LMFDB - Embedded newform 82.5.e.a.3.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,5,Mod(3,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	82.e (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.47633697288$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	82.3
Dual form			82.5.e.a.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 2.00000i) q^{2} +(-6.17854 + 14.9163i) q^{3} -8.00000i q^{4} +(-15.3528 - 15.3528i) q^{5} +(-17.4755 - 42.1897i) q^{6} +(22.0538 - 53.2426i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-127.046 - 127.046i) q^{9} +61.4114 q^{10} +(83.2830 + 34.4969i) q^{11} +(119.331 + 49.4283i) q^{12} +(-67.8795 + 163.876i) q^{13} +(62.3776 + 150.593i) q^{14} +(323.866 - 134.150i) q^{15} -64.0000 q^{16} +(-126.148 - 304.547i) q^{17} +508.186 q^{18} +(161.625 + 390.198i) q^{19} +(-122.823 + 122.823i) q^{20} +(657.924 + 657.924i) q^{21} +(-235.560 + 97.5720i) q^{22} -688.349i q^{23} +(-337.518 + 139.804i) q^{24} -153.580i q^{25} +(-191.992 - 463.510i) q^{26} +(1471.80 - 609.641i) q^{27} +(-425.941 - 176.431i) q^{28} +(438.038 - 1057.52i) q^{29} +(-379.433 + 916.032i) q^{30} -936.544i q^{31} +(128.000 - 128.000i) q^{32} +(-1029.13 + 1029.13i) q^{33} +(861.389 + 356.799i) q^{34} +(-1156.02 + 478.837i) q^{35} +(-1016.37 + 1016.37i) q^{36} +1388.73 q^{37} +(-1103.65 - 457.145i) q^{38} +(-2025.02 - 2025.02i) q^{39} -491.291i q^{40} +(953.792 + 1384.21i) q^{41} -2631.69 q^{42} +(-661.387 + 661.387i) q^{43} +(275.975 - 666.264i) q^{44} +3901.05i q^{45} +(1376.70 + 1376.70i) q^{46} +(-883.211 - 2132.26i) q^{47} +(395.427 - 954.644i) q^{48} +(-650.645 - 650.645i) q^{49} +(307.160 + 307.160i) q^{50} +5322.13 q^{51} +(1311.00 + 543.036i) q^{52} +(-2183.05 - 904.248i) q^{53} +(-1724.33 + 4162.89i) q^{54} +(-749.004 - 1808.26i) q^{55} +(1204.74 - 499.021i) q^{56} -6818.92 q^{57} +(1238.96 + 2991.11i) q^{58} -1164.44 q^{59} +(-1073.20 - 2590.93i) q^{60} +(548.607 - 548.607i) q^{61} +(1873.09 + 1873.09i) q^{62} +(-9566.15 + 3962.43i) q^{63} +512.000i q^{64} +(3558.10 - 1473.81i) q^{65} -4116.54i q^{66} +(-3128.19 - 7552.13i) q^{67} +(-2436.38 + 1009.18i) q^{68} +(10267.6 + 4252.99i) q^{69} +(1354.36 - 3269.71i) q^{70} +(3367.37 - 8129.56i) q^{71} -4065.49i q^{72} +(-3900.01 + 3900.01i) q^{73} +(-2777.46 + 2777.46i) q^{74} +(2290.85 + 948.901i) q^{75} +(3121.58 - 1293.00i) q^{76} +(3673.42 - 3673.42i) q^{77} +8100.09 q^{78} +(6099.03 + 2526.30i) q^{79} +(982.582 + 982.582i) q^{80} +11167.3i q^{81} +(-4676.01 - 860.840i) q^{82} -12570.4 q^{83} +(5263.39 - 5263.39i) q^{84} +(-2738.94 + 6612.39i) q^{85} -2645.55i q^{86} +(13067.8 + 13067.8i) q^{87} +(780.576 + 1884.48i) q^{88} +(860.411 - 2077.22i) q^{89} +(-7802.10 - 7802.10i) q^{90} +(7228.17 + 7228.17i) q^{91} -5506.79 q^{92} +(13969.8 + 5786.47i) q^{93} +(6030.94 + 2498.10i) q^{94} +(3509.24 - 8472.06i) q^{95} +(1118.44 + 2700.14i) q^{96} +(7775.29 - 3220.63i) q^{97} +2602.58 q^{98} +(-6198.09 - 14963.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 56 q^{2} + 16 q^{3} - 16 q^{6} + 448 q^{8} + 24 q^{9} + 328 q^{11} - 64 q^{12} - 348 q^{13} + 192 q^{14} + 1036 q^{15} - 1792 q^{16} - 1832 q^{17} - 96 q^{18} - 504 q^{19} + 2004 q^{21} - 856 q^{22}+ \cdots + 11544 q^{99}+O(q^{100}) $ 28 * q - 56 * q^2 + 16 * q^3 - 16 * q^6 + 448 * q^8 + 24 * q^9 + 328 * q^11 - 64 * q^12 - 348 * q^13 + 192 * q^14 + 1036 * q^15 - 1792 * q^16 - 1832 * q^17 - 96 * q^18 - 504 * q^19 + 2004 * q^21 - 856 * q^22 + 384 * q^24 + 384 * q^26 + 964 * q^27 - 768 * q^28 - 4 * q^29 - 4456 * q^30 + 3584 * q^32 - 748 * q^33 + 3576 * q^34 - 1104 * q^35 + 192 * q^36 + 5488 * q^37 + 256 * q^38 + 1232 * q^39 - 3760 * q^41 - 8016 * q^42 + 4756 * q^43 + 800 * q^44 - 2320 * q^46 - 4240 * q^47 - 1024 * q^48 + 2088 * q^49 - 6280 * q^50 + 29792 * q^51 + 1248 * q^52 - 10492 * q^53 - 1992 * q^54 + 14840 * q^55 + 1536 * q^56 - 33512 * q^57 + 2192 * q^58 - 11376 * q^59 + 9536 * q^60 - 3360 * q^61 + 2224 * q^62 - 13912 * q^63 + 41300 * q^65 + 15440 * q^67 + 352 * q^68 - 1004 * q^69 - 6792 * q^70 - 28392 * q^71 + 4284 * q^73 - 10976 * q^74 + 23812 * q^75 + 3008 * q^76 - 16524 * q^77 - 4928 * q^78 - 22236 * q^79 + 16752 * q^82 - 4024 * q^83 + 16032 * q^84 - 16616 * q^85 - 4628 * q^87 + 3648 * q^88 - 54412 * q^89 + 18336 * q^90 + 59948 * q^91 + 9280 * q^92 - 26800 * q^93 - 3240 * q^94 - 47636 * q^95 + 1024 * q^96 + 46764 * q^97 - 8352 * q^98 + 11544 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$	−6.17854	+	14.9163i	−0.686504	+	1.65737i	0.0652035	+	0.997872i	$0.479230\pi$
$3$	−6.17854	+	14.9163i	−0.686504	+	1.65737i	−0.751708	+	0.659496i	$0.770770\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−15.3528	−	15.3528i	−0.614114	−	0.614114i	0.329901	−	0.944015i	$-0.392984\pi$
$5$	−15.3528	−	15.3528i	−0.614114	−	0.614114i	−0.944015	+	0.329901i	$0.892984\pi$
$6$	−17.4755	−	42.1897i	−0.485432	−	1.17194i
$7$	22.0538	−	53.2426i	0.450078	−	1.08658i	−0.522214	−	0.852815i	$-0.674894\pi$
$7$	22.0538	−	53.2426i	0.450078	−	1.08658i	0.972292	−	0.233770i	$-0.0751063\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	−127.046	−	127.046i	−1.56847	−	1.56847i
$10$	61.4114			0.614114
$11$	83.2830	+	34.4969i	0.688289	+	0.285099i	0.699287	−	0.714841i	$-0.253501\pi$
$11$	83.2830	+	34.4969i	0.688289	+	0.285099i	−0.0109982	+	0.999940i	$0.503501\pi$
$12$	119.331	+	49.4283i	0.828684	+	0.343252i
$13$	−67.8795	+	163.876i	−0.401654	+	0.969678i	0.585611	+	0.810592i	$0.300855\pi$
$13$	−67.8795	+	163.876i	−0.401654	+	0.969678i	−0.987265	+	0.159086i	$0.949145\pi$
$14$	62.3776	+	150.593i	0.318253	+	0.768331i
$15$	323.866	−	134.150i	1.43940	−	0.596221i
$16$	−64.0000			−0.250000
$17$	−126.148	−	304.547i	−0.436497	−	1.05380i	−0.977150	−	0.212551i	$-0.931823\pi$
$17$	−126.148	−	304.547i	−0.436497	−	1.05380i	0.540653	−	0.841245i	$-0.318177\pi$
$18$	508.186			1.56847
$19$	161.625	+	390.198i	0.447716	+	1.08088i	0.973176	+	0.230063i	$0.0738932\pi$
$19$	161.625	+	390.198i	0.447716	+	1.08088i	−0.525460	+	0.850818i	$0.676107\pi$
$20$	−122.823	+	122.823i	−0.307057	+	0.307057i
$21$	657.924	+	657.924i	1.49189	+	1.49189i
$22$	−235.560	+	97.5720i	−0.486694	+	0.201595i
$23$		−	688.349i		−	1.30123i	−0.759409	−	0.650613i	$-0.774512\pi$
$23$		−	688.349i		−	1.30123i	0.759409	−	0.650613i	$-0.225488\pi$
$24$	−337.518	+	139.804i	−0.585968	+	0.242716i
$25$		−	153.580i		−	0.245728i
$26$	−191.992	−	463.510i	−0.284012	−	0.685666i
$27$	1471.80	−	609.641i	2.01894	−	0.836270i
$28$	−425.941	−	176.431i	−0.543292	−	0.225039i
$29$	438.038	−	1057.52i	0.520854	−	1.25745i	−0.416520	−	0.909127i	$-0.636750\pi$
$29$	438.038	−	1057.52i	0.520854	−	1.25745i	0.937373	−	0.348326i	$-0.113250\pi$
$30$	−379.433	+	916.032i	−0.421592	+	1.01781i
$31$		−	936.544i		−	0.974551i	−0.873248	−	0.487276i	$-0.837991\pi$
$31$		−	936.544i		−	0.974551i	0.873248	−	0.487276i	$-0.162009\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	−1029.13	+	1029.13i	−0.945027	+	0.945027i
$34$	861.389	+	356.799i	0.745146	+	0.308650i
$35$	−1156.02	+	478.837i	−0.943686	+	0.390888i
$36$	−1016.37	+	1016.37i	−0.784237	+	0.784237i
$37$	1388.73			1.01441			0.507206	−	0.861825i	$-0.330679\pi$
$37$	1388.73			1.01441			0.507206	+	0.861825i	$0.330679\pi$
$38$	−1103.65	−	457.145i	−0.764298	−	0.316583i
$39$	−2025.02	−	2025.02i	−1.33138	−	1.33138i
$40$		−	491.291i		−	0.307057i
$41$	953.792	+	1384.21i	0.567395	+	0.823445i
$41$	953.792	+	1384.21i	0.567395	+	0.823445i
$42$	−2631.69			−1.49189
$43$	−661.387	+	661.387i	−0.357700	+	0.357700i	−0.862965	−	0.505264i	$-0.831395\pi$
$43$	−661.387	+	661.387i	−0.357700	+	0.357700i	0.505264	+	0.862965i	$0.331395\pi$
$44$	275.975	−	666.264i	0.142549	−	0.344144i
$45$			3901.05i			1.92644i
$46$	1376.70	+	1376.70i	0.650613	+	0.650613i
$47$	−883.211	−	2132.26i	−0.399824	−	0.965260i	−0.987707	−	0.156315i	$-0.950039\pi$
$47$	−883.211	−	2132.26i	−0.399824	−	0.965260i	0.587883	−	0.808946i	$-0.299961\pi$
$48$	395.427	−	954.644i	0.171626	−	0.414342i
$49$	−650.645	−	650.645i	−0.270989	−	0.270989i
$50$	307.160	+	307.160i	0.122864	+	0.122864i
$51$	5322.13			2.04619
$52$	1311.00	+	543.036i	0.484839	+	0.200827i
$53$	−2183.05	−	904.248i	−0.777162	−	0.321911i	−0.0413925	−	0.999143i	$-0.513179\pi$
$53$	−2183.05	−	904.248i	−0.777162	−	0.321911i	−0.735770	+	0.677232i	$0.763179\pi$
$54$	−1724.33	+	4162.89i	−0.591333	+	1.42760i
$55$	−749.004	−	1808.26i	−0.247605	−	0.597771i
$56$	1204.74	−	499.021i	0.384166	−	0.159127i
$57$	−6818.92			−2.09878
$58$	1238.96	+	2991.11i	0.368299	+	0.889153i
$59$	−1164.44			−0.334512			−0.167256	−	0.985914i	$-0.553491\pi$
$59$	−1164.44			−0.334512			−0.167256	+	0.985914i	$0.553491\pi$
$60$	−1073.20	−	2590.93i	−0.298110	−	0.719702i
$61$	548.607	−	548.607i	0.147435	−	0.147435i	−0.629536	−	0.776971i	$-0.716755\pi$
$61$	548.607	−	548.607i	0.147435	−	0.147435i	0.776971	+	0.629536i	$0.216755\pi$
$62$	1873.09	+	1873.09i	0.487276	+	0.487276i
