LMFDB - Embedded newform 234.2.z.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.880877 + 1.49133i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.93052 - 0.517281i) q^{5} +(-1.23685 - 1.21252i) q^{6} +(1.87601 + 1.87601i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.44811 + 2.62735i) q^{9} +(-1.73086 + 0.999310i) q^{10} +(-1.12909 - 4.21380i) q^{11} +(1.50853 + 0.851088i) q^{12} +(1.69527 - 3.18215i) q^{13} +(-2.29763 - 1.32654i) q^{14} +(2.47199 + 2.42337i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.21062 + 2.09686i) q^{17} +(0.718758 - 2.91263i) q^{18} +(1.64767 + 6.14918i) q^{19} +(1.41324 - 1.41324i) q^{20} +(-1.14521 + 4.45027i) q^{21} +(2.18123 + 3.77799i) q^{22} -1.22153 q^{23} +(-1.67740 - 0.431653i) q^{24} +(-0.870804 + 0.502759i) q^{25} +(-0.813901 + 3.51249i) q^{26} +(-5.19385 + 0.154769i) q^{27} +(2.56267 + 0.686666i) q^{28} +(-3.87626 - 2.23796i) q^{29} +(-3.01497 - 1.70100i) q^{30} +(2.18253 + 8.14531i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(5.28957 - 5.39568i) q^{33} +(0.626664 - 2.33874i) q^{34} +(4.59209 + 2.65124i) q^{35} +(0.0595757 + 2.99941i) q^{36} +(2.49571 - 9.31410i) q^{37} +(-3.18305 - 5.51321i) q^{38} +(6.23895 - 0.274886i) q^{39} +(-0.999310 + 1.73086i) q^{40} +(-4.85400 - 4.85400i) q^{41} +(-0.0456298 - 4.59503i) q^{42} -10.2840i q^{43} +(-3.08472 - 3.08472i) q^{44} +(-1.43652 + 5.82123i) q^{45} +(1.17991 - 0.316156i) q^{46} +(5.22728 + 1.40065i) q^{47} +(1.73197 - 0.0171989i) q^{48} +0.0387948i q^{49} +(0.711008 - 0.711008i) q^{50} +(-4.19351 + 0.0416426i) q^{51} +(-0.122930 - 3.60346i) q^{52} -0.142416i q^{53} +(4.97681 - 1.49376i) q^{54} +(-4.35944 - 7.55077i) q^{55} -2.65307 q^{56} +(-7.71905 + 7.87389i) q^{57} +(4.32340 + 1.15845i) q^{58} +(-3.88086 - 1.03987i) q^{59} +(3.35249 + 0.862710i) q^{60} -10.0548 q^{61} +(-4.21632 - 7.30289i) q^{62} +(-7.64559 + 2.21226i) q^{63} -1.00000i q^{64} +(1.62668 - 7.02013i) q^{65} +(-3.71283 + 6.58087i) q^{66} +(1.78863 - 1.78863i) q^{67} +2.42124i q^{68} +(-1.07602 - 1.82170i) q^{69} +(-5.12181 - 1.37238i) q^{70} +(7.11876 - 1.90747i) q^{71} +(-0.833850 - 2.88179i) q^{72} +(-4.15800 - 4.15800i) q^{73} +9.64266i q^{74} +(-1.51685 - 0.855784i) q^{75} +(4.50152 + 4.50152i) q^{76} +(5.78695 - 10.0233i) q^{77} +(-5.95521 + 1.88028i) q^{78} +(-0.161842 - 0.280319i) q^{79} +(0.517281 - 1.93052i) q^{80} +(-4.80595 - 7.60939i) q^{81} +(5.94491 + 3.43230i) q^{82} +(-1.01813 + 3.79971i) q^{83} +(1.23336 + 4.42665i) q^{84} +(-1.25246 + 4.67425i) q^{85} +(2.66170 + 9.93360i) q^{86} +(-0.0769806 - 7.75213i) q^{87} +(3.77799 + 2.18123i) q^{88} +(14.2994 + 3.83151i) q^{89} +(-0.119069 - 5.99468i) q^{90} +(9.15006 - 2.78940i) q^{91} +(-1.05788 + 0.610766i) q^{92} +(-10.2248 + 10.4299i) q^{93} -5.41168 q^{94} +(6.36171 + 11.0188i) q^{95} +(-1.66850 + 0.464878i) q^{96} +(-6.20661 + 6.20661i) q^{97} +(-0.0100408 - 0.0374729i) q^{98} +(12.7062 + 3.13555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.880877	+	1.49133i	0.508575	+	0.861018i
$3$	0.880877	+	1.49133i	0.508575	+	0.861018i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.93052	−	0.517281i	0.863354	−	0.231335i	0.200142	−	0.979767i	$-0.435860\pi$
$5$	1.93052	−	0.517281i	0.863354	−	0.231335i	0.663212	+	0.748432i	$0.269193\pi$
$6$	−1.23685	−	1.21252i	−0.504940	−	0.495010i
$7$	1.87601	+	1.87601i	0.709064	+	0.709064i	0.966338	−	0.257275i	$-0.0828245\pi$
$7$	1.87601	+	1.87601i	0.709064	+	0.709064i	−0.257275	+	0.966338i	$0.582825\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.44811	+	2.62735i	−0.482703	+	0.875784i
$10$	−1.73086	+	0.999310i	−0.547345	+	0.316010i
$11$	−1.12909	−	4.21380i	−0.340432	−	1.27051i	−0.897859	−	0.440284i	$-0.854878\pi$
$11$	−1.12909	−	4.21380i	−0.340432	−	1.27051i	0.557427	−	0.830226i	$-0.311789\pi$
$12$	1.50853	+	0.851088i	0.435474	+	0.245688i
$13$	1.69527	−	3.18215i	0.470182	−	0.882569i
$13$	1.69527	−	3.18215i	0.470182	−	0.882569i
$14$	−2.29763	−	1.32654i	−0.614067	−	0.354532i
$15$	2.47199	+	2.42337i	0.638264	+	0.625712i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.21062	+	2.09686i	−0.293619	+	0.508563i	−0.974663	−	0.223680i	$-0.928193\pi$
$17$	−1.21062	+	2.09686i	−0.293619	+	0.508563i	0.681044	+	0.732243i	$0.261526\pi$
$18$	0.718758	−	2.91263i	0.169413	−	0.686512i
$19$	1.64767	+	6.14918i	0.378001	+	1.41072i	0.848910	+	0.528538i	$0.177259\pi$
$19$	1.64767	+	6.14918i	0.378001	+	1.41072i	−0.470909	+	0.882182i	$0.656074\pi$
$20$	1.41324	−	1.41324i	0.316010	−	0.316010i
$21$	−1.14521	+	4.45027i	−0.249905	+	0.971128i
$22$	2.18123	+	3.77799i	0.465039	+	0.805471i
$23$	−1.22153			−0.254707			−0.127353	−	0.991857i	$-0.540648\pi$
$23$	−1.22153			−0.254707			−0.127353	+	0.991857i	$0.540648\pi$
$24$	−1.67740	−	0.431653i	−0.342398	−	0.0881108i
$25$	−0.870804	+	0.502759i	−0.174161	+	0.100552i
$26$	−0.813901	+	3.51249i	−0.159619	+	0.688855i
$27$	−5.19385	+	0.154769i	−0.999556	+	0.0297854i
$28$	2.56267	+	0.686666i	0.484299	+	0.129768i
$29$	−3.87626	−	2.23796i	−0.719803	−	0.415578i	0.0948775	−	0.995489i	$-0.469754\pi$
$29$	−3.87626	−	2.23796i	−0.719803	−	0.415578i	−0.814680	+	0.579911i	$0.803087\pi$
$30$	−3.01497	−	1.70100i	−0.550456	−	0.310559i
$31$	2.18253	+	8.14531i	0.391994	+	1.46294i	0.826840	+	0.562437i	$0.190136\pi$
$31$	2.18253	+	8.14531i	0.391994	+	1.46294i	−0.434847	+	0.900505i	$0.643197\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	5.28957	−	5.39568i	0.920796	−	0.939267i
$34$	0.626664	−	2.33874i	0.107472	−	0.401091i
$35$	4.59209	+	2.65124i	0.776204	+	0.448142i
$36$	0.0595757	+	2.99941i	0.00992928	+	0.499901i
$37$	2.49571	−	9.31410i	0.410291	−	1.53123i	−0.383792	−	0.923420i	$-0.625382\pi$
$37$	2.49571	−	9.31410i	0.410291	−	1.53123i	0.794083	−	0.607809i	$-0.207951\pi$
$38$	−3.18305	−	5.51321i	−0.516359	−	0.894360i
$39$	6.23895	−	0.274886i	0.999031	−	0.0440170i
$40$	−0.999310	+	1.73086i	−0.158005	+	0.273672i
$41$	−4.85400	−	4.85400i	−0.758067	−	0.758067i	0.217903	−	0.975970i	$-0.430078\pi$
$41$	−4.85400	−	4.85400i	−0.758067	−	0.758067i	−0.975970	+	0.217903i	$0.930078\pi$
$42$	−0.0456298	−	4.59503i	−0.00704084	−	0.709029i
$43$		−	10.2840i		−	1.56830i	−0.620573	−	0.784149i	$-0.713100\pi$
$43$		−	10.2840i		−	1.56830i	0.620573	−	0.784149i	$-0.286900\pi$
$44$	−3.08472	−	3.08472i	−0.465039	−	0.465039i
$45$	−1.43652	+	5.82123i	−0.214144	+	0.867778i
$46$	1.17991	−	0.316156i	0.173968	−	0.0466146i
$47$	5.22728	+	1.40065i	0.762477	+	0.204305i	0.619046	−	0.785355i	$-0.287520\pi$
$47$	5.22728	+	1.40065i	0.762477	+	0.204305i	0.143432	+	0.989660i	$0.454186\pi$
$48$	1.73197	−	0.0171989i	0.249988	−	0.00248244i
$49$			0.0387948i			0.00554211i
$50$	0.711008	−	0.711008i	0.100552	−	0.100552i
$51$	−4.19351	+	0.0416426i	−0.587209	+	0.00583113i
$52$	−0.122930	−	3.60346i	−0.0170473	−	0.499709i
$53$		−	0.142416i		−	0.0195624i	−0.999952	−	0.00978119i	$-0.996887\pi$
$53$		−	0.142416i		−	0.0195624i	0.999952	−	0.00978119i	$-0.00311350\pi$
$54$	4.97681	−	1.49376i	0.677259	−	0.203275i
$55$	−4.35944	−	7.55077i	−0.587827	−	1.01815i
$56$	−2.65307			−0.354532
$57$	−7.71905	+	7.87389i	−1.02241	+	1.04292i
$58$	4.32340	+	1.15845i	0.567690	+	0.152112i
