LMFDB - Embedded newform 416.2.bd.a.83.3

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			83.3
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41176 - 0.0832778i) q^{2} +(-2.32196 - 0.961788i) q^{3} +(1.98613 + 0.235136i) q^{4} +(0.932501 - 2.25126i) q^{5} +(3.19796 + 1.55118i) q^{6} +4.08128i q^{7} +(-2.78436 - 0.497357i) q^{8} +(2.34515 + 2.34515i) q^{9} +O(q^{10})$	\(q+(-1.41176 - 0.0832778i) q^{2} +(-2.32196 - 0.961788i) q^{3} +(1.98613 + 0.235136i) q^{4} +(0.932501 - 2.25126i) q^{5} +(3.19796 + 1.55118i) q^{6} +4.08128i q^{7} +(-2.78436 - 0.497357i) q^{8} +(2.34515 + 2.34515i) q^{9} +(-1.50395 + 3.10058i) q^{10} +(-5.01361 - 2.07671i) q^{11} +(-4.38557 - 2.45621i) q^{12} +(3.14807 + 1.75774i) q^{13} +(0.339880 - 5.76179i) q^{14} +(-4.33046 + 4.33046i) q^{15} +(3.88942 + 0.934023i) q^{16} -5.02884 q^{17} +(-3.11549 - 3.50609i) q^{18} +(-0.314391 - 0.759008i) q^{19} +(2.38142 - 4.25202i) q^{20} +(3.92533 - 9.47658i) q^{21} +(6.90507 + 3.34933i) q^{22} +(5.64225 + 5.64225i) q^{23} +(5.98682 + 3.83280i) q^{24} +(-0.663064 - 0.663064i) q^{25} +(-4.29794 - 2.74366i) q^{26} +(-0.304446 - 0.734999i) q^{27} +(-0.959658 + 8.10595i) q^{28} +(-1.61354 + 3.89544i) q^{29} +(6.47420 - 5.75294i) q^{30} +(0.191640 + 0.191640i) q^{31} +(-5.41314 - 1.64252i) q^{32} +(9.64406 + 9.64406i) q^{33} +(7.09952 + 0.418791i) q^{34} +(9.18801 + 3.80580i) q^{35} +(4.10634 + 5.20920i) q^{36} +(4.82258 + 1.99758i) q^{37} +(0.380636 + 1.09772i) q^{38} +(-5.61914 - 7.10917i) q^{39} +(-3.71609 + 5.80451i) q^{40} +4.38078 q^{41} +(-6.33081 + 13.0518i) q^{42} +(-0.182517 - 0.440634i) q^{43} +(-9.46937 - 5.30349i) q^{44} +(7.46639 - 3.09268i) q^{45} +(-7.49562 - 8.43537i) q^{46} +(6.13062 + 6.13062i) q^{47} +(-8.13276 - 5.90956i) q^{48} -9.65685 q^{49} +(0.880869 + 0.991306i) q^{50} +(11.6768 + 4.83668i) q^{51} +(5.83917 + 4.23132i) q^{52} +(3.34267 + 8.06993i) q^{53} +(0.368596 + 1.06300i) q^{54} +(-9.35039 + 9.35039i) q^{55} +(2.02985 - 11.3637i) q^{56} +2.06476i q^{57} +(2.60234 - 5.36505i) q^{58} +(-0.901922 + 2.17743i) q^{59} +(-9.61911 + 7.58261i) q^{60} +(0.967064 - 2.33470i) q^{61} +(-0.254590 - 0.286509i) q^{62} +(-9.57121 + 9.57121i) q^{63} +(7.50527 + 2.76964i) q^{64} +(6.89270 - 5.44803i) q^{65} +(-12.8120 - 14.4182i) q^{66} +(1.21542 - 0.503443i) q^{67} +(-9.98793 - 1.18246i) q^{68} +(-7.67444 - 18.5277i) q^{69} +(-12.6543 - 6.13803i) q^{70} -1.22794 q^{71} +(-5.36335 - 7.69611i) q^{72} -4.96133i q^{73} +(-6.64197 - 3.22171i) q^{74} +(0.901883 + 2.17734i) q^{75} +(-0.445952 - 1.58141i) q^{76} +(8.47562 - 20.4620i) q^{77} +(7.34083 + 10.5044i) q^{78} +3.63284 q^{79} +(5.72961 - 7.88511i) q^{80} -7.95017i q^{81} +(-6.18461 - 0.364822i) q^{82} +(-1.66391 - 4.01702i) q^{83} +(10.0245 - 17.8987i) q^{84} +(-4.68940 + 11.3212i) q^{85} +(0.220975 + 0.637269i) q^{86} +(7.49317 - 7.49317i) q^{87} +(12.9268 + 8.27584i) q^{88} -5.69815 q^{89} +(-10.7983 + 3.74433i) q^{90} +(-7.17381 + 12.8482i) q^{91} +(9.87954 + 12.5329i) q^{92} +(-0.260663 - 0.629297i) q^{93} +(-8.14441 - 9.16550i) q^{94} -2.00189 q^{95} +(10.9894 + 9.02016i) q^{96} +(-6.00369 + 6.00369i) q^{97} +(13.6332 + 0.804201i) q^{98} +(-6.88748 - 16.6279i) 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 $

$2$	−1.41176	−	0.0832778i	−0.998265	−	0.0588863i
$2$	−1.41176	−	0.0832778i	−0.998265	−	0.0588863i
$3$	−2.32196	−	0.961788i	−1.34059	−	0.555289i	−0.406929	−	0.913460i	$-0.633400\pi$
$3$	−2.32196	−	0.961788i	−1.34059	−	0.555289i	−0.933656	+	0.358171i	$0.883400\pi$
$4$	1.98613	+	0.235136i	0.993065	+	0.117568i
$5$	0.932501	−	2.25126i	0.417027	−	1.00679i	−0.566177	−	0.824284i	$-0.691578\pi$
$5$	0.932501	−	2.25126i	0.417027	−	1.00679i	0.983204	−	0.182509i	$-0.0584218\pi$
$6$	3.19796	+	1.55118i	1.30556	+	0.633267i
$7$			4.08128i			1.54258i	0.636484	+	0.771290i	$0.280388\pi$
$7$			4.08128i			1.54258i	−0.636484	+	0.771290i	$0.719612\pi$
$8$	−2.78436	−	0.497357i	−0.984418	−	0.175842i
$9$	2.34515	+	2.34515i	0.781716	+	0.781716i
$10$	−1.50395	+	3.10058i	−0.475590	+	0.980488i
$11$	−5.01361	−	2.07671i	−1.51166	−	0.626150i	−0.535761	−	0.844370i	$-0.679975\pi$
$11$	−5.01361	−	2.07671i	−1.51166	−	0.626150i	−0.975900	+	0.218219i	$0.929975\pi$
$12$	−4.38557	−	2.45621i	−1.26600	−	0.709048i
$13$	3.14807	+	1.75774i	0.873118	+	0.487508i
$13$	3.14807	+	1.75774i	0.873118	+	0.487508i
$14$	0.339880	−	5.76179i	0.0908368	−	1.53990i
$15$	−4.33046	+	4.33046i	−1.11812	+	1.11812i
$16$	3.88942	+	0.934023i	0.972355	+	0.233506i
$17$	−5.02884			−1.21967			−0.609837	−	0.792527i	$-0.708765\pi$
$17$	−5.02884			−1.21967			−0.609837	+	0.792527i	$0.708765\pi$
$18$	−3.11549	−	3.50609i	−0.734328	−	0.826392i
$19$	−0.314391	−	0.759008i	−0.0721263	−	0.174128i	0.883705	−	0.468045i	$-0.155041\pi$
$19$	−0.314391	−	0.759008i	−0.0721263	−	0.174128i	−0.955831	+	0.293916i	$0.905041\pi$
$20$	2.38142	−	4.25202i	0.532502	−	0.950781i
$21$	3.92533	−	9.47658i	0.856577	−	2.06796i
$22$	6.90507	+	3.34933i	1.47217	+	0.714080i
$23$	5.64225	+	5.64225i	1.17649	+	1.17649i	0.980632	+	0.195858i	$0.0627490\pi$
$23$	5.64225	+	5.64225i	1.17649	+	1.17649i	0.195858	+	0.980632i	$0.437251\pi$
$24$	5.98682	+	3.83280i	1.22205	+	0.782368i
$25$	−0.663064	−	0.663064i	−0.132613	−	0.132613i
$26$	−4.29794	−	2.74366i	−0.842896	−	0.538077i
$27$	−0.304446	−	0.734999i	−0.0585907	−	0.141451i
$28$	−0.959658	+	8.10595i	−0.181358	+	1.53188i
$29$	−1.61354	+	3.89544i	−0.299628	+	0.723365i	0.700327	+	0.713822i	$0.253038\pi$
$29$	−1.61354	+	3.89544i	−0.299628	+	0.723365i	−0.999954	+	0.00954272i	$0.996962\pi$
$30$	6.47420	−	5.75294i	1.18202	−	1.05034i
$31$	0.191640	+	0.191640i	0.0344195	+	0.0344195i	0.724107	−	0.689688i	$-0.242252\pi$
$31$	0.191640	+	0.191640i	0.0344195	+	0.0344195i	−0.689688	+	0.724107i	$0.742252\pi$
$32$	−5.41314	−	1.64252i	−0.956918	−	0.290359i
$33$	9.64406	+	9.64406i	1.67882	+	1.67882i
$34$	7.09952	+	0.418791i	1.21756	+	0.0718221i
$35$	9.18801	+	3.80580i	1.55306	+	0.643297i
$36$	4.10634	+	5.20920i	0.684390	+	0.868200i
$37$	4.82258	+	1.99758i	0.792827	+	0.328400i	0.742080	−	0.670312i	$-0.233840\pi$
$37$	4.82258	+	1.99758i	0.792827	+	0.328400i	0.0507475	+	0.998712i	$0.483840\pi$
$38$	0.380636	+	1.09772i	0.0617474	+	0.178073i
$39$	−5.61914	−	7.10917i	−0.899782	−	1.13838i
$40$	−3.71609	+	5.80451i	−0.587566	+	0.917774i
$41$	4.38078			0.684163			0.342082	−	0.939670i	$-0.388868\pi$
$41$	4.38078			0.684163			0.342082	+	0.939670i	$0.388868\pi$
$42$	−6.33081	+	13.0518i	−0.976865	+	2.01393i
$43$	−0.182517	−	0.440634i	−0.0278335	−	0.0671961i	0.909352	−	0.416028i	$-0.136578\pi$
$43$	−0.182517	−	0.440634i	−0.0278335	−	0.0671961i	−0.937185	+	0.348832i	$0.886578\pi$
$44$	−9.46937	−	5.30349i	−1.42756	−	0.799531i
$45$	7.46639	−	3.09268i	1.11302	−	0.461029i
$46$	−7.49562	−	8.43537i	−1.10517	−	1.24373i
$47$	6.13062	+	6.13062i	0.894243	+	0.894243i	0.994919	−	0.100677i	$-0.0321007\pi$
$47$	6.13062	+	6.13062i	0.894243	+	0.894243i	−0.100677	+	0.994919i	$0.532101\pi$
$48$	−8.13276	−	5.90956i	−1.17386	−	0.852972i
$49$	−9.65685			−1.37955
$50$	0.880869	+	0.991306i	0.124574	+	0.140192i
$51$	11.6768	+	4.83668i	1.63508	+	0.677271i
