LMFDB - Embedded newform 416.2.bd.a.83.12

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			83.12
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13073 - 0.849387i) q^{2} +(0.761899 + 0.315589i) q^{3} +(0.557082 + 1.92085i) q^{4} +(-0.560536 + 1.35325i) q^{5} +(-0.593442 - 1.00399i) q^{6} +4.42814i q^{7} +(1.00164 - 2.64513i) q^{8} +(-1.64043 - 1.64043i) q^{9} +O(q^{10})$	\(q+(-1.13073 - 0.849387i) q^{2} +(0.761899 + 0.315589i) q^{3} +(0.557082 + 1.92085i) q^{4} +(-0.560536 + 1.35325i) q^{5} +(-0.593442 - 1.00399i) q^{6} +4.42814i q^{7} +(1.00164 - 2.64513i) q^{8} +(-1.64043 - 1.64043i) q^{9} +(1.78325 - 1.05405i) q^{10} +(-0.0820155 - 0.0339719i) q^{11} +(-0.181758 + 1.63930i) q^{12} +(-3.35512 + 1.32030i) q^{13} +(3.76120 - 5.00701i) q^{14} +(-0.854144 + 0.854144i) q^{15} +(-3.37932 + 2.14014i) q^{16} -5.20503 q^{17} +(0.461515 + 3.24823i) q^{18} +(-0.202500 - 0.488879i) q^{19} +(-2.91166 - 0.322831i) q^{20} +(-1.39747 + 3.37379i) q^{21} +(0.0638817 + 0.108076i) q^{22} +(-3.85867 - 3.85867i) q^{23} +(1.59792 - 1.69922i) q^{24} +(2.01844 + 2.01844i) q^{25} +(4.91516 + 1.35690i) q^{26} +(-1.67891 - 4.05324i) q^{27} +(-8.50578 + 2.46684i) q^{28} +(-1.70159 + 4.10801i) q^{29} +(1.69130 - 0.240303i) q^{30} +(1.48538 + 1.48538i) q^{31} +(5.63889 + 0.450439i) q^{32} +(-0.0517664 - 0.0517664i) q^{33} +(5.88546 + 4.42109i) q^{34} +(-5.99239 - 2.48213i) q^{35} +(2.23716 - 4.06486i) q^{36} +(1.78268 + 0.738412i) q^{37} +(-0.186275 + 0.724790i) q^{38} +(-2.97293 - 0.0529068i) q^{39} +(3.01808 + 2.83816i) q^{40} +10.8195 q^{41} +(4.44581 - 2.62784i) q^{42} +(1.42531 + 3.44101i) q^{43} +(0.0195656 - 0.176464i) q^{44} +(3.13943 - 1.30039i) q^{45} +(1.08559 + 7.64061i) q^{46} +(1.77151 + 1.77151i) q^{47} +(-3.25011 + 0.564096i) q^{48} -12.6084 q^{49} +(-0.567865 - 3.99674i) q^{50} +(-3.96571 - 1.64265i) q^{51} +(-4.40516 - 5.70916i) q^{52} +(4.69207 + 11.3277i) q^{53} +(-1.54439 + 6.00914i) q^{54} +(0.0919452 - 0.0919452i) q^{55} +(11.7130 + 4.43539i) q^{56} -0.436384i q^{57} +(5.41332 - 3.19972i) q^{58} +(-0.387119 + 0.934589i) q^{59} +(-2.11651 - 1.16485i) q^{60} +(-3.01561 + 7.28034i) q^{61} +(-0.417896 - 2.94123i) q^{62} +(7.26403 - 7.26403i) q^{63} +(-5.99344 - 5.29893i) q^{64} +(0.0939708 - 5.28040i) q^{65} +(0.0145639 + 0.102503i) q^{66} +(-4.47221 + 1.85245i) q^{67} +(-2.89963 - 9.99808i) q^{68} +(-1.72217 - 4.15768i) q^{69} +(4.66746 + 7.89647i) q^{70} +11.6070 q^{71} +(-5.98226 + 2.69603i) q^{72} +7.03652i q^{73} +(-1.38853 - 2.34913i) q^{74} +(0.900850 + 2.17484i) q^{75} +(0.826254 - 0.661319i) q^{76} +(0.150432 - 0.363176i) q^{77} +(3.31663 + 2.58499i) q^{78} +2.67686 q^{79} +(-1.00192 - 5.77270i) q^{80} +3.34174i q^{81} +(-12.2338 - 9.18991i) q^{82} +(-3.46051 - 8.35441i) q^{83} +(-7.25905 - 0.804850i) q^{84} +(2.91761 - 7.04373i) q^{85} +(1.31111 - 5.10148i) q^{86} +(-2.59288 + 2.59288i) q^{87} +(-0.172010 + 0.182914i) q^{88} +7.23795 q^{89} +(-4.65437 - 1.19620i) q^{90} +(-5.84645 - 14.8569i) q^{91} +(5.26233 - 9.56153i) q^{92} +(0.662942 + 1.60048i) q^{93} +(-0.498394 - 3.50779i) q^{94} +0.775086 q^{95} +(4.15411 + 2.12276i) q^{96} +(-10.7614 + 10.7614i) q^{97} +(14.2566 + 10.7094i) q^{98} +(0.0788119 + 0.190269i) 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 $

$2$	−1.13073	−	0.849387i	−0.799544	−	0.600608i
$2$	−1.13073	−	0.849387i	−0.799544	−	0.600608i
$3$	0.761899	+	0.315589i	0.439883	+	0.182205i	0.591623	−	0.806215i	$-0.298488\pi$
$3$	0.761899	+	0.315589i	0.439883	+	0.182205i	−0.151740	+	0.988420i	$0.548488\pi$
$4$	0.557082	+	1.92085i	0.278541	+	0.960424i
$5$	−0.560536	+	1.35325i	−0.250679	+	0.605193i	−0.998259	−	0.0589785i	$-0.981216\pi$
$5$	−0.560536	+	1.35325i	−0.250679	+	0.605193i	0.747580	+	0.664172i	$0.231216\pi$
$6$	−0.593442	−	1.00399i	−0.242272	−	0.409878i
$7$			4.42814i			1.67368i	0.547449	+	0.836839i	$0.315599\pi$
$7$			4.42814i			1.67368i	−0.547449	+	0.836839i	$0.684401\pi$
$8$	1.00164	−	2.64513i	0.354132	−	0.935195i
$9$	−1.64043	−	1.64043i	−0.546809	−	0.546809i
$10$	1.78325	−	1.05405i	0.563913	−	0.333319i
$11$	−0.0820155	−	0.0339719i	−0.0247286	−	0.0102429i	0.370285	−	0.928918i	$-0.379260\pi$
$11$	−0.0820155	−	0.0339719i	−0.0247286	−	0.0102429i	−0.395013	+	0.918675i	$0.629260\pi$
$12$	−0.181758	+	1.63930i	−0.0524691	+	0.473226i
$13$	−3.35512	+	1.32030i	−0.930542	+	0.366184i
$13$	−3.35512	+	1.32030i	−0.930542	+	0.366184i
$14$	3.76120	−	5.00701i	1.00522	−	1.33818i
$15$	−0.854144	+	0.854144i	−0.220539	+	0.220539i
$16$	−3.37932	+	2.14014i	−0.844830	+	0.535035i
$17$	−5.20503			−1.26241			−0.631203	−	0.775618i	$-0.717438\pi$
$17$	−5.20503			−1.26241			−0.631203	+	0.775618i	$0.717438\pi$
$18$	0.461515	+	3.24823i	0.108780	+	0.765615i
$19$	−0.202500	−	0.488879i	−0.0464568	−	0.112157i	0.898948	−	0.438056i	$-0.144333\pi$
$19$	−0.202500	−	0.488879i	−0.0464568	−	0.112157i	−0.945404	+	0.325900i	$0.894333\pi$
$20$	−2.91166	−	0.322831i	−0.651067	−	0.0721873i
$21$	−1.39747	+	3.37379i	−0.304953	+	0.736222i
$22$	0.0638817	+	0.108076i	0.0136196	+	0.0230418i
$23$	−3.85867	−	3.85867i	−0.804589	−	0.804589i	0.179220	−	0.983809i	$-0.442643\pi$
$23$	−3.85867	−	3.85867i	−0.804589	−	0.804589i	−0.983809	+	0.179220i	$0.942643\pi$
$24$	1.59792	−	1.69922i	0.326174	−	0.346851i
$25$	2.01844	+	2.01844i	0.403688	+	0.403688i
$26$	4.91516	+	1.35690i	0.963942	+	0.266111i
$27$	−1.67891	−	4.05324i	−0.323106	−	0.780046i
$28$	−8.50578	+	2.46684i	−1.60744	+	0.466188i
$29$	−1.70159	+	4.10801i	−0.315978	+	0.762838i	0.683482	+	0.729968i	$0.260465\pi$
$29$	−1.70159	+	4.10801i	−0.315978	+	0.762838i	−0.999460	+	0.0328703i	$0.989535\pi$
$30$	1.69130	−	0.240303i	0.308788	−	0.0438732i
$31$	1.48538	+	1.48538i	0.266783	+	0.266783i	0.827803	−	0.561020i	$-0.189591\pi$
$31$	1.48538	+	1.48538i	0.266783	+	0.266783i	−0.561020	+	0.827803i	$0.689591\pi$
$32$	5.63889	+	0.450439i	0.996825	+	0.0796271i
$33$	−0.0517664	−	0.0517664i	−0.00901137	−	0.00901137i
$34$	5.88546	+	4.42109i	1.00935	+	0.758210i
$35$	−5.99239	−	2.48213i	−1.01290	−	0.419556i
$36$	2.23716	−	4.06486i	0.372860	−	0.677477i
$37$	1.78268	+	0.738412i	0.293071	+	0.121394i	0.524375	−	0.851488i	$-0.324299\pi$
$37$	1.78268	+	0.738412i	0.293071	+	0.121394i	−0.231304	+	0.972882i	$0.574299\pi$
$38$	−0.186275	+	0.724790i	−0.0302179	+	0.117576i
$39$	−2.97293	−	0.0529068i	−0.476050	−	0.00847186i
$40$	3.01808	+	2.83816i	0.477200	+	0.448753i
$41$	10.8195			1.68971			0.844857	−	0.534992i	$-0.179685\pi$
$41$	10.8195			1.68971			0.844857	+	0.534992i	$0.179685\pi$
$42$	4.44581	−	2.62784i	0.686004	−	0.405485i
$43$	1.42531	+	3.44101i	0.217358	+	0.524749i	0.994519	−	0.104553i	$-0.0333411\pi$
$43$	1.42531	+	3.44101i	0.217358	+	0.524749i	−0.777161	+	0.629301i	$0.783341\pi$
$44$	0.0195656	−	0.176464i	0.00294962	−	0.0266030i
$45$	3.13943	−	1.30039i	0.467999	−	0.193851i
$46$	1.08559	+	7.64061i	0.160062	+	1.12655i
$47$	1.77151	+	1.77151i	0.258401	+	0.258401i	0.824404	−	0.566002i	$-0.191511\pi$
$47$	1.77151	+	1.77151i	0.258401	+	0.258401i	−0.566002	+	0.824404i	$0.691511\pi$
$48$	−3.25011	+	0.564096i	−0.469112	+	0.0814202i
$49$	−12.6084			−1.80120
$50$	−0.567865	−	3.99674i	−0.0803082	−	0.565224i
$51$	−3.96571	−	1.64265i	−0.555310	−	0.230017i
