LMFDB - Embedded newform 99.2.g.b.65.4

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			65.4
Root			$-0.618600 + 1.07145i$ of defining polynomial
Character	$\chi$	$=$	99.65
Dual form			99.2.g.b.32.4

$q$-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} +(2.85069 - 1.69515i) 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} +(0.0528262 + 4.10299i) 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} +(-5.32644 - 2.15152i) 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} +(5.60018 - 4.37606i) 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} +(13.7583 - 0.177139i) 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} +(-8.70905 + 5.17880i) 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} +(2.62074 + 9.59853i) 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

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

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	$-0.977440\pi$
$2$	−0.618600	+	1.07145i	−0.437416	+	0.757627i	0.560073	+	0.828443i	$0.310773\pi$
$3$	−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	−0.0450349	−	0.998985i	$-0.514340\pi$
$5$	1.78348	−	1.02969i	0.797594	−	0.460491i	0.842629	+	0.538494i	$0.181007\pi$
$6$	2.12568	−	0.271060i	0.867806	−	0.110660i
$7$	3.59283	+	2.07432i	1.35796	+	0.784019i	0.989349	−	0.145564i	$-0.0464996\pi$
$7$	3.59283	+	2.07432i	1.35796	+	0.784019i	0.368612	+	0.929583i	$0.379833\pi$
$8$	−3.05506			−1.08013
$9$	−0.800005	+	2.89137i	−0.266668	+	0.963788i
$10$			2.54787i			0.805706i
$11$	2.85069	−	1.69515i	0.859517	−	0.511108i
$11$	2.85069	−	1.69515i	0.859517	−	0.511108i
$12$	0.314140	−	0.749761i	0.0906845	−	0.216437i
$13$	−0.747261	+	0.431431i	−0.207253	+	0.119658i	−0.600034	−	0.799974i	$-0.704846\pi$
$13$	−0.747261	+	0.431431i	−0.207253	+	0.119658i	0.392781	+	0.919632i	$0.371513\pi$
$14$	−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	$-0.672414\pi$
$17$	−4.25136			−1.03111			−0.515553	+	0.856857i	$0.672414\pi$
$18$	−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
$22$	0.0528262	+	4.10299i	0.0112626	+	0.874760i
$23$	−2.25042	+	1.29928i	−0.469244	+	0.270918i	−0.715923	−	0.698179i	$-0.753994\pi$
$23$	−2.25042	+	1.29928i	−0.469244	+	0.270918i	0.246679	+	0.969097i	$0.420661\pi$
$24$	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	$-0.919909\pi$
$29$	−1.44670	+	2.50575i	−0.268645	+	0.465306i	0.699867	+	0.714273i	$0.253242\pi$
$30$	3.51199	−	2.67222i	0.641199	−	0.487879i
$31$	−2.40400	−	4.16385i	−0.431771	−	0.747849i	0.565255	−	0.824916i	$-0.308778\pi$
$31$	−2.40400	−	4.16385i	−0.431771	−	0.747849i	−0.997026	+	0.0770672i	$0.975444\pi$
$32$	−1.29759	−	2.24748i	−0.229383	−	0.397303i
$33$	−5.32644	−	2.15152i	−0.927214	−	0.374532i
$34$	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	$-0.0212164\pi$
$41$	2.82512	+	4.89325i	0.441209	+	0.764197i	−0.556570	+	0.830800i	$0.687883\pi$
$42$	8.19947	+	3.43547i	1.26521	+	0.530105i
$43$	1.96401	+	1.13392i	0.299509	+	0.172922i	0.642222	−	0.766518i	$-0.278013\pi$
$43$	1.96401	+	1.13392i	0.299509	+	0.172922i	−0.342713	+	0.939440i	$0.611346\pi$
$44$	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	0.391206	−	0.920303i	$-0.372058\pi$
$47$	−1.44104	−	0.831985i	−0.210197	−	0.121358i	−0.601403	+	0.798946i	$0.705391\pi$
$48$	−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	$-0.949925\pi$
$53$		−	2.28109i		−	0.313331i	0.987652	−	0.156666i	$-0.0500745\pi$
$54$	−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	−0.0724816	−	0.997370i	$-0.523092\pi$
$59$	5.79946	−	3.34832i	0.755025	−	0.435914i	0.827507	+	0.561456i	$0.189759\pi$
$60$	−0.211760	−	1.66065i	−0.0273381	−	0.214389i
$61$	5.78878	+	3.34215i	0.741177	+	0.427919i	0.822497	−	0.568769i	$-0.192580\pi$
$61$	5.78878	+	3.34215i	0.741177	+	0.427919i	−0.0813198	+	0.996688i	$0.525914\pi$
$62$	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
$66$	5.60018	−	4.37606i	0.689334	−	0.538656i
$67$	−1.08746	−	1.88354i	−0.132855	−	0.230111i	0.791921	−	0.610623i	$-0.209081\pi$
$67$	−1.08746	−	1.88354i	−0.132855	−	0.230111i	−0.924776	+	0.380512i	$0.875748\pi$
$68$	−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	$-0.974247\pi$
$71$		−	1.36195i		−	0.161634i	0.996729	−	0.0808168i	$-0.0257529\pi$
$72$	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
