LMFDB - Embedded newform 462.4.g.b.419.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,4,Mod(419,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("462.419");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	462.g (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:	$27.2588824227$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.10
Character	$\chi$	$=$	462.419
Dual form			462.4.g.b.419.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +(0.124204 + 5.19467i) q^{3} -4.00000 q^{4} -16.3702 q^{5} +(10.3893 - 0.248407i) q^{6} +(-2.94673 - 18.2843i) q^{7} +8.00000i q^{8} +(-26.9691 + 1.29039i) q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +(0.124204 + 5.19467i) q^{3} -4.00000 q^{4} -16.3702 q^{5} +(10.3893 - 0.248407i) q^{6} +(-2.94673 - 18.2843i) q^{7} +8.00000i q^{8} +(-26.9691 + 1.29039i) q^{9} +32.7404i q^{10} +11.0000i q^{11} +(-0.496815 - 20.7787i) q^{12} -42.0621i q^{13} +(-36.5687 + 5.89346i) q^{14} +(-2.03324 - 85.0378i) q^{15} +16.0000 q^{16} -31.6801 q^{17} +(2.58079 + 53.9383i) q^{18} -24.6930i q^{19} +65.4808 q^{20} +(94.6150 - 17.5783i) q^{21} +22.0000 q^{22} +196.552i q^{23} +(-41.5573 + 0.993630i) q^{24} +142.984 q^{25} -84.1243 q^{26} +(-10.0528 - 139.935i) q^{27} +(11.7869 + 73.1373i) q^{28} +38.4732i q^{29} +(-170.076 + 4.06648i) q^{30} -140.949i q^{31} -32.0000i q^{32} +(-57.1413 + 1.36624i) q^{33} +63.3603i q^{34} +(48.2386 + 299.318i) q^{35} +(107.877 - 5.16158i) q^{36} -0.688073 q^{37} -49.3859 q^{38} +(218.499 - 5.22427i) q^{39} -130.962i q^{40} +249.706 q^{41} +(-35.1565 - 189.230i) q^{42} +362.010 q^{43} -44.0000i q^{44} +(441.491 - 21.1240i) q^{45} +393.105 q^{46} +85.0387 q^{47} +(1.98726 + 83.1147i) q^{48} +(-325.634 + 107.758i) q^{49} -285.967i q^{50} +(-3.93479 - 164.568i) q^{51} +168.249i q^{52} +587.604i q^{53} +(-279.871 + 20.1057i) q^{54} -180.072i q^{55} +(146.275 - 23.5738i) q^{56} +(128.272 - 3.06696i) q^{57} +76.9465 q^{58} +226.923 q^{59} +(8.13296 + 340.151i) q^{60} +912.487i q^{61} -281.897 q^{62} +(103.065 + 489.310i) q^{63} -64.0000 q^{64} +688.566i q^{65} +(2.73248 + 114.283i) q^{66} +898.220 q^{67} +126.721 q^{68} +(-1021.02 + 24.4125i) q^{69} +(598.637 - 96.4771i) q^{70} -576.673i q^{71} +(-10.3232 - 215.753i) q^{72} +554.946i q^{73} +1.37615i q^{74} +(17.7591 + 742.753i) q^{75} +98.7719i q^{76} +(201.128 - 32.4140i) q^{77} +(-10.4485 - 436.998i) q^{78} +214.103 q^{79} -261.923 q^{80} +(725.670 - 69.6016i) q^{81} -499.413i q^{82} -596.008 q^{83} +(-378.460 + 70.3130i) q^{84} +518.610 q^{85} -724.021i q^{86} +(-199.856 + 4.77852i) q^{87} -88.0000 q^{88} +1292.48 q^{89} +(-42.2480 - 882.981i) q^{90} +(-769.078 + 123.946i) q^{91} -786.209i q^{92} +(732.181 - 17.5063i) q^{93} -170.077i q^{94} +404.229i q^{95} +(166.229 - 3.97452i) q^{96} -321.385i q^{97} +(215.516 + 651.267i) q^{98} +(-14.1943 - 296.661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 144 q^{4} - 36 q^{7} - 132 q^{9}+O(q^{10}) $ 36 * q - 144 * q^4 - 36 * q^7 - 132 * q^9	$ 36 q - 144 q^{4} - 36 q^{7} - 132 q^{9} - 468 q^{15} + 576 q^{16} + 8 q^{18} + 14 q^{21} + 792 q^{22} + 552 q^{25} + 144 q^{28} - 184 q^{30} + 528 q^{36} - 108 q^{37} - 708 q^{39} + 260 q^{42} + 2688 q^{43} - 912 q^{46} - 2796 q^{49} + 1544 q^{51} - 1784 q^{57} - 1128 q^{58} + 1872 q^{60} + 1030 q^{63} - 2304 q^{64} + 2196 q^{67} - 2544 q^{70} - 32 q^{72} - 384 q^{78} - 4488 q^{79} - 2176 q^{81} - 56 q^{84} + 8328 q^{85} - 3168 q^{88} - 5580 q^{91} + 2956 q^{93} - 44 q^{99}+O(q^{100}) $ 36 * q - 144 * q^4 - 36 * q^7 - 132 * q^9 - 468 * q^15 + 576 * q^16 + 8 * q^18 + 14 * q^21 + 792 * q^22 + 552 * q^25 + 144 * q^28 - 184 * q^30 + 528 * q^36 - 108 * q^37 - 708 * q^39 + 260 * q^42 + 2688 * q^43 - 912 * q^46 - 2796 * q^49 + 1544 * q^51 - 1784 * q^57 - 1128 * q^58 + 1872 * q^60 + 1030 * q^63 - 2304 * q^64 + 2196 * q^67 - 2544 * q^70 - 32 * q^72 - 384 * q^78 - 4488 * q^79 - 2176 * q^81 - 56 * q^84 + 8328 * q^85 - 3168 * q^88 - 5580 * q^91 + 2956 * q^93 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	0.124204	+	5.19467i	0.0239030	+	0.999714i
$3$	0.124204	+	5.19467i	0.0239030	+	0.999714i
$4$	−4.00000			−0.500000
$5$	−16.3702			−1.46420			−0.732098	−	0.681199i	$-0.761459\pi$
$5$	−16.3702			−1.46420			−0.732098	+	0.681199i	$0.761459\pi$
$6$	10.3893	−	0.248407i	0.706905	−	0.0169020i
$7$	−2.94673	−	18.2843i	−0.159108	−	0.987261i
$7$	−2.94673	−	18.2843i	−0.159108	−	0.987261i
$8$			8.00000i			0.353553i
$9$	−26.9691	+	1.29039i	−0.998857	+	0.0477924i
$10$			32.7404i			1.03534i
$11$			11.0000i			0.301511i
$11$			11.0000i			0.301511i
$12$	−0.496815	−	20.7787i	−0.0119515	−	0.499857i
$13$		−	42.0621i		−	0.897380i	−0.893687	−	0.448690i	$-0.851891\pi$
$13$		−	42.0621i		−	0.897380i	0.893687	−	0.448690i	$-0.148109\pi$
$14$	−36.5687	+	5.89346i	−0.698099	+	0.112507i
$15$	−2.03324	−	85.0378i	−0.0349987	−	1.46378i
$16$	16.0000			0.250000
$17$	−31.6801			−0.451974			−0.225987	−	0.974130i	$-0.572561\pi$
$17$	−31.6801			−0.451974			−0.225987	+	0.974130i	$0.572561\pi$
$18$	2.58079	+	53.9383i	0.0337943	+	0.706299i
$19$		−	24.6930i		−	0.298156i	−0.988825	−	0.149078i	$-0.952370\pi$
$19$		−	24.6930i		−	0.298156i	0.988825	−	0.149078i	$-0.0476305\pi$
$20$	65.4808			0.732098
$21$	94.6150	−	17.5783i	0.983176	−	0.182661i
$22$	22.0000			0.213201
$23$			196.552i			1.78191i	0.454089	+	0.890956i	$0.349965\pi$
$23$			196.552i			1.78191i	−0.454089	+	0.890956i	$0.650035\pi$
$24$	−41.5573	+	0.993630i	−0.353452	+	0.00845099i
$25$	142.984			1.14387
$26$	−84.1243			−0.634543
$27$	−10.0528	−	139.935i	−0.0716544	−	0.997430i
$28$	11.7869	+	73.1373i	0.0795542	+	0.493631i
$29$			38.4732i			0.246355i	0.992385	+	0.123178i	$0.0393085\pi$
$29$			38.4732i			0.246355i	−0.992385	+	0.123178i	$0.960692\pi$
$30$	−170.076	+	4.06648i	−1.03505	+	0.0247478i
$31$		−	140.949i		−	0.816617i	−0.912844	−	0.408308i	$-0.866119\pi$
$31$		−	140.949i		−	0.816617i	0.912844	−	0.408308i	$-0.133881\pi$
$32$		−	32.0000i		−	0.176777i
$33$	−57.1413	+	1.36624i	−0.301425	+	0.00720703i
$34$			63.3603i			0.319594i
$35$	48.2386	+	299.318i	0.232966	+	1.44554i
$36$	107.877	−	5.16158i	0.499429	−	0.0238962i
$37$	−0.688073			−0.00305725			−0.00152863	−	0.999999i	$-0.500487\pi$
$37$	−0.688073			−0.00305725			−0.00152863	+	0.999999i	$0.500487\pi$
$38$	−49.3859			−0.210828
$39$	218.499	−	5.22427i	0.897124	−	0.0214501i
$40$		−	130.962i		−	0.517671i
$41$	249.706			0.951161			0.475580	−	0.879672i	$-0.342238\pi$
$41$	249.706			0.951161			0.475580	+	0.879672i	$0.342238\pi$
$42$	−35.1565	−	189.230i	−0.129161	−	0.695210i
$43$	362.010			1.28386			0.641931	−	0.766762i	$-0.278134\pi$
$43$	362.010			1.28386			0.641931	+	0.766762i	$0.278134\pi$
$44$		−	44.0000i		−	0.150756i
$45$	441.491	−	21.1240i	1.46252	−	0.0699774i
$46$	393.105			1.26000
$47$	85.0387			0.263918			0.131959	−	0.991255i	$-0.457873\pi$
$47$	85.0387			0.263918			0.131959	+	0.991255i	$0.457873\pi$
$48$	1.98726	+	83.1147i	0.00597575	+	0.249929i
$49$	−325.634	+	107.758i	−0.949369	+	0.314163i
$50$		−	285.967i		−	0.808838i
$51$	−3.93479	−	164.568i	−0.0108035	−	0.451845i
$52$			168.249i			0.448690i
$53$			587.604i			1.52290i	0.648224	+	0.761450i	$0.275512\pi$
$53$			587.604i			1.52290i	−0.648224	+	0.761450i	$0.724488\pi$
$54$	−279.871	+	20.1057i	−0.705289	+	0.0506673i
$55$		−	180.072i		−	0.441472i
$56$	146.275	−	23.5738i	0.349050	−	0.0562533i
$57$	128.272	−	3.06696i	0.298070	−	0.00712681i
$58$	76.9465			0.174199
$59$	226.923			0.500726			0.250363	−	0.968152i	$-0.419450\pi$
$59$	226.923			0.500726			0.250363	+	0.968152i	$0.419450\pi$
$60$	8.13296	+	340.151i	0.0174993	+	0.731889i
$61$			912.487i			1.91528i	0.287971	+	0.957639i	$0.407019\pi$
$61$			912.487i			1.91528i	−0.287971	+	0.957639i	$0.592981\pi$
$62$	−281.897			−0.577435