$52$	−4.40516	−	5.70916i	−0.610886	−	0.791718i
$53$	4.69207	+	11.3277i	0.644506	+	1.55597i	0.820539	+	0.571591i	$0.193673\pi$
$53$	4.69207	+	11.3277i	0.644506	+	1.55597i	−0.176033	+	0.984384i	$0.556327\pi$
$54$	−1.54439	+	6.00914i	−0.210164	+	0.817741i
$55$	0.0919452	−	0.0919452i	0.0123979	−	0.0123979i
$56$	11.7130	+	4.43539i	1.56522	+	0.592704i
$57$		−	0.436384i		−	0.0578004i
$58$	5.41332	−	3.19972i	0.710804	−	0.420144i
$59$	−0.387119	+	0.934589i	−0.0503986	+	0.121673i	−0.947074	−	0.321016i	$-0.895976\pi$
$59$	−0.387119	+	0.934589i	−0.0503986	+	0.121673i	0.896675	+	0.442689i	$0.145976\pi$
$60$	−2.11651	−	1.16485i	−0.273240	−	0.150382i
$61$	−3.01561	+	7.28034i	−0.386110	+	0.932151i	0.604646	+	0.796494i	$0.293315\pi$
$61$	−3.01561	+	7.28034i	−0.386110	+	0.932151i	−0.990756	+	0.135657i	$0.956685\pi$
$62$	−0.417896	−	2.94123i	−0.0530728	−	0.373537i
$63$	7.26403	−	7.26403i	0.915182	−	0.915182i
$64$	−5.99344	−	5.29893i	−0.749181	−	0.662366i
$65$	0.0939708	−	5.28040i	0.0116556	−	0.654953i
$66$	0.0145639	+	0.102503i	0.00179269	+	0.0126173i
$67$	−4.47221	+	1.85245i	−0.546367	+	0.226313i	−0.638755	−	0.769411i	$-0.720550\pi$
$67$	−4.47221	+	1.85245i	−0.546367	+	0.226313i	0.0923877	+	0.995723i	$0.470550\pi$
$68$	−2.89963	−	9.99808i	−0.351632	−	1.21245i
$69$	−1.72217	−	4.15768i	−0.207324	−	0.500525i
$70$	4.66746	+	7.89647i	0.557868	+	0.943809i
$71$	11.6070			1.37749			0.688746	−	0.725002i	$-0.258161\pi$
$71$	11.6070			1.37749			0.688746	+	0.725002i	$0.258161\pi$
$72$	−5.98226	+	2.69603i	−0.705016	+	0.317730i
$73$			7.03652i			0.823562i	0.911283	+	0.411781i	$0.135093\pi$
$73$			7.03652i			0.823562i	−0.911283	+	0.411781i	$0.864907\pi$
$74$	−1.38853	−	2.34913i	−0.161413	−	0.273081i
$75$	0.900850	+	2.17484i	0.104021	+	0.251129i
$76$	0.826254	−	0.661319i	0.0947778	−	0.0758584i
$77$	0.150432	−	0.363176i	0.0171433	−	0.0413877i
$78$	3.31663	+	2.58499i	0.375535	+	0.292693i
$79$	2.67686			0.301170			0.150585	−	0.988597i	$-0.451884\pi$
$79$	2.67686			0.301170			0.150585	+	0.988597i	$0.451884\pi$
$80$	−1.00192	−	5.77270i	−0.112018	−	0.645408i
$81$			3.34174i			0.371304i
$82$	−12.2338	−	9.18991i	−1.35100	−	1.01486i
$83$	−3.46051	−	8.35441i	−0.379840	−	0.917016i	−0.991995	−	0.126278i	$-0.959697\pi$
$83$	−3.46051	−	8.35441i	−0.379840	−	0.917016i	0.612155	−	0.790738i	$-0.290303\pi$
$84$	−7.25905	−	0.804850i	−0.792027	−	0.0878164i
$85$	2.91761	−	7.04373i	0.316459	−	0.764000i
$86$	1.31111	−	5.10148i	0.141381	−	0.550106i
$87$	−2.59288	+	2.59288i	−0.277986	+	0.277986i
$88$	−0.172010	+	0.182914i	−0.0183363	+	0.0194987i
$89$	7.23795			0.767221			0.383610	−	0.923495i	$-0.374681\pi$
$89$	7.23795			0.767221			0.383610	+	0.923495i	$0.374681\pi$
$90$	−4.65437	−	1.19620i	−0.490614	−	0.126091i
$91$	−5.84645	−	14.8569i	−0.612874	−	1.55743i
$92$	5.26233	−	9.56153i	0.548636	−	0.996858i
$93$	0.662942	+	1.60048i	0.0687439	+	0.165962i
$94$	−0.498394	−	3.50779i	−0.0514054	−	0.361801i
$95$	0.775086			0.0795222
$96$	4.15411	+	2.12276i	0.423977	+	0.216653i
$97$	−10.7614	+	10.7614i	−1.09266	+	1.09266i	−0.0974159	+	0.995244i	$0.531058\pi$
$97$	−10.7614	+	10.7614i	−1.09266	+	1.09266i	−0.995244	+	0.0974159i	$0.968942\pi$
$98$	14.2566	+	10.7094i	1.44014	+	1.08181i
$99$	0.0788119	+	0.190269i	0.00792090	+	0.0191227i
$100$	−2.75268	+	5.00155i	−0.275268	+	0.500155i
$101$	−1.56778	−	3.78497i	−0.156000	−	0.376618i	0.826485	−	0.562959i	$-0.190337\pi$
$101$	−1.56778	−	3.78497i	−0.156000	−	0.376618i	−0.982485	+	0.186341i	$0.940337\pi$
$102$	3.08888	+	5.22581i	0.305845	+	0.517432i
$103$	11.9175	−	11.9175i	1.17426	−	1.17426i	0.193078	−	0.981183i	$-0.438153\pi$
$103$	11.9175	−	11.9175i	1.17426	−	1.17426i	0.981183	−	0.193078i	$-0.0618470\pi$
$104$	0.131741	+	10.1972i	0.0129183	+	0.999917i
$105$	−3.78226	−	3.78226i	−0.369111	−	0.369111i
$106$	4.31613	−	16.7939i	0.419220	−	1.63117i
$107$	−0.954069	+	0.395188i	−0.0922333	+	0.0382043i	−0.428323	−	0.903626i	$-0.640895\pi$
$107$	−0.954069	+	0.395188i	−0.0922333	+	0.0382043i	0.336090	+	0.941830i	$0.390895\pi$
$108$	6.85037	−	5.48291i	0.659177	−	0.527593i
$109$	1.49146	−	0.617783i	0.142856	−	0.0591729i	−0.310110	−	0.950701i	$-0.600366\pi$
$109$	1.49146	−	0.617783i	0.142856	−	0.0591729i	0.452966	+	0.891528i	$0.350366\pi$
$110$	−0.182062	+	0.0258677i	−0.0173589	+	0.00246639i
$111$	1.12519	+	1.12519i	0.106798	+	0.106798i
$112$	−9.47683	−	14.9641i	−0.895477	−	1.41397i
$113$		−	11.3922i		−	1.07168i	−0.844318	−	0.535842i	$-0.819994\pi$
$113$		−	11.3922i		−	1.07168i	0.844318	−	0.535842i	$-0.180006\pi$
$114$	−0.370659	+	0.493430i	−0.0347154	+	0.0462140i
$115$	7.38469	−	3.05884i	0.688626	−	0.285238i
$116$	−8.83879	−	0.980004i	−0.820661	−	0.0909911i
$117$	7.66967	+	3.33798i	0.709061	+	0.308596i
$118$	1.23155	−	0.727949i	0.113374	−	0.0670132i
$119$		−	23.0486i		−	2.11286i
$120$	1.40378	+	3.11487i	0.128147	+	0.284347i
$121$	−7.77260	−	7.77260i	−0.706600	−	0.706600i
$122$	9.59366	−	5.67064i	0.868569	−	0.513396i
$123$	8.24333	+	3.41450i	0.743276	+	0.307875i
$124$	−2.02572	+	3.68068i	−0.181915	+	0.330535i
$125$	−10.6291	+	4.40273i	−0.950699	+	0.393792i
$126$	−14.3836	+	2.04365i	−1.28139	+	0.182063i
$127$	3.91821			0.347685			0.173842	−	0.984773i	$-0.444382\pi$
$127$	3.91821			0.347685			0.173842	+	0.984773i	$0.444382\pi$
$128$	2.27610	+	11.0824i	0.201181	+	0.979554i
$129$			3.07151i			0.270432i
$130$	−4.59136	+	5.89087i	−0.402689	+	0.516663i
$131$	−15.7801	−	6.53635i	−1.37872	−	0.571083i	−0.434579	−	0.900634i	$-0.643103\pi$
$131$	−15.7801	−	6.53635i	−1.37872	−	0.571083i	−0.944138	+	0.329551i	$0.893103\pi$
$132$	0.0705972	−	0.128273i	0.00614470	−	0.0111648i
$133$	2.16482	−	0.896699i	0.187714	−	0.0777537i
$134$	6.63029	+	1.70402i	0.572769	+	0.147205i
$135$	6.42614			0.553074
$136$	−5.21356	+	13.7680i	−0.447059	+	1.18060i
$137$			2.19294i			0.187355i	0.995603	+	0.0936776i	$0.0298623\pi$
$137$			2.19294i			0.187355i	−0.995603	+	0.0936776i	$0.970138\pi$
$138$	−1.58418	+	6.16398i	−0.134854	+	0.524713i
$139$	−5.62670	+	2.33065i	−0.477250	+	0.197684i	−0.608324	−	0.793689i	$-0.708158\pi$
$139$	−5.62670	+	2.33065i	−0.477250	+	0.197684i	0.131073	+	0.991373i	$0.458158\pi$
$140$	1.42954	−	12.8932i	0.120818	−	1.08968i
$141$	0.790643	+	1.90878i	0.0665841	+	0.160748i
$142$	−13.1243	−	9.85881i	−1.10137	−	0.827333i
$143$	0.320025	+	0.00569521i	0.0267618	+	0.000476257i
$144$	9.05427	+	2.03278i	0.754522	+	0.169398i
$145$	−4.60537	−	4.60537i	−0.382455	−	0.382455i
$146$	5.97673	−	7.95638i	0.494638	−	0.658474i
$147$	−9.60632	−	3.97907i	−0.792316	−	0.328188i
$148$	−0.425276	+	3.83562i	−0.0349575	+	0.315286i
$149$	−2.43175	−	1.00726i	−0.199217	−	0.0825183i	0.280844	−	0.959753i	$-0.409386\pi$
$149$	−2.43175	−	1.00726i	−0.199217	−	0.0825183i	−0.480061	+	0.877235i	$0.659386\pi$
$150$	0.828671	−	3.22432i	0.0676607	−	0.263265i
$151$	13.8929			1.13059			0.565296	−	0.824888i	$-0.308762\pi$
$151$	13.8929			1.13059			0.565296	+	0.824888i	$0.308762\pi$
$152$	−1.49598	+	0.0459605i	−0.121340	+	0.00372789i
$153$	8.53847	+	8.53847i	0.690295	+	0.690295i
$154$	−0.478574	+	0.282877i	−0.0385646	+	0.0227949i
$155$	−2.84271	+	1.17749i	−0.228332	+	0.0945783i
$156$	−1.55454	−	5.74003i	−0.124463	−	0.459570i
