LMFDB - Embedded newform 115.2.l.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	115.7
Dual form			115.2.l.a.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43652 + 0.174263i) q^{2} +(-0.128656 + 0.591424i) q^{3} +(3.92662 - 0.564562i) q^{4} +(-1.44483 - 1.70660i) q^{5} +(0.210410 - 1.46344i) q^{6} +(-0.0458364 + 0.0839431i) q^{7} +(-4.69506 + 1.02135i) q^{8} +(2.39567 + 1.09406i) q^{9} +O(q^{10})$	\(q+(-2.43652 + 0.174263i) q^{2} +(-0.128656 + 0.591424i) q^{3} +(3.92662 - 0.564562i) q^{4} +(-1.44483 - 1.70660i) q^{5} +(0.210410 - 1.46344i) q^{6} +(-0.0458364 + 0.0839431i) q^{7} +(-4.69506 + 1.02135i) q^{8} +(2.39567 + 1.09406i) q^{9} +(3.81775 + 3.90638i) q^{10} +(2.37754 - 2.06015i) q^{11} +(-0.171289 + 2.39493i) q^{12} +(5.54369 - 3.02708i) q^{13} +(0.0970531 - 0.212517i) q^{14} +(1.19521 - 0.634940i) q^{15} +(3.64902 - 1.07145i) q^{16} +(2.44442 + 3.26536i) q^{17} +(-6.02774 - 2.24823i) q^{18} +(-0.180176 - 1.25315i) q^{19} +(-6.63676 - 5.88546i) q^{20} +(-0.0437488 - 0.0379085i) q^{21} +(-5.43392 + 5.43392i) q^{22} +(-1.20538 - 4.64188i) q^{23} -2.90817i q^{24} +(-0.824954 + 4.93148i) q^{25} +(-12.9798 + 8.34161i) q^{26} +(-2.04342 + 2.72969i) q^{27} +(-0.132591 + 0.355490i) q^{28} +(-2.05829 - 0.295937i) q^{29} +(-2.80150 + 1.75532i) q^{30} +(-0.614903 - 0.395174i) q^{31} +(0.299649 - 0.111763i) q^{32} +(0.912536 + 1.67119i) q^{33} +(-6.52490 - 7.53014i) q^{34} +(0.209483 - 0.0430589i) q^{35} +(10.0245 + 2.94347i) q^{36} +(-1.47764 - 3.96171i) q^{37} +(0.657380 + 3.02193i) q^{38} +(1.07706 + 3.66812i) q^{39} +(8.52658 + 6.53691i) q^{40} +(-2.69875 - 5.90943i) q^{41} +(0.113201 + 0.0847411i) q^{42} +(-7.06043 - 1.53590i) q^{43} +(8.17261 - 9.43170i) q^{44} +(-1.59419 - 5.66917i) q^{45} +(3.74583 + 11.1000i) q^{46} +(3.91418 + 3.91418i) q^{47} +(0.164211 + 2.29596i) q^{48} +(3.77954 + 5.88108i) q^{49} +(1.15064 - 12.1594i) q^{50} +(-2.24570 + 1.02558i) q^{51} +(20.0590 - 15.0160i) q^{52} +(9.58880 + 5.23588i) q^{53} +(4.50315 - 7.00704i) q^{54} +(-6.95098 - 1.08095i) q^{55} +(0.129470 - 0.440933i) q^{56} +(0.764323 + 0.0546655i) q^{57} +(5.06663 + 0.362372i) q^{58} +(-4.23060 + 14.4081i) q^{59} +(4.33466 - 3.16794i) q^{60} +(1.76179 - 2.74140i) q^{61} +(1.56709 + 0.855694i) q^{62} +(-0.201648 + 0.150952i) q^{63} +(-7.62941 + 3.48424i) q^{64} +(-13.1757 - 5.08724i) q^{65} +(-2.51464 - 3.91285i) q^{66} +(-0.422879 - 5.91261i) q^{67} +(11.4418 + 11.4418i) q^{68} +(2.90040 - 0.115680i) q^{69} +(-0.502905 + 0.141419i) q^{70} +(-4.76419 + 5.49816i) q^{71} +(-12.3652 - 2.68989i) q^{72} +(1.73261 + 1.29702i) q^{73} +(4.29068 + 9.39529i) q^{74} +(-2.81046 - 1.12236i) q^{75} +(-1.41496 - 4.81892i) q^{76} +(0.0639575 + 0.294008i) q^{77} +(-3.26349 - 8.74976i) q^{78} +(-10.8439 - 3.18406i) q^{79} +(-7.10073 - 4.67935i) q^{80} +(3.82255 + 4.41146i) q^{81} +(7.60534 + 13.9281i) q^{82} +(4.53412 - 1.69114i) q^{83} +(-0.193186 - 0.124153i) q^{84} +(2.04090 - 8.88952i) q^{85} +(17.4705 + 2.51188i) q^{86} +(0.439836 - 1.17925i) q^{87} +(-9.05857 + 12.1008i) q^{88} +(6.50253 - 4.17892i) q^{89} +(4.87221 + 13.5352i) q^{90} +0.604105i q^{91} +(-7.35368 - 17.5464i) q^{92} +(0.312826 - 0.312826i) q^{93} +(-10.2191 - 8.85488i) q^{94} +(-1.87830 + 2.11807i) q^{95} +(0.0275477 + 0.191599i) q^{96} +(-6.94271 - 2.58950i) q^{97} +(-10.2338 - 13.6707i) q^{98} +(7.94973 - 2.33425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−2.43652	+	0.174263i	−1.72288	+	0.123223i	−0.897403	−	0.441213i	$-0.854548\pi$
$2$	−2.43652	+	0.174263i	−1.72288	+	0.123223i	−0.825477	+	0.564436i	$0.809094\pi$
$3$	−0.128656	+	0.591424i	−0.0742798	+	0.341459i	−0.999256	−	0.0385663i	$-0.987721\pi$
$3$	−0.128656	+	0.591424i	−0.0742798	+	0.341459i	0.924976	+	0.380025i	$0.124085\pi$
$4$	3.92662	−	0.564562i	1.96331	−	0.282281i
$5$	−1.44483	−	1.70660i	−0.646146	−	0.763214i
$5$	−1.44483	−	1.70660i	−0.646146	−	0.763214i
$6$	0.210410	−	1.46344i	0.0858996	−	0.597445i
$7$	−0.0458364	+	0.0839431i	−0.0173245	+	0.0317275i	−0.886198	−	0.463307i	$-0.846663\pi$
$7$	−0.0458364	+	0.0839431i	−0.0173245	+	0.0317275i	0.868873	+	0.495034i	$0.164845\pi$
$8$	−4.69506	+	1.02135i	−1.65996	+	0.361101i
$9$	2.39567	+	1.09406i	0.798556	+	0.364688i
$10$	3.81775	+	3.90638i	1.20728	+	1.23531i
$11$	2.37754	−	2.06015i	0.716856	−	0.621159i	−0.218099	−	0.975927i	$-0.569986\pi$
$11$	2.37754	−	2.06015i	0.716856	−	0.621159i	0.934954	+	0.354768i	$0.115440\pi$
$12$	−0.171289	+	2.39493i	−0.0494468	+	0.691357i
$13$	5.54369	−	3.02708i	1.53754	−	0.839562i	0.537550	−	0.843232i	$-0.319350\pi$
$13$	5.54369	−	3.02708i	1.53754	−	0.839562i	0.999993	+	0.00366978i	$0.00116813\pi$
$14$	0.0970531	−	0.212517i	0.0259385	−	0.0567974i
$15$	1.19521	−	0.634940i	0.308601	−	0.163941i
$16$	3.64902	−	1.07145i	0.912255	−	0.267862i
$17$	2.44442	+	3.26536i	0.592858	+	0.791966i	0.992176	−	0.124847i	$-0.0398439\pi$
$17$	2.44442	+	3.26536i	0.592858	+	0.791966i	−0.399318	+	0.916813i	$0.630753\pi$
$18$	−6.02774	−	2.24823i	−1.42075	−	0.529913i
$19$	−0.180176	−	1.25315i	−0.0413351	−	0.287492i	−0.999996	−	0.00294001i	$-0.999064\pi$
$19$	−0.180176	−	1.25315i	−0.0413351	−	0.287492i	0.958661	−	0.284552i	$-0.0918449\pi$
$20$	−6.63676	−	5.88546i	−1.48403	−	1.31603i
$21$	−0.0437488	−	0.0379085i	−0.00954677	−	0.00827232i
$22$	−5.43392	+	5.43392i	−1.15852	+	1.15852i
$23$	−1.20538	−	4.64188i	−0.251338	−	0.967899i
$23$	−1.20538	−	4.64188i	−0.251338	−	0.967899i
$24$		−	2.90817i		−	0.593628i
$25$	−0.824954	+	4.93148i	−0.164991	+	0.986295i
$26$	−12.9798	+	8.34161i	−2.54555	+	1.63592i
$27$	−2.04342	+	2.72969i	−0.393257	+	0.525329i
$28$	−0.132591	+	0.355490i	−0.0250573	+	0.0671813i
$29$	−2.05829	−	0.295937i	−0.382214	−	0.0549541i	−0.0514700	−	0.998675i	$-0.516391\pi$
$29$	−2.05829	−	0.295937i	−0.382214	−	0.0549541i	−0.330744	+	0.943720i	$0.607300\pi$
$30$	−2.80150	+	1.75532i	−0.511482	+	0.320477i
$31$	−0.614903	−	0.395174i	−0.110440	−	0.0709753i	0.484255	−	0.874927i	$-0.339091\pi$
$31$	−0.614903	−	0.395174i	−0.110440	−	0.0709753i	−0.594695	+	0.803952i	$0.702727\pi$
$32$	0.299649	−	0.111763i	0.0529710	−	0.0197572i
$33$	0.912536	+	1.67119i	0.158852	+	0.290916i
$34$	−6.52490	−	7.53014i	−1.11901	−	1.29141i
$35$	0.209483	−	0.0430589i	0.0354090	−	0.00727828i
$36$	10.0245	+	2.94347i	1.67076	+	0.490578i
$37$	−1.47764	−	3.96171i	−0.242923	−	0.651301i	0.757075	−	0.653328i	$-0.226628\pi$
$37$	−1.47764	−	3.96171i	−0.242923	−	0.651301i	−0.999998	+	0.00202662i	$0.999355\pi$
$38$	0.657380	+	3.02193i	0.106641	+	0.490221i
$39$	1.07706	+	3.66812i	0.172467	+	0.587370i
$40$	8.52658	+	6.53691i	1.34817	+	1.03358i
$41$	−2.69875	−	5.90943i	−0.421473	−	0.922898i	−0.994634	−	0.103455i	$-0.967010\pi$
$41$	−2.69875	−	5.90943i	−0.421473	−	0.922898i	0.573161	−	0.819443i	$-0.305717\pi$
$42$	0.113201	+	0.0847411i	0.0174673	+	0.0130758i
$43$	−7.06043	−	1.53590i	−1.07671	−	0.234223i	−0.360958	−	0.932582i	$-0.617550\pi$
$43$	−7.06043	−	1.53590i	−1.07671	−	0.234223i	−0.715747	+	0.698359i	$0.753914\pi$
$44$	8.17261	−	9.43170i	1.23207	−	1.42188i
$45$	−1.59419	−	5.66917i	−0.237648	−	0.845110i
$46$	3.74583	+	11.1000i	0.552293	+	1.63660i
$47$	3.91418	+	3.91418i	0.570942	+	0.570942i	0.932392	−	0.361450i	$-0.117718\pi$
$47$	3.91418	+	3.91418i	0.570942	+	0.570942i	−0.361450	+	0.932392i	$0.617718\pi$
$48$	0.164211	+	2.29596i	0.0237018	+	0.331394i
$49$	3.77954	+	5.88108i	0.539934	+	0.840154i
$50$	1.15064	−	12.1594i	0.162725	−	1.71960i
$51$	−2.24570	+	1.02558i	−0.314461	+	0.143610i
$52$	20.0590	−	15.0160i	2.78168	−	2.08234i
$53$	9.58880	+	5.23588i	1.31712	+	0.719203i	0.975368	−	0.220586i	$-0.0707968\pi$
$53$	9.58880	+	5.23588i	1.31712	+	0.719203i	0.341755	+	0.939789i	$0.388979\pi$
$54$	4.50315	−	7.00704i	0.612801	−	0.953538i
$55$	−6.95098	−	1.08095i	−0.937271	−	0.145755i
$56$	0.129470	−	0.440933i	0.0173011	−	0.0589221i
$57$	0.764323	+	0.0546655i	0.101237	+	0.00724062i
$58$	5.06663	+	0.362372i	0.665281	+	0.0475818i
$59$	−4.23060	+	14.4081i	−0.550777	+	1.87577i	−0.0729150	+	0.997338i	$0.523230\pi$
$59$	−4.23060	+	14.4081i	−0.550777	+	1.87577i	−0.477862	+	0.878435i	$0.658588\pi$
$60$	4.33466	−	3.16794i	0.559603	−	0.408979i
$61$	1.76179	−	2.74140i	0.225574	−	0.351000i	−0.709957	−	0.704245i	$-0.751285\pi$
$61$	1.76179	−	2.74140i	0.225574	−	0.351000i	0.935531	+	0.353245i	$0.114922\pi$
$62$	1.56709	+	0.855694i	0.199020	+	0.108673i
$63$	−0.201648	+	0.150952i	−0.0254052	+	0.0190181i
$64$	−7.62941	+	3.48424i	−0.953677	+	0.435530i
$65$	−13.1757	−	5.08724i	−1.63424	−	0.630995i
$66$	−2.51464	−	3.91285i	−0.309531	−	0.481639i
$67$	−0.422879	−	5.91261i	−0.0516628	−	0.722341i	−0.955598	−	0.294672i	$-0.904790\pi$
$67$	−0.422879	−	5.91261i	−0.0516628	−	0.722341i	0.903936	−	0.427669i	$-0.140665\pi$
$68$	11.4418	+	11.4418i	1.38752	+	1.38752i
$69$	2.90040	−	0.115680i	0.349167	−	0.0139263i
$70$	−0.502905	+	0.141419i	−0.0601087	+	0.0169028i
$71$	−4.76419	+	5.49816i	−0.565405	+	0.652512i	−0.964402	−	0.264440i	$-0.914813\pi$
$71$	−4.76419	+	5.49816i	−0.565405	+	0.652512i	0.398997	+	0.916952i	$0.369358\pi$
$72$	−12.3652	−	2.68989i	−1.45726	−	0.317007i
$73$	1.73261	+	1.29702i	0.202787	+	0.151805i	0.695845	−	0.718192i	$-0.255030\pi$
$73$	1.73261	+	1.29702i	0.202787	+	0.151805i	−0.493058	+	0.869996i	$0.664121\pi$
$74$	4.29068	+	9.39529i	0.498782	+	1.09218i
$75$	−2.81046	−	1.12236i	−0.324523	−	0.129599i
$76$	−1.41496	−	4.81892i	−0.162307	−	0.552768i
$77$	0.0639575	+	0.294008i	0.00728864	+	0.0335053i
