LMFDB - Embedded newform 120.2.w.c.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11940 - 0.864261i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 + 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(1.10573 - 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +O(q^{10})$	\(q+(-1.11940 - 0.864261i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 + 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(1.10573 - 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +(0.00136610 - 3.16228i) q^{10} +0.510276 q^{11} +(-0.543207 - 3.42125i) q^{12} +(0.750647 - 0.750647i) q^{13} +(-4.10544 + 0.528041i) q^{14} +(-2.05292 - 3.28413i) q^{15} +(-3.48771 + 1.95854i) q^{16} +(3.14698 + 3.14698i) q^{17} +(-2.78656 - 3.19923i) q^{18} +6.01198 q^{19} +(-2.73456 + 3.53867i) q^{20} +(-3.91945 + 3.21529i) q^{21} +(-0.571203 - 0.441012i) q^{22} +(-2.54575 + 2.54575i) q^{23} +(-2.34878 + 4.29921i) q^{24} +(-1.26945 + 4.83617i) q^{25} +(-1.48903 + 0.191519i) q^{26} +(-4.97150 - 1.51135i) q^{27} +(5.05199 + 2.95708i) q^{28} -5.10739i q^{29} +(-0.540308 + 5.45051i) q^{30} -4.56672 q^{31} +(5.59683 + 0.821906i) q^{32} +(-0.879551 - 0.0868061i) q^{33} +(-0.802913 - 6.24253i) q^{34} +(6.49090 + 0.837710i) q^{35} +(0.354305 + 5.98953i) q^{36} +(-6.76263 - 6.76263i) q^{37} +(-6.72981 - 5.19592i) q^{38} +(-1.42157 + 1.16618i) q^{39} +(6.11940 - 1.59781i) q^{40} -4.24355i q^{41} +(7.16627 - 0.211772i) q^{42} +(-5.95972 + 5.95972i) q^{43} +(0.258254 + 0.987336i) q^{44} +(2.97989 + 6.01001i) q^{45} +(5.04990 - 0.649518i) q^{46} +(-3.33849 - 3.33849i) q^{47} +(6.34486 - 2.78257i) q^{48} -1.56672i q^{49} +(5.60073 - 4.31647i) q^{50} +(-4.88902 - 5.95972i) q^{51} +(1.83234 + 1.07252i) q^{52} +(5.75871 + 5.75871i) q^{53} +(4.25889 + 5.98848i) q^{54} +(0.696910 + 0.903452i) q^{55} +(-3.09950 - 7.67638i) q^{56} +(-10.3627 - 1.02273i) q^{57} +(-4.41411 + 5.71720i) q^{58} -1.16514i q^{59} +(5.31548 - 5.63433i) q^{60} -4.92929i q^{61} +(5.11198 + 3.94684i) q^{62} +(7.30283 - 4.87536i) q^{63} +(-5.55474 - 5.75716i) q^{64} +(2.35423 + 0.303835i) q^{65} +(0.909545 + 0.857332i) q^{66} +(7.98415 + 7.98415i) q^{67} +(-4.49639 + 7.68180i) q^{68} +(4.82112 - 3.95497i) q^{69} +(-6.54191 - 6.54756i) q^{70} -5.09150i q^{71} +(4.77991 - 7.01088i) q^{72} +(-3.20654 - 3.20654i) q^{73} +(1.72540 + 13.4148i) q^{74} +(3.01082 - 8.12003i) q^{75} +(3.04271 + 11.6326i) q^{76} +(1.05608 - 1.05608i) q^{77} +(2.59918 - 0.0768090i) q^{78} +7.31215i q^{79} +(-8.23097 - 3.50017i) q^{80} +(8.31215 + 3.45081i) q^{81} +(-3.66754 + 4.75023i) q^{82} +(-4.77995 - 4.77995i) q^{83} +(-8.20494 - 5.95647i) q^{84} +(-1.27378 + 9.86975i) q^{85} +(11.8220 - 1.52055i) q^{86} +(-0.868848 + 8.80349i) q^{87} +(0.564226 - 1.32842i) q^{88} -12.6431 q^{89} +(1.85853 - 9.30300i) q^{90} -3.10712i q^{91} +(-6.21420 - 3.63736i) q^{92} +(7.87155 + 0.776871i) q^{93} +(0.851777 + 6.62243i) q^{94} +(8.21087 + 10.6443i) q^{95} +(-9.50730 - 2.36881i) q^{96} +(10.8789 - 10.8789i) q^{97} +(-1.35405 + 1.75378i) q^{98} +(1.50129 + 0.299251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.11940	−	0.864261i	−0.791534	−	0.611125i
$2$	−1.11940	−	0.864261i	−0.791534	−	0.611125i
$3$	−1.72368	−	0.170116i	−0.995165	−	0.0982164i
$3$	−1.72368	−	0.170116i	−0.995165	−	0.0982164i
$4$	0.506107	+	1.93490i	0.253054	+	0.967452i
$5$	1.36575	+	1.77052i	0.610783	+	0.791798i
$5$	1.36575	+	1.77052i	0.610783	+	0.791798i
$6$	1.78246	+	1.68013i	0.727685	+	0.685911i
$7$	2.06963	−	2.06963i	0.782246	−	0.782246i	−0.197964	−	0.980209i	$-0.563433\pi$
$7$	2.06963	−	2.06963i	0.782246	−	0.782246i	0.980209	+	0.197964i	$0.0634328\pi$
$8$	1.10573	−	2.60334i	0.390933	−	0.920419i
$9$	2.94212	+	0.586449i	0.980707	+	0.195483i
$10$	0.00136610	−	3.16228i	0.000431999	−	1.00000i
$11$	0.510276			0.153854			0.0769270	−	0.997037i	$-0.475489\pi$
$11$	0.510276			0.153854			0.0769270	+	0.997037i	$0.475489\pi$
$12$	−0.543207	−	3.42125i	−0.156810	−	0.987629i
$13$	0.750647	−	0.750647i	0.208192	−	0.208192i	−0.595307	−	0.803499i	$-0.702969\pi$
$13$	0.750647	−	0.750647i	0.208192	−	0.208192i	0.803499	+	0.595307i	$0.202969\pi$
$14$	−4.10544	+	0.528041i	−1.09722	+	0.141125i
$15$	−2.05292	−	3.28413i	−0.530062	−	0.847959i
$16$	−3.48771	+	1.95854i	−0.871928	+	0.489635i
$17$	3.14698	+	3.14698i	0.763254	+	0.763254i	0.976909	−	0.213656i	$-0.0685370\pi$
$17$	3.14698	+	3.14698i	0.763254	+	0.763254i	−0.213656	+	0.976909i	$0.568537\pi$
$18$	−2.78656	−	3.19923i	−0.656799	−	0.754066i
$19$	6.01198			1.37924			0.689622	−	0.724170i	$-0.257777\pi$
$19$	6.01198			1.37924			0.689622	+	0.724170i	$0.257777\pi$
$20$	−2.73456	+	3.53867i	−0.611466	+	0.791270i
$21$	−3.91945	+	3.21529i	−0.855293	+	0.701634i
$22$	−0.571203	−	0.441012i	−0.121781	−	0.0940240i
$23$	−2.54575	+	2.54575i	−0.530825	+	0.530825i	−0.920818	−	0.389993i	$-0.872478\pi$
$23$	−2.54575	+	2.54575i	−0.530825	+	0.530825i	0.389993	+	0.920818i	$0.372478\pi$
$24$	−2.34878	+	4.29921i	−0.479443	+	0.877573i
$25$	−1.26945	+	4.83617i	−0.253889	+	0.967233i
$26$	−1.48903	+	0.191519i	−0.292023	+	0.0375599i
$27$	−4.97150	−	1.51135i	−0.956766	−	0.290859i
$28$	5.05199	+	2.95708i	0.954736	+	0.558835i
$29$		−	5.10739i		−	0.948418i	−0.880412	−	0.474209i	$-0.842734\pi$
$29$		−	5.10739i		−	0.948418i	0.880412	−	0.474209i	$-0.157266\pi$
$30$	−0.540308	+	5.45051i	−0.0986463	+	0.995123i
$31$	−4.56672			−0.820207			−0.410104	−	0.912039i	$-0.634507\pi$
$31$	−4.56672			−0.820207			−0.410104	+	0.912039i	$0.634507\pi$
$32$	5.59683	+	0.821906i	0.989389	+	0.145294i
$33$	−0.879551	−	0.0868061i	−0.153110	−	0.0151110i
$34$	−0.802913	−	6.24253i	−0.137699	−	1.07058i
$35$	6.49090	+	0.837710i	1.09716	+	0.141599i
$36$	0.354305	+	5.98953i	0.0590509	+	0.998255i
$37$	−6.76263	−	6.76263i	−1.11177	−	1.11177i	−0.992911	−	0.118858i	$-0.962077\pi$
$37$	−6.76263	−	6.76263i	−1.11177	−	1.11177i	−0.118858	−	0.992911i	$-0.537923\pi$
$38$	−6.72981	−	5.19592i	−1.09172	−	0.842890i
$39$	−1.42157	+	1.16618i	−0.227633	+	0.186738i
$40$	6.11940	−	1.59781i	0.967561	−	0.252636i
$41$		−	4.24355i		−	0.662732i	−0.943502	−	0.331366i	$-0.892491\pi$
$41$		−	4.24355i		−	0.662732i	0.943502	−	0.331366i	$-0.107509\pi$
$42$	7.16627	−	0.211772i	1.10578	−	0.0326771i
$43$	−5.95972	+	5.95972i	−0.908848	+	0.908848i	−0.996179	−	0.0873310i	$-0.972166\pi$
$43$	−5.95972	+	5.95972i	−0.908848	+	0.908848i	0.0873310	+	0.996179i	$0.472166\pi$
$44$	0.258254	+	0.987336i	0.0389333	+	0.148846i
$45$	2.97989	+	6.01001i	0.444216	+	0.895920i
$46$	5.04990	−	0.649518i	0.744567	−	0.0957661i
$47$	−3.33849	−	3.33849i	−0.486969	−	0.486969i	0.420379	−	0.907349i	$-0.361897\pi$
$47$	−3.33849	−	3.33849i	−0.486969	−	0.486969i	−0.907349	+	0.420379i	$0.861897\pi$
$48$	6.34486	−	2.78257i	0.915802	−	0.401630i
$49$		−	1.56672i		−	0.223817i
$50$	5.60073	−	4.31647i	0.792062	−	0.610440i
$51$	−4.88902	−	5.95972i	−0.684599	−	0.834527i
$52$	1.83234	+	1.07252i	0.254100	+	0.148732i
$53$	5.75871	+	5.75871i	0.791019	+	0.791019i	0.981660	−	0.190641i	$-0.0610565\pi$
$53$	5.75871	+	5.75871i	0.791019	+	0.791019i	−0.190641	+	0.981660i	$0.561057\pi$
$54$	4.25889	+	5.98848i	0.579562	+	0.814928i
$55$	0.696910	+	0.903452i	0.0939714	+	0.121821i
$56$	−3.09950	−	7.67638i	−0.414188	−	1.02580i
$57$	−10.3627	−	1.02273i	−1.37257	−	0.135464i
$58$	−4.41411	+	5.71720i	−0.579602	+	0.750706i
$59$		−	1.16514i		−	0.151689i	−0.997120	−	0.0758444i	$-0.975835\pi$
$59$		−	1.16514i		−	0.151689i	0.997120	−	0.0758444i	$-0.0241652\pi$
$60$	5.31548	−	5.63433i	0.686226	−	0.727389i
$61$		−	4.92929i		−	0.631131i	−0.948904	−	0.315565i	$-0.897806\pi$
$61$		−	4.92929i		−	0.631131i	0.948904	−	0.315565i	$-0.102194\pi$
$62$	5.11198	+	3.94684i	0.649222	+	0.501249i
$63$	7.30283	−	4.87536i	0.920070	−	0.614238i
$64$	−5.55474	−	5.75716i	−0.694342	−	0.719645i
$65$	2.35423	+	0.303835i	0.292006	+	0.0376861i
$66$	0.909545	+	0.857332i	0.111957	+	0.105530i
$67$	7.98415	+	7.98415i	0.975419	+	0.975419i	0.999705	−	0.0242864i	$-0.00773136\pi$
$67$	7.98415	+	7.98415i	0.975419	+	0.975419i	−0.0242864	+	0.999705i	$0.507731\pi$
$68$	−4.49639	+	7.68180i	−0.545267	+	0.931555i
$69$	4.82112	−	3.95497i	0.580395	−	0.476123i
$70$	−6.54191	−	6.54756i	−0.781908	−	0.782584i
$71$		−	5.09150i		−	0.604250i	−0.953268	−	0.302125i	$-0.902304\pi$
$71$		−	5.09150i		−	0.604250i	0.953268	−	0.302125i	$-0.0976959\pi$
$72$	4.77991	−	7.01088i	0.563317	−	0.826241i
$73$	−3.20654	−	3.20654i	−0.375297	−	0.375297i	0.494105	−	0.869402i	$-0.335496\pi$
$73$	−3.20654	−	3.20654i	−0.375297	−	0.375297i	−0.869402	+	0.494105i	$0.835496\pi$
$74$	1.72540	+	13.4148i	0.200574	+	1.55943i
$75$	3.01082	−	8.12003i	0.347660	−	0.937621i
$76$	3.04271	+	11.6326i	0.349023	+	1.33435i
$77$	1.05608	−	1.05608i	0.120352	−	0.120352i
$78$	2.59918	−	0.0768090i	0.294300	−	0.00869691i
$79$			7.31215i			0.822682i	0.911482	+	0.411341i	$0.134939\pi$
$79$			7.31215i			0.822682i	−0.911482	+	0.411341i	$0.865061\pi$
$80$	−8.23097	−	3.50017i	−0.920250	−	0.391331i
$81$	8.31215	+	3.45081i	0.923573	+	0.383423i
$82$	−3.66754	+	4.75023i	−0.405012	+	0.524575i
