LMFDB - Embedded newform 162.4.e.a.37.1

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			37.1
Character	$\chi$	$=$	162.37
Dual form			162.4.e.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-18.7075 + 6.80898i) q^{5} +(-3.26433 - 18.5129i) q^{7} +(4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-18.7075 + 6.80898i) q^{5} +(-3.26433 - 18.5129i) q^{7} +(4.00000 + 6.92820i) q^{8} +(19.9081 - 34.4819i) q^{10} +(17.8591 + 6.50019i) q^{11} +(40.8543 + 34.2808i) q^{13} +(28.8010 + 24.1669i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(50.6294 - 87.6927i) q^{17} +(18.7636 + 32.4995i) q^{19} +(13.8280 + 78.4227i) q^{20} +(-35.7182 + 13.0004i) q^{22} +(-11.1641 + 63.3146i) q^{23} +(207.853 - 174.410i) q^{25} -106.663 q^{26} -75.1940 q^{28} +(147.733 - 123.963i) q^{29} +(-2.55555 + 14.4933i) q^{31} +(30.0702 - 10.9446i) q^{32} +(35.1668 + 199.441i) q^{34} +(187.121 + 324.104i) q^{35} +(-39.9846 + 69.2554i) q^{37} +(-70.5281 - 25.6701i) q^{38} +(-122.004 - 102.374i) q^{40} +(190.896 + 160.181i) q^{41} +(473.183 + 172.225i) q^{43} +(38.0106 - 65.8362i) q^{44} +(-64.2913 - 111.356i) q^{46} +(-90.9577 - 515.847i) q^{47} +(-9.75774 + 3.55153i) q^{49} +(-94.2330 + 534.422i) q^{50} +(163.417 - 137.123i) q^{52} -35.1308 q^{53} -378.359 q^{55} +(115.204 - 96.6676i) q^{56} +(-66.9768 + 379.844i) q^{58} +(-403.999 + 147.044i) q^{59} +(-73.0632 - 414.362i) q^{61} +(-14.7168 - 25.4903i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-997.700 - 363.133i) q^{65} +(-388.003 - 325.573i) q^{67} +(-310.275 - 260.352i) q^{68} +(-703.347 - 255.997i) q^{70} +(444.756 - 770.339i) q^{71} +(-98.2491 - 170.172i) q^{73} +(-27.7730 - 157.509i) q^{74} +(141.056 - 51.3402i) q^{76} +(62.0394 - 351.843i) q^{77} +(-348.281 + 292.242i) q^{79} +318.530 q^{80} -498.395 q^{82} +(22.6820 - 19.0324i) q^{83} +(-350.052 + 1985.25i) q^{85} +(-946.366 + 344.449i) q^{86} +(26.4019 + 149.732i) q^{88} +(110.079 + 190.662i) q^{89} +(501.276 - 868.236i) q^{91} +(241.656 + 87.9557i) q^{92} +(802.515 + 673.390i) q^{94} +(-572.309 - 480.224i) q^{95} +(1367.72 + 497.809i) q^{97} +(10.3840 - 17.9856i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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
$5$	−18.7075	+	6.80898i	−1.67325	+	0.609013i	−0.992360	−	0.123372i	$-0.960629\pi$
$5$	−18.7075	+	6.80898i	−1.67325	+	0.609013i	−0.680890	+	0.732385i	$0.738407\pi$
$6$		0			0
$7$	−3.26433	−	18.5129i	−0.176257	−	0.999604i	−0.936683	−	0.350179i	$-0.886121\pi$
$7$	−3.26433	−	18.5129i	−0.176257	−	0.999604i	0.760426	−	0.649425i	$-0.224990\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$		0			0
$10$	19.9081	−	34.4819i	0.629550	−	1.09041i
$11$	17.8591	+	6.50019i	0.489521	+	0.178171i	0.574975	−	0.818171i	$-0.305012\pi$
$11$	17.8591	+	6.50019i	0.489521	+	0.178171i	−0.0854541	+	0.996342i	$0.527234\pi$
$12$		0			0
$13$	40.8543	+	34.2808i	0.871611	+	0.731369i	0.964437	−	0.264314i	$-0.0851454\pi$
$13$	40.8543	+	34.2808i	0.871611	+	0.731369i	−0.0928255	+	0.995682i	$0.529590\pi$
$14$	28.8010	+	24.1669i	0.549813	+	0.461348i
$15$		0			0
$16$	−15.0351	−	5.47232i	−0.234923	−	0.0855050i
$17$	50.6294	−	87.6927i	0.722320	−	1.25109i	−0.237748	−	0.971327i	$-0.576409\pi$
$17$	50.6294	−	87.6927i	0.722320	−	1.25109i	0.960068	−	0.279767i	$-0.0902573\pi$
$18$		0			0
$19$	18.7636	+	32.4995i	0.226561	+	0.392416i	0.956787	−	0.290791i	$-0.0939183\pi$
$19$	18.7636	+	32.4995i	0.226561	+	0.392416i	−0.730225	+	0.683206i	$0.760585\pi$
$20$	13.8280	+	78.4227i	0.154602	+	0.876792i
$21$		0			0
$22$	−35.7182	+	13.0004i	−0.346143	+	0.125986i
$23$	−11.1641	+	63.3146i	−0.101212	+	0.574000i	0.891454	+	0.453111i	$0.149686\pi$
$23$	−11.1641	+	63.3146i	−0.101212	+	0.574000i	−0.992666	+	0.120890i	$0.961425\pi$
$24$		0			0
$25$	207.853	−	174.410i	1.66283	−	1.39528i
$26$	−106.663			−0.804552
$27$		0			0
$28$	−75.1940			−0.507512
$29$	147.733	−	123.963i	0.945978	−	0.793770i	−0.0326375	−	0.999467i	$-0.510391\pi$
$29$	147.733	−	123.963i	0.945978	−	0.793770i	0.978616	+	0.205697i	$0.0659462\pi$
$30$		0			0
$31$	−2.55555	+	14.4933i	−0.0148062	+	0.0839699i	−0.991315	−	0.131505i	$-0.958019\pi$
$31$	−2.55555	+	14.4933i	−0.0148062	+	0.0839699i	0.976509	+	0.215475i	$0.0691301\pi$
$32$	30.0702	−	10.9446i	0.166116	−	0.0604612i
$33$		0			0
$34$	35.1668	+	199.441i	0.177384	+	1.00599i
$35$	187.121	+	324.104i	0.903694	+	1.56524i
$36$		0			0
$37$	−39.9846	+	69.2554i	−0.177660	+	0.307717i	−0.941079	−	0.338188i	$-0.890186\pi$
$37$	−39.9846	+	69.2554i	−0.177660	+	0.307717i	0.763418	+	0.645904i	$0.223519\pi$
$38$	−70.5281	−	25.6701i	−0.301083	−	0.109585i
$39$		0			0
$40$	−122.004	−	102.374i	−0.482263	−	0.404667i
$41$	190.896	+	160.181i	0.727146	+	0.610148i	0.929352	−	0.369195i	$-0.120367\pi$
$41$	190.896	+	160.181i	0.727146	+	0.610148i	−0.202206	+	0.979343i	$0.564811\pi$
$42$		0			0
$43$	473.183	+	172.225i	1.67813	+	0.610791i	0.993052	−	0.117676i	$-0.0375445\pi$
$43$	473.183	+	172.225i	1.67813	+	0.610791i	0.685081	+	0.728467i	$0.259767\pi$
$44$	38.0106	−	65.8362i	0.130234	−	0.225572i
$45$		0			0
$46$	−64.2913	−	111.356i	−0.206070	−	0.356925i
$47$	−90.9577	−	515.847i	−0.282288	−	1.60094i	−0.714814	−	0.699314i	$-0.753489\pi$
$47$	−90.9577	−	515.847i	−0.282288	−	1.60094i	0.432526	−	0.901621i	$-0.357622\pi$
$48$		0			0
$49$	−9.75774	+	3.55153i	−0.0284482	+	0.0103543i
$50$	−94.2330	+	534.422i	−0.266531	+	1.51157i
$51$		0			0
$52$	163.417	−	137.123i	0.435806	−	0.365684i
$53$	−35.1308			−0.0910487			−0.0455244	−	0.998963i	$-0.514496\pi$
$53$	−35.1308			−0.0910487			−0.0455244	+	0.998963i	$0.514496\pi$
$54$		0			0
$55$	−378.359			−0.927599
$56$	115.204	−	96.6676i	0.274907	−	0.230674i
$57$		0			0
$58$	−66.9768	+	379.844i	−0.151629	+	0.859931i
$59$	−403.999	+	147.044i	−0.891461	+	0.324465i	−0.746826	−	0.665020i	$-0.768423\pi$
$59$	−403.999	+	147.044i	−0.891461	+	0.324465i	−0.144635	+	0.989485i	$0.546201\pi$
$60$		0			0
$61$	−73.0632	−	414.362i	−0.153357	−	0.869732i	−0.960272	−	0.279065i	$-0.909976\pi$
$61$	−73.0632	−	414.362i	−0.153357	−	0.869732i	0.806915	−	0.590667i	$-0.201135\pi$
$62$	−14.7168	−	25.4903i	−0.0301458	−	0.0522141i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	−997.700	−	363.133i	−1.90384	−	0.692940i
$66$		0			0
$67$	−388.003	−	325.573i	−0.707495	−	0.593658i	0.216400	−	0.976305i	$-0.430568\pi$
$67$	−388.003	−	325.573i	−0.707495	−	0.593658i	−0.923895	+	0.382646i	$0.875013\pi$
$68$	−310.275	−	260.352i	−0.553329	−	0.464298i
$69$		0			0
$70$	−703.347	−	255.997i	−1.20094	−	0.437108i
$71$	444.756	−	770.339i	0.743419	−	1.28764i	−0.207510	−	0.978233i	$-0.566536\pi$
$71$	444.756	−	770.339i	0.743419	−	1.28764i	0.950930	−	0.309407i	$-0.100131\pi$
$72$		0			0
$73$	−98.2491	−	170.172i	−0.157523	−	0.272838i	0.776452	−	0.630177i	$-0.217018\pi$
$73$	−98.2491	−	170.172i	−0.157523	−	0.272838i	−0.933975	+	0.357339i	$0.883684\pi$
$74$	−27.7730	−	157.509i	−0.0436290	−	0.247433i
$75$		0			0
$76$	141.056	−	51.3402i	0.212898	−	0.0774886i
$77$	62.0394	−	351.843i	0.0918188	−	0.520731i
$78$		0			0
$79$	−348.281	+	292.242i	−0.496009	+	0.416201i	−0.856174	−	0.516688i	$-0.827165\pi$
$79$	−348.281	+	292.242i	−0.496009	+	0.416201i	0.360165	+	0.932889i	$0.382720\pi$
$80$	318.530			0.445159
$81$		0			0
$82$	−498.395			−0.671201
$83$	22.6820	−	19.0324i	0.0299960	−	0.0251697i	−0.627666	−	0.778482i	$-0.715990\pi$
$83$	22.6820	−	19.0324i	0.0299960	−	0.0251697i	0.657662	+	0.753313i	$0.271545\pi$
