LMFDB - Embedded newform 189.2.v.a.43.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(22,189)] 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("189.22"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.v (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [54,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	189.43
Dual form			189.2.v.a.22.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00215 + 1.68000i) q^{2} +(1.58061 - 0.708280i) q^{3} +(0.838893 + 4.75760i) q^{4} +(-3.29720 - 1.20008i) q^{5} +(4.35453 + 1.23735i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-3.69957 + 6.40784i) q^{8} +(1.99668 - 2.23903i) q^{9} +(-4.58534 - 7.94204i) q^{10} +(-0.308948 + 0.112448i) q^{11} +(4.69568 + 6.92576i) q^{12} +(-1.82041 + 1.52750i) q^{13} +(2.00215 - 1.68000i) q^{14} +(-6.06160 + 0.438472i) q^{15} +(-9.09294 + 3.30956i) q^{16} +(-1.28196 - 2.22042i) q^{17} +(7.75922 - 1.12845i) q^{18} +(2.50633 - 4.34109i) q^{19} +(2.94352 - 16.6935i) q^{20} +(-0.423048 - 1.67959i) q^{21} +(-0.807473 - 0.293896i) q^{22} +(0.785944 + 4.45731i) q^{23} +(-1.30905 + 12.7486i) q^{24} +(5.60111 + 4.69989i) q^{25} -6.21093 q^{26} +(1.57012 - 4.95325i) q^{27} +4.83099 q^{28} +(-7.49985 - 6.29312i) q^{29} +(-12.8728 - 9.30560i) q^{30} +(1.70905 + 9.69250i) q^{31} +(-9.85965 - 3.58862i) q^{32} +(-0.408683 + 0.396559i) q^{33} +(1.16363 - 6.59930i) q^{34} +(-1.75440 + 3.03872i) q^{35} +(12.3274 + 7.62110i) q^{36} +(1.70374 + 2.95097i) q^{37} +(12.3111 - 4.48086i) q^{38} +(-1.79546 + 3.70375i) q^{39} +(19.8881 - 16.6881i) q^{40} +(-5.18169 + 4.34795i) q^{41} +(1.97471 - 4.07351i) q^{42} +(0.843380 - 0.306965i) q^{43} +(-0.794157 - 1.37552i) q^{44} +(-9.27048 + 4.98636i) q^{45} +(-5.91471 + 10.2446i) q^{46} +(-0.875085 + 4.96285i) q^{47} +(-12.0283 + 11.6715i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(3.31843 + 18.8197i) q^{50} +(-3.59896 - 2.60164i) q^{51} +(-8.79438 - 7.37936i) q^{52} +6.97774 q^{53} +(11.4651 - 7.27934i) q^{54} +1.15361 q^{55} +(5.66806 + 4.75607i) q^{56} +(0.886834 - 8.63677i) q^{57} +(-4.44335 - 25.1995i) q^{58} +(6.88347 + 2.50538i) q^{59} +(-7.17111 - 28.4708i) q^{60} +(0.157688 - 0.894295i) q^{61} +(-12.8616 + 22.2770i) q^{62} +(-1.85830 - 2.35515i) q^{63} +(-4.03508 - 6.98896i) q^{64} +(7.83538 - 2.85185i) q^{65} +(-1.48446 + 0.107380i) q^{66} +(4.46899 - 3.74993i) q^{67} +(9.48844 - 7.96175i) q^{68} +(4.39930 + 6.48862i) q^{69} +(-8.61762 + 3.13656i) q^{70} +(-5.46530 - 9.46618i) q^{71} +(6.96050 + 21.0778i) q^{72} +(2.95135 - 5.11188i) q^{73} +(-1.54649 + 8.77057i) q^{74} +(12.1820 + 3.46156i) q^{75} +(22.7557 + 8.28240i) q^{76} +(0.0570914 + 0.323781i) q^{77} +(-9.81708 + 4.39907i) q^{78} +(-0.653105 - 0.548021i) q^{79} +33.9530 q^{80} +(-1.02654 - 8.94127i) q^{81} -17.6791 q^{82} +(-1.71116 - 1.43583i) q^{83} +(7.63593 - 3.42169i) q^{84} +(1.56219 + 8.85963i) q^{85} +(2.20427 + 0.802290i) q^{86} +(-16.3116 - 4.63500i) q^{87} +(0.422426 - 2.39570i) q^{88} +(0.107492 - 0.186182i) q^{89} +(-26.9379 - 5.59099i) q^{90} +(1.18819 + 2.05800i) q^{91} +(-20.5468 + 7.47842i) q^{92} +(9.56634 + 14.1096i) q^{93} +(-10.0896 + 8.46622i) q^{94} +(-13.4735 + 11.3056i) q^{95} +(-18.1261 + 1.31117i) q^{96} +(-2.73245 + 0.994531i) q^{97} +(-1.30681 - 2.26346i) q^{98} +(-0.365096 + 0.916268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27}+ \cdots - 117 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	2.00215	+	1.68000i	1.41573	+	1.18794i	0.953580	+	0.301139i	$0.0973667\pi$
$2$	2.00215	+	1.68000i	1.41573	+	1.18794i	0.462151	+	0.886801i	$0.347078\pi$
$3$	1.58061	−	0.708280i	0.912568	−	0.408925i
$3$	1.58061	−	0.708280i	0.912568	−	0.408925i
$4$	0.838893	+	4.75760i	0.419447	+	2.37880i
$5$	−3.29720	−	1.20008i	−1.47455	−	0.536693i	−0.525220	−	0.850966i	$-0.676017\pi$
$5$	−3.29720	−	1.20008i	−1.47455	−	0.536693i	−0.949333	+	0.314273i	$0.898239\pi$
$6$	4.35453	+	1.23735i	1.77773	+	0.505147i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	−3.69957	+	6.40784i	−1.30799	+	2.26551i
$9$	1.99668	−	2.23903i	0.665560	−	0.746344i
$10$	−4.58534	−	7.94204i	−1.45001	−	2.51149i
$11$	−0.308948	+	0.112448i	−0.0931514	+	0.0339044i	−0.388175	−	0.921585i	$-0.626895\pi$
$11$	−0.308948	+	0.112448i	−0.0931514	+	0.0339044i	0.295024	+	0.955490i	$0.404672\pi$
$12$	4.69568	+	6.92576i	1.35553	+	1.99929i
$13$	−1.82041	+	1.52750i	−0.504890	+	0.423653i	−0.859327	−	0.511427i	$-0.829117\pi$
$13$	−1.82041	+	1.52750i	−0.504890	+	0.423653i	0.354437	+	0.935080i	$0.384673\pi$
$14$	2.00215	−	1.68000i	0.535096	−	0.448999i
$15$	−6.06160	+	0.438472i	−1.56510	+	0.113213i
$16$	−9.09294	+	3.30956i	−2.27324	+	0.827390i
$17$	−1.28196	−	2.22042i	−0.310921	−	0.538531i	0.667641	−	0.744483i	$-0.267304\pi$
$17$	−1.28196	−	2.22042i	−0.310921	−	0.538531i	−0.978562	+	0.205952i	$0.933971\pi$
$18$	7.75922	−	1.12845i	1.82887	−	0.265978i
$19$	2.50633	−	4.34109i	0.574991	−	0.995914i	−0.421051	−	0.907037i	$-0.638339\pi$
$19$	2.50633	−	4.34109i	0.574991	−	0.995914i	0.996043	−	0.0888772i	$-0.0283279\pi$
$20$	2.94352	−	16.6935i	0.658190	−	3.73278i
$21$	−0.423048	−	1.67959i	−0.0923167	−	0.366517i
$22$	−0.807473	−	0.293896i	−0.172154	−	0.0626588i
$23$	0.785944	+	4.45731i	0.163881	+	0.929414i	0.950211	+	0.311607i	$0.100867\pi$
$23$	0.785944	+	4.45731i	0.163881	+	0.929414i	−0.786330	+	0.617806i	$0.788022\pi$
$24$	−1.30905	+	12.7486i	−0.267208	+	2.60231i
$25$	5.60111	+	4.69989i	1.12022	+	0.939978i
$26$	−6.21093			−1.21806
$27$	1.57012	−	4.95325i	0.302170	−	0.953254i
$28$	4.83099			0.912972
$29$	−7.49985	−	6.29312i	−1.39269	−	1.16860i	−0.964238	−	0.265036i	$-0.914616\pi$
$29$	−7.49985	−	6.29312i	−1.39269	−	1.16860i	−0.428448	−	0.903566i	$-0.640940\pi$
$30$	−12.8728	−	9.30560i	−2.35025	−	1.69896i
$31$	1.70905	+	9.69250i	0.306954	+	1.74082i	0.614161	+	0.789181i	$0.289495\pi$
$31$	1.70905	+	9.69250i	0.306954	+	1.74082i	−0.307207	+	0.951643i	$0.599394\pi$
$32$	−9.85965	−	3.58862i	−1.74296	−	0.634384i
$33$	−0.408683	+	0.396559i	−0.0711427	+	0.0690320i
$34$	1.16363	−	6.59930i	0.199562	−	1.13177i
$35$	−1.75440	+	3.03872i	−0.296548	+	0.513637i
$36$	12.3274	+	7.62110i	2.05457	+	1.27018i
$37$	1.70374	+	2.95097i	0.280094	+	0.485137i	0.971408	−	0.237418i	$-0.0763011\pi$
$37$	1.70374	+	2.95097i	0.280094	+	0.485137i	−0.691314	+	0.722555i	$0.742968\pi$
$38$	12.3111	−	4.48086i	1.99712	−	0.726892i
$39$	−1.79546	+	3.70375i	−0.287504	+	0.593075i
$40$	19.8881	−	16.6881i	3.14459	−	2.63863i
$41$	−5.18169	+	4.34795i	−0.809244	+	0.679036i	−0.950427	−	0.310947i	$-0.899354\pi$
$41$	−5.18169	+	4.34795i	−0.809244	+	0.679036i	0.141183	+	0.989983i	$0.454909\pi$
$42$	1.97471	−	4.07351i	0.304704	−	0.628556i
$43$	0.843380	−	0.306965i	0.128614	−	0.0468118i	−0.276911	−	0.960896i	$-0.589311\pi$
$43$	0.843380	−	0.306965i	0.128614	−	0.0468118i	0.405525	+	0.914084i	$0.367089\pi$
$44$	−0.794157	−	1.37552i	−0.119724	−	0.207368i
$45$	−9.27048	+	4.98636i	−1.38196	+	0.743323i
$46$	−5.91471	+	10.2446i	−0.872076	+	1.51048i
$47$	−0.875085	+	4.96285i	−0.127644	+	0.723907i	0.852058	+	0.523448i	$0.175354\pi$
$47$	−0.875085	+	4.96285i	−0.127644	+	0.723907i	−0.979702	+	0.200459i	$0.935757\pi$
$48$	−12.0283	+	11.6715i	−1.73614	+	1.68463i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	3.31843	+	18.8197i	0.469297	+	2.66151i
$51$	−3.59896	−	2.60164i	−0.503955	−	0.364303i
$52$	−8.79438	−	7.37936i	−1.21956	−	1.02333i
$53$	6.97774			0.958466			0.479233	−	0.877688i	$-0.340915\pi$
$53$	6.97774			0.958466			0.479233	+	0.877688i	$0.340915\pi$
$54$	11.4651	−	7.27934i	1.56020	−	0.990593i
$55$	1.15361			0.155553
$56$	5.66806	+	4.75607i	0.757427	+	0.635557i
$57$	0.886834	−	8.63677i	0.117464	−	1.14397i
$58$	−4.44335	−	25.1995i	−0.583441	−	3.30886i
$59$	6.88347	+	2.50538i	0.896151	+	0.326172i	0.748709	−	0.662899i	$-0.230674\pi$
$59$	6.88347	+	2.50538i	0.896151	+	0.326172i	0.147442	+	0.989071i	$0.452896\pi$
$60$	−7.17111	−	28.4708i	−0.925786	−	3.67557i
$61$	0.157688	−	0.894295i	0.0201899	−	0.114503i	−0.973047	−	0.230606i	$-0.925929\pi$
$61$	0.157688	−	0.894295i	0.0201899	−	0.114503i	0.993237	+	0.116103i	$0.0370403\pi$
$62$	−12.8616	+	22.2770i	−1.63343	+	2.82918i
$63$	−1.85830	−	2.35515i	−0.234123	−	0.296721i
$64$	−4.03508	−	6.98896i	−0.504385	−	0.873620i
$65$	7.83538	−	2.85185i	0.971859	−	0.353728i
$66$	−1.48446	+	0.107380i	−0.182725	+	0.0132176i
$67$	4.46899	−	3.74993i	0.545974	−	0.458126i	−0.327601	−	0.944816i	$-0.606240\pi$
$67$	4.46899	−	3.74993i	0.545974	−	0.458126i	0.873575	+	0.486690i	$0.161796\pi$
$68$	9.48844	−	7.96175i	1.15064	−	0.965504i
$69$	4.39930	+	6.48862i	0.529613	+	0.781138i
$70$	−8.61762	+	3.13656i	−1.03000	+	0.374890i
$71$	−5.46530	−	9.46618i	−0.648612	−	1.12343i	−0.983455	−	0.181155i	$-0.942016\pi$
$71$	−5.46530	−	9.46618i	−0.648612	−	1.12343i	0.334843	−	0.942274i	$-0.391317\pi$
$72$	6.96050	+	21.0778i	0.820303	+	2.48405i
$73$	2.95135	−	5.11188i	0.345429	−	0.598301i	−0.640003	−	0.768373i	$-0.721067\pi$
$73$	2.95135	−	5.11188i	0.345429	−	0.598301i	0.985432	+	0.170072i	$0.0544001\pi$
$74$	−1.54649	+	8.77057i	−0.179776	+	1.01956i
$75$	12.1820	+	3.46156i	1.40666	+	0.399707i
$76$	22.7557	+	8.28240i	2.61026	+	0.950056i
$77$	0.0570914	+	0.323781i	0.00650616	+	0.0368983i
$78$	−9.81708	+	4.39907i	−1.11157	+	0.498097i
