LMFDB - Embedded newform 324.3.j.a.199.4

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			199.4
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90220 - 0.617774i) q^{2} +(3.23671 + 2.35025i) q^{4} +(5.80978 - 2.11459i) q^{5} +(7.71693 - 1.36070i) q^{7} +(-4.70494 - 6.47020i) q^{8} +O(q^{10})$	\(q+(-1.90220 - 0.617774i) q^{2} +(3.23671 + 2.35025i) q^{4} +(5.80978 - 2.11459i) q^{5} +(7.71693 - 1.36070i) q^{7} +(-4.70494 - 6.47020i) q^{8} +(-12.3577 + 0.433234i) q^{10} +(5.58301 - 15.3392i) q^{11} +(0.501591 + 0.420885i) q^{13} +(-15.5197 - 2.17899i) q^{14} +(4.95261 + 15.2142i) q^{16} +(-16.2536 + 28.1521i) q^{17} +(22.1106 - 12.7656i) q^{19} +(23.7744 + 6.81015i) q^{20} +(-20.0961 + 25.7292i) q^{22} +(-11.4625 - 2.02115i) q^{23} +(10.1309 - 8.50086i) q^{25} +(-0.694114 - 1.11048i) q^{26} +(28.1755 + 13.7326i) q^{28} +(-0.277178 + 0.232580i) q^{29} +(-17.8485 - 3.14718i) q^{31} +(-0.0219106 - 32.0000i) q^{32} +(48.3092 - 43.5097i) q^{34} +(41.9564 - 24.2235i) q^{35} +(16.6488 - 28.8366i) q^{37} +(-49.9451 + 10.6233i) q^{38} +(-41.0165 - 27.6414i) q^{40} +(-13.6788 - 11.4779i) q^{41} +(-1.58745 + 4.36148i) q^{43} +(54.1216 - 36.5271i) q^{44} +(20.5554 + 10.9259i) q^{46} +(58.2666 - 10.2740i) q^{47} +(11.6546 - 4.24194i) q^{49} +(-24.5226 + 9.91170i) q^{50} +(0.634319 + 2.54115i) q^{52} +65.6694 q^{53} -100.923i q^{55} +(-45.1117 - 43.5281i) q^{56} +(0.670929 - 0.271180i) q^{58} +(7.73105 + 21.2409i) q^{59} +(-11.4644 - 65.0179i) q^{61} +(32.0072 + 17.0129i) q^{62} +(-19.7271 + 60.8838i) q^{64} +(3.80413 + 1.38459i) q^{65} +(-20.4878 + 24.4165i) q^{67} +(-118.773 + 52.9200i) q^{68} +(-94.7739 + 20.1584i) q^{70} +(-56.4127 - 32.5699i) q^{71} +(27.4849 + 47.6052i) q^{73} +(-49.4838 + 44.5677i) q^{74} +(101.568 + 10.6471i) q^{76} +(22.2116 - 125.968i) q^{77} +(-18.8412 - 22.4541i) q^{79} +(60.9453 + 77.9184i) q^{80} +(18.9290 + 30.2835i) q^{82} +(11.6992 + 13.9426i) q^{83} +(-34.8999 + 197.927i) q^{85} +(5.71404 - 7.31571i) q^{86} +(-125.515 + 36.0468i) q^{88} +(37.7308 + 65.3517i) q^{89} +(4.44344 + 2.56542i) q^{91} +(-32.3507 - 33.4818i) q^{92} +(-117.182 - 16.4524i) q^{94} +(101.464 - 120.920i) q^{95} +(144.082 + 52.4414i) q^{97} +(-24.7900 + 0.869083i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.90220	−	0.617774i	−0.951099	−	0.308887i
$2$	−1.90220	−	0.617774i	−0.951099	−	0.308887i
$3$		0			0
$3$		0			0
$4$	3.23671	+	2.35025i	0.809178	+	0.587564i
$5$	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	0.407310	−	0.913290i	$-0.366467\pi$
$7$	7.71693	−	1.36070i	1.10242	−	0.194386i	0.695110	+	0.718904i	$0.255356\pi$
$8$	−4.70494	−	6.47020i	−0.588118	−	0.808775i
$9$		0			0
$10$	−12.3577	+	0.433234i	−1.23577	+	0.0433234i
$11$	5.58301	−	15.3392i	0.507547	−	1.39447i	−0.376214	−	0.926533i	$-0.622774\pi$
$11$	5.58301	−	15.3392i	0.507547	−	1.39447i	0.883760	−	0.467940i	$-0.155004\pi$
$12$		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	$0.714205\pi$
$14$	−15.5197	−	2.17899i	−1.10855	−	0.155642i
$15$		0			0
$16$	4.95261	+	15.2142i	0.309538	+	0.950887i
$17$	−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	0.211526	−	0.977372i	$-0.432157\pi$
$19$	22.1106	−	12.7656i	1.16372	−	0.671873i	0.952192	+	0.305499i	$0.0988234\pi$
$20$	23.7744	+	6.81015i	1.18872	+	0.340508i
$21$		0			0
$22$	−20.0961	+	25.7292i	−0.913461	+	1.16951i
$23$	−11.4625	−	2.02115i	−0.498371	−	0.0878763i	−0.0811881	−	0.996699i	$-0.525871\pi$
$23$	−11.4625	−	2.02115i	−0.498371	−	0.0878763i	−0.417183	+	0.908823i	$0.636983\pi$
$24$		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	−0.121816	−	0.992553i	$-0.538872\pi$
$31$	−17.8485	−	3.14718i	−0.575759	−	0.101522i	−0.453943	+	0.891031i	$0.649983\pi$
$32$	−0.0219106	−	32.0000i	−0.000684705	−	1.00000i
$33$		0			0
$34$	48.3092	−	43.5097i	1.42086	−	1.27970i
$35$	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	$0.0181020\pi$
$38$	−49.9451	+	10.6233i	−1.31434	+	0.279560i
$39$		0			0
$40$	−41.0165	−	27.6414i	−1.02541	−	0.691036i
$41$	−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	−0.956782	−	0.290807i	$-0.906076\pi$
$43$	−1.58745	+	4.36148i	−0.0369174	+	0.101430i	0.919864	+	0.392237i	$0.128299\pi$
$44$	54.1216	−	36.5271i	1.23004	−	0.830161i
$45$		0			0
$46$	20.5554	+	10.9259i	0.446856	+	0.237519i
$47$	58.2666	−	10.2740i	1.23972	−	0.218595i	0.484922	−	0.874558i	$-0.338848\pi$
$47$	58.2666	−	10.2740i	1.23972	−	0.218595i	0.754794	+	0.655962i	$0.227737\pi$
$48$		0			0
$49$	11.6546	−	4.24194i	0.237850	−	0.0865702i
$50$	−24.5226	+	9.91170i	−0.490453	+	0.198234i
$51$		0			0
$52$	0.634319	+	2.54115i	0.0121984	+	0.0488683i
$53$	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
$56$	−45.1117	−	43.5281i	−0.805567	−	0.777288i
$57$		0			0
$58$	0.670929	−	0.271180i	0.0115677	−	0.00467552i
$59$	7.73105	+	21.2409i	0.131035	+	0.360015i	0.987808	−	0.155679i	$-0.0497565\pi$
$59$	7.73105	+	21.2409i	0.131035	+	0.360015i	−0.856773	+	0.515694i	$0.827534\pi$
$60$		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	$-0.237568\pi$
$62$	32.0072	+	17.0129i	0.516245	+	0.274402i
$63$		0			0
$64$	−19.7271	+	60.8838i	−0.308235	+	0.951310i
$65$	3.80413	+	1.38459i	0.0585251	+	0.0213014i
$66$		0			0
$67$	−20.4878	+	24.4165i	−0.305789	+	0.364425i	−0.896953	−	0.442127i	$-0.854224\pi$