$84$		0			0
$85$	−350.052	+	1985.25i	−0.446689	+	2.53330i
$86$	−946.366	+	344.449i	−1.18662	+	0.431894i
$87$		0			0
$88$	26.4019	+	149.732i	0.0319824	+	0.181381i
$89$	110.079	+	190.662i	0.131105	+	0.227080i	0.924103	−	0.382144i	$-0.124814\pi$
$89$	110.079	+	190.662i	0.131105	+	0.227080i	−0.792998	+	0.609224i	$0.791481\pi$
$90$		0			0
$91$	501.276	−	868.236i	0.577451	−	1.00017i
$92$	241.656	+	87.9557i	0.273852	+	0.0996741i
$93$		0			0
$94$	802.515	+	673.390i	0.880565	+	0.738882i
$95$	−572.309	−	480.224i	−0.618080	−	0.518631i
$96$		0			0
$97$	1367.72	+	497.809i	1.43166	+	0.521081i	0.937406	−	0.348238i	$-0.113220\pi$
$97$	1367.72	+	497.809i	1.43166	+	0.521081i	0.494252	+	0.869319i	$0.335442\pi$
$98$	10.3840	−	17.9856i	0.0107035	−	0.0185389i
$99$		0			0
$100$	−542.666	−	939.926i	−0.542666	−	0.939926i
$101$	276.963	+	1570.73i	0.272860	+	1.54746i	0.745680	+	0.666305i	$0.232125\pi$
$101$	276.963	+	1570.73i	0.272860	+	1.54746i	−0.472820	+	0.881159i	$0.656764\pi$
$102$		0			0
$103$	−290.094	+	105.586i	−0.277513	+	0.101006i	−0.477027	−	0.878889i	$-0.658286\pi$
$103$	−290.094	+	105.586i	−0.277513	+	0.101006i	0.199515	+	0.979895i	$0.436063\pi$
$104$	−74.0874	+	420.170i	−0.0698545	+	0.396164i
$105$		0			0
$106$	53.8235	−	45.1632i	0.0493188	−	0.0413834i
$107$	1594.74			1.44084			0.720418	−	0.693540i	$-0.243950\pi$
$107$	1594.74			1.44084			0.720418	+	0.693540i	$0.243950\pi$
$108$		0			0
$109$	−290.868			−0.255597			−0.127798	−	0.991800i	$-0.540791\pi$
$109$	−290.868			−0.255597			−0.127798	+	0.991800i	$0.540791\pi$
$110$	579.680	−	486.409i	0.502458	−	0.421612i
$111$		0			0
$112$	−52.2292	+	296.207i	−0.0440643	+	0.249901i
$113$	1250.83	−	455.266i	1.04131	−	0.379008i	0.235936	−	0.971769i	$-0.424184\pi$
$113$	1250.83	−	455.266i	1.04131	−	0.379008i	0.805378	+	0.592761i	$0.201962\pi$
$114$		0			0
$115$	−222.256	−	1260.47i	−0.180221	−	1.02209i
$116$	−385.704	−	668.059i	−0.308722	−	0.534722i
$117$		0			0
$118$	429.927	−	744.655i	0.335406	−	0.580941i
$119$	−1788.72	−	651.040i	−1.37791	−	0.501519i
$120$		0			0
$121$	−742.909	−	623.375i	−0.558159	−	0.468351i
$122$	644.633	+	540.911i	0.478380	+	0.401408i
$123$		0			0
$124$	55.3172	+	20.1338i	0.0400616	+	0.0145812i
$125$	−1456.61	+	2522.92i	−1.04226	+	1.80526i
$126$		0			0
$127$	177.940	+	308.201i	0.124328	+	0.215342i	0.921470	−	0.388450i	$-0.126989\pi$
$127$	177.940	+	308.201i	0.124328	+	0.215342i	−0.797142	+	0.603792i	$0.793656\pi$
$128$	−22.2270	−	126.055i	−0.0153485	−	0.0870455i
$129$		0			0
$130$	1995.40	−	726.266i	1.34622	−	0.489983i
$131$	−46.4862	+	263.636i	−0.0310039	+	0.175832i	−0.996378	−	0.0850388i	$-0.972899\pi$
$131$	−46.4862	+	263.636i	−0.0310039	+	0.175832i	0.965374	+	0.260871i	$0.0840097\pi$
$132$		0			0
$133$	540.410	−	453.458i	0.352327	−	0.295638i
$134$	1013.00			0.653062
$135$		0			0
$136$	810.070			0.510757
$137$	−17.7465	+	14.8910i	−0.0110670	+	0.00928633i	−0.648304	−	0.761381i	$-0.724522\pi$
$137$	−17.7465	+	14.8910i	−0.0110670	+	0.00928633i	0.637237	+	0.770668i	$0.280077\pi$
$138$		0			0
$139$	217.013	−	1230.74i	0.132423	−	0.751007i	−0.844197	−	0.536033i	$-0.819922\pi$
$139$	217.013	−	1230.74i	0.132423	−	0.751007i	0.976620	−	0.214974i	$-0.0689667\pi$
$140$	1406.69	−	511.995i	0.849195	−	0.309082i
$141$		0			0
$142$	308.924	+	1751.99i	0.182566	+	1.03538i
$143$	506.790	+	877.786i	0.296363	+	0.513316i
$144$		0			0
$145$	−1919.66	+	3324.95i	−1.09944	+	1.90429i
$146$	369.296	+	134.413i	0.209337	+	0.0761923i
$147$		0			0
$148$	245.040	+	205.613i	0.136096	+	0.114198i
$149$	1277.71	+	1072.13i	0.702512	+	0.589478i	0.922487	−	0.386028i	$-0.126153\pi$
$149$	1277.71	+	1072.13i	0.702512	+	0.589478i	−0.219975	+	0.975506i	$0.570598\pi$
$150$		0			0
$151$	−731.635	−	266.293i	−0.394302	−	0.143514i	0.137257	−	0.990535i	$-0.456171\pi$
$151$	−731.635	−	266.293i	−0.394302	−	0.143514i	−0.531559	+	0.847021i	$0.678394\pi$
$152$	−150.109	+	259.996i	−0.0801015	+	0.138740i
$153$		0			0
$154$	357.271	+	618.811i	0.186946	+	0.323800i
$155$	−50.8763	−	288.534i	−0.0263644	−	0.149520i
$156$		0			0
$157$	2479.22	−	902.364i	1.26028	−	0.458704i	0.376416	−	0.926451i	$-0.377157\pi$
$157$	2479.22	−	902.364i	1.26028	−	0.458704i	0.883862	+	0.467747i	$0.154934\pi$
$158$	157.898	−	895.483i	0.0795043	−	0.450891i
$159$		0			0
$160$	−488.016	+	409.494i	−0.241132	+	0.202333i
$161$	1208.58			0.591612
$162$		0			0
$163$	2231.98			1.07253			0.536265	−	0.844050i	$-0.319835\pi$
$163$	2231.98			1.07253			0.536265	+	0.844050i	$0.319835\pi$
$164$	763.585	−	640.724i	0.363573	−	0.305074i
$165$		0			0
$166$	−10.2832	+	58.3188i	−0.00480801	+	0.0272676i
$167$	−1426.51	+	519.207i	−0.660997	+	0.240583i	−0.650667	−	0.759363i	$-0.725511\pi$
$167$	−1426.51	+	519.207i	−0.660997	+	0.240583i	−0.0103303	+	0.999947i	$0.503288\pi$
$168$		0			0
$169$	112.394	+	637.417i	0.0511579	+	0.290131i
$170$	−2015.87	−	3491.59i	−0.909472	−	1.57525i
$171$		0			0
$172$	1007.10	−	1744.35i	0.446458	−	0.773288i
$173$	1214.86	+	442.173i	0.533897	+	0.194322i	0.594877	−	0.803816i	$-0.297201\pi$
$173$	1214.86	+	442.173i	0.533897	+	0.194322i	−0.0609808	+	0.998139i	$0.519423\pi$
$174$		0			0
$175$	−3907.33	−	3278.64i	−1.68781	−	1.41624i
$176$	−232.942	−	195.462i	−0.0997652	−	0.0837130i
$177$		0			0
$178$	−413.761	−	150.597i	−0.174229	−	0.0634140i
$179$	−46.2091	+	80.0365i	−0.0192951	+	0.0334202i	−0.875512	−	0.483197i	$-0.839476\pi$
$179$	−46.2091	+	80.0365i	−0.0192951	+	0.0334202i	0.856217	+	0.516617i	$0.172809\pi$
$180$		0			0
$181$	−362.472	−	627.820i	−0.148853	−	0.257820i	0.781951	−	0.623340i	$-0.214225\pi$
$181$	−362.472	−	627.820i	−0.148853	−	0.257820i	−0.930804	+	0.365519i	$0.880891\pi$
$182$	348.183	+	1974.64i	0.141808	+	0.804233i
$183$		0			0
$184$	−483.313	+	175.911i	−0.193643	+	0.0704803i
$185$	276.454	−	1567.85i	0.109867	−	0.623085i
$186$		0			0
$187$	1474.22	−	1237.01i	0.576499	−	0.483740i
$188$	−2095.22			−0.812816
$189$		0			0
$190$	1494.19			0.570527
$191$	−965.308	+	809.989i	−0.365692	+	0.306852i	−0.807055	−	0.590477i	$-0.798940\pi$
$191$	−965.308	+	809.989i	−0.365692	+	0.306852i	0.441362	+	0.897329i	$0.354495\pi$
$192$		0			0
$193$	−588.801	+	3339.25i	−0.219600	+	1.24541i	0.653143	+	0.757234i	$0.273450\pi$
$193$	−588.801	+	3339.25i	−0.219600	+	1.24541i	−0.872743	+	0.488179i	$0.837661\pi$
$194$	−2735.44	+	995.618i	−1.01233	+	0.368460i
$195$		0			0
$196$	7.21263	+	40.9048i	0.00262851	+	0.0149070i
$197$	1063.84	+	1842.62i	0.384748	+	0.666403i	0.991734	−	0.128309i	$-0.0409549\pi$
$197$	1063.84	+	1842.62i	0.384748	+	0.666403i	−0.606986	+	0.794713i	$0.707622\pi$
$198$		0			0
$199$	168.821	−	292.406i	0.0601376	−	0.104161i	−0.834389	−	0.551176i	$-0.814179\pi$
$199$	168.821	−	292.406i	0.0601376	−	0.104161i	0.894527	+	0.447014i	$0.147513\pi$
$200$	2039.76	+	742.411i	0.721164	+	0.262482i
$201$		0			0
$202$	−2443.63	−	2050.45i	−0.851154	−	0.714203i
$203$	−2777.16	−	2330.32i	−0.960191	−	0.805696i
$204$		0			0
$205$	−4661.86	−	1696.78i	−1.58829	−	0.578089i
$206$	308.711	−	534.704i	0.104412	−	0.180848i
$207$		0			0
$208$	−426.652	−	738.983i	−0.142226	−	0.246343i
$209$	123.849	+	702.380i	0.0409894	+	0.232462i
$210$		0			0
$211$	3015.25	−	1097.46i	0.983784	−	0.358068i	0.200474	−	0.979699i	$-0.435752\pi$
$211$	3015.25	−	1097.46i	0.983784	−	0.358068i	0.783310	+	0.621631i	$0.213530\pi$
$212$	−24.4016	+	138.388i	−0.00790522	+	0.0448327i
$213$		0			0
$214$	−2443.29	+	2050.16i	−0.780465	+	0.654888i