$77$	13.7583	−	0.177139i	1.56791	−	0.0201869i
$78$	−1.47149	+	1.11964i	−0.166614	+	0.126774i
$79$	−9.22261	−	5.32468i	−1.03762	−	0.599073i	−0.118465	−	0.992958i	$-0.537797\pi$
$79$	−9.22261	−	5.32468i	−1.03762	−	0.599073i	−0.919160	+	0.393885i	$0.871131\pi$
$80$		−	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	$-0.943959\pi$
$83$	−3.10289	+	5.37436i	−0.340586	+	0.589913i	0.643955	+	0.765063i	$0.277292\pi$
$84$	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
$88$	−8.70905	+	5.17880i	−0.928388	+	0.552062i
$89$			7.44670i			0.789349i	0.918821	+	0.394674i	$0.129143\pi$
$89$			7.44670i			0.789349i	−0.918821	+	0.394674i	$0.870857\pi$
$90$	−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	−0.463546	−	0.886073i	$-0.653423\pi$
$97$	5.27494	−	9.13646i	0.535589	−	0.927667i	0.999135	−	0.0415940i	$-0.0132436\pi$
$98$	−12.6333			−1.27616
$99$	2.62074	+	9.59853i	0.263394	+	0.964688i
$100$	−0.356204			−0.0356204
$101$	0.517315	−	0.896016i	0.0514748	−	0.0891569i	−0.839140	−	0.543916i	$-0.816941\pi$
$101$	0.517315	−	0.896016i	0.0514748	−	0.0891569i	0.890615	+	0.454759i	$0.150274\pi$
$102$	−9.03704	+	1.15237i	−0.894801	+	0.114102i
$103$	3.91199	+	6.77576i	0.385460	+	0.667636i	0.991833	−	0.127544i	$-0.0407095\pi$
$103$	3.91199	+	6.77576i	0.385460	+	0.667636i	−0.606373	+	0.795180i	$0.707376\pi$
$104$	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	$-0.375498\pi$
$107$	7.88709			0.762473			0.381237	+	0.924477i	$0.375498\pi$
$108$	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	$0.991735\pi$
$110$	4.31902	+	7.26319i	0.411803	+	0.692518i
$111$	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	−0.732370	−	0.680907i	$-0.761586\pi$
$113$	−5.40938	+	3.12311i	−0.508872	+	0.293797i	0.223498	+	0.974704i	$0.428252\pi$
$114$	−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
$121$	5.25291	−	9.66472i	0.477538	−	0.878611i
$122$	−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	$-0.0491391\pi$
$131$	4.13059	+	7.15440i	0.360892	+	0.625083i	−0.627216	+	0.778845i	$0.715806\pi$
$132$	−0.375442	−	2.66986i	−0.0326780	−	0.232381i
$133$	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	0.778982	−	0.627046i	$-0.215736\pi$
$137$	7.32054	+	4.22652i	0.625436	+	0.361096i	−0.153546	+	0.988141i	$0.549069\pi$
$138$	−4.43149	+	3.37185i	−0.377233	+	0.287031i
$139$	−7.02666	+	4.05684i	−0.595993	+	0.344097i	−0.767464	−	0.641092i	$-0.778482\pi$
$139$	−7.02666	+	4.05684i	−0.595993	+	0.344097i	0.171470	+	0.985189i	$0.445148\pi$
$140$	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	$-0.301549\pi$
$149$	−5.01907	−	8.69329i	−0.411179	−	0.712182i	−0.995019	+	0.0996863i	$0.968216\pi$
$150$	−0.628487	+	1.50002i	−0.0513158	+	0.122476i
$151$	9.87222	+	5.69973i	0.803390	+	0.463838i	0.844655	−	0.535311i	$-0.179805\pi$
$151$	9.87222	+	5.69973i	0.803390	+	0.463838i	−0.0412650	+	0.999148i	$0.513139\pi$
$152$			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	0.779921	−	0.625878i	$-0.215259\pi$
$157$	−1.90538	−	3.30021i	−0.152066	−	0.263386i	−0.931987	+	0.362492i	$0.881926\pi$
$158$	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
$165$	−11.7150	+	1.64739i	−0.912009	+	0.128249i
$166$	−3.83889	−	6.64916i	−0.297956	−	0.516075i
$167$	−2.80467	−	4.85783i	−0.217032	−	0.375910i	0.736868	−	0.676037i	$-0.236304\pi$
$167$	−2.80467	−	4.85783i	−0.217032	−	0.375910i	−0.953899	+	0.300127i	$0.902971\pi$
$168$	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	0.124891	+	0.992171i	$0.460142\pi$
$173$	−10.4803	+	18.1523i	−0.796800	+	1.38010i	−0.921690	+	0.387927i	$0.873191\pi$
$174$	−2.39601	+	5.71857i	−0.181641	+	0.433524i
$175$	−2.72679	+	1.57431i	−0.206126	+	0.119007i
$176$	−0.121308	−	9.42193i	−0.00914393	−	0.710205i
$177$	−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	$-0.829897\pi$
$179$		−	13.6285i		−	1.01864i	0.860577	−	0.509321i	$-0.170103\pi$
$180$	−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
$187$	−12.1193	+	7.20671i	−0.886254	+	0.527007i
$188$		−	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	0.999996	−	0.00288872i	$-0.000919510\pi$
$191$	20.6958	+	11.9487i	1.49749	+	0.864577i	0.497496	+	0.867466i	$0.334253\pi$
$192$	−9.32690	−	12.2580i	−0.673111	−	0.884642i
