LMFDB - Embedded newform 216.2.v.b.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.521940 + 1.31437i) q^{2} +(1.24100 - 1.20827i) q^{3} +(-1.45516 - 1.37205i) q^{4} +(3.07462 + 1.11907i) q^{5} +(0.940397 + 2.26178i) q^{6} +(-1.33825 - 0.235969i) q^{7} +(2.56289 - 1.19649i) q^{8} +(0.0801499 - 2.99893i) q^{9} +O(q^{10})$	\(q+(-0.521940 + 1.31437i) q^{2} +(1.24100 - 1.20827i) q^{3} +(-1.45516 - 1.37205i) q^{4} +(3.07462 + 1.11907i) q^{5} +(0.940397 + 2.26178i) q^{6} +(-1.33825 - 0.235969i) q^{7} +(2.56289 - 1.19649i) q^{8} +(0.0801499 - 2.99893i) q^{9} +(-3.07564 + 3.45711i) q^{10} +(-0.982057 - 2.69818i) q^{11} +(-3.46366 + 0.0555201i) q^{12} +(2.36880 + 2.82303i) q^{13} +(1.00864 - 1.63580i) q^{14} +(5.16774 - 2.32622i) q^{15} +(0.234968 + 3.99309i) q^{16} +(1.94027 - 1.12022i) q^{17} +(3.89988 + 1.67061i) q^{18} +(-1.22444 + 2.12079i) q^{19} +(-2.93864 - 5.84695i) q^{20} +(-1.94588 + 1.32413i) q^{21} +(4.05899 + 0.117497i) q^{22} +(1.08869 + 6.17426i) q^{23} +(1.73485 - 4.58152i) q^{24} +(4.37075 + 3.66750i) q^{25} +(-4.94689 + 1.64004i) q^{26} +(-3.52406 - 3.81851i) q^{27} +(1.62360 + 2.17951i) q^{28} +(-5.00298 - 4.19800i) q^{29} +(0.360273 + 8.00649i) q^{30} +(-4.65080 + 0.820062i) q^{31} +(-5.37106 - 1.77532i) q^{32} +(-4.47887 - 2.16184i) q^{33} +(0.459678 + 3.13493i) q^{34} +(-3.85054 - 2.22311i) q^{35} +(-4.23131 + 4.25395i) q^{36} +(-3.70698 + 2.14023i) q^{37} +(-2.14843 - 2.71630i) q^{38} +(6.35067 + 0.641210i) q^{39} +(9.21887 - 0.810714i) q^{40} +(7.28211 + 8.67848i) q^{41} +(-0.724774 - 3.24873i) q^{42} +(-3.24005 + 1.17928i) q^{43} +(-2.27298 + 5.27370i) q^{44} +(3.60244 - 9.13088i) q^{45} +(-8.68352 - 1.79165i) q^{46} +(2.21737 - 12.5753i) q^{47} +(5.11634 + 4.67151i) q^{48} +(-4.84262 - 1.76257i) q^{49} +(-7.10173 + 3.83059i) q^{50} +(1.05434 - 3.73456i) q^{51} +(0.426350 - 7.35806i) q^{52} -4.14210 q^{53} +(6.85829 - 2.63890i) q^{54} -9.39487i q^{55} +(-3.71212 + 0.996444i) q^{56} +(1.04297 + 4.11136i) q^{57} +(8.12900 - 4.38468i) q^{58} +(3.92440 - 10.7822i) q^{59} +(-10.7116 - 3.70537i) q^{60} +(-9.59806 - 1.69240i) q^{61} +(1.34957 - 6.54091i) q^{62} +(-0.814916 + 3.99440i) q^{63} +(5.13680 - 6.13297i) q^{64} +(4.12400 + 11.3306i) q^{65} +(5.17917 - 4.75856i) q^{66} +(-6.64683 + 5.57735i) q^{67} +(-4.36039 - 1.03205i) q^{68} +(8.81126 + 6.34681i) q^{69} +(4.93175 - 3.90072i) q^{70} +(3.19451 + 5.53306i) q^{71} +(-3.38279 - 7.78182i) q^{72} +(-2.87137 + 4.97336i) q^{73} +(-0.878236 - 5.98943i) q^{74} +(9.85543 - 0.729710i) q^{75} +(4.69159 - 1.40610i) q^{76} +(0.677549 + 3.84257i) q^{77} +(-4.15746 + 8.01248i) q^{78} +(-5.31972 + 6.33979i) q^{79} +(-3.74612 + 12.5402i) q^{80} +(-8.98715 - 0.480728i) q^{81} +(-15.2076 + 5.04177i) q^{82} +(-1.56022 + 1.85940i) q^{83} +(4.64833 + 0.743017i) q^{84} +(7.21919 - 1.27294i) q^{85} +(0.141094 - 4.87415i) q^{86} +(-11.2810 + 0.835263i) q^{87} +(-5.74526 - 5.74011i) q^{88} +(1.06132 + 0.612754i) q^{89} +(10.1211 + 9.50073i) q^{90} +(-2.50390 - 4.33688i) q^{91} +(6.88717 - 10.4783i) q^{92} +(-4.78077 + 6.63713i) q^{93} +(15.3714 + 9.47803i) q^{94} +(-6.13801 + 5.15040i) q^{95} +(-8.81054 + 4.28654i) q^{96} +(16.9633 - 6.17414i) q^{97} +(4.84423 - 5.44506i) q^{98} +(-8.17036 + 2.72886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.521940	+	1.31437i	−0.369067	+	0.929403i
$2$	−0.521940	+	1.31437i	−0.369067	+	0.929403i
$3$	1.24100	−	1.20827i	0.716490	−	0.697597i
$3$	1.24100	−	1.20827i	0.716490	−	0.697597i
$4$	−1.45516	−	1.37205i	−0.727579	−	0.686024i
$5$	3.07462	+	1.11907i	1.37501	+	0.500464i	0.920662	−	0.390360i	$-0.127649\pi$
$5$	3.07462	+	1.11907i	1.37501	+	0.500464i	0.454350	+	0.890823i	$0.349872\pi$
$6$	0.940397	+	2.26178i	0.383916	+	0.923368i
$7$	−1.33825	−	0.235969i	−0.505810	−	0.0891880i	−0.0850807	−	0.996374i	$-0.527115\pi$
$7$	−1.33825	−	0.235969i	−0.505810	−	0.0891880i	−0.420730	+	0.907186i	$0.638226\pi$
$8$	2.56289	−	1.19649i	0.906118	−	0.423025i
$9$	0.0801499	−	2.99893i	0.0267166	−	0.999643i
$10$	−3.07564	+	3.45711i	−0.972604	+	1.09324i
$11$	−0.982057	−	2.69818i	−0.296101	−	0.813531i	−0.995142	−	0.0984497i	$-0.968612\pi$
$11$	−0.982057	−	2.69818i	−0.296101	−	0.813531i	0.699041	−	0.715082i	$-0.253611\pi$
$12$	−3.46366	+	0.0555201i	−0.999872	+	0.0160273i
$13$	2.36880	+	2.82303i	0.656987	+	0.782967i	0.986950	−	0.161027i	$-0.0514806\pi$
$13$	2.36880	+	2.82303i	0.656987	+	0.782967i	−0.329963	+	0.943994i	$0.607036\pi$
$14$	1.00864	−	1.63580i	0.269570	−	0.437185i
$15$	5.16774	−	2.32622i	1.33430	−	0.600627i
$16$	0.234968	+	3.99309i	0.0587419	+	0.998273i
$17$	1.94027	−	1.12022i	0.470585	−	0.271692i	−0.245900	−	0.969295i	$-0.579083\pi$
$17$	1.94027	−	1.12022i	0.470585	−	0.271692i	0.716484	+	0.697603i	$0.245750\pi$
$18$	3.89988	+	1.67061i	0.919211	+	0.393766i
$19$	−1.22444	+	2.12079i	−0.280906	+	0.486544i	−0.971608	−	0.236596i	$-0.923968\pi$
$19$	−1.22444	+	2.12079i	−0.280906	+	0.486544i	0.690702	+	0.723139i	$0.257302\pi$
$20$	−2.93864	−	5.84695i	−0.657100	−	1.30742i
$21$	−1.94588	+	1.32413i	−0.424626	+	0.288949i
$22$	4.05899	+	0.117497i	0.865380	+	0.0250505i
$23$	1.08869	+	6.17426i	0.227007	+	1.28742i	0.858810	+	0.512294i	$0.171204\pi$
$23$	1.08869	+	6.17426i	0.227007	+	1.28742i	−0.631803	+	0.775129i	$0.717685\pi$
$24$	1.73485	−	4.58152i	0.354124	−	0.935198i
$25$	4.37075	+	3.66750i	0.874151	+	0.733500i
$26$	−4.94689	+	1.64004i	−0.970164	+	0.321638i
$27$	−3.52406	−	3.81851i	−0.678206	−	0.734872i
$28$	1.62360	+	2.17951i	0.306832	+	0.411889i
$29$	−5.00298	−	4.19800i	−0.929030	−	0.779549i	0.0466128	−	0.998913i	$-0.485157\pi$
$29$	−5.00298	−	4.19800i	−0.929030	−	0.779549i	−0.975643	+	0.219364i	$0.929602\pi$
$30$	0.360273	+	8.00649i	0.0657765	+	1.46178i
$31$	−4.65080	+	0.820062i	−0.835309	+	0.147287i	−0.574913	−	0.818215i	$-0.694964\pi$
$31$	−4.65080	+	0.820062i	−0.835309	+	0.147287i	−0.260396	+	0.965502i	$0.583853\pi$
$32$	−5.37106	−	1.77532i	−0.949478	−	0.313835i
$33$	−4.47887	−	2.16184i	−0.779671	−	0.376328i
$34$	0.459678	+	3.13493i	0.0788341	+	0.537635i
$35$	−3.85054	−	2.22311i	−0.650860	−	0.375774i
$36$	−4.23131	+	4.25395i	−0.705218	+	0.708991i
$37$	−3.70698	+	2.14023i	−0.609424	+	0.351851i	−0.772740	−	0.634723i	$-0.781114\pi$
$37$	−3.70698	+	2.14023i	−0.609424	+	0.351851i	0.163316	+	0.986574i	$0.447781\pi$
$38$	−2.14843	−	2.71630i	−0.348522	−	0.440642i
$39$	6.35067	+	0.641210i	1.01692	+	0.102676i
$40$	9.21887	−	0.810714i	1.45763	−	0.128185i
$41$	7.28211	+	8.67848i	1.13727	+	1.35535i	0.925821	+	0.377963i	$0.123375\pi$
$41$	7.28211	+	8.67848i	1.13727	+	1.35535i	0.211454	+	0.977388i	$0.432180\pi$
$42$	−0.724774	−	3.24873i	−0.111835	−	0.501290i
$43$	−3.24005	+	1.17928i	−0.494103	+	0.179839i	−0.577040	−	0.816716i	$-0.695792\pi$
$43$	−3.24005	+	1.17928i	−0.494103	+	0.179839i	0.0829367	+	0.996555i	$0.473570\pi$
$44$	−2.27298	+	5.27370i	−0.342665	+	0.795041i
$45$	3.60244	−	9.13088i	0.537021	−	1.36115i
$46$	−8.68352	−	1.79165i	−1.28032	−	0.264164i
$47$	2.21737	−	12.5753i	0.323437	−	1.83430i	−0.197002	−	0.980403i	$-0.563121\pi$
$47$	2.21737	−	12.5753i	0.323437	−	1.83430i	0.520439	−	0.853899i	$-0.325768\pi$
$48$	5.11634	+	4.67151i	0.738480	+	0.674275i
$49$	−4.84262	−	1.76257i	−0.691803	−	0.251796i
$50$	−7.10173	+	3.83059i	−1.00434	+	0.541727i
$51$	1.05434	−	3.73456i	0.147638	−	0.522943i
$52$	0.426350	−	7.35806i	0.0591241	−	1.02038i
$53$	−4.14210			−0.568961			−0.284481	−	0.958682i	$-0.591821\pi$
$53$	−4.14210			−0.568961			−0.284481	+	0.958682i	$0.591821\pi$
$54$	6.85829	−	2.63890i	0.933296	−	0.359109i
$55$		−	9.39487i		−	1.26680i
$56$	−3.71212	+	0.996444i	−0.496053	+	0.133155i
$57$	1.04297	+	4.11136i	0.138145	+	0.544563i
$58$	8.12900	−	4.38468i	1.06739	−	0.575737i
$59$	3.92440	−	10.7822i	0.510913	−	1.40372i	−0.369373	−	0.929281i	$-0.620428\pi$
$59$	3.92440	−	10.7822i	0.510913	−	1.40372i	0.880287	−	0.474442i	$-0.157350\pi$
$60$	−10.7116	−	3.70537i	−1.38286	−	0.478362i
$61$	−9.59806	−	1.69240i	−1.22891	−	0.216689i	−0.478750	−	0.877951i	$-0.658910\pi$
$61$	−9.59806	−	1.69240i	−1.22891	−	0.216689i	−0.750155	+	0.661262i	$0.770021\pi$
$62$	1.34957	−	6.54091i	0.171396	−	0.830697i
$63$	−0.814916	+	3.99440i	−0.102670	+	0.503247i
$64$	5.13680	−	6.13297i	0.642100	−	0.766621i
$65$	4.12400	+	11.3306i	0.511519	+	1.40539i
$66$	5.17917	−	4.75856i	0.637511	−	0.585738i
$67$	−6.64683	+	5.57735i	−0.812039	+	0.681382i	−0.951094	−	0.308903i	$-0.900038\pi$
$67$	−6.64683	+	5.57735i	−0.812039	+	0.681382i	0.139054	+	0.990285i	$0.455594\pi$
$68$	−4.36039	−	1.03205i	−0.528775	−	0.125155i
$69$	8.81126	+	6.34681i	1.06075	+	0.764066i
$70$	4.93175	−	3.90072i	0.589457	−	0.466225i
$71$	3.19451	+	5.53306i	0.379119	+	0.656653i	0.990934	−	0.134348i	$-0.0428939\pi$
$71$	3.19451	+	5.53306i	0.379119	+	0.656653i	−0.611816	+	0.791000i	$0.709561\pi$
$72$	−3.38279	−	7.78182i	−0.398665	−	0.917096i
$73$	−2.87137	+	4.97336i	−0.336069	+	0.582088i	−0.983690	−	0.179875i	$-0.942431\pi$
$73$	−2.87137	+	4.97336i	−0.336069	+	0.582088i	0.647621	+	0.761963i	$0.275764\pi$
$74$	−0.878236	−	5.98943i	−0.102093	−	0.696257i
$75$	9.85543	−	0.729710i	1.13801	−	0.0842597i
$76$	4.69159	−	1.40610i	0.538162	−	0.161290i
$77$	0.677549	+	3.84257i	0.0772138	+	0.437901i
$78$	−4.15746	+	8.01248i	−0.470739	+	0.907234i
$79$	−5.31972	+	6.33979i	−0.598515	+	0.713283i	−0.977219	−	0.212236i	$-0.931926\pi$
