LMFDB - Embedded newform 483.3.b.a.323.10

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			323.10
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.79

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.27803i q^{2} +(2.67440 + 1.35925i) q^{3} -6.74548 q^{4} +7.86031i q^{5} +(4.45568 - 8.76677i) q^{6} -2.64575 q^{7} +8.99976i q^{8} +(5.30485 + 7.27039i) q^{9} +O(q^{10})$	\(q-3.27803i q^{2} +(2.67440 + 1.35925i) q^{3} -6.74548 q^{4} +7.86031i q^{5} +(4.45568 - 8.76677i) q^{6} -2.64575 q^{7} +8.99976i q^{8} +(5.30485 + 7.27039i) q^{9} +25.7663 q^{10} -3.39386i q^{11} +(-18.0401 - 9.16882i) q^{12} -23.9904 q^{13} +8.67285i q^{14} +(-10.6842 + 21.0216i) q^{15} +2.51956 q^{16} +16.3389i q^{17} +(23.8325 - 17.3895i) q^{18} -31.6901 q^{19} -53.0216i q^{20} +(-7.07580 - 3.59625i) q^{21} -11.1252 q^{22} +4.79583i q^{23} +(-12.2330 + 24.0690i) q^{24} -36.7845 q^{25} +78.6413i q^{26} +(4.30499 + 26.6546i) q^{27} +17.8469 q^{28} -18.0976i q^{29} +(68.9095 + 35.0230i) q^{30} +1.17290 q^{31} +27.7398i q^{32} +(4.61312 - 9.07655i) q^{33} +53.5594 q^{34} -20.7964i q^{35} +(-35.7838 - 49.0422i) q^{36} +60.4140 q^{37} +103.881i q^{38} +(-64.1600 - 32.6091i) q^{39} -70.7409 q^{40} +46.8719i q^{41} +(-11.7886 + 23.1947i) q^{42} +8.34441 q^{43} +22.8932i q^{44} +(-57.1475 + 41.6978i) q^{45} +15.7209 q^{46} +10.6473i q^{47} +(6.73831 + 3.42472i) q^{48} +7.00000 q^{49} +120.581i q^{50} +(-22.2087 + 43.6968i) q^{51} +161.827 q^{52} -46.3640i q^{53} +(87.3745 - 14.1119i) q^{54} +26.6768 q^{55} -23.8111i q^{56} +(-84.7521 - 43.0749i) q^{57} -59.3244 q^{58} -40.6082i q^{59} +(72.0698 - 141.801i) q^{60} +49.0241 q^{61} -3.84480i q^{62} +(-14.0353 - 19.2356i) q^{63} +101.010 q^{64} -188.572i q^{65} +(-29.7532 - 15.1220i) q^{66} -67.3317 q^{67} -110.214i q^{68} +(-6.51876 + 12.8260i) q^{69} -68.1713 q^{70} +124.310i q^{71} +(-65.4317 + 47.7424i) q^{72} +26.8073 q^{73} -198.039i q^{74} +(-98.3766 - 49.9995i) q^{75} +213.765 q^{76} +8.97931i q^{77} +(-106.894 + 210.318i) q^{78} -82.1030 q^{79} +19.8045i q^{80} +(-24.7171 + 77.1367i) q^{81} +153.647 q^{82} +60.8160i q^{83} +(47.7297 + 24.2584i) q^{84} -128.429 q^{85} -27.3532i q^{86} +(24.5992 - 48.4002i) q^{87} +30.5439 q^{88} +14.3856i q^{89} +(136.687 + 187.331i) q^{90} +63.4727 q^{91} -32.3502i q^{92} +(3.13681 + 1.59427i) q^{93} +34.9022 q^{94} -249.094i q^{95} +(-37.7055 + 74.1875i) q^{96} +168.915 q^{97} -22.9462i q^{98} +(24.6747 - 18.0039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$		−	3.27803i		−	1.63901i	−0.573069	−	0.819507i	$-0.694247\pi$
$2$		−	3.27803i		−	1.63901i	0.573069	−	0.819507i	$-0.305753\pi$
$3$	2.67440	+	1.35925i	0.891467	+	0.453085i
$3$	2.67440	+	1.35925i	0.891467	+	0.453085i
$4$	−6.74548			−1.68637
$5$			7.86031i			1.57206i	0.618187	+	0.786031i	$0.287868\pi$
$5$			7.86031i			1.57206i	−0.618187	+	0.786031i	$0.712132\pi$
$6$	4.45568	−	8.76677i	0.742613	−	1.46113i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			8.99976i			1.12497i
$9$	5.30485	+	7.27039i	0.589428	+	0.807821i
$10$	25.7663			2.57663
$11$		−	3.39386i		−	0.308533i	−0.988029	−	0.154266i	$-0.950699\pi$
$11$		−	3.39386i		−	0.308533i	0.988029	−	0.154266i	$-0.0493014\pi$
$12$	−18.0401	−	9.16882i	−1.50334	−	0.764069i
$13$	−23.9904			−1.84542			−0.922708	−	0.385499i	$-0.874029\pi$
$13$	−23.9904			−1.84542			−0.922708	+	0.385499i	$0.874029\pi$
$14$			8.67285i			0.619489i
$15$	−10.6842	+	21.0216i	−0.712278	+	1.40144i
$16$	2.51956			0.157472
$17$			16.3389i			0.961111i	0.876964	+	0.480556i	$0.159565\pi$
$17$			16.3389i			0.961111i	−0.876964	+	0.480556i	$0.840435\pi$
$18$	23.8325	−	17.3895i	1.32403	−	0.966081i
$19$	−31.6901			−1.66790			−0.833950	−	0.551840i	$-0.813926\pi$
$19$	−31.6901			−1.66790			−0.833950	+	0.551840i	$0.813926\pi$
$20$		−	53.0216i		−	2.65108i
$21$	−7.07580	−	3.59625i	−0.336943	−	0.171250i
$22$	−11.1252			−0.505690
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−12.2330	+	24.0690i	−0.509707	+	1.00287i
$25$	−36.7845			−1.47138
$26$			78.6413i			3.02466i
$27$	4.30499	+	26.6546i	0.159444	+	0.987207i
$28$	17.8469			0.637388
$29$		−	18.0976i		−	0.624055i	−0.950073	−	0.312027i	$-0.898992\pi$
$29$		−	18.0976i		−	0.624055i	0.950073	−	0.312027i	$-0.101008\pi$
$30$	68.9095	+	35.0230i	2.29698	+	1.16743i
$31$	1.17290			0.0378355			0.0189178	−	0.999821i	$-0.493978\pi$
$31$	1.17290			0.0378355			0.0189178	+	0.999821i	$0.493978\pi$
$32$			27.7398i			0.866870i
$33$	4.61312	−	9.07655i	0.139792	−	0.275047i
$34$	53.5594			1.57528
$35$		−	20.7964i		−	0.594184i
$36$	−35.7838	−	49.0422i	−0.993993	−	1.36228i
$37$	60.4140			1.63281			0.816405	−	0.577480i	$-0.195964\pi$
$37$	60.4140			1.63281			0.816405	+	0.577480i	$0.195964\pi$
$38$			103.881i			2.73371i
$39$	−64.1600	−	32.6091i	−1.64513	−	0.836130i
$40$	−70.7409			−1.76852
$41$			46.8719i			1.14322i	0.820527	+	0.571608i	$0.193680\pi$
$41$			46.8719i			1.14322i	−0.820527	+	0.571608i	$0.806320\pi$
$42$	−11.7886	+	23.1947i	−0.280681	+	0.552255i
$43$	8.34441			0.194056			0.0970280	−	0.995282i	$-0.469066\pi$
$43$	8.34441			0.194056			0.0970280	+	0.995282i	$0.469066\pi$
$44$			22.8932i			0.520300i
$45$	−57.1475	+	41.6978i	−1.26995	+	0.926618i
$46$	15.7209			0.341758
$47$			10.6473i			0.226539i	0.993564	+	0.113269i	$0.0361323\pi$
$47$			10.6473i			0.226539i	−0.993564	+	0.113269i	$0.963868\pi$
$48$	6.73831	+	3.42472i	0.140381	+	0.0713484i
$49$	7.00000			0.142857
$50$			120.581i			2.41161i
$51$	−22.2087	+	43.6968i	−0.435465	+	0.856799i
$52$	161.827			3.11205
$53$		−	46.3640i		−	0.874793i	−0.899269	−	0.437397i	$-0.855901\pi$
$53$		−	46.3640i		−	0.874793i	0.899269	−	0.437397i	$-0.144099\pi$
$54$	87.3745	−	14.1119i	1.61805	−	0.261331i
$55$	26.6768			0.485033
$56$		−	23.8111i		−	0.425199i
$57$	−84.7521	−	43.0749i	−1.48688	−	0.755700i
$58$	−59.3244			−1.02284
$59$		−	40.6082i		−	0.688275i	−0.938919	−	0.344138i	$-0.888171\pi$
$59$		−	40.6082i		−	0.688275i	0.938919	−	0.344138i	$-0.111829\pi$
$60$	72.0698	−	141.801i	1.20116	−	2.36335i
$61$	49.0241			0.803673			0.401837	−	0.915711i	$-0.368372\pi$
$61$	49.0241			0.803673			0.401837	+	0.915711i	$0.368372\pi$
$62$		−	3.84480i		−	0.0620130i
$63$	−14.0353	−	19.2356i	−0.222783	−	0.305328i
$64$	101.010			1.57829
$65$		−	188.572i		−	2.90111i
$66$	−29.7532	−	15.1220i	−0.450806	−	0.229120i
$67$	−67.3317			−1.00495			−0.502475	−	0.864592i	$-0.667577\pi$
$67$	−67.3317			−1.00495			−0.502475	+	0.864592i	$0.667577\pi$
$68$		−	110.214i		−	1.62079i
$69$	−6.51876	+	12.8260i	−0.0944748	+	0.185884i
$70$	−68.1713			−0.973876
$71$			124.310i			1.75085i	0.483353	+	0.875426i	$0.339419\pi$
$71$			124.310i			1.75085i	−0.483353	+	0.875426i	$0.660581\pi$
$72$	−65.4317	+	47.7424i	−0.908774	+	0.663089i
$73$	26.8073			0.367224			0.183612	−	0.982999i	$-0.441221\pi$
$73$	26.8073			0.367224			0.183612	+	0.982999i	$0.441221\pi$
$74$		−	198.039i		−	2.67620i
$75$	−98.3766	−	49.9995i	−1.31169	−	0.666660i
$76$	213.765			2.81270
$77$			8.97931i			0.116614i
$78$	−106.894	+	210.318i	−1.37043	+	2.69639i
$79$	−82.1030			−1.03928			−0.519640	−	0.854386i	$-0.673934\pi$