$63$	103.065	+	489.310i	0.206110	+	0.978529i
$64$	−64.0000			−0.125000
$65$			688.566i			1.31394i
$66$	2.73248	+	114.283i	0.00509614	+	0.213140i
$67$	898.220			1.63784			0.818918	−	0.573910i	$-0.194574\pi$
$67$	898.220			1.63784			0.818918	+	0.573910i	$0.194574\pi$
$68$	126.721			0.225987
$69$	−1021.02	+	24.4125i	−1.78140	+	0.0425931i
$70$	598.637	−	96.4771i	1.02215	−	0.164732i
$71$		−	576.673i		−	0.963923i	−0.876192	−	0.481961i	$-0.839925\pi$
$71$		−	576.673i		−	0.963923i	0.876192	−	0.481961i	$-0.160075\pi$
$72$	−10.3232	−	215.753i	−0.0168972	−	0.353149i
$73$			554.946i			0.889746i	0.895594	+	0.444873i	$0.146751\pi$
$73$			554.946i			0.889746i	−0.895594	+	0.444873i	$0.853249\pi$
$74$			1.37615i			0.00216181i
$75$	17.7591	+	742.753i	0.0273419	+	1.14354i
$76$			98.7719i			0.149078i
$77$	201.128	−	32.4140i	0.297670	−	0.0479730i
$78$	−10.4485	−	436.998i	−0.0151675	−	0.634362i
$79$	214.103			0.304917			0.152458	−	0.988310i	$-0.451281\pi$
$79$	214.103			0.304917			0.152458	+	0.988310i	$0.451281\pi$
$80$	−261.923			−0.366049
$81$	725.670	−	69.6016i	0.995432	−	0.0954755i
$82$		−	499.413i		−	0.672572i
$83$	−596.008			−0.788197			−0.394099	−	0.919068i	$-0.628943\pi$
$83$	−596.008			−0.788197			−0.394099	+	0.919068i	$0.628943\pi$
$84$	−378.460	+	70.3130i	−0.491588	+	0.0913307i
$85$	518.610			0.661779
$86$		−	724.021i		−	0.907827i
$87$	−199.856	+	4.77852i	−0.246285	+	0.00588863i
$88$	−88.0000			−0.106600
$89$	1292.48			1.53935			0.769677	−	0.638434i	$-0.220418\pi$
$89$	1292.48			1.53935			0.769677	+	0.638434i	$0.220418\pi$
$90$	−42.2480	−	882.981i	−0.0494815	−	1.03416i
$91$	−769.078	+	123.946i	−0.885948	+	0.142781i
$92$		−	786.209i		−	0.890956i
$93$	732.181	−	17.5063i	0.816383	−	0.0195196i
$94$		−	170.077i		−	0.186618i
$95$			404.229i			0.436558i
$96$	166.229	−	3.97452i	0.176726	−	0.00422550i
$97$		−	321.385i		−	0.336409i	−0.985752	−	0.168205i	$-0.946203\pi$
$97$		−	321.385i		−	0.336409i	0.985752	−	0.168205i	$-0.0537969\pi$
$98$	215.516	+	651.267i	0.222147	+	0.671305i
$99$	−14.1943	−	296.661i	−0.0144099	−	0.301167i
$100$	−571.935			−0.571935
$101$	−747.867			−0.736787			−0.368394	−	0.929670i	$-0.620092\pi$
$101$	−747.867			−0.736787			−0.368394	+	0.929670i	$0.620092\pi$
$102$	−329.136	+	7.86958i	−0.319503	+	0.00763926i
$103$		−	1374.44i		−	1.31483i	−0.753528	−	0.657416i	$-0.771649\pi$
$103$		−	1374.44i		−	1.31483i	0.753528	−	0.657416i	$-0.228351\pi$
$104$	336.497			0.317272
$105$	−1548.87	+	287.760i	−1.43956	+	0.267452i
$106$	1175.21			1.07685
$107$		−	642.574i		−	0.580560i	−0.956942	−	0.290280i	$-0.906252\pi$
$107$		−	642.574i		−	0.580560i	0.956942	−	0.290280i	$-0.0937485\pi$
$108$	40.2113	+	559.742i	0.0358272	+	0.498715i
$109$	−593.818			−0.521812			−0.260906	−	0.965364i	$-0.584021\pi$
$109$	−593.818			−0.521812			−0.260906	+	0.965364i	$0.584021\pi$
$110$	−360.145			−0.312168
$111$	−0.0854611	−	3.57431i	−7.30776e−5	−	0.00305638i
$112$	−47.1477	−	292.549i	−0.0397771	−	0.246815i
$113$		−	1750.48i		−	1.45727i	−0.684905	−	0.728633i	$-0.740156\pi$
$113$		−	1750.48i		−	1.45727i	0.684905	−	0.728633i	$-0.259844\pi$
$114$	−6.13391	−	256.544i	−0.00503942	−	0.210768i
$115$		−	3217.60i		−	2.60907i
$116$		−	153.893i		−	0.123178i
$117$	54.2767	+	1134.38i	0.0428879	+	0.896354i
$118$		−	453.846i		−	0.354067i
$119$	93.3528	+	579.250i	0.0719129	+	0.446217i
$120$	680.302	−	16.2659i	0.517523	−	0.0123739i
$121$	−121.000			−0.0909091
$122$	1824.97			1.35431
$123$	31.0145	+	1297.14i	0.0227356	+	0.950889i
$124$			563.794i			0.408308i
$125$	−294.396			−0.210653
$126$	978.621	−	206.130i	0.691924	−	0.145742i
$127$	−1581.57			−1.10505			−0.552527	−	0.833495i	$-0.686336\pi$
$127$	−1581.57			−1.10505			−0.552527	+	0.833495i	$0.686336\pi$
$128$			128.000i			0.0883883i
$129$	44.9630	+	1880.52i	0.0306882	+	1.28350i
$130$	1377.13			0.929096
$131$	604.960			0.403478			0.201739	−	0.979439i	$-0.435341\pi$
$131$	604.960			0.403478			0.201739	+	0.979439i	$0.435341\pi$
$132$	228.565	−	5.46496i	0.150713	−	0.00360351i
$133$	−451.494	+	72.7635i	−0.294357	+	0.0474391i
$134$		−	1796.44i		−	1.15813i
$135$	164.567	+	2290.77i	0.104916	+	1.46043i
$136$		−	253.441i		−	0.159797i
$137$		−	4.17891i		−	0.00260604i	−0.999999	−	0.00130302i	$-0.999585\pi$
$137$		−	4.17891i		−	0.00260604i	0.999999	−	0.00130302i	$-0.000414765\pi$
$138$	48.8250	+	2042.05i	0.0301178	+	1.25964i
$139$			1737.28i			1.06010i	0.847966	+	0.530050i	$0.177827\pi$
$139$			1737.28i			1.06010i	−0.847966	+	0.530050i	$0.822173\pi$
$140$	−192.954	−	1197.27i	−0.116483	−	0.722772i
$141$	10.5621	+	441.748i	0.00630844	+	0.263843i
$142$	−1153.35			−0.681596
$143$	462.684			0.270570
$144$	−431.506	+	20.6463i	−0.249714	+	0.0119481i
$145$		−	629.815i		−	0.360712i
$146$	1109.89			0.629146
$147$	−600.212	−	1678.17i	−0.336766	−	0.941588i
$148$	2.75229			0.00152863
$149$		−	929.923i		−	0.511290i	−0.966771	−	0.255645i	$-0.917712\pi$
$149$		−	929.923i		−	0.511290i	0.966771	−	0.255645i	$-0.0822879\pi$
$150$	1485.51	−	35.5182i	0.808607	−	0.0193337i
$151$	1794.01			0.966850			0.483425	−	0.875386i	$-0.339393\pi$
$151$	1794.01			0.966850			0.483425	+	0.875386i	$0.339393\pi$
$152$	197.544			0.105414
$153$	854.386	−	40.8799i	0.451458	−	0.0216009i
$154$	−64.8280	−	402.255i	−0.0339220	−	0.210485i
$155$			2307.36i			1.19569i
$156$	−873.995	+	20.8971i	−0.448562	+	0.0107250i
$157$		−	2126.28i		−	1.08086i	−0.841387	−	0.540432i	$-0.818261\pi$
$157$		−	2126.28i		−	1.08086i	0.841387	−	0.540432i	$-0.181739\pi$
$158$		−	428.205i		−	0.215609i
$159$	−3052.41	+	72.9826i	−1.52246	+	0.0364019i
$160$			523.847i			0.258836i
$161$	3593.83	−	579.186i	1.75921	−	0.283517i
$162$	−139.203	−	1451.34i	−0.0675114	−	0.703877i
$163$	1663.18			0.799204			0.399602	−	0.916689i	$-0.369148\pi$
$163$	1663.18			0.799204			0.399602	+	0.916689i	$0.369148\pi$
$164$	−998.826			−0.475580
$165$	935.416	−	22.3656i	0.441346	−	0.0105525i
$166$			1192.02i			0.557340i
$167$	−2667.44			−1.23601			−0.618003	−	0.786176i	$-0.712058\pi$
$167$	−2667.44			−1.23601			−0.618003	+	0.786176i	$0.712058\pi$
$168$	140.626	+	756.920i	0.0645806	+	0.347605i
$169$	427.776			0.194709
$170$		−	1037.22i		−	0.467948i
$171$	31.8637	+	665.948i	0.0142496	+	0.297815i
$172$	−1448.04			−0.641931
$173$	−276.215			−0.121389			−0.0606943	−	0.998156i	$-0.519331\pi$
$173$	−276.215			−0.121389			−0.0606943	+	0.998156i	$0.519331\pi$
$174$	9.55703	+	399.711i	0.00416389	+	0.174150i
$175$	−421.334	−	2614.36i	−0.181999	−	1.12930i
$176$			176.000i			0.0753778i
$177$	28.1847	+	1178.79i	0.0119689	+	0.500583i
$178$		−	2584.96i		−	1.08849i
$179$			2607.96i			1.08898i	0.838766	+	0.544492i	$0.183277\pi$
$179$			2607.96i			1.08898i	−0.838766	+	0.544492i	$0.816723\pi$
$180$	−1765.96	+	84.4961i	−0.731261	+	0.0349887i
$181$		−	4625.21i		−	1.89939i	−0.313178	−	0.949694i	$-0.601394\pi$
$181$		−	4625.21i		−	1.89939i	0.313178	−	0.949694i	$-0.398606\pi$
$182$	247.892	+	1538.16i	0.100961	+	0.626460i
$183$	−4740.07	+	113.334i	−1.91473	+	0.0457809i
$184$	−1572.42			−0.630001
$185$	11.2639			0.00447642
$186$	−35.0127	−	1464.36i	−0.0138024	−	0.577270i
$187$		−	348.482i		−	0.136275i
$188$	−340.155			−0.131959
$189$	−2529.00	+	596.161i	−0.973323	+	0.229441i
$190$	808.458			0.308693
$191$			1782.19i			0.675158i	0.941297	+	0.337579i	$0.109608\pi$
$191$			1782.19i			0.675158i	−0.941297	+	0.337579i	$0.890392\pi$
$192$	−7.94904	−	332.459i	−0.00298788	−	0.124964i
$193$	−381.000			−0.142098			−0.0710492	−	0.997473i	$-0.522635\pi$
$193$	−381.000			−0.142098			−0.0710492	+	0.997473i	$0.522635\pi$
$194$	−642.769			−0.237877
$195$	−3576.87	+	85.5224i	−1.31356	+	0.0314071i
$196$	1302.53	−	431.032i	0.474685	−	0.157082i
$197$			4462.69i			1.61398i	0.590568	+	0.806988i	$0.298904\pi$
$197$			4462.69i			1.61398i	−0.590568	+	0.806988i	$0.701096\pi$