$59$	−3.88086	−	1.03987i	−0.505245	−	0.135380i	−0.00281160	−	0.999996i	$-0.500895\pi$
$59$	−3.88086	−	1.03987i	−0.505245	−	0.135380i	−0.502433	+	0.864616i	$0.667562\pi$
$60$	3.35249	+	0.862710i	0.432804	+	0.111375i
$61$	−10.0548			−1.28738			−0.643689	−	0.765287i	$-0.722597\pi$
$61$	−10.0548			−1.28738			−0.643689	+	0.765287i	$0.722597\pi$
$62$	−4.21632	−	7.30289i	−0.535474	−	0.927467i
$63$	−7.64559	+	2.21226i	−0.963254	+	0.278719i
$64$		−	1.00000i		−	0.125000i
$65$	1.62668	−	7.02013i	0.201765	−	0.870740i
$66$	−3.71283	+	6.58087i	−0.457018	+	0.810049i
$67$	1.78863	−	1.78863i	0.218516	−	0.218516i	−0.589357	−	0.807873i	$-0.700619\pi$
$67$	1.78863	−	1.78863i	0.218516	−	0.218516i	0.807873	+	0.589357i	$0.200619\pi$
$68$			2.42124i			0.293619i
$69$	−1.07602	−	1.82170i	−0.129538	−	0.219307i
$70$	−5.12181	−	1.37238i	−0.612173	−	0.164031i
$71$	7.11876	−	1.90747i	0.844841	−	0.226375i	0.189663	−	0.981849i	$-0.439260\pi$
$71$	7.11876	−	1.90747i	0.844841	−	0.226375i	0.655178	+	0.755475i	$0.272594\pi$
$72$	−0.833850	−	2.88179i	−0.0982701	−	0.339622i
$73$	−4.15800	−	4.15800i	−0.486657	−	0.486657i	0.420592	−	0.907250i	$-0.361822\pi$
$73$	−4.15800	−	4.15800i	−0.486657	−	0.486657i	−0.907250	+	0.420592i	$0.861822\pi$
$74$			9.64266i			1.12094i
$75$	−1.51685	−	0.855784i	−0.175151	−	0.0988174i
$76$	4.50152	+	4.50152i	0.516359	+	0.516359i
$77$	5.78695	−	10.0233i	0.659484	−	1.14226i
$78$	−5.95521	+	1.88028i	−0.674295	+	0.212899i
$79$	−0.161842	−	0.280319i	−0.0182087	−	0.0315383i	0.856777	−	0.515686i	$-0.172463\pi$
$79$	−0.161842	−	0.280319i	−0.0182087	−	0.0315383i	−0.874986	+	0.484148i	$0.839130\pi$
$80$	0.517281	−	1.93052i	0.0578338	−	0.215839i
$81$	−4.80595	−	7.60939i	−0.533995	−	0.845488i
$82$	5.94491	+	3.43230i	0.656505	+	0.379034i
$83$	−1.01813	+	3.79971i	−0.111754	+	0.417072i	−0.999024	−	0.0441792i	$-0.985933\pi$
$83$	−1.01813	+	3.79971i	−0.111754	+	0.417072i	0.887269	+	0.461252i	$0.152599\pi$
$84$	1.23336	+	4.42665i	0.134570	+	0.482987i
$85$	−1.25246	+	4.67425i	−0.135849	+	0.506994i
$86$	2.66170	+	9.93360i	0.287018	+	1.07117i
$87$	−0.0769806	−	7.75213i	−0.00825319	−	0.831115i
$88$	3.77799	+	2.18123i	0.402735	+	0.232519i
$89$	14.2994	+	3.83151i	1.51573	+	0.406140i	0.918335	−	0.395805i	$-0.129534\pi$
$89$	14.2994	+	3.83151i	1.51573	+	0.406140i	0.597399	+	0.801944i	$0.296201\pi$
$90$	−0.119069	−	5.99468i	−0.0125510	−	0.631895i
$91$	9.15006	−	2.78940i	0.959187	−	0.292408i
$92$	−1.05788	+	0.610766i	−0.110291	+	0.0636767i
$93$	−10.2248	+	10.4299i	−1.06026	+	1.08153i
$94$	−5.41168			−0.558172
$95$	6.36171	+	11.0188i	0.652698	+	1.13051i
$96$	−1.66850	+	0.464878i	−0.170290	+	0.0474465i
$97$	−6.20661	+	6.20661i	−0.630185	+	0.630185i	−0.948115	−	0.317929i	$-0.897013\pi$
$97$	−6.20661	+	6.20661i	−0.630185	+	0.630185i	0.317929	+	0.948115i	$0.397013\pi$
$98$	−0.0100408	−	0.0374729i	−0.00101428	−	0.00378533i
$99$	12.7062	+	3.13555i	1.27702	+	0.315134i
$100$	−0.502759	+	0.870804i	−0.0502759	+	0.0870804i
$101$	−1.76687	+	3.06031i	−0.175810	+	0.304512i	−0.940441	−	0.339956i	$-0.889588\pi$
$101$	−1.76687	+	3.06031i	−0.175810	+	0.304512i	0.764631	+	0.644468i	$0.222921\pi$
$102$	4.03984	−	1.12558i	0.400004	−	0.111449i
$103$	−12.1415	−	7.00991i	−1.19634	−	0.690707i	−0.236603	−	0.971606i	$-0.576034\pi$
$103$	−12.1415	−	7.00991i	−1.19634	−	0.690707i	−0.959737	+	0.280899i	$0.909367\pi$
$104$	1.05138	+	3.44885i	0.103097	+	0.338188i
$105$	0.0911967	+	9.18372i	0.00889989	+	0.896239i
$106$	0.0368600	+	0.137563i	0.00358016	+	0.0133613i
$107$	8.57787	−	4.95244i	0.829254	−	0.478770i	−0.0243429	−	0.999704i	$-0.507749\pi$
$107$	8.57787	−	4.95244i	0.829254	−	0.478770i	0.853597	+	0.520933i	$0.174416\pi$
$108$	−4.42062	+	2.73096i	−0.425374	+	0.262787i
$109$	5.54653	−	5.54653i	0.531261	−	0.531261i	−0.389687	−	0.920948i	$-0.627417\pi$
$109$	5.54653	−	5.54653i	0.531261	−	0.531261i	0.920948	+	0.389687i	$0.127417\pi$
$110$	6.16518	+	6.16518i	0.587827	+	0.587827i
$111$	16.0888	−	4.48267i	1.52708	−	0.425476i
$112$	2.56267	−	0.686666i	0.242150	−	0.0648838i
$113$	−11.6666	+	6.73569i	−1.09750	+	0.633640i	−0.935562	−	0.353161i	$-0.885107\pi$
$113$	−11.6666	+	6.73569i	−1.09750	+	0.633640i	−0.161935	+	0.986801i	$0.551773\pi$
$114$	5.41812	−	9.60343i	0.507453	−	0.899444i
$115$	−2.35819	+	0.631875i	−0.219902	+	0.0589226i
$116$	−4.47591			−0.415578
$117$	5.90569	+	9.06216i	0.545981	+	0.837797i
$118$	4.01776			0.369865
$119$	−6.20485	+	1.66258i	−0.568797	+	0.152409i
$120$	−3.46154	+	0.0343740i	−0.315994	+	0.00313790i
$121$	−6.95503	+	4.01549i	−0.632276	+	0.365044i
$122$	9.71214	−	2.60236i	0.879296	−	0.235607i
$123$	2.96312	−	11.5147i	0.267175	−	1.03824i
$124$	5.96278	+	5.96278i	0.535474	+	0.535474i
$125$	−8.48722	+	8.48722i	−0.759120	+	0.759120i
$126$	6.81250	−	4.11571i	0.606905	−	0.366656i
$127$	−2.38546	+	1.37724i	−0.211675	+	0.122211i	−0.602090	−	0.798429i	$-0.705665\pi$
$127$	−2.38546	+	1.37724i	−0.211675	+	0.122211i	0.390415	+	0.920639i	$0.372332\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	15.3368	−	9.05896i	1.35033	−	0.797597i
$130$	0.245691	+	7.20194i	0.0215485	+	0.631652i
$131$	−0.591828	−	0.341692i	−0.0517083	−	0.0298538i	0.473923	−	0.880566i	$-0.342837\pi$
$131$	−0.591828	−	0.341692i	−0.0517083	−	0.0298538i	−0.525631	+	0.850713i	$0.676171\pi$
$132$	1.88306	−	7.31758i	0.163900	−	0.636914i
$133$	−8.44487	+	14.6269i	−0.732263	+	1.26832i
$134$	−1.26475	+	2.19061i	−0.109258	+	0.189240i
$135$	−9.94676	+	2.98546i	−0.856081	+	0.256948i
$136$	−0.626664	−	2.33874i	−0.0537360	−	0.200545i
$137$	15.9277	−	15.9277i	1.36079	−	1.36079i	0.487884	−	0.872908i	$-0.337769\pi$
$137$	15.9277	−	15.9277i	1.36079	−	1.36079i	0.872908	−	0.487884i	$-0.162231\pi$
$138$	1.51085	+	1.48114i	0.128612	+	0.126083i
$139$	9.77449	+	16.9299i	0.829062	+	1.43598i	0.898775	+	0.438410i	$0.144458\pi$
$139$	9.77449	+	16.9299i	0.829062	+	1.43598i	−0.0697133	+	0.997567i	$0.522208\pi$
$140$	5.30248			0.448142
$141$	2.51577	+	9.02938i	0.211866	+	0.760411i
$142$	−6.38250	+	3.68494i	−0.535608	+	0.309233i
$143$	−15.3231	−	3.55060i	−1.28138	−	0.296916i
$144$	1.55130	+	2.56778i	0.129275	+	0.213981i
$145$	−8.64084	−	2.31531i	−0.717582	−	0.192276i
$146$	5.09249	+	2.94015i	0.421458	+	0.243329i
$147$	−0.0578557	+	0.0341734i	−0.00477185	+	0.00281858i
$148$	−2.49571	−	9.31410i	−0.205146	−	0.765614i
$149$	−1.27189	+	4.74676i	−0.104197	+	0.388869i	−0.998253	−	0.0590865i	$-0.981181\pi$
$149$	−1.27189	+	4.74676i	−0.104197	+	0.388869i	0.894056	+	0.447956i	$0.147848\pi$
$150$	1.68666	+	0.434034i	0.137715	+	0.0354388i
$151$	1.03704	−	3.87030i	0.0843934	−	0.314961i	−0.910805	−	0.412836i	$-0.864538\pi$
$151$	1.03704	−	3.87030i	0.0843934	−	0.314961i	0.995199	+	0.0978758i	$0.0312048\pi$
$152$	−5.51321	−	3.18305i	−0.447180	−	0.258180i
$153$	−3.75607	−	6.21721i	−0.303660	−	0.502631i
$154$	−2.99555	+	11.1795i	−0.241388	+	0.900872i
$155$	8.42683	+	14.5957i	0.676859	+	1.17235i
$156$	5.26564	−	3.35753i	0.421589	−	0.268818i
$157$	0.0374157	−	0.0648059i	0.00298610	−	0.00517207i	−0.864528	−	0.502584i	$-0.832383\pi$
$157$	0.0374157	−	0.0648059i	0.00298610	−	0.00517207i	0.867515	+	0.497412i	$0.165716\pi$
$158$	0.228879	+	0.228879i	0.0182087	+	0.0182087i
