LMFDB - Embedded newform 403.2.bs.a.4.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(4,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 18]))

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

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

chi := DirichletCharacter("403.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bs (of order $30$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	403.4
Dual form			403.2.bs.a.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.364510 + 1.71488i) q^{2} +(-0.797644 - 0.885874i) q^{3} +(-0.980870 - 0.436711i) q^{4} +3.57659i q^{5} +(1.80992 - 1.04496i) q^{6} +(0.0329582 - 0.0740253i) q^{7} +(-0.954559 + 1.31384i) q^{8} +(0.165050 - 1.57034i) q^{9} +O(q^{10})$	\(q+(-0.364510 + 1.71488i) q^{2} +(-0.797644 - 0.885874i) q^{3} +(-0.980870 - 0.436711i) q^{4} +3.57659i q^{5} +(1.80992 - 1.04496i) q^{6} +(0.0329582 - 0.0740253i) q^{7} +(-0.954559 + 1.31384i) q^{8} +(0.165050 - 1.57034i) q^{9} +(-6.13344 - 1.30370i) q^{10} +(-0.0769876 + 0.00809172i) q^{11} +(0.395514 + 1.21727i) q^{12} +(-2.41736 + 2.67514i) q^{13} +(0.114931 + 0.0835025i) q^{14} +(3.16841 - 2.85285i) q^{15} +(-3.34202 - 3.71169i) q^{16} +(-0.393147 + 3.74054i) q^{17} +(2.63279 + 0.855446i) q^{18} +(1.72739 + 1.55535i) q^{19} +(1.56194 - 3.50817i) q^{20} +(-0.0918660 + 0.0298491i) q^{21} +(0.0141864 - 0.134974i) q^{22} +(1.36132 - 0.606098i) q^{23} +(1.92529 - 0.202356i) q^{24} -7.79200 q^{25} +(-3.70639 - 5.12061i) q^{26} +(-4.41597 + 3.20839i) q^{27} +(-0.0646554 + 0.0582160i) q^{28} +(-4.71782 - 1.00280i) q^{29} +(3.73739 + 6.47334i) q^{30} +(-0.935150 - 5.48867i) q^{31} +(4.77048 - 2.75424i) q^{32} +(0.0685769 + 0.0617470i) q^{33} +(-6.27129 - 2.03767i) q^{34} +(0.264758 + 0.117878i) q^{35} +(-0.847678 + 1.46822i) q^{36} +(-9.56193 - 5.52058i) q^{37} +(-3.29690 + 2.39534i) q^{38} +(4.29803 + 0.00767347i) q^{39} +(-4.69906 - 3.41407i) q^{40} +(0.179754 - 0.845678i) q^{41} +(-0.0177016 - 0.168420i) q^{42} +(-4.87542 + 5.41470i) q^{43} +(0.0790485 + 0.0256844i) q^{44} +(5.61647 + 0.590315i) q^{45} +(0.543174 + 2.55543i) q^{46} +(11.4478 + 3.71960i) q^{47} +(-0.622344 + 5.92121i) q^{48} +(4.67952 + 5.19713i) q^{49} +(2.84026 - 13.3624i) q^{50} +(3.62724 - 2.63534i) q^{51} +(3.53938 - 1.56827i) q^{52} +(5.44280 + 3.95443i) q^{53} +(-3.89235 - 8.74236i) q^{54} +(-0.0289408 - 0.275353i) q^{55} +(0.0657967 + 0.113963i) q^{56} -2.77087i q^{57} +(3.43938 - 7.72498i) q^{58} +(1.92245 + 9.04442i) q^{59} +(-4.35366 + 1.41459i) q^{60} +(0.787045 + 1.36320i) q^{61} +(9.75330 + 0.397000i) q^{62} +(-0.110805 - 0.0639735i) q^{63} +(-0.102503 - 0.315473i) q^{64} +(-9.56786 - 8.64592i) q^{65} +(-0.130886 + 0.0950941i) q^{66} +(10.3712 + 5.98779i) q^{67} +(2.01916 - 3.49729i) q^{68} +(-1.62277 - 0.722506i) q^{69} +(-0.298654 + 0.411062i) q^{70} +(4.26214 + 0.447969i) q^{71} +(1.90563 + 1.71583i) q^{72} +(4.60271 + 6.33509i) q^{73} +(12.9526 - 14.3853i) q^{74} +(6.21524 + 6.90272i) q^{75} +(-1.01511 - 2.27997i) q^{76} +(-0.00193838 + 0.00596572i) q^{77} +(-1.57983 + 7.36782i) q^{78} +(-0.437356 - 0.317758i) q^{79} +(13.2752 - 11.9530i) q^{80} +(1.73113 + 0.367964i) q^{81} +(1.38472 + 0.616516i) q^{82} +(-6.28282 + 2.04141i) q^{83} +(0.103144 + 0.0108409i) q^{84} +(-13.3784 - 1.40613i) q^{85} +(-7.50845 - 10.3345i) q^{86} +(2.87478 + 4.97927i) q^{87} +(0.0628580 - 0.108873i) q^{88} +(10.3155 - 1.08420i) q^{89} +(-3.05958 + 9.41642i) q^{90} +(0.118356 + 0.267114i) q^{91} -1.59997 q^{92} +(-4.11635 + 5.20643i) q^{93} +(-10.5515 + 18.2758i) q^{94} +(-5.56285 + 6.17817i) q^{95} +(-6.24505 - 2.02914i) q^{96} +(6.21335 - 13.9554i) q^{97} +(-10.6182 + 6.13043i) q^{98} +0.122232i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9}+O(q^{10}) $ 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9	$ 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + 3 q^{10} - 18 q^{11} - 46 q^{12} - q^{13} - 32 q^{14} + 18 q^{15} + 21 q^{16} - 15 q^{17} - 15 q^{19} + 51 q^{20} - 10 q^{22} - 4 q^{23} - 51 q^{24} - 296 q^{25} - 6 q^{26} - 52 q^{27} + 21 q^{28} + q^{29} + 60 q^{30} + 138 q^{32} + 69 q^{33} - 10 q^{35} + 128 q^{36} - 18 q^{37} + 32 q^{38} - 14 q^{39} + 60 q^{40} - 15 q^{41} - 49 q^{42} - 36 q^{43} + 6 q^{45} - 69 q^{46} + 21 q^{48} - 23 q^{49} + 117 q^{50} + 8 q^{51} + 26 q^{52} - 48 q^{53} + 75 q^{54} + 46 q^{55} - 98 q^{56} - 21 q^{58} - 105 q^{59} - 74 q^{61} - 3 q^{62} - 90 q^{63} + 90 q^{64} + 89 q^{65} - 8 q^{66} + 6 q^{67} - 182 q^{68} + 29 q^{69} + 3 q^{71} - 183 q^{72} - 53 q^{74} - 38 q^{75} + 144 q^{76} - 128 q^{78} - 72 q^{79} - 72 q^{80} + 11 q^{81} - 11 q^{82} - 33 q^{84} + 72 q^{85} - 18 q^{87} - 14 q^{88} + 81 q^{89} - 34 q^{90} - 48 q^{91} + 8 q^{92} + 72 q^{93} - 6 q^{94} + 141 q^{97} + 96 q^{98}+O(q^{100}) $ 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9 + 3 * q^10 - 18 * q^11 - 46 * q^12 - q^13 - 32 * q^14 + 18 * q^15 + 21 * q^16 - 15 * q^17 - 15 * q^19 + 51 * q^20 - 10 * q^22 - 4 * q^23 - 51 * q^24 - 296 * q^25 - 6 * q^26 - 52 * q^27 + 21 * q^28 + q^29 + 60 * q^30 + 138 * q^32 + 69 * q^33 - 10 * q^35 + 128 * q^36 - 18 * q^37 + 32 * q^38 - 14 * q^39 + 60 * q^40 - 15 * q^41 - 49 * q^42 - 36 * q^43 + 6 * q^45 - 69 * q^46 + 21 * q^48 - 23 * q^49 + 117 * q^50 + 8 * q^51 + 26 * q^52 - 48 * q^53 + 75 * q^54 + 46 * q^55 - 98 * q^56 - 21 * q^58 - 105 * q^59 - 74 * q^61 - 3 * q^62 - 90 * q^63 + 90 * q^64 + 89 * q^65 - 8 * q^66 + 6 * q^67 - 182 * q^68 + 29 * q^69 + 3 * q^71 - 183 * q^72 - 53 * q^74 - 38 * q^75 + 144 * q^76 - 128 * q^78 - 72 * q^79 - 72 * q^80 + 11 * q^81 - 11 * q^82 - 33 * q^84 + 72 * q^85 - 18 * q^87 - 14 * q^88 + 81 * q^89 - 34 * q^90 - 48 * q^91 + 8 * q^92 + 72 * q^93 - 6 * q^94 + 141 * q^97 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.364510	+	1.71488i	−0.257747	+	1.21261i	0.638700	+	0.769456i	$0.279473\pi$
$2$	−0.364510	+	1.71488i	−0.257747	+	1.21261i	−0.896447	+	0.443150i	$0.853861\pi$
$3$	−0.797644	−	0.885874i	−0.460520	−	0.511459i	0.467498	−	0.883994i	$-0.345155\pi$
$3$	−0.797644	−	0.885874i	−0.460520	−	0.511459i	−0.928018	+	0.372535i	$0.878489\pi$
$4$	−0.980870	−	0.436711i	−0.490435	−	0.218356i
$5$			3.57659i			1.59950i	0.600333	+	0.799750i	$0.295035\pi$
$5$			3.57659i			1.59950i	−0.600333	+	0.799750i	$0.704965\pi$
$6$	1.80992	−	1.04496i	0.738897	−	0.426602i
$7$	0.0329582	−	0.0740253i	0.0124570	−	0.0279789i	−0.907210	−	0.420678i	$-0.861792\pi$
$7$	0.0329582	−	0.0740253i	0.0124570	−	0.0279789i	0.919667	+	0.392699i	$0.128459\pi$
$8$	−0.954559	+	1.31384i	−0.337488	+	0.464512i
$9$	0.165050	−	1.57034i	0.0550165	−	0.523447i
$10$	−6.13344	−	1.30370i	−1.93956	−	0.412267i
$11$	−0.0769876	+	0.00809172i	−0.0232126	+	0.00243975i	−0.116128	−	0.993234i	$-0.537048\pi$
$11$	−0.0769876	+	0.00809172i	−0.0232126	+	0.00243975i	0.0929150	+	0.995674i	$0.470382\pi$
$12$	0.395514	+	1.21727i	0.114175	+	0.351395i
$13$	−2.41736	+	2.67514i	−0.670456	+	0.741949i
$13$	−2.41736	+	2.67514i	−0.670456	+	0.741949i
$14$	0.114931	+	0.0835025i	0.0307167	+	0.0223170i
$15$	3.16841	−	2.85285i	0.818079	−	0.736602i
$16$	−3.34202	−	3.71169i	−0.835505	−	0.927922i
$17$	−0.393147	+	3.74054i	−0.0953521	+	0.907215i	0.837374	+	0.546630i	$0.184090\pi$
$17$	−0.393147	+	3.74054i	−0.0953521	+	0.907215i	−0.932726	+	0.360585i	$0.882577\pi$
$18$	2.63279	+	0.855446i	0.620555	+	0.201631i
$19$	1.72739	+	1.55535i	0.396291	+	0.356822i	0.843053	−	0.537831i	$-0.180756\pi$
$19$	1.72739	+	1.55535i	0.396291	+	0.356822i	−0.446762	+	0.894653i	$0.647423\pi$
$20$	1.56194	−	3.50817i	0.349260	−	0.784450i
$21$	−0.0918660	+	0.0298491i	−0.0200468	+	0.00651360i
$22$	0.0141864	−	0.134974i	0.00302454	−	0.0287766i
$23$	1.36132	−	0.606098i	0.283855	−	0.126380i	−0.259871	−	0.965643i	$-0.583680\pi$
$23$	1.36132	−	0.606098i	0.283855	−	0.126380i	0.543725	+	0.839263i	$0.317013\pi$
$24$	1.92529	−	0.202356i	0.392999	−	0.0413058i
$25$	−7.79200			−1.55840
$26$	−3.70639	−	5.12061i	−0.726884	−	1.00424i
$27$	−4.41597	+	3.20839i	−0.849853	+	0.617454i
$28$	−0.0646554	+	0.0582160i	−0.0122187	+	0.0110018i
$29$	−4.71782	−	1.00280i	−0.876077	−	0.186216i	−0.252140	−	0.967691i	$-0.581134\pi$
$29$	−4.71782	−	1.00280i	−0.876077	−	0.186216i	−0.623937	+	0.781475i	$0.714468\pi$
$30$	3.73739	+	6.47334i	0.682350	+	1.18186i
$31$	−0.935150	−	5.48867i	−0.167958	−	0.985794i
$31$	−0.935150	−	5.48867i	−0.167958	−	0.985794i
$32$	4.77048	−	2.75424i	0.843309	−	0.486885i
$33$	0.0685769	+	0.0617470i	0.0119377	+	0.0107488i
$34$	−6.27129	−	2.03767i	−1.07552	−	0.349457i
$35$	0.264758	+	0.117878i	0.0447523	+	0.0199250i
$36$	−0.847678	+	1.46822i	−0.141280	+	0.244704i
$37$	−9.56193	−	5.52058i	−1.57197	−	0.907578i	−0.995927	−	0.0901597i	$-0.971262\pi$
$37$	−9.56193	−	5.52058i	−1.57197	−	0.907578i	−0.576044	−	0.817418i	$-0.695404\pi$
$38$	−3.29690	+	2.39534i	−0.534827	+	0.388575i
$39$	4.29803	+	0.00767347i	0.688235	+	0.00122874i
$40$	−4.69906	−	3.41407i	−0.742987	−	0.539811i
$41$	0.179754	−	0.845678i	0.0280729	−	0.132073i	−0.961879	−	0.273474i	$-0.911827\pi$
$41$	0.179754	−	0.845678i	0.0280729	−	0.132073i	0.989952	+	0.141401i	$0.0451607\pi$
$42$	−0.0177016	−	0.168420i	−0.00273142	−	0.0259877i
$43$	−4.87542	+	5.41470i	−0.743494	+	0.825734i	−0.989651	−	0.143496i	$-0.954166\pi$
$43$	−4.87542	+	5.41470i	−0.743494	+	0.825734i	0.246157	+	0.969230i	$0.420832\pi$
$44$	0.0790485	+	0.0256844i	0.0119170	+	0.00387207i
$45$	5.61647	+	0.590315i	0.837254	+	0.0879989i
$46$	0.543174	+	2.55543i	0.0800867	+	0.376778i
$47$	11.4478	+	3.71960i	1.66983	+	0.542560i	0.982896	−	0.184162i	$-0.0589572\pi$
$47$	11.4478	+	3.71960i	1.66983	+	0.542560i	0.686932	+	0.726722i	$0.258957\pi$
$48$	−0.622344	+	5.92121i	−0.0898277	+	0.854653i
$49$	4.67952	+	5.19713i	0.668503	+	0.742448i
$50$	2.84026	−	13.3624i	0.401673	−	1.88972i
$51$	3.62724	−	2.63534i	0.507915	−	0.369022i
$52$	3.53938	−	1.56827i	0.490824	−	0.217480i
$53$	5.44280	+	3.95443i	0.747626	+	0.543182i	0.895090	−	0.445885i	$-0.147111\pi$
