LMFDB - Embedded newform 162.4.e.a.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	162.127
Dual form			162.4.e.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(19.8413 + 7.22164i) q^{5} +(-3.38399 + 19.1916i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(19.8413 + 7.22164i) q^{5} +(-3.38399 + 19.1916i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-21.1147 - 36.5717i) q^{10} +(-20.6574 + 7.51869i) q^{11} +(-57.4742 + 48.2266i) q^{13} +(29.8568 - 25.0528i) q^{14} +(-15.0351 + 5.47232i) q^{16} +(-22.5870 - 39.1219i) q^{17} +(-10.9300 + 18.9313i) q^{19} +(-14.6661 + 83.1755i) q^{20} +(41.3149 + 15.0374i) q^{22} +(9.15342 + 51.9116i) q^{23} +(245.769 + 206.225i) q^{25} +150.055 q^{26} -77.9506 q^{28} +(92.8070 + 77.8743i) q^{29} +(-26.8524 - 152.288i) q^{31} +(30.0702 + 10.9446i) q^{32} +(-15.6888 + 88.9756i) q^{34} +(-205.737 + 356.348i) q^{35} +(91.7574 + 158.928i) q^{37} +(41.0834 - 14.9531i) q^{38} +(129.398 - 108.578i) q^{40} +(213.053 - 178.773i) q^{41} +(-188.260 + 68.5209i) q^{43} +(-43.9664 - 76.1520i) q^{44} +(52.7125 - 91.3006i) q^{46} +(-3.39621 + 19.2608i) q^{47} +(-34.5507 - 12.5754i) q^{49} +(-111.423 - 631.909i) q^{50} +(-229.897 - 192.906i) q^{52} +646.915 q^{53} -464.168 q^{55} +(119.427 + 100.211i) q^{56} +(-42.0753 - 238.621i) q^{58} +(-415.902 - 151.376i) q^{59} +(-21.3384 + 121.016i) q^{61} +(-154.637 + 267.839i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-1488.64 + 541.820i) q^{65} +(222.612 - 186.793i) q^{67} +(138.421 - 116.149i) q^{68} +(773.320 - 281.465i) q^{70} +(40.8070 + 70.6797i) q^{71} +(170.673 - 295.614i) q^{73} +(63.7340 - 361.453i) q^{74} +(-82.1668 - 29.9063i) q^{76} +(-74.3910 - 421.892i) q^{77} +(907.990 + 761.894i) q^{79} -337.835 q^{80} -556.242 q^{82} +(-716.377 - 601.112i) q^{83} +(-165.632 - 939.345i) q^{85} +(376.519 + 137.042i) q^{86} +(-30.5387 + 173.194i) q^{88} +(704.011 - 1219.38i) q^{89} +(-731.052 - 1266.22i) q^{91} +(-198.134 + 72.1149i) q^{92} +(29.9645 - 25.1432i) q^{94} +(-353.581 + 296.689i) q^{95} +(-65.8521 + 23.9682i) q^{97} +(36.7680 + 63.6841i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−1.53209	−	1.28558i	−0.541675	−	0.454519i
$2$	−1.53209	−	1.28558i	−0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.694593	+	3.93923i	0.0868241	+	0.492404i
$5$	19.8413	+	7.22164i	1.77466	+	0.645923i	0.999907	+	0.0136580i	$0.00434760\pi$
$5$	19.8413	+	7.22164i	1.77466	+	0.645923i	0.774752	+	0.632265i	$0.217875\pi$
$6$		0			0
$7$	−3.38399	+	19.1916i	−0.182718	+	1.03625i	0.746133	+	0.665796i	$0.231908\pi$
$7$	−3.38399	+	19.1916i	−0.182718	+	1.03625i	−0.928852	+	0.370451i	$0.879203\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$		0			0
$10$	−21.1147	−	36.5717i	−0.667704	−	1.15650i
$11$	−20.6574	+	7.51869i	−0.566223	+	0.206088i	−0.609240	−	0.792986i	$-0.708525\pi$
$11$	−20.6574	+	7.51869i	−0.566223	+	0.206088i	0.0430168	+	0.999074i	$0.486303\pi$
$12$		0			0
$13$	−57.4742	+	48.2266i	−1.22619	+	1.02890i	−0.227714	+	0.973728i	$0.573125\pi$
$13$	−57.4742	+	48.2266i	−1.22619	+	1.02890i	−0.998477	+	0.0551684i	$0.982430\pi$
$14$	29.8568	−	25.0528i	0.569969	−	0.478261i
$15$		0			0
$16$	−15.0351	+	5.47232i	−0.234923	+	0.0855050i
$17$	−22.5870	−	39.1219i	−0.322245	−	0.558145i	0.658706	−	0.752400i	$-0.271104\pi$
$17$	−22.5870	−	39.1219i	−0.322245	−	0.558145i	−0.980951	+	0.194256i	$0.937771\pi$
$18$		0			0
$19$	−10.9300	+	18.9313i	−0.131974	+	0.228586i	−0.924438	−	0.381333i	$-0.875465\pi$
$19$	−10.9300	+	18.9313i	−0.131974	+	0.228586i	0.792463	+	0.609920i	$0.208798\pi$
$20$	−14.6661	+	83.1755i	−0.163972	+	0.929931i
$21$		0			0
$22$	41.3149	+	15.0374i	0.400380	+	0.145726i
$23$	9.15342	+	51.9116i	0.0829835	+	0.470623i	0.997774	+	0.0666931i	$0.0212448\pi$
$23$	9.15342	+	51.9116i	0.0829835	+	0.470623i	−0.914790	+	0.403930i	$0.867644\pi$
$24$		0			0
$25$	245.769	+	206.225i	1.96615	+	1.64980i
$26$	150.055			1.13185
$27$		0			0
$28$	−77.9506			−0.526117
$29$	92.8070	+	77.8743i	0.594270	+	0.498651i	0.889598	−	0.456744i	$-0.150985\pi$
$29$	92.8070	+	77.8743i	0.594270	+	0.498651i	−0.295328	+	0.955396i	$0.595429\pi$
$30$		0			0
$31$	−26.8524	−	152.288i	−0.155575	−	0.882312i	−0.958258	−	0.285906i	$-0.907706\pi$
$31$	−26.8524	−	152.288i	−0.155575	−	0.882312i	0.802682	−	0.596407i	$-0.203405\pi$
$32$	30.0702	+	10.9446i	0.166116	+	0.0604612i
$33$		0			0
$34$	−15.6888	+	88.9756i	−0.0791355	+	0.448800i
$35$	−205.737	+	356.348i	−0.993599	+	1.72096i
$36$		0			0
$37$	91.7574	+	158.928i	0.407698	+	0.706153i	0.994631	−	0.103482i	$-0.0329984\pi$
$37$	91.7574	+	158.928i	0.407698	+	0.706153i	−0.586934	+	0.809635i	$0.699665\pi$
$38$	41.0834	−	14.9531i	0.175384	−	0.0638347i
$39$		0			0
$40$	129.398	−	108.578i	0.511491	−	0.429192i
$41$	213.053	−	178.773i	0.811544	−	0.680967i	−0.139431	−	0.990232i	$-0.544527\pi$
$41$	213.053	−	178.773i	0.811544	−	0.680967i	0.950976	+	0.309265i	$0.100083\pi$
$42$		0			0
$43$	−188.260	+	68.5209i	−0.667659	+	0.243008i	−0.653539	−	0.756892i	$-0.726717\pi$
$43$	−188.260	+	68.5209i	−0.667659	+	0.243008i	−0.0141192	+	0.999900i	$0.504494\pi$
$44$	−43.9664	−	76.1520i	−0.150640	−	0.260917i
$45$		0			0
$46$	52.7125	−	91.3006i	0.168957	−	0.292642i
$47$	−3.39621	+	19.2608i	−0.0105402	+	0.0597762i	−0.989624	−	0.143680i	$-0.954106\pi$
$47$	−3.39621	+	19.2608i	−0.0105402	+	0.0597762i	0.979084	+	0.203456i	$0.0652175\pi$
$48$		0			0
$49$	−34.5507	−	12.5754i	−0.100731	−	0.0366630i
$50$	−111.423	−	631.909i	−0.315151	−	1.78731i
$51$		0			0
$52$	−229.897	−	192.906i	−0.613096	−	0.514448i
$53$	646.915			1.67662			0.838308	−	0.545197i	$-0.183545\pi$
$53$	646.915			1.67662			0.838308	+	0.545197i	$0.183545\pi$
$54$		0			0
$55$	−464.168			−1.13797
$56$	119.427	+	100.211i	0.284984	+	0.239130i
$57$		0			0
$58$	−42.0753	−	238.621i	−0.0952544	−	0.540214i
$59$	−415.902	−	151.376i	−0.917726	−	0.334025i	−0.160392	−	0.987053i	$-0.551276\pi$
$59$	−415.902	−	151.376i	−0.917726	−	0.334025i	−0.757333	+	0.653029i	$0.773498\pi$
$60$		0			0
$61$	−21.3384	+	121.016i	−0.0447886	+	0.254009i	−0.998978	−	0.0451936i	$-0.985610\pi$
$61$	−21.3384	+	121.016i	−0.0447886	+	0.254009i	0.954190	+	0.299203i	$0.0967206\pi$
$62$	−154.637	+	267.839i	−0.316757	+	0.548639i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−1488.64	+	541.820i	−2.84066	+	1.03392i
$66$		0			0
$67$	222.612	−	186.793i	0.405916	−	0.340604i	−0.416859	−	0.908971i	$-0.636869\pi$
$67$	222.612	−	186.793i	0.405916	−	0.340604i	0.822775	+	0.568367i	$0.192425\pi$
$68$	138.421	−	116.149i	0.246854	−	0.207135i
$69$		0			0
$70$	773.320	−	281.465i	1.32042	−	0.480594i
$71$	40.8070	+	70.6797i	0.0682098	+	0.118143i	0.898113	−	0.439764i	$-0.144938\pi$
$71$	40.8070	+	70.6797i	0.0682098	+	0.118143i	−0.829904	+	0.557907i	$0.811605\pi$
$72$		0			0
$73$	170.673	−	295.614i	0.273640	−	0.473958i	−0.696151	−	0.717895i	$-0.745106\pi$
$73$	170.673	−	295.614i	0.273640	−	0.473958i	0.969791	+	0.243937i	$0.0784390\pi$
$74$	63.7340	−	361.453i	0.100121	−	0.567812i
$75$		0			0
$76$	−82.1668	−	29.9063i	−0.124015	−	0.0451379i
$77$	−74.3910	−	421.892i	−0.110099	−	0.624403i
$78$		0			0
$79$	907.990	+	761.894i	1.29312	+	1.08506i	0.991290	+	0.131700i	$0.0420434\pi$
$79$	907.990	+	761.894i	1.29312	+	1.08506i	0.301834	+	0.953360i	$0.402401\pi$
$80$	−337.835			−0.472138
$81$		0			0
$82$	−556.242			−0.749106
$83$	−716.377	−	601.112i	−0.947381	−	0.794947i	0.0314737	−	0.999505i	$-0.489980\pi$