$79$	−82.1030			−1.03928			−0.519640	+	0.854386i	$0.673934\pi$
$80$			19.8045i			0.247556i
$81$	−24.7171	+	77.1367i	−0.305149	+	0.952305i
$82$	153.647			1.87375
$83$			60.8160i			0.732723i	0.930473	+	0.366361i	$0.119397\pi$
$83$			60.8160i			0.732723i	−0.930473	+	0.366361i	$0.880603\pi$
$84$	47.7297	+	24.2584i	0.568210	+	0.288791i
$85$	−128.429			−1.51093
$86$		−	27.3532i		−	0.318061i
$87$	24.5992	−	48.4002i	0.282750	−	0.556325i
$88$	30.5439			0.347090
$89$			14.3856i			0.161636i	0.996729	+	0.0808180i	$0.0257533\pi$
$89$			14.3856i			0.161636i	−0.996729	+	0.0808180i	$0.974247\pi$
$90$	136.687	+	187.331i	1.51874	+	2.08146i
$91$	63.4727			0.697502
$92$		−	32.3502i		−	0.351632i
$93$	3.13681	+	1.59427i	0.0337291	+	0.0171427i
$94$	34.9022			0.371300
$95$		−	249.094i		−	2.62204i
$96$	−37.7055	+	74.1875i	−0.392766	+	0.772786i
$97$	168.915			1.74140			0.870698	−	0.491818i	$-0.163667\pi$
$97$	168.915			1.74140			0.870698	+	0.491818i	$0.163667\pi$
$98$		−	22.9462i		−	0.234145i
$99$	24.6747	−	18.0039i	0.249239	−	0.181858i
$100$	248.129			2.48129
$101$			44.2308i			0.437929i	0.975733	+	0.218964i	$0.0702679\pi$
$101$			44.2308i			0.437929i	−0.975733	+	0.218964i	$0.929732\pi$
$102$	143.239	+	72.8008i	1.40431	+	0.713734i
$103$	56.8851			0.552283			0.276141	−	0.961117i	$-0.410944\pi$
$103$	56.8851			0.552283			0.276141	+	0.961117i	$0.410944\pi$
$104$		−	215.908i		−	2.07604i
$105$	28.2677	−	55.6180i	0.269216	−	0.529695i
$106$	−151.983			−1.43380
$107$		−	68.8756i		−	0.643697i	−0.946791	−	0.321848i	$-0.895696\pi$
$107$		−	68.8756i		−	0.643697i	0.946791	−	0.321848i	$-0.104304\pi$
$108$	−29.0392	−	179.798i	−0.268882	−	1.66480i
$109$	164.705			1.51105			0.755525	−	0.655119i	$-0.227382\pi$
$109$	164.705			1.51105			0.755525	+	0.655119i	$0.227382\pi$
$110$		−	87.4474i		−	0.794976i
$111$	161.571	+	82.1180i	1.45560	+	0.739802i
$112$	−6.66612			−0.0595190
$113$		−	20.6428i		−	0.182680i	−0.995820	−	0.0913400i	$-0.970885\pi$
$113$		−	20.6428i		−	0.182680i	0.995820	−	0.0913400i	$-0.0291150\pi$
$114$	−141.201	+	277.820i	−1.23860	+	2.43702i
$115$	−37.6967			−0.327798
$116$			122.077i			1.05239i
$117$	−127.266	−	174.420i	−1.08774	−	1.49077i
$118$	−133.115			−1.12809
$119$		−	43.2286i		−	0.363266i
$120$	−189.190	−	96.1549i	−1.57658	−	0.801291i
$121$	109.482			0.904808
$122$		−	160.702i		−	1.31723i
$123$	−63.7108	+	125.354i	−0.517974	+	1.01914i
$124$	−7.91178			−0.0638047
$125$		−	92.6300i		−	0.741040i
$126$	−63.0550	+	46.0082i	−0.500436	+	0.365144i
$127$	−135.542			−1.06726			−0.533630	−	0.845718i	$-0.679173\pi$
$127$	−135.542			−1.06726			−0.533630	+	0.845718i	$0.679173\pi$
$128$		−	220.155i		−	1.71996i
$129$	22.3163	+	11.3422i	0.172995	+	0.0879238i
$130$	−618.145			−4.75496
$131$			220.225i			1.68110i	0.541731	+	0.840552i	$0.317769\pi$
$131$			220.225i			1.68110i	−0.541731	+	0.840552i	$0.682231\pi$
$132$	−31.1177	+	61.2257i	−0.235740	+	0.463831i
$133$	83.8441			0.630407
$134$			220.715i			1.64713i
$135$	−209.513	+	33.8386i	−1.55195	+	0.250656i
$136$	−147.046			−1.08122
$137$		−	84.9650i		−	0.620182i	−0.950707	−	0.310091i	$-0.899640\pi$
$137$		−	84.9650i		−	0.620182i	0.950707	−	0.310091i	$-0.100360\pi$
$138$	42.0439	+	21.3687i	0.304666	+	0.154846i
$139$	−90.9061			−0.654000			−0.327000	−	0.945024i	$-0.606038\pi$
$139$	−90.9061			−0.654000			−0.327000	+	0.945024i	$0.606038\pi$
$140$			140.282i			1.00201i
$141$	−14.4724	+	28.4752i	−0.102641	+	0.201952i
$142$	407.493			2.86967
$143$			81.4201i			0.569371i
$144$	13.3659	+	18.3182i	0.0928186	+	0.127209i
$145$	142.253			0.981053
$146$		−	87.8752i		−	0.601885i
$147$	18.7208	+	9.51478i	0.127352	+	0.0647264i
$148$	−407.521			−2.75352
$149$			39.2335i			0.263312i	0.991295	+	0.131656i	$0.0420294\pi$
$149$			39.2335i			0.263312i	−0.991295	+	0.131656i	$0.957971\pi$
$150$	−163.900	+	322.481i	−1.09267	+	2.14988i
$151$	−221.936			−1.46977			−0.734886	−	0.678190i	$-0.762765\pi$
$151$	−221.936			−1.46977			−0.734886	+	0.678190i	$0.762765\pi$
$152$		−	285.203i		−	1.87634i
$153$	−118.790	+	86.6754i	−0.776406	+	0.566506i
$154$	29.4344			0.191133
$155$			9.21937i			0.0594798i
$156$	432.790	+	219.964i	2.77429	+	1.41002i
$157$	−81.6655			−0.520162			−0.260081	−	0.965587i	$-0.583749\pi$
$157$	−81.6655			−0.520162			−0.260081	+	0.965587i	$0.583749\pi$
$158$			269.136i			1.70339i
$159$	63.0206	−	123.996i	0.396356	−	0.779850i
$160$	−218.044			−1.36277
$161$		−	12.6886i		−	0.0788110i
$162$	252.856	+	81.0234i	1.56084	+	0.500144i
$163$	−135.825			−0.833281			−0.416641	−	0.909071i	$-0.636793\pi$
$163$	−135.825			−0.833281			−0.416641	+	0.909071i	$0.636793\pi$
$164$		−	316.173i		−	1.92788i
$165$	71.3445	+	36.2606i	0.432391	+	0.219761i
$166$	199.357			1.20094
$167$			55.1142i			0.330025i	0.986291	+	0.165013i	$0.0527665\pi$
$167$			55.1142i			0.330025i	−0.986291	+	0.165013i	$0.947234\pi$
$168$	32.3654	−	63.6805i	0.192651	−	0.379051i
$169$	406.540			2.40556
$170$			420.993i			2.47643i
$171$	−168.111	−	230.399i	−0.983107	−	1.34736i
$172$	−56.2870			−0.327250
$173$		−	53.0281i		−	0.306521i	−0.988186	−	0.153260i	$-0.951023\pi$
$173$		−	53.0281i		−	0.306521i	0.988186	−	0.153260i	$-0.0489773\pi$
$174$	−158.657	−	80.6370i	−0.911824	−	0.463431i
$175$	97.3227			0.556130
$176$		−	8.55103i		−	0.0485854i
$177$	55.1969	−	108.603i	0.311847	−	0.613575i
$178$	47.1564			0.264924
$179$			246.703i			1.37823i	0.724651	+	0.689116i	$0.242001\pi$
$179$			246.703i			1.37823i	−0.724651	+	0.689116i	$0.757999\pi$
$180$	385.487	−	281.272i	2.14160	−	1.56262i
$181$	−201.867			−1.11529			−0.557644	−	0.830080i	$-0.688294\pi$
$181$	−201.867			−1.11529			−0.557644	+	0.830080i	$0.688294\pi$
$182$		−	208.065i		−	1.14322i
$183$	131.110	+	66.6362i	0.716449	+	0.364132i
$184$	−43.1613			−0.234572
$185$			474.873i			2.56688i
$186$	5.22607	−	10.2826i	0.0280971	−	0.0552825i
$187$	55.4519			0.296534
$188$		−	71.8213i		−	0.382028i
$189$	−11.3899	−	70.5214i	−0.0602643	−	0.373129i
$190$	−816.538			−4.29757
$191$		−	129.938i		−	0.680302i	−0.940371	−	0.340151i	$-0.889522\pi$
$191$		−	129.938i		−	0.680302i	0.940371	−	0.340151i	$-0.110478\pi$
$192$	270.142	+	137.299i	1.40699	+	0.715097i
$193$	−273.104			−1.41505			−0.707525	−	0.706689i	$-0.750188\pi$
$193$	−273.104			−1.41505			−0.707525	+	0.706689i	$0.750188\pi$
$194$		−	553.710i		−	2.85417i
$195$	256.318	−	504.318i	1.31445	−	2.58624i
$196$	−47.2183			−0.240910
$197$		−	167.057i		−	0.848004i	−0.905661	−	0.424002i	$-0.860625\pi$
$197$		−	167.057i		−	0.848004i	0.905661	−	0.424002i	$-0.139375\pi$
$198$	−59.0174	−	80.8844i	−0.298068	−	0.408507i
$199$	−269.022			−1.35187			−0.675934	−	0.736962i	$-0.736259\pi$
$199$	−269.022			−1.35187			−0.675934	+	0.736962i	$0.736259\pi$
$200$		−	331.052i		−	1.65526i
$201$	−180.072	−	91.5209i	−0.895881	−	0.455328i
$202$	144.990			0.717772
$203$			47.8817i			0.235871i
$204$	149.808	−	294.756i	0.734355	−	1.44488i
$205$	−368.428			−1.79721
$206$		−	186.471i		−	0.905200i
$207$	−34.8676	+	25.4412i	−0.168442	+	0.122904i
$208$	−60.4452			−0.290602
$209$			107.552i			0.514602i
$210$	−182.318	−	92.6622i	−0.868179	−	0.441249i
