LMFDB - Embedded newform 64.2.i.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

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("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	64.29
Dual form			64.2.i.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12131 - 0.861781i) q^{2} +(0.416408 + 0.0828287i) q^{3} +(0.514666 + 1.93265i) q^{4} +(1.82421 - 2.73012i) q^{5} +(-0.395542 - 0.451729i) q^{6} +(0.00395016 - 0.00163621i) q^{7} +(1.08842 - 2.61062i) q^{8} +(-2.60510 - 1.07907i) q^{9} +O(q^{10})$	\(q+(-1.12131 - 0.861781i) q^{2} +(0.416408 + 0.0828287i) q^{3} +(0.514666 + 1.93265i) q^{4} +(1.82421 - 2.73012i) q^{5} +(-0.395542 - 0.451729i) q^{6} +(0.00395016 - 0.00163621i) q^{7} +(1.08842 - 2.61062i) q^{8} +(-2.60510 - 1.07907i) q^{9} +(-4.39827 + 1.48924i) q^{10} +(0.744179 + 3.74124i) q^{11} +(0.0542323 + 0.847398i) q^{12} +(2.10744 + 3.15401i) q^{13} +(-0.00583940 - 0.00156948i) q^{14} +(0.985749 - 0.985749i) q^{15} +(-3.47024 + 1.98933i) q^{16} +(-0.937106 - 0.937106i) q^{17} +(1.99120 + 3.45500i) q^{18} +(-6.36144 + 4.25058i) q^{19} +(6.21522 + 2.12045i) q^{20} +(0.00178040 - 0.000354144i) q^{21} +(2.38968 - 4.83641i) q^{22} +(0.0154938 - 0.0374052i) q^{23} +(0.669461 - 0.996931i) q^{24} +(-2.21242 - 5.34125i) q^{25} +(0.354974 - 5.35277i) q^{26} +(-2.05445 - 1.37274i) q^{27} +(0.00519522 + 0.00679216i) q^{28} +(0.237387 - 1.19343i) q^{29} +(-1.95483 + 0.255828i) q^{30} -5.05566i q^{31} +(5.60558 + 0.759932i) q^{32} +1.61952i q^{33} +(0.243204 + 1.85837i) q^{34} +(0.00273887 - 0.0137692i) q^{35} +(0.744702 - 5.59010i) q^{36} +(5.65766 + 3.78033i) q^{37} +(10.7962 + 0.715962i) q^{38} +(0.616312 + 1.48791i) q^{39} +(-5.14182 - 7.73385i) q^{40} +(-1.75731 + 4.24251i) q^{41} +(-0.00230158 - 0.00113721i) q^{42} +(10.6807 - 2.12452i) q^{43} +(-6.84749 + 3.36372i) q^{44} +(-7.69825 + 5.14381i) q^{45} +(-0.0496084 + 0.0285906i) q^{46} +(-7.35399 - 7.35399i) q^{47} +(-1.60981 + 0.540938i) q^{48} +(-4.94973 + 4.94973i) q^{49} +(-2.12219 + 7.89581i) q^{50} +(-0.312599 - 0.467838i) q^{51} +(-5.01095 + 5.69619i) q^{52} +(-1.15910 - 5.82718i) q^{53} +(1.12067 + 3.30975i) q^{54} +(11.5716 + 4.79311i) q^{55} +(2.79065e-5 - 0.0120933i) q^{56} +(-3.00102 + 1.24307i) q^{57} +(-1.29466 + 1.13362i) q^{58} +(3.18115 - 4.76093i) q^{59} +(2.41243 + 1.39777i) q^{60} +(2.17097 + 0.431834i) q^{61} +(-4.35688 + 5.66896i) q^{62} -0.0120562 q^{63} +(-5.63069 - 5.68290i) q^{64} +12.4552 q^{65} +(1.39567 - 1.81598i) q^{66} +(-2.42928 - 0.483215i) q^{67} +(1.32880 - 2.29339i) q^{68} +(0.00954995 - 0.0142925i) q^{69} +(-0.0149372 + 0.0130792i) q^{70} +(-10.9250 + 4.52528i) q^{71} +(-5.65249 + 5.62646i) q^{72} +(4.86044 + 2.01326i) q^{73} +(-3.08617 - 9.11458i) q^{74} +(-0.478860 - 2.40739i) q^{75} +(-11.4889 - 10.1068i) q^{76} +(0.00906108 + 0.0135609i) q^{77} +(0.591177 - 2.19953i) q^{78} +(10.3833 - 10.3833i) q^{79} +(-0.899323 + 13.1031i) q^{80} +(5.23979 + 5.23979i) q^{81} +(5.62660 - 3.24275i) q^{82} +(0.0153741 - 0.0102727i) q^{83} +(0.00160075 + 0.00325862i) q^{84} +(-4.26790 + 0.848937i) q^{85} +(-13.8072 - 6.82218i) q^{86} +(0.197700 - 0.477289i) q^{87} +(10.5769 + 2.12927i) q^{88} +(-3.25895 - 7.86780i) q^{89} +(13.0650 + 0.866416i) q^{90} +(0.0134853 + 0.00901061i) q^{91} +(0.0802652 + 0.0106928i) q^{92} +(0.418754 - 2.10522i) q^{93} +(1.90856 + 14.5836i) q^{94} +25.1215i q^{95} +(2.27126 + 0.780744i) q^{96} -8.60967i q^{97} +(9.81577 - 1.28459i) q^{98} +(2.09840 - 10.5493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$

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 $

$2$	−1.12131	−	0.861781i	−0.792885	−	0.609371i
$2$	−1.12131	−	0.861781i	−0.792885	−	0.609371i
$3$	0.416408	+	0.0828287i	0.240413	+	0.0478212i	0.313826	−	0.949480i	$-0.398389\pi$
$3$	0.416408	+	0.0828287i	0.240413	+	0.0478212i	−0.0734129	+	0.997302i	$0.523389\pi$
$4$	0.514666	+	1.93265i	0.257333	+	0.966323i
$5$	1.82421	−	2.73012i	0.815812	−	1.22095i	−0.156596	−	0.987663i	$-0.550052\pi$
$5$	1.82421	−	2.73012i	0.815812	−	1.22095i	0.972408	−	0.233286i	$-0.0749479\pi$
$6$	−0.395542	−	0.451729i	−0.161479	−	0.184418i
$7$	0.00395016	−	0.00163621i	0.00149302	−	0.000618429i	−0.381937	−	0.924188i	$-0.624743\pi$
$7$	0.00395016	−	0.00163621i	0.00149302	−	0.000618429i	0.383430	+	0.923570i	$0.374743\pi$
$8$	1.08842	−	2.61062i	0.384814	−	0.922994i
$9$	−2.60510	−	1.07907i	−0.868368	−	0.359690i
$10$	−4.39827	+	1.48924i	−1.39086	+	0.470939i
$11$	0.744179	+	3.74124i	0.224379	+	1.12803i	0.914579	+	0.404408i	$0.132523\pi$
$11$	0.744179	+	3.74124i	0.224379	+	1.12803i	−0.690200	+	0.723619i	$0.742477\pi$
$12$	0.0542323	+	0.847398i	0.0156555	+	0.244623i
$13$	2.10744	+	3.15401i	0.584499	+	0.874764i	0.999383	−	0.0351100i	$-0.0111782\pi$
$13$	2.10744	+	3.15401i	0.584499	+	0.874764i	−0.414885	+	0.909874i	$0.636178\pi$
$14$	−0.00583940	−	0.00156948i	−0.00156065	−	0.000419461i
$15$	0.985749	−	0.985749i	0.254519	−	0.254519i
$16$	−3.47024	+	1.98933i	−0.867560	+	0.497333i
$17$	−0.937106	−	0.937106i	−0.227282	−	0.227282i	0.584274	−	0.811556i	$-0.301379\pi$
$17$	−0.937106	−	0.937106i	−0.227282	−	0.227282i	−0.811556	+	0.584274i	$0.801379\pi$
$18$	1.99120	+	3.45500i	0.469331	+	0.814351i
$19$	−6.36144	+	4.25058i	−1.45941	+	0.975150i	−0.463383	+	0.886158i	$0.653364\pi$
$19$	−6.36144	+	4.25058i	−1.45941	+	0.975150i	−0.996032	+	0.0889916i	$0.971636\pi$
$20$	6.21522	+	2.12045i	1.38977	+	0.474148i
$21$	0.00178040		0.000354144i	0.000388516		7.72806e-5i
$22$	2.38968	−	4.83641i	0.509481	−	1.03113i
$23$	0.0154938	−	0.0374052i	0.00323067	−	0.00779953i	−0.922256	−	0.386580i	$-0.873656\pi$
$23$	0.0154938	−	0.0374052i	0.00323067	−	0.00779953i	0.925487	+	0.378780i	$0.123656\pi$
$24$	0.669461	−	0.996931i	0.136653	−	0.203498i
$25$	−2.21242	−	5.34125i	−0.442484	−	1.06825i
$26$	0.354974	−	5.35277i	0.0696161	−	1.04976i
$27$	−2.05445	−	1.37274i	−0.395379	−	0.264184i
$28$	0.00519522	+	0.00679216i	0.000981805	+	0.00128360i
$29$	0.237387	−	1.19343i	0.0440817	−	0.221613i	−0.952465	−	0.304648i	$-0.901461\pi$
$29$	0.237387	−	1.19343i	0.0440817	−	0.221613i	0.996547	+	0.0830345i	$0.0264612\pi$
$30$	−1.95483	+	0.255828i	−0.356901	+	0.0467077i
$31$		−	5.05566i		−	0.908024i	−0.890996	−	0.454012i	$-0.849992\pi$
$31$		−	5.05566i		−	0.908024i	0.890996	−	0.454012i	$-0.150008\pi$
$32$	5.60558	+	0.759932i	0.990936	+	0.134338i
$33$			1.61952i			0.281923i
$34$	0.243204	+	1.85837i	0.0417092	+	0.318707i
$35$	0.00273887	−	0.0137692i	0.000462953	−	0.00232742i
$36$	0.744702	−	5.59010i	0.124117	−	0.931684i
$37$	5.65766	+	3.78033i	0.930113	+	0.621482i	0.925598	−	0.378508i	$-0.123563\pi$
$37$	5.65766	+	3.78033i	0.930113	+	0.621482i	0.00451536	+	0.999990i	$0.498563\pi$
$38$	10.7962	+	0.715962i	1.75138	+	0.116144i
$39$	0.616312	+	1.48791i	0.0986889	+	0.238256i
$40$	−5.14182	−	7.73385i	−0.812992	−	1.22283i
$41$	−1.75731	+	4.24251i	−0.274445	+	0.662569i	−0.999663	−	0.0259502i	$-0.991739\pi$
$41$	−1.75731	+	4.24251i	−0.274445	+	0.662569i	0.725218	+	0.688519i	$0.241739\pi$
$42$	−0.00230158	−	0.00113721i	−0.000355141	−	0.000175476i
$43$	10.6807	−	2.12452i	1.62879	−	0.323986i	0.705682	−	0.708528i	$-0.250641\pi$
$43$	10.6807	−	2.12452i	1.62879	−	0.323986i	0.923108	+	0.384542i	$0.125641\pi$
$44$	−6.84749	+	3.36372i	−1.03230	+	0.507100i
$45$	−7.69825	+	5.14381i	−1.14759	+	0.766794i
$46$	−0.0496084	+	0.0285906i	−0.00731436	+	0.00421545i
$47$	−7.35399	−	7.35399i	−1.07269	−	1.07269i	−0.997142	−	0.0755469i	$-0.975930\pi$
$47$	−7.35399	−	7.35399i	−1.07269	−	1.07269i	−0.0755469	−	0.997142i	$-0.524070\pi$
$48$	−1.60981	+	0.540938i	−0.232356	+	0.0780777i
$49$	−4.94973	+	4.94973i	−0.707105	+	0.707105i
$50$	−2.12219	+	7.89581i	−0.300123	+	1.11664i
$51$	−0.312599	−	0.467838i	−0.0437726	−	0.0655104i
$52$	−5.01095	+	5.69619i	−0.694894	+	0.789920i
$53$	−1.15910	−	5.82718i	−0.159214	−	0.800424i	−0.975023	−	0.222103i	$-0.928708\pi$
$53$	−1.15910	−	5.82718i	−0.159214	−	0.800424i	0.815809	−	0.578322i	$-0.196292\pi$
$54$	1.12067	+	3.30975i	0.152504	+	0.450400i
$55$	11.5716	+	4.79311i	1.56031	+	0.646303i
$56$	2.79065e−5	−	0.0120933i	3.72916e−6	−	0.00161603i
$57$	−3.00102	+	1.24307i	−0.397495	+	0.164648i
$58$	−1.29466	+	1.13362i	−0.169997	+	0.148852i
$59$	3.18115	−	4.76093i	0.414151	−	0.619820i	−0.564480	−	0.825447i	$-0.690923\pi$
$59$	3.18115	−	4.76093i	0.414151	−	0.619820i	0.978631	+	0.205627i	$0.0659232\pi$
$60$	2.41243	+	1.39777i	0.311444	+	0.180452i
$61$	2.17097	+	0.431834i	0.277965	+	0.0552906i	0.332104	−	0.943243i	$-0.392241\pi$
$61$	2.17097	+	0.431834i	0.277965	+	0.0552906i	−0.0541393	+	0.998533i	$0.517241\pi$
$62$	−4.35688	+	5.66896i	−0.553324	+	0.719958i
$63$	−0.0120562			−0.00151893
$64$	−5.63069	−	5.68290i	−0.703836	−	0.710363i
$65$	12.4552			1.54488
$66$	1.39567	−	1.81598i	0.171796	−	0.223532i
$67$	−2.42928	−	0.483215i	−0.296784	−	0.0590341i	0.0444523	−	0.999012i	$-0.485846\pi$
$67$	−2.42928	−	0.483215i	−0.296784	−	0.0590341i	−0.341237	+	0.939977i	$0.610846\pi$
$68$	1.32880	−	2.29339i	0.161140	−	0.278114i
$69$	0.00954995	−	0.0142925i	0.00114968	−	0.00172062i
$70$	−0.0149372	+	0.0130792i	−0.00178533	+	0.00156327i
$71$	−10.9250	+	4.52528i	−1.29656	+	0.537052i	−0.920933	−	0.389720i	$-0.872572\pi$
$71$	−10.9250	+	4.52528i	−1.29656	+	0.537052i	−0.375624	+	0.926772i	$0.622572\pi$
$72$	−5.65249	+	5.62646i	−0.666152	+	0.663085i
$73$	4.86044	+	2.01326i	0.568872	+	0.235635i	0.648532	−	0.761188i	$-0.275383\pi$
$73$	4.86044	+	2.01326i	0.568872	+	0.235635i	−0.0796597	+	0.996822i	$0.525383\pi$