$157$	−2.58769	+	6.24724i	−0.206520	+	0.498584i	−0.992871	−	0.119197i	$-0.961968\pi$
$157$	−2.58769	+	6.24724i	−0.206520	+	0.498584i	0.786350	+	0.617781i	$0.211968\pi$
$158$	−3.02680	−	2.27369i	−0.240799	−	0.180885i
$159$			10.1113i			0.801879i
$160$	−3.77036	+	7.37836i	−0.298073	+	0.583311i
$161$	17.0867	−	17.0867i	1.34662	−	1.34662i
$162$	2.83843	−	3.77859i	0.223008	−	0.296874i
$163$	9.35483	+	22.5846i	0.732727	+	1.76896i	0.633289	+	0.773916i	$0.281705\pi$
$163$	9.35483	+	22.5846i	0.732727	+	1.76896i	0.0994381	+	0.995044i	$0.468295\pi$
$164$	6.02732	+	20.7825i	0.470655	+	1.62284i
$165$	0.0990699	−	0.0410361i	0.00771258	−	0.00319466i
$166$	−3.18324	+	12.3859i	−0.247068	+	0.961329i
$167$		−	5.82368i		−	0.450650i	−0.974284	−	0.225325i	$-0.927656\pi$
$167$		−	5.82368i		−	0.450650i	0.974284	−	0.225325i	$-0.0723444\pi$
$168$	7.52437	+	7.07581i	0.580518	+	0.545911i
$169$	9.51364	−	8.85949i	0.731819	−	0.681499i
$170$	−9.28187	+	5.48635i	−0.711887	+	0.420784i
$171$	−0.469783	+	1.13416i	−0.0359252	+	0.0867312i
$172$	−5.81564	+	4.65473i	−0.443438	+	0.354920i
$173$	−9.05584	+	21.8627i	−0.688503	+	1.66219i	0.0592728	+	0.998242i	$0.481122\pi$
$173$	−9.05584	+	21.8627i	−0.688503	+	1.66219i	−0.747776	+	0.663951i	$0.768878\pi$
$174$	5.13420	−	0.729478i	0.389223	−	0.0553016i
$175$	−8.93792	+	8.93792i	−0.675644	+	0.675644i
$176$	0.349861	−	0.0607227i	0.0263718	−	0.00457714i
$177$	−0.589892	+	0.589892i	−0.0443390	+	0.0443390i
$178$	−8.18413	−	6.14782i	−0.613427	−	0.460799i
$179$	17.7076	+	7.33471i	1.32352	+	0.548222i	0.928801	−	0.370578i	$-0.120840\pi$
$179$	17.7076	+	7.33471i	1.32352	+	0.548222i	0.394723	+	0.918800i	$0.370840\pi$
$180$	4.24678	+	5.30594i	0.316536	+	0.395482i
$181$	20.0512	−	8.30547i	1.49039	−	0.617341i	0.518990	−	0.854780i	$-0.326308\pi$
$181$	20.0512	−	8.30547i	1.49039	−	0.617341i	0.971402	+	0.237439i	$0.0763081\pi$
$182$	−6.00855	+	21.7650i	−0.445384	+	1.61333i
$183$	−4.59519	+	4.59519i	−0.339686	+	0.339686i
$184$	−14.0717	+	6.34171i	−1.03738	+	0.467517i
$185$	−1.99852	+	1.99852i	−0.146934	+	0.146934i
$186$	0.609825	−	2.37280i	0.0447145	−	0.173982i
$187$	0.426893	+	0.176825i	0.0312175	+	0.0129307i
$188$	−2.41593	+	4.38968i	−0.176200	+	0.320150i
$189$	17.9483	−	7.43442i	1.30555	−	0.540775i
$190$	−0.876410	−	0.658349i	−0.0635815	−	0.0477616i
$191$		−	1.38990i		−	0.100570i	−0.998735	−	0.0502848i	$-0.983987\pi$
$191$		−	1.38990i		−	0.100570i	0.998735	−	0.0502848i	$-0.0160129\pi$
$192$	−2.89412	−	5.92871i	−0.208865	−	0.427868i
$193$	11.9901	+	11.9901i	0.863064	+	0.863064i	0.991693	−	0.128629i	$-0.0410576\pi$
$193$	11.9901	+	11.9901i	0.863064	+	0.863064i	−0.128629	+	0.991693i	$0.541058\pi$
$194$	21.3089	−	3.02761i	1.52989	−	0.217370i
$195$	1.73803	−	3.99348i	0.124463	−	0.285979i
$196$	−7.02391	−	24.2188i	−0.501708	−	1.72991i
$197$	−9.43446	+	22.7768i	−0.672178	+	1.62278i	0.105725	+	0.994395i	$0.466284\pi$
$197$	−9.43446	+	22.7768i	−0.672178	+	1.62278i	−0.777902	+	0.628385i	$0.783716\pi$
$198$	0.0724972	−	0.282084i	0.00515215	−	0.0200468i
$199$	−1.71805	+	1.71805i	−0.121790	+	0.121790i	−0.765375	−	0.643585i	$-0.777446\pi$
$199$	−1.71805	+	1.71805i	−0.121790	+	0.121790i	0.643585	+	0.765375i	$0.277446\pi$
$200$	7.36078	−	3.31729i	0.520486	−	0.234568i
$201$	−3.99198			−0.281573
$202$	−1.44217	+	5.61142i	−0.101471	+	0.394818i
$203$	−18.1908	−	7.53488i	−1.27674	−	0.528845i
$204$	0.946058	−	8.53262i	0.0662373	−	0.597403i
$205$	−6.06469	+	14.6415i	−0.423576	+	1.02260i
$206$	−23.5979	+	3.35284i	−1.64414	+	0.233603i
$207$			12.6597i			0.879913i
$208$	8.51240	−	11.6421i	0.590229	−	0.807236i
$209$			0.0469750i			0.00324933i
$210$	1.06410	+	7.48931i	0.0734296	+	0.516812i
$211$	2.74986	−	6.63875i	0.189308	−	0.457030i	−0.800519	−	0.599308i	$-0.795443\pi$
$211$	2.74986	−	6.63875i	0.189308	−	0.457030i	0.989827	+	0.142278i	$0.0454426\pi$
$212$	−19.1449	+	15.3232i	−1.31487	+	1.05240i
$213$	8.84333	+	3.66303i	0.605935	+	0.250987i
$214$	1.41446	+	0.363524i	0.0966904	+	0.0248500i
$215$	−5.45549			−0.372062
$216$	−12.4030	+	0.381053i	−0.843917	+	0.0259273i
$217$	−6.57748	+	6.57748i	−0.446509	+	0.446509i
$218$	−2.21117	−	0.568284i	−0.149759	−	0.0384891i
$219$	−2.22065	+	5.36112i	−0.150057	+	0.362271i
$220$	0.227834	+	0.125392i	0.0153606	+	0.00845392i
$221$	17.4635	−	6.87218i	1.17472	−	0.462273i
$222$	−0.316559	−	2.22800i	−0.0212461	−	0.149534i
$223$	−12.3724	−	12.3724i	−0.828516	−	0.828516i	0.158795	−	0.987312i	$-0.449239\pi$
$223$	−12.3724	−	12.3724i	−0.828516	−	0.828516i	−0.987312	+	0.158795i	$0.949239\pi$
$224$	−1.99460	+	24.9698i	−0.133270	+	1.66836i
$225$		−	6.62220i		−	0.441480i
$226$	−9.67636	+	12.8814i	−0.643662	+	0.856859i
$227$	−12.0964	+	5.01049i	−0.802866	+	0.332558i	−0.746104	−	0.665830i	$-0.768078\pi$
$227$	−12.0964	+	5.01049i	−0.802866	+	0.332558i	−0.0567624	+	0.998388i	$0.518078\pi$
$228$	0.838227	−	0.243101i	0.0555129	−	0.0160998i
$229$	−21.1131	−	8.74532i	−1.39519	−	0.577907i	−0.446692	−	0.894688i	$-0.647398\pi$
$229$	−21.1131	−	8.74532i	−1.39519	−	0.577907i	−0.948499	+	0.316781i	$0.897398\pi$
$230$	−10.9482	−	2.81375i	−0.721903	−	0.185533i
$231$	0.229228	−	0.229228i	0.0150821	−	0.0150821i
$232$	9.16184	+	8.61567i	0.601504	+	0.565647i
$233$	6.56126	−	6.56126i	0.429843	−	0.429843i	−0.458732	−	0.888575i	$-0.651696\pi$
$233$	6.56126	−	6.56126i	0.429843	−	0.429843i	0.888575	+	0.458732i	$0.151696\pi$
$234$	−5.83706	−	10.2889i	−0.381581	−	0.672604i
$235$	−3.39030	+	1.40431i	−0.221159	+	0.0916069i
$236$	−2.01086	−	0.222955i	−0.130896	−	0.0145131i
$237$	2.03950	+	0.844788i	0.132480	+	0.0548749i
$238$	−19.5772	+	26.0616i	−1.26900	+	1.68932i
$239$	3.16368	−	3.16368i	0.204641	−	0.204641i	−0.597344	−	0.801985i	$-0.703777\pi$
$239$	3.16368	−	3.16368i	0.204641	−	0.204641i	0.801985	+	0.597344i	$0.203777\pi$
$240$	1.05844	−	4.71441i	0.0683218	−	0.304314i
$241$	7.48202	−	7.48202i	0.481959	−	0.481959i	−0.423798	−	0.905757i	$-0.639303\pi$
$241$	7.48202	−	7.48202i	0.481959	−	0.481959i	0.905757	+	0.423798i	$0.139303\pi$
$242$	2.18673	+	15.3906i	0.140568	+	0.989347i
$243$	−6.09133	+	14.7058i	−0.390759	+	0.943376i
$244$	−15.6644	−	1.73679i	−1.00281	−	0.111187i
$245$	7.06745	−	17.0623i	0.451523	−	1.09007i
$246$	−6.42072	−	10.8626i	−0.409370	−	0.692577i
$247$	1.32488	+	1.37289i	0.0843000	+	0.0873548i
$248$	5.41685	−	2.44122i	0.343971	−	0.155018i
$249$		−	7.45732i		−	0.472588i
$250$	15.7583	+	4.04997i	0.996640	+	0.256143i
$251$	20.0195	−	8.29236i	1.26362	−	0.523409i	0.352602	−	0.935773i	$-0.385297\pi$
$251$	20.0195	−	8.29236i	1.26362	−	0.523409i	0.911019	+	0.412364i	$0.135297\pi$
$252$	17.9998	+	9.90644i	1.13388	+	0.624047i
$253$	0.185384	+	0.447558i	0.0116550	+	0.0281377i
$254$	−4.43042	−	3.32808i	−0.277989	−	0.208822i
$255$	4.44585	−	4.44585i	0.278410	−	0.278410i
$256$	6.83960	−	14.4644i	0.427475	−	0.904027i
$257$		−	27.1552i		−	1.69389i	−0.531679	−	0.846946i	$-0.678439\pi$
$257$		−	27.1552i		−	1.69389i	0.531679	−	0.846946i	$-0.321561\pi$
$258$	2.60890	−	3.47304i	0.162423	−	0.216222i
$259$	−3.26979	+	7.89396i	−0.203175	+	0.490507i
$260$	10.1952	−	2.76111i	0.632279	−	0.171237i
$261$	9.53022	−	3.94755i	0.589906	−	0.244347i
$262$	12.2911	+	20.7943i	0.759348	+	1.28467i