$211$	212.134			1.00537			0.502686	−	0.864469i	$-0.332345\pi$
$211$	212.134			1.00537			0.502686	+	0.864469i	$0.332345\pi$
$212$			312.748i			1.47522i
$213$	−168.970	+	332.456i	−0.793285	+	1.56083i
$214$	−225.776			−1.05503
$215$			65.5896i			0.305068i
$216$	−239.885	+	38.7439i	−1.11058	+	0.179370i
$217$	−3.10320			−0.0143005
$218$		−	539.906i		−	2.47663i
$219$	71.6936	+	36.4380i	0.327368	+	0.166383i
$220$	−179.948			−0.817945
$221$		−	391.977i		−	1.77365i
$222$	269.185	−	529.635i	1.21255	−	2.38574i
$223$	351.091			1.57440			0.787199	−	0.616699i	$-0.211531\pi$
$223$	351.091			1.57440			0.787199	+	0.616699i	$0.211531\pi$
$224$		−	73.3927i		−	0.327646i
$225$	−195.136	−	267.438i	−0.867273	−	1.18861i
$226$	−67.6679			−0.299415
$227$		−	228.647i		−	1.00725i	−0.863921	−	0.503627i	$-0.831998\pi$
$227$		−	228.647i		−	1.00725i	0.863921	−	0.503627i	$-0.168002\pi$
$228$	571.693	+	290.561i	2.50743	+	1.27439i
$229$	41.8201			0.182621			0.0913104	−	0.995822i	$-0.470894\pi$
$229$	41.8201			0.182621			0.0913104	+	0.995822i	$0.470894\pi$
$230$			123.571i			0.537265i
$231$	−12.2052	+	24.0143i	−0.0528363	+	0.103958i
$232$	162.874			0.702043
$233$			149.567i			0.641917i	0.947093	+	0.320958i	$0.104005\pi$
$233$			149.567i			0.641917i	−0.947093	+	0.320958i	$0.895995\pi$
$234$	−571.753	+	417.180i	−2.44339	+	1.78282i
$235$	−83.6913			−0.356133
$236$			273.922i			1.16069i
$237$	−219.577	−	111.599i	−0.926483	−	0.470882i
$238$	−141.705			−0.595398
$239$		−	362.705i		−	1.51760i	−0.651326	−	0.758798i	$-0.725787\pi$
$239$		−	362.705i		−	1.51760i	0.651326	−	0.758798i	$-0.274213\pi$
$240$	−26.9194	+	52.9652i	−0.112164	+	0.220688i
$241$	153.485			0.636866			0.318433	−	0.947945i	$-0.396843\pi$
$241$	153.485			0.636866			0.318433	+	0.947945i	$0.396843\pi$
$242$		−	358.884i		−	1.48299i
$243$	−170.952	+	172.698i	−0.703506	+	0.710690i
$244$	−330.691			−1.35529
$245$			55.0222i			0.224580i
$246$	410.915	+	208.846i	1.67039	+	0.848967i
$247$	760.259			3.07797
$248$			10.5558i			0.0425638i
$249$	−82.6645	+	162.646i	−0.331986	+	0.653199i
$250$	−303.644			−1.21458
$251$			311.691i			1.24180i	0.783891	+	0.620899i	$0.213232\pi$
$251$			311.691i			1.24180i	−0.783891	+	0.620899i	$0.786768\pi$
$252$	94.6749	+	129.754i	0.375694	+	0.514895i
$253$	16.2764			0.0643335
$254$			444.311i			1.74926i
$255$	−343.470	−	174.567i	−1.34694	−	0.684578i
$256$	−317.634			−1.24076
$257$			495.212i			1.92690i	0.267897	+	0.963448i	$0.413671\pi$
$257$			495.212i			1.92690i	−0.267897	+	0.963448i	$0.586329\pi$
$258$	37.1800	−	73.1535i	0.144108	−	0.283541i
$259$	−159.840			−0.617144
$260$			1272.01i			4.89234i
$261$	131.577	−	96.0050i	0.504125	−	0.367835i
$262$	721.903			2.75535
$263$			393.406i			1.49584i	0.663788	+	0.747921i	$0.268948\pi$
$263$			393.406i			1.49584i	−0.663788	+	0.747921i	$0.731052\pi$
$264$	81.6867	+	41.5170i	0.309419	+	0.157261i
$265$	364.436			1.37523
$266$		−	274.844i		−	1.03325i
$267$	−19.5537	+	38.4729i	−0.0732349	+	0.144093i
$268$	454.184			1.69472
$269$		−	487.709i		−	1.81304i	−0.422159	−	0.906522i	$-0.638728\pi$
$269$		−	487.709i		−	1.81304i	0.422159	−	0.906522i	$-0.361272\pi$
$270$	110.924	+	686.791i	0.410829	+	2.54367i
$271$	54.6334			0.201599			0.100800	−	0.994907i	$-0.467860\pi$
$271$	54.6334			0.201599			0.100800	+	0.994907i	$0.467860\pi$
$272$			41.1668i			0.151348i
$273$	169.751	+	86.2755i	0.621800	+	0.316028i
$274$	−278.518			−1.01649
$275$			124.842i			0.453969i
$276$	43.9721	−	86.5174i	0.159319	−	0.313469i
$277$	−160.335			−0.578826			−0.289413	−	0.957204i	$-0.593460\pi$
$277$	−160.335			−0.578826			−0.289413	+	0.957204i	$0.593460\pi$
$278$			297.993i			1.07192i
$279$	6.22207	+	8.52745i	0.0223013	+	0.0305643i
$280$	187.163			0.668439
$281$		−	152.868i		−	0.544016i	−0.962295	−	0.272008i	$-0.912312\pi$
$281$		−	152.868i		−	0.544016i	0.962295	−	0.272008i	$-0.0876877\pi$
$282$	93.3426	+	47.4411i	0.331002	+	0.168231i
$283$	−21.1061			−0.0745800			−0.0372900	−	0.999304i	$-0.511873\pi$
$283$	−21.1061			−0.0745800			−0.0372900	+	0.999304i	$0.511873\pi$
$284$		−	838.533i		−	2.95258i
$285$	338.582	−	666.178i	1.18801	−	2.33747i
$286$	266.898			0.933208
$287$		−	124.011i		−	0.432095i
$288$	−201.679	+	147.156i	−0.700276	+	0.510957i
$289$	22.0407			0.0762654
$290$		−	466.309i		−	1.60796i
$291$	451.748	+	229.599i	1.55240	+	0.789001i
$292$	−180.828			−0.619275
$293$			49.3930i			0.168577i	0.996441	+	0.0842884i	$0.0268617\pi$
$293$			49.3930i			0.168577i	−0.996441	+	0.0842884i	$0.973138\pi$
$294$	31.1897	−	61.3674i	0.106088	−	0.208733i
$295$	319.193			1.08201
$296$			543.711i			1.83686i
$297$	90.4620	−	14.6106i	0.304586	−	0.0491938i
$298$	128.609			0.431572
$299$		−	115.054i		−	0.384796i
$300$	663.597	+	337.271i	2.21199	+	1.12424i
$301$	−22.0772			−0.0733463
$302$			727.512i			2.40898i
$303$	−60.1210	+	118.291i	−0.198419	+	0.390399i
$304$	−79.8450			−0.262648
$305$			385.345i			1.26342i
$306$	284.124	+	389.397i	0.928511	+	1.27254i
$307$	−485.494			−1.58141			−0.790707	−	0.612194i	$-0.790287\pi$
$307$	−485.494			−1.58141			−0.790707	+	0.612194i	$0.790287\pi$
$308$		−	60.5697i		−	0.196655i
$309$	152.134	+	77.3214i	0.492342	+	0.250231i
$310$	30.2214			0.0974883
$311$		−	57.4886i		−	0.184851i	−0.995720	−	0.0924253i	$-0.970538\pi$
$311$		−	57.4886i		−	0.184851i	0.995720	−	0.0924253i	$-0.0294619\pi$
$312$	293.474	−	577.424i	0.940621	−	1.85072i
$313$	−291.362			−0.930868			−0.465434	−	0.885083i	$-0.654102\pi$
$313$	−291.362			−0.930868			−0.465434	+	0.885083i	$0.654102\pi$
$314$			267.702i			0.852554i
$315$	151.198	−	110.322i	0.479994	−	0.350229i
$316$	553.824			1.75261
$317$			226.273i			0.713796i	0.934143	+	0.356898i	$0.116166\pi$
$317$			226.273i			0.713796i	−0.934143	+	0.356898i	$0.883834\pi$
$318$	−406.463	−	206.583i	−1.27818	−	0.649633i
$319$	−61.4207			−0.192541
$320$			793.972i			2.48116i
$321$	93.6194	−	184.201i	0.291649	−	0.573835i
$322$	−41.5935			−0.129172
$323$		−	517.781i		−	1.60304i
$324$	166.729	−	520.324i	0.514595	−	1.60594i
$325$	882.476			2.71531
$326$			445.238i			1.36576i
$327$	440.486	+	223.875i	1.34705	+	0.684634i
$328$	−421.835			−1.28608
$329$		−	28.1702i		−	0.0856236i
$330$	118.863	−	233.869i	0.360192	−	0.708695i
$331$	238.677			0.721078			0.360539	−	0.932744i	$-0.382593\pi$
$331$	238.677			0.721078			0.360539	+	0.932744i	$0.382593\pi$
$332$		−	410.233i		−	1.23564i
$333$	320.487	+	439.233i	0.962424	+	1.31902i
$334$	180.666			0.540916
$335$		−	529.248i		−	1.57985i
$336$	−17.8279	−	9.06096i	−0.0530592	−	0.0269672i
$337$	−589.672			−1.74977			−0.874884	−	0.484333i	$-0.839062\pi$
$337$	−589.672			−1.74977			−0.874884	+	0.484333i	$0.839062\pi$
$338$		−	1332.65i		−	3.94275i
$339$	28.0589	−	55.2073i	0.0827696	−	0.162853i
$340$	866.313			2.54798
$341$		−	3.98066i		−	0.0116735i
$342$	−755.256	+	551.074i	−2.20835	+	1.61133i
$343$	−18.5203			−0.0539949
$344$			75.0976i			0.218307i
$345$	−100.816	−	51.2395i	−0.292221	−	0.148520i
$346$	−173.828			−0.502392
$347$			474.996i			1.36887i	0.729076	+	0.684433i	$0.239950\pi$
$347$			474.996i			1.36887i	−0.729076	+	0.684433i	$0.760050\pi$
$348$	−165.934	+	326.483i	−0.476821	+	0.938169i