$215$	−10024.7			−3.17992
$216$		0			0
$217$	276.655			0.0865463
$218$	445.635	−	373.932i	0.138450	−	0.116174i
$219$		0			0
$220$	−262.806	+	1490.44i	−0.0805380	+	0.456754i
$221$	5074.61	−	1847.01i	1.54459	−	0.562186i
$222$		0			0
$223$	149.088	+	845.523i	0.0447700	+	0.253903i	0.998976	−	0.0452477i	$-0.0144077\pi$
$223$	149.088	+	845.523i	0.0447700	+	0.253903i	−0.954206	+	0.299151i	$0.903297\pi$
$224$	−300.776	−	520.960i	−0.0897163	−	0.155393i
$225$		0			0
$226$	−1331.11	+	2305.55i	−0.391788	+	0.678597i
$227$	2159.56	+	786.014i	0.631431	+	0.229822i	0.637854	−	0.770157i	$-0.279822\pi$
$227$	2159.56	+	786.014i	0.631431	+	0.229822i	−0.00642319	+	0.999979i	$0.502045\pi$
$228$		0			0
$229$	−2760.81	−	2316.59i	−0.796678	−	0.668493i	0.150710	−	0.988578i	$-0.451844\pi$
$229$	−2760.81	−	2316.59i	−0.796678	−	0.668493i	−0.947389	+	0.320085i	$0.896288\pi$
$230$	1960.95	+	1645.43i	0.562179	+	0.471725i
$231$		0			0
$232$	1449.77	+	527.674i	0.410268	+	0.149325i
$233$	2705.00	−	4685.20i	0.760560	−	1.31733i	−0.182002	−	0.983298i	$-0.558258\pi$
$233$	2705.00	−	4685.20i	0.760560	−	1.31733i	0.942562	−	0.334031i	$-0.108409\pi$
$234$		0			0
$235$	5213.98	+	9030.88i	1.44733	+	2.50685i
$236$	298.624	+	1693.58i	0.0823676	+	0.467130i
$237$		0			0
$238$	3577.44	−	1302.08i	0.974331	−	0.354627i
$239$	257.506	−	1460.39i	0.0696932	−	0.395250i	−0.929928	−	0.367741i	$-0.880131\pi$
$239$	257.506	−	1460.39i	0.0696932	−	0.395250i	0.999622	−	0.0275090i	$-0.00875748\pi$
$240$		0			0
$241$	−3192.71	+	2679.01i	−0.853364	+	0.716058i	−0.960528	−	0.278184i	$-0.910268\pi$
$241$	−3192.71	+	2679.01i	−0.853364	+	0.716058i	0.107164	+	0.994241i	$0.465823\pi$
$242$	1939.60			0.515215
$243$		0			0
$244$	−1683.02			−0.441574
$245$	158.361	−	132.880i	0.0412951	−	0.0346507i
$246$		0			0
$247$	−347.536	+	1970.98i	−0.0895272	+	0.507734i
$248$	−110.634	+	40.2677i	−0.0283278	+	0.0103105i
$249$		0			0
$250$	−1011.75	−	5737.92i	−0.255955	−	1.45159i
$251$	−1054.94	−	1827.21i	−0.265287	−	0.459491i	0.702352	−	0.711830i	$-0.252133\pi$
$251$	−1054.94	−	1827.21i	−0.265287	−	0.459491i	−0.967639	+	0.252339i	$0.918800\pi$
$252$		0			0
$253$	−610.938	+	1058.17i	−0.151815	+	0.262952i
$254$	−668.836	−	243.436i	−0.165223	−	0.0601361i
$255$		0			0
$256$	196.107	+	164.554i	0.0478778	+	0.0401742i
$257$	−622.096	−	522.001i	−0.150993	−	0.126698i	0.564162	−	0.825664i	$-0.309199\pi$
$257$	−622.096	−	522.001i	−0.150993	−	0.126698i	−0.715155	+	0.698966i	$0.753644\pi$
$258$		0			0
$259$	1412.64	+	514.160i	0.338909	+	0.123353i
$260$	−2123.46	+	3677.94i	−0.506505	+	0.877293i
$261$		0			0
$262$	−267.703	−	463.675i	−0.0631250	−	0.109336i
$263$	−229.752	−	1302.99i	−0.0538674	−	0.305497i	0.945956	−	0.324295i	$-0.105127\pi$
$263$	−229.752	−	1302.99i	−0.0538674	−	0.305497i	−0.999823	+	0.0187979i	$0.994016\pi$
$264$		0			0
$265$	657.209	−	239.205i	0.152347	−	0.0554499i
$266$	−245.002	+	1389.48i	−0.0564739	+	0.320279i
$267$		0			0
$268$	−1552.01	+	1302.29i	−0.353747	+	0.296829i
$269$	−5994.88			−1.35879			−0.679395	−	0.733773i	$-0.737758\pi$
$269$	−5994.88			−1.35879			−0.679395	+	0.733773i	$0.737758\pi$
$270$		0			0
$271$	−4184.09			−0.937880			−0.468940	−	0.883230i	$-0.655364\pi$
$271$	−4184.09			−0.937880			−0.468940	+	0.883230i	$0.655364\pi$
$272$	−1241.10	+	1041.41i	−0.276664	+	0.232149i
$273$		0			0
$274$	8.04559	−	45.6288i	0.00177391	−	0.0100604i
$275$	4845.77	−	1763.72i	1.06259	−	0.386750i
$276$		0			0
$277$	1453.87	+	8245.29i	0.315359	+	1.78849i	0.570199	+	0.821507i	$0.306866\pi$
$277$	1453.87	+	8245.29i	0.315359	+	1.78849i	−0.254840	+	0.966983i	$0.582023\pi$
$278$	1249.73	+	2164.59i	0.269617	+	0.466991i
$279$		0			0
$280$	−1496.97	+	2592.83i	−0.319504	+	0.553398i
$281$	−534.451	−	194.524i	−0.113462	−	0.0412966i	0.284666	−	0.958627i	$-0.408117\pi$
$281$	−534.451	−	194.524i	−0.113462	−	0.0412966i	−0.398127	+	0.917330i	$0.630340\pi$
$282$		0			0
$283$	−4161.58	−	3491.98i	−0.874135	−	0.733487i	0.0908295	−	0.995866i	$-0.471048\pi$
$283$	−4161.58	−	3491.98i	−0.874135	−	0.733487i	−0.964965	+	0.262380i	$0.915493\pi$
$284$	−2725.62	−	2287.07i	−0.569492	−	0.477861i
$285$		0			0
$286$	−1904.91	−	693.330i	−0.393845	−	0.143348i
$287$	2342.27	−	4056.93i	0.481742	−	0.834401i
$288$		0			0
$289$	−2670.17	−	4624.87i	−0.543491	−	0.941354i
$290$	−1333.38	−	7561.98i	−0.269996	−	1.53122i
$291$		0			0
$292$	−738.592	+	268.825i	−0.148023	+	0.0538761i
$293$	245.407	−	1391.77i	0.0489312	−	0.277502i	−0.950519	−	0.310667i	$-0.899448\pi$
$293$	245.407	−	1391.77i	0.0489312	−	0.277502i	0.999450	+	0.0331648i	$0.0105586\pi$
$294$		0			0
$295$	6556.60	−	5501.64i	1.29403	−	1.08582i
$296$	−639.754			−0.125625
$297$		0			0
$298$	−3335.87			−0.648463
$299$	−2626.58	+	2203.96i	−0.508023	+	0.426282i
$300$		0			0
$301$	1643.75	−	9322.19i	0.314766	−	1.78512i
$302$	1463.27	−	532.587i	0.278814	−	0.101480i
$303$		0			0
$304$	−104.265	−	591.313i	−0.0196710	−	0.111560i
$305$	4188.21	+	7254.20i	0.786284	+	1.36188i
$306$		0			0
$307$	3179.20	−	5506.53i	0.591030	−	1.02369i	−0.403064	−	0.915172i	$-0.632055\pi$
$307$	3179.20	−	5506.53i	0.591030	−	1.02369i	0.994094	−	0.108522i	$-0.0346119\pi$
$308$	−1342.90	−	488.775i	−0.248438	−	0.0904239i
$309$		0			0
$310$	448.879	+	376.654i	0.0822406	+	0.0690081i
$311$	4187.28	+	3513.54i	0.763469	+	0.640626i	0.939027	−	0.343843i	$-0.111729\pi$
$311$	4187.28	+	3513.54i	0.763469	+	0.640626i	−0.175559	+	0.984469i	$0.556173\pi$
$312$		0			0
$313$	2995.27	+	1090.19i	0.540903	+	0.196873i	0.598000	−	0.801496i	$-0.295962\pi$
$313$	2995.27	+	1090.19i	0.540903	+	0.196873i	−0.0570970	+	0.998369i	$0.518184\pi$
$314$	−2638.33	+	4569.73i	−0.474171	+	0.821289i
$315$		0			0
$316$	909.297	+	1574.95i	0.161873	+	0.280373i
$317$	248.792	+	1410.97i	0.0440805	+	0.249993i	0.998883	−	0.0472472i	$-0.0150449\pi$
$317$	248.792	+	1410.97i	0.0440805	+	0.249993i	−0.954803	+	0.297240i	$0.903934\pi$
$318$		0			0
$319$	3444.17	−	1253.57i	0.604503	−	0.220021i
$320$	221.249	−	1254.76i	0.0386505	−	0.219198i
$321$		0			0
$322$	−1851.65	+	1553.72i	−0.320462	+	0.268899i
$323$	3799.96			0.654599
$324$		0			0
$325$	14470.6			2.46980
$326$	−3419.60	+	2869.38i	−0.580963	+	0.487486i
$327$		0			0
$328$	−346.181	+	1963.29i	−0.0582764	+	0.330502i
$329$	−9252.91	+	3367.78i	−1.55055	+	0.564353i
$330$		0			0
$331$	−1961.87	−	11126.3i	−0.325783	−	1.84761i	−0.504114	−	0.863637i	$-0.668181\pi$
$331$	−1961.87	−	11126.3i	−0.325783	−	1.84761i	0.178331	−	0.983971i	$-0.442930\pi$
$332$	−59.2185	−	102.569i	−0.00978926	−	0.0169555i
$333$		0			0
$334$	1518.06	−	2629.35i	0.248696	−	0.430754i
$335$	9475.40	+	3448.76i	1.54536	+	0.562466i
$336$		0			0
$337$	8173.02	+	6857.98i	1.32111	+	1.10854i	0.986069	+	0.166334i	$0.0531931\pi$
$337$	8173.02	+	6857.98i	1.32111	+	1.10854i	0.335037	+	0.942205i	$0.391251\pi$
$338$	−991.645	−	832.089i	−0.159581	−	0.133904i
$339$		0			0
$340$	7577.20	+	2757.88i	1.20862	+	0.439902i
$341$	−139.849	+	242.225i	−0.0222089	+	0.0384670i
$342$		0			0
$343$	−3126.34	−	5414.98i	−0.492148	−	0.852425i
$344$	699.525	+	3967.21i	0.109639	+	0.621795i
$345$		0			0
$346$	−2429.72	+	884.346i	−0.377522	+	0.137407i
$347$	458.283	−	2599.05i	0.0708989	−	0.402088i	−0.928619	−	0.371035i	$-0.879003\pi$
$347$	458.283	−	2599.05i	0.0708989	−	0.402088i	0.999518	−	0.0310526i	$-0.00988594\pi$
$348$		0			0
$349$	−6429.22	+	5394.76i	−0.986098	+	0.827434i	−0.984998	−	0.172565i	$-0.944795\pi$
