LMFDB - Embedded newform 256.2.m.a.109.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

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("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			109.29
Character	$\chi$	$=$	256.109
Dual form			256.2.m.a.101.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35577 + 0.402339i) q^{2} +(1.68530 + 0.422145i) q^{3} +(1.67625 + 1.09096i) q^{4} +(-2.39151 + 1.13110i) q^{5} +(2.11503 + 1.25039i) q^{6} +(0.208482 - 0.687274i) q^{7} +(1.83368 + 2.15352i) q^{8} +(0.0162507 + 0.00868620i) q^{9} +O(q^{10})$	\(q+(1.35577 + 0.402339i) q^{2} +(1.68530 + 0.422145i) q^{3} +(1.67625 + 1.09096i) q^{4} +(-2.39151 + 1.13110i) q^{5} +(2.11503 + 1.25039i) q^{6} +(0.208482 - 0.687274i) q^{7} +(1.83368 + 2.15352i) q^{8} +(0.0162507 + 0.00868620i) q^{9} +(-3.69743 + 0.571318i) q^{10} +(1.17974 + 0.174997i) q^{11} +(2.36443 + 2.54621i) q^{12} +(-1.23067 - 3.43948i) q^{13} +(0.559172 - 0.847908i) q^{14} +(-4.50788 + 0.896673i) q^{15} +(1.61961 + 3.65744i) q^{16} +(-0.537376 - 0.106891i) q^{17} +(0.0185375 + 0.0183148i) q^{18} +(4.13592 - 3.74858i) q^{19} +(-5.24274 - 0.713039i) q^{20} +(0.641483 - 1.07025i) q^{21} +(1.52905 + 0.711910i) q^{22} +(-4.28702 - 0.422235i) q^{23} +(2.18119 + 4.40339i) q^{24} +(1.26795 - 1.54500i) q^{25} +(-0.284669 - 5.15831i) q^{26} +(-3.83818 - 3.47872i) q^{27} +(1.09926 - 0.924595i) q^{28} +(2.12192 - 2.86108i) q^{29} +(-6.47243 - 0.598008i) q^{30} +(-2.95256 + 1.22299i) q^{31} +(0.724295 + 5.61029i) q^{32} +(1.91433 + 0.792941i) q^{33} +(-0.685554 - 0.361127i) q^{34} +(0.278788 + 1.87943i) q^{35} +(0.0177639 + 0.0322891i) q^{36} +(-0.0770981 - 1.56937i) q^{37} +(7.11557 - 3.41818i) q^{38} +(-0.622078 - 6.31606i) q^{39} +(-6.82109 - 3.07608i) q^{40} +(3.14596 + 3.83337i) q^{41} +(1.30031 - 1.19292i) q^{42} +(-0.0455819 - 0.181973i) q^{43} +(1.78661 + 1.58038i) q^{44} +(-0.0486887 - 0.00239192i) q^{45} +(-5.64235 - 2.29729i) q^{46} +(-7.82385 + 5.22773i) q^{47} +(1.18555 + 6.84758i) q^{48} +(5.39141 + 3.60242i) q^{49} +(2.34067 - 1.58453i) q^{50} +(-0.860514 - 0.406993i) q^{51} +(1.68944 - 7.10803i) q^{52} +(7.14557 + 9.63469i) q^{53} +(-3.80408 - 6.26061i) q^{54} +(-3.01928 + 0.915890i) q^{55} +(1.86234 - 0.811269i) q^{56} +(8.55268 - 4.57150i) q^{57} +(4.02797 - 3.02524i) q^{58} +(-2.90868 + 8.12921i) q^{59} +(-8.53456 - 3.41487i) q^{60} +(-5.48610 - 9.15301i) q^{61} +(-4.49506 + 0.470170i) q^{62} +(0.00935779 - 0.00935779i) q^{63} +(-1.27526 + 7.89770i) q^{64} +(6.83354 + 6.83354i) q^{65} +(2.27637 + 1.84526i) q^{66} +(-3.99902 + 2.39692i) q^{67} +(-0.784161 - 0.765431i) q^{68} +(-7.04666 - 2.52133i) q^{69} +(-0.378196 + 2.66025i) q^{70} +(-1.49561 - 2.79810i) q^{71} +(0.0110927 + 0.0509239i) q^{72} +(-3.97595 - 13.1069i) q^{73} +(0.526890 - 2.15873i) q^{74} +(2.78908 - 2.06853i) q^{75} +(11.0224 - 1.77142i) q^{76} +(0.366225 - 0.774318i) q^{77} +(1.69780 - 8.81344i) q^{78} +(-4.73946 + 7.09310i) q^{79} +(-8.01023 - 6.91485i) q^{80} +(-5.03066 - 7.52891i) q^{81} +(2.72291 + 6.46293i) q^{82} +(0.550022 - 11.1960i) q^{83} +(2.24289 - 1.09417i) q^{84} +(1.40604 - 0.352195i) q^{85} +(0.0114161 - 0.265054i) q^{86} +(4.78385 - 3.92600i) q^{87} +(1.78640 + 2.86147i) q^{88} +(2.95716 - 0.291255i) q^{89} +(-0.0650485 - 0.0228322i) q^{90} +(-2.62044 + 0.128734i) q^{91} +(-6.72547 - 5.38474i) q^{92} +(-5.49222 + 0.814693i) q^{93} +(-12.7107 + 3.93978i) q^{94} +(-5.65106 + 13.6429i) q^{95} +(-1.14770 + 9.76076i) q^{96} +(4.62605 + 11.1683i) q^{97} +(5.86014 + 7.05324i) q^{98} +(0.0176515 + 0.0130913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{55}{64}\right)$	$1$

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 $

$2$	1.35577	+	0.402339i	0.958677	+	0.284496i
$2$	1.35577	+	0.402339i	0.958677	+	0.284496i
$3$	1.68530	+	0.422145i	0.973006	+	0.243725i	0.696714	−	0.717349i	$-0.254645\pi$
$3$	1.68530	+	0.422145i	0.973006	+	0.243725i	0.276291	+	0.961074i	$0.410895\pi$
$4$	1.67625	+	1.09096i	0.838124	+	0.545480i
$5$	−2.39151	+	1.13110i	−1.06951	+	0.505842i	−0.879480	−	0.475935i	$-0.842110\pi$
$5$	−2.39151	+	1.13110i	−1.06951	+	0.505842i	−0.190033	+	0.981778i	$0.560860\pi$
$6$	2.11503	+	1.25039i	0.863459	+	0.510470i
$7$	0.208482	−	0.687274i	0.0787989	−	0.259765i	−0.908686	−	0.417481i	$-0.862913\pi$
$7$	0.208482	−	0.687274i	0.0787989	−	0.259765i	0.987485	+	0.157716i	$0.0504130\pi$
$8$	1.83368	+	2.15352i	0.648303	+	0.761383i
$9$	0.0162507	+	0.00868620i	0.00541691	+	0.00289540i
$10$	−3.69743	+	0.571318i	−1.16923	+	0.180667i
$11$	1.17974	+	0.174997i	0.355704	+	0.0527637i	0.322191	−	0.946675i	$-0.395581\pi$
$11$	1.17974	+	0.174997i	0.355704	+	0.0527637i	0.0335126	+	0.999438i	$0.489331\pi$
$12$	2.36443	+	2.54621i	0.682552	+	0.735027i
$13$	−1.23067	−	3.43948i	−0.341325	−	0.953941i	−0.982454	−	0.186507i	$-0.940283\pi$
$13$	−1.23067	−	3.43948i	−0.341325	−	0.953941i	0.641128	−	0.767434i	$-0.278467\pi$
$14$	0.559172	−	0.847908i	0.149445	−	0.226613i
$15$	−4.50788	+	0.896673i	−1.16393	+	0.231520i
$16$	1.61961	+	3.65744i	0.404902	+	0.914360i
$17$	−0.537376	−	0.106891i	−0.130333	−	0.0259248i	0.129493	−	0.991580i	$-0.458665\pi$
$17$	−0.537376	−	0.106891i	−0.130333	−	0.0259248i	−0.259826	+	0.965656i	$0.583665\pi$
$18$	0.0185375	+	0.0183148i	0.00436934	+	0.00431684i
$19$	4.13592	−	3.74858i	0.948844	−	0.859982i	−0.0414257	−	0.999142i	$-0.513190\pi$
$19$	4.13592	−	3.74858i	0.948844	−	0.859982i	0.990270	+	0.139159i	$0.0444400\pi$
$20$	−5.24274	−	0.713039i	−1.17231	−	0.159440i
$21$	0.641483	−	1.07025i	0.139983	−	0.233548i
$22$	1.52905	+	0.711910i	0.325994	+	0.151780i
$23$	−4.28702	−	0.422235i	−0.893906	−	0.0880421i	−0.359377	−	0.933192i	$-0.617011\pi$
$23$	−4.28702	−	0.422235i	−0.893906	−	0.0880421i	−0.534529	+	0.845150i	$0.679511\pi$
$24$	2.18119	+	4.40339i	0.445234	+	0.898837i
$25$	1.26795	−	1.54500i	0.253590	−	0.309000i
$26$	−0.284669	−	5.15831i	−0.0558282	−	1.01163i
$27$	−3.83818	−	3.47872i	−0.738658	−	0.669481i
$28$	1.09926	−	0.924595i	0.207740	−	0.174732i
$29$	2.12192	−	2.86108i	0.394031	−	0.531289i	−0.560992	−	0.827821i	$-0.689580\pi$
$29$	2.12192	−	2.86108i	0.394031	−	0.531289i	0.955023	+	0.296532i	$0.0958302\pi$
$30$	−6.47243	−	0.598008i	−1.18170	−	0.109181i
$31$	−2.95256	+	1.22299i	−0.530296	+	0.219656i	−0.631733	−	0.775186i	$-0.717656\pi$
$31$	−2.95256	+	1.22299i	−0.530296	+	0.219656i	0.101437	+	0.994842i	$0.467656\pi$
$32$	0.724295	+	5.61029i	0.128039	+	0.991769i
$33$	1.91433	+	0.792941i	0.333242	+	0.138033i
$34$	−0.685554	−	0.361127i	−0.117572	−	0.0619327i
$35$	0.278788	+	1.87943i	0.0471237	+	0.317682i
$36$	0.0177639	+	0.0322891i	0.00296066	+	0.00538152i
$37$	−0.0770981	−	1.56937i	−0.0126749	−	0.258003i	−0.996767	−	0.0803446i	$-0.974398\pi$
$37$	−0.0770981	−	1.56937i	−0.0126749	−	0.258003i	0.984092	−	0.177658i	$-0.0568521\pi$
$38$	7.11557	−	3.41818i	1.15430	−	0.554503i
$39$	−0.622078	−	6.31606i	−0.0996122	−	1.01138i
$40$	−6.82109	−	3.07608i	−1.07851	−	0.486370i
$41$	3.14596	+	3.83337i	0.491317	+	0.598672i	0.958360	−	0.285563i	$-0.0921806\pi$
$41$	3.14596	+	3.83337i	0.491317	+	0.598672i	−0.467043	+	0.884235i	$0.654681\pi$
$42$	1.30031	−	1.19292i	0.200642	−	0.184072i
$43$	−0.0455819	−	0.181973i	−0.00695118	−	0.0277506i	0.966456	−	0.256831i	$-0.0826783\pi$
$43$	−0.0455819	−	0.181973i	−0.00695118	−	0.0277506i	−0.973408	+	0.229080i	$0.926428\pi$
$44$	1.78661	+	1.58038i	0.269342	+	0.238252i
$45$	−0.0486887	−	0.00239192i	−0.00725808	−	0.000356566i
$46$	−5.64235	−	2.29729i	−0.831920	−	0.338717i
$47$	−7.82385	+	5.22773i	−1.14123	+	0.762543i	−0.974705	−	0.223495i	$-0.928253\pi$
$47$	−7.82385	+	5.22773i	−1.14123	+	0.762543i	−0.166521	+	0.986038i	$0.553253\pi$
$48$	1.18555	+	6.84758i	0.171120	+	0.988362i
$49$	5.39141	+	3.60242i	0.770201	+	0.514632i
$50$	2.34067	−	1.58453i	0.331020	−	0.224086i
$51$	−0.860514	−	0.406993i	−0.120496	−	0.0569904i
$52$	1.68944	−	7.10803i	0.234283	−	0.985706i
$53$	7.14557	+	9.63469i	0.981520	+	1.32343i	0.946038	+	0.324056i	$0.105046\pi$
$53$	7.14557	+	9.63469i	0.981520	+	1.32343i	0.0354815	+	0.999370i	$0.488704\pi$
$54$	−3.80408	−	6.26061i	−0.517670	−	0.851961i
$55$	−3.01928	+	0.915890i	−0.407120	+	0.123499i
$56$	1.86234	−	0.811269i	0.248866	−	0.108410i
$57$	8.55268	−	4.57150i	1.13283	−	0.605510i
$58$	4.02797	−	3.02524i	0.528898	−	0.397234i
$59$	−2.90868	+	8.12921i	−0.378678	+	1.05833i	0.589434	+	0.807816i	$0.299351\pi$
$59$	−2.90868	+	8.12921i	−0.378678	+	1.05833i	−0.968112	+	0.250517i	$0.919399\pi$
$60$	−8.53456	−	3.41487i	−1.10181	−	0.440858i
$61$	−5.48610	−	9.15301i	−0.702424	−	1.17192i	−0.977588	−	0.210526i	$-0.932482\pi$
$61$	−5.48610	−	9.15301i	−0.702424	−	1.17192i	0.275165	−	0.961397i	$-0.411268\pi$
$62$	−4.49506	+	0.470170i	−0.570874	+	0.0597116i
$63$	0.00935779	−	0.00935779i	0.00117897	−	0.00117897i
$64$	−1.27526	+	7.89770i	−0.159407	+	0.987213i
$65$	6.83354	+	6.83354i	0.847596	+	0.847596i
$66$	2.27637	+	1.84526i	0.280202	+	0.227136i
$67$	−3.99902	+	2.39692i	−0.488558	+	0.292831i	−0.737092	−	0.675793i	$-0.763801\pi$
$67$	−3.99902	+	2.39692i	−0.488558	+	0.292831i	0.248533	+	0.968623i	$0.420051\pi$
$68$	−0.784161	−	0.765431i	−0.0950935	−	0.0928222i
$69$	−7.04666	−	2.52133i	−0.848318	−	0.303533i
$70$	−0.378196	+	2.66025i	−0.0452030	+	0.317961i
$71$	−1.49561	−	2.79810i	−0.177497	−	0.332073i	0.777402	−	0.629004i	$-0.216537\pi$
$71$	−1.49561	−	2.79810i	−0.177497	−	0.332073i	−0.954899	+	0.296931i	$0.904037\pi$
$72$	0.0110927	+	0.0509239i	0.00130729	+	0.00600144i
