LMFDB - Embedded newform 197.2.h.a.10.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,2,Mod(4,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(98))

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

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

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

chi := DirichletCharacter("197.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.h (of order $98$, degree $42$, 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:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$16$ over $\Q(\zeta_{98})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{98}]$

Embedding invariants

Embedding label			10.7
Character	$\chi$	$=$	197.10
Dual form			197.2.h.a.138.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0948264 - 0.735455i) q^{2} +(2.28285 + 0.840110i) q^{3} +(1.40269 - 0.367828i) q^{4} +(-2.90046 + 1.28395i) q^{5} +(0.401389 - 1.75860i) q^{6} +(2.08662 + 0.269040i) q^{7} +(-0.960086 - 2.37143i) q^{8} +(2.22129 + 1.89101i) q^{9} +(1.21932 + 2.01140i) q^{10} +(-0.116259 - 0.178605i) q^{11} +(3.51114 + 0.338716i) q^{12} +(-0.0451466 - 0.703194i) q^{13} -1.56013i q^{14} +(-7.69997 + 0.494354i) q^{15} +(0.873982 - 0.492217i) q^{16} +(-2.22411 - 0.0713227i) q^{17} +(1.18011 - 1.81297i) q^{18} +(-3.40504 + 4.26979i) q^{19} +(-3.59616 + 2.86784i) q^{20} +(4.53742 + 2.36717i) q^{21} +(-0.120331 + 0.102440i) q^{22} +(-1.18168 - 0.392344i) q^{23} +(-0.199470 - 6.22020i) q^{24} +(3.40263 - 3.74667i) q^{25} +(-0.512887 + 0.0998847i) q^{26} +(-0.0988449 - 0.175509i) q^{27} +(3.02583 - 0.390138i) q^{28} +(0.837505 - 8.68162i) q^{29} +(1.09374 + 5.61610i) q^{30} +(1.15479 - 1.19241i) q^{31} +(-3.50530 - 4.69679i) q^{32} +(-0.115354 - 0.505398i) q^{33} +(0.158449 + 1.64249i) q^{34} +(-6.39758 + 1.89877i) q^{35} +(3.81133 + 1.83544i) q^{36} +(-0.0852870 - 0.0480328i) q^{37} +(3.46313 + 2.09937i) q^{38} +(0.487698 - 1.64322i) q^{39} +(5.82948 + 5.64554i) q^{40} +(-0.237173 + 7.39594i) q^{41} +(1.31068 - 3.56154i) q^{42} +(-10.3915 + 6.76412i) q^{43} +(-0.228770 - 0.207763i) q^{44} +(-8.87069 - 2.63278i) q^{45} +(-0.176497 + 0.906275i) q^{46} +(0.514564 + 0.737666i) q^{47} +(2.40869 - 0.389418i) q^{48} +(-2.48947 - 0.652816i) q^{49} +(-3.07817 - 2.14720i) q^{50} +(-5.01738 - 2.03131i) q^{51} +(-0.321981 - 0.969756i) q^{52} +(13.0226 + 2.53616i) q^{53} +(-0.119706 + 0.0893389i) q^{54} +(0.566522 + 0.368765i) q^{55} +(-1.36532 - 5.20658i) q^{56} +(-11.3603 + 6.88668i) q^{57} +(-6.46436 + 0.207299i) q^{58} +(-6.69957 + 11.0516i) q^{59} +(-10.6188 + 3.52569i) q^{60} +(-4.18825 - 11.3808i) q^{61} +(-0.986472 - 0.736223i) q^{62} +(4.12622 + 4.54343i) q^{63} +(-1.68079 + 1.62775i) q^{64} +(1.03381 + 1.98162i) q^{65} +(-0.360759 + 0.132763i) q^{66} +(8.56126 - 5.97196i) q^{67} +(-3.14596 + 0.718045i) q^{68} +(-2.36798 - 1.88840i) q^{69} +(2.00312 + 4.52508i) q^{70} +(-0.0712288 + 0.0836694i) q^{71} +(2.35177 - 7.08316i) q^{72} +(0.800554 - 1.42146i) q^{73} +(-0.0272385 + 0.0672796i) q^{74} +(10.9153 - 5.69451i) q^{75} +(-3.20566 + 7.24165i) q^{76} +(-0.194536 - 0.403958i) q^{77} +(-1.25476 - 0.202860i) q^{78} +(13.5067 + 5.97904i) q^{79} +(-1.90297 + 2.54980i) q^{80} +(-1.47495 - 9.12310i) q^{81} +(5.46187 - 0.526900i) q^{82} +(3.32615 + 4.17086i) q^{83} +(7.23529 + 1.65141i) q^{84} +(6.54250 - 2.64876i) q^{85} +(5.96010 + 7.00107i) q^{86} +(9.20541 - 19.1152i) q^{87} +(-0.311930 + 0.447175i) q^{88} +(8.24270 + 8.51127i) q^{89} +(-1.09511 + 6.77365i) q^{90} +(0.0949835 - 1.47944i) q^{91} +(-1.80184 - 0.115682i) q^{92} +(3.63797 - 1.75195i) q^{93} +(0.493726 - 0.448389i) q^{94} +(4.39400 - 16.7562i) q^{95} +(-4.05627 - 13.6669i) q^{96} +(-2.57767 + 4.94091i) q^{97} +(-0.244049 + 1.89280i) q^{98} +(0.0794989 - 0.616578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 42 q^{2} - 42 q^{3} - 56 q^{4} - 42 q^{5} - 21 q^{6} - 56 q^{7} - 28 q^{8} - 42 q^{9} - 56 q^{10} - 28 q^{11} - 28 q^{12} - 42 q^{13} + 70 q^{15} - 56 q^{16} - 42 q^{17} - 21 q^{18} - 7 q^{19} - 49 q^{20}+ \cdots + 259 q^{99}+O(q^{100}) $ 672 * q - 42 * q^2 - 42 * q^3 - 56 * q^4 - 42 * q^5 - 21 * q^6 - 56 * q^7 - 28 * q^8 - 42 * q^9 - 56 * q^10 - 28 * q^11 - 28 * q^12 - 42 * q^13 + 70 * q^15 - 56 * q^16 - 42 * q^17 - 21 * q^18 - 7 * q^19 - 49 * q^20 - 42 * q^21 - 84 * q^22 - 42 * q^23 - 56 * q^24 - 42 * q^25 - 42 * q^26 + 119 * q^28 + 119 * q^29 + 77 * q^30 - 70 * q^31 - 56 * q^32 - 49 * q^33 - 70 * q^34 - 42 * q^35 - 301 * q^36 + 7 * q^37 - 28 * q^38 - 63 * q^39 - 56 * q^40 - 28 * q^41 + 112 * q^42 - 28 * q^43 + 126 * q^44 - 56 * q^45 - 56 * q^46 - 7 * q^47 + 42 * q^48 - 42 * q^49 - 182 * q^50 - 70 * q^51 + 49 * q^52 - 42 * q^53 - 63 * q^54 - 84 * q^55 + 77 * q^56 + 175 * q^57 + 126 * q^58 - 42 * q^59 + 84 * q^60 - 14 * q^61 - 56 * q^62 + 7 * q^63 - 14 * q^64 - 133 * q^65 + 63 * q^66 - 112 * q^67 - 49 * q^68 - 49 * q^69 + 168 * q^70 + 91 * q^71 + 392 * q^72 - 56 * q^73 - 56 * q^74 - 91 * q^75 - 161 * q^76 - 49 * q^77 + 84 * q^78 + 42 * q^79 - 70 * q^80 - 14 * q^81 - 42 * q^82 - 35 * q^83 + 245 * q^84 + 322 * q^85 + 63 * q^86 - 49 * q^87 - 133 * q^88 + 28 * q^89 + 196 * q^90 - 126 * q^91 - 7 * q^93 - 210 * q^94 + 84 * q^95 - 49 * q^96 - 42 * q^97 + 280 * q^98 + 259 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{45}{98}\right)$

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 $

$2$	−0.0948264	−	0.735455i	−0.0670524	−	0.520045i	−0.990624	−	0.136619i	$-0.956377\pi$
$2$	−0.0948264	−	0.735455i	−0.0670524	−	0.520045i	0.923571	−	0.383427i	$-0.125256\pi$
$3$	2.28285	+	0.840110i	1.31800	+	0.485038i	0.904892	−	0.425642i	$-0.139952\pi$
$3$	2.28285	+	0.840110i	1.31800	+	0.485038i	0.413113	+	0.910680i	$0.364441\pi$
$4$	1.40269	−	0.367828i	0.701344	−	0.183914i
$5$	−2.90046	+	1.28395i	−1.29712	+	0.574198i	−0.933910	−	0.357508i	$-0.883627\pi$
$5$	−2.90046	+	1.28395i	−1.29712	+	0.574198i	−0.363213	+	0.931706i	$0.618320\pi$
$6$	0.401389	−	1.75860i	0.163866	−	0.717945i
$7$	2.08662	+	0.269040i	0.788668	+	0.101687i	0.511669	−	0.859183i	$-0.329027\pi$
$7$	2.08662	+	0.269040i	0.788668	+	0.101687i	0.276999	+	0.960870i	$0.410660\pi$
$8$	−0.960086	−	2.37143i	−0.339442	−	0.838428i
$9$	2.22129	+	1.89101i	0.740428	+	0.630336i
$10$	1.21932	+	2.01140i	0.385584	+	0.636062i
$11$	−0.116259	−	0.178605i	−0.0350533	−	0.0538513i	0.820129	−	0.572179i	$-0.193902\pi$
$11$	−0.116259	−	0.178605i	−0.0350533	−	0.0538513i	−0.855182	+	0.518328i	$0.826555\pi$
$12$	3.51114	+	0.338716i	1.01358	+	0.0977788i
$13$	−0.0451466	−	0.703194i	−0.0125214	−	0.195031i	−0.999430	−	0.0337519i	$-0.989254\pi$
$13$	−0.0451466	−	0.703194i	−0.0125214	−	0.195031i	0.986909	−	0.161279i	$-0.0515619\pi$
$14$		−	1.56013i		−	0.416961i
$15$	−7.69997	+	0.494354i	−1.98812	+	0.127642i
$16$	0.873982	−	0.492217i	0.218495	−	0.123054i
$17$	−2.22411	−	0.0713227i	−0.539425	−	0.0172983i	−0.238850	−	0.971056i	$-0.576770\pi$
$17$	−2.22411	−	0.0713227i	−0.539425	−	0.0172983i	−0.300575	+	0.953758i	$0.597179\pi$
$18$	1.18011	−	1.81297i	0.278156	−	0.427322i
$19$	−3.40504	+	4.26979i	−0.781170	+	0.979557i	0.218822	+	0.975765i	$0.429778\pi$
$19$	−3.40504	+	4.26979i	−0.781170	+	0.979557i	−0.999993	+	0.00379200i	$0.998793\pi$
$20$	−3.59616	+	2.86784i	−0.804126	+	0.641269i
$21$	4.53742	+	2.36717i	0.990145	+	0.516558i
$22$	−0.120331	+	0.102440i	−0.0256547	+	0.0218402i
$23$	−1.18168	−	0.392344i	−0.246397	−	0.0818093i	0.189244	−	0.981930i	$-0.439396\pi$
$23$	−1.18168	−	0.392344i	−0.246397	−	0.0818093i	−0.435640	+	0.900121i	$0.643478\pi$
$24$	−0.199470	−	6.22020i	−0.0407166	−	1.26969i
$25$	3.40263	−	3.74667i	0.680525	−	0.749334i
$26$	−0.512887	+	0.0998847i	−0.100585	+	0.0195890i
$27$	−0.0988449	−	0.175509i	−0.0190227	−	0.0337767i
$28$	3.02583	−	0.390138i	0.571829	−	0.0737292i
$29$	0.837505	−	8.68162i	0.155521	−	1.61214i	−0.506221	−	0.862404i	$-0.668958\pi$
$29$	0.837505	−	8.68162i	0.155521	−	1.61214i	0.661742	−	0.749732i	$-0.269817\pi$
$30$	1.09374	+	5.61610i	0.199688	+	1.02536i
$31$	1.15479	−	1.19241i	0.207406	−	0.214164i	−0.606620	−	0.794992i	$-0.707475\pi$
$31$	1.15479	−	1.19241i	0.207406	−	0.214164i	0.814026	+	0.580828i	$0.197271\pi$
$32$	−3.50530	−	4.69679i	−0.619656	−	0.830282i
$33$	−0.115354	−	0.505398i	−0.0200805	−	0.0879785i
$34$	0.158449	+	1.64249i	0.0271738	+	0.281685i
$35$	−6.39758	+	1.89877i	−1.08139	+	0.320950i
$36$	3.81133	+	1.83544i	0.635222	+	0.305907i
$37$	−0.0852870	−	0.0480328i	−0.0140211	−	0.00789654i	0.483691	−	0.875239i	$-0.339296\pi$
$37$	−0.0852870	−	0.0480328i	−0.0140211	−	0.00789654i	−0.497712	+	0.867342i	$0.665826\pi$
$38$	3.46313	+	2.09937i	0.561793	+	0.340562i
$39$	0.487698	−	1.64322i	0.0780942	−	0.263125i
$40$	5.82948	+	5.64554i	0.921722	+	0.892638i
$41$	−0.237173	+	7.39594i	−0.0370403	+	1.15505i	0.797223	+	0.603685i	$0.206302\pi$
$41$	−0.237173	+	7.39594i	−0.0370403	+	1.15505i	−0.834263	+	0.551367i	$0.814107\pi$
$42$	1.31068	−	3.56154i	0.202242	−	0.549557i
$43$	−10.3915	+	6.76412i	−1.58469	+	1.03152i	−0.614579	+	0.788856i	$0.710674\pi$
$43$	−10.3915	+	6.76412i	−1.58469	+	1.03152i	−0.970111	+	0.242663i	$0.921979\pi$
$44$	−0.228770	−	0.207763i	−0.0344884	−	0.0313215i
$45$	−8.87069	−	2.63278i	−1.32236	−	0.392471i
$46$	−0.176497	+	0.906275i	−0.0260231	+	0.133623i
$47$	0.514564	+	0.737666i	0.0750568	+	0.107600i	0.855934	−	0.517085i	$-0.172983\pi$
$47$	0.514564	+	0.737666i	0.0750568	+	0.107600i	−0.780877	+	0.624684i	$0.785228\pi$
$48$	2.40869	−	0.389418i	0.347664	−	0.0562076i
$49$	−2.48947	−	0.652816i	−0.355638	−	0.0932594i
$50$	−3.07817	−	2.14720i	−0.435319	−	0.303659i
$51$	−5.01738	−	2.03131i	−0.702574	−	0.284441i
$52$	−0.321981	−	0.969756i	−0.0446507	−	0.134481i
$53$	13.0226	+	2.53616i	1.78879	+	0.348368i	0.973148	−	0.230182i	$-0.0739321\pi$
$53$	13.0226	+	2.53616i	1.78879	+	0.348368i	0.815647	+	0.578550i	$0.196381\pi$
$54$	−0.119706	+	0.0893389i	−0.0162899	+	0.0121575i
