LMFDB - Embedded newform 99.2.g.b.32.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(32,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.g (of order $6$, degree $2$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15x^{14} + 150x^{12} + 837x^{10} + 3372x^{8} + 8010x^{6} + 13761x^{4} + 13392x^{2} + 8649 $ x^16 + 15x^14 + 150x^12 + 837x^10 + 3372x^8 + 8010x^6 + 13761x^4 + 13392*x^2 + 8649
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.5
Root			$0.618600 + 1.07145i$ of defining polynomial
Character	$\chi$	$=$	99.32
Dual form			99.2.g.b.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618600 + 1.07145i) q^{2} +(-1.04881 + 1.37841i) q^{3} +(0.234668 - 0.406456i) q^{4} +(1.78348 + 1.02969i) q^{5} +(-2.12568 - 0.271060i) q^{6} +(-3.59283 + 2.07432i) q^{7} +3.05506 q^{8} +(-0.800005 - 2.89137i) q^{9} +O(q^{10})$	\(q+(0.618600 + 1.07145i) q^{2} +(-1.04881 + 1.37841i) q^{3} +(0.234668 - 0.406456i) q^{4} +(1.78348 + 1.02969i) q^{5} +(-2.12568 - 0.271060i) q^{6} +(-3.59283 + 2.07432i) q^{7} +3.05506 q^{8} +(-0.800005 - 2.89137i) q^{9} +2.54787i q^{10} +(-0.0426982 - 3.31635i) q^{11} +(0.314140 + 0.749761i) q^{12} +(0.747261 + 0.431431i) q^{13} +(-4.44505 - 2.56635i) q^{14} +(-3.28985 + 1.37841i) q^{15} +(1.42053 + 2.46043i) q^{16} +4.25136 q^{17} +(2.60306 - 2.64576i) q^{18} -5.55362i q^{19} +(0.837047 - 0.483270i) q^{20} +(0.908931 - 7.12794i) q^{21} +(3.52688 - 2.09724i) q^{22} +(-2.25042 - 1.29928i) q^{23} +(-3.20417 + 4.21112i) q^{24} +(-0.379477 - 0.657274i) q^{25} +1.06753i q^{26} +(4.82453 + 1.92976i) q^{27} +1.94710i q^{28} +(1.44670 + 2.50575i) q^{29} +(-3.51199 - 2.67222i) q^{30} +(-2.40400 + 4.16385i) q^{31} +(1.29759 - 2.24748i) q^{32} +(4.61606 + 3.41936i) q^{33} +(2.62989 + 4.55511i) q^{34} -8.54363 q^{35} +(-1.36295 - 0.353343i) q^{36} -11.7136 q^{37} +(5.95041 - 3.43547i) q^{38} +(-1.37842 + 0.577540i) q^{39} +(5.44863 + 3.14577i) q^{40} +(-2.82512 + 4.89325i) q^{41} +(8.19947 - 3.43547i) q^{42} +(-1.96401 + 1.13392i) q^{43} +(-1.35797 - 0.760885i) q^{44} +(1.55042 - 5.98043i) q^{45} -3.21494i q^{46} +(-1.44104 + 0.831985i) q^{47} +(-4.88132 - 0.622450i) q^{48} +(5.10561 - 8.84317i) q^{49} +(0.469489 - 0.813180i) q^{50} +(-4.45886 + 5.86010i) q^{51} +(0.350716 - 0.202486i) q^{52} +2.28109i q^{53} +(0.916822 + 6.36297i) q^{54} +(3.33866 - 5.95859i) q^{55} +(-10.9763 + 6.33718i) q^{56} +(7.65514 + 5.82468i) q^{57} +(-1.78985 + 3.10012i) q^{58} +(5.79946 + 3.34832i) q^{59} +(-0.211760 + 1.66065i) q^{60} +(-5.78878 + 3.34215i) q^{61} -5.94845 q^{62} +(8.87190 + 8.72871i) q^{63} +8.89286 q^{64} +(0.888481 + 1.53889i) q^{65} +(-0.808167 + 7.06108i) q^{66} +(-1.08746 + 1.88354i) q^{67} +(0.997657 - 1.72799i) q^{68} +(4.15119 - 1.73929i) q^{69} +(-5.28509 - 9.15404i) q^{70} +1.36195i q^{71} +(-2.44406 - 8.83330i) q^{72} -11.1781i q^{73} +(-7.24604 - 12.5505i) q^{74} +(1.30399 + 0.166280i) q^{75} +(-2.25730 - 1.30325i) q^{76} +(7.03258 + 11.8265i) q^{77} +(-1.47149 - 1.11964i) q^{78} +(9.22261 - 5.32468i) q^{79} +5.85081i q^{80} +(-7.71999 + 4.62621i) q^{81} -6.99047 q^{82} +(3.10289 + 5.37436i) q^{83} +(-2.68390 - 2.04214i) q^{84} +(7.58220 + 4.37759i) q^{85} +(-2.42988 - 1.40289i) q^{86} +(-4.97125 - 0.633917i) q^{87} +(-0.130446 - 10.1317i) q^{88} -7.44670i q^{89} +(7.36681 - 2.03830i) q^{90} -3.57971 q^{91} +(-1.05620 + 0.609797i) q^{92} +(-3.21814 - 7.68076i) q^{93} +(-1.78286 - 1.02933i) q^{94} +(5.71851 - 9.90475i) q^{95} +(1.73703 + 4.14578i) q^{96} +(5.27494 + 9.13646i) q^{97} +12.6333 q^{98} +(-9.55462 + 2.77655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9	$ 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9} - 12 q^{11} + 12 q^{12} - 6 q^{14} - 30 q^{15} - 2 q^{16} + 36 q^{20} + 6 q^{22} + 12 q^{23} - 12 q^{25} + 18 q^{27} - 4 q^{31} + 18 q^{33} - 18 q^{36} - 28 q^{37} + 66 q^{38} - 54 q^{42} - 42 q^{45} - 30 q^{47} + 42 q^{48} + 10 q^{49} + 20 q^{55} - 120 q^{56} - 6 q^{58} - 36 q^{59} + 30 q^{60} + 40 q^{64} + 54 q^{66} + 8 q^{67} + 96 q^{69} + 24 q^{75} + 72 q^{77} - 42 q^{78} + 30 q^{81} + 12 q^{82} - 72 q^{86} - 6 q^{88} - 12 q^{91} + 18 q^{92} - 24 q^{93} - 4 q^{97} - 36 q^{99}+O(q^{100}) $ 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9 - 12 * q^11 + 12 * q^12 - 6 * q^14 - 30 * q^15 - 2 * q^16 + 36 * q^20 + 6 * q^22 + 12 * q^23 - 12 * q^25 + 18 * q^27 - 4 * q^31 + 18 * q^33 - 18 * q^36 - 28 * q^37 + 66 * q^38 - 54 * q^42 - 42 * q^45 - 30 * q^47 + 42 * q^48 + 10 * q^49 + 20 * q^55 - 120 * q^56 - 6 * q^58 - 36 * q^59 + 30 * q^60 + 40 * q^64 + 54 * q^66 + 8 * q^67 + 96 * q^69 + 24 * q^75 + 72 * q^77 - 42 * q^78 + 30 * q^81 + 12 * q^82 - 72 * q^86 - 6 * q^88 - 12 * q^91 + 18 * q^92 - 24 * q^93 - 4 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.618600	+	1.07145i	0.437416	+	0.757627i	0.997489	−	0.0708158i	$-0.0225603\pi$
$2$	0.618600	+	1.07145i	0.437416	+	0.757627i	−0.560073	+	0.828443i	$0.689227\pi$
$3$	−1.04881	+	1.37841i	−0.605529	+	0.795823i
$3$	−1.04881	+	1.37841i	−0.605529	+	0.795823i
$4$	0.234668	−	0.406456i	0.117334	−	0.203228i
$5$	1.78348	+	1.02969i	0.797594	+	0.460491i	0.842629	−	0.538494i	$-0.181007\pi$
$5$	1.78348	+	1.02969i	0.797594	+	0.460491i	−0.0450349	+	0.998985i	$0.514340\pi$
$6$	−2.12568	−	0.271060i	−0.867806	−	0.110660i
$7$	−3.59283	+	2.07432i	−1.35796	+	0.784019i	−0.989349	−	0.145564i	$-0.953500\pi$
$7$	−3.59283	+	2.07432i	−1.35796	+	0.784019i	−0.368612	+	0.929583i	$0.620167\pi$
$8$	3.05506			1.08013
$9$	−0.800005	−	2.89137i	−0.266668	−	0.963788i
$10$			2.54787i			0.805706i
$11$	−0.0426982	−	3.31635i	−0.0128740	−	0.999917i
$11$	−0.0426982	−	3.31635i	−0.0128740	−	0.999917i
$12$	0.314140	+	0.749761i	0.0906845	+	0.216437i
$13$	0.747261	+	0.431431i	0.207253	+	0.119658i	0.600034	−	0.799974i	$-0.295154\pi$
$13$	0.747261	+	0.431431i	0.207253	+	0.119658i	−0.392781	+	0.919632i	$0.628487\pi$
$14$	−4.44505	−	2.56635i	−1.18799	−	0.685886i
$15$	−3.28985	+	1.37841i	−0.849436	+	0.355903i
$16$	1.42053	+	2.46043i	0.355132	+	0.615106i
$17$	4.25136			1.03111			0.515553	−	0.856857i	$-0.327586\pi$
$17$	4.25136			1.03111			0.515553	+	0.856857i	$0.327586\pi$
$18$	2.60306	−	2.64576i	0.613548	−	0.623612i
$19$		−	5.55362i		−	1.27409i	−0.770827	−	0.637044i	$-0.780157\pi$
$19$		−	5.55362i		−	1.27409i	0.770827	−	0.637044i	$-0.219843\pi$
$20$	0.837047	−	0.483270i	0.187169	−	0.108062i
$21$	0.908931	−	7.12794i	0.198345	−	1.55544i
$22$	3.52688	−	2.09724i	0.751933	−	0.447134i
$23$	−2.25042	−	1.29928i	−0.469244	−	0.270918i	0.246679	−	0.969097i	$-0.420661\pi$
$23$	−2.25042	−	1.29928i	−0.469244	−	0.270918i	−0.715923	+	0.698179i	$0.753994\pi$
$24$	−3.20417	+	4.21112i	−0.654049	+	0.859590i
$25$	−0.379477	−	0.657274i	−0.0758955	−	0.131455i
$26$			1.06753i			0.209361i
$27$	4.82453	+	1.92976i	0.928480	+	0.371382i
$28$			1.94710i			0.367968i
$29$	1.44670	+	2.50575i	0.268645	+	0.465306i	0.968512	−	0.248966i	$-0.0800909\pi$
$29$	1.44670	+	2.50575i	0.268645	+	0.465306i	−0.699867	+	0.714273i	$0.746758\pi$
$30$	−3.51199	−	2.67222i	−0.641199	−	0.487879i
$31$	−2.40400	+	4.16385i	−0.431771	+	0.747849i	−0.997026	−	0.0770672i	$-0.975444\pi$
$31$	−2.40400	+	4.16385i	−0.431771	+	0.747849i	0.565255	+	0.824916i	$0.308778\pi$
$32$	1.29759	−	2.24748i	0.229383	−	0.397303i
$33$	4.61606	+	3.41936i	0.803553	+	0.595234i
$34$	2.62989	+	4.55511i	0.451023	+	0.781195i
$35$	−8.54363			−1.44414
$36$	−1.36295	−	0.353343i	−0.227158	−	0.0588905i
$37$	−11.7136			−1.92571			−0.962853	−	0.270028i	$-0.912967\pi$
$37$	−11.7136			−1.92571			−0.962853	+	0.270028i	$0.912967\pi$
$38$	5.95041	−	3.43547i	0.965284	−	0.557307i
$39$	−1.37842	+	0.577540i	−0.220724	+	0.0924805i
$40$	5.44863	+	3.14577i	0.861504	+	0.497389i
$41$	−2.82512	+	4.89325i	−0.441209	+	0.764197i	−0.997779	−	0.0666039i	$-0.978784\pi$
$41$	−2.82512	+	4.89325i	−0.441209	+	0.764197i	0.556570	+	0.830800i	$0.312117\pi$
$42$	8.19947	−	3.43547i	1.26521	−	0.530105i
$43$	−1.96401	+	1.13392i	−0.299509	+	0.172922i	−0.642222	−	0.766518i	$-0.721987\pi$
$43$	−1.96401	+	1.13392i	−0.299509	+	0.172922i	0.342713	+	0.939440i	$0.388654\pi$
$44$	−1.35797	−	0.760885i	−0.204722	−	0.114708i
$45$	1.55042	−	5.98043i	0.231123	−	0.891511i
$46$		−	3.21494i		−	0.474017i
$47$	−1.44104	+	0.831985i	−0.210197	+	0.121358i	−0.601403	−	0.798946i	$-0.705391\pi$
$47$	−1.44104	+	0.831985i	−0.210197	+	0.121358i	0.391206	+	0.920303i	$0.372058\pi$
$48$	−4.88132	−	0.622450i	−0.704558	−	0.0898430i
$49$	5.10561	−	8.84317i	0.729372	−	1.26331i
$50$	0.469489	−	0.813180i	0.0663958	−	0.115001i
$51$	−4.45886	+	5.86010i	−0.624366	+	0.820579i
$52$	0.350716	−	0.202486i	0.0486355	−	0.0280797i
$53$			2.28109i			0.313331i	0.987652	+	0.156666i	$0.0500745\pi$
$53$			2.28109i			0.313331i	−0.987652	+	0.156666i	$0.949925\pi$
$54$	0.916822	+	6.36297i	0.124764	+	0.865891i
$55$	3.33866	−	5.95859i	0.450185	−	0.803457i
$56$	−10.9763	+	6.33718i	−1.46677	+	0.846841i
$57$	7.65514	+	5.82468i	1.01395	+	0.771498i
$58$	−1.78985	+	3.10012i	−0.235019	+	0.407065i
$59$	5.79946	+	3.34832i	0.755025	+	0.435914i	0.827507	−	0.561456i	$-0.189759\pi$
$59$	5.79946	+	3.34832i	0.755025	+	0.435914i	−0.0724816	+	0.997370i	$0.523092\pi$