$198$	−593.321	+	28.3887i	−0.212957	+	0.0101894i
$199$		−	179.841i		−	0.0640632i	−0.999487	−	0.0320316i	$-0.989802\pi$
$199$		−	179.841i		−	0.0640632i	0.999487	−	0.0320316i	$-0.0101977\pi$
$200$			1143.87i			0.404419i
$201$	111.562	+	4665.95i	0.0391492	+	1.63737i
$202$			1495.73i			0.520987i
$203$	703.457	−	113.370i	0.243217	−	0.0391972i
$204$	15.7392	+	658.271i	0.00540177	+	0.225923i
$205$	−4087.75			−1.39269
$206$	−2748.88			−0.929727
$207$	−253.630	−	5300.85i	−0.0851618	−	1.77988i
$208$		−	672.994i		−	0.224345i
$209$	271.623			0.0898973
$210$	575.520	+	3097.74i	0.189117	+	1.01792i
$211$	3581.92			1.16867			0.584335	−	0.811512i	$-0.301355\pi$
$211$	3581.92			1.16867			0.584335	+	0.811512i	$0.301355\pi$
$212$		−	2350.42i		−	0.761450i
$213$	2995.63	−	71.6249i	0.963647	−	0.0230407i
$214$	−1285.15			−0.410518
$215$	−5926.18			−1.87983
$216$	1119.48	−	80.4227i	0.352645	−	0.0253337i
$217$	−2577.15	+	415.337i	−0.806214	+	0.129931i
$218$			1187.64i			0.368976i
$219$	−2882.76	+	68.9263i	−0.889492	+	0.0212676i
$220$			720.289i			0.220736i
$221$			1332.53i			0.405593i
$222$	−7.14862	+	0.170922i	−0.00216119	+	5.16737e-5i
$223$			1969.42i			0.591400i	0.955281	+	0.295700i	$0.0955529\pi$
$223$			1969.42i			0.591400i	−0.955281	+	0.295700i	$0.904447\pi$
$224$	−585.099	+	94.2953i	−0.174525	+	0.0281267i
$225$	−3856.15	+	184.505i	−1.14256	+	0.0546682i
$226$	−3500.95			−1.03044
$227$	2161.25			0.631925			0.315962	−	0.948772i	$-0.397673\pi$
$227$	2161.25			0.631925			0.315962	+	0.948772i	$0.397673\pi$
$228$	−513.087	+	12.2678i	−0.149035	+	0.00356341i
$229$			2253.26i			0.650215i	0.945677	+	0.325108i	$0.105401\pi$
$229$			2253.26i			0.650215i	−0.945677	+	0.325108i	$0.894599\pi$
$230$	−6435.20			−1.84489
$231$	193.361	+	1040.77i	0.0550745	+	0.296439i
$232$	−307.786			−0.0870997
$233$		−	4714.46i		−	1.32556i	−0.748816	−	0.662778i	$-0.769377\pi$
$233$		−	4714.46i		−	1.32556i	0.748816	−	0.662778i	$-0.230623\pi$
$234$	2268.76	−	108.553i	0.633818	−	0.0303263i
$235$	−1392.10			−0.386428
$236$	−907.692			−0.250363
$237$	26.5923	+	1112.19i	0.00728843	+	0.304830i
$238$	1158.50	−	186.706i	0.315523	−	0.0508501i
$239$			2593.70i			0.701976i	0.936380	+	0.350988i	$0.114154\pi$
$239$			2593.70i			0.701976i	−0.936380	+	0.350988i	$0.885846\pi$
$240$	−32.5318	−	1360.60i	−0.00874967	−	0.365944i
$241$			5913.35i			1.58055i	0.612752	+	0.790275i	$0.290062\pi$
$241$			5913.35i			1.58055i	−0.612752	+	0.790275i	$0.709938\pi$
$242$			242.000i			0.0642824i
$243$	451.688	+	3760.97i	0.119242	+	0.992865i
$244$		−	3649.95i		−	0.957639i
$245$	5330.69	−	1764.02i	1.39006	−	0.459996i
$246$	2594.28	−	62.0289i	0.672380	−	0.0160765i
$247$	−1038.64			−0.267559
$248$	1127.59			0.288718
$249$	−74.0264	−	3096.06i	−0.0188403	−	0.787972i
$250$			588.793i			0.148954i
$251$	−1645.32			−0.413751			−0.206876	−	0.978367i	$-0.566330\pi$
$251$	−1645.32			−0.413751			−0.206876	+	0.978367i	$0.566330\pi$
$252$	−412.259	−	1957.24i	−0.103055	−	0.489264i
$253$	−2162.08			−0.537267
$254$			3163.14i			0.781391i
$255$	64.4133	+	2694.01i	0.0158185	+	0.661590i
$256$	256.000			0.0625000
$257$	6514.61			1.58121			0.790603	−	0.612329i	$-0.209767\pi$
$257$	6514.61			1.58121			0.790603	+	0.612329i	$0.209767\pi$
$258$	3761.05	−	89.9260i	0.907568	−	0.0216998i
$259$	2.02756	+	12.5809i	0.000486435	+	0.00301831i
$260$		−	2754.26i		−	0.656970i
$261$	−49.6456	−	1037.59i	−0.0117739	−	0.246074i
$262$		−	1209.92i		−	0.285302i
$263$			2823.46i			0.661984i	0.943633	+	0.330992i	$0.107383\pi$
$263$			2823.46i			0.661984i	−0.943633	+	0.330992i	$0.892617\pi$
$264$	−10.9299	−	457.131i	−0.00254807	−	0.106570i
$265$		−	9619.21i		−	2.22982i
$266$	145.527	+	902.989i	0.0335445	+	0.208142i
$267$	160.531	+	6714.00i	0.0367952	+	1.53891i
$268$	−3592.88			−0.818918
$269$	−3556.49			−0.806109			−0.403054	−	0.915176i	$-0.632051\pi$
$269$	−3556.49			−0.806109			−0.403054	+	0.915176i	$0.632051\pi$
$270$	4581.55	−	329.134i	1.03268	−	0.0741869i
$271$		−	2668.56i		−	0.598169i	−0.954227	−	0.299084i	$-0.903319\pi$
$271$		−	2668.56i		−	0.598169i	0.954227	−	0.299084i	$-0.0966812\pi$
$272$	−506.882			−0.112994
$273$	−739.379	−	3979.71i	−0.163917	−	0.882282i
$274$	−8.35781			−0.00184275
$275$			1572.82i			0.344890i
$276$	4084.10	−	97.6501i	0.890702	−	0.0212965i
$277$	5791.72			1.25628			0.628142	−	0.778099i	$-0.283816\pi$
$277$	5791.72			1.25628			0.628142	+	0.778099i	$0.283816\pi$
$278$	3474.55			0.749604
$279$	181.879	+	3801.26i	0.0390280	+	0.815683i
$280$	−2394.55	+	385.909i	−0.511077	+	0.0823659i
$281$			8193.87i			1.73952i	0.493475	+	0.869760i	$0.335727\pi$
$281$			8193.87i			1.73952i	−0.493475	+	0.869760i	$0.664273\pi$
$282$	883.495	−	21.1242i	0.186565	−	0.00446074i
$283$			6898.16i			1.44895i	0.689300	+	0.724476i	$0.257918\pi$
$283$			6898.16i			1.44895i	−0.689300	+	0.724476i	$0.742082\pi$
$284$			2306.69i			0.481961i
$285$	−2099.84	+	50.2067i	−0.436433	+	0.0104351i
$286$		−	925.367i		−	0.191322i
$287$	−735.817	−	4565.72i	−0.151338	−	0.939044i
$288$	41.2926	+	863.013i	0.00844858	+	0.176575i
$289$	−3909.37			−0.795719
$290$	−1259.63			−0.255062
$291$	1669.49	−	39.9172i	0.336313	−	0.00804119i
$292$		−	2219.78i		−	0.444873i
$293$	5541.18			1.10484			0.552422	−	0.833565i	$-0.313704\pi$
$293$	5541.18			1.10484			0.552422	+	0.833565i	$0.313704\pi$
$294$	−3356.35	+	1200.42i	−0.665803	+	0.238130i
$295$	−3714.78			−0.733162
$296$		−	5.50458i		−	0.00108090i
$297$	1539.29	−	110.581i	0.300736	−	0.0216046i
$298$	−1859.85			−0.361537
$299$	8267.41			1.59905
$300$	−71.0364	−	2971.01i	−0.0136710	−	0.571771i
$301$	−1066.75	−	6619.12i	−0.204273	−	1.26751i
$302$		−	3588.02i		−	0.683666i
$303$	−92.8878	−	3884.92i	−0.0176114	−	0.736577i
$304$		−	395.087i		−	0.0745389i
$305$		−	14937.6i		−	2.80434i
$306$	−81.7597	−	1708.77i	−0.0152742	−	0.319229i
$307$		−	8349.12i		−	1.55215i	−0.630642	−	0.776074i	$-0.717208\pi$
$307$		−	8349.12i		−	1.55215i	0.630642	−	0.776074i	$-0.282792\pi$
$308$	−804.511	+	129.656i	−0.148835	+	0.0239865i
$309$	7139.76	−	170.711i	1.31446	−	0.0314284i
$310$	4614.72			0.845478
$311$	−4923.86			−0.897771			−0.448885	−	0.893589i	$-0.648179\pi$
$311$	−4923.86			−0.897771			−0.448885	+	0.893589i	$0.648179\pi$
$312$	41.7942	+	1747.99i	0.00758375	+	0.317181i
$313$			7958.52i			1.43720i	0.695426	+	0.718598i	$0.255216\pi$
$313$			7958.52i			1.43720i	−0.695426	+	0.718598i	$0.744784\pi$
$314$	−4252.56			−0.764287
$315$	−1687.19	−	8010.11i	−0.301786	−	1.43276i
$316$	−856.410			−0.152458
$317$			1466.80i			0.259885i	0.991522	+	0.129942i	$0.0414793\pi$
$317$			1466.80i			0.259885i	−0.991522	+	0.129942i	$0.958521\pi$
$318$	145.965	+	6104.82i	0.0257400	+	1.07654i
$319$	−423.206			−0.0742789
$320$	1047.69			0.183024
$321$	3337.96	−	79.8100i	0.580394	−	0.0138771i
$322$	−1158.37	−	7187.65i	−0.200477	−	1.24395i
$323$			782.277i			0.134759i
$324$	−2902.68	+	278.407i	−0.497716	+	0.0477378i
$325$		−	6014.20i		−	1.02649i
$326$		−	3326.36i		−	0.565122i
$327$	−73.7544	−	3084.69i	−0.0124729	−	0.521662i
$328$			1997.65i			0.336286i
$329$	−250.586	−	1554.88i	−0.0419916	−	0.260556i
$330$	−44.7313	−	1870.83i	−0.00746175	−	0.312078i
$331$	5039.30			0.836812			0.418406	−	0.908260i	$-0.362589\pi$
$331$	5039.30			0.836812			0.418406	+	0.908260i	$0.362589\pi$
$332$	2384.03			0.394099
$333$	18.5567	−	0.887885i	0.00305376	−	0.000146113i
$334$			5334.88i			0.873988i
$335$	−14704.0			−2.39811
$336$	1513.84	−	281.252i	0.245794	−	0.0456654i
$337$	2680.38			0.433263			0.216632	−	0.976253i	$-0.430493\pi$
$337$	2680.38			0.433263			0.216632	+	0.976253i	$0.430493\pi$
$338$		−	855.552i		−	0.137680i
$339$	9093.14	−	217.416i	1.45685	−	0.0348330i
$340$	−2074.44			−0.330889
$341$	1550.43			0.246219
$342$	1331.90	−	63.7273i	0.210587	−	0.0100760i