$79$	−0.653105	−	0.548021i	−0.0734801	−	0.0616571i	0.605308	−	0.795991i	$-0.293050\pi$
$79$	−0.653105	−	0.548021i	−0.0734801	−	0.0616571i	−0.678788	+	0.734334i	$0.737494\pi$
$80$	33.9530			3.79606
$81$	−1.02654	−	8.94127i	−0.114060	−	0.993474i
$82$	−17.6791			−1.95233
$83$	−1.71116	−	1.43583i	−0.187824	−	0.157603i	0.544027	−	0.839068i	$-0.316899\pi$
$83$	−1.71116	−	1.43583i	−0.187824	−	0.157603i	−0.731851	+	0.681465i	$0.761343\pi$
$84$	7.63593	−	3.42169i	0.833149	−	0.373337i
$85$	1.56219	+	8.85963i	0.169443	+	0.960962i
$86$	2.20427	+	0.802290i	0.237693	+	0.0865131i
$87$	−16.3116	−	4.63500i	−1.74879	−	0.496924i
$88$	0.422426	−	2.39570i	0.0450308	−	0.255382i
$89$	0.107492	−	0.186182i	0.0113941	−	0.0197352i	−0.860272	−	0.509835i	$-0.829706\pi$
$89$	0.107492	−	0.186182i	0.0113941	−	0.0197352i	0.871666	+	0.490100i	$0.163040\pi$
$90$	−26.9379	−	5.59099i	−2.83951	−	0.589342i
$91$	1.18819	+	2.05800i	0.124556	+	0.215737i
$92$	−20.5468	+	7.47842i	−2.14215	+	0.779679i
$93$	9.56634	+	14.1096i	0.991984	+	1.46310i
$94$	−10.0896	+	8.46622i	−1.04067	+	0.873224i
$95$	−13.4735	+	11.3056i	−1.38236	+	1.15993i
$96$	−18.1261	+	1.31117i	−1.84998	+	0.133820i
$97$	−2.73245	+	0.994531i	−0.277438	+	0.100979i	−0.476992	−	0.878908i	$-0.658273\pi$
$97$	−2.73245	+	0.994531i	−0.277438	+	0.100979i	0.199554	+	0.979887i	$0.436051\pi$
$98$	−1.30681	−	2.26346i	−0.132008	−	0.228644i
$99$	−0.365096	+	0.916268i	−0.0366936	+	0.0920884i
$100$	−17.6615	+	30.5906i	−1.76615	+	3.05906i
$101$	−0.958894	+	5.43816i	−0.0954135	+	0.541117i	0.899206	+	0.437525i	$0.144145\pi$
$101$	−0.958894	+	5.43816i	−0.0954135	+	0.541117i	−0.994620	+	0.103592i	$0.966966\pi$
$102$	−2.83489	−	11.2551i	−0.280696	−	1.11442i
$103$	−4.15162	−	1.51106i	−0.409071	−	0.148890i	0.129285	−	0.991608i	$-0.458732\pi$
$103$	−4.15162	−	1.51106i	−0.409071	−	0.148890i	−0.538355	+	0.842718i	$0.680954\pi$
$104$	−3.05327	−	17.3160i	−0.299398	−	1.69797i
$105$	−0.620774	+	6.04565i	−0.0605814	+	0.589995i
$106$	13.9705	+	11.7226i	1.35693	+	1.13860i
$107$	−13.6243			−1.31711			−0.658556	−	0.752532i	$-0.728832\pi$
$107$	−13.6243			−1.31711			−0.658556	+	0.752532i	$0.728832\pi$
$108$	24.8828	+	3.31475i	2.39434	+	0.318962i
$109$	11.0039			1.05398			0.526989	−	0.849872i	$-0.323321\pi$
$109$	11.0039			1.05398			0.526989	+	0.849872i	$0.323321\pi$
$110$	2.30970	+	1.93807i	0.220221	+	0.184788i
$111$	4.78307	+	3.45762i	0.453989	+	0.328183i
$112$	1.68031	+	9.52950i	0.158774	+	0.900453i
$113$	−1.17069	−	0.426096i	−0.110129	−	0.0400837i	0.286368	−	0.958120i	$-0.407552\pi$
$113$	−1.17069	−	0.426096i	−0.110129	−	0.0400837i	−0.396497	+	0.918036i	$0.629774\pi$
$114$	16.2853	−	15.8022i	1.52526	−	1.48001i
$115$	2.75773	−	15.6398i	0.257159	−	1.45842i
$116$	23.6486	−	40.9605i	2.19571	−	3.80309i
$117$	−0.214642	+	7.12589i	−0.0198436	+	0.658789i
$118$	9.57267	+	16.5804i	0.881236	+	1.52635i
$119$	−2.40930	+	0.876912i	−0.220860	+	0.0803864i
$120$	19.6156	−	40.4639i	1.79065	−	3.69383i
$121$	−8.34368	+	7.00118i	−0.758517	+	0.636471i
$122$	1.81813	−	1.52559i	0.164606	−	0.138121i
$123$	−5.11068	+	10.5425i	−0.460815	+	0.950587i
$124$	−44.6793	+	16.2619i	−4.01232	+	1.46037i
$125$	−4.05572	−	7.02470i	−0.362754	−	0.628309i
$126$	0.236070	−	7.83730i	0.0210308	−	0.698202i
$127$	6.39662	−	11.0793i	0.567608	−	0.983126i	−0.429193	−	0.903213i	$-0.641202\pi$
$127$	6.39662	−	11.0793i	0.567608	−	0.983126i	0.996802	−	0.0799139i	$-0.0254645\pi$
$128$	0.0186594	−	0.105822i	0.00164927	−	0.00935347i
$129$	1.11564	−	1.08254i	0.0982267	−	0.0953125i
$130$	20.4787	+	7.45363i	1.79610	+	0.653727i
$131$	−1.25242	−	7.10283i	−0.109424	−	0.620577i	−0.989360	−	0.145485i	$-0.953526\pi$
$131$	−1.25242	−	7.10283i	−0.109424	−	0.620577i	0.879936	−	0.475092i	$-0.157585\pi$
$132$	−2.22951	−	1.61168i	−0.194054	−	0.140279i
$133$	−3.83992	−	3.22207i	−0.332963	−	0.279389i
$134$	15.2474			1.31718
$135$	−11.1213	+	14.4476i	−0.957170	+	1.24345i
$136$	18.9708			1.62673
$137$	7.02318	+	5.89315i	0.600031	+	0.503486i	0.891456	−	0.453108i	$-0.149685\pi$
$137$	7.02318	+	5.89315i	0.600031	+	0.503486i	−0.291425	+	0.956594i	$0.594129\pi$
$138$	−2.09285	+	20.3820i	−0.178155	+	1.73503i
$139$	−3.10976	−	17.6363i	−0.263766	−	1.49589i	−0.772526	−	0.634983i	$-0.781007\pi$
$139$	−3.10976	−	17.6363i	−0.263766	−	1.49589i	0.508760	−	0.860909i	$-0.330104\pi$
$140$	−15.9288	−	5.79759i	−1.34623	−	0.489986i
$141$	2.13192	+	8.46416i	0.179540	+	0.712811i
$142$	4.96085	−	28.1344i	0.416305	−	2.36099i
$143$	0.390647	−	0.676621i	0.0326676	−	0.0565819i
$144$	−10.7455	+	26.9675i	−0.895457	+	2.24729i
$145$	17.1762	+	29.7501i	1.42641	+	2.47061i
$146$	14.4970	−	5.27647i	1.19978	−	0.436684i
$147$	−1.72754	+	0.124963i	−0.142485	+	0.0103068i
$148$	−12.6103	+	10.5813i	−1.03656	+	0.869776i
$149$	15.3512	−	12.8812i	1.25762	−	1.05527i	0.261690	−	0.965152i	$-0.415720\pi$
$149$	15.3512	−	12.8812i	1.25762	−	1.05527i	0.995931	−	0.0901176i	$-0.0287243\pi$
$150$	18.5748	+	27.3964i	1.51663	+	2.23690i
$151$	0.536388	−	0.195229i	0.0436506	−	0.0158875i	−0.320103	−	0.947383i	$-0.603717\pi$
$151$	0.536388	−	0.195229i	0.0436506	−	0.0158875i	0.363753	+	0.931495i	$0.381495\pi$
$152$	18.5447	+	32.1203i	1.50417	+	2.60530i
$153$	−7.53126	−	1.56312i	−0.608866	−	0.126371i
$154$	−0.429647	+	0.744171i	−0.0346220	+	0.0599670i
$155$	5.99672	−	34.0091i	0.481668	−	2.73168i
$156$	−19.1272	−	5.43504i	−1.53140	−	0.435151i
$157$	−7.56674	−	2.75407i	−0.603891	−	0.219798i	0.0219369	−	0.999759i	$-0.493017\pi$
$157$	−7.56674	−	2.75407i	−0.603891	−	0.219798i	−0.625828	+	0.779961i	$0.715239\pi$
$158$	−0.386938	−	2.19444i	−0.0307831	−	0.174580i
$159$	11.0291	−	4.94219i	0.874665	−	0.391941i
$160$	28.2026	+	23.6648i	2.22961	+	1.87087i
$161$	4.52607			0.356704
$162$	12.9661	−	19.6263i	1.01871	−	1.54199i
$163$	−1.88855			−0.147923			−0.0739614	−	0.997261i	$-0.523564\pi$
$163$	−1.88855			−0.147923			−0.0739614	+	0.997261i	$0.523564\pi$
$164$	−25.0327	−	21.0049i	−1.95473	−	1.64021i
$165$	1.82341	−	0.817080i	0.141953	−	0.0636096i
$166$	−1.01379	−	5.74949i	−0.0786854	−	0.446247i
$167$	−4.73464	−	1.72327i	−0.366378	−	0.133351i	0.152269	−	0.988339i	$-0.451342\pi$
$167$	−4.73464	−	1.72327i	−0.366378	−	0.133351i	−0.518647	+	0.854988i	$0.673564\pi$
$168$	12.3276	+	3.50294i	0.951099	+	0.270257i
$169$	−1.27681	+	7.24114i	−0.0982161	+	0.557011i
$170$	−11.7564	+	20.3628i	−0.901678	+	1.56175i
$171$	−4.71550	−	14.2795i	−0.360603	−	1.09198i
$172$	2.16792	+	3.75495i	0.165303	+	0.286313i
$173$	16.2893	−	5.92883i	1.23845	−	0.450760i	0.361969	−	0.932190i	$-0.382105\pi$
$173$	16.2893	−	5.92883i	1.23845	−	0.450760i	0.876485	+	0.481430i	$0.159882\pi$
$174$	−24.8715	−	36.6835i	−1.88550	−	2.78097i
$175$	5.60111	−	4.69989i	0.423404	−	0.355278i
$176$	2.43710	−	2.04497i	0.183703	−	0.154145i
$177$	12.6546	−	0.915385i	0.951178	−	0.0688045i
$178$	0.528001	−	0.192177i	0.0395753	−	0.0144042i
$179$	5.86658	+	10.1612i	0.438489	+	0.759485i	0.997573	−	0.0696257i	$-0.0221805\pi$
$179$	5.86658	+	10.1612i	0.438489	+	0.759485i	−0.559084	+	0.829111i	$0.688847\pi$
$180$	−31.5000	−	39.9222i	−2.34787	−	2.97563i
$181$	−6.59159	+	11.4170i	−0.489949	+	0.848617i	−0.999933	−	0.0115671i	$-0.996318\pi$
$181$	−6.59159	+	11.4170i	−0.489949	+	0.848617i	0.509984	+	0.860184i	$0.329651\pi$
$182$	−1.07852	+	6.11657i	−0.0799450	+	0.453390i
$183$	−0.384166	−	1.52522i	−0.0283984	−	0.112748i
$184$	−31.4694	−	11.4539i	−2.31995	−	0.844394i
$185$	−2.07618	−	11.7746i	−0.152644	−	0.865685i
$186$	−4.55093	+	44.3210i	−0.333690	+	3.24977i
$187$	0.645741	+	0.541841i	0.0472213	+	0.0396234i
$188$	−24.3454			−1.77557
$189$	−4.60535	−	2.40639i	−0.334990	−	0.175039i
$190$	−45.9695			−3.33498
$191$	−0.292258	−	0.245234i	−0.0211470	−	0.0177445i	0.632153	−	0.774844i	$-0.282171\pi$
$191$	−0.292258	−	0.245234i	−0.0211470	−	0.0177445i	−0.653300	+	0.757099i	$0.726616\pi$
$192$	−11.3280	−	8.18889i	−0.817531	−	0.590982i
$193$	−1.86312	−	10.5663i	−0.134110	−	0.760577i	−0.975475	−	0.220110i	$-0.929359\pi$
$193$	−1.86312	−	10.5663i	−0.134110	−	0.760577i	0.841365	−	0.540467i	$-0.181753\pi$
$194$	−7.14158	−	2.59932i	−0.512736	−	0.186621i
$195$	10.3648	−	10.0573i	0.742239	−	0.720219i
$196$	0.838893	−	4.75760i	0.0599209	−	0.339829i
$197$	0.207469	−	0.359346i	0.0147815	−	0.0256024i	−0.858540	−	0.512747i	$-0.828628\pi$
$197$	0.207469	−	0.359346i	0.0147815	−	0.0256024i	0.873322	+	0.487144i	$0.161961\pi$
$198$	−2.27031	+	1.22114i	−0.161344	+	0.0867827i
$199$	−9.85935	−	17.0769i	−0.698910	−	1.21055i	−0.968845	−	0.247670i	$-0.920335\pi$
$199$	−9.85935	−	17.0769i	−0.698910	−	1.21055i	0.269934	−	0.962879i	$-0.412998\pi$
$200$	−50.8378	+	18.5035i	−3.59478	+	1.30839i
$201$	4.40775	−	9.09248i	0.310899	−	0.641334i
$202$	−11.0559	+	9.27704i	−0.777894	+	0.652730i
$203$	−7.49985	+	6.29312i	−0.526386	+	0.441690i
$204$	9.35842	−	19.3049i	0.655220	−	1.35161i
$205$	22.3030	−	8.11762i	1.55771	−	0.566959i
$206$	−5.77355	−	10.0001i	−0.402263	−	0.696739i
$207$	11.5493	+	7.14007i	0.802735	+	0.496269i
$208$	11.4975	−	19.9143i	0.797208	−	1.38080i
$209$	−0.286179	+	1.62300i	−0.0197954	+	0.112266i
$210$	−11.3996	+	11.0614i	−0.786645	+	0.763307i
$211$	−15.6464	−	5.69483i	−1.07714	−	0.392048i	−0.258300	−	0.966065i	$-0.583162\pi$
$211$	−15.6464	−	5.69483i	−1.07714	−	0.392048i	−0.818844	+	0.574016i	$0.805385\pi$
