LMFDB - Embedded newform 171.3.ba.c.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(10,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("171.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.ba (of order $18$, degree $6$, 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:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 48 x^{16} + 936 x^{14} + 9539 x^{12} + 54576 x^{10} + 176517 x^{8} + 313396 x^{6} + 277917 x^{4} + \cdots + 8427 $ x^18 + 48x^16 + 936x^14 + 9539x^12 + 54576x^10 + 176517x^8 + 313396x^6 + 277917x^4 + 96435x^2 + 8427
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			91.2
Root			$-0.707729i$ of defining polynomial
Character	$\chi$	$=$	171.91
Dual form			171.3.ba.c.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.242057 + 0.665047i) q^{2} +(2.68048 + 2.24919i) q^{4} +(-5.34756 + 4.48713i) q^{5} +(-0.504300 + 0.873473i) q^{7} +(-4.59629 + 2.65367i) q^{8} +O(q^{10})$	\(q+(-0.242057 + 0.665047i) q^{2} +(2.68048 + 2.24919i) q^{4} +(-5.34756 + 4.48713i) q^{5} +(-0.504300 + 0.873473i) q^{7} +(-4.59629 + 2.65367i) q^{8} +(-1.68974 - 4.64252i) q^{10} +(-3.17026 - 5.49105i) q^{11} +(-18.8398 - 3.32196i) q^{13} +(-0.458832 - 0.546814i) q^{14} +(1.77821 + 10.0847i) q^{16} +(17.6556 + 6.42612i) q^{17} +(-3.75932 + 18.6244i) q^{19} -24.4264 q^{20} +(4.41919 - 0.779223i) q^{22} +(-4.24742 - 3.56401i) q^{23} +(4.12079 - 23.3702i) q^{25} +(6.76956 - 11.7252i) q^{26} +(-3.31638 + 1.20706i) q^{28} +(15.9133 + 43.7213i) q^{29} +(-11.5290 - 6.65625i) q^{31} +(-28.0441 - 4.94493i) q^{32} +(-8.54735 + 10.1863i) q^{34} +(-1.22262 - 6.93381i) q^{35} +33.7511i q^{37} +(-11.4761 - 7.00830i) q^{38} +(12.6716 - 34.8148i) q^{40} +(-14.6890 + 2.59006i) q^{41} +(54.4444 - 45.6843i) q^{43} +(3.85260 - 21.8492i) q^{44} +(3.39835 - 1.96204i) q^{46} +(61.8359 - 22.5064i) q^{47} +(23.9914 + 41.5543i) q^{49} +(14.5448 + 8.39745i) q^{50} +(-43.0279 - 51.2786i) q^{52} +(2.12547 - 2.53303i) q^{53} +(41.5922 + 15.1383i) q^{55} -5.35299i q^{56} -32.9287 q^{58} +(15.3099 - 42.0637i) q^{59} +(42.0127 + 35.2529i) q^{61} +(7.21739 - 6.05611i) q^{62} +(-10.4037 + 18.0198i) q^{64} +(115.653 - 66.7721i) q^{65} +(21.4253 + 58.8655i) q^{67} +(32.8720 + 56.9359i) q^{68} +(4.90726 + 0.865282i) q^{70} +(50.5020 + 60.1860i) q^{71} +(-23.2374 - 131.786i) q^{73} +(-22.4461 - 8.16971i) q^{74} +(-51.9666 + 41.4669i) q^{76} +6.39505 q^{77} +(24.2864 - 4.28235i) q^{79} +(-54.7607 - 45.9497i) q^{80} +(1.83306 - 10.3958i) q^{82} +(-56.6745 + 98.1632i) q^{83} +(-123.249 + 44.8590i) q^{85} +(17.2035 + 47.2663i) q^{86} +(29.1429 + 16.8256i) q^{88} +(-153.275 - 27.0266i) q^{89} +(12.4025 - 14.7808i) q^{91} +(-3.36899 - 19.1065i) q^{92} +46.5717i q^{94} +(-63.4669 - 116.463i) q^{95} +(43.5508 - 119.655i) q^{97} +(-33.4428 + 5.89688i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8}+O(q^{10}) $ 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8	$ 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8} - 78 q^{10} - 15 q^{11} + 36 q^{13} + 39 q^{14} - 3 q^{16} + 30 q^{17} + 54 q^{19} + 30 q^{20} + 132 q^{22} - 69 q^{23} + 138 q^{25} - 48 q^{26} - 246 q^{28} + 162 q^{29} + 72 q^{31} + 21 q^{32} - 285 q^{34} - 54 q^{35} + 204 q^{38} - 51 q^{40} - 30 q^{41} + 402 q^{43} - 471 q^{44} - 99 q^{46} + 105 q^{47} + 66 q^{49} - 567 q^{50} - 3 q^{52} + 36 q^{53} - 15 q^{55} - 48 q^{58} + 180 q^{59} + 93 q^{61} - 189 q^{62} - 183 q^{64} + 891 q^{65} - 354 q^{67} - 153 q^{68} + 372 q^{70} - 144 q^{71} - 453 q^{73} + 489 q^{74} - 150 q^{76} + 36 q^{77} - 96 q^{79} - 144 q^{80} + 249 q^{82} + 99 q^{83} - 573 q^{85} + 33 q^{86} + 360 q^{88} - 795 q^{89} + 414 q^{91} - 285 q^{92} - 198 q^{95} - 483 q^{97} + 39 q^{98}+O(q^{100}) $ 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8 - 78 * q^10 - 15 * q^11 + 36 * q^13 + 39 * q^14 - 3 * q^16 + 30 * q^17 + 54 * q^19 + 30 * q^20 + 132 * q^22 - 69 * q^23 + 138 * q^25 - 48 * q^26 - 246 * q^28 + 162 * q^29 + 72 * q^31 + 21 * q^32 - 285 * q^34 - 54 * q^35 + 204 * q^38 - 51 * q^40 - 30 * q^41 + 402 * q^43 - 471 * q^44 - 99 * q^46 + 105 * q^47 + 66 * q^49 - 567 * q^50 - 3 * q^52 + 36 * q^53 - 15 * q^55 - 48 * q^58 + 180 * q^59 + 93 * q^61 - 189 * q^62 - 183 * q^64 + 891 * q^65 - 354 * q^67 - 153 * q^68 + 372 * q^70 - 144 * q^71 - 453 * q^73 + 489 * q^74 - 150 * q^76 + 36 * q^77 - 96 * q^79 - 144 * q^80 + 249 * q^82 + 99 * q^83 - 573 * q^85 + 33 * q^86 + 360 * q^88 - 795 * q^89 + 414 * q^91 - 285 * q^92 - 198 * q^95 - 483 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.242057	+	0.665047i	−0.121029	+	0.332524i	−0.985382	−	0.170362i	$-0.945506\pi$
$2$	−0.242057	+	0.665047i	−0.121029	+	0.332524i	0.864353	+	0.502886i	$0.167728\pi$
$3$		0			0
$3$		0			0
$4$	2.68048	+	2.24919i	0.670120	+	0.562298i
$5$	−5.34756	+	4.48713i	−1.06951	+	0.897426i	−0.995008	−	0.0997943i	$-0.968182\pi$
$5$	−5.34756	+	4.48713i	−1.06951	+	0.897426i	−0.0745031	+	0.997221i	$0.523737\pi$
$6$		0			0
$7$	−0.504300	+	0.873473i	−0.0720429	+	0.124782i	−0.899797	−	0.436310i	$-0.856285\pi$
$7$	−0.504300	+	0.873473i	−0.0720429	+	0.124782i	0.827754	+	0.561092i	$0.189619\pi$
$8$	−4.59629	+	2.65367i	−0.574537	+	0.331709i
$9$		0			0
$10$	−1.68974	−	4.64252i	−0.168974	−	0.464252i
$11$	−3.17026	−	5.49105i	−0.288205	−	0.499186i	0.685176	−	0.728377i	$-0.259725\pi$
$11$	−3.17026	−	5.49105i	−0.288205	−	0.499186i	−0.973381	+	0.229191i	$0.926392\pi$
$12$		0			0
$13$	−18.8398	−	3.32196i	−1.44921	−	0.255535i	−0.607009	−	0.794695i	$-0.707631\pi$
$13$	−18.8398	−	3.32196i	−1.44921	−	0.255535i	−0.842203	+	0.539160i	$0.818742\pi$
$14$	−0.458832	−	0.546814i	−0.0327737	−	0.0390582i
$15$		0			0
$16$	1.77821	+	10.0847i	0.111138	+	0.630297i
$17$	17.6556	+	6.42612i	1.03857	+	0.378007i	0.804336	−	0.594175i	$-0.202521\pi$
$17$	17.6556	+	6.42612i	1.03857	+	0.378007i	0.234229	+	0.972181i	$0.424743\pi$
$18$		0			0
$19$	−3.75932	+	18.6244i	−0.197859	+	0.980231i
$19$	−3.75932	+	18.6244i	−0.197859	+	0.980231i
$20$	−24.4264			−1.22132
$21$		0			0
$22$	4.41919	−	0.779223i	0.200872	−	0.0354192i
$23$	−4.24742	−	3.56401i	−0.184670	−	0.154957i	0.545766	−	0.837938i	$-0.316239\pi$
$23$	−4.24742	−	3.56401i	−0.184670	−	0.154957i	−0.730436	+	0.682981i	$0.760683\pi$
$24$		0			0
$25$	4.12079	−	23.3702i	0.164832	−	0.934808i
$26$	6.76956	−	11.7252i	0.260368	−	0.450970i
$27$		0			0
$28$	−3.31638	+	1.20706i	−0.118442	+	0.0431094i
$29$	15.9133	+	43.7213i	0.548733	+	1.50763i	0.835423	+	0.549608i	$0.185223\pi$
$29$	15.9133	+	43.7213i	0.548733	+	1.50763i	−0.286690	+	0.958023i	$0.592555\pi$
$30$		0			0
$31$	−11.5290	−	6.65625i	−0.371902	−	0.214718i	0.302387	−	0.953185i	$-0.402216\pi$
$31$	−11.5290	−	6.65625i	−0.371902	−	0.214718i	−0.674289	+	0.738468i	$0.735550\pi$
$32$	−28.0441	−	4.94493i	−0.876379	−	0.154529i
$33$		0			0
$34$	−8.54735	+	10.1863i	−0.251393	+	0.299598i
$35$	−1.22262	−	6.93381i	−0.0349319	−	0.198109i
$36$		0			0
$37$			33.7511i			0.912193i	0.889930	+	0.456096i	$0.150753\pi$
$37$			33.7511i			0.912193i	−0.889930	+	0.456096i	$0.849247\pi$
$38$	−11.4761	−	7.00830i	−0.302003	−	0.184429i
$39$		0			0
$40$	12.6716	−	34.8148i	0.316789	−	0.870371i
$41$	−14.6890	+	2.59006i	−0.358268	+	0.0631723i	−0.349885	−	0.936793i	$-0.613779\pi$
$41$	−14.6890	+	2.59006i	−0.358268	+	0.0631723i	−0.00838270	+	0.999965i	$0.502668\pi$
$42$		0			0
$43$	54.4444	−	45.6843i	1.26615	−	1.06242i	0.271149	−	0.962537i	$-0.412596\pi$
$43$	54.4444	−	45.6843i	1.26615	−	1.06242i	0.994999	−	0.0998873i	$-0.0318482\pi$
$44$	3.85260	−	21.8492i	0.0875591	−	0.496572i
$45$		0			0
$46$	3.39835	−	1.96204i	0.0738773	−	0.0426531i
$47$	61.8359	−	22.5064i	1.31566	−	0.478860i	0.413594	−	0.910462i	$-0.364273\pi$
$47$	61.8359	−	22.5064i	1.31566	−	0.478860i	0.902064	+	0.431601i	$0.142051\pi$
$48$		0			0
$49$	23.9914	+	41.5543i	0.489620	+	0.848046i
$50$	14.5448	+	8.39745i	0.290896	+	0.167949i
$51$		0			0
$52$	−43.0279	−	51.2786i	−0.827460	−	0.986128i
