LMFDB - Embedded newform 136.4.h.a.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(101,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("136.101");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	136.101
Dual form			136.4.h.a.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.64160 - 1.01092i) q^{2} -6.38011 q^{3} +(5.95609 + 5.34088i) q^{4} -16.9716 q^{5} +(16.8537 + 6.44977i) q^{6} +31.4494i q^{7} +(-10.3344 - 20.1296i) q^{8} +13.7058 q^{9} +O(q^{10})$	\(q+(-2.64160 - 1.01092i) q^{2} -6.38011 q^{3} +(5.95609 + 5.34088i) q^{4} -16.9716 q^{5} +(16.8537 + 6.44977i) q^{6} +31.4494i q^{7} +(-10.3344 - 20.1296i) q^{8} +13.7058 q^{9} +(44.8322 + 17.1569i) q^{10} -16.9532 q^{11} +(-38.0005 - 34.0754i) q^{12} +37.9820i q^{13} +(31.7927 - 83.0766i) q^{14} +108.281 q^{15} +(6.94996 + 63.6215i) q^{16} +(-68.0599 - 16.7586i) q^{17} +(-36.2051 - 13.8554i) q^{18} -85.6684i q^{19} +(-101.084 - 90.6434i) q^{20} -200.650i q^{21} +(44.7836 + 17.1383i) q^{22} -23.5064i q^{23} +(65.9346 + 128.429i) q^{24} +163.036 q^{25} +(38.3967 - 100.333i) q^{26} +84.8186 q^{27} +(-167.967 + 187.315i) q^{28} -55.2526 q^{29} +(-286.034 - 109.463i) q^{30} -218.364i q^{31} +(45.9572 - 175.088i) q^{32} +108.163 q^{33} +(162.845 + 113.072i) q^{34} -533.747i q^{35} +(81.6328 + 73.2009i) q^{36} -99.9450 q^{37} +(-86.6038 + 226.302i) q^{38} -242.329i q^{39} +(175.391 + 341.632i) q^{40} +233.138i q^{41} +(-202.841 + 530.037i) q^{42} +266.763i q^{43} +(-100.975 - 90.5451i) q^{44} -232.609 q^{45} +(-23.7630 + 62.0944i) q^{46} +630.370 q^{47} +(-44.3415 - 405.912i) q^{48} -646.062 q^{49} +(-430.676 - 164.816i) q^{50} +(434.229 + 106.921i) q^{51} +(-202.857 + 226.224i) q^{52} +526.469i q^{53} +(-224.057 - 85.7447i) q^{54} +287.724 q^{55} +(633.062 - 325.010i) q^{56} +546.574i q^{57} +(145.955 + 55.8559i) q^{58} -260.113i q^{59} +(644.930 + 578.315i) q^{60} +363.306 q^{61} +(-220.748 + 576.829i) q^{62} +431.038i q^{63} +(-298.400 + 416.054i) q^{64} -644.616i q^{65} +(-285.724 - 109.344i) q^{66} +297.080i q^{67} +(-315.865 - 463.315i) q^{68} +149.973i q^{69} +(-539.574 + 1409.94i) q^{70} +663.955i q^{71} +(-141.641 - 275.891i) q^{72} -878.743i q^{73} +(264.015 + 101.036i) q^{74} -1040.19 q^{75} +(457.545 - 510.249i) q^{76} -533.168i q^{77} +(-244.975 + 640.136i) q^{78} -1135.44i q^{79} +(-117.952 - 1079.76i) q^{80} -911.208 q^{81} +(235.683 - 615.856i) q^{82} -79.0370i q^{83} +(1071.65 - 1195.09i) q^{84} +(1155.09 + 284.420i) q^{85} +(269.675 - 704.680i) q^{86} +352.518 q^{87} +(175.201 + 341.261i) q^{88} -742.706 q^{89} +(614.460 + 235.149i) q^{90} -1194.51 q^{91} +(125.545 - 140.006i) q^{92} +1393.18i q^{93} +(-1665.18 - 637.252i) q^{94} +1453.93i q^{95} +(-293.212 + 1117.08i) q^{96} +216.022i q^{97} +(1706.64 + 653.116i) q^{98} -232.357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.64160	−	1.01092i	−0.933946	−	0.357414i
$2$	−2.64160	−	1.01092i	−0.933946	−	0.357414i
$3$	−6.38011			−1.22785			−0.613926	−	0.789364i	$-0.710411\pi$
$3$	−6.38011			−1.22785			−0.613926	+	0.789364i	$0.710411\pi$
$4$	5.95609	+	5.34088i	0.744511	+	0.667610i
$5$	−16.9716			−1.51799			−0.758994	−	0.651098i	$-0.774309\pi$
$5$	−16.9716			−1.51799			−0.758994	+	0.651098i	$0.774309\pi$
$6$	16.8537	+	6.44977i	1.14675	+	0.438851i
$7$			31.4494i			1.69811i	0.528308	+	0.849053i	$0.322827\pi$
$7$			31.4494i			1.69811i	−0.528308	+	0.849053i	$0.677173\pi$
$8$	−10.3344	−	20.1296i	−0.456720	−	0.889610i
$9$	13.7058			0.507621
$10$	44.8322	+	17.1569i	1.41772	+	0.542550i
$11$	−16.9532			−0.464690			−0.232345	−	0.972633i	$-0.574640\pi$
$11$	−16.9532			−0.464690			−0.232345	+	0.972633i	$0.574640\pi$
$12$	−38.0005	−	34.0754i	−0.914149	−	0.819727i
$13$			37.9820i			0.810331i	0.914243	+	0.405166i	$0.132786\pi$
$13$			37.9820i			0.810331i	−0.914243	+	0.405166i	$0.867214\pi$
$14$	31.7927	−	83.0766i	0.606926	−	1.58594i
$15$	108.281			1.86387
$16$	6.94996	+	63.6215i	0.108593	+	0.994086i
$17$	−68.0599	−	16.7586i	−0.970997	−	0.239091i
$17$	−68.0599	−	16.7586i	−0.970997	−	0.239091i
$18$	−36.2051	−	13.8554i	−0.474091	−	0.181431i
$19$		−	85.6684i		−	1.03440i	−0.855863	−	0.517202i	$-0.826974\pi$
$19$		−	85.6684i		−	1.03440i	0.855863	−	0.517202i	$-0.173026\pi$
$20$	−101.084	−	90.6434i	−1.13016	−	1.01342i
$21$		−	200.650i		−	2.08502i
$22$	44.7836	+	17.1383i	0.433995	+	0.166086i
$23$		−	23.5064i		−	0.213105i	−0.994307	−	0.106553i	$-0.966019\pi$
$23$		−	23.5064i		−	0.213105i	0.994307	−	0.106553i	$-0.0339812\pi$
$24$	65.9346	+	128.429i	0.560785	+	1.09231i
$25$	163.036			1.30429
$26$	38.3967	−	100.333i	0.289623	−	0.756806i
$27$	84.8186			0.604569
$28$	−167.967	+	187.315i	−1.13367	+	1.26426i
$29$	−55.2526			−0.353798			−0.176899	−	0.984229i	$-0.556607\pi$
$29$	−55.2526			−0.353798			−0.176899	+	0.984229i	$0.556607\pi$
$30$	−286.034	−	109.463i	−1.74075	−	0.666171i
$31$		−	218.364i		−	1.26514i	−0.774504	−	0.632569i	$-0.782000\pi$
$31$		−	218.364i		−	1.26514i	0.774504	−	0.632569i	$-0.218000\pi$
$32$	45.9572	−	175.088i	0.253880	−	0.967236i
$33$	108.163			0.570570
$34$	162.845	+	113.072i	0.821405	+	0.570346i
$35$		−	533.747i		−	2.57770i
$36$	81.6328	+	73.2009i	0.377929	+	0.338893i
$37$	−99.9450			−0.444077			−0.222039	−	0.975038i	$-0.571271\pi$
$37$	−99.9450			−0.444077			−0.222039	+	0.975038i	$0.571271\pi$
$38$	−86.6038	+	226.302i	−0.369710	+	0.966078i
$39$		−	242.329i		−	0.994967i
$40$	175.391	+	341.632i	0.693296	+	1.35042i
$41$			233.138i			0.888049i	0.896015	+	0.444024i	$0.146450\pi$
$41$			233.138i			0.888049i	−0.896015	+	0.444024i	$0.853550\pi$
$42$	−202.841	+	530.037i	−0.745216	+	1.94730i
$43$			266.763i			0.946068i	0.881044	+	0.473034i	$0.156841\pi$
$43$			266.763i			0.946068i	−0.881044	+	0.473034i	$0.843159\pi$
$44$	−100.975	−	90.5451i	−0.345967	−	0.310232i
$45$	−232.609			−0.770563
$46$	−23.7630	+	62.0944i	−0.0761667	+	0.199029i
$47$	630.370			1.95636			0.978179	−	0.207763i	$-0.0666183\pi$
$47$	630.370			1.95636			0.978179	+	0.207763i	$0.0666183\pi$
$48$	−44.3415	−	405.912i	−0.133336	−	1.22059i
$49$	−646.062			−1.88356
$50$	−430.676	−	164.816i	−1.21813	−	0.466170i
$51$	434.229	+	106.921i	1.19224	+	0.293569i
$52$	−202.857	+	226.224i	−0.540986	+	0.603301i
$53$			526.469i			1.36445i	0.731141	+	0.682227i	$0.238988\pi$
$53$			526.469i			1.36445i	−0.731141	+	0.682227i	$0.761012\pi$
$54$	−224.057	−	85.7447i	−0.564635	−	0.216081i
$55$	287.724			0.705393
$56$	633.062	−	325.010i	1.51065	−	0.775559i
$57$			546.574i			1.27010i
$58$	145.955	+	55.8559i	0.330429	+	0.126452i
$59$		−	260.113i		−	0.573963i	−0.957936	−	0.286982i	$-0.907348\pi$
$59$		−	260.113i		−	0.573963i	0.957936	−	0.286982i	$-0.0926518\pi$
$60$	644.930	+	578.315i	1.38767	+	1.24434i
$61$	363.306			0.762567			0.381283	−	0.924458i	$-0.375482\pi$
$61$	363.306			0.762567			0.381283	+	0.924458i	$0.375482\pi$
$62$	−220.748	+	576.829i	−0.452178	+	1.18157i
$63$			431.038i			0.861994i
$64$	−298.400	+	416.054i	−0.582813	+	0.812606i
$65$		−	644.616i		−	1.23007i
$66$	−285.724	−	109.344i	−0.532882	−	0.203930i
$67$			297.080i			0.541704i	0.962621	+	0.270852i	$0.0873053\pi$
$67$			297.080i			0.541704i	−0.962621	+	0.270852i	$0.912695\pi$
$68$	−315.865	−	463.315i	−0.563298	−	0.826254i
$69$			149.973i			0.261662i
$70$	−539.574	+	1409.94i	−0.921307	+	2.40744i
$71$			663.955i			1.10982i	0.831912	+	0.554908i	$0.187247\pi$
$71$			663.955i			1.10982i	−0.831912	+	0.554908i	$0.812753\pi$
$72$	−141.641	−	275.891i	−0.231841	−	0.451585i
$73$		−	878.743i		−	1.40889i	−0.709758	−	0.704446i	$-0.751195\pi$
$73$		−	878.743i		−	1.40889i	0.709758	−	0.704446i	$-0.248805\pi$
$74$	264.015	+	101.036i	0.414744	+	0.158719i
$75$	−1040.19			−1.60147
$76$	457.545	−	510.249i	0.690579	−	0.770125i
$77$		−	533.168i		−	0.789092i
