LMFDB - Embedded newform 189.2.be.a.20.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(20,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 9]))

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

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

chi := DirichletCharacter("189.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			20.14
Character	$\chi$	$=$	189.20
Dual form			189.2.be.a.104.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.157445 + 0.432576i) q^{2} +(0.888001 - 1.48710i) q^{3} +(1.36976 - 1.14936i) q^{4} +(0.725040 + 4.11191i) q^{5} +(0.783093 + 0.149993i) q^{6} +(-1.09969 + 2.40638i) q^{7} +(1.51017 + 0.871900i) q^{8} +(-1.42291 - 2.64109i) q^{9} +O(q^{10})$	\(q+(0.157445 + 0.432576i) q^{2} +(0.888001 - 1.48710i) q^{3} +(1.36976 - 1.14936i) q^{4} +(0.725040 + 4.11191i) q^{5} +(0.783093 + 0.149993i) q^{6} +(-1.09969 + 2.40638i) q^{7} +(1.51017 + 0.871900i) q^{8} +(-1.42291 - 2.64109i) q^{9} +(-1.66456 + 0.961033i) q^{10} +(-1.36185 - 0.240131i) q^{11} +(-0.492866 - 3.05759i) q^{12} +(1.43469 - 3.94178i) q^{13} +(-1.21408 - 0.0968290i) q^{14} +(6.75864 + 2.57317i) q^{15} +(0.481603 - 2.73131i) q^{16} +(-1.18976 - 2.06072i) q^{17} +(0.918441 - 1.03134i) q^{18} +(-4.72301 - 2.72683i) q^{19} +(5.71920 + 4.79898i) q^{20} +(2.60199 + 3.77222i) q^{21} +(-0.110541 - 0.626912i) q^{22} +(-1.01769 - 1.21284i) q^{23} +(2.63764 - 1.47153i) q^{24} +(-11.6836 + 4.25249i) q^{25} +1.93100 q^{26} +(-5.19109 - 0.229289i) q^{27} +(1.25949 + 4.56010i) q^{28} +(0.495461 + 1.36127i) q^{29} +(-0.0489817 + 3.32875i) q^{30} +(1.18509 + 1.41234i) q^{31} +(4.69194 - 0.827315i) q^{32} +(-1.56642 + 1.81197i) q^{33} +(0.704097 - 0.839111i) q^{34} +(-10.6921 - 2.77712i) q^{35} +(-4.98460 - 1.98221i) q^{36} +(3.37083 + 5.83846i) q^{37} +(0.435948 - 2.47239i) q^{38} +(-4.58780 - 5.63383i) q^{39} +(-2.49023 + 6.84186i) q^{40} +(6.07454 + 2.21095i) q^{41} +(-1.22210 + 1.71947i) q^{42} +(0.819766 - 4.64912i) q^{43} +(-2.14140 + 1.23634i) q^{44} +(9.82823 - 7.76576i) q^{45} +(0.364414 - 0.631183i) q^{46} +(-2.18349 - 1.83217i) q^{47} +(-3.63405 - 3.14159i) q^{48} +(-4.58135 - 5.29257i) q^{49} +(-3.67905 - 4.38452i) q^{50} +(-4.12100 - 0.0606394i) q^{51} +(-2.56536 - 7.04826i) q^{52} +11.6368i q^{53} +(-0.718125 - 2.28164i) q^{54} -5.77391i q^{55} +(-3.75885 + 2.67523i) q^{56} +(-8.24910 + 4.60214i) q^{57} +(-0.510844 + 0.428649i) q^{58} +(-1.15353 - 6.54201i) q^{59} +(12.2152 - 4.24350i) q^{60} +(1.37654 - 1.64050i) q^{61} +(-0.424356 + 0.735006i) q^{62} +(7.92022 - 0.519671i) q^{63} +(-1.67684 - 2.90438i) q^{64} +(17.2484 + 3.04137i) q^{65} +(-1.03044 - 0.392313i) q^{66} +(9.25483 + 3.36848i) q^{67} +(-3.99819 - 1.45522i) q^{68} +(-2.70732 + 0.436403i) q^{69} +(-0.482108 - 5.06240i) q^{70} +(-9.79394 + 5.65453i) q^{71} +(0.153924 - 5.22913i) q^{72} +(7.69650 + 4.44358i) q^{73} +(-1.99486 + 2.37738i) q^{74} +(-4.05122 + 21.1509i) q^{75} +(-9.60349 + 1.69335i) q^{76} +(2.07547 - 3.01307i) q^{77} +(1.71473 - 2.87159i) q^{78} +(-2.14212 + 0.779666i) q^{79} +11.5801 q^{80} +(-4.95067 + 7.51604i) q^{81} +2.97580i q^{82} +(-10.9949 + 4.00181i) q^{83} +(7.89974 + 2.17639i) q^{84} +(7.61088 - 6.38628i) q^{85} +(2.14017 - 0.377369i) q^{86} +(2.46430 + 0.472010i) q^{87} +(-1.84726 - 1.55004i) q^{88} +(-4.23831 + 7.34097i) q^{89} +(4.90668 + 3.02878i) q^{90} +(7.90771 + 7.78717i) q^{91} +(-2.78798 - 0.491595i) q^{92} +(3.15264 - 0.508187i) q^{93} +(0.448772 - 1.23299i) q^{94} +(7.78811 - 21.3976i) q^{95} +(2.93615 - 7.71202i) q^{96} +(5.77859 + 1.01892i) q^{97} +(1.56813 - 2.81507i) q^{98} +(1.30358 + 3.93845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.157445	+	0.432576i	0.111330	+	0.305877i	0.982829	−	0.184521i	$-0.0590735\pi$
$2$	0.157445	+	0.432576i	0.111330	+	0.305877i	−0.871498	+	0.490399i	$0.836851\pi$
$3$	0.888001	−	1.48710i	0.512688	−	0.858575i
$3$	0.888001	−	1.48710i	0.512688	−	0.858575i
$4$	1.36976	−	1.14936i	0.684878	−	0.574681i
$5$	0.725040	+	4.11191i	0.324248	+	1.83890i	0.514909	+	0.857245i	$0.327826\pi$
$5$	0.725040	+	4.11191i	0.324248	+	1.83890i	−0.190661	+	0.981656i	$0.561063\pi$
$6$	0.783093	+	0.149993i	0.319696	+	0.0612342i
$7$	−1.09969	+	2.40638i	−0.415645	+	0.909527i
$7$	−1.09969	+	2.40638i	−0.415645	+	0.909527i
$8$	1.51017	+	0.871900i	0.533927	+	0.308263i
$9$	−1.42291	−	2.64109i	−0.474302	−	0.880362i
$10$	−1.66456	+	0.961033i	−0.526379	+	0.303905i
$11$	−1.36185	−	0.240131i	−0.410614	−	0.0724023i	−0.0354742	−	0.999371i	$-0.511294\pi$
$11$	−1.36185	−	0.240131i	−0.410614	−	0.0724023i	−0.375140	+	0.926968i	$0.622405\pi$
$12$	−0.492866	−	3.05759i	−0.142278	−	0.882651i
$13$	1.43469	−	3.94178i	0.397912	−	1.09325i	−0.565388	−	0.824825i	$-0.691274\pi$
$13$	1.43469	−	3.94178i	0.397912	−	1.09325i	0.963300	−	0.268428i	$-0.0865042\pi$
$14$	−1.21408	−	0.0968290i	−0.324477	−	0.0258786i
$15$	6.75864	+	2.57317i	1.74507	+	0.664391i
$16$	0.481603	−	2.73131i	0.120401	−	0.682827i
$17$	−1.18976	−	2.06072i	−0.288559	−	0.499799i	0.684907	−	0.728630i	$-0.259843\pi$
$17$	−1.18976	−	2.06072i	−0.288559	−	0.499799i	−0.973466	+	0.228832i	$0.926509\pi$
$18$	0.918441	−	1.03134i	0.216479	−	0.243089i
$19$	−4.72301	−	2.72683i	−1.08353	−	0.625578i	−0.151686	−	0.988429i	$-0.548470\pi$
$19$	−4.72301	−	2.72683i	−1.08353	−	0.625578i	−0.931847	+	0.362851i	$0.881804\pi$
$20$	5.71920	+	4.79898i	1.27885	+	1.07308i
$21$	2.60199	+	3.77222i	0.567801	+	0.823166i
$22$	−0.110541	−	0.626912i	−0.0235675	−	0.133658i
$23$	−1.01769	−	1.21284i	−0.212203	−	0.252894i	0.649435	−	0.760417i	$-0.275006\pi$
$23$	−1.01769	−	1.21284i	−0.212203	−	0.252894i	−0.861638	+	0.507523i	$0.830561\pi$
$24$	2.63764	−	1.47153i	0.538405	−	0.300374i
$25$	−11.6836	+	4.25249i	−2.33673	+	0.850499i
$26$	1.93100			0.378701
$27$	−5.19109	−	0.229289i	−0.999026	−	0.0441267i
$28$	1.25949	+	4.56010i	0.238021	+	0.861778i
$29$	0.495461	+	1.36127i	0.0920048	+	0.252781i	0.977156	−	0.212522i	$-0.0681677\pi$
$29$	0.495461	+	1.36127i	0.0920048	+	0.252781i	−0.885152	+	0.465303i	$0.845945\pi$
$30$	−0.0489817	+	3.32875i	−0.00894280	+	0.607745i
$31$	1.18509	+	1.41234i	0.212849	+	0.253663i	0.861896	−	0.507085i	$-0.169277\pi$
$31$	1.18509	+	1.41234i	0.212849	+	0.253663i	−0.649048	+	0.760748i	$0.724832\pi$
$32$	4.69194	−	0.827315i	0.829425	−	0.146250i
$33$	−1.56642	+	1.81197i	−0.272680	+	0.315423i
$34$	0.704097	−	0.839111i	0.120752	−	0.143906i
$35$	−10.6921	−	2.77712i	−1.80730	−	0.469418i
$36$	−4.98460	−	1.98221i	−0.830766	−	0.330368i
$37$	3.37083	+	5.83846i	0.554162	+	0.959836i	0.997968	+	0.0637138i	$0.0202945\pi$
$37$	3.37083	+	5.83846i	0.554162	+	0.959836i	−0.443806	+	0.896123i	$0.646372\pi$
$38$	0.435948	−	2.47239i	0.0707202	−	0.401074i
$39$	−4.58780	−	5.63383i	−0.734636	−	0.902135i
$40$	−2.49023	+	6.84186i	−0.393741	+	1.08179i
$41$	6.07454	+	2.21095i	0.948684	+	0.345293i	0.769589	−	0.638539i	$-0.220461\pi$
$41$	6.07454	+	2.21095i	0.948684	+	0.345293i	0.179095	+	0.983832i	$0.442683\pi$
$42$	−1.22210	+	1.71947i	−0.188574	+	0.265321i
$43$	0.819766	−	4.64912i	0.125013	−	0.708985i	−0.856287	−	0.516500i	$-0.827234\pi$
$43$	0.819766	−	4.64912i	0.125013	−	0.708985i	0.981300	−	0.192484i	$-0.0616544\pi$
$44$	−2.14140	+	1.23634i	−0.322829	+	0.186385i
$45$	9.82823	−	7.76576i	1.46511	−	1.15765i
$46$	0.364414	−	0.631183i	0.0537299	−	0.0930629i
$47$	−2.18349	−	1.83217i	−0.318495	−	0.267249i	0.469497	−	0.882934i	$-0.344435\pi$
$47$	−2.18349	−	1.83217i	−0.318495	−	0.267249i	−0.787993	+	0.615685i	$0.788880\pi$
$48$	−3.63405	−	3.14159i	−0.524530	−	0.453450i
$49$	−4.58135	−	5.29257i	−0.654478	−	0.756081i
$50$	−3.67905	−	4.38452i	−0.520297	−	0.620065i
$51$	−4.12100	−	0.0606394i	−0.577055	−	0.00849121i
$52$	−2.56536	−	7.04826i	−0.355751	−	0.977417i
$53$			11.6368i			1.59844i	0.601040	+	0.799219i	$0.294753\pi$
$53$			11.6368i			1.59844i	−0.601040	+	0.799219i	$0.705247\pi$
$54$	−0.718125	−	2.28164i	−0.0977244	−	0.310492i
$55$		−	5.77391i		−	0.778554i
$56$	−3.75885	+	2.67523i	−0.502298	+	0.357493i
$57$	−8.24910	+	4.60214i	−1.09262	+	0.609568i
$58$	−0.510844	+	0.428649i	−0.0670771	+	0.0562843i
$59$	−1.15353	−	6.54201i	−0.150177	−	0.851698i	−0.963063	−	0.269275i	$-0.913216\pi$
$59$	−1.15353	−	6.54201i	−0.150177	−	0.851698i	0.812886	−	0.582423i	$-0.197895\pi$
$60$	12.2152	−	4.24350i	1.57697	−	0.547833i
$61$	1.37654	−	1.64050i	0.176248	−	0.210045i	−0.670687	−	0.741741i	$-0.734001\pi$
$61$	1.37654	−	1.64050i	0.176248	−	0.210045i	0.846935	+	0.531696i	$0.178445\pi$
$62$	−0.424356	+	0.735006i	−0.0538933	+	0.0933459i
$63$	7.92022	−	0.519671i	0.997854	−	0.0654724i
$64$	−1.67684	−	2.90438i	−0.209606	−	0.363048i
$65$	17.2484	+	3.04137i	2.13941	+	0.377235i
$66$	−1.03044	−	0.392313i	−0.126838	−	0.0482904i
$67$	9.25483	+	3.36848i	1.13066	+	0.411525i	0.838531	−	0.544854i	$-0.183415\pi$
$67$	9.25483	+	3.36848i	1.13066	+	0.411525i	0.292126	+	0.956380i	$0.405637\pi$
$68$	−3.99819	−	1.45522i	−0.484852	−	0.176472i
$69$	−2.70732	+	0.436403i	−0.325922	+	0.0525368i
$70$	−0.482108	−	5.06240i	−0.0576229	−	0.605073i
$71$	−9.79394	+	5.65453i	−1.16233	+	0.671069i	−0.951860	−	0.306532i	$-0.900831\pi$
$71$	−9.79394	+	5.65453i	−1.16233	+	0.671069i	−0.210466	+	0.977601i	$0.567498\pi$
$72$	0.153924	−	5.22913i	0.0181401	−	0.616259i
$73$	7.69650	+	4.44358i	0.900807	+	0.520081i	0.877462	−	0.479646i	$-0.159235\pi$
