LMFDB - Embedded newform 483.3.b.a.323.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(323,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("483.323");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.b (of order $2$, degree $1$, 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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.17
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.72

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.71288i q^{2} +(-2.93253 - 0.632651i) q^{3} -3.35974 q^{4} -2.46348i q^{5} +(-1.71631 + 7.95562i) q^{6} +2.64575 q^{7} -1.73695i q^{8} +(8.19950 + 3.71054i) q^{9} -6.68313 q^{10} -11.8962i q^{11} +(9.85255 + 2.12554i) q^{12} -17.4275 q^{13} -7.17762i q^{14} +(-1.55852 + 7.22423i) q^{15} -18.1511 q^{16} +0.203562i q^{17} +(10.0663 - 22.2443i) q^{18} -27.0623 q^{19} +8.27664i q^{20} +(-7.75875 - 1.67384i) q^{21} -32.2730 q^{22} +4.79583i q^{23} +(-1.09888 + 5.09366i) q^{24} +18.9313 q^{25} +47.2788i q^{26} +(-21.6978 - 16.0687i) q^{27} -8.88904 q^{28} +14.7351i q^{29} +(19.5985 + 4.22809i) q^{30} +15.3304 q^{31} +42.2941i q^{32} +(-7.52615 + 34.8860i) q^{33} +0.552240 q^{34} -6.51774i q^{35} +(-27.5482 - 12.4665i) q^{36} +6.24119 q^{37} +73.4169i q^{38} +(51.1067 + 11.0255i) q^{39} -4.27893 q^{40} -27.1454i q^{41} +(-4.54093 + 21.0486i) q^{42} -6.41913 q^{43} +39.9682i q^{44} +(9.14083 - 20.1993i) q^{45} +13.0105 q^{46} +60.7602i q^{47} +(53.2287 + 11.4833i) q^{48} +7.00000 q^{49} -51.3584i q^{50} +(0.128784 - 0.596952i) q^{51} +58.5519 q^{52} +34.4701i q^{53} +(-43.5926 + 58.8637i) q^{54} -29.3060 q^{55} -4.59553i q^{56} +(79.3611 + 17.1210i) q^{57} +39.9746 q^{58} -7.86711i q^{59} +(5.23623 - 24.2715i) q^{60} -3.37527 q^{61} -41.5897i q^{62} +(21.6938 + 9.81717i) q^{63} +42.1344 q^{64} +42.9322i q^{65} +(94.6418 + 20.4176i) q^{66} -63.0208 q^{67} -0.683916i q^{68} +(3.03409 - 14.0639i) q^{69} -17.6819 q^{70} -28.2348i q^{71} +(6.44502 - 14.2421i) q^{72} -54.3051 q^{73} -16.9316i q^{74} +(-55.5166 - 11.9769i) q^{75} +90.9223 q^{76} -31.4744i q^{77} +(29.9110 - 138.647i) q^{78} -26.3806 q^{79} +44.7148i q^{80} +(53.4637 + 60.8492i) q^{81} -73.6423 q^{82} -6.93649i q^{83} +(26.0674 + 5.62366i) q^{84} +0.501470 q^{85} +17.4144i q^{86} +(9.32219 - 43.2112i) q^{87} -20.6631 q^{88} +92.9215i q^{89} +(-54.7983 - 24.7980i) q^{90} -46.1088 q^{91} -16.1128i q^{92} +(-44.9571 - 9.69883i) q^{93} +164.835 q^{94} +66.6673i q^{95} +(26.7574 - 124.029i) q^{96} -170.087 q^{97} -18.9902i q^{98} +(44.1414 - 97.5430i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30}+ \cdots - 248 q^{99}+O(q^{100}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	2.71288i		−	1.35644i	−0.734858	−	0.678221i	$-0.762751\pi$
$2$		−	2.71288i		−	1.35644i	0.734858	−	0.678221i	$-0.237249\pi$
$3$	−2.93253	−	0.632651i	−0.977511	−	0.210884i
$3$	−2.93253	−	0.632651i	−0.977511	−	0.210884i
$4$	−3.35974			−0.839935
$5$		−	2.46348i		−	0.492695i	−0.969182	−	0.246348i	$-0.920770\pi$
$5$		−	2.46348i		−	0.492695i	0.969182	−	0.246348i	$-0.0792305\pi$
$6$	−1.71631	+	7.95562i	−0.286052	+	1.32594i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$		−	1.73695i		−	0.217119i
$9$	8.19950	+	3.71054i	0.911056	+	0.412283i
$10$	−6.68313			−0.668313
$11$		−	11.8962i		−	1.08147i	−0.841192	−	0.540737i	$-0.818145\pi$
$11$		−	11.8962i		−	1.08147i	0.841192	−	0.540737i	$-0.181855\pi$
$12$	9.85255	+	2.12554i	0.821046	+	0.177129i
$13$	−17.4275			−1.34058			−0.670289	−	0.742100i	$-0.733830\pi$
$13$	−17.4275			−1.34058			−0.670289	+	0.742100i	$0.733830\pi$
$14$		−	7.17762i		−	0.512687i
$15$	−1.55852	+	7.22423i	−0.103901	+	0.481615i
$16$	−18.1511			−1.13444
$17$			0.203562i			0.0119742i	0.999982	+	0.00598712i	$0.00190577\pi$
$17$			0.203562i			0.0119742i	−0.999982	+	0.00598712i	$0.998094\pi$
$18$	10.0663	−	22.2443i	0.559237	−	1.23579i
$19$	−27.0623			−1.42433			−0.712165	−	0.702012i	$-0.752285\pi$
$19$	−27.0623			−1.42433			−0.712165	+	0.702012i	$0.752285\pi$
$20$			8.27664i			0.413832i
$21$	−7.75875	−	1.67384i	−0.369464	−	0.0797066i
$22$	−32.2730			−1.46696
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−1.09888	+	5.09366i	−0.0457868	+	0.212236i
$25$	18.9313			0.757251
$26$			47.2788i			1.81842i
$27$	−21.6978	−	16.0687i	−0.803624	−	0.595138i
$28$	−8.88904			−0.317466
$29$			14.7351i			0.508107i	0.967190	+	0.254054i	$0.0817640\pi$
$29$			14.7351i			0.508107i	−0.967190	+	0.254054i	$0.918236\pi$
$30$	19.5985	+	4.22809i	0.653283	+	0.140936i
$31$	15.3304			0.494531			0.247265	−	0.968948i	$-0.420468\pi$
$31$	15.3304			0.494531			0.247265	+	0.968948i	$0.420468\pi$
$32$			42.2941i			1.32169i
$33$	−7.52615	+	34.8860i	−0.228065	+	1.05715i
$34$	0.552240			0.0162424
$35$		−	6.51774i		−	0.186221i
$36$	−27.5482	−	12.4665i	−0.765228	−	0.346291i
$37$	6.24119			0.168681			0.0843405	−	0.996437i	$-0.473122\pi$
$37$	6.24119			0.168681			0.0843405	+	0.996437i	$0.473122\pi$
$38$			73.4169i			1.93202i
$39$	51.1067	+	11.0255i	1.31043	+	0.282706i
$40$	−4.27893			−0.106973
$41$		−	27.1454i		−	0.662083i	−0.943616	−	0.331041i	$-0.892600\pi$
$41$		−	27.1454i		−	0.662083i	0.943616	−	0.331041i	$-0.107400\pi$
$42$	−4.54093	+	21.0486i	−0.108117	+	0.501157i
$43$	−6.41913			−0.149282			−0.0746411	−	0.997210i	$-0.523781\pi$
$43$	−6.41913			−0.149282			−0.0746411	+	0.997210i	$0.523781\pi$
$44$			39.9682i			0.908368i
$45$	9.14083	−	20.1993i	0.203130	−	0.448873i
$46$	13.0105			0.282838
$47$			60.7602i			1.29277i	0.763011	+	0.646385i	$0.223720\pi$
$47$			60.7602i			1.29277i	−0.763011	+	0.646385i	$0.776280\pi$
$48$	53.2287	+	11.4833i	1.10893	+	0.239236i
$49$	7.00000			0.142857
$50$		−	51.3584i		−	1.02717i
$51$	0.128784	−	0.596952i	0.00252517	−	0.0117050i
$52$	58.5519			1.12600
$53$			34.4701i			0.650380i	0.945649	+	0.325190i	$0.105428\pi$
$53$			34.4701i			0.650380i	−0.945649	+	0.325190i	$0.894572\pi$
$54$	−43.5926	+	58.8637i	−0.807270	+	1.09007i
$55$	−29.3060			−0.532837
$56$		−	4.59553i		−	0.0820631i
$57$	79.3611	+	17.1210i	1.39230	+	0.300368i
$58$	39.9746			0.689218
$59$		−	7.86711i		−	0.133341i	−0.997775	−	0.0666705i	$-0.978762\pi$
$59$		−	7.86711i		−	0.133341i	0.997775	−	0.0666705i	$-0.0212376\pi$
$60$	5.23623	−	24.2715i	0.0872705	−	0.404525i
$61$	−3.37527			−0.0553324			−0.0276662	−	0.999617i	$-0.508808\pi$
$61$	−3.37527			−0.0553324			−0.0276662	+	0.999617i	$0.508808\pi$
$62$		−	41.5897i		−	0.670802i
$63$	21.6938	+	9.81717i	0.344347	+	0.155828i
$64$	42.1344			0.658351
$65$			42.9322i			0.660496i
$66$	94.6418	+	20.4176i	1.43397	+	0.309357i
$67$	−63.0208			−0.940608			−0.470304	−	0.882504i	$-0.655856\pi$
$67$	−63.0208			−0.940608			−0.470304	+	0.882504i	$0.655856\pi$
$68$		−	0.683916i		−	0.0100576i
$69$	3.03409	−	14.0639i	0.0439723	−	0.203825i
$70$	−17.6819			−0.252598
$71$		−	28.2348i		−	0.397673i	−0.980033	−	0.198836i	$-0.936284\pi$
$71$		−	28.2348i		−	0.397673i	0.980033	−	0.198836i	$-0.0637162\pi$
$72$	6.44502	−	14.2421i	0.0895142	−	0.197807i
$73$	−54.3051			−0.743905			−0.371953	−	0.928252i	$-0.621312\pi$
$73$	−54.3051			−0.743905			−0.371953	+	0.928252i	$0.621312\pi$
$74$		−	16.9316i		−	0.228806i
$75$	−55.5166	−	11.9769i	−0.740222	−	0.159692i