$67$	−20.4878	+	24.4165i	−0.305789	+	0.364425i	0.591164	+	0.806551i	$0.298669\pi$
$68$	−118.773	+	52.9200i	−1.74666	+	0.778236i
$69$		0			0
$70$	−94.7739	+	20.1584i	−1.35391	+	0.287977i
$71$	−56.4127	−	32.5699i	−0.794545	−	0.458731i	0.0470150	−	0.998894i	$-0.485029\pi$
$71$	−56.4127	−	32.5699i	−0.794545	−	0.458731i	−0.841560	+	0.540163i	$0.818362\pi$
$72$		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	$0.710459\pi$
$74$	−49.4838	+	44.5677i	−0.668701	+	0.602267i
$75$		0			0
$76$	101.568	+	10.6471i	1.33642	+	0.140094i
$77$	22.2116	−	125.968i	0.288463	−	1.63595i
$78$		0			0
$79$	−18.8412	−	22.4541i	−0.238496	−	0.284229i	0.633498	−	0.773744i	$-0.281618\pi$
$79$	−18.8412	−	22.4541i	−0.238496	−	0.284229i	−0.871995	+	0.489515i	$0.837174\pi$
$80$	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	0.831903	−	0.554921i	$-0.187251\pi$
$83$	11.6992	+	13.9426i	0.140954	+	0.167983i	−0.690949	+	0.722904i	$0.742807\pi$
$84$		0			0
$85$	−34.8999	+	197.927i	−0.410586	+	2.32855i
$86$	5.71404	−	7.31571i	0.0664424	−	0.0850663i
$87$		0			0
$88$	−125.515	+	36.0468i	−1.42631	+	0.409623i
$89$	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
$92$	−32.3507	−	33.4818i	−0.351638	−	0.363932i
$93$		0			0
$94$	−117.182	−	16.4524i	−1.24661	−	0.175026i
$95$	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	$0.321009\pi$
$98$	−24.7900	+	0.869083i	−0.252959	+	0.00886820i
$99$		0			0
$100$	52.7701	−	3.70457i	0.527701	−	0.0370457i
$101$	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	0.906056	−	0.423158i	$-0.139079\pi$
$103$	−6.18247	−	16.9862i	−0.0600240	−	0.164915i	−0.966080	+	0.258244i	$0.916856\pi$
$104$	0.363255	−	5.22563i	0.00349283	−	0.0502465i
$105$		0			0
$106$	−124.916	−	40.5688i	−1.17845	−	0.382725i
$107$			26.1902i			0.244769i	0.992483	+	0.122384i	$0.0390540\pi$
$107$			26.1902i			0.244769i	−0.992483	+	0.122384i	$0.960946\pi$
$108$		0			0
$109$	−68.9277			−0.632364			−0.316182	−	0.948699i	$-0.602401\pi$
$109$	−68.9277			−0.632364			−0.316182	+	0.948699i	$0.602401\pi$
$110$	−62.3476	+	191.976i	−0.566797	+	1.74523i
$111$		0			0
$112$	58.9210	+	110.668i	0.526080	+	0.988106i
$113$	−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
$116$	−1.44377	+	0.101355i	−0.0124463	+	0.000873754i
$117$		0			0
$118$	−1.58393	−	45.1804i	−0.0134231	−	0.382885i
$119$	−87.1214	+	239.364i	−0.732112	+	2.01146i
$120$		0			0
$121$	−111.430	−	93.5006i	−0.920906	−	0.772732i
$122$	−18.3588	+	130.759i	−0.150482	+	1.07180i
$123$		0			0
$124$	−50.3739	−	52.1351i	−0.406241	−	0.420445i
$125$	−36.4003	+	63.0472i	−0.291202	+	0.504377i
$126$		0			0
$127$	−34.2929	+	19.7990i	−0.270022	+	0.155898i	−0.628898	−	0.777488i	$-0.716494\pi$
$127$	−34.2929	+	19.7990i	−0.270022	+	0.155898i	0.358875	+	0.933385i	$0.383160\pi$
$128$	75.1372	−	103.626i	0.587009	−	0.809580i
$129$		0			0
$130$	−6.38084	−	4.98385i	−0.0490834	−	0.0383373i
$131$	−90.0826	−	15.8840i	−0.687654	−	0.121252i	−0.181106	−	0.983464i	$-0.557968\pi$
$131$	−90.0826	−	15.8840i	−0.687654	−	0.121252i	−0.506548	+	0.862212i	$0.669079\pi$
$132$		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	−0.0596412	−	0.998220i	$-0.518996\pi$
$139$	−63.5365	−	11.2032i	−0.457097	−	0.0805985i	−0.397456	+	0.917621i	$0.630107\pi$
$140$	192.732	+	20.2036i	1.37666	+	0.144311i
$141$		0			0
$142$	87.1873	+	96.8047i	0.613995	+	0.681723i
$143$	9.25642	−	5.34420i	0.0647302	−	0.0373720i
$144$		0			0
$145$	−1.11853	+	1.93736i	−0.00771402	+	0.0133611i
$146$	−22.8724	−	107.534i	−0.156660	−	0.736534i
$147$		0			0
$148$	121.661	−	54.2068i	0.822033	−	0.366262i
$149$	−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	−0.915499	−	0.402320i	$-0.868204\pi$
$151$	6.70741	−	18.4285i	0.0444200	−	0.122043i	0.959919	+	0.280277i	$0.0904263\pi$
$152$	−186.625	−	82.9990i	−1.22780	−	0.546046i
$153$		0			0
$154$	−120.071	+	225.895i	−0.779681	+	1.46685i
$155$	−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	$0.524112\pi$
$158$	21.9682	+	54.3517i	0.139039	+	0.343998i
$159$		0			0
$160$	−67.7940	−	185.867i	−0.423713	−	1.16167i
$161$	−91.2058			−0.566496
$162$		0			0
$163$			82.7053i			0.507394i	0.967284	+	0.253697i	$0.0816467\pi$
$163$			82.7053i			0.507394i	−0.967284	+	0.253697i	$0.918353\pi$
$164$	−17.2984	−	69.2991i	−0.105478	−	0.422556i
$165$		0			0
$166$	−13.6409	−	33.7490i	−0.0821738	−	0.203307i
$167$	39.4378	+	108.354i	0.236154	+	0.648829i	0.999994	+	0.00342276i	$0.00108950\pi$
$167$	39.4378	+	108.354i	0.236154	+	0.648829i	−0.763840	+	0.645406i	$0.776688\pi$
$168$		0			0
$169$	−29.2721	−	166.010i	−0.173208	−	0.982309i
$170$	188.660	−	354.936i	1.10977	−	2.08786i
$171$		0			0
$172$	−15.3887	+	10.3859i	−0.0894691	+	0.0603833i
$173$	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
$176$	261.024	+	8.97201i	1.48309	+	0.0509773i
$177$		0			0
$178$	−31.3989	−	147.621i	−0.176399	−	0.829331i
$179$	−282.005	−	162.816i	−1.57545	−	0.909585i	−0.995483	−	0.0949444i	$-0.969733\pi$
$179$	−282.005	−	162.816i	−1.57545	−	0.909585i	−0.579966	−	0.814641i	$-0.696934\pi$
$180$		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	$0.989548\pi$
$182$	−6.86746	−	7.62498i	−0.0377333	−	0.0418955i
$183$		0			0
$184$	40.8533	+	83.6743i	0.222029	+	0.454752i
$185$	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	0.988339	−	0.152267i	$-0.0486573\pi$
