LMFDB - Embedded newform 98.2.g.a.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			51.1
Character	$\chi$	$=$	98.51
Dual form			98.2.g.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.955573 - 0.294755i) q^{2} +(-0.692327 + 1.76402i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-4.01065 + 0.604508i) q^{5} +(1.18152 - 1.48158i) q^{6} +(-2.17740 - 1.50297i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.433294 - 0.402038i) q^{9} +O(q^{10})$	\(q+(-0.955573 - 0.294755i) q^{2} +(-0.692327 + 1.76402i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-4.01065 + 0.604508i) q^{5} +(1.18152 - 1.48158i) q^{6} +(-2.17740 - 1.50297i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.433294 - 0.402038i) q^{9} +(4.01065 + 0.604508i) q^{10} +(-0.843363 + 0.782526i) q^{11} +(-1.56573 + 1.06750i) q^{12} +(1.46590 + 6.42254i) q^{13} +(1.63766 + 2.07800i) q^{14} +(1.71032 - 7.49339i) q^{15} +(0.365341 + 0.930874i) q^{16} +(0.0145130 + 0.193663i) q^{17} +(0.295541 + 0.511892i) q^{18} +(0.979457 - 1.69647i) q^{19} +(-3.65429 - 1.75981i) q^{20} +(4.15874 - 2.80044i) q^{21} +(1.03655 - 0.499175i) q^{22} +(-0.204205 + 2.72492i) q^{23} +(1.81082 - 0.558565i) q^{24} +(10.9420 - 3.37517i) q^{25} +(0.492300 - 6.56928i) q^{26} +(-4.11287 + 1.98065i) q^{27} +(-0.952403 - 2.46839i) q^{28} +(-1.09337 - 0.526541i) q^{29} +(-3.84305 + 6.65635i) q^{30} +(-2.49765 - 4.32606i) q^{31} +(-0.0747301 - 0.997204i) q^{32} +(-0.796509 - 2.02947i) q^{33} +(0.0432149 - 0.189337i) q^{34} +(9.64136 + 4.71162i) q^{35} +(-0.131528 - 0.576262i) q^{36} +(-1.86576 + 1.27206i) q^{37} +(-1.43599 + 1.33240i) q^{38} +(-12.3444 - 1.86061i) q^{39} +(2.97322 + 2.75875i) q^{40} +(4.89552 + 6.13878i) q^{41} +(-4.79942 + 1.45021i) q^{42} +(-3.11862 + 3.91062i) q^{43} +(-1.13763 + 0.171470i) q^{44} +(1.98083 + 1.35050i) q^{45} +(0.998318 - 2.54367i) q^{46} +(-9.22092 - 2.84428i) q^{47} -1.89502 q^{48} +(2.48217 + 6.54514i) q^{49} -11.4508 q^{50} +(-0.351673 - 0.108477i) q^{51} +(-2.40676 + 6.13232i) q^{52} +(2.18578 + 1.49024i) q^{53} +(4.51395 - 0.680368i) q^{54} +(2.90939 - 3.64826i) q^{55} +(0.182521 + 2.63945i) q^{56} +(2.31450 + 2.90229i) q^{57} +(0.889598 + 0.825426i) q^{58} +(9.10037 + 1.37166i) q^{59} +(5.63430 - 5.22787i) q^{60} +(2.29690 - 1.56600i) q^{61} +(1.11156 + 4.87006i) q^{62} +(0.339205 + 1.52663i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-9.76170 - 24.8724i) q^{65} +(0.162925 + 2.17408i) q^{66} +(-0.900787 - 1.56021i) q^{67} +(-0.0971030 + 0.168187i) q^{68} +(-4.66544 - 2.24676i) q^{69} +(-7.82425 - 7.34414i) q^{70} +(2.51616 - 1.21172i) q^{71} +(-0.0441716 + 0.589429i) q^{72} +(-10.3660 + 3.19750i) q^{73} +(2.15782 - 0.665599i) q^{74} +(-1.62160 + 21.6387i) q^{75} +(1.76492 - 0.849941i) q^{76} +(3.01245 - 0.436328i) q^{77} +(11.2475 + 5.41652i) q^{78} +(-3.35704 + 5.81456i) q^{79} +(-2.02798 - 3.51256i) q^{80} +(-0.778977 - 10.3947i) q^{81} +(-2.86858 - 7.30903i) q^{82} +(0.923281 - 4.04516i) q^{83} +(5.01366 + 0.0288720i) q^{84} +(-0.175278 - 0.767941i) q^{85} +(4.13274 - 2.81766i) q^{86} +(1.68580 - 1.56420i) q^{87} +(1.13763 + 0.171470i) q^{88} +(3.61856 + 3.35753i) q^{89} +(-1.49475 - 1.87436i) q^{90} +(6.46101 - 16.1877i) q^{91} +(-1.70373 + 2.13641i) q^{92} +(9.36044 - 1.41086i) q^{93} +(7.97289 + 5.43582i) q^{94} +(-2.90273 + 7.39604i) q^{95} +(1.81082 + 0.558565i) q^{96} +9.02920 q^{97} +(-0.442683 - 6.98599i) q^{98} +0.680029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{21}\right)$

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 $

$2$	−0.955573	−	0.294755i	−0.675692	−	0.208423i
$2$	−0.955573	−	0.294755i	−0.675692	−	0.208423i
$3$	−0.692327	+	1.76402i	−0.399715	+	1.01846i	0.579381	+	0.815057i	$0.303294\pi$
$3$	−0.692327	+	1.76402i	−0.399715	+	1.01846i	−0.979096	+	0.203400i	$0.934801\pi$
$4$	0.826239	+	0.563320i	0.413119	+	0.281660i
$5$	−4.01065	+	0.604508i	−1.79362	+	0.270344i	−0.959595	−	0.281385i	$-0.909206\pi$
$5$	−4.01065	+	0.604508i	−1.79362	+	0.270344i	−0.834023	+	0.551730i	$0.813968\pi$
$6$	1.18152	−	1.48158i	0.482355	−	0.604853i
$7$	−2.17740	−	1.50297i	−0.822981	−	0.568069i
$7$	−2.17740	−	1.50297i	−0.822981	−	0.568069i
$8$	−0.623490	−	0.781831i	−0.220437	−	0.276419i
$9$	−0.433294	−	0.402038i	−0.144431	−	0.134013i
$10$	4.01065	+	0.604508i	1.26828	+	0.191162i
$11$	−0.843363	+	0.782526i	−0.254283	+	0.235941i	−0.797006	−	0.603972i	$-0.793584\pi$
$11$	−0.843363	+	0.782526i	−0.254283	+	0.235941i	0.542722	+	0.839912i	$0.317394\pi$
$12$	−1.56573	+	1.06750i	−0.451989	+	0.308161i
$13$	1.46590	+	6.42254i	0.406568	+	1.78129i	0.599813	+	0.800140i	$0.295242\pi$
$13$	1.46590	+	6.42254i	0.406568	+	1.78129i	−0.193245	+	0.981151i	$0.561901\pi$
$14$	1.63766	+	2.07800i	0.437683	+	0.555368i
$15$	1.71032	−	7.49339i	0.441602	−	1.93478i
$16$	0.365341	+	0.930874i	0.0913353	+	0.232718i
$17$	0.0145130	+	0.193663i	0.00351993	+	0.0469702i	0.998687	−	0.0512243i	$-0.0163123\pi$
$17$	0.0145130	+	0.193663i	0.00351993	+	0.0469702i	−0.995167	+	0.0981944i	$0.968693\pi$
$18$	0.295541	+	0.511892i	0.0696597	+	0.120654i
$19$	0.979457	−	1.69647i	0.224703	−	0.389197i	−0.731527	−	0.681812i	$-0.761192\pi$
$19$	0.979457	−	1.69647i	0.224703	−	0.389197i	0.956230	+	0.292615i	$0.0945255\pi$
$20$	−3.65429	−	1.75981i	−0.817124	−	0.393506i
$21$	4.15874	−	2.80044i	0.907512	−	0.611106i
$22$	1.03655	−	0.499175i	0.220993	−	0.106425i
$23$	−0.204205	+	2.72492i	−0.0425796	+	0.568186i	0.934590	+	0.355726i	$0.115766\pi$
$23$	−0.204205	+	2.72492i	−0.0425796	+	0.568186i	−0.977170	+	0.212460i	$0.931853\pi$
$24$	1.81082	−	0.558565i	0.369633	−	0.114017i
$25$	10.9420	−	3.37517i	2.18841	−	0.675034i
$26$	0.492300	−	6.56928i	0.0965479	−	1.28834i
$27$	−4.11287	+	1.98065i	−0.791521	+	0.381177i
$28$	−0.952403	−	2.46839i	−0.179987	−	0.466481i
$29$	−1.09337	−	0.526541i	−0.203035	−	0.0977763i	0.329603	−	0.944119i	$-0.393085\pi$
$29$	−1.09337	−	0.526541i	−0.203035	−	0.0977763i	−0.532638	+	0.846343i	$0.678799\pi$
$30$	−3.84305	+	6.65635i	−0.701641	+	1.21528i
$31$	−2.49765	−	4.32606i	−0.448591	−	0.776983i	0.549703	−	0.835360i	$-0.314741\pi$
$31$	−2.49765	−	4.32606i	−0.448591	−	0.776983i	−0.998295	+	0.0583772i	$0.981407\pi$
$32$	−0.0747301	−	0.997204i	−0.0132105	−	0.176282i
$33$	−0.796509	−	2.02947i	−0.138654	−	0.353286i
$34$	0.0432149	−	0.189337i	0.00741129	−	0.0324710i
$35$	9.64136	+	4.71162i	1.62969	+	0.796410i
$36$	−0.131528	−	0.576262i	−0.0219213	−	0.0960437i
$37$	−1.86576	+	1.27206i	−0.306730	+	0.209125i	−0.706896	−	0.707318i	$-0.749905\pi$
$37$	−1.86576	+	1.27206i	−0.306730	+	0.209125i	0.400166	+	0.916443i	$0.368953\pi$
$38$	−1.43599	+	1.33240i	−0.232948	+	0.216144i
$39$	−12.3444	−	1.86061i	−1.97668	−	0.297937i
$40$	2.97322	+	2.75875i	0.470108	+	0.436197i
$41$	4.89552	+	6.13878i	0.764551	+	0.958717i	0.999913	−	0.0131909i	$-0.00419893\pi$
$41$	4.89552	+	6.13878i	0.764551	+	0.958717i	−0.235362	+	0.971908i	$0.575628\pi$
$42$	−4.79942	+	1.45021i	−0.740567	+	0.223773i
$43$	−3.11862	+	3.91062i	−0.475585	+	0.596364i	−0.960529	−	0.278181i	$-0.910269\pi$
$43$	−3.11862	+	3.91062i	−0.475585	+	0.596364i	0.484944	+	0.874545i	$0.338840\pi$
$44$	−1.13763	+	0.171470i	−0.171504	+	0.0258501i
$45$	1.98083	+	1.35050i	0.295284	+	0.201321i
$46$	0.998318	−	2.54367i	0.147194	−	0.375044i
$47$	−9.22092	−	2.84428i	−1.34501	−	0.414880i	−0.463102	−	0.886305i	$-0.653264\pi$
$47$	−9.22092	−	2.84428i	−1.34501	−	0.414880i	−0.881906	+	0.471425i	$0.843740\pi$
$48$	−1.89502			−0.273522
$49$	2.48217	+	6.54514i	0.354596	+	0.935020i
$50$	−11.4508			−1.61938
$51$	−0.351673	−	0.108477i	−0.0492441	−	0.0151898i
$52$	−2.40676	+	6.13232i	−0.333757	+	0.850400i
$53$	2.18578	+	1.49024i	0.300239	+	0.204700i	0.704064	−	0.710137i	$-0.251367\pi$
$53$	2.18578	+	1.49024i	0.300239	+	0.204700i	−0.403824	+	0.914837i	$0.632319\pi$
$54$	4.51395	−	0.680368i	0.614271	−	0.0925864i
$55$	2.90939	−	3.64826i	0.392302	−	0.491931i
$56$	0.182521	+	2.63945i	0.0243904	+	0.352711i
$57$	2.31450	+	2.90229i	0.306563	+	0.384418i
$58$	0.889598	+	0.825426i	0.116810	+	0.108384i
$59$	9.10037	+	1.37166i	1.18477	+	0.178575i	0.711721	−	0.702462i	$-0.247916\pi$
$59$	9.10037	+	1.37166i	1.18477	+	0.178575i	0.473047	+	0.881037i	$0.343154\pi$
$60$	5.63430	−	5.22787i	0.727386	−	0.674915i
$61$	2.29690	−	1.56600i	0.294088	−	0.200506i	−0.407283	−	0.913302i	$-0.633524\pi$
$61$	2.29690	−	1.56600i	0.294088	−	0.200506i	0.701371	+	0.712796i	$0.252571\pi$
$62$	1.11156	+	4.87006i	0.141168	+	0.618498i
$63$	0.339205	+	1.52663i	0.0427358	+	0.192337i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	−9.76170	−	24.8724i	−1.21079	−	3.08504i
$66$	0.162925	+	2.17408i	0.0200547	+	0.267611i
$67$	−0.900787	−	1.56021i	−0.110049	−	0.190610i	0.805741	−	0.592268i	$-0.201767\pi$
$67$	−0.900787	−	1.56021i	−0.110049	−	0.190610i	−0.915790	+	0.401658i	$0.868434\pi$
$68$	−0.0971030	+	0.168187i	−0.0117755	+	0.0203957i
$69$	−4.66544	−	2.24676i	−0.561653	−	0.270478i
$70$	−7.82425	−	7.34414i	−0.935177	−	0.877793i
$71$	2.51616	−	1.21172i	0.298613	−	0.143805i	−0.278578	−	0.960414i	$-0.589863\pi$
$71$	2.51616	−	1.21172i	0.298613	−	0.143805i	0.577191	+	0.816609i	$0.304149\pi$
$72$	−0.0441716	+	0.589429i	−0.00520567	+	0.0694649i
$73$	−10.3660	+	3.19750i	−1.21325	+	0.374239i	−0.834369	−	0.551206i	$-0.814168\pi$
$73$	−10.3660	+	3.19750i	−1.21325	+	0.374239i	−0.378883	+	0.925445i	$0.623692\pi$
$74$	2.15782	−	0.665599i	0.250841	−	0.0773743i
$75$	−1.62160	+	21.6387i	−0.187246	+	2.49862i
$76$	1.76492	−	0.849941i	0.202450	−	0.0974949i