$83$	−716.377	−	601.112i	−0.947381	−	0.794947i	−0.978855	+	0.204558i	$0.934424\pi$
$84$		0			0
$85$	−165.632	−	939.345i	−0.211356	−	1.19866i
$86$	376.519	+	137.042i	0.472106	+	0.171833i
$87$		0			0
$88$	−30.5387	+	173.194i	−0.0369936	+	0.209801i
$89$	704.011	−	1219.38i	0.838483	−	1.45230i	−0.0526797	−	0.998611i	$-0.516776\pi$
$89$	704.011	−	1219.38i	0.838483	−	1.45230i	0.891163	−	0.453684i	$-0.149890\pi$
$90$		0			0
$91$	−731.052	−	1266.22i	−0.842144	−	1.45864i
$92$	−198.134	+	72.1149i	−0.224532	+	0.0817228i
$93$		0			0
$94$	29.9645	−	25.1432i	0.0328788	−	0.0275886i
$95$	−353.581	+	296.689i	−0.381859	+	0.320418i
$96$		0			0
$97$	−65.8521	+	23.9682i	−0.0689306	+	0.0250887i	−0.376255	−	0.926516i	$-0.622788\pi$
$97$	−65.8521	+	23.9682i	−0.0689306	+	0.0250887i	0.307325	+	0.951605i	$0.400566\pi$
$98$	36.7680	+	63.6841i	0.0378993	+	0.0656435i
$99$		0			0
$100$	−641.658	+	1111.38i	−0.641658	+	1.11138i
$101$	40.0683	−	227.239i	0.0394747	−	0.223872i	−0.958688	−	0.284459i	$-0.908186\pi$
$101$	40.0683	−	227.239i	0.0394747	−	0.223872i	0.998163	+	0.0605867i	$0.0192972\pi$
$102$		0			0
$103$	1151.25	+	419.022i	1.10132	+	0.400849i	0.827804	−	0.561018i	$-0.189590\pi$
$103$	1151.25	+	419.022i	1.10132	+	0.400849i	0.273519	+	0.961867i	$0.411812\pi$
$104$	104.227	+	591.100i	0.0982719	+	0.557328i
$105$		0			0
$106$	−991.131	−	831.658i	−0.908181	−	0.762054i
$107$	151.086			0.136505			0.0682526	−	0.997668i	$-0.478258\pi$
$107$	151.086			0.136505			0.0682526	+	0.997668i	$0.478258\pi$
$108$		0			0
$109$	225.539			0.198190			0.0990952	−	0.995078i	$-0.468405\pi$
$109$	225.539			0.198190			0.0990952	+	0.995078i	$0.468405\pi$
$110$	711.146	+	596.722i	0.616410	+	0.517229i
$111$		0			0
$112$	−54.1439	−	307.065i	−0.0456796	−	0.259062i
$113$	202.546	+	73.7208i	0.168619	+	0.0613723i	0.424950	−	0.905217i	$-0.360292\pi$
$113$	202.546	+	73.7208i	0.168619	+	0.0613723i	−0.256331	+	0.966589i	$0.582514\pi$
$114$		0			0
$115$	−193.271	+	1096.10i	−0.156719	+	0.888796i
$116$	−242.302	+	419.679i	−0.193941	+	0.335916i
$117$		0			0
$118$	442.594	+	766.595i	0.345288	+	0.598057i
$119$	827.246	−	301.093i	0.637256	−	0.231942i
$120$		0			0
$121$	−649.406	+	544.916i	−0.487908	+	0.409404i
$122$	188.268	−	157.976i	0.139713	−	0.117233i
$123$		0			0
$124$	581.245	−	211.556i	0.420946	−	0.153212i
$125$	2067.43	+	3580.89i	1.47933	+	2.56228i
$126$		0			0
$127$	−431.304	+	747.041i	−0.301355	+	0.521962i	−0.976443	−	0.215775i	$-0.930772\pi$
$127$	−431.304	+	747.041i	−0.301355	+	0.521962i	0.675088	+	0.737737i	$0.264105\pi$
$128$	−22.2270	+	126.055i	−0.0153485	+	0.0870455i
$129$		0			0
$130$	2977.28	+	1083.64i	2.00865	+	0.731088i
$131$	142.714	+	809.371i	0.0951830	+	0.539809i	0.994691	+	0.102906i	$0.0328139\pi$
$131$	142.714	+	809.371i	0.0951830	+	0.539809i	−0.899508	+	0.436904i	$0.856075\pi$
$132$		0			0
$133$	−326.335	−	273.827i	−0.212758	−	0.178525i
$134$	−581.198			−0.374686
$135$		0			0
$136$	−361.393			−0.227862
$137$	808.851	+	678.707i	0.504415	+	0.423254i	0.859159	−	0.511709i	$-0.170988\pi$
$137$	808.851	+	678.707i	0.504415	+	0.423254i	−0.354744	+	0.934964i	$0.615432\pi$
$138$		0			0
$139$	−475.647	−	2697.53i	−0.290243	−	1.64605i	−0.685931	−	0.727667i	$-0.740605\pi$
$139$	−475.647	−	2697.53i	−0.290243	−	1.64605i	0.395687	−	0.918385i	$-0.370506\pi$
$140$	−1546.64	−	562.931i	−0.933678	−	0.339831i
$141$		0			0
$142$	28.3442	−	160.748i	0.0167507	−	0.0949977i
$143$	824.670	−	1428.37i	0.482254	−	0.835289i
$144$		0			0
$145$	1279.03	+	2215.34i	0.732536	+	1.26879i
$146$	−641.519	+	233.494i	−0.363647	+	0.132357i
$147$		0			0
$148$	−562.322	+	471.844i	−0.312315	+	0.262063i
$149$	−27.0754	+	22.7190i	−0.0148866	+	0.0124914i	−0.650201	−	0.759763i	$-0.725315\pi$
$149$	−27.0754	+	22.7190i	−0.0148866	+	0.0124914i	0.635314	+	0.772254i	$0.280871\pi$
$150$		0			0
$151$	−2261.30	+	823.045i	−1.21869	+	0.443566i	−0.869709	−	0.493565i	$-0.835693\pi$
$151$	−2261.30	+	823.045i	−1.21869	+	0.443566i	−0.348978	+	0.937131i	$0.613471\pi$
$152$	87.4400	+	151.451i	0.0466600	+	0.0808175i
$153$		0			0
$154$	−428.400	+	742.011i	−0.224166	+	0.388266i
$155$	566.980	−	3215.50i	0.293813	−	1.66629i
$156$		0			0
$157$	−227.755	−	82.8962i	−0.115776	−	0.0421391i	0.283482	−	0.958977i	$-0.408510\pi$
$157$	−227.755	−	82.8962i	−0.115776	−	0.0421391i	−0.399259	+	0.916838i	$0.630732\pi$
$158$	−411.649	−	2334.58i	−0.207272	−	1.17550i
$159$		0			0
$160$	517.593	+	434.312i	0.255746	+	0.214596i
$161$	−1027.24			−0.502844
$162$		0			0
$163$	1663.76			0.799483			0.399742	−	0.916628i	$-0.369100\pi$
$163$	1663.76			0.799483			0.399742	+	0.916628i	$0.369100\pi$
$164$	852.213	+	715.091i	0.405772	+	0.340483i
$165$		0			0
$166$	324.779	+	1841.91i	0.151854	+	0.861206i
$167$	1418.63	+	516.340i	0.657348	+	0.239255i	0.649091	−	0.760711i	$-0.275149\pi$
$167$	1418.63	+	516.340i	0.657348	+	0.239255i	0.00825699	+	0.999966i	$0.497372\pi$
$168$		0			0
$169$	595.977	−	3379.95i	0.271268	−	1.53844i
$170$	−953.836	+	1652.09i	−0.430329	+	0.745351i
$171$		0			0
$172$	−400.683	−	694.004i	−0.177627	−	0.307659i
$173$	−703.622	+	256.097i	−0.309222	+	0.112548i	−0.491970	−	0.870612i	$-0.663723\pi$
$173$	−703.622	+	256.097i	−0.309222	+	0.112548i	0.182748	+	0.983160i	$0.441501\pi$
$174$		0			0
$175$	−4789.46	+	4018.83i	−2.06885	+	1.73597i
$176$	269.442	−	226.088i	0.115397	−	0.0968298i
$177$		0			0
$178$	−2646.21	+	963.143i	−1.11428	+	0.405565i
$179$	−2102.26	−	3641.23i	−0.877824	−	1.52044i	−0.853724	−	0.520726i	$-0.825661\pi$
$179$	−2102.26	−	3641.23i	−0.877824	−	1.52044i	−0.0241001	−	0.999710i	$-0.507672\pi$
$180$		0			0
$181$	1893.95	−	3280.42i	0.777770	−	1.34714i	−0.155455	−	0.987843i	$-0.549684\pi$
$181$	1893.95	−	3280.42i	0.777770	−	1.34714i	0.933225	−	0.359294i	$-0.116982\pi$
$182$	−507.784	+	2879.78i	−0.206810	+	1.17288i
$183$		0			0
$184$	396.268	+	144.230i	0.158768	+	0.0577867i
$185$	672.861	+	3815.98i	0.267404	+	1.51652i
$186$		0			0
$187$	760.736	+	638.333i	0.297490	+	0.249623i
$188$	−78.2319			−0.0303492
$189$		0			0
$190$	923.133			0.352480
$191$	348.017	+	292.021i	0.131841	+	0.110628i	0.706324	−	0.707889i	$-0.250352\pi$
$191$	348.017	+	292.021i	0.131841	+	0.110628i	−0.574483	+	0.818517i	$0.694797\pi$
$192$		0			0
$193$	−16.3847	−	92.9224i	−0.00611087	−	0.0346565i	0.981600	−	0.190950i	$-0.0611567\pi$
$193$	−16.3847	−	92.9224i	−0.00611087	−	0.0346565i	−0.987711	+	0.156293i	$0.950046\pi$
$194$	131.704	+	47.9364i	0.0487413	+	0.0177404i
$195$		0			0
$196$	25.5388	−	144.838i	0.00930715	−	0.0527835i
$197$	1576.68	−	2730.88i	0.570221	−	0.987651i	−0.426322	−	0.904571i	$-0.640191\pi$
$197$	1576.68	−	2730.88i	0.570221	−	0.987651i	0.996543	−	0.0830797i	$-0.0264756\pi$
$198$		0			0
$199$	−1554.07	−	2691.73i	−0.553593	−	0.958852i	−0.998011	−	0.0630325i	$-0.979923\pi$
$199$	−1554.07	−	2691.73i	−0.553593	−	0.958852i	0.444418	−	0.895820i	$-0.353411\pi$
$200$	2411.84	−	877.839i	0.852716	−	0.310363i
$201$		0			0
$202$	−353.521	+	296.639i	−0.123137	+	0.103324i
$203$	−1808.59	+	1517.59i	−0.625311	+	0.524698i
$204$		0			0
$205$	5518.28	−	2008.49i	1.88007	−	0.684288i
$206$	−1225.14	−	2122.00i	−0.414366	−	0.717703i
$207$		0			0
$208$	600.218	−	1039.61i	0.200085	−	0.346557i
$209$	83.4471	−	473.252i	0.0276180	−	0.156629i
$210$		0			0
$211$	−2062.72	−	750.770i	−0.673003	−	0.244953i	−0.0171629	−	0.999853i	$-0.505463\pi$
$211$	−2062.72	−	750.770i	−0.673003	−	0.244953i	−0.655840	+	0.754899i	$0.727686\pi$