$53$	2.12547	−	2.53303i	0.0401032	−	0.0477931i	−0.745620	−	0.666371i	$-0.767847\pi$
$53$	2.12547	−	2.53303i	0.0401032	−	0.0477931i	0.785723	+	0.618578i	$0.212291\pi$
$54$		0			0
$55$	41.5922	+	15.1383i	0.756222	+	0.275242i
$56$		−	5.35299i		−	0.0955890i
$57$		0			0
$58$	−32.9287			−0.567736
$59$	15.3099	−	42.0637i	0.259490	−	0.712944i	−0.739709	−	0.672927i	$-0.765037\pi$
$59$	15.3099	−	42.0637i	0.259490	−	0.712944i	0.999199	−	0.0400165i	$-0.0127410\pi$
$60$		0			0
$61$	42.0127	+	35.2529i	0.688733	+	0.577916i	0.918544	−	0.395320i	$-0.129366\pi$
$61$	42.0127	+	35.2529i	0.688733	+	0.577916i	−0.229811	+	0.973235i	$0.573811\pi$
$62$	7.21739	−	6.05611i	0.116410	−	0.0976792i
$63$		0			0
$64$	−10.4037	+	18.0198i	−0.162558	+	0.281559i
$65$	115.653	−	66.7721i	1.77927	−	1.02726i
$66$		0			0
$67$	21.4253	+	58.8655i	0.319780	+	0.878590i	0.990578	+	0.136949i	$0.0437297\pi$
$67$	21.4253	+	58.8655i	0.319780	+	0.878590i	−0.670798	+	0.741640i	$0.734048\pi$
$68$	32.8720	+	56.9359i	0.483411	+	0.837293i
$69$		0			0
$70$	4.90726	+	0.865282i	0.0701037	+	0.0123612i
$71$	50.5020	+	60.1860i	0.711296	+	0.847690i	0.993754	−	0.111590i	$-0.0355942\pi$
$71$	50.5020	+	60.1860i	0.711296	+	0.847690i	−0.282458	+	0.959280i	$0.591150\pi$
$72$		0			0
$73$	−23.2374	−	131.786i	−0.318321	−	1.80529i	−0.552962	−	0.833206i	$-0.686503\pi$
$73$	−23.2374	−	131.786i	−0.318321	−	1.80529i	0.234641	−	0.972082i	$-0.424609\pi$
$74$	−22.4461	−	8.16971i	−0.303326	−	0.110402i
$75$		0			0
$76$	−51.9666	+	41.4669i	−0.683771	+	0.545617i
$77$	6.39505			0.0830526
$78$		0			0
$79$	24.2864	−	4.28235i	0.307423	−	0.0542070i	−0.0178084	−	0.999841i	$-0.505669\pi$
$79$	24.2864	−	4.28235i	0.307423	−	0.0542070i	0.325231	+	0.945634i	$0.394558\pi$
$80$	−54.7607	−	45.9497i	−0.684509	−	0.574371i
$81$		0			0
$82$	1.83306	−	10.3958i	0.0223544	−	0.126778i
$83$	−56.6745	+	98.1632i	−0.682826	+	1.18269i	0.291289	+	0.956635i	$0.405916\pi$
$83$	−56.6745	+	98.1632i	−0.682826	+	1.18269i	−0.974115	+	0.226054i	$0.927417\pi$
$84$		0			0
$85$	−123.249	+	44.8590i	−1.44999	+	0.527753i
$86$	17.2035	+	47.2663i	0.200041	+	0.549608i
$87$		0			0
$88$	29.1429	+	16.8256i	0.331169	+	0.191201i
$89$	−153.275	−	27.0266i	−1.72220	−	0.303670i	−0.776837	−	0.629701i	$-0.783177\pi$
$89$	−153.275	−	27.0266i	−1.72220	−	0.303670i	−0.945359	+	0.326032i	$0.894288\pi$
$90$		0			0
$91$	12.4025	−	14.7808i	0.136292	−	0.162426i
$92$	−3.36899	−	19.1065i	−0.0366195	−	0.207679i
$93$		0			0
$94$			46.5717i			0.495443i
$95$	−63.4669	−	116.463i	−0.668073	−	1.22593i
$96$		0			0
$97$	43.5508	−	119.655i	0.448977	−	1.23355i	−0.484460	−	0.874813i	$-0.660984\pi$
$97$	43.5508	−	119.655i	0.448977	−	1.23355i	0.933437	−	0.358741i	$-0.116794\pi$
$98$	−33.4428	+	5.89688i	−0.341254	+	0.0601722i
$99$		0			0
$100$	63.6097	−	53.3749i	0.636097	−	0.533749i
$101$	−11.6382	+	66.0033i	−0.115229	+	0.653498i	0.871407	+	0.490561i	$0.163208\pi$
$101$	−11.6382	+	66.0033i	−0.115229	+	0.653498i	−0.986636	+	0.162937i	$0.947903\pi$
$102$		0			0
$103$	−97.1329	+	56.0797i	−0.943038	+	0.544463i	−0.890911	−	0.454178i	$-0.849933\pi$
$103$	−97.1329	+	56.0797i	−0.943038	+	0.544463i	−0.0521263	+	0.998640i	$0.516600\pi$
$104$	95.4084	−	34.7258i	0.917389	−	0.333902i
$105$		0			0
$106$	1.17010	+	2.02668i	0.0110387	+	0.0191196i
$107$	−40.1577	−	23.1851i	−0.375306	−	0.216683i	0.300468	−	0.953792i	$-0.402857\pi$
$107$	−40.1577	−	23.1851i	−0.375306	−	0.216683i	−0.675774	+	0.737109i	$0.736190\pi$
$108$		0			0
$109$	39.6870	+	47.2971i	0.364101	+	0.433919i	0.916729	−	0.399509i	$-0.130819\pi$
$109$	39.6870	+	47.2971i	0.364101	+	0.433919i	−0.552628	+	0.833428i	$0.686375\pi$
$110$	−20.1354	+	23.9964i	−0.183049	+	0.218149i
$111$		0			0
$112$	−9.70551	−	3.53252i	−0.0866564	−	0.0315403i
$113$			27.3673i			0.242188i	0.992641	+	0.121094i	$0.0386403\pi$
$113$			27.3673i			0.242188i	−0.992641	+	0.121094i	$0.961360\pi$
$114$		0			0
$115$	38.7055			0.336569
$116$	−55.6824	+	152.986i	−0.480021	+	1.31885i
$117$		0			0
$118$	24.2685	+	20.3637i	0.205665	+	0.172573i
$119$	−14.5168	+	12.1810i	−0.121990	+	0.102361i
$120$		0			0
$121$	40.3989	−	69.9730i	0.333875	−	0.578289i
$122$	−33.6143	+	19.4072i	−0.275527	+	0.159076i
$123$		0			0
$124$	−15.9320	−	43.7728i	−0.128484	−	0.353006i
$125$	−4.43029	−	7.67348i	−0.0354423	−	0.0613879i
$126$		0			0
$127$	1.50322	+	0.265059i	0.0118364	+	0.00208708i	0.179563	−	0.983746i	$-0.442532\pi$
$127$	1.50322	+	0.265059i	0.0118364	+	0.00208708i	−0.167727	+	0.985834i	$0.553643\pi$
$128$	−82.6837	−	98.5386i	−0.645966	−	0.769833i
$129$		0			0
$130$	16.4120	+	93.0772i	0.126246	+	0.715979i
$131$	95.0832	+	34.6075i	0.725826	+	0.264179i	0.678397	−	0.734696i	$-0.262675\pi$
$131$	95.0832	+	34.6075i	0.725826	+	0.264179i	0.0474290	+	0.998875i	$0.484897\pi$
$132$		0			0
$133$	−14.3721	−	12.6759i	−0.108061	−	0.0953078i
$134$	−44.3345			−0.330854
$135$		0			0
$136$	−98.2032	+	17.3159i	−0.722082	+	0.127323i
$137$	−17.5368	−	14.7151i	−0.128006	−	0.107410i	0.576537	−	0.817071i	$-0.304404\pi$
$137$	−17.5368	−	14.7151i	−0.128006	−	0.107410i	−0.704543	+	0.709661i	$0.748848\pi$
$138$		0			0
$139$	−38.6935	+	219.442i	−0.278371	+	1.57872i	0.449677	+	0.893191i	$0.351539\pi$
$139$	−38.6935	+	219.442i	−0.278371	+	1.57872i	−0.728047	+	0.685527i	$0.759572\pi$
$140$	12.3183	−	21.3358i	0.0879875	−	0.152399i
$141$		0			0
$142$	−52.2509	+	19.0178i	−0.367964	+	0.133928i
$143$	41.4859	+	113.981i	0.290111	+	0.797073i
$144$		0			0
$145$	−281.280	−	162.397i	−1.93986	−	1.11998i
$146$	93.2688	+	16.4458i	0.638827	+	0.112642i
$147$		0			0
$148$	−75.9127	+	90.4693i	−0.512924	+	0.611279i
$149$	4.98879	+	28.2929i	0.0334818	+	0.189885i	0.996961	−	0.0778969i	$-0.0248205\pi$
$149$	4.98879	+	28.2929i	0.0334818	+	0.189885i	−0.963480	+	0.267782i	$0.913709\pi$
$150$		0			0
$151$		−	53.6268i		−	0.355144i	−0.984108	−	0.177572i	$-0.943176\pi$
$151$		−	53.6268i		−	0.355144i	0.984108	−	0.177572i	$-0.0568243\pi$
$152$	−32.1441	−	95.5791i	−0.211474	−	0.628810i
$153$		0			0
$154$	−1.54797	+	4.25301i	−0.0100517	+	0.0276169i
$155$	91.5192	−	16.1373i	0.590446	−	0.104112i
$156$		0			0
$157$	−74.4671	+	62.4853i	−0.474313	+	0.397996i	−0.848365	−	0.529412i	$-0.822413\pi$
$157$	−74.4671	+	62.4853i	−0.474313	+	0.397996i	0.374052	+	0.927408i	$0.377968\pi$
$158$	−3.03074	+	17.1882i	−0.0191819	+	0.108786i
$159$		0			0
$160$	172.156	−	99.3943i	1.07598	−	0.621215i
$161$	5.25504	−	1.91268i	0.0326400	−	0.0118800i
$162$		0			0
$163$	71.0293	+	123.026i	0.435762	+	0.754763i	0.997358	−	0.0726495i	$-0.0231454\pi$
$163$	71.0293	+	123.026i	0.435762	+	0.754763i	−0.561595	+	0.827412i	$0.689812\pi$
$164$	−45.1991	−	26.0957i	−0.275604	−	0.159120i
$165$		0			0
$166$	−51.5647	−	61.4524i	−0.310631	−	0.370195i
$167$	−101.724	+	121.230i	−0.609125	+	0.725927i	−0.979160	−	0.203091i	$-0.934901\pi$
$167$	−101.724	+	121.230i	−0.609125	+	0.725927i	0.370035	+	0.929018i	$0.379346\pi$
$168$		0			0
$169$	185.093	+	67.3683i	1.09522	+	0.398629i
$170$		−	92.8250i		−	0.546030i
$171$		0			0
$172$	248.690			1.44587
$173$	−27.1974	+	74.7243i	−0.157210	+	0.431932i	−0.993144	−	0.116899i	$-0.962705\pi$
$173$	−27.1974	+	74.7243i	−0.157210	+	0.431932i	0.835933	+	0.548831i	$0.184927\pi$
$174$		0			0
$175$	18.3351	+	15.3850i	0.104772	+	0.0879142i
$176$	49.7384	−	41.7355i	0.282605	−	0.237134i
$177$		0			0
$178$	55.0754	−	95.3935i	0.309413	−	0.535918i
$179$	273.268	−	157.771i	1.52664	−	0.881404i	0.527137	−	0.849780i	$-0.323265\pi$
$179$	273.268	−	157.771i	1.52664	−	0.881404i	0.999500	−	0.0316238i	$-0.0100679\pi$
$180$		0			0
$181$	−52.6294	−	144.598i	−0.290770	−	0.798884i	−0.995954	−	0.0898599i	$-0.971358\pi$
$181$	−52.6294	−	144.598i	−0.290770	−	0.798884i	0.705185	−	0.709024i	$-0.250864\pi$
$182$	6.82778	+	11.8261i	0.0375153	+	0.0649784i
$183$		0			0
$184$	28.9801	+	5.10997i	0.157500	+	0.0277716i
$185$	−151.446	−	180.486i	−0.818626	−	0.975600i
$186$		0			0
$187$	−20.6867	−	117.320i	−0.110624	−	0.627381i
$188$	216.371	+	78.7527i	1.15091	+	0.418897i
$189$		0			0
