LMFDB - Embedded newform 354.5.b.a.119.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.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:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.17
Character	$\chi$	$=$	354.119
Dual form			354.5.b.a.119.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} +(-3.47377 - 8.30259i) q^{3} -8.00000 q^{4} -12.2691i q^{5} +(-23.4833 + 9.82529i) q^{6} -13.7545 q^{7} +22.6274i q^{8} +(-56.8659 + 57.6825i) q^{9} +O(q^{10})$	\(q-2.82843i q^{2} +(-3.47377 - 8.30259i) q^{3} -8.00000 q^{4} -12.2691i q^{5} +(-23.4833 + 9.82529i) q^{6} -13.7545 q^{7} +22.6274i q^{8} +(-56.8659 + 57.6825i) q^{9} -34.7024 q^{10} +99.2007i q^{11} +(27.7901 + 66.4207i) q^{12} +260.029 q^{13} +38.9037i q^{14} +(-101.866 + 42.6201i) q^{15} +64.0000 q^{16} +146.049i q^{17} +(163.151 + 160.841i) q^{18} +122.407 q^{19} +98.1531i q^{20} +(47.7801 + 114.198i) q^{21} +280.582 q^{22} +119.270i q^{23} +(187.866 - 78.6023i) q^{24} +474.468 q^{25} -735.473i q^{26} +(676.453 + 271.759i) q^{27} +110.036 q^{28} +101.923i q^{29} +(120.548 + 288.120i) q^{30} -392.523 q^{31} -181.019i q^{32} +(823.623 - 344.600i) q^{33} +413.088 q^{34} +168.756i q^{35} +(454.927 - 461.460i) q^{36} +351.161 q^{37} -346.219i q^{38} +(-903.280 - 2158.91i) q^{39} +277.619 q^{40} +1983.59i q^{41} +(323.002 - 135.142i) q^{42} -74.1789 q^{43} -793.606i q^{44} +(707.715 + 697.696i) q^{45} +337.347 q^{46} +2077.48i q^{47} +(-222.321 - 531.366i) q^{48} -2211.81 q^{49} -1342.00i q^{50} +(1212.58 - 507.339i) q^{51} -2080.23 q^{52} -2036.56i q^{53} +(768.650 - 1913.30i) q^{54} +1217.11 q^{55} -311.230i q^{56} +(-425.213 - 1016.29i) q^{57} +288.282 q^{58} -453.188i q^{59} +(814.925 - 340.961i) q^{60} +6462.13 q^{61} +1110.22i q^{62} +(782.165 - 793.396i) q^{63} -512.000 q^{64} -3190.33i q^{65} +(-974.676 - 2329.56i) q^{66} +1258.62 q^{67} -1168.39i q^{68} +(990.252 - 414.317i) q^{69} +477.315 q^{70} -6889.63i q^{71} +(-1305.21 - 1286.73i) q^{72} -1079.08 q^{73} -993.235i q^{74} +(-1648.19 - 3939.31i) q^{75} -979.255 q^{76} -1364.46i q^{77} +(-6106.33 + 2554.86i) q^{78} -3529.62 q^{79} -785.225i q^{80} +(-93.5374 - 6560.33i) q^{81} +5610.45 q^{82} +5606.23i q^{83} +(-382.241 - 913.586i) q^{84} +1791.89 q^{85} +209.810i q^{86} +(846.226 - 354.057i) q^{87} -2244.66 q^{88} -836.835i q^{89} +(1973.38 - 2001.72i) q^{90} -3576.58 q^{91} -954.163i q^{92} +(1363.53 + 3258.95i) q^{93} +5876.00 q^{94} -1501.83i q^{95} +(-1502.93 + 628.819i) q^{96} -5760.76 q^{97} +6255.95i q^{98} +(-5722.14 - 5641.14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−3.47377	−	8.30259i	−0.385974	−	0.922510i
$3$	−3.47377	−	8.30259i	−0.385974	−	0.922510i
$4$	−8.00000			−0.500000
$5$		−	12.2691i		−	0.490766i	−0.969426	−	0.245383i	$-0.921086\pi$
$5$		−	12.2691i		−	0.490766i	0.969426	−	0.245383i	$-0.0789137\pi$
$6$	−23.4833	+	9.82529i	−0.652313	+	0.272925i
$7$	−13.7545			−0.280705			−0.140353	−	0.990102i	$-0.544824\pi$
$7$	−13.7545			−0.280705			−0.140353	+	0.990102i	$0.544824\pi$
$8$			22.6274i			0.353553i
$9$	−56.8659	+	57.6825i	−0.702048	+	0.712129i
$10$	−34.7024			−0.347024
$11$			99.2007i			0.819841i	0.912121	+	0.409920i	$0.134444\pi$
$11$			99.2007i			0.819841i	−0.912121	+	0.409920i	$0.865556\pi$
$12$	27.7901	+	66.4207i	0.192987	+	0.461255i
$13$	260.029			1.53863			0.769316	−	0.638868i	$-0.220597\pi$
$13$	260.029			1.53863			0.769316	+	0.638868i	$0.220597\pi$
$14$			38.9037i			0.198488i
$15$	−101.866	+	42.6201i	−0.452736	+	0.189423i
$16$	64.0000			0.250000
$17$			146.049i			0.505359i	0.967550	+	0.252679i	$0.0813118\pi$
$17$			146.049i			0.505359i	−0.967550	+	0.252679i	$0.918688\pi$
$18$	163.151	+	160.841i	0.503552	+	0.496423i
$19$	122.407			0.339077			0.169539	−	0.985524i	$-0.445772\pi$
$19$	122.407			0.339077			0.169539	+	0.985524i	$0.445772\pi$
$20$			98.1531i			0.245383i
$21$	47.7801	+	114.198i	0.108345	+	0.258953i
$22$	280.582			0.579715
$23$			119.270i			0.225464i	0.993625	+	0.112732i	$0.0359601\pi$
$23$			119.270i			0.225464i	−0.993625	+	0.112732i	$0.964040\pi$
$24$	187.866	−	78.6023i	0.326156	−	0.136462i
$25$	474.468			0.759149
$26$		−	735.473i		−	1.08798i
$27$	676.453	+	271.759i	0.927919	+	0.372783i
$28$	110.036			0.140353
$29$			101.923i			0.121193i	0.998162	+	0.0605964i	$0.0193003\pi$
$29$			101.923i			0.121193i	−0.998162	+	0.0605964i	$0.980700\pi$
$30$	120.548	+	288.120i	0.133942	+	0.320133i
$31$	−392.523			−0.408452			−0.204226	−	0.978924i	$-0.565468\pi$
$31$	−392.523			−0.408452			−0.204226	+	0.978924i	$0.565468\pi$
$32$		−	181.019i		−	0.176777i
$33$	823.623	−	344.600i	0.756311	−	0.316437i
$34$	413.088			0.357343
$35$			168.756i			0.137760i
$36$	454.927	−	461.460i	0.351024	−	0.356065i
$37$	351.161			0.256509			0.128255	−	0.991741i	$-0.459062\pi$
$37$	351.161			0.256509			0.128255	+	0.991741i	$0.459062\pi$
$38$		−	346.219i		−	0.239764i
$39$	−903.280	−	2158.91i	−0.593872	−	1.41940i
$40$	277.619			0.173512
$41$			1983.59i			1.18001i	0.807400	+	0.590004i	$0.200874\pi$
$41$			1983.59i			1.18001i	−0.807400	+	0.590004i	$0.799126\pi$
$42$	323.002	−	135.142i	0.183107	−	0.0766114i
$43$	−74.1789			−0.0401184			−0.0200592	−	0.999799i	$-0.506385\pi$
$43$	−74.1789			−0.0401184			−0.0200592	+	0.999799i	$0.506385\pi$
$44$		−	793.606i		−	0.409920i
$45$	707.715	+	697.696i	0.349489	+	0.344541i
$46$	337.347			0.159427
$47$			2077.48i			0.940461i	0.882544	+	0.470231i	$0.155829\pi$
$47$			2077.48i			0.940461i	−0.882544	+	0.470231i	$0.844171\pi$
$48$	−222.321	−	531.366i	−0.0964935	−	0.230627i
$49$	−2211.81			−0.921205
$50$		−	1342.00i		−	0.536799i
$51$	1212.58	−	507.339i	0.466198	−	0.195055i
$52$	−2080.23			−0.769316
$53$		−	2036.56i		−	0.725011i	−0.931982	−	0.362505i	$-0.881921\pi$
$53$		−	2036.56i		−	0.725011i	0.931982	−	0.362505i	$-0.118079\pi$
$54$	768.650	−	1913.30i	0.263597	−	0.656138i
$55$	1217.11			0.402350
$56$		−	311.230i		−	0.0992442i
$57$	−425.213	−	1016.29i	−0.130875	−	0.312802i
$58$	288.282			0.0856963
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	814.925	−	340.961i	0.226368	−	0.0947114i
$61$	6462.13			1.73667			0.868333	−	0.495982i	$-0.165192\pi$
$61$	6462.13			1.73667			0.868333	+	0.495982i	$0.165192\pi$
$62$			1110.22i			0.288819i
$63$	782.165	−	793.396i	0.197068	−	0.199898i
$64$	−512.000			−0.125000
$65$		−	3190.33i		−	0.755108i
$66$	−974.676	−	2329.56i	−0.223755	−	0.534793i
$67$	1258.62			0.280379			0.140189	−	0.990125i	$-0.455229\pi$
$67$	1258.62			0.280379			0.140189	+	0.990125i	$0.455229\pi$
$68$		−	1168.39i		−	0.252679i
$69$	990.252	−	414.317i	0.207992	−	0.0870231i
$70$	477.315			0.0974113
$71$		−	6889.63i		−	1.36672i	−0.730082	−	0.683359i	$-0.760518\pi$
$71$		−	6889.63i		−	1.36672i	0.730082	−	0.683359i	$-0.239482\pi$
$72$	−1305.21	−	1286.73i	−0.251776	−	0.248212i
$73$	−1079.08			−0.202492			−0.101246	−	0.994861i	$-0.532283\pi$
$73$	−1079.08			−0.202492			−0.101246	+	0.994861i	$0.532283\pi$
$74$		−	993.235i		−	0.181380i
$75$	−1648.19	−	3939.31i	−0.293012	−	0.700322i
$76$	−979.255			−0.169539
$77$		−	1364.46i		−	0.230133i
$78$	−6106.33	+	2554.86i	−1.00367	+	0.419931i
$79$	−3529.62			−0.565554			−0.282777	−	0.959186i	$-0.591256\pi$
