LMFDB - Embedded newform 416.2.bd.a.83.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.20
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.649485 + 1.25625i) q^{2} +(-2.66851 - 1.10533i) q^{3} +(-1.15634 - 1.63183i) q^{4} +(1.60908 - 3.88465i) q^{5} +(3.12173 - 2.63443i) q^{6} -1.17091i q^{7} +(2.80102 - 0.392804i) q^{8} +(3.77787 + 3.77787i) q^{9} +O(q^{10})$	\(q+(-0.649485 + 1.25625i) q^{2} +(-2.66851 - 1.10533i) q^{3} +(-1.15634 - 1.63183i) q^{4} +(1.60908 - 3.88465i) q^{5} +(3.12173 - 2.63443i) q^{6} -1.17091i q^{7} +(2.80102 - 0.392804i) q^{8} +(3.77787 + 3.77787i) q^{9} +(3.83503 + 4.54443i) q^{10} +(-3.31067 - 1.37133i) q^{11} +(1.28199 + 5.63270i) q^{12} +(-3.33290 - 1.37543i) q^{13} +(1.47096 + 0.760488i) q^{14} +(-8.58767 + 8.58767i) q^{15} +(-1.32576 + 3.77391i) q^{16} +6.08573 q^{17} +(-7.19962 + 2.29229i) q^{18} +(-0.319274 - 0.770796i) q^{19} +(-8.19974 + 1.86623i) q^{20} +(-1.29425 + 3.12459i) q^{21} +(3.87296 - 3.26839i) q^{22} +(-0.578255 - 0.578255i) q^{23} +(-7.90873 - 2.04786i) q^{24} +(-8.96587 - 8.96587i) q^{25} +(3.89255 - 3.29364i) q^{26} +(-2.58948 - 6.25155i) q^{27} +(-1.91073 + 1.35397i) q^{28} +(-1.30968 + 3.16185i) q^{29} +(-5.21072 - 16.3658i) q^{30} +(4.38495 + 4.38495i) q^{31} +(-3.87992 - 4.11658i) q^{32} +(7.31880 + 7.31880i) q^{33} +(-3.95259 + 7.64522i) q^{34} +(-4.54858 - 1.88408i) q^{35} +(1.79635 - 10.5333i) q^{36} +(-4.91174 - 2.03451i) q^{37} +(1.17568 + 0.0995312i) q^{38} +(7.37357 + 7.35430i) q^{39} +(2.98114 - 11.5130i) q^{40} -8.78281 q^{41} +(-3.08468 - 3.65527i) q^{42} +(-2.06989 - 4.99717i) q^{43} +(1.59049 + 6.98819i) q^{44} +(20.7546 - 8.59683i) q^{45} +(1.10200 - 0.350866i) q^{46} +(-1.27536 - 1.27536i) q^{47} +(7.70922 - 8.60531i) q^{48} +5.62897 q^{49} +(17.0866 - 5.44020i) q^{50} +(-16.2398 - 6.72676i) q^{51} +(1.60950 + 7.02919i) q^{52} +(2.81667 + 6.80004i) q^{53} +(9.53535 + 0.807250i) q^{54} +(-10.6543 + 10.6543i) q^{55} +(-0.459938 - 3.27974i) q^{56} +2.40978i q^{57} +(-3.12147 - 3.69887i) q^{58} +(-3.05374 + 7.37238i) q^{59} +(23.9439 + 4.08338i) q^{60} +(-2.37361 + 5.73039i) q^{61} +(-8.35657 + 2.66065i) q^{62} +(4.42355 - 4.42355i) q^{63} +(7.69141 - 2.20050i) q^{64} +(-10.7059 + 10.7340i) q^{65} +(-13.9477 + 4.44081i) q^{66} +(10.8065 - 4.47619i) q^{67} +(-7.03717 - 9.93090i) q^{68} +(0.903915 + 2.18224i) q^{69} +(5.32112 - 4.49048i) q^{70} -13.1613 q^{71} +(12.0658 + 9.09792i) q^{72} -4.94824i q^{73} +(5.74596 - 4.84900i) q^{74} +(14.0152 + 33.8358i) q^{75} +(-0.888621 + 1.41230i) q^{76} +(-1.60570 + 3.87650i) q^{77} +(-14.0279 + 4.48656i) q^{78} -1.13679 q^{79} +(12.5271 + 11.2226i) q^{80} +3.51644i q^{81} +(5.70430 - 11.0334i) q^{82} +(1.90343 + 4.59529i) q^{83} +(6.59539 - 1.50109i) q^{84} +(9.79241 - 23.6410i) q^{85} +(7.62206 + 0.645273i) q^{86} +(6.98981 - 6.98981i) q^{87} +(-9.81192 - 2.54066i) q^{88} -2.57921 q^{89} +(-2.67999 + 31.6565i) q^{90} +(-1.61050 + 3.90252i) q^{91} +(-0.274956 + 1.61227i) q^{92} +(-6.85446 - 16.5481i) q^{93} +(2.43050 - 0.773848i) q^{94} -3.50801 q^{95} +(5.80341 + 15.2737i) q^{96} +(1.72686 - 1.72686i) q^{97} +(-3.65593 + 7.07140i) q^{98} +(-7.32660 - 17.6880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.649485	+	1.25625i	−0.459255	+	0.888305i
$2$	−0.649485	+	1.25625i	−0.459255	+	0.888305i
$3$	−2.66851	−	1.10533i	−1.54067	−	0.638165i	−0.559067	−	0.829122i	$-0.688841\pi$
$3$	−2.66851	−	1.10533i	−1.54067	−	0.638165i	−0.981598	+	0.190958i	$0.938841\pi$
$4$	−1.15634	−	1.63183i	−0.578170	−	0.815916i
$5$	1.60908	−	3.88465i	0.719601	−	1.73727i	0.0451150	−	0.998982i	$-0.485635\pi$
$5$	1.60908	−	3.88465i	0.719601	−	1.73727i	0.674486	−	0.738288i	$-0.264365\pi$
$6$	3.12173	−	2.63443i	1.27444	−	1.07550i
$7$		−	1.17091i		−	0.442563i	−0.975210	−	0.221281i	$-0.928976\pi$
$7$		−	1.17091i		−	0.442563i	0.975210	−	0.221281i	$-0.0710239\pi$
$8$	2.80102	−	0.392804i	0.990310	−	0.138877i
$9$	3.77787	+	3.77787i	1.25929	+	1.25929i
$10$	3.83503	+	4.54443i	1.21274	+	1.43707i
$11$	−3.31067	−	1.37133i	−0.998206	−	0.413470i	−0.177067	−	0.984199i	$-0.556661\pi$
$11$	−3.31067	−	1.37133i	−0.998206	−	0.413470i	−0.821139	+	0.570728i	$0.806661\pi$
$12$	1.28199	+	5.63270i	0.370077	+	1.62602i
$13$	−3.33290	−	1.37543i	−0.924379	−	0.381474i
$13$	−3.33290	−	1.37543i	−0.924379	−	0.381474i
$14$	1.47096	+	0.760488i	0.393130	+	0.203249i
$15$	−8.58767	+	8.58767i	−2.21733	+	2.21733i
$16$	−1.32576	+	3.77391i	−0.331439	+	0.943477i
$17$	6.08573			1.47601			0.738004	−	0.674797i	$-0.235769\pi$
$17$	6.08573			1.47601			0.738004	+	0.674797i	$0.235769\pi$
$18$	−7.19962	+	2.29229i	−1.69697	+	0.540298i
$19$	−0.319274	−	0.770796i	−0.0732465	−	0.176833i	0.883016	−	0.469343i	$-0.155509\pi$
$19$	−0.319274	−	0.770796i	−0.0732465	−	0.176833i	−0.956262	+	0.292511i	$0.905509\pi$
$20$	−8.19974	+	1.86623i	−1.83352	+	0.417303i
$21$	−1.29425	+	3.12459i	−0.282428	+	0.681841i
$22$	3.87296	−	3.26839i	0.825719	−	0.696823i
$23$	−0.578255	−	0.578255i	−0.120574	−	0.120574i	0.644245	−	0.764819i	$-0.277172\pi$
$23$	−0.578255	−	0.578255i	−0.120574	−	0.120574i	−0.764819	+	0.644245i	$0.777172\pi$
$24$	−7.90873	−	2.04786i	−1.61436	−	0.418017i
$25$	−8.96587	−	8.96587i	−1.79317	−	1.79317i
$26$	3.89255	−	3.29364i	0.763391	−	0.645936i
$27$	−2.58948	−	6.25155i	−0.498345	−	1.20311i
$28$	−1.91073	+	1.35397i	−0.361094	+	0.255876i
$29$	−1.30968	+	3.16185i	−0.243202	+	0.587142i	−0.997597	−	0.0692788i	$-0.977930\pi$
$29$	−1.30968	+	3.16185i	−0.243202	+	0.587142i	0.754395	+	0.656420i	$0.227930\pi$
$30$	−5.21072	−	16.3658i	−0.951344	−	2.98798i
$31$	4.38495	+	4.38495i	0.787561	+	0.787561i	0.981094	−	0.193533i	$-0.0619947\pi$
$31$	4.38495	+	4.38495i	0.787561	+	0.787561i	−0.193533	+	0.981094i	$0.561995\pi$
$32$	−3.87992	−	4.11658i	−0.685879	−	0.727715i
$33$	7.31880	+	7.31880i	1.27404	+	1.27404i
$34$	−3.95259	+	7.64522i	−0.677864	+	1.31114i
$35$	−4.54858	−	1.88408i	−0.768851	−	0.318468i
$36$	1.79635	−	10.5333i	0.299392	−	1.75556i
$37$	−4.91174	−	2.03451i	−0.807485	−	0.334471i	−0.0595350	−	0.998226i	$-0.518962\pi$
$37$	−4.91174	−	2.03451i	−0.807485	−	0.334471i	−0.747950	+	0.663755i	$0.768962\pi$
$38$	1.17568	+	0.0995312i	0.190720	+	0.0161461i
$39$	7.37357	+	7.35430i	1.18072	+	1.17763i
$40$	2.98114	−	11.5130i	0.471360	−	1.82037i
$41$	−8.78281			−1.37164			−0.685822	−	0.727769i	$-0.740557\pi$
$41$	−8.78281			−1.37164			−0.685822	+	0.727769i	$0.740557\pi$
$42$	−3.08468	−	3.65527i	−0.475976	−	0.564021i
$43$	−2.06989	−	4.99717i	−0.315656	−	0.762061i	−0.999475	−	0.0324088i	$-0.989682\pi$
$43$	−2.06989	−	4.99717i	−0.315656	−	0.762061i	0.683819	−	0.729652i	$-0.260318\pi$
$44$	1.59049	+	6.98819i	0.239775	+	1.05351i
$45$	20.7546	−	8.59683i	3.09391	−	1.28154i
$46$	1.10200	−	0.350866i	0.162481	−	0.0517324i
$47$	−1.27536	−	1.27536i	−0.186030	−	0.186030i	0.607947	−	0.793978i	$-0.291993\pi$
$47$	−1.27536	−	1.27536i	−0.186030	−	0.186030i	−0.793978	+	0.607947i	$0.791993\pi$
$48$	7.70922	−	8.60531i	1.11273	−	1.24207i
$49$	5.62897			0.804138
$50$	17.0866	−	5.44020i	2.41641	−	0.769361i
$51$	−16.2398	−	6.72676i	−2.27403	−	0.941935i
$52$	1.60950	+	7.02919i	0.223197	+	0.974773i