$79$	−5.31972	+	6.33979i	−0.598515	+	0.713283i	0.378703	+	0.925518i	$0.376370\pi$
$80$	−3.74612	+	12.5402i	−0.418828	+	1.40204i
$81$	−8.98715	−	0.480728i	−0.998572	−	0.0534142i
$82$	−15.2076	+	5.04177i	−1.67940	+	0.556771i
$83$	−1.56022	+	1.85940i	−0.171257	+	0.204096i	−0.844845	−	0.535011i	$-0.820308\pi$
$83$	−1.56022	+	1.85940i	−0.171257	+	0.204096i	0.673589	+	0.739106i	$0.264752\pi$
$84$	4.64833	+	0.743017i	0.507175	+	0.0810698i
$85$	7.21919	−	1.27294i	0.783032	−	0.138070i
$86$	0.141094	−	4.87415i	0.0152146	−	0.525593i
$87$	−11.2810	+	0.835263i	−1.20945	+	0.0895495i
$88$	−5.74526	−	5.74011i	−0.612447	−	0.611897i
$89$	1.06132	+	0.612754i	0.112500	+	0.0649518i	0.555194	−	0.831721i	$-0.312644\pi$
$89$	1.06132	+	0.612754i	0.112500	+	0.0649518i	−0.442694	+	0.896673i	$0.645977\pi$
$90$	10.1211	+	9.50073i	1.06686	+	1.00146i
$91$	−2.50390	−	4.33688i	−0.262480	−	0.454628i
$92$	6.88717	−	10.4783i	0.718037	−	1.09243i
$93$	−4.78077	+	6.63713i	−0.495743	+	0.688239i
$94$	15.3714	+	9.47803i	1.58544	+	0.977584i
$95$	−6.13801	+	5.15040i	−0.629747	+	0.528420i
$96$	−8.81054	+	4.28654i	−0.899222	+	0.437493i
$97$	16.9633	−	6.17414i	1.72236	−	0.626889i	0.724324	−	0.689460i	$-0.242152\pi$
$97$	16.9633	−	6.17414i	1.72236	−	0.626889i	0.998041	+	0.0625705i	$0.0199298\pi$
$98$	4.84423	−	5.44506i	0.489341	−	0.550034i
$99$	−8.17036	+	2.72886i	−0.821152	+	0.274261i
$100$	−1.32815	−	11.3337i	−0.132815	−	1.13337i
$101$	−3.06146	+	17.3624i	−0.304627	+	1.72763i	0.320628	+	0.947205i	$0.396106\pi$
$101$	−3.06146	+	17.3624i	−0.304627	+	1.72763i	−0.625255	+	0.780420i	$0.715005\pi$
$102$	4.35831	+	3.33502i	0.431537	+	0.330216i
$103$	3.18775	−	8.75828i	0.314099	−	0.862979i	−0.677720	−	0.735320i	$-0.737032\pi$
$103$	3.18775	−	8.75828i	0.314099	−	0.862979i	0.991818	−	0.127658i	$-0.0407461\pi$
$104$	9.44871	+	4.40085i	0.926522	+	0.431539i
$105$	−7.46464	+	1.89363i	−0.728474	+	0.184800i
$106$	2.16193	−	5.44427i	0.209985	−	0.528794i
$107$			3.23586i			0.312823i	0.987692	+	0.156411i	$0.0499926\pi$
$107$			3.23586i			0.312823i	−0.987692	+	0.156411i	$0.950007\pi$
$108$	−0.111111	+	10.3917i	−0.0106916	+	0.999943i
$109$		−	7.62757i		−	0.730589i	−0.930892	−	0.365295i	$-0.880968\pi$
$109$		−	7.62757i		−	0.730589i	0.930892	−	0.365295i	$-0.119032\pi$
$110$	12.3484	+	4.90356i	1.17737	+	0.467536i
$111$	−2.01437	+	7.13506i	−0.191196	+	0.677230i
$112$	0.627802	−	5.39920i	0.0593217	−	0.510176i
$113$	2.66170	−	7.31296i	0.250392	−	0.687946i	−0.749278	−	0.662255i	$-0.769599\pi$
$113$	2.66170	−	7.31296i	0.250392	−	0.687946i	0.999670	−	0.0256902i	$-0.00817836\pi$
$114$	−5.94823	−	0.775028i	−0.557103	−	0.0725881i
$115$	−3.56213	+	20.2018i	−0.332170	+	1.88383i
$116$	1.52027	+	12.9731i	0.141153	+	1.20452i
$117$	8.65592	−	6.87760i	0.800240	−	0.635834i
$118$	12.1235	+	10.7858i	1.11606	+	0.992912i
$119$	−2.86090	+	1.04128i	−0.262258	+	0.0954542i
$120$	10.4610	−	12.1450i	0.954958	−	1.10868i
$121$	2.11076	−	1.77114i	0.191887	−	0.161012i
$122$	7.23405	−	11.7321i	0.654940	−	1.06218i
$123$	19.5231	+	1.97119i	1.76034	+	0.177736i
$124$	7.89281	+	5.18780i	0.708796	+	0.465879i
$125$	1.15436	+	1.99942i	0.103249	+	0.178833i
$126$	−4.82480	−	3.15594i	−0.429827	−	0.281153i
$127$	9.21001	+	5.31740i	0.817256	+	0.471843i	0.849469	−	0.527638i	$-0.176922\pi$
$127$	9.21001	+	5.31740i	0.817256	+	0.471843i	−0.0322133	+	0.999481i	$0.510256\pi$
$128$	5.37991	+	9.95272i	0.475521	+	0.879704i
$129$	−2.59600	+	5.37835i	−0.228565	+	0.473538i
$130$	−17.0451	−	0.493411i	−1.49496	−	0.0432750i
$131$	18.4239	−	3.24863i	1.60970	−	0.283834i	0.704784	−	0.709422i	$-0.251044\pi$
$131$	18.4239	−	3.24863i	1.60970	−	0.283834i	0.904917	+	0.425588i	$0.139933\pi$
$132$	3.55131	+	9.29104i	0.309102	+	0.808681i
$133$	2.13905	−	2.54922i	0.185479	−	0.221045i
$134$	−3.86148	−	11.6475i	−0.333581	−	1.00619i
$135$	−6.56197	−	15.6841i	−0.564765	−	1.34988i
$136$	3.63236	−	5.19251i	0.311473	−	0.445254i
$137$	−4.50049	+	5.36347i	−0.384502	+	0.458232i	−0.923230	−	0.384248i	$-0.874461\pi$
$137$	−4.50049	+	5.36347i	−0.384502	+	0.458232i	0.538727	+	0.842480i	$0.318905\pi$
$138$	−12.9410	+	8.26864i	−1.10161	+	0.703873i
$139$	2.26112	+	12.8235i	0.191786	+	1.08767i	0.916922	+	0.399067i	$0.130666\pi$
$139$	2.26112	+	12.8235i	0.191786	+	1.08767i	−0.725136	+	0.688606i	$0.758223\pi$
$140$	2.55293	+	8.51810i	0.215762	+	0.719911i
$141$	−12.4427	−	18.2852i	−1.04786	−	1.53989i
$142$	−8.93985	+	1.31086i	−0.750215	+	0.110005i
$143$	5.29073	−	9.16382i	0.442433	−	0.766317i
$144$	11.9938	−	0.384605i	0.999486	−	0.0320505i
$145$	−10.6844	−	18.5059i	−0.887292	−	1.53684i
$146$	−5.03818	−	6.36985i	−0.416962	−	0.527173i
$147$	−8.13935	+	3.66387i	−0.671322	+	0.302191i
$148$	8.33073	+	1.97179i	0.684782	+	0.162080i
$149$	−5.35782	+	4.49574i	−0.438929	+	0.368305i	−0.835309	−	0.549781i	$-0.814711\pi$
$149$	−5.35782	+	4.49574i	−0.438929	+	0.368305i	0.396379	+	0.918087i	$0.370267\pi$
$150$	−4.18483	+	13.3346i	−0.341690	+	1.08876i
$151$	3.81995	+	10.4952i	0.310863	+	0.854089i	0.992483	+	0.122383i	$0.0390535\pi$
$151$	3.81995	+	10.4952i	0.310863	+	0.854089i	−0.681620	+	0.731706i	$0.738724\pi$
$152$	−0.600587	+	6.90040i	−0.0487141	+	0.559696i
$153$	−3.20393	−	5.90852i	−0.259023	−	0.477675i
$154$	−5.40421	−	1.11504i	−0.435484	−	0.0898523i
$155$	−15.2172	−	2.68320i	−1.22227	−	0.215519i
$156$	−8.36145	−	9.64648i	−0.669452	−	0.772337i
$157$	2.38479	−	6.55217i	0.190327	−	0.522920i	−0.807422	−	0.589974i	$-0.799138\pi$
$157$	2.38479	−	6.55217i	0.190327	−	0.522920i	0.997749	+	0.0670544i	$0.0213601\pi$
$158$	−5.55629	−	10.3011i	−0.442034	−	0.819511i
$159$	−5.14034	+	5.00479i	−0.407655	+	0.396906i
$160$	−14.5273	−	11.4690i	−1.14848	−	0.906706i
$161$		−	8.51960i		−	0.671438i
$162$	5.32261	−	11.5616i	0.418184	−	0.908363i
$163$	−2.76444			−0.216528			−0.108264	−	0.994122i	$-0.534529\pi$
$163$	−2.76444			−0.216528			−0.108264	+	0.994122i	$0.534529\pi$
$164$	1.31068	−	22.6200i	0.102347	−	1.76632i
$165$	−11.3516	−	11.6590i	−0.883719	−	0.907652i
$166$	−1.62961	−	3.02121i	−0.126482	−	0.234491i
$167$	14.0653	+	5.11934i	1.08840	+	0.396146i	0.823029	−	0.567999i	$-0.192282\pi$
$167$	14.0653	+	5.11934i	1.08840	+	0.396146i	0.265374	+	0.964146i	$0.414505\pi$
$168$	−3.40275	+	5.72184i	−0.262528	+	0.441449i
$169$	−0.100838	+	0.571881i	−0.00775677	+	0.0439908i
$170$	−2.09487	+	10.1531i	−0.160669	+	0.778709i
$171$	6.26197	+	3.84199i	0.478865	+	0.293805i
$172$	6.33282	+	2.72946i	0.482873	+	0.208120i
$173$	7.26501	−	2.64425i	0.552349	−	0.201038i	−0.0507411	−	0.998712i	$-0.516158\pi$
$173$	7.26501	−	2.64425i	0.552349	−	0.201038i	0.603090	+	0.797673i	$0.293936\pi$
$174$	4.79017	−	15.2634i	0.363142	−	1.15712i
$175$	−4.98374	−	5.93939i	−0.376735	−	0.448975i
$176$	10.5433	−	4.55543i	0.794733	−	0.343378i
$177$	−8.15768	−	18.1224i	−0.613169	−	1.36217i
$178$	−1.35933	+	1.07515i	−0.101886	+	0.0805860i
$179$	−5.90573	+	3.40968i	−0.441415	+	0.254851i	−0.704198	−	0.710004i	$-0.748693\pi$
$179$	−5.90573	+	3.40968i	−0.441415	+	0.254851i	0.262782	+	0.964855i	$0.415360\pi$
$180$	−17.7701	+	8.34414i	−1.32451	+	0.621935i
$181$	5.60659	+	3.23697i	0.416734	+	0.240602i	0.693679	−	0.720284i	$-0.255989\pi$
$181$	5.60659	+	3.23697i	0.416734	+	0.240602i	−0.276945	+	0.960886i	$0.589322\pi$
$182$	7.00716	−	1.02747i	0.519405	−	0.0761610i
$183$	−13.9560	+	9.49682i	−1.03166	+	0.702025i
$184$	10.1777	+	14.5213i	0.750307	+	1.07053i
$185$	−13.7926	+	2.43201i	−1.01405	+	0.178805i
$186$	−6.22840	−	9.74791i	−0.456689	−	0.714751i
$187$	−4.92800	−	4.13508i	−0.360371	−	0.302387i
$188$	−20.4806	+	15.2568i	−1.49370	+	1.11271i
$189$	3.81502	+	5.94168i	0.277502	+	0.432194i
$190$	−3.56588	−	10.7558i	−0.258696	−	0.780311i
$191$	6.03023	+	5.05997i	0.436332	+	0.366126i	0.834335	−	0.551258i	$-0.185852\pi$
$191$	6.03023	+	5.05997i	0.436332	+	0.366126i	−0.398003	+	0.917384i	$0.630296\pi$
$192$	−1.03554	−	13.8177i	−0.0747340	−	0.997204i
$193$	−3.98502	−	22.6002i	−0.286848	−	1.62680i	−0.698609	−	0.715504i	$-0.746197\pi$
$193$	−3.98502	−	22.6002i	−0.286848	−	1.62680i	0.411761	−	0.911292i	$-0.364914\pi$
$194$	−0.738699	+	25.5187i	−0.0530355	+	1.83213i
$195$	18.8083	+	9.07832i	1.34689	+	0.650112i
$196$	4.62845	+	9.20913i	0.330603	+	0.657795i
$197$	9.17303	−	15.8882i	0.653551	−	1.13198i	−0.328704	−	0.944433i	$-0.606612\pi$
$197$	9.17303	−	15.8882i	0.653551	−	1.13198i	0.982255	−	0.187551i	$-0.0600550\pi$
$198$	0.677693	−	12.1632i	0.0481616	−	0.864401i
$199$	1.73990	−	1.00453i	0.123338	−	0.0712092i	−0.437062	−	0.899432i	$-0.643981\pi$
$199$	1.73990	−	1.00453i	0.123338	−	0.0712092i	0.560400	+	0.828222i	$0.310648\pi$
$200$	15.5899	+	4.16981i	1.10237	+	0.294850i
$201$	−1.50973	+	14.9527i	−0.106488	+	1.05468i
$202$	−21.2228	−	13.0860i	−1.49323	−	0.920731i
$203$	5.70463	+	6.79852i	0.400387	+	0.477162i
$204$	−6.65823	+	3.98777i	−0.466170	+	0.279199i
$205$	12.6779	+	34.8322i	0.885463	+	2.43279i
$206$	9.84784	+	8.76119i	0.686131	+	0.610421i
$207$	18.6034	−	2.77004i	1.29303	−	0.192531i
$208$	−10.7160	+	10.1222i	−0.743022	+	0.701846i
$209$	6.92475	+	1.22102i	0.478995	+	0.0844598i
$210$	1.40715	−	10.7997i	0.0971027	−	0.745249i
$211$	4.02245	+	1.46405i	0.276917	+	0.100790i	0.476746	−	0.879041i	$-0.341816\pi$
$211$	4.02245	+	1.46405i	0.276917	+	0.100790i	−0.199828	+	0.979831i	$0.564038\pi$