$76$	90.9223			1.19635
$77$		−	31.4744i		−	0.408759i
$78$	29.9110	−	138.647i	0.383474	−	1.77752i
$79$	−26.3806			−0.333932			−0.166966	−	0.985963i	$-0.553397\pi$
$79$	−26.3806			−0.333932			−0.166966	+	0.985963i	$0.553397\pi$
$80$			44.7148i			0.558935i
$81$	53.4637	+	60.8492i	0.660046	+	0.751225i
$82$	−73.6423			−0.898077
$83$		−	6.93649i		−	0.0835722i	−0.999127	−	0.0417861i	$-0.986695\pi$
$83$		−	6.93649i		−	0.0835722i	0.999127	−	0.0417861i	$-0.0133048\pi$
$84$	26.0674	+	5.62366i	0.310326	+	0.0669484i
$85$	0.501470			0.00589965
$86$			17.4144i			0.202493i
$87$	9.32219	−	43.2112i	0.107152	−	0.496681i
$88$	−20.6631			−0.234808
$89$			92.9215i			1.04406i	0.852926	+	0.522031i	$0.174825\pi$
$89$			92.9215i			1.04406i	−0.852926	+	0.522031i	$0.825175\pi$
$90$	−54.7983	−	24.7980i	−0.608870	−	0.275534i
$91$	−46.1088			−0.506691
$92$		−	16.1128i		−	0.175139i
$93$	−44.9571	−	9.69883i	−0.483409	−	0.104288i
$94$	164.835			1.75357
$95$			66.6673i			0.701761i
$96$	26.7574	−	124.029i	0.278723	−	1.29197i
$97$	−170.087			−1.75347			−0.876736	−	0.480972i	$-0.840284\pi$
$97$	−170.087			−1.75347			−0.876736	+	0.480972i	$0.840284\pi$
$98$		−	18.9902i		−	0.193777i
$99$	44.1414	−	97.5430i	0.445873	−	0.985283i
$100$	−63.6042			−0.636042
$101$		−	18.5230i		−	0.183396i	−0.995787	−	0.0916979i	$-0.970771\pi$
$101$		−	18.5230i		−	0.183396i	0.995787	−	0.0916979i	$-0.0292294\pi$
$102$	−1.61946	−	0.349376i	−0.0158771	−	0.00342525i
$103$	64.9633			0.630712			0.315356	−	0.948973i	$-0.397876\pi$
$103$	64.9633			0.630712			0.315356	+	0.948973i	$0.397876\pi$
$104$			30.2707i			0.291064i
$105$	−4.12346	+	19.1135i	−0.0392711	+	0.182033i
$106$	93.5135			0.882202
$107$		−	101.916i		−	0.952483i	−0.879315	−	0.476242i	$-0.841999\pi$
$107$		−	101.916i		−	0.952483i	0.879315	−	0.476242i	$-0.158001\pi$
$108$	72.8991	+	53.9867i	0.674992	+	0.499877i
$109$	66.2966			0.608225			0.304113	−	0.952636i	$-0.401640\pi$
$109$	66.2966			0.608225			0.304113	+	0.952636i	$0.401640\pi$
$110$			79.5039i			0.722762i
$111$	−18.3025	−	3.94850i	−0.164887	−	0.0355721i
$112$	−48.0233			−0.428780
$113$			36.2110i			0.320451i	0.987080	+	0.160226i	$0.0512222\pi$
$113$			36.2110i			0.320451i	−0.987080	+	0.160226i	$0.948778\pi$
$114$	46.4473	−	215.297i	0.407432	−	1.88857i
$115$	11.8144			0.102734
$116$		−	49.5062i		−	0.426777i
$117$	−142.897	−	64.6655i	−1.22134	−	0.552697i
$118$	−21.3426			−0.180869
$119$			0.538575i			0.00452584i
$120$	12.5481	+	2.70707i	0.104568	+	0.0225589i
$121$	−20.5199			−0.169586
$122$			9.15673i			0.0750552i
$123$	−17.1736	+	79.6048i	−0.139623	+	0.647193i
$124$	−51.5063			−0.415374
$125$		−	108.224i		−	0.865789i
$126$	26.6329	−	58.8529i	0.211372	−	0.467087i
$127$	38.1195			0.300154			0.150077	−	0.988674i	$-0.452048\pi$
$127$	38.1195			0.300154			0.150077	+	0.988674i	$0.452048\pi$
$128$			54.8703i			0.428674i
$129$	18.8243	+	4.06107i	0.145925	+	0.0314812i
$130$	116.470			0.895925
$131$		−	201.997i		−	1.54196i	−0.636857	−	0.770982i	$-0.719766\pi$
$131$		−	201.997i		−	1.54196i	0.636857	−	0.770982i	$-0.280234\pi$
$132$	25.2859	−	117.208i	0.191560	−	0.887940i
$133$	−71.6001			−0.538347
$134$			170.968i			1.27588i
$135$	−39.5849	+	53.4521i	−0.293221	+	0.395942i
$136$	0.353577			0.00259983
$137$		−	51.6647i		−	0.377114i	−0.982062	−	0.188557i	$-0.939619\pi$
$137$		−	51.6647i		−	0.377114i	0.982062	−	0.188557i	$-0.0603811\pi$
$138$	−38.1538	−	8.23113i	−0.276477	−	0.0596459i
$139$	−164.094			−1.18053			−0.590266	−	0.807209i	$-0.700977\pi$
$139$	−164.094			−1.18053			−0.590266	+	0.807209i	$0.700977\pi$
$140$			21.8979i			0.156414i
$141$	38.4400	−	178.181i	0.272624	−	1.26370i
$142$	−76.5976			−0.539420
$143$			207.321i			1.44980i
$144$	−148.830	−	67.3504i	−1.03354	−	0.467711i
$145$	36.2996			0.250342
$146$			147.323i			1.00906i
$147$	−20.5277	−	4.42856i	−0.139644	−	0.0301263i
$148$	−20.9688			−0.141681
$149$		−	115.751i		−	0.776850i	−0.921480	−	0.388425i	$-0.873019\pi$
$149$		−	115.751i		−	0.776850i	0.921480	−	0.388425i	$-0.126981\pi$
$150$	−32.4920	+	150.610i	−0.216613	+	1.00407i
$151$	61.6599			0.408343			0.204172	−	0.978935i	$-0.434550\pi$
$151$	61.6599			0.408343			0.204172	+	0.978935i	$0.434550\pi$
$152$			47.0058i			0.309249i
$153$	−0.755326	+	1.66911i	−0.00493677	+	0.0109092i
$154$	−85.3865			−0.554457
$155$		−	37.7662i		−	0.243653i
$156$	−171.705	−	37.0429i	−1.10068	−	0.237455i
$157$	36.0816			0.229819			0.114910	−	0.993376i	$-0.463342\pi$
$157$	36.0816			0.229819			0.114910	+	0.993376i	$0.463342\pi$
$158$			71.5676i			0.452960i
$159$	21.8076	−	101.085i	0.137155	−	0.635753i
$160$	104.190			0.651190
$161$			12.6886i			0.0788110i
$162$	165.077	−	145.041i	1.01899	−	0.895315i
$163$	−263.142			−1.61437			−0.807184	−	0.590300i	$-0.799009\pi$
$163$	−263.142			−1.61437			−0.807184	+	0.590300i	$0.799009\pi$
$164$			91.2015i			0.556107i
$165$	85.9409	+	18.5405i	0.520854	+	0.112367i
$166$	−18.8179			−0.113361
$167$		−	305.453i		−	1.82906i	−0.404517	−	0.914530i	$-0.632560\pi$
$167$		−	305.453i		−	1.82906i	0.404517	−	0.914530i	$-0.367440\pi$
$168$	−2.90737	+	13.4766i	−0.0173058	+	0.0802176i
$169$	134.718			0.797147
$170$		−	1.36043i		−	0.00800253i
$171$	−221.897	−	100.416i	−1.29765	−	0.587227i
$172$	21.5666			0.125387
$173$			282.283i			1.63169i	0.578269	+	0.815847i	$0.303729\pi$
$173$			282.283i			1.63169i	−0.578269	+	0.815847i	$0.696271\pi$
$174$	−117.227	−	25.2900i	−0.673718	−	0.145345i
$175$	50.0875			0.286214
$176$			215.929i			1.22687i
$177$	−4.97714	+	23.0706i	−0.0281194	+	0.130342i
$178$	252.085			1.41621
$179$		−	252.363i		−	1.40985i	−0.709282	−	0.704925i	$-0.750981\pi$
$179$		−	252.363i		−	1.40985i	0.709282	−	0.704925i	$-0.249019\pi$
$180$	−30.7108	+	67.8644i	−0.170616	+	0.377024i
$181$	−340.899			−1.88342			−0.941711	−	0.336424i	$-0.890783\pi$
$181$	−340.899			−1.88342			−0.941711	+	0.336424i	$0.890783\pi$
$182$			125.088i			0.687296i
$183$	9.89811	+	2.13537i	0.0540880	+	0.0116687i
$184$	8.33011			0.0452724
$185$		−	15.3750i		−	0.0831083i
$186$	−26.3118	+	121.963i	−0.141461	+	0.655717i
$187$	2.42162			0.0129498
$188$		−	204.139i		−	1.08584i
$189$	−57.4071	−	42.5138i	−0.303741	−	0.224941i
$190$	180.861			0.951898
$191$		−	260.176i		−	1.36218i	−0.732200	−	0.681090i	$-0.761506\pi$
$191$		−	260.176i		−	1.36218i	0.732200	−	0.681090i	$-0.238494\pi$
$192$	−123.561	−	26.6564i	−0.643545	−	0.138836i
$193$	−266.038			−1.37843			−0.689217	−	0.724555i	$-0.742045\pi$
$193$	−266.038			−1.37843			−0.689217	+	0.724555i	$0.742045\pi$
$194$			461.426i			2.37848i
$195$	27.1611	−	125.900i	0.139288	−	0.645642i
$196$	−23.5182			−0.119991
$197$		−	136.564i		−	0.693220i	−0.938009	−	0.346610i	$-0.887333\pi$
$197$		−	136.564i		−	0.693220i	0.938009	−	0.346610i	$-0.112667\pi$
$198$	−264.623	−	119.751i	−1.33648	−	0.604801i
$199$	35.3878			0.177828			0.0889141	−	0.996039i	$-0.471660\pi$
$199$	35.3878			0.177828			0.0889141	+	0.996039i	$0.471660\pi$
$200$		−	32.8827i		−	0.164413i
$201$	184.810	+	39.8702i	0.919455	+	0.198359i
$202$	−50.2507			−0.248766
$203$			38.9854i			0.192046i
$204$	−0.432680	+	2.00561i	−0.00212098	+	0.00983140i
$205$	−66.8720			−0.326205
$206$		−	176.238i		−	0.855524i