$63$	−9566.15	+	3962.43i	−2.41022	+	0.998344i
$64$			512.000i			0.125000i
$65$	3558.10	−	1473.81i	0.842154	−	0.348832i
$66$		−	4116.54i		−	0.945027i
$67$	−3128.19	−	7552.13i	−0.696858	−	1.68236i	−0.730485	−	0.682929i	$-0.760706\pi$
$67$	−3128.19	−	7552.13i	−0.696858	−	1.68236i	0.0336275	−	0.999434i	$-0.489294\pi$
$68$	−2436.38	+	1009.18i	−0.526898	+	0.218248i
$69$	10267.6	+	4252.99i	2.15661	+	0.893298i
$70$	1354.36	−	3269.71i	0.276399	−	0.667287i
$71$	3367.37	−	8129.56i	0.667997	−	1.61269i	−0.116959	−	0.993137i	$-0.537315\pi$
$71$	3367.37	−	8129.56i	0.667997	−	1.61269i	0.784956	−	0.619551i	$-0.212685\pi$
$72$		−	4065.49i		−	0.784237i
$73$	−3900.01	+	3900.01i	−0.731847	+	0.731847i	−0.970986	−	0.239138i	$-0.923135\pi$
$73$	−3900.01	+	3900.01i	−0.731847	+	0.731847i	0.239138	+	0.970986i	$0.423135\pi$
$74$	−2777.46	+	2777.46i	−0.507206	+	0.507206i
$75$	2290.85	+	948.901i	0.407262	+	0.168693i
$76$	3121.58	−	1293.00i	0.540440	−	0.223858i
$77$	3673.42	−	3673.42i	0.619567	−	0.619567i
$78$	8100.09			1.33138
$79$	6099.03	+	2526.30i	0.977251	+	0.404791i	0.813407	−	0.581695i	$-0.197610\pi$
$79$	6099.03	+	2526.30i	0.977251	+	0.404791i	0.163845	+	0.986486i	$0.447610\pi$
$80$	982.582	+	982.582i	0.153528	+	0.153528i
$81$			11167.3i			1.70207i
$82$	−4676.01	−	860.840i	−0.695420	−	0.128025i
$83$	−12570.4			−1.82471			−0.912356	−	0.409397i	$-0.865739\pi$
$83$	−12570.4			−1.82471			−0.912356	+	0.409397i	$0.865739\pi$
$84$	5263.39	−	5263.39i	0.745945	−	0.745945i
$85$	−2738.94	+	6612.39i	−0.379092	+	0.915210i
$86$		−	2645.55i		−	0.357700i
$87$	13067.8	+	13067.8i	1.72649	+	1.72649i
$88$	780.576	+	1884.48i	0.100798	+	0.243347i
$89$	860.411	−	2077.22i	0.108624	−	0.262242i	−0.860216	−	0.509931i	$-0.829671\pi$
$89$	860.411	−	2077.22i	0.108624	−	0.262242i	0.968840	+	0.247689i	$0.0796711\pi$
$90$	−7802.10	−	7802.10i	−0.963222	−	0.963222i
$91$	7228.17	+	7228.17i	0.872862	+	0.872862i
$92$	−5506.79			−0.650613
$93$	13969.8	+	5786.47i	1.61519	+	0.669034i
$94$	6030.94	+	2498.10i	0.682542	+	0.282718i
$95$	3509.24	−	8472.06i	0.388836	−	0.938732i
$96$	1118.44	+	2700.14i	0.121358	+	0.292984i
$97$	7775.29	−	3220.63i	0.826367	−	0.342292i	0.0709035	−	0.997483i	$-0.477412\pi$
$97$	7775.29	−	3220.63i	0.826367	−	0.342292i	0.755463	+	0.655191i	$0.227412\pi$
$98$	2602.58			0.270989
$99$	−6198.09	−	14963.5i	−0.632394	−	1.52673i
$100$	−1228.64			−0.122864
$101$	−3977.12	−	9601.61i	−0.389875	−	0.941242i	−0.989965	−	0.141309i	$-0.954869\pi$
$101$	−3977.12	−	9601.61i	−0.389875	−	0.941242i	0.600090	−	0.799932i	$-0.295131\pi$
$102$	−10644.3	+	10644.3i	−1.02309	+	1.02309i
$103$	−1871.20	−	1871.20i	−0.176378	−	0.176378i	0.613397	−	0.789775i	$-0.289803\pi$
$103$	−1871.20	−	1871.20i	−0.176378	−	0.176378i	−0.789775	+	0.613397i	$0.789803\pi$
$104$	−3708.08	+	1535.94i	−0.342833	+	0.142006i
$105$		−	20202.0i		−	1.83238i
$106$	6174.59	−	2557.60i	0.549537	−	0.227626i
$107$			6878.67i			0.600809i	0.953812	+	0.300405i	$0.0971217\pi$
$107$			6878.67i			0.600809i	−0.953812	+	0.300405i	$0.902878\pi$
$108$	−4877.13	−	11774.4i	−0.418135	−	1.00947i
$109$	−14504.3	+	6007.86i	−1.22079	+	0.505670i	−0.897662	−	0.440684i	$-0.854736\pi$
$109$	−14504.3	+	6007.86i	−1.22079	+	0.505670i	−0.323132	+	0.946354i	$0.604736\pi$
$110$	5114.52	+	2118.50i	0.422688	+	0.175083i
$111$	−8580.32	+	20714.7i	−0.696398	+	1.68125i
$112$	−1411.44	+	3407.53i	−0.112520	+	0.271646i
$113$		−	3332.44i		−	0.260979i	−0.991450	−	0.130490i	$-0.958345\pi$
$113$		−	3332.44i		−	0.260979i	0.991450	−	0.130490i	$-0.0416549\pi$
$114$	13637.8	−	13637.8i	1.04939	−	1.04939i
$115$	−10568.1	+	10568.1i	−0.799101	+	0.799101i
$116$	−8460.14	−	3504.31i	−0.628726	−	0.260427i
$117$	29443.7	−	12196.0i	2.15090	−	0.890931i
$118$	2328.87	−	2328.87i	0.167256	−	0.167256i
$119$	−18996.9			−1.34150
$120$	7328.25	+	3035.46i	0.508906	+	0.210796i
$121$	−4606.74	−	4606.74i	−0.314646	−	0.314646i
$122$			2194.43i			0.147435i
$123$	−26540.4	+	5674.65i	−1.75427	+	0.375084i
$124$	−7492.35			−0.487276
$125$	−11953.4	+	11953.4i	−0.765019	+	0.765019i
$126$	11207.4	−	27057.2i	0.705936	−	1.70428i
$127$			24046.7i			1.49090i	0.666561	+	0.745451i	$0.267766\pi$
$127$			24046.7i			1.49090i	−0.666561	+	0.745451i	$0.732234\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	−5779.05	−	13951.9i	−0.347278	−	0.838403i
$130$	−4168.57	+	10063.8i	−0.246661	+	0.595493i
$131$	−15076.1	−	15076.1i	−0.878511	−	0.878511i	0.114869	−	0.993381i	$-0.463355\pi$
$131$	−15076.1	−	15076.1i	−0.878511	−	0.878511i	−0.993381	+	0.114869i	$0.963355\pi$
$132$	8233.07	+	8233.07i	0.472513	+	0.472513i
$133$	24339.6			1.37598
$134$	21360.6	+	8847.87i	1.18961	+	0.492753i
$135$	−31956.1	−	13236.7i	−1.75342	−	0.726291i
$136$	2854.39	−	6891.11i	0.154325	−	0.372573i
$137$	1227.07	+	2962.42i	0.0653776	+	0.157836i	0.953192	−	0.302367i	$-0.0977768\pi$
$137$	1227.07	+	2962.42i	0.0653776	+	0.157836i	−0.887814	+	0.460203i	$0.847777\pi$
$138$	−29041.2	+	12029.3i	−1.52495	+	0.631657i
$139$	30115.2			1.55868			0.779338	−	0.626604i	$-0.215555\pi$
$139$	30115.2			1.55868			0.779338	+	0.626604i	$0.215555\pi$
$140$	3830.70	+	9248.12i	0.195444	+	0.471843i
$141$	37262.4			1.87427
$142$	9524.37	+	22993.9i	0.472345	+	1.14034i
$143$	−11306.4	+	11306.4i	−0.552908	+	0.552908i
$144$	8130.97	+	8130.97i	0.392119	+	0.392119i
$145$	−22961.0	+	9510.78i	−1.09208	+	0.452356i
$146$		−	15600.1i		−	0.731847i
$147$	13725.3	−	5685.19i	0.635164	−	0.263094i
$148$		−	11109.8i		−	0.507206i
$149$	3804.38	+	9184.59i	0.171361	+	0.413701i	0.986106	−	0.166118i	$-0.0531232\pi$
$149$	3804.38	+	9184.59i	0.171361	+	0.413701i	−0.814745	+	0.579819i	$0.803123\pi$
$150$	−6479.50	+	2683.90i	−0.287978	+	0.119284i
$151$	19199.9	+	7952.86i	0.842064	+	0.348794i	0.761667	−	0.647969i	$-0.224381\pi$
$151$	19199.9	+	7952.86i	0.842064	+	0.348794i	0.0803967	+	0.996763i	$0.474381\pi$
$152$	−3657.16	+	8829.17i	−0.158291	+	0.382149i
$153$	−22665.0	+	54718.2i	−0.968218	+	2.33749i
$154$			14693.7i			0.619567i
$155$	−14378.6	+	14378.6i	−0.598485	+	0.598485i
$156$	−16200.2	+	16200.2i	−0.665688	+	0.665688i
$157$	−22391.2	−	9274.74i	−0.908402	−	0.376272i	−0.120957	−	0.992658i	$-0.538596\pi$
$157$	−22391.2	−	9274.74i	−0.908402	−	0.376272i	−0.787445	+	0.616385i	$0.788596\pi$
$158$	−17250.7	+	7145.45i	−0.691021	+	0.286230i
$159$	26976.1	−	26976.1i	1.06705	−	1.06705i
$160$	−3930.33			−0.153528
$161$	−36649.5	−	15180.7i	−1.41389	−	0.585654i
$162$	−22334.5	−	22334.5i	−0.851033	−	0.851033i
$163$		−	34619.0i		−	1.30299i	−0.758655	−	0.651493i	$-0.774143\pi$
$163$		−	34619.0i		−	1.30299i	0.758655	−	0.651493i	$-0.225857\pi$
$164$	11073.7	−	7630.33i	0.411723	−	0.283698i
$165$	31600.3			1.16071
$166$	25140.9	−	25140.9i	0.912356	−	0.912356i
$167$	−776.824	+	1875.42i	−0.0278541	+	0.0672458i	−0.937195	−	0.348807i	$-0.886587\pi$
$167$	−776.824	+	1875.42i	−0.0278541	+	0.0672458i	0.909340	+	0.416053i	$0.136587\pi$
$168$			21053.6i			0.745945i
$169$	−2051.91	−	2051.91i	−0.0718430	−	0.0718430i
$170$	−7746.90	−	18702.7i	−0.268059	−	0.647151i
$171$	29039.3	−	70107.2i	0.993104	−	2.39756i
$172$	5291.10	+	5291.10i	0.178850	+	0.178850i
$173$	18910.2	+	18910.2i	0.631836	+	0.631836i	0.948528	−	0.316692i	$-0.102572\pi$
$173$	18910.2	+	18910.2i	0.631836	+	0.631836i	−0.316692	+	0.948528i	$0.602572\pi$
$174$	−52271.3			−1.72649
$175$	−8177.01	−	3387.03i	−0.267004	−	0.110597i
$176$	−5330.11	−	2207.80i	−0.172072	−	0.0712746i
$177$	7194.51	−	17369.1i	0.229644	−	0.554409i
$178$	2433.61	+	5875.26i	0.0768088	+	0.185433i
$179$	−932.003	+	386.048i	−0.0290878	+	0.0120486i	−0.397180	−	0.917741i	$-0.630011\pi$
$179$	−932.003	+	386.048i	−0.0290878	+	0.0120486i	0.368092	+	0.929789i	$0.380011\pi$
$180$	31208.4			0.963222
$181$	8959.60	+	21630.4i	0.273484	+	0.660248i	0.999627	−	0.0272947i	$-0.00868925\pi$
$181$	8959.60	+	21630.4i	0.273484	+	0.660248i	−0.726144	+	0.687543i	$0.758689\pi$
$182$	−28912.7			−0.872862
$183$	4793.60	+	11572.8i	0.143140	+	0.345570i
$184$	11013.6	−	11013.6i	0.325307	−	0.325307i
$185$	−21320.9	−	21320.9i	−0.622964	−	0.622964i
$186$	−39512.5	+	16366.6i	−1.14211	+	0.473078i
$187$		−	29715.3i		−	0.849761i
$188$	−17058.1	+	7065.69i	−0.482630	+	0.199912i
$189$		−	91807.7i		−	2.57013i
$190$	9925.64	+	23962.6i	0.274948	+	0.663784i
$191$	5503.42	−	2279.59i	0.150857	−	0.0624870i	−0.305977	−	0.952039i	$-0.598983\pi$
$191$	5503.42	−	2279.59i	0.150857	−	0.0624870i	0.456834	+	0.889552i	$0.348983\pi$
$192$	−7637.15	−	3163.41i	−0.207171	−	0.0858130i
$193$	−16409.4	+	39615.9i	−0.440534	+	1.06354i	0.535228	+	0.844708i	$0.320226\pi$
$193$	−16409.4	+	39615.9i	−0.440534	+	1.06354i	−0.975762	+	0.218835i	$0.929774\pi$
$194$	−9109.32	+	21991.8i	−0.242037	+	0.584330i
$195$			62179.8i			1.63523i
$196$	−5205.16	+	5205.16i	−0.135495	+	0.135495i
$197$	23441.0	−	23441.0i	0.604010	−	0.604010i	−0.337365	−	0.941374i	$-0.609535\pi$
$197$	23441.0	−	23441.0i	0.604010	−	0.604010i	0.941374	+	0.337365i	$0.109535\pi$