$73$	−3.97595	−	13.1069i	−0.465349	−	1.53405i	−0.804869	−	0.593453i	$-0.797764\pi$
$73$	−3.97595	−	13.1069i	−0.465349	−	1.53405i	0.339519	−	0.940599i	$-0.389736\pi$
$74$	0.526890	−	2.15873i	0.0612497	−	0.250947i
$75$	2.78908	−	2.06853i	0.322056	−	0.238853i
$76$	11.0224	−	1.77142i	1.26435	−	0.203196i
$77$	0.366225	−	0.774318i	0.0417352	−	0.0882418i
$78$	1.69780	−	8.81344i	0.192238	−	0.997925i
$79$	−4.73946	+	7.09310i	−0.533231	+	0.798036i	−0.996085	−	0.0883979i	$-0.971825\pi$
$79$	−4.73946	+	7.09310i	−0.533231	+	0.798036i	0.462854	+	0.886434i	$0.346825\pi$
$80$	−8.01023	−	6.91485i	−0.895571	−	0.773104i
$81$	−5.03066	−	7.52891i	−0.558962	−	0.836545i
$82$	2.72291	+	6.46293i	0.300695	+	0.713711i
$83$	0.550022	−	11.1960i	0.0603728	−	1.22892i	−0.757236	−	0.653142i	$-0.773451\pi$
$83$	0.550022	−	11.1960i	0.0603728	−	1.22892i	0.817608	−	0.575775i	$-0.195299\pi$
$84$	2.24289	−	1.09417i	0.244719	−	0.119384i
$85$	1.40604	−	0.352195i	0.152507	−	0.0382009i
$86$	0.0114161	−	0.265054i	0.00123103	−	0.0285815i
$87$	4.78385	−	3.92600i	0.512883	−	0.420912i
$88$	1.78640	+	2.86147i	0.190430	+	0.305034i
$89$	2.95716	−	0.291255i	0.313458	−	0.0308729i	0.0599352	−	0.998202i	$-0.480911\pi$
$89$	2.95716	−	0.291255i	0.313458	−	0.0308729i	0.253523	+	0.967329i	$0.418411\pi$
$90$	−0.0650485	−	0.0228322i	−0.00685671	−	0.00240673i
$91$	−2.62044	+	0.128734i	−0.274697	+	0.0134950i
$92$	−6.72547	−	5.38474i	−0.701179	−	0.561398i
$93$	−5.49222	+	0.814693i	−0.569516	+	0.0844798i
$94$	−12.7107	+	3.93978i	−1.31101	+	0.406358i
$95$	−5.65106	+	13.6429i	−0.579787	+	1.39973i
$96$	−1.14770	+	9.76076i	−0.117137	+	0.996203i
$97$	4.62605	+	11.1683i	0.469704	+	1.13397i	0.964293	+	0.264839i	$0.0853188\pi$
$97$	4.62605	+	11.1683i	0.469704	+	1.13397i	−0.494589	+	0.869127i	$0.664681\pi$
$98$	5.86014	+	7.05324i	0.591963	+	0.712485i
$99$	0.0176515	+	0.0130913i	0.00177404	+	0.00131572i
$100$	3.81093	−	1.20652i	0.381093	−	0.120652i
$101$	6.07177	−	6.69916i	0.604164	−	0.666592i	−0.359675	−	0.933078i	$-0.617113\pi$
$101$	6.07177	−	6.69916i	0.604164	−	0.666592i	0.963839	+	0.266486i	$0.0858625\pi$
$102$	−1.00291	−	0.898008i	−0.0993032	−	0.0889160i
$103$	13.9632	+	11.4593i	1.37583	+	1.12912i	0.977276	+	0.211971i	$0.0679882\pi$
$103$	13.9632	+	11.4593i	1.37583	+	1.12912i	0.398555	+	0.917144i	$0.369512\pi$
$104$	5.15033	−	8.95716i	0.505032	−	0.878322i
$105$	−0.323553	+	3.28509i	−0.0315755	+	0.320592i
$106$	5.81137	+	15.9374i	0.564450	+	1.54798i
$107$	−5.45827	−	3.27156i	−0.527671	−	0.316274i	0.225342	−	0.974280i	$-0.427650\pi$
$107$	−5.45827	−	3.27156i	−0.527671	−	0.316274i	−0.753013	+	0.658006i	$0.771400\pi$
$108$	−2.63859	−	10.0185i	−0.253898	−	0.964031i
$109$	8.83302	+	9.74573i	0.846050	+	0.933472i	0.998495	−	0.0548401i	$-0.0174649\pi$
$109$	8.83302	+	9.74573i	0.846050	+	0.933472i	−0.152446	+	0.988312i	$0.548715\pi$
$110$	−4.46197	+	0.0269650i	−0.425432	+	0.00257102i
$111$	0.532567	−	2.67740i	0.0505490	−	0.254127i
$112$	2.85132	−	0.350604i	0.269425	−	0.0331290i
$113$	2.72002	+	13.6745i	0.255878	+	1.28639i	0.868373	+	0.495911i	$0.165166\pi$
$113$	2.72002	+	13.6745i	0.255878	+	1.28639i	−0.612495	+	0.790474i	$0.709834\pi$
$114$	13.4348	−	2.75685i	1.25828	−	0.258203i
$115$	10.7300	−	3.83927i	1.00058	−	0.358013i
$116$	6.67819	−	2.48094i	0.620054	−	0.230350i
$117$	0.00987679	−	0.0665839i	0.000913109	−	0.00615568i
$118$	−7.21421	+	9.85110i	−0.664122	+	0.906867i
$119$	−0.185497	+	0.347040i	−0.0170044	+	0.0318131i
$120$	−10.1970	−	8.06358i	−0.930854	−	0.736101i
$121$	−9.16519	−	2.78023i	−0.833199	−	0.252748i
$122$	−3.75531	−	14.6167i	−0.339990	−	1.32333i
$123$	3.68364	+	7.78841i	0.332143	+	0.702257i
$124$	−6.28346	−	1.17109i	−0.564271	−	0.105167i
$125$	1.92926	−	7.70204i	0.172558	−	0.688892i
$126$	0.0164520	−	0.00892205i	0.00146566	−	0.000794839i
$127$		−	10.4476i		−	0.927076i	−0.886077	−	0.463538i	$-0.846580\pi$
$127$		−	10.4476i		−	0.927076i	0.886077	−	0.463538i	$-0.153420\pi$
$128$	−4.90651	+	10.1944i	−0.433679	+	0.901068i
$129$		−	0.325921i		−	0.0286957i
$130$	6.51534	+	12.0141i	0.571433	+	1.05371i
$131$	−3.60480	+	14.3912i	−0.314953	+	1.25736i	0.581252	+	0.813723i	$0.302563\pi$
$131$	−3.60480	+	14.3912i	−0.314953	+	1.25736i	−0.896205	+	0.443640i	$0.853687\pi$
$132$	2.34382	+	3.41762i	0.204004	+	0.297466i
$133$	−1.71403	−	3.62402i	−0.148626	−	0.314242i
$134$	−6.38615	+	1.64072i	−0.551679	+	0.141737i
$135$	13.1138	+	3.97803i	1.12866	+	0.342374i
$136$	−0.755183	−	1.35325i	−0.0647564	−	0.116040i
$137$	−6.64279	+	12.4278i	−0.567532	+	1.06178i	0.420466	+	0.907309i	$0.361867\pi$
$137$	−6.64279	+	12.4278i	−0.567532	+	1.06178i	−0.987998	+	0.154469i	$0.950633\pi$
$138$	−8.53924	−	6.25350i	−0.726909	−	0.532333i
$139$	3.03092	−	20.4328i	0.257079	−	1.73309i	−0.348505	−	0.937307i	$-0.613310\pi$
$139$	3.03092	−	20.4328i	0.257079	−	1.73309i	0.605584	−	0.795781i	$-0.292940\pi$
$140$	−1.58307	+	3.45454i	−0.133794	+	0.291962i
$141$	−15.3924	+	5.50747i	−1.29627	+	0.463813i
$142$	−0.901932	−	4.39533i	−0.0756884	−	0.368848i
$143$	−0.849961	−	4.27304i	−0.0710773	−	0.357330i
$144$	−0.00544940	+	0.0735043i	−0.000454117	+	0.00612536i
$145$	−1.83842	+	9.24238i	−0.152673	+	0.767538i
$146$	−0.117057	−	19.3697i	−0.00968773	−	1.60305i
$147$	7.56537	+	8.34710i	0.623981	+	0.688457i
$148$	1.58288	−	2.71476i	0.130112	−	0.223152i
$149$	14.8149	+	8.87971i	1.21368	+	0.727454i	0.970166	−	0.242442i	$-0.0779484\pi$
$149$	14.8149	+	8.87971i	1.21368	+	0.727454i	0.243518	+	0.969896i	$0.421698\pi$
$150$	4.61362	−	1.68230i	0.376700	−	0.137359i
$151$	−1.68690	+	17.1274i	−0.137278	+	1.39381i	0.641795	+	0.766877i	$0.278190\pi$
$151$	−1.68690	+	17.1274i	−0.137278	+	1.39381i	−0.779073	+	0.626933i	$0.784310\pi$
$152$	15.6566	+	2.03308i	1.26991	+	0.164905i
$153$	−0.00780428	−	0.00640480i	−0.000630938	−	0.000517798i
$154$	0.808057	−	0.902454i	0.0651151	−	0.0727218i
$155$	5.67774	−	6.26443i	0.456047	−	0.503171i
$156$	5.84782	−	11.2659i	0.468200	−	0.901997i
$157$	−10.2800	−	7.62420i	−0.820437	−	0.608477i	0.101930	−	0.994792i	$-0.467498\pi$
$157$	−10.2800	−	7.62420i	−0.820437	−	0.608477i	−0.922367	+	0.386314i	$0.873748\pi$
$158$	−9.27947	+	7.70978i	−0.738235	+	0.613357i
$159$	7.97517	+	19.2538i	0.632472	+	1.52692i
$160$	−8.07795	−	12.5978i	−0.638618	−	0.995944i
$161$	−1.18396	+	2.85833i	−0.0933091	+	0.225268i
$162$	−3.79126	−	12.2315i	−0.297870	−	0.960999i
$163$	12.9556	−	1.92178i	1.01476	−	0.150525i	0.381421	−	0.924401i	$-0.375435\pi$
$163$	12.9556	−	1.92178i	1.01476	−	0.150525i	0.633337	+	0.773876i	$0.281685\pi$
$164$	1.09136	+	9.85780i	0.0852209	+	0.769765i
$165$	−5.47502	+	0.268971i	−0.426230	+	0.0209393i
$166$	5.25027	−	14.9579i	0.407500	−	1.16096i
$167$	−0.434587	+	0.0428031i	−0.0336293	+	0.00331220i	−0.114818	−	0.993387i	$-0.536628\pi$
$167$	−0.434587	+	0.0428031i	−0.0336293	+	0.00331220i	0.0811885	+	0.996699i	$0.474128\pi$
$168$	3.48107	−	0.581049i	0.268571	−	0.0448289i
$169$	−0.266359	+	0.218595i	−0.0204892	+	0.0168150i
$170$	2.04798	+	0.0882079i	0.157073	+	0.00676523i
$171$	0.0997725	−	0.0249917i	0.00762980	−	0.00191116i
$172$	0.122119	−	0.354760i	0.00931149	−	0.0270502i
$173$	−0.487770	+	9.92878i	−0.0370844	+	0.754871i	0.906193	+	0.422865i	$0.138976\pi$
$173$	−0.487770	+	9.92878i	−0.0370844	+	0.754871i	−0.943277	+	0.332006i	$0.892274\pi$
$174$	8.06540	−	3.39805i	0.611437	−	0.257605i
$175$	−0.797494	−	1.19353i	−0.0602849	−	0.0902227i
$176$	1.27067	+	4.59824i	0.0957803	+	0.346605i
$177$	−8.33368	+	12.4722i	−0.626398	+	0.937471i
$178$	4.12642	+	0.794904i	0.309289	+	0.0595806i
$179$	0.298351	−	0.630810i	0.0222998	−	0.0471490i	−0.892532	−	0.450984i	$-0.851073\pi$
$179$	0.298351	−	0.630810i	0.0222998	−	0.0471490i	0.914832	+	0.403835i	$0.132323\pi$
$180$	−0.0790047	−	0.0571269i	−0.00588866	−	0.00425798i
$181$	10.0211	−	7.43219i	0.744866	−	0.552430i	−0.155358	−	0.987858i	$-0.549653\pi$
$181$	10.0211	−	7.43219i	0.744866	−	0.552430i	0.900223	+	0.435428i	$0.143403\pi$
$182$	−3.60452	−	0.879770i	−0.267185	−	0.0652129i
$183$	−5.38181	−	17.7415i	−0.397835	−	1.31149i
$184$	−6.95173	−	10.0064i	−0.512488	−	0.737683i
$185$	1.95949	+	3.66595i	0.144065	+	0.269526i
$186$	−7.77399	−	1.10519i	−0.570017	−	0.0810365i
$187$	−0.615256	−	0.220142i	−0.0449920	−	0.0160984i
$188$	−18.8180	+	0.227454i	−1.37244	+	0.0165888i
$189$	−3.19103	+	1.91263i	−0.232113	+	0.139123i
$190$	−13.1506	+	16.2230i	−0.954046	+	1.17694i
$191$	−3.32059	−	3.32059i	−0.240270	−	0.240270i	0.576692	−	0.816962i	$-0.304343\pi$
$191$	−3.32059	−	3.32059i	−0.240270	−	0.240270i	−0.816962	+	0.576692i	$0.804343\pi$
$192$	−5.48316	+	12.7716i	−0.395713	+	0.921712i
$193$	8.44646	−	8.44646i	0.607989	−	0.607989i	−0.334431	−	0.942420i	$-0.608544\pi$
$193$	8.44646	−	8.44646i	0.607989	−	0.607989i	0.942420	+	0.334431i	$0.108544\pi$
$194$	1.77845	+	17.0029i	0.127685	+	1.22074i
$195$	8.63179	+	14.4013i	0.618135	+	1.03130i
$196$	5.10723	+	11.9204i	0.364802	+	0.851455i
$197$	6.38113	−	17.8341i	0.454637	−	1.27062i	−0.467580	−	0.883951i	$-0.654874\pi$
$197$	6.38113	−	17.8341i	0.454637	−	1.27062i	0.922217	−	0.386674i	$-0.126376\pi$
$198$	0.0186643	+	0.0248507i	0.00132642	+	0.00176606i
$199$	14.1337	−	7.55462i	1.00191	−	0.535533i	0.112992	−	0.993596i	$-0.463957\pi$
$199$	14.1337	−	7.55462i	1.00191	−	0.535533i	0.888920	+	0.458063i	$0.151457\pi$
$200$	5.65219	−	0.102484i	0.399671	−	0.00724670i
$201$	−7.75138	+	2.35136i	−0.546740	+	0.165852i
$202$	10.9273	−	6.63965i	0.768841	−	0.467164i
$203$	−1.52396	−	2.05482i	−0.106961	−	0.144220i
$204$	−0.998421	−	1.62101i	−0.0699034	−	0.113493i