$191$	127.352	+	151.772i	0.666762	+	0.794616i	−0.321577	+	0.946883i	$0.604213\pi$
$192$		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	$0.944504\pi$
$194$	−241.675	−	188.764i	−1.24575	−	0.973009i
$195$		0			0
$196$	47.6923	+	13.6614i	0.243328	+	0.0697011i
$197$	−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	0.821530	−	0.570165i	$-0.193121\pi$
$199$	146.965	+	84.8503i	0.738518	+	0.426383i	−0.0830125	+	0.996549i	$0.526454\pi$
$200$	−102.668	−	25.5531i	−0.513339	−	0.127766i
$201$		0			0
$202$	46.3968	−	330.458i	0.229687	−	1.63593i
$203$	−1.82249	+	2.17196i	−0.00897780	+	0.0106993i
$204$		0			0
$205$	−103.742	−	37.7588i	−0.506056	−	0.184189i
$206$	1.26666	+	36.1305i	0.00614882	+	0.175391i
$207$		0			0
$208$	−3.91924	+	9.71578i	−0.0188425	+	0.0467105i
$209$	−72.3699	−	410.430i	−0.346267	−	1.96378i
$210$		0			0
$211$	12.7388	+	34.9995i	0.0603733	+	0.165874i	0.966212	−	0.257748i	$-0.0829805\pi$
$211$	12.7388	+	34.9995i	0.0603733	+	0.165874i	−0.905839	+	0.423623i	$0.860758\pi$
$212$	212.553	+	154.340i	1.00261	+	0.728018i
$213$		0			0
$214$	16.1796	−	49.8190i	0.0756058	−	0.232799i
$215$			28.6960i			0.133470i
$216$		0			0
$217$	−142.018			−0.654463
$218$	131.114	+	42.5817i	0.601440	+	0.195329i
$219$		0			0
$220$	237.195	−	326.659i	1.07816	−	1.48481i
$221$	−20.0014	+	7.27993i	−0.0905042	+	0.0329408i
$222$		0			0
$223$	−401.905	+	70.8667i	−1.80227	+	0.317788i	−0.971178	−	0.238354i	$-0.923392\pi$
$223$	−401.905	+	70.8667i	−1.80227	+	0.317788i	−0.831087	+	0.556142i	$0.812281\pi$
$224$	−43.7116	−	246.912i	−0.195141	−	1.10229i
$225$		0			0
$226$	242.211	−	8.49141i	1.07173	−	0.0375726i
$227$	114.765	−	315.313i	0.505571	−	1.38905i	−0.380191	−	0.924908i	$-0.624142\pi$
$227$	114.765	−	315.313i	0.505571	−	1.38905i	0.885763	−	0.464138i	$-0.153636\pi$
$228$		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	$0.531128\pi$
$230$	142.526	+	20.0108i	0.619678	+	0.0870035i
$231$		0			0
$232$	2.80895	+	0.699124i	0.0121075	+	0.00301346i
$233$	−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
$236$	−24.8983	+	86.9205i	−0.105501	+	0.368307i
$237$		0			0
$238$	313.595	−	401.496i	1.31763	−	1.68696i
$239$	277.323	+	48.8996i	1.16035	+	0.204601i	0.720490	−	0.693466i	$-0.243917\pi$
$239$	277.323	+	48.8996i	1.16035	+	0.204601i	0.439860	+	0.898067i	$0.355028\pi$
$240$		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
$248$	63.6134	+	130.291i	0.256506	+	0.525367i
$249$		0			0
$250$	108.189	−	97.4410i	0.432758	−	0.389764i
$251$	68.9864	−	39.8293i	0.274846	−	0.158683i	−0.356242	−	0.934394i	$-0.615942\pi$
$251$	68.9864	−	39.8293i	0.274846	−	0.158683i	0.631088	+	0.775711i	$0.282609\pi$
$252$		0			0
$253$	−94.9984	+	164.542i	−0.375488	+	0.650364i
$254$	77.4631	−	16.4764i	0.304973	−	0.0648676i
$255$		0			0
$256$	−206.943	+	150.700i	−0.808373	+	0.588671i
$257$	−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
$260$	9.05873	+	13.4222i	0.0348413	+	0.0516238i
$261$		0			0
$262$	161.542	+	85.8652i	0.616574	+	0.327730i
$263$	−286.514	+	50.5202i	−1.08941	+	0.192092i	−0.689372	−	0.724407i	$-0.742114\pi$
$263$	−286.514	+	50.5202i	−1.08941	+	0.192092i	−0.400036	+	0.916499i	$0.631002\pi$
$264$		0			0
$265$	381.525	−	138.864i	1.43972	−	0.524014i
$266$	−370.968	+	149.940i	−1.39461	+	0.563683i
$267$		0			0
$268$	−123.698	+	30.8774i	−0.461560	+	0.115214i
$269$	−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	$0.0828833\pi$
$271$			139.540i			0.514906i	−0.966291	+	0.257453i	$0.917117\pi$
$272$	−508.809	−	107.859i	−1.87062	−	0.396542i
$273$		0			0
$274$	−135.613	+	54.8128i	−0.494937	+	0.200047i
$275$	−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	$0.695016\pi$
$278$	113.938	+	60.5618i	0.409849	+	0.217848i
$279$		0			0
$280$	−354.133	−	157.496i	−1.26476	−	0.562486i
$281$	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	$0.524516\pi$
$283$	−295.868	+	352.602i	−1.04547	+	1.24594i	−0.968527	+	0.248908i	$0.919928\pi$
$284$	−106.044	−	238.004i	−0.373395	−	0.838041i
$285$		0			0
$286$	−20.9091	+	4.44735i	−0.0731086	+	0.0155502i
$287$	−121.176	−	69.9611i	−0.422217	−	0.243767i
$288$		0			0
$289$	−383.859	−	664.864i	−1.32823	−	2.30057i
$290$	3.32452	−	2.99423i	0.0114639	−	0.0103249i
$291$		0			0
$292$	−22.9237	+	218.681i	−0.0785059	+	0.748907i
$293$	−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
$302$	−24.1434	+	30.9109i	−0.0799452	+	0.102354i
$303$		0			0
$304$	303.723	+	273.173i	0.999090	+	0.898594i
$305$	−204.092	−	353.497i	−0.669153	−	1.15901i
$306$		0			0
$307$	−378.645	−	218.611i	−1.23337	−	0.712087i	−0.265640	−	0.964072i	$-0.585583\pi$
$307$	−378.645	−	218.611i	−1.23337	−	0.712087i	−0.967731	+	0.251985i	$0.918916\pi$
$308$	367.951	−	355.521i	1.19464	−	1.15429i
$309$		0			0
$310$	221.930	+	31.1592i	0.715904	+	0.100514i
$311$	−96.7434	+	115.294i	−0.311072	+	0.370721i	−0.898816	−	0.438326i	$-0.855572\pi$
$311$	−96.7434	+	115.294i	−0.311072	+	0.370721i	0.587744	+	0.809047i	$0.300016\pi$
$312$		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	$0.163332\pi$
$314$	258.673	−	9.06851i	0.823798	−	0.0288806i
$315$		0			0
$316$	−8.21076	−	116.959i	−0.0259834	−	0.370124i
$317$	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
$320$	14.1343	+	395.436i	0.0441695	+	1.23574i
$321$		0			0