$77$	3.01245	−	0.436328i	0.343301	−	0.0497242i
$78$	11.2475	+	5.41652i	1.27353	+	0.613300i
$79$	−3.35704	+	5.81456i	−0.377696	+	0.654189i	−0.990727	−	0.135870i	$-0.956617\pi$
$79$	−3.35704	+	5.81456i	−0.377696	+	0.654189i	0.613030	+	0.790059i	$0.289950\pi$
$80$	−2.02798	−	3.51256i	−0.226735	−	0.392716i
$81$	−0.778977	−	10.3947i	−0.0865530	−	1.15497i
$82$	−2.86858	−	7.30903i	−0.316782	−	0.807148i
$83$	0.923281	−	4.04516i	0.101343	−	0.444014i	−0.898643	−	0.438682i	$-0.855446\pi$
$83$	0.923281	−	4.04516i	0.101343	−	0.444014i	0.999986	−	0.00533214i	$-0.00169728\pi$
$84$	5.01366	+	0.0288720i	0.547035	+	0.00315019i
$85$	−0.175278	−	0.767941i	−0.0190115	−	0.0832949i
$86$	4.13274	−	2.81766i	0.445645	−	0.303836i
$87$	1.68580	−	1.56420i	0.180737	−	0.167699i
$88$	1.13763	+	0.171470i	0.121272	+	0.0182788i
$89$	3.61856	+	3.35753i	0.383566	+	0.355897i	0.848266	−	0.529571i	$-0.177647\pi$
$89$	3.61856	+	3.35753i	0.383566	+	0.355897i	−0.464699	+	0.885468i	$0.653838\pi$
$90$	−1.49475	−	1.87436i	−0.157561	−	0.197575i
$91$	6.46101	−	16.1877i	0.677298	−	1.69693i
$92$	−1.70373	+	2.13641i	−0.177626	+	0.222736i
$93$	9.36044	−	1.41086i	0.970632	−	0.146299i
$94$	7.97289	+	5.43582i	0.822341	+	0.560663i
$95$	−2.90273	+	7.39604i	−0.297814	+	0.758817i
$96$	1.81082	+	0.558565i	0.184817	+	0.0570084i
$97$	9.02920			0.916776			0.458388	−	0.888752i	$-0.348427\pi$
$97$	9.02920			0.916776			0.458388	+	0.888752i	$0.348427\pi$
$98$	−0.442683	−	6.98599i	−0.0447177	−	0.705691i
$99$	0.680029			0.0683455
$100$	10.9420	+	3.37517i	1.09420	+	0.337517i
$101$	−1.39368	+	3.55103i	−0.138676	+	0.353341i	−0.983293	−	0.182030i	$-0.941733\pi$
$101$	−1.39368	+	3.55103i	−0.138676	+	0.353341i	0.844617	+	0.535371i	$0.179828\pi$
$102$	0.304075	+	0.207315i	0.0301079	+	0.0205272i
$103$	12.3810	−	1.86614i	1.21994	−	0.183876i	0.492661	−	0.870221i	$-0.336024\pi$
$103$	12.3810	−	1.86614i	1.21994	−	0.183876i	0.727276	+	0.686345i	$0.240786\pi$
$104$	4.10737	−	5.15047i	0.402760	−	0.505045i
$105$	−14.9864	+	13.7456i	−1.46252	+	1.34143i
$106$	−1.64941	−	2.06830i	−0.160205	−	0.200891i
$107$	7.94052	+	7.36773i	0.767640	+	0.712265i	0.963306	−	0.268405i	$-0.0864966\pi$
$107$	7.94052	+	7.36773i	0.767640	+	0.712265i	−0.195667	+	0.980670i	$0.562687\pi$
$108$	−4.51395	−	0.680368i	−0.434355	−	0.0654685i
$109$	−13.5644	+	12.5859i	−1.29923	+	1.20551i	−0.334466	+	0.942408i	$0.608556\pi$
$109$	−13.5644	+	12.5859i	−1.29923	+	1.20551i	−0.964767	+	0.263105i	$0.915253\pi$
$110$	−3.85548	+	2.62862i	−0.367606	+	0.250629i
$111$	−0.952215	−	4.17192i	−0.0903802	−	0.395982i
$112$	0.603579	−	2.57598i	0.0570329	−	0.243408i
$113$	1.53313	−	6.71707i	0.144225	−	0.631889i	−0.850202	−	0.526457i	$-0.823520\pi$
$113$	1.53313	−	6.71707i	0.144225	−	0.631889i	0.994426	−	0.105432i	$-0.0336226\pi$
$114$	−1.35621	−	3.45556i	−0.127021	−	0.323643i
$115$	−0.828245	−	11.0522i	−0.0772343	−	1.03062i
$116$	−0.606777	−	1.05097i	−0.0563378	−	0.0975800i
$117$	1.94694	−	3.37219i	0.179994	−	0.311759i
$118$	−8.29177	−	3.99310i	−0.763319	−	0.367595i
$119$	0.259469	−	0.443495i	0.0237854	−	0.0406551i
$120$	−6.92493	+	3.33487i	−0.632157	+	0.304431i
$121$	−0.723118	+	9.64933i	−0.0657380	+	0.877212i
$122$	−2.65644	+	0.819404i	−0.240503	+	0.0741853i
$123$	−14.2182	+	4.38574i	−1.28201	+	0.395449i
$124$	0.373299	−	4.98133i	0.0335233	−	0.447337i
$125$	−23.5729	+	11.3521i	−2.10843	+	1.01536i
$126$	0.125846	−	1.55878i	0.0112112	−	0.138868i
$127$	−0.262303	−	0.126318i	−0.0232756	−	0.0112089i	0.422210	−	0.906498i	$-0.361255\pi$
$127$	−0.262303	−	0.126318i	−0.0232756	−	0.0112089i	−0.445485	+	0.895289i	$0.646969\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.73931	−	8.20873i	−0.417273	−	0.722738i
$130$	1.99674	+	26.6447i	0.175126	+	2.33690i
$131$	0.333434	+	0.849576i	0.0291323	+	0.0742278i	0.944700	−	0.327937i	$-0.106353\pi$
$131$	0.333434	+	0.849576i	0.0291323	+	0.0742278i	−0.915567	+	0.402164i	$0.868258\pi$
$132$	0.485136	−	2.12552i	0.0422257	−	0.185003i
$133$	−4.68241	+	2.22180i	−0.406017	+	0.192655i
$134$	0.400888	+	1.75640i	0.0346314	+	0.151730i
$135$	15.2979	−	10.4300i	1.31664	−	0.897668i
$136$	0.142363	−	0.132094i	0.0122075	−	0.0113269i
$137$	8.94796	+	1.34869i	0.764476	+	0.115226i	0.519695	−	0.854352i	$-0.326046\pi$
$137$	8.94796	+	1.34869i	0.764476	+	0.115226i	0.244781	+	0.969578i	$0.421284\pi$
$138$	3.79593	+	3.52211i	0.323131	+	0.299822i
$139$	−11.5164	−	14.4412i	−0.976812	−	1.22488i	−0.974385	−	0.224886i	$-0.927799\pi$
$139$	−11.5164	−	14.4412i	−0.976812	−	1.22488i	−0.00242640	−	0.999997i	$-0.500772\pi$
$140$	5.31192	+	9.32410i	0.448939	+	0.788030i
$141$	11.4012	−	14.2967i	0.960158	−	1.20400i
$142$	−2.76153	+	0.416234i	−0.231743	+	0.0349296i
$143$	−6.26209	−	4.26942i	−0.523662	−	0.357027i
$144$	0.215946	−	0.550223i	0.0179955	−	0.0458519i
$145$	4.70344	+	1.45082i	0.390600	+	0.120484i
$146$	10.8480			0.897784
$147$	−13.2642	−	0.152774i	−1.09401	−	0.0126006i
$148$	−2.25814			−0.185618
$149$	5.58447	+	1.72258i	0.457498	+	0.141119i	0.514934	−	0.857230i	$-0.327816\pi$
$149$	5.58447	+	1.72258i	0.457498	+	0.141119i	−0.0574363	+	0.998349i	$0.518293\pi$
$150$	7.92767	−	20.1994i	0.647291	−	1.64927i
$151$	0.190151	+	0.129643i	0.0154743	+	0.0105502i	0.571032	−	0.820927i	$-0.306543\pi$
$151$	0.190151	+	0.129643i	0.0154743	+	0.0105502i	−0.555558	+	0.831478i	$0.687495\pi$
$152$	−1.93703	+	0.291961i	−0.157114	+	0.0236812i
$153$	0.0715714	−	0.0897477i	0.00578621	−	0.00725567i
$154$	−3.00723	−	0.470993i	−0.242329	−	0.0379537i
$155$	12.6323	+	15.8405i	1.01465	+	1.27234i
$156$	−9.15127	−	8.49114i	−0.732688	−	0.679835i
$157$	2.79129	+	0.420719i	0.222769	+	0.0335771i	0.259478	−	0.965749i	$-0.416449\pi$
$157$	2.79129	+	0.420719i	0.222769	+	0.0335771i	−0.0367091	+	0.999326i	$0.511687\pi$
$158$	4.92177	−	4.56673i	0.391555	−	0.363310i
$159$	−4.14208	+	2.82402i	−0.328488	+	0.223959i
$160$	0.902535	+	3.95426i	0.0713516	+	0.312612i
$161$	4.54011	−	5.62635i	0.357811	−	0.443418i
$162$	−2.31953	+	10.1625i	−0.182239	+	0.798443i
$163$	3.63814	+	9.26984i	0.284961	+	0.726070i	0.999646	+	0.0266225i	$0.00847522\pi$
$163$	3.63814	+	9.26984i	0.284961	+	0.726070i	−0.714684	+	0.699447i	$0.753430\pi$
$164$	0.586766	+	7.82984i	0.0458187	+	0.611408i
$165$	4.42136	+	7.65801i	0.344202	+	0.596175i
$166$	−2.07459	+	3.59330i	−0.161020	+	0.278894i
$167$	13.7557	+	6.62438i	1.06445	+	0.512610i	0.882313	−	0.470664i	$-0.155986\pi$
$167$	13.7557	+	6.62438i	1.06445	+	0.512610i	0.182133	+	0.983274i	$0.441700\pi$
$168$	−4.78240	−	1.50539i	−0.368970	−	0.116143i
$169$	−27.3875	+	13.1891i	−2.10673	+	1.01455i
$170$	−0.0588642	+	0.785488i	−0.00451468	+	0.0602442i
$171$	−1.10644	+	0.341291i	−0.0846114	+	0.0260991i
$172$	−4.77965	+	1.47433i	−0.364445	+	0.112416i
$173$	0.354351	−	4.72848i	0.0269408	−	0.359500i	−0.967399	−	0.253256i	$-0.918499\pi$
$173$	0.354351	−	4.72848i	0.0269408	−	0.359500i	0.994340	−	0.106244i	$-0.0338824\pi$
$174$	−2.07196	+	0.997804i	−0.157075	+	0.0756433i
$175$	−28.8980	−	9.09642i	−2.18448	−	0.687625i
$176$	−1.03655	−	0.499175i	−0.0781328	−	0.0376268i
$177$	−8.72007	+	15.1036i	−0.655441	+	1.13526i
$178$	−2.46814	−	4.27495i	−0.184995	−	0.320421i
$179$	0.0906257	+	1.20932i	0.00677368	+	0.0903885i	0.999566	−	0.0294591i	$-0.00937847\pi$
$179$	0.0906257	+	1.20932i	0.00677368	+	0.0903885i	−0.992792	+	0.119848i	$0.961759\pi$
$180$	0.875869	+	2.23168i	0.0652834	+	0.166339i
$181$	4.27441	−	18.7274i	0.317714	−	1.39200i	−0.523837	−	0.851819i	$-0.675500\pi$
$181$	4.27441	−	18.7274i	0.317714	−	1.39200i	0.841551	−	0.540178i	$-0.181643\pi$
$182$	−10.9454	+	13.5641i	−0.811324	+	1.00544i
$183$	1.17225	+	5.13596i	0.0866552	+	0.379661i
$184$	2.25775	−	1.53931i	0.166444	−	0.113479i
$185$	6.71396	−	6.22965i	0.493620	−	0.458013i
$186$	−9.36044	−	1.41086i	−0.686341	−	0.103449i
$187$	−0.163786	−	0.151971i	−0.0119772	−	0.0111132i
$188$	−6.01644	−	7.54438i	−0.438794	−	0.550230i
$189$	11.9322	+	1.86883i	0.867942	+	0.135937i
$190$	4.95379	−	6.21186i	0.359386	−	0.450655i
$191$	14.9836	−	2.25841i	1.08417	−	0.163413i	0.417437	−	0.908706i	$-0.362928\pi$
$191$	14.9836	−	2.25841i	1.08417	−	0.163413i	0.666737	+	0.745293i	$0.267690\pi$
$192$	−1.56573	−	1.06750i	−0.112997	−	0.0770402i
$193$	5.79215	−	14.7582i	0.416928	−	1.06232i	−0.555995	−	0.831186i	$-0.687663\pi$
$193$	5.79215	−	14.7582i	0.416928	−	1.06232i	0.972923	−	0.231130i	$-0.0742422\pi$
$194$	−8.62806	−	2.66140i	−0.619458	−	0.191078i
$195$	50.6337			3.62595
$196$	−1.63614	+	6.80610i	−0.116867	+	0.486150i
$197$	22.5155			1.60416			0.802081	−	0.597216i	$-0.203726\pi$
$197$	22.5155			1.60416			0.802081	+	0.597216i	$0.203726\pi$
$198$	−0.649817	−	0.200442i	−0.0461805	−	0.0142448i
$199$	−4.18073	+	10.6523i	−0.296364	+	0.755123i	0.702684	+	0.711502i	$0.251985\pi$
$199$	−4.18073	+	10.6523i	−0.296364	+	0.755123i	−0.999048	+	0.0436210i	$0.986111\pi$
$200$	−9.46106	−	6.45044i	−0.668998	−	0.456115i
$201$	3.37588	−	0.508832i	0.238116	−	0.0358902i
$202$	2.37845	−	2.98248i	0.167347	−	0.209846i
$203$	1.58934	+	2.78980i	0.111550	+	0.195806i
$204$	−0.229459	−	0.287732i	−0.0160653	−	0.0201453i
$205$	−23.3452	−	21.6611i	−1.63050	−	1.51288i
$206$	−12.3810	−	1.86614i	−0.862625	−	0.130020i
$207$	1.18400	−	1.09859i	0.0822939	−	0.0763576i
$208$	−5.44302	+	3.71099i	−0.377405	+	0.257311i
$209$	0.501494	+	2.19719i	0.0346891	+	0.151983i
$210$	18.3721	−	8.71759i	1.26780	−	0.601571i
$211$	−2.98175	+	13.0639i	−0.205272	+	0.899355i	0.762393	+	0.647115i	$0.224025\pi$
$211$	−2.98175	+	13.0639i	−0.205272	+	0.899355i	−0.967665	+	0.252241i	$0.918833\pi$
