LMFDB - Embedded newform 128.2.k.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

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("128.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	128.13
Dual form			128.2.k.a.69.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36942 - 0.353095i) q^{2} +(-0.855442 - 2.82001i) q^{3} +(1.75065 + 0.967074i) q^{4} +(-0.0181846 - 0.184631i) q^{5} +(0.175731 + 4.16385i) q^{6} +(1.98359 - 2.96866i) q^{7} +(-2.05591 - 1.94248i) q^{8} +(-4.72629 + 3.15801i) q^{9} +O(q^{10})$	\(q+(-1.36942 - 0.353095i) q^{2} +(-0.855442 - 2.82001i) q^{3} +(1.75065 + 0.967074i) q^{4} +(-0.0181846 - 0.184631i) q^{5} +(0.175731 + 4.16385i) q^{6} +(1.98359 - 2.96866i) q^{7} +(-2.05591 - 1.94248i) q^{8} +(-4.72629 + 3.15801i) q^{9} +(-0.0402899 + 0.259259i) q^{10} +(-3.55038 + 1.89772i) q^{11} +(1.22958 - 5.76413i) q^{12} +(-4.45994 - 0.439266i) q^{13} +(-3.76460 + 3.36496i) q^{14} +(-0.505107 + 0.209222i) q^{15} +(2.12954 + 3.38601i) q^{16} +(2.85923 + 1.18433i) q^{17} +(7.58738 - 2.65582i) q^{18} +(5.20552 - 4.27206i) q^{19} +(0.146717 - 0.340810i) q^{20} +(-10.0685 - 3.05425i) q^{21} +(5.53206 - 1.34516i) q^{22} +(0.310799 - 1.56249i) q^{23} +(-3.71911 + 7.45938i) q^{24} +(4.87017 - 0.968737i) q^{25} +(5.95245 + 2.17632i) q^{26} +(6.11472 + 5.01822i) q^{27} +(6.34349 - 3.27879i) q^{28} +(1.66397 - 3.11306i) q^{29} +(0.765581 - 0.108163i) q^{30} +(-2.12713 + 2.12713i) q^{31} +(-1.72066 - 5.38882i) q^{32} +(8.38874 + 8.38874i) q^{33} +(-3.49731 - 2.63143i) q^{34} +(-0.584178 - 0.312249i) q^{35} +(-11.3281 + 0.957886i) q^{36} +(-0.363413 + 0.442819i) q^{37} +(-8.63701 + 4.01222i) q^{38} +(2.57649 + 12.9529i) q^{39} +(-0.321256 + 0.414908i) q^{40} +(1.19574 + 0.237847i) q^{41} +(12.7096 + 7.73770i) q^{42} +(-0.201123 + 0.663013i) q^{43} +(-8.05071 - 0.111244i) q^{44} +(0.669012 + 0.815194i) q^{45} +(-0.977325 + 2.02998i) q^{46} +(3.20111 - 7.72816i) q^{47} +(7.72691 - 8.90186i) q^{48} +(-2.19950 - 5.31007i) q^{49} +(-7.01138 - 0.393020i) q^{50} +(0.893926 - 9.07618i) q^{51} +(-7.38299 - 5.08209i) q^{52} +(1.56257 + 2.92337i) q^{53} +(-6.60175 - 9.03116i) q^{54} +(0.414940 + 0.621002i) q^{55} +(-9.84465 + 2.25021i) q^{56} +(-16.5003 - 11.0251i) q^{57} +(-3.37789 + 3.67557i) q^{58} +(11.3185 - 1.11477i) q^{59} +(-1.08660 - 0.122201i) q^{60} +(10.2039 - 3.09531i) q^{61} +(3.66402 - 2.16186i) q^{62} +20.2950i q^{63} +(0.453546 + 7.98713i) q^{64} +0.831432i q^{65} +(-8.52573 - 14.4498i) q^{66} +(-4.23438 + 1.28449i) q^{67} +(3.86016 + 4.83843i) q^{68} +(-4.67213 + 0.460164i) q^{69} +(0.689733 + 0.633872i) q^{70} +(-13.1426 - 8.78163i) q^{71} +(15.8512 + 2.68814i) q^{72} +(6.13916 + 9.18790i) q^{73} +(0.654023 - 0.478089i) q^{74} +(-6.89800 - 12.9052i) q^{75} +(13.2444 - 2.44475i) q^{76} +(-1.40884 + 14.3042i) q^{77} +(1.04529 - 18.6477i) q^{78} +(1.76236 + 4.25472i) q^{79} +(0.586438 - 0.454752i) q^{80} +(2.39485 - 5.78169i) q^{81} +(-1.55349 - 0.747923i) q^{82} +(3.20230 + 3.90202i) q^{83} +(-14.6727 - 15.0839i) q^{84} +(0.166670 - 0.549439i) q^{85} +(0.509529 - 0.836931i) q^{86} +(-10.2023 - 2.02937i) q^{87} +(10.9856 + 2.99500i) q^{88} +(1.78282 + 8.96285i) q^{89} +(-0.628321 - 1.35257i) q^{90} +(-10.1507 + 12.3687i) q^{91} +(2.05515 - 2.43481i) q^{92} +(7.81816 + 4.17889i) q^{93} +(-7.11245 + 9.45284i) q^{94} +(-0.883415 - 0.883415i) q^{95} +(-13.7246 + 9.46210i) q^{96} +(3.16077 - 3.16077i) q^{97} +(1.13710 + 8.04837i) q^{98} +(10.7871 - 20.1813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 32 q^{50} - 16 q^{51} + 80 q^{52} - 16 q^{53} + 112 q^{54} - 16 q^{55} + 96 q^{56} - 16 q^{57} + 128 q^{58} - 16 q^{59} + 176 q^{60} - 16 q^{61} + 80 q^{62} + 176 q^{64} + 176 q^{66} - 16 q^{67} + 80 q^{68} - 16 q^{69} + 176 q^{70} - 16 q^{71} + 128 q^{72} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 112 q^{76} - 16 q^{77} + 80 q^{78} - 16 q^{79} + 32 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−1.36942	−	0.353095i	−0.968329	−	0.249676i
$2$	−1.36942	−	0.353095i	−0.968329	−	0.249676i
$3$	−0.855442	−	2.82001i	−0.493890	−	1.62814i	−0.749964	−	0.661479i	$-0.769929\pi$
$3$	−0.855442	−	2.82001i	−0.493890	−	1.62814i	0.256074	−	0.966657i	$-0.417571\pi$
$4$	1.75065	+	0.967074i	0.875324	+	0.483537i
$5$	−0.0181846	−	0.184631i	−0.00813239	−	0.0825695i	0.990262	−	0.139218i	$-0.0444587\pi$
$5$	−0.0181846	−	0.184631i	−0.00813239	−	0.0825695i	−0.998394	+	0.0566480i	$0.981959\pi$
$6$	0.175731	+	4.16385i	0.0717418	+	1.69988i
$7$	1.98359	−	2.96866i	0.749728	−	1.12205i	−0.238809	−	0.971067i	$-0.576757\pi$
$7$	1.98359	−	2.96866i	0.749728	−	1.12205i	0.988537	−	0.150981i	$-0.0482431\pi$
$8$	−2.05591	−	1.94248i	−0.726875	−	0.686770i
$9$	−4.72629	+	3.15801i	−1.57543	+	1.05267i
$10$	−0.0402899	+	0.259259i	−0.0127408	+	0.0819850i
$11$	−3.55038	+	1.89772i	−1.07048	+	0.572184i	−0.909895	−	0.414838i	$-0.863838\pi$
$11$	−3.55038	+	1.89772i	−1.07048	+	0.572184i	−0.160585	+	0.987022i	$0.551338\pi$
$12$	1.22958	−	5.76413i	0.354950	−	1.66396i
$13$	−4.45994	−	0.439266i	−1.23697	−	0.121830i	−0.541693	−	0.840577i	$-0.682216\pi$
$13$	−4.45994	−	0.439266i	−1.23697	−	0.121830i	−0.695273	+	0.718746i	$0.744716\pi$
$14$	−3.76460	+	3.36496i	−1.00613	+	0.899323i
$15$	−0.505107	+	0.209222i	−0.130418	+	0.0540209i
$16$	2.12954	+	3.38601i	0.532384	+	0.846503i
$17$	2.85923	+	1.18433i	0.693464	+	0.287242i	0.701443	−	0.712726i	$-0.252540\pi$
$17$	2.85923	+	1.18433i	0.693464	+	0.287242i	−0.00797851	+	0.999968i	$0.502540\pi$
$18$	7.58738	−	2.65582i	1.78836	−	0.625984i
$19$	5.20552	−	4.27206i	1.19423	−	0.980078i	0.194228	−	0.980956i	$-0.437780\pi$
$19$	5.20552	−	4.27206i	1.19423	−	0.980078i	1.00000		0.000878713i	$0.000279703\pi$
$20$	0.146717	−	0.340810i	0.0328069	−	0.0762074i
$21$	−10.0685	−	3.05425i	−2.19713	−	0.666492i
$22$	5.53206	−	1.34516i	1.17944	−	0.286789i
$23$	0.310799	−	1.56249i	0.0648062	−	0.325803i	−0.934759	−	0.355282i	$-0.884385\pi$
$23$	0.310799	−	1.56249i	0.0648062	−	0.325803i	0.999565	+	0.0294793i	$0.00938491\pi$
$24$	−3.71911	+	7.45938i	−0.759160	+	1.52264i
$25$	4.87017	−	0.968737i	0.974034	−	0.193747i
$26$	5.95245	+	2.17632i	1.16737	+	0.426812i
$27$	6.11472	+	5.01822i	1.17678	+	0.965758i
$28$	6.34349	−	3.27879i	1.19881	−	0.619634i
$29$	1.66397	−	3.11306i	0.308991	−	0.578082i	−0.678715	−	0.734401i	$-0.737463\pi$
$29$	1.66397	−	3.11306i	0.308991	−	0.578082i	0.987706	+	0.156320i	$0.0499630\pi$
$30$	0.765581	−	0.108163i	0.139775	−	0.0197478i
$31$	−2.12713	+	2.12713i	−0.382043	+	0.382043i	−0.871838	−	0.489795i	$-0.837072\pi$
$31$	−2.12713	+	2.12713i	−0.382043	+	0.382043i	0.489795	+	0.871838i	$0.337072\pi$
$32$	−1.72066	−	5.38882i	−0.304172	−	0.952617i
$33$	8.38874	+	8.38874i	1.46029	+	1.46029i
$34$	−3.49731	−	2.63143i	−0.599784	−	0.451286i
$35$	−0.584178	−	0.312249i	−0.0987440	−	0.0527798i
$36$	−11.3281	+	0.957886i	−1.88802	+	0.159648i
$37$	−0.363413	+	0.442819i	−0.0597447	+	0.0727991i	−0.802025	−	0.597290i	$-0.796244\pi$
$37$	−0.363413	+	0.442819i	−0.0597447	+	0.0727991i	0.742281	+	0.670089i	$0.233744\pi$
$38$	−8.63701	+	4.01222i	−1.40111	+	0.650868i
$39$	2.57649	+	12.9529i	0.412568	+	2.07412i
$40$	−0.321256	+	0.414908i	−0.0507951	+	0.0656028i
$41$	1.19574	+	0.237847i	0.186743	+	0.0371455i	0.287576	−	0.957758i	$-0.407151\pi$
$41$	1.19574	+	0.237847i	0.186743	+	0.0371455i	−0.100833	+	0.994903i	$0.532151\pi$
$42$	12.7096	+	7.73770i	1.96114	+	1.19395i
$43$	−0.201123	+	0.663013i	−0.0306709	+	0.101109i	−0.970940	−	0.239325i	$-0.923074\pi$
$43$	−0.201123	+	0.663013i	−0.0306709	+	0.101109i	0.940269	+	0.340434i	$0.110574\pi$
$44$	−8.05071	−	0.111244i	−1.21369	−	0.0167706i
$45$	0.669012	+	0.815194i	0.0997304	+	0.121522i
$46$	−0.977325	+	2.02998i	−0.144099	+	0.299304i
$47$	3.20111	−	7.72816i	0.466930	−	1.12727i	−0.498567	−	0.866851i	$-0.666140\pi$
$47$	3.20111	−	7.72816i	0.466930	−	1.12727i	0.965496	−	0.260417i	$-0.0838599\pi$
$48$	7.72691	−	8.90186i	1.11528	−	1.28487i
$49$	−2.19950	−	5.31007i	−0.314215	−	0.758581i
$50$	−7.01138	−	0.393020i	−0.991560	−	0.0555814i
$51$	0.893926	−	9.07618i	0.125175	−	1.27092i
$52$	−7.38299	−	5.08209i	−1.02384	−	0.704760i
$53$	1.56257	+	2.92337i	0.214636	+	0.401556i	0.966081	−	0.258240i	$-0.0831427\pi$
$53$	1.56257	+	2.92337i	0.214636	+	0.401556i	−0.751445	+	0.659796i	$0.770643\pi$
$54$	−6.60175	−	9.03116i	−0.898384	−	1.22899i
$55$	0.414940	+	0.621002i	0.0559505	+	0.0837359i
$56$	−9.84465	+	2.25021i	−1.31555	+	0.300697i
$57$	−16.5003	−	11.0251i	−2.18552	−	1.46032i
$58$	−3.37789	+	3.67557i	−0.443538	+	0.482626i
$59$	11.3185	−	1.11477i	1.47354	−	0.145131i	0.670878	−	0.741567i	$-0.265917\pi$
$59$	11.3185	−	1.11477i	1.47354	−	0.145131i	0.802660	+	0.596437i	$0.203417\pi$
$60$	−1.08660	−	0.122201i	−0.140279	−	0.0157761i
$61$	10.2039	−	3.09531i	1.30647	−	0.396313i	0.441105	−	0.897456i	$-0.354587\pi$
$61$	10.2039	−	3.09531i	1.30647	−	0.396313i	0.865365	+	0.501142i	$0.167087\pi$
$62$	3.66402	−	2.16186i	0.465331	−	0.274557i
$63$			20.2950i			2.55692i
$64$	0.453546	+	7.98713i	0.0566933	+	0.998392i
$65$			0.831432i			0.103126i
$66$	−8.52573	−	14.4498i	−1.04944	−	1.77864i
$67$	−4.23438	+	1.28449i	−0.517312	+	0.156925i	−0.538136	−	0.842858i	$-0.680871\pi$
$67$	−4.23438	+	1.28449i	−0.517312	+	0.156925i	0.0208236	+	0.999783i	$0.493371\pi$
$68$	3.86016	+	4.83843i	0.468114	+	0.586745i
$69$	−4.67213	+	0.460164i	−0.562458	+	0.0553973i
$70$	0.689733	+	0.633872i	0.0824389	+	0.0757622i
$71$	−13.1426	−	8.78163i	−1.55974	−	1.04219i	−0.972536	−	0.232752i	$-0.925227\pi$
