LMFDB - Embedded newform 162.4.e.a.73.2

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			73.2
Character	$\chi$	$=$	162.73
Dual form			162.4.e.a.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-3.46830 + 2.91025i) q^{5} +(22.9979 - 8.37056i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-3.46830 + 2.91025i) q^{5} +(22.9979 - 8.37056i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-4.52754 - 7.84193i) q^{10} +(24.6741 + 20.7040i) q^{11} +(0.761088 + 4.31634i) q^{13} +(8.49969 + 48.2041i) q^{14} +(12.2567 + 10.2846i) q^{16} +(16.1926 + 28.0463i) q^{17} +(-62.8139 + 108.797i) q^{19} +(17.0180 - 6.19404i) q^{20} +(-49.3481 + 41.4080i) q^{22} +(138.497 + 50.4088i) q^{23} +(-18.1465 + 102.914i) q^{25} -8.76586 q^{26} -97.8955 q^{28} +(21.0451 - 119.353i) q^{29} +(148.527 + 54.0595i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(-60.8641 + 22.1527i) q^{34} +(-55.4033 + 95.9613i) q^{35} +(-151.315 - 262.086i) q^{37} +(-192.473 - 161.504i) q^{38} +(6.28960 + 35.6701i) q^{40} +(80.0317 + 453.882i) q^{41} +(121.198 + 101.697i) q^{43} +(-64.4194 - 111.578i) q^{44} +(-147.385 + 255.279i) q^{46} +(-99.9785 + 36.3892i) q^{47} +(196.085 - 164.535i) q^{49} +(-196.398 - 71.4831i) q^{50} +(3.04435 - 17.2654i) q^{52} +91.3423 q^{53} -145.831 q^{55} +(33.9988 - 192.817i) q^{56} +(227.770 + 82.9016i) q^{58} +(251.602 - 211.119i) q^{59} +(592.165 - 215.531i) q^{61} +(-158.059 + 273.767i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-15.2013 - 12.7554i) q^{65} +(-158.815 - 900.683i) q^{67} +(-22.4945 - 127.572i) q^{68} +(-169.766 - 142.450i) q^{70} +(-534.661 - 926.060i) q^{71} +(371.350 - 643.197i) q^{73} +(568.760 - 207.012i) q^{74} +(384.946 - 323.008i) q^{76} +(740.756 + 269.613i) q^{77} +(-188.846 + 1071.00i) q^{79} -72.4407 q^{80} -921.768 q^{82} +(128.937 - 731.236i) q^{83} +(-137.782 - 50.1487i) q^{85} +(-242.395 + 203.394i) q^{86} +(242.138 - 88.1309i) q^{88} +(-587.989 + 1018.43i) q^{89} +(53.6337 + 92.8962i) q^{91} +(-451.615 - 378.950i) q^{92} +(-36.9506 - 209.557i) q^{94} +(-98.7685 - 560.144i) q^{95} +(376.407 + 315.843i) q^{97} +(255.971 + 443.355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$2$	−0.347296	+	1.96962i	−0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	−	1.36808i	−0.469846	−	0.171010i
$5$	−3.46830	+	2.91025i	−0.310214	+	0.260301i	−0.784580	−	0.620027i	$-0.787122\pi$
$5$	−3.46830	+	2.91025i	−0.310214	+	0.260301i	0.474366	+	0.880328i	$0.342677\pi$
$6$		0			0
$7$	22.9979	−	8.37056i	1.24177	−	0.451968i	0.364158	−	0.931337i	$-0.381357\pi$
$7$	22.9979	−	8.37056i	1.24177	−	0.451968i	0.877613	+	0.479369i	$0.159135\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$		0			0
$10$	−4.52754	−	7.84193i	−0.143173	−	0.247984i
$11$	24.6741	+	20.7040i	0.676319	+	0.567499i	0.914928	−	0.403617i	$-0.132247\pi$
$11$	24.6741	+	20.7040i	0.676319	+	0.567499i	−0.238609	+	0.971116i	$0.576692\pi$
$12$		0			0
$13$	0.761088	+	4.31634i	0.0162375	+	0.0920876i	0.991850	−	0.127414i	$-0.0406678\pi$
$13$	0.761088	+	4.31634i	0.0162375	+	0.0920876i	−0.975612	+	0.219502i	$0.929557\pi$
$14$	8.49969	+	48.2041i	0.162260	+	0.920221i
$15$		0			0
$16$	12.2567	+	10.2846i	0.191511	+	0.160697i
$17$	16.1926	+	28.0463i	0.231016	+	0.400132i	0.958107	−	0.286409i	$-0.0924617\pi$
$17$	16.1926	+	28.0463i	0.231016	+	0.400132i	−0.727091	+	0.686541i	$0.759128\pi$
$18$		0			0
$19$	−62.8139	+	108.797i	−0.758447	+	1.31367i	0.185196	+	0.982702i	$0.440708\pi$
$19$	−62.8139	+	108.797i	−0.758447	+	1.31367i	−0.943642	+	0.330967i	$0.892625\pi$
$20$	17.0180	−	6.19404i	0.190267	−	0.0692515i
$21$		0			0
$22$	−49.3481	+	41.4080i	−0.478230	+	0.401282i
$23$	138.497	+	50.4088i	1.25559	+	0.456998i	0.882287	−	0.470711i	$-0.156003\pi$
$23$	138.497	+	50.4088i	1.25559	+	0.456998i	0.373304	+	0.927709i	$0.378225\pi$
$24$		0			0
$25$	−18.1465	+	102.914i	−0.145172	+	0.823310i
$26$	−8.76586			−0.0661203
$27$		0			0
$28$	−97.8955			−0.660733
$29$	21.0451	−	119.353i	0.134758	−	0.764251i	−0.840270	−	0.542168i	$-0.817604\pi$
$29$	21.0451	−	119.353i	0.134758	−	0.764251i	0.975028	−	0.222082i	$-0.0712854\pi$
$30$		0			0
$31$	148.527	+	54.0595i	0.860525	+	0.313206i	0.734324	−	0.678799i	$-0.237499\pi$
$31$	148.527	+	54.0595i	0.860525	+	0.313206i	0.126201	+	0.992005i	$0.459721\pi$
$32$	−24.5134	+	20.5692i	−0.135419	+	0.113630i
$33$		0			0
$34$	−60.8641	+	22.1527i	−0.307003	+	0.111740i
$35$	−55.4033	+	95.9613i	−0.267568	+	0.463441i
$36$		0			0
$37$	−151.315	−	262.086i	−0.672327	−	1.16450i	−0.977243	−	0.212125i	$-0.931962\pi$
$37$	−151.315	−	262.086i	−0.672327	−	1.16450i	0.304916	−	0.952379i	$-0.401372\pi$
$38$	−192.473	−	161.504i	−0.821664	−	0.689458i
$39$		0			0
$40$	6.28960	+	35.6701i	0.0248618	+	0.140998i
$41$	80.0317	+	453.882i	0.304850	+	1.72889i	0.624210	+	0.781257i	$0.285421\pi$
$41$	80.0317	+	453.882i	0.304850	+	1.72889i	−0.319360	+	0.947634i	$0.603468\pi$
$42$		0			0
$43$	121.198	+	101.697i	0.429824	+	0.360666i	0.831885	−	0.554947i	$-0.187262\pi$
$43$	121.198	+	101.697i	0.429824	+	0.360666i	−0.402061	+	0.915613i	$0.631706\pi$
$44$	−64.4194	−	111.578i	−0.220718	−	0.382295i
$45$		0			0
$46$	−147.385	+	255.279i	−0.472408	+	0.818235i
$47$	−99.9785	+	36.3892i	−0.310284	+	0.112934i	−0.492469	−	0.870330i	$-0.663905\pi$
$47$	−99.9785	+	36.3892i	−0.310284	+	0.112934i	0.182184	+	0.983264i	$0.441683\pi$
$48$		0			0
$49$	196.085	−	164.535i	0.571677	−	0.479694i
$50$	−196.398	−	71.4831i	−0.555498	−	0.202185i
$51$		0			0
$52$	3.04435	−	17.2654i	0.00811876	−	0.0460438i
$53$	91.3423			0.236733			0.118366	−	0.992970i	$-0.462234\pi$
$53$	91.3423			0.236733			0.118366	+	0.992970i	$0.462234\pi$
$54$		0			0
$55$	−145.831			−0.357524
$56$	33.9988	−	192.817i	0.0811299	−	0.460111i
$57$		0			0
$58$	227.770	+	82.9016i	0.515650	+	0.187681i
$59$	251.602	−	211.119i	0.555182	−	0.465853i	−0.321509	−	0.946906i	$-0.604190\pi$
$59$	251.602	−	211.119i	0.555182	−	0.465853i	0.876691	+	0.481053i	$0.159746\pi$
$60$		0			0
$61$	592.165	−	215.531i	1.24293	−	0.452391i	0.364926	−	0.931036i	$-0.381094\pi$
$61$	592.165	−	215.531i	1.24293	−	0.452391i	0.878008	+	0.478645i	$0.158872\pi$
$62$	−158.059	+	273.767i	−0.323767	+	0.560781i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−15.2013	−	12.7554i	−0.0290076	−	0.0243402i
$66$		0			0
$67$	−158.815	−	900.683i	−0.289587	−	1.64233i	−0.688426	−	0.725307i	$-0.741698\pi$
$67$	−158.815	−	900.683i	−0.289587	−	1.64233i	0.398839	−	0.917021i	$-0.369413\pi$
$68$	−22.4945	−	127.572i	−0.0401155	−	0.227506i
$69$		0			0
$70$	−169.766	−	142.450i	−0.289869	−	0.243229i
$71$	−534.661	−	926.060i	−0.893698	−	1.54793i	−0.835408	−	0.549631i	$-0.814768\pi$
$71$	−534.661	−	926.060i	−0.893698	−	1.54793i	−0.0582906	−	0.998300i	$-0.518565\pi$
$72$		0			0
$73$	371.350	−	643.197i	0.595387	−	1.03124i	−0.398105	−	0.917340i	$-0.630332\pi$
$73$	371.350	−	643.197i	0.595387	−	1.03124i	0.993492	−	0.113901i	$-0.0363345\pi$
$74$	568.760	−	207.012i	0.893472	−	0.325197i
$75$		0			0
$76$	384.946	−	323.008i	0.581004	−	0.487520i
$77$	740.756	+	269.613i	1.09632	+	0.399030i
$78$		0			0
$79$	−188.846	+	1071.00i	−0.268948	+	1.52528i	0.488605	+	0.872505i	$0.337506\pi$
$79$	−188.846	+	1071.00i	−0.268948	+	1.52528i	−0.757553	+	0.652774i	$0.773605\pi$
$80$	−72.4407			−0.101239
$81$		0			0
$82$	−921.768			−1.24137
$83$	128.937	−	731.236i	0.170514	−	0.967030i	−0.772682	−	0.634793i	$-0.781085\pi$
$83$	128.937	−	731.236i	0.170514	−	0.967030i	0.943196	−	0.332237i	$-0.107804\pi$