$79$	−3529.62			−0.565554			−0.282777	+	0.959186i	$0.591256\pi$
$80$		−	785.225i		−	0.122691i
$81$	−93.5374	−	6560.33i	−0.0142566	−	0.999898i
$82$	5610.45			0.834392
$83$			5606.23i			0.813795i	0.913474	+	0.406898i	$0.133389\pi$
$83$			5606.23i			0.813795i	−0.913474	+	0.406898i	$0.866611\pi$
$84$	−382.241	−	913.586i	−0.0541724	−	0.129477i
$85$	1791.89			0.248013
$86$			209.810i			0.0283680i
$87$	846.226	−	354.057i	0.111802	−	0.0467773i
$88$	−2244.66			−0.289858
$89$		−	836.835i		−	0.105648i	−0.998604	−	0.0528238i	$-0.983178\pi$
$89$		−	836.835i		−	0.105648i	0.998604	−	0.0528238i	$-0.0168222\pi$
$90$	1973.38	−	2001.72i	0.243627	−	0.247126i
$91$	−3576.58			−0.431902
$92$		−	954.163i		−	0.112732i
$93$	1363.53	+	3258.95i	0.157652	+	0.376801i
$94$	5876.00			0.665007
$95$		−	1501.83i		−	0.166408i
$96$	−1502.93	+	628.819i	−0.163078	+	0.0682312i
$97$	−5760.76			−0.612260			−0.306130	−	0.951990i	$-0.599034\pi$
$97$	−5760.76			−0.612260			−0.306130	+	0.951990i	$0.599034\pi$
$98$			6255.95i			0.651390i
$99$	−5722.14	−	5641.14i	−0.583833	−	0.575568i
$100$	−3795.75			−0.379575
$101$		−	12607.0i		−	1.23586i	−0.786234	−	0.617929i	$-0.787972\pi$
$101$		−	12607.0i		−	1.23586i	0.786234	−	0.617929i	$-0.212028\pi$
$102$	−1434.97	−	3429.70i	−0.137925	−	0.329652i
$103$	10112.2			0.953176			0.476588	−	0.879127i	$-0.341873\pi$
$103$	10112.2			0.953176			0.476588	+	0.879127i	$0.341873\pi$
$104$			5883.78i			0.543989i
$105$	1401.12	−	586.220i	0.127085	−	0.0531719i
$106$	−5760.25			−0.512660
$107$			3566.81i			0.311539i	0.987793	+	0.155770i	$0.0497858\pi$
$107$			3566.81i			0.311539i	−0.987793	+	0.155770i	$0.950214\pi$
$108$	−5411.62	−	2174.07i	−0.463959	−	0.186391i
$109$	17230.9			1.45029			0.725146	−	0.688595i	$-0.241772\pi$
$109$	17230.9			1.45029			0.725146	+	0.688595i	$0.241772\pi$
$110$		−	3442.50i		−	0.284504i
$111$	−1219.85	−	2915.55i	−0.0990060	−	0.236632i
$112$	−880.291			−0.0701763
$113$			1649.46i			0.129177i	0.997912	+	0.0645884i	$0.0205734\pi$
$113$			1649.46i			0.129177i	−0.997912	+	0.0645884i	$0.979427\pi$
$114$	−2874.51	+	1202.68i	−0.221184	+	0.0925426i
$115$	1463.34			0.110650
$116$		−	815.385i		−	0.0605964i
$117$	−14786.8	+	14999.1i	−1.08019	+	1.09571i
$118$	−1281.81			−0.0920575
$119$		−	2008.83i		−	0.141857i
$120$	−964.383	−	2304.96i	−0.0669711	−	0.160066i
$121$	4800.21			0.327861
$122$		−	18277.7i		−	1.22801i
$123$	16469.0	−	6890.54i	1.08857	−	0.455452i
$124$	3140.18			0.204226
$125$		−	13489.5i		−	0.863330i
$126$	−2244.06	−	2212.30i	−0.141349	−	0.139348i
$127$	15566.1			0.965099			0.482549	−	0.875869i	$-0.339711\pi$
$127$	15566.1			0.965099			0.482549	+	0.875869i	$0.339711\pi$
$128$			1448.15i			0.0883883i
$129$	257.680	+	615.877i	0.0154846	+	0.0370096i
$130$	−9023.62			−0.533942
$131$			8396.93i			0.489303i	0.969611	+	0.244652i	$0.0786736\pi$
$131$			8396.93i			0.489303i	−0.969611	+	0.244652i	$0.921326\pi$
$132$	−6588.98	+	2756.80i	−0.378156	+	0.158219i
$133$	−1683.65			−0.0951807
$134$		−	3559.92i		−	0.198258i
$135$	3334.25	−	8299.49i	0.182949	−	0.455391i
$136$	−3304.70			−0.178671
$137$			12806.1i			0.682302i	0.940009	+	0.341151i	$0.110817\pi$
$137$			12806.1i			0.682302i	−0.940009	+	0.341151i	$0.889183\pi$
$138$	−1171.87	−	2800.86i	−0.0615346	−	0.147073i
$139$	10105.4			0.523028			0.261514	−	0.965200i	$-0.415778\pi$
$139$	10105.4			0.523028			0.261514	+	0.965200i	$0.415778\pi$
$140$		−	1350.05i		−	0.0688802i
$141$	17248.5	−	7216.68i	0.867585	−	0.362994i
$142$	−19486.8			−0.966416
$143$			25795.1i			1.26143i
$144$	−3639.42	+	3691.68i	−0.175512	+	0.178032i
$145$	1250.51			0.0594773
$146$			3052.10i			0.143183i
$147$	7683.32	+	18363.8i	0.355561	+	0.849820i
$148$	−2809.29			−0.128255
$149$			23941.9i			1.07841i	0.842173	+	0.539207i	$0.181276\pi$
$149$			23941.9i			1.07841i	−0.842173	+	0.539207i	$0.818724\pi$
$150$	−11142.1	+	4661.79i	−0.495203	+	0.207191i
$151$	−11966.9			−0.524843			−0.262421	−	0.964953i	$-0.584521\pi$
$151$	−11966.9			−0.524843			−0.262421	+	0.964953i	$0.584521\pi$
$152$			2769.75i			0.119882i
$153$	−8424.45	−	8305.19i	−0.359881	−	0.354786i
$154$	−3859.28			−0.162729
$155$			4815.92i			0.200454i
$156$	7226.24	+	17271.3i	0.296936	+	0.709702i
$157$	19724.5			0.800214			0.400107	−	0.916469i	$-0.368973\pi$
$157$	19724.5			0.800214			0.400107	+	0.916469i	$0.368973\pi$
$158$			9983.27i			0.399907i
$159$	−16908.7	+	7074.51i	−0.668829	+	0.279835i
$160$	−2220.95			−0.0867559
$161$		−	1640.51i		−	0.0632888i
$162$	−18555.4	+	264.564i	−0.707035	+	0.0100809i
$163$	22991.3			0.865342			0.432671	−	0.901552i	$-0.357571\pi$
$163$	22991.3			0.865342			0.432671	+	0.901552i	$0.357571\pi$
$164$		−	15868.7i		−	0.590004i
$165$	−4227.95	−	10105.1i	−0.155297	−	0.371172i
$166$	15856.8			0.575440
$167$			21323.8i			0.764597i	0.924039	+	0.382299i	$0.124867\pi$
$167$			21323.8i			0.764597i	−0.924039	+	0.382299i	$0.875133\pi$
$168$	−2584.01	+	1081.14i	−0.0915537	+	0.0383057i
$169$	39054.0			1.36739
$170$		−	5068.24i		−	0.175372i
$171$	−6960.78	+	7060.73i	−0.238049	+	0.241467i
$172$	593.431			0.0200592
$173$		−	24537.4i		−	0.819853i	−0.912119	−	0.409927i	$-0.865554\pi$
$173$		−	24537.4i		−	0.819853i	0.912119	−	0.409927i	$-0.134446\pi$
$174$	−1001.43	−	2393.49i	−0.0330765	−	0.0790557i
$175$	−6526.09			−0.213097
$176$			6348.85i			0.204960i
$177$	−3762.63	+	1574.27i	−0.120101	+	0.0502495i
$178$	−2366.93			−0.0747041
$179$			34985.4i			1.09189i	0.837820	+	0.545947i	$0.183830\pi$
$179$			34985.4i			1.09189i	−0.837820	+	0.545947i	$0.816170\pi$
$180$	−5661.72	−	5581.57i	−0.174744	−	0.172271i
$181$	60124.1			1.83524			0.917618	−	0.397464i	$-0.130110\pi$
$181$	60124.1			1.83524			0.917618	+	0.397464i	$0.130110\pi$
$182$			10116.1i			0.305401i
$183$	−22447.9	−	53652.4i	−0.670308	−	1.60209i
$184$	−2698.78			−0.0797135
$185$		−	4308.45i		−	0.125886i
$186$	9217.71	−	3856.65i	0.266439	−	0.111477i
$187$	−14488.1			−0.414314
$188$		−	16619.8i		−	0.470231i
$189$	−9304.30	−	3737.92i	−0.260471	−	0.104642i
$190$	−4247.81			−0.117668
$191$		−	2703.84i		−	0.0741165i	−0.999313	−	0.0370582i	$-0.988201\pi$
$191$		−	2703.84i		−	0.0741165i	0.999313	−	0.0370582i	$-0.0117987\pi$
$192$	1778.57	+	4250.92i	0.0482467	+	0.115314i
$193$	41468.3			1.11327			0.556637	−	0.830756i	$-0.312091\pi$
$193$	41468.3			1.11327			0.556637	+	0.830756i	$0.312091\pi$
$194$			16293.9i			0.432933i
$195$	−26488.0	+	11082.5i	−0.696595	+	0.291452i
$196$	17694.5			0.460602
$197$			40857.7i			1.05279i	0.850241	+	0.526394i	$0.176456\pi$
$197$			40857.7i			1.05279i	−0.850241	+	0.526394i	$0.823544\pi$
$198$	−15955.6	+	16184.7i	−0.406988	+	0.412832i
$199$	−60734.3			−1.53366			−0.766828	−	0.641853i	$-0.778166\pi$
$199$	−60734.3			−1.53366			−0.766828	+	0.641853i	$0.778166\pi$
$200$			10736.0i			0.268400i
$201$	−4372.15	−	10449.8i	−0.108219	−	0.258652i
$202$	−35657.9			−0.873883
$203$		−	1401.91i		−	0.0340194i
$204$	−9700.66	+	4058.71i	−0.233099	+	0.0975277i
$205$	24337.0			0.579107
$206$		−	28601.8i		−	0.673997i
$207$	−6879.81	−	6782.41i	−0.160559	−	0.158286i
$208$	16641.9			0.384658
$209$			12142.9i			0.277989i
$210$	−1658.08	−	3962.95i	−0.0375982	−	0.0898629i
$211$	58628.7			1.31688			0.658439	−	0.752634i	$-0.271217\pi$