$74$	−3.08617	−	9.11458i	−0.358759	−	1.05955i
$75$	−0.478860	−	2.40739i	−0.0552940	−	0.277982i
$76$	−11.4889	−	10.1068i	−1.31786	−	1.15933i
$77$	0.00906108	+	0.0135609i	0.00103261	+	0.00154540i
$78$	0.591177	−	2.19953i	0.0669376	−	0.249048i
$79$	10.3833	−	10.3833i	1.16822	−	1.16822i	0.185589	−	0.982627i	$-0.440581\pi$
$79$	10.3833	−	10.3833i	1.16822	−	1.16822i	0.982627	−	0.185589i	$-0.0594194\pi$
$80$	−0.899323	+	13.1031i	−0.100547	+	1.46498i
$81$	5.23979	+	5.23979i	0.582199	+	0.582199i
$82$	5.62660	−	3.24275i	0.621354	−	0.358102i
$83$	0.0153741	−	0.0102727i	0.00168753	−	0.00112757i	−0.554726	−	0.832033i	$-0.687177\pi$
$83$	0.0153741	−	0.0102727i	0.00168753	−	0.00112757i	0.556414	+	0.830905i	$0.312177\pi$
$84$	0.00160075	+	0.00325862i	0.000174656	+	0.000355545i
$85$	−4.26790	+	0.848937i	−0.462918	+	0.0920802i
$86$	−13.8072	−	6.82218i	−1.48887	−	0.735654i
$87$	0.197700	−	0.477289i	0.0211956	−	0.0511708i
$88$	10.5769	+	2.12927i	1.12751	+	0.226981i
$89$	−3.25895	−	7.86780i	−0.345448	−	0.833985i	−0.997145	−	0.0755058i	$-0.975943\pi$
$89$	−3.25895	−	7.86780i	−0.345448	−	0.833985i	0.651698	−	0.758479i	$-0.274057\pi$
$90$	13.0650	+	0.866416i	1.37717	+	0.0913282i
$91$	0.0134853	+	0.00901061i	0.00141365	+	0.000944569i
$92$	0.0802652	+	0.0106928i	0.00836822	+	0.00111480i
$93$	0.418754	−	2.10522i	0.0434228	−	0.218301i
$94$	1.90856	+	14.5836i	0.196853	+	1.50419i
$95$			25.1215i			2.57741i
$96$	2.27126	+	0.780744i	0.231810	+	0.0796844i
$97$		−	8.60967i		−	0.874180i	−0.899418	−	0.437090i	$-0.856009\pi$
$97$		−	8.60967i		−	0.874180i	0.899418	−	0.437090i	$-0.143991\pi$
$98$	9.81577	−	1.28459i	0.991542	−	0.129763i
$99$	2.09840	−	10.5493i	0.210897	−	1.06025i
$100$	9.18409	−	7.02478i	0.918409	−	0.702478i
$101$	−0.973870	−	0.650719i	−0.0969036	−	0.0647489i	0.506174	−	0.862431i	$-0.331059\pi$
$101$	−0.973870	−	0.650719i	−0.0969036	−	0.0647489i	−0.603078	+	0.797682i	$0.706059\pi$
$102$	−0.0526538	+	0.793983i	−0.00521350	+	0.0786160i
$103$	−1.43691	−	3.46901i	−0.141583	−	0.341812i	0.837143	−	0.546984i	$-0.184224\pi$
$103$	−1.43691	−	3.46901i	−0.141583	−	0.341812i	−0.978726	+	0.205173i	$0.934224\pi$
$104$	10.5277	−	2.06884i	1.03233	−	0.202867i
$105$	0.00228097	−	0.00550676i	0.000222600	−	0.000537404i
$106$	−3.72205	+	7.53295i	−0.361517	+	0.731665i
$107$	−11.9550	+	2.37799i	−1.15573	+	0.229889i	−0.735497	−	0.677527i	$-0.763051\pi$
$107$	−11.9550	+	2.37799i	−1.15573	+	0.229889i	−0.420233	+	0.907416i	$0.638051\pi$
$108$	1.59566	−	4.67702i	0.153543	−	0.450047i
$109$	−7.72304	+	5.16037i	−0.739733	+	0.494274i	−0.867442	−	0.497538i	$-0.834238\pi$
$109$	−7.72304	+	5.16037i	−0.739733	+	0.494274i	0.127709	+	0.991812i	$0.459238\pi$
$110$	−8.84472	−	15.3467i	−0.843311	−	1.46326i
$111$	2.04277	+	2.04277i	0.193892	+	0.193892i
$112$	−0.0104530	+	0.0135362i	−0.000987719	+	0.00127905i
$113$	−1.39520	+	1.39520i	−0.131250	+	0.131250i	−0.769680	−	0.638430i	$-0.779584\pi$
$113$	−1.39520	+	1.39520i	−0.131250	+	0.131250i	0.638430	+	0.769680i	$0.279584\pi$
$114$	4.43633	+	1.19237i	0.415500	+	0.111675i
$115$	−0.0738571	−	0.110535i	−0.00688721	−	0.0103074i
$116$	2.42864	−	0.155430i	0.225494	−	0.0144313i
$117$	−2.08671	−	10.4906i	−0.192916	−	0.969855i
$118$	−7.66993	+	2.59701i	−0.706074	+	0.239074i
$119$	−0.00523502	−	0.00216842i	−0.000479894	−	0.000198778i
$120$	−1.50051	−	3.64632i	−0.136977	−	0.332862i
$121$	−3.28042	+	1.35879i	−0.298220	+	0.123527i
$122$	−2.06219	−	2.35512i	−0.186701	−	0.213223i
$123$	−1.08316	+	1.62106i	−0.0976650	+	0.146166i
$124$	9.77081	−	2.60198i	0.877444	−	0.233664i
$125$	−2.51619	−	0.500501i	−0.225055	−	0.0447662i
$126$	0.0135187	+	0.0103898i	0.00120434	+	0.000925595i
$127$	−7.55255			−0.670180			−0.335090	−	0.942186i	$-0.608767\pi$
$127$	−7.55255			−0.670180			−0.335090	+	0.942186i	$0.608767\pi$
$128$	1.41632	+	11.2247i	0.125186	+	0.992133i
$129$	4.62349			0.407076
$130$	−13.9662	−	10.7337i	−1.22491	−	0.941408i
$131$	9.31194	+	1.85226i	0.813588	+	0.161833i	0.584312	−	0.811529i	$-0.301364\pi$
$131$	9.31194	+	1.85226i	0.813588	+	0.161833i	0.229276	+	0.973362i	$0.426364\pi$
$132$	−3.12996	+	0.833512i	−0.272428	+	0.0725479i
$133$	−0.0181739	+	0.0271991i	−0.00157587	+	0.00235846i
$134$	2.30755	+	2.63535i	0.199342	+	0.227659i
$135$	−7.49550	+	3.10474i	−0.645110	+	0.267213i
$136$	−3.46639	+	1.42646i	−0.297241	+	0.122318i
$137$	14.3885	+	5.95992i	1.22929	+	0.509190i	0.900353	−	0.435160i	$-0.143308\pi$
$137$	14.3885	+	5.95992i	1.22929	+	0.509190i	0.328941	+	0.944350i	$0.393308\pi$
$138$	−0.0230255	+	0.00779634i	−0.00196006	+	0.000663669i
$139$	2.16053	+	10.8617i	0.183254	+	0.921278i	0.957509	+	0.288404i	$0.0931247\pi$
$139$	2.16053	+	10.8617i	0.183254	+	0.921278i	−0.774255	+	0.632874i	$0.781875\pi$
$140$	0.0280206	−	0.00179328i	0.00236818	−	0.000151560i
$141$	−2.45314	−	3.67138i	−0.206591	−	0.309186i
$142$	16.1501	+	4.34072i	1.35528	+	0.364265i
$143$	−10.2316	+	10.2316i	−0.855608	+	0.855608i
$144$	11.1870	−	1.43779i	0.932247	−	0.119816i
$145$	−2.82516	−	2.82516i	−0.234616	−	0.234616i
$146$	−3.71507	−	6.44613i	−0.307461	−	0.533485i
$147$	−2.47109	+	1.65113i	−0.203812	+	0.136183i
$148$	−4.39423	+	12.8799i	−0.361204	+	1.05872i
$149$	−9.18533	+	1.82708i	−0.752492	+	0.149680i	−0.556410	−	0.830908i	$-0.687822\pi$
$149$	−9.18533	+	1.82708i	−0.752492	+	0.149680i	−0.196081	+	0.980588i	$0.562822\pi$
$150$	−1.53770	+	3.11210i	−0.125552	+	0.254102i
$151$	−3.59266	+	8.67346i	−0.292367	+	0.705836i	−1.00000		0.000744261i	$-0.999763\pi$
$151$	−3.59266	+	8.67346i	−0.292367	+	0.705836i	0.707633	+	0.706580i	$0.249763\pi$
$152$	4.17274	+	21.2337i	0.338454	+	1.72228i
$153$	1.43006	+	3.45246i	0.115613	+	0.279115i
$154$	0.00152624	−	0.0230146i	0.000122988	−	0.00185457i
$155$	−13.8026	−	9.22260i	−1.10865	−	0.740777i
$156$	−2.55841	+	1.95689i	−0.204836	+	0.156677i
$157$	2.82136	−	14.1839i	0.225169	−	1.13200i	−0.688405	−	0.725327i	$-0.741689\pi$
$157$	2.82136	−	14.1839i	0.225169	−	1.13200i	0.913574	−	0.406673i	$-0.133311\pi$
$158$	−20.5911	+	2.69476i	−1.63814	+	0.214383i
$159$		−	2.52249i		−	0.200046i
$160$	12.3005	−	13.9177i	0.972437	−	1.10029i
$161$		0	0.000173108i		0	1.36428e-5i
$162$	−1.35987	−	10.3910i	−0.106841	−	0.816393i
$163$	0.390869	−	1.96503i	0.0306152	−	0.153913i	−0.962454	−	0.271445i	$-0.912498\pi$
$163$	0.390869	−	1.96503i	0.0306152	−	0.153913i	0.993069	+	0.117532i	$0.0374984\pi$
$164$	−9.10370	−	1.21278i	−0.710879	−	0.0947018i
$165$	4.42150	+	2.95435i	0.344213	+	0.229996i
$166$	−0.0260919	−	0.00173031i	−0.00202512	−	0.000134298i
$167$	−1.10126	−	2.65868i	−0.0852182	−	0.205735i	0.875526	−	0.483171i	$-0.160515\pi$
$167$	−1.10126	−	2.65868i	−0.0852182	−	0.205735i	−0.960744	+	0.277436i	$0.910515\pi$
$168$	0.00101329	−	0.00503341i	7.81769e−5	−	0.000388336i
$169$	−0.531568	+	1.28332i	−0.0408898	+	0.0987168i
$170$	5.51723	+	2.72607i	0.423152	+	0.209080i
$171$	21.1589	−	4.20876i	1.61806	−	0.321852i
$172$	9.60293	+	19.5486i	0.732216	+	1.49056i
$173$	14.0323	−	9.37606i	1.06685	−	0.712849i	0.107258	−	0.994231i	$-0.465793\pi$
$173$	14.0323	−	9.37606i	1.06685	−	0.712849i	0.959596	+	0.281382i	$0.0907929\pi$
$174$	−0.633001	+	0.364815i	−0.0479877	+	0.0276565i
$175$	−0.0174788	−	0.0174788i	−0.00132127	−	0.00132127i
$176$	−10.0251	−	11.5026i	−0.755667	−	0.867040i
$177$	1.71900	−	1.71900i	0.129208	−	0.129208i
$178$	−3.12603	+	11.6307i	−0.234306	+	0.871760i
$179$	1.71795	+	2.57110i	0.128406	+	0.192173i	0.890102	−	0.455762i	$-0.150633\pi$
$179$	1.71795	+	2.57110i	0.128406	+	0.192173i	−0.761696	+	0.647934i	$0.775633\pi$
$180$	−13.9032	−	12.2307i	−1.03628	−	0.911619i
$181$	1.87395	+	9.42097i	0.139289	+	0.700256i	0.985805	+	0.167892i	$0.0536960\pi$
$181$	1.87395	+	9.42097i	0.139289	+	0.700256i	−0.846516	+	0.532363i	$0.821304\pi$
$182$	−0.00735604	−	0.0217251i	−0.000545266	−	0.00161037i
$183$	0.868243	+	0.359638i	0.0641823	+	0.0265852i
$184$	−0.0807872	−	0.0811609i	−0.00595571	−	0.00598326i
$185$	20.6415	−	8.55000i	1.51760	−	0.628609i
$186$	−2.28379	+	1.99972i	−0.167456	+	0.146627i
$187$	2.80857	−	4.20332i	0.205383	−	0.307377i
$188$	10.4278	−	17.9975i	0.760526	−	1.31260i
$189$	−0.0103615	−	0.00206103i	−0.000753687	−	0.000149918i
$190$	21.6492	−	28.1689i	1.57060	−	2.04359i
$191$	13.3038			0.962632			0.481316	−	0.876547i	$-0.340159\pi$
$191$	13.3038			0.962632			0.481316	+	0.876547i	$0.340159\pi$
$192$	−1.87396	−	2.83279i	−0.135241	−	0.204439i
$193$	−15.7913			−1.13669			−0.568343	−	0.822792i	$-0.692415\pi$
$193$	−15.7913			−1.13669			−0.568343	+	0.822792i	$0.692415\pi$
$194$	−7.41966	+	9.65410i	−0.532700	+	0.693124i
$195$	5.18646	+	1.03165i	0.371410	+	0.0738781i
$196$	−12.1135	−	7.01863i	−0.865253	−	0.501330i
$197$	−5.35865	+	8.01978i	−0.381788	+	0.571386i	−0.971740	−	0.236052i	$-0.924146\pi$
$197$	−5.35865	+	8.01978i	−0.381788	+	0.571386i	0.589953	+	0.807438i	$0.299146\pi$
$198$	−11.4442	+	10.0207i	−0.813302	+	0.712141i
$199$	18.5879	−	7.69936i	1.31766	−	0.545793i	0.390551	−	0.920581i	$-0.372285\pi$
$199$	18.5879	−	7.69936i	1.31766	−	0.545793i	0.927110	+	0.374788i	$0.122285\pi$
$200$	−16.3520	−	0.0377340i	−1.15626	−	0.00266820i
$201$	−0.971549	−	0.402429i	−0.0685278	−	0.0283851i
$202$	0.531231	+	1.56892i	0.0373773	+	0.110389i
$203$	−0.00101498	−	0.00510263i	−7.12374e−5	−	0.000358135i
$204$	0.743281	−	0.844923i	0.0520400	−	0.0591565i
$205$	8.37689	+	12.5369i	0.585067	+	0.875615i
$206$	−1.37831	+	5.12813i	−0.0960312	+	0.357294i
$207$	−0.0807257	+	0.0807257i	−0.00561082	+	0.00561082i
$208$	−13.5877	−	6.75276i	−0.942136	−	0.468219i