$212$	449.342	+	2548.35i	0.145571	+	0.825572i
$213$		0			0
$214$	−231.478	−	194.233i	−0.0739415	−	0.0620443i
$215$	−4230.15			−1.34183
$216$		0			0
$217$	3013.51			0.942721
$218$	−345.546	−	289.948i	−0.107355	−	0.0900814i
$219$		0			0
$220$	−322.407	−	1828.46i	−0.0988032	−	0.560341i
$221$	3184.89	+	1159.21i	0.969407	+	0.352835i
$222$		0			0
$223$	−494.574	+	2804.87i	−0.148516	+	0.842278i	0.815960	+	0.578109i	$0.196209\pi$
$223$	−494.574	+	2804.87i	−0.148516	+	0.842278i	−0.964476	+	0.264170i	$0.914902\pi$
$224$	−311.802	+	540.057i	−0.0930052	+	0.161090i
$225$		0			0
$226$	−215.545	−	373.335i	−0.0634418	−	0.109884i
$227$	9.06506	−	3.29941i	0.00265052	−	0.000964712i	−0.340695	−	0.940174i	$-0.610662\pi$
$227$	9.06506	−	3.29941i	0.00265052	−	0.000964712i	0.343345	+	0.939209i	$0.388440\pi$
$228$		0			0
$229$	−2343.01	+	1966.02i	−0.676115	+	0.567328i	−0.914868	−	0.403753i	$-0.867706\pi$
$229$	−2343.01	+	1966.02i	−0.676115	+	0.567328i	0.238753	+	0.971080i	$0.423261\pi$
$230$	1705.22	−	1430.85i	0.488866	−	0.410207i
$231$		0			0
$232$	910.757	−	331.488i	0.257733	−	0.0938072i
$233$	−2291.32	−	3968.68i	−0.644246	−	1.11587i	−0.984475	−	0.175525i	$-0.943838\pi$
$233$	−2291.32	−	3968.68i	−0.644246	−	1.11587i	0.340229	−	0.940343i	$-0.389495\pi$
$234$		0			0
$235$	−206.480	+	357.634i	−0.0573160	+	0.0992743i
$236$	307.422	−	1743.48i	0.0847944	−	0.480893i
$237$		0			0
$238$	−1654.49	−	602.186i	−0.450608	−	0.164008i
$239$	−703.025	−	3987.05i	−0.190272	−	1.07908i	−0.918993	−	0.394274i	$-0.870996\pi$
$239$	−703.025	−	3987.05i	−0.190272	−	1.07908i	0.728721	−	0.684810i	$-0.240115\pi$
$240$		0			0
$241$	−2704.94	−	2269.71i	−0.722988	−	0.606659i	0.205222	−	0.978715i	$-0.434208\pi$
$241$	−2704.94	−	2269.71i	−0.722988	−	0.606659i	−0.928210	+	0.372056i	$0.878653\pi$
$242$	1695.48			0.450370
$243$		0			0
$244$	−491.533			−0.128964
$245$	−594.715	−	499.025i	−0.155081	−	0.130129i
$246$		0			0
$247$	−284.800	−	1615.18i	−0.0733659	−	0.416079i
$248$	−1162.49	−	423.112i	−0.297654	−	0.108337i
$249$		0			0
$250$	1436.02	−	8144.08i	0.363288	−	2.06031i
$251$	−2574.75	+	4459.59i	−0.647476	+	1.12146i	0.336248	+	0.941774i	$0.390842\pi$
$251$	−2574.75	+	4459.59i	−0.647476	+	1.12146i	−0.983724	+	0.179688i	$0.942491\pi$
$252$		0			0
$253$	−579.394	−	1003.54i	−0.143977	−	0.249375i
$254$	1621.17	−	590.059i	0.400478	−	0.145762i
$255$		0			0
$256$	196.107	−	164.554i	0.0478778	−	0.0401742i
$257$	−2998.39	+	2515.95i	−0.727761	+	0.610664i	−0.929520	−	0.368771i	$-0.879779\pi$
$257$	−2998.39	+	2515.95i	−0.727761	+	0.610664i	0.201759	+	0.979435i	$0.435334\pi$
$258$		0			0
$259$	−3360.59	+	1223.16i	−0.806244	+	0.293449i
$260$	−3168.35	−	5487.74i	−0.755742	−	1.30898i
$261$		0			0
$262$	821.857	−	1423.50i	0.193796	−	0.335664i
$263$	−813.380	+	4612.91i	−0.190704	+	1.08154i	0.727701	+	0.685894i	$0.240589\pi$
$263$	−813.380	+	4612.91i	−0.190704	+	1.08154i	−0.918405	+	0.395641i	$0.870522\pi$
$264$		0			0
$265$	12835.6	+	4671.79i	2.97542	+	1.08296i
$266$	147.948	+	839.056i	0.0341026	+	0.193405i
$267$		0			0
$268$	890.447	+	747.174i	0.202958	+	0.170302i
$269$	2589.41			0.586912			0.293456	−	0.955973i	$-0.405195\pi$
$269$	2589.41			0.586912			0.293456	+	0.955973i	$0.405195\pi$
$270$		0			0
$271$	7508.62			1.68309			0.841543	−	0.540191i	$-0.181648\pi$
$271$	7508.62			1.68309			0.841543	+	0.540191i	$0.181648\pi$
$272$	553.686	+	464.598i	0.123427	+	0.103568i
$273$		0			0
$274$	−366.703	−	2079.68i	−0.0808517	−	0.458533i
$275$	−6627.50	−	2412.21i	−1.45329	−	0.528953i
$276$		0			0
$277$	−1006.86	+	5710.18i	−0.218398	+	1.23860i	0.656514	+	0.754314i	$0.272030\pi$
$277$	−1006.86	+	5710.18i	−0.218398	+	1.23860i	−0.874912	+	0.484283i	$0.839081\pi$
$278$	−2739.14	+	4744.33i	−0.590945	+	1.02355i
$279$		0			0
$280$	1645.90	+	2850.78i	0.351290	+	0.608453i
$281$	5546.05	−	2018.60i	1.17740	−	0.428539i	0.322118	−	0.946700i	$-0.395605\pi$
$281$	5546.05	−	2018.60i	1.17740	−	0.428539i	0.855283	+	0.518160i	$0.173383\pi$
$282$		0			0
$283$	−1533.13	+	1286.45i	−0.322032	+	0.270217i	−0.789444	−	0.613823i	$-0.789631\pi$
$283$	−1533.13	+	1286.45i	−0.322032	+	0.270217i	0.467412	+	0.884040i	$0.345186\pi$
$284$	−250.080	+	209.842i	−0.0522517	+	0.0438444i
$285$		0			0
$286$	−3099.74	+	1128.21i	−0.640880	+	0.233261i
$287$	2709.96	+	4693.79i	0.557366	+	0.965386i
$288$		0			0
$289$	1436.15	−	2487.49i	0.292316	−	0.506307i
$290$	888.405	−	5038.39i	0.179893	−	1.02022i
$291$		0			0
$292$	1283.04	+	466.988i	0.257138	+	0.0935904i
$293$	529.884	+	3005.12i	0.105652	+	0.599184i	0.990958	+	0.134174i	$0.0428381\pi$
$293$	529.884	+	3005.12i	0.105652	+	0.599184i	−0.885305	+	0.465010i	$0.846051\pi$
$294$		0			0
$295$	−7158.85	−	6006.99i	−1.41290	−	1.18556i
$296$	1468.12			0.288286
$297$		0			0
$298$	70.6889			0.0137413
$299$	−3029.61	−	2542.14i	−0.585976	−	0.491692i
$300$		0			0
$301$	−677.955	−	3844.87i	−0.129823	−	0.736262i
$302$	4522.59	+	1646.09i	0.861742	+	0.313648i
$303$		0			0
$304$	60.7352	−	344.447i	0.0114586	−	0.0649847i
$305$	−1297.32	+	2247.02i	−0.243555	+	0.421849i
$306$		0			0
$307$	4301.59	+	7450.57i	0.799689	+	1.38510i	0.919819	+	0.392344i	$0.128336\pi$
$307$	4301.59	+	7450.57i	0.799689	+	1.38510i	−0.120130	+	0.992758i	$0.538331\pi$
$308$	1610.26	−	586.086i	0.297899	−	0.108427i
$309$		0			0
$310$	−5002.44	+	4197.54i	−0.916514	+	0.769046i
$311$	1912.48	−	1604.76i	0.348704	−	0.292598i	−0.451565	−	0.892238i	$-0.649134\pi$
$311$	1912.48	−	1604.76i	0.348704	−	0.292598i	0.800270	+	0.599640i	$0.204690\pi$
$312$		0			0
$313$	56.0623	−	20.4050i	0.0101240	−	0.00368485i	−0.336953	−	0.941521i	$-0.609396\pi$
$313$	56.0623	−	20.4050i	0.0101240	−	0.00368485i	0.347077	+	0.937837i	$0.387174\pi$
$314$	242.372	+	419.801i	0.0435600	+	0.0754482i
$315$		0			0
$316$	−2370.59	+	4105.99i	−0.422013	+	0.730949i
$317$	−347.977	+	1973.48i	−0.0616541	+	0.349658i	0.938338	+	0.345719i	$0.112365\pi$
$317$	−347.977	+	1973.48i	−0.0616541	+	0.349658i	−0.999992	+	0.00393894i	$0.998746\pi$
$318$		0			0
$319$	−2502.67	−	910.896i	−0.439255	−	0.159876i
$320$	−234.657	−	1330.81i	−0.0409930	−	0.232483i
$321$		0			0
$322$	1573.82	+	1320.60i	0.272378	+	0.228553i
$323$	987.506			0.170112
$324$		0			0
$325$	−24070.9			−4.10835
$326$	−2549.03	−	2138.89i	−0.433060	−	0.363381i
$327$		0			0
$328$	−386.362	−	2191.17i	−0.0650405	−	0.368863i
$329$	−358.153	−	130.357i	−0.0600171	−	0.0218444i
$330$		0			0
$331$	−476.542	+	2702.60i	−0.0791333	+	0.448787i	0.919336	+	0.393474i	$0.128727\pi$
$331$	−476.542	+	2702.60i	−0.0791333	+	0.448787i	−0.998469	+	0.0553133i	$0.982384\pi$
$332$	1870.33	−	3239.50i	0.309179	−	0.535515i
$333$		0			0
$334$	−1509.68	−	2614.84i	−0.247323	−	0.428376i
$335$	5765.86	−	2098.60i	0.940366	−	0.342265i
$336$		0			0
$337$	−1466.58	+	1230.61i	−0.237062	+	0.198918i	−0.753577	−	0.657359i	$-0.771673\pi$
$337$	−1466.58	+	1230.61i	−0.237062	+	0.198918i	0.516515	+	0.856278i	$0.327229\pi$
$338$	−5258.27	+	4412.21i	−0.846190	+	0.710038i
$339$		0			0
$340$	3585.25	−	1304.92i	0.571875	−	0.208145i
$341$	1699.71	+	2943.98i	0.269925	+	0.467523i
$342$		0			0
$343$	−2983.87	+	5168.21i	−0.469719	+	0.813578i
$344$	−278.312	+	1578.38i	−0.0436208	+	0.247386i
$345$		0			0
$346$	1407.24	+	512.195i	0.218653	+	0.0795831i
$347$	−363.893	−	2063.74i	−0.0562963	−	0.319272i	0.943635	−	0.330988i	$-0.107382\pi$
$347$	−363.893	−	2063.74i	−0.0562963	−	0.319272i	−0.999931	+	0.0117155i	$0.996271\pi$
