LMFDB - Embedded newform 55.3.c.a.21.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,3,Mod(21,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(55, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("55.21"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$8$
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} + 30x^{6} + 280x^{4} + 890x^{2} + 895 $ x^8 + 30x^6 + 280x^4 + 890*x^2 + 895
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.2
Root			$-3.15955i$ of defining polynomial
Character	$\chi$	$=$	55.21
Dual form			55.3.c.a.21.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.15955i q^{2} -3.03112 q^{3} -5.98274 q^{4} -2.23607 q^{5} +9.57697i q^{6} -5.67155i q^{7} +6.26455i q^{8} +0.187686 q^{9} +7.06496i q^{10} +(10.8573 + 1.76614i) q^{11} +18.1344 q^{12} -17.2349i q^{13} -17.9195 q^{14} +6.77779 q^{15} -4.13780 q^{16} +3.43437i q^{17} -0.593004i q^{18} -18.5738i q^{19} +13.3778 q^{20} +17.1911i q^{21} +(5.58019 - 34.3041i) q^{22} +15.7918 q^{23} -18.9886i q^{24} +5.00000 q^{25} -54.4546 q^{26} +26.7112 q^{27} +33.9314i q^{28} +52.6031i q^{29} -21.4147i q^{30} +27.5484 q^{31} +38.1318i q^{32} +(-32.9097 - 5.35337i) q^{33} +10.8510 q^{34} +12.6820i q^{35} -1.12288 q^{36} -40.1425 q^{37} -58.6848 q^{38} +52.2411i q^{39} -14.0080i q^{40} -74.8398i q^{41} +54.3162 q^{42} -9.72983i q^{43} +(-64.9563 - 10.5663i) q^{44} -0.419679 q^{45} -49.8949i q^{46} +18.2212 q^{47} +12.5422 q^{48} +16.8335 q^{49} -15.7977i q^{50} -10.4100i q^{51} +103.112i q^{52} -75.2040 q^{53} -84.3952i q^{54} +(-24.2776 - 3.94920i) q^{55} +35.5297 q^{56} +56.2994i q^{57} +166.202 q^{58} +1.75672 q^{59} -40.5497 q^{60} -48.5900i q^{61} -87.0404i q^{62} -1.06447i q^{63} +103.928 q^{64} +38.5385i q^{65} +(-16.9142 + 103.980i) q^{66} -35.4901 q^{67} -20.5469i q^{68} -47.8668 q^{69} +40.0693 q^{70} +110.499 q^{71} +1.17577i q^{72} +50.7154i q^{73} +126.832i q^{74} -15.1556 q^{75} +111.122i q^{76} +(10.0167 - 61.5777i) q^{77} +165.058 q^{78} +12.7481i q^{79} +9.25240 q^{80} -82.6540 q^{81} -236.460 q^{82} -112.062i q^{83} -102.850i q^{84} -7.67948i q^{85} -30.7419 q^{86} -159.446i q^{87} +(-11.0640 + 68.0161i) q^{88} +66.3600 q^{89} +1.32600i q^{90} -97.7488 q^{91} -94.4781 q^{92} -83.5024 q^{93} -57.5709i q^{94} +41.5323i q^{95} -115.582i q^{96} +65.1302 q^{97} -53.1863i q^{98} +(2.03776 + 0.331479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} - 48 q^{12} + 20 q^{15} + 88 q^{16} - 20 q^{20} + 80 q^{22} + 8 q^{23} + 40 q^{25} - 100 q^{26} - 16 q^{27} + 36 q^{31} - 152 q^{33} + 80 q^{34} - 216 q^{36}+ \cdots - 184 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 - 48 * q^12 + 20 * q^15 + 88 * q^16 - 20 * q^20 + 80 * q^22 + 8 * q^23 + 40 * q^25 - 100 * q^26 - 16 * q^27 + 36 * q^31 - 152 * q^33 + 80 * q^34 - 216 * q^36 - 88 * q^37 - 160 * q^38 + 280 * q^42 + 12 * q^44 - 8 * q^47 + 488 * q^48 + 172 * q^49 - 152 * q^53 - 20 * q^55 - 80 * q^56 + 160 * q^58 - 16 * q^59 - 300 * q^60 - 588 * q^64 + 180 * q^66 - 88 * q^67 + 8 * q^69 + 60 * q^70 + 276 * q^71 + 40 * q^75 + 160 * q^77 + 160 * q^78 + 320 * q^80 - 320 * q^81 - 520 * q^82 + 420 * q^86 - 520 * q^88 + 444 * q^89 - 40 * q^91 - 368 * q^92 - 104 * q^93 + 312 * q^97 - 184 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	3.15955i		−	1.57977i	−0.613253	−	0.789887i	$-0.710139\pi$
$2$		−	3.15955i		−	1.57977i	0.613253	−	0.789887i	$-0.289861\pi$
$3$	−3.03112			−1.01037			−0.505187	−	0.863010i	$-0.668576\pi$
$3$	−3.03112			−1.01037			−0.505187	+	0.863010i	$0.668576\pi$
$4$	−5.98274			−1.49568
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$			9.57697i			1.59616i
$7$		−	5.67155i		−	0.810221i	−0.914268	−	0.405111i	$-0.867233\pi$
$7$		−	5.67155i		−	0.810221i	0.914268	−	0.405111i	$-0.132767\pi$
$8$			6.26455i			0.783069i
$9$	0.187686			0.0208540
$10$			7.06496i			0.706496i
$11$	10.8573	+	1.76614i	0.987026	+	0.160558i
$11$	10.8573	+	1.76614i	0.987026	+	0.160558i
$12$	18.1344			1.51120
$13$		−	17.2349i		−	1.32576i	−0.748724	−	0.662882i	$-0.769333\pi$
$13$		−	17.2349i		−	1.32576i	0.748724	−	0.662882i	$-0.230667\pi$
$14$	−17.9195			−1.27997
$15$	6.77779			0.451853
$16$	−4.13780			−0.258612
$17$			3.43437i			0.202022i	0.994885	+	0.101011i	$0.0322077\pi$
$17$			3.43437i			0.202022i	−0.994885	+	0.101011i	$0.967792\pi$
$18$		−	0.593004i		−	0.0329446i
$19$		−	18.5738i		−	0.977569i	−0.872405	−	0.488784i	$-0.837441\pi$
$19$		−	18.5738i		−	0.977569i	0.872405	−	0.488784i	$-0.162559\pi$
$20$	13.3778			0.668890
$21$			17.1911i			0.818626i
$22$	5.58019	−	34.3041i	0.253645	−	1.55928i
$23$	15.7918			0.686599			0.343300	−	0.939226i	$-0.388455\pi$
$23$	15.7918			0.686599			0.343300	+	0.939226i	$0.388455\pi$
$24$		−	18.9886i		−	0.791192i
$25$	5.00000			0.200000
$26$	−54.4546			−2.09441
$27$	26.7112			0.989303
$28$			33.9314i			1.21184i
$29$			52.6031i			1.81390i	0.421238	+	0.906950i	$0.361596\pi$
$29$			52.6031i			1.81390i	−0.421238	+	0.906950i	$0.638404\pi$
$30$		−	21.4147i		−	0.713825i
$31$	27.5484			0.888657			0.444328	−	0.895864i	$-0.353442\pi$
$31$	27.5484			0.888657			0.444328	+	0.895864i	$0.353442\pi$
$32$			38.1318i			1.19162i
$33$	−32.9097	−	5.35337i	−0.997265	−	0.162223i
$34$	10.8510			0.319148
$35$			12.6820i			0.362342i
$36$	−1.12288			−0.0311910
$37$	−40.1425			−1.08493			−0.542467	−	0.840077i	$-0.682510\pi$
$37$	−40.1425			−1.08493			−0.542467	+	0.840077i	$0.682510\pi$
$38$	−58.6848			−1.54434
$39$			52.2411i			1.33952i
$40$		−	14.0080i		−	0.350199i
$41$		−	74.8398i		−	1.82536i	−0.408675	−	0.912680i	$-0.634009\pi$
$41$		−	74.8398i		−	1.82536i	0.408675	−	0.912680i	$-0.365991\pi$
$42$	54.3162			1.29324
$43$		−	9.72983i		−	0.226275i	−0.993579	−	0.113138i	$-0.963910\pi$
$43$		−	9.72983i		−	0.226275i	0.993579	−	0.113138i	$-0.0360901\pi$
$44$	−64.9563	−	10.5663i	−1.47628	−	0.240144i
$45$	−0.419679			−0.00932620
$46$		−	49.8949i		−	1.08467i
$47$	18.2212			0.387686			0.193843	−	0.981033i	$-0.437905\pi$
$47$	18.2212			0.387686			0.193843	+	0.981033i	$0.437905\pi$
$48$	12.5422			0.261295
$49$	16.8335			0.343541
$50$		−	15.7977i		−	0.315955i
$51$		−	10.4100i		−	0.204117i
$52$			103.112i			1.98292i
$53$	−75.2040			−1.41894			−0.709471	−	0.704734i	$-0.751066\pi$
$53$	−75.2040			−1.41894			−0.709471	+	0.704734i	$0.751066\pi$
$54$		−	84.3952i		−	1.56287i
$55$	−24.2776	−	3.94920i	−0.441412	−	0.0718036i
$56$	35.5297			0.634459
$57$			56.2994i			0.987709i
$58$	166.202			2.86555
$59$	1.75672			0.0297750			0.0148875	−	0.999889i	$-0.495261\pi$
$59$	1.75672			0.0297750			0.0148875	+	0.999889i	$0.495261\pi$
$60$	−40.5497			−0.675829
$61$		−	48.5900i		−	0.796557i	−0.917265	−	0.398278i	$-0.869608\pi$
$61$		−	48.5900i		−	0.796557i	0.917265	−	0.398278i	$-0.130392\pi$
$62$		−	87.0404i		−	1.40388i