$209$	−20.6365	−	20.6365i	−1.42746	−	1.42746i
$210$	−0.00730329	+	0.00420907i	−0.000503975	+	0.000290454i
$211$	−4.13413	+	2.76234i	−0.284605	+	0.190167i	−0.689676	−	0.724118i	$-0.742247\pi$
$211$	−4.13413	+	2.76234i	−0.284605	+	0.190167i	0.405071	+	0.914285i	$0.367247\pi$
$212$	10.6653	−	5.23917i	0.732497	−	0.359828i
$213$	−4.92407	+	0.979459i	−0.337392	+	0.0671114i
$214$	15.4545	+	7.63611i	1.05645	+	0.521993i
$215$	13.6836	−	33.0352i	0.933215	−	2.25298i
$216$	−5.81980	+	3.86927i	−0.395987	+	0.263271i
$217$	−0.00827212	−	0.0199707i	−0.000561548	−	0.00135570i
$218$	13.1070	+	0.869206i	0.887720	+	0.0588700i
$219$	1.85717	+	1.24092i	0.125496	+	0.0838538i
$220$	−3.30789	+	24.8307i	−0.223018	+	1.67408i
$221$	0.980744	−	4.93053i	0.0659720	−	0.331664i
$222$	−0.530155	−	4.05101i	−0.0355817	−	0.271886i
$223$		−	9.81113i		−	0.657002i	−0.944504	−	0.328501i	$-0.893457\pi$
$223$		−	9.81113i		−	0.657002i	0.944504	−	0.328501i	$-0.106543\pi$
$224$	0.0233863	−	0.00617005i	0.00156257	−	0.000412254i
$225$			16.3019i			1.08679i
$226$	2.76682	−	0.362093i	0.184046	−	0.0240861i
$227$	0.254036	−	1.27712i	0.0168609	−	0.0847657i	−0.971439	−	0.237291i	$-0.923741\pi$
$227$	0.254036	−	1.27712i	0.0168609	−	0.0847657i	0.988300	+	0.152525i	$0.0487405\pi$
$228$	−3.94693	−	5.16015i	−0.261392	−	0.341740i
$229$	10.8067	+	7.22083i	0.714129	+	0.477166i	0.858798	−	0.512314i	$-0.171212\pi$
$229$	10.8067	+	7.22083i	0.714129	+	0.477166i	−0.144669	+	0.989480i	$0.546212\pi$
$230$	−0.0124404	+	0.187592i	−0.000820294	+	0.0123695i
$231$	0.00264988	+	0.00639737i	0.000174349	+	0.000420916i
$232$	−2.85720	−	1.91867i	−0.187585	−	0.125967i
$233$	−6.27298	+	15.1443i	−0.410957	+	0.992138i	0.573925	+	0.818908i	$0.305420\pi$
$233$	−6.27298	+	15.1443i	−0.410957	+	0.992138i	−0.984881	+	0.173230i	$0.944580\pi$
$234$	−6.70075	+	13.5615i	−0.438042	+	0.886541i
$235$	−33.4925	+	6.66208i	−2.18481	+	0.434586i
$236$	10.8384	+	3.69775i	0.705521	+	0.240703i
$237$	5.18374	−	3.46367i	0.336720	−	0.224989i
$238$	0.00400137	+	0.00694291i	0.000259370	+	0.000450042i
$239$	8.29613	+	8.29613i	0.536632	+	0.536632i	0.922538	−	0.385906i	$-0.126111\pi$
$239$	8.29613	+	8.29613i	0.536632	+	0.536632i	−0.385906	+	0.922538i	$0.626111\pi$
$240$	−1.45980	+	5.38176i	−0.0942298	+	0.347391i
$241$	−5.76496	+	5.76496i	−0.371353	+	0.371353i	−0.867970	−	0.496617i	$-0.834576\pi$
$241$	−5.76496	+	5.76496i	−0.371353	+	0.371353i	0.496617	+	0.867970i	$0.334576\pi$
$242$	4.84934	+	1.30338i	0.311727	+	0.0837842i
$243$	5.86610	+	8.77924i	0.376311	+	0.563189i
$244$	0.282744	+	4.41797i	0.0181008	+	0.282832i
$245$	4.48403	+	22.5428i	0.286474	+	1.44020i
$246$	2.61155	−	0.884263i	0.166507	−	0.0563786i
$247$	−26.8127	−	11.1062i	−1.70605	−	0.706670i
$248$	−13.1984	−	5.50268i	−0.838101	−	0.349421i
$249$	0.00725277	−	0.00300420i	0.000459626	−	0.000190383i
$250$	2.39010	+	2.72962i	0.151163	+	0.172637i
$251$	−11.1940	+	16.7529i	−0.706556	+	1.05744i	0.288438	+	0.957499i	$0.406864\pi$
$251$	−11.1940	+	16.7529i	−0.706556	+	1.05744i	−0.994994	+	0.0999372i	$0.968136\pi$
$252$	−0.00620489	−	0.0233003i	−0.000390871	−	0.00146778i
$253$	0.151472	+	0.0301297i	0.00952297	+	0.00189424i
$254$	8.46873	+	6.50864i	0.531376	+	0.408389i
$255$	−1.84750			−0.115695
$256$	8.08511	−	13.8069i	0.505320	−	0.862932i
$257$	−9.06360			−0.565372			−0.282686	−	0.959213i	$-0.591225\pi$
$257$	−9.06360			−0.565372			−0.282686	+	0.959213i	$0.591225\pi$
$258$	−5.18436	−	3.98444i	−0.322764	−	0.248061i
$259$	0.0285341	+	0.00567578i	0.00177302	+	0.000352676i
$260$	6.41028	+	24.0716i	0.397549	+	1.49286i
$261$	−1.90621	+	2.85284i	−0.117991	+	0.176586i
$262$	−8.84531	−	10.1018i	−0.546465	−	0.624092i
$263$	6.45410	−	2.67338i	0.397977	−	0.164847i	−0.174713	−	0.984619i	$-0.555900\pi$
$263$	6.45410	−	2.67338i	0.397977	−	0.164847i	0.572690	+	0.819772i	$0.305900\pi$
$264$	4.22796	+	1.76272i	0.260213	+	0.108488i
$265$	−18.0234	−	7.46552i	−1.10717	−	0.458603i
$266$	0.0438182	−	0.0148367i	0.00268667	−	0.000909697i
$267$	−0.705372	−	3.54615i	−0.0431681	−	0.217021i
$268$	−0.316386	−	4.94364i	−0.0193264	−	0.301981i
$269$	−3.01896	−	4.51820i	−0.184069	−	0.275479i	0.727947	−	0.685634i	$-0.240475\pi$
$269$	−3.01896	−	4.51820i	−0.184069	−	0.275479i	−0.912016	+	0.410154i	$0.865475\pi$
$270$	11.0804	+	2.97811i	0.674330	+	0.181242i
$271$	2.26040	−	2.26040i	0.137309	−	0.137309i	−0.635111	−	0.772421i	$-0.719046\pi$
$271$	2.26040	−	2.26040i	0.137309	−	0.137309i	0.772421	+	0.635111i	$0.219046\pi$
$272$	5.11620	+	1.38777i	0.310215	+	0.0841457i
$273$	0.00486906	+	0.00486906i	0.000294689	+	0.000294689i
$274$	−10.9978	−	19.0827i	−0.664403	−	1.15283i
$275$	18.3365	−	12.2520i	1.10573	−	0.738826i
$276$	0.0325374	+	0.0111008i	0.00195852	+	0.000668190i
$277$	3.69695	−	0.735369i	0.222128	−	0.0441841i	−0.0827713	−	0.996569i	$-0.526377\pi$
$277$	3.69695	−	0.735369i	0.222128	−	0.0441841i	0.304900	+	0.952385i	$0.401377\pi$
$278$	6.93780	−	14.0412i	0.416102	−	0.842137i
$279$	−5.45541	+	13.1705i	−0.326607	+	0.788499i
$280$	−0.0329652	−	0.0221368i	−0.00197005	−	0.00132293i
$281$	9.02095	+	21.7785i	0.538145	+	1.29920i	0.926016	+	0.377483i	$0.123210\pi$
$281$	9.02095	+	21.7785i	0.538145	+	1.29920i	−0.387872	+	0.921713i	$0.626790\pi$
$282$	−0.413203	+	6.23082i	−0.0246059	+	0.371040i
$283$	−1.15851	−	0.774093i	−0.0688664	−	0.0460151i	0.520660	−	0.853764i	$-0.325686\pi$
$283$	−1.15851	−	0.774093i	−0.0688664	−	0.0460151i	−0.589527	+	0.807749i	$0.700686\pi$
$284$	−14.3685	−	18.7851i	−0.852612	−	1.11469i
$285$	−2.08078	+	10.4608i	−0.123255	+	0.619643i
$286$	20.2902	−	2.65537i	1.19978	−	0.157016i
$287$			0.0196339i			0.00115895i
$288$	−13.7831	−	8.02851i	−0.812176	−	0.473084i
$289$		−	15.2437i		−	0.896686i
$290$	0.733204	+	5.60254i	0.0430552	+	0.328992i
$291$	0.713128	−	3.58514i	0.0418043	−	0.210164i
$292$	−1.38942	+	10.4297i	−0.0813096	+	0.610351i
$293$	−22.0407	−	14.7271i	−1.28763	−	0.860367i	−0.292246	−	0.956343i	$-0.594403\pi$
$293$	−22.0407	−	14.7271i	−1.28763	−	0.860367i	−0.995384	+	0.0959763i	$0.969403\pi$
$294$	4.19376	+	0.278114i	0.244585	+	0.0162199i
$295$	−7.19484	−	17.3699i	−0.418900	−	1.01131i
$296$	16.0269	−	10.6554i	0.931545	−	0.619334i
$297$	3.60687	−	8.70775i	0.209292	−	0.505275i
$298$	11.8741	+	5.86703i	0.687850	+	0.339868i
$299$	0.150628	−	0.0299619i	0.00871107	−	0.00173274i
$300$	4.40618	−	2.16447i	0.254391	−	0.124966i
$301$	0.0387143	−	0.0258680i	0.00223145	−	0.00149101i
$302$	11.5031	−	6.62953i	0.661930	−	0.381487i
$303$	−0.351629	−	0.351629i	−0.0202005	−	0.0202005i
$304$	13.6199	−	27.4055i	0.781155	−	1.57182i
$305$	5.13927	−	5.13927i	0.294274	−	0.294274i
$306$	1.37173	−	5.10367i	0.0784167	−	0.291757i
$307$	−5.73461	−	8.58245i	−0.327292	−	0.489826i	0.630935	−	0.775835i	$-0.282671\pi$
$307$	−5.73461	−	8.58245i	−0.327292	−	0.489826i	−0.958227	+	0.286009i	$0.907671\pi$
$308$	−0.0215449	+	0.0244912i	−0.00122764	+	0.00139551i
$309$	−0.311007	−	1.56354i	−0.0176926	−	0.0889467i
$310$	7.52910	+	22.2362i	0.427624	+	1.26293i
$311$	6.73800	+	2.79097i	0.382077	+	0.158261i	0.565451	−	0.824782i	$-0.308702\pi$
$311$	6.73800	+	2.79097i	0.382077	+	0.158261i	−0.183374	+	0.983043i	$0.558702\pi$
$312$	4.55517	+	0.0105115i	0.257886	+	0.000595099i
$313$	−27.9648	+	11.5834i	−1.58067	+	0.654733i	−0.988519	−	0.151097i	$-0.951720\pi$
$313$	−27.9648	+	11.5834i	−1.58067	+	0.654733i	−0.592147	+	0.805830i	$0.701720\pi$
$314$	−15.3870	+	13.4732i	−0.868341	+	0.760334i
$315$	−0.0219930	+	0.0329148i	−0.00123916	+	0.00185454i
$316$	25.4113	+	14.7234i	1.42949	+	0.828254i
$317$	17.8912	+	3.55879i	1.00487	+	0.199881i	0.669983	−	0.742377i	$-0.266301\pi$
$317$	17.8912	+	3.55879i	1.00487	+	0.199881i	0.334888	+	0.942258i	$0.391301\pi$
$318$	−2.17383	+	2.82849i	−0.121903	+	0.158614i
$319$	4.64155			0.259877
$320$	−25.7866	+	5.00567i	−1.44151	+	0.279825i
$321$	−5.17511			−0.288846
$322$	−0.000149181	0	0.000194107i	−8.31353e−6	0	1.08172e-5i
$323$	9.94459	+	1.97810i	0.553332	+	0.110065i
$324$	−7.42992	+	12.8234i	−0.412774	+	0.712411i
$325$	12.1838	−	18.2343i	0.675836	−	1.01146i
$326$	−2.13171	+	1.86656i	−0.118065	+	0.103379i
$327$	−3.64336	+	1.50913i	−0.201478	+	0.0834551i
$328$	9.16290	+	9.20529i	0.505937	+	0.508277i
$329$	−0.0410821	−	0.0170168i	−0.00226493	−	0.000938164i
$330$	−2.41186	−	7.12310i	−0.132768	−	0.392114i
$331$	2.03401	+	10.2257i	0.111799	+	0.562054i	0.995561	+	0.0941165i	$0.0300026\pi$
$331$	2.03401	+	10.2257i	0.111799	+	0.562054i	−0.883762	+	0.467937i	$0.844997\pi$
$332$	0.0277659	+	0.0244257i	0.00152385	+	0.00134054i
$333$	−10.6596	−	15.9531i	−0.584140	−	0.874227i
$334$	−1.05635	+	3.93025i	−0.0578008	+	0.215054i
$335$	−5.75076	+	5.75076i	−0.314198	+	0.314198i
$336$	−0.00547391	+	0.00477078i	−0.000298626	+	0.000260267i
$337$	20.0673	+	20.0673i	1.09313	+	1.09313i	0.995192	+	0.0979408i	$0.0312256\pi$
$337$	20.0673	+	20.0673i	1.09313	+	1.09313i	0.0979408	+	0.995192i	$0.468774\pi$
$338$	1.70199	−	0.980900i	0.0925761	−	0.0533539i
$339$	−0.696537	+	0.465411i	−0.0378307	+	0.0252777i
$340$	−3.83723	−	7.81141i	−0.208103	−	0.423633i
$341$	18.9145	−	3.76232i	1.02428	−	0.203741i
$342$	−27.3527	−	13.5150i	−1.47906	−	0.730808i
$343$	−0.0229069	+	0.0553022i	−0.00123686	+	0.00298604i
$344$	6.07875	−	30.1956i	0.327744	−	1.62804i
$345$	−0.0215992	−	0.0521451i	−0.00116286	−	0.00280740i
$346$	−23.8146	−	1.57929i	−1.28028	−	0.0849032i
$347$	19.0808	+	12.7494i	1.02431	+	0.684424i	0.949820	−	0.312798i	$-0.101266\pi$
$347$	19.0808	+	12.7494i	1.02431	+	0.684424i	0.0744929	+	0.997222i	$0.476266\pi$