$53$	2.81667	+	6.80004i	0.386899	+	0.934057i	0.990593	+	0.136841i	$0.0436949\pi$
$53$	2.81667	+	6.80004i	0.386899	+	0.934057i	−0.603694	+	0.797216i	$0.706305\pi$
$54$	9.53535	+	0.807250i	1.29760	+	0.109853i
$55$	−10.6543	+	10.6543i	−1.43662	+	1.43662i
$56$	−0.459938	−	3.27974i	−0.0614618	−	0.438274i
$57$			2.40978i			0.319183i
$58$	−3.12147	−	3.69887i	−0.409869	−	0.485685i
$59$	−3.05374	+	7.37238i	−0.397563	+	0.959801i	0.590680	+	0.806906i	$0.298860\pi$
$59$	−3.05374	+	7.37238i	−0.397563	+	0.959801i	−0.988242	+	0.152895i	$0.951140\pi$
$60$	23.9439	+	4.08338i	3.09115	+	0.527162i
$61$	−2.37361	+	5.73039i	−0.303909	+	0.733701i	0.695969	+	0.718072i	$0.254975\pi$
$61$	−2.37361	+	5.73039i	−0.303909	+	0.733701i	−0.999878	+	0.0156294i	$0.995025\pi$
$62$	−8.35657	+	2.66065i	−1.06128	+	0.337903i
$63$	4.42355	−	4.42355i	0.557314	−	0.557314i
$64$	7.69141	−	2.20050i	0.961426	−	0.275063i
$65$	−10.7059	+	10.7340i	−1.32791	+	1.33139i
$66$	−13.9477	+	4.44081i	−1.71684	+	0.546626i
$67$	10.8065	−	4.47619i	1.32022	−	0.546853i	0.392371	−	0.919807i	$-0.371655\pi$
$67$	10.8065	−	4.47619i	1.32022	−	0.546853i	0.927850	+	0.372954i	$0.121655\pi$
$68$	−7.03717	−	9.93090i	−0.853383	−	1.20430i
$69$	0.903915	+	2.18224i	0.108819	+	0.262711i
$70$	5.32112	−	4.49048i	0.635995	−	0.536715i
$71$	−13.1613			−1.56196			−0.780980	−	0.624556i	$-0.785280\pi$
$71$	−13.1613			−1.56196			−0.780980	+	0.624556i	$0.785280\pi$
$72$	12.0658	+	9.09792i	1.42197	+	1.07220i
$73$		−	4.94824i		−	0.579148i	−0.957156	−	0.289574i	$-0.906486\pi$
$73$		−	4.94824i		−	0.579148i	0.957156	−	0.289574i	$-0.0935136\pi$
$74$	5.74596	−	4.84900i	0.667954	−	0.563685i
$75$	14.0152	+	33.8358i	1.61834	+	3.90702i
$76$	−0.888621	+	1.41230i	−0.101932	+	0.162002i
$77$	−1.60570	+	3.87650i	−0.182987	+	0.441769i
$78$	−14.0279	+	4.48656i	−1.58834	+	0.508003i
$79$	−1.13679			−0.127899			−0.0639494	−	0.997953i	$-0.520370\pi$
$79$	−1.13679			−0.127899			−0.0639494	+	0.997953i	$0.520370\pi$
$80$	12.5271	+	11.2226i	1.40057	+	1.25473i
$81$			3.51644i			0.390715i
$82$	5.70430	−	11.0334i	0.629934	−	1.21844i
$83$	1.90343	+	4.59529i	0.208929	+	0.504399i	0.993255	−	0.115950i	$-0.0369911\pi$
$83$	1.90343	+	4.59529i	0.208929	+	0.504399i	−0.784326	+	0.620349i	$0.786991\pi$
$84$	6.59539	−	1.50109i	0.719616	−	0.163782i
$85$	9.79241	−	23.6410i	1.06214	−	2.56422i
$86$	7.62206	+	0.645273i	0.821908	+	0.0695816i
$87$	6.98981	−	6.98981i	0.749386	−	0.749386i
$88$	−9.81192	−	2.54066i	−1.04595	−	0.270836i
$89$	−2.57921			−0.273396			−0.136698	−	0.990613i	$-0.543649\pi$
$89$	−2.57921			−0.273396			−0.136698	+	0.990613i	$0.543649\pi$
$90$	−2.67999	+	31.6565i	−0.282496	+	3.33689i
$91$	−1.61050	+	3.90252i	−0.168826	+	0.409096i
$92$	−0.274956	+	1.61227i	−0.0286662	+	0.168091i
$93$	−6.85446	−	16.5481i	−0.710774	−	1.71596i
$94$	2.43050	−	0.773848i	0.250687	−	0.0798163i
$95$	−3.50801			−0.359914
$96$	5.80341	+	15.2737i	0.592308	+	1.55887i
$97$	1.72686	−	1.72686i	0.175336	−	0.175336i	−0.613983	−	0.789319i	$-0.710434\pi$
$97$	1.72686	−	1.72686i	0.175336	−	0.175336i	0.789319	+	0.613983i	$0.210434\pi$
$98$	−3.65593	+	7.07140i	−0.369305	+	0.714320i
$99$	−7.32660	−	17.6880i	−0.736351	−	1.77771i
$100$	−4.26321	+	24.9984i	−0.426321	+	2.49984i
$101$	0.728280	+	1.75822i	0.0724666	+	0.174950i	0.955962	−	0.293489i	$-0.0948165\pi$
$101$	0.728280	+	1.75822i	0.0724666	+	0.174950i	−0.883496	+	0.468439i	$0.844817\pi$
$102$	18.9980	−	16.0324i	1.88109	−	1.58745i
$103$	8.20901	−	8.20901i	0.808858	−	0.808858i	−0.175603	−	0.984461i	$-0.556187\pi$
$103$	8.20901	−	8.20901i	0.808858	−	0.808858i	0.984461	+	0.175603i	$0.0561875\pi$
$104$	−9.87578	−	2.54342i	−0.968400	−	0.249402i
$105$	10.0554	+	10.0554i	0.981306	+	0.981306i
$106$	−10.3719	−	0.878074i	−1.00741	−	0.0852861i
$107$	8.64845	−	3.58231i	0.836077	−	0.346315i	0.0767717	−	0.997049i	$-0.475539\pi$
$107$	8.64845	−	3.58231i	0.836077	−	0.346315i	0.759306	+	0.650734i	$0.225539\pi$
$108$	−7.20717	+	11.4545i	−0.693511	+	1.10221i
$109$	4.92636	−	2.04056i	0.471860	−	0.195451i	−0.134065	−	0.990972i	$-0.542803\pi$
$109$	4.92636	−	2.04056i	0.471860	−	0.195451i	0.605925	+	0.795522i	$0.292803\pi$
$110$	−6.46466	−	20.3042i	−0.616381	−	1.93593i
$111$	10.8582	+	10.8582i	1.03062	+	1.03062i
$112$	4.41891	+	1.55234i	0.417547	+	0.146683i
$113$		−	7.38227i		−	0.694466i	−0.937779	−	0.347233i	$-0.887121\pi$
$113$		−	7.38227i		−	0.694466i	0.937779	−	0.347233i	$-0.112879\pi$
$114$	−3.02729	−	1.56512i	−0.283532	−	0.146587i
$115$	−3.17678	+	1.31586i	−0.296236	+	0.122705i
$116$	6.67406	−	1.51899i	0.619670	−	0.141035i
$117$	−7.39507	−	17.7874i	−0.683675	−	1.64445i
$118$	−7.27821	−	8.62451i	−0.670013	−	0.793950i
$119$		−	7.12585i		−	0.653226i
$120$	−20.6810	+	27.4275i	−1.88790	+	2.50378i
$121$	1.30186	+	1.30186i	0.118351	+	0.118351i
$122$	−5.65720	−	6.70365i	−0.512179	−	0.606920i
$123$	23.4370	+	9.70793i	2.11324	+	0.875334i
$124$	2.08502	−	12.2260i	0.187240	−	1.09793i
$125$	−29.8328	+	12.3572i	−2.66833	+	1.10526i
$126$	2.68406	+	8.43011i	0.239115	+	0.751014i
$127$	−14.5896			−1.29461			−0.647307	−	0.762230i	$-0.724105\pi$
$127$	−14.5896			−1.29461			−0.647307	+	0.762230i	$0.724105\pi$
$128$	−2.23107	+	11.0915i	−0.197200	+	0.980363i
$129$			15.6229i			1.37552i
$130$	−6.53126	−	20.4209i	−0.572829	−	1.79103i
$131$	−2.12109	−	0.878586i	−0.185321	−	0.0767624i	0.288093	−	0.957602i	$-0.406979\pi$
$131$	−2.12109	−	0.878586i	−0.185321	−	0.0767624i	−0.473414	+	0.880840i	$0.656979\pi$
$132$	3.48004	−	20.4061i	0.302899	−	1.77612i
$133$	−0.902533	+	0.373841i	−0.0782595	+	0.0324162i
$134$	−1.39542	+	16.4829i	−0.120546	+	1.42390i
$135$	−28.4518			−2.44874
$136$	17.0463	−	2.39050i	1.46170	−	0.204984i
$137$		−	0.877245i		−	0.0749481i	−0.999298	−	0.0374740i	$-0.988069\pi$
$137$		−	0.877245i		−	0.0749481i	0.999298	−	0.0374740i	$-0.0119312\pi$
$138$	−3.32853	−	0.281788i	−0.283343	−	0.0239874i
$139$	13.9638	−	5.78398i	1.18439	−	0.490591i	0.298466	−	0.954420i	$-0.403525\pi$
$139$	13.9638	−	5.78398i	1.18439	−	0.490591i	0.885924	+	0.463830i	$0.153525\pi$
$140$	2.18519	+	9.60117i	0.184683	+	0.811447i
$141$	1.99362	+	4.81301i	0.167893	+	0.405329i
$142$	8.54807	−	16.5339i	0.717338	−	1.38750i
$143$	9.14798	+	9.12408i	0.764993	+	0.762994i
$144$	−19.2659	+	9.24878i	−1.60549	+	0.770732i
$145$	10.1753	+	10.1753i	0.845015	+	0.845015i
$146$	6.21624	+	3.21381i	0.514460	+	0.265977i
$147$	−15.0210	−	6.22189i	−1.23891	−	0.513173i
$148$	2.35966	+	10.3677i	0.193963	+	0.852222i
$149$	3.80070	+	1.57430i	0.311365	+	0.128972i	0.532894	−	0.846182i	$-0.321105\pi$
$149$	3.80070	+	1.57430i	0.311365	+	0.128972i	−0.221528	+	0.975154i	$0.571105\pi$
$150$	−51.6090	−	4.36914i	−4.21386	−	0.356739i
$151$	1.81108			0.147384			0.0736919	−	0.997281i	$-0.476522\pi$
$151$	1.81108			0.147384			0.0736919	+	0.997281i	$0.476522\pi$
$152$	−1.19706	−	2.03360i	−0.0970947	−	0.164947i
$153$	22.9911	+	22.9911i	1.85872	+	1.85872i
$154$	−3.82699	−	4.53489i	−0.308388	−	0.365432i
$155$	24.0897	−	9.97830i	1.93493	−	0.801476i
$156$	3.47464	−	20.5365i	0.278194	−	1.64424i
$157$	7.07948	−	17.0914i	0.565004	−	1.36404i	−0.340716	−	0.940166i	$-0.610670\pi$