$83$	−4.77995	−	4.77995i	−0.524668	−	0.524668i	0.394310	−	0.918978i	$-0.370984\pi$
$83$	−4.77995	−	4.77995i	−0.524668	−	0.524668i	−0.918978	+	0.394310i	$0.870984\pi$
$84$	−8.20494	−	5.95647i	−0.895233	−	0.649904i
$85$	−1.27378	+	9.86975i	−0.138161	+	1.07052i
$86$	11.8220	−	1.52055i	1.27480	−	0.163965i
$87$	−0.868848	+	8.80349i	−0.0931502	+	0.943833i
$88$	0.564226	−	1.32842i	0.0601467	−	0.141610i
$89$	−12.6431			−1.34017			−0.670083	−	0.742286i	$-0.733741\pi$
$89$	−12.6431			−1.34017			−0.670083	+	0.742286i	$0.733741\pi$
$90$	1.85853	−	9.30300i	0.195907	−	0.980623i
$91$		−	3.10712i		−	0.325715i
$92$	−6.21420	−	3.63736i	−0.647875	−	0.379221i
$93$	7.87155	+	0.776871i	0.816241	+	0.0805578i
$94$	0.851777	+	6.62243i	0.0878541	+	0.683052i
$95$	8.21087	+	10.6443i	0.842418	+	1.09208i
$96$	−9.50730	−	2.36881i	−0.970335	−	0.241766i
$97$	10.8789	−	10.8789i	1.10458	−	1.10458i	0.110732	−	0.993850i	$-0.464680\pi$
$97$	10.8789	−	10.8789i	1.10458	−	1.10458i	0.993850	−	0.110732i	$-0.0353195\pi$
$98$	−1.35405	+	1.75378i	−0.136780	+	0.177159i
$99$	1.50129	+	0.299251i	0.150886	+	0.0300759i
$100$	−10.0000	−	0.00863998i	−1.00000	−	0.000863998i
$101$	−6.41002			−0.637821			−0.318911	−	0.947785i	$-0.603317\pi$
$101$	−6.41002			−0.637821			−0.318911	+	0.947785i	$0.603317\pi$
$102$	0.322010	+	10.8967i	0.0318838	+	1.07893i
$103$	−1.86309	−	1.86309i	−0.183575	−	0.183575i	0.609336	−	0.792912i	$-0.291436\pi$
$103$	−1.86309	−	1.86309i	−0.183575	−	0.183575i	−0.792912	+	0.609336i	$0.791436\pi$
$104$	−1.12418	−	2.78420i	−0.110235	−	0.273013i
$105$	−11.0457	−	2.54815i	−1.07795	−	0.248674i
$106$	−1.46927	−	11.4233i	−0.142708	−	1.10953i
$107$	−10.0319	+	10.0319i	−0.969824	+	0.969824i	−0.999558	−	0.0297341i	$-0.990534\pi$
$107$	−10.0319	+	10.0319i	−0.969824	+	0.969824i	0.0297341	+	0.999558i	$0.490534\pi$
$108$	0.408206	−	10.3843i	0.0392797	−	0.999228i
$109$	−12.6448			−1.21115			−0.605577	−	0.795786i	$-0.707058\pi$
$109$	−12.6448			−1.21115			−0.605577	+	0.795786i	$0.707058\pi$
$110$	0.000697089	−	1.61364i	6.64648e−5	−	0.153854i
$111$	10.5062	+	12.8070i	0.997200	+	1.21559i
$112$	−3.16482	+	11.2717i	−0.299047	+	1.06508i
$113$	−1.88933	+	1.88933i	−0.177733	+	0.177733i	−0.790367	−	0.612634i	$-0.790110\pi$
$113$	−1.88933	+	1.88933i	−0.177733	+	0.177733i	0.612634	+	0.790367i	$0.290110\pi$
$114$	10.7161	+	10.1009i	1.00365	+	0.946039i
$115$	−7.98415	−	1.03043i	−0.744525	−	0.0960878i
$116$	9.88231	−	2.58489i	0.917549	−	0.240001i
$117$	2.64871	−	1.76828i	0.244874	−	0.163477i
$118$	−1.00699	+	1.30426i	−0.0927008	+	0.120067i
$119$	13.0261			1.19410
$120$	−10.8197	+	1.71310i	−0.987696	+	0.156384i
$121$	−10.7396			−0.976329
$122$	−4.26019	+	5.51784i	−0.385700	+	0.499562i
$123$	−0.721896	+	7.31452i	−0.0650912	+	0.659528i
$124$	−2.31125	−	8.83617i	−0.207556	−	0.793511i
$125$	−10.2963	+	4.35743i	−0.920925	+	0.389740i
$126$	−12.3884	−	0.854070i	−1.10364	−	0.0760866i
$127$	0.964015	−	0.964015i	0.0855425	−	0.0855425i	−0.663041	−	0.748583i	$-0.730734\pi$
$127$	0.964015	−	0.964015i	0.0855425	−	0.0855425i	0.748583	+	0.663041i	$0.230734\pi$
$128$	1.24228	+	11.2453i	0.109803	+	0.993953i
$129$	11.2865	−	9.25878i	0.993718	−	0.815190i
$130$	−2.37273	−	2.37478i	−0.208102	−	0.208282i
$131$	7.59234			0.663346			0.331673	−	0.943395i	$-0.392387\pi$
$131$	7.59234			0.663346			0.331673	+	0.943395i	$0.392387\pi$
$132$	−0.277186	−	1.74578i	−0.0241259	−	0.151951i
$133$	12.4426	−	12.4426i	1.07891	−	1.07891i
$134$	−2.03706	−	15.8378i	−0.175975	−	1.36818i
$135$	−4.11397	−	10.8662i	−0.354074	−	0.935217i
$136$	11.6723	−	4.71295i	1.00089	−	0.404132i
$137$	−0.713542	−	0.713542i	−0.0609620	−	0.0609620i	0.675968	−	0.736931i	$-0.263726\pi$
$137$	−0.713542	−	0.713542i	−0.0609620	−	0.0609620i	−0.736931	+	0.675968i	$0.763726\pi$
$138$	−8.81488	+	0.260491i	−0.750373	+	0.0221744i
$139$	9.01457			0.764606			0.382303	−	0.924037i	$-0.375131\pi$
$139$	9.01457			0.764606			0.382303	+	0.924037i	$0.375131\pi$
$140$	1.66420	+	12.9833i	0.140651	+	1.09729i
$141$	5.18655	+	6.32241i	0.436787	+	0.532443i
$142$	−4.40038	+	5.69942i	−0.369272	+	0.478284i
$143$	0.383038	−	0.383038i	0.0320312	−	0.0320312i
$144$	−11.4099	+	3.71689i	−0.950821	+	0.309741i
$145$	9.04271	−	6.97542i	0.750956	−	0.579277i
$146$	0.818111	+	6.36069i	0.0677073	+	0.526414i
$147$	−0.266524	+	2.70052i	−0.0219825	+	0.222735i
$148$	9.66243	−	16.5077i	0.794247	−	1.35692i
$149$		−	13.1573i		−	1.07789i	−0.842341	−	0.538944i	$-0.818823\pi$
$149$		−	13.1573i		−	1.07789i	0.842341	−	0.538944i	$-0.181177\pi$
$150$	−10.3881	+	6.48742i	−0.848188	+	0.529695i
$151$	2.75982			0.224591			0.112295	−	0.993675i	$-0.464180\pi$
$151$	2.75982			0.224591			0.112295	+	0.993675i	$0.464180\pi$
$152$	6.64761	−	15.6512i	0.539192	−	1.26948i
$153$	7.41324	+	11.1043i	0.599325	+	0.897731i
$154$	−2.09491	+	0.269447i	−0.168812	+	0.0217126i
$155$	−6.23700	−	8.08545i	−0.500968	−	0.649439i
$156$	−2.97591	−	2.16039i	−0.238263	−	0.172970i
$157$	4.38090	+	4.38090i	0.349634	+	0.349634i	0.859973	−	0.510339i	$-0.170480\pi$
$157$	4.38090	+	4.38090i	0.349634	+	0.349634i	−0.510339	+	0.859973i	$0.670480\pi$
$158$	6.31961	−	8.18522i	0.502761	−	0.651181i
$159$	−8.94650	−	10.9058i	−0.709504	−	0.864886i
$160$	6.18868	+	11.0318i	0.489258	+	0.872139i
$161$			10.5375i			0.830472i
$162$	−6.32222	−	11.0467i	−0.496720	−	0.867911i
$163$	0.470868	−	0.470868i	0.0368812	−	0.0368812i	−0.688426	−	0.725307i	$-0.741698\pi$
$163$	0.470868	−	0.470868i	0.0368812	−	0.0368812i	0.725307	+	0.688426i	$0.241698\pi$
$164$	8.21087	−	2.14769i	0.641162	−	0.167707i
$165$	−1.04756	−	1.67581i	−0.0815522	−	0.130462i
$166$	1.21955	+	9.48180i	0.0946553	+	0.735930i
$167$	0.495354	+	0.495354i	0.0383316	+	0.0383316i	0.726013	−	0.687681i	$-0.241371\pi$
$167$	0.495354	+	0.495354i	0.0383316	+	0.0383316i	−0.687681	+	0.726013i	$0.741371\pi$
$168$	4.03666	+	13.7589i	0.311435	+	1.06152i
$169$			11.8731i			0.913312i
$170$	9.95591	−	9.94731i	0.763583	−	0.762924i
$171$	17.6880	+	3.52572i	1.35263	+	0.269619i
$172$	−14.5477	−	8.51523i	−1.10925	−	0.649280i
$173$	−2.32674	−	2.32674i	−0.176899	−	0.176899i	0.613104	−	0.790002i	$-0.289921\pi$
$173$	−2.32674	−	2.32674i	−0.176899	−	0.176899i	−0.790002	+	0.613104i	$0.789921\pi$
$174$	8.58109	−	9.10370i	0.650531	−	0.690150i
$175$	7.38178	+	12.6363i	0.558010	+	0.955218i
$176$	−1.77970	+	0.999395i	−0.134150	+	0.0753323i
$177$	−0.198209	+	2.00833i	−0.0148983	+	0.150955i
$178$	14.1527	+	10.9269i	1.06079	+	0.819008i
$179$			13.9141i			1.03999i	0.854169	+	0.519996i	$0.174066\pi$
$179$			13.9141i			1.03999i	−0.854169	+	0.519996i	$0.825934\pi$
$180$	−10.1207	+	8.80751i	−0.754349	+	0.656473i
$181$			5.80972i			0.431833i	0.976412	+	0.215917i	$0.0692740\pi$
$181$			5.80972i			0.431833i	−0.976412	+	0.215917i	$0.930726\pi$
$182$	−2.68536	+	3.47811i	−0.199052	+	0.257814i
$183$	−0.838550	+	8.49650i	−0.0619874	+	0.628079i
$184$	3.81254	+	9.44235i	0.281064	+	0.696099i
$185$	2.73727	−	21.2094i	0.201248	−	1.55935i
$186$	−8.13998	−	7.67270i	−0.596852	−	0.562589i
$187$	1.60583	+	1.60583i	0.117430	+	0.117430i
$188$	4.77003	−	8.14930i	0.347890	−	0.594349i
$189$	−13.4171	+	7.16122i	−0.975950	+	0.520902i
$190$	0.00821298	−	19.0116i	0.000595832	−	1.37924i
$191$		−	13.8456i		−	1.00183i	−0.865497	−	0.500914i	$-0.832997\pi$
$191$		−	13.8456i		−	1.00183i	0.865497	−	0.500914i	$-0.167003\pi$
$192$	8.59519	+	10.8684i	0.620304	+	0.784361i
$193$	4.57254	+	4.57254i	0.329138	+	0.329138i	0.852259	−	0.523120i	$-0.175232\pi$
$193$	4.57254	+	4.57254i	0.329138	+	0.329138i	−0.523120	+	0.852259i	$0.675232\pi$
$194$	−21.5800	+	2.77562i	−1.54935	+	0.199278i
$195$	−4.00624	−	0.924205i	−0.286893	−	0.0661837i
$196$	3.03145	−	0.792928i	0.216532	−	0.0566377i
$197$	−3.85757	+	3.85757i	−0.274840	+	0.274840i	−0.831045	−	0.556205i	$-0.812257\pi$
$197$	−3.85757	+	3.85757i	−0.274840	+	0.274840i	0.556205	+	0.831045i	$0.312257\pi$
$198$	−1.42192	−	1.63249i	−0.101051	−	0.116016i
$199$		−	5.91833i		−	0.419540i	−0.977751	−	0.209770i	$-0.932729\pi$
$199$		−	5.91833i		−	0.419540i	0.977751	−	0.209770i	$-0.0672714\pi$
$200$	11.1865	+	8.65227i	0.791006	+	0.611808i
$201$	−12.4039	−	15.1203i	−0.874900	−	1.06650i
$202$	7.17537	+	5.53993i	0.504858	+	0.389788i
$203$	−10.5704	−	10.5704i	−0.741896	−	0.741896i
$204$	9.05712	−	12.4760i	0.634125	−	0.873497i
$205$	7.51328	−	5.79564i	0.524750	−	0.404785i
$206$	0.475344	+	3.69573i	0.0331188	+	0.257494i
$207$	−8.98285	+	5.99695i	−0.624351	+	0.416817i
$208$	−1.14787	+	4.08821i	−0.0795904	+	0.283467i
$209$	3.06777			0.212202
$210$	10.1623	+	12.3988i	0.701265	+	0.855596i
$211$		−	6.95372i		−	0.478714i	−0.970932	−	0.239357i	$-0.923063\pi$
$211$		−	6.95372i		−	0.478714i	0.970932	−	0.239357i	$-0.0769366\pi$
$212$	−8.22802	+	14.0571i	−0.565103	+	0.965444i
$213$	−0.866144	+	8.77609i	−0.0593472	+	0.601328i
$214$	19.8999	−	2.55953i	1.36033	−	0.174966i
$215$	−18.6913	−	2.41228i	−1.27473	−	0.164516i
$216$	−9.43167	+	11.2714i	−0.641744	+	0.766919i
$217$	−9.45141	+	9.45141i	−0.641604	+	0.641604i
$218$	14.1546	+	10.9284i	0.958671	+	0.740166i