$55$	0.566522	+	0.368765i	0.0763898	+	0.0497243i
$56$	−1.36532	−	5.20658i	−0.182449	−	0.695758i
$57$	−11.3603	+	6.88668i	−1.50471	+	0.912163i
$58$	−6.46436	+	0.207299i	−0.848812	+	0.0272197i
$59$	−6.69957	+	11.0516i	−0.872210	+	1.43880i	0.0262057	+	0.999657i	$0.491658\pi$
$59$	−6.69957	+	11.0516i	−0.872210	+	1.43880i	−0.898416	+	0.439146i	$0.855281\pi$
$60$	−10.6188	+	3.52569i	−1.37088	+	0.455164i
$61$	−4.18825	−	11.3808i	−0.536250	−	1.45716i	−0.859641	−	0.510899i	$-0.829313\pi$
$61$	−4.18825	−	11.3808i	−0.536250	−	1.45716i	0.323391	−	0.946266i	$-0.395177\pi$
$62$	−0.986472	−	0.736223i	−0.125282	−	0.0935004i
$63$	4.12622	+	4.54343i	0.519855	+	0.572418i
$64$	−1.68079	+	1.62775i	−0.210099	+	0.203469i
$65$	1.03381	+	1.98162i	0.128228	+	0.245790i
$66$	−0.360759	+	0.132763i	−0.0444063	+	0.0163419i
$67$	8.56126	−	5.97196i	1.04592	−	0.729592i	0.0822338	−	0.996613i	$-0.473795\pi$
$67$	8.56126	−	5.97196i	1.04592	−	0.729592i	0.963691	+	0.267022i	$0.0860395\pi$
$68$	−3.14596	+	0.718045i	−0.381504	+	0.0870757i
$69$	−2.36798	−	1.88840i	−0.285071	−	0.227337i
$70$	2.00312	+	4.52508i	0.239418	+	0.540850i
$71$	−0.0712288	+	0.0836694i	−0.00845331	+	0.00992973i	−0.765656	−	0.643250i	$-0.777586\pi$
$71$	−0.0712288	+	0.0836694i	−0.00845331	+	0.00992973i	0.757203	+	0.653179i	$0.226565\pi$
$72$	2.35177	−	7.08316i	0.277159	−	0.834758i
$73$	0.800554	−	1.42146i	0.0936978	−	0.166370i	−0.820490	−	0.571661i	$-0.806299\pi$
$73$	0.800554	−	1.42146i	0.0936978	−	0.166370i	0.914188	+	0.405291i	$0.132830\pi$
$74$	−0.0272385	+	0.0672796i	−0.00316641	+	0.00782109i
$75$	10.9153	−	5.69451i	1.26039	−	0.657545i
$76$	−3.20566	+	7.24165i	−0.367715	+	0.830674i
$77$	−0.194536	−	0.403958i	−0.0221694	−	0.0460353i
$78$	−1.25476	−	0.202860i	−0.142073	−	0.0229693i
$79$	13.5067	+	5.97904i	1.51963	+	0.672694i	0.985025	−	0.172409i	$-0.0551552\pi$
$79$	13.5067	+	5.97904i	1.51963	+	0.672694i	0.534603	+	0.845104i	$0.320461\pi$
$80$	−1.90297	+	2.54980i	−0.212758	+	0.285076i
$81$	−1.47495	−	9.12310i	−0.163884	−	1.01368i
$82$	5.46187	−	0.526900i	0.603163	−	0.0581864i
$83$	3.32615	+	4.17086i	0.365093	+	0.457812i	0.930117	−	0.367262i	$-0.119705\pi$
$83$	3.32615	+	4.17086i	0.365093	+	0.457812i	−0.565025	+	0.825074i	$0.691133\pi$
$84$	7.23529	+	1.65141i	0.789435	+	0.180183i
$85$	6.54250	−	2.64876i	0.709633	−	0.287299i
$86$	5.96010	+	7.00107i	0.642694	+	0.754945i
$87$	9.20541	−	19.1152i	0.986924	−	2.04937i
$88$	−0.311930	+	0.447175i	−0.0332519	+	0.0476691i
$89$	8.24270	+	8.51127i	0.873725	+	0.902193i	0.995913	−	0.0903142i	$-0.0287871\pi$
$89$	8.24270	+	8.51127i	0.873725	+	0.902193i	−0.122188	+	0.992507i	$0.538991\pi$
$90$	−1.09511	+	6.77365i	−0.115435	+	0.714006i
$91$	0.0949835	−	1.47944i	0.00995698	−	0.155088i
$92$	−1.80184	−	0.115682i	−0.187855	−	0.0120607i
$93$	3.63797	−	1.75195i	0.377240	−	0.181669i
$94$	0.493726	−	0.448389i	0.0509239	−	0.0462478i
$95$	4.39400	−	16.7562i	0.450815	−	1.71915i
$96$	−4.05627	−	13.6669i	−0.413991	−	1.39487i
$97$	−2.57767	+	4.94091i	−0.261723	+	0.501673i	−0.981237	−	0.192804i	$-0.938242\pi$
$97$	−2.57767	+	4.94091i	−0.261723	+	0.501673i	0.719515	+	0.694477i	$0.244364\pi$
$98$	−0.244049	+	1.89280i	−0.0246527	+	0.191201i
$99$	0.0794989	−	0.616578i	0.00798994	−	0.0619684i
$100$	3.39469	−	6.50699i	0.339469	−	0.650699i
$101$	0.860703	+	2.90000i	0.0856432	+	0.288560i	0.990570	−	0.137007i	$-0.0437482\pi$
$101$	0.860703	+	2.90000i	0.0856432	+	0.288560i	−0.904927	+	0.425567i	$0.860075\pi$
$102$	−1.01816	+	3.88268i	−0.100813	+	0.384443i
$103$	12.0791	−	10.9699i	1.19019	−	1.08090i	0.195213	−	0.980761i	$-0.437460\pi$
$103$	12.0791	−	10.9699i	1.19019	−	1.08090i	0.994974	−	0.100135i	$-0.0319276\pi$
$104$	−1.62423	+	0.782189i	−0.159269	+	0.0767000i
$105$	−16.1999	−	1.04007i	−1.58095	−	0.101500i
$106$	0.630340	−	9.81805i	0.0612240	−	0.953613i
$107$	0.0294330	−	0.182054i	0.00284540	−	0.0175998i	−0.985720	−	0.168393i	$-0.946142\pi$
$107$	0.0294330	−	0.182054i	0.00284540	−	0.0175998i	0.988565	+	0.150794i	$0.0481829\pi$
$108$	−0.203206	−	0.209826i	−0.0195535	−	0.0201906i
$109$	−10.0840	+	14.4562i	−0.965872	+	1.38465i	−0.0431993	+	0.999066i	$0.513755\pi$
$109$	−10.0840	+	14.4562i	−0.965872	+	1.38465i	−0.922673	+	0.385584i	$0.874000\pi$
$110$	0.217489	−	0.451620i	0.0207367	−	0.0430603i
$111$	−0.154345	−	0.181302i	−0.0146498	−	0.0172084i
$112$	1.95609	−	0.791934i	0.184833	−	0.0748308i
$113$	2.67561	+	0.610692i	0.251701	+	0.0574490i	0.346509	−	0.938046i	$-0.387367\pi$
$113$	2.67561	+	0.610692i	0.251701	+	0.0574490i	−0.0948088	+	0.995495i	$0.530224\pi$
$114$	6.14210	+	7.70195i	0.575260	+	0.721354i
$115$	3.93115	−	0.379233i	0.366582	−	0.0353637i
$116$	−2.01858	−	12.4857i	−0.187421	−	1.15926i
$117$	1.22946	−	1.64737i	0.113664	−	0.152299i
$118$	8.76329	+	3.87925i	0.806726	+	0.357114i
$119$	−4.62167	−	0.747196i	−0.423668	−	0.0684954i
$120$	8.56496	+	17.7853i	0.781870	+	1.62357i
$121$	4.43423	−	10.0170i	0.403112	−	0.910637i
$122$	−7.97293	+	4.15947i	−0.721835	+	0.376581i
$123$	−6.75484	+	16.6846i	−0.609063	+	1.50440i
$124$	1.18120	−	2.09735i	0.106075	−	0.188347i
$125$	−0.0611355	+	0.184130i	−0.00546812	+	0.0164691i
$126$	2.95021	−	3.46549i	0.262826	−	0.308730i
$127$	−3.25045	−	7.34283i	−0.288431	−	0.651570i	0.710193	−	0.704007i	$-0.248607\pi$
$127$	−3.25045	−	7.34283i	−0.288431	−	0.651570i	−0.998624	+	0.0524362i	$0.983301\pi$
$128$	−7.80752	−	6.22629i	−0.690094	−	0.550332i
$129$	−29.4049	+	6.71147i	−2.58895	+	0.590912i
$130$	1.35936	−	0.948230i	0.119224	−	0.0831653i
$131$	16.3890	−	6.03131i	1.43191	−	0.526958i	0.492673	−	0.870215i	$-0.336020\pi$
$131$	16.3890	−	6.03131i	1.43191	−	0.526958i	0.939241	+	0.343257i	$0.111530\pi$
$132$	−0.347705	−	0.666485i	−0.0302638	−	0.0580101i
$133$	−8.25377	+	7.99333i	−0.715693	+	0.693110i
$134$	−5.20395	−	5.73012i	−0.449552	−	0.495007i
$135$	0.512039	+	0.382145i	0.0440693	+	0.0328898i
$136$	1.96620	+	5.34279i	0.168600	+	0.458141i
$137$	14.2066	−	4.71692i	1.21375	−	0.402993i	0.364611	−	0.931160i	$-0.381202\pi$
$137$	14.2066	−	4.71692i	1.21375	−	0.402993i	0.849141	+	0.528166i	$0.177120\pi$
$138$	−1.16429	+	1.92061i	−0.0991107	+	0.163493i
$139$	−0.259522	+	0.00832237i	−0.0220124	+	0.000705894i	−0.0430558	−	0.999073i	$-0.513709\pi$
$139$	−0.259522	+	0.00832237i	−0.0220124	+	0.000705894i	0.0210434	+	0.999779i	$0.493301\pi$
$140$	−8.27538	+	5.01659i	−0.699398	+	0.423979i
$141$	0.554952	+	2.11627i	0.0467354	+	0.178222i
$142$	0.0682895	+	0.0444515i	0.00573073	+	0.00373029i
$143$	−0.120345	+	0.0898158i	−0.0100638	+	0.00751078i
$144$	2.87215	+	0.559351i	0.239346	+	0.0466126i
$145$	8.71758	+	26.2560i	0.723956	+	2.18044i
$146$	−1.12134	−	0.453979i	−0.0928025	−	0.0375716i
$147$	−5.13465	−	3.58171i	−0.423499	−	0.295414i
$148$	−0.137299	−	0.0360040i	−0.0112859	−	0.00295951i
$149$	−11.4600	+	1.85277i	−0.938843	+	0.151785i	−0.609822	−	0.792538i	$-0.708759\pi$
$149$	−11.4600	+	1.85277i	−0.938843	+	0.151785i	−0.329020	+	0.944323i	$0.606718\pi$
$150$	−5.22311	−	7.48773i	−0.426466	−	0.611370i
$151$	−0.276124	+	1.41784i	−0.0224707	+	0.115382i	−0.991098	−	0.133137i	$-0.957495\pi$
$151$	−0.276124	+	1.41784i	−0.0224707	+	0.115382i	0.968627	+	0.248519i	$0.0799439\pi$
$152$	13.3946	+	3.97546i	1.08645	+	0.322452i
$153$	−4.80550	−	4.36423i	−0.388502	−	0.352827i
$154$	−0.278646	+	0.181378i	−0.0224539	+	0.0146159i
$155$	−1.81842	+	4.94123i	−0.146059	+	0.396889i
$156$	0.0796669	−	2.48431i	0.00637846	−	0.198904i
$157$	−6.08949	−	5.89734i	−0.485994	−	0.470659i	0.411674	−	0.911331i	$-0.364944\pi$
$157$	−6.08949	−	5.89734i	−0.485994	−	0.470659i	−0.897668	+	0.440672i	$0.854740\pi$
$158$	3.11652	−	10.5006i	0.247937	−	0.835381i
$159$	27.5981	+	16.7301i	2.18867	+	1.32678i
$160$	16.1974	+	9.12220i	1.28052	+	0.721174i
$161$	−2.36015	−	1.13659i	−0.186006	−	0.0895758i
$162$	−6.56977	+	1.94987i	−0.516170	+	0.153196i
$163$	0.184736	+	1.91498i	0.0144696	+	0.149993i	0.999785	−	0.0207537i	$-0.00660658\pi$
$163$	0.184736	+	1.91498i	0.0144696	+	0.149993i	−0.985315	+	0.170746i	$0.945382\pi$
$164$	2.38775	+	10.4614i	0.186452	+	0.816901i
$165$	0.983482	+	1.31778i	0.0765640	+	0.102589i
$166$	2.75208	−	2.84174i	0.213603	−	0.220562i
$167$	−4.11357	−	21.1223i	−0.318318	−	1.63449i	−0.702819	−	0.711369i	$-0.748076\pi$
$167$	−4.11357	−	21.1223i	−0.318318	−	1.63449i	0.384501	−	0.923124i	$-0.374373\pi$
$168$	1.25726	−	13.0329i	0.0970000	−	1.00551i
$169$	12.4008	−	1.59891i	0.953910	−	0.122993i
$170$	−2.56845	−	4.56054i	−0.196991	−	0.349777i
$171$	−15.6378	+	3.04546i	−1.19585	+	0.232892i
$172$	−12.0880	+	13.3102i	−0.921701	+	1.01490i
$173$	0.605936	+	18.8953i	0.0460684	+	1.43658i	0.718037	+	0.696004i	$0.245041\pi$
$173$	0.605936	+	18.8953i	0.0460684	+	1.43658i	−0.671969	+	0.740579i	$0.734551\pi$
$174$	−14.9313	−	4.95754i	−1.13194	−	0.375830i
$175$	8.10799	−	6.90243i	0.612906	−	0.521775i
$176$	−0.189520	−	0.0988726i	−0.0142856	−	0.00745280i
$177$	−24.5787	+	19.6009i	−1.84745	+	1.47329i
$178$	5.47803	−	6.86923i	0.410596	−	0.514871i
$179$	−3.08332	+	4.73681i	−0.230458	+	0.354046i	−0.934408	−	0.356204i	$-0.884071\pi$
$179$	−3.08332	+	4.73681i	−0.230458	+	0.354046i	0.703950	+	0.710250i	$0.251418\pi$
$180$	−13.4112	−	0.430072i	−0.999613	−	0.0320556i
$181$	−13.2582	+	7.46686i	−0.985472	+	0.555008i	−0.897453	−	0.441111i	$-0.854584\pi$
$181$	−13.2582	+	7.46686i	−0.985472	+	0.555008i	−0.0880198	+	0.996119i	$0.528054\pi$
$182$	−1.09707	+	0.0704344i	−0.0813204	+	0.00522094i
$183$		−	29.4993i		−	2.18065i
$184$	0.204095	+	3.17895i	0.0150461	+	0.234355i
$185$	0.309043	+	0.0298130i	0.0227213	+	0.00219189i
$186$	−1.63346	−	2.50943i	−0.119771	−	0.184001i
$187$	0.245833	+	0.405527i	0.0179771	+	0.0296551i
$188$	0.993106	+	0.845443i	0.0724297	+	0.0616603i
$189$	−0.159033	−	0.392814i	−0.0115679	−	0.0285730i
$190$	−12.7401	−	1.64266i	−0.924266	−	0.119171i
$191$	−0.518155	+	2.27019i	−0.0374924	+	0.164265i	−0.990208	−	0.139597i	$-0.955419\pi$