$63$		−	1.06447i		−	0.0168964i
$64$	103.928			1.62387
$65$			38.5385i			0.592900i
$66$	−16.9142	+	103.980i	−0.256276	+	1.57545i
$67$	−35.4901			−0.529702			−0.264851	−	0.964289i	$-0.585323\pi$
$67$	−35.4901			−0.529702			−0.264851	+	0.964289i	$0.585323\pi$
$68$		−	20.5469i		−	0.302161i
$69$	−47.8668			−0.693721
$70$	40.0693			0.572418
$71$	110.499			1.55632			0.778159	−	0.628067i	$-0.216154\pi$
$71$	110.499			1.55632			0.778159	+	0.628067i	$0.216154\pi$
$72$			1.17577i			0.0163301i
$73$			50.7154i			0.694732i	0.937730	+	0.347366i	$0.112924\pi$
$73$			50.7154i			0.694732i	−0.937730	+	0.347366i	$0.887076\pi$
$74$			126.832i			1.71395i
$75$	−15.1556			−0.202075
$76$			111.122i			1.46213i
$77$	10.0167	−	61.5777i	0.130087	−	0.799710i
$78$	165.058			2.11613
$79$			12.7481i			0.161368i	0.996740	+	0.0806842i	$0.0257105\pi$
$79$			12.7481i			0.161368i	−0.996740	+	0.0806842i	$0.974289\pi$
$80$	9.25240			0.115655
$81$	−82.6540			−1.02042
$82$	−236.460			−2.88366
$83$		−	112.062i		−	1.35015i	−0.737749	−	0.675075i	$-0.764111\pi$
$83$		−	112.062i		−	1.35015i	0.737749	−	0.675075i	$-0.235889\pi$
$84$		−	102.850i		−	1.22441i
$85$		−	7.67948i		−	0.0903468i
$86$	−30.7419			−0.357463
$87$		−	159.446i		−	1.83272i
$88$	−11.0640	+	68.0161i	−0.125728	+	0.772910i
$89$	66.3600			0.745618			0.372809	−	0.927908i	$-0.378395\pi$
$89$	66.3600			0.745618			0.372809	+	0.927908i	$0.378395\pi$
$90$			1.32600i			0.0147333i
$91$	−97.7488			−1.07416
$92$	−94.4781			−1.02694
$93$	−83.5024			−0.897875
$94$		−	57.5709i		−	0.612456i
$95$			41.5323i			0.437182i
$96$		−	115.582i		−	1.20398i
$97$	65.1302			0.671445			0.335723	−	0.941961i	$-0.391020\pi$
$97$	65.1302			0.671445			0.335723	+	0.941961i	$0.391020\pi$
$98$		−	53.1863i		−	0.542717i
$99$	2.03776	+	0.331479i	0.0205835	+	0.00334828i
$100$	−29.9137			−0.299137
$101$			172.019i			1.70316i	0.524229	+	0.851578i	$0.324354\pi$
$101$			172.019i			1.70316i	−0.524229	+	0.851578i	$0.675646\pi$
$102$	−32.8908			−0.322459
$103$	28.3278			0.275027			0.137514	−	0.990500i	$-0.456089\pi$
$103$	28.3278			0.275027			0.137514	+	0.990500i	$0.456089\pi$
$104$	107.969			1.03816
$105$		−	38.4406i		−	0.366101i
$106$			237.610i			2.24161i
$107$			63.2464i			0.591088i	0.955329	+	0.295544i	$0.0955009\pi$
$107$			63.2464i			0.591088i	−0.955329	+	0.295544i	$0.904499\pi$
$108$	−159.806			−1.47968
$109$		−	128.641i		−	1.18020i	−0.807331	−	0.590098i	$-0.799089\pi$
$109$		−	128.641i		−	1.18020i	0.807331	−	0.590098i	$-0.200911\pi$
$110$	−12.4777	+	76.7063i	−0.113433	+	0.697330i
$111$	121.677			1.09619
$112$			23.4677i			0.209533i
$113$	−35.4694			−0.313889			−0.156944	−	0.987607i	$-0.550164\pi$
$113$	−35.4694			−0.313889			−0.156944	+	0.987607i	$0.550164\pi$
$114$	177.881			1.56036
$115$	−35.3115			−0.307056
$116$		−	314.711i		−	2.71302i
$117$		−	3.23476i		−	0.0276475i
$118$		−	5.55045i		−	0.0470377i
$119$	19.4782			0.163682
$120$			42.4598i			0.353832i
$121$	114.762	+	38.3509i	0.948442	+	0.316949i
$122$	−153.522			−1.25838
$123$			226.848i			1.84430i
$124$	−164.815			−1.32915
$125$	−11.1803			−0.0894427
$126$	−3.36325			−0.0266925
$127$			210.686i			1.65895i	0.558547	+	0.829473i	$0.311359\pi$
$127$			210.686i			1.65895i	−0.558547	+	0.829473i	$0.688641\pi$
$128$		−	175.838i		−	1.37374i
$129$			29.4923i			0.228622i
$130$	121.764			0.936647
$131$			131.724i			1.00553i	0.864424	+	0.502764i	$0.167684\pi$
$131$			131.724i			1.00553i	−0.864424	+	0.502764i	$0.832316\pi$
$132$	196.890	+	32.0278i	1.49159	+	0.242635i
$133$	−105.342			−0.792047
$134$			112.133i			0.836810i
$135$	−59.7280			−0.442430
$136$	−21.5148			−0.158197
$137$	167.934			1.22580			0.612898	−	0.790162i	$-0.290004\pi$
$137$	167.934			1.22580			0.612898	+	0.790162i	$0.290004\pi$
$138$			151.237i			1.09592i
$139$		−	90.6142i		−	0.651901i	−0.945387	−	0.325950i	$-0.894316\pi$
$139$		−	90.6142i		−	0.651901i	0.945387	−	0.325950i	$-0.105684\pi$
$140$		−	75.8729i		−	0.541949i
$141$	−55.2308			−0.391708
$142$		−	349.125i		−	2.45863i
$143$	30.4392	−	187.125i	0.212862	−	1.30856i
$144$	−0.776608			−0.00539311
$145$		−	117.624i		−	0.811201i
$146$	160.238			1.09752
$147$	−51.0244			−0.347105
$148$	240.162			1.62272
$149$			72.8977i			0.489246i	0.969618	+	0.244623i	$0.0786642\pi$
$149$			72.8977i			0.489246i	−0.969618	+	0.244623i	$0.921336\pi$
$150$			47.8848i			0.319232i
$151$		−	237.180i		−	1.57073i	−0.619035	−	0.785364i	$-0.712476\pi$
$151$		−	237.180i		−	1.57073i	0.619035	−	0.785364i	$-0.287524\pi$
$152$	116.357			0.765504
$153$			0.644584i			0.00421296i
$154$	−194.558	−	31.6483i	−1.26336	−	0.205509i
$155$	−61.6000			−0.397419
$156$		−	312.545i		−	2.00349i
$157$	105.915			0.674620			0.337310	−	0.941394i	$-0.390483\pi$
$157$	105.915			0.674620			0.337310	+	0.941394i	$0.390483\pi$
$158$	40.2783			0.254926
$159$	227.952			1.43366
$160$		−	85.2653i		−	0.532908i
$161$		−	89.5639i		−	0.556297i
$162$			261.149i			1.61203i
$163$	143.233			0.878730			0.439365	−	0.898309i	$-0.355203\pi$
$163$	143.233			0.878730			0.439365	+	0.898309i	$0.355203\pi$
$164$			447.747i			2.73016i
$165$	73.5884	+	11.9705i	0.445991	+	0.0725484i
$166$	−354.067			−2.13293
$167$		−	35.5974i		−	0.213158i	−0.994304	−	0.106579i	$-0.966010\pi$
$167$		−	35.5974i		−	0.213158i	0.994304	−	0.106579i	$-0.0339897\pi$
$168$	−107.695			−0.641041
$169$	−128.043			−0.757650
$170$	−24.2637			−0.142728
$171$		−	3.48605i		−	0.0203862i
$172$			58.2110i			0.338436i
$173$			196.047i			1.13322i	0.823987	+	0.566609i	$0.191745\pi$
$173$			196.047i			1.13322i	−0.823987	+	0.566609i	$0.808255\pi$
$174$	−503.778			−2.89528
$175$		−	28.3578i		−	0.162044i
$176$	−44.9253	−	7.30791i	−0.255257	−	0.0415222i
$177$	−5.32484			−0.0300838
$178$		−	209.668i		−	1.17791i
$179$	−65.1824			−0.364148			−0.182074	−	0.983285i	$-0.558281\pi$
$179$	−65.1824			−0.364148			−0.182074	+	0.983285i	$0.558281\pi$
$180$	2.51083			0.0139491
$181$	−157.016			−0.867493			−0.433746	−	0.901035i	$-0.642809\pi$
$181$	−157.016			−0.867493			−0.433746	+	0.901035i	$0.642809\pi$
$182$			308.842i			1.69693i
$183$			147.282i			0.804820i
$184$			98.9285i			0.537655i
$185$	89.7615			0.485197
$186$			263.830i			1.41844i
$187$	−6.06556	+	37.2879i	−0.0324361	+	0.199401i
$188$	−109.013			−0.579856
$189$		−	151.494i		−	0.801554i
$190$	131.223			0.690648
$191$	161.967			0.847995			0.423997	−	0.905663i	$-0.360627\pi$
$191$	161.967			0.847995			0.423997	+	0.905663i	$0.360627\pi$
$192$	−315.018			−1.64072
$193$			0.742915i			0.00384930i	0.999998	+	0.00192465i	$0.000612635\pi$
$193$			0.742915i			0.00384930i	−0.999998	+	0.00192465i	$0.999387\pi$
$194$		−	205.782i		−	1.06073i
$195$		−	116.815i		−	0.599050i
$196$	−100.711			−0.513829
$197$		−	43.0945i		−	0.218754i	−0.994000	−	0.109377i	$-0.965114\pi$