$78$	−3.26349	−	8.74976i	−0.369518	−	0.990716i
$79$	−10.8439	−	3.18406i	−1.22004	−	0.358235i	−0.392555	−	0.919729i	$-0.628409\pi$
$79$	−10.8439	−	3.18406i	−1.22004	−	0.358235i	−0.827481	+	0.561494i	$0.810227\pi$
$80$	−7.10073	−	4.67935i	−0.793886	−	0.523167i
$81$	3.82255	+	4.41146i	0.424728	+	0.490162i
$82$	7.60534	+	13.9281i	0.839870	+	1.53811i
$83$	4.53412	−	1.69114i	0.497684	−	0.185627i	−0.0880718	−	0.996114i	$-0.528070\pi$
$83$	4.53412	−	1.69114i	0.497684	−	0.185627i	0.585756	+	0.810488i	$0.300798\pi$
$84$	−0.193186	−	0.124153i	−0.0210784	−	0.0135462i
$85$	2.04090	−	8.88952i	0.221366	−	0.964203i
$86$	17.4705	+	2.51188i	1.88389	+	0.270863i
$87$	0.439836	−	1.17925i	0.0471553	−	0.126428i
$88$	−9.05857	+	12.1008i	−0.965647	+	1.28995i
$89$	6.50253	−	4.17892i	0.689267	−	0.442965i	−0.148558	−	0.988904i	$-0.547463\pi$
$89$	6.50253	−	4.17892i	0.689267	−	0.442965i	0.837825	+	0.545939i	$0.183827\pi$
$90$	4.87221	+	13.5352i	0.513576	+	1.42674i
$91$			0.604105i			0.0633274i
$92$	−7.35368	−	17.5464i	−0.766674	−	1.82934i
$93$	0.312826	−	0.312826i	0.0324386	−	0.0324386i
$94$	−10.2191	−	8.85488i	−1.05402	−	0.913311i
$95$	−1.87830	+	2.11807i	−0.192710	+	0.217310i
$96$	0.0275477	+	0.191599i	0.00281158	+	0.0195550i
$97$	−6.94271	−	2.58950i	−0.704926	−	0.262924i	−0.0286682	−	0.999589i	$-0.509127\pi$
$97$	−6.94271	−	2.58950i	−0.704926	−	0.262924i	−0.676258	+	0.736665i	$0.736399\pi$
$98$	−10.2338	−	13.6707i	−1.03377	−	1.38095i
$99$	7.94973	−	2.33425i	0.798978	−	0.234601i
$100$	−0.455155	+	19.8298i	−0.0455155	+	1.98298i
$101$	2.92025	−	6.39446i	0.290576	−	0.636273i	−0.706897	−	0.707316i	$-0.749906\pi$
$101$	2.92025	−	6.39446i	0.290576	−	0.636273i	0.997473	+	0.0710434i	$0.0226329\pi$
$102$	5.29297	−	2.89018i	0.524082	−	0.286171i
$103$	−1.18384	+	16.5523i	−0.116647	+	1.63094i	0.516059	+	0.856553i	$0.327398\pi$
$103$	−1.18384	+	16.5523i	−0.116647	+	1.63094i	−0.632707	+	0.774392i	$0.718056\pi$
$104$	−22.9363	+	19.8744i	−2.24909	+	1.94884i
$105$	−0.00148525	+	0.129433i	−0.000144945	+	0.0126313i
$106$	−24.2757	−	11.0863i	−2.35787	−	1.07680i
$107$	−9.22530	+	2.00684i	−0.891843	+	0.194009i	−0.635062	−	0.772461i	$-0.719026\pi$
$107$	−9.22530	+	2.00684i	−0.891843	+	0.194009i	−0.256781	+	0.966470i	$0.582662\pi$
$108$	−6.48266	+	11.8721i	−0.623794	+	1.14239i
$109$	0.978111	−	6.80291i	0.0936860	−	0.651600i	−0.887823	−	0.460185i	$-0.847783\pi$
$109$	0.978111	−	6.80291i	0.0936860	−	0.651600i	0.981509	−	0.191416i	$-0.0613078\pi$
$110$	17.1246	+	1.42245i	1.63276	+	0.135625i
$111$	2.53316	−	0.364213i	0.240437	−	0.0345696i
$112$	−0.0773171	+	0.355421i	−0.00730578	+	0.0335841i
$113$	−12.5972	+	0.900972i	−1.18505	+	0.0847563i	−0.649912	−	0.760010i	$-0.725194\pi$
$113$	−12.5972	+	0.900972i	−1.18505	+	0.0847563i	−0.535136	+	0.844766i	$0.679740\pi$
$114$	−1.87181			−0.175311
$115$	−6.18027	+	8.76381i	−0.576313	+	0.817229i
$116$	−8.24918			−0.765917
$117$	16.5927	−	1.18673i	1.53399	−	0.109713i
$118$	7.79713	−	35.8428i	0.717784	−	3.29960i
$119$	−0.386148	+	0.0555196i	−0.0353981	+	0.00508948i
$120$	−4.96308	+	4.20181i	−0.453065	+	0.383571i
$121$	−0.156984	+	1.09185i	−0.0142713	+	0.0992588i
$122$	−3.81491	+	6.98649i	−0.345386	+	0.632527i
$123$	3.84219	−	0.835816i	0.346438	−	0.0753630i
$124$	−2.63759	−	1.20455i	−0.236862	−	0.108171i
$125$	9.60796	−	5.71726i	0.859362	−	0.511367i
$126$	0.465014	−	0.402937i	0.0414267	−	0.0358964i
$127$	0.224930	−	3.14493i	0.0199593	−	0.279067i	−0.977665	−	0.210171i	$-0.932598\pi$
$127$	0.224930	−	3.14493i	0.0199593	−	0.279067i	0.997624	−	0.0688958i	$-0.0219476\pi$
$128$	17.4207	−	9.51240i	1.53978	−	0.840785i
$129$	1.81674	−	3.97810i	0.159955	−	0.350252i
$130$	32.9893	+	10.0991i	2.89336	+	0.885752i
$131$	15.4950	−	4.54975i	1.35381	−	0.397513i	0.477231	−	0.878778i	$-0.341640\pi$
$131$	15.4950	−	4.54975i	1.35381	−	0.397513i	0.876576	+	0.481264i	$0.159822\pi$
$132$	4.52667	+	6.04692i	0.393996	+	0.526317i
$133$	0.113452	+	0.0423154i	0.00983752	+	0.00366921i
$134$	2.06070	+	14.3325i	0.178018	+	1.23814i
$135$	7.61088	−	0.456631i	0.655040	−	0.0393005i
$136$	−14.8118	−	12.8345i	−1.27010	−	1.10055i
$137$	−15.7336	+	15.7336i	−1.34421	+	1.34421i	−0.452387	+	0.891822i	$0.649427\pi$
$137$	−15.7336	+	15.7336i	−1.34421	+	1.34421i	−0.891822	+	0.452387i	$0.850573\pi$
$138$	−7.04672	+	0.787290i	−0.599856	+	0.0670186i
$139$			13.6355i			1.15655i	0.815843	+	0.578274i	$0.196273\pi$
$139$			13.6355i			1.15655i	−0.815843	+	0.578274i	$0.803727\pi$
$140$	0.798249	−	0.287342i	0.0674644	−	0.0242848i
$141$	−2.81852	+	1.81135i	−0.237362	+	0.152544i
$142$	10.6499	−	14.2266i	0.893720	−	1.19387i
$143$	6.94410	−	18.6179i	0.580695	−	1.55690i
$144$	9.91406	+	1.42543i	0.826172	+	0.118786i
$145$	2.46882	+	3.94025i	0.205024	+	0.327220i
$146$	−4.44757	−	2.85828i	−0.368084	−	0.236553i
$147$	−3.96447	+	1.47867i	−0.326984	+	0.121959i
$148$	−8.03877	−	14.7219i	−0.660783	−	1.21013i
$149$	1.54695	+	1.78527i	0.126731	+	0.146255i	0.815569	−	0.578660i	$-0.196424\pi$
$149$	1.54695	+	1.78527i	0.126731	+	0.146255i	−0.688838	+	0.724916i	$0.741879\pi$
$150$	7.04332	+	2.24490i	0.575084	+	0.183295i
$151$	−14.7257	−	4.32387i	−1.19836	−	0.351872i	−0.379137	−	0.925341i	$-0.623779\pi$
$151$	−14.7257	−	4.32387i	−1.19836	−	0.351872i	−0.819227	+	0.573469i	$0.805597\pi$
$152$	2.12584	+	5.69959i	0.172428	+	0.462298i
$153$	2.28350	+	10.4971i	0.184610	+	0.848637i
$154$	−0.207069	−	0.705211i	−0.0166861	−	0.0568275i
$155$	0.214024	+	1.62035i	0.0171908	+	0.130150i
$156$	6.30008	+	13.7953i	0.504410	+	1.10450i
$157$	3.96788	+	2.97032i	0.316671	+	0.237057i	0.745775	−	0.666198i	$-0.232080\pi$
$157$	3.96788	+	2.97032i	0.316671	+	0.237057i	−0.429103	+	0.903255i	$0.641170\pi$
$158$	26.9763	+	5.86833i	2.14612	+	0.466859i
$159$	−4.33028	+	4.99741i	−0.343414	+	0.396321i
$160$	−0.623677	−	0.349902i	−0.0493060	−	0.0276622i
$161$	0.444904	+	0.111584i	0.0350633	+	0.00879406i
$162$	−10.0825	−	10.0825i	−0.792154	−	0.792154i
$163$	0.265944	+	3.71838i	0.0208303	+	0.291246i	0.997180	+	0.0750481i	$0.0239110\pi$
$163$	0.265944	+	3.71838i	0.0208303	+	0.291246i	−0.976350	+	0.216198i	$0.930634\pi$
$164$	−13.9332	−	21.6805i	−1.08800	−	1.69296i
$165$	1.53359	−	3.97191i	0.119389	−	0.309212i
$166$	−10.7528	+	4.91062i	−0.834576	+	0.381138i
$167$	−6.84307	+	5.12266i	−0.529532	+	0.396403i	−0.830319	−	0.557289i	$-0.811842\pi$
$167$	−6.84307	+	5.12266i	−0.529532	+	0.396403i	0.300787	+	0.953691i	$0.402751\pi$
$168$	0.244121	+	0.133300i	0.0188343	+	0.0102843i
$169$	14.5409	−	22.6261i	1.11853	−	1.74047i
$170$	−3.42357	+	22.0151i	−0.262576	+	1.68848i
$171$	0.939385	−	3.19925i	0.0718366	−	0.244653i
$172$	−28.5907	−	2.04485i	−2.18002	−	0.155918i
$173$	−14.9903	−	1.07213i	−1.13969	−	0.0815125i	−0.511296	−	0.859405i	$-0.670834\pi$
$173$	−14.9903	−	1.07213i	−1.13969	−	0.0815125i	−0.628397	+	0.777892i	$0.716289\pi$
$174$	−0.866169	+	2.94990i	−0.0656641	+	0.223631i
$175$	−0.376150	−	0.295290i	−0.0284343	−	0.0223218i
$176$	6.46835	−	10.0649i	0.487570	−	0.758674i
$177$	−7.97699	−	4.35577i	−0.599587	−	0.327399i
$178$	−15.1153	+	11.3152i	−1.13294	+	0.848108i
$179$	−3.80224	+	1.73642i	−0.284192	+	0.129786i	−0.552411	−	0.833572i	$-0.686292\pi$
$179$	−3.80224	+	1.73642i	−0.284192	+	0.129786i	0.268219	+	0.963358i	$0.413565\pi$
$180$	−9.46039	−	21.3607i	−0.705136	−	1.59213i
$181$	6.78991	+	10.5653i	0.504690	+	0.785313i	0.996340	−	0.0854799i	$-0.0272423\pi$
$181$	6.78991	+	10.5653i	0.504690	+	0.785313i	−0.491650	+	0.870793i	$0.663606\pi$
$182$	−0.105273	−	1.47191i	−0.00780338	−	0.109106i
$183$	1.39466	+	1.39466i	0.103096	+	0.103096i
$184$	10.4003	+	20.5628i	0.766720	+	1.51591i
$185$	−4.62611	+	8.24572i	−0.340119	+	0.606238i
$186$	−0.707693	+	0.816721i	−0.0518906	+	0.0598849i
$187$	12.5388	+	2.72766i	0.916931	+	0.199466i
$188$	17.5793	+	13.1597i	1.28210	+	0.959769i
$189$	−0.135476	−	0.296650i	−0.00985440	−	0.0215781i
$190$	4.20741	−	5.48804i	0.305238	−	0.398144i
$191$	−7.21811	−	24.5826i	−0.522284	−	1.77874i	−0.621212	−	0.783643i	$-0.713359\pi$
$191$	−7.21811	−	24.5826i	−0.522284	−	1.77874i	0.0989277	−	0.995095i	$-0.468459\pi$
$192$	−1.07909	−	4.96048i	−0.0778764	−	0.357992i
$193$	0.380734	+	1.02079i	0.0274058	+	0.0734779i	0.949932	−	0.312456i	$-0.101152\pi$
$193$	0.380734	+	1.02079i	0.0274058	+	0.0734779i	−0.922526	+	0.385934i	$0.873879\pi$
$194$	17.3673	+	5.09950i	1.24690	+	0.366123i
$195$	4.70385	−	7.13791i	0.336850	−	0.511156i
$196$	18.1610	+	20.9590i	1.29722	+	1.49707i
$197$	−0.885839	−	1.62229i	−0.0631134	−	0.115584i	0.844218	−	0.536001i	$-0.180066\pi$
$197$	−0.885839	−	1.62229i	−0.0631134	−	0.115584i	−0.907331	+	0.420417i	$0.861884\pi$
$198$	−18.9629	+	7.07280i	−1.34764	+	0.502642i
$199$	−3.94008	−	2.53214i	−0.279305	−	0.179498i	0.393487	−	0.919330i	$-0.371269\pi$
$199$	−3.94008	−	2.53214i	−0.279305	−	0.179498i	−0.672792	+	0.739832i	$0.734905\pi$
$200$	−1.16354	−	23.9962i	−0.0822748	−	1.69678i
$201$	3.55127	+	0.510595i	0.250487	+	0.0360146i
$202$	−6.00094	+	16.0891i	−0.422224	+	1.13203i
$203$	0.119186	−	0.159214i	0.00836524	−	0.0111746i
$204$	−8.23901	+	5.29489i	−0.576846	+	0.370716i
$205$	−6.18580	+	13.1438i	−0.432035	+	0.918001i
$206$		−	40.5363i		−	2.82429i
$207$	2.19084	−	12.4392i	0.152274	−	0.864581i
$208$	16.9857	−	16.9857i	1.17774	−	1.17774i
$209$	−3.01005	−	2.60823i	−0.208210	−	0.180415i
$210$	−0.0189366	−	0.315624i	−0.00130675	−	0.0217802i
$211$	−0.879981	−	6.12040i	−0.0605804	−	0.421346i	−0.997432	−	0.0716189i	$-0.977183\pi$