$212$	0.966493	+	2.46258i	0.0663790	+	0.169131i
$213$	0.395491	+	5.27746i	0.0270986	+	0.361606i
$214$	−5.41607	−	9.38091i	−0.370235	−	0.641266i
$215$	10.1437	−	17.5694i	0.691793	−	1.19822i
$216$	4.11287	+	1.98065i	0.279845	+	0.134766i
$217$	−1.06353	+	13.1735i	−0.0721975	+	0.894273i
$218$	16.6715	−	8.02859i	1.12914	−	0.543765i
$219$	1.53623	−	20.4996i	0.103809	−	1.38523i
$220$	4.45899	−	1.37542i	0.300625	−	0.0927306i
$221$	−1.22253	+	0.377101i	−0.0822364	+	0.0253666i
$222$	−0.319786	+	4.26725i	−0.0214626	+	0.286399i
$223$	2.04361	−	0.984151i	0.136850	−	0.0659036i	−0.364206	−	0.931319i	$-0.618659\pi$
$223$	2.04361	−	0.984151i	0.136850	−	0.0659036i	0.501056	+	0.865415i	$0.332945\pi$
$224$	−1.33605	+	2.28363i	−0.0892685	+	0.152582i
$225$	−6.09806	−	2.93667i	−0.406537	−	0.195778i
$226$	−3.44491	+	5.96675i	−0.229152	+	0.396903i
$227$	−4.96698	−	8.60306i	−0.329670	−	0.571005i	0.652776	−	0.757551i	$-0.273604\pi$
$227$	−4.96698	−	8.60306i	−0.329670	−	0.571005i	−0.982446	+	0.186546i	$0.940271\pi$
$228$	0.277411	+	3.70179i	0.0183720	+	0.245157i
$229$	−5.41138	−	13.7880i	−0.357594	−	0.911135i	−0.990575	−	0.136968i	$-0.956264\pi$
$229$	−5.41138	−	13.7880i	−0.357594	−	0.911135i	0.632981	−	0.774167i	$-0.281831\pi$
$230$	−2.46623	+	10.8053i	−0.162619	+	0.712479i
$231$	−1.31591	+	5.61611i	−0.0865806	+	0.369513i
$232$	0.270041	+	1.18313i	0.0177291	+	0.0776761i
$233$	−21.3792	+	14.5761i	−1.40060	+	0.954910i	−0.401356	+	0.915922i	$0.631461\pi$
$233$	−21.3792	+	14.5761i	−1.40060	+	0.954910i	−0.999240	+	0.0389875i	$0.987587\pi$
$234$	−2.85441	+	2.64851i	−0.186599	+	0.173138i
$235$	38.7013	+	5.83328i	2.52459	+	0.380521i
$236$	6.74640	+	6.25974i	0.439153	+	0.407475i
$237$	−7.93284	−	9.94746i	−0.515293	−	0.646157i
$238$	−0.378663	+	0.347312i	−0.0245451	+	0.0225129i
$239$	−10.3868	+	13.0246i	−0.671863	+	0.842490i	−0.994577	−	0.104007i	$-0.966834\pi$
$239$	−10.3868	+	13.0246i	−0.671863	+	0.842490i	0.322713	+	0.946497i	$0.395405\pi$
$240$	7.60025	−	1.14555i	0.490594	−	0.0739451i
$241$	−3.41873	−	2.33085i	−0.220220	−	0.150143i	0.448185	−	0.893941i	$-0.352070\pi$
$241$	−3.41873	−	2.33085i	−0.220220	−	0.150143i	−0.668405	+	0.743797i	$0.733023\pi$
$242$	3.53518	−	9.00750i	0.227250	−	0.579024i
$243$	5.78941	+	1.78580i	0.371391	+	0.114559i
$244$	2.77995			0.177968
$245$	−13.9117	−	24.7498i	−0.888787	−	1.58120i
$246$	14.8793			0.948668
$247$	12.3314	+	3.80374i	0.784629	+	0.242026i
$248$	−1.82499	+	4.64999i	−0.115887	+	0.295275i
$249$	6.49653	+	4.42926i	0.411701	+	0.280693i
$250$	25.8717	−	3.89954i	1.63627	−	0.246628i
$251$	−16.2264	+	20.3472i	−1.02420	+	1.28431i	−0.0661173	+	0.997812i	$0.521061\pi$
$251$	−16.2264	+	20.3472i	−1.02420	+	1.28431i	−0.958082	+	0.286494i	$0.907510\pi$
$252$	−0.579714	+	1.45244i	−0.0365186	+	0.0914950i
$253$	−1.96011	−	2.45790i	−0.123231	−	0.154527i
$254$	0.213416	+	0.198022i	0.0133909	+	0.0124250i
$255$	1.47601	+	0.222473i	0.0924315	+	0.0139318i
$256$	−0.733052	+	0.680173i	−0.0458157	+	0.0425108i
$257$	−7.88981	+	5.37918i	−0.492153	+	0.335544i	−0.783833	−	0.620972i	$-0.786738\pi$
$257$	−7.88981	+	5.37918i	−0.492153	+	0.335544i	0.291680	+	0.956516i	$0.405786\pi$
$258$	2.10919	+	9.24097i	0.131313	+	0.575318i
$259$	5.97438	+	0.0344045i	0.371230	+	0.00213779i
$260$	5.94563	−	26.0495i	0.368732	−	1.61552i
$261$	0.262063	+	0.667725i	0.0162213	+	0.0413311i
$262$	−0.0682035	−	0.910113i	−0.00421363	−	0.0562269i
$263$	−13.6430	−	23.6303i	−0.841261	−	1.45711i	−0.888829	−	0.458239i	$-0.848480\pi$
$263$	−13.6430	−	23.6303i	−0.841261	−	1.45711i	0.0475675	−	0.998868i	$-0.484853\pi$
$264$	−1.09009	+	1.88809i	−0.0670904	+	0.116204i
$265$	−9.66725	−	4.65550i	−0.593854	−	0.285985i
$266$	5.12927	−	0.742931i	0.314496	−	0.0455520i
$267$	−8.42797	+	4.05870i	−0.515783	+	0.248388i
$268$	0.134632	−	1.79654i	0.00822394	−	0.109741i
$269$	1.16540	−	0.359477i	0.0710555	−	0.0219177i	−0.259024	−	0.965871i	$-0.583401\pi$
$269$	1.16540	−	0.359477i	0.0710555	−	0.0219177i	0.330079	+	0.943953i	$0.392925\pi$
$270$	−17.6926	+	5.45744i	−1.07674	+	0.332129i
$271$	−2.20355	+	29.4043i	−0.133856	+	1.78618i	0.376695	+	0.926337i	$0.377060\pi$
$271$	−2.20355	+	29.4043i	−0.133856	+	1.78618i	−0.510551	+	0.859847i	$0.670559\pi$
$272$	−0.174974	+	0.0842628i	−0.0106093	+	0.00510918i
$273$	24.0822	+	22.6045i	1.45752	+	1.36809i
$274$	−8.15290	−	3.92623i	−0.492534	−	0.237192i
$275$	−6.58695	+	11.4089i	−0.397208	+	0.687984i
$276$	−2.58913	−	4.48450i	−0.155847	−	0.269935i
$277$	0.147481	+	1.96800i	0.00886129	+	0.118246i	0.999880	−	0.0154758i	$-0.00492628\pi$
$277$	0.147481	+	1.96800i	0.00886129	+	0.118246i	−0.991019	+	0.133722i	$0.957307\pi$
$278$	6.74819	+	17.1941i	0.404730	+	1.03123i
$279$	−0.657022	+	2.87860i	−0.0393349	+	0.172337i
$280$	−2.32760	−	10.4756i	−0.139100	−	0.626035i
$281$	−5.44807	−	23.8695i	−0.325004	−	1.42394i	−0.828524	−	0.559954i	$-0.810819\pi$
$281$	−5.44807	−	23.8695i	−0.325004	−	1.42394i	0.503520	−	0.863984i	$-0.332038\pi$
$282$	−15.1087	+	10.3010i	−0.899713	+	0.613414i
$283$	2.54052	−	2.35726i	0.151018	−	0.140125i	−0.601045	−	0.799215i	$-0.705249\pi$
$283$	2.54052	−	2.35726i	0.151018	−	0.140125i	0.752064	+	0.659090i	$0.229058\pi$
$284$	2.76153	+	0.416234i	0.163867	+	0.0246990i
$285$	−11.0371	−	10.2409i	−0.653782	−	0.606621i
$286$	4.72545	+	5.92553i	0.279422	+	0.350384i
$287$	−1.43312	−	20.7244i	−0.0845942	−	1.22332i
$288$	−0.368534	+	0.462126i	−0.0217160	+	0.0272311i
$289$	16.7728	−	2.52810i	0.986637	−	0.148712i
$290$	−4.06684	−	2.77273i	−0.238813	−	0.162820i
$291$	−6.25116	+	15.9277i	−0.366449	+	0.933698i
$292$	−10.3660	−	3.19750i	−0.606626	−	0.187119i
$293$	−28.0242			−1.63719			−0.818596	−	0.574370i	$-0.805247\pi$
$293$	−28.0242			−1.63719			−0.818596	+	0.574370i	$0.805247\pi$
$294$	12.6299	+	4.05569i	0.736591	+	0.236532i
$295$	−37.3276			−2.17330
$296$	2.15782	+	0.665599i	0.125421	+	0.0386872i
$297$	1.91873	−	4.88883i	0.111336	−	0.283679i
$298$	−4.82863	−	3.29210i	−0.279715	−	0.190706i
$299$	−17.8003	+	2.68296i	−1.02942	+	0.155159i
$300$	−13.5293	+	16.9652i	−0.781116	+	0.979489i
$301$	12.6680	−	3.82782i	0.730173	−	0.220632i
$302$	−0.143490	−	0.179931i	−0.00825693	−	0.0103539i
$303$	−5.29921	−	4.91695i	−0.304432	−	0.282471i
$304$	1.93703	+	0.291961i	0.111097	+	0.0167451i
$305$	−8.26541	+	7.66918i	−0.473276	+	0.439136i
$306$	−0.0948453	+	0.0646644i	−0.00542194	+	0.00369662i
$307$	−1.67790	−	7.35135i	−0.0957627	−	0.419564i	0.904209	−	0.427090i	$-0.140461\pi$
$307$	−1.67790	−	7.35135i	−0.0957627	−	0.419564i	−0.999972	+	0.00752643i	$0.997604\pi$
$308$	2.73480	+	1.33646i	0.155830	+	0.0761521i
$309$	−5.27980	+	23.1323i	−0.300357	+	1.31595i
$310$	−7.40207	−	18.8602i	−0.420409	−	1.07118i
$311$	1.26103	+	16.8273i	0.0715067	+	0.954190i	0.911422	+	0.411473i	$0.134985\pi$
$311$	1.26103	+	16.8273i	0.0715067	+	0.954190i	−0.839915	+	0.542717i	$0.817395\pi$
$312$	6.24190	+	10.8113i	0.353378	+	0.612068i
$313$	13.2872	−	23.0141i	0.751037	−	1.30083i	−0.196283	−	0.980547i	$-0.562887\pi$
$313$	13.2872	−	23.0141i	0.751037	−	1.30083i	0.947321	−	0.320287i	$-0.103779\pi$
$314$	−2.54327	−	1.22478i	−0.143525	−	0.0691181i
$315$	−2.28329	−	5.91771i	−0.128649	−	0.333425i
$316$	−6.04918	+	2.91313i	−0.340293	+	0.163876i
$317$	−1.27756	+	17.0478i	−0.0717548	+	0.957501i	0.838887	+	0.544305i	$0.183207\pi$
$317$	−1.27756	+	17.0478i	−0.0717548	+	0.957501i	−0.910642	+	0.413196i	$0.864412\pi$
$318$	4.79045	−	1.47766i	0.268635	−	0.0828630i
$319$	1.33414	−	0.411529i	0.0746977	−	0.0230412i
$320$	0.303102	−	4.04461i	0.0169439	−	0.226101i
$321$	−18.4943	+	8.90637i	−1.03225	+	0.497105i
$322$	−5.99680	+	4.03816i	−0.334189	+	0.225038i
$323$	0.342758	+	0.165064i	0.0190716	+	0.00918438i
$324$	5.21193	−	9.02733i	0.289552	−	0.501519i
$325$	37.7171	+	65.3279i	2.09217	+	3.62374i
$326$	−0.744178	−	9.93037i	−0.0412162	−	0.549992i
$327$	−12.8108	−	32.6414i	−0.708440	−	1.80508i
$328$	1.74719	−	7.65494i	0.0964724	−	0.422673i
$329$	15.8028	+	20.0519i	0.871236	+	1.10550i
$330$	−1.96769	−	8.62101i	−0.108318	−	0.474571i
$331$	−25.7995	+	17.5898i	−1.41807	+	0.966823i	−0.419823	+	0.907606i	$0.637908\pi$
$331$	−25.7995	+	17.5898i	−1.41807	+	0.966823i	−0.998245	+	0.0592169i	$0.981140\pi$
$332$	3.04157	−	2.82216i	0.166928	−	0.154886i
$333$	1.31984	+	0.198934i	0.0723267	+	0.0109015i
$334$	−11.1920	−	10.3846i	−0.612397	−	0.568222i
$335$	4.55590	+	5.71292i	0.248915	+	0.312130i
$336$	4.12621	+	2.84815i	0.225103	+	0.155379i
$337$	15.5303	−	19.4743i	0.845987	−	1.06083i	−0.151392	−	0.988474i	$-0.548375\pi$
$337$	15.5303	−	19.4743i	0.845987	−	1.06083i	0.997379	−	0.0723602i	$-0.0230531\pi$
$338$	30.0583	−	4.53056i	1.63496	−	0.246430i
$339$	10.7876	+	7.35488i	0.585903	+	0.399462i
$340$	0.287776	−	0.733240i	0.0156068	−	0.0397655i
$341$	5.49168	+	1.69396i	0.297391	+	0.0917330i
$342$	1.15788			0.0626109
$343$	4.43245	−	17.9820i	0.239330	−	0.970938i
$344$	5.00187			0.269683
$345$	20.0697	+	6.19067i	1.08051	+	0.333294i
$346$	−1.73235	+	4.41396i	−0.0931318	+	0.237296i
$347$	7.41353	+	5.05446i	0.397979	+	0.271338i	0.745728	−	0.666250i	$-0.232102\pi$
$347$	7.41353	+	5.05446i	0.397979	+	0.271338i	−0.347749	+	0.937588i	$0.613054\pi$
$348$	2.27402	−	0.342753i	0.121900	−	0.0183735i
$349$	11.4046	−	14.3009i	0.610474	−	0.765510i	−0.376495	−	0.926419i	$-0.622871\pi$
$349$	11.4046	−	14.3009i	0.610474	−	0.765510i	0.986969	+	0.160908i	$0.0514423\pi$
$350$	24.9329	+	17.2101i	1.33272	+	0.919920i
$351$	−18.7499	−	23.5116i	−1.00079	−	1.25496i