$197$		−	43.0945i		−	0.218754i	0.994000	−	0.109377i	$-0.0348855\pi$
$198$	1.04732	−	6.43841i	0.00528952	−	0.0325172i
$199$	−201.933			−1.01474			−0.507370	−	0.861729i	$-0.669382\pi$
$199$	−201.933			−1.01474			−0.507370	+	0.861729i	$0.669382\pi$
$200$			31.3228i			0.156614i
$201$	107.575			0.535197
$202$	543.501			2.69060
$203$	298.341			1.46966
$204$			62.2802i			0.305295i
$205$			167.347i			0.816326i
$206$		−	89.5031i		−	0.434481i
$207$	2.96390			0.0143184
$208$			71.3147i			0.342859i
$209$	32.8038	−	201.661i	0.156956	−	0.964886i
$210$	−121.455			−0.578356
$211$		−	53.4705i		−	0.253415i	−0.991940	−	0.126707i	$-0.959559\pi$
$211$		−	53.4705i		−	0.253415i	0.991940	−	0.126707i	$-0.0404409\pi$
$212$	449.926			2.12229
$213$	−334.934			−1.57246
$214$	199.830			0.933785
$215$			21.7566i			0.101193i
$216$			167.334i			0.774693i
$217$		−	156.242i		−	0.720009i
$218$	−406.449			−1.86444
$219$		−	153.725i		−	0.701939i
$220$	145.247	+	23.6270i	0.660213	+	0.107396i
$221$	59.1911			0.267833
$222$		−	384.444i		−	1.73173i
$223$	−282.600			−1.26726			−0.633632	−	0.773635i	$-0.718437\pi$
$223$	−282.600			−1.26726			−0.633632	+	0.773635i	$0.718437\pi$
$224$	216.266			0.965475
$225$	0.938431			0.00417081
$226$			112.067i			0.495873i
$227$		−	111.251i		−	0.490092i	−0.969511	−	0.245046i	$-0.921197\pi$
$227$		−	111.251i		−	0.490092i	0.969511	−	0.245046i	$-0.0788031\pi$
$228$		−	336.825i		−	1.47730i
$229$	−53.3814			−0.233107			−0.116553	−	0.993184i	$-0.537185\pi$
$229$	−53.3814			−0.233107			−0.116553	+	0.993184i	$0.537185\pi$
$230$			111.568i			0.485080i
$231$	−30.3619	+	186.649i	−0.131437	+	0.808006i
$232$	−329.535			−1.42041
$233$		−	42.7082i		−	0.183297i	−0.995791	−	0.0916485i	$-0.970786\pi$
$233$		−	42.7082i		−	0.183297i	0.995791	−	0.0916485i	$-0.0292136\pi$
$234$	−10.2204			−0.0436768
$235$	−40.7439			−0.173378
$236$	−10.5100			−0.0445340
$237$		−	38.6411i		−	0.163042i
$238$		−	61.5423i		−	0.258581i
$239$		−	216.974i		−	0.907840i	−0.891042	−	0.453920i	$-0.850025\pi$
$239$		−	216.974i		−	0.907840i	0.891042	−	0.453920i	$-0.149975\pi$
$240$	−28.0451			−0.116855
$241$			155.081i			0.643488i	0.946827	+	0.321744i	$0.104269\pi$
$241$			155.081i			0.643488i	−0.946827	+	0.321744i	$0.895731\pi$
$242$	121.171	−	362.594i	0.500708	−	1.49832i
$243$	10.1334			0.0417013
$244$			290.701i			1.19140i
$245$	−37.6409			−0.153636
$246$	716.738			2.91357
$247$	−320.118			−1.29603
$248$			172.578i			0.695880i
$249$			339.675i			1.36416i
$250$			35.3248i			0.141299i
$251$	−116.539			−0.464300			−0.232150	−	0.972680i	$-0.574576\pi$
$251$	−116.539			−0.464300			−0.232150	+	0.972680i	$0.574576\pi$
$252$			6.36846i			0.0252717i
$253$	171.456	+	27.8904i	0.677692	+	0.110239i
$254$	665.673			2.62076
$255$			23.2774i			0.0912840i
$256$	−139.857			−0.546317
$257$	−85.7024			−0.333472			−0.166736	−	0.986002i	$-0.553323\pi$
$257$	−85.7024			−0.333472			−0.166736	+	0.986002i	$0.553323\pi$
$258$	93.1822			0.361171
$259$			227.670i			0.879037i
$260$		−	230.566i		−	0.886791i
$261$			9.87288i			0.0378271i
$262$	416.189			1.58851
$263$			398.864i			1.51659i	0.651911	+	0.758296i	$0.273968\pi$
$263$			398.864i			1.51659i	−0.651911	+	0.758296i	$0.726032\pi$
$264$	33.5365	−	206.165i	0.127032	−	0.780928i
$265$	168.161			0.634570
$266$			332.834i			1.25125i
$267$	−201.145			−0.753353
$268$	212.328			0.792268
$269$	−237.209			−0.881819			−0.440910	−	0.897552i	$-0.645344\pi$
$269$	−237.209			−0.881819			−0.440910	+	0.897552i	$0.645344\pi$
$270$			188.713i			0.698939i
$271$			34.0378i			0.125601i	0.998026	+	0.0628003i	$0.0200031\pi$
$271$			34.0378i			0.125601i	−0.998026	+	0.0628003i	$0.979997\pi$
$272$		−	14.2107i		−	0.0522453i
$273$	296.288			1.08530
$274$		−	530.595i		−	1.93648i
$275$	54.2865	+	8.83068i	0.197405	+	0.0321116i
$276$	286.374			1.03759
$277$			202.654i			0.731604i	0.930693	+	0.365802i	$0.119205\pi$
$277$			202.654i			0.731604i	−0.930693	+	0.365802i	$0.880795\pi$
$278$	−286.300			−1.02986
$279$	5.17045			0.0185321
$280$	−79.4469			−0.283739
$281$			100.966i			0.359311i	0.983730	+	0.179655i	$0.0574982\pi$
$281$			100.966i			0.359311i	−0.983730	+	0.179655i	$0.942502\pi$
$282$			174.504i			0.618809i
$283$			162.113i			0.572836i	0.958105	+	0.286418i	$0.0924646\pi$
$283$			162.113i			0.572836i	−0.958105	+	0.286418i	$0.907535\pi$
$284$	−661.084			−2.32776
$285$		−	125.889i		−	0.441717i
$286$	−591.229	−	96.1741i	−2.06723	−	0.336273i
$287$	−424.458			−1.47895
$288$			7.15681i			0.0248500i
$289$	277.205			0.959187
$290$	−371.639			−1.28151
$291$	−197.417			−0.678410
$292$		−	303.417i		−	1.03910i
$293$		−	372.772i		−	1.27226i	−0.771582	−	0.636130i	$-0.780534\pi$
$293$		−	372.772i		−	1.27226i	0.771582	−	0.636130i	$-0.219466\pi$
$294$			161.214i			0.548347i
$295$	−3.92815			−0.0133158
$296$		−	251.475i		−	0.849578i
$297$	290.011	+	47.1756i	0.976468	+	0.158840i
$298$	230.324			0.772898
$299$		−	272.170i		−	0.910268i
$300$	90.6720			0.302240
$301$	−55.1832			−0.183333
$302$	−749.381			−2.48139
$303$		−	521.409i		−	1.72082i
$304$			76.8547i			0.252811i
$305$			108.650i			0.356231i
$306$	2.03659			0.00665553
$307$			445.994i			1.45275i	0.687300	+	0.726374i	$0.258796\pi$
$307$			445.994i			1.45275i	−0.687300	+	0.726374i	$0.741204\pi$
$308$	−59.9274	+	368.403i	−0.194570	+	1.19611i
$309$	−85.8650			−0.277880
$310$			194.628i			0.627833i
$311$	−249.222			−0.801357			−0.400679	−	0.916219i	$-0.631226\pi$
$311$	−249.222			−0.801357			−0.400679	+	0.916219i	$0.631226\pi$
$312$	−327.267			−1.04893
$313$	463.222			1.47994			0.739971	−	0.672638i	$-0.234839\pi$
$313$	463.222			1.47994			0.739971	+	0.672638i	$0.234839\pi$
$314$		−	334.644i		−	1.06575i
$315$			2.38023i			0.00755629i
$316$		−	76.2686i		−	0.241356i
$317$	167.548			0.528542			0.264271	−	0.964448i	$-0.414869\pi$
$317$	167.548			0.528542			0.264271	+	0.964448i	$0.414869\pi$
$318$		−	720.226i		−	2.26486i
$319$	−92.9042	+	571.127i	−0.291236	+	1.79037i
$320$	−232.390			−0.726219
$321$		−	191.707i		−	0.597220i
$322$	−282.981			−0.878824
$323$	63.7893			0.197490
$324$	494.497			1.52623
$325$		−	86.1747i		−	0.265153i
$326$		−	452.551i		−	1.38819i
$327$			389.928i			1.19244i
$328$	468.838			1.42938
$329$		−	103.343i		−	0.314112i
$330$	37.8213	−	232.506i	0.114610	−	0.704564i
$331$	8.98005			0.0271301			0.0135650	−	0.999908i	$-0.495682\pi$
$331$	8.98005			0.0271301			0.0135650	+	0.999908i	$0.495682\pi$
$332$			670.440i			2.01940i
$333$	−7.53420			−0.0226252
$334$	−112.472			−0.336742
$335$	79.3582			0.236890
$336$		−	71.1335i		−	0.211707i
$337$		−	263.901i		−	0.783090i	−0.920159	−	0.391545i	$-0.871941\pi$
$337$		−	263.901i		−	0.783090i	0.920159	−	0.391545i	$-0.128059\pi$
$338$			404.557i			1.19692i
$339$	107.512			0.317145
$340$			45.9443i			0.135130i