$193$	13.1143	−	7.57157i	0.943991	−	0.545013i	0.0527816	−	0.998606i	$-0.483191\pi$
$193$	13.1143	−	7.57157i	0.943991	−	0.545013i	0.891209	+	0.453593i	$0.149858\pi$
$194$	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	$-0.434382\pi$
$197$	5.74588			0.409377			0.204689	+	0.978827i	$0.434382\pi$
$198$	−11.9055	−	3.12967i	−0.846087	−	0.222416i
$199$	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
$209$	−9.41424	−	15.8317i	−0.651196	−	1.09510i
$210$	18.1610	−	2.31583i	1.25323	−	0.159808i
$211$	−10.1616	+	5.86680i	−0.699553	+	0.403887i	−0.807181	−	0.590304i	$-0.799008\pi$
$211$	−10.1616	+	5.86680i	−0.699553	+	0.403887i	0.107628	+	0.994191i	$0.465674\pi$
$212$	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
$220$	3.20538	−	0.0412695i	0.216107	−	0.00278239i
$221$	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	−0.933052	−	0.359740i	$-0.882865\pi$
$223$	−2.31437	+	4.00861i	−0.154982	+	0.268437i	0.778071	+	0.628177i	$0.216199\pi$
$224$		−	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	−0.191018	−	0.981587i	$-0.561179\pi$
$227$	11.3687	−	19.6912i	0.754570	−	1.30695i	0.945588	−	0.325367i	$-0.105488\pi$
$228$	−4.16389	−	1.74462i	−0.275760	−	0.115540i
$229$	−1.79384	−	3.10702i	−0.118540	−	0.205318i	0.800649	−	0.599133i	$-0.204488\pi$
$229$	−1.79384	−	3.10702i	−0.118540	−	0.205318i	−0.919189	+	0.393816i	$0.871155\pi$
$230$	−3.31039	−	5.73376i	−0.218280	−	0.378073i
$231$	−14.6740	−	18.7788i	−0.965480	−	1.23555i
$232$	4.41975	−	7.65523i	0.290171	−	0.502590i
$233$	−18.6774			−1.22360			−0.611799	−	0.791013i	$-0.709554\pi$
$233$	−18.6774			−1.22360			−0.611799	+	0.791013i	$0.709554\pi$
$234$	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	−0.974811	−	0.223033i	$-0.928404\pi$
$239$	−10.5212	−	18.2232i	−0.680557	−	1.17876i	0.294254	−	0.955727i	$-0.404929\pi$
$240$	−8.06479	+	6.13638i	−0.520580	+	0.396101i
$241$	0.881555	+	0.508966i	0.0567860	+	0.0327854i	0.528124	−	0.849167i	$-0.322896\pi$
$241$	0.881555	+	0.508966i	0.0567860	+	0.0327854i	−0.471338	+	0.881953i	$0.656229\pi$
$242$	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	$-0.657333\pi$
$251$		−	27.8935i		−	1.76062i	0.474396	−	0.880312i	$-0.342667\pi$
$252$	−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	0.456393	−	0.889778i	$-0.349141\pi$
$257$	23.3280	−	13.4684i	1.45516	−	0.840137i	0.998767	+	0.0496416i	$0.0158079\pi$
$258$	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	−0.439523	−	0.898231i	$-0.644852\pi$
$263$	9.05134	−	15.6774i	0.558130	−	0.966709i	0.997653	−	0.0684777i	$-0.0218142\pi$
$264$	16.2726	+	6.57304i	1.00151	+	0.404543i
$265$	−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	$-0.878423\pi$
$269$		−	12.2263i		−	0.745451i	0.927942	−	0.372726i	$-0.121577\pi$
$270$	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
$275$	0.0324060	+	2.51696i	0.00195416	+	0.151778i
$276$	0.267202	+	2.09543i	0.0160837	+	0.126130i
$277$	25.7169	+	14.8477i	1.54518	+	0.892110i	0.998499	+	0.0547699i	$0.0174425\pi$
$277$	25.7169	+	14.8477i	1.54518	+	0.892110i	0.546682	+	0.837341i	$0.315891\pi$
$278$		−	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	$-0.808481\pi$
$281$	1.30747	−	2.26461i	0.0779973	−	0.135095i	0.902386	+	0.430929i	$0.141814\pi$
$282$	−3.28871	−	1.37793i	−0.195840	−	0.0820544i
$283$	−1.80894	+	1.04439i	−0.107530	+	0.0620827i	−0.552801	−	0.833314i	$-0.686441\pi$
$283$	−1.80894	+	1.04439i	−0.107530	+	0.0620827i	0.445270	+	0.895396i	$0.353108\pi$
$284$	0.553572	−	0.319605i	0.0328485	−	0.0189651i
$285$	−7.65514	+	18.2706i	−0.453452	+	1.08226i
$286$	−1.80963	−	3.04321i	−0.107006	−	0.179949i
$287$			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	0.850850	+	0.525409i	$0.176088\pi$
$293$	15.0707	+	26.1033i	0.880442	+	1.52497i	0.0295925	+	0.999562i	$0.490579\pi$
$294$	13.2499	+	17.4138i	0.772751	+	1.01560i
$295$	6.89546	−	11.9433i	0.401469	−	0.695365i
$296$	35.7858			2.08001
$297$	10.4820	−	13.6794i	0.608228	−	0.793762i
$298$	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	$-0.170396\pi$
$308$	3.30064	+	5.55059i	0.188071	+	0.316274i
$309$	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	−0.986135	−	0.165943i	$-0.946933\pi$
$311$	−23.5517	+	13.5976i	−1.33549	+	0.771047i	−0.349357	+	0.936990i	$0.613600\pi$
$312$	−4.21116	−	1.76442i	−0.238410	−	0.0998907i