$349$	−6429.22	+	5394.76i	−0.986098	+	0.827434i	−0.00109985	+	0.999999i	$0.500350\pi$
$350$	10201.3			1.55795
$351$		0			0
$352$	608.169			0.0920895
$353$	1773.40	−	1488.06i	0.267390	−	0.224367i	−0.499227	−	0.866471i	$-0.666383\pi$
$353$	1773.40	−	1488.06i	0.267390	−	0.224367i	0.766617	+	0.642104i	$0.221938\pi$
$354$		0			0
$355$	−3075.05	+	17439.5i	−0.459737	+	2.60730i
$356$	827.522	−	301.193i	0.123198	−	0.0448405i
$357$		0			0
$358$	−32.0965	−	182.028i	−0.00473842	−	0.0268729i
$359$	−1498.69	−	2595.81i	−0.220328	−	0.381620i	0.734579	−	0.678523i	$-0.237380\pi$
$359$	−1498.69	−	2595.81i	−0.220328	−	0.381620i	−0.954908	+	0.296903i	$0.904046\pi$
$360$		0			0
$361$	2725.35	−	4720.45i	0.397340	−	0.688213i
$362$	1362.45	+	495.891i	0.197814	+	0.0719985i
$363$		0			0
$364$	−3072.00	−	2577.71i	−0.442353	−	0.371178i
$365$	2996.70	+	2514.53i	0.429738	+	0.360593i
$366$		0			0
$367$	−4858.38	−	1768.31i	−0.691023	−	0.251512i	−0.0274496	−	0.999623i	$-0.508739\pi$
$367$	−4858.38	−	1768.31i	−0.691023	−	0.251512i	−0.663573	+	0.748112i	$0.730961\pi$
$368$	514.331	−	890.847i	0.0728569	−	0.126192i
$369$		0			0
$370$	1592.04	+	2757.49i	0.223692	+	0.387446i
$371$	114.678	+	650.373i	0.0160480	+	0.0910126i
$372$		0			0
$373$	8916.97	−	3245.51i	1.23781	−	0.450526i	0.361544	−	0.932355i	$-0.382250\pi$
$373$	8916.97	−	3245.51i	1.23781	−	0.450526i	0.876265	+	0.481829i	$0.160027\pi$
$374$	−668.355	+	3790.43i	−0.0924059	+	0.524060i
$375$		0			0
$376$	3210.06	−	2693.56i	0.440282	−	0.369441i
$377$	10285.1			1.40506
$378$		0			0
$379$	−13171.1			−1.78511			−0.892553	−	0.450943i	$-0.851088\pi$
$379$	−13171.1			−1.78511			−0.892553	+	0.450943i	$0.851088\pi$
$380$	−2289.24	+	1920.90i	−0.309040	+	0.259316i
$381$		0			0
$382$	437.635	−	2481.95i	0.0586161	−	0.332428i
$383$	−9651.19	+	3512.74i	−1.28760	+	0.468650i	−0.892940	−	0.450175i	$-0.851361\pi$
$383$	−9651.19	+	3512.74i	−1.28760	+	0.468650i	−0.394665	+	0.918825i	$0.629139\pi$
$384$		0			0
$385$	1235.09	+	7004.54i	0.163496	+	0.927232i
$386$	−3390.77	−	5872.98i	−0.447113	−	0.774422i
$387$		0			0
$388$	2910.99	−	5041.99i	0.380885	−	0.659711i
$389$	−10031.5	−	3651.18i	−1.30750	−	0.475893i	−0.408071	−	0.912950i	$-0.633798\pi$
$389$	−10031.5	−	3651.18i	−1.30750	−	0.475893i	−0.899433	+	0.437058i	$0.856021\pi$
$390$		0			0
$391$	4987.00	+	4184.59i	0.645021	+	0.541237i
$392$	−63.6366	−	53.3975i	−0.00819932	−	0.00688005i
$393$		0			0
$394$	−3998.73	−	1455.42i	−0.511302	−	0.186099i
$395$	4525.60	−	7838.57i	0.576475	−	0.998484i
$396$		0			0
$397$	−3310.20	−	5733.43i	−0.418474	−	0.724817i	0.577313	−	0.816523i	$-0.304101\pi$
$397$	−3310.20	−	5733.43i	−0.418474	−	0.724817i	−0.995786	+	0.0917058i	$0.970768\pi$
$398$	117.262	+	665.024i	0.0147683	+	0.0837554i
$399$		0			0
$400$	−4079.52	+	1484.82i	−0.509940	+	0.185603i
$401$	−1782.77	+	10110.6i	−0.222014	+	1.25910i	0.646299	+	0.763085i	$0.276316\pi$
$401$	−1782.77	+	10110.6i	−0.222014	+	1.25910i	−0.868312	+	0.496018i	$0.834795\pi$
$402$		0			0
$403$	−601.246	+	504.506i	−0.0743182	+	0.0623603i
$404$	6379.86			0.785668
$405$		0			0
$406$	7250.66			0.886316
$407$	−1164.26	+	976.933i	−0.141795	+	0.118980i
$408$		0			0
$409$	−2203.19	+	12494.9i	−0.266359	+	1.51060i	0.498777	+	0.866730i	$0.333783\pi$
$409$	−2203.19	+	12494.9i	−0.266359	+	1.51060i	−0.765136	+	0.643868i	$0.777328\pi$
$410$	9323.73	−	3393.56i	1.12309	−	0.408771i
$411$		0			0
$412$	214.429	+	1216.09i	0.0256411	+	0.145418i
$413$	4040.99	+	6999.20i	0.481463	+	0.833918i
$414$		0			0
$415$	−294.732	+	510.491i	−0.0348622	+	0.0603832i
$416$	1603.69	+	583.694i	0.189008	+	0.0687932i
$417$		0			0
$418$	−1092.71	−	916.892i	−0.127862	−	0.107289i
$419$	−8548.03	−	7172.65i	−0.996656	−	0.836293i	−0.0101380	−	0.999949i	$-0.503227\pi$
$419$	−8548.03	−	7172.65i	−0.996656	−	0.836293i	−0.986518	+	0.163655i	$0.947672\pi$
$420$		0			0
$421$	−2442.88	−	889.135i	−0.282800	−	0.102931i	0.196726	−	0.980459i	$-0.436969\pi$
$421$	−2442.88	−	889.135i	−0.282800	−	0.102931i	−0.479526	+	0.877528i	$0.659191\pi$
$422$	−3208.76	+	5557.74i	−0.370142	+	0.641105i
$423$		0			0
$424$	−140.523	−	243.393i	−0.0160953	−	0.0278779i
$425$	−4770.96	−	27057.5i	−0.544531	−	3.08819i
$426$		0			0
$427$	−7432.55	+	2705.23i	−0.842357	+	0.306593i
$428$	1107.70	−	6282.05i	0.125099	−	0.709473i
$429$		0			0
$430$	15358.8	−	12887.6i	1.72248	−	1.44533i
$431$	5744.90			0.642047			0.321024	−	0.947071i	$-0.395973\pi$
$431$	5744.90			0.642047			0.321024	+	0.947071i	$0.395973\pi$
$432$		0			0
$433$	−13112.6			−1.45531			−0.727655	−	0.685943i	$-0.759390\pi$
$433$	−13112.6			−1.45531			−0.727655	+	0.685943i	$0.759390\pi$
$434$	−423.860	+	355.660i	−0.0468800	+	0.0393370i
$435$		0			0
$436$	−202.034	+	1145.79i	−0.0221920	+	0.125857i
$437$	−2267.17	+	825.183i	−0.248178	+	0.0903292i
$438$		0			0
$439$	864.432	+	4902.44i	0.0939797	+	0.532985i	0.995055	+	0.0993232i	$0.0316678\pi$
$439$	864.432	+	4902.44i	0.0939797	+	0.532985i	−0.901076	+	0.433662i	$0.857221\pi$
$440$	−1513.44	−	2621.35i	−0.163978	−	0.284018i
$441$		0			0
$442$	−5400.28	+	9353.57i	−0.581143	+	1.00657i
$443$	11439.6	+	4163.68i	1.22689	+	0.446552i	0.872532	−	0.488557i	$-0.162477\pi$
$443$	11439.6	+	4163.68i	1.22689	+	0.446552i	0.354360	+	0.935109i	$0.384699\pi$
$444$		0			0
$445$	−3357.51	−	2817.29i	−0.357666	−	0.300117i
$446$	−1315.40	−	1103.75i	−0.139655	−	0.117184i
$447$		0			0
$448$	1130.55	+	411.486i	0.119226	+	0.0433948i
$449$	−4202.08	+	7278.21i	−0.441667	+	0.764989i	−0.997813	−	0.0660951i	$-0.978946\pi$
$449$	−4202.08	+	7278.21i	−0.441667	+	0.764989i	0.556147	+	0.831084i	$0.312279\pi$
$450$		0			0
$451$	2368.03	+	4101.55i	0.247242	+	0.428236i
$452$	−924.579	−	5243.55i	−0.0962136	−	0.545654i
$453$		0			0
$454$	−4319.11	+	1572.03i	−0.446489	+	0.162509i
$455$	−3465.83	+	19655.7i	−0.357101	+	2.02522i
$456$		0			0
$457$	6061.46	−	5086.17i	0.620445	−	0.520615i	−0.277499	−	0.960726i	$-0.589505\pi$
$457$	6061.46	−	5086.17i	0.620445	−	0.520615i	0.897943	+	0.440111i	$0.145061\pi$
$458$	7207.96			0.735384
$459$		0			0
$460$	−5119.68			−0.518927
$461$	1602.29	−	1344.48i	0.161879	−	0.135832i	−0.558250	−	0.829673i	$-0.688527\pi$
$461$	1602.29	−	1344.48i	0.161879	−	0.135832i	0.720129	+	0.693840i	$0.244083\pi$
$462$		0			0
$463$	2459.81	−	13950.3i	0.246905	−	1.40027i	−0.569122	−	0.822253i	$-0.692717\pi$
$463$	2459.81	−	13950.3i	0.246905	−	1.40027i	0.816027	−	0.578014i	$-0.196172\pi$
$464$	−2899.55	+	1055.35i	−0.290103	+	0.105589i
$465$		0			0
$466$	1878.87	+	10655.6i	0.186775	+	1.05925i
$467$	−5512.32	−	9547.62i	−0.546210	−	0.946063i	−0.998530	−	0.0542071i	$-0.982737\pi$
$467$	−5512.32	−	9547.62i	−0.546210	−	0.946063i	0.452320	−	0.891856i	$-0.350596\pi$
$468$		0			0
$469$	−4760.74	+	8245.85i	−0.468722	+	0.811851i
$470$	−19598.2	−	7133.15i	−1.92339	−	0.700059i
$471$		0			0
$472$	−2634.74	−	2210.81i	−0.256936	−	0.215595i
$473$	7331.14	+	6151.56i	0.712656	+	0.597989i
$474$		0			0
$475$	9568.30	+	3482.58i	0.924261	+	0.336403i
$476$	−3807.03	+	6593.97i	−0.366586	+	0.634945i
$477$		0			0
$478$	1482.92	+	2568.49i	0.141898	+	0.245774i
$479$	1704.65	+	9667.56i	0.162604	+	0.922175i	0.951500	+	0.307648i	$0.0995420\pi$
$479$	1704.65	+	9667.56i	0.162604	+	0.922175i	−0.788896	+	0.614527i	$0.789347\pi$
$480$		0			0
$481$	−4007.68	+	1458.68i	−0.379905	+	0.138274i
$482$	1447.46	−	8208.95i	0.136784	−	0.775741i
$483$		0			0
$484$	−2971.64	+	2493.50i	−0.279079	+	0.234175i
$485$	−28976.2			−2.71287