$211$	58628.7			1.31688			0.658439	+	0.752634i	$0.271217\pi$
$212$			16292.4i			0.362505i
$213$	−57201.7	+	23933.0i	−1.26081	+	0.527518i
$214$	10088.5			0.220292
$215$			910.111i			0.0196887i
$216$	−6149.20	+	15306.4i	−0.131799	+	0.328069i
$217$	5398.97			0.114655
$218$		−	48736.4i		−	1.02551i
$219$	3748.47	+	8959.15i	0.0781566	+	0.186801i
$220$	−9736.86			−0.201175
$221$			37976.9i			0.777562i
$222$	−8246.42	+	3450.26i	−0.167324	+	0.0700078i
$223$	−70876.4			−1.42525			−0.712626	−	0.701544i	$-0.752494\pi$
$223$	−70876.4			−1.42525			−0.712626	+	0.701544i	$0.752494\pi$
$224$			2489.84i			0.0496221i
$225$	−26981.1	+	27368.5i	−0.532959	+	0.540612i
$226$	4665.37			0.0913418
$227$			60839.4i			1.18068i	0.807153	+	0.590342i	$0.201007\pi$
$227$			60839.4i			1.18068i	−0.807153	+	0.590342i	$0.798993\pi$
$228$	3401.70	+	8130.35i	0.0654375	+	0.156401i
$229$	16812.8			0.320605			0.160302	−	0.987068i	$-0.448753\pi$
$229$	16812.8			0.320605			0.160302	+	0.987068i	$0.448753\pi$
$230$		−	4138.96i		−	0.0782413i
$231$	−11328.6	+	4739.82i	−0.212300	+	0.0888255i
$232$	−2306.26			−0.0428481
$233$			86695.7i			1.59693i	0.602041	+	0.798465i	$0.294354\pi$
$233$			86695.7i			1.59693i	−0.602041	+	0.798465i	$0.705646\pi$
$234$	42423.9	+	41823.3i	0.774781	+	0.763813i
$235$	25488.9			0.461546
$236$			3625.50i			0.0650945i
$237$	12261.1	+	29305.0i	0.218289	+	0.521729i
$238$	−5681.84			−0.100308
$239$		−	51947.2i		−	0.909423i	−0.890639	−	0.454712i	$-0.849742\pi$
$239$		−	51947.2i		−	0.909423i	0.890639	−	0.454712i	$-0.150258\pi$
$240$	−6519.40	+	2727.69i	−0.113184	+	0.0473557i
$241$	24365.1			0.419502			0.209751	−	0.977755i	$-0.432735\pi$
$241$	24365.1			0.419502			0.209751	+	0.977755i	$0.432735\pi$
$242$		−	13577.1i		−	0.231833i
$243$	−54142.8	+	23565.7i	−0.916913	+	0.399087i
$244$	−51697.0			−0.868333
$245$			27137.0i			0.452096i
$246$	−19489.4	−	46581.2i	−0.322053	−	0.769734i
$247$	31829.3			0.521715
$248$		−	8881.77i		−	0.144410i
$249$	46546.2	−	19474.7i	0.750734	−	0.314104i
$250$	−38154.2			−0.610467
$251$			60218.4i			0.955832i	0.878405	+	0.477916i	$0.158608\pi$
$251$			60218.4i			0.955832i	−0.878405	+	0.477916i	$0.841392\pi$
$252$	−6257.32	+	6347.17i	−0.0985342	+	0.0999491i
$253$	−11831.7			−0.184844
$254$		−	44027.5i		−	0.682428i
$255$	−6224.61	−	14877.3i	−0.0957265	−	0.228794i
$256$	4096.00			0.0625000
$257$		−	16459.0i		−	0.249194i	−0.992207	−	0.124597i	$-0.960236\pi$
$257$		−	16459.0i		−	0.249194i	0.992207	−	0.124597i	$-0.0397638\pi$
$258$	1741.96	−	728.829i	0.0261697	−	0.0109493i
$259$	−4830.07			−0.0720035
$260$			25522.7i			0.377554i
$261$	−5879.18	−	5795.95i	−0.0863050	−	0.0850832i
$262$	23750.1			0.345990
$263$		−	25950.3i		−	0.375173i	−0.982248	−	0.187586i	$-0.939934\pi$
$263$		−	25950.3i		−	0.375173i	0.982248	−	0.187586i	$-0.0600664\pi$
$264$	7797.41	+	18636.5i	0.111877	+	0.267396i
$265$	−24986.8			−0.355810
$266$			4762.09i			0.0673029i
$267$	−6947.89	+	2906.97i	−0.0974610	+	0.0407772i
$268$	−10069.0			−0.140189
$269$		−	48565.3i		−	0.671154i	−0.942013	−	0.335577i	$-0.891069\pi$
$269$		−	48565.3i		−	0.671154i	0.942013	−	0.335577i	$-0.108931\pi$
$270$	−23474.5	−	9430.67i	−0.322010	−	0.129365i
$271$	−81750.6			−1.11315			−0.556574	−	0.830798i	$-0.687884\pi$
$271$	−81750.6			−1.11315			−0.556574	+	0.830798i	$0.687884\pi$
$272$			9347.12i			0.126340i
$273$	12424.2	+	29694.9i	0.166703	+	0.398434i
$274$	36221.2			0.482460
$275$			47067.6i			0.622381i
$276$	−7922.02	+	3314.54i	−0.103996	+	0.0435116i
$277$	−3043.02			−0.0396593			−0.0198297	−	0.999803i	$-0.506312\pi$
$277$	−3043.02			−0.0396593			−0.0198297	+	0.999803i	$0.506312\pi$
$278$		−	28582.4i		−	0.369836i
$279$	22321.2	−	22641.7i	0.286753	−	0.290871i
$280$	−3818.52			−0.0487057
$281$		−	55816.0i		−	0.706880i	−0.935457	−	0.353440i	$-0.885012\pi$
$281$		−	55816.0i		−	0.706880i	0.935457	−	0.353440i	$-0.114988\pi$
$282$	−20411.8	−	48786.0i	−0.256675	−	0.613475i
$283$	33849.7			0.422651			0.211326	−	0.977416i	$-0.432222\pi$
$283$	33849.7			0.422651			0.211326	+	0.977416i	$0.432222\pi$
$284$			55117.0i			0.683359i
$285$	−12469.1	+	5217.00i	−0.153513	+	0.0642290i
$286$	72959.5			0.891969
$287$		−	27283.4i		−	0.331234i
$288$	10441.6	+	10293.8i	0.125888	+	0.124106i
$289$	62190.8			0.744612
$290$		−	3536.98i		−	0.0420568i
$291$	20011.5	+	47829.2i	0.236316	+	0.564816i
$292$	8632.63			0.101246
$293$		−	39360.0i		−	0.458479i	−0.973370	−	0.229239i	$-0.926376\pi$
$293$		−	39360.0i		−	0.458479i	0.973370	−	0.229239i	$-0.0736239\pi$
$294$	51940.6	−	21731.7i	0.600914	−	0.251420i
$295$	−5560.22			−0.0638923
$296$			7945.88i			0.0906898i
$297$	−26958.7	+	67104.6i	−0.305623	+	0.760746i
$298$	67717.9			0.762554
$299$			31013.7i			0.346906i
$300$	13185.5	+	31514.5i	0.146506	+	0.350161i
$301$	1020.30			0.0112614
$302$			33847.6i			0.371120i
$303$	−104671.	+	43793.7i	−1.14009	+	0.477009i
$304$	7834.04			0.0847693
$305$		−	79284.8i		−	0.852296i
$306$	−23490.6	+	23827.9i	−0.250872	+	0.254474i
$307$	−138520.			−1.46973			−0.734863	−	0.678216i	$-0.762753\pi$
$307$	−138520.			−1.46973			−0.734863	+	0.678216i	$0.762753\pi$
$308$			10915.7i			0.115067i
$309$	−35127.6	−	83957.8i	−0.367901	−	0.879314i
$310$	13621.5			0.141743
$311$		−	17651.4i		−	0.182498i	−0.995828	−	0.0912489i	$-0.970914\pi$
$311$		−	17651.4i		−	0.182498i	0.995828	−	0.0912489i	$-0.0290859\pi$
$312$	48850.6	−	20438.9i	0.501835	−	0.209966i
$313$	52909.4			0.540062			0.270031	−	0.962852i	$-0.412966\pi$
$313$	52909.4			0.540062			0.270031	+	0.962852i	$0.412966\pi$
$314$		−	55789.2i		−	0.565836i
$315$	−9734.29	−	9596.49i	−0.0981032	−	0.0967144i
$316$	28237.0			0.282777
$317$		−	34547.5i		−	0.343794i	−0.985115	−	0.171897i	$-0.945010\pi$
$317$		−	34547.5i		−	0.343794i	0.985115	−	0.171897i	$-0.0549897\pi$
$318$	20009.7	+	47825.0i	0.197873	+	0.472934i
$319$	−10110.9			−0.0993588
$320$			6281.80i			0.0613457i
$321$	29613.8	−	12390.3i	0.287398	−	0.120246i
$322$	−4640.06			−0.0447519
$323$			17877.4i			0.171356i
$324$	748.299	+	52482.7i	0.00712829	+	0.499949i
$325$	123375.			1.16805
$326$		−	65029.1i		−	0.611889i
$327$	−59856.2	−	143061.i	−0.559775	−	1.33791i
$328$	−44883.6			−0.417196
$329$		−	28574.8i		−	0.263992i
$330$	−28581.7	+	11958.4i	−0.262458	+	0.109811i
$331$	88180.4			0.804852			0.402426	−	0.915453i	$-0.368167\pi$
$331$	88180.4			0.804852			0.402426	+	0.915453i	$0.368167\pi$
$332$		−	44849.9i		−	0.406898i
$333$	−19969.1	+	20255.9i	−0.180082	+	0.182668i
$334$	60313.0			0.540652
$335$		−	15442.2i		−	0.137600i
$336$	3057.92	+	7308.69i	0.0270862	+	0.0647383i
$337$	−65395.0			−0.575818			−0.287909	−	0.957658i	$-0.592960\pi$
$337$	−65395.0			−0.575818			−0.287909	+	0.957658i	$0.592960\pi$
$338$		−	110462.i		−	0.966891i
$339$	13694.8	−	5729.83i	0.119167	−	0.0498589i
$340$	−14335.1			−0.124006
$341$		−	38938.5i		−	0.334866i
$342$	19970.8	+	19688.1i	0.170743	+	0.168326i
$343$	63447.1			0.539292
$344$		−	1678.48i		−	0.0141840i
$345$	−5083.32	−	12149.5i	−0.0427080	−	0.102076i
$346$	−69402.2			−0.579724
$347$		−	121812.i		−	1.01165i	−0.862636	−	0.505825i	$-0.831188\pi$
$347$		−	121812.i		−	1.01165i	0.862636	−	0.505825i	$-0.168812\pi$
$348$	−6769.81	+	2832.46i	−0.0559008	+	0.0233886i