$207$	−17.7951	+	39.3234i	−0.0859668	+	0.189968i
$208$	316.328			1.52081
$209$			321.939i			1.54038i
$210$	51.8527	+	11.1865i	0.246918	+	0.0532689i
$211$	−49.5778			−0.234966			−0.117483	−	0.993075i	$-0.537483\pi$
$211$	−49.5778			−0.234966			−0.117483	+	0.993075i	$0.537483\pi$
$212$		−	115.811i		−	0.546277i
$213$	−17.8628	+	82.7994i	−0.0838627	+	0.388729i
$214$	−276.485			−1.29199
$215$			15.8134i			0.0735506i
$216$	−27.9105	+	37.6880i	−0.129215	+	0.174482i
$217$	40.5606			0.186915
$218$		−	179.855i		−	0.825023i
$219$	159.251	+	34.3562i	0.727176	+	0.156878i
$220$	98.4607			0.447549
$221$		−	3.54758i		−	0.0160524i
$222$	−10.7118	+	49.6526i	−0.0482515	+	0.223660i
$223$	−394.062			−1.76709			−0.883547	−	0.468342i	$-0.844851\pi$
$223$	−394.062			−1.76709			−0.883547	+	0.468342i	$0.844851\pi$
$224$			111.900i			0.499552i
$225$	155.227	+	70.2453i	0.689899	+	0.312202i
$226$	98.2362			0.434674
$227$			75.6079i			0.333074i	0.986035	+	0.166537i	$0.0532586\pi$
$227$			75.6079i			0.333074i	−0.986035	+	0.166537i	$0.946741\pi$
$228$	−266.633	−	57.5221i	−1.16944	−	0.252290i
$229$	73.2421			0.319834			0.159917	−	0.987130i	$-0.448877\pi$
$229$	73.2421			0.319834			0.159917	+	0.987130i	$0.448877\pi$
$230$		−	32.0511i		−	0.139353i
$231$	−19.9123	+	92.2998i	−0.0862006	+	0.399566i
$232$	25.5941			0.110320
$233$			151.085i			0.648436i	0.945982	+	0.324218i	$0.105101\pi$
$233$			151.085i			0.648436i	−0.945982	+	0.324218i	$0.894899\pi$
$234$	−175.430	+	387.663i	−0.749701	+	1.65668i
$235$	149.681			0.636942
$236$			26.4315i			0.111998i
$237$	77.3621	+	16.6898i	0.326422	+	0.0704209i
$238$	1.46109			0.00613904
$239$		−	403.356i		−	1.68768i	−0.536593	−	0.843841i	$-0.680289\pi$
$239$		−	403.356i		−	1.68768i	0.536593	−	0.843841i	$-0.319711\pi$
$240$	28.2889	−	131.128i	0.117870	−	0.546365i
$241$	405.045			1.68069			0.840343	−	0.542056i	$-0.182354\pi$
$241$	405.045			1.68069			0.840343	+	0.542056i	$0.182354\pi$
$242$			55.6680i			0.230033i
$243$	−118.288	−	212.266i	−0.486781	−	0.873524i
$244$	11.3400			0.0464756
$245$		−	17.2443i		−	0.0703850i
$246$	215.959	+	46.5899i	0.877881	+	0.189390i
$247$	471.628			1.90943
$248$		−	26.6282i		−	0.107372i
$249$	−4.38838	+	20.3415i	−0.0176240	+	0.0816928i
$250$	−293.598			−1.17439
$251$		−	100.182i		−	0.399133i	−0.979884	−	0.199567i	$-0.936047\pi$
$251$		−	100.182i		−	0.399133i	0.979884	−	0.199567i	$-0.0639534\pi$
$252$	−72.8857	−	32.9832i	−0.289229	−	0.130886i
$253$	57.0522			0.225503
$254$		−	103.414i		−	0.407141i
$255$	−1.47058	−	0.317256i	−0.00576697	−	0.00124414i
$256$	317.395			1.23982
$257$		−	288.377i		−	1.12209i	−0.827786	−	0.561044i	$-0.810400\pi$
$257$		−	288.377i		−	1.12209i	0.827786	−	0.561044i	$-0.189600\pi$
$258$	11.0172	−	51.0682i	0.0427024	−	0.197939i
$259$	16.5126			0.0637554
$260$		−	144.241i		−	0.554774i
$261$	−54.6753	+	120.821i	−0.209484	+	0.462914i
$262$	−547.995			−2.09159
$263$		−	507.686i		−	1.93036i	−0.261580	−	0.965182i	$-0.584244\pi$
$263$		−	507.686i		−	1.93036i	0.261580	−	0.965182i	$-0.415756\pi$
$264$	60.5953	+	13.0725i	0.229527	+	0.0495172i
$265$	84.9163			0.320439
$266$			194.243i			0.730236i
$267$	58.7869	−	272.495i	0.220176	−	1.02058i
$268$	211.733			0.790050
$269$		−	201.692i		−	0.749786i	−0.927068	−	0.374893i	$-0.877679\pi$
$269$		−	201.692i		−	0.749786i	0.927068	−	0.374893i	$-0.122321\pi$
$270$	145.009	+	107.389i	0.537072	+	0.397738i
$271$	412.413			1.52182			0.760910	−	0.648858i	$-0.224753\pi$
$271$	412.413			1.52182			0.760910	+	0.648858i	$0.224753\pi$
$272$		−	3.69488i		−	0.0135841i
$273$	135.216	+	29.1708i	0.495296	+	0.106853i
$274$	−140.160			−0.511534
$275$		−	225.211i		−	0.818948i
$276$	−10.1938	+	47.2512i	−0.0369339	+	0.171200i
$277$	171.831			0.620329			0.310165	−	0.950683i	$-0.399616\pi$
$277$	171.831			0.620329			0.310165	+	0.950683i	$0.399616\pi$
$278$			445.168i			1.60132i
$279$	125.702	+	56.8843i	0.450545	+	0.203886i
$280$	−11.3210			−0.0404321
$281$			387.163i			1.37780i	0.724855	+	0.688902i	$0.241907\pi$
$281$			387.163i			1.37780i	−0.724855	+	0.688902i	$0.758093\pi$
$282$	−483.385	−	104.283i	−1.71413	−	0.369799i
$283$	321.435			1.13581			0.567907	−	0.823093i	$-0.307753\pi$
$283$	321.435			1.13581			0.567907	+	0.823093i	$0.307753\pi$
$284$			94.8615i			0.334019i
$285$	42.1772	−	195.504i	0.147990	−	0.685979i
$286$	562.439			1.96657
$287$		−	71.8200i		−	0.250244i
$288$	−156.934	+	346.790i	−0.544909	+	1.20413i
$289$	288.959			0.999857
$290$		−	98.4766i		−	0.339574i
$291$	498.785	+	107.606i	1.71404	+	0.369779i
$292$	182.451			0.624832
$293$			459.424i			1.56800i	0.620760	+	0.784000i	$0.286824\pi$
$293$			459.424i			1.56800i	−0.620760	+	0.784000i	$0.713176\pi$
$294$	−12.0142	+	55.6894i	−0.0408645	+	0.189420i
$295$	−19.3804			−0.0656964
$296$		−	10.8406i		−	0.0366238i
$297$	−191.157	+	258.122i	−0.643626	+	0.869098i
$298$	−314.018			−1.05375
$299$		−	83.5794i		−	0.279530i
$300$	186.521	+	40.2393i	0.621738	+	0.134131i
$301$	−16.9834			−0.0564233
$302$		−	167.276i		−	0.553894i
$303$	−11.7186	+	54.3192i	−0.0386752	+	0.179271i
$304$	491.210			1.61582
$305$			8.31491i			0.0272620i
$306$	4.52810	+	2.04911i	0.0147977	+	0.00669644i
$307$	100.073			0.325971			0.162986	−	0.986628i	$-0.447888\pi$
$307$	100.073			0.325971			0.162986	+	0.986628i	$0.447888\pi$
$308$			105.746i			0.343331i
$309$	−190.507	−	41.0991i	−0.616528	−	0.133007i
$310$	−102.455			−0.330501
$311$			464.199i			1.49260i	0.665609	+	0.746300i	$0.268172\pi$
$311$			464.199i			1.49260i	−0.665609	+	0.746300i	$0.731828\pi$
$312$	19.1508	−	88.7698i	0.0613807	−	0.284519i
$313$	−394.898			−1.26165			−0.630827	−	0.775923i	$-0.717284\pi$
$313$	−394.898			−1.26165			−0.630827	+	0.775923i	$0.717284\pi$
$314$		−	97.8853i		−	0.311737i
$315$	24.1844	−	53.4423i	0.0767758	−	0.169658i
$316$	88.6321			0.280481
$317$		−	264.405i		−	0.834084i	−0.908887	−	0.417042i	$-0.863067\pi$
$317$		−	264.405i		−	0.834084i	0.908887	−	0.417042i	$-0.136933\pi$
$318$	−274.231	−	59.1614i	−0.862363	−	0.186042i
$319$	175.292			0.549505
$320$		−	103.797i		−	0.324366i
$321$	−64.4771	+	298.871i	−0.200863	+	0.931063i
$322$	34.4226			0.106903
$323$		−	5.50885i		−	0.0170553i
$324$	−179.624	−	204.438i	−0.554396	−	0.630980i
$325$	−329.925			−1.01515
$326$			713.873i			2.18980i
$327$	−194.417	−	41.9426i	−0.594547	−	0.128265i
$328$	−47.1502			−0.143751
$329$			160.756i			0.488621i
$330$	50.2982	−	233.148i	0.152419	−	0.706508i
$331$	−138.493			−0.418407			−0.209204	−	0.977872i	$-0.567087\pi$
$331$	−138.493			−0.418407			−0.209204	+	0.977872i	$0.567087\pi$
$332$			23.3048i			0.0701952i
$333$	51.1747	+	23.1582i	0.153678	+	0.0695442i
$334$	−828.659			−2.48101
$335$			155.250i			0.463433i
$336$	140.830	+	30.3820i	0.419137	+	0.0904227i
$337$	167.452			0.496889			0.248445	−	0.968646i	$-0.420081\pi$
$337$	167.452			0.496889			0.248445	+	0.968646i	$0.420081\pi$
$338$		−	365.474i		−	1.08128i
$339$	22.9089	−	106.190i	0.0675780	−	0.313245i
$340$	−1.68481			−0.00495532
$341$		−	182.374i		−	0.534822i
$342$	−272.416	+	601.982i	−0.796539	+	1.76018i
$343$	18.5203			0.0539949
$344$			11.1497i			0.0324119i
$345$	−34.6462	−	7.47441i	−0.100424	−	0.0216649i
$346$	765.801			2.21330