$198$	42323.2	+	17530.8i	1.07956	+	0.447170i
$199$	55159.4	−	22847.8i	1.39288	−	0.576949i	0.444985	−	0.895538i	$-0.353209\pi$
$199$	55159.4	−	22847.8i	1.39288	−	0.576949i	0.947893	+	0.318589i	$0.103209\pi$
$200$	2457.28	−	2457.28i	0.0614320	−	0.0614320i
$201$	131978.			3.26669
$202$	27157.4	+	11249.0i	0.665558	+	0.275683i
$203$	−46644.6	−	46644.6i	−1.13190	−	1.13190i
$204$		−	42577.0i		−	1.02309i
$205$	6608.17	−	35895.0i	0.157244	−	0.854135i
$206$	7484.79			0.176378
$207$	−87452.3	+	87452.3i	−2.04094	+	2.04094i
$208$	4344.29	−	10488.0i	0.100413	−	0.242420i
$209$			38072.4i			0.871601i
$210$	40404.0	+	40404.0i	0.916191	+	0.916191i
$211$	−5567.76	−	13441.8i	−0.125059	−	0.301919i	0.848933	−	0.528500i	$-0.177245\pi$
$211$	−5567.76	−	13441.8i	−0.125059	−	0.301919i	−0.973992	+	0.226581i	$0.927245\pi$
$212$	−7233.99	+	17464.4i	−0.160956	+	0.388581i
$213$	100458.	+	100458.i	2.21423	+	2.21423i
$214$	−13757.3	−	13757.3i	−0.300405	−	0.300405i
$215$	20308.4			0.439337
$216$	33303.1	+	13794.6i	0.713802	+	0.295666i
$217$	−49864.1	−	20654.4i	−1.05893	−	0.438624i
$218$	16992.8	−	41024.2i	0.357562	−	0.863232i
$219$	−34077.4	−	82270.2i	−0.710524	−	1.71536i
$220$	−14466.1	+	5992.04i	−0.298885	+	0.123802i
$221$	58470.7			1.19716
$222$	−24268.8	−	58590.1i	−0.492427	−	1.18883i
$223$	36521.7			0.734414			0.367207	−	0.930139i	$-0.380314\pi$
$223$	36521.7			0.734414			0.367207	+	0.930139i	$0.380314\pi$
$224$	−3992.17	−	9637.95i	−0.0795633	−	0.192083i
$225$	−19511.8	+	19511.8i	−0.385418	+	0.385418i
$226$	6664.89	+	6664.89i	0.130490	+	0.130490i
$227$	60485.0	−	25053.7i	1.17380	−	0.486206i	0.291356	−	0.956615i	$-0.405894\pi$
$227$	60485.0	−	25053.7i	1.17380	−	0.486206i	0.882449	+	0.470409i	$0.155894\pi$
$228$			54551.4i			1.04939i
$229$	−50553.8	+	20940.1i	−0.964013	+	0.399307i	−0.808480	−	0.588523i	$-0.799710\pi$
$229$	−50553.8	+	20940.1i	−0.964013	+	0.399307i	−0.155533	+	0.987831i	$0.549710\pi$
$230$		−	42272.5i		−	0.799101i
$231$	32097.5	+	77490.2i	0.601516	+	1.45219i
$232$	23928.9	−	9911.67i	0.444577	−	0.184150i
$233$	63815.5	+	26433.3i	1.17548	+	0.486899i	0.883000	−	0.469373i	$-0.155520\pi$
$233$	63815.5	+	26433.3i	1.17548	+	0.486899i	0.292478	+	0.956272i	$0.405520\pi$
$234$	−34495.4	+	83279.2i	−0.629984	+	1.52092i
$235$	−19176.5	+	46296.1i	−0.347242	+	0.838317i
$236$			9315.49i			0.167256i
$237$	−75366.1	+	75366.1i	−1.34177	+	1.34177i
$238$	37993.9	−	37993.9i	0.670748	−	0.670748i
$239$	−77644.9	−	32161.6i	−1.35931	−	0.563043i	−0.420438	−	0.907321i	$-0.638124\pi$
$239$	−77644.9	−	32161.6i	−1.35931	−	0.563043i	−0.938868	+	0.344278i	$0.888124\pi$
$240$	−20727.4	+	8585.58i	−0.359851	+	0.149055i
$241$	−54974.8	+	54974.8i	−0.946520	+	0.946520i	−0.998641	−	0.0521211i	$-0.983402\pi$
$241$	−54974.8	+	54974.8i	−0.946520	+	0.946520i	0.0521211	+	0.998641i	$0.483402\pi$
$242$	18427.0			0.314646
$243$	−47358.1	−	19616.4i	−0.802013	−	0.332205i
$244$	−4388.85	−	4388.85i	−0.0737177	−	0.0737177i
$245$			19978.5i			0.332836i
$246$	41731.5	−	64430.1i	0.689594	−	1.06468i
$247$	−74915.0			−1.22793
$248$	14984.7	−	14984.7i	0.243638	−	0.243638i
$249$	77667.0	−	187505.i	1.25267	−	3.02422i
$250$		−	47813.7i		−	0.765019i
$251$	63151.6	+	63151.6i	1.00239	+	1.00239i	0.999997	+	0.00239267i	$0.000761613\pi$
$251$	63151.6	+	63151.6i	1.00239	+	1.00239i	0.00239267	+	0.999997i	$0.499238\pi$
$252$	31699.4	+	76529.2i	0.499172	+	1.20511i
$253$	23745.9	−	57327.7i	0.370978	−	0.895620i
$254$	−48093.5	−	48093.5i	−0.745451	−	0.745451i
$255$	−81709.8	−	81709.8i	−1.25659	−	1.25659i
$256$	4096.00			0.0625000
$257$	−59912.0	−	24816.4i	−0.907084	−	0.375727i	−0.120145	−	0.992756i	$-0.538336\pi$
$257$	−59912.0	−	24816.4i	−0.907084	−	0.375727i	−0.786940	+	0.617030i	$0.788336\pi$
$258$	39461.8	+	16345.6i	0.592841	+	0.245563i
$259$	30626.8	−	73939.6i	0.456564	−	1.10224i
$260$	−11790.5	−	28464.8i	−0.174416	−	0.421077i
$261$	−190005.	+	78702.7i	−2.78923	+	1.15534i
$262$	60304.5			0.878511
$263$	−46979.8	−	113419.i	−0.679203	−	1.63974i	−0.765472	−	0.643469i	$-0.777495\pi$
$263$	−46979.8	−	113419.i	−0.679203	−	1.63974i	0.0862694	−	0.996272i	$-0.472505\pi$
$264$	−32932.3			−0.472513
$265$	19633.2	+	47398.8i	0.279576	+	0.674956i
$266$	−48679.3	+	48679.3i	−0.687988	+	0.687988i
$267$	25668.3	+	25668.3i	0.360060	+	0.360060i
$268$	−60417.0	+	25025.5i	−0.841182	+	0.348429i
$269$		−	6524.18i		−	0.0901615i	−0.998983	−	0.0450808i	$-0.985645\pi$
$269$		−	6524.18i		−	0.0901615i	0.998983	−	0.0450808i	$-0.0143545\pi$
$270$	90385.5	−	37438.9i	1.23986	−	0.513565i
$271$		−	19336.1i		−	0.263287i	−0.991297	−	0.131644i	$-0.957975\pi$
$271$		−	19336.1i		−	0.263287i	0.991297	−	0.131644i	$-0.0420254\pi$
$272$	8073.44	+	19491.0i	0.109124	+	0.263449i
$273$	−152477.	+	63158.1i	−2.04588	+	0.847430i
$274$	−8378.98	−	3470.69i	−0.111607	−	0.0462290i
$275$	5298.04	−	12790.6i	0.0700568	−	0.169132i
$276$	34023.9	−	82141.0i	0.446649	−	1.07831i
$277$		−	56205.4i		−	0.732519i	−0.930513	−	0.366259i	$-0.880638\pi$
$277$		−	56205.4i		−	0.732519i	0.930513	−	0.366259i	$-0.119362\pi$
$278$	−60230.4	+	60230.4i	−0.779338	+	0.779338i
$279$	−118984.	+	118984.i	−1.52856	+	1.52856i
$280$	−26157.6	−	10834.8i	−0.333643	−	0.138200i
$281$	−48049.8	+	19902.9i	−0.608526	+	0.252060i	−0.665598	−	0.746310i	$-0.731823\pi$
$281$	−48049.8	+	19902.9i	−0.608526	+	0.252060i	0.0570724	+	0.998370i	$0.481823\pi$
$282$	−74524.8	+	74524.8i	−0.937136	+	0.937136i
$283$	−59434.1			−0.742100			−0.371050	−	0.928613i	$-0.621002\pi$
$283$	−59434.1			−0.742100			−0.371050	+	0.928613i	$0.621002\pi$
$284$	−65036.5	−	26939.0i	−0.806344	−	0.333999i
$285$	104690.	+	104690.i	1.28889	+	1.28889i
$286$		−	45225.6i		−	0.552908i
$287$	94733.9	−	20255.2i	1.15012	−	0.245908i
$288$	−32523.9			−0.392119
$289$	−17777.5	+	17777.5i	−0.212850	+	0.212850i
$290$	26900.5	−	64943.6i	0.319864	−	0.772219i
$291$			135877.i			1.60458i
$292$	31200.1	+	31200.1i	0.365924	+	0.365924i
$293$	−639.541	−	1543.99i	−0.00744960	−	0.0179849i	0.920111	−	0.391658i	$-0.128098\pi$
$293$	−639.541	−	1543.99i	−0.00744960	−	0.0179849i	−0.927561	+	0.373673i	$0.878098\pi$
$294$	−16080.1	+	38820.9i	−0.186035	+	0.449129i
$295$	17877.4	+	17877.4i	0.205428	+	0.205428i
$296$	22219.7	+	22219.7i	0.253603	+	0.253603i
$297$	143607.			1.62803
$298$	−25977.9	−	10760.4i	−0.292531	−	0.121170i
$299$	112804.	+	46724.8i	1.26177	+	0.522643i
$300$	7591.21	−	18326.8i	0.0843467	−	0.203631i
$301$	20627.9	+	49800.1i	0.227678	+	0.549664i
$302$	−54305.5	+	22494.1i	−0.595429	+	0.246635i
$303$	167793.			1.82763
$304$	−10344.0	−	24972.7i	−0.111929	−	0.270220i
$305$	−16845.4			−0.181084
$306$	−64106.4	−	154766.i	−0.684634	−	1.65285i
$307$	−71109.2	+	71109.2i	−0.754482	+	0.754482i	−0.975312	−	0.220830i	$-0.929123\pi$
$307$	−71109.2	+	71109.2i	−0.754482	+	0.754482i	0.220830	+	0.975312i	$0.429123\pi$
$308$	−29387.3	−	29387.3i	−0.309784	−	0.309784i
$309$	39472.6	−	16350.1i	0.413408	−	0.171239i
$310$		−	57514.4i		−	0.598485i
$311$	44794.7	−	18554.6i	0.463133	−	0.191836i	−0.138901	−	0.990306i	$-0.544357\pi$
$311$	44794.7	−	18554.6i	0.463133	−	0.191836i	0.602034	+	0.798470i	$0.294357\pi$
$312$		−	64800.8i		−	0.665688i
$313$	−7588.71	−	18320.8i	−0.0774604	−	0.187006i	0.880406	−	0.474221i	$-0.157270\pi$
$313$	−7588.71	−	18320.8i	−0.0774604	−	0.187006i	−0.957866	+	0.287216i	$0.907270\pi$
$314$	63331.9	−	26232.9i	0.642337	−	0.266065i
$315$	207702.	+	86033.1i	2.09324	+	0.867050i
$316$	20210.4	−	48792.2i	0.202395	−	0.488626i
$317$	−49296.4	+	119012.i	−0.490565	+	1.18433i	0.463869	+	0.885904i	$0.346461\pi$
$317$	−49296.4	+	119012.i	−0.490565	+	1.18433i	−0.954433	+	0.298424i	$0.903539\pi$
$318$			107904.i			1.06705i
$319$	72962.2	−	72962.2i	0.716996	−	0.716996i
$320$	7860.66	−	7860.66i	0.0767642	−	0.0767642i
$321$	−102604.	−	42500.1i	−0.995762	−	0.412458i
$322$	103660.	−	42937.6i	0.999773	−	0.414120i
$323$	98445.0	−	98445.0i	0.943602	−	0.943602i
$324$	89338.0			0.851033
$325$	25168.0	+	10424.9i	0.238277	+	0.0986977i
$326$	69238.0	+	69238.0i	0.651493	+	0.651493i
$327$		−	253470.i		−	2.37045i
$328$	−6886.72	+	37408.1i	−0.0640125	+	0.347710i
$329$	−133005.			−1.22879
$330$	−63200.6	+	63200.6i	−0.580354	+	0.580354i
$331$	−46017.0	+	111095.i	−0.420013	+	1.01400i	0.562330	+	0.826913i	$0.309905\pi$
$331$	−46017.0	+	111095.i	−0.420013	+	1.01400i	−0.982343	+	0.187088i	$0.940095\pi$
$332$			100564.i			0.912356i
$333$	−176433.	−	176433.i	−1.59108	−	1.59108i
$334$	−2197.19	−	5304.48i	−0.0196958	−	0.0475500i
$335$	−67920.0	+	163973.i	−0.605213	+	1.46111i
$336$	−42107.1	−	42107.1i	−0.372973	−	0.372973i
$337$	−21914.0	−	21914.0i	−0.192957	−	0.192957i	0.604015	−	0.796973i	$-0.293567\pi$
$337$	−21914.0	−	21914.0i	−0.192957	−	0.192957i	−0.796973	+	0.604015i	$0.793567\pi$
$338$	8207.63			0.0718430
$339$	49707.8	+	20589.6i	0.432539	+	0.179163i
$340$	52899.1	+	21911.5i	0.457605	+	0.189546i
$341$	32307.9	−	77998.1i	0.277843	−	0.670773i