$343$	2929.84	+	5636.46i	0.461214	+	0.887289i
$344$			2896.08i			0.453914i
$345$	16714.4	−	399.638i	2.60832	−	0.0623646i
$346$			552.430i			0.0858348i
$347$		−	2.73501i		−	0.000423122i	−1.00000		0.000211561i	$-0.999933\pi$
$347$		−	2.73501i		−	0.000423122i	1.00000		0.000211561i	$-6.73419e-5\pi$
$348$	799.423	−	19.1141i	0.123142	−	0.00294431i
$349$		−	11882.3i		−	1.82248i	−0.411881	−	0.911238i	$-0.635128\pi$
$349$		−	11882.3i		−	1.82248i	0.411881	−	0.911238i	$-0.364872\pi$
$350$	−5228.72	+	842.668i	−0.798534	+	0.128693i
$351$	−5885.99	+	422.844i	−0.895073	+	0.0643012i
$352$	352.000			0.0533002
$353$	−3121.10			−0.470593			−0.235297	−	0.971924i	$-0.575606\pi$
$353$	−3121.10			−0.470593			−0.235297	+	0.971924i	$0.575606\pi$
$354$	2357.58	−	56.3694i	0.353966	−	0.00846327i
$355$			9440.26i			1.41137i
$356$	−5169.91			−0.769677
$357$	−2997.42	+	556.882i	−0.444370	+	0.0825583i
$358$	5215.92			0.770027
$359$			6036.25i			0.887413i	0.896172	+	0.443707i	$0.146337\pi$
$359$			6036.25i			0.887413i	−0.896172	+	0.443707i	$0.853663\pi$
$360$	168.992	+	3531.92i	0.0247407	+	0.517080i
$361$	6249.26			0.911103
$362$	−9250.43			−1.34307
$363$	−15.0286	−	628.555i	−0.00217300	−	0.0908831i
$364$	3076.31	−	495.783i	0.442974	−	0.0713904i
$365$		−	9084.57i		−	1.30276i
$366$	226.668	+	9480.13i	0.0323720	+	1.35392i
$367$			1149.16i			0.163448i	0.996655	+	0.0817240i	$0.0260426\pi$
$367$			1149.16i			0.163448i	−0.996655	+	0.0817240i	$0.973957\pi$
$368$			3144.84i			0.445478i
$369$	−6734.37	+	322.220i	−0.950074	+	0.0454582i
$370$		−	22.5278i		−	0.00316531i
$371$	10744.0	−	1731.51i	1.50350	−	0.242306i
$372$	−2928.72	+	70.0253i	−0.408192	+	0.00975980i
$373$	11123.7			1.54414			0.772068	−	0.635540i	$-0.219223\pi$
$373$	11123.7			1.54414			0.772068	+	0.635540i	$0.219223\pi$
$374$	−696.963			−0.0963612
$375$	−36.5651	−	1529.29i	−0.00503524	−	0.210593i
$376$			680.309i			0.0933092i
$377$	1618.27			0.221074
$378$	1192.32	+	5058.01i	0.162239	+	0.688243i
$379$	3299.81			0.447229			0.223615	−	0.974678i	$-0.428214\pi$
$379$	3299.81			0.447229			0.223615	+	0.974678i	$0.428214\pi$
$380$		−	1616.92i		−	0.218279i
$381$	−196.437	−	8215.74i	−0.0264141	−	1.10474i
$382$	3564.39			0.477409
$383$	−3164.70			−0.422215			−0.211108	−	0.977463i	$-0.567707\pi$
$383$	−3164.70			−0.422215			−0.211108	+	0.977463i	$0.567707\pi$
$384$	−664.917	+	15.8981i	−0.0883631	+	0.00211275i
$385$	−3292.50	+	530.624i	−0.435848	+	0.0702419i
$386$			762.000i			0.100479i
$387$	−9763.11	+	467.136i	−1.28239	+	0.0613588i
$388$			1285.54i			0.168205i
$389$		−	13938.1i		−	1.81669i	−0.418226	−	0.908343i	$-0.637348\pi$
$389$		−	13938.1i		−	1.81669i	0.418226	−	0.908343i	$-0.362652\pi$
$390$	171.045	+	7153.74i	0.0222082	+	0.928830i
$391$		−	6226.80i		−	0.805378i
$392$	−862.064	−	2605.07i	−0.111073	−	0.335653i
$393$	75.1383	+	3142.57i	0.00964434	+	0.403363i
$394$	8925.37			1.14125
$395$	−3504.90			−0.446458
$396$	56.7773	+	1186.64i	0.00720497	+	0.150583i
$397$		−	1554.13i		−	0.196473i	−0.995163	−	0.0982364i	$-0.968680\pi$
$397$		−	1554.13i		−	0.196473i	0.995163	−	0.0982364i	$-0.0313201\pi$
$398$	−359.682			−0.0452995
$399$	−434.059	−	2336.33i	−0.0544615	−	0.293139i
$400$	2287.74			0.285967
$401$		−	11581.1i		−	1.44223i	−0.692816	−	0.721114i	$-0.743630\pi$
$401$		−	11581.1i		−	1.44223i	0.692816	−	0.721114i	$-0.256370\pi$
$402$	9331.91	−	223.124i	1.15779	−	0.0276827i
$403$	−5928.60			−0.732815
$404$	2991.47			0.368394
$405$	−11879.4	+	1139.39i	−1.45751	+	0.139795i
$406$	−226.740	−	1406.91i	−0.0277166	−	0.171980i
$407$		−	7.56880i		−	0.000921797i
$408$	1316.54	−	31.4783i	0.159751	−	0.00381963i
$409$			13632.1i			1.64808i	0.566532	+	0.824040i	$0.308285\pi$
$409$			13632.1i			1.64808i	−0.566532	+	0.824040i	$0.691715\pi$
$410$			8175.49i			0.984778i
$411$	21.7080	−	0.519036i	0.00260530	−	6.22923e-5i
$412$			5497.76i			0.657416i
$413$	−668.681	−	4149.14i	−0.0796698	−	0.494348i
$414$	−10601.7	+	507.260i	−1.25856	+	0.0602185i
$415$	9756.77			1.15408
$416$	−1345.99			−0.158636
$417$	−9024.58	+	215.776i	−1.05980	+	0.0253396i
$418$		−	543.245i		−	0.0635670i
$419$	9173.45			1.06958			0.534788	−	0.844986i	$-0.320391\pi$
$419$	9173.45			1.06958			0.534788	+	0.844986i	$0.320391\pi$
$420$	6195.47	−	1151.04i	0.719781	−	0.133726i
$421$	9918.05			1.14816			0.574081	−	0.818799i	$-0.305360\pi$
$421$	9918.05			1.14816			0.574081	+	0.818799i	$0.305360\pi$
$422$		−	7163.84i		−	0.826375i
$423$	−2293.42	+	109.733i	−0.263617	+	0.0126133i
$424$	−4700.84			−0.538426
$425$	−4529.74			−0.516999
$426$	−143.250	−	5991.25i	−0.0162922	−	0.681401i
$427$	16684.2	−	2688.85i	1.89088	−	0.304737i
$428$			2570.29i			0.290280i
$429$	57.4670	+	2403.49i	0.00646744	+	0.270493i
$430$			11852.4i			1.32924i
$431$			2562.34i			0.286365i	0.989696	+	0.143183i	$0.0457336\pi$
$431$			2562.34i			0.286365i	−0.989696	+	0.143183i	$0.954266\pi$
$432$	−160.845	−	2238.97i	−0.0179136	−	0.249357i
$433$			12284.7i			1.36343i	0.731620	+	0.681713i	$0.238765\pi$
$433$			12284.7i			1.36343i	−0.731620	+	0.681713i	$0.761235\pi$
$434$	830.675	+	5154.30i	0.0918748	+	0.570079i
$435$	3271.68	−	78.2253i	0.360609	−	0.00862211i
$436$	2375.27			0.260906
$437$	4853.46			0.531287
$438$	137.853	+	5765.52i	0.0150385	+	0.628966i
$439$			11478.1i			1.24788i	0.781473	+	0.623939i	$0.214469\pi$
$439$			11478.1i			1.24788i	−0.781473	+	0.623939i	$0.785531\pi$
$440$	1440.58			0.156084
$441$	8643.01	−	3326.34i	0.933270	−	0.359177i
$442$	2665.07			0.286797
$443$			12101.8i			1.29791i	0.760826	+	0.648956i	$0.224794\pi$
$443$			12101.8i			1.29791i	−0.760826	+	0.648956i	$0.775206\pi$
$444$	0.341845	+	14.2972i	3.65388e−5	+	0.00152819i
$445$	−21158.1			−2.25391
$446$	3938.85			0.418183
$447$	4830.64	−	115.500i	0.511144	−	0.0122214i
$448$	188.591	+	1170.20i	0.0198886	+	0.123408i
$449$			7199.29i			0.756694i	0.925664	+	0.378347i	$0.123507\pi$
$449$			7199.29i			0.756694i	−0.925664	+	0.378347i	$0.876493\pi$
$450$	369.010	+	7712.29i	0.0386563	+	0.807913i
$451$			2746.77i			0.286786i
$452$			7001.91i			0.728633i
$453$	222.823	+	9319.28i	0.0231106	+	0.966574i
$454$		−	4322.49i		−	0.446838i
$455$	12590.0	−	2029.02i	1.29720	−	0.209059i
$456$	24.5357	+	1026.17i	0.00251971	+	0.105384i
$457$	−8641.08			−0.884491			−0.442246	−	0.896894i	$-0.645818\pi$
$457$	−8641.08			−0.884491			−0.442246	+	0.896894i	$0.645818\pi$
$458$	4506.51			0.459772
$459$	318.475	+	4433.18i	0.0323859	+	0.450812i
$460$			12870.4i			1.30453i
$461$	5655.54			0.571377			0.285688	−	0.958323i	$-0.407778\pi$
$461$	5655.54			0.571377			0.285688	+	0.958323i	$0.407778\pi$
$462$	2081.53	−	386.722i	0.209614	−	0.0389436i
$463$	−1955.07			−0.196242			−0.0981209	−	0.995175i	$-0.531283\pi$
$463$	−1955.07			−0.196242			−0.0981209	+	0.995175i	$0.531283\pi$
$464$			615.572i			0.0615888i
$465$	−11986.0	+	286.582i	−1.19534	+	0.0285805i
$466$	−9428.92			−0.937310
$467$	12888.9			1.27715			0.638573	−	0.769561i	$-0.279525\pi$
$467$	12888.9			1.27715			0.638573	+	0.769561i	$0.279525\pi$
$468$	−217.107	−	4537.52i	−0.0214440	−	0.448177i
$469$	−2646.81	−	16423.4i	−0.260594	−	1.61697i
$470$			2784.20i			0.273246i
$471$	11045.3	−	264.092i	1.08056	−	0.0258359i
$472$			1815.38i			0.177034i
$473$			3982.11i			0.387099i
$474$	2224.38	−	53.1847i	0.215547	−	0.00515370i
$475$		−	3530.69i		−	0.341051i
$476$	−373.411	−	2317.00i	−0.0359565	−	0.223108i
$477$	−758.241	−	15847.2i	−0.0727830	−	1.52116i
$478$	5187.39			0.496372
$479$	−3950.39			−0.376822			−0.188411	−	0.982090i	$-0.560334\pi$
$479$	−3950.39			−0.376822			−0.188411	+	0.982090i	$0.560334\pi$
$480$	−2721.21	+	65.0637i	−0.258762	+	0.00618695i
$481$			28.9418i			0.00274352i
$482$	11826.7			1.11762
$483$	3455.05	+	18596.8i	0.325487	+	1.75193i
$484$	484.000			0.0454545
$485$			5261.13i			0.492569i