$349$	−191.105			−0.547578			−0.273789	−	0.961790i	$-0.588277\pi$
$349$	−191.105			−0.547578			−0.273789	+	0.961790i	$0.588277\pi$
$350$		−	319.027i		−	0.911505i
$351$	−103.279	−	639.455i	−0.294241	−	1.82181i
$352$	94.1452			0.267458
$353$			141.969i			0.402179i	0.979573	+	0.201090i	$0.0644482\pi$
$353$			141.969i			0.402179i	−0.979573	+	0.201090i	$0.935552\pi$
$354$	−356.003	−	180.937i	−1.00566	−	0.511122i
$355$	−977.119			−2.75245
$356$		−	97.0378i		−	0.272578i
$357$	58.7587	−	115.611i	0.164590	−	0.323840i
$358$	808.701			2.25894
$359$		−	230.391i		−	0.641757i	−0.947120	−	0.320878i	$-0.896022\pi$
$359$		−	230.391i		−	0.641757i	0.947120	−	0.320878i	$-0.103978\pi$
$360$	−375.270	−	514.314i	−1.04242	−	1.42865i
$361$	643.262			1.78189
$362$			661.726i			1.82797i
$363$	292.798	+	148.814i	0.806606	+	0.409955i
$364$	−428.153			−1.17625
$365$			210.714i			0.577298i
$366$	218.436	−	429.783i	0.596818	−	1.17427i
$367$	−169.606			−0.462143			−0.231071	−	0.972937i	$-0.574223\pi$
$367$	−169.606			−0.462143			−0.231071	+	0.972937i	$0.574223\pi$
$368$			12.0834i			0.0328353i
$369$	−340.777	+	248.648i	−0.923514	+	0.673844i
$370$	1556.65			4.20715
$371$			122.668i			0.330641i
$372$	−21.1593	−	10.7541i	−0.0568798	−	0.0289089i
$373$	311.454			0.834996			0.417498	−	0.908678i	$-0.362907\pi$
$373$	311.454			0.834996			0.417498	+	0.908678i	$0.362907\pi$
$374$		−	181.773i		−	0.486024i
$375$	125.908	−	247.730i	0.335754	−	0.660613i
$376$	−95.8233			−0.254849
$377$			434.169i			1.15164i
$378$	−231.171	+	37.3366i	−0.611564	+	0.0987740i
$379$	618.185			1.63110			0.815548	−	0.578689i	$-0.196436\pi$
$379$	618.185			1.63110			0.815548	+	0.578689i	$0.196436\pi$
$380$			1680.26i			4.42173i
$381$	−362.494	−	184.236i	−0.951428	−	0.483560i
$382$	−425.939			−1.11502
$383$			45.6916i			0.119299i	0.998219	+	0.0596496i	$0.0189983\pi$
$383$			45.6916i			0.119299i	−0.998219	+	0.0596496i	$0.981002\pi$
$384$	299.247	−	588.784i	0.779289	−	1.53329i
$385$	−70.5802			−0.183325
$386$			895.245i			2.31929i
$387$	44.2658	+	60.6671i	0.114382	+	0.156762i
$388$	−1139.42			−2.93664
$389$		−	678.896i		−	1.74523i	−0.488406	−	0.872617i	$-0.662421\pi$
$389$		−	678.896i		−	1.74523i	0.488406	−	0.872617i	$-0.337579\pi$
$390$	−1653.17	−	840.217i	−4.23889	−	2.15440i
$391$	−78.3586			−0.200406
$392$			62.9983i			0.160710i
$393$	−299.341	+	588.969i	−0.761683	+	1.49865i
$394$	−547.617			−1.38989
$395$		−	645.356i		−	1.63381i
$396$	−166.443	+	121.445i	−0.420309	+	0.306680i
$397$	326.580			0.822620			0.411310	−	0.911495i	$-0.365071\pi$
$397$	326.580			0.822620			0.411310	+	0.911495i	$0.365071\pi$
$398$			881.861i			2.21573i
$399$	224.233	+	113.966i	0.561987	+	0.285628i
$400$	−92.6807			−0.231702
$401$			490.528i			1.22326i	0.791144	+	0.611630i	$0.209486\pi$
$401$			490.528i			1.22326i	−0.791144	+	0.611630i	$0.790514\pi$
$402$	−300.008	+	590.281i	−0.746289	+	1.46836i
$403$	−28.1384			−0.0698223
$404$		−	298.358i		−	0.738510i
$405$	−606.318	−	194.284i	−1.49708	−	0.479714i
$406$	156.958			0.386595
$407$		−	205.037i		−	0.503775i
$408$	−393.260	−	199.873i	−0.963873	−	0.489885i
$409$	278.884			0.681867			0.340933	−	0.940087i	$-0.389257\pi$
$409$	278.884			0.681867			0.340933	+	0.940087i	$0.389257\pi$
$410$			1207.72i			2.94565i
$411$	115.489	−	227.231i	0.280995	−	0.552872i
$412$	−383.717			−0.931353
$413$			107.439i			0.260144i
$414$	83.3969	+	114.297i	0.201442	+	0.276079i
$415$	−478.033			−1.15189
$416$		−	665.490i		−	1.59974i
$417$	−243.119	−	123.565i	−0.583020	−	0.296318i
$418$	352.558			0.843440
$419$		−	336.443i		−	0.802968i	−0.915866	−	0.401484i	$-0.868495\pi$
$419$		−	336.443i		−	0.802968i	0.915866	−	0.401484i	$-0.131505\pi$
$420$	−190.679	+	375.170i	−0.453997	+	0.893262i
$421$	−329.184			−0.781909			−0.390955	−	0.920410i	$-0.627855\pi$
$421$	−329.184			−0.781909			−0.390955	+	0.920410i	$0.627855\pi$
$422$		−	695.380i		−	1.64782i
$423$	−77.4102	+	56.4825i	−0.183003	+	0.133528i
$424$	417.265			0.984116
$425$		−	601.018i		−	1.41416i
$426$	1089.80	+	553.887i	2.55822	+	1.30021i
$427$	−129.706			−0.303760
$428$			464.599i			1.08551i
$429$	−110.671	+	217.750i	−0.257974	+	0.507576i
$430$	215.005			0.500011
$431$		−	378.205i		−	0.877507i	−0.898608	−	0.438753i	$-0.855420\pi$
$431$		−	378.205i		−	0.877507i	0.898608	−	0.438753i	$-0.144580\pi$
$432$	10.8467	+	67.1578i	0.0251081	+	0.155458i
$433$	−129.143			−0.298251			−0.149125	−	0.988818i	$-0.547646\pi$
$433$	−129.143			−0.298251			−0.149125	+	0.988818i	$0.547646\pi$
$434$			10.1724i			0.0234387i
$435$	380.441	+	193.358i	0.874577	+	0.444501i
$436$	−1111.01			−2.54819
$437$		−	151.980i		−	0.347781i
$438$	119.445	−	235.014i	0.272705	−	0.536561i
$439$	−193.938			−0.441771			−0.220886	−	0.975300i	$-0.570895\pi$
$439$	−193.938			−0.441771			−0.220886	+	0.975300i	$0.570895\pi$
$440$			240.085i			0.545647i
$441$	37.1340	+	50.8927i	0.0842040	+	0.115403i
$442$	−1284.91			−2.90704
$443$			351.448i			0.793337i	0.917962	+	0.396669i	$0.129834\pi$
$443$			351.448i			0.793337i	−0.917962	+	0.396669i	$0.870166\pi$
$444$	−1089.88	−	553.925i	−2.45467	−	1.24758i
$445$	−113.075			−0.254102
$446$		−	1150.89i		−	2.58046i
$447$	−53.3283	+	104.926i	−0.119303	+	0.234734i
$448$	−267.248			−0.596536
$449$		−	259.899i		−	0.578840i	−0.957202	−	0.289420i	$-0.906538\pi$
$449$		−	259.899i		−	0.578840i	0.957202	−	0.289420i	$-0.0934624\pi$
$450$	−876.669	+	639.663i	−1.94815	+	1.42147i
$451$	159.077			0.352720
$452$			139.246i			0.308066i
$453$	−593.545	−	301.667i	−1.31025	−	0.665932i
$454$	−749.511			−1.65091
$455$			498.915i			1.09652i
$456$	387.664	−	762.748i	0.850140	−	1.67269i
$457$	530.125			1.16001			0.580005	−	0.814613i	$-0.303051\pi$
$457$	530.125			1.16001			0.580005	+	0.814613i	$0.303051\pi$
$458$		−	137.088i		−	0.299318i
$459$	−435.506	+	70.3388i	−0.948816	+	0.153244i
$460$	254.282			0.552788
$461$		−	546.434i		−	1.18532i	−0.805451	−	0.592662i	$-0.798077\pi$
$461$		−	546.434i		−	1.18532i	0.805451	−	0.592662i	$-0.201923\pi$
$462$	78.7195	+	40.0089i	0.170389	+	0.0865994i
$463$	3.67058			0.00792782			0.00396391	−	0.999992i	$-0.498738\pi$
$463$	3.67058			0.00792782			0.00396391	+	0.999992i	$0.498738\pi$
$464$		−	45.5979i		−	0.0982714i
$465$	−12.5315	+	24.6563i	−0.0269494	+	0.0530243i
$466$	490.284			1.05211
$467$		−	172.889i		−	0.370211i	−0.982719	−	0.185106i	$-0.940737\pi$
$467$		−	172.889i		−	0.370211i	0.982719	−	0.185106i	$-0.0592627\pi$
$468$	858.467	+	1176.54i	1.83433	+	2.51398i
$469$	178.143			0.379836
$470$			274.343i			0.583708i
$471$	−218.406	−	111.004i	−0.463708	−	0.235678i
$472$	365.464			0.774289
$473$		−	28.3198i		−	0.0598726i
$474$	−365.825	+	719.778i	−0.771782	+	1.51852i
$475$	1165.70			2.45412
$476$			291.598i			0.612600i
$477$	337.085	−	245.954i	0.706676	−	0.515628i
$478$	−1188.96			−2.48736
$479$		−	762.171i		−	1.59117i	−0.605841	−	0.795586i	$-0.707163\pi$
$479$		−	762.171i		−	1.59117i	0.605841	−	0.795586i	$-0.292837\pi$
$480$	−583.137	−	296.377i	−1.21487	−	0.617452i
$481$	−1449.36			−3.01321
$482$		−	503.128i		−	1.04383i
$483$	17.2470	−	33.9344i	0.0357081	−	0.0702575i