$212$	6.02741	+	5.68316i	0.413964	+	0.390321i
$213$	10.6498	+	3.00667i	0.729714	+	0.206013i
$214$	−4.25314	−	1.68893i	−0.290738	−	0.115453i
$215$	−11.2816			−0.769401
$216$	−13.6006	−	5.56989i	−0.925404	−	0.378983i
$217$	6.41744			0.435644
$218$	10.0255	+	3.98113i	0.679011	+	0.269636i
$219$	2.44582	+	9.64134i	0.165273	+	0.651501i
$220$	−12.8902	+	13.6710i	−0.869058	+	0.921700i
$221$	7.75851	+	2.82387i	0.521894	+	0.189954i
$222$	−8.32675	−	6.37171i	−0.558855	−	0.427641i
$223$	−14.9594	−	2.63774i	−1.00175	−	0.176636i	−0.351366	−	0.936238i	$-0.614283\pi$
$223$	−14.9594	−	2.63774i	−1.00175	−	0.176636i	−0.650388	+	0.759602i	$0.725394\pi$
$224$	6.76889	+	3.64322i	0.452265	+	0.243423i
$225$	11.3489	−	12.8136i	0.756592	−	0.854242i
$226$	8.22272	+	7.31540i	0.546967	+	0.486613i
$227$	−6.27979	−	17.2536i	−0.416805	−	1.14516i	−0.953502	−	0.301386i	$-0.902551\pi$
$227$	−6.27979	−	17.2536i	−0.416805	−	1.14516i	0.536698	−	0.843775i	$-0.319672\pi$
$228$	4.12330	−	7.41368i	0.273072	−	0.490983i
$229$	−13.7865	−	16.4302i	−0.911040	−	1.08574i	−0.996000	−	0.0893510i	$-0.971521\pi$
$229$	−13.7865	−	16.4302i	−0.911040	−	1.08574i	0.0849601	−	0.996384i	$-0.472924\pi$
$230$	−24.6936	−	15.2261i	−1.62824	−	1.00398i
$231$	5.48371	+	3.94995i	0.360802	+	0.259888i
$232$	−17.8450	−	4.77297i	−1.17158	−	0.313361i
$233$	4.91994	−	2.84053i	0.322316	−	0.186089i	−0.330108	−	0.943943i	$-0.607085\pi$
$233$	4.91994	−	2.84053i	0.322316	−	0.186089i	0.652424	+	0.757854i	$0.273752\pi$
$234$	4.52187	+	14.9668i	0.295604	+	0.978411i
$235$	20.8903	−	36.1830i	1.36273	−	2.36032i
$236$	−20.5043	+	10.3053i	−1.33472	+	0.670820i
$237$	1.05845	+	14.2953i	0.0687536	+	0.928582i
$238$	0.124583	−	4.30378i	0.00807552	−	0.278973i
$239$	−1.83559	−	10.4102i	−0.118735	−	0.673377i	−0.984833	−	0.173504i	$-0.944491\pi$
$239$	−1.83559	−	10.4102i	−0.118735	−	0.673377i	0.866099	−	0.499873i	$-0.166620\pi$
$240$	10.5031	+	20.0887i	0.677970	+	1.29672i
$241$	5.42614	+	4.55307i	0.349528	+	0.293289i	0.800601	−	0.599198i	$-0.204514\pi$
$241$	5.42614	+	4.55307i	0.349528	+	0.293289i	−0.451072	+	0.892487i	$0.648958\pi$
$242$	1.22625	+	3.69875i	0.0788261	+	0.237765i
$243$	−11.7339	+	10.2624i	−0.752729	+	0.658330i
$244$	11.6446	+	15.6317i	0.745472	+	1.00072i
$245$	−12.9168	−	10.8385i	−0.825223	−	0.692444i
$246$	−12.7807	+	24.6318i	−0.814871	+	1.57046i
$247$	−8.88752	+	1.56711i	−0.565499	+	0.0997128i
$248$	−10.9383	+	7.66639i	−0.694582	+	0.486816i
$249$	0.310432	+	4.19269i	0.0196729	+	0.265701i
$250$	−3.23049	+	0.473690i	−0.204314	+	0.0299588i
$251$	−1.58934	−	0.917608i	−0.100318	−	0.0579189i	0.449001	−	0.893531i	$-0.351780\pi$
$251$	−1.58934	−	0.917608i	−0.100318	−	0.0579189i	−0.549320	+	0.835612i	$0.685113\pi$
$252$	6.66634	−	4.69438i	0.419940	−	0.295718i
$253$	15.5901	−	9.00095i	0.980142	−	0.565885i
$254$	−11.7961	+	9.33003i	−0.740154	+	0.585418i
$255$	7.42094	−	10.3025i	0.464718	−	0.645166i
$256$	−15.8896	+	1.87650i	−0.993099	+	0.117281i
$257$	−4.18774	−	4.99076i	−0.261224	−	0.311315i	0.619451	−	0.785035i	$-0.287355\pi$
$257$	−4.18774	−	4.99076i	−0.261224	−	0.311315i	−0.880675	+	0.473720i	$0.842911\pi$
$258$	−5.71421	−	6.21929i	−0.355751	−	0.387196i
$259$	5.46589	−	1.98942i	0.339634	−	0.123617i
$260$	9.54505	−	22.1461i	0.591959	−	1.37344i
$261$	−12.9905	+	14.6671i	−0.804091	+	0.907872i
$262$	−5.34624	+	25.9114i	−0.330292	+	1.60081i
$263$	−0.191952	+	1.08861i	−0.0118363	+	0.0671268i	−0.990154	−	0.139984i	$-0.955295\pi$
$263$	−0.191952	+	1.08861i	−0.0118363	+	0.0671268i	0.978318	+	0.207111i	$0.0664060\pi$
$264$	−14.0655	−	0.181614i	−0.865670	−	0.0111776i
$265$	−12.7354	−	4.63530i	−0.782329	−	0.284744i
$266$	2.23417	+	4.14205i	0.136986	+	0.253965i
$267$	2.05747	−	0.521940i	0.125915	−	0.0319422i
$268$	17.3246	+	1.00384i	1.05827	+	0.0613195i
$269$	2.45873			0.149911			0.0749556	−	0.997187i	$-0.476118\pi$
$269$	2.45873			0.149911			0.0749556	+	0.997187i	$0.476118\pi$
$270$	24.0398	−	0.438713i	1.46301	−	0.0266992i
$271$			10.4347i			0.633866i	0.948448	+	0.316933i	$0.102653\pi$
$271$			10.4347i			0.633866i	−0.948448	+	0.316933i	$0.897347\pi$
$272$	4.92902	+	7.48446i	0.298866	+	0.453812i
$273$	−8.34746	−	2.35666i	−0.505211	−	0.142632i
$274$	−4.70062	−	8.71473i	−0.283975	−	0.526476i
$275$	5.60324	−	15.3948i	0.337888	−	0.928339i
$276$	−4.11364	−	21.3251i	−0.247612	−	1.28362i
$277$	8.82313	+	1.55576i	0.530130	+	0.0934763i	0.432305	−	0.901727i	$-0.357700\pi$
$277$	8.82313	+	1.55576i	0.530130	+	0.0934763i	0.0978251	+	0.995204i	$0.468811\pi$
$278$	−18.0350	−	3.72112i	−1.08167	−	0.223178i
$279$	2.08655	+	14.0132i	0.124918	+	0.838945i
$280$	−12.5284	−	1.09043i	−0.748718	−	0.0651659i
$281$	8.31065	+	22.8333i	0.495772	+	1.36212i	0.895326	+	0.445412i	$0.146943\pi$
$281$	8.31065	+	22.8333i	0.495772	+	1.36212i	−0.399554	+	0.916710i	$0.630835\pi$
$282$	30.5279	−	6.81061i	1.81791	−	0.405566i
$283$	−5.06269	+	4.24810i	−0.300946	+	0.252524i	−0.780738	−	0.624859i	$-0.785157\pi$
$283$	−5.06269	+	4.24810i	−0.300946	+	0.252524i	0.479792	+	0.877382i	$0.340712\pi$
$284$	2.94310	−	12.4345i	0.174641	−	0.737851i
$285$	−1.39416	+	13.8080i	−0.0825830	+	0.817917i
$286$	9.28324	+	11.7370i	0.548930	+	0.694021i
$287$	−7.69742	−	13.3323i	−0.454364	−	0.786982i
$288$	−5.75454	+	15.9651i	−0.339090	+	0.940754i
$289$	−5.99024	+	10.3754i	−0.352367	+	0.610317i
$290$	29.9004	−	4.38432i	1.75581	−	0.257456i
$291$	13.5914	−	28.1584i	0.796741	−	1.65068i
$292$	11.0020	−	3.29737i	0.643843	−	0.192964i
$293$	−5.28397	−	29.9669i	−0.308693	−	1.75068i	−0.605593	−	0.795775i	$-0.707064\pi$
$293$	−5.28397	−	29.9669i	−0.308693	−	1.75068i	0.296900	−	0.954908i	$-0.404047\pi$
$294$	−0.567441	−	12.6105i	−0.0330938	−	0.735457i
$295$	24.1321	−	28.7595i	1.40502	−	1.67444i
$296$	−6.93981	+	9.92054i	−0.403368	+	0.576620i
$297$	−6.84219	+	13.2585i	−0.397024	+	0.769338i
$298$	−3.11263	−	9.38868i	−0.180310	−	0.543872i
$299$	−14.8512	+	17.6990i	−0.858869	+	1.02356i
$300$	−15.3424	−	12.4603i	−0.885794	−	0.719395i
$301$	4.61427	−	0.813620i	0.265962	−	0.0468963i
$302$	−15.7884	−	0.457033i	−0.908522	−	0.0262993i
$303$	17.1793	+	25.2458i	0.986924	+	1.45033i
$304$	−8.75623	−	4.39099i	−0.502204	−	0.251840i
$305$	−27.6165	−	15.9444i	−1.58131	−	0.912973i
$306$	9.43826	−	1.12728i	0.539549	−	0.0644421i
$307$	2.83374	+	4.90819i	0.161730	+	0.280125i	0.935489	−	0.353355i	$-0.114959\pi$
$307$	2.83374	+	4.90819i	0.161730	+	0.280125i	−0.773759	+	0.633480i	$0.781626\pi$
$308$	4.28625	−	6.52117i	0.244232	−	0.371578i
$309$	−6.62640	−	14.7207i	−0.376963	−	0.837430i
$310$	11.4692	−	18.6006i	0.651405	−	1.05644i
$311$	−0.654416	+	0.549121i	−0.0371085	+	0.0311378i	−0.661153	−	0.750251i	$-0.729933\pi$
$311$	−0.654416	+	0.549121i	−0.0371085	+	0.0311378i	0.624045	+	0.781389i	$0.285488\pi$
$312$	17.0433	−	5.95519i	0.964884	−	0.337146i
$313$	22.1803	−	8.07297i	1.25370	−	0.456311i	0.372053	−	0.928212i	$-0.378654\pi$
$313$	22.1803	−	8.07297i	1.25370	−	0.456311i	0.881652	+	0.471900i	$0.156432\pi$
$314$	7.36728	+	6.55435i	0.415760	+	0.369883i
$315$	−6.97557	+	11.3693i	−0.393029	+	0.640588i
$316$	16.4395	−	1.92649i	0.924796	−	0.108373i
$317$	3.58128	−	20.3104i	0.201145	−	1.14075i	−0.702248	−	0.711932i	$-0.747820\pi$
$317$	3.58128	−	20.3104i	0.201145	−	1.14075i	0.903392	−	0.428815i	$-0.141069\pi$
$318$	−3.89522	−	9.36853i	−0.218433	−	0.525361i
$319$	−6.41374	+	17.6216i	−0.359101	+	0.986621i
$320$	22.6569	−	13.1081i	1.26656	−	0.732765i
$321$	3.90981	+	4.01570i	0.218224	+	0.224134i
$322$	11.1979	+	4.44672i	0.624037	+	0.247806i
$323$			5.48655i			0.305280i
$324$	12.4181	+	13.0303i	0.689897	+	0.723908i
$325$			21.0263i			1.16633i
$326$	1.44287	−	3.63351i	0.0799134	−	0.201242i
$327$	−9.21620	−	9.46580i	−0.509657	−	0.523460i
$328$	29.0470	+	13.5290i	1.60385	+	0.747013i
$329$	−5.93479	+	16.3057i	−0.327196	+	0.898962i
$330$	21.2491	−	8.83491i	1.16973	−	0.486346i
$331$	3.26084	−	18.4932i	0.179232	−	1.01648i	−0.753913	−	0.656975i	$-0.771836\pi$
$331$	3.26084	−	18.4932i	0.179232	−	1.01648i	0.933145	−	0.359501i	$-0.117053\pi$
$332$	4.82156	−	0.565021i	0.264617	−	0.0310095i
$333$	6.12127	+	11.2885i	0.335444	+	0.618606i
$334$	−14.0699	+	15.8150i	−0.769873	+	0.865360i
$335$	−26.6779	+	9.70997i	−1.45757	+	0.530512i
$336$	−5.74460	−	7.45895i	−0.313394	−	0.406919i
$337$	−5.59075	+	4.69119i	−0.304547	+	0.255546i	−0.782234	−	0.622985i	$-0.785920\pi$
$337$	−5.59075	+	4.69119i	−0.304547	+	0.255546i	0.477687	+	0.878530i	$0.341475\pi$
$338$	−0.699033	−	0.431026i	−0.0380224	−	0.0234447i
$339$	−5.53289	−	12.2914i	−0.300506	−	0.667579i
$340$	−12.2516	−	8.05276i	−0.664436	−	0.436722i
$341$	6.78002	+	11.7433i	0.367159	+	0.635938i
$342$	−8.31819	+	6.22528i	−0.449796	+	0.336625i
$343$	14.3026	+	8.25759i	0.772266	+	0.445868i
$344$	−6.89289	+	6.89907i	−0.371640	+	0.371973i
$345$	19.9888	+	29.3745i	1.07616	+	1.58147i
$346$	−0.316368	+	10.9291i	−0.0170081	+	0.587551i
$347$	−22.5534	+	3.97677i	−1.21073	+	0.213484i	−0.742331	−	0.670034i	$-0.766280\pi$
$347$	−22.5534	+	3.97677i	−1.21073	+	0.213484i	−0.468398	+	0.883518i	$0.655169\pi$
$348$	17.5617	+	14.2627i	0.941405	+	0.764559i
$349$	−10.5079	+	12.5229i	−0.562476	+	0.670333i	−0.970069	−	0.242831i	$-0.921924\pi$
$349$	−10.5079	+	12.5229i	−0.562476	+	0.670333i	0.407592	+	0.913164i	$0.366368\pi$
$350$	10.4078	−	3.45049i	0.556320	−	0.184437i
$351$	2.43195	−	18.9938i	0.129808	−	1.01381i