$486$		0			0
$487$	−9211.57			−0.857117			−0.428559	−	0.903514i	$-0.640978\pi$
$487$	−9211.57			−0.857117			−0.428559	+	0.903514i	$0.640978\pi$
$488$	2578.53	−	2163.65i	0.239190	−	0.200704i
$489$		0			0
$490$	−71.7949	+	407.169i	−0.00661911	+	0.0375388i
$491$	−5350.10	+	1947.28i	−0.491745	+	0.178981i	−0.575977	−	0.817466i	$-0.695378\pi$
$491$	−5350.10	+	1947.28i	−0.491745	+	0.178981i	0.0842325	+	0.996446i	$0.473156\pi$
$492$		0			0
$493$	−3390.99	−	19231.3i	−0.309782	−	1.75686i
$494$	−2001.38	−	3466.50i	−0.182280	−	0.315719i
$495$		0			0
$496$	117.735	−	203.923i	0.0106582	−	0.0184605i
$497$	−15713.1	−	5719.08i	−1.41816	−	0.516169i
$498$		0			0
$499$	5232.12	+	4390.27i	0.469382	+	0.393858i	0.846569	−	0.532279i	$-0.178664\pi$
$499$	5232.12	+	4390.27i	0.469382	+	0.393858i	−0.377187	+	0.926137i	$0.623109\pi$
$500$	8926.62	+	7490.32i	0.798421	+	0.669955i
$501$		0			0
$502$	3965.27	+	1443.24i	0.352547	+	0.128317i
$503$	537.543	−	931.052i	0.0476498	−	0.0825319i	−0.841217	−	0.540698i	$-0.818160\pi$
$503$	537.543	−	931.052i	0.0476498	−	0.0825319i	0.888867	+	0.458166i	$0.151494\pi$
$504$		0			0
$505$	−15876.4	−	27498.7i	−1.39899	−	2.42312i
$506$	−424.353	−	2406.62i	−0.0372822	−	0.211438i
$507$		0			0
$508$	1337.67	−	486.873i	0.116830	−	0.0425226i
$509$	2125.66	−	12055.2i	0.185105	−	1.04978i	−0.740716	−	0.671818i	$-0.765514\pi$
$509$	2125.66	−	12055.2i	0.185105	−	1.04978i	0.925821	−	0.377962i	$-0.123375\pi$
$510$		0			0
$511$	−2829.67	+	2374.38i	−0.244965	+	0.205550i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	1624.18			0.139376
$515$	4708.00	−	3950.49i	0.402834	−	0.338018i
$516$		0			0
$517$	1728.68	−	9803.81i	0.147054	−	0.833987i
$518$	−2825.29	+	1028.32i	−0.239645	+	0.0872235i
$519$		0			0
$520$	−1474.94	−	8364.80i	−0.124385	−	0.705425i
$521$	−1862.88	−	3226.61i	−0.156650	−	0.271325i	0.777009	−	0.629490i	$-0.216736\pi$
$521$	−1862.88	−	3226.61i	−0.156650	−	0.271325i	−0.933658	+	0.358165i	$0.883403\pi$
$522$		0			0
$523$	−1861.15	+	3223.61i	−0.155607	+	0.269520i	−0.933280	−	0.359150i	$-0.883067\pi$
$523$	−1861.15	+	3223.61i	−0.155607	+	0.269520i	0.777673	+	0.628669i	$0.216400\pi$
$524$	1006.23	+	366.239i	0.0838885	+	0.0305329i
$525$		0			0
$526$	2027.09	+	1700.93i	0.168033	+	0.140997i
$527$	1141.57	+	957.888i	0.0943595	+	0.0791770i
$528$		0			0
$529$	7549.14	+	2747.66i	0.620460	+	0.225829i
$530$	−699.388	+	1211.37i	−0.0573197	+	0.0992807i
$531$		0			0
$532$	−1410.91	−	2443.77i	−0.114983	−	0.199156i
$533$	2307.80	+	13088.2i	0.187546	+	1.06362i
$534$		0			0
$535$	−29833.6	+	10858.6i	−2.41088	+	0.877489i
$536$	703.625	−	3990.46i	0.0567015	−	0.321570i
$537$		0			0
$538$	9184.69	−	7706.87i	0.736023	−	0.617596i
$539$	−197.350			−0.0157708
$540$		0			0
$541$	11303.9			0.898321			0.449161	−	0.893451i	$-0.351723\pi$
$541$	11303.9			0.898321			0.449161	+	0.893451i	$0.351723\pi$
$542$	6410.40	−	5378.96i	0.508026	−	0.426285i
$543$		0			0
$544$	562.669	−	3191.05i	0.0443460	−	0.251499i
$545$	5441.41	−	1980.51i	0.427678	−	0.155662i
$546$		0			0
$547$	1388.53	+	7874.73i	0.108536	+	0.615538i	0.989749	+	0.142818i	$0.0456165\pi$
$547$	1388.53	+	7874.73i	0.108536	+	0.615538i	−0.881213	+	0.472719i	$0.843272\pi$
$548$	46.3327	+	80.2506i	0.00361174	+	0.00625572i
$549$		0			0
$550$	−5156.76	+	8931.78i	−0.399791	+	0.692459i
$551$	6800.74	+	2475.27i	0.525810	+	0.191379i
$552$		0			0
$553$	6547.16	+	5493.72i	0.503461	+	0.422454i
$554$	−12827.4	−	10763.5i	−0.983726	−	0.825444i
$555$		0			0
$556$	−4697.43	−	1709.73i	−0.358301	−	0.130411i
$557$	10198.1	−	17663.6i	0.775775	−	1.34368i	−0.158583	−	0.987346i	$-0.550693\pi$
$557$	10198.1	−	17663.6i	0.775775	−	1.34368i	0.934358	−	0.356336i	$-0.115974\pi$
$558$		0			0
$559$	13427.6	+	23257.2i	1.01597	+	1.75971i
$560$	−1039.79	−	5896.92i	−0.0784624	−	0.444983i
$561$		0			0
$562$	1068.90	−	389.049i	0.0802294	−	0.0292011i
$563$	−3069.29	+	17406.8i	−0.229761	+	1.30304i	0.623611	+	0.781735i	$0.285665\pi$
$563$	−3069.29	+	17406.8i	−0.229761	+	1.30304i	−0.853371	+	0.521303i	$0.825446\pi$
$564$		0			0
$565$	−20300.1	+	17033.8i	−1.51156	+	1.26835i
$566$	10865.1			0.806881
$567$		0			0
$568$	7116.09			0.525677
$569$	6079.62	−	5101.41i	0.447928	−	0.375856i	−0.390738	−	0.920502i	$-0.627780\pi$
$569$	6079.62	−	5101.41i	0.447928	−	0.375856i	0.838666	+	0.544646i	$0.183336\pi$
$570$		0			0
$571$	873.647	−	4954.70i	0.0640298	−	0.363131i	−0.935911	−	0.352237i	$-0.885421\pi$
$571$	873.647	−	4954.70i	0.0640298	−	0.363131i	0.999941	−	0.0108940i	$-0.00346774\pi$
$572$	3809.82	−	1386.66i	0.278490	−	0.101362i
$573$		0			0
$574$	1626.92	+	9226.74i	0.118304	+	0.670935i
$575$	8722.19	+	15107.3i	0.632592	+	1.09568i
$576$		0			0
$577$	6776.42	−	11737.1i	0.488918	−	0.846831i	−0.511000	−	0.859580i	$-0.670725\pi$
$577$	6776.42	−	11737.1i	0.488918	−	0.846831i	0.999919	+	0.0127491i	$0.00405827\pi$
$578$	10036.6	+	3653.01i	0.722259	+	0.262881i
$579$		0			0
$580$	11764.4	+	9871.47i	0.842221	+	0.706708i
$581$	−426.387	−	357.782i	−0.0304467	−	0.0255478i
$582$		0			0
$583$	−627.405	−	228.357i	−0.0445702	−	0.0162222i
$584$	785.993	−	1361.38i	0.0556928	−	0.0964628i
$585$		0			0
$586$	1413.24	+	2447.81i	0.0996255	+	0.172556i
$587$	2477.56	+	14051.0i	0.174208	+	0.987982i	0.939054	+	0.343769i	$0.111704\pi$
$587$	2477.56	+	14051.0i	0.174208	+	0.987982i	−0.764846	+	0.644213i	$0.777185\pi$
$588$		0			0
$589$	−518.975	+	188.892i	−0.0363056	+	0.0132142i
$590$	−2972.52	+	16858.0i	−0.207418	+	1.17633i
$591$		0			0
$592$	980.160	−	822.452i	0.0680479	−	0.0570989i
$593$	−5141.13			−0.356022			−0.178011	−	0.984029i	$-0.556966\pi$
$593$	−5141.13			−0.356022			−0.178011	+	0.984029i	$0.556966\pi$
$594$		0			0
$595$	37895.4			2.61102
$596$	5110.85	−	4288.51i	0.351256	−	0.294739i
$597$		0			0
$598$	1190.79	−	6753.33i	0.0814301	−	0.461813i
$599$	−2123.17	+	772.770i	−0.144825	+	0.0527121i	−0.413416	−	0.910542i	$-0.635664\pi$
$599$	−2123.17	+	772.770i	−0.144825	+	0.0527121i	0.268591	+	0.963254i	$0.413442\pi$
$600$		0			0
$601$	−798.615	−	4529.17i	−0.0542033	−	0.307402i	0.945638	−	0.325221i	$-0.105439\pi$
$601$	−798.615	−	4529.17i	−0.0542033	−	0.307402i	−0.999841	+	0.0178191i	$0.994328\pi$
$602$	9466.00	+	16395.6i	0.640873	+	1.11002i
$603$		0			0
$604$	−1557.18	+	2697.11i	−0.104902	+	0.181695i
$605$	18142.5	+	6603.34i	1.21917	+	0.443742i
$606$		0			0
$607$	8379.78	+	7031.47i	0.560337	+	0.470179i	0.878423	−	0.477883i	$-0.158596\pi$
$607$	8379.78	+	7031.47i	0.560337	+	0.470179i	−0.318086	+	0.948062i	$0.603040\pi$
$608$	919.920	+	771.905i	0.0613613	+	0.0514883i
$609$		0			0
$610$	−15742.5	−	5729.82i	−1.04491	−	0.380317i
$611$	13967.6	−	24192.7i	0.924829	−	1.60185i
$612$		0			0
$613$	264.516	+	458.155i	0.0174286	+	0.0301871i	0.874608	−	0.484830i	$-0.161119\pi$
$613$	264.516	+	458.155i	0.0174286	+	0.0301871i	−0.857180	+	0.515018i	$0.827785\pi$
$614$	2208.25	+	12523.6i	0.145143	+	0.823145i
$615$		0			0
$616$	2685.80	−	977.551i	0.175672	−	0.0639394i
$617$	2339.88	−	13270.1i	0.152674	−	0.865858i	−0.808207	−	0.588898i	$-0.799562\pi$
$617$	2339.88	−	13270.1i	0.152674	−	0.865858i	0.960881	−	0.276960i	$-0.0893269\pi$
$618$		0			0
$619$	−2290.88	+	1922.28i	−0.148753	+	0.124819i	−0.714127	−	0.700016i	$-0.753176\pi$
$619$	−2290.88	+	1922.28i	−0.148753	+	0.124819i	0.565374	+	0.824835i	$0.308732\pi$
$620$	−1171.94			−0.0759132
$621$		0			0
$622$	−10932.2			−0.704729
$623$	3170.38	−	2660.26i	0.203882	−	0.171077i