$190$	92.8164	−	14.0176i	0.488507	−	0.0737771i
$191$	−126.605			−0.662855			−0.331427	−	0.943481i	$-0.607530\pi$
$191$	−126.605			−0.662855			−0.331427	+	0.943481i	$0.607530\pi$
$192$		0			0
$193$	72.6347	−	12.8075i	0.376346	−	0.0663599i	0.0177241	−	0.999843i	$-0.494358\pi$
$193$	72.6347	−	12.8075i	0.376346	−	0.0663599i	0.358622	+	0.933483i	$0.383247\pi$
$194$	69.0343	+	57.9266i	0.355847	+	0.298591i
$195$		0			0
$196$	−29.1551	+	165.347i	−0.148750	+	0.843605i
$197$	149.599	−	259.114i	0.759388	−	1.31530i	−0.183776	−	0.982968i	$-0.558832\pi$
$197$	149.599	−	259.114i	0.759388	−	1.31530i	0.943163	−	0.332330i	$-0.107835\pi$
$198$		0			0
$199$	203.339	−	74.0095i	1.02181	−	0.371907i	0.223850	−	0.974624i	$-0.428137\pi$
$199$	203.339	−	74.0095i	1.02181	−	0.371907i	0.797955	+	0.602717i	$0.205915\pi$
$200$	43.0764	+	118.351i	0.215382	+	0.591757i
$201$		0			0
$202$	−41.0782	−	23.7165i	−0.203358	−	0.117409i
$203$	−46.2145	−	8.14885i	−0.227657	−	0.0401421i
$204$		0			0
$205$	66.9282	−	79.7619i	0.326479	−	0.389083i
$206$	−13.7839	−	78.1725i	−0.0669122	−	0.379478i
$207$		0			0
$208$		−	195.901i		−	0.941833i
$209$	114.185	−	38.4015i	0.546342	−	0.183739i
$210$		0			0
$211$	−51.3222	+	141.007i	−0.243233	+	0.668277i	0.756662	+	0.653806i	$0.226829\pi$
$211$	−51.3222	+	141.007i	−0.243233	+	0.668277i	−0.999895	+	0.0144713i	$0.995393\pi$
$212$	11.3946	−	2.00917i	0.0537479	−	0.00947720i
$213$		0			0
$214$	25.1397	−	21.0947i	0.117475	−	0.0985732i
$215$	−86.1530	+	488.598i	−0.400712	+	2.27255i
$216$		0			0
$217$	11.6281	−	6.71349i	0.0535857	−	0.0309377i
$218$	−41.0614	+	14.9451i	−0.188355	+	0.0685556i
$219$		0			0
$220$	77.4381	+	134.127i	0.351992	+	0.609667i
$221$	−311.280	−	179.718i	−1.40851	−	0.813202i
$222$		0			0
$223$	−114.961	−	137.005i	−0.515519	−	0.614372i	0.443996	−	0.896029i	$-0.353560\pi$
$223$	−114.961	−	137.005i	−0.515519	−	0.614372i	−0.959515	+	0.281657i	$0.909116\pi$
$224$	18.4619	−	22.0021i	0.0824193	−	0.0982235i
$225$		0			0
$226$	−18.2005	−	6.62445i	−0.0805333	−	0.0293117i
$227$		−	300.657i		−	1.32448i	−0.749291	−	0.662241i	$-0.769606\pi$
$227$		−	300.657i		−	1.32448i	0.749291	−	0.662241i	$-0.230394\pi$
$228$		0			0
$229$	−423.152			−1.84782			−0.923912	−	0.382605i	$-0.875027\pi$
$229$	−423.152			−1.84782			−0.923912	+	0.382605i	$0.875027\pi$
$230$	−9.36895	+	25.7410i	−0.0407346	+	0.111917i
$231$		0			0
$232$	−189.164	−	158.727i	−0.815362	−	0.684170i
$233$	188.868	−	158.479i	0.810592	−	0.680168i	−0.140157	−	0.990129i	$-0.544761\pi$
$233$	188.868	−	158.479i	0.810592	−	0.680168i	0.950749	+	0.309962i	$0.100316\pi$
$234$		0			0
$235$	−229.682	+	397.820i	−0.977369	+	1.69285i
$236$	135.647	−	78.3160i	0.574776	−	0.331847i
$237$		0			0
$238$	−4.58706	−	12.6028i	−0.0192734	−	0.0529531i
$239$	207.326	+	359.098i	0.867471	+	1.50250i	0.864573	+	0.502508i	$0.167589\pi$
$239$	207.326	+	359.098i	0.867471	+	1.50250i	0.00289799	+	0.999996i	$0.499078\pi$
$240$		0			0
$241$	251.284	+	44.3081i	1.04267	+	0.183851i	0.668656	−	0.743572i	$-0.266870\pi$
$241$	251.284	+	44.3081i	1.04267	+	0.183851i	0.374014	+	0.927423i	$0.377981\pi$
$242$	36.7565	+	43.8047i	0.151886	+	0.181011i
$243$		0			0
$244$	33.3239	+	188.989i	0.136573	+	0.774546i
$245$	−314.755	−	114.561i	−1.28471	−	0.467597i
$246$		0			0
$247$	132.694	−	338.390i	0.537223	−	1.37000i
$248$	70.6540			0.284895
$249$		0			0
$250$	6.17562	−	1.08893i	0.0247025	−	0.00435571i
$251$	136.308	+	114.376i	0.543061	+	0.455683i	0.872583	−	0.488465i	$-0.162443\pi$
$251$	136.308	+	114.376i	0.543061	+	0.455683i	−0.329522	+	0.944148i	$0.606888\pi$
$252$		0			0
$253$	−6.10472	+	34.6216i	−0.0241293	+	0.136844i
$254$	−0.540143	+	0.935556i	−0.00212655	+	0.00368329i
$255$		0			0
$256$	7.33653	−	2.67028i	0.0286583	−	0.0104308i
$257$	−110.492	−	303.575i	−0.429931	−	1.18123i	−0.945855	−	0.324591i	$-0.894773\pi$
$257$	−110.492	−	303.575i	−0.429931	−	1.18123i	0.515924	−	0.856635i	$-0.327449\pi$
$258$		0			0
$259$	−29.4807	−	17.0207i	−0.113825	−	0.0657170i
$260$	460.188	+	81.1436i	1.76995	+	0.312091i
$261$		0			0
$262$	−46.0312	+	54.8578i	−0.175692	+	0.209381i
$263$	12.6227	+	71.5870i	0.0479952	+	0.272194i	0.999356	−	0.0358850i	$-0.0114250\pi$
$263$	12.6227	+	71.5870i	0.0479952	+	0.272194i	−0.951361	+	0.308079i	$0.900314\pi$
$264$		0			0
$265$			23.0828i			0.0871049i
$266$	11.9090	−	6.48981i	0.0447706	−	0.0243978i
$267$		0			0
$268$	−74.9697	+	205.977i	−0.279738	+	0.768573i
$269$	−395.721	+	69.7763i	−1.47108	+	0.259391i	−0.851008	−	0.525152i	$-0.824008\pi$
$269$	−395.721	+	69.7763i	−1.47108	+	0.259391i	−0.620074	+	0.784544i	$0.712897\pi$
$270$		0			0
$271$	12.9049	−	10.8285i	0.0476196	−	0.0399576i	−0.618667	−	0.785653i	$-0.712327\pi$
$271$	12.9049	−	10.8285i	0.0476196	−	0.0399576i	0.666287	+	0.745696i	$0.267883\pi$
$272$	−33.4103	+	189.479i	−0.122832	+	0.696615i
$273$		0			0
$274$	14.0312	−	8.10090i	0.0512087	−	0.0295653i
$275$	−141.391	+	51.4621i	−0.514149	+	0.187135i
$276$		0			0
$277$	−29.6827	−	51.4119i	−0.107158	−	0.185603i	0.807460	−	0.589922i	$-0.200842\pi$
$277$	−29.6827	−	51.4119i	−0.107158	−	0.185603i	−0.914618	+	0.404320i	$0.867508\pi$
$278$	−136.573	−	78.8506i	−0.491270	−	0.283635i
$279$		0			0
$280$	24.0196	+	28.6254i	0.0857841	+	0.102234i
$281$	−38.2465	+	45.5804i	−0.136109	+	0.162208i	−0.829793	−	0.558071i	$-0.811542\pi$
$281$	−38.2465	+	45.5804i	−0.136109	+	0.162208i	0.693685	+	0.720279i	$0.255986\pi$
$282$		0			0
$283$	15.1683	+	5.52080i	0.0535981	+	0.0195081i	0.368680	−	0.929556i	$-0.379810\pi$
$283$	15.1683	+	5.52080i	0.0535981	+	0.0195081i	−0.315082	+	0.949064i	$0.602032\pi$
$284$			274.916i			0.968015i
$285$		0			0
$286$	−85.8451			−0.300158
$287$	5.14530	−	14.1366i	0.0179279	−	0.0492565i
$288$		0			0
$289$	49.0387	+	41.1484i	0.169684	+	0.142382i
$290$	176.088	−	147.755i	0.607200	−	0.509501i
$291$		0			0
$292$	234.125	−	405.516i	0.801796	−	1.38875i
$293$	108.314	−	62.5352i	0.369673	−	0.213431i	−0.303643	−	0.952786i	$-0.598203\pi$
$293$	108.314	−	62.5352i	0.369673	−	0.213431i	0.673316	+	0.739355i	$0.264870\pi$
$294$		0			0
$295$	106.875	+	293.636i	0.362287	+	0.995375i
$296$	−89.5644	−	155.130i	−0.302582	−	0.524088i
$297$		0			0
$298$	−20.0237	−	3.53071i	−0.0671935	−	0.0118480i
$299$	68.1808	+	81.2548i	0.228030	+	0.271755i
$300$		0			0
$301$	12.4477	+	70.5943i	0.0413544	+	0.234533i
$302$	35.6644	+	12.9808i	0.118094	+	0.0429827i
$303$		0			0
$304$	−194.507	−	4.79366i	−0.639826	−	0.0157686i
$305$	−382.850			−1.25524
$306$		0			0
$307$	−103.954	+	18.3300i	−0.338614	+	0.0597068i	−0.340370	−	0.940292i	$-0.610552\pi$
$307$	−103.954	+	18.3300i	−0.338614	+	0.0597068i	0.00175580	+	0.999998i	$0.499441\pi$
$308$	17.1418	+	14.3837i	0.0556552	+	0.0467003i
$309$		0			0
$310$	−11.4208	+	64.7708i	−0.0368414	+	0.208938i
$311$	−139.497	+	241.616i	−0.448543	+	0.776899i	−0.998291	−	0.0584312i	$-0.981390\pi$
$311$	−139.497	+	241.616i	−0.448543	+	0.776899i	0.549749	+	0.835330i	$0.314724\pi$
$312$		0			0
$313$	244.049	−	88.8266i	0.779709	−	0.283791i	0.0786579	−	0.996902i	$-0.474937\pi$
$313$	244.049	−	88.8266i	0.779709	−	0.283791i	0.701051	+	0.713111i	$0.252714\pi$
$314$	−23.5304	−	64.6492i	−0.0749375	−	0.205889i
$315$		0			0
$316$	74.7311	+	43.1460i	0.236491	+	0.136538i
$317$	−421.691	−	74.3554i	−1.33025	−	0.234560i	−0.537068	−	0.843539i	$-0.680468\pi$
$317$	−421.691	−	74.3554i	−1.33025	−	0.234560i	−0.793186	+	0.608979i	$0.791579\pi$
$318$		0			0
$319$	189.627	−	225.988i	0.594441	−	0.708427i
$320$	−25.2227	−	143.045i	−0.0788208	−	0.447015i
$321$		0			0
$322$			3.95783i			0.0122914i
$323$	−186.055	+	304.667i	−0.576023	+	0.943241i
$324$		0			0
$325$	−155.270	+	426.599i	−0.477752	+	1.31261i
$326$	−99.0115	+	17.4584i	−0.303716	+	0.0535534i
$327$		0			0
$328$	60.6417	−	50.8844i	0.184883	−	0.155136i
$329$	−11.5251	+	65.3620i	−0.0350307	+	0.198669i
$330$		0			0
$331$	157.466	−	90.9131i	0.475728	−	0.274662i	−0.242906	−	0.970050i	$-0.578101\pi$
$331$	157.466	−	90.9131i	0.475728	−	0.274662i	0.718635	+	0.695388i	$0.244767\pi$