$159$	0.212389	−	0.125451i	0.0168436	−	0.00994893i
$160$			1.99862i			0.158005i
$161$	−2.29160	−	2.29160i	−0.180603	−	0.180603i
$162$	6.61165	+	6.10623i	0.519460	+	0.479751i
$163$	18.0329	−	4.83191i	1.41245	−	0.378464i	0.529649	−	0.848217i	$-0.322324\pi$
$163$	18.0329	−	4.83191i	1.41245	−	0.378464i	0.882798	+	0.469752i	$0.155657\pi$
$164$	−6.63068	−	1.77669i	−0.517769	−	0.138736i
$165$	7.42054	−	13.1527i	0.577688	−	1.02393i
$166$		−	3.93375i		−	0.305318i
$167$	−12.8699	+	12.8699i	−0.995905	+	0.995905i	−0.999992	−	0.00408714i	$-0.998699\pi$
$167$	−12.8699	+	12.8699i	−0.995905	+	0.995905i	0.00408714	+	0.999992i	$0.498699\pi$
$168$	−2.33703	−	3.95660i	−0.180306	−	0.305258i
$169$	−7.25214	−	10.7892i	−0.557857	−	0.829937i
$170$		−	4.83914i		−	0.371145i
$171$	−18.5421	−	4.57569i	−1.41795	−	0.349912i
$172$	−5.14201	−	8.90622i	−0.392075	−	0.679093i
$173$	−4.39545			−0.334180			−0.167090	−	0.985942i	$-0.553437\pi$
$173$	−4.39545			−0.334180			−0.167090	+	0.985942i	$0.553437\pi$
$174$	2.08076	+	7.46806i	0.157742	+	0.566152i
$175$	−2.57681	−	0.690454i	−0.194789	−	0.0521934i
$176$	−4.21380	−	1.12909i	−0.317627	−	0.0851080i
$177$	−1.86777	−	6.70363i	−0.140390	−	0.503875i
$178$	−14.8038			−1.10959
$179$	5.44340	+	9.42824i	0.406859	+	0.704700i	0.994536	−	0.104396i	$-0.0332909\pi$
$179$	5.44340	+	9.42824i	0.406859	+	0.704700i	−0.587677	+	0.809095i	$0.699958\pi$
$180$	1.66655	+	5.75960i	0.124217	+	0.429295i
$181$			3.13809i			0.233253i	0.993176	+	0.116626i	$0.0372080\pi$
$181$			3.13809i			0.233253i	−0.993176	+	0.116626i	$0.962792\pi$
$182$	−8.11633	+	5.06256i	−0.601622	+	0.375262i
$183$	−8.85700	−	14.9949i	−0.654728	−	1.10846i
$184$	0.863753	−	0.863753i	0.0636767	−	0.0636767i
$185$		−	19.2720i		−	1.41691i
$186$	7.17692	−	12.7209i	0.526238	−	0.932739i
$187$	10.2026	+	2.73379i	0.746091	+	0.199914i
$188$	5.22728	−	1.40065i	0.381239	−	0.102153i
$189$	−10.0340	−	9.45334i	−0.729869	−	0.687629i
$190$	−8.99682	−	8.99682i	−0.652698	−	0.652698i
$191$			16.6360i			1.20374i	0.798595	+	0.601869i	$0.205577\pi$
$191$			16.6360i			1.20374i	−0.798595	+	0.601869i	$0.794423\pi$
$192$	1.49133	−	0.880877i	0.107627	−	0.0635718i
$193$	−10.8194	−	10.8194i	−0.778799	−	0.778799i	0.200827	−	0.979627i	$-0.435637\pi$
$193$	−10.8194	−	10.8194i	−0.778799	−	0.778799i	−0.979627	+	0.200827i	$0.935637\pi$
$194$	4.38873	−	7.60151i	0.315093	−	0.545757i
$195$	11.9022	−	3.75796i	0.852335	−	0.269113i
$196$	0.0193974	+	0.0335972i	0.00138553	+	0.00239980i
$197$	−5.36725	+	20.0309i	−0.382401	+	1.42714i	0.459822	+	0.888011i	$0.347913\pi$
$197$	−5.36725	+	20.0309i	−0.382401	+	1.42714i	−0.842223	+	0.539129i	$0.818753\pi$
$198$	−13.0848	+	0.259896i	−0.929894	+	0.0184700i
$199$	5.37244	+	3.10178i	0.380842	+	0.219879i	0.678185	−	0.734892i	$-0.262767\pi$
$199$	5.37244	+	3.10178i	0.380842	+	0.219879i	−0.297342	+	0.954771i	$0.596100\pi$
$200$	0.260247	−	0.971255i	0.0184022	−	0.0686781i
$201$	4.24299	+	1.09187i	0.299277	+	0.0770143i
$202$	0.914599	−	3.41333i	0.0643510	−	0.240161i
$203$	−3.07346	−	11.4703i	−0.215714	−	0.805057i
$204$	−3.61086	+	2.13282i	−0.252811	+	0.149327i
$205$	−11.8816	−	6.85985i	−0.829848	−	0.479113i
$206$	13.5421	+	3.62860i	0.943524	+	0.252816i
$207$	1.76891	−	3.20939i	0.122948	−	0.223068i
$208$	−1.90819	−	3.05922i	−0.132309	−	0.212119i
$209$	24.0511	−	13.8859i	1.66365	−	0.960508i
$210$	−2.46501	−	8.84719i	−0.170102	−	0.610514i
$211$	−8.45099			−0.581790			−0.290895	−	0.956755i	$-0.593953\pi$
$211$	−8.45099			−0.581790			−0.290895	+	0.956755i	$0.593953\pi$
$212$	−0.0712081	−	0.123336i	−0.00489059	−	0.00847076i
$213$	9.11541	+	8.93615i	0.624577	+	0.612295i
$214$	−7.00381	+	7.00381i	−0.478770	+	0.478770i
$215$	−5.31973	−	19.8535i	−0.362802	−	1.35400i
$216$	3.56317	−	3.78204i	0.242443	−	0.257335i
$217$	−11.1862	+	19.3751i	−0.759370	+	1.31527i
$218$	−3.92199	+	6.79308i	−0.265630	+	0.460086i
$219$	2.53825	−	9.86363i	0.171519	−	0.666522i
$220$	−7.55077	−	4.35944i	−0.509073	−	0.293913i
$221$	4.62019	+	7.40711i	0.310787	+	0.498256i
$222$	−14.3804	+	8.49401i	−0.965147	+	0.570080i
$223$	2.84796	+	10.6287i	0.190713	+	0.711752i	0.993335	+	0.115264i	$0.0367713\pi$
$223$	2.84796	+	10.6287i	0.190713	+	0.711752i	−0.802621	+	0.596489i	$0.796562\pi$
$224$	−2.29763	+	1.32654i	−0.153517	+	0.0886329i
$225$	−0.0599044	−	3.01596i	−0.00399362	−	0.201064i
$226$	9.52570	−	9.52570i	0.633640	−	0.633640i
$227$	5.59976	+	5.59976i	0.371669	+	0.371669i	0.868085	−	0.496416i	$-0.165351\pi$
$227$	5.59976	+	5.59976i	0.371669	+	0.371669i	−0.496416	+	0.868085i	$0.665351\pi$
$228$	−2.74795	+	10.6785i	−0.181987	+	0.707202i
$229$	−1.40853	+	0.377414i	−0.0930780	+	0.0249402i	−0.305057	−	0.952334i	$-0.598676\pi$
$229$	−1.40853	+	0.377414i	−0.0930780	+	0.0249402i	0.211979	+	0.977274i	$0.432009\pi$
$230$	2.11429	−	1.22069i	0.139412	−	0.0804898i
$231$	20.0456	−	0.199058i	1.31890	−	0.0130970i
$232$	4.32340	−	1.15845i	0.283845	−	0.0760561i
$233$	−4.39305			−0.287799			−0.143899	−	0.989592i	$-0.545964\pi$
$233$	−4.39305			−0.287799			−0.143899	+	0.989592i	$0.545964\pi$
$234$	−8.04992	−	7.22487i	−0.526240	−	0.472305i
$235$	10.8159			0.705551
$236$	−3.88086	+	1.03987i	−0.252622	+	0.0676899i
$237$	0.275484	−	0.488286i	0.0178946	−	0.0317176i
$238$	5.56311	−	3.21187i	0.360603	−	0.208194i
$239$	−8.98867	+	2.40851i	−0.581429	+	0.155793i	−0.537533	−	0.843243i	$-0.680644\pi$
$239$	−8.98867	+	2.40851i	−0.581429	+	0.155793i	−0.0438958	+	0.999036i	$0.513977\pi$
$240$	3.33470	−	0.929115i	0.215254	−	0.0599741i
$241$	1.17890	+	1.17890i	0.0759395	+	0.0759395i	0.744056	−	0.668117i	$-0.232899\pi$
$241$	1.17890	+	1.17890i	0.0759395	+	0.0759395i	−0.668117	+	0.744056i	$0.732899\pi$
$242$	5.67876	−	5.67876i	0.365044	−	0.365044i
$243$	7.11463	−	13.8702i	0.456404	−	0.889773i
$244$	−8.70767	+	5.02738i	−0.557451	+	0.321845i
$245$	0.0200678	+	0.0748940i	0.00128208	+	0.00478480i
$246$	0.118063	+	11.8892i	0.00752743	+	0.758030i
$247$	22.3609	+	5.18138i	1.42279	+	0.329683i
$248$	−7.30289	−	4.21632i	−0.463734	−	0.267737i
$249$	−6.56346	+	1.82872i	−0.415942	+	0.115890i
$250$	6.00137	−	10.3947i	0.379560	−	0.657418i
$251$	−3.88661	+	6.73180i	−0.245321	+	0.424908i	−0.962222	−	0.272267i	$-0.912227\pi$
$251$	−3.88661	+	6.73180i	−0.245321	+	0.424908i	0.716901	+	0.697175i	$0.245560\pi$
$252$	−5.51514	+	5.73867i	−0.347421	+	0.361502i
$253$	1.37921	+	5.14729i	0.0867104	+	0.323608i
$254$	1.94772	−	1.94772i	0.122211	−	0.122211i
$255$	−8.07410	+	2.24961i	−0.505620	+	0.140876i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	25.7870			1.60855			0.804274	−	0.594259i	$-0.202555\pi$
$257$	25.7870			1.60855			0.804274	+	0.594259i	$0.202555\pi$
$258$	−12.4696	+	12.7197i	−0.776324	+	0.791897i
$259$	22.1553	−	12.7913i	1.37666	−	0.794816i
$260$	−2.10132	−	6.89295i	−0.130318	−	0.427483i
$261$	11.4931	−	6.94348i	0.711408	−	0.429790i
$262$	0.660098	+	0.176873i	0.0407810	+	0.0109272i
$263$	−23.1774	−	13.3815i	−1.42918	−	0.825136i	−0.432122	−	0.901815i	$-0.642235\pi$
$263$	−23.1774	−	13.3815i	−1.42918	−	0.825136i	−0.997056	+	0.0766793i	$0.975568\pi$
$264$	0.0750292	+	7.55561i	0.00461773	+	0.465016i
$265$	−0.0736692	−	0.274937i	−0.00452546	−	0.0168893i
$266$	4.37139	−	16.3142i	0.268027	−	1.00029i