$71$	−13.1426	−	8.78163i	−1.55974	−	1.04219i	−0.587208	−	0.809436i	$-0.699773\pi$
$72$	15.8512	+	2.68814i	1.86808	+	0.316800i
$73$	6.13916	+	9.18790i	0.718534	+	1.07536i	0.993492	+	0.113906i	$0.0363362\pi$
$73$	6.13916	+	9.18790i	0.718534	+	1.07536i	−0.274958	+	0.961456i	$0.588664\pi$
$74$	0.654023	−	0.478089i	0.0760287	−	0.0555767i
$75$	−6.89800	−	12.9052i	−0.796512	−	1.49017i
$76$	13.2444	−	2.44475i	1.51924	−	0.280432i
$77$	−1.40884	+	14.3042i	−0.160552	+	1.63011i
$78$	1.04529	−	18.6477i	0.118356	−	2.11144i
$79$	1.76236	+	4.25472i	0.198281	+	0.478694i	0.991478	−	0.130272i	$-0.0415849\pi$
$79$	1.76236	+	4.25472i	0.198281	+	0.478694i	−0.793197	+	0.608965i	$0.791585\pi$
$80$	0.586438	−	0.454752i	0.0655658	−	0.0508428i
$81$	2.39485	−	5.78169i	0.266095	−	0.642410i
$82$	−1.55349	−	0.747923i	−0.171554	−	0.0825943i
$83$	3.20230	+	3.90202i	0.351498	+	0.428302i	0.918504	−	0.395412i	$-0.129398\pi$
$83$	3.20230	+	3.90202i	0.351498	+	0.428302i	−0.567005	+	0.823714i	$0.691898\pi$
$84$	−14.6727	−	15.0839i	−1.60093	−	1.64579i
$85$	0.166670	−	0.549439i	0.0180779	−	0.0595950i
$86$	0.509529	−	0.836931i	0.0549439	−	0.0902486i
$87$	−10.2023	−	2.02937i	−1.09380	−	0.217571i
$88$	10.9856	+	2.99500i	1.17106	+	0.319268i
$89$	1.78282	+	8.96285i	0.188979	+	0.950060i	0.952561	+	0.304349i	$0.0984389\pi$
$89$	1.78282	+	8.96285i	0.188979	+	0.950060i	−0.763582	+	0.645711i	$0.776561\pi$
$90$	−0.628321	−	1.35257i	−0.0662308	−	0.142573i
$91$	−10.1507	+	12.3687i	−1.06409	+	1.29659i
$92$	2.05515	−	2.43481i	0.214264	−	0.253847i
$93$	7.81816	+	4.17889i	0.810706	+	0.433331i
$94$	−7.11245	+	9.45284i	−0.733593	+	0.974986i
$95$	−0.883415	−	0.883415i	−0.0906365	−	0.0906365i
$96$	−13.7246	+	9.46210i	−1.40076	+	0.965721i
$97$	3.16077	−	3.16077i	0.320928	−	0.320928i	−0.528195	−	0.849123i	$-0.677131\pi$
$97$	3.16077	−	3.16077i	0.320928	−	0.320928i	0.849123	+	0.528195i	$0.177131\pi$
$98$	1.13710	+	8.04837i	0.114864	+	0.813009i
$99$	10.7871	−	20.1813i	1.08415	−	2.02830i
$100$	9.46279	+	3.01390i	0.946279	+	0.301390i
$101$	−3.01337	−	2.47301i	−0.299842	−	0.246074i	0.472427	−	0.881370i	$-0.343378\pi$
$101$	−3.01337	−	2.47301i	−0.299842	−	0.246074i	−0.772269	+	0.635296i	$0.780878\pi$
$102$	−4.42892	+	12.1135i	−0.438528	+	1.19942i
$103$	−18.1171	+	3.60372i	−1.78513	+	0.355085i	−0.973429	−	0.228987i	$-0.926459\pi$
$103$	−18.1171	+	3.60372i	−1.78513	+	0.355085i	−0.811702	+	0.584072i	$0.801459\pi$
$104$	8.31598	+	9.56644i	0.815449	+	0.938067i
$105$	−0.380818	+	1.91450i	−0.0371640	+	0.186836i
$106$	−1.10760	−	4.55507i	−0.107580	−	0.442427i
$107$	−2.21823	−	0.672892i	−0.214444	−	0.0650509i	0.181235	−	0.983440i	$-0.441991\pi$
$107$	−2.21823	−	0.672892i	−0.214444	−	0.0650509i	−0.395679	+	0.918389i	$0.629491\pi$
$108$	5.85174	+	14.6985i	0.563084	+	1.41437i
$109$	−1.65005	+	1.35416i	−0.158046	+	0.129705i	−0.710093	−	0.704108i	$-0.751347\pi$
$109$	−1.65005	+	1.35416i	−0.158046	+	0.129705i	0.552047	+	0.833813i	$0.313847\pi$
$110$	−0.348957	−	0.996929i	−0.0332717	−	0.0950534i
$111$	1.55964	+	0.646022i	0.148034	+	0.0613177i
$112$	14.2760	+	0.394605i	1.34896	+	0.0372867i
$113$	8.27185	−	3.42631i	0.778150	−	0.322320i	0.0419816	−	0.999118i	$-0.486633\pi$
$113$	8.27185	−	3.42631i	0.778150	−	0.322320i	0.736169	+	0.676798i	$0.236633\pi$
$114$	18.7030	+	20.9243i	1.75169	+	1.95974i
$115$	−0.294137	−	0.0289699i	−0.0274284	−	0.00270146i
$116$	5.92358	−	3.84070i	0.549991	−	0.356600i
$117$	22.4662	−	12.0084i	2.07700	−	1.11018i
$118$	−15.8934	−	2.46990i	−1.46311	−	0.227372i
$119$	9.18742	−	6.13883i	0.842209	−	0.562746i
$120$	1.44486	+	0.551017i	0.131897	+	0.0503008i
$121$	2.89261	−	4.32909i	0.262964	−	0.393554i
$122$	−15.0663	+	0.635859i	−1.36404	+	0.0575679i
$123$	−0.352153	−	3.57547i	−0.0317525	−	0.322389i
$124$	−5.78094	+	1.66676i	−0.519144	+	0.149680i
$125$	−0.536695	−	1.76925i	−0.0480035	−	0.158246i
$126$	7.16604	−	27.7924i	0.638402	−	2.47594i
$127$	1.41307			0.125389			0.0626947	−	0.998033i	$-0.480031\pi$
$127$	1.41307			0.125389			0.0626947	+	0.998033i	$0.480031\pi$
$128$	2.19912	−	11.0979i	0.194376	−	0.980927i
$129$	2.04175			0.179766
$130$	0.293574	−	1.13858i	0.0257482	−	0.0998604i
$131$	5.41851	+	17.8624i	0.473417	+	1.56065i	0.790631	+	0.612293i	$0.209753\pi$
$131$	5.41851	+	17.8624i	0.473417	+	1.56065i	−0.317214	+	0.948354i	$0.602747\pi$
$132$	6.57320	+	22.7983i	0.572124	+	1.98433i
$133$	−2.35665	−	23.9274i	−0.204347	−	2.07477i
$134$	6.25221	−	0.263868i	0.540109	−	0.0227947i
$135$	0.815327	−	1.22022i	0.0701722	−	0.105020i
$136$	−3.57778	−	7.98887i	−0.306792	−	0.685040i
$137$	5.32195	−	3.55602i	0.454685	−	0.303811i	−0.307057	−	0.951691i	$-0.599344\pi$
$137$	5.32195	−	3.55602i	0.454685	−	0.303811i	0.761742	+	0.647880i	$0.224344\pi$
$138$	6.56061	+	1.01954i	0.558476	+	0.0867893i
$139$	−3.65288	+	1.95250i	−0.309833	+	0.165609i	−0.618984	−	0.785404i	$-0.712455\pi$
$139$	−3.65288	+	1.95250i	−0.309833	+	0.165609i	0.309150	+	0.951013i	$0.399955\pi$
$140$	−0.720721	−	1.11158i	−0.0609120	−	0.0939458i
$141$	−24.5319	−	2.41618i	−2.06596	−	0.203479i
$142$	14.8971	+	16.6664i	1.25014	+	1.39861i
$143$	16.6681	−	6.90416i	1.39386	−	0.577355i
$144$	−20.7579	−	9.27819i	−1.72982	−	0.773182i
$145$	−0.605027	−	0.250610i	−0.0502448	−	0.0208121i
$146$	−5.16291	−	14.7498i	−0.427286	−	1.22071i
$147$	−13.0929	+	10.7451i	−1.07989	+	0.886240i
$148$	−1.06445	+	0.423774i	−0.0874970	+	0.0348340i
$149$	2.85267	+	0.865347i	0.233700	+	0.0708920i	0.404962	−	0.914333i	$-0.367285\pi$
$149$	2.85267	+	0.865347i	0.233700	+	0.0708920i	−0.171263	+	0.985225i	$0.554785\pi$
$150$	4.88951	+	20.1084i	0.399227	+	1.64185i
$151$	−1.07742	+	5.41653i	−0.0876788	+	0.440791i	0.911862	+	0.410496i	$0.134645\pi$
$151$	−1.07742	+	5.41653i	−0.0876788	+	0.440791i	−0.999541	+	0.0302947i	$0.990355\pi$
$152$	−19.0005	−	1.32864i	−1.54114	−	0.107767i
$153$	−17.2537	+	3.43197i	−1.39488	+	0.277458i
$154$	6.98003	−	19.0910i	0.562467	−	1.53840i
$155$	0.431415	+	0.354053i	0.0346521	+	0.0284382i
$156$	−8.01586	+	25.1676i	−0.641782	+	2.01502i
$157$	−10.6633	+	19.9496i	−0.851023	+	1.59215i	−0.0459740	+	0.998943i	$0.514639\pi$
$157$	−10.6633	+	19.9496i	−0.851023	+	1.59215i	−0.805049	+	0.593209i	$0.797861\pi$
$158$	−0.911104	−	6.44880i	−0.0724835	−	0.513039i
$159$	6.90725	−	6.90725i	0.547781	−	0.547781i
$160$	−0.963654	+	0.415680i	−0.0761835	+	0.0328624i
$161$	−4.02201	−	4.02201i	−0.316979	−	0.316979i
$162$	−5.32106	+	7.07198i	−0.418062	+	0.555627i
$163$	−16.8486	−	9.00579i	−1.31969	−	0.705388i	−0.347079	−	0.937836i	$-0.612826\pi$
$163$	−16.8486	−	9.00579i	−1.31969	−	0.705388i	−0.972609	+	0.232448i	$0.925326\pi$
$164$	1.86330	+	1.57275i	0.145499	+	0.122811i
$165$	1.39628	−	1.70137i	0.108700	−	0.132451i
$166$	−3.00753	−	6.47424i	−0.233430	−	0.502498i
$167$	1.57994	+	7.94287i	0.122259	+	0.614638i	0.992524	+	0.122053i	$0.0389478\pi$
$167$	1.57994	+	7.94287i	0.122259	+	0.614638i	−0.870265	+	0.492585i	$0.836052\pi$
$168$	14.7672	+	25.8371i	1.13931	+	1.99338i
$169$	6.94792	+	1.38203i	0.534456	+	0.106310i
$170$	−0.422246	+	0.693564i	−0.0323848	+	0.0531940i
$171$	−11.1116	+	36.6301i	−0.849726	+	2.80117i
$172$	−0.993278	+	0.966202i	−0.0757367	+	0.0736722i
$173$	3.78812	+	4.61583i	0.288005	+	0.350935i	0.896835	−	0.442366i	$-0.145861\pi$
$173$	3.78812	+	4.61583i	0.288005	+	0.350935i	−0.608830	+	0.793301i	$0.708361\pi$
$174$	13.2547	+	6.38145i	1.00484	+	0.483776i
$175$	6.78459	−	16.3794i	0.512867	−	1.23817i
$176$	−13.9864	−	7.98037i	−1.05426	−	0.601543i
$177$	−12.8260	−	30.9646i	−0.964058	−	2.32744i
$178$	0.723296	−	12.9034i	0.0542134	−	0.967154i
$179$	−2.00384	+	20.3453i	−0.149774	+	1.52068i	0.567199	+	0.823581i	$0.308027\pi$
$179$	−2.00384	+	20.3453i	−0.149774	+	1.52068i	−0.716973	+	0.697101i	$0.754473\pi$
$180$	0.382852	+	2.07410i	0.0285361	+	0.154594i
$181$	−7.85658	−	14.6986i	−0.583975	−	1.09254i	−0.984356	−	0.176191i	$-0.943622\pi$
$181$	−7.85658	−	14.6986i	−0.583975	−	1.09254i	0.400381	−	0.916349i	$-0.368878\pi$
$182$	18.2680	−	13.3539i	1.35412	−	0.989854i
$183$	−17.4576	−	26.1272i	−1.29050	−	1.93138i
$184$	−3.67409	+	2.60863i	−0.270857	+	0.192311i
$185$	0.0883668	+	0.0590448i	0.00649685	+	0.00434106i
$186$	−9.23084	−	8.48323i	−0.676838	−	0.622021i
$187$	−12.3989	+	1.22118i	−0.906695	+	0.0893017i
$188$	13.0777	−	10.4336i	0.953791	−	0.760947i
$189$	27.0265	−	8.19841i	1.96589	−	0.596346i
$190$	0.897841	+	1.52170i	0.0651363	+	0.110396i
$191$		−	4.21640i		−	0.305088i	−0.988297	−	0.152544i	$-0.951253\pi$
$191$		−	4.21640i		−	0.305088i	0.988297	−	0.152544i	$-0.0487466\pi$
$192$	22.1358	−	8.11154i	1.59752	−	0.585400i
$193$		−	6.41458i		−	0.461732i	−0.972986	−	0.230866i	$-0.925844\pi$
$193$		−	6.41458i		−	0.461732i	0.972986	−	0.230866i	$-0.0741559\pi$
$194$	−5.44450	+	3.21239i	−0.390892	+	0.230636i
$195$	2.34465	−	0.711242i	0.167904	−	0.0509331i
$196$	1.28467	−	11.4231i	0.0917624	−	0.815939i
$197$	14.6772	−	1.44558i	1.04571	−	0.102993i	0.439454	−	0.898265i	$-0.355172\pi$
$197$	14.6772	−	1.44558i	1.04571	−	0.102993i	0.606253	+	0.795272i	$0.292672\pi$
$198$	−21.8981	+	23.8279i	−1.55623	+	1.69338i
$199$	16.5145	+	11.0346i	1.17068	+	0.782223i	0.979916	−	0.199413i	$-0.0639034\pi$
$199$	16.5145	+	11.0346i	1.17068	+	0.782223i	0.190764	+	0.981636i	$0.438903\pi$
$200$	−11.8944	−	7.46857i	−0.841060	−	0.528107i
$201$	7.24454	+	10.8422i	0.510990	+	0.764751i
$202$	3.25338	+	4.45061i	0.228907	+	0.313144i
$203$	−5.94099	−	11.1148i	−0.416976	−	0.780107i