$332$	−372.703	+	135.653i	−1.12260	+	0.408593i
$333$		0			0
$334$	−56.0006	−	96.9958i	−0.167666	−	0.290407i
$335$	−378.710	−	218.648i	−1.13048	−	0.652682i
$336$		0			0
$337$	23.3632	+	27.8432i	0.0693269	+	0.0826206i	0.799593	−	0.600542i	$-0.205048\pi$
$337$	23.3632	+	27.8432i	0.0693269	+	0.0826206i	−0.730266	+	0.683163i	$0.760604\pi$
$338$	−89.6062	+	106.789i	−0.265107	+	0.315942i
$339$		0			0
$340$	−431.264	−	156.967i	−1.26842	−	0.461668i
$341$			84.4081i			0.247531i
$342$		0			0
$343$	−97.8168			−0.285180
$344$	−129.011	+	354.456i	−0.375033	+	1.03039i
$345$		0			0
$346$	−43.1118	−	36.1751i	−0.124601	−	0.104552i
$347$	474.726	−	398.343i	1.36809	−	1.14796i	0.394697	−	0.918812i	$-0.370850\pi$
$347$	474.726	−	398.343i	1.36809	−	1.14796i	0.973391	−	0.229150i	$-0.0735947\pi$
$348$		0			0
$349$	−78.3305	+	135.672i	−0.224443	+	0.388746i	−0.956152	−	0.292871i	$-0.905389\pi$
$349$	−78.3305	+	135.672i	−0.224443	+	0.388746i	0.731709	+	0.681617i	$0.238723\pi$
$350$	−14.6699	+	8.46967i	−0.0419140	+	0.0241991i
$351$		0			0
$352$	61.7542	+	169.668i	0.175438	+	0.482012i
$353$	280.147	+	485.229i	0.793617	+	1.37459i	0.923713	+	0.383084i	$0.125138\pi$
$353$	280.147	+	485.229i	0.793617	+	1.37459i	−0.130096	+	0.991501i	$0.541529\pi$
$354$		0			0
$355$	−540.125	−	95.2386i	−1.52148	−	0.268278i
$356$	−350.064	−	417.190i	−0.983326	−	1.17188i
$357$		0			0
$358$	38.7789	+	219.926i	0.108321	+	0.614318i
$359$	395.428	+	143.924i	1.10147	+	0.400903i	0.827858	−	0.560937i	$-0.189559\pi$
$359$	395.428	+	143.924i	1.10147	+	0.400903i	0.273613	+	0.961840i	$0.411781\pi$
$360$		0			0
$361$	−332.735	−	140.030i	−0.921704	−	0.387895i
$362$	108.904			0.300839
$363$		0			0
$364$	66.4895	−	11.7239i	0.182663	−	0.0322085i
$365$	715.605	+	600.464i	1.96056	+	1.64511i
$366$		0			0
$367$	−2.80817	+	15.9259i	−0.00765168	+	0.0433948i	−0.988395	−	0.151909i	$-0.951458\pi$
$367$	−2.80817	+	15.9259i	−0.00765168	+	0.0433948i	0.980743	+	0.195303i	$0.0625692\pi$
$368$	28.3893	−	49.1717i	0.0771448	−	0.133619i
$369$		0			0
$370$	156.690	−	57.0306i	0.423487	−	0.154137i
$371$	1.14066	+	3.13395i	0.00307457	+	0.00844730i
$372$		0			0
$373$	274.684	+	158.589i	0.736419	+	0.425172i	0.820766	−	0.571265i	$-0.193547\pi$
$373$	274.684	+	158.589i	0.736419	+	0.425172i	−0.0843469	+	0.996436i	$0.526880\pi$
$374$	83.0309	+	14.6406i	0.222008	+	0.0391460i
$375$		0			0
$376$	−224.491	+	267.538i	−0.597052	+	0.711538i
$377$	−154.561	−	876.562i	−0.409977	−	2.32510i
$378$		0			0
$379$		−	461.855i		−	1.21861i	−0.792934	−	0.609307i	$-0.791448\pi$
$379$		−	461.855i		−	1.21861i	0.792934	−	0.609307i	$-0.208552\pi$
$380$	91.8268	−	454.927i	0.241649	−	1.19718i
$381$		0			0
$382$	30.6458	−	84.1985i	0.0802245	−	0.220415i
$383$	637.438	−	112.397i	1.66433	−	0.293466i	0.739303	−	0.673373i	$-0.235155\pi$
$383$	637.438	−	112.397i	1.66433	−	0.293466i	0.925025	+	0.379907i	$0.124044\pi$
$384$		0			0
$385$	−34.1979	+	28.6954i	−0.0888256	+	0.0745336i
$386$	−9.06421	+	51.4057i	−0.0234824	+	0.133175i
$387$		0			0
$388$	385.863	−	222.778i	0.994493	−	0.574171i
$389$	79.8138	−	29.0498i	0.205177	−	0.0746782i	−0.237387	−	0.971415i	$-0.576291\pi$
$389$	79.8138	−	29.0498i	0.205177	−	0.0746782i	0.442564	+	0.896737i	$0.354069\pi$
$390$		0			0
$391$	−52.0880	−	90.2191i	−0.133217	−	0.230739i
$392$	−220.543	−	127.330i	−0.562609	−	0.324822i
$393$		0			0
$394$	136.111	+	162.211i	0.345460	+	0.411703i
$395$	−110.658	+	131.877i	−0.280146	+	0.333865i
$396$		0			0
$397$	182.689	+	66.4933i	0.460174	+	0.167490i	0.561696	−	0.827344i	$-0.310149\pi$
$397$	182.689	+	66.4933i	0.460174	+	0.167490i	−0.101522	+	0.994833i	$0.532371\pi$
$398$			153.145i			0.384786i
$399$		0			0
$400$	243.010			0.607525
$401$	136.802	−	375.859i	0.341151	−	0.937305i	−0.643910	−	0.765101i	$-0.722689\pi$
$401$	136.802	−	375.859i	0.341151	−	0.937305i	0.985061	−	0.172204i	$-0.0550888\pi$
$402$		0			0
$403$	195.091	+	163.701i	0.484097	+	0.406205i
$404$	−179.650	+	150.744i	−0.444678	+	0.373129i
$405$		0			0
$406$	16.6059	−	28.7623i	0.0409013	−	0.0708431i
$407$	185.329	−	107.000i	0.455354	−	0.262899i
$408$		0			0
$409$	117.529	+	322.910i	0.287358	+	0.789510i	0.996434	+	0.0843776i	$0.0268902\pi$
$409$	117.529	+	322.910i	0.287358	+	0.789510i	−0.709076	+	0.705132i	$0.750888\pi$
$410$	36.8450	+	63.8174i	0.0898659	+	0.155652i
$411$		0			0
$412$	−386.497	−	68.1498i	−0.938099	−	0.165412i
$413$	29.0207	+	34.5855i	0.0702680	+	0.0837422i
$414$		0			0
$415$	−137.401	−	779.239i	−0.331087	−	1.87769i
$416$	511.917	+	186.323i	1.23057	+	0.447891i
$417$		0			0
$418$	−2.10061	+	85.2341i	−0.00502538	+	0.203909i
$419$	−218.717			−0.521997			−0.260998	−	0.965339i	$-0.584052\pi$
$419$	−218.717			−0.521997			−0.260998	+	0.965339i	$0.584052\pi$
$420$		0			0
$421$	133.710	−	23.5766i	0.317600	−	0.0560015i	−0.0125756	−	0.999921i	$-0.504003\pi$
$421$	133.710	−	23.5766i	0.317600	−	0.0560015i	0.330176	+	0.943919i	$0.392892\pi$
$422$	−81.3531	−	68.2634i	−0.192780	−	0.161762i
$423$		0			0
$424$	−3.04743	+	17.2829i	−0.00718734	+	0.0407615i
$425$	222.935	−	386.134i	0.524552	−	0.908551i
$426$		0			0
$427$	−51.9794	+	18.9190i	−0.121732	+	0.0443067i
$428$	−55.4944	−	152.470i	−0.129660	−	0.356237i
$429$		0			0
$430$	−304.087	−	175.565i	−0.707179	−	0.408290i
$431$	71.1607	+	12.5475i	0.165106	+	0.0291126i	0.255590	−	0.966785i	$-0.417730\pi$
$431$	71.1607	+	12.5475i	0.165106	+	0.0291126i	−0.0904840	+	0.995898i	$0.528841\pi$
$432$		0			0
$433$	−324.779	+	387.057i	−0.750067	+	0.893895i	−0.997177	−	0.0750923i	$-0.976075\pi$
$433$	−324.779	+	387.057i	−0.750067	+	0.893895i	0.247109	+	0.968988i	$0.420519\pi$
$434$	1.65012	+	9.35829i	0.00380212	+	0.0215629i
$435$		0			0
$436$			216.043i			0.495511i
$437$	82.3448	−	65.7073i	0.188432	−	0.150360i
$438$		0			0
$439$	28.1483	−	77.3368i	0.0641192	−	0.176166i	−0.903496	−	0.428597i	$-0.859008\pi$
$439$	28.1483	−	77.3368i	0.0641192	−	0.176166i	0.967615	+	0.252431i	$0.0812302\pi$
$440$	−231.342	+	40.7919i	−0.525778	+	0.0927088i
$441$		0			0
$442$	194.868	−	163.514i	0.440879	−	0.369941i
$443$	24.6983	−	140.071i	0.0557524	−	0.316188i	−0.944159	−	0.329490i	$-0.893123\pi$
$443$	24.6983	−	140.071i	0.0557524	−	0.316188i	0.999912	+	0.0133021i	$0.00423433\pi$
$444$		0			0
$445$	940.921	−	543.241i	2.11443	−	1.22077i
$446$	118.942	−	43.2913i	0.266686	−	0.0970657i
$447$		0			0
$448$	−10.4932	−	18.1748i	−0.0234223	−	0.0405687i
$449$	234.051	+	135.129i	0.521271	+	0.300956i	0.737455	−	0.675397i	$-0.236028\pi$
$449$	234.051	+	135.129i	0.521271	+	0.300956i	−0.216183	+	0.976353i	$0.569361\pi$
$450$		0			0
$451$	60.7901	+	72.4468i	0.134790	+	0.160636i
$452$	−61.5542	+	73.3574i	−0.136182	+	0.162295i
$453$		0			0
$454$	199.951	+	72.7764i	0.440422	+	0.160300i
$455$			134.693i			0.296028i
$456$		0			0
$457$	−703.941			−1.54035			−0.770177	−	0.637831i	$-0.779832\pi$
$457$	−703.941			−1.54035			−0.770177	+	0.637831i	$0.779832\pi$
$458$	102.427	−	281.416i	0.223640	−	0.614445i
$459$		0			0
$460$	103.749	+	87.0560i	0.225542	+	0.189252i
$461$	−54.9805	+	46.1341i	−0.119264	+	0.100074i	−0.700469	−	0.713683i	$-0.747026\pi$
$461$	−54.9805	+	46.1341i	−0.119264	+	0.100074i	0.581205	+	0.813757i	$0.302581\pi$
$462$		0			0
$463$	48.6437	−	84.2533i	0.105062	−	0.181973i	−0.808702	−	0.588219i	$-0.799829\pi$
$463$	48.6437	−	84.2533i	0.105062	−	0.181973i	0.913764	+	0.406247i	$0.133163\pi$
$464$	−412.621	+	238.227i	−0.889270	+	0.513420i
$465$		0			0
$466$	59.6792	+	163.967i	0.128067	+	0.351861i
$467$	−53.2974	−	92.3138i	−0.114127	−	0.197674i	0.803303	−	0.595570i	$-0.203074\pi$
$467$	−53.2974	−	92.3138i	−0.114127	−	0.197674i	−0.917431	+	0.397896i	$0.869740\pi$
$468$		0			0
$469$	−62.2222	−	10.9715i	−0.132670	−	0.0233933i
$470$	−208.973	−	249.045i	−0.444624	−	0.529882i
$471$		0			0
$472$	41.2543	+	233.965i	0.0874031	+	0.495688i
$473$	−423.457	−	154.126i	−0.895258	−	0.325847i
$474$		0			0
$475$	419.764	+	164.603i	0.883713	+	0.346533i