$348$	1.02418	+	0.136439i	0.0549018	+	0.00731390i
$349$	−3.50743	+	17.6330i	−0.187748	+	0.943875i	0.765902	+	0.642957i	$0.222293\pi$
$349$	−3.50743	+	17.6330i	−0.187748	+	0.943875i	−0.953650	+	0.300917i	$0.902707\pi$
$350$	0.00453622	+	0.0346621i	0.000242471	+	0.00185276i
$351$		−	9.37271i		−	0.500278i
$352$	1.32846	+	21.5374i	0.0708074	+	1.14794i
$353$		−	13.7997i		−	0.734483i	−0.930126	−	0.367242i	$-0.880302\pi$
$353$		−	13.7997i		−	0.734483i	0.930126	−	0.367242i	$-0.119698\pi$
$354$	−3.40893	+	0.446126i	−0.181182	+	0.0237114i
$355$	−7.57491	+	38.0816i	−0.402034	+	2.02116i
$356$	13.5284	−	10.3477i	0.717003	−	0.548426i
$357$	−0.00200030	−	0.00133656i	−0.000105867	−	7.07380e-5i
$358$	0.289369	−	4.36349i	0.0152936	−	0.230618i
$359$	1.37873	+	3.32855i	0.0727666	+	0.175674i	0.956078	−	0.293113i	$-0.0946912\pi$
$359$	1.37873	+	3.32855i	0.0727666	+	0.175674i	−0.883311	+	0.468787i	$0.844691\pi$
$360$	5.04961	+	25.6958i	0.266138	+	1.35429i
$361$	15.1295	−	36.5259i	0.796291	−	1.92242i
$362$	6.01755	−	12.1788i	0.316275	−	0.640101i
$363$	−1.47854	+	0.294100i	−0.0776031	+	0.0154362i
$364$	−0.0104739	+	0.0306998i	−0.000548981	+	0.00160911i
$365$	14.3629	−	9.59701i	0.751790	−	0.502330i
$366$	−0.663639	−	1.15150i	−0.0346889	−	0.0601899i
$367$	10.8713	+	10.8713i	0.567480	+	0.567480i	0.931422	−	0.363942i	$-0.118569\pi$
$367$	10.8713	+	10.8713i	0.567480	+	0.567480i	−0.363942	+	0.931422i	$0.618569\pi$
$368$	0.0206444	+	0.160627i	0.00107616	+	0.00837328i
$369$	9.15593	−	9.15593i	0.476639	−	0.476639i
$370$	−30.5138	−	8.20130i	−1.58633	−	0.426365i
$371$	−0.0141131	−	0.0211218i	−0.000732716	−	0.00109659i
$372$	4.28416	−	0.274180i	0.222123	−	0.0142156i
$373$	−1.96225	−	9.86488i	−0.101601	−	0.510784i	−0.997751	−	0.0670320i	$-0.978647\pi$
$373$	−1.96225	−	9.86488i	−0.101601	−	0.510784i	0.896150	−	0.443752i	$-0.146353\pi$
$374$	−6.77161	+	2.29284i	−0.350152	+	0.118560i
$375$	−1.00631	−	0.416826i	−0.0519654	−	0.0215248i
$376$	−27.2027	+	11.1943i	−1.40287	+	0.577299i
$377$	4.26435	−	1.76635i	0.219625	−	0.0909717i
$378$	0.00984227	+	0.0112404i	0.000506232	+	0.000578143i
$379$	−6.87637	+	10.2912i	−0.353216	+	0.528625i	−0.964948	−	0.262440i	$-0.915473\pi$
$379$	−6.87637	+	10.2912i	−0.353216	+	0.528625i	0.611733	+	0.791065i	$0.290473\pi$
$380$	−48.5509	+	12.9292i	−2.49061	+	0.663252i
$381$	−3.14494	−	0.625567i	−0.161120	−	0.0320488i
$382$	−14.9177	−	11.4650i	−0.763256	−	0.586601i
$383$	−10.8753			−0.555703			−0.277851	−	0.960624i	$-0.589622\pi$
$383$	−10.8753			−0.555703			−0.277851	+	0.960624i	$0.589622\pi$
$384$	−0.339962	+	4.79137i	−0.0173486	+	0.244508i
$385$	0.0535522			0.00272927
$386$	17.7070	+	13.6087i	0.901261	+	0.692664i
$387$	−30.1168	−	5.99061i	−1.53092	−	0.304520i
$388$	16.6394	−	4.43110i	0.844740	−	0.224955i
$389$	−18.7089	+	27.9998i	−0.948579	+	1.41965i	−0.0412864	+	0.999147i	$0.513146\pi$
$389$	−18.7089	+	27.9998i	−0.948579	+	1.41965i	−0.907292	+	0.420501i	$0.861854\pi$
$390$	−4.92657	−	5.62640i	−0.249466	−	0.284904i
$391$	−0.0495720	+	0.0205334i	−0.00250696	+	0.00103842i
$392$	7.53450	+	18.3093i	0.380549	+	0.924758i
$393$	3.72414	+	1.54259i	0.187858	+	0.0778134i
$394$	12.9200	−	4.37467i	0.650900	−	0.220393i
$395$	−9.40641	−	47.2892i	−0.473288	−	2.37938i
$396$	21.4681	−	1.37393i	1.07881	−	0.0690426i
$397$	3.23990	+	4.84885i	0.162606	+	0.243357i	0.903821	−	0.427911i	$-0.140750\pi$
$397$	3.23990	+	4.84885i	0.162606	+	0.243357i	−0.741215	+	0.671267i	$0.765750\pi$
$398$	−27.4779	−	7.38535i	−1.37734	−	0.370194i
$399$	−0.00982061	+	0.00982061i	−0.000491646	+	0.000491646i
$400$	18.3031	+	14.1342i	0.915157	+	0.706709i
$401$	10.7103	+	10.7103i	0.534846	+	0.534846i	0.922011	−	0.387164i	$-0.126545\pi$
$401$	10.7103	+	10.7103i	0.534846	+	0.534846i	−0.387164	+	0.922011i	$0.626545\pi$
$402$	0.742601	+	1.28851i	0.0370376	+	0.0642650i
$403$	15.9456	−	10.6545i	0.794306	−	0.530739i
$404$	0.756392	−	2.21705i	0.0376319	−	0.110302i
$405$	23.8638	−	4.74680i	1.18580	−	0.235870i
$406$	−0.00325925	+	0.00659632i	−0.000161754	+	0.000327370i
$407$	−9.93281	+	23.9799i	−0.492351	+	1.18864i
$408$	−1.56159	+	0.306874i	−0.0773100	+	0.0151925i
$409$	−6.86070	−	16.5632i	−0.339240	−	0.818998i	−0.997789	−	0.0664600i	$-0.978830\pi$
$409$	−6.86070	−	16.5632i	−0.339240	−	0.818998i	0.658549	−	0.752538i	$-0.271170\pi$
$410$	1.41099	−	21.2768i	0.0696839	−	1.05079i
$411$	5.49784	+	3.67354i	0.271189	+	0.181202i
$412$	5.96484	−	4.56242i	0.293866	−	0.224774i
$413$	0.00477618	−	0.0240115i	0.000235020	−	0.00118153i
$414$	0.160086	−	0.0209505i	0.00786781	−	0.00102966i
$415$		−	0.0607127i		−	0.00298027i
$416$	9.41658	+	19.2815i	0.461686	+	0.945355i
$417$			4.70185i			0.230251i
$418$	5.35573	+	40.9240i	0.261957	+	2.00166i
$419$	−1.60909	+	8.08943i	−0.0786091	+	0.395194i	0.921370	+	0.388687i	$0.127071\pi$
$419$	−1.60909	+	8.08943i	−0.0786091	+	0.395194i	−0.999979	+	0.00650723i	$0.997929\pi$
$420$	0.0118165	+	0.00157418i	0.000576588	+	7.68119e-5i
$421$	−7.34247	−	4.90608i	−0.357850	−	0.239108i	0.363629	−	0.931544i	$-0.381537\pi$
$421$	−7.34247	−	4.90608i	−0.357850	−	0.239108i	−0.721479	+	0.692436i	$0.756537\pi$
$422$	7.01616	+	0.465284i	0.341541	+	0.0226497i
$423$	11.2224	+	27.0934i	0.545654	+	1.31732i
$424$	−16.4741	−	3.31645i	−0.800055	−	0.161061i
$425$	−2.93205	+	7.07859i	−0.142225	+	0.343362i
$426$	6.36549	+	3.14520i	0.308409	+	0.152385i
$427$	0.00928226	−	0.00184636i	0.000449200	−	8.93515e-5i
$428$	−10.7486	−	21.8808i	−0.519554	−	1.05765i
$429$	−5.10798	+	3.41304i	−0.246616	+	0.164783i
$430$	−43.8127	+	25.2503i	−2.11283	+	1.21768i
$431$	−1.32586	−	1.32586i	−0.0638644	−	0.0638644i	0.674453	−	0.738318i	$-0.264379\pi$
$431$	−1.32586	−	1.32586i	−0.0638644	−	0.0638644i	−0.738318	+	0.674453i	$0.764379\pi$
$432$	9.86026	+	0.676750i	0.474402	+	0.0325602i
$433$	10.5008	−	10.5008i	0.504637	−	0.504637i	−0.408238	−	0.912875i	$-0.633857\pi$
$433$	10.5008	−	10.5008i	0.504637	−	0.504637i	0.912875	+	0.408238i	$0.133857\pi$
$434$	−0.00793475	+	0.0295221i	−0.000380880	+	0.00141710i
$435$	−0.942413	−	1.41042i	−0.0451852	−	0.0676245i
$436$	−13.9480	−	12.2700i	−0.667986	−	0.587628i
$437$	0.0604313	+	0.303809i	0.00289082	+	0.0145331i
$438$	−1.01306	−	2.99193i	−0.0484058	−	0.142960i
$439$	24.5596	+	10.1729i	1.17216	+	0.485526i	0.881907	−	0.471423i	$-0.156259\pi$
$439$	24.5596	+	10.1729i	1.17216	+	0.485526i	0.290256	+	0.956949i	$0.406259\pi$
$440$	25.1078	−	24.9921i	1.19697	−	1.19145i
$441$	18.2357	−	7.55347i	0.868366	−	0.359689i
$442$	−5.34876	+	4.68346i	−0.254414	+	0.222770i
$443$	11.9115	−	17.8268i	0.565931	−	0.846976i	−0.432576	−	0.901598i	$-0.642395\pi$
$443$	11.9115	−	17.8268i	0.565931	−	0.846976i	0.998507	+	0.0546213i	$0.0173952\pi$
$444$	−2.89661	+	4.99930i	−0.137467	+	0.237257i
$445$	−27.4251	−	5.45519i	−1.30007	−	0.258601i
$446$	−8.45505	+	11.0013i	−0.400358	+	0.520927i
$447$	−3.97618			−0.188067
$448$	−0.0315405	−	0.0132354i	−0.00149015	−	0.000625313i
$449$	−20.1252			−0.949765			−0.474883	−	0.880049i	$-0.657509\pi$
$449$	−20.1252			−0.949765			−0.474883	+	0.880049i	$0.657509\pi$
$450$	14.0486	−	18.2794i	0.662259	−	0.861700i
$451$	−17.1800	−	3.41732i	−0.808975	−	0.160915i
$452$	−3.41450	−	1.97837i	−0.160605	−	0.0930548i
$453$	−2.21442	+	3.31412i	−0.104043	+	0.155711i
$454$	−1.38545	+	1.21313i	−0.0650226	+	0.0569349i
$455$	0.0492002	−	0.0203794i	0.00230654	−	0.000955401i
$456$	−0.0212012	+	9.18752i	−0.000992835	+	0.430245i
$457$	7.55757	+	3.13045i	0.353528	+	0.146436i	0.552378	−	0.833594i	$-0.313721\pi$
$457$	7.55757	+	3.13045i	0.353528	+	0.146436i	−0.198850	+	0.980030i	$0.563721\pi$
$458$	−5.89491	−	17.4098i	−0.275451	−	0.813508i
$459$	0.638835	+	3.21164i	0.0298182	+	0.149906i
$460$	0.175613	−	0.199628i	0.00818801	−	0.00930771i
$461$	−18.0840	−	27.0647i	−0.842257	−	1.26053i	−0.963447	−	0.267898i	$-0.913671\pi$
$461$	−18.0840	−	27.0647i	−0.842257	−	1.26053i	0.121190	−	0.992629i	$-0.461329\pi$
$462$	0.00254181	−	0.00945704i	0.000118255	−	0.000439981i
$463$	−12.5434	+	12.5434i	−0.582942	+	0.582942i	−0.935710	−	0.352769i	$-0.885240\pi$
$463$	−12.5434	+	12.5434i	−0.582942	+	0.582942i	0.352769	+	0.935710i	$0.385240\pi$
$464$	1.55033	+	4.61371i	0.0719722	+	0.214186i
$465$	−4.98361	−	4.98361i	−0.231109	−	0.231109i
$466$	20.0850	−	11.5755i	0.930422	−	0.536226i
$467$	10.4313	−	6.96995i	0.482702	−	0.322531i	−0.290299	−	0.956936i	$-0.593755\pi$
$467$	10.4313	−	6.96995i	0.482702	−	0.322531i	0.773001	+	0.634405i	$0.218755\pi$
$468$	19.2006	−	9.43201i	0.887549	−	0.435995i
$469$	−0.0103867	+	0.00206604i	−0.000479613	+	9.54010e-5i
$470$	43.2967	+	21.3930i	1.99713	+	0.986785i
$471$	2.34967	−	5.67261i	0.108267	−	0.261380i
$472$	−8.96656	−	13.4867i	−0.412719	−	0.620774i
$473$	15.8967	+	38.3780i	0.730931	+	1.76462i
$474$	−8.79750	−	0.583415i	−0.404082	−	0.0267971i
$475$	36.7776	+	24.5740i	1.68747	+	1.12753i
$476$	0.00149650	−	0.0112335i	6.85918e−5	−	0.000514884i
$477$	−3.26836	+	16.4311i	−0.149648	+	0.752331i
$478$	−2.15307	−	16.4520i	−0.0984792	−	0.752496i
$479$		−	26.9317i		−	1.23054i	−0.788316	−	0.615270i	$-0.789047\pi$
$479$		−	26.9317i		−	1.23054i	0.788316	−	0.615270i	$-0.210953\pi$
$480$	6.27479	−	4.77659i	0.286404	−	0.218020i
$481$			25.8111i			1.17688i
$482$	11.4324	−	1.49616i	0.520733	−	0.0681483i
$483$	1.43383e−5	0	7.20834e-5i	6.52414e−7	0	3.27991e-6i
$484$	−4.31438	−	5.64056i	−0.196108	−	0.256389i
$485$	−23.5055	−	15.7059i	−1.06733	−	0.713166i
$486$	0.988078	−	14.8995i	0.0448201	−	0.675857i
$487$	7.03105	+	16.9745i	0.318607	+	0.769186i	0.999328	+	0.0366435i	$0.0116666\pi$