$78$	−244.975	+	640.136i	−0.355615	+	0.929246i
$79$		−	1135.44i		−	1.61706i	−0.588458	−	0.808528i	$-0.700265\pi$
$79$		−	1135.44i		−	1.61706i	0.588458	−	0.808528i	$-0.299735\pi$
$80$	−117.952	−	1079.76i	−0.164843	−	1.50901i
$81$	−911.208			−1.24994
$82$	235.683	−	615.856i	0.317401	−	0.829390i
$83$		−	79.0370i		−	0.104523i	−0.998633	−	0.0522616i	$-0.983357\pi$
$83$		−	79.0370i		−	0.104523i	0.998633	−	0.0522616i	$-0.0166430\pi$
$84$	1071.65	−	1195.09i	1.39198	−	1.55232i
$85$	1155.09	+	284.420i	1.47396	+	0.362938i
$86$	269.675	−	704.680i	0.338138	−	0.883577i
$87$	352.518			0.434412
$88$	175.201	+	341.261i	0.212233	+	0.413393i
$89$	−742.706			−0.884569			−0.442285	−	0.896875i	$-0.645832\pi$
$89$	−742.706			−0.884569			−0.442285	+	0.896875i	$0.645832\pi$
$90$	614.460	+	235.149i	0.719664	+	0.275410i
$91$	−1194.51			−1.37603
$92$	125.545	−	140.006i	0.142271	−	0.158659i
$93$			1393.18i			1.55340i
$94$	−1665.18	−	637.252i	−1.82713	−	0.699229i
$95$			1453.93i			1.57021i
$96$	−293.212	+	1117.08i	−0.311727	+	1.18762i
$97$			216.022i			0.226121i	0.993588	+	0.113060i	$0.0360654\pi$
$97$			216.022i			0.226121i	−0.993588	+	0.113060i	$0.963935\pi$
$98$	1706.64	+	653.116i	1.75915	+	0.673211i
$99$	−232.357			−0.235886
$100$	971.057	+	870.756i	0.971057	+	0.870756i
$101$		−	1621.96i		−	1.59793i	−0.601378	−	0.798965i	$-0.705381\pi$
$101$		−	1621.96i		−	1.59793i	0.601378	−	0.798965i	$-0.294619\pi$
$102$	−1038.97	−	721.414i	−1.00856	−	0.700301i
$103$	1090.71			1.04340			0.521702	−	0.853128i	$-0.325297\pi$
$103$	1090.71			1.04340			0.521702	+	0.853128i	$0.325297\pi$
$104$	764.562	−	392.521i	0.720879	−	0.370095i
$105$			3405.36i			3.16504i
$106$	532.217	−	1390.72i	0.487674	−	1.27433i
$107$	−542.607			−0.490241			−0.245121	−	0.969493i	$-0.578828\pi$
$107$	−542.607			−0.490241			−0.245121	+	0.969493i	$0.578828\pi$
$108$	505.187	+	453.006i	0.450108	+	0.403616i
$109$	672.264			0.590745			0.295372	−	0.955382i	$-0.404556\pi$
$109$	672.264			0.590745			0.295372	+	0.955382i	$0.404556\pi$
$110$	−760.050	−	290.865i	−0.658800	−	0.252117i
$111$	637.660			0.545261
$112$	−2000.86	+	218.572i	−1.68806	+	0.184402i
$113$		−	1072.51i		−	0.892859i	−0.894819	−	0.446430i	$-0.852695\pi$
$113$		−	1072.51i		−	0.892859i	0.894819	−	0.446430i	$-0.147305\pi$
$114$	552.541	−	1443.83i	0.453950	−	1.18620i
$115$			398.941i			0.323491i
$116$	−329.090	−	295.098i	−0.263407	−	0.236200i
$117$			520.572i			0.411341i
$118$	−262.953	+	687.114i	−0.205142	+	0.536051i
$119$	527.046	−	2140.44i	0.406002	−	1.64886i
$120$	−1119.02	−	2179.65i	−0.851265	−	1.65811i
$121$	−1043.59			−0.784063
$122$	−959.709	−	367.273i	−0.712196	−	0.272552i
$123$		−	1487.44i		−	1.09039i
$124$	1166.26	−	1300.59i	0.844619	−	0.941909i
$125$	−645.532			−0.461905
$126$	435.744	−	1138.63i	0.308088	−	0.805056i
$127$	−2225.91			−1.55526			−0.777629	−	0.628723i	$-0.783578\pi$
$127$	−2225.91			−1.55526			−0.777629	+	0.628723i	$0.783578\pi$
$128$	1208.85	−	797.390i	0.834753	−	0.550625i
$129$		−	1701.98i		−	1.16163i
$130$	−651.654	+	1702.82i	−0.439645	+	1.14882i
$131$	2047.93			1.36586			0.682932	−	0.730482i	$-0.260704\pi$
$131$	2047.93			1.36586			0.682932	+	0.730482i	$0.260704\pi$
$132$	644.230	+	577.688i	0.424796	+	0.380919i
$133$	2694.22			1.75653
$134$	300.324	−	784.767i	0.193612	−	0.505922i
$135$	−1439.51			−0.917728
$136$	366.015	+	1543.21i	0.230776	+	0.973007i
$137$	−1334.03			−0.831926			−0.415963	−	0.909382i	$-0.636555\pi$
$137$	−1334.03			−0.831926			−0.415963	+	0.909382i	$0.636555\pi$
$138$	151.611	−	396.169i	0.0935214	−	0.244378i
$139$	180.979			0.110435			0.0552173	−	0.998474i	$-0.482415\pi$
$139$	180.979			0.110435			0.0552173	+	0.998474i	$0.482415\pi$
$140$	2850.68	−	3179.04i	1.72090	−	1.91913i
$141$	−4021.83			−2.40212
$142$	671.204	−	1753.90i	0.396663	−	1.03651i
$143$		−	643.917i		−	0.376553i
$144$	95.2545	+	871.982i	0.0551241	+	0.504619i
$145$	937.727			0.537062
$146$	−888.338	+	2321.29i	−0.503557	+	1.31583i
$147$	4121.94			2.31274
$148$	−595.281	−	533.795i	−0.330620	−	0.296471i
$149$			2014.02i			1.10735i	0.832733	+	0.553674i	$0.186775\pi$
$149$			2014.02i			1.10735i	−0.832733	+	0.553674i	$0.813225\pi$
$150$	2747.76	+	1051.54i	1.49569	+	0.572388i
$151$	1039.03			0.559965			0.279982	−	0.960005i	$-0.409671\pi$
$151$	1039.03			0.559965			0.279982	+	0.960005i	$0.409671\pi$
$152$	−1724.47	+	885.331i	−0.920217	+	0.472433i
$153$	−932.813	−	229.689i	−0.492899	−	0.121368i
$154$	−538.989	+	1408.41i	−0.282032	+	0.736970i
$155$			3705.99i			1.92047i
$156$	1294.25	−	1443.33i	0.664250	−	0.740764i
$157$			643.115i			0.326918i	0.986550	+	0.163459i	$0.0522652\pi$
$157$			643.115i			0.326918i	−0.986550	+	0.163459i	$0.947735\pi$
$158$	−1147.84	+	2999.39i	−0.577958	+	1.51024i
$159$		−	3358.93i		−	1.67535i
$160$	−779.968	+	2971.53i	−0.385387	+	1.46825i
$161$	739.260			0.361875
$162$	2407.04	+	921.157i	1.16738	+	0.446746i
$163$	163.405			0.0785207			0.0392604	−	0.999229i	$-0.487500\pi$
$163$	163.405			0.0785207			0.0392604	+	0.999229i	$0.487500\pi$
$164$	−1245.16	+	1388.59i	−0.592870	+	0.661162i
$165$	−1835.71			−0.866119
$166$	−79.8999	+	208.784i	−0.0373581	+	0.0976191i
$167$			2676.52i			1.24021i	0.784518	+	0.620106i	$0.212910\pi$
$167$			2676.52i			1.24021i	−0.784518	+	0.620106i	$0.787090\pi$
$168$	−4039.01	+	2073.60i	−1.85486	+	0.952272i
$169$	754.369			0.343363
$170$	−2763.75	−	1919.02i	−1.24688	−	0.865778i
$171$		−	1174.15i		−	0.525085i
$172$	−1424.75	+	1588.86i	−0.631605	+	0.704358i
$173$	−3930.67			−1.72742			−0.863710	−	0.503990i	$-0.831865\pi$
$173$	−3930.67			−1.72742			−0.863710	+	0.503990i	$0.831865\pi$
$174$	−931.210	−	356.367i	−0.405718	−	0.155265i
$175$			5127.38i			2.21482i
$176$	−117.824	−	1078.59i	−0.0504621	−	0.461942i
$177$			1659.55i			0.704742i
$178$	1961.93	+	750.815i	0.826140	+	0.316157i
$179$		−	4416.94i		−	1.84435i	−0.386778	−	0.922173i	$-0.626412\pi$
$179$		−	4416.94i		−	1.84435i	0.386778	−	0.922173i	$-0.373588\pi$
$180$	−1385.44	−	1242.34i	−0.573692	−	0.514436i
$181$	1064.32			0.437075			0.218537	−	0.975829i	$-0.429871\pi$
$181$	1064.32			0.437075			0.218537	+	0.975829i	$0.429871\pi$
$182$	3155.41	+	1207.55i	1.28514	+	0.491811i
$183$	−2317.93			−0.936319
$184$	−473.174	+	242.924i	−0.189581	+	0.0973294i
$185$	1696.23			0.674104
$186$	1408.40	−	3680.23i	0.555207	−	1.45079i
$187$	1153.83	+	284.112i	0.451212	+	0.111103i
$188$	3754.54	+	3366.73i	1.45653	+	1.30608i
$189$			2667.49i			1.02662i
$190$	1469.81	−	3840.71i	0.561216	−	1.46649i
$191$	−214.432			−0.0812342			−0.0406171	−	0.999175i	$-0.512932\pi$
$191$	−214.432			−0.0812342			−0.0406171	+	0.999175i	$0.512932\pi$
$192$	1903.83	−	2654.47i	0.715609	−	0.997760i
$193$			1940.85i			0.723861i	0.932205	+	0.361931i	$0.117882\pi$
$193$			1940.85i			0.723861i	−0.932205	+	0.361931i	$0.882118\pi$
$194$	218.381	−	570.644i	0.0808187	−	0.211185i
$195$			4112.72i			1.51035i
$196$	−3848.00	−	3450.54i	−1.40233	−	1.25749i
$197$	1467.46			0.530723			0.265362	−	0.964149i	$-0.414509\pi$
$197$	1467.46			0.530723			0.265362	+	0.964149i	$0.414509\pi$
$198$	613.794	+	234.894i	0.220305	+	0.0843090i
$199$			179.293i			0.0638681i	0.999490	+	0.0319341i	$0.0101667\pi$
$199$			179.293i			0.0638681i	−0.999490	+	0.0319341i	$0.989833\pi$
$200$	−1684.88	−	3281.85i	−0.595695	−	1.16031i
$201$		−	1895.40i		−	0.665132i
$202$	−1639.67	+	4284.56i	−0.571122	+	1.49238i
$203$		−	1737.66i		−	0.600787i
$204$	2015.25	+	2956.00i	0.691647	+	1.01452i
$205$		−	3956.72i		−	1.34805i
$206$	−2881.21	−	1102.62i	−0.974484	−	0.372927i
$207$		−	322.173i		−	0.108177i
$208$	−2416.47	+	263.973i	−0.805539	+	0.0879964i
$209$			1452.36i			0.480677i
$210$	3442.54	−	8995.59i	1.13123	−	2.95598i
$211$	−4971.54			−1.62206			−0.811030	−	0.585004i	$-0.801093\pi$