$60$	−0.211760	+	1.66065i	−0.0273381	+	0.214389i
$61$	−5.78878	+	3.34215i	−0.741177	+	0.427919i	−0.822497	−	0.568769i	$-0.807420\pi$
$61$	−5.78878	+	3.34215i	−0.741177	+	0.427919i	0.0813198	+	0.996688i	$0.474086\pi$
$62$	−5.94845			−0.755455
$63$	8.87190	+	8.72871i	1.11775	+	1.09971i
$64$	8.89286			1.11161
$65$	0.888481	+	1.53889i	0.110202	+	0.190876i
$66$	−0.808167	+	7.06108i	−0.0994784	+	0.869159i
$67$	−1.08746	+	1.88354i	−0.132855	+	0.230111i	−0.924776	−	0.380512i	$-0.875748\pi$
$67$	−1.08746	+	1.88354i	−0.132855	+	0.230111i	0.791921	+	0.610623i	$0.209081\pi$
$68$	0.997657	−	1.72799i	0.120984	−	0.209550i
$69$	4.15119	−	1.73929i	0.499744	−	0.209386i
$70$	−5.28509	−	9.15404i	−0.631689	−	1.09412i
$71$			1.36195i			0.161634i	0.996729	+	0.0808168i	$0.0257529\pi$
$71$			1.36195i			0.161634i	−0.996729	+	0.0808168i	$0.974247\pi$
$72$	−2.44406	−	8.83330i	−0.288036	−	1.04101i
$73$		−	11.1781i		−	1.30830i	−0.756367	−	0.654148i	$-0.773027\pi$
$73$		−	11.1781i		−	1.30830i	0.756367	−	0.654148i	$-0.226973\pi$
$74$	−7.24604	−	12.5505i	−0.842335	−	1.45897i
$75$	1.30399	+	0.166280i	0.150572	+	0.0192004i
$76$	−2.25730	−	1.30325i	−0.258930	−	0.149494i
$77$	7.03258	+	11.8265i	0.801437	+	1.34776i
$78$	−1.47149	−	1.11964i	−0.166614	−	0.126774i
$79$	9.22261	−	5.32468i	1.03762	−	0.599073i	0.118465	−	0.992958i	$-0.462203\pi$
$79$	9.22261	−	5.32468i	1.03762	−	0.599073i	0.919160	+	0.393885i	$0.128869\pi$
$80$			5.85081i			0.654141i
$81$	−7.71999	+	4.62621i	−0.857776	+	0.514023i
$82$	−6.99047			−0.771968
$83$	3.10289	+	5.37436i	0.340586	+	0.589913i	0.984542	−	0.175150i	$-0.0560411\pi$
$83$	3.10289	+	5.37436i	0.340586	+	0.589913i	−0.643955	+	0.765063i	$0.722708\pi$
$84$	−2.68390	−	2.04214i	−0.292837	−	0.222815i
$85$	7.58220	+	4.37759i	0.822405	+	0.474816i
$86$	−2.42988	−	1.40289i	−0.262020	−	0.151277i
$87$	−4.97125	−	0.633917i	−0.532974	−	0.0679631i
$88$	−0.130446	−	10.1317i	−0.0139056	−	1.08004i
$89$		−	7.44670i		−	0.789349i	−0.918821	−	0.394674i	$-0.870857\pi$
$89$		−	7.44670i		−	0.789349i	0.918821	−	0.394674i	$-0.129143\pi$
$90$	7.36681	−	2.03830i	0.776530	−	0.214856i
$91$	−3.57971			−0.375255
$92$	−1.05620	+	0.609797i	−0.110116	+	0.0635757i
$93$	−3.21814	−	7.68076i	−0.333705	−	0.796458i
$94$	−1.78286	−	1.02933i	−0.183888	−	0.106168i
$95$	5.71851	−	9.90475i	0.586707	−	1.01621i
$96$	1.73703	+	4.14578i	0.177285	+	0.423127i
$97$	5.27494	+	9.13646i	0.535589	+	0.927667i	0.999135	+	0.0415940i	$0.0132436\pi$
$97$	5.27494	+	9.13646i	0.535589	+	0.927667i	−0.463546	+	0.886073i	$0.653423\pi$
$98$	12.6333			1.27616
$99$	−9.55462	+	2.77655i	−0.960275	+	0.279054i
$100$	−0.356204			−0.0356204
$101$	−0.517315	−	0.896016i	−0.0514748	−	0.0891569i	0.839140	−	0.543916i	$-0.183059\pi$
$101$	−0.517315	−	0.896016i	−0.0514748	−	0.0891569i	−0.890615	+	0.454759i	$0.849726\pi$
$102$	−9.03704	−	1.15237i	−0.894801	−	0.114102i
$103$	3.91199	−	6.77576i	0.385460	−	0.667636i	−0.606373	−	0.795180i	$-0.707376\pi$
$103$	3.91199	−	6.77576i	0.385460	−	0.667636i	0.991833	+	0.127544i	$0.0407095\pi$
$104$	2.28293	+	1.31805i	0.223860	+	0.129245i
$105$	8.96062	−	11.7766i	0.874467	−	1.14928i
$106$	−2.44406	+	1.41108i	−0.237388	+	0.137056i
$107$	−7.88709			−0.762473			−0.381237	−	0.924477i	$-0.624502\pi$
$107$	−7.88709			−0.762473			−0.381237	+	0.924477i	$0.624502\pi$
$108$	1.91652	−	1.50811i	0.184417	−	0.145118i
$109$			0.542120i			0.0519257i	0.999663	+	0.0259628i	$0.00826515\pi$
$109$			0.542120i			0.0519257i	−0.999663	+	0.0259628i	$0.991735\pi$
$110$	8.44961	−	0.108789i	0.805639	−	0.0103727i
$111$	12.2853	−	16.1461i	1.16607	−	1.53252i
$112$	−10.2074	−	5.89326i	−0.964510	−	0.556860i
$113$	−5.40938	−	3.12311i	−0.508872	−	0.293797i	0.223498	−	0.974704i	$-0.428252\pi$
$113$	−5.40938	−	3.12311i	−0.508872	−	0.293797i	−0.732370	+	0.680907i	$0.761586\pi$
$114$	−1.50536	+	11.8052i	−0.140990	+	1.10566i
$115$	−2.67571	−	4.63446i	−0.249511	−	0.432166i
$116$	1.35797			0.126084
$117$	0.649613	−	2.50575i	0.0600568	−	0.231657i
$118$			8.28508i			0.762704i
$119$	−15.2744	+	8.81869i	−1.40020	+	0.808408i
$120$	−10.0507	+	4.21112i	−0.917500	+	0.384420i
$121$	−10.9964	+	0.283204i	−0.999669	+	0.0257459i
$122$	−7.16188	−	4.13491i	−0.648406	−	0.374358i
$123$	−3.78187	−	9.02623i	−0.341000	−	0.813868i
$124$	1.12828	+	1.95424i	0.101323	+	0.175496i
$125$		−	11.8599i		−	1.06078i
$126$	−3.86420	+	14.9053i	−0.344250	+	1.32787i
$127$			17.8159i			1.58091i	0.612520	+	0.790455i	$0.290156\pi$
$127$			17.8159i			1.58091i	−0.612520	+	0.790455i	$0.709844\pi$
$128$	2.90595	+	5.03326i	0.256852	+	0.444881i
$129$	0.496865	−	3.89647i	0.0437465	−	0.343065i
$130$	−1.09923	+	1.90392i	−0.0964088	+	0.166985i
$131$	−4.13059	+	7.15440i	−0.360892	+	0.625083i	−0.988108	−	0.153763i	$-0.950861\pi$
$131$	−4.13059	+	7.15440i	−0.360892	+	0.625083i	0.627216	+	0.778845i	$0.284194\pi$
$132$	2.47306	−	1.07381i	0.215252	−	0.0934634i
$133$	11.5200	+	19.9532i	0.998910	+	1.73016i
$134$	−2.69082			−0.232452
$135$	6.61737	+	8.40944i	0.569533	+	0.723769i
$136$	12.9882			1.11373
$137$	7.32054	−	4.22652i	0.625436	−	0.361096i	−0.153546	−	0.988141i	$-0.549069\pi$
$137$	7.32054	−	4.22652i	0.625436	−	0.361096i	0.778982	+	0.627046i	$0.215736\pi$
$138$	4.43149	+	3.37185i	0.377233	+	0.287031i
$139$	7.02666	+	4.05684i	0.595993	+	0.344097i	0.767464	−	0.641092i	$-0.221518\pi$
$139$	7.02666	+	4.05684i	0.595993	+	0.344097i	−0.171470	+	0.985189i	$0.554852\pi$
$140$	−2.00491	+	3.47261i	−0.169446	+	0.293489i
$141$	0.364562	−	2.85893i	0.0307016	−	0.240765i
$142$	−1.45926	+	0.842502i	−0.122458	+	0.0707012i
$143$	1.39887	−	2.49660i	0.116979	−	0.208776i
$144$	5.97756	−	6.07561i	0.498130	−	0.506301i
$145$			5.95859i			0.494834i
$146$	11.9767	−	6.91477i	0.991201	−	0.572270i
$147$	6.83468	+	16.3124i	0.563715	+	1.34542i
$148$	−2.74880	+	4.76107i	−0.225950	+	0.391357i
$149$	5.01907	−	8.69329i	0.411179	−	0.712182i	−0.583840	−	0.811868i	$-0.698451\pi$
$149$	5.01907	−	8.69329i	0.411179	−	0.712182i	0.995019	+	0.0996863i	$0.0317839\pi$
$150$	0.628487	+	1.50002i	0.0513158	+	0.122476i
$151$	−9.87222	+	5.69973i	−0.803390	+	0.463838i	−0.844655	−	0.535311i	$-0.820195\pi$
$151$	−9.87222	+	5.69973i	−0.803390	+	0.463838i	0.0412650	+	0.999148i	$0.486861\pi$
$152$		−	16.9667i		−	1.37618i
$153$	−3.40111	−	12.2922i	−0.274963	−	0.993769i
$154$	−8.32112	+	14.8509i	−0.670535	+	1.19672i
$155$	−8.57494	+	4.95075i	−0.688756	+	0.397653i
$156$	−0.0887258	+	0.695797i	−0.00710375	+	0.0557084i
$157$	−1.90538	+	3.30021i	−0.152066	+	0.263386i	−0.931987	−	0.362492i	$-0.881926\pi$
$157$	−1.90538	+	3.30021i	−0.152066	+	0.263386i	0.779921	+	0.625878i	$0.215259\pi$
$158$	11.4102	+	6.58769i	0.907748	+	0.524089i
$159$	−3.14426	−	2.39242i	−0.249356	−	0.189731i
$160$	4.62842	−	2.67222i	0.365909	−	0.211258i
$161$	10.7805			0.849621
$162$	−9.73232	−	5.40978i	−0.764644	−	0.425032i
$163$	5.80321			0.454542			0.227271	−	0.973832i	$-0.427020\pi$
$163$	5.80321			0.454542			0.227271	+	0.973832i	$0.427020\pi$
$164$	1.32593	+	2.29657i	0.103537	+	0.179332i
$165$	4.71175	+	10.8514i	0.366809	+	0.844784i
$166$	−3.83889	+	6.64916i	−0.297956	+	0.516075i
$167$	2.80467	−	4.85783i	0.217032	−	0.375910i	−0.736868	−	0.676037i	$-0.763696\pi$
$167$	2.80467	−	4.85783i	0.217032	−	0.375910i	0.953899	+	0.300127i	$0.0970292\pi$
$168$	2.77684	−	21.7763i	0.214238	−	1.68008i
$169$	−6.12773	−	10.6135i	−0.471364	−	0.816427i
$170$			10.8319i			0.830769i
$171$	−16.0576	+	4.44292i	−1.22795	+	0.339759i
$172$			1.06438i			0.0811581i
$173$	10.4803	+	18.1523i	0.796800	+	1.38010i	0.921690	+	0.387927i	$0.126809\pi$
$173$	10.4803	+	18.1523i	0.796800	+	1.38010i	−0.124891	+	0.992171i	$0.539858\pi$
$174$	−2.39601	−	5.71857i	−0.181641	−	0.433524i
$175$	2.72679	+	1.57431i	0.206126	+	0.119007i
$176$	8.09898	−	4.81602i	0.610483	−	0.363021i
$177$	−10.6979	+	4.48226i	−0.804100	+	0.336908i
$178$	7.97875	−	4.60653i	0.598032	−	0.345274i
$179$			13.6285i			1.01864i	0.860577	+	0.509321i	$0.170103\pi$
$179$			13.6285i			1.01864i	−0.860577	+	0.509321i	$0.829897\pi$
$180$	−2.06695	−	2.03359i	−0.154061	−	0.151575i
$181$	6.84428			0.508731			0.254366	−	0.967108i	$-0.418133\pi$
$181$	6.84428			0.508731			0.254366	+	0.967108i	$0.418133\pi$
$182$	−2.21441	−	3.83547i	−0.164143	−	0.284304i
$183$	1.46447	−	11.4846i	0.108257	−	0.848964i
$184$	−6.87516	−	3.96938i	−0.506844	−	0.292626i
$185$	−20.8909	−	12.0614i	−1.53593	−	0.886771i
$186$	6.23879	−	8.19938i	0.457450	−	0.601208i
$187$	−0.181526	−	14.0990i	−0.0132745	−	1.03102i
$188$			0.780960i			0.0569573i
$189$	−21.3366	+	3.07433i	−1.55201	+	0.223625i
$190$	14.1499			1.02654
$191$	20.6958	−	11.9487i	1.49749	−	0.864577i	0.497496	−	0.867466i	$-0.334253\pi$
$191$	20.6958	−	11.9487i	1.49749	−	0.864577i	0.999996	+	0.00288872i	$0.000919510\pi$
$192$	−9.32690	+	12.2580i	−0.673111	+	0.884642i
$193$	−13.1143	−	7.57157i	−0.943991	−	0.545013i	−0.0527816	−	0.998606i	$-0.516809\pi$
$193$	−13.1143	−	7.57157i	−0.943991	−	0.545013i	−0.891209	+	0.453593i	$0.850142\pi$
$194$	−6.52615	+	11.3036i	−0.468551	+	0.811553i
$195$	−3.05307	−	0.389317i	−0.218635	−	0.0278796i
$196$	−2.39624	−	4.15041i	−0.171160	−	0.296458i
$197$	−5.74588			−0.409377			−0.204689	−	0.978827i	$-0.565618\pi$