$84$		0			0
$85$	−137.782	−	50.1487i	−0.175819	−	0.0639928i
$86$	−242.395	+	203.394i	−0.303932	+	0.255029i
$87$		0			0
$88$	242.138	−	88.1309i	0.293318	−	0.106759i
$89$	−587.989	+	1018.43i	−0.700301	+	1.21296i	0.268060	+	0.963402i	$0.413617\pi$
$89$	−587.989	+	1018.43i	−0.700301	+	1.21296i	−0.968361	+	0.249554i	$0.919716\pi$
$90$		0			0
$91$	53.6337	+	92.8962i	0.0617839	+	0.107013i
$92$	−451.615	−	378.950i	−0.511784	−	0.429438i
$93$		0			0
$94$	−36.9506	−	209.557i	−0.0405443	−	0.229938i
$95$	−98.7685	−	560.144i	−0.106668	−	0.604942i
$96$		0			0
$97$	376.407	+	315.843i	0.394004	+	0.330608i	0.818170	−	0.574976i	$-0.194989\pi$
$97$	376.407	+	315.843i	0.394004	+	0.330608i	−0.424167	+	0.905584i	$0.639433\pi$
$98$	255.971	+	443.355i	0.263847	+	0.456996i
$99$		0			0
$100$	209.003	−	362.003i	0.209003	−	0.362003i
$101$	388.844	−	141.528i	0.383084	−	0.139431i	−0.143298	−	0.989680i	$-0.545771\pi$
$101$	388.844	−	141.528i	0.383084	−	0.139431i	0.526381	+	0.850249i	$0.323548\pi$
$102$		0			0
$103$	225.031	−	188.824i	0.215272	−	0.180634i	−0.528775	−	0.848762i	$-0.677348\pi$
$103$	225.031	−	188.824i	0.215272	−	0.180634i	0.744047	+	0.668128i	$0.232904\pi$
$104$	32.9489	+	11.9924i	0.0310664	+	0.0113072i
$105$		0			0
$106$	−31.7229	+	179.909i	−0.0290679	+	0.164852i
$107$	−1812.95			−1.63798			−0.818991	−	0.573806i	$-0.805466\pi$
$107$	−1812.95			−1.63798			−0.818991	+	0.573806i	$0.805466\pi$
$108$		0			0
$109$	53.9469			0.0474053			0.0237027	−	0.999719i	$-0.492455\pi$
$109$	53.9469			0.0474053			0.0237027	+	0.999719i	$0.492455\pi$
$110$	50.6465	−	287.231i	0.0438996	−	0.248967i
$111$		0			0
$112$	367.967	+	133.929i	0.310443	+	0.112992i
$113$	−72.9712	+	61.2301i	−0.0607482	+	0.0509738i	−0.672656	−	0.739955i	$-0.734847\pi$
$113$	−72.9712	+	61.2301i	−0.0607482	+	0.0509738i	0.611908	+	0.790929i	$0.290402\pi$
$114$		0			0
$115$	−627.051	+	228.228i	−0.508459	+	0.185064i
$116$	−242.388	+	419.829i	−0.194010	+	0.336035i
$117$		0			0
$118$	328.443	+	568.879i	0.256234	+	0.443810i
$119$	607.159	+	509.467i	0.467716	+	0.392460i
$120$		0			0
$121$	−50.9720	−	289.076i	−0.0382960	−	0.217187i
$122$	218.856	+	1241.19i	0.162412	+	0.921083i
$123$		0			0
$124$	−484.322	−	406.395i	−0.350753	−	0.294317i
$125$	−519.539	−	899.867i	−0.371752	−	0.643893i
$126$		0			0
$127$	−632.288	+	1095.16i	−0.441783	+	0.765191i	−0.997822	−	0.0659652i	$-0.978987\pi$
$127$	−632.288	+	1095.16i	−0.441783	+	0.765191i	0.556039	+	0.831157i	$0.312321\pi$
$128$	120.281	−	43.7786i	0.0830579	−	0.0302306i
$129$		0			0
$130$	30.4026	−	25.5108i	0.0205114	−	0.0172111i
$131$	723.495	+	263.331i	0.482534	+	0.175628i	0.571822	−	0.820378i	$-0.306237\pi$
$131$	723.495	+	263.331i	0.482534	+	0.175628i	−0.0892875	+	0.996006i	$0.528459\pi$
$132$		0			0
$133$	−533.898	+	3027.89i	−0.348082	+	1.97407i
$134$	1829.15			1.17922
$135$		0			0
$136$	259.081			0.163353
$137$	−393.297	+	2230.50i	−0.245268	+	1.39098i	0.574603	+	0.818433i	$0.305157\pi$
$137$	−393.297	+	2230.50i	−0.245268	+	1.39098i	−0.819870	+	0.572549i	$0.805954\pi$
$138$		0			0
$139$	−2322.51	−	845.323i	−1.41721	−	0.515823i	−0.483974	−	0.875083i	$-0.660807\pi$
$139$	−2322.51	−	845.323i	−1.41721	−	0.515823i	−0.933238	+	0.359260i	$0.883029\pi$
$140$	339.531	−	284.900i	0.204969	−	0.171989i
$141$		0			0
$142$	2009.67	−	731.459i	1.18766	−	0.432272i
$143$	−70.5864	+	122.259i	−0.0412778	+	0.0714953i
$144$		0			0
$145$	274.356	+	475.198i	0.157131	+	0.272159i
$146$	1137.88	+	954.797i	0.645013	+	0.541230i
$147$		0			0
$148$	210.205	+	1192.13i	0.116748	+	0.662113i
$149$	−185.816	−	1053.81i	−0.102165	−	0.579408i	−0.992315	−	0.123739i	$-0.960511\pi$
$149$	−185.816	−	1053.81i	−0.102165	−	0.579408i	0.890150	−	0.455668i	$-0.150600\pi$
$150$		0			0
$151$	−2272.45	−	1906.82i	−1.22470	−	1.02765i	−0.998565	−	0.0535492i	$-0.982947\pi$
$151$	−2272.45	−	1906.82i	−1.22470	−	1.02765i	−0.226135	−	0.974096i	$-0.572609\pi$
$152$	502.511	+	870.374i	0.268151	+	0.464452i
$153$		0			0
$154$	−788.296	+	1365.37i	−0.412485	+	0.714445i
$155$	−672.464	+	244.757i	−0.348475	+	0.126834i
$156$		0			0
$157$	−1105.94	+	927.990i	−0.562186	+	0.471730i	−0.879043	−	0.476743i	$-0.841817\pi$
$157$	−1105.94	+	927.990i	−0.562186	+	0.471730i	0.316856	+	0.948474i	$0.397373\pi$
$158$	−2043.88	−	743.910i	−1.02913	−	0.374571i
$159$		0			0
$160$	25.1584	−	142.680i	0.0124309	−	0.0704992i
$161$	3607.09			1.76571
$162$		0			0
$163$	1350.18			0.648800			0.324400	−	0.945920i	$-0.394838\pi$
$163$	1350.18			0.648800			0.324400	+	0.945920i	$0.394838\pi$
$164$	320.127	−	1815.53i	0.152425	−	0.864445i
$165$		0			0
$166$	1395.47	+	507.911i	0.652468	+	0.237479i
$167$	−178.160	+	149.494i	−0.0825536	+	0.0692707i	−0.683131	−	0.730296i	$-0.739382\pi$
$167$	−178.160	+	149.494i	−0.0825536	+	0.0692707i	0.600577	+	0.799567i	$0.294938\pi$
$168$		0			0
$169$	2046.45	−	744.848i	0.931476	−	0.339030i
$170$	146.625	−	253.962i	0.0661507	−	0.114576i
$171$		0			0
$172$	−316.424	−	548.063i	−0.140274	−	0.242962i
$173$	−411.450	−	345.248i	−0.180821	−	0.151727i	0.547885	−	0.836554i	$-0.315433\pi$
$173$	−411.450	−	345.248i	−0.180821	−	0.151727i	−0.728705	+	0.684827i	$0.759878\pi$
$174$		0			0
$175$	444.115	+	2518.70i	0.191839	+	1.08798i
$176$	89.4905	+	507.526i	0.0383273	+	0.217365i
$177$		0			0
$178$	−1801.70	−	1511.81i	−0.758671	−	0.636601i
$179$	−50.8575	−	88.0878i	−0.0212361	−	0.0367821i	0.855212	−	0.518278i	$-0.173427\pi$
$179$	−50.8575	−	88.0878i	−0.0212361	−	0.0367821i	−0.876448	+	0.481496i	$0.840094\pi$
$180$		0			0
$181$	1260.62	−	2183.46i	0.517687	−	0.896659i	−0.482102	−	0.876115i	$-0.660127\pi$
$181$	1260.62	−	2183.46i	0.517687	−	0.896659i	0.999789	−	0.0205445i	$-0.00653997\pi$
$182$	−201.597	+	73.3752i	−0.0821063	+	0.0298842i
$183$		0			0
$184$	903.230	−	757.900i	0.361886	−	0.303658i
$185$	1287.54	+	468.627i	0.511686	+	0.186239i
$186$		0			0
$187$	−181.135	+	1027.27i	−0.0708337	+	0.401718i
$188$	425.580			0.165099
$189$		0			0
$190$	1137.57			0.434358
$191$	−455.081	+	2580.89i	−0.172400	+	0.977732i	0.768701	+	0.639608i	$0.220903\pi$
$191$	−455.081	+	2580.89i	−0.172400	+	0.977732i	−0.941102	+	0.338124i	$0.890208\pi$
$192$		0			0
$193$	49.9936	+	18.1962i	0.0186457	+	0.00678647i	0.351326	−	0.936253i	$-0.385731\pi$
$193$	49.9936	+	18.1962i	0.0186457	+	0.00678647i	−0.332680	+	0.943040i	$0.607953\pi$
$194$	−752.814	+	631.686i	−0.278603	+	0.233775i
$195$		0			0
$196$	−962.137	+	350.189i	−0.350633	+	0.127620i
$197$	857.024	−	1484.41i	0.309951	−	0.536851i	−0.668400	−	0.743802i	$-0.733021\pi$
$197$	857.024	−	1484.41i	0.309951	−	0.536851i	0.978351	+	0.206950i	$0.0663539\pi$
$198$		0			0
$199$	−1420.08	−	2459.65i	−0.505863	−	0.876181i	−0.999977	−	0.00678367i	$-0.997841\pi$
$199$	−1420.08	−	2459.65i	−0.505863	−	0.876181i	0.494114	−	0.869397i	$-0.335493\pi$
$200$	640.421	+	537.377i	0.226423	+	0.189992i
$201$		0			0
$202$	143.711	+	815.026i	0.0500568	+	0.283886i
$203$	−515.056	−	2921.03i	−0.178078	−	1.00993i
$204$		0			0
$205$	−1598.48	−	1341.29i	−0.544600	−	0.456974i
$206$	293.757	+	508.803i	0.0993546	+	0.172087i
$207$		0			0
$208$	−35.0634	+	60.7317i	−0.0116885	+	0.0202451i
$209$	−3802.40	+	1383.96i	−1.25846	+	0.458041i
$210$		0			0
$211$	−1674.18	+	1404.80i	−0.546234	+	0.458345i	−0.873663	−	0.486531i	$-0.838262\pi$
$211$	−1674.18	+	1404.80i	−0.546234	+	0.458345i	0.327429	+	0.944876i	$0.393818\pi$
$212$	−343.335	−	124.964i	−0.111228	−	0.0404837i
$213$		0			0