$219$	4.98156	+	6.07252i	0.336622	+	0.410343i
$220$	−1.39538	+	1.80570i	−0.0940766	+	0.121740i
$221$	4.72454			0.317807
$222$	−0.691978	−	23.4162i	−0.0464425	−	1.57159i
$223$	−16.7218	−	16.7218i	−1.11977	−	1.11977i	−0.991774	−	0.127998i	$-0.959145\pi$
$223$	−16.7218	−	16.7218i	−1.11977	−	1.11977i	−0.127998	−	0.991774i	$-0.540855\pi$
$224$	13.2844	−	9.88231i	0.887601	−	0.660290i
$225$	−6.57103	+	13.4841i	−0.438069	+	0.898941i
$226$	3.74778	−	0.482039i	0.249298	−	0.0320647i
$227$	12.4814	−	12.4814i	0.828416	−	0.828416i	−0.158881	−	0.987298i	$-0.550789\pi$
$227$	12.4814	−	12.4814i	0.828416	−	0.828416i	0.987298	+	0.158881i	$0.0507887\pi$
$228$	−3.26575	−	20.5685i	−0.216280	−	1.36218i
$229$	−1.09678			−0.0724770			−0.0362385	−	0.999343i	$-0.511538\pi$
$229$	−1.09678			−0.0724770			−0.0362385	+	0.999343i	$0.511538\pi$
$230$	8.04689	+	8.05384i	0.530596	+	0.531055i
$231$	−2.00000	+	1.64069i	−0.131590	+	0.107949i
$232$	−13.2963	−	5.64737i	−0.872942	−	0.370768i
$233$	6.98082	−	6.98082i	0.457329	−	0.457329i	−0.440449	−	0.897778i	$-0.645181\pi$
$233$	6.98082	−	6.98082i	0.457329	−	0.457329i	0.897778	+	0.440449i	$0.145181\pi$
$234$	−4.49322	−	0.309768i	−0.293731	−	0.0202502i
$235$	1.35130	−	10.4704i	0.0881492	−	0.683014i
$236$	2.25444	−	0.589688i	0.146752	−	0.0383854i
$237$	1.24391	−	12.6038i	0.0808008	−	0.818704i
$238$	−14.5814	−	11.2580i	−0.945174	−	0.729746i
$239$	−12.3210			−0.796976			−0.398488	−	0.917173i	$-0.630465\pi$
$239$	−12.3210			−0.796976			−0.398488	+	0.917173i	$0.630465\pi$
$240$	13.5921	+	7.43338i	0.877366	+	0.479822i
$241$	−7.03833			−0.453379			−0.226689	−	0.973967i	$-0.572790\pi$
$241$	−7.03833			−0.453379			−0.226689	+	0.973967i	$0.572790\pi$
$242$	12.0219	+	9.28183i	0.772798	+	0.596659i
$243$	−13.7404	−	7.36211i	−0.881449	−	0.472279i
$244$	9.53771	−	2.49475i	0.610589	−	0.159710i
$245$	2.77390	−	2.13975i	0.177218	−	0.136704i
$246$	7.12974	−	7.56395i	0.454575	−	0.482260i
$247$	4.51288	−	4.51288i	0.287148	−	0.287148i
$248$	−5.04954	+	11.8887i	−0.320646	+	0.754934i
$249$	7.42595	+	9.05224i	0.470600	+	0.573662i
$250$	15.2916	+	4.02095i	0.967123	+	0.254307i
$251$	−9.92262			−0.626311			−0.313155	−	0.949702i	$-0.601386\pi$
$251$	−9.92262			−0.626311			−0.313155	+	0.949702i	$0.601386\pi$
$252$	13.1294	+	11.6628i	0.827073	+	0.734688i
$253$	−1.29904	+	1.29904i	−0.0816696	+	0.0816696i
$254$	−1.91228	+	0.245957i	−0.119987	+	0.0154327i
$255$	3.87459	−	16.7956i	0.242636	−	1.05178i
$256$	8.32826	−	13.6616i	0.520516	−	0.853852i
$257$	14.5324	+	14.5324i	0.906508	+	0.906508i	0.995989	−	0.0894809i	$-0.0285208\pi$
$257$	14.5324	+	14.5324i	0.906508	+	0.906508i	−0.0894809	+	0.995989i	$0.528521\pi$
$258$	−20.6361	+	0.609821i	−1.28474	+	0.0379658i
$259$	−27.9923			−1.73935
$260$	0.603601	+	4.70898i	0.0374338	+	0.292039i
$261$	2.99522	−	15.0266i	0.185400	−	0.930120i
$262$	−8.49885	−	6.56176i	−0.525061	−	0.405387i
$263$	−10.8634	+	10.8634i	−0.669867	+	0.669867i	−0.957685	−	0.287818i	$-0.907070\pi$
$263$	−10.8634	+	10.8634i	−0.669867	+	0.669867i	0.287818	+	0.957685i	$0.407070\pi$
$264$	−1.19853	+	2.19379i	−0.0737643	+	0.135018i
$265$	−2.33092	+	18.0608i	−0.143187	+	1.10947i
$266$	−24.6818	+	3.17457i	−1.51334	+	0.194646i
$267$	21.7926	+	2.15079i	1.33369	+	0.131626i
$268$	−11.4077	+	19.4894i	−0.696838	+	1.19050i
$269$			32.3280i			1.97108i	0.169455	+	0.985538i	$0.445799\pi$
$269$			32.3280i			1.97108i	−0.169455	+	0.985538i	$0.554201\pi$
$270$	−4.78610	+	15.7192i	−0.291273	+	0.956640i
$271$	0.306338			0.0186087			0.00930434	−	0.999957i	$-0.497038\pi$
$271$	0.306338			0.0186087			0.00930434	+	0.999957i	$0.497038\pi$
$272$	−17.1392	−	4.81227i	−1.03922	−	0.291787i
$273$	−0.528571	+	5.35567i	−0.0319905	+	0.324140i
$274$	0.182052	+	1.41543i	0.0109982	+	0.0855090i
$275$	−0.647769	+	2.46778i	−0.0390619	+	0.148813i
$276$	10.0925	+	7.32676i	0.607497	+	0.441019i
$277$	6.97897	+	6.97897i	0.419326	+	0.419326i	0.884971	−	0.465645i	$-0.154178\pi$
$277$	6.97897	+	6.97897i	0.419326	+	0.419326i	−0.465645	+	0.884971i	$0.654178\pi$
$278$	−10.0909	−	7.79094i	−0.605212	−	0.467270i
$279$	−13.4358	−	2.67815i	−0.804383	−	0.160337i
$280$	9.35801	−	15.9717i	0.559248	−	0.954494i
$281$			15.4596i			0.922240i	0.887338	+	0.461120i	$0.152552\pi$
$281$			15.4596i			0.922240i	−0.887338	+	0.461120i	$0.847448\pi$
$282$	−0.341607	−	11.5598i	−0.0203424	−	0.688378i
$283$	8.86458	−	8.86458i	0.526945	−	0.526945i	−0.392715	−	0.919660i	$-0.628464\pi$
$283$	8.86458	−	8.86458i	0.526945	−	0.526945i	0.919660	+	0.392715i	$0.128464\pi$
$284$	9.85156	−	2.57684i	0.584583	−	0.152908i
$285$	−12.3421	−	19.7441i	−0.731084	−	1.16954i
$286$	−0.759816	+	0.0977275i	−0.0449289	+	0.00577875i
$287$	−8.78258	−	8.78258i	−0.518419	−	0.518419i
$288$	15.9845	+	5.70040i	0.941898	+	0.335899i
$289$			2.80690i			0.165112i
$290$	−16.1510	−	0.00697721i	−0.948418	−	0.000409716i
$291$	−20.6023	+	16.9010i	−1.20773	+	0.990754i
$292$	4.58150	−	7.82720i	0.268112	−	0.458053i
$293$	−1.49638	−	1.49638i	−0.0874192	−	0.0874192i	0.662045	−	0.749464i	$-0.269689\pi$
$293$	−1.49638	−	1.49638i	−0.0874192	−	0.0874192i	−0.749464	+	0.662045i	$0.769689\pi$
$294$	2.63230	−	2.79261i	0.153519	−	0.162868i
$295$	2.06291	−	1.59130i	0.120107	−	0.0926489i
$296$	−25.0830	+	10.1278i	−1.45792	+	0.588666i
$297$	−2.53684	−	0.771206i	−0.147202	−	0.0447499i
$298$	−11.3713	+	14.7283i	−0.658724	+	0.853186i
$299$			3.82192i			0.221027i
$300$	17.2353	+	1.71605i	0.995080	+	0.0990762i
$301$			24.6688i			1.42189i
$302$	−3.08933	−	2.38520i	−0.177771	−	0.137253i
$303$	11.0488	+	1.09045i	0.634738	+	0.0626445i
$304$	−20.9681	+	11.7747i	−1.20260	+	0.675325i
$305$	8.72738	−	6.73218i	0.499728	−	0.385484i
$306$	1.29866	−	18.8371i	0.0742393	−	1.07685i
$307$	−12.4948	−	12.4948i	−0.713118	−	0.713118i	0.254068	−	0.967186i	$-0.418231\pi$
$307$	−12.4948	−	12.4948i	−0.713118	−	0.713118i	−0.967186	+	0.254068i	$0.918231\pi$
$308$	2.57791	+	1.50893i	0.146890	+	0.0859791i
$309$	2.89442	+	3.52830i	0.164658	+	0.200718i
$310$	−0.00623860	+	14.4412i	−0.000354329	+	0.820207i
$311$			0.224632i			0.0127377i	0.999980	+	0.00636886i	$0.00202728\pi$
$311$			0.224632i			0.0127377i	−0.999980	+	0.00636886i	$0.997973\pi$
$312$	1.46408	+	4.99030i	0.0828874	+	0.282520i
$313$	−12.0383	−	12.0383i	−0.680447	−	0.680447i	0.279654	−	0.960101i	$-0.409780\pi$
$313$	−12.0383	−	12.0383i	−0.680447	−	0.680447i	−0.960101	+	0.279654i	$0.909780\pi$
$314$	−1.11774	−	8.69022i	−0.0630775	−	0.490417i
$315$	18.6058	+	6.27123i	1.04832	+	0.353344i
$316$	−14.1483	+	3.70073i	−0.795905	+	0.208183i
$317$	20.2257	−	20.2257i	1.13599	−	1.13599i	0.146829	−	0.989162i	$-0.453093\pi$
$317$	20.2257	−	20.2257i	1.13599	−	1.13599i	0.989162	−	0.146829i	$-0.0469068\pi$
$318$	0.589252	+	19.9400i	0.0330436	+	1.11818i
$319$		−	2.60618i		−	0.145918i
$320$	2.60674	−	17.6976i	0.145721	−	0.989326i
$321$	18.9984	−	15.5852i	1.06039	−	0.869882i
$322$	9.10715	−	11.7957i	0.507522	−	0.657347i
$323$	18.9196	+	18.9196i	1.05271	+	1.05271i
$324$	−2.47015	+	17.8297i	−0.137230	+	0.990539i
$325$	2.67735	+	4.58316i	0.148513	+	0.254228i
$326$	−0.934042	+	0.120136i	−0.0517318	+	0.00665374i
$327$	21.7956	+	2.15109i	1.20530	+	0.118955i
$328$	−11.0474	−	4.69221i	−0.609991	−	0.259084i
$329$	−13.8189			−0.761860
$330$	−0.275706	+	2.78127i	−0.0151771	+	0.153104i
$331$			12.3308i			0.677760i	0.940830	+	0.338880i	$0.110048\pi$
$331$			12.3308i			0.677760i	−0.940830	+	0.338880i	$0.889952\pi$
$332$	6.82959	−	11.6679i	0.374822	−	0.640361i
$333$	−15.9305	−	23.8624i	−0.872988	−	1.30765i
$334$	−0.126384	−	0.982613i	−0.00691540	−	0.0537662i
$335$	−3.23169	+	25.0404i	−0.176566	+	1.36810i
$336$	7.37262	−	18.8904i	0.402209	−	1.03056i
$337$	10.6723	−	10.6723i	0.581359	−	0.581359i	−0.353918	−	0.935277i	$-0.615151\pi$
$337$	10.6723	−	10.6723i	0.581359	−	0.581359i	0.935277	+	0.353918i	$0.115151\pi$
$338$	10.2614	−	13.2907i	0.558147	−	0.722918i
$339$	3.57799	−	2.93518i	0.194330	−	0.159417i
$340$	−19.7417	+	2.53051i	−1.07064	+	0.137236i
$341$	−2.33029			−0.126192
$342$	−16.7528	−	19.2337i	−0.905886	−	1.04004i
$343$	11.2449	+	11.2449i	0.607166	+	0.607166i
$344$	8.92534	+	22.1050i	0.481222	+	1.19182i
$345$	13.5868	+	3.13435i	0.731488	+	0.168748i
$346$	0.593640	+	4.61546i	0.0319143	+	0.248129i
$347$	8.00457	−	8.00457i	0.429708	−	0.429708i	−0.458821	−	0.888529i	$-0.651728\pi$
$347$	8.00457	−	8.00457i	0.429708	−	0.429708i	0.888529	+	0.458821i	$0.151728\pi$
$348$	−17.4736	+	2.77437i	−0.936685	+	0.148722i
$349$	13.9579			0.747152			0.373576	−	0.927600i	$-0.378132\pi$
$349$	13.9579			0.747152			0.373576	+	0.927600i	$0.378132\pi$
$350$	2.65794	−	20.5249i	0.142073	−	1.09710i
$351$	−4.86633	+	2.59735i	−0.259746	+	0.138636i
$352$	2.85593	+	0.419399i	0.152221	+	0.0223541i
$353$	11.8744	−	11.8744i	0.632008	−	0.632008i	−0.316563	−	0.948571i	$-0.602529\pi$
$353$	11.8744	−	11.8744i	0.632008	−	0.632008i	0.948571	+	0.316563i	$0.102529\pi$
$354$	1.95760	−	2.07682i	0.104045	−	0.110382i
$355$	9.01457	−	6.95372i	0.478444	−	0.369065i
$356$	−6.39876	−	24.4632i	−0.339134	−	1.29655i