$341$	299.101	+	48.6541i	0.877128	+	0.142681i
$342$	−11.0143			−0.0322056
$343$		−	373.378i		−	1.08857i
$344$	60.9530			0.177189
$345$	107.033			0.310242
$346$	619.419			1.79023
$347$		−	611.749i		−	1.76297i	−0.472216	−	0.881483i	$-0.656546\pi$
$347$		−	611.749i		−	1.76297i	0.472216	−	0.881483i	$-0.343454\pi$
$348$			953.925i			2.74117i
$349$			282.223i			0.808662i	0.914613	+	0.404331i	$0.132496\pi$
$349$			282.223i			0.808662i	−0.914613	+	0.404331i	$0.867504\pi$
$350$	−89.5977			−0.255993
$351$		−	460.365i		−	1.31158i
$352$	−67.3459	+	414.008i	−0.191324	+	1.17616i
$353$	−173.629			−0.491868			−0.245934	−	0.969287i	$-0.579095\pi$
$353$	−173.629			−0.491868			−0.245934	+	0.969287i	$0.579095\pi$
$354$			16.8241i			0.0475256i
$355$	−247.082			−0.696007
$356$	−397.015			−1.11521
$357$	−59.0407			−0.165380
$358$			205.947i			0.575271i
$359$			285.384i			0.794941i	0.917615	+	0.397471i	$0.130112\pi$
$359$			285.384i			0.794941i	−0.917615	+	0.397471i	$0.869888\pi$
$360$		−	2.62910i		−	0.00730306i
$361$	16.0139			0.0443597
$362$			496.100i			1.37044i
$363$	−347.856	−	116.246i	−0.958281	−	0.320237i
$364$	584.805			1.60661
$365$		−	113.403i		−	0.310694i
$366$	465.344			1.27143
$367$	−324.275			−0.883582			−0.441791	−	0.897118i	$-0.645657\pi$
$367$	−324.275			−0.883582			−0.441791	+	0.897118i	$0.645657\pi$
$368$	−65.3432			−0.177563
$369$		−	14.0464i		−	0.0380661i
$370$		−	283.606i		−	0.766501i
$371$			426.523i			1.14966i
$372$	499.573			1.34294
$373$			128.367i			0.344148i	0.985084	+	0.172074i	$0.0550469\pi$
$373$			128.367i			0.344148i	−0.985084	+	0.172074i	$0.944953\pi$
$374$	117.813	+	19.1644i	0.315008	+	0.0512418i
$375$	33.8889			0.0903705
$376$			114.148i			0.303585i
$377$	906.611			2.40480
$378$	−478.652			−1.26627
$379$	684.510			1.80610			0.903048	−	0.429540i	$-0.141324\pi$
$379$	684.510			1.80610			0.903048	+	0.429540i	$0.141324\pi$
$380$		−	248.477i		−	0.653886i
$381$		−	638.615i		−	1.67615i
$382$		−	511.742i		−	1.33964i
$383$	338.766			0.884506			0.442253	−	0.896890i	$-0.354179\pi$
$383$	338.766			0.884506			0.442253	+	0.896890i	$0.354179\pi$
$384$			532.987i			1.38799i
$385$	−22.3981	+	137.692i	−0.0581768	+	0.357641i
$386$	2.34727			0.00608102
$387$		−	1.82616i		−	0.00471875i
$388$	−389.657			−1.00427
$389$	−552.950			−1.42146			−0.710732	−	0.703463i	$-0.751636\pi$
$389$	−552.950			−1.42146			−0.710732	+	0.703463i	$0.751636\pi$
$390$	−369.082			−0.946363
$391$			54.2348i			0.138708i
$392$			105.454i			0.269017i
$393$		−	399.272i		−	1.01596i
$394$	−136.159			−0.345581
$395$		−	28.5056i		−	0.0721662i
$396$	−12.1914	−	1.98315i	−0.0307864	−	0.00500796i
$397$	111.881			0.281815			0.140908	−	0.990023i	$-0.454998\pi$
$397$	111.881			0.281815			0.140908	+	0.990023i	$0.454998\pi$
$398$			638.017i			1.60306i
$399$	319.305			0.800263
$400$	−20.6890			−0.0517225
$401$	−284.972			−0.710654			−0.355327	−	0.934742i	$-0.615630\pi$
$401$	−284.972			−0.710654			−0.355327	+	0.934742i	$0.615630\pi$
$402$		−	339.887i		−	0.845490i
$403$		−	474.794i		−	1.17815i
$404$		−	1029.14i		−	2.54738i
$405$	184.820			0.456345
$406$		−	942.623i		−	2.32173i
$407$	−435.839	−	70.8972i	−1.07086	−	0.174195i
$408$	65.2139			0.159838
$409$		−	122.119i		−	0.298580i	−0.988793	−	0.149290i	$-0.952301\pi$
$409$		−	122.119i		−	0.298580i	0.988793	−	0.149290i	$-0.0476989\pi$
$410$	528.740			1.28961
$411$	−509.028			−1.23851
$412$	−169.478			−0.411354
$413$		−	9.96334i		−	0.0241243i
$414$		−	9.36458i		−	0.0226198i
$415$			250.579i			0.603806i
$416$	657.199			1.57980
$417$			274.663i			0.658663i
$418$	−637.158	−	103.645i	−1.52430	−	0.247955i
$419$	407.625			0.972852			0.486426	−	0.873722i	$-0.338300\pi$
$419$	407.625			0.972852			0.486426	+	0.873722i	$0.338300\pi$
$420$			229.980i			0.547571i
$421$	−348.212			−0.827107			−0.413554	−	0.910480i	$-0.635713\pi$
$421$	−348.212			−0.827107			−0.413554	+	0.910480i	$0.635713\pi$
$422$	−168.943			−0.400338
$423$	3.41988			0.00808481
$424$		−	471.119i		−	1.11113i
$425$			17.1718i			0.0404043i
$426$			1058.24i			2.48413i
$427$	−275.580			−0.645387
$428$		−	378.387i		−	0.884081i
$429$	−92.2649	+	567.197i	−0.215070	+	1.32214i
$430$	68.7409			0.159863
$431$			453.606i			1.05245i	0.850346	+	0.526225i	$0.176393\pi$
$431$			453.606i			1.05245i	−0.850346	+	0.526225i	$0.823607\pi$
$432$	−110.525			−0.255846
$433$	760.149			1.75554			0.877771	−	0.479081i	$-0.159030\pi$
$433$	760.149			1.75554			0.877771	+	0.479081i	$0.159030\pi$
$434$	−493.654			−1.13745
$435$			356.533i			0.819616i
$436$			769.628i			1.76520i
$437$		−	293.313i		−	0.671198i
$438$	−485.700			−1.10890
$439$		−	343.308i		−	0.782023i	−0.920386	−	0.391011i	$-0.872125\pi$
$439$		−	343.308i		−	0.782023i	0.920386	−	0.391011i	$-0.127875\pi$
$440$	24.7400	−	152.089i	0.0562272	−	0.345656i
$441$	3.15942			0.00716422
$442$		−	187.017i		−	0.423115i
$443$	47.4703			0.107156			0.0535782	−	0.998564i	$-0.482937\pi$
$443$	47.4703			0.107156			0.0535782	+	0.998564i	$0.482937\pi$
$444$	−727.961			−1.63955
$445$	−148.385			−0.333451
$446$			892.887i			2.00199i
$447$		−	220.962i		−	0.494321i
$448$		−	589.433i		−	1.31570i
$449$	−339.087			−0.755205			−0.377602	−	0.925968i	$-0.623251\pi$
$449$	−339.087			−0.755205			−0.377602	+	0.925968i	$0.623251\pi$
$450$		−	2.96502i		−	0.00658893i
$451$	132.177	−	812.557i	0.293076	−	1.80168i
$452$	212.204			0.469478
$453$			718.921i			1.58702i
$454$	−351.503			−0.774235
$455$	218.573			0.480380
$456$	−352.691			−0.773445
$457$			276.791i			0.605669i	0.953043	+	0.302835i	$0.0979330\pi$
$457$			276.791i			0.605669i	−0.953043	+	0.302835i	$0.902067\pi$
$458$			168.661i			0.368256i
$459$			91.7360i			0.199861i
$460$	211.259			0.459260
$461$			156.898i			0.340342i	0.985415	+	0.170171i	$0.0544321\pi$
$461$			156.898i			0.340342i	−0.985415	+	0.170171i	$0.945568\pi$
$462$	589.727	+	95.9298i	1.27647	+	0.207640i
$463$	407.669			0.880494			0.440247	−	0.897877i	$-0.354891\pi$
$463$	407.669			0.880494			0.440247	+	0.897877i	$0.354891\pi$
$464$		−	217.661i		−	0.469097i
$465$	186.717			0.401542
$466$	−134.939			−0.289568
$467$	749.076			1.60402			0.802008	−	0.597313i	$-0.203765\pi$
$467$	749.076			1.60402			0.802008	+	0.597313i	$0.203765\pi$
$468$			19.3527i			0.0413520i
$469$			201.284i			0.429176i
$470$			128.732i			0.273899i
$471$	−321.042			−0.681618
$472$			11.0051i			0.0233159i
$473$	17.1842	−	105.640i	0.0363302	−	0.223340i
$474$	−122.088			−0.257570
$475$		−	92.8690i		−	0.195514i
$476$	−116.533			−0.244817
$477$	−14.1147			−0.0295907
$478$	−685.539			−1.43418
$479$		−	11.2596i		−	0.0235064i	−0.999931	−	0.0117532i	$-0.996259\pi$
$479$		−	11.2596i		−	0.0235064i	0.999931	−	0.0117532i	$-0.00374124\pi$
$480$			258.449i			0.538436i
$481$			691.854i			1.43837i
$482$	489.984			1.01657
