LMFDB - Embedded newform 153.4.f.a.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(55,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("153.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.f (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:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 $ x^8 + 46x^6 + 561x^4 + 836*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.4
Root			$4.46767i$ of defining polynomial
Character	$\chi$	$=$	153.64
Dual form			153.4.f.a.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.46767i q^{2} -21.8954 q^{4} +(-4.79064 - 4.79064i) q^{5} +(3.33761 - 3.33761i) q^{7} -75.9757i q^{8} +O(q^{10})$	\(q+5.46767i q^{2} -21.8954 q^{4} +(-4.79064 - 4.79064i) q^{5} +(3.33761 - 3.33761i) q^{7} -75.9757i q^{8} +(26.1937 - 26.1937i) q^{10} +(6.70048 - 6.70048i) q^{11} -33.7223 q^{13} +(18.2490 + 18.2490i) q^{14} +240.247 q^{16} +(56.0931 - 42.0305i) q^{17} -27.4317i q^{19} +(104.893 + 104.893i) q^{20} +(36.6360 + 36.6360i) q^{22} +(-58.6134 + 58.6134i) q^{23} -79.0995i q^{25} -184.382i q^{26} +(-73.0784 + 73.0784i) q^{28} +(-147.098 - 147.098i) q^{29} +(-158.115 - 158.115i) q^{31} +705.786i q^{32} +(229.809 + 306.699i) q^{34} -31.9786 q^{35} +(122.947 + 122.947i) q^{37} +149.988 q^{38} +(-363.973 + 363.973i) q^{40} +(60.9335 - 60.9335i) q^{41} -258.362i q^{43} +(-146.710 + 146.710i) q^{44} +(-320.479 - 320.479i) q^{46} -88.9429 q^{47} +320.721i q^{49} +432.490 q^{50} +738.364 q^{52} -541.310i q^{53} -64.1992 q^{55} +(-253.577 - 253.577i) q^{56} +(804.282 - 804.282i) q^{58} +13.5759i q^{59} +(-112.176 + 112.176i) q^{61} +(864.520 - 864.520i) q^{62} -1937.03 q^{64} +(161.551 + 161.551i) q^{65} +357.758 q^{67} +(-1228.18 + 920.277i) q^{68} -174.848i q^{70} +(-679.278 - 679.278i) q^{71} +(-635.175 - 635.175i) q^{73} +(-672.233 + 672.233i) q^{74} +600.630i q^{76} -44.7272i q^{77} +(-319.090 + 319.090i) q^{79} +(-1150.94 - 1150.94i) q^{80} +(333.164 + 333.164i) q^{82} +559.916i q^{83} +(-470.075 - 67.3686i) q^{85} +1412.64 q^{86} +(-509.074 - 509.074i) q^{88} +602.266 q^{89} +(-112.552 + 112.552i) q^{91} +(1283.37 - 1283.37i) q^{92} -486.311i q^{94} +(-131.416 + 131.416i) q^{95} +(-580.502 - 580.502i) q^{97} -1753.60 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{4} - 14 q^{5} + 2 q^{7}+O(q^{10}) $ 8 * q - 36 * q^4 - 14 * q^5 + 2 * q^7	$ 8 q - 36 q^{4} - 14 q^{5} + 2 q^{7} + 78 q^{10} + 108 q^{11} - 88 q^{13} - 108 q^{14} + 420 q^{16} + 10 q^{17} + 306 q^{20} + 30 q^{22} + 22 q^{23} - 764 q^{28} - 46 q^{29} + 610 q^{31} + 1002 q^{34} - 1172 q^{35} - 574 q^{37} + 768 q^{38} - 342 q^{40} + 968 q^{41} - 550 q^{44} - 944 q^{46} + 368 q^{47} - 468 q^{50} + 2564 q^{52} - 1996 q^{55} - 684 q^{56} + 266 q^{58} + 1258 q^{61} + 2516 q^{62} - 3044 q^{64} - 628 q^{65} + 764 q^{67} - 1914 q^{68} - 1266 q^{71} - 1732 q^{73} - 1538 q^{74} + 914 q^{79} - 498 q^{80} - 280 q^{82} - 2498 q^{85} + 4244 q^{86} + 442 q^{88} + 2156 q^{89} - 1632 q^{91} + 1768 q^{92} - 1484 q^{95} + 1836 q^{97} - 6728 q^{98}+O(q^{100}) $ 8 * q - 36 * q^4 - 14 * q^5 + 2 * q^7 + 78 * q^10 + 108 * q^11 - 88 * q^13 - 108 * q^14 + 420 * q^16 + 10 * q^17 + 306 * q^20 + 30 * q^22 + 22 * q^23 - 764 * q^28 - 46 * q^29 + 610 * q^31 + 1002 * q^34 - 1172 * q^35 - 574 * q^37 + 768 * q^38 - 342 * q^40 + 968 * q^41 - 550 * q^44 - 944 * q^46 + 368 * q^47 - 468 * q^50 + 2564 * q^52 - 1996 * q^55 - 684 * q^56 + 266 * q^58 + 1258 * q^61 + 2516 * q^62 - 3044 * q^64 - 628 * q^65 + 764 * q^67 - 1914 * q^68 - 1266 * q^71 - 1732 * q^73 - 1538 * q^74 + 914 * q^79 - 498 * q^80 - 280 * q^82 - 2498 * q^85 + 4244 * q^86 + 442 * q^88 + 2156 * q^89 - 1632 * q^91 + 1768 * q^92 - 1484 * q^95 + 1836 * q^97 - 6728 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$			5.46767i			1.93311i	0.256451	+	0.966557i	$0.417447\pi$
$2$			5.46767i			1.93311i	−0.256451	+	0.966557i	$0.582553\pi$
$3$		0			0
$3$		0			0
$4$	−21.8954			−2.73693
$5$	−4.79064	−	4.79064i	−0.428488	−	0.428488i	0.459625	−	0.888113i	$-0.347984\pi$
$5$	−4.79064	−	4.79064i	−0.428488	−	0.428488i	−0.888113	+	0.459625i	$0.847984\pi$
$6$		0			0
$7$	3.33761	−	3.33761i	0.180214	−	0.180214i	−0.611235	−	0.791449i	$-0.709327\pi$
$7$	3.33761	−	3.33761i	0.180214	−	0.180214i	0.791449	+	0.611235i	$0.209327\pi$
$8$		−	75.9757i		−	3.35769i
$9$		0			0
$10$	26.1937	−	26.1937i	0.828316	−	0.828316i
$11$	6.70048	−	6.70048i	0.183661	−	0.183661i	−0.609288	−	0.792949i	$-0.708545\pi$
$11$	6.70048	−	6.70048i	0.183661	−	0.183661i	0.792949	+	0.609288i	$0.208545\pi$
$12$		0			0
$13$	−33.7223			−0.719452			−0.359726	−	0.933058i	$-0.617130\pi$
$13$	−33.7223			−0.719452			−0.359726	+	0.933058i	$0.617130\pi$
$14$	18.2490	+	18.2490i	0.348374	+	0.348374i
$15$		0			0
$16$	240.247			3.75386
$17$	56.0931	−	42.0305i	0.800269	−	0.599641i
$17$	56.0931	−	42.0305i	0.800269	−	0.599641i
$18$		0			0
$19$		−	27.4317i		−	0.331225i	−0.986191	−	0.165612i	$-0.947040\pi$
$19$		−	27.4317i		−	0.331225i	0.986191	−	0.165612i	$-0.0529601\pi$
$20$	104.893	+	104.893i	1.17274	+	1.17274i
$21$		0			0
$22$	36.6360	+	36.6360i	0.355038	+	0.355038i
$23$	−58.6134	+	58.6134i	−0.531380	+	0.531380i	−0.920983	−	0.389603i	$-0.872612\pi$
$23$	−58.6134	+	58.6134i	−0.531380	+	0.531380i	0.389603	+	0.920983i	$0.372612\pi$
$24$		0			0
$25$		−	79.0995i		−	0.632796i
$26$		−	184.382i		−	1.39078i
$27$		0			0
$28$	−73.0784	+	73.0784i	−0.493233	+	0.493233i
$29$	−147.098	−	147.098i	−0.941908	−	0.941908i	0.0564944	−	0.998403i	$-0.482008\pi$
$29$	−147.098	−	147.098i	−0.941908	−	0.941908i	−0.998403	+	0.0564944i	$0.982008\pi$
$30$		0			0
$31$	−158.115	−	158.115i	−0.916072	−	0.916072i	0.0806685	−	0.996741i	$-0.474294\pi$
$31$	−158.115	−	158.115i	−0.916072	−	0.916072i	−0.996741	+	0.0806685i	$0.974294\pi$
$32$			705.786i			3.89895i
$33$		0			0
$34$	229.809	+	306.699i	1.15918	+	1.54701i
$35$	−31.9786			−0.154439
$36$		0			0
$37$	122.947	+	122.947i	0.546279	+	0.546279i	0.925363	−	0.379083i	$-0.123761\pi$
$37$	122.947	+	122.947i	0.546279	+	0.546279i	−0.379083	+	0.925363i	$0.623761\pi$
$38$	149.988			0.640296
$39$		0			0
$40$	−363.973	+	363.973i	−1.43873	+	1.43873i
$41$	60.9335	−	60.9335i	0.232103	−	0.232103i	−0.581467	−	0.813570i	$-0.697521\pi$
$41$	60.9335	−	60.9335i	0.232103	−	0.232103i	0.813570	+	0.581467i	$0.197521\pi$
$42$		0			0
$43$		−	258.362i		−	0.916274i	−0.888882	−	0.458137i	$-0.848517\pi$
$43$		−	258.362i		−	0.916274i	0.888882	−	0.458137i	$-0.151483\pi$
$44$	−146.710	+	146.710i	−0.502667	+	0.502667i
$45$		0			0
$46$	−320.479	−	320.479i	−1.02722	−	1.02722i
$47$	−88.9429			−0.276035			−0.138018	−	0.990430i	$-0.544073\pi$
$47$	−88.9429			−0.276035			−0.138018	+	0.990430i	$0.544073\pi$
$48$		0			0
$49$			320.721i			0.935046i
$50$	432.490			1.22327
$51$		0			0
$52$	738.364			1.96909
$53$		−	541.310i		−	1.40292i	−0.712710	−	0.701458i	$-0.752533\pi$
$53$		−	541.310i		−	1.40292i	0.712710	−	0.701458i	$-0.247467\pi$
$54$		0			0
$55$	−64.1992			−0.157393
$56$	−253.577	−	253.577i	−0.605102	−	0.605102i
$57$		0			0
$58$	804.282	−	804.282i	1.82082	−	1.82082i