$357$	−22.4528	−	2.21595i	−1.18833	−	0.117281i
$358$	12.0254	−	15.5755i	0.635564	−	0.823189i
$359$	33.8765			1.78793			0.893967	−	0.448133i	$-0.147911\pi$
$359$	33.8765			1.78793			0.893967	+	0.448133i	$0.147911\pi$
$360$	18.9410	−	1.11223i	0.998280	−	0.0586196i
$361$	17.1439			0.902313
$362$	5.02112	−	6.50340i	0.263904	−	0.341811i
$363$	18.5116	+	1.82698i	0.971608	+	0.0958915i
$364$	6.01198	−	1.57254i	0.315114	−	0.0824233i
$365$	1.29789	−	10.0566i	0.0679347	−	0.526385i
$366$	8.28186	−	8.78625i	0.432900	−	0.459265i
$367$	10.7900	−	10.7900i	0.563233	−	0.563233i	−0.366992	−	0.930224i	$-0.619612\pi$
$367$	10.7900	−	10.7900i	0.563233	−	0.563233i	0.930224	+	0.366992i	$0.119612\pi$
$368$	3.89289	−	13.8648i	0.202931	−	0.722752i
$369$	2.48863	−	12.4851i	0.129553	−	0.649946i
$370$	−21.3946	+	21.3761i	−1.11225	+	1.11129i
$371$	23.8368			1.23754
$372$	2.48067	+	15.6239i	0.128617	+	0.810060i
$373$	−25.8380	+	25.8380i	−1.33784	+	1.33784i	−0.439697	+	0.898146i	$0.644914\pi$
$373$	−25.8380	+	25.8380i	−1.33784	+	1.33784i	−0.898146	+	0.439697i	$0.855086\pi$
$374$	−0.409708	−	3.18541i	−0.0211855	−	0.164714i
$375$	18.4887	−	5.75924i	0.954751	−	0.297406i
$376$	−12.3827	+	4.99977i	−0.638588	+	0.257843i
$377$	−3.83385	−	3.83385i	−0.197453	−	0.197453i
$378$	21.2082	+	3.57960i	1.09083	+	0.184115i
$379$	−12.2262			−0.628019			−0.314010	−	0.949420i	$-0.601672\pi$
$379$	−12.2262			−0.628019			−0.314010	+	0.949420i	$0.601672\pi$
$380$	−16.4401	+	21.2744i	−0.843361	+	1.09135i
$381$	−1.82564	+	1.49766i	−0.0935306	+	0.0767272i
$382$	−11.9662	+	15.4987i	−0.612242	+	0.792982i
$383$	21.6256	−	21.6256i	1.10501	−	1.10501i	0.111219	−	0.993796i	$-0.464525\pi$
$383$	21.6256	−	21.6256i	1.10501	−	1.10501i	0.993796	−	0.111219i	$-0.0354754\pi$
$384$	−0.228292	−	19.5946i	−0.0116500	−	0.999932i
$385$	3.31215	+	0.427464i	0.168803	+	0.0217856i
$386$	−1.16663	−	9.07035i	−0.0593798	−	0.461669i
$387$	−21.0293	+	14.0391i	−1.06898	+	0.713649i
$388$	26.5555	+	15.5437i	1.34815	+	0.789112i
$389$		−	6.63941i		−	0.336632i	−0.985733	−	0.168316i	$-0.946167\pi$
$389$		−	6.63941i		−	0.336632i	0.985733	−	0.168316i	$-0.0538328\pi$
$390$	3.68583	+	4.49699i	0.186639	+	0.227714i
$391$	−16.0228			−0.810309
$392$	−4.07870	−	1.73236i	−0.206006	−	0.0874975i
$393$	−13.0867	−	1.29158i	−0.660138	−	0.0651514i
$394$	7.65210	−	0.984213i	0.385507	−	0.0495839i
$395$	−12.9463	+	9.98658i	−0.651398	+	0.502480i
$396$	0.180794	+	3.05631i	0.00908522	+	0.153586i
$397$	14.0596	+	14.0596i	0.705629	+	0.705629i	0.965613	−	0.259984i	$-0.0837172\pi$
$397$	14.0596	+	14.0596i	0.705629	+	0.705629i	−0.259984	+	0.965613i	$0.583717\pi$
$398$	−5.11498	+	6.62498i	−0.256391	+	0.332080i
$399$	−23.5636	+	19.3303i	−1.17966	+	0.967725i
$400$	−5.04435	−	19.3534i	−0.252218	−	0.967671i
$401$			18.1176i			0.904751i	0.891827	+	0.452376i	$0.149423\pi$
$401$			18.1176i			0.904751i	−0.891827	+	0.452376i	$0.850577\pi$
$402$	0.816968	+	27.6458i	0.0407466	+	1.37885i
$403$	−3.42800	+	3.42800i	−0.170761	+	0.170761i
$404$	−3.24416	−	12.4028i	−0.161403	−	0.617062i
$405$	5.24263	+	19.4297i	0.260508	+	0.965472i
$406$	2.69691	+	20.9681i	0.133845	+	1.04063i
$407$	−3.45081	−	3.45081i	−0.171050	−	0.171050i
$408$	−20.9211	+	6.13795i	−1.03575	+	0.303874i
$409$		−	26.3245i		−	1.30166i	−0.759223	−	0.650831i	$-0.774421\pi$
$409$		−	26.3245i		−	1.30166i	0.759223	−	0.650831i	$-0.225579\pi$
$410$	−13.4193	−	0.00579713i	−0.662732	−	0.000286300i
$411$	1.10853	+	1.35130i	0.0546798	+	0.0666548i
$412$	2.66197	−	4.54782i	0.131146	−	0.224055i
$413$	−2.41142	−	2.41142i	−0.118658	−	0.118658i
$414$	15.2383	+	1.05055i	0.748923	+	0.0516317i
$415$	1.93475	−	14.9912i	0.0949732	−	0.735890i
$416$	4.81820	−	3.58428i	0.236232	−	0.175734i
$417$	−15.5382	−	1.53352i	−0.760909	−	0.0750969i
$418$	−3.43406	−	2.65135i	−0.167965	−	0.129682i
$419$		−	12.7809i		−	0.624385i	−0.950019	−	0.312193i	$-0.898937\pi$
$419$		−	12.7809i		−	0.624385i	0.950019	−	0.312193i	$-0.101063\pi$
$420$	−0.659892	−	22.6620i	−0.0321994	−	1.10579i
$421$		−	26.3792i		−	1.28564i	−0.766017	−	0.642821i	$-0.777764\pi$
$421$		−	26.3792i		−	1.28564i	0.766017	−	0.642821i	$-0.222236\pi$
$422$	−6.00983	+	7.78398i	−0.292554	+	0.378918i
$423$	−7.86440	−	11.7801i	−0.382380	−	0.572769i
$424$	21.3594	−	8.62431i	1.03730	−	0.418833i
$425$	−19.2142	+	11.2244i	−0.932026	+	0.544462i
$426$	8.55439	−	9.07537i	0.414462	−	0.439703i
$427$	−10.2018	−	10.2018i	−0.493700	−	0.493700i
$428$	−24.4881	−	14.3336i	−1.18368	−	0.692841i
$429$	−0.725393	+	0.595072i	−0.0350223	+	0.0287303i
$430$	18.8381	+	18.8544i	0.908456	+	0.909241i
$431$			28.6818i			1.38155i	0.723068	+	0.690777i	$0.242731\pi$
$431$			28.6818i			1.38155i	−0.723068	+	0.690777i	$0.757269\pi$
$432$	20.2992	−	4.46572i	0.976646	−	0.214857i
$433$	−2.25457	−	2.25457i	−0.108347	−	0.108347i	0.650855	−	0.759202i	$-0.274411\pi$
$433$	−2.25457	−	2.25457i	−0.108347	−	0.108347i	−0.759202	+	0.650855i	$0.774411\pi$
$434$	18.7484	−	2.41142i	0.899951	−	0.115752i
$435$	−16.7733	+	10.4851i	−0.804220	+	0.502720i
$436$	−6.39964	−	24.4665i	−0.306487	−	1.17173i
$437$	−15.3050	+	15.3050i	−0.732137	+	0.732137i
$438$	−0.328105	−	11.1029i	−0.0156775	−	0.530519i
$439$			11.8510i			0.565620i	0.959176	+	0.282810i	$0.0912665\pi$
$439$			11.8510i			0.565620i	−0.959176	+	0.282810i	$0.908733\pi$
$440$	3.12258	−	0.815323i	0.148863	−	0.0388690i
$441$	0.918802	−	4.60948i	0.0437525	−	0.219499i
$442$	−5.28864	−	4.08323i	−0.251555	−	0.194219i
$443$	−1.66807	−	1.66807i	−0.0792526	−	0.0792526i	0.666369	−	0.745622i	$-0.267847\pi$
$443$	−1.66807	−	1.66807i	−0.0792526	−	0.0792526i	−0.745622	+	0.666369i	$0.767847\pi$
$444$	−19.4631	+	26.8101i	−0.923679	+	1.27235i
$445$	−17.2673	−	22.3848i	−0.818550	−	1.06114i
$446$	4.26636	+	33.1703i	0.202018	+	1.57066i
$447$	−2.23827	+	22.6789i	−0.105866	+	1.07268i
$448$	−23.4114	−	0.418930i	−1.10609	−	0.0197926i
$449$	−34.3414			−1.62067			−0.810336	−	0.585966i	$-0.800715\pi$
$449$	−34.3414			−1.62067			−0.810336	+	0.585966i	$0.800715\pi$
$450$	19.0094	−	9.41502i	0.896112	−	0.443828i
$451$		−	2.16539i		−	0.101964i
$452$	−4.61186	−	2.69946i	−0.216924	−	0.126972i
$453$	−4.75703	−	0.469488i	−0.223505	−	0.0220585i
$454$	−24.7588	+	3.18447i	−1.16199	+	0.149455i
$455$	5.50120	−	4.24355i	0.257900	−	0.198941i
$456$	−14.1208	+	25.8468i	−0.661269	+	1.21039i
$457$	−4.61474	+	4.61474i	−0.215869	+	0.215869i	−0.806755	−	0.590886i	$-0.798778\pi$
$457$	−4.61474	+	4.61474i	−0.215869	+	0.215869i	0.590886	+	0.806755i	$0.298778\pi$
$458$	1.22773	+	0.947900i	0.0573680	+	0.0442925i
$459$	−10.8890	−	20.4014i	−0.508255	−	0.952254i
$460$	−2.04706	−	15.9701i	−0.0954445	−	0.744608i
$461$	20.6452			0.961543			0.480772	−	0.876846i	$-0.340357\pi$
$461$	20.6452			0.961543			0.480772	+	0.876846i	$0.340357\pi$
$462$	3.65678	−	0.108062i	0.170129	−	0.00502751i
$463$	27.1817	+	27.1817i	1.26324	+	1.26324i	0.949512	+	0.313730i	$0.101579\pi$
$463$	27.1817	+	27.1817i	1.26324	+	1.26324i	0.313730	+	0.949512i	$0.398421\pi$
$464$	10.0030	+	17.8131i	0.464378	+	0.826952i
$465$	9.37511	+	14.9977i	0.434760	+	0.695502i
$466$	−13.8476	+	1.78107i	−0.641476	+	0.0825067i
$467$	6.39901	−	6.39901i	0.296111	−	0.296111i	−0.543378	−	0.839488i	$-0.682855\pi$
$467$	6.39901	−	6.39901i	0.296111	−	0.296111i	0.839488	+	0.543378i	$0.182855\pi$
$468$	4.76198	+	4.23007i	0.220123	+	0.195535i
$469$	33.0484			1.52603
$470$	−10.5618	+	10.5527i	−0.487180	+	0.486759i
$471$	−6.80600	−	8.29652i	−0.313604	−	0.382283i
$472$	−3.03326	−	1.28833i	−0.139617	−	0.0593002i
$473$	−3.04110	+	3.04110i	−0.139830	+	0.139830i
$474$	−12.2854	+	13.0336i	−0.564287	+	0.598653i
$475$	−7.63189	+	29.0750i	−0.350175	+	1.33405i
$476$	6.59262	+	25.2043i	0.302172	+	1.15524i
$477$	13.5656	+	20.3200i	0.621127	+	0.930389i
$478$	13.7921	+	10.6485i	0.630834	+	0.487052i
$479$	35.9113			1.64083			0.820414	−	0.571770i	$-0.193743\pi$
$479$	35.9113			1.64083			0.820414	+	0.571770i	$0.193743\pi$
$480$	−8.79059	−	20.0680i	−0.401234	−	0.915976i
$481$	−10.1527			−0.462923
$482$	7.87870	+	6.08295i	0.358865	+	0.277071i
$483$	1.79260	−	18.1632i	0.0815660	−	0.826456i
$484$	−5.43540	−	20.7801i	−0.247064	−	0.944552i
$485$	34.1190	+	4.40337i	1.54927	+	0.199947i
$486$	9.01824	+	20.1164i	0.409076	+	0.912501i
$487$	−23.9090	+	23.9090i	−1.08342	+	1.08342i	−0.0872343	+	0.996188i	$0.527803\pi$
$487$	−23.9090	+	23.9090i	−1.08342	+	1.08342i	−0.996188	+	0.0872343i	$0.972197\pi$
$488$	−12.8326	−	5.45044i	−0.580905	−	0.246730i
$489$	−0.891726	+	0.731522i	−0.0403252	+	0.0330806i
$490$	−4.95440	−	0.00214030i	−0.223817	−	9.66888e-5i
$491$	−30.9507			−1.39678			−0.698392	−	0.715715i	$-0.746101\pi$
$491$	−30.9507			−1.39678			−0.698392	+	0.715715i	$0.746101\pi$
$492$	−14.5182	+	2.30513i	−0.654533	+	0.103923i
$493$	16.0728	−	16.0728i	0.723884	−	0.723884i
$494$	−8.95201	+	1.15141i	−0.402770	+	0.0518043i
$495$	1.52057	+	3.06677i	0.0683444	+	0.137841i
$496$	15.9274	−	8.94409i	0.715161	−	0.401602i
$497$	−10.5375	−	10.5375i	−0.472672	−	0.472672i
$498$	−0.489103	−	16.5510i	−0.0219172	−	0.741669i