$204$	10.3423	−	15.0247i	0.724105	−	1.05194i
$205$	0.0221700	−	0.225096i	0.00154842	−	0.0157214i
$206$	26.0825	+	1.46204i	1.81725	+	0.101865i
$207$	3.46544	+	8.36631i	0.240865	+	0.581499i
$208$	−8.01025	−	16.0368i	−0.555411	−	1.11196i
$209$	−10.3744	+	25.0461i	−0.717613	+	1.73247i
$210$	1.19750	−	2.48730i	0.0826355	−	0.171640i
$211$	10.5966	+	12.9120i	0.729498	+	0.888896i	0.997213	−	0.0746023i	$-0.0237687\pi$
$211$	10.5966	+	12.9120i	0.729498	+	0.888896i	−0.267716	+	0.963498i	$0.586269\pi$
$212$	−0.0915976	+	6.62891i	−0.00629095	+	0.455276i
$213$	−13.5216	+	44.5746i	−0.926482	+	3.05420i
$214$	2.80010	+	1.70472i	0.191411	+	0.116532i
$215$	0.126070	+	0.0250769i	0.00859791	+	0.00171023i
$216$	−2.82354	−	22.1948i	−0.192117	−	1.51016i
$217$	2.09536	+	10.5341i	0.142242	+	0.715099i
$218$	2.73777	−	1.27180i	0.185425	−	0.0861370i
$219$	20.6583	−	25.1722i	1.39596	−	1.70098i
$220$	0.125860	+	1.48843i	0.00848545	+	0.100350i
$221$	−12.2317	−	6.53800i	−0.822796	−	0.439794i
$222$	−1.90770	−	1.43538i	−0.128036	−	0.0963363i
$223$	−5.01101	−	5.01101i	−0.335562	−	0.335562i	0.519132	−	0.854694i	$-0.326255\pi$
$223$	−5.01101	−	5.01101i	−0.335562	−	0.335562i	−0.854694	+	0.519132i	$0.826255\pi$
$224$	−19.4106	−	5.58118i	−1.29693	−	0.372908i
$225$	−19.9586	+	19.9586i	−1.33057	+	1.33057i
$226$	−12.5375	+	1.77133i	−0.833982	+	0.117827i
$227$	7.73543	−	14.4720i	0.513419	−	0.960539i	−0.482971	−	0.875637i	$-0.660442\pi$
$227$	7.73543	−	14.4720i	0.513419	−	0.960539i	0.996389	−	0.0849021i	$-0.0270578\pi$
$228$	−18.2241	−	35.2581i	−1.20692	−	2.33503i
$229$	−6.01251	−	4.93434i	−0.397318	−	0.326071i	0.414427	−	0.910083i	$-0.363982\pi$
$229$	−6.01251	−	4.93434i	−0.397318	−	0.326071i	−0.811745	+	0.584012i	$0.801482\pi$
$230$	0.392569	+	0.143530i	0.0258852	+	0.00946411i
$231$	41.5432	−	8.26345i	2.73334	−	0.543695i
$232$	−9.46803	+	3.16796i	−0.621607	+	0.207987i
$233$	0.254375	−	1.27883i	0.0166646	−	0.0837788i	−0.971558	−	0.236802i	$-0.923901\pi$
$233$	0.254375	−	1.27883i	0.0166646	−	0.0837788i	0.988223	+	0.153023i	$0.0489008\pi$
$234$	−35.0059	+	8.51194i	−2.28841	+	0.556443i
$235$	−1.48507	−	0.450491i	−0.0968753	−	0.0293868i
$236$	20.8927	+	8.99422i	1.36000	+	0.585474i
$237$	10.4908	−	8.60956i	0.681449	−	0.559251i
$238$	−14.7491	+	5.16264i	−0.956040	+	0.334644i
$239$	−4.36764	−	1.80913i	−0.282519	−	0.117023i	0.236924	−	0.971528i	$-0.423861\pi$
$239$	−4.36764	−	1.80913i	−0.282519	−	0.117023i	−0.519443	+	0.854505i	$0.673861\pi$
$240$	−1.78407	−	1.26475i	−0.115161	−	0.0816393i
$241$	4.81238	−	1.99335i	0.309993	−	0.128403i	−0.222263	−	0.974987i	$-0.571344\pi$
$241$	4.81238	−	1.99335i	0.309993	−	0.128403i	0.532256	+	0.846583i	$0.321344\pi$
$242$	−5.48979	+	4.90700i	−0.352897	+	0.315434i
$243$	5.26344	+	0.518404i	0.337650	+	0.0332556i
$244$	20.8567	+	4.44909i	1.33522	+	0.284824i
$245$	−0.940407	+	0.502658i	−0.0600804	+	0.0321136i
$246$	−0.780232	+	5.02067i	−0.0497458	+	0.320106i
$247$	−25.0929	+	16.7665i	−1.59662	+	1.06683i
$248$	8.50508	−	0.241285i	0.540073	−	0.0153216i
$249$	8.26436	−	12.3685i	0.523733	−	0.783821i
$250$	0.110252	+	2.61236i	0.00697293	+	0.165220i
$251$	−0.903865	−	9.17709i	−0.0570514	−	0.579253i	−0.980633	−	0.195852i	$-0.937253\pi$
$251$	−0.903865	−	9.17709i	−0.0570514	−	0.579253i	0.923582	−	0.383401i	$-0.125247\pi$
$252$	−19.6267	+	35.5293i	−1.23637	+	2.23814i
$253$	1.86172	+	6.13726i	0.117045	+	0.385846i
$254$	−1.93509	−	0.498947i	−0.121418	−	0.0313067i
$255$	−1.69200			−0.105957
$256$	−6.93015	+	14.4213i	−0.433134	+	0.901329i
$257$	−22.9792			−1.43340			−0.716700	−	0.697381i	$-0.754348\pi$
$257$	−22.9792			−1.43340			−0.716700	+	0.697381i	$0.754348\pi$
$258$	−2.79603	−	0.720933i	−0.174073	−	0.0448833i
$259$	0.593717	+	1.95722i	0.0368918	+	0.121616i
$260$	−0.804056	+	1.45554i	−0.0498654	+	0.0902691i
$261$	1.96668	+	19.9681i	0.121735	+	1.23599i
$262$	−1.11311	−	26.3745i	−0.0687679	−	1.62942i
$263$	10.2222	−	15.2985i	0.630325	−	0.943348i	−0.369575	−	0.929201i	$-0.620497\pi$
$263$	10.2222	−	15.2985i	0.630325	−	0.943348i	0.999900	−	0.0141470i	$-0.00450328\pi$
$264$	−0.951554	−	33.5415i	−0.0585641	−	2.06434i
$265$	0.511330	−	0.341660i	0.0314108	−	0.0209880i
$266$	−5.22141	+	33.5989i	−0.320145	+	2.06008i
$267$	23.7503	−	12.6948i	1.45349	−	0.776908i
$268$	−8.65510	−	1.84628i	−0.528695	−	0.112779i
$269$	21.7419	+	2.14139i	1.32562	+	0.130563i	0.735926	−	0.677061i	$-0.236747\pi$
$269$	21.7419	+	2.14139i	1.32562	+	0.130563i	0.589698	+	0.807624i	$0.299247\pi$
$270$	−1.54738	+	1.38312i	−0.0941707	+	0.0841737i
$271$	1.11263	−	0.460866i	0.0675874	−	0.0279956i	−0.348634	−	0.937259i	$-0.613354\pi$
$271$	1.11263	−	0.460866i	0.0675874	−	0.0279956i	0.416221	+	0.909263i	$0.363354\pi$
$272$	2.07867	+	12.2034i	0.126038	+	0.739943i
$273$	43.5633	+	18.0445i	2.63657	+	1.09210i
$274$	−8.54363	+	2.99054i	−0.516139	+	0.180665i
$275$	−15.4526	+	12.6816i	−0.931825	+	0.764729i
$276$	−8.62426	−	3.71271i	−0.519120	−	0.223479i
$277$	6.71791	+	2.03786i	0.403640	+	0.122443i	0.485576	−	0.874195i	$-0.338610\pi$
$277$	6.71791	+	2.03786i	0.403640	+	0.122443i	−0.0819353	+	0.996638i	$0.526110\pi$
$278$	5.69176	−	1.38400i	0.341369	−	0.0830065i
$279$	3.33594	−	16.7709i	0.199717	−	1.00405i
$280$	0.594479	+	1.77671i	0.0355269	+	0.106179i
$281$	−8.48893	+	1.68855i	−0.506407	+	0.100731i	−0.441681	−	0.897172i	$-0.645618\pi$
$281$	−8.48893	+	1.68855i	−0.506407	+	0.100731i	−0.0647266	+	0.997903i	$0.520618\pi$
$282$	32.7414	+	11.9709i	1.94972	+	0.712854i
$283$	20.1549	+	16.5407i	1.19808	+	0.983241i	0.999995	+	0.00305658i	$0.000972942\pi$
$283$	20.1549	+	16.5407i	1.19808	+	0.983241i	0.198087	+	0.980184i	$0.436527\pi$
$284$	−14.5157	−	28.0834i	−0.861345	−	1.66645i
$285$	−1.73553	+	3.24695i	−0.102804	+	0.192333i
$286$	−25.2635	+	3.56930i	−1.49386	+	0.211057i
$287$	3.07795	−	3.07795i	0.181686	−	0.181686i
$288$	25.1502	+	20.0353i	1.48199	+	1.18059i
$289$	−5.24828	−	5.24828i	−0.308722	−	0.308722i
$290$	0.740050	+	0.556824i	0.0434572	+	0.0326978i
$291$	−11.6173	−	6.20957i	−0.681018	−	0.364012i
$292$	1.86213	+	22.0218i	0.108973	+	1.28873i
$293$	7.69339	−	9.37442i	0.449453	−	0.547660i	−0.498158	−	0.867086i	$-0.665990\pi$
$293$	7.69339	−	9.37442i	0.449453	−	0.547660i	0.947611	+	0.319426i	$0.103490\pi$
$294$	21.7238	−	10.0915i	1.26696	−	0.588551i
$295$	−0.411643	−	2.06947i	−0.0239668	−	0.120489i
$296$	1.60731	−	0.204476i	0.0934231	−	0.0118849i
$297$	−31.2328	−	6.21259i	−1.81231	−	0.360491i
$298$	−3.60096	−	2.19229i	−0.208598	−	0.126996i
$299$	−2.07250	+	6.83211i	−0.119856	+	0.395111i
$300$	0.404359	−	29.2634i	0.0233457	−	1.68952i
$301$	1.56931	+	1.91221i	0.0904537	+	0.110218i
$302$	3.38799	−	7.03710i	0.194957	−	0.404940i
$303$	−4.39616	+	10.6133i	−0.252553	+	0.609716i
$304$	25.5506	+	8.52844i	1.46543	+	0.489140i
$305$	−0.757042	−	1.82766i	−0.0433481	−	0.104652i
$306$	24.8394	+	1.39236i	1.41997	+	0.0795959i
$307$	0.166408	−	1.68957i	0.00949739	−	0.0964286i	−0.989267	−	0.146116i	$-0.953323\pi$
$307$	0.166408	−	1.68957i	0.00949739	−	0.0964286i	0.998765	+	0.0496877i	$0.0158226\pi$
$308$	−16.2996	+	23.6791i	−0.928755	+	1.34924i
$309$	25.6607	+	48.0077i	1.45978	+	2.73106i
$310$	−0.465776	−	0.637179i	−0.0264543	−	0.0361893i
$311$	4.12505	+	6.17357i	0.233910	+	0.350071i	0.929792	−	0.368085i	$-0.119986\pi$
$311$	4.12505	+	6.17357i	0.233910	+	0.350071i	−0.695882	+	0.718156i	$0.744986\pi$
$312$	19.8637	−	31.6347i	1.12456	−	1.79096i
$313$	−18.3279	−	12.2463i	−1.03595	−	0.692201i	−0.0833816	−	0.996518i	$-0.526572\pi$
$313$	−18.3279	−	12.2463i	−1.03595	−	0.692201i	−0.952571	+	0.304316i	$0.901572\pi$
$314$	21.6467	−	23.5543i	1.22159	−	1.32925i
$315$	3.74708	−	0.369055i	0.211124	−	0.0207939i
$316$	−1.02935	+	9.15286i	−0.0579056	+	0.514888i
$317$	−9.66980	+	2.93330i	−0.543110	+	0.164751i	−0.549906	−	0.835226i	$-0.685337\pi$
$317$	−9.66980	+	2.93330i	−0.543110	+	0.164751i	0.00679632	+	0.999977i	$0.497837\pi$
$318$	−11.8979	+	7.02004i	−0.667200	+	0.393665i
$319$			14.2103i			0.795625i
$320$	1.46643	−	0.228981i	0.0819757	−	0.0128005i
$321$			6.83105i			0.381272i
$322$	4.08769	+	6.92799i	0.227798	+	0.386082i
$323$	19.9433	−	6.04973i	1.10967	−	0.336616i
$324$	9.78387	−	7.80570i	0.543548	−	0.433650i
$325$	−22.1462	+	2.18121i	−1.22845	+	0.120992i
$326$	19.8931	+	18.2819i	1.10177	+	1.01254i
$327$	5.23027	+	3.49476i	0.289235	+	0.193261i
$328$	−1.99632	−	2.81169i	−0.110228	−	0.155250i
$329$	−16.5926	−	24.8325i	−0.914778	−	1.36906i
$330$	−2.51284	+	1.83688i	−0.138327	+	0.101117i
$331$	5.08073	+	9.50537i	0.279262	+	0.522462i	0.981975	−	0.189011i	$-0.0605282\pi$
$331$	5.08073	+	9.50537i	0.279262	+	0.522462i	−0.702713	+	0.711473i	$0.748028\pi$
$332$	1.83257	+	9.92792i	0.100575	+	0.544866i
$333$	0.319167	−	3.24055i	0.0174902	−	0.177581i
$334$	0.640985	−	11.4350i	0.0350731	−	0.625697i
$335$	0.314156	+	0.758441i	0.0171642	+	0.0414380i
$336$	−11.0995	−	40.5962i	−0.605529	−	2.21471i
$337$	10.1316	−	24.4599i	0.551905	−	1.33242i	−0.364140	−	0.931344i	$-0.618637\pi$
$337$	10.1316	−	24.4599i	0.551905	−	1.33242i	0.916046	−	0.401074i	$-0.131363\pi$
$338$	−9.02667	−	4.34586i	−0.490986	−	0.236384i
$339$	−16.7383	−	20.3957i	−0.909102	−	1.10774i
$340$	0.823129	−	0.800691i	0.0446404	−	0.0434236i
$341$	3.51542	−	11.5888i	0.190371	−	0.627569i
$342$	28.1504	−	46.2387i	1.52220	−	2.50030i
$343$	4.38569	+	0.872369i	0.236805	+	0.0471035i
$344$	1.70138	−	0.972419i	0.0917322	−	0.0524293i
$345$	0.169921	+	0.854252i	0.00914826	+	0.0459914i
$346$	−3.55771	−	7.65860i	−0.191264	−	0.411729i