$191$	−0.518155	+	2.27019i	−0.0374924	+	0.164265i	0.952716	+	0.303862i	$0.0982763\pi$
$192$	−5.20449	+	2.30387i	−0.375601	+	0.166268i
$193$	−2.60309	+	0.682610i	−0.187374	+	0.0491353i	−0.346149	−	0.938179i	$-0.612511\pi$
$193$	−2.60309	+	0.682610i	−0.187374	+	0.0491353i	0.158775	+	0.987315i	$0.449246\pi$
$194$	3.87825	+	1.42723i	0.278442	+	0.102469i
$195$	0.695254	+	5.39225i	0.0497882	+	0.386147i
$196$	−3.73207			−0.266576
$197$	−7.43185	−	11.9066i	−0.529498	−	0.848311i
$197$	−7.43185	−	11.9066i	−0.529498	−	0.848311i
$198$	−0.461004			−0.0327621
$199$	2.53337	+	19.6483i	0.179586	+	1.39283i	0.795947	+	0.605366i	$0.206973\pi$
$199$	2.53337	+	19.6483i	0.179586	+	1.39283i	−0.616361	+	0.787463i	$0.711394\pi$
$200$	−12.1518	−	4.47197i	−0.859261	−	0.316216i
$201$	24.5612	−	6.44070i	1.73241	−	0.454292i
$202$	2.05120	−	0.908005i	0.144322	−	0.0638870i
$203$	4.08325	−	17.8899i	0.286588	−	1.25562i
$204$	−7.78499	−	1.00376i	−0.545059	−	0.0702775i
$205$	−8.80808	−	21.7561i	−0.615183	−	1.51951i
$206$	−9.21328	−	7.84338i	−0.641920	−	0.546474i
$207$	−1.88292	−	3.10607i	−0.130872	−	0.215887i
$208$	−0.385582	−	0.592357i	−0.0267353	−	0.0410726i
$209$	1.15847	+	0.111756i	0.0801330	+	0.00773034i
$210$	0.771255	+	12.0129i	0.0532217	+	0.828970i
$211$			5.11121i			0.351870i	0.984402	+	0.175935i	$0.0562949\pi$
$211$			5.11121i			0.351870i	−0.984402	+	0.175935i	$0.943705\pi$
$212$	19.1995	−	1.23265i	1.31863	−	0.0846588i
$213$	−0.232896	+	0.131165i	−0.0159578	+	0.00898726i
$214$	−0.136683	−	0.00438317i	−0.00934348	−	0.000299627i
$215$	21.4553	−	32.9612i	1.46324	−	2.24793i
$216$	−0.321308	+	0.402908i	−0.0218623	+	0.0274144i
$217$	2.73041	−	2.17743i	0.185352	−	0.147814i
$218$	11.5881	+	6.04550i	0.784845	+	0.409453i
$219$	3.02173	−	2.57244i	0.204190	−	0.173829i
$220$	0.930295	+	0.308879i	0.0627205	+	0.0208246i
$221$	0.0502570	+	1.56720i	0.00338065	+	0.105421i
$222$	−0.118704	+	0.130706i	−0.00796687	+	0.00877240i
$223$	−2.39710	+	0.466836i	−0.160522	+	0.0312616i	−0.270779	−	0.962641i	$-0.587281\pi$
$223$	−2.39710	+	0.466836i	−0.160522	+	0.0312616i	0.110258	+	0.993903i	$0.464832\pi$
$224$	−6.05061	−	10.7435i	−0.404273	−	0.717828i
$225$	14.6432	−	1.88803i	0.976212	−	0.125869i
$226$	0.195417	−	2.02570i	0.0129990	−	0.134748i
$227$	−0.303381	−	1.55780i	−0.0201361	−	0.103395i	0.970129	−	0.242591i	$-0.0779972\pi$
$227$	−0.303381	−	1.55780i	−0.0201361	−	0.103395i	−0.990265	+	0.139196i	$0.955548\pi$
$228$	−13.4018	+	13.8385i	−0.887558	+	0.916477i
$229$	−0.288040	−	0.385948i	−0.0190343	−	0.0255042i	0.791795	−	0.610787i	$-0.209147\pi$
$229$	−0.288040	−	0.385948i	−0.0190343	−	0.0255042i	−0.810829	+	0.585283i	$0.800984\pi$
$230$	−0.651686	−	2.85522i	−0.0429709	−	0.188268i
$231$	−0.104727	−	1.08561i	−0.00689054	−	0.0714277i
$232$	−21.3919	+	6.34901i	−1.40445	+	0.416833i
$233$	−0.700077	−	0.337139i	−0.0458636	−	0.0220867i	0.410811	−	0.911720i	$-0.365245\pi$
$233$	−0.700077	−	0.337139i	−0.0458636	−	0.0220867i	−0.456675	+	0.889634i	$0.650960\pi$
$234$	−1.32815	−	0.748001i	−0.0868239	−	0.0488983i
$235$	−2.43959	−	1.47890i	−0.159141	−	0.0964725i
$236$	−5.33230	+	17.9663i	−0.347103	+	1.16951i
$237$	25.8108	+	24.9964i	1.67659	+	1.62369i
$238$	−0.111273	+	3.46989i	−0.00721273	+	0.224919i
$239$	−2.76406	+	7.51085i	−0.178792	+	0.485836i	−0.995880	−	0.0906764i	$-0.971097\pi$
$239$	−2.76406	+	7.51085i	−0.178792	+	0.485836i	0.817088	+	0.576513i	$0.195587\pi$
$240$	−6.48630	+	4.22211i	−0.418689	+	0.272536i
$241$	13.0118	+	11.8170i	0.838163	+	0.761197i	0.973277	−	0.229633i	$-0.0737524\pi$
$241$	13.0118	+	11.8170i	0.838163	+	0.761197i	−0.135114	+	0.990830i	$0.543140\pi$
$242$	−7.78754	−	2.31130i	−0.500602	−	0.148576i
$243$	4.18180	−	21.4727i	0.268263	−	1.37747i
$244$	−10.0610	−	14.4232i	−0.644089	−	0.923349i
$245$	8.05878	−	1.30288i	0.514856	−	0.0832380i
$246$	12.9113	+	3.38574i	0.823194	+	0.215867i
$247$	3.15622	+	2.20164i	0.200825	+	0.140087i
$248$	−3.93643	−	1.59368i	−0.249963	−	0.101199i
$249$	4.08913	+	12.3158i	0.259138	+	0.780482i
$250$	0.141217	+	0.0275020i	0.00893134	+	0.00173938i
$251$	−4.53784	+	3.38668i	−0.286426	+	0.213765i	−0.731696	−	0.681631i	$-0.761271\pi$
$251$	−4.53784	+	3.38668i	−0.286426	+	0.213765i	0.445270	+	0.895396i	$0.353108\pi$
$252$	7.45899	+	4.85527i	0.469873	+	0.305853i
$253$	0.0673058	+	0.256666i	0.00423148	+	0.0161365i
$254$	−5.09209	+	3.08686i	−0.319506	+	0.193687i
$255$	17.1608	−	0.550313i	1.07465	−	0.0344620i
$256$	−6.26466	+	10.3342i	−0.391541	+	0.645889i
$257$	−6.94920	+	2.30729i	−0.433479	+	0.143925i	−0.523521	−	0.852013i	$-0.675382\pi$
$257$	−6.94920	+	2.30729i	−0.433479	+	0.143925i	0.0900413	+	0.995938i	$0.471300\pi$
$258$	7.72434	+	20.9895i	0.480896	+	1.30675i
$259$	−0.165039	−	0.123172i	−0.0102550	−	0.00765351i
$260$	2.17901	+	2.39933i	0.135136	+	0.148800i
$261$	18.2773	−	17.7006i	1.13134	−	1.09564i
$262$	−5.98987	−	11.4815i	−0.370055	−	0.709326i
$263$	−1.81028	+	0.666201i	−0.111627	+	0.0410797i	−0.400567	−	0.916267i	$-0.631187\pi$
$263$	−1.81028	+	0.666201i	−0.111627	+	0.0410797i	0.288940	+	0.957347i	$0.406697\pi$
$264$	−1.08777	+	0.758779i	−0.0669474	+	0.0466996i
$265$	−41.0278	+	9.36434i	−2.52032	+	0.575247i
$266$	6.66141	+	5.31230i	0.408437	+	0.325718i
$267$	11.6665	+	26.3547i	0.713976	+	1.61288i
$268$	9.81212	−	11.5259i	0.599370	−	0.704055i
$269$	−7.61285	+	22.9287i	−0.464164	+	1.39799i	0.409880	+	0.912139i	$0.365571\pi$
$269$	−7.61285	+	22.9287i	−0.464164	+	1.39799i	−0.874044	+	0.485847i	$0.838511\pi$
$270$	0.232496	−	0.412820i	0.0141492	−	0.0251234i
$271$	1.66900	−	4.12247i	0.101385	−	0.250422i	−0.867729	−	0.497038i	$-0.834421\pi$
$271$	1.66900	−	4.12247i	0.101385	−	0.250422i	0.969113	+	0.246616i	$0.0793188\pi$
$272$	−1.97893	+	1.03241i	−0.119991	+	0.0625990i
$273$	1.45973	−	3.29756i	0.0883469	−	0.199577i
$274$	−4.81624	−	10.0010i	−0.290960	−	0.604184i
$275$	−1.06476	−	0.172142i	−0.0642073	−	0.0103805i
$276$	−4.01614	−	1.77783i	−0.241743	−	0.107013i
$277$	8.08738	−	10.8364i	0.485924	−	0.651093i	−0.489352	−	0.872086i	$-0.662767\pi$
$277$	8.08738	−	10.8364i	0.485924	−	0.651093i	0.975275	+	0.220993i	$0.0709298\pi$
$278$	0.0307303	+	0.190078i	0.00184308	+	0.0114001i
$279$	4.81998	−	0.464978i	0.288565	−	0.0278375i
$280$	10.6450	+	13.3484i	0.636162	+	0.797722i
$281$	−27.7660	−	6.33740i	−1.65638	−	0.378058i	−0.710786	−	0.703409i	$-0.751660\pi$
$281$	−27.7660	−	6.33740i	−1.65638	−	0.378058i	−0.945593	+	0.325351i	$0.894517\pi$
$282$	1.50380	−	0.608820i	0.0895499	−	0.0362547i
$283$	−9.53474	−	11.2000i	−0.566781	−	0.665774i	0.401435	−	0.915887i	$-0.368512\pi$
$283$	−9.53474	−	11.2000i	−0.566781	−	0.665774i	−0.968216	+	0.250114i	$0.919532\pi$
$284$	−0.0691358	+	0.143562i	−0.00410246	+	0.00851884i
$285$	24.1079	−	34.5605i	1.42803	−	2.04719i
$286$	0.0774674	+	0.0799915i	0.00458074	+	0.00473000i
$287$	−2.48469	+	15.3687i	−0.146667	+	0.907186i
$288$	1.09538	−	17.0615i	0.0645460	−	1.00536i
$289$	−12.0235	−	0.771935i	−0.707265	−	0.0454079i
$290$	18.4834	−	8.90115i	1.08538	−	0.522693i
$291$	−10.0353	+	9.11383i	−0.588282	+	0.534262i
$292$	0.600073	−	2.28834i	0.0351166	−	0.133915i
$293$	−5.59847	−	18.8631i	−0.327066	−	1.10200i	−0.948037	−	0.318161i	$-0.896935\pi$
$293$	−5.59847	−	18.8631i	−0.327066	−	1.10200i	0.620970	−	0.783834i	$-0.286739\pi$
$294$	−2.14729	+	4.11594i	−0.125232	+	0.240047i
$295$	5.24210	−	40.6567i	0.305207	−	2.36713i
$296$	−0.0320235	+	0.248368i	−0.00186133	+	0.0144361i
$297$	−0.0198551	+	0.0380586i	−0.00115211	+	0.00220838i
$298$	2.44934	+	8.25265i	0.141887	+	0.478063i
$299$	−0.222545	+	0.848661i	−0.0128701	+	0.0490793i
$300$	13.2162	−	12.0026i	0.763035	−	0.692969i
$301$	−23.5029	+	11.3184i	−1.35469	+	0.652382i
$302$	1.06894	+	0.0686283i	0.0615106	+	0.00394911i
$303$	−0.471458	+	7.34334i	−0.0270846	+	0.421864i
$304$	−0.874281	+	5.40774i	−0.0501435	+	0.310155i
$305$	26.7602	+	27.6321i	1.53228	+	1.58221i
$306$	−2.75401	+	3.94808i	−0.157436	+	0.225696i
$307$	4.35132	−	9.03560i	0.248343	−	0.515689i	−0.739114	−	0.673581i	$-0.764755\pi$
$307$	4.35132	−	9.03560i	0.248343	−	0.515689i	0.987456	+	0.157892i	$0.0504697\pi$
$308$	−0.421460	−	0.495071i	−0.0240149	−	0.0282093i
$309$	36.7907	−	14.8949i	2.09295	−	0.847340i
$310$	3.80649	+	0.868806i	0.216194	+	0.0493449i
$311$	18.7223	+	23.4771i	1.06165	+	1.33126i	0.940939	+	0.338575i	$0.109945\pi$
$311$	18.7223	+	23.4771i	1.06165	+	1.33126i	0.120707	+	0.992688i	$0.461484\pi$
$312$	−4.36501	+	0.421087i	−0.247120	+	0.0238394i
$313$	1.23033	+	7.61003i	0.0695424	+	0.430145i	0.998240	+	0.0593061i	$0.0188888\pi$
$313$	1.23033	+	7.61003i	0.0695424	+	0.430145i	−0.928697	+	0.370838i	$0.879070\pi$
$314$	−3.75978	+	5.03777i	−0.212177	+	0.284298i
$315$	−17.8014	−	7.88017i	−1.00300	−	0.443997i
$316$	21.1450	+	3.41856i	1.18950	+	0.192309i
$317$	2.42045	+	5.02613i	0.135946	+	0.282295i	0.957817	−	0.287379i	$-0.0927838\pi$
$317$	2.42045	+	5.02613i	0.135946	+	0.282295i	−0.821871	+	0.569674i	$0.807069\pi$
$318$	9.68722	−	21.8836i	0.543232	−	1.22717i
$319$	−1.64794	+	0.859731i	−0.0922671	+	0.0481357i
$320$	2.78511	−	6.87928i	0.155692	−	0.384563i
$321$	0.220136	−	0.390875i	0.0122868	−	0.0218165i
$322$	−0.612106	+	1.84356i	−0.0341113	+	0.102738i
$323$	7.87771	−	9.25360i	0.438327	−	0.514884i
$324$	−5.42463	−	12.2543i	−0.301368	−	0.680796i
$325$	−2.78825	−	2.22356i	−0.154665	−	0.123341i
$326$	1.39086	−	0.317456i	0.0770328	−	0.0175822i
$327$	−35.1651	+	24.5296i	−1.94463	+	1.35649i
$328$	17.7667	−	6.53830i	0.981000	−	0.361017i
$329$	0.875237	+	1.67766i	0.0482534	+	0.0924927i
$330$	0.875905	−	0.848267i	0.0482170	−	0.0466956i
$331$	3.22278	+	3.54864i	0.177140	+	0.195051i	0.822396	−	0.568916i	$-0.192637\pi$
$331$	3.22278	+	3.54864i	0.177140	+	0.195051i	−0.645256	+	0.763967i	$0.723249\pi$
$332$	6.19971	+	4.62697i	0.340253	+	0.253938i
$333$	−0.0986165	−	0.267973i	−0.00540415	−	0.0146848i
$334$	−15.1444	+	5.02830i	−0.828667	+	0.275136i
