LMFDB - Embedded newform 512.2.o.a.149.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			149.6
Character	$\chi$	$=$	512.149
Dual form			512.2.o.a.189.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35047 + 0.419796i) q^{2} +(0.213123 + 0.0369803i) q^{3} +(1.64754 - 1.13384i) q^{4} +(0.614425 - 1.85989i) q^{5} +(-0.303341 + 0.0395272i) q^{6} +(-0.212885 + 4.33337i) q^{7} +(-1.74898 + 2.22285i) q^{8} +(-2.78058 - 0.994907i) q^{9} +O(q^{10})$	\(q+(-1.35047 + 0.419796i) q^{2} +(0.213123 + 0.0369803i) q^{3} +(1.64754 - 1.13384i) q^{4} +(0.614425 - 1.85989i) q^{5} +(-0.303341 + 0.0395272i) q^{6} +(-0.212885 + 4.33337i) q^{7} +(-1.74898 + 2.22285i) q^{8} +(-2.78058 - 0.994907i) q^{9} +(-0.0489890 + 2.76966i) q^{10} +(-0.695107 - 0.308120i) q^{11} +(0.393059 - 0.180721i) q^{12} +(-4.15589 + 3.58490i) q^{13} +(-1.53164 - 5.94146i) q^{14} +(0.199727 - 0.373664i) q^{15} +(1.42880 - 3.73611i) q^{16} +(1.67328 - 0.894387i) q^{17} +(4.17275 + 0.176318i) q^{18} +(-5.15126 + 2.91815i) q^{19} +(-1.09653 - 3.76091i) q^{20} +(-0.205620 + 0.915669i) q^{21} +(1.06807 + 0.124304i) q^{22} +(2.01759 + 8.05469i) q^{23} +(-0.454949 + 0.409063i) q^{24} +(0.934361 + 0.692969i) q^{25} +(4.10749 - 6.58593i) q^{26} +(-1.12043 - 0.634717i) q^{27} +(4.56263 + 7.38080i) q^{28} +(0.930140 - 0.0228337i) q^{29} +(-0.112864 + 0.588467i) q^{30} +(6.57179 - 4.39113i) q^{31} +(-0.361146 + 5.64531i) q^{32} +(-0.136749 - 0.0913727i) q^{33} +(-1.88426 + 1.91028i) q^{34} +(7.92880 + 3.05848i) q^{35} +(-5.70919 + 1.51359i) q^{36} +(-3.14782 - 0.388246i) q^{37} +(5.73160 - 6.10335i) q^{38} +(-1.01829 + 0.610338i) q^{39} +(3.05965 + 4.61868i) q^{40} +(-3.33202 + 2.47119i) q^{41} +(-0.106710 - 1.32290i) q^{42} +(-5.36853 + 7.62272i) q^{43} +(-1.49458 + 0.280502i) q^{44} +(-3.55888 + 4.56028i) q^{45} +(-6.10602 - 10.0306i) q^{46} +(-0.350969 - 3.56345i) q^{47} +(0.442672 - 0.743414i) q^{48} +(-11.7665 - 1.15890i) q^{49} +(-1.55273 - 0.543594i) q^{50} +(0.389689 - 0.128736i) q^{51} +(-2.78230 + 10.6184i) q^{52} +(-1.19141 - 0.0292474i) q^{53} +(1.77956 + 0.386814i) q^{54} +(-1.00016 + 1.10351i) q^{55} +(-9.26013 - 8.05218i) q^{56} +(-1.20577 + 0.431430i) q^{57} +(-1.24654 + 0.421305i) q^{58} +(1.75939 - 2.03963i) q^{59} +(-0.0946167 - 0.842087i) q^{60} +(-7.71810 + 1.73316i) q^{61} +(-7.03164 + 8.68891i) q^{62} +(4.90325 - 11.8375i) q^{63} +(-1.88216 - 7.77544i) q^{64} +(4.11404 + 9.93216i) q^{65} +(0.223033 + 0.0659896i) q^{66} +(-0.266836 - 0.168972i) q^{67} +(1.74271 - 3.37078i) q^{68} +(0.132131 + 1.79125i) q^{69} +(-11.9916 - 0.801907i) q^{70} +(10.3183 + 4.88019i) q^{71} +(7.07470 - 4.44075i) q^{72} +(-0.000589951 - 0.0120087i) q^{73} +(4.41402 - 0.797124i) q^{74} +(0.173507 + 0.182241i) q^{75} +(-5.17819 + 10.6485i) q^{76} +(1.48318 - 2.94656i) q^{77} +(1.11895 - 1.25172i) q^{78} +(-0.759732 - 0.925736i) q^{79} +(-6.07087 - 4.95297i) q^{80} +(6.63327 + 5.44379i) q^{81} +(3.46240 - 4.73604i) q^{82} +(-0.725152 + 0.0894390i) q^{83} +(0.699457 + 1.74175i) q^{84} +(-0.635357 - 3.66165i) q^{85} +(4.05005 - 12.5479i) q^{86} +(0.199079 + 0.0295305i) q^{87} +(1.90063 - 1.00623i) q^{88} +(-2.37398 + 9.47747i) q^{89} +(2.89177 - 7.65252i) q^{90} +(-14.6500 - 18.7722i) q^{91} +(12.4568 + 10.9828i) q^{92} +(1.56299 - 0.692824i) q^{93} +(1.96989 + 4.66500i) q^{94} +(2.26238 + 11.3738i) q^{95} +(-0.285734 + 1.18979i) q^{96} +(-2.69269 + 13.5371i) q^{97} +(16.3768 - 3.37447i) q^{98} +(1.62625 + 1.54832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{77}{128}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.35047	+	0.419796i	−0.954927	+	0.296840i
$2$	−1.35047	+	0.419796i	−0.954927	+	0.296840i
$3$	0.213123	+	0.0369803i	0.123047	+	0.0213506i	0.232152	−	0.972680i	$-0.425423\pi$
$3$	0.213123	+	0.0369803i	0.123047	+	0.0213506i	−0.109105	+	0.994030i	$0.534798\pi$
$4$	1.64754	−	1.13384i	0.823772	−	0.566922i
$5$	0.614425	−	1.85989i	0.274779	−	0.831769i	−0.716217	−	0.697878i	$-0.754128\pi$
$5$	0.614425	−	1.85989i	0.274779	−	0.831769i	0.990996	−	0.133891i	$-0.0427471\pi$
$6$	−0.303341	+	0.0395272i	−0.123838	+	0.0161369i
$7$	−0.212885	+	4.33337i	−0.0804630	+	1.63786i	0.531559	+	0.847021i	$0.321606\pi$
$7$	−0.212885	+	4.33337i	−0.0804630	+	1.63786i	−0.612022	+	0.790841i	$0.709644\pi$
$8$	−1.74898	+	2.22285i	−0.618357	+	0.785898i
$9$	−2.78058	−	0.994907i	−0.926859	−	0.331636i
$10$	−0.0489890	+	2.76966i	−0.0154917	+	0.875844i
$11$	−0.695107	−	0.308120i	−0.209583	−	0.0929016i	0.297779	−	0.954635i	$-0.403754\pi$
$11$	−0.695107	−	0.308120i	−0.209583	−	0.0929016i	−0.507362	+	0.861733i	$0.669379\pi$
$12$	0.393059	−	0.180721i	0.113466	−	0.0521698i
$13$	−4.15589	+	3.58490i	−1.15264	+	0.994272i	−0.152656	+	0.988279i	$0.548783\pi$
$13$	−4.15589	+	3.58490i	−1.15264	+	0.994272i	−0.999982	+	0.00599276i	$0.998092\pi$
$14$	−1.53164	−	5.94146i	−0.409347	−	1.58792i
$15$	0.199727	−	0.373664i	0.0515694	−	0.0964796i
$16$	1.42880	−	3.73611i	0.357199	−	0.934028i
$17$	1.67328	−	0.894387i	0.405830	−	0.216921i	−0.255835	−	0.966721i	$-0.582350\pi$
$17$	1.67328	−	0.894387i	0.405830	−	0.216921i	0.661665	+	0.749800i	$0.269850\pi$
$18$	4.17275	+	0.176318i	0.983526	+	0.0415586i
$19$	−5.15126	+	2.91815i	−1.18178	+	0.669470i	−0.952692	−	0.303936i	$-0.901699\pi$
$19$	−5.15126	+	2.91815i	−1.18178	+	0.669470i	−0.229087	+	0.973406i	$0.573574\pi$
$20$	−1.09653	−	3.76091i	−0.245192	−	0.840966i
$21$	−0.205620	+	0.915669i	−0.0448700	+	0.199815i
$22$	1.06807	+	0.124304i	0.227713	+	0.0265017i
$23$	2.01759	+	8.05469i	0.420697	+	1.67952i	0.695905	+	0.718134i	$0.255003\pi$
$23$	2.01759	+	8.05469i	0.420697	+	1.67952i	−0.275208	+	0.961385i	$0.588747\pi$
$24$	−0.454949	+	0.409063i	−0.0928661	+	0.0834997i
$25$	0.934361	+	0.692969i	0.186872	+	0.138594i
$26$	4.10749	−	6.58593i	0.805545	−	1.29161i
$27$	−1.12043	−	0.634717i	−0.215627	−	0.122151i
$28$	4.56263	+	7.38080i	0.862256	+	1.39484i
$29$	0.930140	−	0.0228337i	0.172723	−	0.00424010i	0.0619118	−	0.998082i	$-0.480280\pi$
$29$	0.930140	−	0.0228337i	0.172723	−	0.00424010i	0.110811	+	0.993842i	$0.464655\pi$
$30$	−0.112864	+	0.588467i	−0.0206060	+	0.107439i
$31$	6.57179	−	4.39113i	1.18033	−	0.788671i	0.198811	−	0.980038i	$-0.436292\pi$
$31$	6.57179	−	4.39113i	1.18033	−	0.788671i	0.981519	+	0.191367i	$0.0612921\pi$
$32$	−0.361146	+	5.64531i	−0.0638422	+	0.997960i
$33$	−0.136749	−	0.0913727i	−0.0238049	−	0.0159059i
$34$	−1.88426	+	1.91028i	−0.323147	+	0.327610i
$35$	7.92880	+	3.05848i	1.34021	+	0.516977i
$36$	−5.70919	+	1.51359i	−0.951532	+	0.252265i
$37$	−3.14782	−	0.388246i	−0.517498	−	0.0638272i	−0.140571	−	0.990071i	$-0.544894\pi$
$37$	−3.14782	−	0.388246i	−0.517498	−	0.0638272i	−0.376926	+	0.926243i	$0.623019\pi$
$38$	5.73160	−	6.10335i	0.929788	−	0.990095i
$39$	−1.01829	+	0.610338i	−0.163056	+	0.0977323i
$40$	3.05965	+	4.61868i	0.483773	+	0.730278i
$41$	−3.33202	+	2.47119i	−0.520374	+	0.385935i	−0.823766	−	0.566930i	$-0.808131\pi$
$41$	−3.33202	+	2.47119i	−0.520374	+	0.385935i	0.303392	+	0.952866i	$0.401881\pi$
$42$	−0.106710	−	1.32290i	−0.0164656	−	0.204128i
$43$	−5.36853	+	7.62272i	−0.818692	+	1.16245i	0.165650	+	0.986185i	$0.447028\pi$
$43$	−5.36853	+	7.62272i	−0.818692	+	1.16245i	−0.984342	+	0.176269i	$0.943597\pi$
$44$	−1.49458	+	0.280502i	−0.225316	+	0.0422873i
$45$	−3.55888	+	4.56028i	−0.530526	+	0.679806i
$46$	−6.10602	−	10.0306i	−0.900284	−	1.47894i
$47$	−0.350969	−	3.56345i	−0.0511941	−	0.519782i	−0.986247	−	0.165275i	$-0.947149\pi$
$47$	−0.350969	−	3.56345i	−0.0511941	−	0.519782i	0.935053	−	0.354507i	$-0.115351\pi$
$48$	0.442672	−	0.743414i	0.0638942	−	0.107303i
$49$	−11.7665	−	1.15890i	−1.68093	−	0.165557i
$50$	−1.55273	−	0.543594i	−0.219590	−	0.0768758i
$51$	0.389689	−	0.128736i	0.0545674	−	0.0180266i
$52$	−2.78230	+	10.6184i	−0.385836	+	1.47251i
$53$	−1.19141	−	0.0292474i	−0.163652	−	0.00401744i	−0.0573674	−	0.998353i	$-0.518271\pi$
$53$	−1.19141	−	0.0292474i	−0.163652	−	0.00401744i	−0.106285	+	0.994336i	$0.533896\pi$
$54$	1.77956	+	0.386814i	0.242168	+	0.0526388i
$55$	−1.00016	+	1.10351i	−0.134862	+	0.148797i
$56$	−9.26013	−	8.05218i	−1.23744	−	1.07602i
$57$	−1.20577	+	0.431430i	−0.159708	+	0.0571443i
$58$	−1.24654	+	0.421305i	−0.163679	+	0.0553200i
$59$	1.75939	−	2.03963i	0.229054	−	0.265537i	−0.630951	−	0.775822i	$-0.717335\pi$
$59$	1.75939	−	2.03963i	0.229054	−	0.265537i	0.860005	+	0.510286i	$0.170460\pi$
$60$	−0.0946167	−	0.842087i	−0.0122150	−	0.108713i
$61$	−7.71810	+	1.73316i	−0.988201	+	0.221908i	−0.683031	−	0.730390i	$-0.739338\pi$
$61$	−7.71810	+	1.73316i	−0.988201	+	0.221908i	−0.305170	+	0.952298i	$0.598713\pi$
$62$	−7.03164	+	8.68891i	−0.893019	+	1.10349i
$63$	4.90325	−	11.8375i	0.617751	−	1.49138i
$64$	−1.88216	−	7.77544i	−0.235270	−	0.971930i
$65$	4.11404	+	9.93216i	0.510283	+	1.23193i
$66$	0.223033	+	0.0659896i	0.0274535	+	0.00812275i
$67$	−0.266836	−	0.168972i	−0.0325992	−	0.0206432i	0.518598	−	0.855018i	$-0.326454\pi$
$67$	−0.266836	−	0.168972i	−0.0325992	−	0.0206432i	−0.551198	+	0.834375i	$0.685829\pi$
$68$	1.74271	−	3.37078i	0.211334	−	0.408767i
$69$	0.132131	+	1.79125i	0.0159066	+	0.215641i
$70$	−11.9916	−	0.801907i	−1.43326	−	0.0958462i
$71$	10.3183	+	4.88019i	1.22456	+	0.579172i	0.926831	−	0.375479i	$-0.122522\pi$
$71$	10.3183	+	4.88019i	1.22456	+	0.579172i	0.297726	+	0.954651i	$0.403772\pi$
$72$	7.07470	−	4.44075i	0.833761	−	0.523348i
$73$	−0.000589951	−	0.0120087i	−6.90485e−5	−	0.00140551i	0.998761	−	0.0497704i	$-0.0158490\pi$
$73$	−0.000589951	−	0.0120087i	−6.90485e−5	−	0.00140551i	−0.998830	+	0.0483649i	$0.984599\pi$