$211$	−4971.54			−1.62206			−0.811030	+	0.585004i	$0.801093\pi$
$212$	−2811.81	+	3135.69i	−0.910923	+	1.01585i
$213$		−	4236.10i		−	1.36269i
$214$	1433.35	+	548.531i	0.457859	+	0.175219i
$215$		−	4527.40i		−	1.43612i
$216$	−876.549	−	1707.36i	−0.276119	−	0.537831i
$217$	6867.40			2.14834
$218$	−1775.85	−	679.604i	−0.551724	−	0.211140i
$219$			5606.48i			1.72991i
$220$	1713.71	+	1536.70i	0.525173	+	0.470928i
$221$	636.524	−	2585.05i	0.193743	−	0.786829i
$222$	−1684.44	−	644.622i	−0.509245	−	0.194884i
$223$	−2366.12			−0.710526			−0.355263	−	0.934766i	$-0.615609\pi$
$223$	−2366.12			−0.710526			−0.355263	+	0.934766i	$0.615609\pi$
$224$	5506.42	+	1445.32i	1.64247	+	0.431115i
$225$	2234.53			0.662084
$226$	−1084.22	+	2833.14i	−0.319120	+	0.833882i
$227$	−1212.61			−0.354555			−0.177278	−	0.984161i	$-0.556729\pi$
$227$	−1212.61			−0.354555			−0.177278	+	0.984161i	$0.556729\pi$
$228$	−2919.19	+	3255.44i	−0.847929	+	0.945600i
$229$		−	5282.79i		−	1.52444i	−0.647319	−	0.762219i	$-0.724110\pi$
$229$		−	5282.79i		−	1.52444i	0.647319	−	0.762219i	$-0.275890\pi$
$230$	403.297	−	1053.84i	0.115620	−	0.302123i
$231$			3401.67i			0.968888i
$232$	571.003	+	1112.21i	0.161587	+	0.314743i
$233$		−	4674.51i		−	1.31432i	−0.753750	−	0.657161i	$-0.771757\pi$
$233$		−	4674.51i		−	1.31432i	0.753750	−	0.657161i	$-0.228243\pi$
$234$	526.256	−	1375.14i	0.147019	−	0.384171i
$235$	−10698.4			−2.96973
$236$	1389.23	−	1549.26i	0.383184	−	0.427322i
$237$			7244.25i			1.98551i
$238$	−3556.05	+	5121.38i	−0.968508	+	1.39483i
$239$	−1349.21			−0.365159			−0.182579	−	0.983191i	$-0.558445\pi$
$239$	−1349.21			−0.365159			−0.182579	+	0.983191i	$0.558445\pi$
$240$	752.547	+	6888.99i	0.202403	+	1.85284i
$241$			102.634i			0.0274324i	0.999906	+	0.0137162i	$0.00436615\pi$
$241$			102.634i			0.0274324i	−0.999906	+	0.0137162i	$0.995634\pi$
$242$	2756.74	+	1054.98i	0.732273	+	0.280235i
$243$	3523.50			0.930175
$244$	2163.88	+	1940.37i	0.567739	+	0.509097i
$245$	10964.7			2.85922
$246$	−1503.68	+	3929.23i	−0.389721	+	1.01837i
$247$	3253.86			0.838210
$248$	−4395.57	+	2256.66i	−1.12548	+	0.577814i
$249$			504.264i			0.128339i
$250$	1705.24	+	652.581i	0.431395	+	0.165091i
$251$		−	2972.67i		−	0.747542i	−0.927521	−	0.373771i	$-0.878065\pi$
$251$		−	2972.67i		−	0.747542i	0.927521	−	0.373771i	$-0.121935\pi$
$252$	−2302.12	+	2567.30i	−0.575476	+	0.641764i
$253$			398.509i			0.0990278i
$254$	5879.97	+	2250.22i	1.45253	+	0.555871i
$255$	−7369.58	−	1814.63i	−1.80981	−	0.445634i
$256$	−3999.40	+	884.334i	−0.976415	+	0.215902i
$257$	−3315.37			−0.804696			−0.402348	−	0.915487i	$-0.631806\pi$
$257$	−3315.37			−0.804696			−0.402348	+	0.915487i	$0.631806\pi$
$258$	−1720.56	+	4495.94i	−0.415183	+	1.08490i
$259$		−	3143.21i		−	0.754090i
$260$	3442.82	−	3839.39i	0.821210	−	0.915803i
$261$	−757.280			−0.179596
$262$	−5409.80	−	2070.29i	−1.27564	−	0.488179i
$263$	7570.98			1.77508			0.887542	−	0.460727i	$-0.152411\pi$
$263$	7570.98			1.77508			0.887542	+	0.460727i	$0.152411\pi$
$264$	−1117.80	−	2177.28i	−0.260591	−	0.507585i
$265$		−	8935.03i		−	2.07122i
$266$	−7117.04	−	2723.63i	−1.64050	−	0.627807i
$267$	4738.54			1.08612
$268$	−1586.67	+	1769.44i	−0.361647	+	0.403304i
$269$	3376.42			0.765294			0.382647	−	0.923895i	$-0.375013\pi$
$269$	3376.42			0.765294			0.382647	+	0.923895i	$0.375013\pi$
$270$	3802.61	+	1455.23i	0.857109	+	0.328009i
$271$	2671.06			0.598727			0.299364	−	0.954139i	$-0.403226\pi$
$271$	2671.06			0.598727			0.299364	+	0.954139i	$0.403226\pi$
$272$	593.192	−	4446.55i	0.132234	−	0.991219i
$273$	7621.09			1.68956
$274$	3523.97	+	1348.60i	0.776974	+	0.297342i
$275$	−2763.98			−0.606089
$276$	−800.989	+	893.253i	−0.174688	+	0.194810i
$277$	1394.68			0.302521			0.151261	−	0.988494i	$-0.451667\pi$
$277$	1394.68			0.302521			0.151261	+	0.988494i	$0.451667\pi$
$278$	−478.073	−	182.955i	−0.103140	−	0.0394708i
$279$		−	2992.84i		−	0.642211i
$280$	−10744.1	+	5515.95i	−2.29315	+	1.17729i
$281$	5096.22			1.08190			0.540952	−	0.841053i	$-0.318064\pi$
$281$	5096.22			1.08190			0.540952	+	0.841053i	$0.318064\pi$
$282$	10624.0	+	4065.74i	2.24345	+	0.858550i
$283$	6826.58			1.43391			0.716957	−	0.697117i	$-0.245534\pi$
$283$	6826.58			1.43391			0.716957	+	0.697117i	$0.245534\pi$
$284$	−3546.10	+	3954.57i	−0.740925	+	0.826270i
$285$		−	9276.24i		−	1.92799i
$286$	−650.947	+	1700.97i	−0.134585	+	0.351680i
$287$	−7332.03			−1.50800
$288$	629.878	−	2399.72i	0.128875	−	0.490989i
$289$	4351.30	+	2281.17i	0.885671	+	0.464314i
$290$	−2477.10	−	947.965i	−0.501587	−	0.191953i
$291$		−	1378.24i		−	0.277643i
$292$	4693.26	−	5233.87i	0.940591	−	1.04894i
$293$		−	6049.99i		−	1.20630i	−0.797630	−	0.603148i	$-0.793913\pi$
$293$		−	6049.99i		−	1.20630i	0.797630	−	0.603148i	$-0.206087\pi$
$294$	−10888.5	−	4166.95i	−2.15997	−	0.826603i
$295$			4414.54i			0.871269i
$296$	1032.87	+	2011.85i	0.202819	+	0.395056i
$297$	−1437.95			−0.280937
$298$	2036.01	−	5320.23i	0.395781	−	1.03420i
$299$	892.819			0.172686
$300$	−6195.45	−	5555.52i	−1.19231	−	1.06916i
$301$	−8389.52			−1.60652
$302$	−2744.69	−	1050.37i	−0.522977	−	0.200139i
$303$			10348.3i			1.96202i
$304$	5450.36	−	595.392i	1.02829	−	0.112329i
$305$	−6165.89			−1.15757
$306$	2231.92	+	1549.74i	0.416962	+	0.289520i
$307$			5037.11i			0.936427i	0.883615	+	0.468213i	$0.155102\pi$
$307$			5037.11i			0.936427i	−0.883615	+	0.468213i	$0.844898\pi$
$308$	2847.59	−	3175.59i	0.526806	−	0.587488i
$309$	−6958.83			−1.28115
$310$	3746.45	−	9789.73i	0.686400	−	1.79361i
$311$			984.374i			0.179481i	0.995965	+	0.0897407i	$0.0286038\pi$
$311$			984.374i			0.179481i	−0.995965	+	0.0897407i	$0.971396\pi$
$312$	−4877.99	+	2504.33i	−0.885133	+	0.454421i
$313$		−	9356.90i		−	1.68972i	−0.534986	−	0.844861i	$-0.679683\pi$
$313$		−	9356.90i		−	1.68972i	0.534986	−	0.844861i	$-0.320317\pi$
$314$	650.137	−	1698.85i	0.116845	−	0.305324i
$315$		−	7315.41i		−	1.30850i
$316$	6064.27	−	6762.80i	1.07956	−	1.20392i
$317$	−6832.99			−1.21066			−0.605330	−	0.795975i	$-0.706959\pi$
$317$	−6832.99			−1.21066			−0.605330	+	0.795975i	$0.706959\pi$
$318$	−3395.60	+	8872.94i	−0.598792	+	1.56468i
$319$	936.710			0.164407
$320$	5064.34	−	7061.12i	0.884704	−	1.23353i
$321$	3461.89			0.601944
$322$	−1952.83	−	747.332i	−0.337972	−	0.129339i
$323$	−1435.68	+	5830.58i	−0.247317	+	1.00440i
$324$	−5427.23	−	4866.65i	−0.930595	−	0.834474i
$325$			6192.43i			1.05691i
$326$	−431.651	−	165.189i	−0.0733341	−	0.0280644i
$327$	−4289.11			−0.725347
$328$	4692.97	−	2409.34i	0.790017	−	0.405590i
$329$			19824.7i			3.32210i
$330$	4849.20	+	1855.75i	0.808908	+	0.309563i
$331$		−	2231.59i		−	0.370571i	−0.982685	−	0.185286i	$-0.940679\pi$
$331$		−	2231.59i		−	0.370571i	0.982685	−	0.185286i	$-0.0593210\pi$
$332$	422.127	−	470.751i	0.0697808	−	0.0778187i
$333$	−1369.82			−0.225423
$334$	2705.74	−	7070.29i	0.443268	−	1.15829i
$335$		−	5041.94i		−	0.822300i
$336$	12765.7	−	1394.51i	2.07269	−	0.226419i
$337$		−	1078.85i		−	0.174388i	−0.996191	−	0.0871941i	$-0.972210\pi$
$337$		−	1078.85i		−	0.174388i	0.996191	−	0.0871941i	$-0.0277900\pi$
$338$	−1992.74	−	762.605i	−0.320683	−	0.122723i
$339$			6842.72i			1.09630i
$340$	5360.74	+	7863.21i	0.855080	+	1.25424i
$341$			3701.97i			0.587897i
$342$	−1186.97	+	3101.64i	−0.187673	+	0.490402i
$343$		−	9531.09i		−	1.50038i
$344$	5369.82	−	2756.83i	0.841632	−	0.432088i
$345$		−	2545.29i		−	0.397199i
$346$	10383.3	+	3973.59i	1.61332	+	0.617403i
$347$	2410.94			0.372986			0.186493	−	0.982456i	$-0.440288\pi$
$347$	2410.94			0.372986			0.186493	+	0.982456i	$0.440288\pi$
$348$	2099.63	+	1882.76i	0.323425	+	0.290018i
$349$		−	7976.94i		−	1.22348i	−0.791057	−	0.611742i	$-0.790469\pi$