$335$	−17.1639	+	28.3136i	−0.937763	+	1.54694i
$336$	5.13078	−	0.164534i	0.279907	−	0.00897607i
$337$	14.8440	−	8.99849i	0.808602	−	0.490179i	−0.0524945	−	0.998621i	$-0.516717\pi$
$337$	14.8440	−	8.99849i	0.808602	−	0.490179i	0.861096	+	0.508442i	$0.169778\pi$
$338$	−2.35185	−	8.96863i	−0.127924	−	0.487829i
$339$	5.59498	+	3.64193i	0.303878	+	0.197802i
$340$	8.20279	−	6.12190i	0.444859	−	0.332007i
$341$	−0.347225	−	0.0676221i	−0.0188033	−	0.00366194i
$342$	3.72267	+	11.2121i	0.201299	+	0.606281i
$343$	−18.6699	−	7.55859i	−1.00808	−	0.408126i
$344$	26.0174	+	18.1486i	1.40276	+	0.978507i
$345$	9.29283	+	2.43687i	0.500309	+	0.131196i
$346$	13.8392	−	2.23741i	0.744000	−	0.120284i
$347$	−5.38177	−	7.71518i	−0.288909	−	0.414172i	0.649144	−	0.760666i	$-0.275127\pi$
$347$	−5.38177	−	7.71518i	−0.288909	−	0.414172i	−0.938052	+	0.346493i	$0.887372\pi$
$348$	5.88120	−	30.1987i	0.315265	−	1.61882i
$349$	−24.4632	−	7.26056i	−1.30949	−	0.388649i	−0.446912	−	0.894578i	$-0.647476\pi$
$349$	−24.4632	−	7.26056i	−1.30949	−	0.388649i	−0.862575	+	0.505929i	$0.831150\pi$
$350$	−5.84528	−	5.30853i	−0.312443	−	0.283753i
$351$	−0.118954	+	0.0774308i	−0.00634932	+	0.00413295i
$352$	−0.431346	+	1.17211i	−0.0229908	+	0.0624734i
$353$	0.0763716	−	2.38155i	0.00406485	−	0.126757i	−0.995442	−	0.0953655i	$-0.969598\pi$
$353$	0.0763716	−	2.38155i	0.00406485	−	0.126757i	0.999507	−	0.0313914i	$-0.00999383\pi$
$354$	16.7463	+	16.2179i	0.890055	+	0.861970i
$355$	0.0991691	−	0.334134i	0.00526335	−	0.0177340i
$356$	14.6926	+	8.90675i	0.778707	+	0.472057i
$357$	−9.92286	−	5.58845i	−0.525174	−	0.295772i
$358$	3.77609	+	1.81847i	0.199573	+	0.0961092i
$359$	12.5610	−	3.72804i	0.662945	−	0.196759i	0.0644942	−	0.997918i	$-0.479457\pi$
$359$	12.5610	−	3.72804i	0.662945	−	0.196759i	0.598451	+	0.801159i	$0.295783\pi$
$360$	2.27318	+	23.5639i	0.119807	+	1.24193i
$361$	−2.40888	−	10.5540i	−0.126783	−	0.555474i
$362$	6.74877	+	9.04274i	0.354707	+	0.475276i
$363$	18.5381	−	19.1421i	0.972997	−	1.00470i
$364$	−0.410949	−	2.11014i	−0.0215396	−	0.110601i
$365$	−0.496888	+	5.15077i	−0.0260083	+	0.269603i
$366$	−21.6954	+	2.79731i	−1.13404	+	0.146218i
$367$	18.5945	+	33.0163i	0.970623	+	1.72344i	0.614290	+	0.789080i	$0.289442\pi$
$367$	18.5945	+	33.0163i	0.970623	+	1.72344i	0.356333	+	0.934359i	$0.384027\pi$
$368$	−1.22588	+	0.238741i	−0.0639035	+	0.0124452i
$369$	−14.5126	+	15.9800i	−0.755496	+	0.831885i
$370$	−0.00737931	−	0.230114i	−0.000383632	−	0.0119631i
$371$	26.4909	+	8.79559i	1.37534	+	0.456644i
$372$	4.45852	−	3.79559i	0.231163	−	0.196792i
$373$	−25.5099	−	13.3085i	−1.32085	−	0.689089i	−0.351832	−	0.936063i	$-0.614441\pi$
$373$	−25.5099	−	13.3085i	−1.32085	−	0.689089i	−0.969022	+	0.246975i	$0.920564\pi$
$374$	0.274936	−	0.219254i	0.0142166	−	0.0113374i
$375$	−0.294253	+	0.368982i	−0.0151952	+	0.0190541i
$376$	1.25530	−	1.92848i	0.0647371	−	0.0994535i
$377$	−6.14267	−	0.196984i	−0.316364	−	0.0101452i
$378$	−0.273816	+	0.154211i	−0.0140836	+	0.00793173i
$379$	−24.9443	+	1.60148i	−1.28130	+	0.0822625i	−0.689777	−	0.724022i	$-0.742291\pi$
$379$	−24.9443	+	1.60148i	−1.28130	+	0.0822625i	−0.591528	+	0.806284i	$0.701475\pi$
$380$		−	25.1200i		−	1.28863i
$381$	−1.25151	−	19.4933i	−0.0641169	−	0.998673i
$382$	1.71875	+	0.165806i	0.0879391	+	0.00848338i
$383$	−21.0273	−	32.3036i	−1.07444	−	1.65063i	−0.682972	−	0.730445i	$-0.739313\pi$
$383$	−21.0273	−	32.3036i	−1.07444	−	1.65063i	−0.391472	−	0.920190i	$-0.628034\pi$
$384$	−12.5926	−	20.7729i	−0.642615	−	1.06006i
$385$	1.08290	+	0.921889i	0.0551898	+	0.0469838i
$386$	0.748871	+	1.84973i	0.0381165	+	0.0941485i
$387$	−35.8735	−	4.62537i	−1.82355	−	0.235121i
$388$	−1.79826	+	7.87869i	−0.0912928	+	0.399980i
$389$	12.1842	−	5.39360i	0.617765	−	0.273466i	−0.0721079	−	0.997397i	$-0.522973\pi$
$389$	12.1842	−	5.39360i	0.617765	−	0.273466i	0.689873	+	0.723931i	$0.257666\pi$
$390$	3.89983	−	1.02266i	0.197476	−	0.0517842i
$391$	2.60019	+	0.956894i	0.131497	+	0.0483922i
$392$	0.841997	+	6.53036i	0.0425273	+	0.329833i
$393$	42.4806			2.14286
$394$	−8.05205	+	6.59486i	−0.405656	+	0.332244i
$395$	−46.8525			−2.35741
$396$	−0.115282	−	0.894108i	−0.00579316	−	0.0449306i
$397$	−10.7305	−	3.94893i	−0.538549	−	0.198191i	0.0615683	−	0.998103i	$-0.480390\pi$
$397$	−10.7305	−	3.94893i	−0.538549	−	0.198191i	−0.600118	+	0.799912i	$0.704880\pi$
$398$	14.2102	−	3.72635i	0.712293	−	0.186785i
$399$	−25.5574	+	11.3135i	−1.27947	+	0.566384i
$400$	1.12966	−	4.94935i	0.0564829	−	0.247468i
$401$	−19.8510	−	2.55950i	−0.991311	−	0.127815i	−0.384893	−	0.922961i	$-0.625762\pi$
$401$	−19.8510	−	2.55950i	−0.991311	−	0.127815i	−0.606418	+	0.795146i	$0.707394\pi$
$402$	−7.06590	−	17.4529i	−0.352415	−	0.870472i
$403$	−0.890634	−	0.758208i	−0.0443656	−	0.0377690i
$404$	2.27400	+	3.75120i	0.113136	+	0.186629i
$405$	15.9916	+	24.5674i	0.794629	+	1.22076i
$406$	−13.5444	−	1.30661i	−0.672198	−	0.0648462i
$407$	0.00133649	+	0.0208169i	6.62472e−5	+	0.00103185i
$408$			13.8486i			0.685609i
$409$	−33.8791	+	2.17511i	−1.67521	+	0.107552i	−0.872437	−	0.488727i	$-0.837462\pi$
$409$	−33.8791	+	2.17511i	−1.67521	+	0.107552i	−0.802777	+	0.596279i	$0.796645\pi$
$410$	−15.1654	+	8.54100i	−0.748966	+	0.421810i
$411$	36.3943	+	1.16709i	1.79520	+	0.0575685i
$412$	12.9081	−	19.8304i	0.635938	−	0.976972i
$413$	−16.9528	+	21.2581i	−0.834192	+	1.04604i
$414$	−2.10582	+	1.67934i	−0.103496	+	0.0825349i
$415$	−15.0025	−	7.82681i	−0.736445	−	0.384203i
$416$	−3.14450	+	2.67695i	−0.154172	+	0.131248i
$417$	−0.599442	−	0.199028i	−0.0293548	−	0.00974647i
$418$	−0.0276619	−	0.862600i	−0.00135299	−	0.0421911i
$419$	−24.5695	+	27.0538i	−1.20030	+	1.32166i	−0.266515	+	0.963831i	$0.585872\pi$
$419$	−24.5695	+	27.0538i	−1.20030	+	1.32166i	−0.933786	+	0.357833i	$0.883516\pi$
$420$	−23.1060	+	4.49988i	−1.12746	+	0.219572i
$421$	6.11403	+	10.8561i	0.297979	+	0.529093i	0.979177	−	0.203007i	$-0.0650713\pi$
$421$	6.11403	+	10.8561i	0.297979	+	0.529093i	−0.681198	+	0.732099i	$0.738541\pi$
$422$	3.75907	−	0.484678i	0.182989	−	0.0235938i
$423$	−0.251939	+	2.61161i	−0.0122497	+	0.126981i
$424$	−6.48852	−	33.3172i	−0.315111	−	1.61803i
$425$	−7.83502	+	8.09031i	−0.380054	+	0.392437i
$426$	0.118551	+	0.158847i	0.00574379	+	0.00769616i
$427$	−5.67738	−	24.8742i	−0.274748	−	1.20375i
$428$	−0.0256791	−	0.266191i	−0.00124125	−	0.0128668i
$429$	−0.350185	+	0.103933i	−0.0169071	+	0.00501794i
$430$	−26.2760	−	12.6539i	−1.26714	−	0.610223i
$431$	12.3005	+	6.92749i	0.592492	+	0.333685i	0.757730	−	0.652568i	$-0.226308\pi$
$431$	12.3005	+	6.92749i	0.592492	+	0.333685i	−0.165238	+	0.986254i	$0.552839\pi$
$432$	−0.172777	−	0.104739i	−0.00831275	−	0.00503924i
$433$	1.83190	−	6.17228i	0.0880355	−	0.296621i	−0.903108	−	0.429413i	$-0.858721\pi$
$433$	1.83190	−	6.17228i	0.0880355	−	0.296621i	0.991144	+	0.132792i	$0.0423941\pi$
$434$	−1.86032	−	1.80162i	−0.0892981	−	0.0864804i
$435$	−2.15697	+	67.2622i	−0.103419	+	3.22497i
$436$	−8.82732	+	23.9867i	−0.422752	+	1.14875i
$437$	5.69888	−	3.70956i	0.272615	−	0.177452i
$438$	−2.17845	−	1.97841i	−0.104091	−	0.0945323i
$439$	−16.4159	−	4.87214i	−0.783486	−	0.232535i	−0.132055	−	0.991242i	$-0.542158\pi$
$439$	−16.4159	−	4.87214i	−0.783486	−	0.232535i	−0.651431	+	0.758708i	$0.725831\pi$
$440$	0.330591	−	1.69751i	0.0157603	−	0.0809258i
$441$	−4.29534	−	6.15769i	−0.204540	−	0.293224i
$442$	1.14784	−	0.185574i	0.0545971	−	0.00882684i
$443$	0.288868	+	0.0757500i	0.0137245	+	0.00359899i	0.260510	−	0.965471i	$-0.416109\pi$
$443$	0.288868	+	0.0757500i	0.0137245	+	0.00359899i	−0.246786	+	0.969070i	$0.579374\pi$
$444$	−0.283185	−	0.197538i	−0.0134394	−	0.00937473i
$445$	−34.8356	−	14.1034i	−1.65137	−	0.668564i
$446$	0.570646	+	1.71869i	0.0270209	+	0.0813825i
$447$	−27.7181	−	5.39810i	−1.31102	−	0.255321i
$448$	−3.94510	+	2.94430i	−0.186388	+	0.139105i
$449$	20.2182	+	13.1606i	0.954154	+	0.621085i	0.925598	−	0.378507i	$-0.123562\pi$
$449$	20.2182	+	13.1606i	0.954154	+	0.621085i	0.0285553	+	0.999592i	$0.490909\pi$
$450$	−2.77712	−	10.5904i	−0.130915	−	0.499235i
$451$	1.34852	−	0.817482i	0.0634994	−	0.0384937i
$452$	3.97768	−	0.127556i	0.187094	−	0.00599975i
$453$	−1.82149	+	3.00474i	−0.0855811	+	0.141175i
$454$	−1.11692	+	0.370843i	−0.0524197	+	0.0174045i
$455$	1.62403	+	4.41302i	0.0761358	+	0.206886i
$456$	27.2382	+	20.3284i	1.27554	+	0.951963i
$457$	15.1570	+	16.6895i	0.709014	+	0.780703i	0.983504	−	0.180887i	$-0.0578968\pi$
$457$	15.1570	+	16.6895i	0.709014	+	0.780703i	−0.274490	+	0.961590i	$0.588509\pi$
$458$	−0.256534	+	0.248439i	−0.0119870	+	0.0116088i
$459$	0.207324	+	0.397401i	0.00967704	+	0.0185491i
$460$	5.37468	−	1.97793i	0.250596	−	0.0922216i
$461$	16.2082	−	11.3062i	0.754893	−	0.526581i	−0.130486	−	0.991450i	$-0.541654\pi$
$461$	16.2082	−	11.3062i	0.754893	−	0.526581i	0.885379	+	0.464870i	$0.153899\pi$
$462$	−0.788485	+	0.179966i	−0.0366836	+	0.00837280i
$463$	3.89434	+	3.10564i	0.180986	+	0.144331i	0.709792	−	0.704411i	$-0.248789\pi$
$463$	3.89434	+	3.10564i	0.180986	+	0.144331i	−0.528807	+	0.848742i	$0.677360\pi$
$464$	−3.54128	−	7.99981i	−0.164400	−	0.371382i
$465$	−8.30236	+	9.75243i	−0.385013	+	0.452258i
$466$	−0.181565	+	0.546845i	−0.00841084	+	0.0253321i
$467$	9.57075	−	16.9938i	0.442882	−	0.786381i	−0.556118	−	0.831103i	$-0.687710\pi$
$467$	9.57075	−	16.9938i	0.442882	−	0.786381i	0.998999	+	0.0447224i	$0.0142403\pi$
$468$	1.11860	−	2.76297i	0.0517075	−	0.127718i
$469$	19.4708	−	10.1579i	0.899077	−	0.469048i
$470$	−0.856323	+	1.93445i	−0.0394992	+	0.0892295i
$471$	−8.94698	−	18.5786i	−0.412255	−	0.856056i
$472$	32.6404	+	5.27705i	1.50240	+	0.242896i
$473$	2.41621	+	1.06958i	0.111097	+	0.0491794i
$474$	15.9362	−	21.3530i	0.731973	−	0.980778i
$475$	4.41140	+	27.2861i	0.202409	+	1.25197i
$476$	−6.75760	+	0.651898i	−0.309734	+	0.0298797i
$477$	24.1311	+	30.2594i	1.10489	+	1.38548i
$478$	5.78600	+	1.32062i	0.264645	+	0.0604036i