$476$	−66.3094			−0.139305
$477$		0			0
$478$	−289.002	+	50.9589i	−0.604607	+	0.106609i
$479$	459.499	+	385.565i	0.959288	+	0.804938i	0.980837	−	0.194830i	$-0.0624154\pi$
$479$	459.499	+	385.565i	0.959288	+	0.804938i	−0.0215492	+	0.999768i	$0.506860\pi$
$480$		0			0
$481$	112.120	−	635.863i	0.233097	−	1.32196i
$482$	−90.2920	+	156.390i	−0.187328	+	0.324461i
$483$		0			0
$484$	265.671	−	96.6964i	0.548907	−	0.199786i
$485$	304.016	+	835.278i	0.626838	+	1.72222i
$486$		0			0
$487$	381.230	+	220.103i	0.782813	+	0.451957i	0.837426	−	0.546550i	$-0.184059\pi$
$487$	381.230	+	220.103i	0.782813	+	0.451957i	−0.0546135	+	0.998508i	$0.517393\pi$
$488$	−286.652	−	50.5445i	−0.587402	−	0.103575i
$489$		0			0
$490$	152.377	−	181.596i	0.310974	−	0.370605i
$491$	78.0781	+	442.803i	0.159019	+	0.901839i	0.955019	+	0.296544i	$0.0958340\pi$
$491$	78.0781	+	442.803i	0.159019	+	0.901839i	−0.796001	+	0.605296i	$0.793055\pi$
$492$		0			0
$493$			874.187i			1.77320i
$494$	192.926	+	170.158i	0.390539	+	0.344449i
$495$		0			0
$496$	46.6256	−	128.103i	0.0940033	−	0.258272i
$497$	−78.0390	+	13.7604i	−0.157020	+	0.0276869i
$498$		0			0
$499$	201.808	−	169.337i	0.404426	−	0.339354i	−0.417776	−	0.908550i	$-0.637190\pi$
$499$	201.808	−	169.337i	0.404426	−	0.339354i	0.822201	+	0.569197i	$0.192746\pi$
$500$	5.38383	−	30.5332i	0.0107677	−	0.0610664i
$501$		0			0
$502$	−109.060	+	62.9659i	−0.217251	+	0.125430i
$503$	21.7018	−	7.89881i	0.0431448	−	0.0157034i	−0.320358	−	0.947297i	$-0.603803\pi$
$503$	21.7018	−	7.89881i	0.0431448	−	0.0157034i	0.363502	+	0.931593i	$0.381581\pi$
$504$		0			0
$505$	−233.930	−	405.178i	−0.463227	−	0.802333i
$506$	−21.5473	−	12.4404i	−0.0425836	−	0.0245857i
$507$		0			0
$508$	3.43320	+	4.09152i	0.00675826	+	0.00805418i
$509$	−358.632	+	427.401i	−0.704582	+	0.839688i	−0.993037	−	0.117806i	$-0.962414\pi$
$509$	−358.632	+	427.401i	−0.704582	+	0.839688i	0.288455	+	0.957493i	$0.406858\pi$
$510$		0			0
$511$	126.830	+	46.1624i	0.248200	+	0.0903375i
$512$		−	509.007i		−	0.994153i
$513$		0			0
$514$	228.637			0.444819
$515$	267.786	−	735.737i	0.519974	−	1.42862i
$516$		0			0
$517$	−319.620	−	268.193i	−0.618220	−	0.518748i
$518$	18.4556	−	15.4861i	0.0356286	−	0.0298959i
$519$		0			0
$520$	−354.383	+	613.809i	−0.681505	+	1.18040i
$521$	755.639	−	436.268i	1.45036	−	0.837367i	0.451860	−	0.892089i	$-0.350761\pi$
$521$	755.639	−	436.268i	1.45036	−	0.837367i	0.998502	+	0.0547220i	$0.0174272\pi$
$522$		0			0
$523$	252.777	+	694.499i	0.483321	+	1.32791i	0.906629	+	0.421929i	$0.138647\pi$
$523$	252.777	+	694.499i	0.483321	+	1.32791i	−0.423308	+	0.905986i	$0.639131\pi$
$524$	177.030	+	306.625i	0.337843	+	0.585162i
$525$		0			0
$526$	−50.6642	−	8.93347i	−0.0963198	−	0.0169838i
$527$	−160.777	−	191.606i	−0.305080	−	0.363580i
$528$		0			0
$529$	−86.5215	−	490.688i	−0.163557	−	0.927576i
$530$	−15.3512	−	5.58736i	−0.0289644	−	0.0105422i
$531$		0			0
$532$	−10.0135	−	66.3032i	−0.0188223	−	0.124630i
$533$	285.341			0.535349
$534$		0			0
$535$	318.780	−	56.2095i	0.595851	−	0.105065i
$536$	−254.687	−	213.707i	−0.475162	−	0.398708i
$537$		0			0
$538$	49.3827	−	280.063i	0.0917894	−	0.520563i
$539$	152.118	−	263.476i	0.282222	−	0.488823i
$540$		0			0
$541$	−414.686	+	150.933i	−0.766518	+	0.278990i	−0.695539	−	0.718488i	$-0.744835\pi$
$541$	−414.686	+	150.933i	−0.766518	+	0.278990i	−0.0709789	+	0.997478i	$0.522612\pi$
$542$	4.07774	+	11.2035i	0.00752350	+	0.0206707i
$543$		0			0
$544$	−463.359	−	267.521i	−0.851763	−	0.491766i
$545$	−424.457	−	74.8432i	−0.778820	−	0.137327i
$546$		0			0
$547$	−273.163	+	325.543i	−0.499384	+	0.595142i	−0.955578	−	0.294738i	$-0.904768\pi$
$547$	−273.163	+	325.543i	−0.499384	+	0.595142i	0.456195	+	0.889880i	$0.349212\pi$
$548$	−13.9099	−	78.8872i	−0.0253831	−	0.143955i
$549$		0			0
$550$		−	106.488i		−	0.193615i
$551$	−874.105	+	132.012i	−1.58640	+	0.239587i
$552$		0			0
$553$	−8.50713	+	23.3731i	−0.0153836	+	0.0422661i
$554$	41.3763	−	7.29576i	0.0746864	−	0.0131692i
$555$		0			0
$556$	−597.284	+	501.181i	−1.07425	+	0.901404i
$557$	28.4106	−	161.124i	0.0510064	−	0.289272i	−0.948625	−	0.316401i	$-0.897525\pi$
$557$	28.4106	−	161.124i	0.0510064	−	0.289272i	0.999632	+	0.0271292i	$0.00863656\pi$
$558$		0			0
$559$	−1177.48	+	679.818i	−2.10640	+	1.21613i
$560$	67.7516	−	24.6596i	0.120985	−	0.0440350i
$561$		0			0
$562$	−21.0553	−	36.4688i	−0.0374649	−	0.0648912i
$563$	59.6883	+	34.4611i	0.106018	+	0.0612097i	0.552072	−	0.833797i	$-0.313837\pi$
$563$	59.6883	+	34.4611i	0.106018	+	0.0612097i	−0.446053	+	0.895006i	$0.647171\pi$
$564$		0			0
$565$	−122.801	−	146.348i	−0.217346	−	0.259023i
$566$	−7.34319	+	8.75127i	−0.0129738	+	0.0154616i
$567$		0			0
$568$	−391.836	−	142.617i	−0.689852	−	0.251086i
$569$			782.345i			1.37495i	0.726209	+	0.687474i	$0.241280\pi$
$569$			782.345i			1.37495i	−0.726209	+	0.687474i	$0.758720\pi$
$570$		0			0
$571$	293.620			0.514220			0.257110	−	0.966382i	$-0.417230\pi$
$571$	293.620			0.514220			0.257110	+	0.966382i	$0.417230\pi$
$572$	−145.164	+	398.835i	−0.253783	+	0.697264i
$573$		0			0
$574$	8.15606	+	6.84374i	0.0142092	+	0.0119229i
$575$	−100.794	+	84.5764i	−0.175294	+	0.147089i
$576$		0			0
$577$	180.983	−	313.471i	0.313661	−	0.543278i	−0.665491	−	0.746406i	$-0.731778\pi$
$577$	180.983	−	313.471i	0.313661	−	0.543278i	0.979152	+	0.203129i	$0.0651110\pi$
$578$	−39.2358	+	22.6528i	−0.0678821	+	0.0391917i
$579$		0			0
$580$	−388.704	−	1067.96i	−0.670180	−	1.84130i
$581$	−57.1620	−	99.0074i	−0.0983855	−	0.170409i
$582$		0			0
$583$	−20.6473	−	3.64067i	−0.0354156	−	0.00624473i
$584$	456.523	+	544.063i	0.781717	+	0.931615i
$585$		0			0
$586$	15.3706	+	87.1712i	0.0262297	+	0.148756i
$587$	−312.050	−	113.577i	−0.531602	−	0.193487i	0.0622515	−	0.998060i	$-0.480172\pi$
$587$	−312.050	−	113.577i	−0.531602	−	0.193487i	−0.593853	+	0.804573i	$0.702394\pi$
$588$		0			0
$589$	167.309	−	189.697i	0.284057	−	0.322066i
$590$	−221.151			−0.374833
$591$		0			0
$592$	−340.372	+	60.0167i	−0.574952	+	0.101380i
$593$	−834.924	−	700.585i	−1.40797	−	1.18142i	−0.957430	−	0.288666i	$-0.906788\pi$
$593$	−834.924	−	700.585i	−1.40797	−	1.18142i	−0.450537	−	0.892758i	$-0.648767\pi$
$594$		0			0
$595$	22.9714	−	130.277i	0.0386074	−	0.218953i
$596$	−50.2637	+	87.0592i	−0.0843350	+	0.146073i
$597$		0			0
$598$	−70.5420	+	25.6752i	−0.117963	+	0.0429351i
$599$	−68.3102	−	187.681i	−0.114040	−	0.313323i	0.869521	−	0.493895i	$-0.164427\pi$
$599$	−68.3102	−	187.681i	−0.114040	−	0.313323i	−0.983562	+	0.180572i	$0.942205\pi$
$600$		0			0
$601$	543.373	+	313.717i	0.904115	+	0.521991i	0.878533	−	0.477682i	$-0.158523\pi$
$601$	543.373	+	313.717i	0.904115	+	0.521991i	0.0255820	+	0.999673i	$0.491856\pi$
$602$	−49.9616	−	8.80958i	−0.0829927	−	0.0146339i
$603$		0			0
$604$	120.617	−	143.746i	0.199697	−	0.237990i
$605$	97.9425	+	555.460i	0.161888	+	0.918115i
$606$		0			0
$607$			518.700i			0.854531i	0.904126	+	0.427265i	$0.140523\pi$
$607$			518.700i			0.854531i	−0.904126	+	0.427265i	$0.859477\pi$
$608$	197.523	−	503.715i	0.324874	−	0.828478i
$609$		0			0
$610$	92.6716	−	254.613i	0.151921	−	0.417399i
$611$	−1239.74	+	218.599i	−2.02903	+	0.357773i
$612$		0			0
$613$	62.9423	−	52.8148i	0.102679	−	0.0861580i	−0.590003	−	0.807401i	$-0.700873\pi$
$613$	62.9423	−	52.8148i	0.102679	−	0.0861580i	0.692682	+	0.721243i	$0.256429\pi$
$614$	12.9727	−	73.5716i	0.0211281	−	0.119823i
$615$		0			0
$616$	−29.3935	+	16.9704i	−0.0477167	+	0.0275493i
$617$	30.4748	−	11.0919i	0.0493920	−	0.0179772i	−0.317206	−	0.948357i	$-0.602745\pi$
$617$	30.4748	−	11.0919i	0.0493920	−	0.0179772i	0.366598	+	0.930379i	$0.380522\pi$
$618$		0			0
$619$	472.043	+	817.603i	0.762590	+	1.32084i	0.941511	+	0.336981i	$0.109406\pi$
$619$	472.043	+	817.603i	0.762590	+	1.32084i	−0.178922	+	0.983863i	$0.557261\pi$
$620$	281.611	+	162.588i	0.454212	+	0.262239i
$621$		0			0
$622$	−126.920	−	151.257i	−0.204051	−	0.243178i
$623$	100.904	−	120.253i	0.161964	−	0.193022i