$73$	7.69650	+	4.44358i	0.900807	+	0.520081i	0.0233450	+	0.999727i	$0.492568\pi$
$74$	−1.99486	+	2.37738i	−0.231897	+	0.276364i
$75$	−4.05122	+	21.1509i	−0.467794	+	2.44230i
$76$	−9.60349	+	1.69335i	−1.10160	+	0.194241i
$77$	2.07547	−	3.01307i	0.236522	−	0.343371i
$78$	1.71473	−	2.87159i	0.194155	−	0.325143i
$79$	−2.14212	+	0.779666i	−0.241007	+	0.0877193i	−0.459700	−	0.888074i	$-0.652043\pi$
$79$	−2.14212	+	0.779666i	−0.241007	+	0.0877193i	0.218693	+	0.975794i	$0.429821\pi$
$80$	11.5801			1.29469
$81$	−4.95067	+	7.51604i	−0.550075	+	0.835116i
$82$			2.97580i			0.328622i
$83$	−10.9949	+	4.00181i	−1.20685	+	0.439256i	−0.865608	−	0.500722i	$-0.833068\pi$
$83$	−10.9949	+	4.00181i	−1.20685	+	0.439256i	−0.341237	+	0.939977i	$0.610846\pi$
$84$	7.89974	+	2.17639i	0.861932	+	0.237464i
$85$	7.61088	−	6.38628i	0.825515	−	0.692690i
$86$	2.14017	−	0.377369i	0.230780	−	0.0406927i
$87$	2.46430	+	0.472010i	0.264201	+	0.0506047i
$88$	−1.84726	−	1.55004i	−0.196919	−	0.165235i
$89$	−4.23831	+	7.34097i	−0.449260	+	0.778142i	−0.998338	−	0.0576296i	$-0.981646\pi$
$89$	−4.23831	+	7.34097i	−0.449260	+	0.778142i	0.549078	+	0.835771i	$0.314979\pi$
$90$	4.90668	+	3.02878i	0.517210	+	0.319261i
$91$	7.90771	+	7.78717i	0.828953	+	0.816317i
$92$	−2.78798	−	0.491595i	−0.290667	−	0.0512524i
$93$	3.15264	−	0.508187i	0.326914	−	0.0526965i
$94$	0.448772	−	1.23299i	0.0462873	−	0.127173i
$95$	7.78811	−	21.3976i	0.799043	−	2.19535i
$96$	2.93615	−	7.71202i	0.299670	−	0.787105i
$97$	5.77859	+	1.01892i	0.586727	+	0.103456i	0.459128	−	0.888370i	$-0.348162\pi$
$97$	5.77859	+	1.01892i	0.586727	+	0.103456i	0.127599	+	0.991826i	$0.459273\pi$
$98$	1.56813	−	2.81507i	0.158405	−	0.284365i
$99$	1.30358	+	3.93845i	0.131015	+	0.395829i
$100$	−11.1161	+	19.2536i	−1.11161	+	1.92536i
$101$	−3.63389	−	3.04919i	−0.361585	−	0.303406i	0.443837	−	0.896108i	$-0.353617\pi$
$101$	−3.63389	−	3.04919i	−0.361585	−	0.303406i	−0.805422	+	0.592702i	$0.798061\pi$
$102$	−0.622598	−	1.79219i	−0.0616464	−	0.177453i
$103$	13.7651	−	2.42716i	1.35631	−	0.239155i	0.552241	−	0.833685i	$-0.313773\pi$
$103$	13.7651	−	2.42716i	1.35631	−	0.239155i	0.804073	+	0.594530i	$0.202662\pi$
$104$	5.60347	−	4.70187i	0.549466	−	0.461056i
$105$	−13.6245	+	13.4342i	−1.32961	+	1.31104i
$106$	−5.03380	+	1.83215i	−0.488926	+	0.177954i
$107$		−	7.92658i		−	0.766292i	−0.923688	−	0.383146i	$-0.874841\pi$
$107$		−	7.92658i		−	0.766292i	0.923688	−	0.383146i	$-0.125159\pi$
$108$	−7.37406	+	5.65237i	−0.709570	+	0.543900i
$109$	−2.88019			−0.275872			−0.137936	−	0.990441i	$-0.544047\pi$
$109$	−2.88019			−0.275872			−0.137936	+	0.990441i	$0.544047\pi$
$110$	2.49766	−	0.909072i	0.238142	−	0.0866766i
$111$	11.6757	+	0.171804i	1.10820	+	0.0163069i
$112$	6.04295	+	4.16252i	0.571005	+	0.393322i
$113$	6.48938	−	1.14425i	0.610470	−	0.107642i	0.140138	−	0.990132i	$-0.455245\pi$
$113$	6.48938	−	1.14425i	0.610470	−	0.107642i	0.470332	+	0.882490i	$0.344134\pi$
$114$	−3.28955	−	2.84378i	−0.308095	−	0.266344i
$115$	4.24921	−	5.06401i	0.396240	−	0.472221i
$116$	2.24325	+	1.29514i	0.208280	+	0.120251i
$117$	−12.4520	+	1.81965i	−1.15119	+	0.168226i
$118$	2.64830	−	1.52900i	0.243796	−	0.140755i
$119$	6.26725	−	0.596849i	0.574518	−	0.0547131i
$120$	7.96317	+	9.77880i	0.726935	+	0.892678i
$121$	−8.53964	−	3.10817i	−0.776331	−	0.282561i
$122$	0.926371	+	0.337172i	0.0838697	+	0.0305261i
$123$	8.68210	−	7.07010i	0.782839	−	0.637489i
$124$	3.24657	+	0.572458i	0.291551	+	0.0514082i
$125$	−15.5186	−	26.8790i	−1.38803	−	2.40413i
$126$	1.47179	+	3.34428i	0.131118	+	0.297932i
$127$	4.32354	−	7.48859i	0.383652	−	0.664505i	−0.607929	−	0.793991i	$-0.707999\pi$
$127$	4.32354	−	7.48859i	0.383652	−	0.664505i	0.991581	+	0.129486i	$0.0413328\pi$
$128$	7.11724	−	8.48200i	0.629081	−	0.749710i
$129$	−6.18574	−	5.34750i	−0.544624	−	0.470821i
$130$	1.40006	+	7.94011i	0.122793	+	0.696393i
$131$	−0.627073	+	0.526177i	−0.0547876	+	0.0459723i	−0.669770	−	0.742568i	$-0.733607\pi$
$131$	−0.627073	+	0.526177i	−0.0547876	+	0.0459723i	0.614983	+	0.788541i	$0.289163\pi$
$132$	−0.0630135	+	4.28234i	−0.00548462	+	0.372730i
$133$	11.7557	−	8.36669i	1.01935	−	0.725484i
$134$			4.53376i			0.391657i
$135$	−2.82093	−	21.5115i	−0.242787	−	1.85142i
$136$		−	4.14940i		−	0.355808i
$137$	1.76175	+	4.84037i	0.150517	+	0.413541i	0.991920	−	0.126867i	$-0.0404921\pi$
$137$	1.76175	+	4.84037i	0.150517	+	0.413541i	−0.841403	+	0.540408i	$0.818270\pi$
$138$	−0.615030	−	1.10241i	−0.0523548	−	0.0938434i
$139$	6.38256	+	7.60644i	0.541362	+	0.645170i	0.965492	−	0.260431i	$-0.0838647\pi$
$139$	6.38256	+	7.60644i	0.541362	+	0.645170i	−0.424131	+	0.905601i	$0.639420\pi$
$140$	−17.8375	+	8.48516i	−1.50755	+	0.717127i
$141$	−4.66356	+	1.62010i	−0.392742	+	0.136437i
$142$	−3.98802	−	3.34634i	−0.334667	−	0.280819i
$143$	−2.90038	+	5.02361i	−0.242542	+	0.420095i
$144$	−7.89889	+	2.61444i	−0.658241	+	0.217870i
$145$	−5.23818	+	3.02426i	−0.435007	+	0.251151i
$146$	−0.710410	+	4.02894i	−0.0587940	+	0.333437i
$147$	−11.9388	+	2.11309i	−0.984695	+	0.174285i
$148$	11.3277	+	4.12295i	0.931133	+	0.338905i
$149$	−2.14963	+	5.90605i	−0.176104	+	0.483843i	−0.996070	−	0.0885701i	$-0.971770\pi$
$149$	−2.14963	+	5.90605i	−0.176104	+	0.483843i	0.819966	+	0.572413i	$0.193992\pi$
$150$	−9.78721	+	1.57764i	−0.799122	+	0.128814i
$151$	−1.64935	+	9.35394i	−0.134222	+	0.761213i	0.841176	+	0.540762i	$0.181864\pi$
$151$	−1.64935	+	9.35394i	−0.134222	+	0.761213i	−0.975398	+	0.220451i	$0.929247\pi$
$152$	−4.75505	−	8.23599i	−0.385685	−	0.668027i
$153$	−3.74963	+	6.07447i	−0.303140	+	0.491092i
$154$	1.63015	+	0.423406i	0.131361	+	0.0341190i
$155$	−4.94816	+	5.89698i	−0.397446	+	0.473657i
$156$	−12.7595	−	2.44393i	−1.02158	−	0.195671i
$157$	9.71583	−	1.71316i	0.775408	−	0.136725i	0.228079	−	0.973643i	$-0.426756\pi$
$157$	9.71583	−	1.71316i	0.775408	−	0.136725i	0.547329	+	0.836917i	$0.315645\pi$
$158$	−0.674529	−	0.803873i	−0.0536627	−	0.0639527i
$159$	17.3050	+	10.3335i	1.37238	+	0.819500i
$160$	6.80369	+	18.6930i	0.537879	+	1.47781i
$161$	4.03770	−	1.11520i	0.318215	−	0.0878903i
$162$	−4.03071	−	0.958179i	−0.316683	−	0.0752817i
$163$	−0.425059			−0.0332932			−0.0166466	−	0.999861i	$-0.505299\pi$
$163$	−0.425059			−0.0332932			−0.0166466	+	0.999861i	$0.505299\pi$
$164$	10.8618	−	3.95338i	0.848166	−	0.308707i
$165$	−8.58636	−	5.12724i	−0.668447	−	0.399155i
$166$	−3.46217	−	4.12606i	−0.268717	−	0.320244i
$167$	−1.60617	−	9.10902i	−0.124289	−	0.704877i	−0.981728	−	0.190291i	$-0.939057\pi$
$167$	−1.60617	−	9.10902i	−0.124289	−	0.704877i	0.857439	−	0.514586i	$-0.172054\pi$
$168$	0.640461	+	7.96539i	0.0494127	+	0.614543i
$169$	−3.52072	−	2.95424i	−0.270825	−	0.227249i
$170$	3.96084	+	2.28679i	0.303783	+	0.175389i
$171$	−0.481391	+	16.3539i	−0.0368129	+	1.25061i
$172$	−4.22064	−	7.31037i	−0.321821	−	0.557411i
$173$	0.793657	−	4.50105i	0.0603406	−	0.342209i	−0.939659	−	0.342112i	$-0.888858\pi$
$173$	0.793657	−	4.50105i	0.0603406	−	0.342209i	1.00000		9.72430e-5i	$-3.09534e-5\pi$
$174$	0.183812	+	1.14031i	0.0139347	+	0.0864470i
$175$	2.61530	−	32.7917i	0.197698	−	2.47882i
$176$	−1.31174	+	3.60399i	−0.0988765	+	0.271661i
$177$	−10.7529	−	4.09390i	−0.808240	−	0.307717i
$178$	−3.84283	−	0.677594i	−0.288032	−	0.0507878i
$179$	3.72660	−	2.15156i	0.278539	−	0.160815i	−0.354223	−	0.935161i	$-0.615254\pi$
$179$	3.72660	−	2.15156i	0.278539	−	0.160815i	0.632762	+	0.774346i	$0.281921\pi$
$180$	4.53662	−	21.9334i	0.338140	−	1.63482i
$181$	−0.427397	−	0.246758i	−0.0317681	−	0.0183413i	0.484032	−	0.875050i	$-0.339172\pi$
$181$	−0.427397	−	0.246758i	−0.0317681	−	0.0183413i	−0.515800	+	0.856709i	$0.672505\pi$
$182$	−2.12351	+	4.64673i	−0.157405	+	0.344439i
$183$	−1.21721	−	3.50382i	−0.0899788	−	0.259010i
$184$	−0.479419	−	2.71892i	−0.0353432	−	0.200441i
$185$	−21.5632	+	18.0937i	−1.58536	+	1.33027i
$186$	0.716196	+	1.28374i	0.0525140	+	0.0941287i
$187$	1.12543	+	3.09210i	0.0822997	+	0.226117i
$188$	−5.09668			−0.371714
$189$	6.26037	−	12.2396i	0.455375	−	0.890300i
$190$	10.4823			0.760466
$191$	4.69030	+	12.8865i	0.339378	+	0.932433i	0.985571	+	0.169260i	$0.0541377\pi$
$191$	4.69030	+	12.8865i	0.339378	+	0.932433i	−0.646193	+	0.763174i	$0.723640\pi$
$192$	−5.80813	−	0.0854651i	−0.419166	−	0.00616791i
$193$	0.558650	−	0.468763i	0.0402125	−	0.0337423i	−0.622460	−	0.782652i	$-0.713867\pi$
$193$	0.558650	−	0.468763i	0.0402125	−	0.0337423i	0.662672	+	0.748909i	$0.269422\pi$
$194$	0.469048	+	2.66010i	0.0336757	+	0.190984i
$195$	19.8394	−	22.9494i	1.42073	−	1.64344i
$196$	−12.3584	−	1.98390i	−0.882743	−	0.141707i
$197$	−17.3970	−	10.0441i	−1.23948	−	0.715615i	−0.270494	−	0.962722i	$-0.587187\pi$
$197$	−17.3970	−	10.0441i	−1.23948	−	0.715615i	−0.968988	+	0.247106i	$0.920520\pi$
$198$	−1.49844	+	1.18399i	−0.106489	+	0.0841423i
$199$	−6.81702	+	3.93581i	−0.483246	+	0.279002i	−0.721768	−	0.692135i	$-0.756670\pi$
$199$	−6.81702	+	3.93581i	−0.483246	+	0.279002i	0.238522	+	0.971137i	$0.423337\pi$
$200$	−21.3521	−	3.76495i	−1.50982	−	0.266222i
$201$	13.2276	−	10.7716i	0.932999	−	0.759770i
$202$	0.746870	−	2.05201i	0.0525496	−	0.144379i
$203$	−3.82058	−	0.304710i	−0.268152	−	0.0213864i
$204$	−5.71446	+	4.65346i	−0.400092	+	0.325807i
$205$	−4.68694	+	26.5810i	−0.327350	+	1.85650i