$479$	9.89185	−	4.00477i	0.451970	−	0.182982i	−0.137958	−	0.990438i	$-0.544054\pi$
$479$	9.89185	−	4.00477i	0.451970	−	0.182982i	0.589928	+	0.807456i	$0.299156\pi$
$480$	29.3126	+	34.4322i	1.33793	+	1.57161i
$481$	−0.0299259	+	0.0621419i	−0.00136451	+	0.00283343i
$482$	7.45698	−	10.6901i	0.339656	−	0.486923i
$483$	−4.43302	−	4.57745i	−0.201709	−	0.208281i
$484$	2.53531	−	15.6818i	0.115241	−	0.712808i
$485$	1.13256	−	17.6405i	0.0514267	−	0.801013i
$486$	−16.1887	−	1.03935i	−0.734335	−	0.0471459i
$487$	37.1515	−	17.8912i	1.68349	−	0.810728i	0.687037	−	0.726622i	$-0.258911\pi$
$487$	37.1515	−	17.8912i	1.68349	−	0.810728i	0.996457	−	0.0841058i	$-0.0268034\pi$
$488$	−22.9678	+	20.8587i	−1.03970	+	0.944229i
$489$	−1.18707	+	4.52681i	−0.0536812	+	0.204710i
$490$	−1.72240	−	5.80332i	−0.0778099	−	0.262167i
$491$	12.2229	−	23.4289i	0.551610	−	1.05733i	−0.435933	−	0.899979i	$-0.643581\pi$
$491$	12.2229	−	23.4289i	0.551610	−	1.05733i	0.987542	−	0.157353i	$-0.0502962\pi$
$492$	−3.33787	+	25.8879i	−0.150483	+	1.16712i
$493$	−2.48190	+	19.2491i	−0.111779	+	0.866936i
$494$	1.31992	−	2.53003i	0.0593858	−	0.113831i
$495$	0.561070	+	1.89043i	0.0252182	+	0.0849685i
$496$	0.422338	−	1.61056i	0.0189635	−	0.0723161i
$497$	−0.171138	+	0.155423i	−0.00767658	+	0.00697167i
$498$	8.66996	−	4.17523i	0.388510	−	0.187097i
$499$	−20.7033	−	1.32920i	−0.926807	−	0.0595030i	−0.406660	−	0.913580i	$-0.633307\pi$
$499$	−20.7033	−	1.32920i	−0.926807	−	0.0595030i	−0.520147	+	0.854077i	$0.674123\pi$
$500$	−0.0180257	+	0.280765i	−0.000806133	+	0.0125562i
$501$	8.35440	−	51.6749i	0.373247	−	2.30867i
$502$	2.92106	+	3.01623i	0.130373	+	0.134621i
$503$	14.9256	−	21.3970i	0.665502	−	0.954047i	−0.334431	−	0.942420i	$-0.608544\pi$
$503$	14.9256	−	21.3970i	0.665502	−	0.954047i	0.999932	−	0.0116264i	$-0.00370087\pi$
$504$	6.81290	−	14.1471i	0.303471	−	0.630163i
$505$	−6.21987	−	7.30621i	−0.276781	−	0.325122i
$506$	0.182384	−	0.0738391i	0.00810796	−	0.00328255i
$507$	29.6525	+	6.76799i	1.31691	+	0.300577i
$508$	−7.26026	−	9.10408i	−0.322122	−	0.403928i
$509$	26.6833	−	2.57411i	1.18272	−	0.114095i	0.514119	−	0.857719i	$-0.328119\pi$
$509$	26.6833	−	2.57411i	1.18272	−	0.114095i	0.668599	+	0.743624i	$0.266894\pi$
$510$	−2.03203	−	12.5688i	−0.0899797	−	0.556556i
$511$	2.05288	−	2.75067i	0.0908141	−	0.121683i
$512$	−10.0686	−	4.45707i	−0.444973	−	0.196976i
$513$	1.08596	+	0.175569i	0.0479462	+	0.00775157i
$514$	2.35588	+	4.89204i	0.103913	+	0.215778i
$515$	−20.9501	+	47.3266i	−0.923171	+	2.08546i
$516$	−38.7772	+	20.2300i	−1.70707	+	0.890577i
$517$	0.0719280	−	0.177663i	0.00316339	−	0.00781363i
$518$	−0.0749372	+	0.133059i	−0.00329255	+	0.00584626i
$519$	−14.4909	+	43.6442i	−0.636079	+	1.91577i
$520$	3.70673	−	4.35413i	0.162551	−	0.190941i
$521$	−10.9809	−	24.8060i	−0.481081	−	1.08677i	−0.975988	−	0.217824i	$-0.930104\pi$
$521$	−10.9809	−	24.8060i	−0.481081	−	1.08677i	0.494907	−	0.868946i	$-0.335202\pi$
$522$	−14.7512	−	11.7637i	−0.645642	−	0.514882i
$523$	31.6404	−	7.22172i	1.38354	−	0.315784i	0.534971	−	0.844870i	$-0.320322\pi$
$523$	31.6404	−	7.22172i	1.38354	−	0.315784i	0.848568	+	0.529086i	$0.177465\pi$
$524$	20.7702	−	14.4884i	0.907349	−	0.632927i
$525$	24.3081	−	8.94562i	1.06089	−	0.390419i
$526$	0.661624	+	1.26821i	0.0288482	+	0.0552966i
$527$	−2.65342	+	2.56969i	−0.115585	+	0.111938i
$528$	−0.349583	−	0.384929i	−0.0152136	−	0.0167519i
$529$	−17.1901	−	12.8293i	−0.747395	−	0.557795i
$530$	10.7776	+	29.2862i	0.468148	+	1.27211i
$531$	−35.7804	+	11.8799i	−1.55274	+	0.515544i
$532$	−8.63729	+	14.2481i	−0.374474	+	0.617734i
$533$	5.21149	−	0.167122i	0.225735	−	0.00723887i
$534$	18.2764	−	11.0793i	0.790899	−	0.479448i
$535$	0.148378	+	0.565829i	0.00641494	+	0.0244629i
$536$	−22.3817	−	14.5688i	−0.966740	−	0.629278i
$537$	−11.0182	+	8.22310i	−0.475471	+	0.354853i
$538$	17.5849	+	3.42466i	0.758140	+	0.147648i
$539$	0.172827	+	0.520526i	0.00744417	+	0.0224206i
$540$	0.858795	+	0.347688i	0.0369566	+	0.0149621i
$541$	−19.0942	−	13.3193i	−0.820924	−	0.572641i	0.0848539	−	0.996393i	$-0.472958\pi$
$541$	−19.0942	−	13.3193i	−0.820924	−	0.572641i	−0.905778	+	0.423752i	$0.860713\pi$
$542$	−3.19015	−	0.836557i	−0.137029	−	0.0359332i
$543$	−36.5394	+	5.90741i	−1.56806	+	0.253511i
$544$	7.46118	+	10.6962i	0.319895	+	0.458594i
$545$	10.6873	−	54.8768i	0.457792	−	2.35066i
$546$	−2.56363	−	0.760870i	−0.109713	−	0.0325622i
$547$	18.6913	+	16.9749i	0.799180	+	0.725795i	0.965536	−	0.260271i	$-0.0838120\pi$
$547$	18.6913	+	16.9749i	0.799180	+	0.725795i	−0.166355	+	0.986066i	$0.553200\pi$
$548$	18.1924	−	11.8419i	0.777141	−	0.505863i
$549$	12.2179	−	33.2001i	0.521448	−	1.41694i
$550$	−0.0256354	+	0.799405i	−0.00109310	+	0.0340867i
$551$	34.2169	+	33.1372i	1.45769	+	1.41169i
$552$	−2.20475	+	7.42853i	−0.0938403	+	0.316179i
$553$	26.5748	+	16.1098i	1.13008	+	0.685059i
$554$	−8.73655	−	4.92033i	−0.371180	−	0.209045i
$555$	0.680452	+	0.327689i	0.0288836	+	0.0139096i
$556$	−0.360967	+	0.107133i	−0.0153084	+	0.00454346i
$557$	−0.141700	−	1.46887i	−0.00600401	−	0.0622378i	0.991891	−	0.127095i	$-0.0405653\pi$
$557$	−0.141700	−	1.46887i	−0.00600401	−	0.0622378i	−0.997895	+	0.0648572i	$0.979341\pi$
$558$	−0.799032	−	3.50079i	−0.0338257	−	0.148200i
$559$	5.22563	+	7.00187i	0.221021	+	0.296148i
$560$	−4.65676	+	4.80849i	−0.196784	+	0.203196i
$561$	0.220513	+	1.13229i	0.00931005	+	0.0478051i
$562$	−2.02793	+	21.0216i	−0.0855429	+	0.886742i
$563$	−6.14936	+	0.792872i	−0.259165	+	0.0334156i	−0.256363	−	0.966581i	$-0.582524\pi$
$563$	−6.14936	+	0.792872i	−0.259165	+	0.0334156i	−0.00280131	+	0.999996i	$0.500892\pi$
$564$	1.55685	+	2.76434i	0.0655551	+	0.116400i
$565$	−8.54460	+	1.66406i	−0.359474	+	0.0700076i
$566$	−7.33299	+	8.07443i	−0.308228	+	0.339394i
$567$	−0.623187	−	19.4333i	−0.0261714	−	0.816120i
$568$	0.266802	+	0.0885844i	0.0111948	+	0.00371692i
$569$	−7.28938	+	6.20554i	−0.305587	+	0.260150i	−0.787837	−	0.615884i	$-0.788799\pi$
$569$	−7.28938	+	6.20554i	−0.305587	+	0.260150i	0.482250	+	0.876033i	$0.339820\pi$
$570$	−27.7038	−	14.4530i	−1.16038	−	0.605372i
$571$	−20.9740	+	16.7262i	−0.877736	+	0.699971i	−0.954862	−	0.297050i	$-0.903997\pi$
$571$	−20.9740	+	16.7262i	−0.877736	+	0.699971i	0.0771260	+	0.997021i	$0.475426\pi$
$572$	−0.135770	+	0.170250i	−0.00567682	+	0.00711850i
$573$	−3.09008	+	4.74719i	−0.129090	+	0.198317i
$574$	11.5386	+	0.370021i	0.481612	+	0.0154444i
$575$	−5.49079	+	3.09235i	−0.228982	+	0.128960i
$576$	−6.81161	+	0.437320i	−0.283817	+	0.0182217i
$577$		−	34.3610i		−	1.43047i	−0.698886	−	0.715233i	$-0.746321\pi$
$577$		−	34.3610i		−	1.43047i	0.698886	−	0.715233i	$-0.253679\pi$
$578$	0.572423	+	8.91595i	0.0238097	+	0.370855i
$579$	−6.51593	−	0.628584i	−0.270793	−	0.0261231i
$580$	21.8857	+	33.6223i	0.908755	+	1.39609i
$581$	5.81828	+	9.59787i	0.241383	+	0.398187i
$582$	7.65443	+	6.51631i	0.317286	+	0.270110i
$583$	−1.06102	−	2.62075i	−0.0439431	−	0.108540i
$584$	−4.13951	−	0.533730i	−0.171294	−	0.0220859i
$585$	−1.45087	+	6.35668i	−0.0599861	+	0.262816i
$586$	−13.3421	+	5.90615i	−0.551157	+	0.243981i
$587$	−4.25883	+	1.11680i	−0.175781	+	0.0460952i	−0.340496	−	0.940246i	$-0.610595\pi$
$587$	−4.25883	+	1.11680i	−0.175781	+	0.0460952i	0.164715	+	0.986341i	$0.447330\pi$
$588$	−8.51976	−	3.13535i	−0.351349	−	0.129300i
$589$	1.15925	+	8.99093i	0.0477661	+	0.370465i
$590$	−30.3983			−1.25148
$591$	−6.96294	−	33.4246i	−0.286417	−	1.37490i
$592$	−0.0981819			−0.00403525
$593$	0.416190	+	3.22789i	0.0170909	+	0.132553i	0.998118	−	0.0613146i	$-0.0195293\pi$
$593$	0.416190	+	3.22789i	0.0170909	+	0.132553i	−0.981028	+	0.193868i	$0.937897\pi$
$594$	0.0298732	+	0.0109936i	0.00122571	+	0.000451073i
$595$	14.3643	−	3.76677i	0.588880	−	0.154422i
$596$	−15.3933	+	6.81418i	−0.630536	+	0.279120i
$597$	−10.7234	+	46.9824i	−0.438881	+	1.92286i
$598$	0.645255	+	0.0831965i	0.0263865	+	0.00340216i
$599$	−10.0703	−	24.8738i	−0.411460	−	1.01632i	−0.980940	−	0.194310i	$-0.937753\pi$
$599$	−10.0703	−	24.8738i	−0.411460	−	1.01632i	0.569480	−	0.822005i	$-0.307145\pi$
$600$	−23.9838	−	20.4177i	−0.979133	−	0.833548i
$601$	−9.80029	−	16.1666i	−0.399762	−	0.659450i	0.589138	−	0.808033i	$-0.299468\pi$
$601$	−9.80029	−	16.1666i	−0.399762	−	0.659450i	−0.988900	+	0.148583i	$0.952529\pi$
$602$	10.5529	+	16.2121i	0.430103	+	0.660754i
$603$	30.3100	+	2.92397i	1.23432	+	0.119073i
$604$	0.134205	+	2.09035i	0.00546072	+	0.0850552i
$605$			34.7472i			1.41268i
$606$	5.44541	−	0.349607i	0.221205	−	0.0142018i
$607$	21.2227	−	11.9524i	0.861403	−	0.485133i	0.00412796	−	0.999991i	$-0.498686\pi$
$607$	21.2227	−	11.9524i	0.861403	−	0.485133i	0.857275	+	0.514858i	$0.172155\pi$
$608$	31.9900	+	1.02586i	1.29737	+	0.0416040i
$609$	24.3509	−	37.4096i	0.986750	−	1.51591i
$610$	17.7846	−	22.3012i	0.720077	−	0.902948i
$611$	0.495492	−	0.395141i	0.0200454	−	0.0159857i
$612$	−8.34590	−	4.35405i	−0.337363	−	0.176002i
$613$	−11.9070	+	10.1365i	−0.480917	+	0.409411i	−0.855516	−	0.517776i	$-0.826760\pi$
$613$	−11.9070	+	10.1365i	−0.480917	+	0.409411i	0.374599	+	0.927187i	$0.377780\pi$
$614$	−7.05790	−	2.34338i	−0.284834	−	0.0945713i
$615$	−1.82999	−	57.0657i	−0.0737922	−	2.30111i
$616$	−0.771187	+	0.849163i	−0.0310720	+	0.0342137i
$617$	13.5261	−	2.63421i	0.544542	−	0.106049i	0.0886136	−	0.996066i	$-0.471756\pi$
$617$	13.5261	−	2.63421i	0.544542	−	0.106049i	0.455928	+	0.890017i	$0.349307\pi$
$618$	−14.4432	−	25.6454i	−0.580993	−	1.03161i
$619$	44.8004	−	5.77637i	1.80068	−	0.232172i	0.846707	−	0.532060i	$-0.178582\pi$
$619$	44.8004	−	5.77637i	1.80068	−	0.232172i	0.953974	+	0.299888i	$0.0969493\pi$
$620$	−0.733150	+	7.59987i	−0.0294440	+	0.305218i
$621$	0.0479428	+	0.246176i	0.00192388	+	0.00987871i
$622$	15.4910	−	15.9957i	0.621131	−	0.641369i
$623$	14.9095	+	19.9774i	0.597337	+	0.800377i
$624$	−0.382580	−	1.67619i	−0.0153155	−	0.0671015i