$347$	−15.3175	+	18.6644i	−0.822286	+	1.00196i	0.177554	+	0.984111i	$0.443181\pi$
$347$	−15.3175	+	18.6644i	−0.822286	+	1.00196i	−0.999841	+	0.0178478i	$0.994319\pi$
$348$	−15.8981	−	13.4191i	−0.852228	−	0.719339i
$349$	−20.1765	−	10.7846i	−1.08003	−	0.577286i	−0.167320	−	0.985903i	$-0.553511\pi$
$349$	−20.1765	−	10.7846i	−1.08003	−	0.577286i	−0.912706	+	0.408617i	$0.866011\pi$
$350$	−15.0745	+	20.0348i	−0.805765	+	1.07091i
$351$	−25.0670	−	25.0670i	−1.33798	−	1.33798i
$352$	16.3355	+	15.8670i	0.870682	+	0.845716i
$353$	−12.5040	+	12.5040i	−0.665521	+	0.665521i	−0.956676	−	0.291155i	$-0.905960\pi$
$353$	−12.5040	+	12.5040i	−0.665521	+	0.665521i	0.291155	+	0.956676i	$0.405960\pi$
$354$	6.63074	+	46.9325i	0.352420	+	2.49443i
$355$	−1.38237	+	2.58623i	−0.0733685	+	0.137263i
$356$	−5.54664	+	17.4149i	−0.293971	+	0.922988i
$357$	−25.1709	−	20.6572i	−1.33219	−	1.09330i
$358$	9.92795	−	27.1539i	0.524708	−	1.43513i
$359$	3.36685	−	0.669707i	0.177695	−	0.0353458i	−0.105441	−	0.994426i	$-0.533625\pi$
$359$	3.36685	−	0.669707i	0.177695	−	0.0353458i	0.283136	+	0.959080i	$0.408625\pi$
$360$	0.208067	−	2.97551i	0.0109661	−	0.156823i
$361$	5.14022	−	25.8417i	0.270538	−	1.36009i
$362$	5.56898	+	22.9028i	0.292699	+	1.20374i
$363$	−14.6826	−	4.45391i	−0.770635	−	0.233770i
$364$	−29.7318	+	11.8368i	−1.55837	+	0.620415i
$365$	1.58473	−	1.30056i	0.0829488	−	0.0680743i
$366$	14.6815	+	41.9434i	0.767415	+	2.19242i
$367$	18.2022	+	7.53960i	0.950148	+	0.393564i	0.803286	−	0.595593i	$-0.203083\pi$
$367$	18.2022	+	7.53960i	0.950148	+	0.393564i	0.146861	+	0.989157i	$0.453083\pi$
$368$	5.95248	−	2.27502i	0.310295	−	0.118594i
$369$	−6.40253	+	2.65202i	−0.333303	+	0.138058i
$370$	−0.100163	−	0.112059i	−0.00520724	−	0.00582568i
$371$	11.7780	+	1.16003i	0.611483	+	0.0602258i
$372$	9.64555	+	14.8765i	0.500098	+	0.771311i
$373$	−15.6532	+	8.36679i	−0.810490	+	0.433216i	−0.823928	−	0.566694i	$-0.808222\pi$
$373$	−15.6532	+	8.36679i	−0.810490	+	0.433216i	0.0134387	+	0.999910i	$0.495722\pi$
$374$	17.4105	+	2.70566i	0.900276	+	0.139906i
$375$	−4.53019	+	3.02698i	−0.233938	+	0.156312i
$376$	−21.5930	+	9.67033i	−1.11357	+	0.498709i
$377$	−8.78866	+	13.1532i	−0.452639	+	0.677422i
$378$	−39.9056	+	1.68417i	−2.05252	+	0.0866245i
$379$	0.241964	+	2.45670i	0.0124289	+	0.126192i	0.999397	−	0.0347238i	$-0.0110552\pi$
$379$	0.241964	+	2.45670i	0.0124289	+	0.126192i	−0.986968	+	0.160916i	$0.948555\pi$
$380$	−0.692221	−	2.40088i	−0.0355102	−	0.123162i
$381$	−1.20880	−	3.98487i	−0.0619286	−	0.204151i
$382$	−1.48879	+	5.77404i	−0.0761731	+	0.295426i
$383$	−31.2340			−1.59598			−0.797992	−	0.602668i	$-0.794104\pi$
$383$	−31.2340			−1.59598			−0.797992	+	0.602668i	$0.794104\pi$
$384$	−33.1775	+	3.29208i	−1.69308	+	0.167998i
$385$	2.66662			0.135903
$386$	−2.26496	+	8.78429i	−0.115283	+	0.447108i
$387$	−1.14323	−	3.76874i	−0.0581139	−	0.191576i
$388$	8.59011	−	2.47670i	0.436097	−	0.125735i
$389$	2.27446	+	23.0930i	0.115320	+	1.17086i	0.862435	+	0.506167i	$0.168938\pi$
$389$	2.27446	+	23.0930i	0.115320	+	1.17086i	−0.747115	+	0.664694i	$0.768562\pi$
$390$	−3.46196	+	0.146108i	−0.175303	+	0.00739847i
$391$	2.73915	−	4.09943i	0.138525	−	0.207317i
$392$	−5.79272	+	15.1895i	−0.292576	+	0.767187i
$393$	45.7371	−	30.5605i	2.30713	−	1.54157i
$394$	−20.6097	−	3.20283i	−1.03830	−	0.161356i
$395$	0.753506	−	0.402757i	0.0379130	−	0.0202649i
$396$	38.4013	−	24.8984i	1.92974	−	1.25119i
$397$	21.9314	+	2.16005i	1.10070	+	0.108410i	0.632017	−	0.774954i	$-0.282227\pi$
$397$	21.9314	+	2.16005i	1.10070	+	0.108410i	0.468687	+	0.883364i	$0.344727\pi$
$398$	−18.7191	−	20.9423i	−0.938302	−	1.04974i
$399$	−65.4598	+	27.1143i	−3.27709	+	1.35741i
$400$	13.6514	+	14.4275i	0.682568	+	0.721374i
$401$	−21.4657	−	8.89138i	−1.07195	−	0.444014i	−0.224269	−	0.974527i	$-0.571999\pi$
$401$	−21.4657	−	8.89138i	−1.07195	−	0.444014i	−0.847677	+	0.530513i	$0.821999\pi$
$402$	−6.09252	−	17.4056i	−0.303867	−	0.868113i
$403$	10.4212	−	8.55249i	0.519119	−	0.426030i
$404$	−2.88377	−	7.24352i	−0.143473	−	0.360379i
$405$	−1.11103	−	0.337027i	−0.0552075	−	0.0167470i
$406$	4.21115	+	17.3186i	0.208996	+	0.859509i
$407$	0.449907	−	2.26183i	0.0223010	−	0.112115i
$408$	−19.4681	+	16.9234i	−0.963816	+	0.837833i
$409$	−3.95762	+	0.787220i	−0.195692	+	0.0389255i	−0.291963	−	0.956430i	$-0.594308\pi$
$409$	−3.95762	+	0.787220i	−0.195692	+	0.0389255i	0.0962712	+	0.995355i	$0.469308\pi$
$410$	−0.109840	+	0.300424i	−0.00542463	+	0.0148369i
$411$	−14.5806	−	11.9660i	−0.719210	−	0.590240i
$412$	−35.2017	−	11.2117i	−1.73426	−	0.552363i
$413$	19.1419	−	35.8119i	0.941910	−	1.76219i
$414$	−1.79156	−	12.6807i	−0.0880502	−	0.623220i
$415$	0.662201	−	0.662201i	0.0325062	−	0.0325062i
$416$	5.30691	+	24.7896i	0.260193	+	1.21541i
$417$	8.63092	+	8.63092i	0.422658	+	0.422658i
$418$	23.0506	−	30.6355i	1.12744	−	1.49843i
$419$	4.84295	+	2.58861i	0.236594	+	0.126462i	0.585434	−	0.810720i	$-0.300924\pi$
$419$	4.84295	+	2.58861i	0.236594	+	0.126462i	−0.348840	+	0.937182i	$0.613424\pi$
$420$	−2.51814	+	2.98334i	−0.122873	+	0.145572i
$421$	22.6123	−	27.5531i	1.10205	−	1.34286i	0.167975	−	0.985791i	$-0.446277\pi$
$421$	22.6123	−	27.5531i	1.10205	−	1.34286i	0.934079	−	0.357066i	$-0.116223\pi$
$422$	−9.95206	−	21.4235i	−0.484459	−	1.04288i
$423$	9.27621	+	46.6347i	0.451025	+	2.26746i
$424$	2.46607	−	9.04545i	0.119763	−	0.439286i
$425$	15.0722	+	2.99805i	0.731110	+	0.145427i
$426$	34.2558	−	56.2672i	1.65970	−	2.72615i
$427$	11.0514	−	36.4316i	0.534815	−	1.76305i
$428$	−3.23260	−	3.32319i	−0.156254	−	0.160632i
$429$	−33.7284	−	41.0982i	−1.62842	−	1.98424i
$430$	−0.163789	−	0.0788557i	−0.00789861	−	0.00380276i
$431$	9.87867	−	23.8492i	0.475839	−	1.14878i	−0.485704	−	0.874123i	$-0.661437\pi$
$431$	9.87867	−	23.8492i	0.475839	−	1.14878i	0.961543	−	0.274654i	$-0.0885632\pi$
$432$	−3.97024	+	31.3910i	−0.191018	+	1.51030i
$433$	6.14114	+	14.8260i	0.295124	+	0.712493i	0.999995	+	0.00315727i	$0.00100499\pi$
$433$	6.14114	+	14.8260i	0.295124	+	0.712493i	−0.704871	+	0.709336i	$0.748995\pi$
$434$	0.850093	−	15.1655i	0.0408058	−	0.727966i
$435$	−0.189159	+	1.92057i	−0.00906950	+	0.0920842i
$436$	−4.19823	+	0.774939i	−0.201059	+	0.0371128i
$437$	−5.05719	−	9.46135i	−0.241918	−	0.452598i
$438$	−37.1782	+	27.1771i	−1.77644	+	1.29857i
$439$	5.73521	+	8.58335i	0.273727	+	0.409661i	0.942708	−	0.333618i	$-0.108270\pi$
$439$	5.73521	+	8.58335i	0.273727	+	0.409661i	−0.668982	+	0.743279i	$0.733270\pi$
$440$	0.353203	−	2.08274i	0.0168383	−	0.0992906i
$441$	27.1647	+	18.1509i	1.29356	+	0.864328i
$442$	14.4419	+	13.2723i	0.686932	+	0.631298i
$443$	−23.2460	+	2.28953i	−1.10445	+	0.108779i	−0.633767	−	0.773524i	$-0.718492\pi$
$443$	−23.2460	+	2.28953i	−1.10445	+	0.108779i	−0.470682	+	0.882303i	$0.655992\pi$
$444$	2.10562	+	2.63924i	0.0999284	+	0.125253i
$445$	1.62240	−	0.492150i	0.0769092	−	0.0233301i
$446$	5.09283	+	8.63156i	0.241153	+	0.408716i
$447$		−	8.78482i		−	0.415508i
$448$	24.6107	+	14.4968i	1.16275	+	0.684910i
$449$		−	5.48632i		−	0.258916i	−0.991585	−	0.129458i	$-0.958676\pi$
$449$		−	5.48632i		−	0.258916i	0.991585	−	0.129458i	$-0.0413237\pi$
$450$	34.3790	−	20.2845i	1.62064	−	0.956220i
$451$	−4.69670	+	1.42473i	−0.221159	+	0.0670878i
$452$	17.7946	+	2.00122i	0.836988	+	0.0941296i
$453$	16.1964	−	1.59520i	0.760972	−	0.0749492i
$454$	−15.7031	+	17.0869i	−0.736982	+	0.801930i
$455$	2.46824	+	1.64922i	0.115713	+	0.0773168i
$456$	12.5070	+	54.7182i	0.585695	+	2.56241i
$457$	17.3574	+	25.9773i	0.811947	+	1.21516i	0.973587	+	0.228315i	$0.0733216\pi$
$457$	17.3574	+	25.9773i	0.811947	+	1.21516i	−0.161640	+	0.986850i	$0.551678\pi$
$458$	6.49139	+	8.88020i	0.303323	+	0.414944i
$459$	11.5401	+	21.5901i	0.538648	+	1.00774i
$460$	−0.486914	−	0.335168i	−0.0227025	−	0.0156273i
$461$	−0.978656	+	9.93647i	−0.0455806	+	0.462787i	0.945120	+	0.326724i	$0.105945\pi$
$461$	−0.978656	+	9.93647i	−0.0455806	+	0.462787i	−0.990700	+	0.136063i	$0.956555\pi$
$462$	−59.8080	−	3.35251i	−2.78252	−	0.155973i
$463$	2.33920	+	5.64733i	0.108712	+	0.262454i	0.968868	−	0.247577i	$-0.0796342\pi$
$463$	2.33920	+	5.64733i	0.108712	+	0.262454i	−0.860156	+	0.510030i	$0.829634\pi$
$464$	14.0844	−	0.995172i	0.653850	−	0.0461997i
$465$	0.629384	−	1.51947i	0.0291870	−	0.0704636i
$466$	−0.799894	+	1.66144i	−0.0370544	+	0.0769647i
$467$	−5.67882	−	6.91966i	−0.262784	−	0.320204i	0.624857	−	0.780739i	$-0.285157\pi$
$467$	−5.67882	−	6.91966i	−0.262784	−	0.320204i	−0.887641	+	0.460536i	$0.847657\pi$
$468$	50.9434	+	0.703931i	2.35486	+	0.0325392i
$469$	−4.58610	+	15.1183i	−0.211766	+	0.698100i
$470$	1.87463	+	1.14128i	0.0864700	+	0.0526435i
$471$	65.3800	+	13.0049i	3.01255	+	0.599234i
$472$	−25.4352	−	19.6940i	−1.17075	−	0.906491i
$473$	−0.544150	−	2.73562i	−0.0250200	−	0.125784i
$474$	−17.4063	+	8.08590i	−0.799499	+	0.371398i
$475$	21.2133	−	25.8484i	0.973331	−	1.18601i
$476$	22.0206	−	1.86203i	1.00931	−	0.0853460i
$477$	−16.6172	−	8.88208i	−0.760849	−	0.406682i
$478$	5.34235	+	4.01966i	0.244354	+	0.183855i
$479$	−14.1188	−	14.1188i	−0.645104	−	0.645104i	0.306702	−	0.951806i	$-0.400775\pi$
$479$	−14.1188	−	14.1188i	−0.645104	−	0.645104i	−0.951806	+	0.306702i	$0.900775\pi$
$480$	1.99657	+	2.36193i	0.0911307	+	0.107807i
$481$	1.81531	−	1.81531i	0.0827712	−	0.0827712i
$482$	−7.29404	+	1.03052i	−0.332234	+	0.0469389i
$483$	−7.90153	+	14.7827i	−0.359532	+	0.672637i
$484$	9.25049	−	4.78135i	0.420477	−	0.217334i