$263$	−8.18870	−	8.18870i	−0.504937	−	0.504937i	0.408031	−	0.912968i	$-0.366216\pi$
$263$	−8.18870	−	8.18870i	−0.504937	−	0.504937i	−0.912968	+	0.408031i	$0.866216\pi$
$264$	−0.188780	+	0.0850777i	−0.0116186	+	0.00523617i
$265$	−17.9593			−1.10323
$266$	−3.20947	−	0.824853i	−0.196785	−	0.0505750i
$267$	5.51458	+	2.28422i	0.337487	+	0.139792i
$268$	−6.04966	−	7.55847i	−0.369542	−	0.461707i
$269$	−14.6686	−	6.07593i	−0.894360	−	0.370456i	−0.112311	−	0.993673i	$-0.535825\pi$
$269$	−14.6686	−	6.07593i	−0.894360	−	0.370456i	−0.782049	+	0.623217i	$0.785825\pi$
$270$	−7.26621	−	5.45829i	−0.442207	−	0.332181i
$271$	16.9549	+	16.9549i	1.02994	+	1.02994i	0.999538	+	0.0304013i	$0.00967852\pi$
$271$	16.9549	+	16.9549i	1.02994	+	1.02994i	0.0304013	+	0.999538i	$0.490321\pi$
$272$	17.5895	−	11.1395i	1.06652	−	0.675431i
$273$	0.234278	−	13.1645i	0.0141792	−	0.796755i
$274$	1.86265	−	2.47961i	0.112527	−	0.149799i
$275$	−0.0969730	−	0.234114i	−0.00584769	−	0.0141176i
$276$	7.02688	−	5.62419i	0.422968	−	0.338536i
$277$	−16.6022	+	6.87684i	−0.997527	+	0.413189i	−0.820890	−	0.571087i	$-0.806522\pi$
$277$	−16.6022	+	6.87684i	−0.997527	+	0.413189i	−0.176637	+	0.984276i	$0.556522\pi$
$278$	8.34188	+	2.14391i	0.500313	+	0.128583i
$279$		−	4.87333i		−	0.291759i
$280$	−12.5678	+	13.3645i	−0.751067	+	0.798680i
$281$	12.9856			0.774655			0.387327	−	0.921942i	$-0.373398\pi$
$281$	12.9856			0.774655			0.387327	+	0.921942i	$0.373398\pi$
$282$	0.727294	−	2.82987i	0.0433097	−	0.168516i
$283$	26.6736	−	11.0486i	1.58558	−	0.656770i	0.596298	−	0.802763i	$-0.296638\pi$
$283$	26.6736	−	11.0486i	1.58558	−	0.656770i	0.989286	+	0.145993i	$0.0466378\pi$
$284$	6.46603	+	22.2952i	0.383688	+	1.32298i
$285$	0.590538	+	0.244609i	0.0349804	+	0.0144894i
$286$	−0.357023	−	0.278265i	−0.0211112	−	0.0164541i
$287$			47.9100i			2.82804i
$288$	−8.51128	−	9.98910i	−0.501532	−	0.588613i
$289$	10.0924			0.593668
$290$	1.29567	+	9.11916i	0.0760843	+	0.535495i
$291$	−11.5953	+	4.80294i	−0.679731	+	0.281554i
$292$	−13.5161	+	3.91992i	−0.790969	+	0.229396i
$293$	−2.54757	−	1.05524i	−0.148831	−	0.0616478i	0.307025	−	0.951702i	$-0.400667\pi$
$293$	−2.54757	−	1.05524i	−0.148831	−	0.0616478i	−0.455855	+	0.890054i	$0.650667\pi$
$294$	7.48234	+	12.6587i	0.436379	+	0.738272i
$295$	−1.04774	−	1.04774i	−0.0610019	−	0.0610019i
$296$	3.73880	−	3.97581i	0.217313	−	0.231089i
$297$			0.389464i			0.0225990i
$298$	1.89409	+	3.20444i	0.109721	+	0.185628i
$299$	18.0409	+	7.85172i	1.04333	+	0.454077i
$300$	−3.67570	+	2.94196i	−0.212217	+	0.169854i
$301$	−15.2372	+	6.31147i	−0.878260	+	0.363787i
$302$	−15.7091	−	11.8005i	−0.903958	−	0.679042i
$303$		−	3.37854i		−	0.194092i
$304$	1.73058	+	1.21870i	0.0992558	+	0.0698972i
$305$	−8.16178	−	8.16178i	−0.467342	−	0.467342i
$306$	−2.40220	−	16.9071i	−0.137325	−	0.966517i
$307$	1.02924	−	0.426324i	0.0587417	−	0.0243316i	−0.353119	−	0.935578i	$-0.614879\pi$
$307$	1.02924	−	0.426324i	0.0587417	−	0.0243316i	0.411861	+	0.911247i	$0.364879\pi$
$308$	0.781409	+	0.0866390i	0.0445249	+	0.00493672i
$309$	12.8409	−	5.31888i	0.730494	−	0.302581i
$310$	4.21447	+	1.08315i	0.239366	+	0.0615186i
$311$	−23.7860	−	23.7860i	−1.34878	−	1.34878i	−0.886988	−	0.461792i	$-0.847207\pi$
$311$	−23.7860	−	23.7860i	−1.34878	−	1.34878i	−0.461792	−	0.886988i	$-0.652793\pi$
$312$	−3.11775	+	7.81080i	−0.176508	+	0.442200i
$313$	4.80912	−	4.80912i	0.271828	−	0.271828i	−0.558008	−	0.829836i	$-0.688434\pi$
$313$	4.80912	−	4.80912i	0.271828	−	0.271828i	0.829836	+	0.558008i	$0.188434\pi$
$314$	8.23230	−	4.86596i	0.464575	−	0.274602i
$315$	5.75832	+	13.9018i	0.324445	+	0.783279i
$316$	1.49123	+	5.14185i	0.0838883	+	0.289251i
$317$	−1.87317	−	4.52222i	−0.105207	−	0.253993i	0.862506	−	0.506047i	$-0.168894\pi$
$317$	−1.87317	−	4.52222i	−0.105207	−	0.253993i	−0.967713	+	0.252054i	$0.918894\pi$
$318$	8.58842	−	11.4331i	0.481615	−	0.641137i
$319$	0.279114	−	0.279114i	0.0156274	−	0.0156274i
$320$	10.5303	−	5.14041i	0.588663	−	0.287358i
$321$	−0.851621			−0.0475329
$322$	−33.8337	+	4.80716i	−1.88548	+	0.267892i
$323$	1.05402	+	2.54463i	0.0586473	+	0.141587i
$324$	−6.41897	+	1.86162i	−0.356610	+	0.103423i
$325$	−9.43704	−	4.10717i	−0.523473	−	0.227825i
$326$	8.60529	−	33.4828i	0.476603	−	1.85444i
$327$	1.33131			0.0736215
$328$	10.8372	−	28.6189i	0.598383	−	1.58021i
$329$	−7.84449	+	7.84449i	−0.432481	+	0.432481i
$330$	−0.146876	−	0.0377481i	−0.00808528	−	0.00207797i
$331$	8.06324	−	19.4664i	0.443196	−	1.06997i	−0.531625	−	0.846980i	$-0.678418\pi$
$331$	8.06324	−	19.4664i	0.443196	−	1.06997i	0.974821	−	0.222990i	$-0.0715816\pi$
$332$	14.1198	−	11.3012i	0.774923	−	0.620234i
$333$	−1.71305	−	4.13567i	−0.0938746	−	0.226633i
$334$	−4.94656	+	6.58499i	−0.270664	+	0.360315i
$335$		−	7.09039i		−	0.387390i
$336$	−2.49789	−	14.3919i	−0.136271	−	0.785143i
$337$	−11.0327			−0.600990			−0.300495	−	0.953783i	$-0.597152\pi$
$337$	−11.0327			−0.600990			−0.300495	+	0.953783i	$0.597152\pi$
$338$	−18.2825	+	1.93689i	−0.994435	+	0.105353i
$339$	3.59524	−	8.67968i	0.195267	−	0.471415i
$340$	15.1553	+	1.68035i	0.821911	+	0.0911297i
$341$	−0.0713631	−	0.172286i	−0.00386453	−	0.00932980i
$342$	1.49454	−	0.883393i	0.0808152	−	0.0477684i
$343$		−	24.8347i		−	1.34095i
$344$	10.5296	−	0.323496i	0.567716	−	0.0174417i
$345$	6.59172			0.354886
$346$	28.8096	−	17.0288i	1.54881	−	0.915476i
$347$	7.51047	+	18.1319i	0.403183	+	0.973370i	0.986888	+	0.161405i	$0.0516024\pi$
$347$	7.51047	+	18.1319i	0.403183	+	0.973370i	−0.583705	+	0.811966i	$0.698398\pi$
$348$	−6.42499	−	3.53609i	−0.344415	−	0.189554i
$349$	−17.7988	+	7.37251i	−0.952749	+	0.394641i	−0.804263	−	0.594273i	$-0.797440\pi$
$349$	−17.7988	+	7.37251i	−0.952749	+	0.394641i	−0.148485	+	0.988915i	$0.547440\pi$
$350$	17.6981	−	2.51458i	0.946003	−	0.134410i
$351$	10.9844	+	11.3824i	0.586304	+	0.607550i
$352$	−0.447174	−	0.228507i	−0.0238345	−	0.0121795i
$353$	−10.5020	+	10.5020i	−0.558966	+	0.558966i	−0.929013	−	0.370047i	$-0.879342\pi$
$353$	−10.5020	+	10.5020i	−0.558966	+	0.558966i	0.370047	+	0.929013i	$0.379342\pi$
$354$	1.16805	−	0.165959i	0.0620813	−	0.00882064i
$355$	−6.50612	+	15.7072i	−0.345309	+	0.833649i
$356$	4.03213	+	13.9030i	0.213702	+	0.736857i
$357$	7.27388	−	17.5607i	0.384975	−	0.929411i
$358$	−13.7924	−	23.3341i	−0.728950	−	1.23325i
$359$			24.8080i			1.30932i	0.755925	+	0.654658i	$0.227187\pi$
$359$			24.8080i			1.30932i	−0.755925	+	0.654658i	$0.772813\pi$
$360$	−0.295144	−	9.60673i	−0.0155554	−	0.506319i
$361$	13.2370	−	13.2370i	0.696686	−	0.696686i
$362$	−29.7270	−	7.64001i	−1.56241	−	0.401550i
$363$	−3.46899	−	8.37489i	−0.182075	−	0.439568i
$364$	25.2809	−	19.5067i	1.32508	−	1.02243i
$365$	−9.52220	−	3.94422i	−0.498415	−	0.206450i
$366$	9.09899	−	1.29280i	0.475612	−	0.0675759i
$367$	18.2030			0.950190			0.475095	−	0.879935i	$-0.342414\pi$
$367$	18.2030			0.950190			0.475095	+	0.879935i	$0.342414\pi$
$368$	21.2978	+	4.78159i	1.11022	+	0.249257i
$369$	−17.7485	−	17.7485i	−0.923951	−	0.923951i
$370$	3.95729	−	0.562260i	0.205730	−	0.0292305i
$371$	−50.1605	+	20.7771i	−2.60420	+	1.07870i
$372$	−2.70497	+	2.16501i	−0.140246	+	0.112251i
$373$	5.36006	+	12.9403i	0.277533	+	0.670025i	0.999766	−	0.0216251i	$-0.00688403\pi$