$349$		−	7976.94i		−	1.22348i	0.791057	−	0.611742i	$-0.209531\pi$
$350$	5183.36	−	13544.5i	0.791606	−	2.06852i
$351$			3221.58i			0.489901i
$352$	−779.122	+	2968.31i	−0.117975	+	0.449464i
$353$	−8088.38			−1.21955			−0.609775	−	0.792575i	$-0.708740\pi$
$353$	−8088.38			−1.21955			−0.609775	+	0.792575i	$0.708740\pi$
$354$	1677.67	−	4383.86i	0.251884	−	0.658191i
$355$		−	11268.4i		−	1.68469i
$356$	−4423.62	−	3966.70i	−0.658571	−	0.590547i
$357$	−3362.61	+	13656.2i	−0.498511	+	2.02455i
$358$	−4465.17	+	11667.8i	−0.659194	+	1.72252i
$359$	−967.731			−0.142270			−0.0711349	−	0.997467i	$-0.522662\pi$
$359$	−967.731			−0.142270			−0.0711349	+	0.997467i	$0.522662\pi$
$360$	2403.87	+	4682.33i	0.351931	+	0.685501i
$361$	−480.078			−0.0699924
$362$	−2811.52	−	1075.94i	−0.408204	−	0.156217i
$363$	6658.21			0.962714
$364$	−7114.60	−	6379.73i	−1.02447	−	0.918650i
$365$			14913.7i			2.13868i
$366$	6123.04	+	2343.24i	0.874472	+	0.334653i
$367$		−	4898.90i		−	0.696786i	−0.937348	−	0.348393i	$-0.886727\pi$
$367$		−	4898.90i		−	0.696786i	0.937348	−	0.348393i	$-0.113273\pi$
$368$	1495.51	−	163.368i	0.211845	−	0.0231417i
$369$			3195.33i			0.450792i
$370$	−4480.76	−	1714.75i	−0.629577	−	0.240934i
$371$	−16557.1			−2.31699
$372$	−7440.83	+	8297.93i	−1.03707	+	1.15653i
$373$		−	5705.70i		−	0.792037i	−0.918243	−	0.396018i	$-0.870392\pi$
$373$		−	5705.70i		−	0.792037i	0.918243	−	0.396018i	$-0.129608\pi$
$374$	−2760.75	−	1916.94i	−0.381698	−	0.265034i
$375$	4118.57			0.567152
$376$	−6514.49	−	12689.1i	−0.893508	−	1.74040i
$377$		−	2098.60i		−	0.286694i
$378$	2696.62	−	7046.44i	0.366928	−	0.958809i
$379$	6432.14			0.871759			0.435880	−	0.900005i	$-0.356437\pi$
$379$	6432.14			0.871759			0.435880	+	0.900005i	$0.356437\pi$
$380$	−7765.28	+	8659.75i	−1.04829	+	1.16904i
$381$	14201.6			1.90963
$382$	566.443	+	216.773i	0.0758684	+	0.0290342i
$383$	2715.66			0.362307			0.181154	−	0.983455i	$-0.442017\pi$
$383$	2715.66			0.362307			0.181154	+	0.983455i	$0.442017\pi$
$384$	−7712.60	+	5087.43i	−1.02495	+	0.676086i
$385$			9048.72i			1.19783i
$386$	1962.04	−	5126.94i	0.258718	−	0.676047i
$387$			3656.19i			0.480244i
$388$	−1153.75	+	1286.65i	−0.150961	+	0.168349i
$389$			5035.71i			0.656351i	0.944617	+	0.328175i	$0.106434\pi$
$389$			5035.71i			0.656351i	−0.944617	+	0.328175i	$0.893566\pi$
$390$	4157.62	−	10864.2i	0.539819	−	1.41058i
$391$	−393.933	+	1599.84i	−0.0509516	+	0.206924i
$392$	6676.66	+	13005.0i	0.860261	+	1.67564i
$393$	−13066.0			−1.67708
$394$	−3876.45	−	1483.49i	−0.495667	−	0.189688i
$395$			19270.3i			2.45467i
$396$	−1383.94	−	1240.99i	−0.175620	−	0.157480i
$397$	−15566.7			−1.96793			−0.983965	−	0.178364i	$-0.942920\pi$
$397$	−15566.7			−1.96793			−0.983965	+	0.178364i	$0.942920\pi$
$398$	181.251	−	473.621i	0.0228273	−	0.0596494i
$399$	−17189.4			−2.15676
$400$	1133.09	+	10372.6i	0.141637	+	1.29657i
$401$			7961.07i			0.991413i	0.868490	+	0.495707i	$0.165091\pi$
$401$			7961.07i			0.991413i	−0.868490	+	0.495707i	$0.834909\pi$
$402$	−1916.10	+	5006.90i	−0.237727	+	0.621197i
$403$	8293.89			1.02518
$404$	8662.69	−	9660.53i	1.06679	−	1.18968i
$405$	15464.7			1.89740
$406$	−1756.63	+	4590.20i	−0.214730	+	0.561103i
$407$	1694.39			0.206358
$408$	−2335.21	−	9845.83i	−0.283359	−	1.19471i
$409$	−6560.19			−0.793107			−0.396553	−	0.918012i	$-0.629794\pi$
$409$	−6560.19			−0.793107			−0.396553	+	0.918012i	$0.629794\pi$
$410$	−3999.93	+	10452.1i	−0.481810	+	1.25900i
$411$	8511.26			1.02148
$412$	6496.35	+	5825.34i	0.776826	+	0.696587i
$413$	8180.38			0.974650
$414$	−325.691	+	851.052i	−0.0386638	+	0.101031i
$415$			1341.39i			0.158665i
$416$	6650.20	+	1745.54i	0.783781	+	0.205727i
$417$	−1154.66			−0.135597
$418$	1468.21	−	3836.54i	0.171801	−	0.448927i
$419$	1434.48			0.167252			0.0836262	−	0.996497i	$-0.473350\pi$
$419$	1434.48			0.167252			0.0836262	+	0.996497i	$0.473350\pi$
$420$	−18187.6	+	20282.6i	−2.11301	+	2.35641i
$421$		−	2643.35i		−	0.306008i	−0.988226	−	0.153004i	$-0.951105\pi$
$421$		−	2643.35i		−	0.306008i	0.988226	−	0.153004i	$-0.0488947\pi$
$422$	13132.8	+	5025.82i	1.51492	+	0.579746i
$423$	8639.70			0.993089
$424$	10597.6	−	5440.74i	1.21383	−	0.623173i
$425$	−11096.2	−	2732.25i	−1.26646	−	0.311844i
$426$	−4282.36	+	11190.1i	−0.487044	+	1.27268i
$427$			11425.7i			1.29492i
$428$	−3231.81	−	2898.00i	−0.364990	−	0.327290i
$429$			4108.26i			0.462351i
$430$	−4576.83	+	11959.6i	−0.513289	+	1.34126i
$431$			8341.21i			0.932209i	0.884730	+	0.466105i	$0.154343\pi$
$431$			8341.21i			0.932209i	−0.884730	+	0.466105i	$0.845657\pi$
$432$	589.486	+	5396.29i	0.0656520	+	0.600993i
$433$	8380.96			0.930170			0.465085	−	0.885266i	$-0.346024\pi$
$433$	8380.96			0.930170			0.465085	+	0.885266i	$0.346024\pi$
$434$	−18140.9	−	6942.38i	−2.00643	−	0.767845i
$435$	−5982.80			−0.659433
$436$	4004.06	+	3590.48i	0.439816	+	0.394387i
$437$	−2013.75			−0.220437
$438$	5667.69	−	14810.1i	0.618294	−	1.61564i
$439$		−	1500.25i		−	0.163104i	−0.996669	−	0.0815522i	$-0.974012\pi$
$439$		−	1500.25i		−	0.163104i	0.996669	−	0.0815522i	$-0.0259877\pi$
$440$	−2973.45	−	5791.76i	−0.322167	−	0.627525i
$441$	−8854.77			−0.956136
$442$	−4294.72	+	6185.19i	−0.462169	+	0.665610i
$443$		−	14701.3i		−	1.57670i	−0.615224	−	0.788352i	$-0.710934\pi$
$443$		−	14701.3i		−	1.57670i	0.615224	−	0.788352i	$-0.289066\pi$
$444$	3797.96	+	3405.67i	0.405953	+	0.364022i
$445$	12604.9			1.34277
$446$	6250.35	+	2391.96i	0.663593	+	0.253952i
$447$		−	12849.7i		−	1.35966i
$448$	−13084.6	−	9384.50i	−1.37989	−	0.989679i
$449$		−	7233.76i		−	0.760317i	−0.924921	−	0.380158i	$-0.875869\pi$
$449$		−	7233.76i		−	0.760317i	0.924921	−	0.380158i	$-0.124131\pi$
$450$	−5902.74	−	2258.93i	−0.618351	−	0.236638i
$451$		−	3952.43i		−	0.412667i
$452$	5728.14	−	6387.95i	0.596082	−	0.664743i
$453$	−6629.09			−0.687554
$454$	3203.24	+	1225.85i	0.331136	+	0.126723i
$455$	20272.8			2.08879
$456$	11002.3	−	5648.51i	1.12989	−	0.580078i
$457$	5052.69			0.517188			0.258594	−	0.965986i	$-0.416741\pi$
$457$	5052.69			0.517188			0.258594	+	0.965986i	$0.416741\pi$
$458$	−5340.47	+	13955.0i	−0.544855	+	1.42374i
$459$	−5772.75	−	1421.44i	−0.587034	−	0.144547i
$460$	−2130.70	+	2376.13i	−0.215966	+	0.240843i
$461$			9359.80i			0.945616i	0.881165	+	0.472808i	$0.156760\pi$
$461$			9359.80i			0.945616i	−0.881165	+	0.472808i	$0.843240\pi$
$462$	3438.81	−	8985.84i	0.346294	−	0.904890i
$463$	−11043.0			−1.10844			−0.554222	−	0.832369i	$-0.686984\pi$
$463$	−11043.0			−1.10844			−0.554222	+	0.832369i	$0.686984\pi$
$464$	−384.003	−	3515.26i	−0.0384201	−	0.351706i
$465$		−	23644.6i		−	2.35805i
$466$	−4725.54	+	12348.2i	−0.469757	+	1.22751i
$467$			355.180i			0.0351944i	0.999845	+	0.0175972i	$0.00560164\pi$
$467$			355.180i			0.0351944i	−0.999845	+	0.0175972i	$0.994398\pi$
$468$	−2780.32	+	3100.57i	−0.274616	+	0.306248i
$469$	−9342.98			−0.919870
$470$	28260.9	+	10815.2i	2.77357	+	1.06142i
$471$		−	4103.14i		−	0.401407i
$472$	−5235.97	+	2688.11i	−0.510604	+	0.262140i
$473$		−	4522.49i		−	0.439628i
$474$	7323.35	−	19136.4i	0.709647	−	1.85435i
$475$		−	13967.0i		−	1.34916i
$476$	14571.0	−	9933.76i	1.40307	−	0.956540i
$477$			7215.66i			0.692625i
$478$	3564.06	+	1363.94i	0.341039	+	0.130513i
$479$			5089.04i			0.485436i	0.970097	+	0.242718i	$0.0780390\pi$
$479$			5089.04i			0.485436i	−0.970097	+	0.242718i	$0.921961\pi$
$480$	4976.28	−	18958.7i	0.473198	−	1.80280i
$481$		−	3796.11i		−	0.359850i
$482$	103.754	−	271.117i	0.00980473	−	0.0256204i
$483$	−4716.56			−0.444329
$484$	−6215.70	−	5573.68i	−0.583744	−	0.523449i
$485$		−	3666.25i		−	0.343249i
$486$	−9307.67	−	3561.97i	−0.868734	−	0.332457i
$487$			9511.74i			0.885048i	0.896757	+	0.442524i	$0.145917\pi$