$212$	5.85358	+	33.1973i	0.402025	+	2.28000i
$213$	−15.3432	−	11.0914i	−1.05130	−	0.759971i
$214$	−27.2779	−	22.8888i	−1.86468	−	1.56465i
$215$	−3.14918			−0.214772
$216$	25.9309	+	28.3860i	1.76437	+	1.93142i
$217$	9.84202			0.668120
$218$	22.0313	+	18.4865i	1.49215	+	1.25206i
$219$	1.04430	−	10.1703i	0.0705671	−	0.687245i
$220$	0.967757	+	5.48842i	0.0652462	+	0.370029i
$221$	5.72539	+	2.08387i	0.385131	+	0.140176i
$222$	3.76761	+	14.9582i	0.252866	+	1.00393i
$223$	−1.64750	+	9.34342i	−0.110325	+	0.625682i	0.878635	+	0.477494i	$0.158455\pi$
$223$	−1.64750	+	9.34342i	−0.110325	+	0.625682i	−0.988959	+	0.148187i	$0.952656\pi$
$224$	−5.24621	+	9.08671i	−0.350527	+	0.607131i
$225$	21.7068	−	3.15689i	1.44712	−	0.210460i
$226$	−1.62805	−	2.81986i	−0.108296	−	0.187575i
$227$	13.1661	−	4.79209i	0.873868	−	0.318062i	0.134135	−	0.990963i	$-0.457174\pi$
$227$	13.1661	−	4.79209i	0.873868	−	0.318062i	0.739732	+	0.672901i	$0.234952\pi$
$228$	41.8342	−	3.02612i	2.77054	−	0.200410i
$229$	−15.7576	+	13.2222i	−1.04129	+	0.873749i	−0.992151	−	0.125043i	$-0.960093\pi$
$229$	−15.7576	+	13.2222i	−1.04129	+	0.873749i	−0.0491422	+	0.998792i	$0.515649\pi$
$230$	31.7963	−	26.6803i	2.09659	−	1.75925i
$231$	0.319567	+	0.471336i	0.0210260	+	0.0310117i
$232$	68.0714	−	24.7760i	4.46911	−	1.62662i
$233$	7.85140	+	13.5990i	0.514362	+	0.890902i	0.999861	+	0.0166645i	$0.00530471\pi$
$233$	7.85140	+	13.5990i	0.514362	+	0.890902i	−0.485499	+	0.874237i	$0.661362\pi$
$234$	−12.4012	+	13.9065i	−0.810694	+	0.909095i
$235$	8.84117	−	15.3133i	0.576734	−	0.998933i
$236$	−6.14509	+	34.8505i	−0.400011	+	2.26858i
$237$	−1.42046	−	0.403628i	−0.0922687	−	0.0262184i
$238$	−6.29698	−	2.29191i	−0.408172	−	0.148563i
$239$	4.90948	+	27.8431i	0.317568	+	1.80102i	0.557444	+	0.830215i	$0.311782\pi$
$239$	4.90948	+	27.8431i	0.317568	+	1.80102i	−0.239875	+	0.970804i	$0.577107\pi$
$240$	53.6666	−	24.0482i	3.46416	−	1.55231i
$241$	18.4147	+	15.4518i	1.18620	+	0.995336i	0.999918	+	0.0128394i	$0.00408702\pi$
$241$	18.4147	+	15.4518i	1.18620	+	0.995336i	0.186278	+	0.982497i	$0.440357\pi$
$242$	−28.4673			−1.82995
$243$	−7.95547	−	13.4056i	−0.510344	−	0.859970i
$244$	4.38698			0.280848
$245$	2.68790	+	2.25542i	0.171724	+	0.144093i
$246$	−27.9438	+	12.5217i	−1.78163	+	0.798356i
$247$	2.06849	+	11.7310i	0.131615	+	0.746424i
$248$	−68.4307	−	24.9067i	−4.34535	−	1.58158i
$249$	−3.72165	−	1.05752i	−0.235850	−	0.0670175i
$250$	3.68137	−	20.8781i	0.232830	−	1.32045i
$251$	7.79191	−	13.4960i	0.491821	−	0.851859i	−0.508135	−	0.861278i	$-0.669665\pi$
$251$	7.79191	−	13.4960i	0.491821	−	0.851859i	0.999956	+	0.00941867i	$0.00299810\pi$
$252$	9.64595	−	10.8168i	0.607638	−	0.681391i
$253$	−0.744032	−	1.28870i	−0.0467769	−	0.0810199i
$254$	31.4202	−	11.4360i	1.97148	−	0.717559i
$255$	8.74432	+	12.8972i	0.547590	+	0.807653i
$256$	−12.1491	+	10.1943i	−0.759316	+	0.637142i
$257$	5.73016	−	4.80817i	0.357437	−	0.299925i	−0.446331	−	0.894868i	$-0.647270\pi$
$257$	5.73016	−	4.80817i	0.357437	−	0.299925i	0.803768	+	0.594942i	$0.202825\pi$
$258$	4.05235	−	0.293131i	0.252288	−	0.0182495i
$259$	3.20199	−	1.16543i	0.198962	−	0.0724163i
$260$	20.1410	+	34.8852i	1.24909	+	2.16349i
$261$	−29.0653	+	4.22706i	−1.79910	+	0.261648i
$262$	9.42523	−	16.3250i	0.582292	−	1.00856i
$263$	4.48609	−	25.4419i	0.276624	−	1.56881i	−0.457131	−	0.889399i	$-0.651123\pi$
$263$	4.48609	−	25.4419i	0.276624	−	1.56881i	0.733755	−	0.679414i	$-0.237766\pi$
$264$	−1.02913	−	4.08587i	−0.0633387	−	0.251468i
$265$	−23.0070	−	8.37387i	−1.41331	−	0.514403i
$266$	−2.27499	−	12.9021i	−0.139489	−	0.791080i
$267$	0.0380348	−	0.370416i	0.00232769	−	0.0226691i
$268$	21.5896	+	18.1159i	1.31880	+	1.10660i
$269$	0.492770			0.0300447			0.0150223	−	0.999887i	$-0.495218\pi$
$269$	0.492770			0.0300447			0.0150223	+	0.999887i	$0.495218\pi$
$270$	−46.5385	+	10.2424i	−2.83224	+	0.623333i
$271$	−23.6945			−1.43934			−0.719669	−	0.694317i	$-0.755707\pi$
$271$	−23.6945			−1.43934			−0.719669	+	0.694317i	$0.755707\pi$
$272$	19.0054	+	15.9474i	1.15237	+	0.966955i
$273$	3.33570	+	2.41133i	0.201886	+	0.145941i
$274$	4.16095	+	23.5979i	0.251372	+	1.42560i
$275$	−2.25895	−	0.822190i	−0.136220	−	0.0495799i
$276$	−27.1797	+	26.3733i	−1.63603	+	1.58749i
$277$	2.12745	−	12.0654i	0.127826	−	0.724938i	−0.851763	−	0.523927i	$-0.824466\pi$
$277$	2.12745	−	12.0654i	0.127826	−	0.724938i	0.979589	−	0.201011i	$-0.0644225\pi$
$278$	23.4028	−	40.5349i	1.40361	−	2.43112i
$279$	25.1142	+	15.5262i	1.50355	+	0.929529i
$280$	−12.9811	−	22.4839i	−0.775767	−	1.34367i
$281$	−12.5499	+	4.56778i	−0.748662	+	0.272491i	−0.688043	−	0.725670i	$-0.741530\pi$
$281$	−12.5499	+	4.56778i	−0.748662	+	0.272491i	−0.0606193	+	0.998161i	$0.519308\pi$
$282$	−9.95138	+	20.5281i	−0.592596	+	1.22243i
$283$	−2.30721	+	1.93598i	−0.137150	+	0.115082i	−0.708782	−	0.705428i	$-0.750755\pi$
$283$	−2.30721	+	1.93598i	−0.137150	+	0.115082i	0.571632	+	0.820510i	$0.306310\pi$
$284$	40.4515	−	33.9428i	2.40035	−	2.01414i
$285$	−13.2889	+	27.4129i	−0.787167	+	1.62380i
$286$	1.91886	−	0.698407i	0.113464	−	0.0412976i
$287$	3.38211	+	5.85798i	0.199639	+	0.345786i
$288$	−27.7216	+	14.9108i	−1.63351	+	0.878625i
$289$	5.21316	−	9.02945i	0.306656	−	0.531144i
$290$	−15.5909	+	88.4202i	−0.915527	+	5.19221i
$291$	−3.61455	+	3.50731i	−0.211888	+	0.205602i
$292$	26.7962	+	9.75300i	1.56813	+	0.570751i
$293$	−0.738094	−	4.18594i	−0.0431199	−	0.244545i	0.955628	−	0.294577i	$-0.0951788\pi$
$293$	−0.738094	−	4.18594i	−0.0431199	−	0.244545i	−0.998748	+	0.0500319i	$0.984068\pi$
$294$	−3.66872	−	2.65207i	−0.213964	−	0.154672i
$295$	−19.6895	−	16.5215i	−1.14637	−	0.961917i
$296$	−25.2125			−1.46544
$297$	0.0718977	+	1.70686i	0.00417193	+	0.0990419i
$298$	52.3758			3.03405
$299$	−8.23930	−	6.91359i	−0.476491	−	0.399823i
$300$	−6.24929	+	60.8611i	−0.360803	+	3.51382i
$301$	−0.155850	−	0.883871i	−0.00898307	−	0.0509455i
$302$	1.40191	+	0.510255i	0.0806710	+	0.0293618i
$303$	2.33609	+	9.27479i	0.134205	+	0.532823i
$304$	−8.42281	+	47.7681i	−0.483081	+	2.73969i
$305$	−1.59316	+	2.75943i	−0.0912240	+	0.158005i
$306$	−12.4526	−	15.7821i	−0.711870	−	0.902203i
$307$	12.1955	+	21.1232i	0.696034	+	1.20557i	0.969831	+	0.243779i	$0.0783870\pi$
$307$	12.1955	+	21.1232i	0.696034	+	1.20557i	−0.273797	+	0.961787i	$0.588280\pi$
$308$	−1.49253	+	0.543236i	−0.0850446	+	0.0309537i
$309$	−7.63236	+	0.552095i	−0.434190	+	0.0314076i
$310$	69.1416	−	58.0167i	3.92698	−	3.29513i
$311$	−10.8993	+	9.14557i	−0.618041	+	0.518598i	−0.897187	−	0.441651i	$-0.854393\pi$
$311$	−10.8993	+	9.14557i	−0.618041	+	0.518598i	0.279146	+	0.960249i	$0.409949\pi$
$312$	−17.0906	−	25.2073i	−0.967564	−	1.42708i
$313$	−7.28132	+	2.65018i	−0.411564	+	0.149797i	−0.539501	−	0.841985i	$-0.681387\pi$
$313$	−7.28132	+	2.65018i	−0.411564	+	0.149797i	0.127936	+	0.991782i	$0.459165\pi$
$314$	−10.5229	−	18.2262i	−0.593841	−	1.02856i
$315$	3.30080	+	9.99551i	0.185979	+	0.563183i
$316$	2.05938	−	3.56694i	0.115849	−	0.200656i
$317$	2.19724	−	12.4612i	0.123409	−	0.699889i	−0.858830	−	0.512260i	$-0.828808\pi$
$317$	2.19724	−	12.4612i	0.123409	−	0.699889i	0.982240	−	0.187629i	$-0.0600804\pi$
$318$	30.3848	+	8.63392i	1.70389	+	0.484166i
$319$	3.02471	+	1.10091i	0.169351	+	0.0616389i
$320$	4.91713	+	27.8864i	0.274876	+	1.55890i
$321$	−21.5348	+	9.64982i	−1.20195	+	0.538600i
$322$	9.06186	+	7.60380i	0.504998	+	0.423743i
$323$	−12.8521			−0.715107
$324$	41.6778	−	12.3846i	2.31543	−	0.688034i
$325$	−17.3754			−0.963814
$326$	−3.78116	−	3.17277i	−0.209419	−	0.175723i
$327$	17.3928	−	7.79380i	0.961826	−	0.430998i
$328$	−8.69097	−	49.2889i	−0.479879	−	2.72153i
$329$	4.73550	+	1.72358i	0.261077	+	0.0950241i
$330$	5.02344	+	1.42742i	0.276531	+	0.0785771i
$331$	0.178113	−	1.01013i	0.00979000	−	0.0555218i	−0.979521	−	0.201340i	$-0.935470\pi$
$331$	0.178113	−	1.01013i	0.00979000	−	0.0555218i	0.989311	+	0.145818i	$0.0465815\pi$
$332$	5.39564	−	9.34551i	0.296124	−	0.512902i
$333$	10.0092	+	2.07741i	0.548498	+	0.113841i
$334$	−6.58436	−	11.4044i	−0.360280	−	0.624023i
$335$	−19.2354	+	7.00110i	−1.05094	+	0.382511i
$336$	9.40547	+	13.8723i	0.513110	+	0.756798i
$337$	9.90301	−	8.30961i	0.539451	−	0.452653i	−0.331899	−	0.943315i	$-0.607689\pi$
$337$	9.90301	−	8.30961i	0.539451	−	0.452653i	0.871350	+	0.490662i	$0.163245\pi$
$338$	−14.7215	+	12.3528i	−0.800743	+	0.671903i
$339$	−2.15220	+	0.155682i	−0.116892	+	0.00845548i
$340$	−40.8401	+	14.8646i	−2.21486	+	0.806144i
$341$	−1.61791	−	2.80230i	−0.0876147	−	0.151753i
$342$	14.5485	−	36.5117i	0.786691	−	1.97433i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−1.15316	+	6.53988i	−0.0621741	+	0.352607i
$345$	−6.71848	−	26.6738i	−0.361711	−	1.43607i
$346$	42.5740	+	15.4957i	2.28879	+	0.833053i
$347$	4.78492	+	27.1366i	0.256868	+	1.45677i	0.791232	+	0.611516i	$0.209440\pi$
$347$	4.78492	+	27.1366i	0.256868	+	1.45677i	−0.534364	+	0.845254i	$0.679449\pi$
$348$	8.36776	−	81.4926i	0.448559	−	4.36846i
$349$	17.0080	+	14.2714i	0.910417	+	0.763931i	0.972198	−	0.234159i	$-0.0752337\pi$
$349$	17.0080	+	14.2714i	0.910417	+	0.763931i	−0.0617812	+	0.998090i	$0.519678\pi$
$350$	19.1101			1.02148
$351$	4.70785	+	11.4153i	0.251287	+	0.609304i
$352$	3.44966			0.183867