$349$	135049.			1.10877			0.554385	−	0.832260i	$-0.312954\pi$
$349$	135049.			1.10877			0.554385	+	0.832260i	$0.312954\pi$
$350$			18458.6i			0.150682i
$351$	175897.	+	70665.1i	1.42773	+	0.573576i
$352$	17957.3			0.144929
$353$		−	46008.5i		−	0.369223i	−0.982812	−	0.184611i	$-0.940897\pi$
$353$		−	46008.5i		−	0.369223i	0.982812	−	0.184611i	$-0.0591026\pi$
$354$	4452.70	+	10642.3i	0.0355318	+	0.0849239i
$355$	−84529.8			−0.670739
$356$			6694.68i			0.0528238i
$357$	−16678.5	+	6978.22i	−0.130864	+	0.0547530i
$358$	98953.5			0.772085
$359$			102552.i			0.795707i	0.917449	+	0.397854i	$0.130245\pi$
$359$			102552.i			0.795707i	−0.917449	+	0.397854i	$0.869755\pi$
$360$	−15787.1	+	16013.8i	−0.121814	+	0.123563i
$361$	−115338.			−0.885027
$362$		−	170057.i		−	1.29771i
$363$	−16674.8	−	39854.2i	−0.126546	−	0.302455i
$364$	28612.6			0.215951
$365$			13239.4i			0.0993760i
$366$	−151752.	+	63492.3i	−1.13285	+	0.473979i
$367$	123615.			0.917784			0.458892	−	0.888492i	$-0.348247\pi$
$367$	123615.			0.917784			0.458892	+	0.888492i	$0.348247\pi$
$368$			7633.30i			0.0563659i
$369$	−114419.	−	112799.i	−0.840318	−	0.828423i
$370$	−12186.1			−0.0890149
$371$			28011.9i			0.203514i
$372$	−10908.3	−	26071.6i	−0.0788260	−	0.188401i
$373$	−32860.7			−0.236189			−0.118094	−	0.993002i	$-0.537679\pi$
$373$	−32860.7			−0.236189			−0.118094	+	0.993002i	$0.537679\pi$
$374$			40978.6i			0.292964i
$375$	−111998.	+	46859.5i	−0.796430	+	0.333223i
$376$	−47008.0			−0.332503
$377$			26503.0i			0.186471i
$378$	−10572.4	+	26316.5i	−0.0739931	+	0.184181i
$379$	−165010.			−1.14877			−0.574383	−	0.818586i	$-0.694758\pi$
$379$	−165010.			−1.14877			−0.574383	+	0.818586i	$0.694758\pi$
$380$			12014.6i			0.0832038i
$381$	−54072.9	−	129239.i	−0.372503	−	0.890313i
$382$	−7647.62			−0.0524083
$383$		−	157939.i		−	1.07669i	−0.842723	−	0.538347i	$-0.819049\pi$
$383$		−	157939.i		−	1.07669i	0.842723	−	0.538347i	$-0.180951\pi$
$384$	12023.4	−	5030.55i	0.0815391	−	0.0341156i
$385$	−16740.8			−0.112942
$386$		−	117290.i		−	0.787204i
$387$	4218.25	−	4278.82i	0.0281650	−	0.0285695i
$388$	46086.1			0.306130
$389$		−	202974.i		−	1.34134i	−0.741754	−	0.670672i	$-0.766006\pi$
$389$		−	202974.i		−	1.34134i	0.741754	−	0.670672i	$-0.233994\pi$
$390$	31345.9	+	74919.4i	0.206088	+	0.492567i
$391$	−17419.3			−0.113940
$392$		−	50047.6i		−	0.325695i
$393$	69716.3	−	29169.0i	0.451387	−	0.188858i
$394$	115563.			0.744434
$395$			43305.4i			0.277554i
$396$	45777.2	+	45129.1i	0.291916	+	0.287784i
$397$	−66195.4			−0.419998			−0.209999	−	0.977702i	$-0.567346\pi$
$397$	−66195.4			−0.419998			−0.209999	+	0.977702i	$0.567346\pi$
$398$			171782.i			1.08446i
$399$	5848.61	+	13978.7i	0.0367373	+	0.0878051i
$400$	30366.0			0.189787
$401$			77632.6i			0.482787i	0.970427	+	0.241393i	$0.0776044\pi$
$401$			77632.6i			0.482787i	−0.970427	+	0.241393i	$0.922396\pi$
$402$	−29556.5	+	12366.3i	−0.182895	+	0.0765223i
$403$	−102067.			−0.628458
$404$			100856.i			0.617929i
$405$	−80489.7	+	1147.62i	−0.490716	+	0.00699664i
$406$	−3965.19			−0.0240554
$407$			34835.5i			0.210297i
$408$	11479.8	+	27437.6i	0.0689625	+	0.164826i
$409$	48477.7			0.289798			0.144899	−	0.989446i	$-0.453714\pi$
$409$	48477.7			0.289798			0.144899	+	0.989446i	$0.453714\pi$
$410$		−	68835.4i		−	0.409491i
$411$	106324.	−	44485.5i	0.629430	−	0.263351i
$412$	−80898.0			−0.476588
$413$			6233.39i			0.0365447i
$414$	−19183.6	+	19459.0i	−0.111925	+	0.113533i
$415$	68783.7			0.399383
$416$		−	47070.3i		−	0.271994i
$417$	−35103.9	−	83901.1i	−0.201875	−	0.482498i
$418$	34345.2			0.196568
$419$		−	268865.i		−	1.53146i	−0.643161	−	0.765731i	$-0.722377\pi$
$419$		−	268865.i		−	1.53146i	0.643161	−	0.765731i	$-0.277623\pi$
$420$	−11208.9	+	4689.76i	−0.0635426	+	0.0265860i
$421$	23969.2			0.135235			0.0676177	−	0.997711i	$-0.478460\pi$
$421$	23969.2			0.135235			0.0676177	+	0.997711i	$0.478460\pi$
$422$		−	165827.i		−	0.931173i
$423$	−119834.	−	118138.i	−0.669730	−	0.660249i
$424$	46082.0			0.256330
$425$			69295.5i			0.383643i
$426$	67692.6	+	161791.i	0.373011	+	0.891528i
$427$	−88883.7			−0.487491
$428$		−	28534.5i		−	0.155770i
$429$	214166.	−	89606.0i	1.16369	−	0.486881i
$430$	2574.18			0.0139220
$431$		−	9995.14i		−	0.0538064i	−0.999638	−	0.0269032i	$-0.991435\pi$
$431$		−	9995.14i		−	0.0538064i	0.999638	−	0.0269032i	$-0.00856459\pi$
$432$	43293.0	+	17392.6i	0.231980	+	0.0931957i
$433$	94850.5			0.505899			0.252950	−	0.967479i	$-0.418599\pi$
$433$	94850.5			0.505899			0.252950	+	0.967479i	$0.418599\pi$
$434$		−	15270.6i		−	0.0810730i
$435$	−4343.98	−	10382.5i	−0.0229567	−	0.0548684i
$436$	−137847.			−0.725146
$437$			14599.5i			0.0764496i
$438$	25340.3	−	10602.3i	0.132088	−	0.0552650i
$439$	−48534.3			−0.251837			−0.125919	−	0.992041i	$-0.540188\pi$
$439$	−48534.3			−0.251837			−0.125919	+	0.992041i	$0.540188\pi$
$440$			27540.0i			0.142252i
$441$	125777.	−	127583.i	0.646730	−	0.656017i
$442$	107415.			0.549819
$443$		−	280228.i		−	1.42792i	−0.700185	−	0.713961i	$-0.746899\pi$
$443$		−	280228.i		−	1.42792i	0.700185	−	0.713961i	$-0.253101\pi$
$444$	9758.82	+	23324.4i	0.0495030	+	0.118316i
$445$	−10267.2			−0.0518482
$446$			200469.i			1.00781i
$447$	198780.	−	83168.5i	0.994848	−	0.416240i
$448$	7042.33			0.0350881
$449$		−	55081.4i		−	0.273220i	−0.990625	−	0.136610i	$-0.956379\pi$
$449$		−	55081.4i		−	0.273220i	0.990625	−	0.136610i	$-0.0436207\pi$
$450$	77409.8	+	76314.0i	0.382271	+	0.376859i
$451$	−196774.			−0.967419
$452$		−	13195.7i		−	0.0645884i
$453$	41570.3	+	99356.5i	0.202576	+	0.484172i
$454$	172080.			0.834869
$455$			43881.6i			0.211963i
$456$	22996.1	−	9621.47i	0.110592	−	0.0462713i
$457$	388882.			1.86202			0.931011	−	0.364990i	$-0.118928\pi$
$457$	388882.			1.86202			0.931011	+	0.364990i	$0.118928\pi$
$458$		−	47553.8i		−	0.226702i
$459$	−39690.0	+	98795.0i	−0.188389	+	0.468932i
$460$	−11706.8			−0.0553249
$461$			226946.i			1.06788i	0.845524	+	0.533938i	$0.179288\pi$
$461$			226946.i			1.06788i	−0.845524	+	0.533938i	$0.820712\pi$
$462$	13406.2	+	32042.0i	0.0628091	+	0.150119i
$463$	102799.			0.479543			0.239772	−	0.970829i	$-0.422927\pi$
$463$	102799.			0.479543			0.239772	+	0.970829i	$0.422927\pi$
$464$			6523.08i			0.0302982i
$465$	39984.6	−	16729.4i	0.184921	−	0.0773702i
$466$	245213.			1.12920
$467$			46061.5i			0.211205i	0.994408	+	0.105603i	$0.0336772\pi$
$467$			46061.5i			0.211205i	−0.994408	+	0.105603i	$0.966323\pi$
$468$	118294.	−	119993.i	0.540097	−	0.547853i
$469$	−17311.7			−0.0787037
$470$		−	72093.5i		−	0.326362i
$471$	−68518.2	−	163764.i	−0.308862	−	0.738205i
$472$	10254.5			0.0460287
$473$		−	7358.60i		−	0.0328907i
$474$	82887.0	−	34679.5i	0.368918	−	0.154354i
$475$	58078.2			0.257410
$476$			16070.7i			0.0709284i
$477$	117474.	+	115811.i	0.516301	+	0.508992i
$478$	−146929.			−0.643059
$479$		−	172779.i		−	0.753045i	−0.926407	−	0.376523i	$-0.877120\pi$
$479$		−	172779.i		−	0.753045i	0.926407	−	0.376523i	$-0.122880\pi$
$480$	7715.07	+	18439.6i	0.0334855	+	0.0800332i
$481$	91312.1			0.394674
$482$		−	68914.9i		−	0.296633i
$483$	−13620.5	+	5698.74i	−0.0583845	+	0.0244278i
$484$	−38401.7			−0.163930