$499$	19.9194			0.891716			0.445858	−	0.895104i	$-0.352899\pi$
$499$	19.9194			0.891716			0.445858	+	0.895104i	$0.352899\pi$
$500$	−13.6422	−	17.7169i	−0.610098	−	0.792326i
$501$	−0.769562	−	0.938097i	−0.0343815	−	0.0419111i
$502$	11.1074	+	8.57573i	0.495746	+	0.382754i
$503$	−14.6687	+	14.6687i	−0.654047	+	0.654047i	−0.953965	−	0.299918i	$-0.903041\pi$
$503$	−14.6687	+	14.6687i	−0.654047	+	0.654047i	0.299918	+	0.953965i	$0.403041\pi$
$504$	−4.61729	−	24.4025i	−0.205671	−	1.08698i
$505$	−8.75450	−	11.3490i	−0.389570	−	0.505026i
$506$	2.57684	−	0.331433i	0.114555	−	0.0147340i
$507$	2.01979	−	20.4653i	0.0897022	−	0.908896i
$508$	2.35317	+	1.37738i	0.104405	+	0.0611114i
$509$			4.85493i			0.215191i	0.994195	+	0.107595i	$0.0343151\pi$
$509$			4.85493i			0.215191i	−0.994195	+	0.107595i	$0.965685\pi$
$510$	−18.8530	+	15.4523i	−0.834823	+	0.684239i
$511$	−13.2727			−0.587149
$512$	−21.1298	+	8.09503i	−0.933816	+	0.357753i
$513$	−29.8886	−	9.08621i	−1.31961	−	0.401166i
$514$	−3.70778	−	28.8274i	−0.163543	−	1.27152i
$515$	0.754110	−	5.84314i	0.0332301	−	0.257479i
$516$	23.6270	+	17.1523i	1.04012	+	0.755088i
$517$	−1.70355	−	1.70355i	−0.0749222	−	0.0749222i
$518$	31.3345	+	24.1926i	1.37676	+	1.06296i
$519$	3.61473	+	4.40636i	0.158669	+	0.193418i
$520$	3.39412	−	5.79290i	0.148842	−	0.254035i
$521$		−	15.0499i		−	0.659346i	−0.944095	−	0.329673i	$-0.893061\pi$
$521$		−	15.0499i		−	0.659346i	0.944095	−	0.329673i	$-0.106939\pi$
$522$	−16.3397	+	14.2321i	−0.715170	+	0.622920i
$523$	15.6997	−	15.6997i	0.686499	−	0.686499i	−0.274957	−	0.961456i	$-0.588664\pi$
$523$	15.6997	−	15.6997i	0.686499	−	0.686499i	0.961456	+	0.274957i	$0.0886637\pi$
$524$	3.84254	+	14.6904i	0.167862	+	0.641755i
$525$	−10.5742	−	23.0367i	−0.461494	−	1.00541i
$526$	21.5493	−	2.77167i	0.939596	−	0.120851i
$527$	−14.3714	−	14.3714i	−0.626026	−	0.626026i
$528$	3.23763	−	1.41988i	0.140900	−	0.0617923i
$529$			10.0383i			0.436449i
$530$	18.2185	−	18.2028i	0.791361	−	0.790677i
$531$	0.683298	−	3.42800i	0.0296526	−	0.148762i
$532$	30.3725	+	17.7779i	1.31681	+	0.770770i
$533$	−3.18541	−	3.18541i	−0.137976	−	0.137976i
$534$	−22.5358	−	21.2421i	−0.975218	−	0.919235i
$535$	−31.4628	−	4.06056i	−1.36026	−	0.175553i
$536$	29.6137	−	11.9572i	1.27912	−	0.516470i
$537$	2.36701	−	23.9835i	0.102144	−	1.03496i
$538$	27.9399	−	36.1880i	1.20457	−	1.56017i
$539$		−	0.799460i		−	0.0344352i
$540$	18.9430	−	13.4596i	0.815179	−	0.579210i
$541$			1.45079i			0.0623742i	0.999514	+	0.0311871i	$0.00992877\pi$
$541$			1.45079i			0.0623742i	−0.999514	+	0.0311871i	$0.990071\pi$
$542$	−0.342914	−	0.264756i	−0.0147294	−	0.0113722i
$543$	0.988326	−	10.0141i	0.0424131	−	0.429745i
$544$	15.0266	+	20.1996i	0.644258	+	0.866050i
$545$	−17.2697	−	22.3879i	−0.739752	−	0.958990i
$546$	5.22038	−	5.53831i	0.223412	−	0.237018i
$547$	−1.86763	−	1.86763i	−0.0798541	−	0.0798541i	0.666052	−	0.745906i	$-0.267983\pi$
$547$	−1.86763	−	1.86763i	−0.0798541	−	0.0798541i	−0.745906	+	0.666052i	$0.767983\pi$
$548$	1.01951	−	1.74177i	0.0435512	−	0.0744045i
$549$	2.89078	−	14.5026i	0.123375	−	0.618955i
$550$	2.85792	−	2.20259i	0.121862	−	0.0939188i
$551$		−	30.7055i		−	1.30810i
$552$	−4.96530	−	16.9241i	−0.211337	−	0.720339i
$553$	15.1334	+	15.1334i	0.643539	+	0.643539i
$554$	−1.78060	−	13.8439i	−0.0756505	−	0.588171i
$555$	−8.32622	+	36.0925i	−0.353428	+	1.53204i
$556$	4.56234	+	17.4423i	0.193486	+	0.739720i
$557$	−22.6188	+	22.6188i	−0.958389	+	0.958389i	−0.999168	−	0.0407789i	$-0.987016\pi$
$557$	−22.6188	+	22.6188i	−0.958389	+	0.958389i	0.0407789	+	0.999168i	$0.487016\pi$
$558$	12.7254	+	14.6100i	0.538711	+	0.618490i
$559$			8.94729i			0.378430i
$560$	−24.2791	+	9.79099i	−1.02598	+	0.413745i
$561$	−2.49475	−	3.04110i	−0.105328	−	0.128395i
$562$	13.3611	−	17.3054i	0.563604	−	0.729985i
$563$	26.6638	+	26.6638i	1.12375	+	1.12375i	0.991173	+	0.132574i	$0.0423241\pi$
$563$	26.6638	+	26.6638i	1.12375	+	1.12375i	0.132574	+	0.991173i	$0.457676\pi$
$564$	−9.60832	+	13.2353i	−0.404583	+	0.557307i
$565$	−5.92543	−	0.764730i	−0.249285	−	0.0321724i
$566$	−17.5843	+	2.26169i	−0.739123	+	0.0950660i
$567$	24.3450	−	10.0612i	1.02239	−	0.422530i
$568$	−13.2549	−	5.62980i	−0.556163	−	0.236221i
$569$	29.3180			1.22907			0.614537	−	0.788888i	$-0.289343\pi$
$569$	29.3180			1.22907			0.614537	+	0.788888i	$0.289343\pi$
$570$	−3.24832	+	32.7684i	−0.136057	+	1.37252i
$571$		−	28.4036i		−	1.18865i	−0.804224	−	0.594326i	$-0.797419\pi$
$571$		−	28.4036i		−	1.18865i	0.804224	−	0.594326i	$-0.202581\pi$
$572$	0.934999	+	0.547283i	0.0390943	+	0.0228831i
$573$	−2.35535	+	23.8652i	−0.0983960	+	0.996985i
$574$	2.24077	+	17.4216i	0.0935280	+	0.727165i
$575$	−9.07997	−	15.5434i	−0.378661	−	0.648203i
$576$	−12.9664	−	20.1958i	−0.540268	−	0.841493i
$577$	−18.9787	+	18.9787i	−0.790092	+	0.790092i	−0.981509	−	0.191417i	$-0.938692\pi$
$577$	−18.9787	+	18.9787i	−0.790092	+	0.790092i	0.191417	+	0.981509i	$0.438692\pi$
$578$	2.42590	−	3.14204i	0.100904	−	0.130692i
$579$	−7.10371	−	8.65943i	−0.295220	−	0.359874i
$580$	18.0734	+	13.9665i	0.750455	+	0.579926i
$581$	−19.7855			−0.820839
$582$	37.6691	−	1.11317i	1.56143	−	0.0461423i
$583$	2.93853	+	2.93853i	0.121702	+	0.121702i
$584$	−11.8933	+	4.80216i	−0.492147	+	0.198715i
$585$	6.74825	+	2.27456i	0.279006	+	0.0940413i
$586$	0.381782	+	2.96830i	0.0157713	+	0.122619i
$587$	−11.2326	+	11.2326i	−0.463619	+	0.463619i	−0.899840	−	0.436220i	$-0.856317\pi$
$587$	−11.2326	+	11.2326i	−0.463619	+	0.463619i	0.436220	+	0.899840i	$0.356317\pi$
$588$	−5.36013	+	0.851053i	−0.221048	+	0.0350968i
$589$	−27.4550			−1.13127
$590$	−3.68451	−	0.00159170i	−0.151689	−	6.55295e-5i
$591$	7.30543	−	5.99297i	0.300505	−	0.246518i
$592$	36.8310	+	10.3412i	1.51374	+	0.425022i
$593$	−0.161070	+	0.161070i	−0.00661435	+	0.00661435i	−0.710406	−	0.703792i	$-0.751489\pi$
$593$	−0.161070	+	0.161070i	−0.00661435	+	0.00661435i	0.703792	+	0.710406i	$0.251489\pi$
$594$	2.17321	+	3.05578i	0.0891679	+	0.125380i
$595$	17.7905	+	23.0630i	0.729338	+	0.945489i
$596$	25.4581	−	6.65901i	1.04281	−	0.272764i
$597$	−1.00680	+	10.2013i	−0.0412057	+	0.417511i
$598$	3.30313	−	4.27825i	0.135075	−	0.174951i
$599$	−15.6557			−0.639673			−0.319837	−	0.947473i	$-0.603628\pi$
$599$	−15.6557			−0.639673			−0.319837	+	0.947473i	$0.603628\pi$
$600$	−17.8100	−	16.8167i	−0.727092	−	0.686540i
$601$	29.1506			1.18908			0.594540	−	0.804066i	$-0.297334\pi$
$601$	29.1506			1.18908			0.594540	+	0.804066i	$0.297334\pi$
$602$	21.3203	−	27.6142i	0.868949	−	1.12547i
$603$	18.8080	+	28.1726i	0.765922	+	1.14728i
$604$	1.39676	+	5.33998i	0.0568335	+	0.217281i
$605$	−14.6676	−	19.0147i	−0.596325	−	0.773056i
$606$	−11.4256	−	10.7697i	−0.464133	−	0.437489i
$607$	18.7872	−	18.7872i	0.762550	−	0.762550i	−0.214232	−	0.976783i	$-0.568725\pi$
$607$	18.7872	−	18.7872i	0.762550	−	0.762550i	0.976783	+	0.214232i	$0.0687250\pi$
$608$	33.6480	+	4.94129i	1.36461	+	0.200396i
$609$	16.4217	+	20.0181i	0.665443	+	0.811176i
$610$	−15.5878	−	0.00673391i	−0.631131	−	0.000272648i
$611$	−5.01206			−0.202766
$612$	−17.7339	+	19.9639i	−0.716851	+	0.806992i
$613$	−29.5115	+	29.5115i	−1.19196	+	1.19196i	−0.215443	+	0.976516i	$0.569120\pi$
$613$	−29.5115	+	29.5115i	−1.19196	+	1.19196i	−0.976516	+	0.215443i	$0.930880\pi$
$614$	3.18791	+	24.7855i	0.128654	+	1.00026i
$615$	−13.9364	+	8.71168i	−0.561969	+	0.351289i
$616$	−1.58160	−	3.91708i	−0.0637245	−	0.157823i
$617$	29.7517	+	29.7517i	1.19776	+	1.19776i	0.974836	+	0.222923i	$0.0715598\pi$
$617$	29.7517	+	29.7517i	1.19776	+	1.19776i	0.222923	+	0.974836i	$0.428440\pi$
$618$	−0.190638	−	6.45111i	−0.00766859	−	0.259502i
$619$	−12.4498			−0.500402			−0.250201	−	0.968194i	$-0.580497\pi$
$619$	−12.4498			−0.500402			−0.250201	+	0.968194i	$0.580497\pi$
$620$	12.4880	−	16.1601i	0.501529	−	0.649006i
$621$	16.5037	−	8.80867i	0.662271	−	0.353480i
$622$	0.194141	−	0.251453i	0.00778433	−	0.0100823i
$623$	−26.1665	+	26.1665i	−1.04834	+	1.04834i
$624$	2.67403	−	6.85148i	0.107047	−	0.274279i
$625$	−21.7770	−	12.2785i	−0.871080	−	0.491140i
$626$	3.07144	+	23.8799i	0.122759	+	0.954434i
$627$	−5.28785	−	0.521877i	−0.211176	−	0.0208417i
$628$	−6.25942	+	10.6938i	−0.249778	+	0.426730i
$629$		−	42.5637i		−	1.69712i
$630$	−15.4073	−	23.1002i	−0.613841	−	0.920335i
$631$	43.7481			1.74158			0.870791	−	0.491653i	$-0.163607\pi$
$631$	43.7481			1.74158			0.870791	+	0.491653i	$0.163607\pi$
$632$	19.0360	+	8.08524i	0.757212	+	0.321614i
$633$	−1.18294	+	11.9860i	−0.0470176	+	0.476399i
$634$	−40.1210	+	5.16036i	−1.59341	+	0.204944i
$635$	3.02341	+	0.390198i	0.119980	+	0.0154845i
$636$	16.5738	−	22.8301i	0.657193	−	0.905273i
$637$	−1.17605	−	1.17605i	−0.0465969	−	0.0465969i
$638$	−2.25242	+	2.91735i	−0.0891741	+	0.115499i
$639$	2.98590	−	14.9798i	0.118121	−	0.592592i
$640$	−18.2133	+	17.5578i	−0.719945	+	0.694032i
$641$		−	13.3935i		−	0.529013i	−0.964384	−	0.264506i	$-0.914791\pi$
$641$		−	13.3935i		−	0.529013i	0.964384	−	0.264506i	$-0.0852090\pi$
$642$	−34.7365	+	1.02651i	−1.37094	+	0.0405129i