$157$	7.07948	−	17.0914i	0.565004	−	1.36404i	0.905721	−	0.423875i	$-0.139330\pi$
$158$	0.738327	−	1.42809i	0.0587382	−	0.113613i
$159$		−	21.2593i		−	1.68597i
$160$	−22.2346	+	8.44825i	−1.75780	+	0.667893i
$161$	−0.677085	+	0.677085i	−0.0533618	+	0.0533618i
$162$	−4.41753	−	2.28387i	−0.347074	−	0.179438i
$163$	−9.66615	−	23.3361i	−0.757111	−	1.82783i	−0.513887	−	0.857858i	$-0.671795\pi$
$163$	−9.66615	−	23.3361i	−0.757111	−	1.82783i	−0.243225	−	0.969970i	$-0.578205\pi$
$164$	10.1559	+	14.3321i	0.793043	+	1.11915i
$165$	40.2075	−	16.6545i	3.13015	−	1.29655i
$166$	−7.00910	−	0.593380i	−0.544011	−	0.0460552i
$167$		−	7.31826i		−	0.566304i	−0.959075	−	0.283152i	$-0.908620\pi$
$167$		−	7.31826i		−	0.566304i	0.959075	−	0.283152i	$-0.0913801\pi$
$168$	−2.39786	+	9.26041i	−0.184999	+	0.714456i
$169$	9.21641	+	9.16830i	0.708955	+	0.705254i
$170$	23.3390	+	27.6562i	1.79002	+	2.12113i
$171$	1.70579	−	4.11814i	0.130445	−	0.314922i
$172$	−5.76104	+	9.15614i	−0.439275	+	0.698149i
$173$	−2.97042	+	7.17124i	−0.225837	+	0.545219i	−0.995663	−	0.0930351i	$-0.970343\pi$
$173$	−2.97042	+	7.17124i	−0.225837	+	0.545219i	0.769826	+	0.638254i	$0.220343\pi$
$174$	4.24119	+	13.3207i	0.321524	+	1.00984i
$175$	−10.4982	+	10.4982i	−0.793592	+	0.793592i
$176$	9.56441	−	10.6761i	0.720944	−	0.804744i
$177$	16.2979	−	16.2979i	1.22502	−	1.22502i
$178$	1.67516	−	3.24014i	0.125558	−	0.242859i
$179$	21.8964	+	9.06977i	1.63661	+	0.677906i	0.995949	−	0.0899172i	$-0.0286603\pi$
$179$	21.8964	+	9.06977i	1.63661	+	0.677906i	0.640661	+	0.767824i	$0.278660\pi$
$180$	−38.0279	−	23.9272i	−2.83444	−	1.78343i
$181$	−9.22181	+	3.81980i	−0.685452	+	0.283923i	−0.698104	−	0.715997i	$-0.745973\pi$
$181$	−9.22181	+	3.81980i	−0.685452	+	0.283923i	0.0126520	+	0.999920i	$0.495973\pi$
$182$	−3.85656	−	4.55782i	−0.285867	−	0.337848i
$183$	12.6680	−	12.6680i	0.936445	−	0.936445i
$184$	−1.84684	−	1.39256i	−0.136151	−	0.102661i
$185$	−15.8067	+	15.8067i	−1.16213	+	1.16213i
$186$	25.2405	+	2.13682i	1.85072	+	0.156680i
$187$	−20.1479	−	8.34553i	−1.47336	−	0.610285i
$188$	−0.606426	+	3.55593i	−0.0442281	+	0.259343i
$189$	−7.32001	+	3.03205i	−0.532452	+	0.220549i
$190$	2.27840	−	4.40695i	0.165292	−	0.319713i
$191$		−	13.4607i		−	0.973986i	−0.873406	−	0.486993i	$-0.838094\pi$
$191$		−	13.4607i		−	0.973986i	0.873406	−	0.486993i	$-0.161906\pi$
$192$	−22.9569	−	2.62951i	−1.65677	−	0.189768i
$193$	−11.1826	−	11.1826i	−0.804942	−	0.804942i	0.178922	−	0.983863i	$-0.442739\pi$
$193$	−11.1826	−	11.1826i	−0.804942	−	0.804942i	−0.983863	+	0.178922i	$0.942739\pi$
$194$	1.04780	+	3.29093i	0.0752277	+	0.236275i
$195$	40.4335	−	16.8101i	2.89551	−	1.20380i
$196$	−6.50900	−	9.18554i	−0.464929	−	0.656110i
$197$	1.40887	−	3.40131i	0.100378	−	0.242333i	−0.865711	−	0.500545i	$-0.833133\pi$
$197$	1.40887	−	3.40131i	0.100378	−	0.242333i	0.966088	+	0.258211i	$0.0831331\pi$
$198$	26.9791	+	2.28401i	1.91732	+	0.162318i
$199$	0.450416	−	0.450416i	0.0319291	−	0.0319291i	−0.690962	−	0.722891i	$-0.742813\pi$
$199$	0.450416	−	0.450416i	0.0319291	−	0.0319291i	0.722891	+	0.690962i	$0.242813\pi$
$200$	−28.6354	−	21.5917i	−2.02483	−	1.52677i
$201$	−33.7849			−2.38300
$202$	−2.68178	−	0.227036i	−0.188689	−	0.0159742i
$203$	3.70225	+	1.53352i	0.259847	+	0.107632i
$204$	7.80182	+	34.2791i	0.546237	+	2.40002i
$205$	−14.1322	+	34.1182i	−0.987036	+	2.38292i
$206$	4.98096	+	15.6442i	0.347040	+	1.08998i
$207$		−	4.36914i		−	0.303676i
$208$	9.60934	−	10.7546i	0.666288	−	0.745695i
$209$			2.98968i			0.206801i
$210$	−19.1629	+	6.10129i	−1.32237	+	0.421029i
$211$	2.99898	−	7.24017i	0.206458	−	0.498434i	−0.786403	−	0.617714i	$-0.788059\pi$
$211$	2.99898	−	7.24017i	0.206458	−	0.498434i	0.992861	+	0.119281i	$0.0380588\pi$
$212$	7.83950	−	12.4595i	0.538419	−	0.855721i
$213$	35.1211	+	14.5476i	2.40646	+	0.996788i
$214$	−1.11676	+	13.1913i	−0.0763399	+	0.901738i
$215$	−22.7429			−1.55105
$216$	−9.70881	−	16.4936i	−0.660601	−	1.12224i
$217$	5.13439	−	5.13439i	0.348545	−	0.348545i
$218$	−0.636130	+	7.51406i	−0.0430842	+	0.508917i
$219$	−5.46946	+	13.2044i	−0.369592	+	0.892273i
$220$	29.7059	+	5.06603i	2.00277	+	0.341552i
$221$	−20.2831	−	8.37047i	−1.36439	−	0.563059i
$222$	−20.6929	+	6.58842i	−1.38882	+	0.442186i
$223$	−6.82353	−	6.82353i	−0.456937	−	0.456937i	0.440712	−	0.897649i	$-0.354726\pi$
$223$	−6.82353	−	6.82353i	−0.456937	−	0.456937i	−0.897649	+	0.440712i	$0.854726\pi$
$224$	−4.82015	+	4.54304i	−0.322060	+	0.303544i
$225$		−	67.7438i		−	4.51625i
$226$	9.27400	+	4.79467i	0.616897	+	0.318937i
$227$	−6.79022	+	2.81260i	−0.450683	+	0.186679i	−0.596467	−	0.802638i	$-0.703429\pi$
$227$	−6.79022	+	2.81260i	−0.450683	+	0.186679i	0.145785	+	0.989316i	$0.453429\pi$
$228$	3.93236	−	2.78653i	0.260427	−	0.184542i
$229$	−24.2771	−	10.0559i	−1.60428	−	0.664513i	−0.612264	−	0.790654i	$-0.709741\pi$
$229$	−24.2771	−	10.0559i	−1.60428	−	0.664513i	−0.992012	+	0.126141i	$0.959741\pi$
$230$	0.410210	−	4.84547i	0.0270485	−	0.319501i
$231$	8.56966	−	8.56966i	0.563842	−	0.563842i
$232$	−2.42646	+	9.37086i	−0.159305	+	0.615227i
$233$	−10.4632	+	10.4632i	−0.685470	+	0.685470i	−0.961227	−	0.275757i	$-0.911071\pi$
$233$	−10.4632	+	10.4632i	−0.685470	+	0.685470i	0.275757	+	0.961227i	$0.411071\pi$
$234$	27.1485	+	2.26258i	1.77475	+	0.147909i
$235$	−7.00649	+	2.90218i	−0.457053	+	0.189317i
$236$	15.5616	−	3.54178i	1.01298	−	0.230550i
$237$	3.03354	+	1.25653i	0.197049	+	0.0816205i
$238$	8.95186	+	4.62813i	0.580263	+	0.299997i
$239$	0.917498	−	0.917498i	0.0593480	−	0.0593480i	−0.676810	−	0.736158i	$-0.736638\pi$
$239$	0.917498	−	0.917498i	0.0593480	−	0.0593480i	0.736158	+	0.676810i	$0.236638\pi$
$240$	−21.0239	−	43.7942i	−1.35709	−	2.82691i
$241$	2.13052	−	2.13052i	0.137239	−	0.137239i	−0.635150	−	0.772389i	$-0.719062\pi$
$241$	2.13052	−	2.13052i	0.137239	−	0.137239i	0.772389	+	0.635150i	$0.219062\pi$
$242$	−2.48100	+	0.789925i	−0.159485	+	0.0507783i
$243$	−3.88160	+	9.37101i	−0.249005	+	0.601150i
$244$	12.0957	−	2.75295i	0.774350	−	0.176240i
$245$	9.05744	−	21.8666i	0.578659	−	1.39701i
$246$	−27.4176	+	23.1376i	−1.74808	+	1.47520i
$247$	0.00393580	+	3.00812i	0.000250429	+	0.191402i
$248$	14.0048	+	10.5599i	0.889303	+	0.670555i
$249$		−	14.3665i		−	0.910441i
$250$	3.85225	−	45.5033i	0.243637	−	2.87788i
$251$	−11.5073	+	4.76648i	−0.726335	+	0.300858i	−0.715045	−	0.699079i	$-0.753594\pi$
$251$	−11.5073	+	4.76648i	−0.726335	+	0.300858i	−0.0112899	+	0.999936i	$0.503594\pi$
$252$	−12.3336	−	2.10337i	−0.776944	−	0.132500i
$253$	1.12144	+	2.70739i	0.0705042	+	0.170212i
$254$	9.47569	−	18.3282i	0.594558	−	1.15001i
$255$	−52.2623	+	52.2623i	−3.27279	+	3.27279i
$256$	−12.4847	−	10.0066i	−0.780296	−	0.625411i
$257$			2.72221i			0.169807i	0.996389	+	0.0849033i	$0.0270581\pi$
$257$			2.72221i			0.169807i	−0.996389	+	0.0849033i	$0.972942\pi$
$258$	−19.6263	−	10.1468i	−1.22188	−	0.631715i
$259$	−2.38223	+	5.75121i	−0.148024	+	0.357363i
$260$	29.8958	+	5.05816i	1.85406	+	0.313694i
$261$	−16.8929	+	6.99726i	−1.04564	+	0.433119i
$262$	2.48134	−	2.09400i	0.153298	−	0.129368i