$322$	173.491	+	56.3445i	0.538793	+	0.174983i
$323$			829.947i			2.56950i
$324$		0			0
$325$	8.65947			0.0266445
$326$	51.0931	−	157.322i	0.156727	−	0.482582i
$327$		0			0
$328$	−9.90624	+	142.507i	−0.0302019	+	0.434473i
$329$	435.660	−	158.567i	1.32419	−	0.481967i
$330$		0			0
$331$	476.068	−	83.9436i	1.43827	−	0.253606i	0.600499	−	0.799625i	$-0.294969\pi$
$331$	476.068	−	83.9436i	1.43827	−	0.253606i	0.837773	+	0.546019i	$0.183858\pi$
$332$	5.09837	+	72.6242i	0.0153565	+	0.218748i
$333$		0			0
$334$	−8.07997	−	230.475i	−0.0241915	−	0.690045i
$335$	−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	$0.730639\pi$
$338$	−46.8755	+	333.868i	−0.138685	+	0.987775i
$339$		0			0
$340$	−578.139	+	558.609i	−1.70041	+	1.64297i
$341$	−147.924	+	256.212i	−0.433794	+	0.751354i
$342$		0			0
$343$	−248.356	+	143.388i	−0.724069	+	0.418042i
$344$	35.6885	−	10.2494i	0.103746	−	0.0297947i
$345$		0			0
$346$	−330.674	−	258.278i	−0.955705	−	0.746468i
$347$	120.577	+	21.2610i	0.347484	+	0.0612709i	0.344667	−	0.938725i	$-0.387992\pi$
$347$	120.577	+	21.2610i	0.347484	+	0.0612709i	0.00281781	+	0.999996i	$0.499103\pi$
$348$		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
$356$	−31.4693	+	300.202i	−0.0883970	+	0.843263i
$357$		0			0
$358$	435.846	+	483.923i	1.21745	+	1.35174i
$359$	153.103	−	88.3942i	0.426471	−	0.246223i	−0.271371	−	0.962475i	$-0.587477\pi$
$359$	153.103	−	88.3942i	0.426471	−	0.246223i	0.697842	+	0.716252i	$0.254144\pi$
$360$		0			0
$361$	145.420	−	251.875i	0.402827	−	0.697716i
$362$	70.9892	+	333.753i	0.196103	+	0.921971i
$363$		0			0
$364$	8.35275	+	18.7468i	0.0229471	+	0.0515021i
$365$	260.346	+	218.456i	0.713277	+	0.598511i
$366$		0			0
$367$	61.2798	−	168.365i	0.166975	−	0.458760i	−0.827779	−	0.561054i	$-0.810396\pi$
$367$	61.2798	−	168.365i	0.166975	−	0.458760i	0.994754	+	0.102294i	$0.0326182\pi$
$368$	−26.0192	−	184.403i	−0.0707043	−	0.501096i
$369$		0			0
$370$	−193.248	+	363.566i	−0.522292	+	0.982612i
$371$	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	$0.578022\pi$
$374$	−397.694	−	983.939i	−1.06335	−	2.63085i
$375$		0			0
$376$	−340.616	−	328.658i	−0.905893	−	0.874092i
$377$	−0.236919			−0.000628434
$378$		0			0
$379$		−	185.425i		−	0.489248i	−0.969618	−	0.244624i	$-0.921335\pi$
$379$		−	185.425i		−	0.489248i	0.969618	−	0.244624i	$-0.0786646\pi$
$380$	612.603	−	152.917i	1.61211	−	0.402414i
$381$		0			0
$382$	−148.487	−	367.374i	−0.388710	−	0.961713i
$383$	−140.116	−	384.965i	−0.365838	−	1.00513i	−0.976928	−	0.213570i	$-0.931491\pi$
$383$	−140.116	−	384.965i	−0.365838	−	1.00513i	0.611090	−	0.791561i	$-0.290731\pi$
$384$		0			0
$385$	−137.326	−	778.817i	−0.356692	−	2.02290i
$386$	123.864	−	233.031i	0.320890	−	0.603706i
$387$		0			0
$388$	343.100	+	508.366i	0.884278	+	1.31022i
$389$	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
$392$	−82.2805	−	55.4498i	−0.209899	−	0.141453i
$393$		0			0
$394$	14.3875	+	67.6425i	0.0365166	+	0.171682i
$395$	−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	$0.548362\pi$
$398$	−227.138	−	252.193i	−0.570699	−	0.633651i
$399$		0			0
$400$	179.508	+	112.033i	0.448771	+	0.280081i
$401$	−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	$-0.215213\pi$
$410$	174.011	+	135.914i	0.424416	+	0.331497i
$411$		0			0
$412$	19.9110	−	69.5098i	0.0483277	−	0.168713i
$413$	88.5625	+	153.395i	0.214437	+	0.371416i
$414$		0			0
$415$	97.4525	+	56.2643i	0.234825	+	0.135577i
$416$	13.4573	−	16.0601i	0.0323493	−	0.0386061i
$417$		0			0
$418$	−115.891	+	825.427i	−0.277251	+	1.97471i
$419$	−257.110	+	306.412i	−0.613628	+	0.731294i	−0.979961	−	0.199190i	$-0.936169\pi$
$419$	−257.110	+	306.412i	−0.613628	+	0.731294i	0.366333	+	0.930484i	$0.380613\pi$
$420$		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	$0.520725\pi$
$422$	−2.60990	−	74.4456i	−0.00618461	−	0.176411i
$423$		0			0
$424$	−308.971	−	424.894i	−0.728704	−	1.00211i
$425$	74.6527	+	423.376i	0.175653	+	0.996180i
$426$		0			0
$427$	−176.940	−	486.140i	−0.414380	−	1.13850i
$428$	−61.5537	+	84.7703i	−0.143817	+	0.198061i
$429$		0			0
$430$	17.7276	−	54.5855i	0.0412270	−	0.126943i
$431$		−	309.442i		−	0.717964i	−0.933344	−	0.358982i	$-0.883124\pi$
$431$		−	309.442i		−	0.717964i	0.933344	−	0.358982i	$-0.116876\pi$
$432$		0			0
$433$	116.466			0.268974			0.134487	−	0.990915i	$-0.457061\pi$
$433$	116.466			0.268974			0.134487	+	0.990915i	$0.457061\pi$
$434$	270.147	+	87.7352i	0.622459	+	0.202155i
$435$		0			0
$436$	−223.099	−	161.998i	−0.511695	−	0.371554i
$437$	−279.245	+	101.637i	−0.639005	+	0.232579i
$438$		0			0
$439$	−613.148	+	108.115i	−1.39669	+	0.246275i	−0.820784	−	0.571239i	$-0.806463\pi$
$439$	−613.148	+	108.115i	−1.39669	+	0.246275i	−0.575909	+	0.817514i	$0.695352\pi$
$440$	−652.993	+	474.837i	−1.48408	+	1.07918i
$441$		0			0
$442$	42.5440	−	1.49150i	0.0962535	−	0.00337444i
$443$	37.4199	−	102.810i	0.0844694	−	0.232078i	−0.890266	−	0.455441i	$-0.849481\pi$
$443$	37.4199	−	102.810i	0.0844694	−	0.232078i	0.974735	+	0.223364i	$0.0717037\pi$
$444$		0			0
$445$	357.400	+	299.894i	0.803145	+	0.673919i
$446$	808.283	+	113.484i	1.81229	+	0.254448i
$447$		0			0
$448$	−69.3876	+	496.679i	−0.154883	+	1.10866i
$449$	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
$452$	−465.979	−	133.479i	−1.03093	−	0.295308i