$59$			13.5759i			0.0299564i	0.999888	+	0.0149782i	$0.00476789\pi$
$59$			13.5759i			0.0299564i	−0.999888	+	0.0149782i	$0.995232\pi$
$60$		0			0
$61$	−112.176	+	112.176i	−0.235453	+	0.235453i	−0.814964	−	0.579511i	$-0.803243\pi$
$61$	−112.176	+	112.176i	−0.235453	+	0.235453i	0.579511	+	0.814964i	$0.303243\pi$
$62$	864.520	−	864.520i	1.77087	−	1.77087i
$63$		0			0
$64$	−1937.03			−3.78326
$65$	161.551	+	161.551i	0.308276	+	0.308276i
$66$		0			0
$67$	357.758			0.652345			0.326172	−	0.945310i	$-0.394241\pi$
$67$	357.758			0.652345			0.326172	+	0.945310i	$0.394241\pi$
$68$	−1228.18	+	920.277i	−2.19028	+	1.64118i
$69$		0			0
$70$		−	174.848i		−	0.298548i
$71$	−679.278	−	679.278i	−1.13543	−	1.13543i	−0.989259	−	0.146170i	$-0.953305\pi$
$71$	−679.278	−	679.278i	−1.13543	−	1.13543i	−0.146170	−	0.989259i	$-0.546695\pi$
$72$		0			0
$73$	−635.175	−	635.175i	−1.01838	−	1.01838i	−0.999828	−	0.0185509i	$-0.994095\pi$
$73$	−635.175	−	635.175i	−1.01838	−	1.01838i	−0.0185509	−	0.999828i	$-0.505905\pi$
$74$	−672.233	+	672.233i	−1.05602	+	1.05602i
$75$		0			0
$76$			600.630i			0.906540i
$77$		−	44.7272i		−	0.0661965i
$78$		0			0
$79$	−319.090	+	319.090i	−0.454436	+	0.454436i	−0.896824	−	0.442388i	$-0.854132\pi$
$79$	−319.090	+	319.090i	−0.454436	+	0.454436i	0.442388	+	0.896824i	$0.354132\pi$
$80$	−1150.94	−	1150.94i	−1.60848	−	1.60848i
$81$		0			0
$82$	333.164	+	333.164i	0.448681	+	0.448681i
$83$			559.916i			0.740467i	0.928939	+	0.370234i	$0.120722\pi$
$83$			559.916i			0.740467i	−0.928939	+	0.370234i	$0.879278\pi$
$84$		0			0
$85$	−470.075	−	67.3686i	−0.599845	−	0.0859664i
$86$	1412.64			1.77126
$87$		0			0
$88$	−509.074	−	509.074i	−0.616676	−	0.616676i
$89$	602.266			0.717304			0.358652	−	0.933471i	$-0.383237\pi$
$89$	602.266			0.717304			0.358652	+	0.933471i	$0.383237\pi$
$90$		0			0
$91$	−112.552	+	112.552i	−0.129655	+	0.129655i
$92$	1283.37	−	1283.37i	1.45435	−	1.45435i
$93$		0			0
$94$		−	486.311i		−	0.533608i
$95$	−131.416	+	131.416i	−0.141926	+	0.141926i
$96$		0			0
$97$	−580.502	−	580.502i	−0.607640	−	0.607640i	0.334689	−	0.942329i	$-0.391369\pi$
$97$	−580.502	−	580.502i	−0.607640	−	0.607640i	−0.942329	+	0.334689i	$0.891369\pi$
$98$	−1753.60			−1.80755
$99$		0			0
$100$			1731.92i			1.73192i
$101$	−246.217			−0.242570			−0.121285	−	0.992618i	$-0.538701\pi$
$101$	−246.217			−0.242570			−0.121285	+	0.992618i	$0.538701\pi$
$102$		0			0
$103$	−102.854			−0.0983931			−0.0491965	−	0.998789i	$-0.515666\pi$
$103$	−102.854			−0.0983931			−0.0491965	+	0.998789i	$0.515666\pi$
$104$			2562.07i			2.41569i
$105$		0			0
$106$	2959.70			2.71200
$107$	1445.44	+	1445.44i	1.30594	+	1.30594i	0.924317	+	0.381625i	$0.124635\pi$
$107$	1445.44	+	1445.44i	1.30594	+	1.30594i	0.381625	+	0.924317i	$0.375365\pi$
$108$		0			0
$109$	−185.564	+	185.564i	−0.163063	+	0.163063i	−0.783922	−	0.620859i	$-0.786784\pi$
$109$	−185.564	+	185.564i	−0.163063	+	0.163063i	0.620859	+	0.783922i	$0.286784\pi$
$110$		−	351.020i		−	0.304259i
$111$		0			0
$112$	801.850	−	801.850i	0.676498	−	0.676498i
$113$	−211.740	+	211.740i	−0.176273	+	0.176273i	−0.789729	−	0.613456i	$-0.789779\pi$
$113$	−211.740	+	211.740i	−0.176273	+	0.176273i	0.613456	+	0.789729i	$0.289779\pi$
$114$		0			0
$115$	561.591			0.455380
$116$	3220.77	+	3220.77i	2.57794	+	2.57794i
$117$		0			0
$118$	−74.2284			−0.0579092
$119$	46.9353	−	327.498i	0.0361559	−	0.252283i
$120$		0			0
$121$			1241.21i			0.932537i
$122$	−613.340	−	613.340i	−0.455157	−	0.455157i
$123$		0			0
$124$	3461.99	+	3461.99i	2.50723	+	2.50723i
$125$	−977.768	+	977.768i	−0.699634	+	0.699634i
$126$		0			0
$127$			761.059i			0.531757i	0.964007	+	0.265878i	$0.0856619\pi$
$127$			761.059i			0.531757i	−0.964007	+	0.265878i	$0.914338\pi$
$128$		−	4944.76i		−	3.41452i
$129$		0			0
$130$	−883.309	+	883.309i	−0.595933	+	0.595933i
$131$	−1024.15	−	1024.15i	−0.683054	−	0.683054i	0.277633	−	0.960687i	$-0.410450\pi$
$131$	−1024.15	−	1024.15i	−0.683054	−	0.683054i	−0.960687	+	0.277633i	$0.910450\pi$
$132$		0			0
$133$	−91.5565	−	91.5565i	−0.0596914	−	0.0596914i
$134$			1956.10i			1.26106i
$135$		0			0
$136$	−3193.30	−	4261.71i	−2.01341	−	2.68705i
$137$	−1902.77			−1.18660			−0.593301	−	0.804981i	$-0.702176\pi$
$137$	−1902.77			−1.18660			−0.593301	+	0.804981i	$0.702176\pi$
$138$		0			0
$139$	−437.312	−	437.312i	−0.266851	−	0.266851i	0.560979	−	0.827830i	$-0.310425\pi$
$139$	−437.312	−	437.312i	−0.266851	−	0.266851i	−0.827830	+	0.560979i	$0.810425\pi$
$140$	700.185			0.422689
$141$		0			0
$142$	3714.07	−	3714.07i	2.19492	−	2.19492i
$143$	−225.955	+	225.955i	−0.132135	+	0.132135i
$144$		0			0
$145$			1409.38i			0.807193i
$146$	3472.93	−	3472.93i	1.96864	−	1.96864i
$147$		0			0
$148$	−2691.97	−	2691.97i	−1.49513	−	1.49513i
$149$	1398.00			0.768647			0.384323	−	0.923199i	$-0.374435\pi$
$149$	1398.00			0.768647			0.384323	+	0.923199i	$0.374435\pi$
$150$		0			0
$151$			2503.54i			1.34924i	0.738166	+	0.674619i	$0.235692\pi$
$151$			2503.54i			1.34924i	−0.738166	+	0.674619i	$0.764308\pi$
$152$	−2084.15			−1.11215
$153$		0			0
$154$	244.553			0.127965
$155$			1514.94i			0.785052i
$156$		0			0
$157$	−2715.22			−1.38024			−0.690121	−	0.723694i	$-0.742443\pi$
$157$	−2715.22			−1.38024			−0.690121	+	0.723694i	$0.742443\pi$
$158$	−1744.68	−	1744.68i	−0.878478	−	0.878478i
$159$		0			0
$160$	3381.17	−	3381.17i	1.67065	−	1.67065i
$161$			391.257i			0.191524i
$162$		0			0
$163$	2340.59	−	2340.59i	1.12472	−	1.12472i	0.133697	−	0.991022i	$-0.457315\pi$
$163$	2340.59	−	2340.59i	1.12472	−	1.12472i	0.991022	−	0.133697i	$-0.0426850\pi$
$164$	−1334.17	+	1334.17i	−0.635249	+	0.635249i
$165$		0			0
$166$	−3061.44			−1.43141
$167$	−247.639	−	247.639i	−0.114748	−	0.114748i	0.647401	−	0.762149i	$-0.275856\pi$
$167$	−247.639	−	247.639i	−0.114748	−	0.114748i	−0.762149	+	0.647401i	$0.775856\pi$
$168$		0			0
$169$	−1059.81			−0.482389
$170$	368.349	−	2570.22i	0.166183	−	1.15957i
$171$		0			0
$172$			5656.94i			2.50778i
$173$	1478.19	+	1478.19i	0.649622	+	0.649622i	0.952902	−	0.303279i	$-0.0980815\pi$
$173$	1478.19	+	1478.19i	0.649622	+	0.649622i	−0.303279	+	0.952902i	$0.598081\pi$
$174$		0			0
$175$	−264.003	−	264.003i	−0.114039	−	0.114039i
$176$	1609.77	−	1609.77i	0.689437	−	0.689437i
$177$		0			0
$178$			3292.99i			1.38663i
$179$			739.046i			0.308597i	0.988024	+	0.154299i	$0.0493118\pi$
$179$			739.046i			0.308597i	−0.988024	+	0.154299i	$0.950688\pi$
$180$		0			0
$181$	2306.67	−	2306.67i	0.947258	−	0.947258i	−0.0514191	−	0.998677i	$-0.516374\pi$
$181$	2306.67	−	2306.67i	0.947258	−	0.947258i	0.998677	+	0.0514191i	$0.0163744\pi$
$182$	−615.396	−	615.396i	−0.250638	−	0.250638i
$183$		0			0
$184$	4453.19	+	4453.19i	1.78421	+	1.78421i
$185$		−	1177.99i		−	0.468148i
$186$		0			0
$187$	94.2257	−	657.475i	0.0368474	−	0.257109i
$188$	1947.44			0.755489
$189$		0			0
$190$	−718.538	−	718.538i	−0.274359	−	0.274359i
$191$	265.840			0.100710			0.0503548	−	0.998731i	$-0.483965\pi$
$191$	265.840			0.100710			0.0503548	+	0.998731i	$0.483965\pi$
$192$		0			0