$267$	6.88198	+	24.7002i	0.421170	+	1.51163i
$268$	0.654683	−	2.44331i	0.0399911	−	0.149249i
$269$	17.6997	+	10.2189i	1.07917	+	0.623058i	0.930672	−	0.365855i	$-0.119223\pi$
$269$	17.6997	+	10.2189i	1.07917	+	0.623058i	0.148496	+	0.988913i	$0.452557\pi$
$270$	8.83514	−	5.45815i	0.537689	−	0.332172i
$271$	−5.01971	+	18.7338i	−0.304926	+	1.13800i	0.628083	+	0.778146i	$0.283840\pi$
$271$	−5.01971	+	18.7338i	−0.304926	+	1.13800i	−0.933009	+	0.359853i	$0.882827\pi$
$272$	1.21062	+	2.09686i	0.0734047	+	0.127141i
$273$	12.2200	+	11.1886i	0.739587	+	0.677165i
$274$	−11.2626	+	19.5073i	−0.680396	+	1.17848i
$275$	3.10174	+	3.10174i	0.187042	+	0.187042i
$276$	−1.84271	−	1.03963i	−0.110918	−	0.0625784i
$277$		−	10.6829i		−	0.641875i	−0.947100	−	0.320937i	$-0.896002\pi$
$277$		−	10.6829i		−	0.641875i	0.947100	−	0.320937i	$-0.103998\pi$
$278$	−13.8232	−	13.8232i	−0.829062	−	0.829062i
$279$	−24.5611	−	6.06104i	−1.47044	−	0.362865i
$280$	−5.12181	+	1.37238i	−0.306087	+	0.0820156i
$281$	−21.9870	−	5.89140i	−1.31163	−	0.351451i	−0.465797	−	0.884892i	$-0.654232\pi$
$281$	−21.9870	−	5.89140i	−1.31163	−	0.351451i	−0.845838	+	0.533440i	$0.820899\pi$
$282$	−4.76703	−	8.07058i	−0.283872	−	0.480596i
$283$		−	0.508663i		−	0.0302369i	−0.999886	−	0.0151184i	$-0.995187\pi$
$283$		−	0.508663i		−	0.0302369i	0.999886	−	0.0151184i	$-0.00481253\pi$
$284$	5.21129	−	5.21129i	0.309233	−	0.309233i
$285$	−10.8288	+	19.1936i	−0.641440	+	1.13693i
$286$	15.7199	−	0.536277i	0.929537	−	0.0317107i
$287$		−	18.2123i		−	1.07504i
$288$	−2.16303	−	2.07878i	−0.127458	−	0.122493i
$289$	5.56879	+	9.64543i	0.327576	+	0.567378i
$290$	8.94565			0.525307
$291$	−14.7233	−	3.78882i	−0.863097	−	0.222104i
$292$	−5.67994	−	1.52193i	−0.332393	−	0.0890645i
$293$	−20.7377	−	5.55666i	−1.21151	−	0.324624i	−0.404157	−	0.914690i	$-0.632435\pi$
$293$	−20.7377	−	5.55666i	−1.21151	−	0.324624i	−0.807355	+	0.590066i	$0.799102\pi$
$294$	0.0470395	−	0.0479831i	0.00274340	−	0.00279843i
$295$	−8.02997			−0.467523
$296$	4.82133	+	8.35079i	0.280234	+	0.485380i
$297$	6.51646	+	21.7111i	0.378124	+	1.25981i
$298$		−	4.91420i		−	0.284672i
$299$	−2.07082	+	3.88709i	−0.119759	+	0.224797i
$300$	−1.74152	+	0.0172938i	−0.100547	+	0.000998455i
$301$	19.2929	−	19.2929i	1.11202	−	1.11202i
$302$			4.00683i			0.230567i
$303$	−6.12032	+	0.0607763i	−0.351603	+	0.00349151i
$304$	6.14918	+	1.64767i	0.352680	+	0.0945003i
$305$	−19.4109	+	5.20113i	−1.11146	+	0.297816i
$306$	5.23722	+	5.03322i	0.299392	+	0.287730i
$307$	−16.9627	−	16.9627i	−0.968112	−	0.968112i	0.0313952	−	0.999507i	$-0.490005\pi$
$307$	−16.9627	−	16.9627i	−0.968112	−	0.968112i	−0.999507	+	0.0313952i	$0.990005\pi$
$308$		−	11.5739i		−	0.659484i
$309$	−0.241125	−	24.2819i	−0.0137171	−	1.38135i
$310$	−11.9173	−	11.9173i	−0.676859	−	0.676859i
$311$	−16.5307	+	28.6320i	−0.937370	+	1.62357i	−0.167017	+	0.985954i	$0.553413\pi$
$311$	−16.5307	+	28.6320i	−0.937370	+	1.62357i	−0.770353	+	0.637618i	$0.779920\pi$
$312$	−4.21723	+	4.60597i	−0.238753	+	0.260762i
$313$	7.32210	+	12.6823i	0.413870	+	0.716843i	0.995309	−	0.0967464i	$-0.0308436\pi$
$313$	7.32210	+	12.6823i	0.413870	+	0.716843i	−0.581439	+	0.813590i	$0.697510\pi$
$314$	−0.0193678	+	0.0722816i	−0.00109299	+	0.00407908i
$315$	−13.6156	+	8.22574i	−0.767152	+	0.463468i
$316$	−0.280319	−	0.161842i	−0.0157692	−	0.00910433i
$317$	−0.361436	+	1.34890i	−0.0203003	+	0.0757616i	−0.975333	−	0.220739i	$-0.929153\pi$
$317$	−0.361436	+	1.34890i	−0.0203003	+	0.0757616i	0.955033	+	0.296501i	$0.0958197\pi$
$318$	−0.172683	+	0.176147i	−0.00968358	+	0.00987783i
$319$	−5.05369	+	18.8606i	−0.282952	+	1.05599i
$320$	−0.517281	−	1.93052i	−0.0289169	−	0.107919i
$321$	14.9418	+	8.42992i	0.833968	+	0.470512i
$322$	2.80663	+	1.62041i	0.156407	+	0.0903017i
$323$	−14.8887	−	3.98941i	−0.828427	−	0.221976i
$324$	−7.96677	−	4.18695i	−0.442598	−	0.232608i
$325$	0.123608	+	3.62334i	0.00685656	+	0.200987i
$326$	−16.1679	+	9.33453i	−0.895456	+	0.516992i
$327$	13.1575	+	3.38587i	0.727611	+	0.187239i
$328$	6.86459			0.379034
$329$	7.17879	+	12.4340i	0.395780	+	0.685510i
$330$	−3.76353	+	14.6251i	−0.207176	+	0.805083i
$331$	12.3912	−	12.3912i	0.681081	−	0.681081i	−0.279163	−	0.960244i	$-0.590057\pi$
$331$	12.3912	−	12.3912i	0.681081	−	0.681081i	0.960244	+	0.279163i	$0.0900569\pi$
$332$	1.01813	+	3.79971i	0.0558771	+	0.208536i
$333$	20.8574	+	20.0449i	1.14298	+	1.09846i
$334$	9.10041	−	15.7624i	0.497952	−	0.862479i
$335$	2.52776	−	4.37820i	0.138106	−	0.239207i
$336$	3.28144	+	3.21691i	0.179017	+	0.175497i
$337$	22.3033	+	12.8768i	1.21494	+	0.701445i	0.963831	−	0.266514i	$-0.0858719\pi$
$337$	22.3033	+	12.8768i	1.21494	+	0.701445i	0.251108	+	0.967959i	$0.419205\pi$
$338$	9.79748	+	8.54456i	0.532912	+	0.464763i
$339$	−20.3219	−	11.4653i	−1.10373	−	0.622711i
$340$	1.25246	+	4.67425i	0.0679243	+	0.253497i
$341$	31.8585	−	18.3935i	1.72523	−	0.996064i
$342$	19.0945	−	0.379265i	1.03251	−	0.0205083i
$343$	13.0593	−	13.0593i	0.705134	−	0.705134i
$344$	7.27190	+	7.27190i	0.392075	+	0.392075i
$345$	−3.01961	−	2.96023i	−0.162570	−	0.159373i
$346$	4.24568	−	1.13763i	0.228249	−	0.0611592i
$347$	19.4800	−	11.2468i	1.04574	−	0.603758i	0.124286	−	0.992246i	$-0.460336\pi$
$347$	19.4800	−	11.2468i	1.04574	−	0.603758i	0.921453	+	0.388489i	$0.127003\pi$
$348$	−3.94273	−	6.67505i	−0.211353	−	0.357820i
$349$	16.0726	−	4.30665i	0.860348	−	0.230530i	0.198439	−	0.980113i	$-0.436413\pi$
$349$	16.0726	−	4.30665i	0.860348	−	0.230530i	0.661910	+	0.749584i	$0.269746\pi$
$350$	2.66771			0.142595
$351$	−8.31246	+	16.7900i	−0.443686	+	0.896182i
$352$	4.36245			0.232519
$353$	32.4783	−	8.70255i	1.72865	−	0.463190i	0.748777	−	0.662822i	$-0.230641\pi$
$353$	32.4783	−	8.70255i	1.72865	−	0.463190i	0.979871	+	0.199632i	$0.0639748\pi$
$354$	3.53915	+	5.99179i	0.188104	+	0.318460i
$355$	12.7562	−	7.36480i	0.677029	−	0.390883i
$356$	14.2994	−	3.83151i	0.757867	−	0.203070i
$357$	−7.94517	−	7.78892i	−0.420503	−	0.412233i
$358$	−7.69812	−	7.69812i	−0.406859	−	0.406859i
$359$	−18.7010	+	18.7010i	−0.987001	+	0.987001i	−0.999917	−	0.0129158i	$-0.995889\pi$
$359$	−18.7010	+	18.7010i	−0.987001	+	0.987001i	0.0129158	+	0.999917i	$0.495889\pi$
$360$	−3.10046	−	5.13201i	−0.163408	−	0.270481i
$361$	−18.6432	+	10.7636i	−0.981220	+	0.566507i
$362$	−0.812199	−	3.03117i	−0.0426882	−	0.159315i
$363$	−12.1149	−	6.83507i	−0.635869	−	0.358748i
$364$	6.52948	−	6.99072i	0.342238	−	0.366413i
$365$	−10.1780	−	5.87625i	−0.532739	−	0.307577i
$366$	12.4362	+	12.1916i	0.650049	+	0.637266i
$367$	−17.5180	+	30.3421i	−0.914432	+	1.58384i	−0.106702	+	0.994291i	$0.534029\pi$
$367$	−17.5180	+	30.3421i	−0.914432	+	1.58384i	−0.807730	+	0.589552i	$0.799304\pi$
$368$	−0.610766	+	1.05788i	−0.0318384	+	0.0551457i
$369$	19.7823	−	5.72404i	1.02982	−	0.297981i
$370$	4.98797	+	18.6153i	0.259312	+	0.967766i
$371$	0.267174	−	0.267174i	0.0138710	−	0.0138710i
$372$	−3.63998	+	14.1449i	−0.188724	+	0.733381i
$373$	−3.17079	−	5.49197i	−0.164177	−	0.284364i	0.772185	−	0.635397i	$-0.219164\pi$
$373$	−3.17079	−	5.49197i	−0.164177	−	0.284364i	−0.936363	+	0.351034i	$0.885830\pi$
$374$	−10.5625			−0.546176
$375$	−20.1334	−	5.18102i	−1.03969	−	0.267547i