$486$	7521.94	−	903.377i	0.702062	−	0.0843169i
$487$	12091.0			1.12504			0.562522	−	0.826782i	$-0.309831\pi$
$487$	12091.0			1.12504			0.562522	+	0.826782i	$0.309831\pi$
$488$	−7299.89			−0.677153
$489$	206.573	+	8639.66i	0.0191034	+	0.798975i
$490$	−3528.04	−	10661.4i	−0.325267	−	0.982922i
$491$		−	19011.8i		−	1.74743i	−0.486435	−	0.873717i	$-0.661703\pi$
$491$		−	19011.8i		−	1.74743i	0.486435	−	0.873717i	$-0.338297\pi$
$492$	−124.058	−	5188.57i	−0.0113678	−	0.475445i
$493$		−	1218.84i		−	0.111346i
$494$			2077.28i			0.189193i
$495$	232.364	+	4856.40i	0.0210990	+	0.440967i
$496$		−	2255.18i		−	0.204154i
$497$	−10544.1	+	1699.30i	−0.951643	+	0.153368i
$498$	−6192.13	+	148.053i	−0.557180	+	0.0133221i
$499$	−11158.6			−1.00106			−0.500528	−	0.865720i	$-0.666861\pi$
$499$	−11158.6			−1.00106			−0.500528	+	0.865720i	$0.666861\pi$
$500$	1177.59			0.105326
$501$	−331.306	−	13856.5i	−0.0295442	−	1.23565i
$502$			3290.64i			0.292566i
$503$	−2170.64			−0.192414			−0.0962070	−	0.995361i	$-0.530671\pi$
$503$	−2170.64			−0.192414			−0.0962070	+	0.995361i	$0.530671\pi$
$504$	−3914.48	+	824.518i	−0.345962	+	0.0728709i
$505$	12242.7			1.07880
$506$			4324.15i			0.379905i
$507$	53.1314	+	2222.16i	0.00465414	+	0.194654i
$508$	6326.29			0.552527
$509$	2641.20			0.229998			0.114999	−	0.993366i	$-0.463313\pi$
$509$	2641.20			0.229998			0.114999	+	0.993366i	$0.463313\pi$
$510$	5388.02	−	128.827i	0.467815	−	0.0111854i
$511$	10146.8	−	1635.27i	0.878412	−	0.141566i
$512$		−	512.000i		−	0.0441942i
$513$	−3455.42	+	248.234i	−0.297389	+	0.0213642i
$514$		−	13029.2i		−	1.11808i
$515$			22499.9i			1.92517i
$516$	−179.852	−	7522.09i	−0.0153441	−	0.641748i
$517$			935.425i			0.0795744i
$518$	25.1619	−	4.05513i	0.00213427	−	0.000343962i
$519$	−34.3069	−	1434.85i	−0.00290156	−	0.121354i
$520$	−5508.53			−0.464548
$521$	−20521.0			−1.72561			−0.862803	−	0.505541i	$-0.831293\pi$
$521$	−20521.0			−1.72561			−0.862803	+	0.505541i	$0.831293\pi$
$522$	−2075.18	+	99.2912i	−0.174000	+	0.00832540i
$523$			5703.34i			0.476844i	0.971162	+	0.238422i	$0.0766302\pi$
$523$			5703.34i			0.476844i	−0.971162	+	0.238422i	$0.923370\pi$
$524$	−2419.84			−0.201739
$525$	13528.4	−	2513.40i	1.12462	−	0.208941i
$526$	5646.92			0.468094
$527$			4465.27i			0.369090i
$528$	−914.262	+	21.8598i	−0.0753563	+	0.00180176i
$529$	−26465.8			−2.17521
$530$	−19238.4			−1.57672
$531$	−6119.92	+	292.820i	−0.500154	+	0.0239309i
$532$	1805.98	−	291.054i	0.147179	−	0.0237195i
$533$		−	10503.2i		−	0.853553i
$534$	13428.0	−	321.061i	1.08818	−	0.0260181i
$535$			10519.1i			0.850054i
$536$			7185.76i			0.579063i
$537$	−13547.5	+	323.918i	−1.08867	+	0.0260300i
$538$			7112.99i			0.570005i
$539$	−1185.34	−	3581.97i	−0.0947238	−	0.286246i
$540$	−658.268	−	9163.09i	−0.0524580	−	0.730216i
$541$	−5340.72			−0.424428			−0.212214	−	0.977223i	$-0.568067\pi$
$541$	−5340.72			−0.424428			−0.212214	+	0.977223i	$0.568067\pi$
$542$	−5337.13			−0.422969
$543$	24026.4	−	574.468i	1.89885	−	0.0454011i
$544$			1013.76i			0.0798985i
$545$	9720.92			0.764034
$546$	−7959.42	+	1478.76i	−0.623868	+	0.115907i
$547$	−12449.5			−0.973127			−0.486564	−	0.873645i	$-0.661750\pi$
$547$	−12449.5			−0.973127			−0.486564	+	0.873645i	$0.661750\pi$
$548$			16.7156i			0.00130302i
$549$	−1177.47	−	24609.0i	−0.0915357	−	1.91309i
$550$	3145.64			0.243874
$551$	950.018			0.0734521
$552$	−195.300	−	8168.19i	−0.0150589	−	0.629821i
$553$	−630.902	−	3914.72i	−0.0485148	−	0.301032i
$554$		−	11583.4i		−	0.888327i
$555$	1.39902	+	58.5122i	0.000107000	+	0.00447514i
$556$		−	6949.11i		−	0.530050i
$557$		−	7433.27i		−	0.565454i	−0.959200	−	0.282727i	$-0.908761\pi$
$557$		−	7433.27i		−	0.565454i	0.959200	−	0.282727i	$-0.0912391\pi$
$558$	7602.53	−	363.758i	0.576775	−	0.0275970i
$559$		−	15226.9i		−	1.15211i
$560$	771.817	+	4789.09i	0.0582415	+	0.361386i
$561$	1810.25	−	43.2827i	0.136236	−	0.00325739i
$562$	16387.7			1.23003
$563$	−184.243			−0.0137920			−0.00689600	−	0.999976i	$-0.502195\pi$
$563$	−184.243			−0.0137920			−0.00689600	+	0.999976i	$0.502195\pi$
$564$	−42.2485	−	1766.99i	−0.00315422	−	0.131921i
$565$			28655.7i			2.13372i
$566$	13796.3			1.02456
$567$	−3410.97	−	13063.3i	−0.252641	−	0.967560i
$568$	4613.38			0.340798
$569$		−	17738.5i		−	1.30692i	−0.756961	−	0.653460i	$-0.773317\pi$
$569$		−	17738.5i		−	1.30692i	0.756961	−	0.653460i	$-0.226683\pi$
$570$	100.413	+	4199.67i	0.00737870	+	0.308605i
$571$	−23331.1			−1.70994			−0.854970	−	0.518678i	$-0.826424\pi$
$571$	−23331.1			−1.70994			−0.854970	+	0.518678i	$0.826424\pi$
$572$	−1850.73			−0.135285
$573$	−9257.91	+	221.355i	−0.674965	+	0.0161383i
$574$	−9131.43	+	1471.63i	−0.664004	+	0.107012i
$575$			28103.8i			2.03827i
$576$	1726.03	−	82.5852i	0.124857	−	0.00597405i
$577$			14168.6i			1.02226i	0.859503	+	0.511131i	$0.170773\pi$
$577$			14168.6i			1.02226i	−0.859503	+	0.511131i	$0.829227\pi$
$578$			7818.74i			0.562659i
$579$	−47.3216	−	1979.17i	−0.00339658	−	0.142058i
$580$			2519.26i			0.180356i
$581$	1756.27	+	10897.6i	0.125409	+	0.778157i
$582$	−79.8343	−	3338.97i	−0.00568598	−	0.237809i
$583$	−6463.65			−0.459171
$584$	−4439.57			−0.314573
$585$	−888.521	−	18570.0i	−0.0627963	−	1.31244i
$586$		−	11082.4i		−	0.781243i
$587$	3199.22			0.224950			0.112475	−	0.993655i	$-0.464122\pi$
$587$	3199.22			0.224950			0.112475	+	0.993655i	$0.464122\pi$
$588$	2400.85	+	6712.70i	0.168383	+	0.470794i
$589$	−3480.44			−0.243479
$590$			7429.55i			0.518424i
$591$	−23182.2	+	554.282i	−1.61351	+	0.0385789i
$592$	−11.0092			−0.000764314
$593$	14795.7			1.02460			0.512298	−	0.858808i	$-0.328794\pi$
$593$	14795.7			1.02460			0.512298	+	0.858808i	$0.328794\pi$
$594$	−221.162	−	3078.58i	−0.0152768	−	0.212653i
$595$	−1528.20	−	9482.44i	−0.105295	−	0.653348i
$596$			3719.69i			0.255645i
$597$	934.214	−	22.3369i	0.0640449	−	0.00153130i
$598$		−	16534.8i		−	1.13070i
$599$			25047.7i			1.70855i	0.519821	+	0.854275i	$0.325999\pi$
$599$			25047.7i			1.70855i	−0.519821	+	0.854275i	$0.674001\pi$
$600$	−5942.02	+	142.073i	−0.404303	+	0.00966683i
$601$		−	3428.19i		−	0.232677i	−0.993210	−	0.116338i	$-0.962884\pi$
$601$		−	3428.19i		−	0.232677i	0.993210	−	0.116338i	$-0.0371157\pi$
$602$	−13238.2	+	2133.49i	−0.896263	+	0.144443i
$603$	−24224.2	+	1159.06i	−1.63596	+	0.0782761i
$604$	−7176.04			−0.483425
$605$	1980.79			0.133109
$606$	−7769.84	+	185.776i	−0.520838	+	0.0124532i
$607$			16088.3i			1.07579i	0.843012	+	0.537894i	$0.180780\pi$
$607$			16088.3i			1.07579i	−0.843012	+	0.537894i	$0.819220\pi$
$608$	−790.175			−0.0527069
$609$	676.292	+	3640.15i	0.0449996	+	0.242210i
$610$	−29875.2			−1.98297
$611$		−	3576.91i		−	0.236835i
$612$	−3417.55	+	163.519i	−0.225729	+	0.0108005i
$613$	5679.64			0.374223			0.187111	−	0.982339i	$-0.440087\pi$
$613$	5679.64			0.374223			0.187111	+	0.982339i	$0.440087\pi$
$614$	−16698.2			−1.09753
$615$	−507.713	−	21234.5i	−0.0332894	−	1.39229i
$616$	259.312	+	1609.02i	0.0169610	+	0.105242i
$617$		−	27081.3i		−	1.76702i	−0.468411	−	0.883511i	$-0.655173\pi$
$617$		−	27081.3i		−	1.76702i	0.468411	−	0.883511i	$-0.344827\pi$
$618$	−341.421	−	14279.5i	−0.0222233	−	0.929461i
$619$			829.852i			0.0538846i	0.999637	+	0.0269423i	$0.00857703\pi$
$619$			829.852i			0.0538846i	−0.999637	+	0.0269423i	$0.991423\pi$
$620$		−	9229.43i		−	0.597843i
$621$	27504.6	−	1975.91i	1.77733	−	0.127682i
$622$			9847.73i			0.634820i
$623$	−3808.58	−	23632.1i	−0.244924	−	1.51974i
$624$	3495.98	−	83.5884i	0.224281	−	0.00536252i
$625$	−13053.6			−0.835432
$626$	15917.0			1.01625
$627$	33.7365	+	1410.99i	0.00214882	+	0.0898716i
$628$			8505.13i			0.540432i
$629$	21.7982			0.00138180
$630$	−16020.2	+	3374.38i	−1.01311	+	0.213395i
$631$	6723.01			0.424150			0.212075	−	0.977253i	$-0.431978\pi$