$206$	3.21717	+	5.57230i	0.224151	+	0.388240i
$207$	−1.75513	+	4.41356i	−0.121990	+	0.306764i
$208$	−10.0753	−	5.81696i	−0.698594	−	0.403333i
$209$	5.77725	+	4.84769i	0.399620	+	0.335321i
$210$	−7.95639	−	3.77848i	−0.549043	−	0.260740i
$211$	−3.02127	−	17.1345i	−0.207993	−	1.17959i	−0.892660	−	0.450731i	$-0.851163\pi$
$211$	−3.02127	−	17.1345i	−0.207993	−	1.17959i	0.684667	−	0.728856i	$-0.259948\pi$
$212$	13.3749	+	15.9396i	0.918591	+	1.09473i
$213$	−0.288199	+	19.5858i	−0.0197471	+	1.34199i
$214$	3.42885	−	1.24800i	0.234391	−	0.0853114i
$215$	19.7111			1.34429
$216$	−7.63954	−	4.87238i	−0.519805	−	0.331523i
$217$	−4.70186	+	1.29864i	−0.319183	+	0.0881576i
$218$	−0.453471	−	1.24590i	−0.0307129	−	0.0843831i
$219$	13.4425	−	7.49953i	0.908361	−	0.506771i
$220$	−6.63632	−	7.90885i	−0.447420	−	0.533215i
$221$	−9.82985	+	1.73327i	−0.661227	+	0.116592i
$222$	1.76395	+	5.07765i	0.118389	+	0.340790i
$223$	−3.66575	+	4.36867i	−0.245476	+	0.292547i	−0.874688	−	0.484687i	$-0.838934\pi$
$223$	−3.66575	+	4.36867i	−0.245476	+	0.292547i	0.629211	+	0.777234i	$0.283378\pi$
$224$	−3.16886	+	12.2004i	−0.211728	+	0.815173i
$225$	27.8559	+	24.8066i	1.85706	+	1.65377i
$226$	1.51669	+	2.62699i	0.100889	+	0.174745i
$227$	−1.25816	+	7.13538i	−0.0835071	+	0.473592i	0.914162	+	0.405350i	$0.132850\pi$
$227$	−1.25816	+	7.13538i	−0.0835071	+	0.473592i	−0.997669	+	0.0682424i	$0.978261\pi$
$228$	−6.00973	+	15.7850i	−0.398004	+	1.04539i
$229$	−9.81687	+	26.9716i	−0.648717	+	1.78233i	−0.0262929	+	0.999654i	$0.508370\pi$
$229$	−9.81687	+	26.9716i	−0.648717	+	1.78233i	−0.622424	+	0.782680i	$0.713852\pi$
$230$	2.85958	+	1.04080i	0.188555	+	0.0686285i
$231$	−2.63770	−	5.76203i	−0.173548	−	0.379113i
$232$	−0.438656	+	2.48774i	−0.0287992	+	0.163328i
$233$	19.3330	−	11.1619i	1.26655	−	0.731243i	0.292216	−	0.956352i	$-0.405607\pi$
$233$	19.3330	−	11.1619i	1.26655	−	0.731243i	0.974333	+	0.225109i	$0.0722739\pi$
$234$	−2.74764	−	5.09995i	−0.179619	−	0.333394i
$235$	5.95059	−	10.3067i	0.388174	−	0.672336i
$236$	−9.09920	−	7.63513i	−0.592307	−	0.497005i
$237$	−0.742763	+	3.87787i	−0.0482476	+	0.251895i
$238$	1.24493	+	2.61709i	0.0806967	+	0.169641i
$239$	−9.75397	−	11.6243i	−0.630932	−	0.751915i	0.351977	−	0.936009i	$-0.385510\pi$
$239$	−9.75397	−	11.6243i	−0.630932	−	0.751915i	−0.982909	+	0.184093i	$0.941065\pi$
$240$	10.2831	−	17.2207i	0.663772	−	1.11159i
$241$	−2.42697	−	6.66806i	−0.156335	−	0.429527i	0.836654	−	0.547732i	$-0.184508\pi$
$241$	−2.42697	−	6.66806i	−0.156335	−	0.429527i	−0.992989	+	0.118204i	$0.962286\pi$
$242$		−	4.18341i		−	0.268920i
$243$	6.78087	+	14.0364i	0.434993	+	0.900434i
$244$		−	3.82924i		−	0.245142i
$245$	18.4409	−	22.6754i	1.17814	−	1.44868i
$246$	4.42530	+	2.64252i	0.282147	+	0.168481i
$247$	−17.5246	+	14.7049i	−1.11507	+	0.935652i
$248$	0.558279	+	3.16616i	0.0354507	+	0.201051i
$249$	−3.81240	+	19.9041i	−0.241601	+	1.26137i
$250$	9.18389	−	10.9449i	0.580840	−	0.692219i
$251$	−7.15997	+	12.4014i	−0.451934	+	0.782772i	−0.998506	−	0.0546399i	$-0.982599\pi$
$251$	−7.15997	+	12.4014i	−0.451934	+	0.782772i	0.546573	+	0.837412i	$0.315932\pi$
$252$	10.2515	−	9.81502i	0.645783	−	0.618288i
$253$	1.09470	+	1.89608i	0.0688235	+	0.119206i
$254$	3.92010	+	0.691220i	0.245969	+	0.0433710i
$255$	−2.73855	−	16.9891i	−0.171494	−	1.06390i
$256$	−1.51319	−	0.550758i	−0.0945746	−	0.0344223i
$257$	8.77573	+	3.19411i	0.547415	+	0.199243i	0.600898	−	0.799326i	$-0.294810\pi$
$257$	8.77573	+	3.19411i	0.547415	+	0.199243i	−0.0534825	+	0.998569i	$0.517032\pi$
$258$	1.33929	−	3.51774i	0.0833803	−	0.219005i
$259$	−17.7564	+	1.69100i	−1.10333	+	0.105074i
$260$	27.1218	−	15.6588i	1.68202	−	0.971116i
$261$	2.89023	−	3.24551i	0.178901	−	0.200892i
$262$	−0.326341	−	0.188413i	−0.0201614	−	0.0116402i
$263$	15.0368	−	17.9202i	0.927211	−	1.10501i	−0.0670205	−	0.997752i	$-0.521349\pi$
$263$	15.0368	−	17.9202i	0.927211	−	1.10501i	0.994231	−	0.107255i	$-0.0342063\pi$
$264$	−3.94543	+	1.37062i	−0.242824	+	0.0843560i
$265$	−47.8494	+	8.43715i	−2.93937	+	0.518290i
$266$	5.47009	+	3.76793i	0.335393	+	0.231026i
$267$	7.15310	+	12.8216i	0.437763	+	0.784668i
$268$	16.5485	−	6.02314i	1.01086	−	0.367922i
$269$	24.6194			1.50107			0.750536	−	0.660830i	$-0.229796\pi$
$269$	24.6194			1.50107			0.750536	+	0.660830i	$0.229796\pi$
$270$	8.86122	−	4.60714i	0.539277	−	0.280382i
$271$		−	17.4873i		−	1.06228i	−0.847285	−	0.531139i	$-0.821764\pi$
$271$		−	17.4873i		−	1.06228i	0.847285	−	0.531139i	$-0.178236\pi$
$272$	−6.20146	+	2.25715i	−0.376019	+	0.136860i
$273$	18.6023	−	4.84450i	1.12586	−	0.293203i
$274$	−1.81645	+	1.52418i	−0.109736	+	0.0920792i
$275$	16.9325	−	2.98566i	1.02107	−	0.180042i
$276$	−3.20678	+	3.70945i	−0.193025	+	0.223283i
$277$	9.59499	+	8.05115i	0.576507	+	0.483747i	0.883798	−	0.467869i	$-0.154978\pi$
$277$	9.59499	+	8.05115i	0.576507	+	0.483747i	−0.307291	+	0.951616i	$0.599422\pi$
$278$	−2.28546	+	3.95854i	−0.137073	+	0.237417i
$279$	2.04383	−	5.13955i	0.122361	−	0.307697i
$280$	−13.7256	−	13.5164i	−0.820263	−	0.807760i
$281$	−18.0825	−	3.18844i	−1.07871	−	0.190206i	−0.394067	−	0.919082i	$-0.628932\pi$
$281$	−18.0825	−	3.18844i	−1.07871	−	0.190206i	−0.684646	+	0.728876i	$0.740043\pi$
$282$	−1.43507	−	1.76227i	−0.0854570	−	0.104941i
$283$	−2.82503	+	7.76172i	−0.167931	+	0.461386i	−0.994901	−	0.100860i	$-0.967840\pi$
$283$	−2.82503	+	7.76172i	−0.167931	+	0.461386i	0.826970	+	0.562246i	$0.190063\pi$
$284$	−6.91620	+	19.0021i	−0.410401	+	1.12757i
$285$	−24.9045	−	30.5828i	−1.47522	−	1.81157i
$286$	−2.62974	−	0.463694i	−0.155500	−	0.0274188i
$287$	−12.0005	+	12.1863i	−0.708369	+	0.719334i
$288$	−8.86120	−	11.2146i	−0.522151	−	0.660828i
$289$	5.66895	−	9.81891i	0.333468	−	0.577583i
$290$	−2.13295	−	1.78975i	−0.125251	−	0.105098i
$291$	6.64663	−	7.68852i	0.389633	−	0.450709i
$292$	15.6496	−	2.75945i	0.915823	−	0.161484i
$293$	17.0672	−	14.3211i	0.997078	−	0.836648i	0.0105009	−	0.999945i	$-0.496657\pi$
$293$	17.0672	−	14.3211i	0.997078	−	0.836648i	0.986577	+	0.163297i	$0.0522130\pi$
$294$	−2.79377	−	4.83174i	−0.162936	−	0.281793i
$295$	26.0638	−	9.48644i	1.51749	−	0.552322i
$296$			11.7561i			0.683311i
$297$	7.01444	+	1.55880i	0.407019	+	0.0904508i
$298$	−2.89326			−0.167602
$299$	−6.24081	+	2.27147i	−0.360915	+	0.131362i
$300$	18.7609	+	33.6279i	1.08316	+	1.94151i
$301$	10.2861	+	7.08528i	0.592879	+	0.408389i
$302$	−4.30597	+	0.759259i	−0.247781	+	0.0436904i
$303$	−7.76133	+	2.69625i	−0.445877	+	0.154895i
$304$	−9.72243	+	11.5867i	−0.557620	+	0.664546i
$305$	7.74364	+	4.47079i	0.443400	+	0.255997i
$306$	−3.21803	−	0.665605i	−0.183962	−	0.0380501i
$307$	17.0333	−	9.83418i	0.972142	−	0.561266i	0.0722533	−	0.997386i	$-0.476981\pi$
$307$	17.0333	−	9.83418i	0.972142	−	0.561266i	0.899889	+	0.436120i	$0.143648\pi$
$308$	−0.620217	−	6.51263i	−0.0353401	−	0.371091i
$309$	8.61400	−	22.6253i	0.490033	−	1.28711i
$310$	−3.32995	−	1.21200i	−0.189129	−	0.0688372i
$311$	−15.6758	−	5.70554i	−0.888896	−	0.323532i	−0.143101	−	0.989708i	$-0.545708\pi$
$311$	−15.6758	−	5.70554i	−0.888896	−	0.323532i	−0.745794	+	0.666177i	$0.767930\pi$
$312$	−2.01624	−	12.5082i	−0.114147	−	0.708136i
$313$	10.7102	+	1.88851i	0.605379	+	0.106745i	0.467932	−	0.883764i	$-0.344999\pi$
$313$	10.7102	+	1.88851i	0.605379	+	0.106745i	0.137447	+	0.990509i	$0.456110\pi$
$314$	2.27078	+	3.93310i	0.128147	+	0.221958i
$315$	7.87932	+	32.1904i	0.443949	+	1.81373i
$316$	−2.03806	+	3.53002i	−0.114650	+	0.198579i
$317$	−18.2381	+	21.7354i	−1.02436	+	1.22078i	−0.0493075	+	0.998784i	$0.515701\pi$
$317$	−18.2381	+	21.7354i	−1.02436	+	1.22078i	−0.975048	+	0.221995i	$0.928743\pi$
$318$	−1.74543	+	9.11269i	−0.0978790	+	0.511015i
$319$	−0.347861	−	1.97282i	−0.0194765	−	0.110457i
$320$	10.7268	−	9.00082i	0.599644	−	0.503161i
$321$	−11.7876	−	7.03882i	−0.657919	−	0.392868i
$322$	1.11812	+	1.57103i	0.0623106	+	0.0875499i
$323$			12.9771i			0.722065i
$324$	1.85744	+	15.9853i	0.103191	+	0.888070i
$325$			52.1553i			2.89306i
$326$	−0.0669233	−	0.183870i	−0.00370654	−	0.0101836i
$327$	−2.55761	+	4.28312i	−0.141436	+	0.236857i
$328$	7.24589	+	8.63532i	0.400088	+	0.476806i
$329$	6.81007	−	3.23950i	0.375452	−	0.178599i
$330$	0.866044	−	4.52151i	0.0476742	−	0.248901i
$331$	−0.689617	−	0.578657i	−0.0379048	−	0.0318059i	0.623638	−	0.781713i	$-0.285654\pi$
$331$	−0.689617	−	0.578657i	−0.0379048	−	0.0318059i	−0.661543	+	0.749907i	$0.730098\pi$
$332$	−10.4608	+	18.1186i	−0.574110	+	0.994387i
$333$	10.6235	−	17.2102i	0.582163	−	0.943116i
$334$	3.68746	−	2.12896i	0.201769	−	0.116491i
$335$	−7.14076	+	40.4973i	−0.390141	+	2.21260i
$336$	11.5562	−	5.29012i	0.630444	−	0.288600i
$337$	−20.7809	−	7.56364i	−1.13201	−	0.412018i	−0.292988	−	0.956116i	$-0.594650\pi$
$337$	−20.7809	−	7.56364i	−1.13201	−	0.412018i	−0.839021	+	0.544098i	$0.816872\pi$
$338$	0.723612	−	1.98811i	0.0393593	−	0.108139i
$339$	4.06097	−	10.6664i	0.220561	−	0.579321i
$340$	3.08489	−	17.4953i	0.167302	−	0.948816i
$341$	−1.27477	−	2.20797i	−0.0690328	−	0.119568i
$342$	−7.15010	+	2.36660i	−0.386633	+	0.127971i
$343$	17.7740	−	5.20426i	0.959707	−	0.281004i
$344$	5.29156	−	6.30624i	0.285302	−	0.340009i
$345$	−3.75736	−	10.8158i	−0.202290	−	0.582304i
$346$	2.07200	−	0.365350i	0.111392	−	0.0196413i
$347$	17.3948	+	20.7303i	0.933803	+	1.11286i	0.993407	+	0.114641i	$0.0365717\pi$