$342$	82135.7	+	198293.i	0.702230	+	1.69533i
$343$	78844.3	−	32658.4i	0.670166	−	0.277592i
$344$	−21164.4			−0.178850
$345$	−92341.8	−	222933.i	−0.775819	−	1.87299i
$346$	−75640.9			−0.631836
$347$	−11381.0	−	27476.1i	−0.0945193	−	0.228190i	0.869548	−	0.493849i	$-0.164410\pi$
$347$	−11381.0	−	27476.1i	−0.0945193	−	0.228190i	−0.964067	+	0.265659i	$0.914410\pi$
$348$	104543.	−	104543.i	0.863247	−	0.863247i
$349$	132113.	+	132113.i	1.08466	+	1.08466i	0.996068	+	0.0885945i	$0.0282375\pi$
$349$	132113.	+	132113.i	1.08466	+	1.08466i	0.0885945	+	0.996068i	$0.471762\pi$
$350$	23128.1	−	9579.97i	0.188801	−	0.0782038i
$351$			282575.i			2.29361i
$352$	15075.8	−	6244.61i	0.121673	−	0.0503988i
$353$			160825.i			1.29064i	0.763913	+	0.645319i	$0.223276\pi$
$353$			160825.i			1.29064i	−0.763913	+	0.645319i	$0.776724\pi$
$354$	20349.2	+	49127.2i	0.162383	+	0.392027i
$355$	−176511.	+	73113.1i	−1.40060	+	0.580148i
$356$	−16617.7	−	6883.29i	−0.131121	−	0.0543120i
$357$	117373.	−	283364.i	0.920943	−	2.22335i
$358$	1091.91	−	2636.10i	0.00851963	−	0.0205682i
$359$		−	167049.i		−	1.29615i	−0.761578	−	0.648073i	$-0.775575\pi$
$359$		−	167049.i		−	1.29615i	0.761578	−	0.648073i	$-0.224425\pi$
$360$	−62416.8	+	62416.8i	−0.481611	+	0.481611i
$361$	−33980.9	+	33980.9i	−0.260748	+	0.260748i
$362$	−61180.0	−	25341.6i	−0.466866	−	0.193382i
$363$	97178.5	−	40252.6i	0.737491	−	0.305479i
$364$	57825.3	−	57825.3i	0.436431	−	0.436431i
$365$	119753.			0.898875
$366$	−32732.8	−	13558.4i	−0.244355	−	0.101215i
$367$	−39382.9	−	39382.9i	−0.292399	−	0.292399i	0.545628	−	0.838027i	$-0.316291\pi$
$367$	−39382.9	−	39382.9i	−0.292399	−	0.292399i	−0.838027	+	0.545628i	$0.816291\pi$
$368$			44054.3i			0.325307i
$369$	54683.3	−	297035.i	0.401608	−	2.18150i
$370$	85283.8			0.622964
$371$	−96289.2	+	96289.2i	−0.699567	+	0.699567i
$372$	46291.8	−	111758.i	0.334517	−	0.807595i
$373$			6341.58i			0.0455806i	0.999740	+	0.0227903i	$0.00725500\pi$
$373$			6341.58i			0.0455806i	−0.999740	+	0.0227903i	$0.992745\pi$
$374$	59430.6	+	59430.6i	0.424880	+	0.424880i
$375$	−104446.	−	252156.i	−0.742729	−	1.79311i
$376$	19984.8	−	48247.5i	0.141359	−	0.341271i
$377$	143568.	+	143568.i	1.01012	+	1.01012i
$378$	183615.	+	183615.i	1.28507	+	1.28507i
$379$	152182.			1.05946			0.529732	−	0.848165i	$-0.322293\pi$
$379$	152182.			1.05946			0.529732	+	0.848165i	$0.322293\pi$
$380$	−67776.5	−	28073.9i	−0.469366	−	0.194418i
$381$	−358689.	−	148574.i	−2.47097	−	1.02351i
$382$	−6447.65	+	15566.0i	−0.0441850	+	0.106672i
$383$	66624.4	+	160845.i	0.454188	+	1.09651i	0.970715	+	0.240235i	$0.0772247\pi$
$383$	66624.4	+	160845.i	0.454188	+	1.09651i	−0.516527	+	0.856271i	$0.672775\pi$
$384$	21601.1	−	8947.48i	0.146492	−	0.0606790i
$385$	−112795.			−0.760970
$386$	−46412.9	−	112051.i	−0.311504	−	0.752038i
$387$	168054.			1.12209
$388$	−25765.0	−	62202.3i	−0.171146	−	0.413184i
$389$	34514.8	−	34514.8i	0.228090	−	0.228090i	−0.583804	−	0.811894i	$-0.698437\pi$
$389$	34514.8	−	34514.8i	0.228090	−	0.228090i	0.811894	+	0.583804i	$0.198437\pi$
$390$	−124360.	−	124360.i	−0.817617	−	0.817617i
$391$	−209635.	+	86833.5i	−1.37123	+	0.567981i
$392$		−	20820.6i		−	0.135495i
$393$	318029.	−	131732.i	2.05912	−	0.852915i
$394$			93764.0i			0.604010i
$395$	−54851.5	−	132423.i	−0.351556	−	0.848731i
$396$	−119708.	+	49584.7i	−0.763367	+	0.316197i
$397$	−156520.	−	64832.6i	−0.993089	−	0.411351i	−0.173831	−	0.984776i	$-0.555615\pi$
$397$	−156520.	−	64832.6i	−0.993089	−	0.411351i	−0.819258	+	0.573424i	$0.805615\pi$
$398$	−64623.2	+	156014.i	−0.407965	+	0.984914i
$399$	−150383.	+	363058.i	−0.944613	+	2.28050i
$400$			9829.13i			0.0614320i
$401$	172029.	−	172029.i	1.06983	−	1.06983i	0.0724562	−	0.997372i	$-0.476916\pi$
$401$	172029.	−	172029.i	1.06983	−	1.06983i	0.997372	−	0.0724562i	$-0.0230838\pi$
$402$	−263955.	+	263955.i	−1.63335	+	1.63335i
$403$	153477.	+	63572.1i	0.945001	+	0.391432i
$404$	−76812.8	+	31816.9i	−0.470621	+	0.194938i
$405$	171449.	−	171449.i	1.04526	−	1.04526i
$406$	186579.			1.13190
$407$	115657.	+	47906.9i	0.698208	+	0.289207i
$408$	85154.0	+	85154.0i	0.511546	+	0.511546i
$409$		−	114565.i		−	0.684868i	−0.939542	−	0.342434i	$-0.888749\pi$
$409$		−	114565.i		−	0.684868i	0.939542	−	0.342434i	$-0.111251\pi$
$410$	58573.7	+	85006.4i	0.348445	+	0.505689i
$411$	−51769.8			−0.306474
$412$	−14969.6	+	14969.6i	−0.0881892	+	0.0881892i
$413$	−25680.3	+	61997.6i	−0.150556	+	0.363475i
$414$		−	349809.i		−	2.04094i
$415$	192992.	+	192992.i	1.12058	+	1.12058i
$416$	12287.5	+	29664.7i	0.0710030	+	0.171416i
$417$	−186068.	+	449208.i	−1.07004	+	2.58330i
$418$	−76144.8	−	76144.8i	−0.435801	−	0.435801i
$419$	−5960.75	−	5960.75i	−0.0339526	−	0.0339526i	0.689927	−	0.723879i	$-0.257643\pi$
$419$	−5960.75	−	5960.75i	−0.0339526	−	0.0339526i	−0.723879	+	0.689927i	$0.757643\pi$
$420$	−161616.			−0.916191
$421$	−97378.8	−	40335.6i	−0.549415	−	0.227575i	0.0906679	−	0.995881i	$-0.471100\pi$
$421$	−97378.8	−	40335.6i	−0.549415	−	0.227575i	−0.640082	+	0.768306i	$0.721100\pi$
$422$	38019.0	+	15748.0i	0.213489	+	0.0884302i
$423$	−158687.	+	383105.i	−0.886873	+	2.14110i
$424$	−20460.8	−	49396.8i	−0.113813	−	0.274768i
$425$	−46772.4	+	19373.8i	−0.258947	+	0.107260i
$426$	−401830.			−2.21423
$427$	−17110.4	−	41308.2i	−0.0938435	−	0.226558i
$428$	55029.3			0.300405
$429$	−98792.9	−	238507.i	−0.536798	−	1.29595i
$430$	−40616.7	+	40616.7i	−0.219669	+	0.219669i
$431$	221282.	+	221282.i	1.19122	+	1.19122i	0.976725	+	0.214496i	$0.0688110\pi$
$431$	221282.	+	221282.i	1.19122	+	1.19122i	0.214496	+	0.976725i	$0.431189\pi$
$432$	−94195.5	+	39017.0i	−0.504734	+	0.209068i
$433$		−	226169.i		−	1.20631i	−0.797625	−	0.603154i	$-0.793911\pi$
$433$		−	226169.i		−	1.20631i	0.797625	−	0.603154i	$-0.206089\pi$
$434$	141037.	−	58419.4i	0.748778	−	0.310154i
$435$		−	401257.i		−	2.12053i
$436$	48062.9	+	116034.i	0.252835	+	0.610397i
$437$	268592.	−	111255.i	1.40647	−	0.582579i
$438$	232695.	+	96385.6i	1.21294	+	0.502416i
$439$	−39168.6	+	94561.3i	−0.203240	+	0.490664i	−0.992331	−	0.123612i	$-0.960552\pi$
$439$	−39168.6	+	94561.3i	−0.203240	+	0.490664i	0.789091	+	0.614276i	$0.210552\pi$
$440$	16948.0	−	40916.2i	0.0875415	−	0.211344i
$441$			165324.i			0.850079i
$442$	−116941.	+	116941.i	−0.598582	+	0.598582i
$443$	56.7670	−	56.7670i	0.000289260	−	0.000289260i	−0.706962	−	0.707251i	$-0.749935\pi$
$443$	56.7670	−	56.7670i	0.000289260	−	0.000289260i	0.707251	+	0.706962i	$0.249935\pi$
$444$	165718.	+	68642.5i	0.840626	+	0.348199i
$445$	−45100.9	+	18681.4i	−0.227754	+	0.0943387i
$446$	−73043.4	+	73043.4i	−0.367207	+	0.367207i
$447$	−160506.			−0.803296
$448$	27260.2	+	11291.6i	0.135823	+	0.0562598i
$449$	−81437.9	−	81437.9i	−0.403956	−	0.403956i	0.475669	−	0.879625i	$-0.342206\pi$
$449$	−81437.9	−	81437.9i	−0.403956	−	0.403956i	−0.879625	+	0.475669i	$0.842206\pi$
$450$		−	78047.2i		−	0.385418i
$451$	31683.5	+	148184.i	0.155769	+	0.728532i
$452$	−26659.6			−0.130490
$453$	−237255.	+	237255.i	−1.15616	+	1.15616i
$454$	−70862.6	+	171077.i	−0.343799	+	0.830005i
$455$		−	221946.i		−	1.07207i
$456$	−109103.	−	109103.i	−0.524694	−	0.524694i
$457$	76188.6	+	183935.i	0.364802	+	0.880710i	0.994584	+	0.103938i	$0.0331444\pi$
$457$	76188.6	+	183935.i	0.364802	+	0.880710i	−0.629782	+	0.776772i	$0.716856\pi$
$458$	59227.5	−	142988.i	0.282353	−	0.681660i
$459$	−371329.	−	371329.i	−1.76252	−	1.76252i
$460$	84544.9	+	84544.9i	0.399551	+	0.399551i
$461$	299082.			1.40731			0.703653	−	0.710544i	$-0.251551\pi$
$461$	299082.			1.40731			0.703653	+	0.710544i	$0.251551\pi$
$462$	−219175.	−	90785.4i	−1.02685	−	0.425336i
$463$	−100911.	−	41798.7i	−0.470735	−	0.194985i	0.134689	−	0.990888i	$-0.456996\pi$
$463$	−100911.	−	41798.7i	−0.470735	−	0.194985i	−0.605424	+	0.795903i	$0.706996\pi$
$464$	−28034.4	+	67681.1i	−0.130213	+	0.314363i
$465$	−125637.	−	303315.i	−0.581048	−	1.40277i
$466$	−180498.	+	74764.5i	−0.831188	+	0.344289i
$467$	99423.1			0.455883			0.227942	−	0.973675i	$-0.426800\pi$
$467$	99423.1			0.455883			0.227942	+	0.973675i	$0.426800\pi$
$468$	−97567.7	−	235549.i	−0.445466	−	1.07545i
$469$	−471084.			−2.14167
$470$	−54239.2	−	130945.i	−0.245537	−	0.592780i
$471$	276690.	−	276690.i	1.24724	−	1.24724i
$472$	−18631.0	−	18631.0i	−0.0836280	−	0.0836280i
$473$	−77898.1	+	32266.5i	−0.348181	+	0.144221i
$474$		−	301465.i		−	1.34177i
$475$	59926.7	−	24822.4i	0.265603	−	0.110016i
$476$			151975.i			0.670748i
$477$	162467.	+	392230.i	0.714050	+	1.72387i
$478$	219613.	−	90966.7i	0.961174	−	0.398132i
$479$	102492.	+	42453.6i	0.446703	+	0.185030i	0.594684	−	0.803960i	$-0.297277\pi$
$479$	102492.	+	42453.6i	0.446703	+	0.185030i	−0.147981	+	0.988990i	$0.547277\pi$
$480$	24283.7	−	58626.0i	0.105398	−	0.254453i
$481$	−94266.2	+	227579.i	−0.407442	+	0.983652i
$482$		−	219899.i		−	0.946520i
$483$	452881.	−	452881.i	1.94129	−	1.94129i
$484$	−36853.9	+	36853.9i	−0.157323	+	0.157323i