$74$	4.41402	−	0.797124i	0.513119	−	0.0926638i
$75$	0.173507	+	0.182241i	0.0200349	+	0.0210433i
$76$	−5.17819	+	10.6485i	−0.593979	+	1.22147i
$77$	1.48318	−	2.94656i	0.169024	−	0.335792i
$78$	1.11895	−	1.25172i	0.126696	−	0.141729i
$79$	−0.759732	−	0.925736i	−0.0854766	−	0.104153i	0.728516	−	0.685029i	$-0.240210\pi$
$79$	−0.759732	−	0.925736i	−0.0854766	−	0.104153i	−0.813993	+	0.580875i	$0.802710\pi$
$80$	−6.07087	−	4.95297i	−0.678744	−	0.553759i
$81$	6.63327	+	5.44379i	0.737030	+	0.604865i
$82$	3.46240	−	4.73604i	0.382358	−	0.523008i
$83$	−0.725152	+	0.0894390i	−0.0795958	+	0.00981720i	−0.162110	−	0.986773i	$-0.551830\pi$
$83$	−0.725152	+	0.0894390i	−0.0795958	+	0.00981720i	0.0825143	+	0.996590i	$0.473705\pi$
$84$	0.699457	+	1.74175i	0.0763170	+	0.190040i
$85$	−0.635357	−	3.66165i	−0.0689142	−	0.397162i
$86$	4.05005	−	12.5479i	0.436728	−	1.35308i
$87$	0.199079	+	0.0295305i	0.0213435	+	0.00316600i
$88$	1.90063	−	1.00623i	0.202608	−	0.107264i
$89$	−2.37398	+	9.47747i	−0.251642	+	1.00461i	0.704029	+	0.710171i	$0.251383\pi$
$89$	−2.37398	+	9.47747i	−0.251642	+	1.00461i	−0.955670	+	0.294438i	$0.904867\pi$
$90$	2.89177	−	7.65252i	0.304820	−	0.806647i
$91$	−14.6500	−	18.7722i	−1.53574	−	1.96786i
$92$	12.4568	+	10.9828i	1.29871	+	1.14504i
$93$	1.56299	−	0.692824i	0.162074	−	0.0718425i
$94$	1.96989	+	4.66500i	0.203179	+	0.481158i
$95$	2.26238	+	11.3738i	0.232116	+	1.16692i
$96$	−0.285734	+	1.18979i	−0.0291626	+	0.121433i
$97$	−2.69269	+	13.5371i	−0.273401	+	1.37448i	0.563042	+	0.826428i	$0.309631\pi$
$97$	−2.69269	+	13.5371i	−0.273401	+	1.37448i	−0.836444	+	0.548053i	$0.815369\pi$
$98$	16.3768	−	3.37447i	1.65431	−	0.340873i
$99$	1.62625	+	1.54832i	0.163444	+	0.155612i
$100$	2.32512	+	0.0822778i	0.232512	+	0.00822778i
$101$	5.90511	−	1.63416i	0.587580	−	0.162605i	0.0397712	−	0.999209i	$-0.487337\pi$
$101$	5.90511	−	1.63416i	0.587580	−	0.162605i	0.547809	+	0.836604i	$0.315462\pi$
$102$	−0.472221	+	0.337444i	−0.0467569	+	0.0334119i
$103$	−2.41840	−	16.3035i	−0.238292	−	1.60643i	−0.696478	−	0.717578i	$-0.745251\pi$
$103$	−2.41840	−	16.3035i	−0.238292	−	1.60643i	0.458186	−	0.888856i	$-0.348499\pi$
$104$	−0.700146	−	15.5079i	−0.0686549	−	1.52067i
$105$	1.57671	+	0.945042i	0.153871	+	0.0922266i
$106$	1.62124	−	0.460650i	0.157469	−	0.0447423i
$107$	6.45418	−	4.08706i	0.623949	−	0.395111i	−0.185212	−	0.982699i	$-0.559297\pi$
$107$	6.45418	−	4.08706i	0.623949	−	0.395111i	0.809161	+	0.587587i	$0.199922\pi$
$108$	−2.56563	+	0.224671i	−0.246878	+	0.0216190i
$109$	0.0229523	−	0.0829391i	0.00219844	−	0.00794413i	−0.962669	−	0.270683i	$-0.912751\pi$
$109$	0.0229523	−	0.0829391i	0.00219844	−	0.00794413i	0.964867	+	0.262738i	$0.0846256\pi$
$110$	0.887440	−	1.91012i	0.0846141	−	0.182122i
$111$	−0.656514	−	0.199151i	−0.0623136	−	0.0189026i
$112$	15.8858	+	6.98688i	1.50107	+	0.660198i
$113$	−3.23233	−	10.6556i	−0.304072	−	1.00239i	−0.967228	−	0.253909i	$-0.918284\pi$
$113$	−3.23233	−	10.6556i	−0.304072	−	1.00239i	0.663156	−	0.748481i	$-0.269216\pi$
$114$	1.44724	−	1.08881i	0.135546	−	0.101976i
$115$	16.2205	+	1.19650i	1.51257	+	0.111574i
$116$	1.50656	−	1.09225i	0.139880	−	0.101413i
$117$	15.1224	−	5.83337i	1.39807	−	0.539295i
$118$	−1.51978	+	3.49304i	−0.139907	+	0.321561i
$119$	3.51950	+	7.44135i	0.322632	+	0.682148i
$120$	0.481282	+	1.09749i	0.0439348	+	0.100187i
$121$	−6.99891	−	7.72211i	−0.636265	−	0.702010i
$122$	9.69549	−	5.58060i	0.877789	−	0.505244i
$123$	−0.801515	+	0.403449i	−0.0722701	+	0.0363777i
$124$	5.84846	−	14.6860i	0.525207	−	1.31884i
$125$	9.87018	−	6.95136i	0.882815	−	0.621749i
$126$	−1.65237	+	18.0445i	−0.147205	+	1.60754i
$127$	11.7959	+	11.7959i	1.04672	+	1.04672i	0.998854	+	0.0478672i	$0.0152424\pi$
$127$	11.7959	+	11.7959i	1.04672	+	1.04672i	0.0478672	+	0.998854i	$0.484758\pi$
$128$	5.80590	+	9.71038i	0.513174	+	0.858285i
$129$	−1.42605	+	1.42605i	−0.125556	+	0.125556i
$130$	−9.72537	−	11.6860i	−0.852971	−	1.02493i
$131$	−4.29393	−	6.09691i	−0.375162	−	0.532690i	0.585403	−	0.810742i	$-0.300936\pi$
$131$	−4.29393	−	6.09691i	−0.375162	−	0.532690i	−0.960566	+	0.278052i	$0.910311\pi$
$132$	−0.328902	+	0.00451139i	−0.0286272	+	0.000392666i
$133$	−11.5488	−	22.9436i	−1.00141	−	1.98946i
$134$	0.431287	+	0.116175i	0.0372576	+	0.0100360i
$135$	−1.86893	+	1.69390i	−0.160852	+	0.145787i
$136$	−0.938437	+	5.28372i	−0.0804703	+	0.453075i
$137$	−5.15132	+	2.43639i	−0.440107	+	0.208155i	−0.634748	−	0.772720i	$-0.718896\pi$
$137$	−5.15132	+	2.43639i	−0.440107	+	0.208155i	0.194641	+	0.980875i	$0.437646\pi$
$138$	−0.930397	−	2.36356i	−0.0792007	−	0.201200i
$139$	4.43924	+	11.5083i	0.376532	+	0.976122i	0.983421	+	0.181336i	$0.0580420\pi$
$139$	4.43924	+	11.5083i	0.376532	+	0.976122i	−0.606890	+	0.794786i	$0.707583\pi$
$140$	16.5309	−	3.95105i	1.39711	−	0.333925i
$141$	0.0569780	−	0.772431i	0.00479841	−	0.0650504i
$142$	−15.9832	−	2.25898i	−1.34128	−	0.189569i
$143$	3.99337	−	1.21138i	0.333942	−	0.101300i
$144$	−7.68997	+	8.96703i	−0.640831	+	0.747253i
$145$	0.529033	−	1.74399i	0.0439338	−	0.144830i
$146$	0.00583792	+	0.0159698i	0.000483150	+	0.00132167i
$147$	−2.46486	−	0.682119i	−0.203298	−	0.0562602i
$148$	−5.62637	+	2.92948i	−0.462485	+	0.240802i
$149$	−8.07048	−	12.7447i	−0.661160	−	1.04408i	−0.994846	−	0.101401i	$-0.967668\pi$
$149$	−8.07048	−	12.7447i	−0.661160	−	1.04408i	0.333686	−	0.942684i	$-0.391707\pi$
$150$	−0.310821	−	0.173273i	−0.0253784	−	0.0141477i
$151$	−2.55498	+	4.26272i	−0.207921	+	0.346895i	−0.943969	−	0.330034i	$-0.892940\pi$
$151$	−2.55498	+	4.26272i	−0.207921	+	0.346895i	0.736048	+	0.676929i	$0.236690\pi$
$152$	2.52280	−	16.5543i	0.204626	−	1.34273i
$153$	−5.54252	+	0.822155i	−0.448086	+	0.0664673i
$154$	−0.766031	+	4.60188i	−0.0617286	+	0.370830i
$155$	−4.12915	−	14.9208i	−0.331662	−	1.19847i
$156$	−0.985645	+	2.16014i	−0.0789147	+	0.172949i
$157$	14.3161	−	15.0367i	1.14255	−	1.20006i	0.165688	−	0.986178i	$-0.447016\pi$
$157$	14.3161	−	15.0367i	1.14255	−	1.20006i	0.976860	−	0.213878i	$-0.0686094\pi$
$158$	1.41462	+	0.931248i	0.112541	+	0.0740861i
$159$	−0.252835	−	0.0502920i	−0.0200511	−	0.00398841i
$160$	10.2778	+	4.14031i	0.812529	+	0.327321i
$161$	−35.3335	+	7.02827i	−2.78467	+	0.553905i
$162$	−11.2433	−	4.56706i	−0.883358	−	0.358822i
$163$	2.95347	+	6.66293i	0.231334	+	0.521881i	0.991846	−	0.127443i	$-0.0406769\pi$
$163$	2.95347	+	6.66293i	0.231334	+	0.521881i	−0.760512	+	0.649324i	$0.775052\pi$
$164$	−2.68770	+	7.84938i	−0.209874	+	0.612934i
$165$	−0.253965	+	0.198196i	−0.0197712	+	0.0154296i
$166$	0.941751	−	0.425200i	0.0730940	−	0.0330020i
$167$	−1.51345	−	0.379101i	−0.117115	−	0.0293357i	0.183980	−	0.982930i	$-0.441102\pi$
$167$	−1.51345	−	0.379101i	−0.117115	−	0.0293357i	−0.301094	+	0.953594i	$0.597352\pi$
$168$	−1.67577	−	2.05855i	−0.129289	−	0.158820i
$169$	2.51246	−	16.9376i	0.193266	−	1.30289i
$170$	2.39518	+	4.67824i	0.183702	+	0.358804i
$171$	17.2268	−	2.98913i	1.31736	−	0.228584i
$172$	−0.201906	+	18.6458i	−0.0153952	+	1.42173i
$173$	0.292184	+	2.36896i	0.0222143	+	0.180109i	0.999493	−	0.0318512i	$-0.0101403\pi$
$173$	0.292184	+	2.36896i	0.0222143	+	0.180109i	−0.977278	+	0.211960i	$0.932015\pi$
$174$	−0.281247	+	0.0436922i	−0.0213213	+	0.00331230i
$175$	−3.20181	+	3.90141i	−0.242034	+	0.294919i
$176$	−2.14434	+	2.15676i	−0.161636	+	0.162572i
$177$	0.450393	−	0.369628i	0.0338536	−	0.0277830i
$178$	−0.772606	−	13.7956i	−0.0579093	−	1.03403i
$179$	−13.3096	−	6.69950i	−0.994808	−	0.500744i	−0.123955	−	0.992288i	$-0.539558\pi$
$179$	−13.3096	−	6.69950i	−0.994808	−	0.500744i	−0.870853	+	0.491544i	$0.836433\pi$
$180$	−0.692760	+	11.5485i	−0.0516353	+	0.860772i
$181$	12.3809	−	11.7876i	0.920266	−	0.876167i	−0.0723602	−	0.997379i	$-0.523053\pi$
$181$	12.3809	−	11.7876i	0.920266	−	0.876167i	0.992627	+	0.121212i	$0.0386781\pi$
$182$	27.6649	+	19.2013i	2.05066	+	1.42330i
$183$	−1.70900	+	0.0839576i	−0.126333	+	0.00620632i
$184$	−21.4331	−	9.60264i	−1.58007	−	0.707916i
$185$	−2.65619	+	5.61605i	−0.195287	+	0.412900i
$186$	−1.81992	+	1.59177i	−0.133443	+	0.116714i
$187$	−1.43869	+	0.106124i	−0.105207	+	0.00776055i
$188$	−4.61863	−	5.47299i	−0.336848	−	0.399159i
$189$	2.98899	−	4.72013i	0.217417	−	0.343339i
$190$	−7.82994	−	14.4102i	−0.568043	−	1.04543i
$191$	15.9840	−	6.62078i	1.15656	−	0.479063i	0.279832	−	0.960049i	$-0.409721\pi$
$191$	15.9840	−	6.62078i	1.15656	−	0.479063i	0.876728	+	0.480986i	$0.159721\pi$
$192$	−0.113593	−	1.72673i	−0.00819789	−	0.124616i
$193$	−5.38657	−	2.23119i	−0.387734	−	0.160605i	0.180296	−	0.983612i	$-0.442294\pi$
$193$	−5.38657	−	2.23119i	−0.387734	−	0.160605i	−0.568030	+	0.823008i	$0.692294\pi$
$194$	−2.04640	−	19.4118i	−0.146923	−	1.39369i
$195$	0.509501	+	2.26891i	0.0364861	+	0.162480i
$196$	−20.6999	+	11.4321i	−1.47856	+	0.816575i
$197$	6.59611	+	5.68984i	0.469953	+	0.405385i	0.855904	−	0.517135i	$-0.173001\pi$
$197$	6.59611	+	5.68984i	0.469953	+	0.405385i	−0.385951	+	0.922519i	$0.626126\pi$
$198$	−2.84618	−	1.40827i	−0.202269	−	0.100081i
$199$	5.64292	+	15.7709i	0.400016	+	1.11797i	0.957663	+	0.287892i	$0.0929543\pi$
$199$	5.64292	+	15.7709i	0.400016	+	1.11797i	−0.557647	+	0.830078i	$0.688296\pi$
$200$	−3.17454	+	0.864961i	−0.224474	+	0.0611620i
$201$	−0.0506202	−	0.0458794i	−0.00357047	−	0.00323609i
$202$	−7.28866	+	4.68583i	−0.512828	+	0.329694i
$203$	−0.0990661	+	4.03551i	−0.00695308	+	0.283237i
$204$	0.496064	−	0.653945i	0.0347314	−	0.0457853i
$205$	2.54887	+	7.71555i	0.178021	+	0.538877i