$263$	−5.00972	−	5.00972i	−0.308913	−	0.308913i	0.535575	−	0.844488i	$-0.320095\pi$
$263$	−5.00972	−	5.00972i	−0.308913	−	0.308913i	−0.844488	+	0.535575i	$0.820095\pi$
$264$	23.3749	+	17.6252i	1.43863	+	1.08476i
$265$	30.9480			1.90112
$266$	0.116542	−	1.37661i	0.00714566	−	0.0844056i
$267$	6.88266	+	2.85089i	0.421212	+	0.174472i
$268$	−19.8003	−	12.4584i	−1.20950	−	0.761016i
$269$	−17.0614	−	7.06706i	−1.04025	−	0.430886i	−0.203850	−	0.979002i	$-0.565345\pi$
$269$	−17.0614	−	7.06706i	−1.04025	−	0.430886i	−0.836402	+	0.548116i	$0.815345\pi$
$270$	18.4790	−	35.7426i	1.12460	−	2.17523i
$271$	0.151094	+	0.151094i	0.00917833	+	0.00917833i	0.711681	−	0.702503i	$-0.247934\pi$
$271$	0.151094	+	0.151094i	0.00917833	+	0.00917833i	−0.702503	+	0.711681i	$0.747934\pi$
$272$	−8.06821	+	22.9670i	−0.489207	+	1.39258i
$273$	8.61123	−	8.63379i	0.521175	−	0.522541i
$274$	1.10204	+	0.569757i	0.0665767	+	0.0344203i
$275$	17.3879	+	41.9782i	1.04853	+	2.53138i
$276$	2.51583	−	3.99845i	0.151435	−	0.240679i
$277$	−12.1517	+	5.03339i	−0.730124	+	0.302427i	−0.716603	−	0.697481i	$-0.754304\pi$
$277$	−12.1517	+	5.03339i	−0.730124	+	0.302427i	−0.0135211	+	0.999909i	$0.504304\pi$
$278$	−1.80311	+	21.2986i	−0.108143	+	1.27741i
$279$			33.1315i			1.98353i
$280$	−13.4807	−	3.49065i	−0.805628	−	0.208606i
$281$	5.27521			0.314693			0.157346	−	0.987543i	$-0.449706\pi$
$281$	5.27521			0.314693			0.157346	+	0.987543i	$0.449706\pi$
$282$	−7.34118	−	0.621494i	−0.437161	−	0.0370094i
$283$	8.21222	−	3.40161i	0.488166	−	0.202205i	−0.125004	−	0.992156i	$-0.539894\pi$
$283$	8.21222	−	3.40161i	0.488166	−	0.202205i	0.613169	+	0.789951i	$0.289894\pi$
$284$	15.2189	+	21.4771i	0.903078	+	1.27443i
$285$	9.36116	+	3.87752i	0.554508	+	0.229685i
$286$	−17.4036	+	5.56623i	−1.02910	+	0.329138i
$287$			10.2839i			0.607038i
$288$	0.894073	−	30.2097i	0.0526838	−	1.78012i
$289$	20.0362			1.17860
$290$	−19.3915	+	6.17406i	−1.13871	+	0.362553i
$291$	−6.51689	+	2.69938i	−0.382027	+	0.158241i
$292$	−8.07471	+	5.72185i	−0.472536	+	0.334846i
$293$	5.42094	+	2.24543i	0.316695	+	0.131179i	0.535368	−	0.844619i	$-0.320173\pi$
$293$	5.42094	+	2.24543i	0.316695	+	0.131179i	−0.218673	+	0.975798i	$0.570173\pi$
$294$	17.5721	−	14.8291i	1.02483	−	0.864851i
$295$	23.7254	+	23.7254i	1.38135	+	1.38135i
$296$	−14.5570	−	3.76935i	−0.846111	−	0.219089i
$297$			24.2479i			1.40700i
$298$	−4.44621	+	3.75215i	−0.257562	+	0.217356i
$299$	1.13192	+	2.72261i	0.0654605	+	0.157453i
$300$	39.0080	−	61.9962i	2.25213	−	3.57935i
$301$	−5.85123	+	2.42366i	−0.337259	+	0.139697i
$302$	−1.17627	+	2.27518i	−0.0676868	+	0.130922i
$303$		−	5.49683i		−	0.315785i
$304$	3.33219	−	0.183022i	0.191114	−	0.0104970i
$305$	18.4413	+	18.4413i	1.05594	+	1.05594i
$306$	−43.8150	+	13.9503i	−2.50474	+	0.797483i
$307$	17.2813	−	7.15816i	0.986298	−	0.408538i	0.169543	−	0.985523i	$-0.445771\pi$
$307$	17.2813	−	7.15816i	0.986298	−	0.408538i	0.816755	+	0.576985i	$0.195771\pi$
$308$	8.18254	−	1.86232i	0.466244	−	0.106116i
$309$	−30.9795	+	12.8321i	−1.76236	+	0.729995i
$310$	−3.11066	+	36.7435i	−0.176673	+	2.08689i
$311$	−13.6718	−	13.6718i	−0.775254	−	0.775254i	0.203765	−	0.979020i	$-0.434682\pi$
$311$	−13.6718	−	13.6718i	−0.775254	−	0.775254i	−0.979020	+	0.203765i	$0.934682\pi$
$312$	23.5423	+	17.7032i	1.33282	+	1.00224i
$313$	10.2646	−	10.2646i	0.580190	−	0.580190i	−0.354766	−	0.934955i	$-0.615439\pi$
$313$	10.2646	−	10.2646i	0.580190	−	0.580190i	0.934955	+	0.354766i	$0.115439\pi$
$314$	16.8731	+	19.9942i	0.952203	+	1.12834i
$315$	−10.0661	−	24.3018i	−0.567162	−	1.36925i
$316$	1.31451	+	1.85505i	0.0739472	+	0.104355i
$317$	−10.2802	−	24.8186i	−0.577394	−	1.39395i	−0.895143	−	0.445778i	$-0.852927\pi$
$317$	−10.2802	−	24.8186i	−0.577394	−	1.39395i	0.317749	−	0.948175i	$-0.397073\pi$
$318$	26.7071	+	13.8076i	1.49766	+	0.774292i
$319$	8.67187	−	8.67187i	0.485531	−	0.485531i
$320$	3.82788	−	33.4192i	0.213985	−	1.86819i
$321$	−27.0381			−1.50912
$322$	−0.410833	−	1.29035i	−0.0228948	−	0.0719081i
$323$	−1.94302	−	4.69086i	−0.108112	−	0.261006i
$324$	5.73824	−	4.06620i	0.318791	−	0.225900i
$325$	17.5504	+	42.2142i	0.973523	+	2.34162i
$326$	35.5941	+	3.01335i	1.97138	+	0.166894i
$327$	−15.4015			−0.851707
$328$	−24.6008	+	3.44992i	−1.35835	+	0.190490i
$329$	−1.49333	+	1.49333i	−0.0823301	+	0.0823301i
$330$	−5.19191	+	61.3276i	−0.285805	+	3.37597i
$331$	−2.61129	+	6.30422i	−0.143530	+	0.346511i	−0.979254	−	0.202638i	$-0.935048\pi$
$331$	−2.61129	+	6.30422i	−0.143530	+	0.346511i	0.835724	+	0.549150i	$0.185048\pi$
$332$	5.29774	−	8.41980i	0.290751	−	0.462097i
$333$	−10.8698	−	26.2420i	−0.595661	−	1.43805i
$334$	9.19358	+	4.75310i	0.503050	+	0.260078i
$335$		−	49.1819i		−	2.68709i
$336$	−10.0760	−	9.02681i	−0.549693	−	0.492453i
$337$	−23.8737			−1.30048			−0.650242	−	0.759727i	$-0.725332\pi$
$337$	−23.8737			−1.30048			−0.650242	+	0.759727i	$0.725332\pi$
$338$	−17.5036	+	5.62347i	−0.952071	+	0.305876i
$339$	−8.15987	+	19.6997i	−0.443184	+	1.06994i
$340$	−49.9015	+	11.3574i	−2.70629	+	0.615942i
$341$	−8.50395	−	20.5304i	−0.460515	−	1.11178i
$342$	4.06554	+	4.81757i	0.219839	+	0.260504i
$343$		−	14.7874i		−	0.798444i
$344$	−7.76072	−	13.1841i	−0.418430	−	0.710839i
$345$	9.93173			0.534706
$346$	−7.07964	−	8.38921i	−0.380604	−	0.451007i
$347$	3.65275	+	8.81852i	0.196090	+	0.473403i	0.991088	−	0.133209i	$-0.0425282\pi$
$347$	3.65275	+	8.81852i	0.196090	+	0.473403i	−0.794998	+	0.606612i	$0.792528\pi$
$348$	−19.4888	−	3.32361i	−1.04471	−	0.178164i
$349$	−19.0399	+	7.88656i	−1.01918	+	0.422158i	−0.828796	−	0.559552i	$-0.810973\pi$
$349$	−19.0399	+	7.88656i	−1.01918	+	0.422158i	−0.190384	+	0.981710i	$0.560973\pi$
$350$	−6.36999	−	20.0069i	−0.340490	−	1.06941i
$351$	0.0319213	+	24.3974i	0.00170384	+	1.30224i
$352$	7.19998	+	18.9493i	0.383760	+	1.01000i
$353$	12.1301	−	12.1301i	0.645618	−	0.645618i	−0.306313	−	0.951931i	$-0.599095\pi$
$353$	12.1301	−	12.1301i	0.645618	−	0.645618i	0.951931	+	0.306313i	$0.0990955\pi$
$354$	9.88902	+	31.0594i	0.525595	+	1.65079i
$355$	−21.1775	+	51.1271i	−1.12399	+	2.71355i
$356$	2.98245	+	4.20884i	0.158069	+	0.223068i
$357$	−7.87644	+	19.0154i	−0.416865	+	1.00640i
$358$	−25.6153	+	21.6167i	−1.35381	+	1.14248i
$359$		−	12.0535i		−	0.636159i	−0.948064	−	0.318080i	$-0.896962\pi$
$359$		−	12.0535i		−	0.636159i	0.948064	−	0.318080i	$-0.103038\pi$
$360$	54.7571	−	32.2324i	2.88595	−	1.69879i
$361$	12.9428	−	12.9428i	0.681202	−	0.681202i
$362$	1.19079	−	14.0658i	0.0625867	−	0.739283i
$363$	−2.03503	−	4.91301i	−0.106812	−	0.257866i
$364$	8.23055	−	1.88458i	0.431398	−	0.0987787i
$365$	−19.2222	−	7.96210i	−1.00614	−	0.416755i
$366$	7.68653	+	24.1418i	0.401781	+	1.26191i
$367$	33.9046			1.76980			0.884902	−	0.465778i	$-0.154225\pi$
$367$	33.9046			1.76980			0.884902	+	0.465778i	$0.154225\pi$
$368$	2.94891	−	1.41565i	0.153722	−	0.0737961i
$369$	−33.1803	−	33.1803i	−1.72730	−	1.72730i
$370$	−9.59101	−	30.1235i	−0.498613	−	1.56604i
$371$	7.96224	−	3.29807i	0.413379	−	0.171227i
$372$	−19.0777	+	30.3206i	−0.989133	+	1.57205i
$373$	10.4475	+	25.2224i	0.540949	+	1.30597i	0.924054	+	0.382262i	$0.124855\pi$