$453$		0			0
$454$	−413.097	+	528.890i	−0.909906	+	1.16496i
$455$	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	0.764442	−	0.644693i	$-0.223015\pi$
$463$	584.437	+	103.052i	1.26228	+	0.222575i	0.497842	+	0.867268i	$0.334126\pi$
$464$	−4.91127	−	3.06516i	−0.0105846	−	0.00660596i
$465$		0			0
$466$	430.108	−	387.377i	0.922978	−	0.831282i
$467$	578.881	−	334.217i	1.23957	−	0.715668i	0.270567	−	0.962701i	$-0.412789\pi$
$467$	578.881	−	334.217i	1.23957	−	0.715668i	0.969007	+	0.247033i	$0.0794556\pi$
$468$		0			0
$469$	−124.880	+	216.298i	−0.266268	+	0.461190i
$470$	−715.589	+	152.206i	−1.52253	+	0.323842i
$471$		0			0
$472$	101.059	−	149.958i	0.214107	−	0.317709i
$473$	58.0388	+	48.7003i	0.122704	+	0.102961i
$474$		0			0
$475$	115.483	−	317.287i	0.243122	−	0.667972i
$476$	−844.553	+	569.995i	−1.77427	+	1.19747i
$477$		0			0
$478$	−497.315	−	264.340i	−1.04041	−	0.553012i
$479$	190.223	−	33.5414i	0.397125	−	0.0700238i	0.0284804	−	0.999594i	$-0.490933\pi$
$479$	190.223	−	33.5414i	0.397125	−	0.0700238i	0.368644	+	0.929571i	$0.379822\pi$
$480$		0			0
$481$	20.4878	−	7.45695i	0.0425942	−	0.0155030i
$482$	443.715	−	179.343i	0.920570	−	0.372081i
$483$		0			0
$484$	−140.916	−	564.523i	−0.291148	−	1.16637i
$485$	947.974			1.95458
$486$		0			0
$487$		−	614.229i		−	1.26125i	−0.776088	−	0.630625i	$-0.782799\pi$
$487$		−	614.229i		−	1.26125i	0.776088	−	0.630625i	$-0.217201\pi$
$488$	−366.740	+	380.083i	−0.751516	+	0.778858i
$489$		0			0
$490$	−142.186	+	57.4697i	−0.290176	+	0.117285i
$491$	196.037	+	538.608i	0.399261	+	1.09696i	0.962645	+	0.270766i	$0.0872769\pi$
$491$	196.037	+	538.608i	0.399261	+	1.09696i	−0.563384	+	0.826195i	$0.690501\pi$
$492$		0			0
$493$	−2.04247	−	11.5834i	−0.00414293	−	0.0234957i
$494$	−29.5232	−	15.6926i	−0.0597635	−	0.0317663i
$495$		0			0
$496$	−40.5150	−	287.138i	−0.0816835	−	0.578907i
$497$	−479.651	−	174.579i	−0.965093	−	0.351265i
$498$		0			0
$499$	362.757	−	432.317i	0.726968	−	0.866366i	−0.268320	−	0.963330i	$-0.586469\pi$
$499$	362.757	−	432.317i	0.726968	−	0.866366i	0.995288	+	0.0969635i	$0.0309130\pi$
$500$	−265.994	+	118.516i	−0.531988	+	0.237031i
$501$		0			0
$502$	−155.831	+	33.1453i	−0.310421	+	0.0660264i
$503$	527.529	+	304.569i	1.04877	+	0.605505i	0.922303	−	0.386467i	$-0.126305\pi$
$503$	527.529	+	304.569i	1.04877	+	0.605505i	0.126462	+	0.991971i	$0.459638\pi$
$504$		0			0
$505$	515.786	+	893.367i	1.02136	+	1.76904i
$506$	282.355	−	254.304i	0.558014	−	0.502577i
$507$		0			0
$508$	−157.529	−	16.5133i	−0.310096	−	0.0325065i
$509$	−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
$518$	−321.220	+	411.259i	−0.620116	+	0.793936i
$519$		0			0
$520$	−8.93962	−	31.1279i	−0.0171916	−	0.0598614i
$521$	−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	0.638602	−	0.769537i	$-0.279513\pi$
$523$	152.436	+	88.0092i	0.291465	+	0.168278i	−0.347137	+	0.937814i	$0.612846\pi$
$524$	−254.240	−	263.129i	−0.485191	−	0.502155i
$525$		0			0
$526$	576.217	+	80.9016i	1.09547	+	0.153805i
$527$	378.703	−	451.320i	0.718601	−	0.856395i
$528$		0			0
$529$	−369.793	−	134.594i	−0.699041	−	0.254430i
$530$	−811.521	+	28.4502i	−1.53117	+	0.0536797i
$531$		0			0
$532$	798.282	−	56.0411i	1.50053	−	0.105340i
$533$	−2.03030	−	11.5144i	−0.00380918	−	0.0216030i
$534$		0			0
$535$	55.3815	+	152.160i	0.103517	+	0.284410i
$536$	254.373	+	17.6825i	0.474577	+	0.0329898i
$537$		0			0
$538$	139.015	+	45.1478i	0.258393	+	0.0839179i
$539$		−	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	$0.417656\pi$
$542$	86.2039	−	265.432i	0.159048	−	0.489727i
$543$		0			0
$544$	901.222	+	519.498i	1.65666	+	0.954960i
$545$	−400.454	+	145.753i	−0.734779	+	0.267438i
$546$		0			0
$547$	−906.841	+	159.901i	−1.65785	+	0.292323i	−0.922681	−	0.385565i	$-0.874006\pi$
$547$	−906.841	+	159.901i	−1.65785	+	0.292323i	−0.735165	+	0.677888i	$0.762895\pi$
$548$	291.824	−	20.4867i	0.532526	−	0.0373844i
$549$		0			0
$550$	15.1273	+	431.495i	0.0275042	+	0.784536i
$551$	−3.15957	+	8.68084i	−0.00573424	+	0.0157547i
$552$		0			0
$553$	−175.950	−	147.639i	−0.318173	−	0.266979i
$554$	108.737	−	774.470i	0.196275	−	1.39796i
$555$		0			0
$556$	−179.319	−	185.588i	−0.322516	−	0.333792i
$557$	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
$560$	576.334	+	518.363i	1.02917	+	0.925647i
$561$		0			0
$562$	−7.55947	−	5.90444i	−0.0134510	−	0.0105061i
$563$	215.390	+	37.9790i	0.382575	+	0.0674582i	0.361628	−	0.932322i	$-0.382221\pi$
$563$	215.390	+	37.9790i	0.382575	+	0.0674582i	0.0209464	+	0.999781i	$0.493332\pi$
$564$		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	0.108519	−	0.994094i	$-0.465389\pi$
$571$	−73.9483	−	13.0391i	−0.129507	−	0.0228355i	−0.238026	+	0.971259i	$0.576500\pi$
$572$	42.5206	+	4.45732i	0.0743367	+	0.00779252i
$573$		0			0
$574$	187.281	+	207.939i	0.326273	+	0.362264i
$575$	−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	$0.113978\pi$
$578$	319.441	+	1501.84i	0.552666	+	2.59834i
$579$		0			0
$580$	−8.17365	+	3.64182i	−0.0140925	+	0.00627901i
$581$	109.254	+	91.6747i	0.188044	+	0.157788i
$582$		0			0
$583$	366.633	−	1007.32i	0.628873	−	1.72781i
$584$	178.701	−	401.812i	0.305994	−	0.688035i
$585$		0			0
$586$	400.271	−	753.048i	0.683055	−	1.28507i
$587$	−232.812	+	41.0511i	−0.396614	+	0.0699337i	−0.368398	−	0.929668i	$-0.620094\pi$