$206$	10.1101	+	21.0022i	0.704406	+	1.46329i
$207$	2.40358	−	24.4040i	0.167061	−	1.69620i
$208$	7.45565	+	20.6490i	0.516957	+	1.43175i
$209$	4.47982	−	0.441223i	0.309875	−	0.0305201i
$210$	−2.52602	−	0.614357i	−0.174312	−	0.0423946i
$211$	2.42702	+	1.89407i	0.167083	+	0.130393i	0.695309	−	0.718711i	$-0.255268\pi$
$211$	2.42702	+	1.89407i	0.167083	+	0.130393i	−0.528226	+	0.849104i	$0.677143\pi$
$212$	−1.99606	+	1.30268i	−0.137090	+	0.0894687i
$213$	2.01860	+	1.42166i	0.138312	+	0.0974102i
$214$	−7.00045	+	8.22889i	−0.478541	+	0.562516i
$215$	10.8789	+	14.6685i	0.741933	+	1.00038i
$216$	3.37049	−	1.38045i	0.229333	−	0.0939279i
$217$	17.6294	+	29.4129i	1.19676	+	1.99667i
$218$	0.00382100	+	0.121642i	0.000258791	+	0.00823865i
$219$	0.000318355	−	0.00258115i	2.15124e−5	−	0.000174418i
$220$	−0.396603	+	2.95210i	−0.0267390	+	0.199031i
$221$	−3.74769	+	9.71552i	−0.252097	+	0.653537i
$222$	0.970206	−	0.00665361i	0.0651160	−	0.000446561i
$223$	−10.9441	+	16.3790i	−0.732872	+	1.09682i	0.258534	+	0.966002i	$0.416761\pi$
$223$	−10.9441	+	16.3790i	−0.732872	+	1.09682i	−0.991406	+	0.130819i	$0.958239\pi$
$224$	−24.3864	−	2.76678i	−1.62938	−	0.184864i
$225$	−1.90862	−	2.85646i	−0.127242	−	0.190430i
$226$	8.83832	+	13.0331i	0.587916	+	0.866949i
$227$	−0.454702	−	18.5225i	−0.0301796	−	1.22938i	−0.803476	−	0.595337i	$-0.797019\pi$
$227$	−0.454702	−	18.5225i	−0.0301796	−	1.22938i	0.773297	−	0.634044i	$-0.218606\pi$
$228$	−1.49738	+	2.07795i	−0.0991662	+	0.137616i
$229$	−12.1180	+	21.3912i	−0.800779	+	1.41357i	0.107060	+	0.994253i	$0.465856\pi$
$229$	−12.1180	+	21.3912i	−0.800779	+	1.41357i	−0.907839	+	0.419320i	$0.862269\pi$
$230$	−22.4076	+	5.19346i	−1.47751	+	0.342447i
$231$	0.425064	−	0.573132i	0.0279671	−	0.0377093i
$232$	−1.57604	+	2.10750i	−0.103472	+	0.138364i
$233$	20.8674	−	5.22701i	1.36707	−	0.342433i	0.511127	−	0.859505i	$-0.329228\pi$
$233$	20.8674	−	5.22701i	1.36707	−	0.342433i	0.855942	+	0.517072i	$0.172978\pi$
$234$	−17.9736	+	14.2261i	−1.17497	+	0.929991i
$235$	−6.84327	−	1.53671i	−0.446406	−	0.100244i
$236$	0.586060	−	5.35525i	0.0381493	−	0.348597i
$237$	−0.127682	−	0.225391i	−0.00829386	−	0.0146407i
$238$	−7.87683	−	8.57186i	−0.510579	−	0.555631i
$239$	12.4691	+	23.3281i	0.806559	+	1.50897i	0.859942	+	0.510392i	$0.170500\pi$
$239$	12.4691	+	23.3281i	0.806559	+	1.50897i	−0.0533826	+	0.998574i	$0.517000\pi$
$240$	−1.11068	−	1.28009i	−0.0716941	−	0.0826297i
$241$	−4.81122	−	2.57165i	−0.309918	−	0.165655i	0.309104	−	0.951028i	$-0.399971\pi$
$241$	−4.81122	−	2.57165i	−0.309918	−	0.165655i	−0.619022	+	0.785374i	$0.712471\pi$
$242$	12.6935	+	7.49037i	0.815971	+	0.481499i
$243$	3.73571	+	4.33072i	0.239646	+	0.277816i
$244$	−10.7508	+	11.6066i	−0.688248	+	0.743034i
$245$	−9.38508	+	21.1724i	−0.599591	+	1.35265i
$246$	0.913056	−	0.881318i	0.0582143	−	0.0561908i
$247$	10.9468	−	30.5943i	0.696529	−	1.94667i
$248$	−1.73307	+	22.2881i	−0.110050	+	1.41530i
$249$	−0.157854	−	0.00775487i	−0.0100036	−	0.000491445i
$250$	−10.4112	+	13.5311i	−0.658464	+	0.855780i
$251$	−16.1154	−	5.32382i	−1.01720	−	0.336036i	−0.243709	−	0.969848i	$-0.578364\pi$
$251$	−16.1154	−	5.32382i	−1.01720	−	0.336036i	−0.773487	+	0.633812i	$0.781489\pi$
$252$	−5.34355	−	25.0623i	−0.336612	−	1.57878i
$253$	1.07936	−	6.22053i	0.0678591	−	0.391081i
$254$	−20.8820	−	10.9782i	−1.31025	−	0.688833i
$255$		−	0.803878i		−	0.0503408i
$256$	−11.9171	−	10.6763i	−0.744817	−	0.667269i
$257$		−	29.8237i		−	1.86035i	−0.367116	−	0.930175i	$-0.619655\pi$
$257$		−	29.8237i		−	1.86035i	0.367116	−	0.930175i	$-0.380345\pi$
$258$	1.32719	−	2.52448i	0.0826270	−	0.157167i
$259$	2.35254	−	13.5580i	0.146180	−	0.842454i
$260$	18.0396	+	11.6990i	1.11877	+	0.725541i
$261$	−2.60904	−	0.861912i	−0.161496	−	0.0533510i
$262$	8.35828	+	6.43113i	0.516377	+	0.397317i
$263$	−26.1321	−	1.28379i	−1.61137	−	0.0791617i	−0.776687	−	0.629887i	$-0.783101\pi$
$263$	−26.1321	−	1.28379i	−1.61137	−	0.0791617i	−0.834687	+	0.550725i	$0.814351\pi$
$264$	0.442279	−	0.144164i	0.0272204	−	0.00887269i
$265$	−0.786428	+	2.19792i	−0.0483099	+	0.135017i
$266$	25.2280	+	26.1365i	1.54682	+	1.60253i
$267$	−0.856430	+	1.93208i	−0.0524127	+	0.118241i
$268$	−0.631211	+	0.0241615i	−0.0385573	+	0.00147590i
$269$	6.72335	+	7.79423i	0.409930	+	0.475222i	0.923927	−	0.382570i	$-0.124961\pi$
$269$	6.72335	+	7.79423i	0.409930	+	0.475222i	−0.513997	+	0.857792i	$0.671836\pi$
$270$	1.81284	−	3.07212i	0.110326	−	0.186964i
$271$	9.65467	+	5.16053i	0.586479	+	0.313480i	0.737815	−	0.675003i	$-0.235858\pi$
$271$	9.65467	+	5.16053i	0.586479	+	0.313480i	−0.151336	+	0.988482i	$0.548358\pi$
$272$	−0.950752	−	7.52946i	−0.0576478	−	0.456541i
$273$	−2.42804	−	4.54255i	−0.146952	−	0.274928i
$274$	5.93392	−	5.45278i	0.358481	−	0.329414i
$275$	−0.435963	−	0.769583i	−0.0262896	−	0.0464076i
$276$	2.24869	+	2.80135i	0.135355	+	0.168621i
$277$	0.919901	+	0.206571i	0.0552715	+	0.0124116i	0.246649	−	0.969105i	$-0.420670\pi$
$277$	0.919901	+	0.206571i	0.0552715	+	0.0124116i	−0.191378	+	0.981516i	$0.561295\pi$
$278$	−10.8262	−	13.6781i	−0.649313	−	0.820355i
$279$	−22.6422	+	5.67157i	−1.35555	+	0.339548i
$280$	−20.6658	+	12.2754i	−1.23502	+	0.733594i
$281$	14.2145	−	19.1661i	0.847968	−	1.14335i	−0.140223	−	0.990120i	$-0.544782\pi$
$281$	14.2145	−	19.1661i	0.847968	−	1.14335i	0.988190	−	0.153232i	$-0.0489682\pi$
$282$	0.247316	+	1.06706i	0.0147275	+	0.0635428i
$283$	−3.51768	+	6.20958i	−0.209105	+	0.369121i	−0.954840	−	0.297121i	$-0.903973\pi$
$283$	−3.51768	+	6.20958i	−0.209105	+	0.369121i	0.745735	+	0.666243i	$0.232098\pi$
$284$	22.5332	−	3.65901i	1.33710	−	0.217122i
$285$	0.0615599	+	2.50767i	0.00364650	+	0.148542i
$286$	−4.88440	+	3.31233i	−0.288821	+	0.195862i
$287$	−9.99926	−	14.9650i	−0.590238	−	0.883353i
$288$	6.62076	−	15.3379i	0.390132	−	0.903796i
$289$	−7.44475	+	11.1419i	−0.437927	+	0.655404i
$290$	0.0176749	+	2.57729i	0.00103791	+	0.151344i
$291$	−1.07448	+	2.78548i	−0.0629871	+	0.163288i
$292$	−0.0145880	−	0.0191160i	−0.000853697	−	0.00111868i
$293$	2.67866	−	21.7180i	0.156489	−	1.26878i	−0.685015	−	0.728529i	$-0.740204\pi$
$293$	2.67866	−	21.7180i	0.156489	−	1.26878i	0.841504	−	0.540251i	$-0.181671\pi$
$294$	3.61507	−	0.113556i	0.210835	−	0.00662272i
$295$	−2.71247	−	4.52548i	−0.157926	−	0.263484i
$296$	6.36847	−	6.31810i	0.370160	−	0.367232i
$297$	0.583251	+	0.786423i	0.0338437	+	0.0456329i
$298$	16.2491	+	13.8234i	0.941286	+	0.800766i
$299$	−37.2602	−	26.2416i	−2.15481	−	1.51759i
$300$	0.492493	+	0.103519i	0.0284341	+	0.00597667i
$301$	−31.8892	−	24.8866i	−1.83806	−	1.43444i
$302$	1.66095	−	6.82925i	0.0955769	−	0.392979i
$303$	1.31895	−	0.129905i	0.0757714	−	0.00746284i
$304$	3.54244	+	23.4151i	0.203173	+	1.34295i
$305$	−1.51871	+	15.4197i	−0.0869610	+	0.882930i
$306$	7.13987	−	3.43702i	0.408159	−	0.196481i
$307$	7.07977	+	21.4308i	0.404064	+	1.22312i	0.928392	+	0.371603i	$0.121192\pi$
$307$	7.07977	+	21.4308i	0.404064	+	1.22312i	−0.524328	+	0.851516i	$0.675683\pi$
$308$	−0.897347	−	6.53628i	−0.0511311	−	0.372439i
$309$	0.0874935	−	3.56409i	0.00497733	−	0.202754i
$310$	11.8400	+	18.4168i	0.672467	+	1.04600i
$311$	16.9679	+	15.3788i	0.962162	+	0.872053i	0.991838	−	0.127507i	$-0.0406975\pi$
$311$	16.9679	+	15.3788i	0.962162	+	0.872053i	−0.0296759	+	0.999560i	$0.509448\pi$
$312$	0.424269	−	3.33097i	0.0240195	−	0.188579i
$313$	7.55653	+	21.1191i	0.427121	+	1.19372i	0.941751	+	0.336310i	$0.109179\pi$
$313$	7.55653	+	21.1191i	0.427121	+	1.19372i	−0.514631	+	0.857412i	$0.672071\pi$
$314$	−13.0211	+	26.3164i	−0.734825	+	1.48512i
$315$	−19.0038	−	16.3928i	−1.07074	−	0.923627i
$316$	−2.30133	−	0.663773i	−0.129460	−	0.0373402i
$317$	7.21311	+	32.1214i	0.405128	+	1.80412i	0.574429	+	0.818554i	$0.305224\pi$
$317$	7.21311	+	32.1214i	0.405128	+	1.80412i	−0.169301	+	0.985564i	$0.554151\pi$
$318$	0.362558	−	0.0382211i	0.0203313	−	0.00214333i
$319$	−0.653582	−	0.270723i	−0.0365936	−	0.0151576i
$320$	−15.6179	−	1.27681i	−0.873068	−	0.0713759i
$321$	1.52667	−	0.632369i	0.0852106	−	0.0352954i
$322$	44.7664	−	24.3243i	2.49474	−	1.35554i
$323$	−6.00954	+	9.49011i	−0.334380	+	0.528044i
$324$	17.1010	+	1.44778i	0.950056	+	0.0804322i
$325$	−6.36733	+	0.469682i	−0.353196	+	0.0260533i
$326$	−6.78565	−	7.75824i	−0.375822	−	0.429689i
$327$	0.00795879	−	0.0168274i	0.000440122	−	0.000930560i
$328$	0.334520	−	11.7286i	0.0184708	−	0.647606i
$329$	15.5165	−	0.762275i	0.855450	−	0.0420256i
$330$	0.259771	−	0.374272i	0.0142999	−	0.0206030i
$331$	2.11620	−	2.01479i	0.116317	−	0.110743i	−0.629155	−	0.777280i	$-0.716599\pi$
$331$	2.11620	−	2.01479i	0.116317	−	0.110743i	0.745472	+	0.666537i	$0.232224\pi$
$332$	−1.09331	+	0.969564i	−0.0600032	+	0.0532117i
$333$	8.36648	+	4.21133i	0.458480	+	0.230780i
$334$	2.20302	−	0.123377i	0.120544	−	0.00675090i
$335$	−0.478220	+	0.392465i	−0.0261279	+	0.0214426i
$336$	3.12725	+	2.07653i	0.170606	+	0.113284i
$337$	−5.97835	+	7.28464i	−0.325662	+	0.396820i	−0.909944	−	0.414730i	$-0.863876\pi$
$337$	−5.97835	+	7.28464i	−0.325662	+	0.396820i	0.584283	+	0.811550i	$0.301376\pi$
$338$	3.71734	+	23.9285i	0.202197	+	1.30154i
$339$	−0.294837	−	2.39048i	−0.0160133	−	0.129833i
$340$	−5.19852	−	5.31234i	−0.281929	−	0.288102i
$341$	−5.92109	+	1.02741i	−0.320645	+	0.0556372i
$342$	−22.0094	+	11.2685i	−1.19013	+	0.609328i
$343$	3.07064	−	20.7006i	0.165799	−	1.11772i
$344$	−7.55477	−	25.2654i	−0.407326	−	1.36222i
$345$	3.41271	+	0.854841i	0.183734	+	0.0460231i
$346$	−1.38907	−	3.07656i	−0.0746767	−	0.165397i