$313$	−4.40376	+	7.62754i	−0.248915	+	0.431134i	−0.963225	−	0.268695i	$-0.913407\pi$
$313$	−4.40376	+	7.62754i	−0.248915	+	0.431134i	0.714310	+	0.699830i	$0.246741\pi$
$314$	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	0.748332	−	0.663325i	$-0.230855\pi$
$317$	9.75760	+	5.63355i	0.548041	+	0.316412i	−0.200290	+	0.979737i	$0.564189\pi$
$318$	−0.618311	−	4.84886i	−0.0346732	−	0.271911i
$319$	0.123543	+	9.59550i	0.00691706	+	0.537245i
$320$	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
$330$	5.48179	−	13.5710i	0.301763	−	0.747062i
$331$	−15.5610	+	26.9525i	−0.855312	+	1.48144i	0.0210431	+	0.999779i	$0.493301\pi$
$331$	−15.5610	+	26.9525i	−0.855312	+	1.48144i	−0.876355	+	0.481665i	$0.840032\pi$
$332$	−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	−0.711550	+	0.702636i	$0.752006\pi$
$337$	−30.7641	+	17.7616i	−1.67582	+	0.967538i	−0.964275	+	0.264902i	$0.914660\pi$
$338$	−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	$-0.0776838\pi$
$347$	5.13984	+	8.90247i	0.275921	+	0.477910i	−0.694446	+	0.719545i	$0.744350\pi$
$348$	1.42425	+	1.87183i	0.0763478	+	0.100341i
$349$	15.7643	+	9.10150i	0.843841	+	0.487192i	0.858568	−	0.512699i	$-0.171354\pi$
$349$	15.7643	+	9.10150i	0.843841	+	0.487192i	−0.0147267	+	0.999892i	$0.504688\pi$
$350$		−	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	0.346439	−	0.938073i	$-0.387391\pi$
$353$	−5.50002	−	3.17544i	−0.292737	−	0.169012i	−0.639175	+	0.769061i	$0.720724\pi$
$354$	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	$-0.492617\pi$
$359$	0.878883			0.0463857			0.0231928	+	0.999731i	$0.492617\pi$
$360$	−4.73663	−	18.2706i	−0.249643	−	0.962945i
$361$	−11.8427			−0.623301
$362$	−4.23387	+	7.33329i	−0.222527	+	0.385429i
$363$	−18.8312	+	2.89579i	−0.988382	+	0.151990i
$364$	−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	−0.721394	−	0.692524i	$-0.756498\pi$
$367$	4.57947	−	7.93188i	0.239047	−	0.414041i	0.960441	+	0.278484i	$0.0898318\pi$
$368$			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	$-0.578608\pi$
$373$	9.13656	−	5.27499i	0.473073	−	0.273129i	0.717525	+	0.696533i	$0.245275\pi$
$374$	−0.224583	−	17.4433i	−0.0116129	−	0.901971i
$375$	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	0.248045	−	0.968749i	$-0.420212\pi$
$383$	23.7003	−	13.6834i	1.21103	−	0.699187i	0.962983	+	0.269561i	$0.0868787\pi$
$384$	9.98565	−	1.27334i	0.509578	−	0.0649797i
$385$	24.3553	−	14.4828i	1.24126	−	0.738109i
$386$			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	0.202708	−	0.979239i	$-0.435026\pi$
$389$	−10.7290	−	6.19442i	−0.543984	−	0.314069i	−0.746692	+	0.665170i	$0.768359\pi$
$390$	−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
$396$	−3.28638	+	3.31768i	−0.165147	+	0.166720i
$397$	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	−0.487394	−	0.873182i	$-0.662053\pi$
$401$	0.502760	−	0.290268i	0.0251066	−	0.0144953i	0.512501	+	0.858687i	$0.328719\pi$
$402$	−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
$407$	−33.3919	+	19.8564i	−1.65518	+	0.984243i
$408$	−13.6221	−	17.9030i	−0.674395	−	0.886330i
$409$	−7.43480	+	4.29248i	−0.367627	+	0.212250i	−0.672421	−	0.740169i	$-0.734746\pi$
$409$	−7.43480	+	4.29248i	−0.367627	+	0.212250i	0.304794	+	0.952418i	$0.401412\pi$
$410$	−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
$418$	22.7865	−	0.293377i	1.11452	−	0.0143495i
$419$	−2.88622	+	1.66636i	−0.141001	+	0.0814070i	−0.568841	−	0.822447i	$-0.692608\pi$
$419$	−2.88622	+	1.66636i	−0.141001	+	0.0814070i	0.427840	+	0.903855i	$0.359275\pi$
$420$	2.68390	−	6.40568i	0.130961	−	0.312565i
$421$	0.811147	−	1.40495i	0.0395329	−	0.0684730i	−0.845582	−	0.533846i	$-0.820746\pi$
$421$	0.811147	−	1.40495i	0.0395329	−	0.0684730i	0.885115	+	0.465373i	$0.154080\pi$
$422$		−	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
$429$	4.90847	−	0.690243i	0.236983	−	0.0333252i
$430$	−2.88908	+	5.00404i	−0.139324	+	0.241316i
$431$	−34.0188			−1.63863			−0.819313	−	0.573347i	$-0.805645\pi$
$431$	−34.0188			−1.63863			−0.819313	+	0.573347i	$0.805645\pi$
$432$	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	$-0.425963\pi$
$439$	−10.4122	−	6.01151i	−0.496949	−	0.286914i	−0.727453	+	0.686158i	$0.759296\pi$
