LMFDB - Embedded newform 64.2.i.a.53.6

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			53.6
Character	$\chi$	$=$	64.53
Dual form			64.2.i.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.468362 + 1.33441i) q^{2} +(-2.98137 + 0.593031i) q^{3} +(-1.56127 + 1.24997i) q^{4} +(0.914126 + 1.36809i) q^{5} +(-2.18770 - 3.70060i) q^{6} +(2.65574 + 1.10004i) q^{7} +(-2.39921 - 1.49793i) q^{8} +(5.76522 - 2.38803i) q^{9} +O(q^{10})$	\(q+(0.468362 + 1.33441i) q^{2} +(-2.98137 + 0.593031i) q^{3} +(-1.56127 + 1.24997i) q^{4} +(0.914126 + 1.36809i) q^{5} +(-2.18770 - 3.70060i) q^{6} +(2.65574 + 1.10004i) q^{7} +(-2.39921 - 1.49793i) q^{8} +(5.76522 - 2.38803i) q^{9} +(-1.39744 + 1.86057i) q^{10} +(0.246413 - 1.23880i) q^{11} +(3.91346 - 4.65250i) q^{12} +(0.319413 - 0.478036i) q^{13} +(-0.224055 + 4.05906i) q^{14} +(-3.53666 - 3.53666i) q^{15} +(0.875149 - 3.90309i) q^{16} +(-3.38390 + 3.38390i) q^{17} +(5.88682 + 6.57468i) q^{18} +(4.19561 + 2.80342i) q^{19} +(-3.13727 - 0.993326i) q^{20} +(-8.57011 - 1.70470i) q^{21} +(1.76847 - 0.251393i) q^{22} +(0.178010 + 0.429755i) q^{23} +(8.04124 + 3.04308i) q^{24} +(0.877384 - 2.11819i) q^{25} +(0.787494 + 0.202333i) q^{26} +(-8.18962 + 5.47213i) q^{27} +(-5.52137 + 1.60213i) q^{28} +(-1.02242 - 5.14005i) q^{29} +(3.06290 - 6.37578i) q^{30} -10.0065i q^{31} +(5.61819 - 0.660257i) q^{32} +3.83945i q^{33} +(-6.10038 - 2.93060i) q^{34} +(0.922728 + 4.63887i) q^{35} +(-6.01612 + 10.9347i) q^{36} +(0.447703 - 0.299146i) q^{37} +(-1.77583 + 6.91166i) q^{38} +(-0.668798 + 1.61462i) q^{39} +(-0.143878 - 4.65162i) q^{40} +(2.44115 + 5.89346i) q^{41} +(-1.73915 - 12.2344i) q^{42} +(3.80641 + 0.757142i) q^{43} +(1.16375 + 2.24212i) q^{44} +(8.53718 + 5.70436i) q^{45} +(-0.490094 + 0.438819i) q^{46} +(-5.99084 + 5.99084i) q^{47} +(-0.294489 + 12.1555i) q^{48} +(0.893127 + 0.893127i) q^{49} +(3.23746 + 0.178704i) q^{50} +(8.08188 - 12.0954i) q^{51} +(0.0988389 + 1.14560i) q^{52} +(0.810472 - 4.07452i) q^{53} +(-11.1378 - 8.36533i) q^{54} +(1.92004 - 0.795307i) q^{55} +(-4.72389 - 6.61736i) q^{56} +(-14.1712 - 5.86989i) q^{57} +(6.38004 - 3.77172i) q^{58} +(-1.03615 - 1.55070i) q^{59} +(9.94242 + 1.10097i) q^{60} +(-6.47490 + 1.28794i) q^{61} +(13.3528 - 4.68668i) q^{62} +17.9379 q^{63} +(3.51240 + 7.18770i) q^{64} +0.945978 q^{65} +(-5.12339 + 1.79826i) q^{66} +(6.01983 - 1.19742i) q^{67} +(1.05342 - 9.51296i) q^{68} +(-0.785572 - 1.17569i) q^{69} +(-5.75795 + 3.40396i) q^{70} +(-4.20400 - 1.74136i) q^{71} +(-17.4091 - 2.90652i) q^{72} +(-0.911379 + 0.377506i) q^{73} +(0.608868 + 0.457308i) q^{74} +(-1.35965 + 6.83542i) q^{75} +(-10.0547 + 0.867487i) q^{76} +(2.01715 - 3.01887i) q^{77} +(-2.46780 - 0.136220i) q^{78} +(0.152459 + 0.152459i) q^{79} +(6.13976 - 2.37064i) q^{80} +(7.93360 - 7.93360i) q^{81} +(-6.72092 + 6.01776i) q^{82} +(-5.16472 - 3.45096i) q^{83} +(15.5111 - 8.05087i) q^{84} +(-7.72277 - 1.53615i) q^{85} +(0.772445 + 5.43391i) q^{86} +(6.09641 + 14.7180i) q^{87} +(-2.44684 + 2.60303i) q^{88} +(1.48745 - 3.59102i) q^{89} +(-3.61343 + 14.0638i) q^{90} +(1.37414 - 0.918171i) q^{91} +(-0.815104 - 0.448458i) q^{92} +(5.93418 + 29.8331i) q^{93} +(-10.8001 - 5.18832i) q^{94} +8.30263i q^{95} +(-16.3583 + 5.30023i) q^{96} +13.7742i q^{97} +(-0.773486 + 1.61010i) q^{98} +(-1.53767 - 7.73041i) 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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.468362	+	1.33441i	0.331182	+	0.943567i
$2$	0.468362	+	1.33441i	0.331182	+	0.943567i
$3$	−2.98137	+	0.593031i	−1.72129	+	0.342386i	−0.954204	−	0.299155i	$-0.903295\pi$
$3$	−2.98137	+	0.593031i	−1.72129	+	0.342386i	−0.767088	+	0.641542i	$0.778295\pi$
$4$	−1.56127	+	1.24997i	−0.780637	+	0.624985i
$5$	0.914126	+	1.36809i	0.408810	+	0.611827i	0.977553	−	0.210688i	$-0.0675704\pi$
$5$	0.914126	+	1.36809i	0.408810	+	0.611827i	−0.568744	+	0.822515i	$0.692570\pi$
$6$	−2.18770	−	3.70060i	−0.893126	−	1.51076i
$7$	2.65574	+	1.10004i	1.00378	+	0.415778i	0.823181	−	0.567779i	$-0.192197\pi$
$7$	2.65574	+	1.10004i	1.00378	+	0.415778i	0.180596	+	0.983557i	$0.442197\pi$
$8$	−2.39921	−	1.49793i	−0.848248	−	0.529599i
$9$	5.76522	−	2.38803i	1.92174	−	0.796011i
$10$	−1.39744	+	1.86057i	−0.441909	+	0.588365i
$11$	0.246413	−	1.23880i	0.0742963	−	0.373513i	−0.925692	−	0.378277i	$-0.876517\pi$
$11$	0.246413	−	1.23880i	0.0742963	−	0.373513i	0.999989	+	0.00476447i	$0.00151658\pi$
$12$	3.91346	−	4.65250i	1.12972	−	1.34306i
$13$	0.319413	−	0.478036i	0.0885893	−	0.132583i	−0.784528	−	0.620093i	$-0.787095\pi$
$13$	0.319413	−	0.478036i	0.0885893	−	0.132583i	0.873117	+	0.487510i	$0.162095\pi$
$14$	−0.224055	+	4.05906i	−0.0598813	+	1.08483i
$15$	−3.53666	−	3.53666i	−0.913162	−	0.913162i
$16$	0.875149	−	3.90309i	0.218787	−	0.975773i
$17$	−3.38390	+	3.38390i	−0.820715	+	0.820715i	−0.986211	−	0.165495i	$-0.947078\pi$
$17$	−3.38390	+	3.38390i	−0.820715	+	0.820715i	0.165495	+	0.986211i	$0.447078\pi$
$18$	5.88682	+	6.57468i	1.38754	+	1.54967i
$19$	4.19561	+	2.80342i	0.962539	+	0.643148i	0.934313	−	0.356453i	$-0.116014\pi$
$19$	4.19561	+	2.80342i	0.962539	+	0.643148i	0.0282261	+	0.999602i	$0.491014\pi$
$20$	−3.13727	−	0.993326i	−0.701514	−	0.222115i
$21$	−8.57011	−	1.70470i	−1.87015	−	0.371996i
$22$	1.76847	−	0.251393i	0.377040	−	0.0535972i
$23$	0.178010	+	0.429755i	0.0371177	+	0.0896101i	0.941351	−	0.337428i	$-0.109557\pi$
$23$	0.178010	+	0.429755i	0.0371177	+	0.0896101i	−0.904234	+	0.427038i	$0.859557\pi$
$24$	8.04124	+	3.04308i	1.64141	+	0.621166i
$25$	0.877384	−	2.11819i	0.175477	−	0.423638i
$26$	0.787494	+	0.202333i	0.154440	+	0.0396807i
$27$	−8.18962	+	5.47213i	−1.57609	+	1.05311i
$28$	−5.52137	+	1.60213i	−1.04344	+	0.302774i
$29$	−1.02242	−	5.14005i	−0.189858	−	0.954483i	−0.951773	−	0.306805i	$-0.900740\pi$
$29$	−1.02242	−	5.14005i	−0.189858	−	0.954483i	0.761914	−	0.647678i	$-0.224260\pi$
$30$	3.06290	−	6.37578i	0.559206	−	1.16405i
$31$		−	10.0065i		−	1.79722i	−0.438743	−	0.898612i	$-0.644576\pi$
$31$		−	10.0065i		−	1.79722i	0.438743	−	0.898612i	$-0.355424\pi$
$32$	5.61819	−	0.660257i	0.993165	−	0.116718i
$33$			3.83945i			0.668363i
$34$	−6.10038	−	2.93060i	−1.04621	−	0.502593i
$35$	0.922728	+	4.63887i	0.155969	+	0.784111i
$36$	−6.01612	+	10.9347i	−1.00269	+	1.82245i
$37$	0.447703	−	0.299146i	0.0736019	−	0.0491792i	−0.518225	−	0.855244i	$-0.673407\pi$
$37$	0.447703	−	0.299146i	0.0736019	−	0.0491792i	0.591827	+	0.806065i	$0.298407\pi$
$38$	−1.77583	+	6.91166i	−0.288077	+	1.12122i
$39$	−0.668798	+	1.61462i	−0.107093	+	0.258546i
$40$	−0.143878	−	4.65162i	−0.0227491	−	0.735486i
$41$	2.44115	+	5.89346i	0.381244	+	0.920404i	0.991726	+	0.128374i	$0.0409757\pi$
$41$	2.44115	+	5.89346i	0.381244	+	0.920404i	−0.610482	+	0.792030i	$0.709024\pi$
$42$	−1.73915	−	12.2344i	−0.268357	−	1.88781i
$43$	3.80641	+	0.757142i	0.580472	+	0.115463i	0.476589	−	0.879126i	$-0.341873\pi$
$43$	3.80641	+	0.757142i	0.580472	+	0.115463i	0.103883	+	0.994589i	$0.466873\pi$
$44$	1.16375	+	2.24212i	0.175441	+	0.338012i
$45$	8.53718	+	5.70436i	1.27265	+	0.850355i
$46$	−0.490094	+	0.438819i	−0.0722604	+	0.0647003i
$47$	−5.99084	+	5.99084i	−0.873854	+	0.873854i	−0.992890	−	0.119036i	$-0.962020\pi$
$47$	−5.99084	+	5.99084i	−0.873854	+	0.873854i	0.119036	+	0.992890i	$0.462020\pi$
$48$	−0.294489	+	12.1555i	−0.0425058	+	1.75450i
$49$	0.893127	+	0.893127i	0.127590	+	0.127590i
$50$	3.23746	+	0.178704i	0.457846	+	0.0252726i
$51$	8.08188	−	12.0954i	1.13169	−	1.69369i
$52$	0.0988389	+	1.14560i	0.0137065	+	0.158866i
$53$	0.810472	−	4.07452i	0.111327	−	0.559678i	−0.884353	−	0.466820i	$-0.845400\pi$
$53$	0.810472	−	4.07452i	0.111327	−	0.559678i	0.995679	−	0.0928581i	$-0.0296003\pi$
$54$	−11.1378	−	8.36533i	−1.51566	−	1.13838i
$55$	1.92004	−	0.795307i	0.258898	−	0.107239i
$56$	−4.72389	−	6.61736i	−0.631256	−	0.884282i
$57$	−14.1712	−	5.86989i	−1.87702	−	0.777486i
$58$	6.38004	−	3.77172i	0.837740	−	0.495252i
$59$	−1.03615	−	1.55070i	−0.134895	−	0.201884i	0.757872	−	0.652403i	$-0.226239\pi$
$59$	−1.03615	−	1.55070i	−0.134895	−	0.201884i	−0.892767	+	0.450519i	$0.851239\pi$
$60$	9.94242	+	1.10097i	1.28356	+	0.142135i
$61$	−6.47490	+	1.28794i	−0.829026	+	0.164903i	−0.591323	−	0.806435i	$-0.701394\pi$
$61$	−6.47490	+	1.28794i	−0.829026	+	0.164903i	−0.237702	+	0.971338i	$0.576394\pi$
$62$	13.3528	−	4.68668i	1.69580	−	0.595209i
$63$	17.9379			2.25996
$64$	3.51240	+	7.18770i	0.439050	+	0.898463i
$65$	0.945978			0.117334
$66$	−5.12339	+	1.79826i	−0.630645	+	0.221350i
$67$	6.01983	−	1.19742i	0.735439	−	0.146288i	0.186860	−	0.982387i	$-0.440169\pi$
$67$	6.01983	−	1.19742i	0.735439	−	0.146288i	0.548579	+	0.836099i	$0.315169\pi$
$68$	1.05342	−	9.51296i	0.127746	−	1.15362i
$69$	−0.785572	−	1.17569i	−0.0945718	−	0.141537i
$70$	−5.75795	+	3.40396i	−0.688207	+	0.406851i
$71$	−4.20400	−	1.74136i	−0.498924	−	0.206661i	0.119007	−	0.992893i	$-0.462029\pi$
$71$	−4.20400	−	1.74136i	−0.498924	−	0.206661i	−0.617931	+	0.786232i	$0.712029\pi$
$72$	−17.4091	−	2.90652i	−2.05168	−	0.342537i
$73$	−0.911379	+	0.377506i	−0.106669	+	0.0441837i	−0.435380	−	0.900247i	$-0.643386\pi$
$73$	−0.911379	+	0.377506i	−0.106669	+	0.0441837i	0.328711	+	0.944431i	$0.393386\pi$
$74$	0.608868	+	0.457308i	0.0707795	+	0.0531610i
$75$	−1.35965	+	6.83542i	−0.156999	+	0.789286i