$631$	6723.01			0.424150			0.212075	+	0.977253i	$0.431978\pi$
$632$			1712.82i			0.107804i
$633$	444.888	+	18606.9i	0.0279347	+	1.16834i
$634$	2933.59			0.183766
$635$	25890.7			1.61801
$636$	12209.6	−	291.931i	0.761232	−	0.0182009i
$637$	4532.53	+	13696.8i	0.281924	+	0.851945i
$638$			846.411i			0.0525231i
$639$	744.135	+	15552.4i	0.0460681	+	0.962821i
$640$		−	2095.39i		−	0.129418i
$641$			29604.2i			1.82417i	0.409996	+	0.912087i	$0.365530\pi$
$641$			29604.2i			1.82417i	−0.409996	+	0.912087i	$0.634470\pi$
$642$	−159.620	−	6675.91i	−0.00981262	−	0.410401i
$643$		−	22679.2i		−	1.39095i	−0.718552	−	0.695474i	$-0.755195\pi$
$643$		−	22679.2i		−	1.39095i	0.718552	−	0.695474i	$-0.244805\pi$
$644$	−14375.3	+	2316.75i	−0.879606	+	0.141759i
$645$	−736.054	−	30784.6i	−0.0449335	−	1.87929i
$646$	1564.55			0.0952887
$647$	23545.9			1.43074			0.715368	−	0.698748i	$-0.246259\pi$
$647$	23545.9			1.43074			0.715368	+	0.698748i	$0.246259\pi$
$648$	556.813	+	5805.36i	0.0337557	+	0.351938i
$649$			2496.15i			0.150975i
$650$	−12028.4			−0.725835
$651$	−2477.63	−	13335.9i	−0.149164	−	0.802878i
$652$	−6652.72			−0.399602
$653$		−	16958.6i		−	1.01629i	−0.861270	−	0.508147i	$-0.830331\pi$
$653$		−	16958.6i		−	1.01629i	0.861270	−	0.508147i	$-0.169669\pi$
$654$	−6169.38	+	147.509i	−0.368871	+	0.00881965i
$655$	−9903.33			−0.590771
$656$	3995.30			0.237790
$657$	−716.098	−	14966.4i	−0.0425231	−	0.888729i
$658$	−3109.75	+	501.172i	−0.184241	+	0.0296926i
$659$			12123.6i			0.716645i	0.933598	+	0.358323i	$0.116651\pi$
$659$			12123.6i			0.716645i	−0.933598	+	0.358323i	$0.883349\pi$
$660$	−3741.66	+	89.4626i	−0.220673	+	0.00527625i
$661$		−	12958.0i		−	0.762495i	−0.924473	−	0.381248i	$-0.875495\pi$
$661$		−	12958.0i		−	0.762495i	0.924473	−	0.381248i	$-0.124505\pi$
$662$		−	10078.6i		−	0.591716i
$663$	−6922.07	+	165.506i	−0.405477	+	0.00969488i
$664$		−	4768.06i		−	0.278670i
$665$	7391.06	−	1191.15i	0.430997	−	0.0694601i
$666$	−1.77577	−	37.1135i	−0.000103318	−	0.00215934i
$667$	−7562.00			−0.438983
$668$	10669.8			0.618003
$669$	−10230.5	+	244.610i	−0.591231	+	0.0141363i
$670$			29408.1i			1.69572i
$671$	−10037.4			−0.577478
$672$	−562.504	−	3027.68i	−0.0322903	−	0.173803i
$673$	30609.0			1.75318			0.876591	−	0.481236i	$-0.159812\pi$
$673$	30609.0			1.75318			0.876591	+	0.481236i	$0.159812\pi$
$674$		−	5360.77i		−	0.306364i
$675$	−1437.39	−	20008.5i	−0.0819633	−	1.14093i
$676$	−1711.10			−0.0973546
$677$	15821.2			0.898168			0.449084	−	0.893490i	$-0.351750\pi$
$677$	15821.2			0.898168			0.449084	+	0.893490i	$0.351750\pi$
$678$	−434.831	−	18186.3i	−0.0246307	−	1.03015i
$679$	−5876.31	+	947.034i	−0.332124	+	0.0535255i
$680$			4148.88i			0.233974i
$681$	268.435	+	11227.0i	0.0151049	+	0.631744i
$682$		−	3100.87i		−	0.174103i
$683$			4243.03i			0.237709i	0.992912	+	0.118854i	$0.0379222\pi$
$683$			4243.03i			0.237709i	−0.992912	+	0.118854i	$0.962078\pi$
$684$	−127.455	−	2663.79i	−0.00712478	−	0.148907i
$685$			68.4096i			0.00381576i
$686$	11272.9	−	5859.67i	0.627408	−	0.326127i
$687$	−11704.9	+	279.863i	−0.650029	+	0.0155421i
$688$	5792.17			0.320965
$689$	24715.9			1.36662
$690$	−799.276	−	33428.7i	−0.0440984	−	1.84436i
$691$			957.649i			0.0527217i	0.999652	+	0.0263608i	$0.00839188\pi$
$691$			957.649i			0.0527217i	−0.999652	+	0.0263608i	$0.991608\pi$
$692$	1104.86			0.0606943
$693$	−5382.41	+	1133.71i	−0.295038	+	0.0621446i
$694$	−5.47003			−0.000299192
$695$		−	28439.6i		−	1.55219i
$696$	−38.2281	−	1598.85i	−0.00208194	−	0.0870748i
$697$	−7910.73			−0.429900
$698$	−23764.6			−1.28868
$699$	24490.1	−	585.553i	1.32518	−	0.0316848i
$700$	1685.34	+	10457.4i	0.0909996	+	0.564649i
$701$		−	3926.15i		−	0.211539i	−0.994391	−	0.105769i	$-0.966269\pi$
$701$		−	3926.15i		−	0.211539i	0.994391	−	0.105769i	$-0.0337305\pi$
$702$	845.688	+	11772.0i	0.0454678	+	0.632912i
$703$			16.9906i			0.000911537i
$704$		−	704.000i		−	0.0376889i
$705$	−172.904	−	7231.50i	−0.00923680	−	0.386318i
$706$			6242.20i			0.332760i
$707$	2203.76	+	13674.2i	0.117229	+	0.727402i
$708$	−112.739	−	4715.16i	−0.00598444	−	0.250292i
$709$	3398.60			0.180024			0.0900121	−	0.995941i	$-0.471309\pi$
$709$	3398.60			0.180024			0.0900121	+	0.995941i	$0.471309\pi$
$710$	18880.5			0.997990
$711$	−5774.16	+	276.277i	−0.304568	+	0.0145727i
$712$			10339.8i			0.544243i
$713$	27703.8			1.45514
$714$	1113.76	+	5994.83i	0.0583775	+	0.314217i
$715$	−7574.23			−0.396168
$716$		−	10431.8i		−	0.544492i
$717$	−13473.4	+	322.147i	−0.701776	+	0.0167793i
$718$	12072.5			0.627496
$719$	1367.58			0.0709347			0.0354674	−	0.999371i	$-0.488708\pi$
$719$	1367.58			0.0709347			0.0354674	+	0.999371i	$0.488708\pi$
$720$	7063.85	−	337.984i	0.365631	−	0.0174943i
$721$	−25130.7	+	4050.11i	−1.29808	+	0.209201i
$722$		−	12498.5i		−	0.644247i
$723$	−30717.9	+	734.460i	−1.58010	+	0.0377799i
$724$			18500.9i			0.949694i
$725$			5501.04i			0.281798i
$726$	−1257.11	+	30.0573i	−0.0642641	+	0.00153654i
$727$			10111.7i			0.515851i	0.966165	+	0.257925i	$0.0830389\pi$
$727$			10111.7i			0.515851i	−0.966165	+	0.257925i	$0.916961\pi$
$728$	−991.566	−	6152.63i	−0.0504806	−	0.313230i
$729$	−19480.9	+	2813.50i	−0.989731	+	0.142940i
$730$	−18169.1			−0.921192
$731$	−11468.5			−0.580272
$732$	18960.3	−	453.337i	0.957365	−	0.0228905i
$733$			14734.6i			0.742474i	0.928538	+	0.371237i	$0.121066\pi$
$733$			14734.6i			0.742474i	−0.928538	+	0.371237i	$0.878934\pi$
$734$	2298.31			0.115575
$735$	9825.59	+	27472.1i	0.493092	+	1.37867i
$736$	6289.67			0.315001
$737$			9880.42i			0.493826i
$738$	644.439	+	13468.7i	0.0321438	+	0.671804i
$739$	30536.3			1.52002			0.760010	−	0.649911i	$-0.225194\pi$
$739$	30536.3			1.52002			0.760010	+	0.649911i	$0.225194\pi$
$740$	−45.0556			−0.00223821
$741$	−129.003	−	5395.38i	−0.00639546	−	0.267482i
$742$	−3463.02	−	21487.9i	−0.171336	−	1.06313i
$743$			11599.9i			0.572757i	0.958117	+	0.286378i	$0.0924515\pi$
$743$			11599.9i			0.572757i	−0.958117	+	0.286378i	$0.907549\pi$
$744$	140.051	+	5857.45i	0.00690122	+	0.288635i
$745$			15223.0i			0.748629i
$746$		−	22247.4i		−	1.09187i
$747$	16073.8	−	769.085i	0.787297	−	0.0376698i
$748$			1393.93i			0.0681377i
$749$	−11749.0	+	1893.49i	−0.573164	+	0.0923720i
$750$	−3058.58	+	73.1302i	−0.148911	+	0.00356045i
$751$	−27449.7			−1.33376			−0.666881	−	0.745164i	$-0.732371\pi$
$751$	−27449.7			−1.33376			−0.666881	+	0.745164i	$0.732371\pi$
$752$	1360.62			0.0659796
$753$	−204.355	−	8546.88i	−0.00988990	−	0.413633i
$754$		−	3236.53i		−	0.156323i
$755$	−29368.3			−1.41566
$756$	10116.0	−	2384.65i	0.486661	−	0.114721i
$757$	14645.9			0.703192			0.351596	−	0.936152i	$-0.385639\pi$
$757$	14645.9			0.703192			0.351596	+	0.936152i	$0.385639\pi$
$758$		−	6599.62i		−	0.316239i
$759$	−268.538	−	11231.3i	−0.0128423	−	0.537113i
$760$	−3233.83			−0.154347
$761$	−18805.8			−0.895810			−0.447905	−	0.894081i	$-0.647830\pi$
$761$	−18805.8			−0.895810			−0.447905	+	0.894081i	$0.647830\pi$
$762$	−16431.5	+	392.874i	−0.781168	+	0.0186776i
$763$	1749.82	+	10857.6i	0.0830246	+	0.515164i
$764$		−	7128.78i		−	0.337579i
$765$	−13986.5	+	669.212i	−0.661023	+	0.0316280i
$766$			6329.39i			0.298551i
$767$		−	9544.87i		−	0.449342i
$768$	31.7961	+	1329.83i	0.00149394	+	0.0624821i
$769$			2659.13i			0.124695i	0.998054	+	0.0623477i	$0.0198588\pi$
$769$			2659.13i			0.124695i	−0.998054	+	0.0623477i	$0.980141\pi$
$770$	1061.25	+	6585.00i	0.0496685	+	0.308191i
$771$	809.138	+	33841.2i	0.0377956	+	1.58075i
$772$	1524.00			0.0710492
$773$	−39680.4			−1.84632			−0.923160	−	0.384416i	$-0.874403\pi$
$773$	−39680.4			−1.84632			−0.923160	+	0.384416i	$0.874403\pi$
$774$	934.272	+	19526.2i	0.0433872	+	0.906790i
$775$		−	20153.3i		−	0.934103i
$776$	2571.08			0.118939
$777$	−65.1020	+	12.0951i	−0.00300582	+	0.000558443i