$353$	10.6062	+	8.89963i	0.564509	+	0.473680i	0.879819	−	0.475309i	$-0.157664\pi$
$353$	10.6062	+	8.89963i	0.564509	+	0.473680i	−0.315309	+	0.948989i	$0.602108\pi$
$354$	26.8742	+	19.4270i	1.42835	+	1.03253i
$355$	6.66000	+	37.7707i	0.353476	+	2.00466i
$356$	0.975953	+	0.355218i	0.0517254	+	0.0188265i
$357$	−3.18707	+	3.09252i	−0.168678	+	0.163673i
$358$	−5.32509	+	30.2001i	−0.281440	+	1.59613i
$359$	1.18334	−	2.04960i	0.0624543	−	0.108174i	−0.833108	−	0.553111i	$-0.813441\pi$
$359$	1.18334	−	2.04960i	0.0624543	−	0.108174i	0.895562	+	0.444937i	$0.146774\pi$
$360$	2.34498	−	77.8511i	0.123592	−	4.10311i
$361$	−3.06337	−	5.30590i	−0.161230	−	0.279258i
$362$	−32.3779	+	11.7846i	−1.70174	+	0.619383i
$363$	−8.22935	+	16.9758i	−0.431929	+	0.891000i
$364$	−8.79438	+	7.37936i	−0.460951	+	0.386783i
$365$	−15.8659	+	13.3130i	−0.830457	+	0.696837i
$366$	1.79322	−	3.69912i	0.0937329	−	0.193356i
$367$	−8.02424	+	2.92059i	−0.418862	+	0.152453i	−0.542849	−	0.839831i	$-0.682654\pi$
$367$	−8.02424	+	2.92059i	−0.418862	+	0.152453i	0.123986	+	0.992284i	$0.460432\pi$
$368$	−21.8983	−	37.9289i	−1.14153	−	1.97718i
$369$	−0.610966	+	20.2834i	−0.0318056	+	1.05591i
$370$	15.6245	−	27.0624i	0.812279	−	1.40691i
$371$	1.21167	−	6.87173i	0.0629069	−	0.356763i
$372$	−59.1027	+	57.3493i	−3.06433	+	2.97342i
$373$	−34.0106	−	12.3788i	−1.76100	−	0.640951i	−0.761030	−	0.648717i	$-0.775306\pi$
$373$	−34.0106	−	12.3788i	−1.76100	−	0.640951i	−0.999970	+	0.00776552i	$0.997528\pi$
$374$	0.382575	+	2.16969i	0.0197825	+	0.112192i
$375$	−11.3860	−	8.23077i	−0.587969	−	0.425035i
$376$	−28.5637	−	23.9678i	−1.47306	−	1.23605i
$377$	23.2655			1.19824
$378$	−5.17786	−	12.5549i	−0.266320	−	0.645757i
$379$	−8.57465			−0.440450			−0.220225	−	0.975449i	$-0.570679\pi$
$379$	−8.57465			−0.440450			−0.220225	+	0.975449i	$0.570679\pi$
$380$	−65.0906	−	54.6175i	−3.33908	−	2.80182i
$381$	2.26337	−	22.0426i	0.115956	−	1.12928i
$382$	−0.173151	−	0.981987i	−0.00885917	−	0.0502428i
$383$	−3.27371	−	1.19153i	−0.167279	−	0.0608844i	0.257023	−	0.966405i	$-0.417258\pi$
$383$	−3.27371	−	1.19153i	−0.167279	−	0.0608844i	−0.424302	+	0.905521i	$0.639480\pi$
$384$	−0.0454586	−	0.180480i	−0.00231980	−	0.00921011i
$385$	0.200323	−	1.13609i	0.0102094	−	0.0579003i
$386$	14.0211	−	24.2853i	0.713656	−	1.23609i
$387$	0.996655	−	2.50127i	0.0506628	−	0.127147i
$388$	−7.02382	−	12.1656i	−0.356580	−	0.617615i
$389$	−17.9466	+	6.53202i	−0.909927	+	0.331186i	−0.754224	−	0.656617i	$-0.771987\pi$
$389$	−17.9466	+	6.53202i	−0.909927	+	0.331186i	−0.155703	+	0.987804i	$0.549764\pi$
$390$	37.6481	−	2.72332i	1.90639	−	0.137901i
$391$	8.88955	−	7.45922i	0.449564	−	0.377229i
$392$	5.66806	−	4.75607i	0.286280	−	0.240218i
$393$	−7.01038	−	10.3398i	−0.353627	−	0.521572i
$394$	1.01908	−	0.370916i	0.0513407	−	0.0186865i
$395$	1.49575	+	2.59071i	0.0752593	+	0.130353i
$396$	−4.66551	−	0.968331i	−0.234451	−	0.0486605i
$397$	7.24191	−	12.5434i	0.363461	−	0.629533i	−0.625067	−	0.780571i	$-0.714928\pi$
$397$	7.24191	−	12.5434i	0.363461	−	0.629533i	0.988528	+	0.151038i	$0.0482616\pi$
$398$	8.94932	−	50.7541i	0.448589	−	2.54408i
$399$	−8.35156	−	2.37312i	−0.418101	−	0.118805i
$400$	−66.4852	−	24.1986i	−3.32426	−	1.20993i
$401$	6.11108	+	34.6577i	0.305173	+	1.73072i	0.622690	+	0.782469i	$0.286040\pi$
$401$	6.11108	+	34.6577i	0.305173	+	1.73072i	−0.317517	+	0.948253i	$0.602849\pi$
$402$	24.1003	−	10.7995i	1.20201	−	0.538628i
$403$	−17.9165	−	15.0337i	−0.892484	−	0.748883i
$404$	−26.6770			−1.32723
$405$	−7.34557	+	30.7131i	−0.365004	+	1.52615i
$406$	−25.5882			−1.26992
$407$	−0.858200	−	0.720115i	−0.0425394	−	0.0356948i
$408$	29.9855	−	13.4366i	1.48450	−	0.665212i
$409$	0.541327	+	3.07002i	0.0267669	+	0.151803i	0.995262	−	0.0972304i	$-0.0309984\pi$
$409$	0.541327	+	3.07002i	0.0267669	+	0.151803i	−0.968495	+	0.249033i	$0.919887\pi$
$410$	58.2914	+	21.2163i	2.87881	+	1.04780i
$411$	15.2749	+	4.34042i	0.753457	+	0.214097i
$412$	3.70628	−	21.0193i	0.182595	−	1.03555i
$413$	3.66262	−	6.34384i	0.180226	−	0.312160i
$414$	11.1282	+	33.6984i	0.546919	+	1.65618i
$415$	3.91891	+	6.78776i	0.192372	+	0.333198i
$416$	23.4302	−	8.52790i	1.14876	−	0.418115i
$417$	−17.4068	−	25.6736i	−0.852413	−	1.25724i
$418$	−3.29962	+	2.76871i	−0.161390	+	0.135422i
$419$	−1.33321	+	1.11870i	−0.0651317	+	0.0546520i	−0.674772	−	0.738026i	$-0.735758\pi$
$419$	−1.33321	+	1.11870i	−0.0651317	+	0.0546520i	0.609641	+	0.792678i	$0.291314\pi$
$420$	−29.2835	+	2.11826i	−1.42889	+	0.103360i
$421$	−32.8485	+	11.9559i	−1.60094	+	0.582694i	−0.979619	−	0.200864i	$-0.935625\pi$
$421$	−32.8485	+	11.9559i	−1.60094	+	0.582694i	−0.621319	+	0.783558i	$0.713403\pi$
$422$	−21.7591	−	37.6879i	−1.05922	−	1.83462i
$423$	9.36473	+	11.8686i	0.455329	+	0.577070i
$424$	−25.8146	+	44.7122i	−1.25367	+	2.17142i
$425$	3.25533	−	18.4619i	0.157907	−	0.895533i
$426$	−12.0858	−	47.9833i	−0.585560	−	2.32480i
$427$	−0.853326	−	0.310585i	−0.0412954	−	0.0150303i
$428$	−11.4293	−	64.8190i	−0.552458	−	3.13314i
$429$	0.138226	−	1.34616i	0.00667360	−	0.0649934i
$430$	−6.30512	−	5.29062i	−0.304060	−	0.255136i
$431$	−5.07549			−0.244478			−0.122239	−	0.992501i	$-0.539007\pi$
$431$	−5.07549			−0.244478			−0.122239	+	0.992501i	$0.539007\pi$
$432$	2.11609	+	50.2361i	0.101810	+	2.41698i
$433$	−17.1982			−0.826492			−0.413246	−	0.910619i	$-0.635605\pi$
$433$	−17.1982			−0.826492			−0.413246	+	0.910619i	$0.635605\pi$
$434$	19.7052	+	16.5346i	0.945878	+	0.793686i
$435$	48.2204	+	34.8579i	2.31199	+	1.67131i
$436$	9.23106	+	52.3519i	0.442087	+	2.50720i
$437$	21.3194	+	7.75963i	1.01985	+	0.371194i
$438$	19.1769	−	18.6080i	0.916309	−	0.889124i
$439$	−2.95767	+	16.7738i	−0.141162	+	0.800570i	0.829207	+	0.558942i	$0.188793\pi$
$439$	−2.95767	+	16.7738i	−0.141162	+	0.800570i	−0.970369	+	0.241628i	$0.922319\pi$
$440$	−4.26786	+	7.39216i	−0.203462	+	0.352407i
$441$	−2.64206	+	1.42110i	−0.125812	+	0.0676713i
$442$	7.96216	+	13.7909i	0.378721	+	0.655965i
$443$	−14.1938	+	5.16612i	−0.674367	+	0.245450i	−0.656427	−	0.754389i	$-0.727933\pi$
$443$	−14.1938	+	5.16612i	−0.674367	+	0.245450i	−0.0179401	+	0.999839i	$0.505711\pi$
$444$	−12.4375	+	25.6565i	−0.590257	+	1.21760i
$445$	−0.577857	+	0.484880i	−0.0273930	+	0.0229855i
$446$	−18.9955	+	15.9391i	−0.899462	+	0.754738i
$447$	15.1409	−	31.2332i	0.716138	−	1.47728i
$448$	−7.58347	+	2.76016i	−0.358285	+	0.130405i
$449$	−7.06546	−	12.2377i	−0.333440	−	0.577535i	0.649744	−	0.760153i	$-0.274876\pi$
$449$	−7.06546	−	12.2377i	−0.333440	−	0.577535i	−0.983184	+	0.182618i	$0.941543\pi$
$450$	48.7639	+	30.1469i	2.29875	+	1.42114i
$451$	1.11196	−	1.92596i	0.0523599	−	0.0906901i
$452$	1.04511	−	5.92712i	0.0491579	−	0.278788i
$453$	0.709545	−	0.688495i	0.0333374	−	0.0323483i
$454$	34.4113	+	12.5247i	1.61500	+	0.587812i
$455$	−1.44792	−	8.21156i	−0.0678795	−	0.384964i
$456$	52.0621	+	37.6350i	2.43803	+	1.76242i
$457$	17.4919	+	14.6774i	0.818237	+	0.686582i	0.952558	−	0.304356i	$-0.0984411\pi$
$457$	17.4919	+	14.6774i	0.818237	+	0.686582i	−0.134322	+	0.990938i	$0.542886\pi$
$458$	−53.7624			−2.51215
$459$	−13.0111	+	2.86355i	−0.607308	+	0.133659i
$460$	76.7216			3.57716
$461$	20.5560	+	17.2485i	0.957386	+	0.803342i	0.980526	−	0.196390i	$-0.0629218\pi$
$461$	20.5560	+	17.2485i	0.957386	+	0.803342i	−0.0231398	+	0.999732i	$0.507366\pi$
$462$	−0.152025	+	1.48056i	−0.00707286	+	0.0688817i
$463$	−4.18053	−	23.7090i	−0.194286	−	1.10185i	−0.913432	−	0.406990i	$-0.866578\pi$
$463$	−4.18053	−	23.7090i	−0.194286	−	1.10185i	0.719147	−	0.694858i	$-0.244533\pi$
$464$	89.0231	+	32.4018i	4.13280	+	1.50421i
$465$	−14.6095	−	58.0026i	−0.677497	−	2.68981i
$466$	−7.12671	+	40.4176i	−0.330139	+	1.87231i
$467$	0.873689	−	1.51327i	0.0404295	−	0.0700259i	−0.845103	−	0.534604i	$-0.820461\pi$
$467$	0.873689	−	1.51327i	0.0404295	−	0.0700259i	0.885532	+	0.464578i	$0.153794\pi$
$468$	−34.0822	+	4.95668i	−1.57545	+	0.229123i
$469$	−2.91692	−	5.05226i	−0.134691	−	0.233292i
$470$	43.4277	−	15.8064i	2.00317	−	0.729095i
$471$	−13.9107	+	1.00625i	−0.640973	+	0.0463655i
$472$	−41.5199	+	34.8393i	−1.91111	+	1.60361i
$473$	−0.226043	+	0.189673i	−0.0103935	+	0.00872117i
$474$	−2.16587	−	3.19449i	−0.0994818	−	0.146728i
$475$	34.4409	−	12.5355i	1.58026	−	0.575166i
$476$	−6.19314	−	10.7268i	−0.283862	−	0.491664i
$477$	13.9323	−	15.6234i	0.637917	−	0.715346i
$478$	−36.9469	+	63.9938i	−1.68991	+	2.92701i
$479$	0.743652	−	4.21746i	0.0339783	−	0.192701i	−0.963094	−	0.269165i	$-0.913252\pi$
$479$	0.743652	−	4.21746i	0.0339783	−	0.192701i	0.997072	+	0.0764648i	$0.0243633\pi$
$480$	61.3387	+	17.4296i	2.79972	+	0.795548i
$481$	−7.60913	−	2.76950i	−0.346946	−	0.126278i
$482$	10.9100	+	61.8734i	0.496935	+	2.81826i
$483$	7.15397	−	3.20572i	0.325517	−	0.145865i
$484$	−40.3083	−	33.8227i	−1.83219	−	1.53739i
$485$	10.2030			0.463293
$486$	6.59342	−	40.2052i	0.299083	−	1.82374i
$487$	−41.2245			−1.86806			−0.934030	−	0.357194i	$-0.883733\pi$
$487$	−41.2245			−1.86806			−0.934030	+	0.357194i	$0.883733\pi$
$488$	5.14712	+	4.31894i	0.232999	+	0.195509i
$489$	−2.98507	+	1.33762i	−0.134990	+	0.0604894i
$490$	1.59247	+	9.03136i	0.0719405	+	0.407995i
$491$	17.1068	+	6.22637i	0.772020	+	0.280992i	0.697841	−	0.716253i	$-0.254144\pi$
$491$	17.1068	+	6.22637i	0.772020	+	0.280992i	0.0741788	+	0.997245i	$0.476366\pi$