$487$	7.03105	+	16.9745i	0.318607	+	0.769186i	−0.680721	+	0.732543i	$0.738333\pi$
$488$	3.49028	−	5.19757i	0.157998	−	0.235283i
$489$	0.325522	−	0.785879i	0.0147206	−	0.0355387i
$490$	14.3989	−	29.1416i	0.650478	−	1.31649i
$491$	20.1722	−	4.01251i	0.910360	−	0.181082i	0.282372	−	0.959305i	$-0.408879\pi$
$491$	20.1722	−	4.01251i	0.910360	−	0.181082i	0.627988	+	0.778223i	$0.283879\pi$
$492$	−3.69040	−	1.25906i	−0.166376	−	0.0567626i
$493$	−1.34082	+	0.895909i	−0.0603876	+	0.0403497i
$494$	20.4942	+	35.5602i	0.922078	+	1.59993i
$495$	−24.9731	−	24.9731i	−1.12246	−	1.12246i
$496$	10.0574	+	17.5444i	0.451590	+	0.787765i
$497$	−0.0357511	+	0.0357511i	−0.00160366	+	0.00160366i
$498$	−0.0107216	−	0.00288167i	−0.000480444	−	0.000129131i
$499$	−18.9433	−	28.3507i	−0.848019	−	1.26915i	−0.961277	−	0.275584i	$-0.911129\pi$
$499$	−18.9433	−	28.3507i	−0.848019	−	1.26915i	0.113258	−	0.993566i	$-0.463871\pi$
$500$	−0.327705	−	5.12050i	−0.0146554	−	0.228996i
$501$	−0.238359	−	1.19831i	−0.0106491	−	0.0535366i
$502$	26.9892	−	9.13847i	1.20459	−	0.407870i
$503$	−35.9878	−	14.9066i	−1.60462	−	0.664654i	−0.612557	−	0.790427i	$-0.709859\pi$
$503$	−35.9878	−	14.9066i	−1.60462	−	0.664654i	−0.992059	+	0.125773i	$0.959859\pi$
$504$	−0.0131222	+	0.0314741i	−0.000584507	+	0.00140197i
$505$	−3.55309	+	1.47174i	−0.158110	+	0.0654914i
$506$	−0.143882	−	0.164321i	−0.00639633	−	0.00730494i
$507$	−0.327645	+	0.490355i	−0.0145512	+	0.0217774i
$508$	−3.88703	−	14.5964i	−0.172459	−	0.647610i
$509$	−0.774360	−	0.154030i	−0.0343229	−	0.00682725i	0.177899	−	0.984049i	$-0.443070\pi$
$509$	−0.774360	−	0.154030i	−0.0343229	−	0.00682725i	−0.212222	+	0.977222i	$0.568070\pi$
$510$	2.07162	+	1.59214i	0.0917329	+	0.0705013i
$511$	0.0224937			0.000995061
$512$	−20.9645	+	8.51421i	−0.926507	+	0.376278i
$513$	18.9042			0.834640
$514$	10.1631	+	7.81084i	0.448275	+	0.344521i
$515$	−12.0921	−	2.40526i	−0.532840	−	0.105988i
$516$	2.37955	+	8.93558i	0.104754	+	0.393367i
$517$	22.0404	−	32.9857i	0.969334	−	1.45071i
$518$	−0.0271042	−	0.0309544i	−0.00119089	−	0.00136006i
$519$	6.61976	−	2.74199i	0.290575	−	0.120360i
$520$	13.5565	−	32.5159i	0.594493	−	1.42592i
$521$	−33.2921	−	13.7900i	−1.45855	−	0.604152i	−0.494336	−	0.869271i	$-0.664589\pi$
$521$	−33.2921	−	13.7900i	−1.45855	−	0.604152i	−0.964216	+	0.265119i	$0.914589\pi$
$522$	4.59597	−	1.55618i	0.201160	−	0.0681121i
$523$	−7.25392	−	36.4679i	−0.317192	−	1.59463i	−0.729759	−	0.683704i	$-0.760368\pi$
$523$	−7.25392	−	36.4679i	−0.317192	−	1.59463i	0.412567	−	0.910927i	$-0.364632\pi$
$524$	1.21277	+	18.9500i	0.0529802	+	0.827833i
$525$	−0.00583057	−	0.00872606i	−0.000254467	−	0.000380837i
$526$	−9.54090	−	2.56434i	−0.416003	−	0.111811i
$527$	−4.73769	+	4.73769i	−0.206377	+	0.206377i
$528$	−3.22177	−	5.62013i	−0.140209	−	0.244585i
$529$	16.2623	+	16.2623i	0.707056	+	0.707056i
$530$	13.7761	+	23.9034i	0.598396	+	1.03830i
$531$	−13.4246	+	8.97003i	−0.582578	+	0.389266i
$532$	−0.0619197	−	0.0211252i	−0.00268456	−	0.000915894i
$533$	−17.0843	+	3.39828i	−0.740004	+	0.147196i
$534$	−2.26506	+	4.58420i	−0.0980189	+	0.198378i
$535$	−15.3162	+	36.9765i	−0.662176	+	1.59863i
$536$	−3.90557	+	5.81600i	−0.168695	+	0.251213i
$537$	0.502408	+	1.21292i	0.0216805	+	0.0523414i
$538$	−0.508510	+	7.66798i	−0.0219234	+	0.330590i
$539$	−22.2016	−	14.8347i	−0.956293	−	0.638974i
$540$	−9.85803	−	12.8882i	−0.424222	−	0.554621i
$541$	−5.78826	+	29.0995i	−0.248857	+	1.25109i	0.630976	+	0.775803i	$0.282655\pi$
$541$	−5.78826	+	29.0995i	−0.248857	+	1.25109i	−0.879832	+	0.475284i	$0.842345\pi$
$542$	−4.48257	+	0.586634i	−0.192543	+	0.0251981i
$543$			4.07818i			0.175012i
$544$	−4.54088	−	5.96516i	−0.194689	−	0.255754i
$545$			30.4985i			1.30641i
$546$	−0.00126365	−	0.00965579i	−5.40794e−5	−	0.000413230i
$547$	0.451950	−	2.27210i	0.0193240	−	0.0971482i	−0.969920	−	0.243425i	$-0.921729\pi$
$547$	0.451950	−	2.27210i	0.0193240	−	0.0971482i	0.989244	+	0.146277i	$0.0467290\pi$
$548$	−4.11314	+	30.8753i	−0.175705	+	1.31893i
$549$	−5.18963	−	3.46760i	−0.221488	−	0.147994i
$550$	−31.1194	−	2.06372i	−1.32694	−	0.0879972i
$551$	3.56262	+	8.60094i	0.151773	+	0.366412i
$552$	−0.0269180	−	0.0404875i	−0.00114571	−	0.00172326i
$553$	0.0240265	−	0.0580052i	0.00102171	−	0.00246663i
$554$	−4.77915	−	2.36139i	−0.203047	−	0.100326i
$555$	9.30348	−	1.85058i	0.394911	−	0.0785526i
$556$	−19.8799	+	9.76568i	−0.843095	+	0.414157i
$557$	−23.1321	+	15.4564i	−0.980138	+	0.654907i	−0.938881	−	0.344241i	$-0.888136\pi$
$557$	−23.1321	+	15.4564i	−0.980138	+	0.654907i	−0.0412566	+	0.999149i	$0.513136\pi$
$558$	17.4673	−	10.0669i	0.739450	−	0.426164i
$559$	29.2097	+	29.2097i	1.23544	+	1.23544i
$560$	0.0178870	+	0.0532310i	0.000755865	+	0.00224942i
$561$	1.51766	−	1.51766i	0.0640758	−	0.0640758i
$562$	8.65304	−	32.1945i	0.365006	−	1.35804i
$563$	17.2728	+	25.8506i	0.727962	+	1.08947i	0.992156	+	0.125003i	$0.0398941\pi$
$563$	17.2728	+	25.8506i	0.727962	+	1.08947i	−0.264194	+	0.964470i	$0.585106\pi$
$564$	5.83293	−	6.63058i	0.245611	−	0.279198i
$565$	1.26393	+	6.35423i	0.0531741	+	0.267324i
$566$	0.631950	+	1.86638i	0.0265629	+	0.0784499i
$567$	0.0292714	+	0.0121246i	0.00122928	+	0.000509186i
$568$	−0.0771811	+	33.4464i	−0.00323845	+	1.40338i
$569$	−12.4056	+	5.13855i	−0.520068	+	0.215419i	−0.627247	−	0.778821i	$-0.715818\pi$
$569$	−12.4056	+	5.13855i	−0.520068	+	0.215419i	0.107179	+	0.994240i	$0.465818\pi$
$570$	11.3481	−	9.93659i	0.475320	−	0.416198i
$571$	23.8379	−	35.6759i	0.997583	−	1.49299i	0.132612	−	0.991168i	$-0.457664\pi$
$571$	23.8379	−	35.6759i	0.997583	−	1.49299i	0.864971	−	0.501821i	$-0.167336\pi$
$572$	−25.0399	−	14.5082i	−1.04697	−	0.606618i
$573$	5.53982	+	1.10194i	0.231429	+	0.0460342i
$574$	0.0169201	−	0.0220157i	0.000706233	−	0.000918917i
$575$	−0.234069			−0.00976137
$576$	8.53628	+	20.8804i	0.355678	+	0.870019i
$577$	37.4884			1.56066			0.780331	−	0.625367i	$-0.215051\pi$
$577$	37.4884			1.56066			0.780331	+	0.625367i	$0.215051\pi$
$578$	−13.1367	+	17.0929i	−0.546415	+	0.710969i
$579$	−6.57564	−	1.30798i	−0.273274	−	0.0543576i
$580$	4.00601	−	6.91403i	0.166341	−	0.287090i
$581$	4.39220e−5	0	6.57339e-5i	1.82219e−6	0	2.72710e-6i
$582$	−3.88924	+	3.40548i	−0.161214	+	0.141162i
$583$	20.9383	−	8.67293i	0.867176	−	0.359196i
$584$	10.5461	−	10.4975i	0.436399	−	0.434390i
$585$	−32.4472	−	13.4401i	−1.34153	−	0.555679i
$586$	12.0228	+	35.5079i	0.496659	+	1.46682i
$587$	7.98597	+	40.1482i	0.329616	+	1.65709i	0.689642	+	0.724150i	$0.257768\pi$
$587$	7.98597	+	40.1482i	0.329616	+	1.65709i	−0.360026	+	0.932942i	$0.617232\pi$
$588$	−4.46283	−	3.92596i	−0.184044	−	0.161904i
$589$	21.4895	+	32.1613i	0.885459	+	1.32518i
$590$	−6.90140	+	25.6774i	−0.284126	+	1.05712i
$591$	−2.89565	+	2.89565i	−0.119111	+	0.119111i
$592$	−27.1538	−	1.86367i	−1.11601	−	0.0765965i
$593$	8.81442	+	8.81442i	0.361965	+	0.361965i	0.864536	−	0.502571i	$-0.167612\pi$
$593$	8.81442	+	8.81442i	0.361965	+	0.361965i	−0.502571	+	0.864536i	$0.667612\pi$
$594$	−11.5486	+	6.65575i	−0.473845	+	0.273089i
$595$	−0.0154698	+	0.0103366i	−0.000634201	+	0.000423760i
$596$	−8.25846	−	16.8117i	−0.338280	−	0.688632i
$597$	8.37787	−	1.66646i	0.342884	−	0.0682038i
$598$	−0.194722	−	0.0962123i	−0.00796276	−	0.00393441i
$599$	11.2451	−	27.1482i	0.459464	−	1.10924i	−0.509150	−	0.860678i	$-0.670040\pi$
$599$	11.2451	−	27.1482i	0.459464	−	1.10924i	0.968615	−	0.248567i	$-0.0799597\pi$
$600$	−6.80599	−	1.37013i	−0.277853	−	0.0559353i
$601$	−7.36797	−	17.7879i	−0.300546	−	0.725582i	−0.999941	−	0.0108469i	$-0.996547\pi$
$601$	−7.36797	−	17.7879i	−0.300546	−	0.725582i	0.699395	−	0.714735i	$-0.253453\pi$
$602$	−0.0657032	−	0.00435718i	−0.00267786	−	0.000177585i
$603$	5.80712	+	3.88019i	0.236484	+	0.158014i
$604$	−18.6117	−	2.47942i	−0.757301	−	0.100886i
$605$	−2.27450	+	11.4347i	−0.0924715	+	0.464886i
$606$	0.0912572	+	0.697312i	0.00370707	+	0.0283263i
$607$		−	43.8540i		−	1.77998i	−0.455983	−	0.889989i	$-0.650712\pi$
$607$		−	43.8540i		−	1.77998i	0.455983	−	0.889989i	$-0.349288\pi$
$608$	−38.8897	+	18.9927i	−1.57719	+	0.770255i
$609$		−	0.00220885i		−	8.95070e-5i
$610$	−10.1916	+	1.33378i	−0.412648	+	0.0540032i
$611$	7.69644	−	38.6926i	0.311364	−	1.56533i
$612$	−5.93638	+	4.54065i	−0.239964	+	0.183545i
$613$	−5.12461	−	3.42415i	−0.206981	−	0.138300i	0.447759	−	0.894154i	$-0.352222\pi$
$613$	−5.12461	−	3.42415i	−0.206981	−	0.138300i	−0.654740	+	0.755854i	$0.727222\pi$
$614$	−0.965930	+	14.5656i	−0.0389817	+	0.587818i
$615$	2.44979	+	5.91431i	0.0987850	+	0.238488i
$616$	0.0452646	−	0.00889514i	0.00182376	−	0.000358396i
$617$	1.79100	−	4.32387i	0.0721031	−	0.174072i	−0.883719	−	0.468018i	$-0.844968\pi$
$617$	1.79100	−	4.32387i	0.0721031	−	0.174072i	0.955822	+	0.293945i	$0.0949684\pi$
$618$	−0.998694	+	2.02123i	−0.0401734	+	0.0813058i
$619$	−11.2620	+	2.24014i	−0.452656	+	0.0900389i	−0.416153	−	0.909295i	$-0.636622\pi$
$619$	−11.2620	+	2.24014i	−0.452656	+	0.0900389i	−0.0365033	+	0.999334i	$0.511622\pi$
$620$	10.7203	−	31.4221i	0.430537	−	1.26194i
$621$	−0.0831787	+	0.0555782i	−0.00333785	+	0.00223028i
$622$	−5.15017	−	8.93622i	−0.206503	−	0.358310i
$623$	−0.0257467	−	0.0257467i	−0.00103152	−	0.00103152i
$624$	−5.09870	−	3.93735i	−0.204111	−	0.157620i
$625$	14.4836	−	14.4836i	0.579343	−	0.579343i
$626$	41.3396	+	11.1110i	1.65226	+	0.444085i
$627$	−6.88391	−	10.3025i	−0.274917	−	0.411442i
$628$	28.8645	−	1.84729i	1.15182	−	0.0737149i