$624$		0			0
$625$	4181.46	−	23714.2i	0.267613	−	1.51771i
$626$	−5990.54	+	2180.38i	−0.382476	+	0.139210i
$627$		0			0
$628$	−1832.57	−	10393.0i	−0.116445	−	0.660392i
$629$	4048.79	+	7012.72i	0.256655	+	0.444540i
$630$		0			0
$631$	3601.04	−	6237.18i	0.227187	−	0.393500i	−0.729786	−	0.683675i	$-0.760380\pi$
$631$	3601.04	−	6237.18i	0.227187	−	0.393500i	0.956973	+	0.290176i	$0.0937138\pi$
$632$	−3417.84	−	1243.99i	−0.215118	−	0.0782964i
$633$		0			0
$634$	−2195.08	−	1841.89i	−0.137504	−	0.115380i
$635$	−5427.35	−	4554.09i	−0.339178	−	0.284604i
$636$		0			0
$637$	−520.395	−	189.408i	−0.0323686	−	0.0117812i
$638$	−3665.21	+	6348.32i	−0.227440	+	0.393938i
$639$		0			0
$640$	1274.12	+	2206.84i	0.0786937	+	0.136302i
$641$	908.877	+	5154.50i	0.0560039	+	0.317614i	0.999921	−	0.0125686i	$-0.00400082\pi$
$641$	908.877	+	5154.50i	0.0560039	+	0.317614i	−0.943917	+	0.330182i	$0.892890\pi$
$642$		0			0
$643$	13793.5	−	5020.43i	0.845978	−	0.307911i	0.117578	−	0.993064i	$-0.462487\pi$
$643$	13793.5	−	5020.43i	0.845978	−	0.307911i	0.728399	+	0.685153i	$0.240265\pi$
$644$	839.472	−	4760.88i	0.0513662	−	0.291312i
$645$		0			0
$646$	−5821.88	+	4885.13i	−0.354580	+	0.297528i
$647$	−21420.8			−1.30161			−0.650804	−	0.759246i	$-0.725568\pi$
$647$	−21420.8			−1.30161			−0.650804	+	0.759246i	$0.725568\pi$
$648$		0			0
$649$	−8170.88			−0.494199
$650$	−22170.3	+	18603.1i	−1.33783	+	1.12257i
$651$		0			0
$652$	1550.32	−	8792.29i	0.0931214	−	0.528118i
$653$	26911.9	−	9795.13i	1.61278	−	0.587003i	0.630792	−	0.775952i	$-0.282730\pi$
$653$	26911.9	−	9795.13i	1.61278	−	0.587003i	0.981987	+	0.188949i	$0.0605081\pi$
$654$		0			0
$655$	−925.452	−	5248.50i	−0.0552067	−	0.313093i
$656$	−1993.58	−	3452.98i	−0.118653	−	0.205513i
$657$		0			0
$658$	9846.74	−	17055.1i	0.583383	−	1.01045i
$659$	−23098.8	−	8407.28i	−1.36541	−	0.496967i	−0.447684	−	0.894192i	$-0.647751\pi$
$659$	−23098.8	−	8407.28i	−1.36541	−	0.496967i	−0.917721	+	0.397225i	$0.869973\pi$
$660$		0			0
$661$	16315.1	+	13690.0i	0.960035	+	0.805565i	0.980959	−	0.194216i	$-0.0622163\pi$
$661$	16315.1	+	13690.0i	0.960035	+	0.805565i	−0.0209239	+	0.999781i	$0.506661\pi$
$662$	17309.5	+	14524.4i	1.01624	+	0.852729i
$663$		0			0
$664$	222.589	+	81.0156i	0.0130092	+	0.00473496i
$665$	−7022.15	+	12162.7i	−0.409484	+	0.709248i
$666$		0			0
$667$	6199.36	+	10737.6i	0.359880	+	0.623331i
$668$	1054.43	+	5979.98i	0.0610737	+	0.346366i
$669$		0			0
$670$	−18950.8	+	6897.52i	−1.09274	+	0.397723i
$671$	1388.59	−	7875.07i	0.0798895	−	0.453076i
$672$		0			0
$673$	3443.32	−	2889.28i	0.197221	−	0.165488i	−0.538829	−	0.842415i	$-0.681133\pi$
$673$	3443.32	−	2889.28i	0.197221	−	0.165488i	0.736050	+	0.676927i	$0.236689\pi$
$674$	−21338.2			−1.21946
$675$		0			0
$676$	2589.00			0.147303
$677$	−13437.0	+	11275.0i	−0.762817	+	0.640079i	−0.938858	−	0.344303i	$-0.888115\pi$
$677$	−13437.0	+	11275.0i	−0.762817	+	0.640079i	0.176042	+	0.984383i	$0.443671\pi$
$678$		0			0
$679$	4751.21	−	26945.5i	0.268534	−	1.52293i
$680$	−15154.4	+	5515.75i	−0.854625	+	0.311058i
$681$		0			0
$682$	−97.1380	−	550.897i	−0.00545397	−	0.0309310i
$683$	11754.0	+	20358.5i	0.658497	+	1.14055i	0.981005	+	0.193984i	$0.0621410\pi$
$683$	11754.0	+	20358.5i	0.658497	+	1.14055i	−0.322507	+	0.946567i	$0.604526\pi$
$684$		0			0
$685$	230.599	−	399.410i	0.0128624	−	0.0222783i
$686$	11751.2	+	4277.09i	0.654028	+	0.238047i
$687$		0			0
$688$	−6171.88	−	5178.82i	−0.342007	−	0.286978i
$689$	−1435.24	−	1204.31i	−0.0793591	−	0.0665902i
$690$		0			0
$691$	11204.1	+	4077.97i	0.616824	+	0.224506i	0.631486	−	0.775387i	$-0.282445\pi$
$691$	11204.1	+	4077.97i	0.616824	+	0.224506i	−0.0146625	+	0.999892i	$0.504667\pi$
$692$	2585.65	−	4478.48i	0.142040	−	0.246021i
$693$		0			0
$694$	2639.15	+	4571.14i	0.144353	+	0.250026i
$695$	4320.31	+	24501.7i	0.235797	+	1.33727i
$696$		0			0
$697$	23711.7	−	8630.34i	1.28858	−	0.469006i
$698$	2914.77	−	16530.5i	0.158060	−	0.896401i
$699$		0			0
$700$	−15629.3	+	13114.6i	−0.843904	+	0.708120i
$701$	−11342.2			−0.611110			−0.305555	−	0.952174i	$-0.598842\pi$
$701$	−11342.2			−0.611110			−0.305555	+	0.952174i	$0.598842\pi$
$702$		0			0
$703$	−3001.02			−0.161004
$704$	−931.769	+	781.847i	−0.0498826	+	0.0418565i
$705$		0			0
$706$	−803.995	+	4559.68i	−0.0428594	+	0.243068i
$707$	28174.8	−	10254.8i	1.49876	−	0.545503i
$708$		0			0
$709$	2189.65	+	12418.1i	0.115986	+	0.657790i	0.986257	+	0.165217i	$0.0528325\pi$
$709$	2189.65	+	12418.1i	0.115986	+	0.657790i	−0.870271	+	0.492573i	$0.836056\pi$
$710$	−17708.5	−	30672.0i	−0.936039	−	1.62127i
$711$		0			0
$712$	−880.630	+	1525.30i	−0.0463525	+	0.0802850i
$713$	−889.105	−	323.608i	−0.0467002	−	0.0169975i
$714$		0			0
$715$	−15457.6	−	12970.5i	−0.808506	−	0.678417i
$716$	283.186	+	237.621i	0.0147809	+	0.0124027i
$717$		0			0
$718$	5633.24	+	2050.33i	0.292800	+	0.106571i
$719$	−3953.43	+	6847.54i	−0.205060	+	0.355174i	−0.950152	−	0.311788i	$-0.899072\pi$
$719$	−3953.43	+	6847.54i	−0.205060	+	0.355174i	0.745092	+	0.666962i	$0.232406\pi$
$720$		0			0
$721$	2901.66	+	5025.82i	0.149880	+	0.259600i
$722$	1893.01	+	10735.8i	0.0975770	+	0.553387i
$723$		0			0
$724$	−2724.90	+	991.782i	−0.139876	+	0.0509106i
$725$	9086.51	−	51532.2i	0.465468	−	2.63980i
$726$		0			0
$727$	3788.33	−	3178.78i	0.193262	−	0.162166i	−0.541022	−	0.841008i	$-0.681963\pi$
$727$	3788.33	−	3178.78i	0.193262	−	0.162166i	0.734284	+	0.678842i	$0.237518\pi$
$728$	8020.42			0.408320
$729$		0			0
$730$	−7823.82			−0.396675
$731$	39059.8	−	32775.1i	1.97630	−	1.65832i
$732$		0			0
$733$	−721.183	+	4090.03i	−0.0363404	+	0.206097i	−0.997572	−	0.0696466i	$-0.977813\pi$
$733$	−721.183	+	4090.03i	−0.0363404	+	0.206097i	0.961231	+	0.275743i	$0.0889239\pi$
$734$	9716.76	−	3536.61i	0.488627	−	0.177846i
$735$		0			0
$736$	357.250	+	2026.07i	0.0178919	+	0.101470i
$737$	−4813.11	−	8336.55i	−0.240561	−	0.416663i
$738$		0			0
$739$	−17308.8	+	29979.7i	−0.861588	+	1.49231i	0.00880839	+	0.999961i	$0.497196\pi$
$739$	−17308.8	+	29979.7i	−0.861588	+	1.49231i	−0.870396	+	0.492352i	$0.836137\pi$
$740$	−5984.10	−	2178.04i	−0.297270	−	0.108198i
$741$		0			0
$742$	−1011.80	−	849.002i	−0.0500598	−	0.0420052i
$743$	−15671.7	−	13150.1i	−0.773807	−	0.649301i	0.167874	−	0.985808i	$-0.446310\pi$
$743$	−15671.7	−	13150.1i	−0.773807	−	0.649301i	−0.941681	+	0.336507i	$0.890754\pi$
$744$		0			0
$745$	−31202.9	−	11356.9i	−1.53448	−	0.558505i
$746$	−9489.24	+	16435.8i	−0.465718	+	0.806647i
$747$		0			0
$748$	−3848.90	−	6666.50i	−0.188141	−	0.325871i
$749$	−5205.76	−	29523.3i	−0.253958	−	1.44026i
$750$		0			0
$751$	−33951.8	+	12357.5i	−1.64969	+	0.600440i	−0.988694	−	0.149946i	$-0.952090\pi$
$751$	−33951.8	+	12357.5i	−1.64969	+	0.600440i	−0.661000	+	0.750386i	$0.729868\pi$
$752$	−1455.32	+	8253.55i	−0.0705720	+	0.400234i
$753$		0			0
$754$	−15757.7	+	13222.3i	−0.761088	+	0.638629i
$755$	15500.3			0.747169
$756$		0			0
$757$	−21683.2			−1.04107			−0.520536	−	0.853840i	$-0.674268\pi$
$757$	−21683.2			−1.04107			−0.520536	+	0.853840i	$0.674268\pi$
$758$	20179.3	−	16932.5i	0.966947	−	0.811365i
$759$		0			0
$760$	1037.86	−	5885.97i	0.0495355	−	0.280930i
$761$	−9111.22	+	3316.21i	−0.434010	+	0.157967i	−0.549780	−	0.835309i	$-0.685289\pi$
$761$	−9111.22	+	3316.21i	−0.434010	+	0.157967i	0.115771	+	0.993276i	$0.463066\pi$
$762$		0			0
$763$	949.487	+	5384.81i	0.0450508	+	0.255496i
$764$	2520.24	+	4365.18i	0.119344	+	0.206710i