$487$			9511.74i			0.885048i	−0.896757	+	0.442524i	$0.854083\pi$
$488$	−3754.55	−	7313.20i	−0.348280	−	0.678387i
$489$	−1042.54			−0.0964118
$490$	−28964.4	−	11084.4i	−2.67036	−	1.02193i
$491$			3368.35i			0.309596i	0.987946	+	0.154798i	$0.0494727\pi$
$491$			3368.35i			0.309596i	−0.987946	+	0.154798i	$0.950527\pi$
$492$	7944.26	−	8859.34i	0.727957	−	0.811809i
$493$	3760.49	+	925.955i	0.343537	+	0.0845901i
$494$	−8595.38	−	3289.38i	−0.782843	−	0.299588i
$495$	3943.47			0.358073
$496$	13892.6	−	1517.62i	1.25766	−	0.137385i
$497$	−20880.9			−1.88458
$498$	509.770	−	1332.06i	0.0458702	−	0.119862i
$499$	3357.63			0.301219			0.150609	−	0.988593i	$-0.451876\pi$
$499$	3357.63			0.301219			0.150609	+	0.988593i	$0.451876\pi$
$500$	−3844.85	−	3447.71i	−0.343894	−	0.308373i
$501$		−	17076.5i		−	1.52280i
$502$	−3005.13	+	7852.60i	−0.267182	+	0.698164i
$503$		−	7313.91i		−	0.648332i	−0.946000	−	0.324166i	$-0.894916\pi$
$503$		−	7313.91i		−	0.648332i	0.946000	−	0.324166i	$-0.105084\pi$
$504$	8676.61	−	4454.51i	0.766839	−	0.393690i
$505$			27527.3i			2.42564i
$506$	402.860	−	1052.70i	0.0353939	−	0.0924866i
$507$	−4812.95			−0.421599
$508$	−13257.7	−	11888.3i	−1.15791	−	1.03831i
$509$			2096.88i			0.182598i	0.995824	+	0.0912992i	$0.0291020\pi$
$509$			2096.88i			0.182598i	−0.995824	+	0.0912992i	$0.970898\pi$
$510$	17633.0	+	12243.6i	1.53099	+	1.06305i
$511$	27635.9			2.39245
$512$	11458.8	+	1707.01i	0.989085	+	0.147343i
$513$		−	7266.28i		−	0.625368i
$514$	8757.86	+	3351.56i	0.751543	+	0.287609i
$515$	−18511.1			−1.58388
$516$	9090.05	−	10137.1i	0.775518	−	0.864848i
$517$	−10686.8			−0.909100
$518$	−3177.53	+	8303.09i	−0.269522	+	0.704280i
$519$	25078.1			2.12102
$520$	−12975.9	+	6661.72i	−1.09429	+	0.561799i
$521$			2114.29i			0.177790i	0.996041	+	0.0888952i	$0.0283336\pi$
$521$			2114.29i			0.177790i	−0.996041	+	0.0888952i	$0.971666\pi$
$522$	2000.43	+	765.548i	0.167733	+	0.0641899i
$523$		−	23308.0i		−	1.94874i	−0.224956	−	0.974369i	$-0.572224\pi$
$523$		−	23308.0i		−	1.94874i	0.224956	−	0.974369i	$-0.427776\pi$
$524$	12197.6	+	10937.7i	1.01690	+	0.911865i
$525$		−	32713.2i		−	2.71947i
$526$	−19999.5	−	7653.65i	−1.65783	−	0.634439i
$527$	−3659.46	+	14861.8i	−0.302483	+	1.22845i
$528$	751.731	+	6881.52i	0.0619600	+	0.567196i
$529$	11614.5			0.954586
$530$	−9032.58	+	23602.8i	−0.740284	+	1.93441i
$531$		−	3565.05i		−	0.291356i
$532$	16047.0	+	14389.5i	1.30775	+	1.17268i
$533$	−8855.03			−0.719614
$534$	−12517.3	−	4790.28i	−1.01438	−	0.388194i
$535$	9208.92			0.744180
$536$	5980.10	−	3070.15i	0.481905	−	0.247407i
$537$			28180.6i			2.26458i
$538$	−8919.15	−	3413.29i	−0.714743	−	0.273526i
$539$	10952.8			0.875272
$540$	−8573.85	−	7688.25i	−0.683258	−	0.612685i
$541$	14647.3			1.16402			0.582012	−	0.813180i	$-0.302266\pi$
$541$	14647.3			1.16402			0.582012	+	0.813180i	$0.302266\pi$
$542$	−7055.86	−	2700.22i	−0.559179	−	0.213993i
$543$	−6790.50			−0.536663
$544$	−6062.07	+	11146.3i	−0.477774	+	0.878483i
$545$	−11409.4			−0.896744
$546$	−20131.9	−	7704.31i	−1.57796	−	0.603871i
$547$	10058.4			0.786225			0.393112	−	0.919490i	$-0.371398\pi$
$547$	10058.4			0.786225			0.393112	+	0.919490i	$0.371398\pi$
$548$	−7945.60	−	7124.90i	−0.619378	−	0.555402i
$549$	4979.39			0.387095
$550$	7301.34	+	2794.16i	0.566055	+	0.216625i
$551$			4733.41i			0.365971i
$552$	3018.90	−	1549.88i	0.232777	−	0.119506i
$553$	35709.0			2.74593
$554$	−3684.19	−	1409.91i	−0.282539	−	0.108125i
$555$	−10822.1			−0.827700
$556$	1077.92	+	966.586i	0.0822198	+	0.0737273i
$557$			5805.51i			0.441629i	0.975316	+	0.220815i	$0.0708715\pi$
$557$			5805.51i			0.441629i	−0.975316	+	0.220815i	$0.929128\pi$
$558$	−3025.52	+	7905.89i	−0.229535	+	0.599790i
$559$	−10132.2			−0.766629
$560$	33957.8	−	3709.52i	2.56246	−	0.279921i
$561$	−7361.59	−	1812.66i	−0.554022	−	0.136418i
$562$	−13462.2	−	5151.87i	−1.01044	−	0.386688i
$563$		−	14344.9i		−	1.07383i	−0.843637	−	0.536914i	$-0.819590\pi$
$563$		−	14344.9i		−	1.07383i	0.843637	−	0.536914i	$-0.180410\pi$
$564$	−23954.3	−	21480.1i	−1.78840	−	1.60368i
$565$			18202.2i			1.35535i
$566$	−18033.1	−	6901.11i	−1.33920	−	0.512501i
$567$		−	28656.9i		−	2.12253i
$568$	13365.1	−	6861.57i	0.987304	−	0.506875i
$569$	5022.54			0.370045			0.185023	−	0.982734i	$-0.440764\pi$
$569$	5022.54			0.370045			0.185023	+	0.982734i	$0.440764\pi$
$570$	−9377.53	+	24504.1i	−0.689090	+	1.80064i
$571$	−10463.8			−0.766895			−0.383448	−	0.923563i	$-0.625263\pi$
$571$	−10463.8			−0.766895			−0.383448	+	0.923563i	$0.625263\pi$
$572$	3439.08	−	3835.22i	0.251390	−	0.280348i
$573$	1368.10			0.0997436
$574$	19368.3	+	7412.08i	1.40839	+	0.538980i
$575$		−	3832.39i		−	0.277950i
$576$	−4089.81	+	5702.34i	−0.295848	+	0.412496i
$577$	−8108.14			−0.585002			−0.292501	−	0.956265i	$-0.594488\pi$
$577$	−8108.14			−0.585002			−0.292501	+	0.956265i	$0.594488\pi$
$578$	−9188.31	−	10424.8i	−0.661217	−	0.750195i
$579$		−	12382.8i		−	0.888794i
$580$	5585.18	+	5008.29i	0.399848	+	0.358548i
$581$	2485.66			0.177492
$582$	−1393.29	+	3640.77i	−0.0992334	+	0.259304i
$583$		−	8925.34i		−	0.634047i
$584$	−17688.7	+	9081.28i	−1.25337	+	0.643469i
$585$		−	8834.96i		−	0.624411i
$586$	−6116.05	+	15981.7i	−0.431146	+	1.12661i
$587$		−	1358.60i		−	0.0955290i	−0.998859	−	0.0477645i	$-0.984790\pi$
$587$		−	1358.60i		−	0.0955290i	0.998859	−	0.0477645i	$-0.0152097\pi$
$588$	24550.7	+	22014.8i	1.72186	+	1.54401i
$589$	−18706.9			−1.30866
$590$	4462.74	−	11661.4i	0.311403	−	0.813718i
$591$	−9362.57			−0.651649
$592$	−694.614	−	6358.65i	−0.0482237	−	0.441451i
$593$	5036.78			0.348796			0.174398	−	0.984675i	$-0.444202\pi$
$593$	5036.78			0.348796			0.174398	+	0.984675i	$0.444202\pi$
$594$	3798.48	+	1453.65i	0.262380	+	0.100411i
$595$	−8944.83	+	36326.7i	−0.616306	+	2.50294i
$596$	−10756.6	+	11995.7i	−0.739277	+	0.824433i
$597$		−	1143.91i		−	0.0784206i
$598$	−2358.47	−	902.567i	−0.161279	−	0.0617203i
$599$	8533.60			0.582093			0.291046	−	0.956709i	$-0.405997\pi$
$599$	8533.60			0.582093			0.291046	+	0.956709i	$0.405997\pi$
$600$	10749.7	+	20938.5i	0.731425	+	1.42469i
$601$		−	22493.8i		−	1.52669i	−0.645991	−	0.763345i	$-0.723555\pi$
$601$		−	22493.8i		−	1.52669i	0.645991	−	0.763345i	$-0.276445\pi$
$602$	22161.7	+	8481.12i	1.50041	+	0.574194i
$603$			4071.71i			0.274980i
$604$	6188.52	+	5549.31i	0.416900	+	0.373838i
$605$	17711.4			1.19020
$606$	10461.3	−	27336.0i	0.701253	−	1.83242i
$607$		−	8404.23i		−	0.561972i	−0.959712	−	0.280986i	$-0.909339\pi$
$607$		−	8404.23i		−	0.561972i	0.959712	−	0.280986i	$-0.0906615\pi$
$608$	−14999.5	−	3937.08i	−1.00051	−	0.262615i
$609$			11086.5i			0.737678i
$610$	16287.8	+	6233.21i	1.08111	+	0.413730i
$611$			23942.7i			1.58530i
$612$	−4329.17	−	6350.09i	−0.285942	−	0.419424i
$613$		−	7225.59i		−	0.476083i	−0.971255	−	0.238042i	$-0.923495\pi$
$613$		−	7225.59i		−	0.476083i	0.971255	−	0.238042i	$-0.0765055\pi$
$614$	5092.11	−	13306.0i	0.334692	−	0.874572i
$615$			25244.3i			1.65520i
$616$	−10732.4	+	5509.97i	−0.701985	+	0.360394i
$617$			8559.44i			0.558493i	0.960219	+	0.279247i	$0.0900847\pi$
$617$			8559.44i			0.558493i	−0.960219	+	0.279247i	$0.909915\pi$
$618$	18382.4	+	7034.81i	1.19652	+	0.457899i
$619$	−2742.20			−0.178059			−0.0890294	−	0.996029i	$-0.528377\pi$
$619$	−2742.20			−0.178059			−0.0890294	+	0.996029i	$0.528377\pi$
$620$	−19793.2	+	22073.2i	−1.28212	+	1.42981i
$621$		−	1993.78i		−	0.128837i
$622$	995.122	−	2600.32i	0.0641491	−	0.167626i
$623$		−	23357.6i		−	1.50209i
$624$	15417.3	−	1684.18i	0.989083	−	0.108047i
$625$	−9423.76			−0.603121
$626$	−9459.06	+	24717.2i	−0.603930	+	1.57811i
$627$		−	9266.18i		−	0.590200i
$628$	−3434.80	+	3830.45i	−0.218254	+	0.243394i
$629$	6802.25	+	1674.94i	0.431198	+	0.106175i