$778$	−27876.2			−1.28459
$779$		−	6165.99i		−	0.283594i
$780$	14307.5	−	342.090i	0.656782	−	0.0157036i
$781$	6343.40			0.290634
$782$	−12453.6			−0.569489
$783$	5383.77	−	386.765i	0.245722	−	0.0176524i
$784$	−5210.14	+	1724.13i	−0.237342	+	0.0785408i
$785$			34807.7i			1.58260i
$786$	6285.14	−	150.277i	0.285221	−	0.00681958i
$787$			33967.4i			1.53851i	0.638943	+	0.769254i	$0.279372\pi$
$787$			33967.4i			1.53851i	−0.638943	+	0.769254i	$0.720628\pi$
$788$		−	17850.7i		−	0.806988i
$789$	−14666.9	+	350.684i	−0.661795	+	0.0158234i
$790$			7009.81i			0.315693i
$791$	−32006.3	+	5158.18i	−1.43870	+	0.231863i
$792$	2373.28	−	113.555i	0.106479	−	0.00509468i
$793$	38381.1			1.71873
$794$	−3108.27			−0.138927
$795$	49968.6	−	1194.74i	2.22919	−	0.0532995i
$796$			719.364i			0.0320316i
$797$	26774.3			1.18996			0.594978	−	0.803742i	$-0.297161\pi$
$797$	26774.3			1.18996			0.594978	+	0.803742i	$0.297161\pi$
$798$	−4672.65	+	868.119i	−0.207281	+	0.0385101i
$799$	−2694.04			−0.119284
$800$		−	4575.48i		−	0.202209i
$801$	−34857.0	+	1667.81i	−1.53759	+	0.0735693i
$802$	−23162.3			−1.01981
$803$	−6104.40			−0.268269
$804$	−446.249	−	18663.8i	−0.0195746	−	0.818684i
$805$	−58831.7	+	9481.40i	−2.57583	+	0.415125i
$806$			11857.2i			0.518179i
$807$	−441.730	−	18474.8i	−0.0192684	−	0.805878i
$808$		−	5982.93i		−	0.260494i
$809$			7419.75i			0.322453i	0.986917	+	0.161226i	$0.0515450\pi$
$809$			7419.75i			0.322453i	−0.986917	+	0.161226i	$0.948455\pi$
$810$	2278.79	+	23758.7i	0.0988499	+	1.03061i
$811$			28899.8i			1.25131i	0.780102	+	0.625653i	$0.215167\pi$
$811$			28899.8i			1.25131i	−0.780102	+	0.625653i	$0.784833\pi$
$812$	−2813.83	+	453.481i	−0.121608	+	0.0195986i
$813$	13862.3	−	331.445i	0.597998	−	0.0142980i
$814$	−15.1376			−0.000651809
$815$	−27226.6			−1.17019
$816$	−62.9566	−	2633.08i	−0.00270089	−	0.112961i
$817$		−	8939.11i		−	0.382790i
$818$	27264.2			1.16537
$819$	20581.4	−	4335.12i	0.878112	−	0.184959i
$820$	16351.0			0.696343
$821$		−	8215.36i		−	0.349230i	−0.984637	−	0.174615i	$-0.944132\pi$
$821$		−	8215.36i		−	0.349230i	0.984637	−	0.174615i	$-0.0558681\pi$
$822$	−1.03807	−	43.4161i	−4.40473e−5	−	0.00184223i
$823$	−39922.7			−1.69091			−0.845455	−	0.534047i	$-0.820671\pi$
$823$	−39922.7			−1.69091			−0.845455	+	0.534047i	$0.820671\pi$
$824$	10995.5			0.464863
$825$	−8170.28	+	195.350i	−0.344791	+	0.00824390i
$826$	−8298.27	+	1337.36i	−0.349557	+	0.0563351i
$827$		−	16669.0i		−	0.700892i	−0.936583	−	0.350446i	$-0.886030\pi$
$827$		−	16669.0i		−	0.700892i	0.936583	−	0.350446i	$-0.113970\pi$
$828$	1014.52	+	21203.4i	0.0425809	+	0.889938i
$829$		−	7749.25i		−	0.324659i	−0.986737	−	0.162330i	$-0.948099\pi$
$829$		−	7749.25i		−	0.324659i	0.986737	−	0.162330i	$-0.0519008\pi$
$830$		−	19513.5i		−	0.816054i
$831$	719.353	+	30086.1i	0.0300290	+	1.25593i
$832$			2691.98i			0.112172i
$833$	10316.1	−	3413.79i	0.429090	−	0.141994i
$834$	431.552	+	18049.2i	0.0179178	+	0.749390i
$835$	43666.6			1.80975
$836$	−1086.49			−0.0449486
$837$	−19723.7	+	1416.93i	−0.814518	+	0.0585142i
$838$		−	18346.9i		−	0.756305i
$839$	17801.1			0.732494			0.366247	−	0.930518i	$-0.380643\pi$
$839$	17801.1			0.732494			0.366247	+	0.930518i	$0.380643\pi$
$840$	−2302.08	−	12390.9i	−0.0945586	−	0.508962i
$841$	22908.8			0.939309
$842$		−	19836.1i		−	0.811873i
$843$	−42564.4	+	1017.71i	−1.73902	+	0.0415798i
$844$	−14327.7			−0.584335
$845$	−7002.79			−0.285092
$846$	219.467	+	4586.84i	0.00891894	+	0.186405i
$847$	356.554	+	2212.40i	0.0144644	+	0.0897510i
$848$			9401.67i			0.380725i
$849$	−35833.7	+	856.777i	−1.44854	+	0.0346343i
$850$			9059.48i			0.365574i
$851$		−	135.242i		−	0.00544776i
$852$	−11982.5	+	286.500i	−0.481824	+	0.0115203i
$853$			21670.5i			0.869852i	0.900466	+	0.434926i	$0.143225\pi$
$853$			21670.5i			0.869852i	−0.900466	+	0.434926i	$0.856775\pi$
$854$	−5377.70	−	33368.4i	−0.215482	−	1.33705i
$855$	−521.615	−	10901.7i	−0.0208641	−	0.436059i
$856$	5140.59			0.205259
$857$	−31217.5			−1.24431			−0.622153	−	0.782896i	$-0.713742\pi$
$857$	−31217.5			−1.24431			−0.622153	+	0.782896i	$0.713742\pi$
$858$	4806.97	−	114.934i	0.191267	−	0.00457317i
$859$			8272.15i			0.328570i	0.986413	+	0.164285i	$0.0525317\pi$
$859$			8272.15i			0.328570i	−0.986413	+	0.164285i	$0.947468\pi$
$860$	23704.7			0.939913
$861$	23626.0	−	4389.41i	0.935158	−	0.173740i
$862$	5124.67			0.202491
$863$			6061.63i			0.239097i	0.992828	+	0.119548i	$0.0381446\pi$
$863$			6061.63i			0.239097i	−0.992828	+	0.119548i	$0.961855\pi$
$864$	−4477.94	+	321.691i	−0.176322	+	0.0126668i
$865$	4521.70			0.177737
$866$	24569.3			0.964088
$867$	−485.558	−	20307.9i	−0.0190201	−	0.795492i
$868$	10308.6	−	1661.35i	0.403107	−	0.0649653i
$869$			2355.13i			0.0919359i
$870$	−156.451	−	6543.36i	−0.00609675	−	0.254989i
$871$		−	37781.1i		−	1.46976i
$872$		−	4750.54i		−	0.184488i
$873$	414.713	+	8667.47i	0.0160778	+	0.336025i
$874$		−	9706.92i		−	0.375677i
$875$	867.506	+	5382.84i	0.0335166	+	0.207969i
$876$	11531.0	−	275.705i	0.444746	−	0.0106338i
$877$	32258.6			1.24207			0.621036	−	0.783782i	$-0.286712\pi$
$877$	32258.6			1.24207			0.621036	+	0.783782i	$0.286712\pi$
$878$	22956.1			0.882383
$879$	688.235	+	28784.6i	0.0264091	+	1.10453i
$880$		−	2881.16i		−	0.110368i
$881$	−13631.7			−0.521299			−0.260649	−	0.965434i	$-0.583937\pi$
$881$	−13631.7			−0.521299			−0.260649	+	0.965434i	$0.583937\pi$
$882$	−6652.67	−	17286.0i	−0.253976	−	0.659921i
$883$	33248.1			1.26714			0.633571	−	0.773685i	$-0.281588\pi$
$883$	33248.1			1.26714			0.633571	+	0.773685i	$0.281588\pi$
$884$		−	5330.14i		−	0.202796i
$885$	−461.389	−	19297.0i	−0.0175248	−	0.732952i
$886$	24203.6			0.917762
$887$	−26749.2			−1.01257			−0.506285	−	0.862366i	$-0.668982\pi$
$887$	−26749.2			−1.01257			−0.506285	+	0.862366i	$0.668982\pi$
$888$	28.5945	−	0.683689i	0.00108059	−	2.58368e-5i
$889$	4660.46	+	28918.0i	0.175823	+	1.09098i
$890$			42316.3i			1.59376i
$891$	765.618	+	7982.37i	0.0287869	+	0.300134i
$892$		−	7877.69i		−	0.295700i
$893$		−	2099.86i		−	0.0786887i
$894$	−231.000	−	9661.28i	−0.00864182	−	0.361433i
$895$		−	42692.8i		−	1.59448i
$896$	2340.39	−	377.181i	0.0872624	−	0.0140633i
$897$	1026.84	+	42946.4i	0.0382222	+	1.59860i
$898$	14398.6			0.535064
$899$	5422.75			0.201178
$900$	15424.6	−	738.021i	0.571281	−	0.0273341i
$901$		−	18615.4i		−	0.688311i
$902$	5493.54			0.202788
$903$	34251.6	−	6363.51i	1.26226	−	0.234512i
$904$	14003.8			0.515221
$905$			75715.7i			2.78108i
$906$	18638.6	−	445.645i	0.683471	−	0.0163417i
$907$	43808.5			1.60379			0.801895	−	0.597465i	$-0.203825\pi$
$907$	43808.5			1.60379			0.801895	+	0.597465i	$0.203825\pi$
$908$	−8644.99			−0.315962
$909$	20169.3	−	965.043i	0.735945	−	0.0352128i
$910$	−4058.04	−	25179.9i	−0.147827	−	0.917260i
$911$			25508.8i			0.927711i	0.885911	+	0.463855i	$0.153534\pi$
$911$			25508.8i			0.927711i	−0.885911	+	0.463855i	$0.846466\pi$
$912$	2052.35	−	49.0713i	0.0745176	−	0.00178170i
$913$		−	6556.09i		−	0.237650i
$914$			17282.2i			0.625430i
$915$	77595.9	−	1855.30i	2.80354	−	0.0670322i
$916$		−	9013.02i		−	0.325108i
$917$	−1782.65	−	11061.3i	−0.0641968	−	0.398338i
$918$	8866.35	−	636.950i	0.318773	−	0.0229003i
$919$	−22395.1			−0.803859			−0.401930	−	0.915671i	$-0.631660\pi$
$919$	−22395.1			−0.803859			−0.401930	+	0.915671i	$0.631660\pi$
$920$	25740.8			0.922445
$921$	43370.9	−	1036.99i	1.55170	−	0.0371010i
$922$		−	11311.1i		−	0.404024i
$923$	−24256.1			−0.865005
$924$	−773.444	−	4163.06i	−0.0275373	−	0.148219i
$925$	−98.3831			−0.00349710
$926$			3910.15i			0.138764i
$927$	1773.57	+	37067.5i	0.0628389	+	1.31333i
$928$	1231.14			0.0435498
$929$	40004.2			1.41280			0.706402	−	0.707810i	$-0.250317\pi$
$929$	40004.2			1.41280			0.706402	+	0.707810i	$0.250317\pi$