$373$	5.36006	+	12.9403i	0.277533	+	0.670025i	−0.722233	+	0.691650i	$0.756884\pi$
$374$	−0.332506	−	0.562538i	−0.0171935	−	0.0290882i
$375$	−9.48778			−0.489947
$376$	6.46029	−	2.91147i	0.333164	−	0.150147i
$377$	0.285263	−	16.0295i	0.0146918	−	0.825559i
$378$	−26.6093	−	6.83875i	−1.36863	−	0.351747i
$379$	−12.9510	−	5.36446i	−0.665246	−	0.275554i	0.0243981	−	0.999702i	$-0.492233\pi$
$379$	−12.9510	−	5.36446i	−0.665246	−	0.275554i	−0.689644	+	0.724148i	$0.742233\pi$
$380$	0.431787	+	1.48882i	0.0221502	+	0.0763750i
$381$	2.98528	+	1.23654i	0.152940	+	0.0633500i
$382$	−1.18056	+	1.57160i	−0.0604029	+	0.0804098i
$383$	4.68870	+	4.68870i	0.239582	+	0.239582i	0.816677	−	0.577095i	$-0.195814\pi$
$383$	4.68870	+	4.68870i	0.239582	+	0.239582i	−0.577095	+	0.816677i	$0.695814\pi$
$384$	−1.76332	+	9.16198i	−0.0899841	+	0.467545i
$385$	0.407146	+	0.407146i	0.0207501	+	0.0207501i
$386$	−3.37327	−	23.7417i	−0.171695	−	1.20842i
$387$	3.30660	−	7.98284i	0.168084	−	0.405790i
$388$	−26.6661	−	14.6761i	−1.35377	−	0.745066i
$389$	−0.464024	−	1.12025i	−0.0235270	−	0.0567991i	0.911679	−	0.410902i	$-0.134786\pi$
$389$	−0.464024	−	1.12025i	−0.0235270	−	0.0567991i	−0.935206	+	0.354103i	$0.884786\pi$
$390$	−5.35725	+	3.03926i	−0.271275	+	0.153899i
$391$	20.0845	+	20.0845i	1.01572	+	1.01572i
$392$	−12.6290	+	33.3508i	−0.637863	+	1.68447i
$393$	−9.96007	−	9.96007i	−0.502419	−	0.502419i
$394$	30.0141	−	17.7408i	1.51209	−	0.893769i
$395$	−1.50048	+	3.62247i	−0.0754972	+	0.182266i
$396$	−0.321573	+	0.257381i	−0.0161596	+	0.0129339i
$397$	6.34168	+	15.3102i	0.318280	+	0.768395i	0.999346	+	0.0361730i	$0.0115167\pi$
$397$	6.34168	+	15.3102i	0.318280	+	0.768395i	−0.681066	+	0.732222i	$0.738483\pi$
$398$	3.40194	−	0.483355i	0.170524	−	0.0242284i
$399$	1.93237			0.0967393
$400$	−11.1407	−	2.50121i	−0.557035	−	0.125060i
$401$	−9.37303	+	9.37303i	−0.468067	+	0.468067i	−0.901288	−	0.433221i	$-0.857377\pi$
$401$	−9.37303	+	9.37303i	−0.468067	+	0.468067i	0.433221	+	0.901288i	$0.357377\pi$
$402$	4.51384	+	3.39074i	0.225130	+	0.169115i
$403$	−6.94479	−	3.02250i	−0.345944	−	0.150561i
$404$	6.39696	−	5.12001i	0.318261	−	0.254730i
$405$	−4.52222	−	1.87316i	−0.224711	−	0.0930783i
$406$	14.1688	+	23.9709i	0.703185	+	1.18966i
$407$	−0.121122	−	0.121122i	−0.00600381	−	0.00600381i
$408$	−8.31723	+	8.84448i	−0.411764	+	0.437867i
$409$			35.6106i			1.76083i	0.474205	+	0.880414i	$0.342736\pi$
$409$			35.6106i			1.76083i	−0.474205	+	0.880414i	$0.657264\pi$
$410$	19.2938	−	11.4042i	0.952852	−	0.563214i
$411$	−0.692066	+	1.67080i	−0.0341371	+	0.0824143i
$412$	29.5306	+	16.2526i	1.45487	+	0.800709i
$413$	−4.13849	−	1.71422i	−0.203642	−	0.0843511i
$414$	10.7530	−	14.3147i	0.528482	−	0.703529i
$415$	13.2454			0.650190
$416$	−19.5139	+	5.93373i	−0.956746	+	0.290925i
$417$	−5.02250			−0.245953
$418$	0.0399000	−	0.0531158i	0.00195157	−	0.00259798i
$419$	−14.1804	−	5.87373i	−0.692760	−	0.286951i	0.00838968	−	0.999965i	$-0.497329\pi$
$419$	−14.1804	−	5.87373i	−0.692760	−	0.286951i	−0.701149	+	0.713014i	$0.747329\pi$
$420$	5.15813	−	9.37219i	0.251691	−	0.457316i
$421$	10.1987	−	24.6219i	0.497056	−	1.20000i	−0.454007	−	0.890998i	$-0.650006\pi$
$421$	10.1987	−	24.6219i	0.497056	−	1.20000i	0.951062	−	0.309000i	$-0.0999943\pi$
$422$	−8.74820	+	5.17091i	−0.425856	+	0.251716i
$423$		−	5.81206i		−	0.282592i
$424$	34.6629	−	1.06494i	1.68338	−	0.0517178i
$425$	−10.5060	−	10.5060i	−0.509618	−	0.509618i
$426$	−6.88806	−	11.6533i	−0.333727	−	0.564604i
$427$	−32.2383	−	13.3535i	−1.56012	−	0.646223i
$428$	−1.29059	−	1.61247i	−0.0623831	−	0.0779417i
$429$	0.242029	+	0.105335i	0.0116853	+	0.00508564i
$430$	6.16867	+	4.63383i	0.297480	+	0.223463i
$431$	−27.3112	+	27.3112i	−1.31553	+	1.31553i	−0.398263	+	0.917271i	$0.630387\pi$
$431$	−27.3112	+	27.3112i	−1.31553	+	1.31553i	−0.917271	+	0.398263i	$0.869613\pi$
$432$	14.3481	+	10.1041i	0.690321	+	0.486133i
$433$	1.48060			0.0711530			0.0355765	−	0.999367i	$-0.488673\pi$
$433$	1.48060			0.0711530			0.0355765	+	0.999367i	$0.488673\pi$
$434$	13.0242	−	1.85050i	0.625180	−	0.0888268i
$435$	−2.05542	−	4.96223i	−0.0985501	−	0.237921i
$436$	2.01753	+	2.52071i	0.0966224	+	0.120720i
$437$	−1.10504	+	2.66781i	−0.0528614	+	0.127619i
$438$	7.06461	−	4.17577i	0.337560	−	0.199526i
$439$	16.7362	+	16.7362i	0.798773	+	0.798773i	0.982902	−	0.184129i	$-0.0589464\pi$
$439$	16.7362	+	16.7362i	0.798773	+	0.798773i	−0.184129	+	0.982902i	$0.558946\pi$
$440$	−0.151111	−	0.335303i	−0.00720396	−	0.0159849i
$441$	20.6831	+	20.6831i	0.984911	+	0.984911i
$442$	−25.5836	−	7.06273i	−1.21689	−	0.335940i
$443$	6.39532	+	15.4397i	0.303851	+	0.733560i	0.999879	+	0.0155461i	$0.00494869\pi$
$443$	6.39532	+	15.4397i	0.303851	+	0.733560i	−0.696029	+	0.718014i	$0.745051\pi$
$444$	−1.53450	+	2.78814i	−0.0728240	+	0.132319i
$445$	−4.05713	+	9.79478i	−0.192326	+	0.464317i
$446$	3.48083	+	24.4987i	0.164822	+	1.16005i
$447$	−1.53487	−	1.53487i	−0.0725967	−	0.0725967i
$448$	23.4644	−	26.5398i	1.10859	−	1.25389i
$449$	−3.57167	−	3.57167i	−0.168557	−	0.168557i	0.617788	−	0.786345i	$-0.288029\pi$
$449$	−3.57167	−	3.57167i	−0.168557	−	0.168557i	−0.786345	+	0.617788i	$0.788029\pi$
$450$	−5.62482	+	7.48790i	−0.265156	+	0.352983i
$451$	−0.887363	−	0.367558i	−0.0417843	−	0.0173076i
$452$	21.8826	−	6.34637i	1.02927	−	0.298508i
$453$	10.5850	+	4.38446i	0.497328	+	0.206000i
$454$	17.9336	+	4.60904i	0.841664	+	0.216313i
$455$	23.3823	+	0.416115i	1.09618	+	0.0195078i
$456$	−1.15429	−	0.437098i	−0.0540547	−	0.0204690i
$457$	39.1564			1.83166			0.915829	−	0.401569i	$-0.131535\pi$
$457$	39.1564			1.83166			0.915829	+	0.401569i	$0.131535\pi$
$458$	16.4449	+	27.8217i	0.768421	+	1.30002i
$459$	8.73876	+	21.0972i	0.407890	+	0.984734i
$460$	9.98944	+	12.4808i	0.465760	+	0.581922i
$461$	12.3866	−	5.13069i	0.576901	−	0.238960i	−0.0751030	−	0.997176i	$-0.523929\pi$
$461$	12.3866	−	5.13069i	0.576901	−	0.238960i	0.652004	+	0.758216i	$0.273929\pi$
$462$	−0.453898	+	0.0644908i	−0.0211173	+	0.00300038i
$463$	−23.8205	−	23.8205i	−1.10703	−	1.10703i	−0.993539	−	0.113493i	$-0.963796\pi$
$463$	−23.8205	−	23.8205i	−1.10703	−	1.10703i	−0.113493	−	0.993539i	$-0.536204\pi$
$464$	−3.04149	−	17.5239i	−0.141198	−	0.813527i
$465$	−2.53746			−0.117672
$466$	−12.9920	+	1.84594i	−0.601845	+	0.0855113i
$467$	−22.4031	−	9.27965i	−1.03669	−	0.429411i	−0.201567	−	0.979475i	$-0.564603\pi$
$467$	−22.4031	−	9.27965i	−1.03669	−	0.429411i	−0.835123	+	0.550064i	$0.814603\pi$
$468$	−2.13911	+	16.5918i	−0.0988806	+	0.766957i
$469$	−8.20289	−	19.8035i	−0.378774	−	0.914442i
$470$	5.02630	+	1.29179i	0.231846	+	0.0595858i
$471$	−3.94312	+	3.94312i	−0.181689	+	0.181689i
$472$	2.08436	+	1.96010i	0.0959403	+	0.0902210i
$473$		−	0.330636i		−	0.0152027i
$474$	−1.58856	−	2.68755i	−0.0729650	−	0.123443i
$475$	0.578038	−	1.39551i	0.0265222	−	0.0640303i
$476$	44.2728	−	12.8400i	2.02924	−	0.588518i
$477$	10.8852	−	26.2792i	0.498399	−	1.20324i
$478$	−6.26444	+	0.890064i	−0.286529	+	0.0407106i
$479$	17.6355	−	17.6355i	0.805785	−	0.805785i	−0.178208	−	0.983993i	$-0.557030\pi$
$479$	17.6355	−	17.6355i	0.805785	−	0.805785i	0.983993	+	0.178208i	$0.0570299\pi$
$480$	−5.20116	+	4.43168i	−0.237400	+	0.202278i