$347$			407.284i			1.17373i	0.809685	+	0.586865i	$0.199638\pi$
$347$			407.284i			1.17373i	−0.809685	+	0.586865i	$0.800362\pi$
$348$	−31.3201	+	145.178i	−0.0900004	+	0.417179i
$349$	140.756			0.403312			0.201656	−	0.979456i	$-0.435368\pi$
$349$	140.756			0.403312			0.201656	+	0.979456i	$0.435368\pi$
$350$		−	135.882i		−	0.388233i
$351$	378.139	+	280.038i	1.07732	+	0.797828i
$352$	503.139			1.42937
$353$			366.450i			1.03810i	0.854743	+	0.519051i	$0.173715\pi$
$353$			366.450i			1.03810i	−0.854743	+	0.519051i	$0.826285\pi$
$354$	62.5878	+	13.5024i	0.176802	+	0.0381424i
$355$	−69.5557			−0.195931
$356$		−	312.192i		−	0.876945i
$357$	0.340730	−	1.57939i	0.000954426	−	0.00442406i
$358$	−684.632			−1.91238
$359$		−	375.644i		−	1.04636i	−0.852221	−	0.523181i	$-0.824745\pi$
$359$		−	375.644i		−	1.04636i	0.852221	−	0.523181i	$-0.175255\pi$
$360$	−35.0851	−	15.8772i	−0.0974587	−	0.0441032i
$361$	371.367			1.02872
$362$			924.820i			2.55475i
$363$	60.1751	+	12.9819i	0.165772	+	0.0357628i
$364$	154.914			0.425587
$365$			133.779i			0.366519i
$366$	5.79302	−	26.8524i	0.0158279	−	0.0733673i
$367$	−519.664			−1.41598			−0.707989	−	0.706223i	$-0.750398\pi$
$367$	−519.664			−1.41598			−0.707989	+	0.706223i	$0.750398\pi$
$368$		−	87.0496i		−	0.236548i
$369$	100.724	−	222.579i	0.272965	−	0.603195i
$370$	−41.7107			−0.112732
$371$			91.1994i			0.245820i
$372$	151.044	+	32.5856i	0.406032	+	0.0875956i
$373$	−121.541			−0.325847			−0.162923	−	0.986639i	$-0.552092\pi$
$373$	−121.541			−0.325847			−0.162923	+	0.986639i	$0.552092\pi$
$374$		−	6.56957i		−	0.0175657i
$375$	−68.4679	+	317.370i	−0.182581	+	0.846319i
$376$	105.537			0.280684
$377$		−	256.796i		−	0.681157i
$378$	−115.335	+	155.739i	−0.305119	+	0.412007i
$379$	−739.079			−1.95008			−0.975039	−	0.222035i	$-0.928730\pi$
$379$	−739.079			−1.95008			−0.975039	+	0.222035i	$0.928730\pi$
$380$		−	223.985i		−	0.589434i
$381$	−111.787	−	24.1164i	−0.293404	−	0.0632975i
$382$	−705.828			−1.84772
$383$		−	298.359i		−	0.779006i	−0.921025	−	0.389503i	$-0.872647\pi$
$383$		−	298.359i		−	0.779006i	0.921025	−	0.389503i	$-0.127353\pi$
$384$	34.7138	−	160.909i	0.0904005	−	0.419034i
$385$	−77.5365			−0.201393
$386$			721.729i			1.86977i
$387$	−52.6337	−	23.8185i	−0.136004	−	0.0615464i
$388$	571.447			1.47280
$389$			379.341i			0.975170i	0.873076	+	0.487585i	$0.162122\pi$
$389$			379.341i			0.975170i	−0.873076	+	0.487585i	$0.837878\pi$
$390$	−341.553	−	73.6850i	−0.875776	−	0.188936i
$391$	−0.976249			−0.00249680
$392$		−	12.1586i		−	0.0310169i
$393$	−127.794	+	592.364i	−0.325175	+	1.50729i
$394$	−370.483			−0.940312
$395$			64.9881i			0.164527i
$396$	−148.304	+	327.719i	−0.374504	+	0.827574i
$397$	−191.873			−0.483308			−0.241654	−	0.970362i	$-0.577690\pi$
$397$	−191.873			−0.483308			−0.241654	+	0.970362i	$0.577690\pi$
$398$		−	96.0030i		−	0.241214i
$399$	209.970	+	45.2979i	0.526240	+	0.113529i
$400$	−343.624			−0.859059
$401$		−	651.879i		−	1.62563i	−0.582520	−	0.812816i	$-0.697933\pi$
$401$		−	651.879i		−	1.62563i	0.582520	−	0.812816i	$-0.302067\pi$
$402$	108.163	−	501.369i	0.269063	−	1.24719i
$403$	−267.171			−0.662956
$404$			62.2324i			0.154041i
$405$	149.901	−	131.707i	0.370125	−	0.325202i
$406$	105.763			0.260500
$407$		−	74.2466i		−	0.182424i
$408$	−1.03688	−	0.223691i	−0.00254136	−	0.000548262i
$409$	−36.9551			−0.0903547			−0.0451773	−	0.998979i	$-0.514385\pi$
$409$	−36.9551			−0.0903547			−0.0451773	+	0.998979i	$0.514385\pi$
$410$			181.416i			0.442478i
$411$	−32.6857	+	151.508i	−0.0795273	+	0.368634i
$412$	−218.260			−0.529757
$413$		−	20.8144i		−	0.0503981i
$414$	106.680	+	48.2761i	0.257681	+	0.116609i
$415$	−17.0879			−0.0411756
$416$		−	737.080i		−	1.77183i
$417$	481.211	+	103.814i	1.15398	+	0.248955i
$418$	873.382			2.08943
$419$		−	701.950i		−	1.67530i	−0.546209	−	0.837649i	$-0.683929\pi$
$419$		−	701.950i		−	1.67530i	0.546209	−	0.837649i	$-0.316071\pi$
$420$	13.8538	−	64.2164i	0.0329851	−	0.152896i
$421$	460.821			1.09459			0.547293	−	0.836941i	$-0.315658\pi$
$421$	460.821			1.09459			0.547293	+	0.836941i	$0.315658\pi$
$422$			134.499i			0.318718i
$423$	−225.453	+	498.204i	−0.532987	+	1.17779i
$424$	59.8728			0.141210
$425$			3.85369i			0.00906751i
$426$	224.625	+	48.4596i	0.527289	+	0.113755i
$427$	−8.93014			−0.0209137
$428$			342.410i			0.800024i
$429$	131.162	−	607.977i	0.305739	−	1.41719i
$430$	42.8999			0.0997671
$431$		−	479.527i		−	1.11259i	−0.830985	−	0.556296i	$-0.812222\pi$
$431$		−	479.527i		−	1.11259i	0.830985	−	0.556296i	$-0.187778\pi$
$432$	393.840	+	291.665i	0.911666	+	0.675150i
$433$	−414.291			−0.956792			−0.478396	−	0.878144i	$-0.658782\pi$
$433$	−414.291			−0.956792			−0.478396	+	0.878144i	$0.658782\pi$
$434$		−	110.036i		−	0.253539i
$435$	−106.450	−	22.9650i	−0.244712	−	0.0527931i
$436$	−222.739			−0.510870
$437$		−	129.786i		−	0.296994i
$438$	93.2044	−	432.031i	0.212795	−	0.986372i
$439$	517.906			1.17974			0.589871	−	0.807498i	$-0.299179\pi$
$439$	517.906			1.17974			0.589871	+	0.807498i	$0.299179\pi$
$440$			50.9031i			0.115689i
$441$	57.3965	+	25.9738i	0.130151	+	0.0588975i
$442$	−9.62417			−0.0217741
$443$			646.657i			1.45972i	0.683595	+	0.729861i	$0.260415\pi$
$443$			646.657i			1.45972i	−0.683595	+	0.729861i	$0.739585\pi$
$444$	61.4917	+	13.2659i	0.138495	+	0.0298782i
$445$	228.910			0.514404
$446$			1069.04i			2.39696i
$447$	−73.2298	+	339.443i	−0.163825	+	0.759379i
$448$	111.477			0.248833
$449$			586.052i			1.30524i	0.757686	+	0.652619i	$0.226330\pi$
$449$			586.052i			1.30524i	−0.757686	+	0.652619i	$0.773670\pi$
$450$	190.567	−	421.113i	0.423483	−	0.935807i
$451$	−322.927			−0.716025
$452$		−	121.660i		−	0.269158i
$453$	−180.820	−	39.0092i	−0.399160	−	0.0861130i
$454$	205.115			0.451796
$455$			113.588i			0.249644i
$456$	29.7383	−	137.846i	0.0652155	−	0.302294i
$457$	190.005			0.415765			0.207882	−	0.978154i	$-0.433343\pi$
$457$	190.005			0.415765			0.207882	+	0.978154i	$0.433343\pi$
$458$		−	198.697i		−	0.433837i
$459$	3.27098	−	4.41686i	0.00712632	−	0.00962278i
$460$	−39.6934			−0.0862900
$461$		−	162.346i		−	0.352161i	−0.984376	−	0.176081i	$-0.943658\pi$
$461$		−	162.346i		−	0.352161i	0.984376	−	0.176081i	$-0.0563419\pi$
$462$	250.399	+	54.0199i	0.541988	+	0.116926i
$463$	−648.331			−1.40028			−0.700141	−	0.714004i	$-0.746880\pi$
$463$	−648.331			−1.40028			−0.700141	+	0.714004i	$0.746880\pi$
$464$		−	267.459i		−	0.576419i
$465$	−23.8928	+	110.751i	−0.0513824	+	0.238173i
$466$	409.877			0.879565
$467$		−	164.780i		−	0.352848i	−0.984314	−	0.176424i	$-0.943547\pi$
$467$		−	164.780i		−	0.352848i	0.984314	−	0.176424i	$-0.0564530\pi$
$468$	480.097	+	217.259i	1.02585	+	0.464229i
$469$	−166.737			−0.355516
$470$		−	406.068i		−	0.863975i
$471$	−105.811	−	22.8271i	−0.224651	−	0.0484652i
$472$	−13.6648			−0.0289508
$473$			76.3634i			0.161445i
$474$	45.2774	−	209.875i	0.0955219	−	0.442773i
$475$	−512.324			−1.07858
$476$		−	1.80947i		−	0.00380141i
$477$	−127.903	+	282.638i	−0.268140	+	0.592532i
$478$	−1094.26			−2.28924
$479$			460.802i			0.962009i	0.876718	+	0.481004i	$0.159728\pi$
$479$			460.802i			0.962009i	−0.876718	+	0.481004i	$0.840272\pi$