$352$	0.484555	+	16.2355i	0.0258269	+	0.865357i
$353$	2.82906	−	3.37155i	0.150576	−	0.179449i	−0.685484	−	0.728088i	$-0.740409\pi$
$353$	2.82906	−	3.37155i	0.150576	−	0.179449i	0.836060	+	0.548639i	$0.184854\pi$
$354$	28.0775	−	1.26342i	1.49230	−	0.0671500i
$355$	3.63003	+	20.5869i	0.192662	+	1.09264i
$356$	−0.703661	−	2.34784i	−0.0372940	−	0.124435i
$357$	−2.29222	+	4.74898i	−0.121317	+	0.251343i
$358$	−1.39915	−	9.54199i	−0.0739475	−	0.504310i
$359$	1.38464	−	2.39827i	0.0730784	−	0.126576i	−0.827171	−	0.561951i	$-0.810051\pi$
$359$	1.38464	−	2.39827i	0.0730784	−	0.126576i	0.900249	+	0.435375i	$0.143384\pi$
$360$	−1.69238	−	27.7117i	−0.0891964	−	1.46054i
$361$	6.50149	+	11.2609i	0.342184	+	0.592679i
$362$	−7.18088	+	5.67965i	−0.377419	+	0.298516i
$363$	0.479428	−	4.74835i	0.0251634	−	0.249224i
$364$	−2.30684	+	9.74631i	−0.120911	+	0.510845i
$365$	−14.3939	+	12.0779i	−0.753413	+	0.632188i
$366$	−5.19816	−	23.3002i	−0.271712	−	1.21792i
$367$	−3.78468	−	10.3983i	−0.197559	−	0.542788i	0.800869	−	0.598839i	$-0.204371\pi$
$367$	−3.78468	−	10.3983i	−0.197559	−	0.542788i	−0.998428	+	0.0560511i	$0.982149\pi$
$368$	−24.3986	+	5.79799i	−1.27186	+	0.302241i
$369$	26.6098	−	21.1430i	1.38525	−	1.10066i
$370$	4.00235	−	19.3980i	0.208072	−	1.00846i
$371$	5.54316	+	0.977409i	0.287787	+	0.0507445i
$372$	16.0632	−	3.09863i	0.832841	−	0.160656i
$373$	−3.74325	+	10.2845i	−0.193818	+	0.532510i	−0.998092	−	0.0617485i	$-0.980332\pi$
$373$	−3.74325	+	10.2845i	−0.193818	+	0.532510i	0.804274	+	0.594259i	$0.202555\pi$
$374$	8.00716	−	4.31897i	0.414040	−	0.223328i
$375$	3.84840	+	1.08648i	0.198731	+	0.0561058i
$376$	−9.36345	−	34.8823i	−0.482883	−	1.79892i
$377$		−	24.0678i		−	1.23955i
$378$	−9.80080	+	1.91316i	−0.504099	+	0.0984024i
$379$	−9.42607			−0.484185			−0.242092	−	0.970253i	$-0.577834\pi$
$379$	−9.42607			−0.484185			−0.242092	+	0.970253i	$0.577834\pi$
$380$	15.9984	+	0.926998i	0.820699	+	0.0475540i
$381$	17.8545	−	4.52933i	0.914712	−	0.232044i
$382$	−9.79810	+	5.28498i	−0.501315	+	0.270403i
$383$	12.6302	+	4.59701i	0.645372	+	0.234896i	0.643908	−	0.765103i	$-0.277312\pi$
$383$	12.6302	+	4.59701i	0.645372	+	0.234896i	0.00146378	+	0.999999i	$0.499534\pi$
$384$	18.7021	+	5.85089i	0.954386	+	0.298577i
$385$	−2.21690	+	12.5727i	−0.112984	+	0.640762i
$386$	31.7850	+	6.55812i	1.61781	+	0.333800i
$387$	3.27689	+	9.81120i	0.166574	+	0.498732i
$388$	−33.1555	−	14.2901i	−1.68322	−	0.725472i
$389$	−7.86520	+	2.86270i	−0.398781	+	0.145145i	−0.533623	−	0.845723i	$-0.679170\pi$
$389$	−7.86520	+	2.86270i	−0.398781	+	0.145145i	0.134841	+	0.990867i	$0.456948\pi$
$390$	−21.7491	+	19.9828i	−1.10131	+	1.01187i
$391$	9.02886	+	10.7602i	0.456609	+	0.544165i
$392$	−14.5200	+	1.27690i	−0.733371	+	0.0644932i
$393$	18.9387	−	26.2926i	0.955333	−	1.32629i
$394$	16.0952	+	20.3495i	0.810865	+	1.02519i
$395$	−23.4508	+	13.5393i	−1.17994	+	0.681237i
$396$	15.6333	+	7.23920i	0.785602	+	0.363784i
$397$	−18.5938	−	10.7351i	−0.933195	−	0.538780i	−0.0453741	−	0.998970i	$-0.514448\pi$
$397$	−18.5938	−	10.7351i	−0.933195	−	0.538780i	−0.887820	+	0.460190i	$0.847781\pi$
$398$	0.412206	+	2.81118i	0.0206620	+	0.140912i
$399$	−0.425600	−	5.74813i	−0.0213066	−	0.287766i
$400$	−13.6177	+	18.3146i	−0.680884	+	0.915728i
$401$	−28.7000	+	5.06058i	−1.43321	+	0.252713i	−0.835716	−	0.549161i	$-0.814947\pi$
$401$	−28.7000	+	5.06058i	−1.43321	+	0.252713i	−0.597492	+	0.801875i	$0.703836\pi$
$402$	−18.8654	−	9.78874i	−0.940921	−	0.488218i
$403$	−13.3319	−	11.1868i	−0.664108	−	0.557253i
$404$	28.2770	−	21.0646i	1.40683	−	1.04800i
$405$	−27.0941	−	11.5353i	−1.34632	−	0.573194i
$406$	−11.9133	+	3.94960i	−0.591246	+	0.196016i
$407$	9.41517	+	7.90027i	0.466693	+	0.391602i
$408$	−1.76622	−	10.8328i	−0.0874408	−	0.536303i
$409$	3.08156	+	17.4764i	0.152373	+	0.864152i	0.961148	+	0.276034i	$0.0890201\pi$
$409$	3.08156	+	17.4764i	0.152373	+	0.864152i	−0.808775	+	0.588119i	$0.799869\pi$
$410$	−52.3997	−	1.51683i	−2.58784	−	0.0749111i
$411$	0.895447	+	12.0939i	0.0441692	+	0.596547i
$412$	−16.6555	+	8.37093i	−0.820556	+	0.412406i
$413$	−7.79609	+	13.5032i	−0.383621	+	0.664450i
$414$	−6.06901	+	25.8977i	−0.298276	+	1.27280i
$415$	−6.87789	+	3.97095i	−0.337622	+	0.194926i
$416$	−7.71119	−	19.3680i	−0.378072	−	0.949595i
$417$	18.3003	+	13.1818i	0.896170	+	0.645517i
$418$	−5.21918	+	8.46441i	−0.255278	+	0.414008i
$419$	23.7288	+	28.2789i	1.15923	+	1.38151i	0.910792	+	0.412866i	$0.135472\pi$
$419$	23.7288	+	28.2789i	1.15923	+	1.38151i	0.248436	+	0.968648i	$0.420084\pi$
$420$	13.4604	+	7.48631i	0.656799	+	0.365295i
$421$	−8.97583	−	24.6609i	−0.437455	−	1.20190i	−0.941142	−	0.338012i	$-0.890246\pi$
$421$	−8.97583	−	24.6609i	−0.437455	−	1.20190i	0.503687	−	0.863886i	$-0.331977\pi$
$422$	−4.02379	+	4.52286i	−0.195875	+	0.220169i
$423$	−37.5348	−	7.65765i	−1.82501	−	0.372328i
$424$	−10.6157	+	4.95600i	−0.515546	+	0.240685i
$425$	12.5888	+	2.21975i	0.610648	+	0.107674i
$426$	−9.51045	+	12.4286i	−0.460783	+	0.602165i
$427$	12.4452	+	4.52969i	0.602267	+	0.219207i
$428$	4.43976	−	4.70869i	0.214604	−	0.227603i
$429$	−4.50661	−	17.7649i	−0.217581	−	0.857699i
$430$	5.88833	−	14.8283i	0.283961	−	0.715083i
$431$	12.1132			0.583473			0.291736	−	0.956499i	$-0.405767\pi$
$431$	12.1132			0.583473			0.291736	+	0.956499i	$0.405767\pi$
$432$	14.4196	−	14.9691i	0.693764	−	0.720203i
$433$	21.9408			1.05441			0.527203	−	0.849739i	$-0.323241\pi$
$433$	21.9408			1.05441			0.527203	+	0.849739i	$0.323241\pi$
$434$	−3.34952	+	8.43491i	−0.160782	+	0.404889i
$435$	−35.6196	−	10.0561i	−1.70783	−	0.482155i
$436$	−10.4654	+	11.0993i	−0.501202	+	0.531561i
$437$	−14.4274	−	5.25114i	−0.690155	−	0.251196i
$438$	−13.9489	−	1.81748i	−0.666504	−	0.0868425i
$439$	−18.3248	−	3.23116i	−0.874596	−	0.154215i	−0.281708	−	0.959500i	$-0.590901\pi$
$439$	−18.3248	−	3.23116i	−0.874596	−	0.154215i	−0.592888	+	0.805285i	$0.702012\pi$
$440$	−11.2409	−	24.0780i	−0.535889	−	1.14787i
$441$	−5.67396	+	14.3814i	−0.270188	+	0.684829i
$442$	−7.76109	+	8.72370i	−0.369158	+	0.414944i
$443$	0.178768	+	0.491160i	0.00849351	+	0.0233357i	0.943867	−	0.330326i	$-0.107159\pi$
$443$	0.178768	+	0.491160i	0.00849351	+	0.0233357i	−0.935373	+	0.353662i	$0.884936\pi$
$444$	12.7209	−	7.61882i	0.603706	−	0.361573i
$445$	2.57744	+	3.07168i	0.122183	+	0.145612i
$446$	11.2749	−	18.2855i	0.533881	−	0.865842i
$447$	−1.21695	+	12.0529i	−0.0575598	+	0.570083i
$448$	−8.32151	+	6.99531i	−0.393154	+	0.330497i
$449$	8.98007	−	5.18465i	0.423796	−	0.244679i	−0.272904	−	0.962041i	$-0.587984\pi$
$449$	8.98007	−	5.18465i	0.423796	−	0.244679i	0.696700	+	0.717363i	$0.254651\pi$
$450$	10.9185	+	21.6046i	0.514702	+	1.01845i
$451$	16.2646	−	28.1712i	0.765872	−	1.32653i
$452$	−13.9069	+	6.98953i	−0.654127	+	0.328760i
$453$	17.4216	+	8.40900i	0.818540	+	0.395089i
$454$	25.9553	+	0.751339i	1.21814	+	0.0352621i
$455$	−2.84526	−	16.1363i	−0.133388	−	0.756481i
$456$	7.59224	+	9.28905i	0.355539	+	0.435000i
$457$	−5.85958	−	4.91677i	−0.274099	−	0.229997i	0.495367	−	0.868684i	$-0.335033\pi$
$457$	−5.85958	−	4.91677i	−0.274099	−	0.229997i	−0.769467	+	0.638687i	$0.779478\pi$
$458$	28.7911	−	9.54511i	1.34532	−	0.446014i
$459$	−11.1152	−	3.46123i	−0.518812	−	0.161556i
$460$	32.9014	−	24.5095i	1.53403	−	1.14276i
$461$	−3.98250	−	3.34172i	−0.185484	−	0.155639i	0.545318	−	0.838229i	$-0.316409\pi$
$461$	−3.98250	−	3.34172i	−0.185484	−	0.155639i	−0.730801	+	0.682590i	$0.760853\pi$
$462$	−8.05388	+	5.14601i	−0.374701	+	0.239414i
$463$	24.6573	−	4.34774i	1.14592	−	0.202057i	0.431727	−	0.902004i	$-0.357904\pi$
$463$	24.6573	−	4.34774i	1.14592	−	0.202057i	0.714194	+	0.699948i	$0.246793\pi$
$464$	15.5875	−	20.9638i	0.723630	−	0.973218i
$465$	−22.1265	+	15.0567i	−1.02609	+	0.698235i
$466$	1.16560	+	7.94923i	0.0539956	+	0.368241i
$467$	5.51602	+	3.18467i	0.255251	+	0.147369i	0.622166	−	0.782885i	$-0.286253\pi$
$467$	5.51602	+	3.18467i	0.255251	+	0.147369i	−0.366915	+	0.930254i	$0.619586\pi$
$468$	−22.0321	−	1.86834i	−1.01844	−	0.0863641i
$469$	10.2112	−	5.89543i	0.471509	−	0.272226i
$470$	36.6545	+	46.3430i	1.69075	+	2.13764i
$471$	−4.95729	−	11.0127i	−0.228420	−	0.507439i
$472$	−2.84304	−	32.3291i	−0.130862	−	1.48807i
$473$	6.36383	+	7.58412i	0.292609	+	0.348718i
$474$	−19.3419	−	6.07011i	−0.888402	−	0.278810i
$475$	−13.1297	+	4.77883i	−0.602434	+	0.219268i
$476$	5.59175	+	2.41006i	0.256297	+	0.110465i
$477$	−0.331989	+	12.4219i	−0.0152007	+	0.568758i
$478$	14.6409	+	3.02082i	0.669660	+	0.138169i
$479$	3.99003	−	22.6286i	0.182309	−	1.03393i	−0.747055	−	0.664762i	$-0.768533\pi$
$479$	3.99003	−	22.6286i	0.182309	−	1.03393i	0.929364	−	0.369164i	$-0.120356\pi$
$480$	−31.8860	+	3.31987i	−1.45539	+	0.151531i
$481$	−14.8230	−	5.39513i	−0.675871	−	0.245997i
$482$	−8.81656	+	4.75555i	−0.401583	+	0.216609i
$483$	−10.2940	−	10.5728i	−0.468393	−	0.481079i
$484$	−5.50157	−	0.318779i	−0.250071	−	0.0144900i
$485$	59.0651			2.68201
$486$	−7.36419	−	20.7790i	−0.334047	−	0.942557i
$487$			17.1809i			0.778541i	0.921124	+	0.389270i	$0.127273\pi$
$487$			17.1809i			0.778541i	−0.921124	+	0.389270i	$0.872727\pi$
$488$	−26.6237	+	7.14660i	−1.20520	+	0.323511i
$489$	−3.43067	+	3.34020i	−0.155140	+	0.151049i
$490$	20.9876	−	11.3205i	0.948122	−	0.511406i