$76$	−10.0547	+	0.867487i	−1.15335	+	0.0995076i
$77$	2.01715	−	3.01887i	0.229875	−	0.344033i
$78$	−2.46780	−	0.136220i	−0.279423	−	0.0154238i
$79$	0.152459	+	0.152459i	0.0171530	+	0.0171530i	0.715631	−	0.698478i	$-0.246139\pi$
$79$	0.152459	+	0.152459i	0.0171530	+	0.0171530i	−0.698478	+	0.715631i	$0.746139\pi$
$80$	6.13976	−	2.37064i	0.686446	−	0.265045i
$81$	7.93360	−	7.93360i	0.881511	−	0.881511i
$82$	−6.72092	+	6.01776i	−0.742201	+	0.664550i
$83$	−5.16472	−	3.45096i	−0.566902	−	0.378792i	0.238840	−	0.971059i	$-0.423233\pi$
$83$	−5.16472	−	3.45096i	−0.566902	−	0.378792i	−0.805741	+	0.592267i	$0.798233\pi$
$84$	15.5111	−	8.05087i	1.69240	−	0.878422i
$85$	−7.72277	−	1.53615i	−0.837652	−	0.166619i
$86$	0.772445	+	5.43391i	0.0832949	+	0.585954i
$87$	6.09641	+	14.7180i	0.653604	+	1.57794i
$88$	−2.44684	+	2.60303i	−0.260834	+	0.277484i
$89$	1.48745	−	3.59102i	0.157669	−	0.380648i	−0.825228	−	0.564799i	$-0.808954\pi$
$89$	1.48745	−	3.59102i	0.157669	−	0.380648i	0.982898	+	0.184151i	$0.0589537\pi$
$90$	−3.61343	+	14.0638i	−0.380889	+	1.48245i
$91$	1.37414	−	0.918171i	0.144049	−	0.0962505i
$92$	−0.815104	−	0.448458i	−0.0849805	−	0.0467549i
$93$	5.93418	+	29.8331i	0.615345	+	3.09355i
$94$	−10.8001	−	5.18832i	−1.11394	−	0.535135i
$95$			8.30263i			0.851832i
$96$	−16.3583	+	5.30023i	−1.66957	+	0.540952i
$97$			13.7742i			1.39856i	0.714849	+	0.699279i	$0.246495\pi$
$97$			13.7742i			1.39856i	−0.714849	+	0.699279i	$0.753505\pi$
$98$	−0.773486	+	1.61010i	−0.0781339	+	0.162645i
$99$	−1.53767	−	7.73041i	−0.154542	−	0.776936i
$100$	1.27784	+	4.40378i	0.127784	+	0.440378i
$101$	3.34129	−	2.23258i	0.332470	−	0.222150i	−0.378118	−	0.925757i	$-0.623429\pi$
$101$	3.34129	−	2.23258i	0.332470	−	0.222150i	0.710589	+	0.703608i	$0.248429\pi$
$102$	19.9254	+	5.11948i	1.97291	+	0.506904i
$103$	3.02140	−	7.29430i	0.297707	−	0.718728i	−0.702270	−	0.711911i	$-0.747830\pi$
$103$	3.02140	−	7.29430i	0.297707	−	0.718728i	0.999977	−	0.00681740i	$-0.00217006\pi$
$104$	−1.48240	+	0.668448i	−0.145362	+	0.0655467i
$105$	−5.50198	−	13.2830i	−0.536938	−	1.29628i
$106$	5.81665	−	0.826852i	0.564963	−	0.0803110i
$107$	−5.40913	−	1.07594i	−0.522920	−	0.104015i	−0.0734296	−	0.997300i	$-0.523394\pi$
$107$	−5.40913	−	1.07594i	−0.522920	−	0.104015i	−0.449490	+	0.893285i	$0.648394\pi$
$108$	5.94624	−	18.7803i	0.572177	−	1.80713i
$109$	−3.62995	−	2.42545i	−0.347686	−	0.232316i	0.369448	−	0.929251i	$-0.379547\pi$
$109$	−3.62995	−	2.42545i	−0.347686	−	0.232316i	−0.717134	+	0.696935i	$0.754547\pi$
$110$	1.96054	+	2.18962i	0.186930	+	0.208772i
$111$	−1.15736	+	1.15736i	−0.109852	+	0.109852i
$112$	6.61775	−	9.40290i	0.625318	−	0.888491i
$113$	−11.6929	−	11.6929i	−1.09998	−	1.09998i	−0.994412	−	0.105567i	$-0.966334\pi$
$113$	−11.6929	−	11.6929i	−1.09998	−	1.09998i	−0.105567	−	0.994412i	$-0.533666\pi$
$114$	1.19557	−	21.6593i	0.111975	−	2.02858i
$115$	−0.425218	+	0.636384i	−0.0396518	+	0.0593431i
$116$	8.02118	+	6.74702i	0.744748	+	0.626445i
$117$	0.699923	−	3.51875i	0.0647079	−	0.325309i
$118$	1.58397	−	2.10893i	0.145816	−	0.194142i
$119$	−12.7092	+	5.26432i	−1.16505	+	0.482580i
$120$	3.18751	+	13.7829i	0.290978	+	1.25820i
$121$	8.68876	+	3.59900i	0.789888	+	0.327182i
$122$	−4.75123	−	8.03691i	−0.430156	−	0.727628i
$123$	−10.7730	−	16.1229i	−0.971366	−	1.45375i
$124$	12.5079	+	15.6229i	1.12324	+	1.40298i
$125$	11.7687	−	2.34095i	1.05263	−	0.209381i
$126$	8.40144	+	23.9364i	0.748459	+	2.13243i
$127$	−21.9517			−1.94790			−0.973949	−	0.226767i	$-0.927185\pi$
$127$	−21.9517			−1.94790			−0.973949	+	0.226767i	$0.927185\pi$
$128$	−7.94623	+	8.05341i	−0.702354	+	0.711828i
$129$	−11.7973			−1.03870
$130$	0.443060	+	1.26232i	0.0388590	+	0.110713i
$131$	−7.05871	+	1.40406i	−0.616722	+	0.122674i	−0.493558	−	0.869713i	$-0.664304\pi$
$131$	−7.05871	+	1.40406i	−0.616722	+	0.122674i	−0.123164	+	0.992386i	$0.539304\pi$
$132$	−4.79920	−	5.99444i	−0.417717	−	0.521749i
$133$	8.05858	+	12.0605i	0.698768	+	1.04578i
$134$	4.41730	+	7.47207i	0.381597	+	0.645488i
$135$	−14.9727	−	6.20189i	−1.28864	−	0.533774i
$136$	13.1875	−	3.04982i	1.13082	−	0.261520i
$137$	10.2318	−	4.23815i	0.874161	−	0.362089i	0.0999315	−	0.994994i	$-0.468138\pi$
$137$	10.2318	−	4.23815i	0.874161	−	0.362089i	0.774229	+	0.632905i	$0.218138\pi$
$138$	1.20092	−	1.59892i	0.102229	−	0.136109i
$139$	−0.752410	+	3.78262i	−0.0638186	+	0.320838i	−0.999486	−	0.0320443i	$-0.989798\pi$
$139$	−0.752410	+	3.78262i	−0.0638186	+	0.320838i	0.935668	+	0.352882i	$0.114798\pi$
$140$	−7.23907	−	6.08916i	−0.611813	−	0.514628i
$141$	14.3081	−	21.4136i	1.20496	−	1.80335i
$142$	0.354676	−	6.42543i	0.0297638	−	0.539210i
$143$	−0.513484	−	0.513484i	−0.0429397	−	0.0429397i
$144$	−4.27528	−	24.5921i	−0.356273	−	2.04934i
$145$	6.09741	−	6.09741i	0.506362	−	0.506362i
$146$	−0.930601	−	1.03934i	−0.0770171	−	0.0860163i
$147$	−3.19239	−	2.13309i	−0.263304	−	0.175934i
$148$	−0.325064	+	1.02666i	−0.0267201	+	0.0843912i
$149$	21.8201	+	4.34028i	1.78757	+	0.355569i	0.974114	−	0.226059i	$-0.0725841\pi$
$149$	21.8201	+	4.34028i	1.78757	+	0.355569i	0.813455	+	0.581628i	$0.197584\pi$
$150$	−9.75803	+	1.38713i	−0.796740	+	0.113259i
$151$	2.99065	+	7.22006i	0.243375	+	0.587560i	0.997614	−	0.0690406i	$-0.0219938\pi$
$151$	2.99065	+	7.22006i	0.243375	+	0.587560i	−0.754239	+	0.656600i	$0.771994\pi$
$152$	−5.86681	−	13.0107i	−0.475861	−	1.05531i
$153$	−11.4281	+	27.5898i	−0.923904	+	2.23050i
$154$	4.97316	+	1.27776i	0.400748	+	0.102965i
$155$	13.6898	−	9.14722i	1.09959	−	0.734723i
$156$	−0.974052	−	3.35684i	−0.0779865	−	0.268762i
$157$	−4.09955	−	20.6098i	−0.327180	−	1.64484i	−0.697970	−	0.716127i	$-0.745913\pi$
$157$	−4.09955	−	20.6098i	−0.327180	−	1.64484i	0.370790	−	0.928717i	$-0.379087\pi$
$158$	−0.132036	+	0.274849i	−0.0105042	+	0.0218658i
$159$			12.6283i			1.00149i
$160$	6.03902	+	7.08261i	0.477427	+	0.559930i
$161$			1.33714i			0.105381i
$162$	14.3024	+	6.87083i	1.12370	+	0.539824i
$163$	3.99966	+	20.1077i	0.313278	+	1.57495i	0.741293	+	0.671182i	$0.234213\pi$
$163$	3.99966	+	20.1077i	0.313278	+	1.57495i	−0.428015	+	0.903772i	$0.640787\pi$
$164$	−11.1780	−	6.14994i	−0.872851	−	0.480229i
$165$	−5.25270	+	3.50974i	−0.408922	+	0.273233i
$166$	2.18601	−	8.50812i	0.169667	−	0.660359i
$167$	5.57052	−	13.4484i	0.431060	−	1.04067i	−0.547886	−	0.836553i	$-0.684567\pi$
$167$	5.57052	−	13.4484i	0.431060	−	1.04067i	0.978946	−	0.204118i	$-0.0654326\pi$
$168$	18.0079	+	16.9274i	1.38934	+	1.30597i
$169$	4.84839	+	11.7051i	0.372953	+	0.900389i
$170$	−1.56720	−	11.0248i	−0.120199	−	0.845562i
$171$	30.8833	+	6.14307i	2.36170	+	0.469772i
$172$	−6.88925	+	3.57579i	−0.525301	+	0.272652i
$173$	−15.4616	−	10.3311i	−1.17552	−	0.785459i	−0.194796	−	0.980844i	$-0.562405\pi$
$173$	−15.4616	−	10.3311i	−1.17552	−	0.785459i	−0.980727	+	0.195384i	$0.937405\pi$
$174$	−16.7845	+	15.0285i	−1.27243	+	1.13930i
$175$	4.66021	−	4.66021i	0.352279	−	0.352279i
$176$	−4.61951	−	2.04591i	−0.348208	−	0.154216i
$177$	4.00874	+	4.00874i	0.301315	+	0.301315i
$178$	5.48854	+	0.302961i	0.411384	+	0.0227079i
$179$	−5.99376	+	8.97030i	−0.447995	+	0.670472i	−0.984891	−	0.173177i	$-0.944597\pi$
$179$	−5.99376	+	8.97030i	−0.447995	+	0.670472i	0.536896	+	0.843648i	$0.319597\pi$
$180$	−20.4591	+	1.76515i	−1.52493	+	0.131567i
$181$	0.698076	−	3.50946i	0.0518876	−	0.260856i	−0.946130	−	0.323786i	$-0.895044\pi$
$181$	0.698076	−	3.50946i	0.0518876	−	0.260856i	0.998018	+	0.0629294i	$0.0200443\pi$
$182$	1.86881	+	1.40362i	0.138525	+	0.104043i
$183$	18.5403	−	7.67963i	1.37054	−	0.567694i
$184$	0.216660	−	1.29772i	0.0159724	−	0.0956691i
$185$	0.818514	+	0.339039i	0.0601783	+	0.0249267i
$186$	−37.0301	+	21.8913i	−2.71518	+	1.60515i
$187$	3.35814	+	5.02581i	0.245572	+	0.367524i
$188$	1.86497	−	16.8417i	0.136017	−	1.22831i
$189$	−27.7691	+	5.52362i	−2.01991	+	0.401784i
$190$	−11.0791	+	3.88864i	−0.803761	+	0.282112i
$191$	−0.722126			−0.0522512			−0.0261256	−	0.999659i	$-0.508317\pi$
$191$	−0.722126			−0.0522512			−0.0261256	+	0.999659i	$0.508317\pi$
$192$	−14.7343	−	19.3462i	−1.06335	−	1.39619i
$193$	−5.30778			−0.382063			−0.191031	−	0.981584i	$-0.561183\pi$
$193$	−5.30778			−0.382063			−0.191031	+	0.981584i	$0.561183\pi$
$194$	−18.3804	+	6.45131i	−1.31963	+	0.463177i
$195$	−2.82031	+	0.560994i	−0.201966	+	0.0401736i
$196$	−2.51080	−	0.278034i	−0.179343	−	0.0198595i
$197$	8.28629	+	12.4013i	0.590373	+	0.883556i	0.999583	−	0.0288843i	$-0.00919543\pi$
$197$	8.28629	+	12.4013i	0.590373	+	0.883556i	−0.409209	+	0.912441i	$0.634195\pi$
$198$	9.59531	−	5.67251i	0.681909	−	0.403128i
$199$	−0.443861	−	0.183853i	−0.0314644	−	0.0130330i	0.366896	−	0.930262i	$-0.380421\pi$
$199$	−0.443861	−	0.183853i	−0.0314644	−	0.0130330i	−0.398360	+	0.917229i	$0.630421\pi$
$200$	−5.27793	+	3.76772i	−0.373206	+	0.266418i
$201$	−17.2372	+	7.13989i	−1.21582	+	0.503609i
$202$	4.54409	+	3.41297i	0.319721	+	0.240136i
$203$	2.93900	−	14.7753i	0.206277	−	1.03703i
$204$	2.50085	+	28.9863i	0.175094	+	2.02945i
$205$	−5.83124	+	8.72707i	−0.407272	+	0.609525i
$206$	11.1487	+	0.615393i	0.776764	+	0.0428765i
$207$	2.05254	+	2.05254i	0.142661	+	0.142661i
$208$	−1.58628	−	1.66505i	−0.109989	−	0.115451i
$209$	4.50673	−	4.50673i	0.311737	−	0.311737i
$210$	15.1479	−	13.5631i	1.04531	−	0.935943i