$52$	5.83917	+	4.23132i	0.809748	+	0.586778i
$53$	3.34267	+	8.06993i	0.459152	+	1.10849i	0.968741	+	0.248073i	$0.0797972\pi$
$53$	3.34267	+	8.06993i	0.459152	+	1.10849i	−0.509590	+	0.860418i	$0.670203\pi$
$54$	0.368596	+	1.06300i	0.0501596	+	0.144655i
$55$	−9.35039	+	9.35039i	−1.26081	+	1.26081i
$56$	2.02985	−	11.3637i	0.271250	−	1.51854i
$57$			2.06476i			0.273485i
$58$	2.60234	−	5.36505i	0.341704	−	0.704466i
$59$	−0.901922	+	2.17743i	−0.117420	+	0.283478i	−0.971652	−	0.236414i	$-0.924028\pi$
$59$	−0.901922	+	2.17743i	−0.117420	+	0.283478i	0.854232	+	0.519892i	$0.174028\pi$
$60$	−9.61911	+	7.58261i	−1.24182	+	0.978911i
$61$	0.967064	−	2.33470i	0.123820	−	0.298928i	−0.849799	−	0.527106i	$-0.823277\pi$
$61$	0.967064	−	2.33470i	0.123820	−	0.298928i	0.973619	+	0.228179i	$0.0732770\pi$
$62$	−0.254590	−	0.286509i	−0.0323330	−	0.0363866i
$63$	−9.57121	+	9.57121i	−1.20586	+	1.20586i
$64$	7.50527	+	2.76964i	0.938159	+	0.346204i
$65$	6.89270	−	5.44803i	0.854934	−	0.675745i
$66$	−12.8120	−	14.4182i	−1.57704	−	1.77476i
$67$	1.21542	−	0.503443i	0.148487	−	0.0615053i	−0.307202	−	0.951644i	$-0.599393\pi$
$67$	1.21542	−	0.503443i	0.148487	−	0.0615053i	0.455689	+	0.890139i	$0.349393\pi$
$68$	−9.98793	−	1.18246i	−1.21121	−	0.143395i
$69$	−7.67444	−	18.5277i	−0.923894	−	2.23048i
$70$	−12.6543	−	6.13803i	−1.51248	−	0.733635i
$71$	−1.22794			−0.145730			−0.0728649	−	0.997342i	$-0.523214\pi$
$71$	−1.22794			−0.145730			−0.0728649	+	0.997342i	$0.523214\pi$
$72$	−5.36335	−	7.69611i	−0.632077	−	0.906995i
$73$		−	4.96133i		−	0.580679i	−0.956924	−	0.290340i	$-0.906232\pi$
$73$		−	4.96133i		−	0.580679i	0.956924	−	0.290340i	$-0.0937683\pi$
$74$	−6.64197	−	3.22171i	−0.772113	−	0.374517i
$75$	0.901883	+	2.17734i	0.104140	+	0.251417i
$76$	−0.445952	−	1.58141i	−0.0511541	−	0.181400i
$77$	8.47562	−	20.4620i	0.965886	−	2.33186i
$78$	7.34083	+	10.5044i	0.831186	+	1.18939i
$79$	3.63284			0.408726			0.204363	−	0.978895i	$-0.434488\pi$
$79$	3.63284			0.408726			0.204363	+	0.978895i	$0.434488\pi$
$80$	5.72961	−	7.88511i	0.640590	−	0.881582i
$81$		−	7.95017i		−	0.883353i
$82$	−6.18461	−	0.364822i	−0.682976	−	0.0402879i
$83$	−1.66391	−	4.01702i	−0.182637	−	0.440926i	0.805871	−	0.592091i	$-0.201697\pi$
$83$	−1.66391	−	4.01702i	−0.182637	−	0.440926i	−0.988509	+	0.151165i	$0.951697\pi$
$84$	10.0245	−	17.8987i	1.09376	−	1.95291i
$85$	−4.68940	+	11.3212i	−0.508637	+	1.22796i
$86$	0.220975	+	0.637269i	0.0238283	+	0.0687185i
$87$	7.49317	−	7.49317i	0.803353	−	0.803353i
$88$	12.9268	+	8.27584i	1.37800	+	0.882207i
$89$	−5.69815			−0.604003			−0.302002	−	0.953307i	$-0.597655\pi$
$89$	−5.69815			−0.604003			−0.302002	+	0.953307i	$0.597655\pi$
$90$	−10.7983	+	3.74433i	−1.13824	+	0.394688i
$91$	−7.17381	+	12.8482i	−0.752020	+	1.34685i
$92$	9.87954	+	12.5329i	1.03001	+	1.30665i
$93$	−0.260663	−	0.629297i	−0.0270295	−	0.0652551i
$94$	−8.14441	−	9.16550i	−0.840032	−	0.945350i
$95$	−2.00189			−0.205390
$96$	10.9894	+	9.02016i	1.12160	+	0.920616i
$97$	−6.00369	+	6.00369i	−0.609582	+	0.609582i	−0.942837	−	0.333255i	$-0.891853\pi$
$97$	−6.00369	+	6.00369i	−0.609582	+	0.609582i	0.333255	+	0.942837i	$0.391853\pi$
$98$	13.6332	+	0.804201i	1.37716	+	0.0812366i
$99$	−6.88748	−	16.6279i	−0.692218	−	1.67116i
$100$	−1.16102	−	1.47284i	−0.116102	−	0.147284i
$101$	6.66507	+	16.0909i	0.663200	+	1.60111i	0.792760	+	0.609534i	$0.208643\pi$
$101$	6.66507	+	16.0909i	0.663200	+	1.60111i	−0.129560	+	0.991572i	$0.541357\pi$
$102$	−16.0820	−	7.80065i	−1.59236	−	0.772379i
$103$	0.433438	−	0.433438i	0.0427079	−	0.0427079i	−0.685430	−	0.728138i	$-0.740386\pi$
$103$	0.433438	−	0.433438i	0.0427079	−	0.0427079i	0.728138	+	0.685430i	$0.240386\pi$
$104$	−7.89113	−	6.45988i	−0.773789	−	0.633443i
$105$	−17.6738	−	17.6738i	−1.72479	−	1.72479i
$106$	−4.04701	−	11.6712i	−0.393080	−	1.13360i
$107$	−17.7981	+	7.37223i	−1.72061	+	0.712700i	−0.720802	+	0.693141i	$0.756226\pi$
$107$	−17.7981	+	7.37223i	−1.72061	+	0.712700i	−0.999809	+	0.0195591i	$0.993774\pi$
$108$	−0.431845	−	1.53139i	−0.0415543	−	0.147358i
$109$	−18.5076	+	7.66609i	−1.77271	+	0.734278i	−0.778392	+	0.627778i	$0.783965\pi$
$109$	−18.5076	+	7.66609i	−1.77271	+	0.734278i	−0.994313	+	0.106500i	$0.966035\pi$
$110$	13.9792	−	12.4218i	1.33286	−	1.18437i
$111$	−9.27660	−	9.27660i	−0.880496	−	0.880496i
$112$	−3.81201	+	15.8738i	−0.360201	+	1.49994i
$113$			12.6033i			1.18562i	0.805342	+	0.592810i	$0.201981\pi$
$113$			12.6033i			1.18562i	−0.805342	+	0.592810i	$0.798019\pi$
$114$	0.171949	−	2.91495i	0.0161045	−	0.273010i
$115$	17.9635	−	7.44075i	1.67511	−	0.693853i
$116$	−4.12067	+	7.35745i	−0.382594	+	0.683122i
$117$	3.26055	+	11.5049i	0.301438	+	1.06362i
$118$	1.45463	−	2.99890i	0.133909	−	0.276071i
$119$		−	20.5241i		−	1.88144i
$120$	14.2113	−	9.90377i	1.29731	−	0.904086i
$121$	13.0454	+	13.0454i	1.18595	+	1.18595i
$122$	−1.55969	+	3.21550i	−0.141208	+	0.291118i
$123$	−10.1720	−	4.21339i	−0.917179	−	0.379908i
$124$	0.335560	+	0.425683i	0.0301342	+	0.0382275i
$125$	9.14525	−	3.78809i	0.817976	−	0.338817i
$126$	14.3093	−	12.7152i	1.27478	−	1.13276i
$127$	−21.0498			−1.86787			−0.933935	−	0.357443i	$-0.883649\pi$
$127$	−21.0498			−1.86787			−0.933935	+	0.357443i	$0.883649\pi$
$128$	−10.3650	−	4.53508i	−0.916144	−	0.400848i
$129$			1.19868i			0.105538i
$130$	−10.1845	+	7.11730i	−0.893242	+	0.624229i
$131$	13.1722	+	5.45609i	1.15086	+	0.476701i	0.874821	−	0.484446i	$-0.160979\pi$
$131$	13.1722	+	5.45609i	1.15086	+	0.476701i	0.276037	+	0.961147i	$0.410979\pi$
$132$	16.8867	+	21.4220i	1.46980	+	1.86455i
$133$	3.09772	−	1.28312i	0.268607	−	0.111261i
$134$	−1.75780	+	0.609523i	−0.151851	+	0.0526547i
$135$	−1.93857			−0.166845
$136$	14.0021	+	2.50113i	1.20067	+	0.214470i
$137$		−	0.383127i		−	0.0327328i	−0.999866	−	0.0163664i	$-0.994790\pi$
$137$		−	0.383127i		−	0.0327328i	0.999866	−	0.0163664i	$-0.00520981\pi$
$138$	9.29151	+	26.7958i	0.790946	+	2.28101i
$139$	0.507582	−	0.210247i	0.0430525	−	0.0178329i	−0.361053	−	0.932545i	$-0.617583\pi$
$139$	0.507582	−	0.210247i	0.0430525	−	0.0178329i	0.404106	+	0.914712i	$0.367583\pi$
$140$	17.3537	+	9.71924i	1.46666	+	0.821426i
$141$	−8.33871	−	20.1314i	−0.702246	−	1.69537i
$142$	1.73356	+	0.102260i	0.145477	+	0.00858148i
$143$	−12.1329	−	15.3502i	−1.01461	−	1.28365i
$144$	6.93085	+	11.3117i	0.577571	+	0.942642i
$145$	7.26500	+	7.26500i	0.603326	+	0.603326i
$146$	−0.413168	+	7.00420i	−0.0341940	+	0.579672i
$147$	22.4228	+	9.28784i	1.84940	+	0.766048i
$148$	9.10856	+	5.10141i	0.748719	+	0.419334i
$149$	−10.4486	−	4.32793i	−0.855979	−	0.354558i	−0.0888453	−	0.996045i	$-0.528318\pi$
$149$	−10.4486	−	4.32793i	−0.855979	−	0.354558i	−0.767134	+	0.641487i	$0.778318\pi$
$150$	−1.09192	−	3.14898i	−0.0891547	−	0.257113i
$151$	3.40279			0.276915			0.138457	−	0.990368i	$-0.455786\pi$
$151$	3.40279			0.276915			0.138457	+	0.990368i	$0.455786\pi$
$152$	0.497880	+	2.26971i	0.0403834	+	0.184098i
$153$	−11.7934	−	11.7934i	−0.953439	−	0.953439i
$154$	−13.6696	+	28.1815i	−1.10152	+	2.27093i
$155$	0.610135	−	0.252726i	0.0490072	−	0.0202994i
$156$	−9.48871	−	15.4410i	−0.759705	−	1.23627i