$440$	−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	0.924259	−	0.381766i	$-0.124684\pi$
$443$	22.2214	+	12.8295i	1.05577	+	0.609548i	0.131510	+	0.991315i	$0.458017\pi$
$444$	−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	$0.151364\pi$
$449$			19.4014i			0.915608i	−0.889053	+	0.457804i	$0.848636\pi$
$450$	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	$-0.240930\pi$
$457$	10.5984	+	6.11897i	0.495770	+	0.286233i	−0.231195	+	0.972907i	$0.574263\pi$
$458$	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	0.176596	+	0.984283i	$0.443491\pi$
$461$	−16.4063	+	28.4165i	−0.764116	+	1.32349i	−0.940713	+	0.339205i	$0.889842\pi$
$462$	29.1978	−	4.10588i	1.35841	−	0.191023i
$463$	2.52075	+	4.36606i	0.117149	+	0.202908i	0.918637	−	0.395103i	$-0.129291\pi$
$463$	2.52075	+	4.36606i	0.117149	+	0.202908i	−0.801488	+	0.598011i	$0.795958\pi$
$464$	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	$-0.931713\pi$
$467$		−	9.20108i		−	0.425775i	0.977077	−	0.212888i	$-0.0682868\pi$
$468$	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
$473$	7.52097	−	0.0968329i	0.345814	−	0.00445238i
$474$	−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	$-0.729964\pi$
$479$	6.98309	−	12.0951i	0.319065	−	0.552637i	0.980293	+	0.197548i	$0.0632977\pi$
$480$	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
$484$	5.16097	−	0.132918i	0.234590	−	0.00604171i
$485$		−	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	$-0.309929\pi$
$491$	−9.63961	−	16.6963i	−0.435029	−	0.753493i	−0.997298	+	0.0734617i	$0.976595\pi$
$492$	4.55625	−	0.580998i	0.205412	−	0.0261934i
$493$	6.15043	−	10.6529i	0.277001	−	0.479781i
$494$	−5.92868			−0.266744
$495$	14.5575	+	14.4202i	0.654312	+	0.648139i
$496$	−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	−0.943951	−	0.330086i	$-0.892922\pi$
$499$	−16.9288	−	29.3216i	−0.757838	−	1.31261i	0.186112	−	0.982528i	$-0.440411\pi$
$500$	−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	$-0.528522\pi$
$503$	−4.01382			−0.178967			−0.0894836	+	0.995988i	$0.528522\pi$
$504$	27.1042	−	26.6668i	1.20732	−	1.18783i
$505$		−	2.13070i		−	0.0948148i
$506$	−5.44981	−	9.16480i	−0.242274	−	0.407425i
$507$	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	−0.426474	−	0.904500i	$-0.640245\pi$
$509$	3.23995	−	1.87059i	0.143608	−	0.0829123i	0.570083	+	0.821587i	$0.306911\pi$
$510$	−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
$517$	−5.51831	+	0.0710486i	−0.242695	+	0.00312471i
$518$	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	$0.0941903\pi$
$521$			13.3122i			0.583216i	−0.956538	+	0.291608i	$0.905810\pi$
$522$	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
$528$	−12.8600	+	10.0490i	−0.559660	+	0.437327i
$529$	−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	$-0.473164\pi$
$547$	−17.2285	−	9.94686i	−0.736636	−	0.425297i	−0.820845	+	0.571151i	$0.806497\pi$
$548$			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	$-0.541257\pi$
$557$	−6.10079			−0.258499			−0.129249	+	0.991612i	$0.541257\pi$
$558$	−4.75879	+	17.1992i	−0.201456	+	0.728098i
$559$	−1.95684			−0.0827655
$560$	12.1365	−	21.0210i	0.512859	−	0.888297i
$561$	22.6446	+	9.14691i	0.956057	+	0.386183i
$562$	1.61761	+	2.80177i	0.0682346	+	0.118186i
$563$	−0.00492939	−	0.00853795i	−0.000207749	−	0.000359832i	0.865922	−	0.500180i	$-0.166733\pi$
$563$	−0.00492939	−	0.00853795i	−0.000207749	−	0.000359832i	−0.866129	+	0.499820i	$0.833399\pi$
$564$	−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	$-0.787076\pi$
$569$	3.45428	−	5.98299i	0.144811	−	0.250820i	0.929302	+	0.369320i	$0.120409\pi$
$570$	−14.8405	−	19.5043i	−0.621600	−	0.816944i
$571$	16.6286	−	9.60053i	0.695886	−	0.401770i	−0.109927	−	0.993940i	$-0.535062\pi$
$571$	16.6286	−	9.60053i	0.695886	−	0.401770i	0.805813	+	0.592170i	$0.201729\pi$
$572$	−1.34303	+	0.0172916i	−0.0561548	+	0.000722997i
$573$	−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
$583$	−3.86679	−	6.50268i	−0.160146	−	0.269314i
$584$			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	−0.999310	−	0.0371404i	$-0.988175\pi$
$587$	−37.0963	−	21.4176i	−1.53113	−	0.883998i	−0.531820	−	0.846858i	$-0.678492\pi$
$588$	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	$-0.352716\pi$
$593$	21.7398			0.892745			0.446373	+	0.894847i	$0.352716\pi$