$630$	−7395.28	+	19324.4i	−0.467675	+	1.22207i
$631$	1273.16			0.0803226			0.0401613	−	0.999193i	$-0.487213\pi$
$631$	1273.16			0.0803226			0.0401613	+	0.999193i	$0.487213\pi$
$632$	−22856.0	+	11734.1i	−1.43855	+	0.738542i
$633$	31718.9			1.99165
$634$	18050.0	+	6907.60i	1.13069	+	0.432706i
$635$	37777.4			2.36086
$636$	17939.6	−	20006.1i	1.11848	−	1.24731i
$637$		−	24538.7i		−	1.52631i
$638$	−2474.41	−	946.937i	−0.153547	−	0.0587611i
$639$			9100.01i			0.563366i
$640$	−20516.2	+	13533.0i	−1.26714	+	0.835842i
$641$		−	19703.0i		−	1.21408i	−0.794673	−	0.607038i	$-0.792357\pi$
$641$		−	19703.0i		−	1.21408i	0.794673	−	0.607038i	$-0.207643\pi$
$642$	−9144.93	−	3499.69i	−0.562183	−	0.215143i
$643$	18714.6			1.14780			0.573898	−	0.818927i	$-0.305431\pi$
$643$	18714.6			1.14780			0.573898	+	0.818927i	$0.305431\pi$
$644$	4403.10	+	3948.30i	0.269420	+	0.241591i
$645$			28885.3i			1.76334i
$646$	9686.74	−	13950.7i	0.589968	−	0.849664i
$647$	25866.7			1.57175			0.785877	−	0.618383i	$-0.212212\pi$
$647$	25866.7			1.57175			0.785877	+	0.618383i	$0.212212\pi$
$648$	9416.78	+	18342.2i	0.570874	+	1.11196i
$649$			4409.75i			0.266715i
$650$	6260.04	−	16357.9i	0.377752	−	0.987093i
$651$	−43814.7			−2.63784
$652$	973.255	+	872.728i	0.0584595	+	0.0524212i
$653$	−18847.5			−1.12949			−0.564747	−	0.825264i	$-0.691026\pi$
$653$	−18847.5			−1.12949			−0.564747	+	0.825264i	$0.691026\pi$
$654$	11330.1	+	4335.95i	0.677435	+	0.259249i
$655$	−34756.7			−2.07337
$656$	−14832.6	+	1620.30i	−0.882797	+	0.0964359i
$657$		−	12043.9i		−	0.715183i
$658$	20041.2	−	52368.9i	1.18736	−	3.10267i
$659$		−	25605.6i		−	1.51359i	−0.653655	−	0.756793i	$-0.726765\pi$
$659$		−	25605.6i		−	1.51359i	0.653655	−	0.756793i	$-0.273235\pi$
$660$	−10933.6	−	9804.30i	−0.644835	−	0.578230i
$661$		−	778.018i		−	0.0457812i	−0.999738	−	0.0228906i	$-0.992713\pi$
$661$		−	778.018i		−	0.0457812i	0.999738	−	0.0228906i	$-0.00728694\pi$
$662$	−2255.95	+	5894.96i	−0.132447	+	0.346094i
$663$	−4061.09	+	16492.9i	−0.237888	+	0.966110i
$664$	−1590.98	+	816.799i	−0.0929850	+	0.0477379i
$665$	−45725.2			−2.66639
$666$	3618.52	+	1384.78i	0.210533	+	0.0805693i
$667$			1298.79i			0.0753963i
$668$	−14295.0	+	15941.6i	−0.827978	+	0.923351i
$669$	15096.1			0.872421
$670$	−5096.99	+	13318.8i	−0.293901	+	0.767984i
$671$	−6159.20			−0.354357
$672$	−35131.5	−	9221.32i	−2.01671	−	0.529345i
$673$			3472.98i			0.198921i	0.995042	+	0.0994603i	$0.0317116\pi$
$673$			3472.98i			0.198921i	−0.995042	+	0.0994603i	$0.968288\pi$
$674$	−1090.63	+	2849.89i	−0.0623287	+	0.162869i
$675$	13828.5			0.788532
$676$	4493.09	+	4028.99i	0.255638	+	0.229233i
$677$	−16399.1			−0.930971			−0.465485	−	0.885056i	$-0.654120\pi$
$677$	−16399.1			−0.930971			−0.465485	+	0.885056i	$0.654120\pi$
$678$	6917.43	−	18075.7i	0.391832	−	1.02388i
$679$	−6793.76			−0.383977
$680$	−6211.87	−	26190.7i	−0.350315	−	1.47701i
$681$	7736.61			0.435342
$682$	3742.39	−	9779.11i	0.210122	−	0.549064i
$683$	−15721.5			−0.880773			−0.440386	−	0.897808i	$-0.645159\pi$
$683$	−15721.5			−0.880773			−0.440386	+	0.897808i	$0.645159\pi$
$684$	6271.00	−	6993.35i	0.350552	−	0.390932i
$685$	22640.7			1.26285
$686$	−9635.16	+	25177.3i	−0.536257	+	1.40128i
$687$			33704.8i			1.87179i
$688$	−16971.9	+	1853.99i	−0.940474	+	0.102736i
$689$	−19996.3			−1.10566
$690$	−2573.08	+	6723.63i	−0.141964	+	0.370963i
$691$	−1949.68			−0.107336			−0.0536680	−	0.998559i	$-0.517091\pi$
$691$	−1949.68			−0.107336			−0.0536680	+	0.998559i	$0.517091\pi$
$692$	−23411.4	−	20993.3i	−1.28608	−	1.15324i
$693$		−	7307.47i		−	0.400560i
$694$	−6368.73	−	2437.26i	−0.348348	−	0.133310i
$695$	−3071.50			−0.167638
$696$	−3643.06	−	7096.04i	−0.198405	−	0.386458i
$697$	3907.05	−	15867.3i	0.212325	−	0.862293i
$698$	−8064.04	+	21071.9i	−0.437290	+	1.14267i
$699$			29823.8i			1.61379i
$700$	−27384.7	+	30539.1i	−1.47864	+	1.64896i
$701$			22499.1i			1.21224i	0.795373	+	0.606120i	$0.207275\pi$
$701$			22499.1i			1.21224i	−0.795373	+	0.606120i	$0.792725\pi$
$702$	3256.75	−	8510.12i	0.175097	−	0.457541i
$703$			8562.13i			0.459356i
$704$	5058.85	−	7053.46i	0.270827	−	0.377610i
$705$	68256.9			3.64639
$706$	21366.2	+	8176.69i	1.13899	+	0.435884i
$707$	51009.5			2.71345
$708$	−8863.45	+	9884.42i	−0.470493	+	0.524688i
$709$	−16693.4			−0.884249			−0.442124	−	0.896954i	$-0.645775\pi$
$709$	−16693.4			−0.884249			−0.442124	+	0.896954i	$0.645775\pi$
$710$	−11391.4	+	29766.6i	−0.602130	+	1.57341i
$711$		−	15562.1i		−	0.820851i
$712$	7675.42	+	14950.4i	0.404001	+	0.786922i
$713$	−5132.94			−0.269607
$714$	22688.0	−	32675.0i	1.18918	−	1.71265i
$715$			10928.3i			0.571602i
$716$	23590.4	−	26307.7i	1.23130	−	1.37314i
$717$	8608.09			0.448361
$718$	2556.36	+	978.297i	0.132872	+	0.0508492i
$719$			10356.6i			0.537183i	0.963254	+	0.268592i	$0.0865582\pi$
$719$			10356.6i			0.537183i	−0.963254	+	0.268592i	$0.913442\pi$
$720$	−1616.62	−	14798.9i	−0.0836778	−	0.766006i
$721$			34302.1i			1.77181i
$722$	1268.17	+	485.320i	0.0653691	+	0.0250162i
$723$		−	654.814i		−	0.0336830i
$724$	6339.21	+	5684.43i	0.325407	+	0.291796i
$725$	−9008.17			−0.461455
$726$	−17588.3	−	6730.90i	−0.899123	−	0.344087i
$727$	3948.22			0.201419			0.100709	−	0.994916i	$-0.467889\pi$
$727$	3948.22			0.201419			0.100709	+	0.994916i	$0.467889\pi$
$728$	12344.5	+	24045.0i	0.628460	+	1.22413i
$729$	2122.30			0.107824
$730$	15076.5	−	39396.0i	0.764394	−	1.99741i
$731$	4470.56	−	18155.8i	0.226197	−	0.918630i
$732$	−13805.8	−	12379.8i	−0.697100	−	0.625096i
$733$		−	5717.09i		−	0.288084i	−0.989572	−	0.144042i	$-0.953990\pi$
$733$		−	5717.09i		−	0.288084i	0.989572	−	0.144042i	$-0.0460101\pi$
$734$	−4952.39	+	12940.9i	−0.249041	+	0.650761i
$735$	−69956.1			−3.51070
$736$	−4115.69	−	1080.29i	−0.206123	−	0.0541031i
$737$		−	5036.47i		−	0.251724i
$738$	3230.22	−	8440.78i	0.161119	−	0.421016i
$739$		−	10447.9i		−	0.520070i	−0.965599	−	0.260035i	$-0.916266\pi$
$739$		−	10447.9i		−	0.520070i	0.965599	−	0.260035i	$-0.0837340\pi$
$740$	10102.9	+	9059.36i	0.501878	+	0.450039i
$741$	−20760.0			−1.02920
$742$	43737.2	+	16737.9i	2.16394	+	0.828122i
$743$		−	20595.5i		−	1.01692i	−0.861084	−	0.508462i	$-0.830214\pi$
$743$		−	20595.5i		−	1.01692i	0.861084	−	0.508462i	$-0.169786\pi$
$744$	28044.2	−	14397.7i	1.38192	−	0.709470i
$745$		−	34181.2i		−	1.68094i
$746$	−5767.99	+	15072.2i	−0.283085	+	0.739720i
$747$		−	1083.26i		−	0.0530582i
$748$	5354.93	+	7854.69i	0.261759	+	0.383952i
$749$		−	17064.6i		−	0.832481i
$750$	−10879.6	−	4163.54i	−0.529689	−	0.202708i
$751$			1116.08i			0.0542294i	0.999632	+	0.0271147i	$0.00863194\pi$
$751$			1116.08i			0.0542294i	−0.999632	+	0.0271147i	$0.991368\pi$
$752$	4381.04	+	40105.1i	0.212447	+	1.94479i
$753$			18965.9i			0.917872i
$754$	−2121.52	+	5543.67i	−0.102468	+	0.267757i
$755$	−17633.9			−0.850020
$756$	−14246.8	+	15887.8i	−0.685383	+	0.764331i
$757$		−	4961.25i		−	0.238203i	−0.992882	−	0.119101i	$-0.961999\pi$
$757$		−	4961.25i		−	0.238203i	0.992882	−	0.119101i	$-0.0380014\pi$
$758$	−16991.1	−	6502.37i	−0.814176	−	0.311579i
$759$		−	2542.53i		−	0.121591i
$760$	29267.1	−	15025.5i	1.39688	−	0.717148i
$761$	9166.77			0.436656			0.218328	−	0.975875i	$-0.429940\pi$
$761$	9166.77			0.436656			0.218328	+	0.975875i	$0.429940\pi$
$762$	−37514.8	−	14356.6i	−1.78349	−	0.682527i
$763$			21142.3i			1.00315i
$764$	−1277.17	−	1145.25i	−0.0604798	−	0.0542328i
$765$	15831.4	+	3898.20i	0.748214	+	0.184235i
$766$	−7173.68	−	2745.31i	−0.338376	−	0.129494i
$767$	9879.61			0.465100
$768$	25516.6	−	5642.14i	1.19889	−	0.265095i
$769$	−20783.7			−0.974616			−0.487308	−	0.873230i	$-0.662021\pi$
$769$	−20783.7			−0.974616			−0.487308	+	0.873230i	$0.662021\pi$
$770$	9147.52	−	23903.1i	0.428122	−	1.11871i