$197$	−5.74588			−0.409377			−0.204689	+	0.978827i	$0.565618\pi$
$198$	−8.88542	−	8.51969i	−0.631459	−	0.605468i
$199$	4.42831			0.313914			0.156957	−	0.987605i	$-0.449832\pi$
$199$	4.42831			0.313914			0.156957	+	0.987605i	$0.449832\pi$
$200$	−1.15933	−	2.00801i	−0.0819768	−	0.141988i
$201$	−1.45575	−	3.47444i	−0.102680	−	0.245068i
$202$	0.640023	−	1.10855i	0.0450318	−	0.0779974i
$203$	−10.3955	−	6.00182i	−0.729618	−	0.421245i
$204$	1.33552	+	3.18751i	0.0935054	+	0.223170i
$205$	−10.0771	+	5.81799i	−0.703812	+	0.406346i
$206$	9.67983			0.674426
$207$	−1.95635	+	7.54621i	−0.135975	+	0.524498i
$208$			2.45144i			0.169977i
$209$	−18.4178	+	0.237130i	−1.27398	+	0.0164026i
$210$	18.1610	+	2.31583i	1.25323	+	0.159808i
$211$	10.1616	+	5.86680i	0.699553	+	0.403887i	0.807181	−	0.590304i	$-0.200992\pi$
$211$	10.1616	+	5.86680i	0.699553	+	0.403887i	−0.107628	+	0.994191i	$0.534326\pi$
$212$	0.927162	+	0.535297i	0.0636777	+	0.0367644i
$213$	−1.87732	−	1.42842i	−0.128632	−	0.0978739i
$214$	−4.87895	−	8.45060i	−0.333518	−	0.577671i
$215$	−4.67035			−0.318516
$216$	14.7392	+	5.89552i	1.00288	+	0.401140i
$217$		−	19.9466i		−	1.35407i
$218$	−0.580853	+	0.335355i	−0.0393403	+	0.0227131i
$219$	15.4079	+	11.7237i	1.04117	+	0.792212i
$220$	−1.63843	−	2.75531i	−0.110463	−	0.185763i
$221$	3.17688	+	1.83417i	0.213700	+	0.123380i
$222$	24.8994	+	3.17509i	1.67114	+	0.213098i
$223$	−2.31437	−	4.00861i	−0.154982	−	0.268437i	0.778071	−	0.628177i	$-0.216199\pi$
$223$	−2.31437	−	4.00861i	−0.154982	−	0.268437i	−0.933052	+	0.359740i	$0.882865\pi$
$224$			10.7664i			0.719362i
$225$	−1.59684	+	1.62303i	−0.106456	+	0.108202i
$226$		−	7.72783i		−	0.514047i
$227$	−11.3687	−	19.6912i	−0.754570	−	1.30695i	−0.945588	−	0.325367i	$-0.894512\pi$
$227$	−11.3687	−	19.6912i	−0.754570	−	1.30695i	0.191018	−	0.981587i	$-0.438821\pi$
$228$	4.16389	−	1.74462i	0.275760	−	0.115540i
$229$	−1.79384	+	3.10702i	−0.118540	+	0.205318i	−0.919189	−	0.393816i	$-0.871155\pi$
$229$	−1.79384	+	3.10702i	−0.118540	+	0.205318i	0.800649	+	0.599133i	$0.204488\pi$
$230$	3.31039	−	5.73376i	0.218280	−	0.378073i
$231$	−23.6775	−	2.70998i	−1.55787	−	0.178304i
$232$	4.41975	+	7.65523i	0.290171	+	0.502590i
$233$	18.6774			1.22360			0.611799	−	0.791013i	$-0.290446\pi$
$233$	18.6774			1.22360			0.611799	+	0.791013i	$0.290446\pi$
$234$	3.08663	−	0.854032i	0.201779	−	0.0558298i
$235$	−3.42675			−0.223536
$236$	2.72189	−	1.57148i	0.177180	−	0.102295i
$237$	−2.33318	+	18.2971i	−0.151556	+	1.18852i
$238$	−18.8975	−	10.9105i	−1.22494	−	0.707222i
$239$	10.5212	−	18.2232i	0.680557	−	1.17876i	−0.294254	−	0.955727i	$-0.595071\pi$
$239$	10.5212	−	18.2232i	0.680557	−	1.17876i	0.974811	−	0.223033i	$-0.0715956\pi$
$240$	−8.06479	−	6.13638i	−0.520580	−	0.396101i
$241$	−0.881555	+	0.508966i	−0.0567860	+	0.0327854i	−0.528124	−	0.849167i	$-0.677104\pi$
$241$	−0.881555	+	0.508966i	−0.0567860	+	0.0327854i	0.471338	+	0.881953i	$0.343771\pi$
$242$	−7.10579	−	11.6068i	−0.456777	−	0.746115i
$243$	1.71999	−	15.4933i	0.110337	−	0.993894i
$244$			3.13718i			0.200837i
$245$	18.2114	−	10.5144i	1.16349	−	0.671739i
$246$	7.33166	−	9.63571i	0.467450	−	0.614350i
$247$	2.39601	−	4.15001i	0.152454	−	0.264059i
$248$	−7.34436	+	12.7208i	−0.466368	+	0.807772i
$249$	−10.6624	−	1.35963i	−0.675701	−	0.0861632i
$250$	12.7072	−	7.33652i	0.803676	−	0.464002i
$251$			27.8935i			1.76062i	0.474396	+	0.880312i	$0.342667\pi$
$251$			27.8935i			1.76062i	−0.474396	+	0.880312i	$0.657333\pi$
$252$	5.62978	−	1.55769i	0.354643	−	0.0981253i
$253$	−4.21277	+	7.51865i	−0.264855	+	0.472693i
$254$	−19.0888	+	11.0209i	−1.19774	+	0.691516i
$255$	−13.9864	+	5.86010i	−0.875860	+	0.366974i
$256$	5.29761	−	9.17573i	0.331101	−	0.573483i
$257$	23.3280	+	13.4684i	1.45516	+	0.840137i	0.998767	−	0.0496416i	$-0.0158079\pi$
$257$	23.3280	+	13.4684i	1.45516	+	0.840137i	0.456393	+	0.889778i	$0.349141\pi$
$258$	4.48222	−	1.87799i	0.279051	−	0.116919i
$259$	42.0850	−	24.2978i	2.61503	−	1.50979i
$260$	0.833990			0.0517219
$261$	6.08768	−	6.18754i	0.376818	−	0.382999i
$262$	−10.2207			−0.631440
$263$	−9.05134	−	15.6774i	−0.558130	−	0.966709i	−0.997653	−	0.0684777i	$-0.978186\pi$
$263$	−9.05134	−	15.6774i	−0.558130	−	0.966709i	0.439523	−	0.898231i	$-0.355148\pi$
$264$	14.1023	+	10.4464i	0.867939	+	0.642929i
$265$	−2.34881	+	4.06826i	−0.144286	+	0.249911i
$266$	−14.2525	+	24.6861i	−0.873879	+	1.51360i
$267$	10.2646	+	7.81016i	0.628182	+	0.477974i
$268$	0.510385	+	0.884013i	0.0311767	+	0.0539997i
$269$			12.2263i			0.745451i	0.927942	+	0.372726i	$0.121577\pi$
$269$			12.2263i			0.745451i	−0.927942	+	0.372726i	$0.878423\pi$
$270$	−4.91676	+	12.2922i	−0.299224	+	0.748082i
$271$			14.9816i			0.910067i	0.890474	+	0.455033i	$0.150373\pi$
$271$			14.9816i			0.910067i	−0.890474	+	0.455033i	$0.849627\pi$
$272$	6.03918	+	10.4602i	0.366179	+	0.634240i
$273$	3.75442	−	4.93429i	0.227228	−	0.298637i
$274$	9.05698	+	5.22905i	0.547152	+	0.315898i
$275$	−2.16355	+	1.28654i	−0.130467	+	0.0775815i
$276$	0.267202	−	2.09543i	0.0160837	−	0.126130i
$277$	−25.7169	+	14.8477i	−1.54518	+	0.892110i	−0.546682	+	0.837341i	$0.684109\pi$
$277$	−25.7169	+	14.8477i	−1.54518	+	0.892110i	−0.998499	+	0.0547699i	$0.982557\pi$
$278$			10.0383i			0.602055i
$279$	13.9624	+	3.61974i	0.835908	+	0.216708i
$280$	−26.1013			−1.55985
$281$	−1.30747	−	2.26461i	−0.0779973	−	0.135095i	0.824388	−	0.566024i	$-0.191519\pi$
$281$	−1.30747	−	2.26461i	−0.0779973	−	0.135095i	−0.902386	+	0.430929i	$0.858186\pi$
$282$	3.28871	−	1.37793i	0.195840	−	0.0820544i
$283$	1.80894	+	1.04439i	0.107530	+	0.0620827i	0.552801	−	0.833314i	$-0.313559\pi$
$283$	1.80894	+	1.04439i	0.107530	+	0.0620827i	−0.445270	+	0.895396i	$0.646892\pi$
$284$	0.553572	+	0.319605i	0.0328485	+	0.0189651i
$285$	7.65514	+	18.2706i	0.453452	+	1.08226i
$286$	3.54032	−	0.0455818i	0.209343	−	0.00269531i
$287$		−	23.4408i		−	1.38367i
$288$	−7.53637	−	1.95380i	−0.444085	−	0.115129i
$289$	1.07409			0.0631815
$290$	−6.38432	+	3.68599i	−0.374900	+	0.216449i
$291$	−18.1261	−	2.31139i	−1.06257	−	0.135496i
$292$	−4.54340	−	2.62313i	−0.265882	−	0.153507i
$293$	−15.0707	+	26.1033i	−0.880442	+	1.52497i	−0.0295925	+	0.999562i	$0.509421\pi$
$293$	−15.0707	+	26.1033i	−0.880442	+	1.52497i	−0.850850	+	0.525409i	$0.823912\pi$
$294$	−13.2499	+	17.4138i	−0.772751	+	1.01560i
$295$	6.89546	+	11.9433i	0.401469	+	0.695365i
$296$	−35.7858			−2.08001
$297$	6.19375	−	16.0822i	0.359398	−	0.933185i
$298$	12.4192			0.719425
$299$	−1.12110	−	1.94180i	−0.0648348	−	0.112297i
$300$	0.373589	−	0.490994i	0.0215692	−	0.0283475i
$301$	4.70424	−	8.14798i	0.271148	−	0.469642i
$302$	−12.2139	−	7.05171i	−0.702832	−	0.405780i
$303$	1.77764	+	0.226679i	0.102123	+	0.0130223i
$304$	13.6643	−	7.88907i	0.783700	−	0.452469i
$305$	−13.7655			−0.788212
$306$	11.0666	−	11.2481i	0.632633	−	0.643011i
$307$		−	17.8758i		−	1.02022i	−0.860108	−	0.510112i	$-0.829604\pi$
$307$		−	17.8758i		−	1.02022i	0.860108	−	0.510112i	$-0.170396\pi$
$308$	6.45727	−	0.0831378i	0.367937	−	0.00473721i
$309$	5.23683	+	12.4988i	0.297913	+	0.711031i
$310$	−10.6089	−	6.12506i	−0.602546	−	0.347880i
$311$	−23.5517	−	13.5976i	−1.33549	−	0.771047i	−0.349357	−	0.936990i	$-0.613600\pi$
$311$	−23.5517	−	13.5976i	−1.33549	−	0.771047i	−0.986135	+	0.165943i	$0.946933\pi$
$312$	−4.21116	+	1.76442i	−0.238410	+	0.0998907i
$313$	−4.40376	−	7.62754i	−0.248915	−	0.431134i	0.714310	−	0.699830i	$-0.246741\pi$
$313$	−4.40376	−	7.62754i	−0.248915	−	0.431134i	−0.963225	+	0.268695i	$0.913407\pi$
$314$	−4.71467			−0.266064
$315$	6.83494	+	24.7027i	0.385105	+	1.39184i
$316$		−	4.99811i		−	0.281166i
$317$	9.75760	−	5.63355i	0.548041	−	0.316412i	−0.200290	−	0.979737i	$-0.564189\pi$
$317$	9.75760	−	5.63355i	0.548041	−	0.316412i	0.748332	+	0.663325i	$0.230855\pi$
$318$	0.618311	−	4.84886i	0.0346732	−	0.271911i
$319$	8.24818	−	4.90474i	0.461809	−	0.274613i
$320$	15.8602	+	9.15688i	0.886611	+	0.511885i
$321$	8.27204	−	10.8716i	0.461700	−	0.606794i
$322$	6.66881	+	11.5507i	0.371638	+	0.643696i
$323$		−	23.6105i		−	1.31372i
$324$	0.0687216	+	4.22346i	0.00381787	+	0.234636i
$325$		−	0.654874i		−	0.0363258i
$326$	3.58987	+	6.21783i	0.198824	+	0.344374i
$327$	−0.747261	−	0.568579i	−0.0413236	−	0.0314425i
$328$	−8.63091	+	14.9492i	−0.476562	+	0.825430i
$329$	3.45161	−	5.97836i	0.190293	−	0.329598i
$330$	−8.71207	+	11.7611i	−0.479583	+	0.647427i
$331$	−15.5610	−	26.9525i	−0.855312	−	1.48144i	−0.876355	−	0.481665i	$-0.840032\pi$
$331$	−15.5610	−	26.9525i	−0.855312	−	1.48144i	0.0210431	−	0.999779i	$-0.493301\pi$
$332$	2.91259			0.159849
$333$	9.37094	+	33.8683i	0.513524	+	1.85597i
$334$	6.93987			0.379733
$335$	−3.87893	+	2.23950i	−0.211929	+	0.122357i
$336$	18.8289	−	7.88907i	1.02720	−	0.430384i
$337$	30.7641	+	17.7616i	1.67582	+	0.967538i	0.964275	+	0.264902i	$0.0853396\pi$
$337$	30.7641	+	17.7616i	1.67582	+	0.967538i	0.711550	+	0.702636i	$0.247994\pi$
$338$	7.58124	−	13.1311i	0.412365	−	0.714237i
$339$	9.97832	−	4.18079i	0.541948	−	0.227069i
$340$	3.55859	−	2.05455i	0.192992	−	0.111424i
$341$	13.9114	+	7.79471i	0.753346	+	0.422107i