$347$	−24.2277	+	18.9075i	−1.30061	+	1.01501i	−0.302525	+	0.953141i	$0.597830\pi$
$347$	−24.2277	+	18.9075i	−1.30061	+	1.01501i	−0.998085	+	0.0618642i	$0.980295\pi$
$348$	0.361474	−	0.177071i	0.0193770	−	0.00949201i
$349$	1.11605	+	2.51777i	0.0597409	+	0.134773i	0.941593	−	0.336752i	$-0.109329\pi$
$349$	1.11605	+	2.51777i	0.0597409	+	0.134773i	−0.881852	+	0.471526i	$0.843704\pi$
$350$	2.68615	−	6.61285i	0.143581	−	0.353472i
$351$	6.93179	−	1.37882i	0.369992	−	0.0735959i
$352$	1.99047	−	3.81282i	0.106092	−	0.203224i
$353$	−23.6948	−	4.71318i	−1.26115	−	0.250857i	−0.481148	−	0.876640i	$-0.659780\pi$
$353$	−23.6948	−	4.71318i	−1.26115	−	0.250857i	−0.779998	+	0.625782i	$0.784780\pi$
$354$	−0.453075	+	0.688245i	−0.0240806	+	0.0365798i
$355$	15.4165	−	16.1924i	0.818220	−	0.859404i
$356$	6.83473	+	18.3063i	0.362240	+	0.970230i
$357$	0.474902	+	1.71608i	0.0251345	+	0.0908244i
$358$	20.7867	+	3.46016i	1.09861	+	0.182875i
$359$	−8.63648	+	1.28110i	−0.455816	+	0.0676139i	−0.370691	−	0.928756i	$-0.620879\pi$
$359$	−8.63648	+	1.28110i	−0.455816	+	0.0676139i	−0.0851253	+	0.996370i	$0.527129\pi$
$360$	−3.91244	−	15.8867i	−0.206204	−	0.837302i
$361$	8.25190	−	13.7675i	0.434310	−	0.724603i
$362$	−11.7717	+	21.1163i	−0.618706	+	1.10985i
$363$	−1.20606	−	1.90458i	−0.0633019	−	0.0999646i
$364$	−45.4212	−	14.3173i	−2.38072	−	0.750428i
$365$	−0.0226974	−	0.00628122i	−0.00118804	−	0.000328774i
$366$	2.27270	−	0.830811i	0.118796	−	0.0434272i
$367$	4.33866	−	14.3026i	0.226476	−	0.746592i	−0.767889	−	0.640583i	$-0.778693\pi$
$367$	4.33866	−	14.3026i	0.226476	−	0.746592i	0.994365	−	0.106009i	$-0.0338073\pi$
$368$	32.9760	+	3.97056i	1.71899	+	0.206980i
$369$	11.7235	−	3.55630i	0.610303	−	0.185133i
$370$	1.22952	−	8.69936i	0.0639196	−	0.452258i
$371$	0.380373	−	5.15659i	0.0197480	−	0.267717i
$372$	1.78953	−	2.91364i	0.0927830	−	0.151065i
$373$	−11.5810	−	30.0225i	−0.599639	−	1.55451i	−0.815914	−	0.578174i	$-0.803766\pi$
$373$	−11.5810	−	30.0225i	−0.599639	−	1.55451i	0.216275	−	0.976333i	$-0.430609\pi$
$374$	1.89836	−	0.747272i	0.0981616	−	0.0386405i
$375$	2.36062	−	1.11649i	0.121902	−	0.0576554i
$376$	8.53486	+	5.45223i	0.440152	+	0.281177i
$377$	−3.78371	+	3.42935i	−0.194871	+	0.176621i
$378$	−2.05505	+	7.62916i	−0.105701	+	0.392402i
$379$	11.7397	+	23.3229i	0.603030	+	1.19801i	0.964116	+	0.265482i	$0.0855311\pi$
$379$	11.7397	+	23.3229i	0.603030	+	1.19801i	−0.361086	+	0.932533i	$0.617594\pi$
$380$	16.6234	+	16.1736i	0.852765	+	0.829687i
$381$	2.07777	+	2.95020i	0.106447	+	0.151144i
$382$	−18.8065	+	15.6512i	−0.962226	+	0.800784i
$383$	−7.92638	+	7.92638i	−0.405019	+	0.405019i	−0.879997	−	0.474978i	$-0.842456\pi$
$383$	−7.92638	+	7.92638i	−0.405019	+	0.405019i	0.474978	+	0.879997i	$0.342456\pi$
$384$	0.878277	+	2.28421i	0.0448194	+	0.116566i
$385$	−4.56899	−	4.56899i	−0.232857	−	0.232857i
$386$	8.21106	+	0.751900i	0.417932	+	0.0382707i
$387$	22.5115	−	15.8544i	1.14432	−	0.805924i
$388$	10.9126	+	25.3560i	0.554003	+	1.28726i
$389$	32.0043	−	16.1096i	1.62268	−	0.816788i	0.623285	−	0.781994i	$-0.285797\pi$
$389$	32.0043	−	16.1096i	1.62268	−	0.816788i	0.999395	−	0.0347940i	$-0.0110775\pi$
$390$	−1.64054	−	2.85021i	−0.0830722	−	0.144326i
$391$	10.5800	+	11.6732i	0.535054	+	0.590341i
$392$	23.1554	−	24.1284i	1.16953	−	1.21867i
$393$	−0.689669	−	1.45818i	−0.0347892	−	0.0735556i
$394$	−11.2964	−	4.91495i	−0.569106	−	0.247612i
$395$	−2.18857	+	0.844224i	−0.110119	+	0.0424775i
$396$	4.43487	+	0.707009i	0.222860	+	0.0355285i
$397$	37.8673	+	2.79326i	1.90051	+	0.140190i	0.972579	−	0.232573i	$-0.0747146\pi$
$397$	37.8673	+	2.79326i	1.90051	+	0.140190i	0.927927	+	0.372763i	$0.121590\pi$
$398$	−14.2412	−	18.9293i	−0.713845	−	0.948839i
$399$	−1.61286	−	5.31688i	−0.0807439	−	0.266177i
$400$	3.92402	−	2.50076i	0.196201	−	0.125038i
$401$	34.0904	+	10.3412i	1.70240	+	0.516416i	0.983839	−	0.179053i	$-0.0573034\pi$
$401$	34.0904	+	10.3412i	1.70240	+	0.516416i	0.718556	+	0.695469i	$0.244803\pi$
$402$	0.0876211	+	0.0407087i	0.00437014	+	0.00203037i
$403$	−11.5699	+	41.8083i	−0.576339	+	2.08262i
$404$	7.87603	−	9.38782i	0.391847	−	0.467062i
$405$	14.2005	−	8.99236i	0.705628	−	0.446834i
$406$	−1.56030	−	5.49142i	−0.0774365	−	0.272535i
$407$	2.06844	+	1.23978i	0.102529	+	0.0614534i
$408$	−0.395396	+	1.09138i	−0.0195750	+	0.0540313i
$409$	0.520620	+	3.50974i	0.0257430	+	0.173545i	0.998235	−	0.0593922i	$-0.0189163\pi$
$409$	0.520620	+	3.50974i	0.0257430	+	0.173545i	−0.972492	+	0.232937i	$0.925166\pi$
$410$	−6.68113	−	9.34962i	−0.329958	−	0.461745i
$411$	−1.18796	+	0.328754i	−0.0585979	+	0.0162162i
$412$	−22.4701	−	24.1187i	−1.10702	−	1.18824i
$413$	8.46392	+	8.05832i	0.416482	+	0.396524i
$414$	6.99872	+	33.9659i	0.343969	+	1.66933i
$415$	−0.279205	+	1.40366i	−0.0137056	+	0.0689028i
$416$	−18.7370	−	24.7560i	−0.918657	−	1.21376i
$417$	0.520524	+	2.61685i	0.0254902	+	0.128148i
$418$	−5.86464	+	2.47647i	−0.286849	+	0.121128i
$419$	−8.13831	+	3.60746i	−0.397582	+	0.176236i	−0.594336	−	0.804217i	$-0.702585\pi$
$419$	−8.13831	+	3.60746i	−0.397582	+	0.176236i	0.196754	+	0.980453i	$0.436960\pi$
$420$	3.66922	−	0.230742i	0.179040	−	0.0112590i
$421$	12.5790	+	16.1185i	0.613063	+	0.785568i	0.990060	−	0.140647i	$-0.0449182\pi$
$421$	12.5790	+	16.1185i	0.613063	+	0.785568i	−0.376997	+	0.926215i	$0.623043\pi$
$422$	−4.07274	−	1.53903i	−0.198258	−	0.0749187i
$423$	−2.56940	+	10.2576i	−0.124929	+	0.498743i
$424$	2.14876	−	2.59717i	0.104353	−	0.126130i
$425$	2.18323	+	0.323852i	0.105902	+	0.0157091i
$426$	−3.32286	−	1.07251i	−0.160993	−	0.0519631i
$427$	−5.86735	−	33.8144i	−0.283941	−	1.63639i
$428$	5.99945	−	14.0516i	0.289994	−	0.679212i
$429$	0.895876	−	0.110496i	0.0432533	−	0.00533478i
$430$	−20.8494	−	15.2424i	−1.00545	−	0.735055i
$431$	−6.63386	−	5.44426i	−0.319542	−	0.262241i	0.460924	−	0.887440i	$-0.347518\pi$
$431$	−6.63386	−	5.44426i	−0.319542	−	0.262241i	−0.780466	+	0.625199i	$0.785018\pi$
$432$	−3.97224	+	3.27918i	−0.191115	+	0.157770i
$433$	8.87450	+	10.8136i	0.426481	+	0.519669i	0.941273	−	0.337646i	$-0.109631\pi$
$433$	8.87450	+	10.8136i	0.426481	+	0.519669i	−0.514792	+	0.857315i	$0.672131\pi$
$434$	−36.1554	−	32.3205i	−1.73551	−	1.55143i
$435$	0.177242	−	0.352120i	0.00849812	−	0.0168829i
$436$	−0.0562250	−	0.162670i	−0.00269269	−	0.00779049i
$437$	−33.8979	−	35.6041i	−1.62156	−	1.70318i
$438$	0.000653627		0.00361941i	3.12315e−5		0.000172942i
$439$	−0.493716	−	10.0498i	−0.0235638	−	0.479652i	−0.981357	−	0.192194i	$-0.938440\pi$
$439$	−0.493716	−	10.0498i	−0.0235638	−	0.479652i	0.957793	−	0.287458i	$-0.0928102\pi$
$440$	−0.703678	−	4.15322i	−0.0335465	−	0.197997i
$441$	31.5647	+	14.9290i	1.50308	+	0.710905i
$442$	0.982613	−	14.6938i	0.0467381	−	0.698912i
$443$	0.292212	+	3.96143i	0.0138834	+	0.188213i	0.999782	+	0.0208702i	$0.00664367\pi$
$443$	0.292212	+	3.96143i	0.0138834	+	0.188213i	−0.985899	+	0.167343i	$0.946481\pi$
$444$	−1.30744	+	0.416274i	−0.0620485	+	0.0197555i
$445$	16.1684	+	10.2385i	0.766457	+	0.485354i
$446$	7.90387	−	26.7137i	0.374259	−	1.26493i
$447$	−1.24870	−	3.01463i	−0.0590616	−	0.142587i
$448$	34.0946	−	6.50083i	1.61082	−	0.307136i
$449$	−1.46152	+	3.52842i	−0.0689733	+	0.166516i	−0.954607	−	0.297868i	$-0.903724\pi$
$449$	−1.46152	+	3.52842i	−0.0689733	+	0.166516i	0.885634	+	0.464385i	$0.153724\pi$
$450$	3.77667	+	3.05633i	0.178034	+	0.144077i
$451$	3.07753	−	0.691083i	0.144915	−	0.0325418i
$452$	−17.4071	−	13.8905i	−0.818762	−	0.653356i
$453$	−0.702161	+	0.814000i	−0.0329904	+	0.0382450i
$454$	8.38972	+	24.8232i	0.393749	+	1.16501i
$455$	−43.9156	+	15.7133i	−2.05880	+	0.736649i
$456$	1.14985	−	3.43480i	0.0538467	−	0.160849i
$457$	4.14873	−	4.57742i	0.194069	−	0.214123i	−0.636141	−	0.771573i	$-0.719470\pi$
$457$	4.14873	−	4.57742i	0.194069	−	0.214123i	0.830210	+	0.557450i	$0.188220\pi$
$458$	7.38504	−	33.9753i	0.345080	−	1.58756i
$459$	−2.44248	−	0.0599595i	−0.114005	−	0.00279867i
$460$	28.0806	−	16.4202i	1.30927	−	0.765597i
$461$	−24.2927	+	8.02523i	−1.13142	+	0.373772i	−0.817644	−	0.575723i	$-0.804720\pi$
$461$	−24.2927	+	8.02523i	−1.13142	+	0.373772i	−0.313780	+	0.949496i	$0.601595\pi$
$462$	−0.333438	+	0.952438i	−0.0155129	+	0.0443114i
$463$	−8.74882	−	0.861683i	−0.406592	−	0.0400458i	−0.107346	−	0.994222i	$-0.534235\pi$
$463$	−8.74882	−	0.861683i	−0.406592	−	0.0400458i	−0.299246	+	0.954176i	$0.596735\pi$
$464$	1.24367	−	3.50773i	0.0577361	−	0.162842i
$465$	−0.328240	−	3.33267i	−0.0152217	−	0.154549i
$466$	−25.9865	+	15.8190i	−1.20380	+	0.732800i
$467$	−1.72853	+	2.21491i	−0.0799870	+	0.102494i	−0.826672	−	0.562683i	$-0.809769\pi$
$467$	−1.72853	+	2.21491i	−0.0799870	+	0.102494i	0.746686	+	0.665177i	$0.231644\pi$
$468$	18.3007	−	26.7572i	0.845952	−	1.23685i
$469$	0.789024	−	1.12033i	0.0364337	−	0.0517319i
$470$	9.88674	−	0.797495i	0.456041	−	0.0367857i
$471$	3.60715	−	2.67524i	0.166209	−	0.123269i
$472$	1.45665	+	7.47813i	0.0670479	+	0.344209i
$473$	6.08041	−	3.64446i	0.279578	−	0.167572i
$474$	0.267049	+	0.250783i	0.0122660	+	0.0115189i
$475$	−6.83532	−	0.843057i	−0.313626	−	0.0386821i
$476$	14.2359	+	8.26939i	0.652499	+	0.379027i
$477$	3.28371	+	1.26666i	0.150351	+	0.0579966i
$478$	−26.6322	−	26.2694i	−1.21813	−	1.20153i
$479$	8.65024	+	5.77990i	0.395239	+	0.264091i	0.737270	−	0.675598i	$-0.236115\pi$
$479$	8.65024	+	5.77990i	0.395239	+	0.264091i	−0.342030	+	0.939689i	$0.611115\pi$
$480$	2.03732	+	1.26247i	0.0929905	+	0.0576237i
$481$	14.4738	−	9.67109i	0.659949	−	0.440964i
$482$	7.57698	+	1.45321i	0.345122	+	0.0661919i