$157$	−4.98873	+	12.0438i	−0.398144	+	0.961204i	0.589963	+	0.807431i	$0.299142\pi$
$157$	−4.98873	+	12.0438i	−0.398144	+	0.961204i	−0.988106	+	0.153773i	$0.950858\pi$
$158$	−5.12869	−	0.302535i	−0.408017	−	0.0240684i
$159$		−	21.9530i		−	1.74099i
$160$	−8.74549	+	10.6547i	−0.691392	+	0.842330i
$161$	−23.0276	+	23.0276i	−1.81483	+	1.81483i
$162$	−0.662073	+	11.2237i	−0.0520174	+	0.881820i
$163$	−7.07053	−	17.0698i	−0.553806	−	1.33701i	−0.914599	−	0.404361i	$-0.867494\pi$
$163$	−7.07053	−	17.0698i	−0.553806	−	1.33701i	0.360793	−	0.932646i	$-0.382506\pi$
$164$	8.70080	+	1.03008i	0.679419	+	0.0804359i
$165$	30.7044	−	12.7182i	2.39033	−	0.990107i
$166$	2.01451	+	5.80964i	0.156356	+	0.450915i
$167$		−	11.5788i		−	0.895998i	−0.894034	−	0.447999i	$-0.852137\pi$
$167$		−	11.5788i		−	0.895998i	0.894034	−	0.447999i	$-0.147863\pi$
$168$	−15.6427	+	24.4339i	−1.20686	+	1.88511i
$169$	6.82073	+	11.0670i	0.524672	+	0.851305i
$170$	7.56311	−	15.5923i	0.580064	−	1.19588i
$171$	1.04269	−	2.51728i	0.0797367	−	0.192501i
$172$	−0.258893	−	0.918073i	−0.0197404	−	0.0700024i
$173$	7.53433	−	18.1895i	0.572824	−	1.38292i	−0.326316	−	0.945261i	$-0.605807\pi$
$173$	7.53433	−	18.1895i	0.572824	−	1.38292i	0.899141	−	0.437660i	$-0.144193\pi$
$174$	−11.2026	+	9.95455i	−0.849265	+	0.754652i
$175$	2.70615	−	2.70615i	0.204566	−	0.204566i
$176$	−17.5604	−	12.7600i	−1.32366	−	0.961822i
$177$	4.18846	−	4.18846i	0.314824	−	0.314824i
$178$	8.04442	+	0.474530i	0.602955	+	0.0355675i
$179$	13.8516	+	5.73752i	1.03532	+	0.428842i	0.834629	−	0.550813i	$-0.185682\pi$
$179$	13.8516	+	5.73752i	1.03532	+	0.428842i	0.200688	+	0.979655i	$0.435682\pi$
$180$	15.5564	−	4.38684i	1.15951	−	0.326976i
$181$	3.31975	−	1.37509i	0.246755	−	0.102209i	−0.255878	−	0.966709i	$-0.582365\pi$
$181$	3.31975	−	1.37509i	0.246755	−	0.102209i	0.502633	+	0.864500i	$0.332365\pi$
$182$	11.1977	−	17.5411i	0.830026	−	1.30023i
$183$	−4.49097	+	4.49097i	−0.331982	+	0.331982i
$184$	−12.9038	−	18.5162i	−0.951282	−	1.36503i
$185$	8.99412	−	8.99412i	0.661261	−	0.661261i
$186$	0.315588	+	0.910124i	0.0231400	+	0.0667335i
$187$	25.2127	+	10.4434i	1.84373	+	0.763699i
$188$	10.7347	+	13.6177i	0.782906	+	0.993175i
$189$	2.99974	−	1.24253i	0.218199	−	0.0903809i
$190$	2.82619	+	0.166713i	0.205033	+	0.0120946i
$191$			7.19460i			0.520583i	0.965530	+	0.260291i	$0.0838186\pi$
$191$			7.19460i			0.520583i	−0.965530	+	0.260291i	$0.916181\pi$
$192$	−14.7632	−	13.6495i	−1.06544	−	0.985066i
$193$	3.29081	+	3.29081i	0.236878	+	0.236878i	0.815556	−	0.578678i	$-0.196431\pi$
$193$	3.29081	+	3.29081i	0.236878	+	0.236878i	−0.578678	+	0.815556i	$0.696431\pi$
$194$	8.97574	−	7.97579i	0.644421	−	0.572628i
$195$	−21.2444	+	6.02081i	−1.52134	+	0.431159i
$196$	−19.1798	−	2.27068i	−1.36998	−	0.162191i
$197$	−3.64521	+	8.80032i	−0.259711	+	0.626997i	−0.998919	−	0.0464798i	$-0.985200\pi$
$197$	−3.64521	+	8.80032i	−0.259711	+	0.626997i	0.739209	+	0.673476i	$0.235200\pi$
$198$	8.33874	+	24.0481i	0.592608	+	1.70902i
$199$	−0.471555	+	0.471555i	−0.0334277	+	0.0334277i	−0.723623	−	0.690195i	$-0.757525\pi$
$199$	−0.471555	+	0.471555i	−0.0334277	+	0.0334277i	0.690195	+	0.723623i	$0.257525\pi$
$200$	1.51643	+	2.17599i	0.107228	+	0.153865i
$201$	−3.30636			−0.233213
$202$	−8.06947	−	23.2716i	−0.567766	−	1.63738i
$203$	−15.8984	−	6.58533i	−1.11585	−	0.462199i
$204$	22.0543	+	12.3519i	1.54411	+	0.864807i
$205$	4.08509	−	9.86227i	0.285315	−	0.688811i
$206$	−0.648005	+	0.575814i	−0.0451487	+	0.0401189i
$207$			26.4638i			1.83936i
$208$	10.6024	+	9.77695i	0.735146	+	0.677909i
$209$			4.45827i			0.308385i
$210$	23.4794	+	26.4230i	1.62023	+	1.82336i
$211$	6.32727	−	15.2754i	0.435587	−	1.05160i	−0.541869	−	0.840463i	$-0.682283\pi$
$211$	6.32727	−	15.2754i	0.435587	−	1.05160i	0.977456	−	0.211138i	$-0.0677169\pi$
$212$	4.74145	+	16.8139i	0.325644	+	1.15478i
$213$	2.85123	+	1.18102i	0.195363	+	0.0809220i
$214$	25.7406	−	8.92562i	1.75959	−	0.610143i
$215$	−1.16218			−0.0792599
$216$	0.482131	+	2.19792i	0.0328048	+	0.149549i
$217$	−0.782136	+	0.782136i	−0.0530948	+	0.0530948i
$218$	26.7667	−	9.28141i	1.81287	−	0.628616i
$219$	−4.77174	+	11.5200i	−0.322445	+	0.778450i
$220$	−20.7697	+	16.3725i	−1.40029	+	1.10383i
$221$	−15.8312	−	8.83938i	−1.06492	−	0.594601i
$222$	12.3238	+	13.8689i	0.827119	+	0.930817i
$223$	−0.726413	−	0.726413i	−0.0486442	−	0.0486442i	0.682366	−	0.731010i	$-0.260951\pi$
$223$	−0.726413	−	0.726413i	−0.0486442	−	0.0486442i	−0.731010	+	0.682366i	$0.760951\pi$
$224$	6.70358	−	22.0926i	0.447902	−	1.47612i
$225$		−	3.10997i		−	0.207331i
$226$	1.04958	−	17.7928i	0.0698167	−	1.18356i
$227$	−16.4646	+	6.81986i	−1.09279	+	0.452650i	−0.854980	−	0.518660i	$-0.826431\pi$
$227$	−16.4646	+	6.81986i	−1.09279	+	0.452650i	−0.237814	+	0.971311i	$0.576431\pi$
$228$	−0.485501	+	4.10089i	−0.0321531	+	0.271588i
$229$	−2.86404	−	1.18632i	−0.189261	−	0.0783944i	0.286040	−	0.958218i	$-0.407661\pi$
$229$	−2.86404	−	1.18632i	−0.189261	−	0.0783944i	−0.475301	+	0.879823i	$0.657661\pi$
$230$	−25.9799	+	9.00858i	−1.71306	+	0.594008i
$231$	−39.3601	+	39.3601i	−2.58971	+	2.58971i
$232$	6.43010	−	10.0438i	0.422157	−	0.659407i
$233$	−5.64563	+	5.64563i	−0.369858	+	0.369858i	−0.867425	−	0.497568i	$-0.834227\pi$
$233$	−5.64563	+	5.64563i	−0.369858	+	0.369858i	0.497568	+	0.867425i	$0.334227\pi$
$234$	−3.64501	−	16.5136i	−0.238282	−	1.07953i
$235$	19.5184	−	8.08479i	1.27324	−	0.527393i
$236$	−2.30333	+	4.11259i	−0.149934	+	0.267707i
$237$	−8.43531	−	3.49402i	−0.547932	−	0.226961i
$238$	−1.70920	+	28.9751i	−0.110791	+	1.87818i
$239$	13.2034	−	13.2034i	0.854054	−	0.854054i	−0.136575	−	0.990630i	$-0.543610\pi$
$239$	13.2034	−	13.2034i	0.854054	−	0.854054i	0.990630	+	0.136575i	$0.0436096\pi$
$240$	−20.8877	+	12.7982i	−1.34830	+	0.826123i
$241$	8.07597	−	8.07597i	0.520219	−	0.520219i	−0.397419	−	0.917637i	$-0.630094\pi$
$241$	8.07597	−	8.07597i	0.520219	−	0.520219i	0.917637	+	0.397419i	$0.130094\pi$
$242$	−17.3306	−	19.5034i	−1.11405	−	1.25372i
$243$	−8.55972	+	20.6650i	−0.549106	+	1.32566i
$244$	2.46969	−	4.40962i	0.158106	−	0.282297i
$245$	−9.00502	+	21.7401i	−0.575310	+	1.38892i
$246$	14.0096	+	6.79539i	0.893216	+	0.433258i
$247$	0.344408	−	2.94203i	0.0219142	−	0.187197i
$248$	−0.438280	−	0.628907i	−0.0278308	−	0.0399356i
$249$			10.9277i			0.692515i
$250$	−13.2264	+	4.58627i	−0.836508	+	0.290061i
$251$	25.2518	−	10.4597i	1.59388	−	0.660207i	0.603348	−	0.797478i	$-0.293833\pi$
$251$	25.2518	−	10.4597i	1.59388	−	0.660207i	0.990534	+	0.137271i	$0.0438330\pi$
$252$	−21.2602	+	16.7591i	−1.33927	+	1.05573i
$253$	−16.5707	−	40.0053i	−1.04179	−	2.51511i
$254$	29.7173	+	1.75298i	1.86463	+	0.109992i
$255$	21.7772	−	21.7772i	1.36374	−	1.36374i
$256$	14.2552	+	7.26562i	0.890950	+	0.454101i
$257$			21.6825i			1.35252i	0.736665	+	0.676258i	$0.236399\pi$
$257$			21.6825i			1.35252i	−0.736665	+	0.676258i	$0.763601\pi$
$258$	0.0998233	−	1.69225i	0.00621473	−	0.105355i
$259$	−8.15268	+	19.6823i	−0.506583	+	1.22300i
$260$	14.9708	−	9.19977i	0.928451	−	0.570546i
$261$	−12.9194	+	5.35139i	−0.799690	+	0.331243i
$262$	−18.1416	−	8.79964i	−1.12079	−	0.543644i
$263$	20.4644	+	20.4644i	1.26189	+	1.26189i	0.950175	+	0.311716i	$0.100904\pi$