$376$	−4.68665	+	2.70584i	−0.241696	+	0.139543i
$377$	−13.6928	+	8.54089i	−0.705215	+	0.439878i
$378$	12.1388	+	6.53422i	0.624354	+	0.336084i
$379$	−33.0310	−	8.85063i	−1.69669	−	0.454626i	−0.724587	−	0.689184i	$-0.757969\pi$
$379$	−33.0310	−	8.85063i	−1.69669	−	0.454626i	−0.972102	+	0.234557i	$0.924636\pi$
$380$	11.0188	+	6.36171i	0.565253	+	0.326349i
$381$	−4.15522	−	2.34431i	−0.212878	−	0.120103i
$382$	−4.30571	−	16.0691i	−0.220299	−	0.822168i
$383$	4.33535	−	16.1798i	0.221526	−	0.826747i	−0.762240	−	0.647294i	$-0.775901\pi$
$383$	4.33535	−	16.1798i	0.221526	−	0.826747i	0.983767	−	0.179453i	$-0.0574327\pi$
$384$	−1.21252	+	1.23685i	−0.0618763	+	0.0631175i
$385$	5.98696	−	22.3436i	0.305124	−	1.13874i
$386$	13.2510	+	7.65049i	0.674460	+	0.389400i
$387$	27.0197	+	14.8924i	1.37349	+	0.757023i
$388$	−2.27178	+	8.47838i	−0.115332	+	0.430425i
$389$	−5.63377	−	9.75798i	−0.285644	−	0.494749i	0.687121	−	0.726543i	$-0.258874\pi$
$389$	−5.63377	−	9.75798i	−0.285644	−	0.494749i	−0.972765	+	0.231793i	$0.925541\pi$
$390$	−10.5240	+	6.71043i	−0.532904	+	0.339796i
$391$	1.47881	−	2.56138i	0.0747867	−	0.129534i
$392$	−0.0274320	−	0.0274320i	−0.00138553	−	0.00138553i
$393$	−0.0117534	−	1.18360i	−0.000592882	−	0.0597046i
$394$		−	20.7375i		−	1.04474i
$395$	−0.457443	−	0.457443i	−0.0230164	−	0.0230164i
$396$	12.5717	−	3.63763i	0.631749	−	0.182798i
$397$	5.64532	−	1.51266i	0.283331	−	0.0759182i	−0.114355	−	0.993440i	$-0.536480\pi$
$397$	5.64532	−	1.51266i	0.283331	−	0.0759182i	0.397686	+	0.917522i	$0.369813\pi$
$398$	−5.99218	−	1.60560i	−0.300361	−	0.0804814i
$399$	−29.2524	+	0.290484i	−1.46445	+	0.0145424i
$400$			1.00552i			0.0502759i
$401$	19.6086	−	19.6086i	0.979208	−	0.979208i	−0.0205800	−	0.999788i	$-0.506551\pi$
$401$	19.6086	−	19.6086i	0.979208	−	0.979208i	0.999788	+	0.0205800i	$0.00655127\pi$
$402$	−4.38101	+	0.0435046i	−0.218505	+	0.00216981i
$403$	29.6196	+	6.86334i	1.47546	+	0.341887i
$404$			3.53374i			0.175810i
$405$	−13.2142	−	12.2040i	−0.656618	−	0.606424i
$406$	5.93746	+	10.2840i	0.294671	+	0.510386i
$407$	−42.0657			−2.08512
$408$	2.93581	−	2.99470i	0.145344	−	0.148260i
$409$	−3.94653	−	1.05747i	−0.195144	−	0.0522885i	0.159923	−	0.987129i	$-0.448875\pi$
$409$	−3.94653	−	1.05747i	−0.195144	−	0.0522885i	−0.355067	+	0.934841i	$0.615542\pi$
$410$	13.2522	+	3.55092i	0.654481	+	0.175368i
$411$	37.7837	+	9.72303i	1.86373	+	0.479602i
$412$	−14.0198			−0.690707
$413$	−5.32970	−	9.23132i	−0.262258	−	0.454243i
$414$	−0.877986	+	3.55786i	−0.0431507	+	0.174859i
$415$			7.86207i			0.385934i
$416$	2.63495	+	2.46110i	0.129189	+	0.120665i
$417$	−16.6379	+	29.4901i	−0.814762	+	1.44414i
$418$	−19.6376	+	19.6376i	−0.960508	+	0.960508i
$419$			18.4321i			0.900466i	0.892911	+	0.450233i	$0.148659\pi$
$419$			18.4321i			0.900466i	−0.892911	+	0.450233i	$0.851341\pi$
$420$	4.67084	+	7.90774i	0.227914	+	0.385858i
$421$	31.1461	+	8.34557i	1.51797	+	0.406738i	0.919072	−	0.394090i	$-0.128940\pi$
$421$	31.1461	+	8.34557i	1.51797	+	0.406738i	0.598895	+	0.800828i	$0.295607\pi$
$422$	8.16303	−	2.18728i	0.397370	−	0.106475i
$423$	−11.2497	+	11.7056i	−0.546978	+	0.569147i
$424$	0.100703	+	0.100703i	0.00489059	+	0.00489059i
$425$		−	2.43460i		−	0.118095i
$426$	−11.1177	−	6.27242i	−0.538652	−	0.303900i
$427$	−18.8628	−	18.8628i	−0.912833	−	0.912833i
$428$	4.95244	−	8.57787i	0.239385	−	0.414627i
$429$	−8.20262	−	25.9793i	−0.396026	−	1.25429i
$430$	10.2769	+	17.8002i	0.495597	+	0.858400i
$431$	3.39947	−	12.6870i	0.163747	−	0.611112i	−0.834450	−	0.551084i	$-0.814214\pi$
$431$	3.39947	−	12.6870i	0.163747	−	0.611112i	0.998197	−	0.0600279i	$-0.0191190\pi$
$432$	−2.46289	+	4.57539i	−0.118496	+	0.220133i
$433$	4.72346	+	2.72709i	0.226995	+	0.131056i	0.609185	−	0.793028i	$-0.291497\pi$
$433$	4.72346	+	2.72709i	0.226995	+	0.131056i	−0.382190	+	0.924084i	$0.624830\pi$
$434$	5.79041	−	21.6101i	0.277949	−	1.03732i
$435$	−4.15864	−	14.9258i	−0.199392	−	0.715638i
$436$	2.03017	−	7.57670i	0.0972275	−	0.362858i
$437$	−2.01268	−	7.51142i	−0.0962795	−	0.359320i
$438$	0.101135	+	10.1845i	0.00483239	+	0.486633i
$439$	2.61857	+	1.51183i	0.124978	+	0.0721559i	0.561186	−	0.827690i	$-0.310345\pi$
$439$	2.61857	+	1.51183i	0.124978	+	0.0721559i	−0.436208	+	0.899846i	$0.643679\pi$
$440$	8.42179	+	2.25661i	0.401493	+	0.107580i
$441$	−0.101927	−	0.0561791i	−0.00485369	−	0.00267519i
$442$	−6.37986	−	5.95893i	−0.303459	−	0.283437i
$443$	−3.45678	+	1.99577i	−0.164237	+	0.0948221i	−0.579865	−	0.814712i	$-0.696895\pi$
$443$	−3.45678	+	1.99577i	−0.164237	+	0.0948221i	0.415629	+	0.909534i	$0.363562\pi$
$444$	11.6920	−	11.9265i	0.554876	−	0.566006i
$445$	29.5872			1.40257
$446$	−5.50183	−	9.52946i	−0.260519	−	0.451233i
$447$	−8.19934	+	2.28451i	−0.387816	+	0.108054i
$448$	1.87601	−	1.87601i	0.0886329	−	0.0886329i
$449$	3.46480	+	12.9308i	0.163514	+	0.610242i	0.998225	+	0.0595540i	$0.0189679\pi$
$449$	3.46480	+	12.9308i	0.163514	+	0.610242i	−0.834711	+	0.550688i	$0.814365\pi$
$450$	0.838450	+	2.89769i	0.0395249	+	0.136598i
$451$	−14.9732	+	25.9344i	−0.705061	+	1.22120i
$452$	−6.73569	+	11.6666i	−0.316820	+	0.548749i
$453$	6.68539	−	1.86269i	0.314107	−	0.0875167i
$454$	−6.85828	−	3.95963i	−0.321875	−	0.185835i
$455$	16.2215	−	10.1181i	0.760474	−	0.474346i
$456$	−0.109490	−	11.0259i	−0.00512733	−	0.516334i
$457$	0.346703	+	1.29391i	0.0162181	+	0.0605267i	0.973561	−	0.228429i	$-0.0733588\pi$
$457$	0.346703	+	1.29391i	0.0162181	+	0.0605267i	−0.957343	+	0.288955i	$0.906692\pi$
$458$	1.26285	−	0.729107i	0.0590091	−	0.0340689i
$459$	5.96325	−	11.0781i	0.278341	−	0.517082i
$460$	−1.72631	+	1.72631i	−0.0804898	+	0.0804898i
$461$	3.58563	+	3.58563i	0.166999	+	0.166999i	0.785659	−	0.618660i	$-0.212324\pi$
$461$	3.58563	+	3.58563i	0.166999	+	0.166999i	−0.618660	+	0.785659i	$0.712324\pi$
$462$	−19.3110	+	5.38046i	−0.898431	+	0.250321i
$463$	7.47439	−	2.00276i	0.347364	−	0.0930760i	−0.0809185	−	0.996721i	$-0.525785\pi$
$463$	7.47439	−	2.00276i	0.347364	−	0.0930760i	0.428283	+	0.903645i	$0.359119\pi$
$464$	−3.87626	+	2.23796i	−0.179951	+	0.103895i
$465$	−14.3439	+	25.4242i	−0.665185	+	1.17902i
$466$	4.24336	−	1.13701i	0.196570	−	0.0526708i
$467$	−10.4397			−0.483093			−0.241546	−	0.970389i	$-0.577655\pi$
$467$	−10.4397			−0.483093			−0.241546	+	0.970389i	$0.577655\pi$
$468$	9.64556	+	4.89522i	0.445866	+	0.226282i
$469$	6.71095			0.309883
$470$	−10.4474	+	2.79936i	−0.481900	+	0.129125i
$471$	0.129605	−	0.00128701i	0.00597190	−	5.93025e-5i
$472$	3.47948	−	2.00888i	0.160156	−	0.0924662i
$473$	−43.3348	+	11.6115i	−1.99254	+	0.533899i
$474$	−0.139719	+	0.542948i	−0.00641751	+	0.0249384i
$475$	−4.52635	−	4.52635i	−0.207683	−	0.207683i
$476$	−4.54226	+	4.54226i	−0.208194	+	0.208194i
$477$	0.374177	+	0.206234i	0.0171324	+	0.00944282i
$478$	8.05902	−	4.65288i	0.368611	−	0.212818i
$479$	−1.71493	−	6.40022i	−0.0783573	−	0.292433i	0.915616	−	0.402053i	$-0.131703\pi$
$479$	−1.71493	−	6.40022i	−0.0783573	−	0.292433i	−0.993974	+	0.109620i	$0.965037\pi$
$480$	−2.98060	+	1.76054i	−0.136045	+	0.0803573i
$481$	−25.4080	−	23.7316i	−1.15850	−	1.08207i
$482$	−1.44385	−	0.833607i	−0.0657655	−	0.0379697i