$348$		0			0
$349$	3899.78	+	3272.30i	0.598138	+	0.501898i	0.890847	−	0.454304i	$-0.150112\pi$
$349$	3899.78	+	3272.30i	0.598138	+	0.501898i	−0.292708	+	0.956202i	$0.594557\pi$
$350$	12504.4			1.90968
$351$		0			0
$352$	−703.462			−0.106519
$353$	886.133	+	743.554i	0.133609	+	0.112112i	0.707143	−	0.707070i	$-0.249984\pi$
$353$	886.133	+	743.554i	0.133609	+	0.112112i	−0.573534	+	0.819182i	$0.694428\pi$
$354$		0			0
$355$	299.239	+	1697.07i	0.0447379	+	0.253721i
$356$	5292.43	+	1926.29i	0.787916	+	0.286778i
$357$		0			0
$358$	−1460.22	+	8281.30i	−0.215572	+	1.22257i
$359$	6630.20	−	11483.9i	0.974732	−	1.68829i	0.293915	−	0.955831i	$-0.405042\pi$
$359$	6630.20	−	11483.9i	0.974732	−	1.68829i	0.680817	−	0.732454i	$-0.261625\pi$
$360$		0			0
$361$	3190.57	+	5526.23i	0.465165	+	0.805690i
$362$	−7118.93	+	2591.08i	−1.03360	+	0.376199i
$363$		0			0
$364$	4480.15	−	3759.29i	0.645120	−	0.541320i
$365$	5521.18	−	4632.82i	0.791758	−	0.664364i
$366$		0			0
$367$	12931.8	−	4706.78i	1.83933	−	0.669460i	0.849424	−	0.527711i	$-0.176950\pi$
$367$	12931.8	−	4706.78i	1.83933	−	0.669460i	0.989903	−	0.141749i	$-0.0452727\pi$
$368$	−421.700	−	730.405i	−0.0597354	−	0.103465i
$369$		0			0
$370$	3874.85	−	6711.44i	0.544443	−	0.943003i
$371$	−2189.16	+	12415.3i	−0.306349	+	1.73739i
$372$		0			0
$373$	5243.32	+	1908.41i	0.727853	+	0.264917i	0.679256	−	0.733902i	$-0.262303\pi$
$373$	5243.32	+	1908.41i	0.727853	+	0.264917i	0.0485971	+	0.998818i	$0.484525\pi$
$374$	−344.890	−	1955.97i	−0.0476840	−	0.270430i
$375$		0			0
$376$	119.858	+	100.573i	0.0164394	+	0.0137943i
$377$	−9089.62			−1.24175
$378$		0			0
$379$	11164.1			1.51310			0.756548	−	0.653938i	$-0.226884\pi$
$379$	11164.1			1.51310			0.756548	+	0.653938i	$0.226884\pi$
$380$	−1414.32	−	1186.76i	−0.190929	−	0.160209i
$381$		0			0
$382$	−157.778	−	894.805i	−0.0211326	−	0.119849i
$383$	1952.92	+	710.803i	0.260547	+	0.0948312i	0.468991	−	0.883203i	$-0.344618\pi$
$383$	1952.92	+	710.803i	0.260547	+	0.0948312i	−0.208444	+	0.978034i	$0.566840\pi$
$384$		0			0
$385$	1570.74	−	8908.11i	0.207928	−	1.17922i
$386$	−94.3559	+	163.429i	−0.0124419	+	0.0215501i
$387$		0			0
$388$	−140.157	−	242.758i	−0.0183386	−	0.0317634i
$389$	−13276.8	+	4832.36i	−1.73049	+	0.629847i	−0.998666	−	0.0516445i	$-0.983554\pi$
$389$	−13276.8	+	4832.36i	−1.73049	+	0.629847i	−0.731826	+	0.681492i	$0.761332\pi$
$390$		0			0
$391$	1824.13	−	1530.63i	0.235935	−	0.197973i
$392$	−225.328	+	189.072i	−0.0290326	+	0.0243612i
$393$		0			0
$394$	−5926.36	+	2157.02i	−0.757781	+	0.275810i
$395$	12513.6	+	21674.1i	1.59399	+	2.76087i
$396$		0			0
$397$	−4445.26	+	7699.42i	−0.561968	+	0.973357i	0.435357	+	0.900258i	$0.356622\pi$
$397$	−4445.26	+	7699.42i	−0.561968	+	0.973357i	−0.997325	+	0.0730988i	$0.976711\pi$
$398$	−1079.45	+	6121.84i	−0.135949	+	0.771005i
$399$		0			0
$400$	−4823.69	−	1755.68i	−0.602961	−	0.219460i
$401$	1791.12	+	10157.9i	0.223053	+	1.26499i	0.866373	+	0.499397i	$0.166445\pi$
$401$	1791.12	+	10157.9i	0.223053	+	1.26499i	−0.643320	+	0.765597i	$0.722444\pi$
$402$		0			0
$403$	8887.64	+	7457.62i	1.09857	+	0.921813i
$404$	922.977			0.113663
$405$		0			0
$406$	4721.89			0.577201
$407$	−3090.41	−	2593.16i	−0.376378	−	0.315818i
$408$		0			0
$409$	1231.32	+	6983.18i	0.148863	+	0.844245i	0.964184	+	0.265235i	$0.0854495\pi$
$409$	1231.32	+	6983.18i	0.148863	+	0.844245i	−0.815321	+	0.579010i	$0.803439\pi$
$410$	−11036.6	−	4016.98i	−1.32941	−	0.483865i
$411$		0			0
$412$	−850.971	+	4826.10i	−0.101758	+	0.577099i
$413$	4312.55	−	7469.56i	0.513818	−	0.889959i
$414$		0			0
$415$	−9872.83	−	17100.3i	−1.16780	−	2.02269i
$416$	−2256.08	+	821.147i	−0.265898	+	0.0967789i
$417$		0			0
$418$	−736.249	+	617.787i	−0.0861511	+	0.0722893i
$419$	6322.42	−	5305.14i	0.737161	−	0.618551i	−0.194913	−	0.980821i	$-0.562442\pi$
$419$	6322.42	−	5305.14i	0.737161	−	0.618551i	0.932073	+	0.362269i	$0.117998\pi$
$420$		0			0
$421$	−13756.0	+	5006.77i	−1.59246	+	0.579608i	−0.977865	−	0.209235i	$-0.932903\pi$
$421$	−13756.0	+	5006.77i	−1.59246	+	0.579608i	−0.614595	+	0.788843i	$0.710680\pi$
$422$	2195.10	+	3802.03i	0.253213	+	0.438578i
$423$		0			0
$424$	2587.66	−	4481.96i	0.296387	−	0.513357i
$425$	2516.71	−	14273.0i	0.287243	−	1.62904i
$426$		0			0
$427$	−2250.28	−	819.037i	−0.255033	−	0.0928243i
$428$	104.943	+	595.164i	0.0118519	+	0.0672157i
$429$		0			0
$430$	6480.96	+	5438.17i	0.726836	+	0.609888i
$431$	−16589.3			−1.85401			−0.927003	−	0.375054i	$-0.877624\pi$
$431$	−16589.3			−1.85401			−0.927003	+	0.375054i	$0.877624\pi$
$432$		0			0
$433$	−8865.65			−0.983963			−0.491981	−	0.870606i	$-0.663727\pi$
$433$	−8865.65			−0.983963			−0.491981	+	0.870606i	$0.663727\pi$
$434$	−4616.97	−	3874.09i	−0.510649	−	0.428485i
$435$		0			0
$436$	156.658	+	888.452i	0.0172077	+	0.0975897i
$437$	−1082.80	−	394.108i	−0.118530	−	0.0431413i
$438$		0			0
$439$	2112.71	−	11981.8i	0.229690	−	1.30264i	−0.623822	−	0.781567i	$-0.714421\pi$
$439$	2112.71	−	11981.8i	0.229690	−	1.30264i	0.853512	−	0.521073i	$-0.174468\pi$
$440$	−1856.67	+	3215.85i	−0.201167	+	0.348431i
$441$		0			0
$442$	−3389.29	−	5870.42i	−0.364733	−	0.631736i
$443$	7948.99	−	2893.20i	0.852524	−	0.310293i	0.121455	−	0.992597i	$-0.461244\pi$
$443$	7948.99	−	2893.20i	0.852524	−	0.310293i	0.731069	+	0.682304i	$0.239022\pi$
$444$		0			0
$445$	22774.4	−	19110.0i	2.42609	−	2.03573i
$446$	4363.60	−	3661.50i	0.463280	−	0.388738i
$447$		0			0
$448$	1171.99	−	426.571i	0.123597	−	0.0449856i
$449$	−3293.61	−	5704.70i	−0.346181	−	0.599603i	0.639387	−	0.768885i	$-0.279188\pi$
$449$	−3293.61	−	5704.70i	−0.346181	−	0.599603i	−0.985568	+	0.169283i	$0.945855\pi$
$450$		0			0
$451$	−3057.00	+	5294.87i	−0.319176	+	0.552829i
$452$	−149.716	+	849.082i	−0.0155798	+	0.0883572i
$453$		0			0
$454$	−18.1301	−	6.59882i	−0.00187420	−	0.000682154i
$455$	−5360.84	−	30402.8i	−0.552352	−	3.13254i
$456$		0			0
$457$	−3545.15	−	2974.74i	−0.362878	−	0.304491i	0.443059	−	0.896493i	$-0.353893\pi$
$457$	−3545.15	−	2974.74i	−0.362878	−	0.304491i	−0.805937	+	0.592002i	$0.798338\pi$
$458$	6117.16			0.624096
$459$		0			0
$460$	−4452.02			−0.451253
$461$	−2098.19	−	1760.59i	−0.211979	−	0.177872i	0.530616	−	0.847613i	$-0.321961\pi$
$461$	−2098.19	−	1760.59i	−0.211979	−	0.177872i	−0.742595	+	0.669741i	$0.766405\pi$
$462$		0			0
$463$	−2884.26	−	16357.4i	−0.289509	−	1.64189i	−0.688719	−	0.725029i	$-0.741827\pi$
$463$	−2884.26	−	16357.4i	−0.289509	−	1.64189i	0.399210	−	0.916860i	$-0.369285\pi$
$464$	−1821.51	−	662.977i	−0.182245	−	0.0663317i
$465$		0			0
$466$	−1591.53	+	9026.04i	−0.158211	+	0.897260i
$467$	−4425.24	+	7664.75i	−0.438492	+	0.759491i	−0.997573	−	0.0696222i	$-0.977821\pi$
$467$	−4425.24	+	7664.75i	−0.438492	+	0.759491i	0.559081	+	0.829113i	$0.311154\pi$
$468$		0			0
$469$	2831.54	+	4904.38i	0.278782	+	0.482864i
$470$	776.111	−	282.481i	0.0761687	−	0.0277232i
$471$		0			0
$472$	−2712.37	+	2275.95i	−0.264506	+	0.221947i
$473$	3373.77	−	2830.93i	0.327963	−	0.275193i
$474$		0			0
$475$	−6590.37	+	2398.70i	−0.636604	+	0.231705i
$476$	1760.67	+	3049.57i	0.169538	+	0.293649i
$477$		0			0
$478$	−4048.56	+	7012.31i	−0.387399	+	0.670995i
$479$	543.260	−	3080.98i	0.0518208	−	0.293890i	−0.947873	−	0.318649i	$-0.896771\pi$
$479$	543.260	−	3080.98i	0.0518208	−	0.293890i	0.999693	+	0.0247591i	$0.00788186\pi$
$480$		0			0
$481$	−12938.3	−	4709.14i	−1.22647	−	0.446400i