$629$	−1.75926	−	8.84440i	−0.0701463	−	0.352649i
$630$	0.0530263	−	0.0179545i	0.00211262	−	0.000715325i
$631$	−37.1958	−	15.4070i	−1.48074	−	0.613344i	−0.511463	−	0.859305i	$-0.670896\pi$
$631$	−37.1958	−	15.4070i	−1.48074	−	0.613344i	−0.969280	+	0.245961i	$0.920896\pi$
$632$	−15.8055	−	38.4084i	−0.628710	−	1.52780i
$633$	−1.95028	+	0.807834i	−0.0775168	+	0.0321085i
$634$	−16.9947	−	19.4088i	−0.674945	−	0.770823i
$635$	−13.7774	+	20.6194i	−0.546741	+	0.818256i
$636$	4.87508	−	1.29824i	0.193309	−	0.0514785i
$637$	−26.0428	−	5.18023i	−1.03185	−	0.205248i
$638$	−5.20461	−	4.00000i	−0.206052	−	0.158362i
$639$	33.3438			1.31906
$640$	33.2285	+	16.6095i	1.31347	+	0.656549i
$641$	−38.2377			−1.51030			−0.755150	−	0.655552i	$-0.772436\pi$
$641$	−38.2377			−1.51030			−0.755150	+	0.655552i	$0.772436\pi$
$642$	5.80289	+	4.45981i	0.229022	+	0.176015i
$643$	31.9223	+	6.34974i	1.25889	+	0.250409i	0.779059	−	0.626951i	$-0.215697\pi$
$643$	31.9223	+	6.34974i	1.25889	+	0.250409i	0.479833	+	0.877360i	$0.340697\pi$
$644$	0.000334556	0	8.90925e-5i	1.31833e−5	0	3.51074e-6i
$645$	8.43423	−	12.6227i	0.332098	−	0.497019i
$646$	−9.44626	−	10.7881i	−0.371658	−	0.424453i
$647$	33.6773	−	13.9496i	1.32399	−	0.548416i	0.395057	−	0.918657i	$-0.370725\pi$
$647$	33.6773	−	13.9496i	1.32399	−	0.548416i	0.928936	+	0.370241i	$0.120725\pi$
$648$	19.3822	−	7.97602i	0.761405	−	0.313328i
$649$	20.1791	+	8.35847i	0.792100	+	0.328099i
$650$	−29.3758	+	9.94655i	−1.15221	+	0.390136i
$651$	−0.00179043	−	0.00900112i	−7.01726e−5	−	0.000352782i
$652$	3.99888	−	0.255922i	0.156608	−	0.0100227i
$653$	11.3012	+	16.9135i	0.442252	+	0.661876i	0.983898	−	0.178730i	$-0.0571989\pi$
$653$	11.3012	+	16.9135i	0.442252	+	0.661876i	−0.541647	+	0.840606i	$0.682199\pi$
$654$	5.38587	+	1.44758i	0.210604	+	0.0566049i
$655$	22.0438	−	22.0438i	0.861324	−	0.861324i
$656$	−2.34149	−	18.2184i	−0.0914200	−	0.711309i
$657$	−10.4895	−	10.4895i	−0.409235	−	0.409235i
$658$	0.0314010	+	0.0544848i	0.00122414	+	0.00212404i
$659$	−17.0076	+	11.3641i	−0.662522	+	0.442683i	−0.840835	−	0.541291i	$-0.817936\pi$
$659$	−17.0076	+	11.3641i	−0.662522	+	0.442683i	0.178314	+	0.983974i	$0.442936\pi$
$660$	−3.43412	+	10.0657i	−0.133673	+	0.391807i
$661$	19.3511	−	3.84916i	0.752669	−	0.149715i	0.196177	−	0.980568i	$-0.437147\pi$
$661$	19.3511	−	3.84916i	0.752669	−	0.149715i	0.556491	+	0.830853i	$0.312147\pi$
$662$	6.53154	−	13.2190i	0.253855	−	0.513771i
$663$	0.816779	−	1.97188i	0.0317211	−	0.0765814i
$664$	−0.0100845	−	0.0513169i	−0.000391355	−	0.00199148i
$665$	0.0411040	+	0.0992339i	0.00159395	+	0.00384812i
$666$	−1.79548	+	27.0746i	−0.0695734	+	1.04912i
$667$	−0.0409623	−	0.0273701i	−0.00158607	−	0.00105978i
$668$	4.57151	−	3.49668i	0.176877	−	0.135291i
$669$	0.812643	−	4.08543i	0.0314186	−	0.157952i
$670$	11.4043	−	1.49248i	0.440586	−	0.0576595i
$671$			8.44350i			0.325958i
$672$	0.0102493		0.000632197i	0.000395376		2.43875e-5i
$673$		−	18.1114i		−	0.698141i	−0.937096	−	0.349071i	$-0.886497\pi$
$673$		−	18.1114i		−	0.698141i	0.937096	−	0.349071i	$-0.113503\pi$
$674$	−5.20800	−	39.7952i	−0.200605	−	1.53285i
$675$	−2.78684	+	14.0104i	−0.107266	+	0.539260i
$676$	−2.75378	−	0.366853i	−0.105915	−	0.0141097i
$677$	36.0379	+	24.0797i	1.38505	+	0.925459i	0.999997	+	0.00256429i	$0.000816241\pi$
$677$	36.0379	+	24.0797i	1.38505	+	0.925459i	0.385051	+	0.922895i	$0.374184\pi$
$678$	1.18212	+	0.0783932i	0.0453989	+	0.00301067i
$679$	−0.0140872	−	0.0340096i	−0.000540618	−	0.00130517i
$680$	−2.42901	+	12.0659i	−0.0931482	+	0.462705i
$681$	0.211565	−	0.510763i	0.00810719	−	0.0195725i
$682$	−24.4512	−	12.0814i	−0.936286	−	0.462621i
$683$	−7.09855	+	1.41199i	−0.271618	+	0.0540283i	−0.329020	−	0.944323i	$-0.606718\pi$
$683$	−7.09855	+	1.41199i	−0.271618	+	0.0540283i	0.0574017	+	0.998351i	$0.481718\pi$
$684$	19.0238	+	38.7265i	0.727393	+	1.48075i
$685$	42.5190	−	28.4103i	1.62457	−	1.08550i
$686$	0.0733441	−	0.0422700i	0.00280029	−	0.00161388i
$687$	3.90192	+	3.90192i	0.148868	+	0.148868i
$688$	−32.8382	+	28.6200i	−1.25194	+	1.09113i
$689$	15.9362	−	15.9362i	0.607122	−	0.607122i
$690$	−0.0207183	+	0.0770845i	−0.000788732	+	0.00293456i
$691$	−5.75781	−	8.61717i	−0.219037	−	0.327812i	0.705636	−	0.708575i	$-0.250662\pi$
$691$	−5.75781	−	8.61717i	−0.219037	−	0.327812i	−0.924673	+	0.380762i	$0.875662\pi$
$692$	25.3425	+	22.2939i	0.963379	+	0.847486i
$693$	−0.00897194	−	0.0451050i	−0.000340816	−	0.00171340i
$694$	−10.4083	−	30.7395i	−0.395094	−	1.16686i
$695$	33.5951	+	13.9155i	1.27433	+	0.527846i
$696$	−1.03084	−	1.03561i	−0.0390739	−	0.0392547i
$697$	5.62247	−	2.32890i	0.212966	−	0.0882134i
$698$	19.1287	−	16.7494i	0.724033	−	0.633975i
$699$	−3.86650	+	5.78663i	−0.146245	+	0.218871i
$700$	0.0247846	−	0.0427761i	0.000936770	−	0.00161678i
$701$	−3.24093	−	0.644660i	−0.122408	−	0.0243485i	0.133506	−	0.991048i	$-0.457376\pi$
$701$	−3.24093	−	0.644660i	−0.122408	−	0.0243485i	−0.255914	+	0.966700i	$0.582376\pi$
$702$	−8.07722	+	10.5097i	−0.304855	+	0.396663i
$703$	−52.0595			−1.96346
$704$	17.0709	−	25.2949i	0.643383	−	0.953336i
$705$	−14.4984			−0.546040
$706$	−11.8923	+	15.4737i	−0.447573	+	0.582361i
$707$	−0.00491165		0.000976988i	−0.000184722		3.67434e-5i
$708$	4.20692	+	2.43750i	0.158106	+	0.0916070i
$709$	−2.09343	+	3.13304i	−0.0786204	+	0.117664i	−0.868696	−	0.495346i	$-0.835041\pi$
$709$	−2.09343	+	3.13304i	−0.0786204	+	0.117664i	0.790075	+	0.613010i	$0.210041\pi$
$710$	41.3119	−	36.1734i	1.55041	−	1.35756i
$711$	−38.2540	+	15.8453i	−1.43464	+	0.594246i
$712$	−24.0869	−	0.0555832i	−0.902696	−	0.00208307i
$713$	−0.189108	−	0.0783312i	−0.00708216	−	0.00293353i
$714$	0.00109113	+	0.00322251i	4.08346e−5	+	0.000120599i
$715$	9.26894	+	46.5981i	0.346639	+	1.74267i
$716$	−4.08485	+	4.64345i	−0.152658	+	0.173534i
$717$	2.76742	+	4.14173i	0.103351	+	0.154676i
$718$	1.32250	−	4.92049i	0.0493552	−	0.183631i
$719$	−7.91252	+	7.91252i	−0.295087	+	0.295087i	−0.839086	−	0.543999i	$-0.816910\pi$
$719$	−7.91252	+	7.91252i	−0.295087	+	0.295087i	0.543999	+	0.839086i	$0.316910\pi$
$720$	16.4820	−	33.1646i	0.614249	−	1.23597i
$721$	−0.0113520	−	0.0113520i	−0.000422772	−	0.000422772i
$722$	−48.4422	+	27.9185i	−1.80283	+	1.03902i
$723$	−2.87808	+	1.92307i	−0.107037	+	0.0715197i
$724$	−17.2429	+	8.47033i	−0.640829	+	0.314797i
$725$	−6.89958	+	1.37241i	−0.256244	+	0.0509701i
$726$	1.91135	+	0.944401i	0.0709368	+	0.0350500i
$727$	−8.92195	+	21.5395i	−0.330897	+	0.798855i	0.667625	+	0.744498i	$0.267311\pi$
$727$	−8.92195	+	21.5395i	−0.330897	+	0.798855i	−0.998522	+	0.0543573i	$0.982689\pi$
$728$	0.0382010	−	0.0253978i	0.00141582	−	0.000941304i
$729$	−6.79175	−	16.3967i	−0.251546	−	0.607286i
$730$	−24.3758	−	1.61651i	−0.902189	−	0.0598296i
$731$	−11.9998	−	8.01804i	−0.443830	−	0.296558i
$732$	−0.248198	+	1.86310i	−0.00917366	+	0.0688621i
$733$	7.50416	−	37.7260i	0.277173	−	1.39344i	−0.551719	−	0.834030i	$-0.686028\pi$
$733$	7.50416	−	37.7260i	0.277173	−	1.39344i	0.828891	−	0.559410i	$-0.188972\pi$
$734$	−2.82141	−	21.5589i	−0.104140	−	0.795752i
$735$			9.75839i			0.359944i
$736$	0.115277	−	0.197904i	0.00424916	−	0.00729483i
$737$		−	9.44814i		−	0.348027i
$738$	−18.1570	+	2.37621i	−0.668369	+	0.0874695i
$739$	−7.52317	+	37.8215i	−0.276744	+	1.39129i	0.553018	+	0.833170i	$0.313476\pi$
$739$	−7.52317	+	37.8215i	−0.276744	+	1.39129i	−0.829762	+	0.558118i	$0.811524\pi$
$740$	27.1476	+	35.4924i	0.997966	+	1.30473i
$741$	−10.2451	−	6.84557i	−0.376364	−	0.251478i
$742$	−0.00237719	+	0.0358464i	−8.72694e−5	+	0.00131596i
$743$	−12.5644	−	30.3333i	−0.460945	−	1.11282i	−0.968010	−	0.250912i	$-0.919270\pi$
$743$	−12.5644	−	30.3333i	−0.460945	−	1.11282i	0.507065	−	0.861908i	$-0.330730\pi$
$744$	−5.04015	−	3.38457i	−0.184781	−	0.124084i
$745$	−11.7678	+	28.4101i	−0.431140	+	1.04086i
$746$	−6.30109	+	12.7526i	−0.230699	+	0.466906i
$747$	−0.0511361	+	0.0101716i	−0.00187097	+	0.000372159i
$748$	9.56899	+	3.26466i	0.349877	+	0.119368i
$749$	−0.0433331	+	0.0289543i	−0.00158336	+	0.00105797i
$750$	0.769167	+	1.33461i	0.0280860	+	0.0487329i
$751$	−24.4143	−	24.4143i	−0.890890	−	0.890890i	0.103716	−	0.994607i	$-0.466927\pi$
$751$	−24.4143	−	24.4143i	−0.890890	−	0.890890i	−0.994607	+	0.103716i	$0.966927\pi$
$752$	40.1496	+	10.8906i	1.46411	+	0.397138i
$753$	−6.04887	+	6.04887i	−0.220433	+	0.220433i
$754$	−6.30386	−	1.69431i	−0.229573	−	0.0617032i
$755$	17.1258	+	25.6306i	0.623273	+	0.932795i
$756$	−0.00134946	−	0.0210858i	−4.90795e−5	−	0.000766884i
$757$	5.87409	+	29.5310i	0.213497	+	1.07332i	0.927683	+	0.373368i	$0.121797\pi$
$757$	5.87409	+	29.5310i	0.213497	+	1.07332i	−0.714186	+	0.699956i	$0.753203\pi$
$758$	16.5793	−	5.61370i	0.602188	−	0.203899i
$759$	0.0605786	+	0.0250925i	0.00219886	+	0.000910799i
$760$	65.5827	+	27.3427i	2.37893	+	0.991824i
$761$	−9.91298	+	4.10609i	−0.359345	+	0.148846i	−0.555050	−	0.831817i	$-0.687301\pi$
$761$	−9.91298	+	4.10609i	−0.359345	+	0.148846i	0.195704	+	0.980663i	$0.437301\pi$
$762$	2.98735	+	3.41170i	0.108220	+	0.123593i
$763$	−0.0220638	+	0.0330208i	−0.000798763	+	0.00119543i
$764$	6.84703	+	25.7116i	0.247717	+	0.930213i
$765$	12.0344	+	2.39379i	0.435104	+	0.0865475i
$766$	12.1946	+	9.37214i	0.440608	+	0.338629i
$767$	21.7201			0.784267
$768$	4.51031	−	5.07963i	0.162752	−	0.183295i
$769$	1.10123			0.0397113			0.0198557	−	0.999803i	$-0.493679\pi$
$769$	1.10123			0.0397113			0.0198557	+	0.999803i	$0.493679\pi$
$770$	−0.0600485	−	0.0461503i	−0.00216400	−	0.00166314i
$771$	−3.77415	−	0.750726i	−0.135923	−	0.0270367i
