LMFDB - Embedded newform 324.3.j.a.199.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.19
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.278075 + 1.98057i) q^{2} +(-3.84535 + 1.10150i) q^{4} +(5.80978 - 2.11459i) q^{5} +(-7.71693 + 1.36070i) q^{7} +(-3.25089 - 7.30970i) q^{8} +O(q^{10})$	\(q+(0.278075 + 1.98057i) q^{2} +(-3.84535 + 1.10150i) q^{4} +(5.80978 - 2.11459i) q^{5} +(-7.71693 + 1.36070i) q^{7} +(-3.25089 - 7.30970i) q^{8} +(5.80365 + 10.9187i) q^{10} +(-5.58301 + 15.3392i) q^{11} +(0.501591 + 0.420885i) q^{13} +(-4.84086 - 14.9056i) q^{14} +(13.5734 - 8.47127i) q^{16} +(-16.2536 + 28.1521i) q^{17} +(-22.1106 + 12.7656i) q^{19} +(-20.0114 + 14.5308i) q^{20} +(-31.9329 - 6.79212i) q^{22} +(11.4625 + 2.02115i) q^{23} +(10.1309 - 8.50086i) q^{25} +(-0.694114 + 1.11048i) q^{26} +(28.1755 - 13.7326i) q^{28} +(-0.277178 + 0.232580i) q^{29} +(17.8485 + 3.14718i) q^{31} +(20.5524 + 24.5275i) q^{32} +(-60.2770 - 24.3631i) q^{34} +(-41.9564 + 24.2235i) q^{35} +(16.6488 - 28.8366i) q^{37} +(-31.4316 - 40.2420i) q^{38} +(-34.3439 - 35.5934i) q^{40} +(-13.6788 - 11.4779i) q^{41} +(1.58745 - 4.36148i) q^{43} +(4.57256 - 65.1342i) q^{44} +(-0.815602 + 23.2644i) q^{46} +(-58.2666 + 10.2740i) q^{47} +(11.6546 - 4.24194i) q^{49} +(19.6537 + 17.7012i) q^{50} +(-2.39240 - 1.06595i) q^{52} +65.6694 q^{53} +100.923i q^{55} +(35.0332 + 51.9850i) q^{56} +(-0.537718 - 0.484297i) q^{58} +(-7.73105 - 21.2409i) q^{59} +(-11.4644 - 65.0179i) q^{61} +(-1.26999 + 36.2255i) q^{62} +(-42.8634 + 47.5261i) q^{64} +(3.80413 + 1.38459i) q^{65} +(20.4878 - 24.4165i) q^{67} +(31.4914 - 126.158i) q^{68} +(-59.6435 - 76.3617i) q^{70} +(56.4127 + 32.5699i) q^{71} +(27.4849 + 47.6052i) q^{73} +(61.7427 + 24.9555i) q^{74} +(70.9619 - 73.4429i) q^{76} +(22.2116 - 125.968i) q^{77} +(18.8412 + 22.4541i) q^{79} +(60.9453 - 77.9184i) q^{80} +(18.9290 - 30.2835i) q^{82} +(-11.6992 - 13.9426i) q^{83} +(-34.8999 + 197.927i) q^{85} +(9.07966 + 1.93124i) q^{86} +(130.275 - 9.05592i) q^{88} +(37.7308 + 65.3517i) q^{89} +(-4.44344 - 2.56542i) q^{91} +(-46.3037 + 4.85390i) q^{92} +(-36.5509 - 112.544i) q^{94} +(-101.464 + 120.920i) q^{95} +(144.082 + 52.4414i) q^{97} +(11.6423 + 21.9033i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.278075	+	1.98057i	0.139037	+	0.990287i
$2$	0.278075	+	1.98057i	0.139037	+	0.990287i
$3$		0			0
$3$		0			0
$4$	−3.84535	+	1.10150i	−0.961337	+	0.275374i
$5$	5.80978	−	2.11459i	1.16196	−	0.422917i	0.312160	−	0.950030i	$-0.398948\pi$
$5$	5.80978	−	2.11459i	1.16196	−	0.422917i	0.849796	+	0.527112i	$0.176725\pi$
$6$		0			0
$7$	−7.71693	+	1.36070i	−1.10242	+	0.194386i	−0.695110	−	0.718904i	$-0.744644\pi$
$7$	−7.71693	+	1.36070i	−1.10242	+	0.194386i	−0.407310	+	0.913290i	$0.633533\pi$
$8$	−3.25089	−	7.30970i	−0.406361	−	0.913712i
$9$		0			0
$10$	5.80365	+	10.9187i	0.580365	+	1.09187i
$11$	−5.58301	+	15.3392i	−0.507547	+	1.39447i	0.376214	+	0.926533i	$0.377226\pi$
$11$	−5.58301	+	15.3392i	−0.507547	+	1.39447i	−0.883760	+	0.467940i	$0.844996\pi$
$12$		0			0
$13$	0.501591	+	0.420885i	0.0385839	+	0.0323758i	0.661876	−	0.749614i	$-0.269761\pi$
$13$	0.501591	+	0.420885i	0.0385839	+	0.0323758i	−0.623292	+	0.781989i	$0.714205\pi$
$14$	−4.84086	−	14.9056i	−0.345776	−	1.06468i
$15$		0			0
$16$	13.5734	−	8.47127i	0.848338	−	0.529455i
$17$	−16.2536	+	28.1521i	−0.956094	+	1.65600i	−0.224250	+	0.974532i	$0.571993\pi$
$17$	−16.2536	+	28.1521i	−0.956094	+	1.65600i	−0.731844	+	0.681472i	$0.761340\pi$
$18$		0			0
$19$	−22.1106	+	12.7656i	−1.16372	+	0.671873i	−0.952192	−	0.305499i	$-0.901177\pi$
$19$	−22.1106	+	12.7656i	−1.16372	+	0.671873i	−0.211526	+	0.977372i	$0.567843\pi$
$20$	−20.0114	+	14.5308i	−1.00057	+	0.726538i
$21$		0			0
$22$	−31.9329	−	6.79212i	−1.45150	−	0.308733i
$23$	11.4625	+	2.02115i	0.498371	+	0.0878763i	0.417183	−	0.908823i	$-0.363017\pi$
$23$	11.4625	+	2.02115i	0.498371	+	0.0878763i	0.0811881	+	0.996699i	$0.474129\pi$
$24$		0			0
$25$	10.1309	−	8.50086i	0.405237	−	0.340034i
$26$	−0.694114	+	1.11048i	−0.0266967	+	0.0427106i
$27$		0			0
$28$	28.1755	−	13.7326i	1.00627	−	0.490448i
$29$	−0.277178	+	0.232580i	−0.00955787	+	0.00802000i	−0.647554	−	0.762020i	$-0.724208\pi$
$29$	−0.277178	+	0.232580i	−0.00955787	+	0.00802000i	0.637996	+	0.770040i	$0.279764\pi$
$30$		0			0
$31$	17.8485	+	3.14718i	0.575759	+	0.101522i	0.453943	−	0.891031i	$-0.350017\pi$
$31$	17.8485	+	3.14718i	0.575759	+	0.101522i	0.121816	+	0.992553i	$0.461128\pi$
$32$	20.5524	+	24.5275i	0.642263	+	0.766484i
$33$		0			0
$34$	−60.2770	−	24.3631i	−1.77285	−	0.716561i
$35$	−41.9564	+	24.2235i	−1.19875	+	0.692100i
$36$		0			0
$37$	16.6488	−	28.8366i	0.449968	−	0.779368i	−0.548415	−	0.836206i	$-0.684769\pi$
$37$	16.6488	−	28.8366i	0.449968	−	0.779368i	0.998383	+	0.0568384i	$0.0181020\pi$
$38$	−31.4316	−	40.2420i	−0.827148	−	1.05900i
$39$		0			0
$40$	−34.3439	−	35.5934i	−0.858599	−	0.889836i
$41$	−13.6788	−	11.4779i	−0.333629	−	0.279948i	0.460548	−	0.887635i	$-0.347653\pi$
$41$	−13.6788	−	11.4779i	−0.333629	−	0.279948i	−0.794176	+	0.607687i	$0.792097\pi$
$42$		0			0
$43$	1.58745	−	4.36148i	0.0369174	−	0.101430i	−0.919864	−	0.392237i	$-0.871701\pi$
$43$	1.58745	−	4.36148i	0.0369174	−	0.101430i	0.956782	+	0.290807i	$0.0939237\pi$
$44$	4.57256	−	65.1342i	0.103922	−	1.48032i
$45$		0			0
$46$	−0.815602	+	23.2644i	−0.0177305	+	0.505748i
$47$	−58.2666	+	10.2740i	−1.23972	+	0.218595i	−0.754794	−	0.655962i	$-0.772263\pi$
$47$	−58.2666	+	10.2740i	−1.23972	+	0.218595i	−0.484922	+	0.874558i	$0.661152\pi$
$48$		0			0
$49$	11.6546	−	4.24194i	0.237850	−	0.0865702i
$50$	19.6537	+	17.7012i	0.393075	+	0.354024i
$51$		0			0
$52$	−2.39240	−	1.06595i	−0.0460076	−	0.0204990i
$53$	65.6694			1.23905			0.619523	−	0.784979i	$-0.287326\pi$
$53$	65.6694			1.23905			0.619523	+	0.784979i	$0.287326\pi$
$54$		0			0
$55$			100.923i			1.83497i
$56$	35.0332	+	51.9850i	0.625594	+	0.928303i
$57$		0			0
$58$	−0.537718	−	0.484297i	−0.00927101	−	0.00834995i
$59$	−7.73105	−	21.2409i	−0.131035	−	0.360015i	0.856773	−	0.515694i	$-0.172466\pi$
$59$	−7.73105	−	21.2409i	−0.131035	−	0.360015i	−0.987808	+	0.155679i	$0.950244\pi$
$60$		0			0
$61$	−11.4644	−	65.0179i	−0.187941	−	1.06587i	−0.922118	−	0.386909i	$-0.873543\pi$
$61$	−11.4644	−	65.0179i	−0.187941	−	1.06587i	0.734177	−	0.678959i	$-0.237568\pi$
$62$	−1.26999	+	36.2255i	−0.0204837	+	0.584283i
$63$		0			0
$64$	−42.8634	+	47.5261i	−0.669741	+	0.742595i
$65$	3.80413	+	1.38459i	0.0585251	+	0.0213014i
$66$		0			0
$67$	20.4878	−	24.4165i	0.305789	−	0.364425i	−0.591164	−	0.806551i	$-0.701331\pi$
$67$	20.4878	−	24.4165i	0.305789	−	0.364425i	0.896953	+	0.442127i	$0.145776\pi$
$68$	31.4914	−	126.158i	0.463108	−	1.85526i
$69$		0			0
$70$	−59.6435	−	76.3617i	−0.852050	−	1.09088i
$71$	56.4127	+	32.5699i	0.794545	+	0.458731i	0.841560	−	0.540163i	$-0.181638\pi$
$71$	56.4127	+	32.5699i	0.794545	+	0.458731i	−0.0470150	+	0.998894i	$0.514971\pi$
$72$		0			0
$73$	27.4849	+	47.6052i	0.376505	+	0.652126i	0.990551	−	0.137144i	$-0.0437924\pi$
$73$	27.4849	+	47.6052i	0.376505	+	0.652126i	−0.614046	+	0.789270i	$0.710459\pi$
$74$	61.7427	+	24.9555i	0.834360	+	0.337236i
$75$		0			0
$76$	70.9619	−	73.4429i	0.933709	−	0.966354i
$77$	22.2116	−	125.968i	0.288463	−	1.63595i
$78$		0			0
$79$	18.8412	+	22.4541i	0.238496	+	0.284229i	0.871995	−	0.489515i	$-0.162826\pi$
$79$	18.8412	+	22.4541i	0.238496	+	0.284229i	−0.633498	+	0.773744i	$0.718382\pi$
$80$	60.9453	−	77.9184i	0.761816	−	0.973980i
$81$		0			0
$82$	18.9290	−	30.2835i	0.230842	−	0.369311i