$480$	−305.542	−	65.9162i	−0.636545	−	0.137325i
$481$	−108.768			−0.226130
$482$		−	1098.84i		−	2.27975i
$483$	8.02745	−	37.2097i	0.0166200	−	0.0770387i
$484$	68.9414			0.142441
$485$			419.005i			0.863927i
$486$	−575.854	+	320.901i	−1.18488	+	0.660291i
$487$	−772.371			−1.58598			−0.792989	−	0.609236i	$-0.791476\pi$
$487$	−772.371			−1.58598			−0.792989	+	0.609236i	$0.791476\pi$
$488$			5.86268i			0.0120137i
$489$	771.672	+	166.477i	1.57806	+	0.340444i
$490$	−46.7819			−0.0954732
$491$			718.102i			1.46253i	0.682093	+	0.731265i	$0.261070\pi$
$491$			718.102i			1.46253i	−0.682093	+	0.731265i	$0.738930\pi$
$492$	57.6988	−	267.452i	0.117274	−	0.543601i
$493$	−2.99951			−0.00608420
$494$		−	1279.47i		−	2.59003i
$495$	−240.295	−	108.741i	−0.485444	−	0.219679i
$496$	−278.265			−0.561017
$497$		−	74.7022i		−	0.150306i
$498$	55.1841	+	11.9052i	0.110812	+	0.0239060i
$499$	357.562			0.716557			0.358278	−	0.933615i	$-0.383364\pi$
$499$	357.562			0.716557			0.358278	+	0.933615i	$0.383364\pi$
$500$			363.603i			0.727207i
$501$	−193.245	+	895.751i	−0.385719	+	1.78793i
$502$	−271.783			−0.541401
$503$		−	815.005i		−	1.62029i	−0.586231	−	0.810144i	$-0.699389\pi$
$503$		−	815.005i		−	1.62029i	0.586231	−	0.810144i	$-0.300611\pi$
$504$	17.0519	−	37.6811i	0.0338332	−	0.0747641i
$505$	−45.6309			−0.0903582
$506$		−	154.776i		−	0.305882i
$507$	−395.065	−	85.2295i	−0.779221	−	0.168105i
$508$	−128.072			−0.252110
$509$			113.144i			0.222287i	0.993804	+	0.111143i	$0.0354513\pi$
$509$			113.144i			0.222287i	−0.993804	+	0.111143i	$0.964549\pi$
$510$	−0.860678	+	3.98951i	−0.00168760	+	0.00782257i
$511$	−143.678			−0.281170
$512$		−	641.574i		−	1.25307i
$513$	587.193	+	434.856i	1.14463	+	0.847673i
$514$	−782.333			−1.52205
$515$		−	160.036i		−	0.310749i
$516$	−63.2448	−	13.6442i	−0.122568	−	0.0264422i
$517$	722.816			1.39810
$518$		−	44.7969i		−	0.0864805i
$519$	178.587	−	827.804i	0.344098	−	1.59500i
$520$	74.5711			0.143406
$521$		−	765.070i		−	1.46846i	−0.678898	−	0.734232i	$-0.737542\pi$
$521$		−	765.070i		−	1.46846i	0.678898	−	0.734232i	$-0.262458\pi$
$522$	327.772	+	148.328i	0.627916	+	0.284153i
$523$	−210.103			−0.401727			−0.200863	−	0.979619i	$-0.564375\pi$
$523$	−210.103			−0.401727			−0.200863	+	0.979619i	$0.564375\pi$
$524$			678.659i			1.29515i
$525$	−146.883	−	31.6879i	−0.279778	−	0.0603579i
$526$	−1377.29			−2.61843
$527$			3.12070i			0.00592163i
$528$	136.608	−	633.220i	0.258727	−	1.19928i
$529$	−23.0000			−0.0434783
$530$		−	230.368i		−	0.434657i
$531$	29.1913	−	64.5064i	0.0549741	−	0.121481i
$532$	240.558			0.452176
$533$			473.077i			0.887573i
$534$	−739.249	−	159.482i	−1.38436	−	0.298656i
$535$	−251.067			−0.469284
$536$			109.464i			0.204224i
$537$	−159.658	+	740.063i	−0.297314	+	1.37814i
$538$	−547.168			−1.01704
$539$		−	83.2735i		−	0.154496i
$540$	132.995	−	179.585i	0.246287	−	0.332565i
$541$	367.908			0.680052			0.340026	−	0.940416i	$-0.389564\pi$
$541$	367.908			0.680052			0.340026	+	0.940416i	$0.389564\pi$
$542$		−	1118.83i		−	2.06426i
$543$	999.699	+	215.670i	1.84107	+	0.397183i
$544$	−8.60946			−0.0158262
$545$		−	163.320i		−	0.299670i
$546$	79.1371	−	366.825i	0.144940	−	0.671840i
$547$	−569.598			−1.04131			−0.520656	−	0.853766i	$-0.674313\pi$
$547$	−569.598			−1.04131			−0.520656	+	0.853766i	$0.674313\pi$
$548$			173.580i			0.316752i
$549$	−27.6756	−	12.5241i	−0.0504109	−	0.0228126i
$550$	−610.970			−1.11085
$551$		−	398.766i		−	0.723713i
$552$	−24.4283	−	5.27006i	−0.0442542	−	0.00954721i
$553$	−69.7966			−0.126215
$554$		−	466.158i		−	0.841440i
$555$	−9.72704	+	45.0878i	−0.0175262	+	0.0812393i
$556$	551.313			0.991570
$557$			107.533i			0.193057i	0.995330	+	0.0965283i	$0.0307738\pi$
$557$			107.533i			0.193057i	−0.995330	+	0.0965283i	$0.969226\pi$
$558$	154.320	−	341.015i	0.276560	−	0.611138i
$559$	111.869			0.200124
$560$			118.304i			0.211258i
$561$	−7.10147	−	1.53204i	−0.0126586	−	0.00273091i
$562$	1050.33			1.86891
$563$			317.566i			0.564061i	0.959405	+	0.282031i	$0.0910080\pi$
$563$			317.566i			0.564061i	−0.959405	+	0.282031i	$0.908992\pi$
$564$	−129.149	+	598.643i	−0.228987	+	1.06142i
$565$	89.2049			0.157885
$566$		−	872.017i		−	1.54067i
$567$	141.452	+	160.992i	0.249474	+	0.283936i
$568$	−49.0423			−0.0863421
$569$			381.386i			0.670275i	0.942169	+	0.335137i	$0.108783\pi$
$569$			381.386i			0.670275i	−0.942169	+	0.335137i	$0.891217\pi$
$570$	−530.380	−	114.422i	−0.930491	−	0.200740i
$571$	327.683			0.573875			0.286938	−	0.957949i	$-0.407363\pi$
$571$	327.683			0.573875			0.286938	+	0.957949i	$0.407363\pi$
$572$		−	696.546i		−	1.21774i
$573$	−164.601	+	762.976i	−0.287262	+	1.33155i
$574$	−194.839			−0.339441
$575$			90.7913i			0.157898i
$576$	345.482	+	156.342i	0.599794	+	0.271427i
$577$	555.461			0.962670			0.481335	−	0.876537i	$-0.340152\pi$
$577$	555.461			0.962670			0.481335	+	0.876537i	$0.340152\pi$
$578$		−	783.911i		−	1.35625i
$579$	780.164	+	168.309i	1.34743	+	0.290689i
$580$	−121.957			−0.210271
$581$		−	18.3522i		−	0.0315873i
$582$	291.922	−	1353.15i	0.501583	−	2.32499i
$583$	410.064			0.703369
$584$			94.3251i			0.161516i
$585$	−159.302	+	352.023i	−0.272311	+	0.601749i
$586$	1246.36			2.12690
$587$		−	819.154i		−	1.39549i	−0.716345	−	0.697747i	$-0.754186\pi$
$587$		−	819.154i		−	1.39549i	0.716345	−	0.697747i	$-0.245814\pi$
$588$	68.9679	+	14.8788i	0.117292	+	0.0253041i
$589$	−414.877			−0.704375
$590$			52.5769i			0.0891134i
$591$	−86.3976	+	400.479i	−0.146189	+	0.677630i
$592$	−113.285			−0.191359
$593$		−	476.584i		−	0.803684i	−0.915709	−	0.401842i	$-0.868370\pi$
$593$		−	476.584i		−	0.803684i	0.915709	−	0.401842i	$-0.131630\pi$
$594$	700.255	+	518.586i	1.17888	+	0.873041i
$595$	1.32677			0.00222986
$596$			388.892i			0.652504i
$597$	−103.776	−	22.3881i	−0.173829	−	0.0375011i
$598$	−226.741			−0.379166
$599$			1095.07i			1.82816i	0.405532	+	0.914081i	$0.367086\pi$
$599$			1095.07i			1.82816i	−0.405532	+	0.914081i	$0.632914\pi$
$600$	−20.8033	+	96.4295i	−0.0346721	+	0.160716i
$601$	−225.787			−0.375686			−0.187843	−	0.982199i	$-0.560150\pi$
$601$	−225.787			−0.375686			−0.187843	+	0.982199i	$0.560150\pi$
$602$			46.0741i			0.0765350i
$603$	−516.739	−	233.841i	−0.856947	−	0.387796i
$604$	−207.161			−0.342982
$605$			50.5502i			0.0835540i
$606$	147.362	+	31.7912i	0.243171	+	0.0524607i
$607$	1126.99			1.85666			0.928329	−	0.371761i	$-0.121246\pi$
$607$	1126.99			1.85666			0.928329	+	0.371761i	$0.121246\pi$
$608$		−	1144.57i		−	1.88252i
$609$	24.6642	−	114.326i	0.0404995	−	0.187728i
$610$	22.5574			0.0369793
$611$		−	1058.90i		−	1.73306i
$612$	2.53770	−	5.60777i	0.00414657	−	0.00916302i
$613$	486.028			0.792868			0.396434	−	0.918063i	$-0.370248\pi$
$613$	486.028			0.792868			0.396434	+	0.918063i	$0.370248\pi$
$614$		−	271.487i		−	0.442161i
$615$	196.105	+	42.3067i	0.318869	+	0.0687914i
$616$	−54.6694			−0.0887491
$617$		−	825.783i		−	1.33838i	−0.743089	−	0.669192i	$-0.766640\pi$
$617$		−	825.783i		−	1.33838i	0.743089	−	0.669192i	$-0.233360\pi$
$618$	−111.497	+	516.824i	−0.180416	+	0.836285i
$619$	666.565			1.07684			0.538421	−	0.842676i	$-0.319021\pi$