$594$	8.17263	+	19.6930i	0.335327	+	0.808015i
$595$	−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	−0.678183	−	0.734893i	$-0.737232\pi$
$599$	−9.32083	+	5.38138i	−0.380839	+	0.219877i	0.297344	+	0.954770i	$0.403899\pi$
$600$	−3.98377	+	0.507997i	−0.162637	+	0.0207389i
$601$	−22.6605	−	13.0831i	−0.924343	−	0.533670i	−0.0393250	−	0.999226i	$-0.512521\pi$
$601$	−22.6605	−	13.0831i	−0.924343	−	0.533670i	−0.885018	+	0.465557i	$0.845854\pi$
$602$	−11.6402			−0.474418
$603$	6.31599	−	1.63741i	0.257207	−	0.0666806i
$604$			5.35017i			0.217695i
$605$	−0.583225	−	22.6457i	−0.0237115	−	0.920677i
$606$	0.856773	−	2.04487i	0.0348040	−	0.0830671i
$607$	16.9909	−	9.80971i	0.689640	−	0.398164i	−0.113837	−	0.993499i	$-0.536314\pi$
$607$	16.9909	−	9.80971i	0.689640	−	0.398164i	0.803477	+	0.595335i	$0.202981\pi$
$608$	−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
$616$	−42.0326	+	0.541172i	−1.69354	+	0.0218044i
$617$	16.5667	−	9.56478i	0.666950	−	0.385064i	−0.127970	−	0.991778i	$-0.540846\pi$
$617$	16.5667	−	9.56478i	0.666950	−	0.385064i	0.794920	+	0.606714i	$0.207513\pi$
$618$	10.1523	+	13.3427i	0.408385	+	0.536723i
$619$	−16.6869	+	28.9026i	−0.670704	+	1.16169i	0.307001	+	0.951709i	$0.400675\pi$
$619$	−16.6869	+	28.9026i	−0.670704	+	1.16169i	−0.977705	+	0.209984i	$0.932659\pi$
$620$		−	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
$627$	−11.9488	+	29.5810i	−0.477187	+	1.18135i
$628$	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	0.890606	−	0.454776i	$-0.150281\pi$
$641$	23.8511	+	13.7704i	0.942062	+	0.543900i	0.0514559	+	0.998675i	$0.483614\pi$
$642$	16.7654	−	2.13787i	0.661679	−	0.0843751i
$643$	−20.3147	−	35.1861i	−0.801133	−	1.38760i	−0.918871	−	0.394558i	$-0.870898\pi$
$643$	−20.3147	−	35.1861i	−0.801133	−	1.38760i	0.117738	−	0.993045i	$-0.462436\pi$
$644$	−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	$-0.733436\pi$
$647$		−	37.7946i		−	1.48586i	0.669371	−	0.742929i	$-0.266564\pi$
$648$	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	−0.982434	−	0.186610i	$-0.940250\pi$
$653$	−33.5277	+	19.3573i	−1.31204	+	0.757508i	−0.329608	+	0.944118i	$0.606917\pi$
$654$	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	−0.372706	−	0.927949i	$-0.621570\pi$
$659$	15.8461	−	27.4462i	0.617275	−	1.06915i	0.989981	−	0.141202i	$-0.0450967\pi$
$660$	−3.41872	−	4.37503i	−0.133073	−	0.170298i
$661$	13.4387	+	23.2766i	0.522706	+	0.905353i	0.999651	+	0.0264199i	$0.00841069\pi$
$661$	13.4387	+	23.2766i	0.522706	+	0.905353i	−0.476945	+	0.878933i	$0.658256\pi$
$662$	−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
$671$	22.1675	−	0.285408i	0.855767	−	0.0110181i
$672$	−14.8405	+	11.2919i	−0.572485	+	0.435595i
$673$	−14.7738	−	8.52968i	−0.569490	−	0.328795i	0.187456	−	0.982273i	$-0.439976\pi$
$673$	−14.7738	−	8.52968i	−0.569490	−	0.328795i	−0.756946	+	0.653478i	$0.773309\pi$
$674$		−	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	$-0.851150\pi$
$677$	−1.45562	+	2.52120i	−0.0559439	+	0.0968978i	0.836697	+	0.547666i	$0.184483\pi$
$678$	−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
$682$	16.9572	−	10.0835i	0.649326	−	0.386119i
$683$		−	20.5133i		−	0.784918i	−0.919770	−	0.392459i	$-0.871625\pi$
$683$		−	20.5133i		−	0.784918i	0.919770	−	0.392459i	$-0.128375\pi$
$684$	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	−0.936439	−	0.350830i	$-0.885900\pi$
$691$	−4.32135	+	7.48480i	−0.164392	+	0.284735i	0.772047	+	0.635565i	$0.219233\pi$
$692$	−9.83751			−0.373966
$693$	−10.4946	+	39.9221i	−0.398655	+	1.51652i
$694$	−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	$-0.694163\pi$
$701$	−30.3341			−1.14570			−0.572852	+	0.819659i	$0.694163\pi$
$702$	−2.06008	−	5.15034i	−0.0777527	−	0.194387i
$703$			65.0530i			2.45352i
$704$	25.3508	−	15.0747i	0.955445	−	0.568151i
$705$	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	−0.881421	−	0.472332i	$-0.843412\pi$
$709$	−0.842981	+	1.46009i	−0.0316588	+	0.0548347i	0.849762	+	0.527167i	$0.176746\pi$
$710$	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
$715$	0.0758731	+	5.89303i	0.00283749	+	0.220387i
$716$	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	$0.108023\pi$
$719$			17.8522i			0.665775i	−0.942967	+	0.332887i	$0.891977\pi$