$83$	−11.6992	−	13.9426i	−0.140954	−	0.167983i	0.690949	−	0.722904i	$-0.257193\pi$
$83$	−11.6992	−	13.9426i	−0.140954	−	0.167983i	−0.831903	+	0.554921i	$0.812749\pi$
$84$		0			0
$85$	−34.8999	+	197.927i	−0.410586	+	2.32855i
$86$	9.07966	+	1.93124i	0.105577	+	0.0224563i
$87$		0			0
$88$	130.275	−	9.05592i	1.48039	−	0.102908i
$89$	37.7308	+	65.3517i	0.423942	+	0.734289i	0.996321	−	0.0857002i	$-0.0273127\pi$
$89$	37.7308	+	65.3517i	0.423942	+	0.734289i	−0.572379	+	0.819989i	$0.693979\pi$
$90$		0			0
$91$	−4.44344	−	2.56542i	−0.0488291	−	0.0281915i
$92$	−46.3037	+	4.85390i	−0.503301	+	0.0527597i
$93$		0			0
$94$	−36.5509	−	112.544i	−0.388839	−	1.19728i
$95$	−101.464	+	120.920i	−1.06804	+	1.27284i
$96$		0			0
$97$	144.082	+	52.4414i	1.48538	+	0.540633i	0.952228	−	0.305388i	$-0.0987863\pi$
$97$	144.082	+	52.4414i	1.48538	+	0.540633i	0.533149	+	0.846021i	$0.321009\pi$
$98$	11.6423	+	21.9033i	0.118799	+	0.223503i
$99$		0			0
$100$	−29.5933	+	43.8480i	−0.295933	+	0.438480i
$101$	28.9732	+	164.315i	0.286863	+	1.62688i	0.698554	+	0.715557i	$0.253827\pi$
$101$	28.9732	+	164.315i	0.286863	+	1.62688i	−0.411691	+	0.911324i	$0.635062\pi$
$102$		0			0
$103$	6.18247	+	16.9862i	0.0600240	+	0.164915i	0.966080	−	0.258244i	$-0.0831437\pi$
$103$	6.18247	+	16.9862i	0.0600240	+	0.164915i	−0.906056	+	0.423158i	$0.860921\pi$
$104$	1.44592	−	5.03473i	0.0139031	−	0.0484109i
$105$		0			0
$106$	18.2610	+	130.063i	0.172274	+	1.22701i
$107$		−	26.1902i		−	0.244769i	−0.992483	−	0.122384i	$-0.960946\pi$
$107$		−	26.1902i		−	0.244769i	0.992483	−	0.122384i	$-0.0390540\pi$
$108$		0			0
$109$	−68.9277			−0.632364			−0.316182	−	0.948699i	$-0.602401\pi$
$109$	−68.9277			−0.632364			−0.316182	+	0.948699i	$0.602401\pi$
$110$	−199.886	+	28.0642i	−1.81714	+	0.255129i
$111$		0			0
$112$	−93.2182	+	83.8417i	−0.832306	+	0.748586i
$113$	−113.872	+	41.4460i	−1.00772	+	0.366779i	−0.792555	−	0.609800i	$-0.791250\pi$
$113$	−113.872	+	41.4460i	−1.00772	+	0.366779i	−0.215161	+	0.976579i	$0.569028\pi$
$114$		0			0
$115$	70.8687	−	12.4961i	0.616249	−	0.108661i
$116$	0.809660	−	1.19966i	0.00697983	−	0.0103419i
$117$		0			0
$118$	39.9193	−	21.2185i	0.338299	−	0.179818i
$119$	87.1214	−	239.364i	0.732112	−	2.01146i
$120$		0			0
$121$	−111.430	−	93.5006i	−0.920906	−	0.772732i
$122$	125.585	−	40.7860i	1.02938	−	0.334311i
$123$		0			0
$124$	−72.1005	+	7.55810i	−0.581456	+	0.0609524i
$125$	−36.4003	+	63.0472i	−0.291202	+	0.504377i
$126$		0			0
$127$	34.2929	−	19.7990i	0.270022	−	0.155898i	−0.358875	−	0.933385i	$-0.616840\pi$
$127$	34.2929	−	19.7990i	0.270022	−	0.155898i	0.628898	+	0.777488i	$0.283506\pi$
$128$	−106.048	−	71.6784i	−0.828501	−	0.559987i
$129$		0			0
$130$	−1.68445	+	7.91938i	−0.0129573	+	0.0609183i
$131$	90.0826	+	15.8840i	0.687654	+	0.121252i	0.506548	−	0.862212i	$-0.330921\pi$
$131$	90.0826	+	15.8840i	0.687654	+	0.121252i	0.181106	+	0.983464i	$0.442032\pi$
$132$		0			0
$133$	153.256	−	128.597i	1.15230	−	0.966896i
$134$	54.0557	+	33.7881i	0.403401	+	0.252150i
$135$		0			0
$136$	258.622	+	27.2897i	1.90163	+	0.200659i
$137$	56.0251	−	47.0107i	0.408943	−	0.343144i	−0.414995	−	0.909824i	$-0.636217\pi$
$137$	56.0251	−	47.0107i	0.408943	−	0.343144i	0.823938	+	0.566680i	$0.191772\pi$
$138$		0			0
$139$	63.5365	+	11.2032i	0.457097	+	0.0805985i	0.397456	−	0.917621i	$-0.369893\pi$
$139$	63.5365	+	11.2032i	0.457097	+	0.0805985i	0.0596412	+	0.998220i	$0.481004\pi$
$140$	134.655	−	139.363i	0.961819	−	0.995447i
$141$		0			0
$142$	−48.8201	+	120.786i	−0.343804	+	0.850609i
$143$	−9.25642	+	5.34420i	−0.0647302	+	0.0373720i
$144$		0			0
$145$	−1.11853	+	1.93736i	−0.00771402	+	0.0133611i
$146$	−86.6427	+	67.6736i	−0.593443	+	0.463518i
$147$		0			0
$148$	−32.2571	+	129.225i	−0.217953	+	0.873145i
$149$	−84.8762	−	71.2196i	−0.569639	−	0.477984i	0.311887	−	0.950119i	$-0.399039\pi$
$149$	−84.8762	−	71.2196i	−0.569639	−	0.477984i	−0.881526	+	0.472135i	$0.843483\pi$
$150$		0			0
$151$	−6.70741	+	18.4285i	−0.0444200	+	0.122043i	−0.959919	−	0.280277i	$-0.909574\pi$
$151$	−6.70741	+	18.4285i	−0.0444200	+	0.122043i	0.915499	+	0.402320i	$0.131796\pi$
$152$	165.192	+	120.123i	1.08679	+	0.790281i
$153$		0			0
$154$	255.666	+	8.96312i	1.66017	+	0.0582021i
$155$	110.351	−	19.4579i	0.711942	−	0.125535i
$156$		0			0
$157$	−121.611	+	44.2628i	−0.774592	+	0.281929i	−0.698916	−	0.715204i	$-0.746334\pi$
$157$	−121.611	+	44.2628i	−0.774592	+	0.281929i	−0.0756765	+	0.997132i	$0.524112\pi$
$158$	−39.2327	+	43.5603i	−0.248308	+	0.275698i
$159$		0			0
$160$	171.270	+	99.0395i	1.07044	+	0.618997i
$161$	−91.2058			−0.566496
$162$		0			0
$163$		−	82.7053i		−	0.507394i	−0.967284	−	0.253697i	$-0.918353\pi$
$163$		−	82.7053i		−	0.507394i	0.967284	−	0.253697i	$-0.0816467\pi$
$164$	65.2425	+	29.0692i	0.397820	+	0.177251i
$165$		0			0
$166$	24.3610	−	27.0482i	0.146753	−	0.162941i
$167$	−39.4378	−	108.354i	−0.236154	−	0.648829i	−0.999994	−	0.00342276i	$-0.998911\pi$
$167$	−39.4378	−	108.354i	−0.236154	−	0.648829i	0.763840	−	0.645406i	$-0.223312\pi$
$168$		0			0
$169$	−29.2721	−	166.010i	−0.173208	−	0.982309i
$170$	−401.714	−	14.0832i	−2.36302	−	0.0828425i
$171$		0			0
$172$	−1.30014	+	18.5200i	−0.00755895	+	0.107674i
$173$	197.141	+	71.7535i	1.13954	+	0.414760i	0.841749	−	0.539870i	$-0.181527\pi$
$173$	197.141	+	71.7535i	1.13954	+	0.414760i	0.297795	+	0.954630i	$0.403749\pi$
$174$		0			0
$175$	−66.6126	+	79.3858i	−0.380643	+	0.453633i
$176$	54.1621	+	255.501i	0.307739	+	1.45171i
$177$		0			0
$178$	−118.942	+	92.9014i	−0.668213	+	0.521918i
$179$	282.005	+	162.816i	1.57545	+	0.909585i	0.995483	+	0.0949444i	$0.0302673\pi$
$179$	282.005	+	162.816i	1.57545	+	0.909585i	0.579966	+	0.814641i	$0.303066\pi$
$180$		0			0
$181$	−85.3049	−	147.752i	−0.471298	−	0.816312i	0.528163	−	0.849143i	$-0.322881\pi$
$181$	−85.3049	−	147.752i	−0.471298	−	0.816312i	−0.999461	+	0.0328313i	$0.989548\pi$
$182$	3.84540	−	9.51395i	0.0211286	−	0.0522745i
$183$		0			0
$184$	−22.4894	−	90.3582i	−0.122225	−	0.491077i
$185$	35.7485	−	202.740i	0.193235	−	1.09589i
$186$		0			0
$187$	−341.086	−	406.491i	−1.82399	−	2.17375i
$188$	212.739	−	103.687i	1.13159	−	0.551529i
$189$		0			0
$190$	−267.706	−	167.332i	−1.40898	−	0.880695i
$191$	−127.352	−	151.772i	−0.666762	−	0.794616i	0.321577	−	0.946883i	$-0.395787\pi$
$191$	−127.352	−	151.772i	−0.666762	−	0.794616i	−0.988339	+	0.152267i	$0.951343\pi$
$192$		0			0
$193$	−22.9132	+	129.947i	−0.118721	+	0.673303i	0.866119	+	0.499838i	$0.166607\pi$
$193$	−22.9132	+	129.947i	−0.118721	+	0.673303i	−0.984840	+	0.173465i	$0.944504\pi$
$194$	−63.7986	+	299.947i	−0.328859	+	1.54612i
$195$		0			0
$196$	−40.1436	+	29.1493i	−0.204814	+	0.148721i
$197$	−17.2889	−	29.9453i	−0.0877610	−	0.152007i	0.818803	−	0.574074i	$-0.194638\pi$
$197$	−17.2889	−	29.9453i	−0.0877610	−	0.152007i	−0.906564	+	0.422067i	$0.861305\pi$
$198$		0			0
$199$	−146.965	−	84.8503i	−0.738518	−	0.426383i	0.0830125	−	0.996549i	$-0.473546\pi$
$199$	−146.965	−	84.8503i	−0.738518	−	0.426383i	−0.821530	+	0.570165i	$0.806879\pi$
$200$	−95.0733	−	46.4187i	−0.475367	−	0.232094i
$201$		0			0
$202$	−317.381	+	103.075i	−1.57119	+	0.510274i
$203$	1.82249	−	2.17196i	0.00897780	−	0.0106993i
$204$		0			0
$205$	−103.742	−	37.7588i	−0.506056	−	0.184189i
$206$	−31.9232	+	16.9683i	−0.154967	+	0.0823703i
$207$		0			0
$208$	10.3737	+	1.46373i	0.0498737	+	0.00703715i
$209$	−72.3699	−	410.430i	−0.346267	−	1.96378i
$210$		0			0
$211$	−12.7388	−	34.9995i	−0.0603733	−	0.165874i	0.905839	−	0.423623i	$-0.139242\pi$
$211$	−12.7388	−	34.9995i	−0.0603733	−	0.165874i	−0.966212	+	0.257748i	$0.917019\pi$