$624$		0			0
$625$	615.612	+	224.065i	0.984980	+	0.358503i
$626$			183.805i			0.293619i
$627$		0			0
$628$	−340.149			−0.541639
$629$	−216.889	+	595.897i	−0.344815	+	0.947372i
$630$		0			0
$631$	639.120	+	536.285i	1.01287	+	0.849897i	0.988715	−	0.149811i	$-0.0478666\pi$
$631$	639.120	+	536.285i	1.01287	+	0.849897i	0.0241532	+	0.999708i	$0.492311\pi$
$632$	−100.264	+	84.1311i	−0.158645	+	0.133119i
$633$		0			0
$634$	151.523	−	262.446i	0.238996	−	0.413953i
$635$	−9.22793	+	5.32775i	−0.0145322	+	0.00839015i
$636$		0			0
$637$	−313.950	−	862.570i	−0.492857	−	1.35411i
$638$	104.392	+	180.813i	0.163624	+	0.283406i
$639$		0			0
$640$	884.311	+	155.928i	1.38174	+	0.243637i
$641$	356.342	+	424.672i	0.555916	+	0.662514i	0.968677	−	0.248325i	$-0.0798800\pi$
$641$	356.342	+	424.672i	0.555916	+	0.662514i	−0.412761	+	0.910839i	$0.635436\pi$
$642$		0			0
$643$	57.3587	+	325.297i	0.0892048	+	0.505906i	0.996370	+	0.0851305i	$0.0271307\pi$
$643$	57.3587	+	325.297i	0.0892048	+	0.505906i	−0.907165	+	0.420775i	$0.861758\pi$
$644$	18.3880	+	6.69269i	0.0285528	+	0.0103924i
$645$		0			0
$646$	−157.582	−	197.483i	−0.243935	−	0.305701i
$647$	330.991			0.511578			0.255789	−	0.966733i	$-0.417665\pi$
$647$	330.991			0.511578			0.255789	+	0.966733i	$0.417665\pi$
$648$		0			0
$649$	−279.510	+	49.2852i	−0.430678	+	0.0759402i
$650$	−246.125	−	206.523i	−0.378653	−	0.317728i
$651$		0			0
$652$	−86.3170	+	489.528i	−0.132388	+	0.750810i
$653$	−251.736	+	436.020i	−0.385508	+	0.667719i	−0.991839	−	0.127493i	$-0.959307\pi$
$653$	−251.736	+	436.020i	−0.385508	+	0.667719i	0.606332	+	0.795212i	$0.292640\pi$
$654$		0			0
$655$	−663.751	+	241.586i	−1.01336	+	0.368833i
$656$	−52.2403	−	143.529i	−0.0796346	−	0.218794i
$657$		0			0
$658$	−40.6791	−	23.4861i	−0.0618224	−	0.0356932i
$659$	−172.200	−	30.3635i	−0.261305	−	0.0460751i	0.0414607	−	0.999140i	$-0.486799\pi$
$659$	−172.200	−	30.3635i	−0.261305	−	0.0460751i	−0.302766	+	0.953065i	$0.597910\pi$
$660$		0			0
$661$	401.271	−	478.216i	0.607067	−	0.723474i	−0.371723	−	0.928344i	$-0.621233\pi$
$661$	401.271	−	478.216i	0.607067	−	0.723474i	0.978789	+	0.204870i	$0.0656772\pi$
$662$	22.3457	+	126.729i	0.0337548	+	0.191433i
$663$		0			0
$664$		−	601.582i		−	0.905998i
$665$	133.734	+	3.29590i	0.201104	+	0.00495624i
$666$		0			0
$667$	88.2328	−	242.418i	0.132283	−	0.363445i
$668$	−545.338	+	96.1578i	−0.816375	+	0.143949i
$669$		0			0
$670$	237.081	−	198.935i	0.353853	−	0.296918i
$671$	60.3840	−	342.455i	0.0899910	−	0.510364i
$672$		0			0
$673$	106.458	−	61.4634i	0.158184	−	0.0913274i	−0.418819	−	0.908070i	$-0.637556\pi$
$673$	106.458	−	61.4634i	0.158184	−	0.0913274i	0.577002	+	0.816743i	$0.304222\pi$
$674$	−24.1723	+	8.79798i	−0.0358639	+	0.0130534i
$675$		0			0
$676$	344.614	+	596.889i	0.509784	+	0.882971i
$677$	815.455	+	470.803i	1.20451	+	0.695426i	0.961555	−	0.274611i	$-0.0885491\pi$
$677$	815.455	+	470.803i	1.20451	+	0.695426i	0.242958	+	0.970037i	$0.421882\pi$
$678$		0			0
$679$	82.5526	+	98.3823i	0.121580	+	0.144893i
$680$	447.448	−	533.248i	0.658012	−	0.784189i
$681$		0			0
$682$	−56.1354	−	20.4316i	−0.0823100	−	0.0299584i
$683$		−	17.3276i		−	0.0253698i	−0.999920	−	0.0126849i	$-0.995962\pi$
$683$		−	17.3276i		−	0.0253698i	0.999920	−	0.0126849i	$-0.00403784\pi$
$684$		0			0
$685$	159.808			0.233296
$686$	23.6773	−	65.0528i	0.0345150	−	0.0948292i
$687$		0			0
$688$	557.528	+	467.821i	0.810360	+	0.679973i
$689$	−48.4579	+	40.6610i	−0.0703308	+	0.0590145i
$690$		0			0
$691$	192.257	−	333.000i	0.278231	−	0.481910i	−0.692714	−	0.721212i	$-0.743585\pi$
$691$	192.257	−	333.000i	0.278231	−	0.481910i	0.970945	+	0.239302i	$0.0769187\pi$
$692$	−240.971	+	139.125i	−0.348224	+	0.201047i
$693$		0			0
$694$	150.006	+	412.137i	0.216147	+	0.593858i
$695$	−777.749	−	1347.10i	−1.11906	−	1.93827i
$696$		0			0
$697$	−275.987	−	48.6640i	−0.395964	−	0.0698192i
$698$	−71.2681	−	84.9340i	−0.102103	−	0.121682i
$699$		0			0
$700$	14.5432	+	82.4784i	0.0207759	+	0.117826i
$701$	620.285	+	225.765i	0.884857	+	0.322062i	0.744168	−	0.667992i	$-0.232846\pi$
$701$	620.285	+	225.765i	0.884857	+	0.322062i	0.140689	+	0.990054i	$0.455068\pi$
$702$		0			0
$703$	−628.594	−	126.881i	−0.894159	−	0.180485i
$704$	131.930			0.187401
$705$		0			0
$706$	−390.512	+	68.8578i	−0.553133	+	0.0975323i
$707$	−51.7830	−	43.4511i	−0.0732433	−	0.0614584i
$708$		0			0
$709$	−97.3388	+	552.036i	−0.137290	+	0.778612i	0.835947	+	0.548810i	$0.184919\pi$
$709$	−97.3388	+	552.036i	−0.137290	+	0.778612i	−0.973237	+	0.229802i	$0.926192\pi$
$710$	194.080	−	336.156i	0.273351	−	0.473459i
$711$		0			0
$712$	776.219	−	282.521i	1.09019	−	0.396798i
$713$	25.2454	+	69.3611i	0.0354073	+	0.0972807i
$714$		0			0
$715$	−733.298	−	423.370i	−1.02559	−	0.592126i
$716$	1087.35	+	191.729i	1.51864	+	0.267778i
$717$		0			0
$718$	−191.433	+	228.141i	−0.266619	+	0.317745i
$719$	−176.762	−	1002.46i	−0.245844	−	1.39425i	−0.818525	−	0.574470i	$-0.805208\pi$
$719$	−176.762	−	1002.46i	−0.245844	−	1.39425i	0.572682	−	0.819778i	$-0.305903\pi$
$720$		0			0
$721$		−	113.124i		−	0.156899i
$722$	173.668	−	187.389i	0.240537	−	0.259542i
$723$		0			0
$724$	184.156	−	505.966i	0.254360	−	0.698848i
$725$	1087.35	−	191.729i	1.49979	−	0.264454i
$726$		0			0
$727$	405.027	−	339.858i	0.557122	−	0.467481i	−0.320222	−	0.947342i	$-0.603758\pi$
$727$	405.027	−	339.858i	0.557122	−	0.467481i	0.877344	+	0.479862i	$0.159313\pi$
$728$	−17.7824	+	100.849i	−0.0244264	+	0.138529i
$729$		0			0
$730$	−572.555	+	330.565i	−0.784321	+	0.452828i
$731$	1254.82	−	456.717i	1.71658	−	0.624785i
$732$		0			0
$733$	−86.5772	−	149.956i	−0.118113	−	0.204579i	0.800907	−	0.598789i	$-0.204351\pi$
$733$	−86.5772	−	149.956i	−0.118113	−	0.204579i	−0.919020	+	0.394211i	$0.871018\pi$
$734$	−9.91175	−	5.72255i	−0.0135037	−	0.00779639i
$735$		0			0
$736$	101.491	+	120.953i	0.137896	+	0.164338i
$737$	255.310	−	304.266i	0.346417	−	0.412844i
$738$		0			0
$739$	−1157.10	−	421.151i	−1.56577	−	0.569893i	−0.593720	−	0.804671i	$-0.702342\pi$
$739$	−1157.10	−	421.151i	−1.56577	−	0.569893i	−0.972049	+	0.234778i	$0.924564\pi$
$740$		−	824.420i		−	1.11408i
$741$		0			0
$742$	−2.36033			−0.00318104
$743$	−245.007	+	673.150i	−0.329753	+	0.905989i	0.658421	+	0.752650i	$0.271225\pi$
$743$	−245.007	+	673.150i	−0.329753	+	0.905989i	−0.988174	+	0.153339i	$0.950997\pi$
$744$		0			0
$745$	−153.632	−	128.912i	−0.206217	−	0.173037i
$746$	−171.959	+	144.290i	−0.230508	+	0.193419i
$747$		0			0
$748$	208.425	−	361.003i	0.278643	−	0.482625i
$749$	40.5031	−	23.3845i	0.0540762	−	0.0312209i
$750$		0			0
$751$	−398.964	−	1096.15i	−0.531244	−	1.45958i	−0.857592	−	0.514331i	$-0.828040\pi$
$751$	−398.964	−	1096.15i	−0.531244	−	1.45958i	0.326348	−	0.945250i	$-0.394182\pi$
$752$	336.929	+	583.578i	0.448044	+	0.776035i
$753$		0			0
$754$	620.368	+	109.388i	0.822769	+	0.145076i
$755$	240.631	+	286.772i	0.318716	+	0.379831i
$756$		0			0
$757$	125.803	+	713.466i	0.166187	+	0.942491i	0.947833	+	0.318769i	$0.103269\pi$
$757$	125.803	+	713.466i	0.166187	+	0.942491i	−0.781646	+	0.623722i	$0.785620\pi$
$758$	307.155	+	111.795i	0.405218	+	0.147487i
$759$		0			0
$760$	600.768	+	366.880i	0.790485	+	0.482737i
$761$	295.133			0.387823			0.193912	−	0.981019i	$-0.437883\pi$
$761$	295.133			0.387823			0.193912	+	0.981019i	$0.437883\pi$
$762$		0			0
$763$	−61.3269	+	10.8136i	−0.0803761	+	0.0141725i
$764$	−339.363	−	284.759i	−0.444192	−	0.372722i
$765$		0			0
$766$	−79.5469	+	451.133i	−0.103847	+	0.588946i
$767$	−428.169	+	741.610i	−0.558239	+	0.966897i
$768$		0			0
$769$	−378.622	+	137.807i	−0.492356	+	0.179203i	−0.576253	−	0.817272i	$-0.695486\pi$
$769$	−378.622	+	137.807i	−0.492356	+	0.179203i	0.0838969	+	0.996474i	$0.473263\pi$
$770$	−10.8060	−	29.6891i	−0.0140337	−	0.0385573i
$771$		0			0
$772$	223.503	+	129.039i	0.289511	+	0.167149i
$773$	−166.209	−	29.3071i	−0.215018	−	0.0379134i	0.0651015	−	0.997879i	$-0.479263\pi$