$587$	−232.812	+	41.0511i	−0.396614	+	0.0699337i	−0.0282156	+	0.999602i	$0.508983\pi$
$588$		0			0
$589$	−434.818	+	158.261i	−0.738232	+	0.268694i
$590$	−104.740	−	259.139i	−0.177526	−	0.439218i
$591$		0			0
$592$	521.181	+	110.482i	0.880373	+	0.186625i
$593$	−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
$596$	−107.336	−	429.998i	−0.180093	−	0.721473i
$597$		0			0
$598$	5.71186	+	14.1318i	0.00955160	+	0.0236317i
$599$	−286.623	−	787.490i	−0.478502	−	1.31467i	−0.910764	−	0.412927i	$-0.864507\pi$
$599$	−286.623	−	787.490i	−0.478502	−	1.31467i	0.432262	−	0.901748i	$-0.357716\pi$
$600$		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	$0.930159\pi$
$602$	34.1404	−	64.2299i	0.0567116	−	0.106694i
$603$		0			0
$604$	65.0216	−	43.8835i	0.107652	−	0.0726548i
$605$	−845.097	−	307.590i	−1.39685	−	0.508413i
$606$		0			0
$607$	−262.383	+	312.696i	−0.432262	+	0.515150i	−0.937573	−	0.347787i	$-0.886933\pi$
$607$	−262.383	+	312.696i	−0.432262	+	0.515150i	0.505312	+	0.862937i	$0.331378\pi$
$608$	−408.983	−	707.261i	−0.672670	−	1.16326i
$609$		0			0
$610$	169.842	+	798.504i	0.278429	+	1.30902i
$611$	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	$0.827209\pi$
$614$	585.205	+	649.757i	0.953103	+	1.05824i
$615$		0			0
$616$	−919.546	+	448.960i	−1.49277	+	0.728831i
$617$	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	0.612497	−	0.790473i	$-0.290165\pi$
$619$	−168.570	−	200.894i	−0.272326	−	0.324545i	−0.884823	+	0.465928i	$0.845721\pi$
$620$	−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
$626$	−973.446	−	760.325i	−1.55503	−	1.21458i
$627$		0			0
$628$	−497.649	−	142.551i	−0.792434	−	0.226992i
$629$	541.207	+	937.398i	0.860424	+	1.49030i
$630$		0			0
$631$	370.756	+	214.056i	0.587569	+	0.339233i	0.764136	−	0.645055i	$-0.223166\pi$
$631$	370.756	+	214.056i	0.587569	+	0.339233i	−0.176567	+	0.984289i	$0.556499\pi$
$632$	−56.6357	+	227.552i	−0.0896135	+	0.360050i
$633$		0			0
$634$	26.8862	−	191.495i	0.0424072	−	0.302043i
$635$	−157.367	+	187.543i	−0.247822	+	0.295343i
$636$		0			0
$637$	7.63122	+	2.77754i	0.0119799	+	0.00436034i
$638$	−0.413877	−	11.8055i	−0.000648709	−	0.0185040i
$639$		0			0
$640$	217.404	−	760.930i	0.339694	−	1.18895i
$641$	−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	$0.0496382\pi$
$643$	212.800	+	584.664i	0.330949	+	0.909275i	−0.656916	+	0.753963i	$0.728140\pi$
$644$	−295.207	−	214.357i	−0.458396	−	0.332852i
$645$		0			0
$646$	512.719	−	1578.72i	0.793683	−	2.44384i
$647$		−	668.799i		−	1.03369i	−0.856078	−	0.516846i	$-0.827106\pi$
$647$		−	668.799i		−	1.03369i	0.856078	−	0.516846i	$-0.172894\pi$
$648$		0			0
$649$	368.981			0.568537
$650$	−16.4720	−	5.34959i	−0.0253416	−	0.00823014i
$651$		0			0
$652$	−194.378	+	267.693i	−0.298126	+	0.410572i
$653$	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
$656$	106.881	−	264.957i	0.162928	−	0.403898i
$657$		0			0
$658$	−926.670	+	32.4871i	−1.40831	+	0.0493725i
$659$	127.048	−	349.061i	0.192789	−	0.529683i	−0.805205	−	0.592997i	$-0.797945\pi$
$659$	127.048	−	349.061i	0.192789	−	0.529683i	0.997994	+	0.0633137i	$0.0201669\pi$
$660$		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	$0.780497\pi$
$662$	−957.433	−	134.425i	−1.44627	−	0.203059i
$663$		0			0
$664$	35.1672	−	141.295i	0.0529627	−	0.212794i
$665$	618.455	−	1071.19i	0.930007	−	1.61082i
$666$		0			0
$667$	3.64724	−	2.10574i	0.00546813	−	0.00315703i
$668$	−127.012	+	443.401i	−0.190137	+	0.663773i
$669$		0			0
$670$	242.604	−	310.607i	0.362096	−	0.463592i
$671$	−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
$680$	1444.83	−	705.425i	2.12475	−	1.03739i
$681$		0			0
$682$	439.661	−	395.982i	0.644665	−	0.580618i
$683$	−718.255	+	414.685i	−1.05162	+	0.607152i	−0.923102	−	0.384555i	$-0.874355\pi$
$683$	−718.255	+	414.685i	−1.05162	+	0.607152i	−0.128517	+	0.991707i	$0.541022\pi$
$684$		0			0
$685$	226.086	−	391.592i	0.330052	−	0.571667i
$686$	561.003	−	119.325i	0.817789	−	0.173943i
$687$		0			0
$688$	−74.2183	−	2.55106i	−0.107875	−	0.00370793i
$689$	32.9392	+	27.6392i	0.0478072	+	0.0401150i
$690$		0			0
$691$	438.513	−	1204.80i	0.634606	−	1.74357i	−0.0334337	−	0.999441i	$-0.510644\pi$
$691$	438.513	−	1204.80i	0.634606	−	1.74357i	0.668040	−	0.744125i	$-0.267134\pi$
$692$	469.450	+	695.577i	0.678396	+	1.00517i
$693$		0			0
$694$	−216.227	−	114.932i	−0.311566	−	0.165608i
$695$	−392.823	+	69.2653i	−0.565213	+	0.0996623i
$696$		0			0
$697$	545.455	−	198.529i	0.782575	−	0.284834i
$698$	1042.22	−	421.249i	1.49315	−	0.603509i
$699$		0			0
$700$	402.183	−	100.392i	0.574547	−	0.143418i
$701$	−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
$704$	823.773	+	642.513i	1.17013	+	0.912660i
$705$		0			0
$706$	−405.902	+	164.060i	−0.574931	+	0.232379i
$707$	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	$-0.267569\pi$
$710$	711.241	+	378.048i	1.00175	+	0.532463i
$711$		0			0
$712$	245.318	−	551.602i	0.344547	−	0.774722i
$713$	198.229	+	72.1493i	0.278020	+	0.101191i
$714$		0			0
$715$	42.4770	−	50.6221i	0.0594084	−	0.0708002i
$716$	−530.111	−	1189.77i	−0.740379	−	1.66169i
$717$		0			0
$718$	−345.840	+	73.5601i	−0.481671	+	0.102451i
$719$	596.030	+	344.118i	0.828971	+	0.478606i	0.853500	−	0.521093i	$-0.174475\pi$