$212$	−252.522	+	72.3346i	−1.19114	+	0.341201i
$213$		0			0
$214$	51.8717	−	7.28285i	0.242391	−	0.0340320i
$215$		−	28.6960i		−	0.133470i
$216$		0			0
$217$	−142.018			−0.654463
$218$	−19.1671	−	136.516i	−0.0879223	−	0.626222i
$219$		0			0
$220$	−111.166	−	388.085i	−0.505302	−	1.76402i
$221$	−20.0014	+	7.27993i	−0.0905042	+	0.0329408i
$222$		0			0
$223$	401.905	−	70.8667i	1.80227	−	0.317788i	0.831087	−	0.556142i	$-0.187719\pi$
$223$	401.905	−	70.8667i	1.80227	−	0.317788i	0.971178	+	0.238354i	$0.0766080\pi$
$224$	−191.976	−	161.311i	−0.857037	−	0.720140i
$225$		0			0
$226$	−113.752	−	214.007i	−0.503326	−	0.946932i
$227$	−114.765	+	315.313i	−0.505571	+	1.38905i	0.380191	+	0.924908i	$0.375858\pi$
$227$	−114.765	+	315.313i	−0.505571	+	1.38905i	−0.885763	+	0.464138i	$0.846364\pi$
$228$		0			0
$229$	198.202	+	166.312i	0.865513	+	0.726251i	0.963148	−	0.268971i	$-0.0866836\pi$
$229$	198.202	+	166.312i	0.865513	+	0.726251i	−0.0976357	+	0.995222i	$0.531128\pi$
$230$	44.4562	+	136.886i	0.193288	+	0.595156i
$231$		0			0
$232$	2.60117	+	1.27000i	0.0112119	+	0.00547412i
$233$	−144.710	+	250.644i	−0.621071	+	1.07573i	0.368215	+	0.929741i	$0.379969\pi$
$233$	−144.710	+	250.644i	−0.621071	+	1.07573i	−0.989287	+	0.145987i	$0.953364\pi$
$234$		0			0
$235$	−316.791	+	182.899i	−1.34805	+	0.778295i
$236$	53.1253	+	73.1629i	0.225107	+	0.310012i
$237$		0			0
$238$	498.304	+	105.989i	2.09372	+	0.445333i
$239$	−277.323	−	48.8996i	−1.16035	−	0.204601i	−0.439860	−	0.898067i	$-0.644972\pi$
$239$	−277.323	−	48.8996i	−1.16035	−	0.204601i	−0.720490	+	0.693466i	$0.756083\pi$
$240$		0			0
$241$	−183.310	+	153.815i	−0.760622	+	0.638238i	−0.938289	−	0.345853i	$-0.887590\pi$
$241$	−183.310	+	153.815i	−0.760622	+	0.638238i	0.177666	+	0.984091i	$0.443145\pi$
$242$	154.199	−	246.695i	0.637186	−	1.01940i
$243$		0			0
$244$	115.702	+	237.389i	0.474187	+	0.972904i
$245$	58.7409	−	49.2894i	0.239759	−	0.201181i
$246$		0			0
$247$	−16.4633	−	2.90293i	−0.0666532	−	0.0117528i
$248$	−35.0187	−	140.699i	−0.141205	−	0.567333i
$249$		0			0
$250$	−134.992	−	54.5616i	−0.539966	−	0.218247i
$251$	−68.9864	+	39.8293i	−0.274846	+	0.158683i	−0.631088	−	0.775711i	$-0.717391\pi$
$251$	−68.9864	+	39.8293i	−0.274846	+	0.158683i	0.356242	+	0.934394i	$0.384058\pi$
$252$		0			0
$253$	−94.9984	+	164.542i	−0.375488	+	0.650364i
$254$	48.7494	+	62.4139i	0.191927	+	0.245724i
$255$		0			0
$256$	112.475	−	229.968i	0.439356	−	0.898313i
$257$	−165.964	−	139.261i	−0.645776	−	0.541870i	0.260010	−	0.965606i	$-0.416274\pi$
$257$	−165.964	−	139.261i	−0.645776	−	0.541870i	−0.905786	+	0.423736i	$0.860719\pi$
$258$		0			0
$259$	−89.2398	+	245.184i	−0.344555	+	0.946658i
$260$	−16.1533	−	1.13400i	−0.0621282	−	0.00436152i
$261$		0			0
$262$	−6.40971	+	182.832i	−0.0244646	+	0.697833i
$263$	286.514	−	50.5202i	1.08941	−	0.192092i	0.400036	−	0.916499i	$-0.368998\pi$
$263$	286.514	−	50.5202i	1.08941	−	0.192092i	0.689372	+	0.724407i	$0.257886\pi$
$264$		0			0
$265$	381.525	−	138.864i	1.43972	−	0.524014i
$266$	297.313	+	267.776i	1.11772	+	1.00668i
$267$		0			0
$268$	−51.8882	+	116.457i	−0.193613	+	0.434541i
$269$	−73.0815			−0.271678			−0.135839	−	0.990731i	$-0.543373\pi$
$269$	−73.0815			−0.271678			−0.135839	+	0.990731i	$0.543373\pi$
$270$		0			0
$271$		−	139.540i		−	0.514906i	−0.966291	−	0.257453i	$-0.917117\pi$
$271$		−	139.540i		−	0.514906i	0.966291	−	0.257453i	$-0.0828833\pi$
$272$	17.8670	+	519.808i	0.0656876	+	1.91106i
$273$		0			0
$274$	108.687	+	97.8895i	0.396669	+	0.357261i
$275$	73.8353	+	202.861i	0.268492	+	0.737676i
$276$		0			0
$277$	67.9022	+	385.092i	0.245134	+	1.39023i	0.820181	+	0.572104i	$0.193873\pi$
$277$	67.9022	+	385.092i	0.245134	+	1.39023i	−0.575047	+	0.818121i	$0.695016\pi$
$278$	−4.52086	+	128.954i	−0.0162621	+	0.463863i
$279$		0			0
$280$	313.462	+	227.940i	1.11951	+	0.814073i
$281$	4.50680	+	1.64034i	0.0160384	+	0.00583752i	0.350027	−	0.936740i	$-0.386172\pi$
$281$	4.50680	+	1.64034i	0.0160384	+	0.00583752i	−0.333988	+	0.942577i	$0.608395\pi$
$282$		0			0
$283$	295.868	−	352.602i	1.04547	−	1.24594i	0.0769436	−	0.997035i	$-0.475484\pi$
$283$	295.868	−	352.602i	1.04547	−	1.24594i	0.968527	−	0.248908i	$-0.0800717\pi$
$284$	−252.802	−	63.1042i	−0.890148	−	0.222198i
$285$		0			0
$286$	−13.1586	−	16.8469i	−0.0460090	−	0.0589054i
$287$	121.176	+	69.9611i	0.422217	+	0.243767i
$288$		0			0
$289$	−383.859	−	664.864i	−1.32823	−	2.30057i
$290$	−4.14811	−	1.67661i	−0.0143038	−	0.00578140i
$291$		0			0
$292$	−158.126	−	152.784i	−0.541527	−	0.523233i
$293$	−74.0451	+	419.931i	−0.252714	+	1.43321i	0.549160	+	0.835717i	$0.314948\pi$
$293$	−74.0451	+	419.931i	−0.252714	+	1.43321i	−0.801874	+	0.597493i	$0.796163\pi$
$294$		0			0
$295$	−89.8313	−	107.057i	−0.304513	−	0.362904i
$296$	−264.910	−	27.9532i	−0.894968	−	0.0944367i
$297$		0			0
$298$	117.454	−	187.908i	0.394140	−	0.630564i
$299$	4.89883	+	5.83820i	0.0163840	+	0.0195257i
$300$		0			0
$301$	−6.31555	+	35.8173i	−0.0209819	+	0.118994i
$302$	−38.3641	−	8.16004i	−0.127033	−	0.0270200i
$303$		0			0
$304$	−191.976	+	360.578i	−0.631500	+	1.18611i
$305$	−204.092	−	353.497i	−0.669153	−	1.15901i
$306$		0			0
$307$	378.645	+	218.611i	1.23337	+	0.712087i	0.967731	−	0.251985i	$-0.0810835\pi$
$307$	378.645	+	218.611i	1.23337	+	0.712087i	0.265640	+	0.964072i	$0.414417\pi$
$308$	53.3423	+	508.859i	0.173189	+	1.65214i
$309$		0			0
$310$	69.2236	+	213.148i	0.223302	+	0.687573i
$311$	96.7434	−	115.294i	0.311072	−	0.370721i	−0.587744	−	0.809047i	$-0.699984\pi$
$311$	96.7434	−	115.294i	0.311072	−	0.370721i	0.898816	+	0.438326i	$0.144428\pi$
$312$		0			0
$313$	580.349	+	211.230i	1.85415	+	0.674856i	0.982935	+	0.183955i	$0.0588900\pi$
$313$	580.349	+	211.230i	1.85415	+	0.674856i	0.871216	+	0.490901i	$0.163332\pi$
$314$	−121.483	−	228.551i	−0.386888	−	0.727870i
$315$		0			0
$316$	−97.1841	−	65.5903i	−0.307545	−	0.207564i
$317$	16.7895	+	95.2178i	0.0529636	+	0.300372i	0.999770	−	0.0214312i	$-0.00682229\pi$
$317$	16.7895	+	95.2178i	0.0529636	+	0.300372i	−0.946807	+	0.321803i	$0.895711\pi$
$318$		0			0
$319$	−2.02010	−	5.55019i	−0.00633261	−	0.0173987i
$320$	−148.529	+	366.754i	−0.464153	+	1.14611i
$321$		0			0
$322$	−25.3621	−	180.640i	−0.0787641	−	0.560993i
$323$		−	829.947i		−	2.56950i
$324$		0			0
$325$	8.65947			0.0266445
$326$	163.804	−	22.9983i	0.502466	−	0.0705468i
$327$		0			0
$328$	−39.4315	+	137.301i	−0.120218	+	0.418601i
$329$	435.660	−	158.567i	1.32419	−	0.481967i
$330$		0			0
$331$	−476.068	+	83.9436i	−1.43827	+	0.253606i	−0.837773	−	0.546019i	$-0.816142\pi$
$331$	−476.068	+	83.9436i	−1.43827	+	0.253606i	−0.600499	+	0.799625i	$0.705031\pi$
$332$	60.3452	+	40.7274i	0.181763	+	0.122673i
$333$		0			0
$334$	203.637	−	108.240i	0.609692	−	0.324072i
$335$	67.3991	−	185.177i	0.201191	−	0.552769i
$336$		0			0
$337$	−13.6506	−	11.4542i	−0.0405062	−	0.0339888i	0.622310	−	0.782771i	$-0.286194\pi$
$337$	−13.6506	−	11.4542i	−0.0405062	−	0.0339888i	−0.662816	+	0.748782i	$0.730639\pi$
$338$	320.656	−	104.139i	0.948686	−	0.308103i
$339$		0			0
$340$	−83.8136	−	799.540i	−0.246511	−	2.35159i
$341$	−147.924	+	256.212i	−0.433794	+	0.751354i
$342$		0			0
$343$	248.356	−	143.388i	0.724069	−	0.418042i
$344$	−37.0417	+	2.57492i	−0.107679	+	0.00748522i
$345$		0			0
$346$	−87.2931	+	410.405i	−0.252292	+	1.18614i
$347$	−120.577	−	21.2610i	−0.347484	−	0.0612709i	−0.00281781	−	0.999996i	$-0.500897\pi$
$347$	−120.577	−	21.2610i	−0.347484	−	0.0612709i	−0.344667	+	0.938725i	$0.612008\pi$
$348$		0			0
$349$	−430.567	+	361.288i	−1.23372	+	1.03521i	−0.235727	+	0.971819i	$0.575747\pi$