$211$	−12.2014	−	8.15273i	−0.839980	−	0.561257i	0.0594948	−	0.998229i	$-0.481051\pi$
$211$	−12.2014	−	8.15273i	−0.839980	−	0.561257i	−0.899475	+	0.436972i	$0.856051\pi$
$212$	3.82766	+	7.37450i	0.262884	+	0.506483i
$213$	13.5664	+	2.69852i	0.929551	+	0.184899i
$214$	−1.09769	−	7.72190i	−0.0750365	−	0.527858i
$215$	2.44370	+	5.89962i	0.166659	+	0.402351i
$216$	27.8455	−	0.861281i	1.89465	−	0.0586028i
$217$	11.0076	−	26.5748i	0.747246	−	1.80401i
$218$	1.53641	−	5.97982i	0.104059	−	0.405004i
$219$	2.49328	−	1.66596i	0.168480	−	0.112575i
$220$	−2.00360	+	3.64168i	−0.135083	+	0.245522i
$221$	0.536762	+	2.69848i	0.0361065	+	0.181520i
$222$	−2.08646	−	1.00233i	−0.140034	−	0.0672718i
$223$		−	20.5439i		−	1.37572i	−0.725843	−	0.687860i	$-0.758550\pi$
$223$		−	20.5439i		−	1.37572i	0.725843	−	0.687860i	$-0.241450\pi$
$224$	15.6468	+	4.42679i	1.04544	+	0.295777i
$225$		−	14.3071i		−	0.953804i
$226$	10.1266	−	21.0796i	0.673610	−	1.40220i
$227$	3.83215	+	19.2655i	0.254348	+	1.27870i	0.870931	+	0.491406i	$0.163517\pi$
$227$	3.83215	+	19.2655i	0.254348	+	1.27870i	−0.616582	+	0.787290i	$0.711483\pi$
$228$	29.4623	−	8.54903i	1.95119	−	0.566174i
$229$	−18.1422	+	12.1223i	−1.19887	+	0.801061i	−0.984447	−	0.175680i	$-0.943788\pi$
$229$	−18.1422	+	12.1223i	−1.19887	+	0.801061i	−0.214425	+	0.976740i	$0.568788\pi$
$230$	−1.04835	−	0.269355i	−0.0691261	−	0.0177607i
$231$	−4.22357	+	10.1966i	−0.277891	+	0.670887i
$232$	−5.24644	+	13.8636i	−0.344446	+	0.910187i
$233$	−1.49754	−	3.61539i	−0.0981074	−	0.236852i	0.867204	−	0.497953i	$-0.165915\pi$
$233$	−1.49754	−	3.61539i	−0.0981074	−	0.236852i	−0.965312	+	0.261100i	$0.915915\pi$
$234$	5.02326	−	0.714070i	0.328381	−	0.0466802i
$235$	−13.6724	−	2.71960i	−0.891887	−	0.177407i
$236$	3.55604	+	1.12592i	0.231478	+	0.0732910i
$237$	−0.544950	−	0.364124i	−0.0353983	−	0.0236524i
$238$	−12.9772	−	14.4936i	−0.841190	−	0.939481i
$239$	4.87803	−	4.87803i	0.315534	−	0.315534i	−0.531515	−	0.847049i	$-0.678377\pi$
$239$	4.87803	−	4.87803i	0.315534	−	0.315534i	0.847049	+	0.531515i	$0.178377\pi$
$240$	−16.8990	+	10.7088i	−1.09083	+	0.691250i
$241$	1.70539	+	1.70539i	0.109854	+	0.109854i	0.759897	−	0.650043i	$-0.225249\pi$
$241$	1.70539	+	1.70539i	0.109854	+	0.109854i	−0.650043	+	0.759897i	$0.725249\pi$
$242$	−0.733039	+	13.2800i	−0.0471215	+	0.853669i
$243$	−2.53170	+	3.78895i	−0.162409	+	0.243062i
$244$	8.49920	−	10.1042i	0.544106	−	0.646858i
$245$	−0.405444	+	2.03831i	−0.0259029	+	0.130223i
$246$	16.4688	−	21.9269i	1.05001	−	1.39801i
$247$	2.68027	−	1.11020i	0.170541	−	0.0706405i
$248$	−14.9891	+	24.0077i	−0.951808	+	1.52449i
$249$	17.4444	+	7.22572i	1.10550	+	0.457912i
$250$	8.63581	+	14.6079i	0.546177	+	0.923882i
$251$	−0.380597	−	0.569604i	−0.0240231	−	0.0359531i	0.819264	−	0.573417i	$-0.194382\pi$
$251$	−0.380597	−	0.569604i	−0.0240231	−	0.0359531i	−0.843287	+	0.537464i	$0.819382\pi$
$252$	−28.0060	+	22.4218i	−1.76421	+	1.41244i
$253$	0.576245	−	0.114622i	0.0362282	−	0.00720625i
$254$	−10.2813	−	29.2925i	−0.645109	−	1.83797i
$255$	23.9354			1.49889
$256$	−14.4682	−	6.83157i	−0.904264	−	0.426973i
$257$	24.3404			1.51831			0.759156	−	0.650908i	$-0.225612\pi$
$257$	24.3404			1.51831			0.759156	+	0.650908i	$0.225612\pi$
$258$	−5.52542	−	15.7424i	−0.343997	−	0.980079i
$259$	1.51806	−	0.301960i	0.0943275	−	0.0187629i
$260$	−1.47693	+	1.18244i	−0.0915953	+	0.0733321i
$261$	−18.1691	−	27.1919i	−1.12464	−	1.68314i
$262$	−5.17963	−	8.76157i	−0.319998	−	0.541291i
$263$	9.60085	+	3.97680i	0.592014	+	0.245220i	0.658517	−	0.752566i	$-0.271184\pi$
$263$	9.60085	+	3.97680i	0.592014	+	0.245220i	−0.0665030	+	0.997786i	$0.521184\pi$
$264$	5.75124	−	9.21165i	0.353964	−	0.566938i
$265$	6.31516	−	2.61583i	0.387937	−	0.160689i
$266$	−12.3193	+	16.4021i	−0.755344	+	1.00568i
$267$	−2.30505	+	11.5883i	−0.141067	+	0.709190i
$268$	−7.90186	+	9.39411i	−0.482683	+	0.573836i
$269$	−17.3303	+	25.9367i	−1.05665	+	1.58139i	−0.271136	+	0.962541i	$0.587399\pi$
$269$	−17.3303	+	25.9367i	−1.05665	+	1.58139i	−0.785513	+	0.618845i	$0.787601\pi$
$270$	1.26319	−	22.8844i	0.0768754	−	1.39270i
$271$	11.8443	+	11.8443i	0.719491	+	0.719491i	0.968501	−	0.249010i	$-0.0801053\pi$
$271$	11.8443	+	11.8443i	0.719491	+	0.719491i	−0.249010	+	0.968501i	$0.580105\pi$
$272$	10.2462	+	16.1691i	0.621269	+	0.980394i
$273$	−3.55231	+	3.55231i	−0.214996	+	0.214996i
$274$	10.4476	+	11.6684i	0.631162	+	0.704912i
$275$	−2.40782	−	1.60885i	−0.145197	−	0.0970176i
$276$	2.69607	+	0.853635i	0.162285	+	0.0513828i
$277$	−25.5130	−	5.07485i	−1.53293	−	0.304918i	−0.644741	−	0.764401i	$-0.723035\pi$
$277$	−25.5130	−	5.07485i	−1.53293	−	0.304918i	−0.888187	+	0.459483i	$0.848035\pi$
$278$	−5.39995	+	0.767617i	−0.323867	+	0.0460386i
$279$	−23.8959	−	57.6898i	−1.43061	−	3.45380i
$280$	4.73489	−	12.5118i	0.282964	−	0.747722i
$281$	−9.37710	+	22.6383i	−0.559391	+	1.35049i	0.350858	+	0.936429i	$0.385890\pi$
$281$	−9.37710	+	22.6383i	−0.559391	+	1.35049i	−0.910249	+	0.414061i	$0.864110\pi$
$282$	35.2759	+	9.06351i	2.10065	+	0.539724i
$283$	−19.3155	+	12.9062i	−1.14819	+	0.767195i	−0.975979	−	0.217865i	$-0.930091\pi$
$283$	−19.3155	+	12.9062i	−1.14819	+	0.767195i	−0.172210	+	0.985060i	$0.555091\pi$
$284$	8.74024	−	2.53615i	0.518638	−	0.150493i
$285$	−4.92372	−	24.7532i	−0.291656	−	1.46625i
$286$	0.444699	−	0.925692i	0.0262956	−	0.0547373i
$287$			18.3369i			1.08239i
$288$	30.8134	−	17.2230i	1.81570	−	1.01487i
$289$		−	5.90150i		−	0.347147i
$290$	10.9922	+	5.28061i	0.645484	+	0.310088i
$291$	−8.16852	−	41.0659i	−0.478847	−	2.40733i
$292$	0.951041	−	1.72859i	0.0556555	−	0.101158i
$293$	23.5455	−	15.7326i	1.37554	−	0.919109i	0.375573	−	0.926793i	$-0.377446\pi$
$293$	23.5455	−	15.7326i	1.37554	−	0.919109i	0.999970	+	0.00768446i	$0.00244606\pi$
$294$	1.35121	−	5.25900i	0.0788040	−	0.306711i
$295$	1.17433	−	2.83507i	0.0683719	−	0.165064i
$296$	−1.52223	+	0.0470838i	−0.0884779	+	0.00273669i
$297$	4.76086	+	11.4937i	0.276253	+	0.666934i
$298$	4.42800	+	31.1496i	0.256507	+	1.80445i
$299$	0.262297	+	0.0521741i	0.0151690	+	0.00301731i
$300$	−6.42129	−	12.3715i	−0.370733	−	0.714268i
$301$	9.27596	+	6.19800i	0.534657	+	0.357247i
$302$	−8.23377	+	7.37234i	−0.473800	+	0.424230i
$303$	−8.63761	+	8.63761i	−0.496218	+	0.496218i
$304$	14.6138	−	13.9224i	0.838158	−	0.798507i
$305$	−7.68088	−	7.68088i	−0.439806	−	0.439806i
$306$	−42.1684	−	2.32765i	−2.41061	−	0.133063i
$307$	−6.01712	+	9.00525i	−0.343415	+	0.513957i	−0.962469	−	0.271392i	$-0.912516\pi$
$307$	−6.01712	+	9.00525i	−0.343415	+	0.513957i	0.619054	+	0.785348i	$0.287516\pi$
$308$	0.624184	+	7.23466i	0.0355662	+	0.412233i
$309$	−4.68215	+	23.5388i	−0.266358	+	1.33907i
$310$	18.6179	+	13.9835i	1.05742	+	0.794210i
$311$	−6.91332	+	2.86359i	−0.392018	+	0.162379i	−0.569981	−	0.821658i	$-0.693049\pi$
$311$	−6.91332	+	2.86359i	−0.392018	+	0.162379i	0.177963	+	0.984037i	$0.443049\pi$
$312$	4.02318	−	2.87200i	0.227768	−	0.162595i
$313$	−20.9463	−	8.67625i	−1.18396	−	0.490411i	−0.298174	−	0.954511i	$-0.596378\pi$
$313$	−20.9463	−	8.67625i	−1.18396	−	0.490411i	−0.885783	+	0.464101i	$0.846378\pi$
$314$	25.5818	−	15.1233i	1.44366	−	0.853459i
$315$	16.3975	+	24.5406i	0.923894	+	1.38271i
$316$	−0.428600	−	0.0474611i	−0.0241106	−	0.00266989i
$317$	−12.9479	+	2.57551i	−0.727229	+	0.144655i	−0.544802	−	0.838565i	$-0.683395\pi$
$317$	−12.9479	+	2.57551i	−0.727229	+	0.144655i	−0.182427	+	0.983219i	$0.558395\pi$
$318$	−16.8512	+	5.91460i	−0.944969	+	0.331674i
$319$	−6.61944			−0.370617
$320$	−6.62262	+	11.3757i	−0.370216	+	0.635923i
$321$	16.7647			0.935712
$322$	−1.78428	+	0.626265i	−0.0994343	+	0.0349004i
$323$	−23.6840	+	4.71104i	−1.31781	+	0.262129i
$324$	−2.46975	+	22.3033i	−0.137209	+	1.23907i
$325$	−0.732323	−	1.09600i	−0.0406220	−	0.0607951i
$326$	−24.9585	+	14.7548i	−1.38232	+	0.817195i
$327$	12.2606	+	5.07850i	0.678012	+	0.280842i
$328$	2.97117	−	17.7963i	0.164056	−	0.982637i
$329$	−22.5003	+	9.31994i	−1.24048	+	0.513825i
$330$	−7.14359	−	5.36540i	−0.393242	−	0.295356i
$331$	0.994900	−	5.00170i	0.0546846	−	0.274918i	−0.943763	−	0.330624i	$-0.892741\pi$
$331$	0.994900	−	5.00170i	0.0546846	−	0.274918i	0.998447	+	0.0557056i	$0.0177408\pi$
$332$	12.3771	−	1.06786i	0.679283	−	0.0586064i
$333$	1.86674	−	2.79377i	0.102297	−	0.153098i
$334$	20.5547	+	1.13459i	1.12470	+	0.0620822i
$335$	7.14106	+	7.14106i	0.390158	+	0.390158i
$336$	−14.1537	+	31.9580i	−0.772149	+	1.74345i
$337$	−9.51763	+	9.51763i	−0.518459	+	0.518459i	−0.917105	−	0.398646i	$-0.869480\pi$
$337$	−9.51763	+	9.51763i	−0.518459	+	0.518459i	0.398646	+	0.917105i	$0.369480\pi$
$338$	−13.3485	+	11.9519i	−0.726061	+	0.650099i
$339$	41.7952	+	27.9267i	2.27000	+	1.51677i
$340$	13.9775	−	7.25487i	0.758036	−	0.393451i
$341$	−12.3961	−	2.46574i	−0.671286	−	0.133527i
$342$	6.26723	+	44.0880i	0.338893	+	2.38401i
$343$	−6.31088	−	15.2358i	−0.340755	−	0.822656i
$344$	−7.99822	−	7.51829i	−0.431235	−	0.405359i
$345$	0.890336	−	2.14946i	0.0479341	−	0.115723i
$346$	6.54425	−	25.4707i	0.351821	−	1.36931i
$347$	24.8873	−	16.6292i	1.33602	−	0.892701i	0.337210	−	0.941430i	$-0.390517\pi$
$347$	24.8873	−	16.6292i	1.33602	−	0.892701i	0.998812	+	0.0487284i	$0.0155169\pi$
$348$	−27.9153	−	15.3585i	−1.49642	−	0.823305i