$485$	−0.641055	−	0.526100i	−0.0291088	−	0.0238890i
$486$	−7.02484	−	2.56841i	−0.318653	−	0.116505i
$487$	−42.6111	+	8.47587i	−1.93089	+	0.384078i	−0.931078	+	0.364821i	$0.881130\pi$
$487$	−42.6111	+	8.47587i	−1.93089	+	0.384078i	−0.999815	+	0.0192578i	$0.993870\pi$
$488$	−26.9908	−	13.4571i	−1.22182	−	0.609174i
$489$	−10.9834	+	55.2174i	−0.496687	+	2.49702i
$490$	1.46530	−	0.356299i	0.0661956	−	0.0160960i
$491$	10.0699	+	3.05466i	0.454447	+	0.137855i	0.509206	−	0.860645i	$-0.329939\pi$
$491$	10.0699	+	3.05466i	0.454447	+	0.137855i	−0.0547590	+	0.998500i	$0.517439\pi$
$492$	2.84124	−	6.59994i	0.128093	−	0.297548i
$493$	8.44455	−	6.93027i	0.380324	−	0.312124i
$494$	40.2830	−	14.1003i	1.81242	−	0.634404i
$495$	−3.92226	−	1.62465i	−0.176292	−	0.0730227i
$496$	−11.7323	−	2.67268i	−0.526794	−	0.120007i
$497$	−52.1393	+	21.5968i	−2.33877	+	0.968750i
$498$	−15.6847	+	14.0196i	−0.702847	+	0.628234i
$499$	−11.3278	−	1.11569i	−0.507100	−	0.0499450i	−0.158767	−	0.987316i	$-0.550752\pi$
$499$	−11.3278	−	1.11569i	−0.507100	−	0.0499450i	−0.348333	+	0.937371i	$0.613252\pi$
$500$	0.771428	−	3.61635i	0.0344993	−	0.161728i
$501$	21.0475	−	11.2501i	0.940331	−	0.502618i
$502$	−2.00261	+	12.8865i	−0.0893808	+	0.575152i
$503$	−6.53040	+	4.36348i	−0.291176	+	0.194558i	−0.692575	−	0.721345i	$-0.743524\pi$
$503$	−6.53040	+	4.36348i	−0.291176	+	0.194558i	0.401399	+	0.915903i	$0.368524\pi$
$504$	39.4225	−	41.7246i	1.75602	−	1.85856i
$505$	−0.401798	+	0.601333i	−0.0178798	+	0.0267590i
$506$	−0.382447	−	9.06188i	−0.0170018	−	0.402850i
$507$	−2.04621	−	20.7755i	−0.0908753	−	0.922672i
$508$	2.47378	+	1.36654i	0.109756	+	0.0606304i
$509$	6.80937	+	22.4475i	0.301820	+	0.994967i	0.968372	+	0.249509i	$0.0802692\pi$
$509$	6.80937	+	22.4475i	0.301820	+	0.994967i	−0.666553	+	0.745458i	$0.732231\pi$
$510$	2.31707	+	0.597437i	0.102602	+	0.0264550i
$511$	39.4533			1.74531
$512$	14.5824	−	17.3018i	0.644457	−	0.764641i
$513$	53.2685			2.35186
$514$	31.4682	+	8.11382i	1.38800	+	0.357885i
$515$	0.994810	+	3.27945i	0.0438366	+	0.144510i
$516$	3.57439	+	1.97453i	0.157354	+	0.0869237i
$517$	3.30072	+	33.5127i	0.145165	+	1.47389i
$518$	−0.121965	−	2.88991i	−0.00535885	−	0.126975i
$519$	9.77620	−	14.6311i	0.429128	−	0.642235i
$520$	1.61504	−	1.70935i	0.0708242	−	0.0749600i
$521$	22.4400	−	14.9939i	0.983114	−	0.656896i	0.0434722	−	0.999055i	$-0.486158\pi$
$521$	22.4400	−	14.9939i	0.983114	−	0.656896i	0.939642	+	0.342159i	$0.111158\pi$
$522$	4.35740	−	28.0392i	0.190718	−	1.22724i
$523$	−6.86704	+	3.67051i	−0.300275	+	0.160500i	−0.614653	−	0.788798i	$-0.710704\pi$
$523$	−6.86704	+	3.67051i	−0.300275	+	0.160500i	0.314378	+	0.949298i	$0.398204\pi$
$524$	−7.78838	+	36.5109i	−0.340237	+	1.59499i
$525$	−51.9941	−	5.12097i	−2.26921	−	0.223498i
$526$	−19.4003	+	17.3408i	−0.845893	+	0.756095i
$527$	−8.60115	+	3.56271i	−0.374672	+	0.155194i
$528$	−10.5402	+	46.2685i	−0.458705	+	2.01358i
$529$	18.9044	+	7.83047i	0.821932	+	0.340455i
$530$	−0.820866	+	0.287329i	−0.0356562	+	0.0124808i
$531$	−49.9739	+	41.0125i	−2.16868	+	1.77979i
$532$	19.0139	−	44.1676i	0.824359	−	1.91491i
$533$	−5.22845	−	1.58603i	−0.226469	−	0.0686987i
$534$	−37.0067	+	8.99845i	−1.60143	+	0.389401i
$535$	−0.0838993	+	0.421790i	−0.00362728	+	0.0182356i
$536$	11.2006	+	5.58441i	0.483792	+	0.241210i
$537$	59.0883	−	11.7534i	2.54985	−	0.507197i
$538$	−29.0177	−	10.6094i	−1.25104	−	0.457404i
$539$	17.8861	+	14.6787i	0.770409	+	0.632258i
$540$	2.60740	−	1.34770i	0.112204	−	0.0579957i
$541$	14.3555	−	26.8573i	0.617192	−	1.15468i	−0.358083	−	0.933690i	$-0.616570\pi$
$541$	14.3555	−	26.8573i	0.617192	−	1.15468i	0.975275	−	0.220995i	$-0.0709304\pi$
$542$	−1.68639	+	0.238258i	−0.0724367	+	0.0102340i
$543$	−34.7295	+	34.7295i	−1.49038	+	1.49038i
$544$	1.46239	−	17.4457i	0.0626995	−	0.747977i
$545$	0.280026	+	0.280026i	0.0119950	+	0.0119950i
$546$	−53.2853	−	40.0926i	−2.28040	−	1.71581i
$547$	13.7308	+	7.33926i	0.587086	+	0.313804i	0.738062	−	0.674733i	$-0.235741\pi$
$547$	13.7308	+	7.33926i	0.587086	+	0.313804i	−0.150975	+	0.988538i	$0.548241\pi$
$548$	12.7558	−	1.07861i	0.544901	−	0.0460759i
$549$	−38.4514	+	46.8532i	−1.64107	+	1.99964i
$550$	25.6389	−	11.9103i	1.09325	−	0.507856i
$551$	−4.63738	−	23.3137i	−0.197559	−	0.993196i
$552$	10.4993	+	8.12945i	0.446882	+	0.346013i
$553$	16.1266	+	3.20779i	0.685774	+	0.136409i
$554$	−8.48012	−	5.16275i	−0.360286	−	0.219344i
$555$	0.0909145	−	0.299705i	0.00385911	−	0.0127218i
$556$	−8.28312	−	0.114455i	−0.351283	−	0.00485399i
$557$	−6.19624	−	7.55014i	−0.262543	−	0.319910i	0.625009	−	0.780618i	$-0.285095\pi$
$557$	−6.19624	−	7.55014i	−0.262543	−	0.319910i	−0.887552	+	0.460708i	$0.847595\pi$
$558$	−10.4900	+	21.7886i	−0.444079	+	0.922384i
$559$	1.18824	−	2.86865i	0.0502570	−	0.121331i
$560$	−0.186747	−	2.64298i	−0.00789152	−	0.111686i
$561$	14.0503	+	33.9203i	0.593203	+	1.43212i
$562$	12.2212	+	0.685052i	0.515519	+	0.0288972i
$563$	−0.914565	+	9.28573i	−0.0385443	+	0.391347i	0.956486	+	0.291777i	$0.0942466\pi$
$563$	−0.914565	+	9.28573i	−0.0385443	+	0.391347i	−0.995031	+	0.0995696i	$0.968253\pi$
$564$	−40.6101	−	27.9540i	−1.70999	−	1.17708i
$565$	−0.783024	−	1.46494i	−0.0329421	−	0.0616303i
$566$	−21.7601	−	29.7678i	−0.914647	−	1.25123i
$567$	−12.4134	−	18.5780i	−0.521316	−	0.780204i
$568$	9.96197	+	43.5836i	0.417995	+	1.82873i
$569$	−4.65631	−	3.11125i	−0.195203	−	0.130430i	0.454128	−	0.890936i	$-0.349951\pi$
$569$	−4.65631	−	3.11125i	−0.195203	−	0.130430i	−0.649331	+	0.760506i	$0.724951\pi$
$570$	3.52317	−	3.83365i	0.147569	−	0.160574i
$571$	−17.5989	+	1.73334i	−0.736491	+	0.0725380i	−0.459306	−	0.888278i	$-0.651902\pi$
$571$	−17.5989	+	1.73334i	−0.736491	+	0.0725380i	−0.277186	+	0.960816i	$0.589402\pi$
$572$	35.8568	+	4.03254i	1.49925	+	0.168609i
$573$	−11.8903	+	3.60689i	−0.496725	+	0.150680i
$574$	−5.30183	+	3.12821i	−0.221294	+	0.130569i
$575$		−	7.91069i		−	0.329899i
$576$	−27.3670	−	36.3172i	−1.14029	−	1.51322i
$577$		−	35.1438i		−	1.46305i	−0.681812	−	0.731527i	$-0.738808\pi$
$577$		−	35.1438i		−	1.46305i	0.681812	−	0.731527i	$-0.261192\pi$
$578$	5.33398	+	9.04027i	0.221864	+	0.376026i
$579$	−18.0892	+	5.48730i	−0.751762	+	0.228045i
$580$	−0.816831	−	1.02384i	−0.0339170	−	0.0425125i
$581$	17.9358	−	1.76652i	0.744104	−	0.0732878i
$582$	13.7164	+	12.6055i	0.568565	+	0.522517i
$583$	−11.0955	−	7.41375i	−0.459527	−	0.307046i
$584$	5.22574	−	30.8147i	0.216243	−	1.27512i
$585$	−2.62567	−	3.92959i	−0.108558	−	0.162469i
$586$	−13.8456	+	10.1211i	−0.571956	+	0.418098i
$587$	−13.0138	−	24.3471i	−0.537137	−	1.00491i	−0.993360	−	0.115047i	$-0.963298\pi$
$587$	−13.0138	−	24.3471i	−0.537137	−	1.00491i	0.456224	−	0.889865i	$-0.349202\pi$
$588$	−33.3124	+	6.14904i	−1.37378	+	0.253582i
$589$	−1.98559	+	20.1600i	−0.0818147	+	0.830679i
$590$	−0.167005	+	2.97933i	−0.00687548	+	0.122657i
$591$	−16.6320	−	40.1533i	−0.684150	−	1.65169i
$592$	−2.27329	−	0.287519i	−0.0934317	−	0.0118169i
$593$	7.67814	−	18.5367i	0.315303	−	0.761210i	−0.684188	−	0.729306i	$-0.739843\pi$
$593$	7.67814	−	18.5367i	0.315303	−	0.761210i	0.999491	−	0.0319037i	$-0.0101570\pi$
$594$	40.5773	+	19.5358i	1.66491	+	0.801564i
$595$	−1.30049	−	1.58465i	−0.0533149	−	0.0649643i
$596$	4.15716	+	4.27366i	0.170284	+	0.175056i
$597$	16.9906	−	56.0105i	0.695379	−	2.29236i
$598$	5.25051	−	8.62427i	0.214709	−	0.352673i
$599$	8.08396	+	1.60800i	0.330302	+	0.0657011i	0.357456	−	0.933930i	$-0.383644\pi$
$599$	8.08396	+	1.60800i	0.330302	+	0.0657011i	−0.0271538	+	0.999631i	$0.508644\pi$
$600$	−10.8865	+	39.9313i	−0.444440	+	1.63019i
$601$	3.07283	+	15.4482i	0.125343	+	0.630143i	0.991472	+	0.130322i	$0.0416011\pi$
$601$	3.07283	+	15.4482i	0.125343	+	0.630143i	−0.866128	+	0.499822i	$0.833399\pi$
$602$	−1.47386	−	3.17275i	−0.0600702	−	0.129312i
$603$	15.9565	−	19.4431i	0.649799	−	0.791783i
$604$	−7.12436	+	8.44050i	−0.289886	+	0.343439i
$605$	−0.851886	−	0.455343i	−0.0346341	−	0.0185123i
$606$	9.76770	−	12.9818i	0.396786	−	0.527350i
$607$	24.4406	+	24.4406i	0.992015	+	0.992015i	0.999968	−	0.00795323i	$-0.00253162\pi$
$607$	24.4406	+	24.4406i	0.992015	+	0.992015i	−0.00795323	+	0.999968i	$0.502532\pi$
$608$	−31.9783	−	20.7008i	−1.29689	−	0.839530i
$609$	−26.2617	+	26.2617i	−1.06418	+	1.06418i
$610$	0.391374	+	2.77015i	0.0158463	+	0.112160i
$611$	−17.6715	+	33.0610i	−0.714912	+	1.33751i
$612$	−33.5240	−	10.6774i	−1.35513	−	0.431608i
$613$	−23.2748	−	19.1011i	−0.940060	−	0.771487i	0.0336135	−	0.999435i	$-0.489298\pi$
$613$	−23.2748	−	19.1011i	−0.940060	−	0.771487i	−0.973673	+	0.227948i	$0.926798\pi$
$614$	−0.824460	+	2.25497i	−0.0332725	+	0.0910034i
$615$	−0.653738	+	0.130037i	−0.0263613	+	0.00524358i
$616$	30.6820	−	26.6715i	1.23621	−	1.07462i
$617$	−1.09037	+	5.48166i	−0.0438967	+	0.220683i	−0.996507	−	0.0835101i	$-0.973387\pi$
$617$	−1.09037	+	5.48166i	−0.0438967	+	0.220683i	0.952610	+	0.304193i	$0.0983869\pi$
$618$	−18.1891	−	74.8036i	−0.731672	−	3.00904i
$619$	1.23693	+	0.375219i	0.0497165	+	0.0150813i	0.315045	−	0.949077i	$-0.397980\pi$
$619$	1.23693	+	0.375219i	0.0497165	+	0.0150813i	−0.265328	+	0.964158i	$0.585480\pi$
$620$	0.412860	+	1.03703i	0.0165809	+	0.0416482i
$621$	9.74140	−	7.99456i	0.390909	−	0.320811i
$622$	−3.46909	−	9.91077i	−0.139098	−	0.397386i
$623$	30.1440	+	12.4861i	1.20769	+	0.500244i
$624$	−38.3718	+	36.3076i	−1.53610	+	1.45347i
$625$	22.6211	−	9.36996i	0.904844	−	0.374799i
$626$	20.7745	+	23.2419i	0.830318	+	0.928931i
$627$	79.5050	+	7.83056i	3.17512	+	0.312722i