$349$	−430.567	+	361.288i	−1.23372	+	1.03521i	−0.997989	+	0.0633910i	$0.979808\pi$
$350$	−175.753	−	109.856i	−0.502151	−	0.313874i
$351$		0			0
$352$	−490.977	+	178.320i	−1.39482	+	0.506592i
$353$	167.688	−	140.707i	0.475038	−	0.398604i	−0.373590	−	0.927594i	$-0.621873\pi$
$353$	167.688	−	140.707i	0.475038	−	0.398604i	0.848628	+	0.528990i	$0.177429\pi$
$354$		0			0
$355$	396.617	+	69.9343i	1.11723	+	0.196998i
$356$	−217.073	−	209.740i	−0.609755	−	0.589157i
$357$		0			0
$358$	−244.050	+	603.807i	−0.681704	+	1.68661i
$359$	−153.103	+	88.3942i	−0.426471	+	0.246223i	−0.697842	−	0.716252i	$-0.745856\pi$
$359$	−153.103	+	88.3942i	−0.426471	+	0.246223i	0.271371	+	0.962475i	$0.412523\pi$
$360$		0			0
$361$	145.420	−	251.875i	0.402827	−	0.697716i
$362$	268.913	−	210.039i	0.742855	−	0.580218i
$363$		0			0
$364$	19.9124	+	4.97051i	0.0547044	+	0.0136553i
$365$	260.346	+	218.456i	0.713277	+	0.598511i
$366$		0			0
$367$	−61.2798	+	168.365i	−0.166975	+	0.458760i	−0.994754	−	0.102294i	$-0.967382\pi$
$367$	−61.2798	+	168.365i	−0.166975	+	0.458760i	0.827779	+	0.561054i	$0.189604\pi$
$368$	172.707	−	69.6683i	0.469314	−	0.189316i
$369$		0			0
$370$	411.482	+	14.4257i	1.11211	+	0.0389883i
$371$	−506.766	+	89.3566i	−1.36595	+	0.240853i
$372$		0			0
$373$	−392.445	+	142.838i	−1.05213	+	0.382945i	−0.809467	−	0.587165i	$-0.800244\pi$
$373$	−392.445	+	142.838i	−1.05213	+	0.382945i	−0.242665	+	0.970110i	$0.578022\pi$
$374$	710.237	−	788.581i	1.89903	−	2.10851i
$375$		0			0
$376$	264.518	+	392.512i	0.703505	+	1.04391i
$377$	−0.236919			−0.000628434
$378$		0			0
$379$			185.425i			0.489248i	0.969618	+	0.244624i	$0.0786646\pi$
$379$			185.425i			0.489248i	−0.969618	+	0.244624i	$0.921335\pi$
$380$	256.971	−	576.742i	0.676241	−	1.51774i
$381$		0			0
$382$	265.182	−	294.433i	0.694193	−	0.770768i
$383$	140.116	+	384.965i	0.365838	+	1.00513i	0.976928	+	0.213570i	$0.0685091\pi$
$383$	140.116	+	384.965i	0.365838	+	1.00513i	−0.611090	+	0.791561i	$0.709269\pi$
$384$		0			0
$385$	−137.326	−	778.817i	−0.356692	−	2.02290i
$386$	−263.742	−	9.24624i	−0.683270	−	0.0239540i
$387$		0			0
$388$	−611.808	−	42.9502i	−1.57682	−	0.110696i
$389$	222.006	+	80.8034i	0.570708	+	0.207721i	0.611224	−	0.791458i	$-0.290678\pi$
$389$	222.006	+	80.8034i	0.570708	+	0.207721i	−0.0405151	+	0.999179i	$0.512900\pi$
$390$		0			0
$391$	−243.207	+	289.843i	−0.622013	+	0.741286i
$392$	−68.8952	−	71.4018i	−0.175753	−	0.182147i
$393$		0			0
$394$	54.5013	−	42.5690i	0.138328	−	0.108043i
$395$	156.944	+	90.6119i	0.397328	+	0.229397i
$396$		0			0
$397$	309.808	+	536.603i	0.780373	+	1.35165i	0.931724	+	0.363166i	$0.118304\pi$
$397$	309.808	+	536.603i	0.780373	+	1.35165i	−0.151351	+	0.988480i	$0.548362\pi$
$398$	127.185	−	314.670i	0.319560	−	0.790628i
$399$		0			0
$400$	65.4982	−	201.208i	0.163745	−	0.503019i
$401$	−45.9110	+	260.374i	−0.114491	+	0.649312i	0.872510	+	0.488597i	$0.162491\pi$
$401$	−45.9110	+	260.374i	−0.114491	+	0.649312i	−0.987001	+	0.160715i	$0.948620\pi$
$402$		0			0
$403$	7.62807	+	9.09078i	0.0189282	+	0.0225578i
$404$	−292.404	−	599.935i	−0.723773	−	1.48499i
$405$		0			0
$406$	4.80852	+	3.00561i	0.0118437	+	0.00740299i
$407$	349.380	+	416.375i	0.858427	+	1.02303i
$408$		0			0
$409$	106.775	−	605.553i	0.261065	−	1.48057i	−0.518948	−	0.854806i	$-0.673676\pi$
$409$	106.775	−	605.553i	0.261065	−	1.48057i	0.780012	−	0.625764i	$-0.215213\pi$
$410$	45.9363	−	215.968i	0.112040	−	0.526750i
$411$		0			0
$412$	−42.4840	−	58.5079i	−0.103116	−	0.142009i
$413$	88.5625	+	153.395i	0.214437	+	0.371416i
$414$		0			0
$415$	−97.4525	−	56.2643i	−0.234825	−	0.135577i
$416$	−0.0143466	+	20.9530i	−3.44870e−5	+	0.0503677i
$417$		0			0
$418$	792.763	−	257.464i	1.89656	−	0.615943i
$419$	257.110	−	306.412i	0.613628	−	0.731294i	−0.366333	−	0.930484i	$-0.619387\pi$
$419$	257.110	−	306.412i	0.613628	−	0.731294i	0.979961	+	0.199190i	$0.0638312\pi$
$420$		0			0
$421$	221.666	+	80.6799i	0.526523	+	0.191639i	0.591585	−	0.806242i	$-0.298502\pi$
$421$	221.666	+	80.6799i	0.526523	+	0.191639i	−0.0650621	+	0.997881i	$0.520725\pi$
$422$	65.7767	−	34.9626i	0.155869	−	0.0828497i
$423$		0			0
$424$	−213.484	−	480.024i	−0.503500	−	1.13213i
$425$	74.6527	+	423.376i	0.175653	+	0.996180i
$426$		0			0
$427$	176.940	+	486.140i	0.414380	+	1.13850i
$428$	28.8485	+	100.711i	0.0674029	+	0.235305i
$429$		0			0
$430$	56.8346	−	7.97964i	0.132173	−	0.0185573i
$431$			309.442i			0.717964i	0.933344	+	0.358982i	$0.116876\pi$
$431$			309.442i			0.717964i	−0.933344	+	0.358982i	$0.883124\pi$
$432$		0			0
$433$	116.466			0.268974			0.134487	−	0.990915i	$-0.457061\pi$
$433$	116.466			0.268974			0.134487	+	0.990915i	$0.457061\pi$
$434$	−39.4918	−	281.278i	−0.0909949	−	0.648106i
$435$		0			0
$436$	265.051	−	75.9236i	0.607915	−	0.174137i
$437$	−279.245	+	101.637i	−0.639005	+	0.232579i
$438$		0			0
$439$	613.148	−	108.115i	1.39669	−	0.246275i	0.575909	−	0.817514i	$-0.304648\pi$
$439$	613.148	−	108.115i	1.39669	−	0.246275i	0.820784	+	0.571239i	$0.193537\pi$
$440$	737.718	−	328.090i	1.67663	−	0.745659i
$441$		0			0
$442$	−19.9803	−	37.5900i	−0.0452044	−	0.0850452i
$443$	−37.4199	+	102.810i	−0.0844694	+	0.232078i	−0.974735	−	0.223364i	$-0.928296\pi$
$443$	−37.4199	+	102.810i	−0.0844694	+	0.232078i	0.890266	+	0.455441i	$0.150519\pi$
$444$		0			0
$445$	357.400	+	299.894i	0.803145	+	0.673919i
$446$	252.117	+	776.297i	0.565284	+	1.74058i
$447$		0			0
$448$	266.105	−	425.080i	0.593985	−	0.948839i
$449$	190.260	−	329.541i	0.423742	−	0.733943i	−0.572560	−	0.819863i	$-0.694049\pi$
$449$	190.260	−	329.541i	0.423742	−	0.733943i	0.996302	+	0.0859196i	$0.0273828\pi$
$450$		0			0
$451$	252.430	−	145.740i	0.559712	−	0.323150i
$452$	392.225	−	284.804i	0.867753	−	0.630097i
$453$		0			0
$454$	−656.415	−	139.619i	−1.44585	−	0.307531i
$455$	−31.2402	−	5.50850i	−0.0686599	−	0.0121066i
$456$		0			0
$457$	158.495	−	132.993i	0.346815	−	0.291013i	−0.452694	−	0.891666i	$-0.649537\pi$
$457$	158.495	−	132.993i	0.346815	−	0.291013i	0.799510	+	0.600653i	$0.205093\pi$
$458$	−274.277	+	438.802i	−0.598859	+	0.958082i
$459$		0			0
$460$	−258.750	+	126.113i	−0.562501	+	0.274159i
$461$	91.9134	−	77.1245i	0.199378	−	0.167298i	−0.537632	−	0.843179i	$-0.680681\pi$
$461$	91.9134	−	77.1245i	0.199378	−	0.167298i	0.737011	+	0.675881i	$0.236237\pi$
$462$		0			0
$463$	−584.437	−	103.052i	−1.26228	−	0.222575i	−0.497842	−	0.867268i	$-0.665874\pi$
$463$	−584.437	−	103.052i	−1.26228	−	0.222575i	−0.764442	+	0.644693i	$0.776985\pi$
$464$	−1.79200	+	5.50496i	−0.00386208	+	0.0118641i
$465$		0			0
$466$	−536.660	−	216.910i	−1.15163	−	0.465473i
$467$	−578.881	+	334.217i	−1.23957	+	0.715668i	−0.969007	−	0.247033i	$-0.920544\pi$
$467$	−578.881	+	334.217i	−1.23957	+	0.715668i	−0.270567	+	0.962701i	$0.587211\pi$
$468$		0			0
$469$	−124.880	+	216.298i	−0.266268	+	0.461190i
$470$	−450.337	−	576.568i	−0.958164	−	1.22674i
$471$		0			0
$472$	−130.132	+	125.563i	−0.275703	+	0.266024i
$473$	58.0388	+	48.7003i	0.122704	+	0.102961i
$474$		0			0
$475$	−115.483	+	317.287i	−0.243122	+	0.667972i
$476$	−71.3535	+	1016.40i	−0.149902	+	2.13530i
$477$		0			0
$478$	19.7326	−	562.857i	0.0412816	−	1.17753i
$479$	−190.223	+	33.5414i	−0.397125	+	0.0700238i	−0.368644	−	0.929571i	$-0.620178\pi$
$479$	−190.223	+	33.5414i	−0.397125	+	0.0700238i	−0.0284804	+	0.999594i	$0.509067\pi$
$480$		0			0
$481$	20.4878	−	7.45695i	0.0425942	−	0.0155030i
$482$	−355.617	−	320.287i	−0.737794	−	0.664496i
$483$		0			0
$484$	531.476	+	236.803i	1.09809	+	0.489262i
$485$	947.974			1.95458
$486$		0			0