$491$	4.32122	−	11.8724i	0.195014	−	0.535796i	−0.803189	−	0.595724i	$-0.796865\pi$
$491$	4.32122	−	11.8724i	0.195014	−	0.535796i	0.998203	+	0.0599285i	$0.0190873\pi$
$492$	−25.7046	−	29.6550i	−1.15885	−	1.33695i
$493$	−14.4098	−	2.54084i	−0.648985	−	0.114433i
$494$	2.57898	−	12.4995i	0.116034	−	0.562377i
$495$	−28.1745	−	0.752998i	−1.26635	−	0.0338447i
$496$	−4.36737	−	18.3784i	−0.196101	−	0.825214i
$497$	−2.96942	−	8.15841i	−0.133197	−	0.365955i
$498$	−5.67278	−	1.78031i	−0.254204	−	0.0797774i
$499$	1.80634	−	1.51570i	0.0808628	−	0.0678519i	−0.601460	−	0.798903i	$-0.705414\pi$
$499$	1.80634	−	1.51570i	0.0808628	−	0.0678519i	0.682323	+	0.731051i	$0.260970\pi$
$500$	1.06351	−	4.49331i	0.0475618	−	0.200947i
$501$	23.6405	−	10.6416i	1.05618	−	0.475432i
$502$	2.03562	−	1.61006i	0.0908543	−	0.0718603i
$503$	−9.09713	−	15.7567i	−0.405621	−	0.702556i	0.588773	−	0.808299i	$-0.299611\pi$
$503$	−9.09713	−	15.7567i	−0.405621	−	0.702556i	−0.994394	+	0.105743i	$0.966278\pi$
$504$	2.69074	+	11.2122i	0.119855	+	0.499433i
$505$	−28.8426	+	49.9569i	−1.28348	+	2.22305i
$506$	3.69352	+	25.1892i	0.164197	+	1.11980i
$507$	0.565848	+	0.831542i	0.0251302	+	0.0369301i
$508$	−6.10628	−	20.3742i	−0.270923	−	0.903960i
$509$	2.07234	+	11.7528i	0.0918549	+	0.520935i	0.995666	+	0.0930030i	$0.0296466\pi$
$509$	2.07234	+	11.7528i	0.0918549	+	0.520935i	−0.903811	+	0.427932i	$0.859242\pi$
$510$	9.66802	+	15.1312i	0.428107	+	0.670019i
$511$	5.01617	−	5.97804i	0.221902	−	0.264453i
$512$	5.82699	−	21.8643i	0.257519	−	0.966273i
$513$	12.4133	−	2.79827i	0.548059	−	0.123547i
$514$	8.74547	−	2.89939i	0.385746	−	0.127886i
$515$	19.6023	−	23.3611i	0.863779	−	1.02941i
$516$	11.1570	−	4.26452i	0.491157	−	0.187735i
$517$	−36.1081	+	6.36683i	−1.58803	+	0.280013i
$518$	−0.238022	+	8.22258i	−0.0104581	+	0.361279i
$519$	5.82089	−	12.0596i	0.255509	−	0.529359i
$520$	24.1264	+	24.1047i	1.05801	+	1.05706i
$521$	12.2664	+	7.08202i	0.537402	+	0.310269i	0.744025	−	0.668152i	$-0.232914\pi$
$521$	12.2664	+	7.08202i	0.537402	+	0.310269i	−0.206624	+	0.978421i	$0.566248\pi$
$522$	−12.4978	−	24.7297i	−0.547015	−	1.08239i
$523$	8.17227	+	14.1548i	0.357349	+	0.618946i	0.987517	−	0.157513i	$-0.0503475\pi$
$523$	8.17227	+	14.1548i	0.357349	+	0.618946i	−0.630168	+	0.776459i	$0.717014\pi$
$524$	−31.2669	−	20.5512i	−1.36590	−	0.897782i
$525$	−13.3612	−	1.34905i	−0.583131	−	0.0588772i
$526$	−1.33066	−	0.820488i	−0.0580195	−	0.0357750i
$527$	−8.10516	+	6.80104i	−0.353066	+	0.296258i
$528$	7.58004	−	18.3925i	0.329879	−	0.800431i
$529$	−15.3234	+	5.57725i	−0.666233	+	0.242489i
$530$	12.7396	−	14.3197i	0.553374	−	0.622009i
$531$	−32.0205	−	12.6332i	−1.38957	−	0.548234i
$532$	−6.61030	+	0.774638i	−0.286593	+	0.0335848i
$533$	−7.24972	+	41.1152i	−0.314020	+	1.78090i
$534$	−0.387852	+	2.97671i	−0.0167840	+	0.128815i
$535$	−3.62116	+	9.94906i	−0.156556	+	0.430135i
$536$	−10.3618	+	22.2470i	−0.447562	+	0.960925i
$537$	−3.20918	+	11.3671i	−0.138486	+	0.490528i
$538$	−1.28331	+	3.23169i	−0.0553273	+	0.139328i
$539$			14.7972i			0.637360i
$540$	−11.9707	+	31.8262i	−0.515136	+	1.36958i
$541$		−	10.8601i		−	0.466912i	−0.972367	−	0.233456i	$-0.924996\pi$
$541$		−	10.8601i		−	0.466912i	0.972367	−	0.233456i	$-0.0750035\pi$
$542$	−13.7152	−	5.44631i	−0.589117	−	0.233939i
$543$	10.8689	−	2.75723i	0.466429	−	0.118324i
$544$	−12.4100	+	2.57214i	−0.532076	+	0.110280i
$545$	8.53579	−	23.4519i	0.365633	−	1.00457i
$546$	7.45441	−	9.74165i	0.319019	−	0.416904i
$547$	0.544866	−	3.09009i	0.0232968	−	0.132123i	−0.970941	−	0.239318i	$-0.923076\pi$
$547$	0.544866	−	3.09009i	0.0232968	−	0.132123i	0.994238	+	0.107196i	$0.0341872\pi$
$548$	13.9079	−	1.62981i	0.594114	−	0.0696221i
$549$	−5.84466	+	28.6482i	−0.249444	+	1.22268i
$550$	17.3099	+	15.3999i	0.738098	+	0.656653i
$551$	15.0289	−	5.47009i	0.640255	−	0.233034i
$552$	30.1762	+	5.72355i	1.28438	+	0.243610i
$553$	8.61510	−	7.22893i	0.366351	−	0.307405i
$554$	−6.64999	+	10.7849i	−0.282531	+	0.458206i
$555$	−14.1781	+	19.6834i	−0.601826	+	0.835513i
$556$	14.3041	−	21.7625i	0.606630	−	0.922937i
$557$	−4.03028	−	6.98066i	−0.170769	−	0.295780i	0.767920	−	0.640546i	$-0.221292\pi$
$557$	−4.03028	−	6.98066i	−0.170769	−	0.295780i	−0.938689	+	0.344766i	$0.887958\pi$
$558$	−19.5076	−	4.57152i	−0.825821	−	0.193528i
$559$	−11.0042	−	6.35327i	−0.465427	−	0.268715i
$560$	7.97233	−	15.8979i	0.336893	−	0.671810i
$561$	−11.1119	+	0.822744i	−0.469146	+	0.0347363i
$562$	−34.3492	−	0.994318i	−1.44893	−	0.0419428i
$563$	1.45495	−	0.256547i	0.0613187	−	0.0108121i	−0.142905	−	0.989736i	$-0.545644\pi$
$563$	1.45495	−	0.256547i	0.0613187	−	0.0108121i	0.204223	+	0.978924i	$0.434533\pi$
$564$	−6.98203	+	43.6798i	−0.293996	+	1.83925i
$565$	16.3674	−	19.5060i	0.688583	−	0.820622i
$566$	−2.94118	−	8.87152i	−0.123627	−	0.372898i
$567$	11.9136	+	2.76403i	0.500324	+	0.116078i
$568$	14.8074	+	10.3584i	0.621307	+	0.434628i
$569$	6.48819	−	7.73232i	0.271999	−	0.324156i	−0.612703	−	0.790314i	$-0.709918\pi$
$569$	6.48819	−	7.73232i	0.271999	−	0.324156i	0.884702	+	0.466158i	$0.154362\pi$
$570$	−17.4212	−	9.03941i	−0.729696	−	0.378619i
$571$	−4.99821	−	28.3463i	−0.209169	−	1.18626i	−0.890743	−	0.454507i	$-0.849816\pi$
$571$	−4.99821	−	28.3463i	−0.209169	−	1.18626i	0.681575	−	0.731749i	$-0.261295\pi$
$572$	−20.2721	+	6.07566i	−0.847617	+	0.254036i
$573$	13.5973	−	1.00677i	0.568036	−	0.0420582i
$574$	21.5412	−	3.15862i	0.899114	−	0.131838i
$575$	−17.8857	+	30.9789i	−0.745885	+	1.29191i
$576$	−17.9806	−	15.8965i	−0.749192	−	0.662352i
$577$	5.35695	+	9.27852i	0.223013	+	0.386270i	0.955721	−	0.294273i	$-0.0950774\pi$
$577$	5.35695	+	9.27852i	0.223013	+	0.386270i	−0.732709	+	0.680543i	$0.761744\pi$
$578$	−10.5106	−	13.2887i	−0.437183	−	0.552739i
$579$	−32.2526	−	23.2318i	−1.34037	−	0.965479i
$580$	−9.84354	+	41.5886i	−0.408731	+	1.72687i
$581$	2.52673	−	2.12018i	0.104826	−	0.0879597i
$582$	29.9168	+	32.5612i	1.24009	+	1.34970i
$583$	4.06778	+	11.1761i	0.168470	+	0.462868i
$584$	−1.40841	+	16.1818i	−0.0582803	+	0.669606i
$585$	34.3102	−	11.4594i	1.41855	−	0.473789i
$586$	42.1456	+	8.69579i	1.74102	+	0.359220i
$587$	−7.19613	−	1.26887i	−0.297016	−	0.0523720i	0.0231543	−	0.999732i	$-0.492629\pi$
$587$	−7.19613	−	1.26887i	−0.297016	−	0.0523720i	−0.320171	+	0.947360i	$0.603740\pi$
$588$	16.8710	+	5.83607i	0.695750	+	0.240676i
$589$	3.95545	−	10.8675i	0.162981	−	0.447788i
$590$	25.2052	+	46.7293i	1.03768	+	1.92382i
$591$	−7.81353	−	30.8007i	−0.321406	−	1.26697i
$592$	−9.41714	−	14.2994i	−0.387042	−	0.587703i
$593$		−	13.1080i		−	0.538281i	−0.963101	−	0.269140i	$-0.913260\pi$
$593$		−	13.1080i		−	0.538281i	0.963101	−	0.269140i	$-0.0867395\pi$
$594$	−13.8555	−	15.9133i	−0.568497	−	0.652933i
$595$	−9.96145			−0.408380
$596$	13.9648	+	0.809169i	0.572022	+	0.0331448i
$597$	0.945461	−	3.34889i	0.0386951	−	0.137061i
$598$	−15.5117	−	28.7579i	−0.634319	−	1.17600i
$599$	−6.88675	−	2.50657i	−0.281385	−	0.102416i	0.197473	−	0.980308i	$-0.436727\pi$
$599$	−6.88675	−	2.50657i	−0.281385	−	0.102416i	−0.478857	+	0.877893i	$0.658949\pi$
$600$	24.3853	−	13.6621i	0.995525	−	0.557755i
$601$	0.0524110	−	0.297238i	0.00213789	−	0.0121246i	−0.983720	−	0.179707i	$-0.942485\pi$
$601$	0.0524110	−	0.297238i	0.00213789	−	0.0121246i	0.985858	+	0.167583i	$0.0535961\pi$
$602$	−1.33897	+	6.48953i	−0.0545723	+	0.264494i
$603$	16.1933	+	20.3804i	0.659444	+	0.829953i
$604$	8.84132	−	20.5134i	0.359748	−	0.834676i
$605$	8.47180	−	3.08348i	0.344428	−	0.125361i
$606$	−42.1490	+	9.40321i	−1.71219	+	0.381979i
$607$	−9.41990	−	11.2262i	−0.382342	−	0.455657i	0.540210	−	0.841530i	$-0.318345\pi$
$607$	−9.41990	−	11.2262i	−0.382342	−	0.455657i	−0.922552	+	0.385873i	$0.873900\pi$
$608$	10.3416	−	9.21713i	0.419408	−	0.373804i
$609$	15.2939	+	1.54419i	0.619740	+	0.0625736i
$610$	35.3710	−	27.9764i	1.43213	−	1.13273i
$611$	40.7530	−	23.5288i	1.64869	−	0.951873i
$612$	−3.44454	+	12.9938i	−0.139237	+	0.525242i
$613$	−11.7747	−	6.79811i	−0.475574	−	0.274573i	0.242996	−	0.970027i	$-0.421870\pi$
$613$	−11.7747	−	6.79811i	−0.475574	−	0.274573i	−0.718570	+	0.695454i	$0.755203\pi$
$614$	−7.93024	+	1.16282i	−0.320038	+	0.0469276i
$615$	57.8201	+	27.9084i	2.33153	+	1.12537i
$616$	6.33409	+	9.03739i	0.255208	+	0.364127i
$617$	−21.9238	+	3.86576i	−0.882620	+	0.155630i	−0.596547	−	0.802578i	$-0.703461\pi$
$617$	−21.9238	+	3.86576i	−0.882620	+	0.155630i	−0.286073	+	0.958208i	$0.592350\pi$
$618$	22.8071	−	1.02626i	0.917435	−	0.0412824i
$619$	−26.2499	−	22.0263i	−1.05507	−	0.885311i	−0.0614548	−	0.998110i	$-0.519574\pi$
$619$	−26.2499	−	22.0263i	−1.05507	−	0.885311i	−0.993618	+	0.112799i	$0.964018\pi$
$620$	18.4619	+	24.7831i	0.741447	+	0.995315i
$621$	19.7399	−	25.9156i	0.792133	−	1.03996i
$622$	−0.380184	−	1.14676i	−0.0152440	−	0.0459807i
$623$	−1.27572	−	1.07046i	−0.0511106	−	0.0428869i
$624$	−1.06821	+	25.5095i	−0.0427626	+	1.02120i
$625$	−3.64210	−	20.6554i	−0.145684	−	0.826216i
$626$	−0.965882	+	33.3668i	−0.0386044	+	1.33361i
$627$	10.0689	−	6.85171i	0.402114	−	0.273631i
$628$	−12.4601	+	6.26238i	−0.497214	+	0.249896i
$629$	−4.79503	+	8.30523i	−0.191190	+	0.331151i
$630$	−11.3027	−	15.1026i	−0.450311	−	0.601702i
$631$	4.33363	−	2.50202i	0.172519	−	0.0996040i	−0.411254	−	0.911521i	$-0.634909\pi$
$631$	4.33363	−	2.50202i	0.172519	−	0.0996040i	0.583773	+	0.811917i	$0.301576\pi$