$625$	2.37085	+	24.5763i	0.0948340	+	0.983054i
$626$	5.48017	−	1.62649i	0.219032	−	0.0650075i
$627$	2.55073	+	1.22836i	0.101866	+	0.0490562i
$628$	−10.7109	−	6.03224i	−0.427410	−	0.240713i
$629$	0.186262	+	0.112913i	0.00742673	+	0.00450213i
$630$	−4.10746	+	13.8394i	−0.163645	+	0.551375i
$631$	−24.7903	−	24.0080i	−0.986885	−	0.955745i	0.0121387	−	0.999926i	$-0.496136\pi$
$631$	−24.7903	−	24.0080i	−0.986885	−	0.955745i	−0.999024	+	0.0441817i	$0.985932\pi$
$632$	1.21123	−	37.7707i	0.0481803	−	1.50244i
$633$	−4.29398	+	11.6681i	−0.170670	+	0.463767i
$634$	3.46697	−	2.25675i	0.137691	−	0.0896268i
$635$	18.8556	+	17.1241i	0.748261	+	0.679551i
$636$	44.8652	+	13.3158i	1.77902	+	0.528005i
$637$	−0.346665	+	1.78005i	−0.0137354	+	0.0705283i
$638$	0.788562	+	1.13046i	0.0312195	+	0.0447555i
$639$	−0.316439	+	0.0511594i	−0.0125181	+	0.00202384i
$640$	30.6396	+	8.03465i	1.21114	+	0.317597i
$641$	19.1115	+	13.3313i	0.754858	+	0.526556i	0.885368	−	0.464891i	$-0.153906\pi$
$641$	19.1115	+	13.3313i	0.754858	+	0.526556i	−0.130510	+	0.991447i	$0.541661\pi$
$642$	−0.308345	−	0.124835i	−0.0121694	−	0.00492685i
$643$	7.68098	+	23.1339i	0.302908	+	0.912311i	0.983697	+	0.179832i	$0.0575553\pi$
$643$	7.68098	+	23.1339i	0.302908	+	0.912311i	−0.680789	+	0.732479i	$0.738363\pi$
$644$	−3.72863	−	0.726150i	−0.146928	−	0.0286143i
$645$	76.6703	−	57.2206i	3.01889	−	2.25306i
$646$	−7.55263	−	4.91622i	−0.297154	−	0.193426i
$647$	−2.21264	−	8.43775i	−0.0869878	−	0.331722i	0.909475	−	0.415759i	$-0.136484\pi$
$647$	−2.21264	−	8.43775i	−0.0869878	−	0.331722i	−0.996463	+	0.0840367i	$0.973219\pi$
$648$	−20.2187	+	12.2567i	−0.794267	+	0.481489i
$649$	2.75276	−	0.0882756i	0.108055	−	0.00346512i
$650$	−1.37093	+	2.26149i	−0.0537722	+	0.0887029i
$651$	8.06240	−	2.67690i	0.315990	−	0.104916i
$652$	0.963510	+	2.61817i	0.0377340	+	0.102535i
$653$	−10.0369	−	7.49074i	−0.392775	−	0.293135i	0.383487	−	0.923546i	$-0.374723\pi$
$653$	−10.0369	−	7.49074i	−0.392775	−	0.293135i	−0.776262	+	0.630411i	$0.782886\pi$
$654$	21.3750	+	23.5363i	0.835829	+	0.920341i
$655$	−39.7917	+	38.5361i	−1.55479	+	1.50573i
$656$	3.43313	+	6.58066i	0.134041	+	0.256932i
$657$	4.46626	−	1.64362i	0.174245	−	0.0641239i
$658$	1.15085	−	0.802784i	0.0448649	−	0.0312958i
$659$	−35.4265	+	8.08586i	−1.38002	+	0.314981i	−0.847212	−	0.531256i	$-0.821720\pi$
$659$	−35.4265	+	8.08586i	−1.38002	+	0.314981i	−0.532808	+	0.846236i	$0.678863\pi$
$660$	1.86423	+	1.48668i	0.0725652	+	0.0578688i
$661$	1.13120	+	2.55540i	0.0439986	+	0.0993935i	0.935060	−	0.354488i	$-0.115345\pi$
$661$	1.13120	+	2.55540i	0.0439986	+	0.0993935i	−0.891062	+	0.453882i	$0.850039\pi$
$662$	2.30426	−	2.70672i	0.0895577	−	0.105200i
$663$	−1.20189	+	3.61990i	−0.0466776	+	0.140585i
$664$	6.69752	−	11.8921i	0.259914	−	0.461504i
$665$	13.6767	−	33.7817i	0.530359	−	1.31000i
$666$	−0.187731	+	0.0979389i	−0.00727441	+	0.00379506i
$667$	−4.39584	+	9.93027i	−0.170207	+	0.384502i
$668$	−13.5394	−	28.1149i	−0.523856	−	1.08780i
$669$	−5.86442	−	0.948114i	−0.226732	−	0.0366562i
$670$	22.4510	+	9.93839i	0.867357	+	0.383953i
$671$	−1.54575	+	2.07116i	−0.0596729	+	0.0799562i
$672$	−4.78694	−	29.6089i	−0.184660	−	1.14219i
$673$	−21.5507	+	2.07897i	−0.830717	+	0.0801383i	−0.502622	−	0.864506i	$-0.667631\pi$
$673$	−21.5507	+	2.07897i	−0.830717	+	0.0801383i	−0.328095	+	0.944645i	$0.606407\pi$
$674$	−8.02559	−	10.0638i	−0.309134	−	0.387642i
$675$	−0.993907	−	0.226853i	−0.0382555	−	0.00873157i
$676$	16.8064	−	6.80414i	0.646398	−	0.261698i
$677$	8.89401	+	10.4474i	0.341825	+	0.401527i	0.905415	−	0.424528i	$-0.139560\pi$
$677$	8.89401	+	10.4474i	0.341825	+	0.401527i	−0.563590	+	0.826054i	$0.690580\pi$
$678$	2.14792	−	4.46021i	0.0824905	−	0.171293i
$679$	−6.70791	+	9.61630i	−0.257426	+	0.369040i
$680$	−12.5627	−	12.9720i	−0.481758	−	0.497455i
$681$	0.616148	−	3.81109i	0.0236108	−	0.146041i
$682$	−0.0168069	+	0.261781i	−0.000643569	+	0.0100241i
$683$	−26.9304	−	1.72899i	−1.03046	−	0.0661579i	−0.460361	−	0.887732i	$-0.652280\pi$
$683$	−26.9304	−	1.72899i	−1.03046	−	0.0661579i	−0.570102	+	0.821574i	$0.693096\pi$
$684$	−20.8147	+	10.0238i	−0.795870	+	0.383271i
$685$	−35.1494	+	31.9217i	−1.34299	+	1.21967i
$686$	−3.78861	+	14.4476i	−0.144650	+	0.551612i
$687$	−0.333315	−	1.12305i	−0.0127167	−	0.0428469i
$688$	−5.75257	+	11.0266i	−0.219315	+	0.420385i
$689$	1.19548	−	9.27193i	0.0455443	−	0.353233i
$690$	0.911000	−	7.06554i	0.0346812	−	0.268980i
$691$	6.50609	−	12.4710i	0.247503	−	0.474417i	−0.730526	−	0.682885i	$-0.760725\pi$
$691$	6.50609	−	12.4710i	0.247503	−	0.474417i	0.978029	+	0.208467i	$0.0668475\pi$
$692$	7.80016	+	26.2813i	0.296518	+	0.999066i
$693$	0.331768	−	1.26517i	0.0126028	−	0.0480600i
$694$	−5.16383	+	4.68966i	−0.196016	+	0.178017i
$695$	0.742047	−	0.357351i	0.0281475	−	0.0135551i
$696$	−54.1685	−	3.47773i	−2.05325	−	0.131823i
$697$	1.05500	−	16.4324i	0.0399609	−	0.622423i
$698$	−3.02006	+	18.6801i	−0.114311	+	0.707053i
$699$	−1.31494	−	1.35778i	−0.0497355	−	0.0513560i
$700$	8.83406	−	12.6643i	0.333896	−	0.478665i
$701$	4.21055	−	8.74331i	0.159030	−	0.330230i	−0.806195	−	0.591650i	$-0.798477\pi$
$701$	4.21055	−	8.74331i	0.159030	−	0.330230i	0.965225	+	0.261420i	$0.0841909\pi$
$702$	0.0682269	+	0.0801432i	0.00257506	+	0.00302481i
$703$	0.495496	−	0.200604i	0.0186880	−	0.00756592i
$704$	0.486131	+	0.110956i	0.0183217	+	0.00418182i
$705$	−4.32679	−	5.42562i	−0.162956	−	0.204341i
$706$	−1.75876	+	0.169666i	−0.0661919	+	0.00638545i
$707$	1.01575	+	6.28275i	0.0382011	+	0.236287i
$708$	−27.2665	+	36.5347i	−1.02474	+	1.37306i
$709$	−5.63198	−	2.49311i	−0.211514	−	0.0936308i	0.296310	−	0.955092i	$-0.404244\pi$
$709$	−5.63198	−	2.49311i	−0.211514	−	0.0936308i	−0.507824	+	0.861461i	$0.669550\pi$
$710$	−0.255144	−	0.0412497i	−0.00957539	−	0.00154807i
$711$	18.6959	+	38.8225i	0.701152	+	1.45596i
$712$	12.2702	−	27.7186i	0.459845	−	1.03880i
$713$	−1.83242	+	0.955974i	−0.0686248	+	0.0358015i
$714$	−3.16911	+	7.82775i	−0.118601	+	0.292946i
$715$	0.233737	−	0.415024i	0.00874126	−	0.0155210i
$716$	−2.58261	+	7.77840i	−0.0965165	+	0.290692i
$717$	−12.6199	+	14.8240i	−0.471298	+	0.553614i
$718$	−3.93293	−	8.88455i	−0.146775	−	0.331568i
$719$	22.8029	+	18.1847i	0.850404	+	0.678175i	0.948422	−	0.317010i	$-0.102679\pi$
$719$	22.8029	+	18.1847i	0.850404	+	0.678175i	−0.0980181	+	0.995185i	$0.531250\pi$
$720$	−9.04872	+	2.06531i	−0.337226	+	0.0769696i
$721$	28.1558	−	19.6402i	1.04858	−	0.731441i
$722$	−7.53357	+	2.77242i	−0.280370	+	0.103179i
$723$	19.7764	+	37.9077i	0.735493	+	1.40980i
$724$	−15.8506	+	15.3504i	−0.589081	+	0.570493i
$725$	−29.6774	−	32.6781i	−1.10219	−	1.21364i
$726$	−15.8361	−	11.8188i	−0.587731	−	0.438635i
$727$	−3.82383	−	10.3906i	−0.141818	−	0.385366i	0.847566	−	0.530690i	$-0.178067\pi$
$727$	−3.82383	−	10.3906i	−0.141818	−	0.385366i	−0.989384	+	0.145324i	$0.953577\pi$
$728$	−3.59959	+	1.19515i	−0.133410	+	0.0442951i
$729$	13.2136	−	21.7971i	0.489391	−	0.807302i
$730$	3.83528	−	0.122990i	0.141950	−	0.00455206i
$731$	23.5942	−	14.3030i	0.872664	−	0.529014i
$732$	−10.8507	−	41.3783i	−0.401052	−	1.52939i
$733$	27.2266	+	17.7226i	1.00564	+	0.654598i	0.939263	−	0.343197i	$-0.111510\pi$
$733$	27.2266	+	17.7226i	1.00564	+	0.654598i	0.0663745	+	0.997795i	$0.478857\pi$
$734$	22.5188	−	16.8062i	0.831184	−	0.620329i
$735$	19.4915	+	3.79598i	0.718957	+	0.140017i
$736$	2.29938	+	6.92536i	0.0847563	+	0.255272i
$737$	−2.06194	−	0.834787i	−0.0759526	−	0.0307498i
$738$	13.1287	+	9.15805i	0.483276	+	0.337112i
$739$	23.5963	+	6.18767i	0.868002	+	0.227617i	0.660691	−	0.750658i	$-0.270263\pi$
$739$	23.5963	+	6.18767i	0.868002	+	0.227617i	0.207311	+	0.978275i	$0.433529\pi$
$740$	0.444456	−	0.0718563i	0.0163385	−	0.00264149i
$741$	5.35555	+	7.67759i	0.196741	+	0.282043i
$742$	3.95672	−	20.3169i	0.145256	−	0.745858i
$743$	−40.6176	−	12.0551i	−1.49011	−	0.442258i	−0.566010	−	0.824398i	$-0.691514\pi$
$743$	−40.6176	−	12.0551i	−1.49011	−	0.442258i	−0.924104	+	0.382140i	$0.875187\pi$
$744$	−7.64741	−	6.94517i	−0.280368	−	0.254622i
$745$	30.8605	−	20.0879i	1.13064	−	0.735965i
$746$	−7.36880	+	20.0234i	−0.269791	+	0.733109i
$747$	−0.498801	+	15.5545i	−0.0182502	+	0.569108i
$748$	0.493991	+	0.478404i	0.0180621	+	0.0174922i
$749$	0.110395	−	0.371958i	0.00403375	−	0.0135911i
$750$	0.299272	+	0.181421i	0.0109279	+	0.00662455i
$751$	1.41433	+	0.796536i	0.0516097	+	0.0290660i	0.516307	−	0.856403i	$-0.327306\pi$
$751$	1.41433	+	0.796536i	0.0516097	+	0.0290660i	−0.464697	+	0.885470i	$0.653837\pi$
$752$	0.812811	+	0.391429i	0.0296402	+	0.0142740i
$753$	−13.2044	+	3.91899i	−0.481195	+	0.142816i
$754$	0.437615	+	4.53634i	0.0159370	+	0.165204i
$755$	−1.01954	−	4.46691i	−0.0371050	−	0.162567i
$756$	−0.367561	−	0.492498i	−0.0133681	−	0.0179120i
$757$	−27.8882	+	28.7969i	−1.01361	+	1.04664i	−0.0147080	+	0.999892i	$0.504682\pi$
$757$	−27.8882	+	28.7969i	−1.01361	+	1.04664i	−0.998907	+	0.0467485i	$0.985114\pi$
$758$	3.54320	+	18.1936i	0.128695	+	0.660821i
$759$	−0.0619788	+	0.642475i	−0.00224969	+	0.0233204i
$760$	−43.9549	+	5.66735i	−1.59441	+	0.205576i
$761$	−6.99588	−	12.4219i	−0.253600	−	0.450293i	0.714927	−	0.699199i	$-0.246460\pi$
$761$	−6.99588	−	12.4219i	−0.253600	−	0.450293i	−0.968528	+	0.248906i	$0.919929\pi$
$762$	−14.2178	+	2.76891i	−0.515056	+	0.100307i
$763$	−24.9308	+	27.4515i	−0.902554	+	0.993812i
$764$	0.108228	+	3.37495i	0.00391556	+	0.122102i
$765$	19.5416	+	6.48825i	0.706527	+	0.234583i
$766$	−21.7639	+	18.5279i	−0.786361	+	0.669439i
$767$	8.07392	+	4.21216i	0.291532	+	0.152092i
$768$	−22.9832	+	18.3285i	−0.829334	+	0.661372i
$769$	8.57138	−	10.7482i	0.309092	−	0.387589i	−0.602887	−	0.797827i	$-0.705983\pi$
$769$	8.57138	−	10.7482i	0.309092	−	0.387589i	0.911979	+	0.410238i	$0.134554\pi$
$770$	0.575320	−	0.883846i	0.0207331	−	0.0318516i
$771$	−17.8024	−	0.570888i	−0.641137	−	0.0205600i