$482$	1226.32	+	6954.80i	0.115886	+	0.657225i
$483$		0			0
$484$	−2597.62	−	2179.67i	−0.243954	−	0.204702i
$485$	−1479.68			−0.138534
$486$		0			0
$487$	−3744.20			−0.348390			−0.174195	−	0.984711i	$-0.555732\pi$
$487$	−3744.20			−0.348390			−0.174195	+	0.984711i	$0.555732\pi$
$488$	753.072	+	631.902i	0.0698565	+	0.0586165i
$489$		0			0
$490$	269.622	+	1529.10i	0.0248577	+	0.140975i
$491$	−6489.00	−	2361.80i	−0.596425	−	0.217081i	0.0261281	−	0.999659i	$-0.491682\pi$
$491$	−6489.00	−	2361.80i	−0.596425	−	0.217081i	−0.622553	+	0.782578i	$0.713904\pi$
$492$		0			0
$493$	950.356	−	5389.74i	0.0868192	−	0.492376i
$494$	−1640.10	+	2840.73i	−0.149375	+	0.258726i
$495$		0			0
$496$	1237.10	+	2142.71i	0.111990	+	0.193973i
$497$	−1494.55	+	543.970i	−0.134888	+	0.0490954i
$498$		0			0
$499$	4623.81	−	3879.84i	0.414810	−	0.348067i	−0.411375	−	0.911466i	$-0.634951\pi$
$499$	4623.81	−	3879.84i	0.414810	−	0.348067i	0.826185	+	0.563399i	$0.190507\pi$
$500$	−12669.9	+	10631.3i	−1.13323	+	0.950896i
$501$		0			0
$502$	9677.88	−	3522.46i	0.860448	−	0.313177i
$503$	1524.27	+	2640.11i	0.135117	+	0.234029i	0.925642	−	0.378400i	$-0.123526\pi$
$503$	1524.27	+	2640.11i	0.135117	+	0.234029i	−0.790525	+	0.612429i	$0.790192\pi$
$504$		0			0
$505$	2436.04	−	4219.35i	0.214658	−	0.371799i
$506$	−402.443	+	2282.37i	−0.0353572	+	0.200521i
$507$		0			0
$508$	−3242.35	−	1180.12i	−0.283181	−	0.103069i
$509$	−2881.10	−	16339.5i	−0.250889	−	1.42286i	−0.806408	−	0.591359i	$-0.798592\pi$
$509$	−2881.10	−	16339.5i	−0.250889	−	1.42286i	0.555519	−	0.831504i	$-0.312519\pi$
$510$		0			0
$511$	5095.74	+	4275.83i	0.441139	+	0.370160i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	7828.25			0.671769
$515$	19816.3	+	16627.9i	1.69556	+	1.42274i
$516$		0			0
$517$	−74.6594	−	423.415i	−0.00635110	−	0.0360189i
$518$	6721.19	+	2446.31i	0.570100	+	0.207500i
$519$		0			0
$520$	−2200.71	+	12480.9i	−0.185592	+	1.05254i
$521$	6090.09	−	10548.3i	0.512115	−	0.887008i	−0.487787	−	0.872963i	$-0.662196\pi$
$521$	6090.09	−	10548.3i	0.512115	−	0.887008i	0.999901	−	0.0140456i	$-0.00447101\pi$
$522$		0			0
$523$	−3841.09	−	6652.96i	−0.321145	−	0.556240i	0.659579	−	0.751635i	$-0.270735\pi$
$523$	−3841.09	−	6652.96i	−0.321145	−	0.556240i	−0.980725	+	0.195395i	$0.937401\pi$
$524$	−3089.17	+	1124.37i	−0.257540	+	0.0937369i
$525$		0			0
$526$	7176.41	−	6021.72i	0.594879	−	0.499163i
$527$	−5351.27	+	4490.25i	−0.442324	+	0.371154i
$528$		0			0
$529$	8822.21	−	3211.02i	0.725093	−	0.263912i
$530$	−13659.4	−	23658.8i	−1.11948	−	1.93900i
$531$		0			0
$532$	852.000	−	1475.71i	0.0694340	−	0.120263i
$533$	−3623.46	+	20549.7i	−0.294464	+	1.66999i
$534$		0			0
$535$	2997.75	+	1091.09i	0.242250	+	0.0881719i
$536$	−403.696	−	2289.47i	−0.0325317	−	0.184497i
$537$		0			0
$538$	−3967.21	−	3328.88i	−0.317916	−	0.266763i
$539$	808.279			0.0645919
$540$		0			0
$541$	−4267.11			−0.339108			−0.169554	−	0.985521i	$-0.554233\pi$
$541$	−4267.11			−0.339108			−0.169554	+	0.985521i	$0.554233\pi$
$542$	−11503.9	−	9652.89i	−0.911686	−	0.764995i
$543$		0			0
$544$	−251.021	−	1423.61i	−0.0197839	−	0.112200i
$545$	4474.99	+	1628.76i	0.351720	+	0.128016i
$546$		0			0
$547$	−2499.30	+	14174.3i	−0.195361	+	1.10795i	0.716543	+	0.697543i	$0.245724\pi$
$547$	−2499.30	+	14174.3i	−0.195361	+	1.10795i	−0.911904	+	0.410404i	$0.865388\pi$
$548$	−2111.76	+	3657.68i	−0.164617	+	0.285124i
$549$		0			0
$550$	7052.84	+	12215.9i	0.546789	+	0.947067i
$551$	−2488.64	+	905.792i	−0.192413	+	0.0700328i
$552$		0			0
$553$	−17694.6	+	14847.5i	−1.36067	+	1.14174i
$554$	8883.46	−	7454.11i	0.681267	−	0.571651i
$555$		0			0
$556$	10295.8	−	3747.37i	0.785322	−	0.285834i
$557$	−1455.19	−	2520.47i	−0.110698	−	0.191734i	0.805354	−	0.592794i	$-0.201975\pi$
$557$	−1455.19	−	2520.47i	−0.110698	−	0.191734i	−0.916052	+	0.401060i	$0.868642\pi$
$558$		0			0
$559$	7515.55	−	13017.3i	0.568647	−	0.984926i
$560$	1143.23	−	6483.58i	0.0862683	−	0.489252i
$561$		0			0
$562$	−11092.1	−	4037.20i	−0.832549	−	0.303023i
$563$	3303.06	+	18732.6i	0.247260	+	1.40228i	0.815185	+	0.579201i	$0.196635\pi$
$563$	3303.06	+	18732.6i	0.247260	+	1.40228i	−0.567925	+	0.823080i	$0.692254\pi$
$564$		0			0
$565$	3486.39	+	2925.43i	0.259599	+	0.217830i
$566$	4002.71			0.297255
$567$		0			0
$568$	652.911			0.0482316
$569$	−5508.72	−	4622.37i	−0.405866	−	0.340562i	0.416890	−	0.908957i	$-0.363120\pi$
$569$	−5508.72	−	4622.37i	−0.405866	−	0.340562i	−0.822756	+	0.568395i	$0.807565\pi$
$570$		0			0
$571$	3292.28	+	18671.4i	0.241292	+	1.36843i	0.828949	+	0.559324i	$0.188939\pi$
$571$	3292.28	+	18671.4i	0.241292	+	1.36843i	−0.587658	+	0.809110i	$0.699950\pi$
$572$	6199.49	+	2256.43i	0.453171	+	0.164941i
$573$		0			0
$574$	1882.32	−	10675.2i	0.136875	−	0.776259i
$575$	−8455.84	+	14645.9i	−0.613274	+	1.06222i
$576$		0			0
$577$	−5734.85	−	9933.06i	−0.413770	−	0.716670i	0.581529	−	0.813526i	$-0.302455\pi$
$577$	−5734.85	−	9933.06i	−0.413770	−	0.716670i	−0.995298	+	0.0968558i	$0.969121\pi$
$578$	−5398.16	+	1964.77i	−0.388467	+	0.141390i
$579$		0			0
$580$	−7838.35	+	6577.16i	−0.561155	+	0.470865i
$581$	13960.5	−	11714.2i	0.996866	−	0.836470i
$582$		0			0
$583$	−13363.6	+	4863.96i	−0.949338	+	0.345531i
$584$	−1365.38	−	2364.91i	−0.0967464	−	0.167570i
$585$		0			0
$586$	3051.48	−	5285.31i	0.215112	−	0.372584i
$587$	1915.32	−	10862.3i	0.134674	−	0.763775i	−0.840412	−	0.541948i	$-0.817687\pi$
$587$	1915.32	−	10862.3i	0.134674	−	0.763775i	0.975086	−	0.221827i	$-0.0712020\pi$
$588$		0			0
$589$	3176.51	+	1156.15i	0.222217	+	0.0808803i
$590$	3245.56	+	18406.5i	0.226470	+	1.28438i
$591$		0			0
$592$	−2249.29	−	1887.38i	−0.156157	−	0.131032i
$593$	7985.38			0.552985			0.276492	−	0.961016i	$-0.410828\pi$
$593$	7985.38			0.552985			0.276492	+	0.961016i	$0.410828\pi$
$594$		0			0
$595$	18588.0			1.28073
$596$	−108.302	−	90.8759i	−0.00744331	−	0.00624568i
$597$		0			0
$598$	1373.51	+	7789.58i	0.0939249	+	0.532675i
$599$	9742.32	+	3545.91i	0.664541	+	0.241873i	0.652196	−	0.758051i	$-0.273848\pi$
$599$	9742.32	+	3545.91i	0.664541	+	0.241873i	0.0123455	+	0.999924i	$0.496070\pi$
$600$		0			0
$601$	1866.12	−	10583.3i	0.126657	−	0.718306i	−0.853653	−	0.520842i	$-0.825618\pi$
$601$	1866.12	−	10583.3i	0.126657	−	0.718306i	0.980310	−	0.197465i	$-0.0632707\pi$
$602$	−3904.19	+	6762.25i	−0.264324	+	0.457822i
$603$		0			0
$604$	−4812.84	−	8336.09i	−0.324225	−	0.561574i
$605$	−16820.2	+	6122.07i	−1.13031	+	0.411401i
$606$		0			0
$607$	6705.45	−	5626.54i	0.448378	−	0.376234i	−0.390455	−	0.920622i	$-0.627682\pi$
$607$	6705.45	−	5626.54i	0.448378	−	0.376234i	0.838834	+	0.544388i	$0.183238\pi$
$608$	−535.864	+	449.643i	−0.0357437	+	0.0299925i
$609$		0			0
$610$	4876.32	−	1774.84i	0.323666	−	0.117805i
$611$	−733.691	−	1270.79i	−0.0485793	−	0.0841418i
$612$		0			0
$613$	−4445.77	+	7700.29i	−0.292925	+	0.507360i	−0.974500	−	0.224388i	$-0.927962\pi$
$613$	−4445.77	+	7700.29i	−0.292925	+	0.507360i	0.681575	+	0.731748i	$0.261295\pi$
$614$	2987.85	−	16944.9i	0.196384	−	1.11375i
$615$		0			0
$616$	−3220.52	−	1172.17i	−0.210647	−	0.0766691i
$617$	1945.98	+	11036.2i	0.126973	+	0.720098i	0.980117	+	0.198423i	$0.0635818\pi$
$617$	1945.98	+	11036.2i	0.126973	+	0.720098i	−0.853144	+	0.521676i	$0.825307\pi$
$618$		0			0
$619$	1771.15	+	1486.17i	0.115006	+	0.0965012i	0.698477	−	0.715633i	$-0.253861\pi$
$619$	1771.15	+	1486.17i	0.115006	+	0.0965012i	−0.583471	+	0.812134i	$0.698306\pi$