$483$	−7.79029	+	0.191241i	−0.354470	+	0.00870176i
$484$	−20.2867	−	4.78684i	−0.922122	−	0.217584i
$485$	23.5230	+	13.3256i	1.06813	+	0.605085i
$486$	−6.86299	−	4.28028i	−0.311311	−	0.194158i
$487$	22.6391	+	16.7903i	1.02587	+	0.760840i	0.971345	−	0.237672i	$-0.0763844\pi$
$487$	22.6391	+	16.7903i	1.02587	+	0.760840i	0.0545287	+	0.998512i	$0.482634\pi$
$488$	9.64622	−	20.1875i	0.436664	−	0.913843i
$489$	0.383056	+	1.52924i	0.0173224	+	0.0691548i
$490$	3.78620	−	32.5325i	0.171043	−	1.46967i
$491$	−2.42654	+	10.8059i	−0.109508	+	0.487661i	0.889990	+	0.455980i	$0.150711\pi$
$491$	−2.42654	+	10.8059i	−0.109508	+	0.487661i	−0.999498	+	0.0316813i	$0.989914\pi$
$492$	−0.863083	+	1.57349i	−0.0389108	+	0.0709385i
$493$	1.53596	−	0.870112i	0.0691763	−	0.0391879i
$494$	−1.94000	+	45.9121i	−0.0872848	+	2.06568i
$495$	3.87891	−	2.07332i	0.174344	−	0.0931888i
$496$	−7.01600	−	30.8270i	−0.315028	−	1.38417i
$497$	−23.3443	+	43.6741i	−1.04714	+	1.95905i
$498$	0.216433	−	0.0557937i	0.00969858	−	0.00250018i
$499$	−10.7989	+	9.31522i	−0.483426	+	0.417006i	−0.860713	−	0.509090i	$-0.829982\pi$
$499$	−10.7989	+	9.31522i	−0.483426	+	0.417006i	0.377287	+	0.926096i	$0.376857\pi$
$500$	8.37978	−	22.6439i	0.374755	−	1.01267i
$501$	−0.308533	−	0.136763i	−0.0137842	−	0.00611013i
$502$	23.9983	+	0.424475i	1.07110	+	0.0189453i
$503$	11.2600	+	4.02887i	0.502056	+	0.179639i	0.575724	−	0.817644i	$-0.304720\pi$
$503$	11.2600	+	4.02887i	0.502056	+	0.179639i	−0.0736674	+	0.997283i	$0.523470\pi$
$504$	17.7373	+	31.6027i	0.790084	+	1.40770i
$505$	0.588880	−	11.9869i	0.0262048	−	0.533411i
$506$	1.15370	+	8.85376i	0.0512883	+	0.393598i
$507$	1.16182	−	3.51689i	0.0515983	−	0.156190i
$508$	32.8091	+	6.05957i	1.45567	+	0.268850i
$509$	−2.22967	−	0.386884i	−0.0988283	−	0.0171483i	0.121333	−	0.992612i	$-0.461283\pi$
$509$	−2.22967	−	0.386884i	−0.0988283	−	0.0171483i	−0.220161	+	0.975464i	$0.570658\pi$
$510$	0.337465	+	1.08561i	0.0149432	+	0.0480718i
$511$	0.0521639			0.00230759
$512$	20.5755	+	9.41529i	0.909318	+	0.416101i
$513$	7.62384			0.336601
$514$	12.5199	+	40.2760i	0.552227	+	1.77650i
$515$	−31.8087	−	5.51934i	−1.40166	−	0.243211i
$516$	−0.732560	+	3.96639i	−0.0322492	+	0.174610i
$517$	−0.854007	+	2.58512i	−0.0375592	+	0.113693i
$518$	2.51456	+	19.2973i	0.110483	+	0.847874i
$519$	−0.0253340	+	0.515686i	−0.00111204	+	0.0226361i
$520$	−29.2731	−	8.22622i	−1.28371	−	0.360744i
$521$	−36.9501	−	13.2209i	−1.61881	−	0.579220i	−0.637299	−	0.770616i	$-0.719949\pi$
$521$	−36.9501	−	13.2209i	−1.61881	−	0.579220i	−0.981513	+	0.191396i	$0.938699\pi$
$522$	3.88527	+	0.0687215i	0.170053	+	0.00300786i
$523$	38.8619	+	17.2263i	1.69931	+	0.753254i	0.999232	+	0.0391912i	$0.0124781\pi$
$523$	38.8619	+	17.2263i	1.69931	+	0.753254i	0.700082	+	0.714063i	$0.253147\pi$
$524$	−13.9874	−	5.17628i	−0.611042	−	0.226127i
$525$	−0.826654	+	0.713077i	−0.0360781	+	0.0311212i
$526$	35.8296	−	9.23642i	1.56224	−	0.402727i
$527$	7.06908	−	13.2253i	0.307934	−	0.576104i
$528$	−0.536765	+	0.380356i	−0.0233597	+	0.0165529i
$529$	−40.5231	+	21.6601i	−1.76187	+	0.941742i
$530$	0.139371	−	3.29836i	0.00605390	−	0.143272i
$531$	−6.92137	+	3.92091i	−0.300362	+	0.170153i
$532$	−45.0416	−	24.7060i	−1.95280	−	1.07114i
$533$	4.98854	−	22.2150i	0.216077	−	0.962237i
$534$	0.345507	−	2.96874i	0.0149516	−	0.128470i
$535$	−3.63588	−	14.5153i	−0.157193	−	0.627549i
$536$	0.842289	−	0.297609i	0.0363813	−	0.0128548i
$537$	−2.58884	−	1.92001i	−0.111717	−	0.0828546i
$538$	−12.3517	−	7.70345i	−0.532518	−	0.332119i
$539$	7.82191	+	4.43106i	0.336914	+	0.190859i
$540$	−1.15852	+	4.90984i	−0.0498549	+	0.211286i
$541$	−11.9449	+	0.293232i	−0.513553	+	0.0126070i	−0.280495	−	0.959856i	$-0.590498\pi$
$541$	−11.9449	+	0.293232i	−0.513553	+	0.0126070i	−0.233059	+	0.972463i	$0.574873\pi$
$542$	−15.2047	−	2.91615i	−0.653098	−	0.125260i
$543$	3.07457	−	2.05436i	0.131942	−	0.0881611i
$544$	4.44480	+	9.76920i	0.190569	+	0.418851i
$545$	−0.140155	−	0.0936487i	−0.00600359	−	0.00401147i
$546$	5.18595	+	5.11530i	0.221938	+	0.218915i
$547$	21.9129	+	8.45275i	0.936929	+	0.361414i	0.779703	−	0.626149i	$-0.215370\pi$
$547$	21.9129	+	8.45275i	0.936929	+	0.361414i	0.157226	+	0.987563i	$0.449745\pi$
$548$	−5.72453	+	9.85485i	−0.244540	+	0.420978i
$549$	23.1851	+	2.85961i	0.989516	+	0.122045i
$550$	0.911823	+	0.856283i	0.0388803	+	0.0365121i
$551$	−4.72476	+	2.83191i	−0.201282	+	0.120643i
$552$	−4.21278	−	2.83915i	−0.179308	−	0.120842i
$553$	4.17330	−	3.09513i	0.177467	−	0.131618i
$554$	−1.32902	+	0.107203i	−0.0564645	+	0.00455461i
$555$	−0.773779	+	1.09868i	−0.0328451	+	0.0466364i
$556$	20.3625	+	13.9270i	0.863561	+	0.590637i
$557$	−14.4533	+	18.5201i	−0.612404	+	0.784724i	−0.989973	−	0.141258i	$-0.954885\pi$
$557$	−14.4533	+	18.5201i	−0.612404	+	0.784724i	0.377568	+	0.925982i	$0.376760\pi$
$558$	28.1967	−	17.1644i	1.19366	−	0.726625i
$559$	−5.01566	−	50.9248i	−0.212140	−	2.15389i
$560$	22.7555	−	25.2530i	0.961594	−	1.06713i
$561$	−0.310542	−	0.0305857i	−0.0131111	−	0.00129133i
$562$	−11.1505	+	31.8504i	−0.470354	+	1.34353i
$563$	−28.3237	+	9.35687i	−1.19370	+	0.394345i	−0.840815	−	0.541322i	$-0.817924\pi$
$563$	−28.3237	+	9.35687i	−1.19370	+	0.394345i	−0.352884	+	0.935667i	$0.614799\pi$
$564$	−0.781943	−	1.33722i	−0.0329257	−	0.0563070i
$565$	−21.8042	−	0.535263i	−0.917309	−	0.0225187i
$566$	2.14378	−	9.86257i	0.0901096	−	0.414555i
$567$	−25.0021	+	27.5856i	−1.04999	+	1.15848i
$568$	−28.8944	+	14.4007i	−1.21238	+	0.604241i
$569$	20.1500	−	7.20978i	0.844732	−	0.302250i	0.121274	−	0.992619i	$-0.461302\pi$
$569$	20.1500	−	7.20978i	0.844732	−	0.302250i	0.723457	+	0.690369i	$0.242552\pi$
$570$	−1.13585	−	3.36070i	−0.0475753	−	0.140764i
$571$	18.8991	−	21.9093i	0.790903	−	0.916876i	−0.207209	−	0.978297i	$-0.566438\pi$
$571$	18.8991	−	21.9093i	0.790903	−	0.916876i	0.998112	+	0.0614205i	$0.0195631\pi$
$572$	5.20574	−	6.52365i	0.217663	−	0.272767i
$573$	3.65139	−	0.819948i	0.152539	−	0.0342538i
$574$	19.7859	+	16.0121i	0.825849	+	0.668332i
$575$	−3.69649	+	8.92411i	−0.154154	+	0.372161i
$576$	−2.50234	+	23.4928i	−0.104264	+	0.978866i
$577$	−11.0762	−	26.7403i	−0.461108	−	1.11321i	−0.967943	−	0.251170i	$-0.919185\pi$
$577$	−11.0762	−	26.7403i	−0.461108	−	1.11321i	0.506835	−	0.862043i	$-0.330815\pi$
$578$	5.37662	−	18.1720i	0.223638	−	0.755857i
$579$	−1.06549	−	0.674716i	−0.0442803	−	0.0280402i
$580$	−1.10581	−	3.47314i	−0.0459161	−	0.144214i
$581$	−0.233199	−	3.16140i	−0.00967471	−	0.131157i
$582$	0.281720	−	4.21278i	0.0116777	−	0.174625i
$583$	0.819144	+	0.387426i	0.0339255	+	0.0160456i
$584$	0.0277255	+	0.0196916i	0.00114729	+	0.000814844i
$585$	−1.55782	−	31.7102i	−0.0644081	−	1.31106i
$586$	5.49968	+	30.4541i	0.227190	+	1.25805i
$587$	3.62525	+	3.80772i	0.149630	+	0.157161i	0.794787	−	0.606889i	$-0.207583\pi$
$587$	3.62525	+	3.80772i	0.149630	+	0.157161i	−0.645156	+	0.764051i	$0.723208\pi$
$588$	−4.83438	+	1.67095i	−0.199366	+	0.0689086i
$589$	−21.0390	+	41.7974i	−0.866898	+	1.72223i
$590$	5.56288	+	4.97284i	0.229020	+	0.204729i
$591$	1.19537	+	1.45656i	0.0491710	+	0.0599150i
$592$	−5.94812	+	11.2059i	−0.244466	+	0.460558i
$593$	18.2230	+	14.9553i	0.748330	+	0.614139i	0.929290	−	0.369352i	$-0.120420\pi$
$593$	18.2230	+	14.9553i	0.748330	+	0.614139i	−0.180959	+	0.983491i	$0.557920\pi$
$594$	−1.11780	−	0.817196i	−0.0458639	−	0.0335299i
$595$	16.0026	−	1.97373i	0.656042	−	0.0809150i
$596$	−27.7469	−	11.8468i	−1.13656	−	0.485262i
$597$	0.619422	+	3.56982i	0.0253513	+	0.146103i
$598$	61.3348	+	19.7968i	2.50817	+	0.809552i
$599$	−30.9145	−	4.58574i	−1.26313	−	0.187368i	−0.518637	−	0.854995i	$-0.673560\pi$
$599$	−30.9145	−	4.58574i	−1.26313	−	0.187368i	−0.744496	+	0.667627i	$0.767310\pi$
$600$	−0.708555	+	0.0669472i	−0.0289266	+	0.00273311i
$601$	1.99797	−	7.97636i	0.0814991	−	0.325363i	−0.915543	−	0.402220i	$-0.868239\pi$
$601$	1.99797	−	7.97636i	0.0814991	−	0.325363i	0.997042	+	0.0768575i	$0.0244887\pi$
$602$	53.5128	+	20.2217i	2.18102	+	0.824174i
$603$	0.573846	+	0.735316i	0.0233688	+	0.0299444i
$604$	0.623824	+	9.91996i	0.0253830	+	0.403637i
$605$	−18.6626	+	8.27256i	−0.758742	+	0.336327i
$606$	−1.72666	+	0.729120i	−0.0701409	+	0.0296185i
$607$	2.81303	+	14.1420i	0.114177	+	0.574008i	0.994942	+	0.100453i	$0.0320293\pi$
$607$	2.81303	+	14.1420i	0.114177	+	0.574008i	−0.880764	+	0.473555i	$0.842971\pi$
$608$	−14.6135	−	30.1343i	−0.592657	−	1.22211i
$609$	−0.170348	+	0.856396i	−0.00690284	+	0.0347029i
$610$	−4.42216	−	21.4614i	−0.179048	−	0.868948i
$611$	14.2332	+	13.5511i	0.575813	+	0.548220i
$612$	−8.19935	+	7.63889i	−0.331439	+	0.308784i
$613$	−40.4025	+	11.1809i	−1.63184	+	0.451591i	−0.957878	−	0.287175i	$-0.907284\pi$
$613$	−40.4025	+	11.1809i	−1.63184	+	0.451591i	−0.673962	+	0.738766i	$0.735409\pi$
$614$	−18.5576	−	25.9696i	−0.748923	−	1.04805i
$615$	0.257900	+	1.73862i	0.0103995	+	0.0701079i
$616$	3.95574	+	8.45036i	0.159381	+	0.340475i
$617$	35.1993	+	21.0977i	1.41707	+	0.849360i	0.998274	−	0.0587203i	$-0.0187020\pi$
$617$	35.1993	+	21.0977i	1.41707	+	0.849360i	0.418797	+	0.908080i	$0.362452\pi$
$618$	1.37803	+	4.84993i	0.0554326	+	0.195093i
$619$	−31.0762	+	19.6788i	−1.24906	+	0.790958i	−0.984833	−	0.173503i	$-0.944491\pi$
$619$	−31.0762	+	19.6788i	−1.24906	+	0.790958i	−0.264225	+	0.964461i	$0.585116\pi$
$620$	−23.7209	−	19.9009i	−0.952653	−	0.799240i
$621$	2.85187	−	10.3053i	0.114442	−	0.413539i
$622$	−29.3706	−	13.6456i	−1.17765	−	0.547138i
$623$	−40.5640	−	12.3050i	−1.62516	−	0.492988i
$624$	0.825365	+	4.67649i	0.0330410	+	0.187209i