$619$	666.565			1.07684			0.538421	+	0.842676i	$0.319021\pi$
$620$			126.885i			0.204653i
$621$	77.0629	−	104.059i	0.124095	−	0.167567i
$622$	1259.32			2.02463
$623$			245.847i			0.394618i
$624$	−927.644	−	200.126i	−1.48661	−	0.320714i
$625$	206.676			0.330681
$626$			1071.31i			1.71136i
$627$	203.675	−	944.096i	0.324840	−	1.50574i
$628$	−121.225			−0.193033
$629$			1.27047i			0.00201983i
$630$	−144.983	−	65.6094i	−0.230131	−	0.104142i
$631$	−977.985			−1.54990			−0.774949	−	0.632024i	$-0.782224\pi$
$631$	−977.985			−1.54990			−0.774949	+	0.632024i	$0.782224\pi$
$632$			45.8218i			0.0725029i
$633$	145.389	+	31.3655i	0.229682	+	0.0495505i
$634$	−717.299			−1.13139
$635$		−	93.9065i		−	0.147884i
$636$	−73.2678	+	339.619i	−0.115201	+	0.533992i
$637$	−121.993			−0.191511
$638$		−	475.547i		−	0.745371i
$639$	104.766	−	231.511i	0.163953	−	0.362302i
$640$	135.172			0.211206
$641$			106.244i			0.165747i	0.996560	+	0.0828737i	$0.0264098\pi$
$641$			106.244i			0.165747i	−0.996560	+	0.0828737i	$0.973590\pi$
$642$	810.803	+	174.919i	1.26293	+	0.272459i
$643$	360.637			0.560866			0.280433	−	0.959874i	$-0.409522\pi$
$643$	360.637			0.560866			0.280433	+	0.959874i	$0.409522\pi$
$644$		−	42.6303i		−	0.0661962i
$645$	10.0044	−	46.3733i	0.0155106	−	0.0718965i
$646$	−14.9449			−0.0231345
$647$		−	143.629i		−	0.221992i	−0.993821	−	0.110996i	$-0.964596\pi$
$647$		−	143.629i		−	0.221992i	0.993821	−	0.110996i	$-0.0354041\pi$
$648$	105.692	−	92.8638i	0.163105	−	0.143308i
$649$	−93.5889			−0.144205
$650$			895.049i			1.37700i
$651$	−118.945	−	25.6607i	−0.182711	−	0.0394173i
$652$	884.089			1.35596
$653$			655.723i			1.00417i	0.864818	+	0.502085i	$0.167433\pi$
$653$			655.723i			1.00417i	−0.864818	+	0.502085i	$0.832567\pi$
$654$	−113.785	+	527.431i	−0.173984	+	0.806469i
$655$	−497.616			−0.759718
$656$			492.719i			0.751096i
$657$	−445.275	−	201.501i	−0.677739	−	0.306699i
$658$	436.113			0.662786
$659$			65.0443i			0.0987015i	0.998782	+	0.0493507i	$0.0157152\pi$
$659$			65.0443i			0.0987015i	−0.998782	+	0.0493507i	$0.984285\pi$
$660$	−288.739	−	62.2913i	−0.437484	−	0.0943807i
$661$	−238.965			−0.361521			−0.180760	−	0.983527i	$-0.557856\pi$
$661$	−238.965			−0.361521			−0.180760	+	0.983527i	$0.557856\pi$
$662$			375.715i			0.567545i
$663$	−2.24438	+	10.4034i	−0.00338519	+	0.0156914i
$664$	−12.0483			−0.0181451
$665$			176.385i			0.265241i
$666$	62.8256	−	138.831i	0.0943327	−	0.208455i
$667$	−70.6671			−0.105948
$668$			1026.24i			1.53629i
$669$	1155.60	+	249.304i	1.72735	+	0.372652i
$670$	421.176			0.628620
$671$			40.1530i			0.0598405i
$672$	70.7934	−	328.149i	0.105347	−	0.488317i
$673$	−353.825			−0.525744			−0.262872	−	0.964831i	$-0.584670\pi$
$673$	−353.825			−0.525744			−0.262872	+	0.964831i	$0.584670\pi$
$674$		−	454.277i		−	0.674001i
$675$	−410.768	−	304.201i	−0.608545	−	0.450669i
$676$	−452.617			−0.669552
$677$		−	746.674i		−	1.10292i	−0.834203	−	0.551458i	$-0.814072\pi$
$677$		−	746.674i		−	1.10292i	0.834203	−	0.551458i	$-0.185928\pi$
$678$	−288.081	−	62.1493i	−0.424898	−	0.0916656i
$679$	−450.007			−0.662750
$680$		−	0.871028i		−	0.00128092i
$681$	47.8334	−	221.723i	0.0702400	−	0.325584i
$682$	−494.760			−0.725455
$683$		−	1170.89i		−	1.71433i	−0.515044	−	0.857164i	$-0.672224\pi$
$683$		−	1170.89i		−	1.71433i	0.515044	−	0.857164i	$-0.327776\pi$
$684$	745.518	+	337.371i	1.08994	+	0.493232i
$685$	−127.275			−0.185802
$686$		−	50.2433i		−	0.0732410i
$687$	−214.785	−	46.3367i	−0.312642	−	0.0674479i
$688$	116.514			0.169352
$689$		−	600.728i		−	0.871884i
$690$	−20.2772	+	93.9910i	−0.0293872	+	0.136219i
$691$	739.843			1.07069			0.535343	−	0.844635i	$-0.320183\pi$
$691$	739.843			1.07069			0.535343	+	0.844635i	$0.320183\pi$
$692$		−	948.397i		−	1.37052i
$693$	116.787	−	258.075i	0.168524	−	0.372402i
$694$	1104.92			1.59210
$695$			404.241i			0.581642i
$696$	−75.0556	−	16.1922i	−0.107839	−	0.0232646i
$697$	5.52577			0.00792794
$698$		−	381.855i		−	0.547070i
$699$	95.5844	−	443.063i	0.136745	−	0.633853i
$700$	−168.281			−0.240401
$701$		−	941.941i		−	1.34371i	−0.740683	−	0.671855i	$-0.765498\pi$
$701$		−	941.941i		−	1.34371i	0.740683	−	0.671855i	$-0.234502\pi$
$702$	759.710	−	1025.85i	1.08221	−	1.46132i
$703$	−168.901			−0.240257
$704$		−	501.240i		−	0.711989i
$705$	−438.945	−	94.6961i	−0.622618	−	0.134321i
$706$	994.137			1.40813
$707$		−	49.0072i		−	0.0693171i
$708$	16.7219	−	77.5112i	0.0236185	−	0.109479i
$709$	−637.979			−0.899829			−0.449914	−	0.893072i	$-0.648546\pi$
$709$	−637.979			−0.899829			−0.449914	+	0.893072i	$0.648546\pi$
$710$			188.696i			0.265770i
$711$	−216.308	−	97.8865i	−0.304231	−	0.137674i
$712$	161.400			0.226685
$713$			73.5222i			0.103117i
$714$	−4.28470	−	0.924361i	−0.00600098	−	0.00129462i
$715$	510.731			0.714309
$716$			847.875i			1.18418i
$717$	−255.184	+	1182.86i	−0.355905	+	1.64973i
$718$	−1019.08			−1.41933
$719$		−	537.161i		−	0.747094i	−0.927611	−	0.373547i	$-0.878141\pi$
$719$		−	537.161i		−	0.747094i	0.927611	−	0.373547i	$-0.121859\pi$
$720$	−165.916	+	366.639i	−0.230439	+	0.509221i
$721$	171.877			0.238387
$722$		−	1007.48i		−	1.39540i
$723$	−1187.81	−	256.252i	−1.64289	−	0.354429i
$724$	1145.33			1.58195
$725$			278.955i			0.384765i
$726$	35.2184	−	163.248i	0.0485102	−	0.224860i
$727$	−427.656			−0.588248			−0.294124	−	0.955767i	$-0.595028\pi$
$727$	−427.656			−0.588248			−0.294124	+	0.955767i	$0.595028\pi$
$728$			80.0887i			0.110012i
$729$	212.593	+	697.313i	0.291622	+	0.956534i
$730$	362.928			0.497161
$731$		−	1.30669i		−	0.00178754i
$732$	−33.2551	−	7.17430i	−0.0454304	−	0.00980095i
$733$	312.467			0.426285			0.213143	−	0.977021i	$-0.431630\pi$
$733$	312.467			0.426285			0.213143	+	0.977021i	$0.431630\pi$
$734$			1409.79i			1.92069i
$735$	−10.9097	+	50.5696i	−0.0148431	+	0.0688021i
$736$	−202.835			−0.275591
$737$			749.708i			1.01724i
$738$	−603.831	−	273.253i	−0.818199	−	0.370262i
$739$	−958.939			−1.29762			−0.648809	−	0.760951i	$-0.724732\pi$
$739$	−958.939			−1.29762			−0.648809	+	0.760951i	$0.724732\pi$
$740$			51.6561i			0.0698056i
$741$	−1383.07	−	298.376i	−1.86648	−	0.402667i
$742$	247.413			0.333441
$743$			1477.85i			1.98903i	0.104587	+	0.994516i	$0.466648\pi$
$743$			1477.85i			1.98903i	−0.104587	+	0.994516i	$0.533352\pi$
$744$	−16.8464	+	78.0881i	−0.0226430	+	0.104957i
$745$	−285.149			−0.382750
$746$			329.726i			0.441992i
$747$	25.7382	−	56.8758i	0.0344554	−	0.0761390i
$748$	−8.13601			−0.0108770
$749$		−	269.644i		−	0.360005i
$750$	860.987	+	185.745i	1.14798	+	0.247660i
$751$	−305.724			−0.407089			−0.203544	−	0.979066i	$-0.565246\pi$
$751$	−305.724			−0.407089			−0.203544	+	0.979066i	$0.565246\pi$
$752$		−	1102.86i		−	1.46658i
$753$	−63.3805	+	293.788i	−0.0841707	+	0.390157i
$754$	−696.658			−0.923950
$755$		−	151.898i		−	0.201189i
$756$	192.873	+	142.835i	0.255123	+	0.188936i
$757$	−987.031			−1.30387			−0.651936	−	0.758274i	$-0.726043\pi$
$757$	−987.031			−1.30387			−0.651936	+	0.758274i	$0.726043\pi$
$758$			2005.04i			2.64517i
$759$	−167.308	−	36.0942i	−0.220432	−	0.0475549i
$760$	115.798			0.152365
$761$		−	6.19475i		−	0.00814028i	−0.999992	−	0.00407014i	$-0.998704\pi$