$263$	20.4644	+	20.4644i	1.26189	+	1.26189i	0.311716	+	0.950175i	$0.399096\pi$
$264$	−22.0560	−	31.6490i	−1.35745	−	1.94786i
$265$	21.2845			1.30750
$266$	−4.48010	+	1.55348i	−0.274692	+	0.0952502i
$267$	13.2309	+	5.48042i	0.809718	+	0.335396i
$268$	2.53236	−	0.714113i	0.154688	−	0.0436214i
$269$	−8.00369	−	3.31524i	−0.487993	−	0.202133i	0.125100	−	0.992144i	$-0.460075\pi$
$269$	−8.00369	−	3.31524i	−0.487993	−	0.202133i	−0.613093	+	0.790011i	$0.710075\pi$
$270$	2.73679	+	0.161440i	0.166556	+	0.00982490i
$271$	−11.3718	−	11.3718i	−0.690790	−	0.690790i	0.271615	−	0.962406i	$-0.412442\pi$
$271$	−11.3718	−	11.3718i	−0.690790	−	0.690790i	−0.962406	+	0.271615i	$0.912442\pi$
$272$	−19.5593	−	4.69705i	−1.18596	−	0.284801i
$273$	29.0145	−	22.9333i	1.75604	−	1.38798i
$274$	−0.0319060	+	0.540883i	−0.00192751	+	0.0326760i
$275$	1.94736	+	4.70134i	0.117430	+	0.283501i
$276$	−10.8859	−	38.6030i	−0.655253	−	2.32363i
$277$	−13.2672	+	5.49546i	−0.797149	+	0.330190i	−0.743814	−	0.668387i	$-0.766985\pi$
$277$	−13.2672	+	5.49546i	−0.797149	+	0.330190i	−0.0533353	+	0.998577i	$0.516985\pi$
$278$	−0.734092	+	0.254548i	−0.0440279	+	0.0152668i
$279$			0.898848i			0.0538126i
$280$	−23.6898	−	15.1664i	−1.41574	−	0.906367i
$281$	−15.5005			−0.924680			−0.462340	−	0.886703i	$-0.652990\pi$
$281$	−15.5005			−0.924680			−0.462340	+	0.886703i	$0.652990\pi$
$282$	10.0957	+	29.1151i	0.601193	+	1.73378i
$283$	−21.0167	+	8.70540i	−1.24931	+	0.517482i	−0.906613	−	0.421962i	$-0.861341\pi$
$283$	−21.0167	+	8.70540i	−1.24931	+	0.517482i	−0.342700	+	0.939445i	$0.611341\pi$
$284$	−2.43885	−	0.288734i	−0.144719	−	0.0171332i
$285$	4.64832	+	1.92540i	0.275342	+	0.114051i
$286$	15.8504	+	22.6812i	0.937255	+	1.34117i
$287$			17.8792i			1.05538i
$288$	−8.84268	−	16.5466i	−0.521060	−	0.975017i
$289$	8.28927			0.487604
$290$	−9.65142	−	10.8615i	−0.566751	−	0.637806i
$291$	19.7146	−	8.16606i	1.15569	−	0.478703i
$292$	1.16659	−	9.85384i	0.0682694	−	0.576652i
$293$	−9.09251	−	3.76624i	−0.531190	−	0.220026i	0.100934	−	0.994893i	$-0.467817\pi$
$293$	−9.09251	−	3.76624i	−0.531190	−	0.220026i	−0.632124	+	0.774867i	$0.717817\pi$
$294$	−30.8822	−	14.9795i	−1.80109	−	0.873624i
$295$	4.06092	+	4.06092i	0.236436	+	0.236436i
$296$	−12.4343	−	7.96051i	−0.722727	−	0.462695i
$297$			4.31724i			0.250512i
$298$	14.3904	+	6.98013i	0.833615	+	0.404348i
$299$	7.84463	+	27.6798i	0.453667	+	1.60076i
$300$	1.27928	+	4.53654i	0.0738595	+	0.261917i
$301$	1.79835	−	0.744902i	0.103655	−	0.0429354i
$302$	−4.80391	−	0.283376i	−0.276434	−	0.0163065i
$303$		−	43.7729i		−	2.51469i
$304$	−0.513870	−	3.24575i	−0.0294725	−	0.186157i
$305$	−4.35422	−	4.35422i	−0.249322	−	0.249322i
$306$	15.6673	+	17.6316i	0.895640	+	1.00793i
$307$	−9.54787	+	3.95486i	−0.544926	+	0.225716i	−0.638126	−	0.769932i	$-0.720290\pi$
$307$	−9.54787	+	3.95486i	−0.544926	+	0.225716i	0.0932006	+	0.995647i	$0.470290\pi$
$308$	21.6450	−	38.6472i	1.23334	−	2.20213i
$309$	−1.42330	+	0.589551i	−0.0809688	+	0.0335384i
$310$	−0.882410	+	0.305978i	−0.0501175	+	0.0173784i
$311$	4.17141	+	4.17141i	0.236539	+	0.236539i	0.815415	−	0.578876i	$-0.196509\pi$
$311$	4.17141	+	4.17141i	0.236539	+	0.236539i	−0.578876	+	0.815415i	$0.696509\pi$
$312$	12.1099	+	22.5892i	0.685587	+	1.27886i
$313$	11.7738	−	11.7738i	0.665493	−	0.665493i	−0.291176	−	0.956669i	$-0.594047\pi$
$313$	11.7738	−	11.7738i	0.665493	−	0.665493i	0.956669	+	0.291176i	$0.0940465\pi$
$314$	8.04587	−	16.5876i	0.454054	−	0.936091i
$315$	12.6221	+	30.4724i	0.711174	+	1.71693i
$316$	7.21528	+	0.854212i	0.405891	+	0.0480532i
$317$	3.40385	+	8.21762i	0.191179	+	0.461547i	0.990183	−	0.139779i	$-0.0446392\pi$
$317$	3.40385	+	8.21762i	0.191179	+	0.461547i	−0.799004	+	0.601326i	$0.794639\pi$
$318$	−1.82820	+	30.9924i	−0.102520	+	1.73797i
$319$	16.1794	−	16.1794i	0.905870	−	0.905870i
$320$	13.2338	−	14.3136i	0.739794	−	0.800155i
$321$	48.4171			2.70238
$322$	34.4271	−	30.5917i	1.91855	−	1.70481i
$323$	1.58102	+	3.81693i	0.0879706	+	0.212380i
$324$	1.86938	−	15.7901i	0.103854	−	0.877227i
$325$	−0.921883	−	3.25287i	−0.0511369	−	0.180437i
$326$	8.56035	+	24.6872i	0.474114	+	1.36730i
$327$	50.3471			2.78420
$328$	−12.1977	−	2.17881i	−0.673503	−	0.120305i
$329$	−25.0208	+	25.0208i	−1.37944	+	1.37944i
$330$	−44.4063	+	15.3980i	−2.44449	+	0.847632i
$331$	2.16552	−	5.22803i	0.119028	−	0.287358i	−0.853125	−	0.521707i	$-0.825296\pi$
$331$	2.16552	−	5.22803i	0.119028	−	0.287358i	0.972153	+	0.234348i	$0.0752956\pi$
$332$	−2.36018	−	8.36958i	−0.129532	−	0.459340i
$333$	6.62505	+	15.9943i	0.363051	+	0.876482i
$334$	−0.964261	+	16.3465i	−0.0527620	+	0.894443i
$335$		−	3.20568i		−	0.175145i
$336$	24.1186	−	33.1921i	1.31578	−	1.81078i
$337$	11.3814			0.619987			0.309993	−	0.950739i	$-0.399673\pi$
$337$	11.3814			0.619987			0.309993	+	0.950739i	$0.399673\pi$
$338$	−8.70760	−	16.1919i	−0.473631	−	0.880723i
$339$	12.1217	−	29.2644i	0.658361	−	1.58942i
$340$	−11.9758	+	21.3828i	−0.649478	+	1.15964i
$341$	−0.562828	−	1.35879i	−0.0304788	−	0.0735824i
$342$	−1.68166	+	3.46696i	−0.0909340	+	0.187472i
$343$		−	10.8434i		−	0.585486i
$344$	0.289039	+	1.31766i	0.0155839	+	0.0710434i
$345$	−48.8671			−2.63092
$346$	−12.1514	+	25.0517i	−0.653265	+	1.34679i
$347$	−12.3099	−	29.7188i	−0.660831	−	1.59539i	−0.796504	−	0.604633i	$-0.793320\pi$
$347$	−12.3099	−	29.7188i	−0.660831	−	1.59539i	0.135674	−	0.990754i	$-0.456680\pi$
$348$	16.6443	−	13.1205i	0.892230	−	0.703333i
$349$	14.2094	−	5.88572i	0.760610	−	0.315055i	0.0315479	−	0.999502i	$-0.489956\pi$
$349$	14.2094	−	5.88572i	0.760610	−	0.315055i	0.729063	+	0.684447i	$0.239956\pi$
$350$	−4.04580	+	3.59507i	−0.216257	+	0.192165i
$351$	0.333514	−	2.84897i	0.0178016	−	0.152067i
$352$	23.7284	+	19.4765i	1.26473	+	1.03810i
$353$	3.38776	−	3.38776i	0.180312	−	0.180312i	−0.611180	−	0.791492i	$-0.709305\pi$
$353$	3.38776	−	3.38776i	0.180312	−	0.180312i	0.791492	+	0.611180i	$0.209305\pi$
$354$	−6.26190	+	5.56429i	−0.332816	+	0.295739i
$355$	−1.14506	+	2.76441i	−0.0607732	+	0.146720i
$356$	−11.3173	−	1.33984i	−0.599814	−	0.0710116i
$357$	−19.7399	+	47.6562i	−1.04474	+	2.52223i
$358$	−19.0773	−	9.25353i	−1.00827	−	0.489064i
$359$		−	0.527036i		−	0.0278159i	−0.999903	−	0.0139080i	$-0.995573\pi$
$359$		−	0.527036i		−	0.0278159i	0.999903	−	0.0139080i	$-0.00442718\pi$
$360$	−22.3272	+	4.89766i	−1.17675	+	0.258129i
$361$	12.9578	−	12.9578i	0.681988	−	0.681988i
$362$	−4.80121	+	1.66483i	−0.252346	+	0.0875015i
$363$	−17.7440	−	42.8379i	−0.931320	−	2.24841i
$364$	−17.2692	+	23.8313i	−0.905152	+	1.24910i
$365$	−11.1692	−	4.62644i	−0.584624	−	0.242159i
$366$	6.71417	−	5.96617i	0.350955	−	0.311857i
$367$	−4.38036			−0.228653			−0.114327	−	0.993443i	$-0.536471\pi$
$367$	−4.38036			−0.228653			−0.114327	+	0.993443i	$0.536471\pi$
$368$	16.6751	+	27.2151i	0.869249	+	1.41868i
$369$	10.2736	+	10.2736i	0.534822	+	0.534822i
$370$	−13.4465	+	11.9485i	−0.699053	+	0.621174i
$371$	−32.9357	+	13.6424i	−1.70993	+	0.708278i
$372$	−0.369741	−	1.31116i	−0.0191702	−	0.0679803i
$373$	−9.46245	−	22.8444i	−0.489947	−	1.18284i	−0.954747	−	0.297421i	$-0.903874\pi$