$483$	1.39891	−	5.43614i	0.0636524	−	0.247353i
$484$	−4.01549	+	6.95503i	−0.182522	+	0.316138i
$485$	−8.77141	+	15.1925i	−0.398289	+	0.689857i
$486$	−3.28234	+	15.2390i	−0.148890	+	0.691254i
$487$	−4.31888	−	16.1183i	−0.195707	−	0.730390i	−0.992083	−	0.125587i	$-0.959919\pi$
$487$	−4.31888	−	16.1183i	−0.195707	−	0.730390i	0.796375	−	0.604803i	$-0.206748\pi$
$488$	7.10978	−	7.10978i	0.321845	−	0.321845i
$489$	23.0907	+	22.6367i	1.04420	+	1.02367i
$490$	−0.0387680	−	0.0671481i	−0.00175136	−	0.00303344i
$491$	−15.3717			−0.693715			−0.346858	−	0.937918i	$-0.612751\pi$
$491$	−15.3717			−0.693715			−0.346858	+	0.937918i	$0.612751\pi$
$492$	−3.19120	−	11.4536i	−0.143870	−	0.516366i
$493$	9.38535	−	5.41864i	0.422695	−	0.244043i
$494$	−22.9400	+	0.782586i	−1.03212	+	0.0352102i
$495$	26.1515	−	0.519433i	1.17542	−	0.0233468i
$496$	8.14531	+	2.18253i	0.365735	+	0.0979985i
$497$	16.9332	+	9.77642i	0.759560	+	0.438532i
$498$	5.86650	−	3.46515i	0.262884	−	0.155277i
$499$	5.78088	+	21.5745i	0.258788	+	0.965808i	0.965944	+	0.258751i	$0.0833109\pi$
$499$	5.78088	+	21.5745i	0.258788	+	0.965808i	−0.707157	+	0.707057i	$0.750022\pi$
$500$	−3.10654	+	11.5938i	−0.138929	+	0.518489i
$501$	−30.5301	−	7.85643i	−1.36398	−	0.351000i
$502$	2.01186	−	7.50835i	0.0897936	−	0.335114i
$503$	20.4381	+	11.8000i	0.911291	+	0.526134i	0.880846	−	0.473402i	$-0.156974\pi$
$503$	20.4381	+	11.8000i	0.911291	+	0.526134i	0.0304450	+	0.999536i	$0.490308\pi$
$504$	3.84194	−	6.97056i	0.171134	−	0.310493i
$505$	−1.82794	+	6.82195i	−0.0813421	+	0.303573i
$506$	−2.66444	−	4.61494i	−0.118449	−	0.205159i
$507$	9.70195	−	20.3193i	0.430879	−	0.902410i
$508$	−1.37724	+	2.38546i	−0.0611053	+	0.105838i
$509$	3.56579	+	3.56579i	0.158051	+	0.158051i	0.781702	−	0.623652i	$-0.214352\pi$
$509$	3.56579	+	3.56579i	0.158051	+	0.158051i	−0.623652	+	0.781702i	$0.714352\pi$
$510$	7.21674	−	4.26269i	0.319563	−	0.188755i
$511$		−	15.6009i		−	0.690142i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−9.50945	−	31.6829i	−0.419852	−	1.39883i
$514$	−24.9083	+	6.67416i	−1.09866	+	0.294385i
$515$	−27.0655	−	7.25219i	−1.19265	−	0.319570i
$516$	8.75261	−	15.5137i	0.385312	−	0.682953i
$517$		−	23.6082i		−	1.03829i
$518$	−18.0897	+	18.0897i	−0.794816	+	0.794816i
$519$	−3.87185	−	6.55505i	−0.169956	−	0.287735i
$520$	3.81374	+	6.11422i	0.167244	+	0.268126i
$521$		−	42.7218i		−	1.87168i	−0.352428	−	0.935839i	$-0.614644\pi$
$521$		−	42.7218i		−	1.87168i	0.352428	−	0.935839i	$-0.385356\pi$
$522$	−9.30442	+	9.68153i	−0.407243	+	0.423749i
$523$	5.91448	+	10.2442i	0.258622	+	0.447946i	0.965873	−	0.259016i	$-0.0833983\pi$
$523$	5.91448	+	10.2442i	0.258622	+	0.447946i	−0.707251	+	0.706962i	$0.750065\pi$
$524$	−0.683384			−0.0298538
$525$	−1.24016	−	4.45107i	−0.0541251	−	0.194261i
$526$	25.8510	+	6.92675i	1.12716	+	0.302021i
$527$	−19.7218	−	5.28443i	−0.859094	−	0.230193i
$528$	−2.02801	−	7.27874i	−0.0882578	−	0.316767i
$529$	−21.5079			−0.935124
$530$	0.142318	+	0.246502i	0.00618190	+	0.0107074i
$531$	8.35202	−	8.69053i	0.362447	−	0.377137i
$532$			16.8897i			0.732263i
$533$	−23.6750	+	7.21732i	−1.02548	+	0.312617i
$534$	−13.0404	−	22.0773i	−0.564312	−	0.955380i
$535$	13.9979	−	13.9979i	0.605184	−	0.605184i
$536$			2.52950i			0.109258i
$537$	−9.26562	+	16.4230i	−0.399841	+	0.708705i
$538$	−19.7414	−	5.28970i	−0.851113	−	0.228055i
$539$	0.163474	−	0.0438026i	0.00704130	−	0.00188671i
$540$	−7.12142	+	7.55887i	−0.306457	+	0.325282i
$541$	−1.16137	−	1.16137i	−0.0499311	−	0.0499311i	0.681700	−	0.731631i	$-0.261241\pi$
$541$	−1.16137	−	1.16137i	−0.0499311	−	0.0499311i	−0.731631	+	0.681700i	$0.761241\pi$
$542$		−	19.3947i		−	0.833073i
$543$	−4.67992	+	2.76428i	−0.200835	+	0.118626i
$544$	−1.71208	−	1.71208i	−0.0734047	−	0.0734047i
$545$	7.83856	−	13.5768i	0.335767	−	0.581566i
$546$	−14.6994	−	7.64460i	−0.629077	−	0.327159i
$547$	0.539713	+	0.934811i	0.0230765	+	0.0399696i	0.877333	−	0.479882i	$-0.159321\pi$
$547$	0.539713	+	0.934811i	0.0230765	+	0.0399696i	−0.854257	+	0.519852i	$0.825987\pi$
$548$	5.82993	−	21.7576i	0.249042	−	0.929439i
$549$	14.5604	−	26.4174i	0.621422	−	1.12747i
$550$	−3.79884	−	2.19326i	−0.161983	−	0.0935209i
$551$	7.37483	−	27.5232i	0.314178	−	1.17253i
$552$	2.04900	+	0.527278i	0.0872112	+	0.0224424i
$553$	0.222263	−	0.829496i	0.00945158	−	0.0352738i
$554$	2.76495	+	10.3189i	0.117471	+	0.438409i
$555$	28.7409	−	16.9763i	1.21998	−	0.720603i
$556$	16.9299	+	9.77449i	0.717989	+	0.414531i
$557$	22.0126	+	5.89827i	0.932705	+	0.249918i	0.693008	−	0.720930i	$-0.256285\pi$
$557$	22.0126	+	5.89827i	0.932705	+	0.249918i	0.239697	+	0.970848i	$0.422952\pi$
$558$	25.2930	−	0.502381i	1.07074	−	0.0212675i
$559$	−32.7253	−	17.4342i	−1.38413	−	0.737386i
$560$	4.59209	−	2.65124i	0.194051	−	0.112035i
$561$	4.91030	+	17.6236i	0.207313	+	0.744069i
$562$	22.7626			0.960183
$563$	−6.38715	−	11.0629i	−0.269186	−	0.466245i	0.699466	−	0.714666i	$-0.253421\pi$
$563$	−6.38715	−	11.0629i	−0.269186	−	0.466245i	−0.968652	+	0.248422i	$0.920088\pi$
$564$	6.69341	+	6.56179i	0.281844	+	0.276301i
$565$	−19.0383	+	19.0383i	−0.800946	+	0.800946i
$566$	0.131652	+	0.491331i	0.00553374	+	0.0206522i
$567$	5.25926	−	23.2913i	0.220868	−	0.978141i
$568$	−3.68494	+	6.38250i	−0.154617	+	0.267804i
$569$	−1.93959	+	3.35946i	−0.0813117	+	0.140836i	−0.903814	−	0.427926i	$-0.859244\pi$
$569$	−1.93959	+	3.35946i	−0.0813117	+	0.140836i	0.822502	+	0.568762i	$0.192578\pi$
$570$	5.49210	−	21.3423i	0.230039	−	0.893930i
$571$	4.28302	+	2.47280i	0.179239	+	0.103483i	0.586935	−	0.809634i	$-0.300334\pi$
$571$	4.28302	+	2.47280i	0.179239	+	0.103483i	−0.407696	+	0.913118i	$0.633668\pi$
$572$	−15.0455	+	4.58661i	−0.629082	+	0.191776i
$573$	−24.8097	+	14.6543i	−1.03644	+	0.612191i
$574$	4.71368	+	17.5917i	0.196745	+	0.734263i
$575$	1.06371	−	0.614136i	0.0443599	−	0.0256112i
$576$	2.62735	+	1.44811i	0.109473	+	0.0603379i
$577$	−9.91809	+	9.91809i	−0.412896	+	0.412896i	−0.882746	−	0.469850i	$-0.844308\pi$
$577$	−9.91809	+	9.91809i	−0.412896	+	0.412896i	0.469850	+	0.882746i	$0.344308\pi$
$578$	−7.87546	−	7.87546i	−0.327576	−	0.327576i
$579$	6.60471	−	25.6659i	0.274482	−	1.06664i
$580$	−8.64084	+	2.31531i	−0.358791	+	0.0961378i
$581$	−9.03829	+	5.21826i	−0.374972	+	0.216490i
$582$	15.2023	−	0.150962i	0.630154	−	0.00625759i
$583$	−0.600114	+	0.160800i	−0.0248542	+	0.00665966i
$584$	5.88030			0.243329
$585$	16.0887	+	14.4398i	0.665187	+	0.597011i
$586$	21.4693			0.886888
$587$	39.5886	−	10.6077i	1.63400	−	0.437828i	0.678926	−	0.734207i	$-0.262446\pi$
$587$	39.5886	−	10.6077i	1.63400	−	0.437828i	0.955070	+	0.296379i	$0.0957792\pi$
$588$	−0.0330178	+	0.0585229i	−0.00136163	+	0.00241344i
$589$	−46.4909	+	26.8416i	−1.91563	+	1.10599i
$590$	7.75636	−	2.07831i	0.319324	−	0.0855627i
$591$	−34.6005	+	9.64041i	−1.42327	+	0.396553i
$592$	−6.81839	−	6.81839i	−0.280234	−	0.280234i
$593$	5.71700	−	5.71700i	0.234769	−	0.234769i	−0.579911	−	0.814680i	$-0.696913\pi$
$593$	5.71700	−	5.71700i	0.234769	−	0.234769i	0.814680	+	0.579911i	$0.196913\pi$
$594$	−11.9137	−	19.2847i	−0.488824	−	0.791262i
$595$	−11.1186	+	6.41930i	−0.455816	+	0.263166i
$596$	1.27189	+	4.74676i	0.0520986	+	0.194435i