$349$	2.77238	+	13.9377i	0.148402	+	0.746067i	0.981276	+	0.192605i	$0.0616936\pi$
$349$	2.77238	+	13.9377i	0.148402	+	0.746067i	−0.832874	+	0.553462i	$0.813306\pi$
$350$	8.40128	+	4.03594i	0.449067	+	0.215730i
$351$			5.66280i			0.302258i
$352$	0.566468	−	7.12252i	0.0301928	−	0.379632i
$353$		−	22.9803i		−	1.22312i	−0.791199	−	0.611558i	$-0.790543\pi$
$353$		−	22.9803i		−	1.22312i	0.791199	−	0.611558i	$-0.209457\pi$
$354$	−3.47174	+	7.22683i	−0.184521	+	0.384102i
$355$	−1.46066	−	7.34326i	−0.0775240	−	0.389740i
$356$	2.16635	+	7.46584i	0.114817	+	0.395689i
$357$	34.7689	−	23.2318i	1.84016	−	1.22956i
$358$	−14.7773	−	3.79676i	−0.781003	−	0.200665i
$359$	2.63107	−	6.35196i	0.138862	−	0.335244i	−0.839115	−	0.543954i	$-0.816927\pi$
$359$	2.63107	−	6.35196i	0.138862	−	0.335244i	0.977978	+	0.208710i	$0.0669266\pi$
$360$	−11.9377	−	26.4741i	−0.629173	−	1.39531i
$361$	2.47302	+	5.97039i	0.130159	+	0.314231i
$362$	5.01000	−	0.712185i	0.263320	−	0.0374316i
$363$	−28.0387	−	5.57725i	−1.47165	−	0.292730i
$364$	−0.997722	+	3.15115i	−0.0522948	+	0.165165i
$365$	−1.34958	−	0.901757i	−0.0706400	−	0.0472001i
$366$	18.9313	+	21.1434i	0.989554	+	1.10518i
$367$	−2.41091	+	2.41091i	−0.125848	+	0.125848i	−0.767226	−	0.641377i	$-0.778363\pi$
$367$	−2.41091	+	2.41091i	−0.125848	+	0.125848i	0.641377	+	0.767226i	$0.278363\pi$
$368$	1.83316	−	0.318691i	0.0955600	−	0.0166129i
$369$	28.1476	+	28.1476i	1.46530	+	1.46530i
$370$	−0.0690550	+	1.25102i	−0.00359000	+	0.0650375i
$371$	6.63456	−	9.92931i	0.344449	−	0.515504i
$372$	−46.5554	−	39.1601i	−2.41378	−	2.03036i
$373$	2.78301	−	13.9911i	0.144099	−	0.724433i	−0.839400	−	0.543515i	$-0.817093\pi$
$373$	2.78301	−	13.9911i	0.144099	−	0.724433i	0.983498	−	0.180918i	$-0.0579068\pi$
$374$	−5.13364	+	6.83502i	−0.265454	+	0.353431i
$375$	−33.6987	+	13.9585i	−1.74019	+	0.720812i
$376$	23.3471	−	5.39940i	1.20404	−	0.278453i
$377$	−2.78370	−	1.15305i	−0.143368	−	0.0593849i
$378$	−20.3768	−	34.4682i	−1.04807	−	1.77285i
$379$	14.2902	+	21.3867i	0.734036	+	1.09856i	0.991223	+	0.132201i	$0.0422044\pi$
$379$	14.2902	+	21.3867i	0.734036	+	1.09856i	−0.257187	+	0.966362i	$0.582796\pi$
$380$	−10.3780	−	12.9627i	−0.532382	−	0.664972i
$381$	65.4461	−	13.0180i	3.35290	−	0.666934i
$382$	−0.338217	−	0.963608i	−0.0173047	−	0.0493025i
$383$	21.5847			1.10293			0.551463	−	0.834199i	$-0.314070\pi$
$383$	21.5847			1.10293			0.551463	+	0.834199i	$0.314070\pi$
$384$	18.9147	−	28.7225i	0.965237	−	1.46574i
$385$	5.97401			0.304464
$386$	−2.48597	−	7.08273i	−0.126532	−	0.360502i
$387$	23.7529	−	4.72474i	1.20743	−	0.240172i
$388$	−17.2173	−	21.5053i	−0.874077	−	1.09177i
$389$	3.94394	+	5.90253i	0.199966	+	0.299270i	0.917877	−	0.396864i	$-0.129902\pi$
$389$	3.94394	+	5.90253i	0.199966	+	0.299270i	−0.717911	+	0.696135i	$0.754902\pi$
$390$	−2.06952	−	3.50068i	−0.104794	−	0.177264i
$391$	−2.05662	−	0.851878i	−0.104007	−	0.0430813i
$392$	−0.804954	−	3.48064i	−0.0406563	−	0.175799i
$393$	20.2119	−	8.37206i	1.01956	−	0.422315i
$394$	−12.6674	+	16.8656i	−0.638173	+	0.849675i
$395$	−0.0692105	+	0.347944i	−0.00348236	+	0.0175070i
$396$	12.0635	+	10.1472i	0.606214	+	0.509918i
$397$	−7.40790	+	11.0867i	−0.371792	+	0.556426i	−0.969439	−	0.245334i	$-0.921102\pi$
$397$	−7.40790	+	11.0867i	−0.371792	+	0.556426i	0.597647	+	0.801759i	$0.296102\pi$
$398$	0.0374469	−	0.678400i	0.00187704	−	0.0340051i
$399$	−31.1778	−	31.1778i	−1.56084	−	1.56084i
$400$	−7.49965	−	5.27824i	−0.374983	−	0.263912i
$401$	−8.50260	+	8.50260i	−0.424600	+	0.424600i	−0.886784	−	0.462184i	$-0.847066\pi$
$401$	−8.50260	+	8.50260i	−0.424600	+	0.424600i	0.462184	+	0.886784i	$0.347066\pi$
$402$	−17.6008	−	19.6574i	−0.877846	−	0.980421i
$403$	−4.78347	−	3.19622i	−0.238282	−	0.159215i
$404$	−2.42601	+	7.66217i	−0.120698	+	0.381207i
$405$	18.1061	+	3.60154i	0.899702	+	0.178962i
$406$	21.0928	−	2.99840i	1.04682	−	0.148808i
$407$	−0.260262	−	0.628329i	−0.0129007	−	0.0311451i
$408$	−37.5082	+	16.9132i	−1.85693	+	0.837330i
$409$	10.8420	−	26.1750i	0.536104	−	1.29427i	−0.391320	−	0.920255i	$-0.627981\pi$
$409$	10.8420	−	26.1750i	0.536104	−	1.29427i	0.927423	−	0.374014i	$-0.122019\pi$
$410$	−14.3766	−	3.69381i	−0.710009	−	0.182424i
$411$	−27.9914	+	18.7032i	−1.38071	+	0.922563i
$412$	4.40043	+	15.1650i	0.216793	+	0.747128i
$413$	−1.04590	−	5.25807i	−0.0514651	−	0.258733i
$414$	−1.77759	+	3.70025i	−0.0873636	+	0.181857i
$415$		−	10.2204i		−	0.501699i
$416$	1.47890	−	2.89659i	0.0725089	−	0.142017i
$417$		−	11.7236i		−	0.574106i
$418$	8.12459	+	3.90302i	0.397387	+	0.190903i
$419$	−4.06419	−	20.4320i	−0.198549	−	0.998171i	−0.943581	−	0.331142i	$-0.892566\pi$
$419$	−4.06419	−	20.4320i	−0.198549	−	0.998171i	0.745032	−	0.667028i	$-0.232434\pi$
$420$	25.1934	+	13.8610i	1.22931	+	0.676348i
$421$	−18.4939	+	12.3572i	−0.901337	+	0.602254i	−0.917553	−	0.397614i	$-0.869838\pi$
$421$	−18.4939	+	12.3572i	−0.901337	+	0.602254i	0.0162157	+	0.999869i	$0.494838\pi$
$422$	5.16436	−	20.1001i	0.251397	−	0.978456i
$423$	−20.2322	+	48.8449i	−0.983723	+	2.37492i
$424$	−8.04784	+	8.56158i	−0.390838	+	0.415787i
$425$	4.19876	+	10.1367i	0.203670	+	0.491703i
$426$	2.75306	+	19.3669i	0.133386	+	0.938329i
$427$	−18.6125	−	3.70225i	−0.900720	−	0.179164i
$428$	9.79002	−	5.08141i	0.473219	−	0.245619i
$429$	1.83540	+	1.22637i	0.0886137	+	0.0592098i
$430$	−6.72795	+	6.02405i	−0.324450	+	0.290505i
$431$	9.16945	−	9.16945i	0.441677	−	0.441677i	−0.450898	−	0.892575i	$-0.648896\pi$
$431$	9.16945	−	9.16945i	0.441677	−	0.441677i	0.892575	+	0.450898i	$0.148896\pi$
$432$	14.1911	+	36.7538i	0.682769	+	1.76832i
$433$	9.06306	+	9.06306i	0.435543	+	0.435543i	0.890509	−	0.454966i	$-0.150349\pi$
$433$	9.06306	+	9.06306i	0.435543	+	0.435543i	−0.454966	+	0.890509i	$0.650349\pi$
$434$	40.6171	+	2.24201i	1.94968	+	0.107620i
$435$	−14.5627	+	21.7946i	−0.698226	+	1.04497i
$436$	8.69909	−	0.750530i	0.416611	−	0.0359439i
$437$	−0.457921	+	2.30212i	−0.0219053	+	0.110125i
$438$	3.39082	+	2.54678i	0.162020	+	0.121690i
$439$	37.3964	−	15.4901i	1.78483	−	0.739301i	0.793395	−	0.608707i	$-0.208312\pi$
$439$	37.3964	−	15.4901i	1.78483	−	0.739301i	0.991436	−	0.130594i	$-0.0416884\pi$
$440$	−5.79789	−	0.967984i	−0.276404	−	0.0461468i
$441$	7.28190	+	3.01626i	0.346757	+	0.143631i
$442$	−3.34947	+	1.98013i	−0.159318	+	0.0941850i
$443$	−0.953921	−	1.42764i	−0.0453222	−	0.0678294i	0.808117	−	0.589023i	$-0.200487\pi$
$443$	−0.953921	−	1.42764i	−0.0453222	−	0.0678294i	−0.853439	+	0.521193i	$0.825487\pi$
$444$	0.360291	−	3.25363i	0.0170987	−	0.154411i
$445$	6.27255	−	1.24769i	0.297347	−	0.0591460i
$446$	27.4139	−	9.62198i	1.29808	−	0.455614i
$447$	−67.6275			−3.19867
$448$	1.42123	+	22.9525i	0.0671470	+	1.08440i
$449$	−24.6119			−1.16151			−0.580754	−	0.814079i	$-0.697242\pi$
$449$	−24.6119			−1.16151			−0.580754	+	0.814079i	$0.697242\pi$
$450$	19.0914	−	6.70089i	0.899978	−	0.315883i
$451$	7.90236	−	1.57188i	0.372108	−	0.0740168i
$452$	32.8717	+	3.64005i	1.54615	+	0.171214i
$453$	−13.1979	−	19.7521i	−0.620093	−	0.928034i
$454$	−23.9131	+	14.1369i	−1.12230	+	0.663476i
$455$	2.51227	+	1.04062i	0.117777	+	0.0487849i
$456$	25.2069	+	35.3105i	1.18042	+	1.65357i
$457$	0.962960	−	0.398871i	0.0450454	−	0.0186584i	−0.360047	−	0.932934i	$-0.617239\pi$
$457$	0.962960	−	0.398871i	0.0450454	−	0.0186584i	0.405092	+	0.914276i	$0.367239\pi$
$458$	−24.6731	−	18.5315i	−1.15290	−	0.865919i
$459$	9.19571	−	46.2300i	0.429219	−	2.15783i
$460$	−0.131579	−	1.52508i	−0.00613491	−	0.0711072i
$461$	−7.72794	+	11.5657i	−0.359926	+	0.538667i	−0.966602	−	0.256282i	$-0.917502\pi$
$461$	−7.72794	+	11.5657i	−0.359926	+	0.538667i	0.606676	+	0.794949i	$0.292502\pi$
$462$	−15.5846	−	0.860250i	−0.725059	−	0.0400224i
$463$	8.29596	+	8.29596i	0.385546	+	0.385546i	0.873095	−	0.487549i	$-0.162109\pi$
$463$	8.29596	+	8.29596i	0.385546	+	0.385546i	−0.487549	+	0.873095i	$0.662109\pi$
$464$	−20.9568	−	0.507716i	−0.972896	−	0.0235701i
$465$	−35.3897	+	35.3897i	−1.64116	+	1.64116i
$466$	4.12300	−	3.69164i	0.190994	−	0.171012i
$467$	−0.240041	−	0.160391i	−0.0111078	−	0.00742199i	0.550004	−	0.835162i	$-0.314626\pi$
$467$	−0.240041	−	0.160391i	−0.0111078	−	0.00742199i	−0.561112	+	0.827740i	$0.689626\pi$
$468$	3.30556	+	6.36861i	0.152800	+	0.294389i
$469$	17.3043	+	3.44205i	0.799040	+	0.158939i
$470$	−2.77457	−	19.5182i	−0.127981	−	0.900309i
$471$	24.4445	+	59.0143i	1.12634	+	2.71924i
$472$	0.163083	+	5.27253i	0.00750651	+	0.242688i
$473$	1.87590	−	4.52882i	0.0862539	−	0.208235i
$474$	0.230655	−	0.897726i	0.0105943	−	0.0412339i
$475$	9.61934	−	6.42743i	0.441365	−	0.294911i
$476$	13.2623	−	24.1052i	0.607876	−	1.10486i
$477$	−5.05753	−	25.4259i	−0.231568	−	1.16417i
$478$	8.79395	+	4.22458i	0.402226	+	0.193228i
$479$		−	27.3994i		−	1.25191i	−0.779860	−	0.625954i	$-0.784710\pi$
$479$		−	27.3994i		−	1.25191i	0.779860	−	0.625954i	$-0.215290\pi$
$480$	−22.2047	−	17.5345i	−1.01350	−	0.800338i
$481$		−	0.309569i		−	0.0141151i
$482$	−1.47694	+	3.07443i	−0.0672730	+	0.140036i
$483$	−0.792964	−	3.98650i	−0.0360811	−	0.181392i
$484$	−18.0642	+	5.24167i	−0.821099	+	0.238258i
$485$	−18.8443	+	12.5913i	−0.855675	+	0.571744i
$486$	−6.24175	−	1.60371i	−0.283132	−	0.0727456i
$487$	−11.7477	+	28.3614i	−0.532338	+	1.28518i	0.397633	+	0.917544i	$0.369832\pi$