$492$	−54.4444	−	15.4705i	−2.45454	−	0.697466i
$493$	−4.35886	+	24.7203i	−0.196313	+	1.11335i
$494$	−15.5666	+	26.9622i	−0.700376	+	1.21309i
$495$	2.30339	−	2.58297i	0.103530	−	0.116096i
$496$	−47.6182	−	82.4771i	−2.13812	−	3.70333i
$497$	−10.2714	+	3.73849i	−0.460736	+	0.167694i
$498$	−5.67466	−	8.36968i	−0.254288	−	0.375054i
$499$	−7.49376	+	6.28801i	−0.335467	+	0.281490i	−0.794923	−	0.606710i	$-0.792489\pi$
$499$	−7.49376	+	6.28801i	−0.335467	+	0.281490i	0.459456	+	0.888200i	$0.348044\pi$
$500$	30.0184	−	25.1884i	1.34246	−	1.12646i
$501$	−8.70420	+	0.629627i	−0.388875	+	0.0281297i
$502$	38.2738	−	13.9305i	1.70824	−	0.621750i
$503$	17.9132	+	31.0265i	0.798708	+	1.38340i	0.920458	+	0.390842i	$0.127816\pi$
$503$	17.9132	+	31.0265i	0.798708	+	1.38340i	−0.121750	+	0.992561i	$0.538851\pi$
$504$	21.9663	−	3.19463i	0.978457	−	0.142300i
$505$	9.68790	−	16.7799i	0.431106	−	0.746698i
$506$	0.675357	−	3.83014i	0.0300233	−	0.170271i
$507$	3.11061	+	12.3498i	0.138147	+	0.548473i
$508$	58.0768	+	21.1382i	2.57674	+	0.937858i
$509$	−6.48936	−	36.8030i	−0.287636	−	1.63126i	−0.695716	−	0.718317i	$-0.744913\pi$
$509$	−6.48936	−	36.8030i	−0.287636	−	1.63126i	0.408080	−	0.912946i	$-0.366199\pi$
$510$	−4.15987	+	40.5125i	−0.184202	+	1.79392i
$511$	−4.52173	−	3.79418i	−0.200029	−	0.167845i
$512$	−41.6655			−1.84137
$513$	−17.5673	−	19.2305i	−0.775614	−	0.849048i
$514$	19.5503			0.862329
$515$	11.8753	+	9.96457i	0.523289	+	0.439091i
$516$	6.08621	+	4.39964i	0.267930	+	0.193683i
$517$	−0.287707	−	1.63167i	−0.0126533	−	0.0717606i
$518$	8.36878	+	3.04599i	0.367703	+	0.133833i
$519$	21.5479	−	20.9086i	0.945846	−	0.917784i
$520$	−10.7133	+	60.7584i	−0.469811	+	2.66443i
$521$	−15.9281	+	27.5883i	−0.697824	+	1.20867i	0.271396	+	0.962468i	$0.412515\pi$
$521$	−15.9281	+	27.5883i	−0.697824	+	1.20867i	−0.969220	+	0.246198i	$0.920819\pi$
$522$	−65.2944	−	40.3665i	−2.85786	−	1.76679i
$523$	−0.367822	−	0.637086i	−0.0160837	−	0.0278578i	0.857872	−	0.513864i	$-0.171786\pi$
$523$	−0.367822	−	0.637086i	−0.0160837	−	0.0278578i	−0.873955	+	0.486006i	$0.838453\pi$
$524$	32.7418	−	11.9170i	1.43033	−	0.520598i
$525$	5.52436	−	11.3959i	0.241103	−	0.497356i
$526$	51.7242	−	43.4017i	2.25528	−	1.89241i
$527$	19.3305	−	16.2202i	0.842049	−	0.706563i
$528$	2.40370	−	4.95845i	0.104608	−	0.215789i
$529$	2.36302	−	0.860068i	0.102740	−	0.0373943i
$530$	−31.9953	−	55.4175i	−1.38979	−	2.40718i
$531$	19.3537	−	10.4099i	0.839879	−	0.451750i
$532$	12.1081	−	20.9718i	0.524951	−	0.909241i
$533$	2.79127	−	15.8301i	0.120903	−	0.685677i
$534$	0.698451	−	0.677729i	0.0302249	−	0.0293282i
$535$	44.9221	+	16.3503i	1.94215	+	0.706885i
$536$	7.49560	+	42.5096i	0.323760	+	1.83614i
$537$	16.4698	+	11.9058i	0.710724	+	0.513772i
$538$	0.986597	+	0.827853i	0.0425352	+	0.0356913i
$539$	0.328776			0.0141614
$540$	−78.0655	−	40.7908i	−3.35940	−	1.75536i
$541$	4.13866			0.177935			0.0889674	−	0.996035i	$-0.471643\pi$
$541$	4.13866			0.177935			0.0889674	+	0.996035i	$0.471643\pi$
$542$	−47.4399	−	39.8068i	−2.03772	−	1.70985i
$543$	−2.33235	+	22.7145i	−0.100091	+	0.974773i
$544$	4.67144	+	26.4930i	0.200286	+	1.13588i
$545$	−36.2819	−	13.2055i	−1.55415	−	0.565663i
$546$	2.62752	+	10.4318i	0.112448	+	0.446441i
$547$	−3.84645	+	21.8143i	−0.164462	+	0.932712i	0.785155	+	0.619300i	$0.212583\pi$
$547$	−3.84645	+	21.8143i	−0.164462	+	0.932712i	−0.949617	+	0.313413i	$0.898528\pi$
$548$	−22.1455	+	38.3572i	−0.946011	+	1.63854i
$549$	−1.68750	−	2.13869i	−0.0720208	−	0.0912771i
$550$	−3.14147	−	5.44118i	−0.133953	−	0.232013i
$551$	−46.1161	+	16.7849i	−1.96461	+	0.715060i
$552$	−57.8535	+	4.18489i	−2.46241	+	0.178121i
$553$	−0.653105	+	0.548021i	−0.0277729	+	0.0233042i
$554$	24.5293	−	20.5825i	1.04215	−	0.874468i
$555$	−11.6213	−	17.1406i	−0.493298	−	0.727576i
$556$	81.2977	−	29.5900i	3.44779	−	1.25489i
$557$	0.700682	+	1.21362i	0.0296888	+	0.0514226i	0.880488	−	0.474068i	$-0.157215\pi$
$557$	0.700682	+	1.21362i	0.0296888	+	0.0514226i	−0.850799	+	0.525491i	$0.823882\pi$
$558$	24.1984	+	73.2777i	1.02440	+	3.10209i
$559$	−1.06641	+	1.84707i	−0.0451041	+	0.0781226i
$560$	5.89588	−	33.4372i	0.249146	−	1.41298i
$561$	1.40444	+	0.399076i	0.0592956	+	0.0168490i
$562$	−32.8005	−	11.9384i	−1.38361	−	0.503592i
$563$	−1.05858	−	6.00352i	−0.0446139	−	0.253018i	0.954341	−	0.298718i	$-0.0965592\pi$
$563$	−1.05858	−	6.00352i	−0.0446139	−	0.253018i	−0.998955	+	0.0457004i	$0.985448\pi$
$564$	−38.4806	+	17.2433i	−1.62033	+	0.726075i
$565$	3.34864	+	2.80985i	0.140879	+	0.118211i
$566$	−7.87183			−0.330878
$567$	−8.98368	−	0.541694i	−0.377279	−	0.0227490i
$568$	80.8770			3.39352
$569$	18.8667	+	15.8311i	0.790935	+	0.663673i	0.945977	−	0.324235i	$-0.105107\pi$
$569$	18.8667	+	15.8311i	0.790935	+	0.663673i	−0.155042	+	0.987908i	$0.549551\pi$
$570$	−72.6600	+	32.5592i	−3.04339	+	1.36376i
$571$	−4.75575	−	26.9712i	−0.199022	−	1.12871i	−0.906574	−	0.422047i	$-0.861312\pi$
$571$	−4.75575	−	26.9712i	−0.199022	−	1.12871i	0.707552	−	0.706661i	$-0.249800\pi$
$572$	3.54680	+	1.29093i	0.148299	+	0.0539765i
$573$	−0.635641	−	0.180619i	−0.0265543	−	0.00754548i
$574$	−3.06994	+	17.4105i	−0.128137	+	0.726699i
$575$	−16.5467	+	28.6598i	−0.690046	+	1.19519i
$576$	−23.7053	−	4.92005i	−0.987720	−	0.205002i
$577$	20.5067	+	35.5186i	0.853705	+	1.47866i	0.877842	+	0.478951i	$0.158983\pi$
$577$	20.5067	+	35.5186i	0.853705	+	1.47866i	−0.0241371	+	0.999709i	$0.507684\pi$
$578$	25.6070	−	9.32018i	1.06511	−	0.387669i
$579$	−10.4287	−	15.3816i	−0.433404	−	0.639237i
$580$	−127.130	+	106.675i	−5.27879	+	4.42943i
$581$	−1.71116	+	1.43583i	−0.0709908	+	0.0595684i
$582$	−13.1291	+	0.949710i	−0.544220	+	0.0393667i
$583$	−2.15576	+	0.784633i	−0.0892825	+	0.0324962i
$584$	21.8374	+	37.8235i	0.903638	+	1.56515i
$585$	9.25937	−	23.2379i	0.382828	−	0.960769i
$586$	5.55461	−	9.62087i	0.229459	−	0.397434i
$587$	−1.87320	+	10.6235i	−0.0773154	+	0.438477i	0.921436	+	0.388529i	$0.127017\pi$
$587$	−1.87320	+	10.6235i	−0.0773154	+	0.438477i	−0.998752	+	0.0499481i	$0.984094\pi$
$588$	−2.04374	−	8.11410i	−0.0842826	−	0.334620i
$589$	46.3594	+	16.8735i	1.91021	+	0.695258i
$590$	−11.6652	−	66.1568i	−0.480250	−	2.72363i
$591$	0.0734102	−	0.714933i	0.00301969	−	0.0294084i
$592$	−25.2585	−	21.1944i	−1.03812	−	0.871084i
$593$	33.8232			1.38895			0.694475	−	0.719516i	$-0.255637\pi$
$593$	33.8232			1.38895			0.694475	+	0.719516i	$0.255637\pi$
$594$	−2.72357	+	3.53817i	−0.111749	+	0.145173i
$595$	8.99630			0.368812
$596$	74.1617	+	62.2290i	3.03778	+	2.54900i
$597$	−27.6790	−	20.0088i	−1.13283	−	0.818905i
$598$	−4.88144	−	27.6840i	−0.199617	−	1.13208i
$599$	−45.6141	−	16.6022i	−1.86374	−	0.678347i	−0.975907	−	0.218186i	$-0.929986\pi$
$599$	−45.6141	−	16.6022i	−1.86374	−	0.678347i	−0.887836	−	0.460161i	$-0.847792\pi$
$600$	−67.2493	+	65.2542i	−2.74544	+	2.66399i
$601$	1.44066	−	8.17040i	0.0587658	−	0.333277i	−0.941224	−	0.337783i	$-0.890323\pi$
$601$	1.44066	−	8.17040i	0.0587658	−	0.333277i	0.999990	+	0.00450545i	$0.00143414\pi$
$602$	1.17287	−	2.03147i	0.0478026	−	0.0827965i
$603$	0.526932	−	17.4936i	0.0214583	−	0.712395i
$604$	1.37879	+	2.38814i	0.0561024	+	0.0971722i
$605$	35.9128	−	13.0712i	1.46006	−	0.531420i
$606$	−10.9044	+	22.4941i	−0.442963	+	0.913761i
$607$	0.953898	−	0.800415i	0.0387175	−	0.0324879i	−0.623224	−	0.782044i	$-0.714177\pi$
$607$	0.953898	−	0.800415i	0.0387175	−	0.0324879i	0.661941	+	0.749556i	$0.269733\pi$
$608$	−40.2900	+	33.8074i	−1.63398	+	1.37107i
$609$	−7.39707	+	15.2590i	−0.299745	+	0.618325i
$610$	−7.82558	+	2.84828i	−0.316849	+	0.115323i
$611$	−5.98776	−	10.3711i	−0.242239	−	0.419570i
$612$	1.11877	−	37.1420i	0.0452236	−	1.50138i
$613$	21.5040	−	37.2460i	0.868539	−	1.50435i	0.00504868	−	0.999987i	$-0.498393\pi$
$613$	21.5040	−	37.2460i	0.868539	−	1.50435i	0.863490	−	0.504366i	$-0.168274\pi$
$614$	−11.0698	+	62.7802i	−0.446743	+	2.53360i
$615$	29.5028	−	28.6276i	1.18967	−	1.15437i
$616$	−2.28595	−	0.832018i	−0.0921035	−	0.0335229i
$617$	−3.75376	−	21.2886i	−0.151121	−	0.857048i	−0.962247	−	0.272177i	$-0.912256\pi$
$617$	−3.75376	−	21.2886i	−0.151121	−	0.857048i	0.811127	−	0.584871i	$-0.198855\pi$
$618$	−16.2086	−	11.7170i	−0.652006	−	0.471326i
$619$	−19.4601	−	16.3289i	−0.782166	−	0.656315i	0.161627	−	0.986852i	$-0.448326\pi$
$619$	−19.4601	−	16.3289i	−0.782166	−	0.656315i	−0.943793	+	0.330537i	$0.892770\pi$
$620$	166.832			6.70015
$621$	23.3122	+	3.10553i	0.935487	+	0.124621i
$622$	−37.1865			−1.49104
$623$	−0.164688	−	0.138189i	−0.00659807	−	0.00553644i
$624$	4.06825	−	39.6202i	0.162860	−	1.58608i
$625$	−1.40607	−	7.97420i	−0.0562427	−	0.318968i
$626$	−19.0306	−	6.92656i	−0.760615	−	0.276841i
$627$	0.697201	+	2.76804i	0.0278435	+	0.110545i
$628$	6.75506	−	38.3099i	0.269556	−	1.52873i
$629$	4.36826	−	7.56606i	0.174174	−	0.301678i
$630$	−10.1838	+	25.5578i	−0.405731	+	1.01825i
$631$	−15.2296	−	26.3784i	−0.606279	−	1.05011i	−0.991848	−	0.127427i	$-0.959328\pi$
$631$	−15.2296	−	26.3784i	−0.606279	−	1.05011i	0.385569	−	0.922679i	$-0.374005\pi$
$632$	5.92783	−	2.15755i	0.235797	−	0.0858229i
$633$	−28.7645	+	2.08071i	−1.14329	+	0.0827008i
$634$	25.3340	−	21.2577i	1.00614	−	0.844253i
$635$	−34.3870	+	28.8541i	−1.36461	+	1.14504i
$636$	32.7652	+	48.3261i	1.29922	+	1.91626i