$53$	5.44280	+	3.95443i	0.747626	+	0.543182i	−0.147464	+	0.989067i	$0.547111\pi$
$54$	−3.89235	−	8.74236i	−0.529682	−	1.18968i
$55$	−0.0289408	−	0.275353i	−0.00390237	−	0.0371286i
$56$	0.0657967	+	0.113963i	0.00879246	+	0.0152290i
$57$		−	2.77087i		−	0.367010i
$58$	3.43938	−	7.72498i	0.451613	−	1.01434i
$59$	1.92245	+	9.04442i	0.250282	+	1.17748i	0.906266	+	0.422709i	$0.138921\pi$
$59$	1.92245	+	9.04442i	0.250282	+	1.17748i	−0.655984	+	0.754775i	$0.727746\pi$
$60$	−4.35366	+	1.41459i	−0.562056	+	0.182623i
$61$	0.787045	+	1.36320i	0.100771	+	0.174540i	0.912002	−	0.410185i	$-0.134536\pi$
$61$	0.787045	+	1.36320i	0.100771	+	0.174540i	−0.811232	+	0.584725i	$0.801202\pi$
$62$	9.75330	+	0.397000i	1.23867	+	0.0504190i
$63$	−0.110805	−	0.0639735i	−0.0139602	−	0.00805990i
$64$	−0.102503	−	0.315473i	−0.0128129	−	0.0394342i
$65$	−9.56786	−	8.64592i	−1.18675	−	1.07239i
$66$	−0.130886	+	0.0950941i	−0.0161109	+	0.0117053i
$67$	10.3712	+	5.98779i	1.26704	+	0.731526i	0.974427	−	0.224705i	$-0.0721420\pi$
$67$	10.3712	+	5.98779i	1.26704	+	0.731526i	0.292613	+	0.956231i	$0.405475\pi$
$68$	2.01916	−	3.49729i	0.244860	−	0.424109i
$69$	−1.62277	−	0.722506i	−0.195359	−	0.0869795i
$70$	−0.298654	+	0.411062i	−0.0356960	+	0.0491313i
$71$	4.26214	+	0.447969i	0.505823	+	0.0531641i	0.354003	−	0.935244i	$-0.384820\pi$
$71$	4.26214	+	0.447969i	0.505823	+	0.0531641i	0.151819	+	0.988408i	$0.451487\pi$
$72$	1.90563	+	1.71583i	0.224580	+	0.202213i
$73$	4.60271	+	6.33509i	0.538706	+	0.741466i	0.988426	−	0.151704i	$-0.0484761\pi$
$73$	4.60271	+	6.33509i	0.538706	+	0.741466i	−0.449720	+	0.893170i	$0.648476\pi$
$74$	12.9526	−	14.3853i	1.50571	−	1.67226i
$75$	6.21524	+	6.90272i	0.717674	+	0.797058i
$76$	−1.01511	−	2.27997i	−0.116441	−	0.261530i
$77$	−0.00193838	+	0.00596572i	−0.000220899	+	0.000679857i
$78$	−1.57983	+	7.36782i	−0.178881	+	0.834242i
$79$	−0.437356	−	0.317758i	−0.0492064	−	0.0357506i	0.562910	−	0.826518i	$-0.309682\pi$
$79$	−0.437356	−	0.317758i	−0.0492064	−	0.0357506i	−0.612117	+	0.790768i	$0.709682\pi$
$80$	13.2752	−	11.9530i	1.48421	−	1.33639i
$81$	1.73113	+	0.367964i	0.192348	+	0.0408849i
$82$	1.38472	+	0.616516i	0.152916	+	0.0680828i
$83$	−6.28282	+	2.04141i	−0.689629	+	0.224074i	−0.632806	−	0.774310i	$-0.718097\pi$
$83$	−6.28282	+	2.04141i	−0.689629	+	0.224074i	−0.0568228	+	0.998384i	$0.518097\pi$
$84$	0.103144	+	0.0108409i	0.0112539	+	0.00118284i
$85$	−13.3784	−	1.40613i	−1.45109	−	0.152516i
$86$	−7.50845	−	10.3345i	−0.809656	−	1.11440i
$87$	2.87478	+	4.97927i	0.308209	+	0.533834i
$88$	0.0628580	−	0.108873i	0.00670068	−	0.0116059i
$89$	10.3155	−	1.08420i	1.09344	−	0.114925i	0.459404	−	0.888227i	$-0.348063\pi$
$89$	10.3155	−	1.08420i	1.09344	−	0.114925i	0.634038	+	0.773302i	$0.281396\pi$
$90$	−3.05958	+	9.41642i	−0.322508	+	0.992578i
$91$	0.118356	+	0.267114i	0.0124071	+	0.0280011i
$92$	−1.59997			−0.166808
$93$	−4.11635	+	5.20643i	−0.426846	+	0.539882i
$94$	−10.5515	+	18.2758i	−1.08831	+	1.88500i
$95$	−5.56285	+	6.17817i	−0.570736	+	0.633867i
$96$	−6.24505	−	2.02914i	−0.637382	−	0.207098i
$97$	6.21335	−	13.9554i	0.630870	−	1.41696i	−0.261300	−	0.965258i	$-0.584151\pi$
$97$	6.21335	−	13.9554i	0.630870	−	1.41696i	0.892170	−	0.451700i	$-0.149182\pi$
$98$	−10.6182	+	6.13043i	−1.07260	+	0.619267i
$99$			0.122232i			0.0122848i
$100$	7.64293	+	3.40285i	0.764293	+	0.340285i
$101$	−11.9811	+	5.33433i	−1.19216	+	0.530786i	−0.904305	−	0.426887i	$-0.859610\pi$
$101$	−11.9811	+	5.33433i	−1.19216	+	0.530786i	−0.287859	+	0.957673i	$0.592944\pi$
$102$	3.19714	+	7.18090i	0.316565	+	0.711016i
$103$	0.852050	+	2.62234i	0.0839550	+	0.258387i	0.984218	−	0.176959i	$-0.0566260\pi$
$103$	0.852050	+	2.62234i	0.0839550	+	0.258387i	−0.900263	+	0.435346i	$0.856626\pi$
$104$	−1.20718	−	5.72960i	−0.118373	−	0.561833i
$105$	−0.106758	−	0.328567i	−0.0104185	−	0.0320649i
$106$	−8.76534	+	7.89235i	−0.851365	+	0.766572i
$107$	14.3312	−	6.38065i	1.38545	−	0.616840i	0.427559	−	0.903987i	$-0.359373\pi$
$107$	14.3312	−	6.38065i	1.38545	−	0.616840i	0.957887	+	0.287147i	$0.0927068\pi$
$108$	5.73263	−	1.21851i	0.551622	−	0.117251i
$109$	13.1387	+	4.26902i	1.25846	+	0.408898i	0.860945	−	0.508698i	$-0.169873\pi$
$109$	13.1387	+	4.26902i	1.25846	+	0.408898i	0.397514	+	0.917596i	$0.369873\pi$
$110$	0.482748	+	0.0507388i	0.0460282	+	0.00483776i
$111$	2.73648	+	12.8741i	0.259735	+	1.22196i
$112$	−0.384906	+	0.125064i	−0.0363702	+	0.0118174i
$113$	2.66380	+	1.18600i	0.250589	+	0.111570i	0.528188	−	0.849128i	$-0.322872\pi$
$113$	2.66380	+	1.18600i	0.250589	+	0.111570i	−0.277598	+	0.960697i	$0.589538\pi$
$114$	4.75171	+	1.01001i	0.445039	+	0.0945959i
$115$	2.16777	+	4.86888i	0.202145	+	0.454026i
$116$	4.18963	+	3.04394i	0.388997	+	0.282623i
$117$	3.80189	+	4.23762i	0.351485	+	0.391768i
$118$	−16.2109			−1.49233
$119$	0.263938	+	0.152384i	0.0241951	+	0.0139691i
$120$	0.723746	+	6.88598i	0.0660687	+	0.628601i
$121$	−10.7538	+	2.28578i	−0.977615	+	0.207798i
$122$	−2.62462	+	0.852791i	−0.237622	+	0.0772081i
$123$	−0.892544	+	0.515310i	−0.0804779	+	0.0464640i
$124$	−1.47970	+	5.79206i	−0.132881	+	0.520142i
$125$		−	9.98583i		−	0.893160i
$126$	0.150097	−	0.166699i	0.0133717	−	0.0148508i
$127$	2.01098	+	2.23342i	0.178445	+	0.198184i	0.825731	−	0.564064i	$-0.190763\pi$
$127$	2.01098	+	2.23342i	0.178445	+	0.198184i	−0.647286	+	0.762247i	$0.724096\pi$
$128$	11.5350	−	1.21237i	1.01956	−	0.107160i
$129$	8.68559			0.764723
$130$	18.3143	−	13.2563i	1.60627	−	1.16265i
$131$	0.750616	−	0.545354i	0.0655816	−	0.0476478i	−0.554511	−	0.832176i	$-0.687095\pi$
$131$	0.750616	−	0.545354i	0.0655816	−	0.0476478i	0.620093	+	0.784528i	$0.287095\pi$
$132$	−0.0402994	−	0.0905140i	−0.00350762	−	0.00787824i
$133$	0.172067	−	0.0766092i	0.0149201	−	0.00664286i
$134$	−14.0488	+	15.6027i	−1.21363	+	1.34787i
$135$	−11.4751	−	15.7941i	−0.987618	−	1.35934i
$136$	−4.53919	−	4.08710i	−0.389232	−	0.350466i
$137$	2.58265	+	12.1504i	0.220651	+	1.03808i	0.939403	+	0.342815i	$0.111380\pi$
$137$	2.58265	+	12.1504i	0.220651	+	1.03808i	−0.718752	+	0.695266i	$0.755286\pi$
$138$	1.83053	−	2.51951i	0.155825	−	0.214475i
$139$	4.08675	−	0.868665i	0.346633	−	0.0736792i	−0.0313052	−	0.999510i	$-0.509966\pi$
$139$	4.08675	−	0.868665i	0.346633	−	0.0736792i	0.377939	+	0.925831i	$0.376633\pi$
$140$	−0.208215	−	0.231246i	−0.0175974	−	0.0195438i
$141$	−5.83614	−	13.1082i	−0.491492	−	1.10391i
$142$	−2.32181	+	7.14578i	−0.194842	+	0.599661i
$143$	0.164461	−	0.225513i	0.0137529	−	0.0188583i
$144$	−6.38022	+	4.63550i	−0.531685	+	0.386292i
$145$	3.58662	−	16.8737i	0.297852	−	1.40128i
$146$	−12.5417	+	5.58391i	−1.03796	+	0.462128i
$147$	0.871412	−	8.29093i	0.0718728	−	0.683824i
$148$	6.96811	+	9.59078i	0.572775	+	0.788357i
$149$	−7.21825	+	4.16746i	−0.591342	+	0.341412i	−0.765628	−	0.643283i	$-0.777572\pi$
$149$	−7.21825	+	4.16746i	−0.591342	+	0.341412i	0.174286	+	0.984695i	$0.444238\pi$
$150$	−14.1029	+	8.14231i	−1.15150	+	0.664817i
$151$	7.57038	+	10.4197i	0.616069	+	0.847946i	0.997059	−	0.0766330i	$-0.0244170\pi$
$151$	7.57038	+	10.4197i	0.616069	+	0.847946i	−0.380991	+	0.924579i	$0.624417\pi$
$152$	−3.69237	+	0.784839i	−0.299491	+	0.0636588i
$153$	5.80904	+	1.23475i	0.469633	+	0.0998237i
$154$	−0.00952396	−	0.00549866i	−0.000767463	−	0.000443095i
$155$	19.6307	−	3.34465i	1.57678	−	0.268649i
$156$	−4.21245	−	1.88452i	−0.337266	−	0.150883i
$157$	−1.99901	−	6.15233i	−0.159539	−	0.491010i	0.839054	−	0.544049i	$-0.183109\pi$
$157$	−1.99901	−	6.15233i	−0.159539	−	0.491010i	−0.998592	+	0.0530389i	$0.983109\pi$
$158$	0.704339	−	0.634190i	0.0560342	−	0.0504534i
$159$	−0.838296	−	7.97586i	−0.0664812	−	0.632527i
$160$	9.85077	+	17.0620i	0.778772	+	1.34887i
$161$		−	0.120748i		−	0.00951628i
$162$	−1.26203	+	2.83457i	−0.0991545	+	0.222705i
$163$	−14.3810	−	1.51151i	−1.12641	−	0.118390i	−0.477052	−	0.878875i	$-0.658295\pi$
$163$	−14.3810	−	1.51151i	−1.12641	−	0.118390i	−0.649356	+	0.760485i	$0.724961\pi$
$164$	−0.545633	+	0.750999i	−0.0426068	+	0.0586432i
$165$	−0.220844	+	0.245272i	−0.0171926	+	0.0190944i
$166$	−1.21063	−	11.5184i	−0.0939635	−	0.894003i
$167$	0.173434	−	0.815940i	0.0134207	−	0.0631394i	−0.970928	−	0.239373i	$-0.923058\pi$
$167$	0.173434	−	0.815940i	0.0134207	−	0.0631394i	0.984348	+	0.176234i	$0.0563914\pi$
$168$	0.0484747	−	0.149190i	0.00373990	−	0.0115102i
$169$	−1.31270	−	12.9336i	−0.100977	−	0.994889i
$170$	7.28790	−	22.4298i	0.558956	−	1.72029i
$171$	2.72754	−	2.45589i	0.208580	−	0.187806i
$172$	7.14681	−	3.18197i	0.544939	−	0.242623i
$173$	−10.7312	+	2.28099i	−0.815878	+	0.173420i	−0.596906	−	0.802311i	$-0.703604\pi$
$173$	−10.7312	+	2.28099i	−0.815878	+	0.173420i	−0.218972	+	0.975731i	$0.570270\pi$
$174$	−9.58676	+	3.11493i	−0.726770	+	0.236142i
$175$	−0.256810	+	0.576805i	−0.0194130	+	0.0436024i
$176$	0.287328	+	0.258711i	0.0216582	+	0.0195011i
$177$	6.47878	−	8.91728i	0.486975	−	0.670264i
$178$	−1.90082	+	18.0851i	−0.142473	+	1.35554i
$179$	−2.20457	−	20.9751i	−0.164777	−	1.56775i	−0.694445	−	0.719546i	$-0.744350\pi$
$179$	−2.20457	−	20.9751i	−0.164777	−	1.56775i	0.529668	−	0.848205i	$-0.322317\pi$
$180$	−5.25123	−	3.03180i	−0.391403	−	0.225977i
$181$	−19.8268			−1.47371			−0.736856	−	0.676050i	$-0.763690\pi$
$181$	−19.8268			−1.47371			−0.736856	+	0.676050i	$0.763690\pi$
$182$	−0.501211	+	0.105601i	−0.0371522	+	0.00782765i
$183$	0.579843	−	1.78457i	0.0428632	−	0.131919i
$184$	−0.503145	+	2.36711i	−0.0370923	+	0.174506i
$185$	19.7449	−	34.1991i	1.45167	−	2.51437i
$186$	−7.42797	−	8.95686i	−0.544646	−	0.656749i
$187$		−	0.291157i		−	0.0212915i
$188$	−9.60437	−	8.64781i	−0.700471	−	0.630707i
$189$	0.0919596	+	0.432636i	0.00668908	+	0.0314696i
$190$	−8.56713	−	11.7916i	−0.621525	−	0.855456i
$191$	−1.99636	−	3.45780i	−0.144452	−	0.250197i	0.784717	−	0.619855i	$-0.212808\pi$
$191$	−1.99636	−	3.45780i	−0.144452	−	0.250197i	−0.929168	+	0.369657i	$0.879475\pi$
$192$	−0.197708	+	0.342441i	−0.0142684	+	0.0247135i