$487$	−11.7477	+	28.3614i	−0.532338	+	1.28518i	−0.929971	+	0.367633i	$0.880168\pi$
$488$	17.4639	+	6.60893i	0.790552	+	0.299172i
$489$	−23.8489	−	57.5764i	−1.07849	−	2.60369i
$490$	−2.90982	+	0.413639i	−0.131452	+	0.0186863i
$491$	1.43618	+	0.285675i	0.0648141	+	0.0128923i	0.227391	−	0.973804i	$-0.426981\pi$
$491$	1.43618	+	0.285675i	0.0648141	+	0.0128923i	−0.162577	+	0.986696i	$0.551981\pi$
$492$	36.9727	+	11.7063i	1.66686	+	0.527763i
$493$	20.8531	+	13.9336i	0.939178	+	0.627539i
$494$	2.73680	+	3.05658i	0.123134	+	0.137522i
$495$	9.17024	−	9.17024i	0.412172	−	0.412172i
$496$	−39.0564	−	8.75720i	−1.75368	−	0.393210i
$497$	−9.24919	−	9.24919i	−0.414883	−	0.414883i
$498$	−1.47172	+	26.6622i	−0.0659495	+	1.19476i
$499$	8.33594	−	12.4756i	0.373168	−	0.558485i	−0.596592	−	0.802544i	$-0.703479\pi$
$499$	8.33594	−	12.4756i	0.373168	−	0.558485i	0.969760	+	0.244059i	$0.0784791\pi$
$500$	−15.4481	+	18.3654i	−0.690861	+	0.821328i
$501$	−8.63244	+	43.3982i	−0.385669	+	1.93889i
$502$	0.581825	−	0.774652i	0.0259681	−	0.0345744i
$503$	−9.56425	+	3.96164i	−0.426449	+	0.176641i	−0.585577	−	0.810617i	$-0.699132\pi$
$503$	−9.56425	+	3.96164i	−0.426449	+	0.176641i	0.159128	+	0.987258i	$0.449132\pi$
$504$	−43.0367	−	26.8698i	−1.91701	−	1.19687i
$505$	6.10871	+	2.53031i	0.271834	+	0.112597i
$506$	0.422844	+	0.715260i	0.0187977	+	0.0317972i
$507$	−21.3963	−	32.0218i	−0.950242	−	1.42214i
$508$	34.2726	−	27.4390i	1.52060	−	1.21741i
$509$	−1.27790	+	0.254190i	−0.0566419	+	0.0112668i	−0.223330	−	0.974743i	$-0.571693\pi$
$509$	−1.27790	+	0.254190i	−0.0566419	+	0.0112668i	0.166688	+	0.986010i	$0.446693\pi$
$510$	11.2104	+	31.9395i	0.496406	+	1.41430i
$511$	−2.83566			−0.125442
$512$	2.33971	−	22.5061i	0.103402	−	0.994640i
$513$	−49.7011			−2.19436
$514$	11.4001	+	32.4800i	0.502838	+	1.43263i
$515$	12.7412	−	2.53437i	0.561443	−	0.111678i
$516$	18.4188	−	14.7463i	0.810844	−	0.649169i
$517$	5.94524	+	8.89768i	0.261471	+	0.391320i
$518$	1.11394	+	1.88428i	0.0489436	+	0.0827904i
$519$	52.2233	+	21.6316i	2.29235	+	0.949522i
$520$	−2.26960	−	1.41701i	−0.0995284	−	0.0621400i
$521$	−30.4733	+	12.6225i	−1.33506	+	0.553001i	−0.932095	−	0.362214i	$-0.882021\pi$
$521$	−30.4733	+	12.6225i	−1.33506	+	0.553001i	−0.402967	+	0.915215i	$0.632021\pi$
$522$	27.7753	−	36.9806i	1.21569	−	1.61860i
$523$	0.709853	−	3.56867i	0.0310397	−	0.156047i	−0.962157	−	0.272496i	$-0.912151\pi$
$523$	0.709853	−	3.56867i	0.0310397	−	0.156047i	0.993197	+	0.116448i	$0.0371510\pi$
$524$	9.26554	−	11.0153i	0.404767	−	0.481206i
$525$	−11.1302	+	16.6574i	−0.485760	+	0.726991i
$526$	−0.809988	+	14.6740i	−0.0353172	+	0.639817i
$527$	33.8610	+	33.8610i	1.47501	+	1.47501i
$528$	14.9857	+	3.36010i	0.652170	+	0.146229i
$529$	16.1105	−	16.1105i	0.700455	−	0.700455i
$530$	6.44835	+	7.20183i	0.280099	+	0.312827i
$531$	−9.67673	−	6.46579i	−0.419934	−	0.280591i
$532$	−27.6569	−	8.75678i	−1.19908	−	0.379655i
$533$	3.59702	+	0.715492i	0.155804	+	0.0309914i
$534$	−16.5430	+	2.35164i	−0.715887	+	0.101765i
$535$	−3.47264	−	8.38370i	−0.150135	−	0.362459i
$536$	−16.2365	−	6.14444i	−0.701309	−	0.265399i
$537$	12.5499	−	30.2982i	0.541570	−	1.30747i
$538$	−42.7269	−	10.9779i	−1.84209	−	0.473292i
$539$	1.32649	−	0.886330i	0.0571358	−	0.0381769i
$540$	31.1287	−	9.03257i	1.33956	−	0.388700i
$541$	0.728776	+	3.66380i	0.0313325	+	0.157519i	0.993284	−	0.115701i	$-0.0369113\pi$
$541$	0.728776	+	3.66380i	0.0313325	+	0.157519i	−0.961952	+	0.273220i	$0.911911\pi$
$542$	−10.2577	+	21.3525i	−0.440605	+	0.917170i
$543$			10.8770i			0.466776i
$544$	−16.7771	+	21.2456i	−0.719314	+	0.910898i
$545$		−	7.18326i		−	0.307697i
$546$	−6.40399	−	3.07645i	−0.274066	−	0.131660i
$547$	2.21811	+	11.1512i	0.0948394	+	0.476790i	0.998791	+	0.0491555i	$0.0156530\pi$
$547$	2.21811	+	11.1512i	0.0948394	+	0.476790i	−0.903952	+	0.427635i	$0.859347\pi$
$548$	−10.6771	+	19.4063i	−0.456102	+	0.828998i
$549$	−34.2536	+	22.8875i	−1.46191	+	0.976815i
$550$	1.01913	−	3.96653i	0.0434559	−	0.169134i
$551$	10.1200	−	24.4319i	0.431128	−	1.04083i
$552$	0.123644	+	3.99746i	0.00526266	+	0.170143i
$553$	0.237181	+	0.572605i	0.0100859	+	0.0243496i
$554$	−5.17742	−	36.4215i	−0.219968	−	1.54740i
$555$	−2.64135	−	0.525397i	−0.112119	−	0.0223019i
$556$	−3.55344	−	6.84619i	−0.150700	−	0.290343i
$557$	−15.2399	−	10.1830i	−0.645734	−	0.431466i	0.189107	−	0.981956i	$-0.439441\pi$
$557$	−15.2399	−	10.1830i	−0.645734	−	0.431466i	−0.834841	+	0.550491i	$0.814441\pi$
$558$	65.7897	−	58.9066i	2.78510	−	2.49371i
$559$	1.57776	−	1.57776i	0.0667321	−	0.0667321i
$560$	18.9134	+	0.458211i	0.799239	+	0.0193630i
$561$	−12.9923	−	12.9923i	−0.548536	−	0.548536i
$562$	−34.6006	−	1.90991i	−1.45954	−	0.0805648i
$563$	2.21898	−	3.32093i	0.0935187	−	0.139961i	−0.781760	−	0.623579i	$-0.785678\pi$
$563$	2.21898	−	3.32093i	0.0935187	−	0.139961i	0.875279	+	0.483619i	$0.160678\pi$
$564$	4.42750	+	51.3173i	0.186431	+	2.16085i
$565$	5.30813	−	26.6858i	0.223315	−	1.12268i
$566$	−26.2688	−	19.7300i	−1.10416	−	0.829312i
$567$	29.7969	−	12.3423i	1.25135	−	0.518327i
$568$	7.47785	+	10.4752i	0.313764	+	0.439529i
$569$	27.7449	+	11.4923i	1.16313	+	0.481783i	0.878915	−	0.476978i	$-0.158268\pi$
$569$	27.7449	+	11.4923i	1.16313	+	0.481783i	0.284213	+	0.958761i	$0.408268\pi$
$570$	30.7247	−	18.1637i	1.28692	−	0.760794i
$571$	17.3752	+	26.0038i	0.727128	+	1.08822i	0.992280	+	0.124017i	$0.0395777\pi$
$571$	17.3752	+	26.0038i	0.727128	+	1.08822i	−0.265152	+	0.964207i	$0.585422\pi$
$572$	1.44353	+	0.159849i	0.0603569	+	0.00668363i
$573$	2.15292	−	0.428243i	0.0899396	−	0.0178901i
$574$	−24.4688	+	8.58831i	−1.02131	+	0.358469i
$575$	1.06649			0.0444756
$576$	37.4142	+	33.0510i	1.55893	+	1.37712i
$577$	−4.61192			−0.191997			−0.0959984	−	0.995381i	$-0.530604\pi$
$577$	−4.61192			−0.191997			−0.0959984	+	0.995381i	$0.530604\pi$
$578$	7.87499	−	2.76404i	0.327557	−	0.114969i
$579$	15.8244	−	3.14768i	0.657642	−	0.130813i
$580$	−1.89814	+	17.1413i	−0.0788161	+	0.711753i
$581$	−9.91996	−	14.8463i	−0.411549	−	0.615927i
$582$	50.9727	−	30.1338i	2.11289	−	1.24909i
$583$	−4.84781	−	2.00803i	−0.200776	−	0.0831640i
$584$	2.75207	+	0.459470i	0.113881	+	0.0190130i
$585$	5.45377	−	2.25903i	0.225486	−	0.0933992i
$586$	32.0215	+	24.0507i	1.32280	+	0.993524i
$587$	−4.06182	+	20.4202i	−0.167649	+	0.842831i	0.801810	+	0.597579i	$0.203871\pi$
$587$	−4.06182	+	20.4202i	−0.167649	+	0.842831i	−0.969459	+	0.245252i	$0.921129\pi$
$588$	7.65049	−	0.660061i	0.315501	−	0.0272204i
$589$	28.0525	−	41.9835i	1.15588	−	1.72990i
$590$	4.33314	+	0.239185i	0.178393	+	0.00984707i
$591$	−32.0588	−	32.0588i	−1.31872	−	1.31872i
$592$	−0.775785	−	2.00922i	−0.0318846	−	0.0825785i
$593$	−3.69463	+	3.69463i	−0.151720	+	0.151720i	−0.778886	−	0.627166i	$-0.784215\pi$
$593$	−3.69463	+	3.69463i	−0.151720	+	0.151720i	0.627166	+	0.778886i	$0.284215\pi$
$594$	−13.1075	+	11.7361i	−0.537806	+	0.481540i
$595$	−18.8199	−	12.5750i	−0.771539	−	0.515526i
$596$	−39.4923	+	20.4981i	−1.61767	+	0.839633i
$597$	1.43234	+	0.284911i	0.0586218	+	0.0116606i
$598$	0.0532287	+	0.374447i	0.00217668	+	0.0153123i
$599$	−4.44136	−	10.7224i	−0.181469	−	0.438105i	0.806801	−	0.590824i	$-0.201197\pi$
$599$	−4.44136	−	10.7224i	−0.181469	−	0.438105i	−0.988270	+	0.152719i	$0.951197\pi$
$600$	13.5011	−	14.3629i	0.551179	−	0.586364i
$601$	−4.16840	+	10.0634i	−0.170033	+	0.410495i	−0.985809	−	0.167873i	$-0.946310\pi$
$601$	−4.16840	+	10.0634i	−0.170033	+	0.410495i	0.815776	+	0.578368i	$0.196310\pi$
$602$	−3.92613	+	15.2808i	−0.160017	+	0.622799i
$603$	31.8462	−	21.2789i	1.29688	−	0.866546i
$604$	−13.6941	−	7.53427i	−0.557204	−	0.306565i
$605$	3.01888	+	15.1769i	0.122735	+	0.617030i
$606$	−15.5716	−	7.48054i	−0.632553	−	0.303876i
$607$			29.1457i			1.18299i	0.806310	+	0.591493i	$0.201461\pi$
$607$			29.1457i			1.18299i	−0.806310	+	0.591493i	$0.798539\pi$
$608$	25.4227	+	12.9800i	1.03103	+	0.526407i
$609$			45.7937i			1.85565i
$610$	6.65197	−	13.8468i	0.269330	−	0.560642i
$611$	0.950281	+	4.77739i	0.0384443	+	0.193272i
$612$	−16.6441	−	57.3599i	−0.672796	−	2.31864i
$613$	−5.29850	+	3.54035i	−0.214005	+	0.142993i	−0.657953	−	0.753059i	$-0.728577\pi$
$613$	−5.29850	+	3.54035i	−0.214005	+	0.142993i	0.443948	+	0.896052i	$0.353577\pi$
$614$	−14.8348	−	3.81155i	−0.598686	−	0.153822i
$615$	12.2096	−	29.4767i	0.492340	−	1.18862i
$616$	−9.36163	+	4.22136i	−0.377191	+	0.170083i
$617$	3.88763	+	9.38556i	0.156510	+	0.377849i	0.982612	−	0.185673i	$-0.0594464\pi$
$617$	3.88763	+	9.38556i	0.156510	+	0.377849i	−0.826102	+	0.563521i	$0.809446\pi$
$618$	−33.6032	+	4.77678i	−1.35172	+	0.192150i
$619$	−3.09719	−	0.616070i	−0.124487	−	0.0247620i	0.132454	−	0.991189i	$-0.457714\pi$
$619$	−3.09719	−	0.616070i	−0.124487	−	0.0247620i	−0.256940	+	0.966427i	$0.582714\pi$
$620$	−9.93975	+	31.3931i	−0.399190	+	1.26078i
$621$	−3.80951	−	2.54544i	−0.152871	−	0.102145i
$622$	−7.05913	−	7.88397i	−0.283045	−	0.316118i
$623$	7.90057	−	7.90057i	0.316530	−	0.316530i
$624$	5.71671	+	4.02341i	0.228852	+	0.161065i
$625$	5.85477	+	5.85477i	0.234191	+	0.234191i
$626$	1.76716	−	32.0145i	0.0706301	−	1.27956i
$627$	−10.7636	+	16.1089i	−0.429856	+	0.643326i
$628$	32.1622	+	27.0533i	1.28341	+	1.07954i
$629$	−0.502703	+	2.52726i	−0.0200441	+	0.100768i
$630$	−25.0671	+	33.3748i	−0.998698	+	1.32968i