$193$	25.1722	−	25.1722i	0.00938825	−	0.00938825i	−0.702397	−	0.711785i	$-0.747887\pi$
$193$	25.1722	−	25.1722i	0.00938825	−	0.00938825i	0.711785	+	0.702397i	$0.247887\pi$
$194$	3174.00	−	3174.00i	1.17464	−	1.17464i
$195$		0			0
$196$		−	7022.32i		−	2.55916i
$197$	−446.683	+	446.683i	−0.161547	+	0.161547i	−0.783252	−	0.621704i	$-0.786441\pi$
$197$	−446.683	+	446.683i	−0.161547	+	0.161547i	0.621704	+	0.783252i	$0.286441\pi$
$198$		0			0
$199$	2696.51	+	2696.51i	0.960554	+	0.960554i	0.999251	−	0.0386973i	$-0.0123208\pi$
$199$	2696.51	+	2696.51i	0.960554	+	0.960554i	−0.0386973	+	0.999251i	$0.512321\pi$
$200$	−6009.64			−2.12473
$201$		0			0
$202$		−	1346.24i		−	0.468915i
$203$	−981.909			−0.339490
$204$		0			0
$205$	−583.821			−0.198906
$206$		−	562.371i		−	0.190205i
$207$		0			0
$208$	−8101.67			−2.70072
$209$	−183.806	−	183.806i	−0.0608331	−	0.0608331i
$210$		0			0
$211$	1667.04	−	1667.04i	0.543903	−	0.543903i	−0.380768	−	0.924671i	$-0.624340\pi$
$211$	1667.04	−	1667.04i	0.543903	−	0.543903i	0.924671	+	0.380768i	$0.124340\pi$
$212$			11852.2i			3.83969i
$213$		0			0
$214$	−7903.18	+	7903.18i	−2.52454	+	2.52454i
$215$	−1237.72	+	1237.72i	−0.392612	+	0.392612i
$216$		0			0
$217$	−1055.45			−0.330178
$218$	−1014.61	−	1014.61i	−0.315219	−	0.315219i
$219$		0			0
$220$	1405.67			0.430774
$221$	−1891.59	+	1417.36i	−0.575755	+	0.431413i
$222$		0			0
$223$		−	5273.08i		−	1.58346i	−0.610871	−	0.791730i	$-0.709181\pi$
$223$		−	5273.08i		−	1.58346i	0.610871	−	0.791730i	$-0.290819\pi$
$224$	2355.64	+	2355.64i	0.702645	+	0.702645i
$225$		0			0
$226$	−1157.72	−	1157.72i	−0.340755	−	0.340755i
$227$	2472.24	−	2472.24i	0.722857	−	0.722857i	−0.246329	−	0.969186i	$-0.579224\pi$
$227$	2472.24	−	2472.24i	0.722857	−	0.722857i	0.969186	+	0.246329i	$0.0792244\pi$
$228$		0			0
$229$			1982.99i			0.572226i	0.958196	+	0.286113i	$0.0923633\pi$
$229$			1982.99i			0.572226i	−0.958196	+	0.286113i	$0.907637\pi$
$230$			3070.60i			0.880301i
$231$		0			0
$232$	−11175.9	+	11175.9i	−3.16263	+	3.16263i
$233$	10.2611	+	10.2611i	0.00288509	+	0.00288509i	0.708548	−	0.705663i	$-0.249351\pi$
$233$	10.2611	+	10.2611i	0.00288509	+	0.00288509i	−0.705663	+	0.708548i	$0.749351\pi$
$234$		0			0
$235$	426.094	+	426.094i	0.118278	+	0.118278i
$236$		−	297.250i		−	0.0819886i
$237$		0			0
$238$	1790.65	+	256.627i	0.487693	+	0.0698934i
$239$	5365.31			1.45210			0.726052	−	0.687640i	$-0.241353\pi$
$239$	5365.31			1.45210			0.726052	+	0.687640i	$0.241353\pi$
$240$		0			0
$241$	−119.928	−	119.928i	−0.0320551	−	0.0320551i	0.690898	−	0.722953i	$-0.257216\pi$
$241$	−119.928	−	119.928i	−0.0320551	−	0.0320551i	−0.722953	+	0.690898i	$0.757216\pi$
$242$	−6786.51			−1.80270
$243$		0			0
$244$	2456.14	−	2456.14i	0.644418	−	0.644418i
$245$	1536.46	−	1536.46i	0.400656	−	0.400656i
$246$		0			0
$247$			925.060i			0.238300i
$248$	−12012.9	+	12012.9i	−3.07588	+	3.07588i
$249$		0			0
$250$	−5346.11	−	5346.11i	−1.35247	−	1.35247i
$251$	4824.87			1.21332			0.606659	−	0.794962i	$-0.292509\pi$
$251$	4824.87			1.21332			0.606659	+	0.794962i	$0.292509\pi$
$252$		0			0
$253$			785.475i			0.195187i
$254$	−4161.22			−1.02795
$255$		0			0
$256$	11540.1			2.81740
$257$		−	5583.38i		−	1.35518i	−0.735439	−	0.677591i	$-0.763024\pi$
$257$		−	5583.38i		−	1.35518i	0.735439	−	0.677591i	$-0.236976\pi$
$258$		0			0
$259$	820.697			0.196894
$260$	−3537.24	−	3537.24i	−0.843731	−	0.843731i
$261$		0			0
$262$	5599.69	−	5599.69i	1.32042	−	1.32042i
$263$		−	4116.11i		−	0.965059i	−0.875880	−	0.482529i	$-0.839718\pi$
$263$		−	4116.11i		−	0.965059i	0.875880	−	0.482529i	$-0.160282\pi$
$264$		0			0
$265$	−2593.22	+	2593.22i	−0.601133	+	0.601133i
$266$	500.601	−	500.601i	0.115390	−	0.115390i
$267$		0			0
$268$	−7833.27			−1.78542
$269$	−4277.93	−	4277.93i	−0.969629	−	0.969629i	0.0299232	−	0.999552i	$-0.490474\pi$
$269$	−4277.93	−	4277.93i	−0.969629	−	0.969629i	−0.999552	+	0.0299232i	$0.990474\pi$
$270$		0			0
$271$	6555.61			1.46947			0.734733	−	0.678357i	$-0.237308\pi$
$271$	6555.61			1.46947			0.734733	+	0.678357i	$0.237308\pi$
$272$	13476.2	−	10097.7i	3.00410	−	2.25097i
$273$		0			0
$274$		−	10403.7i		−	2.29384i
$275$	−530.005	−	530.005i	−0.116220	−	0.116220i
$276$		0			0
$277$	1725.33	+	1725.33i	0.374241	+	0.374241i	0.869019	−	0.494778i	$-0.164751\pi$
$277$	1725.33	+	1725.33i	0.374241	+	0.374241i	−0.494778	+	0.869019i	$0.664751\pi$
$278$	2391.08	−	2391.08i	0.515854	−	0.515854i
$279$		0			0
$280$			2429.60i			0.518558i
$281$		−	519.764i		−	0.110343i	−0.998477	−	0.0551717i	$-0.982429\pi$
$281$		−	519.764i		−	0.110343i	0.998477	−	0.0551717i	$-0.0175706\pi$
$282$		0			0
$283$	3290.24	−	3290.24i	0.691112	−	0.691112i	−0.271365	−	0.962477i	$-0.587475\pi$
$283$	3290.24	−	3290.24i	0.691112	−	0.691112i	0.962477	+	0.271365i	$0.0874749\pi$
$284$	14873.1	+	14873.1i	3.10759	+	3.10759i
$285$		0			0
$286$	−1235.45	−	1235.45i	−0.255432	−	0.255432i
$287$		−	406.744i		−	0.0836563i
$288$		0			0
$289$	1379.87	−	4715.25i	0.280860	−	0.959749i
$290$	−7706.05			−1.56040
$291$		0			0
$292$	13907.4	+	13907.4i	2.78723	+	2.78723i
$293$	−1856.79			−0.370220			−0.185110	−	0.982718i	$-0.559264\pi$
$293$	−1856.79			−0.370220			−0.185110	+	0.982718i	$0.559264\pi$
$294$		0			0
$295$	65.0371	−	65.0371i	0.0128360	−	0.0128360i
$296$	9340.97	−	9340.97i	1.83423	−	1.83423i
$297$		0			0
$298$			7643.79i			1.48588i
$299$	1976.58	−	1976.58i	0.382302	−	0.382302i
$300$		0			0
$301$	−862.310	−	862.310i	−0.165125	−	0.165125i
$302$	−13688.5			−2.60823
$303$		0			0
$304$		−	6590.39i		−	1.24337i
$305$	1074.79			0.201777
$306$		0			0
$307$	759.641			0.141221			0.0706107	−	0.997504i	$-0.477505\pi$
$307$	759.641			0.141221			0.0706107	+	0.997504i	$0.477505\pi$
$308$			979.321i			0.181175i
$309$		0			0
$310$	−8283.21			−1.51760
$311$	722.960	+	722.960i	0.131818	+	0.131818i	0.769937	−	0.638120i	$-0.220287\pi$
$311$	722.960	+	722.960i	0.131818	+	0.131818i	−0.638120	+	0.769937i	$0.720287\pi$
$312$		0			0
$313$	−2786.70	+	2786.70i	−0.503238	+	0.503238i	−0.912443	−	0.409205i	$-0.865806\pi$
$313$	−2786.70	+	2786.70i	−0.503238	+	0.503238i	0.409205	+	0.912443i	$0.365806\pi$
$314$		−	14845.9i		−	2.66817i
$315$		0			0
$316$	6986.63	−	6986.63i	1.24376	−	1.24376i
$317$	−3806.81	+	3806.81i	−0.674485	+	0.674485i	−0.958747	−	0.284262i	$-0.908252\pi$
$317$	−3806.81	+	3806.81i	−0.674485	+	0.674485i	0.284262	+	0.958747i	$0.408252\pi$
$318$		0			0
$319$	−1971.25			−0.345984
$320$	9279.61	+	9279.61i	1.62108	+	1.62108i
$321$		0			0
$322$	−2139.27			−0.370238
$323$	−1152.97	−	1538.73i	−0.198616	−	0.265069i
$324$		0			0
$325$			2667.41i			0.455266i
$326$	12797.6	+	12797.6i	2.17421	+	2.17421i
$327$		0			0
$328$	−4629.47	−	4629.47i	−0.779328	−	0.779328i
$329$	−296.857	+	296.857i	−0.0497454	+	0.0497454i
$330$		0			0
$331$		−	1697.70i		−	0.281915i	−0.990016	−	0.140958i	$-0.954982\pi$
$331$		−	1697.70i		−	0.281915i	0.990016	−	0.140958i	$-0.0450181\pi$
$332$		−	12259.6i		−	2.02661i
$333$		0			0
$334$	1354.01	−	1354.01i	0.221820	−	0.221820i
$335$	−1713.89	−	1713.89i	−0.279522	−	0.279522i
$336$		0			0