$625$	−5.17587	−	17.0626i	−0.207035	−	0.682502i
$626$	−19.0706	−	25.3485i	−0.762214	−	1.01313i
$627$	0.971068	+	0.0716303i	0.0387807	+	0.00286064i
$628$	6.53716	−	41.0058i	0.260861	−	1.63631i
$629$	−5.61442	+	2.16572i	−0.223862	+	0.0863530i
$630$	32.5456	+	14.1602i	1.29665	+	0.564158i
$631$	6.09453	+	12.8858i	0.242619	+	0.512976i	0.988149	−	0.153497i	$-0.0490534\pi$
$631$	6.09453	+	12.8858i	0.242619	+	0.512976i	−0.745530	+	0.666472i	$0.767803\pi$
$632$	3.38653	−	0.0696825i	0.134709	−	0.00277182i
$633$	0.447211	+	0.493421i	0.0177750	+	0.0196117i
$634$	−23.2255	−	40.3510i	−0.922403	−	1.60254i
$635$	29.1869	−	14.6915i	1.15825	−	0.583012i
$636$	−0.473580	+	0.203817i	−0.0187787	+	0.00808187i
$637$	53.0550	−	37.3655i	2.10211	−	1.48048i
$638$	0.996292	+	0.0912321i	0.0394436	+	0.00361191i
$639$	−23.8355	−	23.8355i	−0.942918	−	0.942918i
$640$	21.6275	−	4.83204i	0.854904	−	0.191003i
$641$	−24.9714	+	24.9714i	−0.986312	+	0.986312i	−0.999908	−	0.0135953i	$-0.995672\pi$
$641$	−24.9714	+	24.9714i	−0.986312	+	0.986312i	0.0135953	+	0.999908i	$0.495672\pi$
$642$	−1.79626	+	1.49489i	−0.0708929	+	0.0589985i
$643$	14.8373	+	21.0674i	0.585127	+	0.830817i	0.996752	−	0.0805367i	$-0.0256634\pi$
$643$	14.8373	+	21.0674i	0.585127	+	0.830817i	−0.411624	+	0.911354i	$0.635038\pi$
$644$	−50.2445	+	51.6420i	−1.97991	+	2.03498i
$645$	1.77609	+	3.52849i	0.0699336	+	0.138934i
$646$	4.13181	−	15.3389i	0.162564	−	0.603501i
$647$	−32.6467	+	29.5892i	−1.28347	+	1.16327i	−0.306043	+	0.952018i	$0.599005\pi$
$647$	−32.6467	+	29.5892i	−1.28347	+	1.16327i	−0.977431	+	0.211255i	$0.932245\pi$
$648$	−23.7022	+	5.22374i	−0.931109	+	0.205208i
$649$	−1.85142	+	0.875654i	−0.0726744	+	0.0343724i
$650$	8.40172	−	3.30727i	0.329543	−	0.129722i
$651$	2.66953	+	6.92050i	0.104627	+	0.271236i
$652$	12.4207	+	7.62869i	0.486432	+	0.298763i
$653$	−2.15393	+	29.2001i	−0.0842898	+	1.14269i	0.775262	+	0.631640i	$0.217618\pi$
$653$	−2.15393	+	29.2001i	−0.0842898	+	1.14269i	−0.859551	+	0.511049i	$0.829257\pi$
$654$	−0.00368402	+	0.0260660i	−0.000144057	+	0.00101926i
$655$	−13.9779	+	4.24015i	−0.546161	+	0.165676i
$656$	4.47187	+	15.9796i	0.174597	+	0.623899i
$657$	−0.0103072	+	0.0339781i	−0.000402121	+	0.00132561i
$658$	−20.6345	+	7.54317i	−0.804418	+	0.294064i
$659$	2.14575	+	0.593809i	0.0835865	+	0.0231315i	0.308255	−	0.951304i	$-0.400255\pi$
$659$	2.14575	+	0.593809i	0.0835865	+	0.0231315i	−0.224669	+	0.974435i	$0.572130\pi$
$660$	−0.193695	+	0.614494i	−0.00753957	+	0.0239191i
$661$	−12.1226	−	19.1436i	−0.471513	−	0.744601i	0.522643	−	0.852552i	$-0.324946\pi$
$661$	−12.1226	−	19.1436i	−0.471513	−	0.744601i	−0.994156	+	0.107951i	$0.965571\pi$
$662$	−2.01207	+	3.60929i	−0.0782013	+	0.140279i
$663$	−1.15800	+	1.93201i	−0.0449731	+	0.0750330i
$664$	1.06946	−	1.76833i	0.0415033	−	0.0686247i
$665$	−49.7684	+	7.38245i	−1.92994	+	0.286279i
$666$	−13.0666	−	2.17507i	−0.506320	−	0.0842822i
$667$	2.06056	+	7.44592i	0.0797853	+	0.288307i
$668$	−2.92332	+	1.09144i	−0.113107	+	0.0422289i
$669$	−2.93814	+	3.08603i	−0.113595	+	0.119313i
$670$	0.481067	−	0.730767i	0.0185852	−	0.0282320i
$671$	5.89892	+	1.17337i	0.227725	+	0.0452974i
$672$	−5.09498	−	1.49148i	−0.196543	−	0.0575352i
$673$	8.88345	−	1.76703i	0.342432	−	0.0681139i	−0.0208787	−	0.999782i	$-0.506646\pi$
$673$	8.88345	−	1.76703i	0.342432	−	0.0681139i	0.363311	+	0.931668i	$0.381646\pi$
$674$	5.01553	−	12.3474i	0.193191	−	0.475603i
$675$	−0.607048	−	1.36948i	−0.0233653	−	0.0527113i
$676$	−15.0652	−	30.7542i	−0.579432	−	1.18285i
$677$	21.2436	−	16.5787i	0.816458	−	0.637170i	−0.118092	−	0.993003i	$-0.537678\pi$
$677$	21.2436	−	16.5787i	0.816458	−	0.637170i	0.934550	+	0.355833i	$0.115803\pi$
$678$	1.40168	+	3.10450i	0.0538312	+	0.119227i
$679$	−58.0879	−	14.5503i	−2.22921	−	0.558388i
$680$	9.25055	+	4.99184i	0.354742	+	0.191428i
$681$	0.588061	−	3.96438i	0.0225345	−	0.151916i
$682$	7.56497	−	3.87313i	0.289677	−	0.148310i
$683$	33.9652	−	5.89352i	1.29964	−	0.225509i	0.521312	−	0.853366i	$-0.325443\pi$
$683$	33.9652	−	5.89352i	1.29964	−	0.225509i	0.778329	+	0.627857i	$0.216068\pi$
$684$	24.9926	−	24.4572i	0.955617	−	0.935143i
$685$	1.36633	+	11.0779i	0.0522046	+	0.423264i
$686$	4.54320	+	29.2445i	0.173460	+	1.11656i
$687$	−3.37368	+	4.11084i	−0.128714	+	0.156838i
$688$	20.8088	+	30.9487i	0.793328	+	1.17991i
$689$	5.05622	−	4.14953i	0.192626	−	0.158084i
$690$	−4.96763	+	0.278205i	−0.189114	+	0.0105911i
$691$	10.0610	+	5.06427i	0.382738	+	0.192654i	0.630540	−	0.776157i	$-0.282833\pi$
$691$	10.0610	+	5.06427i	0.382738	+	0.192654i	−0.247803	+	0.968811i	$0.579708\pi$
$692$	3.16742	+	3.57168i	0.120407	+	0.135775i
$693$	−7.05565	+	6.71753i	−0.268022	+	0.255178i
$694$	24.7815	−	35.7046i	0.940693	−	1.35533i
$695$	24.1318	−	1.18552i	0.915371	−	0.0449693i
$696$	−0.413826	+	0.390874i	−0.0156860	+	0.0148161i
$697$	−3.36520	+	7.11511i	−0.127466	+	0.269504i
$698$	−2.56415	−	2.93166i	−0.0970543	−	0.110965i
$699$	4.64062	−	0.342313i	0.175524	−	0.0129475i
$700$	−0.851523	+	10.0581i	−0.0321846	+	0.380160i
$701$	6.26152	−	9.88801i	0.236494	−	0.373465i	−0.705712	−	0.708499i	$-0.749373\pi$
$701$	6.26152	−	9.88801i	0.236494	−	0.373465i	0.942206	+	0.335034i	$0.108748\pi$
$702$	−8.78236	+	4.77199i	−0.331469	+	0.180107i
$703$	17.3482	−	7.18585i	0.654299	−	0.271019i
$704$	−1.08746	+	5.98469i	−0.0409853	+	0.225557i
$705$	−1.40163	−	0.580574i	−0.0527884	−	0.0218657i
$706$	33.9777	−	3.58194i	1.27877	−	0.134808i
$707$	5.82433	+	25.9369i	0.219047	+	0.975459i
$708$	0.322942	−	1.11965i	0.0121369	−	0.0420792i
$709$	−6.44818	−	5.56224i	−0.242166	−	0.208894i	0.523685	−	0.851912i	$-0.324557\pi$
$709$	−6.44818	−	5.56224i	−0.242166	−	0.208894i	−0.765851	+	0.643018i	$0.777682\pi$
$710$	−14.0220	+	28.3391i	−0.526235	+	1.06355i
$711$	1.19147	+	3.32995i	0.0446838	+	0.124883i
$712$	−16.9150	−	21.8529i	−0.633916	−	0.818972i
$713$	48.6284	+	44.0742i	1.82115	+	1.65059i
$714$	−1.36174	−	2.11815i	−0.0509619	−	0.0792697i
$715$	0.200600	−	8.17153i	0.00750201	−	0.305598i
$716$	−29.5244	+	4.05331i	−1.10338	+	0.151479i
$717$	1.79477	+	5.43286i	0.0670270	+	0.202894i
$718$	11.1255	−	5.35565i	0.415201	−	0.199871i
$719$	2.72256	−	27.6426i	0.101534	−	1.03090i	−0.800529	−	0.599294i	$-0.795448\pi$
$719$	2.72256	−	27.6426i	0.101534	−	1.03090i	0.902064	−	0.431603i	$-0.142052\pi$
$720$	11.9528	+	19.8121i	0.445454	+	0.738352i
$721$	71.1641	−	7.00906i	2.65029	−	0.261031i
$722$	−5.36443	+	22.0567i	−0.199643	+	0.820864i
$723$	−0.930281	−	0.725998i	−0.0345975	−	0.0270002i
$724$	7.03279	−	33.4586i	0.261372	−	1.24348i
$725$	0.884909	+	0.623223i	0.0328647	+	0.0231459i
$726$	2.42829	+	2.06578i	0.0901222	+	0.0766683i
$727$	−12.9663	−	17.4830i	−0.480892	−	0.648408i	0.494424	−	0.869221i	$-0.335379\pi$
$727$	−12.9663	−	17.4830i	−0.480892	−	0.648408i	−0.975316	+	0.220813i	$0.929129\pi$
$728$	67.3504	+	0.267397i	2.49617	+	0.00991040i
$729$	−12.5987	−	21.0196i	−0.466617	−	0.778504i
$730$	0.0332890	−	0.00104567i	0.00123208	−	3.87019e-5i
$731$	−2.16539	+	17.5565i	−0.0800897	+	0.649350i
$732$	−2.72045	+	2.07606i	−0.100551	+	0.0767333i
$733$	−13.5333	+	35.0837i	−0.499863	+	1.29585i	0.421389	+	0.906880i	$0.361543\pi$
$733$	−13.5333	+	35.0837i	−0.499863	+	1.29585i	−0.921252	+	0.388966i	$0.872832\pi$
$734$	0.144954	+	21.1367i	0.00535034	+	0.780168i
$735$	−2.78314	+	4.16526i	−0.102658	+	0.153638i
$736$	−46.1999	+	8.48104i	−1.70295	+	0.312615i
$737$	0.133416	+	0.199671i	0.00491443	+	0.00735497i
$738$	−14.3394	+	9.72416i	−0.527840	+	0.357951i
$739$	−0.887058	−	36.1347i	−0.0326310	−	1.32924i	−0.763095	−	0.646286i	$-0.776321\pi$
$739$	−0.887058	−	36.1347i	−0.0326310	−	1.32924i	0.730464	−	0.682951i	$-0.239304\pi$
$740$	1.99153	+	12.2644i	0.0732100	+	0.450848i
$741$	3.46440	−	6.11553i	0.127268	−	0.224659i
$742$	1.65103	+	7.12351i	0.0606113	+	0.261512i
$743$	3.01417	−	4.06414i	0.110579	−	0.149099i	−0.744451	−	0.667677i	$-0.767289\pi$
$743$	3.01417	−	4.06414i	0.110579	−	0.149099i	0.855030	+	0.518578i	$0.173539\pi$
$744$	−1.19358	+	4.68602i	−0.0437587	+	0.171798i
$745$	−28.6624	+	7.17956i	−1.05011	+	0.263039i
$746$	28.2431	+	35.6829i	1.03405	+	1.30644i
$747$	2.10533	+	0.472767i	0.0770298	+	0.0172976i
$748$	−2.24997	+	1.80609i	−0.0822671	+	0.0660372i
$749$	16.3368	+	28.8384i	0.596933	+	1.05373i
$750$	−2.71926	+	2.49877i	−0.0992932	+	0.0912422i
$751$	11.1808	+	20.9179i	0.407995	+	0.763304i	0.999061	−	0.0433184i	$-0.0137930\pi$
$751$	11.1808	+	20.9179i	0.407995	+	0.763304i	−0.591067	+	0.806623i	$0.701293\pi$
$752$	−13.8149	−	3.78019i	−0.503778	−	0.137849i
$753$	−3.23769	−	1.73058i	−0.117988	−	0.0630659i
$754$	3.67016	−	6.21962i	0.133659	−	0.226505i
$755$	6.35835	+	7.37110i	0.231404	+	0.268262i
$756$	−0.427400	−	11.1657i	−0.0155444	−	0.406091i
$757$	−12.8119	+	28.9031i	−0.465656	+	1.05050i	0.515431	+	0.856931i	$0.327632\pi$
$757$	−12.8119	+	28.9031i	−0.465656	+	1.05050i	−0.981086	+	0.193571i	$0.937993\pi$
$758$	−25.6450	−	26.5685i	−0.931469	−	0.965013i
$759$	0.460075	−	1.28582i	0.0166997	−	0.0466724i
$760$	−29.2391	−	14.8635i	−1.06061	−	0.539156i
$761$	12.3457	+	0.606503i	0.447530	+	0.0219857i	0.271585	−	0.962414i	$-0.412452\pi$
$761$	12.3457	+	0.606503i	0.447530	+	0.0219857i	0.175944	+	0.984400i	$0.443702\pi$
$762$	−4.04445	−	3.11193i	−0.146515	−	0.112733i
$763$	0.354520	+	0.117118i	0.0128345	+	0.00423994i
$764$	18.8274	−	29.0314i	0.681151	−	1.05032i
$765$	−1.87634	+	10.8136i	−0.0678394	+	0.390968i
$766$	7.37688	−	14.0318i	0.266538	−	0.506990i
$767$			14.7837i			0.533809i