$773$	−166.209	−	29.3071i	−0.215018	−	0.0379134i	−0.280119	+	0.959965i	$0.590374\pi$
$774$		0			0
$775$	−203.066	+	242.005i	−0.262021	+	0.312264i
$776$	117.352	+	665.538i	0.151227	+	0.857652i
$777$		0			0
$778$			60.1117i			0.0772644i
$779$	6.98223	−	283.310i	0.00896307	−	0.363684i
$780$		0			0
$781$	170.380	−	468.114i	0.218156	−	0.599378i
$782$	72.6083	−	12.8028i	0.0928495	−	0.0163719i
$783$		0			0
$784$	−376.402	+	315.839i	−0.480105	+	0.402856i
$785$	117.837	−	668.288i	0.150111	−	0.851322i
$786$		0			0
$787$	−413.425	+	238.691i	−0.525318	+	0.303293i	−0.739108	−	0.673587i	$-0.764753\pi$
$787$	−413.425	+	238.691i	−0.525318	+	0.303293i	0.213790	+	0.976880i	$0.431419\pi$
$788$	983.795	−	358.072i	1.24847	−	0.454406i
$789$		0			0
$790$	−60.9187	−	105.514i	−0.0771122	−	0.133562i
$791$	−23.9046	−	13.8013i	−0.0302207	−	0.0174479i
$792$		0			0
$793$	−674.401	−	803.720i	−0.850442	−	1.01352i
$794$	−88.4424	+	105.402i	−0.111388	+	0.132748i
$795$		0			0
$796$	711.509	+	258.968i	0.893855	+	0.325337i
$797$		−	964.886i		−	1.21065i	−0.795979	−	0.605324i	$-0.793044\pi$
$797$		−	964.886i		−	1.21065i	0.795979	−	0.605324i	$-0.206956\pi$
$798$		0			0
$799$	1236.38			1.54741
$800$	−231.128	+	635.019i	−0.288910	+	0.793774i
$801$		0			0
$802$	216.850	+	181.959i	0.270387	+	0.226882i
$803$	−649.975	+	545.394i	−0.809433	+	0.679195i
$804$		0			0
$805$	−19.5192	+	33.8082i	−0.0242474	+	0.0419978i
$806$	−156.092	+	90.1197i	−0.193663	+	0.111811i
$807$		0			0
$808$	−121.659	−	334.254i	−0.150568	−	0.413681i
$809$	−83.6869	−	144.950i	−0.103445	−	0.179172i	0.809657	−	0.586903i	$-0.199653\pi$
$809$	−83.6869	−	144.950i	−0.103445	−	0.179172i	−0.913102	+	0.407732i	$0.866320\pi$
$810$		0			0
$811$	1129.00	+	199.074i	1.39211	+	0.245467i	0.818899	−	0.573938i	$-0.194585\pi$
$811$	1129.00	+	199.074i	1.39211	+	0.245467i	0.573214	+	0.819405i	$0.305696\pi$
$812$	−105.549	−	125.788i	−0.129986	−	0.154911i
$813$		0			0
$814$	26.2997	+	149.153i	0.0323092	+	0.183234i
$815$	−931.868	−	339.172i	−1.14340	−	0.416162i
$816$		0			0
$817$	646.167	+	1185.73i	0.790902	+	1.45133i
$818$	−243.199			−0.297309
$819$		0			0
$820$	358.800	−	63.2661i	0.437561	−	0.0771537i
$821$	−683.038	−	573.137i	−0.831959	−	0.698097i	0.123781	−	0.992310i	$-0.460498\pi$
$821$	−683.038	−	573.137i	−0.831959	−	0.698097i	−0.955740	+	0.294213i	$0.904943\pi$
$822$		0			0
$823$	197.568	−	1120.46i	0.240058	−	1.36144i	−0.591637	−	0.806204i	$-0.701518\pi$
$823$	197.568	−	1120.46i	0.240058	−	1.36144i	0.831695	−	0.555232i	$-0.187371\pi$
$824$	297.634	−	515.517i	0.361206	−	0.625628i
$825$		0			0
$826$	−30.0257	+	10.9285i	−0.0363507	+	0.0132306i
$827$	172.111	+	472.871i	0.208115	+	0.571791i	0.999203	−	0.0399109i	$-0.0127074\pi$
$827$	172.111	+	472.871i	0.208115	+	0.571791i	−0.791088	+	0.611702i	$0.790485\pi$
$828$		0			0
$829$	98.7997	+	57.0420i	0.119179	+	0.0688082i	0.558405	−	0.829569i	$-0.311414\pi$
$829$	98.7997	+	57.0420i	0.119179	+	0.0688082i	−0.439225	+	0.898377i	$0.644747\pi$
$830$	551.490	+	97.2426i	0.664446	+	0.117160i
$831$		0			0
$832$	255.865	−	304.928i	0.307530	−	0.366500i
$833$	156.550	+	887.837i	0.187935	+	1.06583i
$834$		0			0
$835$		−	1104.73i		−	1.32303i
$836$	392.444	+	153.890i	0.469431	+	0.184079i
$837$		0			0
$838$	52.9420	−	145.457i	0.0631766	−	0.173576i
$839$	1066.40	−	188.034i	1.27103	−	0.224117i	0.502864	−	0.864366i	$-0.332280\pi$
$839$	1066.40	−	188.034i	1.27103	−	0.224117i	0.768168	+	0.640248i	$0.221169\pi$
$840$		0			0
$841$	−1014.08	+	850.912i	−1.20580	+	1.01179i
$842$	−16.6859	+	94.6302i	−0.0198169	+	0.112387i
$843$		0			0
$844$	−454.719	+	262.532i	−0.538766	+	0.311057i
$845$	−1292.08	+	470.280i	−1.52909	+	0.556545i
$846$		0			0
$847$	40.7464	+	70.5748i	0.0481067	+	0.0833232i
$848$	29.3245	+	16.9305i	0.0345808	+	0.0199652i
$849$		0			0
$850$	202.835	+	241.729i	0.238629	+	0.284387i
$851$	120.289	−	143.355i	0.141350	−	0.168455i
$852$		0			0
$853$	214.717	+	78.1506i	0.251720	+	0.0916185i	0.464798	−	0.885417i	$-0.346127\pi$
$853$	214.717	+	78.1506i	0.251720	+	0.0916185i	−0.213079	+	0.977035i	$0.568349\pi$
$854$		−	39.1483i		−	0.0458411i
$855$		0			0
$856$	246.102			0.287503
$857$	−92.4587	+	254.028i	−0.107886	+	0.296416i	−0.981875	−	0.189532i	$-0.939303\pi$
$857$	−92.4587	+	254.028i	−0.107886	+	0.296416i	0.873988	+	0.485947i	$0.161525\pi$
$858$		0			0
$859$	−357.479	−	299.961i	−0.416157	−	0.349197i	0.410542	−	0.911842i	$-0.365340\pi$
$859$	−357.479	−	299.961i	−0.416157	−	0.349197i	−0.826699	+	0.562644i	$0.809784\pi$
$860$	−1329.88	+	1115.90i	−1.54637	+	1.29756i
$861$		0			0
$862$	−25.5697	+	44.2880i	−0.0296632	+	0.0513782i
$863$	−770.849	+	445.050i	−0.893221	+	0.515701i	−0.874995	−	0.484133i	$-0.839135\pi$
$863$	−770.849	+	445.050i	−0.893221	+	0.515701i	−0.0182261	+	0.999834i	$0.505802\pi$
$864$		0			0
$865$	−189.858	−	521.631i	−0.219489	−	0.603041i
$866$	−178.796	−	309.683i	−0.206462	−	0.357602i
$867$		0			0
$868$	46.2688	+	8.15845i	0.0533051	+	0.00939913i
$869$	−100.509	−	119.782i	−0.115660	−	0.137839i
$870$		0			0
$871$	−208.099	−	1180.19i	−0.238919	−	1.35498i
$872$	−307.924	−	112.075i	−0.353124	−	0.128527i
$873$		0			0
$874$	23.7663	+	70.6682i	0.0271926	+	0.0808560i
$875$	8.93678			0.0102135
$876$		0			0
$877$	−257.119	+	45.3370i	−0.293180	+	0.0516956i	−0.318304	−	0.947989i	$-0.603113\pi$
$877$	−257.119	+	45.3370i	−0.293180	+	0.0516956i	0.0251236	+	0.999684i	$0.492002\pi$
$878$	44.6192	+	37.4399i	0.0508191	+	0.0426423i
$879$		0			0
$880$	−78.7064	+	446.366i	−0.0894391	+	0.507234i
$881$	42.0790	−	72.8830i	0.0477628	−	0.0827275i	−0.841156	−	0.540793i	$-0.818124\pi$
$881$	42.0790	−	72.8830i	0.0477628	−	0.0827275i	0.888918	+	0.458066i	$0.151458\pi$
$882$		0			0
$883$	−454.849	+	165.551i	−0.515118	+	0.187488i	−0.586481	−	0.809963i	$-0.699487\pi$
$883$	−454.849	+	165.551i	−0.515118	+	0.187488i	0.0713634	+	0.997450i	$0.477265\pi$
$884$	−430.161	−	1181.86i	−0.486608	−	1.33694i
$885$		0			0
$886$	87.1756	+	50.3308i	0.0983923	+	0.0568068i
$887$	−1169.55	−	206.224i	−1.31855	−	0.232496i	−0.530279	−	0.847823i	$-0.677913\pi$
$887$	−1169.55	−	206.224i	−1.31855	−	0.232496i	−0.788272	+	0.615327i	$0.789024\pi$
$888$		0			0
$889$	−0.989598	+	1.17936i	−0.00111316	+	0.00132661i
$890$	133.524	+	757.253i	0.150027	+	0.850846i
$891$		0			0
$892$		−	625.808i		−	0.701578i
$893$	186.707	+	1236.26i	0.209079	+	1.38439i
$894$		0			0
$895$	−753.375	+	2069.88i	−0.841760	+	2.31272i
$896$	127.768	−	22.5290i	0.142598	−	0.0251440i
$897$		0			0
$898$	−146.521	+	122.946i	−0.163164	+	0.136911i
$899$	107.557	−	609.984i	0.119640	−	0.678513i
$900$		0			0
$901$	53.8040	−	31.0637i	0.0597159	−	0.0344770i
$902$	−62.8952	+	22.8920i	−0.0697286	+	0.0253792i
$903$		0			0
$904$	−72.6237	−	125.788i	−0.0803360	−	0.139146i
$905$	930.269	+	537.091i	1.02792	+	0.593471i
$906$		0			0
$907$	−101.853	−	121.384i	−0.112297	−	0.133830i	0.706968	−	0.707246i	$-0.250062\pi$
$907$	−101.853	−	121.384i	−0.112297	−	0.133830i	−0.819265	+	0.573416i	$0.805618\pi$
$908$	676.236	−	805.906i	0.744753	−	0.887562i
$909$		0			0
$910$	−89.5771	−	32.6034i	−0.0984363	−	0.0358279i
$911$		−	45.3584i		−	0.0497897i	−0.999690	−	0.0248948i	$-0.992075\pi$
$911$		−	45.3584i		−	0.0497897i	0.999690	−	0.0248948i	$-0.00792509\pi$
$912$		0			0
$913$	718.692			0.787176
$914$	170.394	−	468.154i	0.186427	−	0.512204i
$915$		0			0
$916$	−1134.25	−	951.749i	−1.23826	−	1.03903i
$917$	−78.1792	+	65.6001i	−0.0852553	+	0.0715377i
$918$		0			0
$919$	−112.912	+	195.569i	−0.122864	+	0.212806i	−0.920896	−	0.389809i	$-0.872541\pi$
$919$	−112.912	+	195.569i	−0.122864	+	0.212806i	0.798032	+	0.602615i	$0.205874\pi$
$920$	−177.902	+	102.712i	−0.193371	+	0.111643i
$921$		0			0
$922$	−17.3729	−	47.7318i	−0.0188427	−	0.0517698i
$923$	−751.511	−	1301.65i	−0.814205	−	1.41024i
$924$		0			0
$925$	788.770	+	139.081i	0.852725	+	0.150358i
$926$	44.2579	+	52.7445i	0.0477947	+	0.0569595i
$927$		0			0
$928$	−230.074	−	1304.82i	−0.247925	−	1.40605i