$483$			271.479i			0.562068i
$484$	−686.588	−	229.443i	−1.41857	−	0.474056i
$485$	−145.636			−0.300279
$486$		−	32.0170i		−	0.0658786i
$487$	−734.846			−1.50892			−0.754462	−	0.656344i	$-0.772102\pi$
$487$	−734.846			−1.50892			−0.754462	+	0.656344i	$0.772102\pi$
$488$	304.394			0.623759
$489$	−434.156			−0.887845
$490$			118.928i			0.242711i
$491$			347.360i			0.707455i	0.935349	+	0.353727i	$0.115086\pi$
$491$			347.360i			0.707455i	−0.935349	+	0.353727i	$0.884914\pi$
$492$		−	1357.17i		−	2.75848i
$493$	−180.658			−0.366447
$494$			1011.43i			2.04743i
$495$	−4.55658	−	0.741210i	−0.00920521	−	0.00149739i
$496$	−113.990			−0.229818
$497$		−	626.698i		−	1.26096i
$498$	1073.22			2.15506
$499$	875.439			1.75439			0.877193	−	0.480138i	$-0.159413\pi$
$499$	875.439			1.75439			0.877193	+	0.480138i	$0.159413\pi$
$500$	66.8890			0.133778
$501$			107.900i			0.215369i
$502$			368.211i			0.733488i
$503$			505.554i			1.00508i	0.864554	+	0.502539i	$0.167601\pi$
$503$			505.554i			1.00508i	−0.864554	+	0.502539i	$0.832399\pi$
$504$	6.66844			0.0132310
$505$		−	384.645i		−	0.761674i
$506$	88.1211	−	541.723i	0.174152	−	1.07060i
$507$	388.113			0.765509
$508$		−	1260.48i		−	2.48126i
$509$	−778.269			−1.52902			−0.764508	−	0.644614i	$-0.777018\pi$
$509$	−778.269			−1.52902			−0.764508	+	0.644614i	$0.777018\pi$
$510$	73.5461			0.144208
$511$	287.635			0.562887
$512$		−	261.468i		−	0.510679i
$513$		−	496.128i		−	0.967111i
$514$			270.781i			0.526811i
$515$	−63.3429			−0.122996
$516$		−	176.445i		−	0.341947i
$517$	197.833	+	32.1812i	0.382656	+	0.0622460i
$518$	719.336			1.38868
$519$		−	594.241i		−	1.14497i
$520$	−241.426			−0.464281
$521$	−273.723			−0.525380			−0.262690	−	0.964880i	$-0.584610\pi$
$521$	−273.723			−0.525380			−0.262690	+	0.964880i	$0.584610\pi$
$522$	31.1938			0.0597583
$523$			628.316i			1.20137i	0.799486	+	0.600685i	$0.205105\pi$
$523$			628.316i			1.20137i	−0.799486	+	0.600685i	$0.794895\pi$
$524$		−	788.071i		−	1.50395i
$525$			85.9557i			0.163725i
$526$	1260.23			2.39587
$527$			94.6112i			0.179528i
$528$	136.174	+	22.1512i	0.257905	+	0.0419529i
$529$	−279.620			−0.528582
$530$		−	531.313i		−	1.00248i
$531$	0.329713			0.000620928
$532$	630.235			1.18465
$533$	−1289.86			−2.42000
$534$			635.528i			1.19013i
$535$		−	141.423i		−	0.264343i
$536$		−	222.329i		−	0.414794i
$537$	197.576			0.367925
$538$			749.474i			1.39307i
$539$	182.766	+	29.7303i	0.339084	+	0.0551582i
$540$	357.337			0.661735
$541$		−	543.648i		−	1.00490i	−0.864608	−	0.502448i	$-0.832433\pi$
$541$		−	543.648i		−	1.00490i	0.864608	−	0.502448i	$-0.167567\pi$
$542$	107.544			0.198421
$543$	475.935			0.876492
$544$	−130.959			−0.240733
$545$			287.651i			0.527800i
$546$		−	936.137i		−	1.71454i
$547$		−	421.038i		−	0.769722i	−0.922975	−	0.384861i	$-0.874249\pi$
$547$		−	421.038i		−	0.769722i	0.922975	−	0.384861i	$-0.125751\pi$
$548$	−1004.71			−1.83340
$549$		−	9.11967i		−	0.0166114i
$550$	27.9009	−	171.521i	0.0507290	−	0.311856i
$551$	977.040			1.77321
$552$		−	299.864i		−	0.543232i
$553$	72.3016			0.130744
$554$	640.296			1.15577
$555$	−272.078			−0.490230
$556$			542.121i			0.975038i
$557$			940.508i			1.68852i	0.535930	+	0.844262i	$0.319961\pi$
$557$			940.508i			1.68852i	−0.535930	+	0.844262i	$0.680039\pi$
$558$		−	16.3363i		−	0.0292765i
$559$	−167.693			−0.299987
$560$		−	52.4754i		−	0.0937062i
$561$	18.3854	−	113.024i	0.0327726	−	0.201469i
$562$	319.008			0.567629
$563$		−	285.806i		−	0.507649i	−0.967250	−	0.253824i	$-0.918312\pi$
$563$		−	285.806i		−	0.507649i	0.967250	−	0.253824i	$-0.0816885\pi$
$564$	330.431			0.585871
$565$	79.3120			0.140375
$566$	512.203			0.904952
$567$			468.776i			0.826765i
$568$			692.224i			1.21870i
$569$		−	307.137i		−	0.539783i	−0.962891	−	0.269892i	$-0.913012\pi$
$569$		−	307.137i		−	0.539783i	0.962891	−	0.269892i	$-0.0869879\pi$
$570$	−397.753			−0.697813
$571$			390.713i			0.684261i	0.939652	+	0.342130i	$0.111148\pi$
$571$			390.713i			0.684261i	−0.939652	+	0.342130i	$0.888852\pi$
$572$	−182.110	+	1119.52i	−0.318374	+	1.95720i
$573$	−490.941			−0.856791
$574$			1341.09i			2.33640i
$575$	78.9589			0.137320
$576$	19.5059			0.0338643
$577$	−119.491			−0.207090			−0.103545	−	0.994625i	$-0.533019\pi$
$577$	−119.491			−0.207090			−0.103545	+	0.994625i	$0.533019\pi$
$578$		−	875.843i		−	1.51530i
$579$		−	2.25186i		−	0.00388923i
$580$			703.714i			1.21330i
$581$	−635.568			−1.09392
$582$			623.749i			1.07173i
$583$	−816.511	−	132.820i	−1.40053	−	0.227822i
$584$	−317.710			−0.544023
$585$			7.23314i			0.0123643i
$586$	−1177.79			−2.00988
$587$	−340.259			−0.579658			−0.289829	−	0.957078i	$-0.593598\pi$
$587$	−340.259			−0.579658			−0.289829	+	0.957078i	$0.593598\pi$
$588$	305.266			0.519159
$589$		−	511.678i		−	0.868723i
$590$			12.4112i			0.0210359i
$591$			130.625i			0.221023i
$592$	166.102			0.280577
$593$			752.004i			1.26813i	0.773278	+	0.634067i	$0.218616\pi$
$593$			752.004i			1.26813i	−0.773278	+	0.634067i	$0.781384\pi$
$594$	149.053	−	916.303i	0.250932	−	1.54260i
$595$	−43.5546			−0.0732009
$596$		−	436.128i		−	0.731758i
$597$	612.083			1.02527
$598$	−859.935			−1.43802
$599$	274.841			0.458833			0.229416	−	0.973328i	$-0.426318\pi$
$599$	274.841			0.458833			0.229416	+	0.973328i	$0.426318\pi$
$600$		−	94.9431i		−	0.158238i
$601$		−	397.025i		−	0.660608i	−0.943875	−	0.330304i	$-0.892849\pi$
$601$		−	397.025i		−	0.660608i	0.943875	−	0.330304i	$-0.107151\pi$
$602$			174.354i			0.289625i
$603$	−6.66100			−0.0110464
$604$			1418.98i			2.34931i
$605$	−256.615	−	85.7552i	−0.424156	−	0.141744i
$606$	−1647.42			−2.71851
$607$		−	351.597i		−	0.579238i	−0.957142	−	0.289619i	$-0.906471\pi$
$607$		−	351.597i		−	0.579238i	0.957142	−	0.289619i	$-0.0935286\pi$
$608$	708.252			1.16489
$609$	−904.308			−1.48491
$610$	343.286			0.562764
$611$		−	314.042i		−	0.513980i
$612$		−	3.85637i		−	0.00630127i
$613$		−	547.965i		−	0.893907i	−0.894557	−	0.446953i	$-0.852509\pi$
$613$		−	547.965i		−	0.893907i	0.894557	−	0.446953i	$-0.147491\pi$
$614$	1409.14			2.29501
$615$		−	507.248i		−	0.824794i
$616$	385.757	+	62.7503i	0.626228	+	0.101867i
$617$	−1124.68			−1.82282			−0.911408	−	0.411505i	$-0.865003\pi$
$617$	−1124.68			−1.82282			−0.911408	+	0.411505i	$0.865003\pi$
$618$			271.295i			0.438988i
$619$	82.7193			0.133634			0.0668169	−	0.997765i	$-0.478716\pi$
$619$	82.7193			0.133634			0.0668169	+	0.997765i	$0.478716\pi$
$620$	368.537			0.594414
$621$	421.817			0.679254
$622$			787.429i			1.26596i
$623$		−	376.364i		−	0.604116i
$624$		−	216.163i		−	0.346416i
$625$	25.0000			0.0400000
$626$		−	1463.57i		−	2.33797i
$627$	−99.4324	+	611.259i	−0.158584	+	0.974895i
$628$	−633.663			−1.00902
$629$		−	137.864i		−	0.219180i
$630$	7.52045			0.0119372