$485$	−168819.	−	69927.0i	−0.717690	−	0.297277i
$486$	133949.	−	55483.5i	0.567109	−	0.234904i
$487$	−38561.2	+	38561.2i	−0.162589	+	0.162589i	−0.783713	−	0.621123i	$-0.786677\pi$
$487$	−38561.2	+	38561.2i	−0.162589	+	0.162589i	0.621123	+	0.783713i	$0.286677\pi$
$488$	17555.4			0.0737177
$489$	516388.	+	213895.i	2.15953	+	0.894505i
$490$	−39957.0	−	39957.0i	−0.166418	−	0.166418i
$491$			106643.i			0.442353i	0.975234	+	0.221177i	$0.0709898\pi$
$491$			106643.i			0.442353i	−0.975234	+	0.221177i	$0.929010\pi$
$492$	45397.2	+	212323.i	0.187542	+	0.877136i
$493$	−377321.			−1.55245
$494$	149830.	−	149830.i	0.613967	−	0.613967i
$495$	−134574.	+	324891.i	−0.549226	+	1.32595i
$496$			59938.8i			0.243638i
$497$	−358576.	−	358576.i	−1.45167	−	1.45167i
$498$	219675.	+	530343.i	0.885774	+	2.13845i
$499$	130225.	−	314392.i	0.522992	−	1.26261i	−0.413045	−	0.910711i	$-0.635535\pi$
$499$	130225.	−	314392.i	0.522992	−	1.26261i	0.936037	−	0.351903i	$-0.114465\pi$
$500$	95627.4	+	95627.4i	0.382510	+	0.382510i
$501$	−23174.7	−	23174.7i	−0.0923291	−	0.0923291i
$502$	−252606.			−1.00239
$503$	−55428.0	−	22959.0i	−0.219075	−	0.0907440i	0.270447	−	0.962735i	$-0.412829\pi$
$503$	−55428.0	−	22959.0i	−0.219075	−	0.0907440i	−0.489522	+	0.871991i	$0.662829\pi$
$504$	−216457.	−	89659.5i	−0.852140	−	0.352968i
$505$	−86351.9	+	208472.i	−0.338602	+	0.817457i
$506$	67163.6	+	162147.i	0.262321	+	0.633299i
$507$	43284.7	−	17929.1i	0.168391	−	0.0697497i
$508$	192374.			0.745451
$509$	161460.	+	389799.i	0.623204	+	1.50455i	0.847921	+	0.530122i	$0.177854\pi$
$509$	161460.	+	389799.i	0.623204	+	1.50455i	−0.224718	+	0.974424i	$0.572146\pi$
$510$	326839.			1.25659
$511$	121637.	+	293657.i	0.465826	+	1.12460i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	475762.	+	475762.i	1.80782	+	1.80782i
$514$	169457.	−	70191.3i	0.641405	−	0.265679i
$515$			57456.4i			0.216633i
$516$	−111615.	+	46232.4i	−0.419202	+	0.173639i
$517$		−	208049.i		−	0.778367i
$518$	86625.6	+	209133.i	0.322840	+	0.779404i
$519$	−398909.	+	165233.i	−1.48094	+	0.613427i
$520$	80510.6	+	33348.6i	0.297746	+	0.123331i
$521$	−95292.1	+	230055.i	−0.351060	+	0.847534i	0.645430	+	0.763820i	$0.276678\pi$
$521$	−95292.1	+	230055.i	−0.351060	+	0.847534i	−0.996490	+	0.0837143i	$0.973322\pi$
$522$	222605.	−	537415.i	0.816946	−	1.97228i
$523$		−	134753.i		−	0.492648i	−0.969188	−	0.246324i	$-0.920777\pi$
$523$		−	134753.i		−	0.492648i	0.969188	−	0.246324i	$-0.0792227\pi$
$524$	−120609.	+	120609.i	−0.439256	+	0.439256i
$525$	101044.	−	101044.i	0.366599	−	0.366599i
$526$	320798.	+	132879.i	1.15947	+	0.480269i
$527$	−285222.	+	118143.i	−1.02698	+	0.425388i
$528$	65864.6	−	65864.6i	0.236257	−	0.236257i
$529$	−193983.			−0.693190
$530$	−134064.	−	55531.2i	−0.477266	−	0.197690i
$531$	147937.	+	147937.i	0.524673	+	0.524673i
$532$		−	194717.i		−	0.687988i
$533$	−291581.	+	62343.6i	−1.02637	+	0.219451i
$534$	−102673.			−0.360060
$535$	105607.	−	105607.i	0.368965	−	0.368965i
$536$	70782.9	−	170885.i	0.246376	−	0.594805i
$537$		−	16287.3i		−	0.0564807i
$538$	13048.4	+	13048.4i	0.0450808	+	0.0450808i
$539$	−31742.4	−	76632.9i	−0.109260	−	0.263777i
$540$	−105893.	+	255649.i	−0.363146	+	0.876711i
$541$	−219085.	−	219085.i	−0.748545	−	0.748545i	0.225661	−	0.974206i	$-0.427546\pi$
$541$	−219085.	−	219085.i	−0.748545	−	0.748545i	−0.974206	+	0.225661i	$0.927546\pi$
$542$	38672.1	+	38672.1i	0.131644	+	0.131644i
$543$	−378003.			−1.28202
$544$	−55128.9	−	22835.1i	−0.186287	−	0.0771624i
$545$	314919.	+	130444.i	1.06025	+	0.439168i
$546$	178638.	−	431270.i	0.599223	−	1.44665i
$547$	−196122.	−	473481.i	−0.655469	−	1.58244i	−0.804728	−	0.593644i	$-0.797689\pi$
$547$	−196122.	−	473481.i	−0.655469	−	1.58244i	0.149259	−	0.988798i	$-0.452311\pi$
$548$	23699.3	−	9816.58i	0.0789178	−	0.0326888i
$549$	−139397.			−0.462497
$550$	14985.1	+	36177.3i	0.0495376	+	0.119594i
$551$	483439.			1.59235
$552$	96234.2	+	232330.i	0.315828	+	0.762477i
$553$	269014.	−	269014.i	0.879679	−	0.879679i
$554$	112411.	+	112411.i	0.366259	+	0.366259i
$555$	449762.	−	186298.i	1.46015	−	0.604813i
$556$		−	240921.i		−	0.779338i
$557$	−123817.	+	51286.5i	−0.399088	+	0.165308i	−0.573195	−	0.819419i	$-0.694296\pi$
$557$	−123817.	+	51286.5i	−0.399088	+	0.165308i	0.174107	+	0.984727i	$0.444296\pi$
$558$		−	475938.i		−	1.52856i
$559$	−63490.6	−	153280.i	−0.203182	−	0.490525i
$560$	73985.0	−	30645.6i	0.235921	−	0.0977219i
$561$	443242.	+	183597.i	1.40837	+	0.583364i
$562$	56293.8	−	135905.i	0.178233	−	0.430293i
$563$	215810.	−	521011.i	0.680855	−	1.64373i	−0.0815813	−	0.996667i	$-0.525997\pi$
$563$	215810.	−	521011.i	0.680855	−	1.64373i	0.762436	−	0.647063i	$-0.224003\pi$
$564$		−	298099.i		−	0.937136i
$565$	−51162.5	+	51162.5i	−0.160271	+	0.160271i
$566$	118868.	−	118868.i	0.371050	−	0.371050i
$567$	594574.	+	246281.i	1.84944	+	0.766062i
$568$	183951.	−	76195.0i	0.570171	−	0.236173i
$569$	−241292.	+	241292.i	−0.745278	+	0.745278i	−0.973588	−	0.228310i	$-0.926680\pi$
$569$	−241292.	+	241292.i	−0.745278	+	0.745278i	0.228310	+	0.973588i	$0.426680\pi$
$570$	−418760.			−1.28889
$571$	−349258.	−	144667.i	−1.07121	−	0.443709i	−0.223791	−	0.974637i	$-0.571843\pi$
$571$	−349258.	−	144667.i	−1.07121	−	0.443709i	−0.847417	+	0.530928i	$0.821843\pi$
$572$	90451.3	+	90451.3i	0.276454	+	0.276454i
$573$			96175.2i			0.292923i
$574$	−148957.	+	229978.i	−0.452104	+	0.698012i
$575$	−105717.			−0.319748
$576$	65047.8	−	65047.8i	0.196059	−	0.196059i
$577$	167981.	−	405542.i	0.504555	−	1.21810i	−0.442423	−	0.896807i	$-0.645881\pi$
$577$	167981.	−	405542.i	0.504555	−	1.21810i	0.946978	−	0.321298i	$-0.104119\pi$
$578$		−	71109.8i		−	0.212850i
$579$	−489537.	−	489537.i	−1.46025	−	1.46025i
$580$	76086.2	+	183688.i	0.226178	+	0.546041i
$581$	−277226.	+	669284.i	−0.821263	+	1.98270i
$582$	−271755.	−	271755.i	−0.802290	−	0.802290i
$583$	−150617.	−	150617.i	−0.443136	−	0.443136i
$584$	−124800.			−0.365924
$585$	−639287.	−	264801.i	−1.86803	−	0.773763i
$586$	4367.06	+	1808.90i	0.0127173	+	0.00526767i
$587$	−17341.0	+	41864.8i	−0.0503265	+	0.121499i	−0.947043	−	0.321106i	$-0.895946\pi$
$587$	−17341.0	+	41864.8i	−0.0503265	+	0.121499i	0.896717	+	0.442605i	$0.145946\pi$
$588$	−45481.5	−	109802.i	−0.131547	−	0.317582i
$589$	365437.	−	151369.i	1.05337	−	0.436322i
$590$	−71509.6			−0.205428
$591$	204822.	+	494485.i	0.586411	+	1.41572i
$592$	−88878.6			−0.253603
$593$	109968.	+	265486.i	0.312721	+	0.754974i	0.999602	+	0.0282050i	$0.00897913\pi$
$593$	109968.	+	265486.i	0.312721	+	0.754974i	−0.686881	+	0.726769i	$0.741021\pi$
$594$	−287214.	+	287214.i	−0.814015	+	0.814015i
$595$	291657.	+	291657.i	0.823832	+	0.823832i
$596$	73476.7	−	30435.0i	0.206851	−	0.0856804i
$597$			963940.i			2.70459i
$598$	−319057.	+	132158.i	−0.892207	+	0.369564i
$599$		−	569608.i		−	1.58753i	−0.608223	−	0.793766i	$-0.708117\pi$
$599$		−	569608.i		−	1.58753i	0.608223	−	0.793766i	$-0.291883\pi$
$600$	21471.2	+	51836.0i	0.0596421	+	0.143989i
$601$	432066.	−	178968.i	1.19619	−	0.495480i	0.306427	−	0.951894i	$-0.400867\pi$
$601$	432066.	−	178968.i	1.19619	−	0.495480i	0.889767	+	0.456415i	$0.150867\pi$
$602$	−140856.	−	58344.5i	−0.388671	−	0.160993i
$603$	−562045.	+	1.35690e6i	−1.54574	+	3.73175i
$604$	63622.8	−	153599.i	0.174397	−	0.421032i
$605$			141453.i			0.386457i
$606$	−335587.	+	335587.i	−0.913817	+	0.913817i
$607$	−148515.	+	148515.i	−0.403081	+	0.403081i	−0.879317	−	0.476236i	$-0.842001\pi$
$607$	−148515.	+	148515.i	−0.403081	+	0.403081i	0.476236	+	0.879317i	$0.342001\pi$
$608$	70633.4	+	29257.3i	0.191075	+	0.0791457i
$609$	983962.	−	407570.i	2.65304	−	1.09892i
$610$	33690.7	−	33690.7i	0.0905421	−	0.0905421i
$611$	409377.			1.09658
$612$	437746.	+	181320.i	1.16874	+	0.484109i
$613$	138857.	+	138857.i	0.369527	+	0.369527i	0.867305	−	0.497778i	$-0.165851\pi$
$613$	138857.	+	138857.i	0.369527	+	0.369527i	−0.497778	+	0.867305i	$0.665851\pi$
$614$		−	284437.i		−	0.754482i
$615$	494592.	+	320348.i	1.30767	+	0.846978i
$616$	117549.			0.309784
$617$	86024.3	−	86024.3i	0.225970	−	0.225970i	−0.585037	−	0.811007i	$-0.698920\pi$
$617$	86024.3	−	86024.3i	0.225970	−	0.225970i	0.811007	+	0.585037i	$0.198920\pi$
$618$	−46245.1	+	111645.i	−0.121085	+	0.292324i
$619$		−	397530.i		−	1.03750i	−0.854926	−	0.518751i	$-0.826397\pi$
$619$		−	397530.i		−	1.03750i	0.854926	−	0.518751i	$-0.173603\pi$
$620$	115029.	+	115029.i	0.299243	+	0.299243i
$621$	−419646.	−	1.01311e6i	−1.08818	−	2.62709i
$622$	−52480.3	+	126699.i	−0.135649	+	0.327485i
$623$	−91621.1	−	91621.1i	−0.236058	−	0.236058i
$624$	129602.	+	129602.i	0.332844	+	0.332844i
$625$	271051.			0.693889
$626$	51819.0	+	21464.1i	0.132233	+	0.0547727i
$627$	−567900.	−	235232.i	−1.44456	−	0.598358i
$628$	−74197.9	+	179130.i	−0.188136	+	0.454201i
$629$	−175185.	−	422933.i	−0.442787	−	1.06898i
$630$	−587470.	+	243338.i	−1.48015	+	0.613097i
$631$	22900.8			0.0575165			0.0287583	−	0.999586i	$-0.490845\pi$