$373$	−9.46245	−	22.8444i	−0.489947	−	1.18284i	0.464800	−	0.885416i	$-0.346126\pi$
$374$	−34.7245	−	16.8433i	−1.79556	−	0.870944i
$375$	−24.8782			−1.28471
$376$	−14.0207	−	20.1189i	−0.723063	−	1.03755i
$377$	−11.9267	+	9.42695i	−0.614257	+	0.485512i
$378$	−4.33838	+	1.50434i	−0.223142	+	0.0773751i
$379$	−16.5864	−	6.87033i	−0.851989	−	0.352905i	−0.0864194	−	0.996259i	$-0.527543\pi$
$379$	−16.5864	−	6.87033i	−0.851989	−	0.352905i	−0.765569	+	0.643354i	$0.777543\pi$
$380$	−3.97602	−	0.470718i	−0.203965	−	0.0241473i
$381$	48.8769	+	20.2455i	2.50404	+	1.03721i
$382$	0.599150	−	10.1570i	0.0306552	−	0.519679i
$383$	10.0660	+	10.0660i	0.514350	+	0.514350i	0.915856	−	0.401506i	$-0.131513\pi$
$383$	10.0660	+	10.0660i	0.514350	+	0.514350i	−0.401506	+	0.915856i	$0.631513\pi$
$384$	19.7053	+	20.4992i	1.00558	+	1.04610i
$385$	−38.1616	−	38.1616i	−1.94489	−	1.94489i
$386$	−4.37178	−	4.91989i	−0.222518	−	0.250416i
$387$	0.605324	−	1.46138i	0.0307704	−	0.0742862i
$388$	−13.3358	+	10.5124i	−0.677022	+	0.533687i
$389$	−8.92458	−	21.5458i	−0.452494	−	1.09242i	−0.971371	−	0.237569i	$-0.923650\pi$
$389$	−8.92458	−	21.5458i	−0.452494	−	1.09242i	0.518876	−	0.854849i	$-0.326350\pi$
$390$	30.4934	−	6.73074i	1.54409	−	0.340824i
$391$	−28.3740	−	28.3740i	−1.43493	−	1.43493i
$392$	26.8881	+	4.80290i	1.35805	+	0.242583i
$393$	−25.3377	−	25.3377i	−1.27812	−	1.27812i
$394$	5.87903	−	12.1204i	0.296181	−	0.610615i
$395$	3.38762	−	8.17845i	0.170450	−	0.411502i
$396$	−9.76962	−	34.6446i	−0.490942	−	1.74095i
$397$	2.66187	+	6.42632i	0.133595	+	0.322528i	0.976494	−	0.215545i	$-0.0691527\pi$
$397$	2.66187	+	6.42632i	0.133595	+	0.322528i	−0.842899	+	0.538072i	$0.819153\pi$
$398$	0.704993	−	0.626452i	0.0353381	−	0.0314012i
$399$	−8.42688			−0.421872
$400$	−1.95962	−	3.19825i	−0.0979810	−	0.159913i
$401$	0.803747	−	0.803747i	0.0401372	−	0.0401372i	−0.686753	−	0.726891i	$-0.740965\pi$
$401$	0.803747	−	0.803747i	0.0401372	−	0.0401372i	0.726891	+	0.686753i	$0.240965\pi$
$402$	4.66778	+	0.275346i	0.232808	+	0.0137330i
$403$	0.266444	+	0.940148i	0.0132725	+	0.0468321i
$404$	9.45414	+	33.5258i	0.470361	+	1.66797i
$405$	−17.8979	−	7.41355i	−0.889353	−	0.368382i
$406$	21.8963	+	10.6209i	1.08669	+	0.527105i
$407$	−20.0302	−	20.0302i	−0.992858	−	0.992858i
$408$	−30.1068	−	19.2746i	−1.49051	−	0.954233i
$409$			29.7864i			1.47284i	0.676523	+	0.736422i	$0.263486\pi$
$409$			29.7864i			1.47284i	−0.676523	+	0.736422i	$0.736514\pi$
$410$	−6.58847	+	13.5830i	−0.325381	+	0.670814i
$411$	−0.368487	+	0.889607i	−0.0181761	+	0.0438811i
$412$	0.962780	−	0.758946i	0.0474328	−	0.0373906i
$413$	−8.88671	−	3.68100i	−0.437287	−	0.181130i
$414$	2.20385	−	37.3606i	0.108313	−	1.83617i
$415$	−10.5949			−0.520086
$416$	−14.1539	−	14.6856i	−0.693950	−	0.720023i
$417$	−1.38080			−0.0676180
$418$	0.371275	−	6.29400i	0.0181596	−	0.307850i
$419$	25.9952	+	10.7676i	1.26995	+	0.526030i	0.912949	−	0.408075i	$-0.133800\pi$
$419$	25.9952	+	10.7676i	1.26995	+	0.526030i	0.357000	+	0.934104i	$0.383800\pi$
$420$	−30.9468	−	39.2583i	−1.51005	−	1.91561i
$421$	−1.89731	+	4.58051i	−0.0924692	+	0.223240i	−0.963347	−	0.268260i	$-0.913551\pi$
$421$	−1.89731	+	4.58051i	−0.0924692	+	0.223240i	0.870877	+	0.491500i	$0.163551\pi$
$422$	−10.2047	+	21.0383i	−0.496756	+	1.02413i
$423$			28.7544i			1.39809i
$424$	−5.29356	−	24.1321i	−0.257078	−	1.17196i
$425$	3.33445	+	3.33445i	0.161744	+	0.161744i
$426$	−3.92690	−	1.90476i	−0.190259	−	0.0922858i
$427$	9.52856	+	3.94686i	0.461119	+	0.191002i
$428$	−37.0829	+	10.4572i	−1.79247	+	0.505468i
$429$	13.4085	+	47.3119i	0.647369	+	2.28424i
$430$	1.64072	+	0.0967836i	0.0791223	+	0.00466732i
$431$	−2.77766	+	2.77766i	−0.133795	+	0.133795i	−0.770833	−	0.637038i	$-0.780160\pi$
$431$	−2.77766	+	2.77766i	−0.133795	+	0.133795i	0.637038	+	0.770833i	$0.280160\pi$
$432$	−0.497615	−	3.14308i	−0.0239415	−	0.151222i
$433$	8.92614			0.428963			0.214481	−	0.976728i	$-0.431194\pi$
$433$	8.92614			0.428963			0.214481	+	0.976728i	$0.431194\pi$
$434$	1.16932	−	1.03905i	0.0561293	−	0.0498762i
$435$	−9.88167	−	23.8565i	−0.473790	−	1.14383i
$436$	−38.5610	+	10.8740i	−1.84674	+	0.520772i
$437$	2.50864	−	6.05638i	0.120004	−	0.289716i
$438$	7.69592	−	15.8661i	0.367725	−	0.758112i
$439$	29.2150	+	29.2150i	1.39435	+	1.39435i	0.815262	+	0.579092i	$0.196593\pi$
$439$	29.2150	+	29.2150i	1.39435	+	1.39435i	0.579092	+	0.815262i	$0.303407\pi$
$440$	30.6853	−	21.3843i	1.46286	−	1.01946i
$441$	−22.6468	−	22.6468i	−1.07842	−	1.07842i
$442$	21.6137	+	13.7975i	1.02806	+	0.656278i
$443$	−2.68733	−	6.48779i	−0.127679	−	0.308244i	0.847094	−	0.531443i	$-0.178350\pi$
$443$	−2.68733	−	6.48779i	−0.127679	−	0.308244i	−0.974773	+	0.223199i	$0.928350\pi$
$444$	−16.2433	−	20.6058i	−0.770871	−	0.977908i
$445$	−5.31353	+	12.8280i	−0.251886	+	0.608106i
$446$	0.965026	+	1.08601i	0.0456953	+	0.0514243i
$447$	20.0986	+	20.0986i	0.950631	+	0.950631i
$448$	−11.3037	+	30.6311i	−0.534048	+	1.44718i
$449$	−11.8449	−	11.8449i	−0.558998	−	0.558998i	0.370024	−	0.929022i	$-0.379349\pi$
$449$	−11.8449	−	11.8449i	−0.558998	−	0.558998i	−0.929022	+	0.370024i	$0.879349\pi$
$450$	−0.258991	+	4.39053i	−0.0122090	+	0.206972i
$451$	−21.9635	−	9.09760i	−1.03422	−	0.428389i
$452$	−2.96350	+	25.0318i	−0.139391	+	1.17740i
$453$	−7.90114	−	3.27276i	−0.371228	−	0.153768i
$454$	23.8120	−	8.25687i	1.11755	−	0.387514i
$455$	22.2349	+	28.1310i	1.04239	+	1.31880i
$456$	1.02692	−	5.74904i	0.0480901	−	0.269223i
$457$	9.11658			0.426456			0.213228	−	0.977002i	$-0.431602\pi$
$457$	9.11658			0.426456			0.213228	+	0.977002i	$0.431602\pi$
$458$	3.94454	+	1.91331i	0.184316	+	0.0894033i
$459$	1.53101	+	3.69619i	0.0714616	+	0.172524i
$460$	37.4275	−	10.5544i	1.74507	−	0.492101i
$461$	−2.45318	+	1.01614i	−0.114256	+	0.0473265i	−0.439079	−	0.898448i	$-0.644695\pi$
$461$	−2.45318	+	1.01614i	−0.114256	+	0.0473265i	0.324823	+	0.945775i	$0.394695\pi$
$462$	58.8448	−	52.2892i	2.73771	−	2.43271i
$463$	16.2353	+	16.2353i	0.754519	+	0.754519i	0.975319	−	0.220800i	$-0.0708668\pi$
$463$	16.2353	+	16.2353i	0.754519	+	0.754519i	−0.220800	+	0.975319i	$0.570867\pi$
$464$	−9.91418	+	13.6439i	−0.460254	+	0.633403i
$465$	−1.65978			−0.0769704
$466$	8.44043	−	7.50012i	0.390995	−	0.347436i
$467$	35.4210	+	14.6719i	1.63909	+	0.678933i	0.996206	−	0.0870301i	$-0.0277376\pi$
$467$	35.4210	+	14.6719i	1.63909	+	0.678933i	0.642884	+	0.765963i	$0.277738\pi$
$468$	3.77066	+	23.6168i	0.174299	+	1.09169i
$469$	2.05469	+	4.96046i	0.0948768	+	0.229053i
$470$	−28.2286	+	9.78833i	−1.30209	+	0.451502i
$471$	23.1673	−	23.1673i	1.06749	−	1.06749i
$472$	3.59423	−	5.61417i	0.165438	−	0.258413i
$473$			2.58820i			0.119006i
$474$	11.6176	+	5.63519i	0.533616	+	0.258833i
$475$	−0.294809	+	0.711733i	−0.0135268	+	0.0326565i
$476$	4.82597	−	40.7636i	0.221198	−	1.86839i
$477$	−11.0861	+	26.7643i	−0.507599	+	1.22545i
$478$	−19.7395	+	17.5404i	−0.902864	+	0.802280i
$479$	−14.9516	+	14.9516i	−0.683157	+	0.683157i	−0.960710	−	0.277553i	$-0.910477\pi$
$479$	−14.9516	+	14.9516i	−0.683157	+	0.683157i	0.277553	+	0.960710i	$0.410477\pi$
$480$	30.5543	−	16.3286i	1.39461	−	0.745293i