$771$	21152.4			0.988047
$772$	−10365.8	+	11559.9i	−0.483257	+	0.538922i
$773$			5877.33i			0.273471i	0.990608	+	0.136735i	$0.0436610\pi$
$773$			5877.33i			0.273471i	−0.990608	+	0.136735i	$0.956339\pi$
$774$	3696.11	−	9658.18i	0.171646	−	0.448522i
$775$		−	35601.2i		−	1.65010i
$776$	4348.44	−	2232.46i	0.201160	−	0.103274i
$777$			20054.0i			0.925911i
$778$	5090.69	−	13302.3i	0.234589	−	0.612996i
$779$	19972.5			0.918601
$780$	−21965.5	+	24495.7i	−1.00832	+	1.12447i
$781$		−	11256.2i		−	0.515720i
$782$	2657.92	−	3827.91i	0.121544	−	0.175046i
$783$	−4686.45			−0.213895
$784$	−4490.10	−	41103.4i	−0.204542	−	1.87242i
$785$		−	10914.7i		−	0.496258i
$786$	34515.1	+	13208.7i	1.56630	+	0.599411i
$787$	14361.8			0.650497			0.325249	−	0.945629i	$-0.394552\pi$
$787$	14361.8			0.650497			0.325249	+	0.945629i	$0.394552\pi$
$788$	8740.34	+	7837.55i	0.395129	+	0.354316i
$789$	−48303.7			−2.17954
$790$	19480.7	−	50904.5i	0.877333	−	2.29253i
$791$	33729.7			1.51617
$792$	2401.27	+	4677.25i	0.107734	+	0.209847i
$793$			13799.1i			0.617932i
$794$	41120.9	+	15736.6i	1.83794	+	0.703365i
$795$			57006.4i			2.54316i
$796$	−957.584	+	1067.89i	−0.0426390	+	0.0475505i
$797$			12746.4i			0.566500i	0.959046	+	0.283250i	$0.0914126\pi$
$797$			12746.4i			0.566500i	−0.959046	+	0.283250i	$0.908587\pi$
$798$	45407.5	+	17377.1i	2.01429	+	0.770854i
$799$	−42902.9	−	10564.1i	−1.89962	−	0.467748i
$800$	7492.67	−	28545.7i	0.331133	−	1.26155i
$801$	−10179.4			−0.449026
$802$	8047.99	−	21029.9i	0.354345	−	0.925927i
$803$			14897.5i			0.654698i
$804$	10123.1	−	11289.2i	0.444049	−	0.495198i
$805$	−12546.4			−0.549322
$806$	−21909.1	−	8384.45i	−0.957464	−	0.366414i
$807$	−21541.9			−0.939668
$808$	−32649.4	+	16762.0i	−1.42154	+	0.729807i
$809$			2526.26i			0.109788i	0.998492	+	0.0548940i	$0.0174821\pi$
$809$			2526.26i			0.109788i	−0.998492	+	0.0548940i	$0.982518\pi$
$810$	−40851.5	−	15633.5i	−1.77207	−	0.678156i
$811$	−41464.8			−1.79535			−0.897674	−	0.440661i	$-0.854744\pi$
$811$	−41464.8			−1.79535			−0.897674	+	0.440661i	$0.854744\pi$
$812$	9280.63	−	10349.7i	0.401092	−	0.447293i
$813$	−17041.6			−0.735149
$814$	−4475.90	−	1712.89i	−0.192727	−	0.0737552i
$815$	−2773.25			−0.119194
$816$	−3784.63	+	28369.4i	−0.162363	+	1.21707i
$817$	22853.1			0.978617
$818$	17329.4	+	6631.82i	0.740719	+	0.283467i
$819$	−16371.7			−0.698501
$820$	21132.4	−	23566.6i	0.899970	−	1.00364i
$821$	32212.7			1.36934			0.684672	−	0.728851i	$-0.259945\pi$
$821$	32212.7			1.36934			0.684672	+	0.728851i	$0.259945\pi$
$822$	−22483.3	−	8604.19i	−0.954010	−	0.365092i
$823$			32272.8i			1.36690i	0.729998	+	0.683449i	$0.239521\pi$
$823$			32272.8i			1.36690i	−0.729998	+	0.683449i	$0.760479\pi$
$824$	−11271.8	−	21955.5i	−0.476544	−	0.928223i
$825$	17634.5			0.744188
$826$	−21609.3	−	8269.70i	−0.910270	−	0.348353i
$827$	19046.7			0.800869			0.400434	−	0.916325i	$-0.368859\pi$
$827$	19046.7			0.800869			0.400434	+	0.916325i	$0.368859\pi$
$828$	1720.69	−	1918.89i	0.0722198	−	0.0805387i
$829$			44471.8i			1.86317i	0.363519	+	0.931587i	$0.381575\pi$
$829$			44471.8i			1.86317i	−0.363519	+	0.931587i	$0.618425\pi$
$830$	1356.03	−	3543.40i	0.0567091	−	0.148185i
$831$	−8898.23			−0.371452
$832$	−15802.6	−	11333.8i	−0.658480	−	0.472272i
$833$	43970.9	+	10827.1i	1.82893	+	0.450343i
$834$	3050.16	+	1167.27i	0.126641	+	0.0484644i
$835$		−	45424.9i		−	1.88263i
$836$	−7756.86	+	8650.35i	−0.320905	+	0.357869i
$837$		−	18521.3i		−	0.764863i
$838$	−3789.31	−	1450.14i	−0.156205	−	0.0597783i
$839$			19481.8i			0.801652i	0.916154	+	0.400826i	$0.131277\pi$
$839$			19481.8i			0.801652i	−0.916154	+	0.400826i	$0.868723\pi$
$840$	68548.5	−	35192.3i	2.81565	−	1.44554i
$841$	−21336.1			−0.874827
$842$	−2672.22	+	6982.68i	−0.109371	+	0.285795i
$843$	−32514.5			−1.32842
$844$	−29610.9	−	26552.4i	−1.20764	−	1.08290i
$845$	−12802.9			−0.521221
$846$	−22822.6	−	8734.03i	−0.927491	−	0.354943i
$847$		−	32820.2i		−	1.33142i
$848$	−33494.7	+	3658.93i	−1.35638	+	0.148170i
$849$	−43554.3			−1.76064
$850$	26549.7	+	18434.9i	1.07135	+	0.743895i
$851$			2349.35i			0.0946352i
$852$	22624.5	−	25230.6i	0.909746	−	1.01454i
$853$	18815.4			0.755250			0.377625	−	0.925959i	$-0.376741\pi$
$853$	18815.4			0.755250			0.377625	+	0.925959i	$0.376741\pi$
$854$	11550.5	−	30182.2i	0.462822	−	1.20938i
$855$			19927.3i			0.797073i
$856$	5607.52	+	10922.5i	0.223903	+	0.436124i
$857$			25870.9i			1.03119i	0.856831	+	0.515597i	$0.172430\pi$
$857$			25870.9i			1.03119i	−0.856831	+	0.515597i	$0.827570\pi$
$858$	4153.11	−	10852.4i	0.165251	−	0.431811i
$859$		−	12038.7i		−	0.478179i	−0.970997	−	0.239090i	$-0.923151\pi$
$859$		−	12038.7i		−	0.478179i	0.970997	−	0.239090i	$-0.0768490\pi$
$860$	24180.3	−	26965.6i	0.958769	−	1.06921i
$861$	46779.1			1.85160
$862$	8432.29	−	22034.1i	0.333184	−	0.870633i
$863$	−30028.8			−1.18446			−0.592231	−	0.805768i	$-0.701753\pi$
$863$	−30028.8			−1.18446			−0.592231	+	0.805768i	$0.701753\pi$
$864$	3898.02	−	14850.8i	0.153488	−	0.584760i
$865$	66709.9			2.62220
$866$	−22139.1	−	8472.47i	−0.868728	−	0.332455i
$867$	−27761.8	−	14554.1i	−1.08747	−	0.570109i
$868$	40902.8	+	36678.0i	1.59946	+	1.43425i
$869$			19249.4i			0.751429i
$870$	15804.2	+	6048.12i	0.615875	+	0.235690i
$871$	−11283.7			−0.438959
$872$	−6947.44	−	13532.4i	−0.269805	−	0.525533i
$873$			2960.75i			0.114784i
$874$	5319.53	+	2035.74i	0.205876	+	0.0787872i
$875$		−	20301.6i		−	0.784364i
$876$	−29943.5	+	33392.7i	−1.15491	+	1.28794i
$877$	8698.98			0.334941			0.167471	−	0.985877i	$-0.446440\pi$
$877$	8698.98			0.334941			0.167471	+	0.985877i	$0.446440\pi$
$878$	−1516.63	+	3963.05i	−0.0582957	+	0.152331i
$879$			38599.6i			1.48115i
$880$	1999.67	+	18305.4i	0.0766008	+	0.701222i
$881$			32363.6i			1.23764i	0.785535	+	0.618818i	$0.212388\pi$
$881$			32363.6i			1.23764i	−0.785535	+	0.618818i	$0.787612\pi$
$882$	23390.8	+	8951.45i	0.892979	+	0.341736i
$883$			16933.1i			0.645350i	0.946510	+	0.322675i	$0.104582\pi$
$883$			16933.1i			0.645350i	−0.946510	+	0.322675i	$0.895418\pi$
$884$	17597.6	−	11997.2i	0.669539	−	0.456458i
$885$		−	28165.2i		−	1.06979i
$886$	−14861.8	+	38835.0i	−0.563536	+	1.47256i
$887$		−	22920.8i		−	0.867649i	−0.900997	−	0.433824i	$-0.857164\pi$
$887$		−	22920.8i		−	0.867649i	0.900997	−	0.433824i	$-0.142836\pi$
$888$	−6589.83	−	12835.8i	−0.249032	−	0.485070i
$889$		−	70003.5i		−	2.64099i
$890$	−33297.1	−	12742.5i	−1.25407	−	0.479923i
$891$	15447.9			0.580835
$892$	−14092.8	−	12637.2i	−0.528995	−	0.474355i
$893$		−	54002.8i		−	2.02367i
$894$	−12990.0	+	33943.6i	−0.485961	+	1.26985i
$895$			74962.7i			2.79969i
$896$	25077.4	+	38017.6i	0.935019	+	1.41750i
$897$	−5696.28			−0.212033
$898$	−7312.74	+	19108.7i	−0.271748	+	0.710095i
$899$			12065.2i			0.447604i
$900$	13309.1	+	11934.4i	0.492929	+	0.442014i
$901$	8822.86	−	35831.4i	0.326229	−	1.32488i
$902$	−3995.59	+	10440.7i	−0.147493	+	0.385409i
$903$	53526.0			1.97257
$904$	−21589.1	+	11083.7i	−0.794297	+	0.407787i
$905$	−18063.3			−0.663475
$906$	17511.4	+	6701.47i	0.642138	+	0.245741i
$907$	−16129.5			−0.590485			−0.295243	−	0.955422i	$-0.595400\pi$
$907$	−16129.5			−0.590485			−0.295243	+	0.955422i	$0.595400\pi$
$908$	−7222.44	−	6476.43i	−0.263970	−	0.236705i
$909$		−	22230.2i		−	0.811143i
$910$	−53552.5	−	20494.1i	−1.95082	−	0.746564i
$911$		−	14344.1i		−	0.521670i	−0.965383	−	0.260835i	$-0.916002\pi$
$911$		−	14344.1i		−	0.521670i	0.965383	−	0.260835i	$-0.0839978\pi$
$912$	−34773.9	+	3798.66i	−1.26258	+	0.137924i
$913$			1339.93i			0.0485709i
$914$	−13347.2	−	5107.86i	−0.483026	−	0.184850i
$915$	39339.1			1.42132
$916$	28214.7	−	31464.7i	1.01773	−	1.13496i
$917$			64406.0i			2.31938i
$918$	13812.3	+	9590.65i	0.496595	+	0.344813i