$631$	22900.8			0.0575165			0.0287583	+	0.999586i	$0.490845\pi$
$632$	57163.6	+	138005.i	0.143115	+	0.345511i
$633$	234902.			0.586245
$634$	−139431.	−	336617.i	−0.346882	−	0.837446i
$635$	369186.	−	369186.i	0.915583	−	0.915583i
$636$	−215809.	−	215809.i	−0.533525	−	0.533525i
$637$	150790.	−	62459.4i	0.371616	−	0.153928i
$638$			291849.i			0.716996i
$639$	−1.46064e6	+	605019.i	−3.57720	+	1.48172i
$640$			31442.6i			0.0767642i
$641$	−92850.4	−	224161.i	−0.225979	−	0.545561i	0.769702	−	0.638403i	$-0.220405\pi$
$641$	−92850.4	−	224161.i	−0.225979	−	0.545561i	−0.995681	+	0.0928424i	$0.970405\pi$
$642$	290209.	−	120208.i	0.704110	−	0.291652i
$643$	234913.	+	97304.1i	0.568179	+	0.235347i	0.648231	−	0.761443i	$-0.275509\pi$
$643$	234913.	+	97304.1i	0.568179	+	0.235347i	−0.0800528	+	0.996791i	$0.525509\pi$
$644$	−121446.	+	293196.i	−0.292827	+	0.706946i
$645$	−125476.	+	302926.i	−0.301607	+	0.728143i
$646$			393780.i			0.943602i
$647$	−60286.4	+	60286.4i	−0.144016	+	0.144016i	−0.775439	−	0.631423i	$-0.782471\pi$
$647$	−60286.4	+	60286.4i	−0.144016	+	0.144016i	0.631423	+	0.775439i	$0.282471\pi$
$648$	−178676.	+	178676.i	−0.425516	+	0.425516i
$649$	−96977.6	−	40169.5i	−0.230241	−	0.0953689i
$650$	−71185.9	+	29486.2i	−0.168487	+	0.0697898i
$651$	616174.	−	616174.i	1.45392	−	1.45392i
$652$	−276952.			−0.651493
$653$	−270884.	−	112204.i	−0.635268	−	0.263136i	0.0417218	−	0.999129i	$-0.486716\pi$
$653$	−270884.	−	112204.i	−0.635268	−	0.263136i	−0.676989	+	0.735993i	$0.736716\pi$
$654$	506940.	+	506940.i	1.18522	+	1.18522i
$655$			462923.i			1.07901i
$656$	−61042.7	−	88589.6i	−0.141849	−	0.205861i
$657$	990966.			2.29577
$658$	266011.	−	266011.i	0.614395	−	0.614395i
$659$	−216804.	+	523411.i	−0.499225	+	1.20524i	0.450676	+	0.892688i	$0.351183\pi$
$659$	−216804.	+	523411.i	−0.499225	+	1.20524i	−0.949902	+	0.312549i	$0.898817\pi$
$660$		−	252802.i		−	0.580354i
$661$	−375427.	−	375427.i	−0.859256	−	0.859256i	0.131995	−	0.991250i	$-0.457862\pi$
$661$	−375427.	−	375427.i	−0.859256	−	0.859256i	−0.991250	+	0.131995i	$0.957862\pi$
$662$	−130156.	−	314224.i	−0.296994	−	0.717007i
$663$	−361263.	+	872167.i	−0.821858	+	1.98414i
$664$	−201127.	−	201127.i	−0.456178	−	0.456178i
$665$	−373683.	−	373683.i	−0.845006	−	0.845006i
$666$	705732.			1.59108
$667$	−727941.	−	301523.i	−1.63623	−	0.677749i
$668$	15003.3	+	6214.59i	0.0336229	+	0.0139271i
$669$	−225651.	+	544769.i	−0.504179	+	1.21719i
$670$	−192107.	−	463787.i	−0.427950	−	1.03316i
$671$	64614.8	−	26764.3i	0.143512	−	0.0594445i
$672$	168428.			0.372973
$673$	298059.	+	719578.i	0.658070	+	1.58872i	0.800781	+	0.598957i	$0.204418\pi$
$673$	298059.	+	719578.i	0.658070	+	1.58872i	−0.142711	+	0.989764i	$0.545582\pi$
$674$	87655.8			0.192957
$675$	−93628.8	−	226040.i	−0.205495	−	0.496109i
$676$	−16415.3	+	16415.3i	−0.0359215	+	0.0359215i
$677$	149870.	+	149870.i	0.326993	+	0.326993i	0.851442	−	0.524449i	$-0.175729\pi$
$677$	149870.	+	149870.i	0.326993	+	0.326993i	−0.524449	+	0.851442i	$0.675729\pi$
$678$	−140595.	+	58236.3i	−0.305851	+	0.126688i
$679$		−	485004.i		−	1.05198i
$680$	−149621.	+	61975.2i	−0.323575	+	0.134029i
$681$			1.05701e6i			2.27921i
$682$	91380.5	+	220612.i	0.196465	+	0.474308i
$683$	−34282.7	+	14200.4i	−0.0734910	+	0.0304410i	−0.419126	−	0.907928i	$-0.637663\pi$
$683$	−34282.7	+	14200.4i	−0.0734910	+	0.0304410i	0.345635	+	0.938369i	$0.387663\pi$
$684$	−560857.	−	232315.i	−1.19878	−	0.496552i
$685$	26642.5	−	64320.6i	0.0567797	−	0.137078i
$686$	−92371.9	+	223005.i	−0.196287	+	0.473879i
$687$		−	883456.i		−	1.87185i
$688$	42328.8	−	42328.8i	0.0894250	−	0.0894250i
$689$	296368.	−	296368.i	0.624300	−	0.624300i
$690$	630549.	+	261182.i	1.32441	+	0.548587i
$691$	345559.	−	143135.i	0.723714	−	0.299772i	0.00974773	−	0.999952i	$-0.496897\pi$
$691$	345559.	−	143135.i	0.723714	−	0.299772i	0.713966	+	0.700181i	$0.246897\pi$
$692$	151282.	−	151282.i	0.315918	−	0.315918i
$693$	−933389.			−1.94355
$694$	77714.2	+	32190.3i	0.161355	+	0.0668352i
$695$	−462354.	−	462354.i	−0.957205	−	0.957205i
$696$			418171.i			0.863247i
$697$	301239.	−	465089.i	0.620077	−	0.957350i
$698$	−528452.			−1.08466
$699$	−788573.	+	788573.i	−1.61394	+	1.61394i
$700$	−27096.2	+	65416.1i	−0.0552984	+	0.133502i
$701$			146351.i			0.297825i	0.988850	+	0.148912i	$0.0475772\pi$
$701$			146351.i			0.297825i	−0.988850	+	0.148912i	$0.952423\pi$
$702$	−565150.	−	565150.i	−1.14680	−	1.14680i
$703$	224454.	+	541879.i	0.454168	+	1.09646i
$704$	−17662.4	+	42640.9i	−0.0356373	+	0.0860361i
$705$	−572084.	−	572084.i	−1.15102	−	1.15102i
$706$	−321650.	−	321650.i	−0.645319	−	0.645319i
$707$	−598925.			−1.19821
$708$	−138953.	−	57556.1i	−0.277205	−	0.114822i
$709$	126738.	+	52496.8i	0.252125	+	0.104434i	0.505167	−	0.863022i	$-0.331431\pi$
$709$	126738.	+	52496.8i	0.252125	+	0.104434i	−0.253042	+	0.967455i	$0.581431\pi$
$710$	206795.	−	499248.i	0.410226	−	0.990374i
$711$	−453902.	−	1.09582e6i	−0.897890	−	2.16770i
$712$	47002.0	−	19468.9i	0.0927164	−	0.0384044i
$713$	−644669.			−1.26811
$714$	331982.	+	801475.i	0.651205	+	1.57215i
$715$	347171.			0.679097
$716$	3088.39	+	7456.03i	0.00602429	+	0.0145439i
$717$	959464.	−	959464.i	1.86634	−	1.86634i
$718$	334097.	+	334097.i	0.648073	+	0.648073i
$719$	538687.	−	223132.i	1.04203	−	0.431622i	0.204988	−	0.978765i	$-0.434285\pi$
$719$	538687.	−	223132.i	1.04203	−	0.431622i	0.837039	+	0.547143i	$0.184285\pi$
$720$		−	249667.i		−	0.481611i
$721$	−140895.	+	58360.5i	−0.271034	+	0.112266i
$722$		−	135924.i		−	0.260748i
$723$	−480357.	−	1.15969e6i	−0.918942	−	2.21852i
$724$	173043.	−	71676.8i	0.330124	−	0.136742i
$725$	−162414.	−	67274.0i	−0.308992	−	0.127988i
$726$	−113852.	+	274862.i	−0.216006	+	0.521485i
$727$	−250288.	+	604249.i	−0.473556	+	1.14327i	0.489025	+	0.872270i	$0.337353\pi$
$727$	−250288.	+	604249.i	−0.473556	+	1.14327i	−0.962581	+	0.270995i	$0.912647\pi$
$728$			231301.i			0.436431i
$729$	−54403.9	+	54403.9i	−0.102371	+	0.102371i
$730$	−239505.	+	239505.i	−0.449438	+	0.449438i
$731$	284856.	+	117991.i	0.533078	+	0.220808i
$732$	92582.2	−	38348.8i	0.172785	−	0.0715698i
$733$	246405.	−	246405.i	0.458608	−	0.458608i	−0.439590	−	0.898198i	$-0.644876\pi$
$733$	246405.	−	246405.i	0.458608	−	0.458608i	0.898198	+	0.439590i	$0.144876\pi$
$734$	157532.			0.292399
$735$	−298006.	−	123438.i	−0.551632	−	0.228494i
$736$	−88108.7	−	88108.7i	−0.162653	−	0.162653i
$737$		−	736877.i		−	1.35662i
$738$	484703.	+	703437.i	0.889945	+	1.29155i
$739$	838341.			1.53508			0.767542	−	0.640999i	$-0.221480\pi$
$739$	838341.			1.53508			0.767542	+	0.640999i	$0.221480\pi$
$740$	−170568.	+	170568.i	−0.311482	+	0.311482i
$741$	462865.	−	1.11746e6i	0.842982	−	2.03514i
$742$		−	385157.i		−	0.699567i
$743$	−92640.1	−	92640.1i	−0.167811	−	0.167811i	0.618205	−	0.786017i	$-0.287860\pi$
$743$	−92640.1	−	92640.1i	−0.167811	−	0.167811i	−0.786017	+	0.618205i	$0.787860\pi$
$744$	130933.	+	316100.i	0.236539	+	0.571056i
$745$	82601.5	−	199418.i	0.148825	−	0.359295i
$746$	−12683.2	−	12683.2i	−0.0227903	−	0.0227903i
$747$	1.59703e6	+	1.59703e6i	2.86202	+	2.86202i
$748$	−237722.			−0.424880
$749$	366238.	+	151701.i	0.652830	+	0.270411i
$750$	713204.	+	295419.i	1.26792	+	0.525189i
$751$	−97867.8	+	236274.i	−0.173524	+	0.418924i	−0.986584	−	0.163256i	$-0.947800\pi$
$751$	−97867.8	+	236274.i	−0.173524	+	0.418924i	0.813060	+	0.582180i	$0.197800\pi$
$752$	56525.5	+	136465.i	0.0999560	+	0.241315i
$753$	−1.33217e6	+	551804.i	−2.34947	+	0.973184i
$754$	−574270.			−1.01012
$755$	−172674.	−	416872.i	−0.302924	−	0.731322i
$756$	−734461.			−1.28507
$757$	159029.	+	383931.i	0.277515	+	0.669980i	0.999766	−	0.0216515i	$-0.00689242\pi$
$757$	159029.	+	383931.i	0.277515	+	0.669980i	−0.722251	+	0.691631i	$0.756892\pi$
$758$	−304365.	+	304365.i	−0.529732	+	0.529732i
$759$	708403.	+	708403.i	1.22969	+	1.22969i
$760$	191701.	−	79405.1i	0.331892	−	0.137474i
$761$			530641.i			0.916287i	0.888878	+	0.458144i	$0.151485\pi$
$761$			530641.i			0.916287i	−0.888878	+	0.458144i	$0.848515\pi$
$762$	1.01453e6	−	420230.i	1.74724	−	0.723731i
$763$			904741.i			1.55409i
$764$	−18236.7	−	44027.3i	−0.0312435	−	0.0754285i
$765$	1.18805e6	−	492108.i	2.03008	−	0.840886i
$766$	−454940.	−	188442.i	−0.775347	−	0.321159i
$767$	79041.3	−	190823.i	0.134358	−	0.324369i
$768$	−25307.3	+	61097.2i	−0.0429065	+	0.103586i
$769$			612584.i			1.03589i	0.855415	+	0.517944i	$0.173302\pi$
$769$			612584.i			1.03589i	−0.855415	+	0.517944i	$0.826698\pi$
$770$	225590.	−	225590.i	0.380485	−	0.380485i
$771$	740337.	−	740337.i	1.24543	−	1.24543i
$772$	316927.	+	131276.i	0.531771	+	0.220267i
$773$	36523.6	−	15128.6i	0.0611244	−	0.0253185i	−0.351912	−	0.936033i	$-0.614468\pi$
$773$	36523.6	−	15128.6i	0.0611244	−	0.0253185i	0.413036	+	0.910715i	$0.364468\pi$
$774$	−336108.	+	336108.i	−0.561043	+	0.561043i
$775$	−143834.			−0.239475
$776$	175935.	+	72874.5i	0.292165	+	0.121019i