$211$	−0.879981	−	6.12040i	−0.0605804	−	0.421346i	0.936852	−	0.349727i	$-0.113726\pi$
$212$	40.6075	+	15.1458i	2.78894	+	1.04022i
$213$	−2.63880	−	3.52503i	−0.180808	−	0.241531i
$214$	22.1279	−	6.49734i	1.51263	−	0.444149i
$215$	7.57992	+	14.2684i	0.516946	+	0.973098i
$216$	6.80603	−	14.9031i	0.463091	−	1.01403i
$217$	0.0613570	−	0.0335035i	0.00416519	−	0.00227436i
$218$	−1.19769	+	16.7459i	−0.0811177	+	1.13417i
$219$	−0.989999	+	0.857839i	−0.0668979	+	0.0579674i
$220$	−27.9041	−	0.320201i	−1.88130	−	0.0215880i
$221$	23.4356	+	10.7027i	1.57645	+	0.719941i
$222$	−6.10862	+	1.32885i	−0.409984	+	0.0891865i
$223$	−6.44396	+	11.8012i	−0.431519	+	0.790268i	−0.999462	−	0.0327997i	$-0.989558\pi$
$223$	−6.44396	+	11.8012i	−0.431519	+	0.790268i	0.567943	+	0.823068i	$0.307739\pi$
$224$	−0.00435308	+	0.0302763i	−0.000290852	+	0.00202292i
$225$	−7.37167	+	10.9116i	−0.491444	+	0.727441i
$226$	30.5364	−	4.39047i	2.03125	−	0.292050i
$227$	3.91042	−	17.9759i	0.259544	−	1.19310i	−0.644142	−	0.764906i	$-0.722785\pi$
$227$	3.91042	−	17.9759i	0.259544	−	1.19310i	0.903685	−	0.428197i	$-0.140851\pi$
$228$	3.03207	−	0.216858i	0.200804	−	0.0143618i
$229$	−10.2756			−0.679029			−0.339515	−	0.940601i	$-0.610263\pi$
$229$	−10.2756			−0.679029			−0.339515	+	0.940601i	$0.610263\pi$
$230$	13.5311	−	22.4302i	0.892217	−	1.47900i
$231$	−0.182112			−0.0119821
$232$	9.96604	−	0.712785i	0.654302	−	0.0467966i
$233$	−2.86542	+	13.1721i	−0.187720	+	0.862934i	0.782868	+	0.622188i	$0.213756\pi$
$233$	−2.86542	+	13.1721i	−0.187720	+	0.862934i	−0.970588	+	0.240747i	$0.922608\pi$
$234$	−40.2215	+	5.78298i	−2.62936	+	0.378046i
$235$	1.02462	−	12.3352i	0.0668390	−	0.804662i
$236$	−8.47767	+	58.9635i	−0.551849	+	3.83820i
$237$	3.27827	−	6.00370i	0.212946	−	0.389982i
$238$	0.931181	−	0.202566i	0.0603595	−	0.0131304i
$239$	14.5181	+	6.63020i	0.939098	+	0.428872i	0.825340	−	0.564637i	$-0.190984\pi$
$239$	14.5181	+	6.63020i	0.939098	+	0.428872i	0.113759	+	0.993508i	$0.463711\pi$
$240$	3.68103	−	3.59751i	0.237610	−	0.232218i
$241$	−1.29613	+	1.12310i	−0.0834909	+	0.0723453i	−0.695606	−	0.718423i	$-0.744864\pi$
$241$	−1.29613	+	1.12310i	−0.0834909	+	0.0723453i	0.612115	+	0.790768i	$0.290319\pi$
$242$	0.192225	−	2.68766i	0.0123567	−	0.172770i
$243$	−12.0790	+	6.59562i	−0.774867	+	0.423109i
$244$	5.37019	−	11.7591i	0.343791	−	0.752798i
$245$	4.57586	−	14.9473i	0.292341	−	0.954948i
$246$	−9.21591	+	2.70604i	−0.587585	+	0.172531i
$247$	−4.79223	−	6.40167i	−0.304922	−	0.407328i
$248$	3.29062	+	1.22734i	0.208954	+	0.0779359i
$249$	0.416836	+	2.89916i	0.0264159	+	0.183727i
$250$	−22.4137	+	15.6045i	−1.41757	+	0.986917i
$251$	−5.90729	−	5.11869i	−0.372865	−	0.323089i	0.448190	−	0.893938i	$-0.352069\pi$
$251$	−5.90729	−	5.11869i	−0.372865	−	0.323089i	−0.821055	+	0.570849i	$0.806614\pi$
$252$	−0.706572	+	0.706572i	−0.0445099	+	0.0445099i
$253$	−12.4288	−	8.55301i	−0.781393	−	0.537723i
$254$			7.70187i			0.483259i
$255$	4.99489	+	2.35073i	0.312792	+	0.147208i
$256$	−26.6763	+	17.1438i	−1.66727	+	1.07149i
$257$	−1.81881	+	2.42965i	−0.113455	+	0.151557i	−0.853674	−	0.520808i	$-0.825631\pi$
$257$	−1.81881	+	2.42965i	−0.113455	+	0.151557i	0.740219	+	0.672365i	$0.234722\pi$
$258$	−3.73328	+	10.0093i	−0.232424	+	0.623152i
$259$	0.400288	+	0.0575527i	0.0248727	+	0.00357615i
$260$	−54.6080	−	12.5372i	−3.38664	−	0.777522i
$261$	−4.60719	−	2.96086i	−0.285178	−	0.183273i
$262$	−36.9611	+	13.7858i	−2.28346	+	0.851688i
$263$	−0.801783	−	1.46836i	−0.0494401	−	0.0905427i	0.851791	−	0.523882i	$-0.175517\pi$
$263$	−0.801783	−	1.46836i	−0.0494401	−	0.0905427i	−0.901231	+	0.433340i	$0.857335\pi$
$264$	−5.99128	−	6.91430i	−0.368738	−	0.425546i
$265$	−4.91860	−	23.9292i	−0.302147	−	1.46996i
$266$	−0.283802	−	0.0833317i	−0.0174010	−	0.00510939i
$267$	1.63492	+	4.38339i	0.100056	+	0.268259i
$268$	−4.99852	−	22.9778i	−0.305333	−	1.40359i
$269$	0.143996	+	0.490404i	0.00877957	+	0.0299005i	0.963766	−	0.266748i	$-0.0859492\pi$
$269$	0.143996	+	0.490404i	0.00877957	+	0.0299005i	−0.954987	+	0.296649i	$0.904131\pi$
$270$	−18.4645	+	2.43889i	−1.12371	+	0.148426i
$271$	6.20474	+	13.5865i	0.376911	+	0.825320i	0.999099	+	0.0424520i	$0.0135170\pi$
$271$	6.20474	+	13.5865i	0.376911	+	0.825320i	−0.622187	+	0.782868i	$0.713756\pi$
$272$	12.4184	+	9.29629i	0.752975	+	0.563670i
$273$	−0.357282	−	0.0777219i	−0.0216237	−	0.00470395i
$274$	35.5933	−	41.0769i	2.15027	−	2.48155i
$275$	8.19822	+	13.4243i	0.494371	+	0.809517i
$276$	11.3234	−	2.09169i	0.681591	−	0.125905i
$277$	11.9905	+	11.9905i	0.720439	+	0.720439i	0.968695	−	0.248255i	$-0.0798572\pi$
$277$	11.9905	+	11.9905i	0.720439	+	0.720439i	−0.248255	+	0.968695i	$0.579857\pi$
$278$	−2.37617	−	33.2232i	−0.142513	−	1.99259i
$279$	−1.04076	−	1.61945i	−0.0623084	−	0.0969538i
$280$	−0.939556	+	0.416119i	−0.0561492	+	0.0248679i
$281$	−7.89033	+	3.60339i	−0.470698	+	0.214960i	−0.636619	−	0.771179i	$-0.719668\pi$
$281$	−7.89033	+	3.60339i	−0.470698	+	0.214960i	0.165921	+	0.986139i	$0.446940\pi$
$282$	6.55173	−	4.90456i	0.390150	−	0.292063i
$283$	19.6863	+	10.7495i	1.17023	+	0.638994i	0.942328	−	0.334690i	$-0.108632\pi$
$283$	19.6863	+	10.7495i	1.17023	+	0.638994i	0.227902	+	0.973684i	$0.426813\pi$
$284$	−15.6031	+	24.2789i	−0.925873	+	1.44069i
$285$	−1.01102	−	1.38337i	−0.0598878	−	0.0819440i
$286$	−13.6750	+	46.5729i	−0.808622	+	2.75391i
$287$	0.619756	+	0.0443259i	0.0365831	+	0.00261647i
$288$	0.840136	+	0.0600877i	0.0495055	+	0.00354070i
$289$	0.102058	−	0.347578i	0.00600341	−	0.0204457i
$290$	−6.70197	−	9.17026i	−0.393553	−	0.538496i
$291$	2.42471	−	3.77293i	0.142139	−	0.221173i
$292$	7.53556	+	4.11473i	0.440985	+	0.240796i
$293$	−1.23196	+	0.922231i	−0.0719717	+	0.0538773i	−0.634658	−	0.772793i	$-0.718859\pi$
$293$	−1.23196	+	0.922231i	−0.0719717	+	0.0538773i	0.562686	+	0.826671i	$0.309768\pi$
$294$	9.40183	−	4.29367i	0.548326	−	0.250412i
$295$	30.7013	−	13.5973i	1.78750	−	0.791663i
$296$	10.9839	+	17.0913i	0.638427	+	0.993411i
$297$	0.765258	+	10.6997i	0.0444048	+	0.620860i
$298$	−4.08028	−	4.08028i	−0.236364	−	0.236364i
$299$	−20.7336	−	22.0844i	−1.19906	−	1.27717i
$300$	−11.6692	−	2.82041i	−0.673723	−	0.162837i
$301$	0.452553	−	0.522274i	0.0260847	−	0.0301034i
$302$	36.6331	+	7.96904i	2.10800	+	0.458567i
$303$	3.40613	+	2.54980i	0.195677	+	0.146482i
$304$	−2.00015	−	4.37972i	−0.114716	−	0.251194i
$305$	−7.22395	+	0.954178i	−0.413642	+	0.0546361i
$306$	−7.39304	−	25.1784i	−0.422632	−	1.43935i
$307$	−2.68617	−	12.3481i	−0.153308	−	0.704744i	−0.988054	−	0.154109i	$-0.950749\pi$
$307$	−2.68617	−	12.3481i	−0.153308	−	0.704744i	0.834746	−	0.550635i	$-0.185614\pi$
$308$	0.417123	+	1.11835i	0.0237678	+	0.0637239i
$309$	−9.63710	−	2.82971i	−0.548235	−	0.160976i
$310$	−0.803842	−	3.91072i	−0.0456552	−	0.222114i
$311$	11.9401	+	13.7796i	0.677060	+	0.781369i	0.985464	−	0.169887i	$-0.0543401\pi$
$311$	11.9401	+	13.7796i	0.677060	+	0.781369i	−0.308403	+	0.951256i	$0.599795\pi$
$312$	−8.80329	−	16.1220i	−0.498388	−	0.912729i
$313$	14.5770	−	5.43694i	0.823942	−	0.307314i	0.0981003	−	0.995177i	$-0.468723\pi$
$313$	14.5770	−	5.43694i	0.823942	−	0.307314i	0.725841	+	0.687862i	$0.241451\pi$
$314$	−10.1854	−	6.54578i	−0.574797	−	0.369400i
$315$	0.548960	+	0.126033i	0.0309304	+	0.00710115i
$316$	−44.3775	−	6.38053i	−2.49643	−	0.358933i
$317$	−0.488281	+	1.30913i	−0.0274246	+	0.0735281i	−0.949940	−	0.312431i	$-0.898857\pi$
$317$	−0.488281	+	1.30913i	−0.0274246	+	0.0735281i	0.922516	+	0.385959i	$0.126129\pi$
$318$	9.67995	−	12.9309i	0.542825	−	0.725129i
$319$	−5.50334	+	3.53678i	−0.308128	+	0.198022i
$320$	16.9694	+	7.98623i	0.948616	+	0.446444i
$321$		−	5.71425i		−	0.318938i
$322$	−1.10346	−	0.194347i	−0.0614935	−	0.0108305i
$323$	3.65156	−	3.65156i	0.203178	−	0.203178i
$324$	17.5002	+	15.1640i	0.972235	+	0.842446i
$325$	10.3547	+	29.8358i	0.574375	+	1.65499i
$326$	−1.29595	−	9.01356i	−0.0717763	−	0.499215i
$327$	3.89756	+	1.45371i	0.215536	+	0.0803906i
$328$	18.7064	+	24.9888i	1.03289	+	1.37977i
$329$	−0.507980	+	0.149156i	−0.0280058	+	0.00822326i
$330$	−3.04445	+	9.94487i	−0.167592	+	0.547447i
$331$	−5.40674	+	11.8391i	−0.297181	+	0.650736i	−0.998041	−	0.0625632i	$-0.980073\pi$
$331$	−5.40674	+	11.8391i	−0.297181	+	0.650736i	0.700860	+	0.713299i	$0.252800\pi$
$332$	16.8490	−	9.20025i	0.924709	−	0.504929i
$333$	0.794429	−	11.1076i	0.0435345	−	0.608691i
$334$	15.7806	−	13.6739i	0.863475	−	0.748205i
$335$	−9.47947	+	9.26438i	−0.517919	+	0.506167i
$336$	−0.200257	−	0.0914544i	−0.0109249	−	0.00498924i
$337$	7.64534	−	1.66314i	0.416468	−	0.0905971i	0.000551425	−	1.00000i	$-0.499824\pi$
$337$	7.64534	−	1.66314i	0.416468	−	0.0905971i	0.415917	+	0.909403i	$0.363461\pi$
$338$	−31.4864	+	57.6630i	−1.71263	+	3.13645i
$339$	1.08786	−	7.56621i	0.0590843	−	0.410940i
$340$	2.99514	−	36.0579i	0.162434	−	1.95552i
$341$	−2.27607	+	0.327250i	−0.123256	+	0.0177216i
$342$	−1.73132	+	7.95874i	−0.0936190	+	0.430360i
$343$	−1.33471	+	0.0954600i	−0.0720673	+	0.00515436i
$344$	34.7178			1.87186
$345$	−4.38799	−	4.78268i	−0.236241	−	0.257491i
$346$	36.7111			1.97360
$347$	−11.9285	+	0.853140i	−0.640353	+	0.0457990i	−0.387741	−	0.921769i	$-0.626744\pi$
$347$	−11.9285	+	0.853140i	−0.640353	+	0.0457990i	−0.252613	+	0.967567i	$0.581290\pi$
$348$	1.06131	−	4.87876i	0.0568921	−	0.261529i
$349$	12.4737	−	1.79345i	0.667704	−	0.0960013i	0.199876	−	0.979821i	$-0.435946\pi$