$205$	−11.8595	−	5.60913i	−0.828304	−	0.391759i
$206$	14.3204	+	21.1541i	0.997748	+	1.47388i
$207$	−0.0659996	−	0.0440996i	−0.00458729	−	0.00306513i
$208$	10.5865	−	10.0717i	0.734042	−	0.698347i
$209$	5.53528	−	3.69856i	0.382883	−	0.255835i
$210$	−1.76038	+	4.32366i	−0.121478	+	0.298361i
$211$	−20.2191	−	0.993299i	−1.39194	−	0.0683815i	−0.660775	−	0.750584i	$-0.729772\pi$
$211$	−20.2191	−	0.993299i	−1.39194	−	0.0683815i	−0.731163	+	0.682203i	$0.761022\pi$
$212$	1.46668	+	23.9457i	0.100732	+	1.64459i
$213$	−1.33935	−	5.34698i	−0.0917707	−	0.366369i
$214$	−6.08391	−	6.63157i	−0.415887	−	0.453325i
$215$	0.314839	+	0.383632i	0.0214718	+	0.0261635i
$216$	0.453503	−	14.6444i	0.0308569	−	0.996428i
$217$	0.224973	+	2.28419i	0.0152722	+	0.155061i
$218$	8.05449	+	16.7669i	0.545519	+	1.13560i
$219$	−1.16762	−	23.7675i	−0.0789006	−	1.60606i
$220$	−6.06027	−	1.75866i	−0.408583	−	0.118569i
$221$	0.293682	+	1.97984i	0.0197552	+	0.133179i
$222$	1.79926	−	3.41567i	0.120758	−	0.229245i
$223$	−14.4430	−	5.98248i	−0.967174	−	0.400616i	−0.157514	−	0.987517i	$-0.550348\pi$
$223$	−14.4430	−	5.98248i	−0.967174	−	0.400616i	−0.809659	+	0.586900i	$0.800348\pi$
$224$	4.00681	+	0.671858i	0.267716	+	0.0448904i
$225$	0.0340253	−	0.0140937i	0.00226835	−	0.000939583i
$226$	−1.81403	+	19.6339i	−0.120668	+	1.30603i
$227$	9.86100	−	13.2960i	0.654497	−	0.882488i	−0.343904	−	0.939005i	$-0.611750\pi$
$227$	9.86100	−	13.2960i	0.654497	−	0.882488i	0.998402	+	0.0565171i	$0.0179996\pi$
$228$	19.3237	+	1.66767i	1.27975	+	0.110444i
$229$	−4.92344	−	4.46235i	−0.325350	−	0.294880i	0.492499	−	0.870313i	$-0.336084\pi$
$229$	−4.92344	−	4.46235i	−0.325350	−	0.294880i	−0.817849	+	0.575433i	$0.804834\pi$
$230$	16.0922	−	0.888072i	1.06109	−	0.0585577i
$231$	0.944072	−	1.15036i	0.0621154	−	0.0756878i
$232$	10.0523	−	0.676705i	0.659965	−	0.0444279i
$233$	4.96588	+	0.489097i	0.325326	+	0.0320418i	0.259362	−	0.965780i	$-0.416488\pi$
$233$	4.96588	+	0.489097i	0.325326	+	0.0320418i	0.0659639	+	0.997822i	$0.478988\pi$
$234$	0.0401800	−	0.0862989i	0.00262665	−	0.00564154i
$235$	12.7977	−	21.3517i	0.834831	−	1.39283i
$236$	−13.7443	+	10.4533i	−0.894679	+	0.680453i
$237$	−10.9817	+	9.95324i	−0.713338	+	0.646532i
$238$	−0.391119	+	0.395875i	−0.0253525	+	0.0256608i
$239$	10.8458	+	2.15737i	0.701558	+	0.139549i	0.532965	−	0.846137i	$-0.321078\pi$
$239$	10.8458	+	2.15737i	0.701558	+	0.139549i	0.168593	+	0.985686i	$0.446078\pi$
$240$	−10.5805	−	15.0350i	−0.682970	−	0.970508i
$241$	−9.82517	+	1.95435i	−0.632895	+	0.125891i	−0.501104	−	0.865387i	$-0.667073\pi$
$241$	−9.82517	+	1.95435i	−0.632895	+	0.125891i	−0.131791	+	0.991278i	$0.542073\pi$
$242$	−11.3073	−	7.45687i	−0.726863	−	0.479346i
$243$	−0.0645114	−	0.180297i	−0.00413841	−	0.0115661i
$244$	0.789510	−	21.3278i	0.0505432	−	1.36537i
$245$	−16.9683	−	2.51701i	−1.08406	−	0.160806i
$246$	1.86061	+	12.0414i	0.118628	+	0.767732i
$247$	−17.9831	−	9.61216i	−1.14424	−	0.611607i
$248$	−8.04777	−	4.11582i	−0.511034	−	0.261355i
$249$	5.65326	−	18.6363i	0.358261	−	1.18103i
$250$	5.71447	−	9.66602i	0.361415	−	0.611332i
$251$	−14.2278	+	6.72926i	−0.898052	+	0.424747i	−0.820107	−	0.572211i	$-0.806086\pi$
$251$	−14.2278	+	6.72926i	−0.898052	+	0.424747i	−0.0779452	+	0.996958i	$0.524836\pi$
$252$	0.0258949	−	0.00547699i	0.00163123	−	0.000345018i
$253$	−4.98367	−	1.24834i	−0.313320	−	0.0784827i
$254$	4.20348	−	14.1646i	0.263750	−	0.888766i
$255$	2.51827			0.157700
$256$	−10.7537	+	11.8472i	−0.672108	+	0.740453i
$257$	−26.5301			−1.65490			−0.827452	−	0.561537i	$-0.810210\pi$
$257$	−26.5301			−1.65490			−0.827452	+	0.561537i	$0.810210\pi$
$258$	0.131130	−	0.441875i	0.00816383	−	0.0275099i
$259$	−1.09466	−	0.274198i	−0.0680188	−	0.0170378i
$260$	3.99958	+	18.9098i	0.248043	+	1.17274i
$261$	0.0593346	−	0.0280632i	0.00367272	−	0.00173707i
$262$	−10.6774	+	18.0608i	−0.659654	+	1.11580i
$263$	0.271107	−	0.893719i	0.0167172	−	0.0551091i	−0.948185	−	0.317719i	$-0.897083\pi$
$263$	0.271107	−	0.893719i	0.0167172	−	0.0551091i	0.964902	+	0.262610i	$0.0845832\pi$
$264$	1.80265	+	5.57654i	0.110946	+	0.343212i
$265$	−27.9864	−	14.9591i	−1.71919	−	0.918928i
$266$	−0.865759	−	5.60297i	−0.0530831	−	0.343540i
$267$	5.10664	+	0.757498i	0.312521	+	0.0463581i
$268$	−9.31830	−	0.344943i	−0.569206	−	0.0210707i
$269$	−7.37128	−	20.6014i	−0.449435	−	1.25609i	−0.926192	−	0.377052i	$-0.876938\pi$
$269$	−7.37128	−	20.6014i	−0.449435	−	1.25609i	0.476757	−	0.879035i	$-0.341812\pi$
$270$	16.1788	+	10.6695i	0.984613	+	0.649325i
$271$	−2.46900	+	0.491114i	−0.149981	+	0.0298331i	−0.269510	−	0.962998i	$-0.586862\pi$
$271$	−2.46900	+	0.491114i	−0.149981	+	0.0298331i	0.119529	+	0.992831i	$0.461862\pi$
$272$	−0.479393	−	2.13854i	−0.0290674	−	0.129668i
$273$	−4.47056	−	0.889249i	−0.270570	−	0.0538198i
$274$	−14.0063	+	14.1766i	−0.846152	+	0.856441i
$275$	1.76622	−	1.60081i	0.106507	−	0.0965322i
$276$	−9.06126	−	11.9140i	−0.545424	−	0.717139i
$277$	8.56329	−	14.2870i	0.514518	−	0.858421i	−0.485356	−	0.874317i	$-0.661310\pi$
$277$	8.56329	−	14.2870i	0.514518	−	0.858421i	0.999874	+	0.0158954i	$0.00505986\pi$
$278$	12.3302	−	26.4828i	0.739514	−	1.58833i
$279$	−0.0586044	−	0.00577203i	−0.00350855	−	0.000345562i
$280$	−3.53618	+	4.04665i	−0.211327	+	0.241833i
$281$	12.3702	−	15.0732i	0.737946	−	0.899190i	−0.259843	−	0.965651i	$-0.583671\pi$
$281$	12.3702	−	15.0732i	0.737946	−	0.899190i	0.997789	+	0.0664607i	$0.0211707\pi$
$282$	−23.0844	+	1.27395i	−1.37466	+	0.0758626i
$283$	4.52251	+	4.09896i	0.268835	+	0.243658i	0.794834	−	0.606828i	$-0.207558\pi$
$283$	4.52251	+	4.09896i	0.268835	+	0.243658i	−0.525998	+	0.850486i	$0.676308\pi$
$284$	0.545595	−	6.32195i	0.0323751	−	0.375139i
$285$	−15.2830	+	20.6067i	−0.905285	+	1.22064i
$286$	0.566855	−	6.13526i	0.0335189	−	0.362785i
$287$	3.29045	−	1.36295i	0.194229	−	0.0804524i
$288$	−0.0369618	+	0.0974627i	−0.00217799	+	0.00574305i
$289$	−15.4286	−	6.39074i	−0.907565	−	0.375926i
$290$	−6.21106	+	11.7909i	−0.364726	+	0.692386i
$291$	3.08164	+	20.7747i	0.180649	+	1.21783i
$292$	7.63449	−	26.3081i	0.446775	−	1.53956i
$293$	0.195750	+	3.98458i	0.0114358	+	0.232781i	0.997709	+	0.0676574i	$0.0215525\pi$
$293$	0.195750	+	3.98458i	0.0114358	+	0.232781i	−0.986273	+	0.165124i	$0.947198\pi$
$294$	6.89857	+	14.3606i	0.402333	+	0.837528i
$295$	−2.23881	−	22.7311i	−0.130349	−	1.32345i
$296$	3.23829	−	3.04375i	0.188222	−	0.176914i
$297$	−3.91927	−	4.77565i	−0.227419	−	0.277111i
$298$	16.5130	+	17.9995i	0.956573	+	1.04268i
$299$	3.82363	+	15.2648i	0.221126	+	0.882784i
$300$	6.93187	−	0.424579i	0.400212	−	0.0245131i
$301$	−0.134568	−	0.00661092i	−0.00775640	−	0.000381047i
$302$	−9.17809	+	22.5422i	−0.528140	+	1.29716i
$303$	13.0607	−	8.72691i	0.750320	−	0.501348i
$304$	20.4088	+	9.05564i	1.17052	+	0.519376i
$305$	23.4730	+	15.6842i	1.34406	+	0.898072i
$306$	−0.00800394	−	0.0118234i	−0.000457555	−	0.000675900i
$307$	−7.39148	−	3.49591i	−0.421854	−	0.199522i	0.204827	−	0.978798i	$-0.434337\pi$
$307$	−7.39148	−	3.49591i	−0.421854	−	0.199522i	−0.626681	+	0.779276i	$0.715587\pi$
$308$	1.45863	−	0.898411i	0.0831134	−	0.0511917i
$309$	18.6946	+	25.2067i	1.06350	+	1.43396i
$310$	10.2182	−	6.20877i	0.580352	−	0.352634i
$311$	−13.3724	+	4.05647i	−0.758278	+	0.230021i	−0.645668	−	0.763618i	$-0.723421\pi$
$311$	−13.3724	+	4.05647i	−0.758278	+	0.230021i	−0.112610	+	0.993639i	$0.535921\pi$
$312$	12.4610	−	12.9213i	0.705468	−	0.731523i
$313$	17.6561	−	9.43736i	0.997980	−	0.533431i	0.110303	−	0.993898i	$-0.464818\pi$
$313$	17.6561	−	9.43736i	0.997980	−	0.533431i	0.887677	+	0.460467i	$0.152318\pi$
$314$	−10.8699	−	14.4728i	−0.613424	−	0.816745i
$315$	−0.0117946	+	0.0329638i	−0.000664552	+	0.00185730i
$316$	−15.6828	+	6.71923i	−0.882227	+	0.377986i
$317$	5.79223	+	9.66375i	0.325324	+	0.542770i	0.976326	−	0.216306i	$-0.0694009\pi$
$317$	5.79223	+	9.66375i	0.325324	+	0.542770i	−0.651002	+	0.759076i	$0.725651\pi$
$318$	3.06599	+	29.3125i	0.171932	+	1.64376i
$319$	3.00399	−	3.00399i	0.168191	−	0.168191i
$320$	−5.88329	−	20.3298i	−0.328886	−	1.13647i
$321$	−7.81773	−	7.81773i	−0.436343	−	0.436343i
$322$	−2.75520	+	3.39890i	−0.153541	+	0.189413i
$323$	−2.62323	+	1.57230i	−0.145960	+	0.0874853i
$324$	−0.218879	−	18.1086i	−0.0121600	−	1.00603i
$325$	−6.87443	−	2.45971i	−0.381325	−	0.136440i
$326$	18.3380	+	2.60703i	1.01565	+	0.144390i
$327$	10.7721	+	20.1532i	0.595700	+	1.11448i
$328$	−2.48654	+	13.8040i	−0.137296	+	0.762201i
$329$	1.96175	+	6.46702i	0.108155	+	0.356538i
$330$	−7.53111	−	1.83815i	−0.414574	−	0.101187i
$331$	−7.82426	+	5.80286i	−0.430060	+	0.318954i	−0.788985	−	0.614412i	$-0.789393\pi$
$331$	−7.82426	+	5.80286i	−0.430060	+	0.318954i	0.358925	+	0.933366i	$0.383143\pi$
$332$	13.1363	−	18.1671i	0.720950	−	0.997052i
$333$	0.0123789	−	0.0261731i	0.000678362	−	0.00143428i
$334$	−0.606423	−	0.116820i	−0.0331820	−	0.00639209i
$335$	6.85253	−	10.2555i	0.374394	−	0.560320i
$336$	4.95333	+	0.612799i	0.270226	+	0.0334309i
$337$	3.87035	+	5.79239i	0.210832	+	0.315532i	0.921781	−	0.387712i	$-0.126734\pi$
$337$	3.87035	+	5.79239i	0.210832	+	0.315532i	−0.710949	+	0.703243i	$0.751734\pi$
$338$	−0.449072	+	0.189199i	−0.0244263	+	0.0102911i
$339$	−1.18856	+	24.1938i	−0.0645539	+	1.31402i
$340$	2.74110	+	0.943570i	0.148657	+	0.0511723i
$341$	−3.69726	+	0.926116i	−0.200218	+	0.0501520i
$342$	0.145324	+	0.00625922i	0.00785823	+	0.000338460i
$343$	7.48609	−	6.14368i	0.404211	−	0.331727i
$344$	0.308300	−	0.431841i	0.0166224	−	0.0232833i
$345$	19.7040	−	1.94067i	1.06083	−	0.104482i