$484$	−738.506			−1.52584
$485$			1327.73i			2.73758i
$486$	566.108	+	560.385i	1.16483	+	1.15306i
$487$	−287.944			−0.591261			−0.295630	−	0.955302i	$-0.595530\pi$
$487$	−287.944			−0.591261			−0.295630	+	0.955302i	$0.595530\pi$
$488$			441.205i			0.904108i
$489$	−363.250	−	184.621i	−0.742843	−	0.377547i
$490$	180.364			0.368091
$491$			339.119i			0.690671i	0.938479	+	0.345335i	$0.112235\pi$
$491$			339.119i			0.690671i	−0.938479	+	0.345335i	$0.887765\pi$
$492$	429.760	−	845.574i	0.873496	−	1.71865i
$493$	295.695			0.599786
$494$		−	2492.15i		−	5.04484i
$495$	141.517	+	193.951i	0.285892	+	0.391820i
$496$	2.95519			0.00595805
$497$		−	328.895i		−	0.661760i
$498$	533.160	+	270.977i	1.07060	+	0.544130i
$499$	58.8433			0.117922			0.0589612	−	0.998260i	$-0.481221\pi$
$499$	58.8433			0.117922			0.0589612	+	0.998260i	$0.481221\pi$
$500$			624.833i			1.24967i
$501$	−74.9143	+	147.398i	−0.149529	+	0.294207i
$502$	1021.73			2.03532
$503$			120.228i			0.239021i	0.992833	+	0.119510i	$0.0381325\pi$
$503$			120.228i			0.239021i	−0.992833	+	0.119510i	$0.961867\pi$
$504$	173.116	−	126.314i	0.343484	−	0.250624i
$505$	−347.668			−0.688452
$506$		−	53.3545i		−	0.105444i
$507$	1087.25	+	552.591i	2.14448	+	1.08992i
$508$	914.296			1.79980
$509$			694.034i			1.36353i	0.731573	+	0.681763i	$0.238786\pi$
$509$			694.034i			1.36353i	−0.731573	+	0.681763i	$0.761214\pi$
$510$	−572.237	+	1125.91i	−1.12203	+	2.20766i
$511$	−70.9255			−0.138797
$512$			160.594i			0.313660i
$513$	−136.426	−	844.687i	−0.265937	−	1.64656i
$514$	1623.32			3.15821
$515$			447.135i			0.868223i
$516$	−150.534	−	76.5084i	−0.291733	−	0.148272i
$517$	36.1355			0.0698947
$518$			523.961i			1.01151i
$519$	72.0787	−	141.818i	0.138880	−	0.273253i
$520$	1697.10			3.26366
$521$			711.657i			1.36594i	0.730445	+	0.682972i	$0.239313\pi$
$521$			711.657i			1.36594i	−0.730445	+	0.682972i	$0.760687\pi$
$522$	−314.707	−	431.312i	−0.602888	−	0.826268i
$523$	858.949			1.64235			0.821175	−	0.570677i	$-0.193319\pi$
$523$	858.949			1.64235			0.821175	+	0.570677i	$0.193319\pi$
$524$		−	1485.52i		−	2.83496i
$525$	260.280	+	132.286i	0.495771	+	0.251974i
$526$	1289.60			2.45171
$527$			19.1639i			0.0363641i
$528$	11.6230	−	22.8689i	0.0220133	−	0.0433123i
$529$	−23.0000			−0.0434783
$530$		−	1194.63i		−	2.25402i
$531$	295.238	−	215.421i	0.556003	−	0.405689i
$532$	−565.569			−1.06310
$533$		−	1124.48i		−	2.10971i
$534$	126.115	+	64.0976i	0.236171	+	0.120033i
$535$	541.383			1.01193
$536$		−	605.969i		−	1.13054i
$537$	−335.333	+	659.784i	−0.624456	+	1.22865i
$538$	−1598.72			−2.97160
$539$		−	23.7570i		−	0.0440761i
$540$	1413.27	−	228.258i	2.61716	−	0.422699i
$541$	443.975			0.820656			0.410328	−	0.911938i	$-0.365414\pi$
$541$	443.975			0.820656			0.410328	+	0.911938i	$0.365414\pi$
$542$		−	179.090i		−	0.330424i
$543$	−539.874	−	274.389i	−0.994242	−	0.505320i
$544$	−453.238			−0.833158
$545$			1294.63i			2.37547i
$546$	282.814	−	556.450i	0.517974	−	1.01914i
$547$	423.466			0.774161			0.387080	−	0.922046i	$-0.373484\pi$
$547$	423.466			0.774161			0.387080	+	0.922046i	$0.373484\pi$
$548$			573.129i			1.04586i
$549$	260.065	+	356.424i	0.473708	+	0.649224i
$550$	409.234			0.744062
$551$			573.515i			1.04086i
$552$	−115.431	−	58.6672i	−0.209114	−	0.106281i
$553$	217.224			0.392811
$554$			525.583i			0.948705i
$555$	−645.473	+	1270.00i	−1.16301	+	2.28829i
$556$	613.205			1.10289
$557$		−	193.895i		−	0.348106i	−0.984736	−	0.174053i	$-0.944314\pi$
$557$		−	193.895i		−	0.348106i	0.984736	−	0.174053i	$-0.0556864\pi$
$558$	27.9532	−	20.3961i	0.0500954	−	0.0365522i
$559$	−200.186			−0.358114
$560$		−	52.3978i		−	0.0935675i
$561$	148.301	+	75.3733i	0.264351	+	0.134355i
$562$	−501.107			−0.891650
$563$			95.1493i			0.169004i	0.996423	+	0.0845020i	$0.0269299\pi$
$563$			95.1493i			0.169004i	−0.996423	+	0.0845020i	$0.973070\pi$
$564$	97.6235	−	192.079i	0.173091	−	0.340566i
$565$	162.259			0.287184
$566$			69.1865i			0.122238i
$567$	65.3953	−	204.084i	0.115336	−	0.359937i
$568$	−1118.76			−1.96965
$569$			783.443i			1.37688i	0.725295	+	0.688439i	$0.241704\pi$
$569$			783.443i			1.37688i	−0.725295	+	0.688439i	$0.758296\pi$
$570$	−2183.75	−	1109.88i	−3.83114	−	1.94716i
$571$	166.563			0.291704			0.145852	−	0.989306i	$-0.453408\pi$
$571$	166.563			0.291704			0.145852	+	0.989306i	$0.453408\pi$
$572$		−	549.218i		−	0.960171i
$573$	176.618	−	347.505i	0.308235	−	0.606467i
$574$	−406.513			−0.708210
$575$		−	176.412i		−	0.306804i
$576$	535.844	+	734.384i	0.930285	+	1.27497i
$577$	−137.716			−0.238676			−0.119338	−	0.992854i	$-0.538077\pi$
$577$	−137.716			−0.238676			−0.119338	+	0.992854i	$0.538077\pi$
$578$		−	72.2500i		−	0.125000i
$579$	−730.391	−	371.219i	−1.26147	−	0.641138i
$580$	−959.563			−1.65442
$581$		−	160.904i		−	0.276943i
$582$	752.633	−	1480.84i	1.29318	−	2.54440i
$583$	−157.353			−0.269902
$584$			241.259i			0.413115i
$585$	1370.99	−	1000.35i	2.34358	−	1.71000i
$586$	161.912			0.276300
$587$			444.114i			0.756583i	0.925687	+	0.378291i	$0.123488\pi$
$587$			444.114i			0.756583i	−0.925687	+	0.378291i	$0.876512\pi$
$588$	−126.281	−	64.1818i	−0.214763	−	0.109153i
$589$	−37.1694			−0.0631059
$590$		−	1046.33i		−	1.77343i
$591$	227.073	−	446.777i	0.384218	−	0.755968i
$592$	152.217			0.257122
$593$		−	91.5757i		−	0.154428i	−0.997015	−	0.0772139i	$-0.975398\pi$
$593$		−	91.5757i		−	0.154428i	0.997015	−	0.0772139i	$-0.0246024\pi$
$594$	−47.8938	−	296.537i	−0.0806293	−	0.499221i
$595$	339.791			0.571077
$596$		−	264.649i		−	0.444041i
$597$	−719.472	−	365.669i	−1.20515	−	0.612511i
$598$	−377.150			−0.630686
$599$		−	189.720i		−	0.316728i	−0.987381	−	0.158364i	$-0.949378\pi$
$599$		−	189.720i		−	0.316728i	0.987381	−	0.158364i	$-0.0506220\pi$
$600$	449.984	−	885.365i	0.749973	−	1.47561i
$601$	884.569			1.47183			0.735915	−	0.677074i	$-0.236752\pi$
$601$	884.569			1.47183			0.735915	+	0.677074i	$0.236752\pi$
$602$			72.3698i			0.120216i
$603$	−357.185	−	489.528i	−0.592346	−	0.811820i
$604$	1497.06			2.47858
$605$			860.560i			1.42241i
$606$	387.761	+	197.078i	0.639870	+	0.325212i
$607$	−418.551			−0.689541			−0.344771	−	0.938687i	$-0.612043\pi$
$607$	−418.551			−0.689541			−0.344771	+	0.938687i	$0.612043\pi$
$608$		−	879.078i		−	1.44585i
$609$	−65.0835	+	128.055i	−0.106869	+	0.210271i
$610$	1263.17			2.07077
$611$		−	255.434i		−	0.418058i
$612$	801.296	−	584.667i	1.30931	−	0.955338i
$613$	−869.313			−1.41813			−0.709065	−	0.705143i	$-0.750883\pi$
$613$	−869.313			−1.41813			−0.709065	+	0.705143i	$0.750883\pi$
$614$			1591.46i			2.59196i
$615$	−985.323	−	500.787i	−1.60215	−	0.814288i
$616$	−80.8116			−0.131188
$617$			846.429i			1.37185i	0.727674	+	0.685923i	$0.240601\pi$
$617$			846.429i			1.37185i	−0.727674	+	0.685923i	$0.759399\pi$
$618$	253.462	−	498.699i	0.410132	−	0.806956i
$619$	−707.051			−1.14225			−0.571123	−	0.820864i	$-0.693492\pi$
$619$	−707.051			−1.14225			−0.571123	+	0.820864i	$0.693492\pi$
$620$		−	62.1890i		−	0.100305i
$621$	−127.831	+	20.6460i	−0.205847	+	0.0332464i
$622$	−188.449			−0.302973
$623$		−	38.0607i		−	0.0610927i