$347$	17.3948	+	20.7303i	0.933803	+	1.11286i	−0.0596042	+	0.998222i	$0.518984\pi$
$348$	3.91801	−	2.18584i	0.210027	−	0.117173i
$349$	−3.61775	−	9.93968i	−0.193654	−	0.532059i	0.804423	−	0.594057i	$-0.202475\pi$
$349$	−3.61775	−	9.93968i	−0.193654	−	0.532059i	−0.998076	+	0.0619986i	$0.980253\pi$
$350$	14.5967	−	4.03157i	0.780225	−	0.215496i
$351$	−8.35142	+	20.1332i	−0.445766	+	1.07463i
$352$	−6.58839			−0.351162
$353$	0.727677	−	0.264853i	0.0387303	−	0.0140967i	−0.322582	−	0.946541i	$-0.604551\pi$
$353$	0.727677	−	0.264853i	0.0387303	−	0.0140967i	0.361313	+	0.932445i	$0.382329\pi$
$354$	0.0779296	−	5.29602i	0.00414191	−	0.281481i
$355$	−30.3519	−	36.1720i	−1.61091	−	1.91981i
$356$	2.63198	+	14.9267i	0.139495	+	0.791113i
$357$	4.67776	−	9.85001i	0.247573	−	0.521318i
$358$	1.51745	+	1.27329i	0.0801995	+	0.0672953i
$359$	−2.11285	−	1.21985i	−0.111512	−	0.0643813i	0.443207	−	0.896419i	$-0.353841\pi$
$359$	−2.11285	−	1.21985i	−0.111512	−	0.0643813i	−0.554719	+	0.832038i	$0.687174\pi$
$360$	21.6133	−	3.15841i	1.13912	−	0.166463i
$361$	5.37123	+	9.30324i	0.282696	+	0.489644i
$362$	0.0394500	−	0.223732i	0.00207345	−	0.0117591i
$363$	−12.2054	+	9.93920i	−0.640616	+	0.521673i
$364$	19.7819	+	1.57770i	1.03685	+	0.0826940i
$365$	−12.6913	+	34.8691i	−0.664293	+	1.82513i
$366$	1.32403	−	1.07819i	0.0692079	−	0.0563581i
$367$	−32.2888	−	5.69339i	−1.68546	−	0.297193i	−0.752883	−	0.658155i	$-0.771337\pi$
$367$	−32.2888	−	5.69339i	−1.68546	−	0.297193i	−0.932580	+	0.360962i	$0.882448\pi$
$368$	−3.80275	+	2.19552i	−0.198232	+	0.114449i
$369$	−2.80419	−	19.1894i	−0.145981	−	0.998959i
$370$	−11.2219	−	6.47897i	−0.583399	−	0.336825i
$371$	−28.0026	−	12.7969i	−1.45382	−	0.664383i
$372$	3.73426	−	4.31962i	0.193612	−	0.223962i
$373$	4.41268	+	25.0256i	0.228480	+	1.29577i	0.855919	+	0.517109i	$0.172992\pi$
$373$	4.41268	+	25.0256i	0.228480	+	1.29577i	−0.627439	+	0.778666i	$0.715897\pi$
$374$	−1.16037	+	0.973669i	−0.0600015	+	0.0503472i
$375$	−53.7522	−	0.790950i	−2.77575	−	0.0408445i
$376$	−1.69999	−	4.67068i	−0.0876703	−	0.240872i
$377$	6.07665			0.312963
$378$	6.28022	+	0.781024i	0.323019	+	0.0401715i
$379$	−18.7107			−0.961102			−0.480551	−	0.876967i	$-0.659563\pi$
$379$	−18.7107			−0.961102			−0.480551	+	0.876967i	$0.659563\pi$
$380$	−13.9258	−	38.2609i	−0.714380	−	1.96274i
$381$	−7.29695	−	13.0794i	−0.373834	−	0.670078i
$382$	−4.83592	+	4.05782i	−0.247427	+	0.207616i
$383$	−1.87324	−	10.6237i	−0.0957180	−	0.542844i	−0.994525	−	0.104499i	$-0.966676\pi$
$383$	−1.87324	−	10.6237i	−0.0957180	−	0.542844i	0.898807	−	0.438345i	$-0.144435\pi$
$384$	−6.29343	−	18.1161i	−0.321160	−	0.924481i
$385$	13.8942	+	6.34954i	0.708116	+	0.323602i
$386$	0.290732	+	0.167854i	0.0147979	+	0.00854356i
$387$	−13.4452	+	4.45020i	−0.683457	+	0.226216i
$388$	9.08637	−	5.24602i	0.461291	−	0.266326i
$389$	4.97680	+	0.877544i	0.252334	+	0.0444932i	0.298384	−	0.954446i	$-0.403552\pi$
$389$	4.97680	+	0.877544i	0.252334	+	0.0444932i	−0.0460504	+	0.998939i	$0.514663\pi$
$390$	13.0509	+	4.96881i	0.660861	+	0.251605i
$391$	−1.28851	+	3.54016i	−0.0651629	+	0.179034i
$392$	−2.30404	−	11.9872i	−0.116372	−	0.605444i
$393$	0.225634	+	1.39976i	0.0113817	+	0.0706087i
$394$	1.60579	−	9.10690i	0.0808987	−	0.458799i
$395$	−4.75903	−	8.24289i	−0.239453	−	0.414745i
$396$	6.31230	+	3.89643i	0.317205	+	0.195803i
$397$	17.8034	+	10.2788i	0.893528	+	0.515878i	0.875095	−	0.483952i	$-0.160799\pi$
$397$	17.8034	+	10.2788i	0.893528	+	0.515878i	0.0184329	+	0.999830i	$0.494132\pi$
$398$	−2.77584	−	2.32921i	−0.139140	−	0.116753i
$399$	−2.00302	−	24.9114i	−0.100276	−	1.24713i
$400$	5.98799	+	33.9596i	0.299400	+	1.69798i
$401$	−19.5802	−	23.3347i	−0.977786	−	1.16528i	−0.986241	−	0.165316i	$-0.947136\pi$
$401$	−19.5802	−	23.3347i	−0.977786	−	1.16528i	0.00845455	−	0.999964i	$-0.497309\pi$
$402$	6.74214	+	4.02599i	0.336267	+	0.200798i
$403$	7.26736	−	2.64510i	0.362013	−	0.131762i
$404$	−8.48216			−0.422003
$405$	−34.4947	−	14.9073i	−1.71406	−	0.740748i
$406$	−0.469721	−	1.70067i	−0.0233118	−	0.0844027i
$407$	−3.18858	−	8.76056i	−0.158052	−	0.434245i
$408$	−6.17056	−	3.68467i	−0.305488	−	0.182419i
$409$	0.623352	+	0.742883i	0.0308228	+	0.0367332i	0.781236	−	0.624236i	$-0.214590\pi$
$409$	0.623352	+	0.742883i	0.0308228	+	0.0367332i	−0.750413	+	0.660969i	$0.770145\pi$
$410$	−12.2362	+	2.15758i	−0.604304	+	0.106555i
$411$	8.76254	+	1.67836i	0.432224	+	0.0827876i
$412$	16.0651	−	19.1457i	0.791472	−	0.943240i
$413$	17.0111	+	4.41837i	0.837062	+	0.217414i
$414$	−2.18554	−	0.0643331i	−0.107413	−	0.00316180i
$415$	−24.4268	−	42.3085i	−1.19906	−	2.07684i
$416$	3.47039	−	19.6815i	0.170150	−	0.964967i
$417$	16.9792	−	2.73695i	0.831476	−	0.134029i
$418$	−1.18739	+	3.26234i	−0.0580774	+	0.159566i
$419$	32.6552	+	11.8855i	1.59531	+	0.580646i	0.978461	−	0.206434i	$-0.0661858\pi$
$419$	32.6552	+	11.8855i	1.59531	+	0.580646i	0.616851	+	0.787080i	$0.288408\pi$
$420$	−3.22150	+	34.0610i	−0.157193	+	1.66200i
$421$	1.63994	−	9.30054i	0.0799256	−	0.453280i	−0.918411	−	0.395627i	$-0.870527\pi$
$421$	1.63994	−	9.30054i	0.0799256	−	0.453280i	0.998337	−	0.0576531i	$-0.0183617\pi$
$422$	6.93628	−	4.00466i	0.337653	−	0.194944i
$423$	−1.73201	+	8.37380i	−0.0842131	+	0.407148i
$424$	−10.1461	+	17.5736i	−0.492739	+	0.853450i
$425$	22.6639	+	19.0173i	1.09936	+	0.922474i
$426$	−8.51770	+	2.95900i	−0.412684	+	0.143364i
$427$	2.43390	+	5.11654i	0.117784	+	0.247607i
$428$	−9.11051	−	10.8575i	−0.440373	−	0.524816i
$429$	4.89504	+	8.77412i	0.236335	+	0.423618i
$430$	3.10341	+	8.52656i	0.149660	+	0.411187i
$431$		−	34.0032i		−	1.63788i	−0.573882	−	0.818938i	$-0.694563\pi$
$431$		−	34.0032i		−	1.63788i	0.573882	−	0.818938i	$-0.305437\pi$
$432$	−3.12630	+	14.0680i	−0.150414	+	0.676849i
$433$		−	36.2251i		−	1.74087i	−0.492286	−	0.870433i	$-0.663839\pi$
$433$		−	36.2251i		−	1.74087i	0.492286	−	0.870433i	$-0.336161\pi$
$434$	−1.30204	−	1.82945i	−0.0625001	−	0.0878162i
$435$	−0.154140	+	10.4752i	−0.00739045	+	0.502248i
$436$	−3.94516	+	3.31038i	−0.188939	+	0.158539i
$437$	1.49936	+	8.50332i	0.0717243	+	0.406769i
$438$	5.36057	+	4.63415i	0.256138	+	0.221428i
$439$	−24.9337	+	29.7148i	−1.19002	+	1.41821i	−0.305196	+	0.952290i	$0.598722\pi$
$439$	−24.9337	+	29.7148i	−1.19002	+	1.41821i	−0.884825	+	0.465923i	$0.845723\pi$
$440$	5.03427	−	8.71962i	0.240000	−	0.415692i
$441$	−7.45930	+	19.6306i	−0.355205	+	0.934789i
$442$	−2.29743	−	3.97926i	−0.109278	−	0.189274i
$443$	−12.4872	−	2.20183i	−0.593285	−	0.104612i	−0.131059	−	0.991375i	$-0.541838\pi$
$443$	−12.4872	−	2.20183i	−0.593285	−	0.104612i	−0.462225	+	0.886762i	$0.652949\pi$
$444$	16.1903	−	13.1842i	0.768356	−	0.625695i
$445$	−33.2584	−	12.1051i	−1.57660	−	0.573834i
$446$	−2.46693	−	0.897889i	−0.116813	−	0.0425163i
$447$	6.87399	+	8.44128i	0.325129	+	0.399259i
$448$	8.83306	−	0.841199i	0.417323	−	0.0397429i
$449$	−14.9676	+	8.64153i	−0.706363	+	0.407819i	−0.809713	−	0.586826i	$-0.800377\pi$
$449$	−14.9676	+	8.64153i	−0.706363	+	0.407819i	0.103350	+	0.994645i	$0.467044\pi$
$450$	−6.34495	+	15.9555i	−0.299104	+	0.752148i
$451$	−7.74171	−	4.46968i	−0.364543	−	0.210469i
$452$	7.57371	−	9.02599i	0.356237	−	0.424547i
$453$	12.4456	+	10.7591i	0.584744	+	0.505505i
$454$	−3.28469	+	0.579179i	−0.154158	+	0.0271822i
$455$	−26.2867	+	38.1618i	−1.23234	+	1.78905i
$456$	−16.4702	−	0.242354i	−0.771287	−	0.0113493i
$457$	−34.2674	+	12.4723i	−1.60296	+	0.583430i	−0.980031	−	0.198847i	$-0.936280\pi$
$457$	−34.2674	+	12.4723i	−1.60296	+	0.583430i	−0.622931	+	0.782277i	$0.714058\pi$
$458$	−13.2129			−0.617397
$459$	5.70364	+	10.9702i	0.266223	+	0.512045i
$460$		−	11.8203i		−	0.551126i
$461$	9.14600	−	3.32887i	0.425972	−	0.155041i	−0.120133	−	0.992758i	$-0.538332\pi$
$461$	9.14600	−	3.32887i	0.425972	−	0.155041i	0.546105	+	0.837717i	$0.316110\pi$
$462$	2.07722	−	2.04820i	0.0966411	−	0.0952911i
$463$	−16.0196	+	13.4420i	−0.744493	+	0.624704i	−0.934040	−	0.357168i	$-0.883742\pi$
$463$	−16.0196	+	13.4420i	−0.744493	+	0.624704i	0.189547	+	0.981872i	$0.439298\pi$
$464$	3.95666	−	0.697665i	0.183683	−	0.0323883i
$465$	4.37541	+	12.5949i	0.202905	+	0.584075i
$466$	7.87227	+	6.60562i	0.364676	+	0.305999i
$467$	−6.75996	+	11.7086i	−0.312813	+	0.541809i	−0.978970	−	0.204003i	$-0.934605\pi$
$467$	−6.75996	+	11.7086i	−0.312813	+	0.541809i	0.666157	+	0.745812i	$0.267938\pi$
$468$	−14.9648	+	16.8043i	−0.691748	+	0.776781i
$469$	−18.2833	+	18.5663i	−0.844246	+	0.857314i
$470$	5.39533	+	0.951342i	0.248868	+	0.0438821i
$471$	6.08003	−	15.9697i	0.280153	−	0.735843i
$472$	3.96194	−	10.8853i	0.182363	−	0.501039i
$473$	−2.23280	+	6.13457i	−0.102664	+	0.282068i
$474$	−1.79442	+	0.289250i	−0.0824204	+	0.0132857i
$475$	66.7778	+	11.7747i	3.06397	+	0.540261i
$476$	7.89861	−	8.02088i	0.362032	−	0.367636i
$477$	30.7338	−	16.5581i	1.40720	−	0.758143i
$478$	3.49269	−	6.04952i	0.159752	−	0.276699i
$479$	7.30076	+	6.12607i	0.333580	+	0.279907i	0.794157	−	0.607713i	$-0.207913\pi$
$479$	7.30076	+	6.12607i	0.333580	+	0.279907i	−0.460576	+	0.887620i	$0.652357\pi$
$480$	33.8399	+	6.48166i	1.54457	+	0.295846i
$481$	27.8500	−	4.91071i	1.26985	−	0.223909i
$482$	2.50233	−	2.09970i	0.113978	−	0.0956387i
$483$	1.92707	−	6.99474i	0.0876846	−	0.318272i
$484$	−15.2696	+	5.55769i	−0.694075	+	0.252622i