$193$	−0.912747	+	0.0959336i	−0.0657010	+	0.00690545i	−0.137322	−	0.990526i	$-0.543849\pi$
$193$	−0.912747	+	0.0959336i	−0.0657010	+	0.00690545i	0.0716209	+	0.997432i	$0.477183\pi$
$194$	21.6671	+	15.7421i	1.55561	+	1.13021i
$195$	−0.0274448	+	15.3723i	−0.00196537	+	1.10083i
$196$	−2.32035	−	7.14131i	−0.165739	−	0.510094i
$197$	−9.56120	+	1.00492i	−0.681207	+	0.0715978i	−0.438811	−	0.898579i	$-0.644600\pi$
$197$	−9.56120	+	1.00492i	−0.681207	+	0.0715978i	−0.242397	+	0.970177i	$0.577934\pi$
$198$	−0.209614	−	0.0445549i	−0.0148966	−	0.00316638i
$199$	12.4118	−	2.63821i	0.879850	−	0.187018i	0.254228	−	0.967144i	$-0.418179\pi$
$199$	12.4118	−	2.63821i	0.879850	−	0.187018i	0.625622	+	0.780127i	$0.284845\pi$
$200$	7.43792	−	10.2374i	0.525940	−	0.723895i
$201$	−2.96807	−	13.9637i	−0.209351	−	0.984921i
$202$	−4.78053	−	22.4906i	−0.336357	−	1.58243i
$203$	−0.229724	+	0.316188i	−0.0161234	+	0.0221920i
$204$	−4.70873	+	1.00087i	−0.329677	+	0.0700751i
$205$	3.02464	+	0.642908i	0.211250	+	0.0449026i
$206$	−4.80759	+	0.505298i	−0.334961	+	0.0352058i
$207$	−0.727097	−	2.23777i	−0.0505367	−	0.155536i
$208$	18.0081	+	0.0321508i	1.24864	+	0.00222925i
$209$	−0.145573	−	0.105765i	−0.0100695	−	0.00731592i
$210$	0.602369	−	0.0633115i	0.0415674	−	0.00436891i
$211$	7.49459	−	12.9810i	0.515949	−	0.893650i	−0.483879	−	0.875135i	$-0.660773\pi$
$211$	7.49459	−	12.9810i	0.515949	−	0.893650i	0.999829	−	0.0185155i	$-0.00589401\pi$
$212$	−3.61174	−	6.25571i	−0.248055	−	0.429644i
$213$	−3.00282	−	4.13303i	−0.205750	−	0.283191i
$214$	5.71822	+	26.9021i	0.390889	+	1.83899i
$215$	−19.3662	−	17.4374i	−1.32076	−	1.18922i
$216$		−	8.86446i		−	0.603150i
$217$	−0.437121	−	0.111672i	−0.0296737	−	0.00758078i
$218$	−12.1101	+	20.9753i	−0.820197	+	1.42062i
$219$	1.94076	−	9.13056i	0.131144	−	0.616986i
$220$	−0.0918627	+	0.282724i	−0.00619338	+	0.0190613i
$221$	−9.05608	−	10.0940i	−0.609178	−	0.678994i
$222$	−23.0751			−1.54870
$223$	14.5832	+	8.41960i	0.976562	+	0.563818i	0.901230	−	0.433340i	$-0.142665\pi$
$223$	14.5832	+	8.41960i	0.976562	+	0.563818i	0.0753317	+	0.997159i	$0.475998\pi$
$224$	−0.0466569	−	0.443911i	−0.00311740	−	0.0296600i
$225$	−1.28607	+	12.2361i	−0.0857377	+	0.815740i
$226$	−3.00484	+	4.13580i	−0.199879	+	0.275109i
$227$	0.135620	+	0.122113i	0.00900139	+	0.00810489i	0.673619	−	0.739079i	$-0.264739\pi$
$227$	0.135620	+	0.122113i	0.00900139	+	0.00810489i	−0.664618	+	0.747184i	$0.731406\pi$
$228$	−1.21007	+	2.71786i	−0.0801388	+	0.179995i
$229$	3.61666	−	1.17512i	0.238995	−	0.0776543i	−0.187070	−	0.982347i	$-0.559899\pi$
$229$	3.61666	−	1.17512i	0.238995	−	0.0776543i	0.426066	+	0.904692i	$0.359899\pi$
$230$	−9.13974	+	1.94271i	−0.602657	+	0.128099i
$231$	0.00683101	−	0.00304136i	0.000449448	−	0.000200107i
$232$	5.82096	−	5.24121i	0.382165	−	0.344103i
$233$	−4.80972	+	14.8028i	−0.315095	+	0.969763i	0.660620	+	0.750720i	$0.270293\pi$
$233$	−4.80972	+	14.8028i	−0.315095	+	0.969763i	−0.975715	+	0.219043i	$0.929707\pi$
$234$	−8.65285	+	4.97515i	−0.565655	+	0.325236i
$235$	−13.3035	+	40.9439i	−0.867824	+	2.67089i
$236$	2.06413	−	9.71096i	0.134363	−	0.632129i
$237$	0.0673613	+	0.640900i	0.00437559	+	0.0416309i
$238$	−0.357529	+	0.397077i	−0.0231752	+	0.0257387i
$239$	−17.6239	+	24.2572i	−1.14000	+	1.56907i	−0.372482	+	0.928039i	$0.621493\pi$
$239$	−17.6239	+	24.2572i	−1.14000	+	1.56907i	−0.767515	+	0.641031i	$0.778507\pi$
$240$	−21.1777	−	2.22587i	−1.36702	−	0.143679i
$241$	3.23784	−	7.27230i	0.208567	−	0.468450i	−0.778725	−	0.627366i	$-0.784133\pi$
$241$	3.23784	−	7.27230i	0.208567	−	0.468450i	0.987292	+	0.158916i	$0.0507998\pi$
$242$		−	19.2746i		−	1.23902i
$243$	7.13279	+	12.3544i	0.457569	+	0.792533i
$244$	−0.176663	−	1.68084i	−0.0113097	−	0.107604i
$245$	−18.5880	+	16.7367i	−1.18754	+	1.06927i
$246$	−0.558357	−	1.71844i	−0.0355995	−	0.109564i
$247$	−8.33651	+	0.861157i	−0.530439	+	0.0547941i
$248$	8.10388	+	4.01062i	0.514597	+	0.254675i
$249$	6.81989	+	3.93746i	0.432193	+	0.249527i
$250$	17.1245	+	3.63993i	1.08305	+	0.230210i
$251$	12.0468	−	2.56062i	0.760386	−	0.161625i	0.188629	−	0.982048i	$-0.439596\pi$
$251$	12.0468	−	2.56062i	0.760386	−	0.161625i	0.571756	+	0.820423i	$0.306262\pi$
$252$	0.0807477	+	0.111140i	0.00508663	+	0.00700114i
$253$	−0.0999003	+	0.0576775i	−0.00628068	+	0.00362615i
$254$	−4.56307	+	2.63449i	−0.286313	+	0.165303i
$255$	9.42554	+	12.9731i	0.590250	+	0.812410i
$256$	−2.05618	+	19.5633i	−0.128511	+	1.22270i
$257$	10.9642	−	4.88156i	0.683925	−	0.304503i	−0.0352033	−	0.999380i	$-0.511208\pi$
$257$	10.9642	−	4.88156i	0.683925	−	0.304503i	0.719129	+	0.694877i	$0.244541\pi$
$258$	−3.16598	+	14.8948i	−0.197105	+	0.927308i
$259$	−0.723807	+	0.525877i	−0.0449752	+	0.0326764i
$260$	5.60905	+	12.6589i	0.347859	+	0.785073i
$261$	−2.35342	+	7.24308i	−0.145673	+	0.448335i
$262$	0.661613	+	1.48601i	0.0408746	+	0.0918058i
$263$	−19.1918	−	21.3146i	−1.18342	−	1.31432i	−0.938705	−	0.344721i	$-0.887973\pi$
$263$	−19.1918	−	21.3146i	−1.18342	−	1.31432i	−0.244711	−	0.969596i	$-0.578693\pi$
$264$	−0.146586	+	0.0311579i	−0.00902176	+	0.00191763i
$265$	−14.1434	+	19.4667i	−0.868820	+	1.19583i
$266$	0.0686557	+	0.323000i	0.00420955	+	0.0198044i
$267$	−9.18858	−	8.27343i	−0.562332	−	0.506326i
$268$	−7.55782	−	10.4025i	−0.461668	−	0.635431i
$269$	10.7963	−	11.9905i	0.658263	−	0.731075i	−0.317897	−	0.948125i	$-0.602977\pi$
$269$	10.7963	−	11.9905i	0.658263	−	0.731075i	0.976161	+	0.217050i	$0.0696434\pi$
$270$	31.2678	−	13.9213i	1.90290	−	0.847226i
$271$	0.832979	+	1.87090i	0.0505999	+	0.113649i	0.937076	−	0.349124i	$-0.113521\pi$
$271$	0.832979	+	1.87090i	0.0505999	+	0.113649i	−0.886476	+	0.462774i	$0.846854\pi$
$272$	15.1976	−	11.0417i	0.921492	−	0.669503i
$273$	0.142223	−	0.317910i	0.00860775	−	0.0192408i
$274$	−21.7780			−1.31566
$275$	0.599887	−	0.0630507i	0.0361745	−	0.00380210i
$276$	1.27620	+	1.41737i	0.0768185	+	0.0853156i
$277$	2.39747	−	2.66266i	0.144050	−	0.159984i	−0.666802	−	0.745235i	$-0.732337\pi$
$277$	2.39747	−	2.66266i	0.144050	−	0.159984i	0.810852	+	0.585251i	$0.199004\pi$
$278$			7.32494i			0.439320i
$279$	−8.77344	+	0.562603i	−0.525252	+	0.0336822i
$280$	−0.407600	+	0.235328i	−0.0243588	+	0.0140635i
$281$	8.30828	−	2.69952i	0.495630	−	0.161040i	−0.0505270	−	0.998723i	$-0.516090\pi$
$281$	8.30828	−	2.69952i	0.495630	−	0.161040i	0.546157	+	0.837683i	$0.316090\pi$
$282$	24.6064	−	5.23024i	1.46529	−	0.311456i
$283$	0.623499	+	5.93220i	0.0370632	+	0.352633i	0.997299	+	0.0734437i	$0.0233989\pi$
$283$	0.623499	+	5.93220i	0.0370632	+	0.352633i	−0.960236	+	0.279189i	$0.909934\pi$
$284$	−3.98497	−	2.30072i	−0.236464	−	0.136523i
$285$	9.91025			0.587033
$286$	0.326781	+	0.364233i	0.0193230	+	0.0215375i
$287$	−0.0566772	−	0.0411784i	−0.00334555	−	0.00243068i
$288$	−3.53773	−	7.94587i	−0.208463	−	0.468215i
$289$	2.79141	+	0.593333i	0.164201	+	0.0349019i
$290$	27.6291	+	12.3013i	1.62244	+	0.722355i
$291$	−17.3188	+	5.62721i	−1.01524	+	0.329873i
$292$	−1.74805	−	8.22395i	−0.102297	−	0.481270i
$293$	−8.40749	−	0.883663i	−0.491171	−	0.0516242i	−0.144294	−	0.989535i	$-0.546091\pi$
$293$	−8.40749	−	0.883663i	−0.491171	−	0.0516242i	−0.346877	+	0.937911i	$0.612758\pi$
$294$	13.9003	+	4.51649i	0.810684	+	0.263407i
$295$	−32.3482	+	6.87582i	−1.88338	+	0.400326i
$296$	16.3806	−	7.29310i	0.952102	−	0.423903i
$297$	0.314013	−	0.282739i	0.0182209	−	0.0164062i
$298$	−4.51559	−	13.8976i	−0.261581	−	0.805063i
$299$	−1.66941	+	5.10687i	−0.0965445	+	0.295338i
$300$	−3.08184	−	9.48494i	−0.177930	−	0.547613i
$301$	0.240140	+	0.539363i	0.0138414	+	0.0310884i
$302$	−20.6281	+	9.18423i	−1.18701	+	0.528493i
$303$	14.2822	+	6.35885i	0.820491	+	0.365306i
$304$		−	11.6095i		−	0.665853i
$305$	−4.87562	+	2.81494i	−0.279177	+	0.161183i
$306$	−4.23491	+	9.51176i	−0.242094	+	0.543751i
$307$	7.70396	+	2.50317i	0.439688	+	0.142863i	0.520492	−	0.853867i	$-0.325749\pi$
$307$	7.70396	+	2.50317i	0.439688	+	0.142863i	−0.0808037	+	0.996730i	$0.525749\pi$
$308$	0.00450660	−	0.00500508i	0.000256787	−	0.000285191i
$309$	1.64343	−	2.84650i	0.0934914	−	0.161932i
$310$	−1.41991	+	34.8836i	−0.0806452	+	1.98125i
$311$	18.8701			1.07003			0.535013	−	0.844844i	$-0.320307\pi$
$311$	18.8701			1.07003			0.535013	+	0.844844i	$0.320307\pi$
$312$	−4.11280	+	5.63959i	−0.232842	+	0.319279i
$313$	2.99199	−	9.20838i	0.169117	−	0.520489i	−0.830199	−	0.557467i	$-0.811773\pi$
$313$	2.99199	−	9.20838i	0.169117	−	0.520489i	0.999316	+	0.0369784i	$0.0117733\pi$
$314$	11.2792	−	1.18549i	0.636522	−	0.0669012i
$315$	0.228807	−	0.396305i	0.0128918	−	0.0223293i
$316$	0.290221	+	0.502678i	0.0163262	+	0.0282778i
$317$	19.4870	+	26.8216i	1.09450	+	1.50645i	0.842478	+	0.538731i	$0.181096\pi$
$317$	19.4870	+	26.8216i	1.09450	+	1.50645i	0.252023	+	0.967721i	$0.418904\pi$
$318$	13.9832	+	1.46970i	0.784141	+	0.0824166i
$319$	0.371328	+	0.0390281i	0.0207904	+	0.00218516i
$320$	1.12832	−	0.366613i	0.0630749	−	0.0204943i
$321$	−17.0836	−	7.60611i	−0.953514	−	0.424532i
$322$	0.207069	+	0.0440139i	0.0115395	+	0.00245280i
$323$	−6.49697	+	5.84990i	−0.361501	+	0.325497i
$324$	−1.53732	−	1.11693i	−0.0854068	−	0.0620517i
$325$	18.8361	−	20.8446i	1.04484	−	1.15625i
$326$	7.83408	−	24.1108i	0.433889	−	1.33537i
$327$	−6.69819	−	15.0444i	−0.370411	−	0.831957i
$328$	0.939497	+	1.04342i	0.0518751	+	0.0576131i
$329$	0.652642	−	0.724833i	0.0359813	−	0.0399613i
$330$	−0.340113	−	0.468125i	−0.0187226	−	0.0257694i
$331$	−3.32920	−	2.99763i	−0.182989	−	0.164764i	0.572545	−	0.819873i	$-0.305956\pi$
$331$	−3.32920	−	2.99763i	−0.182989	−	0.164764i	−0.755535	+	0.655109i	$0.772623\pi$
$332$	7.05414	+	0.741419i	0.387146	+	0.0406907i
$333$	−10.2474	+	14.1043i	−0.561554	+	0.772913i
$334$	1.33603	+	0.594837i	0.0731041	+	0.0325480i
$335$	−21.4159	+	37.0934i	−1.17007	+	2.02663i
$336$	0.417808	+	0.241222i	0.0227933	+	0.0131597i
$337$	−15.8619	+	11.5244i	−0.864055	+	0.627773i	−0.928985	−	0.370117i	$-0.879318\pi$