$346$	−4.65604	+	13.2649i	−0.250310	+	0.713127i
$347$	−36.2776	+	1.78220i	−1.94748	+	0.0956736i	−0.984662	−	0.174473i	$-0.944178\pi$
$347$	−36.2776	+	1.78220i	−1.94748	+	0.0956736i	−0.962819	+	0.270147i	$0.912928\pi$
$348$	12.3020	−	1.36196i	0.659458	−	0.0730088i
$349$	20.5517	−	3.04855i	1.10011	−	0.163185i	0.428101	−	0.903731i	$-0.359183\pi$
$349$	20.5517	−	3.04855i	1.10011	−	0.163185i	0.672006	+	0.740546i	$0.265433\pi$
$350$	−0.601017	−	1.93903i	−0.0321257	−	0.103645i
$351$	−7.24149	+	17.4825i	−0.386522	+	0.933147i
$352$	−0.127309	+	6.74542i	−0.00678561	+	0.359532i
$353$	−9.73552	−	23.5036i	−0.518169	−	1.25097i	−0.939027	−	0.343844i	$-0.888271\pi$
$353$	−9.73552	−	23.5036i	−0.518169	−	1.25097i	0.420857	−	0.907127i	$-0.361729\pi$
$354$	−16.3167	+	13.5566i	−0.867221	+	0.720524i
$355$	6.74169	+	4.99998i	0.357812	+	0.265371i
$356$	5.27468	+	2.73793i	0.279557	+	0.145110i
$357$	−0.459117	+	0.506558i	−0.0242991	+	0.0268099i
$358$	0.658296	−	0.735198i	0.0347920	−	0.0388564i
$359$	0.424715	+	0.348554i	0.0224156	+	0.0183960i	0.645534	−	0.763731i	$-0.276635\pi$
$359$	0.424715	+	0.348554i	0.0224156	+	0.0183960i	−0.623119	+	0.782127i	$0.714135\pi$
$360$	−0.0841282	−	0.109238i	−0.00443395	−	0.00575734i
$361$	1.19166	−	12.0991i	0.0627187	−	0.636794i
$362$	16.5767	−	6.04447i	0.871250	−	0.317690i
$363$	−14.2724	−	8.55454i	−0.749106	−	0.448997i
$364$	−4.53295	−	2.64301i	−0.237591	−	0.138531i
$365$	24.3337	+	26.8481i	1.27369	+	1.40530i
$366$	−0.158448	−	26.2187i	−0.00828220	−	1.37047i
$367$	3.91362	−	19.6751i	0.204289	−	1.02703i	−0.733463	−	0.679729i	$-0.762097\pi$
$367$	3.91362	−	19.6751i	0.204289	−	1.02703i	0.937753	−	0.347304i	$-0.112903\pi$
$368$	−5.39900	−	16.3634i	−0.281443	−	0.853000i
$369$	0.0178268	+	0.0896215i	0.000928028	+	0.00466551i
$370$	1.18167	+	5.75858i	0.0614323	+	0.299374i
$371$	8.11139	−	2.90230i	0.421123	−	0.150680i
$372$	−10.0951	−	4.62617i	−0.523407	−	0.239856i
$373$	−1.03078	+	6.94895i	−0.0533717	+	0.359803i	0.945994	+	0.324185i	$0.105090\pi$
$373$	−1.03078	+	6.94895i	−0.0533717	+	0.359803i	−0.999365	+	0.0356181i	$0.988660\pi$
$374$	−0.745577	−	0.546004i	−0.0385528	−	0.0282332i
$375$	6.50275	−	12.1658i	0.335801	−	0.628239i
$376$	−25.6044	−	7.26282i	−1.32045	−	0.374551i
$377$	−12.4520	−	3.77727i	−0.641311	−	0.194539i
$378$	−5.09584	+	1.30922i	−0.262102	+	0.0673390i
$379$	14.6992	+	31.0788i	0.755047	+	1.59641i	0.801862	+	0.597509i	$0.203843\pi$
$379$	14.6992	+	31.0788i	0.755047	+	1.59641i	−0.0468147	+	0.998904i	$0.514907\pi$
$380$	−24.3564	+	16.7037i	−1.24946	+	0.856883i
$381$	4.41040	−	17.6073i	0.225952	−	0.902050i
$382$	−3.16597	−	5.83797i	−0.161985	−	0.298697i
$383$		−	6.37768i		−	0.325884i	−0.986636	−	0.162942i	$-0.947902\pi$
$383$		−	6.37768i		−	0.325884i	0.986636	−	0.162942i	$-0.0520984\pi$
$384$	−12.5724	+	15.1093i	−0.641585	+	0.771046i
$385$			2.26602i			0.115487i
$386$	14.8498	−	8.05315i	0.755836	−	0.409895i
$387$	0.000839915	−	0.00335313i	4.26953e−5	−	0.000170449i
$388$	−4.42974	+	23.7676i	−0.224886	+	1.20662i
$389$	13.8972	+	29.3833i	0.704618	+	1.48979i	0.864489	+	0.502652i	$0.167642\pi$
$389$	13.8972	+	29.3833i	0.704618	+	1.48979i	−0.159870	+	0.987138i	$0.551108\pi$
$390$	5.90857	+	22.9978i	0.299192	+	1.16454i
$391$	2.25861	+	0.685142i	0.114223	+	0.0346491i
$392$	2.12823	+	18.2162i	0.107492	+	0.920055i
$393$	−12.1503	+	22.7316i	−0.612902	+	1.14666i
$394$	15.8267	−	21.6116i	0.797338	−	1.08878i
$395$	3.31145	−	22.3240i	0.166617	−	1.12324i
$396$	0.0153063	+	0.0412013i	0.000769168	+	0.00207044i
$397$	−20.1238	+	7.20041i	−1.00998	+	0.361378i	−0.789327	−	0.613973i	$-0.789570\pi$
$397$	−20.1238	+	7.20041i	−1.00998	+	0.361378i	−0.220658	+	0.975351i	$0.570820\pi$
$398$	22.2016	−	4.55582i	1.11287	−	0.228363i
$399$	−1.35879	−	6.83111i	−0.0680247	−	0.341983i
$400$	7.70433	+	2.13515i	0.385217	+	0.106758i
$401$	3.34794	−	16.8312i	0.167188	−	0.840512i	−0.802591	−	0.596529i	$-0.796546\pi$
$401$	3.34794	−	16.8312i	0.167188	−	0.840512i	0.969780	−	0.243983i	$-0.0784540\pi$
$402$	−11.4552	+	0.0692271i	−0.571332	+	0.00345273i
$403$	7.84007	+	8.65019i	0.390542	+	0.430897i
$404$	17.4863	−	4.60539i	0.869976	−	0.229127i
$405$	20.5468	+	12.3153i	1.02098	+	0.611950i
$406$	−1.23941	−	3.39903i	−0.0615110	−	0.168691i
$407$	0.183680	−	1.86493i	0.00910467	−	0.0924413i
$408$	−0.701439	−	2.59942i	−0.0347264	−	0.128691i
$409$	10.4396	+	8.56757i	0.516206	+	0.423639i	0.856089	−	0.516829i	$-0.172888\pi$
$409$	10.4396	+	8.56757i	0.516206	+	0.423639i	−0.339883	+	0.940468i	$0.610388\pi$
$410$	−13.8220	−	12.3763i	−0.682622	−	0.611220i
$411$	−16.4414	+	18.1403i	−0.810994	+	0.894794i
$412$	10.9041	+	34.4418i	0.537206	+	1.69683i
$413$	4.98059	+	3.69386i	0.245079	+	0.181763i
$414$	−0.0717377	−	0.0863432i	−0.00352571	−	0.00424354i
$415$	11.3483	+	27.3973i	0.557068	+	1.34488i
$416$	18.4051	−	9.39560i	0.902386	−	0.460657i
$417$	13.7336	−	33.1558i	0.672537	−	1.62365i
$418$	8.99266	−	2.78735i	0.439846	−	0.136334i
$419$	25.6946	−	3.81144i	1.25527	−	0.186201i	0.514221	−	0.857657i	$-0.328081\pi$
$419$	25.6946	−	3.81144i	1.25527	−	0.186201i	0.741044	+	0.671456i	$0.234331\pi$
$420$	−4.12626	+	5.15364i	−0.201341	+	0.251472i
$421$	39.4446	−	1.93779i	1.92241	−	0.0944420i	0.947871	−	0.318655i	$-0.103231\pi$
$421$	39.4446	−	1.93779i	1.92241	−	0.0944420i	0.974540	+	0.224213i	$0.0719811\pi$
$422$	−27.0128	−	9.48160i	−1.31496	−	0.461557i
$423$	−0.172552	+	0.0169949i	−0.00838979	+	0.000826322i
$424$	−7.64578	+	33.0550i	−0.371312	+	1.60529i
$425$	−0.846512	+	0.694714i	−0.0410619	+	0.0336986i
$426$	0.335442	−	7.78817i	0.0162522	−	0.377338i
$427$	−7.43438	+	1.86222i	−0.359775	+	0.0901190i
$428$	−5.58027	−	11.4387i	−0.269732	−	0.552911i
$429$	0.371406	−	7.56015i	0.0179317	−	0.365007i
$430$	0.272500	+	0.646791i	0.0131411	+	0.0311910i
$431$	4.61705	+	6.90991i	0.222396	+	0.332839i	0.925843	−	0.377909i	$-0.123357\pi$
$431$	4.61705	+	6.90991i	0.222396	+	0.332839i	−0.703447	+	0.710748i	$0.748357\pi$
$432$	6.50687	−	19.6721i	0.313062	−	0.946474i
$433$	−15.3300	+	22.9430i	−0.736714	+	1.10257i	0.254078	+	0.967184i	$0.418228\pi$
$433$	−15.3300	+	22.9430i	−0.736714	+	1.10257i	−0.990793	+	0.135387i	$0.956772\pi$
$434$	−0.614006	+	3.18736i	−0.0294732	+	0.152998i
$435$	−6.99991	+	14.8001i	−0.335620	+	0.709609i
$436$	4.17411	+	25.9727i	0.199904	+	1.24387i
$437$	−19.3136	+	14.3239i	−0.923892	+	0.685205i
$438$	7.97955	−	32.6931i	0.381278	−	1.56214i
$439$	−1.42679	−	4.70351i	−0.0680972	−	0.224486i	0.916286	−	0.400524i	$-0.131172\pi$
$439$	−1.42679	−	4.70351i	−0.0680972	−	0.224486i	−0.984383	+	0.176038i	$0.943672\pi$
$440$	−7.50878	−	4.82263i	−0.357967	−	0.229910i
$441$	0.0563229	+	0.105373i	0.00268204	+	0.00501775i
$442$	−0.398401	+	2.80238i	−0.0189500	+	0.133295i
$443$	−14.1795	−	5.07351i	−0.673688	−	0.241050i	−0.0222515	−	0.999752i	$-0.507083\pi$
$443$	−14.1795	−	5.07351i	−0.673688	−	0.241050i	−0.651437	+	0.758703i	$0.725833\pi$
$444$	3.81365	−	3.90697i	0.180988	−	0.185416i
$445$	−6.74263	+	4.04137i	−0.319631	+	0.191580i
$446$	−17.1744	−	13.9219i	−0.813233	−	0.659219i
$447$	21.2190	+	21.2190i	1.00362	+	1.00362i
$448$	5.16202	+	2.52298i	0.243882	+	0.119200i
$449$	19.4801	−	19.4801i	0.919321	−	0.919321i	−0.0776587	−	0.996980i	$-0.524744\pi$
$449$	19.4801	−	19.4801i	0.919321	−	0.919321i	0.996980	+	0.0776587i	$0.0247444\pi$
$450$	0.0518011	−	0.00541824i	0.00244193	−	0.000255418i
$451$	3.04058	+	5.07290i	0.143175	+	0.238874i
$452$	−10.3589	+	25.8892i	−0.487241	+	1.21773i
$453$	−10.0732	+	28.1527i	−0.473279	+	1.32273i
$454$	18.7188	−	14.0589i	0.878516	−	0.659819i
$455$	6.12118	−	3.27184i	0.286965	−	0.153386i
$456$	25.5277	+	10.0357i	1.19544	+	0.469963i
$457$	14.3881	−	4.36460i	0.673049	−	0.204167i	0.0647818	−	0.997899i	$-0.479365\pi$
$457$	14.3881	−	4.36460i	0.673049	−	0.204167i	0.608267	+	0.793732i	$0.291865\pi$
$458$	−4.87970	−	8.03083i	−0.228013	−	0.375256i
$459$	1.69070	+	2.27965i	0.0789152	+	0.106405i
$460$	22.1747	+	5.27048i	1.03390	+	0.245737i
$461$	19.9467	+	9.43408i	0.929010	+	0.439389i	0.831299	−	0.555826i	$-0.187598\pi$
$461$	19.9467	+	9.43408i	0.929010	+	0.439389i	0.0977111	+	0.995215i	$0.468848\pi$
$462$	1.74278	−	1.17978i	0.0810815	−	0.0548886i
$463$	−9.07346	−	6.06269i	−0.421680	−	0.281757i	0.326572	−	0.945172i	$-0.394106\pi$
$463$	−9.07346	−	6.06269i	−0.421680	−	0.281757i	−0.748252	+	0.663415i	$0.769106\pi$
$464$	13.9009	+	3.12697i	0.645333	+	0.145166i
$465$	12.2132	−	8.16058i	0.566372	−	0.378438i
$466$	6.53583	+	2.66107i	0.302767	+	0.123272i
$467$	−25.0442	−	1.23034i	−1.15891	−	0.0569334i	−0.539487	−	0.841994i	$-0.681382\pi$
$467$	−25.0442	−	1.23034i	−1.15891	−	0.0569334i	−0.619419	+	0.785061i	$0.712632\pi$
$468$	0.0891964	−	0.100836i	0.00412310	−	0.00466114i
$469$	0.813617	+	3.24814i	0.0375693	+	0.149985i
$470$	25.9414	−	23.7991i	1.19659	−	1.09777i
$471$	−14.1064	−	17.1887i	−0.649988	−	0.792013i
$472$	−22.8400	+	8.64246i	−1.05129	+	0.397802i
$473$	−0.0219298	−	0.222657i	−0.00100833	−	0.0102378i
$474$	−18.8933	+	9.07598i	−0.867797	+	0.416873i
$475$	−0.547421	−	11.1430i	−0.0251174	−	0.511276i
$476$	−0.689545	+	0.379355i	−0.0316052	+	0.0173877i
$477$	0.0324320	+	0.218639i	0.00148496	+	0.0100108i
$478$	13.8365	+	7.28860i	0.632866	+	0.333373i
$479$	−21.8781	−	9.06221i	−0.999637	−	0.414063i	−0.177973	−	0.984035i	$-0.556954\pi$
$479$	−21.8781	−	9.06221i	−0.999637	−	0.414063i	−0.821664	+	0.569972i	$0.806954\pi$
$480$	−8.29564	−	24.6411i	−0.378642	−	1.12471i
$481$	−5.30293	+	2.19655i	−0.241793	+	0.100154i