$632$	−6.04832	+	22.6132i	−0.240589	+	0.899505i
$633$	6.76083	−	3.04334i	0.268719	−	0.120962i
$634$	24.8263	+	15.3080i	0.985978	+	0.607957i
$635$	22.3667	+	26.6556i	0.887597	+	1.05780i
$636$	14.3468	−	0.229970i	0.568888	−	0.00911891i
$637$	−6.49542	−	17.8460i	−0.257358	−	0.707085i
$638$	−19.8138	−	17.6275i	−0.784436	−	0.697878i
$639$	16.8493	−	9.13664i	0.666547	−	0.361440i
$640$	5.40340	+	36.6213i	0.213588	+	1.44759i
$641$	21.6772	+	3.82227i	0.856197	+	0.150971i	0.584482	−	0.811407i	$-0.301298\pi$
$641$	21.6772	+	3.82227i	0.856197	+	0.150971i	0.271716	+	0.962378i	$0.412409\pi$
$642$	−7.31882	+	3.04300i	−0.288851	+	0.120098i
$643$	17.8842	+	6.50931i	0.705283	+	0.256702i	0.669665	−	0.742663i	$-0.266438\pi$
$643$	17.8842	+	6.50931i	0.705283	+	0.256702i	0.0356184	+	0.999365i	$0.488660\pi$
$644$	−11.6893	+	12.3974i	−0.460623	+	0.488524i
$645$	−14.0005	+	13.6313i	−0.551268	+	0.536732i
$646$	−7.21138	−	2.86365i	−0.283728	−	0.112669i
$647$	10.3985			0.408809			0.204405	−	0.978886i	$-0.434474\pi$
$647$	10.3985			0.408809			0.204405	+	0.978886i	$0.434474\pi$
$648$	−23.6083	+	9.52103i	−0.927420	+	0.374021i
$649$	−32.9463			−1.29325
$650$	−27.6365	−	10.9745i	−1.08399	−	0.430454i
$651$	7.96402	−	7.75402i	0.312135	−	0.303904i
$652$	4.02270	+	3.79295i	0.157541	+	0.148543i
$653$	14.2393	+	5.18267i	0.557225	+	0.202813i	0.605254	−	0.796033i	$-0.293072\pi$
$653$	14.2393	+	5.18267i	0.557225	+	0.202813i	−0.0480285	+	0.998846i	$0.515294\pi$
$654$	17.2519	−	7.17295i	0.674603	−	0.280485i
$655$	60.2819	+	10.6293i	2.35541	+	0.415322i
$656$	−32.9429	+	31.1173i	−1.28621	+	1.21493i
$657$	14.6846	+	9.00966i	0.572902	+	0.351500i
$658$	−18.3342	−	16.3111i	−0.714741	−	0.635874i
$659$	3.21036	+	8.82040i	0.125058	+	0.343594i	0.986384	−	0.164459i	$-0.0525877\pi$
$659$	3.21036	+	8.82040i	0.125058	+	0.343594i	−0.861326	+	0.508053i	$0.830365\pi$
$660$	0.521604	+	32.5406i	0.0203034	+	1.26664i
$661$	15.4507	+	18.4135i	0.600964	+	0.716201i	0.977673	−	0.210131i	$-0.0673889\pi$
$661$	15.4507	+	18.4135i	0.600964	+	0.716201i	−0.376709	+	0.926332i	$0.622944\pi$
$662$	22.6050	+	13.9383i	0.878567	+	0.541727i
$663$	13.0403	−	5.86999i	0.506443	−	0.227972i
$664$	−1.77391	+	6.63223i	−0.0688412	+	0.257381i
$665$	9.42952	−	5.44414i	0.365661	−	0.211115i
$666$	−18.0323	+	2.15372i	−0.698736	+	0.0834548i
$667$	20.4729	−	35.4600i	0.792712	−	1.37302i
$668$	−13.4432	−	26.7477i	−0.520133	−	1.03490i
$669$	−21.7517	+	14.8016i	−0.840968	+	0.572262i
$670$	1.16174	−	40.1328i	0.0448819	−	1.55046i
$671$	4.85945	+	27.5593i	0.187597	+	1.06392i
$672$	12.8022	−	3.65744i	0.493855	−	0.141089i
$673$	7.81263	+	6.55558i	0.301155	+	0.252699i	0.780825	−	0.624750i	$-0.214799\pi$
$673$	7.81263	+	6.55558i	0.301155	+	0.252699i	−0.479670	+	0.877449i	$0.659244\pi$
$674$	−3.24795	−	9.79685i	−0.125106	−	0.377361i
$675$	−1.39844	−	29.6142i	−0.0538259	−	1.13985i
$676$	0.931383	−	0.693822i	0.0358224	−	0.0266855i
$677$	33.3112	+	27.9514i	1.28025	+	1.07426i	0.993209	+	0.116342i	$0.0371170\pi$
$677$	33.3112	+	27.9514i	1.28025	+	1.07426i	0.287044	+	0.957917i	$0.407327\pi$
$678$	19.0434	−	0.856906i	0.731356	−	0.0329093i
$679$	−24.1580	+	4.25972i	−0.927101	+	0.163473i
$680$	16.9789	−	11.9001i	0.651112	−	0.456349i
$681$	−28.6403	−	13.8240i	−1.09750	−	0.529735i
$682$	−18.9739	+	2.78217i	−0.726549	+	0.106535i
$683$	29.8941	+	17.2593i	1.14386	+	0.660411i	0.947385	−	0.320097i	$-0.103716\pi$
$683$	29.8941	+	17.2593i	1.14386	+	0.660411i	0.196480	+	0.980508i	$0.437049\pi$
$684$	−3.84076	−	14.1824i	−0.146855	−	0.542279i
$685$	−19.8394	+	11.4543i	−0.758024	+	0.437645i
$686$	−18.3186	+	14.4890i	−0.699409	+	0.553191i
$687$	−36.9612	−	3.73187i	−1.41016	−	0.142380i
$688$	−5.47029	−	12.6607i	−0.208553	−	0.482686i
$689$	−9.81181	−	11.6933i	−0.373800	−	0.445478i
$690$	−49.0420	+	10.9410i	−1.86700	+	0.416517i
$691$	−28.1515	+	10.2463i	−1.07093	+	0.389788i	−0.816526	−	0.577309i	$-0.804103\pi$
$691$	−28.1515	+	10.2463i	−1.07093	+	0.389788i	−0.254408	+	0.967097i	$0.581881\pi$
$692$	−14.1998	−	6.12015i	−0.539794	−	0.232653i
$693$	11.5779	−	1.72394i	0.439808	−	0.0654870i
$694$	6.54454	−	31.7192i	0.248427	−	1.20404i
$695$	−7.39827	+	41.9577i	−0.280632	+	1.59154i
$696$	−27.9126	+	15.6384i	−1.05802	+	0.592771i
$697$	23.8510	+	8.68106i	0.903422	+	0.328819i
$698$	−10.9752	−	20.3475i	−0.415418	−	0.770165i
$699$	2.67350	−	9.46973i	0.101121	−	0.358178i
$700$	−0.897001	+	15.4807i	−0.0339035	+	0.585114i
$701$	−44.3573			−1.67535			−0.837677	−	0.546167i	$-0.816087\pi$
$701$	−44.3573			−1.67535			−0.837677	+	0.546167i	$0.816087\pi$
$702$	23.6956	+	13.1101i	0.894334	+	0.494809i
$703$		−	10.4823i		−	0.395348i
$704$	−21.5925	−	7.83708i	−0.813797	−	0.295371i
$705$	−17.7942	−	70.1442i	−0.670168	−	2.64178i
$706$	2.95487	+	5.47819i	0.111208	+	0.206175i
$707$	8.19400	−	22.5128i	0.308167	−	0.846682i
$708$	−12.9941	+	37.5637i	−0.488350	+	1.41173i
$709$	19.2193	+	3.38888i	0.721795	+	0.127272i	0.522465	−	0.852660i	$-0.325012\pi$
$709$	19.2193	+	3.38888i	0.721795	+	0.127272i	0.199330	+	0.979932i	$0.436123\pi$
$710$	−28.9536	−	5.97392i	−1.08661	−	0.224197i
$711$	18.5862	+	16.4616i	0.697038	+	0.617358i
$712$	3.45320	+	0.300555i	0.129414	+	0.0112638i
$713$	−10.1266	−	27.8225i	−0.379242	−	1.04196i
$714$	−5.04553	−	5.49151i	−0.188824	−	0.205515i
$715$	26.5220	−	22.2546i	0.991865	−	0.832274i
$716$	13.2720	+	3.14133i	0.495999	+	0.117397i
$717$	−14.8563	−	10.7011i	−0.554818	−	0.399639i
$718$	2.42952	+	3.07168i	0.0906688	+	0.114634i
$719$	20.6637	+	35.7906i	0.770626	+	1.33476i	0.937220	+	0.348737i	$0.113389\pi$
$719$	20.6637	+	35.7906i	0.770626	+	1.33476i	−0.166595	+	0.986025i	$0.553277\pi$
$720$	37.3069	+	12.2394i	1.39035	+	0.456137i
$721$	−6.33269	+	10.9685i	−0.235842	+	0.408490i
$722$	−18.1944	+	2.66787i	−0.677127	+	0.0992879i
$723$	12.2352	−	0.905910i	0.455031	−	0.0336912i
$724$	−3.71720	−	12.4028i	−0.138149	−	0.460947i
$725$	−6.47064	−	36.6968i	−0.240314	−	1.36289i
$726$	5.99087	+	3.10850i	0.222342	+	0.115367i
$727$	−5.83712	+	6.95641i	−0.216487	+	0.257999i	−0.863348	−	0.504609i	$-0.831637\pi$
$727$	−5.83712	+	6.95641i	−0.216487	+	0.257999i	0.646861	+	0.762608i	$0.276081\pi$
$728$	−11.6063	−	8.11903i	−0.430157	−	0.300911i
$729$	−2.16199	+	26.9133i	−0.0800736	+	0.996789i
$730$	−8.36216	−	25.2230i	−0.309498	−	0.933544i
$731$	−4.96552	+	5.91768i	−0.183657	+	0.218873i
$732$	33.3383	+	5.32900i	1.23222	+	0.196965i
$733$	44.2086	−	7.79517i	1.63288	−	0.287921i	0.719337	−	0.694661i	$-0.244446\pi$
$733$	44.2086	−	7.79517i	1.63288	−	0.287921i	0.913544	+	0.406740i	$0.133335\pi$
$734$	15.6427	+	0.452814i	0.577381	+	0.0167137i
$735$	−29.1255	+	2.15650i	−1.07431	+	0.0795435i
$736$	5.11387	−	35.0951i	0.188500	−	1.29362i
$737$	21.5762	+	12.4571i	0.794771	+	0.458861i
$738$	13.9010	+	46.0106i	0.511704	+	1.69367i
$739$	24.0347	+	41.6292i	0.884129	+	1.53136i	0.846709	+	0.532057i	$0.178581\pi$
$739$	24.0347	+	41.6292i	0.884129	+	1.53136i	0.0374202	+	0.999300i	$0.488086\pi$
$740$	23.4073	+	15.3852i	0.860468	+	0.565570i
$741$	−9.13589	+	12.6833i	−0.335615	+	0.465934i
$742$	−4.17788	+	6.77564i	−0.153375	+	0.248741i
$743$	−32.1593	+	26.9848i	−1.17981	+	0.989977i	−0.179828	+	0.983698i	$0.557554\pi$
$743$	−32.1593	+	26.9848i	−1.17981	+	0.989977i	−0.999980	+	0.00627899i	$0.998001\pi$
$744$	−4.31130	+	22.7304i	−0.158060	+	0.833337i
$745$	−21.5043	+	7.82693i	−0.787857	+	0.286756i
$746$	−11.5639	−	10.2879i	−0.423385	−	0.376667i
$747$	5.45116	+	4.82803i	0.199447	+	0.176648i
$748$	1.49748	+	12.7786i	0.0547534	+	0.467233i
$749$	0.763565	−	4.33039i	0.0279000	−	0.158229i
$750$	−3.43668	+	4.49116i	−0.125490	+	0.163994i
$751$	13.3606	−	36.7079i	0.487534	−	1.33949i	−0.415371	−	0.909652i	$-0.636348\pi$
$751$	13.3606	−	36.7079i	0.487534	−	1.33949i	0.902906	−	0.429838i	$-0.141429\pi$
$752$	50.7355	+	5.89937i	1.85013	+	0.215128i
$753$	−3.08109	+	0.781613i	−0.112281	+	0.0284836i
$754$	31.6341	+	12.5619i	1.15204	+	0.457479i
$755$			36.5436i			1.32996i
$756$	2.60082	−	13.8805i	0.0945909	−	0.504828i
$757$			46.6422i			1.69524i	0.530604	+	0.847620i	$0.321965\pi$
$757$			46.6422i			1.69524i	−0.530604	+	0.847620i	$0.678035\pi$
$758$	4.91984	−	12.3894i	0.178697	−	0.450003i
$759$	8.47167	−	30.0073i	0.307502	−	1.08920i
$760$	−9.56861	+	20.5440i	−0.347090	+	0.745209i
$761$	7.07189	−	19.4299i	0.256356	−	0.704332i	−0.743029	−	0.669259i	$-0.766612\pi$
$761$	7.07189	−	19.4299i	0.256356	−	0.704332i	0.999385	−	0.0350727i	$-0.0111663\pi$
$762$	−3.36573	+	25.8315i	−0.121927	+	0.935776i
$763$	−1.79987	+	10.2076i	−0.0651598	+	0.369540i
$764$	−1.83242	−	15.6368i	−0.0662947	−	0.565720i
$765$	−3.23884	−	21.7519i	−0.117100	−	0.786441i
$766$	−12.6344	+	14.2014i	−0.456499	+	0.513118i
$767$	39.7346	−	14.4622i	1.43473	−	0.522200i
$768$	−17.4516	+	21.5277i	−0.629731	+	0.776813i
$769$	−31.2082	+	26.1868i	−1.12540	+	0.944321i	−0.998864	−	0.0476419i	$-0.984829\pi$
$769$	−31.2082	+	26.1868i	−1.12540	+	0.944321i	−0.126533	+	0.991962i	$0.540385\pi$
$770$	−15.3681	−	9.47601i	−0.553828	−	0.341492i
$771$	−11.2272	−	1.13358i	−0.404337	−	0.0408249i
$772$	−25.2097	+	38.3545i	−0.907317	+	1.38041i
$773$	−10.3871	−	17.9910i	−0.373598	−	0.647090i	0.616518	−	0.787341i	$-0.288543\pi$
$773$	−10.3871	−	17.9910i	−0.373598	−	0.647090i	−0.990116	+	0.140250i	$0.955209\pi$
$774$	−14.6059	−	0.813794i	−0.524999	−	0.0292512i