$485$			70679.5i			0.300476i
$486$	66653.8	+	153139.i	0.282197	+	0.648356i
$487$	−52425.1			−0.221046			−0.110523	−	0.993874i	$-0.535253\pi$
$487$	−52425.1			−0.221046			−0.110523	+	0.993874i	$0.535253\pi$
$488$			146221.i			0.614004i
$489$	−79866.3	−	190887.i	−0.333999	−	0.798286i
$490$	76755.1			0.319680
$491$			369341.i			1.53202i	0.642829	+	0.766010i	$0.277761\pi$
$491$			369341.i			1.53202i	−0.642829	+	0.766010i	$0.722239\pi$
$492$	−131752.	+	55124.3i	−0.544284	+	0.227726i
$493$	−14885.7			−0.0612459
$494$		−	90027.0i		−	0.368909i
$495$	−69212.0	+	70205.8i	−0.282469	+	0.286525i
$496$	−25121.4			−0.102113
$497$			94763.7i			0.383645i
$498$	−55082.9	−	131653.i	−0.222105	−	0.530849i
$499$	5814.24			0.0233503			0.0116751	−	0.999932i	$-0.496284\pi$
$499$	5814.24			0.0233503			0.0116751	+	0.999932i	$0.496284\pi$
$500$			107916.i			0.431665i
$501$	177043.	−	74074.1i	0.705348	−	0.295115i
$502$	170323.			0.675876
$503$			335859.i			1.32746i	0.747972	+	0.663730i	$0.231027\pi$
$503$			335859.i			1.32746i	−0.747972	+	0.663730i	$0.768973\pi$
$504$	17952.5	+	17698.4i	0.0706747	+	0.0696742i
$505$	−154677.			−0.606516
$506$			33465.1i			0.130705i
$507$	−135665.	−	324250.i	−0.527777	−	1.26143i
$508$	−124529.			−0.482549
$509$			438764.i			1.69354i	0.531958	+	0.846771i	$0.321456\pi$
$509$			438764.i			1.69354i	−0.531958	+	0.846771i	$0.678544\pi$
$510$	−42079.5	+	17605.9i	−0.161782	+	0.0676888i
$511$	14842.2			0.0568405
$512$		−	11585.2i		−	0.0441942i
$513$	82802.5	+	33265.1i	0.314636	+	0.126402i
$514$	−46553.1			−0.176207
$515$		−	124069.i		−	0.467786i
$516$	−2061.44	−	4927.01i	−0.00774232	−	0.0185048i
$517$	−206087.			−0.771029
$518$			13661.5i			0.0509142i
$519$	−203724.	+	85237.1i	−0.756322	+	0.316442i
$520$	72189.0			0.266971
$521$			229428.i			0.845222i	0.906311	+	0.422611i	$0.138886\pi$
$521$			229428.i			0.845222i	−0.906311	+	0.422611i	$0.861114\pi$
$522$	−16393.4	+	16628.8i	−0.0601629	+	0.0610268i
$523$	−306214.			−1.11949			−0.559746	−	0.828664i	$-0.689101\pi$
$523$	−306214.			−1.11949			−0.559746	+	0.828664i	$0.689101\pi$
$524$		−	67175.5i		−	0.244652i
$525$	22670.1	+	54183.5i	0.0822499	+	0.196584i
$526$	−73398.6			−0.265287
$527$		−	57327.4i		−	0.206415i
$528$	52711.9	−	22054.4i	0.189078	−	0.0791093i
$529$	265616.			0.949166
$530$			70673.3i			0.251596i
$531$	26141.0	+	25770.9i	0.0927114	+	0.0913989i
$532$	13469.2			0.0475903
$533$			515792.i			1.81560i
$534$	8222.15	+	19651.6i	0.0288339	+	0.0689153i
$535$	43761.8			0.152893
$536$			28479.3i			0.0991289i
$537$	290469.	−	121531.i	1.00728	−	0.421442i
$538$	−137364.			−0.474577
$539$		−	219413.i		−	0.755241i
$540$	−26674.0	+	66396.0i	−0.0914745	+	0.227695i
$541$	−341615.			−1.16719			−0.583596	−	0.812044i	$-0.698355\pi$
$541$	−341615.			−1.16719			−0.583596	+	0.812044i	$0.698355\pi$
$542$			231226.i			0.787114i
$543$	−208857.	−	499186.i	−0.708353	−	1.69302i
$544$	26437.6			0.0893357
$545$		−	211409.i		−	0.711753i
$546$	83989.8	−	35140.9i	0.281735	−	0.117877i
$547$	−230474.			−0.770277			−0.385139	−	0.922859i	$-0.625846\pi$
$547$	−230474.			−0.770277			−0.385139	+	0.922859i	$0.625846\pi$
$548$		−	102449.i		−	0.341151i
$549$	−367475.	+	372752.i	−1.21922	+	1.23673i
$550$	133127.			0.440090
$551$			12476.1i			0.0410937i
$552$	9374.93	+	22406.9i	0.0307673	+	0.0735364i
$553$	48548.3			0.158754
$554$			8606.96i			0.0280434i
$555$	−35771.3	+	14966.5i	−0.116131	+	0.0485887i
$556$	−80843.4			−0.261514
$557$			384542.i			1.23946i	0.784814	+	0.619731i	$0.212758\pi$
$557$			384542.i			1.23946i	−0.784814	+	0.619731i	$0.787242\pi$
$558$	−64040.3	−	63133.8i	−0.205677	−	0.202765i
$559$	−19288.7			−0.0617274
$560$			10800.4i			0.0344401i
$561$	50328.4	+	120289.i	0.159914	+	0.382208i
$562$	−157871.			−0.499840
$563$		−	294921.i		−	0.930441i	−0.885195	−	0.465221i	$-0.845975\pi$
$563$		−	294921.i		−	0.930441i	0.885195	−	0.465221i	$-0.154025\pi$
$564$	−137988.	+	57733.4i	−0.433792	+	0.181497i
$565$	20237.4			0.0633955
$566$		−	95741.4i		−	0.298860i
$567$	1286.56	+	90234.4i	0.00400189	+	0.280676i
$568$	155895.			0.483208
$569$			479532.i			1.48113i	0.671985	+	0.740565i	$0.265442\pi$
$569$			479532.i			1.48113i	−0.671985	+	0.740565i	$0.734558\pi$
$570$	14755.9	+	35267.8i	0.0454167	+	0.108550i
$571$	−276903.			−0.849288			−0.424644	−	0.905360i	$-0.639601\pi$
$571$	−276903.			−0.849288			−0.424644	+	0.905360i	$0.639601\pi$
$572$		−	206361.i		−	0.630717i
$573$	−22448.9	+	9392.52i	−0.0683732	+	0.0286070i
$574$	−77169.2			−0.234218
$575$			56590.0i			0.171161i
$576$	29115.3	−	29533.4i	0.0877560	−	0.0890162i
$577$	−582400.			−1.74932			−0.874661	−	0.484734i	$-0.838916\pi$
$577$	−582400.			−1.74932			−0.874661	+	0.484734i	$0.838916\pi$
$578$		−	175902.i		−	0.526521i
$579$	−144051.	−	344295.i	−0.429695	−	1.02701i
$580$	−10004.1			−0.0297386
$581$		−	77111.2i		−	0.228436i
$582$	135281.	−	56601.1i	0.399385	−	0.167101i
$583$	202028.			0.594393
$584$		−	24416.8i		−	0.0715917i
$585$	184026.	+	181421.i	0.537735	+	0.530122i
$586$	−111327.			−0.324194
$587$			106008.i			0.307654i	0.988098	+	0.153827i	$0.0491598\pi$
$587$			106008.i			0.307654i	−0.988098	+	0.153827i	$0.950840\pi$
$588$	−61466.5	−	146910.i	−0.177781	−	0.424910i
$589$	−48047.5			−0.138497
$590$			15726.7i			0.0451786i
$591$	339224.	−	141930.i	0.971207	−	0.406349i
$592$	22474.3			0.0641274
$593$			478029.i			1.35939i	0.733493	+	0.679697i	$0.237889\pi$
$593$			478029.i			1.35939i	−0.733493	+	0.679697i	$0.762111\pi$
$594$	189800.	+	76250.6i	0.537928	+	0.216108i
$595$	−24646.7			−0.0696184
$596$		−	191535.i		−	0.539207i
$597$	210977.	+	504252.i	0.591951	+	1.41481i
$598$	87720.1			0.245300
$599$		−	300951.i		−	0.838769i	−0.907809	−	0.419385i	$-0.862246\pi$
$599$		−	300951.i		−	0.838769i	0.907809	−	0.419385i	$-0.137754\pi$
$600$	89136.5	−	37294.3i	0.247601	−	0.103595i
$601$	−49277.8			−0.136428			−0.0682138	−	0.997671i	$-0.521730\pi$
$601$	−49277.8			−0.136428			−0.0682138	+	0.997671i	$0.521730\pi$
$602$		−	2885.83i		−	0.00796303i
$603$	−71572.6	+	72600.3i	−0.196839	+	0.199666i
$604$	95735.5			0.262421
$605$		−	58894.5i		−	0.160903i
$606$	123867.	+	296053.i	0.337296	+	0.806166i
$607$	−400389.			−1.08669			−0.543344	−	0.839510i	$-0.682842\pi$
$607$	−400389.			−1.08669			−0.543344	+	0.839510i	$0.682842\pi$
$608$		−	22158.0i		−	0.0599410i
$609$	−11639.5	+	4869.90i	−0.0313833	+	0.0131306i
$610$	−224251.			−0.602664
$611$			540205.i			1.44702i
$612$	67395.6	+	66441.5i	0.179940	+	0.177393i
$613$	−155148.			−0.412881			−0.206441	−	0.978459i	$-0.566188\pi$
$613$	−155148.			−0.412881			−0.206441	+	0.978459i	$0.566188\pi$
$614$			391794.i			1.03925i
$615$	−84541.0	−	202060.i	−0.223520	−	0.534232i
$616$	30874.2			0.0813645
$617$		−	139266.i		−	0.365825i	−0.983129	−	0.182913i	$-0.941447\pi$
$617$		−	139266.i		−	0.365825i	0.983129	−	0.182913i	$-0.0585525\pi$
$618$	−237469.	+	99355.8i	−0.621769	+	0.260145i
$619$	−668571.			−1.74488			−0.872441	−	0.488719i	$-0.837464\pi$
$619$	−668571.			−1.74488			−0.872441	+	0.488719i	$0.837464\pi$
$620$		−	38527.3i		−	0.100227i
$621$	−32412.8	+	80680.7i	−0.0840490	+	0.209212i
$622$	−49925.6			−0.129045
$623$			11510.3i			0.0296558i