$482$	−14.1070	−	1.30339i	−0.642557	−	0.0593678i
$483$	−3.20195	+	4.31733i	−0.145694	+	0.196445i
$484$	−12.3300	−	14.6592i	−0.560455	−	0.666328i
$485$	−23.6956	−	21.4765i	−1.07596	−	0.975196i
$486$	−0.0149223	−	0.270398i	−0.000676891	−	0.0122655i
$487$	−4.86038	+	5.92238i	−0.220245	+	0.268369i	−0.871397	−	0.490578i	$-0.836786\pi$
$487$	−4.86038	+	5.92238i	−0.220245	+	0.268369i	0.651153	+	0.758947i	$0.274286\pi$
$488$	9.65141	−	28.5981i	0.436899	−	1.29457i
$489$	22.6452	+	2.23036i	1.02405	+	0.100860i
$490$	−21.9925	−	10.2395i	−0.993518	−	0.462573i
$491$	−10.2106	+	17.0354i	−0.460799	+	0.768796i	−0.997170	−	0.0751861i	$-0.976045\pi$
$491$	−10.2106	+	17.0354i	−0.460799	+	0.768796i	0.536371	+	0.843983i	$0.319795\pi$
$492$	−2.32215	+	17.0740i	−0.104691	+	0.769756i
$493$	−1.44609	+	1.31066i	−0.0651287	+	0.0590292i
$494$	−20.5137	−	20.2672i	−0.922953	−	0.911865i
$495$	−0.0570212	−	0.0113422i	−0.00256291	−	0.000509795i
$496$	−9.25501	−	8.81805i	−0.415562	−	0.395942i
$497$	−2.23487	+	0.444543i	−0.100247	+	0.0199405i
$498$	15.1627	−	22.9921i	0.679455	−	1.03030i
$499$	−5.34321	−	14.9333i	−0.239195	−	0.668505i	−0.999814	−	0.0193060i	$-0.993854\pi$
$499$	−5.34321	−	14.9333i	−0.239195	−	0.668505i	0.760619	−	0.649199i	$-0.224896\pi$
$500$	11.6365	−	10.8058i	0.520402	−	0.483249i
$501$	−0.750476	−	0.111323i	−0.0335288	−	0.00497353i
$502$	−21.9971	+	3.39895i	−0.981781	+	0.151703i
$503$	−0.350024	−	0.187092i	−0.0156068	−	0.00834202i	0.463575	−	0.886058i	$-0.346567\pi$
$503$	−0.350024	−	0.187092i	−0.0156068	−	0.00834202i	−0.479182	+	0.877716i	$0.659067\pi$
$504$	0.0373113	+	0.00299298i	0.00166198	+	0.000133318i
$505$	−6.94326	+	22.8889i	−0.308971	+	1.01854i
$506$	−6.25447	−	3.69759i	−0.278045	−	0.164378i
$507$	−0.541173	+	0.255956i	−0.0240343	+	0.0113674i
$508$	11.3979	−	17.5128i	0.505702	−	0.777004i
$509$	41.5680	+	10.4122i	1.84247	+	0.461514i	0.997330	−	0.0730322i	$-0.0232676\pi$
$509$	41.5680	+	10.4122i	1.84247	+	0.461514i	0.845139	+	0.534547i	$0.179518\pi$
$510$	3.41421	+	1.01320i	0.151184	+	0.0448652i
$511$	−9.83698			−0.435162
$512$	−19.3462	+	11.7356i	−0.854991	+	0.518643i
$513$	−28.9147			−1.27661
$514$	−35.9689	−	10.6741i	−1.58652	−	0.470814i
$515$	−46.3545	−	11.6112i	−2.04262	−	0.511651i
$516$	0.355567	−	0.546324i	0.0156530	−	0.0240506i
$517$	−10.1449	+	4.79819i	−0.446173	+	0.211024i
$518$	−1.37379	−	0.812174i	−0.0603609	−	0.0356849i
$519$	−5.01342	+	16.5270i	−0.220065	+	0.725456i
$520$	−2.18563	+	27.2466i	−0.0958461	+	1.19484i
$521$	−27.2456	−	14.5631i	−1.19365	−	0.638019i	−0.249769	−	0.968305i	$-0.580355\pi$
$521$	−27.2456	−	14.5631i	−1.19365	−	0.638019i	−0.943881	+	0.330286i	$0.892855\pi$
$522$	0.0917353	−	0.0141747i	0.00401514	−	0.000620411i
$523$	13.2523	+	1.96579i	0.579481	+	0.0859579i	0.430035	−	0.902812i	$-0.358501\pi$
$523$	13.2523	+	1.96579i	0.579481	+	0.0859579i	0.149446	+	0.988770i	$0.452251\pi$
$524$	−21.7428	+	20.1905i	−0.949836	+	0.882025i
$525$	−0.840169	−	2.34812i	−0.0366680	−	0.102480i
$526$	0.727138	−	1.10261i	0.0317047	−	0.0480759i
$527$	1.71736	−	0.341604i	0.0748094	−	0.0148805i
$528$	0.200331	+	8.28580i	0.00871830	+	0.360593i
$529$	−4.35777	−	0.866815i	−0.189468	−	0.0376876i
$530$	−31.9247	−	31.5411i	−1.38672	−	1.37006i
$531$	−0.117880	+	0.106840i	−0.00511556	+	0.00463647i
$532$	1.08052	−	7.94470i	0.0468464	−	0.344446i
$533$	9.31317	−	15.5381i	0.403398	−	0.673029i
$534$	6.61868	+	3.08160i	0.286418	+	0.133354i
$535$	16.7539	+	1.65012i	0.724336	+	0.0713409i
$536$	−12.4947	−	4.21678i	−0.539690	−	0.182137i
$537$	0.769103	−	0.937154i	0.0331892	−	0.0404412i
$538$	−1.70507	−	30.8965i	−0.0735109	−	1.33204i
$539$	5.73002	+	5.19339i	0.246810	+	0.223695i
$540$	17.6421	+	20.9748i	0.759195	+	0.902612i
$541$	14.0128	−	18.8940i	0.602456	−	0.812318i	−0.391720	−	0.920084i	$-0.628120\pi$
$541$	14.0128	−	18.8940i	0.602456	−	0.812318i	0.994176	+	0.107766i	$0.0343699\pi$
$542$	−3.54500	−	0.327533i	−0.152271	−	0.0140688i
$543$	20.0260	−	8.29506i	0.859400	−	0.355975i
$544$	0.210469	−	3.09226i	0.00902381	−	0.132579i
$545$	−32.1476	−	13.3160i	−1.37705	−	0.570393i
$546$	−5.70329	−	3.00430i	−0.244078	−	0.128572i
$547$	0.511235	+	3.44647i	0.0218588	+	0.147360i	0.997358	−	0.0726427i	$-0.0231433\pi$
$547$	0.511235	+	3.44647i	0.0218588	+	0.147360i	−0.975499	+	0.220003i	$0.929393\pi$
$548$	−24.6932	+	13.5850i	−1.05484	+	0.580323i
$549$	−0.00964834	−	0.196397i	−0.000411781	−	0.00838200i
$550$	3.03866	−	1.45971i	0.129569	−	0.0622424i
$551$	−1.94888	−	19.7874i	−0.0830253	−	0.842970i
$552$	−7.49156	−	19.7984i	−0.318862	−	0.842676i
$553$	3.88681	+	4.73609i	0.165284	+	0.201399i
$554$	17.3581	−	15.9246i	0.737474	−	0.676570i
$555$	1.75476	+	7.00539i	0.0744854	+	0.297362i
$556$	27.3720	−	30.9438i	1.16083	−	1.31231i
$557$	−16.6789	−	0.819380i	−0.706706	−	0.0347182i	−0.307459	−	0.951561i	$-0.599479\pi$
$557$	−16.6789	−	0.819380i	−0.706706	−	0.0347182i	−0.399247	+	0.916843i	$0.630729\pi$
$558$	−0.0771320	−	0.0314044i	−0.00326526	−	0.00132945i
$559$	−0.569797	+	0.380726i	−0.0240999	+	0.0161030i
$560$	−6.42239	+	4.06360i	−0.271395	+	0.171718i
$561$	−0.943956	−	0.630732i	−0.0398539	−	0.0266295i
$562$	22.8358	−	15.4588i	0.963269	−	0.652090i
$563$	−38.4953	−	18.2069i	−1.62238	−	0.767331i	−0.622502	−	0.782618i	$-0.713884\pi$
$563$	−38.4953	−	18.2069i	−1.62238	−	0.767331i	−0.999883	+	0.0152875i	$0.995134\pi$
$564$	−31.8098	−	7.56057i	−1.33944	−	0.318357i
$565$	−21.9721	−	29.6260i	−0.924374	−	1.24637i
$566$	4.48233	+	7.37685i	0.188406	+	0.310072i
$567$	−6.22323	+	1.88779i	−0.261351	+	0.0792799i
$568$	3.28327	−	8.35163i	0.137763	−	0.350427i
$569$	−2.70358	+	1.44510i	−0.113340	+	0.0605815i	−0.527093	−	0.849808i	$-0.676718\pi$
$569$	−2.70358	+	1.44510i	−0.113340	+	0.0605815i	0.413752	+	0.910389i	$0.364218\pi$
$570$	−29.0111	+	21.7891i	−1.21514	+	0.912645i
$571$	6.68867	−	18.6936i	0.279912	−	0.782301i	−0.716494	−	0.697593i	$-0.754254\pi$
$571$	6.68867	−	18.6936i	0.279912	−	0.782301i	0.996406	−	0.0847081i	$-0.0269958\pi$
$572$	3.23698	−	8.08995i	0.135345	−	0.338258i
$573$	−4.19441	−	6.99795i	−0.175224	−	0.292343i
$574$	5.00948	−	0.523976i	0.209092	−	0.0218704i
$575$	−6.08808	+	6.08808i	−0.253891	+	0.253891i
$576$	−0.0893249	+	0.117266i	−0.00372187	+	0.00488610i
$577$	30.3757	+	30.3757i	1.26456	+	1.26456i	0.948860	+	0.315697i	$0.102238\pi$
$577$	30.3757	+	30.3757i	1.26456	+	1.26456i	0.315697	+	0.948860i	$0.397762\pi$
$578$	−18.3465	−	14.8719i	−0.763112	−	0.618590i
$579$	17.8004	−	10.6692i	0.739759	−	0.443395i
$580$	−13.1647	+	13.4869i	−0.546636	+	0.560012i
$581$	−7.58002	−	2.71218i	−0.314472	−	0.112520i
$582$	−4.18046	+	29.4057i	−0.173286	+	1.21890i
$583$	6.74384	+	12.6168i	0.279301	+	0.522536i
$584$	20.9354	−	32.5962i	0.866313	−	1.34884i
$585$	0.0516925	+	0.170407i	0.00213722	+	0.00704548i
$586$	−1.33776	+	5.48094i	−0.0552622	+	0.226416i
$587$	−10.5130	+	7.79694i	−0.433916	+	0.321814i	−0.790514	−	0.612444i	$-0.790187\pi$
$587$	−10.5130	+	7.79694i	−0.433916	+	0.321814i	0.356598	+	0.934258i	$0.383937\pi$
$588$	3.57507	+	22.2453i	0.147433	+	0.917382i
$589$	−7.62707	+	16.1261i	−0.314268	+	0.664464i
$590$	6.11026	−	31.7189i	0.251555	−	1.30585i
$591$	18.2826	−	27.3619i	0.752047	−	1.12552i
$592$	5.61500	−	2.82375i	0.230775	−	0.116055i
$593$	6.06198	+	9.07240i	0.248936	+	0.372559i	0.934802	−	0.355169i	$-0.115577\pi$
$593$	6.06198	+	9.07240i	0.248936	+	0.372559i	−0.685866	+	0.727727i	$0.740577\pi$
$594$	−3.39222	−	8.05158i	−0.139185	−	0.330360i
$595$	0.0510802	−	1.03976i	0.00209409	−	0.0426261i
$596$	15.1460	+	31.0471i	0.620405	+	1.27174i
$597$	27.0086	−	6.76530i	1.10539	−	0.276885i
$598$	−0.957634	+	22.2340i	−0.0391606	+	0.909215i
$599$	27.9991	−	22.9783i	1.14401	−	0.938867i	0.145290	−	0.989389i	$-0.453588\pi$
$599$	27.9991	−	22.9783i	1.14401	−	0.938867i	0.998723	+	0.0505219i	$0.0160885\pi$
$600$	9.56888	+	2.21333i	0.390648	+	0.0903587i
$601$	2.46772	−	0.243050i	0.100661	−	0.00991420i	−0.0475614	−	0.998868i	$-0.515145\pi$
$601$	2.46772	−	0.243050i	0.100661	−	0.00991420i	0.148222	+	0.988954i	$0.452645\pi$
$602$	−0.179785	−	0.0631050i	−0.00732747	−	0.00257197i
$603$	−0.0858072	+	0.00421544i	−0.00349434	+	0.000171666i
$604$	−21.5130	+	26.8695i	−0.875352	+	1.09330i
$605$	25.0633	−	3.71779i	1.01897	−	0.151150i
$606$	21.2186	−	6.57687i	0.861946	−	0.267167i
$607$	−18.2051	+	43.9509i	−0.738921	+	1.78391i	−0.128696	+	0.991684i	$0.541079\pi$
$607$	−18.2051	+	43.9509i	−0.738921	+	1.78391i	−0.610225	+	0.792228i	$0.708921\pi$
$608$	24.0262	+	20.4886i	0.974393	+	0.830924i
$609$	−1.70089	−	4.10632i	−0.0689237	−	0.166396i
$610$	25.5137	+	30.7083i	1.03302	+	1.24334i
$611$	27.6092	+	20.4764i	1.11695	+	0.828387i
$612$	−0.00609451	−	0.0192502i	−0.000246356	−	0.000778143i
$613$	5.81818	−	6.41938i	0.234994	−	0.259276i	−0.612025	−	0.790838i	$-0.709645\pi$
$613$	5.81818	−	6.41938i	0.234994	−	0.259276i	0.847019	+	0.531562i	$0.178395\pi$
$614$	−8.61463	−	7.71354i	−0.347658	−	0.311293i
$615$	−17.6189	−	14.4595i	−0.710463	−	0.583062i
$616$	2.33905	−	0.631178i	0.0942428	−	0.0254309i
$617$	−0.721675	+	7.32729i	−0.0290535	+	0.294985i	0.969668	+	0.244427i	$0.0786000\pi$
$617$	−0.721675	+	7.32729i	−0.0290535	+	0.294985i	−0.998721	+	0.0505580i	$0.983900\pi$
$618$	15.2040	+	41.6962i	0.611594	+	1.67727i
$619$	25.5143	+	15.2927i	1.02551	+	0.614664i	0.924880	−	0.380260i	$-0.124166\pi$
$619$	25.5143	+	15.2927i	1.02551	+	0.614664i	0.100626	+	0.994924i	$0.467916\pi$
$620$	16.3515	−	4.30653i	0.656694	−	0.172954i
$621$	14.9855	+	16.5340i	0.601349	+	0.663486i