$337$	−15.8619	+	11.5244i	−0.864055	+	0.627773i	0.0649303	+	0.997890i	$0.479318\pi$
$338$	22.6580	+	2.46329i	1.23243	+	0.133985i
$339$	−1.07412	−	3.30580i	−0.0583381	−	0.179546i
$340$	12.5084	+	7.22172i	0.678363	+	0.391653i
$341$	0.116408	+	0.414992i	0.00630383	+	0.0224731i
$342$	3.21735	+	5.57261i	0.173974	+	0.301332i
$343$	1.07840	−	0.350394i	0.0582283	−	0.0189195i
$344$	−2.46016	−	11.5742i	−0.132643	−	0.624037i
$345$	2.58411	−	5.80400i	0.139124	−	0.312477i
$346$		−	19.2342i		−	1.03404i
$347$	7.95448	+	13.7776i	0.427019	+	0.739618i	0.996607	−	0.0823122i	$-0.0262305\pi$
$347$	7.95448	+	13.7776i	0.427019	+	0.739618i	−0.569588	+	0.821931i	$0.692897\pi$
$348$	−0.645284	−	6.13947i	−0.0345909	−	0.329110i
$349$	−8.07968	−	18.1473i	−0.432495	−	0.971401i	−0.989979	−	0.141213i	$-0.954900\pi$
$349$	−8.07968	−	18.1473i	−0.432495	−	0.971401i	0.557484	−	0.830188i	$-0.311767\pi$
$350$	−0.895544	−	0.650651i	−0.0478689	−	0.0347788i
$351$	2.09213	−	19.5692i	0.111670	−	1.04452i
$352$	−0.344981	+	0.250643i	−0.0183875	+	0.0133593i
$353$	6.11992	−	28.7920i	0.325731	−	1.53244i	−0.445146	−	0.895458i	$-0.646848\pi$
$353$	6.11992	−	28.7920i	0.325731	−	1.53244i	0.770877	−	0.636984i	$-0.219818\pi$
$354$	12.9305	+	14.3608i	0.687249	+	0.763268i
$355$	−1.60220	+	15.2439i	−0.0850359	+	0.809063i
$356$	−10.5917	−	3.44144i	−0.561357	−	0.182396i
$357$	−0.0755349	−	0.355364i	−0.00399773	−	0.0188078i
$358$	36.7734	+	3.86504i	1.94354	+	0.204274i
$359$	−20.8978	−	6.79010i	−1.10294	−	0.358368i	−0.299708	−	0.954031i	$-0.596889\pi$
$359$	−20.8978	−	6.79010i	−1.10294	−	0.358368i	−0.803234	+	0.595663i	$0.796889\pi$
$360$	−6.13683	+	6.81564i	−0.323439	+	0.359216i
$361$	−1.42127	−	13.5225i	−0.0748039	−	0.711712i
$362$	7.22705	−	34.0006i	0.379845	−	1.78703i
$363$	10.6026	+	7.70323i	0.556492	+	0.404315i
$364$	0.000560047	−	0.313691i	2.93545e−5	−	0.0164419i
$365$	−22.6580	+	16.4620i	−1.18597	+	0.861661i
$366$	2.84898	+	1.64486i	0.148918	+	0.0859781i
$367$	−5.67969	+	9.83751i	−0.296477	+	0.513514i	−0.975327	−	0.220763i	$-0.929145\pi$
$367$	−5.67969	+	9.83751i	−0.296477	+	0.513514i	0.678850	+	0.734277i	$0.262479\pi$
$368$	−6.79920	−	3.02720i	−0.354433	−	0.157804i
$369$	−1.29834	−	0.421855i	−0.0675886	−	0.0219609i
$370$	51.4503	+	46.3261i	2.67477	+	2.40838i
$371$	0.472113	−	0.272574i	0.0245109	−	0.0141514i
$372$	6.31131	−	3.30917i	0.327226	−	0.171573i
$373$	−11.7455	−	20.3439i	−0.608161	−	1.05337i	−0.991543	−	0.129776i	$-0.958574\pi$
$373$	−11.7455	−	20.3439i	−0.608161	−	1.05337i	0.383382	−	0.923590i	$-0.374759\pi$
$374$	0.499300	+	0.106129i	0.0258182	+	0.00548782i
$375$	−8.84618	+	7.96514i	−0.456815	+	0.411318i
$376$	−15.8145	+	11.4899i	−0.815572	+	0.592547i
$377$	14.0873	−	10.1967i	0.725534	−	0.525155i
$378$	−0.775441			−0.0398844
$379$	−19.5846	+	2.05842i	−1.00599	+	0.105734i	−0.593169	−	0.805078i	$-0.702123\pi$
$379$	−19.5846	+	2.05842i	−1.00599	+	0.105734i	−0.412822	+	0.910812i	$0.635457\pi$
$380$	8.15451	−	3.63062i	0.418317	−	0.186247i
$381$	0.374480	−	3.56294i	0.0191852	−	0.182535i
$382$	6.65741	−	2.16313i	0.340623	−	0.110675i
$383$	−3.65674	+	8.21317i	−0.186851	+	0.419673i	−0.982545	−	0.186025i	$-0.940439\pi$
$383$	−3.65674	+	8.21317i	−0.186851	+	0.419673i	0.795694	+	0.605698i	$0.207106\pi$
$384$	−10.2748	−	9.25147i	−0.524334	−	0.472112i
$385$	−0.0213369	−	0.00693279i	−0.00108743	−	0.000353328i
$386$	0.168190	−	1.60022i	0.00856066	−	0.0814493i
$387$	7.69825	+	8.54977i	0.391324	+	0.434609i
$388$	−12.1890	+	10.9750i	−0.618801	+	0.557171i
$389$	0.294793	+	0.214180i	0.0149466	+	0.0108593i	0.595233	−	0.803553i	$-0.297060\pi$
$389$	0.294793	+	0.214180i	0.0149466	+	0.0108593i	−0.580287	+	0.814412i	$0.697060\pi$
$390$	−26.3517	−	5.65041i	−1.33437	−	0.286120i
$391$	1.73194	+	5.33036i	0.0875879	+	0.269568i
$392$	−11.2951	+	1.18716i	−0.570487	+	0.0599606i
$393$	−1.08184	−	0.229952i	−0.0545716	−	0.0115995i
$394$	1.76183	−	16.7627i	0.0887595	−	0.844491i
$395$	1.13649	−	1.56424i	0.0571830	−	0.0787057i
$396$	0.0533803	−	0.119894i	0.00268246	−	0.00602490i
$397$	−14.1718	+	8.18210i	−0.711263	+	0.410648i	−0.811529	−	0.584313i	$-0.801364\pi$
$397$	−14.1718	+	8.18210i	−0.711263	+	0.410648i	0.100265	+	0.994961i	$0.468031\pi$
$398$			22.2465i			1.11511i
$399$	−0.205114	−	0.0913228i	−0.0102686	−	0.00457186i
$400$	26.0410	+	28.9215i	1.30205	+	1.44607i
$401$	0.509157	−	2.39540i	0.0254261	−	0.119620i	−0.963604	−	0.267333i	$-0.913858\pi$
$401$	0.509157	−	2.39540i	0.0254261	−	0.119620i	0.989030	+	0.147712i	$0.0471910\pi$
$402$	25.0280			1.24828
$403$	16.9435	+	10.7665i	0.844017	+	0.536316i
$404$	14.0815			0.700579
$405$	−1.31606	+	6.19155i	−0.0653953	+	0.307661i
$406$	−0.458488	−	0.509203i	−0.0227544	−	0.0252713i
$407$	0.780821	+	0.347644i	0.0387039	+	0.0172321i
$408$			7.28120i			0.360473i
$409$	29.0404	−	16.7665i	1.43596	−	0.829051i	0.438392	−	0.898784i	$-0.355548\pi$
$409$	29.0404	−	16.7665i	1.43596	−	0.829051i	0.997566	+	0.0697333i	$0.0222148\pi$
$410$	−2.20502	+	4.95257i	−0.108898	+	0.244590i
$411$	8.70370	−	11.9796i	0.429322	−	0.590911i
$412$	0.309456	−	2.94428i	0.0152458	−	0.145054i
$413$	0.732877	+	0.155778i	0.0360625	+	0.00766532i
$414$	4.10256	−	0.431196i	0.201630	−	0.0211921i
$415$	−7.30129	−	22.4711i	−0.358406	−	1.10306i
$416$	−4.16403	+	19.4197i	−0.204158	+	0.952127i
$417$	−4.02930	−	2.92746i	−0.197316	−	0.143358i
$418$	0.234438	−	0.211089i	0.0114667	−	0.0103247i
$419$	8.51752	+	9.45966i	0.416108	+	0.462135i	0.914363	−	0.404896i	$-0.132692\pi$
$419$	8.51752	+	9.45966i	0.416108	+	0.462135i	−0.498255	+	0.867031i	$0.666026\pi$
$420$	−0.0387734	+	0.368904i	−0.00189195	+	0.0180007i
$421$	20.6428	+	6.70726i	1.00607	+	0.326892i	0.765289	−	0.643687i	$-0.222596\pi$
$421$	20.6428	+	6.70726i	1.00607	+	0.326892i	0.240782	+	0.970579i	$0.422596\pi$
$422$	19.5291	+	17.5841i	0.950661	+	0.855979i
$423$	7.73050	−	17.3630i	0.375870	−	0.844217i
$424$	−10.3909	+	3.37622i	−0.504629	+	0.163964i
$425$	3.06340	−	29.1463i	0.148597	−	1.41380i
$426$	8.18223	−	3.64296i	0.396430	−	0.176502i
$427$	0.126851	−	0.0133326i	0.00613876	−	0.000645209i
$428$	−16.8435			−0.814162
$429$	−0.330957	+	0.0341877i	−0.0159787	+	0.00165060i
$430$	36.9622	−	26.8546i	1.78248	−	1.29505i
$431$	−17.1512	+	15.4430i	−0.826143	+	0.743863i	−0.969312	−	0.245836i	$-0.920938\pi$
$431$	−17.1512	+	15.4430i	−0.826143	+	0.743863i	0.143168	+	0.989698i	$0.454271\pi$
$432$	26.6668	+	5.66820i	1.28301	+	0.272711i
$433$	1.73396	+	3.00331i	0.0833290	+	0.144330i	0.904678	−	0.426096i	$-0.140111\pi$
$433$	1.73396	+	3.00331i	0.0833290	+	0.144330i	−0.821349	+	0.570426i	$0.806778\pi$
$434$	0.350839	−	0.708907i	0.0168408	−	0.0340286i
$435$	−17.8088	+	10.2819i	−0.853867	+	0.492980i
$436$	−11.0230	−	9.92518i	−0.527907	−	0.475330i
$437$	3.29423	+	1.07036i	0.157584	+	0.0512022i
$438$	14.9504	+	6.65636i	0.714359	+	0.318053i
$439$	19.3969	−	33.5964i	0.925764	−	1.60347i	0.135435	−	0.990786i	$-0.456757\pi$
$439$	19.3969	−	33.5964i	0.925764	−	1.60347i	0.790328	−	0.612683i	$-0.209910\pi$
$440$	0.389395	+	0.224817i	0.0185637	+	0.0107177i
$441$	8.93363	−	6.49066i	0.425411	−	0.309079i
$442$	20.6110	−	11.8508i	0.980367	−	0.563684i
$443$	12.5609	+	9.12606i	0.596788	+	0.433592i	0.844737	−	0.535181i	$-0.179757\pi$
$443$	12.5609	+	9.12606i	0.596788	+	0.433592i	−0.247949	+	0.968773i	$0.579757\pi$
$444$	2.93815	−	13.8229i	0.139438	−	0.656005i
$445$	3.87776	+	36.8944i	0.183823	+	1.74896i
$446$	−19.7544	+	21.9394i	−0.935396	+	1.03886i
$447$	9.44944	+	3.07031i	0.446943	+	0.145221i
$448$	−0.0267313	−	0.00280958i	−0.00126294	−	0.000132740i
$449$	−2.54883	−	11.9913i	−0.120287	−	0.565905i	−0.996472	−	0.0839299i	$-0.973253\pi$
$449$	−2.54883	−	11.9913i	−0.120287	−	0.565905i	0.876185	−	0.481975i	$-0.160081\pi$
$450$	−20.5147	−	6.66563i	−0.967073	−	0.314221i
$451$	−0.00699587	+	0.0665612i	−0.000329422	+	0.00313425i
$452$	−2.09490	−	2.32662i	−0.0985359	−	0.109435i
$453$	3.19210	−	15.0176i	0.149978	−	0.705590i
$454$	−0.258844	+	0.188061i	−0.0121481	+	0.00882613i
$455$	−0.955357	+	0.423310i	−0.0447878	+	0.0198451i
$456$	3.64047	+	2.64496i	0.170481	+	0.123861i
$457$	−0.694206	−	1.55921i	−0.0324736	−	0.0729368i	0.896580	−	0.442881i	$-0.146044\pi$
$457$	−0.694206	−	1.55921i	−0.0324736	−	0.0729368i	−0.929054	+	0.369944i	$0.879377\pi$
$458$	0.696893	+	6.63049i	0.0325636	+	0.309822i
$459$	−10.2650	−	17.7795i	−0.479129	−	0.829875i
$460$		−	5.72243i		−	0.266810i
$461$	5.64532	−	12.6796i	0.262929	−	0.590548i	−0.733046	−	0.680179i	$-0.761902\pi$
$461$	5.64532	−	12.6796i	0.262929	−	0.590548i	0.995975	+	0.0896312i	$0.0285688\pi$
$462$	0.00272561	+	0.0128230i	0.000126807	+	0.000596580i
$463$	−3.13677	+	1.01920i	−0.145778	+	0.0473662i	−0.380997	−	0.924576i	$-0.624419\pi$
$463$	−3.13677	+	1.01920i	−0.145778	+	0.0473662i	0.235219	+	0.971942i	$0.424419\pi$
$464$	12.0449	+	20.8625i	0.559173	+	0.968515i
$465$	−18.6213	−	14.7225i	−0.863540	−	0.682739i
$466$	−23.6319	−	13.6439i	−1.09473	−	0.632040i
$467$	−10.9776	−	33.7854i	−0.507981	−	1.56340i	−0.795701	−	0.605689i	$-0.792898\pi$
$467$	−10.9776	−	33.7854i	−0.507981	−	1.56340i	0.287721	−	0.957714i	$-0.407102\pi$
$468$	−1.87854	−	5.81688i	−0.0868358	−	0.268885i
$469$	0.785063	−	0.570382i	0.0362509	−	0.0263378i
$470$	−65.3649	−	37.7384i	−3.01506	−	1.74074i
$471$	−3.85569	+	6.67824i	−0.177661	+	0.307717i
$472$	−13.7180	−	6.10765i	−0.631422	−	0.281127i
$473$	0.331532	−	0.456315i	0.0152439	−	0.0209814i
$474$	−1.12362	−	0.118098i	−0.0516097	−	0.00542440i
$475$	−13.4598	−	12.1193i	−0.617579	−	0.556071i
$476$	−0.192340	−	0.264734i	−0.00881591	−	0.0121341i
$477$	7.10813	−	7.89438i	0.325459	−	0.361459i
$478$	−35.1743	−	39.0650i	−1.60883	−	1.78679i
$479$	0.832846	+	1.87060i	0.0380537	+	0.0854701i	0.931572	−	0.363556i	$-0.118438\pi$
$479$	0.832846	+	1.87060i	0.0380537	+	0.0854701i	−0.893518	+	0.449026i	$0.851771\pi$
$480$	7.25740	−	22.3360i	0.331253	−	1.01949i
$481$	37.8830	−	12.2342i	1.72732	−	0.557831i
$482$	11.2909	+	8.20334i	0.514288	+	0.373652i