$637$	2.23306	−	0.812767i	0.0884771	−	0.0322030i
$638$	4.20640	+	7.28570i	0.166533	+	0.288443i
$639$	−32.1075	−	6.66395i	−1.27015	−	0.263622i
$640$	−0.188519	+	0.326525i	−0.00745188	+	0.0129070i
$641$	−2.47840	+	14.0557i	−0.0978909	+	0.555167i	0.895932	+	0.444191i	$0.146509\pi$
$641$	−2.47840	+	14.0557i	−0.0978909	+	0.555167i	−0.993823	+	0.110976i	$0.964602\pi$
$642$	−59.3275	−	16.8581i	−2.34147	−	0.665335i
$643$	20.4760	+	7.45266i	0.807496	+	0.293904i	0.712589	−	0.701582i	$-0.247523\pi$
$643$	20.4760	+	7.45266i	0.807496	+	0.293904i	0.0949066	+	0.995486i	$0.469745\pi$
$644$	3.79689	+	21.5332i	0.149618	+	0.848528i
$645$	−4.97763	+	2.23050i	−0.195994	+	0.0878258i
$646$	−25.7317	−	21.5915i	−1.01240	−	0.849504i
$647$	44.4776			1.74860			0.874298	−	0.485389i	$-0.161322\pi$
$647$	44.4776			1.74860			0.874298	+	0.485389i	$0.161322\pi$
$648$	61.0919	+	26.5009i	2.39992	+	1.04105i
$649$	−2.40836			−0.0945364
$650$	−34.7881	−	29.1907i	−1.36450	−	1.14495i
$651$	15.5564	−	6.97090i	0.609705	−	0.273211i
$652$	−1.58429	−	8.98498i	−0.0620458	−	0.351879i
$653$	−2.67503	−	0.973633i	−0.104682	−	0.0381012i	0.289148	−	0.957284i	$-0.406628\pi$
$653$	−2.67503	−	0.973633i	−0.104682	−	0.0381012i	−0.393830	+	0.919183i	$0.628850\pi$
$654$	47.9166	+	13.6156i	1.87369	+	0.532414i
$655$	−4.39450	+	24.9225i	−0.171707	+	0.973801i
$656$	32.7270	−	56.6848i	1.27777	−	2.21317i
$657$	−5.55278	−	16.8150i	−0.216634	−	0.656014i
$658$	6.58555	+	11.4065i	0.256731	+	0.444672i
$659$	14.5443	−	5.29368i	0.566564	−	0.206212i	−0.0428267	−	0.999083i	$-0.513636\pi$
$659$	14.5443	−	5.29368i	0.566564	−	0.206212i	0.609391	+	0.792870i	$0.291414\pi$
$660$	5.41699	+	7.98964i	0.210856	+	0.310996i
$661$	10.2102	−	8.56735i	0.397130	−	0.333231i	−0.422253	−	0.906478i	$-0.638761\pi$
$661$	10.2102	−	8.56735i	0.397130	−	0.333231i	0.819383	+	0.573247i	$0.194316\pi$
$662$	2.05363	−	1.72320i	0.0798166	−	0.0669741i
$663$	10.5256	−	0.761380i	0.408780	−	0.0295695i
$664$	15.5311	−	5.65286i	0.602724	−	0.219374i
$665$	8.79423	+	15.2320i	0.341025	+	0.590673i
$666$	16.5498	+	20.9747i	0.641290	+	0.812752i
$667$	22.1559	−	38.3752i	0.857881	−	1.48589i
$668$	4.22676	−	23.9712i	0.163538	−	0.927472i
$669$	4.01370	+	15.9352i	0.155178	+	0.616091i
$670$	−50.2739	−	18.2982i	−1.94225	−	0.706921i
$671$	0.0518441	+	0.294023i	0.00200142	+	0.0113506i
$672$	−1.85631	+	18.0784i	−0.0716086	+	0.697388i
$673$	10.7285	+	9.00232i	0.413555	+	0.347014i	0.825705	−	0.564102i	$-0.190778\pi$
$673$	10.7285	+	9.00232i	0.413555	+	0.347014i	−0.412150	+	0.911116i	$0.635222\pi$
$674$	33.7874			1.30144
$675$	32.0742	−	20.3643i	1.23454	−	0.783824i
$676$	−35.5216			−1.36621
$677$	−19.5771	−	16.4272i	−0.752410	−	0.631347i	0.183729	−	0.982977i	$-0.441183\pi$
$677$	−19.5771	−	16.4272i	−0.752410	−	0.631347i	−0.936139	+	0.351630i	$0.885628\pi$
$678$	−4.57057	−	3.30400i	−0.175532	−	0.126889i
$679$	0.504937	+	2.86364i	0.0193777	+	0.109896i
$680$	−62.5505	−	22.7665i	−2.39870	−	0.873056i
$681$	17.4165	−	16.8998i	0.667400	−	0.647600i
$682$	1.46858	−	8.32871i	0.0562347	−	0.318923i
$683$	−1.69604	+	2.93763i	−0.0648971	+	0.112405i	−0.896648	−	0.442743i	$-0.854005\pi$
$683$	−1.69604	+	2.93763i	−0.0648971	+	0.112405i	0.831751	+	0.555149i	$0.187339\pi$
$684$	63.9804	−	34.4135i	2.44635	−	1.31583i
$685$	−16.0846	−	27.8593i	−0.614560	−	1.06445i
$686$	−2.45600	+	0.893910i	−0.0937704	+	0.0341296i
$687$	−15.5417	+	32.0600i	−0.592953	+	1.22317i
$688$	−6.65289	+	5.58244i	−0.253639	+	0.212828i
$689$	−12.7023	+	10.6585i	−0.483920	+	0.406057i
$690$	31.3606	−	64.6919i	1.19388	−	2.46278i
$691$	1.64934	−	0.600311i	0.0627439	−	0.0228369i	−0.310458	−	0.950587i	$-0.600482\pi$
$691$	1.64934	−	0.600311i	0.0627439	−	0.0228369i	0.373201	+	0.927750i	$0.378260\pi$
$692$	41.8720	+	72.5244i	1.59173	+	2.75696i
$693$	0.838950	+	0.518658i	0.0318691	+	0.0197022i
$694$	−36.0094	+	62.3702i	−1.36690	+	2.36754i
$695$	−10.9115	+	61.8824i	−0.413898	+	2.34733i
$696$	90.0464	−	87.3749i	3.41320	−	3.31194i
$697$	16.2970	+	5.93162i	0.617293	+	0.224676i
$698$	10.0765	+	57.1469i	0.381403	+	2.16304i
$699$	22.0419	+	15.9338i	0.833703	+	0.602673i
$700$	27.0589	+	22.7051i	1.02273	+	0.858174i
$701$	−49.6210			−1.87416			−0.937079	−	0.349118i	$-0.886481\pi$
$701$	−49.6210			−1.87416			−0.937079	+	0.349118i	$0.886481\pi$
$702$	−9.75190	+	30.7643i	−0.368062	+	1.16112i
$703$	17.0806			0.644206
$704$	2.03253	+	1.70549i	0.0766037	+	0.0642781i
$705$	3.12834	−	30.4665i	0.117820	−	1.14744i
$706$	6.28372	+	35.6367i	0.236491	+	1.34121i
$707$	5.18903	+	1.88865i	0.195153	+	0.0710301i
$708$	14.9709	+	59.4376i	0.562641	+	2.23380i
$709$	1.44806	−	8.21236i	0.0543831	−	0.308422i	−0.945467	−	0.325717i	$-0.894394\pi$
$709$	1.44806	−	8.21236i	0.0543831	−	0.308422i	0.999850	+	0.0172952i	$0.00550550\pi$
$710$	−50.1205	+	86.8113i	−1.88099	+	3.25797i
$711$	−2.53108	+	0.368103i	−0.0949229	+	0.0138049i
$712$	0.795349	+	1.37758i	0.0298070	+	0.0516272i
$713$	−41.8593	+	15.2355i	−1.56764	+	0.570575i
$714$	−11.5764	+	0.837392i	−0.433236	+	0.0313386i
$715$	−2.10004	+	1.76215i	−0.0785372	+	0.0659005i
$716$	−43.4216	+	36.4350i	−1.62274	+	1.36164i
$717$	27.4807	+	40.5319i	1.02628	+	1.51369i
$718$	5.81255	−	2.11560i	0.216923	−	0.0789534i
$719$	9.33949	+	16.1765i	0.348304	+	0.603280i	0.985948	−	0.167051i	$-0.0534243\pi$
$719$	9.33949	+	16.1765i	0.348304	+	0.603280i	−0.637644	+	0.770331i	$0.720091\pi$
$720$	67.7933	−	76.0219i	2.52651	−	2.83317i
$721$	−2.20903	+	3.82615i	−0.0822685	+	0.142493i
$722$	2.78062	−	15.7697i	0.103484	−	0.586886i
$723$	40.0507	+	11.3805i	1.48950	+	0.423246i
$724$	−59.8470	−	21.7825i	−2.22420	−	0.809541i
$725$	−12.4305	−	70.4969i	−0.461658	−	2.61819i
$726$	−44.9958	+	20.1628i	−1.66995	+	0.748311i
$727$	3.52947	+	2.96158i	0.130901	+	0.109839i	0.705888	−	0.708324i	$-0.250548\pi$
$727$	3.52947	+	2.96158i	0.130901	+	0.109839i	−0.574987	+	0.818163i	$0.694993\pi$
$728$	−17.5831			−0.651673
$729$	−22.0695	−	15.5544i	−0.817387	−	0.576089i
$730$	−54.1317			−2.00350
$731$	−1.76277	−	1.47914i	−0.0651985	−	0.0547080i
$732$	6.93412	−	3.10721i	0.256293	−	0.114846i
$733$	−6.38556	−	36.2143i	−0.235856	−	1.33761i	−0.840803	−	0.541341i	$-0.817917\pi$
$733$	−6.38556	−	36.2143i	−0.235856	−	1.33761i	0.604947	−	0.796265i	$-0.293194\pi$
$734$	−20.9723	−	7.63329i	−0.774102	−	0.281750i
$735$	5.84600	+	1.66116i	0.215633	+	0.0612728i
$736$	8.24646	−	46.7680i	0.303969	−	1.72389i
$737$	−0.959015	+	1.66106i	−0.0353258	+	0.0611860i
$738$	−35.2994	+	39.5840i	−1.29939	+	1.45711i
$739$	15.7426	+	27.2670i	0.579101	+	1.00303i	0.995583	+	0.0938889i	$0.0299298\pi$
$739$	15.7426	+	27.2670i	0.579101	+	1.00303i	−0.416481	+	0.909144i	$0.636737\pi$
$740$	54.2771	−	19.7552i	1.99526	−	0.726217i
$741$	11.5783	+	17.0771i	0.425339	+	0.627342i
$742$	13.9705	−	11.7226i	0.512872	−	0.430350i
$743$	33.0732	−	27.7517i	1.21334	−	1.01811i	0.214191	−	0.976792i	$-0.431289\pi$
$743$	33.0732	−	27.7517i	1.21334	−	1.01811i	0.999146	−	0.0413184i	$-0.0131558\pi$
$744$	−125.803	+	9.10012i	−4.61218	+	0.333627i
$745$	−66.0746	+	24.0492i	−2.42079	+	0.881094i
$746$	−47.2977	−	81.9220i	−1.73169	−	2.99938i
$747$	−6.63151	+	0.964441i	−0.242634	+	0.0352871i
$748$	−2.03616	+	3.52673i	−0.0744492	+	0.128950i
$749$	−2.36584	+	13.4173i	−0.0864458	+	0.490258i
$750$	−8.96870	−	35.6076i	−0.327491	−	1.30021i
$751$	34.1005	+	12.4116i	1.24435	+	0.452905i	0.878487	−	0.477766i	$-0.158553\pi$
$751$	34.1005	+	12.4116i	1.24435	+	0.452905i	0.365858	+	0.930671i	$0.380776\pi$
$752$	−8.46777	−	48.0231i	−0.308788	−	1.75122i
$753$	2.75707	−	26.8508i	0.100473	−	0.978497i
$754$	46.5810	+	39.0861i	1.69638	+	1.42343i
$755$	−2.00287			−0.0728919
$756$	7.58524	−	23.9291i	0.275872	−	0.870294i
$757$	40.9390			1.48795			0.743977	−	0.668205i	$-0.232937\pi$
$757$	40.9390			1.48795			0.743977	+	0.668205i	$0.232937\pi$
$758$	−17.1677	−	14.4054i	−0.623559	−	0.523229i
$759$	−2.08879	−	1.50996i	−0.0758182	−	0.0548079i
$760$	−22.5984	−	128.162i	−0.819732	−	4.64893i
$761$	−4.78591	−	1.74193i	−0.173489	−	0.0631449i	0.253815	−	0.967253i	$-0.418314\pi$
$761$	−4.78591	−	1.74193i	−0.173489	−	0.0631449i	−0.427304	+	0.904108i	$0.640537\pi$
$762$	41.5633	−	40.3302i	1.50568	−	1.46101i
$763$	1.91080	−	10.8367i	0.0691756	−	0.392314i
$764$	0.921550	−	1.59617i	0.0333405	−	0.0577474i
$765$	22.9562	+	14.1920i	0.829983	+	0.513115i
$766$	−4.55267	−	7.88545i	−0.164495	−	0.284913i
$767$	−16.3577	+	5.95371i	−0.590642	+	0.214976i
$768$	−11.9826	+	24.7181i	−0.432384	+	0.891939i
$769$	−31.6855	+	26.5873i	−1.14261	+	0.958762i	−0.999521	−	0.0309485i	$-0.990147\pi$
$769$	−31.6855	+	26.5873i	−1.14261	+	0.958762i	−0.143087	+	0.989710i	$0.545703\pi$
$770$	2.30970	−	1.93807i	0.0832358	−	0.0698431i
$771$	5.65163	−	11.6584i	0.203539	−	0.419867i
$772$	48.7071	−	17.7279i	1.75301	−	0.638043i
$773$	−0.613389	−	1.06242i	−0.0220621	−	0.0382126i	0.854784	−	0.518985i	$-0.173690\pi$
$773$	−0.613389	−	1.06242i	−0.0220621	−	0.0382126i	−0.876846	+	0.480772i	$0.840356\pi$
$774$	6.19758	−	3.33352i	0.222767	−	0.119821i
$775$	−35.9811	+	62.3211i	−1.29248	+	2.23864i
$776$	3.73609	−	21.1884i	0.134118	−	0.760621i
$777$	4.23566	−	4.11000i	0.151954	−	0.147445i
$778$	−46.9055	−	17.0722i	−1.68164	−	0.612068i
$779$	5.88783	+	33.3916i	0.210954	+	1.19638i
$780$	56.5436	+	40.8746i	2.02459	+	1.46355i