$487$			614.229i			1.26125i	0.776088	+	0.630625i	$0.217201\pi$
$487$			614.229i			1.26125i	−0.776088	+	0.630625i	$0.782799\pi$
$488$	−437.992	+	295.168i	−0.897525	+	0.604852i
$489$		0			0
$490$	113.956	+	102.634i	0.232563	+	0.209458i
$491$	−196.037	−	538.608i	−0.399261	−	1.09696i	−0.962645	−	0.270766i	$-0.912723\pi$
$491$	−196.037	−	538.608i	−0.399261	−	1.09696i	0.563384	−	0.826195i	$-0.309499\pi$
$492$		0			0
$493$	−2.04247	−	11.5834i	−0.00414293	−	0.0234957i
$494$	1.17143	−	33.4141i	0.00237131	−	0.0676399i
$495$		0			0
$496$	268.926	−	108.482i	0.542190	−	0.218714i
$497$	−479.651	−	174.579i	−0.965093	−	0.351265i
$498$		0			0
$499$	−362.757	+	432.317i	−0.726968	+	0.866366i	−0.995288	−	0.0969635i	$-0.969087\pi$
$499$	−362.757	+	432.317i	−0.726968	+	0.866366i	0.268320	+	0.963330i	$0.413531\pi$
$500$	70.5256	−	282.533i	0.141051	−	0.565066i
$501$		0			0
$502$	−98.0683	−	125.557i	−0.195355	−	0.250114i
$503$	−527.529	−	304.569i	−1.04877	−	0.605505i	−0.126462	−	0.991971i	$-0.540362\pi$
$503$	−527.529	−	304.569i	−1.04877	−	0.605505i	−0.922303	+	0.386467i	$0.873695\pi$
$504$		0			0
$505$	515.786	+	893.367i	1.02136	+	1.76904i
$506$	−352.304	−	142.396i	−0.696253	−	0.281416i
$507$		0			0
$508$	−110.059	+	113.907i	−0.216653	+	0.224227i
$509$	−34.7796	+	197.245i	−0.0683294	+	0.387515i	0.931394	+	0.364012i	$0.118593\pi$
$509$	−34.7796	+	197.245i	−0.0683294	+	0.387515i	−0.999724	+	0.0235034i	$0.992518\pi$
$510$		0			0
$511$	−276.875	−	329.967i	−0.541831	−	0.645729i
$512$	486.746	+	158.817i	0.950675	+	0.310189i
$513$		0			0
$514$	229.666	−	367.430i	0.446820	−	0.714844i
$515$	71.8376	+	85.6127i	0.139490	+	0.166238i
$516$		0			0
$517$	167.709	−	951.123i	0.324388	−	1.83970i
$518$	−510.421	−	108.566i	−0.985369	−	0.209588i
$519$		0			0
$520$	−2.24587	−	32.3082i	−0.00431898	−	0.0621311i
$521$	−328.565	−	569.091i	−0.630643	−	1.09231i	−0.987420	−	0.158117i	$-0.949458\pi$
$521$	−328.565	−	569.091i	−0.630643	−	1.09231i	0.356777	−	0.934190i	$-0.383876\pi$
$522$		0			0
$523$	−152.436	−	88.0092i	−0.291465	−	0.168278i	0.347137	−	0.937814i	$-0.387154\pi$
$523$	−152.436	−	88.0092i	−0.291465	−	0.168278i	−0.638602	+	0.769537i	$0.720487\pi$
$524$	−363.895	+	38.1462i	−0.694457	+	0.0727981i
$525$		0			0
$526$	179.732	+	553.415i	0.341695	+	1.05212i
$527$	−378.703	+	451.320i	−0.718601	+	0.856395i
$528$		0			0
$529$	−369.793	−	134.594i	−0.699041	−	0.254430i
$530$	381.122	+	717.023i	0.719098	+	1.35287i
$531$		0			0
$532$	−447.674	+	663.312i	−0.841493	+	1.24683i
$533$	−2.03030	−	11.5144i	−0.00380918	−	0.0216030i
$534$		0			0
$535$	−55.3815	−	152.160i	−0.103517	−	0.284410i
$536$	−245.081	−	70.3847i	−0.457240	−	0.131315i
$537$		0			0
$538$	−20.3221	−	144.743i	−0.0377735	−	0.269040i
$539$			202.455i			0.375613i
$540$		0			0
$541$	276.793			0.511632			0.255816	−	0.966725i	$-0.417656\pi$
$541$	276.793			0.511632			0.255816	+	0.966725i	$0.417656\pi$
$542$	276.369	−	38.8025i	0.509905	−	0.0715913i
$543$		0			0
$544$	−1024.55	+	179.933i	−1.88336	+	0.330759i
$545$	−400.454	+	145.753i	−0.734779	+	0.267438i
$546$		0			0
$547$	906.841	−	159.901i	1.65785	−	0.292323i	0.735165	−	0.677888i	$-0.237105\pi$
$547$	906.841	−	159.901i	1.65785	−	0.292323i	0.922681	+	0.385565i	$0.125994\pi$
$548$	−163.654	+	242.484i	−0.298639	+	0.442489i
$549$		0			0
$550$	−381.249	+	202.647i	−0.693180	+	0.368449i
$551$	3.15957	−	8.68084i	0.00573424	−	0.0157547i
$552$		0			0
$553$	−175.950	−	147.639i	−0.318173	−	0.266979i
$554$	−743.822	+	241.570i	−1.34264	+	0.436047i
$555$		0			0
$556$	−256.660	+	26.9050i	−0.461619	+	0.0483903i
$557$	141.868	−	245.723i	0.254701	−	0.441155i	−0.710113	−	0.704088i	$-0.751356\pi$
$557$	141.868	−	245.723i	0.254701	−	0.441155i	0.964814	+	0.262932i	$0.0846896\pi$
$558$		0			0
$559$	2.63193	−	1.51954i	0.00470828	−	0.00271833i
$560$	−364.287	+	684.219i	−0.650512	+	1.22182i
$561$		0			0
$562$	−1.99559	+	9.38219i	−0.00355087	+	0.0166943i
$563$	−215.390	−	37.9790i	−0.382575	−	0.0674582i	−0.0209464	−	0.999781i	$-0.506668\pi$
$563$	−215.390	−	37.9790i	−0.382575	−	0.0674582i	−0.361628	+	0.932322i	$0.617779\pi$
$564$		0			0
$565$	−573.929	+	481.584i	−1.01580	+	0.852361i
$566$	780.628	+	487.939i	1.37920	+	0.862083i
$567$		0			0
$568$	54.6846	−	518.241i	0.0962757	−	0.912396i
$569$	−684.667	+	574.503i	−1.20328	+	1.00967i	−0.203750	+	0.979023i	$0.565313\pi$
$569$	−684.667	+	574.503i	−1.20328	+	1.00967i	−0.999530	+	0.0306492i	$0.990243\pi$
$570$		0			0
$571$	73.9483	+	13.0391i	0.129507	+	0.0228355i	0.238026	−	0.971259i	$-0.423500\pi$
$571$	73.9483	+	13.0391i	0.129507	+	0.0228355i	−0.108519	+	0.994094i	$0.534611\pi$
$572$	29.7076	−	30.7462i	0.0519363	−	0.0537521i
$573$		0			0
$574$	−104.867	+	259.453i	−0.182695	+	0.452009i
$575$	133.308	−	76.9652i	0.231839	−	0.133853i
$576$		0			0
$577$	95.0734	−	164.672i	0.164772	−	0.285393i	−0.771802	−	0.635863i	$-0.780645\pi$
$577$	95.0734	−	164.672i	0.164772	−	0.285393i	0.936574	+	0.350469i	$0.113978\pi$
$578$	1210.07	−	945.144i	2.09355	−	1.63520i
$579$		0			0
$580$	2.16716	−	8.68187i	0.00373648	−	0.0149687i
$581$	109.254	+	91.6747i	0.188044	+	0.157788i
$582$		0			0
$583$	−366.633	+	1007.32i	−0.628873	+	1.72781i
$584$	258.629	−	355.665i	0.442858	−	0.609016i
$585$		0			0
$586$	−852.294	−	29.8796i	−1.45443	−	0.0509891i
$587$	232.812	−	41.0511i	0.396614	−	0.0699337i	0.0282156	−	0.999602i	$-0.491017\pi$
$587$	232.812	−	41.0511i	0.396614	−	0.0699337i	0.368398	+	0.929668i	$0.379906\pi$
$588$		0			0
$589$	−434.818	+	158.261i	−0.738232	+	0.268694i
$590$	187.054	−	207.687i	0.317041	−	0.352013i
$591$		0			0
$592$	−18.3015	−	532.448i	−0.0309147	−	0.899405i
$593$	−447.411			−0.754487			−0.377243	−	0.926114i	$-0.623128\pi$
$593$	−447.411			−0.754487			−0.377243	+	0.926114i	$0.623128\pi$
$594$		0			0
$595$		−	1574.88i		−	2.64685i
$596$	404.827	+	180.373i	0.679239	+	0.302640i
$597$		0			0
$598$	−10.2007	+	11.3260i	−0.0170581	+	0.0189397i
$599$	286.623	+	787.490i	0.478502	+	1.31467i	0.910764	+	0.412927i	$0.135493\pi$
$599$	286.623	+	787.490i	0.478502	+	1.31467i	−0.432262	+	0.901748i	$0.642284\pi$
$600$		0			0
$601$	9.36443	+	53.1083i	0.0155814	+	0.0883666i	0.991607	−	0.129290i	$-0.0412698\pi$
$601$	9.36443	+	53.1083i	0.0155814	+	0.0883666i	−0.976025	+	0.217657i	$0.930159\pi$
$602$	−72.6950	−	2.54853i	−0.120756	−	0.00423344i
$603$		0			0
$604$	5.49346	−	78.2521i	0.00909512	−	0.129556i
$605$	−845.097	−	307.590i	−1.39685	−	0.508413i
$606$		0			0
$607$	262.383	−	312.696i	0.432262	−	0.515150i	−0.505312	−	0.862937i	$-0.668622\pi$
$607$	262.383	−	312.696i	0.432262	−	0.515150i	0.937573	+	0.347787i	$0.113067\pi$
$608$	−767.535	−	279.955i	−1.26239	−	0.460453i
$609$		0			0
$610$	643.375	−	502.518i	1.05471	−	0.823799i
$611$	−33.5502	−	19.3702i	−0.0549103	−	0.0317025i
$612$		0			0
$613$	11.7936	+	20.4271i	0.0192391	+	0.0333231i	0.875485	−	0.483246i	$-0.160542\pi$
$613$	11.7936	+	20.4271i	0.0192391	+	0.0333231i	−0.856246	+	0.516569i	$0.827209\pi$
$614$	−327.683	+	810.724i	−0.533686	+	1.32040i
$615$		0			0
$616$	−992.999	+	247.149i	−1.61201	+	0.401216i
$617$	107.264	−	608.323i	0.173847	−	0.985937i	−0.765619	−	0.643295i	$-0.777567\pi$
$617$	107.264	−	608.323i	0.173847	−	0.985937i	0.939466	−	0.342642i	$-0.111322\pi$
$618$		0			0
$619$	168.570	+	200.894i	0.272326	+	0.324545i	0.884823	−	0.465928i	$-0.154279\pi$
$619$	168.570	+	200.894i	0.272326	+	0.324545i	−0.612497	+	0.790473i	$0.709835\pi$
$620$	−402.906	+	196.374i	−0.649848	+	0.316732i
$621$		0			0
$622$	255.251	+	159.547i	0.410371	+	0.256506i
$623$	−380.091	−	452.974i	−0.610097	−	0.727086i
$624$		0			0