$631$	317.879			0.503771			0.251885	−	0.967757i	$-0.418949\pi$
$631$	317.879			0.503771			0.251885	+	0.967757i	$0.418949\pi$
$632$	−79.8612			−0.126363
$633$			162.076i			0.256043i
$634$		−	529.375i		−	0.834976i
$635$		−	471.108i		−	0.741903i
$636$	−1363.78			−2.14431
$637$		−	290.125i		−	0.455454i
$638$	1804.50	+	293.535i	2.82838	+	0.460086i
$639$	20.7391			0.0324555
$640$			393.186i			0.614353i
$641$	432.182			0.674230			0.337115	−	0.941463i	$-0.390549\pi$
$641$	432.182			0.674230			0.337115	+	0.941463i	$0.390549\pi$
$642$	−605.709			−0.943472
$643$	229.511			0.356937			0.178469	−	0.983946i	$-0.442886\pi$
$643$	229.511			0.356937			0.178469	+	0.983946i	$0.442886\pi$
$644$			535.837i			0.832045i
$645$		−	65.9467i		−	0.102243i
$646$		−	201.545i		−	0.311989i
$647$	−768.342			−1.18755			−0.593773	−	0.804633i	$-0.702362\pi$
$647$	−768.342			−1.18755			−0.593773	+	0.804633i	$0.702362\pi$
$648$		−	517.790i		−	0.799059i
$649$	19.0733	+	3.10261i	0.0293887	+	0.00478060i
$650$	−272.273			−0.418881
$651$			473.588i			0.727478i
$652$	−856.926			−1.31430
$653$	624.977			0.957085			0.478543	−	0.878064i	$-0.341165\pi$
$653$	624.977			0.957085			0.478543	+	0.878064i	$0.341165\pi$
$654$	1231.99			1.88378
$655$		−	294.544i		−	0.449686i
$656$			309.672i			0.472061i
$657$			9.51859i			0.0144880i
$658$	−326.516			−0.496225
$659$		−	1104.04i		−	1.67533i	−0.546185	−	0.837665i	$-0.683920\pi$
$659$		−	1104.04i		−	1.67533i	0.546185	−	0.837665i	$-0.316080\pi$
$660$	−440.260	−	71.6163i	−0.667061	−	0.108510i
$661$	246.985			0.373653			0.186827	−	0.982393i	$-0.440180\pi$
$661$	246.985			0.373653			0.186827	+	0.982393i	$0.440180\pi$
$662$		−	28.3729i		−	0.0428594i
$663$	−179.415			−0.270611
$664$	702.021			1.05726
$665$	235.552			0.354214
$666$			23.8047i			0.0357427i
$667$			830.697i			1.24542i
$668$			212.970i			0.318817i
$669$	856.594			1.28041
$670$		−	250.736i		−	0.374233i
$671$	85.8165	−	527.555i	0.127893	−	0.786223i
$672$	−655.529			−0.975490
$673$			715.709i			1.06346i	0.846914	+	0.531730i	$0.178458\pi$
$673$			715.709i			1.06346i	−0.846914	+	0.531730i	$0.821542\pi$
$674$	−833.808			−1.23710
$675$	133.556			0.197861
$676$	766.047			1.13321
$677$		−	946.798i		−	1.39852i	−0.714867	−	0.699260i	$-0.753513\pi$
$677$		−	946.798i		−	1.39852i	0.714867	−	0.699260i	$-0.246487\pi$
$678$		−	339.689i		−	0.501017i
$679$		−	369.389i		−	0.544019i
$680$	48.1085			0.0707478
$681$			337.215i			0.495176i
$682$	153.725	−	945.023i	0.225403	−	1.38566i
$683$	67.4542			0.0987616			0.0493808	−	0.998780i	$-0.484275\pi$
$683$	67.4542			0.0987616			0.0493808	+	0.998780i	$0.484275\pi$
$684$			20.8561i			0.0304914i
$685$	−375.512			−0.548193
$686$	−1179.71			−1.71969
$687$	161.805			0.235525
$688$			40.2601i			0.0585176i
$689$			1296.13i			1.88118i
$690$		−	338.177i		−	0.490112i
$691$	−396.379			−0.573632			−0.286816	−	0.957986i	$-0.592597\pi$
$691$	−396.379			−0.573632			−0.286816	+	0.957986i	$0.592597\pi$
$692$		−	1172.90i		−	1.69494i
$693$	1.88000	−	11.5573i	0.00271284	−	0.0166772i
$694$	−1932.85			−2.78509
$695$			202.620i			0.291539i
$696$	998.860			1.43514
$697$	257.027			0.368762
$698$	891.697			1.27750
$699$			129.454i			0.185198i
$700$			169.657i			0.242367i
$701$			884.194i			1.26133i	0.776054	+	0.630666i	$0.217218\pi$
$701$			884.194i			1.26133i	−0.776054	+	0.630666i	$0.782782\pi$
$702$	−1454.55			−2.07200
$703$			745.600i			1.06060i
$704$	1128.38	+	183.551i	1.60281	+	0.260726i
$705$	123.500			0.175177
$706$			548.590i			0.777040i
$707$	975.613			1.37993
$708$	31.8571			0.0449959
$709$	−902.302			−1.27264			−0.636320	−	0.771425i	$-0.719544\pi$
$709$	−902.302			−1.27264			−0.636320	+	0.771425i	$0.719544\pi$
$710$			780.668i			1.09953i
$711$			2.39265i			0.00336518i
$712$			415.716i			0.583871i
$713$	435.038			0.610151
$714$			186.542i			0.261263i
$715$	−68.0642	+	418.423i	−0.0951946	+	0.585208i
$716$	389.969			0.544650
$717$			657.673i			0.917257i
$718$	901.684			1.25583
$719$	1021.01			1.42004			0.710021	−	0.704180i	$-0.248685\pi$
$719$	1021.01			1.42004			0.710021	+	0.704180i	$0.248685\pi$
$720$	1.73655			0.00241187
$721$		−	160.663i		−	0.222833i
$722$		−	50.5966i		−	0.0700784i
$723$		−	470.068i		−	0.650163i
$724$	939.387			1.29750
$725$			263.016i			0.362780i
$726$	−367.285	+	1099.07i	−0.505902	+	1.51387i
$727$	637.169			0.876436			0.438218	−	0.898869i	$-0.355610\pi$
$727$	637.169			0.876436			0.438218	+	0.898869i	$0.355610\pi$
$728$		−	612.352i		−	0.841143i
$729$	713.170			0.978285
$730$	−358.303			−0.490826
$731$	33.4158			0.0457125
$732$		−	881.150i		−	1.20376i
$733$		−	261.937i		−	0.357349i	−0.983908	−	0.178674i	$-0.942819\pi$
$733$		−	261.937i		−	0.357349i	0.983908	−	0.178674i	$-0.0571809\pi$
$734$			1024.56i			1.39586i
$735$	114.094			0.155230
$736$			602.169i			0.818164i
$737$	−385.326	−	62.6803i	−0.522830	−	0.0850478i
$738$	−44.3802			−0.0601358
$739$			734.865i			0.994404i	0.867635	+	0.497202i	$0.165639\pi$
$739$			734.865i			0.994404i	−0.867635	+	0.497202i	$0.834361\pi$
$740$	−537.019			−0.725702
$741$	970.317			1.30947
$742$	1347.62			1.81620
$743$		−	161.161i		−	0.216905i	−0.994102	−	0.108453i	$-0.965410\pi$
$743$		−	161.161i		−	0.216905i	0.994102	−	0.108453i	$-0.0345896\pi$
$744$		−	523.105i		−	0.703098i
$745$		−	163.004i		−	0.218797i
$746$	405.583			0.543676
$747$		−	21.0326i		−	0.0281561i
$748$	36.2886	−	223.084i	0.0485142	−	0.298241i
$749$	358.705			0.478912
$750$		−	107.074i		−	0.142765i
$751$	1141.77			1.52033			0.760167	−	0.649728i	$-0.225117\pi$
$751$	1141.77			1.52033			0.760167	+	0.649728i	$0.225117\pi$
$752$	−75.3958			−0.100260
$753$	353.244			0.469116
$754$		−	2864.48i		−	3.79904i
$755$			530.350i			0.702451i
$756$			906.348i			1.19887i
$757$	119.677			0.158094			0.0790469	−	0.996871i	$-0.474812\pi$
$757$	119.677			0.158094			0.0790469	+	0.996871i	$0.474812\pi$
$758$		−	2162.74i		−	2.85322i
$759$	−519.704	−	84.5392i	−0.684721	−	0.111382i
$760$	−260.181			−0.342344
$761$			157.280i			0.206676i	0.994646	+	0.103338i	$0.0329523\pi$
$761$			157.280i			0.206676i	−0.994646	+	0.103338i	$0.967048\pi$
$762$	−2017.73			−2.64794
$763$	−729.596			−0.956221
$764$	−969.006			−1.26833
$765$		−	1.44133i		−	0.00188409i
$766$		−	1070.35i		−	1.39732i
$767$		−	30.2770i		−	0.0394746i
$768$	423.924			0.551984
$769$		−	1498.58i		−	1.94874i	−0.224947	−	0.974371i	$-0.572221\pi$
$769$		−	1498.58i		−	1.94874i	0.224947	−	0.974371i	$-0.427779\pi$
$770$	435.044	+	70.7678i	0.564992	+	0.0919062i
$771$	259.774			0.336931
$772$		−	4.44466i		−	0.00575734i
$773$	−1528.87			−1.97784			−0.988920	−	0.148450i	$-0.952572\pi$
$773$	−1528.87			−1.97784			−0.988920	+	0.148450i	$0.952572\pi$
$774$	−5.76982			−0.00745455
$775$	137.742			0.177731
$776$			408.012i			0.525788i
$777$		−	690.096i		−	0.888155i