$624$	−57809.9	−	138170.i	−0.148468	−	0.354851i
$625$	131038.			0.335456
$626$		−	149650.i		−	0.381882i
$627$	100817.	−	42181.4i	0.256448	−	0.107297i
$628$	−157796.			−0.400107
$629$			51286.7i			0.129629i
$630$	−27143.0	+	27532.7i	−0.0683874	+	0.0693695i
$631$	−98077.3			−0.246326			−0.123163	−	0.992386i	$-0.539304\pi$
$631$	−98077.3			−0.246326			−0.123163	+	0.992386i	$0.539304\pi$
$632$		−	79866.2i		−	0.199953i
$633$	−203662.	−	486770.i	−0.508281	−	1.21483i
$634$	−97715.2			−0.243099
$635$		−	190982.i		−	0.473637i
$636$	135269.	−	56596.1i	0.334415	−	0.139918i
$637$	−575135.			−1.41740
$638$			28597.8i			0.0702573i
$639$	397411.	+	391785.i	0.973281	+	0.959502i
$640$	17767.6			0.0433780
$641$			55525.7i			0.135138i	0.997715	+	0.0675690i	$0.0215243\pi$
$641$			55525.7i			0.135138i	−0.997715	+	0.0675690i	$0.978476\pi$
$642$	−35045.0	−	83760.5i	−0.0850268	−	0.203221i
$643$	−648100.			−1.56755			−0.783773	−	0.621047i	$-0.786707\pi$
$643$	−648100.			−1.56755			−0.783773	+	0.621047i	$0.786707\pi$
$644$			13124.1i			0.0316444i
$645$	7556.28	−	3161.51i	0.0181630	−	0.00759933i
$646$	50564.8			0.121167
$647$			523397.i			1.25032i	0.780495	+	0.625162i	$0.214967\pi$
$647$			523397.i			1.25032i	−0.780495	+	0.625162i	$0.785033\pi$
$648$	148443.	−	2116.51i	0.353517	−	0.00504046i
$649$	44956.5			0.106734
$650$		−	348958.i		−	0.825937i
$651$	−18754.8	−	44825.4i	−0.0442537	−	0.105770i
$652$	−183930.			−0.432671
$653$		−	140906.i		−	0.330448i	−0.986256	−	0.165224i	$-0.947165\pi$
$653$		−	140906.i		−	0.330448i	0.986256	−	0.165224i	$-0.0528347\pi$
$654$	−404638.	+	169299.i	−0.946044	+	0.395821i
$655$	103023.			0.240133
$656$			126950.i			0.295002i
$657$	61362.8	−	62243.9i	0.142159	−	0.144200i
$658$	−80821.7			−0.186671
$659$			183122.i			0.421668i	0.977522	+	0.210834i	$0.0676179\pi$
$659$			183122.i			0.421668i	−0.977522	+	0.210834i	$0.932382\pi$
$660$	33823.6	+	80841.2i	0.0776483	+	0.185586i
$661$	110121.			0.252039			0.126019	−	0.992028i	$-0.459780\pi$
$661$	110121.			0.252039			0.126019	+	0.992028i	$0.459780\pi$
$662$		−	249412.i		−	0.569116i
$663$	315306.	−	131923.i	0.717308	−	0.300119i
$664$	−126855.			−0.287720
$665$			20657.0i			0.0467114i
$666$	57292.2	+	56481.2i	0.129166	+	0.127337i
$667$	−12156.4			−0.0273246
$668$		−	170591.i		−	0.382299i
$669$	246208.	+	588457.i	0.550110	+	1.31481i
$670$	−43677.1			−0.0972981
$671$			641048.i			1.42379i
$672$	20672.1	−	8649.12i	0.0457769	−	0.0191528i
$673$	−43976.4			−0.0970933			−0.0485466	−	0.998821i	$-0.515459\pi$
$673$	−43976.4			−0.0970933			−0.0485466	+	0.998821i	$0.515459\pi$
$674$			184965.i			0.407165i
$675$	320955.	+	128941.i	0.704428	+	0.282998i
$676$	−312432.			−0.683695
$677$		−	164857.i		−	0.359691i	−0.983695	−	0.179845i	$-0.942440\pi$
$677$		−	164857.i		−	0.359691i	0.983695	−	0.179845i	$-0.0575597\pi$
$678$	−16206.4	−	38734.7i	−0.0352555	−	0.0842637i
$679$	79236.6			0.171865
$680$			40545.9i			0.0876858i
$681$	505125.	−	211342.i	1.08919	−	0.455713i
$682$	−110135.			−0.236786
$683$			46654.3i			0.100012i	0.998749	+	0.0500058i	$0.0159240\pi$
$683$			46654.3i			0.100012i	−0.998749	+	0.0500058i	$0.984076\pi$
$684$	55686.2	−	56485.9i	0.119024	−	0.120733i
$685$	157120.			0.334850
$686$		−	179456.i		−	0.381337i
$687$	−58403.8	−	139590.i	−0.123745	−	0.295761i
$688$	−4747.45			−0.0100296
$689$		−	529563.i		−	1.11553i
$690$	−34364.1	+	14377.8i	−0.0721783	+	0.0301991i
$691$	631487.			1.32254			0.661270	−	0.750148i	$-0.270018\pi$
$691$	631487.			1.32254			0.661270	+	0.750148i	$0.270018\pi$
$692$			196299.i			0.409927i
$693$	78705.5	+	77591.3i	0.163885	+	0.161565i
$694$	−344536.			−0.715345
$695$		−	123985.i		−	0.256684i
$696$	8011.40	+	19147.9i	0.0165383	+	0.0395278i
$697$	−289701.			−0.596327
$698$		−	381977.i		−	0.784018i
$699$	719799.	−	301161.i	1.47318	−	0.616373i
$700$	52208.7			0.106548
$701$			77978.3i			0.158686i	0.996847	+	0.0793429i	$0.0252822\pi$
$701$			77978.3i			0.158686i	−0.996847	+	0.0793429i	$0.974718\pi$
$702$	199871.	−	497513.i	0.405579	−	1.00955i
$703$	42984.6			0.0869765
$704$		−	50790.8i		−	0.102480i
$705$	−88542.4	−	211624.i	−0.178145	−	0.425781i
$706$	−130132.			−0.261080
$707$			173403.i			0.346911i
$708$	30101.0	−	12594.1i	0.0600503	−	0.0251248i
$709$	117080.			0.232911			0.116456	−	0.993196i	$-0.462847\pi$
$709$	117080.			0.232911			0.116456	+	0.993196i	$0.462847\pi$
$710$			239086.i			0.474284i
$711$	200715.	−	203597.i	0.397046	−	0.402747i
$712$	18935.4			0.0373521
$713$		−	46816.3i		−	0.0920912i
$714$	19737.4	+	47174.0i	0.0387162	+	0.0925350i
$715$	316483.			0.619069
$716$		−	279883.i		−	0.545947i
$717$	−431296.	+	180452.i	−0.838952	+	0.351014i
$718$	290060.			0.562650
$719$		−	793068.i		−	1.53410i	−0.641590	−	0.767048i	$-0.721725\pi$
$719$		−	793068.i		−	1.53410i	0.641590	−	0.767048i	$-0.278275\pi$
$720$	45293.7	+	44652.5i	0.0873722	+	0.0861353i
$721$	−139089.			−0.267561
$722$			326224.i			0.625808i
$723$	−84638.7	−	202293.i	−0.161917	−	0.386995i
$724$	−480993.			−0.917618
$725$			48359.3i			0.0920034i
$726$	−112725.	+	47163.5i	−0.213868	+	0.0894814i
$727$	247925.			0.469084			0.234542	−	0.972106i	$-0.424641\pi$
$727$	247925.			0.469084			0.234542	+	0.972106i	$0.424641\pi$
$728$		−	80928.8i		−	0.152700i
$729$	383735.	+	367664.i	0.722066	+	0.691824i
$730$	37446.6			0.0702695
$731$		−	10833.7i		−	0.0202742i
$732$	179583.	+	429219.i	0.335154	+	0.801045i
$733$	596277.			1.10979			0.554894	−	0.831921i	$-0.312759\pi$
$733$	596277.			1.10979			0.554894	+	0.831921i	$0.312759\pi$
$734$		−	349637.i		−	0.648971i
$735$	225308.	−	94267.7i	0.417063	−	0.174497i
$736$	21590.2			0.0398567
$737$			124856.i			0.229866i
$738$	−319043.	+	323625.i	−0.585783	+	0.594195i
$739$	473645.			0.867290			0.433645	−	0.901084i	$-0.357227\pi$
$739$	473645.			0.867290			0.433645	+	0.901084i	$0.357227\pi$
$740$			34467.6i			0.0629430i
$741$	−110568.	−	264266.i	−0.201369	−	0.481288i
$742$	79229.6			0.143906
$743$			666726.i			1.20773i	0.797087	+	0.603865i	$0.206373\pi$
$743$			666726.i			1.20773i	−0.797087	+	0.603865i	$0.793627\pi$
$744$	−73741.7	+	30853.2i	−0.133219	+	0.0557384i
$745$	293746.			0.529249
$746$			92944.0i			0.167011i
$747$	−323382.	−	318804.i	−0.579527	−	0.571323i
$748$	115905.			0.207157
$749$		−	49059.9i		−	0.0874507i
$750$	132539.	+	316778.i	0.235624	+	0.563161i
$751$	282650.			0.501152			0.250576	−	0.968097i	$-0.419380\pi$
$751$	282650.			0.501152			0.250576	+	0.968097i	$0.419380\pi$
$752$			132959.i			0.235115i
$753$	499969.	−	209185.i	0.881765	−	0.368926i
$754$	74961.7			0.131855
$755$			146824.i			0.257575i
$756$	74434.4	+	29903.3i	0.130236	+	0.0523210i
$757$	−480430.			−0.838374			−0.419187	−	0.907900i	$-0.637685\pi$
$757$	−480430.			−0.838374			−0.419187	+	0.907900i	$0.637685\pi$
$758$			466719.i			0.812301i
$759$	41100.6	+	98233.8i	0.0713451	+	0.170521i
$760$	33982.5			0.0588339
$761$			993660.i			1.71581i	0.513811	+	0.857903i	$0.328233\pi$
$761$			993660.i			1.71581i	−0.513811	+	0.857903i	$0.671767\pi$
$762$	−365542.	+	152941.i	−0.629546	+	0.263399i
$763$	−237003.			−0.407104
$764$			21630.7i			0.0370582i
$765$	−101898.	+	103361.i	−0.174117	+	0.176617i
$766$	−446720.			−0.761338