$720$	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
$726$	8.54630	−	21.9680i	0.317183	−	0.815308i
$727$	−13.8248	+	23.9453i	−0.512734	+	0.888081i	0.487157	+	0.873314i	$0.338034\pi$
$727$	−13.8248	+	23.9453i	−0.512734	+	0.888081i	−0.999891	+	0.0147668i	$0.995299\pi$
$728$	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	$-0.586789\pi$
$733$	11.6445	−	6.72297i	0.430100	−	0.248318i	0.699389	+	0.714741i	$0.253455\pi$
$734$	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	$-0.219858\pi$
$743$	−4.53380	−	7.85278i	−0.166329	−	0.288090i	−0.937126	+	0.348990i	$0.886525\pi$
$744$	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	0.964850	−	0.262802i	$-0.0846467\pi$
$751$	6.98349	+	12.0958i	0.254831	+	0.441381i	−0.710018	+	0.704183i	$0.751313\pi$
$752$	−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
$759$	14.7821	−	2.07870i	0.536558	−	0.0754521i
$760$	17.4704	+	30.2596i	0.633718	+	1.09763i
$761$	8.01546	+	13.8832i	0.290560	+	0.503265i	0.973942	−	0.226796i	$-0.0728250\pi$
$761$	8.01546	+	13.8832i	0.290560	+	0.503265i	−0.683382	+	0.730061i	$0.739492\pi$
$762$	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	$-0.616801\pi$
$769$	7.49374	−	4.32651i	0.270231	−	0.156018i	0.628993	+	0.777411i	$0.283468\pi$
$770$	0.451328	+	35.0544i	0.0162647	+	1.26327i
$771$	−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	$0.0529248\pi$
$773$			9.20292i			0.331006i	−0.986209	+	0.165503i	$0.947075\pi$
$774$	−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
$781$	−2.30871	−	3.88250i	−0.0826122	−	0.138927i
$782$			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	$-0.411003\pi$
$787$	34.9642	−	20.1866i	1.24634	−	0.719575i	0.970378	+	0.241593i	$0.0776699\pi$
$788$	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
$792$	−8.00652	−	29.3241i	−0.284499	−	1.04199i
$793$	−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	−0.510134	−	0.860095i	$-0.670404\pi$
$797$	−0.574131	+	0.331475i	−0.0203368	+	0.0117414i	0.489797	+	0.871836i	$0.337071\pi$
$798$	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
$803$	−18.9486	−	31.8653i	−0.668680	−	1.12450i
$804$	−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	$-0.876347\pi$
$809$	−52.6473			−1.85098			−0.925490	+	0.378772i	$0.876347\pi$
$810$	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
$814$	−0.618786	−	48.0608i	−0.0216884	−	1.68453i
$815$	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	$-0.781886\pi$
$821$	4.61093	−	7.98637i	0.160923	−	0.278726i	0.935200	+	0.354120i	$0.115220\pi$
$822$	16.7068	+	6.99992i	0.582716	+	0.244150i
$823$	−2.85199	−	4.93978i	−0.0994140	−	0.172190i	0.812028	−	0.583618i	$-0.198363\pi$
$823$	−2.85199	−	4.93978i	−0.0994140	−	0.172190i	−0.911442	+	0.411428i	$0.865030\pi$
$824$	−11.9514	−	20.7004i	−0.416346	−	0.721132i
$825$	3.43540	−	2.68447i	0.119605	−	0.0934614i
$826$	−17.1859	+	29.7669i	−0.597974	+	1.03572i
$827$	35.5680			1.23682			0.618411	−	0.785855i	$-0.287777\pi$
$827$	35.5680			1.23682			0.618411	+	0.785855i	$0.287777\pi$
$828$	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	0.919793	−	0.392403i	$-0.128356\pi$
$839$	30.1200	+	17.3898i	1.03986	+	0.600363i	0.120066	+	0.992766i	$0.461689\pi$
$840$	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	$-0.296440\pi$
$853$	5.85013	+	3.37757i	0.200305	+	0.115646i	−0.396493	+	0.918038i	$0.629773\pi$
$854$	−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	$-0.897656\pi$
$857$	−5.87551	+	10.1767i	−0.200704	+	0.347629i	0.748052	+	0.663640i	$0.230989\pi$
$858$	−2.29682	+	5.68615i	−0.0784123	+	0.194122i
$859$	−26.5699	−	46.0204i	−0.906552	−	1.57019i	−0.818820	−	0.574050i	$-0.805371\pi$
$859$	−26.5699	−	46.0204i	−0.906552	−	1.57019i	−0.0877320	−	0.996144i	$-0.527962\pi$
$860$	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	$0.287274\pi$
$863$			46.1145i			1.56976i	−0.619651	+	0.784878i	$0.712726\pi$
$864$	−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
$869$	−35.3170	+	0.454708i	−1.19805	+	0.0154249i
$870$	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	$-0.960021\pi$
$877$	−40.8587	+	23.5898i	−1.37970	+	0.796570i	−0.387577	+	0.921837i	$0.626688\pi$
$878$	12.8820	−	7.43745i	0.434748	−	0.251002i
$879$	20.1746	−	48.1509i	0.680473	−	1.62409i