$337$	−7987.91	−	7987.91i	−1.29119	−	1.29119i	−0.934054	−	0.357131i	$-0.883755\pi$
$337$	−7987.91	−	7987.91i	−1.29119	−	1.29119i	−0.357131	−	0.934054i	$-0.616245\pi$
$338$		−	5794.69i		−	0.932514i
$339$		0			0
$340$	10292.5	+	1475.06i	1.64173	+	0.235284i
$341$	−2118.89			−0.336493
$342$		0			0
$343$	2215.24	+	2215.24i	0.348722	+	0.348722i
$344$	−19629.2			−3.07656
$345$		0			0
$346$	−8082.26	+	8082.26i	−1.25579	+	1.25579i
$347$	2544.06	−	2544.06i	0.393580	−	0.393580i	−0.482381	−	0.875961i	$-0.660228\pi$
$347$	2544.06	−	2544.06i	0.393580	−	0.393580i	0.875961	+	0.482381i	$0.160228\pi$
$348$		0			0
$349$		−	3741.37i		−	0.573842i	−0.957954	−	0.286921i	$-0.907368\pi$
$349$		−	3741.37i		−	0.573842i	0.957954	−	0.286921i	$-0.0926318\pi$
$350$	1443.48	−	1443.48i	0.220450	−	0.220450i
$351$		0			0
$352$	4729.10	+	4729.10i	0.716085	+	0.716085i
$353$	5726.82			0.863478			0.431739	−	0.901999i	$-0.357900\pi$
$353$	5726.82			0.863478			0.431739	+	0.901999i	$0.357900\pi$
$354$		0			0
$355$			6508.36i			0.973036i
$356$	−13186.9			−1.96321
$357$		0			0
$358$	−4040.86			−0.596554
$359$			6048.82i			0.889260i	0.895714	+	0.444630i	$0.146665\pi$
$359$			6048.82i			0.889260i	−0.895714	+	0.444630i	$0.853335\pi$
$360$		0			0
$361$	6106.50			0.890290
$362$	12612.1	+	12612.1i	1.83116	+	1.83116i
$363$		0			0
$364$	2464.37	−	2464.37i	0.354857	−	0.354857i
$365$			6085.79i			0.872726i
$366$		0			0
$367$	−2432.09	+	2432.09i	−0.345924	+	0.345924i	−0.858589	−	0.512665i	$-0.828658\pi$
$367$	−2432.09	+	2432.09i	−0.345924	+	0.345924i	0.512665	+	0.858589i	$0.328658\pi$
$368$	−14081.7	+	14081.7i	−1.99472	+	1.99472i
$369$		0			0
$370$	6440.85			0.904984
$371$	−1806.68	−	1806.68i	−0.252825	−	0.252825i
$372$		0			0
$373$	−6816.14			−0.946184			−0.473092	−	0.881013i	$-0.656862\pi$
$373$	−6816.14			−0.946184			−0.473092	+	0.881013i	$0.656862\pi$
$374$	3594.86	+	515.195i	0.497021	+	0.0712303i
$375$		0			0
$376$			6757.50i			0.926839i
$377$	4960.46	+	4960.46i	0.677658	+	0.677658i
$378$		0			0
$379$	4184.48	+	4184.48i	0.567130	+	0.567130i	0.931323	−	0.364193i	$-0.118655\pi$
$379$	4184.48	+	4184.48i	0.567130	+	0.567130i	−0.364193	+	0.931323i	$0.618655\pi$
$380$	2877.40	−	2877.40i	0.388441	−	0.388441i
$381$		0			0
$382$			1453.53i			0.194683i
$383$			7584.88i			1.01193i	0.862554	+	0.505965i	$0.168863\pi$
$383$			7584.88i			1.01193i	−0.862554	+	0.505965i	$0.831137\pi$
$384$		0			0
$385$	−214.272	+	214.272i	−0.0283644	+	0.0283644i
$386$	137.633	+	137.633i	0.0181486	+	0.0181486i
$387$		0			0
$388$	12710.3	+	12710.3i	1.66307	+	1.66307i
$389$		−	1389.74i		−	0.181137i	−0.995890	−	0.0905687i	$-0.971132\pi$
$389$		−	1389.74i		−	0.181137i	0.995890	−	0.0905687i	$-0.0288685\pi$
$390$		0			0
$391$	−824.253	+	5751.36i	−0.106609	+	0.743884i
$392$	24367.0			3.13959
$393$		0			0
$394$	−2442.32	−	2442.32i	−0.312290	−	0.312290i
$395$	3057.30			0.389441
$396$		0			0
$397$	9672.31	−	9672.31i	1.22277	−	1.22277i	0.256126	−	0.966643i	$-0.417554\pi$
$397$	9672.31	−	9672.31i	1.22277	−	1.22277i	0.966643	−	0.256126i	$-0.0824461\pi$
$398$	−14743.6	+	14743.6i	−1.85686	+	1.85686i
$399$		0			0
$400$		−	19003.4i		−	2.37543i
$401$	−9399.33	+	9399.33i	−1.17052	+	1.17052i	−0.188439	+	0.982085i	$0.560343\pi$
$401$	−9399.33	+	9399.33i	−1.17052	+	1.17052i	−0.982085	+	0.188439i	$0.939657\pi$
$402$		0			0
$403$	5331.99	+	5331.99i	0.659070	+	0.659070i
$404$	5391.04			0.663897
$405$		0			0
$406$		−	5368.76i		−	0.656273i
$407$	1647.60			0.200660
$408$		0			0
$409$	−6570.02			−0.794295			−0.397147	−	0.917755i	$-0.630000\pi$
$409$	−6570.02			−0.794295			−0.397147	+	0.917755i	$0.630000\pi$
$410$		−	3192.14i		−	0.384509i
$411$		0			0
$412$	2252.03			0.269295
$413$	45.3110	+	45.3110i	0.00539856	+	0.00539856i
$414$		0			0
$415$	2682.36	−	2682.36i	0.317281	−	0.317281i
$416$		−	23800.7i		−	2.80511i
$417$		0			0
$418$	1004.99	−	1004.99i	0.117597	−	0.117597i
$419$	9830.40	−	9830.40i	1.14617	−	1.14617i	0.158874	−	0.987299i	$-0.449214\pi$
$419$	9830.40	−	9830.40i	1.14617	−	1.14617i	0.987299	−	0.158874i	$-0.0507865\pi$
$420$		0			0
$421$	3041.18			0.352062			0.176031	−	0.984385i	$-0.443674\pi$
$421$	3041.18			0.352062			0.176031	+	0.984385i	$0.443674\pi$
$422$	9114.80	+	9114.80i	1.05143	+	1.05143i
$423$		0			0
$424$	−41126.4			−4.71055
$425$	−3324.60	−	4436.93i	−0.379451	−	0.506407i
$426$		0			0
$427$			748.797i			0.0848638i
$428$	−31648.5	−	31648.5i	−3.57427	−	3.57427i
$429$		0			0
$430$	−6767.43	−	6767.43i	−0.758964	−	0.758964i
$431$	−4422.43	+	4422.43i	−0.494248	+	0.494248i	−0.909642	−	0.415394i	$-0.863644\pi$
$431$	−4422.43	+	4422.43i	−0.494248	+	0.494248i	0.415394	+	0.909642i	$0.363644\pi$
$432$		0			0
$433$			10180.7i			1.12992i	0.825119	+	0.564959i	$0.191108\pi$
$433$			10180.7i			1.12992i	−0.825119	+	0.564959i	$0.808892\pi$
$434$		−	5770.86i		−	0.638272i
$435$		0			0
$436$	4063.01	−	4063.01i	0.446292	−	0.446292i
$437$	1607.87	+	1607.87i	0.176006	+	0.176006i
$438$		0			0
$439$	−7042.71	−	7042.71i	−0.765672	−	0.765672i	0.211669	−	0.977341i	$-0.432110\pi$
$439$	−7042.71	−	7042.71i	−0.765672	−	0.765672i	−0.977341	+	0.211669i	$0.932110\pi$
$440$			4877.58i			0.528476i
$441$		0			0
$442$	−7749.69	−	10342.6i	−0.833971	−	1.11300i
$443$	−6833.02			−0.732836			−0.366418	−	0.930450i	$-0.619416\pi$
$443$	−6833.02			−0.732836			−0.366418	+	0.930450i	$0.619416\pi$
$444$		0			0
$445$	−2885.24	−	2885.24i	−0.307356	−	0.307356i
$446$	28831.5			3.06101
$447$		0			0
$448$	−6465.05	+	6465.05i	−0.681796	+	0.681796i
$449$	−4645.28	+	4645.28i	−0.488251	+	0.488251i	−0.907754	−	0.419503i	$-0.862204\pi$
$449$	−4645.28	+	4645.28i	−0.488251	+	0.488251i	0.419503	+	0.907754i	$0.362204\pi$
$450$		0			0
$451$		−	816.567i		−	0.0852564i
$452$	4636.14	−	4636.14i	0.482446	−	0.482446i
$453$		0			0
$454$	13517.4	+	13517.4i	1.39737	+	1.39737i
$455$	1078.39			0.111111
$456$		0			0
$457$			10031.6i			1.02682i	0.858144	+	0.513410i	$0.171618\pi$
$457$			10031.6i			1.02682i	−0.858144	+	0.513410i	$0.828382\pi$
$458$	−10842.4			−1.10618
$459$		0			0
$460$	−12296.3			−1.24634
$461$			1359.04i			0.137304i	0.997641	+	0.0686518i	$0.0218698\pi$
$461$			1359.04i			0.137304i	−0.997641	+	0.0686518i	$0.978130\pi$
$462$		0			0
$463$	81.1156			0.00814203			0.00407102	−	0.999992i	$-0.498704\pi$
$463$	81.1156			0.00814203			0.00407102	+	0.999992i	$0.498704\pi$
$464$	−35339.8	−	35339.8i	−3.53579	−	3.53579i
$465$		0			0
$466$	−56.1043	+	56.1043i	−0.00557721	+	0.00557721i
$467$			10790.7i			1.06924i	0.845094	+	0.534618i	$0.179545\pi$
$467$			10790.7i			1.06924i	−0.845094	+	0.534618i	$0.820455\pi$
$468$		0			0
$469$	1194.06	−	1194.06i	0.117562	−	0.117562i
$470$	−2329.74	+	2329.74i	−0.228644	+	0.228644i
$471$		0			0
$472$	1031.44			0.100584
$473$	−1731.15	−	1731.15i	−0.168284	−	0.168284i
$474$		0			0
$475$	−2169.84			−0.209598
$476$	−1027.67	+	7170.72i	−0.0989561	+	0.690482i
$477$		0			0
$478$			29335.7i			2.80708i
$479$	1974.01	+	1974.01i	0.188298	+	0.188298i	0.794960	−	0.606662i	$-0.207492\pi$
$479$	1974.01	+	1974.01i	0.188298	+	0.188298i	−0.606662	+	0.794960i	$0.707492\pi$