$373$	10.4475	+	25.2224i	0.540949	+	1.30597i	−0.383105	+	0.923705i	$0.625145\pi$
$374$	23.5698	−	19.8905i	1.21877	−	1.02852i
$375$	93.2679			4.81633
$376$	−4.07328	−	3.07134i	−0.210063	−	0.158392i
$377$	8.71393	−	8.73676i	0.448790	−	0.449966i
$378$	0.945217	−	11.1650i	0.0486167	−	0.574268i
$379$	−7.62534	−	3.15852i	−0.391687	−	0.162242i	0.178143	−	0.984005i	$-0.442991\pi$
$379$	−7.62534	−	3.15852i	−0.391687	−	0.162242i	−0.569830	+	0.821762i	$0.692991\pi$
$380$	4.05645	+	5.72449i	0.208092	+	0.293660i
$381$	38.9324	+	16.1263i	1.99457	+	0.826176i
$382$	16.9101	+	8.74255i	0.865196	+	0.447308i
$383$	4.27322	+	4.27322i	0.218351	+	0.218351i	0.807803	−	0.589452i	$-0.200656\pi$
$383$	4.27322	+	4.27322i	0.218351	+	0.218351i	−0.589452	+	0.807803i	$0.700656\pi$
$384$	18.2135	−	27.1318i	0.929453	−	1.38457i
$385$	12.4752	+	12.4752i	0.635794	+	0.635794i
$386$	21.3111	−	6.78524i	1.08471	−	0.345360i
$387$	11.0588	−	26.6984i	0.562153	−	1.35716i
$388$	−4.81477	−	0.821109i	−0.244433	−	0.0416855i
$389$	10.4526	+	25.2347i	0.529965	+	1.27945i	0.931545	+	0.363626i	$0.118461\pi$
$389$	10.4526	+	25.2347i	0.529965	+	1.27945i	−0.401580	+	0.915824i	$0.631539\pi$
$390$	−5.14319	+	61.7126i	−0.260436	+	3.12494i
$391$	−3.51911	−	3.51911i	−0.177969	−	0.177969i
$392$	15.7668	−	2.21108i	0.796346	−	0.111676i
$393$	4.68903	+	4.68903i	0.236530	+	0.236530i
$394$	3.35786	+	3.97899i	0.169167	+	0.200459i
$395$	−1.82918	+	4.41603i	−0.0920361	+	0.222195i
$396$	−20.3918	+	32.4091i	−1.02473	+	1.62862i
$397$	−0.687094	−	1.65879i	−0.0344843	−	0.0832524i	0.905699	−	0.423921i	$-0.139347\pi$
$397$	−0.687094	−	1.65879i	−0.0344843	−	0.0832524i	−0.940183	+	0.340669i	$0.889347\pi$
$398$	0.273298	+	0.858374i	0.0136992	+	0.0430264i
$399$	2.82164			0.141259
$400$	45.7229	−	21.9498i	2.28615	−	1.09749i
$401$	−5.82409	+	5.82409i	−0.290841	+	0.290841i	−0.837413	−	0.546571i	$-0.815933\pi$
$401$	−5.82409	+	5.82409i	−0.290841	+	0.290841i	0.546571	+	0.837413i	$0.315933\pi$
$402$	21.9427	−	42.4423i	1.09440	−	2.11683i
$403$	−8.58342	−	20.6458i	−0.427571	−	1.02844i
$404$	2.02699	−	3.22154i	0.100846	−	0.160277i
$405$	13.6601	+	5.65821i	0.678778	+	0.281159i
$406$	−4.33104	+	3.65496i	−0.214946	+	0.181393i
$407$	13.4712	+	13.4712i	0.667743	+	0.667743i
$408$	−48.1304	−	12.4627i	−2.38281	−	0.616996i
$409$			36.9758i			1.82834i	0.405334	+	0.914169i	$0.367155\pi$
$409$			36.9758i			1.82834i	−0.405334	+	0.914169i	$0.632845\pi$
$410$	−33.6824	−	39.9128i	−1.66345	−	1.97115i
$411$	−0.969648	+	2.34094i	−0.0478292	+	0.115470i
$412$	−22.8881	−	3.90333i	−1.12762	−	0.192303i
$413$	8.63239	+	3.57565i	0.424772	+	0.175946i
$414$	5.48874	+	2.83769i	0.269757	+	0.139465i
$415$	20.9139			1.02662
$416$	7.26932	+	19.0567i	0.356408	+	0.934330i
$417$	−43.6557			−2.13783
$418$	−3.75580	−	1.94175i	−0.183702	−	0.0949743i
$419$	19.5129	+	8.08249i	0.953265	+	0.394855i	0.804457	−	0.594011i	$-0.202456\pi$
$419$	19.5129	+	8.08249i	0.953265	+	0.394855i	0.148808	+	0.988866i	$0.452456\pi$
$420$	4.78127	−	28.0362i	0.233302	−	1.36803i
$421$	6.73895	−	16.2693i	0.328436	−	0.792915i	−0.670273	−	0.742115i	$-0.733823\pi$
$421$	6.73895	−	16.2693i	0.328436	−	0.792915i	0.998709	−	0.0508000i	$-0.0161771\pi$
$422$	7.14769	+	8.46985i	0.347944	+	0.412306i
$423$		−	9.63629i		−	0.468532i
$424$	10.5606	+	17.9406i	0.512869	+	0.871274i
$425$	−54.5639	−	54.5639i	−2.64674	−	2.64674i
$426$	−41.0861	+	34.6725i	−1.99063	+	1.67989i
$427$	6.70978	+	2.77928i	0.324709	+	0.134499i
$428$	−15.8463	−	9.97047i	−0.765959	−	0.481941i
$429$	−14.3263	−	34.4593i	−0.691683	−	1.66371i
$430$	14.7711	−	28.5708i	0.712328	−	1.37781i
$431$	24.1693	−	24.1693i	1.16419	−	1.16419i	0.180647	−	0.983548i	$-0.442181\pi$
$431$	24.1693	−	24.1693i	1.16419	−	1.16419i	0.983548	−	0.180647i	$-0.0578191\pi$
$432$	27.0258	−	1.48440i	1.30028	−	0.0714184i
$433$	17.0527			0.819503			0.409751	−	0.912197i	$-0.365615\pi$
$433$	17.0527			0.819503			0.409751	+	0.912197i	$0.365615\pi$
$434$	3.11538	+	9.78479i	0.149543	+	0.469685i
$435$	−15.9058	−	38.4001i	−0.762627	−	1.84114i
$436$	−9.02640	−	5.67941i	−0.432286	−	0.271994i
$437$	−0.261095	+	0.630338i	−0.0124899	+	0.0301532i
$438$	−13.0358	−	15.4471i	−0.622874	−	0.738091i
$439$	14.8974	+	14.8974i	0.711015	+	0.711015i	0.966748	−	0.255733i	$-0.0823166\pi$
$439$	14.8974	+	14.8974i	0.711015	+	0.711015i	−0.255733	+	0.966748i	$0.582317\pi$
$440$	−25.6577	+	34.0278i	−1.22318	+	1.62221i
$441$	21.2655	+	21.2655i	1.01264	+	1.01264i
$442$	23.6890	−	20.0442i	1.12677	−	0.953407i
$443$	8.24934	+	19.9157i	0.391938	+	0.946222i	0.989518	+	0.144413i	$0.0461293\pi$
$443$	8.24934	+	19.9157i	0.391938	+	0.946222i	−0.597579	+	0.801810i	$0.703871\pi$
$444$	5.16301	−	30.2746i	0.245026	−	1.43677i
$445$	−4.15015	+	10.0193i	−0.196736	+	0.474963i
$446$	13.0038	−	4.14030i	0.615750	−	0.196049i
$447$	−8.40208	−	8.40208i	−0.397405	−	0.397405i
$448$	−2.57659	−	9.00595i	−0.121732	−	0.425491i
$449$	−11.8229	−	11.8229i	−0.557959	−	0.557959i	0.370767	−	0.928726i	$-0.379095\pi$
$449$	−11.8229	−	11.8229i	−0.557959	−	0.557959i	−0.928726	+	0.370767i	$0.879095\pi$
$450$	85.1032	+	43.9985i	4.01181	+	2.07411i
$451$	29.0770	+	12.0441i	1.36918	+	0.567134i
$452$	−12.0466	+	8.53642i	−0.566626	+	0.401519i
$453$	−4.83289	−	2.00185i	−0.227069	−	0.0940551i
$454$	0.876806	−	10.3570i	0.0411505	−	0.486077i
$455$	12.5685	+	12.5357i	0.589222	+	0.587682i
$456$	0.946571	+	6.74984i	0.0443273	+	0.316090i
$457$	21.0769			0.985937			0.492969	−	0.870047i	$-0.335912\pi$
$457$	21.0769			0.985937			0.492969	+	0.870047i	$0.335912\pi$
$458$	28.4004	−	23.9670i	1.32706	−	1.11990i
$459$	−15.7589	−	38.0453i	−0.735561	−	1.77580i
$460$	5.82070	+	3.66238i	0.271392	+	0.170759i
$461$	30.6138	−	12.6806i	1.42583	−	0.590597i	0.469509	−	0.882928i	$-0.344431\pi$
$461$	30.6138	−	12.6806i	1.42583	−	0.590597i	0.956317	+	0.292331i	$0.0944309\pi$
$462$	5.19979	+	16.3315i	0.241916	+	0.759811i
$463$	−8.82577	−	8.82577i	−0.410168	−	0.410168i	0.471629	−	0.881797i	$-0.343666\pi$
$463$	−8.82577	−	8.82577i	−0.410168	−	0.410168i	−0.881797	+	0.471629i	$0.843666\pi$
$464$	−10.1962	−	9.13447i	−0.473348	−	0.424057i
$465$	−75.3131			−3.49256
$466$	−6.34876	−	19.9402i	−0.294101	−	0.923711i
$467$	5.72180	+	2.37005i	0.264773	+	0.109673i	0.511121	−	0.859509i	$-0.329230\pi$
$467$	5.72180	+	2.37005i	0.264773	+	0.109673i	−0.246347	+	0.969182i	$0.579230\pi$
$468$	−20.4749	+	32.6358i	−0.946452	+	1.50859i
$469$	−5.24121	−	12.6534i	−0.242017	−	0.584280i
$470$	0.904733	−	10.6868i	0.0417322	−	0.492947i
$471$	−37.7834	+	37.7834i	−1.74097	+	1.74097i
$472$	−5.65768	+	21.8497i	−0.260416	+	1.00571i
$473$			19.3825i			0.891208i
$474$	−3.54876	+	2.99479i	−0.163000	+	0.137555i
$475$	−4.04829	+	9.77343i	−0.185748	+	0.448436i
$476$	−11.6282	+	8.23990i	−0.532977	+	0.377675i
$477$	−15.0486	+	36.3306i	−0.689030	+	1.66347i
$478$	0.556708	+	1.74851i	0.0254632	+	0.0799749i
$479$	−24.3109	+	24.3109i	−1.11079	+	1.11079i	−0.117750	+	0.993043i	$0.537568\pi$
$479$	−24.3109	+	24.3109i	−1.11079	+	1.11079i	−0.993043	+	0.117750i	$0.962432\pi$
$480$	68.6713	+	2.03237i	3.13440	+	0.0927644i