$622$	−19.7620	+	0.119428i	−0.792384	+	0.00478862i
$623$	0.416344	−	2.09310i	0.0166805	−	0.0838583i
$624$	22.0931	−	12.5048i	0.884431	−	0.500591i
$625$	6.04754	+	30.4030i	0.241902	+	1.21612i
$626$	27.7347	−	5.69122i	1.10850	−	0.227467i
$627$	10.8899	−	3.89647i	0.434901	−	0.155610i
$628$	−8.91419	−	23.9952i	−0.355715	−	0.957511i
$629$	−0.126320	+	0.851582i	−0.00503672	+	0.0339548i
$630$	−0.0292535	+	0.0399460i	−0.00116549	+	0.00159149i
$631$	−21.9345	+	41.0365i	−0.873197	+	1.63364i	−0.104044	+	0.994573i	$0.533178\pi$
$631$	−21.9345	+	41.0365i	−0.873197	+	1.63364i	−0.769153	+	0.639064i	$0.779322\pi$
$632$	−23.9657	+	2.79996i	−0.953306	+	0.111376i
$633$	−33.6558	−	10.2094i	−1.33770	−	0.405786i
$634$	3.96485	+	15.4323i	0.157464	+	0.612895i
$635$	11.8173	+	24.9855i	0.468954	+	0.991520i
$636$	−7.63674	+	40.9746i	−0.302816	+	1.62475i
$637$	5.75544	−	22.9770i	0.228039	−	0.910383i
$638$	5.28135	−	2.86411i	0.209091	−	0.113391i
$639$		−	0.0584623i		−	0.00231273i
$640$	0.203068	−	29.9298i	0.00802699	−	1.18308i
$641$			0.532062i			0.0210152i	0.999945	+	0.0105076i	$0.00334474\pi$
$641$			0.532062i			0.0210152i	−0.999945	+	0.0105076i	$0.996655\pi$
$642$	−7.45370	−	13.7444i	−0.294174	−	0.542450i
$643$	4.05056	−	16.1707i	0.159738	−	0.637712i	−0.836259	−	0.548334i	$-0.815262\pi$
$643$	4.05056	−	16.1707i	0.159738	−	0.637712i	0.995998	−	0.0893775i	$-0.0284878\pi$
$644$	−5.10294	+	3.49962i	−0.201084	+	0.137904i
$645$	0.368648	+	0.779441i	0.0145155	+	0.0306905i
$646$	−4.18910	+	1.07626i	−0.164818	+	0.0423449i
$647$	4.69664	+	1.42471i	0.184644	+	0.0560111i	0.381252	−	0.924471i	$-0.375493\pi$
$647$	4.69664	+	1.42471i	0.184644	+	0.0560111i	−0.196609	+	0.980482i	$0.562993\pi$
$648$	6.98902	−	24.6392i	0.274555	−	0.967918i
$649$	−4.85406	+	9.08131i	−0.190539	+	0.356473i
$650$	−8.33053	−	6.10066i	−0.326750	−	0.239287i
$651$	−0.585112	+	3.94451i	−0.0229324	+	0.154597i
$652$	23.8133	+	10.9126i	0.932601	+	0.427372i
$653$	−6.53726	+	2.33907i	−0.255823	+	0.0915348i	−0.461678	−	0.887048i	$-0.652752\pi$
$653$	−6.53726	+	2.33907i	−0.255823	+	0.0915348i	0.205855	+	0.978582i	$0.434002\pi$
$654$	6.49615	+	31.6573i	0.254020	+	1.23790i
$655$	−7.65693	−	38.4940i	−0.299181	−	1.50408i
$656$	−8.92508	+	17.7147i	−0.348466	+	0.691644i
$657$	0.0492374	−	0.247533i	0.00192093	−	0.00965719i
$658$	0.0577566	+	9.55711i	0.00225158	+	0.372575i
$659$	−22.7026	−	25.0485i	−0.884368	−	0.975750i	0.115477	−	0.993310i	$-0.463160\pi$
$659$	−22.7026	−	25.0485i	−0.884368	−	0.975750i	−0.999846	+	0.0175599i	$0.994410\pi$
$660$	−9.47093	−	5.52218i	−0.368655	−	0.214950i
$661$	22.7408	+	13.6303i	0.884516	+	0.530158i	0.882752	−	0.469840i	$-0.155688\pi$
$661$	22.7408	+	13.6303i	0.884516	+	0.530158i	0.00176439	+	0.999998i	$0.499438\pi$
$662$	−12.9426	+	4.71937i	−0.503030	+	0.183424i
$663$	−0.340839	+	3.46059i	−0.0132371	+	0.134398i
$664$	25.1192	−	19.3453i	0.974816	−	0.750743i
$665$	8.19824	+	6.72812i	0.317914	+	0.260905i
$666$	0.0273135	−	0.0305042i	0.00105838	−	0.00118202i
$667$	−10.3048	+	11.3696i	−0.399002	+	0.440231i
$668$	−0.775171	−	0.402369i	−0.0299923	−	0.0155681i
$669$	−21.8152	−	16.1793i	−0.843425	−	0.625527i
$670$	13.4167	−	11.1472i	0.518332	−	0.430652i
$671$	−4.87040	−	11.7582i	−0.188020	−	0.453920i
$672$	6.46904	+	2.82373i	0.249549	+	0.108928i
$673$	−10.5365	+	25.4374i	−0.406153	+	0.980540i	0.579987	+	0.814626i	$0.303058\pi$
$673$	−10.5365	+	25.4374i	−0.406153	+	0.980540i	−0.986140	+	0.165914i	$0.946942\pi$
$674$	2.91682	+	9.41037i	0.112352	+	0.362474i
$675$	−10.2413	+	1.51915i	−0.394186	+	0.0584720i
$676$	−0.684963	+	0.0758324i	−0.0263447	+	0.00291663i
$677$	−15.4616	+	0.759580i	−0.594238	+	0.0291930i	−0.343965	−	0.938982i	$-0.611770\pi$
$677$	−15.4616	+	0.759580i	−0.594238	+	0.0291930i	−0.250272	+	0.968175i	$0.580520\pi$
$678$	−11.3455	+	32.3231i	−0.435722	+	1.24136i
$679$	8.64011	−	0.850977i	0.331577	−	0.0326575i
$680$	3.33668	+	2.38212i	0.127956	+	0.0913501i
$681$	22.2315	−	18.2449i	0.851914	−	0.699148i
$682$	−5.38527	−	0.231948i	−0.206213	−	0.00888173i
$683$	−4.68109	+	1.17255i	−0.179117	+	0.0448665i	−0.331501	−	0.943455i	$-0.607555\pi$
$683$	−4.68109	+	1.17255i	−0.179117	+	0.0448665i	0.152384	+	0.988321i	$0.451305\pi$
$684$	0.194508	+	0.0669556i	0.00743722	+	0.00256011i
$685$	1.82923	−	37.2348i	0.0698912	−	1.42267i
$686$	12.6213	−	5.31750i	0.481883	−	0.203023i
$687$	−6.41370	−	9.59878i	−0.244698	−	0.366216i
$688$	0.591731	−	0.461439i	0.0225595	−	0.0175922i
$689$	24.3445	−	36.4341i	0.927452	−	1.38803i
$690$	27.4950	+	5.29656i	1.04672	+	0.201637i
$691$	0.789660	−	1.66960i	0.0300401	−	0.0635144i	−0.888411	−	0.459048i	$-0.848190\pi$
$691$	0.789660	−	1.66960i	0.0300401	−	0.0635144i	0.918451	+	0.395534i	$0.129440\pi$
$692$	−11.6495	+	16.1110i	−0.442849	+	0.612447i
$693$	0.0126773	−	0.00940213i	0.000481571	−	0.000357157i
$694$	−49.9012	−	12.1796i	−1.89422	−	0.462331i
$695$	15.8630	+	52.2935i	0.601720	+	1.98360i
$696$	17.2267	+	3.10307i	0.652978	+	0.117622i
$697$	−1.28081	−	2.39623i	−0.0485143	−	0.0907638i
$698$	29.0900	+	4.13559i	1.10107	+	0.156534i
$699$	8.16251	+	2.92059i	0.308734	+	0.110467i
$700$	−0.0346982	−	2.87069i	−0.00131147	−	0.108502i
$701$	40.9386	−	24.5376i	1.54623	−	0.926773i	0.550461	−	0.834861i	$-0.314452\pi$
$701$	40.9386	−	24.5376i	1.54623	−	0.926773i	0.995767	−	0.0919125i	$-0.0292980\pi$
$702$	−16.8517	+	20.7888i	−0.636027	+	0.784622i
$703$	−6.20177	−	6.20177i	−0.233904	−	0.233904i
$704$	−2.88654	+	9.09404i	−0.108791	+	0.342745i
$705$	30.5814	−	30.5814i	1.15176	−	1.15176i
$706$	−3.74275	−	35.7826i	−0.140860	−	1.34669i
$707$	−3.33831	−	5.56963i	−0.125550	−	0.209467i
$708$	−27.5760	+	11.8148i	−1.03637	+	0.444029i
$709$	−8.72147	+	24.3749i	−0.327542	+	0.915418i	0.659034	+	0.752113i	$0.270965\pi$
$709$	−8.72147	+	24.3749i	−0.327542	+	0.915418i	−0.986576	+	0.163305i	$0.947785\pi$
$710$	7.12852	+	9.49128i	0.267529	+	0.356201i
$711$	−0.138632	+	0.0741002i	−0.00519910	+	0.00277898i
$712$	6.04970	+	5.83422i	0.226722	+	0.218647i
$713$	13.1741	−	3.99632i	0.493374	−	0.149663i
$714$	−0.826267	+	0.502057i	−0.0309223	+	0.0187890i
$715$	6.86592	+	9.25762i	0.256771	+	0.346215i
$716$	1.18830	−	0.731905i	0.0444088	−	0.0273526i
$717$	17.3677	+	8.21431i	0.648608	+	0.306769i
$718$	0.435580	+	0.643440i	0.0162557	+	0.0240130i
$719$	11.9104	+	7.95831i	0.444185	+	0.296795i	0.757477	−	0.652862i	$-0.226432\pi$
$719$	11.9104	+	7.95831i	0.444185	+	0.296795i	−0.313292	+	0.949657i	$0.601432\pi$
$720$	−0.0701083	−	0.181950i	−0.00261278	−	0.00678087i
$721$	10.7867	−	7.20746i	0.401719	−	0.268420i
$722$	6.48355	−	15.9242i	0.241293	−	0.592637i
$723$	−17.3833	−	0.853988i	−0.646493	−	0.0317602i
$724$	24.9061	−	1.52551i	0.925629	−	0.0566951i
$725$	−1.72988	−	6.90607i	−0.0642462	−	0.256485i
$726$	−15.9083	−	17.3404i	−0.590413	−	0.643561i
$727$	5.83276	+	7.10724i	0.216325	+	0.263593i	0.869855	−	0.493308i	$-0.164212\pi$
$727$	5.83276	+	7.10724i	0.216325	+	0.263593i	−0.653530	+	0.756901i	$0.726712\pi$
$728$	−5.08227	−	5.40710i	−0.188361	−	0.200400i
$729$	2.63001	+	26.7029i	0.0974077	+	0.988997i
$730$	22.1890	+	46.1904i	0.821252	+	1.70958i
$731$	0.00504337	+	0.102660i	0.000186536	+	0.00379703i
$732$	10.3340	−	35.6104i	0.381955	−	1.31620i
$733$	4.16065	+	28.0488i	0.153677	+	1.03601i	0.919538	+	0.393001i	$0.128563\pi$
$733$	4.16065	+	28.0488i	0.153677	+	1.03601i	−0.765861	+	0.643006i	$0.777687\pi$
$734$	13.2220	−	25.1004i	0.488035	−	0.926473i
$735$	−27.5340	−	11.4050i	−1.01561	−	0.420678i
$736$	−0.736208	−	24.3573i	−0.0271370	−	0.897821i
$737$	−5.13725	+	2.12792i	−0.189233	+	0.0783828i
$738$	−0.0118890	+	0.128679i	−0.000437642	+	0.00473674i
$739$	1.23595	−	1.66649i	0.0454653	−	0.0613029i	−0.779890	−	0.625917i	$-0.784725\pi$
$739$	1.23595	−	1.66649i	0.0454653	−	0.0613029i	0.825355	+	0.564614i	$0.190975\pi$
$740$	−0.714815	+	8.28276i	−0.0262771	+	0.304480i
$741$	−26.2491	−	23.7908i	−0.964285	−	0.873977i
$742$	12.1649	−	0.671340i	0.446589	−	0.0246457i
$743$	−20.8839	+	25.4471i	−0.766155	+	0.933562i	−0.999243	−	0.0388934i	$-0.987617\pi$
$743$	−20.8839	+	25.4471i	−0.766155	+	0.933562i	0.233089	+	0.972455i	$0.425117\pi$
$744$	−11.8254	−	10.3337i	−0.433540	−	0.378851i
$745$	−45.4737	−	4.47877i	−1.66603	−	0.164090i
$746$	−4.19333	+	9.00648i	−0.153529	+	0.329751i
$747$	0.106189	−	0.177165i	0.00388524	−	0.00648213i
$748$	−0.791155	−	1.04023i	−0.0289275	−	0.0380347i
$749$	−3.38641	+	3.06927i	−0.123737	+	0.112149i
$750$	13.7110	−	13.8778i	0.500656	−	0.506744i
$751$	21.0331	+	4.18373i	0.767507	+	0.152667i	0.563290	−	0.826259i	$-0.309535\pi$
$751$	21.0331	+	4.18373i	0.767507	+	0.152667i	0.204217	+	0.978926i	$0.434535\pi$
$752$	−31.7917	−	20.1484i	−1.15932	−	0.734736i
$753$	−26.8188	+	5.33459i	−0.977331	+	0.194403i
$754$	−15.3624	−	10.1310i	−0.559464	−	0.368951i
$755$	−15.3386	−	42.8684i	−0.558227	−	1.56014i
$756$	−7.43556	−	0.275248i	−0.270429	−	0.0100107i
$757$	−19.4491	−	2.88500i	−0.706889	−	0.104857i	−0.216401	−	0.976305i	$-0.569432\pi$
$757$	−19.4491	−	2.88500i	−0.706889	−	0.104857i	−0.490489	+	0.871447i	$0.663182\pi$
$758$	7.42457	+	48.0500i	0.269673	+	1.74525i
$759$	−7.87197	−	4.20766i	−0.285734	−	0.152728i
$760$	−39.7423	+	12.8470i	−1.44161	+	0.466008i
$761$	−2.17085	+	7.15634i	−0.0786933	+	0.259417i	−0.987456	−	0.157897i	$-0.949529\pi$
$761$	−2.17085	+	7.15634i	−0.0786933	+	0.259417i	0.908762	+	0.417314i	$0.137029\pi$
$762$	13.0636	−	22.0971i	0.473245	−	0.800492i
$763$	8.53952	−	4.03889i	0.309151	−	0.146218i
$764$	−1.94350	−	9.18877i	−0.0703133	−	0.332438i