$342$	−14.6936	−	14.4564i	−0.794537	−	0.781714i
$343$			13.3222i			0.719330i
$344$	−6.00018	+	3.46420i	−0.323508	+	0.186777i
$345$	9.19447	+	1.17245i	0.495014	+	0.0631225i
$346$	−12.9662	+	22.4581i	−0.697066	+	1.20735i
$347$	−5.13984	+	8.90247i	−0.275921	+	0.477910i	−0.970367	−	0.241635i	$-0.922316\pi$
$347$	−5.13984	+	8.90247i	−0.275921	+	0.477910i	0.694446	+	0.719545i	$0.255650\pi$
$348$	−1.42425	+	1.87183i	−0.0763478	+	0.100341i
$349$	−15.7643	+	9.10150i	−0.843841	+	0.487192i	−0.858568	−	0.512699i	$-0.828646\pi$
$349$	−15.7643	+	9.10150i	−0.843841	+	0.487192i	0.0147267	+	0.999892i	$0.495312\pi$
$350$			3.89549i			0.208222i
$351$	2.77262	+	3.52348i	0.147992	+	0.188070i
$352$	−7.50885	−	4.20728i	−0.400223	−	0.224249i
$353$	−5.50002	+	3.17544i	−0.292737	+	0.169012i	−0.639175	−	0.769061i	$-0.720724\pi$
$353$	−5.50002	+	3.17544i	−0.292737	+	0.169012i	0.346439	+	0.938073i	$0.387391\pi$
$354$	−11.4202	−	8.68946i	−0.606977	−	0.461840i
$355$	−1.40238	+	2.42900i	−0.0744308	+	0.128918i
$356$	−3.02676	−	1.74750i	−0.160418	−	0.0926173i
$357$	3.86420	−	30.3034i	0.204515	−	1.60383i
$358$	−14.6022	+	8.43060i	−0.771751	+	0.445571i
$359$	−0.878883			−0.0463857			−0.0231928	−	0.999731i	$-0.507383\pi$
$359$	−0.878883			−0.0463857			−0.0231928	+	0.999731i	$0.507383\pi$
$360$	4.73663	−	18.2706i	0.249643	−	0.962945i
$361$	−11.8427			−0.623301
$362$	4.23387	+	7.33329i	0.222527	+	0.385429i
$363$	11.1427	−	15.4545i	0.584840	−	0.811149i
$364$	−0.840041	+	1.45499i	−0.0440301	+	0.0762624i
$365$	11.5100	−	19.9358i	0.602459	−	1.04349i
$366$	13.2110	−	5.53525i	0.690552	−	0.289332i
$367$	4.57947	+	7.93188i	0.239047	+	0.414041i	0.960441	−	0.278484i	$-0.0898318\pi$
$367$	4.57947	+	7.93188i	0.239047	+	0.414041i	−0.721394	+	0.692524i	$0.756498\pi$
$368$		−	7.38264i		−	0.384847i
$369$	16.4083	+	4.25383i	0.854180	+	0.221445i
$370$		−	29.8447i		−	1.55155i
$371$	−4.73170	−	8.19555i	−0.245658	−	0.425492i
$372$	−3.87708	−	0.494393i	−0.201017	−	0.0256331i
$373$	−9.13656	−	5.27499i	−0.473073	−	0.273129i	0.244452	−	0.969661i	$-0.421392\pi$
$373$	−9.13656	−	5.27499i	−0.473073	−	0.273129i	−0.717525	+	0.696533i	$0.754725\pi$
$374$	14.9940	−	8.91614i	0.775324	−	0.461043i
$375$	16.3477	+	12.4387i	0.844193	+	0.642333i
$376$	−4.40247	+	2.54177i	−0.227040	+	0.131082i
$377$			2.49660i			0.128581i
$378$	−16.4928	−	20.9593i	−0.848299	−	1.07803i
$379$	15.2267			0.782145			0.391072	−	0.920360i	$-0.372104\pi$
$379$	15.2267			0.782145			0.391072	+	0.920360i	$0.372104\pi$
$380$	−2.68390	−	4.64865i	−0.137681	−	0.238470i
$381$	−24.5576	−	18.6855i	−1.25812	−	0.957287i
$382$	25.6048	+	14.7829i	1.31006	+	0.756361i
$383$	23.7003	+	13.6834i	1.21103	+	0.699187i	0.962983	−	0.269561i	$-0.0868787\pi$
$383$	23.7003	+	13.6834i	1.21103	+	0.699187i	0.248045	+	0.968749i	$0.420212\pi$
$384$	−9.98565	−	1.27334i	−0.509578	−	0.0649797i
$385$	0.364797	+	28.3337i	0.0185918	+	1.44402i
$386$		−	18.7351i		−	0.953591i
$387$	4.84980	+	4.77153i	0.246529	+	0.242551i
$388$	4.95143			0.251371
$389$	−10.7290	+	6.19442i	−0.543984	+	0.314069i	−0.746692	−	0.665170i	$-0.768359\pi$
$389$	−10.7290	+	6.19442i	−0.543984	+	0.314069i	0.202708	+	0.979239i	$0.435026\pi$
$390$	−1.47149	−	3.51203i	−0.0745120	−	0.177839i
$391$	−9.56734	−	5.52371i	−0.483841	−	0.279346i
$392$	15.5979	−	27.0164i	0.787815	−	1.36454i
$393$	−5.52946	−	13.1972i	−0.278925	−	0.665712i
$394$	−3.55441	−	6.15641i	−0.179068	−	0.310156i
$395$	21.9311			1.10347
$396$	−1.11361	+	4.53510i	−0.0559612	+	0.227897i
$397$	12.3514			0.619900			0.309950	−	0.950753i	$-0.399688\pi$
$397$	12.3514			0.619900			0.309950	+	0.950753i	$0.399688\pi$
$398$	2.73935	+	4.74470i	0.137311	+	0.237830i
$399$	−39.5859	−	5.04786i	−1.98177	−	0.252709i
$400$	1.07812	−	1.86735i	0.0539058	−	0.0933676i
$401$	0.502760	+	0.290268i	0.0251066	+	0.0144953i	0.512501	−	0.858687i	$-0.328719\pi$
$401$	0.502760	+	0.290268i	0.0251066	+	0.0144953i	−0.487394	+	0.873182i	$0.662053\pi$
$402$	2.82216	−	3.70904i	0.140756	−	0.184990i
$403$	−3.59283	+	2.07432i	−0.178971	+	0.103329i
$404$	−0.485588			−0.0241589
$405$	−18.5320	+	0.301541i	−0.920861	+	0.0149837i
$406$		−	14.8509i		−	0.737038i
$407$	0.500150	+	38.8464i	0.0247915	+	1.92555i
$408$	−13.6221	+	17.9030i	−0.674395	+	0.886330i
$409$	7.43480	+	4.29248i	0.367627	+	0.212250i	0.672421	−	0.740169i	$-0.265254\pi$
$409$	7.43480	+	4.29248i	0.367627	+	0.212250i	−0.304794	+	0.952418i	$0.598588\pi$
$410$	−12.4673	−	7.19802i	−0.615718	−	0.355485i
$411$	−1.85199	+	14.5235i	−0.0913517	+	0.716390i
$412$	−1.83603	−	3.18010i	−0.0904549	−	0.156672i
$413$	−27.7819			−1.36706
$414$	−9.29556	+	2.57196i	−0.456852	+	0.126405i
$415$			12.7801i			0.627348i
$416$	1.93927	−	1.11964i	0.0950805	−	0.0548948i
$417$	−12.9616	+	5.43074i	−0.634732	+	0.265944i
$418$	−11.6473	−	19.5870i	−0.569688	−	0.958030i
$419$	−2.88622	−	1.66636i	−0.141001	−	0.0814070i	0.427840	−	0.903855i	$-0.359275\pi$
$419$	−2.88622	−	1.66636i	−0.141001	−	0.0814070i	−0.568841	+	0.822447i	$0.692608\pi$
$420$	−2.68390	−	6.40568i	−0.130961	−	0.312565i
$421$	0.811147	+	1.40495i	0.0395329	+	0.0684730i	0.885115	−	0.465373i	$-0.154080\pi$
$421$	0.811147	+	1.40495i	0.0395329	+	0.0684730i	−0.845582	+	0.533846i	$0.820746\pi$
$422$			14.5168i			0.706667i
$423$	3.55841	+	3.50098i	0.173016	+	0.170224i
$424$			6.96886i			0.338438i
$425$	−1.61330	−	2.79431i	−0.0782563	−	0.135544i
$426$	0.369170	−	2.89507i	0.0178863	−	0.140267i
$427$	13.8654	−	24.0156i	0.670993	−	1.16219i
$428$	−1.85084	+	3.20575i	−0.0894639	+	0.154956i
$429$	1.97418	+	4.54666i	0.0953144	+	0.219515i
$430$	−2.88908	−	5.00404i	−0.139324	−	0.241316i
$431$	34.0188			1.63863			0.819313	−	0.573347i	$-0.194355\pi$
$431$	34.0188			1.63863			0.819313	+	0.573347i	$0.194355\pi$
$432$	2.10535	+	14.6117i	0.101294	+	0.703004i
$433$	−28.6069			−1.37476			−0.687380	−	0.726298i	$-0.741239\pi$
$433$	−28.6069			−1.37476			−0.687380	+	0.726298i	$0.741239\pi$
$434$	21.3718	−	12.3390i	1.02588	−	0.592291i
$435$	−8.21336	−	6.24942i	−0.393800	−	0.299637i
$436$	0.220348	+	0.127218i	0.0105527	+	0.00609263i
$437$	−7.21570	+	12.4980i	−0.345174	+	0.597859i
$438$	−3.02993	+	23.7610i	−0.144776	+	1.13535i
$439$	10.4122	−	6.01151i	0.496949	−	0.286914i	−0.230503	−	0.973071i	$-0.574037\pi$
$439$	10.4122	−	6.01151i	0.496949	−	0.286914i	0.727453	+	0.686158i	$0.240704\pi$
$440$	10.1998	−	18.2039i	0.486257	−	0.867836i
$441$	−29.6533	−	7.68760i	−1.41206	−	0.366076i
$442$			4.53847i			0.215873i
$443$	22.2214	−	12.8295i	1.05577	−	0.609548i	0.131510	−	0.991315i	$-0.458017\pi$
$443$	22.2214	−	12.8295i	1.05577	−	0.609548i	0.924259	+	0.381766i	$0.124684\pi$
$444$	−3.67972	−	8.78241i	−0.174632	−	0.416795i
$445$	7.66779	−	13.2810i	0.363488	−	0.629580i
$446$	2.86334	−	4.95946i	0.135583	−	0.234837i
$447$	6.71884	+	16.0359i	0.317790	+	0.758473i
$448$	−31.9505	+	18.4466i	−1.50952	+	0.871521i
$449$		−	19.4014i		−	0.915608i	−0.889053	−	0.457804i	$-0.848636\pi$
$449$		−	19.4014i		−	0.915608i	0.889053	−	0.457804i	$-0.151364\pi$
$450$	−2.72679	−	0.706918i	−0.128542	−	0.0333244i
$451$	16.3483	+	9.16014i	0.769813	+	0.431334i
$452$	−2.53881	+	1.46578i	−0.119416	+	0.0689447i
$453$	2.49752	−	19.5859i	0.117344	−	0.920224i
$454$	14.0654	−	24.3620i	0.660123	−	1.14337i
$455$	−6.38432	−	3.68599i	−0.299301	−	0.172802i
$456$	23.3869	+	17.7948i	1.09519	+	0.833316i
$457$	−10.5984	+	6.11897i	−0.495770	+	0.286233i	−0.726965	−	0.686674i	$-0.759070\pi$
$457$	−10.5984	+	6.11897i	−0.495770	+	0.286233i	0.231195	+	0.972907i	$0.425737\pi$
$458$	−4.43867			−0.207406
$459$	20.5108	+	8.20409i	0.957362	+	0.382934i
$460$	−2.51161			−0.117104
$461$	16.4063	+	28.4165i	0.764116	+	1.32349i	0.940713	+	0.339205i	$0.110158\pi$
$461$	16.4063	+	28.4165i	0.764116	+	1.32349i	−0.176596	+	0.984283i	$0.556509\pi$
$462$	−11.7433	−	27.0456i	−0.546349	−	1.25828i
$463$	2.52075	−	4.36606i	0.117149	−	0.202908i	−0.801488	−	0.598011i	$-0.795958\pi$
$463$	2.52075	−	4.36606i	0.117149	−	0.202908i	0.918637	+	0.395103i	$0.129291\pi$
$464$	−4.11014	+	7.11898i	−0.190809	+	0.330490i
$465$	2.16933	−	17.0121i	0.100600	−	0.788919i
$466$	11.5539	+	20.0119i	0.535222	+	0.927032i
$467$			9.20108i			0.425775i	0.977077	+	0.212888i	$0.0682868\pi$
$467$			9.20108i			0.425775i	−0.977077	+	0.212888i	$0.931713\pi$
$468$	−0.866035	−	0.852058i	−0.0400325	−	0.0393864i
$469$		−	9.02299i		−	0.416643i
$470$	−2.11979	−	3.67158i	−0.0977785	−	0.169357i
$471$	−2.55065	−	6.08767i	−0.117528	−	0.280505i
$472$	17.7177	+	10.2293i	0.815524	+	0.470843i
$473$	3.84434	+	6.46493i	0.176763	+	0.297258i
$474$	−21.0476	+	8.81869i	−0.966750	+	0.405056i
$475$	−3.65025	+	2.10747i	−0.167485	+	0.0966975i
$476$			8.27784i			0.379414i
$477$	6.59546	−	1.82488i	0.301985	−	0.0835555i
$478$	26.0336			1.19075
$479$	−6.98309	−	12.0951i	−0.319065	−	0.552637i	0.661228	−	0.750185i	$-0.270036\pi$
$479$	−6.98309	−	12.0951i	−0.319065	−	0.552637i	−0.980293	+	0.197548i	$0.936702\pi$
$480$	−1.17092	+	9.18249i	−0.0534450	+	0.419121i
$481$	−8.75312	−	5.05362i	−0.399108	−	0.230425i
$482$	−1.09066	−	0.629693i	−0.0496782	−	0.0286817i
$483$	−11.3067	+	14.8599i	−0.514470	+	0.676148i
$484$	−2.46538	+	4.53599i	−0.112063	+	0.206182i
$485$			21.7262i			0.986536i