$768$	−2.14499	−	2.71606i	−0.0774006	−	0.0980074i
$769$		−	19.5065i		−	0.703423i	−0.936108	−	0.351711i	$-0.885600\pi$
$769$		−	19.5065i		−	0.703423i	0.936108	−	0.351711i	$-0.114400\pi$
$770$	8.08833	+	4.25225i	0.291483	+	0.153240i
$771$	1.10289	−	6.35611i	0.0397196	−	0.228910i
$772$	−11.4044	+	2.43155i	−0.410455	+	0.0875133i
$773$	45.0300	+	14.8759i	1.61962	+	0.535049i	0.973597	−	0.228272i	$-0.0733076\pi$
$773$	45.0300	+	14.8759i	1.61962	+	0.535049i	0.646019	+	0.763321i	$0.276433\pi$
$774$	−23.7455	+	30.8611i	−0.853515	+	1.10928i
$775$	9.18335	+	0.451149i	0.329876	+	0.0162057i
$776$	−25.3815	−	29.6615i	−0.911142	−	1.06478i
$777$	1.00276	−	2.80253i	0.0359738	−	0.100540i
$778$	−36.4581	+	35.1908i	−1.30709	+	1.26165i
$779$	9.95276	−	22.4531i	0.356595	−	0.804465i
$780$	3.41201	+	3.16043i	0.122170	+	0.113162i
$781$	−5.66864	−	6.57153i	−0.202840	−	0.235148i
$782$	−19.1884	−	11.3229i	−0.686175	−	0.404907i
$783$	−1.05665	−	0.564792i	−0.0377616	−	0.0201840i
$784$	−21.1418	+	42.3052i	−0.755063	+	1.51090i
$785$	−19.1704	−	35.8653i	−0.684220	−	1.28009i
$786$	1.54352	+	1.67971i	0.0550554	+	0.0599134i
$787$	−11.7169	−	20.6832i	−0.417662	−	0.737276i	0.579304	−	0.815111i	$-0.303324\pi$
$787$	−11.7169	−	20.6832i	−0.417662	−	0.737276i	−0.996966	+	0.0778349i	$0.975199\pi$
$788$	17.3188	+	1.89531i	0.616956	+	0.0675175i
$789$	−5.52187	−	1.23998i	−0.196584	−	0.0441444i
$790$	2.60120	−	2.05885i	0.0925464	−	0.0732506i
$791$	46.8626	−	11.7385i	1.66624	−	0.417372i
$792$	−6.28596	+	0.906943i	−0.223362	+	0.0322268i
$793$	25.8624	−	34.8714i	0.918401	−	1.23832i
$794$	−52.3113	+	12.1243i	−1.85646	+	0.430276i
$795$	−0.248886	+	0.439345i	−0.00882707	+	0.0155819i
$796$	27.1787	+	19.5851i	0.963323	+	0.694174i
$797$	−0.883975	−	36.0091i	−0.0313120	−	1.27551i	−0.785504	−	0.618856i	$-0.787596\pi$
$797$	−0.883975	−	36.0091i	−0.0313120	−	1.27551i	0.754192	−	0.656653i	$-0.228029\pi$
$798$	4.41012	+	6.50322i	0.156117	+	0.230211i
$799$	−3.77437	−	5.64874i	−0.133528	−	0.199838i
$800$	−4.24947	+	5.02450i	−0.150241	+	0.177643i
$801$	16.0302	−	23.9910i	0.566401	−	0.847679i
$802$	−50.3793	+	0.345498i	−1.77896	+	0.0122000i
$803$	−0.00329005	+	0.00852912i	−0.000116103	+	0.000300986i
$804$	−0.135419	−	0.0181930i	−0.00477586	−	0.000641618i
$805$	−8.63797	+	70.0348i	−0.304448	+	2.46840i
$806$	−1.92611	−	61.3179i	−0.0678443	−	2.15983i
$807$	1.14467	+	1.90976i	0.0402942	+	0.0672267i
$808$	−6.69539	+	15.9843i	−0.235543	+	0.562326i
$809$	−13.3475	−	17.9970i	−0.469274	−	0.632742i	0.503639	−	0.863914i	$-0.331994\pi$
$809$	−13.3475	−	17.9970i	−0.469274	−	0.632742i	−0.972913	+	0.231172i	$0.925744\pi$
$810$	−15.4024	+	18.1052i	−0.541185	+	0.636153i
$811$	−6.00063	−	4.22612i	−0.210711	−	0.148399i	0.465652	−	0.884968i	$-0.345820\pi$
$811$	−6.00063	−	4.22612i	−0.210711	−	0.148399i	−0.676363	+	0.736569i	$0.736445\pi$
$812$	4.41242	+	6.76100i	0.154845	+	0.237264i
$813$	1.86679	+	1.45686i	0.0654713	+	0.0510943i
$814$	−3.31382	−	0.805959i	−0.116149	−	0.0282489i
$815$	14.2070	−	1.39927i	0.497650	−	0.0490143i
$816$	0.0758151	−	1.63986i	0.00265406	−	0.0574066i
$817$	5.41041	−	54.9328i	0.189286	−	1.92185i
$818$	−2.17645	−	4.52124i	−0.0760979	−	0.158081i
$819$	22.0588	+	66.7730i	0.770798	+	2.33324i
$820$	12.9476	+	9.82168i	0.452150	+	0.342988i
$821$	−1.14120	+	46.4874i	−0.0398282	+	1.62242i	0.564325	+	0.825553i	$0.309137\pi$
$821$	−1.14120	+	46.4874i	−0.0398282	+	1.62242i	−0.604153	+	0.796869i	$0.706488\pi$
$822$	1.46630	−	0.942674i	0.0511431	−	0.0328795i
$823$	33.8592	+	30.6882i	1.18026	+	1.06972i	0.996226	+	0.0868026i	$0.0276649\pi$
$823$	33.8592	+	30.6882i	1.18026	+	1.06972i	0.184032	+	0.982920i	$0.441085\pi$
$824$	40.4701	+	23.1387i	1.40984	+	0.806076i
$825$	−0.0644543	−	0.180138i	−0.00224401	−	0.00627159i
$826$	−14.8131	−	7.32941i	−0.515414	−	0.255023i
$827$	−36.4071	−	31.4050i	−1.26600	−	1.09206i	−0.991450	−	0.130486i	$-0.958346\pi$
$827$	−36.4071	−	31.4050i	−1.26600	−	1.09206i	−0.274550	−	0.961573i	$-0.588529\pi$
$828$	−23.7103	−	42.9319i	−0.823990	−	1.49199i
$829$	−10.0019	−	44.5404i	−0.347379	−	1.54695i	−0.768442	−	0.639919i	$-0.778968\pi$
$829$	−10.0019	−	44.5404i	−0.347379	−	1.54695i	0.421063	−	0.907031i	$-0.361657\pi$
$830$	−0.212191	−	2.01281i	−0.00736527	−	0.0698656i
$831$	0.188413	+	0.0780432i	0.00653598	+	0.00270729i
$832$	35.6962	+	25.5666i	1.23754	+	0.886361i
$833$	−20.7252	+	8.58466i	−0.718086	+	0.297441i
$834$	−1.80149	−	3.31547i	−0.0623806	−	0.114805i
$835$	−1.63499	+	2.58193i	−0.0565812	+	0.0893514i
$836$	6.88041	−	5.80634i	0.237964	−	0.200817i
$837$	−10.1504	+	0.748737i	−0.350848	+	0.0258801i
$838$	9.47615	−	8.28820i	0.327348	−	0.286311i
$839$	−0.239996	+	0.507429i	−0.00828559	+	0.0175184i	−0.908090	−	0.418776i	$-0.862459\pi$
$839$	−0.239996	+	0.507429i	−0.00828559	+	0.0175184i	0.899804	+	0.436294i	$0.143709\pi$
$840$	−4.85831	+	1.85193i	−0.167628	+	0.0638978i
$841$	−28.1004	+	1.38049i	−0.968980	+	0.0476030i
$842$	−23.7541	−	16.4870i	−0.818619	−	0.568178i
$843$	3.73821	−	3.55907i	0.128751	−	0.122581i
$844$	6.14619	+	0.368693i	0.211561	+	0.0126909i
$845$	−29.9584	−	15.0798i	−1.03060	−	0.518761i
$846$	−0.836204	−	14.9312i	−0.0287493	−	0.513347i
$847$	34.9528	−	28.6850i	1.20099	−	0.985628i
$848$	−1.81155	+	4.40945i	−0.0622090	+	0.151421i
$849$	−0.979332	+	1.19332i	−0.0336106	+	0.0409546i
$850$	−3.08434	+	0.479158i	−0.105792	+	0.0164350i
$851$	−3.22381	−	26.1380i	−0.110511	−	0.895999i
$852$	4.93766	+	0.0534673i	0.169161	+	0.00183176i
$853$	−1.77984	+	0.308832i	−0.0609406	+	0.0105742i	−0.201350	−	0.979519i	$-0.564533\pi$
$853$	−1.77984	+	0.308832i	−0.0609406	+	0.0105742i	0.140410	+	0.990093i	$0.455158\pi$
$854$	22.1188	+	43.2022i	0.756890	+	1.47835i
$855$	5.02510	−	33.8765i	0.171855	−	1.15855i
$856$	−2.20326	+	21.4949i	−0.0753059	+	0.734680i
$857$	−18.9261	−	4.74075i	−0.646505	−	0.161941i	−0.0941603	−	0.995557i	$-0.530017\pi$
$857$	−18.9261	−	4.74075i	−0.646505	−	0.161941i	−0.552344	+	0.833616i	$0.686267\pi$
$858$	−1.16347	+	0.525306i	−0.0397202	+	0.0179337i
$859$	1.88325	−	1.46970i	0.0642556	−	0.0501456i	−0.582593	−	0.812764i	$-0.697962\pi$
$859$	1.88325	−	1.46970i	0.0642556	−	0.0501456i	0.646848	+	0.762619i	$0.276087\pi$
$860$	34.5552	+	11.8320i	1.17832	+	0.403467i
$861$	−1.57766	−	3.55915i	−0.0537666	−	0.121296i
$862$	11.2443	+	4.56746i	0.382983	+	0.155568i
$863$	−4.39349	+	0.873919i	−0.149556	+	0.0297485i	−0.269300	−	0.963056i	$-0.586792\pi$
$863$	−4.39349	+	0.873919i	−0.149556	+	0.0297485i	0.119744	+	0.992805i	$0.461792\pi$
$864$	3.98782	−	6.09597i	0.135668	−	0.207389i
$865$	4.58554	+	0.912121i	0.155913	+	0.0310130i
$866$	−16.5243	−	10.8780i	−0.561517	−	0.369649i
$867$	−1.99868	+	2.09928i	−0.0678787	+	0.0712952i
$868$	62.3948	+	28.4700i	2.11782	+	0.966334i
$869$	0.242858	+	0.877574i	0.00823838	+	0.0297697i
$870$	−0.0915422	+	0.549934i	−0.00310357	+	0.0186445i
$871$	1.71469	−	0.254350i	0.0581000	−	0.00861832i
$872$	0.144218	+	0.196078i	0.00488385	+	0.00664005i
$873$	20.9554	−	34.9619i	0.709231	−	1.18328i
$874$	60.7246	+	33.8521i	2.05404	+	1.14507i
$875$	28.0216	+	44.2510i	0.947304	+	1.49596i
$876$	−0.00240212	−	0.00461352i	−8.11601e−5	−	0.000155877i
$877$	−27.8896	−	7.71810i	−0.941765	−	0.260622i	−0.238171	−	0.971223i	$-0.576548\pi$
$877$	−27.8896	−	7.71810i	−0.941765	−	0.260622i	−0.703595	+	0.710602i	$0.748423\pi$
$878$	4.88562	+	13.3647i	0.164882	+	0.451038i
$879$	1.37402	−	4.52955i	0.0463447	−	0.152778i
$880$	2.69380	+	5.31340i	0.0908079	+	0.179115i
$881$	12.1974	−	3.70004i	0.410941	−	0.124658i	−0.0780438	−	0.996950i	$-0.524867\pi$
$881$	12.1974	−	3.70004i	0.410941	−	0.124658i	0.488985	+	0.872292i	$0.337367\pi$
$882$	−48.8944	−	6.91045i	−1.64636	−	0.232687i
$883$	3.42339	−	46.4098i	0.115206	−	1.56181i	−0.562697	−	0.826663i	$-0.690236\pi$
$883$	3.42339	−	46.4098i	0.115206	−	1.56181i	0.677903	−	0.735151i	$-0.262889\pi$
$884$	4.84140	+	20.2560i	0.162834	+	0.681284i
$885$	−0.410735	−	1.06479i	−0.0138067	−	0.0357926i
$886$	−2.05761	−	5.22712i	−0.0691269	−	0.175609i
$887$	15.2407	−	7.20830i	0.511732	−	0.242031i	−0.154206	−	0.988039i	$-0.549282\pi$
$887$	15.2407	−	7.20830i	0.511732	−	0.242031i	0.665937	+	0.746008i	$0.268032\pi$
$888$	1.59091	−	1.11102i	0.0533875	−	0.0372835i
$889$	−53.6274	+	48.6051i	−1.79861	+	1.63016i
$890$	−26.1331	−	7.03942i	−0.875983	−	0.235962i
$891$	−2.93350	−	5.82785i	−0.0982758	−	0.195240i
$892$	0.540349	+	39.3941i	0.0180922	+	1.31901i
$893$	12.2066	+	17.3321i	0.408479	+	0.579995i
$894$	2.95187	+	3.54697i	0.0987252	+	0.118629i
$895$	−20.6381	+	20.6381i	−0.689856	+	0.689856i
$896$	−43.3147	+	23.0919i	−1.44704	+	0.771448i
$897$	−6.97057	−	6.97057i	−0.232741	−	0.232741i
$898$	0.492524	−	5.37857i	0.0164357	−	0.179485i
$899$	6.01242	−	4.23443i	0.200526	−	0.141226i
$900$	−6.38331	−	2.54206i	−0.212777	−	0.0847352i
$901$	−2.01972	+	1.01664i	−0.0672866	+	0.0338692i
$902$	−3.86600	+	2.22522i	−0.128724	+	0.0740918i
$903$	−5.87601	−	6.48318i	−0.195541	−	0.215747i
$904$	29.3390	+	11.4513i	0.975801	+	0.380865i
$905$	−14.3165	−	30.2698i	−0.475898	−	1.00620i
$906$	0.606534	−	1.39405i	0.0201508	−	0.0463141i
$907$	−29.0129	+	11.1915i	−0.963358	+	0.371608i	−0.789902	−	0.613233i	$-0.789869\pi$
$907$	−29.0129	+	11.1915i	−0.963358	+	0.371608i	−0.173456	+	0.984842i	$0.555494\pi$
$908$	−21.7507	−	30.0010i	−0.721824	−	0.995620i
$909$	−18.0455	−	1.33111i	−0.598530	−	0.0441502i
$910$	52.7104	−	39.6559i	1.74733	−	1.31458i
$911$	5.36491	+	17.6857i	0.177748	+	0.585955i	0.999862	+	0.0166323i	$0.00529448\pi$
$911$	5.36491	+	17.6857i	0.177748	+	0.585955i	−0.822114	+	0.569323i	$0.807206\pi$