$628$	−37.9604	+	24.6125i	−1.51478	+	0.982147i
$629$	−1.56352	+	0.835720i	−0.0623417	+	0.0333224i
$630$	−5.26165	−	0.817681i	−0.209629	−	0.0325772i
$631$	−25.1773	+	16.8229i	−1.00229	+	0.669710i	−0.944463	−	0.328617i	$-0.893417\pi$
$631$	−25.1773	+	16.8229i	−1.00229	+	0.669710i	−0.0578280	+	0.998327i	$0.518417\pi$
$632$	4.64145	−	12.1707i	0.184627	−	0.484124i
$633$	27.3472	−	40.9279i	1.08695	−	1.62674i
$634$	14.2778	−	0.602579i	0.567044	−	0.0239315i
$635$	−0.0256960	−	0.260896i	−0.00101972	−	0.0103534i
$636$	18.7720	−	5.41234i	0.744358	−	0.214613i
$637$	7.47712	+	24.6488i	0.296254	+	0.976620i
$638$	5.01759	−	19.4600i	0.198648	−	0.770427i
$639$	89.8484			3.55435
$640$	−2.08901	−	0.204215i	−0.0825754	−	0.00807229i
$641$	14.4273			0.569844			0.284922	−	0.958551i	$-0.408032\pi$
$641$	14.4273			0.569844			0.284922	+	0.958551i	$0.408032\pi$
$642$	2.41201	−	9.35461i	0.0951945	−	0.369197i
$643$	−8.64999	−	28.5152i	−0.341122	−	1.12453i	−0.944895	−	0.327373i	$-0.893836\pi$
$643$	−8.64999	−	28.5152i	−0.341122	−	1.12453i	0.603773	−	0.797157i	$-0.293664\pi$
$644$	−3.15154	−	10.9307i	−0.124188	−	0.430730i
$645$	−0.0371285	−	0.376972i	−0.00146193	−	0.0148432i
$646$	−29.4470	+	1.24278i	−1.15857	+	0.0488964i
$647$	−23.9337	+	35.8193i	−0.940930	+	1.40820i	−0.0282158	+	0.999602i	$0.508983\pi$
$647$	−23.9337	+	35.8193i	−0.940930	+	1.40820i	−0.912714	+	0.408599i	$0.866017\pi$
$648$	−16.1544	+	7.23469i	−0.634606	+	0.284205i
$649$	−38.0694	+	25.4371i	−1.49435	+	0.998495i
$650$	31.0977	+	4.83271i	1.21975	+	0.189554i
$651$	27.9138	−	14.9202i	1.09403	−	0.584769i
$652$	−20.7868	−	32.0599i	−0.814074	−	1.25556i
$653$	4.53369	+	0.446530i	0.177417	+	0.0174741i	0.186335	−	0.982486i	$-0.440339\pi$
$653$	4.53369	+	0.446530i	0.177417	+	0.0174741i	−0.00891843	+	0.999960i	$0.502839\pi$
$654$	−5.92849	−	6.63259i	−0.231822	−	0.259355i
$655$	3.19943	−	1.32525i	0.125012	−	0.0517816i
$656$	1.74102	+	4.55529i	0.0679753	+	0.177854i
$657$	−58.0309	−	24.0372i	−2.26400	−	0.937780i
$658$	13.9540	+	39.8650i	0.543985	+	1.55410i
$659$	17.1674	−	14.0889i	0.668748	−	0.548827i	−0.237598	−	0.971363i	$-0.576360\pi$
$659$	17.1674	−	14.0889i	0.668748	−	0.548827i	0.906346	+	0.422537i	$0.138860\pi$
$660$	4.08974	−	1.62819i	0.159193	−	0.0633774i
$661$	−6.80109	−	2.06309i	−0.264532	−	0.0802448i	0.155233	−	0.987878i	$-0.450387\pi$
$661$	−6.80109	−	2.06309i	−0.264532	−	0.0802448i	−0.419764	+	0.907633i	$0.637887\pi$
$662$	−3.60137	−	14.8109i	−0.139971	−	0.575641i
$663$	−7.97372	+	40.0866i	−0.309674	+	1.55683i
$664$	0.995937	−	14.2426i	0.0386498	−	0.552721i
$665$	−4.37490	+	0.870221i	−0.169651	+	0.0337457i
$666$	−1.58130	+	4.32500i	−0.0612740	+	0.167590i
$667$	−4.34698	−	3.56748i	−0.168316	−	0.138133i
$668$	−4.91543	+	15.4331i	−0.190184	+	0.597124i
$669$	−9.84448	+	18.4177i	−0.380610	+	0.712071i
$670$	−0.162412	−	1.14955i	−0.00627452	−	0.0444112i
$671$	−30.3536	+	30.3536i	−1.17179	+	1.17179i
$672$	0.865663	+	59.5127i	0.0333937	+	2.29575i
$673$	−17.2984	−	17.2984i	−0.666805	−	0.666805i	0.290170	−	0.956975i	$-0.406288\pi$
$673$	−17.2984	−	17.2984i	−0.666805	−	0.666805i	−0.956975	+	0.290170i	$0.906288\pi$
$674$	−22.5112	+	29.9186i	−0.867099	+	1.15242i
$675$	34.6411	+	18.5160i	1.33334	+	0.712683i
$676$	10.8268	+	9.13860i	0.416417	+	0.351485i
$677$	12.5235	−	15.2599i	0.481316	−	0.586486i	−0.474572	−	0.880217i	$-0.657397\pi$
$677$	12.5235	−	15.2599i	0.481316	−	0.586486i	0.955888	+	0.293731i	$0.0948970\pi$
$678$	15.7203	+	33.8406i	0.603734	+	1.29964i
$679$	−3.11357	−	15.6530i	−0.119488	−	0.600705i
$680$	−1.40993	+	0.805843i	−0.0540685	+	0.0309027i
$681$	−47.4284	−	9.43409i	−1.81746	−	0.361515i
$682$	−8.90606	+	14.6287i	−0.341031	+	0.560162i
$683$	9.88232	−	32.5776i	0.378136	−	1.24655i	−0.537061	−	0.843543i	$-0.680466\pi$
$683$	9.88232	−	32.5776i	0.378136	−	1.24655i	0.915198	−	0.403005i	$-0.132034\pi$
$684$	−54.8765	+	53.3806i	−2.09826	+	2.04106i
$685$	−0.753329	−	0.917934i	−0.0287832	−	0.0350724i
$686$	−5.69785	−	2.74321i	−0.217545	−	0.104736i
$687$	−8.77156	+	21.1764i	−0.334656	+	0.807931i
$688$	−2.67327	+	0.730906i	−0.101917	+	0.0278655i
$689$	−5.68485	−	13.7244i	−0.216575	−	0.522860i
$690$	0.0689376	−	1.22983i	0.00262441	−	0.0468189i
$691$	3.26926	−	33.1933i	0.124368	−	1.26273i	−0.707081	−	0.707133i	$-0.749988\pi$
$691$	3.26926	−	33.1933i	0.124368	−	1.26273i	0.831449	−	0.555601i	$-0.187512\pi$
$692$	2.16781	+	11.7441i	0.0824076	+	0.446443i
$693$	−38.5141	−	72.0548i	−1.46303	−	2.73714i
$694$	27.5665	−	20.1510i	1.04641	−	0.764921i
$695$	0.426919	+	0.638930i	0.0161940	+	0.0242360i
$696$	17.0331	+	23.9900i	0.645636	+	0.909338i
$697$	3.13720	+	2.09621i	0.118830	+	0.0793996i
$698$	23.8223	+	21.8929i	0.901687	+	0.828659i
$699$	−3.82391	+	0.376623i	−0.144634	+	0.0142452i
$700$	27.7176	−	22.1134i	1.04763	−	0.835810i
$701$	−42.7376	+	12.9643i	−1.61418	+	0.489655i	−0.963052	−	0.269317i	$-0.913202\pi$
$701$	−42.7376	+	12.9643i	−1.61418	+	0.489655i	−0.651124	+	0.758972i	$0.725702\pi$
$702$	25.4763	+	43.1784i	0.961542	+	1.62966i
$703$			3.85763i			0.145493i
$704$	−16.7676	−	27.4967i	−0.631953	−	1.03632i
$705$			4.57329i			0.172240i
$706$	21.5384	−	12.7082i	0.810608	−	0.478279i
$707$	−13.3188	+	4.04022i	−0.500906	+	0.151948i
$708$	7.49132	−	66.6118i	0.281541	−	2.50342i
$709$	31.5967	−	3.11200i	1.18664	−	0.116874i	0.514627	−	0.857414i	$-0.327930\pi$
$709$	31.5967	−	3.11200i	1.18664	−	0.116874i	0.672012	+	0.740540i	$0.265430\pi$
$710$	2.80624	−	3.05354i	0.105316	−	0.114597i
$711$	−21.7659	−	14.5435i	−0.816285	−	0.545424i
$712$	13.7448	−	21.8899i	0.515109	−	0.820359i
$713$	2.66251	+	3.98473i	0.0997119	+	0.149229i
$714$	27.1757	+	37.1762i	1.01702	+	1.39129i
$715$	−1.57782	−	2.95190i	−0.0590073	−	0.110395i
$716$	−23.1835	+	33.6797i	−0.866407	+	1.25867i
$717$	−1.36552	+	13.8644i	−0.0509965	+	0.517776i
$718$	−4.84711	−	0.271702i	−0.180893	−	0.0101398i
$719$	−8.96048	−	21.6325i	−0.334170	−	0.806757i	−0.998252	−	0.0590976i	$-0.981178\pi$
$719$	−8.96048	−	21.6325i	−0.334170	−	0.806757i	0.664083	−	0.747659i	$-0.268822\pi$
$720$	−1.33557	+	4.00127i	−0.0497737	+	0.149118i
$721$	−25.2388	+	60.9318i	−0.939941	+	2.26922i
$722$	−16.1637	+	33.5732i	−0.601551	+	1.24947i
$723$	−9.73800	−	11.8658i	−0.362160	−	0.441294i
$724$	0.460551	−	33.3300i	0.0171162	−	1.23870i
$725$	5.08806	−	16.7731i	0.188966	−	0.622937i
$726$	18.5340	+	11.2836i	0.687862	+	0.418775i
$727$	0.0206944	+	0.00411637i	0.000767513	+	0.000152668i	0.195474	−	0.980709i	$-0.437375\pi$
$727$	0.0206944	+	0.00411637i	0.000767513	+	0.000152668i	−0.194707	+	0.980862i	$0.562375\pi$
$728$	44.8950	−	5.71138i	1.66392	−	0.211678i
$729$	−6.70332	−	33.6999i	−0.248271	−	1.24814i
$730$	−2.62939	+	1.22145i	−0.0973182	+	0.0452080i
$731$	−1.36028	+	1.65751i	−0.0503118	+	0.0613051i
$732$	−5.29524	−	62.6223i	−0.195718	−	2.31459i
$733$	19.7243	+	10.5428i	0.728533	+	0.389409i	0.793574	−	0.608474i	$-0.208218\pi$
$733$	19.7243	+	10.5428i	0.728533	+	0.389409i	−0.0650413	+	0.997883i	$0.520718\pi$
$734$	−22.2644	−	16.7520i	−0.821793	−	0.618329i
$735$	2.22197	+	2.22197i	0.0819585	+	0.0819585i
$736$	−8.95477	+	1.01368i	−0.330077	+	0.0373646i
$737$	12.5961	−	12.5961i	0.463983	−	0.463983i
$738$	9.70420	−	1.37103i	0.357217	−	0.0504685i
$739$	0.547472	−	1.02425i	0.0201391	−	0.0376776i	−0.871650	−	0.490128i	$-0.836950\pi$
$739$	0.547472	−	1.02425i	0.0201391	−	0.0376776i	0.891790	+	0.452450i	$0.149450\pi$
$740$	0.0975984	+	0.188824i	0.00358779	+	0.00694130i
$741$	68.7474	+	56.4195i	2.52550	+	2.07262i
$742$	−15.7195	−	5.74732i	−0.577080	−	0.210991i
$743$	−19.7561	+	3.92973i	−0.724781	+	0.144168i	−0.543675	−	0.839296i	$-0.682968\pi$
$743$	−19.7561	+	3.92973i	−0.724781	+	0.144168i	−0.181106	+	0.983464i	$0.557968\pi$
$744$	−7.95603	−	23.7781i	−0.291682	−	0.871746i
$745$	0.107895	−	0.542427i	0.00395298	−	0.0198730i
$746$	24.3901	−	5.93063i	0.892985	−	0.217136i
$747$	−27.4576	−	8.32918i	−1.00462	−	0.304749i
$748$	−22.8870	−	9.85276i	−0.836833	−	0.360253i
$749$	−6.39765	+	5.25042i	−0.233765	+	0.191846i
$750$	7.27257	−	2.54563i	0.265557	−	0.0929533i
$751$	3.91003	+	1.61959i	0.142679	+	0.0590995i	0.452880	−	0.891571i	$-0.350396\pi$
$751$	3.91003	+	1.61959i	0.142679	+	0.0590995i	−0.310201	+	0.950671i	$0.600396\pi$
$752$	32.9845	−	5.61841i	1.20282	−	0.204882i
$753$	−25.1063	+	10.3994i	−0.914925	+	0.378975i
$754$	16.6797	−	14.9090i	0.607440	−	0.542955i
$755$	1.01965	+	0.100427i	0.0371090	+	0.00365491i
$756$	55.2424	+	11.7841i	2.00915	+	0.428584i
$757$	−17.2218	+	9.20527i	−0.625939	+	0.334571i	−0.753685	−	0.657236i	$-0.771726\pi$
$757$	−17.2218	+	9.20527i	−0.625939	+	0.334571i	0.127747	+	0.991807i	$0.459226\pi$
$758$	0.536097	−	3.44970i	0.0194719	−	0.125299i
$759$	15.7146	−	10.5001i	0.570403	−	0.381131i
$760$	0.100208	+	3.53224i	0.00363492	+	0.128128i
$761$	0.641169	−	0.959578i	0.0232424	−	0.0347847i	−0.819667	−	0.572841i	$-0.805841\pi$
$761$	0.641169	−	0.959578i	0.0232424	−	0.0347847i	0.842909	+	0.538056i	$0.180841\pi$
$762$	0.248319	+	5.88380i	0.00899566	+	0.213148i
$763$	0.747012	+	7.58454i	0.0270436	+	0.274579i
$764$	4.07757	−	7.38143i	0.147521	−	0.267051i
$765$	0.947398	+	3.12315i	0.0342533	+	0.112918i
$766$	42.7726	+	11.0286i	1.54544	+	0.398479i
$767$	−50.9694			−1.84040
$768$	46.5965	+	7.20655i	1.68141	+	0.260044i
$769$	16.9050			0.609611			0.304805	−	0.952415i	$-0.401409\pi$
$769$	16.9050			0.609611			0.304805	+	0.952415i	$0.401409\pi$
$770$	−3.65173	−	0.941568i	−0.131599	−	0.0339318i