$597$	0.106694	+	10.7443i	0.00436670	+	0.439737i
$598$	0.994206	−	4.29061i	0.0406561	−	0.175456i
$599$	33.2498	+	19.1968i	1.35855	+	0.784359i	0.989428	−	0.145022i	$-0.0463254\pi$
$599$	33.2498	+	19.1968i	1.35855	+	0.784359i	0.369121	+	0.929381i	$0.379659\pi$
$600$	1.67770	−	0.467443i	0.0684920	−	0.0190833i
$601$	−10.4558	+	18.1099i	−0.426500	+	0.738719i	−0.996559	−	0.0828841i	$-0.973587\pi$
$601$	−10.4558	+	18.1099i	−0.426500	+	0.738719i	0.570059	+	0.821604i	$0.306920\pi$
$602$	−13.6421	+	23.6289i	−0.556011	+	0.963040i
$603$	2.10922	+	7.28949i	0.0858943	+	0.296851i
$604$	−1.03704	−	3.87030i	−0.0421967	−	0.157480i
$605$	−11.3497	+	11.3497i	−0.461430	+	0.461430i
$606$	5.89604	−	1.64276i	0.239510	−	0.0667326i
$607$	−17.5417	−	30.3832i	−0.711997	−	1.23322i	−0.964106	−	0.265516i	$-0.914458\pi$
$607$	−17.5417	−	30.3832i	−0.711997	−	1.23322i	0.252109	−	0.967699i	$-0.418876\pi$
$608$	−6.36610			−0.258180
$609$	14.3986	−	14.6875i	0.583462	−	0.595166i
$610$	17.4033	−	10.0478i	0.704640	−	0.406824i
$611$	13.3187	−	14.2595i	0.538817	−	0.576878i
$612$	−6.36145	−	3.50623i	−0.257147	−	0.141731i
$613$	37.3103	+	9.99725i	1.50695	+	0.403785i	0.915420	−	0.402500i	$-0.131859\pi$
$613$	37.3103	+	9.99725i	1.50695	+	0.403785i	0.591527	+	0.806285i	$0.298525\pi$
$614$	20.7750	+	11.9944i	0.838409	+	0.484056i
$615$	−0.235963	−	23.7621i	−0.00951496	−	0.958179i
$616$	2.99555	+	11.1795i	0.120694	+	0.450436i
$617$	2.02021	−	7.53952i	0.0813305	−	0.303530i	−0.913264	−	0.407369i	$-0.866446\pi$
$617$	2.02021	−	7.53952i	0.0813305	−	0.303530i	0.994594	+	0.103840i	$0.0331129\pi$
$618$	6.51752	+	23.3921i	0.262173	+	0.940967i
$619$	−7.39770	+	27.6086i	−0.297339	+	1.10968i	0.642003	+	0.766702i	$0.278104\pi$
$619$	−7.39770	+	27.6086i	−0.297339	+	1.10968i	−0.939342	+	0.342982i	$0.888563\pi$
$620$	14.5957	+	8.42683i	0.586177	+	0.338430i
$621$	6.34445	−	0.189056i	0.254594	−	0.00758654i
$622$	8.55692	−	31.9348i	0.343101	−	1.28047i
$623$	19.6378	+	34.0137i	0.786773	+	1.36273i
$624$	2.88141	−	5.54053i	0.115349	−	0.221799i
$625$	−9.48067	+	16.4210i	−0.379227	+	0.656840i
$626$	−10.3550	−	10.3550i	−0.413870	−	0.413870i
$627$	41.8945	+	23.6363i	1.67310	+	0.943941i
$628$		−	0.0748314i		−	0.00298610i
$629$	16.5090	+	16.5090i	0.658256	+	0.658256i
$630$	11.0227	−	11.4694i	0.439154	−	0.456953i
$631$	−2.02779	+	0.543345i	−0.0807251	+	0.0216302i	−0.298956	−	0.954267i	$-0.596638\pi$
$631$	−2.02779	+	0.543345i	−0.0807251	+	0.0216302i	0.218230	+	0.975897i	$0.429972\pi$
$632$	0.312655	+	0.0837756i	0.0124367	+	0.00333242i
$633$	−7.44429	−	12.6032i	−0.295884	−	0.500932i
$634$		−	1.39648i		−	0.0554613i
$635$	−3.89275	+	3.89275i	−0.154479	+	0.154479i
$636$	0.121209	−	0.214838i	0.00480624	−	0.00851890i
$637$	0.123451	+	0.0657675i	0.00489129	+	0.00260580i
$638$		−	19.5260i		−	0.773040i
$639$	−5.29716	+	21.4657i	−0.209553	+	0.849170i
$640$	0.999310	+	1.73086i	0.0395012	+	0.0684181i
$641$	19.2923			0.762001			0.381001	−	0.924575i	$-0.375580\pi$
$641$	19.2923			0.762001			0.381001	+	0.924575i	$0.375580\pi$
$642$	−16.6145	−	4.27547i	−0.655720	−	0.168739i
$643$	−16.0158	−	4.29141i	−0.631600	−	0.169237i	−0.0712046	−	0.997462i	$-0.522684\pi$
$643$	−16.0158	−	4.29141i	−0.631600	−	0.169237i	−0.560396	+	0.828225i	$0.689351\pi$
$644$	−3.13038	−	0.838784i	−0.123354	−	0.0330527i
$645$	24.9220	−	25.4219i	0.981303	−	1.00099i
$646$	15.4139			0.606451
$647$	19.1754	+	33.2127i	0.753861	+	1.30573i	0.945939	+	0.324346i	$0.105144\pi$
$647$	19.1754	+	33.2127i	0.753861	+	1.30573i	−0.192077	+	0.981380i	$0.561522\pi$
$648$	8.77897	+	1.98233i	0.344871	+	0.0778732i
$649$			17.5273i			0.688006i
$650$	−1.05719	−	3.46788i	−0.0414662	−	0.136022i
$651$	−38.7483	+	0.384780i	−1.51866	+	0.0150807i
$652$	13.2010	−	13.2010i	0.516992	−	0.516992i
$653$			14.7649i			0.577793i	0.957360	+	0.288897i	$0.0932884\pi$
$653$			14.7649i			0.577793i	−0.957360	+	0.288897i	$0.906712\pi$
$654$	−13.5855	+	0.134907i	−0.531235	+	0.00527530i
$655$	−1.31929	−	0.353502i	−0.0515488	−	0.0138125i
$656$	−6.63068	+	1.77669i	−0.258885	+	0.0693680i
$657$	16.9458	−	4.90329i	0.661118	−	0.191296i
$658$	−10.1523	−	10.1523i	−0.395780	−	0.395780i
$659$		−	7.99000i		−	0.311246i	−0.987817	−	0.155623i	$-0.950261\pi$
$659$		−	7.99000i		−	0.311246i	0.987817	−	0.155623i	$-0.0497385\pi$
$660$	−0.149955	−	15.1008i	−0.00583698	−	0.587798i
$661$	−17.2742	−	17.2742i	−0.671887	−	0.671887i	0.286264	−	0.958151i	$-0.407587\pi$
$661$	−17.2742	−	17.2742i	−0.671887	−	0.671887i	−0.958151	+	0.286264i	$0.907587\pi$
$662$	−8.76189	+	15.1760i	−0.340540	+	0.589833i
$663$	−6.97660	+	13.4150i	−0.270949	+	0.520994i
$664$	−1.96687	−	3.40673i	−0.0763295	−	0.132207i
$665$	−8.73674	+	32.6060i	−0.338796	+	1.26440i
$666$	−25.3347	−	13.9636i	−0.981699	−	0.541080i
$667$	4.73497	+	2.73374i	0.183339	+	0.105851i
$668$	−4.71072	+	17.5806i	−0.182263	+	0.680215i
$669$	−13.3422	+	13.6098i	−0.515839	+	0.526187i
$670$	−1.30846	+	4.88325i	−0.0505503	+	0.188656i
$671$	11.3527	+	42.3687i	0.438265	+	1.63563i
$672$	−4.00223	−	2.25800i	−0.154389	−	0.0871042i
$673$	−43.1736	−	24.9263i	−1.66422	−	0.960838i	−0.970666	−	0.240433i	$-0.922710\pi$
$673$	−43.1736	−	24.9263i	−1.66422	−	0.960838i	−0.693554	−	0.720405i	$-0.743956\pi$
$674$	−24.8761	−	6.66553i	−0.958192	−	0.256747i
$675$	4.44501	−	2.74603i	0.171088	−	0.105695i
$676$	−11.6751	−	5.71764i	−0.449043	−	0.219909i
$677$	7.87586	−	4.54713i	0.302694	−	0.174760i	−0.340959	−	0.940078i	$-0.610752\pi$
$677$	7.87586	−	4.54713i	0.302694	−	0.174760i	0.643652	+	0.765318i	$0.277418\pi$
$678$	22.5969	+	5.81496i	0.867829	+	0.223322i
$679$	−23.2873			−0.893683
$680$	−2.41957	−	4.19082i	−0.0927863	−	0.160711i
$681$	−3.41837	+	13.2838i	−0.130992	+	0.509035i
$682$	−26.0123	+	26.0123i	−0.996064	+	0.996064i
$683$	7.08606	+	26.4455i	0.271141	+	1.01191i	0.958384	+	0.285483i	$0.0921540\pi$
$683$	7.08606	+	26.4455i	0.271141	+	1.01191i	−0.687243	+	0.726427i	$0.741179\pi$
$684$	−18.3458	+	5.30837i	−0.701467	+	0.202971i
$685$	22.5096	−	38.9877i	0.860047	−	1.48965i
$686$	−9.23429	+	15.9943i	−0.352567	+	0.610664i
$687$	−1.80359	−	1.76812i	−0.0688111	−	0.0674579i
$688$	−8.90622	−	5.14201i	−0.339546	−	0.196037i
$689$	−0.453190	−	0.241433i	−0.0172651	−	0.00919788i
$690$	3.68288	+	2.07783i	0.140205	+	0.0791015i
$691$	−0.505728	−	1.88740i	−0.0192388	−	0.0718002i	0.955639	−	0.294540i	$-0.0951665\pi$
$691$	−0.505728	−	1.88740i	−0.0192388	−	0.0718002i	−0.974878	+	0.222740i	$0.928500\pi$
$692$	−3.80657	+	2.19773i	−0.144704	+	0.0835450i
$693$	17.9546	+	29.7192i	0.682038	+	1.12894i
$694$	−15.9053	+	15.9053i	−0.603758	+	0.603758i
$695$	27.6274	+	27.6274i	1.04797	+	1.04797i
$696$	5.53602	+	5.42715i	0.209842	+	0.205716i
$697$	16.0545	−	4.30179i	0.608107	−	0.162942i
$698$	−14.4103	+	8.31981i	−0.545439	+	0.314909i
$699$	−3.86974	−	6.55148i	−0.146367	−	0.247800i
$700$	−2.57681	+	0.690454i	−0.0973943	+	0.0260967i
$701$	−8.14720			−0.307715			−0.153858	−	0.988093i	$-0.549170\pi$
$701$	−8.14720			−0.307715			−0.153858	+	0.988093i	$0.549170\pi$
$702$	3.68365	−	18.3693i	0.139031	−	0.693304i
$703$	61.3862			2.31522
$704$	−4.21380	+	1.12909i	−0.158814	+	0.0425540i
$705$	9.52748	+	16.1300i	0.358825	+	0.607492i