$772$	−8.12726	−	30.5191i	−0.292506	−	1.09841i
$773$	−6.65537	+	9.96046i	−0.239377	+	0.358253i	−0.931634	−	0.363398i	$-0.881616\pi$
$773$	−6.65537	+	9.96046i	−0.239377	+	0.358253i	0.692257	+	0.721651i	$0.256616\pi$
$774$	28.6076	+	32.6714i	1.02828	+	1.17435i
$775$	−27.0036	+	11.1852i	−0.969997	+	0.401786i
$776$	−22.4766	−	9.37094i	−0.806863	−	0.336397i
$777$	0.0114117	+	0.00472688i	0.000409392	+	0.000169576i
$778$	45.1082	−	15.2735i	1.61721	−	0.547581i
$779$	−6.85413	−	34.4581i	−0.245575	−	1.23459i
$780$	0.675476	+	10.5545i	0.0241859	+	0.377913i
$781$	−25.0603	−	37.5054i	−0.896728	−	1.34205i
$782$	0.0732808	+	0.0196959i	0.00262051	+	0.000704326i
$783$	−2.12596	+	2.12596i	−0.0759756	+	0.0759756i
$784$	7.33009	−	27.0234i	0.261789	−	0.965122i
$785$	−33.5771	−	33.5771i	−1.19842	−	1.19842i
$786$	−2.84654	−	4.93912i	−0.101533	−	0.176173i
$787$	−4.26735	+	2.85135i	−0.152115	+	0.101640i	−0.629298	−	0.777164i	$-0.716658\pi$
$787$	−4.26735	+	2.85135i	−0.152115	+	0.101640i	0.477184	+	0.878804i	$0.341658\pi$
$788$	−18.2573	−	6.22886i	−0.650390	−	0.221894i
$789$	2.90897	−	0.578630i	0.103562	−	0.0205998i
$790$	−30.2055	+	61.1321i	−1.07466	+	2.17498i
$791$	−0.00322843	+	0.00779413i	−0.000114790	+	0.000277127i
$792$	−25.2564	−	16.9602i	−0.897447	−	0.602655i
$793$	3.21319	+	7.75733i	0.114104	+	0.275471i
$794$	0.545724	−	8.22914i	0.0193670	−	0.292041i
$795$	−6.88671	−	4.60155i	−0.244246	−	0.163200i
$796$	24.4467	+	31.9612i	0.866490	+	1.13284i
$797$	2.59385	−	13.0402i	0.0918788	−	0.461906i	−0.907266	−	0.420557i	$-0.861835\pi$
$797$	2.59385	−	13.0402i	0.0918788	−	0.461906i	0.999145	−	0.0413486i	$-0.0131654\pi$
$798$	0.0194752	−	0.00254871i	0.000689413	−	9.02235e-5i
$799$			13.7829i			0.487605i
$800$	−8.34290	−	31.6221i	−0.294966	−	1.11801i
$801$			24.0131i			0.848460i
$802$	−2.77961	−	21.2395i	−0.0981514	−	0.749992i
$803$	−3.91506	+	19.6823i	−0.138159	+	0.694574i
$804$	0.277730	−	2.08478i	0.00979477	−	0.0735244i
$805$	−0.000472606	0	0.000315785i	−1.66572e−5	0	1.11300e-5i
$806$	−27.0618	−	1.79463i	−0.953211	−	0.0632131i
$807$	−0.882884	−	2.13147i	−0.0310790	−	0.0750313i
$808$	−2.75876	+	1.83415i	−0.0970528	+	0.0645252i
$809$	15.4001	−	37.1792i	0.541439	−	1.30715i	−0.382268	−	0.924052i	$-0.624857\pi$
$809$	15.4001	−	37.1792i	0.541439	−	1.30715i	0.923707	−	0.383099i	$-0.125143\pi$
$810$	−30.8494	−	15.2427i	−1.08394	−	0.535575i
$811$	−6.30322	+	1.25379i	−0.221336	+	0.0440265i	−0.304512	−	0.952508i	$-0.598494\pi$
$811$	−6.30322	+	1.25379i	−0.221336	+	0.0440265i	0.0831764	+	0.996535i	$0.473494\pi$
$812$	0.00933921	−	0.00458774i	0.000327742	−	0.000160998i
$813$	1.12847	−	0.754021i	0.0395773	−	0.0264447i
$814$	31.8032	−	18.3290i	1.11470	−	0.642430i
$815$	−4.65175	−	4.65175i	−0.162944	−	0.162944i
$816$	2.01548	+	1.00164i	0.0705559	+	0.0350646i
$817$	−58.9141	+	58.9141i	−2.06114	+	2.06114i
$818$	−6.58090	+	24.4849i	−0.230096	+	0.856094i
$819$	−0.0254076	−	0.0380252i	−0.000887814	−	0.00132871i
$820$	−19.9181	+	22.6419i	−0.695570	+	0.790688i
$821$	−5.61594	−	28.2332i	−0.195998	−	0.985346i	−0.946063	−	0.323983i	$-0.894978\pi$
$821$	−5.61594	−	28.2332i	−0.195998	−	0.985346i	0.750065	−	0.661364i	$-0.230022\pi$
$822$	−2.99899	−	8.85711i	−0.104602	−	0.308927i
$823$	43.0603	+	17.8362i	1.50099	+	0.621729i	0.973675	−	0.227942i	$-0.0731997\pi$
$823$	43.0603	+	17.8362i	1.50099	+	0.621729i	0.527313	+	0.849671i	$0.323200\pi$
$824$	−10.6202	−	0.0245073i	−0.369973	−	0.000853752i
$825$	8.65027	−	3.58306i	0.301164	−	0.124746i
$826$	−0.0260482	+	0.0228082i	−0.000906333	+	0.000793600i
$827$	−14.1694	+	21.2060i	−0.492717	+	0.737404i	−0.991611	−	0.129260i	$-0.958740\pi$
$827$	−14.1694	+	21.2060i	−0.492717	+	0.737404i	0.498893	+	0.866663i	$0.333740\pi$
$828$	−0.197561	−	0.114467i	−0.00686571	−	0.00397802i
$829$	12.9770	+	2.58128i	0.450709	+	0.0896515i	0.415225	−	0.909719i	$-0.363703\pi$
$829$	12.9770	+	2.58128i	0.450709	+	0.0896515i	0.0354836	+	0.999370i	$0.488703\pi$
$830$	−0.0523211	+	0.0680777i	−0.00181609	+	0.00236301i
$831$	1.60035			0.0555155
$832$	6.05757	−	29.7356i	0.210009	−	1.03090i
$833$	9.27685			0.321424
$834$	4.05197	−	5.27223i	0.140308	−	0.182562i
$835$	−9.26747	−	1.84341i	−0.320714	−	0.0637940i
$836$	29.2622	−	50.5039i	1.01205	−	1.74672i
$837$	−6.94010	+	10.3866i	−0.239885	+	0.359013i
$838$	8.77560	−	7.68406i	0.303148	−	0.265442i
$839$	9.50389	−	3.93664i	0.328111	−	0.135908i	−0.212546	−	0.977151i	$-0.568176\pi$
$839$	9.50389	−	3.93664i	0.328111	−	0.135908i	0.540657	+	0.841243i	$0.318176\pi$
$840$	−0.0118934	−	0.0119484i	−0.000410361	−	0.000412260i
$841$	25.4246	+	10.5312i	0.876710	+	0.363145i
$842$	4.00520	+	11.8288i	0.138028	+	0.407648i
$843$	1.95251	+	9.81593i	0.0672480	+	0.338079i
$844$	−7.46631	−	6.56812i	−0.257001	−	0.226084i
$845$	2.53393	+	3.79229i	0.0871697	+	0.130459i
$846$	10.7647	−	40.0513i	0.370099	−	1.37699i
$847$	−0.0107349	+	0.0107349i	−0.000368855	+	0.000368855i
$848$	15.6145	+	17.9159i	0.536205	+	0.615233i
$849$	−0.418296	−	0.418296i	−0.0143559	−	0.0143559i
$850$	9.38793	−	5.41050i	0.322003	−	0.185579i
$851$	0.229062	−	0.153055i	0.00785216	−	0.00524664i
$852$	−4.42720	−	9.01240i	−0.151673	−	0.308760i
$853$	−28.4463	+	5.65832i	−0.973982	+	0.193737i	−0.656333	−	0.754471i	$-0.727893\pi$
$853$	−28.4463	+	5.65832i	−0.973982	+	0.193737i	−0.317649	+	0.948208i	$0.602893\pi$
$854$	−0.0119994	−	0.00592895i	−0.000410612	−	0.000202884i
$855$	27.1078	−	65.4441i	0.927068	−	2.23814i
$856$	−6.80398	+	33.7981i	−0.232555	+	1.15520i
$857$	−10.4076	−	25.1262i	−0.355517	−	0.858294i	−0.995919	−	0.0902541i	$-0.971232\pi$
$857$	−10.4076	−	25.1262i	−0.355517	−	0.858294i	0.640402	−	0.768040i	$-0.278768\pi$
$858$	8.66892	+	0.574888i	0.295952	+	0.0196264i
$859$	21.6667	+	14.4772i	0.739258	+	0.493957i	0.867284	−	0.497814i	$-0.165864\pi$
$859$	21.6667	+	14.4772i	0.739258	+	0.493957i	−0.128025	+	0.991771i	$0.540864\pi$
$860$	70.8878	+	9.44352i	2.41725	+	0.322021i
$861$	−0.00162625	+	0.00817572i	−5.54225e−5	+	0.000278628i
$862$	0.344096	+	2.62930i	0.0117200	+	0.0895542i
$863$			36.8745i			1.25522i	0.778527	+	0.627611i	$0.215967\pi$
$863$			36.8745i			1.25522i	−0.778527	+	0.627611i	$0.784033\pi$
$864$	−10.4732	−	9.25624i	−0.356305	−	0.314904i
$865$		−	55.4138i		−	1.88412i
$866$	−20.8241	+	2.72525i	−0.707630	+	0.0926076i
$867$	1.26261	−	6.34758i	0.0428806	−	0.215575i
$868$	0.0343389	−	0.0262653i	0.00116554	−	0.000891503i
$869$	46.5736	+	31.1195i	1.57990	+	1.05566i
$870$	−0.158739	+	2.39367i	−0.00538175	+	0.0811530i
$871$	−3.59551	−	8.68032i	−0.121829	−	0.294122i
$872$	5.06587	+	25.7786i	0.171552	+	0.872973i
$873$	−9.29043	+	22.4291i	−0.314434	+	0.759110i
$874$	0.194055	−	0.392742i	0.00656399	−	0.0132847i
$875$	−0.0107583	+	0.00213995i	−0.000363696	+	7.23437e-5i
$876$	−1.44244	+	4.22791i	−0.0487356	+	0.142848i
$877$	−31.7570	+	21.2194i	−1.07236	+	0.716527i	−0.960803	−	0.277231i	$-0.910583\pi$
$877$	−31.7570	+	21.2194i	−1.07236	+	0.716527i	−0.111555	+	0.993758i	$0.535583\pi$
$878$	−18.7720	−	32.5719i	−0.633525	−	1.09925i
$879$	−7.95808	−	7.95808i	−0.268419	−	0.268419i
$880$	−49.6913	+	6.38651i	−1.67509	+	0.215289i
$881$	11.0483	−	11.0483i	0.372227	−	0.372227i	−0.496061	−	0.868288i	$-0.665221\pi$
$881$	11.0483	−	11.0483i	0.372227	−	0.372227i	0.868288	+	0.496061i	$0.165221\pi$
$882$	−26.9573	−	7.24540i	−0.907698	−	0.243965i
$883$	8.22590	+	12.3109i	0.276824	+	0.414296i	0.943664	−	0.330904i	$-0.107354\pi$
$883$	8.22590	+	12.3109i	0.276824	+	0.414296i	−0.666841	+	0.745200i	$0.732354\pi$
$884$	10.0337	−	0.642145i	0.337471	−	0.0215977i
$885$	−1.55726	−	7.82889i	−0.0523469	−	0.263165i
$886$	−28.7192	+	9.72424i	−0.964842	+	0.326692i
$887$	−16.4158	−	6.79963i	−0.551187	−	0.228309i	0.0896672	−	0.995972i	$-0.471420\pi$
$887$	−16.4158	−	6.79963i	−0.551187	−	0.228309i	−0.640854	+	0.767663i	$0.721420\pi$
$888$	7.55631	−	3.10952i	0.253573	−	0.104348i
$889$	−0.0298338	+	0.0123575i	−0.00100059	+	0.000414459i
$890$	26.0508	+	29.7514i	0.873224	+	0.997268i
$891$	−15.7040	+	23.5027i	−0.526104	+	0.787370i
$892$	18.9614	−	5.04945i	0.634876	−	0.169068i
$893$	78.0407	+	15.5233i	2.61153	+	0.519466i
$894$	4.45852	+	3.42660i	0.149115	+	0.114603i
$895$	10.1533			0.339388
$896$	0.0239607	+	0.0420220i	0.000800469	+	0.00140386i
$897$	0.0652046			0.00217712
$898$	22.5665	+	17.3435i	0.753055	+	0.578760i
$899$	−6.03355	−	1.20015i	−0.201230	−	0.0400272i
$900$	−31.5057	+	8.39001i	−1.05019	+	0.279667i
$901$	−4.37449	+	6.54688i	−0.145735	+	0.218108i
$902$	16.3191	+	18.6373i	0.543367	+	0.620554i
$903$	0.0182635	−	0.00756501i	0.000607773	−	0.000251748i
$904$	2.12378	+	5.16092i	0.0706359	+	0.171650i
$905$	29.1389	+	12.0697i	0.968610	+	0.401212i
$906$	5.33910	−	1.80780i	0.177380	−	0.0600602i
$907$	−7.14940	−	35.9424i	−0.237392	−	1.19345i	−0.897066	−	0.441897i	$-0.854306\pi$
$907$	−7.14940	−	35.9424i	−0.237392	−	1.19345i	0.659674	−	0.751552i	$-0.270694\pi$
$908$	2.59897	−	0.166331i	0.0862499	−	0.00551988i
$909$	1.83486	+	2.74606i	0.0608585	+	0.0910811i
$910$	−0.0727312	−	0.0195482i	−0.00241102	−	0.000648018i
$911$	39.4695	−	39.4695i	1.30768	−	1.30768i	0.384602	−	0.923083i	$-0.374339\pi$
$911$	39.4695	−	39.4695i	1.30768	−	1.30768i	0.923083	−	0.384602i	$-0.125661\pi$
$912$	7.94140	−	10.2838i	0.262966	−	0.340530i
$913$	0.0498736	+	0.0498736i	0.00165057	+	0.00165057i
$914$	−5.77661	−	10.0232i	−0.191073	−	0.331537i
$915$	2.56571	−	1.71436i	0.0848199	−	0.0566748i
$916$	−8.39346	+	24.6019i	−0.277328	+	0.812870i
$917$	0.0398143	−	0.00791956i	0.00131479	−	0.000261527i