$767$		−	117842.i		−	0.200313i
$768$	−14228.5	−	34007.4i	−0.0241234	−	0.0576569i
$769$	326385.			0.551922			0.275961	−	0.961169i	$-0.411004\pi$
$769$	326385.			0.551922			0.275961	+	0.961169i	$0.411004\pi$
$770$			47350.0i			0.0798618i
$771$	−136652.	+	57174.7i	−0.229884	+	0.0961823i
$772$	−331747.			−0.556637
$773$		−	760578.i		−	1.27287i	−0.771329	−	0.636436i	$-0.780408\pi$
$773$		−	760578.i		−	1.27287i	0.771329	−	0.636436i	$-0.219592\pi$
$774$	−12102.3	−	11931.0i	−0.0202017	−	0.0199157i
$775$	−186239.			−0.310076
$776$		−	130351.i		−	0.216467i
$777$	16778.5	+	40102.0i	0.0277915	+	0.0664239i
$778$	−574096.			−0.948474
$779$			242806.i			0.400114i
$780$	211904.	−	88659.7i	0.348297	−	0.145726i
$781$	683456.			1.12049
$782$			49269.2i			0.0805678i
$783$	−27698.5	+	68946.2i	−0.0451786	+	0.112457i
$784$	−141556.			−0.230301
$785$		−	242002.i		−	0.392717i
$786$	−82502.3	−	197187.i	−0.133543	−	0.319179i
$787$	32438.5			0.0523735			0.0261867	−	0.999657i	$-0.491664\pi$
$787$	32438.5			0.0523735			0.0261867	+	0.999657i	$0.491664\pi$
$788$		−	326861.i		−	0.526394i
$789$	−215455.	+	90145.3i	−0.346100	+	0.144807i
$790$	122486.			0.196261
$791$		−	22687.5i		−	0.0362606i
$792$	127644.	−	129477.i	0.203494	−	0.206416i
$793$	1.68034e6			2.67209
$794$			187229.i			0.296983i
$795$	86798.2	+	207455.i	0.137334	+	0.328239i
$796$	485874.			0.766828
$797$		−	801779.i		−	1.26223i	−0.775690	−	0.631114i	$-0.782598\pi$
$797$		−	801779.i		−	1.26223i	0.775690	−	0.631114i	$-0.217402\pi$
$798$	39537.6	−	16542.4i	0.0620876	−	0.0259772i
$799$	−303413.			−0.475270
$800$		−	85887.9i		−	0.134200i
$801$	48270.7	+	47587.4i	0.0752348	+	0.0741697i
$802$	219578.			0.341382
$803$		−	107045.i		−	0.166011i
$804$	34977.2	+	83598.4i	0.0541094	+	0.129326i
$805$	−20127.6			−0.0310600
$806$			288690.i			0.444387i
$807$	−403218.	+	168705.i	−0.619146	+	0.259048i
$808$	285263.			0.436942
$809$		−	195914.i		−	0.299342i	−0.988736	−	0.149671i	$-0.952179\pi$
$809$		−	195914.i		−	0.299342i	0.988736	−	0.149671i	$-0.0478215\pi$
$810$	3245.97	+	227659.i	0.00494737	+	0.346988i
$811$	−669833.			−1.01841			−0.509207	−	0.860644i	$-0.670061\pi$
$811$	−669833.			−1.01841			−0.509207	+	0.860644i	$0.670061\pi$
$812$			11215.3i			0.0170097i
$813$	283983.	+	678742.i	0.429646	+	1.02689i
$814$	98529.6			0.148702
$815$		−	282083.i		−	0.424680i
$816$	77605.3	−	32469.7i	0.116550	−	0.0487638i
$817$	−9080.01			−0.0136032
$818$		−	137116.i		−	0.204918i
$819$	203385.	−	206306.i	0.303216	−	0.307570i
$820$	−194696.			−0.289554
$821$			801586.i			1.18922i	0.804013	+	0.594612i	$0.202694\pi$
$821$			801586.i			1.18922i	−0.804013	+	0.594612i	$0.797306\pi$
$822$	−125824.	−	300730.i	−0.186217	−	0.445074i
$823$	18836.2			0.0278096			0.0139048	−	0.999903i	$-0.495574\pi$
$823$	18836.2			0.0278096			0.0139048	+	0.999903i	$0.495574\pi$
$824$			228814.i			0.336999i
$825$	390783.	−	163502.i	0.574153	−	0.240223i
$826$	17630.7			0.0258410
$827$		−	164850.i		−	0.241033i	−0.992711	−	0.120517i	$-0.961545\pi$
$827$		−	164850.i		−	0.241033i	0.992711	−	0.120517i	$-0.0384551\pi$
$828$	55038.5	+	54259.3i	0.0802797	+	0.0791432i
$829$	782012.			1.13790			0.568950	−	0.822372i	$-0.307350\pi$
$829$	782012.			1.13790			0.568950	+	0.822372i	$0.307350\pi$
$830$		−	194550.i		−	0.282406i
$831$	10570.7	+	25264.9i	0.0153075	+	0.0365861i
$832$	−133135.			−0.192329
$833$		−	323032.i		−	0.465539i
$834$	−237308.	+	99288.7i	−0.341178	+	0.142747i
$835$	261625.			0.375238
$836$		−	97142.8i		−	0.138995i
$837$	−265523.	−	106671.i	−0.379010	−	0.152264i
$838$	−760465.			−1.08291
$839$		−	949739.i		−	1.34921i	−0.738178	−	0.674606i	$-0.764313\pi$
$839$		−	949739.i		−	1.34921i	0.738178	−	0.674606i	$-0.235687\pi$
$840$	13264.7	+	31703.6i	0.0187991	+	0.0449314i
$841$	696893.			0.985312
$842$		−	67795.3i		−	0.0956258i
$843$	−463417.	+	193892.i	−0.652104	+	0.272837i
$844$	−469030.			−0.658439
$845$		−	479160.i		−	0.671069i
$846$	−334144.	+	338942.i	−0.466867	+	0.473571i
$847$	−66024.7			−0.0920322
$848$		−	130340.i		−	0.181253i
$849$	−117586.	−	281040.i	−0.163132	−	0.389900i
$850$	195997.			0.271276
$851$			41883.1i			0.0578336i
$852$	457614.	−	191464.i	0.630406	−	0.263759i
$853$	599509.			0.823944			0.411972	−	0.911197i	$-0.364840\pi$
$853$	599509.			0.823944			0.411972	+	0.911197i	$0.364840\pi$
$854$			251401.i			0.344708i
$855$	86629.2	+	85402.8i	0.118504	+	0.116826i
$856$	−80707.8			−0.110146
$857$		−	320117.i		−	0.435861i	−0.975964	−	0.217930i	$-0.930069\pi$
$857$		−	320117.i		−	0.435861i	0.975964	−	0.217930i	$-0.0699306\pi$
$858$	−253444.	−	605752.i	−0.344277	−	0.822850i
$859$	1.25703e6			1.70356			0.851782	−	0.523897i	$-0.175522\pi$
$859$	1.25703e6			1.70356			0.851782	+	0.523897i	$0.175522\pi$
$860$		−	7280.89i		−	0.00984436i
$861$	−226523.	+	94776.2i	−0.305567	+	0.127848i
$862$	−28270.5			−0.0380469
$863$		−	557567.i		−	0.748644i	−0.927299	−	0.374322i	$-0.877876\pi$
$863$		−	557567.i		−	0.748644i	0.927299	−	0.374322i	$-0.122124\pi$
$864$	49193.6	−	122451.i	0.0658993	−	0.164034i
$865$	−301053.			−0.402356
$866$		−	268278.i		−	0.357725i
$867$	−216036.	−	516344.i	−0.287401	−	0.686912i
$868$	−43191.8			−0.0573273
$869$		−	350141.i		−	0.463664i
$870$	−29366.1	+	12286.6i	−0.0387978	+	0.0162328i
$871$	327278.			0.431400
$872$			389891.i			0.512756i
$873$	327591.	−	332295.i	0.429836	−	0.436008i
$874$	41293.7			0.0540581
$875$			185542.i			0.242341i
$876$	−29987.7	−	71673.2i	−0.0390783	−	0.0934003i
$877$	378196.			0.491720			0.245860	−	0.969305i	$-0.420930\pi$
$877$	378196.			0.491720			0.245860	+	0.969305i	$0.420930\pi$
$878$			137276.i			0.178076i
$879$	−326789.	+	136727.i	−0.422951	+	0.176961i
$880$	77894.9			0.100587
$881$		−	1.03649e6i		−	1.33541i	−0.744425	−	0.667706i	$-0.767276\pi$
$881$		−	1.03649e6i		−	1.33541i	0.744425	−	0.667706i	$-0.232724\pi$
$882$	−360859.	−	355750.i	−0.463874	−	0.457307i
$883$	−1.46415e6			−1.87787			−0.938934	−	0.344098i	$-0.888185\pi$
$883$	−1.46415e6			−1.87787			−0.938934	+	0.344098i	$0.888185\pi$
$884$		−	303815.i		−	0.388781i
$885$	19314.9	+	46164.2i	0.0246607	+	0.0589412i
$886$	−792606.			−1.00969
$887$			1.49799e6i			1.90398i	0.306129	+	0.951990i	$0.400966\pi$
$887$			1.49799e6i			1.90398i	−0.306129	+	0.951990i	$0.599034\pi$
$888$	65971.3	−	27602.1i	0.0836622	−	0.0350039i
$889$	−214104.			−0.270908
$890$			29040.2i			0.0366622i
$891$	650790.	−	9278.98i	0.819758	−	0.0116881i
$892$	567011.			0.712626
$893$			254298.i			0.318889i
$894$	−235236.	−	562234.i	−0.294326	−	0.703464i
$895$	429240.			0.535864
$896$		−	19918.7i		−	0.0248111i
$897$	257494.	−	107734.i	0.320024	−	0.133897i
$898$	−155794.			−0.193196
$899$		−	40007.2i		−	0.0495015i
$900$	215848.	−	218948.i	0.266480	−	0.270306i
$901$	297436.			0.366391
$902$			556561.i			0.684068i
$903$	−3544.27	−	8471.10i	−0.00434662	−	0.0103888i
$904$	−37323.0			−0.0456709
$905$		−	737672.i		−	0.900671i
$906$	281023.	−	117579.i	0.342362	−	0.143243i
$907$	−714881.			−0.868999			−0.434499	−	0.900672i	$-0.643075\pi$
$907$	−714881.			−0.868999			−0.434499	+	0.900672i	$0.643075\pi$
$908$		−	486716.i		−	0.590342i
$909$	727202.	+	716907.i	0.880090	+	0.867632i
$910$	124116.			0.149880