$643$	12.4335	−	12.4335i	0.490331	−	0.490331i	−0.418080	−	0.908410i	$-0.637297\pi$
$643$	12.4335	−	12.4335i	0.490331	−	0.490331i	0.908410	+	0.418080i	$0.137297\pi$
$644$	−20.3891	+	5.33311i	−0.803442	+	0.210154i
$645$	31.8073	+	7.33766i	1.25241	+	0.288920i
$646$	−4.82710	−	37.5300i	−0.189920	−	1.47660i
$647$	−0.352589	−	0.352589i	−0.0138617	−	0.0138617i	0.700142	−	0.714004i	$-0.253120\pi$
$647$	−0.352589	−	0.352589i	−0.0138617	−	0.0138617i	−0.714004	+	0.700142i	$0.753120\pi$
$648$	18.1746	−	17.8237i	0.713965	−	0.700181i
$649$		−	0.594545i		−	0.0233380i
$650$	0.964026	−	7.44431i	0.0378122	−	0.291990i
$651$	17.8990	−	14.6833i	0.701517	−	0.575485i
$652$	1.14939	+	0.672775i	0.0450138	+	0.0263479i
$653$	−10.5497	−	10.5497i	−0.412841	−	0.412841i	0.469886	−	0.882727i	$-0.344295\pi$
$653$	−10.5497	−	10.5497i	−0.412841	−	0.412841i	−0.882727	+	0.469886i	$0.844295\pi$
$654$	−22.5389	−	21.2450i	−0.881339	−	0.830745i
$655$	10.3692	+	13.4423i	0.405160	+	0.525236i
$656$	8.31116	+	14.8003i	0.324496	+	0.577854i
$657$	−7.55356	−	11.3145i	−0.294692	−	0.441421i
$658$	15.4688	+	11.9431i	0.603038	+	0.465591i
$659$		−	30.8600i		−	1.20213i	−0.799199	−	0.601067i	$-0.794742\pi$
$659$		−	30.8600i		−	1.20213i	0.799199	−	0.601067i	$-0.205258\pi$
$660$	2.71236	−	2.87506i	0.105579	−	0.111912i
$661$		−	44.1992i		−	1.71915i	−0.511009	−	0.859575i	$-0.670728\pi$
$661$		−	44.1992i		−	1.71915i	0.511009	−	0.859575i	$-0.329272\pi$
$662$	10.6570	−	13.8030i	0.414196	−	0.536470i
$663$	−8.14357	−	0.803718i	−0.316270	−	0.0312138i
$664$	−17.7292	+	7.15852i	−0.688025	+	0.277804i
$665$	39.0232	+	5.03630i	1.51326	+	0.195299i
$666$	−2.79072	+	40.4797i	−0.108138	+	1.56856i
$667$	13.0021	+	13.0021i	0.503444	+	0.503444i
$668$	−0.707760	+	1.20916i	−0.0273841	+	0.0467840i
$669$	25.9783	+	31.6675i	1.00438	+	1.22434i
$670$	25.2590	−	25.2372i	0.975840	−	0.974997i
$671$		−	2.51530i		−	0.0971021i
$672$	−24.5791	+	14.7740i	−0.948160	+	0.569920i
$673$	13.1276	+	13.1276i	0.506033	+	0.506033i	0.913306	−	0.407274i	$-0.133520\pi$
$673$	13.1276	+	13.1276i	0.506033	+	0.506033i	−0.407274	+	0.913306i	$0.633520\pi$
$674$	−21.1703	+	2.72292i	−0.815448	+	0.104883i
$675$	13.6202	−	22.1244i	0.524242	−	0.851570i
$676$	−22.9732	+	6.00904i	−0.883586	+	0.231117i
$677$	−23.1658	+	23.1658i	−0.890334	+	0.890334i	−0.994554	−	0.104220i	$-0.966765\pi$
$677$	−23.1658	+	23.1658i	−0.890334	+	0.890334i	0.104220	+	0.994554i	$0.466765\pi$
$678$	−6.54196	+	0.193323i	−0.251242	+	0.00742452i
$679$		−	45.0304i		−	1.72811i
$680$	24.2858	+	14.2293i	0.931320	+	0.545670i
$681$	−23.6371	+	19.3905i	−0.905775	+	0.743047i
$682$	2.60852	+	2.01398i	0.0998855	+	0.0771192i
$683$	−14.8655	−	14.8655i	−0.568814	−	0.568814i	0.362982	−	0.931796i	$-0.381759\pi$
$683$	−14.8655	−	14.8655i	−0.568814	−	0.568814i	−0.931796	+	0.362982i	$0.881759\pi$
$684$	2.13008	+	36.0090i	0.0814455	+	1.37684i
$685$	0.288816	−	2.23786i	0.0110351	−	0.0855042i
$686$	−2.86899	−	22.3060i	−0.109539	−	0.851647i
$687$	1.89049	+	0.186579i	0.0721266	+	0.00711843i
$688$	9.11344	−	32.4581i	0.347447	−	1.23745i
$689$	8.64552			0.329368
$690$	−12.5001	−	15.2511i	−0.475872	−	0.580600i
$691$			47.2699i			1.79823i	0.437710	+	0.899116i	$0.355790\pi$
$691$			47.2699i			1.79823i	−0.437710	+	0.899116i	$0.644210\pi$
$692$	3.32444	−	5.67960i	0.126376	−	0.215906i
$693$	3.72646	−	2.48778i	0.141557	−	0.0945031i
$694$	−15.8783	+	2.04227i	−0.602733	+	0.0775235i
$695$	12.3117	+	15.9604i	0.467008	+	0.605414i
$696$	21.9577	+	11.9961i	0.832306	+	0.454713i
$697$	13.3544	−	13.3544i	0.505833	−	0.505833i
$698$	−15.6245	−	12.0633i	−0.591396	−	0.456603i
$699$	−13.2202	+	10.8451i	−0.500035	+	0.410201i
$700$	−20.7142	+	20.6784i	−0.782921	+	0.781570i
$701$	−7.65973			−0.289304			−0.144652	−	0.989483i	$-0.546206\pi$
$701$	−7.65973			−0.289304			−0.144652	+	0.989483i	$0.546206\pi$
$702$	7.69216	+	1.29831i	0.290322	+	0.0490015i
$703$	−40.6568	−	40.6568i	−1.53340	−	1.53340i
$704$	−2.83445	−	2.93774i	−0.106827	−	0.110720i
$705$	−4.11039	+	17.8177i	−0.154806	+	0.671054i
$706$	−23.5547	+	3.02960i	−0.886492	+	0.114021i
$707$	−13.2664	+	13.2664i	−0.498933	+	0.498933i
$708$	−3.98625	+	0.632915i	−0.149812	+	0.0237864i
$709$	43.9829			1.65181			0.825906	−	0.563808i	$-0.190664\pi$
$709$	43.9829			1.65181			0.825906	+	0.563808i	$0.190664\pi$
$710$	−16.1007	−	0.00695550i	−0.604250	−	0.000261035i
$711$	−4.28821	+	21.5132i	−0.160820	+	0.806810i
$712$	−13.9798	+	32.9143i	−0.523915	+	1.23351i
$713$	11.6257	−	11.6257i	0.435387	−	0.435387i
$714$	23.2185	+	21.8856i	0.868931	+	0.819050i
$715$	1.20131	+	0.155040i	0.0449264	+	0.00579816i
$716$	−26.9225	+	7.04204i	−1.00614	+	0.263174i
$717$	21.2373	+	2.09599i	0.793123	+	0.0782762i
$718$	−37.9213	−	29.2781i	−1.41521	−	1.09265i
$719$	−14.6227			−0.545333			−0.272666	−	0.962109i	$-0.587906\pi$
$719$	−14.6227			−0.545333			−0.272666	+	0.962109i	$0.587906\pi$
$720$	−22.1638	−	15.1250i	−0.825997	−	0.563674i
$721$	−7.71179			−0.287202
$722$	−19.1909	−	14.8168i	−0.714212	−	0.551425i
$723$	12.1318	+	1.19733i	0.451186	+	0.0445292i
$724$	−11.2413	+	2.94034i	−0.417778	+	0.109277i
$725$	24.7002	+	6.48356i	0.917342	+	0.240793i
$726$	−19.1429	−	18.0440i	−0.710460	−	0.669675i
$727$	−22.1109	+	22.1109i	−0.820048	+	0.820048i	−0.986115	−	0.166067i	$-0.946893\pi$
$727$	−22.1109	+	22.1109i	−0.820048	+	0.820048i	0.166067	+	0.986115i	$0.446893\pi$
$728$	−8.08889	−	3.43563i	−0.299794	−	0.127333i
$729$	22.4316	+	15.0274i	0.830802	+	0.556569i
$730$	−10.1444	+	10.1356i	−0.375459	+	0.375135i
$731$	−37.5102			−1.38736
$732$	−16.8643	+	2.67763i	−0.623323	+	0.0989679i
$733$	−8.64610	+	8.64610i	−0.319351	+	0.319351i	−0.848518	−	0.529167i	$-0.822505\pi$
$733$	−8.64610	+	8.64610i	−0.319351	+	0.319351i	0.529167	+	0.848518i	$0.322505\pi$
$734$	−21.4037	+	2.75294i	−0.790023	+	0.101613i
$735$	−5.14531	+	3.21635i	−0.189788	+	0.118637i
$736$	−16.3405	+	12.1557i	−0.602318	+	0.448067i
$737$	4.07412	+	4.07412i	0.150072	+	0.150072i
$738$	−13.5761	+	11.8249i	−0.499743	+	0.435282i
$739$	29.8509			1.09808			0.549041	−	0.835796i	$-0.314993\pi$
$739$	29.8509			1.09808			0.549041	+	0.835796i	$0.314993\pi$
$740$	42.4235	−	5.43788i	1.55952	−	0.199901i
$741$	−8.54646	+	7.01103i	−0.313962	+	0.257557i
$742$	−26.6828	−	20.6012i	−0.979558	−	0.756293i
$743$	6.78930	−	6.78930i	0.249075	−	0.249075i	−0.571516	−	0.820591i	$-0.693644\pi$
$743$	6.78930	−	6.78930i	0.249075	−	0.249075i	0.820591	+	0.571516i	$0.193644\pi$
$744$	10.7262	−	19.6333i	0.393243	−	0.719791i
$745$	23.2952	−	17.9696i	0.853470	−	0.658355i
$746$	51.2539	−	6.59227i	1.87654	−	0.241360i
$747$	−11.2600	−	16.8664i	−0.411982	−	0.617110i
$748$	−2.29440	+	3.91984i	−0.0838916	+	0.143324i
$749$			41.5247i			1.51728i
$750$	−25.6737	−	9.53215i	−0.937470	−	0.348065i
$751$	22.5357			0.822339			0.411170	−	0.911559i	$-0.365120\pi$
$751$	22.5357			0.822339			0.411170	+	0.911559i	$0.365120\pi$
$752$	18.1823	+	5.10513i	0.663039	+	0.186165i
$753$	17.1034	+	1.68800i	0.623282	+	0.0615140i
$754$	0.978161	+	7.60505i	0.0356225	+	0.276959i
$755$	3.76922	+	4.88630i	0.137176	+	0.177831i
$756$	−20.6468	−	22.3364i	−0.750916	−	0.812368i
$757$	−33.9790	−	33.9790i	−1.23499	−	1.23499i	−0.962025	−	0.272963i	$-0.911996\pi$
$757$	−33.9790	−	33.9790i	−1.23499	−	1.23499i	−0.272963	−	0.962025i	$-0.588004\pi$
$758$	13.6860	+	10.5666i	0.497099	+	0.383798i
$759$	2.46010	−	2.01813i	0.0892961	−	0.0732535i
$760$	36.7897	−	9.60599i	1.33450	−	0.348446i
$761$			34.4290i			1.24805i	0.781404	+	0.624025i	$0.214504\pi$
$761$			34.4290i			1.24805i	−0.781404	+	0.624025i	$0.785496\pi$
$762$	3.33799	−	0.0986416i	0.120923	−	0.00357341i
$763$	−26.1701	+	26.1701i	−0.947421	+	0.947421i
$764$	26.7898	−	7.00733i	0.969222	−	0.253516i
$765$	−9.53573	+	28.2910i	−0.344765	+	1.02286i
$766$	−42.8977	+	5.51751i	−1.54996	+	0.199356i
$767$	−0.874612	−	0.874612i	−0.0315804	−	0.0315804i
$768$	−16.6793	+	22.1315i	−0.601862	+	0.798600i
$769$			14.8941i			0.537094i	0.963267	+	0.268547i	$0.0865434\pi$
$769$			14.8941i			0.537094i	−0.963267	+	0.268547i	$0.913457\pi$
$770$	−3.33818	−	3.34107i	−0.120300	−	0.120404i
$771$	−22.5770	−	27.5214i	−0.813091	−	0.991159i
$772$	−6.53323	+	11.1616i	−0.235136	+	0.401715i
$773$	7.32969	+	7.32969i	0.263631	+	0.263631i	0.826527	−	0.562897i	$-0.190313\pi$
$773$	7.32969	+	7.32969i	0.263631	+	0.263631i	−0.562897	+	0.826527i	$0.690313\pi$
$774$	35.6736	+	2.45939i	1.28226	+	0.0884008i
$775$	5.79721	−	22.0854i	0.208242	−	0.793332i
$776$	−16.2923	−	40.3504i	−0.584861	−	1.44850i
$777$	48.2496	+	4.76193i	1.73094	+	0.170833i
$778$	−5.73818	+	7.43215i	−0.205724	+	0.266455i
$779$		−	25.5122i		−	0.914069i
$780$	−0.239341	−	8.21945i	−0.00856977	−	0.294303i
$781$		−	2.59807i		−	0.0929663i
$782$	17.9359	+	13.8479i	0.641387	+	0.495199i
$783$	−7.71905	+	25.3914i	−0.275856	+	0.907414i
$784$	3.06848	+	5.46427i	0.109589	+	0.195152i
$785$	−1.77323	+	13.7397i	−0.0632893	+	0.490390i
$786$	13.5330	+	12.7561i	0.482707	+	0.454996i
$787$	−4.66068	−	4.66068i	−0.166135	−	0.166135i	0.619143	−	0.785278i	$-0.287480\pi$