$912$	−0.110925	+	5.12130i	−0.00367308	+	0.169583i
$913$	0.531616	+	0.161264i	0.0175939	+	0.00533706i
$914$	−3.68116	+	7.92329i	−0.121762	+	0.262079i
$915$	−0.893898	+	3.23013i	−0.0295514	+	0.106785i
$916$	4.28941	+	48.9829i	0.141726	+	1.61844i
$917$	27.3343	−	17.3093i	0.902659	−	0.571602i
$918$	3.32367	−	0.944369i	0.109697	−	0.0311688i
$919$	13.3984	+	8.03069i	0.441972	+	0.264908i	0.717733	−	0.696318i	$-0.245180\pi$
$919$	13.3984	+	8.03069i	0.441972	+	0.264908i	−0.275761	+	0.961226i	$0.588930\pi$
$920$	−31.0289	+	33.9632i	−1.02299	+	1.11973i
$921$	0.716345	+	4.82920i	0.0236044	+	0.159128i
$922$	29.4377	−	21.0358i	0.969477	−	0.692778i
$923$	−60.3768	+	16.7085i	−1.98733	+	0.549967i
$924$	0.0504688	−	1.42622i	0.00166030	−	0.0469191i
$925$	−2.67215	−	2.54410i	−0.0878598	−	0.0836495i
$926$	12.1768	−	2.50904i	0.400153	−	0.0824521i
$927$	−9.49594	+	47.7393i	−0.311888	+	1.56796i
$928$	−0.207013	+	5.25918i	−0.00679554	+	0.172641i
$929$	2.55953	+	12.8676i	0.0839755	+	0.422173i	0.999788	+	0.0205683i	$0.00654755\pi$
$929$	2.55953	+	12.8676i	0.0839755	+	0.422173i	−0.915813	+	0.401605i	$0.868452\pi$
$930$	1.84232	+	4.36288i	0.0604120	+	0.143065i
$931$	63.9943	−	28.3667i	2.09733	−	0.929681i
$932$	28.4533	−	32.2721i	0.932020	−	1.05711i
$933$	3.04754	+	3.90506i	0.0997719	+	0.127846i
$934$	1.40452	−	3.71680i	0.0459574	−	0.121618i
$935$	−0.686587	+	2.74101i	−0.0224538	+	0.0896405i
$936$	−13.4821	+	43.8174i	−0.440675	+	1.43222i
$937$	−0.642280	−	0.0952732i	−0.0209824	−	0.00311244i	0.136231	−	0.990677i	$-0.456501\pi$
$937$	−0.642280	−	0.0952732i	−0.0209824	−	0.00311244i	−0.157213	+	0.987565i	$0.550251\pi$
$938$	−0.595245	+	1.84420i	−0.0194354	+	0.0602152i
$939$	0.829479	+	4.78041i	0.0270690	+	0.156003i
$940$	−13.0170	+	5.22740i	−0.424567	+	0.170499i
$941$	50.2625	−	6.19929i	1.63851	−	0.202091i	0.750160	−	0.661256i	$-0.229976\pi$
$941$	50.2625	−	6.19929i	1.63851	−	0.202091i	0.888351	+	0.459165i	$0.151851\pi$
$942$	−3.74829	+	5.12710i	−0.122126	+	0.167050i
$943$	−26.6273	−	21.8525i	−0.867105	−	0.711615i
$944$	−5.10646	−	9.48751i	−0.166201	−	0.308792i
$945$	−6.94242	−	8.45936i	−0.225837	−	0.275183i
$946$	−6.68149	+	7.47426i	−0.217234	+	0.243009i
$947$	−13.3969	+	26.6151i	−0.435340	+	0.864873i	0.563898	+	0.825845i	$0.309301\pi$
$947$	−13.3969	+	26.6151i	−0.435340	+	0.864873i	−0.999238	+	0.0390283i	$0.987574\pi$
$948$	−0.465920	−	0.226569i	−0.0151324	−	0.00735863i
$949$	0.0455018	+	0.0477921i	0.00147705	+	0.00155140i
$950$	9.58481	−	1.73091i	0.310972	−	0.0561583i
$951$	0.349417	+	7.11255i	0.0113306	+	0.230640i
$952$	−22.6966	−	5.19142i	−0.735600	−	0.168255i
$953$	−36.2989	−	17.1681i	−1.17584	−	0.556130i	−0.263137	−	0.964759i	$-0.584757\pi$
$953$	−36.2989	−	17.1681i	−1.17584	−	0.556130i	−0.912701	+	0.408629i	$0.866007\pi$
$954$	−4.96629	−	0.332109i	−0.160790	−	0.0107524i
$955$	−2.49298	−	33.7965i	−0.0806708	−	1.09363i
$956$	46.9937	+	24.2960i	1.51989	+	0.785788i
$957$	−0.129282	−	0.0818669i	−0.00417909	−	0.00264638i
$958$	−14.1083	−	4.17426i	−0.455818	−	0.134864i
$959$	−9.46116	−	22.8413i	−0.305517	−	0.737583i
$960$	−3.28132	−	0.849674i	−0.105904	−	0.0274231i
$961$	12.0433	−	29.0750i	0.388492	−	0.937903i
$962$	−15.4866	+	19.1366i	−0.499307	+	0.616988i
$963$	−22.0126	+	4.94309i	−0.709346	+	0.159289i
$964$	−10.8425	+	1.21826i	−0.349215	+	0.0392377i
$965$	−7.45942	+	8.64754i	−0.240127	+	0.278374i
$966$	10.4403	−	3.52859i	0.335910	−	0.113531i
$967$	−17.0656	+	6.10618i	−0.548794	+	0.196362i	−0.596663	−	0.802492i	$-0.703507\pi$
$967$	−17.0656	+	6.10618i	−0.548794	+	0.196362i	0.0478689	+	0.998854i	$0.484757\pi$
$968$	29.4061	−	2.05177i	0.945147	−	0.0659464i
$969$	−1.63172	+	1.80032i	−0.0524184	+	0.0578348i
$970$	−37.3612	−	8.12101i	−1.19960	−	0.260750i
$971$	40.8242	+	1.00218i	1.31011	+	0.0321615i	0.673595	−	0.739101i	$-0.264749\pi$
$971$	40.8242	+	1.00218i	1.31011	+	0.0321615i	0.636517	+	0.771262i	$0.280374\pi$
$972$	11.0651	+	2.89935i	0.354913	+	0.0929966i
$973$	−50.8149	+	16.7870i	−1.62905	+	0.538165i
$974$	−37.6219	−	13.1710i	−1.20548	−	0.422026i
$975$	−1.37439	−	0.135366i	−0.0440158	−	0.00433518i
$976$	−4.55233	+	31.3120i	−0.145717	+	1.00227i
$977$	3.49180	+	35.4528i	0.111713	+	1.13424i	0.873639	+	0.486574i	$0.161754\pi$
$977$	3.49180	+	35.4528i	0.111713	+	1.13424i	−0.761927	+	0.647663i	$0.775746\pi$
$978$	−1.15928	−	1.90439i	−0.0370696	−	0.0608958i
$979$	4.57037	−	5.85638i	0.146070	−	0.187171i
$980$	8.54386	+	45.5236i	0.272924	+	1.45420i
$981$	−0.146337	+	0.207783i	−0.00467220	+	0.00663401i
$982$	−1.25928	−	15.6116i	−0.0401854	−	0.498187i
$983$	−22.4253	+	16.6318i	−0.715257	+	0.530471i	−0.891021	−	0.453962i	$-0.850010\pi$
$983$	−22.4253	+	16.6318i	−0.715257	+	0.530471i	0.175764	+	0.984432i	$0.443760\pi$
$984$	0.505023	−	2.48727i	0.0160996	−	0.0792914i
$985$	14.6353	−	8.77206i	0.466320	−	0.279501i
$986$	−1.70900	+	1.81985i	−0.0544258	+	0.0579559i
$987$	3.33510	+	0.411346i	0.106158	+	0.0130933i
$988$	−16.6538	−	62.8174i	−0.529827	−	1.99849i
$989$	−72.2301	−	27.8622i	−2.29678	−	0.885968i
$990$	−4.36798	+	4.42831i	−0.138824	+	0.140741i
$991$	33.6641	+	22.4936i	1.06937	+	0.714533i	0.960150	−	0.279484i	$-0.0901635\pi$
$991$	33.6641	+	22.4936i	1.06937	+	0.714533i	0.109224	+	0.994017i	$0.465164\pi$
$992$	22.4159	+	38.6857i	0.711707	+	1.22827i
$993$	0.525519	−	0.351141i	0.0166769	−	0.0111431i
$994$	13.1916	−	68.7805i	0.418412	−	2.18159i
$995$	32.7993	−	0.805178i	1.03981	−	0.0255259i
$996$	−0.268864	+	0.166205i	−0.00851929	+	0.00526642i
$997$	27.3090	+	15.4704i	0.864886	+	0.489952i	0.860153	−	0.510037i	$-0.170368\pi$
$997$	27.3090	+	15.4704i	0.864886	+	0.489952i	0.00473352	+	0.999989i	$0.498493\pi$
$998$	10.6731	−	17.1133i	0.337853	−	0.541711i
$999$	3.28049	+	2.43298i	0.103790	+	0.0769759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.149.6	✓	4032
512.189	even	128	inner	512.2.o.a.189.6	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.149.6	✓	4032	1.1	even	1	trivial
512.2.o.a.189.6	yes	4032	512.189	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35047 + 0.419796i) q^{2} +(0.213123 + 0.0369803i) q^{3} +(1.64754 - 1.13384i) q^{4} +(0.614425 - 1.85989i) q^{5} +(-0.303341 + 0.0395272i) q^{6} +(-0.212885 + 4.33337i) q^{7} +(-1.74898 + 2.22285i) q^{8} +(-2.78058 - 0.994907i) q^{9} +O(q^{10})\)	\(q+(-1.35047 + 0.419796i) q^{2} +(0.213123 + 0.0369803i) q^{3} +(1.64754 - 1.13384i) q^{4} +(0.614425 - 1.85989i) q^{5} +(-0.303341 + 0.0395272i) q^{6} +(-0.212885 + 4.33337i) q^{7} +(-1.74898 + 2.22285i) q^{8} +(-2.78058 - 0.994907i) q^{9} +(-0.0489890 + 2.76966i) q^{10} +(-0.695107 - 0.308120i) q^{11} +(0.393059 - 0.180721i) q^{12} +(-4.15589 + 3.58490i) q^{13} +(-1.53164 - 5.94146i) q^{14} +(0.199727 - 0.373664i) q^{15} +(1.42880 - 3.73611i) q^{16} +(1.67328 - 0.894387i) q^{17} +(4.17275 + 0.176318i) q^{18} +(-5.15126 + 2.91815i) q^{19} +(-1.09653 - 3.76091i) q^{20} +(-0.205620 + 0.915669i) q^{21} +(1.06807 + 0.124304i) q^{22} +(2.01759 + 8.05469i) q^{23} +(-0.454949 + 0.409063i) q^{24} +(0.934361 + 0.692969i) q^{25} +(4.10749 - 6.58593i) q^{26} +(-1.12043 - 0.634717i) q^{27} +(4.56263 + 7.38080i) q^{28} +(0.930140 - 0.0228337i) q^{29} +(-0.112864 + 0.588467i) q^{30} +(6.57179 - 4.39113i) q^{31} +(-0.361146 + 5.64531i) q^{32} +(-0.136749 - 0.0913727i) q^{33} +(-1.88426 + 1.91028i) q^{34} +(7.92880 + 3.05848i) q^{35} +(-5.70919 + 1.51359i) q^{36} +(-3.14782 - 0.388246i) q^{37} +(5.73160 - 6.10335i) q^{38} +(-1.01829 + 0.610338i) q^{39} +(3.05965 + 4.61868i) q^{40} +(-3.33202 + 2.47119i) q^{41} +(-0.106710 - 1.32290i) q^{42} +(-5.36853 + 7.62272i) q^{43} +(-1.49458 + 0.280502i) q^{44} +(-3.55888 + 4.56028i) q^{45} +(-6.10602 - 10.0306i) q^{46} +(-0.350969 - 3.56345i) q^{47} +(0.442672 - 0.743414i) q^{48} +(-11.7665 - 1.15890i) q^{49} +(-1.55273 - 0.543594i) q^{50} +(0.389689 - 0.128736i) q^{51} +(-2.78230 + 10.6184i) q^{52} +(-1.19141 - 0.0292474i) q^{53} +(1.77956 + 0.386814i) q^{54} +(-1.00016 + 1.10351i) q^{55} +(-9.26013 - 8.05218i) q^{56} +(-1.20577 + 0.431430i) q^{57} +(-1.24654 + 0.421305i) q^{58} +(1.75939 - 2.03963i) q^{59} +(-0.0946167 - 0.842087i) q^{60} +(-7.71810 + 1.73316i) q^{61} +(-7.03164 + 8.68891i) q^{62} +(4.90325 - 11.8375i) q^{63} +(-1.88216 - 7.77544i) q^{64} +(4.11404 + 9.93216i) q^{65} +(0.223033 + 0.0659896i) q^{66} +(-0.266836 - 0.168972i) q^{67} +(1.74271 - 3.37078i) q^{68} +(0.132131 + 1.79125i) q^{69} +(-11.9916 - 0.801907i) q^{70} +(10.3183 + 4.88019i) q^{71} +(7.07470 - 4.44075i) q^{72} +(-0.000589951 - 0.0120087i) q^{73} +(4.41402 - 0.797124i) q^{74} +(0.173507 + 0.182241i) q^{75} +(-5.17819 + 10.6485i) q^{76} +(1.48318 - 2.94656i) q^{77} +(1.11895 - 1.25172i) q^{78} +(-0.759732 - 0.925736i) q^{79} +(-6.07087 - 4.95297i) q^{80} +(6.63327 + 5.44379i) q^{81} +(3.46240 - 4.73604i) q^{82} +(-0.725152 + 0.0894390i) q^{83} +(0.699457 + 1.74175i) q^{84} +(-0.635357 - 3.66165i) q^{85} +(4.05005 - 12.5479i) q^{86} +(0.199079 + 0.0295305i) q^{87} +(1.90063 - 1.00623i) q^{88} +(-2.37398 + 9.47747i) q^{89} +(2.89177 - 7.65252i) q^{90} +(-14.6500 - 18.7722i) q^{91} +(12.4568 + 10.9828i) q^{92} +(1.56299 - 0.692824i) q^{93} +(1.96989 + 4.66500i) q^{94} +(2.26238 + 11.3738i) q^{95} +(-0.285734 + 1.18979i) q^{96} +(-2.69269 + 13.5371i) q^{97} +(16.3768 - 3.37447i) q^{98} +(1.62625 + 1.54832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

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Database

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