$911$			1.20498e6i			1.45192i	0.687737	+	0.725960i	$0.258604\pi$
$911$			1.20498e6i			1.45192i	−0.687737	+	0.725960i	$0.741396\pi$
$912$	−27213.6	−	65042.8i	−0.0327188	−	0.0782005i
$913$	−556143.			−0.667182
$914$		−	1.09992e6i		−	1.31665i
$915$	−658269.	+	275417.i	−0.786251	+	0.328964i
$916$	−134503.			−0.160302
$917$		−	115496.i		−	0.137350i
$918$	279435.	+	112260.i	0.331585	+	0.133211i
$919$	291832.			0.345542			0.172771	−	0.984962i	$-0.444728\pi$
$919$	291832.			0.345542			0.172771	+	0.984962i	$0.444728\pi$
$920$			33111.7i			0.0391206i
$921$	481187.	+	1.15008e6i	0.567276	+	1.35584i
$922$	641900.			0.755102
$923$		−	1.79150e6i		−	2.10288i
$924$	90628.5	−	37918.5i	0.106150	−	0.0444128i
$925$	166615.			0.194729
$926$		−	290760.i		−	0.339088i
$927$	−575042.	+	583300.i	−0.669176	+	0.678785i
$928$	18450.1			0.0214241
$929$		−	56979.5i		−	0.0660218i	−0.999455	−	0.0330109i	$-0.989490\pi$
$929$		−	56979.5i		−	0.0660218i	0.999455	−	0.0330109i	$-0.0105096\pi$
$930$	−47317.8	−	113093.i	−0.0547090	−	0.130759i
$931$	−270741.			−0.312360
$932$		−	693566.i		−	0.798465i
$933$	−146552.	+	61316.7i	−0.168356	+	0.0704394i
$934$	130282.			0.149345
$935$			177757.i			0.203331i
$936$	−339391.	−	334587.i	−0.387390	−	0.381906i
$937$	1.01366e6			1.15455			0.577274	−	0.816551i	$-0.304117\pi$
$937$	1.01366e6			1.15455			0.577274	+	0.816551i	$0.304117\pi$
$938$			48965.0i			0.0556519i
$939$	−183795.	−	439285.i	−0.208450	−	0.498213i
$940$	−203911.			−0.230773
$941$		−	527263.i		−	0.595454i	−0.954651	−	0.297727i	$-0.903772\pi$
$941$		−	527263.i		−	0.595454i	0.954651	−	0.297727i	$-0.0962285\pi$
$942$	−463195.	+	193799.i	−0.521990	+	0.218398i
$943$	−236584.			−0.266049
$944$		−	29004.0i		−	0.0325472i
$945$	−45861.0	+	114156.i	−0.0513547	+	0.127830i
$946$	−20813.3			−0.0232572
$947$			133943.i			0.149355i	0.997208	+	0.0746773i	$0.0237927\pi$
$947$			133943.i			0.149355i	−0.997208	+	0.0746773i	$0.976207\pi$
$948$	−98088.6	−	234440.i	−0.109144	−	0.260864i
$949$	−280592.			−0.311561
$950$		−	164270.i		−	0.182017i
$951$	−286834.	+	120010.i	−0.317154	+	0.132696i
$952$	45454.7			0.0501539
$953$		−	1.44973e6i		−	1.59625i	−0.602491	−	0.798126i	$-0.705825\pi$
$953$		−	1.44973e6i		−	1.59625i	0.602491	−	0.798126i	$-0.294175\pi$
$954$	327562.	−	332265.i	0.359912	−	0.365080i
$955$	−33173.8			−0.0363738
$956$			415577.i			0.454712i
$957$	35122.7	+	83946.3i	0.0383499	+	0.0916595i
$958$	−488694.			−0.532483
$959$		−	176142.i		−	0.191526i
$960$	52155.2	−	21821.5i	0.0565920	−	0.0236778i
$961$	−769447.			−0.833167
$962$		−	258270.i		−	0.279077i
$963$	−205743.	−	202830.i	−0.221856	−	0.218716i
$964$	−194921.			−0.209751
$965$		−	508781.i		−	0.546357i
$966$	16118.5	+	38524.5i	0.0172731	+	0.0412841i
$967$	−1.55427e6			−1.66216			−0.831079	−	0.556155i	$-0.812276\pi$
$967$	−1.55427e6			−1.66216			−0.831079	+	0.556155i	$0.812276\pi$
$968$			108616.i			0.115916i
$969$	148428.	−	62101.8i	0.158077	−	0.0661388i
$970$	199912.			0.212469
$971$		−	329144.i		−	0.349098i	−0.984649	−	0.174549i	$-0.944153\pi$
$971$		−	329144.i		−	0.349098i	0.984649	−	0.174549i	$-0.0558467\pi$
$972$	433142.	−	188525.i	0.458457	−	0.199543i
$973$	−138995.			−0.146817
$974$			148281.i			0.156303i
$975$	−428577.	−	1.02434e6i	−0.450837	−	1.07754i
$976$	413576.			0.434166
$977$		−	559562.i		−	0.586218i	−0.956079	−	0.293109i	$-0.905310\pi$
$977$		−	559562.i		−	0.586218i	0.956079	−	0.293109i	$-0.0946899\pi$
$978$	−539910.	+	225896.i	−0.564474	+	0.236173i
$979$	83014.6			0.0866142
$980$		−	217096.i		−	0.226048i
$981$	−979852.	+	993922.i	−1.01817	+	1.03280i
$982$	1.04465e6			1.08330
$983$		−	638722.i		−	0.661005i	−0.943805	−	0.330503i	$-0.892782\pi$
$983$		−	638722.i		−	0.661005i	0.943805	−	0.330503i	$-0.107218\pi$
$984$	155915.	+	372650.i	0.161027	+	0.384867i
$985$	501288.			0.516672
$986$			42103.3i			0.0433074i
$987$	−237245.	+	99262.1i	−0.243535	+	0.101894i
$988$	−254635.			−0.260858
$989$		−	8847.34i		−	0.00904524i
$990$	198572.	+	195761.i	0.202604	+	0.199736i
$991$	−1.11620e6			−1.13657			−0.568285	−	0.822832i	$-0.692393\pi$
$991$	−1.11620e6			−1.13657			−0.568285	+	0.822832i	$0.692393\pi$
$992$			71054.2i			0.0722048i
$993$	−306318.	−	732125.i	−0.310652	−	0.742484i
$994$	268032.			0.271278
$995$			745158.i			0.752665i
$996$	−372370.	+	155798.i	−0.375367	+	0.157052i
$997$	−1.11762e6			−1.12436			−0.562179	−	0.827016i	$-0.690037\pi$
$997$	−1.11762e6			−1.12436			−0.562179	+	0.827016i	$0.690037\pi$
$998$		−	16445.2i		−	0.0165111i
$999$	237544.	+	95431.2i	0.238020	+	0.0956223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.b.a.119.17	✓	76
3.2	odd	2	inner	354.5.b.a.119.55	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.b.a.119.17	✓	76	1.1	even	1	trivial
354.5.b.a.119.55	yes	76	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} +(-3.47377 - 8.30259i) q^{3} -8.00000 q^{4} -12.2691i q^{5} +(-23.4833 + 9.82529i) q^{6} -13.7545 q^{7} +22.6274i q^{8} +(-56.8659 + 57.6825i) q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} +(-3.47377 - 8.30259i) q^{3} -8.00000 q^{4} -12.2691i q^{5} +(-23.4833 + 9.82529i) q^{6} -13.7545 q^{7} +22.6274i q^{8} +(-56.8659 + 57.6825i) q^{9} -34.7024 q^{10} +99.2007i q^{11} +(27.7901 + 66.4207i) q^{12} +260.029 q^{13} +38.9037i q^{14} +(-101.866 + 42.6201i) q^{15} +64.0000 q^{16} +146.049i q^{17} +(163.151 + 160.841i) q^{18} +122.407 q^{19} +98.1531i q^{20} +(47.7801 + 114.198i) q^{21} +280.582 q^{22} +119.270i q^{23} +(187.866 - 78.6023i) q^{24} +474.468 q^{25} -735.473i q^{26} +(676.453 + 271.759i) q^{27} +110.036 q^{28} +101.923i q^{29} +(120.548 + 288.120i) q^{30} -392.523 q^{31} -181.019i q^{32} +(823.623 - 344.600i) q^{33} +413.088 q^{34} +168.756i q^{35} +(454.927 - 461.460i) q^{36} +351.161 q^{37} -346.219i q^{38} +(-903.280 - 2158.91i) q^{39} +277.619 q^{40} +1983.59i q^{41} +(323.002 - 135.142i) q^{42} -74.1789 q^{43} -793.606i q^{44} +(707.715 + 697.696i) q^{45} +337.347 q^{46} +2077.48i q^{47} +(-222.321 - 531.366i) q^{48} -2211.81 q^{49} -1342.00i q^{50} +(1212.58 - 507.339i) q^{51} -2080.23 q^{52} -2036.56i q^{53} +(768.650 - 1913.30i) q^{54} +1217.11 q^{55} -311.230i q^{56} +(-425.213 - 1016.29i) q^{57} +288.282 q^{58} -453.188i q^{59} +(814.925 - 340.961i) q^{60} +6462.13 q^{61} +1110.22i q^{62} +(782.165 - 793.396i) q^{63} -512.000 q^{64} -3190.33i q^{65} +(-974.676 - 2329.56i) q^{66} +1258.62 q^{67} -1168.39i q^{68} +(990.252 - 414.317i) q^{69} +477.315 q^{70} -6889.63i q^{71} +(-1305.21 - 1286.73i) q^{72} -1079.08 q^{73} -993.235i q^{74} +(-1648.19 - 3939.31i) q^{75} -979.255 q^{76} -1364.46i q^{77} +(-6106.33 + 2554.86i) q^{78} -3529.62 q^{79} -785.225i q^{80} +(-93.5374 - 6560.33i) q^{81} +5610.45 q^{82} +5606.23i q^{83} +(-382.241 - 913.586i) q^{84} +1791.89 q^{85} +209.810i q^{86} +(846.226 - 354.057i) q^{87} -2244.66 q^{88} -836.835i q^{89} +(1973.38 - 2001.72i) q^{90} -3576.58 q^{91} -954.163i q^{92} +(1363.53 + 3258.95i) q^{93} +5876.00 q^{94} -1501.83i q^{95} +(-1502.93 + 628.819i) q^{96} -5760.76 q^{97} +6255.95i q^{98} +(-5722.14 - 5641.14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

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