$772$	−3.40024	+	1.91498i	−0.122377	+	0.0689215i
$773$	−14.5071	+	0.931389i	−0.521785	+	0.0334997i	−0.322735	−	0.946490i	$-0.604602\pi$
$773$	−14.5071	+	0.931389i	−0.521785	+	0.0334997i	−0.199051	+	0.979989i	$0.563786\pi$
$774$			26.8220i			0.964095i
$775$	−0.538268	−	8.38395i	−0.0193351	−	0.301161i
$776$	14.1918	+	1.36907i	0.509456	+	0.0491467i
$777$	−0.273281	−	0.419833i	−0.00980391	−	0.0150614i
$778$	−5.12214	−	8.44950i	−0.183637	−	0.302929i
$779$	−30.7715	−	26.1962i	−1.10250	−	0.938575i
$780$	2.95865	+	7.30791i	0.105937	+	0.261665i
$781$	0.0232247	+	0.00299450i	0.000831046	+	0.000107151i
$782$	0.457186	−	2.00306i	0.0163489	−	0.0716294i
$783$	−1.60649	+	0.711143i	−0.0574111	+	0.0254142i
$784$	−2.49708	+	0.654811i	−0.0891814	+	0.0233861i
$785$	25.2342	+	9.28640i	0.900646	+	0.331446i
$786$	−4.02829	−	31.2426i	−0.143684	−	1.11439i
$787$	−42.4707			−1.51392			−0.756959	−	0.653462i	$-0.773316\pi$
$787$	−42.4707			−1.51392			−0.756959	+	0.653462i	$0.773316\pi$
$788$	−14.8042	−	13.9676i	−0.527376	−	0.497576i
$789$	−4.69229			−0.167050
$790$	4.44286	+	34.4579i	0.158070	+	1.22596i
$791$	5.41869	+	1.99413i	0.192666	+	0.0709030i
$792$	−1.53850	+	0.403442i	−0.0546681	+	0.0143357i
$793$	−7.81384	+	3.45896i	−0.277478	+	0.122831i
$794$	−1.88672	+	8.26628i	−0.0669573	+	0.293359i
$795$	−101.528	−	13.0905i	−3.60081	−	0.464273i
$796$	10.7807	+	26.6286i	0.382112	+	0.943824i
$797$	−11.0600	−	9.41554i	−0.391766	−	0.333516i	0.430529	−	0.902577i	$-0.358327\pi$
$797$	−11.0600	−	9.41554i	−0.391766	−	0.333516i	−0.822295	+	0.569061i	$0.807307\pi$
$798$	10.7441	+	17.7235i	0.380337	+	0.627405i
$799$	−1.09183	−	1.67735i	−0.0386262	−	0.0593403i
$800$	−29.5245	−	2.84820i	−1.04385	−	0.100699i
$801$	2.21452	+	34.4930i	0.0782463	+	1.21875i
$802$			14.8422i			0.524097i
$803$	−0.346952	+	0.0222750i	−0.0122437	+	0.000786069i
$804$	32.0826	−	18.0686i	1.13147	−	0.637230i
$805$	8.30484	+	0.266320i	0.292707	+	0.00938655i
$806$	−0.473172	+	0.726919i	−0.0166668	+	0.0256046i
$807$	−36.6416	+	45.9471i	−1.28985	+	1.61742i
$808$	6.05079	−	4.82535i	0.212866	−	0.169755i
$809$	29.7397	+	15.5152i	1.04559	+	0.545484i	0.896364	−	0.443319i	$-0.146199\pi$
$809$	29.7397	+	15.5152i	1.04559	+	0.545484i	0.149227	+	0.988803i	$0.452322\pi$
$810$	16.5518	−	14.0908i	0.581571	−	0.495098i
$811$	13.9640	+	4.63636i	0.490341	+	0.162804i	0.549583	−	0.835439i	$-0.314787\pi$
$811$	13.9640	+	4.63636i	0.490341	+	0.162804i	−0.0592418	+	0.998244i	$0.518868\pi$
$812$	−0.852878	−	26.5959i	−0.0299301	−	0.933332i
$813$	7.27341	−	8.00883i	0.255090	−	0.280882i
$814$	0.0151831	−	0.00295692i	0.000532169	−	0.000103640i
$815$	−2.99455	−	5.31713i	−0.104894	−	0.186251i
$816$	−5.38495	+	0.694312i	−0.188511	+	0.0243058i
$817$	6.50215	−	67.4016i	0.227482	−	2.35808i
$818$	4.81233	+	24.7103i	0.168259	+	0.863976i
$819$	3.00863	−	3.10665i	0.105130	−	0.108555i
$820$	−20.3575	−	27.2772i	−0.710914	−	0.952560i
$821$	5.21248	+	22.8374i	0.181917	+	0.797030i	0.980717	+	0.195433i	$0.0626113\pi$
$821$	5.21248	+	22.8374i	0.181917	+	0.797030i	−0.798800	+	0.601596i	$0.794532\pi$
$822$	−2.59280	−	26.8770i	−0.0904341	−	0.937444i
$823$	15.7149	−	4.66411i	0.547788	−	0.162581i	0.00122606	−	0.999999i	$-0.499610\pi$
$823$	15.7149	−	4.66411i	0.547788	−	0.162581i	0.546562	+	0.837419i	$0.315936\pi$
$824$	−37.6113	−	18.1127i	−1.31025	−	0.630984i
$825$	−2.28606	−	1.28749i	−0.0795905	−	0.0448246i
$826$	17.2420	+	10.4522i	0.599925	+	0.363678i
$827$	1.67481	−	5.64300i	0.0582390	−	0.196226i	−0.924515	−	0.381147i	$-0.875529\pi$
$827$	1.67481	−	5.64300i	0.0582390	−	0.196226i	0.982754	+	0.184920i	$0.0592027\pi$
$828$	−3.78364	−	3.66425i	−0.131491	−	0.127342i
$829$	−0.757761	+	23.6298i	−0.0263181	+	0.820696i	0.898207	+	0.439574i	$0.144870\pi$
$829$	−0.757761	+	23.6298i	−0.0263181	+	0.820696i	−0.924525	+	0.381122i	$0.875538\pi$
$830$	−4.33363	+	11.7759i	−0.150423	+	0.408747i
$831$	27.5660	−	17.9435i	0.956254	−	0.622453i
$832$	1.22051	+	1.10843i	0.0423136	+	0.0384281i
$833$	5.49028	+	1.62949i	0.190227	+	0.0564584i
$834$	−0.0895336	+	0.459736i	−0.00310029	+	0.0159194i
$835$	39.0511	+	55.9827i	1.35142	+	1.93736i
$836$	1.66608	−	0.269359i	0.0576225	−	0.00931596i
$837$	−0.323425	−	0.0848119i	−0.0111792	−	0.00293153i
$838$	22.2267	+	15.5044i	0.767808	+	0.535590i
$839$	10.4923	+	4.24787i	0.362235	+	0.146653i	0.549151	−	0.835723i	$-0.314951\pi$
$839$	10.4923	+	4.24787i	0.362235	+	0.146653i	−0.186916	+	0.982376i	$0.559849\pi$
$840$	13.0868	+	39.4155i	0.451539	+	1.35996i
$841$	−46.2038	−	8.99819i	−1.59324	−	0.310282i
$842$	7.40438	−	5.52603i	0.255172	−	0.190440i
$843$	−58.0614	−	37.7938i	−1.99974	−	1.30169i
$844$	1.88005	+	7.16944i	0.0647139	+	0.246782i
$845$	−33.9151	+	20.5596i	−1.16672	+	0.707270i
$846$	1.94461	−	0.0623599i	0.0668571	−	0.00214398i
$847$	11.9475	−	19.7087i	0.410522	−	0.677199i
$848$	12.6299	−	4.19341i	0.433712	−	0.144002i
$849$	−12.3571	−	33.5783i	−0.424095	−	1.15240i
$850$	6.69302	+	4.99513i	0.229569	+	0.171332i
$851$	0.0819363	+	0.0902210i	0.00280874	+	0.00309274i
$852$	−0.278435	+	0.269649i	−0.00953902	+	0.00923802i
$853$	14.7171	+	28.2099i	0.503904	+	0.965890i	0.995472	+	0.0950508i	$0.0303014\pi$
$853$	14.7171	+	28.2099i	0.503904	+	0.965890i	−0.491568	+	0.870839i	$0.663576\pi$
$854$	−17.7555	+	6.53420i	−0.607581	+	0.223596i
$855$	41.4465	−	28.9113i	1.41744	−	0.988745i
$856$	−0.459986	+	0.104989i	−0.0157220	+	0.00358845i
$857$	2.00703	+	1.60056i	0.0685590	+	0.0546740i	0.657170	−	0.753743i	$-0.271753\pi$
$857$	2.00703	+	1.60056i	0.0685590	+	0.0546740i	−0.588611	+	0.808417i	$0.700325\pi$
$858$	0.109645	+	0.247690i	0.00374322	+	0.00845599i
$859$	7.54944	−	8.86800i	0.257583	−	0.302572i	−0.617474	−	0.786591i	$-0.711844\pi$
$859$	7.54944	−	8.86800i	0.257583	−	0.302572i	0.875057	+	0.484019i	$0.160823\pi$
$860$	17.9711	−	54.1261i	0.612809	−	1.84568i
$861$	−18.5836	+	32.9970i	−0.633327	+	1.12454i
$862$	3.92845	−	9.70335i	0.133804	−	0.330497i
$863$	−16.7277	+	8.72685i	−0.569419	+	0.297065i	−0.722750	−	0.691109i	$-0.757122\pi$
$863$	−16.7277	+	8.72685i	−0.569419	+	0.297065i	0.153331	+	0.988175i	$0.451000\pi$
$864$	−0.477847	+	1.07947i	−0.0162567	+	0.0367242i
$865$	−26.0180	−	54.0270i	−0.884640	−	1.83697i
$866$	−4.71315	−	0.761985i	−0.160159	−	0.0258933i
$867$	−26.7994	−	11.8633i	−0.910155	−	0.402898i
$868$	3.02899	−	4.05858i	0.102811	−	0.137757i
$869$	−0.502394	−	3.10748i	−0.0170425	−	0.105414i
$870$	49.6728	−	4.79188i	1.68407	−	0.162460i
$871$	−4.58596	−	5.75062i	−0.155389	−	0.194852i
$872$	43.9633	+	10.0343i	1.48879	+	0.339806i
$873$	−15.0690	+	6.10078i	−0.510010	+	0.206480i
$874$	−3.26862	−	3.83951i	−0.110563	−	0.129873i
$875$	−0.177105	+	0.367762i	−0.00598723	+	0.0124326i
$876$	3.29233	−	4.71981i	0.111238	−	0.159467i
$877$	27.8345	+	28.7414i	0.939905	+	0.970529i	0.999617	−	0.0276867i	$-0.00881408\pi$
$877$	27.8345	+	28.7414i	0.939905	+	0.970529i	−0.0597118	+	0.998216i	$0.519018\pi$
$878$	−2.02658	+	12.5351i	−0.0683939	+	0.423040i
$879$	3.06662	−	47.7650i	0.103434	−	1.61107i
$880$	0.676643	+	0.0434419i	0.0228096	+	0.00146443i
$881$	19.4293	−	9.35667i	0.654591	−	0.315234i	−0.0769472	−	0.997035i	$-0.524517\pi$
$881$	19.4293	−	9.35667i	0.654591	−	0.315234i	0.731538	+	0.681801i	$0.238803\pi$
$882$	−4.12140	+	3.74294i	−0.138775	+	0.126031i
$883$	−8.53160	+	32.5347i	−0.287111	+	1.09488i	0.653921	+	0.756563i	$0.273123\pi$
$883$	−8.53160	+	32.5347i	−0.287111	+	1.09488i	−0.941032	+	0.338317i	$0.890142\pi$
$884$	0.646954	+	2.17980i	0.0217594	+	0.0733147i
$885$	46.1231	−	88.4093i	1.55041	−	2.97185i
$886$	0.0283185	−	0.219632i	0.000951377	−	0.00737870i
$887$	−0.319518	+	2.47812i	−0.0107284	+	0.0832071i	−0.996281	−	0.0861611i	$-0.972540\pi$
$887$	−0.319518	+	2.47812i	−0.0107284	+	0.0832071i	0.985553	+	0.169368i	$0.0541727\pi$
$888$	−0.281761	+	0.540084i	−0.00945529	+	0.0181240i
$889$	−4.80694	−	16.1962i	−0.161220	−	0.543202i
$890$	−7.06907	+	26.9574i	−0.236956	+	0.903614i
$891$	−1.45795	+	1.32407i	−0.0488432	+	0.0443581i
$892$	−3.19067	+	1.53655i	−0.106832	+	0.0514474i
$893$	−4.90179	−	0.314705i	−0.164032	−	0.0105312i
$894$	−1.34165	+	20.8973i	−0.0448715	+	0.698910i
$895$	2.86123	−	17.6977i	0.0956405	−	0.591570i
$896$	−14.6162	−	15.0924i	−0.488293	−	0.504203i
$897$	−1.22101	+	1.75040i	−0.0407682	+	0.0584443i
$898$	7.76179	−	16.1175i	0.259014	−	0.537849i
$899$	−9.38494	−	11.0241i	−0.313005	−	0.367674i
$900$	19.8453	−	8.03449i	0.661511	−	0.267816i
$901$	−28.7828	−	6.56949i	−0.958894	−	0.218861i
$902$	−0.729097	−	0.914259i	−0.0242763	−	0.0304415i
$903$	−63.1624	+	6.09320i	−2.10191	+	0.202769i
$904$	−1.12061	−	6.93135i	−0.0372709	−	0.230533i
$905$	28.8677	−	38.6801i	0.959595	−	1.28577i
$906$	2.38258	+	1.05470i	0.0791558	+	0.0350399i
$907$	26.1318	+	4.22478i	0.867692	+	0.140282i	0.577207	−	0.816598i	$-0.304143\pi$
$907$	26.1318	+	4.22478i	0.867692	+	0.140282i	0.290485	+	0.956880i	$0.406183\pi$
$908$	−0.998550	−	2.07351i	−0.0331380	−	0.0688118i
$909$	−3.57205	+	8.06931i	−0.118477	+	0.267642i
$910$	3.09158	−	1.61287i	0.102485	−	0.0534662i
$911$	2.34877	−	5.80151i	0.0778182	−	0.192213i	−0.883012	−	0.469351i	$-0.844488\pi$
$911$	2.34877	−	5.80151i	0.0778182	−	0.192213i	0.960830	+	0.277138i	$0.0893860\pi$
$912$	−6.53895	+	11.6106i	−0.216526	+	0.384464i
$913$	0.358241	−	1.07897i	0.0118561	−	0.0357085i
$914$	10.8371	−	12.7299i	0.358460	−	0.421067i
$915$	37.8755	+	85.5614i	1.25213	+	2.82857i
$916$	−0.545993	−	0.435415i	−0.0180401	−	0.0143865i
$917$	35.8203	−	8.17574i	1.18289	−	0.269987i
$918$	0.272611	−	0.190161i	0.00899749	−	0.00627626i
$919$	41.1096	−	15.1287i	1.35608	−	0.499051i	0.439264	−	0.898358i	$-0.355239\pi$
$919$	41.1096	−	15.1287i	1.35608	−	0.499051i	0.916817	+	0.399307i	$0.130749\pi$
$920$	−4.67357	−	8.95836i	−0.154083	−	0.295348i
$921$	17.5243	−	16.9713i	0.577446	−	0.559225i
$922$	−9.85215	−	10.8483i	−0.324463	−	0.357270i
$923$	0.0620516	+	0.0463103i	0.00204245	+	0.00152432i
