	+	1.29347i
$958$	1.89014	−	10.7195i	0.0610676	−	0.346331i
$959$	−8.79943	−	8.22097i	−0.284148	−	0.265469i
$960$	−0.698542	−	2.79738i	−0.0225454	−	0.0902850i
$961$	7.93739	+	45.0152i	0.256045	+	1.45210i
$962$	22.3174			0.719542
$963$	11.1950	+	34.3699i	0.360755	+	1.10755i
$964$	−6.42394			−0.206901
$965$	34.8248	+	12.6752i	1.12105	+	0.408029i
$966$	−12.0191	+	0.202934i	−0.386707	+	0.00652928i
$967$	14.2453	+	11.9533i	0.458099	+	0.384391i	0.842431	−	0.538804i	$-0.181124\pi$
$967$	14.2453	+	11.9533i	0.458099	+	0.384391i	−0.384332	+	0.923195i	$0.625568\pi$
$968$	−0.626850	+	3.55504i	−0.0201477	+	0.114263i
$969$	39.8248	−	17.7485i	1.27936	−	0.570162i
$970$	−21.7126	+	18.2190i	−0.697148	+	0.584977i
$971$	−20.3346	+	35.2206i	−0.652569	+	1.13028i	0.329928	+	0.944006i	$0.392975\pi$
$971$	−20.3346	+	35.2206i	−0.652569	+	1.13028i	−0.982497	+	0.186277i	$0.940358\pi$
$972$	−2.67906	+	15.3565i	−0.0859309	+	0.492561i
$973$	12.6619	+	24.9078i	0.405922	+	0.798508i
$974$	2.35758	+	13.3705i	0.0755416	+	0.428418i
$975$	7.04433	+	5.11410i	0.225599	+	0.163782i
$976$	−7.23297	−	6.06918i	−0.231522	−	0.194270i
$977$	−3.31135	+	18.7796i	−0.105940	+	0.600813i	0.884901	+	0.465778i	$0.154226\pi$
$977$	−3.31135	+	18.7796i	−0.105940	+	0.600813i	−0.990841	+	0.135034i	$0.956885\pi$
$978$	14.7806	−	30.3326i	0.472631	−	0.969929i
$979$	17.5802	+	6.39866i	0.561865	+	0.204502i
$980$	−11.5865	−	1.23966i	−0.370117	−	0.0395995i
$981$	−2.89673	−	0.613524i	−0.0924856	−	0.0195883i
$982$	9.70905	+	16.8166i	0.309828	+	0.536638i
$983$	−40.2390	−	14.6458i	−1.28343	−	0.467129i	−0.391862	−	0.920024i	$-0.628169\pi$
$983$	−40.2390	−	14.6458i	−1.28343	−	0.467129i	−0.891564	+	0.452895i	$0.850391\pi$
$984$	6.88549	−	6.65407i	0.219501	−	0.212124i
$985$	−1.02289	−	0.858307i	−0.0325920	−	0.0273479i
$986$	10.8402	−	61.4780i	0.345223	−	1.95786i
$987$	−2.61365	−	0.901619i	−0.0831932	−	0.0286988i
$988$	6.10090	−	5.11926i	0.194095	−	0.162865i
$989$	−1.63081	−	2.82465i	−0.0518568	−	0.0898187i
$990$	11.9823	−	6.38225i	0.380822	−	0.202841i
$991$	−10.2263	+	17.7125i	−0.324850	+	0.562656i	−0.981482	−	0.191555i	$-0.938647\pi$
$991$	−10.2263	+	17.7125i	−0.324850	+	0.562656i	0.656632	+	0.754211i	$0.271980\pi$
$992$	6.70932	−	5.62979i	0.213021	−	0.178746i
$993$	2.69800	−	5.53681i	0.0856183	−	0.175705i
$994$	1.88067	+	1.75704i	0.0596512	+	0.0557298i
$995$	−3.73770	+	1.36041i	−0.118493	+	0.0431279i
$996$	1.59567	−	15.2349i	0.0505607	−	0.482738i
$997$	31.5413	−	26.4663i	0.998923	−	0.838196i	0.0120883	−	0.999927i	$-0.496152\pi$
$997$	31.5413	−	26.4663i	0.998923	−	0.838196i	0.986835	+	0.161731i	$0.0517076\pi$
$998$	7.67086	+	13.2863i	0.242817	+	0.420571i
$999$	−50.2937	+	10.7475i	−1.59122	+	0.340035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.a.121.2	yes	72
7.4	even	3		378.2.v.b.67.9	✓	72
27.25	even	9		378.2.v.b.79.9	yes	72
189.25	even	9	inner	378.2.w.a.25.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.9	✓	72	7.4	even	3
378.2.v.b.79.9	yes	72	27.25	even	9
378.2.w.a.25.2	yes	72	189.25	even	9	inner