$481$	−6.95604	−	0.123791i	−0.317168	−	0.00564437i
$482$	−14.8152	+	2.10498i	−0.674816	+	0.0958792i
$483$	18.4108	−	7.62598i	0.837718	−	0.346994i
$484$	10.6000	−	19.2600i	0.481819	−	0.875453i
$485$	−8.53079	−	20.5951i	−0.387363	−	0.935178i
$486$	19.3785	−	11.4543i	0.879028	−	0.519578i
$487$	−35.2443			−1.59707			−0.798537	−	0.601946i	$-0.794392\pi$
$487$	−35.2443			−1.59707			−0.798537	+	0.601946i	$0.794392\pi$
$488$	16.2369	+	15.2690i	0.735010	+	0.691193i
$489$			20.1594i			0.911641i
$490$	−22.4839	+	13.2898i	−1.01572	+	0.600373i
$491$	9.25922	+	22.3537i	0.417863	+	1.00881i	0.982966	+	0.183789i	$0.0588365\pi$
$491$	9.25922	+	22.3537i	0.417863	+	1.00881i	−0.565103	+	0.825020i	$0.691164\pi$
$492$	−1.96653	+	17.7363i	−0.0886578	+	0.799616i
$493$	8.85684	−	21.3823i	0.398892	−	0.963011i
$494$	−0.331960	−	2.67769i	−0.0149356	−	0.120475i
$495$	−0.301659			−0.0135586
$496$	−8.19852	−	1.84066i	−0.368124	−	0.0826479i
$497$			51.3972i			2.30548i
$498$	−6.33415	+	8.43218i	−0.283840	+	0.377855i
$499$	−11.0548	−	26.6886i	−0.494880	−	1.19475i	−0.952209	−	0.305448i	$-0.901194\pi$
$499$	−11.0548	−	26.6886i	−0.494880	−	1.19475i	0.457329	−	0.889297i	$-0.348806\pi$
$500$	−14.3783	−	17.9643i	−0.643016	−	0.803387i
$501$	1.83789	−	4.43706i	0.0821109	−	0.198233i
$502$	−29.6800	−	7.62795i	−1.32468	−	0.340452i
$503$	−19.4771	+	19.4771i	−0.868439	+	0.868439i	−0.992300	−	0.123861i	$-0.960472\pi$
$503$	−19.4771	+	19.4771i	−0.868439	+	0.868439i	0.123861	+	0.992300i	$0.460472\pi$
$504$	−11.9384	−	26.4902i	−0.531778	−	1.17997i
$505$	6.00082			0.267033
$506$	0.170531	−	0.663528i	0.00758102	−	0.0294974i
$507$	10.0444	−	3.74764i	0.446087	−	0.166439i
$508$	2.18276	+	7.52628i	0.0968445	+	0.333925i
$509$	1.98303	+	4.78746i	0.0878963	+	0.212200i	0.961715	−	0.274051i	$-0.0883638\pi$
$509$	1.98303	+	4.78746i	0.0878963	+	0.212200i	−0.873819	+	0.486252i	$0.838364\pi$
$510$	−8.80328	+	1.25079i	−0.389816	+	0.0553858i
$511$	−31.1587			−1.37838
$512$	−20.0196	+	10.5458i	−0.884750	+	0.466065i
$513$	−1.64156	+	1.64156i	−0.0724769	+	0.0724769i
$514$	−23.0652	+	30.7050i	−1.01736	+	1.35434i
$515$	9.44717	+	22.8075i	0.416292	+	1.00502i
$516$	−5.89991	+	1.71108i	−0.259729	+	0.0753263i
$517$	−0.0851096	−	0.205473i	−0.00374312	−	0.00903668i
$518$	10.4023	−	6.14859i	0.457049	−	0.270154i
$519$	−13.7993	+	13.7993i	−0.605721	+	0.605721i
$520$	−13.8732	−	5.53761i	−0.608381	−	0.242840i
$521$	−9.54267	−	9.54267i	−0.418072	−	0.418072i	0.466467	−	0.884539i	$-0.345527\pi$
$521$	−9.54267	−	9.54267i	−0.418072	−	0.418072i	−0.884539	+	0.466467i	$0.845527\pi$
$522$	−14.1291	−	3.63126i	−0.618412	−	0.158936i
$523$	30.4823	−	12.6262i	1.33290	−	0.552104i	0.401417	−	0.915896i	$-0.368518\pi$
$523$	30.4823	−	12.6262i	1.33290	−	0.552104i	0.931480	+	0.363792i	$0.118518\pi$
$524$	3.76450	−	33.9525i	0.164453	−	1.48322i
$525$	−9.63051	+	3.98909i	−0.420310	+	0.174098i
$526$	2.30380	+	16.2146i	0.100450	+	0.706988i
$527$	−7.73147	−	7.73147i	−0.336788	−	0.336788i
$528$	0.285722	+	0.0641478i	0.0124345	+	0.00279167i
$529$			6.77873i			0.294727i
$530$	20.3070	+	15.2544i	0.882081	+	0.662608i
$531$	2.16817	−	0.898083i	0.0940903	−	0.0389735i
$532$	2.92841	+	3.65876i	0.126963	+	0.158628i
$533$	−36.3005	+	14.2849i	−1.57235	+	0.618746i
$534$	−4.29530	−	7.26684i	−0.185876	−	0.314467i
$535$		−	1.51261i		−	0.0653960i
$536$	0.420441	+	13.6851i	0.0181603	+	0.591104i
$537$	11.1766	+	11.1766i	0.482307	+	0.482307i
$538$	11.4253	+	19.3295i	0.492581	+	0.833355i
$539$	1.03408	+	0.428331i	0.0445411	+	0.0184495i
$540$	3.57989	+	12.3437i	0.154054	+	0.531186i
$541$	−9.10140	+	3.76992i	−0.391300	+	0.162082i	−0.569654	−	0.821885i	$-0.692923\pi$
$541$	−9.10140	+	3.76992i	−0.391300	+	0.162082i	0.178354	+	0.983966i	$0.442923\pi$
$542$	−4.77008	−	33.5727i	−0.204892	−	1.44207i
$543$	17.8981			0.768081
$544$	−29.3506	−	2.34455i	−1.25840	−	0.100522i
$545$			2.36461i			0.101289i
$546$	−11.4467	+	14.6865i	−0.489874	+	0.628524i
$547$	−2.79092	−	1.15604i	−0.119331	−	0.0494286i	0.322219	−	0.946665i	$-0.395571\pi$
$547$	−2.79092	−	1.15604i	−0.119331	−	0.0494286i	−0.441550	+	0.897237i	$0.645571\pi$
$548$	−4.21230	+	1.22165i	−0.179940	+	0.0521861i
$549$	16.8897	−	6.99596i	0.720837	−	0.298580i
$550$	−0.0892032	+	0.347086i	−0.00380364	+	0.0147998i
$551$	2.35289			0.100237
$552$	−12.7226	+	0.390871i	−0.541509	+	0.0166366i
$553$			11.8535i			0.504062i
$554$	24.6136	+	6.32584i	1.04573	+	0.268759i
$555$	−2.15338	+	0.891958i	−0.0914058	+	0.0378615i
$556$	−7.61137	−	9.50967i	−0.322794	−	0.403300i
$557$	−2.55398	−	6.16585i	−0.108216	−	0.261255i	0.860490	−	0.509467i	$-0.170157\pi$
$557$	−2.55398	−	6.16585i	−0.108216	−	0.261255i	−0.968706	+	0.248211i	$0.920157\pi$
$558$	−4.13934	+	5.51040i	−0.175232	+	0.233274i
$559$	−9.32523	−	9.66315i	−0.394415	−	0.408708i
$560$	25.5623	−	4.43665i	1.08020	−	0.187483i
$561$	0.269446	+	0.269446i	0.0113760	+	0.0113760i
$562$	−14.6831	−	11.0298i	−0.619370	−	0.465263i
$563$	−21.1106	−	8.74428i	−0.889704	−	0.368528i	−0.109452	−	0.993992i	$-0.534910\pi$
$563$	−21.1106	−	8.74428i	−0.889704	−	0.368528i	−0.780253	+	0.625464i	$0.784910\pi$
$564$	−3.22603	+	2.58205i	−0.135840	+	0.108724i
$565$	15.4165	+	6.38572i	0.648576	+	0.268649i
$566$	−39.5451	−	10.1633i	−1.66220	−	0.427197i
$567$	−14.7977			−0.621444
$568$	11.6260	−	30.7019i	0.487815	−	1.28822i
$569$	9.41072	+	9.41072i	0.394518	+	0.394518i	0.876294	−	0.481776i	$-0.160008\pi$
$569$	9.41072	+	9.41072i	0.394518	+	0.394518i	−0.481776	+	0.876294i	$0.660008\pi$
$570$	−0.459969	−	0.778181i	−0.0192660	−	0.0325944i
$571$	−2.24706	+	0.930764i	−0.0940367	+	0.0389513i	−0.429206	−	0.903207i	$-0.641207\pi$
$571$	−2.24706	+	0.930764i	−0.0940367	+	0.0389513i	0.335169	+	0.942158i	$0.391207\pi$
$572$	0.167340	+	0.617892i	0.00699685	+	0.0258353i
$573$	0.438637	−	1.05896i	0.0183243	−	0.0442388i
$574$	40.6942	−	54.1731i	1.69854	−	2.26114i
$575$		−	15.5770i		−	0.649606i
$576$	1.13931	+	18.5243i	0.0474711	+	0.771846i
$577$	−4.32632	+	4.32632i	−0.180107	+	0.180107i	−0.791402	−	0.611295i	$-0.790649\pi$
$577$	−4.32632	+	4.32632i	−0.180107	+	0.180107i	0.611295	+	0.791402i	$0.290649\pi$
$578$	−11.4117	−	8.57232i	−0.474664	−	0.356562i
$579$	5.35129	+	12.9192i	0.222392	+	0.536902i
$580$	6.28065	−	11.4118i	0.260790	−	0.473849i
$581$	36.9945	−	15.3236i	1.53479	−	0.635730i
$582$	17.1907	+	4.41812i	0.712578	+	0.183137i
$583$		−	1.08844i		−	0.0450787i
$584$	18.6125	+	7.04804i	0.770192	+	0.291650i
$585$	−8.81626	+	8.50795i	−0.364507	+	0.351761i
$586$	1.98430	+	3.35707i	0.0819707	+	0.138679i
$587$	2.63033	−	6.35017i	0.108565	−	0.262100i	−0.860255	−	0.509864i	$-0.829696\pi$
$587$	2.63033	−	6.35017i	0.108565	−	0.262100i	0.968820	+	0.247764i	$0.0796958\pi$
$588$	2.29168	−	20.6690i	0.0945072	−	0.852373i
$589$	0.425383	−	1.02696i	0.0175276	−	0.0423153i
$590$	0.294770	+	2.07465i	0.0121355	+	0.0854118i
$591$	−14.3762	+	14.3762i	−0.591359	+	0.591359i
$592$	−7.60456	+	1.31986i	−0.312546	+	0.0542461i
$593$	−5.38876	+	5.38876i	−0.221290	+	0.221290i	−0.809041	−	0.587752i	$-0.800013\pi$
$593$	−5.38876	+	5.38876i	−0.221290	+	0.221290i	0.587752	+	0.809041i	$0.300013\pi$
$594$	0.330806	−	0.440377i	0.0135731	−	0.0180689i
$595$	31.1906	+	12.9196i	1.27869	+	0.529650i