$761$		−	6.19475i		−	0.00814028i	0.999992	−	0.00407014i	$-0.00129557\pi$
$762$	−65.4249	+	303.265i	−0.0858595	+	0.397985i
$763$	175.404			0.229888
$764$			874.125i			1.14414i
$765$	4.11181	+	1.86073i	0.00537491	+	0.00243232i
$766$	−809.414			−1.05668
$767$			137.104i			0.178754i
$768$	−930.770	−	200.800i	−1.21194	−	0.261459i
$769$	1302.35			1.69357			0.846784	−	0.531936i	$-0.178535\pi$
$769$	1302.35			1.69357			0.846784	+	0.531936i	$0.178535\pi$
$770$			210.347i			0.273179i
$771$	−182.442	+	845.675i	−0.236630	+	1.09685i
$772$	893.818			1.15779
$773$			889.502i			1.15071i	0.817903	+	0.575357i	$0.195137\pi$
$773$			889.502i			1.15071i	−0.817903	+	0.575357i	$0.804863\pi$
$774$	−64.6167	+	142.789i	−0.0834842	+	0.184482i
$775$	290.225			0.374484
$776$			295.432i			0.380711i
$777$	−48.4239	−	10.4468i	−0.0623216	−	0.0134450i
$778$	1029.11			1.32276
$779$			734.617i			0.943025i
$780$	−91.2544	+	422.992i	−0.116993	+	0.542298i
$781$	−335.887			−0.430073
$782$			2.64845i			0.00338677i
$783$	236.774	−	319.720i	0.302394	−	0.408327i
$784$	−127.058			−0.162063
$785$		−	88.8863i		−	0.113231i
$786$	1607.01	+	346.690i	2.04455	+	0.441081i
$787$	744.117			0.945511			0.472756	−	0.881194i	$-0.343259\pi$
$787$	744.117			0.945511			0.472756	+	0.881194i	$0.343259\pi$
$788$			458.821i			0.582260i
$789$	−321.188	+	1488.80i	−0.407082	+	1.88695i
$790$	176.305			0.223171
$791$			95.8053i			0.121119i
$792$	−169.427	−	76.6713i	−0.213923	−	0.0968073i
$793$	58.8226			0.0741773
$794$			520.530i			0.655580i
$795$	−249.020	−	53.7224i	−0.313233	−	0.0675754i
$796$	−118.894			−0.149364
$797$			254.923i			0.319854i	0.987129	+	0.159927i	$0.0511258\pi$
$797$			254.923i			0.319854i	−0.987129	+	0.159927i	$0.948874\pi$
$798$	122.888	−	569.623i	0.153995	−	0.713814i
$799$	−12.3685			−0.0154799
$800$			800.681i			1.00085i
$801$	−344.789	+	761.910i	−0.430449	+	0.951199i
$802$	−1768.47			−2.20508
$803$			646.025i			0.804514i
$804$	−620.915	−	133.953i	−0.772283	−	0.166609i
$805$	31.2580			0.0388298
$806$			724.805i			0.899262i
$807$	−127.601	+	591.470i	−0.158118	+	0.732924i
$808$	−32.1735			−0.0398186
$809$			318.703i			0.393947i	0.980409	+	0.196974i	$0.0631113\pi$
$809$			318.703i			0.393947i	−0.980409	+	0.196974i	$0.936889\pi$
$810$	−357.305	−	406.663i	−0.441117	−	0.502053i
$811$	−472.259			−0.582317			−0.291158	−	0.956675i	$-0.594041\pi$
$811$	−472.259			−0.582317			−0.291158	+	0.956675i	$0.594041\pi$
$812$		−	130.981i		−	0.161307i
$813$	−1209.41	−	260.914i	−1.48760	−	0.320927i
$814$	−201.422			−0.247448
$815$			648.244i			0.795391i
$816$	−2.33757	+	10.8353i	−0.00286467	+	0.0132786i
$817$	173.716			0.212627
$818$			100.255i			0.122561i
$819$	−378.070	−	171.089i	−0.461624	−	0.208900i
$820$	224.673			0.273991
$821$			958.561i			1.16755i	0.811914	+	0.583776i	$0.198426\pi$
$821$			958.561i			1.16755i	−0.811914	+	0.583776i	$0.801574\pi$
$822$	411.025	+	88.6726i	0.500030	+	0.107874i
$823$	−195.658			−0.237737			−0.118869	−	0.992910i	$-0.537927\pi$
$823$	−195.658			−0.237737			−0.118869	+	0.992910i	$0.537927\pi$
$824$		−	112.838i		−	0.136939i
$825$	−142.480	+	660.438i	−0.172703	+	0.800530i
$826$	−56.4671			−0.0683621
$827$			1140.23i			1.37876i	0.724401	+	0.689379i	$0.242117\pi$
$827$			1140.23i			1.37876i	−0.724401	+	0.689379i	$0.757883\pi$
$828$	59.7871	−	132.117i	0.0722066	−	0.159561i
$829$	175.521			0.211726			0.105863	−	0.994381i	$-0.466240\pi$
$829$	175.521			0.211726			0.105863	+	0.994381i	$0.466240\pi$
$830$			46.3575i			0.0558524i
$831$	−503.901	−	108.709i	−0.606379	−	0.130817i
$832$	−734.298			−0.882570
$833$			1.42493i			0.00171061i
$834$	281.636	−	1305.47i	0.337693	−	1.56531i
$835$	−752.476			−0.901169
$836$		−	1081.63i		−	1.29382i
$837$	−332.638	−	246.341i	−0.397417	−	0.294314i
$838$	−1904.31			−2.27245
$839$		−	496.368i		−	0.591618i	−0.955247	−	0.295809i	$-0.904411\pi$
$839$		−	496.368i		−	0.591618i	0.955247	−	0.295809i	$-0.0955893\pi$
$840$	33.1992	+	7.16224i	0.0395228	+	0.00852647i
$841$	623.877			0.741827
$842$		−	1250.15i		−	1.48474i
$843$	244.939	−	1135.37i	0.290556	−	1.34682i
$844$	166.569			0.197356
$845$		−	331.874i		−	0.392751i
$846$	1351.57	+	611.629i	1.59760	+	0.722965i
$847$	−54.2904			−0.0640973
$848$		−	625.671i		−	0.737819i
$849$	−942.620	−	203.356i	−1.11027	−	0.239525i
$850$	10.4546			0.0122996
$851$			29.9317i			0.0351724i
$852$	60.0142	−	278.184i	0.0704393	−	0.326508i
$853$	463.297			0.543138			0.271569	−	0.962419i	$-0.412457\pi$
$853$	463.297			0.543138			0.271569	+	0.962419i	$0.412457\pi$
$854$			24.2264i			0.0283682i
$855$	−247.372	+	546.639i	−0.289324	+	0.639344i
$856$	−177.022			−0.206802
$857$		−	222.851i		−	0.260036i	−0.991512	−	0.130018i	$-0.958496\pi$
$857$		−	222.851i		−	0.260036i	0.991512	−	0.130018i	$-0.0415036\pi$
$858$	−1649.37	−	355.828i	−1.92234	−	0.414717i
$859$	794.060			0.924400			0.462200	−	0.886776i	$-0.347060\pi$
$859$	794.060			0.924400			0.462200	+	0.886776i	$0.347060\pi$
$860$		−	53.1289i		−	0.0617777i
$861$	−45.4370	+	210.615i	−0.0527724	+	0.244616i
$862$	−1300.90			−1.50917
$863$			1099.90i			1.27451i	0.770652	+	0.637256i	$0.219931\pi$
$863$			1099.90i			1.27451i	−0.770652	+	0.637256i	$0.780069\pi$
$864$	679.611	−	917.690i	0.786587	−	1.06214i
$865$	695.397			0.803927
$866$			1123.92i			1.29783i
$867$	−847.381	−	182.810i	−0.977371	−	0.210854i
$868$	−136.273			−0.156996
$869$			313.830i			0.361139i
$870$	−62.3014	+	288.786i	−0.0716107	+	0.331938i
$871$	1098.29			1.26096
$872$		−	115.154i		−	0.132057i
$873$	−1394.63	−	631.114i	−1.59751	−	0.722926i
$874$	−352.095			−0.402855
$875$		−	286.333i		−	0.327238i
$876$	−535.044	−	115.428i	−0.610780	−	0.131767i
$877$	602.030			0.686465			0.343233	−	0.939250i	$-0.388478\pi$
$877$	602.030			0.686465			0.343233	+	0.939250i	$0.388478\pi$
$878$		−	1405.02i		−	1.60025i
$879$	290.655	−	1347.28i	0.330666	−	1.53274i
$880$	531.937			0.604474
$881$		−	244.099i		−	0.277071i	−0.990357	−	0.138535i	$-0.955761\pi$
$881$		−	244.099i		−	0.277071i	0.990357	−	0.138535i	$-0.0442395\pi$
$882$	70.4639	−	155.710i	0.0798911	−	0.176542i
$883$	1191.85			1.34977			0.674885	−	0.737923i	$-0.264193\pi$
$883$	1191.85			1.34977			0.674885	+	0.737923i	$0.264193\pi$
$884$			11.9189i			0.0134830i
$885$	56.8338	+	12.2611i	0.0642190	+	0.0138543i
$886$	1754.31			1.98003
$887$			31.9382i			0.0360070i	0.999838	+	0.0180035i	$0.00573100\pi$
$887$			31.9382i			0.0360070i	−0.999838	+	0.0180035i	$0.994269\pi$
$888$	−6.85834	+	31.7905i	−0.00772336	+	0.0358001i
$889$	100.855			0.113447
$890$		−	621.006i		−	0.697760i
$891$	723.875	−	636.016i	0.812430	−	0.713823i
$892$	1323.95			1.48424
$893$		−	1644.31i		−	1.84133i
$894$	920.869	+	198.664i	1.03005	+	0.222219i
$895$	−621.691			−0.694626
$896$			145.173i			0.162024i
$897$	−52.8766	+	245.099i	−0.0589483	+	0.273243i
$898$	1589.89			1.77048
$899$			225.896i			0.251275i
$900$	−521.523	−	236.006i	−0.579470	−	0.262229i
$901$	−7.01681			−0.00778780
$902$			876.065i			0.971247i
$903$	49.8045	+	10.7446i	0.0551545	+	0.0118988i
$904$	62.8966			0.0695759
$905$			839.797i			0.927953i
$906$	−105.827	+	490.543i	−0.116807	+	0.541438i
$907$	712.067			0.785080			0.392540	−	0.919735i	$-0.371596\pi$