$625$	−135.571	+	768.863i	−0.216914	+	1.23018i
$626$	−256.976	+	1208.16i	−0.410504	+	1.92997i
$627$		0			0
$628$	418.881	−	304.160i	0.667009	−	0.484331i
$629$	541.207	+	937.398i	0.860424	+	1.49030i
$630$		0			0
$631$	−370.756	−	214.056i	−0.587569	−	0.339233i	0.176567	−	0.984289i	$-0.443501\pi$
$631$	−370.756	−	214.056i	−0.587569	−	0.339233i	−0.764136	+	0.645055i	$0.776834\pi$
$632$	102.882	−	210.719i	0.162788	−	0.333417i
$633$		0			0
$634$	−183.917	+	59.7305i	−0.290090	+	0.0942121i
$635$	157.367	−	187.543i	0.247822	−	0.295343i
$636$		0			0
$637$	7.63122	+	2.77754i	0.0119799	+	0.00436034i
$638$	10.4308	−	5.54433i	0.0163492	−	0.00869018i
$639$		0			0
$640$	−767.686	−	192.188i	−1.19951	−	0.300293i
$641$	−69.5087	−	394.203i	−0.108438	−	0.614982i	−0.989791	−	0.142524i	$-0.954478\pi$
$641$	−69.5087	−	394.203i	−0.108438	−	0.614982i	0.881353	−	0.472458i	$-0.156633\pi$
$642$		0			0
$643$	−212.800	−	584.664i	−0.330949	−	0.909275i	−0.987865	−	0.155312i	$-0.950362\pi$
$643$	−212.800	−	584.664i	−0.330949	−	0.909275i	0.656916	−	0.753963i	$-0.271860\pi$
$644$	350.718	−	100.463i	0.544593	−	0.155998i
$645$		0			0
$646$	1643.77	−	230.788i	2.54454	−	0.357256i
$647$			668.799i			1.03369i	0.856078	+	0.516846i	$0.172894\pi$
$647$			668.799i			1.03369i	−0.856078	+	0.516846i	$0.827106\pi$
$648$		0			0
$649$	368.981			0.568537
$650$	2.40798	+	17.1507i	0.00370459	+	0.0263857i
$651$		0			0
$652$	91.0995	+	318.031i	0.139723	+	0.487777i
$653$	1204.33	−	438.339i	1.84430	−	0.671269i	0.856366	−	0.516368i	$-0.172717\pi$
$653$	1204.33	−	438.339i	1.84430	−	0.671269i	0.987930	−	0.154901i	$-0.0495057\pi$
$654$		0			0
$655$	556.948	−	98.2050i	0.850303	−	0.149931i
$656$	−282.900	−	39.9170i	−0.431250	−	0.0608491i
$657$		0			0
$658$	435.200	+	818.763i	0.661399	+	1.24432i
$659$	−127.048	+	349.061i	−0.192789	+	0.529683i	−0.997994	−	0.0633137i	$-0.979833\pi$
$659$	−127.048	+	349.061i	−0.192789	+	0.529683i	0.805205	+	0.592997i	$0.202055\pi$
$660$		0			0
$661$	−184.368	−	154.703i	−0.278923	−	0.234044i	0.492584	−	0.870265i	$-0.336052\pi$
$661$	−184.368	−	154.703i	−0.278923	−	0.234044i	−0.771507	+	0.636221i	$0.780497\pi$
$662$	−298.639	−	919.545i	−0.451117	−	1.38904i
$663$		0			0
$664$	−63.8832	+	130.843i	−0.0962096	+	0.197053i
$665$	618.455	−	1071.19i	0.930007	−	1.61082i
$666$		0			0
$667$	−3.64724	+	2.10574i	−0.00546813	+	0.00315703i
$668$	271.004	+	373.220i	0.405694	+	0.558712i
$669$		0			0
$670$	385.500	+	81.9957i	0.575373	+	0.122382i
$671$	1061.33	+	187.141i	1.58171	+	0.278899i
$672$		0			0
$673$	−7.13513	+	5.98709i	−0.0106020	+	0.00889612i	−0.648073	−	0.761578i	$-0.724425\pi$
$673$	−7.13513	+	5.98709i	−0.0106020	+	0.00889612i	0.637471	+	0.770474i	$0.279980\pi$
$674$	18.8900	−	30.2211i	0.0280267	−	0.0448385i
$675$		0			0
$676$	295.421	+	606.124i	0.437013	+	0.896634i
$677$	−511.434	+	429.144i	−0.755441	+	0.633890i	−0.936936	−	0.349501i	$-0.886351\pi$
$677$	−511.434	+	429.144i	−0.755441	+	0.633890i	0.181495	+	0.983392i	$0.441907\pi$
$678$		0			0
$679$	−1183.23	−	208.635i	−1.74260	−	0.307267i
$680$	1560.24	−	388.331i	2.29447	−	0.571075i
$681$		0			0
$682$	−548.580	−	221.728i	−0.804370	−	0.325115i
$683$	718.255	−	414.685i	1.05162	−	0.607152i	0.128517	−	0.991707i	$-0.458978\pi$
$683$	718.255	−	414.685i	1.05162	−	0.607152i	0.923102	+	0.384555i	$0.125645\pi$
$684$		0			0
$685$	226.086	−	391.592i	0.330052	−	0.571667i
$686$	353.053	+	452.014i	0.514654	+	0.658913i
$687$		0			0
$688$	−15.4002	−	72.6478i	−0.0223840	−	0.105593i
$689$	32.9392	+	27.6392i	0.0478072	+	0.0401150i
$690$		0			0
$691$	−438.513	+	1204.80i	−0.634606	+	1.74357i	0.0334337	+	0.999441i	$0.489356\pi$
$691$	−438.513	+	1204.80i	−0.634606	+	1.74357i	−0.668040	+	0.744125i	$0.732866\pi$
$692$	−837.112	−	58.7670i	−1.20970	−	0.0849234i
$693$		0			0
$694$	8.57951	−	244.724i	0.0123624	−	0.352628i
$695$	392.823	−	69.2653i	0.565213	−	0.0996623i
$696$		0			0
$697$	545.455	−	198.529i	0.782575	−	0.284834i
$698$	−835.288	−	752.304i	−1.19669	−	1.07780i
$699$		0			0
$700$	168.705	−	378.640i	0.241008	−	0.540914i
$701$	−711.655			−1.01520			−0.507600	−	0.861593i	$-0.669467\pi$
$701$	−711.655			−1.01520			−0.507600	+	0.861593i	$0.669467\pi$
$702$		0			0
$703$			850.128i			1.20929i
$704$	−489.705	−	922.829i	−0.695603	−	1.31084i
$705$		0			0
$706$	325.311	+	292.992i	0.460780	+	0.415003i
$707$	−447.168	−	1228.58i	−0.632487	−	1.73774i
$708$		0			0
$709$	−152.146	−	862.861i	−0.214592	−	1.21701i	−0.881613	−	0.471972i	$-0.843542\pi$
$709$	−152.146	−	862.861i	−0.214592	−	1.21701i	0.667021	−	0.745039i	$-0.267569\pi$
$710$	−28.2208	+	804.977i	−0.0397476	+	1.13377i
$711$		0			0
$712$	355.043	−	488.252i	0.498655	−	0.685748i
$713$	198.229	+	72.1493i	0.278020	+	0.101191i
$714$		0			0
$715$	−42.4770	+	50.6221i	−0.0594084	+	0.0708002i
$716$	−1263.75	−	315.456i	−1.76501	−	0.440581i
$717$		0			0
$718$	−217.645	−	278.652i	−0.303127	−	0.388095i
$719$	−596.030	−	344.118i	−0.828971	−	0.478606i	0.0245295	−	0.999699i	$-0.492191\pi$
$719$	−596.030	−	344.118i	−0.828971	−	0.478606i	−0.853500	+	0.521093i	$0.825525\pi$
$720$		0			0
$721$	−70.8229	−	122.669i	−0.0982287	−	0.170137i
$722$	539.296	+	217.976i	0.746947	+	0.301905i
$723$		0			0
$724$	490.776	+	474.196i	0.677867	+	0.654968i
$725$	−0.830942	+	4.71251i	−0.00114613	+	0.00650001i
$726$		0			0
$727$	−288.835	−	344.220i	−0.397297	−	0.473481i	0.529897	−	0.848062i	$-0.322231\pi$
$727$	−288.835	−	344.220i	−0.397297	−	0.473481i	−0.927194	+	0.374582i	$0.877786\pi$
$728$	−4.30733	+	40.8202i	−0.00591666	+	0.0560716i
$729$		0			0
$730$	−360.273	+	576.382i	−0.493525	+	0.789565i
$731$	96.9828	+	115.580i	0.132671	+	0.158112i
$732$		0			0
$733$	113.082	−	641.322i	0.154273	−	0.874928i	−0.805174	−	0.593039i	$-0.797928\pi$
$733$	113.082	−	641.322i	0.154273	−	0.874928i	0.959447	−	0.281889i	$-0.0909609\pi$
$734$	−350.500	−	74.5512i	−0.477520	−	0.101568i
$735$		0			0
$736$	186.009	+	322.687i	0.252729	+	0.438433i
$737$	260.145	+	450.584i	0.352978	+	0.611376i
$738$		0			0
$739$	51.6835	+	29.8395i	0.0699371	+	0.0403782i	0.534561	−	0.845130i	$-0.320477\pi$
$739$	51.6835	+	29.8395i	0.0699371	+	0.0403782i	−0.464624	+	0.885508i	$0.653810\pi$
$740$	85.8516	+	818.981i	0.116016	+	1.10673i
$741$		0			0
$742$	−317.896	−	978.841i	−0.428432	−	1.31919i
$743$	537.178	−	640.184i	0.722985	−	0.861620i	−0.271932	−	0.962316i	$-0.587663\pi$
$743$	537.178	−	640.184i	0.722985	−	0.861620i	0.994917	+	0.100696i	$0.0321071\pi$
$744$		0			0
$745$	−643.712	−	234.292i	−0.864042	−	0.314486i
$746$	−392.031	−	737.547i	−0.525511	−	0.988670i
$747$		0			0
$748$	1759.34	+	1187.39i	2.35206	+	1.58742i
$749$	35.6372	+	202.108i	0.0475797	+	0.269838i
$750$		0			0
$751$	−453.840	−	1246.91i	−0.604314	−	1.66034i	−0.742431	−	0.669923i	$-0.766327\pi$
$751$	−453.840	−	1246.91i	−0.604314	−	1.66034i	0.138117	−	0.990416i	$-0.455895\pi$
$752$	−703.843	+	633.045i	−0.935962	+	0.841816i
$753$		0			0
$754$	−0.0658814	−	0.469237i	−8.73758e−5	−	0.000622330i
$755$			121.249i			0.160594i
$756$		0			0
$757$	−399.002			−0.527084			−0.263542	−	0.964648i	$-0.584891\pi$
$757$	−399.002			−0.527084			−0.263542	+	0.964648i	$0.584891\pi$
$758$	−367.248	+	51.5621i	−0.484496	+	0.0680238i
$759$		0			0
$760$	1213.74	+	348.573i	1.59702	+	0.458649i
$761$	−597.774	+	217.572i	−0.785511	+	0.285903i	−0.703469	−	0.710726i	$-0.748367\pi$
$761$	−597.774	+	217.572i	−0.785511	+	0.285903i	−0.0820425	+	0.996629i	$0.526144\pi$
$762$		0			0
$763$	531.910	−	93.7901i	0.697130	−	0.122923i
$764$	656.887	+	443.338i	0.859800	+	0.580285i
$765$		0			0
$766$	−723.489	+	384.559i	−0.944503	+	0.502035i