$481$	13.5720	+	13.5365i	0.618830	+	0.617213i
$482$	1.29273	+	4.06022i	0.0588824	+	0.184938i
$483$	2.55521	−	1.05840i	0.116266	−	0.0481590i
$484$	0.619025	−	3.62980i	0.0281375	−	0.164991i
$485$	−3.92960	−	9.48688i	−0.178434	−	0.430777i
$486$	−9.25131	−	10.9626i	−0.419648	−	0.497273i
$487$	12.3216			0.558347			0.279173	−	0.960241i	$-0.409940\pi$
$487$	12.3216			0.558347			0.279173	+	0.960241i	$0.409940\pi$
$488$	−4.39759	+	16.9833i	−0.199070	+	0.768798i
$489$			72.9571i			3.29923i
$490$	21.5873	+	25.5804i	0.975214	+	1.15561i
$491$	−10.9257	−	26.3770i	−0.493071	−	1.19038i	−0.953149	−	0.302500i	$-0.902179\pi$
$491$	−10.9257	−	26.3770i	−0.493071	−	1.19038i	0.460079	−	0.887878i	$-0.347821\pi$
$492$	−11.2594	−	49.4709i	−0.507614	−	2.23032i
$493$	−7.97038	+	19.2422i	−0.358968	+	0.866625i
$494$	−3.78151	−	1.94878i	−0.170138	−	0.0876799i
$495$	−80.5007			−3.61824
$496$	−22.3618	+	10.7350i	−1.00407	+	0.482016i
$497$			15.4107i			0.691265i
$498$	18.0480	+	9.33083i	0.808749	+	0.418124i
$499$	−11.2643	−	27.1944i	−0.504260	−	1.21739i	−0.947143	−	0.320811i	$-0.896044\pi$
$499$	−11.2643	−	27.1944i	−0.504260	−	1.21739i	0.442883	−	0.896579i	$-0.353956\pi$
$500$	54.6617	+	34.3931i	2.44454	+	1.53811i
$501$	−8.08912	+	19.5289i	−0.361395	+	0.872485i
$502$	1.48591	−	17.5518i	0.0663196	−	0.783377i
$503$	−1.69822	+	1.69822i	−0.0757201	+	0.0757201i	−0.743953	−	0.668232i	$-0.767051\pi$
$503$	−1.69822	+	1.69822i	−0.0757201	+	0.0757201i	0.668232	+	0.743953i	$0.267051\pi$
$504$	10.6528	−	14.1280i	0.474516	−	0.629312i
$505$	8.00195			0.356082
$506$	−4.12952	−	0.349599i	−0.183580	−	0.0155416i
$507$	−14.4601	−	34.6529i	−0.642194	−	1.53899i
$508$	16.8705	+	23.8077i	0.748506	+	1.05630i
$509$	−14.3177	−	34.5659i	−0.634619	−	1.53211i	−0.833755	−	0.552135i	$-0.813813\pi$
$509$	−14.3177	−	34.5659i	−0.634619	−	1.53211i	0.199135	−	0.979972i	$-0.436187\pi$
$510$	−31.7111	−	99.5982i	−1.40419	−	4.41028i
$511$	−5.79395			−0.256309
$512$	20.6794	−	9.18486i	0.913910	−	0.405917i
$513$	−3.99192	+	3.99192i	−0.176247	+	0.176247i
$514$	−3.41978	−	1.76803i	−0.150840	−	0.0779845i
$515$	−18.6802	−	45.0981i	−0.823150	−	1.98726i
$516$	25.4940	−	18.0654i	1.12231	−	0.795285i
$517$	2.47337	+	5.97124i	0.108779	+	0.262615i
$518$	−5.67775	−	6.72800i	−0.249466	−	0.295611i
$519$	15.8532	−	15.8532i	0.695879	−	0.695879i
$520$	−25.7712	+	34.2714i	−1.13014	+	1.50290i
$521$	10.0602	+	10.0602i	0.440744	+	0.440744i	0.892262	−	0.451518i	$-0.149117\pi$
$521$	10.0602	+	10.0602i	0.440744	+	0.440744i	−0.451518	+	0.892262i	$0.649117\pi$
$522$	2.18134	−	25.7663i	0.0954747	−	1.12776i
$523$	−37.3586	+	15.4745i	−1.63358	+	0.676651i	−0.995626	−	0.0934244i	$-0.970219\pi$
$523$	−37.3586	+	15.4745i	−1.63358	+	0.676651i	−0.637953	+	0.770075i	$0.720219\pi$
$524$	1.01900	+	4.47722i	0.0445152	+	0.195588i
$525$	39.6187	−	16.4106i	1.72910	−	0.716217i
$526$	9.54722	−	3.03974i	0.416278	−	0.132539i
$527$	26.6857	+	26.6857i	1.16245	+	1.16245i
$528$	−37.3234	+	17.9175i	−1.62429	+	0.779759i
$529$		−	22.3312i		−	0.970924i
$530$	−20.1003	+	38.8785i	−0.873100	+	1.68877i
$531$	−39.3885	+	16.3152i	−1.70931	+	0.708021i
$532$	1.65368	+	1.04050i	0.0716962	+	0.0451112i
$533$	29.2722	+	12.0801i	1.26792	+	0.523247i
$534$	−8.05162	+	6.79475i	−0.348428	+	0.294037i
$535$		−	39.3604i		−	1.70170i
$536$	28.5109	−	16.7827i	1.23148	−	0.724902i
$537$	−48.4056	−	48.4056i	−2.08885	−	2.08885i
$538$	19.9591	−	16.8435i	0.860499	−	0.726174i
$539$	−18.6357	−	7.71915i	−0.802696	−	0.332487i
$540$	32.8999	+	46.4286i	1.41579	+	1.99797i
$541$	24.4765	−	10.1385i	1.05233	−	0.435889i	0.211606	−	0.977355i	$-0.432131\pi$
$541$	24.4765	−	10.1385i	1.05233	−	0.435889i	0.840723	+	0.541466i	$0.182131\pi$
$542$	−0.287946	+	0.0916792i	−0.0123683	+	0.00393796i
$543$	28.8307			1.23724
$544$	−23.6122	−	25.0524i	−1.01236	−	1.07411i
$545$		−	22.4206i		−	0.960394i
$546$	5.25336	+	16.4254i	0.224823	+	0.702942i
$547$	−29.7748	−	12.3331i	−1.27308	−	0.527326i	−0.359179	−	0.933269i	$-0.616943\pi$
$547$	−29.7748	−	12.3331i	−1.27308	−	0.527326i	−0.913898	+	0.405943i	$0.866943\pi$
$548$	−1.43152	+	1.01439i	−0.0611514	+	0.0433327i
$549$	−30.6158	+	12.6815i	−1.30665	+	0.541233i
$550$	−64.0284	−	5.42056i	−2.73018	−	0.231133i
$551$	2.85529			0.121640
$552$	3.38908	+	5.75745i	0.144249	+	0.245053i
$553$			1.33108i			0.0566032i
$554$	1.56912	−	18.5347i	0.0666656	−	0.787464i
$555$	59.6521	−	24.7087i	2.53209	−	1.04883i
$556$	−25.5853	−	16.0983i	−1.08506	−	0.682719i
$557$	−0.740188	−	1.78697i	−0.0313628	−	0.0757165i	0.907422	−	0.420220i	$-0.138047\pi$
$557$	−0.740188	−	1.78697i	−0.0313628	−	0.0757165i	−0.938785	+	0.344504i	$0.888047\pi$
$558$	−41.6216	−	21.5184i	−1.76198	−	0.910948i
$559$	0.0255163	+	19.5020i	0.00107922	+	0.824848i
$560$	13.1407	−	14.6681i	0.555295	−	0.619839i
$561$	44.5403	+	44.5403i	1.88049	+	1.88049i
$562$	−3.42617	+	6.62700i	−0.144524	+	0.279543i
$563$	2.45736	+	1.01787i	0.103565	+	0.0428982i	0.433865	−	0.900978i	$-0.357150\pi$
$563$	2.45736	+	1.01787i	0.103565	+	0.0428982i	−0.330299	+	0.943876i	$0.607150\pi$
$564$	5.54874	−	8.81872i	0.233644	−	0.371335i
$565$	−28.6776	−	11.8786i	−1.20647	−	0.499738i
$566$	−1.06043	+	12.5259i	−0.0445730	+	0.526503i
$567$	4.11743			0.172916
$568$	−36.8651	+	5.16981i	−1.54682	+	0.216921i
$569$	14.4821	+	14.4821i	0.607123	+	0.607123i	0.942193	−	0.335070i	$-0.108760\pi$
$569$	14.4821	+	14.4821i	0.607123	+	0.607123i	−0.335070	+	0.942193i	$0.608760\pi$
$570$	−10.9511	+	9.24159i	−0.458690	+	0.387088i
$571$	9.42378	−	3.90346i	0.394373	−	0.163355i	−0.176679	−	0.984269i	$-0.556535\pi$
$571$	9.42378	−	3.90346i	0.394373	−	0.163355i	0.571052	+	0.820914i	$0.306535\pi$
$572$	4.31079	−	25.4785i	0.180243	−	1.06531i
$573$	−14.8786	+	35.9202i	−0.621563	+	1.50059i
$574$	−12.9191	−	6.67922i	−0.539235	−	0.278785i
$575$			10.3691i			0.432422i
$576$	37.3703	+	20.7439i	1.55710	+	0.864330i
$577$	−21.5632	+	21.5632i	−0.897689	+	0.897689i	−0.995231	−	0.0975428i	$-0.968902\pi$
$577$	−21.5632	+	21.5632i	−0.897689	+	0.897689i	0.0975428	+	0.995231i	$0.468902\pi$
$578$	−13.0132	+	25.1705i	−0.541277	+	1.04695i
$579$	17.4804	+	42.2014i	0.726461	+	1.75383i
$580$	4.83830	−	28.3706i	0.200899	−	1.17802i
$581$	5.38068	−	2.22875i	0.223228	−	0.0924641i
$582$	0.841512	−	9.94006i	0.0348818	−	0.412029i
$583$		−	26.3753i		−	1.09235i
$584$	−1.94369	−	13.8601i	−0.0804304	−	0.573536i
$585$	−80.9972	+	0.105976i	−3.34882	+	0.00438157i
$586$	−6.34164	+	5.35170i	−0.261971	+	0.221077i
$587$	−13.9825	+	33.7567i	−0.577119	+	1.39329i	0.318268	+	0.948001i	$0.396899\pi$
$587$	−13.9825	+	33.7567i	−0.577119	+	1.39329i	−0.895387	+	0.445288i	$0.853101\pi$
$588$	7.21625	+	31.7063i	0.297593	+	1.30755i
$589$	1.97990	−	4.77990i	0.0815804	−	0.196953i
$590$	−45.2144	+	14.3958i	−1.86145	+	0.592667i
$591$	−7.51916	+	7.51916i	−0.309297	+	0.309297i
$592$	14.1898	−	15.8392i	0.583198	−	0.650986i
$593$	11.7675	−	11.7675i	0.483234	−	0.483234i	−0.422929	−	0.906163i	$-0.638998\pi$
$593$	11.7675	−	11.7675i	0.483234	−	0.483234i	0.906163	+	0.422929i	$0.138998\pi$
$594$	−30.4615	−	15.7486i	−1.24985	−	0.646174i
$595$	−27.6815	−	11.4660i	−1.13483	−	0.470062i