$778$			1747.07i			2.24559i
$779$	−1390.06			−1.78441
$780$			698.872i			0.895990i
$781$	1199.72	+	195.155i	1.53613	+	0.249879i
$782$	171.357			0.219127
$783$			1405.09i			1.79450i
$784$	−69.6537			−0.0888440
$785$	−236.834			−0.301699
$786$	−1261.52			−1.60498
$787$		−	930.613i		−	1.18248i	−0.806495	−	0.591241i	$-0.798638\pi$
$787$		−	930.613i		−	1.18248i	0.806495	−	0.591241i	$-0.201362\pi$
$788$			257.823i			0.327187i
$789$		−	1209.00i		−	1.53232i
$790$	−90.0649			−0.114006
$791$			201.167i			0.254319i
$792$	−2.07657	+	12.7657i	−0.00262193	+	0.0161183i
$793$	−837.445			−1.05605
$794$		−	353.492i		−	0.445204i
$795$	−509.717			−0.641153
$796$	1208.11			1.51773
$797$	−332.628			−0.417350			−0.208675	−	0.977985i	$-0.566915\pi$
$797$	−332.628			−0.417350			−0.208675	+	0.977985i	$0.566915\pi$
$798$		−	1008.86i		−	1.26423i
$799$			62.5784i			0.0783210i
$800$			190.659i			0.238324i
$801$	12.4549			0.0155491
$802$			900.383i			1.12267i
$803$	−89.5703	+	550.632i	−0.111545	+	0.685719i
$804$	−643.591			−0.800486
$805$			200.271i			0.248784i
$806$	−1500.13			−1.86121
$807$	719.010			0.890966
$808$	−1077.62			−1.33369
$809$			870.764i			1.07635i	0.842834	+	0.538173i	$0.180885\pi$
$809$			870.764i			1.07635i	−0.842834	+	0.538173i	$0.819115\pi$
$810$		−	583.947i		−	0.720922i
$811$		−	1369.14i		−	1.68821i	−0.536180	−	0.844103i	$-0.680133\pi$
$811$		−	1369.14i		−	1.68821i	0.536180	−	0.844103i	$-0.319867\pi$
$812$	−1784.90			−2.19815
$813$		−	103.173i		−	0.126904i
$814$	−224.003	+	1377.05i	−0.275188	+	1.69171i
$815$	−320.279			−0.392980
$816$			43.0744i			0.0527873i
$817$	−180.720			−0.221199
$818$	−385.842			−0.471689
$819$	−18.3461			−0.0224006
$820$		−	1001.19i		−	1.22097i
$821$			759.486i			0.925075i	0.886600	+	0.462537i	$0.153061\pi$
$821$			759.486i			0.925075i	−0.886600	+	0.462537i	$0.846939\pi$
$822$			1608.30i			1.95657i
$823$	252.673			0.307015			0.153507	−	0.988148i	$-0.450943\pi$
$823$	252.673			0.307015			0.153507	+	0.988148i	$0.450943\pi$
$824$			177.461i			0.215366i
$825$	−164.549	−	26.7668i	−0.199453	−	0.0324447i
$826$	−31.4797			−0.0381110
$827$			172.995i			0.209184i	0.994515	+	0.104592i	$0.0333536\pi$
$827$			172.995i			0.209184i	−0.994515	+	0.104592i	$0.966646\pi$
$828$	−17.7322			−0.0214157
$829$	1145.40			1.38167			0.690834	−	0.723013i	$-0.257244\pi$
$829$	1145.40			1.38167			0.690834	+	0.723013i	$0.257244\pi$
$830$	791.717			0.953876
$831$		−	614.270i		−	0.739193i
$832$		−	1791.19i		−	2.15287i
$833$			57.8125i			0.0694027i
$834$	867.809			1.04054
$835$			79.5983i			0.0953273i
$836$	−196.257	+	1206.49i	−0.234757	+	1.44317i
$837$	735.849			0.879151
$838$		−	1287.91i		−	1.53689i
$839$	−41.7126			−0.0497170			−0.0248585	−	0.999691i	$-0.507914\pi$
$839$	−41.7126			−0.0497170			−0.0248585	+	0.999691i	$0.507914\pi$
$840$	240.813			0.286682
$841$	−1926.09			−2.29023
$842$			1100.19i			1.30664i
$843$		−	306.041i		−	0.363038i
$844$			319.900i			0.379029i
$845$	286.312			0.338831
$846$		−	10.8053i		−	0.0127722i
$847$	217.509	−	650.876i	0.256799	−	0.768448i
$848$	311.179			0.366956
$849$		−	491.383i		−	0.578778i
$850$	54.2552			0.0638297
$851$	−633.922			−0.744915
$852$	2003.82			2.35191
$853$			725.094i			0.850052i	0.905181	+	0.425026i	$0.139735\pi$
$853$			725.094i			0.850052i	−0.905181	+	0.425026i	$0.860265\pi$
$854$			870.709i			1.01957i
$855$			7.79504i			0.00911700i
$856$	−396.211			−0.462863
$857$		−	302.221i		−	0.352650i	−0.984332	−	0.176325i	$-0.943579\pi$
$857$		−	302.221i		−	0.352650i	0.984332	−	0.176325i	$-0.0564210\pi$
$858$	1792.09	+	291.515i	2.08868	+	0.339761i
$859$	−207.101			−0.241096			−0.120548	−	0.992708i	$-0.538465\pi$
$859$	−207.101			−0.241096			−0.120548	+	0.992708i	$0.538465\pi$
$860$		−	130.164i		−	0.151353i
$861$	1286.58			1.49429
$862$	1433.19			1.66263
$863$	482.444			0.559032			0.279516	−	0.960141i	$-0.409826\pi$
$863$	482.444			0.559032			0.279516	+	0.960141i	$0.409826\pi$
$864$			1018.54i			1.17887i
$865$		−	438.374i		−	0.506791i
$866$		−	2401.73i		−	2.77336i
$867$	−840.242			−0.969137
$868$			934.755i			1.07691i
$869$	−22.5149	+	138.410i	−0.0259090	+	0.159275i
$870$	1126.48			1.29481
$871$			611.669i			0.702260i
$872$	805.881			0.924176
$873$	12.2240			0.0140023
$874$	−926.738			−1.06034
$875$			63.4099i			0.0724684i
$876$			919.694i			1.04988i
$877$			377.864i			0.430860i	0.976519	+	0.215430i	$0.0691153\pi$
$877$			377.864i			0.430860i	−0.976519	+	0.215430i	$0.930885\pi$
$878$	−1084.70			−1.23542
$879$			1129.92i			1.28546i
$880$	100.456	+	16.3410i	0.114155	+	0.0185693i
$881$	−1459.75			−1.65693			−0.828463	−	0.560045i	$-0.810784\pi$
$881$	−1459.75			−1.65693			−0.828463	+	0.560045i	$0.810784\pi$
$882$		−	9.98233i		−	0.0113178i
$883$	−353.252			−0.400059			−0.200029	−	0.979790i	$-0.564104\pi$
$883$	−353.252			−0.400059			−0.200029	+	0.979790i	$0.564104\pi$
$884$	−354.125			−0.400594
$885$	11.9067			0.0134539
$886$		−	149.985i		−	0.169283i
$887$		−	174.064i		−	0.196239i	−0.995175	−	0.0981194i	$-0.968717\pi$
$887$		−	174.064i		−	0.196239i	0.995175	−	0.0981194i	$-0.0312827\pi$
$888$			762.251i			0.858391i
$889$	1194.92			1.34411
$890$			468.831i			0.526776i
$891$	−897.398	−	145.978i	−1.00718	−	0.163836i
$892$	1690.72			1.89543
$893$		−	338.438i		−	0.378990i
$894$	−698.138			−0.780915
$895$	145.752			0.162852
$896$	−997.275			−1.11303
$897$			824.981i			0.919711i
$898$			1071.36i			1.19305i
$899$			1449.13i			1.61193i
$900$	−5.61439			−0.00623821
$901$		−	258.278i		−	0.286657i
$902$	−2567.31	−	417.620i	−2.84624	−	0.462993i
$903$	167.267			0.185235
$904$		−	222.200i		−	0.245797i
$905$	351.099			0.387955
$906$	2271.46			2.50713
$907$	−1341.78			−1.47936			−0.739679	−	0.672960i	$-0.765023\pi$
$907$	−1341.78			−1.47936			−0.739679	+	0.672960i	$0.765023\pi$
$908$			665.586i			0.733024i
$909$			32.2855i			0.0355176i
$910$		−	690.591i		−	0.758892i
$911$	81.8460			0.0898419			0.0449210	−	0.998991i	$-0.485696\pi$
$911$	81.8460			0.0898419			0.0449210	+	0.998991i	$0.485696\pi$
$912$		−	232.956i		−	0.255434i
$913$	197.918	−	1216.70i	0.216777	−	1.33263i
$914$	874.534			0.956821
$915$		−	329.333i		−	0.359926i
$916$	319.367			0.348654
$917$	747.080			0.814700
$918$	289.844			0.315734
$919$			146.259i			0.159150i	0.996829	+	0.0795752i	$0.0253564\pi$
$919$			146.259i			0.159150i	−0.996829	+	0.0795752i	$0.974644\pi$
$920$		−	221.211i		−	0.240446i
$921$		−	1351.86i		−	1.46782i
$922$	495.726			0.537664
$923$		−	1904.44i		−	2.06331i
$924$	181.647	−	1116.67i	0.196588	−	1.20852i
$925$	−200.713			−0.216987
$926$		−	1288.05i		−	1.39098i
$927$	5.31674			0.00573543
$928$	−2005.85			−2.16148
$929$	−624.735			−0.672481			−0.336240	−	0.941776i	$-0.609155\pi$
$929$	−624.735			−0.672481			−0.336240	+	0.941776i	$0.609155\pi$