$787$	−4.66068	−	4.66068i	−0.166135	−	0.166135i	−0.785278	+	0.619143i	$0.787480\pi$
$788$	−9.41637	−	5.51168i	−0.335444	−	0.196346i
$789$	20.5731	−	16.8770i	0.732421	−	0.600837i
$790$	23.1231	+	0.00998914i	0.822682	+	0.000355398i
$791$			7.82040i			0.278061i
$792$	2.43907	−	3.57749i	0.0866687	−	0.127120i
$793$	−3.70016	−	3.70016i	−0.131396	−	0.131396i
$794$	−3.58713	−	27.8894i	−0.127303	−	0.989757i
$795$	7.09018	−	30.7345i	0.251463	−	1.09004i
$796$	11.4514	−	2.99531i	0.405884	−	0.106166i
$797$	27.8720	−	27.8720i	0.987276	−	0.987276i	−0.0126440	−	0.999920i	$-0.504025\pi$
$797$	27.8720	−	27.8720i	0.987276	−	0.987276i	0.999920	+	0.0126440i	$0.00402483\pi$
$798$	43.0835	−	1.27317i	1.52514	−	0.0450697i
$799$		−	21.0123i		−	0.743362i
$800$	−11.0797	+	26.0238i	−0.391728	+	0.920081i
$801$	−37.1975	−	7.41454i	−1.31431	−	0.261980i
$802$	15.6584	−	20.2809i	0.552916	−	0.716142i
$803$	−1.63622	−	1.63622i	−0.0577410	−	0.0577410i
$804$	22.9787	−	31.6528i	0.810396	−	1.11631i
$805$	−18.6568	+	14.3916i	−0.657566	+	0.507238i
$806$	6.79998	−	0.874612i	0.239519	−	0.0308069i
$807$	5.49951	−	55.7231i	0.193592	−	1.96155i
$808$	−7.08773	+	16.6875i	−0.249346	+	0.587063i
$809$	−18.8285			−0.661975			−0.330988	−	0.943635i	$-0.607382\pi$
$809$	−18.8285			−0.661975			−0.330988	+	0.943635i	$0.607382\pi$
$810$	10.9238	−	26.2806i	0.383822	−	0.923407i
$811$			37.4113i			1.31369i	0.754026	+	0.656845i	$0.228109\pi$
$811$			37.4113i			1.31369i	−0.754026	+	0.656845i	$0.771891\pi$
$812$	15.1030	−	25.8025i	0.530010	−	0.905489i
$813$	−0.528027	−	0.0521129i	−0.0185187	−	0.00182768i
$814$	0.880433	+	6.84523i	0.0308592	+	0.239925i
$815$	1.47677	+	0.190590i	0.0517289	+	0.00667609i
$816$	28.7238	+	11.2104i	1.00553	+	0.392444i
$817$	−35.8297	+	35.8297i	−1.25352	+	1.25352i
$818$	−22.7512	+	29.4676i	−0.795477	+	1.03031i
$819$	1.82217	−	9.14153i	0.0636717	−	0.319431i
$820$	15.0165	+	11.6043i	0.524400	+	0.405238i
$821$	−14.3129			−0.499523			−0.249761	−	0.968307i	$-0.580352\pi$
$821$	−14.3129			−0.499523			−0.249761	+	0.968307i	$0.580352\pi$
$822$	−0.0730123	−	2.47070i	−0.00254660	−	0.0861757i
$823$	10.8660	+	10.8660i	0.378766	+	0.378766i	0.870657	−	0.491891i	$-0.163694\pi$
$823$	10.8660	+	10.8660i	0.378766	+	0.378766i	−0.491891	+	0.870657i	$0.663694\pi$
$824$	−6.91031	+	2.79018i	−0.240732	+	0.0972006i
$825$	1.53635	−	4.14346i	0.0534889	−	0.144257i
$826$	0.615244	+	4.78343i	0.0214071	+	0.166437i
$827$	2.49596	−	2.49596i	0.0867932	−	0.0867932i	−0.662377	−	0.749170i	$-0.730452\pi$
$827$	2.49596	−	2.49596i	0.0867932	−	0.0867932i	0.749170	+	0.662377i	$0.230452\pi$
$828$	−16.1498	−	14.3459i	−0.561245	−	0.498553i
$829$	−49.1212			−1.70605			−0.853026	−	0.521869i	$-0.825235\pi$
$829$	−49.1212			−1.70605			−0.853026	+	0.521869i	$0.825235\pi$
$830$	−15.1221	+	15.1090i	−0.524895	+	0.524441i
$831$	−10.8423	−	13.2167i	−0.376114	−	0.458483i
$832$	−8.49125	−	0.151945i	−0.294381	−	0.00526773i
$833$	4.93043	−	4.93043i	0.170829	−	0.170829i
$834$	16.0681	+	15.1457i	0.556392	+	0.524452i
$835$	−0.200501	+	1.55356i	−0.00693863	+	0.0537632i
$836$	1.55262	+	5.93585i	0.0536985	+	0.205296i
$837$	22.7034	+	6.90191i	0.784746	+	0.238565i
$838$	−11.0460	+	14.3069i	−0.381577	+	0.494223i
$839$	−26.9749			−0.931277			−0.465638	−	0.884975i	$-0.654175\pi$
$839$	−26.9749			−0.931277			−0.465638	+	0.884975i	$0.654175\pi$
$840$	−18.8472	+	25.9382i	−0.650291	+	0.894952i
$841$	2.91458			0.100503
$842$	−22.7985	+	29.5288i	−0.785687	+	1.01763i
$843$	2.62992	−	26.6473i	0.0905792	−	0.917782i
$844$	13.4548	−	3.51933i	0.463133	−	0.121140i
$845$	−21.0214	+	16.2156i	−0.723159	+	0.557835i
$846$	−1.37769	+	19.9835i	−0.0473660	+	0.687048i
$847$	−22.2270	+	22.2270i	−0.763729	+	0.763729i
$848$	−31.3634	−	8.80606i	−1.07702	−	0.302401i
$849$	−16.7877	+	13.7717i	−0.576151	+	0.472642i
$850$	31.2092	+	4.04153i	1.07047	+	0.138623i
$851$	34.4319			1.18031
$852$	−17.4193	+	2.76574i	−0.596774	+	0.0947526i
$853$	16.4190	−	16.4190i	0.562174	−	0.562174i	−0.367750	−	0.929925i	$-0.619872\pi$
$853$	16.4190	−	16.4190i	0.562174	−	0.562174i	0.929925	+	0.367750i	$0.119872\pi$
$854$	2.60287	+	20.2369i	0.0890683	+	0.692492i
$855$	17.9150	+	36.1321i	0.612681	+	1.23569i
$856$	15.0239	+	37.2091i	0.513508	+	1.27178i
$857$	−24.4641	−	24.4641i	−0.835678	−	0.835678i	0.152608	−	0.988287i	$-0.451233\pi$
$857$	−24.4641	−	24.4641i	−0.835678	−	0.835678i	−0.988287	+	0.152608i	$0.951233\pi$
$858$	1.32630	−	0.0391938i	0.0452792	−	0.00133806i
$859$	1.68121			0.0573622			0.0286811	−	0.999589i	$-0.490869\pi$
$859$	1.68121			0.0573622			0.0286811	+	0.999589i	$0.490869\pi$
$860$	−4.79225	−	37.3867i	−0.163415	−	1.27488i
$861$	13.6443	+	16.6324i	0.464995	+	0.566830i
$862$	24.7886	−	32.1064i	0.844302	−	1.09355i
$863$	23.0950	−	23.0950i	0.786161	−	0.786161i	−0.194701	−	0.980863i	$-0.562374\pi$
$863$	23.0950	−	23.0950i	0.786161	−	0.786161i	0.980863	+	0.194701i	$0.0623737\pi$
$864$	−26.5824	−	12.5449i	−0.904353	−	0.426785i
$865$	0.941779	−	7.29727i	0.0320215	−	0.248115i
$866$	0.575226	+	4.47229i	0.0195470	+	0.151975i
$867$	0.477499	−	4.83819i	0.0162167	−	0.164314i
$868$	−23.0710	−	13.5042i	−0.783081	−	0.458361i
$869$			3.73122i			0.126573i
$870$	27.8379	+	2.75956i	0.943792	+	0.0935580i
$871$	11.9866			0.406149
$872$	−13.9817	+	32.9188i	−0.473481	+	1.11477i
$873$	38.3869	−	25.6271i	1.29920	−	0.867345i
$874$	30.3599	−	3.90489i	1.02694	−	0.132085i
$875$	−12.2912	+	30.3277i	−0.415517	+	1.02526i
$876$	−9.22855	+	12.7122i	−0.311804	+	0.429505i
$877$	−14.2900	−	14.2900i	−0.482539	−	0.482539i	0.423403	−	0.905942i	$-0.360836\pi$
$877$	−14.2900	−	14.2900i	−0.482539	−	0.482539i	−0.905942	+	0.423403i	$0.860836\pi$
$878$	10.2424	−	13.2660i	0.345664	−	0.447707i
$879$	2.32471	+	2.83382i	0.0784105	+	0.0955825i
$880$	−4.20007	−	1.78605i	−0.141584	−	0.0602078i
$881$		−	45.2886i		−	1.52581i	−0.646509	−	0.762906i	$-0.723772\pi$
$881$		−	45.2886i		−	1.52581i	0.646509	−	0.762906i	$-0.276228\pi$
$882$	−5.01230	+	4.36576i	−0.168773	+	0.147003i
$883$	3.68252	−	3.68252i	0.123927	−	0.123927i	−0.642423	−	0.766350i	$-0.722071\pi$
$883$	3.68252	−	3.68252i	0.123927	−	0.123927i	0.766350	+	0.642423i	$0.222071\pi$
$884$	2.39112	+	9.14153i	0.0804221	+	0.307463i
$885$	−3.82649	+	2.39195i	−0.128626	+	0.0804045i
$886$	0.425589	+	3.30889i	0.0142980	+	0.111164i
$887$	14.7506	+	14.7506i	0.495277	+	0.495277i	0.909964	−	0.414687i	$-0.136109\pi$
$887$	14.7506	+	14.7506i	0.495277	+	0.495277i	−0.414687	+	0.909964i	$0.636109\pi$
$888$	44.9579	−	13.1900i	1.50869	−	0.442628i
$889$		−	3.99030i		−	0.133830i
$890$	−0.0172717	+	39.9810i	−0.000578950	+	1.34017i
$891$	4.24150	+	1.76087i	0.142095	+	0.0589912i
$892$	23.8920	−	40.8180i	0.799964	−	1.36669i
$893$	−20.0710	−	20.0710i	−0.671649	−	0.671649i
$894$	22.1060	−	23.4523i	0.739336	−	0.784363i
$895$	−24.6352	+	19.0032i	−0.823463	+	0.635209i
$896$	25.8446	+	20.7025i	0.863409	+	0.691623i
$897$	0.650169	−	6.58775i	0.0217085	−	0.219959i
$898$	38.4417	+	29.6799i	1.28282	+	0.990432i
$899$			23.3240i			0.777899i
$900$	−29.4161	−	5.88991i	−0.980538	−	0.196330i
$901$			36.2450i			1.20750i
$902$	−1.87146	+	2.42393i	−0.0623127	+	0.0807080i
$903$	4.19655	−	42.5210i	0.139653	−	1.41501i
$904$	2.82948	+	7.00763i	0.0941070	+	0.233070i
$905$	−10.2862	+	7.93464i	−0.341925	+	0.263756i
$906$	4.91925	+	4.63686i	0.163431	+	0.154049i
$907$	−8.08868	−	8.08868i	−0.268580	−	0.268580i	0.559948	−	0.828528i	$-0.310821\pi$
$907$	−8.08868	−	8.08868i	−0.268580	−	0.268580i	−0.828528	+	0.559948i	$0.810821\pi$
$908$	30.4671	+	17.8333i	1.01109	+	0.591820i
$909$	−18.8591	−	3.75915i	−0.625516	−	0.124683i
$910$	−9.82558	−	0.00424464i	−0.325715	−	0.000140709i
$911$		−	38.7011i		−	1.28222i	−0.767448	−	0.641112i	$-0.778473\pi$
$911$		−	38.7011i		−	1.28222i	0.767448	−	0.641112i	$-0.221527\pi$
$912$	38.1452	−	16.7288i	1.26311	−	0.553945i
$913$	−2.43910	−	2.43910i	−0.0807223	−	0.0807223i
$914$	9.15408	−	1.17740i	0.302790	−	0.0389448i
$915$	−16.1884	+	10.1194i	−0.535173	+	0.334538i
$916$	−0.555086	−	2.12216i	−0.0183406	−	0.0701180i
$917$	15.7133	−	15.7133i	0.518899	−	0.518899i
$918$	−5.44296	+	32.2482i	−0.179644	+	1.06435i
$919$			39.9611i			1.31819i	0.752058	+	0.659097i	$0.229061\pi$
$919$			39.9611i			1.31819i	−0.752058	+	0.659097i	$0.770939\pi$
$920$	−11.5108	+	19.6461i	−0.379501	+	0.647711i
$921$	19.4115	+	23.6626i	0.639630	+	0.779710i
$922$	−23.1102	−	17.8428i	−0.761094	−	0.587623i
$923$	−3.82192	−	3.82192i	−0.125800	−	0.125800i
$924$	−4.18679	−	3.03945i	−0.137735	−	0.0999904i
$925$	41.2900	−	24.1204i	1.35761	−	0.793074i
$926$	−6.93510	−	53.9193i	−0.227901	−	1.77190i
$927$	−4.38882	−	6.57403i	−0.144148	−	0.215920i
$928$	4.19779	−	28.5852i	0.137799	−	0.938354i
$929$	0.568113			0.0186392			0.00931959	−	0.999957i	$-0.497033\pi$
$929$	0.568113			0.0186392			0.00931959	+	0.999957i	$0.497033\pi$
$930$	2.46744	−	24.8910i	0.0809104	−	0.816207i
$931$		−	9.41909i		−	0.308698i
$932$	17.0403	+	9.97418i	0.558173	+	0.326715i
$933$	0.0382135	−	0.387193i	0.00125105	−	0.0126761i