$880$	−9.91802	−	16.6789i	−0.334336	−	0.562245i
$881$			17.0910i			0.575812i	0.957659	+	0.287906i	$0.0929590\pi$
$881$			17.0910i			0.575812i	−0.957659	+	0.287906i	$0.907041\pi$
$882$	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	$-0.267874\pi$
$887$	−9.31066	−	16.1265i	−0.312621	−	0.541476i	−0.978929	+	0.204201i	$0.934540\pi$
$888$	−37.5324	−	49.3274i	−1.25951	−	1.65532i
$889$	−36.9560	+	64.0096i	−1.23946	+	2.14681i
$890$	−18.9732			−0.635983
$891$	−29.8495	−	0.101358i	−0.999994	−	0.00339562i
$892$	−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
$902$	−19.9277	+	11.8499i	−0.663520	+	0.394559i
$903$	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	−0.356911	−	0.934138i	$-0.616170\pi$
$907$	18.9894	−	32.8906i	0.630532	−	1.09211i	0.987443	−	0.157975i	$-0.0504966\pi$
$908$	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	0.709217	−	0.704991i	$-0.249049\pi$
$911$	13.6814	+	7.89896i	0.453285	+	0.261704i	−0.255931	+	0.966695i	$0.582382\pi$
$912$	3.45685	+	27.1090i	0.114468	+	0.897670i
$913$	0.264975	+	20.5805i	0.00876941	+	0.681116i
$914$	−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
$924$	4.18924	−	10.3711i	0.137816	−	0.341185i
$925$	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	−0.999384	−	0.0351041i	$-0.988824\pi$
$929$	−46.6177	−	26.9147i	−1.52948	−	0.883044i	−0.530093	−	0.847940i	$-0.677843\pi$
$930$	−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	$-0.319205\pi$
$941$	−14.1440	−	24.4982i	−0.461082	−	0.798618i	−0.999015	+	0.0443696i	$0.985872\pi$
$942$	−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	0.281190	−	0.959652i	$-0.409271\pi$
$947$	−12.5955	−	7.27199i	−0.409297	−	0.236308i	−0.690488	+	0.723344i	$0.742604\pi$
$948$	−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	$-0.540355\pi$
$953$	−7.80664			−0.252882			−0.126441	+	0.991974i	$0.540355\pi$
$954$	−6.03521	+	5.93781i	−0.195397	+	0.192244i
$955$	49.2138			1.59252
$956$	4.93795	−	8.55278i	0.159705	−	0.276617i
$957$	13.0969	−	10.2341i	0.423363	−	0.330822i
$958$	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	$-0.645817\pi$
$967$	3.52549	−	2.03544i	0.113372	−	0.0654554i	0.555614	+	0.831441i	$0.312483\pi$
$968$	−16.0480	+	29.5263i	−0.515802	+	0.949012i
$969$	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	$0.123746\pi$
$971$			23.6225i			0.758084i	−0.925380	+	0.379042i	$0.876254\pi$
$972$	−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	−0.868070	−	0.496441i	$-0.834640\pi$
$977$	−27.2616	+	15.7395i	−0.872175	+	0.503550i	−0.00410429	+	0.999992i	$0.501306\pi$
$978$	12.3358	−	1.57302i	0.394455	−	0.0502995i
$979$	12.6233	+	21.2283i	0.403442	+	0.678458i
$980$			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	0.878438	−	0.477857i	$-0.158586\pi$
$983$	28.3373	+	16.3606i	0.903821	+	0.521821i	0.0253828	+	0.999678i	$0.491920\pi$
$984$	−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
$990$	−24.4558	+	6.67729i	−0.777255	+	0.212218i
$991$	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	$-0.467429\pi$
$997$	−22.3641	−	12.9119i	−0.708277	−	0.408924i	−0.810423	+	0.585846i	$0.800763\pi$
$998$	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.65.4	yes	16
3.2	odd	2		297.2.g.b.197.5		16
9.2	odd	6		891.2.d.b.890.7		16
9.4	even	3		297.2.g.b.98.4		16
9.5	odd	6	inner	99.2.g.b.32.5	yes	16
9.7	even	3		891.2.d.b.890.10		16
11.10	odd	2	inner	99.2.g.b.65.5	yes	16
33.32	even	2		297.2.g.b.197.4		16
99.32	even	6	inner	99.2.g.b.32.4	✓	16
99.43	odd	6		891.2.d.b.890.8		16
99.65	even	6		891.2.d.b.890.9		16
99.76	odd	6		297.2.g.b.98.5		16

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

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} +(2.85069 - 1.69515i) 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} +(0.0528262 + 4.10299i) 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} +(-5.32644 - 2.15152i) 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} +(5.60018 - 4.37606i) 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} +(13.7583 - 0.177139i) 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} +(-8.70905 + 5.17880i) 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} +(2.62074 + 9.59853i) 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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