$485$			24.4998i			1.11248i
$486$	−5.00418	+	5.14319i	−0.226994	+	0.233300i
$487$	16.1416			0.731447			0.365724	−	0.930724i	$-0.380822\pi$
$487$	16.1416			0.731447			0.365724	+	0.930724i	$0.380822\pi$
$488$	3.50918	−	1.27724i	0.158853	−	0.0578178i
$489$	−0.377453	+	0.632104i	−0.0170690	+	0.0285847i
$490$	12.7122	+	4.40696i	0.574281	+	0.199086i
$491$	18.8388	−	3.32178i	0.850181	−	0.149910i	0.268453	−	0.963293i	$-0.413488\pi$
$491$	18.8388	−	3.32178i	0.850181	−	0.149910i	0.581729	+	0.813383i	$0.302377\pi$
$492$	3.76626	−	19.6632i	0.169796	−	0.886485i
$493$	2.21572	−	2.64059i	0.0997908	−	0.118926i
$494$	−9.12015	−	5.26552i	−0.410335	−	0.236907i
$495$	−15.2494	+	8.21574i	−0.685410	+	0.369270i
$496$	4.42827	−	2.55666i	0.198835	−	0.114797i
$497$	−2.83663	−	29.7862i	−0.127240	−	1.33609i
$498$	−9.21025	+	1.48464i	−0.412721	+	0.0665282i
$499$	37.5122	+	13.6533i	1.67928	+	0.611207i	0.993210	−	0.116332i	$-0.0371138\pi$
$499$	37.5122	+	13.6533i	1.67928	+	0.611207i	0.686066	+	0.727539i	$0.259336\pi$
$500$	−52.1504	−	18.9812i	−2.33224	−	0.848865i
$501$	−14.9723	−	5.70030i	−0.668911	−	0.254671i
$502$	−6.49186	−	1.14469i	−0.289746	−	0.0510900i
$503$	−14.1117	−	24.4422i	−0.629211	−	1.08982i	−0.987710	−	0.156295i	$-0.950045\pi$
$503$	−14.1117	−	24.4422i	−0.629211	−	1.08982i	0.358500	−	0.933530i	$-0.383288\pi$
$504$	12.4140	+	6.12085i	0.552965	+	0.272644i
$505$	9.90328	−	17.1530i	0.440690	−	0.763298i
$506$	−0.647845	+	0.772071i	−0.0288002	+	0.0343227i
$507$	−7.51964	+	2.61228i	−0.333959	+	0.116016i
$508$	−2.68491	−	15.2269i	−0.119123	−	0.675583i
$509$	−1.16032	+	0.973624i	−0.0514303	+	0.0431551i	−0.668140	−	0.744035i	$-0.732909\pi$
$509$	−1.16032	+	0.973624i	−0.0514303	+	0.0431551i	0.616710	+	0.787190i	$0.288465\pi$
$510$	6.91792	−	3.85948i	0.306330	−	0.170901i
$511$	−19.1567	+	13.6341i	−0.847444	+	0.603139i
$512$		−	22.8862i		−	1.01144i
$513$	23.8924	+	15.2382i	1.05487	+	0.672782i
$514$			4.29906i			0.189624i
$515$	19.9605	+	54.8410i	0.879564	+	2.41658i
$516$	−14.6192	−	0.215117i	−0.643573	−	0.00947000i
$517$	2.53364	+	3.01947i	0.111429	+	0.132796i
$518$	−3.52714	−	7.41477i	−0.154974	−	0.325786i
$519$	−5.98873	−	5.17719i	−0.262876	−	0.227253i
$520$	23.3964	+	19.6319i	1.02600	+	0.860916i
$521$	5.51610	−	9.55416i	0.241665	−	0.418575i	−0.719524	−	0.694468i	$-0.755640\pi$
$521$	5.51610	−	9.55416i	0.241665	−	0.418575i	0.961189	+	0.275892i	$0.0889733\pi$
$522$	1.85898	+	0.739255i	0.0813654	+	0.0323563i
$523$	11.2904	−	6.51851i	0.493695	−	0.285035i	−0.232411	−	0.972618i	$-0.574662\pi$
$523$	11.2904	−	6.51851i	0.493695	−	0.285035i	0.726106	+	0.687583i	$0.241328\pi$
$524$	−0.254170	+	1.44147i	−0.0111035	+	0.0629708i
$525$	−46.4420	−	33.0083i	−2.02690	−	1.44060i
$526$	10.1193	+	3.68313i	0.441223	+	0.160592i
$527$	1.50046	−	4.12248i	0.0653611	−	0.179578i
$528$	4.19465	+	5.15104i	0.182549	+	0.224170i
$529$	3.55863	−	20.1820i	0.154723	−	0.877478i
$530$	−11.1833	−	19.3701i	−0.485774	−	0.841385i
$531$	−15.6366	+	12.3553i	−0.678573	+	0.536173i
$532$	6.48604	−	24.9718i	0.281206	−	1.08267i
$533$	17.4302	−	20.7725i	0.754985	−	0.899756i
$534$	−4.42008	+	5.11295i	−0.191276	+	0.221259i
$535$	32.5934	−	5.74709i	1.40913	−	0.248468i
$536$	11.0394	+	13.1563i	0.476831	+	0.568265i
$537$	0.109660	−	7.45240i	0.00473218	−	0.321595i
$538$	3.87619	+	10.6498i	0.167115	+	0.459144i
$539$	4.96820	+	8.30782i	0.213996	+	0.357843i
$540$	−28.5885	−	26.2233i	−1.23025	−	1.12847i
$541$	34.4095			1.47938			0.739689	−	0.672949i	$-0.234972\pi$
$541$	34.4095			1.47938			0.739689	+	0.672949i	$0.234972\pi$
$542$	7.56458	−	2.75328i	0.324927	−	0.118264i
$543$	−0.746481	+	0.416459i	−0.0320346	+	0.0178719i
$544$	−7.28714	−	8.68448i	−0.312434	−	0.372344i
$545$	−2.08825	−	11.8431i	−0.0894510	−	0.507302i
$546$	5.02445	+	7.28417i	0.215027	+	0.311734i
$547$	26.9501	+	22.6138i	1.15230	+	0.966896i	0.999771	−	0.0214028i	$-0.00681326\pi$
$547$	26.9501	+	22.6138i	1.15230	+	0.966896i	0.152531	+	0.988299i	$0.451258\pi$
$548$	7.97651	+	4.60524i	0.340740	+	0.196726i
$549$	−6.29140	−	1.30129i	−0.268511	−	0.0555377i
$550$	3.95746	+	6.85453i	0.168747	+	0.292278i
$551$	1.37188	−	7.78032i	0.0584441	−	0.331453i
$552$	−4.46902	−	1.70146i	−0.190214	−	0.0724191i
$553$	0.479497	−	6.01214i	0.0203903	−	0.255662i
$554$	−1.97205	+	5.41817i	−0.0837845	+	0.230196i
$555$	7.75887	+	48.1338i	0.329346	+	2.04316i
$556$	17.4851	+	3.08310i	0.741534	+	0.130752i
$557$	19.3350	−	11.1631i	0.819251	−	0.472995i	−0.0309069	−	0.999522i	$-0.509840\pi$
$557$	19.3350	−	11.1631i	0.819251	−	0.472995i	0.850158	+	0.526527i	$0.176506\pi$
$558$	2.54503	+	0.0749152i	0.107740	+	0.00317141i
$559$	−17.1497	−	9.90139i	−0.725356	−	0.418784i
$560$	−12.7345	+	27.8661i	−0.538132	+	1.17756i
$561$	5.59763	+	1.07216i	0.236332	+	0.0452667i
$562$	−1.46776	−	8.32406i	−0.0619136	−	0.351129i
$563$	14.2562	−	11.9624i	0.600826	−	0.504153i	−0.290885	−	0.956758i	$-0.593950\pi$
$563$	14.2562	−	11.9624i	0.600826	−	0.504153i	0.891711	+	0.452605i	$0.149505\pi$
$564$	−4.52586	+	7.57925i	−0.190573	+	0.319144i
$565$	9.41012	+	25.8541i	0.395887	+	1.08769i
$566$	−3.80232			−0.159823
$567$	−12.6422	−	20.1785i	−0.530924	−	0.847419i
$568$	−19.7207			−0.827464
$569$	−10.4577	−	28.7324i	−0.438411	−	1.20452i	−0.940526	−	0.339723i	$-0.889667\pi$
$569$	−10.4577	−	28.7324i	−0.438411	−	1.20452i	0.502115	−	0.864801i	$-0.332555\pi$
$570$	9.30830	−	15.5882i	0.389882	−	0.652917i
$571$	−26.3530	+	22.1128i	−1.10284	+	0.925390i	−0.997613	−	0.0690584i	$-0.978001\pi$
$571$	−26.3530	+	22.1128i	−1.10284	+	0.925390i	−0.105224	+	0.994449i	$0.533556\pi$
$572$	1.80113	+	10.2147i	0.0753090	+	0.427098i
$573$	23.3284	+	4.46830i	0.974559	+	0.186666i
$574$	−7.16092	−	3.27247i	−0.298891	−	0.136590i
$575$	17.0479	+	9.84261i	0.710947	+	0.410465i
$576$	−5.28472	+	8.56136i	−0.220197	+	0.356723i
$577$	2.61437	−	1.50941i	0.108838	−	0.0628374i	−0.444593	−	0.895733i	$-0.646652\pi$
$577$	2.61437	−	1.50941i	0.108838	−	0.0628374i	0.553431	+	0.832895i	$0.313318\pi$
$578$	5.13997	+	0.906315i	0.213794	+	0.0376977i
$579$	−0.201014	−	1.24703i	−0.00835384	−	0.0518247i
$580$	−3.69905	+	10.1631i	−0.153595	+	0.421998i
$581$	2.46112	−	30.8587i	0.102105	−	1.28023i
$582$	4.37234	+	1.66466i	0.181239	+	0.0690022i
$583$	2.79436	−	15.8476i	0.115731	−	0.656341i
$584$	7.74871	+	13.4212i	0.320644	+	0.555371i
$585$	−16.5104	−	49.8822i	−0.682622	−	2.06238i
$586$	8.88211	+	5.12809i	0.366916	+	0.211839i
$587$	−3.99771	−	3.35448i	−0.165003	−	0.138454i	0.556547	−	0.830816i	$-0.312126\pi$
$587$	−3.99771	−	3.35448i	−0.165003	−	0.138454i	−0.721550	+	0.692362i	$0.756570\pi$
$588$	−13.9245	+	16.6164i	−0.574238	+	0.685249i
$589$	−1.74599	−	9.90202i	−0.0719424	−	0.408006i
$590$	8.20721	+	9.78097i	0.337886	+	0.402676i
$591$	−30.3851	+	16.9517i	−1.24988	+	0.697301i
$592$	17.5700	−	6.39497i	0.722124	−	0.262832i
$593$	−38.2020			−1.56877			−0.784385	−	0.620274i	$-0.787021\pi$
$593$	−38.2020			−1.56877			−0.784385	+	0.620274i	$0.787021\pi$
$594$	0.430087	+	3.27970i	0.0176467	+	0.134568i
$595$	6.99820	+	25.3376i	0.286898	+	1.03874i
$596$	3.84373	+	10.5605i	0.157445	+	0.432577i
$597$	−0.200600	+	13.6326i	−0.00820999	+	0.557944i
$598$	−1.96516	−	2.34199i	−0.0803616	−	0.0957712i
$599$	−13.2464	+	2.33569i	−0.541231	+	0.0954337i	−0.437579	−	0.899180i	$-0.644164\pi$
$599$	−13.2464	+	2.33569i	−0.541231	+	0.0954337i	−0.103652	+	0.994614i	$0.533053\pi$
$600$	−24.5595	+	28.4093i	−1.00264	+	1.15980i
$601$	−7.32851	+	8.73377i	−0.298936	+	0.356258i	−0.894514	−	0.447039i	$-0.852478\pi$
$601$	−7.32851	+	8.73377i	−0.298936	+	0.356258i	0.595578	+	0.803297i	$0.296923\pi$
$602$	−1.44543	+	5.56505i	−0.0589115	+	0.226814i
$603$	−4.27231	−	29.2358i	−0.173982	−	1.19057i
$604$	8.49185	+	14.7083i	0.345528	+	0.598473i
$605$	6.58894	−	37.3678i	0.267879	−	1.51922i
$606$	−2.38831	−	2.93286i	−0.0970186	−	0.119139i
$607$	−6.95549	+	19.1101i	−0.282315	+	0.775654i	0.714771	+	0.699359i	$0.246531\pi$
$607$	−6.95549	+	19.1101i	−0.282315	+	0.775654i	−0.997085	+	0.0762945i	$0.975691\pi$
$608$	−24.4160	−	8.88671i	−0.990201	−	0.360404i
$609$	−3.84582	+	5.41099i	−0.155840	+	0.219264i
$610$	−0.714762	+	4.05361i	−0.0289399	+	0.164126i
$611$	−10.3547	+	5.97826i	−0.418904	+	0.241855i
$612$	1.84569	+	12.6302i	0.0746075	+	0.510546i
$613$	−15.2811	+	26.4677i	−0.617199	+	1.06902i	0.372796	+	0.927913i	$0.378399\pi$
$613$	−15.2811	+	26.4677i	−0.617199	+	1.06902i	−0.989994	+	0.141106i	$0.954934\pi$
$614$	6.93583	+	5.81985i	0.279907	+	0.234870i
$615$	35.3665	+	30.5739i	1.42611	+	1.23286i
$616$	5.76141	−	2.74065i	0.232134	−	0.110424i
$617$	10.8908	+	12.9791i	0.438446	+	0.522519i	0.939339	−	0.342990i	$-0.111440\pi$
$617$	10.8908	+	12.9791i	0.438446	+	0.522519i	−0.500894	+	0.865509i	$0.666995\pi$
$618$	11.1434	+	0.163972i	0.448253	+	0.00659592i
$619$	−11.9681	−	32.8822i	−0.481040	−	1.32165i	−0.908603	−	0.417661i	$-0.862850\pi$
$619$	−11.9681	−	32.8822i	−0.481040	−	1.32165i	0.427563	−	0.903985i	$-0.359372\pi$
$620$			13.7646i			0.552802i
$621$	5.00484	+	6.52929i	0.200837	+	0.262011i
$622$		−	7.67930i		−	0.307912i
$623$	−13.0043	−	18.2718i	−0.521008	−	0.732045i
$624$	−17.5972	+	9.81742i	−0.704453	+	0.393011i
$625$	51.6495	−	43.3391i	2.06598	−	1.73356i
$626$	0.869350	+	4.93033i	0.0347462	+	0.197056i
$627$	12.3392	−	4.28657i	0.492779	−	0.171189i