$352$	0.843363	+	0.782526i	0.0449514	+	0.0417088i
$353$	−14.6600	−	2.20965i	−0.780275	−	0.117608i	−0.253186	−	0.967418i	$-0.581478\pi$
$353$	−14.6600	−	2.20965i	−0.780275	−	0.117608i	−0.527089	+	0.849810i	$0.676717\pi$
$354$	12.7845	−	11.8623i	0.679490	−	0.630474i
$355$	−9.35894	+	6.38082i	−0.496721	+	0.338659i
$356$	1.09843	+	4.81253i	0.0582165	+	0.255063i
$357$	0.602697	+	0.764751i	0.0318981	+	0.0404749i
$358$	0.269853	−	1.18230i	0.0142622	−	0.0624866i
$359$	−4.89726	−	12.4780i	−0.258468	−	0.658565i	0.741455	−	0.671002i	$-0.234136\pi$
$359$	−4.89726	−	12.4780i	−0.258468	−	0.658565i	−0.999923	+	0.0124379i	$0.996041\pi$
$360$	−0.179158	−	2.39070i	−0.00944245	−	0.126001i
$361$	7.58133	+	13.1312i	0.399017	+	0.691118i
$362$	−9.60450	+	16.6355i	−0.504801	+	0.874342i
$363$	−16.5210	−	7.95609i	−0.867127	−	0.417586i
$364$	14.4572	−	9.73525i	0.757761	−	0.510266i
$365$	39.6416	−	19.0904i	2.07494	−	0.999237i
$366$	0.393681	−	5.25331i	0.0205780	−	0.274595i
$367$	15.4157	−	4.75511i	0.804693	−	0.248215i	0.134993	−	0.990847i	$-0.456899\pi$
$367$	15.4157	−	4.75511i	0.804693	−	0.248215i	0.669700	+	0.742632i	$0.266423\pi$
$368$	−2.61116	+	0.805438i	−0.136116	+	0.0419863i
$369$	0.346827	−	4.62808i	0.0180551	−	0.240928i
$370$	−8.25190	+	3.97391i	−0.428996	+	0.206594i
$371$	−2.51954	−	6.53000i	−0.130808	−	0.339021i
$372$	8.52872	+	4.10722i	0.442194	+	0.212949i
$373$	−0.162161	+	0.280871i	−0.00839638	+	0.0145430i	−0.870193	−	0.492711i	$-0.836006\pi$
$373$	−0.162161	+	0.280871i	−0.00839638	+	0.0145430i	0.861797	+	0.507254i	$0.169339\pi$
$374$	0.111715	+	0.193496i	0.00577666	+	0.0100055i
$375$	−3.70520	−	49.4425i	−0.191336	−	2.55320i
$376$	3.52540	+	8.98258i	0.181809	+	0.463241i
$377$	1.77895	−	7.79409i	0.0916206	−	0.401416i
$378$	−10.8513	−	5.30289i	−0.558129	−	0.272751i
$379$	1.37942	+	6.04361i	0.0708558	+	0.310440i	0.997920	−	0.0644628i	$-0.0205334\pi$
$379$	1.37942	+	6.04361i	0.0708558	+	0.310440i	−0.927064	+	0.374902i	$0.877676\pi$
$380$	−6.56468	+	4.47573i	−0.336761	+	0.229600i
$381$	0.404427	−	0.375254i	0.0207194	−	0.0192248i
$382$	−14.9836	−	2.25841i	−0.766627	−	0.115550i
$383$	23.7504	+	22.0371i	1.21359	+	1.12605i	0.988423	+	0.151725i	$0.0484827\pi$
$383$	23.7504	+	22.0371i	1.21359	+	1.12605i	0.225165	+	0.974321i	$0.427708\pi$
$384$	1.18152	+	1.48158i	0.0602943	+	0.0756067i
$385$	−11.8181	+	3.57101i	−0.602308	+	0.181996i
$386$	−9.88487	+	12.3952i	−0.503126	+	0.630901i
$387$	2.92349	−	0.440646i	0.148610	−	0.0223993i
$388$	7.46028	+	5.08633i	0.378738	+	0.258219i
$389$	5.66497	−	14.4341i	0.287225	−	0.731838i	−0.712325	−	0.701850i	$-0.752358\pi$
$389$	5.66497	−	14.4341i	0.287225	−	0.731838i	0.999550	−	0.0299885i	$-0.00954706\pi$
$390$	−48.3842	−	14.9245i	−2.45003	−	0.755734i
$391$	−0.530680			−0.0268377
$392$	3.56959	−	6.02147i	0.180291	−	0.304130i
$393$	−1.72951			−0.0872424
$394$	−21.5152	−	6.63655i	−1.08392	−	0.334345i
$395$	9.94896	−	25.3495i	0.500587	−	1.27547i
$396$	0.561866	+	0.383074i	0.0282348	+	0.0192502i
$397$	−6.77790	+	1.02160i	−0.340173	+	0.0512729i	−0.316908	−	0.948456i	$-0.602644\pi$
$397$	−6.77790	+	1.02160i	−0.340173	+	0.0512729i	−0.0232657	+	0.999729i	$0.507406\pi$
$398$	7.13481	−	8.94677i	0.357636	−	0.448461i
$399$	−0.677548	−	9.79808i	−0.0339198	−	0.490518i
$400$	7.13943	+	8.95256i	0.356972	+	0.447628i
$401$	−13.0460	−	12.1050i	−0.651488	−	0.604493i	0.283585	−	0.958947i	$-0.408476\pi$
$401$	−13.0460	−	12.1050i	−0.651488	−	0.604493i	−0.935073	+	0.354454i	$0.884667\pi$
$402$	−3.37588	−	0.508832i	−0.168373	−	0.0253782i
$403$	24.1229	−	22.3828i	1.20165	−	1.11497i
$404$	−3.15188	+	2.14892i	−0.156812	+	0.106913i
$405$	9.40790	+	41.2187i	0.467482	+	2.04817i
$406$	−0.696424	−	3.13432i	−0.0345629	−	0.155554i
$407$	0.578099	−	2.53282i	0.0286553	−	0.125547i
$408$	0.134454	+	0.342583i	0.00665646	+	0.0169604i
$409$	1.49040	+	19.8880i	0.0736954	+	0.983397i	0.904401	+	0.426684i	$0.140318\pi$
$409$	1.49040	+	19.8880i	0.0736954	+	0.983397i	−0.830705	+	0.556712i	$0.812063\pi$
$410$	15.9233	+	27.5799i	0.786394	+	1.36207i
$411$	−8.57402	+	14.8506i	−0.422925	+	0.732528i
$412$	11.2809	+	5.43259i	0.555770	+	0.267645i
$413$	−17.7536	−	16.6642i	−0.873599	−	0.819993i
$414$	−1.45522	+	0.700796i	−0.0715200	+	0.0344422i
$415$	−1.25763	+	16.7819i	−0.0617344	+	0.823789i
$416$	6.29503	−	1.94176i	0.308639	−	0.0952026i
$417$	33.4476	−	10.3172i	1.63794	−	0.505237i
$418$	0.168419	−	2.24739i	0.00823763	−	0.109924i
$419$	7.17059	−	3.45318i	0.350306	−	0.168699i	−0.250453	−	0.968129i	$-0.580579\pi$
$419$	7.17059	−	3.45318i	0.350306	−	0.168699i	0.600759	+	0.799430i	$0.294865\pi$
$420$	−20.1255	+	2.91500i	−0.982023	+	0.142238i
$421$	5.09136	+	2.45187i	0.248138	+	0.119497i	0.553819	−	0.832637i	$-0.313170\pi$
$421$	5.09136	+	2.45187i	0.248138	+	0.119497i	−0.305681	+	0.952134i	$0.598884\pi$
$422$	6.69993	−	11.6046i	0.326147	−	0.564904i
$423$	2.85186	+	4.93956i	0.138662	+	0.240170i
$424$	−0.197695	−	2.63806i	−0.00960092	−	0.128115i
$425$	0.812447	+	2.07008i	0.0394095	+	0.100414i
$426$	1.17764	−	5.15957i	0.0570568	−	0.249982i
$427$	−7.35493	−	0.0423546i	−0.355930	−	0.00204968i
$428$	2.41038	+	10.5606i	0.116510	+	0.510464i
$429$	11.8668	−	8.09062i	0.572932	−	0.390619i
$430$	−14.8717	+	13.7989i	−0.717177	+	0.665443i
$431$	−14.5685	−	2.19584i	−0.701739	−	0.105770i	−0.211525	−	0.977373i	$-0.567843\pi$
$431$	−14.5685	−	2.19584i	−0.701739	−	0.105770i	−0.490213	+	0.871602i	$0.663081\pi$
$432$	−3.34633	−	3.10495i	−0.161001	−	0.149387i
$433$	−2.44771	−	3.06934i	−0.117630	−	0.147503i	0.719530	−	0.694461i	$-0.244357\pi$
$433$	−2.44771	−	3.06934i	−0.117630	−	0.147503i	−0.837160	+	0.546958i	$0.815786\pi$
$434$	4.89923	−	12.2747i	0.235171	−	0.589205i
$435$	−5.81559	+	7.29252i	−0.278836	+	0.349650i
$436$	−18.2973	+	2.75788i	−0.876283	+	0.132078i
$437$	4.42274	+	3.01537i	0.211568	+	0.144245i
$438$	−7.51034	+	19.1360i	−0.358858	+	0.914355i
$439$	30.0657	+	9.27405i	1.43496	+	0.442626i	0.912162	−	0.409831i	$-0.134412\pi$
$439$	30.0657	+	9.27405i	1.43496	+	0.442626i	0.522797	+	0.852457i	$0.324888\pi$
$440$	−4.66630			−0.222457
$441$	1.55588	−	3.83389i	0.0740897	−	0.182566i
$442$	1.27937			0.0608535
$443$	−19.1493	−	5.90678i	−0.909811	−	0.280639i	−0.195693	−	0.980665i	$-0.562696\pi$
$443$	−19.1493	−	5.90678i	−0.909811	−	0.280639i	−0.714118	+	0.700026i	$0.753172\pi$
$444$	1.56337	−	3.98341i	0.0741944	−	0.189044i
$445$	−16.5424	−	11.2784i	−0.784186	−	0.534649i
$446$	−2.24290	+	0.338063i	−0.106204	+	0.0160077i
$447$	−6.90495	+	8.65853i	−0.326593	+	0.409534i
$448$	1.94980	−	1.78837i	0.0921196	−	0.0844925i
$449$	−0.269388	−	0.337802i	−0.0127132	−	0.0159419i	0.775434	−	0.631428i	$-0.217531\pi$
$449$	−0.269388	−	0.337802i	−0.0127132	−	0.0159419i	−0.788147	+	0.615486i	$0.788960\pi$
$450$	4.96154	+	4.60364i	0.233889	+	0.217018i
$451$	−8.93246	−	1.34635i	−0.420613	−	0.0633972i
$452$	5.05059	−	4.68626i	0.237560	−	0.220423i
$453$	−0.360339	+	0.245675i	−0.0169302	+	0.0115428i
$454$	2.21051	+	9.68489i	0.103744	+	0.454534i
$455$	−16.1273	+	68.8288i	−0.756059	+	3.22674i
$456$	0.826036	−	3.61910i	0.0386827	−	0.169480i
$457$	9.77557	+	24.9077i	0.457282	+	1.16513i	0.954686	+	0.297616i	$0.0961915\pi$
$457$	9.77557	+	24.9077i	0.457282	+	1.16513i	−0.497404	+	0.867519i	$0.665713\pi$
$458$	1.10689	+	14.7705i	0.0517217	+	0.690178i
$459$	−0.443269	−	0.767764i	−0.0206900	−	0.0358362i
$460$	5.54158	−	9.59829i	0.258377	−	0.447523i
$461$	23.0181	+	11.0849i	1.07206	+	0.516276i	0.884769	−	0.466029i	$-0.154316\pi$
$461$	23.0181	+	11.0849i	1.07206	+	0.516276i	0.187289	+	0.982305i	$0.440030\pi$
$462$	2.91283	−	4.97873i	0.135517	−	0.231631i
$463$	25.6284	−	12.3420i	1.19105	−	0.573581i	0.269941	−	0.962877i	$-0.412996\pi$
$463$	25.6284	−	12.3420i	1.19105	−	0.573581i	0.921113	+	0.389295i	$0.127281\pi$
$464$	0.0906890	−	1.21016i	0.00421013	−	0.0561803i
$465$	−36.6886	+	11.3169i	−1.70139	+	0.524810i
$466$	24.7257	−	7.62687i	1.14540	−	0.353308i
$467$	2.47148	−	32.9796i	0.114367	−	1.52612i	−0.584812	−	0.811169i	$-0.698832\pi$
$467$	2.47148	−	32.9796i	0.114367	−	1.52612i	0.699179	−	0.714947i	$-0.253549\pi$
$468$	3.50826	−	1.68949i	0.162169	−	0.0780966i
$469$	−0.383568	+	4.75106i	−0.0177115	+	0.219383i
$470$	−35.2625	−	16.9815i	−1.62654	−	0.783299i
$471$	−2.67464	+	4.63262i	−0.123241	+	0.213460i
$472$	−4.60158	−	7.97018i	−0.211805	−	0.366857i
$473$	−0.430039	−	5.73847i	−0.0197732	−	0.263855i
$474$	4.64834	+	11.8438i	0.213505	+	0.544002i
$475$	4.99138	−	21.8687i	0.229020	−	1.00340i
$476$	0.464213	−	0.220269i	0.0212771	−	0.0100960i
$477$	−0.347951	−	1.52447i	−0.0159316	−	0.0698009i
$478$	13.7644	−	9.38438i	0.629567	−	0.429232i
$479$	12.4453	−	11.5475i	0.568638	−	0.527619i	−0.342609	−	0.939478i	$-0.611311\pi$
$479$	12.4453	−	11.5475i	0.568638	−	0.527619i	0.911248	+	0.411859i	$0.135120\pi$
$480$	−7.60025	−	1.14555i	−0.346902	−	0.0522871i
$481$	−10.9049	−	10.1182i	−0.497219	−	0.461352i
$482$	2.57982	+	3.23499i	0.117507	+	0.147350i
$483$	6.78174	+	11.9041i	0.308580	+	0.541656i
$484$	−6.03313	+	7.56531i	−0.274233	+	0.343878i
$485$	−36.2130	+	5.45823i	−1.64435	+	0.247845i
$486$	−5.00583	−	3.41292i	−0.227069	−	0.154813i
$487$	−13.5067	+	34.4145i	−0.612046	+	1.55947i	0.202445	+	0.979294i	$0.435111\pi$
$487$	−13.5067	+	34.4145i	−0.612046	+	1.55947i	−0.814492	+	0.580175i	$0.802984\pi$
$488$	−2.65644	−	0.819404i	−0.120251	−	0.0370927i
$489$	−18.8710			−0.853375
$490$	5.99854	+	27.7508i	0.270986	+	1.25365i
$491$	3.76589			0.169952			0.0849762	−	0.996383i	$-0.472919\pi$