$481$	11.6706	+	14.7653i	0.532134	+	0.673242i
$482$	−12.0739	+	10.7288i	−0.549950	+	0.488682i
$483$	75.6169	−	31.3215i	3.44069	−	1.42518i
$484$	22.8424	+	28.9773i	1.03829	+	1.31715i
$485$	7.91740	+	19.1143i	0.359511	+	0.867935i
$486$	13.8052	−	28.4612i	0.626217	−	1.29102i
$487$	−1.17258			−0.0531348			−0.0265674	−	0.999647i	$-0.508458\pi$
$487$	−1.17258			−0.0531348			−0.0265674	+	0.999647i	$0.508458\pi$
$488$	−3.85383	+	6.01966i	−0.174455	+	0.272497i
$489$			46.4357i			2.09989i
$490$	14.5234	−	29.9418i	0.656100	−	1.35263i
$491$	2.70855	+	6.53902i	0.122235	+	0.295102i	0.973138	−	0.230221i	$-0.0739448\pi$
$491$	2.70855	+	6.53902i	0.122235	+	0.295102i	−0.850903	+	0.525322i	$0.823945\pi$
$492$	−19.2122	−	10.7601i	−0.866153	−	0.485105i
$493$	8.11426	−	19.5896i	0.365448	−	0.882269i
$494$	−0.731227	+	4.12476i	−0.0328995	+	0.185582i
$495$	−43.8561			−1.97119
$496$	0.566372	+	0.924364i	0.0254309	+	0.0415052i
$497$		−	5.01157i		−	0.224800i
$498$	0.910035	−	15.4273i	0.0407796	−	0.691313i
$499$	−6.81288	−	16.4477i	−0.304986	−	0.736302i	−0.999853	−	0.0171632i	$-0.994537\pi$
$499$	−6.81288	−	16.4477i	−0.304986	−	0.736302i	0.694866	−	0.719139i	$-0.255463\pi$
$500$	19.0544	−	5.37325i	0.852137	−	0.240299i
$501$	−11.1364	+	26.8856i	−0.497537	+	1.20116i
$502$	−36.5206	+	12.6636i	−1.62999	+	0.565204i
$503$	17.3525	−	17.3525i	0.773708	−	0.773708i	−0.205045	−	0.978753i	$-0.565734\pi$
$503$	17.3525	−	17.3525i	0.773708	−	0.773708i	0.978753	+	0.205045i	$0.0657339\pi$
$504$	31.4100	−	21.8894i	1.39911	−	0.975029i
$505$	42.4400			1.88855
$506$	20.0624	+	57.8579i	0.891880	+	2.57210i
$507$	−5.19341	−	32.2572i	−0.230647	−	1.43259i
$508$	−41.8077	−	4.94958i	−1.85492	−	0.219602i
$509$	12.8446	+	31.0097i	0.569329	+	1.37448i	0.902122	+	0.431482i	$0.142009\pi$
$509$	12.8446	+	31.0097i	0.569329	+	1.37448i	−0.332793	+	0.943000i	$0.607991\pi$
$510$	−32.5578	+	28.9306i	−1.44168	+	1.28107i
$511$	20.2486			0.895744
$512$	−19.5199	−	11.4444i	−0.862664	−	0.505778i
$513$	−0.462154	+	0.462154i	−0.0204046	+	0.0204046i
$514$	1.80567	−	30.6104i	0.0796446	−	1.35017i
$515$	−0.571598	−	1.37996i	−0.0251876	−	0.0608083i
$516$	−0.281853	+	2.38073i	−0.0124079	+	0.104806i
$517$	−18.0050	−	43.4680i	−0.791861	−	1.91172i
$518$	13.1487	−	27.1077i	0.577721	−	1.19105i
$519$	−34.9888	+	34.9888i	−1.53584	+	1.53584i
$520$	−21.9013	+	11.7411i	−0.960437	+	0.514882i
$521$	−23.5185	−	23.5185i	−1.03036	−	1.03036i	−0.999524	−	0.0308404i	$-0.990182\pi$
$521$	−23.5185	−	23.5185i	−1.03036	−	1.03036i	−0.0308404	−	0.999524i	$-0.509818\pi$
$522$	18.6847	−	6.47897i	0.817808	−	0.283577i
$523$	−4.09508	+	1.69624i	−0.179065	+	0.0741713i	−0.470415	−	0.882445i	$-0.655896\pi$
$523$	−4.09508	+	1.69624i	−0.179065	+	0.0741713i	0.291349	+	0.956617i	$0.405896\pi$
$524$	24.8787	+	13.9338i	1.08683	+	0.608699i
$525$	−8.88632	+	3.68084i	−0.387831	+	0.160645i
$526$	−27.1866	−	30.5951i	−1.18539	−	1.33401i
$527$	−0.963727	−	0.963727i	−0.0419806	−	0.0419806i
$528$	28.5020	+	46.5176i	1.24039	+	2.02442i
$529$			40.6699i			1.76826i
$530$	−30.0486	−	1.77253i	−1.30523	−	0.0769937i
$531$	−7.22155	+	2.99126i	−0.313388	+	0.129810i
$532$	6.45419	−	1.82005i	0.279825	−	0.0789093i
$533$	13.7910	+	7.70026i	0.597356	+	0.333535i
$534$	−18.2224	−	8.83887i	−0.788562	−	0.382495i
$535$			46.9428i			2.02951i
$536$	−3.63455	+	0.797267i	−0.156989	+	0.0344367i
$537$	−26.6446	−	26.6446i	−1.14980	−	1.14980i
$538$	11.0232	+	5.34684i	0.475244	+	0.230519i
$539$	48.4157	+	20.0544i	2.08541	+	0.863806i
$540$	−3.85025	−	0.455828i	−0.165688	−	0.0196157i
$541$	19.1499	−	7.93214i	0.823318	−	0.341029i	0.0690638	−	0.997612i	$-0.477999\pi$
$541$	19.1499	−	7.93214i	0.823318	−	0.341029i	0.754254	+	0.656583i	$0.227999\pi$
$542$	15.1073	+	17.0013i	0.648914	+	0.730270i
$543$	−9.03088			−0.387552
$544$	27.2219	+	8.25997i	1.16713	+	0.354143i
$545$			48.8140i			2.09096i
$546$	−42.8714	+	29.9600i	−1.83473	+	1.28217i
$547$	−7.91096	−	3.27683i	−0.338248	−	0.140107i	0.207093	−	0.978321i	$-0.433600\pi$
$547$	−7.91096	−	3.27683i	−0.338248	−	0.140107i	−0.545341	+	0.838214i	$0.683600\pi$
$548$	0.0900872	−	0.760940i	0.00384833	−	0.0325058i
$549$	7.74313	−	3.20731i	0.330469	−	0.136885i
$550$	−2.35768	−	6.79933i	−0.100532	−	0.289924i
$551$	3.46395			0.147569
$552$	12.1535	+	55.4047i	0.517286	+	2.35818i
$553$			14.8266i			0.630492i
$554$	19.1878	−	6.65340i	0.815210	−	0.282676i
$555$	−29.5344	+	12.2336i	−1.25367	+	0.519286i
$556$	1.05756	−	0.298227i	0.0448505	−	0.0126477i
$557$	11.8548	+	28.6200i	0.502304	+	1.21267i	0.948226	+	0.317596i	$0.102876\pi$
$557$	11.8548	+	28.6200i	0.502304	+	1.21267i	−0.445922	+	0.895072i	$0.647124\pi$
$558$	0.0748541	−	1.26896i	0.00316883	−	0.0537192i
$559$	0.199943	−	1.70796i	0.00845667	−	0.0722392i
$560$	32.1813	+	23.3842i	1.35991	+	0.988161i
$561$	−48.4985	−	48.4985i	−2.04761	−	2.04761i
$562$	21.8829	+	1.29084i	0.923075	+	0.0544510i
$563$	−9.90386	−	4.10231i	−0.417398	−	0.172892i	0.164093	−	0.986445i	$-0.447530\pi$
$563$	−9.90386	−	4.10231i	−0.417398	−	0.172892i	−0.581491	+	0.813553i	$0.697530\pi$
$564$	−11.8281	−	41.9443i	−0.498054	−	1.76618i
$565$	28.3733	+	11.7526i	1.19367	+	0.494436i
$566$	30.3955	−	10.5397i	1.27762	−	0.443017i
$567$	32.4469			1.36264
$568$	3.41902	+	0.610724i	0.143459	+	0.0256254i
$569$	−8.00079	−	8.00079i	−0.335411	−	0.335411i	0.519226	−	0.854637i	$-0.326220\pi$
$569$	−8.00079	−	8.00079i	−0.335411	−	0.335411i	−0.854637	+	0.519226i	$0.826220\pi$
$570$	−6.40196	−	3.10530i	−0.268149	−	0.130067i
$571$	−23.8277	+	9.86976i	−0.997159	+	0.413037i	−0.820755	−	0.571281i	$-0.806447\pi$
$571$	−23.8277	+	9.86976i	−0.997159	+	0.413037i	−0.176404	+	0.984318i	$0.556447\pi$
$572$	−20.4881	−	33.3404i	−0.856652	−	1.39403i
$573$	6.91968	−	16.7056i	0.289074	−	0.697885i
$574$	1.48894	−	25.2411i	0.0621472	−	1.05354i
$575$		−	7.48235i		−	0.312035i
$576$	11.1058	+	24.0962i	0.462741	+	1.00401i
$577$	3.30559	−	3.30559i	0.137613	−	0.137613i	−0.634944	−	0.772558i	$-0.718977\pi$
$577$	3.30559	−	3.30559i	0.137613	−	0.137613i	0.772558	+	0.634944i	$0.218977\pi$
$578$	−11.7024	−	0.690312i	−0.486758	−	0.0287132i
$579$	−4.47608	−	10.8062i	−0.186019	−	0.449091i
$580$	12.7210	+	16.1375i	0.528210	+	0.670073i
$581$	16.3946	−	6.79087i	0.680163	−	0.281733i
$582$	−28.5123	+	9.88672i	−1.18187	+	0.409818i
$583$		−	47.4012i		−	1.96316i
$584$	−2.46755	+	13.8141i	−0.102108	+	0.571631i
$585$	28.9408	+	3.38796i	1.19656	+	0.140075i
$586$	12.5228	+	6.07423i	0.517312	+	0.250924i
$587$	12.4595	−	30.0798i	0.514257	−	1.24153i	−0.427128	−	0.904191i	$-0.640475\pi$
$587$	12.4595	−	30.0798i	0.514257	−	1.24153i	0.941385	−	0.337334i	$-0.109525\pi$
$588$	42.3508	+	23.7193i	1.74652	+	0.978167i
$589$	0.0852062	−	0.205706i	0.00351086	−	0.00847597i
$590$	−5.39485	−	6.07122i	−0.222103	−	0.249948i
$591$	16.9281	−	16.9281i	0.696328	−	0.696328i
$592$	16.8913	+	12.2738i	0.694227	+	0.504451i
$593$	29.2021	−	29.2021i	1.19919	−	1.19919i	0.224775	−	0.974411i	$-0.427835\pi$
$593$	29.2021	−	29.2021i	1.19919	−	1.19919i	0.974411	−	0.224775i	$-0.0721646\pi$
$594$	0.359531	−	6.09491i	0.0147517	−	0.250077i
$595$	−46.2051	−	19.1388i	−1.89422	−	0.784613i
$596$	−19.7345	−	11.0527i	−0.808358	−	0.452735i