$480$		0			0
$481$	−4146.04	−	4146.04i	−0.393021	−	0.393021i
$482$	655.729	−	655.729i	0.0619661	−	0.0619661i
$483$		0			0
$484$		−	27176.8i		−	2.55229i
$485$			5561.95i			0.520733i
$486$		0			0
$487$	4575.10	−	4575.10i	0.425703	−	0.425703i	−0.461459	−	0.887162i	$-0.652674\pi$
$487$	4575.10	−	4575.10i	0.425703	−	0.425703i	0.887162	+	0.461459i	$0.152674\pi$
$488$	8522.63	+	8522.63i	0.790576	+	0.790576i
$489$		0			0
$490$	8400.85	+	8400.85i	0.774514	+	0.774514i
$491$			221.719i			0.0203789i	0.999948	+	0.0101895i	$0.00324346\pi$
$491$			221.719i			0.0203789i	−0.999948	+	0.0101895i	$0.996757\pi$
$492$		0			0
$493$	−14433.8	−	2068.57i	−1.31859	−	0.188973i
$494$	−5057.93			−0.460662
$495$		0			0
$496$	−37986.6	−	37986.6i	−3.43881	−	3.43881i
$497$	−4534.33			−0.409241
$498$		0			0
$499$	−5125.17	+	5125.17i	−0.459788	+	0.459788i	−0.898586	−	0.438798i	$-0.855404\pi$
$499$	−5125.17	+	5125.17i	−0.459788	+	0.459788i	0.438798	+	0.898586i	$0.355404\pi$
$500$	21408.7	−	21408.7i	1.91485	−	1.91485i
$501$		0			0
$502$			26380.8i			2.34548i
$503$	5194.90	−	5194.90i	0.460495	−	0.460495i	−0.438323	−	0.898818i	$-0.644427\pi$
$503$	5194.90	−	5194.90i	0.460495	−	0.460495i	0.898818	+	0.438323i	$0.144427\pi$
$504$		0			0
$505$	1179.54	+	1179.54i	0.103938	+	0.103938i
$506$	−4294.72			−0.377320
$507$		0			0
$508$		−	16663.7i		−	1.45538i
$509$	1656.30			0.144232			0.0721162	−	0.997396i	$-0.477025\pi$
$509$	1656.30			0.144232			0.0721162	+	0.997396i	$0.477025\pi$
$510$		0			0
$511$	−4239.93			−0.367052
$512$			23539.3i			2.03184i
$513$		0			0
$514$	30528.1			2.61972
$515$	492.736	+	492.736i	0.0421602	+	0.0421602i
$516$		0			0
$517$	−595.960	+	595.960i	−0.0506969	+	0.0506969i
$518$			4487.30i			0.380619i
$519$		0			0
$520$	12274.0	−	12274.0i	1.03510	−	1.03510i
$521$	12169.0	−	12169.0i	1.02329	−	1.02329i	0.0235669	−	0.999722i	$-0.492498\pi$
$521$	12169.0	−	12169.0i	1.02329	−	1.02329i	0.999722	−	0.0235669i	$-0.00750228\pi$
$522$		0			0
$523$	22280.9			1.86286			0.931429	−	0.363922i	$-0.118563\pi$
$523$	22280.9			1.86286			0.931429	+	0.363922i	$0.118563\pi$
$524$	22424.1	+	22424.1i	1.86947	+	1.86947i
$525$		0			0
$526$	22505.6			1.86557
$527$	−15514.8	−	2223.49i	−1.28242	−	0.183789i
$528$		0			0
$529$			5295.94i			0.435271i
$530$	−14178.9	−	14178.9i	−1.16206	−	1.16206i
$531$		0			0
$532$	2004.67	+	2004.67i	0.163371	+	0.163371i
$533$	−2054.81	+	2054.81i	−0.166987	+	0.166987i
$534$		0			0
$535$		−	13849.2i		−	1.11916i
$536$		−	27180.9i		−	2.19037i
$537$		0			0
$538$	23390.3	−	23390.3i	1.87440	−	1.87440i
$539$	2148.98	+	2148.98i	0.171731	+	0.171731i
$540$		0			0
$541$	−6005.23	−	6005.23i	−0.477237	−	0.477237i	0.427010	−	0.904247i	$-0.359567\pi$
$541$	−6005.23	−	6005.23i	−0.477237	−	0.477237i	−0.904247	+	0.427010i	$0.859567\pi$
$542$			35843.9i			2.84064i
$543$		0			0
$544$	29664.6	+	39589.7i	2.33797	+	3.12021i
$545$	1777.94			0.139741
$546$		0			0
$547$	8851.45	+	8851.45i	0.691885	+	0.691885i	0.962646	−	0.270762i	$-0.0872756\pi$
$547$	8851.45	+	8851.45i	0.691885	+	0.691885i	−0.270762	+	0.962646i	$0.587276\pi$
$548$	41662.0			3.24765
$549$		0			0
$550$	2897.89	−	2897.89i	0.224666	−	0.224666i
$551$	−4035.15	+	4035.15i	−0.311984	+	0.311984i
$552$		0			0
$553$			2130.00i			0.163792i
$554$	−9433.52	+	9433.52i	−0.723451	+	0.723451i
$555$		0			0
$556$	9575.15	+	9575.15i	0.730354	+	0.730354i
$557$	−21449.2			−1.63165			−0.815827	−	0.578295i	$-0.803718\pi$
$557$	−21449.2			−1.63165			−0.815827	+	0.578295i	$0.803718\pi$
$558$		0			0
$559$			8712.53i			0.659215i
$560$	−7682.76			−0.579742
$561$		0			0
$562$	2841.90			0.213306
$563$			9661.93i			0.723271i	0.932319	+	0.361636i	$0.117782\pi$
$563$			9661.93i			0.723271i	−0.932319	+	0.361636i	$0.882218\pi$
$564$		0			0
$565$	2028.74			0.151061
$566$	17990.0	+	17990.0i	1.33600	+	1.33600i
$567$		0			0
$568$	−51608.7	+	51608.7i	−3.81242	+	3.81242i
$569$		−	22571.3i		−	1.66298i	−0.555537	−	0.831492i	$-0.687487\pi$
$569$		−	22571.3i		−	1.66298i	0.555537	−	0.831492i	$-0.312513\pi$
$570$		0			0
$571$	−12344.5	+	12344.5i	−0.904732	+	0.904732i	−0.995841	−	0.0911089i	$-0.970959\pi$
$571$	−12344.5	+	12344.5i	−0.904732	+	0.904732i	0.0911089	+	0.995841i	$0.470959\pi$
$572$	4947.39	−	4947.39i	0.361645	−	0.361645i
$573$		0			0
$574$	2223.94			0.161717
$575$	4636.29	+	4636.29i	0.336255	+	0.336255i
$576$		0			0
$577$	−22153.0			−1.59834			−0.799168	−	0.601108i	$-0.794726\pi$
$577$	−22153.0			−1.59834			−0.799168	+	0.601108i	$0.794726\pi$
$578$	25781.4	+	7544.66i	1.85530	+	0.542935i
$579$		0			0
$580$		−	30859.1i		−	2.20923i
$581$	1868.78	+	1868.78i	0.133443	+	0.133443i
$582$		0			0
$583$	−3627.03	−	3627.03i	−0.257661	−	0.257661i
$584$	−48257.9	+	48257.9i	−3.41940	+	3.41940i
$585$		0			0
$586$		−	10152.3i		−	0.715678i
$587$		−	16152.5i		−	1.13575i	−0.823116	−	0.567873i	$-0.807766\pi$
$587$		−	16152.5i		−	1.13575i	0.823116	−	0.567873i	$-0.192234\pi$
$588$		0			0
$589$	−4337.36	+	4337.36i	−0.303426	+	0.303426i
$590$	355.602	+	355.602i	0.0248134	+	0.0248134i
$591$		0			0
$592$	29537.6	+	29537.6i	2.05065	+	2.05065i
$593$			8336.26i			0.577284i	0.957437	+	0.288642i	$0.0932037\pi$
$593$			8336.26i			0.577284i	−0.957437	+	0.288642i	$0.906796\pi$
$594$		0			0
$595$	−1793.78	+	1344.08i	−0.123593	+	0.0926080i
$596$	−30609.8			−2.10373
$597$		0			0
$598$	10807.3	+	10807.3i	0.739033	+	0.739033i
$599$	9798.73			0.668390			0.334195	−	0.942504i	$-0.391536\pi$
$599$	9798.73			0.668390			0.334195	+	0.942504i	$0.391536\pi$
$600$		0			0
$601$	−5458.38	+	5458.38i	−0.370469	+	0.370469i	−0.867648	−	0.497179i	$-0.834369\pi$
$601$	−5458.38	+	5458.38i	−0.370469	+	0.370469i	0.497179	+	0.867648i	$0.334369\pi$
$602$	4714.83	−	4714.83i	0.319206	−	0.319206i
$603$		0			0
$604$		−	54816.1i		−	3.69277i
$605$	5946.18	−	5946.18i	0.399581	−	0.399581i
$606$		0			0
$607$	−17165.0	−	17165.0i	−1.14779	−	1.14779i	−0.986987	−	0.160799i	$-0.948593\pi$
$607$	−17165.0	−	17165.0i	−1.14779	−	1.14779i	−0.160799	−	0.986987i	$-0.551407\pi$
$608$	19360.9			1.29143
$609$		0			0
$610$			5876.58i			0.390059i
$611$	2999.36			0.198594
$612$		0			0
$613$	−12662.6			−0.834318			−0.417159	−	0.908833i	$-0.636974\pi$
$613$	−12662.6			−0.834318			−0.417159	+	0.908833i	$0.636974\pi$
$614$			4153.47i			0.272997i
$615$		0			0
$616$	−3398.18			−0.222267
$617$	−13203.5	−	13203.5i	−0.861514	−	0.861514i	0.130000	−	0.991514i	$-0.458502\pi$
$617$	−13203.5	−	13203.5i	−0.861514	−	0.861514i	−0.991514	+	0.130000i	$0.958502\pi$
$618$		0			0
$619$	13686.4	−	13686.4i	0.888697	−	0.888697i	−0.105701	−	0.994398i	$-0.533709\pi$
$619$	13686.4	−	13686.4i	0.888697	−	0.888697i	0.994398	+	0.105701i	$0.0337087\pi$
$620$		−	33170.3i		−	2.14863i
$621$		0			0
$622$	−3952.91	+	3952.91i	−0.254819	+	0.254819i
$623$	2010.13	−	2010.13i	0.129268	−	0.129268i
$624$		0			0
$625$	−519.171			−0.0332269
$626$	−15236.8	−	15236.8i	−0.972816	−	0.972816i
$627$		0			0
$628$	59450.9			3.77763
$629$	12064.0	+	1728.94i	0.764742	+	0.109599i
$630$		0			0
$631$		−	6088.34i		−	0.384109i	−0.981384	−	0.192055i	$-0.938485\pi$