$491$	3.76589			0.169952			0.0849762	+	0.996383i	$0.472919\pi$
$492$	−14.2182	−	4.38574i	−0.641007	−	0.197725i
$493$	0.0861034	−	0.219388i	0.00387790	−	0.00988073i
$494$	−10.6624	−	7.26950i	−0.479724	−	0.327070i
$495$	−2.72736	+	0.411083i	−0.122586	+	0.0184768i
$496$	3.11452	−	3.90548i	0.139846	−	0.175361i
$497$	−7.29987	−	1.14331i	−0.327444	−	0.0512844i
$498$	−4.90236	−	6.14736i	−0.219680	−	0.275470i
$499$	5.66666	+	5.25789i	0.253674	+	0.235375i	0.796751	−	0.604308i	$-0.206550\pi$
$499$	5.66666	+	5.25789i	0.253674	+	0.235375i	−0.543077	+	0.839683i	$0.682741\pi$
$500$	−25.8717	−	3.89954i	−1.15702	−	0.174393i
$501$	−21.2090	+	19.6790i	−0.947546	+	0.879194i
$502$	21.5029	−	14.6604i	0.959723	−	0.654328i
$503$	7.34435	+	32.1777i	0.327469	+	1.43473i	0.823938	+	0.566679i	$0.191772\pi$
$503$	7.34435	+	32.1777i	0.327469	+	1.43473i	−0.496470	+	0.868054i	$0.665371\pi$
$504$	0.982073	−	1.21704i	0.0437450	−	0.0542111i
$505$	3.44293	−	15.0845i	0.153208	−	0.671249i
$506$	1.14855	+	2.92645i	0.0510591	+	0.130097i
$507$	−4.30478	−	57.4433i	−0.191182	−	2.55115i
$508$	−0.145567	−	0.252130i	−0.00645850	−	0.0111864i
$509$	6.94879	−	12.0357i	0.308000	−	0.533471i	−0.669925	−	0.742429i	$-0.733674\pi$
$509$	6.94879	−	12.0357i	0.308000	−	0.533471i	0.977925	+	0.208958i	$0.0670071\pi$
$510$	−1.34486	−	0.647652i	−0.0595515	−	0.0286785i
$511$	27.3768	+	8.61757i	1.21108	+	0.381219i
$512$	0.900969	−	0.433884i	0.0398176	−	0.0191751i
$513$	−0.668260	+	8.91731i	−0.0295044	+	0.393709i
$514$	9.12483	−	2.81464i	0.402479	−	0.124148i
$515$	−48.5278	+	14.9688i	−2.13839	+	0.659606i
$516$	0.708338	−	9.45212i	0.0311829	−	0.416106i
$517$	10.0023	−	4.81685i	0.439901	−	0.211845i
$518$	−5.69882	−	1.79386i	−0.250392	−	0.0788175i
$519$	8.09580	+	3.89873i	0.355366	+	0.171135i
$520$	−13.3597	+	23.1397i	−0.585862	+	1.01474i
$521$	−0.476825	−	0.825886i	−0.0208901	−	0.0361827i	0.855391	−	0.517982i	$-0.173317\pi$
$521$	−0.476825	−	0.825886i	−0.0208901	−	0.0361827i	−0.876281	+	0.481800i	$0.839983\pi$
$522$	−0.0536046	−	0.715304i	−0.00234621	−	0.0313080i
$523$	2.08801	+	5.32016i	0.0913022	+	0.232634i	0.969229	−	0.246161i	$-0.0791690\pi$
$523$	2.08801	+	5.32016i	0.0913022	+	0.232634i	−0.877927	+	0.478795i	$0.841074\pi$
$524$	−0.203087	+	0.889782i	−0.00887190	+	0.0388703i
$525$	36.0531	−	44.6789i	1.57349	−	1.94995i
$526$	6.07169	+	26.6018i	0.264738	+	1.15989i
$527$	0.801548	−	0.546486i	0.0349160	−	0.0238053i
$528$	1.59819	−	1.48290i	0.0695521	−	0.0645349i
$529$	15.3596	+	2.31509i	0.667809	+	0.100656i
$530$	7.86553	+	7.29814i	0.341657	+	0.317011i
$531$	−3.39168	−	4.25303i	−0.147186	−	0.184566i
$532$	−5.12038	−	0.801955i	−0.221996	−	0.0347692i
$533$	−32.2502	+	40.4405i	−1.39691	+	1.75167i
$534$	9.24986	−	1.39419i	0.400281	−	0.0603326i
$535$	−36.3005	−	24.7493i	−1.56941	−	1.07000i
$536$	−0.658189	+	1.67704i	−0.0284294	+	0.0724370i
$537$	−2.19600	−	0.677376i	−0.0947644	−	0.0292309i
$538$	−1.21958			−0.0525798
$539$	−7.21511	−	3.57756i	−0.310777	−	0.154096i
$540$	18.5152			0.796766
$541$	10.5101	+	3.24194i	0.451865	+	0.139382i	0.512330	−	0.858788i	$-0.328782\pi$
$541$	10.5101	+	3.24194i	0.451865	+	0.139382i	−0.0604654	+	0.998170i	$0.519258\pi$
$542$	10.7727	−	27.4484i	0.462728	−	1.17901i
$543$	30.0762	+	20.5056i	1.29069	+	0.879980i
$544$	0.192037	−	0.0289449i	0.00823351	−	0.00124100i
$545$	46.7938	−	58.6775i	2.00443	−	2.51347i
$546$	−16.3495	−	28.6986i	−0.699695	−	1.22819i
$547$	−25.8420	−	32.4049i	−1.10493	−	1.38553i	−0.914865	−	0.403760i	$-0.867703\pi$
$547$	−25.8420	−	32.4049i	−1.10493	−	1.38553i	−0.190061	−	0.981772i	$-0.560869\pi$
$548$	6.63341	+	6.15490i	0.283365	+	0.262924i
$549$	−1.62482	−	0.244903i	−0.0693458	−	0.0104522i
$550$	9.65715	−	8.96052i	0.411782	−	0.382078i
$551$	−1.96417	+	1.33915i	−0.0836766	+	0.0570497i
$552$	1.15227	+	5.04842i	0.0490438	+	0.214875i
$553$	16.0487	−	7.61513i	0.682462	−	0.323828i
$554$	0.439150	−	1.92404i	0.0186577	−	0.0817446i
$555$	6.34097	+	16.1565i	0.269159	+	0.685806i
$556$	−1.38033	−	18.4193i	−0.0585392	−	0.781152i
$557$	0.127122	+	0.220181i	0.00538631	+	0.00932937i	0.868706	−	0.495328i	$-0.164952\pi$
$557$	0.127122	+	0.220181i	0.00538631	+	0.00932937i	−0.863320	+	0.504657i	$0.831619\pi$
$558$	1.47632	−	2.55705i	0.0624974	−	0.108249i
$559$	−29.6877	−	14.2968i	−1.25566	−	0.604692i
$560$	−0.863541	+	10.6962i	−0.0364913	+	0.451999i
$561$	0.381474	−	0.183708i	0.0161058	−	0.00775616i
$562$	−1.82965	+	24.4149i	−0.0771790	+	1.02988i
$563$	15.2341	−	4.69910i	0.642041	−	0.198044i	0.0433963	−	0.999058i	$-0.486182\pi$
$563$	15.2341	−	4.69910i	0.642041	−	0.198044i	0.598645	+	0.801014i	$0.295706\pi$
$564$	17.4738	−	5.38995i	0.735779	−	0.226958i
$565$	−2.08831	+	27.8666i	−0.0878561	+	1.17236i
$566$	−3.12247	+	1.50370i	−0.131247	+	0.0632053i
$567$	−13.9268	+	23.8043i	−0.584870	+	0.999686i
$568$	−2.51616	−	1.21172i	−0.105576	−	0.0508426i
$569$	13.7566	−	23.8272i	0.576707	−	0.998886i	−0.419147	−	0.907919i	$-0.637671\pi$
$569$	13.7566	−	23.8272i	0.576707	−	0.998886i	0.995854	−	0.0909677i	$-0.0289960\pi$
$570$	7.52820	+	13.0392i	0.315321	+	0.546153i
$571$	0.421294	+	5.62178i	0.0176306	+	0.235264i	0.999057	+	0.0434238i	$0.0138266\pi$
$571$	0.421294	+	5.62178i	0.0176306	+	0.235264i	−0.981426	+	0.191840i	$0.938554\pi$
$572$	−2.76893	−	7.05512i	−0.115775	−	0.294990i
$573$	−6.38965	+	27.9949i	−0.266932	+	1.16950i
$574$	−4.73918	+	20.2261i	−0.197810	+	0.844221i
$575$	6.96267	+	30.5054i	0.290363	+	1.27216i
$576$	0.488375	−	0.332968i	0.0203489	−	0.0138737i
$577$	15.8805	−	14.7350i	0.661115	−	0.613425i	−0.276536	−	0.961004i	$-0.589187\pi$
$577$	15.8805	−	14.7350i	0.661115	−	0.613425i	0.937651	+	0.347579i	$0.112996\pi$
$578$	−16.7728	−	2.52810i	−0.697658	−	0.105155i
$579$	22.0236	+	20.4349i	0.915271	+	0.849247i
$580$	3.06889	+	3.84827i	0.127429	+	0.159791i
$581$	−8.09010	+	7.42028i	−0.335634	+	0.307845i
$582$	10.6682	−	13.3775i	0.442211	−	0.554515i
$583$	−3.00955	+	0.453617i	−0.124643	+	0.0187869i
$584$	8.96301	+	6.11088i	0.370892	+	0.252870i
$585$	−5.76996	+	14.7016i	−0.238559	+	0.607837i
$586$	26.7792	+	8.26028i	1.10624	+	0.341229i
$587$	−10.6404			−0.439177			−0.219589	−	0.975593i	$-0.570472\pi$
$587$	−10.6404			−0.439177			−0.219589	+	0.975593i	$0.570472\pi$
$588$	−10.8734	−	7.59823i	−0.448410	−	0.313346i
$589$	−9.78536			−0.403199
$590$	35.6693	+	11.0025i	1.46848	+	0.452966i
$591$	−15.5881	+	39.7177i	−0.641207	+	1.63377i
$592$	−1.86576	−	1.27206i	−0.0766825	−	0.0522812i
$593$	−41.9376	+	6.32107i	−1.72217	+	0.259575i	−0.934357	−	0.356339i	$-0.884025\pi$
$593$	−41.9376	+	6.32107i	−1.72217	+	0.259575i	−0.787813	+	0.615914i	$0.788787\pi$
$594$	−3.27449	+	4.10608i	−0.134354	+	0.168475i
$595$	−0.772541	+	1.93555i	−0.0316711	+	0.0793500i
$596$	3.64374	+	4.56911i	0.149254	+	0.187158i
$597$	−15.8965	−	14.7498i	−0.650599	−	0.603668i
$598$	17.8003	+	2.68296i	0.727907	+	0.109714i
$599$	−23.8520	+	22.1314i	−0.974566	+	0.904265i	−0.995428	−	0.0955174i	$-0.969549\pi$
$599$	−23.8520	+	22.1314i	−0.974566	+	0.904265i	0.0208619	+	0.999782i	$0.493359\pi$
$600$	17.9289	−	12.2237i	0.731942	−	0.499030i
$601$	1.48966	+	6.52664i	0.0607646	+	0.266227i	0.996180	−	0.0873235i	$-0.0278314\pi$
$601$	1.48966	+	6.52664i	0.0607646	+	0.266227i	−0.935415	+	0.353551i	$0.884974\pi$
$602$	−13.2335	−	0.0762073i	−0.539357	−	0.00310598i
$603$	−0.236957	+	1.03818i	−0.00964965	+	0.0422779i
$604$	0.0840797	+	0.214232i	0.00342116	+	0.00871696i
$605$	−2.93293	−	39.1372i	−0.119241	−	1.59116i
$606$	3.61449	+	6.26048i	0.146829	+	0.254314i
$607$	6.44239	−	11.1585i	0.261488	−	0.452911i	−0.705149	−	0.709059i	$-0.749120\pi$
$607$	6.44239	−	11.1585i	0.261488	−	0.452911i	0.966638	+	0.256148i	$0.0824533\pi$
$608$	−1.76492	−	0.849941i	−0.0715770	−	0.0344696i
$609$	−6.02161	+	0.872178i	−0.244008	+	0.0353424i
$610$	10.1587	−	4.89219i	0.411315	−	0.198079i
$611$	4.75050	−	63.3911i	0.192185	−	2.56453i
$612$	0.109692	−	0.0338354i	0.00443403	−	0.00136772i
$613$	1.32708	−	0.409351i	0.0536004	−	0.0165335i	−0.267839	−	0.963464i	$-0.586310\pi$
$613$	1.32708	−	0.409351i	0.0536004	−	0.0165335i	0.321439	+	0.946930i	$0.395833\pi$
$614$	−0.563495	+	7.51932i	−0.0227408	+	0.303455i
$615$	54.3732	−	26.1847i	2.19254	−	1.05587i
$616$	−2.21937	−	2.08319i	−0.0894209	−	0.0839339i
$617$	13.2951	+	6.40260i	0.535242	+	0.257759i	0.681922	−	0.731425i	$-0.261144\pi$
$617$	13.2951	+	6.40260i	0.535242	+	0.257759i	−0.146680	+	0.989184i	$0.546859\pi$
$618$	11.8636	−	20.5484i	0.477224	−	0.826576i
$619$	−1.73415	−	3.00363i	−0.0697013	−	0.120726i	0.829069	−	0.559147i	$-0.188871\pi$
$619$	−1.73415	−	3.00363i	−0.0697013	−	0.120726i	−0.898770	+	0.438421i	$0.855538\pi$
$620$	1.51408	+	20.2041i	0.0608071	+	0.811414i
$621$	−4.55726	−	11.6117i	−0.182876	−	0.465962i
$622$	3.75493	−	16.4514i	0.150559	−	0.659642i
$623$	−2.83280	−	12.7493i	−0.113494	−	0.510789i
$624$	−2.77791	−	12.1708i	−0.111205	−	0.487222i
$625$	40.3750	−	27.5272i	1.61500	−	1.10109i
$626$	−19.4804	+	18.0752i	−0.778594	+	0.722430i
$627$	−4.22308	−	0.636527i	−0.168654	−	0.0254205i
$628$	2.06927	+	1.92000i	0.0825730	+	0.0766165i
$629$	−0.273428	−	0.342868i	−0.0109023	−	0.0136710i
$630$	0.437576	+	6.32781i	0.0174334	+	0.252106i
$631$	15.4361	−	19.3562i	0.614499	−	0.770558i	−0.373059	−	0.927807i	$-0.621691\pi$
$631$	15.4361	−	19.3562i	0.614499	−	0.770558i	0.987559	+	0.157250i	$0.0502627\pi$
$632$	6.63909	−	1.00068i	0.264089	−	0.0398050i
$633$	−20.9806	−	14.3043i	−0.833905	−	0.568547i
$634$	6.24573	−	15.9139i	0.248050	−	0.632020i