$349$	12.4737	−	1.79345i	0.667704	−	0.0960013i	0.467827	+	0.883820i	$0.345037\pi$
$350$	0.967956	+	0.653931i	0.0517394	+	0.0349541i
$351$	−3.06509	+	21.3182i	−0.163602	+	1.13788i
$352$	0.482179	−	0.883045i	0.0257002	−	0.0470665i
$353$	−14.9431	+	3.25067i	−0.795339	+	0.173015i	−0.591836	−	0.806059i	$-0.701597\pi$
$353$	−14.9431	+	3.25067i	−0.795339	+	0.173015i	−0.203504	+	0.979074i	$0.565233\pi$
$354$	20.1951	+	9.22281i	1.07336	+	0.490187i
$355$	16.2666	+	0.186660i	0.863340	+	0.00990687i
$356$	23.1737	−	20.0801i	1.22820	−	1.06424i
$357$	0.0168447	−	0.235520i	0.000891516	−	0.0124650i
$358$	8.96163	−	4.89342i	0.473637	−	0.258625i
$359$	13.0593	−	28.5960i	0.689245	−	1.50924i	−0.163296	−	0.986577i	$-0.552213\pi$
$359$	13.0593	−	28.5960i	0.689245	−	1.50924i	0.852541	−	0.522660i	$-0.175060\pi$
$360$	13.2750	+	24.9889i	0.699656	+	1.31703i
$361$	16.6924	−	4.90134i	0.878550	−	0.257965i
$362$	−18.3849	−	24.5593i	−0.966289	−	1.29081i
$363$	−0.625547	−	0.233317i	−0.0328327	−	0.0122460i
$364$	0.341055	+	2.37209i	0.0178761	+	0.124331i
$365$	−0.289837	−	4.83084i	−0.0151707	−	0.252858i
$366$	−3.64116	−	3.15509i	−0.190327	−	0.164919i
$367$	12.0510	−	12.0510i	0.629058	−	0.629058i	−0.318773	−	0.947831i	$-0.603271\pi$
$367$	12.0510	−	12.0510i	0.629058	−	0.629058i	0.947831	+	0.318773i	$0.103271\pi$
$368$	−9.37198	−	15.6468i	−0.488548	−	0.815647i
$369$		−	17.1096i		−	0.890691i
$370$	9.83469	−	20.8970i	0.511281	−	1.08638i
$371$	−0.879032	+	0.564919i	−0.0456371	+	0.0293292i
$372$	1.05174	−	1.40496i	0.0545301	−	0.0728437i
$373$	5.01630	−	13.4492i	0.259734	−	0.696374i	−0.739984	−	0.672625i	$-0.765167\pi$
$373$	5.01630	−	13.4492i	0.259734	−	0.696374i	0.999718	−	0.0237494i	$-0.00756039\pi$
$374$	−31.0265	−	4.46093i	−1.60434	−	0.230669i
$375$	2.14520	+	6.41794i	0.110777	+	0.331421i
$376$	−22.3751	−	14.3796i	−1.15391	−	0.741570i
$377$	−12.3063	+	4.59002i	−0.633808	+	0.236398i
$378$	0.381784	+	0.699186i	0.0196369	+	0.0359622i
$379$	22.6656	+	26.1575i	1.16426	+	1.34362i	0.928288	+	0.371861i	$0.121280\pi$
$379$	22.6656	+	26.1575i	1.16426	+	1.34362i	0.235967	+	0.971761i	$0.424174\pi$
$380$	−6.17959	+	9.37728i	−0.317006	+	0.481044i
$381$	1.83105	+	0.537643i	0.0938073	+	0.0275443i
$382$	21.8709	+	58.6382i	1.11901	+	3.00019i
$383$	−5.89153	−	27.0829i	−0.301043	−	1.38387i	−0.840478	−	0.541846i	$-0.817726\pi$
$383$	−5.89153	−	27.0829i	−0.301043	−	1.38387i	0.539435	−	0.842027i	$-0.318638\pi$
$384$	3.38458	+	11.5268i	0.172719	+	0.588225i
$385$	0.409346	−	0.533940i	0.0208622	−	0.0272121i
$386$	−1.10555	−	2.42082i	−0.0562711	−	0.123216i
$387$	−15.2341	−	11.4041i	−0.774390	−	0.579701i
$388$	−28.7233	−	6.24838i	−1.45821	−	0.317213i
$389$	−4.44937	+	5.13485i	−0.225592	+	0.260347i	−0.857250	−	0.514900i	$-0.827829\pi$
$389$	−4.44937	+	5.13485i	−0.225592	+	0.260347i	0.631658	+	0.775247i	$0.282375\pi$
$390$	−10.2171	+	18.2114i	−0.517365	+	0.922168i
$391$	12.2110	−	15.2827i	0.617535	−	0.772878i
$392$	−23.7518	−	23.7518i	−1.19965	−	1.19965i
$393$	0.697296	+	9.74948i	0.0351739	+	0.491796i
$394$	2.44107	+	3.79838i	0.122979	+	0.191360i
$395$	10.2337	+	23.1066i	0.514912	+	1.16262i
$396$	29.8977	−	13.6538i	1.50242	−	0.686131i
$397$	−2.03432	+	1.52287i	−0.102099	+	0.0764306i	−0.649108	−	0.760697i	$-0.724858\pi$
$397$	−2.03432	+	1.52287i	−0.102099	+	0.0764306i	0.547008	+	0.837127i	$0.315767\pi$
$398$	10.0413	+	5.48299i	0.503327	+	0.274837i
$399$	−0.0396226	+	0.0616540i	−0.00198361	+	0.00308656i
$400$	2.27355	+	18.8789i	0.113677	+	0.943947i
$401$	−1.75048	+	5.96159i	−0.0874148	+	0.297707i	−0.991584	−	0.129468i	$-0.958673\pi$
$401$	−1.75048	+	5.96159i	−0.0874148	+	0.297707i	0.904169	+	0.427175i	$0.140491\pi$
$402$	−8.74171	−	0.625219i	−0.435997	−	0.0311831i
$403$	−4.60505	−	0.329360i	−0.229394	−	0.0164066i
$404$	7.85665	−	26.7573i	0.390883	−	1.33122i
$405$	2.00566	−	12.8973i	0.0996623	−	0.640874i
$406$	−0.262655	+	0.408698i	−0.0130353	+	0.0202834i
$407$	−11.6749	−	6.37496i	−0.578702	−	0.315995i
$408$	9.49623	−	7.10879i	0.470134	−	0.351938i
$409$	−25.1842	+	11.5013i	−1.24528	+	0.568700i	−0.925484	−	0.378786i	$-0.876342\pi$
$409$	−25.1842	+	11.5013i	−1.24528	+	0.568700i	−0.319796	+	0.947487i	$0.603614\pi$
$410$	12.7814	−	33.1030i	0.631226	−	1.63484i
$411$	−7.28098	−	11.3294i	−0.359144	−	0.558839i
$412$	4.69630	+	65.6628i	0.231370	+	3.23498i
$413$	−1.01554	−	1.01554i	−0.0499717	−	0.0499717i
$414$	−3.17033	+	30.6900i	−0.155813	+	1.50833i
$415$	−9.43710	−	5.29451i	−0.463249	−	0.259898i
$416$	1.32285	−	1.52665i	0.0648579	−	0.0748500i
$417$	−8.06435	−	1.75429i	−0.394913	−	0.0859081i
$418$	7.78857	+	5.83045i	0.380952	+	0.285177i
$419$	1.38831	+	3.03998i	0.0678234	+	0.148513i	0.940508	−	0.339772i	$-0.110350\pi$
$419$	1.38831	+	3.03998i	0.0678234	+	0.148513i	−0.872684	+	0.488285i	$0.837623\pi$
$420$	0.0672409	+	0.509072i	0.00328102	+	0.0248402i
$421$	2.63836	+	8.98542i	0.128586	+	0.437923i	0.998468	−	0.0553372i	$-0.0176234\pi$
$421$	2.63836	+	8.98542i	0.128586	+	0.437923i	−0.869882	+	0.493260i	$0.835805\pi$
$422$	3.21065	+	14.7591i	0.156292	+	0.718463i
$423$	5.09470	+	13.6594i	0.247713	+	0.664144i
$424$	−50.3677	−	14.7893i	−2.44607	−	0.718231i
$425$	−18.1196	+	9.36081i	−0.878928	+	0.454066i
$426$	7.04377	+	8.12895i	0.341272	+	0.393849i
$427$	0.149367	+	0.273546i	0.00722840	+	0.0132378i
$428$	−35.0912	+	13.0884i	−1.69620	+	0.632650i
$429$	10.1176	+	6.50221i	0.488484	+	0.313930i
$430$	−20.9551	−	33.4444i	−1.01054	−	1.61283i
$431$	−21.7087	−	3.12124i	−1.04567	−	0.150345i	−0.401995	−	0.915642i	$-0.631683\pi$
$431$	−21.7087	−	3.12124i	−1.04567	−	0.150345i	−0.643677	+	0.765297i	$0.722592\pi$
$432$	−4.53176	+	12.1501i	−0.218034	+	0.584573i
$433$	−8.20216	+	10.9568i	−0.394171	+	0.526550i	−0.953096	−	0.302668i	$-0.902123\pi$
$433$	−8.20216	+	10.9568i	−0.394171	+	0.526550i	0.558926	+	0.829218i	$0.311214\pi$
$434$	−0.143659	+	0.0923241i	−0.00689586	+	0.00443170i
$435$	−2.64798	+	0.953181i	−0.126961	+	0.0457016i
$436$		−	27.2646i		−	1.30574i
$437$	−5.59979	+	2.34687i	−0.267874	+	0.112266i
$438$	2.26266	−	2.26266i	0.108114	−	0.108114i
$439$	3.27951	+	2.84171i	0.156523	+	0.135628i	0.729601	−	0.683873i	$-0.239706\pi$
$439$	3.27951	+	2.84171i	0.156523	+	0.135628i	−0.573079	+	0.819500i	$0.694251\pi$
$440$	33.7393	−	2.02426i	1.60846	−	0.0965029i
$441$	2.62024	+	18.2242i	0.124773	+	0.867817i
$442$	−58.9664	−	21.9933i	−2.80475	−	1.04612i
$443$	−6.70091	−	8.95137i	−0.318370	−	0.425293i	0.612597	−	0.790395i	$-0.290125\pi$
$443$	−6.70091	−	8.95137i	−0.318370	−	0.425293i	−0.930967	+	0.365103i	$0.881034\pi$
$444$	9.74112	−	2.86025i	0.462293	−	0.135741i
$445$	−16.5268	−	5.05939i	−0.783444	−	0.239838i
$446$	13.6443	−	29.8769i	0.646077	−	1.41471i
$447$	−1.25488	+	0.685215i	−0.0593537	+	0.0324096i
$448$	0.0572272	−	0.800141i	0.00270373	−	0.0378031i
$449$	−0.888899	+	0.770235i	−0.0419497	+	0.0363496i	−0.675583	−	0.737284i	$-0.736108\pi$
$449$	−0.888899	+	0.770235i	−0.0419497	+	0.0363496i	0.633634	+	0.773633i	$0.281563\pi$
$450$	16.0597	−	27.8710i	0.757062	−	1.31385i
$451$	−18.5907	−	8.49009i	−0.875402	−	0.399783i
$452$	−48.9559	+	10.6497i	−2.30269	+	0.500919i
$453$	4.45180	−	8.15286i	0.209164	−	0.383055i
$454$	−6.39527	+	44.4801i	−0.300145	+	2.08755i
$455$	1.03096	−	0.872827i	0.0483324	−	0.0409188i
$456$	−3.64438	+	0.523982i	−0.170664	+	0.0245377i
$457$	−5.77039	+	26.5261i	−0.269928	+	1.24084i	0.619952	+	0.784640i	$0.287152\pi$
$457$	−5.77039	+	26.5261i	−0.269928	+	1.24084i	−0.889879	+	0.456197i	$0.849211\pi$
$458$	25.0366	−	1.79066i	1.16989	−	0.0836718i
$459$	−13.9084			−0.649188
$460$	−19.3198	+	37.9013i	−0.900792	+	1.76716i
$461$	−12.8545			−0.598693			−0.299346	−	0.954145i	$-0.596769\pi$
$461$	−12.8545			−0.598693			−0.299346	+	0.954145i	$0.596769\pi$
$462$	0.443719	−	0.0317354i	0.0206437	−	0.00147647i
$463$	0.864576	−	3.97439i	0.0401803	−	0.184706i	−0.952683	−	0.303967i	$-0.901689\pi$
$463$	0.864576	−	3.97439i	0.0401803	−	0.184706i	0.992863	+	0.119261i	$0.0380525\pi$
$464$	−7.82781	+	1.12547i	−0.363397	+	0.0522486i
$465$	−0.985848	−	0.0818891i	−0.0457176	−	0.00379752i
$466$	4.68623	−	32.5935i	0.217086	−	1.50986i
$467$	−1.25694	+	2.30191i	−0.0581642	+	0.106520i	−0.905144	−	0.425106i	$-0.860237\pi$
$467$	−1.25694	+	2.30191i	−0.0581642	+	0.106520i	0.846979	+	0.531626i	$0.178419\pi$
$468$	64.4831	−	14.0274i	2.98073	−	0.648418i
$469$	0.515706	+	0.235515i	0.0238131	+	0.0108751i
$470$	−0.346932	+	30.2336i	−0.0160028	+	1.39457i
$471$	−2.26721	+	1.96455i	−0.104467	+	0.0905216i
$472$	5.14724	−	71.9678i	0.236921	−	3.31259i
$473$	−19.9506	+	10.8939i	−0.917332	+	0.500901i
$474$	−6.94134	+	15.1994i	−0.318826	+	0.698132i
$475$	6.32851	+	0.145259i	0.290372	+	0.00666495i
$476$	−1.48491	+	0.436009i	−0.0680607	+	0.0199844i
$477$	17.2432	+	23.0342i	0.789511	+	1.05466i
$478$	−36.5291	−	13.6246i	−1.67080	−	0.623176i
$479$	5.97482	+	41.5558i	0.272996	+	1.89873i	0.416590	+	0.909094i	$0.363225\pi$
$479$	5.97482	+	41.5558i	0.272996	+	1.89873i	−0.143594	+	0.989637i	$0.545866\pi$
$480$	0.287180	−	0.323840i	0.0131079	−	0.0147812i
$481$	−20.1840	−	17.4896i	−0.920312	−	0.797455i
$482$	2.96232	−	2.96232i	0.134930	−	0.134930i
$483$	−0.123233	+	0.248771i	−0.00560731	+	0.0113195i
$484$			4.37589i			0.198904i
$485$	5.61178	+	15.5898i	0.254818	+	0.707896i
$486$	28.2813	−	18.1753i	1.28287	−	0.824448i
$487$	8.78731	−	11.7385i	0.398191	−	0.531921i	−0.555975	−	0.831199i	$-0.687655\pi$