$483$	−0.106967	+	0.0963140i	−0.00486719	+	0.00438244i
$484$	11.5463	+	2.45423i	0.524830	+	0.111556i
$485$	49.9128	+	22.2226i	2.26642	+	1.00908i
$486$	−23.7863	+	7.72863i	−1.07897	+	0.350578i
$487$	−24.6800	−	2.59397i	−1.11836	−	0.117544i	−0.472738	−	0.881203i	$-0.656734\pi$
$487$	−24.6800	−	2.59397i	−1.11836	−	0.117544i	−0.645620	+	0.763659i	$0.723401\pi$
$488$	−2.54231	−	0.267207i	−0.115085	−	0.0120959i
$489$	10.1319	+	13.9454i	0.458182	+	0.630633i
$490$	−21.9260	−	37.9770i	−0.990517	−	1.71563i
$491$	−10.4275	+	18.0609i	−0.470586	+	0.815078i	−0.999434	−	0.0336382i	$-0.989291\pi$
$491$	−10.4275	+	18.0609i	−0.470586	+	0.815078i	0.528849	+	0.848716i	$0.322624\pi$
$492$	1.10051	−	0.115668i	0.0496149	−	0.00521473i
$493$	5.60583	−	17.2530i	0.252474	−	0.777034i
$494$	1.56195	−	14.6100i	0.0702757	−	0.657337i
$495$	−0.437175			−0.0196496
$496$	−17.2469	+	21.8142i	−0.774410	+	0.979488i
$497$	0.173633	−	0.300742i	0.00778852	−	0.0134901i
$498$	−9.23821	+	10.2601i	−0.413974	+	0.459765i
$499$	29.5244	+	9.59305i	1.32169	+	0.429444i	0.883076	−	0.469231i	$-0.155469\pi$
$499$	29.5244	+	9.59305i	1.32169	+	0.429444i	0.438616	+	0.898674i	$0.355469\pi$
$500$	−4.36092	+	9.79480i	−0.195026	+	0.438037i
$501$	−0.861158	+	0.497190i	−0.0384737	+	0.0222128i
$502$			21.5922i			0.963707i
$503$	7.60562	+	3.38624i	0.339118	+	0.150985i	0.569228	−	0.822180i	$-0.307242\pi$
$503$	7.60562	+	3.38624i	0.339118	+	0.150985i	−0.230110	+	0.973165i	$0.573909\pi$
$504$	0.189821	−	0.0845138i	0.00845530	−	0.00376454i
$505$	−19.0787	−	42.8515i	−0.848992	−	1.90687i
$506$	−0.0624955	−	0.192341i	−0.00277827	−	0.00855062i
$507$	−10.4104	+	11.4793i	−0.462343	+	0.509812i
$508$	−0.997148	−	3.06891i	−0.0442413	−	0.136161i
$509$	−30.4887	+	27.4521i	−1.35139	+	1.21679i	−0.397145	+	0.917756i	$0.629999\pi$
$509$	−30.4887	+	27.4521i	−1.35139	+	1.21679i	−0.954241	+	0.299038i	$0.903334\pi$
$510$	−25.6832	+	11.4349i	−1.13727	+	0.506345i
$511$	0.620654	−	0.131924i	0.0274561	−	0.00583598i
$512$	−10.7376	−	3.48885i	−0.474538	−	0.154187i
$513$	−12.6183	−	1.32623i	−0.557110	−	0.0585546i
$514$	4.37476	+	20.5816i	0.192962	+	0.907817i
$515$	−9.37904	+	3.04743i	−0.413290	+	0.134286i
$516$	−8.51943	−	3.79309i	−0.375047	−	0.166982i
$517$	−0.911433	−	0.193731i	−0.0400848	−	0.00852029i
$518$	−0.637983	−	1.43293i	−0.0280313	−	0.0629594i
$519$	10.5803	+	7.68707i	0.464426	+	0.337425i
$520$	20.4924	−	4.31758i	0.898652	−	0.189338i
$521$	−4.31189			−0.188907			−0.0944536	−	0.995529i	$-0.530110\pi$
$521$	−4.31189			−0.188907			−0.0944536	+	0.995529i	$0.530110\pi$
$522$	−11.5632	−	6.67601i	−0.506107	−	0.292201i
$523$	−2.10679	−	20.0447i	−0.0921234	−	0.876495i	−0.938817	−	0.344415i	$-0.888077\pi$
$523$	−2.10679	−	20.0447i	−0.0921234	−	0.876495i	0.846694	−	0.532080i	$-0.178589\pi$
$524$	−0.974419	+	0.207119i	−0.0425677	+	0.00904804i
$525$	0.715820	−	0.232584i	0.0312409	−	0.0101508i
$526$	43.5477	−	25.1423i	1.89877	−	1.09626i
$527$	20.8983	−	1.34012i	0.910342	−	0.0583764i
$528$		−	0.460896i		−	0.0200579i
$529$	−13.9042	+	15.4421i	−0.604529	+	0.671398i
$530$	−28.2277	−	31.3500i	−1.22613	−	1.36176i
$531$	14.5201	−	1.52613i	0.630120	−	0.0662283i
$532$	−0.202231			−0.00876784
$533$	1.82777	+	2.52518i	0.0791695	+	0.109378i
$534$	17.5373	−	12.7416i	0.758914	−	0.551383i
$535$	22.8210	+	51.2567i	0.986636	+	2.21602i
$536$	−17.7669	+	7.91033i	−0.767412	+	0.341674i
$537$	−16.8228	+	18.6836i	−0.725958	+	0.806258i
$538$	16.6270	+	22.8851i	0.716841	+	0.986647i
$539$	−0.402319	−	0.362249i	−0.0173291	−	0.0156032i
$540$	4.35810	+	20.5033i	0.187543	+	0.882320i
$541$	6.85191	−	9.43085i	0.294587	−	0.405464i	−0.635911	−	0.771763i	$-0.719375\pi$
$541$	6.85191	−	9.43085i	0.294587	−	0.405464i	0.930497	+	0.366299i	$0.119375\pi$
$542$	−3.51201	+	0.746501i	−0.150854	+	0.0320650i
$543$	15.8147	+	17.5640i	0.678674	+	0.753744i
$544$	8.42684	+	18.9270i	0.361298	+	0.811488i
$545$	−15.2685	+	46.9918i	−0.654033	+	2.01291i
$546$	0.493337	+	0.359778i	0.0211129	+	0.0153971i
$547$	32.4808	−	23.5987i	1.38878	−	1.00901i	0.392779	−	0.919633i	$-0.371514\pi$
$547$	32.4808	−	23.5987i	1.38878	−	1.00901i	0.995998	−	0.0893727i	$-0.0284862\pi$
$548$	2.77298	−	13.0459i	0.118456	−	0.557292i
$549$	2.27060	−	1.01093i	0.0969067	−	0.0431456i
$550$	−0.110540	+	1.05172i	−0.00471345	+	0.0448455i
$551$	−6.58981	−	9.07009i	−0.280735	−	0.386399i
$552$	2.49829	−	1.44239i	0.106334	−	0.0613921i
$553$	−0.0379366	+	0.0219027i	−0.00161323	+	0.000931398i
$554$	3.69225	+	5.08195i	0.156869	+	0.215911i
$555$	−46.0455	+	9.78726i	−1.95452	+	0.415446i
$556$	−4.38792	−	0.932682i	−0.186089	−	0.0395545i
$557$	32.7196	+	18.8907i	1.38637	+	0.800423i	0.992904	−	0.118915i	$-0.0379417\pi$
$557$	32.7196	+	18.8907i	1.38637	+	0.800423i	0.393469	+	0.919338i	$0.371275\pi$
$558$	2.23320	−	15.2505i	0.0945391	−	0.645605i
$559$	−2.69939	−	26.1317i	−0.114172	−	1.10525i
$560$	−0.447301	−	1.37665i	−0.0189019	−	0.0581741i
$561$	−0.257928	+	0.232239i	−0.0108897	+	0.00980515i
$562$	1.60092	+	15.2317i	0.0675307	+	0.642512i
$563$	2.51944	+	4.36380i	0.106182	+	0.183912i	0.914220	−	0.405217i	$-0.132804\pi$
$563$	2.51944	+	4.36380i	0.106182	+	0.183912i	−0.808039	+	0.589129i	$0.799471\pi$
$564$			15.4061i			0.648715i
$565$	−4.24184	+	9.52732i	−0.178455	+	0.400818i
$566$	−10.4003	−	1.09312i	−0.437158	−	0.0459471i
$567$	0.0842937	−	0.116020i	0.00354000	−	0.00487239i
$568$	−4.65702	+	5.17214i	−0.195404	+	0.217018i
$569$	0.446526	+	4.24841i	0.0187194	+	0.178103i	0.999887	−	0.0150572i	$-0.00479304\pi$
$569$	0.446526	+	4.24841i	0.0187194	+	0.178103i	−0.981167	+	0.193160i	$0.938126\pi$
$570$	−3.61238	+	16.9949i	−0.151306	+	0.711839i
$571$	4.18260	−	12.8727i	0.175036	−	0.538707i	−0.824599	−	0.565718i	$-0.808599\pi$
$571$	4.18260	−	12.8727i	0.175036	−	0.538707i	0.999635	+	0.0270113i	$0.00859901\pi$
$572$	−0.259798	+	0.149377i	−0.0108627	+	0.00624576i
$573$	−1.47079	+	4.52661i	−0.0614430	+	0.189102i
$574$	0.0912756	−	0.0821849i	0.00380977	−	0.00343033i
$575$	−10.6074	+	4.72272i	−0.442359	+	0.196951i
$576$	−0.512319	+	0.108897i	−0.0213466	+	0.00453737i
$577$	−38.6811	+	12.5683i	−1.61032	+	0.523224i	−0.969630	−	0.244578i	$-0.921351\pi$
$577$	−38.6811	+	12.5683i	−1.61032	+	0.523224i	−0.640688	+	0.767802i	$0.721351\pi$
$578$	−2.03499	+	4.57067i	−0.0846446	+	0.190115i
$579$	0.813032	+	0.732058i	0.0337885	+	0.0304233i
$580$	−10.8869	+	14.9846i	−0.452056	+	0.622201i
$581$	−0.0559542	+	0.532369i	−0.00232137	+	0.0220864i
$582$	−3.33715	−	31.7509i	−0.138329	−	1.31612i
$583$	−0.451026	−	0.260400i	−0.0186796	−	0.0107847i
$584$	−12.7168			−0.526226
$585$	−15.1562	+	13.5978i	−0.626633	+	0.562200i
$586$	4.58000	−	14.0958i	0.189198	−	0.582291i
$587$	−6.54326	+	30.7836i	−0.270069	+	1.27058i	0.608728	+	0.793379i	$0.291680\pi$
$587$	−6.54326	+	30.7836i	−0.270069	+	1.27058i	−0.878797	+	0.477196i	$0.841653\pi$
$588$	−4.47548	+	7.75176i	−0.184566	+	0.319677i
$589$	6.92143	−	10.9356i	0.285193	−	0.450592i
$590$		−	57.9797i		−	2.38699i
$591$	8.51667	+	7.66844i	0.350329	+	0.315438i
$592$	11.4655	+	53.9408i	0.471228	+	2.21695i
$593$	12.1057	+	16.6620i	0.497121	+	0.684228i	0.981681	−	0.190530i	$-0.0610205\pi$
$593$	12.1057	+	16.6620i	0.497121	+	0.684228i	−0.484561	+	0.874758i	$0.661020\pi$
$594$	0.370403	+	0.641557i	0.0151978	+	0.0263234i
$595$	−0.545017	+	0.943996i	−0.0223435	+	0.0387001i
$596$	8.90014	−	0.935443i	0.364564	−	0.0383172i
$597$	−12.2373	−	8.89094i	−0.500840	−	0.363882i
$598$	−8.14918	−	4.72435i	−0.333245	−	0.193193i
$599$	8.02164	+	24.6881i	0.327755	+	1.00873i	0.970181	+	0.242380i	$0.0779280\pi$
$599$	8.02164	+	24.6881i	0.327755	+	1.00873i	−0.642426	+	0.766348i	$0.722072\pi$
$600$	−15.0019	+	1.57676i	−0.612449	+	0.0643710i
$601$	−30.8354	−	6.55426i	−1.25780	−	0.267354i	−0.469659	−	0.882848i	$-0.655623\pi$
$601$	−30.8354	−	6.55426i	−1.25780	−	0.267354i	−0.788142	+	0.615494i	$0.788957\pi$
$602$	−1.01248	+	0.215209i	−0.0412656	+	0.00877126i
$603$	11.1146	−	15.2980i	0.452623	−	0.622982i
$604$	−2.87514	−	13.5265i	−0.116988	−	0.550384i
$605$	−8.17531	−	38.4618i	−0.332374	−	1.56369i
$606$	−16.1107	+	22.1745i	−0.654452	+	0.900776i
$607$	32.3490	−	6.87600i	1.31301	−	0.279088i	0.502378	−	0.864648i	$-0.332459\pi$
$607$	32.3490	−	6.87600i	1.31301	−	0.279088i	0.810629	+	0.585560i	$0.199125\pi$
$608$	12.5243	+	2.66212i	0.507927	+	0.107963i
$609$	0.463340	−	0.0486990i	0.0187755	−	0.00197338i
$610$	−3.05008	−	9.38719i	−0.123494	−	0.380076i
$611$	−37.6239	+	21.6327i	−1.52210	+	0.875164i
$612$	−5.15869	−	3.74800i	−0.208528	−	0.151504i
$613$	−36.8404	+	3.87208i	−1.48797	+	0.156392i	−0.813350	−	0.581774i	$-0.802359\pi$
$613$	−36.8404	+	3.87208i	−1.48797	+	0.156392i	−0.674619	+	0.738166i	$0.735692\pi$
$614$	−7.10081	+	12.2990i	−0.286565	+	0.496346i
$615$	−1.84305	−	3.19226i	−0.0743191	−	0.128724i
$616$	−0.00598769	−	0.00824135i	−0.000241251	−	0.000332053i
$617$	9.67713	+	45.5273i	0.389586	+	1.83286i	0.536742	+	0.843747i	$0.319655\pi$
$617$	9.67713	+	45.5273i	0.389586	+	1.83286i	−0.147155	+	0.989113i	$0.547012\pi$
$618$	4.28238	+	3.85587i	0.172263	+	0.155106i
$619$		−	29.9297i		−	1.20297i	−0.798882	−	0.601487i	$-0.794575\pi$
$619$		−	29.9297i		−	1.20297i	0.798882	−	0.601487i	$-0.205425\pi$
$620$	−20.7158	−	5.29229i	−0.831968	−	0.212544i
$621$	−4.06694	+	7.04415i	−0.163201	+	0.282672i
$622$	−6.87834	+	32.3600i	−0.275796	+	1.29752i
$623$	0.259722	−	0.799343i	0.0104056	−	0.0320250i
$624$	−14.3356	−	15.9786i	−0.573884	−	0.639655i
$625$	−3.24477			−0.129791
$626$	14.7007	+	8.48746i	0.587558	+	0.339227i
$627$	0.0224211	+	0.213322i	0.000895412	+	0.00851927i
$628$	−0.726021	+	6.90763i	−0.0289714	+	0.275644i
$629$	24.4092	−	33.5964i	0.973259	−	1.33958i
$630$	0.596215	+	0.536835i	0.0237538	+	0.0213880i
$631$	14.5890	−	32.7675i	0.580780	−	1.30445i	−0.349271	−	0.937022i	$-0.613571\pi$
$631$	14.5890	−	32.7675i	0.580780	−	1.30445i	0.930051	−	0.367431i	$-0.119762\pi$
$632$	0.834965	−	0.271297i	0.0332131	−	0.0107916i