$596$	0.580117	−	5.23215i	0.0237625	−	0.214317i
$597$	−1.85118	+	0.766785i	−0.0757639	+	0.0313824i
$598$	−13.7302	−	24.2019i	−0.561468	−	0.989687i
$599$	−20.7593	+	20.7593i	−0.848201	+	0.848201i	−0.989909	−	0.141707i	$-0.954741\pi$
$599$	−20.7593	+	20.7593i	−0.848201	+	0.848201i	0.141707	+	0.989909i	$0.454741\pi$
$600$	6.65508	−	0.204461i	0.271692	−	0.00834710i
$601$	−24.2621	+	24.2621i	−0.989673	+	0.989673i	−0.999947	−	0.0102740i	$-0.996730\pi$
$601$	−24.2621	+	24.2621i	−0.989673	+	0.989673i	0.0102740	+	0.999947i	$0.496730\pi$
$602$	22.5900	+	5.80578i	0.920701	+	0.236626i
$603$	10.3751	+	4.29752i	0.422508	+	0.175009i
$604$	7.73951	+	26.6862i	0.314916	+	1.08585i
$605$	14.8751	−	6.16148i	0.604760	−	0.250500i
$606$	−2.86969	+	3.82020i	−0.116573	+	0.155185i
$607$		−	16.2739i		−	0.660539i	−0.943887	−	0.330270i	$-0.892860\pi$
$607$		−	16.2739i		−	0.660539i	0.943887	−	0.330270i	$-0.107140\pi$
$608$	−0.921668	−	2.84795i	−0.0373786	−	0.115500i
$609$	−11.4816	−	11.4816i	−0.465260	−	0.465260i
$610$	2.29622	+	16.1612i	0.0929713	+	0.654350i
$611$	−8.28254	−	3.60471i	−0.335076	−	0.145831i
$612$	−11.6445	+	21.1577i	−0.470700	+	0.855251i
$613$	−1.47246	+	3.55482i	−0.0594720	+	0.143578i	−0.950822	−	0.309737i	$-0.899759\pi$
$613$	−1.47246	+	3.55482i	−0.0594720	+	0.143578i	0.891350	+	0.453315i	$0.149759\pi$
$614$	−1.52590	−	0.392166i	−0.0615803	−	0.0158265i
$615$	−9.24137	+	9.24137i	−0.372648	+	0.372648i
$616$	−0.809969	−	0.761684i	−0.0326346	−	0.0306891i
$617$	11.3506			0.456960			0.228480	−	0.973549i	$-0.426624\pi$
$617$	11.3506			0.456960			0.228480	+	0.973549i	$0.426624\pi$
$618$	−19.0373	−	4.89271i	−0.765794	−	0.196814i
$619$	16.6465	+	6.89520i	0.669079	+	0.277141i	0.691253	−	0.722613i	$-0.257059\pi$
$619$	16.6465	+	6.89520i	0.669079	+	0.277141i	−0.0221745	+	0.999754i	$0.507059\pi$
$620$	−3.84541	−	4.80446i	−0.154435	−	0.192952i
$621$	−9.16177	+	22.1185i	−0.367649	+	0.887584i
$622$	6.69192	+	47.0990i	0.268321	+	1.88850i
$623$			32.0506i			1.28408i
$624$	10.1597	−	6.18370i	0.406714	−	0.247546i
$625$		−	2.57928i		−	0.103171i
$626$	−9.52260	+	1.35299i	−0.380600	+	0.0540764i
$627$	−0.0148248	+	0.0357902i	−0.000592045	+	0.00142932i
$628$	−13.4416	−	1.49034i	−0.536377	−	0.0594710i
$629$	−9.27892	−	3.84346i	−0.369975	−	0.153249i
$630$	5.29695	−	20.6102i	0.211035	−	0.821130i
$631$	23.9623			0.953925			0.476962	−	0.878924i	$-0.341738\pi$
$631$	23.9623			0.953925			0.476962	+	0.878924i	$0.341738\pi$
$632$	2.68124	−	7.08065i	0.106654	−	0.281653i
$633$	4.19023	−	4.19023i	0.166547	−	0.166547i
$634$	−1.72308	+	6.70444i	−0.0684323	+	0.266267i
$635$	−2.19630	+	5.30233i	−0.0871574	+	0.210416i
$636$	−19.4223	+	5.63283i	−0.770144	+	0.223356i
$637$	42.3026	−	16.6468i	1.67609	−	0.659570i
$638$	−0.552677	+	0.0785255i	−0.0218807	+	0.00310885i
$639$	−19.0404	−	19.0404i	−0.753225	−	0.753225i
$640$	−16.2731	−	3.13194i	−0.643252	−	0.123801i
$641$		−	22.0173i		−	0.869631i	−0.900519	−	0.434816i	$-0.856814\pi$
$641$		−	22.0173i		−	0.869631i	0.900519	−	0.434816i	$-0.143186\pi$
$642$	0.962950	+	0.723356i	0.0380046	+	0.0285486i
$643$	41.1722	−	17.0541i	1.62367	−	0.672547i	0.629171	−	0.777267i	$-0.283394\pi$
$643$	41.1722	−	17.0541i	1.62367	−	0.672547i	0.994502	+	0.104719i	$0.0333945\pi$
$644$	42.3397	+	23.3023i	1.66842	+	0.918240i
$645$	−4.15654	−	1.72169i	−0.163663	−	0.0677916i
$646$	0.969570	−	3.77255i	0.0381472	−	0.148429i
$647$	0.290186	−	0.290186i	0.0114084	−	0.0114084i	−0.701380	−	0.712788i	$-0.747432\pi$
$647$	0.290186	−	0.290186i	0.0114084	−	0.0114084i	0.712788	+	0.701380i	$0.247432\pi$
$648$	8.83934	+	3.34721i	0.347242	+	0.131491i
$649$	0.0634996	−	0.0634996i	0.00249258	−	0.00249258i
$650$	7.18213	+	12.6598i	0.281706	+	0.496558i
$651$	−7.08716	+	2.93560i	−0.277768	+	0.115055i
$652$	−38.1701	+	30.5507i	−1.49486	+	1.19646i
$653$	4.74963	+	1.96736i	0.185867	+	0.0769888i	0.473676	−	0.880699i	$-0.342927\pi$
$653$	4.74963	+	1.96736i	0.185867	+	0.0769888i	−0.287809	+	0.957688i	$0.592927\pi$
$654$	−1.50534	−	1.13080i	−0.0588636	−	0.0442176i
$655$	17.6907	−	17.6907i	0.691231	−	0.691231i
$656$	−36.5624	+	23.1552i	−1.42752	+	0.904057i
$657$	11.5429	−	11.5429i	0.450331	−	0.450331i
$658$	15.5330	−	2.20696i	0.605538	−	0.0860361i
$659$	19.1384	−	46.2042i	0.745526	−	1.79986i	0.163766	−	0.986499i	$-0.447636\pi$
$659$	19.1384	−	46.2042i	0.745526	−	1.79986i	0.581761	−	0.813360i	$-0.302364\pi$
$660$	0.134014	+	0.167438i	0.00521650	+	0.00651751i
$661$	4.38987	−	10.5981i	0.170746	−	0.412217i	−0.815223	−	0.579148i	$-0.803385\pi$
$661$	4.38987	−	10.5981i	0.170746	−	0.412217i	0.985969	+	0.166930i	$0.0533855\pi$
$662$	−25.6518	+	15.1623i	−0.996986	+	0.589301i
$663$	15.4742	+	0.275381i	0.600968	+	0.0106949i
$664$	−25.5647	+	0.785414i	−0.992103	+	0.0304800i
$665$			3.43219i			0.133095i
$666$	−1.57580	+	6.13135i	−0.0610608	+	0.237585i
$667$	22.4174	−	9.28557i	0.868003	−	0.359539i
$668$	11.1864	−	3.24427i	0.432815	−	0.125525i
$669$	−5.52192	−	13.3311i	−0.213490	−	0.515410i
$670$	−6.02249	+	8.01729i	−0.232669	+	0.309735i
$671$	0.494654	−	0.494654i	0.0190959	−	0.0190959i
$672$	−9.39987	+	18.3950i	−0.362608	+	0.709602i
$673$			26.0684i			1.00486i	0.864617	+	0.502432i	$0.167561\pi$
$673$			26.0684i			1.00486i	−0.864617	+	0.502432i	$0.832439\pi$
$674$	12.4750	+	9.37104i	0.480518	+	0.360959i
$675$	4.79244	−	11.5700i	0.184461	−	0.445329i
$676$	22.3176	+	13.3388i	0.858370	+	0.513031i
$677$	−45.7110	+	18.9341i	−1.75682	+	0.727697i	−0.759830	+	0.650122i	$0.774718\pi$
$677$	−45.7110	+	18.9341i	−1.75682	+	0.727697i	−0.996986	+	0.0775757i	$0.975282\pi$
$678$	−11.4376	+	6.76059i	−0.439260	+	0.259639i
$679$	−47.6532	−	47.6532i	−1.82876	−	1.82876i
$680$	−15.7092	−	14.7727i	−0.602420	−	0.566508i
$681$	−10.7975			−0.413761
$682$	−0.0656453	+	0.255423i	−0.00251369	+	0.00978065i
$683$	−9.00430	−	3.72970i	−0.344540	−	0.142713i	0.203702	−	0.979033i	$-0.434703\pi$
$683$	−9.00430	−	3.72970i	−0.344540	−	0.142713i	−0.548242	+	0.836320i	$0.684703\pi$
$684$	−2.44025	−	0.270564i	−0.0933054	−	0.0103453i
$685$	−2.96760	−	1.22922i	−0.113386	−	0.0469661i
$686$	−21.0943	+	28.0812i	−0.805383	+	1.07215i
$687$	−13.3261	−	13.3261i	−0.508423	−	0.508423i
$688$	−12.1808	−	8.57789i	−0.464389	−	0.327029i
$689$	−30.6983	−	31.8107i	−1.16951	−	1.21189i
$690$	−7.45343	−	5.59893i	−0.283747	−	0.213148i
$691$	15.8264	+	38.2082i	0.602064	+	1.45351i	0.871453	+	0.490479i	$0.163178\pi$
$691$	15.8264	+	38.2082i	0.602064	+	1.45351i	−0.269390	+	0.963031i	$0.586822\pi$
$692$	−47.0399	−	5.21556i	−1.78819	−	0.198266i
$693$	−0.842536	+	0.348990i	−0.0320053	+	0.0132570i
$694$	6.90871	−	26.8815i	0.262251	−	1.02041i
$695$		−	8.92076i		−	0.338384i
$696$	4.26139	+	9.45565i	0.161528	+	0.358415i
$697$	−56.3156			−2.13311
$698$	26.3877	+	6.78180i	0.998789	+	0.256695i
$699$	7.06968	−	2.92836i	0.267400	−	0.110761i
$700$	−22.1476	−	12.1892i	−0.837099	−	0.460710i
$701$	−29.7671	−	12.3299i	−1.12429	−	0.465695i	−0.258452	−	0.966024i	$-0.583212\pi$
$701$	−29.7671	−	12.3299i	−1.12429	−	0.465695i	−0.865835	+	0.500329i	$0.833212\pi$
$702$	−2.75224	−	22.2004i	−0.103877	−	0.837901i
$703$		−	1.02105i		−	0.0385095i
$704$	0.311540	+	0.638203i	0.0117416	+	0.0240532i
$705$	−3.02625			−0.113975