$929$	−1671.31	−	608.307i	−1.79904	−	0.654798i	−0.998454	−	0.0555823i	$-0.982298\pi$
$929$	−1671.31	−	608.307i	−1.79904	−	0.654798i	−0.800588	−	0.599215i	$-0.795479\pi$
$930$		0			0
$931$	−864.113	+	290.609i	−0.928156	+	0.312147i
$932$	862.707			0.925651
$933$		0			0
$934$	74.2941	−	13.1001i	0.0795440	−	0.0140258i
$935$	637.055	+	534.553i	0.681342	+	0.571714i
$936$		0			0
$937$	13.0564	−	74.0467i	0.0139343	−	0.0790252i	−0.977048	−	0.213021i	$-0.931670\pi$
$937$	13.0564	−	74.0467i	0.0139343	−	0.0790252i	0.990982	+	0.133996i	$0.0427808\pi$
$938$	22.3579	−	38.7250i	0.0238357	−	0.0412847i
$939$		0			0
$940$	−1510.43	+	549.752i	−1.60684	+	0.584843i
$941$	185.275	+	509.040i	0.196892	+	0.540957i	0.998370	−	0.0570673i	$-0.0181750\pi$
$941$	185.275	+	509.040i	0.196892	+	0.540957i	−0.801478	+	0.598024i	$0.795953\pi$
$942$		0			0
$943$	71.6213	+	41.3506i	0.0759505	+	0.0438500i
$944$	451.426	+	79.5986i	0.478205	+	0.0843205i
$945$		0			0
$946$	205.002	−	244.312i	0.216704	−	0.258258i
$947$	−51.0229	−	289.365i	−0.0538784	−	0.305560i	0.945945	−	0.324326i	$-0.105137\pi$
$947$	−51.0229	−	289.365i	−0.0538784	−	0.305560i	−0.999824	+	0.0187660i	$0.994026\pi$
$948$		0			0
$949$			2560.01i			2.69759i
$950$	−211.076	+	239.319i	−0.222185	+	0.251915i
$951$		0			0
$952$	34.3989	−	94.5102i	0.0361333	−	0.0992755i
$953$	1226.21	−	216.215i	1.28669	−	0.226878i	0.511871	−	0.859063i	$-0.328953\pi$
$953$	1226.21	−	216.215i	1.28669	−	0.226878i	0.774818	+	0.632185i	$0.217842\pi$
$954$		0			0
$955$	677.029	−	568.095i	0.708931	−	0.594863i
$956$	−251.949	+	1428.87i	−0.263544	+	1.49464i
$957$		0			0
$958$	−367.644	+	212.260i	−0.383762	+	0.221565i
$959$	21.6971	−	7.89709i	0.0226247	−	0.00823472i
$960$		0			0
$961$	−391.889	−	678.771i	−0.407793	−	0.706318i
$962$	395.740	+	228.480i	0.411372	+	0.237506i
$963$		0			0
$964$	573.904	+	683.952i	0.595336	+	0.709493i
$965$	−330.950	+	394.410i	−0.342953	+	0.408715i
$966$		0			0
$967$	91.2073	+	33.1968i	0.0943199	+	0.0343296i	0.388749	−	0.921344i	$-0.372907\pi$
$967$	91.2073	+	33.1968i	0.0943199	+	0.0343296i	−0.294429	+	0.955673i	$0.595130\pi$
$968$			428.822i			0.442998i
$969$		0			0
$970$	−629.089			−0.648546
$971$	252.747	−	694.418i	0.260296	−	0.715157i	−0.738851	−	0.673868i	$-0.764631\pi$
$971$	252.747	−	694.418i	0.260296	−	0.715157i	0.999147	−	0.0412887i	$-0.0131463\pi$
$972$		0			0
$973$	−172.163	−	144.462i	−0.176941	−	0.148471i
$974$	−238.659	+	200.258i	−0.245029	+	0.205604i
$975$		0			0
$976$	−280.809	+	486.375i	−0.287714	+	0.498335i
$977$	−1043.75	+	602.610i	−1.06832	+	0.616796i	−0.927722	−	0.373271i	$-0.878236\pi$
$977$	−1043.75	+	602.610i	−1.06832	+	0.616796i	−0.140599	+	0.990067i	$0.544903\pi$
$978$		0			0
$979$	337.518	+	927.324i	0.344758	+	0.947216i
$980$	−586.024	−	1015.02i	−0.597983	−	1.03574i
$981$		0			0
$982$	−313.385	−	55.2581i	−0.319129	−	0.0562710i
$983$	423.850	+	505.125i	0.431181	+	0.513861i	0.937262	−	0.348624i	$-0.113351\pi$
$983$	423.850	+	505.125i	0.431181	+	0.513861i	−0.506082	+	0.862485i	$0.668907\pi$
$984$		0			0
$985$	362.686	+	2056.90i	0.368210	+	2.08822i
$986$	−581.376	−	211.603i	−0.589631	−	0.214608i
$987$		0			0
$988$	1116.79	−	608.595i	1.13035	−	0.615987i
$989$	−394.067			−0.398450
$990$		0			0
$991$	933.288	−	164.564i	0.941763	−	0.166058i	0.318370	−	0.947967i	$-0.396865\pi$
$991$	933.288	−	164.564i	0.941763	−	0.166058i	0.623394	+	0.781908i	$0.285753\pi$
$992$	290.405	+	243.678i	0.292747	+	0.245644i
$993$		0			0
$994$	9.73862	−	55.2305i	0.00979741	−	0.0555639i
$995$	−755.278	+	1308.18i	−0.759074	+	1.31475i
$996$		0			0
$997$	128.652	−	46.8254i	0.129039	−	0.0469663i	−0.276694	−	0.960958i	$-0.589239\pi$
$997$	128.652	−	46.8254i	0.129039	−	0.0469663i	0.405732	+	0.913992i	$0.367017\pi$
$998$	63.7682	+	175.202i	0.0638960	+	0.175553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.ba.c.91.2		18
3.2	odd	2		57.3.k.a.34.2	✓	18
19.14	odd	18	inner	171.3.ba.c.109.2		18
57.14	even	18		57.3.k.a.52.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.k.a.34.2	✓	18	3.2	odd	2
57.3.k.a.52.2	yes	18	57.14	even	18
171.3.ba.c.91.2		18	1.1	even	1	trivial
171.3.ba.c.109.2		18	19.14	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.242057 + 0.665047i) q^{2} +(2.68048 + 2.24919i) q^{4} +(-5.34756 + 4.48713i) q^{5} +(-0.504300 + 0.873473i) q^{7} +(-4.59629 + 2.65367i) q^{8} +O(q^{10})\)	\(q+(-0.242057 + 0.665047i) q^{2} +(2.68048 + 2.24919i) q^{4} +(-5.34756 + 4.48713i) q^{5} +(-0.504300 + 0.873473i) q^{7} +(-4.59629 + 2.65367i) q^{8} +(-1.68974 - 4.64252i) q^{10} +(-3.17026 - 5.49105i) q^{11} +(-18.8398 - 3.32196i) q^{13} +(-0.458832 - 0.546814i) q^{14} +(1.77821 + 10.0847i) q^{16} +(17.6556 + 6.42612i) q^{17} +(-3.75932 + 18.6244i) q^{19} -24.4264 q^{20} +(4.41919 - 0.779223i) q^{22} +(-4.24742 - 3.56401i) q^{23} +(4.12079 - 23.3702i) q^{25} +(6.76956 - 11.7252i) q^{26} +(-3.31638 + 1.20706i) q^{28} +(15.9133 + 43.7213i) q^{29} +(-11.5290 - 6.65625i) q^{31} +(-28.0441 - 4.94493i) q^{32} +(-8.54735 + 10.1863i) q^{34} +(-1.22262 - 6.93381i) q^{35} +33.7511i q^{37} +(-11.4761 - 7.00830i) q^{38} +(12.6716 - 34.8148i) q^{40} +(-14.6890 + 2.59006i) q^{41} +(54.4444 - 45.6843i) q^{43} +(3.85260 - 21.8492i) q^{44} +(3.39835 - 1.96204i) q^{46} +(61.8359 - 22.5064i) q^{47} +(23.9914 + 41.5543i) q^{49} +(14.5448 + 8.39745i) q^{50} +(-43.0279 - 51.2786i) q^{52} +(2.12547 - 2.53303i) q^{53} +(41.5922 + 15.1383i) q^{55} -5.35299i q^{56} -32.9287 q^{58} +(15.3099 - 42.0637i) q^{59} +(42.0127 + 35.2529i) q^{61} +(7.21739 - 6.05611i) q^{62} +(-10.4037 + 18.0198i) q^{64} +(115.653 - 66.7721i) q^{65} +(21.4253 + 58.8655i) q^{67} +(32.8720 + 56.9359i) q^{68} +(4.90726 + 0.865282i) q^{70} +(50.5020 + 60.1860i) q^{71} +(-23.2374 - 131.786i) q^{73} +(-22.4461 - 8.16971i) q^{74} +(-51.9666 + 41.4669i) q^{76} +6.39505 q^{77} +(24.2864 - 4.28235i) q^{79} +(-54.7607 - 45.9497i) q^{80} +(1.83306 - 10.3958i) q^{82} +(-56.6745 + 98.1632i) q^{83} +(-123.249 + 44.8590i) q^{85} +(17.2035 + 47.2663i) q^{86} +(29.1429 + 16.8256i) q^{88} +(-153.275 - 27.0266i) q^{89} +(12.4025 - 14.7808i) q^{91} +(-3.36899 - 19.1065i) q^{92} +46.5717i q^{94} +(-63.4669 - 116.463i) q^{95} +(43.5508 - 119.655i) q^{97} +(-33.4428 + 5.89688i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8}+O(q^{10}) \) 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8	\( 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8} - 78 q^{10} - 15 q^{11} + 36 q^{13} + 39 q^{14} - 3 q^{16} + 30 q^{17} + 54 q^{19} + 30 q^{20} + 132 q^{22} - 69 q^{23} + 138 q^{25} - 48 q^{26} - 246 q^{28} + 162 q^{29} + 72 q^{31} + 21 q^{32} - 285 q^{34} - 54 q^{35} + 204 q^{38} - 51 q^{40} - 30 q^{41} + 402 q^{43} - 471 q^{44} - 99 q^{46} + 105 q^{47} + 66 q^{49} - 567 q^{50} - 3 q^{52} + 36 q^{53} - 15 q^{55} - 48 q^{58} + 180 q^{59} + 93 q^{61} - 189 q^{62} - 183 q^{64} + 891 q^{65} - 354 q^{67} - 153 q^{68} + 372 q^{70} - 144 q^{71} - 453 q^{73} + 489 q^{74} - 150 q^{76} + 36 q^{77} - 96 q^{79} - 144 q^{80} + 249 q^{82} + 99 q^{83} - 573 q^{85} + 33 q^{86} + 360 q^{88} - 795 q^{89} + 414 q^{91} - 285 q^{92} - 198 q^{95} - 483 q^{97} + 39 q^{98}+O(q^{100}) \) 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8 - 78 * q^10 - 15 * q^11 + 36 * q^13 + 39 * q^14 - 3 * q^16 + 30 * q^17 + 54 * q^19 + 30 * q^20 + 132 * q^22 - 69 * q^23 + 138 * q^25 - 48 * q^26 - 246 * q^28 + 162 * q^29 + 72 * q^31 + 21 * q^32 - 285 * q^34 - 54 * q^35 + 204 * q^38 - 51 * q^40 - 30 * q^41 + 402 * q^43 - 471 * q^44 - 99 * q^46 + 105 * q^47 + 66 * q^49 - 567 * q^50 - 3 * q^52 + 36 * q^53 - 15 * q^55 - 48 * q^58 + 180 * q^59 + 93 * q^61 - 189 * q^62 - 183 * q^64 + 891 * q^65 - 354 * q^67 - 153 * q^68 + 372 * q^70 - 144 * q^71 - 453 * q^73 + 489 * q^74 - 150 * q^76 + 36 * q^77 - 96 * q^79 - 144 * q^80 + 249 * q^82 + 99 * q^83 - 573 * q^85 + 33 * q^86 + 360 * q^88 - 795 * q^89 + 414 * q^91 - 285 * q^92 - 198 * q^95 - 483 * q^97 + 39 * q^98

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