$719$	596.030	+	344.118i	0.828971	+	0.478606i	−0.0245295	+	0.999699i	$0.507809\pi$
$720$		0			0
$721$	−70.8229	−	122.669i	−0.0982287	−	0.170137i
$722$	−432.220	+	389.280i	−0.598643	+	0.539169i
$723$		0			0
$724$	71.1484	−	678.720i	0.0982713	−	0.937459i
$725$	−0.830942	+	4.71251i	−0.00114613	+	0.00650001i
$726$		0			0
$727$	288.835	+	344.220i	0.397297	+	0.473481i	0.927194	−	0.374582i	$-0.122214\pi$
$727$	288.835	+	344.220i	0.397297	+	0.473481i	−0.529897	+	0.848062i	$0.677769\pi$
$728$	−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	$-0.0909609\pi$
$734$	−220.578	+	282.406i	−0.300515	+	0.384750i
$735$		0			0
$736$	−64.4258	+	366.845i	−0.0875350	+	0.498431i
$737$	260.145	+	450.584i	0.352978	+	0.611376i
$738$		0			0
$739$	−51.6835	−	29.8395i	−0.0699371	−	0.0403782i	0.464624	−	0.885508i	$-0.346190\pi$
$739$	−51.6835	−	29.8395i	−0.0699371	−	0.0403782i	−0.534561	+	0.845130i	$0.679523\pi$
$740$	592.197	−	572.192i	0.800267	−	0.773232i
$741$		0			0
$742$	−1019.17	−	143.093i	−1.37355	−	0.192848i
$743$	−537.178	+	640.184i	−0.722985	+	0.861620i	−0.994917	−	0.100696i	$-0.967893\pi$
$743$	−537.178	+	640.184i	−0.722985	+	0.861620i	0.271932	+	0.962316i	$0.412337\pi$
$744$		0			0
$745$	−643.712	−	234.292i	−0.864042	−	0.314486i
$746$	834.751	−	29.2646i	1.11897	−	0.0392287i
$747$		0			0
$748$	148.641	+	2117.33i	0.198718	+	2.83066i
$749$	35.6372	+	202.108i	0.0475797	+	0.269838i
$750$		0			0
$751$	453.840	+	1246.91i	0.604314	+	1.66034i	0.742431	+	0.669923i	$0.233673\pi$
$751$	453.840	+	1246.91i	0.604314	+	1.66034i	−0.138117	+	0.990416i	$0.544105\pi$
$752$	444.882	+	835.597i	0.591598	+	1.11117i
$753$		0			0
$754$	0.450668	+	0.146363i	0.000597702	+	0.000194115i
$755$		−	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	$0.584891\pi$
$758$	−114.551	+	352.715i	−0.151122	+	0.465323i
$759$		0			0
$760$	−1259.76	−	87.5709i	−1.65758	−	0.115225i
$761$	−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
$764$	55.4982	+	790.550i	0.0726417	+	1.03475i
$765$		0			0
$766$	28.7068	+	818.840i	0.0374762	+	1.06898i
$767$	−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	$0.969243\pi$
$770$	−219.910	+	1566.30i	−0.285598	+	2.03416i
$771$		0			0
$772$	−379.573	+	366.751i	−0.491675	+	0.475066i
$773$	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
$776$	−338.589	−	1178.97i	−0.436326	−	1.51929i
$777$		0			0
$778$	−372.380	−	290.853i	−0.478638	−	0.373847i
$779$	−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	0.291364	−	0.956612i	$-0.405891\pi$
$787$	187.288	+	33.0239i	0.237977	+	0.0419618i	−0.0533875	+	0.998574i	$0.517002\pi$
$788$	14.4198	−	137.558i	0.0182992	−	0.174566i
$789$		0			0
$790$	242.562	+	269.318i	0.307040	+	0.340909i
$791$	−822.346	+	474.782i	−1.03963	+	0.600230i
$792$		0			0
$793$	21.6146	−	37.4376i	0.0272568	−	0.0472101i
$794$	−257.817	−	1212.12i	−0.324706	−	1.52660i
$795$		0			0
$796$	276.264	+	620.041i	0.347065	+	0.778946i
$797$	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
$800$	−272.250	−	324.004i	−0.340312	−	0.405004i
$801$		0			0
$802$	248.184	−	466.921i	0.309456	−	0.582195i
$803$	883.674	−	155.816i	1.10047	−	0.194042i
$804$		0			0
$805$	−529.886	+	192.863i	−0.658243	+	0.239581i
$806$	8.89405	+	22.0049i	0.0110348	+	0.0273013i
$807$		0			0
$808$	926.834	−	960.555i	1.14707	−	1.18881i
$809$	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	$0.0115258\pi$
$811$			58.7187i			0.0724029i	−0.999345	+	0.0362014i	$0.988474\pi$
$812$	−11.0035	+	2.74669i	−0.0135512	+	0.00338263i
$813$		0			0
$814$	407.364	+	1007.86i	0.500448	+	1.23816i
$815$	174.887	+	480.499i	0.214586	+	0.589570i
$816$		0			0
$817$	20.5773	+	116.700i	0.0251864	+	0.142839i
$818$	−577.203	+	1085.92i	−0.705627	+	1.32753i
$819$		0			0
$820$	−247.039	−	366.034i	−0.301267	−	0.446382i
$821$	−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	−0.997069	−	0.0765119i	$-0.975622\pi$
$823$	−616.081	+	734.217i	−0.748580	+	0.892123i	0.248489	+	0.968635i	$0.420066\pi$
$824$	−80.8160	+	119.921i	−0.0980777	+	0.145535i
$825$		0			0
$826$	−73.7002	−	346.499i	−0.0892254	−	0.419490i
$827$	−729.172	−	420.987i	−0.881707	−	0.509054i	−0.0104861	−	0.999945i	$-0.503338\pi$
$827$	−729.172	−	420.987i	−0.881707	−	0.509054i	−0.871221	+	0.490891i	$0.836671\pi$
$828$		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	$0.639894\pi$
$830$	−150.615	−	167.229i	−0.181464	−	0.201481i
$831$		0			0
$832$	−35.5200	+	22.2360i	−0.0426923	+	0.0267259i
$833$	−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	0.808210	−	0.588894i	$-0.200437\pi$
$839$	73.7634	+	87.9078i	0.0879182	+	0.104777i	−0.720292	+	0.693671i	$0.755992\pi$
$840$		0			0
$841$	−146.015	+	828.094i	−0.173621	+	0.984654i
$842$	−371.811	−	290.409i	−0.441581	−	0.344903i
$843$		0			0
$844$	−41.0260	+	143.223i	−0.0486090	+	0.169695i
$845$	−521.107	−	902.585i	−0.616695	−	1.06815i
$846$		0			0
$847$	−987.122	−	569.915i	−1.16543	−	0.672863i
$848$	325.235	+	999.107i	0.383531	+	1.17819i
$849$		0			0
$850$	119.547	−	851.464i	0.140643	−	1.00172i
$851$	−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	$0.448176\pi$
$854$	36.2513	+	1034.04i	0.0424489	+	1.21082i
$855$		0			0
$856$	169.456	−	123.224i	0.197963	−	0.143953i
$857$	−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	$-0.803696\pi$
$859$	−483.287	−	1327.82i	−0.562616	−	1.54577i	0.253171	−	0.967422i	$-0.418526\pi$