$924$	−0.546216	−	1.48425i	−0.0179692	−	0.0488281i
$925$	−0.470163	+	0.156105i	−0.0154589	+	0.00513269i
$926$	1.91477	−	3.15861i	0.0629232	−	0.103798i
$927$	47.5752	−	1.52565i	1.56258	−	0.0501088i
$928$	−43.7114	+	26.4981i	−1.43490	+	0.869843i
$929$	4.05698	+	15.4710i	0.133105	+	0.507588i	0.999959	+	0.00902605i	$0.00287312\pi$
$929$	4.05698	+	15.4710i	0.133105	+	0.507588i	−0.866854	+	0.498562i	$0.833862\pi$
$930$	7.95976	+	5.18123i	0.261011	+	0.169899i
$931$	11.2641	−	8.40664i	0.369167	−	0.275517i
$932$	−1.10600	−	0.215393i	−0.0362282	−	0.00705544i
$933$	23.0170	+	69.3235i	0.753542	+	2.26955i
$934$	−13.4058	−	5.42739i	−0.438650	−	0.177590i
$935$	−1.23370	−	0.860578i	−0.0403464	−	0.0281439i
$936$	−5.08701	−	1.33397i	−0.166274	−	0.0436022i
$937$	43.1565	−	6.97721i	1.40986	−	0.227935i	0.593201	−	0.805054i	$-0.297864\pi$
$937$	43.1565	−	6.97721i	1.40986	−	0.227935i	0.816660	+	0.577119i	$0.195823\pi$
$938$	−9.31702	−	13.3566i	−0.304212	−	0.436110i
$939$	−3.58460	+	18.4062i	−0.116979	+	0.600663i
$940$	−3.96596	−	1.17708i	−0.129355	−	0.0383920i
$941$	2.36996	+	2.15234i	0.0772585	+	0.0701641i	0.710014	−	0.704187i	$-0.248688\pi$
$941$	2.36996	+	2.15234i	0.0772585	+	0.0701641i	−0.632756	+	0.774352i	$0.718076\pi$
$942$	−12.8153	+	8.34184i	−0.417545	+	0.271792i
$943$	3.18201	−	8.64655i	0.103621	−	0.281571i
$944$	−0.415493	+	12.9566i	−0.0135231	+	0.421701i
$945$	0.965619	+	0.935150i	0.0314116	+	0.0304204i
$946$	0.557510	−	1.87844i	0.0181262	−	0.0610732i
$947$	−6.07412	−	3.68217i	−0.197382	−	0.119654i	0.416237	−	0.909256i	$-0.363349\pi$
$947$	−6.07412	−	3.68217i	−0.197382	−	0.119654i	−0.613620	+	0.789602i	$0.710287\pi$
$948$	45.3989	+	25.5682i	1.47449	+	0.830416i
$949$	−1.03571	−	0.498771i	−0.0336205	−	0.0161908i
$950$	19.6494	−	5.83183i	0.637509	−	0.189209i
$951$	1.30304	+	13.5073i	0.0422539	+	0.438006i
$952$	2.66528	+	11.6774i	0.0863822	+	0.378465i
$953$	26.7590	+	35.8546i	0.866809	+	1.16144i	0.985695	+	0.168537i	$0.0539043\pi$
$953$	26.7590	+	35.8546i	0.866809	+	1.16144i	−0.118886	+	0.992908i	$0.537932\pi$
$954$	19.9662	−	20.6167i	0.646429	−	0.667491i
$955$	−1.41191	−	7.24986i	−0.0456883	−	0.234600i
$956$	−1.11441	+	11.5521i	−0.0360427	+	0.373621i
$957$	−4.48428	+	0.578184i	−0.144956	+	0.0186900i
$958$	−3.88333	−	6.89525i	−0.125465	−	0.222776i
$959$	30.9128	−	6.02027i	0.998227	−	0.194405i
$960$	12.1373	−	13.3646i	0.391731	−	0.431339i
$961$	0.905284	+	28.2301i	0.0292027	+	0.910648i
$962$	0.0485403	+	0.0161165i	0.00156500	+	0.000519617i
$963$	0.409644	−	0.348735i	0.0132006	−	0.0112378i
$964$	22.5981	+	11.7894i	0.727835	+	0.379711i
$965$	6.67371	−	5.32211i	0.214834	−	0.171325i
$966$	−2.94614	+	3.69435i	−0.0947906	+	0.118864i
$967$	−5.30671	+	8.15253i	−0.170652	+	0.262168i	−0.913099	−	0.407737i	$-0.866318\pi$
$967$	−5.30671	+	8.15253i	−0.170652	+	0.262168i	0.742447	+	0.669905i	$0.233665\pi$
$968$	−28.0119	−	0.898287i	−0.900337	−	0.0288720i
$969$	25.7577	−	14.5065i	0.827456	−	0.466015i
$970$	−13.0812	+	0.839840i	−0.420011	+	0.0269656i
$971$		−	47.1295i		−	1.51246i	−0.654308	−	0.756229i	$-0.727040\pi$
$971$		−	47.1295i		−	1.51246i	0.654308	−	0.756229i	$-0.272960\pi$
$972$	−2.03249	−	31.6576i	−0.0651920	−	1.01542i
$973$	−0.543763	−	0.0524561i	−0.0174322	−	0.00168167i
$974$	−16.6811	−	25.6267i	−0.534498	−	0.821132i
$975$	−4.49713	−	7.41849i	−0.144024	−	0.237582i
$976$	−9.26229	−	7.88510i	−0.296479	−	0.252396i
$977$	−7.36170	−	18.1835i	−0.235522	−	0.581743i	0.762335	−	0.647183i	$-0.224053\pi$
$977$	−7.36170	−	18.1835i	−0.235522	−	0.581743i	−0.997857	+	0.0654396i	$0.979155\pi$
$978$	3.44183	+	0.443775i	0.110058	+	0.0141904i
$979$	0.561866	−	2.46169i	0.0179573	−	0.0786761i
$980$	10.8247	−	4.79178i	0.345783	−	0.153068i
$981$	−49.7362	+	13.0424i	−1.58795	+	0.416411i
$982$	−18.3900	−	6.76768i	−0.586848	−	0.215965i
$983$	−2.86546	−	22.2239i	−0.0913940	−	0.708834i	−0.971999	−	0.234983i	$-0.924496\pi$
$983$	−2.86546	−	22.2239i	−0.0913940	−	0.708834i	0.880605	−	0.473850i	$-0.157136\pi$
$984$	46.0516			1.46807
$985$	36.8432	+	24.9925i	1.17392	+	0.796328i
$986$	14.3922			0.458341
$987$	0.588611	+	4.56515i	0.0187357	+	0.145310i
$988$	5.23701	+	1.92727i	0.166612	+	0.0613146i
$989$	14.9333	−	3.91596i	0.474850	−	0.124520i
$990$	1.33712	−	0.591904i	0.0424965	−	0.0188120i
$991$	8.21135	−	35.9763i	0.260842	−	1.14282i	−0.659498	−	0.751706i	$-0.729231\pi$
$991$	8.21135	−	35.9763i	0.260842	−	1.14282i	0.920340	−	0.391118i	$-0.127912\pi$
$992$	−9.64840	−	1.24402i	−0.306337	−	0.0394978i
$993$	4.37588	+	10.8085i	0.138864	+	0.342998i
$994$	0.130535	+	0.111126i	0.00414032	+	0.00352470i
$995$	−32.5753	−	53.7363i	−1.03270	−	1.70355i
$996$	10.2659	+	15.7711i	0.325286	+	0.499727i
$997$	−17.9630	−	1.73287i	−0.568895	−	0.0548806i	−0.192429	−	0.981311i	$-0.561636\pi$
$997$	−17.9630	−	1.73287i	−0.568895	−	0.0548806i	−0.376466	+	0.926430i	$0.622861\pi$
$998$	0.985656	+	15.3524i	0.0312004	+	0.485972i
$999$			0.0197164i			0.000623800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.h.a.10.7	✓	672
197.138	even	98	inner	197.2.h.a.138.7	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.h.a.10.7	✓	672	1.1	even	1	trivial
197.2.h.a.138.7	yes	672	197.138	even	98	inner

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.h (of order \(98\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0948264 - 0.735455i) q^{2} +(2.28285 + 0.840110i) q^{3} +(1.40269 - 0.367828i) q^{4} +(-2.90046 + 1.28395i) q^{5} +(0.401389 - 1.75860i) q^{6} +(2.08662 + 0.269040i) q^{7} +(-0.960086 - 2.37143i) q^{8} +(2.22129 + 1.89101i) q^{9} +(1.21932 + 2.01140i) q^{10} +(-0.116259 - 0.178605i) q^{11} +(3.51114 + 0.338716i) q^{12} +(-0.0451466 - 0.703194i) q^{13} -1.56013i q^{14} +(-7.69997 + 0.494354i) q^{15} +(0.873982 - 0.492217i) q^{16} +(-2.22411 - 0.0713227i) q^{17} +(1.18011 - 1.81297i) q^{18} +(-3.40504 + 4.26979i) q^{19} +(-3.59616 + 2.86784i) q^{20} +(4.53742 + 2.36717i) q^{21} +(-0.120331 + 0.102440i) q^{22} +(-1.18168 - 0.392344i) q^{23} +(-0.199470 - 6.22020i) q^{24} +(3.40263 - 3.74667i) q^{25} +(-0.512887 + 0.0998847i) q^{26} +(-0.0988449 - 0.175509i) q^{27} +(3.02583 - 0.390138i) q^{28} +(0.837505 - 8.68162i) q^{29} +(1.09374 + 5.61610i) q^{30} +(1.15479 - 1.19241i) q^{31} +(-3.50530 - 4.69679i) q^{32} +(-0.115354 - 0.505398i) q^{33} +(0.158449 + 1.64249i) q^{34} +(-6.39758 + 1.89877i) q^{35} +(3.81133 + 1.83544i) q^{36} +(-0.0852870 - 0.0480328i) q^{37} +(3.46313 + 2.09937i) q^{38} +(0.487698 - 1.64322i) q^{39} +(5.82948 + 5.64554i) q^{40} +(-0.237173 + 7.39594i) q^{41} +(1.31068 - 3.56154i) q^{42} +(-10.3915 + 6.76412i) q^{43} +(-0.228770 - 0.207763i) q^{44} +(-8.87069 - 2.63278i) q^{45} +(-0.176497 + 0.906275i) q^{46} +(0.514564 + 0.737666i) q^{47} +(2.40869 - 0.389418i) q^{48} +(-2.48947 - 0.652816i) q^{49} +(-3.07817 - 2.14720i) q^{50} +(-5.01738 - 2.03131i) q^{51} +(-0.321981 - 0.969756i) q^{52} +(13.0226 + 2.53616i) q^{53} +(-0.119706 + 0.0893389i) q^{54} +(0.566522 + 0.368765i) q^{55} +(-1.36532 - 5.20658i) q^{56} +(-11.3603 + 6.88668i) q^{57} +(-6.46436 + 0.207299i) q^{58} +(-6.69957 + 11.0516i) q^{59} +(-10.6188 + 3.52569i) q^{60} +(-4.18825 - 11.3808i) q^{61} +(-0.986472 - 0.736223i) q^{62} +(4.12622 + 4.54343i) q^{63} +(-1.68079 + 1.62775i) q^{64} +(1.03381 + 1.98162i) q^{65} +(-0.360759 + 0.132763i) q^{66} +(8.56126 - 5.97196i) q^{67} +(-3.14596 + 0.718045i) q^{68} +(-2.36798 - 1.88840i) q^{69} +(2.00312 + 4.52508i) q^{70} +(-0.0712288 + 0.0836694i) q^{71} +(2.35177 - 7.08316i) q^{72} +(0.800554 - 1.42146i) q^{73} +(-0.0272385 + 0.0672796i) q^{74} +(10.9153 - 5.69451i) q^{75} +(-3.20566 + 7.24165i) q^{76} +(-0.194536 - 0.403958i) q^{77} +(-1.25476 - 0.202860i) q^{78} +(13.5067 + 5.97904i) q^{79} +(-1.90297 + 2.54980i) q^{80} +(-1.47495 - 9.12310i) q^{81} +(5.46187 - 0.526900i) q^{82} +(3.32615 + 4.17086i) q^{83} +(7.23529 + 1.65141i) q^{84} +(6.54250 - 2.64876i) q^{85} +(5.96010 + 7.00107i) q^{86} +(9.20541 - 19.1152i) q^{87} +(-0.311930 + 0.447175i) q^{88} +(8.24270 + 8.51127i) q^{89} +(-1.09511 + 6.77365i) q^{90} +(0.0949835 - 1.47944i) q^{91} +(-1.80184 - 0.115682i) q^{92} +(3.63797 - 1.75195i) q^{93} +(0.493726 - 0.448389i) q^{94} +(4.39400 - 16.7562i) q^{95} +(-4.05627 - 13.6669i) q^{96} +(-2.57767 + 4.94091i) q^{97} +(-0.244049 + 1.89280i) q^{98} +(0.0794989 - 0.616578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 42 q^{2} - 42 q^{3} - 56 q^{4} - 42 q^{5} - 21 q^{6} - 56 q^{7} - 28 q^{8} - 42 q^{9} - 56 q^{10} - 28 q^{11} - 28 q^{12} - 42 q^{13} + 70 q^{15} - 56 q^{16} - 42 q^{17} - 21 q^{18} - 7 q^{19} - 49 q^{20}+ \cdots + 259 q^{99}+O(q^{100}) \) 672 * q - 42 * q^2 - 42 * q^3 - 56 * q^4 - 42 * q^5 - 21 * q^6 - 56 * q^7 - 28 * q^8 - 42 * q^9 - 56 * q^10 - 28 * q^11 - 28 * q^12 - 42 * q^13 + 70 * q^15 - 56 * q^16 - 42 * q^17 - 21 * q^18 - 7 * q^19 - 49 * q^20 - 42 * q^21 - 84 * q^22 - 42 * q^23 - 56 * q^24 - 42 * q^25 - 42 * q^26 + 119 * q^28 + 119 * q^29 + 77 * q^30 - 70 * q^31 - 56 * q^32 - 49 * q^33 - 70 * q^34 - 42 * q^35 - 301 * q^36 + 7 * q^37 - 28 * q^38 - 63 * q^39 - 56 * q^40 - 28 * q^41 + 112 * q^42 - 28 * q^43 + 126 * q^44 - 56 * q^45 - 56 * q^46 - 7 * q^47 + 42 * q^48 - 42 * q^49 - 182 * q^50 - 70 * q^51 + 49 * q^52 - 42 * q^53 - 63 * q^54 - 84 * q^55 + 77 * q^56 + 175 * q^57 + 126 * q^58 - 42 * q^59 + 84 * q^60 - 14 * q^61 - 56 * q^62 + 7 * q^63 - 14 * q^64 - 133 * q^65 + 63 * q^66 - 112 * q^67 - 49 * q^68 - 49 * q^69 + 168 * q^70 + 91 * q^71 + 392 * q^72 - 56 * q^73 - 56 * q^74 - 91 * q^75 - 161 * q^76 - 49 * q^77 + 84 * q^78 + 42 * q^79 - 70 * q^80 - 14 * q^81 - 42 * q^82 - 35 * q^83 + 245 * q^84 + 322 * q^85 + 63 * q^86 - 49 * q^87 - 133 * q^88 + 28 * q^89 + 196 * q^90 - 126 * q^91 - 7 * q^93 - 210 * q^94 + 84 * q^95 - 49 * q^96 - 42 * q^97 + 280 * q^98 + 259 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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