$635$	1.12837	+	0.348055i	0.0447778	+	0.0138121i
$636$	−5.01317			−0.198785
$637$	−38.3978	+	25.5364i	−1.52137	+	1.01179i
$638$	−1.39617			−0.0552750
$639$	−1.57739	−	0.486561i	−0.0624007	−	0.0192481i
$640$	−1.48181	+	3.77558i	−0.0585735	+	0.149243i
$641$	8.80727	+	6.00469i	0.347866	+	0.237171i	0.724630	−	0.689138i	$-0.242011\pi$
$641$	8.80727	+	6.00469i	0.347866	+	0.237171i	−0.376764	+	0.926309i	$0.622963\pi$
$642$	20.2978	−	3.05940i	0.801091	−	0.120745i
$643$	−21.9626	+	27.5402i	−0.866120	+	1.08608i	0.129406	+	0.991592i	$0.458693\pi$
$643$	−21.9626	+	27.5402i	−0.866120	+	1.08608i	−0.995526	+	0.0944886i	$0.969878\pi$
$644$	6.92065	−	2.09117i	0.272712	−	0.0824036i
$645$	23.9700	+	30.0574i	0.943817	+	1.18351i
$646$	−0.278877	−	0.258760i	−0.0109723	−	0.0101808i
$647$	46.5591	+	7.01766i	1.83043	+	0.275893i	0.971645	−	0.236445i	$-0.0759824\pi$
$647$	46.5591	+	7.01766i	1.83043	+	0.275893i	0.858784	+	0.512338i	$0.171220\pi$
$648$	−7.64124	+	7.09003i	−0.300176	+	0.278523i
$649$	−8.74828	+	5.96448i	−0.343400	+	0.234126i
$650$	−16.7857	−	73.5429i	−0.658389	−	2.88459i
$651$	−22.5019	−	10.9964i	−0.881920	−	0.430984i
$652$	−2.21591	+	9.70854i	−0.0867818	+	0.380216i
$653$	−10.2697	−	26.1667i	−0.401884	−	1.02398i	−0.978367	−	0.206875i	$-0.933671\pi$
$653$	−10.2697	−	26.1667i	−0.401884	−	1.02398i	0.576484	−	0.817109i	$-0.304424\pi$
$654$	2.62044	+	34.9673i	0.102467	+	1.36733i
$655$	−1.85086	−	3.20579i	−0.0723192	−	0.125261i
$656$	−3.92590	+	6.79986i	−0.153281	+	0.265490i
$657$	5.77705	+	2.78208i	0.225384	+	0.108539i
$658$	−9.19033	−	23.8190i	−0.358276	−	0.928561i
$659$	−16.9548	+	8.16502i	−0.660466	+	0.318064i	−0.733921	−	0.679235i	$-0.762312\pi$
$659$	−16.9548	+	8.16502i	−0.660466	+	0.318064i	0.0734547	+	0.997299i	$0.476598\pi$
$660$	−0.660817	+	8.81798i	−0.0257223	+	0.343240i
$661$	12.9730	−	4.00163i	0.504590	−	0.155645i	−0.0320013	−	0.999488i	$-0.510188\pi$
$661$	12.9730	−	4.00163i	0.504590	−	0.155645i	0.536591	+	0.843843i	$0.319712\pi$
$662$	29.8380	−	9.20380i	1.15969	−	0.357716i
$663$	0.181178	−	2.41765i	0.00703636	−	0.0938937i
$664$	−3.73829	+	1.80026i	−0.145074	+	0.0698638i
$665$	17.4364	−	11.7414i	0.676155	−	0.455314i
$666$	−1.20257	−	0.579125i	−0.0465985	−	0.0224406i
$667$	1.65806	−	2.87184i	0.0642002	−	0.111198i
$668$	7.63382	+	13.2222i	0.295361	+	0.511581i
$669$	0.321215	+	4.28632i	0.0124189	+	0.165719i
$670$	−2.66958	−	6.80198i	−0.103135	−	0.262784i
$671$	−0.711684	+	3.11809i	−0.0274743	+	0.120373i
$672$	−3.10339	−	3.93783i	−0.119716	−	0.151905i
$673$	4.62747	+	20.2743i	0.178376	+	0.781515i	0.982380	+	0.186892i	$0.0598415\pi$
$673$	4.62747	+	20.2743i	0.178376	+	0.781515i	−0.804005	+	0.594623i	$0.797301\pi$
$674$	−20.5804	+	14.0315i	−0.792729	+	0.540474i
$675$	−38.3181	+	35.5540i	−1.47486	+	1.36847i
$676$	−30.0583	−	4.53056i	−1.15609	−	0.174252i
$677$	−1.47439	−	1.36803i	−0.0566653	−	0.0525778i	0.651332	−	0.758793i	$-0.274211\pi$
$677$	−1.47439	−	1.36803i	−0.0566653	−	0.0525778i	−0.707997	+	0.706215i	$0.750401\pi$
$678$	−8.14047	−	10.2078i	−0.312633	−	0.392029i
$679$	−19.6602	−	13.5706i	−0.754490	−	0.520792i
$680$	−0.491117	+	0.615841i	−0.0188335	+	0.0236164i
$681$	18.6147	−	2.80572i	0.713318	−	0.107515i
$682$	−4.74840	−	3.23740i	−0.181825	−	0.123967i
$683$	9.04931	−	23.0573i	0.346262	−	0.882261i	−0.646582	−	0.762844i	$-0.723802\pi$
$683$	9.04931	−	23.0573i	0.346262	−	0.882261i	0.992844	−	0.119417i	$-0.0381025\pi$
$684$	−1.10644	−	0.341291i	−0.0423057	−	0.0130496i
$685$	−36.7024			−1.40233
$686$	−9.53582	+	15.8767i	−0.364079	+	0.606173i
$687$	28.0687			1.07089
$688$	−4.77965	−	1.47433i	−0.182223	−	0.0562082i
$689$	−6.36697	+	16.2228i	−0.242562	+	0.618038i
$690$	−17.3533	−	11.8313i	−0.660628	−	0.450409i
$691$	21.4815	−	3.23781i	0.817194	−	0.123172i	0.272874	−	0.962050i	$-0.412026\pi$
$691$	21.4815	−	3.23781i	0.817194	−	0.123172i	0.544320	+	0.838878i	$0.316788\pi$
$692$	2.95643	−	3.70724i	0.112386	−	0.140928i
$693$	−1.48070	−	1.02206i	−0.0562471	−	0.0388249i
$694$	−5.59434	−	7.01508i	−0.212358	−	0.266289i
$695$	54.9182	+	50.9567i	2.08317	+	1.93290i
$696$	−2.27402	−	0.342753i	−0.0861964	−	0.0129920i
$697$	−1.11781	+	1.03717i	−0.0423399	+	0.0392857i
$698$	−15.1132	+	10.3040i	−0.572043	+	0.390012i
$699$	−10.9111	−	47.8047i	−0.412696	−	1.80814i
$700$	−18.7524	−	23.7946i	−0.708776	−	0.899353i
$701$	−9.35041	+	40.9668i	−0.353160	+	1.54730i	0.416677	+	0.909055i	$0.363195\pi$
$701$	−9.35041	+	40.9668i	−0.353160	+	1.54730i	−0.769837	+	0.638240i	$0.779663\pi$
$702$	10.9867	+	27.9936i	0.414666	+	1.05655i
$703$	0.330569	+	4.41114i	0.0124676	+	0.166369i
$704$	−0.575241	−	0.996347i	−0.0216802	−	0.0375512i
$705$	−37.0839	+	64.2313i	−1.39666	+	2.41909i
$706$	13.3574	+	6.43260i	0.502713	+	0.242094i
$707$	8.37169	−	5.63738i	0.314850	−	0.212015i
$708$	−15.7130	+	7.56699i	−0.590532	+	0.284385i
$709$	2.25312	−	30.0658i	0.0846178	−	1.12915i	−0.779684	−	0.626173i	$-0.784620\pi$
$709$	2.25312	−	30.0658i	0.0846178	−	1.12915i	0.864302	−	0.502973i	$-0.167761\pi$
$710$	10.8239	−	3.33874i	0.406215	−	0.125301i
$711$	3.79226	−	1.16976i	0.142221	−	0.0438693i
$712$	0.368889	−	4.92249i	0.0138247	−	0.184478i
$713$	12.2982	−	5.92250i	0.460571	−	0.221800i
$714$	−0.350506	−	0.908423i	−0.0131174	−	0.0339969i
$715$	27.6960	+	13.3377i	1.03577	+	0.498801i
$716$	−0.606353	+	1.05023i	−0.0226605	+	0.0392491i
$717$	−15.7846	−	27.3397i	−0.589486	−	1.02102i
$718$	1.00173	+	13.3671i	0.0373842	+	0.498857i
$719$	13.0836	+	33.3366i	0.487938	+	1.24325i	0.936870	+	0.349679i	$0.113709\pi$
$719$	13.0836	+	33.3366i	0.487938	+	1.24325i	−0.448932	+	0.893566i	$0.648195\pi$
$720$	−0.533472	+	2.33729i	−0.0198813	+	0.0871058i
$721$	−29.7632	−	14.5449i	−1.10844	−	0.541681i
$722$	−3.37401	−	14.7825i	−0.125568	−	0.550148i
$723$	6.47855	−	4.41700i	0.240940	−	0.164270i
$724$	14.0812	−	13.0654i	0.523324	−	0.485573i
$725$	−13.7409	−	2.07111i	−0.510324	−	0.0769190i
$726$	13.4419	+	12.4723i	0.498876	+	0.462889i
$727$	23.9313	+	30.0090i	0.887564	+	1.11297i	0.992949	+	0.118539i	$0.0378211\pi$
$727$	23.9313	+	30.0090i	0.887564	+	1.11297i	−0.105385	+	0.994431i	$0.533607\pi$
$728$	−16.6844	+	5.04142i	−0.618365	+	0.186847i
$729$	12.3392	−	15.4728i	0.457007	−	0.573068i
$730$	−43.5074	+	6.55769i	−1.61028	+	0.242711i
$731$	−0.802603	−	0.547205i	−0.0296853	−	0.0202391i
$732$	−1.92463	+	4.90388i	−0.0711364	+	0.181253i
$733$	10.0635	+	3.10418i	0.371704	+	0.114656i	0.474979	−	0.879997i	$-0.342456\pi$
$733$	10.0635	+	3.10418i	0.371704	+	0.114656i	−0.103274	+	0.994653i	$0.532932\pi$
$734$	−16.1324			−0.595458
$735$	53.2905	−	7.40562i	1.96565	−	0.273160i
$736$	2.73256			0.100724
$737$	1.98059	+	0.610932i	0.0729561	+	0.0225040i
$738$	−1.69557	+	4.32024i	−0.0624147	+	0.159030i
$739$	−33.2828	−	22.6918i	−1.22433	−	0.834733i	−0.233833	−	0.972277i	$-0.575127\pi$
$739$	−33.2828	−	22.6918i	−1.22433	−	0.834733i	−0.990496	+	0.137544i	$0.956079\pi$
$740$	9.05662	−	1.36507i	0.332928	−	0.0501808i
$741$	−15.2472	+	19.1194i	−0.560121	+	0.702370i
$742$	0.482850	+	6.98254i	0.0177260	+	0.256337i
$743$	−8.12540	−	10.1889i	−0.298092	−	0.373796i	0.610118	−	0.792311i	$-0.291122\pi$
$743$	−8.12540	−	10.1889i	−0.298092	−	0.373796i	−0.908210	+	0.418515i	$0.862551\pi$
$744$	−6.93919	−	6.43863i	−0.254403	−	0.236052i
$745$	−23.4387	−	3.53281i	−0.858727	−	0.129432i
$746$	0.237745	−	0.220595i	0.00870446	−	0.00807656i
$747$	−2.02636	+	1.38155i	−0.0741406	+	0.0505482i
$748$	−0.0497180	−	0.217829i	−0.00181787	−	0.00796460i
$749$	−6.21626	−	27.9769i	−0.227137	−	1.02225i
$750$	−11.0328	+	48.3380i	−0.402862	+	1.76506i
$751$	−3.54754	−	9.03897i	−0.129451	−	0.329837i	0.851423	−	0.524480i	$-0.175740\pi$
$751$	−3.54754	−	9.03897i	−0.129451	−	0.329837i	−0.980874	+	0.194643i	$0.937645\pi$
$752$	−0.721117	−	9.62264i	−0.0262964	−	0.350902i
$753$	−24.6590	−	42.7106i	−0.898622	−	1.55646i
$754$	−3.99727	+	6.92347i	−0.145572	+	0.252138i
$755$	−0.840999	−	0.405004i	−0.0306071	−	0.0147396i
$756$	8.80612	+	8.26576i	0.320275	+	0.300623i
$757$	13.9035	−	6.69559i	0.505333	−	0.243355i	−0.163807	−	0.986492i	$-0.552377\pi$
$757$	13.9035	−	6.69559i	0.505333	−	0.243355i	0.669139	+	0.743137i	$0.266663\pi$
$758$	0.463255	−	6.18170i	0.0168262	−	0.224530i
$759$	5.69281	−	1.75600i	0.206636	−	0.0637387i
$760$	7.59228	−	2.34191i	0.275401	−	0.0849499i
$761$	−1.51478	+	20.2133i	−0.0549106	+	0.732730i	0.900010	+	0.435869i	$0.143559\pi$
$761$	−1.51478	+	20.2133i	−0.0549106	+	0.732730i	−0.954921	+	0.296861i	$0.904060\pi$
$762$	−0.497068	+	0.239375i	−0.0180069	+	0.00867165i
$763$	48.4514	−	7.01777i	1.75406	−	0.254060i
$764$	13.6522	+	6.57457i	0.493920	+	0.237859i
$765$	−0.232795	+	0.403212i	−0.00841671	+	0.0145782i
$766$	−16.1997	−	28.0586i	−0.585318	−	1.01380i
$767$	4.53072	+	60.4582i	0.163595	+	2.18302i
$768$	−0.692327	−	1.76402i	−0.0249822	−	0.0636536i
$769$	−3.44780	+	15.1058i	−0.124331	+	0.544729i	0.873945	+	0.486026i	$0.161554\pi$
$769$	−3.44780	+	15.1058i	−0.124331	+	0.544729i	−0.998275	+	0.0587035i	$0.981303\pi$
$770$	12.3457	+	0.0710946i	0.444907	+	0.00256207i
$771$	−4.02665	−	17.6419i	−0.145016	−	0.635359i
$772$	13.0993	−	8.93093i	0.471453	−	0.321431i
$773$	−26.8019	+	24.8685i	−0.963996	+	0.894458i	−0.994464	−	0.105078i	$-0.966491\pi$
$773$	−26.8019	+	24.8685i	−0.963996	+	0.894458i	0.0304677	+	0.999536i	$0.490300\pi$
$774$	−2.92349	−	0.440646i	−0.105083	−	0.0158387i
$775$	−41.9305	−	38.9059i	−1.50619	−	1.39754i
$776$	−5.62961	−	7.05931i	−0.202091	−	0.253415i
$777$	−4.19692	+	10.5151i	−0.150564	+	0.377228i