$214$	629.630	−	3570.81i	0.201124	−	1.14063i
$215$	−716.312			−0.227219
$216$		0			0
$217$	3868.33			1.21013
$218$	−18.7356	+	106.255i	−0.00582080	+	0.0330114i
$219$		0			0
$220$	548.144	+	199.508i	0.167981	+	0.0611402i
$221$	−108.734	+	91.2384i	−0.0330960	+	0.0277709i
$222$		0			0
$223$	4505.42	−	1639.84i	1.35294	−	0.492430i	0.439076	−	0.898450i	$-0.355306\pi$
$223$	4505.42	−	1639.84i	1.35294	−	0.492430i	0.913864	+	0.406020i	$0.133084\pi$
$224$	−391.582	+	678.240i	−0.116802	+	0.202307i
$225$		0			0
$226$	−95.2571	−	164.990i	−0.0280372	−	0.0485619i
$227$	−3087.30	−	2590.55i	−0.902692	−	0.757448i	0.0680231	−	0.997684i	$-0.478331\pi$
$227$	−3087.30	−	2590.55i	−0.902692	−	0.757448i	−0.970715	+	0.240236i	$0.922775\pi$
$228$		0			0
$229$	44.9488	+	254.917i	0.0129707	+	0.0735608i	0.990606	−	0.136747i	$-0.0436646\pi$
$229$	44.9488	+	254.917i	0.0129707	+	0.0735608i	−0.977635	+	0.210307i	$0.932554\pi$
$230$	−231.749	−	1314.31i	−0.0664394	−	0.376796i
$231$		0			0
$232$	−742.720	−	623.216i	−0.210181	−	0.176363i
$233$	−1769.46	−	3064.79i	−0.497515	−	0.861721i	0.502481	−	0.864588i	$-0.332421\pi$
$233$	−1769.46	−	3064.79i	−0.497515	−	0.861721i	−0.999996	+	0.00286708i	$0.999087\pi$
$234$		0			0
$235$	240.854	−	417.171i	0.0668578	−	0.115801i
$236$	−1234.54	+	449.336i	−0.340516	+	0.123938i
$237$		0			0
$238$	−1214.32	+	1018.93i	−0.330725	+	0.277511i
$239$	−4652.33	−	1693.31i	−1.25914	−	0.458289i	−0.375659	−	0.926758i	$-0.622583\pi$
$239$	−4652.33	−	1693.31i	−1.25914	−	0.458289i	−0.883480	+	0.468469i	$0.844806\pi$
$240$		0			0
$241$	111.526	−	632.497i	0.0298093	−	0.169057i	−0.966269	−	0.257536i	$-0.917089\pi$
$241$	111.526	−	632.497i	0.0298093	−	0.169057i	0.996078	+	0.0884788i	$0.0282006\pi$
$242$	587.072			0.155944
$243$		0			0
$244$	−2520.68			−0.661352
$245$	−201.244	+	1141.31i	−0.0524777	+	0.297616i
$246$		0			0
$247$	−517.411	−	188.322i	−0.133288	−	0.0485128i
$248$	968.644	−	812.789i	0.248020	−	0.208114i
$249$		0			0
$250$	1952.83	−	710.771i	0.494030	−	0.179812i
$251$	3484.64	−	6035.57i	0.876288	−	1.51777i	0.0209032	−	0.999782i	$-0.493346\pi$
$251$	3484.64	−	6035.57i	0.876288	−	1.51777i	0.855385	−	0.517993i	$-0.173321\pi$
$252$		0			0
$253$	2373.62	+	4111.23i	0.589834	+	1.02162i
$254$	−1937.44	−	1625.71i	−0.478606	−	0.401598i
$255$		0			0
$256$	44.4539	+	252.111i	0.0108530	+	0.0615505i
$257$	237.378	+	1346.24i	0.0576158	+	0.326755i	0.999969	−	0.00786421i	$-0.00250328\pi$
$257$	237.378	+	1346.24i	0.0576158	+	0.326755i	−0.942353	+	0.334620i	$0.891392\pi$
$258$		0			0
$259$	−5673.75	−	4760.84i	−1.36119	−	1.14218i
$260$	39.6878	+	68.7413i	0.00946667	+	0.0163967i
$261$		0			0
$262$	−769.927	+	1333.55i	−0.181551	+	0.314455i
$263$	4898.27	−	1782.82i	1.14844	−	0.417999i	0.303487	−	0.952836i	$-0.401849\pi$
$263$	4898.27	−	1782.82i	1.14844	−	0.417999i	0.844955	+	0.534837i	$0.179627\pi$
$264$		0			0
$265$	−316.802	+	265.829i	−0.0734378	+	0.0616216i
$266$	−5778.35	−	2103.15i	−1.33193	−	0.484783i
$267$		0			0
$268$	−635.259	+	3602.73i	−0.144793	+	0.821164i
$269$	456.576			0.103487			0.0517433	−	0.998660i	$-0.483522\pi$
$269$	456.576			0.103487			0.0517433	+	0.998660i	$0.483522\pi$
$270$		0			0
$271$	−2314.46			−0.518795			−0.259397	−	0.965771i	$-0.583524\pi$
$271$	−2314.46			−0.518795			−0.259397	+	0.965771i	$0.583524\pi$
$272$	−89.9779	+	510.290i	−0.0200578	+	0.113753i
$273$		0			0
$274$	−4256.64	−	1549.29i	−0.938514	−	0.341591i
$275$	−2578.47	+	2163.60i	−0.565410	+	0.474435i
$276$		0			0
$277$	5578.74	−	2030.49i	1.21009	−	0.440435i	0.343352	−	0.939207i	$-0.388438\pi$
$277$	5578.74	−	2030.49i	1.21009	−	0.440435i	0.866733	+	0.498772i	$0.166215\pi$
$278$	2471.56	−	4280.87i	0.533217	−	0.923558i
$279$		0			0
$280$	443.226	+	767.690i	0.0945994	+	0.163851i
$281$	6130.68	+	5144.25i	1.30151	+	1.09210i	0.989881	+	0.141897i	$0.0453203\pi$
$281$	6130.68	+	5144.25i	1.30151	+	1.09210i	0.311633	+	0.950203i	$0.399124\pi$
$282$		0			0
$283$	−249.287	−	1413.78i	−0.0523625	−	0.296963i	0.947369	−	0.320144i	$-0.103731\pi$
$283$	−249.287	−	1413.78i	−0.0523625	−	0.296963i	−0.999731	+	0.0231818i	$0.992620\pi$
$284$	742.743	+	4212.31i	0.155189	+	0.880121i
$285$		0			0
$286$	−216.289	−	181.488i	−0.0447184	−	0.0375232i
$287$	5639.81	+	9768.44i	1.15996	+	2.00910i
$288$		0			0
$289$	1932.10	−	3346.50i	0.393263	−	0.681152i
$290$	−1031.24	+	375.341i	−0.208815	+	0.0760026i
$291$		0			0
$292$	−2275.77	+	1909.59i	−0.456093	+	0.382707i
$293$	6482.49	+	2359.43i	1.29253	+	0.470442i	0.894556	−	0.446955i	$-0.147492\pi$
$293$	6482.49	+	2359.43i	1.29253	+	0.470442i	0.397973	+	0.917397i	$0.369714\pi$
$294$		0			0
$295$	−258.222	+	1464.45i	−0.0509635	+	0.289028i
$296$	−2421.05			−0.475407
$297$		0			0
$298$	2140.14			0.416023
$299$	−112.173	+	636.166i	−0.0216961	+	0.123045i
$300$		0			0
$301$	3638.55	+	1324.32i	0.696753	+	0.253597i
$302$	4544.91	−	3813.63i	0.865994	−	0.726655i
$303$		0			0
$304$	−1888.82	+	687.475i	−0.356353	+	0.129702i
$305$	−1426.56	+	2470.87i	−0.267818	+	0.463875i
$306$		0			0
$307$	3133.51	+	5427.39i	0.582537	+	1.00898i	0.995178	+	0.0980892i	$0.0312730\pi$
$307$	3133.51	+	5427.39i	0.582537	+	1.00898i	−0.412641	+	0.910894i	$0.635394\pi$
$308$	−2415.48	−	2026.83i	−0.446866	−	0.374965i
$309$		0			0
$310$	−248.533	−	1409.50i	−0.0455345	−	0.258239i
$311$	−1170.33	−	6637.24i	−0.213386	−	1.21017i	−0.883685	−	0.468081i	$-0.844945\pi$
$311$	−1170.33	−	6637.24i	−0.213386	−	1.21017i	0.670299	−	0.742091i	$-0.266166\pi$
$312$		0			0
$313$	−1353.53	−	1135.75i	−0.244429	−	0.205100i	0.512340	−	0.858783i	$-0.328779\pi$
$313$	−1353.53	−	1135.75i	−0.244429	−	0.205100i	−0.756769	+	0.653683i	$0.773223\pi$
$314$	−1443.70	−	2500.55i	−0.259466	−	0.449409i
$315$		0			0
$316$	2175.05	−	3767.29i	0.387202	−	0.670654i
$317$	−1174.97	+	427.656i	−0.208180	+	0.0757714i	−0.444006	−	0.896024i	$-0.646443\pi$
$317$	−1174.97	+	427.656i	−0.208180	+	0.0757714i	0.235825	+	0.971795i	$0.424221\pi$
$318$		0			0
$319$	2990.35	−	2509.20i	0.524851	−	0.440402i
$320$	272.288	+	99.1047i	0.0475667	+	0.0173129i
$321$		0			0
$322$	−1252.73	+	7104.59i	−0.216807	+	1.22957i
$323$	−4068.47			−0.700853
$324$		0			0
$325$	−458.022			−0.0781738
$326$	−468.913	+	2659.34i	−0.0796648	+	0.451801i
$327$		0			0
$328$	3464.72	+	1261.05i	0.583253	+	0.212287i
$329$	−1994.70	+	1673.75i	−0.334260	+	0.280477i
$330$		0			0
$331$	−4395.80	+	1599.94i	−0.729955	+	0.265682i	−0.680146	−	0.733077i	$-0.738084\pi$
$331$	−4395.80	+	1599.94i	−0.729955	+	0.265682i	−0.0498094	+	0.998759i	$0.515861\pi$
$332$	−1485.03	+	2572.15i	−0.245487	+	0.425196i
$333$		0			0
$334$	−232.572	−	402.826i	−0.0381011	−	0.0659930i
$335$	3172.03	+	2661.65i	0.517333	+	0.434094i
$336$		0			0
$337$	−613.237	−	3477.84i	−0.0991251	−	0.562166i	−0.993405	−	0.114658i	$-0.963423\pi$
$337$	−613.237	−	3477.84i	−0.0991251	−	0.562166i	0.894280	−	0.447508i	$-0.147688\pi$
$338$	756.339	+	4289.41i	0.121714	+	0.690275i
$339$		0			0
$340$	449.285	+	376.995i	0.0716644	+	0.0601336i
$341$	2545.52	+	4408.97i	0.404246	+	0.700174i
$342$		0			0
$343$	−1064.97	+	1844.58i	−0.167647	+	0.290373i
$344$	1189.37	−	432.894i	0.186414	−	0.0678491i
$345$		0			0
$346$	822.901	−	690.496i	0.127860	−	0.107287i
$347$	5446.80	+	1982.47i	0.842649	+	0.306699i	0.727040	−	0.686595i	$-0.240896\pi$
$347$	5446.80	+	1982.47i	0.842649	+	0.306699i	0.115610	+	0.993295i	$0.463118\pi$
$348$		0			0
$349$	−1174.56	+	6661.27i	−0.180151	+	1.02169i	0.751877	+	0.659304i	$0.229149\pi$