$775$	−23.3351	−	13.4725i	−0.838221	−	0.483947i
$776$	36.0878	−	36.1202i	1.29548	−	1.29664i
$777$	4.37939	−	9.07315i	0.157110	−	0.325498i
$778$	0.342504	−	11.8320i	0.0122794	−	0.424197i
$779$	−27.3218	+	4.81757i	−0.978905	+	0.172607i
$780$	−14.9132	−	39.0163i	−0.533978	−	1.39701i
$781$	11.7920	−	14.0531i	0.421950	−	0.502861i
$782$	−18.8554	+	6.25113i	−0.674268	+	0.223540i
$783$	1.60072	+	33.8979i	0.0572051	+	1.21141i
$784$	5.90025	−	19.7512i	0.210723	−	0.705399i
$785$	14.6647	−	17.4767i	0.523405	−	0.623769i
$786$	24.6734	+	38.6158i	0.880072	+	1.37738i
$787$	5.43029	+	30.7967i	0.193569	+	1.09778i	0.914442	+	0.404717i	$0.132630\pi$
$787$	5.43029	+	30.7967i	0.193569	+	1.09778i	−0.720873	+	0.693067i	$0.756259\pi$
$788$	−35.1475	+	10.5339i	−1.25208	+	0.375256i
$789$	1.07713	+	1.58290i	0.0383469	+	0.0563526i
$790$	−5.55583	−	37.8898i	−0.197668	−	1.34806i
$791$	−5.28765	+	9.15848i	−0.188007	+	0.325638i
$792$	−17.6747	+	16.7696i	−0.628042	+	0.595880i
$793$	−17.9582	−	31.1045i	−0.637715	−	1.10455i
$794$	23.8148	−	18.8361i	0.845155	−	0.668468i
$795$	−21.4053	+	9.63544i	−0.759168	+	0.341734i
$796$	−3.91009	−	0.925473i	−0.138589	−	0.0328025i
$797$	34.7586	−	29.1659i	1.23121	−	1.03311i	0.233052	−	0.972464i	$-0.425129\pi$
$797$	34.7586	−	29.1659i	1.23121	−	1.03311i	0.998159	−	0.0606447i	$-0.0193157\pi$
$798$	7.77733	+	2.44078i	0.275314	+	0.0864027i
$799$	−9.78479	−	26.8835i	−0.346161	−	0.951069i
$800$	−16.9646	−	27.4578i	−0.599789	−	0.970780i
$801$	1.92267	−	3.13371i	0.0679342	−	0.110724i
$802$	8.32817	−	40.3638i	0.294078	−	1.42530i
$803$	16.2389	+	2.86335i	0.573057	+	0.101045i
$804$	22.7127	−	19.6871i	0.801014	−	0.694309i
$805$	9.53403	−	26.1945i	0.336030	−	0.923236i
$806$	21.6620	−	11.6843i	0.763013	−	0.411560i
$807$	3.05127	−	2.97081i	0.107410	−	0.104578i
$808$	12.9279	+	48.1610i	0.454800	+	1.69430i
$809$		−	4.07482i		−	0.143263i	−0.997431	−	0.0716315i	$-0.977179\pi$
$809$		−	4.07482i		−	0.143263i	0.997431	−	0.0716315i	$-0.0228206\pi$
$810$	29.3032	−	29.5911i	1.02961	−	1.03972i
$811$	−27.7403			−0.974095			−0.487047	−	0.873376i	$-0.661926\pi$
$811$	−27.7403			−0.974095			−0.487047	+	0.873376i	$0.661926\pi$
$812$	1.02675	−	17.7199i	0.0360319	−	0.621848i
$813$	12.6080	+	12.9495i	0.442183	+	0.454159i
$814$	−15.2981	+	8.25159i	−0.536197	+	0.289218i
$815$	−8.49962	−	3.09361i	−0.297729	−	0.108364i
$816$	15.1602	+	3.33259i	0.530713	+	0.116664i
$817$	1.46624	−	8.31544i	0.0512971	−	0.290921i
$818$	−24.5789	−	5.07131i	−0.859382	−	0.177314i
$819$	−13.2067	+	7.16141i	−0.461478	+	0.250240i
$820$	29.3432	−	68.0811i	1.02471	−	2.37749i
$821$	−20.0519	+	7.29828i	−0.699815	+	0.254712i	−0.667332	−	0.744761i	$-0.732564\pi$
$821$	−20.0519	+	7.29828i	−0.699815	+	0.254712i	−0.0324830	+	0.999472i	$0.510341\pi$
$822$	−16.3632	−	5.13532i	−0.570734	−	0.179115i
$823$	−8.84276	−	10.5384i	−0.308239	−	0.367345i	0.589579	−	0.807710i	$-0.299293\pi$
$823$	−8.84276	−	10.5384i	−0.308239	−	0.367345i	−0.897819	+	0.440365i	$0.854849\pi$
$824$	−2.30938	−	26.2606i	−0.0804510	−	0.914832i
$825$	−11.6475	−	25.8751i	−0.405513	−	0.900856i
$826$	−13.6792	−	17.2949i	−0.475960	−	0.601765i
$827$	−39.9803	+	23.0826i	−1.39025	+	0.802662i	−0.993343	−	0.115196i	$-0.963250\pi$
$827$	−39.9803	+	23.0826i	−1.39025	+	0.802662i	−0.396909	+	0.917858i	$0.629917\pi$
$828$	−30.8716	−	21.4940i	−1.07286	−	0.746967i
$829$	−48.1207	−	27.7825i	−1.67130	−	0.964925i	−0.966912	−	0.255110i	$-0.917888\pi$
$829$	−48.1207	−	27.7825i	−1.67130	−	0.964925i	−0.704387	−	0.709816i	$-0.748778\pi$
$830$	−1.62947	−	11.1127i	−0.0565598	−	0.385728i
$831$	12.8293	−	8.73006i	0.445042	−	0.302843i
$832$	29.4816	−	0.0264502i	1.02209	−	0.000916994i
$833$	−11.3704	+	2.00492i	−0.393963	+	0.0694663i
$834$	−26.8775	+	17.1733i	−0.930692	+	0.594663i
$835$	37.5165	+	31.4801i	1.29831	+	1.08941i
$836$	−8.40131	−	11.2779i	−0.290565	−	0.390053i
$837$	19.5211	+	14.8692i	0.674749	+	0.513954i
$838$	−49.5540	+	16.4286i	−1.71182	+	0.567518i
$839$	−35.4959	−	29.7846i	−1.22546	−	1.02828i	−0.998521	−	0.0543696i	$-0.982685\pi$
$839$	−35.4959	−	29.7846i	−1.22546	−	1.02828i	−0.226935	−	0.973910i	$-0.572870\pi$
$840$	−16.8653	+	13.7846i	−0.581909	+	0.475613i
$841$	2.37082	+	13.4456i	0.0817525	+	0.463641i
$842$	37.0985	+	1.07390i	1.27850	+	0.0370091i
$843$	37.9024	+	18.2946i	1.30543	+	0.630098i
$844$	−3.84455	−	7.64943i	−0.132335	−	0.263304i
$845$	−0.950013	+	1.64547i	−0.0326814	+	0.0566059i
$846$	29.6559	−	45.3380i	1.01959	−	1.55875i
$847$	−3.24265	+	1.87215i	−0.111419	+	0.0643277i
$848$	−0.973260	−	16.5398i	−0.0334219	−	0.567979i
$849$	−1.14992	+	11.3890i	−0.0394651	+	0.390870i
$850$	−9.48819	+	15.3879i	−0.325442	+	0.527799i
$851$	−17.2501	−	20.5578i	−0.591325	−	0.704713i
$852$	−11.3719	−	18.9872i	−0.389594	−	0.650492i
$853$	7.11678	+	19.5532i	0.243674	+	0.669489i	0.999885	+	0.0151612i	$0.00482613\pi$
$853$	7.11678	+	19.5532i	0.243674	+	0.669489i	−0.756211	+	0.654328i	$0.772952\pi$
$854$	−12.4494	+	13.9935i	−0.426009	+	0.478846i
$855$	14.9537	+	18.8203i	0.511407	+	0.643639i
$856$	3.87169	+	8.29316i	0.132332	+	0.283454i
$857$	−52.7015	−	9.29269i	−1.80025	−	0.317432i	−0.829676	−	0.558245i	$-0.811475\pi$
$857$	−52.7015	−	9.29269i	−1.80025	−	0.317432i	−0.970572	+	0.240813i	$0.922586\pi$
$858$	25.7019	+	3.34885i	0.877450	+	0.114328i
$859$	−6.25960	−	2.27831i	−0.213575	−	0.0777349i	0.233017	−	0.972473i	$-0.425140\pi$
$859$	−6.25960	−	2.27831i	−0.213575	−	0.0777349i	−0.446592	+	0.894738i	$0.647362\pi$
$860$	16.4166	+	15.4789i	0.559800	+	0.527827i
$861$	−25.6616	−	7.24479i	−0.874544	−	0.246902i
$862$	−6.32237	+	15.9213i	−0.215341	+	0.542281i
$863$	−26.7202			−0.909566			−0.454783	−	0.890602i	$-0.650283\pi$
$863$	−26.7202			−0.909566			−0.454783	+	0.890602i	$0.650283\pi$
$864$	12.1489	+	26.7657i	0.413313	+	0.910589i
$865$	25.2963			0.860099
$866$	−11.4518	+	28.8384i	−0.389147	+	0.979968i
$867$	5.10244	+	20.1137i	0.173288	+	0.683096i
$868$	−9.33838	−	8.80503i	−0.316965	−	0.298862i
$869$	22.3302	+	8.12751i	0.757499	+	0.275707i
$870$	31.8088	−	41.5687i	1.07842	−	1.40931i
$871$	−31.4900	−	5.55254i	−1.06700	−	0.188141i
$872$	−9.12635	−	19.5486i	−0.309057	−	0.662000i
$873$	−17.1562	−	51.3667i	−0.580650	−	1.73850i
$874$	14.4322	−	16.2222i	0.488176	−	0.548724i
$875$	−1.07302	−	2.94811i	−0.0362748	−	0.0996643i
$876$	9.66933	−	17.3854i	0.326696	−	0.587400i
$877$	19.4723	+	23.2062i	0.657534	+	0.783618i	0.987030	−	0.160539i	$-0.0513232\pi$
$877$	19.4723	+	23.2062i	0.657534	+	0.783618i	−0.329496	+	0.944157i	$0.606879\pi$
$878$	13.8114	−	22.3992i	0.466112	−	0.755936i
$879$	−42.7656	−	30.8043i	−1.44245	−	1.03900i
$880$	37.5146	−	2.20749i	1.26462	−	0.0744145i
$881$	−26.4220	+	15.2548i	−0.890181	+	0.513946i	−0.874002	−	0.485923i	$-0.838484\pi$
$881$	−26.4220	+	15.2548i	−0.890181	+	0.513946i	−0.0161793	+	0.999869i	$0.505150\pi$
$882$	−15.9411	−	14.9639i	−0.536764	−	0.503862i
$883$	−21.5979	+	37.4087i	−0.726827	+	1.25890i	0.231391	+	0.972861i	$0.425672\pi$
$883$	−21.5979	+	37.4087i	−0.726827	+	1.25890i	−0.958218	+	0.286040i	$0.907661\pi$
$884$	−7.41538	−	14.7542i	−0.249406	−	0.496238i
$885$	−4.80148	−	64.8486i	−0.161400	−	2.17986i
$886$	−0.738875	−	0.0213885i	−0.0248230	−	0.000718560i
$887$	−7.61863	−	43.2074i	−0.255809	−	1.45076i	−0.793989	−	0.607933i	$-0.791999\pi$
$887$	−7.61863	−	43.2074i	−0.255809	−	1.45076i	0.538180	−	0.842830i	$-0.319112\pi$
$888$	3.37444	+	20.6966i	0.113239	+	0.694531i
$889$	−11.0705	−	9.28928i	−0.371294	−	0.311553i
$890$	−5.38260	+	1.78449i	−0.180425	+	0.0598164i
$891$	7.52880	+	24.7210i	0.252224	+	0.828186i
$892$	18.1491	+	24.3633i	0.607678	+	0.815744i
$893$	23.9547	+	20.1004i	0.801612	+	0.672633i
$894$	−15.2069	−	7.89042i	−0.508593	−	0.263895i
$895$	−21.9736	+	3.87453i	−0.734495	+	0.129511i
$896$	−4.85112	−	14.5887i	−0.162065	−	0.487374i
$897$	2.95490	+	39.9088i	0.0986613	+	1.33251i
$898$	2.12751	+	14.5092i	0.0709959	+	0.484180i
$899$	26.7105	+	15.4213i	0.890845	+	0.514329i
$900$	−34.0953	+	3.07464i	−1.13651	+	0.102488i
$901$	−8.03679	+	4.64005i	−0.267744	+	0.154582i
$902$	28.5383	+	36.0815i	0.950222	+	1.20138i
$903$	4.74322	−	6.58500i	0.157844	−	0.219135i
$904$	−1.92828	−	21.9270i	−0.0641336	−	0.729282i
$905$	13.6157	+	16.2266i	0.452603	+	0.539391i
$906$	−20.1456	+	18.5096i	−0.669293	+	0.614939i
$907$	35.4010	−	12.8849i	1.17547	−	0.427836i	0.320870	−	0.947123i	$-0.396025\pi$
$907$	35.4010	−	12.8849i	1.17547	−	0.427836i	0.854600	+	0.519287i	$0.173802\pi$
$908$	−14.5347	+	33.7229i	−0.482350	+	1.11913i
$909$	51.8233	+	10.5727i	1.71887	+	0.350675i
$910$	22.6942	+	4.68243i	0.752305	+	0.155221i
$911$	−4.75504	+	26.9672i	−0.157541	+	0.893462i	0.798884	+	0.601485i	$0.205424\pi$
$911$	−4.75504	+	26.9672i	−0.157541	+	0.893462i	−0.956425	+	0.291977i	$0.905687\pi$
$912$	−16.1720	+	5.13072i	−0.535508	+	0.169895i
$913$	6.54922	+	2.38372i	0.216748	+	0.0788897i
$914$	9.52082	−	5.13542i	0.314921	−	0.169865i
$915$	−53.5372	+	13.5813i	−1.76988	+	0.448985i
$916$	−2.48138	+	42.8243i	−0.0819871	+	1.41495i
$917$	−25.4223			−0.839518
$918$	10.3508	−	12.8029i	0.341627	−	0.422560i
$919$		−	40.1046i		−	1.32293i	−0.749976	−	0.661465i	$-0.769935\pi$
$919$		−	40.1046i		−	1.32293i	0.749976	−	0.661465i	$-0.230065\pi$
$920$	15.0421	+	56.0371i	0.495922	+	1.84749i
$921$	9.44710	+	2.66711i	0.311293	+	0.0878843i