$706$	20.7952	−	2.95462i	0.782638	−	0.111199i
$707$	16.7603	−	6.94236i	0.630338	−	0.261094i
$708$	−1.46171	−	0.804475i	−0.0549345	−	0.0302340i
$709$	39.2898	+	16.2744i	1.47556	+	0.611196i	0.968119	−	0.250492i	$-0.0805922\pi$
$709$	39.2898	+	16.2744i	1.47556	+	0.611196i	0.507439	+	0.861688i	$0.330592\pi$
$710$	20.6981	−	12.2343i	0.776786	−	0.459144i
$711$	−4.39119	−	4.39119i	−0.164683	−	0.164683i
$712$	7.24980	−	19.1453i	0.271698	−	0.717501i
$713$		−	11.4632i		−	0.429301i
$714$	−23.1406	+	13.6780i	−0.866015	+	0.511886i
$715$	−0.187092	+	0.429882i	−0.00699686	+	0.0160767i
$716$	−4.22430	+	38.0996i	−0.157870	+	1.42385i
$717$	3.40882	−	1.41198i	0.127305	−	0.0527314i
$718$	21.0716	−	28.0510i	0.786385	−	1.04686i
$719$			3.70520i			0.138181i	0.997610	+	0.0690903i	$0.0220097\pi$
$719$			3.70520i			0.138181i	−0.997610	+	0.0690903i	$0.977990\pi$
$720$	−7.82611	+	11.1133i	−0.291662	+	0.414167i
$721$	52.7721	+	52.7721i	1.96534	+	1.96534i
$722$	−26.2108	+	3.72409i	−0.975466	+	0.138596i
$723$	8.06178	−	3.33930i	0.299821	−	0.124190i
$724$	27.1237	+	33.8885i	1.00804	+	1.25945i
$725$	−11.7263	+	4.85720i	−0.435505	+	0.180392i
$726$	−3.19104	+	12.4162i	−0.118431	+	0.460809i
$727$	−8.45304	−	8.45304i	−0.313506	−	0.313506i	0.532760	−	0.846266i	$-0.321155\pi$
$727$	−8.45304	−	8.45304i	−0.313506	−	0.313506i	−0.846266	+	0.532760i	$0.821155\pi$
$728$	−45.1545	+	0.583369i	−1.67354	+	0.0216211i
$729$	−2.19307	+	2.19307i	−0.0812247	+	0.0812247i
$730$	7.41682	+	12.5479i	0.274509	+	0.464417i
$731$	−7.41879	−	17.9105i	−0.274394	−	0.662446i
$732$	−11.3866	−	6.26676i	−0.420859	−	0.231626i
$733$	4.15509	+	10.0313i	0.153472	+	0.370513i	0.981851	−	0.189654i	$-0.0607367\pi$
$733$	4.15509	+	10.0313i	0.153472	+	0.370513i	−0.828379	+	0.560168i	$0.810737\pi$
$734$	−20.5826	−	15.4614i	−0.759718	−	0.570691i
$735$	10.7694	−	10.7694i	0.397234	−	0.397234i
$736$	−20.0206	−	23.4967i	−0.737967	−	0.866101i
$737$	0.429721			0.0158290
$738$	4.99334	+	35.1441i	0.183807	+	1.29367i
$739$	−2.58772	−	6.24731i	−0.0951909	−	0.229811i	0.869111	−	0.494618i	$-0.164692\pi$
$739$	−2.58772	−	6.24731i	−0.0951909	−	0.229811i	−0.964302	+	0.264807i	$0.914692\pi$
$740$	−4.95218	−	2.72551i	−0.182046	−	0.100192i
$741$	0.576155	+	1.46412i	0.0211656	+	0.0537857i
$742$	74.3656	+	19.1124i	2.73005	+	0.701639i
$743$	34.5815			1.26867			0.634336	−	0.773057i	$-0.281273\pi$
$743$	34.5815			1.26867			0.634336	+	0.773057i	$0.281273\pi$
$744$	4.89752	−	0.150465i	0.179552	−	0.00551630i
$745$	2.72617	−	2.72617i	0.0998791	−	0.0998791i
$746$	4.93060	−	19.1847i	0.180522	−	0.702403i
$747$	−8.02808	+	19.3815i	−0.293732	+	0.709132i
$748$	−0.101839	+	0.918503i	−0.00372362	+	0.0335838i
$749$	−1.74995	−	4.22475i	−0.0639417	−	0.154369i
$750$	10.7281	+	8.05880i	0.391734	+	0.294266i
$751$			51.8570i			1.89229i	0.323746	+	0.946144i	$0.395058\pi$
$751$			51.8570i			1.89229i	−0.323746	+	0.946144i	$0.604942\pi$
$752$	−9.77778	−	2.19522i	−0.356559	−	0.0800513i
$753$	17.8698			0.651213
$754$	−13.9378	+	17.8826i	−0.507584	+	0.651247i
$755$	−7.78749	+	18.8007i	−0.283416	+	0.684227i
$756$	24.2791	+	30.3344i	0.883021	+	1.10325i
$757$	−1.37725	−	3.32498i	−0.0500570	−	0.120848i	0.896873	−	0.442288i	$-0.145833\pi$
$757$	−1.37725	−	3.32498i	−0.0500570	−	0.120848i	−0.946930	+	0.321440i	$0.895833\pi$
$758$	10.0875	+	17.0661i	0.366394	+	0.619869i
$759$			0.399499i			0.0145009i
$760$	0.776356	−	2.05021i	0.0281614	−	0.0743688i
$761$	−12.5408			−0.454605			−0.227303	−	0.973824i	$-0.572991\pi$
$761$	−12.5408			−0.454605			−0.227303	+	0.973824i	$0.572991\pi$
$762$	−2.32523	−	3.93385i	−0.0842341	−	0.142508i
$763$	2.73563	+	6.60439i	0.0990364	+	0.239095i
$764$	2.66979	−	0.774288i	0.0965895	−	0.0280128i
$765$	−16.3408	+	6.76860i	−0.590804	+	0.244719i
$766$	−1.31911	−	9.28417i	−0.0476615	−	0.335451i
$767$	0.0648984	−	3.64677i	0.00234335	−	0.131677i
$768$	9.77590	−	8.86194i	0.352757	−	0.319778i
$769$	−23.2047	+

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)

\(f(q)\)	\(=\)	\(q+(-1.13073 - 0.849387i) q^{2} +(0.761899 + 0.315589i) q^{3} +(0.557082 + 1.92085i) q^{4} +(-0.560536 + 1.35325i) q^{5} +(-0.593442 - 1.00399i) q^{6} +4.42814i q^{7} +(1.00164 - 2.64513i) q^{8} +(-1.64043 - 1.64043i) q^{9} +O(q^{10})\)	\(q+(-1.13073 - 0.849387i) q^{2} +(0.761899 + 0.315589i) q^{3} +(0.557082 + 1.92085i) q^{4} +(-0.560536 + 1.35325i) q^{5} +(-0.593442 - 1.00399i) q^{6} +4.42814i q^{7} +(1.00164 - 2.64513i) q^{8} +(-1.64043 - 1.64043i) q^{9} +(1.78325 - 1.05405i) q^{10} +(-0.0820155 - 0.0339719i) q^{11} +(-0.181758 + 1.63930i) q^{12} +(-3.35512 + 1.32030i) q^{13} +(3.76120 - 5.00701i) q^{14} +(-0.854144 + 0.854144i) q^{15} +(-3.37932 + 2.14014i) q^{16} -5.20503 q^{17} +(0.461515 + 3.24823i) q^{18} +(-0.202500 - 0.488879i) q^{19} +(-2.91166 - 0.322831i) q^{20} +(-1.39747 + 3.37379i) q^{21} +(0.0638817 + 0.108076i) q^{22} +(-3.85867 - 3.85867i) q^{23} +(1.59792 - 1.69922i) q^{24} +(2.01844 + 2.01844i) q^{25} +(4.91516 + 1.35690i) q^{26} +(-1.67891 - 4.05324i) q^{27} +(-8.50578 + 2.46684i) q^{28} +(-1.70159 + 4.10801i) q^{29} +(1.69130 - 0.240303i) q^{30} +(1.48538 + 1.48538i) q^{31} +(5.63889 + 0.450439i) q^{32} +(-0.0517664 - 0.0517664i) q^{33} +(5.88546 + 4.42109i) q^{34} +(-5.99239 - 2.48213i) q^{35} +(2.23716 - 4.06486i) q^{36} +(1.78268 + 0.738412i) q^{37} +(-0.186275 + 0.724790i) q^{38} +(-2.97293 - 0.0529068i) q^{39} +(3.01808 + 2.83816i) q^{40} +10.8195 q^{41} +(4.44581 - 2.62784i) q^{42} +(1.42531 + 3.44101i) q^{43} +(0.0195656 - 0.176464i) q^{44} +(3.13943 - 1.30039i) q^{45} +(1.08559 + 7.64061i) q^{46} +(1.77151 + 1.77151i) q^{47} +(-3.25011 + 0.564096i) q^{48} -12.6084 q^{49} +(-0.567865 - 3.99674i) q^{50} +(-3.96571 - 1.64265i) q^{51} +(-4.40516 - 5.70916i) q^{52} +(4.69207 + 11.3277i) q^{53} +(-1.54439 + 6.00914i) q^{54} +(0.0919452 - 0.0919452i) q^{55} +(11.7130 + 4.43539i) q^{56} -0.436384i q^{57} +(5.41332 - 3.19972i) q^{58} +(-0.387119 + 0.934589i) q^{59} +(-2.11651 - 1.16485i) q^{60} +(-3.01561 + 7.28034i) q^{61} +(-0.417896 - 2.94123i) q^{62} +(7.26403 - 7.26403i) q^{63} +(-5.99344 - 5.29893i) q^{64} +(0.0939708 - 5.28040i) q^{65} +(0.0145639 + 0.102503i) q^{66} +(-4.47221 + 1.85245i) q^{67} +(-2.89963 - 9.99808i) q^{68} +(-1.72217 - 4.15768i) q^{69} +(4.66746 + 7.89647i) q^{70} +11.6070 q^{71} +(-5.98226 + 2.69603i) q^{72} +7.03652i q^{73} +(-1.38853 - 2.34913i) q^{74} +(0.900850 + 2.17484i) q^{75} +(0.826254 - 0.661319i) q^{76} +(0.150432 - 0.363176i) q^{77} +(3.31663 + 2.58499i) q^{78} +2.67686 q^{79} +(-1.00192 - 5.77270i) q^{80} +3.34174i q^{81} +(-12.2338 - 9.18991i) q^{82} +(-3.46051 - 8.35441i) q^{83} +(-7.25905 - 0.804850i) q^{84} +(2.91761 - 7.04373i) q^{85} +(1.31111 - 5.10148i) q^{86} +(-2.59288 + 2.59288i) q^{87} +(-0.172010 + 0.182914i) q^{88} +7.23795 q^{89} +(-4.65437 - 1.19620i) q^{90} +(-5.84645 - 14.8569i) q^{91} +(5.26233 - 9.56153i) q^{92} +(0.662942 + 1.60048i) q^{93} +(-0.498394 - 3.50779i) q^{94} +0.775086 q^{95} +(4.15411 + 2.12276i) q^{96} +(-10.7614 + 10.7614i) q^{97} +(14.2566 + 10.7094i) q^{98} +(0.0788119 + 0.190269i) 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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