$349$	−1174.56	+	6661.27i	−0.180151	+	1.02169i	−0.932028	+	0.362386i	$0.881962\pi$
$350$	−5115.11			−0.781183
$351$		0			0
$352$	−1030.71			−0.156071
$353$	1112.84	−	6311.21i	0.167791	−	0.951591i	−0.778349	−	0.627832i	$-0.783942\pi$
$353$	1112.84	−	6311.21i	0.167791	−	0.951591i	0.946140	−	0.323758i	$-0.104947\pi$
$354$		0			0
$355$	4549.43	+	1655.86i	0.680165	+	0.247560i
$356$	3603.41	−	3023.62i	0.536461	−	0.450145i
$357$		0			0
$358$	191.162	−	69.5772i	0.0282213	−	0.0102717i
$359$	−4273.15	+	7401.31i	−0.628212	+	1.08809i	0.359699	+	0.933069i	$0.382880\pi$
$359$	−4273.15	+	7401.31i	−0.628212	+	1.08809i	−0.987910	+	0.155026i	$0.950454\pi$
$360$		0			0
$361$	−4461.66	−	7727.82i	−0.650483	−	1.12667i
$362$	3862.77	+	3241.25i	0.560836	+	0.470597i
$363$		0			0
$364$	−74.5071	−	422.551i	−0.0107287	−	0.0608453i
$365$	583.911	+	3311.52i	0.0837350	+	0.474885i
$366$		0			0
$367$	3523.11	+	2956.24i	0.501103	+	0.420476i	0.857986	−	0.513674i	$-0.171716\pi$
$367$	3523.11	+	2956.24i	0.501103	+	0.420476i	−0.356882	+	0.934149i	$0.616160\pi$
$368$	1179.08	+	2042.23i	0.167022	+	0.289290i
$369$		0			0
$370$	−1370.17	+	2373.21i	−0.192519	+	0.333452i
$371$	2100.68	−	764.587i	0.293968	−	0.106996i
$372$		0			0
$373$	−3980.52	+	3340.05i	−0.552556	+	0.463650i	−0.875806	−	0.482664i	$-0.839669\pi$
$373$	−3980.52	+	3340.05i	−0.552556	+	0.463650i	0.323249	+	0.946314i	$0.395225\pi$
$374$	−1960.41	−	713.533i	−0.271044	−	0.0986521i
$375$		0			0
$376$	−147.802	+	838.229i	−0.0202721	+	0.114969i
$377$	531.185			0.0725661
$378$		0			0
$379$	−7624.79			−1.03340			−0.516701	−	0.856166i	$-0.672840\pi$
$379$	−7624.79			−1.03340			−0.516701	+	0.856166i	$0.672840\pi$
$380$	−395.074	+	2240.57i	−0.0533338	+	0.302471i
$381$		0			0
$382$	−4925.32	−	1792.67i	−0.659689	−	0.240107i
$383$	−1282.75	+	1076.35i	−0.171137	+	0.143601i	−0.724333	−	0.689450i	$-0.757852\pi$
$383$	−1282.75	+	1076.35i	−0.171137	+	0.143601i	0.553196	+	0.833051i	$0.313408\pi$
$384$		0			0
$385$	−3353.81	+	1220.69i	−0.443963	+	0.161589i
$386$	−53.2021	+	92.1487i	−0.00701532	+	0.0121509i
$387$		0			0
$388$	−982.729	−	1702.14i	−0.128584	−	0.222714i
$389$	−5619.41	−	4715.24i	−0.732430	−	0.614582i	0.198363	−	0.980129i	$-0.436438\pi$
$389$	−5619.41	−	4715.24i	−0.732430	−	0.614582i	−0.930793	+	0.365547i	$0.880882\pi$
$390$		0			0
$391$	828.839	+	4700.58i	0.107203	+	0.607976i
$392$	−355.591	−	2016.66i	−0.0458165	−	0.259838i
$393$		0			0
$394$	2626.07	+	2203.54i	0.335786	+	0.281758i
$395$	−2461.90	−	4264.14i	−0.313600	−	0.543170i
$396$		0			0
$397$	−3345.27	+	5794.18i	−0.422907	+	0.732497i	−0.996222	−	0.0868378i	$-0.972324\pi$
$397$	−3345.27	+	5794.18i	−0.422907	+	0.732497i	0.573315	+	0.819335i	$0.305657\pi$
$398$	5337.75	−	1942.78i	0.672255	−	0.244681i
$399$		0			0
$400$	−1280.84	+	1074.75i	−0.160105	+	0.134344i
$401$	2511.22	+	914.011i	0.312730	+	0.113824i	0.493617	−	0.869680i	$-0.335675\pi$
$401$	2511.22	+	914.011i	0.312730	+	0.113824i	−0.180887	+	0.983504i	$0.557897\pi$
$402$		0			0
$403$	−120.297	+	682.239i	−0.0148695	+	0.0843294i
$404$	−1655.20			−0.203835
$405$		0			0
$406$	5932.18			0.725146
$407$	1692.66	−	9599.55i	0.206148	−	1.16912i
$408$		0			0
$409$	−9133.07	−	3324.16i	−1.10416	−	0.401881i	−0.275311	−	0.961355i	$-0.588781\pi$
$409$	−9133.07	−	3324.16i	−1.10416	−	0.401881i	−0.828848	+	0.559474i	$0.811003\pi$
$410$	3196.97	−	2682.58i	0.385090	−	0.323129i
$411$		0			0
$412$	−1104.17	+	401.884i	−0.132035	+	0.0480568i
$413$	4019.13	−	6961.35i	0.478859	−	0.829408i
$414$		0			0
$415$	1680.89	+	2911.38i	0.198823	+	0.344371i
$416$	−107.441	−	90.1534i	−0.0126628	−	0.0106253i
$417$		0			0
$418$	−1405.31	−	7969.91i	−0.164440	−	0.932586i
$419$	−1570.68	−	8907.75i	−0.183133	−	1.03860i	−0.928331	−	0.371754i	$-0.878756\pi$
$419$	−1570.68	−	8907.75i	−0.183133	−	1.03860i	0.745199	−	0.666843i	$-0.232355\pi$
$420$		0			0
$421$	10508.0	+	8817.25i	1.21646	+	1.02073i	0.999002	+	0.0446579i	$0.0142198\pi$
$421$	10508.0	+	8817.25i	1.21646	+	1.02073i	0.217454	+	0.976070i	$0.430225\pi$
$422$	−2185.49	−	3785.38i	−0.252104	−	0.436657i
$423$		0			0
$424$	365.369	−	632.838i	0.0418488	−	0.0724843i
$425$	−3180.19	+	1157.50i	−0.362969	+	0.132110i
$426$		0			0
$427$	11814.5	−	9913.52i	1.33897	−	1.12353i
$428$	6814.45	+	2480.26i	0.769600	+	0.280112i
$429$		0			0
$430$	248.773	−	1410.86i	0.0278997	−	0.158227i
$431$	−10042.6			−1.12235			−0.561175	−	0.827697i	$-0.689651\pi$
$431$	−10042.6			−1.12235			−0.561175	+	0.827697i	$0.689651\pi$
$432$		0			0
$433$	−4558.11			−0.505886			−0.252943	−	0.967481i	$-0.581399\pi$
$433$	−4558.11			−0.505886			−0.252943	+	0.967481i	$0.581399\pi$
$434$	−1343.46	+	7619.12i	−0.148590	+	0.842695i
$435$		0			0
$436$	−202.774	−	73.8038i	−0.0222732	−	0.00810679i
$437$	−14183.8	+	11901.7i	−1.55264	+	1.30282i
$438$		0			0
$439$	2506.94	−	912.450i	0.272550	−	0.0992001i	−0.202129	−	0.979359i	$-0.564786\pi$
$439$	2506.94	−	912.450i	0.272550	−	0.0992001i	0.474680	+	0.880159i	$0.342564\pi$
$440$	−583.323	+	1010.35i	−0.0632019	+	0.109469i
$441$		0			0
$442$	−141.942	−	245.850i	−0.0152748	−	0.0264568i
$443$	−508.935	−	427.047i	−0.0545829	−	0.0458005i	0.615088	−	0.788458i	$-0.289120\pi$
$443$	−508.935	−	427.047i	−0.0545829	−	0.0458005i	−0.669671	+	0.742658i	$0.733565\pi$
$444$		0			0
$445$	−924.554	−	5243.41i	−0.0984900	−	0.558565i
$446$	1665.14	+	9443.47i	0.176786	+	1.00260i
$447$		0			0
$448$	−1199.88	−	1006.82i	−0.126538	−	0.106178i
$449$	−1869.94	−	3238.83i	−0.196543	−	0.340423i	0.750862	−	0.660459i	$-0.229638\pi$
$449$	−1869.94	−	3238.83i	−0.196543	−	0.340423i	−0.947405	+	0.320036i	$0.896305\pi$
$450$		0			0
$451$	−7422.47	+	12856.1i	−0.774968	+	1.34228i
$452$	358.050	−	130.319i	0.0372594	−	0.0135613i
$453$		0			0
$454$	6174.59	−	5181.10i	0.638299	−	0.535597i
$455$	−456.369	−	166.105i	−0.0470218	−	0.0171145i
$456$		0			0
$457$	1303.14	−	7390.49i	0.133388	−	0.756483i	−0.842580	−	0.538571i	$-0.818964\pi$
$457$	1303.14	−	7390.49i	0.133388	−	0.756483i	0.975968	−	0.217912i	$-0.0699246\pi$
$458$	−517.700			−0.0528177
$459$		0			0
$460$	2669.17			0.270545
$461$	2838.76	−	16099.4i	0.286799	−	1.62652i	−0.411990	−	0.911188i	$-0.635166\pi$
$461$	2838.76	−	16099.4i	0.286799	−	1.62652i	0.698789	−	0.715328i	$-0.253723\pi$
$462$		0			0
$463$	17419.3	+	6340.11i	1.74847	+	0.636393i	0.999652	−	0.0263781i	$-0.00839739\pi$
$463$	17419.3	+	6340.11i	1.74847	+	0.636393i	0.748822	+	0.662771i	$0.230620\pi$
$464$	1485.44	−	1246.43i	0.148620	−	0.124707i
$465$		0			0
$466$	6650.98	−	2420.76i	0.661161	−	0.240643i
$467$	−3399.79	+	5888.61i	−0.336881	+	0.583495i	−0.983844	−	0.179026i	$-0.942705\pi$
$467$	−3399.79	+	5888.61i	−0.336881	+	0.583495i	0.646963	+	0.762521i	$0.276039\pi$
$468$		0			0
$469$	−11191.6	−	19384.5i	−1.10188	−	1.90851i
$470$	738.019	+	619.271i	0.0724304	+	0.0607763i
$471$		0			0
$472$	−456.268	−	2587.62i	−0.0444946	−	0.252341i
$473$	884.905	+	5018.54i	0.0860211	+	0.487850i
$474$		0			0
$475$	−10056.8	−	8438.69i	−0.971451	−	0.815144i
$476$	−1585.18	−	2745.61i	−0.152640	−	0.264380i
$477$		0			0
$478$	4950.90	−	8575.22i	0.473743	−	0.820547i
$479$	8298.03	−	3020.24i	0.791538	−	0.288096i	0.0855629	−	0.996333i	$-0.472731\pi$
$479$	8298.03	−	3020.24i	0.791538	−	0.288096i	0.705975	+	0.708236i	$0.250509\pi$
$480$		0			0
$481$	1016.09	−	852.599i	0.0963194	−	0.0808216i
$482$	1207.04	+	439.328i	0.114065	+	0.0415163i
$483$		0			0
$484$	−203.888	+	1156.31i	−0.0191480	+	0.108594i