$620$	13060.4			0.845999
$621$		0			0
$622$	−4993.14			−0.321876
$623$	21019.5	+	17637.5i	1.35173	+	1.13424i
$624$		0			0
$625$	8196.63	+	46485.4i	0.524585	+	2.97507i
$626$	−112.125	−	40.8100i	−0.00715878	−	0.00260558i
$627$		0			0
$628$	168.350	−	954.760i	0.0106973	−	0.0606673i
$629$	4145.05	−	7179.45i	0.262757	−	0.455109i
$630$		0			0
$631$	10314.0	+	17864.4i	0.650703	+	1.12705i	0.982953	+	0.183860i	$0.0588592\pi$
$631$	10314.0	+	17864.4i	0.650703	+	1.12705i	−0.332249	+	0.943192i	$0.607808\pi$
$632$	8910.51	−	3243.16i	0.560825	−	0.204123i
$633$		0			0
$634$	3070.19	−	2576.19i	0.192323	−	0.161378i
$635$	−13952.5	+	11707.5i	−0.871949	+	0.731652i
$636$		0			0
$637$	2592.24	−	943.499i	0.161238	−	0.0586857i
$638$	2663.28	+	4612.94i	0.165267	+	0.286251i
$639$		0			0
$640$	−1351.34	+	2340.59i	−0.0834630	+	0.144562i
$641$	−1825.80	+	10354.6i	−0.112504	+	0.638040i	0.875452	+	0.483305i	$0.160564\pi$
$641$	−1825.80	+	10354.6i	−0.112504	+	0.638040i	−0.987956	+	0.154735i	$0.950548\pi$
$642$		0			0
$643$	−13089.4	−	4764.15i	−0.802792	−	0.292192i	−0.0921491	−	0.995745i	$-0.529374\pi$
$643$	−13089.4	−	4764.15i	−0.802792	−	0.292192i	−0.710643	+	0.703553i	$0.751596\pi$
$644$	−713.514	−	4046.54i	−0.0436590	−	0.247603i
$645$		0			0
$646$	−1512.95	−	1269.51i	−0.0921457	−	0.0773194i
$647$	14641.7			0.889683			0.444841	−	0.895609i	$-0.353260\pi$
$647$	14641.7			0.889683			0.444841	+	0.895609i	$0.353260\pi$
$648$		0			0
$649$	9729.62			0.588476
$650$	36878.8	+	30945.0i	2.22539	+	1.86733i
$651$		0			0
$652$	1155.64	+	6553.93i	0.0694144	+	0.393669i
$653$	889.188	+	323.638i	0.0532873	+	0.0193950i	0.368526	−	0.929617i	$-0.379862\pi$
$653$	889.188	+	323.638i	0.0532873	+	0.0193950i	−0.315239	+	0.949012i	$0.602085\pi$
$654$		0			0
$655$	−3013.36	+	17089.6i	−0.179758	+	1.01946i
$656$	−2224.97	+	3853.76i	−0.132424	+	0.229366i
$657$		0			0
$658$	381.139	+	660.151i	0.0225810	+	0.0391115i
$659$	10370.4	−	3774.52i	0.613010	−	0.223117i	−0.0168097	−	0.999859i	$-0.505351\pi$
$659$	10370.4	−	3774.52i	0.613010	−	0.223117i	0.629820	+	0.776741i	$0.283129\pi$
$660$		0			0
$661$	−216.154	+	181.375i	−0.0127192	+	0.0106727i	−0.649125	−	0.760682i	$-0.724865\pi$
$661$	−216.154	+	181.375i	−0.0127192	+	0.0106727i	0.636406	+	0.771354i	$0.280420\pi$
$662$	4204.51	−	3528.00i	0.246847	−	0.207129i
$663$		0			0
$664$	−7030.13	+	2558.76i	−0.410877	+	0.149547i
$665$	−4497.42	−	7789.76i	−0.262259	−	0.454247i
$666$		0			0
$667$	−3193.08	+	5530.58i	−0.185362	+	0.321057i
$668$	−1048.61	+	5946.97i	−0.0607365	+	0.344454i
$669$		0			0
$670$	−11531.7	−	4197.20i	−0.664939	−	0.242018i
$671$	−469.087	−	2660.32i	−0.0269879	−	0.153056i
$672$		0			0
$673$	−24529.4	−	20582.6i	−1.40496	−	1.17890i	−0.958847	−	0.283922i	$-0.908364\pi$
$673$	−24529.4	−	20582.6i	−1.40496	−	1.17890i	−0.446111	−	0.894978i	$-0.647191\pi$
$674$	3828.97			0.218823
$675$		0			0
$676$	13728.4			0.781086
$677$	−24698.5	−	20724.5i	−1.40213	−	1.17653i	−0.960145	−	0.279501i	$-0.909831\pi$
$677$	−24698.5	−	20724.5i	−1.40213	−	1.17653i	−0.441983	−	0.897024i	$-0.645725\pi$
$678$		0			0
$679$	−237.145	−	1344.91i	−0.0134032	−	0.0760133i
$680$	−7170.50	−	2609.85i	−0.404377	−	0.147181i
$681$		0			0
$682$	1180.60	−	6695.54i	0.0662869	−	0.375932i
$683$	−1007.06	+	1744.27i	−0.0564187	+	0.0977201i	−0.892855	−	0.450344i	$-0.851302\pi$
$683$	−1007.06	+	1744.27i	−0.0564187	+	0.0977201i	0.836437	+	0.548064i	$0.184635\pi$
$684$		0			0
$685$	11147.3	+	19307.6i	0.621774	+	1.07694i
$686$	11215.7	−	4082.17i	0.624222	−	0.227198i
$687$		0			0
$688$	2455.53	−	2060.43i	0.136070	−	0.114176i
$689$	−37180.9	+	31198.5i	−2.05585	+	1.72506i
$690$		0			0
$691$	5873.56	−	2137.80i	0.323359	−	0.117693i	−0.175240	−	0.984526i	$-0.556070\pi$
$691$	5873.56	−	2137.80i	0.323359	−	0.117693i	0.498599	+	0.866833i	$0.333848\pi$
$692$	−1497.56	−	2593.85i	−0.0822667	−	0.142490i
$693$		0			0
$694$	−2095.58	+	3629.65i	−0.114621	+	0.198530i
$695$	10043.1	−	56957.4i	0.548140	−	3.10866i
$696$		0			0
$697$	−11806.2	−	4297.10i	−0.641594	−	0.233521i
$698$	−1768.02	−	10026.9i	−0.0958744	−	0.543731i
$699$		0			0
$700$	−19157.8	−	16075.3i	−1.03443	−	0.867987i
$701$	−12250.3			−0.660037			−0.330019	−	0.943974i	$-0.607055\pi$
$701$	−12250.3			−0.660037			−0.330019	+	0.943974i	$0.607055\pi$
$702$		0			0
$703$	−4011.63			−0.215223
$704$	1077.77	+	904.353i	0.0576987	+	0.0484149i
$705$		0			0
$706$	−401.740	−	2278.38i	−0.0214160	−	0.121456i
$707$	4225.48	+	1537.95i	0.224774	+	0.0818111i
$708$		0			0
$709$	4152.58	−	23550.5i	0.219963	−	1.24747i	−0.652122	−	0.758114i	$-0.726121\pi$
$709$	4152.58	−	23550.5i	0.219963	−	1.24747i	0.872084	−	0.489356i	$-0.162768\pi$
$710$	1723.25	−	2984.76i	0.0910879	−	0.157769i
$711$		0			0
$712$	−5632.09	−	9755.06i	−0.296449	−	0.513464i
$713$	7659.71	−	2787.91i	0.402326	−	0.146435i
$714$		0			0
$715$	26677.7	−	22385.2i	1.39537	−	1.17085i
$716$	12883.4	−	10810.5i	0.672452	−	0.564254i
$717$		0			0
$718$	−24921.4	+	9070.65i	−1.29535	+	0.471468i
$719$	−12187.4	−	21109.3i	−0.632149	−	1.09491i	−0.987112	−	0.160034i	$-0.948840\pi$
$719$	−12187.4	−	21109.3i	−0.632149	−	1.09491i	0.354962	−	0.934881i	$-0.384494\pi$
$720$		0			0
$721$	−11937.5	+	20676.4i	−0.616611	+	1.06800i
$722$	2216.15	−	12568.4i	0.114233	−	0.647849i
$723$		0			0
$724$	14237.9	+	5182.16i	0.730864	+	0.266013i
$725$	6749.48	+	38278.2i	0.345751	+	1.96085i
$726$		0			0
$727$	−7628.04	−	6400.69i	−0.389145	−	0.326531i	0.427135	−	0.904188i	$-0.359523\pi$
$727$	−7628.04	−	6400.69i	−0.389145	−	0.326531i	−0.816280	+	0.577656i	$0.803967\pi$
$728$	−11696.8			−0.595486
$729$		0			0
$730$	−14414.8			−0.730842
$731$	6932.90	+	5817.39i	0.350783	+	0.294342i
$732$		0			0
$733$	58.2016	+	330.077i	0.00293277	+	0.0166326i	0.986239	−	0.165326i	$-0.0528675\pi$
$733$	58.2016	+	330.077i	0.00293277	+	0.0166326i	−0.983306	+	0.181958i	$0.941756\pi$
$734$	−25863.5	−	9413.56i	−1.30060	−	0.473380i
$735$		0			0
$736$	−292.909	+	1661.17i	−0.0146695	+	0.0831951i
$737$	−3194.15	+	5532.42i	−0.159644	+	0.276512i
$738$		0			0
$739$	6777.14	+	11738.4i	0.337349	+	0.584306i	0.983933	−	0.178537i	$-0.0571363\pi$
$739$	6777.14	+	11738.4i	0.337349	+	0.584306i	−0.646584	+	0.762843i	$0.723803\pi$
$740$	−14564.7	+	5301.11i	−0.723524	+	0.263341i
$741$		0			0
$742$	19314.8	−	16207.0i	0.955619	−	0.801859i
$743$	−1284.31	+	1077.66i	−0.0634140	+	0.0532107i	−0.673944	−	0.738783i	$-0.735401\pi$
$743$	−1284.31	+	1077.66i	−0.0634140	+	0.0532107i	0.610530	+	0.791993i	$0.290957\pi$
$744$		0			0
$745$	−701.280	+	255.245i	−0.0344871	+	0.0125523i
$746$	−5579.83	−	9664.55i	−0.273850	−	0.474322i
$747$		0			0
$748$	−1986.14	+	3440.10i	−0.0970862	+	0.168158i
$749$	−511.275	+	2899.58i	−0.0249420	+	0.141453i
$750$		0			0
$751$	−27042.5	−	9842.67i	−1.31397	−	0.478248i	−0.412452	−	0.910979i	$-0.635327\pi$
$751$	−27042.5	−	9842.67i	−1.31397	−	0.478248i	−0.901523	+	0.432732i	$0.857550\pi$
$752$	−54.3393	−	308.173i	−0.00263504	−	0.0149441i
$753$		0			0
$754$	13926.1	+	11685.4i	0.672625	+	0.564399i
$755$	−50810.8			−2.44926
$756$		0			0
$757$	1878.31			0.0901828			0.0450914	−	0.998983i	$-0.485642\pi$
$757$	1878.31			0.0901828			0.0450914	+	0.998983i	$0.485642\pi$
$758$	−17104.5	−	14352.3i	−0.819607	−	0.687732i
$759$		0			0
$760$	641.202	+	3636.44i	0.0306037	+	0.173562i
$761$	−24957.1	−	9083.65i	−1.18882	−	0.432697i	−0.329514	−	0.944151i	$-0.606885\pi$