$633$	−17.4776	+	3.71497i	−0.694671	+	0.147657i
$634$	−53.0992	+	23.6413i	−2.10884	+	0.938915i
$635$	−7.98802	+	7.19244i	−0.316995	+	0.285423i
$636$	−2.66089	+	8.18937i	−0.105511	+	0.324730i
$637$	−25.2151	−	0.0450178i	−0.999060	−	0.00178367i
$638$	−0.202281	+	0.622558i	−0.00800840	+	0.0246473i
$639$	1.40693	−	6.61908i	0.0556572	−	0.261847i
$640$	4.33616	+	41.2558i	0.171402	+	1.63078i
$641$	−25.3085	+	28.1080i	−0.999627	+	1.11020i	−0.00571941	+	0.999984i	$0.501821\pi$
$641$	−25.3085	+	28.1080i	−0.999627	+	1.11020i	−0.993908	+	0.110215i	$0.964846\pi$
$642$	19.2708	−	26.5239i	0.760556	−	1.04682i
$643$	37.3318	+	3.92373i	1.47222	+	0.154737i	0.806399	−	0.591372i	$-0.201414\pi$
$643$	37.3318	+	3.92373i	1.47222	+	0.154737i	0.665824	+	0.746109i	$0.268080\pi$
$644$	−0.0527320	+	0.118438i	−0.00207793	+	0.00466712i
$645$			31.0648i			1.22317i
$646$	−7.66369	−	13.2739i	−0.301524	−	0.522255i
$647$	−3.74115	−	35.5946i	−0.147080	−	1.39937i	−0.780304	−	0.625401i	$-0.784936\pi$
$647$	−3.74115	−	35.5946i	−0.147080	−	1.39937i	0.633224	−	0.773969i	$-0.281731\pi$
$648$	−2.13591	+	1.92319i	−0.0839066	+	0.0755499i
$649$	−0.221190	−	0.680752i	−0.00868246	−	0.0267219i
$650$	28.8802	+	39.8998i	1.13278	+	1.56500i
$651$	0.249740	+	0.476309i	0.00978809	+	0.0186680i
$652$	13.4458	+	7.76294i	0.526579	+	0.304020i
$653$	−25.1213	−	5.33969i	−0.983071	−	0.208958i	−0.311782	−	0.950154i	$-0.600926\pi$
$653$	−25.1213	−	5.33969i	−0.983071	−	0.208958i	−0.671289	+	0.741195i	$0.734259\pi$
$654$	28.2409	−	6.00280i	1.10431	−	0.234728i
$655$	1.95051	+	2.68464i	0.0762127	+	0.104898i
$656$	−3.73963	+	2.15908i	−0.146008	+	0.0842979i
$657$	10.7079	−	6.18222i	0.417756	−	0.241192i
$658$	1.00511	+	1.38342i	0.0391833	+	0.0539311i
$659$	1.40452	−	13.3631i	0.0547123	−	0.520552i	−0.932503	−	0.361161i	$-0.882380\pi$
$659$	1.40452	−	13.3631i	0.0547123	−	0.520552i	0.987216	−	0.159391i	$-0.0509530\pi$
$660$	0.323732	−	0.144135i	0.0126012	−	0.00561043i
$661$	−0.310572	+	1.46113i	−0.0120799	+	0.0568313i	−0.983775	−	0.179408i	$-0.942582\pi$
$661$	−0.310572	+	1.46113i	−0.0120799	+	0.0568313i	0.971695	+	0.236240i	$0.0759150\pi$
$662$	6.35411	−	4.61653i	0.246959	−	0.179426i
$663$	−1.71846	+	16.0739i	−0.0667394	+	0.624260i
$664$	3.31524	−	10.2033i	0.128656	−	0.395963i
$665$	0.274000	+	0.615413i	0.0106252	+	0.0238647i
$666$	−20.4520	−	22.7143i	−0.792500	−	0.880160i
$667$	−7.03026	+	1.49433i	−0.272213	+	0.0578606i
$668$	−0.526446	+	0.724591i	−0.0203688	+	0.0280353i
$669$	−4.17348	−	19.6347i	−0.161356	−	0.759121i
$670$	−55.8046	−	50.2467i	−2.15592	−	1.94120i
$671$	−0.0716234	−	0.0985811i	−0.00276499	−	0.00380568i
$672$	−0.356033	+	0.395415i	−0.0137343	+	0.0152535i
$673$	15.1169	−	6.73048i	0.582714	−	0.259441i	−0.0941393	−	0.995559i	$-0.530010\pi$
$673$	15.1169	−	6.73048i	0.582714	−	0.259441i	0.676853	+	0.736118i	$0.263343\pi$
$674$	−13.9811	−	31.4021i	−0.538533	−	1.20957i
$675$	34.4092	−	24.9997i	1.32441	−	0.962241i
$676$	−4.36065	+	13.2594i	−0.167717	+	0.509977i
$677$	−19.0895			−0.733667			−0.366834	−	0.930287i	$-0.619558\pi$
$677$	−19.0895			−0.733667			−0.366834	+	0.930287i	$0.619558\pi$
$678$	6.06059	−	0.636993i	0.232755	−	0.0244636i
$679$	−0.828273	−	0.919890i	−0.0317862	−	0.0353022i
$680$	14.6179	−	16.2348i	0.560570	−	0.622576i
$681$		−	0.217544i		−	0.00833631i
$682$	−0.754096	+	0.0483570i	−0.0288758	+	0.00185168i
$683$	40.8382	−	23.5779i	1.56263	−	0.902184i	0.565638	−	0.824653i	$-0.308630\pi$
$683$	40.8382	−	23.5779i	1.56263	−	0.902184i	0.996990	−	0.0775305i	$-0.0247035\pi$
$684$	−3.74787	+	1.21776i	−0.143303	+	0.0465621i
$685$	−43.4571	+	9.23709i	−1.66041	+	0.352931i
$686$	0.207797	+	1.97706i	0.00793373	+	0.0754844i
$687$	−3.92581	−	2.26657i	−0.149779	−	0.0864750i
$688$	36.3914			1.38741
$689$	−23.7359	+	5.00094i	−0.904264	+	0.190521i
$690$	9.01126	+	6.54706i	0.343053	+	0.249242i
$691$	−4.27102	−	9.59287i	−0.162477	−	0.364930i	0.813899	−	0.581006i	$-0.197341\pi$
$691$	−4.27102	−	9.59287i	−0.162477	−	0.364930i	−0.976377	+	0.216076i	$0.930674\pi$
$692$	11.5220	+	2.44909i	0.438002	+	0.0931003i
$693$	0.00904829	+	0.00402856i	0.000343716	+	0.000153032i
$694$	−26.5264	+	8.61895i	−1.00693	+	0.327171i
$695$	3.10686	+	14.6166i	0.117850	+	0.554440i
$696$	−9.28610	−	0.976009i	−0.351989	−	0.0369955i
$697$	3.09262	+	1.00485i	0.117142	+	0.0380616i
$698$	34.0656	−	7.24086i	1.28940	−	0.274071i
$699$	16.9498	−	7.54656i	0.641102	−	0.285437i
$700$	0.503795	−	0.453619i	0.0190417	−	0.0171452i
$701$	10.6060	+	32.6418i	0.400582	+	1.23287i	0.924528	+	0.381114i	$0.124459\pi$
$701$	10.6060	+	32.6418i	0.400582	+	1.23287i	−0.523946	+	0.851752i	$0.675541\pi$
$702$	32.7962	+	10.7209i	1.23781	+	0.404635i
$703$	−7.93076	−	24.4084i	−0.299114	−	0.920579i
$704$	0.0104442	+	0.0234581i	0.000393631	+	0.000884110i
$705$	46.8826	−	20.8735i	1.76570	−	0.786141i
$706$	47.1441	+	20.9899i	1.77429	+	0.789966i
$707$			1.06272i			0.0399675i
$708$	−10.2491	+	5.91733i	−0.385185	+	0.222387i
$709$	9.14917	−	20.5494i	0.343604	−	0.771748i	−0.656248	−	0.754546i	$-0.727857\pi$
$709$	9.14917	−	20.5494i	0.343604	−	0.771748i	0.999852	−	0.0172025i	$-0.00547601\pi$
$710$	−25.5575	−	8.30415i	−0.959157	−	0.311649i
$711$	−0.571174	+	0.634353i	−0.0214207	+	0.0237901i
$712$	−8.42230	+	14.5879i	−0.315639	+	0.546703i
$713$	−4.59971	−	6.90504i	−0.172261	−	0.258596i
$714$	0.636941			0.0238369
$715$	0.806567	+	0.588208i	0.0301639	+	0.0219977i
$716$	−6.99766	+	21.5366i	−0.261515	+	0.804860i
$717$	35.5465	−	3.73608i	1.32751	−	0.139527i
$718$	19.2617	−	33.3622i	0.718840	−	1.24507i
$719$	16.9759	+	29.4031i	0.633094	+	1.09655i	0.986916	+	0.161238i	$0.0515487\pi$
$719$	16.9759	+	29.4031i	0.633094	+	1.09655i	−0.353822	+	0.935313i	$0.615118\pi$
$720$	−16.5793	−	22.8194i	−0.617873	−	0.850430i
$721$	0.222202	+	0.0233543i	0.00827522	+	0.000869761i
$722$	23.7076	+	2.49177i	0.882306	+	0.0927341i
$723$	−9.02498	+	2.93239i	−0.335642	+	0.109057i
$724$	19.4475	+	8.65857i	0.722760	+	0.321793i
$725$	36.7612	+	7.81384i	1.36528	+	0.290199i
$726$	−17.0749	+	15.3743i	−0.633709	+	0.570594i
$727$	−31.8278	−	23.1243i	−1.18043	−	0.857632i	−0.188209	−	0.982129i	$-0.560268\pi$
$727$	−31.8278	−	23.1243i	−1.18043	−	0.857632i	−0.992220	+	0.124497i	$0.960268\pi$
$728$	−0.463922	−	0.0994757i	−0.0171941	−	0.00368681i
$729$	6.89567	−	21.2227i	0.255395	−	0.786026i
$730$	−19.9714	−	44.8564i	−0.739173	−	1.66021i
$731$	−18.3372	−	20.3655i	−0.678224	−	0.753245i
$732$	−1.34809	+	1.49721i	−0.0498270	+	0.0553385i
$733$	26.0574	+	35.8649i	0.962452	+	1.32470i	0.945769	+	0.324841i	$0.105311\pi$
$733$	26.0574	+	35.8649i	0.962452	+	1.32470i	0.0166835	+	0.999861i	$0.494689\pi$
$734$	−14.7999	−	13.3259i	−0.546274	−	0.491867i
$735$	29.6532	+	3.11668i	1.09378	+	0.114961i
$736$	4.82480	−	6.64077i	0.177845	−	0.244782i
$737$	−0.846903	−	0.377065i	−0.0311961	−	0.0138894i
$738$	1.19669	−	2.07272i	0.0440507	−	0.0762980i
$739$	20.3564	+	11.7528i	0.748821	+	0.432332i	0.825268	−	0.564742i	$-0.191024\pi$
$739$	20.3564	+	11.7528i	0.748821	+	0.432332i	−0.0764468	+	0.997074i	$0.524358\pi$
$740$	−34.3023	+	24.9221i	−1.26098	+	0.916153i
$741$	7.41244	+	6.69819i	0.272303	+	0.246064i
$742$	0.295344	+	0.908975i	0.0108424	+	0.0333695i
$743$	−34.3845	−	19.8519i	−1.26145	−	0.728296i	−0.288092	−	0.957603i	$-0.593021\pi$
$743$	−34.3845	−	19.8519i	−1.26145	−	0.728296i	−0.973354	+	0.229306i	$0.926354\pi$
$744$	−2.91111	−	10.3781i	−0.106726	−	0.380478i
$745$	−14.9053	−	25.8167i	−0.546088	−	0.945852i
$746$	39.1688	−	12.7267i	1.43407	−	0.465958i
$747$	2.16874	+	10.2031i	0.0793500	+	0.373312i
$748$	−0.127151	+	0.285587i	−0.00464912	+	0.0104421i
$749$		−	1.27116i		−	0.0464473i
$750$	−10.4348	−	18.0735i	−0.381024	−	0.659953i
$751$	−2.59496	−	24.6894i	−0.0946915	−	0.900930i	−0.934000	−	0.357274i	$-0.883706\pi$
$751$	−2.59496	−	24.6894i	−0.0946915	−	0.900930i	0.839308	−	0.543656i	$-0.182960\pi$
$752$	−24.4526	−	54.9215i	−0.891696	−	2.00278i
$753$	−11.8774	−	8.62945i	−0.432837	−	0.314475i
$754$	12.3511	+	27.8749i	0.449801	+	1.01514i
$755$	−37.2671	+	27.0761i	−1.35629	+	0.985402i
$756$	0.0987367	−	0.464520i	0.00359102	−	0.0168944i
$757$	−9.63962	−	10.7059i	−0.350358	−	0.389112i	0.542046	−	0.840349i	$-0.317650\pi$
$757$	−9.63962	−	10.7059i	−0.350358	−	0.389112i	−0.892404	+	0.451237i	$0.850983\pi$
$758$	3.60881	−	34.3356i	0.131078	−	1.24712i
$759$	0.130780	+	0.0424929i	0.00474701	+	0.00154240i
$760$	−2.80705	−	13.2061i	−0.101822	−	0.479036i
$761$	12.7478	+	1.33985i	0.462109	+	0.0485696i	0.332723	−	0.943025i	$-0.392033\pi$
$761$	12.7478	+	1.33985i	0.462109	+	0.0485696i	0.129386	+	0.991594i	$0.458699\pi$
$762$	5.97353	+	1.94092i	0.216398	+	0.0703121i
$763$	0.749044	−	0.831898i	0.0271172	−	0.0301167i
$764$	0.448110	+	4.26348i	0.0162120	+	0.154247i
$765$	−4.41620	+	20.7766i	−0.159668	+	0.751178i
$766$	−12.7517	−	9.26466i	−0.460738	−	0.334746i
$767$	−28.8423	−	16.7208i	−1.04144	−	0.603755i
$768$	18.9707	−	13.7830i	0.684545	−	0.497351i
$769$	39.7191	+	22.9319i	1.43231	+	0.826944i	0.997297	−	0.0734805i	$-0.0234107\pi$
$769$	39.7191	+	22.9319i	1.43231	+	0.826944i	0.435012	+	0.900425i	$0.356744\pi$
$770$	0.0196665	−	0.0340633i	0.000708730	−	0.00122756i
$771$	−13.0699	−	5.81911i	−0.470702	−	0.209570i
$772$	0.937181	+	0.304509i	0.0337299	+	0.0109595i
$773$	−25.0662	−	22.5697i	−0.901569	−	0.811776i	0.0811840	−	0.996699i	$-0.474130\pi$
$773$	−25.0662	−	22.5697i	−0.901569	−	0.811776i	−0.982753	+	0.184923i	$0.940797\pi$
$774$	−17.4679	+	10.0851i	−0.627872	+	0.362502i
$775$	7.28669	+	42.7677i	0.261746	+	1.53626i
$776$	12.4041	+	21.4846i	0.445283	+	0.771252i
$777$	1.04320	+	0.221739i	0.0374246	+	0.00795485i
$778$	−0.474749	+	0.427466i	−0.0170206	+	0.0153254i
$779$	1.62583	−	1.18124i	0.0582514	−	0.0423222i
$780$	6.74017	−	15.0662i	0.241337	−	0.539457i
$781$	−0.331756			−0.0118712
$782$	−9.77226	+	1.02711i	−0.349455	+	0.0367292i
$783$	24.0511	−	10.7082i	0.859517	−	0.382681i
$784$	3.65109	−	34.7378i	0.130396	−	1.24064i