$765$	0.0259084	+	0.00648972i	0.000936721	+	0.000234636i
$766$	2.56599	−	8.64669i	0.0927129	−	0.312418i
$767$	31.5399			1.13884
$768$	−23.1245	+	15.4265i	−0.834432	+	0.556655i
$769$	30.9035			1.11441			0.557203	−	0.830376i	$-0.311874\pi$
$769$	30.9035			1.11441			0.557203	+	0.830376i	$0.311874\pi$
$770$	−0.911709	+	3.07222i	−0.0328557	+	0.110715i
$771$	−44.7111	−	11.1995i	−1.61023	−	0.403342i
$772$	23.3731	−	4.94360i	0.841216	−	0.177924i
$773$	−15.3153	+	7.24358i	−0.550852	+	0.260534i	−0.682653	−	0.730743i	$-0.739174\pi$
$773$	−15.3153	+	7.24358i	−0.550852	+	0.260534i	0.131801	+	0.991276i	$0.457924\pi$
$774$	0.00248783	−	0.00420816i	8.94232e−5	−	0.000151259i
$775$	−1.85418	+	6.11240i	−0.0666040	+	0.219564i
$776$	−15.5684	+	30.4413i	−0.558872	+	1.09278i
$777$	−1.72907	−	0.924209i	−0.0620302	−	0.0331558i
$778$	7.01951	+	45.4285i	0.251661	+	1.62869i
$779$	27.3811	+	4.06161i	0.981031	+	0.145522i
$780$	−1.24221	+	33.5570i	−0.0444782	+	1.20153i
$781$	−1.27477	−	3.56274i	−0.0456148	−	0.127485i
$782$	2.78651	+	1.83762i	0.0996452	+	0.0657133i
$783$	−18.0972	+	3.59976i	−0.646742	+	0.128645i
$784$	−4.44367	+	25.5533i	−0.158703	+	0.912616i
$785$	33.2085	+	6.60558i	1.18526	+	0.235763i
$786$	−25.6189	+	25.9304i	−0.913796	+	0.924908i
$787$	−16.8451	+	15.2675i	−0.600462	+	0.544227i	−0.914190	−	0.405286i	$-0.867172\pi$
$787$	−16.8451	+	15.2675i	−0.600462	+	0.544227i	0.313728	+	0.949513i	$0.398422\pi$
$788$	30.1526	−	22.9327i	1.07414	−	0.816945i
$789$	0.834174	−	1.39174i	0.0296974	−	0.0495471i
$790$	13.4714	−	28.9340i	0.479290	−	1.02942i
$791$	9.96518	+	0.981485i	0.354321	+	0.0348976i
$792$	0.00417496	+	0.0620179i	0.000148351	+	0.00220371i
$793$	−24.7301	+	30.1337i	−0.878190	+	1.07008i
$794$	−30.1803	+	1.66555i	−1.07106	+	0.0591081i
$795$	−40.8505	−	37.0248i	−1.44882	−	1.31313i
$796$	31.9334	+	2.75590i	1.13185	+	0.0976803i
$797$	2.79314	−	3.76611i	0.0989380	−	0.133402i	−0.750964	−	0.660343i	$-0.770411\pi$
$797$	2.79314	−	3.76611i	0.0989380	−	0.133402i	0.849902	+	0.526940i	$0.176661\pi$
$798$	0.906205	−	9.80814i	0.0320793	−	0.347204i
$799$	4.76314	−	1.97296i	0.168508	−	0.0697983i
$800$	9.58628	+	5.99453i	0.338926	+	0.211939i
$801$	0.0505859	+	0.0209534i	0.00178736	+	0.000740351i
$802$	11.3109	−	21.4724i	0.399402	−	0.758215i
$803$	−2.39689	−	16.1585i	−0.0845844	−	0.570222i
$804$	−15.5585	−	4.51500i	−0.548705	−	0.159232i
$805$	−0.401607	−	8.17489i	−0.0141548	−	0.288127i
$806$	7.14906	+	14.8821i	0.251815	+	0.524198i
$807$	−3.72604	−	37.8311i	−0.131163	−	1.33172i
$808$	25.5604	+	0.791544i	0.899212	+	0.0278464i
$809$	−19.2161	−	23.4149i	−0.675601	−	0.823223i	0.316509	−	0.948590i	$-0.397489\pi$
$809$	−19.2161	−	23.4149i	−0.675601	−	0.823223i	−0.992110	+	0.125367i	$0.959989\pi$
$810$	22.9019	+	24.9635i	0.804690	+	0.877127i
$811$	9.43167	+	37.6533i	0.331191	+	1.32219i	0.875466	+	0.483280i	$0.160555\pi$
$811$	9.43167	+	37.6533i	0.331191	+	1.32219i	−0.544275	+	0.838907i	$0.683195\pi$
$812$	−0.312804	−	5.10698i	−0.0109773	−	0.179220i
$813$	−4.36831	−	0.214601i	−0.153203	−	0.00752640i
$814$	0.999363	−	2.45453i	0.0350276	−	0.0860311i
$815$	−28.8096	+	19.2500i	−1.00916	+	0.674296i
$816$	0.0948551	−	3.80645i	0.00332059	−	0.133252i
$817$	−0.870663	−	0.581759i	−0.0304607	−	0.0203532i
$818$	10.7067	+	15.8159i	0.374351	+	0.552992i
$819$	−0.0437023	−	0.0206696i	−0.00152708	−	0.000722255i
$820$	−13.7601	−	22.3405i	−0.480525	−	0.780166i
$821$	6.10146	+	8.22686i	0.212942	+	0.287120i	0.896745	−	0.442547i	$-0.145925\pi$
$821$	6.10146	+	8.22686i	0.212942	+	0.287120i	−0.683803	+	0.729667i	$0.739675\pi$
$822$	−29.5893	+	17.9791i	−1.03205	+	0.627094i
$823$	−35.6273	+	10.8074i	−1.24189	+	0.376723i	−0.841818	−	0.539762i	$-0.818514\pi$
$823$	−35.6273	+	10.8074i	−1.24189	+	0.376723i	−0.400070	+	0.916484i	$0.631014\pi$
$824$	0.926212	+	51.0825i	0.0322661	+	1.77954i
$825$	3.65237	−	1.95223i	0.127159	−	0.0679680i
$826$	5.26637	+	7.01192i	0.183241	+	0.243976i
$827$	−0.314763	+	0.879705i	−0.0109454	+	0.0305903i	−0.946893	−	0.321550i	$-0.895796\pi$
$827$	−0.314763	+	0.879705i	−0.0109454	+	0.0305903i	0.935947	+	0.352141i	$0.114546\pi$
$828$	−0.0625208	−	0.145925i	−0.00217275	−	0.00507124i
$829$	−19.8617	−	33.1372i	−0.689824	−	1.15090i	−0.980958	−	0.194219i	$-0.937783\pi$
$829$	−19.8617	−	33.1372i	−0.689824	−	1.15090i	0.291135	−	0.956682i	$-0.405967\pi$
$830$	4.36279	+	41.7105i	0.151435	+	1.44779i
$831$	20.4628	−	20.4628i	0.709848	−	0.709848i
$832$	28.7334	−	5.33321i	0.996152	−	0.184896i
$833$	−2.51215	−	2.51215i	−0.0870407	−	0.0870407i
$834$	31.9595	−	39.4263i	1.10667	−	1.36522i
$835$	0.990902	−	0.593924i	0.0342916	−	0.0205536i
$836$	13.3135	−	0.160921i	0.460456	−	0.00556556i
$837$	15.5869	+	5.57709i	0.538762	+	0.192772i
$838$	36.3696	+	5.17050i	1.25637	+	0.178612i
$839$	1.31847	+	2.46668i	0.0455185	+	0.0851592i	0.903652	−	0.428267i	$-0.140876\pi$
$839$	1.31847	+	2.46668i	0.0455185	+	0.0851592i	−0.858134	+	0.513427i	$0.828376\pi$
$840$	−7.66778	+	5.32702i	−0.264564	+	0.183800i
$841$	4.73503	+	15.6093i	0.163277	+	0.538252i
$842$	54.2576	+	13.2429i	1.86984	+	0.456380i
$843$	27.2106	−	20.1807i	0.937181	−	0.695061i
$844$	−32.8085	−	23.7232i	−1.12932	−	0.816587i
$845$	0.389747	−	0.824050i	0.0134077	−	0.0283482i
$846$	−0.240780	−	0.0463832i	−0.00827818	−	0.00159469i
$847$	−3.82156	+	5.71937i	−0.131310	+	0.196520i
$848$	−23.6653	+	41.7389i	−0.812668	+	1.43332i
$849$	5.89141	+	8.81712i	0.202193	+	0.302603i
$850$	−1.42719	+	0.601291i	−0.0489522	+	0.0206241i
$851$	−0.332121	+	6.76047i	−0.0113850	+	0.231746i
$852$	3.58827	−	10.4240i	0.122932	−	0.357122i
$853$	−16.3884	+	4.10508i	−0.561128	+	0.140555i	−0.513159	−	0.858294i	$-0.671525\pi$
$853$	−16.3884	+	4.10508i	−0.561128	+	0.140555i	−0.0479691	+	0.998849i	$0.515275\pi$
$854$	−10.8286	−	0.466395i	−0.370547	−	0.0159597i
$855$	−0.210338	+	0.172620i	−0.00719342	+	0.00590349i
$856$	−2.96335	−	17.7535i	−0.101285	−	0.606801i
$857$	10.5806	−	1.04210i	0.361427	−	0.0355975i	0.0843260	−	0.996438i	$-0.473126\pi$
$857$	10.5806	−	1.04210i	0.361427	−	0.0355975i	0.277101	+	0.960841i	$0.410626\pi$
$858$	3.54528	−	10.1004i	0.121034	−	0.344823i
$859$	32.7321	−	1.60803i	1.11680	−	0.0548651i	0.517720	−	0.855550i	$-0.326781\pi$
$859$	32.7321	−	1.60803i	1.11680	−	0.0548651i	0.599085	+	0.800685i	$0.295531\pi$
$860$	0.109220	+	0.986539i	0.00372437	+	0.0336407i
$861$	6.12075	−	0.907927i	0.208595	−	0.0309421i
$862$	3.47956	+	11.2259i	0.118514	+	0.382355i
$863$	17.9322	−	43.2922i	0.610420	−	1.47368i	−0.252120	−	0.967696i	$-0.581128\pi$
$863$	17.9322	−	43.2922i	0.610420	−	1.47368i	0.862540	−	0.505989i	$-0.168872\pi$
$864$	16.7367	−	24.0529i	0.569394	−	0.818298i
$865$	−10.0639	−	24.2964i	−0.342184	−	0.826104i
$866$	−30.0149	+	24.9377i	−1.01995	+	0.847417i
$867$	−23.3039	−	17.2834i	−0.791443	−	0.586974i
$868$	−2.11485	+	4.07431i	−0.0717828	+	0.138291i
$869$	−6.83259	+	7.53860i	−0.231780	+	0.255729i
$870$	−15.4449	+	17.2492i	−0.523632	+	0.584803i
$871$	13.1656	+	10.8048i	0.446100	+	0.366105i
$872$	−4.79068	+	36.8926i	−0.162233	+	1.24934i
$873$	−0.0218331	+	0.221675i	−0.000738939	+	0.00750257i
$874$	−31.9479	+	11.6494i	−1.08065	+	0.394047i
$875$	−4.89120	−	2.93167i	−0.165353	−	0.0991086i
$876$	23.9722	−	41.1140i	0.809945	−	1.38911i
$877$	−0.210927	−	0.232722i	−0.00712249	−	0.00785846i	0.737379	−	0.675479i	$-0.236063\pi$
$877$	−0.210927	−	0.232722i	−0.00712249	−	0.00785846i	−0.744502	+	0.667620i	$0.767313\pi$
$878$	−0.0420068	−	6.95095i	−0.00141766	−	0.234583i
$879$	−1.35217	+	6.79782i	−0.0456076	+	0.229285i
$880$	−8.23987	−	9.55947i	−0.277766	−	0.322250i
$881$	−7.96782	−	40.0569i	−0.268443	−	1.34955i	−0.845992	−	0.533196i	$-0.820991\pi$
$881$	−7.96782	−	40.0569i	−0.268443	−	1.34955i	0.577549	−	0.816356i	$-0.304009\pi$
$882$	0.0339656	+	0.165523i	0.00114368	+	0.00557344i
$883$	37.2168	−	13.3164i	1.25245	−	0.448132i	0.374650	−	0.927166i	$-0.377763\pi$
$883$	37.2168	−	13.3164i	1.25245	−	0.448132i	0.877796	+	0.479034i	$0.159013\pi$
$884$	−1.66765	+	3.63910i	−0.0560890	+	0.122396i
$885$	5.82273	−	39.2536i	0.195729	−	1.31950i
$886$	−17.1829	−	12.5835i	−0.577272	−	0.422751i
$887$	12.2089	−	22.8412i	0.409934	−	0.766933i	−0.589223	−	0.807970i	$-0.700566\pi$
$887$	12.2089	−	22.8412i	0.409934	−	0.766933i	0.999158	+	0.0410370i	$0.0130662\pi$
$888$	6.74237	−	3.76259i	0.226259	−	0.126264i
$889$	−7.18037	−	2.17814i	−0.240822	−	0.0730525i
$890$	−10.7675	+	2.76637i	−0.360927	+	0.0927290i
$891$	−4.61731	−	9.76248i	−0.154686	−	0.327055i
$892$	−17.6834	−	25.7848i	−0.592083	−	0.863340i
$893$	−12.7623	+	50.9498i	−0.427072	+	1.70497i
$894$	20.2309	+	37.3053i	0.676623	+	1.24768i
$895$			1.84605i			0.0617067i
$896$	5.98344	+	5.49747i	0.199893	+	0.183658i
$897$			27.3398i			0.912848i
$898$	34.2482	−	18.5730i	1.14288	−	0.619789i
$899$	−2.76603	+	11.0426i	−0.0922521	+	0.368291i
$900$	0.0724105	+	0.0134957i	0.00241368	+	0.000449856i
$901$	−2.81000	−	5.94124i	−0.0936146	−	0.197931i
$902$	2.08132	+	8.10105i	0.0693002	+	0.269735i
$903$	−0.223997	−	0.0679487i	−0.00745415	−	0.00226119i
$904$	−24.4605	+	30.9322i	−0.813545	+	1.02879i
$905$	−15.5591	+	29.1090i	−0.517202	+	0.967616i
$906$	−24.9839	+	34.1158i	−0.830033	+	1.13342i
$907$	5.00096	−	33.7138i	0.166054	−	1.11945i	−0.732559	−	0.680704i	$-0.761674\pi$
$907$	5.00096	−	33.7138i	0.166054	−	1.11945i	0.898613	−	0.438743i	$-0.144576\pi$
$908$	31.0349	−	11.5294i	1.02993	−	0.382618i
$909$	0.156861	−	0.0561257i	0.00520275	−	0.00186157i
$910$	9.61533	−	1.97309i	0.318745	−	0.0654072i
$911$	−2.79979	−	14.0755i	−0.0927613	−	0.466343i	−0.999046	−	0.0436744i	$-0.986094\pi$