$631$	−29.9605	+	12.4100i	−1.19271	+	0.494036i	−0.888636	−	0.458613i	$-0.848347\pi$
$631$	−29.9605	+	12.4100i	−1.19271	+	0.494036i	−0.304073	+	0.952649i	$0.598347\pi$
$632$	−0.137408	−	0.594155i	−0.00546579	−	0.0236342i
$633$	41.2117	+	17.0705i	1.63802	+	0.678490i
$634$	−9.50110	−	16.0715i	−0.377337	−	0.638282i
$635$	−20.0666	−	30.0318i	−0.796319	−	1.19178i
$636$	−15.7849	−	19.7162i	−0.625914	−	0.781797i
$637$	0.712223	−	0.141670i	0.0282193	−	0.00561317i
$638$	−3.10029	−	8.83301i	−0.122742	−	0.349702i
$639$	−28.3954			−1.12331
$640$	−18.2816	−	3.50930i	−0.722644	−	0.138717i
$641$	27.6811			1.09334			0.546668	−	0.837349i	$-0.315896\pi$
$641$	27.6811			1.09334			0.546668	+	0.837349i	$0.315896\pi$
$642$	7.85193	+	22.3708i	0.309891	+	0.882907i
$643$	42.4514	−	8.44410i	1.67412	−	0.333003i	0.735386	−	0.677649i	$-0.237001\pi$
$643$	42.4514	−	8.44410i	1.67412	−	0.333003i	0.938733	+	0.344646i	$0.112001\pi$
$644$	−1.67138	−	2.08764i	−0.0658617	−	0.0822645i
$645$	−10.7842	−	16.1397i	−0.424629	−	0.635502i
$646$	−17.3791	−	29.3976i	−0.683772	−	1.15663i
$647$	−35.3075	−	14.6248i	−1.38808	−	0.574962i	−0.441451	−	0.897285i	$-0.645536\pi$
$647$	−35.3075	−	14.6248i	−1.38808	−	0.574962i	−0.946630	+	0.322324i	$0.895536\pi$
$648$	−30.9183	+	7.15036i	−1.21459	+	0.280893i
$649$	−2.17633	+	0.901466i	−0.0854285	+	0.0353856i
$650$	1.11951	−	1.49054i	0.0439109	−	0.0584638i
$651$	−17.0581	+	85.7570i	−0.668560	+	3.36108i
$652$	−31.3785	−	26.3941i	−1.22888	−	1.03367i
$653$	13.3150	−	19.9272i	0.521055	−	0.779813i	−0.473853	−	0.880604i	$-0.657137\pi$
$653$	13.3150	−	19.9272i	0.521055	−	0.779813i	0.994908	+	0.100791i	$0.0321372\pi$
$654$	−1.03438	+	18.7392i	−0.0404475	+	0.732759i
$655$	−8.37343	−	8.37343i	−0.327177	−	0.327177i
$656$	25.1391	−	4.37037i	0.981516	−	0.170634i
$657$	−4.35281	+	4.35281i	−0.169819	+	0.169819i
$658$	−22.9749	−	25.6594i	−0.895654	−	1.00031i
$659$	17.2984	+	11.5584i	0.673852	+	0.450253i	0.844839	−	0.535020i	$-0.179696\pi$
$659$	17.2984	+	11.5584i	0.673852	+	0.450253i	−0.170988	+	0.985273i	$0.554696\pi$
$660$	3.81383	−	12.0454i	0.148453	−	0.468866i
$661$	14.9381	+	2.97137i	0.581025	+	0.115573i	0.476848	−	0.878986i	$-0.341779\pi$
$661$	14.9381	+	2.97137i	0.581025	+	0.115573i	0.104177	+	0.994559i	$0.466779\pi$
$662$	7.14027	−	1.01501i	0.277514	−	0.0394494i
$663$	−3.20057	−	7.72685i	−0.124300	−	0.300086i
$664$	7.22194	+	16.0160i	0.280266	+	0.621540i
$665$	−9.13327	+	22.0497i	−0.354173	+	0.855049i
$666$	4.60233	+	1.18249i	0.178337	+	0.0458204i
$667$	2.02696	−	1.35437i	0.0784842	−	0.0524415i
$668$	8.11303	+	27.9597i	0.313902	+	1.08179i
$669$	12.1832	+	61.2489i	0.471028	+	2.36802i
$670$	−6.18446	+	12.8737i	−0.238927	+	0.497353i
$671$			8.33848i			0.321903i
$672$	−49.2740	−	3.91886i	−1.90079	−	0.151173i
$673$			33.8371i			1.30432i	0.758080	+	0.652162i	$0.226138\pi$
$673$			33.8371i			1.30432i	−0.758080	+	0.652162i	$0.773862\pi$
$674$	−17.1581	−	8.24268i	−0.660905	−	0.317496i
$675$	4.40558	+	22.1483i	0.169571	+	0.852490i
$676$	−22.2006	−	12.2144i	−0.853870	−	0.469786i
$677$	28.0419	−	18.7370i	1.07774	−	0.720121i	0.115768	−	0.993276i	$-0.463067\pi$
$677$	28.0419	−	18.7370i	1.07774	−	0.720121i	0.961970	+	0.273155i	$0.0880672\pi$
$678$	−17.6902	+	68.8515i	−0.679387	+	2.64423i
$679$	−15.1522	+	36.5807i	−0.581489	+	1.40384i
$680$	16.2275	+	15.2537i	0.622295	+	0.584954i
$681$	−22.8501	−	55.1649i	−0.875616	−	2.11392i
$682$	−2.51557	−	17.6963i	−0.0963263	−	0.677625i
$683$	14.0115	+	2.78707i	0.536137	+	0.106644i	0.455730	−	0.890118i	$-0.349378\pi$
$683$	14.0115	+	2.78707i	0.536137	+	0.106644i	0.0804066	+	0.996762i	$0.474378\pi$
$684$	−55.8959	+	29.0122i	−2.13723	+	1.10931i
$685$	15.1513	+	10.1238i	0.578901	+	0.386809i
$686$	17.3750	−	15.5571i	0.663379	−	0.593975i
$687$	46.8998	−	46.8998i	1.78934	−	1.78934i
$688$	6.28637	−	14.1942i	0.239666	−	0.541147i
$689$	−1.68889	−	1.68889i	−0.0643415	−	0.0643415i
$690$	3.28525	+	0.181342i	0.125067	+	0.00690358i
$691$	10.9236	−	16.3483i	0.415552	−	0.621918i	−0.563357	−	0.826214i	$-0.690490\pi$
$691$	10.9236	−	16.3483i	0.415552	−	0.621918i	0.978909	+	0.204296i	$0.0654904\pi$
$692$	37.0533	−	3.19685i	1.40856	−	0.121526i
$693$	4.42013	−	22.2215i	0.167907	−	0.844125i
$694$	33.8463	+	25.4213i	1.28479	+	0.964979i
$695$	−5.86275	+	2.42843i	−0.222387	+	0.0921156i
$696$	7.42006	−	44.4436i	0.281257	−	1.68463i
$697$	−28.2035	−	11.6823i	−1.06828	−	0.442497i
$698$	−17.3000	+	10.2274i	−0.654816	+	0.387111i
$699$	6.60877	+	9.89072i	0.249967	+	0.374101i
$700$	−1.45074	+	13.1010i	−0.0548328	+	0.495171i
$701$	11.0341	−	2.19482i	0.416753	−	0.0828974i	0.0177402	−	0.999843i	$-0.494353\pi$
$701$	11.0341	−	2.19482i	0.416753	−	0.0828974i	0.399013	+	0.916945i	$0.369353\pi$
$702$	−7.55647	+	2.65224i	−0.285201	+	0.100102i
$703$	2.71702			0.102474
$704$	9.76964	−	2.58002i	0.368207	−	0.0972383i
$705$	42.3751			1.59594
$706$	30.6650	−	10.7631i	1.15409	−	0.405075i
$707$	11.3295	−	2.25358i	0.426091	−	0.0847548i
$708$	−11.2695	−	1.24793i	−0.423536	−	0.0469003i
$709$	−23.4418	−	35.0831i	−0.880374	−	1.31757i	−0.947476	−	0.319827i	$-0.896375\pi$
$709$	−23.4418	−	35.0831i	−0.880374	−	1.31757i	0.0671017	−	0.997746i	$-0.478625\pi$
$710$	9.11476	−	5.38842i	0.342071	−	0.202224i
$711$	1.24304	+	0.514884i	0.0466176	+	0.0193097i
$712$	−8.94781	+	6.38751i	−0.335333	+	0.239382i
$713$	4.30035	−	1.78127i	0.161050	−	0.0667089i
$714$	47.2851	+	35.5148i	1.76960	+	1.32911i
$715$	0.233101	−	1.17188i	0.00871749	−	0.0438258i
$716$	−1.85470	−	21.4971i	−0.0693135	−	0.803385i
$717$	−11.6504	+	17.4360i	−0.435091	+	0.651160i
$718$	9.70838	+	0.535892i	0.362314	+	0.0199993i
$719$	−9.10621	−	9.10621i	−0.339604	−	0.339604i	0.516614	−	0.856218i	$-0.327192\pi$
$719$	−9.10621	−	9.10621i	−0.339604	−	0.339604i	−0.856218	+	0.516614i	$0.827192\pi$
$720$	29.7359	−	28.3292i	1.10819	−	1.05577i
$721$	16.0481	−	16.0481i	0.597663	−	0.597663i
$722$	−6.80865	+	6.09631i	−0.253392	+	0.226881i
$723$	−6.09576	−	4.07305i	−0.226704	−	0.151479i
$724$	3.29684	+	6.35181i	0.122526	+	0.236063i
$725$	−11.7847	−	2.34411i	−0.437671	−	0.0870582i
$726$	−5.68997	−	40.0272i	−0.211175	−	1.48555i
$727$	8.28934	+	20.0122i	0.307435	+	0.742213i	0.999787	+	0.0206529i	$0.00657449\pi$
$727$	8.28934	+	20.0122i	0.307435	+	0.742213i	−0.692352	+	0.721560i	$0.743426\pi$
$728$	−4.67221	+	0.144515i	−0.173163	+	0.00535607i
$729$	−7.57994	+	18.2996i	−0.280739	+	0.677763i
$730$	0.571219	−	2.22323i	0.0211418	−	0.0822854i
$731$	−15.4426	+	10.3184i	−0.571165	+	0.381640i
$732$	−19.3471	+	35.1648i	−0.715090	+	1.29973i
$733$	−1.86746	−	9.38837i	−0.0689763	−	0.346767i	0.930850	−	0.365401i	$-0.119068\pi$
$733$	−1.86746	−	9.38837i	−0.0689763	−	0.346767i	−0.999826	+	0.0186340i	$0.994068\pi$
$734$	−4.34630	−	2.08795i	−0.160425	−	0.0770676i
$735$		−	6.31738i		−	0.233020i
$736$	1.28384	+	2.29691i	0.0473232	+	0.0846653i
$737$		−	7.75244i		−	0.285565i
$738$	−24.3770	+	50.7435i	−0.897329	+	1.86789i
$739$	−3.72209	−	18.7122i	−0.136919	−	0.688340i	−0.986875	−	0.161486i	$-0.948371\pi$
$739$	−3.72209	−	18.7122i	−0.136919	−	0.688340i	0.849956	−	0.526854i	$-0.176629\pi$
$740$	−1.70171	+	0.493784i	−0.0625562	+	0.0181519i
$741$	−7.33247	+	4.89940i	−0.269365	+	0.179984i
$742$	16.3571	+	4.20267i	0.600488	+	0.154285i
$743$	−2.74886	+	6.63633i	−0.100846	+	0.243463i	−0.966248	−	0.257615i	$-0.917063\pi$
$743$	−2.74886	+	6.63633i	−0.100846	+	0.243463i	0.865402	+	0.501079i	$0.167063\pi$
$744$	30.4507	−	80.4648i	1.11638	−	2.94998i
$745$	14.0084	+	33.8193i	0.513228	+	1.23904i
$746$	19.9733	−	2.83926i	0.731274	−	0.103953i
$747$	−38.0168	−	7.56200i	−1.39096	−	0.276679i
$748$	−11.5251	−	3.64909i	−0.421399	−	0.133424i
$749$	−13.1817	−	8.80771i	−0.481648	−	0.321827i
$750$	−34.4094	−	38.4301i	−1.25645	−	1.40327i
$751$	−1.88191	+	1.88191i	−0.0686719	+	0.0686719i	−0.740609	−	0.671937i	$-0.765463\pi$
$751$	−1.88191	+	1.88191i	−0.0686719	+	0.0686719i	0.671937	+	0.740609i	$0.265463\pi$
$752$	18.1399	+	28.6257i	0.661494	+	1.04387i
$753$	1.47249	+	1.47249i	0.0536606	+	0.0536606i
$754$	0.234850	−	4.25462i	0.00855275	−	0.154944i
$755$	−7.14383	+	10.6915i	−0.259991	+	0.389104i
$756$	36.4508	−	43.3345i	1.32570	−	1.57606i
$757$	7.70412	−	38.7312i	0.280011	−	1.40771i	−0.543023	−	0.839718i	$-0.682720\pi$
$757$	7.70412	−	38.7312i	0.280011	−	1.40771i	0.823034	−	0.567992i	$-0.192280\pi$
$758$	−21.8456	+	29.0856i	−0.793468	+	1.05644i
$759$	−1.65002	+	0.683463i	−0.0598921	+	0.0248081i
$760$	12.4368	−	19.9197i	0.451130	−	0.722565i
$761$	−7.53878	−	3.12266i	−0.273280	−	0.113196i	0.241835	−	0.970317i	$-0.422251\pi$
$761$	−7.53878	−	3.12266i	−0.273280	−	0.113196i	−0.515115	+	0.857121i	$0.672251\pi$
$762$	48.0238	+	81.2344i	1.73972	+	2.94281i
$763$	−6.97211	−	10.4345i	−0.252407	−	0.377754i
$764$	1.12744	−	0.902636i	0.0407892	−	0.0326562i
$765$	−48.1919	+	9.58596i	−1.74238	+	0.346581i
$766$	10.1095	+	28.8027i	0.365270	+	1.04068i
$767$	−1.07225			−0.0387167
$768$	47.1864	+	11.7873i	1.70269	+	0.425338i
$769$	3.77877			0.136266			0.0681330	−	0.997676i	$-0.478296\pi$
$769$	3.77877			0.136266			0.0681330	+	0.997676i	$0.478296\pi$
$770$	2.79800	+	7.97175i	0.100833	+	0.287282i
$771$	−72.5677	+	14.4346i	−2.61346	+	0.519850i
$772$	8.28690	−	6.63457i	0.298252	−	0.238783i
$773$	−2.84091	−	4.25173i	−0.102181	−	0.152924i	0.776856	−	0.629678i	$-0.216813\pi$