$486$	17.6642	−	7.74127i	0.801265	−	0.351151i
$487$	−28.9483			−1.31177			−0.655886	−	0.754860i	$-0.727705\pi$
$487$	−28.9483			−1.31177			−0.655886	+	0.754860i	$0.727705\pi$
$488$	−17.6851	+	10.2105i	−0.800566	+	0.462207i
$489$	−6.08645	+	7.99918i	−0.275239	+	0.361735i
$490$	22.5312	+	13.0084i	1.01786	+	0.587660i
$491$	9.63961	−	16.6963i	0.435029	−	0.753493i	−0.562269	−	0.826955i	$-0.690071\pi$
$491$	9.63961	−	16.6963i	0.435029	−	0.753493i	0.997298	+	0.0734617i	$0.0234047\pi$
$492$	−4.55625	−	0.580998i	−0.205412	−	0.0261934i
$493$	6.15043	+	10.6529i	0.277001	+	0.479781i
$494$	5.92868			0.266744
$495$	−19.8994	−	4.88639i	−0.894412	−	0.219627i
$496$	−13.6598			−0.613342
$497$	−2.82512	−	4.89325i	−0.126724	−	0.219492i
$498$	−5.13898	−	12.2652i	−0.230283	−	0.549619i
$499$	−16.9288	+	29.3216i	−0.757838	+	1.31261i	0.186112	+	0.982528i	$0.440411\pi$
$499$	−16.9288	+	29.3216i	−0.757838	+	1.31261i	−0.943951	+	0.330086i	$0.892922\pi$
$500$	−4.82052	−	2.78313i	−0.215580	−	0.124465i
$501$	3.75450	+	8.96089i	0.167739	+	0.400343i
$502$	−29.8864	+	17.2549i	−1.33390	+	0.770126i
$503$	4.01382			0.178967			0.0894836	−	0.995988i	$-0.471478\pi$
$503$	4.01382			0.178967			0.0894836	+	0.995988i	$0.471478\pi$
$504$	27.1042	+	26.6668i	1.20732	+	1.18783i
$505$		−	2.13070i		−	0.0948148i
$506$	−10.6619	+	0.137272i	−0.473977	+	0.00610248i
$507$	21.0566	+	2.68507i	0.935156	+	0.119248i
$508$	7.24140	+	4.18082i	0.321285	+	0.185494i
$509$	3.23995	+	1.87059i	0.143608	+	0.0829123i	0.570083	−	0.821587i	$-0.306911\pi$
$509$	3.23995	+	1.87059i	0.143608	+	0.0829123i	−0.426474	+	0.904500i	$0.640245\pi$
$510$	−14.9308	−	11.3606i	−0.661145	−	0.503055i
$511$	23.1869	+	40.1609i	1.02573	+	1.77662i
$512$	24.7322			1.09302
$513$	10.7171	−	26.7936i	0.473173	−	1.18297i
$514$			33.3263i			1.46996i
$515$	13.9539	−	8.05627i	0.614881	−	0.355002i
$516$	−1.46715	−	1.11633i	−0.0645875	−	0.0491436i
$517$	2.82068	+	4.74347i	0.124054	+	0.208618i
$518$	52.0675	+	30.0612i	2.28772	+	1.32081i
$519$	−36.0131	−	4.59227i	−1.58080	−	0.201578i
$520$	2.71436	+	4.70142i	0.119033	+	0.206171i
$521$		−	13.3122i		−	0.583216i	−0.956538	−	0.291608i	$-0.905810\pi$
$521$		−	13.3122i		−	0.583216i	0.956538	−	0.291608i	$-0.0941903\pi$
$522$	10.3955	+	2.69501i	0.454997	+	0.117957i
$523$		−	19.7745i		−	0.864678i	−0.901711	−	0.432339i	$-0.857688\pi$
$523$		−	19.7745i		−	0.864678i	0.901711	−	0.432339i	$-0.142312\pi$
$524$	1.93863	+	3.35781i	0.0846895	+	0.146687i
$525$	−5.02993	+	2.10747i	−0.219524	+	0.0919777i
$526$	11.1983	−	19.3961i	0.488270	−	0.845709i
$527$	−10.2203	+	17.7020i	−0.445202	+	0.771112i
$528$	−1.85584	+	16.2148i	−0.0807650	+	0.705657i
$529$	−8.12375	−	14.0707i	−0.353207	−	0.611772i
$530$	−5.81190			−0.252453
$531$	5.04162	−	19.4470i	0.218788	−	0.843929i
$532$	10.8135			0.468823
$533$	−4.22220	+	2.43769i	−0.182884	+	0.105588i
$534$	−2.01850	+	15.8293i	−0.0873491	+	0.685001i
$535$	−14.0664	−	8.12125i	−0.608145	−	0.351112i
$536$	−3.32227	+	5.75434i	−0.143500	+	0.248550i
$537$	−18.7856	−	14.2937i	−0.810659	−	0.616818i
$538$	−13.0998	+	7.56320i	−0.564774	+	0.326073i
$539$	−29.5450	−	16.5544i	−1.27260	−	0.713048i
$540$	4.97095	−	0.716249i	0.213916	−	0.0308225i
$541$		−	23.4225i		−	1.00701i	−0.863992	−	0.503506i	$-0.832043\pi$
$541$		−	23.4225i		−	1.00701i	0.863992	−	0.503506i	$-0.167957\pi$
$542$	−16.0520	+	9.26761i	−0.689492	+	0.398078i
$543$	−7.17834	+	9.43420i	−0.308052	+	0.404860i
$544$	5.51651	−	9.55487i	0.236518	−	0.409662i
$545$	−0.558215	+	0.966857i	−0.0239113	+	0.0414156i
$546$	7.60932	+	0.970315i	0.325649	+	0.0415256i
$547$	17.2285	−	9.94686i	0.736636	−	0.425297i	−0.0842088	−	0.996448i	$-0.526836\pi$
$547$	17.2285	−	9.94686i	0.736636	−	0.425297i	0.820845	+	0.571151i	$0.193503\pi$
$548$		−	3.96730i		−	0.169475i
$549$	14.2944	+	14.0637i	0.610072	+	0.600226i
$550$	−2.71683	−	1.52227i	−0.115846	−	0.0649098i
$551$	13.9160	−	8.03440i	0.592841	−	0.342277i
$552$	12.6821	−	5.31365i	0.539788	−	0.226164i
$553$	−22.0902	+	38.2613i	−0.939369	+	1.62704i
$554$	−31.8170	−	18.3696i	−1.35177	−	0.780447i
$555$	38.5360	−	16.1461i	1.63576	−	0.685364i
$556$	3.29786	−	1.90402i	0.139860	−	0.0807484i
$557$	6.10079			0.258499			0.129249	−	0.991612i	$-0.458743\pi$
$557$	6.10079			0.258499			0.129249	+	0.991612i	$0.458743\pi$
$558$	4.75879	+	17.1992i	0.201456	+	0.728098i
$559$	−1.95684			−0.0827655
$560$	−12.1365	−	21.0210i	−0.512859	−	0.888297i
$561$	19.6245	+	14.5369i	0.828549	+	0.613750i
$562$	1.61761	−	2.80177i	0.0682346	−	0.118186i
$563$	0.00492939	−	0.00853795i	0.000207749	−	0.000359832i	−0.865922	−	0.500180i	$-0.833267\pi$
$563$	0.00492939	−	0.00853795i	0.000207749	−	0.000359832i	0.866129	+	0.499820i	$0.166601\pi$
$564$	−1.07648	−	0.819077i	−0.0453280	−	0.0344893i
$565$	−6.43167	−	11.1400i	−0.270582	−	0.468662i
$566$			2.58424i			0.108624i
$567$	18.1403	−	32.6349i	0.761822	−	1.37054i
$568$			4.16084i			0.174585i
$569$	−3.45428	−	5.98299i	−0.144811	−	0.250820i	0.784491	−	0.620140i	$-0.212924\pi$
$569$	−3.45428	−	5.98299i	−0.144811	−	0.250820i	−0.929302	+	0.369320i	$0.879591\pi$
$570$	−14.8405	+	19.5043i	−0.621600	+	0.816944i
$571$	−16.6286	−	9.60053i	−0.695886	−	0.401770i	0.109927	−	0.993940i	$-0.464938\pi$
$571$	−16.6286	−	9.60053i	−0.695886	−	0.401770i	−0.805813	+	0.592170i	$0.798271\pi$
$572$	−0.686489	−	1.15445i	−0.0287035	−	0.0482700i
$573$	−5.23571	+	41.0590i	−0.218725	+	1.71527i
$574$	25.1156	−	14.5005i	1.04830	−	0.605238i
$575$			1.97219i			0.0822459i
$576$	−7.11433	−	25.7125i	−0.296430	−	1.07135i
$577$	25.0209			1.04163			0.520816	−	0.853669i	$-0.325628\pi$
$577$	25.0209			1.04163			0.520816	+	0.853669i	$0.325628\pi$
$578$	0.664430	+	1.15083i	0.0276366	+	0.0478681i
$579$	24.1911	−	10.1358i	1.00535	−	0.421228i
$580$	2.42191	+	1.39829i	0.100564	+	0.0580608i
$581$	−22.2963	−	12.8728i	−0.925006	−	0.534052i
$582$	−8.73631	−	20.8510i	−0.362132	−	0.864303i
$583$	7.56488	−	0.0973983i	0.313305	−	0.00403383i
$584$		−	34.1497i		−	1.41313i
$585$	3.73872	−	3.80005i	0.154577	−	0.157113i
$586$	−37.2911			−1.54048
$587$	−37.0963	+	21.4176i	−1.53113	+	0.883998i	−0.531820	+	0.846858i	$0.678492\pi$
$587$	−37.0963	+	21.4176i	−1.53113	+	0.883998i	−0.999310	+	0.0371404i	$0.988175\pi$
$588$	8.23414	+	1.04999i	0.339570	+	0.0433009i
$589$	23.1244	+	13.3509i	0.952826	+	0.550114i
$590$	−8.53107	+	14.7762i	−0.351218	+	0.608328i
$591$	6.02633	−	7.92016i	0.247890	−	0.325792i
$592$	−16.6395	−	28.8205i	−0.683879	−	1.18451i
$593$	−21.7398			−0.892745			−0.446373	−	0.894847i	$-0.647284\pi$
$593$	−21.7398			−0.892745			−0.446373	+	0.894847i	$0.647284\pi$
$594$	21.0627	−	3.31219i	0.864213	−	0.135901i
$595$	−36.3221			−1.48906
$596$	−2.35563	−	4.08007i	−0.0964902	−	0.167126i
$597$	−4.64444	+	6.10400i	−0.190084	+	0.249820i
$598$	1.38702	−	2.40240i	0.0567196	−	0.0982413i
$599$	−9.32083	−	5.38138i	−0.380839	−	0.219877i	0.297344	−	0.954770i	$-0.403899\pi$
$599$	−9.32083	−	5.38138i	−0.380839	−	0.219877i	−0.678183	+	0.734893i	$0.737232\pi$
$600$	3.98377	+	0.507997i	0.162637	+	0.0207389i
$601$	22.6605	−	13.0831i	0.924343	−	0.533670i	0.0393250	−	0.999226i	$-0.487479\pi$
$601$	22.6605	−	13.0831i	0.924343	−	0.533670i	0.885018	+	0.465557i	$0.154146\pi$
$602$	11.6402			0.474418
$603$	6.31599	+	1.63741i	0.257207	+	0.0666806i
$604$			5.35017i			0.217695i
$605$	−19.9033	−	10.8177i	−0.809186	−	0.439804i
$606$	0.856773	+	2.04487i	0.0348040	+	0.0830671i
$607$	−16.9909	−	9.80971i	−0.689640	−	0.398164i	0.113837	−	0.993499i	$-0.463686\pi$
$607$	−16.9909	−	9.80971i	−0.689640	−	0.398164i	−0.803477	+	0.595335i	$0.797019\pi$
$608$	−12.4817	−	7.20630i	−0.506199	−	0.292254i
$609$	19.1758	−	8.03440i	0.777042	−	0.325570i
$610$	−8.51536	−	14.7490i	−0.344777	−	0.597171i
$611$	−1.43578			−0.0580854
$612$	−5.79439	−	1.50219i	−0.234224	−	0.0607224i
$613$		−	33.5233i		−	1.35399i	−0.735987	−	0.676996i	$-0.763282\pi$
$613$		−	33.5233i		−	1.35399i	0.735987	−	0.676996i	$-0.236718\pi$
$614$	19.1530	−	11.0580i	0.772950	−	0.446263i
$615$	2.54934	−	19.9922i	0.102799	−	0.806164i
$616$	21.4850	+	36.1307i	0.865654	+	1.45575i
$617$	16.5667	+	9.56478i	0.666950	+	0.385064i	0.794920	−	0.606714i	$-0.207513\pi$
$617$	16.5667	+	9.56478i	0.666950	+	0.385064i	−0.127970	+	0.991778i	$0.540846\pi$
$618$	−10.1523	+	13.3427i	−0.408385	+	0.536723i
$619$	−16.6869	−	28.9026i	−0.670704	−	1.16169i	−0.977705	−	0.209984i	$-0.932659\pi$
$619$	−16.6869	−	28.9026i	−0.670704	−	1.16169i	0.307001	−	0.951709i	$-0.400675\pi$
$620$			4.64712i			0.186633i
$621$	−8.34990	−	10.6112i	−0.335070	−	0.425811i
$622$		−	33.6458i		−	1.34907i
$623$	15.4468	+	26.7547i	0.618865	+	1.07190i
$624$	−3.37908	−	2.57109i	−0.135271	−	0.102926i
$625$	10.3146	−	17.8654i	0.412584	−	0.714617i
$626$	5.44834	−	9.43680i	0.217759	−	0.377170i
$627$	18.9898	−	25.6358i	0.758381	−	1.02380i
$628$	0.894261	+	1.54890i	0.0356849	+	0.0618080i
$629$	−49.7988			−1.98561
$630$	−22.2396	+	22.6044i	−0.886046	+	0.900581i
$631$	14.2718			0.568152			0.284076	−	0.958802i	$-0.408313\pi$
$631$	14.2718			0.568152			0.284076	+	0.958802i	$0.408313\pi$
$632$	28.1757	−	16.2672i	1.12077	−	0.647075i
$633$	−18.7444	+	7.85365i	−0.745022	+	0.312155i