$777$	913677.	+	913677.i	1.51339	+	1.51339i
$778$			138059.i			0.228090i
$779$	−385960.	+	595891.i	−0.636015	+	0.981956i
$780$	497438.			0.817617
$781$	560890.	−	560890.i	0.919550	−	0.919550i
$782$	245602.	−	592936.i	0.401623	−	0.969604i
$783$		−	1.82350e6i		−	2.97429i
$784$	41641.3	+	41641.3i	0.0677473	+	0.0677473i
$785$	201375.	+	486162.i	0.326788	+	0.788936i
$786$	−372594.	+	899521.i	−0.603102	+	1.45602i
$787$	443785.	+	443785.i	0.716512	+	0.716512i	0.967889	−	0.251377i	$-0.0808835\pi$
$787$	443785.	+	443785.i	0.716512	+	0.716512i	−0.251377	+	0.967889i	$0.580884\pi$
$788$	−187528.	−	187528.i	−0.302005	−	0.302005i
$789$	1.98206e6			3.18393
$790$	374550.	+	155144.i	0.600144	+	0.248588i
$791$	−177428.	−	73493.2i	−0.283576	−	0.117461i
$792$	140247.	−	338586.i	0.223585	−	0.539782i
$793$	52664.1	+	127142.i	0.0837468	+	0.202183i
$794$	442705.	−	183374.i	0.702220	−	0.290869i
$795$	−828320.			−1.31058
$796$	−182782.	−	441275.i	−0.288475	−	0.696439i
$797$	335562.			0.528271			0.264135	−	0.964486i	$-0.414913\pi$
$797$	335562.			0.528271			0.264135	+	0.964486i	$0.414913\pi$
$798$	−425348.	−	1.02688e6i	−0.667942	−	1.61256i
$799$	−537959.	+	537959.i	−0.842666	+	0.842666i
$800$	−19658.3	−	19658.3i	−0.0307160	−	0.0307160i
$801$	−373215.	+	154591.i	−0.581693	+	0.240945i
$802$			688118.i			1.06983i
$803$	−459343.	+	190266.i	−0.712371	+	0.295074i
$804$		−	1.05582e6i		−	1.63335i
$805$	329607.	+	795742.i	0.508633	+	1.22795i
$806$	−434097.	+	179809.i	−0.668216	+	0.276784i
$807$	97316.7	+	40309.9i	0.149431	+	0.0618963i
$808$	89991.8	−	217260.i	0.137842	−	0.332779i
$809$	139225.	−	336120.i	0.212726	−	0.513566i	−0.781114	−	0.624388i	$-0.785348\pi$
$809$	139225.	−	336120.i	0.212726	−	0.513566i	0.993840	+	0.110822i	$0.0353483\pi$
$810$			685796.i			1.04526i
$811$	−233057.	+	233057.i	−0.354341	+	0.354341i	−0.861722	−	0.507381i	$-0.830614\pi$
$811$	−233057.	+	233057.i	−0.354341	+	0.354341i	0.507381	+	0.861722i	$0.330614\pi$
$812$	−373157.	+	373157.i	−0.565952	+	0.565952i
$813$	288423.	+	119469.i	0.436364	+	0.180748i
$814$	−327129.	+	135501.i	−0.493707	+	0.204500i
$815$	−531500.	+	531500.i	−0.800181	+	0.800181i
$816$	−340616.			−0.511546
$817$	−364969.	−	151175.i	−0.546779	−	0.226483i
$818$	229131.	+	229131.i	0.342434	+	0.342434i
$819$		−	1.83663e6i		−	2.73812i
$820$	−287160.	−	52865.4i	−0.427067	−	0.0786219i
$821$	−337947.			−0.501374			−0.250687	−	0.968068i	$-0.580656\pi$
$821$	−337947.			−0.501374			−0.250687	+	0.968068i	$0.580656\pi$
$822$	103540.	−	103540.i	0.153237	−	0.153237i
$823$	11642.7	−	28107.9i	0.0171891	−	0.0414981i	−0.915052	−	0.403336i	$-0.867851\pi$
$823$	11642.7	−	28107.9i	0.0171891	−	0.0414981i	0.932241	+	0.361838i	$0.117851\pi$
$824$		−	59878.3i		−	0.0881892i
$825$	158055.	+	158055.i	0.232220	+	0.232220i
$826$	−72634.8	−	175356.i	−0.106459	−	0.257016i
$827$	−277363.	+	669614.i	−0.405544	+	0.979070i	0.580751	+	0.814081i	$0.302759\pi$
$827$	−277363.	+	669614.i	−0.405544	+	0.979070i	−0.986295	+	0.164989i	$0.947241\pi$
$828$	699618.	+	699618.i	1.02047	+	1.02047i
$829$	515905.	+	515905.i	0.750690	+	0.750690i	0.974608	−	0.223918i	$-0.0718848\pi$
$829$	515905.	+	515905.i	0.750690	+	0.750690i	−0.223918	+	0.974608i	$0.571885\pi$
$830$	−771969.			−1.12058
$831$	838378.	+	347267.i	1.21405	+	0.502877i
$832$	−83904.3	−	34754.3i	−0.121210	−	0.0502067i
$833$	−116075.	+	280229.i	−0.167281	+	0.403853i
$834$	−526279.	−	1.27055e6i	−0.756631	−	1.82667i
$835$	40719.5	−	16866.6i	0.0584022	−	0.0241910i
$836$	304579.			0.435801
$837$	−570956.	−	1.37841e6i	−0.814988	−	1.96756i
$838$	23843.0			0.0339526
$839$	−131182.	−	316701.i	−0.186359	−	0.449910i	0.802895	−	0.596121i	$-0.203292\pi$
$839$	−131182.	−	316701.i	−0.186359	−	0.449910i	−0.989253	+	0.146211i	$0.953292\pi$
$840$	323232.	−	323232.i	0.458095	−	0.458095i
$841$	−426343.	−	426343.i	−0.602792	−	0.602792i
$842$	275429.	−	114086.i	0.388495	−	0.160920i
$843$		−	839696.i		−	1.18159i
$844$	−107534.	+	44542.1i	−0.150960	+	0.0625296i
$845$			63005.2i			0.0882395i
$846$	−448835.	−	1.08358e6i	−0.627114	−	1.51399i
$847$	−346871.	+	143679.i	−0.483505	+	0.200275i
$848$	139715.	+	57871.9i	0.194291	+	0.0804778i
$849$	367216.	−	886537.i	0.509455	−	1.22993i
$850$	54797.2	−	132292.i	0.0758439	−	0.183103i
$851$		−	955930.i		−	1.31998i
$852$	803661.	−	803661.i	1.10712	−	1.10712i
$853$	−553460.	+	553460.i	−0.760656	+	0.760656i	−0.976441	−	0.215785i	$-0.930769\pi$
$853$	−553460.	+	553460.i	−0.760656	+	0.760656i	0.215785	+	0.976441i	$0.430769\pi$
$854$	116837.	+	48395.5i	0.160201	+	0.0663574i
$855$	−1.52218e6	+	630508.i	−2.08226	+	0.862499i
$856$	−110059.	+	110059.i	−0.150202	+	0.150202i
$857$	−1.13467e6			−1.54493			−0.772463	−	0.635059i	$-0.780976\pi$
$857$	−1.13467e6			−1.54493			−0.772463	+	0.635059i	$0.780976\pi$
$858$	674600.	+	279428.i	0.916372	+	0.379574i
$859$	−590940.	−	590940.i	−0.800861	−	0.800861i	0.182369	−	0.983230i	$-0.441623\pi$
$859$	−590940.	−	590940.i	−0.800861	−	0.800861i	−0.983230	+	0.182369i	$0.941623\pi$
$860$		−	162467.i		−	0.219669i
$861$	−283184.	+	1.53823e6i	−0.381999	+	2.07498i
$862$	−885130.			−1.19122
$863$	−203953.	+	203953.i	−0.273848	+	0.273848i	−0.830647	−	0.556799i	$-0.812029\pi$
$863$	−203953.	+	203953.i	−0.273848	+	0.273848i	0.556799	+	0.830647i	$0.312029\pi$
$864$	110357.	−	266425.i	0.147833	−	0.356901i
$865$		−	580652.i		−	0.776039i
$866$	452339.	+	452339.i	0.603154	+	0.603154i
$867$	−155335.	−	375013.i	−0.206649	−	0.498894i
$868$	−165235.	+	398912.i	−0.219312	+	0.529466i
$869$	420795.	+	420795.i	0.557226	+	0.557226i
$870$	802514.	+	802514.i	1.06026	+	1.06026i
$871$	1.44995e6			1.91125
$872$	−328194.	−	135942.i	−0.431616	−	0.178781i
$873$	−1.39699e6	−	578653.i	−1.83301	−	0.759259i
$874$	−314676.	+	759694.i	−0.411946	+	0.994525i
$875$	372813.	+	900051.i	0.486940	+	1.17558i
$876$	−658162.	+	272620.i	−0.857678	+	0.355262i
$877$	−1.41541e6			−1.84028			−0.920140	−	0.391589i	$-0.871925\pi$
$877$	−1.41541e6			−1.84028			−0.920140	+	0.391589i	$0.871925\pi$
$878$	−110785.	−	267460.i	−0.143712	−	0.346952i
$879$	26982.1			0.0349218
$880$	47936.3	+	115728.i	0.0619012	+	0.149443i
$881$	948581.	−	948581.i	1.22214	−	1.22214i	0.255277	−	0.966868i	$-0.417833\pi$
$881$	948581.	−	948581.i	1.22214	−	1.22214i	0.966868	−	0.255277i	$-0.0821666\pi$
$882$	−330648.	−	330648.i	−0.425039	−	0.425039i
$883$	754013.	−	312322.i	0.967069	−	0.400573i	0.157449	−	0.987527i	$-0.449673\pi$
$883$	754013.	−	312322.i	0.967069	−	0.400573i	0.809620	+	0.586954i	$0.199673\pi$
$884$		−	467765.i		−	0.598582i
$885$	−377121.	+	156209.i	−0.481498	+	0.199443i
$886$			227.068i			0.000289260i
$887$	2220.10	+	5359.78i	0.00282179	+	0.00681240i	0.925284	−	0.379275i	$-0.123826\pi$
$887$	2220.10	+	5359.78i	0.00282179	+	0.00681240i	−0.922462	+	0.386087i	$0.873826\pi$
$888$	−468720.	+	194150.i	−0.594413	+	0.246214i
$889$	1.28031e6	+	530323.i	1.61999	+	0.671022i
$890$	52839.0	−	127565.i	0.0667075	−	0.161046i
$891$	−385236.	+	930042.i	−0.485256	+	1.17151i
$892$		−	292174.i		−	0.367207i
$893$	689254.	−	689254.i	0.864324	−	0.864324i
$894$	321011.	−	321011.i	0.401648	−	0.401648i
$895$	20235.8	+	8381.96i	0.0252624	+	0.0104640i
$896$	−77103.6	+	31937.4i	−0.0960414	+	0.0397817i
$897$	−1.39392e6	+	1.39392e6i	−1.73242	+	1.73242i
$898$	325752.			0.403956
$899$	−990411.	−	410242.i	−1.22545	−	0.507599i
$900$	156094.	+	156094.i	0.192709	+	0.192709i
$901$			778910.i			0.959484i
$902$	−359735.	−	233001.i	−0.442150	−	0.286382i
$903$	−870285.			−1.06730
$904$	53319.1	−	53319.1i	0.0652448	−	0.0652448i
$905$	194533.	−	469644.i	0.237517	−	0.573418i
$906$		−	949018.i		−	1.15616i
$907$	792015.	+	792015.i	0.962762	+	0.962762i	0.999331	−	0.0365691i	$-0.0116429\pi$
$907$	792015.	+	792015.i	0.962762	+	0.962762i	−0.0365691	+	0.999331i	$0.511643\pi$
$908$	−200430.	−	483880.i	−0.243103	−	0.586902i
$909$	−714571.	+	1.72513e6i	−0.864804	+	2.08782i
$910$	443892.	+	443892.i	0.536037	+	0.536037i
$911$	215638.	+	215638.i	0.259830	+	0.259830i	0.824985	−	0.565155i	$-0.191184\pi$
$911$	215638.	+	215638.i	0.259830	+	0.259830i	−0.565155	+	0.824985i	$0.691184\pi$
$912$	436411.			0.524694
$913$	−1.04690e6	−	433642.i	−1.25593	−	0.520223i
$914$	−520248.	−	215494.i	−0.622756	−	0.257954i
$915$	104080.	−	251271.i	0.124315	−	0.300123i
$916$	167521.	+	404431.i	0.199654	+	0.482007i
$917$	−1.13518e6	+	470207.i	−1.34998	+	0.559178i
$918$	1.48532e6			1.76252
$919$	190536.	+	459993.i	0.225603	+	0.544654i	0.995633	−	0.0933539i	$-0.0297588\pi$
$919$	190536.	+	459993.i	0.225603	+	0.544654i	−0.770030	+	0.638008i	$0.779759\pi$
$920$	−338180.			−0.399551
$921$	−621336.	−	1.50004e6i	−0.732500	−	1.76841i
$922$	−598164.	+	598164.i	−0.703653	+	0.703653i
$923$	1.10366e6	+	1.10366e6i	1.29548	+	1.29548i
$924$	619921.	−	256780.i	0.726094	−	0.300758i
$925$		−	213281.i		−	0.249269i
$926$	285419.	−	118225.i	0.332860	−	0.137875i
$927$			475458.i			0.553290i