$765$		0			0
$766$	10270.6	−	17789.2i	0.484453	−	0.839097i
$767$	−21545.9	−	7842.06i	−1.01431	−	0.369179i
$768$		0			0
$769$	20593.0	+	17279.6i	0.965673	+	0.810296i	0.981867	−	0.189573i	$-0.0607104\pi$
$769$	20593.0	+	17279.6i	0.965673	+	0.810296i	−0.0161937	+	0.999869i	$0.505155\pi$
$770$	−10897.1	−	9143.77i	−0.510007	−	0.427946i
$771$		0			0
$772$	12745.1	+	4638.84i	0.594180	+	0.216264i
$773$	−19542.6	+	33848.7i	−0.909311	+	1.57497i	−0.0942873	+	0.995545i	$0.530057\pi$
$773$	−19542.6	+	33848.7i	−0.909311	+	1.57497i	−0.815024	+	0.579428i	$0.803276\pi$
$774$		0			0
$775$	1996.58	+	3458.18i	0.0925412	+	0.160286i
$776$	2021.95	+	11467.1i	0.0935360	+	0.530469i
$777$		0			0
$778$	20063.1	−	7302.36i	0.924545	−	0.336507i
$779$	−1623.90	+	9209.61i	−0.0746885	+	0.423580i
$780$		0			0
$781$	12950.3	−	10866.6i	0.593339	−	0.497871i
$782$	−13020.1			−0.595395
$783$		0			0
$784$	166.143			0.00756849
$785$	−40235.9	+	33762.0i	−1.82940	+	1.53505i
$786$		0			0
$787$	−734.308	+	4164.47i	−0.0332595	+	0.188624i	−0.996911	−	0.0785379i	$-0.974975\pi$
$787$	−734.308	+	4164.47i	−0.0332595	+	0.188624i	0.963652	+	0.267162i	$0.0860859\pi$
$788$	7997.45	−	2910.84i	0.361545	−	0.131592i
$789$		0			0
$790$	3143.45	+	17827.4i	0.141568	+	0.802873i
$791$	−12511.4	−	21670.4i	−0.562396	−	0.974099i
$792$		0			0
$793$	11219.7	−	19433.2i	0.502427	−	0.870229i
$794$	12442.3	+	4528.62i	0.556120	+	0.202411i
$795$		0			0
$796$	−1034.59	−	868.127i	−0.0460681	−	0.0386557i
$797$	12995.9	+	10904.9i	0.577589	+	0.484655i	0.884154	−	0.467195i	$-0.154735\pi$
$797$	12995.9	+	10904.9i	0.577589	+	0.484655i	−0.306565	+	0.951850i	$0.599180\pi$
$798$		0			0
$799$	−49841.1	−	18140.7i	−2.20682	−	0.803218i
$800$	4341.33	−	7519.41i	0.191862	−	0.332314i
$801$		0			0
$802$	−10266.6	−	17782.3i	−0.452027	−	0.782934i
$803$	−648.490	−	3677.77i	−0.0284990	−	0.161626i
$804$		0			0
$805$	−22609.6	+	8229.20i	−0.989916	+	0.360300i
$806$	272.583	−	1545.90i	0.0119123	−	0.0675581i
$807$		0			0
$808$	−9774.51	+	8201.79i	−0.425577	+	0.357101i
$809$	19066.3			0.828598			0.414299	−	0.910141i	$-0.364027\pi$
$809$	19066.3			0.828598			0.414299	+	0.910141i	$0.364027\pi$
$810$		0			0
$811$	20991.4			0.908886			0.454443	−	0.890776i	$-0.349838\pi$
$811$	20991.4			0.908886			0.454443	+	0.890776i	$0.349838\pi$
$812$	−11108.7	+	9321.27i	−0.480095	+	0.402848i
$813$		0			0
$814$	527.834	−	2993.50i	0.0227280	−	0.128897i
$815$	−41754.8	+	15197.5i	−1.79461	+	0.653185i
$816$		0			0
$817$	3281.40	+	18609.8i	0.140516	+	0.796907i
$818$	−12687.7	−	21975.7i	−0.542316	−	0.939319i
$819$		0			0
$820$	−9922.10	+	17185.6i	−0.422555	+	0.731886i
$821$	−11497.9	−	4184.91i	−0.488771	−	0.177898i	0.0858657	−	0.996307i	$-0.472634\pi$
$821$	−11497.9	−	4184.91i	−0.488771	−	0.177898i	−0.574637	+	0.818409i	$0.694857\pi$
$822$		0			0
$823$	−16831.4	−	14123.2i	−0.712885	−	0.598181i	0.212522	−	0.977156i	$-0.431832\pi$
$823$	−16831.4	−	14123.2i	−0.712885	−	0.598181i	−0.925407	+	0.378975i	$0.876277\pi$
$824$	−1891.89	−	1587.49i	−0.0799845	−	0.0671150i
$825$		0			0
$826$	−15189.2	−	5528.40i	−0.639828	−	0.232879i
$827$	4466.52	−	7736.24i	0.187807	−	0.325291i	−0.756712	−	0.653748i	$-0.773195\pi$
$827$	4466.52	−	7736.24i	0.187807	−	0.325291i	0.944519	+	0.328458i	$0.106529\pi$
$828$		0			0
$829$	16840.1	+	29167.9i	0.705526	+	1.22201i	0.966501	+	0.256662i	$0.0826227\pi$
$829$	16840.1	+	29167.9i	0.705526	+	1.22201i	−0.260975	+	0.965346i	$0.584044\pi$
$830$	−204.719	−	1161.02i	−0.00856131	−	0.0485536i
$831$		0			0
$832$	−3207.37	+	1167.39i	−0.133649	+	0.0486441i
$833$	−182.585	+	1035.49i	−0.00759449	+	0.0430705i
$834$		0			0
$835$	23151.2	−	19426.1i	0.959496	−	0.805112i
$836$	2852.86			0.118024
$837$		0			0
$838$	22317.3			0.919975
$839$	−11884.9	+	9972.60i	−0.489049	+	0.410361i	−0.853685	−	0.520789i	$-0.825638\pi$
$839$	−11884.9	+	9972.60i	−0.489049	+	0.410361i	0.364637	+	0.931150i	$0.381193\pi$
$840$		0			0
$841$	2223.20	−	12608.4i	0.0911558	−	0.516970i
$842$	4885.76	−	1778.27i	0.199970	−	0.0727830i
$843$		0			0
$844$	−2228.78	−	12640.1i	−0.0908979	−	0.515508i
$845$	−6442.77	−	11159.2i	−0.262293	−	0.454306i
$846$		0			0
$847$	−9115.39	+	15788.3i	−0.369786	+	0.640488i
$848$	528.194	+	192.247i	0.0213895	+	0.00778512i
$849$		0			0
$850$	42093.9	+	35321.0i	1.69860	+	1.42530i
$851$	−3938.49	−	3304.78i	−0.158648	−	0.133122i
$852$		0			0
$853$	12337.8	+	4490.59i	0.495238	+	0.180252i	0.577551	−	0.816355i	$-0.304009\pi$
$853$	12337.8	+	4490.59i	0.495238	+	0.180252i	−0.0823132	+	0.996607i	$0.526231\pi$
$854$	7909.56	−	13699.8i	0.316931	−	0.548941i
$855$		0			0
$856$	6378.97	+	11048.7i	0.254706	+	0.441164i
$857$	6201.70	+	35171.6i	0.247195	+	1.40191i	0.815339	+	0.578983i	$0.196550\pi$
$857$	6201.70	+	35171.6i	0.247195	+	1.40191i	−0.568144	+	0.822929i	$0.692338\pi$
$858$		0			0
$859$	−8581.22	+	3123.31i	−0.340847	+	0.124058i	−0.506772	−	0.862080i	$-0.669161\pi$
$859$	−8581.22	+	3123.31i	−0.340847	+	0.124058i	0.165925	+	0.986138i	$0.446939\pi$
$860$	−6963.12	+	39489.8i	−0.276093	+	1.56580i
$861$		0			0
$862$	−8801.70	+	7385.51i	−0.347781	+	0.291823i
$863$	42351.7			1.67053			0.835266	−	0.549846i	$-0.185313\pi$
$863$	42351.7			1.67053			0.835266	+	0.549846i	$0.185313\pi$
$864$		0			0
$865$	−25737.8			−1.01169
$866$	20089.6	−	16857.2i	0.788306	−	0.661467i
$867$		0			0
$868$	192.162	−	1089.81i	0.00751430	−	0.0426157i
$869$	−8119.62	+	2955.30i	−0.316961	+	0.115364i
$870$		0			0
$871$	−4690.68	−	26602.1i	−0.182477	−	1.03488i
$872$	−1163.47	−	2015.19i	−0.0451836	−	0.0782602i
$873$		0			0
$874$	2412.67	−	4178.88i	0.0933752	−	0.161731i
$875$	51461.5	+	18730.4i	1.98825	+	0.723663i
$876$		0			0
$877$	−6051.11	−	5077.48i	−0.232989	−	0.195501i	0.518817	−	0.854885i	$-0.326373\pi$
$877$	−6051.11	−	5077.48i	−0.232989	−	0.195501i	−0.751806	+	0.659384i	$0.770817\pi$
$878$	−7626.84	−	6399.68i	−0.293159	−	0.245989i
$879$		0			0
$880$	5688.66	+	2070.50i	0.217915	+	0.0793144i
$881$	4073.72	−	7055.89i	0.155786	−	0.269829i	−0.777559	−	0.628810i	$-0.783542\pi$
$881$	4073.72	−	7055.89i	0.155786	−	0.269829i	0.933345	+	0.358981i	$0.116876\pi$
$882$		0			0
$883$	−311.142	−	538.914i	−0.0118582	−	0.0205390i	0.860035	−	0.510234i	$-0.170441\pi$
$883$	−311.142	−	538.914i	−0.0118582	−	0.0205390i	−0.871894	+	0.489695i	$0.837108\pi$
$884$	−3751.00	−	21273.0i	−0.142715	−	0.809375i
$885$		0			0
$886$	−22879.3	+	8327.37i	−0.867544	+	0.315760i
$887$	−113.791	+	645.341i	−0.00430748	+	0.0244289i	−0.986886	−	0.161420i	$-0.948393\pi$
$887$	−113.791	+	645.341i	−0.00430748	+	0.0244289i	0.982578	+	0.185849i	$0.0595036\pi$
$888$		0			0
$889$	5124.85	−	4300.26i	0.193343	−	0.162234i
$890$	8765.85			0.330148
$891$		0			0
$892$	3434.27			0.128910
$893$	15058.1	−	12635.2i	0.564277	−	0.473485i
$894$		0			0
$895$	319.491	−	1811.92i	0.0119323	−	0.0676713i
$896$	−2261.10	+	822.972i	−0.0843057	+	0.0306848i
$897$		0			0
$898$	−2918.73	−	16553.0i	−0.108463	−	0.615122i
$899$	1419.09	+	2457.93i	0.0526465	+	0.0911864i
$900$		0			0
$901$	−1778.65	+	3080.71i	−0.0657663	+	0.113911i
$902$	−8900.89	−	3239.66i	−0.328567	−	0.119589i
$903$		0			0
$904$	8157.51	+	6844.97i	0.300127	+	0.251836i
$905$	11055.8	+	9276.89i	0.406084	+	0.340745i
$906$		0			0
$907$	27516.8	+	10015.3i	1.00737	+	0.366651i	0.792421	−	0.609975i	$-0.208820\pi$
$907$	27516.8	+	10015.3i	1.00737	+	0.366651i	0.214945	+	0.976626i	$0.431043\pi$
$908$	4596.30	−	7961.03i	0.167989	−	0.290965i