$485$	−2224.67			−0.208283
$486$		0			0
$487$	1131.64			0.105297			0.0526485	−	0.998613i	$-0.483234\pi$
$487$	1131.64			0.105297			0.0526485	+	0.998613i	$0.483234\pi$
$488$	875.422	−	4964.76i	0.0812059	−	0.460542i
$489$		0			0
$490$	−2178.06	−	792.748i	−0.200805	−	0.0730872i
$491$	633.891	−	531.897i	0.0582629	−	0.0488884i	−0.613191	−	0.789935i	$-0.710114\pi$
$491$	633.891	−	531.897i	0.0582629	−	0.0488884i	0.671454	+	0.741046i	$0.265670\pi$
$492$		0			0
$493$	3688.18	−	1342.39i	0.336932	−	0.122633i
$494$	550.617	−	953.697i	0.0501487	−	0.0868601i
$495$		0			0
$496$	1264.48	+	2190.14i	0.114469	+	0.198266i
$497$	−20047.7	−	16822.0i	−1.80938	−	1.51825i
$498$		0			0
$499$	−1137.44	−	6450.75i	−0.102042	−	0.578708i	−0.992361	−	0.123371i	$-0.960630\pi$
$499$	−1137.44	−	6450.75i	−0.102042	−	0.578708i	0.890319	−	0.455338i	$-0.150481\pi$
$500$	721.735	+	4093.17i	0.0645540	+	0.366104i
$501$		0			0
$502$	10677.5	+	8959.52i	0.949327	+	0.796580i
$503$	3035.09	+	5256.94i	0.269042	+	0.465995i	0.968615	−	0.248567i	$-0.0799596\pi$
$503$	3035.09	+	5256.94i	0.269042	+	0.465995i	−0.699573	+	0.714561i	$0.746626\pi$
$504$		0			0
$505$	−936.748	+	1622.49i	−0.0825440	+	0.142970i
$506$	−8921.89	+	3247.30i	−0.783846	+	0.285297i
$507$		0			0
$508$	3874.89	−	3251.42i	0.338426	−	0.283973i
$509$	6484.86	+	2360.30i	0.564708	+	0.205537i	0.608569	−	0.793501i	$-0.291744\pi$
$509$	6484.86	+	2360.30i	0.564708	+	0.205537i	−0.0438614	+	0.999038i	$0.513966\pi$
$510$		0			0
$511$	3156.36	−	17900.6i	0.273247	−	1.54966i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−2734.02			−0.234615
$515$	−230.952	+	1309.79i	−0.0197611	+	0.112071i
$516$		0			0
$517$	−3220.28	−	1172.09i	−0.273941	−	0.0997065i
$518$	11347.5	−	9521.68i	0.962510	−	0.807642i
$519$		0			0
$520$	−149.177	+	54.2961i	−0.0125805	+	0.00457893i
$521$	2702.42	−	4680.73i	0.227246	−	0.393602i	−0.729745	−	0.683720i	$-0.760361\pi$
$521$	2702.42	−	4680.73i	0.227246	−	0.393602i	0.956991	+	0.290118i	$0.0936944\pi$
$522$		0			0
$523$	928.208	+	1607.70i	0.0776056	+	0.134417i	0.902216	−	0.431284i	$-0.141939\pi$
$523$	928.208	+	1607.70i	0.0776056	+	0.134417i	−0.824611	+	0.565700i	$0.808606\pi$
$524$	−2359.19	−	1979.60i	−0.196683	−	0.165037i
$525$		0			0
$526$	1810.33	+	10266.9i	0.150065	+	0.851059i
$527$	888.866	+	5041.01i	0.0734717	+	0.416679i
$528$		0			0
$529$	7319.90	+	6142.12i	0.601619	+	0.504818i
$530$	−413.556	−	716.300i	−0.0338938	−	0.0587059i
$531$		0			0
$532$	6149.20	−	10650.7i	0.501131	−	0.867984i
$533$	−1898.20	+	690.889i	−0.154259	+	0.0561458i
$534$		0			0
$535$	6287.84	−	5276.12i	0.508125	−	0.426368i
$536$	−6875.37	−	2502.43i	−0.554050	−	0.201658i
$537$		0			0
$538$	−158.567	+	899.279i	−0.0127069	+	0.0720644i
$539$	8244.75			0.658862
$540$		0			0
$541$	−10652.7			−0.846575			−0.423288	−	0.905995i	$-0.639124\pi$
$541$	−10652.7			−0.846575			−0.423288	+	0.905995i	$0.639124\pi$
$542$	803.804	−	4558.60i	0.0637017	−	0.361270i
$543$		0			0
$544$	−973.826	−	354.444i	−0.0767508	−	0.0279350i
$545$	−187.104	+	156.999i	−0.0147058	+	0.0123396i
$546$		0			0
$547$	−15471.6	+	5631.18i	−1.20935	+	0.440168i	−0.866479	−	0.499213i	$-0.833622\pi$
$547$	−15471.6	+	5631.18i	−1.20935	+	0.440168i	−0.342873	+	0.939382i	$0.611400\pi$
$548$	4529.82	−	7845.88i	0.353110	−	0.611604i
$549$		0			0
$550$	−3365.96	−	5830.01i	−0.260954	−	0.451986i
$551$	11663.3	+	9786.65i	0.901765	+	0.756671i
$552$		0			0
$553$	4621.81	+	26211.6i	0.355405	+	2.01560i
$554$	2061.82	+	11693.1i	0.158120	+	0.896740i
$555$		0			0
$556$	7573.30	+	6354.75i	0.577661	+	0.484715i
$557$	−1388.77	−	2405.43i	−0.105645	−	0.182982i	0.808357	−	0.588693i	$-0.200357\pi$
$557$	−1388.77	−	2405.43i	−0.105645	−	0.182982i	−0.914002	+	0.405711i	$0.867024\pi$
$558$		0			0
$559$	−346.716	+	600.530i	−0.0262335	+	0.0454378i
$560$	−1665.99	+	606.369i	−0.125716	+	0.0457567i
$561$		0			0
$562$	−12261.4	+	10288.5i	−0.920309	+	0.772231i
$563$	−933.067	−	339.608i	−0.0698474	−	0.0254224i	0.306860	−	0.951755i	$-0.400722\pi$
$563$	−933.067	−	339.608i	−0.0698474	−	0.0254224i	−0.376708	+	0.926332i	$0.622944\pi$
$564$		0			0
$565$	74.8911	−	424.729i	0.00557645	−	0.0316256i
$566$	2871.18			0.213224
$567$		0			0
$568$	−8554.57			−0.631940
$569$	−2471.04	+	14014.0i	−0.182059	+	1.03251i	0.747617	+	0.664130i	$0.231198\pi$
$569$	−2471.04	+	14014.0i	−0.182059	+	1.03251i	−0.929676	+	0.368378i	$0.879913\pi$
$570$		0			0
$571$	−4489.20	−	1633.93i	−0.329014	−	0.119751i	0.172231	−	0.985057i	$-0.444902\pi$
$571$	−4489.20	−	1633.93i	−0.329014	−	0.119751i	−0.501245	+	0.865305i	$0.667125\pi$
$572$	432.579	−	362.977i	0.0316207	−	0.0265329i
$573$		0			0
$574$	−21198.8	+	7715.72i	−1.54150	+	0.561059i
$575$	−7700.99	+	13338.5i	−0.558527	+	0.967398i
$576$		0			0
$577$	8181.08	+	14170.0i	0.590265	+	1.02237i	0.994197	+	0.107579i	$0.0343099\pi$
$577$	8181.08	+	14170.0i	0.590265	+	1.02237i	−0.403932	+	0.914789i	$0.632357\pi$
$578$	5920.30	+	4967.72i	0.426042	+	0.357492i
$579$		0			0
$580$	−381.131	−	2161.50i	−0.0272855	−	0.154744i
$581$	−3155.58	−	17896.2i	−0.225328	−	1.27790i
$582$		0			0
$583$	2253.79	+	1891.15i	0.160107	+	0.134346i
$584$	−2970.80	−	5145.58i	−0.210501	−	0.364599i
$585$		0			0
$586$	−6898.52	+	11948.6i	−0.486306	+	0.842307i
$587$	10734.1	−	3906.91i	0.754762	−	0.274711i	0.0641541	−	0.997940i	$-0.479565\pi$
$587$	10734.1	−	3906.91i	0.754762	−	0.274711i	0.690608	+	0.723229i	$0.257343\pi$
$588$		0			0
$589$	−15211.1	+	12763.6i	−1.06411	+	0.892895i
$590$	−2794.72	−	1017.19i	−0.195011	−	0.0709783i
$591$		0			0
$592$	840.820	−	4768.53i	0.0583742	−	0.331056i
$593$	20596.0			1.42627			0.713133	−	0.701029i	$-0.247275\pi$
$593$	20596.0			1.42627			0.713133	+	0.701029i	$0.247275\pi$
$594$		0			0
$595$	−3588.48			−0.247250
$596$	−743.263	+	4215.25i	−0.0510826	+	0.289704i
$597$		0			0
$598$	−1214.04	−	441.876i	−0.0830200	−	0.0302168i
$599$	−8207.24	+	6886.70i	−0.559831	+	0.469754i	−0.878254	−	0.478195i	$-0.841291\pi$
$599$	−8207.24	+	6886.70i	−0.559831	+	0.469754i	0.318423	+	0.947949i	$0.396847\pi$
$600$		0			0
$601$	−6945.97	+	2528.13i	−0.471434	+	0.171588i	−0.566802	−	0.823854i	$-0.691820\pi$
$601$	−6945.97	+	2528.13i	−0.471434	+	0.171588i	0.0953676	+	0.995442i	$0.469597\pi$
$602$	−3872.07	+	6706.61i	−0.262149	+	0.454055i
$603$		0			0
$604$	5932.96	+	10276.2i	0.399683	+	0.692271i
$605$	1018.07	+	854.262i	0.0684139	+	0.0574061i
$606$		0			0
$607$	697.910	+	3958.04i	0.0466677	+	0.264666i	0.999210	−	0.0397405i	$-0.0126531\pi$
$607$	697.910	+	3958.04i	0.0466677	+	0.264666i	−0.952542	+	0.304406i	$0.901542\pi$
$608$	−698.081	−	3959.01i	−0.0465640	−	0.264078i
$609$		0			0
$610$	−4371.23	−	3667.90i	−0.290141	−	0.243457i
$611$	−233.161	−	403.846i	−0.0154381	−	0.0267396i
$612$		0			0
$613$	7422.64	−	12856.4i	0.489067	−	0.847088i	−0.510854	−	0.859667i	$-0.670671\pi$
$613$	7422.64	−	12856.4i	0.489067	−	0.847088i	0.999921	+	0.0125792i	$0.00400420\pi$
$614$	−11778.1	+	4286.89i	−0.774148	+	0.281767i
$615$		0			0
$616$	4830.96	−	4053.66i	0.315982	−	0.265140i
$617$	−10394.6	−	3783.32i	−0.678233	−	0.246857i	−0.0201444	−	0.999797i	$-0.506413\pi$
$617$	−10394.6	−	3783.32i	−0.678233	−	0.246857i	−0.658089	+	0.752940i	$0.728635\pi$
$618$		0			0
$619$	3080.61	−	17471.0i	0.200033	−	1.13444i	−0.705035	−	0.709173i	$-0.749069\pi$
$619$	3080.61	−	17471.0i	0.200033	−	1.13444i	0.905067	−	0.425268i	$-0.139820\pi$
$620$	2862.48			0.185420
$621$		0			0
$622$	13479.3			0.868922
$623$	−4997.73	+	28343.5i	−0.321396	+	1.82273i