$631$		−	6088.34i		−	0.384109i	0.981384	−	0.192055i	$-0.0615151\pi$
$632$	24243.1	+	24243.1i	1.52585	+	1.52585i
$633$		0			0
$634$	−20814.4	−	20814.4i	−1.30386	−	1.30386i
$635$	3645.96	−	3645.96i	0.227851	−	0.227851i
$636$		0			0
$637$		−	10815.4i		−	0.672720i
$638$		−	10778.1i		−	0.668826i
$639$		0			0
$640$	−23688.6	+	23688.6i	−1.46308	+	1.46308i
$641$	−6462.87	−	6462.87i	−0.398234	−	0.398234i	0.479376	−	0.877610i	$-0.340863\pi$
$641$	−6462.87	−	6462.87i	−0.398234	−	0.398234i	−0.877610	+	0.479376i	$0.840863\pi$
$642$		0			0
$643$	−17003.8	−	17003.8i	−1.04287	−	1.04287i	−0.999039	−	0.0438299i	$-0.986044\pi$
$643$	−17003.8	−	17003.8i	−1.04287	−	1.04287i	−0.0438299	−	0.999039i	$-0.513956\pi$
$644$		−	8566.75i		−	0.524188i
$645$		0			0
$646$	8413.28	−	6304.07i	0.512409	−	0.383948i
$647$	−22785.1			−1.38451			−0.692253	−	0.721655i	$-0.743382\pi$
$647$	−22785.1			−1.38451			−0.692253	+	0.721655i	$0.743382\pi$
$648$		0			0
$649$	90.9649	+	90.9649i	0.00550182	+	0.00550182i
$650$	−14584.5			−0.880082
$651$		0			0
$652$	−51248.3	+	51248.3i	−3.07828	+	3.07828i
$653$	5235.78	−	5235.78i	0.313770	−	0.313770i	−0.532598	−	0.846368i	$-0.678784\pi$
$653$	5235.78	−	5235.78i	0.313770	−	0.313770i	0.846368	+	0.532598i	$0.178784\pi$
$654$		0			0
$655$			9812.63i			0.585361i
$656$	14639.1	−	14639.1i	0.871281	−	0.871281i
$657$		0			0
$658$	−1623.11	−	1623.11i	−0.0961635	−	0.0961635i
$659$	18416.5			1.08863			0.544314	−	0.838882i	$-0.316790\pi$
$659$	18416.5			1.08863			0.544314	+	0.838882i	$0.316790\pi$
$660$		0			0
$661$			23526.7i			1.38439i	0.721709	+	0.692197i	$0.243357\pi$
$661$			23526.7i			1.38439i	−0.721709	+	0.692197i	$0.756643\pi$
$662$	9282.45			0.544974
$663$		0			0
$664$	42540.0			2.48626
$665$			877.228i			0.0511541i
$666$		0			0
$667$	17243.8			1.00102
$668$	5422.16	+	5422.16i	0.314057	+	0.314057i
$669$		0			0
$670$	9370.99	−	9370.99i	0.540348	−	0.540348i
$671$			1503.26i			0.0864870i
$672$		0			0
$673$	14333.6	−	14333.6i	0.820979	−	0.820979i	−0.165269	−	0.986248i	$-0.552849\pi$
$673$	14333.6	−	14333.6i	0.820979	−	0.820979i	0.986248	+	0.165269i	$0.0528493\pi$
$674$	43675.3	−	43675.3i	2.49601	−	2.49601i
$675$		0			0
$676$	23205.0			1.32027
$677$	−23854.8	−	23854.8i	−1.35423	−	1.35423i	−0.880866	−	0.473366i	$-0.843039\pi$
$677$	−23854.8	−	23854.8i	−1.35423	−	1.35423i	−0.473366	−	0.880866i	$-0.656961\pi$
$678$		0			0
$679$	−3874.98			−0.219010
$680$	−5118.38	+	35714.3i	−0.288648	+	2.01409i
$681$		0			0
$682$		−	11585.4i		−	0.650480i
$683$	−466.809	−	466.809i	−0.0261522	−	0.0261522i	0.693910	−	0.720062i	$-0.255887\pi$
$683$	−466.809	−	466.809i	−0.0261522	−	0.0261522i	−0.720062	+	0.693910i	$0.755887\pi$
$684$		0			0
$685$	9115.48	+	9115.48i	0.508445	+	0.508445i
$686$	−12112.2	+	12112.2i	−0.674120	+	0.674120i
$687$		0			0
$688$		−	62070.6i		−	3.43956i
$689$			18254.2i			1.00933i
$690$		0			0
$691$	15237.1	−	15237.1i	0.838850	−	0.838850i	−0.149858	−	0.988708i	$-0.547882\pi$
$691$	15237.1	−	15237.1i	0.838850	−	0.838850i	0.988708	+	0.149858i	$0.0478815\pi$
$692$	−32365.6	−	32365.6i	−1.77797	−	1.77797i
$693$		0			0
$694$	13910.1	+	13910.1i	0.760836	+	0.760836i
$695$			4190.01i			0.228685i
$696$		0			0
$697$	856.879	−	5979.01i	0.0465662	−	0.324923i
$698$	20456.6			1.10930
$699$		0			0
$700$	5780.47	+	5780.47i	0.312116	+	0.312116i
$701$	13156.7			0.708878			0.354439	−	0.935079i	$-0.384672\pi$
$701$	13156.7			0.708878			0.354439	+	0.935079i	$0.384672\pi$
$702$		0			0
$703$	3372.65	−	3372.65i	0.180941	−	0.180941i
$704$	−12979.0	+	12979.0i	−0.694837	+	0.694837i
$705$		0			0
$706$			31312.4i			1.66920i
$707$	−821.777	+	821.777i	−0.0437145	+	0.0437145i
$708$		0			0
$709$	23107.7	+	23107.7i	1.22402	+	1.22402i	0.966191	+	0.257828i	$0.0830069\pi$
$709$	23107.7	+	23107.7i	1.22402	+	1.22402i	0.257828	+	0.966191i	$0.416993\pi$
$710$	−35585.6			−1.88099
$711$		0			0
$712$		−	45757.6i		−	2.40848i
$713$	18535.3			0.973565
$714$		0			0
$715$	2164.94			0.113237
$716$		−	16181.7i		−	0.844609i
$717$		0			0
$718$	−33073.0			−1.71904
$719$	−9521.59	−	9521.59i	−0.493874	−	0.493874i	0.415650	−	0.909524i	$-0.363554\pi$
$719$	−9521.59	−	9521.59i	−0.493874	−	0.493874i	−0.909524	+	0.415650i	$0.863554\pi$
$720$		0			0
$721$	−343.286	+	343.286i	−0.0177318	+	0.0177318i
$722$			33388.3i			1.72103i
$723$		0			0
$724$	−50505.6	+	50505.6i	−2.59258	+	2.59258i
$725$	−11635.4	+	11635.4i	−0.596036	+	0.596036i
$726$		0			0
$727$	−32562.8			−1.66119			−0.830596	−	0.556875i	$-0.812000\pi$
$727$	−32562.8			−1.66119			−0.830596	+	0.556875i	$0.812000\pi$
$728$	8551.20	+	8551.20i	0.435341	+	0.435341i
$729$		0			0
$730$	−33275.1			−1.68708
$731$	−10859.1	−	14492.3i	−0.549436	−	0.733265i
$732$		0			0
$733$		−	36291.9i		−	1.82875i	−0.404869	−	0.914375i	$-0.632683\pi$
$733$		−	36291.9i		−	1.82875i	0.404869	−	0.914375i	$-0.367317\pi$
$734$	−13297.9	−	13297.9i	−0.668710	−	0.668710i
$735$		0			0
$736$	−41368.5	−	41368.5i	−2.07182	−	2.07182i
$737$	2397.15	−	2397.15i	0.119810	−	0.119810i
$738$		0			0
$739$		−	13314.8i		−	0.662776i	−0.943495	−	0.331388i	$-0.892483\pi$
$739$		−	13314.8i		−	0.662776i	0.943495	−	0.331388i	$-0.107517\pi$
$740$			25792.6i			1.28129i
$741$		0			0
$742$	9878.34	−	9878.34i	0.488740	−	0.488740i
$743$	−2986.28	−	2986.28i	−0.147451	−	0.147451i	0.629527	−	0.776978i	$-0.283249\pi$
$743$	−2986.28	−	2986.28i	−0.147451	−	0.147451i	−0.776978	+	0.629527i	$0.783249\pi$
$744$		0			0
$745$	−6697.30	−	6697.30i	−0.329356	−	0.329356i
$746$		−	37268.4i		−	1.82908i
$747$		0			0
$748$	−2063.11	+	14395.7i	−0.100849	+	0.703689i
$749$	9648.62			0.470698
$750$		0			0
$751$	25948.6	+	25948.6i	1.26082	+	1.26082i	0.950695	+	0.310129i	$0.100372\pi$
$751$	25948.6	+	25948.6i	1.26082	+	1.26082i	0.310129	+	0.950695i	$0.399628\pi$
$752$	−21368.3			−1.03620
$753$		0			0
$754$	−27122.2	+	27122.2i	−1.30999	+	1.30999i
$755$	11993.5	−	11993.5i	0.578132	−	0.578132i
$756$		0			0
$757$			8664.38i			0.416000i	0.978129	+	0.208000i	$0.0666955\pi$
$757$			8664.38i			0.416000i	−0.978129	+	0.208000i	$0.933305\pi$
$758$	−22879.4	+	22879.4i	−1.09633	+	1.09633i
$759$		0			0
$760$	9984.40	+	9984.40i	0.476543	+	0.476543i
$761$	30593.6			1.45731			0.728657	−	0.684879i	$-0.240145\pi$
$761$	30593.6			1.45731			0.728657	+	0.684879i	$0.240145\pi$
$762$		0			0
$763$			1238.68i			0.0587724i
$764$	−5820.69			−0.275635
$765$		0			0
$766$	−41471.6			−1.95618
$767$		−	457.809i		−	0.0215522i
$768$		0			0
$769$	24560.3			1.15171			0.575857	−	0.817550i	$-0.304668\pi$
$769$	24560.3			1.15171			0.575857	+	0.817550i	$0.304668\pi$
$770$	−1171.57	−	1171.57i	−0.0548317	−	0.0548317i
$771$		0			0
$772$	−551.156	+	551.156i	−0.0256950	+	0.0256950i
$773$			4421.49i			0.205731i	0.994695	+	0.102865i	$0.0328011\pi$
$773$			4421.49i			0.205731i	−0.994695	+	0.102865i	$0.967199\pi$
$774$		0			0
$775$	−12506.8	+	12506.8i	−0.579687	+	0.579687i
$776$	−44104.1	+	44104.1i	−2.04026	+	2.04026i
$777$		0			0
$778$	7598.63			0.350159
$779$	−1671.51	−	1671.51i	−0.0768782	−	0.0768782i
$780$		0			0
$781$	−9102.98			−0.417068
$782$	−31446.5	−	4506.74i	−1.43801	−	0.206088i