$628$	11.3393	−	13.5136i	0.452486	−	0.539252i
$629$	8.02096	−	13.8927i	0.319817	−	0.553939i
$630$	−12.6842	+	8.47662i	−0.505353	+	0.337717i
$631$	8.12831	+	14.0786i	0.323583	+	0.560462i	0.981225	−	0.192869i	$-0.0617792\pi$
$631$	8.12831	+	14.0786i	0.323583	+	0.560462i	−0.657642	+	0.753331i	$0.728446\pi$
$632$	−3.91476	−	0.690278i	−0.155721	−	0.0274578i
$633$	−28.1635	−	10.7225i	−1.11940	−	0.426182i
$634$	−12.2737	−	4.46726i	−0.487450	−	0.177417i
$635$	33.9271	+	12.3485i	1.34636	+	0.490034i
$636$	35.5806	−	5.73538i	1.41086	−	0.227423i
$637$	−27.4350	+	10.4655i	−1.08701	+	0.414657i
$638$	0.798625	−	0.461087i	0.0316179	−	0.0182546i
$639$	28.8700	+	17.8208i	1.14208	+	0.704978i
$640$	40.0375	+	23.1157i	1.58262	+	0.913727i
$641$	17.7198	−	21.1176i	0.699889	−	0.834095i	−0.292625	−	0.956227i	$-0.594529\pi$
$641$	17.7198	−	21.1176i	0.699889	−	0.834095i	0.992514	+	0.122132i	$0.0389731\pi$
$642$	1.18893	−	6.20725i	0.0469233	−	0.244981i
$643$	−14.1593	+	2.49667i	−0.558390	+	0.0984592i	−0.445719	−	0.895173i	$-0.647052\pi$
$643$	−14.1593	+	2.49667i	−0.558390	+	0.0984592i	−0.112671	+	0.993632i	$0.535941\pi$
$644$	4.24889	−	6.16833i	0.167430	−	0.243066i
$645$	17.5035	−	29.3123i	0.689200	−	1.15417i
$646$	−5.61357	+	2.04317i	−0.220863	+	0.0803876i
$647$	22.9189			0.901035			0.450518	−	0.892768i	$-0.351239\pi$
$647$	22.9189			0.901035			0.450518	+	0.892768i	$0.351239\pi$
$648$	−14.0296	+	7.03405i	−0.551135	+	0.276323i
$649$			9.18625i			0.360592i
$650$	−22.5611	+	8.21158i	−0.884921	+	0.322085i
$651$	−2.24405	+	8.14531i	−0.0879512	+	0.319240i
$652$	−0.582228	+	0.488547i	−0.0228018	+	0.0191330i
$653$	−26.7113	+	4.70992i	−1.04529	+	0.184313i	−0.669823	−	0.742521i	$-0.733630\pi$
$653$	−26.7113	+	4.70992i	−1.04529	+	0.184313i	−0.375470	+	0.926834i	$0.622519\pi$
$654$	−2.25546	−	0.432007i	−0.0881953	−	0.0168928i
$655$	−2.61824	−	2.19697i	−0.102303	−	0.0858426i
$656$	8.96431	−	15.5266i	0.349998	−	0.606214i
$657$	0.784462	−	26.6499i	0.0306048	−	1.03971i
$658$	2.47354	+	2.43583i	0.0964285	+	0.0949586i
$659$	2.75685	+	0.486108i	0.107392	+	0.0189361i	0.227086	−	0.973875i	$-0.427080\pi$
$659$	2.75685	+	0.486108i	0.107392	+	0.0189361i	−0.119694	+	0.992811i	$0.538191\pi$
$660$	−17.6543	+	2.84576i	−0.687192	+	0.110771i
$661$	9.01985	−	24.7818i	0.350832	−	0.963902i	−0.631272	−	0.775561i	$-0.717467\pi$
$661$	9.01985	−	24.7818i	0.350832	−	0.963902i	0.982104	−	0.188341i	$-0.0603109\pi$
$662$	0.141737	−	0.389418i	0.00550875	−	0.0151352i
$663$	−6.15139	+	16.1571i	−0.238900	+	0.627489i
$664$	−20.0934	−	3.54300i	−0.779774	−	0.137495i
$665$	42.9264	+	42.2720i	1.66461	+	1.63924i
$666$	9.11735	+	1.88580i	0.353290	+	0.0730732i
$667$	1.14677	−	1.98626i	0.0444031	−	0.0769084i
$668$	−12.6696	−	10.6311i	−0.490202	−	0.411328i
$669$	3.24144	+	9.33069i	0.125321	+	0.360746i
$670$	−18.6424	+	3.28716i	−0.720219	+	0.126994i
$671$	−2.26859	+	1.90357i	−0.0875778	+	0.0734865i
$672$	15.3292	+	15.5464i	0.591336	+	0.599714i
$673$	−27.5049	+	10.0110i	−1.06024	+	0.385895i	−0.812518	−	0.582937i	$-0.801904\pi$
$673$	−27.5049	+	10.0110i	−1.06024	+	0.385895i	−0.247720	+	0.968832i	$0.579681\pi$
$674$		−	10.1802i		−	0.392126i
$675$	61.6258	−	19.3962i	2.37198	−	0.746558i
$676$	−8.21802			−0.316078
$677$	−40.9538	+	14.9060i	−1.57398	+	0.572883i	−0.973885	−	0.227043i	$-0.927094\pi$
$677$	−40.9538	+	14.9060i	−1.57398	+	0.572883i	−0.600099	+	0.799926i	$0.704872\pi$
$678$	5.25342	+	0.0773026i	0.201756	+	0.00296879i
$679$	−8.80660	+	12.7850i	−0.337966	+	0.490643i
$680$	17.0620	−	3.00848i	0.654296	−	0.115370i
$681$	9.49375	+	8.20724i	0.363801	+	0.314502i
$682$	0.754408	−	0.899069i	0.0288878	−	0.0344271i
$683$	−41.6692	−	24.0577i	−1.59443	−	0.920542i	−0.992534	−	0.121965i	$-0.961081\pi$
$683$	−41.6692	−	24.0577i	−1.59443	−	0.920542i	−0.601892	−	0.798578i	$-0.705586\pi$
$684$	18.1372	+	22.9542i	0.693492	+	0.877674i
$685$	−18.6258	+	10.7536i	−0.711656	+	0.410875i
$686$	5.04966	+	6.86923i	0.192797	+	0.262268i
$687$	31.3920	+	38.5495i	1.19768	+	1.47075i
$688$	−12.3034	−	4.47807i	−0.469062	−	0.170725i
$689$	45.8697	+	16.6952i	1.74750	+	0.636037i
$690$	4.08708	−	3.32824i	0.155593	−	0.126704i
$691$	2.19447	+	0.386945i	0.0834817	+	0.0147201i	0.215233	−	0.976563i	$-0.430949\pi$
$691$	2.19447	+	0.386945i	0.0834817	+	0.0147201i	−0.131751	+	0.991283i	$0.542060\pi$
$692$	−4.08622	−	7.07754i	−0.155335	−	0.269048i
$693$	−10.9110	−	1.19418i	−0.414473	−	0.0453631i
$694$	−6.22872	+	10.7885i	−0.236439	+	0.409524i
$695$	−26.6494	+	31.7595i	−1.01087	+	1.20471i
$696$	3.30999	+	2.86144i	0.125465	+	0.108463i
$697$	−2.67108	−	15.1484i	−0.101174	−	0.573788i
$698$	3.73007	−	3.12990i	0.141185	−	0.118468i
$699$	0.568899	−	38.6619i	0.0215178	−	1.46233i
$700$	−34.1072	−	47.9226i	−1.28913	−	1.81130i
$701$		−	21.8097i		−	0.823740i	−0.911243	−	0.411870i	$-0.864876\pi$
$701$		−	21.8097i		−	0.823740i	0.911243	−	0.411870i	$-0.135124\pi$
$702$	−10.0240	−	0.442758i	−0.378332	−	0.0167108i
$703$		−	36.7668i		−	1.38669i
$704$	1.58618	+	4.35800i	0.0597815	+	0.164248i
$705$	−10.0430	−	18.0015i	−0.378239	−	0.677975i
$706$	0.229138	+	0.273076i	0.00862371	+	0.0102773i
$707$	11.3337	−	5.39134i	0.426247	−	0.202762i
$708$	−19.4343	+	6.75137i	−0.730385	+	0.253732i
$709$	−30.0452	−	25.2109i	−1.12837	−	0.946817i	−0.129375	−	0.991596i	$-0.541297\pi$
$709$	−30.0452	−	25.2109i	−1.12837	−	0.946817i	−0.998997	+	0.0447792i	$0.985742\pi$
$710$	10.8684	−	18.8246i	0.407883	−	0.706474i
$711$	5.10720	+	4.54812i	0.191535	+	0.170568i
$712$	−12.8012	+	7.39077i	−0.479745	+	0.276981i
$713$	0.506877	−	2.87464i	0.0189827	−	0.107656i
$714$	4.99736	+	0.472653i	0.187022	+	0.0176886i
$715$	−22.7595	−	8.28378i	−0.851157	−	0.309796i
$716$	2.63162	−	7.23032i	0.0983483	−	0.270210i
$717$	−25.9480	+	4.18267i	−0.969047	+	0.156205i
$718$	0.195022	−	1.10603i	0.00727816	−	0.0412765i
$719$	0.795849	+	1.37845i	0.0296802	+	0.0514075i	0.880484	−	0.474076i	$-0.157218\pi$
$719$	0.795849	+	1.37845i	0.0296802	+	0.0514075i	−0.850804	+	0.525483i	$0.823884\pi$
$720$	−16.4774	−	30.5839i	−0.614075	−	1.13980i
$721$	−9.29672	+	35.7932i	−0.346228	+	1.33301i
$722$	−3.17869	+	3.78821i	−0.118298	+	0.140983i
$723$	−12.0712	−	2.31210i	−0.448933	−	0.0859879i
$724$	−0.869043	+	0.153236i	−0.0322977	+	0.00569496i
$725$	−11.5776	−	13.7976i	−0.429980	−	0.512430i
$726$	−6.22113	−	3.71487i	−0.230888	−	0.137872i
$727$	1.90536	+	5.23493i	0.0706659	+	0.194153i	0.969998	−	0.243114i	$-0.0781688\pi$
$727$	1.90536	+	5.23493i	0.0706659	+	0.194153i	−0.899332	+	0.437267i	$0.855947\pi$
$728$	5.15239	+	18.6547i	0.190960	+	0.691390i
$729$	26.8949	+	2.38052i	0.996106	+	0.0881674i
$730$	−17.0817			−0.632222
$731$	−10.5559	+	3.84202i	−0.390423	+	0.142102i
$732$	−5.69444	−	3.40037i	−0.210473	−	0.125681i
$733$	10.0493	+	11.9762i	0.371178	+	0.442352i	0.919009	−	0.394236i	$-0.128991\pi$
$733$	10.0493	+	11.9762i	0.371178	+	0.442352i	−0.547831	+	0.836589i	$0.684546\pi$
$734$	−2.62088	−	14.8638i	−0.0967385	−	0.548631i
$735$	−17.3449	−	47.5591i	−0.639778	−	1.75425i
$736$	−5.77834	−	4.84860i	−0.212993	−	0.178722i
$737$	−11.7948	−	6.80975i	−0.434468	−	0.250840i
$738$	7.85935	−	4.23429i	0.289307	−	0.155866i
$739$	−2.30238	−	3.98783i	−0.0846943	−	0.146695i	0.820567	−	0.571551i	$-0.193658\pi$
$739$	−2.30238	−	3.98783i	−0.0846943	−	0.146695i	−0.905261	+	0.424856i	$0.860325\pi$
$740$	−8.74015	+	49.5678i	−0.321294	+	1.82215i
$741$	6.30572	+	39.1188i	0.231646	+	1.43707i
$742$	1.12678	−	14.1280i	0.0413654	−	0.518657i
$743$	6.72183	−	18.4681i	0.246600	−	0.677528i	−0.753205	−	0.657786i	$-0.771493\pi$
$743$	6.72183	−	18.4681i	0.246600	−	0.677528i	0.999805	−	0.0197424i	$-0.00628462\pi$
$744$	5.20413	+	1.98134i	0.190793	+	0.0726393i
$745$	−25.8437	−	4.55694i	−0.946840	−	0.166953i
$746$	−10.1307	+	5.84896i	−0.370911	+	0.214146i
$747$	26.2138	+	23.3442i	0.959114	+	0.854121i
$748$	5.09550	+	2.94189i	0.186310	+	0.107566i
$749$	19.0744	+	8.71682i	0.696963	+	0.318506i
$750$	−8.12086	−	23.3764i	−0.296532	−	0.853587i
$751$	−2.66294	−	15.1023i	−0.0971722	−	0.551091i	−0.994060	−	0.108833i	$-0.965289\pi$
$751$	−2.66294	−	15.1023i	−0.0971722	−	0.551091i	0.896888	−	0.442258i	$-0.145822\pi$
$752$	−6.05580	+	5.08142i	−0.220832	+	0.185300i
$753$	12.0841	+	21.6601i	0.440368	+	0.789336i
$754$	0.956737	+	2.62861i	0.0348423	+	0.0957284i
$755$	−39.6584			−1.44332
$756$	−5.49255	−	23.9607i	−0.199762	−	0.871442i
$757$	13.1222			0.476934			0.238467	−	0.971151i	$-0.423355\pi$
$757$	13.1222			0.476934			0.238467	+	0.971151i	$0.423355\pi$
$758$	−2.94589	−	8.09378i	−0.107000	−	0.293979i
$759$	3.79176	+	0.0557947i	0.137632	+	0.00202522i
$760$	30.4180	−	25.5237i	1.10338	−	0.925843i
$761$	−7.30569	−	41.4326i	−0.264831	−	1.50193i	−0.769515	−	0.638628i	$-0.779502\pi$
$761$	−7.30569	−	41.4326i	−0.264831	−	1.50193i	0.504684	−	0.863304i	$-0.331609\pi$
$762$	4.50897	−	5.21576i	0.163343	−	0.188947i
$763$	3.16733	−	6.93084i	0.114665	−	0.250913i
$764$	21.2358	+	12.2605i	0.768284	+	0.443569i
$765$	−27.6963	−	11.0139i	−1.00136	−	0.398208i
$766$	4.30061	−	2.48296i	0.155387	−	0.0897129i
$767$	−27.4421	−	4.83879i	−0.990879	−	0.174719i
$768$	−2.16275	+	1.76119i	−0.0780414	+	0.0635515i
$769$	−11.9091	+	32.7199i	−0.429452	+	1.17991i	0.516694	+	0.856170i	$0.327162\pi$
$769$	−11.9091	+	32.7199i	−0.429452	+	1.17991i	−0.946146	+	0.323740i	$0.895060\pi$