$624$		0			0
$625$	−7854.14	−	2858.67i	−0.502665	−	0.182955i
$626$	2707.07	−	2271.50i	0.172837	−	0.145028i
$627$		0			0
$628$	5426.52	−	1975.09i	0.344812	−	0.125501i
$629$	4900.37	−	8487.68i	0.310637	−	0.538038i
$630$		0			0
$631$	13379.2	+	23173.4i	0.844085	+	1.46200i	0.886414	+	0.462894i	$0.153189\pi$
$631$	13379.2	+	23173.4i	0.844085	+	1.46200i	−0.0423292	+	0.999104i	$0.513478\pi$
$632$	6664.73	+	5592.37i	0.419476	+	0.351982i
$633$		0			0
$634$	−434.253	−	2462.77i	−0.0272025	−	0.154273i
$635$	−994.209	−	5638.44i	−0.0621323	−	0.352370i
$636$		0			0
$637$	859.428	+	721.146i	0.0534565	+	0.0448553i
$638$	3903.62	+	6761.27i	0.242235	+	0.419563i
$639$		0			0
$640$	−289.763	+	501.884i	−0.0178967	+	0.0309980i
$641$	−9643.77	+	3510.05i	−0.594237	+	0.216285i	−0.621592	−	0.783341i	$-0.713514\pi$
$641$	−9643.77	+	3510.05i	−0.594237	+	0.216285i	0.0273547	+	0.999626i	$0.491292\pi$
$642$		0			0
$643$	−1883.60	+	1580.53i	−0.115524	+	0.0969362i	−0.698720	−	0.715396i	$-0.746247\pi$
$643$	−1883.60	+	1580.53i	−0.115524	+	0.0969362i	0.583196	+	0.812332i	$0.301802\pi$
$644$	−13558.2	−	4934.79i	−0.829611	−	0.301954i
$645$		0			0
$646$	1412.96	−	8013.32i	0.0860563	−	0.488049i
$647$	17675.5			1.07403			0.537014	−	0.843573i	$-0.319552\pi$
$647$	17675.5			1.07403			0.537014	+	0.843573i	$0.319552\pi$
$648$		0			0
$649$	10579.0			0.639851
$650$	159.069	−	902.128i	0.00959879	−	0.0544375i
$651$		0			0
$652$	−5075.03	−	1847.16i	−0.304836	−	0.110951i
$653$	−4213.50	+	3535.55i	−0.252507	+	0.211879i	−0.760251	−	0.649629i	$-0.774924\pi$
$653$	−4213.50	+	3535.55i	−0.252507	+	0.211879i	0.507744	+	0.861508i	$0.330480\pi$
$654$		0			0
$655$	−3275.65	+	1192.24i	−0.195405	+	0.0711216i
$656$	−3687.07	+	6386.20i	−0.219445	+	0.380090i
$657$		0			0
$658$	−2603.90	−	4510.08i	−0.154271	−	0.267206i
$659$	4006.45	+	3361.81i	0.236827	+	0.198722i	0.753475	−	0.657476i	$-0.228376\pi$
$659$	4006.45	+	3361.81i	0.236827	+	0.198722i	−0.516648	+	0.856198i	$0.672820\pi$
$660$		0			0
$661$	−1515.62	−	8595.52i	−0.0891844	−	0.505790i	−0.996375	−	0.0850699i	$-0.972889\pi$
$661$	−1515.62	−	8595.52i	−0.0891844	−	0.505790i	0.907191	−	0.420720i	$-0.138222\pi$
$662$	−1624.62	−	9213.70i	−0.0953818	−	0.540937i
$663$		0			0
$664$	−4550.40	−	3818.24i	−0.265949	−	0.223157i
$665$	−6960.19	−	12055.4i	−0.405871	−	0.702990i
$666$		0			0
$667$	8931.12	−	15469.1i	0.518462	−	0.898003i
$668$	874.184	−	318.177i	0.0506335	−	0.0184291i
$669$		0			0
$670$	−6344.06	+	5323.30i	−0.365809	+	0.306950i
$671$	19073.5	+	6942.17i	1.09735	+	0.399403i
$672$		0			0
$673$	−1840.83	+	10439.8i	−0.105436	+	0.597959i	0.885609	+	0.464432i	$0.153741\pi$
$673$	−1840.83	+	10439.8i	−0.105436	+	0.597959i	−0.991045	+	0.133527i	$0.957370\pi$
$674$	7062.98			0.403644
$675$		0			0
$676$	−8711.16			−0.495628
$677$	531.290	−	3013.10i	0.0301612	−	0.171053i	−0.966006	−	0.258518i	$-0.916766\pi$
$677$	531.290	−	3013.10i	0.0301612	−	0.171053i	0.996168	+	0.0874657i	$0.0278768\pi$
$678$		0			0
$679$	11300.4	+	4113.00i	0.638687	+	0.232463i
$680$	−898.570	+	753.990i	−0.0506744	+	0.0425209i
$681$		0			0
$682$	−9568.04	+	3482.48i	−0.537213	+	0.195529i
$683$	−11386.6	+	19722.1i	−0.637913	+	1.10490i	0.347977	+	0.937503i	$0.386869\pi$
$683$	−11386.6	+	19722.1i	−0.637913	+	1.10490i	−0.985890	+	0.167394i	$0.946465\pi$
$684$		0			0
$685$	−5127.24	−	8880.64i	−0.285988	−	0.495345i
$686$	−3263.25	−	2738.19i	−0.181620	−	0.152397i
$687$		0			0
$688$	439.572	+	2492.94i	0.0243583	+	0.138143i
$689$	69.5195	+	394.265i	0.00384395	+	0.0218001i
$690$		0			0
$691$	19974.4	+	16760.5i	1.09965	+	0.922719i	0.997402	−	0.0720392i	$-0.0229507\pi$
$691$	19974.4	+	16760.5i	1.09965	+	0.922719i	0.102252	+	0.994759i	$0.467395\pi$
$692$	1074.22	+	1860.60i	0.0590112	+	0.102210i
$693$		0			0
$694$	−5796.36	+	10039.6i	−0.317041	+	0.549132i
$695$	10515.2	−	3827.24i	0.573908	−	0.208885i
$696$		0			0
$697$	−11433.8	+	9594.11i	−0.621358	+	0.521382i
$698$	−12712.2	−	4626.87i	−0.689348	−	0.250902i
$699$		0			0
$700$	1776.46	−	10074.8i	0.0959197	−	0.543988i
$701$	905.740			0.0488008			0.0244004	−	0.999702i	$-0.492232\pi$
$701$	905.740			0.0488008			0.0244004	+	0.999702i	$0.492232\pi$
$702$		0			0
$703$	38018.8			2.03970
$704$	357.962	−	2030.10i	0.0191636	−	0.108682i
$705$		0			0
$706$	12044.2	+	4383.72i	0.642051	+	0.233687i
$707$	7757.95	−	6509.69i	0.412684	−	0.346283i
$708$		0			0
$709$	−25215.2	+	9177.59i	−1.33565	+	0.486138i	−0.908440	−	0.418014i	$-0.862726\pi$
$709$	−25215.2	+	9177.59i	−1.33565	+	0.486138i	−0.427211	+	0.904152i	$0.640504\pi$
$710$	−4841.40	+	8385.55i	−0.255908	+	0.443245i
$711$		0			0
$712$	4703.92	+	8147.42i	0.247594	+	0.428845i
$713$	17845.5	+	14974.2i	0.937334	+	0.786517i
$714$		0			0
$715$	−110.990	−	629.456i	−0.00580530	−	0.0329235i
$716$	70.6505	+	400.679i	0.00368762	+	0.0209135i
$717$		0			0
$718$	−13093.7	−	10986.9i	−0.680573	−	0.571069i
$719$	2729.84	+	4728.21i	0.141593	+	0.245247i	0.928097	−	0.372339i	$-0.121444\pi$
$719$	2729.84	+	4728.21i	0.141593	+	0.245247i	−0.786503	+	0.617586i	$0.788111\pi$
$720$		0			0
$721$	3594.69	−	6226.19i	0.185677	−	0.321603i
$722$	16770.4	−	6103.91i	0.864443	−	0.314632i
$723$		0			0
$724$	−7725.54	+	6482.49i	−0.396571	+	0.332762i
$725$	11901.2	+	4331.67i	0.609652	+	0.221895i
$726$		0			0
$727$	4263.43	−	24179.1i	0.217499	−	1.23350i	−0.659018	−	0.752127i	$-0.729028\pi$
$727$	4263.43	−	24179.1i	0.217499	−	1.23350i	0.876517	−	0.481371i	$-0.159861\pi$
$728$	858.139			0.0436878
$729$		0			0
$730$	−6725.21			−0.340974
$731$	−889.725	+	5045.88i	−0.0450173	+	0.255306i
$732$		0			0
$733$	−11925.8	−	4340.63i	−0.600939	−	0.218724i	0.0235948	−	0.999722i	$-0.492489\pi$
$733$	−11925.8	−	4340.63i	−0.600939	−	0.218724i	−0.624534	+	0.780998i	$0.714711\pi$
$734$	−7046.22	+	5912.48i	−0.354333	+	0.297321i
$735$		0			0
$736$	−4431.90	+	1613.08i	−0.221959	+	0.0807866i
$737$	14729.1	−	25511.6i	0.736166	−	1.27508i
$738$		0			0
$739$	−6519.26	−	11291.7i	−0.324513	−	0.562073i	0.656901	−	0.753977i	$-0.271867\pi$
$739$	−6519.26	−	11291.7i	−0.324513	−	0.562073i	−0.981414	+	0.191904i	$0.938534\pi$
$740$	−4198.45	−	3522.92i	−0.208565	−	0.175007i
$741$		0			0
$742$	776.381	+	4403.08i	0.0384122	+	0.217846i
$743$	−1812.91	−	10281.5i	−0.0895142	−	0.507660i	−0.996291	−	0.0860490i	$-0.972576\pi$
$743$	−1812.91	−	10281.5i	−0.0895142	−	0.507660i	0.906777	−	0.421611i	$-0.138535\pi$
$744$		0			0
$745$	3711.32	+	3114.17i	0.182513	+	0.153147i
$746$	−5196.20	−	9000.08i	−0.255022	−	0.441711i
$747$		0			0
$748$	2086.23	−	3613.46i	0.101979	−	0.176632i
$749$	−41694.0	+	15175.4i	−2.03400	+	0.740315i
$750$		0			0
$751$	11830.6	−	9927.05i	0.574840	−	0.482348i	−0.308408	−	0.951254i	$-0.599796\pi$
$751$	11830.6	−	9927.05i	0.574840	−	0.482348i	0.883248	+	0.468906i	$0.155352\pi$
$752$	−1599.66	−	582.227i	−0.0775711	−	0.0282336i
$753$		0			0
$754$	−184.479	+	1046.23i	−0.00891023	+	0.0505324i
$755$	13430.9			0.647416
$756$		0			0
$757$	31943.3			1.53368			0.766841	−	0.641837i	$-0.221827\pi$
$757$	31943.3			1.53368			0.766841	+	0.641837i	$0.221827\pi$
$758$	2648.06	−	15017.9i	0.126889	−	0.719624i
$759$		0			0
$760$	−4275.86	−	1556.29i	−0.204081	−	0.0742796i
$761$	30790.5	−	25836.3i	1.46670	−	1.23070i	0.547559	−	0.836767i	$-0.315557\pi$
$761$	30790.5	−	25836.3i	1.46670	−	1.23070i	0.919137	−	0.393937i	$-0.128887\pi$
$762$		0			0
$763$	1240.67	−	451.566i	0.0588666	−	0.0214257i
$764$	5241.41	−	9078.39i	0.248204	−	0.429901i