$624$	−161.655	−	82.1605i	−0.259062	−	0.131667i
$625$	−191.512			−0.306420
$626$			955.092i			1.52571i
$627$	−146.190	+	287.637i	−0.233158	+	0.458751i
$628$	550.873			0.877186
$629$			987.097i			1.56931i
$630$	−361.639	−	495.632i	−0.574030	−	0.786717i
$631$	−630.621			−0.999400			−0.499700	−	0.866199i	$-0.666556\pi$
$631$	−630.621			−0.999400			−0.499700	+	0.866199i	$0.666556\pi$
$632$		−	738.907i		−	1.16916i
$633$	567.330	+	288.344i	0.896256	+	0.455519i
$634$	741.730			1.16992
$635$		−	1065.40i		−	1.67780i
$636$	−425.104	+	836.413i	−0.668402	+	1.31511i
$637$	−167.933			−0.263631
$638$			201.339i			0.315578i
$639$	−903.785	+	659.449i	−1.41437	+	1.03200i
$640$	1730.49			2.70389
$641$			332.623i			0.518912i	0.965755	+	0.259456i	$0.0835432\pi$
$641$			332.623i			0.518912i	−0.965755	+	0.259456i	$0.916457\pi$
$642$	−603.816	−	306.887i	−0.940524	−	0.478018i
$643$	369.579			0.574772			0.287386	−	0.957815i	$-0.407214\pi$
$643$	369.579			0.574772			0.287386	+	0.957815i	$0.407214\pi$
$644$			85.5905i			0.132905i
$645$	−89.1531	+	175.413i	−0.138222	+	0.271958i
$646$	−1697.30			−2.62740
$647$			945.419i			1.46124i	0.682787	+	0.730618i	$0.260768\pi$
$647$			945.419i			1.46124i	−0.682787	+	0.730618i	$0.739232\pi$
$648$	−694.211	−	222.448i	−1.07131	−	0.343284i
$649$	−137.819			−0.212355
$650$		−	2892.78i		−	4.45043i
$651$	−8.29922	−	4.21805i	−0.0127484	−	0.00647933i
$652$	916.203			1.40522
$653$			794.309i			1.21640i	0.793784	+	0.608200i	$0.208108\pi$
$653$			794.309i			1.21640i	−0.793784	+	0.608200i	$0.791892\pi$
$654$	733.870	−	1443.93i	1.12213	−	2.20784i
$655$	−1731.03			−2.64280
$656$			118.096i			0.180025i
$657$	142.209	+	194.900i	0.216452	+	0.296651i
$658$	−92.3427			−0.140338
$659$			116.941i			0.177452i	0.996056	+	0.0887259i	$0.0282795\pi$
$659$			116.941i			0.177452i	−0.996056	+	0.0887259i	$0.971720\pi$
$660$	−481.253	−	244.595i	−0.729171	−	0.370598i
$661$	656.482			0.993165			0.496582	−	0.867990i	$-0.334588\pi$
$661$	656.482			0.993165			0.496582	+	0.867990i	$0.334588\pi$
$662$		−	782.390i		−	1.18186i
$663$	532.796	−	1048.30i	0.803614	−	1.58115i
$664$	−547.329			−0.824291
$665$			659.041i			0.991039i
$666$	1439.82	−	1050.57i	2.16189	−	1.57743i
$667$	86.7930			0.130124
$668$		−	371.772i		−	0.556544i
$669$	938.958	+	477.222i	1.40352	+	0.713336i
$670$	−1734.89			−2.58939
$671$		−	166.381i		−	0.247960i
$672$	99.7594	−	196.282i	0.148452	−	0.292086i
$673$	−102.742			−0.152663			−0.0763317	−	0.997082i	$-0.524321\pi$
$673$	−102.742			−0.152663			−0.0763317	+	0.997082i	$0.524321\pi$
$674$			1932.96i			2.86790i
$675$	−158.357	−	980.476i	−0.234603	−	1.45256i
$676$	−2742.31			−4.05666
$677$			1305.08i			1.92774i	0.266378	+	0.963869i	$0.414173\pi$
$677$			1305.08i			1.92774i	−0.266378	+	0.963869i	$0.585827\pi$
$678$	−180.971	−	91.9779i	−0.266919	−	0.135661i
$679$	−446.908			−0.658186
$680$		−	1155.83i		−	1.69975i
$681$	310.789	−	611.494i	0.456372	−	0.897935i
$682$	−13.0487			−0.0191330
$683$			81.4022i			0.119183i	0.998223	+	0.0595917i	$0.0189799\pi$
$683$			81.4022i			0.119183i	−0.998223	+	0.0595917i	$0.981020\pi$
$684$	1133.99	+	1554.15i	1.65788	+	2.27215i
$685$	667.851			0.974966
$686$			60.7100i			0.0884985i
$687$	111.844	+	56.8442i	0.162800	+	0.0827427i
$688$	21.0242			0.0305585
$689$			1112.29i			1.61436i
$690$	−167.965	+	330.479i	−0.243427	+	0.478954i
$691$	759.546			1.09920			0.549599	−	0.835428i	$-0.314780\pi$
$691$	759.546			1.09920			0.549599	+	0.835428i	$0.314780\pi$
$692$			357.700i			0.516907i
$693$	−65.2831	+	47.6339i	−0.0942036	+	0.0687358i
$694$	1557.05			2.24359
$695$		−	714.550i		−	1.02813i
$696$	435.590	+	221.387i	0.625848	+	0.318085i
$697$	−765.834			−1.09876
$698$			626.447i			0.897489i
$699$	−203.299	+	400.001i	−0.290843	+	0.572248i
$700$	−656.488			−0.937840
$701$		−	783.866i		−	1.11821i	−0.829097	−	0.559105i	$-0.811145\pi$
$701$		−	783.866i		−	1.11821i	0.829097	−	0.559105i	$-0.188855\pi$
$702$	−2096.15	+	338.550i	−2.98597	+	0.482265i
$703$	−1914.52			−2.72336
$704$		−	342.815i		−	0.486953i
$705$	−223.824	−	113.758i	−0.317481	−	0.161359i
$706$	465.379			0.659178
$707$		−	117.024i		−	0.165522i
$708$	−372.330	+	732.577i	−0.525889	+	1.03471i
$709$	777.141			1.09611			0.548054	−	0.836443i	$-0.315369\pi$
$709$	777.141			1.09611			0.548054	+	0.836443i	$0.315369\pi$
$710$			3203.03i			4.51130i
$711$	−435.544	−	596.921i	−0.612580	−	0.839551i
$712$	−129.467			−0.181836
$713$			5.62504i			0.00788925i
$714$	−378.975	−	192.613i	−0.530778	−	0.269766i
$715$	−639.988			−0.895088
$716$		−	1664.13i		−	2.32421i
$717$	493.009	−	970.020i	0.687600	−	1.35289i
$718$	−755.228			−1.05185
$719$		−	462.841i		−	0.643729i	−0.946786	−	0.321864i	$-0.895690\pi$
$719$		−	462.841i		−	0.643729i	0.946786	−	0.321864i	$-0.104310\pi$
$720$	−143.987	+	105.060i	−0.199981	+	0.145917i
$721$	−150.504			−0.208743
$722$		−	2108.63i		−	2.92054i
$723$	410.480	+	208.625i	0.567745	+	0.288555i
$724$	1361.69			1.88079
$725$			665.711i			0.918222i
$726$	487.815	−	959.801i	0.671922	−	1.32204i
$727$	−28.6408			−0.0393959			−0.0196979	−	0.999806i	$-0.506270\pi$
$727$	−28.6408			−0.0393959			−0.0196979	+	0.999806i	$0.506270\pi$
$728$			571.239i			0.784668i
$729$	−691.934	+	229.496i	−0.949155	+	0.314809i
$730$	690.726			0.946201
$731$			136.338i			0.186509i
$732$	−884.400	−	449.493i	−1.20820	−	0.614062i
$733$	607.156			0.828317			0.414159	−	0.910205i	$-0.364076\pi$
$733$	607.156			0.828317			0.414159	+	0.910205i	$0.364076\pi$
$734$			555.975i			0.757459i
$735$	−74.7892	+	147.151i	−0.101754	+	0.200206i
$736$	−133.036			−0.180755
$737$			228.514i			0.310060i
$738$	815.076	+	1117.08i	1.10444	+	1.51365i
$739$	−342.591			−0.463588			−0.231794	−	0.972765i	$-0.574459\pi$
$739$	−342.591			−0.463588			−0.231794	+	0.972765i	$0.574459\pi$
$740$		−	3203.24i		−	4.32871i
$741$	2033.24	+	1033.39i	2.74391	+	1.39458i
$742$	402.108			0.541925
$743$			484.627i			0.652257i	0.945325	+	0.326128i	$0.105744\pi$
$743$			484.627i			0.652257i	−0.945325	+	0.326128i	$0.894256\pi$
$744$	−14.3481	+	28.2305i	−0.0192850	+	0.0379442i
$745$	−308.388			−0.413943
$746$		−	1020.95i		−	1.36857i
$747$	−442.156	+	322.620i	−0.591909	+	0.431887i
$748$	−374.050			−0.500066
$749$			182.228i			0.243295i
$750$	−812.066	−	412.729i	−1.08275	−	0.550306i
$751$	357.737			0.476348			0.238174	−	0.971222i	$-0.423451\pi$
$751$	357.737			0.476348			0.238174	+	0.971222i	$0.423451\pi$
$752$			26.8266i			0.0356736i
$753$	−423.668	+	833.588i	−0.562640	+	1.10702i
$754$	1423.22			1.88756
$755$		−	1744.48i		−	2.31057i
$756$	76.8306	+	475.701i	0.101628	+	0.629234i
$757$	1028.55			1.35872			0.679361	−	0.733805i	$-0.262257\pi$
$757$	1028.55			1.35872			0.679361	+	0.733805i	$0.262257\pi$
$758$		−	2026.43i		−	2.67339i
$759$	43.5296	+	22.1238i	0.0573512	+	0.0291486i
$760$	2241.79			2.94972
$761$		−	442.942i		−	0.582053i	−0.956715	−	0.291026i	$-0.906003\pi$
$761$		−	442.942i		−	0.582053i	0.956715	−	0.291026i	$-0.0939968\pi$
$762$	−603.932	+	1188.27i	−0.792561	+	1.55940i
$763$	−435.767			−0.571124
$764$			876.491i			1.14724i
$765$	−681.296	−	933.727i	−0.890583	−	1.22056i