$930$	573.165	+	23971.9i	0.0202095	+	0.845237i
$931$	2660.86	+	8040.86i	0.0936695	+	0.283060i
$932$			18857.8i			0.662778i
$933$	−611.562	−	25577.8i	−0.0214594	−	0.897514i
$934$		−	25777.8i		−	0.903079i
$935$			5704.71i			0.199534i
$936$	−9075.04	+	434.214i	−0.316909	+	0.0151632i
$937$		−	42458.7i		−	1.48033i	−0.672428	−	0.740163i	$-0.734748\pi$
$937$		−	42458.7i		−	1.48033i	0.672428	−	0.740163i	$-0.265252\pi$
$938$	−32846.7	+	5293.62i	−1.14337	+	0.184267i
$939$	−41341.9	+	988.477i	−1.43678	+	0.0343533i
$940$	5568.40			0.193214
$941$	20559.8			0.712254			0.356127	−	0.934438i	$-0.384097\pi$
$941$	20559.8			0.712254			0.356127	+	0.934438i	$0.384097\pi$
$942$	−528.184	−	22090.7i	−0.0182688	−	0.764068i
$943$			49080.4i			1.69489i
$944$	3630.77			0.125182
$945$	41400.3	−	9759.29i	1.42513	−	0.335947i
$946$	7964.23			0.273720
$947$		−	19636.2i		−	0.673803i	−0.941540	−	0.336902i	$-0.890621\pi$
$947$		−	19636.2i		−	0.673803i	0.941540	−	0.336902i	$-0.109379\pi$
$948$	−106.369	−	4448.77i	−0.00364421	−	0.152415i
$949$	23342.2			0.798440
$950$	−7061.38			−0.241159
$951$	−7619.52	+	182.182i	−0.259811	+	0.00621203i
$952$	−4634.00	+	746.822i	−0.157761	+	0.0254251i
$953$		−	29334.8i		−	0.997113i	−0.866857	−	0.498556i	$-0.833864\pi$
$953$		−	29334.8i		−	0.997113i	0.866857	−	0.498556i	$-0.166136\pi$
$954$	−31694.4	+	1516.48i	−1.07562	+	0.0514653i
$955$		−	29174.9i		−	0.988563i
$956$		−	10374.8i		−	0.350988i
$957$	−52.5637	−	2198.41i	−0.00177549	−	0.0742576i
$958$			7900.77i			0.266453i
$959$	−76.4085	+	12.3141i	−0.00257285	+	0.000414644i
$960$	130.127	+	5442.42i	0.00437484	+	0.182972i
$961$	9924.49			0.333137
$962$	57.8836			0.00193996
$963$	829.173	+	17329.7i	0.0277463	+	0.579897i
$964$		−	23653.4i		−	0.790275i
$965$	6237.05			0.208060
$966$	37193.6	−	6910.09i	1.23880	−	0.230154i
$967$	−24966.8			−0.830279			−0.415139	−	0.909758i	$-0.636267\pi$
$967$	−24966.8			−0.830279			−0.415139	+	0.909758i	$0.636267\pi$
$968$		−	968.000i		−	0.0321412i
$969$	−4063.67	+	97.1616i	−0.134720	+	0.00322114i
$970$	10522.3			0.348299
$971$	−15816.9			−0.522749			−0.261374	−	0.965237i	$-0.584176\pi$
$971$	−15816.9			−0.522749			−0.261374	+	0.965237i	$0.584176\pi$
$972$	−1806.75	−	15043.9i	−0.0596210	−	0.496433i
$973$	31764.9	−	5119.29i	1.04660	−	0.168671i
$974$		−	24182.1i		−	0.795527i
$975$	31241.8	−	746.986i	1.02619	−	0.0245361i
$976$			14599.8i			0.478820i
$977$		−	21168.2i		−	0.693173i	−0.938018	−	0.346587i	$-0.887341\pi$
$977$		−	21168.2i		−	0.693173i	0.938018	−	0.346587i	$-0.112659\pi$
$978$	17279.3	−	413.146i	0.564961	−	0.0135081i
$979$			14217.3i			0.464132i
$980$	−21322.8	+	7056.08i	−0.695031	+	0.229998i
$981$	16014.8	−	766.259i	0.521215	−	0.0249386i
$982$	−38023.6			−1.23562
$983$	−11920.1			−0.386766			−0.193383	−	0.981123i	$-0.561946\pi$
$983$	−11920.1			−0.386766			−0.193383	+	0.981123i	$0.561946\pi$
$984$	−10377.1	+	248.116i	−0.336190	+	0.00803825i
$985$		−	73055.1i		−	2.36318i
$986$	−2437.67			−0.0787336
$987$	8045.94	−	1494.83i	0.259478	−	0.0482077i
$988$	4154.56			0.133779
$989$			71154.0i			2.28773i
$990$	9712.79	−	464.728i	0.311811	−	0.0149192i
$991$	−56538.7			−1.81232			−0.906162	−	0.422931i	$-0.861001\pi$
$991$	−56538.7			−1.81232			−0.906162	+	0.422931i	$0.861001\pi$
$992$	−4510.36			−0.144359
$993$	625.900	+	26177.5i	0.0200023	+	0.836573i
$994$	3398.60	+	21088.2i	0.108448	+	0.672913i
$995$			2944.03i			0.0938011i
$996$	296.106	+	12384.3i	0.00942014	+	0.393986i
$997$			23593.7i			0.749469i	0.927132	+	0.374734i	$0.122266\pi$
$997$			23593.7i			0.749469i	−0.927132	+	0.374734i	$0.877734\pi$
$998$			22317.2i			0.707854i
$999$	6.91708	+	96.2858i	0.000219066	+	0.00304940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.4.g.b.419.10	yes	36
3.2	odd	2	inner	462.4.g.b.419.11	yes	36
7.6	odd	2	inner	462.4.g.b.419.9	✓	36
21.20	even	2	inner	462.4.g.b.419.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.4.g.b.419.9	✓	36	7.6	odd	2	inner
462.4.g.b.419.10	yes	36	1.1	even	1	trivial
462.4.g.b.419.11	yes	36	3.2	odd	2	inner
462.4.g.b.419.12	yes	36	21.20	even	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	462.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(0.124204 + 5.19467i) q^{3} -4.00000 q^{4} -16.3702 q^{5} +(10.3893 - 0.248407i) q^{6} +(-2.94673 - 18.2843i) q^{7} +8.00000i q^{8} +(-26.9691 + 1.29039i) q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +(0.124204 + 5.19467i) q^{3} -4.00000 q^{4} -16.3702 q^{5} +(10.3893 - 0.248407i) q^{6} +(-2.94673 - 18.2843i) q^{7} +8.00000i q^{8} +(-26.9691 + 1.29039i) q^{9} +32.7404i q^{10} +11.0000i q^{11} +(-0.496815 - 20.7787i) q^{12} -42.0621i q^{13} +(-36.5687 + 5.89346i) q^{14} +(-2.03324 - 85.0378i) q^{15} +16.0000 q^{16} -31.6801 q^{17} +(2.58079 + 53.9383i) q^{18} -24.6930i q^{19} +65.4808 q^{20} +(94.6150 - 17.5783i) q^{21} +22.0000 q^{22} +196.552i q^{23} +(-41.5573 + 0.993630i) q^{24} +142.984 q^{25} -84.1243 q^{26} +(-10.0528 - 139.935i) q^{27} +(11.7869 + 73.1373i) q^{28} +38.4732i q^{29} +(-170.076 + 4.06648i) q^{30} -140.949i q^{31} -32.0000i q^{32} +(-57.1413 + 1.36624i) q^{33} +63.3603i q^{34} +(48.2386 + 299.318i) q^{35} +(107.877 - 5.16158i) q^{36} -0.688073 q^{37} -49.3859 q^{38} +(218.499 - 5.22427i) q^{39} -130.962i q^{40} +249.706 q^{41} +(-35.1565 - 189.230i) q^{42} +362.010 q^{43} -44.0000i q^{44} +(441.491 - 21.1240i) q^{45} +393.105 q^{46} +85.0387 q^{47} +(1.98726 + 83.1147i) q^{48} +(-325.634 + 107.758i) q^{49} -285.967i q^{50} +(-3.93479 - 164.568i) q^{51} +168.249i q^{52} +587.604i q^{53} +(-279.871 + 20.1057i) q^{54} -180.072i q^{55} +(146.275 - 23.5738i) q^{56} +(128.272 - 3.06696i) q^{57} +76.9465 q^{58} +226.923 q^{59} +(8.13296 + 340.151i) q^{60} +912.487i q^{61} -281.897 q^{62} +(103.065 + 489.310i) q^{63} -64.0000 q^{64} +688.566i q^{65} +(2.73248 + 114.283i) q^{66} +898.220 q^{67} +126.721 q^{68} +(-1021.02 + 24.4125i) q^{69} +(598.637 - 96.4771i) q^{70} -576.673i q^{71} +(-10.3232 - 215.753i) q^{72} +554.946i q^{73} +1.37615i q^{74} +(17.7591 + 742.753i) q^{75} +98.7719i q^{76} +(201.128 - 32.4140i) q^{77} +(-10.4485 - 436.998i) q^{78} +214.103 q^{79} -261.923 q^{80} +(725.670 - 69.6016i) q^{81} -499.413i q^{82} -596.008 q^{83} +(-378.460 + 70.3130i) q^{84} +518.610 q^{85} -724.021i q^{86} +(-199.856 + 4.77852i) q^{87} -88.0000 q^{88} +1292.48 q^{89} +(-42.2480 - 882.981i) q^{90} +(-769.078 + 123.946i) q^{91} -786.209i q^{92} +(732.181 - 17.5063i) q^{93} -170.077i q^{94} +404.229i q^{95} +(166.229 - 3.97452i) q^{96} -321.385i q^{97} +(215.516 + 651.267i) q^{98} +(-14.1943 - 296.661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 144 q^{4} - 36 q^{7} - 132 q^{9}+O(q^{10}) \) 36 * q - 144 * q^4 - 36 * q^7 - 132 * q^9	\( 36 q - 144 q^{4} - 36 q^{7} - 132 q^{9} - 468 q^{15} + 576 q^{16} + 8 q^{18} + 14 q^{21} + 792 q^{22} + 552 q^{25} + 144 q^{28} - 184 q^{30} + 528 q^{36} - 108 q^{37} - 708 q^{39} + 260 q^{42} + 2688 q^{43} - 912 q^{46} - 2796 q^{49} + 1544 q^{51} - 1784 q^{57} - 1128 q^{58} + 1872 q^{60} + 1030 q^{63} - 2304 q^{64} + 2196 q^{67} - 2544 q^{70} - 32 q^{72} - 384 q^{78} - 4488 q^{79} - 2176 q^{81} - 56 q^{84} + 8328 q^{85} - 3168 q^{88} - 5580 q^{91} + 2956 q^{93} - 44 q^{99}+O(q^{100}) \) 36 * q - 144 * q^4 - 36 * q^7 - 132 * q^9 - 468 * q^15 + 576 * q^16 + 8 * q^18 + 14 * q^21 + 792 * q^22 + 552 * q^25 + 144 * q^28 - 184 * q^30 + 528 * q^36 - 108 * q^37 - 708 * q^39 + 260 * q^42 + 2688 * q^43 - 912 * q^46 - 2796 * q^49 + 1544 * q^51 - 1784 * q^57 - 1128 * q^58 + 1872 * q^60 + 1030 * q^63 - 2304 * q^64 + 2196 * q^67 - 2544 * q^70 - 32 * q^72 - 384 * q^78 - 4488 * q^79 - 2176 * q^81 - 56 * q^84 + 8328 * q^85 - 3168 * q^88 - 5580 * q^91 + 2956 * q^93 - 44 * q^99

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