$918$	2.05140	−	4.15177i	0.0677063	−	0.137029i
$919$	−4.30202	+	10.3860i	−0.141910	+	0.342602i	−0.978815	−	0.204747i	$-0.934363\pi$
$919$	−4.30202	+	10.3860i	−0.141910	+	0.342602i	0.836905	+	0.547349i	$0.184363\pi$
$920$	−0.368952	+	0.0725045i	−0.0121640	+	0.00239040i
$921$	−1.67706	−	4.04879i	−0.0552611	−	0.133412i
$922$	−3.04605	+	45.9323i	−0.100316	+	1.51270i
$923$	−37.2965	−	24.9207i	−1.22763	−	0.820276i
$924$	−0.0110001	+	0.00841378i	−0.000361875	+	0.000276793i
$925$	7.67456	−	38.5826i	0.252338	−	1.26859i
$926$	24.8747	−	3.25535i	0.817434	−	0.106978i
$927$			10.5877i			0.347744i
$928$	2.23761	−	6.50944i	0.0734533	−	0.213683i
$929$		−	30.9521i		−	1.01551i	−0.861502	−	0.507754i	$-0.830476\pi$
$929$		−	30.9521i		−	1.01551i	0.861502	−	0.507754i	$-0.169524\pi$
$930$	1.29338	+	9.88295i	0.0424117	+	0.324075i
$931$	10.4482	−	52.5267i	0.342426	−	1.72149i
$932$	−32.4971	−	4.32920i	−1.06448	−	0.141808i
$933$	2.57458	+	1.72028i	0.0842881	+	0.0563195i
$934$	−17.7032	−	1.17401i	−0.579268	−	0.0384147i
$935$	−6.35216	−	15.3355i	−0.207738	−	0.501524i
$936$	−29.6582	−	5.97055i	−0.969407	−	0.195154i
$937$	−9.75061	+	23.5400i	−0.318538	+	0.769020i	0.680794	+	0.732475i	$0.261635\pi$
$937$	−9.75061	+	23.5400i	−0.318538	+	0.769020i	−0.999332	+	0.0365445i	$0.988365\pi$
$938$	0.0134272	+	0.00663440i	0.000438413	+	0.000216621i
$939$	−12.6042	+	2.50714i	−0.411323	+	0.0818173i
$940$	−30.1129	−	61.3004i	−0.982174	−	1.99940i
$941$	−6.60481	+	4.41319i	−0.215311	+	0.143866i	−0.658549	−	0.752538i	$-0.728829\pi$
$941$	−6.60481	+	4.41319i	−0.215311	+	0.143866i	0.443239	+	0.896404i	$0.353829\pi$
$942$	−7.52325	+	4.33584i	−0.245121	+	0.141269i
$943$	0.131465	+	0.131465i	0.00428108	+	0.00428108i
$944$	−1.56828	+	22.8499i	−0.0510433	+	0.743702i
$945$	−0.0245284	+	0.0245284i	−0.000797909	+	0.000797909i
$946$	15.2484	−	56.7331i	0.495767	−	1.84455i
$947$	3.19217	+	4.77741i	0.103731	+	0.155245i	0.879704	−	0.475521i	$-0.157741\pi$
$947$	3.19217	+	4.77741i	0.103731	+	0.155245i	−0.775973	+	0.630767i	$0.782741\pi$
$948$	9.36193	+	8.23571i	0.304061	+	0.267483i
$949$	3.89325	+	19.5727i	0.126380	+	0.635357i
$950$	−20.0616	−	59.2493i	−0.650884	−	1.92230i
$951$	7.15528	+	2.96381i	0.232026	+	0.0961082i
$952$	−0.0113588	+	0.0113065i	−0.000368141	+	0.000366446i
$953$	−6.42092	+	2.65963i	−0.207994	+	0.0861539i	−0.484248	−	0.874931i	$-0.660907\pi$
$953$	−6.42092	+	2.65963i	−0.207994	+	0.0861539i	0.276254	+	0.961085i	$0.410907\pi$
$954$	17.8249	−	15.6078i	0.577102	−	0.505320i
$955$	24.2690	−	36.3211i	0.785327	−	1.17532i
$956$	−11.7638	+	20.3032i	−0.380467	+	0.656653i
$957$	1.93278	+	0.384454i	0.0624779	+	0.0124276i
$958$	−23.2092	+	30.1987i	−0.749857	+	0.975677i
$959$	0.0665886			0.00215026
$960$	−11.1524	−	0.0514707i	−0.359941	−	0.00166121i
$961$	5.44027			0.175493
$962$	22.2435	−	28.9422i	0.717160	−	0.933134i
$963$	33.7099	+	6.70532i	1.08629	+	0.216076i
$964$	−14.1086	−	8.17459i	−0.454409	−	0.263286i
$965$	−28.8067	+	43.1123i	−0.927322	+	1.38784i
$966$	−7.81978e−5	0	6.84713e-5i	−2.51597e−6	0	2.20303e-6i
$967$	−5.39977	+	2.23666i	−0.173645	+	0.0719261i	−0.467812	−	0.883828i	$-0.654958\pi$
$967$	−5.39977	+	2.23666i	−0.173645	+	0.0719261i	0.294167	+	0.955754i	$0.404958\pi$
$968$	−0.0231750	+	10.0429i	−0.000744872	+	0.322790i
$969$	3.97716	+	1.64739i	0.127765	+	0.0529219i
$970$	12.8219	+	37.8677i	0.411686	+	1.21586i
$971$	10.5008	+	52.7912i	0.336987	+	1.69415i	0.662866	+	0.748738i	$0.269340\pi$
$971$	10.5008	+	52.7912i	0.336987	+	1.69415i	−0.325879	+	0.945411i	$0.605660\pi$
$972$	−13.9481	+	15.8555i	−0.447385	+	0.508564i
$973$	0.0263065	+	0.0393704i	0.000843346	+	0.00126216i
$974$	6.74430	−	25.0928i	0.216101	−	0.804026i
$975$	6.58376	−	6.58376i	0.210849	−	0.210849i
$976$	−8.39286	+	2.82022i	−0.268649	+	0.0902731i
$977$	1.68084	+	1.68084i	0.0537748	+	0.0537748i	0.733483	−	0.679708i	$-0.237893\pi$
$977$	1.68084	+	1.68084i	0.0537748	+	0.0537748i	−0.679708	+	0.733483i	$0.737893\pi$
$978$	−1.04227	+	0.600684i	−0.0333280	+	0.0192078i
$979$	27.0101	−	18.0476i	0.863246	−	0.576803i
$980$	−41.2594	+	20.2680i	−1.31798	+	0.647438i
$981$	25.6877	−	5.10961i	0.820146	−	0.163137i
$982$	−26.0772	−	12.8848i	−0.832157	−	0.411170i
$983$	13.7969	−	33.3088i	0.440054	−	1.06238i	−0.535875	−	0.844297i	$-0.680018\pi$
$983$	13.7969	−	33.3088i	0.440054	−	1.06238i	0.975929	−	0.218087i	$-0.0699818\pi$
$984$	3.05304	+	4.59211i	0.0973275	+	0.146391i
$985$	12.1197	+	29.2595i	0.386166	+	0.932287i
$986$	2.27555	+	0.150906i	0.0724684	+	0.00480581i
$987$	−0.0156974	−	0.0104887i	−0.000499655	−	0.000333859i
$988$	7.66475	−	57.5354i	0.243848	−	1.83045i
$989$	0.0860158	−	0.432430i	0.00273514	−	0.0137505i
$990$	6.48120	+	49.5239i	0.205986	+	1.57397i
$991$			57.2499i			1.81860i	0.416137	+	0.909302i	$0.363384\pi$
$991$			57.2499i			1.81860i	−0.416137	+	0.909302i	$0.636616\pi$
$992$	3.84196	−	28.3399i	0.121982	−	0.899793i
$993$			4.42652i			0.140471i
$994$	0.0708977	−	0.00927839i	0.00224874	−	0.000294293i
$995$	12.8880	−	64.7925i	0.408578	−	2.05406i
$996$	0.00953880	+	0.0124709i	0.000302248	+	0.000395155i
$997$	−24.0320	−	16.0577i	−0.761102	−	0.508552i	0.113415	−	0.993548i	$-0.463821\pi$
$997$	−24.0320	−	16.0577i	−0.761102	−	0.508552i	−0.874516	+	0.484996i	$0.838821\pi$
$998$	−3.19078	+	48.1148i	−0.101002	+	1.52305i
$999$	−6.43397	−	15.5330i	−0.203562	−	0.491442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.29.2	✓	56
3.2	odd	2		576.2.bd.a.541.6		56
4.3	odd	2		256.2.i.a.209.3		56
8.3	odd	2		512.2.i.a.161.5		56
8.5	even	2		512.2.i.b.161.3		56
64.11	odd	16		256.2.i.a.49.3		56
64.21	even	16		512.2.i.b.353.3		56
64.43	odd	16		512.2.i.a.353.5		56
64.53	even	16	inner	64.2.i.a.53.2	yes	56
192.53	odd	16		576.2.bd.a.181.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.2	✓	56	1.1	even	1	trivial
64.2.i.a.53.2	yes	56	64.53	even	16	inner
256.2.i.a.49.3		56	64.11	odd	16
256.2.i.a.209.3		56	4.3	odd	2
512.2.i.a.161.5		56	8.3	odd	2
512.2.i.a.353.5		56	64.43	odd	16
512.2.i.b.161.3		56	8.5	even	2
512.2.i.b.353.3		56	64.21	even	16
576.2.bd.a.181.6		56	192.53	odd	16
576.2.bd.a.541.6		56	3.2	odd	2

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12131 - 0.861781i) q^{2} +(0.416408 + 0.0828287i) q^{3} +(0.514666 + 1.93265i) q^{4} +(1.82421 - 2.73012i) q^{5} +(-0.395542 - 0.451729i) q^{6} +(0.00395016 - 0.00163621i) q^{7} +(1.08842 - 2.61062i) q^{8} +(-2.60510 - 1.07907i) q^{9} +O(q^{10})\)	\(q+(-1.12131 - 0.861781i) q^{2} +(0.416408 + 0.0828287i) q^{3} +(0.514666 + 1.93265i) q^{4} +(1.82421 - 2.73012i) q^{5} +(-0.395542 - 0.451729i) q^{6} +(0.00395016 - 0.00163621i) q^{7} +(1.08842 - 2.61062i) q^{8} +(-2.60510 - 1.07907i) q^{9} +(-4.39827 + 1.48924i) q^{10} +(0.744179 + 3.74124i) q^{11} +(0.0542323 + 0.847398i) q^{12} +(2.10744 + 3.15401i) q^{13} +(-0.00583940 - 0.00156948i) q^{14} +(0.985749 - 0.985749i) q^{15} +(-3.47024 + 1.98933i) q^{16} +(-0.937106 - 0.937106i) q^{17} +(1.99120 + 3.45500i) q^{18} +(-6.36144 + 4.25058i) q^{19} +(6.21522 + 2.12045i) q^{20} +(0.00178040 - 0.000354144i) q^{21} +(2.38968 - 4.83641i) q^{22} +(0.0154938 - 0.0374052i) q^{23} +(0.669461 - 0.996931i) q^{24} +(-2.21242 - 5.34125i) q^{25} +(0.354974 - 5.35277i) q^{26} +(-2.05445 - 1.37274i) q^{27} +(0.00519522 + 0.00679216i) q^{28} +(0.237387 - 1.19343i) q^{29} +(-1.95483 + 0.255828i) q^{30} -5.05566i q^{31} +(5.60558 + 0.759932i) q^{32} +1.61952i q^{33} +(0.243204 + 1.85837i) q^{34} +(0.00273887 - 0.0137692i) q^{35} +(0.744702 - 5.59010i) q^{36} +(5.65766 + 3.78033i) q^{37} +(10.7962 + 0.715962i) q^{38} +(0.616312 + 1.48791i) q^{39} +(-5.14182 - 7.73385i) q^{40} +(-1.75731 + 4.24251i) q^{41} +(-0.00230158 - 0.00113721i) q^{42} +(10.6807 - 2.12452i) q^{43} +(-6.84749 + 3.36372i) q^{44} +(-7.69825 + 5.14381i) q^{45} +(-0.0496084 + 0.0285906i) q^{46} +(-7.35399 - 7.35399i) q^{47} +(-1.60981 + 0.540938i) q^{48} +(-4.94973 + 4.94973i) q^{49} +(-2.12219 + 7.89581i) q^{50} +(-0.312599 - 0.467838i) q^{51} +(-5.01095 + 5.69619i) q^{52} +(-1.15910 - 5.82718i) q^{53} +(1.12067 + 3.30975i) q^{54} +(11.5716 + 4.79311i) q^{55} +(2.79065e-5 - 0.0120933i) q^{56} +(-3.00102 + 1.24307i) q^{57} +(-1.29466 + 1.13362i) q^{58} +(3.18115 - 4.76093i) q^{59} +(2.41243 + 1.39777i) q^{60} +(2.17097 + 0.431834i) q^{61} +(-4.35688 + 5.66896i) q^{62} -0.0120562 q^{63} +(-5.63069 - 5.68290i) q^{64} +12.4552 q^{65} +(1.39567 - 1.81598i) q^{66} +(-2.42928 - 0.483215i) q^{67} +(1.32880 - 2.29339i) q^{68} +(0.00954995 - 0.0142925i) q^{69} +(-0.0149372 + 0.0130792i) q^{70} +(-10.9250 + 4.52528i) q^{71} +(-5.65249 + 5.62646i) q^{72} +(4.86044 + 2.01326i) q^{73} +(-3.08617 - 9.11458i) q^{74} +(-0.478860 - 2.40739i) q^{75} +(-11.4889 - 10.1068i) q^{76} +(0.00906108 + 0.0135609i) q^{77} +(0.591177 - 2.19953i) q^{78} +(10.3833 - 10.3833i) q^{79} +(-0.899323 + 13.1031i) q^{80} +(5.23979 + 5.23979i) q^{81} +(5.62660 - 3.24275i) q^{82} +(0.0153741 - 0.0102727i) q^{83} +(0.00160075 + 0.00325862i) q^{84} +(-4.26790 + 0.848937i) q^{85} +(-13.8072 - 6.82218i) q^{86} +(0.197700 - 0.477289i) q^{87} +(10.5769 + 2.12927i) q^{88} +(-3.25895 - 7.86780i) q^{89} +(13.0650 + 0.866416i) q^{90} +(0.0134853 + 0.00901061i) q^{91} +(0.0802652 + 0.0106928i) q^{92} +(0.418754 - 2.10522i) q^{93} +(1.90856 + 14.5836i) q^{94} +25.1215i q^{95} +(2.27126 + 0.780744i) q^{96} -8.60967i q^{97} +(9.81577 - 1.28459i) q^{98} +(2.09840 - 10.5493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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