$770$	−0.559082	+	7.01001i	−0.0201479	+	0.252623i
$771$	12.5428	−	10.2140i	0.451718	−	0.367848i
$772$	0.226436	−	1.28418i	0.00814961	−	0.0462187i
$773$	24.5173	+	42.4653i	0.881827	+	1.52737i	0.849307	+	0.527899i	$0.177020\pi$
$773$	24.5173	+	42.4653i	0.881827	+	1.52737i	0.0325201	+	0.999471i	$0.489647\pi$
$774$	−4.04192	−	5.11540i	−0.145284	−	0.183869i
$775$	−19.8521	−	11.4616i	−0.713109	−	0.411714i
$776$	7.83829	+	6.57711i	0.281378	+	0.236104i
$777$	−13.2531	+	27.9071i	−0.475451	+	1.00116i
$778$	0.403966	+	2.29101i	0.0144829	+	0.0821366i
$779$	−22.6612	−	27.0066i	−0.811923	−	0.967613i
$780$	0.798093	−	54.2377i	0.0285763	−	1.94202i
$781$	14.6957	−	5.34881i	0.525854	−	0.191395i
$782$	−1.73426			−0.0620169
$783$	−2.25986	−	7.18007i	−0.0807608	−	0.256595i
$784$	−16.6620	+	9.96415i	−0.595072	+	0.355862i
$785$	14.0887	+	38.7085i	0.502848	+	1.38156i
$786$	−0.569979	+	0.317989i	−0.0203305	+	0.0113423i
$787$	−12.1134	−	14.4362i	−0.431798	−	0.514596i	0.505642	−	0.862743i	$-0.331256\pi$
$787$	−12.1134	−	14.4362i	−0.431798	−	0.514596i	−0.937440	+	0.348147i	$0.886811\pi$
$788$	−35.3739	+	6.23738i	−1.26014	+	0.222197i
$789$	−13.2963	−	38.2744i	−0.473362	−	1.36260i
$790$	2.81639	−	3.35644i	0.100203	−	0.119417i
$791$	−4.38282	+	16.8743i	−0.155835	+	0.599979i
$792$	−1.46530	+	7.08435i	−0.0520672	+	0.251731i
$793$	−4.49158	−	7.77965i	−0.159501	−	0.276264i
$794$	−1.64331	+	9.31967i	−0.0583189	+	0.330743i
$795$	−29.9435	+	78.6489i	−1.06199	+	2.78939i
$796$	−4.81399	+	13.2263i	−0.170627	+	0.468795i
$797$	18.9831	+	6.90930i	0.672418	+	0.244740i	0.655588	−	0.755118i	$-0.272421\pi$
$797$	18.9831	+	6.90930i	0.672418	+	0.244740i	0.0168292	+	0.999858i	$0.494643\pi$
$798$	10.4607	−	4.78863i	0.370305	−	0.169516i
$799$	−1.17776	+	6.67941i	−0.0416662	+	0.236301i
$800$	−51.3007	+	29.6185i	−1.81375	+	1.04717i
$801$	25.4189	+	0.748226i	0.898132	+	0.0264373i
$802$	7.01124	−	12.1438i	0.247576	−	0.428813i
$803$	−9.41445	−	7.89966i	−0.332229	−	0.278773i
$804$	5.73806	−	29.9577i	0.202366	−	1.05653i
$805$	7.51311	+	15.7941i	0.264802	+	0.556668i
$806$	2.28841	+	2.72723i	0.0806060	+	0.0960624i
$807$	21.8621	−	36.6114i	0.769581	−	1.28878i
$808$	−2.82921	−	7.77320i	−0.0995313	−	0.273460i
$809$			21.6939i			0.762716i	0.924428	+	0.381358i	$0.124543\pi$
$809$			21.6939i			0.762716i	−0.924428	+	0.381358i	$0.875457\pi$
$810$	1.01752	−	17.2686i	0.0357518	−	0.606758i
$811$			15.5791i			0.547057i	0.961864	+	0.273529i	$0.0881908\pi$
$811$			15.5791i			0.547057i	−0.961864	+	0.273529i	$0.911809\pi$
$812$	−5.58349	+	3.97385i	−0.195942	+	0.139455i
$813$	−26.0053	−	15.5287i	−0.912045	−	0.544617i
$814$	3.28758	−	2.75861i	0.115230	−	0.0966891i
$815$	−0.308185	−	1.74780i	−0.0107953	−	0.0612229i
$816$	−2.15031	+	11.2265i	−0.0752759	+	0.393006i
$817$	−16.5491	+	19.7225i	−0.578981	+	0.690003i
$818$	−0.223209	+	0.386610i	−0.00780434	+	0.0135175i
$819$	9.31464	−	31.9654i	0.325480	−	1.11696i
$820$	24.1312	+	41.7965i	0.842698	+	1.45960i
$821$	39.3325	+	6.93539i	1.37271	+	0.242047i	0.810885	−	0.585206i	$-0.198986\pi$
$821$	39.3325	+	6.93539i	1.37271	+	0.242047i	0.561830	+	0.827253i	$0.310098\pi$
$822$	0.653595	+	4.05471i	0.0227968	+	0.141424i
$823$	47.2385	+	17.1934i	1.64663	+	0.599324i	0.988180	−	0.153301i	$-0.0489904\pi$
$823$	47.2385	+	17.1934i	1.64663	+	0.599324i	0.658449	+	0.752625i	$0.271213\pi$
$824$	22.9039	+	8.33635i	0.797896	+	0.290410i
$825$	10.5961	−	27.8316i	0.368911	−	0.968971i
$826$	0.767030	+	8.05425i	0.0266884	+	0.280243i
$827$	−29.4328	+	16.9930i	−1.02348	+	0.590905i	−0.915109	−	0.403206i	$-0.867896\pi$
$827$	−29.4328	+	16.9930i	−1.02348	+	0.590905i	−0.108368	+	0.994111i	$0.534563\pi$
$828$	2.66869	+	8.06278i	0.0927432	+	0.280201i
$829$	−11.4272	−	6.59749i	−0.396883	−	0.229140i	0.288255	−	0.957554i	$-0.406925\pi$
$829$	−11.4272	−	6.59749i	−0.396883	−	0.229140i	−0.685138	+	0.728413i	$0.740258\pi$
$830$	14.4557	−	17.2277i	0.501766	−	0.597982i
$831$	20.4932	−	7.11923i	0.710901	−	0.246963i
$832$	−13.8542	+	2.44287i	−0.480307	+	0.0846912i
$833$	−5.45582	+	15.7378i	−0.189033	+	0.545281i
$834$	3.85723	+	6.91388i	0.133565	+	0.239408i
$835$	36.2909	−	13.2088i	1.25590	−	0.457110i
$836$	13.4852			0.466394
$837$	−5.82808	−	7.60329i	−0.201448	−	0.262808i
$838$			15.9972i			0.552613i
$839$	0.902087	−	0.328333i	0.0311435	−	0.0113353i	−0.326401	−	0.945231i	$-0.605836\pi$
$839$	0.902087	−	0.328333i	0.0311435	−	0.0113353i	0.357545	+	0.933896i	$0.383614\pi$
$840$	−32.2886	+	8.40874i	−1.11406	+	0.290129i
$841$	20.6077	−	17.2919i	0.710611	−	0.596274i
$842$	4.28139	−	0.754924i	0.147546	−	0.0260164i
$843$	−20.7988	+	24.0591i	−0.716349	+	0.828639i
$844$	−23.8321	−	19.9975i	−0.820336	−	0.688343i
$845$	9.59488	−	16.6188i	0.330074	−	0.571705i
$846$	−3.89500	+	0.569187i	−0.133913	+	0.0195690i
$847$	16.8704	−	17.1316i	0.579675	−	0.588649i
$848$	31.7837	+	5.60432i	1.09146	+	0.192453i
$849$	9.03378	+	11.0935i	0.310039	+	0.380728i
$850$	−4.65810	+	12.7980i	−0.159772	+	0.438969i
$851$	3.65063	−	10.0300i	0.125142	−	0.343825i
$852$	22.1163	+	27.1589i	0.757694	+	0.930450i
$853$	18.8229	+	3.31898i	0.644483	+	0.113640i	0.486331	−	0.873775i	$-0.338335\pi$
$853$	18.8229	+	3.31898i	0.644483	+	0.113640i	0.158153	+	0.987415i	$0.449446\pi$
$854$	−1.83009	+	1.85842i	−0.0626243	+	0.0635937i
$855$	−67.5948	+	9.87781i	−2.31169	+	0.337814i
$856$	6.91119	−	11.9705i	0.236220	−	0.409144i
$857$	18.3633	+	15.4086i	0.627277	+	0.526348i	0.900082	−	0.435722i	$-0.143507\pi$
$857$	18.3633	+	15.4086i	0.627277	+	0.526348i	−0.272804	+	0.962070i	$0.587951\pi$
$858$	−3.02477	+	3.49892i	−0.103264	+	0.119451i
$859$	−36.0276	+	6.35264i	−1.22925	+	0.216749i	−0.750301	−	0.661096i	$-0.770092\pi$
$859$	−36.0276	+	6.35264i	−1.22925	+	0.216749i	−0.478944	+	0.877845i	$0.658980\pi$
$860$	26.9994	−	22.6552i	0.920673	−	0.772536i
$861$	7.46570	+	28.6674i	0.254430	+	0.976982i
$862$	14.7090	−	5.35362i	0.500989	−	0.182345i
$863$		−	2.63865i		−	0.0898208i	−0.998991	−	0.0449104i	$-0.985700\pi$
$863$		−	2.63865i		−	0.0898208i	0.998991	−	0.0449104i	$-0.0143002\pi$
$864$	−24.5460	+	3.21886i	−0.835071	+	0.109508i
$865$	19.0833			0.648853
$866$	15.6701	−	5.70345i	0.532492	−	0.193811i
$867$	−9.56762	−	17.1495i	−0.324933	−	0.582427i
$868$	−4.94779	+	7.18296i	−0.167939	+	0.243806i
$869$	3.10447	−	0.547401i	0.105312	−	0.0185693i
$870$	−4.55559	+	1.58259i	−0.154449	+	0.0536548i
$871$	26.5556	−	31.6478i	0.899803	−	1.07234i
$872$	−4.34959	−	2.51124i	−0.147296	−	0.0850413i
$873$	−5.53134	−	16.7116i	−0.187208	−	0.565602i
$874$	−3.44226	+	1.98739i	−0.116436	+	0.0672245i
$875$	81.7469	−	7.78500i	2.76355	−	0.263181i
$876$	9.79330	−	25.7228i	0.330885	−	0.869094i
$877$	−6.60150	−	2.40275i	−0.222917	−	0.0811351i	0.228147	−	0.973627i	$-0.426733\pi$
$877$	−6.60150	−	2.40275i	−0.222917	−	0.0811351i	−0.451064	+	0.892492i	$0.648955\pi$
$878$	−16.7796	−	6.10728i	−0.566284	−	0.206111i
$879$	−6.14113	−	38.0977i	−0.207135	−	1.28501i
$880$	−15.7703	−	2.78074i	−0.531618	−	0.0937386i
$881$	2.09355	+	3.62614i	0.0705336	+	0.122168i	0.899135	−	0.437671i	$-0.144196\pi$
$881$	2.09355	+	3.62614i	0.0705336	+	0.122168i	−0.828602	+	0.559839i	$0.810863\pi$
$882$	−9.66613	−	0.135983i	−0.325476	−	0.00457878i
$883$	−18.5670	+	32.1591i	−0.624831	+	1.08224i	0.363743	+	0.931500i	$0.381499\pi$
$883$	−18.5670	+	32.1591i	−0.624831	+	1.08224i	−0.988574	+	0.150739i	$0.951835\pi$
$884$	−11.4723	+	13.6722i	−0.385857	+	0.459846i
$885$	9.03743	−	47.1833i	0.303790	−	1.58605i
$886$	−1.01358	−	5.74833i	−0.0340520	−	0.193119i
$887$	−16.9146	+	14.1930i	−0.567937	+	0.476555i	−0.880960	−	0.473190i	$-0.843102\pi$
$887$	−16.9146	+	14.1930i	−0.567937	+	0.476555i	0.313024	+	0.949745i	$0.398658\pi$
$888$	17.4825	+	10.4395i	0.586674	+	0.350325i
$889$	13.2658	+	18.6393i	0.444922	+	0.625141i
$890$		−	16.2926i		−	0.546130i
$891$	8.54692	−	9.04692i	0.286333	−	0.303083i
$892$			10.1973i			0.341430i
$893$	5.31665	+	14.6074i	0.177915	+	0.488817i
$894$	−2.56922	+	4.30256i	−0.0859276	+	0.143899i
$895$	11.5489	+	13.7635i	0.386038	+	0.460063i
$896$	12.5841	+	26.4544i	0.420407	+	0.883780i
$897$	−2.16396	+	11.2977i	−0.0722524	+	0.377221i
$898$	−6.09468	−	5.11404i	−0.203382	−	0.170658i
$899$	−1.33540	+	2.31298i	−0.0445381	+	0.0771423i
$900$	66.6675	+	1.96241i	2.22225	+	0.0654138i
$901$	23.9802	−	13.8450i	0.798897	−	0.461243i
$902$	0.714583	−	4.05260i	0.0237930	−	0.134937i
$903$	19.6705	−	9.00463i	0.654595	−	0.299655i
$904$	10.7978	+	3.93007i	0.359129	+	0.130712i
$905$	0.704764	−	1.93632i	0.0234272	−	0.0643656i
$906$	−2.69462	+	7.07761i	−0.0895226	+	0.235138i
$907$	−7.80605	+	44.2703i	−0.259196	+	1.46997i	0.525873	+	0.850563i	$0.323739\pi$
$907$	−7.80605	+	44.2703i	−0.259196	+	1.46997i	−0.785069	+	0.619408i	$0.787373\pi$
$908$	6.47776	+	11.2198i	0.214972	+	0.372343i
$909$	−2.88250	+	13.9361i	−0.0956064	+	0.462232i
$910$	−20.6466	−	5.36262i	−0.684427	−	0.177769i
$911$	−17.2752	+	20.5878i	−0.572353	+	0.682103i	−0.972112	−	0.234517i	$-0.924649\pi$
$911$	−17.2752	+	20.5878i	−0.572353	+	0.682103i	0.399759	+	0.916620i	$0.369094\pi$
$912$	8.59707	+	24.7472i	0.284677	+	0.819463i
$913$	15.9344	−	2.80966i	0.527350	−	0.0929861i
$914$	−10.7904	−	12.8595i	−0.356916	−	0.425356i
$915$	13.5249	−	7.54547i	0.447118	−	0.249445i
$916$	17.5534	+	48.2277i	0.579982	+	1.59349i