$771$	19.6573	+	64.8016i	0.707942	+	2.33377i
$772$	6.20337	−	11.2297i	0.223264	−	0.404165i
$773$	2.88342	+	29.2758i	0.103709	+	1.05298i	0.896367	+	0.443312i	$0.146197\pi$
$773$	2.88342	+	29.2758i	0.103709	+	1.05298i	−0.792658	+	0.609667i	$0.791303\pi$
$774$	0.234851	+	5.56468i	0.00844155	+	0.200018i
$775$	−8.29884	+	12.4201i	−0.298103	+	0.446143i
$776$	−12.6380	+	0.358534i	−0.453678	+	0.0128706i
$777$	5.01150	−	3.34858i	0.179787	−	0.120130i
$778$	5.03932	−	32.4272i	0.180668	−	1.16257i
$779$	7.24054	−	3.87015i	0.259419	−	0.138662i
$780$	4.79248	+	1.02232i	0.171598	+	0.0366048i
$781$	63.3265	+	6.23711i	2.26600	+	0.223181i
$782$	−5.19855	+	4.64668i	−0.185900	+	0.166165i
$783$	25.7968	−	10.6854i	0.921901	−	0.381864i
$784$	13.2960	−	18.7555i	0.474858	−	0.669840i
$785$	3.87722	+	1.60600i	0.138384	+	0.0573206i
$786$	−73.4242	+	25.7008i	−2.61896	+	0.916718i
$787$	27.4757	−	22.5488i	0.979405	−	0.803777i	−0.00115481	−	0.999999i	$-0.500368\pi$
$787$	27.4757	−	22.5488i	0.979405	−	0.803777i	0.980559	+	0.196223i	$0.0628676\pi$
$788$	27.0926	+	11.6632i	0.965133	+	0.415485i
$789$	−51.8865	−	15.7396i	−1.84721	−	0.560345i
$790$	−1.17408	+	0.285487i	−0.0417720	+	0.0101572i
$791$	6.23644	−	31.3527i	0.221742	−	1.11477i
$792$	−61.3792	+	20.5372i	−2.18101	+	0.729758i
$793$	−46.8683	+	9.32268i	−1.66434	+	0.331058i
$794$	−29.2707	−	10.7019i	−1.03878	−	0.379796i
$795$	−1.40090	−	1.14969i	−0.0496848	−	0.0407752i
$796$	18.2397	+	35.2884i	0.646490	+	1.25077i
$797$	−12.1915	+	22.8087i	−0.431845	+	0.807926i	−0.999886	−	0.0150746i	$-0.995201\pi$
$797$	−12.1915	+	22.8087i	−0.431845	+	0.807926i	0.568041	+	0.823000i	$0.307701\pi$
$798$	99.2161	−	14.0175i	3.51221	−	0.496215i
$799$	18.3054	−	18.3054i	0.647598	−	0.647598i
$800$	−13.6002	−	24.5776i	−0.480841	−	0.868949i
$801$	−36.7309	−	36.7309i	−1.29782	−	1.29782i
$802$	26.2562	+	19.7555i	0.927137	+	0.697591i
$803$	−39.2324	−	20.9702i	−1.38448	−	0.740021i
$804$	2.19741	+	25.9869i	0.0774967	+	0.916487i
$805$	−0.669450	+	0.815727i	−0.0235950	+	0.0287506i
$806$	−17.2909	+	8.03230i	−0.609047	+	0.282926i
$807$	−12.5602	−	63.1442i	−0.442138	−	2.22278i
$808$	1.39145	+	10.9377i	0.0489512	+	0.384787i
$809$	−48.9207	−	9.73093i	−1.71996	−	0.342121i	−0.766180	−	0.642627i	$-0.777845\pi$
$809$	−48.9207	−	9.73093i	−1.71996	−	0.342121i	−0.953780	+	0.300505i	$0.902845\pi$
$810$	1.40247	+	0.853832i	0.0492777	+	0.0300006i
$811$	−3.62649	+	11.9549i	−0.127343	+	0.419795i	−0.997309	−	0.0733183i	$-0.976641\pi$
$811$	−3.62649	+	11.9549i	−0.127343	+	0.419795i	0.869965	+	0.493113i	$0.164141\pi$
$812$	0.348259	−	25.2035i	0.0122215	−	0.884469i
$813$	−2.25144	−	2.74339i	−0.0789614	−	0.0962147i
$814$	−1.41476	+	2.93855i	−0.0495871	+	0.102996i
$815$	−1.35636	+	3.27455i	−0.0475113	+	0.114703i
$816$	32.6357	−	16.3012i	1.14248	−	0.570657i
$817$	1.78548	+	4.31053i	0.0624661	+	0.150807i
$818$	5.69763	+	0.319378i	0.199213	+	0.0111668i
$819$	8.91488	−	90.5143i	0.311511	−	3.16283i
$820$	0.256496	−	0.372623i	0.00895723	−	0.0130126i
$821$	24.9294	+	46.6396i	0.870041	+	1.62773i	0.774736	+	0.632285i	$0.217883\pi$
$821$	24.9294	+	46.6396i	0.870041	+	1.62773i	0.0953053	+	0.995448i	$0.469617\pi$
$822$	15.7419	+	21.5349i	0.549063	+	0.751116i
$823$	22.3265	+	33.4139i	0.778252	+	1.16474i	0.982581	+	0.185834i	$0.0594988\pi$
$823$	22.3265	+	33.4139i	0.778252	+	1.16474i	−0.204329	+	0.978902i	$0.565501\pi$
$824$	44.2473	+	27.7832i	1.54143	+	0.967873i
$825$	48.9811	+	32.7281i	1.70530	+	1.13945i
$826$	−38.8583	+	42.2828i	−1.35205	+	1.47121i
$827$	−7.34268	+	0.723191i	−0.255330	+	0.0251478i	−0.224872	−	0.974388i	$-0.572196\pi$
$827$	−7.34268	+	0.723191i	−0.255330	+	0.0251478i	−0.0304577	+	0.999536i	$0.509696\pi$
$828$	−2.02407	+	17.9978i	−0.0703415	+	0.625467i
$829$	20.4649	−	6.20795i	0.710774	−	0.215611i	0.0858630	−	0.996307i	$-0.472635\pi$
$829$	20.4649	−	6.20795i	0.710774	−	0.215611i	0.624911	+	0.780696i	$0.285135\pi$
$830$	−1.14065	+	0.673015i	−0.0395927	+	0.0233607i
$831$		−	20.6879i		−	0.717655i
$832$	1.48569	−	35.8214i	0.0515069	−	1.24188i
$833$		−	17.7876i		−	0.616305i
$834$	−8.77186	−	14.8669i	−0.303745	−	0.514800i
$835$	1.43777	−	0.436143i	0.0497561	−	0.0150933i
$836$	−42.3833	+	33.8140i	−1.46586	+	1.16948i
$837$	−23.6812	+	2.33239i	−0.818542	+	0.0806193i
$838$	−5.71803	−	5.25493i	−0.197526	−	0.181529i
$839$	18.6793	+	12.4811i	0.644882	+	0.430897i	0.834535	−	0.550955i	$-0.185736\pi$
$839$	18.6793	+	12.4811i	0.644882	+	0.430897i	−0.189653	+	0.981851i	$0.560736\pi$
$840$	4.50181	−	3.19631i	0.155327	−	0.110283i
$841$	9.18916	+	13.7525i	0.316867	+	0.474226i
$842$	−40.6947	+	29.7477i	−1.40243	+	1.02517i
$843$	12.0235	+	22.4944i	0.414112	+	0.774750i
$844$	6.06405	+	32.8520i	0.208733	+	1.13081i
$845$	0.128820	−	1.30793i	0.00443155	−	0.0449943i
$846$	3.76339	−	67.1381i	0.129388	−	2.30825i
$847$	−7.11384	−	17.1743i	−0.244434	−	0.590117i
$848$	−6.57100	+	11.5163i	−0.225649	+	0.395472i
$849$	29.4036	−	70.9866i	1.00913	−	2.43625i
$850$	−19.5817	−	9.42753i	−0.671646	−	0.323361i
$851$	0.578954	+	0.705458i	0.0198463	+	0.0241828i
$852$	−66.7784	+	64.9581i	−2.28779	+	2.22543i
$853$	−11.3055	+	37.2693i	−0.387094	+	1.27608i	0.519644	+	0.854383i	$0.326064\pi$
$853$	−11.3055	+	37.2693i	−0.387094	+	1.27608i	−0.906738	+	0.421694i	$0.861436\pi$
$854$	−27.9979	+	45.9881i	−0.958067	+	1.57368i
$855$	6.96511	+	1.38545i	0.238202	+	0.0473813i
$856$	3.25340	+	5.69227i	0.111199	+	0.194558i
$857$	4.91599	+	24.7143i	0.167927	+	0.844226i	0.969266	+	0.246015i	$0.0791213\pi$
$857$	4.91599	+	24.7143i	0.167927	+	0.844226i	−0.801339	+	0.598210i	$0.795879\pi$
$858$	31.6770	+	68.1902i	1.08143	+	2.32798i
$859$	−1.57880	+	1.92377i	−0.0538680	+	0.0656383i	−0.799247	−	0.601002i	$-0.794768\pi$
$859$	−1.57880	+	1.92377i	−0.0538680	+	0.0656383i	0.745379	+	0.666640i	$0.232268\pi$
$860$	0.196453	+	0.165820i	0.00669900	+	0.00565441i
$861$	−11.3129	−	6.04685i	−0.385541	−	0.206076i
$862$	−21.9491	+	29.1716i	−0.747591	+	0.993589i
$863$	27.2221	+	27.2221i	0.926651	+	0.926651i	0.997488	−	0.0708370i	$-0.0225670\pi$
$863$	27.2221	+	27.2221i	0.926651	+	0.926651i	−0.0708370	+	0.997488i	$0.522567\pi$
$864$	16.5209	−	41.5858i	0.562054	−	1.41478i
$865$	0.783341	−	0.783341i	0.0266344	−	0.0266344i
$866$	−3.17483	−	22.4715i	−0.107885	−	0.763613i
$867$	−10.3106	+	19.2898i	−0.350167	+	0.655117i
$868$	−6.51899	+	20.4678i	−0.221269	+	0.694723i
$869$	−14.3313	−	11.7614i	−0.486157	−	0.398979i
$870$	0.937182	−	2.56328i	0.0317735	−	0.0869034i
$871$	19.4493	−	3.86871i	0.659015	−	0.131086i
$872$	6.02279	+	0.421153i	0.203957	+	0.0142620i
$873$	−4.95699	+	24.9205i	−0.167769	+	0.843431i
$874$	3.58469	+	14.7423i	0.121254	+	0.498665i
$875$	−6.31688	−	1.91620i	−0.213549	−	0.0647795i
$876$	60.5088	−	24.0896i	2.04440	−	0.813912i
$877$	−30.9261	+	25.3804i	−1.04430	+	0.857035i	−0.989940	−	0.141487i	$-0.954812\pi$
$877$	−30.9261	+	25.3804i	−1.04430	+	0.857035i	−0.0543597	+	0.998521i	$0.517312\pi$
$878$	−4.82320	−	13.7793i	−0.162775	−	0.465030i
$879$	−33.0173	−	13.6762i	−1.11364	−	0.461287i
$880$	−1.21909	+	2.72744i	−0.0410955	+	0.0919419i
$881$	−7.45550	+	3.08817i	−0.251182	+	0.104043i	−0.504722	−	0.863282i	$-0.668405\pi$
$881$	−7.45550	+	3.08817i	−0.251182	+	0.104043i	0.253540	+	0.967325i	$0.418405\pi$
$882$	−30.7911	−	34.4480i	−1.03679	−	1.15992i
$883$	13.3360	+	1.31348i	0.448791	+	0.0442021i	0.319889	−	0.947455i	$-0.396355\pi$
$883$	13.3360	+	1.31348i	0.448791	+	0.0442021i	0.128903	+	0.991657i	$0.458855\pi$
$884$	−15.0908	−	23.2747i	−0.507557	−	0.782814i
$885$	−5.48380	+	2.93115i	−0.184336	+	0.0985295i
$886$	32.6420	+	5.07270i	1.09663	+	0.170421i
$887$	34.3949	−	22.9820i	1.15487	−	0.771659i	0.177692	−	0.984086i	$-0.443137\pi$
$887$	34.3949	−	22.9820i	1.15487	−	0.771659i	0.977177	+	0.212427i	$0.0681368\pi$
$888$	−1.95159	−	4.35773i	−0.0654910	−	0.146236i
$889$	2.80295	−	4.19492i	0.0940080	−	0.140693i
$890$	−2.39553	+	0.101101i	−0.0802984	+	0.00338891i
$891$	2.46937	+	25.0720i	0.0827271	+	0.839943i
$892$	−3.92650	−	13.6185i	−0.131469	−	0.455982i
$893$	−16.3517	−	53.9044i	−0.547190	−	1.80384i
$894$	−3.10187	+	12.0301i	−0.103742	+	0.402348i
$895$	3.79282			0.126780
$896$	−28.5838	−	28.5422i	−0.954917	−	0.953528i
$897$	21.0396			0.702490
$898$	−1.93719	+	7.51311i	−0.0646450	+	0.250716i
$899$	3.08241	+	10.1614i	0.102804	+	0.338900i
$900$	−54.2418	+	15.6390i	−1.80806	+	0.521300i
$901$	1.00552	+	10.2092i	0.0334986	+	0.340117i
$902$	6.93484	−	0.292677i	0.230905	−	0.00974509i
$903$	4.05001	−	6.06127i	0.134776	−	0.201707i
$904$	−23.6617	−	9.02371i	−0.786978	−	0.300124i
$905$	−2.57095	+	1.71786i	−0.0854614	+	0.0571035i
$906$	−22.7430	−	3.53434i	−0.755584	−	0.117421i
$907$	−13.7067	+	7.32637i	−0.455123	+	0.243268i	−0.682995	−	0.730423i	$-0.739323\pi$
$907$	−13.7067	+	7.32637i	−0.455123	+	0.243268i	0.227873	+	0.973691i	$0.426823\pi$
$908$	27.5375	−	17.8546i	0.913863	−	0.592526i
$909$	22.0519	+	2.17192i	0.731414	+	0.0720380i
$910$	−2.79773	−	3.13001i	−0.0927440	−	0.103759i
$911$	−27.5952	+	11.4303i	−0.914269	+	0.378703i	−0.789689	−	0.613507i	$-0.789758\pi$
$911$	−27.5952	+	11.4303i	−0.914269	+	0.378703i	−0.124580	+	0.992210i	$0.539758\pi$
$912$	2.19328	−	79.3486i	0.0726268	−	2.62750i
$913$	−18.7743	−	7.77659i	−0.621340	−	0.257367i
$914$	−14.5973	−	41.7027i	−0.482835	−	1.37940i
$915$	−4.50643	+	3.69833i	−0.148978	+	0.122263i
$916$	−5.75392	−	14.4528i	−0.190115	−	0.477535i
$917$	63.7755	+	19.3461i	2.10605	+	0.638864i
$918$	−8.18001	−	33.6408i	−0.269980	−	1.11031i