$596$	−1.82590	−	8.02253i	−0.0747918	−	0.328616i
$597$	−1.69980	+	0.704080i	−0.0695682	+	0.0288161i
$598$	−4.15545	−	0.346319i	−0.169929	−	0.0141620i
$599$	−2.74020	+	2.74020i	−0.111962	+	0.111962i	−0.760868	−	0.648907i	$-0.775227\pi$
$599$	−2.74020	+	2.74020i	−0.111962	+	0.111962i	0.648907	+	0.760868i	$0.275227\pi$
$600$	52.5478	+	89.2695i	2.14525	+	3.64441i
$601$	15.8604	−	15.8604i	0.646959	−	0.646959i	−0.305298	−	0.952257i	$-0.598756\pi$
$601$	15.8604	−	15.8604i	0.646959	−	0.646959i	0.952257	+	0.305298i	$0.0987560\pi$
$602$	0.755557	−	8.92476i	0.0307942	−	0.363746i
$603$	57.7359	+	23.9150i	2.35119	+	0.973893i
$604$	−2.09423	−	2.95538i	−0.0852129	−	0.120253i
$605$	7.15205	−	2.96248i	0.290772	−	0.120442i
$606$	6.90541	+	3.57011i	0.280513	+	0.145026i
$607$			18.5226i			0.751810i	0.926658	+	0.375905i	$0.122668\pi$
$607$			18.5226i			0.751810i	−0.926658	+	0.375905i	$0.877332\pi$
$608$	−1.93428	+	4.30494i	−0.0784456	+	0.174588i
$609$	−8.18444	−	8.18444i	−0.331650	−	0.331650i
$610$	−35.1442	+	11.1896i	−1.42295	+	0.453052i
$611$	2.49648	+	6.00481i	0.100997	+	0.242929i
$612$	10.9321	−	64.1031i	0.441905	−	2.59122i
$613$	12.8289	−	30.9717i	0.518155	−	1.25094i	−0.420880	−	0.907116i	$-0.638279\pi$
$613$	12.8289	−	30.9717i	0.518155	−	1.25094i	0.939035	−	0.343821i	$-0.111721\pi$
$614$	−2.23150	+	26.3588i	−0.0900561	+	1.06376i
$615$	75.4239	−	75.4239i	3.04138	−	3.04138i
$616$	−2.97489	+	11.4889i	−0.119862	+	0.462900i
$617$	−23.7726			−0.957050			−0.478525	−	0.878074i	$-0.658828\pi$
$617$	−23.7726			−0.957050			−0.478525	+	0.878074i	$0.658828\pi$
$618$	4.00032	−	47.2524i	0.160917	−	1.90077i
$619$	23.8823	+	9.89238i	0.959912	+	0.397608i	0.806947	−	0.590623i	$-0.201118\pi$
$619$	23.8823	+	9.89238i	0.959912	+	0.397608i	0.152964	+	0.988232i	$0.451118\pi$
$620$	−44.1388	−	27.7721i	−1.77266	−	1.11536i
$621$	−2.11761	+	5.11237i	−0.0849769	+	0.205152i
$622$	26.0548	−	8.29558i	1.04470	−	0.332623i
$623$			3.02003i			0.120995i
$624$	−37.5300	+	18.0771i	−1.50240	+	0.723665i
$625$			72.3754i			2.89502i
$626$	6.22823	+	19.5616i	0.248930	+	0.781840i
$627$	3.30460	−	7.97800i	0.131973	−	0.318611i
$628$	−36.0766	+	8.21091i	−1.43961	+	0.327651i
$629$	−29.8915	−	12.3815i	−1.19185	−	0.493682i
$630$	37.0669	+	3.13803i	1.47678	+	0.125022i
$631$	−22.6639			−0.902237			−0.451118	−	0.892464i	$-0.648975\pi$
$631$	−22.6639			−0.902237			−0.451118	+	0.892464i	$0.648975\pi$
$632$	−3.18417	+	0.446535i	−0.126659	+	0.0177622i
$633$	−16.0056	+	16.0056i	−0.636166	+	0.636166i
$634$	37.8553	+	3.20478i	1.50343	+	0.127278i
$635$	−23.4757	+	56.6753i	−0.931605	+	2.24909i
$636$	−34.6917	+	24.5830i	−1.37561	+	0.974780i
$637$	−18.7608	−	7.74223i	−0.743329	−	0.306758i
$638$	5.26181	+	16.5263i	0.208317	+	0.654282i
$639$	−49.7217	−	49.7217i	−1.96696	−	1.96696i
$640$	39.4968	+	26.5141i	1.56125	+	1.04806i
$641$			4.19416i			0.165659i	0.996564	+	0.0828297i	$0.0263958\pi$
$641$			4.19416i			0.165659i	−0.996564	+	0.0828297i	$0.973604\pi$
$642$	17.5608	−	33.9667i	0.693071	−	1.34056i
$643$	5.46344	−	2.26303i	0.215457	−	0.0892453i	−0.272344	−	0.962200i	$-0.587799\pi$
$643$	5.46344	−	2.26303i	0.215457	−	0.0892453i	0.487801	+	0.872955i	$0.337799\pi$
$644$	1.88783	+	0.321949i	0.0743909	+	0.0126866i
$645$	60.6896	+	25.1385i	2.38965	+	0.989826i
$646$	7.15486	+	0.605720i	0.281504	+	0.0238317i
$647$	−18.8193	+	18.8193i	−0.739863	+	0.739863i	−0.972551	−	0.232689i	$-0.925248\pi$
$647$	−18.8193	+	18.8193i	−0.739863	+	0.739863i	0.232689	+	0.972551i	$0.425248\pi$
$648$	1.38127	+	9.84961i	0.0542614	+	0.386929i
$649$	20.2199	−	20.2199i	0.793699	−	0.793699i
$650$	−64.4304	−	5.36970i	−2.52717	−	0.210617i
$651$	−19.3764	+	8.02596i	−0.759420	+	0.314562i
$652$	−26.9033	+	42.7581i	−1.05362	+	1.67453i
$653$	−13.3176	−	5.51632i	−0.521157	−	0.215870i	0.106568	−	0.994305i	$-0.466014\pi$
$653$	−13.3176	−	5.51632i	−0.521157	−	0.215870i	−0.627725	+	0.778435i	$0.716014\pi$
$654$	10.0031	−	19.3482i	0.391151	−	0.756576i
$655$	−6.82600	+	6.82600i	−0.266714	+	0.266714i
$656$	11.6439	−	33.1455i	0.454617	−	1.29411i
$657$	18.6938	−	18.6938i	0.729315	−	0.729315i
$658$	−0.906106	−	2.84590i	−0.0353237	−	0.110945i
$659$	−12.9850	+	31.3485i	−0.505822	+	1.22116i	0.440446	+	0.897779i	$0.354820\pi$
$659$	−12.9850	+	31.3485i	−0.505822	+	1.22116i	−0.946268	+	0.323384i	$0.895180\pi$
$660$	−73.6709	−	46.3537i	−2.86763	−	1.80431i
$661$	11.8010	−	28.4901i	0.459005	−	1.10814i	−0.509796	−	0.860295i	$-0.670279\pi$
$661$	11.8010	−	28.4901i	0.459005	−	1.10814i	0.968801	−	0.247840i	$-0.0797209\pi$
$662$	−6.22370	−	7.37494i	−0.241891	−	0.286635i
$663$	44.8736	+	44.7563i	1.74275	+	1.73819i
$664$	7.13660	+	12.1238i	0.276954	+	0.470496i
$665$			4.10757i			0.159285i
$666$	40.0264	+	3.38857i	1.55099	+	0.131305i
$667$	2.58569	−	1.07103i	0.100118	−	0.0414703i
$668$	−11.9422	+	8.46239i	−0.462057	+	0.327420i
$669$	10.6664	+	25.7509i	0.412386	+	0.995588i
$670$	61.7849	+	31.9429i	2.38696	+	1.23406i
$671$	15.7165	−	15.7165i	0.606728	−	0.606728i
$672$	17.8842	−	6.79528i	0.689897	−	0.262134i
$673$		−	6.71647i		−	0.258901i	−0.991586	−	0.129450i	$-0.958679\pi$
$673$		−	6.71647i		−	0.258901i	0.991586	−	0.129450i	$-0.0413213\pi$
$674$	15.5056	−	29.9914i	0.597253	−	1.15523i
$675$	−32.8337	+	79.2675i	−1.26377	+	3.05101i
$676$	4.30384	−	25.6413i	0.165532	−	0.986204i
$677$	29.3246	−	12.1466i	1.12703	−	0.466833i	0.260263	−	0.965538i	$-0.416191\pi$
$677$	29.3246	−	12.1466i	1.12703	−	0.466833i	0.866772	+	0.498705i	$0.166191\pi$
$678$	−19.4481	−	23.0455i	−0.746898	−	0.885057i
$679$	−2.02199	−	2.02199i	−0.0775970	−	0.0775970i
$680$	18.1425	−	70.0653i	0.695731	−	2.68688i
$681$	21.2286			0.813483
$682$	31.3145	+	2.65104i	1.19909	+	0.101514i
$683$	−27.3626	−	11.3340i	−1.04700	−	0.433682i	−0.208180	−	0.978091i	$-0.566754\pi$
$683$	−27.3626	−	11.3340i	−1.04700	−	0.433682i	−0.838820	+	0.544409i	$0.816754\pi$
$684$	−8.69259	+	1.97840i	−0.332369	+	0.0756462i
$685$	−3.40779	−	1.41155i	−0.130205	−	0.0539327i
$686$	18.5767	+	9.60418i	0.709262	+	0.366689i
$687$	53.6686	+	53.6686i	2.04758	+	2.04758i
$688$	21.6030	−	1.18655i	0.823607	−	0.0452370i
$689$	−0.0347220	−	26.5379i	−0.00132280	−	1.01102i
$690$	−6.45051	+	12.4768i	−0.245567	+	0.474982i
$691$	1.10611	+	2.67037i	0.0420782	+	0.101586i	0.943521	−	0.331312i	$-0.107491\pi$
$691$	1.10611	+	2.67037i	0.0420782	+	0.101586i	−0.901443	+	0.432898i	$0.857491\pi$
$692$	15.1371	−	3.44515i	0.575426	−	0.130965i
$693$	−20.7110	+	8.57880i	−0.786748	+	0.325882i
$694$	−13.4507	−	1.13872i	−0.510581	−	0.0432251i
$695$		−	63.5512i		−	2.41063i
$696$	16.8330	−	22.3242i	0.638051	−	0.846197i
$697$	−53.4498			−2.02456
$698$	2.45857	−	29.0411i	0.0930584	−	1.09922i
$699$	39.4867	−	16.3559i	1.49352	−	0.618637i
$700$	29.2709	+	4.99184i	1.10634	+	0.188674i
$701$	−6.38088	−	2.64305i	−0.241003	−	0.0998266i	0.258913	−	0.965901i	$-0.416636\pi$
$701$	−6.38088	−	2.64305i	−0.241003	−	0.0998266i	−0.499916	+	0.866074i	$0.666636\pi$
$702$	−30.6700	−	15.8056i	−1.15757	−	0.596546i
$703$			4.43551i			0.167289i
$704$	−28.4814	−	3.26229i	−1.07343	−	0.122952i
$705$	21.9048			0.824981