$487$	8.78731	−	11.7385i	0.398191	−	0.531921i	0.954166	+	0.299278i	$0.0967458\pi$
$488$	−5.47180	+	14.6705i	−0.247697	+	0.664100i
$489$	−2.23335	−	0.321108i	−0.100996	−	0.0145210i
$490$	−8.54441	+	37.2168i	−0.385997	+	1.68128i
$491$	3.25453	+	2.09156i	0.146875	+	0.0943907i	0.612014	−	0.790847i	$-0.290359\pi$
$491$	3.25453	+	2.09156i	0.146875	+	0.0943907i	−0.465139	+	0.885237i	$0.653996\pi$
$492$	14.6149	−	5.45109i	0.658892	−	0.245754i
$493$	−4.06497	−	7.44444i	−0.183077	−	0.335281i
$494$	12.7919	+	14.7627i	0.575536	+	0.664204i
$495$	−15.4696	−	10.1944i	−0.695307	−	0.458205i
$496$	−2.66720	−	0.783160i	−0.119761	−	0.0351649i
$497$	−0.243160	−	0.651936i	−0.0109072	−	0.0292433i
$498$	−1.52085	−	6.99122i	−0.0681508	−	0.313284i
$499$	−7.44046	−	25.3399i	−0.333081	−	1.13437i	−0.940445	−	0.339945i	$-0.889591\pi$
$499$	−7.44046	−	25.3399i	−0.333081	−	1.13437i	0.607364	−	0.794423i	$-0.292227\pi$
$500$	34.4991	−	27.8738i	1.54284	−	1.24655i
$501$	−2.14926	−	4.70621i	−0.0960216	−	0.210258i
$502$	15.2852	+	11.4424i	0.682213	+	0.510698i
$503$	29.6025	+	6.43963i	1.31991	+	0.287129i	0.816714	−	0.577043i	$-0.195793\pi$
$503$	29.6025	+	6.43963i	1.31991	+	0.287129i	0.503197	+	0.864172i	$0.332157\pi$
$504$	0.792575	−	0.914680i	0.0353041	−	0.0407431i
$505$	−15.1320	+	4.25519i	−0.673367	+	0.189353i
$506$	31.7735	+	18.6737i	1.41251	+	0.830147i
$507$	11.5109	+	11.5109i	0.511215	+	0.511215i
$508$	−0.892295	−	12.4759i	−0.0395892	−	0.553529i
$509$	−6.11152	−	9.50972i	−0.270889	−	0.421511i	0.678982	−	0.734155i	$-0.262422\pi$
$509$	−6.11152	−	9.50972i	−0.270889	−	0.421511i	−0.949870	+	0.312644i	$0.898785\pi$
$510$	−12.5798	−	4.85717i	−0.557043	−	0.215079i
$511$	−0.188292	+	0.0859903i	−0.00832957	+	0.00380399i
$512$	30.2307	−	22.6304i	1.33602	−	1.00013i
$513$	3.78889	+	2.06889i	0.167283	+	0.0913437i
$514$	4.00818	−	6.23685i	0.176793	−	0.275095i
$515$	29.9585	−	21.8948i	1.32013	−	0.964801i
$516$	4.88775	−	16.6461i	0.215171	−	0.732805i
$517$	17.3699	+	1.24232i	0.763928	+	0.0546372i
$518$	−0.985339	−	0.0704728i	−0.0432933	−	0.00309640i
$519$	2.56268	−	8.72769i	0.112489	−	0.383103i
$520$	67.0565	+	10.4280i	2.94062	+	0.457296i
$521$	−9.13931	+	14.2210i	−0.400401	+	0.623035i	−0.981650	−	0.190690i	$-0.938928\pi$
$521$	−9.13931	+	14.2210i	−0.400401	+	0.623035i	0.581250	+	0.813725i	$0.302564\pi$
$522$	11.7415	+	6.41134i	0.513911	+	0.280617i
$523$	22.5461	−	16.8778i	0.985871	−	0.738014i	0.0207410	−	0.999785i	$-0.493397\pi$
$523$	22.5461	−	16.8778i	0.985871	−	0.738014i	0.965130	+	0.261771i	$0.0843065\pi$
$524$	58.2744	−	26.6130i	2.54573	−	1.16260i
$525$	0.223036	−	0.184473i	0.00973408	−	0.00805107i
$526$	2.20944	+	3.43796i	0.0963362	+	0.149902i
$527$	−0.212694	−	2.97385i	−0.00926509	−	0.129543i
$528$	5.12045	+	5.12045i	0.222839	+	0.222839i
$529$	−20.0941	+	11.1904i	−0.873658	+	0.486540i
$530$	16.1543	+	57.4467i	0.701696	+	2.49533i
$531$	−25.8985	+	29.8884i	−1.12390	+	1.29705i
$532$	0.469372	+	0.102106i	0.0203498	+	0.00442684i
$533$	−32.8494	−	24.5907i	−1.42286	−	1.06514i
$534$	−4.74738	−	10.3953i	−0.205439	−	0.449849i
$535$	16.7538	+	12.8443i	0.724331	+	0.555309i
$536$	8.02428	+	27.3282i	0.346596	+	1.18040i
$537$	−0.537780	−	2.47213i	−0.0232069	−	0.106680i
$538$	−0.436308	−	1.16979i	−0.0188106	−	0.0504331i
$539$	21.1019	+	6.19608i	0.908924	+	0.266884i
$540$	29.6272	−	6.08983i	1.27495	−	0.262065i
$541$	−16.0995	−	18.5798i	−0.692170	−	0.798807i	0.295502	−	0.955342i	$-0.404513\pi$
$541$	−16.0995	−	18.5798i	−0.692170	−	0.798807i	−0.987672	+	0.156535i	$0.949967\pi$
$542$	−17.4856	−	32.0225i	−0.751071	−	1.37548i
$543$	−7.12214	+	2.65642i	−0.305640	+	0.113998i
$544$	1.09742	+	0.705266i	0.0470513	+	0.0302380i
$545$	−13.0230	+	8.15978i	−0.557845	+	0.349527i
$546$	0.884069	+	0.127110i	0.0378347	+	0.00543980i
$547$	10.3702	−	27.8037i	0.443399	−	1.18880i	−0.502569	−	0.864537i	$-0.667612\pi$
$547$	10.3702	−	27.8037i	0.443399	−	1.18880i	0.945968	−	0.324261i	$-0.105116\pi$
$548$	−52.8971	+	70.6623i	−2.25965	+	3.01854i
$549$	7.21993	−	4.63997i	0.308139	−	0.198029i
$550$	−22.3145	−	31.2800i	−0.951493	−	1.33378i
$551$			2.63266i			0.112155i
$552$	−13.4994	+	3.50544i	−0.574573	+	0.149202i
$553$	0.764326	−	0.764326i	0.0325024	−	0.0325024i
$554$	−31.3046	−	27.1256i	−1.33000	−	1.15246i
$555$	−4.28154	−	3.79686i	−0.181741	−	0.161168i
$556$	7.69809	+	53.5414i	0.326472	+	2.27066i
$557$	2.76255	+	1.03038i	0.117053	+	0.0436584i	0.407308	−	0.913291i	$-0.366468\pi$
$557$	2.76255	+	1.03038i	0.117053	+	0.0436584i	−0.290255	+	0.956949i	$0.593740\pi$
$558$	2.81803	+	3.76445i	0.119297	+	0.159362i
$559$	−43.7901	+	12.8579i	−1.85213	+	0.543833i
$560$	0.718271	−	0.381573i	0.0303525	−	0.0161244i
$561$	−3.22640	+	7.06483i	−0.136219	+	0.298278i
$562$	18.5970	−	10.1547i	0.784468	−	0.428352i
$563$	1.01504	−	14.1921i	0.0427787	−	0.598125i	−0.930174	−	0.367119i	$-0.880344\pi$
$563$	1.01504	−	14.1921i	0.0427787	−	0.598125i	0.972953	−	0.231005i	$-0.0742014\pi$
$564$	−10.0446	+	8.70373i	−0.422956	+	0.366493i
$565$	19.7384	+	20.1967i	0.830401	+	0.849680i
$566$	−49.8393	−	22.7609i	−2.09490	−	0.956711i
$567$	−0.545523	+	0.118671i	−0.0229098	+	0.00498372i
$568$	16.7526	−	30.6801i	0.702924	−	1.28731i
$569$	4.62026	−	32.1346i	0.193691	−	1.34715i	−0.628442	−	0.777857i	$-0.716307\pi$
$569$	4.62026	−	32.1346i	0.193691	−	1.34715i	0.822133	−	0.569295i	$-0.192784\pi$
$570$	2.70445	+	3.19444i	0.113277	+	0.133800i
$571$	−38.3847	+	5.51888i	−1.60635	+	0.230958i	−0.886349	−	0.463017i	$-0.846767\pi$
$571$	−38.3847	+	5.51888i	−1.60635	+	0.230958i	−0.719999	+	0.693975i	$0.755858\pi$
$572$	16.7559	−	77.0256i	0.700599	−	3.22060i
$573$	15.4674	−	1.10625i	0.646160	−	0.0462143i
$574$	−1.51777			−0.0633506
$575$	23.8857	−	2.11494i	0.996103	−	0.0881991i
$576$	−22.0895			−0.920396
$577$	19.3162	−	1.38153i	0.804146	−	0.0575136i	0.336786	−	0.941581i	$-0.390660\pi$
$577$	19.3162	−	1.38153i	0.804146	−	0.0575136i	0.467359	+	0.884067i	$0.345205\pi$
$578$	−0.188096	+	0.864664i	−0.00782377	+	0.0359653i
$579$	−0.652701	+	0.0938443i	−0.0271253	+	0.00390004i
$580$	11.9186	+	14.0780i	0.494894	+	0.584559i
$581$	−0.0658682	+	0.458123i	−0.00273267	+	0.0190062i
$582$	−5.25038	+	9.61536i	−0.217635	+	0.398569i
$583$	33.5845	−	7.30585i	1.39093	−	0.302578i
$584$	−9.45944	−	4.31998i	−0.391434	−	0.178762i
$585$	−25.9988	−	26.6024i	−1.07492	−	1.09987i
$586$	2.84098	−	2.46172i	0.117360	−	0.101693i
$587$	−1.01797	+	14.2331i	−0.0420161	+	0.587462i	0.932214	+	0.361907i	$0.117874\pi$
$587$	−1.01797	+	14.2331i	−0.0420161	+	0.587462i	−0.974230	+	0.225555i	$0.927580\pi$
$588$	−14.7322	+	8.04437i	−0.607544	+	0.331744i
$589$	−0.384421	+	0.841766i	−0.0158398	+	0.0346844i
$590$	−72.4348	+	38.4801i	−2.98209	+	1.58420i
$591$	1.07343	−	0.315188i	0.0441551	−	0.0129651i
$592$	−9.63671	−	12.8731i	−0.396066	−	0.529083i
$593$	22.8943	+	8.53913i	0.940156	+	0.350660i	0.772377	−	0.635164i	$-0.219068\pi$
$593$	22.8943	+	8.53913i	0.940156	+	0.350660i	0.167779	+	0.985825i	$0.446340\pi$
$594$	−3.72913	−	25.9367i	−0.153008	−	1.06420i
$595$	0.652666	+	0.578783i	0.0267567	+	0.0237278i
$596$	7.08218	+	6.13674i	0.290097	+	0.251371i
$597$	2.00448	−	2.00448i	0.0820380	−	0.0820380i
$598$	54.3663	+	50.1959i	2.22320	+	2.05266i
$599$			8.94745i			0.365583i	0.983152	+	0.182791i	$0.0585133\pi$
$599$			8.94745i			0.365583i	−0.983152	+	0.182791i	$0.941487\pi$
$600$	14.3416	+	2.39911i	0.585493	+	0.0979433i
$601$	−8.47434	+	5.44613i	−0.345676	+	0.222152i	−0.701945	−	0.712231i	$-0.747685\pi$
$601$	−8.47434	+	5.44613i	−0.345676	+	0.222152i	0.356270	+	0.934383i	$0.384048\pi$
$602$	−1.01164	+	1.35139i	−0.0412314	+	0.0550787i
$603$	5.45570	−	14.6273i	0.222173	−	0.595670i
$604$	−60.2635	−	8.66458i	−2.45209	−	0.352557i
$605$	2.09016	−	1.30962i	0.0849770	−	0.0532437i
$606$	−8.74343	−	5.61906i	−0.355178	−	0.228259i
$607$	7.54780	−	2.81519i	0.306356	−	0.114265i	−0.191584	−	0.981476i	$-0.561363\pi$
$607$	7.54780	−	2.81519i	0.306356	−	0.114265i	0.497940	+	0.867211i	$0.334090\pi$
$608$	−0.194046	−	0.355368i	−0.00786960	−	0.0144121i
$609$	0.0788290	+	0.0909735i	0.00319431	+	0.00368643i
$610$	17.4350	−	3.58374i	0.705923	−	0.145102i
$611$	33.5475	+	9.85045i	1.35719	+	0.398507i
$612$	14.8927	+	39.9288i	0.602000	+	1.61403i
$613$	−2.93779	−	13.5048i	−0.118656	−	0.545454i	−0.997644	−	0.0686090i	$-0.978144\pi$
$613$	−2.93779	−	13.5048i	−0.118656	−	0.545454i	0.878987	−	0.476845i	$-0.158220\pi$
$614$	8.69672	+	29.6183i	0.350971	+	1.19530i
$615$	−6.97769	−	5.34946i	−0.281368	−	0.215711i
$616$	−0.600569	−	1.31506i	−0.0241976	−	0.0529854i
$617$	−18.8443	−	14.1067i	−0.758644	−	0.567914i	0.148411	−	0.988926i	$-0.452584\pi$
$617$	−18.8443	−	14.1067i	−0.758644	−	0.567914i	−0.907055	+	0.421012i	$0.861675\pi$
$618$	23.9741	+	5.21525i	0.964380	+	0.209788i
$619$	−21.3787	+	24.6723i	−0.859283	+	0.991665i	0.140716	+	0.990050i	$0.455060\pi$
$619$	−21.3787	+	24.6723i	−0.859283	+	0.991665i	−0.999999	+	0.00161538i	$0.999486\pi$
$620$	1.75518	+	6.24166i	0.0704897	+	0.250671i
$621$	15.1340	+	6.19502i	0.607306	+	0.248597i
$622$	−31.4935	−	31.4935i	−1.26278	−	1.26278i
$623$	0.0527391	+	0.737389i	0.00211295	+	0.0295429i
$624$	7.86041	+	12.2310i	0.314668	+	0.489633i
$625$	−23.6389	−	8.13648i	−0.945556	−	0.325459i
$626$	−34.5697	+	15.7875i	−1.38168	+	0.630994i
$627$	1.92983	−	1.44465i	0.0770699	−	0.0576938i
$628$	17.2573	+	9.42319i	0.688640	+	0.376026i
$629$	9.32444	−	14.5091i	0.371790	−	0.578516i