$634$	12.0721	+	6.96983i	0.479445	+	0.276807i
$635$	−18.3449	+	31.7743i	−0.727995	+	1.26092i
$636$	−1.71027	+	0.716581i	−0.0678166	+	0.0284143i
$637$	7.63044	−	4.40544i	0.302329	−	0.174550i
$638$	10.3575	+	5.80341i	0.410057	+	0.229759i
$639$	3.93789	−	1.08956i	0.155781	−	0.0431025i
$640$			11.9689i			0.473113i
$641$	23.8511	−	13.7704i	0.942062	−	0.543900i	0.0514559	−	0.998675i	$-0.483614\pi$
$641$	23.8511	−	13.7704i	0.942062	−	0.543900i	0.890606	+	0.454776i	$0.150281\pi$
$642$	16.7654	+	2.13787i	0.661679	+	0.0843751i
$643$	−20.3147	+	35.1861i	−0.801133	+	1.38760i	0.117738	+	0.993045i	$0.462436\pi$
$643$	−20.3147	+	35.1861i	−0.801133	+	1.38760i	−0.918871	+	0.394558i	$0.870898\pi$
$644$	2.52983	−	4.38179i	0.0996892	−	0.172667i
$645$	4.89830	−	6.43764i	0.192871	−	0.253482i
$646$	25.2974	−	14.6054i	0.995311	−	0.574643i
$647$			37.7946i			1.48586i	0.669371	+	0.742929i	$0.266564\pi$
$647$			37.7946i			1.48586i	−0.669371	+	0.742929i	$0.733436\pi$
$648$	−23.5850	+	14.1334i	−0.926508	+	0.555211i
$649$	10.8566	−	19.3760i	0.426158	−	0.760575i
$650$	0.701662	−	0.405105i	0.0275215	−	0.0158895i
$651$	27.4946	+	20.9202i	1.07760	+	0.819927i
$652$	1.36182	−	2.35875i	0.0533332	−	0.0923758i
$653$	−33.5277	−	19.3573i	−1.31204	−	0.757508i	−0.329608	−	0.944118i	$-0.606917\pi$
$653$	−33.5277	−	19.3573i	−1.31204	−	0.757508i	−0.982434	+	0.186610i	$0.940250\pi$
$654$	0.146947	−	1.15237i	0.00574608	−	0.0450614i
$655$	−14.7336	+	8.50646i	−0.575690	+	0.332375i
$656$	−16.0526			−0.626750
$657$	−32.3199	+	8.94252i	−1.26092	+	0.348881i
$658$	8.54066			0.332950
$659$	−15.8461	−	27.4462i	−0.617275	−	1.06915i	−0.989981	−	0.141202i	$-0.954903\pi$
$659$	−15.8461	−	27.4462i	−0.617275	−	1.06915i	0.372706	−	0.927949i	$-0.378430\pi$
$660$	5.51633	+	0.631365i	0.214723	+	0.0245758i
$661$	13.4387	−	23.2766i	0.522706	−	0.905353i	−0.476945	−	0.878933i	$-0.658256\pi$
$661$	13.4387	−	23.2766i	0.522706	−	0.905353i	0.999651	−	0.0264199i	$-0.00841069\pi$
$662$	19.2521	−	33.3457i	0.748255	−	1.29602i
$663$	−5.86017	+	2.45533i	−0.227590	+	0.0953572i
$664$	9.47952	+	16.4190i	0.367877	+	0.637181i
$665$			47.4481i			1.83996i
$666$	−30.4912	+	30.9914i	−1.18151	+	1.20089i
$667$		−	7.51865i		−	0.291123i
$668$	−1.31633	−	2.27995i	−0.0509303	−	0.0882138i
$669$	7.95283	+	1.01412i	0.307474	+	0.0392081i
$670$	−4.79902	−	2.77071i	−0.185402	−	0.107042i
$671$	11.3309	+	19.0549i	0.437425	+	0.735607i
$672$	−14.8405	−	11.2919i	−0.572485	−	0.435595i
$673$	14.7738	−	8.52968i	0.569490	−	0.328795i	−0.187456	−	0.982273i	$-0.560024\pi$
$673$	14.7738	−	8.52968i	0.569490	−	0.328795i	0.756946	+	0.653478i	$0.226691\pi$
$674$			43.9494i			1.69287i
$675$	−0.562420	−	3.90333i	−0.0216475	−	0.150239i
$676$	−5.75192			−0.221228
$677$	1.45562	+	2.52120i	0.0559439	+	0.0968978i	0.892641	−	0.450768i	$-0.148850\pi$
$677$	1.45562	+	2.52120i	0.0559439	+	0.0968978i	−0.836697	+	0.547666i	$0.815517\pi$
$678$	10.6521	+	8.10500i	0.409091	+	0.311271i
$679$	−37.9039	−	21.8838i	−1.45462	−	0.839824i
$680$	23.1641	+	13.3738i	0.888303	+	0.512862i
$681$	39.0661	+	4.98159i	1.49702	+	0.190895i
$682$	0.253988	+	19.7272i	0.00972572	+	0.755392i
$683$			20.5133i			0.784918i	0.919770	+	0.392459i	$0.128375\pi$
$683$			20.5133i			0.784918i	−0.919770	+	0.392459i	$0.871625\pi$
$684$	−1.96233	+	7.56930i	−0.0750317	+	0.289419i
$685$	17.4080			0.665126
$686$	−14.2740	+	8.24110i	−0.544984	+	0.314647i
$687$	−2.40134	−	5.73130i	−0.0916168	−	0.218663i
$688$	−5.57986	−	3.22154i	−0.212730	−	0.122820i
$689$	−0.984132	+	1.70457i	−0.0374925	+	0.0649388i
$690$	4.43149	+	10.5767i	0.168704	+	0.402647i
$691$	−4.32135	−	7.48480i	−0.164392	−	0.284735i	0.772047	−	0.635565i	$-0.219233\pi$
$691$	−4.32135	−	7.48480i	−0.164392	−	0.284735i	−0.936439	+	0.350830i	$0.885900\pi$
$692$	9.83751			0.373966
$693$	28.5686	−	29.7950i	1.08523	−	1.13182i
$694$	−12.7180			−0.482770
$695$	8.35458	+	14.4706i	0.316907	+	0.548900i
$696$	−15.1875	−	1.93666i	−0.575680	−	0.0734088i
$697$	−12.0106	+	20.8030i	−0.454934	+	0.787968i
$698$	−19.5035	−	11.2604i	−0.738220	−	0.426212i
$699$	−19.5890	+	25.7451i	−0.740925	+	0.973768i
$700$	1.27978	−	0.738881i	0.0483711	−	0.0279271i
$701$	30.3341			1.14570			0.572852	−	0.819659i	$-0.305837\pi$
$701$	30.3341			1.14570			0.572852	+	0.819659i	$0.305837\pi$
$702$	−2.06008	+	5.15034i	−0.0777527	+	0.194387i
$703$			65.0530i			2.45352i
$704$	−0.379709	−	29.4918i	−0.0143108	−	1.11151i
$705$	3.59400	−	4.72345i	0.135358	−	0.177895i
$706$	−6.80463	−	3.92866i	−0.256096	−	0.147857i
$707$	3.71725	+	2.14615i	0.139802	+	0.0807144i
$708$	−0.688597	+	5.40005i	−0.0258790	+	0.202946i
$709$	−0.842981	−	1.46009i	−0.0316588	−	0.0548347i	0.849762	−	0.527167i	$-0.176746\pi$
$709$	−0.842981	−	1.46009i	−0.0316588	−	0.0548347i	−0.881421	+	0.472332i	$0.843412\pi$
$710$	−3.47006			−0.130229
$711$	−22.7737	−	22.4062i	−0.854081	−	0.840297i
$712$		−	22.7501i		−	0.852597i
$713$	10.8200	−	6.24693i	0.405212	−	0.233949i
$714$	34.8589	−	14.6054i	1.30456	−	0.546595i
$715$	5.06557	−	3.01222i	0.189442	−	0.112651i
$716$	5.53939	+	3.19817i	0.207017	+	0.119521i
$717$	14.0843	+	33.6150i	0.525987	+	1.25538i
$718$	−0.543677	−	0.941677i	−0.0202899	−	0.0351431i
$719$		−	17.8522i		−	0.665775i	−0.942967	−	0.332887i	$-0.891977\pi$
$719$		−	17.8522i		−	0.665775i	0.942967	−	0.332887i	$-0.108023\pi$
$720$	16.9168	−	4.68068i	0.630453	−	0.174438i
$721$			32.4589i			1.20883i
$722$	−7.32591	−	12.6888i	−0.272642	−	0.472230i
$723$	0.223020	−	1.74895i	0.00829421	−	0.0650441i
$724$	1.60613	−	2.78190i	0.0596914	−	0.103388i
$725$	1.09798	−	1.90175i	0.0407778	−	0.0706293i
$726$	23.4515	+	2.37867i	0.870367	+	0.0882806i
$727$	−13.8248	−	23.9453i	−0.512734	−	0.888081i	−0.999891	−	0.0147668i	$-0.995299\pi$
$727$	−13.8248	−	23.9453i	−0.512734	−	0.888081i	0.487157	−	0.873314i	$-0.338034\pi$
$728$	−10.9362			−0.405324
$729$	19.5521	+	18.6203i	0.724151	+	0.689641i
$730$	28.4803			1.05410
$731$	−8.34972	+	4.82072i	−0.308826	+	0.178301i
$732$	−4.32431	−	3.29030i	−0.159831	−	0.121613i
$733$	−11.6445	−	6.72297i	−0.430100	−	0.248318i	0.269289	−	0.963059i	$-0.413211\pi$
$733$	−11.6445	−	6.72297i	−0.430100	−	0.248318i	−0.699389	+	0.714741i	$0.746545\pi$
$734$	−5.66573	+	9.81332i	−0.209126	+	0.362216i
$735$	−4.60722	+	36.1303i	−0.169940	+	1.33269i
$736$	−5.84022	+	3.37185i	−0.215273	+	0.124288i
$737$	6.29292	+	3.52599i	0.231803	+	0.129881i
$738$	5.59241	+	20.2120i	0.205859	+	0.744014i
$739$		−	2.47408i		−	0.0910107i	−0.998964	−	0.0455053i	$-0.985510\pi$
$739$		−	2.47408i		−	0.0910107i	0.998964	−	0.0455053i	$-0.0144898\pi$
$740$	−9.80485	+	5.66083i	−0.360433	+	0.208096i
$741$	3.20744	+	7.65523i	0.117828	+	0.281222i
$742$	5.85407	−	10.1395i	0.214910	−	0.372234i
$743$	4.53380	−	7.85278i	0.166329	−	0.288090i	−0.770797	−	0.637080i	$-0.780142\pi$
$743$	4.53380	−	7.85278i	0.166329	−	0.288090i	0.937126	+	0.348990i	$0.113475\pi$
$744$	−9.83161	−	23.4652i	−0.360444	−	0.860276i
$745$	17.9028	−	10.3362i	0.655907	−	0.378688i
$746$		−	13.0524i		−	0.477884i
$747$	13.0569	−	13.2711i	0.477727	−	0.485564i
$748$	−5.77322	−	3.23480i	−0.211090	−	0.118276i
$749$	28.3369	−	16.3603i	1.03541	−	0.597794i
$750$	−3.21474	+	25.2103i	−0.117386	+	0.920551i
$751$	6.98349	−	12.0958i	0.254831	−	0.441381i	−0.710018	−	0.704183i	$-0.751313\pi$
$751$	6.98349	−	12.0958i	0.254831	−	0.441381i	0.964850	+	0.262802i	$0.0846467\pi$
$752$	−4.09408	−	2.36372i	−0.149296	−	0.0861958i
$753$	−38.4486	−	29.2549i	−1.40114	−	1.06611i
$754$	−2.67497	+	1.54440i	−0.0974168	+	0.0562436i
$755$	−23.4758			−0.854373
$756$	−3.75743	+	9.39384i	−0.136656	+	0.341651i
$757$	−7.49099			−0.272265			−0.136132	−	0.990691i	$-0.543467\pi$
$757$	−7.49099			−0.272265			−0.136132	+	0.990691i	$0.543467\pi$
$758$	9.41926	+	16.3146i	0.342123	+	0.592574i
$759$	−5.94535	−	13.6925i	−0.215803	−	0.497007i
$760$	17.4704	−	30.2596i	0.633718	−	1.09763i
$761$	−8.01546	+	13.8832i	−0.290560	+	0.503265i	−0.973942	−	0.226796i	$-0.927175\pi$
$761$	−8.01546	+	13.8832i	−0.290560	+	0.503265i	0.683382	+	0.730061i	$0.260508\pi$
$762$	4.82919	−	37.8710i	0.174943	−	1.37192i
$763$	−1.12453	−	1.94774i	−0.0407107	−	0.0705130i
$764$		−	11.2159i		−	0.405776i
$765$	6.59140	−	25.4250i	0.238313	−	0.919243i
$766$			33.8581i			1.22334i
$767$	2.88914	+	5.00414i	0.104321	+	0.180689i
$768$	7.09170	+	16.9258i	0.255900	+	0.610758i
$769$	−7.49374	−	4.32651i	−0.270231	−	0.156018i	0.358762	−	0.933429i	$-0.383199\pi$
$769$	−7.49374	−	4.32651i	−0.270231	−	0.156018i	−0.628993	+	0.777411i	$0.716532\pi$
$770$	−30.1323	+	17.9181i	−1.08589	+	0.645722i
$771$	−43.0315	+	18.0296i	−1.54974	+	0.649322i
$772$	−6.15502	+	3.55360i	−0.221524	+	0.127897i
$773$		−	9.20292i		−	0.331006i	−0.986209	−	0.165503i	$-0.947075\pi$
$773$		−	9.20292i		−	0.331006i	0.986209	−	0.165503i	$-0.0529248\pi$
$774$	−2.11235	+	8.14798i	−0.0759270	+	0.292873i
$775$	3.64905			0.131078
$776$	16.1153	+	27.9125i	0.578504	+	1.00200i
$777$	−10.6469	+	83.4939i	−0.381954	+	2.99533i
$778$	−13.2740	−	7.66374i	−0.475895	−	0.274758i
$779$	27.1752	+	15.6896i	0.973654	+	0.562139i
$780$	−0.874696	+	1.14958i	−0.0313191	+	0.0411615i
$781$	4.51670	−	0.0581527i	0.161620	−	0.00208087i