$597$	1.54847	−	0.641397i	0.0633746	−	0.0262506i
$598$	−8.76962	−	39.7305i	−0.358616	−	1.62470i
$599$	29.8756	−	29.8756i	1.22068	−	1.22068i	0.253295	−	0.967389i	$-0.418486\pi$
$599$	29.8756	−	29.8756i	1.22068	−	1.22068i	0.967389	−	0.253295i	$-0.0815142\pi$
$600$	−1.42825	−	6.51104i	−0.0583080	−	0.265812i
$601$	−8.07275	+	8.07275i	−0.329294	+	0.329294i	−0.852318	−	0.523024i	$-0.824804\pi$
$601$	−8.07275	+	8.07275i	−0.329294	+	0.329294i	0.523024	+	0.852318i	$0.324804\pi$
$602$	−2.60087	+	0.901859i	−0.106004	+	0.0367570i
$603$	4.03099	+	1.66969i	0.164154	+	0.0679950i
$604$	6.75837	+	0.800119i	0.274994	+	0.0325564i
$605$	41.5334	−	17.2037i	1.68857	−	0.699430i
$606$	−3.64531	+	61.7968i	−0.148081	+	2.51032i
$607$			20.9605i			0.850760i	0.905015	+	0.425380i	$0.139860\pi$
$607$			20.9605i			0.850760i	−0.905015	+	0.425380i	$0.860140\pi$
$608$	0.455162	+	4.62501i	0.0184592	+	0.187569i
$609$	30.5817	+	30.5817i	1.23924	+	1.23924i
$610$	5.78450	+	6.50972i	0.234208	+	0.263571i
$611$	8.52363	+	30.0756i	0.344829	+	1.21673i
$612$	−20.6501	−	26.1963i	−0.834733	−	1.05892i
$613$	−6.32781	+	15.2767i	−0.255578	+	0.617019i	−0.998636	−	0.0522072i	$-0.983374\pi$
$613$	−6.32781	+	15.2767i	−0.255578	+	0.617019i	0.743059	+	0.669226i	$0.233374\pi$
$614$	13.8086	−	4.78818i	0.557272	−	0.193235i
$615$	−18.9708	+	18.9708i	−0.764977	+	0.764977i
$616$	−33.7760	+	52.7579i	−1.36087	+	2.12568i
$617$	−20.2985			−0.817186			−0.408593	−	0.912717i	$-0.633980\pi$
$617$	−20.2985			−0.817186			−0.408593	+	0.912717i	$0.633980\pi$
$618$	2.05845	−	0.713774i	0.0828032	−	0.0287122i
$619$	21.5815	+	8.93936i	0.867435	+	0.359303i	0.771611	−	0.636095i	$-0.219451\pi$
$619$	21.5815	+	8.93936i	0.867435	+	0.359303i	0.0958241	+	0.995398i	$0.469451\pi$
$620$	1.27123	−	0.358482i	0.0510539	−	0.0143970i
$621$	2.42928	−	5.86481i	0.0974838	−	0.235347i
$622$	−5.54165	−	6.23642i	−0.222200	−	0.250058i
$623$		−	23.2558i		−	0.931722i
$624$	−15.2151	−	32.8990i	−0.609090	−	1.31701i
$625$		−	28.8093i		−	1.15237i
$626$	−17.6022	+	15.6413i	−0.703527	+	0.625150i
$627$	4.28791	−	10.3519i	0.171243	−	0.413416i
$628$	−12.7402	+	22.7476i	−0.508389	+	0.907729i
$629$	−24.2520	−	10.0455i	−0.966990	−	0.400541i
$630$	−15.2817	−	44.0709i	−0.608837	−	1.75583i
$631$	15.8099			0.629383			0.314692	−	0.949194i	$-0.398099\pi$
$631$	15.8099			0.629383			0.314692	+	0.949194i	$0.398099\pi$
$632$	−10.1151	−	1.80681i	−0.402357	−	0.0718712i
$633$	−29.3834	+	29.3834i	−1.16788	+	1.16788i
$634$	−4.12107	−	11.8848i	−0.163669	−	0.472004i
$635$	−19.6290	+	47.3886i	−0.778953	+	1.88056i
$636$	5.16195	−	43.6015i	0.204685	−	1.72891i
$637$	−30.4005	−	16.9742i	−1.20451	−	0.672542i
$638$	−24.1888	+	21.4940i	−0.957642	+	0.850955i
$639$	−2.87970	−	2.87970i	−0.113919	−	0.113919i
$640$	−19.8750	+	19.1053i	−0.785628	+	0.755203i
$641$		−	9.61706i		−	0.379851i	−0.981799	−	0.189926i	$-0.939175\pi$
$641$		−	9.61706i		−	0.379851i	0.981799	−	0.189926i	$-0.0608247\pi$
$642$	−68.3533	−	4.03207i	−2.69769	−	0.159133i
$643$	4.73219	−	1.96014i	0.186619	−	0.0773002i	−0.287417	−	0.957806i	$-0.592797\pi$
$643$	4.73219	−	1.96014i	0.186619	−	0.0773002i	0.474036	+	0.880505i	$0.342797\pi$
$644$	−51.1504	+	40.3212i	−2.01561	+	1.58888i
$645$	2.69853	+	1.11777i	0.106255	+	0.0440121i
$646$	−1.91416	−	5.52025i	−0.0753117	−	0.217191i
$647$	15.6163	−	15.6163i	0.613942	−	0.613942i	−0.330029	−	0.943971i	$-0.607058\pi$
$647$	15.6163	−	15.6163i	0.613942	−	0.613942i	0.943971	+	0.330029i	$0.107058\pi$
$648$	−3.95407	+	22.1361i	−0.155331	+	0.869589i
$649$	9.04377	−	9.04377i	0.354999	−	0.354999i
$650$	1.03059	+	4.66904i	0.0404229	+	0.183135i
$651$	2.56834	−	1.06384i	0.100661	−	0.0416952i
$652$	−10.0293	−	35.5653i	−0.392776	−	1.39284i
$653$	−9.14062	−	3.78617i	−0.357700	−	0.148164i	0.196594	−	0.980485i	$-0.437012\pi$
$653$	−9.14062	−	3.78617i	−0.357700	−	0.148164i	−0.554294	+	0.832321i	$0.687012\pi$
$654$	−71.0779	−	4.19279i	−2.77937	−	0.163951i
$655$	24.5661	−	24.5661i	0.959878	−	0.959878i
$656$	17.0387	+	4.09175i	0.665250	+	0.159756i
$657$	11.6351	−	11.6351i	0.453927	−	0.453927i
$658$	37.4070	−	33.2396i	1.45828	−	1.29582i
$659$	−0.237209	+	0.572674i	−0.00924036	+	0.0223082i	−0.928432	−	0.371501i	$-0.878843\pi$
$659$	−0.237209	+	0.572674i	−0.00924036	+	0.0223082i	0.919192	+	0.393810i	$0.128843\pi$
$660$	63.9733	−	18.0402i	2.49016	−	0.702214i
$661$	−11.6004	+	28.0059i	−0.451204	+	1.08930i	0.520661	+	0.853763i	$0.325686\pi$
$661$	−11.6004	+	28.0059i	−0.451204	+	1.08930i	−0.971865	+	0.235539i	$0.924314\pi$
$662$	−3.49257	+	7.20038i	−0.135743	+	0.279851i
$663$	28.2578	+	35.7509i	1.09744	+	1.38845i
$664$	2.63501	+	12.0124i	0.102258	+	0.466171i
$665$		−	8.17028i		−	0.316830i
$666$	−8.02101	−	23.1318i	−0.310808	−	0.896339i
$667$	−31.0831	+	12.8750i	−1.20354	+	0.498523i
$668$	2.72261	−	22.9971i	0.105341	−	0.889784i
$669$	0.988048	+	2.38536i	0.0382001	+	0.0922233i
$670$	−0.266962	+	4.52565i	−0.0103136	+	0.174841i
$671$	−9.69697	+	9.69697i	−0.374347	+	0.374347i
$672$	−36.8138	+	44.8507i	−1.42012	+	1.73015i
$673$		−	31.6025i		−	1.21819i	−0.793099	−	0.609093i	$-0.791534\pi$
$673$		−	31.6025i		−	1.21819i	0.793099	−	0.609093i	$-0.208466\pi$
$674$	−16.0679	−	0.947821i	−0.618911	−	0.0365087i
$675$	−0.285484	+	0.689219i	−0.0109883	+	0.0265281i
$676$	10.9446	+	23.5842i	0.420947	+	0.907085i
$677$	5.79654	−	2.40100i	0.222779	−	0.0922781i	−0.268502	−	0.963279i	$-0.586529\pi$
$677$	5.79654	−	2.40100i	0.222779	−	0.0922781i	0.491281	+	0.871001i	$0.336529\pi$
$678$	−19.5500	+	40.3048i	−0.750814	+	1.54790i
$679$	−24.5027	−	24.5027i	−0.940329	−	0.940329i
$680$	18.6876	−	29.1900i	0.716638	−	1.11938i
$681$	44.7895			1.71634
$682$	0.681421	+	1.96515i	0.0260930	+	0.0752495i
$683$	−8.06538	−	3.34079i	−0.308613	−	0.127832i	0.223002	−	0.974818i	$-0.428415\pi$
$683$	−8.06538	−	3.34079i	−0.308613	−	0.127832i	−0.531615	+	0.846986i	$0.678415\pi$
$684$	2.66283	−	4.75447i	0.101816	−	0.181792i
$685$	−0.862518	−	0.357266i	−0.0329551	−	0.0136505i
$686$	−0.903011	+	15.3082i	−0.0344771	+	0.584470i
$687$	5.50919	+	5.50919i	0.210189	+	0.210189i
$688$	−0.298322	−	1.88429i	−0.0113734	−	0.0718378i
$689$	−3.66182	+	31.2803i	−0.139504	+	1.19168i
$690$	68.9886	+	4.06954i	2.62635	+	0.154925i
$691$	6.60806	+	15.9533i	0.251383	+	0.606891i	0.998316	−	0.0580075i	$-0.0184747\pi$
$691$	6.60806	+	15.9533i	0.251383	+	0.606891i	−0.746934	+	0.664899i	$0.768475\pi$
$692$	19.2412	−	34.3551i	0.731439	−	1.30598i
$693$	67.8629	−	28.1097i	2.57790	−	1.06780i
$694$	14.9037	+	42.9809i	0.565738	+	1.63153i
$695$		−	1.33875i		−	0.0507818i
$696$	−24.5904	+	17.1369i	−0.932098	+	0.649572i
$697$	−22.0303			−0.834456
$698$	−20.5504	+	7.12589i	−0.777843	+	0.269719i
$699$	18.5388	−	7.67904i	0.701203	−	0.290448i
$700$	6.01108	−	4.73845i	0.227198	−	0.179097i
$701$	10.3730	+	4.29664i	0.391783	+	0.162282i	0.569874	−	0.821732i	$-0.306992\pi$
$701$	10.3730	+	4.29664i	0.391783	+	0.162282i	−0.178091	+	0.984014i	$0.556992\pi$
$702$	−0.708097	+	3.99428i	−0.0267254	+	0.150754i
$703$		−	4.28840i		−	0.161740i
$704$	−31.8768	−	29.4721i	−1.20140	−	1.11077i
$705$	−53.0968			−1.99974
$706$	−5.06482	+	4.50057i	−0.190617	+	0.169381i