$919$	7.55101	−	37.9615i	0.249085	−	1.25223i	−0.630386	−	0.776282i	$-0.717104\pi$
$919$	7.55101	−	37.9615i	0.249085	−	1.25223i	0.879471	−	0.475952i	$-0.157896\pi$
$920$	0.548446	+	0.630914i	0.0180817	+	0.0208006i
$921$	−4.90695	+	0.976053i	−0.161690	+	0.0321620i
$922$	4.84871	−	13.2617i	0.159684	−	0.436750i
$923$	54.7580	+	44.9387i	1.80238	+	1.47917i
$924$	80.7188	+	25.7089i	2.65545	+	0.845761i
$925$	−1.34090	+	2.50866i	−0.0440887	+	0.0824841i
$926$	−1.20932	−	8.55955i	−0.0397406	−	0.281284i
$927$	74.2462	−	74.2462i	2.43856	−	2.43856i
$928$	−19.6388	−	3.61030i	−0.644677	−	0.118514i
$929$	40.4538	+	40.4538i	1.32725	+	1.32725i	0.907764	+	0.419482i	$0.137788\pi$
$929$	40.4538	+	40.4538i	1.32725	+	1.32725i	0.419482	+	0.907764i	$0.362212\pi$
$930$	−1.39841	+	1.85856i	−0.0458557	+	0.0609447i
$931$	−34.1345	−	18.2453i	−1.11871	−	0.597964i
$932$	1.68204	−	1.99278i	0.0550971	−	0.0652756i
$933$	13.8808	−	16.9138i	0.454438	−	0.553734i
$934$	5.33342	+	11.4811i	0.174515	+	0.375674i
$935$	0.450937	+	2.26701i	0.0147472	+	0.0741392i
$936$	−69.5147	−	18.9518i	−2.27216	−	0.619461i
$937$	−11.3972	−	2.26705i	−0.372331	−	0.0740611i	0.00537838	−	0.999986i	$-0.498288\pi$
$937$	−11.3972	−	2.26705i	−0.372331	−	0.0740611i	−0.377709	+	0.925924i	$0.623288\pi$
$938$	11.6185	−	19.0841i	0.379358	−	0.623118i
$939$	−18.8563	+	62.1609i	−0.615352	+	2.02854i
$940$	−2.16418	−	2.22482i	−0.0705877	−	0.0725657i
$941$	15.5061	+	18.8942i	0.505484	+	0.615934i	0.961757	−	0.273906i	$-0.0883157\pi$
$941$	15.5061	+	18.8942i	0.505484	+	0.615934i	−0.456272	+	0.889840i	$0.650816\pi$
$942$	−84.9410	−	40.8946i	−2.76753	−	1.33242i
$943$	0.743270	−	1.79441i	0.0242042	−	0.0584341i
$944$	27.8777	+	35.9505i	0.907342	+	1.17009i
$945$	−2.00515	−	4.84085i	−0.0652274	−	0.157473i
$946$	−0.220763	+	3.93837i	−0.00717763	+	0.128047i
$947$	−4.43772	+	45.0569i	−0.144207	+	1.46415i	0.602030	+	0.798473i	$0.294359\pi$
$947$	−4.43772	+	45.0569i	−0.144207	+	1.46415i	−0.746237	+	0.665680i	$0.768141\pi$
$948$	26.6917	−	4.92695i	0.866907	−	0.160020i
$949$	−23.3444	−	43.6742i	−0.757790	−	1.41773i
$950$	−38.1769	+	27.9072i	−1.23862	+	0.905429i
$951$	16.5439	+	24.7597i	0.536473	+	0.802889i
$952$	−30.8131	−	5.22546i	−0.998657	−	0.169358i
$953$	−6.08595	−	4.06650i	−0.197143	−	0.131727i	0.453081	−	0.891470i	$-0.350325\pi$
$953$	−6.08595	−	4.06650i	−0.197143	−	0.131727i	−0.650224	+	0.759743i	$0.725325\pi$
$954$	19.6198	+	18.0308i	0.635214	+	0.583768i
$955$	−0.778479	+	0.0766735i	−0.0251910	+	0.00248110i
$956$	−5.89663	−	7.39098i	−0.190711	−	0.239041i
$957$	40.0733	−	12.1561i	1.29539	−	0.392951i
$958$	14.3494	+	24.3199i	0.463606	+	0.785740i
$959$		−	22.8528i		−	0.737954i
$960$	−1.90017	−	3.93946i	−0.0613278	−	0.127146i
$961$			21.9507i			0.708086i
$962$	−3.12691	+	1.84496i	−0.100816	+	0.0594838i
$963$	12.6090	−	3.82489i	0.406319	−	0.123256i
$964$	10.3525	+	1.16427i	0.333432	+	0.0374985i
$965$	−1.18433	+	0.116646i	−0.0381250	+	0.00375498i
$966$	16.0403	−	17.4538i	0.516087	−	0.561568i
$967$	−34.5171	−	23.0636i	−1.11000	−	0.741676i	−0.141310	−	0.989965i	$-0.545132\pi$
$967$	−34.5171	−	23.0636i	−1.11000	−	0.741676i	−0.968686	+	0.248290i	$0.920132\pi$
$968$	−14.3561	+	3.28140i	−0.461423	+	0.105468i
$969$	−34.1206	−	51.0652i	−1.09611	−	1.64045i
$970$	0.692113	+	0.946808i	0.0222224	+	0.0304002i
$971$	−16.9956	−	31.7966i	−0.545416	−	1.02040i	−0.992069	−	0.125694i	$-0.959884\pi$
$971$	−16.9956	−	31.7966i	−0.545416	−	1.02040i	0.446653	−	0.894707i	$-0.352616\pi$
$972$	8.71310	+	5.99768i	0.279473	+	0.192376i
$973$	−1.44951	+	14.7171i	−0.0464692	+	0.471809i
$974$	61.3455	+	3.43869i	1.96564	+	0.110183i
$975$	25.0958	+	60.5867i	0.803710	+	1.94033i
$976$	32.2102	+	27.9588i	1.03102	+	0.894939i
$977$	−22.3107	+	53.8628i	−0.713782	+	1.72322i	−0.0234565	+	0.999725i	$0.507467\pi$
$977$	−22.3107	+	53.8628i	−0.713782	+	1.72322i	−0.690326	+	0.723498i	$0.742533\pi$
$978$	34.5379	−	71.7378i	1.10440	−	2.29392i
$979$	−23.3387	−	28.4382i	−0.745907	−	0.908890i
$980$	−2.13243	−	0.0294657i	−0.0681180	−	0.000941247i
$981$	3.52217	−	11.6110i	0.112454	−	0.370712i
$982$	−12.7114	−	7.73875i	−0.405636	−	0.246954i
$983$	−5.66571	−	1.12698i	−0.180708	−	0.0359451i	0.103907	−	0.994587i	$-0.466866\pi$
$983$	−5.66571	−	1.12698i	−0.180708	−	0.0359451i	−0.284615	+	0.958642i	$0.591866\pi$
$984$	−6.22127	+	8.03489i	−0.198327	+	0.256143i
$985$	−0.533797	−	2.68358i	−0.0170082	−	0.0855059i
$986$	−14.0112	+	6.50875i	−0.446208	+	0.207281i
$987$	−55.8341	+	68.0341i	−1.77722	+	2.16555i
$988$	−60.1433	+	5.08562i	−1.91341	+	0.161795i
$989$	0.973445	+	0.520317i	0.0309537	+	0.0165451i
$990$	4.79758	+	3.60977i	0.152477	+	0.114726i
$991$	−37.1512	−	37.1512i	−1.18015	−	1.18015i	−0.979706	−	0.200439i	$-0.935763\pi$
$991$	−37.1512	−	37.1512i	−1.18015	−	1.18015i	−0.200439	−	0.979706i	$-0.564237\pi$
$992$	15.1227	+	7.80264i	0.480148	+	0.247734i
$993$	22.4590	−	22.4590i	0.712715	−	0.712715i
$994$	79.0266	−	11.1651i	2.50657	−	0.354135i
$995$	1.73703	−	3.24975i	0.0550674	−	0.103024i
$996$	26.4292	−	13.6606i	0.837442	−	0.432854i
$997$	−35.8649	−	29.4336i	−1.13585	−	0.932172i	−0.137557	−	0.990494i	$-0.543925\pi$
$997$	−35.8649	−	29.4336i	−1.13585	−	0.932172i	−0.998298	+	0.0583224i	$0.981425\pi$
$998$	15.1186	+	5.52762i	0.478570	+	0.174974i
$999$	−4.44434	+	0.884033i	−0.140613	+	0.0279696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.k.a.13.2	✓	240
4.3	odd	2		512.2.k.a.401.14		240
128.59	odd	32		512.2.k.a.369.14		240
128.69	even	32	inner	128.2.k.a.69.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.13.2	✓	240	1.1	even	1	trivial
128.2.k.a.69.2	yes	240	128.69	even	32	inner
512.2.k.a.369.14		240	128.59	odd	32
512.2.k.a.401.14		240	4.3	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36942 - 0.353095i) q^{2} +(-0.855442 - 2.82001i) q^{3} +(1.75065 + 0.967074i) q^{4} +(-0.0181846 - 0.184631i) q^{5} +(0.175731 + 4.16385i) q^{6} +(1.98359 - 2.96866i) q^{7} +(-2.05591 - 1.94248i) q^{8} +(-4.72629 + 3.15801i) q^{9} +O(q^{10})\)	\(q+(-1.36942 - 0.353095i) q^{2} +(-0.855442 - 2.82001i) q^{3} +(1.75065 + 0.967074i) q^{4} +(-0.0181846 - 0.184631i) q^{5} +(0.175731 + 4.16385i) q^{6} +(1.98359 - 2.96866i) q^{7} +(-2.05591 - 1.94248i) q^{8} +(-4.72629 + 3.15801i) q^{9} +(-0.0402899 + 0.259259i) q^{10} +(-3.55038 + 1.89772i) q^{11} +(1.22958 - 5.76413i) q^{12} +(-4.45994 - 0.439266i) q^{13} +(-3.76460 + 3.36496i) q^{14} +(-0.505107 + 0.209222i) q^{15} +(2.12954 + 3.38601i) q^{16} +(2.85923 + 1.18433i) q^{17} +(7.58738 - 2.65582i) q^{18} +(5.20552 - 4.27206i) q^{19} +(0.146717 - 0.340810i) q^{20} +(-10.0685 - 3.05425i) q^{21} +(5.53206 - 1.34516i) q^{22} +(0.310799 - 1.56249i) q^{23} +(-3.71911 + 7.45938i) q^{24} +(4.87017 - 0.968737i) q^{25} +(5.95245 + 2.17632i) q^{26} +(6.11472 + 5.01822i) q^{27} +(6.34349 - 3.27879i) q^{28} +(1.66397 - 3.11306i) q^{29} +(0.765581 - 0.108163i) q^{30} +(-2.12713 + 2.12713i) q^{31} +(-1.72066 - 5.38882i) q^{32} +(8.38874 + 8.38874i) q^{33} +(-3.49731 - 2.63143i) q^{34} +(-0.584178 - 0.312249i) q^{35} +(-11.3281 + 0.957886i) q^{36} +(-0.363413 + 0.442819i) q^{37} +(-8.63701 + 4.01222i) q^{38} +(2.57649 + 12.9529i) q^{39} +(-0.321256 + 0.414908i) q^{40} +(1.19574 + 0.237847i) q^{41} +(12.7096 + 7.73770i) q^{42} +(-0.201123 + 0.663013i) q^{43} +(-8.05071 - 0.111244i) q^{44} +(0.669012 + 0.815194i) q^{45} +(-0.977325 + 2.02998i) q^{46} +(3.20111 - 7.72816i) q^{47} +(7.72691 - 8.90186i) q^{48} +(-2.19950 - 5.31007i) q^{49} +(-7.01138 - 0.393020i) q^{50} +(0.893926 - 9.07618i) q^{51} +(-7.38299 - 5.08209i) q^{52} +(1.56257 + 2.92337i) q^{53} +(-6.60175 - 9.03116i) q^{54} +(0.414940 + 0.621002i) q^{55} +(-9.84465 + 2.25021i) q^{56} +(-16.5003 - 11.0251i) q^{57} +(-3.37789 + 3.67557i) q^{58} +(11.3185 - 1.11477i) q^{59} +(-1.08660 - 0.122201i) q^{60} +(10.2039 - 3.09531i) q^{61} +(3.66402 - 2.16186i) q^{62} +20.2950i q^{63} +(0.453546 + 7.98713i) q^{64} +0.831432i q^{65} +(-8.52573 - 14.4498i) q^{66} +(-4.23438 + 1.28449i) q^{67} +(3.86016 + 4.83843i) q^{68} +(-4.67213 + 0.460164i) q^{69} +(0.689733 + 0.633872i) q^{70} +(-13.1426 - 8.78163i) q^{71} +(15.8512 + 2.68814i) q^{72} +(6.13916 + 9.18790i) q^{73} +(0.654023 - 0.478089i) q^{74} +(-6.89800 - 12.9052i) q^{75} +(13.2444 - 2.44475i) q^{76} +(-1.40884 + 14.3042i) q^{77} +(1.04529 - 18.6477i) q^{78} +(1.76236 + 4.25472i) q^{79} +(0.586438 - 0.454752i) q^{80} +(2.39485 - 5.78169i) q^{81} +(-1.55349 - 0.747923i) q^{82} +(3.20230 + 3.90202i) q^{83} +(-14.6727 - 15.0839i) q^{84} +(0.166670 - 0.549439i) q^{85} +(0.509529 - 0.836931i) q^{86} +(-10.2023 - 2.02937i) q^{87} +(10.9856 + 2.99500i) q^{88} +(1.78282 + 8.96285i) q^{89} +(-0.628321 - 1.35257i) q^{90} +(-10.1507 + 12.3687i) q^{91} +(2.05515 - 2.43481i) q^{92} +(7.81816 + 4.17889i) q^{93} +(-7.11245 + 9.45284i) q^{94} +(-0.883415 - 0.883415i) q^{95} +(-13.7246 + 9.46210i) q^{96} +(3.16077 - 3.16077i) q^{97} +(1.13710 + 8.04837i) q^{98} +(10.7871 - 20.1813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 32 q^{50} - 16 q^{51} + 80 q^{52} - 16 q^{53} + 112 q^{54} - 16 q^{55} + 96 q^{56} - 16 q^{57} + 128 q^{58} - 16 q^{59} + 176 q^{60} - 16 q^{61} + 80 q^{62} + 176 q^{64} + 176 q^{66} - 16 q^{67} + 80 q^{68} - 16 q^{69} + 176 q^{70} - 16 q^{71} + 128 q^{72} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 112 q^{76} - 16 q^{77} + 80 q^{78} - 16 q^{79} + 32 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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