$911$	−2.79979	−	14.0755i	−0.0927613	−	0.466343i	0.906285	−	0.422668i	$-0.138906\pi$
$912$	30.5720	+	23.8769i	1.01234	+	0.790642i
$913$	2.60814	−	13.1120i	0.0863170	−	0.433945i
$914$	21.2631	−	0.128500i	0.703322	−	0.00425039i
$915$	32.9380	+	36.3414i	1.08890	+	1.20141i
$916$	−3.38466	−	12.8513i	−0.111832	−	0.424618i
$917$	9.13915	+	5.47779i	0.301801	+	0.180893i
$918$	1.37502	+	3.77092i	0.0453824	+	0.124459i
$919$	−3.00602	+	30.5207i	−0.0991596	+	1.00678i	0.808901	+	0.587945i	$0.200063\pi$
$919$	−3.00602	+	30.5207i	−0.0991596	+	1.00678i	−0.908061	+	0.418839i	$0.862437\pi$
$920$	27.9433	+	16.0673i	0.921264	+	0.529724i
$921$	−10.9810	−	9.01191i	−0.361838	−	0.296952i
$922$	23.2475	+	20.8158i	0.765616	+	0.685532i
$923$	−7.78340	+	8.58766i	−0.256194	+	0.282666i
$924$	2.83749	−	0.898334i	0.0933466	−	0.0295530i
$925$	−2.52243	−	1.87076i	−0.0829371	−	0.0615103i
$926$	−9.86231	−	11.8703i	−0.324096	−	0.390081i
$927$	0.127374	+	0.307508i	0.00418351	+	0.0100999i
$928$	17.5884	+	9.83233i	0.577367	+	0.322762i
$929$	6.32221	−	15.2632i	0.207425	−	0.500768i	−0.785591	−	0.618746i	$-0.787641\pi$
$929$	6.32221	−	15.2632i	0.207425	−	0.500768i	0.993016	+	0.117978i	$0.0376411\pi$
$930$	19.8416	−	6.15007i	0.650632	−	0.201669i
$931$	35.8024	−	5.31078i	1.17338	−	0.174054i
$932$	7.79046	+	6.23743i	0.255185	+	0.204314i
$933$	−24.2488	+	1.19127i	−0.793871	+	0.0390004i
$934$	−33.4592	−	11.7443i	−1.09482	−	0.384285i
$935$	1.72039	−	0.169444i	0.0562628	−	0.00554140i
$936$	0.161500	−	0.100824i	0.00527880	−	0.00329552i
$937$	24.2599	−	19.9096i	0.792536	−	0.650418i	−0.148428	−	0.988923i	$-0.547421\pi$
$937$	24.2599	−	19.9096i	0.792536	−	0.650418i	0.940964	+	0.338505i	$0.109921\pi$
$938$	−0.203772	+	4.73109i	−0.00665338	+	0.154476i
$939$	33.7396	−	8.45134i	1.10105	−	0.275799i
$940$	44.7460	−	21.8289i	1.45945	−	0.711981i
$941$	−1.39415	+	28.3786i	−0.0454480	+	0.925115i	0.862507	+	0.506046i	$0.168893\pi$
$941$	−1.39415	+	28.3786i	−0.0454480	+	0.925115i	−0.907954	+	0.419069i	$0.862357\pi$
$942$	−12.2094	−	28.9795i	−0.397804	−	0.944204i
$943$	−11.8682	−	17.7621i	−0.386483	−	0.578413i
$944$	−34.4430	+	2.52783i	−1.12103	+	0.0822739i
$945$	5.46799	−	8.18343i	0.177874	−	0.266207i
$946$	0.0598517	−	0.310696i	0.00194595	−	0.0101016i
$947$	16.8978	−	35.7275i	0.549106	−	1.16099i	−0.418429	−	0.908249i	$-0.637419\pi$
$947$	16.8978	−	35.7275i	0.549106	−	1.16099i	0.967535	−	0.252737i	$-0.0813309\pi$
$948$	−29.2666	+	4.70348i	−0.950536	+	0.152762i
$949$	−40.1880	+	29.8055i	−1.30456	+	0.967527i
$950$	3.74108	−	15.3276i	0.121377	−	0.497294i
$951$	5.68212	+	18.7314i	0.184255	+	0.607408i
$952$	−1.08750	+	0.236889i	−0.0352459	+	0.00767761i
$953$	−15.6057	−	29.1961i	−0.505517	−	0.945756i	−0.997186	−	0.0749734i	$-0.976113\pi$
$953$	−15.6057	−	29.1961i	−0.505517	−	0.945756i	0.491668	−	0.870782i	$-0.336387\pi$
$954$	−0.0439963	+	0.309473i	−0.00142443	+	0.0100196i
$955$	11.6971	+	4.18530i	0.378510	+	0.135433i
$956$	15.8267	+	15.4486i	0.511871	+	0.499645i
$957$	6.33072	−	3.79449i	0.204643	−	0.122658i
$958$	−26.0157	−	21.0887i	−0.840529	−	0.681346i
$959$	7.15639	+	7.15639i	0.231092	+	0.231092i
$960$	−1.33295	−	36.7454i	−0.0430208	−	1.18595i
$961$	−14.6984	+	14.6984i	−0.474142	+	0.474142i
$962$	−8.07333	+	0.844446i	−0.260295	+	0.0272260i
$963$	−0.0602835	−	0.100577i	−0.00194261	−	0.00324105i
$964$	−18.6015	−	7.44290i	−0.599115	−	0.239720i
$965$	−10.6460	+	29.7535i	−0.342706	+	0.957800i
$966$	−6.07815	+	4.56506i	−0.195561	+	0.146878i
$967$	−10.1967	+	5.45027i	−0.327905	+	0.175269i	−0.627132	−	0.778913i	$-0.715771\pi$
$967$	−10.1967	+	5.45027i	−0.327905	+	0.175269i	0.299227	+	0.954182i	$0.403271\pi$
$968$	−10.8187	−	24.8354i	−0.347727	−	0.798241i
$969$	−5.08466	+	1.54241i	−0.163343	+	0.0495495i
$970$	−23.4851	−	38.6509i	−0.754061	−	1.24101i
$971$	31.3063	+	42.2117i	1.00467	+	1.35464i	0.934053	+	0.357134i	$0.116246\pi$
$971$	31.3063	+	42.2117i	1.00467	+	1.35464i	0.0706150	+	0.997504i	$0.477504\pi$
$972$	0.0885603	−	0.372602i	0.00284057	−	0.0119512i
$973$	−13.4110	−	6.34295i	−0.429938	−	0.203346i
$974$	−8.97238	+	6.07390i	−0.287493	+	0.194620i
$975$	−10.5471	−	7.04734i	−0.337777	−	0.225695i
$976$	24.5912	−	34.8894i	0.787147	−	1.11678i
$977$	36.7539	−	24.5582i	1.17586	−	0.785686i	0.195079	−	0.980787i	$-0.437504\pi$
$977$	36.7539	−	24.5582i	1.17586	−	0.785686i	0.980783	+	0.195101i	$0.0625035\pi$
$978$	29.8044	+	12.1349i	0.953041	+	0.388032i
$979$	3.53964	+	0.173891i	0.113127	+	0.00555759i
$980$	−25.6971	−	22.7308i	−0.820863	−	0.726110i
$981$	0.0588896	+	0.235101i	0.00188020	+	0.00750618i
$982$	−20.6973	+	18.9880i	−0.660477	+	0.605932i
$983$	−27.0801	−	32.9972i	−0.863721	−	1.05245i	−0.998106	−	0.0615184i	$-0.980406\pi$
$983$	−27.0801	−	32.9972i	−0.863721	−	1.05245i	0.134385	−	0.990929i	$-0.457094\pi$
$984$	−10.0179	+	22.2142i	−0.319357	+	0.708163i
$985$	4.91156	+	49.8679i	0.156495	+	1.58892i
$986$	−2.48790	+	1.19514i	−0.0792309	+	0.0380610i
$987$	0.576110	+	11.7270i	0.0183378	+	0.373274i
$988$	−19.6576	−	35.7312i	−0.625392	−	1.13676i
$989$	0.118575	+	0.799370i	0.00377047	+	0.0254185i
$990$	−0.0727444	−	0.0383193i	−0.00231197	−	0.00121787i
$991$	18.0633	+	7.48206i	0.573799	+	0.237675i	0.650664	−	0.759366i	$-0.274491\pi$
$991$	18.0633	+	7.48206i	0.573799	+	0.237675i	−0.0768643	+	0.997042i	$0.524491\pi$
$992$	−8.99986	−	15.6789i	−0.285746	−	0.497807i
$993$	−15.6358	+	6.47657i	−0.496188	+	0.205528i
$994$	−3.20883	−	0.296474i	−0.101778	−	0.00940358i
$995$	−25.2558	+	34.0535i	−0.800663	+	1.07957i
$996$	29.8078	−	25.0716i	0.944495	−	0.794423i
$997$	−44.9280	−	40.7204i	−1.42288	−	1.28963i	−0.899077	−	0.437791i	$-0.855761\pi$
$997$	−44.9280	−	40.7204i	−1.42288	−	1.28963i	−0.523808	−	0.851836i	$-0.675489\pi$
$998$	−1.23595	−	22.3959i	−0.0391234	−	0.708930i
$999$	−5.16348	+	6.29172i	−0.163365	+	0.199061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.109.29	yes	992
256.101	even	64	inner	256.2.m.a.101.29	✓	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.29	✓	992	256.101	even	64	inner
256.2.m.a.109.29	yes	992	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35577 + 0.402339i) q^{2} +(1.68530 + 0.422145i) q^{3} +(1.67625 + 1.09096i) q^{4} +(-2.39151 + 1.13110i) q^{5} +(2.11503 + 1.25039i) q^{6} +(0.208482 - 0.687274i) q^{7} +(1.83368 + 2.15352i) q^{8} +(0.0162507 + 0.00868620i) q^{9} +O(q^{10})\)	\(q+(1.35577 + 0.402339i) q^{2} +(1.68530 + 0.422145i) q^{3} +(1.67625 + 1.09096i) q^{4} +(-2.39151 + 1.13110i) q^{5} +(2.11503 + 1.25039i) q^{6} +(0.208482 - 0.687274i) q^{7} +(1.83368 + 2.15352i) q^{8} +(0.0162507 + 0.00868620i) q^{9} +(-3.69743 + 0.571318i) q^{10} +(1.17974 + 0.174997i) q^{11} +(2.36443 + 2.54621i) q^{12} +(-1.23067 - 3.43948i) q^{13} +(0.559172 - 0.847908i) q^{14} +(-4.50788 + 0.896673i) q^{15} +(1.61961 + 3.65744i) q^{16} +(-0.537376 - 0.106891i) q^{17} +(0.0185375 + 0.0183148i) q^{18} +(4.13592 - 3.74858i) q^{19} +(-5.24274 - 0.713039i) q^{20} +(0.641483 - 1.07025i) q^{21} +(1.52905 + 0.711910i) q^{22} +(-4.28702 - 0.422235i) q^{23} +(2.18119 + 4.40339i) q^{24} +(1.26795 - 1.54500i) q^{25} +(-0.284669 - 5.15831i) q^{26} +(-3.83818 - 3.47872i) q^{27} +(1.09926 - 0.924595i) q^{28} +(2.12192 - 2.86108i) q^{29} +(-6.47243 - 0.598008i) q^{30} +(-2.95256 + 1.22299i) q^{31} +(0.724295 + 5.61029i) q^{32} +(1.91433 + 0.792941i) q^{33} +(-0.685554 - 0.361127i) q^{34} +(0.278788 + 1.87943i) q^{35} +(0.0177639 + 0.0322891i) q^{36} +(-0.0770981 - 1.56937i) q^{37} +(7.11557 - 3.41818i) q^{38} +(-0.622078 - 6.31606i) q^{39} +(-6.82109 - 3.07608i) q^{40} +(3.14596 + 3.83337i) q^{41} +(1.30031 - 1.19292i) q^{42} +(-0.0455819 - 0.181973i) q^{43} +(1.78661 + 1.58038i) q^{44} +(-0.0486887 - 0.00239192i) q^{45} +(-5.64235 - 2.29729i) q^{46} +(-7.82385 + 5.22773i) q^{47} +(1.18555 + 6.84758i) q^{48} +(5.39141 + 3.60242i) q^{49} +(2.34067 - 1.58453i) q^{50} +(-0.860514 - 0.406993i) q^{51} +(1.68944 - 7.10803i) q^{52} +(7.14557 + 9.63469i) q^{53} +(-3.80408 - 6.26061i) q^{54} +(-3.01928 + 0.915890i) q^{55} +(1.86234 - 0.811269i) q^{56} +(8.55268 - 4.57150i) q^{57} +(4.02797 - 3.02524i) q^{58} +(-2.90868 + 8.12921i) q^{59} +(-8.53456 - 3.41487i) q^{60} +(-5.48610 - 9.15301i) q^{61} +(-4.49506 + 0.470170i) q^{62} +(0.00935779 - 0.00935779i) q^{63} +(-1.27526 + 7.89770i) q^{64} +(6.83354 + 6.83354i) q^{65} +(2.27637 + 1.84526i) q^{66} +(-3.99902 + 2.39692i) q^{67} +(-0.784161 - 0.765431i) q^{68} +(-7.04666 - 2.52133i) q^{69} +(-0.378196 + 2.66025i) q^{70} +(-1.49561 - 2.79810i) q^{71} +(0.0110927 + 0.0509239i) q^{72} +(-3.97595 - 13.1069i) q^{73} +(0.526890 - 2.15873i) q^{74} +(2.78908 - 2.06853i) q^{75} +(11.0224 - 1.77142i) q^{76} +(0.366225 - 0.774318i) q^{77} +(1.69780 - 8.81344i) q^{78} +(-4.73946 + 7.09310i) q^{79} +(-8.01023 - 6.91485i) q^{80} +(-5.03066 - 7.52891i) q^{81} +(2.72291 + 6.46293i) q^{82} +(0.550022 - 11.1960i) q^{83} +(2.24289 - 1.09417i) q^{84} +(1.40604 - 0.352195i) q^{85} +(0.0114161 - 0.265054i) q^{86} +(4.78385 - 3.92600i) q^{87} +(1.78640 + 2.86147i) q^{88} +(2.95716 - 0.291255i) q^{89} +(-0.0650485 - 0.0228322i) q^{90} +(-2.62044 + 0.128734i) q^{91} +(-6.72547 - 5.38474i) q^{92} +(-5.49222 + 0.814693i) q^{93} +(-12.7107 + 3.93978i) q^{94} +(-5.65106 + 13.6429i) q^{95} +(-1.14770 + 9.76076i) q^{96} +(4.62605 + 11.1683i) q^{97} +(5.86014 + 7.05324i) q^{98} +(0.0176515 + 0.0130913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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