$761$	−24957.1	−	9083.65i	−1.18882	−	0.432697i	−0.859310	+	0.511454i	$0.829107\pi$
$762$		0			0
$763$	−763.224	+	4328.46i	−0.0362130	+	0.205374i
$764$	−908.609	+	1573.76i	−0.0430266	+	0.0745242i
$765$		0			0
$766$	−2078.25	−	3599.63i	−0.0980290	−	0.169791i
$767$	31204.0	−	11357.3i	1.46898	−	0.534666i
$768$		0			0
$769$	5064.66	−	4249.75i	0.237498	−	0.199285i	−0.516268	−	0.856427i	$-0.672679\pi$
$769$	5064.66	−	4249.75i	0.237498	−	0.199285i	0.753767	+	0.657142i	$0.228235\pi$
$770$	−13858.6	+	11628.7i	−0.648607	+	0.544246i
$771$		0			0
$772$	354.662	−	129.086i	0.0165344	−	0.00601804i
$773$	12817.3	+	22200.3i	0.596388	+	1.03297i	0.993349	+	0.115139i	$0.0367312\pi$
$773$	12817.3	+	22200.3i	0.596388	+	1.03297i	−0.396962	+	0.917835i	$0.629935\pi$
$774$		0			0
$775$	24806.0	−	42965.3i	1.14975	−	1.99143i
$776$	−97.3518	+	552.109i	−0.00450351	+	0.0255407i
$777$		0			0
$778$	26553.6	+	9664.73i	1.22364	+	0.445369i
$779$	1055.73	+	5987.37i	0.0485566	+	0.275378i
$780$		0			0
$781$	−1374.39	−	1153.25i	−0.0629698	−	0.0528379i
$782$	−4762.47			−0.217782
$783$		0			0
$784$	588.289			0.0267989
$785$	−3920.31	−	3289.53i	−0.178245	−	0.149565i
$786$		0			0
$787$	6185.74	+	35081.1i	0.280175	+	1.58895i	0.722028	+	0.691864i	$0.243210\pi$
$787$	6185.74	+	35081.1i	0.280175	+	1.58895i	−0.441853	+	0.897087i	$0.645679\pi$
$788$	11852.7	+	4314.04i	0.535832	+	0.195027i
$789$		0			0
$790$	8691.83	−	49293.8i	0.391445	−	2.21999i
$791$	−2100.23	+	3637.71i	−0.0944067	+	0.163517i
$792$		0			0
$793$	−4609.79	−	7984.40i	−0.206430	−	0.357546i
$794$	16708.7	−	6081.47i	0.746814	−	0.271818i
$795$		0			0
$796$	9523.89	−	7991.50i	0.424077	−	0.355843i
$797$	9496.50	−	7968.51i	0.422062	−	0.354152i	−0.406885	−	0.913479i	$-0.633385\pi$
$797$	9496.50	−	7968.51i	0.422062	−	0.354152i	0.828947	+	0.559327i	$0.188941\pi$
$798$		0			0
$799$	830.231	−	302.179i	0.0367603	−	0.0133796i
$800$	5133.26	+	8891.07i	0.226860	+	0.392933i
$801$		0			0
$802$	10314.6	−	17865.5i	0.454142	−	0.786598i
$803$	−1303.03	+	7389.86i	−0.0572640	+	0.324760i
$804$		0			0
$805$	−20381.8	−	7418.36i	−0.892377	−	0.324799i
$806$	−4029.33	−	22851.5i	−0.176088	−	0.998646i
$807$		0			0
$808$	−1414.08	−	1186.56i	−0.0615684	−	0.0516620i
$809$	9115.26			0.396138			0.198069	−	0.980188i	$-0.436533\pi$
$809$	9115.26			0.396138			0.198069	+	0.980188i	$0.436533\pi$
$810$		0			0
$811$	20744.0			0.898177			0.449089	−	0.893487i	$-0.351749\pi$
$811$	20744.0			0.898177			0.449089	+	0.893487i	$0.351749\pi$
$812$	−7234.35	−	6070.34i	−0.312655	−	0.262349i
$813$		0			0
$814$	1401.08	+	7945.90i	0.0603289	+	0.342142i
$815$	33011.1	+	12015.1i	1.41881	+	0.516404i
$816$		0			0
$817$	760.487	−	4312.94i	0.0325656	−	0.184689i
$818$	7090.91	−	12281.8i	0.303090	−	0.524968i
$819$		0			0
$820$	11744.9	+	20342.7i	0.500181	+	0.866339i
$821$	−20199.2	+	7351.89i	−0.858655	+	0.312525i	−0.733564	−	0.679620i	$-0.762144\pi$
$821$	−20199.2	+	7351.89i	−0.858655	+	0.312525i	−0.125091	+	0.992145i	$0.539922\pi$
$822$		0			0
$823$	−22050.0	+	18502.1i	−0.933918	+	0.783650i	−0.976517	−	0.215442i	$-0.930881\pi$
$823$	−22050.0	+	18502.1i	−0.933918	+	0.783650i	0.0425984	+	0.999092i	$0.486436\pi$
$824$	7508.08	−	6300.02i	0.317423	−	0.266349i
$825$		0			0
$826$	−16209.9	+	5899.92i	−0.682826	+	0.248528i
$827$	2495.06	+	4321.57i	0.104911	+	0.181712i	0.913702	−	0.406385i	$-0.133211\pi$
$827$	2495.06	+	4321.57i	0.104911	+	0.181712i	−0.808791	+	0.588097i	$0.799877\pi$
$828$		0			0
$829$	8527.42	−	14769.9i	0.357261	−	0.618794i	−0.630241	−	0.776399i	$-0.717044\pi$
$829$	8527.42	−	14769.9i	0.357261	−	0.618794i	0.987502	+	0.157605i	$0.0503773\pi$
$830$	−6857.60	+	38891.4i	−0.286784	+	1.62643i
$831$		0			0
$832$	4512.17	+	1642.29i	0.188018	+	0.0684330i
$833$	288.423	+	1635.73i	0.0119967	+	0.0680368i
$834$		0			0
$835$	24418.7	+	20489.7i	1.01203	+	0.849192i
$836$	1922.21			0.0795228
$837$		0			0
$838$	−16506.7			−0.680445
$839$	−5469.34	−	4589.32i	−0.225057	−	0.188845i	0.523286	−	0.852157i	$-0.324706\pi$
$839$	−5469.34	−	4589.32i	−0.225057	−	0.188845i	−0.748343	+	0.663312i	$0.769150\pi$
$840$		0			0
$841$	−1686.38	−	9563.92i	−0.0691450	−	0.392141i
$842$	27512.0	+	10013.5i	1.12604	+	0.409845i
$843$		0			0
$844$	1524.70	−	8647.02i	0.0621830	−	0.352657i
$845$	36233.7	−	62758.7i	1.47512	−	2.55499i
$846$		0			0
$847$	−8260.22	−	14307.1i	−0.335094	−	0.580400i
$848$	−9726.42	+	3540.13i	−0.393876	+	0.143359i
$849$		0			0
$850$	−22204.8	+	18632.0i	−0.896021	+	0.751851i
$851$	−7410.34	+	6218.01i	−0.298500	+	0.250471i
$852$		0			0
$853$	19955.4	−	7263.17i	0.801007	−	0.291543i	0.0911036	−	0.995841i	$-0.470961\pi$
$853$	19955.4	−	7263.17i	0.801007	−	0.291543i	0.709904	+	0.704299i	$0.248738\pi$
$854$	2394.70	+	4147.75i	0.0959544	+	0.166198i
$855$		0			0
$856$	604.345	−	1046.76i	0.0241309	−	0.0417960i
$857$	3346.70	−	18980.1i	0.133397	−	0.756532i	−0.842566	−	0.538594i	$-0.818956\pi$
$857$	3346.70	−	18980.1i	0.133397	−	0.756532i	0.975963	−	0.217938i	$-0.0699331\pi$
$858$		0			0
$859$	−14774.5	−	5377.49i	−0.586845	−	0.213594i	0.0314960	−	0.999504i	$-0.489973\pi$
$859$	−14774.5	−	5377.49i	−0.586845	−	0.213594i	−0.618341	+	0.785910i	$0.712195\pi$
$860$	−2938.23	−	16663.5i	−0.116503	−	0.660723i
$861$		0			0
$862$	25416.2	+	21326.7i	1.00427	+	0.842682i
$863$	38698.5			1.52643			0.763217	−	0.646142i	$-0.223619\pi$
$863$	38698.5			1.52643			0.763217	+	0.646142i	$0.223619\pi$
$864$		0			0
$865$	−15810.2			−0.621460
$866$	13583.0	+	11397.5i	0.532988	+	0.447230i
$867$		0			0
$868$	2093.16	+	11870.9i	0.0818509	+	0.464199i
$869$	−24485.2	−	8911.88i	−0.955815	−	0.347888i
$870$		0			0
$871$	−3786.03	+	21471.6i	−0.147284	+	0.835291i
$872$	902.158	−	1562.58i	0.0350354	−	0.0606832i
$873$		0			0
$874$	1152.29	+	1995.83i	0.0445961	+	0.0772426i
$875$	−75719.2	+	27559.5i	−2.92546	+	1.06478i
$876$		0			0
$877$	−17652.1	+	14811.9i	−0.679668	+	0.570309i	−0.915909	−	0.401386i	$-0.868529\pi$
$877$	−17652.1	+	14811.9i	−0.679668	+	0.570309i	0.236242	+	0.971694i	$0.424084\pi$
$878$	−18640.3	+	15641.1i	−0.716493	+	0.601209i
$879$		0			0
$880$	6978.80	−	2540.07i	0.267335	−	0.0973022i
$881$	6688.90	+	11585.5i	0.255794	+	0.443049i	0.965111	−	0.261841i	$-0.0843297\pi$
$881$	6688.90	+	11585.5i	0.255794	+	0.443049i	−0.709317	+	0.704890i	$0.750996\pi$
$882$		0			0
$883$	25788.3	−	44666.7i	0.982838	−	1.70233i	0.331663	−	0.943398i	$-0.392390\pi$
$883$	25788.3	−	44666.7i	0.982838	−	1.70233i	0.651175	−	0.758927i	$-0.274276\pi$
$884$	−2354.18	+	13351.2i	−0.0895696	+	0.507974i
$885$		0			0
$886$	−15898.0	−	5786.39i	−0.602825	−	0.219410i
$887$	−532.534	−	3020.15i	−0.0201587	−	0.114326i	0.973068	−	0.230518i	$-0.0740421\pi$
$887$	−532.534	−	3020.15i	−0.0201587	−	0.114326i	−0.993227	+	0.116193i	$0.962931\pi$
$888$		0			0
$889$	−12877.4	−	10805.4i	−0.485818	−	0.407650i
$890$	−59459.8			−2.23943
$891$		0			0
$892$	−11392.6			−0.427636
$893$	−327.513	−	274.816i	−0.0122730	−	0.0102983i
$894$		0			0
$895$	−15416.0	−	87428.4i	−0.575754	−	3.26526i
$896$	−2343.99	−	853.141i	−0.0873963	−	0.0318096i
$897$		0			0
$898$	−2287.72	+	12974.3i	−0.0850135	+	0.482136i
$899$	9367.21	−	16224.5i	0.347513	−	0.601910i
$900$		0			0
$901$	−14611.9	−	25308.6i	−0.540281	−	0.935794i
$902$	11490.5	−	4182.22i	0.424161	−	0.154382i
$903$		0			0
$904$	1320.94	−	1108.40i	0.0485992	−	0.0407796i
$905$	61268.5	−	51410.3i	2.25042	−	1.88833i
$906$		0			0
$907$	9841.74	−	3582.10i	0.360297	−	0.131137i	−0.155528	−	0.987832i	$-0.549708\pi$