$773$	−2.84091	−	4.25173i	−0.102181	−	0.152924i	−0.879037	+	0.476754i	$0.841813\pi$
$774$	17.4297	+	29.4831i	0.626497	+	1.05975i
$775$	−21.1957	−	8.77956i	−0.761373	−	0.315371i
$776$	20.6328	−	33.0472i	0.740675	−	1.18632i
$777$	−4.34681	+	1.80051i	−0.155941	+	0.0645929i
$778$	−6.02917	+	8.02734i	−0.216156	+	0.287794i
$779$	−6.27971	+	31.5702i	−0.224994	+	1.13112i
$780$	3.70204	−	4.40116i	0.132554	−	0.157587i
$781$	−3.19312	+	4.77884i	−0.114259	+	0.171000i
$782$	0.173509	−	3.14335i	0.00620467	−	0.112406i
$783$	36.5002	+	36.5002i	1.30441	+	1.30441i
$784$	4.26758	−	2.70434i	0.152413	−	0.0965835i
$785$	24.4485	−	24.4485i	0.872605	−	0.872605i
$786$	20.6382	+	23.0498i	0.736142	+	0.822158i
$787$	−25.7884	−	17.2312i	−0.919257	−	0.614228i	0.00333965	−	0.999994i	$-0.498937\pi$
$787$	−25.7884	−	17.2312i	−0.919257	−	0.614228i	−0.922596	+	0.385767i	$0.873937\pi$
$788$	−28.4384	−	9.00422i	−1.01308	−	0.320762i
$789$	−30.9820	−	6.16271i	−1.10299	−	0.219398i
$790$	−0.496714	+	0.0706093i	−0.0176723	+	0.00251217i
$791$	−18.1907	−	43.9162i	−0.646786	−	1.56148i
$792$	−7.89043	+	20.8502i	−0.280374	+	0.740879i
$793$	−1.45249	+	3.50662i	−0.0515793	+	0.124524i
$794$	−18.2637	−	4.69254i	−0.648156	−	0.166532i
$795$	−17.2765	+	11.5438i	−0.612736	+	0.409417i
$796$	0.922799	−	0.267768i	0.0327077	−	0.00949077i
$797$	0.860359	+	4.32532i	0.0304755	+	0.153211i	0.993027	−	0.117889i	$-0.0376127\pi$
$797$	0.860359	+	4.32532i	0.0304755	+	0.153211i	−0.962551	+	0.271100i	$0.912613\pi$
$798$	27.0013	−	56.2064i	0.955837	−	1.98968i
$799$		−	40.5448i		−	1.43437i
$800$	3.53076	−	12.4797i	0.124831	−	0.441224i
$801$		−	24.2551i		−	0.857013i
$802$	−15.3282	−	7.36362i	−0.541258	−	0.260018i
$803$	0.243079	+	1.22204i	0.00857807	+	0.0431249i
$804$	17.9874	−	32.6933i	0.634365	−	1.15300i
$805$	−1.82932	+	1.22231i	−0.0644751	+	0.0430809i
$806$	2.02465	−	7.88008i	0.0713151	−	0.277564i
$807$	36.2868	−	87.6041i	1.27736	−	3.08381i
$808$	−11.3607	+	0.351394i	−0.399668	+	0.0123620i
$809$	−4.29079	−	10.3589i	−0.150856	−	0.364199i	0.830327	−	0.557276i	$-0.188153\pi$
$809$	−4.29079	−	10.3589i	−0.150856	−	0.364199i	−0.981184	+	0.193077i	$0.938153\pi$
$810$	3.67433	+	25.8478i	0.129103	+	0.908198i
$811$	3.92167	+	0.780069i	0.137709	+	0.0273919i	0.263463	−	0.964669i	$-0.415135\pi$
$811$	3.92167	+	0.780069i	0.137709	+	0.0273919i	−0.125755	+	0.992061i	$0.540135\pi$
$812$	13.8802	+	26.7420i	0.487098	+	0.938461i
$813$	−42.3363	−	28.2882i	−1.48480	−	0.992110i
$814$	0.716548	−	0.641581i	0.0251150	−	0.0224874i
$815$	−23.8528	+	23.8528i	−0.835528	+	0.835528i
$816$	−40.1365	−	42.1296i	−1.40506	−	1.47483i
$817$	13.8476	+	13.8476i	0.484467	+	0.484467i
$818$	40.0060	+	2.20828i	1.39878	+	0.0772109i
$819$	5.72960	−	8.57495i	0.200208	−	0.299633i
$820$	−1.80441	−	20.9142i	−0.0630129	−	0.730356i
$821$	−7.39036	+	37.1538i	−0.257925	+	1.29668i	0.606970	+	0.794725i	$0.292385\pi$
$821$	−7.39036	+	37.1538i	−0.257925	+	1.29668i	−0.864895	+	0.501953i	$0.832615\pi$
$822$	−38.0678	−	28.5919i	−1.32777	−	0.997258i
$823$	13.1154	−	5.43259i	0.457175	−	0.189368i	−0.142197	−	0.989838i	$-0.545417\pi$
$823$	13.1154	−	5.43259i	0.457175	−	0.189368i	0.599373	+	0.800470i	$0.295417\pi$
$824$	−18.1753	+	12.9747i	−0.633167	+	0.451995i
$825$	8.13270	+	3.36867i	0.283144	+	0.117282i
$826$	6.52654	−	3.85833i	0.227087	−	0.134248i
$827$	13.3036	+	19.9102i	0.462611	+	0.692347i	0.987286	−	0.158956i	$-0.0508129\pi$
$827$	13.3036	+	19.9102i	0.462611	+	0.692347i	−0.524674	+	0.851303i	$0.675813\pi$
$828$	−5.77019	−	0.638962i	−0.200528	−	0.0222055i
$829$	12.2166	−	2.43003i	0.424299	−	0.0843983i	0.0216779	−	0.999765i	$-0.493099\pi$
$829$	12.2166	−	2.43003i	0.424299	−	0.0843983i	0.402621	+	0.915367i	$0.368099\pi$
$830$	13.6381	−	4.78685i	0.473387	−	0.166154i
$831$	79.0731			2.74302
$832$	4.55788	+	0.616795i	0.158016	+	0.0213835i
$833$	−6.04450			−0.209430
$834$	15.6440	−	5.49088i	0.541707	−	0.190134i
$835$	23.4908	−	4.67260i	0.812932	−	0.161702i
$836$	−1.40296	+	12.6695i	−0.0485224	+	0.438185i
$837$	54.7570	+	81.9497i	1.89268	+	2.83259i
$838$	25.3611	−	14.9929i	0.876085	−	0.517920i
$839$	−26.8826	−	11.1351i	−0.928089	−	0.384427i	−0.133136	−	0.991098i	$-0.542505\pi$
$839$	−26.8826	−	11.1351i	−0.928089	−	0.384427i	−0.794953	+	0.606671i	$0.792505\pi$
$840$	−6.69657	+	40.1102i	−0.231054	+	1.38393i
$841$	1.41778	−	0.587262i	0.0488888	−	0.0202504i
$842$	−25.1514	−	18.8907i	−0.866774	−	0.651016i
$843$	14.5314	−	73.0540i	0.500486	−	2.51612i
$844$	29.2404	−	2.52277i	1.00650	−	0.0868374i
$845$	−11.5815	+	17.3329i	−0.398415	+	0.596270i
$846$	−74.6548	−	4.12086i	−2.56669	−	0.141678i
$847$	19.1161	+	19.1161i	0.656836	+	0.656836i
$848$	−15.1939	−	6.72915i	−0.521761	−	0.231080i
$849$	49.9329	−	49.9329i	1.71369	−	1.71369i
$850$	−11.5599	+	10.3505i	−0.396503	+	0.355019i
$851$	0.208255	+	0.139152i	0.00713889	+	0.00477006i
$852$	−24.5539	+	12.7444i	−0.841201	+	0.436617i
$853$	29.6923	+	5.90616i	1.01664	+	0.202223i	0.675165	−	0.737666i	$-0.264072\pi$
$853$	29.6923	+	5.90616i	1.01664	+	0.202223i	0.341479	+	0.939889i	$0.389072\pi$
$854$	−3.77708	−	26.5705i	−0.129249	−	0.909225i
$855$	19.8270	+	47.8665i	0.678068	+	1.63700i
$856$	11.3659	+	10.6839i	0.388480	+	0.365169i
$857$	−0.425175	+	1.02646i	−0.0145237	+	0.0350633i	−0.930975	−	0.365083i	$-0.881041\pi$
$857$	−0.425175	+	1.02646i	−0.0145237	+	0.0350633i	0.916451	+	0.400146i	$0.131041\pi$
$858$	−0.776847	+	3.02355i	−0.0265211	+	0.103222i
$859$	−40.2028	+	26.8627i	−1.37170	+	0.916543i	−0.999931	−	0.0117809i	$-0.996250\pi$
$859$	−40.2028	+	26.8627i	−1.37170	+	0.916543i	−0.371773	+	0.928324i	$0.621250\pi$
$860$	−11.1896	−	6.15637i	−0.381564	−	0.209930i
$861$	−10.8743	−	54.6690i	−0.370596	−	1.86311i
$862$	16.5304	+	7.94114i	0.563027	+	0.270476i
$863$			54.0259i			1.83906i	0.393018	+	0.919531i	$0.371431\pi$
$863$			54.0259i			1.83906i	−0.393018	+	0.919531i	$0.628569\pi$
$864$	−42.3978	+	36.1507i	−1.44240	+	1.22987i
$865$		−	30.5967i		−	1.04032i
$866$	−7.84900	+	16.3386i	−0.266720	+	0.555208i
$867$	3.49977	+	17.5945i	0.118858	+	0.597542i
$868$	16.0317	+	55.2497i	0.544153	+	1.87530i
$869$	0.226435	−	0.151299i	0.00768127	−	0.00513246i
$870$	−35.9034	−	9.22473i	−1.21724	−	0.312748i
$871$	1.35040	−	3.26016i	0.0457567	−	0.110466i
$872$	5.07584	+	11.2566i	0.171890	+	0.381196i
$873$	32.8932	+	79.4113i	1.11327	+	2.68766i
$874$	−3.28644	+	0.467176i	−0.111165	+	0.0158025i
$875$	33.8299	+	6.72919i	1.14366	+	0.227488i
$876$	−1.81030	+	5.71754i	−0.0611643	+	0.193178i
$877$	25.7807	+	17.2261i	0.870552	+	0.581684i	0.908635	−	0.417590i	$-0.137125\pi$
$877$	25.7807	+	17.2261i	0.870552	+	0.581684i	−0.0380835	+	0.999275i	$0.512125\pi$
$878$	38.1851	+	42.6469i	1.28868	+	1.43926i
$879$	−60.8679	+	60.8679i	−2.05302	+	2.05302i
$880$	−1.42383	−	8.19010i	−0.0479974	−	0.276088i
$881$	24.7406	+	24.7406i	0.833533	+	0.833533i	0.987998	−	0.154465i	$-0.0493655\pi$
$881$	24.7406	+	24.7406i	0.833533	+	0.833533i	−0.154465	+	0.987998i	$0.549365\pi$
$882$	−0.614347	+	11.1297i	−0.0206861	+	0.374757i
$883$	−17.5606	+	26.2813i	−0.590962	+	0.884436i	−0.999601	−	0.0282597i	$-0.991003\pi$
$883$	−17.5606	+	26.2813i	−0.590962	+	0.884436i	0.408639	+	0.912696i	$0.366003\pi$
$884$	−4.21106	−	3.54213i	−0.141633	−	0.119135i
$885$	−1.81981	+	9.14880i	−0.0611722	+	0.307534i
$886$	1.45827	−	1.94157i	0.0489917	−	0.0652284i
$887$	−15.7202	+	6.51152i	−0.527833	+	0.218635i	−0.630654	−	0.776064i	$-0.717213\pi$
$887$	−15.7202	+	6.51152i	−0.527833	+	0.218635i	0.102821	+	0.994700i	$0.467213\pi$
$888$	4.51041	−	1.04310i	0.151359	−	0.0350043i
$889$	−58.2981	−	24.1479i	−1.95525	−	0.809893i
$890$	4.60274	+	7.78575i	0.154284	+	0.260979i
$891$	−7.87321	−	11.7831i	−0.263763	−	0.394749i
$892$	25.6792	+	32.0746i	0.859805	+	1.07394i
$893$	−41.9301	+	8.34041i	−1.40314	+	0.279101i
$894$	−31.6742	−	90.2425i	−1.05934	−	3.01816i
$895$	−17.7512			−0.593357
$896$	−29.9623	+	12.6466i	−1.00097	+	0.422493i
$897$	−0.812945			−0.0271434
$898$	−11.5273	−	32.8423i	−0.384671	−	1.09596i
$899$	−51.4340	+	10.2309i	−1.71542	+	0.341218i
$900$	17.8834	+	22.3372i	0.596114	+	0.744575i
$901$	11.0452	+	16.5303i	0.367968	+	0.550704i
$902$	5.79869	+	9.80874i	0.193075	+	0.326595i
$903$	−31.3306	−	12.9776i	−1.04262	−	0.431867i
$904$	10.5386	+	45.5690i	0.350507	+	1.51560i
$905$	5.43938	−	2.25306i	0.180811	−	0.0748944i
$906$	20.1759	−	26.8625i	0.670299	−	0.892447i
$907$	7.39593	−	37.1818i	0.245578	−	1.23460i	−0.639365	−	0.768903i	$-0.720803\pi$
$907$	7.39593	−	37.1818i	0.245578	−	1.23460i	0.884943	−	0.465699i	$-0.154197\pi$
$908$	−30.0643	−	25.2886i	−0.997720	−	0.839233i
$909$	13.9318	−	20.8504i	0.462088	−	0.691564i
$910$	−0.211951	+	3.83978i	−0.00702612	+	0.127287i
$911$	−30.6254	−	30.6254i	−1.01467	−	1.01467i	−0.999891	−	0.0147749i	$-0.995297\pi$
$911$	−30.6254	−	30.6254i	−1.01467	−	1.01467i	−0.0147749	−	0.999891i	$-0.504703\pi$
$912$	−35.3126	+	50.1743i	−1.16932	+	1.66144i
$913$	−5.54770	+	5.54770i	−0.183602	+	0.183602i
$914$	0.983270	+	1.09816i	0.0325237	+	0.0363240i
$915$	27.4545	+	18.3445i	0.907618	+	0.606451i
$916$	13.1725	−	41.6034i	0.435233	−	1.37461i
$917$	−20.2907	−	4.03606i	−0.670057	−	0.133283i
$918$	65.9964	−	9.38157i	2.17821	−	0.309638i
$919$	3.89489	+	9.40310i	0.128481	+	0.310180i	0.975010	−	0.222163i	$-0.0713117\pi$