$766$	149.778			0.195533
$767$			974.208i			1.27015i
$768$	−849.482	−	431.746i	−1.10610	−	0.562169i
$769$	754.699			0.981404			0.490702	−	0.871328i	$-0.336740\pi$
$769$	754.699			0.981404			0.490702	+	0.871328i	$0.336740\pi$
$770$			231.364i			0.300473i
$771$	−673.119	+	1324.40i	−0.873047	+	1.71776i
$772$	1842.22			2.38630
$773$		−	559.131i		−	0.723326i	−0.932309	−	0.361663i	$-0.882209\pi$
$773$		−	559.131i		−	0.723326i	0.932309	−	0.361663i	$-0.117791\pi$
$774$	198.868	−	145.105i	0.256936	−	0.187474i
$775$	−43.1446			−0.0556704
$776$			1520.20i			1.95902i
$777$	−427.477	−	217.264i	−0.550164	−	0.279619i
$778$	−2225.44			−2.86046
$779$		−	1485.37i		−	1.90677i
$780$	−1728.98	+	3401.86i	−2.21665	+	4.36136i
$781$	421.892			0.540195
$782$			256.862i			0.328468i
$783$	482.384	−	77.9100i	0.616071	−	0.0995020i
$784$	17.6369			0.0224961
$785$		−	641.916i		−	0.817728i
$786$	1930.66	+	981.250i	2.45631	+	1.24841i
$787$	−431.461			−0.548235			−0.274117	−	0.961696i	$-0.588386\pi$
$787$	−431.461			−0.548235			−0.274117	+	0.961696i	$0.588386\pi$
$788$			1126.88i			1.43005i
$789$	−534.739	+	1052.13i	−0.677743	+	1.33349i
$790$	−2115.49			−2.67784
$791$			54.6158i			0.0690466i
$792$	162.031	+	222.066i	0.204585	+	0.280387i
$793$	−1176.11			−1.48311
$794$		−	1070.54i		−	1.34829i
$795$	974.648	+	495.361i	1.22597	+	0.623096i
$796$	1814.68			2.27975
$797$			856.896i			1.07515i	0.843215	+	0.537576i	$0.180660\pi$
$797$			856.896i			1.07515i	−0.843215	+	0.537576i	$0.819340\pi$
$798$	373.582	−	735.042i	0.468148	−	0.921105i
$799$	−173.965			−0.217729
$800$		−	1020.40i		−	1.27550i
$801$	−104.589	+	76.3135i	−0.130573	+	0.0952728i
$802$	1607.96			2.00494
$803$		−	90.9803i		−	0.113301i
$804$	1214.67	+	617.352i	1.51079	+	0.767851i
$805$	99.7362			0.123896
$806$			92.2384i			0.114440i
$807$	662.920	−	1304.33i	0.821463	−	1.61627i
$808$	−398.067			−0.492657
$809$			1210.95i			1.49685i	0.663222	+	0.748423i	$0.269189\pi$
$809$			1210.95i			1.49685i	−0.663222	+	0.748423i	$0.730811\pi$
$810$	−636.869	+	1987.53i	−0.786258	+	2.45374i
$811$	−149.681			−0.184563			−0.0922815	−	0.995733i	$-0.529416\pi$
$811$	−149.681			−0.184563			−0.0922815	+	0.995733i	$0.529416\pi$
$812$		−	322.985i		−	0.397765i
$813$	146.112	+	74.2607i	0.179719	+	0.0913415i
$814$	−672.116			−0.825695
$815$		−	1067.63i		−	1.30997i
$816$	−55.9562	+	110.097i	−0.0685737	+	0.134922i
$817$	−264.435			−0.323666
$818$		−	914.188i		−	1.11759i
$819$	336.713	+	461.471i	0.411127	+	0.563457i
$820$	2485.22			3.03076
$821$			696.556i			0.848424i	0.905563	+	0.424212i	$0.139449\pi$
$821$			696.556i			0.848424i	−0.905563	+	0.424212i	$0.860551\pi$
$822$	−744.868	−	378.577i	−0.906166	−	0.460556i
$823$	−1040.39			−1.26414			−0.632069	−	0.774912i	$-0.717794\pi$
$823$	−1040.39			−1.26414			−0.632069	+	0.774912i	$0.717794\pi$
$824$			511.952i			0.621301i
$825$	−169.691	+	333.876i	−0.205687	+	0.404699i
$826$	352.189			0.426379
$827$		−	287.110i		−	0.347171i	−0.984819	−	0.173586i	$-0.944465\pi$
$827$		−	287.110i		−	0.347171i	0.984819	−	0.173586i	$-0.0555353\pi$
$828$	235.198	−	171.613i	0.284056	−	0.207262i
$829$	648.831			0.782667			0.391333	−	0.920249i	$-0.372014\pi$
$829$	648.831			0.782667			0.391333	+	0.920249i	$0.372014\pi$
$830$			1567.01i			1.88796i
$831$	−428.800	−	217.936i	−0.516005	−	0.262258i
$832$	−2423.28			−2.91259
$833$			114.372i			0.137302i
$834$	−405.048	+	796.952i	−0.485669	+	0.955578i
$835$	−433.215			−0.518820
$836$		−	725.488i		−	0.867809i
$837$	5.04933	+	31.2632i	0.00603265	+	0.0373515i
$838$	−1102.87			−1.31608
$839$			66.8090i			0.0796293i	0.999207	+	0.0398147i	$0.0126768\pi$
$839$			66.8090i			0.0796293i	−0.999207	+	0.0398147i	$0.987323\pi$
$840$	500.549	+	254.402i	0.595891	+	0.302860i
$841$	513.477			0.610555
$842$			1079.07i			1.28156i
$843$	207.787	−	408.832i	0.246485	−	0.484972i
$844$	−1430.94			−1.69543
$845$			3195.53i			3.78169i
$846$	185.151	+	253.753i	0.218855	+	0.299944i
$847$	−289.661			−0.341985
$848$		−	116.817i		−	0.137756i
$849$	−56.4463	−	28.6886i	−0.0664856	−	0.0337911i
$850$	−1970.16			−2.31783
$851$			289.735i			0.340464i
$852$	1139.78	−	2242.58i	1.33777	−	2.63213i
$853$	502.007			0.588519			0.294260	−	0.955726i	$-0.404927\pi$
$853$	502.007			0.588519			0.294260	+	0.955726i	$0.404927\pi$
$854$			425.179i			0.497867i
$855$	1811.01	−	1321.41i	2.11814	−	1.54551i
$856$	619.863			0.724139
$857$		−	982.545i		−	1.14649i	−0.819383	−	0.573247i	$-0.805684\pi$
$857$		−	982.545i		−	1.14649i	0.819383	−	0.573247i	$-0.194316\pi$
$858$	713.791	+	362.782i	0.831925	+	0.422823i
$859$	−209.708			−0.244131			−0.122065	−	0.992522i	$-0.538952\pi$
$859$	−209.708			−0.244131			−0.122065	+	0.992522i	$0.538952\pi$
$860$		−	442.433i		−	0.514458i
$861$	168.563	−	331.656i	0.195776	−	0.385199i
$862$	−1239.77			−1.43825
$863$			432.967i			0.501700i	0.968026	+	0.250850i	$0.0807100\pi$
$863$			432.967i			0.501700i	−0.968026	+	0.250850i	$0.919290\pi$
$864$	−739.394	+	119.420i	−0.855780	+	0.138217i
$865$	416.818			0.481870
$866$			423.334i			0.488838i
$867$	58.9457	+	29.9589i	0.0679881	+	0.0345547i
$868$	20.9326			0.0241159
$869$			278.646i			0.320652i
$870$	633.832	−	1247.10i	0.728543	−	1.43344i
$871$	1615.31			1.85455
$872$			1482.30i			1.69989i
$873$	896.071	+	1228.08i	1.02643	+	1.40674i
$874$	−498.196			−0.570018
$875$			245.076i			0.280087i
$876$	−483.607	−	245.792i	−0.552063	−	0.280584i
$877$	585.585			0.667714			0.333857	−	0.942624i	$-0.391650\pi$
$877$	585.585			0.667714			0.333857	+	0.942624i	$0.391650\pi$
$878$			635.733i			0.724069i
$879$	−67.1376	+	132.097i	−0.0763796	+	0.150281i
$880$	67.2138			0.0763793
$881$			321.841i			0.365314i	0.983177	+	0.182657i	$0.0584697\pi$
$881$			321.841i			0.365314i	−0.983177	+	0.182657i	$0.941530\pi$
$882$	166.828	−	121.726i	0.189147	−	0.138012i
$883$	−62.2551			−0.0705040			−0.0352520	−	0.999378i	$-0.511223\pi$
$883$	−62.2551			−0.0705040			−0.0352520	+	0.999378i	$0.511223\pi$
$884$			2644.07i			2.99103i
$885$	853.651	+	433.865i	0.964578	+	0.490243i
$886$	1152.06			1.30029
$887$		−	633.077i		−	0.713728i	−0.934156	−	0.356864i	$-0.883846\pi$
$887$		−	633.077i		−	0.713728i	0.934156	−	0.356864i	$-0.116154\pi$
$888$	−739.042	+	1454.10i	−0.832254	+	1.63750i
$889$	358.611			0.403386
$890$			370.664i			0.416477i
$891$	261.791	+	83.8864i	0.293817	+	0.0941486i
$892$	−2368.27			−2.65502
$893$		−	337.415i		−	0.377844i
$894$	343.951	+	174.812i	0.384733	+	0.195539i
$895$	−1939.17			−2.16667
$896$			582.476i			0.650085i
$897$	156.388	−	307.701i	0.174345	−	0.343033i
$898$	−851.957			−0.948727
$899$		−	21.2267i		−	0.0236114i
$900$	1316.29	+	1804.00i	1.46254	+	2.00444i
$901$	757.537			0.840773
$902$		−	521.458i		−	0.578113i
$903$	−59.0434	−	30.0086i	−0.0653858	−	0.0332321i
$904$	185.781			0.205510
$905$		−	1586.74i		−	1.75330i
$906$	−988.874	+	1945.66i	−1.09147	+	2.14753i
$907$	619.732			0.683277			0.341638	−	0.939831i	$-0.389018\pi$
$907$	619.732			0.683277			0.341638	+	0.939831i	$0.389018\pi$
$908$			1542.33i			1.69860i
$909$	−321.575	+	234.638i	−0.353768	+	0.258128i
$910$	1635.46			1.79721