$778$	−9.66782	+	12.1231i	−0.346608	+	0.434633i
$779$	15.2092	−	2.29242i	0.544926	−	0.0821344i
$780$	41.8355	+	28.5230i	1.49795	+	1.02129i
$781$	−1.17383	+	2.99088i	−0.0420031	+	0.107022i
$782$	0.507104	+	0.156421i	0.0181340	+	0.00559360i
$783$	5.53980			0.197976
$784$	−5.18586	+	4.70180i	−0.185209	+	0.167921i
$785$	−11.4492			−0.408640
$786$	1.65268	+	0.509783i	0.0589490	+	0.0181834i
$787$	−13.1216	+	33.4333i	−0.467734	+	1.19177i	0.481289	+	0.876562i	$0.340169\pi$
$787$	−13.1216	+	33.4333i	−0.467734	+	1.19177i	−0.949023	+	0.315206i	$0.897927\pi$
$788$	18.6032	+	12.6834i	0.662710	+	0.451828i
$789$	51.1297	−	7.70657i	1.82027	−	0.274361i
$790$	−16.9789	+	21.2908i	−0.604081	+	0.757494i
$791$	−13.4338	+	12.3215i	−0.477650	+	0.438103i
$792$	−0.423991	−	0.531668i	−0.0150659	−	0.0188920i
$793$	13.4247	+	12.4563i	0.476726	+	0.442337i
$794$	6.77790	+	1.02160i	0.240539	+	0.0362554i
$795$	14.9053	−	13.8301i	0.528636	−	0.490503i
$796$	−9.45494	+	6.44627i	−0.335122	+	0.228482i
$797$	−3.00021	−	13.1448i	−0.106273	−	0.465612i	−0.999860	−	0.0167224i	$-0.994677\pi$
$797$	−3.00021	−	13.1448i	−0.106273	−	0.465612i	0.893587	−	0.448889i	$-0.148180\pi$
$798$	−2.24059	+	9.56249i	−0.0793160	+	0.338509i
$799$	0.417007	−	1.82703i	0.0147527	−	0.0646356i
$800$	−4.18343	−	10.6592i	−0.147907	−	0.376860i
$801$	−0.218044	−	2.90959i	−0.00770420	−	0.102805i
$802$	8.89845	+	15.4126i	0.314215	+	0.544236i
$803$	6.24020	−	10.8083i	0.220212	−	0.381418i
$804$	3.07592	+	1.48128i	0.108479	+	0.0522408i
$805$	−14.8076	+	25.3098i	−0.521900	+	0.892055i
$806$	−29.6487	+	14.2781i	−1.04433	+	0.502923i
$807$	−0.172710	+	2.30466i	−0.00607969	+	0.0811279i
$808$	3.64525	−	1.12441i	0.128240	−	0.0395567i
$809$	−31.0564	+	9.57963i	−1.09188	+	0.336802i	−0.787855	−	0.615861i	$-0.788808\pi$
$809$	−31.0564	+	9.57963i	−1.09188	+	0.336802i	−0.304029	+	0.952663i	$0.598332\pi$
$810$	3.15949	−	42.1605i	0.111013	−	1.48137i
$811$	−9.52477	+	4.58689i	−0.334460	+	0.161067i	−0.593574	−	0.804779i	$-0.702284\pi$
$811$	−9.52477	+	4.58689i	−0.334460	+	0.161067i	0.259114	+	0.965847i	$0.416569\pi$
$812$	−0.258374	+	3.20035i	−0.00906716	+	0.112310i
$813$	−50.3442	−	24.2445i	−1.76565	−	0.850291i
$814$	−1.29898	+	2.24989i	−0.0455291	+	0.0788587i
$815$	−20.1950	−	34.9788i	−0.707401	−	1.22525i
$816$	−0.0275024	−	0.366994i	−0.000962777	−	0.0128474i
$817$	3.57970	+	9.12092i	0.125238	+	0.319101i
$818$	4.43790	−	19.4437i	0.155167	−	0.679833i
$819$	−9.30756	+	4.41644i	−0.325233	+	0.154323i
$820$	−7.08652	−	31.0481i	−0.247472	−	1.08425i
$821$	−2.80415	+	1.91184i	−0.0978655	+	0.0667236i	−0.611264	−	0.791427i	$-0.709339\pi$
$821$	−2.80415	+	1.91184i	−0.0978655	+	0.0667236i	0.513399	+	0.858150i	$0.328386\pi$
$822$	12.5704	−	11.6636i	0.438443	−	0.406816i
$823$	13.8625	+	2.08943i	0.483215	+	0.0728330i	0.386133	−	0.922443i	$-0.373811\pi$
$823$	13.8625	+	2.08943i	0.483215	+	0.0728330i	0.0970828	+	0.995276i	$0.469049\pi$
$824$	−9.17843	−	8.51634i	−0.319746	−	0.296681i
$825$	−15.5652	−	19.5182i	−0.541912	−	0.679537i
$826$	12.0530	+	21.1569i	0.419378	+	0.736141i
$827$	12.8619	−	16.1283i	0.447253	−	0.560837i	−0.506186	−	0.862424i	$-0.668945\pi$
$827$	12.8619	−	16.1283i	0.447253	−	0.560837i	0.953439	+	0.301587i	$0.0975164\pi$
$828$	1.59713	−	0.240729i	0.0555041	−	0.00836589i
$829$	−9.20103	−	6.27315i	−0.319565	−	0.217876i	0.392904	−	0.919580i	$-0.371471\pi$
$829$	−9.20103	−	6.27315i	−0.319565	−	0.217876i	−0.712469	+	0.701704i	$0.752423\pi$
$830$	6.14829	−	15.6656i	0.213410	−	0.543761i
$831$	−3.57370	−	1.10234i	−0.123970	−	0.0382398i
$832$	−6.58770			−0.228388
$833$	−1.23153	+	0.575694i	−0.0426699	+	0.0199466i
$834$	−35.0027			−1.21204
$835$	−59.1737	−	18.2527i	−2.04779	−	0.631659i
$836$	−0.823367	+	2.09791i	−0.0284767	+	0.0725576i
$837$	18.8409	+	12.8455i	0.651237	+	0.444006i
$838$	−7.86987	+	1.18619i	−0.271860	+	0.0409763i
$839$	−14.4302	+	18.0949i	−0.498186	+	0.624706i	−0.965819	−	0.259217i	$-0.916535\pi$
$839$	−14.4302	+	18.0949i	−0.498186	+	0.624706i	0.467633	+	0.883923i	$0.345107\pi$
$840$	20.0906	+	3.14659i	0.693191	+	0.108568i
$841$	−17.1630	−	21.5217i	−0.591827	−	0.742128i
$842$	−4.14247	−	3.84365i	−0.142759	−	0.132461i
$843$	45.8782	+	6.91502i	1.58013	+	0.238166i
$844$	−9.82279	+	9.11422i	−0.338114	+	0.313724i
$845$	101.869	−	69.4530i	3.50439	−	2.38925i
$846$	−1.26920	−	5.56071i	−0.0436359	−	0.191181i
$847$	16.0772	−	19.9237i	0.552418	−	0.684585i
$848$	−0.588669	+	2.57913i	−0.0202150	+	0.0885676i
$849$	2.39938	+	6.11353i	0.0823466	+	0.209816i
$850$	−0.166185	−	2.21759i	−0.00570010	−	0.0760626i
$851$	−3.08526	−	5.34383i	−0.105761	−	0.183184i
$852$	−2.64613	+	4.58323i	−0.0906549	+	0.157019i
$853$	51.4357	+	24.7701i	1.76112	+	0.848113i	0.972384	+	0.233387i	$0.0749810\pi$
$853$	51.4357	+	24.7701i	1.76112	+	0.848113i	0.788741	+	0.614726i	$0.210733\pi$
$854$	7.01568	+	2.20838i	0.240072	+	0.0755691i
$855$	4.23122	−	2.03765i	0.144705	−	0.0696861i
$856$	0.809487	−	10.8019i	0.0276677	−	0.369200i
$857$	3.28834	−	1.01432i	0.112328	−	0.0346485i	−0.238082	−	0.971245i	$-0.576519\pi$
$857$	3.28834	−	1.01432i	0.112328	−	0.0346485i	0.350409	+	0.936597i	$0.386042\pi$
$858$	−13.7243	+	4.23339i	−0.468540	+	0.144525i
$859$	−2.63515	+	35.1636i	−0.0899102	+	1.19977i	0.751634	+	0.659580i	$0.229266\pi$
$859$	−2.63515	+	35.1636i	−0.0899102	+	1.19977i	−0.841544	+	0.540188i	$0.818353\pi$
$860$	18.2783	−	8.80236i	0.623284	−	0.300158i
$861$	37.5505	+	11.8200i	1.27972	+	0.402825i
$862$	13.2740	+	6.39242i	0.452114	+	0.217727i
$863$	16.9367	−	29.3351i	0.576530	−	0.998580i	−0.419343	−	0.907828i	$-0.637740\pi$
$863$	16.9367	−	29.3351i	0.576530	−	0.998580i	0.995874	−	0.0907521i	$-0.0289271\pi$
$864$	2.28247	+	3.95335i	0.0776511	+	0.134496i
$865$	1.43723	+	19.1785i	0.0488673	+	0.652088i
$866$	1.43427	+	3.65445i	0.0487384	+	0.124183i
$867$	−7.15266	+	31.3379i	−0.242917	+	1.06429i
$868$	−8.29961	+	10.2853i	−0.281707	+	0.349106i
$869$	−1.71885	−	7.53076i	−0.0583079	−	0.255464i
$870$	7.70673	−	5.25436i	0.261283	−	0.178140i
$871$	8.70003	−	8.07245i	0.294789	−	0.273524i
$872$	18.2973	+	2.75788i	0.619626	+	0.0933936i
$873$	−3.91230	−	3.63008i	−0.132411	−	0.122860i
$874$	−3.33745	−	4.18503i	−0.112891	−	0.141561i
$875$	68.3897	+	10.7112i	2.31199	+	0.362105i
$876$	12.8171	−	16.0722i	0.433050	−	0.543028i
$877$	−22.0739	+	3.32710i	−0.745382	+	0.112348i	−0.510742	−	0.859734i	$-0.670629\pi$
$877$	−22.0739	+	3.32710i	−0.745382	+	0.112348i	−0.234640	+	0.972082i	$0.575391\pi$
$878$	−25.9964	−	17.7241i	−0.877337	−	0.598158i
$879$	19.4019	−	49.4352i	0.654410	−	1.66741i
$880$	4.45899	+	1.37542i	0.150313	+	0.0463653i
$881$	31.2017			1.05121			0.525606	−	0.850728i	$-0.323838\pi$
$881$	31.2017			1.05121			0.525606	+	0.850728i	$0.323838\pi$
$882$	−2.61682	+	3.20496i	−0.0881129	+	0.107917i
$883$	13.6978			0.460969			0.230485	−	0.973076i	$-0.425969\pi$
$883$	13.6978			0.460969			0.230485	+	0.973076i	$0.425969\pi$
$884$	−1.22253	−	0.377101i	−0.0411182	−	0.0126833i
$885$	25.8429	−	65.8466i	0.868700	−	2.21341i
$886$	16.5575	+	11.2887i	0.556260	+	0.379252i
$887$	−36.4413	+	5.49264i	−1.22358	+	0.184425i	−0.728881	−	0.684640i	$-0.759959\pi$
$887$	−36.4413	+	5.49264i	−1.22358	+	0.184425i	−0.494698	+	0.869065i	$0.664721\pi$
$888$	−2.66805	+	3.34562i	−0.0895338	+	0.112272i
$889$	0.381287	+	0.669279i	0.0127879	+	0.0224469i
$890$	12.4831	+	15.6533i	0.418435	+	0.524701i
$891$	8.79110	+	8.15695i	0.294513	+	0.273268i
$892$	2.24290	+	0.338063i	0.0750979	+	0.0113192i
$893$	−13.8567	+	12.8572i	−0.463697	+	0.430248i
$894$	9.15033	−	6.23859i	0.306033	−	0.208650i
$895$	−1.09451	−	4.79536i	−0.0365854	−	0.160291i
$896$	−2.39031	+	1.13420i	−0.0798547	+	0.0378910i
$897$	7.59081	−	33.2575i	0.253450	−	1.11044i
$898$	0.157851	+	0.402198i	0.00526756	+	0.0134215i
$899$	0.453019	+	6.04511i	0.0151090	+	0.201616i
$900$	−3.38417	−	5.86155i	−0.112806	−	0.195385i
$901$	−0.256881	+	0.444932i	−0.00855796	+	0.0148228i
$902$	8.13877	+	3.91942i	0.270991	+	0.130503i
$903$	−2.01807	+	24.9968i	−0.0671570	+	0.831840i
$904$	−6.20751	+	2.98938i	−0.206459	+	0.0994252i
$905$	−5.82228	+	77.6930i	−0.193539	+	2.58260i
$906$	0.416744	−	0.128548i	0.0138454	−	0.00427074i
$907$	−6.68959	+	2.06347i	−0.222124	+	0.0685163i	−0.403820	−	0.914839i	$-0.632318\pi$
$907$	−6.68959	+	2.06347i	−0.222124	+	0.0685163i	0.181695	+	0.983355i	$0.441842\pi$
$908$	0.742365	−	9.90618i	0.0246363	−	0.328748i
$909$	2.03152	−	0.978329i	0.0673813	−	0.0324491i
$910$	35.6984	−	61.0173i	1.18339	−	2.02270i
$911$	1.64725	+	0.793272i	0.0545757	+	0.0262823i	0.460973	−	0.887414i	$-0.347501\pi$
$911$	1.64725	+	0.793272i	0.0545757	+	0.0262823i	−0.406397	+	0.913697i	$0.633215\pi$
$912$	−1.85609	+	3.21483i	−0.0614611	+	0.106454i
$913$	2.38678	+	4.13403i	0.0789910	+	0.136816i
$914$	−1.99958	−	26.6826i	−0.0661403	−	0.882581i
$915$	−7.80622	−	19.8899i	−0.258066	−	0.657540i
$916$	3.29595	−	14.4405i	0.108901	−	0.477128i
$917$	0.550865	−	2.35101i	0.0181912	−	0.0776372i
$918$	0.197273	+	0.864310i	0.00651099	+	0.0285265i
$919$	13.2867	−	9.05870i	0.438287	−	0.298819i	−0.324001	−	0.946057i	$-0.605028\pi$
$919$	13.2867	−	9.05870i	0.438287	−	0.298819i	0.762288	+	0.647238i	$0.224076\pi$
$920$	−8.12453	+	7.53846i	−0.267858	+	0.248536i
$921$	14.1296	+	2.12969i	0.465586	+	0.0701758i
$922$	−18.7281	−	17.3771i	−0.616777	−	0.572285i
$923$	11.4707	+	14.3839i	0.377564	+	0.473451i
$924$	−4.25092	+	3.89897i	−0.139845	+	0.128267i
$925$	−16.1219	+	20.2162i	−0.530083	+	0.664703i
$926$	−28.1277	+	4.23957i	−0.924333	+	0.139321i