$930$		−	589.941i		−	0.634345i
$931$		−	312.662i		−	0.335835i
$932$			255.512i			0.274154i
$933$	755.422			0.809670
$934$		−	2366.74i		−	2.53398i
$935$	13.5630	−	83.3783i	0.0145059	−	0.0891747i
$936$	20.2643			0.0216499
$937$			1737.04i			1.85383i	0.375273	+	0.926915i	$0.377549\pi$
$937$			1737.04i			1.85383i	−0.375273	+	0.926915i	$0.622451\pi$
$938$	635.965			0.678001
$939$	−1404.08			−1.49529
$940$	243.760			0.259319
$941$		−	1214.68i		−	1.29084i	−0.763830	−	0.645418i	$-0.776683\pi$
$941$		−	1214.68i		−	1.29084i	0.763830	−	0.645418i	$-0.223317\pi$
$942$			1014.35i			1.07680i
$943$		−	1181.85i		−	1.25329i
$944$	−7.26897			−0.00770018
$945$			338.750i			0.358466i
$946$	−333.773	−	54.2943i	−0.352826	−	0.0573935i
$947$	1465.25			1.54725			0.773627	−	0.633641i	$-0.218440\pi$
$947$	1465.25			1.54725			0.773627	+	0.633641i	$0.218440\pi$
$948$			231.179i			0.243860i
$949$	874.077			0.921051
$950$	−293.424			−0.308867
$951$	−507.857			−0.534025
$952$			122.022i			0.128175i
$953$			464.526i			0.487435i	0.969846	+	0.243717i	$0.0783670\pi$
$953$			464.526i			0.487435i	−0.969846	+	0.243717i	$0.921633\pi$
$954$			44.5962i			0.0467465i
$955$	−362.169			−0.379235
$956$			1298.10i			1.35784i
$957$	281.604	−	1731.15i	0.294257	−	1.80894i
$958$	−35.5751			−0.0371348
$959$		−	952.446i		−	0.993166i
$960$	704.402			0.733752
$961$	−202.088			−0.210289
$962$	2185.95			2.27229
$963$			11.8705i			0.0123266i
$964$		−	927.807i		−	0.962455i
$965$		−	1.66121i		−	0.00172146i
$966$	857.750			0.887940
$967$			667.349i			0.690123i	0.938580	+	0.345062i	$0.112142\pi$
$967$			667.349i			0.690123i	−0.938580	+	0.345062i	$0.887858\pi$
$968$	−240.251	+	718.930i	−0.248193	+	0.742696i
$969$	−193.353			−0.199539
$970$			460.142i			0.474373i
$971$	980.665			1.00995			0.504977	−	0.863133i	$-0.331501\pi$
$971$	980.665			1.00995			0.504977	+	0.863133i	$0.331501\pi$
$972$	−60.6256			−0.0623720
$973$	−513.923			−0.528184
$974$			2321.78i			2.38376i
$975$			261.206i			0.267903i
$976$			201.056i			0.206000i
$977$	342.678			0.350745			0.175372	−	0.984502i	$-0.443887\pi$
$977$	342.678			0.350745			0.175372	+	0.984502i	$0.443887\pi$
$978$			1371.74i			1.40259i
$979$	720.490	+	117.201i	0.735945	+	0.119715i
$980$	225.196			0.229791
$981$		−	24.1442i		−	0.0246118i
$982$	1097.50			1.11762
$983$	−447.215			−0.454949			−0.227475	−	0.973784i	$-0.573047\pi$
$983$	−447.215			−0.454949			−0.227475	+	0.973784i	$0.573047\pi$
$984$	−1421.10			−1.44421
$985$			96.3622i			0.0978297i
$986$			570.799i			0.578903i
$987$			313.244i			0.317370i
$988$	1915.18			1.93844
$989$		−	153.651i		−	0.155360i
$990$	−2.34189	+	14.3967i	−0.00236554	+	0.0145421i
$991$	135.932			0.137166			0.0685831	−	0.997645i	$-0.478152\pi$
$991$	135.932			0.137166			0.0685831	+	0.997645i	$0.478152\pi$
$992$			1050.47i			1.05894i
$993$	−27.2196			−0.0274115
$994$	−1980.08			−1.99203
$995$	451.536			0.453805
$996$		−	2032.19i		−	2.04035i
$997$		−	303.075i		−	0.303987i	−0.988381	−	0.151993i	$-0.951431\pi$
$997$		−	303.075i		−	0.303987i	0.988381	−	0.151993i	$-0.0485693\pi$
$998$		−	2765.99i		−	2.77153i
$999$	−1072.25			−1.07333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.c.a.21.2	✓	8
3.2	odd	2		495.3.b.a.406.7		8
4.3	odd	2		880.3.j.a.241.8		8
5.2	odd	4		275.3.d.c.274.14		16
5.3	odd	4		275.3.d.c.274.3		16
5.4	even	2		275.3.c.f.76.7		8
11.10	odd	2	inner	55.3.c.a.21.7	yes	8
33.32	even	2		495.3.b.a.406.2		8
44.43	even	2		880.3.j.a.241.7		8
55.32	even	4		275.3.d.c.274.4		16
55.43	even	4		275.3.d.c.274.13		16
55.54	odd	2		275.3.c.f.76.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.2	✓	8	1.1	even	1	trivial
55.3.c.a.21.7	yes	8	11.10	odd	2	inner
275.3.c.f.76.2		8	55.54	odd	2
275.3.c.f.76.7		8	5.4	even	2
275.3.d.c.274.3		16	5.3	odd	4
275.3.d.c.274.4		16	55.32	even	4
275.3.d.c.274.13		16	55.43	even	4
275.3.d.c.274.14		16	5.2	odd	4
495.3.b.a.406.2		8	33.32	even	2
495.3.b.a.406.7		8	3.2	odd	2
880.3.j.a.241.7		8	44.43	even	2
880.3.j.a.241.8		8	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.15955i q^{2} -3.03112 q^{3} -5.98274 q^{4} -2.23607 q^{5} +9.57697i q^{6} -5.67155i q^{7} +6.26455i q^{8} +0.187686 q^{9} +7.06496i q^{10} +(10.8573 + 1.76614i) q^{11} +18.1344 q^{12} -17.2349i q^{13} -17.9195 q^{14} +6.77779 q^{15} -4.13780 q^{16} +3.43437i q^{17} -0.593004i q^{18} -18.5738i q^{19} +13.3778 q^{20} +17.1911i q^{21} +(5.58019 - 34.3041i) q^{22} +15.7918 q^{23} -18.9886i q^{24} +5.00000 q^{25} -54.4546 q^{26} +26.7112 q^{27} +33.9314i q^{28} +52.6031i q^{29} -21.4147i q^{30} +27.5484 q^{31} +38.1318i q^{32} +(-32.9097 - 5.35337i) q^{33} +10.8510 q^{34} +12.6820i q^{35} -1.12288 q^{36} -40.1425 q^{37} -58.6848 q^{38} +52.2411i q^{39} -14.0080i q^{40} -74.8398i q^{41} +54.3162 q^{42} -9.72983i q^{43} +(-64.9563 - 10.5663i) q^{44} -0.419679 q^{45} -49.8949i q^{46} +18.2212 q^{47} +12.5422 q^{48} +16.8335 q^{49} -15.7977i q^{50} -10.4100i q^{51} +103.112i q^{52} -75.2040 q^{53} -84.3952i q^{54} +(-24.2776 - 3.94920i) q^{55} +35.5297 q^{56} +56.2994i q^{57} +166.202 q^{58} +1.75672 q^{59} -40.5497 q^{60} -48.5900i q^{61} -87.0404i q^{62} -1.06447i q^{63} +103.928 q^{64} +38.5385i q^{65} +(-16.9142 + 103.980i) q^{66} -35.4901 q^{67} -20.5469i q^{68} -47.8668 q^{69} +40.0693 q^{70} +110.499 q^{71} +1.17577i q^{72} +50.7154i q^{73} +126.832i q^{74} -15.1556 q^{75} +111.122i q^{76} +(10.0167 - 61.5777i) q^{77} +165.058 q^{78} +12.7481i q^{79} +9.25240 q^{80} -82.6540 q^{81} -236.460 q^{82} -112.062i q^{83} -102.850i q^{84} -7.67948i q^{85} -30.7419 q^{86} -159.446i q^{87} +(-11.0640 + 68.0161i) q^{88} +66.3600 q^{89} +1.32600i q^{90} -97.7488 q^{91} -94.4781 q^{92} -83.5024 q^{93} -57.5709i q^{94} +41.5323i q^{95} -115.582i q^{96} +65.1302 q^{97} -53.1863i q^{98} +(2.03776 + 0.331479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} - 48 q^{12} + 20 q^{15} + 88 q^{16} - 20 q^{20} + 80 q^{22} + 8 q^{23} + 40 q^{25} - 100 q^{26} - 16 q^{27} + 36 q^{31} - 152 q^{33} + 80 q^{34} - 216 q^{36}+ \cdots - 184 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 - 48 * q^12 + 20 * q^15 + 88 * q^16 - 20 * q^20 + 80 * q^22 + 8 * q^23 + 40 * q^25 - 100 * q^26 - 16 * q^27 + 36 * q^31 - 152 * q^33 + 80 * q^34 - 216 * q^36 - 88 * q^37 - 160 * q^38 + 280 * q^42 + 12 * q^44 - 8 * q^47 + 488 * q^48 + 172 * q^49 - 152 * q^53 - 20 * q^55 - 80 * q^56 + 160 * q^58 - 16 * q^59 - 300 * q^60 - 588 * q^64 + 180 * q^66 - 88 * q^67 + 8 * q^69 + 60 * q^70 + 276 * q^71 + 40 * q^75 + 160 * q^77 + 160 * q^78 + 320 * q^80 - 320 * q^81 - 520 * q^82 + 420 * q^86 - 520 * q^88 + 444 * q^89 - 40 * q^91 - 368 * q^92 - 104 * q^93 + 312 * q^97 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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