$907$	9841.74	−	3582.10i	0.360297	−	0.131137i	0.515825	+	0.856694i	$0.327486\pi$
$908$	19.2937	+	33.4176i	0.000705157	+	0.00122137i
$909$		0			0
$910$	−30871.8	+	53471.6i	−1.12461	+	1.94787i
$911$	−7998.06	+	45359.3i	−0.290875	+	1.64964i	0.392634	+	0.919695i	$0.371564\pi$
$911$	−7998.06	+	45359.3i	−0.290875	+	1.64964i	−0.683509	+	0.729942i	$0.739547\pi$
$912$		0			0
$913$	19318.1	+	7031.21i	0.700258	+	0.254873i
$914$	1607.24	+	9115.12i	0.0581650	+	0.329870i
$915$		0			0
$916$	−9372.03	−	7864.07i	−0.338057	−	0.283664i
$917$	−16016.0			−0.576768
$918$		0			0
$919$	−7250.25			−0.260243			−0.130122	−	0.991498i	$-0.541537\pi$
$919$	−7250.25			−0.260243			−0.130122	+	0.991498i	$0.541537\pi$
$920$	6820.89	+	5723.41i	0.244433	+	0.205103i
$921$		0			0
$922$	951.242	+	5394.76i	0.0339777	+	0.192697i
$923$	−5753.99	−	2094.28i	−0.205195	−	0.0746849i
$924$		0			0
$925$	−10223.9	+	57982.3i	−0.363414	+	2.06102i
$926$	−16609.8	+	28769.0i	−0.589450	+	1.02096i
$927$		0			0
$928$	1938.41	+	3357.43i	0.0685685	+	0.118764i
$929$	40260.4	−	14653.6i	1.42185	−	0.517512i	0.487267	−	0.873253i	$-0.337994\pi$
$929$	40260.4	−	14653.6i	1.42185	−	0.517512i	0.934584	+	0.355742i	$0.115772\pi$
$930$		0			0
$931$	615.708	−	516.640i	0.0216746	−	0.0181871i
$932$	14042.0	−	11782.7i	0.493521	−	0.414114i
$933$		0			0
$934$	16633.5	−	6054.09i	0.582724	−	0.212094i
$935$	10484.2	+	18159.1i	0.366705	+	0.635152i
$936$		0			0
$937$	−22311.8	+	38645.1i	−0.777902	+	1.34737i	0.155247	+	0.987876i	$0.450383\pi$
$937$	−22311.8	+	38645.1i	−0.777902	+	1.34737i	−0.933149	+	0.359490i	$0.882951\pi$
$938$	1966.77	−	11154.1i	0.0684620	−	0.388267i
$939$		0			0
$940$	−1552.22	−	564.962i	−0.0538594	−	0.0196032i
$941$	−646.880	−	3668.64i	−0.0224099	−	0.127093i	0.971550	−	0.236833i	$-0.0761093\pi$
$941$	−646.880	−	3668.64i	−0.0224099	−	0.127093i	−0.993960	+	0.109740i	$0.964998\pi$
$942$		0			0
$943$	11230.6	+	9423.56i	0.387823	+	0.325422i
$944$	7081.50			0.244156
$945$		0			0
$946$	−8808.30			−0.302730
$947$	−21967.6	−	18433.0i	−0.753803	−	0.632516i	0.182703	−	0.983168i	$-0.441515\pi$
$947$	−21967.6	−	18433.0i	−0.753803	−	0.632516i	−0.936506	+	0.350652i	$0.885960\pi$
$948$		0			0
$949$	4447.17	+	25221.1i	0.152119	+	0.862711i
$950$	13180.7	+	4797.39i	0.450147	+	0.163840i
$951$		0			0
$952$	1222.95	−	6935.70i	0.0416345	−	0.236121i
$953$	−15483.6	+	26818.4i	−0.526300	+	0.911579i	0.473230	+	0.880939i	$0.343088\pi$
$953$	−15483.6	+	26818.4i	−0.526300	+	0.911579i	−0.999530	+	0.0306400i	$0.990245\pi$
$954$		0			0
$955$	4796.24	+	8307.33i	0.162516	+	0.281486i
$956$	15217.6	−	5538.76i	0.514825	−	0.187381i
$957$		0			0
$958$	−4793.15	+	4021.93i	−0.161649	+	0.135640i
$959$	−15762.6	+	13226.4i	−0.530762	+	0.445362i
$960$		0			0
$961$	5523.88	−	2010.53i	0.185421	−	0.0674877i
$962$	13768.6	+	23847.9i	0.461453	+	0.799260i
$963$		0			0
$964$	7062.08	−	12231.9i	0.235949	−	0.408675i
$965$	345.958	−	1962.03i	0.0115407	−	0.0654506i
$966$		0			0
$967$	23508.9	+	8556.55i	0.781795	+	0.284550i	0.701921	−	0.712255i	$-0.252326\pi$
$967$	23508.9	+	8556.55i	0.781795	+	0.284550i	0.0798743	+	0.996805i	$0.474548\pi$
$968$	1177.67	+	6678.88i	0.0391030	+	0.221764i
$969$		0			0
$970$	2267.00	+	1902.24i	0.0750402	+	0.0629662i
$971$	7341.25			0.242628			0.121314	−	0.992614i	$-0.461289\pi$
$971$	7341.25			0.242628			0.121314	+	0.992614i	$0.461289\pi$
$972$		0			0
$973$	53379.4			1.75875
$974$	5736.45	+	4813.46i	0.188714	+	0.158350i
$975$		0			0
$976$	−341.415	−	1936.26i	−0.0111972	−	0.0635022i
$977$	12624.4	+	4594.92i	0.413400	+	0.150465i	0.540343	−	0.841445i	$-0.318294\pi$
$977$	12624.4	+	4594.92i	0.413400	+	0.150465i	−0.126943	+	0.991910i	$0.540517\pi$
$978$		0			0
$979$	−5374.90	+	30482.6i	−0.175467	+	0.995125i
$980$	1552.69	−	2689.34i	0.0506111	−	0.0876609i
$981$		0			0
$982$	6905.45	+	11960.6i	0.224401	+	0.388674i
$983$	13985.0	−	5090.14i	0.453767	−	0.165158i	−0.105018	−	0.994470i	$-0.533490\pi$
$983$	13985.0	−	5090.14i	0.453767	−	0.165158i	0.558785	+	0.829313i	$0.311268\pi$
$984$		0			0
$985$	51004.7	−	42798.0i	1.64989	−	1.38443i
$986$	−8384.94	+	7035.80i	−0.270822	+	0.227247i
$987$		0			0
$988$	6164.75	−	2243.78i	0.198509	−	0.0722513i
$989$	−5280.25	−	9145.66i	−0.169770	−	0.294050i
$990$		0			0
$991$	−25481.5	+	44135.2i	−0.816797	+	1.41473i	0.0912333	+	0.995830i	$0.470919\pi$
$991$	−25481.5	+	44135.2i	−0.816797	+	1.41473i	−0.908030	+	0.418904i	$0.862414\pi$
$992$	859.278	−	4873.21i	0.0275021	−	0.155972i
$993$		0			0
$994$	2989.09	+	1087.94i	0.0953805	+	0.0347157i
$995$	−11396.1	−	64630.3i	−0.363095	−	2.05921i
$996$		0			0
$997$	26569.2	+	22294.2i	0.843987	+	0.708190i	0.958457	−	0.285237i	$-0.0920724\pi$
$997$	26569.2	+	22294.2i	0.843987	+	0.708190i	−0.114469	+	0.993427i	$0.536517\pi$
$998$	−12071.9			−0.382896
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.127.4		24
3.2	odd	2		54.4.e.a.43.2	✓	24
27.5	odd	18		54.4.e.a.49.2	yes	24
27.7	even	9		1458.4.a.e.1.1		12
27.20	odd	18		1458.4.a.h.1.12		12
27.22	even	9	inner	162.4.e.a.37.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.43.2	✓	24	3.2	odd	2
54.4.e.a.49.2	yes	24	27.5	odd	18
162.4.e.a.37.4		24	27.22	even	9	inner
162.4.e.a.127.4		24	1.1	even	1	trivial
1458.4.a.e.1.1		12	27.7	even	9
1458.4.a.h.1.12		12	27.20	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(19.8413 + 7.22164i) q^{5} +(-3.38399 + 19.1916i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(19.8413 + 7.22164i) q^{5} +(-3.38399 + 19.1916i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-21.1147 - 36.5717i) q^{10} +(-20.6574 + 7.51869i) q^{11} +(-57.4742 + 48.2266i) q^{13} +(29.8568 - 25.0528i) q^{14} +(-15.0351 + 5.47232i) q^{16} +(-22.5870 - 39.1219i) q^{17} +(-10.9300 + 18.9313i) q^{19} +(-14.6661 + 83.1755i) q^{20} +(41.3149 + 15.0374i) q^{22} +(9.15342 + 51.9116i) q^{23} +(245.769 + 206.225i) q^{25} +150.055 q^{26} -77.9506 q^{28} +(92.8070 + 77.8743i) q^{29} +(-26.8524 - 152.288i) q^{31} +(30.0702 + 10.9446i) q^{32} +(-15.6888 + 88.9756i) q^{34} +(-205.737 + 356.348i) q^{35} +(91.7574 + 158.928i) q^{37} +(41.0834 - 14.9531i) q^{38} +(129.398 - 108.578i) q^{40} +(213.053 - 178.773i) q^{41} +(-188.260 + 68.5209i) q^{43} +(-43.9664 - 76.1520i) q^{44} +(52.7125 - 91.3006i) q^{46} +(-3.39621 + 19.2608i) q^{47} +(-34.5507 - 12.5754i) q^{49} +(-111.423 - 631.909i) q^{50} +(-229.897 - 192.906i) q^{52} +646.915 q^{53} -464.168 q^{55} +(119.427 + 100.211i) q^{56} +(-42.0753 - 238.621i) q^{58} +(-415.902 - 151.376i) q^{59} +(-21.3384 + 121.016i) q^{61} +(-154.637 + 267.839i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-1488.64 + 541.820i) q^{65} +(222.612 - 186.793i) q^{67} +(138.421 - 116.149i) q^{68} +(773.320 - 281.465i) q^{70} +(40.8070 + 70.6797i) q^{71} +(170.673 - 295.614i) q^{73} +(63.7340 - 361.453i) q^{74} +(-82.1668 - 29.9063i) q^{76} +(-74.3910 - 421.892i) q^{77} +(907.990 + 761.894i) q^{79} -337.835 q^{80} -556.242 q^{82} +(-716.377 - 601.112i) q^{83} +(-165.632 - 939.345i) q^{85} +(376.519 + 137.042i) q^{86} +(-30.5387 + 173.194i) q^{88} +(704.011 - 1219.38i) q^{89} +(-731.052 - 1266.22i) q^{91} +(-198.134 + 72.1149i) q^{92} +(29.9645 - 25.1432i) q^{94} +(-353.581 + 296.689i) q^{95} +(-65.8521 + 23.9682i) q^{97} +(36.7680 + 63.6841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Introduction

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