$630$	−1.35951	−	0.211418i	−0.0541644	−	0.00842309i
$631$	3.78787	−	12.9003i	0.150793	−	0.513553i	−0.849099	−	0.528233i	$-0.822855\pi$
$631$	3.78787	−	12.9003i	0.150793	−	0.513553i	0.999892	+	0.0146800i	$0.00467294\pi$
$632$	54.1649	+	3.87395i	2.15456	+	0.154097i
$633$	3.73297	+	0.266987i	0.148372	+	0.0106118i
$634$	0.961572	−	3.27481i	0.0381889	−	0.130059i
$635$	−5.69211	+	4.16001i	−0.225884	+	0.165085i
$636$	−14.1820	+	22.0676i	−0.562354	+	0.875039i
$637$	38.7551	+	21.1619i	1.53553	+	0.838465i
$638$	12.7927	−	9.57646i	0.506466	−	0.379136i
$639$	−17.4287	+	7.95944i	−0.689471	+	0.314871i
$640$	−41.4037	−	15.9863i	−1.63662	−	0.631914i
$641$	10.9105	+	16.9770i	0.430937	+	0.670552i	0.987024	−	0.160573i	$-0.0513341\pi$
$641$	10.9105	+	16.9770i	0.430937	+	0.670552i	−0.556087	+	0.831124i	$0.687698\pi$
$642$	0.995785	+	13.9229i	0.0393005	+	0.549493i
$643$	11.7335	+	11.7335i	0.462726	+	0.462726i	0.899548	−	0.436822i	$-0.143896\pi$
$643$	11.7335	+	11.7335i	0.462726	+	0.462726i	−0.436822	+	0.899548i	$0.643896\pi$
$644$	1.80996	+	0.186972i	0.0713226	+	0.00736774i
$645$	−9.41389	+	2.64722i	−0.370671	+	0.104234i
$646$	−8.26076	+	9.53343i	−0.325015	+	0.375088i
$647$	21.0852	+	4.58680i	0.828944	+	0.180326i	0.606968	−	0.794726i	$-0.292386\pi$
$647$	21.0852	+	4.58680i	0.828944	+	0.180326i	0.221976	+	0.975052i	$0.428749\pi$
$648$	−22.4527	−	16.8079i	−0.882027	−	0.660277i
$649$	19.6244	+	42.9715i	0.770326	+	1.68678i
$650$	−30.4287	−	70.8910i	−1.19351	−	2.78058i
$651$	0.0119208	+	0.0405984i	0.000467212	+	0.00159118i
$652$	3.14352	+	14.4505i	0.123110	+	0.565926i
$653$	−14.6767	−	39.3497i	−0.574343	−	1.53987i	−0.821094	−	0.570793i	$-0.806636\pi$
$653$	−14.6767	−	39.3497i	−0.574343	−	1.53987i	0.246751	−	0.969079i	$-0.420637\pi$
$654$	−9.74981	−	2.86280i	−0.381248	−	0.111944i
$655$	−30.1522	−	19.8702i	−1.17814	−	0.776392i
$656$	−16.1794	−	18.6720i	−0.631700	−	0.729021i
$657$	2.73174	+	5.00281i	0.106575	+	0.195178i
$658$	1.21171	−	0.451945i	0.0472374	−	0.0176186i
$659$	11.2805	+	7.24953i	0.439426	+	0.282402i	0.741589	−	0.670854i	$-0.234072\pi$
$659$	11.2805	+	7.24953i	0.439426	+	0.282402i	−0.302163	+	0.953256i	$0.597709\pi$
$660$	3.77942	−	16.4620i	0.147114	−	0.640781i
$661$	35.9798	+	5.17311i	1.39945	+	0.201211i	0.800384	−	0.599488i	$-0.204629\pi$
$661$	35.9798	+	5.17311i	1.39945	+	0.201211i	0.599067	+	0.800699i	$0.295538\pi$
$662$	11.1105	−	29.7884i	0.431822	−	1.15776i
$663$	−9.34496	+	12.4834i	−0.362928	+	0.484815i
$664$	−19.5607	+	12.5709i	−0.759103	+	0.487846i
$665$	−0.0917029	−	0.254755i	−0.00355609	−	0.00987898i
$666$			27.2023i			1.05407i
$667$	1.10730	+	9.91104i	0.0428750	+	0.383757i
$668$	−23.9781	+	23.9781i	−0.927739	+	0.927739i
$669$	−6.15047	−	5.32941i	−0.237791	−	0.206047i
$670$	21.4825	−	24.2248i	0.829940	−	0.935885i
$671$	−1.45897	−	10.1474i	−0.0563229	−	0.391734i
$672$	−0.0173461	−	0.00646975i	−0.000669140	−	0.000249576i
$673$	22.5546	+	30.1294i	0.869414	+	1.16140i	0.985754	+	0.168192i	$0.0537928\pi$
$673$	22.5546	+	30.1294i	0.869414	+	1.16140i	−0.116340	+	0.993209i	$0.537116\pi$
$674$	−18.3382	+	5.38458i	−0.706361	+	0.207406i
$675$	−11.7757	−	12.3290i	−0.453246	−	0.474542i
$676$	44.3228	−	97.0535i	1.70472	−	3.73283i
$677$	−25.8171	+	14.0972i	−0.992230	+	0.541799i	−0.891454	−	0.453110i	$-0.850314\pi$
$677$	−25.8171	+	14.0972i	−0.992230	+	0.541799i	−0.100776	+	0.994909i	$0.532132\pi$
$678$	−1.33207	+	18.6248i	−0.0511579	+	0.715281i
$679$	0.535599	−	0.464100i	0.0205544	−	0.0178105i
$680$	−0.502851	+	43.8213i	−0.0192835	+	1.68047i
$681$	10.1283	+	4.62543i	0.388116	+	0.177247i
$682$	5.48867	−	1.19399i	0.210172	−	0.0457201i
$683$	15.8746	−	29.0722i	0.607426	−	1.11242i	−0.375222	−	0.926935i	$-0.622434\pi$
$683$	15.8746	−	29.0722i	0.607426	−	1.11242i	0.982648	−	0.185482i	$-0.0593847\pi$
$684$	1.88243	−	13.0926i	0.0719765	−	0.500608i
$685$	49.5831	+	4.11860i	1.89447	+	0.157364i
$686$	3.23540	−	0.465180i	0.123528	−	0.0177607i
$687$	1.32202	−	6.07722i	0.0504381	−	0.231860i
$688$	−27.4093	+	1.96035i	−1.04497	+	0.0747376i
$689$	69.0068			2.62895
$690$	11.5249	+	10.8884i	0.438744	+	0.414515i
$691$	38.8961			1.47968			0.739839	−	0.672784i	$-0.234902\pi$
$691$	38.8961			1.47968			0.739839	+	0.672784i	$0.234902\pi$
$692$	−59.4666	+	4.25313i	−2.26058	+	0.161680i
$693$	−0.168443	+	0.774319i	−0.00639861	+	0.0294139i
$694$	28.9153	−	4.15739i	1.09761	−	0.157812i
$695$	23.2703	−	19.7009i	0.882693	−	0.747299i
$696$	−0.860636	+	5.98585i	−0.0326223	+	0.226893i
$697$	12.6995	−	23.2575i	0.481030	−	0.880940i
$698$	−30.0800	+	6.54350i	−1.13854	+	0.247675i
$699$	−7.42165	−	3.38935i	−0.280712	−	0.128197i
$700$	−1.64371	−	0.947132i	−0.0621263	−	0.0357982i
$701$	5.09788	−	4.41734i	0.192544	−	0.166841i	−0.553253	−	0.833013i	$-0.686614\pi$
$701$	5.09788	−	4.41734i	0.192544	−	0.166841i	0.745798	+	0.666172i	$0.232068\pi$
$702$	3.75318	−	52.4763i	0.141655	−	1.98059i
$703$	−4.69838	+	2.56551i	−0.177203	+	0.0967600i
$704$	−10.9612	+	24.0017i	−0.413115	+	0.904597i
$705$	7.16353	+	2.19299i	0.269794	+	0.0825929i
$706$	35.8426	−	10.5243i	1.34895	−	0.396089i
$707$	0.402917	+	0.538234i	0.0151533	+	0.0202424i
$708$	−33.7817	−	12.5999i	−1.26959	−	0.473534i
$709$	−5.68230	−	39.5213i	−0.213403	−	1.48425i	−0.761678	−	0.647955i	$-0.775624\pi$
$709$	−5.68230	−	39.5213i	−0.213403	−	1.48425i	0.548275	−	0.836298i	$-0.315285\pi$
$710$	−39.6664	+	2.37987i	−1.48865	+	0.0893149i
$711$	−22.4948	−	19.4919i	−0.843623	−	0.731003i
$712$	−26.2616	+	26.2616i	−0.984197	+	0.984197i
$713$	−1.09316	+	3.33064i	−0.0409392	+	0.124733i
$714$			0.576784i			0.0215856i
$715$	−41.8062	+	15.0488i	−1.56346	+	0.562792i
$716$	−13.9496	+	8.96487i	−0.521321	+	0.335033i
$717$	−5.78910	+	7.73333i	−0.216198	+	0.288807i
$718$	−26.8361	+	71.9504i	−1.00151	+	2.68516i
$719$	−3.35510	−	0.482391i	−0.125124	−	0.0179901i	0.0794682	−	0.996837i	$-0.474678\pi$
$719$	−3.35510	−	0.482391i	−0.125124	−	0.0179901i	−0.204592	+	0.978847i	$0.565587\pi$
$720$	−11.8915	−	18.9788i	−0.443169	−	0.707299i
$721$	−1.33519	−	0.858072i	−0.0497249	−	0.0319563i
$722$	−39.8174	+	14.8511i	−1.48185	+	0.552701i
$723$	−0.497473	−	0.911054i	−0.0185012	−	0.0338825i
$724$	32.6262	+	37.6526i	1.21254	+	1.39935i
$725$	3.15740	−	9.90625i	0.117263	−	0.367909i
$726$	1.56482	+	0.459472i	0.0580758	+	0.0170526i
$727$	−1.84107	−	4.93611i	−0.0682816	−	0.183070i	0.898327	−	0.439328i	$-0.144783\pi$
$727$	−1.84107	−	4.93611i	−0.0682816	−	0.183070i	−0.966609	+	0.256257i	$0.917511\pi$
$728$	−0.617002	−	2.83631i	−0.0228676	−	0.105121i
$729$	2.58681	+	8.80987i	0.0958078	+	0.326291i
$730$	1.54803	+	11.7199i	0.0572952	+	0.433774i
$731$	−12.2434	−	26.8092i	−0.452837	−	0.991575i
$732$	6.26369	+	4.68894i	0.231513	+	0.173308i
$733$	−21.7148	−	4.72377i	−0.802056	−	0.174477i	−0.207189	−	0.978301i	$-0.566432\pi$
$733$	−21.7148	−	4.72377i	−0.802056	−	0.174477i	−0.594867	+	0.803824i	$0.702795\pi$
$734$	−27.2625	+	31.4626i	−1.00628	+	1.16130i
$735$	8.25147	+	4.62934i	0.304360	+	0.170756i
$736$	−0.879983	−	1.25622i	−0.0324366	−	0.0463049i
$737$	−13.1863	−	13.1863i	−0.485723	−	0.485723i
$738$	2.98158	+	41.6879i	0.109753	+	1.53455i
$739$	−9.18790	−	14.2967i	−0.337982	−	0.525911i	0.630110	−	0.776506i	$-0.283010\pi$
$739$	−9.18790	−	14.2967i	−0.337982	−	0.525911i	−0.968092	+	0.250595i	$0.919374\pi$
$740$	−13.5098	+	34.9895i	−0.496628	+	1.28624i
$741$	4.40265	−	2.01062i	0.161735	−	0.0738620i
$742$	2.04333	−	1.52962i	0.0750131	−	0.0561541i
$743$	3.65947	+	1.99822i	0.134253	+	0.0733077i	0.544972	−	0.838454i	$-0.316540\pi$
$743$	3.65947	+	1.99822i	0.134253	+	0.0733077i	−0.410719	+	0.911762i	$0.634722\pi$
$744$	−1.14923	+	1.78824i	−0.0421330	+	0.0655602i
$745$	0.811673	−	5.21943i	0.0297374	−	0.191225i
$746$	−9.87861	+	33.6434i	−0.361681	+	1.23177i
$747$	12.7124	+	0.909212i	0.465124	+	0.0332663i
$748$	50.7752	+	3.63151i	1.85652	+	0.132781i
$749$	0.254394	−	0.866386i	0.00929535	−	0.0316571i
$750$	−6.34523	−	15.2636i	−0.231695	−	0.557348i
$751$	−20.5742	+	32.0140i	−0.750762	+	1.16821i	0.230035	+	0.973182i	$0.426116\pi$
$751$	−20.5742	+	32.0140i	−0.750762	+	1.16821i	−0.980798	+	0.195027i	$0.937521\pi$
$752$	18.4768	+	10.0891i	0.673778	+	0.367911i
$753$	3.78733	−	2.83516i	0.138018	−	0.103319i
$754$	29.1847	−	13.3282i	1.06285	−	0.485385i
$755$	13.8970	+	31.3782i	0.505765	+	1.14197i
$756$	−0.699439	−	1.08835i	−0.0254383	−	0.0395828i
$757$	−1.40789	−	19.6849i	−0.0511707	−	0.715459i	−0.956682	−	0.291136i	$-0.905967\pi$
$757$	−1.40789	−	19.6849i	−0.0511707	−	0.715459i	0.905511	−	0.424323i	$-0.139488\pi$
$758$	−59.7836	−	59.7836i	−2.17144	−	2.17144i
$759$	6.65750	−	6.25029i	0.241652	−	0.226871i
$760$	6.65545	−	11.8629i	0.241419	−	0.430312i
$761$	22.4603	−	25.9206i	0.814185	−	0.939619i	−0.184884	−	0.982760i	$-0.559191\pi$
$761$	22.4603	−	25.9206i	0.814185	−	0.939619i	0.999069	+	0.0431410i	$0.0137365\pi$
$762$	−4.55507	−	0.990895i	−0.165013	−	0.0358963i
$763$	0.526224	+	0.393926i	0.0190506	+	0.0142611i
$764$	−42.2212	−	92.4516i	−1.52751	−	3.34478i
$765$	14.6150	−	19.0634i	0.528407	−	0.689240i
$766$	19.0744	+	64.9614i	0.689186	+	2.34715i
$767$	20.1614	+	92.6804i	0.727985	+	3.34649i
$768$	−6.70719	−	17.9827i	−0.242025	−	0.648893i
$769$	−31.5126	−	9.25292i	−1.13637	−	0.333669i	−0.341163	−	0.940004i	$-0.610821\pi$
$769$	−31.5126	−	9.25292i	−1.13637	−	0.333669i	−0.795209	+	0.606335i	$0.792639\pi$
$770$	−0.904333	+	1.37229i	−0.0325899	+	0.0494539i