$934$	−12.6935	+	1.63263i	−0.415343	+	0.0534213i
$935$	−0.649980	+	5.03630i	−0.0212566	+	0.164705i
$936$	−1.67468	−	8.85073i	−0.0547386	−	0.289295i
$937$	18.2630	−	18.2630i	0.596626	−	0.596626i	−0.342787	−	0.939413i	$-0.611371\pi$
$937$	18.2630	−	18.2630i	0.596626	−	0.596626i	0.939413	+	0.342787i	$0.111371\pi$
$938$	−36.9944	−	28.5624i	−1.20791	−	0.932597i
$939$	18.7023	+	22.7981i	0.610326	+	0.743988i
$940$	20.9431	−	2.68451i	0.683090	−	0.0875590i
$941$	22.3971			0.730125			0.365063	−	0.930983i	$-0.381048\pi$
$941$	22.3971			0.730125			0.365063	+	0.930983i	$0.381048\pi$
$942$	0.448270	+	15.1693i	0.0146054	+	0.494242i
$943$	10.8030	+	10.8030i	0.351795	+	0.351795i
$944$	2.28198	+	4.06369i	0.0742721	+	0.132262i
$945$	−31.0035	−	13.9747i	−1.00854	−	0.454597i
$946$	6.03251	−	0.775901i	0.196134	−	0.0252267i
$947$	15.7486	−	15.7486i	0.511761	−	0.511761i	−0.403305	−	0.915066i	$-0.632139\pi$
$947$	15.7486	−	15.7486i	0.511761	−	0.511761i	0.915066	+	0.403305i	$0.132139\pi$
$948$	25.0167	−	3.97201i	0.812504	−	0.129005i
$949$	−4.81396			−0.156268
$950$	33.6715	−	25.9505i	1.09245	−	0.841946i
$951$	−38.3034	+	31.4219i	−1.24207	+	1.01893i
$952$	14.4033	−	33.9114i	0.466815	−	1.09908i
$953$	−33.3609	+	33.3609i	−1.08067	+	1.08067i	−0.0842194	+	0.996447i	$0.526840\pi$
$953$	−33.3609	+	33.3609i	−1.08067	+	1.08067i	−0.996447	+	0.0842194i	$0.973160\pi$
$954$	2.37644	−	34.4704i	0.0769400	−	1.11602i
$955$	24.5138	−	18.9096i	0.793246	−	0.611900i
$956$	−6.23572	−	23.8399i	−0.201678	−	0.771037i
$957$	−0.443352	+	4.49221i	−0.0143315	+	0.145213i
$958$	−40.1990	−	31.0367i	−1.29877	−	1.00275i
$959$	−2.95353			−0.0953746
$960$	−7.50382	+	30.0615i	−0.242185	+	0.970230i
$961$	−10.1451			−0.327260
$962$	11.3649	+	8.77458i	0.366420	+	0.282904i
$963$	−35.3984	+	23.6319i	−1.14070	+	0.761529i
$964$	−3.56215	−	13.6185i	−0.114729	−	0.438622i
$965$	−1.85080	+	14.3407i	−0.0595793	+	0.461643i
$966$	−17.7044	+	18.7826i	−0.569630	+	0.604322i
$967$	−8.01398	+	8.01398i	−0.257712	+	0.257712i	−0.824123	−	0.566411i	$-0.808332\pi$
$967$	−8.01398	+	8.01398i	−0.257712	+	0.257712i	0.566411	+	0.824123i	$0.308332\pi$
$968$	−11.8751	+	27.9589i	−0.381679	+	0.898632i
$969$	−29.3927	−	35.8297i	−0.944229	−	1.15102i
$970$	−34.3872	−	34.4169i	−1.10411	−	1.10506i
$971$	43.4981			1.39592			0.697961	−	0.716136i	$-0.254091\pi$
$971$	43.4981			1.39592			0.697961	+	0.716136i	$0.254091\pi$
$972$	7.29085	−	30.3124i	0.233854	−	0.972272i
$973$	18.6568	−	18.6568i	0.598110	−	0.598110i
$974$	47.4274	−	6.10011i	1.51967	−	0.195460i
$975$	−3.83521	−	8.35535i	−0.122825	−	0.267585i
$976$	9.65420	+	17.1919i	0.309024	+	0.550301i
$977$	−39.7367	−	39.7367i	−1.27129	−	1.27129i	−0.945411	−	0.325880i	$-0.894339\pi$
$977$	−39.7367	−	39.7367i	−1.27129	−	1.27129i	−0.325880	−	0.945411i	$-0.605661\pi$
$978$	1.63042	−	0.0481810i	0.0521352	−	0.00154066i
$979$	−6.45147			−0.206190
$980$	5.54410	+	4.28429i	0.177100	+	0.136857i
$981$	−37.2026	−	7.41555i	−1.18779	−	0.236760i
$982$	34.6462	+	26.7495i	1.10560	+	0.853609i
$983$	9.14087	−	9.14087i	0.291548	−	0.291548i	−0.546143	−	0.837692i	$-0.683905\pi$
$983$	9.14087	−	9.14087i	0.291548	−	0.291548i	0.837692	+	0.546143i	$0.183905\pi$
$984$	18.2439	+	9.96719i	0.581596	+	0.317742i
$985$	−12.0984	−	1.56140i	−0.385486	−	0.0497504i
$986$	−31.8830	+	4.10079i	−1.01536	+	0.130596i
$987$	23.8193	+	2.35081i	0.758176	+	0.0748271i
$988$	11.0160	+	6.44799i	0.350465	+	0.205138i
$989$		−	30.3439i		−	0.964879i
$990$	0.948366	−	4.74710i	0.0301411	−	0.150873i
$991$	−23.1823			−0.736409			−0.368205	−	0.929745i	$-0.620027\pi$
$991$	−23.1823			−0.736409			−0.368205	+	0.929745i	$0.620027\pi$
$992$	−25.5591	−	3.75342i	−0.811503	−	0.119171i
$993$	2.09766	−	21.2542i	0.0665671	−	0.674483i
$994$	2.68852	+	20.9028i	0.0852747	+	0.662997i
$995$	10.4785	−	8.08297i	0.332191	−	0.256247i
$996$	−13.7569	+	18.9499i	−0.435904	+	0.600451i
$997$	−3.70273	−	3.70273i	−0.117267	−	0.117267i	0.646038	−	0.763305i	$-0.276425\pi$
$997$	−3.70273	−	3.70273i	−0.117267	−	0.117267i	−0.763305	+	0.646038i	$0.776425\pi$
$998$	−22.2978	−	17.2156i	−0.705824	−	0.544949i
$999$	23.3997	+	43.8411i	0.740334	+	1.38707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.w.c.53.4	✓	32
3.2	odd	2	inner	120.2.w.c.53.13	yes	32
4.3	odd	2		480.2.bi.c.113.16		32
5.2	odd	4	inner	120.2.w.c.77.12	yes	32
5.3	odd	4		600.2.w.j.557.5		32
5.4	even	2		600.2.w.j.293.13		32
8.3	odd	2		480.2.bi.c.113.1		32
8.5	even	2	inner	120.2.w.c.53.5	yes	32
12.11	even	2		480.2.bi.c.113.8		32
15.2	even	4	inner	120.2.w.c.77.5	yes	32
15.8	even	4		600.2.w.j.557.12		32
15.14	odd	2		600.2.w.j.293.4		32
20.7	even	4		480.2.bi.c.17.9		32
24.5	odd	2	inner	120.2.w.c.53.12	yes	32
24.11	even	2		480.2.bi.c.113.9		32
40.13	odd	4		600.2.w.j.557.4		32
40.27	even	4		480.2.bi.c.17.8		32
40.29	even	2		600.2.w.j.293.12		32
40.37	odd	4	inner	120.2.w.c.77.13	yes	32
60.47	odd	4		480.2.bi.c.17.1		32
120.29	odd	2		600.2.w.j.293.5		32
120.53	even	4		600.2.w.j.557.13		32
120.77	even	4	inner	120.2.w.c.77.4	yes	32
120.107	odd	4		480.2.bi.c.17.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.4	✓	32	1.1	even	1	trivial
120.2.w.c.53.5	yes	32	8.5	even	2	inner
120.2.w.c.53.12	yes	32	24.5	odd	2	inner
120.2.w.c.53.13	yes	32	3.2	odd	2	inner
120.2.w.c.77.4	yes	32	120.77	even	4	inner
120.2.w.c.77.5	yes	32	15.2	even	4	inner
120.2.w.c.77.12	yes	32	5.2	odd	4	inner
120.2.w.c.77.13	yes	32	40.37	odd	4	inner
480.2.bi.c.17.1		32	60.47	odd	4
480.2.bi.c.17.8		32	40.27	even	4
480.2.bi.c.17.9		32	20.7	even	4
480.2.bi.c.17.16		32	120.107	odd	4
480.2.bi.c.113.1		32	8.3	odd	2
480.2.bi.c.113.8		32	12.11	even	2
480.2.bi.c.113.9		32	24.11	even	2
480.2.bi.c.113.16		32	4.3	odd	2
600.2.w.j.293.4		32	15.14	odd	2
600.2.w.j.293.5		32	120.29	odd	2
600.2.w.j.293.12		32	40.29	even	2
600.2.w.j.293.13		32	5.4	even	2
600.2.w.j.557.4		32	40.13	odd	4
600.2.w.j.557.5		32	5.3	odd	4
600.2.w.j.557.12		32	15.8	even	4
600.2.w.j.557.13		32	120.53	even	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11940 - 0.864261i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 + 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(1.10573 - 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +O(q^{10})\)	\(q+(-1.11940 - 0.864261i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 + 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(1.10573 - 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +(0.00136610 - 3.16228i) q^{10} +0.510276 q^{11} +(-0.543207 - 3.42125i) q^{12} +(0.750647 - 0.750647i) q^{13} +(-4.10544 + 0.528041i) q^{14} +(-2.05292 - 3.28413i) q^{15} +(-3.48771 + 1.95854i) q^{16} +(3.14698 + 3.14698i) q^{17} +(-2.78656 - 3.19923i) q^{18} +6.01198 q^{19} +(-2.73456 + 3.53867i) q^{20} +(-3.91945 + 3.21529i) q^{21} +(-0.571203 - 0.441012i) q^{22} +(-2.54575 + 2.54575i) q^{23} +(-2.34878 + 4.29921i) q^{24} +(-1.26945 + 4.83617i) q^{25} +(-1.48903 + 0.191519i) q^{26} +(-4.97150 - 1.51135i) q^{27} +(5.05199 + 2.95708i) q^{28} -5.10739i q^{29} +(-0.540308 + 5.45051i) q^{30} -4.56672 q^{31} +(5.59683 + 0.821906i) q^{32} +(-0.879551 - 0.0868061i) q^{33} +(-0.802913 - 6.24253i) q^{34} +(6.49090 + 0.837710i) q^{35} +(0.354305 + 5.98953i) q^{36} +(-6.76263 - 6.76263i) q^{37} +(-6.72981 - 5.19592i) q^{38} +(-1.42157 + 1.16618i) q^{39} +(6.11940 - 1.59781i) q^{40} -4.24355i q^{41} +(7.16627 - 0.211772i) q^{42} +(-5.95972 + 5.95972i) q^{43} +(0.258254 + 0.987336i) q^{44} +(2.97989 + 6.01001i) q^{45} +(5.04990 - 0.649518i) q^{46} +(-3.33849 - 3.33849i) q^{47} +(6.34486 - 2.78257i) q^{48} -1.56672i q^{49} +(5.60073 - 4.31647i) q^{50} +(-4.88902 - 5.95972i) q^{51} +(1.83234 + 1.07252i) q^{52} +(5.75871 + 5.75871i) q^{53} +(4.25889 + 5.98848i) q^{54} +(0.696910 + 0.903452i) q^{55} +(-3.09950 - 7.67638i) q^{56} +(-10.3627 - 1.02273i) q^{57} +(-4.41411 + 5.71720i) q^{58} -1.16514i q^{59} +(5.31548 - 5.63433i) q^{60} -4.92929i q^{61} +(5.11198 + 3.94684i) q^{62} +(7.30283 - 4.87536i) q^{63} +(-5.55474 - 5.75716i) q^{64} +(2.35423 + 0.303835i) q^{65} +(0.909545 + 0.857332i) q^{66} +(7.98415 + 7.98415i) q^{67} +(-4.49639 + 7.68180i) q^{68} +(4.82112 - 3.95497i) q^{69} +(-6.54191 - 6.54756i) q^{70} -5.09150i q^{71} +(4.77991 - 7.01088i) q^{72} +(-3.20654 - 3.20654i) q^{73} +(1.72540 + 13.4148i) q^{74} +(3.01082 - 8.12003i) q^{75} +(3.04271 + 11.6326i) q^{76} +(1.05608 - 1.05608i) q^{77} +(2.59918 - 0.0768090i) q^{78} +7.31215i q^{79} +(-8.23097 - 3.50017i) q^{80} +(8.31215 + 3.45081i) q^{81} +(-3.66754 + 4.75023i) q^{82} +(-4.77995 - 4.77995i) q^{83} +(-8.20494 - 5.95647i) q^{84} +(-1.27378 + 9.86975i) q^{85} +(11.8220 - 1.52055i) q^{86} +(-0.868848 + 8.80349i) q^{87} +(0.564226 - 1.32842i) q^{88} -12.6431 q^{89} +(1.85853 - 9.30300i) q^{90} -3.10712i q^{91} +(-6.21420 - 3.63736i) q^{92} +(7.87155 + 0.776871i) q^{93} +(0.851777 + 6.62243i) q^{94} +(8.21087 + 10.6443i) q^{95} +(-9.50730 - 2.36881i) q^{96} +(10.8789 - 10.8789i) q^{97} +(-1.35405 + 1.75378i) q^{98} +(1.50129 + 0.299251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more