$909$		0			0
$910$	−19958.9	−	34569.9i	−0.727069	−	1.25932i
$911$	−4075.80	−	23115.0i	−0.148230	−	0.840653i	−0.964717	−	0.263289i	$-0.915193\pi$
$911$	−4075.80	−	23115.0i	−0.148230	−	0.840653i	0.816487	−	0.577364i	$-0.195918\pi$
$912$		0			0
$913$	528.795	−	192.466i	0.0191682	−	0.00697665i
$914$	−2748.04	+	15584.9i	−0.0994499	+	0.564008i
$915$		0			0
$916$	−11043.2	+	9266.37i	−0.398339	+	0.334246i
$917$	5032.42			0.181227
$918$		0			0
$919$	29530.9			1.05999			0.529997	−	0.848000i	$-0.322193\pi$
$919$	29530.9			1.05999			0.529997	+	0.848000i	$0.322193\pi$
$920$	7843.80	−	6581.73i	0.281090	−	0.235862i
$921$		0			0
$922$	−726.419	+	4119.73i	−0.0259472	+	0.147154i
$923$	44578.1	−	16225.1i	1.58971	−	0.578608i
$924$		0			0
$925$	3767.87	+	21368.7i	0.133932	+	0.759565i
$926$	14165.5	+	24535.3i	0.502706	+	0.870713i
$927$		0			0
$928$	3085.63	−	5344.47i	0.109150	−	0.189053i
$929$	−5528.89	−	2012.35i	−0.195261	−	0.0710690i	0.242539	−	0.970142i	$-0.422020\pi$
$929$	−5528.89	−	2012.35i	−0.195261	−	0.0710690i	−0.437799	+	0.899073i	$0.644242\pi$
$930$		0			0
$931$	−298.513	−	250.482i	−0.0105085	−	0.00881764i
$932$	−16577.2	−	13909.9i	−0.582623	−	0.488879i
$933$		0			0
$934$	20719.6	+	7541.30i	0.725872	+	0.264196i
$935$	−19156.1	+	33179.3i	−0.670023	+	1.16051i
$936$		0			0
$937$	−3493.70	−	6051.27i	−0.121808	−	0.210978i	0.798673	−	0.601766i	$-0.205536\pi$
$937$	−3493.70	−	6051.27i	−0.121808	−	0.210978i	−0.920481	+	0.390788i	$0.872203\pi$
$938$	−3306.78	−	18753.7i	−0.115107	−	0.652803i
$939$		0			0
$940$	39196.3	−	14266.3i	1.36005	−	0.495016i
$941$	−6756.59	+	38318.5i	−0.234068	+	1.32747i	0.610498	+	0.792018i	$0.290969\pi$
$941$	−6756.59	+	38318.5i	−0.234068	+	1.32747i	−0.844567	+	0.535451i	$0.820142\pi$
$942$		0			0
$943$	−12273.0	+	10298.3i	−0.423821	+	0.355628i
$944$	6878.83			0.237168
$945$		0			0
$946$	−19140.2			−0.657826
$947$	−27870.5	+	23386.1i	−0.956355	+	0.802478i	−0.980356	−	0.197234i	$-0.936804\pi$
$947$	−27870.5	+	23386.1i	−0.956355	+	0.802478i	0.0240009	+	0.999712i	$0.492360\pi$
$948$		0			0
$949$	1819.75	−	10320.3i	0.0622463	−	0.353016i
$950$	−19136.6	+	6965.16i	−0.653551	+	0.237873i
$951$		0			0
$952$	−2644.33	−	14996.8i	−0.0900245	−	0.510555i
$953$	2260.41	+	3915.14i	0.0768330	+	0.133079i	0.901882	−	0.431983i	$-0.142186\pi$
$953$	2260.41	+	3915.14i	0.0768330	+	0.133079i	−0.825049	+	0.565061i	$0.808852\pi$
$954$		0			0
$955$	12543.3	−	21725.6i	0.425018	−	0.736152i
$956$	−5573.94	−	2028.75i	−0.188571	−	0.0686344i
$957$		0			0
$958$	−15040.0	−	12620.1i	−0.507225	−	0.425613i
$959$	333.607	+	279.929i	0.0112333	+	0.00942585i
$960$		0			0
$961$	27790.9	+	10115.0i	0.932861	+	0.339534i
$962$	4264.88	−	7386.99i	0.142937	−	0.247574i
$963$		0			0
$964$	8335.58	+	14437.7i	0.278497	+	0.482371i
$965$	−11721.9	−	66478.3i	−0.391028	−	2.21763i
$966$		0			0
$967$	−54378.9	+	19792.3i	−1.80838	+	0.658198i	−0.811071	+	0.584947i	$0.801115\pi$
$967$	−54378.9	+	19792.3i	−1.80838	+	0.658198i	−0.997314	+	0.0732509i	$0.976663\pi$
$968$	1347.23	−	7640.53i	0.0447331	−	0.253694i
$969$		0			0
$970$	44394.1	−	37251.1i	1.46949	−	1.23305i
$971$	−53097.5			−1.75487			−0.877435	−	0.479696i	$-0.840747\pi$
$971$	−53097.5			−1.75487			−0.877435	+	0.479696i	$0.840747\pi$
$972$		0			0
$973$	−23493.0			−0.774050
$974$	14112.9	−	11842.2i	0.464279	−	0.389577i
$975$		0			0
$976$	−1169.01	+	6629.80i	−0.0383393	+	0.217433i
$977$	−27131.6	+	9875.09i	−0.888451	+	0.323370i	−0.745615	−	0.666377i	$-0.767844\pi$
$977$	−27131.6	+	9875.09i	−0.888451	+	0.323370i	−0.142836	+	0.989746i	$0.545622\pi$
$978$		0			0
$979$	726.571	+	4120.59i	0.0237194	+	0.134520i
$980$	−413.450	−	716.117i	−0.0134767	−	0.0233424i
$981$		0			0
$982$	5693.46	−	9861.36i	0.185016	−	0.320457i
$983$	−12936.9	−	4708.64i	−0.419758	−	0.152779i	0.123501	−	0.992344i	$-0.460588\pi$
$983$	−12936.9	−	4708.64i	−0.419758	−	0.152779i	−0.543259	+	0.839565i	$0.682810\pi$
$984$		0			0
$985$	−32448.2	−	27227.2i	−1.04963	−	0.880743i
$986$	29918.6	+	25104.7i	0.966330	+	0.810847i
$987$		0			0
$988$	7522.74	+	2738.05i	0.242237	+	0.0881671i
$989$	−16187.0	+	28036.7i	−0.520441	+	0.901430i
$990$		0			0
$991$	−19335.2	−	33489.5i	−0.619780	−	1.07349i	−0.989526	−	0.144358i	$-0.953888\pi$
$991$	−19335.2	−	33489.5i	−0.619780	−	1.07349i	0.369745	−	0.929133i	$-0.379445\pi$
$992$	81.7777	+	463.784i	0.00261738	+	0.0148439i
$993$		0			0
$994$	31426.1	−	11438.2i	1.00279	−	0.364987i
$995$	−1167.23	+	6619.69i	−0.0371896	+	0.210913i
$996$		0			0
$997$	42753.5	−	35874.5i	1.35809	−	1.13957i	0.381526	−	0.924358i	$-0.375399\pi$
$997$	42753.5	−	35874.5i	1.35809	−	1.13957i	0.976566	−	0.215216i	$-0.0690457\pi$
$998$	−13660.1			−0.433269
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.37.1		24
3.2	odd	2		54.4.e.a.49.1	yes	24
27.4	even	9		1458.4.a.e.1.12		12
27.11	odd	18		54.4.e.a.43.1	✓	24
27.16	even	9	inner	162.4.e.a.127.1		24
27.23	odd	18		1458.4.a.h.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.43.1	✓	24	27.11	odd	18
54.4.e.a.49.1	yes	24	3.2	odd	2
162.4.e.a.37.1		24	1.1	even	1	trivial
162.4.e.a.127.1		24	27.16	even	9	inner
1458.4.a.e.1.12		12	27.4	even	9
1458.4.a.h.1.1		12	27.23	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)

\(f(q)\)	\(=\)	\(q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-18.7075 + 6.80898i) q^{5} +(-3.26433 - 18.5129i) q^{7} +(4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.53209 + 1.28558i) q^{2} +(0.694593 - 3.93923i) q^{4} +(-18.7075 + 6.80898i) q^{5} +(-3.26433 - 18.5129i) q^{7} +(4.00000 + 6.92820i) q^{8} +(19.9081 - 34.4819i) q^{10} +(17.8591 + 6.50019i) q^{11} +(40.8543 + 34.2808i) q^{13} +(28.8010 + 24.1669i) q^{14} +(-15.0351 - 5.47232i) q^{16} +(50.6294 - 87.6927i) q^{17} +(18.7636 + 32.4995i) q^{19} +(13.8280 + 78.4227i) q^{20} +(-35.7182 + 13.0004i) q^{22} +(-11.1641 + 63.3146i) q^{23} +(207.853 - 174.410i) q^{25} -106.663 q^{26} -75.1940 q^{28} +(147.733 - 123.963i) q^{29} +(-2.55555 + 14.4933i) q^{31} +(30.0702 - 10.9446i) q^{32} +(35.1668 + 199.441i) q^{34} +(187.121 + 324.104i) q^{35} +(-39.9846 + 69.2554i) q^{37} +(-70.5281 - 25.6701i) q^{38} +(-122.004 - 102.374i) q^{40} +(190.896 + 160.181i) q^{41} +(473.183 + 172.225i) q^{43} +(38.0106 - 65.8362i) q^{44} +(-64.2913 - 111.356i) q^{46} +(-90.9577 - 515.847i) q^{47} +(-9.75774 + 3.55153i) q^{49} +(-94.2330 + 534.422i) q^{50} +(163.417 - 137.123i) q^{52} -35.1308 q^{53} -378.359 q^{55} +(115.204 - 96.6676i) q^{56} +(-66.9768 + 379.844i) q^{58} +(-403.999 + 147.044i) q^{59} +(-73.0632 - 414.362i) q^{61} +(-14.7168 - 25.4903i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(-997.700 - 363.133i) q^{65} +(-388.003 - 325.573i) q^{67} +(-310.275 - 260.352i) q^{68} +(-703.347 - 255.997i) q^{70} +(444.756 - 770.339i) q^{71} +(-98.2491 - 170.172i) q^{73} +(-27.7730 - 157.509i) q^{74} +(141.056 - 51.3402i) q^{76} +(62.0394 - 351.843i) q^{77} +(-348.281 + 292.242i) q^{79} +318.530 q^{80} -498.395 q^{82} +(22.6820 - 19.0324i) q^{83} +(-350.052 + 1985.25i) q^{85} +(-946.366 + 344.449i) q^{86} +(26.4019 + 149.732i) q^{88} +(110.079 + 190.662i) q^{89} +(501.276 - 868.236i) q^{91} +(241.656 + 87.9557i) q^{92} +(802.515 + 673.390i) q^{94} +(-572.309 - 480.224i) q^{95} +(1367.72 + 497.809i) q^{97} +(10.3840 - 17.9856i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 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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