$781$	2.75295	+	2.31000i	0.0985083	+	0.0826582i
$782$	30.3297			1.08459
$783$	−42.9471	+	27.2677i	−1.53480	+	0.974468i
$784$	9.67651			0.345590
$785$	21.6439	+	18.1614i	0.772506	+	0.648209i
$786$	3.33500	−	32.4792i	0.118956	−	1.15849i
$787$	0.256922	+	1.45708i	0.00915827	+	0.0519391i	0.989044	−	0.147618i	$-0.0471607\pi$
$787$	0.256922	+	1.45708i	0.00915827	+	0.0519391i	−0.979886	+	0.199557i	$0.936050\pi$
$788$	1.88367	+	0.685600i	0.0671030	+	0.0244235i
$789$	−10.9292	−	43.3912i	−0.389089	−	1.54477i
$790$	−1.35769	+	7.69985i	−0.0483045	+	0.273948i
$791$	−0.622910	+	1.07891i	−0.0221481	+	0.0383617i
$792$	−4.52060	−	5.72927i	−0.160632	−	0.203581i
$793$	1.07898	+	1.86885i	0.0383157	+	0.0663648i
$794$	35.5722	−	12.9472i	1.26241	−	0.459480i
$795$	−42.2962	+	3.05954i	−1.50009	+	0.108511i
$796$	72.9741	−	61.2325i	2.58650	−	2.17033i
$797$	23.2710	−	19.5266i	0.824299	−	0.691669i	−0.129675	−	0.991557i	$-0.541393\pi$
$797$	23.2710	−	19.5266i	0.824299	−	0.691669i	0.953975	+	0.299887i	$0.0969490\pi$
$798$	−12.7342	−	18.7820i	−0.450786	−	0.664874i
$799$	12.1414	−	4.41912i	0.429533	−	0.156337i
$800$	−38.3589	−	66.4396i	−1.35619	−	2.34899i
$801$	−0.202240	−	0.612424i	−0.00714579	−	0.0216389i
$802$	−45.9896	+	79.6564i	−1.62395	+	2.81276i
$803$	−0.336993	+	1.91118i	−0.0118922	+	0.0674441i
$804$	46.9560	+	13.3427i	1.65601	+	0.470560i
$805$	−14.9234	−	5.43166i	−0.525980	−	0.191441i
$806$	−10.6148	−	60.1994i	−0.373890	−	2.12043i
$807$	0.778878	−	0.349019i	0.0274178	−	0.0122860i
$808$	−31.2993	−	26.2632i	−1.10111	−	0.923938i
$809$	0.358539			0.0126056			0.00630278	−	0.999980i	$-0.497994\pi$
$809$	0.358539			0.0126056			0.00630278	+	0.999980i	$0.497994\pi$
$810$	−66.3049	+	49.1515i	−2.32972	+	1.72701i
$811$	−7.53287			−0.264515			−0.132257	−	0.991215i	$-0.542223\pi$
$811$	−7.53287			−0.264515			−0.132257	+	0.991215i	$0.542223\pi$
$812$	−36.2317	−	30.4020i	−1.27148	−	1.06690i
$813$	−37.4519	+	16.7823i	−1.31349	+	0.588582i
$814$	−0.508448	−	2.88355i	−0.0178211	−	0.101068i
$815$	6.22694	+	2.26642i	0.218120	+	0.0793893i
$816$	41.3354	+	11.7456i	1.44703	+	0.411178i
$817$	0.781224	−	4.43054i	0.0273316	−	0.155005i
$818$	−4.07381	+	7.05605i	−0.142438	+	0.246709i
$819$	6.98036	+	1.44878i	0.243913	+	0.0506244i
$820$	57.3302	+	99.2988i	2.00206	+	3.46766i
$821$	−32.8475	+	11.9555i	−1.14638	+	0.417250i	−0.844215	−	0.536004i	$-0.819933\pi$
$821$	−32.8475	+	11.9555i	−1.14638	+	0.417250i	−0.302169	+	0.953254i	$0.597711\pi$
$822$	23.2908	+	34.3520i	0.812358	+	1.19817i
$823$	10.4925	−	8.80425i	0.365745	−	0.306897i	−0.441330	−	0.897345i	$-0.645493\pi$
$823$	10.4925	−	8.80425i	0.365745	−	0.306897i	0.807076	+	0.590448i	$0.201049\pi$
$824$	25.0418	−	21.0126i	0.872373	−	0.732008i
$825$	−4.15287	+	0.300402i	−0.144584	+	0.0104587i
$826$	17.9907	−	6.54809i	0.625978	−	0.227837i
$827$	7.79994	+	13.5099i	0.271231	+	0.469785i	0.969177	−	0.246365i	$-0.0792361\pi$
$827$	7.79994	+	13.5099i	0.271231	+	0.469785i	−0.697947	+	0.716150i	$0.745903\pi$
$828$	−24.2809	+	60.9369i	−0.843821	+	2.11770i
$829$	−16.3716	+	28.3564i	−0.568609	+	0.984859i	0.428095	+	0.903734i	$0.359185\pi$
$829$	−16.3716	+	28.3564i	−0.568609	+	0.984859i	−0.996704	+	0.0811257i	$0.974148\pi$
$830$	−3.55720	+	20.1739i	−0.123472	+	0.700245i
$831$	−5.18298	−	20.5775i	−0.179795	−	0.713826i
$832$	18.0212	+	6.55916i	0.624771	+	0.227398i
$833$	0.445220	+	2.52497i	0.0154260	+	0.0874850i
$834$	8.28080	−	80.6457i	0.286741	−	2.79253i
$835$	13.5430	+	11.3639i	0.468675	+	0.393265i
$836$	−7.96168			−0.275360
$837$	50.6928	+	6.75303i	1.75220	+	0.233419i
$838$	−4.54870			−0.157132
$839$	−2.28340	−	1.91600i	−0.0788319	−	0.0661478i	0.602520	−	0.798104i	$-0.294163\pi$
$839$	−2.28340	−	1.91600i	−0.0788319	−	0.0661478i	−0.681352	+	0.731956i	$0.738608\pi$
$840$	−36.4429	−	26.3441i	−1.25740	−	0.908957i
$841$	11.6086	+	65.8354i	0.400295	+	2.27019i
$842$	−85.8534	−	31.2481i	−2.95870	−	1.07688i
$843$	−16.6012	+	16.1087i	−0.571776	+	0.554813i
$844$	13.9681	−	79.2168i	0.480800	−	2.72675i
$845$	12.8999	−	22.3432i	0.443769	−	0.768631i
$846$	−1.18966	+	39.4954i	−0.0409012	+	1.35788i
$847$	5.44595	+	9.43267i	0.187125	+	0.324110i
$848$	−63.4482	+	23.0933i	−2.17882	+	0.793026i
$849$	−2.27560	+	4.69419i	−0.0780983	+	0.161104i
$850$	37.5336	−	31.4945i	1.28739	−	1.08025i
$851$	−11.8144	+	9.91342i	−0.404991	+	0.339828i
$852$	39.8972	−	82.3015i	1.36685	−	2.81960i
$853$	13.3830	−	4.87102i	0.458226	−	0.166781i	−0.102585	−	0.994724i	$-0.532711\pi$
$853$	13.3830	−	4.87102i	0.458226	−	0.166781i	0.560811	+	0.827944i	$0.310489\pi$
$854$	−1.18670	−	2.05543i	−0.0406081	−	0.0703352i
$855$	−1.58865	+	52.7414i	−0.0543306	+	1.80372i
$856$	50.4040	−	87.3023i	1.72277	−	2.98393i
$857$	5.40024	−	30.6263i	0.184469	−	1.04617i	−0.742168	−	0.670214i	$-0.766202\pi$
$857$	5.40024	−	30.6263i	0.184469	−	1.04617i	0.926636	−	0.375959i	$-0.122687\pi$
$858$	2.53830	−	2.46300i	0.0866563	−	0.0840854i
$859$	−48.1882	−	17.5391i	−1.64416	−	0.598426i	−0.656402	−	0.754412i	$-0.727922\pi$
$859$	−48.1882	−	17.5391i	−1.64416	−	0.598426i	−0.987759	+	0.155986i	$0.950144\pi$
$860$	−2.64182	−	14.9825i	−0.0900854	−	0.510900i
$861$	9.49489	+	6.86373i	0.323585	+	0.233915i
$862$	−10.1619	−	8.52683i	−0.346115	−	0.290425i
$863$	37.6511			1.28166			0.640829	−	0.767683i	$-0.278591\pi$
$863$	37.6511			1.28166			0.640829	+	0.767683i	$0.278591\pi$
$864$	−33.2562	+	43.2028i	−1.13140	+	1.46979i
$865$	−60.8242			−2.06809
$866$	−34.4333	−	28.8930i	−1.17009	−	0.981823i
$867$	1.84461	−	17.9645i	0.0626463	−	0.610105i
$868$	8.25640	+	46.8244i	0.280241	+	1.58932i
$869$	0.263400	+	0.0958696i	0.00893522	+	0.00325216i
$870$	37.9831	+	150.801i	1.28775	+	5.11263i
$871$	−2.40735	+	13.6528i	−0.0815701	+	0.462607i
$872$	−40.7095	+	70.5109i	−1.37860	+	2.38780i
$873$	−3.22905	+	8.10381i	−0.109287	+	0.274272i
$874$	29.6484	+	51.3526i	1.00287	+	1.73703i
$875$	−7.62225	+	2.77427i	−0.257679	+	0.0937875i
$876$	49.2622	−	3.56344i	1.66442	−	0.120397i
$877$	4.02403	−	3.37656i	0.135882	−	0.114018i	−0.572314	−	0.820035i	$-0.693954\pi$
$877$	4.02403	−	3.37656i	0.135882	−	0.114018i	0.708195	+	0.706016i	$0.249510\pi$
$878$	−34.1017	+	28.6147i	−1.15088	+	0.965700i
$879$	−4.13146	−	6.09358i	−0.139351	−	0.205531i
$880$	−10.4897	+	3.81795i	−0.353609	+	0.128703i
$881$	−15.0462	−	26.0608i	−0.506920	−	0.878011i	−0.999968	−	0.00800900i	$-0.997451\pi$
$881$	−15.0462	−	26.0608i	−0.506920	−	0.878011i	0.493048	−	0.870002i	$-0.335883\pi$
$882$	−7.67724	−	1.59342i	−0.258506	−	0.0536531i
$883$	10.7214	−	18.5700i	0.360804	−	0.624931i	−0.627289	−	0.778786i	$-0.715836\pi$
$883$	10.7214	−	18.5700i	0.360804	−	0.624931i	0.988093	+	0.153856i	$0.0491690\pi$
$884$	−5.11123	+	28.9872i	−0.171909	+	0.974947i
$885$	−42.8233	−	12.1684i	−1.43949	−	0.409035i
$886$	−37.0971	−	13.5022i	−1.24630	−	0.453617i
$887$	−4.90371	−	27.8103i	−0.164650	−	0.933779i	−0.949424	−	0.313997i	$-0.898332\pi$
$887$	−4.90371	−	27.8103i	−0.164650	−	0.933779i	0.784774	−	0.619782i	$-0.212779\pi$
$888$	−39.8512	+	17.8575i	−1.33732	+	0.599257i
$889$	−9.80019	−	8.22334i	−0.328688	−	0.275802i
$890$	−1.97155			−0.0660866
$891$	1.32257	+	2.64696i	0.0443079	+	0.0886764i
$892$	−45.8343			−1.53465
$893$	19.3509	+	16.2374i	0.647554	+	0.543363i
$894$	82.7860	−	37.0967i	2.76878	−	1.24070i
$895$	−7.14900	−	40.5440i	−0.238965	−	1.35524i
$896$	−0.100975	−	0.0367518i	−0.00337333	−	0.00122779i
$897$	−17.9199	−	5.09199i	−0.598328	−	0.170017i
$898$	6.41332	−	36.3717i	0.214015	−	1.21374i
$899$	48.1784	−	83.4475i	1.60684	−	2.78313i
$900$	33.2290	+	100.624i	1.10763	+	3.35414i
$901$	−8.94518	−	15.4935i	−0.298007	−	0.516164i
$902$	5.46192	−	1.98798i	0.181862	−	0.0661923i
$903$	−0.872367	−	1.28667i	−0.0290306	−	0.0428178i
$904$	7.06139	−	5.92521i	0.234858	−	0.197070i
$905$	35.4351	−	29.7336i	1.17790	−	0.988378i
$906$	2.57729	−	0.186431i	0.0856246	−	0.00619375i
$907$	46.4160	−	16.8941i	1.54122	−	0.560958i	0.574882	−	0.818236i	$-0.305048\pi$
$907$	46.4160	−	16.8941i	1.54122	−	0.560958i	0.966337	+	0.257278i	$0.0828258\pi$
$908$	33.8438	+	58.6192i	1.12315	+	1.94535i
$909$	10.2616	+	13.0053i	0.340356	+	0.431357i
$910$	10.8965	−	18.8733i	0.361215	−	0.625642i
$911$	2.40798	−	13.6564i	0.0797801	−	0.452455i	−0.918581	−	0.395232i	$-0.870664\pi$
$911$	2.40798	−	13.6564i	0.0797801	−	0.452455i	0.998361	−	0.0572233i	$-0.0182247\pi$
$912$	20.5200	+	81.4687i	0.679484	+	2.69770i
$913$	0.690116	+	0.251182i	0.0228395	+	0.00831290i
$914$	10.3632	+	58.7728i	0.342785	+	1.94403i
$915$	−0.563719	+	5.49000i	−0.0186360	+	0.181494i
$916$	−76.1250	−	63.8765i	−2.51524	−	2.11054i
$917$	−7.21240			−0.238174
$918$	−30.8610	−	16.1255i	−1.01856	−	0.532220i
$919$	−4.61654			−0.152286			−0.0761429	−	0.997097i	$-0.524261\pi$
$919$	−4.61654			−0.152286			−0.0761429	+	0.997097i	$0.524261\pi$
$920$	90.0152	+	75.5317i	2.96771	+	2.49021i
$921$	34.2375	+	24.7498i	1.12816	+	0.815535i
$922$	12.1786	+	69.0680i	0.401079	+	2.27463i
$923$	24.4087	+	8.88404i	0.803422	+	0.292422i
$924$	−1.97435	+	1.91577i	−0.0649512	+	0.0630243i
$925$	−4.32638	+	24.5361i	−0.142251	+	0.806743i
$926$	31.4610	−	54.4921i	1.03387	−	1.79072i
$927$	−11.6728	+	6.27849i	−0.383384	+	0.206213i
$928$	51.3623	+	88.9621i	1.68605	+	2.92032i
$929$	21.0412	−	7.65838i	0.690340	−	0.251263i	0.0270592	−	0.999634i	$-0.491386\pi$