$927$	−6.11487	−	4.16905i	−0.200839	−	0.136929i
$928$	−0.443361	+	1.12967i	−0.0145540	+	0.0370831i
$929$	35.0527	+	10.8123i	1.15004	+	0.354741i	0.810436	−	0.585827i	$-0.199230\pi$
$929$	35.0527	+	10.8123i	1.15004	+	0.354741i	0.339605	+	0.940568i	$0.389707\pi$
$930$	38.3943			1.25900
$931$	13.5348	+	2.19975i	0.443585	+	0.0720940i
$932$	−25.8753			−0.847573
$933$	−30.5568	−	9.42552i	−1.00038	−	0.308578i
$934$	−12.0826	+	30.7860i	−0.395355	+	1.00735i
$935$	0.748757	+	0.510494i	0.0244870	+	0.0166949i
$936$	−3.85038	+	0.580351i	−0.125854	+	0.0189694i
$937$	−1.40865	+	1.76639i	−0.0460186	+	0.0577056i	−0.804308	−	0.594212i	$-0.797464\pi$
$937$	−1.40865	+	1.76639i	−0.0460186	+	0.0577056i	0.758290	+	0.651918i	$0.226035\pi$
$938$	1.76693	−	4.42692i	0.0576922	−	0.144544i
$939$	31.3983	+	39.3722i	1.02464	+	1.28486i
$940$	28.6905	+	26.6209i	0.935780	+	0.868277i
$941$	13.6920	+	2.06374i	0.446347	+	0.0672760i	0.368370	−	0.929679i	$-0.379916\pi$
$941$	13.6920	+	2.06374i	0.446347	+	0.0672760i	0.0779768	+	0.996955i	$0.475154\pi$
$942$	3.92130	−	3.63844i	0.127763	−	0.118547i
$943$	−17.7274	+	12.0863i	−0.577284	+	0.393585i
$944$	2.04790	+	8.97242i	0.0666534	+	0.292028i
$945$	−48.9857	−	0.282092i	−1.59351	−	0.00917647i
$946$	−1.28051	+	5.61029i	−0.0416330	+	0.182406i
$947$	10.5580	+	26.9014i	0.343089	+	0.874177i	0.993420	+	0.114526i	$0.0365349\pi$
$947$	10.5580	+	26.9014i	0.343089	+	0.874177i	−0.650331	+	0.759651i	$0.725370\pi$
$948$	−0.950812	−	12.6877i	−0.0308809	−	0.412077i
$949$	−35.7316	−	61.8890i	−1.15990	−	2.00900i
$950$	−11.2155	+	19.4259i	−0.363880	+	0.630258i
$951$	−29.1882	−	14.0563i	−0.946492	−	0.455807i
$952$	−0.508514	+	0.0736539i	−0.0164810	+	0.00238714i
$953$	−13.8742	+	6.68146i	−0.449429	+	0.216434i	−0.644886	−	0.764279i	$-0.723095\pi$
$953$	−13.8742	+	6.68146i	−0.449429	+	0.216434i	0.195457	+	0.980712i	$0.437381\pi$
$954$	−0.116854	+	1.55931i	−0.00378329	+	0.0504844i
$955$	−58.7287	+	18.1154i	−1.90042	+	0.586201i
$956$	−15.9189	+	4.91034i	−0.514855	+	0.158812i
$957$	−0.197718	+	2.63837i	−0.00639133	+	0.0852863i
$958$	−15.2960	+	7.36618i	−0.494192	+	0.237991i
$959$	−17.4563	−	16.3851i	−0.563693	−	0.529104i
$960$	6.92493	+	3.33487i	0.223501	+	0.107632i
$961$	3.02349	−	5.23684i	0.0975319	−	0.168930i
$962$	7.43799	+	12.8830i	0.239810	+	0.415364i
$963$	−0.478473	−	6.38478i	−0.0154186	−	0.205747i
$964$	−1.51167	−	3.85168i	−0.0486877	−	0.124054i
$965$	−14.3089	+	62.6912i	−0.460619	+	2.01810i
$966$	−2.97165	−	13.3742i	−0.0956113	−	0.430308i
$967$	0.270506	+	1.18516i	0.00869887	+	0.0381123i	0.979091	−	0.203422i	$-0.0652064\pi$
$967$	0.270506	+	1.18516i	0.00869887	+	0.0381123i	−0.970392	+	0.241535i	$0.922349\pi$
$968$	7.99501	−	5.45091i	0.256969	−	0.175199i
$969$	−0.528476	+	0.490354i	−0.0169771	+	0.0157524i
$970$	36.2130	+	5.45823i	1.16273	+	0.175253i
$971$	−37.9237	−	35.1881i	−1.21703	−	1.12924i	−0.987777	−	0.155871i	$-0.950181\pi$
$971$	−37.9237	−	35.1881i	−1.21703	−	1.12924i	−0.229252	−	0.973367i	$-0.573628\pi$
$972$	3.77746	+	4.73679i	0.121162	+	0.151933i
$973$	3.37133	+	48.7531i	0.108080	+	1.56295i
$974$	23.0505	−	28.9044i	0.738585	−	0.926156i
$975$	−141.352	+	21.3054i	−4.52690	+	0.682320i
$976$	2.29690	+	1.56600i	0.0735220	+	0.0501264i
$977$	13.5002	−	34.3978i	0.431908	−	1.10048i	−0.534885	−	0.844925i	$-0.679645\pi$
$977$	13.5002	−	34.3978i	0.431908	−	1.10048i	0.966793	−	0.255559i	$-0.0822596\pi$
$978$	18.0326	+	5.56231i	0.576618	+	0.177863i
$979$	−5.67911			−0.181505
$980$	2.44764	−	28.2860i	0.0781871	−	0.903562i
$981$	10.9374			0.349204
$982$	−3.59859	−	1.11002i	−0.114835	−	0.0354220i
$983$	−7.63876	+	19.4632i	−0.243639	+	0.620781i	−0.999420	−	0.0340426i	$-0.989162\pi$
$983$	−7.63876	+	19.4632i	−0.243639	+	0.620781i	0.755782	+	0.654824i	$0.227257\pi$
$984$	12.2938	+	8.38179i	0.391913	+	0.267202i
$985$	−90.3017	+	13.6108i	−2.87725	+	0.433676i
$986$	−0.146944	+	0.184262i	−0.00467964	+	0.00586808i
$987$	−46.3126	+	13.9940i	−1.47415	+	0.445434i
$988$	8.04597	+	10.0893i	0.255977	+	0.320984i
$989$	−10.0193	−	9.29656i	−0.318595	−	0.295613i
$990$	2.72736	+	0.411083i	0.0866812	+	0.0130651i
$991$	18.1971	−	16.8844i	0.578048	−	0.536351i	−0.336049	−	0.941844i	$-0.609091\pi$
$991$	18.1971	−	16.8844i	0.578048	−	0.536351i	0.914098	+	0.405494i	$0.132900\pi$
$992$	−4.12731	+	2.81395i	−0.131042	+	0.0893431i
$993$	−13.1671	−	57.6887i	−0.417844	−	1.83070i
$994$	6.63856	+	3.24419i	0.210562	+	0.102899i
$995$	10.3280	−	45.2500i	0.327420	−	1.43452i
$996$	2.87259	+	7.31925i	0.0910216	+	0.231919i
$997$	−1.09667	−	14.6341i	−0.0347320	−	0.463466i	−0.987271	−	0.159049i	$-0.949157\pi$
$997$	−1.09667	−	14.6341i	−0.0347320	−	0.463466i	0.952539	−	0.304417i	$-0.0984617\pi$
$998$	−3.86511	−	6.69457i	−0.122348	−	0.211913i
$999$	5.15414	−	8.92723i	0.163070	−	0.282445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.a.51.1	yes	24
3.2	odd	2		882.2.z.d.541.2		24
4.3	odd	2		784.2.bg.a.737.2		24
7.2	even	3		686.2.e.f.589.1		24
7.3	odd	6		686.2.g.c.655.1		24
7.4	even	3		686.2.g.a.655.2		24
7.5	odd	6		686.2.e.e.589.4		24
7.6	odd	2		686.2.g.b.471.2		24
49.5	odd	42		4802.2.a.k.1.10		12
49.9	even	21		686.2.e.f.99.1		24
49.15	even	7		686.2.g.a.177.2		24
49.24	odd	42		686.2.g.b.67.2		24
49.25	even	21	inner	98.2.g.a.25.1	✓	24
49.34	odd	14		686.2.g.c.177.1		24
49.40	odd	42		686.2.e.e.99.4		24
49.44	even	21		4802.2.a.i.1.3		12
147.74	odd	42		882.2.z.d.613.2		24
196.123	odd	42		784.2.bg.a.417.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.25.1	✓	24	49.25	even	21	inner
98.2.g.a.51.1	yes	24	1.1	even	1	trivial
686.2.e.e.99.4		24	49.40	odd	42
686.2.e.e.589.4		24	7.5	odd	6
686.2.e.f.99.1		24	49.9	even	21
686.2.e.f.589.1		24	7.2	even	3
686.2.g.a.177.2		24	49.15	even	7
686.2.g.a.655.2		24	7.4	even	3
686.2.g.b.67.2		24	49.24	odd	42
686.2.g.b.471.2		24	7.6	odd	2
686.2.g.c.177.1		24	49.34	odd	14
686.2.g.c.655.1		24	7.3	odd	6
784.2.bg.a.417.2		24	196.123	odd	42
784.2.bg.a.737.2		24	4.3	odd	2
882.2.z.d.541.2		24	3.2	odd	2
882.2.z.d.613.2		24	147.74	odd	42
4802.2.a.i.1.3		12	49.44	even	21
4802.2.a.k.1.10		12	49.5	odd	42

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.955573 - 0.294755i) q^{2} +(-0.692327 + 1.76402i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-4.01065 + 0.604508i) q^{5} +(1.18152 - 1.48158i) q^{6} +(-2.17740 - 1.50297i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.433294 - 0.402038i) q^{9} +O(q^{10})\)	\(q+(-0.955573 - 0.294755i) q^{2} +(-0.692327 + 1.76402i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-4.01065 + 0.604508i) q^{5} +(1.18152 - 1.48158i) q^{6} +(-2.17740 - 1.50297i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.433294 - 0.402038i) q^{9} +(4.01065 + 0.604508i) q^{10} +(-0.843363 + 0.782526i) q^{11} +(-1.56573 + 1.06750i) q^{12} +(1.46590 + 6.42254i) q^{13} +(1.63766 + 2.07800i) q^{14} +(1.71032 - 7.49339i) q^{15} +(0.365341 + 0.930874i) q^{16} +(0.0145130 + 0.193663i) q^{17} +(0.295541 + 0.511892i) q^{18} +(0.979457 - 1.69647i) q^{19} +(-3.65429 - 1.75981i) q^{20} +(4.15874 - 2.80044i) q^{21} +(1.03655 - 0.499175i) q^{22} +(-0.204205 + 2.72492i) q^{23} +(1.81082 - 0.558565i) q^{24} +(10.9420 - 3.37517i) q^{25} +(0.492300 - 6.56928i) q^{26} +(-4.11287 + 1.98065i) q^{27} +(-0.952403 - 2.46839i) q^{28} +(-1.09337 - 0.526541i) q^{29} +(-3.84305 + 6.65635i) q^{30} +(-2.49765 - 4.32606i) q^{31} +(-0.0747301 - 0.997204i) q^{32} +(-0.796509 - 2.02947i) q^{33} +(0.0432149 - 0.189337i) q^{34} +(9.64136 + 4.71162i) q^{35} +(-0.131528 - 0.576262i) q^{36} +(-1.86576 + 1.27206i) q^{37} +(-1.43599 + 1.33240i) q^{38} +(-12.3444 - 1.86061i) q^{39} +(2.97322 + 2.75875i) q^{40} +(4.89552 + 6.13878i) q^{41} +(-4.79942 + 1.45021i) q^{42} +(-3.11862 + 3.91062i) q^{43} +(-1.13763 + 0.171470i) q^{44} +(1.98083 + 1.35050i) q^{45} +(0.998318 - 2.54367i) q^{46} +(-9.22092 - 2.84428i) q^{47} -1.89502 q^{48} +(2.48217 + 6.54514i) q^{49} -11.4508 q^{50} +(-0.351673 - 0.108477i) q^{51} +(-2.40676 + 6.13232i) q^{52} +(2.18578 + 1.49024i) q^{53} +(4.51395 - 0.680368i) q^{54} +(2.90939 - 3.64826i) q^{55} +(0.182521 + 2.63945i) q^{56} +(2.31450 + 2.90229i) q^{57} +(0.889598 + 0.825426i) q^{58} +(9.10037 + 1.37166i) q^{59} +(5.63430 - 5.22787i) q^{60} +(2.29690 - 1.56600i) q^{61} +(1.11156 + 4.87006i) q^{62} +(0.339205 + 1.52663i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-9.76170 - 24.8724i) q^{65} +(0.162925 + 2.17408i) q^{66} +(-0.900787 - 1.56021i) q^{67} +(-0.0971030 + 0.168187i) q^{68} +(-4.66544 - 2.24676i) q^{69} +(-7.82425 - 7.34414i) q^{70} +(2.51616 - 1.21172i) q^{71} +(-0.0441716 + 0.589429i) q^{72} +(-10.3660 + 3.19750i) q^{73} +(2.15782 - 0.665599i) q^{74} +(-1.62160 + 21.6387i) q^{75} +(1.76492 - 0.849941i) q^{76} +(3.01245 - 0.436328i) q^{77} +(11.2475 + 5.41652i) q^{78} +(-3.35704 + 5.81456i) q^{79} +(-2.02798 - 3.51256i) q^{80} +(-0.778977 - 10.3947i) q^{81} +(-2.86858 - 7.30903i) q^{82} +(0.923281 - 4.04516i) q^{83} +(5.01366 + 0.0288720i) q^{84} +(-0.175278 - 0.767941i) q^{85} +(4.13274 - 2.81766i) q^{86} +(1.68580 - 1.56420i) q^{87} +(1.13763 + 0.171470i) q^{88} +(3.61856 + 3.35753i) q^{89} +(-1.49475 - 1.87436i) q^{90} +(6.46101 - 16.1877i) q^{91} +(-1.70373 + 2.13641i) q^{92} +(9.36044 - 1.41086i) q^{93} +(7.97289 + 5.43582i) q^{94} +(-2.90273 + 7.39604i) q^{95} +(1.81082 + 0.558565i) q^{96} +9.02920 q^{97} +(-0.442683 - 6.98599i) q^{98} +0.680029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

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