$785$	22.0044	−	7.14965i	0.785370	−	0.255182i
$786$	0.788682	−	1.77141i	0.0281314	−	0.0631841i
$787$	37.7863	+	34.0229i	1.34693	+	1.21279i	0.956352	+	0.292218i	$0.0943932\pi$
$787$	37.7863	+	34.0229i	1.34693	+	1.21279i	0.390583	+	0.920568i	$0.372273\pi$
$788$	9.81715	+	3.18979i	0.349722	+	0.113631i
$789$	−3.57386	+	34.0030i	−0.127233	+	1.21054i
$790$	2.26824	+	2.51913i	0.0807002	+	0.0896267i
$791$	0.175588	−	0.158100i	0.00624320	−	0.00562140i
$792$	−0.160594	−	0.116678i	−0.00570644	−	0.00414597i
$793$	−5.54933	−	1.18990i	−0.197062	−	0.0422548i
$794$	−8.86559	−	27.2855i	−0.314628	−	0.968326i
$795$	28.5264	−	2.99824i	1.01173	−	0.106337i
$796$	−13.3265	−	2.83264i	−0.472345	−	0.100400i
$797$	−3.76483	+	35.8200i	−0.133357	+	1.26881i	0.699223	+	0.714904i	$0.253529\pi$
$797$	−3.76483	+	35.8200i	−0.133357	+	1.26881i	−0.832580	+	0.553905i	$0.813137\pi$
$798$	0.231374	−	0.318459i	0.00819056	−	0.0112733i
$799$	−18.4140	+	41.3585i	−0.651440	+	1.46316i
$800$	−37.1715	+	21.4610i	−1.31421	+	0.758761i
$801$		−	16.3778i		−	0.578682i
$802$	3.92224	+	1.74629i	0.138499	+	0.0616637i
$803$	−0.405613	−	0.450479i	−0.0143138	−	0.0158971i
$804$	−3.18680	+	14.9927i	−0.112390	+	0.528753i
$805$	0.431866			0.0152213
$806$	−24.6393	+	25.1317i	−0.867883	+	0.885227i
$807$	−19.2337			−0.677059
$808$	4.42823	−	20.8332i	0.155784	−	0.732908i
$809$	11.9629	+	13.2862i	0.420594	+	0.467117i	0.915786	−	0.401667i	$-0.131569\pi$
$809$	11.9629	+	13.2862i	0.420594	+	0.467117i	−0.495192	+	0.868784i	$0.664902\pi$
$810$	−10.1381	−	4.51377i	−0.356216	−	0.158598i
$811$		−	4.04402i		−	0.142005i	−0.997476	−	0.0710023i	$-0.977380\pi$
$811$		−	4.04402i		−	0.142005i	0.997476	−	0.0710023i	$-0.0226198\pi$
$812$	0.363412	−	0.209816i	0.0127533	−	0.00736309i
$813$	0.992962	−	2.23023i	0.0348247	−	0.0782175i
$814$	−0.880786	+	1.21230i	−0.0308715	+	0.0424910i
$815$	5.40603	−	51.4350i	0.189365	−	1.80169i
$816$	−21.9039	−	4.65581i	−0.766789	−	0.162986i
$817$	−16.8435	+	1.77032i	−0.589280	+	0.0619358i
$818$	18.1671	+	55.9126i	0.635198	+	1.95494i
$819$	0.438995	−	0.141772i	0.0153397	−	0.00495392i
$820$	−2.68602	−	1.95150i	−0.0937997	−	0.0681495i
$821$	17.2044	−	15.4909i	0.600438	−	0.540637i	−0.311879	−	0.950122i	$-0.600958\pi$
$821$	17.2044	−	15.4909i	0.600438	−	0.540637i	0.912317	+	0.409485i	$0.134292\pi$
$822$	17.3711	+	19.2925i	0.605886	+	0.672905i
$823$	4.94882	−	47.0849i	0.172505	−	1.64128i	−0.475554	−	0.879687i	$-0.657752\pi$
$823$	4.94882	−	47.0849i	0.172505	−	1.64128i	0.648059	−	0.761590i	$-0.275581\pi$
$824$	−4.25866	−	1.38372i	−0.148358	−	0.0482043i
$825$	−0.534351	−	0.481132i	−0.0186037	−	0.0167509i
$826$	−0.534282	+	1.20002i	−0.0185900	+	0.0417539i
$827$	48.1224	−	15.6359i	1.67338	−	0.543714i	0.689771	−	0.724028i	$-0.257711\pi$
$827$	48.1224	−	15.6359i	1.67338	−	0.543714i	0.983609	+	0.180313i	$0.0577112\pi$
$828$	−0.264074	+	2.51250i	−0.00917720	+	0.0873153i
$829$	17.2322	−	7.67228i	0.598500	−	0.266469i	−0.0850460	−	0.996377i	$-0.527104\pi$
$829$	17.2322	−	7.67228i	0.598500	−	0.266469i	0.683546	+	0.729908i	$0.260437\pi$
$830$	41.1967	−	4.32995i	1.42996	−	0.150295i
$831$	−4.27111			−0.148163
$832$	1.09172	+	0.488403i	0.0378487	+	0.0169323i
$833$	−21.2798	+	15.4607i	−0.737303	+	0.535682i
$834$	6.48897	−	5.84269i	0.224695	−	0.202316i
$835$	2.91828	+	0.620301i	0.100991	+	0.0214664i
$836$	0.0965995	+	0.167315i	0.00334096	+	0.00578672i
$837$	21.7394	+	21.2375i	0.751423	+	0.734074i
$838$	−19.3269	+	11.1584i	−0.667638	+	0.385461i
$839$	11.8721	+	10.6897i	0.409872	+	0.369050i	0.848120	−	0.529804i	$-0.177734\pi$
$839$	11.8721	+	10.6897i	0.409872	+	0.369050i	−0.438249	+	0.898854i	$0.644401\pi$
$840$	0.533591	+	0.173374i	0.0184106	+	0.00598197i
$841$	−5.24062	−	2.33327i	−0.180711	−	0.0804577i
$842$	−19.0267	+	32.9552i	−0.655703	+	1.13571i
$843$	−9.01848	−	5.20682i	−0.310613	−	0.179333i
$844$	−13.0202	+	9.45971i	−0.448173	+	0.325617i
$845$	46.2580	−	4.69498i	1.59132	−	0.161512i
$846$	26.9577	+	19.5859i	0.926823	+	0.673377i
$847$	−0.185219	+	0.871386i	−0.00636419	+	0.0299412i
$848$	−3.51235	−	33.4177i	−0.120614	−	1.14757i
$849$	4.75785	−	5.28413i	0.163289	−	0.181351i
$850$	48.8659	+	15.8775i	1.67609	+	0.544593i
$851$	−16.3629	−	1.71981i	−0.560912	−	0.0589542i
$852$	1.14044	+	5.36533i	0.0390707	+	0.183813i
$853$	8.98029	+	2.91787i	0.307479	+	0.0999060i	0.458692	−	0.888595i	$-0.348318\pi$
$853$	8.98029	+	2.91787i	0.307479	+	0.0999060i	−0.151213	+	0.988501i	$0.548318\pi$
$854$	−0.0233746	+	0.222395i	−0.000799864	+	0.00761020i
$855$	8.78370	+	9.75528i	0.300396	+	0.333624i
$856$	−5.29681	+	24.9195i	−0.181041	+	0.851732i
$857$	−11.4758	+	8.33769i	−0.392007	+	0.284810i	−0.766278	−	0.642510i	$-0.777893\pi$
$857$	−11.4758	+	8.33769i	−0.392007	+	0.284810i	0.374270	+	0.927320i	$0.377893\pi$
$858$	0.0620091	−	0.580015i	0.00211696	−	0.0198014i
$859$	18.3843	+	13.3570i	0.627266	+	0.455735i	0.855452	−	0.517882i	$-0.173279\pi$
$859$	18.3843	+	13.3570i	0.627266	+	0.455735i	−0.228186	+	0.973618i	$0.573279\pi$
$860$	11.3806	+	25.5612i	0.388075	+	0.871630i
$861$	0.00872938	+	0.0830545i	0.000297497	+	0.00283049i
$862$	−20.2312	−	35.0414i	−0.689076	−	1.19352i
$863$		−	18.7050i		−	0.636726i	−0.947969	−	0.318363i	$-0.896867\pi$
$863$		−	18.7050i		−	0.636726i	0.947969	−	0.318363i	$-0.103133\pi$
$864$	−12.2296	+	27.4682i	−0.416060	+	0.934485i
$865$	−8.15816	−	38.3811i	−0.277386	−	1.30500i
$866$	−5.78238	+	1.87881i	−0.196493	+	0.0638446i
$867$	−1.70093	−	2.94610i	−0.0577668	−	0.100055i
$868$	0.379991	+	0.300431i	0.0128977	+	0.0101973i
$869$	0.0362422	+	0.0209245i	0.00122943	+	0.000709814i
$870$	−11.1408	−	34.2879i	−0.377709	−	1.16247i
$871$	−41.0890	+	13.2696i	−1.39225	+	0.449623i
$872$	−18.1505	+	13.1871i	−0.614653	+	0.446571i
$873$	−20.8893	−	12.0604i	−0.706994	−	0.408183i
$874$	−3.03632	+	5.25906i	−0.102705	+	0.177890i
$875$	−0.739204	−	0.329115i	−0.0249897	−	0.0111261i
$876$	−5.89105	+	8.10834i	−0.199040	+	0.273955i
$877$	−23.3167	−	2.45069i	−0.787350	−	0.0827538i	−0.297685	−	0.954664i	$-0.596214\pi$
$877$	−23.3167	−	2.45069i	−0.787350	−	0.0827538i	−0.489666	+	0.871910i	$0.662881\pi$
$878$	50.5436	+	45.5097i	1.70576	+	1.53588i
$879$	5.92337	+	8.15282i	0.199790	+	0.274988i
$880$	−0.925304	+	1.02765i	−0.0311920	+	0.0346422i
$881$	−24.9118	−	27.6674i	−0.839300	−	0.932137i	0.159180	−	0.987250i	$-0.449115\pi$
$881$	−24.9118	−	27.6674i	−0.839300	−	0.932137i	−0.998480	+	0.0551126i	$0.982448\pi$
$882$	7.87434	+	17.6861i	0.265143	+	0.595521i
$883$	−0.793811	+	2.44310i	−0.0267139	+	0.0822169i	−0.963525	−	0.267620i	$-0.913763\pi$
$883$	−0.793811	+	2.44310i	−0.0267139	+	0.0822169i	0.936811	+	0.349837i	$0.113763\pi$
$884$	4.47468	+	13.8558i	0.150500	+	0.466020i
$885$	31.8935	+	23.1719i	1.07209	+	0.778917i
$886$	−20.2287	+	18.2140i	−0.679597	+	0.611912i
$887$	17.3364	+	3.68496i	0.582099	+	0.123729i	0.489544	−	0.871979i	$-0.337163\pi$
$887$	17.3364	+	3.68496i	0.582099	+	0.123729i	0.0925551	+	0.995708i	$0.470497\pi$
$888$	−19.5266	−	8.69382i	−0.655271	−	0.291745i
$889$	0.231608	−	0.0752539i	0.00776787	−	0.00252393i
$890$	−64.6831	−	6.79846i	−2.16818	−	0.227885i
$891$	−0.136253	−	0.0143208i	−0.00456466	−	0.000479765i
$892$	−10.6273	−	14.6272i	−0.355827	−	0.489754i
$893$	13.9895	+	24.2305i	0.468140	+	0.810842i
$894$	−8.70964	+	15.0855i	−0.291294	+	0.504536i
$895$	75.0193	−	7.88484i	2.50762	−	0.263561i
$896$	0.290425	−	0.893837i	0.00970242	−	0.0298610i
$897$	5.85564	−	2.59458i	0.195514	−	0.0866306i
$898$	21.4928			0.717224
$899$	−1.09219	+	26.8323i	−0.0364264	+	0.894908i
$900$	6.60511	−	11.4404i	0.220170	−	0.381346i
$901$	−16.9315	+	18.8044i	−0.564071	+	0.626464i
$902$	−0.111595	−	0.0362593i	−0.00371570	−	0.00120730i
$903$	0.286261	−	0.642953i	0.00952618	−	0.0213962i
$904$	−4.10097	+	2.36769i	−0.136396	+	0.0787484i
$905$		−	70.9122i		−	2.35720i
$906$	24.5900	+	10.9482i	0.816947	+	0.363728i
$907$	−23.4247	+	10.4294i	−0.777805	+	0.346301i	−0.756943	−	0.653481i	$-0.773308\pi$
$907$	−23.4247	+	10.4294i	−0.777805	+	0.346301i	−0.0208620	+	0.999782i	$0.506641\pi$
$908$	−0.0796973	−	0.179003i	−0.00264485	−	0.00594043i
$909$	6.39925	+	19.6949i	0.212250	+	0.653237i
$910$	−0.377691	−	1.79263i	−0.0125203	−	0.0594250i
$911$	1.68471	+	5.18499i	0.0558168	+	0.171786i	0.975078	−	0.221861i	$-0.0712131\pi$
$911$	1.68471	+	5.18499i	0.0558168	+	0.171786i	−0.919262	+	0.393647i	$0.871213\pi$
$912$	−10.2846	+	9.26029i	−0.340557	+	0.306639i
$913$	0.467181	−	0.208002i	0.0154614	−	0.00688387i
$914$	2.92691	−	0.622134i	0.0968136	−	0.0205784i
$915$	6.38269	+	2.07386i	0.211005	+	0.0685597i
$916$	−4.06066	−	0.426792i	−0.134168	−	0.0141016i
$917$	−0.0156311	−	0.0735385i	−0.000516184	−	0.00242845i
$918$	34.2314	−	11.1225i	1.12981	−	0.367096i
$919$	−42.6766	−	19.0008i	−1.40777	−	0.626780i	−0.444614	−	0.895722i	$-0.646659\pi$
$919$	−42.6766	−	19.0008i	−1.40777	−	0.626780i	−0.963156	+	0.268943i	$0.913326\pi$
$920$	−8.46618	−	1.79954i	−0.279122	−	0.0593292i
$921$	−3.92753	−	8.82137i	−0.129416	−	0.290674i
$922$	19.6863	+	14.3029i	0.648333	+	0.471041i
$923$	−11.5015	+	10.3189i	−0.378577	+	0.339650i
$924$	−0.00802853			−0.000264119
$925$	74.5065	+	43.0164i	2.44976	+	1.41437i
$926$	−0.604423	−	5.75070i	−0.0198626	−	0.188980i
$927$	4.25860	−	0.905194i	0.139871	−	0.0297305i
$928$	−25.2682	+	8.21014i	−0.829469	+	0.269511i
$929$	−0.106045	+	0.0612251i	−0.00347922	+	0.00200873i	−0.501739	−	0.865019i	$-0.667306\pi$
$929$	−0.106045	+	0.0612251i	−0.00347922	+	0.00200873i	0.498259	+	0.867028i	$0.333973\pi$
$930$	32.0350	−	26.5668i	1.05047	−	0.871160i
$931$			16.2558i			0.532762i
$932$	11.1823	−	12.4192i	0.366287	−	0.406803i
$933$	−15.0516	−	16.7165i	−0.492768	−	0.547274i
$934$	61.9395	−	6.51011i	2.02672	−	0.213017i
$935$	1.04135			0.0340557
$936$	−9.19668	+	0.950012i	−0.300603	+	0.0310521i
$937$	−29.1249	+	21.1604i	−0.951468	+	0.691282i	−0.951154	−	0.308718i	$-0.900100\pi$
$937$	−29.1249	+	21.1604i	−0.951468	+	0.691282i	−0.000314018		1.00000i	$0.500100\pi$