$911$			1133.98i			1.24476i	0.782714	+	0.622381i	$0.213835\pi$
$911$			1133.98i			1.24476i	−0.782714	+	0.622381i	$0.786165\pi$
$912$	−213.538	−	108.530i	−0.234142	−	0.119002i
$913$	206.401			0.226069
$914$		−	1737.76i		−	1.90127i
$915$	−523.782	+	1030.57i	−0.572439	+	1.12630i
$916$	−282.097			−0.307966
$917$		−	582.659i		−	0.635397i
$918$	230.573	+	1427.60i	0.251169	+	1.55512i
$919$	964.158			1.04914			0.524569	−	0.851368i	$-0.324226\pi$
$919$	964.158			1.04914			0.524569	+	0.851368i	$0.324226\pi$
$920$		−	339.261i		−	0.368762i
$921$	−1298.41	−	659.910i	−1.40978	−	0.716515i
$922$	−1791.23			−1.94276
$923$		−	2982.26i		−	3.23105i
$924$	82.3297	−	161.988i	0.0891014	−	0.175312i
$925$	−2222.30			−2.40248
$926$		−	12.0323i		−	0.0129938i
$927$	301.767	+	413.577i	0.325531	+	0.446146i
$928$	502.024			0.540975
$929$			1479.68i			1.59276i	0.604793	+	0.796382i	$0.293256\pi$
$929$			1479.68i			1.59276i	−0.604793	+	0.796382i	$0.706744\pi$
$930$	80.8241	+	41.0785i	0.0869076	+	0.0441705i
$931$	−221.831			−0.238271
$932$		−	1008.90i		−	1.08251i
$933$	78.1416	−	153.748i	0.0837531	−	0.164788i
$934$	−566.734			−0.606782
$935$			435.869i			0.466170i
$936$	1569.73	−	1145.36i	1.67707	−	1.22367i
$937$	−1694.37			−1.80830			−0.904148	−	0.427219i	$-0.859493\pi$
$937$	−1694.37			−1.80830			−0.904148	+	0.427219i	$0.859493\pi$
$938$		−	583.958i		−	0.622556i
$939$	−779.218	−	396.035i	−0.829838	−	0.421762i
$940$	564.538			0.600572
$941$		−	1689.92i		−	1.79588i	−0.440117	−	0.897940i	$-0.645063\pi$
$941$		−	1689.92i		−	1.79588i	0.440117	−	0.897940i	$-0.354937\pi$
$942$	−363.875	+	715.942i	−0.386279	+	0.760024i
$943$	−224.790			−0.238377
$944$		−	102.315i		−	0.108384i
$945$	554.320	−	89.5285i	0.586582	−	0.0947392i
$946$	−92.8330			−0.0981321
$947$			1264.75i			1.33554i	0.744370	+	0.667768i	$0.232750\pi$
$947$			1264.75i			1.33554i	−0.744370	+	0.667768i	$0.767250\pi$
$948$	1481.15	+	752.788i	1.56239	+	0.794081i
$949$	−643.119			−0.677680
$950$		−	3821.22i		−	4.02233i
$951$	−307.563	+	605.146i	−0.323410	+	0.636326i
$952$	389.047			0.408663
$953$		−	308.177i		−	0.323376i	−0.986842	−	0.161688i	$-0.948306\pi$
$953$		−	308.177i		−	0.323376i	0.986842	−	0.161688i	$-0.0516938\pi$
$954$	−806.246	−	1104.97i	−0.845121	−	1.15825i
$955$	1021.35			1.06948
$956$			2446.62i			2.55923i
$957$	−164.264	−	83.4864i	−0.171644	−	0.0872376i
$958$	−2498.42			−2.60795
$959$			224.796i			0.234407i
$960$	−1079.21	+	2123.40i	−1.12418	+	2.21188i
$961$	−959.624			−0.998568
$962$			4751.03i			4.93870i
$963$	500.752	−	365.375i	0.519992	−	0.379413i
$964$	−1035.33			−1.07399
$965$		−	2146.69i		−	2.22455i
$966$	−111.238	−	56.5362i	−0.115153	−	0.0585261i
$967$	187.391			0.193786			0.0968928	−	0.995295i	$-0.469110\pi$
$967$	187.391			0.193786			0.0968928	+	0.995295i	$0.469110\pi$
$968$			985.309i			1.01788i
$969$	703.796	−	1384.75i	0.726312	−	1.42906i
$970$	4352.33			4.48694
$971$		−	363.101i		−	0.373945i	−0.982365	−	0.186973i	$-0.940132\pi$
$971$		−	363.101i		−	0.373945i	0.982365	−	0.186973i	$-0.0598676\pi$
$972$	1153.15	−	1164.93i	1.18637	−	1.19849i
$973$	240.515			0.247189
$974$			943.889i			0.969085i
$975$	2360.09	+	1199.51i	2.42061	+	1.23027i
$976$	123.519			0.126556
$977$		−	755.765i		−	0.773557i	−0.922173	−	0.386778i	$-0.873588\pi$
$977$		−	755.765i		−	0.773557i	0.922173	−	0.386778i	$-0.126412\pi$
$978$	−605.192	+	1190.74i	−0.618805	+	1.21753i
$979$	48.8228			0.0498700
$980$		−	371.151i		−	0.378725i
$981$	873.733	+	1197.47i	0.890656	+	1.22066i
$982$	1111.64			1.13202
$983$		−	1019.16i		−	1.03678i	−0.855143	−	0.518392i	$-0.826531\pi$
$983$		−	1019.16i		−	1.03678i	0.855143	−	0.518392i	$-0.173469\pi$
$984$	−1128.16	−	573.382i	−1.14650	−	0.582705i
$985$	1313.12			1.33311
$986$		−	969.296i		−	0.983058i
$987$	38.2904	−	75.3384i	0.0387948	−	0.0763307i
$988$	−5128.31			−5.19059
$989$			40.0184i			0.0404635i
$990$	635.776	−	463.895i	0.642198	−	0.468581i
$991$	−1573.93			−1.58823			−0.794114	−	0.607769i	$-0.792065\pi$
$991$	−1573.93			−1.58823			−0.794114	+	0.607769i	$0.792065\pi$
$992$			32.5361i			0.0327985i
$993$	638.318	+	324.423i	0.642818	+	0.326710i
$994$	−1078.13			−1.08463
$995$		−	2114.59i		−	2.12522i
$996$	557.611	−	1097.13i	0.559851	−	1.10153i
$997$	−847.447			−0.849997			−0.424998	−	0.905194i	$-0.639725\pi$
$997$	−847.447			−0.849997			−0.424998	+	0.905194i	$0.639725\pi$
$998$		−	192.890i		−	0.193277i
$999$	260.082	+	1610.31i	0.260342	+	1.61192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.10	✓	88
3.2	odd	2	inner	483.3.b.a.323.79	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.10	✓	88	1.1	even	1	trivial
483.3.b.a.323.79	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)

\(f(q)\)	\(=\)	\(q-3.27803i q^{2} +(2.67440 + 1.35925i) q^{3} -6.74548 q^{4} +7.86031i q^{5} +(4.45568 - 8.76677i) q^{6} -2.64575 q^{7} +8.99976i q^{8} +(5.30485 + 7.27039i) q^{9} +O(q^{10})\)	\(q-3.27803i q^{2} +(2.67440 + 1.35925i) q^{3} -6.74548 q^{4} +7.86031i q^{5} +(4.45568 - 8.76677i) q^{6} -2.64575 q^{7} +8.99976i q^{8} +(5.30485 + 7.27039i) q^{9} +25.7663 q^{10} -3.39386i q^{11} +(-18.0401 - 9.16882i) q^{12} -23.9904 q^{13} +8.67285i q^{14} +(-10.6842 + 21.0216i) q^{15} +2.51956 q^{16} +16.3389i q^{17} +(23.8325 - 17.3895i) q^{18} -31.6901 q^{19} -53.0216i q^{20} +(-7.07580 - 3.59625i) q^{21} -11.1252 q^{22} +4.79583i q^{23} +(-12.2330 + 24.0690i) q^{24} -36.7845 q^{25} +78.6413i q^{26} +(4.30499 + 26.6546i) q^{27} +17.8469 q^{28} -18.0976i q^{29} +(68.9095 + 35.0230i) q^{30} +1.17290 q^{31} +27.7398i q^{32} +(4.61312 - 9.07655i) q^{33} +53.5594 q^{34} -20.7964i q^{35} +(-35.7838 - 49.0422i) q^{36} +60.4140 q^{37} +103.881i q^{38} +(-64.1600 - 32.6091i) q^{39} -70.7409 q^{40} +46.8719i q^{41} +(-11.7886 + 23.1947i) q^{42} +8.34441 q^{43} +22.8932i q^{44} +(-57.1475 + 41.6978i) q^{45} +15.7209 q^{46} +10.6473i q^{47} +(6.73831 + 3.42472i) q^{48} +7.00000 q^{49} +120.581i q^{50} +(-22.2087 + 43.6968i) q^{51} +161.827 q^{52} -46.3640i q^{53} +(87.3745 - 14.1119i) q^{54} +26.6768 q^{55} -23.8111i q^{56} +(-84.7521 - 43.0749i) q^{57} -59.3244 q^{58} -40.6082i q^{59} +(72.0698 - 141.801i) q^{60} +49.0241 q^{61} -3.84480i q^{62} +(-14.0353 - 19.2356i) q^{63} +101.010 q^{64} -188.572i q^{65} +(-29.7532 - 15.1220i) q^{66} -67.3317 q^{67} -110.214i q^{68} +(-6.51876 + 12.8260i) q^{69} -68.1713 q^{70} +124.310i q^{71} +(-65.4317 + 47.7424i) q^{72} +26.8073 q^{73} -198.039i q^{74} +(-98.3766 - 49.9995i) q^{75} +213.765 q^{76} +8.97931i q^{77} +(-106.894 + 210.318i) q^{78} -82.1030 q^{79} +19.8045i q^{80} +(-24.7171 + 77.1367i) q^{81} +153.647 q^{82} +60.8160i q^{83} +(47.7297 + 24.2584i) q^{84} -128.429 q^{85} -27.3532i q^{86} +(24.5992 - 48.4002i) q^{87} +30.5439 q^{88} +14.3856i q^{89} +(136.687 + 187.331i) q^{90} +63.4727 q^{91} -32.3502i q^{92} +(3.13681 + 1.59427i) q^{93} +34.9022 q^{94} -249.094i q^{95} +(-37.7055 + 74.1875i) q^{96} +168.915 q^{97} -22.9462i q^{98} +(24.6747 - 18.0039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) \) 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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