$783$		0			0
$784$			77052.2i			3.51003i
$785$	13007.6	+	13007.6i	0.591417	+	0.591417i
$786$		0			0
$787$	18102.6	+	18102.6i	0.819932	+	0.819932i	0.986098	−	0.166166i	$-0.0531387\pi$
$787$	18102.6	+	18102.6i	0.819932	+	0.819932i	−0.166166	+	0.986098i	$0.553139\pi$
$788$	9780.33	−	9780.33i	0.442144	−	0.442144i
$789$		0			0
$790$			16716.3i			0.752834i
$791$			1413.41i			0.0635336i
$792$		0			0
$793$	3782.82	−	3782.82i	0.169397	−	0.169397i
$794$	52885.0	+	52885.0i	2.36375	+	2.36375i
$795$		0			0
$796$	−59041.2	−	59041.2i	−2.62897	−	2.62897i
$797$			29252.2i			1.30008i	0.759899	+	0.650042i	$0.225249\pi$
$797$			29252.2i			1.30008i	−0.759899	+	0.650042i	$0.774751\pi$
$798$		0			0
$799$	−4989.08	+	3738.32i	−0.220902	+	0.165522i
$800$	55827.3			2.46724
$801$		0			0
$802$	−51392.4	−	51392.4i	−2.26276	−	2.26276i
$803$	−8511.96			−0.374073
$804$		0			0
$805$	1874.37	−	1874.37i	0.0820658	−	0.0820658i
$806$	−29153.6	+	29153.6i	−1.27406	+	1.27406i
$807$		0			0
$808$			18706.5i			0.814473i
$809$	−21127.9	+	21127.9i	−0.918191	+	0.918191i	−0.996898	−	0.0787072i	$-0.974921\pi$
$809$	−21127.9	+	21127.9i	−0.918191	+	0.918191i	0.0787072	+	0.996898i	$0.474921\pi$
$810$		0			0
$811$	5743.99	+	5743.99i	0.248704	+	0.248704i	0.820439	−	0.571735i	$-0.193729\pi$
$811$	5743.99	+	5743.99i	0.248704	+	0.248704i	−0.571735	+	0.820439i	$0.693729\pi$
$812$	21499.3			0.929161
$813$		0			0
$814$			9008.56i			0.387899i
$815$	−22425.9			−0.963858
$816$		0			0
$817$	−7087.31			−0.303493
$818$		−	35922.7i		−	1.53546i
$819$		0			0
$820$	12783.0			0.544393
$821$	−19490.2	−	19490.2i	−0.828518	−	0.828518i	0.158794	−	0.987312i	$-0.449240\pi$
$821$	−19490.2	−	19490.2i	−0.828518	−	0.828518i	−0.987312	+	0.158794i	$0.949240\pi$
$822$		0			0
$823$	13917.8	−	13917.8i	0.589483	−	0.589483i	−0.348008	−	0.937491i	$-0.613142\pi$
$823$	13917.8	−	13917.8i	0.589483	−	0.589483i	0.937491	+	0.348008i	$0.113142\pi$
$824$			7814.39i			0.330373i
$825$		0			0
$826$	−247.745	+	247.745i	−0.0104360	+	0.0104360i
$827$	−21762.7	+	21762.7i	−0.915071	+	0.915071i	−0.996666	−	0.0815942i	$-0.973999\pi$
$827$	−21762.7	+	21762.7i	−0.915071	+	0.915071i	0.0815942	+	0.996666i	$0.473999\pi$
$828$		0			0
$829$	29861.7			1.25108			0.625538	−	0.780194i	$-0.284880\pi$
$829$	29861.7			1.25108			0.625538	+	0.780194i	$0.284880\pi$
$830$	14666.2	+	14666.2i	0.613341	+	0.613341i
$831$		0			0
$832$	65321.0			2.72187
$833$	13480.1	+	17990.2i	0.560692	+	0.748288i
$834$		0			0
$835$			2372.70i			0.0983361i
$836$	4024.51	+	4024.51i	0.166496	+	0.166496i
$837$		0			0
$838$	53749.4	+	53749.4i	2.21568	+	2.21568i
$839$	20354.4	−	20354.4i	0.837558	−	0.837558i	−0.150979	−	0.988537i	$-0.548242\pi$
$839$	20354.4	−	20354.4i	0.837558	−	0.837558i	0.988537	+	0.150979i	$0.0482424\pi$
$840$		0			0
$841$			18886.4i			0.774383i
$842$			16628.2i			0.680576i
$843$		0			0
$844$	−36500.5	+	36500.5i	−1.48862	+	1.48862i
$845$	5077.17	+	5077.17i	0.206698	+	0.206698i
$846$		0			0
$847$	4142.66	+	4142.66i	0.168056	+	0.168056i
$848$		−	130048.i		−	5.26635i
$849$		0			0
$850$	24259.7	−	18177.8i	0.978942	−	0.733522i
$851$	−14412.7			−0.580563
$852$		0			0
$853$	1527.89	+	1527.89i	0.0613293	+	0.0613293i	0.737106	−	0.675777i	$-0.236192\pi$
$853$	1527.89	+	1527.89i	0.0613293	+	0.0613293i	−0.675777	+	0.737106i	$0.736192\pi$
$854$	−4094.18			−0.164051
$855$		0			0
$856$	109818.	−	109818.i	4.38494	−	4.38494i
$857$	17938.8	−	17938.8i	0.715025	−	0.715025i	−0.252557	−	0.967582i	$-0.581271\pi$
$857$	17938.8	−	17938.8i	0.715025	−	0.715025i	0.967582	+	0.252557i	$0.0812715\pi$
$858$		0			0
$859$			4878.89i			0.193790i	0.995295	+	0.0968951i	$0.0308911\pi$
$859$			4878.89i			0.193790i	−0.995295	+	0.0968951i	$0.969109\pi$
$860$	27100.4	−	27100.4i	1.07455	−	1.07455i
$861$		0			0
$862$	−24180.4	−	24180.4i	−0.955438	−	0.955438i
$863$	39426.2			1.55514			0.777569	−	0.628797i	$-0.216452\pi$
$863$	39426.2			1.55514			0.777569	+	0.628797i	$0.216452\pi$
$864$		0			0
$865$		−	14163.0i		−	0.556711i
$866$	−55664.9			−2.18426
$867$		0			0
$868$	23109.6			0.903674
$869$			4276.12i			0.166924i
$870$		0			0
$871$	−12064.4			−0.469330
$872$	14098.4	+	14098.4i	0.547514	+	0.547514i
$873$		0			0
$874$	−8791.29	+	8791.29i	−0.340240	+	0.340240i
$875$			6526.81i			0.252167i
$876$		0			0
$877$	1781.74	−	1781.74i	0.0686034	−	0.0686034i	−0.671973	−	0.740576i	$-0.734553\pi$
$877$	1781.74	−	1781.74i	0.0686034	−	0.0686034i	0.740576	+	0.671973i	$0.234553\pi$
$878$	38507.2	−	38507.2i	1.48013	−	1.48013i
$879$		0			0
$880$	−15423.7			−0.590831
$881$	2784.04	+	2784.04i	0.106466	+	0.106466i	0.758333	−	0.651867i	$-0.226014\pi$
$881$	2784.04	+	2784.04i	0.106466	+	0.106466i	−0.651867	+	0.758333i	$0.726014\pi$
$882$		0			0
$883$	−8794.76			−0.335184			−0.167592	−	0.985856i	$-0.553599\pi$
$883$	−8794.76			−0.335184			−0.167592	+	0.985856i	$0.553599\pi$
$884$	41417.1	−	31033.8i	1.57580	−	1.18075i
$885$		0			0
$886$		−	37360.7i		−	1.41666i
$887$	385.409	+	385.409i	0.0145894	+	0.0145894i	0.714364	−	0.699774i	$-0.246716\pi$
$887$	385.409	+	385.409i	0.0145894	+	0.0145894i	−0.699774	+	0.714364i	$0.746716\pi$
$888$		0			0
$889$	2540.12	+	2540.12i	0.0958300	+	0.0958300i
$890$	15775.5	−	15775.5i	0.594154	−	0.594154i
$891$		0			0
$892$			115456.i			4.33382i
$893$			2439.86i			0.0914298i
$894$		0			0
$895$	3540.51	−	3540.51i	0.132230	−	0.132230i
$896$	−16503.7	−	16503.7i	−0.615345	−	0.615345i
$897$		0			0
$898$	−25398.9	−	25398.9i	−0.943844	−	0.943844i
$899$			46516.6i			1.72571i
$900$		0			0
$901$	−22751.5	−	30363.7i	−0.841247	−	1.12271i
$902$	4464.72			0.164810
$903$		0			0
$904$	16087.1	+	16087.1i	0.591868	+	0.591868i
$905$	−22100.9			−0.811777
$906$		0			0
$907$	1870.27	−	1870.27i	0.0684688	−	0.0684688i	−0.672043	−	0.740512i	$-0.734583\pi$
$907$	1870.27	−	1870.27i	0.0684688	−	0.0684688i	0.740512	+	0.672043i	$0.234583\pi$
$908$	−54130.9	+	54130.9i	−1.97841	+	1.97841i
$909$		0			0
$910$			5896.28i			0.214791i
$911$	576.131	−	576.131i	0.0209529	−	0.0209529i	−0.696553	−	0.717506i	$-0.745284\pi$
$911$	576.131	−	576.131i	0.0209529	−	0.0209529i	0.717506	+	0.696553i	$0.245284\pi$
$912$		0			0
$913$	3751.71	+	3751.71i	0.135995	+	0.135995i
$914$	−54849.3			−1.98496
$915$		0			0
$916$		−	43418.5i		−	1.56614i
$917$	−6836.40			−0.246192
$918$		0			0
$919$	−44667.9			−1.60333			−0.801664	−	0.597774i	$-0.796052\pi$
$919$	−44667.9			−1.60333			−0.801664	+	0.597774i	$0.796052\pi$
$920$		−	42667.3i		−	1.52902i
$921$		0			0
$922$	−7430.81			−0.265424
$923$	22906.8	+	22906.8i	0.816887	+	0.816887i
$924$		0			0
$925$	9725.03	−	9725.03i	0.345683	−	0.345683i
$926$			443.514i			0.0157395i
$927$		0			0
$928$	103819.	−	103819.i	3.67246	−	3.67246i
$929$	−4929.53	+	4929.53i	−0.174093	+	0.174093i	−0.788775	−	0.614682i	$-0.789284\pi$
$929$	−4929.53	+	4929.53i	−0.174093	+	0.174093i	0.614682	+	0.788775i	$0.289284\pi$
$930$		0			0
$931$	8797.93			0.309711
$932$	−224.671	−	224.671i	−0.00789629	−	0.00789629i
$933$		0			0
$934$	−59000.0			−2.06696
$935$	−3601.13	+	2698.33i	−0.125957	+	0.0943794i