$771$	−1.20295	−	1.38828i	−0.0433232	−	0.0499977i
$772$	2.07129	+	3.79329i	0.0745475	+	0.136524i
$773$	5.92343	−	2.20933i	0.213051	−	0.0794639i	−0.240673	−	0.970606i	$-0.577368\pi$
$773$	5.92343	−	2.20933i	0.213051	−	0.0794639i	0.453724	+	0.891142i	$0.350095\pi$
$774$	39.1054	+	25.1315i	1.40561	+	0.903333i
$775$	2.45606	−	2.70638i	0.0882242	−	0.0972159i
$776$	35.2413	+	5.06693i	1.26509	+	0.181892i
$777$	−0.0855376	+	0.229335i	−0.00306864	+	0.00822735i
$778$	9.94617	−	13.2865i	0.356587	−	0.476345i
$779$	−6.91915	+	4.44667i	−0.247904	+	0.159318i
$780$	14.4404	−	30.6835i	0.517050	−	1.09864i
$781$			22.8871i			0.818963i
$782$	−27.0891	+	39.3645i	−0.968703	+	1.40767i
$783$	5.01376	−	5.01376i	0.179177	−	0.179177i
$784$	20.0929	+	17.4106i	0.717603	+	0.621807i
$785$	−0.663758	−	11.0632i	−0.0236905	−	0.394861i
$786$	−3.39795	−	23.6333i	−0.121201	−	0.842971i
$787$	−30.5617	−	11.3989i	−1.08941	−	0.406328i	−0.260364	−	0.965511i	$-0.583842\pi$
$787$	−30.5617	−	11.3989i	−1.08941	−	0.406328i	−0.829045	+	0.559182i	$0.811115\pi$
$788$	−4.39424	−	5.87001i	−0.156538	−	0.209111i
$789$	0.971575	−	0.285280i	0.0345890	−	0.0101562i
$790$	−28.9612	−	54.5164i	−1.03039	−	1.93961i
$791$	0.501781	−	1.09875i	0.0178413	−	0.0390670i
$792$	−34.9404	+	19.0789i	−1.24155	+	0.677939i
$793$	1.46838	−	20.5306i	0.0521435	−	0.729062i
$794$	4.69127	−	4.06501i	0.166487	−	0.144262i
$795$	14.7851	+	0.169660i	0.524373	+	0.00601720i
$796$	−16.9007	−	7.71831i	−0.599031	−	0.273568i
$797$	1.66923	−	0.363120i	0.0591273	−	0.0128624i	−0.182904	−	0.983131i	$-0.558550\pi$
$797$	1.66923	−	0.363120i	0.0591273	−	0.0128624i	0.242032	+	0.970268i	$0.422186\pi$
$798$	0.0857972	−	0.157126i	0.00303719	−	0.00556220i
$799$	−3.21331	+	22.3491i	−0.113679	+	0.790654i
$800$	0.303962	+	1.56991i	0.0107467	+	0.0555048i
$801$	20.1499	−	2.89712i	0.711962	−	0.102365i
$802$	3.22619	−	14.8306i	0.113921	−	0.523686i
$803$	6.79141	−	0.485732i	0.239664	−	0.0171411i
$804$	14.2327			0.501950
$805$	−0.452380	−	0.920492i	−0.0159443	−	0.0324431i
$806$	11.2777			0.397240
$807$	−0.308563	+	0.0220688i	−0.0108619	+	0.000776860i
$808$	−7.17980	+	33.0050i	−0.252584	+	1.16111i
$809$	38.7159	−	5.56650i	1.36118	−	0.195708i	0.577254	−	0.816565i	$-0.304124\pi$
$809$	38.7159	−	5.56650i	1.36118	−	0.195708i	0.783924	+	0.620857i	$0.213215\pi$
$810$	−2.63931	+	31.7741i	−0.0927358	+	1.11643i
$811$	2.94602	−	20.4900i	0.103449	−	0.719503i	−0.870407	−	0.492334i	$-0.836144\pi$
$811$	2.94602	−	20.4900i	0.103449	−	0.719503i	0.973855	−	0.227169i	$-0.0729469\pi$
$812$	0.378113	−	0.692462i	0.0132692	−	0.0243006i
$813$	−8.83365	+	1.92164i	−0.309810	+	0.0673950i
$814$	29.5570	+	13.4982i	1.03597	+	0.473113i
$815$	5.96154	−	5.82627i	0.208823	−	0.204085i
$816$	−7.09575	+	6.14850i	−0.248401	+	0.215241i
$817$	−0.652597	+	9.12450i	−0.0228315	+	0.319226i
$818$	59.3576	−	32.4117i	2.07539	−	1.13325i
$819$	−0.660930	+	1.44723i	−0.0230948	+	0.0505705i
$820$	−16.8688	+	55.1028i	−0.589084	+	1.92427i
$821$	−44.6275	+	13.1038i	−1.55751	+	0.457327i	−0.943335	−	0.331842i	$-0.892330\pi$
$821$	−44.6275	+	13.1038i	−1.55751	+	0.457327i	−0.614177	+	0.789168i	$0.710512\pi$
$822$	19.7145	+	26.3356i	0.687624	+	0.918558i
$823$	−7.58675	−	2.82971i	−0.264457	−	0.0986375i	0.213738	−	0.976891i	$-0.431436\pi$
$823$	−7.58675	−	2.82971i	−0.264457	−	0.0986375i	−0.478195	+	0.878254i	$0.658709\pi$
$824$	−11.3474	−	78.9231i	−0.395306	−	2.74942i
$825$	−8.99421	+	3.12150i	−0.313138	+	0.108677i
$826$	2.65137	+	2.29742i	0.0922528	+	0.0799375i
$827$	−9.84594	+	9.84594i	−0.342377	+	0.342377i	−0.857260	−	0.514883i	$-0.827835\pi$
$827$	−9.84594	+	9.84594i	−0.342377	+	0.342377i	0.514883	+	0.857260i	$0.327835\pi$
$828$	1.57990	−	50.0807i	0.0549055	−	1.74042i
$829$		−	46.2055i		−	1.60478i	−0.596798	−	0.802392i	$-0.703561\pi$
$829$		−	46.2055i		−	1.60478i	0.596798	−	0.802392i	$-0.296439\pi$
$830$	23.9163	+	11.2556i	0.830148	+	0.390689i
$831$	−8.63412	+	5.54881i	−0.299514	+	0.192486i
$832$	−31.7480	+	42.4104i	−1.10066	+	1.47032i
$833$	−9.96506	+	26.7174i	−0.345269	+	0.925702i
$834$	19.9547	+	2.86905i	0.690974	+	0.0993470i
$835$	18.6294	+	4.27702i	0.644695	+	0.148012i
$836$	−13.2918	−	8.54214i	−0.459708	−	0.295436i
$837$	2.33521	−	0.870987i	0.0807166	−	0.0301057i
$838$	−3.91240	−	7.16503i	−0.135152	−	0.247512i
$839$	−8.49280	−	9.80122i	−0.293204	−	0.338376i	0.589966	−	0.807428i	$-0.299141\pi$
$839$	−8.49280	−	9.80122i	−0.293204	−	0.338376i	−0.883170	+	0.469052i	$0.844596\pi$
$840$	−0.125223	−	0.609212i	−0.00432059	−	0.0210198i
$841$	−23.6763	−	6.95200i	−0.816425	−	0.239724i
$842$	−7.99424	−	21.4334i	−0.275500	−	0.738643i
$843$	−1.11599	−	5.13013i	−0.0384368	−	0.176691i
$844$	−6.91070	−	23.5357i	−0.237876	−	0.810132i
$845$	−59.6229	+	7.87531i	−2.05109	+	0.270919i
$846$	−14.7937	−	32.3937i	−0.508617	−	1.11372i
$847$	−0.0844574	−	0.0632240i	−0.00290199	−	0.00217240i
$848$	40.5997	+	8.83192i	1.39420	+	0.303289i
$849$	−8.89030	+	10.2600i	−0.305114	+	0.352121i
$850$	42.5175	−	25.9654i	1.45834	−	0.890605i
$851$	−16.6087	+	11.6344i	−0.569338	+	0.398822i
$852$	−12.3517	−	12.3517i	−0.423161	−	0.423161i
$853$	2.27254	+	31.7743i	0.0778103	+	1.08793i	0.874975	+	0.484168i	$0.160878\pi$
$853$	2.27254	+	31.7743i	0.0778103	+	1.08793i	−0.797165	+	0.603762i	$0.793668\pi$
$854$	−0.411606	−	0.640471i	−0.0140849	−	0.0219165i
$855$	−6.81709	+	3.01921i	−0.233139	+	0.103255i
$856$	41.2637	−	18.8445i	1.41036	−	0.644091i
$857$	26.0647	−	19.5118i	0.890355	−	0.666511i	−0.0528933	−	0.998600i	$-0.516844\pi$
$857$	26.0647	−	19.5118i	0.890355	−	0.666511i	0.943248	+	0.332089i	$0.107753\pi$
$858$	−25.7849	−	14.0796i	−0.880283	−	0.480671i
$859$	−20.4318	+	31.7925i	−0.697124	+	1.08475i	0.294507	+	0.955649i	$0.404844\pi$
$859$	−20.4318	+	31.7925i	−0.697124	+	1.08475i	−0.991632	+	0.129098i	$0.958792\pi$
$860$	37.8189	+	51.7473i	1.28961	+	1.76457i
$861$	−0.105951	+	0.360836i	−0.00361080	+	0.0122972i
$862$	53.4376	+	3.82194i	1.82009	+	0.130176i
$863$	−36.0361	−	2.57735i	−1.22668	−	0.0877340i	−0.557083	−	0.830457i	$-0.688079\pi$
$863$	−36.0361	−	2.57735i	−1.22668	−	0.0877340i	−0.669599	+	0.742723i	$0.733534\pi$
$864$	−0.307230	+	1.04633i	−0.0104522	+	0.0355969i
$865$	19.8287	+	27.1315i	0.674197	+	0.922499i
$866$	18.0754	−	28.1258i	0.614226	−	0.955754i
$867$	0.192435	+	0.105078i	0.00653544	+	0.00356862i
$868$	0.222011	−	0.166195i	0.00753554	−	0.00564103i
$869$	−32.3415	+	14.7699i	−1.09711	+	0.501034i
$870$	6.28576	−	2.78389i	0.213107	−	0.0943828i
$871$	−20.2423	−	31.4976i	−0.685884	−	1.06726i
$872$	2.35585	+	32.9391i	0.0797791	+	1.11546i
$873$	−13.7994	−	13.7994i	−0.467037	−	0.467037i
$874$	13.2350	−	6.69404i	0.447682	−	0.226429i
$875$	0.0395301	+	1.06858i	0.00133636	+	0.0361246i
$876$	−3.40304	+	3.92732i	−0.114978	+	0.132692i
$877$	−40.4838	−	8.80672i	−1.36704	−	0.297382i	−0.531617	−	0.846985i	$-0.678415\pi$
$877$	−40.4838	−	8.80672i	−1.36704	−	0.297382i	−0.835426	+	0.549603i	$0.814779\pi$
$878$	−8.48580	−	6.35239i	−0.286382	−	0.214383i
$879$	−0.386930	−	0.847259i	−0.0130508	−	0.0285773i
$880$	−26.5224	+	3.50323i	−0.894072	+	0.118094i
$881$	−8.90021	−	30.3113i	−0.299856	−	1.02121i	−0.962274	−	0.272081i	$-0.912288\pi$
$881$	−8.90021	−	30.3113i	−0.299856	−	1.02121i	0.662419	−	0.749134i	$-0.269530\pi$
$882$	−9.56007	−	43.9469i	−0.321904	−	1.47977i
$883$	0.0369919	+	0.0991792i	0.00124488	+	0.00333764i	0.937571	−	0.347795i	$-0.113069\pi$
$883$	0.0369919	+	0.0991792i	0.00124488	+	0.00333764i	−0.936326	+	0.351132i	$0.885797\pi$
$884$	98.0650	+	28.7945i	3.29828	+	0.968464i
$885$	4.09182	+	19.9068i	0.137545	+	0.669161i
$886$	17.8868	+	20.6425i	0.600919	+	0.693497i
$887$	−24.5333	−	44.9294i	−0.823748	−	1.50858i	−0.860612	−	0.509262i	$-0.829918\pi$
$887$	−24.5333	−	44.9294i	−0.823748	−	1.50858i	0.0368634	−	0.999320i	$-0.488263\pi$
$888$	−11.5213	+	4.29724i	−0.386631	+	0.144206i
$889$	0.253685	+	0.163033i	0.00850832	+	0.00546796i
$890$	41.1495	+	9.44729i	1.37933	+	0.316674i
$891$	18.1765	+	2.61339i	0.608937	+	0.0875519i
$892$	−18.6404	+	49.9769i	−0.624128	+	1.67335i
$893$	4.19981	−	5.61029i	0.140541	−	0.187741i
$894$	2.93813	−	1.88822i	0.0982657	−	0.0631515i
$895$	8.45695	+	3.98006i	0.282685	+	0.133039i
$896$			1.89836i			0.0634197i
$897$	15.7287	−	9.42104i	0.525167	−	0.314559i
$898$	2.03160	−	2.03160i	0.0677952	−	0.0677952i
$899$	1.14870	+	0.995353i	0.0383113	+	0.0331969i
$900$	−22.7854	+	47.0075i	−0.759514	+	1.56692i
$901$	6.34200	+	44.1096i	0.211283	+	1.46950i
$902$	46.7761	+	17.4466i	1.55747	+	0.580908i
$903$	0.250661	+	0.334844i	0.00834148	+	0.0111429i
$904$	58.2246	−	17.0963i	1.93652	−	0.568614i
$905$	8.22049	−	26.8527i	0.273258	−	0.892613i
$906$	−9.42615	+	20.6404i	−0.313163	+	0.685731i
$907$	10.7261	−	5.85687i	0.356153	−	0.194474i	−0.291204	−	0.956661i	$-0.594056\pi$
$907$	10.7261	−	5.85687i	0.356153	−	0.194474i	0.647357	+	0.762187i	$0.275874\pi$
$908$	5.20620	−	72.7922i	0.172774	−	2.41569i
$909$	13.9919	−	12.1241i	0.464082	−	0.402130i
$910$	−2.35986	+	2.30632i	−0.0782287	+	0.0764537i
$911$	44.1189	+	20.1484i	1.46173	+	0.667548i	0.978178	−	0.207770i	$-0.0666207\pi$
$911$	44.1189	+	20.1484i	1.46173	+	0.667548i	0.483548	+	0.875318i	$0.339348\pi$
$912$	2.84760	−	0.619457i	0.0942935	−	0.0205123i
$913$	7.29605	−	13.3617i	0.241464	−	0.442208i
$914$	9.43715	−	65.6368i	0.312153	−	2.17107i
$915$	0.365084	−	4.39518i	0.0120693	−	0.145300i
$916$	−40.3483	+	5.80120i	−1.33314	+	0.191677i
$917$	−0.328316	+	1.50924i	−0.0108419	+	0.0498396i