$767$	5.06214	−	13.9081i	0.00659992	−	0.0181331i
$768$		0			0
$769$	−825.263	−	692.478i	−1.07316	−	0.900491i	−0.0778283	−	0.996967i	$-0.524799\pi$
$769$	−825.263	−	692.478i	−1.07316	−	0.900491i	−0.995335	+	0.0964755i	$0.969243\pi$
$770$	1504.32	−	488.555i	1.95366	−	0.634487i
$771$		0			0
$772$	−55.0272	−	524.932i	−0.0712788	−	0.679964i
$773$	292.032	−	505.814i	0.377790	−	0.654352i	−0.612950	−	0.790122i	$-0.710017\pi$
$773$	292.032	−	505.814i	0.377790	−	0.654352i	0.990740	+	0.135770i	$0.0433507\pi$
$774$		0			0
$775$	207.576	−	119.844i	0.267840	−	0.154638i
$776$	−85.0625	−	1223.67i	−0.109617	−	1.57690i
$777$		0			0
$778$	−98.3030	+	462.168i	−0.126353	+	0.594046i
$779$	448.968	+	79.1652i	0.576339	+	0.101624i
$780$		0			0
$781$	−814.549	+	683.488i	−1.04296	+	0.875144i
$782$	−641.685	−	401.092i	−0.820569	−	0.512905i
$783$		0			0
$784$	122.258	−	156.307i	0.155942	−	0.199371i
$785$	−612.936	+	514.314i	−0.780810	+	0.655177i
$786$		0			0
$787$	−187.288	−	33.0239i	−0.237977	−	0.0419618i	0.0533875	−	0.998574i	$-0.482998\pi$
$787$	−187.288	−	33.0239i	−0.237977	−	0.0419618i	−0.291364	+	0.956612i	$0.594109\pi$
$788$	99.4666	+	96.1064i	0.126227	+	0.121962i
$789$		0			0
$790$	−135.821	+	336.037i	−0.171926	+	0.425363i
$791$	822.346	−	474.782i	1.03963	−	0.600230i
$792$		0			0
$793$	21.6146	−	37.4376i	0.0272568	−	0.0472101i
$794$	−976.633	+	762.814i	−1.23002	+	0.960723i
$795$		0			0
$796$	658.594	+	164.398i	0.827379	+	0.206530i
$797$	764.881	+	641.812i	0.959700	+	0.805284i	0.980904	−	0.194491i	$-0.0623055\pi$
$797$	764.881	+	641.812i	0.959700	+	0.805284i	−0.0212040	+	0.999775i	$0.506750\pi$
$798$		0			0
$799$	657.809	−	1807.31i	0.823290	−	2.26197i
$800$	416.720	+	73.7732i	0.520900	+	0.0922165i
$801$		0			0
$802$	−528.457	−	18.5266i	−0.658924	−	0.0231005i
$803$	−883.674	+	155.816i	−1.10047	+	0.194042i
$804$		0			0
$805$	−529.886	+	192.863i	−0.658243	+	0.239581i
$806$	−15.8838	+	17.6359i	−0.0197069	+	0.0218807i
$807$		0			0
$808$	1106.90	−	745.955i	1.36993	−	0.923212i
$809$	1272.41			1.57282			0.786410	−	0.617705i	$-0.211937\pi$
$809$	1272.41			1.57282			0.786410	+	0.617705i	$0.211937\pi$
$810$		0			0
$811$		−	58.7187i		−	0.0724029i	−0.999345	−	0.0362014i	$-0.988474\pi$
$811$		−	58.7187i		−	0.0724029i	0.999345	−	0.0362014i	$-0.0115258\pi$
$812$	−4.61571	+	10.3594i	−0.00568437	+	0.0127579i
$813$		0			0
$814$	−727.507	+	807.756i	−0.893744	+	0.992330i
$815$	−174.887	−	480.499i	−0.214586	−	0.589570i
$816$		0			0
$817$	20.5773	+	116.700i	0.0251864	+	0.142839i
$818$	1229.03	+	43.0874i	1.50249	+	0.0526740i
$819$		0			0
$820$	440.514	+	30.9250i	0.537212	+	0.0377134i
$821$	−742.930	−	270.404i	−0.904909	−	0.329360i	−0.152691	−	0.988274i	$-0.548794\pi$
$821$	−742.930	−	270.404i	−0.904909	−	0.329360i	−0.752218	+	0.658914i	$0.771016\pi$
$822$		0			0
$823$	616.081	−	734.217i	0.748580	−	0.892123i	−0.248489	−	0.968635i	$-0.579934\pi$
$823$	616.081	−	734.217i	0.748580	−	0.892123i	0.997069	+	0.0765119i	$0.0243783\pi$
$824$	104.065	−	100.412i	0.126293	−	0.121860i
$825$		0			0
$826$	−279.183	+	218.060i	−0.337994	+	0.263995i
$827$	729.172	+	420.987i	0.881707	+	0.509054i	0.871221	−	0.490891i	$-0.163329\pi$
$827$	729.172	+	420.987i	0.881707	+	0.509054i	0.0104861	+	0.999945i	$0.496662\pi$
$828$		0			0
$829$	473.348	+	819.862i	0.570986	+	0.988977i	0.996465	+	0.0840088i	$0.0267724\pi$
$829$	473.348	+	819.862i	0.570986	+	0.988977i	−0.425479	+	0.904968i	$0.639894\pi$
$830$	84.3364	−	208.658i	0.101610	−	0.251395i
$831$		0			0
$832$	−41.5029	+	5.79808i	−0.0498833	+	0.00696885i
$833$	−70.0104	+	397.049i	−0.0840461	+	0.476649i
$834$		0			0
$835$	−458.249	−	546.120i	−0.548802	−	0.654036i
$836$	730.375	+	1498.53i	0.873654	+	1.79250i
$837$		0			0
$838$	678.368	+	424.020i	0.809508	+	0.505991i
$839$	−73.7634	−	87.9078i	−0.0879182	−	0.104777i	0.720292	−	0.693671i	$-0.244008\pi$
$839$	−73.7634	−	87.9078i	−0.0879182	−	0.104777i	−0.808210	+	0.588894i	$0.799563\pi$
$840$		0			0
$841$	−146.015	+	828.094i	−0.173621	+	0.984654i
$842$	−98.1527	+	461.462i	−0.116571	+	0.548054i
$843$		0			0
$844$	87.5368	+	120.553i	0.103717	+	0.142836i
$845$	−521.107	−	902.585i	−0.616695	−	1.06815i
$846$		0			0
$847$	987.122	+	569.915i	1.16543	+	0.672863i
$848$	891.358	−	556.303i	1.05113	−	0.656018i
$849$		0			0
$850$	−817.769	+	265.586i	−0.962081	+	0.312454i
$851$	249.121	−	296.891i	0.292739	−	0.348873i
$852$		0			0
$853$	785.229	+	285.800i	0.920549	+	0.335053i	0.758457	−	0.651723i	$-0.225954\pi$
$853$	785.229	+	285.800i	0.920549	+	0.335053i	0.162092	+	0.986776i	$0.448176\pi$
$854$	−913.633	+	485.627i	−1.06983	+	0.568649i
$855$		0			0
$856$	−191.443	+	85.1416i	−0.223648	+	0.0994645i
$857$	−134.463	−	762.580i	−0.156900	−	0.889825i	−0.957028	−	0.289996i	$-0.906346\pi$
$857$	−134.463	−	762.580i	−0.156900	−	0.889825i	0.800128	−	0.599830i	$-0.204765\pi$
$858$		0			0
$859$	483.287	+	1327.82i	0.562616	+	1.54577i	0.815787	+	0.578353i	$0.196304\pi$
$859$	483.287	+	1327.82i	0.562616	+	1.54577i	−0.253171	+	0.967422i	$0.581474\pi$
$860$	31.6085	+	110.346i	0.0367541	+	0.128309i
$861$		0			0
$862$	−612.874	+	86.0482i	−0.710990	+	0.0998239i
$863$		−	509.284i		−	0.590132i	−0.955477	−	0.295066i	$-0.904658\pi$
$863$		−	509.284i		−	0.590132i	0.955477	−	0.295066i	$-0.0953417\pi$
$864$		0			0
$865$	1297.07			1.49951
$866$	32.3862	+	230.669i	0.0373974	+	0.266361i
$867$		0			0
$868$	546.110	−	156.433i	0.629159	−	0.180222i
$869$	−449.618	+	163.648i	−0.517398	+	0.188317i
$870$		0			0
$871$	20.5530	−	3.62405i	0.0235970	−	0.00416080i
$872$	224.076	+	503.840i	0.256968	+	0.577799i
$873$		0			0
$874$	−278.951	−	524.803i	−0.319165	−	0.600461i
$875$	195.110	−	536.061i	0.222983	−	0.612641i
$876$		0			0
$877$	295.917	+	248.304i	0.337419	+	0.283128i	0.795715	−	0.605672i	$-0.207095\pi$
$877$	295.917	+	248.304i	0.337419	+	0.283128i	−0.458296	+	0.888800i	$0.651540\pi$
$878$	384.630	+	1184.32i	0.438075	+	1.34889i
$879$		0			0
$880$	854.947	+	1369.87i	0.971531	+	1.55667i
$881$	−590.991	+	1023.63i	−0.670818	+	1.16189i	0.306854	+	0.951757i	$0.400724\pi$
$881$	−590.991	+	1023.63i	−0.670818	+	1.16189i	−0.977672	+	0.210135i	$0.932610\pi$
$882$		0			0
$883$	379.330	−	219.006i	0.429592	−	0.248025i	−0.269581	−	0.962978i	$-0.586885\pi$
$883$	379.330	−	219.006i	0.429592	−	0.248025i	0.699173	+	0.714953i	$0.253552\pi$
$884$	68.8937	−	50.0254i	0.0779340	−	0.0565898i
$885$		0			0
$886$	−214.029	−	45.5240i	−0.241568	−	0.0513814i
$887$	1569.49	+	276.744i	1.76944	+	0.312000i	0.960993	−	0.276572i	$-0.0891984\pi$
$887$	1569.49	+	276.744i	1.76944	+	0.312000i	0.808445	+	0.588572i	$0.200310\pi$
$888$		0			0
$889$	−237.695	+	199.450i	−0.267374	+	0.224353i
$890$	−494.578	+	791.249i	−0.555706	+	0.889044i
$891$		0			0
$892$	−1467.41	+	715.204i	−1.64507	+	0.801798i
$893$	1157.16	−	970.972i	1.29581	−	1.08731i
$894$		0			0
$895$	1982.68	+	349.599i	2.21528	+	0.390614i
$896$	915.900	+	408.837i	1.02221	+	0.456292i
$897$		0			0
$898$	705.586	+	285.188i	0.785731	+	0.317581i
$899$	−5.67920	+	3.27889i	−0.00631724	+	0.00364726i
$900$		0			0
$901$	−1067.36	+	1848.73i	−1.18464	+	2.05186i
$902$	358.844	+	459.429i	0.397832	+	0.509345i
$903$		0			0
$904$	673.143	+	697.633i	0.744627	+	0.771718i
$905$	−808.038	−	678.024i	−0.892859	−	0.749198i
$906$		0			0
$907$	−335.024	+	920.471i	−0.369376	+	1.01485i	0.606224	+	0.795294i	$0.292684\pi$
$907$	−335.024	+	920.471i	−0.369376	+	1.01485i	−0.975599	+	0.219558i	$0.929539\pi$
$908$	93.9937	−	1338.90i	0.103517	−	1.47456i
$909$		0			0
$910$	2.22286	−	63.4054i	0.00244270	−	0.0696762i