$706$	−29.1193	+	16.8120i	−1.09592	+	0.632729i
$707$	−9.05582	+	2.42650i	−0.340579	+	0.0912579i
$708$	−4.96935	−	4.87163i	−0.186760	−	0.183087i
$709$	29.2396	+	29.2396i	1.09811	+	1.09811i	0.994631	+	0.103484i	$0.0329989\pi$
$709$	29.2396	+	29.2396i	1.09811	+	1.09811i	0.103484	+	0.994631i	$0.467001\pi$
$710$	−10.4154	+	10.4154i	−0.390883	+	0.390883i
$711$	0.970861	−	0.0192837i	0.0364101	−	0.000723195i
$712$	−12.8205	+	7.40192i	−0.480468	+	0.277399i
$713$	−2.66603	−	9.94975i	−0.0998436	−	0.372621i
$714$	9.69036	+	5.46716i	0.362653	+	0.204603i
$715$	−31.4181	+	1.07181i	−1.17497	+	0.0400836i
$716$	9.42824	+	5.44340i	0.352350	+	0.203429i
$717$	−11.5098	−	11.2834i	−0.429841	−	0.421388i
$718$	13.2236	−	22.9039i	0.493500	−	0.854768i
$719$	24.0105	−	41.5874i	0.895441	−	1.55095i	0.0621837	−	0.998065i	$-0.480194\pi$
$719$	24.0105	−	41.5874i	0.895441	−	1.55095i	0.833258	−	0.552885i	$-0.186473\pi$
$720$	4.32307	+	4.15468i	0.161111	+	0.154836i
$721$	−9.62694	−	35.9282i	−0.358526	−	1.33804i
$722$	15.2221	−	15.2221i	0.566507	−	0.566507i
$723$	−0.719657	+	2.79659i	−0.0267643	+	0.104006i
$724$	1.56905	+	2.71767i	0.0583132	+	0.101001i
$725$	4.50061			0.167148
$726$	13.4712	+	3.46659i	0.499962	+	0.128657i
$727$	−6.36454	+	3.67457i	−0.236048	+	0.136282i	−0.613359	−	0.789804i	$-0.710182\pi$
$727$	−6.36454	+	3.67457i	−0.236048	+	0.136282i	0.377311	+	0.926087i	$0.376849\pi$
$728$	−4.49767	+	8.44247i	−0.166695	+	0.312899i
$729$	26.9521	−	1.60770i	0.998226	−	0.0595443i
$730$	11.3520	+	3.04177i	0.420158	+	0.112581i
$731$	21.5641	+	12.4500i	0.797578	+	0.460482i
$732$	−15.1678	−	8.55748i	−0.560620	−	0.316293i
$733$	2.01932	+	7.53620i	0.0745852	+	0.278356i	0.993139	−	0.116940i	$-0.0373086\pi$
$733$	2.01932	+	7.53620i	0.0745852	+	0.278356i	−0.918554	+	0.395296i	$0.870642\pi$
$734$	9.06799	−	33.8422i	0.334705	−	1.24914i
$735$	−0.0940142	+	0.0959001i	−0.00346777	+	0.00353733i
$736$	0.316156	−	1.17991i	0.0116537	−	0.0434920i
$737$	−9.55644	−	5.51741i	−0.352016	−	0.203237i
$738$	−17.6267	+	10.6490i	−0.648849	+	0.391996i
$739$	−6.40212	+	23.8930i	−0.235506	+	0.878920i	0.742414	+	0.669941i	$0.233681\pi$
$739$	−6.40212	+	23.8930i	−0.235506	+	0.878920i	−0.977920	+	0.208979i	$0.932986\pi$
$740$	−9.63601	−	16.6901i	−0.354227	−	0.613539i
$741$	11.9700	+	37.9115i	0.439730	+	1.39271i
$742$	−0.188920	+	0.327220i	−0.00693548	+	0.0120126i
$743$	13.9570	+	13.9570i	0.512032	+	0.512032i	0.915149	−	0.403117i	$-0.132073\pi$
$743$	13.9570	+	13.9570i	0.512032	+	0.512032i	−0.403117	+	0.915149i	$0.632073\pi$
$744$	−0.145032	−	14.6051i	−0.00531713	−	0.535447i
$745$			9.82163i			0.359837i
$746$	4.48418	+	4.48418i	0.164177	+	0.164177i
$747$	−8.50881	−	8.17738i	−0.311321	−	0.299195i
$748$	10.2026	−	2.73379i	0.373045	−	0.0999572i
$749$	25.3829	+	6.80134i	0.927473	+	0.248516i
$750$	20.7883	−	0.206434i	0.759083	−	0.00753789i
$751$		−	10.7772i		−	0.393266i	−0.980477	−	0.196633i	$-0.936999\pi$
$751$		−	10.7772i		−	0.393266i	0.980477	−	0.196633i	$-0.0630008\pi$
$752$	3.82664	−	3.82664i	0.139543	−	0.139543i
$753$	−13.4629	+	0.133691i	−0.490617	+	0.00487195i
$754$	11.0157	−	11.7938i	0.401168	−	0.429506i
$755$		−	8.00813i		−	0.291446i
$756$	−13.4164	−	3.16981i	−0.487950	−	0.115285i
$757$	−25.3500	−	43.9076i	−0.921363	−	1.59585i	−0.797308	−	0.603572i	$-0.793744\pi$
$757$	−25.3500	−	43.9076i	−0.921363	−	1.59585i	−0.124055	−	0.992275i	$-0.539590\pi$
$758$	34.1962			1.24206
$759$	−6.46138	+	6.59099i	−0.234533	+	0.239238i
$760$	−12.2899	−	3.29306i	−0.445801	−	0.119452i
$761$	−0.685121	−	0.183578i	−0.0248356	−	0.00665468i	0.246380	−	0.969173i	$-0.420759\pi$
$761$	−0.685121	−	0.183578i	−0.0248356	−	0.00665468i	−0.271215	+	0.962519i	$0.587426\pi$
$762$	4.62038	+	1.18898i	0.167379	+	0.0430723i
$763$	20.8106			0.753396
$764$	8.31799	+	14.4072i	0.300934	+	0.521234i
$765$	−10.4672	−	10.0595i	−0.378443	−	0.363702i
$766$			16.7505i			0.605221i
$767$	−9.88812	+	10.5866i	−0.357039	+	0.382260i
$768$	0.851088	−	1.50853i	0.0307110	−	0.0544342i
$769$	−13.1862	+	13.1862i	−0.475507	+	0.475507i	−0.903691	−	0.428184i	$-0.859153\pi$
$769$	−13.1862	+	13.1862i	−0.475507	+	0.475507i	0.428184	+	0.903691i	$0.359153\pi$
$770$

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.880877 + 1.49133i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.93052 - 0.517281i) q^{5} +(-1.23685 - 1.21252i) q^{6} +(1.87601 + 1.87601i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.44811 + 2.62735i) q^{9} +(-1.73086 + 0.999310i) q^{10} +(-1.12909 - 4.21380i) q^{11} +(1.50853 + 0.851088i) q^{12} +(1.69527 - 3.18215i) q^{13} +(-2.29763 - 1.32654i) q^{14} +(2.47199 + 2.42337i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.21062 + 2.09686i) q^{17} +(0.718758 - 2.91263i) q^{18} +(1.64767 + 6.14918i) q^{19} +(1.41324 - 1.41324i) q^{20} +(-1.14521 + 4.45027i) q^{21} +(2.18123 + 3.77799i) q^{22} -1.22153 q^{23} +(-1.67740 - 0.431653i) q^{24} +(-0.870804 + 0.502759i) q^{25} +(-0.813901 + 3.51249i) q^{26} +(-5.19385 + 0.154769i) q^{27} +(2.56267 + 0.686666i) q^{28} +(-3.87626 - 2.23796i) q^{29} +(-3.01497 - 1.70100i) q^{30} +(2.18253 + 8.14531i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(5.28957 - 5.39568i) q^{33} +(0.626664 - 2.33874i) q^{34} +(4.59209 + 2.65124i) q^{35} +(0.0595757 + 2.99941i) q^{36} +(2.49571 - 9.31410i) q^{37} +(-3.18305 - 5.51321i) q^{38} +(6.23895 - 0.274886i) q^{39} +(-0.999310 + 1.73086i) q^{40} +(-4.85400 - 4.85400i) q^{41} +(-0.0456298 - 4.59503i) q^{42} -10.2840i q^{43} +(-3.08472 - 3.08472i) q^{44} +(-1.43652 + 5.82123i) q^{45} +(1.17991 - 0.316156i) q^{46} +(5.22728 + 1.40065i) q^{47} +(1.73197 - 0.0171989i) q^{48} +0.0387948i q^{49} +(0.711008 - 0.711008i) q^{50} +(-4.19351 + 0.0416426i) q^{51} +(-0.122930 - 3.60346i) q^{52} -0.142416i q^{53} +(4.97681 - 1.49376i) q^{54} +(-4.35944 - 7.55077i) q^{55} -2.65307 q^{56} +(-7.71905 + 7.87389i) q^{57} +(4.32340 + 1.15845i) q^{58} +(-3.88086 - 1.03987i) q^{59} +(3.35249 + 0.862710i) q^{60} -10.0548 q^{61} +(-4.21632 - 7.30289i) q^{62} +(-7.64559 + 2.21226i) q^{63} -1.00000i q^{64} +(1.62668 - 7.02013i) q^{65} +(-3.71283 + 6.58087i) q^{66} +(1.78863 - 1.78863i) q^{67} +2.42124i q^{68} +(-1.07602 - 1.82170i) q^{69} +(-5.12181 - 1.37238i) q^{70} +(7.11876 - 1.90747i) q^{71} +(-0.833850 - 2.88179i) q^{72} +(-4.15800 - 4.15800i) q^{73} +9.64266i q^{74} +(-1.51685 - 0.855784i) q^{75} +(4.50152 + 4.50152i) q^{76} +(5.78695 - 10.0233i) q^{77} +(-5.95521 + 1.88028i) q^{78} +(-0.161842 - 0.280319i) q^{79} +(0.517281 - 1.93052i) q^{80} +(-4.80595 - 7.60939i) q^{81} +(5.94491 + 3.43230i) q^{82} +(-1.01813 + 3.79971i) q^{83} +(1.23336 + 4.42665i) q^{84} +(-1.25246 + 4.67425i) q^{85} +(2.66170 + 9.93360i) q^{86} +(-0.0769806 - 7.75213i) q^{87} +(3.77799 + 2.18123i) q^{88} +(14.2994 + 3.83151i) q^{89} +(-0.119069 - 5.99468i) q^{90} +(9.15006 - 2.78940i) q^{91} +(-1.05788 + 0.610766i) q^{92} +(-10.2248 + 10.4299i) q^{93} -5.41168 q^{94} +(6.36171 + 11.0188i) q^{95} +(-1.66850 + 0.464878i) q^{96} +(-6.20661 + 6.20661i) q^{97} +(-0.0100408 - 0.0374729i) q^{98} +(12.7062 + 3.13555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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