378.2.w.a.121.2	yes	72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.58205 + 0.705062i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.56427 - 0.569347i) q^{5} +(1.72779 - 0.121449i) q^{6} +(0.319985 + 2.62633i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00577 - 2.23089i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.58205 + 0.705062i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.56427 - 0.569347i) q^{5} +(1.72779 - 0.121449i) q^{6} +(0.319985 + 2.62633i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.00577 - 2.23089i) q^{9} -1.66466 q^{10} +(-2.55453 - 0.929774i) q^{11} +(-1.66513 - 0.476814i) q^{12} +(-0.391548 + 2.22058i) q^{13} +(0.597570 - 2.57738i) q^{14} +(-2.07333 + 2.00364i) q^{15} +(0.173648 + 0.984808i) q^{16} +7.12702 q^{17} +(-2.64782 + 1.41034i) q^{18} -3.53203 q^{19} +(1.56427 + 0.569347i) q^{20} +(-2.35796 - 3.92938i) q^{21} +(2.08247 + 1.74740i) q^{22} +(-0.455505 + 2.58330i) q^{23} +(1.40163 + 1.01757i) q^{24} +(-1.70744 + 1.43271i) q^{25} +(1.12742 - 1.95275i) q^{26} +(-1.60032 + 4.94358i) q^{27} +(-1.44305 + 2.21757i) q^{28} +(1.52100 + 8.62604i) q^{29} +(2.63358 - 1.17369i) q^{30} +(6.70932 + 5.62979i) q^{31} +(0.173648 - 0.984808i) q^{32} +(4.69695 - 0.330155i) q^{33} +(-6.69721 - 2.43759i) q^{34} +(1.99584 + 3.92610i) q^{35} +(2.97050 - 0.419674i) q^{36} +(4.94878 + 8.57154i) q^{37} +(3.31903 + 1.20803i) q^{38} +(-0.946199 - 3.78914i) q^{39} +(-1.27520 - 1.07002i) q^{40} +(0.959980 - 5.44432i) q^{41} +(0.871830 + 4.49888i) q^{42} +(-0.952500 + 0.799242i) q^{43} +(-1.35924 - 2.35427i) q^{44} +(1.86742 - 4.63169i) q^{45} +(1.31158 - 2.27172i) q^{46} +(0.462175 - 0.387811i) q^{47} +(-0.969071 - 1.43558i) q^{48} +(-6.79522 + 1.68077i) q^{49} +(2.09449 - 0.762331i) q^{50} +(-11.2753 + 5.02500i) q^{51} +(-1.72731 + 1.44938i) q^{52} +(-2.22157 - 3.84788i) q^{53} +(3.19461 - 4.09810i) q^{54} -4.52534 q^{55} +(2.11448 - 1.59028i) q^{56} +(5.58786 - 2.49030i) q^{57} +(1.52100 - 8.62604i) q^{58} +(1.88446 - 10.6873i) q^{59} +(-2.87618 + 0.202170i) q^{60} +(-7.23297 + 6.06918i) q^{61} +(-4.37920 - 7.58500i) q^{62} +(6.50087 + 4.55397i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.651795 + 3.69651i) q^{65} +(-4.52661 - 1.29621i) q^{66} +(0.977175 - 0.355662i) q^{67} +(5.45962 + 4.58116i) q^{68} +(-1.10075 - 4.40807i) q^{69} +(-0.532666 - 4.37195i) q^{70} +(-0.486389 + 0.842451i) q^{71} +(-2.93489 - 0.621606i) q^{72} +(3.95827 - 6.85593i) q^{73} +(-1.71869 - 9.74720i) q^{74} +(1.69111 - 3.47048i) q^{75} +(-2.70569 - 2.27035i) q^{76} +(1.62448 - 7.00656i) q^{77} +(-0.406826 + 3.88425i) q^{78} +(-0.744351 - 0.270922i) q^{79} +(0.832330 + 1.44164i) q^{80} +(-0.953742 - 8.94932i) q^{81} +(-2.76415 + 4.78765i) q^{82} +(1.53575 + 8.70965i) q^{83} +(0.719455 - 4.52575i) q^{84} +(11.1486 - 4.05775i) q^{85} +(1.16841 - 0.425268i) q^{86} +(-8.48820 - 12.5744i) q^{87} +(0.472059 + 2.67718i) q^{88} -6.88195 q^{89} +(-3.33893 + 3.71367i) q^{90} +(-5.95727 - 0.317783i) q^{91} +(-2.00945 + 1.68613i) q^{92} +(-14.5839 - 4.17613i) q^{93} +(-0.566941 + 0.206350i) q^{94} +(-5.52505 + 2.01095i) q^{95} +(0.419631 + 1.68045i) q^{96} +(13.0432 - 10.9446i) q^{97} +(6.96028 + 0.744693i) q^{98} +(-7.19804 + 3.83397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

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