$911$	1389.49	−	245.005i	1.52524	−	0.268941i	0.652751	−	0.757572i	$-0.273615\pi$
$911$	1389.49	−	245.005i	1.52524	−	0.268941i	0.872490	+	0.488631i	$0.162504\pi$
$912$		0			0
$913$	279.185	−	101.615i	0.305788	−	0.111298i
$914$	307.475	+	276.928i	0.336406	+	0.302985i
$915$		0			0
$916$	−945.349	−	421.207i	−1.03204	−	0.459833i
$917$	−716.775			−0.781652
$918$		0			0
$919$		−	648.911i		−	0.706105i	−0.935603	−	0.353053i	$-0.885144\pi$
$919$		−	648.911i		−	0.706105i	0.935603	−	0.353053i	$-0.114856\pi$
$920$	−321.729	−	477.405i	−0.349705	−	0.518919i
$921$		0			0
$922$	178.310	+	160.595i	0.193394	+	0.174181i
$923$	14.5879	+	40.0800i	0.0158049	+	0.0434236i
$924$		0			0
$925$	−76.4679	−	433.671i	−0.0826680	−	0.468834i
$926$	41.5849	−	1186.18i	0.0449081	−	1.28097i
$927$		0			0
$928$	−11.4013	−	2.01840i	−0.0122859	−	0.00217501i
$929$	146.001	+	53.1400i	0.157159	+	0.0572012i	0.419402	−	0.907801i	$-0.362240\pi$
$929$	146.001	+	53.1400i	0.157159	+	0.0572012i	−0.262243	+	0.965002i	$0.584462\pi$
$930$		0			0
$931$	−203.541	+	242.570i	−0.218626	+	0.260548i
$932$	280.375	−	1123.21i	0.300832	−	1.20516i
$933$		0			0
$934$	−822.914	−	1053.58i	−0.881064	−	1.12803i
$935$	−2841.19	−	1640.36i	−3.03871	−	1.75440i
$936$		0			0
$937$	128.354	+	222.316i	0.136984	+	0.237264i	0.926354	−	0.376655i	$-0.122926\pi$
$937$	128.354	+	222.316i	0.136984	+	0.237264i	−0.789369	+	0.613918i	$0.789592\pi$
$938$	−463.120	−	187.187i	−0.493732	−	0.199559i
$939$		0			0
$940$	1016.71	−	1052.26i	1.08160	−	1.11942i
$941$	112.599	−	638.580i	0.119659	−	0.678618i	−0.864679	−	0.502325i	$-0.832478\pi$
$941$	112.599	−	638.580i	0.119659	−	0.678618i	0.984338	−	0.176293i	$-0.0564108\pi$
$942$		0			0
$943$	−133.595	−	159.212i	−0.141670	−	0.168836i
$944$	−284.874	−	222.819i	−0.301773	−	0.236037i
$945$		0			0
$946$	−80.3155	+	128.493i	−0.0849001	+	0.135827i
$947$	645.804	+	769.639i	0.681947	+	0.812713i	0.990357	−	0.138540i	$-0.0442411\pi$
$947$	645.804	+	769.639i	0.681947	+	0.812713i	−0.308409	+	0.951254i	$0.599797\pi$
$948$		0			0
$949$	−6.25014	+	35.4463i	−0.00658602	+	0.0373512i
$950$	−660.523	−	140.493i	−0.695287	−	0.147887i
$951$		0			0
$952$	−2032.90	+	141.315i	−2.13540	+	0.148440i
$953$	29.9840	+	51.9338i	0.0314628	+	0.0544951i	0.881328	−	0.472505i	$-0.156650\pi$
$953$	29.9840	+	51.9338i	0.0314628	+	0.0544951i	−0.849865	+	0.527000i	$0.823317\pi$
$954$		0			0
$955$	−1060.82	−	612.464i	−1.11081	−	0.641324i
$956$	1120.27	−	117.435i	1.17183	−	0.122840i
$957$		0			0
$958$	−119.327	−	367.423i	−0.124559	−	0.383531i
$959$	−368.375	+	439.012i	−0.384124	+	0.457781i
$960$		0			0
$961$	−594.379	−	216.336i	−0.618500	−	0.225116i
$962$	20.4662	+	38.5040i	0.0212746	+	0.0400249i
$963$		0			0
$964$	535.464	−	793.389i	0.555460	−	0.823018i
$965$	141.664	+	803.418i	0.146802	+	0.832558i
$966$		0			0
$967$	−7.17415	−	19.7108i	−0.00741897	−	0.0203835i	0.935928	−	0.352192i	$-0.114564\pi$
$967$	−7.17415	−	19.7108i	−0.00741897	−	0.0203835i	−0.943347	+	0.331808i	$0.892341\pi$
$968$	−321.216	+	1118.48i	−0.331834	+	1.15545i
$969$		0			0
$970$	263.608	+	1877.53i	0.271761	+	1.93560i
$971$			423.302i			0.435945i	0.975955	+	0.217972i	$0.0699442\pi$
$971$			423.302i			0.435945i	−0.975955	+	0.217972i	$0.930056\pi$
$972$		0			0
$973$	−505.551			−0.519580
$974$	−1216.53	+	170.802i	−1.24900	+	0.175361i
$975$		0			0
$976$	−706.396	−	785.397i	−0.723766	−	0.804710i
$977$	−119.361	+	43.4437i	−0.122171	+	0.0444664i	−0.402382	−	0.915472i	$-0.631818\pi$
$977$	−119.361	+	43.4437i	−0.122171	+	0.0444664i	0.280211	+	0.959938i	$0.409595\pi$
$978$		0			0
$979$	−1213.09	+	213.901i	−1.23912	+	0.218490i
$980$	−171.587	+	254.238i	−0.175089	+	0.259426i
$981$		0			0
$982$	1012.24	−	538.040i	1.03079	−	0.547902i
$983$	−345.481	+	949.200i	−0.351455	+	0.965615i	0.630448	+	0.776232i	$0.282871\pi$
$983$	−345.481	+	949.200i	−0.351455	+	0.965615i	−0.981903	+	0.189384i	$0.939351\pi$
$984$		0			0
$985$	−163.767	−	137.417i	−0.166261	−	0.139509i
$986$	22.3738	−	7.26631i	0.0226915	−	0.00736948i
$987$		0			0
$988$	66.5048	−	6.97153i	0.0673126	−	0.00705620i
$989$	27.0114	−	46.7851i	0.0273118	−	0.0473054i
$990$		0			0
$991$	−1171.38	+	676.298i	−1.18202	+	0.682440i	−0.956481	−	0.291794i	$-0.905748\pi$
$991$	−1171.38	+	676.298i	−1.18202	+	0.682440i	−0.225539	+	0.974234i	$0.572414\pi$
$992$	289.638	+	502.462i	0.291974	+	0.506514i
$993$		0			0
$994$	212.387	−	998.531i	0.213669	−	1.00456i
$995$	−1033.26	−	182.191i	−1.03845	−	0.183107i
$996$		0			0
$997$	1031.88	−	865.848i	1.03498	−	0.868453i	0.0435468	−	0.999051i	$-0.486134\pi$
$997$	1031.88	−	865.848i	1.03498	−	0.868453i	0.991435	+	0.130598i	$0.0416898\pi$
$998$	−957.109	−	598.250i	−0.959027	−	0.599449i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.19		204
3.2	odd	2		108.3.j.a.103.16	yes	204
4.3	odd	2	inner	324.3.j.a.199.4		204
12.11	even	2		108.3.j.a.103.31	yes	204
27.11	odd	18		108.3.j.a.43.31	yes	204
27.16	even	9	inner	324.3.j.a.127.4		204
108.11	even	18		108.3.j.a.43.16	✓	204
108.43	odd	18	inner	324.3.j.a.127.19		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.16	✓	204	108.11	even	18
108.3.j.a.43.31	yes	204	27.11	odd	18
108.3.j.a.103.16	yes	204	3.2	odd	2
108.3.j.a.103.31	yes	204	12.11	even	2
324.3.j.a.127.4		204	27.16	even	9	inner
324.3.j.a.127.19		204	108.43	odd	18	inner
324.3.j.a.199.4		204	4.3	odd	2	inner
324.3.j.a.199.19		204	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.278075 + 1.98057i) q^{2} +(-3.84535 + 1.10150i) q^{4} +(5.80978 - 2.11459i) q^{5} +(-7.71693 + 1.36070i) q^{7} +(-3.25089 - 7.30970i) q^{8} +O(q^{10})\)	\(q+(0.278075 + 1.98057i) q^{2} +(-3.84535 + 1.10150i) q^{4} +(5.80978 - 2.11459i) q^{5} +(-7.71693 + 1.36070i) q^{7} +(-3.25089 - 7.30970i) q^{8} +(5.80365 + 10.9187i) q^{10} +(-5.58301 + 15.3392i) q^{11} +(0.501591 + 0.420885i) q^{13} +(-4.84086 - 14.9056i) q^{14} +(13.5734 - 8.47127i) q^{16} +(-16.2536 + 28.1521i) q^{17} +(-22.1106 + 12.7656i) q^{19} +(-20.0114 + 14.5308i) q^{20} +(-31.9329 - 6.79212i) q^{22} +(11.4625 + 2.02115i) q^{23} +(10.1309 - 8.50086i) q^{25} +(-0.694114 + 1.11048i) q^{26} +(28.1755 - 13.7326i) q^{28} +(-0.277178 + 0.232580i) q^{29} +(17.8485 + 3.14718i) q^{31} +(20.5524 + 24.5275i) q^{32} +(-60.2770 - 24.3631i) q^{34} +(-41.9564 + 24.2235i) q^{35} +(16.6488 - 28.8366i) q^{37} +(-31.4316 - 40.2420i) q^{38} +(-34.3439 - 35.5934i) q^{40} +(-13.6788 - 11.4779i) q^{41} +(1.58745 - 4.36148i) q^{43} +(4.57256 - 65.1342i) q^{44} +(-0.815602 + 23.2644i) q^{46} +(-58.2666 + 10.2740i) q^{47} +(11.6546 - 4.24194i) q^{49} +(19.6537 + 17.7012i) q^{50} +(-2.39240 - 1.06595i) q^{52} +65.6694 q^{53} +100.923i q^{55} +(35.0332 + 51.9850i) q^{56} +(-0.537718 - 0.484297i) q^{58} +(-7.73105 - 21.2409i) q^{59} +(-11.4644 - 65.0179i) q^{61} +(-1.26999 + 36.2255i) q^{62} +(-42.8634 + 47.5261i) q^{64} +(3.80413 + 1.38459i) q^{65} +(20.4878 - 24.4165i) q^{67} +(31.4914 - 126.158i) q^{68} +(-59.6435 - 76.3617i) q^{70} +(56.4127 + 32.5699i) q^{71} +(27.4849 + 47.6052i) q^{73} +(61.7427 + 24.9555i) q^{74} +(70.9619 - 73.4429i) q^{76} +(22.2116 - 125.968i) q^{77} +(18.8412 + 22.4541i) q^{79} +(60.9453 - 77.9184i) q^{80} +(18.9290 - 30.2835i) q^{82} +(-11.6992 - 13.9426i) q^{83} +(-34.8999 + 197.927i) q^{85} +(9.07966 + 1.93124i) q^{86} +(130.275 - 9.05592i) q^{88} +(37.7308 + 65.3517i) q^{89} +(-4.44344 - 2.56542i) q^{91} +(-46.3037 + 4.85390i) q^{92} +(-36.5509 - 112.544i) q^{94} +(-101.464 + 120.920i) q^{95} +(144.082 + 52.4414i) q^{97} +(11.6423 + 21.9033i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

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