$907$	712.067			0.785080			0.392540	+	0.919735i	$0.371596\pi$
$908$		−	254.023i		−	0.279761i
$909$	68.7303	−	151.879i	0.0756109	−	0.167084i
$910$	308.151			0.338628
$911$			448.916i			0.492772i	0.969172	+	0.246386i	$0.0792431\pi$
$911$			448.916i			0.492772i	−0.969172	+	0.246386i	$0.920757\pi$
$912$	−1440.49	−	310.765i	−1.57949	−	0.340751i
$913$	−82.5180			−0.0903812
$914$		−	515.460i		−	0.563961i
$915$	5.26044	−	24.3837i	0.00574911	−	0.0266489i
$916$	−246.074			−0.268640
$917$		−	534.435i		−	0.582808i
$918$	−11.9824	−	8.87379i	−0.0130527	−	0.00966644i
$919$	−1385.55			−1.50767			−0.753836	−	0.657063i	$-0.771799\pi$
$919$	−1385.55			−1.50767			−0.753836	+	0.657063i	$0.771799\pi$
$920$		−	20.5210i		−	0.0223055i
$921$	−293.468	−	63.3114i	−0.318640	−	0.0687420i
$922$	−440.427			−0.477686
$923$			492.061i			0.533111i
$924$	66.9003	−	310.103i	0.0724029	−	0.335610i
$925$	118.154			0.127734
$926$			1758.85i			1.89940i
$927$	532.667	+	241.049i	0.574614	+	0.260032i
$928$	−623.208			−0.671560
$929$			136.819i			0.147275i	0.997285	+	0.0736375i	$0.0234608\pi$
$929$			136.819i			0.147275i	−0.997285	+	0.0736375i	$0.976539\pi$
$930$	300.454	+	64.8185i	0.323068	+	0.0696973i
$931$	−189.436			−0.203476
$932$		−	507.608i		−	0.544644i
$933$	293.676	−	1361.28i	0.314765	−	1.45903i
$934$	−447.029			−0.478618
$935$		−	5.96560i		−	0.00638032i
$936$	−112.321	+	248.205i	−0.120001	+	0.265176i
$937$	−1335.58			−1.42538			−0.712691	−	0.701479i	$-0.752524\pi$
$937$	−1335.58			−1.42538			−0.712691	+	0.701479i	$0.752524\pi$
$938$			452.339i			0.482238i
$939$	1158.05	+	249.833i	1.23328	+	0.266062i
$940$	−502.890			−0.534990
$941$		−	1376.63i		−	1.46295i	−0.681870	−	0.731474i	$-0.738833\pi$
$941$		−	1376.63i		−	1.46295i	0.681870	−	0.731474i	$-0.261167\pi$
$942$	−61.9273	+	287.052i	−0.0657402	+	0.304726i
$943$	130.185			0.138054
$944$			142.797i			0.151268i
$945$	−104.732	+	141.421i	−0.110827	+	0.149652i
$946$	207.165			0.218990
$947$		−	1402.18i		−	1.48066i	−0.672245	−	0.740328i	$-0.734670\pi$
$947$		−	1402.18i		−	1.48066i	0.672245	−	0.740328i	$-0.265330\pi$
$948$	−259.917	−	56.0732i	−0.274174	−	0.0591490i
$949$	946.402			0.997263
$950$			1389.88i			1.46303i
$951$	−167.276	+	775.376i	−0.175895	+	0.815327i
$952$	0.935476			0.000982643
$953$		−	542.925i		−	0.569701i	−0.958572	−	0.284850i	$-0.908056\pi$
$953$		−	542.925i		−	0.569701i	0.958572	−	0.284850i	$-0.0919439\pi$
$954$	766.764	+	346.986i	0.803736	+	0.363717i
$955$	−640.938			−0.671139
$956$			1355.17i			1.41754i
$957$	−514.050	−	110.899i	−0.537147	−	0.115882i
$958$	1250.10			1.30491
$959$		−	136.692i		−	0.142536i
$960$	−65.6674	+	304.389i	−0.0684036	+	0.317072i
$961$	−725.977			−0.755440
$962$			295.076i			0.306732i
$963$	378.163	−	835.658i	0.392692	−	0.867765i
$964$	−1360.85			−1.41167
$965$			655.377i			0.679148i
$966$	−100.946	−	21.7775i	−0.104498	−	0.0225440i
$967$	1738.32			1.79764			0.898819	−	0.438319i	$-0.144426\pi$
$967$	1738.32			1.79764			0.898819	+	0.438319i	$0.144426\pi$
$968$			35.6419i			0.0368202i
$969$	−3.48518	+	16.1549i	−0.00359668	+	0.0166717i
$970$	1136.71			1.17187
$971$			1322.19i			1.36168i	0.732434	+	0.680838i	$0.238384\pi$
$971$			1322.19i			1.36168i	−0.732434	+	0.680838i	$0.761616\pi$
$972$	397.417	+	713.160i	0.408865	+	0.733703i
$973$	−434.152			−0.446199
$974$			2095.35i			2.15129i
$975$	967.516	+	208.728i	0.992324	+	0.214080i
$976$	61.2650			0.0627715
$977$			48.0452i			0.0491762i	0.999698	+	0.0245881i	$0.00782743\pi$
$977$			48.0452i			0.0491762i	−0.999698	+	0.0245881i	$0.992173\pi$
$978$	451.633	−	2093.46i	0.461792	−	2.14055i
$979$	1105.41			1.12913
$980$			57.9365i			0.0591189i
$981$	543.599	+	245.996i	0.554127	+	0.250761i
$982$	1948.13			1.98384
$983$			389.609i			0.396347i	0.980167	+	0.198173i	$0.0635009\pi$
$983$			389.609i			0.396347i	−0.980167	+	0.198173i	$0.936499\pi$
$984$	138.269	+	29.8296i	0.140518	+	0.0303147i
$985$	−336.423			−0.341546
$986$			8.13732i			0.00825286i
$987$	101.703	−	471.423i	0.103042	−	0.477633i
$988$	−1584.55			−1.60379
$989$		−	30.7851i		−	0.0311275i
$990$	−295.003	+	651.892i	−0.297982	+	0.658477i
$991$	1947.58			1.96527			0.982633	−	0.185557i	$-0.0594090\pi$
$991$	1947.58			1.96527			0.982633	+	0.185557i	$0.0594090\pi$
$992$			648.387i			0.653616i
$993$	406.135	+	87.6176i	0.408998	+	0.0882353i
$994$	−202.658			−0.203882
$995$		−	87.1770i		−	0.0876151i
$996$	14.7438	−	68.3422i	0.0148030	−	0.0686166i
$997$	299.524			0.300426			0.150213	−	0.988654i	$-0.452004\pi$
$997$	299.524			0.300426			0.150213	+	0.988654i	$0.452004\pi$
$998$		−	970.024i		−	0.971968i
$999$	−135.420	−	100.288i	−0.135556	−	0.100388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.17	✓	88
3.2	odd	2	inner	483.3.b.a.323.72	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.17	✓	88	1.1	even	1	trivial
483.3.b.a.323.72	yes	88	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.71288i q^{2} +(-2.93253 - 0.632651i) q^{3} -3.35974 q^{4} -2.46348i q^{5} +(-1.71631 + 7.95562i) q^{6} +2.64575 q^{7} -1.73695i q^{8} +(8.19950 + 3.71054i) q^{9} -6.68313 q^{10} -11.8962i q^{11} +(9.85255 + 2.12554i) q^{12} -17.4275 q^{13} -7.17762i q^{14} +(-1.55852 + 7.22423i) q^{15} -18.1511 q^{16} +0.203562i q^{17} +(10.0663 - 22.2443i) q^{18} -27.0623 q^{19} +8.27664i q^{20} +(-7.75875 - 1.67384i) q^{21} -32.2730 q^{22} +4.79583i q^{23} +(-1.09888 + 5.09366i) q^{24} +18.9313 q^{25} +47.2788i q^{26} +(-21.6978 - 16.0687i) q^{27} -8.88904 q^{28} +14.7351i q^{29} +(19.5985 + 4.22809i) q^{30} +15.3304 q^{31} +42.2941i q^{32} +(-7.52615 + 34.8860i) q^{33} +0.552240 q^{34} -6.51774i q^{35} +(-27.5482 - 12.4665i) q^{36} +6.24119 q^{37} +73.4169i q^{38} +(51.1067 + 11.0255i) q^{39} -4.27893 q^{40} -27.1454i q^{41} +(-4.54093 + 21.0486i) q^{42} -6.41913 q^{43} +39.9682i q^{44} +(9.14083 - 20.1993i) q^{45} +13.0105 q^{46} +60.7602i q^{47} +(53.2287 + 11.4833i) q^{48} +7.00000 q^{49} -51.3584i q^{50} +(0.128784 - 0.596952i) q^{51} +58.5519 q^{52} +34.4701i q^{53} +(-43.5926 + 58.8637i) q^{54} -29.3060 q^{55} -4.59553i q^{56} +(79.3611 + 17.1210i) q^{57} +39.9746 q^{58} -7.86711i q^{59} +(5.23623 - 24.2715i) q^{60} -3.37527 q^{61} -41.5897i q^{62} +(21.6938 + 9.81717i) q^{63} +42.1344 q^{64} +42.9322i q^{65} +(94.6418 + 20.4176i) q^{66} -63.0208 q^{67} -0.683916i q^{68} +(3.03409 - 14.0639i) q^{69} -17.6819 q^{70} -28.2348i q^{71} +(6.44502 - 14.2421i) q^{72} -54.3051 q^{73} -16.9316i q^{74} +(-55.5166 - 11.9769i) q^{75} +90.9223 q^{76} -31.4744i q^{77} +(29.9110 - 138.647i) q^{78} -26.3806 q^{79} +44.7148i q^{80} +(53.4637 + 60.8492i) q^{81} -73.6423 q^{82} -6.93649i q^{83} +(26.0674 + 5.62366i) q^{84} +0.501470 q^{85} +17.4144i q^{86} +(9.32219 - 43.2112i) q^{87} -20.6631 q^{88} +92.9215i q^{89} +(-54.7983 - 24.7980i) q^{90} -46.1088 q^{91} -16.1128i q^{92} +(-44.9571 - 9.69883i) q^{93} +164.835 q^{94} +66.6673i q^{95} +(26.7574 - 124.029i) q^{96} -170.087 q^{97} -18.9902i q^{98} +(44.1414 - 97.5430i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30}+ \cdots - 248 q^{99}+O(q^{100}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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