$782$		−	13.6679i		−	0.488762i
$783$	2.14414	+	14.8808i	0.0766251	+	0.531797i
$784$	29.0106			1.03609
$785$	−6.79639	+	3.92390i	−0.242574	+	0.140050i
$786$	10.7196	−	14.0883i	0.382355	−	0.502514i
$787$	−34.9642	−	20.1866i	−1.24634	−	0.719575i	−0.275963	−	0.961168i	$-0.588997\pi$
$787$	−34.9642	−	20.1866i	−1.24634	−	0.719575i	−0.970378	+	0.241593i	$0.922330\pi$
$788$	−1.34837	+	2.33545i	−0.0480338	+	0.0831970i
$789$	31.1029	+	3.96614i	1.10729	+	0.141198i
$790$	13.5666	+	23.4980i	0.482677	+	0.836020i
$791$	25.9133			0.921371
$792$	−29.1900	+	8.48254i	−1.03722	+	0.301414i
$793$	−5.76764			−0.204815
$794$	7.64059	+	13.2339i	0.271154	+	0.469653i
$795$	−3.14426	−	7.50444i	−0.111516	−	0.266155i
$796$	1.03918	−	1.79991i	0.0368328	−	0.0637962i
$797$	−0.574131	−	0.331475i	−0.0203368	−	0.0117414i	0.489797	−	0.871836i	$-0.337071\pi$
$797$	−0.574131	−	0.331475i	−0.0203368	−	0.0117414i	−0.510134	+	0.860095i	$0.670404\pi$
$798$	−19.0793	−	45.5368i	−0.675400	−	1.61198i
$799$	−6.12639	+	3.53707i	−0.216736	+	0.125133i
$800$	−1.96962			−0.0696365
$801$	−21.5311	+	5.95739i	−0.760765	+	0.210494i
$802$			0.718241i			0.0253620i
$803$	−37.0704	+	0.477284i	−1.30819	+	0.0168430i
$804$	−1.75382	−	0.223642i	−0.0618526	−	0.00788724i
$805$	19.2267	+	11.1006i	0.677653	+	0.391243i
$806$	−4.44505	−	2.56635i	−0.156570	−	0.0903958i
$807$	−16.8528	−	12.8231i	−0.593247	−	0.451393i
$808$	−1.58043	−	2.73739i	−0.0555993	−	0.0963009i
$809$	52.6473			1.85098			0.925490	−	0.378772i	$-0.123653\pi$
$809$	52.6473			1.85098			0.925490	+	0.378772i	$0.123653\pi$
$810$	−11.7870	−	19.6695i	−0.414152	−	0.691115i
$811$			23.1946i			0.814474i	0.913323	+	0.407237i	$0.133508\pi$
$811$			23.1946i			0.814474i	−0.913323	+	0.407237i	$0.866492\pi$
$812$	−4.87895	+	2.81687i	−0.171218	+	0.0988526i
$813$	−20.6507	−	15.7128i	−0.724252	−	0.551072i
$814$	−41.3125	+	24.5663i	−1.44800	+	0.861048i
$815$	10.3499	+	5.97551i	0.362540	+	0.209313i
$816$	−20.7523	−	2.64626i	−0.726475	−	0.0926377i
$817$	6.29738	+	10.9074i	0.220317	+	0.381601i
$818$			10.6213i			0.371366i
$819$	2.86378	+	10.3502i	0.100069	+	0.361667i
$820$			5.46117i			0.190712i
$821$	−4.61093	−	7.98637i	−0.160923	−	0.278726i	0.774277	−	0.632847i	$-0.218114\pi$
$821$	−4.61093	−	7.98637i	−0.160923	−	0.278726i	−0.935200	+	0.354120i	$0.884780\pi$
$822$	−16.7068	+	6.99992i	−0.582716	+	0.244150i
$823$	−2.85199	+	4.93978i	−0.0994140	+	0.172190i	−0.911442	−	0.411428i	$-0.865030\pi$
$823$	−2.85199	+	4.93978i	−0.0994140	+	0.172190i	0.812028	+	0.583618i	$0.198363\pi$
$824$	11.9514	−	20.7004i	0.416346	−	0.721132i
$825$	0.495766	−	4.33158i	0.0172604	−	0.150806i
$826$	−17.1859	−	29.7669i	−0.597974	−	1.03572i
$827$	−35.5680			−1.23682			−0.618411	−	0.785855i	$-0.712223\pi$
$827$	−35.5680			−1.23682			−0.618411	+	0.785855i	$0.712223\pi$
$828$	2.60811	+	2.56602i	0.0906381	+	0.0891753i
$829$	−9.38140			−0.325830			−0.162915	−	0.986640i	$-0.552090\pi$
$829$	−9.38140			−0.325830			−0.162915	+	0.986640i	$0.552090\pi$
$830$	−13.6931	+	7.90574i	−0.475296	+	0.274412i
$831$	6.50599	−	51.0207i	0.225690	−	1.76989i
$832$	6.64528	+	3.83666i	0.230384	+	0.133012i
$833$	21.7058	−	37.5955i	0.752061	−	1.30261i
$834$	−13.8368	−	10.5282i	−0.479129	−	0.364562i
$835$	10.0041	−	5.77587i	0.346206	−	0.199882i
$836$	−4.22567	+	7.54165i	−0.146148	+	0.260834i
$837$	−19.6334	+	15.4495i	−0.678628	+	0.534011i
$838$		−	4.12324i		−	0.142435i
$839$	30.1200	−	17.3898i	1.03986	−	0.600363i	0.120066	−	0.992766i	$-0.461689\pi$
$839$	30.1200	−	17.3898i	1.03986	−	0.600363i	0.919793	+	0.392403i	$0.128356\pi$
$840$	27.3753	−	35.9782i	0.944536	−	1.24137i
$841$	10.3141	−	17.8646i	0.355660	−	0.616021i
$842$	−1.00355	+	1.73820i	−0.0345847	+	0.0599024i
$843$	4.49284	+	0.572912i	0.154742	+	0.0197321i
$844$	4.76919	−	2.75349i	0.164162	−	0.0947791i
$845$		−	25.2387i		−	0.868236i
$846$	−1.54988	+	5.97836i	−0.0532861	+	0.205540i
$847$	38.9205	−	23.8275i	1.33733	−	0.818721i
$848$	−5.61244	+	3.24035i	−0.192732	+	0.111274i
$849$	−3.33683	+	1.39809i	−0.114520	+	0.0479822i
$850$	1.99597	−	3.45712i	0.0684612	−	0.118578i
$851$	26.3605	+	15.2192i	0.903626	+	0.521709i
$852$	−1.02114	+	0.427843i	−0.0349835	+	0.0146577i
$853$	−5.85013	+	3.37757i	−0.200305	+	0.115646i	−0.596798	−	0.802392i	$-0.703560\pi$
$853$	−5.85013	+	3.37757i	−0.200305	+	0.115646i	0.396493	+	0.918038i	$0.370227\pi$
$854$	34.3085			1.17401
$855$	−33.2131	−	8.61045i	−1.13586	−	0.294471i
$856$	−24.0955			−0.823569
$857$	5.87551	+	10.1767i	0.200704	+	0.347629i	0.948755	−	0.316012i	$-0.102344\pi$
$857$	5.87551	+	10.1767i	0.200704	+	0.347629i	−0.748052	+	0.663640i	$0.769011\pi$
$858$	−3.65028	+	4.92780i	−0.124619	+	0.168232i
$859$	−26.5699	+	46.0204i	−0.906552	+	1.57019i	−0.0877320	+	0.996144i	$0.527962\pi$
$859$	−26.5699	+	46.0204i	−0.906552	+	1.57019i	−0.818820	+	0.574050i	$0.805371\pi$
$860$	−1.09598	+	1.89829i	−0.0373726	+	0.0647313i
$861$	32.3109	+	24.5849i	1.10115	+	0.837850i
$862$	21.0440	+	36.4493i	0.716762	+	1.24147i
$863$		−	46.1145i		−	1.56976i	−0.619651	−	0.784878i	$-0.712726\pi$
$863$		−	46.1145i		−	1.56976i	0.619651	−	0.784878i	$-0.287274\pi$
$864$	10.5973	−	8.33902i	0.360528	−	0.283699i
$865$			43.1657i			1.46768i
$866$	−17.6962	−	30.6508i	−0.601342	−	1.04156i
$867$	−1.12651	+	1.48053i	−0.0382583	+	0.0502813i
$868$	−8.10743	−	4.68083i	−0.275184	−	0.158878i
$869$	−18.0523	−	30.3581i	−0.612382	−	1.02983i
$870$	1.61514	−	12.6661i	0.0547582	−	0.429420i
$871$	−1.62524	+	0.938332i	−0.0550691	+	0.0317942i
$872$			1.65621i			0.0560863i
$873$	22.1969	−	22.5610i	0.751250	−	0.763573i
$874$	−17.8545			−0.603939
$875$	24.6012	+	42.6105i	0.831672	+	1.44050i
$876$	8.38090	−	3.51149i	0.283164	−	0.118642i
$877$	40.8587	+	23.5898i	1.37970	+	0.796570i	0.992123	−	0.125267i	$-0.0399788\pi$
$877$	40.8587	+	23.5898i	1.37970	+	0.796570i	0.387577	+	0.921837i	$0.373312\pi$
$878$	12.8820	+	7.43745i	0.434748	+	0.251002i
$879$	−20.1746	−	48.1509i	−0.680473	−	1.62409i
$880$	19.4033	−	0.249819i	0.654086	−	0.00842140i
$881$		−	17.0910i		−	0.575812i	−0.957659	−	0.287906i	$-0.907041\pi$
$881$		−	17.0910i		−	0.575812i	0.957659	−	0.287906i	$-0.0929590\pi$
$882$	−10.1067	−	36.5275i	−0.340311	−	1.22995i
$883$	9.98172			0.335912			0.167956	−	0.985795i	$-0.446283\pi$
$883$	9.98172			0.335912			0.167956	+	0.985795i	$0.446283\pi$
$884$	1.49102	−	0.860841i	0.0501484	−	0.0289532i
$885$	−23.6947	−	3.02147i	−0.796489	−	0.101566i
$886$	27.4923	+	15.8727i	0.923621	+	0.533253i
$887$	9.31066	−	16.1265i	0.312621	−	0.541476i	−0.666308	−	0.745677i	$-0.732126\pi$
$887$	9.31066	−	16.1265i	0.312621	−	0.541476i	0.978929	+	0.204201i	$0.0654596\pi$
$888$	37.5324	−	49.3274i	1.25951	−	1.65532i
$889$	−36.9560	−	64.0096i	−1.23946	−	2.14681i
$890$	18.9732			0.635983
$891$	15.6718	+	25.4046i	0.525024	+	0.851088i
$892$	−2.17243			−0.0727385
$893$	4.62053	+	8.00300i	0.154620	+	0.267810i
$894$	−13.0254	+	17.1187i	−0.435633	+	0.572535i
$895$	−14.0331	+	24.3061i	−0.469076	+	0.812463i
$896$	−20.8812	−	12.0557i	−0.697591	−	0.402754i
$897$	3.85241	+	0.491246i	0.128628	+	0.0164022i
$898$	20.7875	−	12.0017i	0.693689	−	0.400502i
$899$	−13.9114			−0.463972
$900$	0.284965	+	1.02992i	0.00949883	+	0.0343305i
$901$			9.69773i			0.323078i
$902$	0.298481	+	23.1828i	0.00993832	+	0.771904i
$903$	6.29738	+	15.0300i	0.209564	+	0.500167i
$904$	−16.5260	−	9.54130i	−0.549647	−	0.317339i
$905$	12.2066	+	7.04749i	0.405761	+	0.234266i
$906$	22.5302	−	9.43985i	0.748515	−	0.313618i
$907$	18.9894	+	32.8906i	0.630532	+	1.09211i	0.987443	+	0.157975i	$0.0504966\pi$
$907$	18.9894	+	32.8906i	0.630532	+	1.09211i	−0.356911	+	0.934138i	$0.616170\pi$
$908$	−10.6715			−0.354146
$909$	−2.17686	+	2.21256i	−0.0722017	+	0.0733861i
$910$		−	9.12061i		−	0.302345i
$911$	13.6814	−	7.89896i	0.453285	−	0.261704i	−0.255931	−	0.966695i	$-0.582382\pi$
$911$	13.6814	−	7.89896i	0.453285	−	0.261704i	0.709217	+	0.704991i	$0.249049\pi$
$912$	−3.45685	+	27.1090i	−0.114468	+	0.897670i
$913$	17.6908	−	10.5197i	0.585479	−	0.348153i
$914$	−13.1123	−	7.57039i	−0.433716	−	0.250406i
$915$	14.4374	−	18.9745i	0.477286	−	0.627277i
$916$	0.841911	+	1.45823i	0.0278175	+	0.0481813i
$917$		−	34.2727i		−	1.13178i
$918$	3.89774	+	27.0513i	0.128645	+	0.892826i
$919$			45.4869i			1.50047i	0.661169	+	0.750237i	$0.270061\pi$
$919$			45.4869i			1.50047i	−0.661169	+	0.750237i	$0.729939\pi$
$920$	−8.17446	−	14.1586i	−0.269504	−	0.466794i
$921$	24.6401	+	18.7483i	0.811918	+	0.617776i
$922$	−20.2978	+	35.1569i	−0.668474	+	1.15783i
$923$	−0.587587	+	1.01773i	−0.0193407	+	0.0334990i
$924$	−6.65784	+	8.98794i	−0.219027	+	0.295681i
$925$	4.44505	+	7.69905i	0.146152	+	0.253143i
$926$	6.23734			0.204972
$927$	−22.7208	−	5.89035i	−0.746250	−	0.193464i
$928$	7.50885			0.246490
$929$	−46.6177	+	26.9147i	−1.52948	+	0.883044i	−0.530093	+	0.847940i	$0.677843\pi$
$929$	−46.6177	+	26.9147i	−1.52948	+	0.883044i	−0.999384	+	0.0351041i	$0.988824\pi$
$930$	19.5695	−	8.19938i	0.641711	−	0.268868i
$931$	−49.1116	−	28.3546i	−1.60957	−	0.929285i
$932$	4.38298	−	7.59155i	0.143569	−	0.248670i
$933$	43.4441	−	18.2025i	1.42230	−	0.595924i
$934$	−9.85847	+	5.69179i	−0.322579	+	0.186241i