$928$	−79293.4	−	191431.i	−0.0920748	−	0.222288i
$929$	−1.49371e6	+	618714.i	−1.73075	+	0.716900i	−0.731358	+	0.681994i	$0.761113\pi$
$929$	−1.49371e6	+	618714.i	−1.73075	+	0.716900i	−0.999391	+	0.0349058i	$0.988887\pi$
$930$	857903.	+	355355.i	0.991911	+	0.410863i
$931$	148720.	−	359041.i	0.171581	−	0.414233i
$932$	211466.	−	510524.i	0.243449	−	0.587739i
$933$			782812.i			0.899279i
$934$	−198846.	+	198846.i	−0.227942	+	0.227942i
$935$	−456214.	+	456214.i	−0.521850	+	0.521850i
$936$	666234.	+	275963.i	0.760458	+	0.314992i
$937$	1.01291e6	−	419562.i	1.15370	−	0.477878i	0.277926	−	0.960602i	$-0.410353\pi$
$937$	1.01291e6	−	419562.i	1.15370	−	0.477878i	0.875772	+	0.482725i	$0.160353\pi$
$938$	942168.	−	942168.i	1.07084	−	1.07084i
$939$	320166.			0.363114
$940$	370369.	+	153412.i	0.419159	+	0.173621i
$941$	−22308.1	−	22308.1i	−0.0251932	−	0.0251932i	0.694398	−	0.719591i	$-0.255671\pi$
$941$	−22308.1	−	22308.1i	−0.0251932	−	0.0251932i	−0.719591	+	0.694398i	$0.755671\pi$
$942$			1.10676e6i			1.24724i
$943$	952821.	−	656541.i	1.07149	−	0.738310i
$944$	74523.9			0.0836280
$945$	−1.40951e6	+	1.40951e6i	−1.57835	+	1.57835i
$946$	91263.3	−	220329.i	0.101980	−	0.246201i
$947$			457204.i			0.509812i	0.966966	+	0.254906i	$0.0820445\pi$
$947$			457204.i			0.509812i	−0.966966	+	0.254906i	$0.917956\pi$
$948$	602929.	+	602929.i	0.670887	+	0.670887i
$949$	−374386.	−	903848.i	−0.415707	−	1.00361i
$950$	−70208.4	+	169498.i	−0.0777933	+	0.187810i
$951$	−1.47064e6	−	1.47064e6i	−1.62609	−	1.62609i
$952$	−303951.	−	303951.i	−0.335374	−	0.335374i
$953$	−1.14328e6			−1.25883			−0.629413	−	0.777071i	$-0.716705\pi$
$953$	−1.14328e6			−1.25883			−0.629413	+	0.777071i	$0.716705\pi$
$954$	−1.10939e6	−	459526.i	−1.21896	−	0.504909i
$955$	−119491.	−	49494.9i	−0.131018	−	0.0542693i
$956$	−257293.	+	621159.i	−0.281521	+	0.679653i
$957$	637527.	+	1.53913e6i	0.696105	+	1.68055i
$958$	−289891.	+	120077.i	−0.315867	+	0.130836i
$959$	184788.			0.200927
$960$	68684.7	+	165819.i	0.0745276	+	0.179926i
$961$	46407.2			0.0502503
$962$	−266625.	−	643690.i	−0.288105	−	0.695547i
$963$	873910.	−	873910.i	0.942354	−	0.942354i
$964$	439798.	+	439798.i	0.473260	+	0.473260i
$965$	860149.	−	356285.i	0.923674	−	0.382598i
$966$			1.81152e6i			1.94129i
$967$	1.20050e6	−	497264.i	1.28384	−	0.531782i	0.366694	−	0.930342i	$-0.380490\pi$
$967$	1.20050e6	−	497264.i	1.28384	−	0.531782i	0.917143	+	0.398559i	$0.130490\pi$
$968$		−	147416.i		−	0.157323i
$969$	860191.	+	2.07668e6i	0.916109	+	2.21168i
$970$	477491.	−	197783.i	0.507483	−	0.210207i
$971$	−1.58007e6	−	654488.i	−1.67587	−	0.694166i	−0.676750	−	0.736213i	$-0.736612\pi$
$971$	−1.58007e6	−	654488.i	−1.67587	−	0.694166i	−0.999116	+	0.0420472i	$0.986612\pi$
$972$	−156931.	+	378865.i	−0.166102	+	0.401007i
$973$	664155.	−	1.60341e6i	0.701526	−	1.69363i
$974$		−	154245.i		−	0.162589i
$975$	−311003.	+	311003.i	−0.327157	+	0.327157i
$976$	−35110.8	+	35110.8i	−0.0368588	+	0.0368588i
$977$	442975.	+	183486.i	0.464077	+	0.192227i	0.602455	−	0.798153i	$-0.294189\pi$
$977$	442975.	+	183486.i	0.464077	+	0.192227i	−0.138379	+	0.990379i	$0.544189\pi$
$978$	−1.46057e6	+	604986.i	−1.52702	+	0.632511i
$979$	143315.	−	143315.i	0.149529	−	0.149529i
$980$	159828.			0.166418
$981$	2.60599e6	+	1.07944e6i	2.70791	+	1.12165i
$982$	−213286.	−	213286.i	−0.221177	−	0.221177i
$983$		−	123768.i		−	0.128086i	−0.997947	−	0.0640428i	$-0.979601\pi$
$983$		−	123768.i		−	0.128086i	0.997947	−	0.0640428i	$-0.0203994\pi$
$984$	−515440.	−	333852.i	−0.532339	−	0.344797i
$985$	−719772.			−0.741861
$986$	754643.	−	754643.i	0.776225	−	0.776225i
$987$	821779.	−	1.98395e6i	0.843569	−	2.03656i
$988$			599320.i			0.613967i
$989$	455265.	+	455265.i	0.465449	+	0.465449i
$990$	−380633.	−	918930.i	−0.388362	−	0.937588i
$991$	18532.5	−	44741.4i	0.0188706	−	0.0455577i	−0.914163	−	0.405346i	$-0.867151\pi$
$991$	18532.5	−	44741.4i	0.0188706	−	0.0455577i	0.933034	+	0.359788i	$0.117151\pi$
$992$	−119878.	−	119878.i	−0.121819	−	0.121819i
$993$	−1.37281e6	−	1.37281e6i	−1.39223	−	1.39223i
$994$	1.43430e6			1.45167
$995$	−1.19763e6	−	496075.i	−1.20970	−	0.501074i
$996$	−1.50004e6	−	621336.i	−1.51211	−	0.626337i
$997$	52682.5	−	127187.i	0.0530000	−	0.127953i	−0.895162	−	0.445742i	$-0.852940\pi$
$997$	52682.5	−	127187.i	0.0530000	−	0.127953i	0.948162	+	0.317788i	$0.102940\pi$
$998$	368333.	+	889235.i	0.369811	+	0.892803i
$999$	2.04394e6	−	846626.i	2.04803	−	0.848322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.e.a.3.1	✓	28
41.14	odd	8	inner	82.5.e.a.55.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.e.a.3.1	✓	28	1.1	even	1	trivial
82.5.e.a.55.1	yes	28	41.14	odd	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	82.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +(-6.17854 + 14.9163i) q^{3} -8.00000i q^{4} +(-15.3528 - 15.3528i) q^{5} +(-17.4755 - 42.1897i) q^{6} +(22.0538 - 53.2426i) q^{7} +(16.0000 + 16.0000i) q^{8} +(-127.046 - 127.046i) q^{9} +61.4114 q^{10} +(83.2830 + 34.4969i) q^{11} +(119.331 + 49.4283i) q^{12} +(-67.8795 + 163.876i) q^{13} +(62.3776 + 150.593i) q^{14} +(323.866 - 134.150i) q^{15} -64.0000 q^{16} +(-126.148 - 304.547i) q^{17} +508.186 q^{18} +(161.625 + 390.198i) q^{19} +(-122.823 + 122.823i) q^{20} +(657.924 + 657.924i) q^{21} +(-235.560 + 97.5720i) q^{22} -688.349i q^{23} +(-337.518 + 139.804i) q^{24} -153.580i q^{25} +(-191.992 - 463.510i) q^{26} +(1471.80 - 609.641i) q^{27} +(-425.941 - 176.431i) q^{28} +(438.038 - 1057.52i) q^{29} +(-379.433 + 916.032i) q^{30} -936.544i q^{31} +(128.000 - 128.000i) q^{32} +(-1029.13 + 1029.13i) q^{33} +(861.389 + 356.799i) q^{34} +(-1156.02 + 478.837i) q^{35} +(-1016.37 + 1016.37i) q^{36} +1388.73 q^{37} +(-1103.65 - 457.145i) q^{38} +(-2025.02 - 2025.02i) q^{39} -491.291i q^{40} +(953.792 + 1384.21i) q^{41} -2631.69 q^{42} +(-661.387 + 661.387i) q^{43} +(275.975 - 666.264i) q^{44} +3901.05i q^{45} +(1376.70 + 1376.70i) q^{46} +(-883.211 - 2132.26i) q^{47} +(395.427 - 954.644i) q^{48} +(-650.645 - 650.645i) q^{49} +(307.160 + 307.160i) q^{50} +5322.13 q^{51} +(1311.00 + 543.036i) q^{52} +(-2183.05 - 904.248i) q^{53} +(-1724.33 + 4162.89i) q^{54} +(-749.004 - 1808.26i) q^{55} +(1204.74 - 499.021i) q^{56} -6818.92 q^{57} +(1238.96 + 2991.11i) q^{58} -1164.44 q^{59} +(-1073.20 - 2590.93i) q^{60} +(548.607 - 548.607i) q^{61} +(1873.09 + 1873.09i) q^{62} +(-9566.15 + 3962.43i) q^{63} +512.000i q^{64} +(3558.10 - 1473.81i) q^{65} -4116.54i q^{66} +(-3128.19 - 7552.13i) q^{67} +(-2436.38 + 1009.18i) q^{68} +(10267.6 + 4252.99i) q^{69} +(1354.36 - 3269.71i) q^{70} +(3367.37 - 8129.56i) q^{71} -4065.49i q^{72} +(-3900.01 + 3900.01i) q^{73} +(-2777.46 + 2777.46i) q^{74} +(2290.85 + 948.901i) q^{75} +(3121.58 - 1293.00i) q^{76} +(3673.42 - 3673.42i) q^{77} +8100.09 q^{78} +(6099.03 + 2526.30i) q^{79} +(982.582 + 982.582i) q^{80} +11167.3i q^{81} +(-4676.01 - 860.840i) q^{82} -12570.4 q^{83} +(5263.39 - 5263.39i) q^{84} +(-2738.94 + 6612.39i) q^{85} -2645.55i q^{86} +(13067.8 + 13067.8i) q^{87} +(780.576 + 1884.48i) q^{88} +(860.411 - 2077.22i) q^{89} +(-7802.10 - 7802.10i) q^{90} +(7228.17 + 7228.17i) q^{91} -5506.79 q^{92} +(13969.8 + 5786.47i) q^{93} +(6030.94 + 2498.10i) q^{94} +(3509.24 - 8472.06i) q^{95} +(1118.44 + 2700.14i) q^{96} +(7775.29 - 3220.63i) q^{97} +2602.58 q^{98} +(-6198.09 - 14963.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 56 q^{2} + 16 q^{3} - 16 q^{6} + 448 q^{8} + 24 q^{9} + 328 q^{11} - 64 q^{12} - 348 q^{13} + 192 q^{14} + 1036 q^{15} - 1792 q^{16} - 1832 q^{17} - 96 q^{18} - 504 q^{19} + 2004 q^{21} - 856 q^{22}+ \cdots + 11544 q^{99}+O(q^{100}) \) 28 * q - 56 * q^2 + 16 * q^3 - 16 * q^6 + 448 * q^8 + 24 * q^9 + 328 * q^11 - 64 * q^12 - 348 * q^13 + 192 * q^14 + 1036 * q^15 - 1792 * q^16 - 1832 * q^17 - 96 * q^18 - 504 * q^19 + 2004 * q^21 - 856 * q^22 + 384 * q^24 + 384 * q^26 + 964 * q^27 - 768 * q^28 - 4 * q^29 - 4456 * q^30 + 3584 * q^32 - 748 * q^33 + 3576 * q^34 - 1104 * q^35 + 192 * q^36 + 5488 * q^37 + 256 * q^38 + 1232 * q^39 - 3760 * q^41 - 8016 * q^42 + 4756 * q^43 + 800 * q^44 - 2320 * q^46 - 4240 * q^47 - 1024 * q^48 + 2088 * q^49 - 6280 * q^50 + 29792 * q^51 + 1248 * q^52 - 10492 * q^53 - 1992 * q^54 + 14840 * q^55 + 1536 * q^56 - 33512 * q^57 + 2192 * q^58 - 11376 * q^59 + 9536 * q^60 - 3360 * q^61 + 2224 * q^62 - 13912 * q^63 + 41300 * q^65 + 15440 * q^67 + 352 * q^68 - 1004 * q^69 - 6792 * q^70 - 28392 * q^71 + 4284 * q^73 - 10976 * q^74 + 23812 * q^75 + 3008 * q^76 - 16524 * q^77 - 4928 * q^78 - 22236 * q^79 + 16752 * q^82 - 4024 * q^83 + 16032 * q^84 - 16616 * q^85 - 4628 * q^87 + 3648 * q^88 - 54412 * q^89 + 18336 * q^90 + 59948 * q^91 + 9280 * q^92 - 26800 * q^93 - 3240 * q^94 - 47636 * q^95 + 1024 * q^96 + 46764 * q^97 - 8352 * q^98 + 11544 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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