$918$	33.8881	−	2.42372i	1.11847	−	0.0799948i
$919$	7.50170			0.247458			0.123729	−	0.992316i	$-0.460515\pi$
$919$	7.50170			0.247458			0.123729	+	0.992316i	$0.460515\pi$
$920$	20.0658	−	47.4588i	0.661551	−	1.56467i
$921$	7.64855			0.252028
$922$	31.3202	−	2.24006i	1.03148	−	0.0737726i
$923$	−9.76777	+	44.9017i	−0.321510	+	1.47796i
$924$	−0.715084	+	0.102814i	−0.0235245	+	0.00338232i
$925$	20.7561	−	4.01872i	0.682455	−	0.132135i
$926$	−1.41397	+	9.83435i	−0.0464658	+	0.323177i
$927$	−20.9453	+	38.3585i	−0.687935	+	1.25986i
$928$	−0.649839	+	0.141364i	−0.0213320	+	0.00464050i
$929$	27.1100	+	12.3807i	0.889450	+	0.406198i	0.807107	−	0.590406i	$-0.201032\pi$
$929$	27.1100	+	12.3807i	0.889450	+	0.406198i	0.0823436	+	0.996604i	$0.473759\pi$
$930$	2.41631	+	0.0277273i	0.0792339	+	0.000909213i
$931$	6.68889	−	5.79596i	0.219220	−	0.189955i
$932$	−3.81492	+	53.3396i	−0.124962	+	1.74720i
$933$	−9.68574	+	5.28882i	−0.317097	+	0.173148i
$934$	2.66142	−	5.82769i	0.0870843	−	0.190688i
$935$	−13.4614	−	25.3397i	−0.440236	−	0.828698i
$936$	−76.6915	+	22.5187i	−2.50674	+	0.736045i
$937$	21.6233	+	28.8853i	0.706401	+	0.943641i	0.999924	−	0.0123109i	$-0.00391877\pi$
$937$	21.6233	+	28.8853i	0.706401	+	0.943641i	−0.293523	+	0.955952i	$0.594828\pi$
$938$	−1.29757	−	0.483969i	−0.0423672	−	0.0158021i
$939$	1.34011	+	9.32069i	0.0437329	+	0.304169i
$940$	−2.94071	−	49.0142i	−0.0959155	−	1.59867i
$941$	8.07733	+	6.99905i	0.263314	+	0.228163i	0.776504	−	0.630112i	$-0.216991\pi$
$941$	8.07733	+	6.99905i	0.263314	+	0.228163i	−0.513191	+	0.858275i	$0.671537\pi$
$942$	5.18175	−	5.18175i	0.168831	−	0.168831i
$943$	−24.1779	+	19.6503i	−0.787340	+	0.639903i
$944$			57.1082i			1.85871i
$945$	−0.310524	+	0.659811i	−0.0101013	+	0.0214636i
$946$	46.7117	−	30.0198i	1.51873	−	0.976028i
$947$	28.2577	−	37.7479i	0.918253	−	1.22664i	−0.0553670	−	0.998466i	$-0.517633\pi$
$947$	28.2577	−	37.7479i	0.918253	−	1.22664i	0.973620	−	0.228176i	$-0.0732762\pi$
$948$	9.48304	−	25.4250i	0.307995	−	0.825766i
$949$	13.5313	+	1.94550i	0.439243	+	0.0631536i
$950$	−15.4449	+	0.748901i	−0.501098	+	0.0242976i
$951$	−0.711431	−	0.457209i	−0.0230697	−	0.0148260i
$952$	1.75628	−	0.655059i	0.0569214	−	0.0212306i
$953$	27.3560	+	50.0987i	0.886146	+	1.62286i	0.777596	+	0.628765i	$0.216439\pi$
$953$	27.3560	+	50.0987i	0.886146	+	1.62286i	0.108550	+	0.994091i	$0.465379\pi$
$954$	−46.0274	−	53.1184i	−1.49019	−	1.71977i
$955$	−31.5238	+	47.8361i	−1.02008	+	1.54794i
$956$	60.7502	+	17.8379i	1.96480	+	0.576918i
$957$	−1.38370	−	3.70983i	−0.0447285	−	0.119922i
$958$	−21.7994	−	100.210i	−0.704307	−	3.23765i
$959$	−0.599554	−	2.04189i	−0.0193606	−	0.0659362i
$960$	−6.90646	+	9.00860i	−0.222905	+	0.290751i
$961$	−12.6559	−	27.7126i	−0.408256	−	0.893955i
$962$	52.2266	+	39.0963i	1.68385	+	1.26052i
$963$	−24.2964	−	5.28535i	−0.782939	−	0.170318i
$964$	−4.45534	+	5.14173i	−0.143497	+	0.165604i
$965$	1.19198	−	2.12462i	0.0383712	−	0.0683939i
$966$	0.256909	−	0.627610i	0.00826590	−	0.0201930i
$967$	−23.1856	−	23.1856i	−0.745599	−	0.745599i	0.228051	−	0.973649i	$-0.426765\pi$
$967$	−23.1856	−	23.1856i	−0.745599	−	0.745599i	−0.973649	+	0.228051i	$0.926765\pi$
$968$	−0.378107	−	5.28662i	−0.0121528	−	0.169919i
$969$	1.68982	+	2.62941i	0.0542849	+	0.0844690i
$970$	−16.3899	−	37.0069i	−0.526250	−	1.18822i
$971$	−16.8073	+	7.67566i	−0.539373	+	0.246324i	−0.666424	−	0.745573i	$-0.732176\pi$
$971$	−16.8073	+	7.67566i	−0.539373	+	0.246324i	0.127051	+	0.991896i	$0.459449\pi$
$972$	−43.7059	+	32.7178i	−1.40187	+	1.04943i
$973$	−1.14461	−	0.625002i	−0.0366944	−	0.0200366i
$974$	−19.3649	+	30.1323i	−0.620491	+	0.965502i
$975$	−18.9778	+	2.28545i	−0.607775	+	0.0731930i
$976$	3.49154	−	11.8911i	0.111761	−	0.380625i
$977$	−29.2062	−	2.08887i	−0.934390	−	0.0668289i	−0.404165	−	0.914686i	$-0.632438\pi$
$977$	−29.2062	−	2.08887i	−0.934390	−	0.0668289i	−0.530225	+	0.847857i	$0.677892\pi$
$978$	5.49756	+	0.393194i	0.175793	+	0.0125729i
$979$	6.85082	−	23.3318i	0.218953	−	0.745686i
$980$	9.52898	−	61.2757i	0.304392	−	1.95738i
$981$	9.78605	−	15.2274i	0.312444	−	0.486173i
$982$	−8.29421	−	4.52898i	−0.264679	−	0.144526i
$983$	−23.3500	+	17.4796i	−0.744750	+	0.557513i	−0.902873	−	0.429907i	$-0.858546\pi$
$983$	−23.3500	+	17.4796i	−0.744750	+	0.557513i	0.158124	+	0.987419i	$0.449456\pi$
$984$	−17.1856	+	7.84842i	−0.547858	+	0.250199i
$985$	−1.48872	+	3.85570i	−0.0474345	+	0.122853i
$986$	11.2017	+	17.4301i	0.356734	+	0.555089i
$987$	−0.0228598	−	0.319621i	−0.000727634	−	0.0101737i
$988$	−22.4314	−	22.4314i	−0.713638	−	0.713638i
$989$	1.38099	+	34.6250i	0.0439130	+	1.10101i
$990$	39.4685	+	22.1431i	1.25439	+	0.703754i
$991$	18.0664	−	20.8497i	0.573898	−	0.662314i	−0.392383	−	0.919802i	$-0.628349\pi$
$991$	18.0664	−	20.8497i	0.573898	−	0.662314i	0.966282	+	0.257488i	$0.0828947\pi$
$992$	−0.228421	−	0.0496900i	−0.00725238	−	0.00157766i
$993$	−6.30631	−	4.72085i	−0.200125	−	0.149812i
$994$	0.706072	+	1.54608i	0.0223952	+	0.0490388i
$995$	1.37139	+	10.3826i	0.0434761	+	0.329152i
$996$	3.27351	+	11.1486i	0.103725	+	0.353256i
$997$	−6.02189	−	27.6822i	−0.190715	−	0.876704i	−0.968664	−	0.248376i	$-0.920103\pi$
$997$	−6.02189	−	27.6822i	−0.190715	−	0.876704i	0.777949	−	0.628328i	$-0.216260\pi$
$998$	22.5446	+	60.4445i	0.713638	+	1.91334i
$999$	13.8337	+	4.06194i	0.437679	+	0.128514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.7.2	✓	200
5.2	odd	4		575.2.r.b.168.2		200
5.3	odd	4	inner	115.2.l.a.53.9	yes	200
5.4	even	2		575.2.r.b.7.9		200
23.10	odd	22	inner	115.2.l.a.102.9	yes	200
115.33	even	44	inner	115.2.l.a.33.2	yes	200
115.79	odd	22		575.2.r.b.332.2		200
115.102	even	44		575.2.r.b.493.9		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.2	✓	200	1.1	even	1	trivial
115.2.l.a.33.2	yes	200	115.33	even	44	inner
115.2.l.a.53.9	yes	200	5.3	odd	4	inner
115.2.l.a.102.9	yes	200	23.10	odd	22	inner
575.2.r.b.7.9		200	5.4	even	2
575.2.r.b.168.2		200	5.2	odd	4
575.2.r.b.332.2		200	115.79	odd	22
575.2.r.b.493.9		200	115.102	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43652 + 0.174263i) q^{2} +(-0.128656 + 0.591424i) q^{3} +(3.92662 - 0.564562i) q^{4} +(-1.44483 - 1.70660i) q^{5} +(0.210410 - 1.46344i) q^{6} +(-0.0458364 + 0.0839431i) q^{7} +(-4.69506 + 1.02135i) q^{8} +(2.39567 + 1.09406i) q^{9} +O(q^{10})\)	\(q+(-2.43652 + 0.174263i) q^{2} +(-0.128656 + 0.591424i) q^{3} +(3.92662 - 0.564562i) q^{4} +(-1.44483 - 1.70660i) q^{5} +(0.210410 - 1.46344i) q^{6} +(-0.0458364 + 0.0839431i) q^{7} +(-4.69506 + 1.02135i) q^{8} +(2.39567 + 1.09406i) q^{9} +(3.81775 + 3.90638i) q^{10} +(2.37754 - 2.06015i) q^{11} +(-0.171289 + 2.39493i) q^{12} +(5.54369 - 3.02708i) q^{13} +(0.0970531 - 0.212517i) q^{14} +(1.19521 - 0.634940i) q^{15} +(3.64902 - 1.07145i) q^{16} +(2.44442 + 3.26536i) q^{17} +(-6.02774 - 2.24823i) q^{18} +(-0.180176 - 1.25315i) q^{19} +(-6.63676 - 5.88546i) q^{20} +(-0.0437488 - 0.0379085i) q^{21} +(-5.43392 + 5.43392i) q^{22} +(-1.20538 - 4.64188i) q^{23} -2.90817i q^{24} +(-0.824954 + 4.93148i) q^{25} +(-12.9798 + 8.34161i) q^{26} +(-2.04342 + 2.72969i) q^{27} +(-0.132591 + 0.355490i) q^{28} +(-2.05829 - 0.295937i) q^{29} +(-2.80150 + 1.75532i) q^{30} +(-0.614903 - 0.395174i) q^{31} +(0.299649 - 0.111763i) q^{32} +(0.912536 + 1.67119i) q^{33} +(-6.52490 - 7.53014i) q^{34} +(0.209483 - 0.0430589i) q^{35} +(10.0245 + 2.94347i) q^{36} +(-1.47764 - 3.96171i) q^{37} +(0.657380 + 3.02193i) q^{38} +(1.07706 + 3.66812i) q^{39} +(8.52658 + 6.53691i) q^{40} +(-2.69875 - 5.90943i) q^{41} +(0.113201 + 0.0847411i) q^{42} +(-7.06043 - 1.53590i) q^{43} +(8.17261 - 9.43170i) q^{44} +(-1.59419 - 5.66917i) q^{45} +(3.74583 + 11.1000i) q^{46} +(3.91418 + 3.91418i) q^{47} +(0.164211 + 2.29596i) q^{48} +(3.77954 + 5.88108i) q^{49} +(1.15064 - 12.1594i) q^{50} +(-2.24570 + 1.02558i) q^{51} +(20.0590 - 15.0160i) q^{52} +(9.58880 + 5.23588i) q^{53} +(4.50315 - 7.00704i) q^{54} +(-6.95098 - 1.08095i) q^{55} +(0.129470 - 0.440933i) q^{56} +(0.764323 + 0.0546655i) q^{57} +(5.06663 + 0.362372i) q^{58} +(-4.23060 + 14.4081i) q^{59} +(4.33466 - 3.16794i) q^{60} +(1.76179 - 2.74140i) q^{61} +(1.56709 + 0.855694i) q^{62} +(-0.201648 + 0.150952i) q^{63} +(-7.62941 + 3.48424i) q^{64} +(-13.1757 - 5.08724i) q^{65} +(-2.51464 - 3.91285i) q^{66} +(-0.422879 - 5.91261i) q^{67} +(11.4418 + 11.4418i) q^{68} +(2.90040 - 0.115680i) q^{69} +(-0.502905 + 0.141419i) q^{70} +(-4.76419 + 5.49816i) q^{71} +(-12.3652 - 2.68989i) q^{72} +(1.73261 + 1.29702i) q^{73} +(4.29068 + 9.39529i) q^{74} +(-2.81046 - 1.12236i) q^{75} +(-1.41496 - 4.81892i) q^{76} +(0.0639575 + 0.294008i) q^{77} +(-3.26349 - 8.74976i) q^{78} +(-10.8439 - 3.18406i) q^{79} +(-7.10073 - 4.67935i) q^{80} +(3.82255 + 4.41146i) q^{81} +(7.60534 + 13.9281i) q^{82} +(4.53412 - 1.69114i) q^{83} +(-0.193186 - 0.124153i) q^{84} +(2.04090 - 8.88952i) q^{85} +(17.4705 + 2.51188i) q^{86} +(0.439836 - 1.17925i) q^{87} +(-9.05857 + 12.1008i) q^{88} +(6.50253 - 4.17892i) q^{89} +(4.87221 + 13.5352i) q^{90} +0.604105i q^{91} +(-7.35368 - 17.5464i) q^{92} +(0.312826 - 0.312826i) q^{93} +(-10.2191 - 8.85488i) q^{94} +(-1.87830 + 2.11807i) q^{95} +(0.0275477 + 0.191599i) q^{96} +(-6.94271 - 2.58950i) q^{97} +(-10.2338 - 13.6707i) q^{98} +(7.94973 - 2.33425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

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