$707$	−65.6715	+	27.2020i	−2.46983	+	1.02304i
$708$	9.30368	−	7.33396i	0.349654	−	0.275627i
$709$	4.44444	+	1.84095i	0.166914	+	0.0691382i	0.464576	−	0.885533i	$-0.346207\pi$
$709$	4.44444	+	1.84095i	0.166914	+	0.0691382i	−0.297662	+	0.954671i	$0.596207\pi$
$710$	1.84676	−	3.80732i	0.0693076	−	0.142886i
$711$	8.51954	+	8.51954i	0.319508	+	0.319508i
$712$	15.8657	+	2.83401i	0.594592	+	0.106209i
$713$			2.16256i			0.0809885i
$714$	31.8366	−	65.6352i	1.19146	−	2.45634i
$715$	−45.8712	+	13.0002i	−1.71549	+	0.486180i
$716$	26.1620	+	14.6525i	0.977718	+	0.547589i
$717$	−43.3565	+	17.9589i	−1.61918	+	0.670686i
$718$	−0.0438904	+	0.744049i	−0.00163798	+	0.0277676i
$719$			11.8616i			0.442364i	0.975233	+	0.221182i	$0.0709915\pi$
$719$			11.8616i			0.442364i	−0.975233	+	0.221182i	$0.929008\pi$
$720$	31.9286	−	5.05496i	1.18991	−	0.188387i
$721$	1.76898	+	1.76898i	0.0658803	+	0.0658803i
$722$	−19.3724	+	17.2142i	−0.720965	+	0.640645i
$723$	−26.5195	+	10.9847i	−0.986269	+	0.408526i
$724$	6.91679	−	1.95051i	0.257061	−	0.0724899i
$725$	3.65281	−	1.51304i	0.135662	−	0.0561930i
$726$	21.4829	+	61.9545i	0.797304	+	2.29935i
$727$	6.70400	+	6.70400i	0.248638	+	0.248638i	0.820411	−	0.571774i	$-0.193745\pi$
$727$	6.70400	+	6.70400i	0.248638	+	0.248638i	−0.571774	+	0.820411i	$0.693745\pi$
$728$	26.3646	−	32.2059i	0.977136	−	1.19363i
$729$	22.8858	−	22.8858i	0.847623	−	0.847623i
$730$	15.3830	+	7.46157i	0.569349	+	0.276165i
$731$	0.917848	+	2.21588i	0.0339478	+	0.0819573i
$732$	−9.97564	+	7.86366i	−0.368710	+	0.290649i
$733$	−0.866703	−	2.09241i	−0.0320124	−	0.0772848i	0.907065	−	0.420991i	$-0.138318\pi$
$733$	−0.866703	−	2.09241i	−0.0320124	−	0.0772848i	−0.939077	+	0.343706i	$0.888318\pi$
$734$	6.18402	+	0.364787i	0.228256	+	0.0134645i
$735$	41.8186	−	41.8186i	1.54250	−	1.54250i
$736$	−21.2748	−	39.8098i	−0.784200	−	1.46741i
$737$	−7.13914			−0.262973
$738$	−13.6483	−	15.3594i	−0.502400	−	0.565387i
$739$	−8.35015	−	20.1590i	−0.307165	−	0.741563i	−0.999795	−	0.0202688i	$-0.993548\pi$
$739$	−8.35015	−	20.1590i	−0.307165	−	0.741563i	0.692629	−	0.721294i	$-0.256452\pi$
$740$	19.9783	−	15.7486i	0.734418	−	0.578932i
$741$	−3.62931	+	6.50003i	−0.133326	+	0.238785i
$742$	47.6333	−	16.5170i	1.74867	−	0.606357i
$743$	4.96816			0.182264			0.0911321	−	0.995839i	$-0.470951\pi$
$743$	4.96816			0.182264			0.0911321	+	0.995839i	$0.470951\pi$
$744$	0.412795	+	1.88183i	0.0151338	+	0.0689912i
$745$	−19.4866	+	19.4866i	−0.713933	+	0.713933i
$746$	11.4563	+	33.0388i	0.419444	+	1.20964i
$747$	5.51842	−	13.3226i	0.201908	−	0.487450i
$748$	47.6200	+	26.6704i	1.74116	+	0.975167i
$749$	−30.0881	−	72.6392i	−1.09940	−	2.65418i
$750$	35.1221	+	2.07181i	1.28248	+	0.0756516i
$751$			13.5718i			0.495244i	0.968857	+	0.247622i	$0.0796491\pi$
$751$			13.5718i			0.495244i	−0.968857	+	0.247622i	$0.920351\pi$
$752$	18.1184	+	29.5707i	0.660711	+	1.07833i
$753$	−68.6938			−2.50334
$754$	17.6227	−	12.3154i	0.641781	−	0.448499i
$755$	3.17310	−	7.66054i	0.115481	−	0.278796i
$756$	6.25003	−	1.76248i	0.227311	−	0.0641008i
$757$	6.68726	+	16.1445i	0.243053	+	0.586781i	0.997583	−	0.0694842i	$-0.0221353\pi$
$757$	6.68726	+	16.1445i	0.243053	+	0.586781i	−0.754530	+	0.656265i	$0.772135\pi$
$758$	22.8439	+	11.0805i	0.829729	+	0.402463i
$759$			108.828i			3.95022i
$760$	5.57398	+	0.995654i	0.202189	+	0.0361162i
$761$	37.6266			1.36396			0.681982	−	0.731369i	$-0.261118\pi$
$761$	37.6266			1.36396			0.681982	+	0.731369i	$0.261118\pi$
$762$	−67.3164	−	32.6521i	−2.43862	−	1.18286i
$763$	−31.2875	−	75.5346i	−1.13268	−	2.73454i
$764$	−1.69171	+	14.2894i	−0.0612040	+	0.516972i
$765$	−37.5473	+	15.5526i	−1.35753	+	0.562305i
$766$	−13.3725	−	15.0491i	−0.483170	−	0.543746i
$767$	−6.66667	+	5.26938i	−0.240719	+	0.190266i
$768$	−26.1121	−	30.5810i	−0.942237	−	1.10350i
$769$	25.6166	−	25.6166i	0.923759	−	0.923759i	−0.0735336	−	0.997293i

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)

\(f(q)\)	\(=\)	\(q+(-1.41176 - 0.0832778i) q^{2} +(-2.32196 - 0.961788i) q^{3} +(1.98613 + 0.235136i) q^{4} +(0.932501 - 2.25126i) q^{5} +(3.19796 + 1.55118i) q^{6} +4.08128i q^{7} +(-2.78436 - 0.497357i) q^{8} +(2.34515 + 2.34515i) q^{9} +O(q^{10})\)	\(q+(-1.41176 - 0.0832778i) q^{2} +(-2.32196 - 0.961788i) q^{3} +(1.98613 + 0.235136i) q^{4} +(0.932501 - 2.25126i) q^{5} +(3.19796 + 1.55118i) q^{6} +4.08128i q^{7} +(-2.78436 - 0.497357i) q^{8} +(2.34515 + 2.34515i) q^{9} +(-1.50395 + 3.10058i) q^{10} +(-5.01361 - 2.07671i) q^{11} +(-4.38557 - 2.45621i) q^{12} +(3.14807 + 1.75774i) q^{13} +(0.339880 - 5.76179i) q^{14} +(-4.33046 + 4.33046i) q^{15} +(3.88942 + 0.934023i) q^{16} -5.02884 q^{17} +(-3.11549 - 3.50609i) q^{18} +(-0.314391 - 0.759008i) q^{19} +(2.38142 - 4.25202i) q^{20} +(3.92533 - 9.47658i) q^{21} +(6.90507 + 3.34933i) q^{22} +(5.64225 + 5.64225i) q^{23} +(5.98682 + 3.83280i) q^{24} +(-0.663064 - 0.663064i) q^{25} +(-4.29794 - 2.74366i) q^{26} +(-0.304446 - 0.734999i) q^{27} +(-0.959658 + 8.10595i) q^{28} +(-1.61354 + 3.89544i) q^{29} +(6.47420 - 5.75294i) q^{30} +(0.191640 + 0.191640i) q^{31} +(-5.41314 - 1.64252i) q^{32} +(9.64406 + 9.64406i) q^{33} +(7.09952 + 0.418791i) q^{34} +(9.18801 + 3.80580i) q^{35} +(4.10634 + 5.20920i) q^{36} +(4.82258 + 1.99758i) q^{37} +(0.380636 + 1.09772i) q^{38} +(-5.61914 - 7.10917i) q^{39} +(-3.71609 + 5.80451i) q^{40} +4.38078 q^{41} +(-6.33081 + 13.0518i) q^{42} +(-0.182517 - 0.440634i) q^{43} +(-9.46937 - 5.30349i) q^{44} +(7.46639 - 3.09268i) q^{45} +(-7.49562 - 8.43537i) q^{46} +(6.13062 + 6.13062i) q^{47} +(-8.13276 - 5.90956i) q^{48} -9.65685 q^{49} +(0.880869 + 0.991306i) q^{50} +(11.6768 + 4.83668i) q^{51} +(5.83917 + 4.23132i) q^{52} +(3.34267 + 8.06993i) q^{53} +(0.368596 + 1.06300i) q^{54} +(-9.35039 + 9.35039i) q^{55} +(2.02985 - 11.3637i) q^{56} +2.06476i q^{57} +(2.60234 - 5.36505i) q^{58} +(-0.901922 + 2.17743i) q^{59} +(-9.61911 + 7.58261i) q^{60} +(0.967064 - 2.33470i) q^{61} +(-0.254590 - 0.286509i) q^{62} +(-9.57121 + 9.57121i) q^{63} +(7.50527 + 2.76964i) q^{64} +(6.89270 - 5.44803i) q^{65} +(-12.8120 - 14.4182i) q^{66} +(1.21542 - 0.503443i) q^{67} +(-9.98793 - 1.18246i) q^{68} +(-7.67444 - 18.5277i) q^{69} +(-12.6543 - 6.13803i) q^{70} -1.22794 q^{71} +(-5.36335 - 7.69611i) q^{72} -4.96133i q^{73} +(-6.64197 - 3.22171i) q^{74} +(0.901883 + 2.17734i) q^{75} +(-0.445952 - 1.58141i) q^{76} +(8.47562 - 20.4620i) q^{77} +(7.34083 + 10.5044i) q^{78} +3.63284 q^{79} +(5.72961 - 7.88511i) q^{80} -7.95017i q^{81} +(-6.18461 - 0.364822i) q^{82} +(-1.66391 - 4.01702i) q^{83} +(10.0245 - 17.8987i) q^{84} +(-4.68940 + 11.3212i) q^{85} +(0.220975 + 0.637269i) q^{86} +(7.49317 - 7.49317i) q^{87} +(12.9268 + 8.27584i) q^{88} -5.69815 q^{89} +(-10.7983 + 3.74433i) q^{90} +(-7.17381 + 12.8482i) q^{91} +(9.87954 + 12.5329i) q^{92} +(-0.260663 - 0.629297i) q^{93} +(-8.14441 - 9.16550i) q^{94} -2.00189 q^{95} +(10.9894 + 9.02016i) q^{96} +(-6.00369 + 6.00369i) q^{97} +(13.6332 + 0.804201i) q^{98} +(-6.88748 - 16.6279i) 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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