$938$	0.691976	+	1.55420i	0.0225938	+	0.0507465i
$939$	−10.5440	+	4.69449i	−0.344091	+	0.153199i
$940$	30.9297	−	34.3509i	1.00881	−	1.12040i
$941$	22.9704	+	31.6160i	0.748812	+	1.03065i	0.998063	+	0.0622127i	$0.0198157\pi$
$941$	22.9704	+	31.6160i	0.748812	+	1.03065i	−0.249251	+	0.968439i	$0.580184\pi$
$942$	−10.0470	−	9.04634i	−0.327348	−	0.294746i
$943$	−0.267861	−	1.26019i	−0.00872275	−	0.0410373i
$944$	27.1452	−	37.3622i	0.883501	−	1.21604i
$945$	−1.54736	+	0.328902i	−0.0503357	+	0.0106992i
$946$	0.661681	+	0.734871i	0.0215131	+	0.0238927i
$947$	−8.28718	−	18.6133i	−0.269297	−	0.604851i	0.727386	−	0.686228i	$-0.240735\pi$
$947$	−8.28718	−	18.6133i	−0.269297	−	0.604851i	−0.996683	+	0.0813771i	$0.974068\pi$
$948$	0.213816	−	0.658057i	0.00694441	−	0.0213727i
$949$	−28.0736	−	3.00134i	−0.911309	−	0.0974277i
$950$	25.6894	−	18.6644i	0.833474	−	0.605555i
$951$	8.21683	−	38.6572i	0.266449	−	1.25354i
$952$	−0.452152	+	0.201311i	−0.0146543	+	0.00652453i
$953$	2.85380	−	27.1521i	0.0924437	−	0.879543i	−0.845784	−	0.533525i	$-0.820867\pi$
$953$	2.85380	−	27.1521i	0.0924437	−	0.879543i	0.938228	−	0.346018i	$-0.112466\pi$
$954$	10.9470	+	15.0672i	0.354421	+	0.487819i
$955$	12.3671	−	7.14016i	0.400191	−	0.231050i
$956$	27.8802	−	16.0966i	0.901710	−	0.520602i
$957$	−0.261613	−	0.360080i	−0.00845676	−	0.0116397i
$958$	−3.51145	+	0.746382i	−0.113450	+	0.0241145i
$959$	0.984559	+	0.209275i	0.0317931	+	0.00675783i
$960$	−1.22477	−	0.707121i	−0.0395293	−	0.0228222i
$961$	−29.2510	+	10.2655i	−0.943580	+	0.331144i
$962$	7.17151	+	69.4244i	0.231219	+	2.23833i
$963$	−7.65444	−	23.5580i	−0.246661	−	0.759144i
$964$	−6.35179	+	5.71918i	−0.204577	+	0.184202i
$965$	−0.343115	−	3.26452i	−0.0110453	−	0.105089i
$966$	−0.126177	−	0.218544i	−0.00405967	−	0.00703155i
$967$		−	5.95599i		−	0.191532i	−0.995404	−	0.0957659i	$-0.969470\pi$
$967$		−	5.95599i		−	0.191532i	0.995404	−	0.0957659i	$-0.0305300\pi$
$968$	7.26195	−	16.3106i	0.233408	−	0.524243i
$969$	10.3645	+	1.08936i	0.332957	+	0.0349952i
$970$	−56.3029	+	77.4943i	−1.80778	+	2.48819i
$971$	−4.27173	+	4.74424i	−0.137086	+	0.152250i	−0.807779	−	0.589486i	$-0.799330\pi$
$971$	−4.27173	+	4.74424i	−0.137086	+	0.152250i	0.670692	+	0.741736i	$0.265997\pi$
$972$	−1.60105	−	15.2330i	−0.0513538	−	0.488598i
$973$	0.0703886	−	0.331152i	0.00225656	−	0.0106163i
$974$	13.4445	−	41.3778i	0.430789	−	1.32583i
$975$	−33.4902	−	0.0597916i	−1.07255	−	0.00191486i
$976$	2.42946	−	7.47712i	0.0777652	−	0.239337i
$977$	−40.9500	+	36.8715i	−1.31011	+	1.17963i	−0.339052	+	0.940768i	$0.610106\pi$
$977$	−40.9500	+	36.8715i	−1.31011	+	1.17963i	−0.971055	+	0.238857i	$0.923227\pi$
$978$	−27.6079	+	12.2918i	−0.882804	+	0.393050i
$979$	−0.785394	+	0.166941i	−0.0251013	+	0.00533544i
$980$	25.5415	−	8.29895i	0.815895	−	0.265100i
$981$	8.87237	−	19.9277i	0.283273	−	0.636241i
$982$	−27.1715	−	24.4653i	−0.867077	−	0.780719i
$983$	−9.18977	+	12.6486i	−0.293108	+	0.403429i	−0.930021	−	0.367507i	$-0.880211\pi$
$983$	−9.18977	+	12.6486i	−0.293108	+	0.403429i	0.636912	+	0.770936i	$0.280211\pi$
$984$	0.174951	−	1.66455i	0.00557725	−	0.0530640i
$985$	−3.59420	−	34.1965i	−0.114521	−	1.08959i
$986$	27.5434	+	15.9022i	0.877162	+	0.506430i
$987$	−1.16269			−0.0370087
$988$	8.55310	+	2.79596i	0.272110	+	0.0889515i
$989$	−3.35516	+	10.3261i	−0.106688	+	0.328351i
$990$	0.159355	−	0.749705i	0.00506462	−	0.0238272i
$991$	1.89710	−	3.28587i	0.0602634	−	0.104379i	−0.834320	−	0.551281i	$-0.814139\pi$
$991$	1.89710	−	3.28587i	0.0602634	−	0.104379i	0.894583	+	0.446902i	$0.147473\pi$
$992$	−19.5782	−	23.6079i	−0.621609	−	0.749553i
$993$			5.34029i			0.169469i
$994$	0.452446	+	0.407385i	0.0143507	+	0.0129215i
$995$	9.43580	+	44.3919i	0.299135	+	1.40732i
$996$	−4.96989	−	6.84046i	−0.157477	−	0.216748i
$997$	28.2757	+	48.9750i	0.895502	+	1.55105i	0.833182	+	0.552998i	$0.186516\pi$
$997$	28.2757	+	48.9750i	0.895502	+	1.55105i	0.0623193	+	0.998056i	$0.480150\pi$
$998$	−27.2129	+	47.1341i	−0.861409	+	1.49200i
$999$	59.9373	−	6.29967i	1.89633	−	0.199313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bs.a.4.7	✓	288
13.10	even	6	inner	403.2.bs.a.283.30	yes	288
31.8	even	5	inner	403.2.bs.a.225.30	yes	288
403.101	even	30	inner	403.2.bs.a.101.7	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bs.a.4.7	✓	288	1.1	even	1	trivial
403.2.bs.a.101.7	yes	288	403.101	even	30	inner
403.2.bs.a.225.30	yes	288	31.8	even	5	inner
403.2.bs.a.283.30	yes	288	13.10	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bs (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.364510 + 1.71488i) q^{2} +(-0.797644 - 0.885874i) q^{3} +(-0.980870 - 0.436711i) q^{4} +3.57659i q^{5} +(1.80992 - 1.04496i) q^{6} +(0.0329582 - 0.0740253i) q^{7} +(-0.954559 + 1.31384i) q^{8} +(0.165050 - 1.57034i) q^{9} +O(q^{10})\)	\(q+(-0.364510 + 1.71488i) q^{2} +(-0.797644 - 0.885874i) q^{3} +(-0.980870 - 0.436711i) q^{4} +3.57659i q^{5} +(1.80992 - 1.04496i) q^{6} +(0.0329582 - 0.0740253i) q^{7} +(-0.954559 + 1.31384i) q^{8} +(0.165050 - 1.57034i) q^{9} +(-6.13344 - 1.30370i) q^{10} +(-0.0769876 + 0.00809172i) q^{11} +(0.395514 + 1.21727i) q^{12} +(-2.41736 + 2.67514i) q^{13} +(0.114931 + 0.0835025i) q^{14} +(3.16841 - 2.85285i) q^{15} +(-3.34202 - 3.71169i) q^{16} +(-0.393147 + 3.74054i) q^{17} +(2.63279 + 0.855446i) q^{18} +(1.72739 + 1.55535i) q^{19} +(1.56194 - 3.50817i) q^{20} +(-0.0918660 + 0.0298491i) q^{21} +(0.0141864 - 0.134974i) q^{22} +(1.36132 - 0.606098i) q^{23} +(1.92529 - 0.202356i) q^{24} -7.79200 q^{25} +(-3.70639 - 5.12061i) q^{26} +(-4.41597 + 3.20839i) q^{27} +(-0.0646554 + 0.0582160i) q^{28} +(-4.71782 - 1.00280i) q^{29} +(3.73739 + 6.47334i) q^{30} +(-0.935150 - 5.48867i) q^{31} +(4.77048 - 2.75424i) q^{32} +(0.0685769 + 0.0617470i) q^{33} +(-6.27129 - 2.03767i) q^{34} +(0.264758 + 0.117878i) q^{35} +(-0.847678 + 1.46822i) q^{36} +(-9.56193 - 5.52058i) q^{37} +(-3.29690 + 2.39534i) q^{38} +(4.29803 + 0.00767347i) q^{39} +(-4.69906 - 3.41407i) q^{40} +(0.179754 - 0.845678i) q^{41} +(-0.0177016 - 0.168420i) q^{42} +(-4.87542 + 5.41470i) q^{43} +(0.0790485 + 0.0256844i) q^{44} +(5.61647 + 0.590315i) q^{45} +(0.543174 + 2.55543i) q^{46} +(11.4478 + 3.71960i) q^{47} +(-0.622344 + 5.92121i) q^{48} +(4.67952 + 5.19713i) q^{49} +(2.84026 - 13.3624i) q^{50} +(3.62724 - 2.63534i) q^{51} +(3.53938 - 1.56827i) q^{52} +(5.44280 + 3.95443i) q^{53} +(-3.89235 - 8.74236i) q^{54} +(-0.0289408 - 0.275353i) q^{55} +(0.0657967 + 0.113963i) q^{56} -2.77087i q^{57} +(3.43938 - 7.72498i) q^{58} +(1.92245 + 9.04442i) q^{59} +(-4.35366 + 1.41459i) q^{60} +(0.787045 + 1.36320i) q^{61} +(9.75330 + 0.397000i) q^{62} +(-0.110805 - 0.0639735i) q^{63} +(-0.102503 - 0.315473i) q^{64} +(-9.56786 - 8.64592i) q^{65} +(-0.130886 + 0.0950941i) q^{66} +(10.3712 + 5.98779i) q^{67} +(2.01916 - 3.49729i) q^{68} +(-1.62277 - 0.722506i) q^{69} +(-0.298654 + 0.411062i) q^{70} +(4.26214 + 0.447969i) q^{71} +(1.90563 + 1.71583i) q^{72} +(4.60271 + 6.33509i) q^{73} +(12.9526 - 14.3853i) q^{74} +(6.21524 + 6.90272i) q^{75} +(-1.01511 - 2.27997i) q^{76} +(-0.00193838 + 0.00596572i) q^{77} +(-1.57983 + 7.36782i) q^{78} +(-0.437356 - 0.317758i) q^{79} +(13.2752 - 11.9530i) q^{80} +(1.73113 + 0.367964i) q^{81} +(1.38472 + 0.616516i) q^{82} +(-6.28282 + 2.04141i) q^{83} +(0.103144 + 0.0108409i) q^{84} +(-13.3784 - 1.40613i) q^{85} +(-7.50845 - 10.3345i) q^{86} +(2.87478 + 4.97927i) q^{87} +(0.0628580 - 0.108873i) q^{88} +(10.3155 - 1.08420i) q^{89} +(-3.05958 + 9.41642i) q^{90} +(0.118356 + 0.267114i) q^{91} -1.59997 q^{92} +(-4.11635 + 5.20643i) q^{93} +(-10.5515 + 18.2758i) q^{94} +(-5.56285 + 6.17817i) q^{95} +(-6.24505 - 2.02914i) q^{96} +(6.21335 - 13.9554i) q^{97} +(-10.6182 + 6.13043i) q^{98} +0.122232i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9}+O(q^{10}) \) 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9	\( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + 3 q^{10} - 18 q^{11} - 46 q^{12} - q^{13} - 32 q^{14} + 18 q^{15} + 21 q^{16} - 15 q^{17} - 15 q^{19} + 51 q^{20} - 10 q^{22} - 4 q^{23} - 51 q^{24} - 296 q^{25} - 6 q^{26} - 52 q^{27} + 21 q^{28} + q^{29} + 60 q^{30} + 138 q^{32} + 69 q^{33} - 10 q^{35} + 128 q^{36} - 18 q^{37} + 32 q^{38} - 14 q^{39} + 60 q^{40} - 15 q^{41} - 49 q^{42} - 36 q^{43} + 6 q^{45} - 69 q^{46} + 21 q^{48} - 23 q^{49} + 117 q^{50} + 8 q^{51} + 26 q^{52} - 48 q^{53} + 75 q^{54} + 46 q^{55} - 98 q^{56} - 21 q^{58} - 105 q^{59} - 74 q^{61} - 3 q^{62} - 90 q^{63} + 90 q^{64} + 89 q^{65} - 8 q^{66} + 6 q^{67} - 182 q^{68} + 29 q^{69} + 3 q^{71} - 183 q^{72} - 53 q^{74} - 38 q^{75} + 144 q^{76} - 128 q^{78} - 72 q^{79} - 72 q^{80} + 11 q^{81} - 11 q^{82} - 33 q^{84} + 72 q^{85} - 18 q^{87} - 14 q^{88} + 81 q^{89} - 34 q^{90} - 48 q^{91} + 8 q^{92} + 72 q^{93} - 6 q^{94} + 141 q^{97} + 96 q^{98}+O(q^{100}) \) 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9 + 3 * q^10 - 18 * q^11 - 46 * q^12 - q^13 - 32 * q^14 + 18 * q^15 + 21 * q^16 - 15 * q^17 - 15 * q^19 + 51 * q^20 - 10 * q^22 - 4 * q^23 - 51 * q^24 - 296 * q^25 - 6 * q^26 - 52 * q^27 + 21 * q^28 + q^29 + 60 * q^30 + 138 * q^32 + 69 * q^33 - 10 * q^35 + 128 * q^36 - 18 * q^37 + 32 * q^38 - 14 * q^39 + 60 * q^40 - 15 * q^41 - 49 * q^42 - 36 * q^43 + 6 * q^45 - 69 * q^46 + 21 * q^48 - 23 * q^49 + 117 * q^50 + 8 * q^51 + 26 * q^52 - 48 * q^53 + 75 * q^54 + 46 * q^55 - 98 * q^56 - 21 * q^58 - 105 * q^59 - 74 * q^61 - 3 * q^62 - 90 * q^63 + 90 * q^64 + 89 * q^65 - 8 * q^66 + 6 * q^67 - 182 * q^68 + 29 * q^69 + 3 * q^71 - 183 * q^72 - 53 * q^74 - 38 * q^75 + 144 * q^76 - 128 * q^78 - 72 * q^79 - 72 * q^80 + 11 * q^81 - 11 * q^82 - 33 * q^84 + 72 * q^85 - 18 * q^87 - 14 * q^88 + 81 * q^89 - 34 * q^90 - 48 * q^91 + 8 * q^92 + 72 * q^93 - 6 * q^94 + 141 * q^97 + 96 * q^98

Introduction

L-functions

Modular forms

Varieties

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