$917$	−0.576594	−	2.08761i	−0.0190408	−	0.0689390i
$918$	−3.84743	+	4.19446i	−0.126984	+	0.138438i
$919$	18.6916			0.616578			0.308289	−	0.951293i	$-0.400244\pi$
$919$	18.6916			0.616578			0.308289	+	0.951293i	$0.400244\pi$
$920$	10.8323	−	3.94265i	0.357132	−	0.129985i
$921$	0.501227	−	34.0629i	0.0165160	−	1.12241i
$922$	2.87998	+	3.43223i	0.0948471	+	0.113034i
$923$	8.23765	+	46.7181i	0.271146	+	1.53774i
$924$	−10.2357	−	4.86090i	−0.336728	−	0.159912i
$925$	−64.2116	−	53.8799i	−2.11126	−	1.77156i
$926$	−8.33689	−	4.81331i	−0.273967	−	0.158175i
$927$	−25.9968	−	32.9012i	−0.853846	−	1.08062i
$928$	3.45087	+	5.97708i	0.113280	+	0.196207i
$929$	−4.56421	+	25.8849i	−0.149747	+	0.849256i	0.813686	+	0.581305i	$0.197458\pi$
$929$	−4.56421	+	25.8849i	−0.149747	+	0.849256i	−0.963432	+	0.267951i	$0.913653\pi$
$930$	−4.75937	+	3.87570i	−0.156066	+	0.127089i
$931$	7.20581	+	37.4894i	0.236161	+	1.22867i
$932$	13.6524	−	37.5098i	0.447201	−	1.22867i
$933$	−22.4049	+	18.2450i	−0.733502	+	0.597313i
$934$	−6.12917	−	1.08074i	−0.200553	−	0.0353628i
$935$	−11.8984	+	6.86956i	−0.389120	+	0.224659i
$936$	−20.3913	−	8.10893i	−0.666509	−	0.265049i
$937$	−46.8366	−	27.0411i	−1.53009	−	0.883396i	−0.999357	−	0.0358542i	$-0.988585\pi$
$937$	−46.8366	−	27.0411i	−1.53009	−	0.883396i	−0.530729	−	0.847541i	$-0.678082\pi$
$938$	−10.9100	−	4.98575i	−0.356223	−	0.162791i
$939$	12.3191	−	14.2502i	0.402019	−	0.465037i
$940$	−3.69530	−	20.9571i	−0.120527	−	0.683544i
$941$	12.2779	−	10.3024i	0.400249	−	0.335849i	−0.420341	−	0.907366i	$-0.638090\pi$
$941$	12.2779	−	10.3024i	0.400249	−	0.335849i	0.820590	+	0.571518i	$0.193645\pi$
$942$	7.86536	+	0.115737i	0.256267	+	0.00377090i
$943$	−3.50048	−	9.61750i	−0.113991	−	0.313189i
$944$	−18.4238			−0.599643
$945$	54.8671	+	16.8679i	1.78483	+	0.548711i
$946$	−3.00521			−0.0977077
$947$	8.01520	+	22.0216i	0.260459	+	0.715605i	0.999137	+	0.0415463i	$0.0132284\pi$
$947$	8.01520	+	22.0216i	0.260459	+	0.715605i	−0.738678	+	0.674059i	$0.764549\pi$
$948$	3.43968	+	6.16545i	0.111716	+	0.200244i
$949$	28.5577	−	23.9628i	0.927022	−	0.777864i
$950$	5.42035	+	30.7403i	0.175859	+	0.997348i
$951$	16.1271	+	46.4229i	0.522956	+	1.50536i
$952$	9.98504	+	4.56307i	0.323617	+	0.147890i
$953$	1.12625	+	0.650242i	0.0364829	+	0.0210634i	0.518131	−	0.855302i	$-0.326628\pi$
$953$	1.12625	+	0.650242i	0.0364829	+	0.0210634i	−0.481648	+	0.876365i	$0.659961\pi$
$954$	12.0015	+	10.6877i	0.388563	+	0.346027i
$955$	−49.5874	+	28.6293i	−1.60461	+	0.926422i
$956$	−26.7211	−	4.71165i	−0.864223	−	0.152386i
$957$	−3.24267	−	1.23456i	−0.104821	−	0.0399078i
$958$	−1.50052	+	4.12265i	−0.0484797	+	0.133197i
$959$	−13.5852	−	1.08348i	−0.438688	−	0.0349875i
$960$	−3.85970	−	23.9445i	−0.124571	−	0.772804i
$961$	4.79284	−	27.1815i	0.154608	−	0.876824i
$962$	6.50909	+	11.2741i	0.209862	+	0.363491i
$963$	−20.9348	+	11.2788i	−0.674614	+	0.363454i
$964$	−10.9884	−	6.34414i	−0.353912	−	0.204331i
$965$	2.33255	+	1.95725i	0.0750876	+	0.0630060i
$966$	3.32916	−	0.267683i	0.107114	−	0.00861257i
$967$	−4.85865	−	27.5548i	−0.156244	−	0.886102i	−0.957640	−	0.287968i	$-0.907020\pi$
$967$	−4.85865	−	27.5548i	−0.156244	−	0.886102i	0.801396	−	0.598134i	$-0.204091\pi$
$968$	−10.1863	−	12.1396i	−0.327401	−	0.390181i
$969$	19.2982	+	11.5237i	0.619947	+	0.370194i
$970$	−10.5980	+	3.85736i	−0.340282	+	0.123852i
$971$	−21.5459			−0.691440			−0.345720	−	0.938338i	$-0.612365\pi$
$971$	−21.5459			−0.691440			−0.345720	+	0.938338i	$0.612365\pi$
$972$	25.4210	+	11.4327i	0.815379	+	0.366705i
$973$	−25.3229	+	6.99412i	−0.811814	+	0.224221i
$974$	2.54141	+	6.98248i	0.0814322	+	0.223733i
$975$	77.5600	+	46.3140i	2.48391	+	1.48324i
$976$	−3.81777	−	4.54984i	−0.122204	−	0.145637i
$977$	43.2803	−	7.63149i	1.38466	−	0.244153i	0.568835	−	0.822451i	$-0.307394\pi$
$977$	43.2803	−	7.63149i	1.38466	−	0.244153i	0.815825	+	0.578298i	$0.196283\pi$
$978$	−0.332861	−	0.0637557i	−0.0106437	−	0.00203868i
$979$	7.53475	−	8.97957i	0.240812	−	0.286988i
$980$	−0.802715	−	52.2550i	−0.0256418	−	1.66922i
$981$	4.09825	+	7.60683i	0.130847	+	0.242868i
$982$	4.40299	+	7.62619i	0.140505	+	0.243362i
$983$	−1.19243	+	6.76260i	−0.0380326	+	0.215694i	−0.997901	−	0.0647570i	$-0.979373\pi$
$983$	−1.19243	+	6.76260i	−0.0380326	+	0.215694i	0.959868	+	0.280451i	$0.0904839\pi$
$984$	19.2759	−	3.10716i	0.614494	−	0.0990527i
$985$	28.6871	−	78.8171i	0.914046	−	2.51132i
$986$	1.49111	+	0.542718i	0.0474865	+	0.0172837i
$987$	1.22992	−	13.0039i	0.0391487	−	0.413919i
$988$	−7.10321	+	40.2843i	−0.225983	+	1.28161i
$989$	−6.47290	+	3.73713i	−0.205826	+	0.118834i
$990$	−5.95487	−	5.30300i	−0.189258	−	0.168540i
$991$	2.09397	−	3.62686i	0.0665171	−	0.115211i	−0.830849	−	0.556498i	$-0.812145\pi$
$991$	2.09397	−	3.62686i	0.0665171	−	0.115211i	0.897366	+	0.441287i	$0.145478\pi$
$992$	6.72882	+	5.64615i	0.213640	+	0.179265i
$993$	−1.47290	+	0.511678i	−0.0467411	+	0.0162376i
$994$	12.4382	−	5.91674i	0.394515	−	0.187667i
$995$	−21.1263	−	25.1773i	−0.669749	−	0.798175i
$996$	17.6549	+	31.6455i	0.559417	+	1.00273i
$997$	8.78012	+	24.1232i	0.278069	+	0.763989i	0.997581	+	0.0695089i	$0.0221432\pi$
$997$	8.78012	+	24.1232i	0.278069	+	0.763989i	−0.719512	+	0.694480i	$0.755635\pi$
$998$			18.3765i			0.581698i
$999$	−16.1596	−	31.0809i	−0.511268	−	0.983355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.20.14	yes	132
3.2	odd	2		567.2.be.a.62.9		132
7.6	odd	2	inner	189.2.be.a.20.13	✓	132
21.20	even	2		567.2.be.a.62.10		132
27.4	even	9		567.2.be.a.503.10		132
27.23	odd	18	inner	189.2.be.a.104.13	yes	132
189.104	even	18	inner	189.2.be.a.104.14	yes	132
189.139	odd	18		567.2.be.a.503.9		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.13	✓	132	7.6	odd	2	inner
189.2.be.a.20.14	yes	132	1.1	even	1	trivial
189.2.be.a.104.13	yes	132	27.23	odd	18	inner
189.2.be.a.104.14	yes	132	189.104	even	18	inner
567.2.be.a.62.9		132	3.2	odd	2
567.2.be.a.62.10		132	21.20	even	2
567.2.be.a.503.9		132	189.139	odd	18
567.2.be.a.503.10		132	27.4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.157445 + 0.432576i) q^{2} +(0.888001 - 1.48710i) q^{3} +(1.36976 - 1.14936i) q^{4} +(0.725040 + 4.11191i) q^{5} +(0.783093 + 0.149993i) q^{6} +(-1.09969 + 2.40638i) q^{7} +(1.51017 + 0.871900i) q^{8} +(-1.42291 - 2.64109i) q^{9} +O(q^{10})\)	\(q+(0.157445 + 0.432576i) q^{2} +(0.888001 - 1.48710i) q^{3} +(1.36976 - 1.14936i) q^{4} +(0.725040 + 4.11191i) q^{5} +(0.783093 + 0.149993i) q^{6} +(-1.09969 + 2.40638i) q^{7} +(1.51017 + 0.871900i) q^{8} +(-1.42291 - 2.64109i) q^{9} +(-1.66456 + 0.961033i) q^{10} +(-1.36185 - 0.240131i) q^{11} +(-0.492866 - 3.05759i) q^{12} +(1.43469 - 3.94178i) q^{13} +(-1.21408 - 0.0968290i) q^{14} +(6.75864 + 2.57317i) q^{15} +(0.481603 - 2.73131i) q^{16} +(-1.18976 - 2.06072i) q^{17} +(0.918441 - 1.03134i) q^{18} +(-4.72301 - 2.72683i) q^{19} +(5.71920 + 4.79898i) q^{20} +(2.60199 + 3.77222i) q^{21} +(-0.110541 - 0.626912i) q^{22} +(-1.01769 - 1.21284i) q^{23} +(2.63764 - 1.47153i) q^{24} +(-11.6836 + 4.25249i) q^{25} +1.93100 q^{26} +(-5.19109 - 0.229289i) q^{27} +(1.25949 + 4.56010i) q^{28} +(0.495461 + 1.36127i) q^{29} +(-0.0489817 + 3.32875i) q^{30} +(1.18509 + 1.41234i) q^{31} +(4.69194 - 0.827315i) q^{32} +(-1.56642 + 1.81197i) q^{33} +(0.704097 - 0.839111i) q^{34} +(-10.6921 - 2.77712i) q^{35} +(-4.98460 - 1.98221i) q^{36} +(3.37083 + 5.83846i) q^{37} +(0.435948 - 2.47239i) q^{38} +(-4.58780 - 5.63383i) q^{39} +(-2.49023 + 6.84186i) q^{40} +(6.07454 + 2.21095i) q^{41} +(-1.22210 + 1.71947i) q^{42} +(0.819766 - 4.64912i) q^{43} +(-2.14140 + 1.23634i) q^{44} +(9.82823 - 7.76576i) q^{45} +(0.364414 - 0.631183i) q^{46} +(-2.18349 - 1.83217i) q^{47} +(-3.63405 - 3.14159i) q^{48} +(-4.58135 - 5.29257i) q^{49} +(-3.67905 - 4.38452i) q^{50} +(-4.12100 - 0.0606394i) q^{51} +(-2.56536 - 7.04826i) q^{52} +11.6368i q^{53} +(-0.718125 - 2.28164i) q^{54} -5.77391i q^{55} +(-3.75885 + 2.67523i) q^{56} +(-8.24910 + 4.60214i) q^{57} +(-0.510844 + 0.428649i) q^{58} +(-1.15353 - 6.54201i) q^{59} +(12.2152 - 4.24350i) q^{60} +(1.37654 - 1.64050i) q^{61} +(-0.424356 + 0.735006i) q^{62} +(7.92022 - 0.519671i) q^{63} +(-1.67684 - 2.90438i) q^{64} +(17.2484 + 3.04137i) q^{65} +(-1.03044 - 0.392313i) q^{66} +(9.25483 + 3.36848i) q^{67} +(-3.99819 - 1.45522i) q^{68} +(-2.70732 + 0.436403i) q^{69} +(-0.482108 - 5.06240i) q^{70} +(-9.79394 + 5.65453i) q^{71} +(0.153924 - 5.22913i) q^{72} +(7.69650 + 4.44358i) q^{73} +(-1.99486 + 2.37738i) q^{74} +(-4.05122 + 21.1509i) q^{75} +(-9.60349 + 1.69335i) q^{76} +(2.07547 - 3.01307i) q^{77} +(1.71473 - 2.87159i) q^{78} +(-2.14212 + 0.779666i) q^{79} +11.5801 q^{80} +(-4.95067 + 7.51604i) q^{81} +2.97580i q^{82} +(-10.9949 + 4.00181i) q^{83} +(7.89974 + 2.17639i) q^{84} +(7.61088 - 6.38628i) q^{85} +(2.14017 - 0.377369i) q^{86} +(2.46430 + 0.472010i) q^{87} +(-1.84726 - 1.55004i) q^{88} +(-4.23831 + 7.34097i) q^{89} +(4.90668 + 3.02878i) q^{90} +(7.90771 + 7.78717i) q^{91} +(-2.78798 - 0.491595i) q^{92} +(3.15264 - 0.508187i) q^{93} +(0.448772 - 1.23299i) q^{94} +(7.78811 - 21.3976i) q^{95} +(2.93615 - 7.71202i) q^{96} +(5.77859 + 1.01892i) q^{97} +(1.56813 - 2.81507i) q^{98} +(1.30358 + 3.93845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more