$765$		0			0
$766$	−1674.51	−	2900.34i	−0.0789850	−	0.136806i
$767$	1102.75	+	925.319i	0.0519141	+	0.0435611i
$768$		0			0
$769$	−4325.81	−	24532.9i	−0.202851	−	1.15043i	−0.900785	−	0.434265i	$-0.857008\pi$
$769$	−4325.81	−	24532.9i	−0.202851	−	1.15043i	0.697934	−	0.716162i	$-0.254103\pi$
$770$	−1239.52	−	7029.65i	−0.0580118	−	0.329001i
$771$		0			0
$772$	−163.021	−	136.790i	−0.00760005	−	0.00637720i
$773$	1510.02	+	2615.44i	0.0702611	+	0.121696i	0.899016	−	0.437916i	$-0.144283\pi$
$773$	1510.02	+	2615.44i	0.0702611	+	0.121696i	−0.828755	+	0.559612i	$0.810950\pi$
$774$		0			0
$775$	−8258.71	+	14304.5i	−0.382789	+	0.663011i
$776$	3693.85	−	1344.45i	0.170878	−	0.0621947i
$777$		0			0
$778$	11238.8	−	9430.49i	0.517906	−	0.434575i
$779$	−54408.0	−	19802.9i	−2.50240	−	0.910799i
$780$		0			0
$781$	5980.88	−	33919.3i	0.274024	−	1.55407i
$782$	−9546.19			−0.436536
$783$		0			0
$784$	4095.54			0.186568
$785$	1135.03	−	6437.09i	0.0516064	−	0.292675i
$786$		0			0
$787$	−15245.5	−	5548.90i	−0.690524	−	0.251330i	−0.0271647	−	0.999631i	$-0.508648\pi$
$787$	−15245.5	−	5548.90i	−0.690524	−	0.251330i	−0.663360	+	0.748301i	$0.730870\pi$
$788$	−5252.15	+	4407.07i	−0.237437	+	0.199233i
$789$		0			0
$790$	9253.73	−	3368.08i	0.416751	−	0.151685i
$791$	−1165.66	+	2018.98i	−0.0523969	+	0.0907541i
$792$		0			0
$793$	1380.99	+	2391.95i	0.0618418	+	0.107113i
$794$	−10250.5	−	8601.19i	−0.458157	−	0.384439i
$795$		0			0
$796$	1972.75	+	11188.0i	0.0878422	+	0.498178i
$797$	1962.09	+	11127.6i	0.0872029	+	0.494552i	0.996859	+	0.0791911i	$0.0252337\pi$
$797$	1962.09	+	11127.6i	0.0872029	+	0.494552i	−0.909657	+	0.415361i	$0.863655\pi$
$798$		0			0
$799$	−2639.49	−	2214.80i	−0.116869	−	0.0980650i
$800$	−1672.02	−	2896.03i	−0.0738936	−	0.127987i
$801$		0			0
$802$	−2672.39	+	4628.71i	−0.117662	+	0.203797i
$803$	22479.5	−	8181.86i	0.987899	−	0.359566i
$804$		0			0
$805$	−12510.5	+	10497.5i	−0.547747	+	0.459614i
$806$	−1301.97	−	473.878i	−0.0568982	−	0.0207092i
$807$		0			0
$808$	574.844	−	3260.10i	0.0250284	−	0.141943i
$809$	−41377.0			−1.79819			−0.899096	−	0.437751i	$-0.855775\pi$
$809$	−41377.0			−1.79819			−0.899096	+	0.437751i	$0.855775\pi$
$810$		0			0
$811$	−22624.0			−0.979576			−0.489788	−	0.871841i	$-0.662926\pi$
$811$	−22624.0			−0.979576			−0.489788	+	0.871841i	$0.662926\pi$
$812$	−2060.22	+	11684.1i	−0.0890390	+	0.504965i
$813$		0			0
$814$	18319.6	+	6667.78i	0.788821	+	0.287108i
$815$	−4682.84	+	3929.37i	−0.201267	+	0.168883i
$816$		0			0
$817$	−18677.2	+	6797.93i	−0.799794	+	0.291101i
$818$	9719.21	−	16834.2i	0.415433	−	0.719551i
$819$		0			0
$820$	4173.35	+	7228.45i	0.177731	+	0.307839i
$821$	1515.28	+	1271.47i	0.0644137	+	0.0540495i	0.674426	−	0.738342i	$-0.264391\pi$
$821$	1515.28	+	1271.47i	0.0644137	+	0.0540495i	−0.610012	+	0.792392i	$0.708836\pi$
$822$		0			0
$823$	−1635.33	−	9274.39i	−0.0692635	−	0.392813i	−0.999655	−	0.0262468i	$-0.991644\pi$
$823$	−1635.33	−	9274.39i	−0.0692635	−	0.392813i	0.930392	−	0.366566i	$-0.119467\pi$
$824$	−408.084	−	2314.36i	−0.0172528	−	0.0978452i
$825$		0			0
$826$	12315.3	+	10333.8i	0.518772	+	0.435301i
$827$	−11859.1	−	20540.6i	−0.498649	−	0.863685i	0.501350	−	0.865245i	$-0.332837\pi$
$827$	−11859.1	−	20540.6i	−0.498649	−	0.863685i	−0.999999	+	0.00155950i	$0.999504\pi$
$828$		0			0
$829$	12982.4	−	22486.1i	0.543903	−	0.942068i	−0.454772	−	0.890608i	$-0.650279\pi$
$829$	12982.4	−	22486.1i	0.543903	−	0.942068i	0.998675	−	0.0514602i	$-0.0163875\pi$
$830$	−6318.07	+	2299.59i	−0.264221	+	0.0961685i
$831$		0			0
$832$	214.881	−	180.307i	0.00895393	−	0.00751324i
$833$	7789.73	+	2835.23i	0.324007	+	0.117929i
$834$		0			0
$835$	182.848	−	1036.98i	0.00757809	−	0.0429775i
$836$	16185.7			0.669611
$837$		0			0
$838$	18090.3			0.745728
$839$	−5192.62	+	29448.8i	−0.213670	+	1.21178i	0.669529	+	0.742786i	$0.266496\pi$
$839$	−5192.62	+	29448.8i	−0.213670	+	1.21178i	−0.883199	+	0.468998i	$0.844615\pi$
$840$		0			0
$841$	9115.96	+	3317.94i	0.373773	+	0.136042i
$842$	−21016.0	+	17634.5i	−0.860165	+	0.721764i
$843$		0			0
$844$	8214.75	−	2989.92i	0.335028	−	0.121940i
$845$	−4930.02	+	8539.04i	−0.200707	+	0.347636i
$846$		0			0
$847$	−3591.98	−	6221.49i	−0.145717	−	0.252388i
$848$	1119.56	+	939.419i	0.0453369	+	0.0380422i
$849$		0			0
$850$	−1175.35	−	6665.75i	−0.0474285	−	0.268980i
$851$	−7745.29	−	43925.7i	−0.311992	−	1.76939i
$852$		0			0
$853$	18800.2	+	15775.3i	0.754640	+	0.633218i	0.936726	−	0.350064i	$-0.113840\pi$
$853$	18800.2	+	15775.3i	0.754640	+	0.633218i	−0.182085	+	0.983283i	$0.558285\pi$
$854$	15422.7	+	26712.9i	0.617979	+	1.07037i
$855$		0			0
$856$	−7251.78	+	12560.5i	−0.289557	+	0.501528i
$857$	−13580.0	+	4942.73i	−0.541290	+	0.197013i	−0.598172	−	0.801367i	$-0.704106\pi$
$857$	−13580.0	+	4942.73i	−0.541290	+	0.197013i	0.0568824	+	0.998381i	$0.481884\pi$
$858$		0			0
$859$	−11420.6	+	9583.03i	−0.453627	+	0.380639i	−0.840780	−	0.541377i	$-0.817903\pi$
$859$	−11420.6	+	9583.03i	−0.453627	+	0.380639i	0.387152	+	0.922016i	$0.373459\pi$
$860$	2692.45	+	979.973i	0.106758	+	0.0388567i
$861$		0			0
$862$	3487.74	−	19780.0i	0.137811	−	0.781565i
$863$	−16242.7			−0.640682			−0.320341	−	0.947302i	$-0.603798\pi$
$863$	−16242.7			−0.640682			−0.320341	+	0.947302i	$0.603798\pi$
$864$		0			0
$865$	2431.79			0.0955877
$866$	1583.01	−	8977.72i	0.0621167	−	0.352281i
$867$		0			0
$868$	−14540.2	−	5292.19i	−0.568577	−	0.206945i
$869$	−26833.6	+	22516.1i	−1.04749	+	0.878948i
$870$		0			0
$871$	3766.79	−	1371.00i	0.146536	−	0.0533347i
$872$	215.788	−	373.755i	0.00838016	−	0.0145149i
$873$		0			0
$874$	−18515.7	−	32070.1i	−0.716593	−	1.24118i
$875$	−19480.7	−	16346.3i	−0.752649	−	0.631548i
$876$		0			0
$877$	452.849	+	2568.23i	0.0174363	+	0.0988861i	0.992284	−	0.123986i	$-0.0395678\pi$
$877$	452.849	+	2568.23i	0.0174363	+	0.0988861i	−0.974848	+	0.222872i	$0.928457\pi$
$878$	926.526	+	5254.59i	0.0356136	+	0.201975i
$879$		0			0
$880$	−1787.41	−	1499.81i	−0.0684698	−	0.0574530i
$881$	−1658.65	−	2872.87i	−0.0634294	−	0.109863i	0.832567	−	0.553925i	$-0.186870\pi$
$881$	−1658.65	−	2872.87i	−0.0634294	−	0.109863i	−0.895996	+	0.444062i	$0.853537\pi$
$882$		0			0
$883$	−7495.97	+	12983.4i	−0.285684	+	0.494820i	−0.972775	−	0.231752i	$-0.925554\pi$
$883$	−7495.97	+	12983.4i	−0.285684	+	0.494820i	0.687091	+	0.726572i	$0.258888\pi$
$884$	533.526	−	194.188i	0.0202991	−	0.00738828i
$885$		0			0
$886$	1017.87	−	854.094i	0.0385959	−	0.0323858i
$887$	40497.6	+	14739.9i	1.53300	+	0.557968i	0.964355	−	0.264612i	$-0.0852439\pi$
$887$	40497.6	+	14739.9i	1.53300	+	0.557968i	0.568649	+	0.822580i	$0.307466\pi$
$888$		0			0
$889$	−5374.25	+	30478.9i	−0.202752	+	1.14986i
$890$	10648.6			0.401058
$891$		0			0
$892$	−19178.3			−0.719884
$893$	2321.01	−	13163.1i	0.0869760	−	0.493265i
$894$		0			0
$895$	432.746	+	157.507i	0.0161621	+	0.00588254i
$896$	2399.75	−	2013.63i	0.0894757	−	0.0750790i
$897$		0			0
$898$	7028.67	−	2558.23i	0.261191	−	0.0950658i
$899$	9577.93	−	16589.5i	0.355330	−	0.615450i
$900$		0			0
$901$	1479.07	+	2561.82i	0.0546890	+	0.0947242i
$902$	−22743.8	−	19084.3i	−0.839562	−	0.704476i
$903$		0			0
$904$	132.330	+	750.480i	0.00486861	+	0.0276113i
$905$	1982.20	+	11241.6i	0.0728073	+	0.412910i
$906$		0			0
$907$	−11031.0	−	9256.15i	−0.403837	−	0.338859i	0.418138	−	0.908384i	$-0.362683\pi$
$907$	−11031.0	−	9256.15i	−0.403837	−	0.338859i	−0.821974	+	0.569524i	$0.807127\pi$