$922$	6.47089	−	3.49032i	0.213107	−	0.114948i
$923$	−8.05281	+	22.1249i	−0.265061	+	0.728250i
$924$	−2.56014	−	13.2717i	−0.0842223	−	0.436608i
$925$	−24.0516	−	4.24094i	−0.790810	−	0.139441i
$926$	−7.15505	+	34.6781i	−0.235130	+	1.13959i
$927$	−26.0100	−	10.2618i	−0.854279	−	0.337042i
$928$	19.4185	+	31.4296i	0.637444	+	1.03173i
$929$	1.55733	+	4.27874i	0.0510945	+	0.140381i	0.962615	−	0.270874i	$-0.0873127\pi$
$929$	1.55733	+	4.27874i	0.0510945	+	0.140381i	−0.911520	+	0.411255i	$0.865091\pi$
$930$	−8.24137	−	36.9411i	−0.270245	−	1.21135i
$931$	9.66755	−	8.11204i	0.316841	−	0.265861i
$932$	−11.0566	−	2.61698i	−0.362172	−	0.0857220i
$933$	−0.148641	+	1.47217i	−0.00486630	+	0.0481967i
$934$	−7.06488	+	5.58790i	−0.231170	+	0.182842i
$935$	−10.5243	−	18.2286i	−0.344181	−	0.596138i
$936$	13.9551	−	27.9833i	0.456138	−	0.914662i
$937$	−20.7897	+	36.0087i	−0.679168	+	1.17635i	0.296063	+	0.955168i	$0.404326\pi$
$937$	−20.7897	+	36.0087i	−0.679168	+	1.17635i	−0.975232	+	0.221186i	$0.929007\pi$
$938$	2.41918	+	16.4984i	0.0789889	+	0.538691i
$939$	17.7713	−	36.8184i	0.579946	−	1.20152i
$940$	−80.0435	+	23.9895i	−2.61073	+	0.782452i
$941$	0.174402	+	0.989083i	0.00568534	+	0.0322432i	0.987518	−	0.157503i	$-0.0503445\pi$
$941$	0.174402	+	0.989083i	0.00568534	+	0.0322432i	−0.981833	+	0.189747i	$0.939233\pi$
$942$	17.0622	−	0.767759i	0.555917	−	0.0250149i
$943$	−45.6553	+	54.4098i	−1.48674	+	1.77183i
$944$	43.9764	+	13.1370i	1.43131	+	0.427574i
$945$	5.08058	+	22.5377i	0.165271	+	0.733151i
$946$	−13.2899	+	4.40600i	−0.432092	+	0.143251i
$947$	17.8652	−	21.2910i	0.580543	−	0.691864i	−0.393216	−	0.919446i	$-0.628638\pi$
$947$	17.8652	−	21.2910i	0.580543	−	0.691864i	0.973759	+	0.227582i	$0.0730821\pi$
$948$	18.0737	−	22.2542i	0.587006	−	0.722783i
$949$	−20.8417	+	3.67495i	−0.676549	+	0.119294i
$950$	0.571758	−	19.7516i	0.0185503	−	0.640828i
$951$	−20.0962	−	29.5324i	−0.651664	−	0.957652i
$952$	−6.08628	+	6.09174i	−0.197257	+	0.197435i
$953$	13.5698	+	7.83453i	0.439569	+	0.253785i	0.703415	−	0.710780i	$-0.251658\pi$
$953$	13.5698	+	7.83453i	0.439569	+	0.253785i	−0.263846	+	0.964565i	$0.584991\pi$
$954$	−16.1537	−	6.91983i	−0.522995	−	0.224038i
$955$	12.8782	+	22.3057i	0.416729	+	0.721796i
$956$	−11.6122	+	17.6670i	−0.375564	+	0.571390i
$957$	13.3323	+	29.6179i	0.430972	+	0.957412i
$958$	27.6598	+	17.0551i	0.893649	+	0.551026i
$959$	7.28838	−	6.11568i	0.235354	−	0.197486i
$960$	12.2790	−	43.6429i	0.396304	−	1.40857i
$961$	−8.17302	+	2.97474i	−0.263646	+	0.0959592i
$962$	14.8279	−	16.6670i	0.478072	−	0.537367i
$963$	9.70413	+	0.259354i	0.312711	+	0.00835757i
$964$	−1.64885	−	14.0704i	−0.0531060	−	0.453176i
$965$	13.0388	−	73.9465i	0.419733	−	2.38042i
$966$	19.2695	−	8.01180i	0.619985	−	0.257776i
$967$	−20.0933	+	55.2059i	−0.646157	+	1.77530i	−0.0147000	+	0.999892i	$0.504679\pi$
$967$	−20.0933	+	55.2059i	−0.646157	+	1.77530i	−0.631457	+	0.775411i	$0.717543\pi$
$968$	3.29048	−	7.06473i	0.105760	−	0.227069i
$969$	6.62925	+	6.80880i	0.212962	+	0.218730i
$970$	−30.8284	+	77.6336i	−0.989841	+	2.49267i
$971$		−	3.85494i		−	0.123711i	−0.998085	−	0.0618554i	$-0.980298\pi$
$971$		−	3.85494i		−	0.123711i	0.998085	−	0.0618554i	$-0.0197018\pi$
$972$	31.1551	+	1.16611i	0.999300	+	0.0374029i
$973$		−	17.6945i		−	0.567261i
$974$	−22.5821	−	8.96739i	−0.723578	−	0.287334i
$975$	25.4056	+	26.0936i	0.813629	+	0.835665i
$976$	4.50266	−	38.7236i	0.144127	−	1.23951i
$977$	1.13249	−	3.11148i	0.0362314	−	0.0995450i	−0.920258	−	0.391313i	$-0.872021\pi$
$977$	1.13249	−	3.11148i	0.0362314	−	0.0995450i	0.956489	+	0.291768i	$0.0942434\pi$
$978$	−2.59968	−	6.25257i	−0.0831284	−	0.199935i
$979$	0.611042	−	3.46539i	0.0195290	−	0.110754i
$980$	3.92506	+	33.4941i	0.125381	+	1.06993i
$981$	−22.8746	−	0.611349i	−0.730328	−	0.0195189i
$982$	13.3494	+	11.8764i	0.425997	+	0.378991i
$983$	52.1125	−	18.9674i	1.66213	−	0.604966i	0.671435	−	0.741063i	$-0.265678\pi$
$983$	52.1125	−	18.9674i	1.66213	−	0.604966i	0.990695	+	0.136097i	$0.0434560\pi$
$984$	52.3940	−	18.3073i	1.67026	−	0.583615i
$985$	45.9836	−	38.5848i	1.46516	−	1.22941i
$986$	10.8607	−	17.6137i	0.345874	−	0.560934i
$987$	12.3367	+	27.4062i	0.392681	+	0.872348i
$988$	15.0829	+	9.91371i	0.479851	+	0.315397i
$989$	−10.8086	−	18.7211i	−0.343694	−	0.595295i
$990$	15.6951	−	36.6389i	0.498824	−	1.16446i
$991$	52.1447	+	30.1057i	1.65643	+	0.956341i	0.974343	+	0.225070i	$0.0722612\pi$
$991$	52.1447	+	30.1057i	1.65643	+	0.956341i	0.682088	+	0.731270i	$0.261072\pi$
$992$	26.4356	+	3.85206i	0.839331	+	0.122303i
$993$	−18.2981	−	26.8900i	−0.580672	−	0.853327i
$994$	12.2731	+	0.355273i	0.389278	+	0.0112686i
$995$	6.47366	−	1.14148i	0.205229	−	0.0361874i
$996$	5.30084	−	6.52695i	0.167964	−	0.206814i
$997$	−20.0612	+	23.9080i	−0.635343	+	0.757172i	−0.983627	−	0.180217i	$-0.942320\pi$
$997$	−20.0612	+	23.9080i	−0.635343	+	0.757172i	0.348284	+	0.937389i	$0.386765\pi$
$998$	1.04939	+	3.16531i	0.0332180	+	0.100196i
$999$	21.2361	+	6.61284i	0.671880	+	0.209221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.11	yes	192
3.2	odd	2		648.2.v.b.35.22		192
4.3	odd	2		864.2.bh.b.335.8		192
8.3	odd	2	inner	216.2.v.b.11.8	✓	192
8.5	even	2		864.2.bh.b.335.7		192
24.11	even	2		648.2.v.b.35.25		192
27.5	odd	18	inner	216.2.v.b.59.8	yes	192
27.22	even	9		648.2.v.b.611.25		192
108.59	even	18		864.2.bh.b.815.7		192
216.5	odd	18		864.2.bh.b.815.8		192
216.59	even	18	inner	216.2.v.b.59.11	yes	192
216.211	odd	18		648.2.v.b.611.22		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.8	✓	192	8.3	odd	2	inner
216.2.v.b.11.11	yes	192	1.1	even	1	trivial
216.2.v.b.59.8	yes	192	27.5	odd	18	inner
216.2.v.b.59.11	yes	192	216.59	even	18	inner
648.2.v.b.35.22		192	3.2	odd	2
648.2.v.b.35.25		192	24.11	even	2
648.2.v.b.611.22		192	216.211	odd	18
648.2.v.b.611.25		192	27.22	even	9
864.2.bh.b.335.7		192	8.5	even	2
864.2.bh.b.335.8		192	4.3	odd	2
864.2.bh.b.815.7		192	108.59	even	18
864.2.bh.b.815.8		192	216.5	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.521940 + 1.31437i) q^{2} +(1.24100 - 1.20827i) q^{3} +(-1.45516 - 1.37205i) q^{4} +(3.07462 + 1.11907i) q^{5} +(0.940397 + 2.26178i) q^{6} +(-1.33825 - 0.235969i) q^{7} +(2.56289 - 1.19649i) q^{8} +(0.0801499 - 2.99893i) q^{9} +O(q^{10})\)	\(q+(-0.521940 + 1.31437i) q^{2} +(1.24100 - 1.20827i) q^{3} +(-1.45516 - 1.37205i) q^{4} +(3.07462 + 1.11907i) q^{5} +(0.940397 + 2.26178i) q^{6} +(-1.33825 - 0.235969i) q^{7} +(2.56289 - 1.19649i) q^{8} +(0.0801499 - 2.99893i) q^{9} +(-3.07564 + 3.45711i) q^{10} +(-0.982057 - 2.69818i) q^{11} +(-3.46366 + 0.0555201i) q^{12} +(2.36880 + 2.82303i) q^{13} +(1.00864 - 1.63580i) q^{14} +(5.16774 - 2.32622i) q^{15} +(0.234968 + 3.99309i) q^{16} +(1.94027 - 1.12022i) q^{17} +(3.89988 + 1.67061i) q^{18} +(-1.22444 + 2.12079i) q^{19} +(-2.93864 - 5.84695i) q^{20} +(-1.94588 + 1.32413i) q^{21} +(4.05899 + 0.117497i) q^{22} +(1.08869 + 6.17426i) q^{23} +(1.73485 - 4.58152i) q^{24} +(4.37075 + 3.66750i) q^{25} +(-4.94689 + 1.64004i) q^{26} +(-3.52406 - 3.81851i) q^{27} +(1.62360 + 2.17951i) q^{28} +(-5.00298 - 4.19800i) q^{29} +(0.360273 + 8.00649i) q^{30} +(-4.65080 + 0.820062i) q^{31} +(-5.37106 - 1.77532i) q^{32} +(-4.47887 - 2.16184i) q^{33} +(0.459678 + 3.13493i) q^{34} +(-3.85054 - 2.22311i) q^{35} +(-4.23131 + 4.25395i) q^{36} +(-3.70698 + 2.14023i) q^{37} +(-2.14843 - 2.71630i) q^{38} +(6.35067 + 0.641210i) q^{39} +(9.21887 - 0.810714i) q^{40} +(7.28211 + 8.67848i) q^{41} +(-0.724774 - 3.24873i) q^{42} +(-3.24005 + 1.17928i) q^{43} +(-2.27298 + 5.27370i) q^{44} +(3.60244 - 9.13088i) q^{45} +(-8.68352 - 1.79165i) q^{46} +(2.21737 - 12.5753i) q^{47} +(5.11634 + 4.67151i) q^{48} +(-4.84262 - 1.76257i) q^{49} +(-7.10173 + 3.83059i) q^{50} +(1.05434 - 3.73456i) q^{51} +(0.426350 - 7.35806i) q^{52} -4.14210 q^{53} +(6.85829 - 2.63890i) q^{54} -9.39487i q^{55} +(-3.71212 + 0.996444i) q^{56} +(1.04297 + 4.11136i) q^{57} +(8.12900 - 4.38468i) q^{58} +(3.92440 - 10.7822i) q^{59} +(-10.7116 - 3.70537i) q^{60} +(-9.59806 - 1.69240i) q^{61} +(1.34957 - 6.54091i) q^{62} +(-0.814916 + 3.99440i) q^{63} +(5.13680 - 6.13297i) q^{64} +(4.12400 + 11.3306i) q^{65} +(5.17917 - 4.75856i) q^{66} +(-6.64683 + 5.57735i) q^{67} +(-4.36039 - 1.03205i) q^{68} +(8.81126 + 6.34681i) q^{69} +(4.93175 - 3.90072i) q^{70} +(3.19451 + 5.53306i) q^{71} +(-3.38279 - 7.78182i) q^{72} +(-2.87137 + 4.97336i) q^{73} +(-0.878236 - 5.98943i) q^{74} +(9.85543 - 0.729710i) q^{75} +(4.69159 - 1.40610i) q^{76} +(0.677549 + 3.84257i) q^{77} +(-4.15746 + 8.01248i) q^{78} +(-5.31972 + 6.33979i) q^{79} +(-3.74612 + 12.5402i) q^{80} +(-8.98715 - 0.480728i) q^{81} +(-15.2076 + 5.04177i) q^{82} +(-1.56022 + 1.85940i) q^{83} +(4.64833 + 0.743017i) q^{84} +(7.21919 - 1.27294i) q^{85} +(0.141094 - 4.87415i) q^{86} +(-11.2810 + 0.835263i) q^{87} +(-5.74526 - 5.74011i) q^{88} +(1.06132 + 0.612754i) q^{89} +(10.1211 + 9.50073i) q^{90} +(-2.50390 - 4.33688i) q^{91} +(6.88717 - 10.4783i) q^{92} +(-4.78077 + 6.63713i) q^{93} +(15.3714 + 9.47803i) q^{94} +(-6.13801 + 5.15040i) q^{95} +(-8.81054 + 4.28654i) q^{96} +(16.9633 - 6.17414i) q^{97} +(4.84423 - 5.44506i) q^{98} +(-8.17036 + 2.72886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

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