$919$	3.89489	+	9.40310i	0.128481	+	0.310180i	−0.846529	+	0.532343i	$0.821312\pi$
$920$	1.97345	−	0.889869i	0.0650626	−	0.0293381i
$921$	12.5988	−	30.4163i	0.415146	−	1.00225i
$922$	−19.0528	−	4.89527i	−0.627469	−	0.161217i
$923$	−2.17524	+	1.45345i	−0.0715990	+	0.0478409i
$924$	−6.15130	−	21.1990i	−0.202363	−	0.697397i
$925$	−0.240840	−	1.21079i	−0.00791878	−	0.0398104i
$926$	−7.18465	+	14.9557i	−0.236102	+	0.491474i
$927$		−	49.2684i		−	1.61819i
$928$	−9.13789	−	28.2027i	−0.299966	−	0.925799i
$929$		−	0.932872i		−	0.0306066i	−0.999883	−	0.0153033i	$-0.995129\pi$
$929$		−	0.932872i		−	0.0306066i	0.999883	−	0.0153033i	$-0.00487137\pi$
$930$	−63.7994	−	30.6490i	−2.09206	−	1.00502i
$931$	1.24341	+	6.25102i	0.0407510	+	0.204869i
$932$	6.85721	+	3.77273i	0.224615	+	0.123580i
$933$	18.9129	−	12.6372i	0.619182	−	0.413724i
$934$	0.101600	−	0.395433i	0.00332444	−	0.0129390i
$935$	−3.80598	+	9.18845i	−0.124469	+	0.300494i
$936$	−6.95011	+	7.39378i	−0.227171	+	0.241673i
$937$	9.77432	+	23.5973i	0.319313	+	0.770890i	0.999291	+	0.0376573i	$0.0119895\pi$
$937$	9.77432	+	23.5973i	0.319313	+	0.770890i	−0.679978	+	0.733233i	$0.738010\pi$
$938$	3.51162	+	24.7031i	0.114658	+	0.806586i
$939$	67.5940	+	13.4453i	2.20585	+	0.438770i
$940$	24.7457	−	12.8440i	0.807117	−	0.418925i
$941$	14.0830	+	9.40994i	0.459092	+	0.306755i	0.763525	−	0.645778i	$-0.223467\pi$
$941$	14.0830	+	9.40994i	0.459092	+	0.306755i	−0.304433	+	0.952534i	$0.598467\pi$
$942$	−67.3001	+	60.2590i	−2.19276	+	1.96334i
$943$	−2.09819	+	2.09819i	−0.0683266	+	0.0683266i
$944$	−6.95931	+	2.68707i	−0.226506	+	0.0874568i
$945$	−32.9413	−	32.9413i	−1.07158	−	1.07158i
$946$	6.92188	+	0.382080i	0.225050	+	0.0124225i
$947$	13.0115	−	19.4731i	0.422818	−	0.632791i	−0.557510	−	0.830171i	$-0.688243\pi$
$947$	13.0115	−	19.4731i	0.422818	−	0.632791i	0.980327	+	0.197379i	$0.0632430\pi$
$948$	1.30596	−	0.112674i	0.0424156	−	0.00365949i
$949$	−0.110645	+	0.556252i	−0.00359170	+	0.0180567i
$950$	13.0821	+	9.82572i	0.424441	+	0.318789i
$951$	37.0752	−	15.3571i	1.20225	−	0.497987i
$952$	38.3776	+	6.40731i	1.24383	+	0.207662i
$953$	44.5204	+	18.4410i	1.44216	+	0.597361i	0.960320	−	0.278899i	$-0.0899695\pi$
$953$	44.5204	+	18.4410i	1.44216	+	0.597361i	0.481838	+	0.876261i	$0.339970\pi$
$954$	31.5597	−	18.6573i	1.02178	−	0.604054i
$955$	−0.660114	−	0.987930i	−0.0213608	−	0.0319687i
$956$	−1.51855	+	13.7133i	−0.0491133	+	0.443521i
$957$	19.7350	−	3.92553i	0.637941	−	0.126894i
$958$	36.5618	−	12.8328i	1.18126	−	0.414610i
$959$	31.8352			1.02801
$960$	12.9983	−	37.8426i	0.419518	−	1.22137i
$961$	−69.1305			−2.23002
$962$	0.413090	−	0.144990i	0.0133186	−	0.00467468i
$963$	−33.7542	+	6.71413i	−1.08771	+	0.216360i
$964$	−4.79428	−	0.530895i	−0.154413	−	0.0170990i
$965$	−4.85198	−	7.26150i	−0.156191	−	0.233756i
$966$	4.94821	−	2.92526i	0.159206	−	0.0941188i
$967$	25.4255	+	10.5316i	0.817629	+	0.338673i	0.751993	−	0.659171i	$-0.229093\pi$
$967$	25.4255	+	10.5316i	0.817629	+	0.338673i	0.0656353	+	0.997844i	$0.479093\pi$
$968$	−15.4551	−	21.6499i	−0.496745	−	0.695855i
$969$	67.8169	−	28.0907i	2.17859	−	0.902402i
$970$	−25.6279	−	19.2486i	−0.822863	−	0.618035i
$971$	3.37327	−	16.9586i	0.108254	−	0.544227i	−0.888154	−	0.459545i	$-0.848012\pi$
$971$	3.37327	−	16.9586i	0.108254	−	0.544227i	0.996408	−	0.0846822i	$-0.0269875\pi$
$972$	−0.783406	−	9.08014i	−0.0251278	−	0.291246i
$973$	−6.15926	+	9.21798i	−0.197457	+	0.295515i
$974$	−43.3477	−	2.39275i	−1.38895	−	0.0766685i
$975$	2.83328	+	2.83328i	0.0907377	+	0.0907377i
$976$	−0.639568	+	26.3992i	−0.0204721	+	0.845019i
$977$	−26.1853	+	26.1853i	−0.837743	+	0.837743i	−0.988562	−	0.150818i	$-0.951809\pi$
$977$	−26.1853	+	26.1853i	−0.837743	+	0.837743i	0.150818	+	0.988562i	$0.451809\pi$
$978$	65.6603	−	58.7907i	2.09958	−	1.87992i
$979$	−4.08204	−	2.72753i	−0.130463	−	0.0871723i
$980$	−1.91481	−	3.68915i	−0.0611664	−	0.117845i
$981$	−26.7195	−	5.31485i	−0.853089	−	0.169690i
$982$	0.291449	+	2.05025i	0.00930050	+	0.0654261i
$983$	−0.628339	−	1.51695i	−0.0200409	−	0.0483831i	0.913542	−	0.406744i	$-0.133336\pi$
$983$	−0.628339	−	1.51695i	−0.0200409	−	0.0483831i	−0.933583	+	0.358361i	$0.883336\pi$
$984$	1.69560	+	54.8193i	0.0540538	+	1.74758i
$985$	−9.39134	+	22.6727i	−0.299233	+	0.722412i
$986$	−8.82627	+	34.3525i	−0.281086	+	1.09401i
$987$	61.5547	−	41.1295i	1.95931	−	1.30917i
$988$	−2.79691	+	5.08358i	−0.0889815	+	0.161730i
$989$	0.352195	+	1.77060i	0.0111991	+	0.0563019i
$990$	16.5318	+	7.94182i	0.525415	+	0.252408i
$991$			0.482249i			0.0153191i	0.999971	+	0.00765957i	$0.00243814\pi$
$991$			0.482249i			0.0153191i	−0.999971	+	0.00765957i	$0.997562\pi$
$992$	−6.60687	−	56.2186i	−0.209768	−	1.78494i
$993$			15.5019i			0.491938i
$994$	8.01019	−	16.6741i	0.254068	−	0.528871i
$995$	−0.154218	−	0.775305i	−0.00488903	−	0.0245788i
$996$	−36.2675	+	10.5237i	−1.14918	+	0.333456i
$997$	−5.71075	+	3.81580i	−0.180861	+	0.120848i	−0.642705	−	0.766114i	$-0.722188\pi$
$997$	−5.71075	+	3.81580i	−0.180861	+	0.120848i	0.461844	+	0.886961i	$0.347188\pi$
$998$	20.5518	+	5.28041i	0.650555	+	0.167149i
$999$	−2.02955	+	4.89978i	−0.0642123	+	0.155022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.53.6	yes	56
3.2	odd	2		576.2.bd.a.181.2		56
4.3	odd	2		256.2.i.a.49.7		56
8.3	odd	2		512.2.i.a.353.1		56
8.5	even	2		512.2.i.b.353.7		56
64.3	odd	16		512.2.i.a.161.1		56
64.29	even	16	inner	64.2.i.a.29.6	✓	56
64.35	odd	16		256.2.i.a.209.7		56
64.61	even	16		512.2.i.b.161.7		56
192.29	odd	16		576.2.bd.a.541.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.6	✓	56	64.29	even	16	inner
64.2.i.a.53.6	yes	56	1.1	even	1	trivial
256.2.i.a.49.7		56	4.3	odd	2
256.2.i.a.209.7		56	64.35	odd	16
512.2.i.a.161.1		56	64.3	odd	16
512.2.i.a.353.1		56	8.3	odd	2
512.2.i.b.161.7		56	64.61	even	16
512.2.i.b.353.7		56	8.5	even	2
576.2.bd.a.181.2		56	3.2	odd	2
576.2.bd.a.541.2		56	192.29	odd	16

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)

\(f(q)\)	\(=\)	\(q+(0.468362 + 1.33441i) q^{2} +(-2.98137 + 0.593031i) q^{3} +(-1.56127 + 1.24997i) q^{4} +(0.914126 + 1.36809i) q^{5} +(-2.18770 - 3.70060i) q^{6} +(2.65574 + 1.10004i) q^{7} +(-2.39921 - 1.49793i) q^{8} +(5.76522 - 2.38803i) q^{9} +O(q^{10})\)	\(q+(0.468362 + 1.33441i) q^{2} +(-2.98137 + 0.593031i) q^{3} +(-1.56127 + 1.24997i) q^{4} +(0.914126 + 1.36809i) q^{5} +(-2.18770 - 3.70060i) q^{6} +(2.65574 + 1.10004i) q^{7} +(-2.39921 - 1.49793i) q^{8} +(5.76522 - 2.38803i) q^{9} +(-1.39744 + 1.86057i) q^{10} +(0.246413 - 1.23880i) q^{11} +(3.91346 - 4.65250i) q^{12} +(0.319413 - 0.478036i) q^{13} +(-0.224055 + 4.05906i) q^{14} +(-3.53666 - 3.53666i) q^{15} +(0.875149 - 3.90309i) q^{16} +(-3.38390 + 3.38390i) q^{17} +(5.88682 + 6.57468i) q^{18} +(4.19561 + 2.80342i) q^{19} +(-3.13727 - 0.993326i) q^{20} +(-8.57011 - 1.70470i) q^{21} +(1.76847 - 0.251393i) q^{22} +(0.178010 + 0.429755i) q^{23} +(8.04124 + 3.04308i) q^{24} +(0.877384 - 2.11819i) q^{25} +(0.787494 + 0.202333i) q^{26} +(-8.18962 + 5.47213i) q^{27} +(-5.52137 + 1.60213i) q^{28} +(-1.02242 - 5.14005i) q^{29} +(3.06290 - 6.37578i) q^{30} -10.0065i q^{31} +(5.61819 - 0.660257i) q^{32} +3.83945i q^{33} +(-6.10038 - 2.93060i) q^{34} +(0.922728 + 4.63887i) q^{35} +(-6.01612 + 10.9347i) q^{36} +(0.447703 - 0.299146i) q^{37} +(-1.77583 + 6.91166i) q^{38} +(-0.668798 + 1.61462i) q^{39} +(-0.143878 - 4.65162i) q^{40} +(2.44115 + 5.89346i) q^{41} +(-1.73915 - 12.2344i) q^{42} +(3.80641 + 0.757142i) q^{43} +(1.16375 + 2.24212i) q^{44} +(8.53718 + 5.70436i) q^{45} +(-0.490094 + 0.438819i) q^{46} +(-5.99084 + 5.99084i) q^{47} +(-0.294489 + 12.1555i) q^{48} +(0.893127 + 0.893127i) q^{49} +(3.23746 + 0.178704i) q^{50} +(8.08188 - 12.0954i) q^{51} +(0.0988389 + 1.14560i) q^{52} +(0.810472 - 4.07452i) q^{53} +(-11.1378 - 8.36533i) q^{54} +(1.92004 - 0.795307i) q^{55} +(-4.72389 - 6.61736i) q^{56} +(-14.1712 - 5.86989i) q^{57} +(6.38004 - 3.77172i) q^{58} +(-1.03615 - 1.55070i) q^{59} +(9.94242 + 1.10097i) q^{60} +(-6.47490 + 1.28794i) q^{61} +(13.3528 - 4.68668i) q^{62} +17.9379 q^{63} +(3.51240 + 7.18770i) q^{64} +0.945978 q^{65} +(-5.12339 + 1.79826i) q^{66} +(6.01983 - 1.19742i) q^{67} +(1.05342 - 9.51296i) q^{68} +(-0.785572 - 1.17569i) q^{69} +(-5.75795 + 3.40396i) q^{70} +(-4.20400 - 1.74136i) q^{71} +(-17.4091 - 2.90652i) q^{72} +(-0.911379 + 0.377506i) q^{73} +(0.608868 + 0.457308i) q^{74} +(-1.35965 + 6.83542i) q^{75} +(-10.0547 + 0.867487i) q^{76} +(2.01715 - 3.01887i) q^{77} +(-2.46780 - 0.136220i) q^{78} +(0.152459 + 0.152459i) q^{79} +(6.13976 - 2.37064i) q^{80} +(7.93360 - 7.93360i) q^{81} +(-6.72092 + 6.01776i) q^{82} +(-5.16472 - 3.45096i) q^{83} +(15.5111 - 8.05087i) q^{84} +(-7.72277 - 1.53615i) q^{85} +(0.772445 + 5.43391i) q^{86} +(6.09641 + 14.7180i) q^{87} +(-2.44684 + 2.60303i) q^{88} +(1.48745 - 3.59102i) q^{89} +(-3.61343 + 14.0638i) q^{90} +(1.37414 - 0.918171i) q^{91} +(-0.815104 - 0.448458i) q^{92} +(5.93418 + 29.8331i) q^{93} +(-10.8001 - 5.18832i) q^{94} +8.30263i q^{95} +(-16.3583 + 5.30023i) q^{96} +13.7742i q^{97} +(-0.773486 + 1.61010i) q^{98} +(-1.53767 - 7.73041i) 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

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