$908$	8060.36	+	13960.9i	0.294595	+	0.510254i
$909$		0			0
$910$	485.657	−	841.183i	0.0176916	−	0.0306428i
$911$	−15733.0	+	5726.35i	−0.572183	+	0.208257i	−0.611875	−	0.790954i	$-0.709584\pi$
$911$	−15733.0	+	5726.35i	−0.572183	+	0.208257i	0.0396923	+	0.999212i	$0.487362\pi$
$912$		0			0
$913$	18320.9	−	15373.0i	0.664110	−	0.557255i
$914$	14103.9	+	5133.38i	0.510409	+	0.185774i
$915$		0			0
$916$	179.795	−	1019.67i	0.00648537	−	0.0367804i
$917$	18843.1			0.678576
$918$		0			0
$919$	−16541.1			−0.593733			−0.296867	−	0.954919i	$-0.595942\pi$
$919$	−16541.1			−0.593733			−0.296867	+	0.954919i	$0.595942\pi$
$920$	−926.995	+	5257.25i	−0.0332197	+	0.188398i
$921$		0			0
$922$	30723.7	+	11182.5i	1.09743	+	0.399433i
$923$	3590.27	−	3012.59i	0.128034	−	0.107433i
$924$		0			0
$925$	29718.1	−	10816.5i	1.05635	−	0.384480i
$926$	−18537.2	+	32107.4i	−0.657852	+	1.13943i
$927$		0			0
$928$	1939.10	+	3358.63i	0.0685929	+	0.118806i
$929$	23703.9	+	19889.9i	0.837136	+	0.702441i	0.956918	−	0.290360i	$-0.0937750\pi$
$929$	23703.9	+	19889.9i	0.837136	+	0.702441i	−0.119782	+	0.992800i	$0.538219\pi$
$930$		0			0
$931$	5584.02	+	31668.5i	0.196572	+	1.11482i
$932$	2458.10	+	13940.6i	0.0863926	+	0.489957i
$933$		0			0
$934$	−10417.6	−	8741.37i	−0.364960	−	0.306238i
$935$	−2361.37	−	4090.02i	−0.0825938	−	0.143057i
$936$		0			0
$937$	−4495.91	+	7787.15i	−0.156750	+	0.271499i	−0.933695	−	0.358069i	$-0.883435\pi$
$937$	−4495.91	+	7787.15i	−0.156750	+	0.271499i	0.776945	+	0.629569i	$0.216768\pi$
$938$	42066.8	−	15311.1i	1.46432	−	0.532968i
$939$		0			0
$940$	−1476.04	+	1238.54i	−0.0512160	+	0.0429753i
$941$	27726.3	+	10091.5i	0.960521	+	0.349601i	0.774238	−	0.632895i	$-0.218134\pi$
$941$	27726.3	+	10091.5i	0.960521	+	0.349601i	0.186283	+	0.982496i	$0.440356\pi$
$942$		0			0
$943$	−11795.5	+	66895.6i	−0.407332	+	2.31010i
$944$	5255.08			0.181185
$945$		0			0
$946$	−10191.9			−0.350283
$947$	7321.49	−	41522.2i	0.251232	−	1.42481i	−0.554331	−	0.832296i	$-0.687026\pi$
$947$	7321.49	−	41522.2i	0.251232	−	1.42481i	0.805563	−	0.592510i	$-0.201863\pi$
$948$		0			0
$949$	3058.89	+	1113.35i	0.104632	+	0.0380829i
$950$	20113.7	−	16877.4i	0.686920	−	0.576394i
$951$		0			0
$952$	5958.33	−	2168.65i	0.202847	−	0.0738303i
$953$	6471.04	−	11208.2i	0.219955	−	0.380974i	−0.734839	−	0.678242i	$-0.762742\pi$
$953$	6471.04	−	11208.2i	0.219955	−	0.380974i	0.954794	+	0.297268i	$0.0960755\pi$
$954$		0			0
$955$	−5932.68	−	10275.7i	−0.201023	−	0.348182i
$956$	15170.5	+	12729.5i	0.513230	+	0.430651i
$957$		0			0
$958$	3066.83	+	17392.9i	0.103429	+	0.586574i
$959$	9625.52	+	54589.0i	0.324113	+	1.83813i
$960$		0			0
$961$	−3683.31	−	3090.66i	−0.123638	−	0.103745i
$962$	1326.41	+	2297.41i	0.0444544	+	0.0769973i
$963$		0			0
$964$	−1284.51	+	2224.84i	−0.0429162	+	0.0743331i
$965$	−226.348	+	82.3840i	−0.00755068	+	0.00274822i
$966$		0			0
$967$	−16941.4	+	14215.5i	−0.563391	+	0.472742i	−0.879445	−	0.476000i	$-0.842086\pi$
$967$	−16941.4	+	14215.5i	−0.563391	+	0.472742i	0.316054	+	0.948741i	$0.397642\pi$
$968$	−2206.67	−	803.161i	−0.0732696	−	0.0266680i
$969$		0			0
$970$	772.621	−	4381.75i	0.0255746	−	0.145041i
$971$	−28669.3			−0.947521			−0.473761	−	0.880654i	$-0.657104\pi$
$971$	−28669.3			−0.947521			−0.473761	+	0.880654i	$0.657104\pi$
$972$		0			0
$973$	−60488.7			−1.99299
$974$	−393.016	+	2228.90i	−0.0129292	+	0.0733251i
$975$		0			0
$976$	9474.65	+	3448.49i	0.310734	+	0.113098i
$977$	21849.3	−	18333.7i	0.715477	−	0.600357i	−0.210653	−	0.977561i	$-0.567559\pi$
$977$	21849.3	−	18333.7i	0.715477	−	0.600357i	0.926130	+	0.377204i	$0.123115\pi$
$978$		0			0
$979$	−35593.6	+	12955.0i	−1.16198	+	0.422925i
$980$	2317.84	−	4014.62i	0.0755517	−	0.130859i
$981$		0			0
$982$	827.485	+	1433.25i	0.0268901	+	0.0465751i
$983$	−35140.5	−	29486.3i	−1.14019	−	0.956733i	−0.140745	−	0.990046i	$-0.544950\pi$
$983$	−35140.5	−	29486.3i	−1.14019	−	0.956733i	−0.999445	+	0.0333132i	$0.989394\pi$
$984$		0			0
$985$	1347.58	+	7642.53i	0.0435915	+	0.247219i
$986$	1363.10	+	7730.51i	0.0440263	+	0.249685i
$987$		0			0
$988$	1687.19	+	1415.72i	0.0543286	+	0.0455871i
$989$	11659.1	+	20194.1i	0.374861	+	0.649278i
$990$		0			0
$991$	4394.23	−	7611.02i	0.140855	−	0.243968i	−0.786964	−	0.616999i	$-0.788348\pi$
$991$	4394.23	−	7611.02i	0.140855	−	0.243968i	0.927819	+	0.373031i	$0.121682\pi$
$992$	−4752.87	+	1729.90i	−0.152121	+	0.0553675i
$993$		0			0
$994$	40095.5	−	33644.1i	1.27943	−	1.07357i
$995$	12083.5	+	4398.02i	0.384996	+	0.140127i
$996$		0			0
$997$	−3060.58	+	17357.4i	−0.0972213	+	0.551370i	0.896823	+	0.442390i	$0.145869\pi$
$997$	−3060.58	+	17357.4i	−0.0972213	+	0.551370i	−0.994044	+	0.108979i	$0.965242\pi$
$998$	13100.5			0.415521
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.73.2		24
3.2	odd	2		54.4.e.a.25.4	yes	24
27.11	odd	18		1458.4.a.h.1.8		12
27.13	even	9	inner	162.4.e.a.91.2		24
27.14	odd	18		54.4.e.a.13.4	✓	24
27.16	even	9		1458.4.a.e.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.13.4	✓	24	27.14	odd	18
54.4.e.a.25.4	yes	24	3.2	odd	2
162.4.e.a.73.2		24	1.1	even	1	trivial
162.4.e.a.91.2		24	27.13	even	9	inner
1458.4.a.e.1.5		12	27.16	even	9
1458.4.a.h.1.8		12	27.11	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)

\(f(q)\)	\(=\)	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-3.46830 + 2.91025i) q^{5} +(22.9979 - 8.37056i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(-0.347296 + 1.96962i) q^{2} +(-3.75877 - 1.36808i) q^{4} +(-3.46830 + 2.91025i) q^{5} +(22.9979 - 8.37056i) q^{7} +(4.00000 - 6.92820i) q^{8} +(-4.52754 - 7.84193i) q^{10} +(24.6741 + 20.7040i) q^{11} +(0.761088 + 4.31634i) q^{13} +(8.49969 + 48.2041i) q^{14} +(12.2567 + 10.2846i) q^{16} +(16.1926 + 28.0463i) q^{17} +(-62.8139 + 108.797i) q^{19} +(17.0180 - 6.19404i) q^{20} +(-49.3481 + 41.4080i) q^{22} +(138.497 + 50.4088i) q^{23} +(-18.1465 + 102.914i) q^{25} -8.76586 q^{26} -97.8955 q^{28} +(21.0451 - 119.353i) q^{29} +(148.527 + 54.0595i) q^{31} +(-24.5134 + 20.5692i) q^{32} +(-60.8641 + 22.1527i) q^{34} +(-55.4033 + 95.9613i) q^{35} +(-151.315 - 262.086i) q^{37} +(-192.473 - 161.504i) q^{38} +(6.28960 + 35.6701i) q^{40} +(80.0317 + 453.882i) q^{41} +(121.198 + 101.697i) q^{43} +(-64.4194 - 111.578i) q^{44} +(-147.385 + 255.279i) q^{46} +(-99.9785 + 36.3892i) q^{47} +(196.085 - 164.535i) q^{49} +(-196.398 - 71.4831i) q^{50} +(3.04435 - 17.2654i) q^{52} +91.3423 q^{53} -145.831 q^{55} +(33.9988 - 192.817i) q^{56} +(227.770 + 82.9016i) q^{58} +(251.602 - 211.119i) q^{59} +(592.165 - 215.531i) q^{61} +(-158.059 + 273.767i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-15.2013 - 12.7554i) q^{65} +(-158.815 - 900.683i) q^{67} +(-22.4945 - 127.572i) q^{68} +(-169.766 - 142.450i) q^{70} +(-534.661 - 926.060i) q^{71} +(371.350 - 643.197i) q^{73} +(568.760 - 207.012i) q^{74} +(384.946 - 323.008i) q^{76} +(740.756 + 269.613i) q^{77} +(-188.846 + 1071.00i) q^{79} -72.4407 q^{80} -921.768 q^{82} +(128.937 - 731.236i) q^{83} +(-137.782 - 50.1487i) q^{85} +(-242.395 + 203.394i) q^{86} +(242.138 - 88.1309i) q^{88} +(-587.989 + 1018.43i) q^{89} +(53.6337 + 92.8962i) q^{91} +(-451.615 - 378.950i) q^{92} +(-36.9506 - 209.557i) q^{94} +(-98.7685 - 560.144i) q^{95} +(376.407 + 315.843i) q^{97} +(255.971 + 443.355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 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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