$935$	14.1939	−	25.3321i	0.464189	−	0.828450i
$936$	1.98461	−	7.65523i	0.0648690	−	0.250219i
$937$		−	12.3751i		−	0.404276i	−0.979357	−	0.202138i	$-0.935211\pi$
$937$		−	12.3751i		−	0.404276i	0.979357	−	0.202138i	$-0.0647890\pi$
$938$	9.66766	−	5.58163i	0.315660	−	0.182247i
$939$	15.1326	+	1.92965i	0.493832	+	0.0629718i
$940$	−0.804146	+	1.39282i	−0.0262284	+	0.0454289i
$941$	14.1440	−	24.4982i	0.461082	−	0.798618i	−0.537933	−	0.842988i	$-0.680795\pi$
$941$	14.1440	−	24.4982i	0.461082	−	0.798618i	0.999015	+	0.0443696i	$0.0141279\pi$
$942$	4.94478	−	6.49873i	0.161110	−	0.211740i
$943$	12.7154	−	7.34123i	0.414070	−	0.239063i
$944$			19.0255i			0.619228i
$945$	−41.2189	−	16.4871i	−1.34085	−	0.536326i
$946$	−4.54872	+	8.11822i	−0.147892	+	0.263946i
$947$	−12.5955	+	7.27199i	−0.409297	+	0.236308i	−0.690488	−	0.723344i	$-0.742604\pi$
$947$	−12.5955	+	7.27199i	−0.409297	+	0.236308i	0.281190	+	0.959652i	$0.409271\pi$
$948$	6.88943	+	5.24206i	0.223758	+	0.170254i
$949$	4.82258	−	8.35295i	0.156547	−	0.271148i
$950$	−4.51609	−	2.60737i	−0.146521	−	0.0845942i
$951$	−2.46852	+	19.3584i	−0.0800474	+	0.627740i
$952$	−46.6643	+	26.9416i	−1.51240	+	0.873184i
$953$	7.80664			0.252882			0.126441	−	0.991974i	$-0.459645\pi$
$953$	7.80664			0.252882			0.126441	+	0.991974i	$0.459645\pi$
$954$	6.03521	+	5.93781i	0.195397	+	0.192244i
$955$	49.2138			1.59252
$956$	−4.93795	−	8.55278i	−0.159705	−	0.276617i
$957$	−1.89003	+	16.5135i	−0.0610959	+	0.533805i
$958$	8.63948	−	14.9640i	0.279129	−	0.483465i
$959$	−17.5343	+	30.3703i	−0.566212	+	0.980708i
$960$	−29.2562	+	12.2580i	−0.944239	+	0.395624i
$961$	3.94159	+	6.82703i	0.127148	+	0.220227i
$962$		−	12.5047i		−	0.403167i
$963$	6.30971	+	22.8044i	0.203327	+	0.734863i
$964$			0.477751i			0.0153873i
$965$	−15.5927	−	27.0074i	−0.501948	−	0.869399i
$966$	−22.9159	−	2.92216i	−0.737306	−	0.0940188i
$967$	−3.52549	−	2.03544i	−0.113372	−	0.0654554i	0.442242	−	0.896896i	$-0.354183\pi$
$967$	−3.52549	−	2.03544i	−0.113372	−	0.0654554i	−0.555614	+	0.831441i	$0.687517\pi$
$968$	−33.5945	+	0.865207i	−1.07977	+	0.0278088i
$969$	32.5448	+	24.7628i	1.04549	+	0.795497i
$970$	−23.2785	+	13.4398i	−0.747427	+	0.431527i
$971$		−	23.6225i		−	0.758084i	−0.925380	−	0.379042i	$-0.876254\pi$
$971$		−	23.6225i		−	0.758084i	0.925380	−	0.379042i	$-0.123746\pi$
$972$	−5.89371	−	4.33487i	−0.189041	−	0.139041i
$973$	−33.6608			−1.07911
$974$	−17.9074	−	31.0166i	−0.573791	−	0.993835i
$975$	0.902681	+	0.686836i	0.0289089	+	0.0219964i
$976$	−16.4462	−	9.49524i	−0.526431	−	0.303935i
$977$	−27.2616	−	15.7395i	−0.872175	−	0.503550i	−0.00410429	−	0.999992i	$-0.501306\pi$
$977$	−27.2616	−	15.7395i	−0.872175	−	0.503550i	−0.868070	+	0.496441i	$0.834640\pi$
$978$	−12.3358	−	1.57302i	−0.394455	−	0.0502995i
$979$	−24.6959	+	0.317961i	−0.789283	+	0.0101621i
$980$		−	9.86954i		−	0.315271i
$981$	1.56747	−	0.433698i	0.0500453	−	0.0138469i
$982$	23.8523			0.761156
$983$	28.3373	−	16.3606i	0.903821	−	0.521821i	0.0253828	−	0.999678i	$-0.491920\pi$
$983$	28.3373	−	16.3606i	0.903821	−	0.521821i	0.878438	+	0.477857i	$0.158586\pi$
$984$	−11.5539	−	27.5757i	−0.368324	−	0.879081i
$985$	−10.2476	−	5.91648i	−0.326517	−	0.188515i
$986$	−7.60932	+	13.1797i	−0.242330	+	0.419728i
$987$	4.62053	+	11.0279i	0.147073	+	0.351021i
$988$	−1.12453	−	1.94774i	−0.0357761	−	0.0619660i
$989$	5.89313			0.187390
$990$	−7.07428	−	24.3439i	−0.224835	−	0.773700i
$991$	34.5499			1.09751			0.548757	−	0.835982i	$-0.315101\pi$
$991$	34.5499			1.09751			0.548757	+	0.835982i	$0.315101\pi$
$992$	6.23879	+	10.8059i	0.198082	+	0.343087i
$993$	53.4720	+	6.81858i	1.69688	+	0.216381i
$994$	3.49524	−	6.05393i	0.110862	−	0.192019i
$995$	7.89778	+	4.55978i	0.250376	+	0.144555i
$996$	−3.05475	+	4.01473i	−0.0967933	+	0.127212i
$997$	22.3641	−	12.9119i	0.708277	−	0.408924i	−0.102146	−	0.994769i	$-0.532571\pi$
$997$	22.3641	−	12.9119i	0.708277	−	0.408924i	0.810423	+	0.585846i	$0.199237\pi$
$998$	−41.8887			−1.32596
$999$	−56.5126	−	22.6044i	−1.78798	−	0.715171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.g.b.32.5	yes	16
3.2	odd	2		297.2.g.b.98.4		16
9.2	odd	6	inner	99.2.g.b.65.4	yes	16
9.4	even	3		891.2.d.b.890.7		16
9.5	odd	6		891.2.d.b.890.10		16
9.7	even	3		297.2.g.b.197.5		16
11.10	odd	2	inner	99.2.g.b.32.4	✓	16
33.32	even	2		297.2.g.b.98.5		16
99.32	even	6		891.2.d.b.890.8		16
99.43	odd	6		297.2.g.b.197.4		16
99.65	even	6	inner	99.2.g.b.65.5	yes	16
99.76	odd	6		891.2.d.b.890.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.g.b.32.4	✓	16	11.10	odd	2	inner
99.2.g.b.32.5	yes	16	1.1	even	1	trivial
99.2.g.b.65.4	yes	16	9.2	odd	6	inner
99.2.g.b.65.5	yes	16	99.65	even	6	inner
297.2.g.b.98.4		16	3.2	odd	2
297.2.g.b.98.5		16	33.32	even	2
297.2.g.b.197.4		16	99.43	odd	6
297.2.g.b.197.5		16	9.7	even	3
891.2.d.b.890.7		16	9.4	even	3
891.2.d.b.890.8		16	99.32	even	6
891.2.d.b.890.9		16	99.76	odd	6
891.2.d.b.890.10		16	9.5	odd	6

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.618600 + 1.07145i) q^{2} +(-1.04881 + 1.37841i) q^{3} +(0.234668 - 0.406456i) q^{4} +(1.78348 + 1.02969i) q^{5} +(-2.12568 - 0.271060i) q^{6} +(-3.59283 + 2.07432i) q^{7} +3.05506 q^{8} +(-0.800005 - 2.89137i) q^{9} +O(q^{10})\)	\(q+(0.618600 + 1.07145i) q^{2} +(-1.04881 + 1.37841i) q^{3} +(0.234668 - 0.406456i) q^{4} +(1.78348 + 1.02969i) q^{5} +(-2.12568 - 0.271060i) q^{6} +(-3.59283 + 2.07432i) q^{7} +3.05506 q^{8} +(-0.800005 - 2.89137i) q^{9} +2.54787i q^{10} +(-0.0426982 - 3.31635i) q^{11} +(0.314140 + 0.749761i) q^{12} +(0.747261 + 0.431431i) q^{13} +(-4.44505 - 2.56635i) q^{14} +(-3.28985 + 1.37841i) q^{15} +(1.42053 + 2.46043i) q^{16} +4.25136 q^{17} +(2.60306 - 2.64576i) q^{18} -5.55362i q^{19} +(0.837047 - 0.483270i) q^{20} +(0.908931 - 7.12794i) q^{21} +(3.52688 - 2.09724i) q^{22} +(-2.25042 - 1.29928i) q^{23} +(-3.20417 + 4.21112i) q^{24} +(-0.379477 - 0.657274i) q^{25} +1.06753i q^{26} +(4.82453 + 1.92976i) q^{27} +1.94710i q^{28} +(1.44670 + 2.50575i) q^{29} +(-3.51199 - 2.67222i) q^{30} +(-2.40400 + 4.16385i) q^{31} +(1.29759 - 2.24748i) q^{32} +(4.61606 + 3.41936i) q^{33} +(2.62989 + 4.55511i) q^{34} -8.54363 q^{35} +(-1.36295 - 0.353343i) q^{36} -11.7136 q^{37} +(5.95041 - 3.43547i) q^{38} +(-1.37842 + 0.577540i) q^{39} +(5.44863 + 3.14577i) q^{40} +(-2.82512 + 4.89325i) q^{41} +(8.19947 - 3.43547i) q^{42} +(-1.96401 + 1.13392i) q^{43} +(-1.35797 - 0.760885i) q^{44} +(1.55042 - 5.98043i) q^{45} -3.21494i q^{46} +(-1.44104 + 0.831985i) q^{47} +(-4.88132 - 0.622450i) q^{48} +(5.10561 - 8.84317i) q^{49} +(0.469489 - 0.813180i) q^{50} +(-4.45886 + 5.86010i) q^{51} +(0.350716 - 0.202486i) q^{52} +2.28109i q^{53} +(0.916822 + 6.36297i) q^{54} +(3.33866 - 5.95859i) q^{55} +(-10.9763 + 6.33718i) q^{56} +(7.65514 + 5.82468i) q^{57} +(-1.78985 + 3.10012i) q^{58} +(5.79946 + 3.34832i) q^{59} +(-0.211760 + 1.66065i) q^{60} +(-5.78878 + 3.34215i) q^{61} -5.94845 q^{62} +(8.87190 + 8.72871i) q^{63} +8.89286 q^{64} +(0.888481 + 1.53889i) q^{65} +(-0.808167 + 7.06108i) q^{66} +(-1.08746 + 1.88354i) q^{67} +(0.997657 - 1.72799i) q^{68} +(4.15119 - 1.73929i) q^{69} +(-5.28509 - 9.15404i) q^{70} +1.36195i q^{71} +(-2.44406 - 8.83330i) q^{72} -11.1781i q^{73} +(-7.24604 - 12.5505i) q^{74} +(1.30399 + 0.166280i) q^{75} +(-2.25730 - 1.30325i) q^{76} +(7.03258 + 11.8265i) q^{77} +(-1.47149 - 1.11964i) q^{78} +(9.22261 - 5.32468i) q^{79} +5.85081i q^{80} +(-7.71999 + 4.62621i) q^{81} -6.99047 q^{82} +(3.10289 + 5.37436i) q^{83} +(-2.68390 - 2.04214i) q^{84} +(7.58220 + 4.37759i) q^{85} +(-2.42988 - 1.40289i) q^{86} +(-4.97125 - 0.633917i) q^{87} +(-0.130446 - 10.1317i) q^{88} -7.44670i q^{89} +(7.36681 - 2.03830i) q^{90} -3.57971 q^{91} +(-1.05620 + 0.609797i) q^{92} +(-3.21814 - 7.68076i) q^{93} +(-1.78286 - 1.02933i) q^{94} +(5.71851 - 9.90475i) q^{95} +(1.73703 + 4.14578i) q^{96} +(5.27494 + 9.13646i) q^{97} +12.6333 q^{98} +(-9.55462 + 2.77655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9	\( 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9} - 12 q^{11} + 12 q^{12} - 6 q^{14} - 30 q^{15} - 2 q^{16} + 36 q^{20} + 6 q^{22} + 12 q^{23} - 12 q^{25} + 18 q^{27} - 4 q^{31} + 18 q^{33} - 18 q^{36} - 28 q^{37} + 66 q^{38} - 54 q^{42} - 42 q^{45} - 30 q^{47} + 42 q^{48} + 10 q^{49} + 20 q^{55} - 120 q^{56} - 6 q^{58} - 36 q^{59} + 30 q^{60} + 40 q^{64} + 54 q^{66} + 8 q^{67} + 96 q^{69} + 24 q^{75} + 72 q^{77} - 42 q^{78} + 30 q^{81} + 12 q^{82} - 72 q^{86} - 6 q^{88} - 12 q^{91} + 18 q^{92} - 24 q^{93} - 4 q^{97} - 36 q^{99}+O(q^{100}) \) 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9 - 12 * q^11 + 12 * q^12 - 6 * q^14 - 30 * q^15 - 2 * q^16 + 36 * q^20 + 6 * q^22 + 12 * q^23 - 12 * q^25 + 18 * q^27 - 4 * q^31 + 18 * q^33 - 18 * q^36 - 28 * q^37 + 66 * q^38 - 54 * q^42 - 42 * q^45 - 30 * q^47 + 42 * q^48 + 10 * q^49 + 20 * q^55 - 120 * q^56 - 6 * q^58 - 36 * q^59 + 30 * q^60 + 40 * q^64 + 54 * q^66 + 8 * q^67 + 96 * q^69 + 24 * q^75 + 72 * q^77 - 42 * q^78 + 30 * q^81 + 12 * q^82 - 72 * q^86 - 6 * q^88 - 12 * q^91 + 18 * q^92 - 24 * q^93 - 4 * q^97 - 36 * q^99

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