$929$	21.0412	−	7.65838i	0.690340	−	0.251263i	0.663281	+	0.748371i	$0.269164\pi$
$930$	68.1942	−	140.674i	2.23618	−	4.61287i
$931$	−3.83992	+	3.22207i	−0.125848	+	0.105599i
$932$	−58.1122	+	48.7620i	−1.90353	+	1.59725i
$933$	−10.7499	+	22.1753i	−0.351936	+	0.725988i
$934$	4.29155	−	1.56200i	0.140424	−	0.0511101i
$935$	−1.47888	−	2.56150i	−0.0483647	−	0.0837701i
$936$	−44.8674	−	27.7381i	−1.46654	−	0.906647i
$937$	15.4071	−	26.6859i	0.503329	−	0.871792i	−0.496663	−	0.867943i	$-0.665442\pi$
$937$	15.4071	−	26.6859i	0.503329	−	0.871792i	0.999993	−	0.00384856i	$-0.00122504\pi$
$938$	2.64769	−	15.0158i	0.0864502	−	0.490283i
$939$	−9.63188	+	9.34612i	−0.314324	+	0.304999i
$940$	80.2716	+	29.2165i	2.61817	+	0.952936i
$941$	1.93875	+	10.9952i	0.0632013	+	0.358432i	0.999964	+	0.00846760i	$0.00269535\pi$
$941$	1.93875	+	10.9952i	0.0632013	+	0.358432i	−0.936763	+	0.349965i	$0.886194\pi$
$942$	−29.5418	−	21.3554i	−0.962525	−	0.695796i
$943$	−23.4527	−	19.6791i	−0.763725	−	0.640841i
$944$	−70.8827			−2.30703
$945$	12.2969	+	13.4612i	0.400019	+	0.437891i
$946$	−0.771222			−0.0250746
$947$	−30.7073	−	25.7665i	−0.997854	−	0.837299i	−0.0111680	−	0.999938i	$-0.503555\pi$
$947$	−30.7073	−	25.7665i	−0.997854	−	0.837299i	−0.986686	+	0.162639i	$0.947999\pi$
$948$	0.728685	−	7.09658i	0.0236666	−	0.230486i
$949$	2.43576	+	13.8139i	0.0790682	+	0.448418i
$950$	90.0153	+	32.7629i	2.92048	+	1.06297i
$951$	−5.35301	−	21.2526i	−0.173583	−	0.689162i
$952$	3.29424	−	18.6826i	0.106767	−	0.605506i
$953$	−15.6058	+	27.0300i	−0.505521	+	0.875587i	0.494459	+	0.869201i	$0.335366\pi$
$953$	−15.6058	+	27.0300i	−0.505521	+	0.875587i	−0.999980	+	0.00638648i	$0.997967\pi$
$954$	54.1418	−	7.87402i	1.75291	−	0.254931i
$955$	0.669333	+	1.15932i	0.0216591	+	0.0375147i
$956$	−128.348	+	46.7147i	−4.15106	+	1.51086i
$957$	5.56065	−	0.402236i	0.179750	−	0.0130024i
$958$	8.57423	−	7.19463i	0.277021	−	0.232448i
$959$	7.02318	−	5.89315i	0.226790	−	0.190300i
$960$	27.5235	+	40.5950i	0.888317	+	1.31020i
$961$	−61.8932	+	22.5273i	−1.99655	+	0.726686i
$962$	−10.5818	−	18.3283i	−0.341172	−	0.590927i
$963$	−27.2034	+	30.5053i	−0.876617	+	0.983019i
$964$	−58.0654	+	100.572i	−1.87016	+	3.23921i
$965$	−6.53733	+	37.0750i	−0.210444	+	1.19349i
$966$	19.7089	+	5.60035i	0.634124	+	0.180188i
$967$	26.5573	+	9.66608i	0.854026	+	0.310840i	0.731681	−	0.681647i	$-0.238736\pi$
$967$	26.5573	+	9.66608i	0.854026	+	0.310840i	0.122345	+	0.992488i	$0.460958\pi$
$968$	−13.9944	−	79.3663i	−0.449798	−	2.55093i
$969$	−20.3141	+	9.10284i	−0.652584	+	0.292425i
$970$	20.4278	+	17.1410i	0.655898	+	0.550364i
$971$	50.1324			1.60883			0.804413	−	0.594070i	$-0.202480\pi$
$971$	50.1324			1.60883			0.804413	+	0.594070i	$0.202480\pi$
$972$	57.1047	−	49.0948i	1.83164	−	1.57472i
$973$	−17.9084			−0.574116
$974$	−82.5375	−	69.2572i	−2.64467	−	2.21914i
$975$	−27.4638	+	12.3066i	−0.879546	+	0.394128i
$976$	1.52587	+	8.65365i	0.0488420	+	0.276997i
$977$	35.6406	+	12.9721i	1.14024	+	0.415014i	0.842001	−	0.539476i	$-0.181378\pi$
$977$	35.6406	+	12.9721i	1.14024	+	0.415014i	0.298242	+	0.954490i	$0.403600\pi$
$978$	−8.22376	−	2.33681i	−0.262967	−	0.0747228i
$979$	−0.0122737	+	0.0696079i	−0.000392271	+	0.00222468i
$980$	−8.47551	+	14.6800i	−0.270740	+	0.468936i
$981$	21.9712	−	24.6380i	0.701486	−	0.786630i
$982$	23.7900	+	41.2056i	0.759171	+	1.31492i
$983$	−11.4456	+	4.16588i	−0.365059	+	0.132871i	−0.518035	−	0.855359i	$-0.673336\pi$
$983$	−11.4456	+	4.16588i	−0.365059	+	0.132871i	0.152976	+	0.988230i	$0.451114\pi$
$984$	−48.6474	−	71.7512i	−1.55082	−	2.28734i
$985$	−1.11531	+	0.935857i	−0.0355368	+	0.0298189i
$986$	−50.2573	+	42.1708i	−1.60052	+	1.34299i
$987$	8.70577	−	0.629741i	0.277108	−	0.0200449i
$988$	−54.0760	+	19.6821i	−1.72039	+	0.626170i
$989$	2.03109	+	3.51795i	0.0645849	+	0.111864i
$990$	8.95113	−	1.30179i	0.284486	−	0.0413736i
$991$	7.59550	−	13.1558i	0.241279	−	0.417907i	−0.719800	−	0.694182i	$-0.755766\pi$
$991$	7.59550	−	13.1558i	0.241279	−	0.417907i	0.961079	+	0.276274i	$0.0890998\pi$
$992$	17.9321	−	101.698i	0.569344	−	3.22891i
$993$	−0.433927	−	1.72278i	−0.0137702	−	0.0546708i
$994$	−26.8455	−	9.77097i	−0.851488	−	0.309916i
$995$	12.0146	+	68.1380i	0.380887	+	2.16012i
$996$	1.90918	−	18.5933i	0.0604947	−	0.589150i
$997$	27.0486	+	22.6965i	0.856639	+	0.718805i	0.961241	−	0.275709i	$-0.0889125\pi$
$997$	27.0486	+	22.6965i	0.856639	+	0.718805i	−0.104602	+	0.994514i	$0.533357\pi$
$998$	−25.5675			−0.809324
$999$	17.2920	−	3.80570i	0.547095	−	0.120407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.a.43.9	yes	54
3.2	odd	2		567.2.v.b.127.1		54
27.5	odd	18		567.2.v.b.442.1		54
27.7	even	9		5103.2.a.i.1.25		27
27.20	odd	18		5103.2.a.f.1.3		27
27.22	even	9	inner	189.2.v.a.22.9	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.22.9	✓	54	27.22	even	9	inner
189.2.v.a.43.9	yes	54	1.1	even	1	trivial
567.2.v.b.127.1		54	3.2	odd	2
567.2.v.b.442.1		54	27.5	odd	18
5103.2.a.f.1.3		27	27.20	odd	18
5103.2.a.i.1.25		27	27.7	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00215 + 1.68000i) q^{2} +(1.58061 - 0.708280i) q^{3} +(0.838893 + 4.75760i) q^{4} +(-3.29720 - 1.20008i) q^{5} +(4.35453 + 1.23735i) q^{6} +(0.173648 - 0.984808i) q^{7} +(-3.69957 + 6.40784i) q^{8} +(1.99668 - 2.23903i) q^{9} +(-4.58534 - 7.94204i) q^{10} +(-0.308948 + 0.112448i) q^{11} +(4.69568 + 6.92576i) q^{12} +(-1.82041 + 1.52750i) q^{13} +(2.00215 - 1.68000i) q^{14} +(-6.06160 + 0.438472i) q^{15} +(-9.09294 + 3.30956i) q^{16} +(-1.28196 - 2.22042i) q^{17} +(7.75922 - 1.12845i) q^{18} +(2.50633 - 4.34109i) q^{19} +(2.94352 - 16.6935i) q^{20} +(-0.423048 - 1.67959i) q^{21} +(-0.807473 - 0.293896i) q^{22} +(0.785944 + 4.45731i) q^{23} +(-1.30905 + 12.7486i) q^{24} +(5.60111 + 4.69989i) q^{25} -6.21093 q^{26} +(1.57012 - 4.95325i) q^{27} +4.83099 q^{28} +(-7.49985 - 6.29312i) q^{29} +(-12.8728 - 9.30560i) q^{30} +(1.70905 + 9.69250i) q^{31} +(-9.85965 - 3.58862i) q^{32} +(-0.408683 + 0.396559i) q^{33} +(1.16363 - 6.59930i) q^{34} +(-1.75440 + 3.03872i) q^{35} +(12.3274 + 7.62110i) q^{36} +(1.70374 + 2.95097i) q^{37} +(12.3111 - 4.48086i) q^{38} +(-1.79546 + 3.70375i) q^{39} +(19.8881 - 16.6881i) q^{40} +(-5.18169 + 4.34795i) q^{41} +(1.97471 - 4.07351i) q^{42} +(0.843380 - 0.306965i) q^{43} +(-0.794157 - 1.37552i) q^{44} +(-9.27048 + 4.98636i) q^{45} +(-5.91471 + 10.2446i) q^{46} +(-0.875085 + 4.96285i) q^{47} +(-12.0283 + 11.6715i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(3.31843 + 18.8197i) q^{50} +(-3.59896 - 2.60164i) q^{51} +(-8.79438 - 7.37936i) q^{52} +6.97774 q^{53} +(11.4651 - 7.27934i) q^{54} +1.15361 q^{55} +(5.66806 + 4.75607i) q^{56} +(0.886834 - 8.63677i) q^{57} +(-4.44335 - 25.1995i) q^{58} +(6.88347 + 2.50538i) q^{59} +(-7.17111 - 28.4708i) q^{60} +(0.157688 - 0.894295i) q^{61} +(-12.8616 + 22.2770i) q^{62} +(-1.85830 - 2.35515i) q^{63} +(-4.03508 - 6.98896i) q^{64} +(7.83538 - 2.85185i) q^{65} +(-1.48446 + 0.107380i) q^{66} +(4.46899 - 3.74993i) q^{67} +(9.48844 - 7.96175i) q^{68} +(4.39930 + 6.48862i) q^{69} +(-8.61762 + 3.13656i) q^{70} +(-5.46530 - 9.46618i) q^{71} +(6.96050 + 21.0778i) q^{72} +(2.95135 - 5.11188i) q^{73} +(-1.54649 + 8.77057i) q^{74} +(12.1820 + 3.46156i) q^{75} +(22.7557 + 8.28240i) q^{76} +(0.0570914 + 0.323781i) q^{77} +(-9.81708 + 4.39907i) q^{78} +(-0.653105 - 0.548021i) q^{79} +33.9530 q^{80} +(-1.02654 - 8.94127i) q^{81} -17.6791 q^{82} +(-1.71116 - 1.43583i) q^{83} +(7.63593 - 3.42169i) q^{84} +(1.56219 + 8.85963i) q^{85} +(2.20427 + 0.802290i) q^{86} +(-16.3116 - 4.63500i) q^{87} +(0.422426 - 2.39570i) q^{88} +(0.107492 - 0.186182i) q^{89} +(-26.9379 - 5.59099i) q^{90} +(1.18819 + 2.05800i) q^{91} +(-20.5468 + 7.47842i) q^{92} +(9.56634 + 14.1096i) q^{93} +(-10.0896 + 8.46622i) q^{94} +(-13.4735 + 11.3056i) q^{95} +(-18.1261 + 1.31117i) q^{96} +(-2.73245 + 0.994531i) q^{97} +(-1.30681 - 2.26346i) q^{98} +(-0.365096 + 0.916268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} - 27 q^{8} - 9 q^{9} - 6 q^{11} + 24 q^{12} - 9 q^{13} - 9 q^{15} - 30 q^{17} - 27 q^{18} - 12 q^{20} - 3 q^{21} - 9 q^{22} - 12 q^{23} + 36 q^{24} + 27 q^{25} + 18 q^{26} + 63 q^{27}+ \cdots - 117 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 - 27 * q^8 - 9 * q^9 - 6 * q^11 + 24 * q^12 - 9 * q^13 - 9 * q^15 - 30 * q^17 - 27 * q^18 - 12 * q^20 - 3 * q^21 - 9 * q^22 - 12 * q^23 + 36 * q^24 + 27 * q^25 + 18 * q^26 + 63 * q^27 + 54 * q^28 + 6 * q^29 - 72 * q^30 - 9 * q^31 - 9 * q^32 - 36 * q^33 - 9 * q^34 - 12 * q^35 + 54 * q^38 + 12 * q^39 - 45 * q^40 - 15 * q^41 - 18 * q^42 - 9 * q^43 - 42 * q^44 - 9 * q^45 - 45 * q^47 - 93 * q^48 + 18 * q^50 + 72 * q^51 - 63 * q^52 + 132 * q^53 + 54 * q^54 - 9 * q^56 + 3 * q^57 - 27 * q^58 - 9 * q^60 - 36 * q^62 - 9 * q^63 - 27 * q^64 + 66 * q^65 + 153 * q^66 + 45 * q^67 + 87 * q^68 - 72 * q^71 - 45 * q^72 - 72 * q^74 - 39 * q^75 + 54 * q^76 + 3 * q^77 - 54 * q^78 - 36 * q^79 + 42 * q^80 + 27 * q^81 + 24 * q^83 - 12 * q^84 + 18 * q^85 - 90 * q^86 - 99 * q^87 + 54 * q^88 - 42 * q^89 - 9 * q^90 + 87 * q^92 + 93 * q^93 - 90 * q^94 + 12 * q^95 + 108 * q^96 - 18 * q^97 - 9 * q^98 - 117 * q^99

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