$936$		0			0
$937$			46241.3i			1.61221i	0.591776	+	0.806103i	$0.298427\pi$
$937$			46241.3i			1.61221i	−0.591776	+	0.806103i	$0.701573\pi$
$938$	6528.71	+	6528.71i	0.227260	+	0.227260i
$939$		0			0
$940$	−9329.51	−	9329.51i	−0.323718	−	0.323718i
$941$	21810.5	−	21810.5i	0.755582	−	0.755582i	−0.219933	−	0.975515i	$-0.570584\pi$
$941$	21810.5	−	21810.5i	0.755582	−	0.755582i	0.975515	+	0.219933i	$0.0705840\pi$
$942$		0			0
$943$			7143.03i			0.246669i
$944$			3261.56i			0.112452i
$945$		0			0
$946$	9465.34	−	9465.34i	0.325312	−	0.325312i
$947$	17699.8	+	17699.8i	0.607355	+	0.607355i	0.942254	−	0.334899i	$-0.108702\pi$
$947$	17699.8	+	17699.8i	0.607355	+	0.607355i	−0.334899	+	0.942254i	$0.608702\pi$
$948$		0			0
$949$	21419.5	+	21419.5i	0.732674	+	0.732674i
$950$		−	11864.0i		−	0.405177i
$951$		0			0
$952$	−24881.9	−	3565.94i	−0.847088	−	0.121400i
$953$	8104.79			0.275488			0.137744	−	0.990468i	$-0.456015\pi$
$953$	8104.79			0.275488			0.137744	+	0.990468i	$0.456015\pi$
$954$		0			0
$955$	−1273.55	−	1273.55i	−0.0431528	−	0.0431528i
$956$	−117476.			−3.97431
$957$		0			0
$958$	−10793.2	+	10793.2i	−0.364001	+	0.364001i
$959$	−6350.70	+	6350.70i	−0.213842	+	0.213842i
$960$		0			0
$961$			20209.5i			0.678377i
$962$	22669.2	−	22669.2i	0.759755	−	0.759755i
$963$		0			0
$964$	2625.89	+	2625.89i	0.0877325	+	0.0877325i
$965$	−241.182			−0.00804550
$966$		0			0
$967$			12592.3i			0.418759i	0.977834	+	0.209379i	$0.0671443\pi$
$967$			12592.3i			0.418759i	−0.977834	+	0.209379i	$0.932856\pi$
$968$	94301.6			3.13117
$969$		0			0
$970$	−30410.9			−1.00664
$971$			43998.8i			1.45416i	0.686553	+	0.727080i	$0.259123\pi$
$971$			43998.8i			1.45416i	−0.686553	+	0.727080i	$0.740877\pi$
$972$		0			0
$973$	−2919.16			−0.0961807
$974$	25015.1	+	25015.1i	0.822933	+	0.822933i
$975$		0			0
$976$	−26949.9	+	26949.9i	−0.883856	+	0.883856i
$977$		−	8709.69i		−	0.285207i	−0.989780	−	0.142604i	$-0.954453\pi$
$977$		−	8709.69i		−	0.285207i	0.989780	−	0.142604i	$-0.0455474\pi$
$978$		0			0
$979$	4035.47	−	4035.47i	0.131741	−	0.131741i
$980$	−33641.4	+	33641.4i	−1.09657	+	1.09657i
$981$		0			0
$982$	−1212.29			−0.0393948
$983$	−24475.0	−	24475.0i	−0.794132	−	0.794132i	0.188031	−	0.982163i	$-0.439789\pi$
$983$	−24475.0	−	24475.0i	−0.794132	−	0.794132i	−0.982163	+	0.188031i	$0.939789\pi$
$984$		0			0
$985$	4279.80			0.138442
$986$	11310.2	−	78919.0i	0.365306	−	2.54898i
$987$		0			0
$988$		−	20254.6i		−	0.652212i
$989$	15143.4	+	15143.4i	0.486889	+	0.486889i
$990$		0			0
$991$	−20930.6	−	20930.6i	−0.670919	−	0.670919i	0.287009	−	0.957928i	$-0.407339\pi$
$991$	−20930.6	−	20930.6i	−0.670919	−	0.670919i	−0.957928	+	0.287009i	$0.907339\pi$
$992$	111595.	−	111595.i	3.57172	−	3.57172i
$993$		0			0
$994$		−	24792.2i		−	0.791109i
$995$		−	25836.0i		−	0.823171i
$996$		0			0
$997$	25813.9	−	25813.9i	0.819993	−	0.819993i	−0.166114	−	0.986107i	$-0.553122\pi$
$997$	25813.9	−	25813.9i	0.819993	−	0.819993i	0.986107	+	0.166114i	$0.0531219\pi$
$998$	−28022.7	−	28022.7i	−0.888822	−	0.888822i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.f.a.64.4		8
3.2	odd	2		17.4.c.a.13.1	yes	8
12.11	even	2		272.4.o.e.81.1		8
17.4	even	4	inner	153.4.f.a.55.1		8
51.2	odd	8		289.4.a.f.1.8		8
51.8	odd	8		289.4.b.c.288.1		8
51.26	odd	8		289.4.b.c.288.2		8
51.32	odd	8		289.4.a.f.1.7		8
51.38	odd	4		17.4.c.a.4.4	✓	8
204.191	even	4		272.4.o.e.225.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.4	✓	8	51.38	odd	4
17.4.c.a.13.1	yes	8	3.2	odd	2
153.4.f.a.55.1		8	17.4	even	4	inner
153.4.f.a.64.4		8	1.1	even	1	trivial
272.4.o.e.81.1		8	12.11	even	2
272.4.o.e.225.1		8	204.191	even	4
289.4.a.f.1.7		8	51.32	odd	8
289.4.a.f.1.8		8	51.2	odd	8
289.4.b.c.288.1		8	51.8	odd	8
289.4.b.c.288.2		8	51.26	odd	8

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+5.46767i q^{2} -21.8954 q^{4} +(-4.79064 - 4.79064i) q^{5} +(3.33761 - 3.33761i) q^{7} -75.9757i q^{8} +O(q^{10})\)	\(q+5.46767i q^{2} -21.8954 q^{4} +(-4.79064 - 4.79064i) q^{5} +(3.33761 - 3.33761i) q^{7} -75.9757i q^{8} +(26.1937 - 26.1937i) q^{10} +(6.70048 - 6.70048i) q^{11} -33.7223 q^{13} +(18.2490 + 18.2490i) q^{14} +240.247 q^{16} +(56.0931 - 42.0305i) q^{17} -27.4317i q^{19} +(104.893 + 104.893i) q^{20} +(36.6360 + 36.6360i) q^{22} +(-58.6134 + 58.6134i) q^{23} -79.0995i q^{25} -184.382i q^{26} +(-73.0784 + 73.0784i) q^{28} +(-147.098 - 147.098i) q^{29} +(-158.115 - 158.115i) q^{31} +705.786i q^{32} +(229.809 + 306.699i) q^{34} -31.9786 q^{35} +(122.947 + 122.947i) q^{37} +149.988 q^{38} +(-363.973 + 363.973i) q^{40} +(60.9335 - 60.9335i) q^{41} -258.362i q^{43} +(-146.710 + 146.710i) q^{44} +(-320.479 - 320.479i) q^{46} -88.9429 q^{47} +320.721i q^{49} +432.490 q^{50} +738.364 q^{52} -541.310i q^{53} -64.1992 q^{55} +(-253.577 - 253.577i) q^{56} +(804.282 - 804.282i) q^{58} +13.5759i q^{59} +(-112.176 + 112.176i) q^{61} +(864.520 - 864.520i) q^{62} -1937.03 q^{64} +(161.551 + 161.551i) q^{65} +357.758 q^{67} +(-1228.18 + 920.277i) q^{68} -174.848i q^{70} +(-679.278 - 679.278i) q^{71} +(-635.175 - 635.175i) q^{73} +(-672.233 + 672.233i) q^{74} +600.630i q^{76} -44.7272i q^{77} +(-319.090 + 319.090i) q^{79} +(-1150.94 - 1150.94i) q^{80} +(333.164 + 333.164i) q^{82} +559.916i q^{83} +(-470.075 - 67.3686i) q^{85} +1412.64 q^{86} +(-509.074 - 509.074i) q^{88} +602.266 q^{89} +(-112.552 + 112.552i) q^{91} +(1283.37 - 1283.37i) q^{92} -486.311i q^{94} +(-131.416 + 131.416i) q^{95} +(-580.502 - 580.502i) q^{97} -1753.60 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{4} - 14 q^{5} + 2 q^{7}+O(q^{10}) \) 8 * q - 36 * q^4 - 14 * q^5 + 2 * q^7	\( 8 q - 36 q^{4} - 14 q^{5} + 2 q^{7} + 78 q^{10} + 108 q^{11} - 88 q^{13} - 108 q^{14} + 420 q^{16} + 10 q^{17} + 306 q^{20} + 30 q^{22} + 22 q^{23} - 764 q^{28} - 46 q^{29} + 610 q^{31} + 1002 q^{34} - 1172 q^{35} - 574 q^{37} + 768 q^{38} - 342 q^{40} + 968 q^{41} - 550 q^{44} - 944 q^{46} + 368 q^{47} - 468 q^{50} + 2564 q^{52} - 1996 q^{55} - 684 q^{56} + 266 q^{58} + 1258 q^{61} + 2516 q^{62} - 3044 q^{64} - 628 q^{65} + 764 q^{67} - 1914 q^{68} - 1266 q^{71} - 1732 q^{73} - 1538 q^{74} + 914 q^{79} - 498 q^{80} - 280 q^{82} - 2498 q^{85} + 4244 q^{86} + 442 q^{88} + 2156 q^{89} - 1632 q^{91} + 1768 q^{92} - 1484 q^{95} + 1836 q^{97} - 6728 q^{98}+O(q^{100}) \) 8 * q - 36 * q^4 - 14 * q^5 + 2 * q^7 + 78 * q^10 + 108 * q^11 - 88 * q^13 - 108 * q^14 + 420 * q^16 + 10 * q^17 + 306 * q^20 + 30 * q^22 + 22 * q^23 - 764 * q^28 - 46 * q^29 + 610 * q^31 + 1002 * q^34 - 1172 * q^35 - 574 * q^37 + 768 * q^38 - 342 * q^40 + 968 * q^41 - 550 * q^44 - 944 * q^46 + 368 * q^47 - 468 * q^50 + 2564 * q^52 - 1996 * q^55 - 684 * q^56 + 266 * q^58 + 1258 * q^61 + 2516 * q^62 - 3044 * q^64 - 628 * q^65 + 764 * q^67 - 1914 * q^68 - 1266 * q^71 - 1732 * q^73 - 1538 * q^74 + 914 * q^79 - 498 * q^80 - 280 * q^82 - 2498 * q^85 + 4244 * q^86 + 442 * q^88 + 2156 * q^89 - 1632 * q^91 + 1768 * q^92 - 1484 * q^95 + 1836 * q^97 - 6728 * q^98

Introduction

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