$919$	9522.14			0.341792			0.170896	−	0.985289i	$-0.445334\pi$
$919$	9522.14			0.341792			0.170896	+	0.985289i	$0.445334\pi$
$920$	8030.52	−	4122.82i	0.287781	−	0.147745i
$921$		−	32137.3i		−	1.14979i
$922$	9461.99	−	24724.8i	0.337976	−	0.883155i
$923$	−25218.3			−0.899319
$924$	−18167.9	+	20260.6i	−0.646840	+	0.721348i
$925$	−16294.6			−0.579205
$926$	29171.1	+	11163.5i	1.03523	+	0.396173i
$927$	14949.0			0.529654
$928$	−2539.26	+	9674.09i	−0.0898223	+	0.342207i
$929$		−	31263.7i		−	1.10412i	−0.833804	−	0.552060i	$-0.813842\pi$
$929$		−	31263.7i		−	1.10412i	0.833804	−	0.552060i	$-0.186158\pi$
$930$	−23902.8	+	62459.5i	−0.842798	+	2.20229i
$931$			55347.1i			1.94836i
$932$	24966.0	−	27841.8i	0.877455	−	0.978527i
$933$		−	6280.41i		−	0.220377i
$934$	359.058	−	938.243i	0.0125789	−	0.0328696i
$935$	−19582.4	−	4821.84i	−0.684935	−	0.168653i
$936$	10478.9	−	5379.80i	0.365933	−	0.187868i
$937$	−32839.4			−1.14495			−0.572475	−	0.819923i	$-0.694016\pi$
$937$	−32839.4			−1.14495			−0.572475	+	0.819923i	$0.694016\pi$
$938$	24680.4	+	9445.00i	0.859109	+	0.328774i
$939$			59698.0i			2.07473i
$940$	−63720.6	−	57138.9i	−2.21100	−	1.98262i
$941$	24835.0			0.860360			0.430180	−	0.902743i	$-0.358450\pi$
$941$	24835.0			0.860360			0.430180	+	0.902743i	$0.358450\pi$
$942$	−4147.94	+	10838.9i	−0.143469	+	0.374893i
$943$	5480.22			0.189248
$944$	16548.8	−	1807.77i	0.570569	−	0.0623284i
$945$		−	45271.6i		−	1.55840i
$946$	−4571.87	+	11946.6i	−0.157129	+	0.410589i
$947$	−27653.2			−0.948901			−0.474451	−	0.880282i	$-0.657353\pi$
$947$	−27653.2			−0.948901			−0.474451	+	0.880282i	$0.657353\pi$
$948$	−38690.7	+	43147.4i	−1.32554	+	1.47823i
$949$	33376.4			1.14167
$950$	−14119.5	+	36895.3i	−0.482209	+	1.26004i
$951$	43595.2			1.48651
$952$	−48532.9	+	11510.9i	−1.65227	+	0.391882i
$953$	−4069.09			−0.138311			−0.0691557	−	0.997606i	$-0.522031\pi$
$953$	−4069.09			−0.138311			−0.0691557	+	0.997606i	$0.522031\pi$
$954$	7294.44	−	19060.9i	0.247554	−	0.646875i
$955$	3639.26			0.123313
$956$	−8036.00	−	7205.96i	−0.271865	−	0.243784i
$957$	−5976.31			−0.201867
$958$	5144.60	−	13443.2i	0.173502	−	0.453372i
$959$		−	41954.4i		−	1.41270i
$960$	−32311.0	+	45050.7i	−1.08629	+	1.51459i
$961$	−17891.7			−0.600575
$962$	−3837.56	+	10027.8i	−0.128615	+	0.336080i
$963$	−7436.85			−0.248857
$964$	−548.155	+	611.295i	−0.0183142	+	0.0204238i
$965$		−	32939.3i		−	1.09881i
$966$	12459.3	+	4768.06i	0.414979	+	0.158809i
$967$	−40221.1			−1.33756			−0.668781	−	0.743459i	$-0.733184\pi$
$967$	−40221.1			−1.33756			−0.668781	+	0.743459i	$0.733184\pi$
$968$	10784.9	+	21007.0i	0.358098	+	0.697511i
$969$	9159.79	−	37199.8i	0.303669	−	1.23326i
$970$	−3706.28	+	9684.75i	−0.122682	+	0.320576i
$971$		−	53301.0i		−	1.76160i	−0.473492	−	0.880798i	$-0.657007\pi$
$971$		−	53301.0i		−	1.76160i	0.473492	−	0.880798i	$-0.342993\pi$
$972$	20986.3	+	18818.6i	0.692526	+	0.620995i
$973$			5691.66i			0.187530i
$974$	9615.60	−	25126.2i	0.316328	−	0.826587i
$975$		−	39508.4i		−	1.29772i
$976$	2524.96	+	23114.1i	0.0828095	+	0.758057i
$977$	5630.94			0.184391			0.0921954	−	0.995741i	$-0.470612\pi$
$977$	5630.94			0.184391			0.0921954	+	0.995741i	$0.470612\pi$
$978$	2753.98	+	1053.93i	0.0900435	+	0.0344589i
$979$	12591.3			0.411050
$980$	65306.8	+	58561.3i	2.12872	+	1.90885i
$981$	9213.89			0.299874
$982$	3405.13	−	8897.84i	0.110654	−	0.289146i
$983$			3678.62i			0.119359i	0.998218	+	0.0596795i	$0.0190079\pi$
$983$			3678.62i			0.119359i	−0.998218	+	0.0596795i	$0.980992\pi$
$984$	−29941.6	+	15371.8i	−0.970024	+	0.498004i
$985$	−24905.2			−0.805631
$986$	−8997.64	−	6247.55i	−0.290612	−	0.201788i
$987$		−	126484.i		−	4.07905i
$988$	19380.3	+	17378.5i	0.624057	+	0.559598i
$989$	6270.63			0.201612
$990$	−10417.1	−	3986.53i	−0.334420	−	0.127980i
$991$			19276.2i			0.617890i	0.951080	+	0.308945i	$0.0999759\pi$
$991$			19276.2i			0.617890i	−0.951080	+	0.308945i	$0.900024\pi$
$992$	−38233.0	−	10035.4i	−1.22369	−	0.321193i
$993$			14237.8i			0.455007i
$994$	55159.1	+	21108.9i	1.76010	+	0.673576i
$995$		−	3042.90i		−	0.0969511i
$996$	−2693.22	+	3003.44i	−0.0856805	+	0.0955499i
$997$	40362.6			1.28214			0.641071	−	0.767481i	$-0.278490\pi$
$997$	40362.6			1.28214			0.641071	+	0.767481i	$0.278490\pi$
$998$	−8869.51	−	3394.29i	−0.281322	−	0.107660i
$999$	−8477.20			−0.268475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.h.a.101.5	✓	52
4.3	odd	2		544.4.h.a.305.42		52
8.3	odd	2		544.4.h.a.305.12		52
8.5	even	2	inner	136.4.h.a.101.8	yes	52
17.16	even	2	inner	136.4.h.a.101.6	yes	52
68.67	odd	2		544.4.h.a.305.11		52
136.67	odd	2		544.4.h.a.305.41		52
136.101	even	2	inner	136.4.h.a.101.7	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.h.a.101.5	✓	52	1.1	even	1	trivial
136.4.h.a.101.6	yes	52	17.16	even	2	inner
136.4.h.a.101.7	yes	52	136.101	even	2	inner
136.4.h.a.101.8	yes	52	8.5	even	2	inner
544.4.h.a.305.11		52	68.67	odd	2
544.4.h.a.305.12		52	8.3	odd	2
544.4.h.a.305.41		52	136.67	odd	2
544.4.h.a.305.42		52	4.3	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.64160 - 1.01092i) q^{2} -6.38011 q^{3} +(5.95609 + 5.34088i) q^{4} -16.9716 q^{5} +(16.8537 + 6.44977i) q^{6} +31.4494i q^{7} +(-10.3344 - 20.1296i) q^{8} +13.7058 q^{9} +O(q^{10})\)	\(q+(-2.64160 - 1.01092i) q^{2} -6.38011 q^{3} +(5.95609 + 5.34088i) q^{4} -16.9716 q^{5} +(16.8537 + 6.44977i) q^{6} +31.4494i q^{7} +(-10.3344 - 20.1296i) q^{8} +13.7058 q^{9} +(44.8322 + 17.1569i) q^{10} -16.9532 q^{11} +(-38.0005 - 34.0754i) q^{12} +37.9820i q^{13} +(31.7927 - 83.0766i) q^{14} +108.281 q^{15} +(6.94996 + 63.6215i) q^{16} +(-68.0599 - 16.7586i) q^{17} +(-36.2051 - 13.8554i) q^{18} -85.6684i q^{19} +(-101.084 - 90.6434i) q^{20} -200.650i q^{21} +(44.7836 + 17.1383i) q^{22} -23.5064i q^{23} +(65.9346 + 128.429i) q^{24} +163.036 q^{25} +(38.3967 - 100.333i) q^{26} +84.8186 q^{27} +(-167.967 + 187.315i) q^{28} -55.2526 q^{29} +(-286.034 - 109.463i) q^{30} -218.364i q^{31} +(45.9572 - 175.088i) q^{32} +108.163 q^{33} +(162.845 + 113.072i) q^{34} -533.747i q^{35} +(81.6328 + 73.2009i) q^{36} -99.9450 q^{37} +(-86.6038 + 226.302i) q^{38} -242.329i q^{39} +(175.391 + 341.632i) q^{40} +233.138i q^{41} +(-202.841 + 530.037i) q^{42} +266.763i q^{43} +(-100.975 - 90.5451i) q^{44} -232.609 q^{45} +(-23.7630 + 62.0944i) q^{46} +630.370 q^{47} +(-44.3415 - 405.912i) q^{48} -646.062 q^{49} +(-430.676 - 164.816i) q^{50} +(434.229 + 106.921i) q^{51} +(-202.857 + 226.224i) q^{52} +526.469i q^{53} +(-224.057 - 85.7447i) q^{54} +287.724 q^{55} +(633.062 - 325.010i) q^{56} +546.574i q^{57} +(145.955 + 55.8559i) q^{58} -260.113i q^{59} +(644.930 + 578.315i) q^{60} +363.306 q^{61} +(-220.748 + 576.829i) q^{62} +431.038i q^{63} +(-298.400 + 416.054i) q^{64} -644.616i q^{65} +(-285.724 - 109.344i) q^{66} +297.080i q^{67} +(-315.865 - 463.315i) q^{68} +149.973i q^{69} +(-539.574 + 1409.94i) q^{70} +663.955i q^{71} +(-141.641 - 275.891i) q^{72} -878.743i q^{73} +(264.015 + 101.036i) q^{74} -1040.19 q^{75} +(457.545 - 510.249i) q^{76} -533.168i q^{77} +(-244.975 + 640.136i) q^{78} -1135.44i q^{79} +(-117.952 - 1079.76i) q^{80} -911.208 q^{81} +(235.683 - 615.856i) q^{82} -79.0370i q^{83} +(1071.65 - 1195.09i) q^{84} +(1155.09 + 284.420i) q^{85} +(269.675 - 704.680i) q^{86} +352.518 q^{87} +(175.201 + 341.261i) q^{88} -742.706 q^{89} +(614.460 + 235.149i) q^{90} -1194.51 q^{91} +(125.545 - 140.006i) q^{92} +1393.18i q^{93} +(-1665.18 - 637.252i) q^{94} +1453.93i q^{95} +(-293.212 + 1117.08i) q^{96} +216.022i q^{97} +(1706.64 + 653.116i) q^{98} -232.357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * q^98

Introduction

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