$706$	7.36013	+	23.1167i	0.277002	+	0.870008i
$707$	2.05872	−	0.852751i	0.0774263	−	0.0320710i
$708$	−45.4413	−	7.74953i	−1.70779	−	0.291245i
$709$	−44.6576	−	18.4978i	−1.67715	−	0.694699i	−0.677969	−	0.735091i	$-0.737140\pi$
$709$	−44.6576	−	18.4978i	−1.67715	−	0.694699i	−0.999184	+	0.0403913i	$0.987140\pi$
$710$	−50.4741	−	59.8106i	−1.89426	−	2.24465i
$711$	−4.29464	−	4.29464i	−0.161062	−	0.161062i
$712$	−7.22442	+	1.01312i	−0.270747	+	0.0379685i
$713$		−	5.07124i		−	0.189919i
$714$	−18.7725	−	22.2450i	−0.702544	−	0.832499i
$715$	50.1637	−	20.8554i	1.87601	−	0.779948i
$716$	−10.5193	−	46.2189i	−0.393124	−	1.72728i
$717$	−3.46249	+	1.43421i	−0.129309	+	0.0535616i
$718$	15.1422	+	7.82856i	0.565103	+	0.292159i
$719$			9.56965i			0.356888i	0.983950	+	0.178444i	$0.0571063\pi$
$719$			9.56965i			0.356888i	−0.983950	+	0.178444i	$0.942894\pi$
$720$	4.92808	+	89.7232i	0.183659	+	3.34378i
$721$	−9.61202	−	9.61202i	−0.357970	−	0.357970i
$722$	7.85330	+	24.6656i	0.292269	+	0.917960i
$723$	−8.04027	+	3.33039i	−0.299021	+	0.123858i
$724$	16.8968	+	10.6315i	0.627965	+	0.395115i
$725$	40.0912	−	16.6063i	1.48895	−	0.616743i
$726$	7.49370	+	0.634406i	0.278117	+	0.0235450i
$727$	−6.78338	−	6.78338i	−0.251582	−	0.251582i	0.570037	−	0.821619i	$-0.306929\pi$
$727$	−6.78338	−	6.78338i	−0.251582	−	0.251582i	−0.821619	+	0.570037i	$0.806929\pi$
$728$	−2.97811	+	11.5637i	−0.110376	+	0.428578i
$729$	28.1757	−	28.1757i	1.04354	−	1.04354i
$730$	22.4869	−	18.9767i	0.832279	−	0.702358i
$731$	−12.5968	−	30.4114i	−0.465910	−	1.12481i
$732$	−35.3205	−	6.02354i	−1.30548	−	0.222637i
$733$	15.1487	+	36.5721i	0.559529	+	1.35082i	0.910140	+	0.414301i	$0.135974\pi$
$733$	15.1487	+	36.5721i	0.559529	+	1.35082i	−0.350611	+	0.936521i	$0.614026\pi$
$734$	−22.0205	+	42.5927i	−0.812791	+	1.57212i
$735$	−48.3397	+	48.3397i	−1.78304	+	1.78304i
$736$	−0.136850	+	4.62402i	−0.00504437	+	0.170443i
$737$	−41.9150			−1.54396
$738$	63.2329	−	20.1327i	2.32763	−	0.741096i
$739$	0.527608	+	1.27376i	0.0194084	+	0.0468560i	0.933287	−	0.359132i	$-0.116927\pi$
$739$	0.527608	+	1.27376i	0.0194084	+	0.0468560i	−0.913878	+	0.405988i	$0.866927\pi$
$740$	44.0719	+	7.51599i	1.62011	+	0.276293i
$741$	3.31447	−	8.03155i	0.121760	−	0.295046i
$742$	−1.02815	+	12.1446i	−0.0377444	+	0.445843i
$743$	6.30691			0.231378			0.115689	−	0.993285i	$-0.463092\pi$
$743$	6.30691			0.231378			0.115689	+	0.993285i	$0.463092\pi$
$744$	−25.6996	−	43.6592i	−0.942194	−	1.60062i
$745$	12.2312	−	12.2312i	0.448117	−	0.448117i
$746$	−38.4712	−	3.25692i	−1.40853	−	0.119244i
$747$	−10.1695	+	24.5513i	−0.372082	+	0.898286i
$748$	9.67929	+	42.5282i	0.353910	+	1.55499i
$749$	−4.19456	−	10.1266i	−0.153266	−	0.370017i
$750$	−60.5761	+	117.168i	−2.21193	+	4.27837i
$751$			18.7423i			0.683918i	0.939715	+	0.341959i	$0.111090\pi$
$751$			18.7423i			0.683918i	−0.939715	+	0.341959i	$0.888910\pi$
$752$	6.50391	−	3.12227i	0.237173	−	0.113858i
$753$	35.9759			1.31104
$754$	5.31602	+	16.6213i	0.193598	+	0.605312i
$755$	2.91417	−	7.03543i	0.106058	−	0.256045i
$756$	13.4122	+	8.43896i	0.487797	+	0.306922i
$757$	14.9181	+	36.0156i	0.542209	+	1.30901i	0.923161	+	0.384414i	$0.125596\pi$
$757$	14.9181	+	36.0156i	0.542209	+	1.30901i	−0.380952	+	0.924595i	$0.624404\pi$
$758$	8.92043	−	7.52794i	0.324005	−	0.273427i
$759$		−	8.46426i		−	0.307233i
$760$	−9.82600	+	1.37796i	−0.356427	+	0.0499839i
$761$	35.1154			1.27293			0.636466	−	0.771305i	$-0.280396\pi$
$761$	35.1154			1.27293			0.636466	+	0.771305i	$0.280396\pi$
$762$	−45.5447	+	38.4351i	−1.64991	+	1.39236i
$763$	−2.38932	−	5.76832i	−0.0864991	−	0.208827i
$764$	−21.9657	+	15.5652i	−0.794691	+	0.563129i
$765$	126.307	−	52.3180i	4.56663	−	1.89156i
$766$	−8.14363	+	2.59285i	−0.294241	+	0.0936836i
$767$	20.3179	−	20.3712i	0.733638	−	0.735561i
$768$	22.2551	+	40.5024i	0.803060	+	1.46151i
$769$	29.9616	−	29.9616i	1.08044	−	1.08044i	0.0839767	−	0.996468i	$-0.473238\pi$

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.649485 + 1.25625i) q^{2} +(-2.66851 - 1.10533i) q^{3} +(-1.15634 - 1.63183i) q^{4} +(1.60908 - 3.88465i) q^{5} +(3.12173 - 2.63443i) q^{6} -1.17091i q^{7} +(2.80102 - 0.392804i) q^{8} +(3.77787 + 3.77787i) q^{9} +O(q^{10})\)	\(q+(-0.649485 + 1.25625i) q^{2} +(-2.66851 - 1.10533i) q^{3} +(-1.15634 - 1.63183i) q^{4} +(1.60908 - 3.88465i) q^{5} +(3.12173 - 2.63443i) q^{6} -1.17091i q^{7} +(2.80102 - 0.392804i) q^{8} +(3.77787 + 3.77787i) q^{9} +(3.83503 + 4.54443i) q^{10} +(-3.31067 - 1.37133i) q^{11} +(1.28199 + 5.63270i) q^{12} +(-3.33290 - 1.37543i) q^{13} +(1.47096 + 0.760488i) q^{14} +(-8.58767 + 8.58767i) q^{15} +(-1.32576 + 3.77391i) q^{16} +6.08573 q^{17} +(-7.19962 + 2.29229i) q^{18} +(-0.319274 - 0.770796i) q^{19} +(-8.19974 + 1.86623i) q^{20} +(-1.29425 + 3.12459i) q^{21} +(3.87296 - 3.26839i) q^{22} +(-0.578255 - 0.578255i) q^{23} +(-7.90873 - 2.04786i) q^{24} +(-8.96587 - 8.96587i) q^{25} +(3.89255 - 3.29364i) q^{26} +(-2.58948 - 6.25155i) q^{27} +(-1.91073 + 1.35397i) q^{28} +(-1.30968 + 3.16185i) q^{29} +(-5.21072 - 16.3658i) q^{30} +(4.38495 + 4.38495i) q^{31} +(-3.87992 - 4.11658i) q^{32} +(7.31880 + 7.31880i) q^{33} +(-3.95259 + 7.64522i) q^{34} +(-4.54858 - 1.88408i) q^{35} +(1.79635 - 10.5333i) q^{36} +(-4.91174 - 2.03451i) q^{37} +(1.17568 + 0.0995312i) q^{38} +(7.37357 + 7.35430i) q^{39} +(2.98114 - 11.5130i) q^{40} -8.78281 q^{41} +(-3.08468 - 3.65527i) q^{42} +(-2.06989 - 4.99717i) q^{43} +(1.59049 + 6.98819i) q^{44} +(20.7546 - 8.59683i) q^{45} +(1.10200 - 0.350866i) q^{46} +(-1.27536 - 1.27536i) q^{47} +(7.70922 - 8.60531i) q^{48} +5.62897 q^{49} +(17.0866 - 5.44020i) q^{50} +(-16.2398 - 6.72676i) q^{51} +(1.60950 + 7.02919i) q^{52} +(2.81667 + 6.80004i) q^{53} +(9.53535 + 0.807250i) q^{54} +(-10.6543 + 10.6543i) q^{55} +(-0.459938 - 3.27974i) q^{56} +2.40978i q^{57} +(-3.12147 - 3.69887i) q^{58} +(-3.05374 + 7.37238i) q^{59} +(23.9439 + 4.08338i) q^{60} +(-2.37361 + 5.73039i) q^{61} +(-8.35657 + 2.66065i) q^{62} +(4.42355 - 4.42355i) q^{63} +(7.69141 - 2.20050i) q^{64} +(-10.7059 + 10.7340i) q^{65} +(-13.9477 + 4.44081i) q^{66} +(10.8065 - 4.47619i) q^{67} +(-7.03717 - 9.93090i) q^{68} +(0.903915 + 2.18224i) q^{69} +(5.32112 - 4.49048i) q^{70} -13.1613 q^{71} +(12.0658 + 9.09792i) q^{72} -4.94824i q^{73} +(5.74596 - 4.84900i) q^{74} +(14.0152 + 33.8358i) q^{75} +(-0.888621 + 1.41230i) q^{76} +(-1.60570 + 3.87650i) q^{77} +(-14.0279 + 4.48656i) q^{78} -1.13679 q^{79} +(12.5271 + 11.2226i) q^{80} +3.51644i q^{81} +(5.70430 - 11.0334i) q^{82} +(1.90343 + 4.59529i) q^{83} +(6.59539 - 1.50109i) q^{84} +(9.79241 - 23.6410i) q^{85} +(7.62206 + 0.645273i) q^{86} +(6.98981 - 6.98981i) q^{87} +(-9.81192 - 2.54066i) q^{88} -2.57921 q^{89} +(-2.67999 + 31.6565i) q^{90} +(-1.61050 + 3.90252i) q^{91} +(-0.274956 + 1.61227i) q^{92} +(-6.85446 - 16.5481i) q^{93} +(2.43050 - 0.773848i) q^{94} -3.50801 q^{95} +(5.80341 + 15.2737i) q^{96} +(1.72686 - 1.72686i) q^{97} +(-3.65593 + 7.07140i) q^{98} +(-7.32660 - 17.6880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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