$860$	−67.4429	+	92.8807i	−0.0784220	+	0.108001i
$861$		0			0
$862$	−191.165	+	588.621i	−0.221770	+	0.682855i
$863$			509.284i			0.590132i	0.955477	+	0.295066i	$0.0953417\pi$
$863$			509.284i			0.590132i	−0.955477	+	0.295066i	$0.904658\pi$
$864$		0			0
$865$	1297.07			1.49951
$866$	−221.541	−	71.9494i	−0.255821	−	0.0830824i
$867$		0			0
$868$	−459.673	−	333.779i	−0.529577	−	0.384539i
$869$	−449.618	+	163.648i	−0.517398	+	0.188317i
$870$		0			0
$871$	−20.5530	+	3.62405i	−0.0235970	+	0.00416080i
$872$	324.301	+	445.976i	0.371904	+	0.511440i
$873$		0			0
$874$	593.968	−	20.8233i	0.679597	−	0.0238252i
$875$	−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	$0.651540\pi$
$878$	1233.12	+	173.131i	1.40446	+	0.197188i
$879$		0			0
$880$	1535.46	−	499.832i	1.74485	−	0.567991i
$881$	−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	−0.699173	−	0.714953i	$-0.746448\pi$
$883$	−379.330	+	219.006i	−0.429592	+	0.248025i	0.269581	+	0.962978i	$0.413115\pi$
$884$	−81.8486	−	23.4454i	−0.0925889	−	0.0265220i
$885$		0			0
$886$	−134.694	+	172.449i	−0.152024	+	0.194637i
$887$	−1569.49	−	276.744i	−1.76944	−	0.312000i	−0.808445	−	0.588572i	$-0.799690\pi$
$887$	−1569.49	−	276.744i	−1.76944	−	0.312000i	−0.960993	+	0.276572i	$0.910802\pi$
$888$		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
$896$	438.824	−	901.916i	0.489759	−	1.00660i
$897$		0			0
$898$	−565.494	+	509.314i	−0.629726	+	0.567164i
$899$	5.67920	−	3.27889i	0.00631724	−	0.00364726i
$900$		0			0
$901$	−1067.36	+	1848.73i	−1.18464	+	2.05186i
$902$	570.206	−	121.283i	0.632158	−	0.134460i
$903$		0			0
$904$	803.924	+	541.773i	0.889297	+	0.599307i
$905$	−808.038	−	678.024i	−0.892859	−	0.749198i
$906$		0			0
$907$	335.024	−	920.471i	0.369376	−	1.01485i	−0.606224	−	0.795294i	$-0.707316\pi$
$907$	335.024	−	920.471i	0.369376	−	1.01485i	0.975599	−	0.219558i	$-0.0704615\pi$
$908$	1112.53	−	750.852i	1.22525	−	0.826930i
$909$		0			0
$910$	−56.0221	−	29.7776i	−0.0615627	−	0.0327227i
$911$	−1389.49	+	245.005i	−1.52524	+	0.268941i	−0.872490	−	0.488631i	$-0.837496\pi$
$911$	−1389.49	+	245.005i	−1.52524	+	0.268941i	−0.652751	+	0.757572i	$0.726385\pi$
$912$		0			0
$913$	279.185	−	101.615i	0.305788	−	0.111298i
$914$	−383.647	+	155.065i	−0.419745	+	0.169655i
$915$		0			0
$916$	250.650	+	1004.13i	0.273635	+	1.09621i
$917$	−716.775			−0.781652
$918$		0			0
$919$			648.911i			0.706105i	0.935603	+	0.353053i	$0.114856\pi$
$919$			648.911i			0.706105i	−0.935603	+	0.353053i	$0.885144\pi$
$920$	414.285	+	399.742i	0.450310	+	0.434502i
$921$		0			0
$922$	−222.483	+	89.9244i	−0.241305	+	0.0975319i
$923$	−14.5879	−	40.0800i	−0.0158049	−	0.0434236i
$924$		0			0
$925$	−76.4679	−	433.671i	−0.0826680	−	0.468834i
$926$	−1048.05	−	557.075i	−1.13181	−	0.601593i
$927$		0			0
$928$	7.44863	+	8.86460i	0.00802654	+	0.00955237i
$929$	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
$932$	−1057.46	+	471.159i	−1.13462	+	0.505536i
$933$		0			0
$934$	−1307.62	+	278.130i	−1.40002	+	0.297783i
$935$	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	$0.789592\pi$
$938$	371.169	−	334.294i	0.395703	−	0.356390i
$939$		0			0
$940$	1455.22	+	152.547i	1.54811	+	0.162284i
$941$	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	0.308409	−	0.951254i	$-0.400203\pi$
$947$	−645.804	−	769.639i	−0.681947	−	0.812713i	−0.990357	+	0.138540i	$0.955759\pi$
$948$		0			0
$949$	−6.25014	+	35.4463i	−0.00658602	+	0.0373512i
$950$	−415.683	+	532.200i	−0.437561	+	0.560210i
$951$		0			0
$952$	1958.63	−	562.500i	2.05739	−	0.590862i
$953$	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
$956$	782.690	+	810.055i	0.818713	+	0.847337i
$957$		0			0
$958$	−382.562	−	53.7122i	−0.399334	−	0.0560670i
$959$	368.375	−	439.012i	0.384124	−	0.457781i
$960$		0			0
$961$	−594.379	−	216.336i	−0.618500	−	0.225116i
$962$	−43.5785	+	1.52777i	−0.0452999	+	0.00158812i
$963$		0			0
$964$	−954.827	+	67.0308i	−0.990484	+	0.0695340i
$965$	141.664	+	803.418i	0.146802	+	0.832558i
$966$		0			0
$967$	7.17415	+	19.7108i	0.00741897	+	0.0203835i	0.943347	−	0.331808i	$-0.107659\pi$
$967$	7.17415	+	19.7108i	0.00741897	+	0.0203835i	−0.935928	+	0.352192i	$0.885436\pi$
$968$	−80.6979	+	1160.89i	−0.0833656	+	1.19926i
$969$		0			0
$970$	−1803.23	−	585.633i	−1.85900	−	0.603745i
$971$		−	423.302i		−	0.435945i	−0.975955	−	0.217972i	$-0.930056\pi$
$971$		−	423.302i		−	0.435945i	0.975955	−	0.217972i	$-0.0699442\pi$
$972$		0			0
$973$	−505.551			−0.519580
$974$	−379.454	+	1168.38i	−0.389583	+	1.19957i
$975$		0			0
$976$	932.417	−	496.430i	0.955345	−	0.508637i
$977$	−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
$980$	305.970	−	21.4797i	0.312214	−	0.0219181i
$981$		0			0
$982$	−40.1639	−	1145.65i	−0.0409001	−	1.16664i
$983$	345.481	−	949.200i	0.351455	−	0.965615i	−0.630448	−	0.776232i	$-0.717129\pi$
$983$	345.481	−	949.200i	0.351455	−	0.965615i	0.981903	−	0.189384i	$-0.0606490\pi$
$984$		0			0
$985$	−163.767	−	137.417i	−0.166261	−	0.139509i
$986$	−3.27074	+	23.2957i	−0.00331718	+	0.0236265i
$987$		0			0
$988$	46.4645	+	48.0890i	0.0470288	+	0.0486731i
$989$	27.0114	−	46.7851i	0.0273118	−	0.0473054i
$990$		0			0
$991$	1171.38	−	676.298i	1.18202	−	0.682440i	0.225539	−	0.974234i	$-0.427586\pi$
$991$	1171.38	−	676.298i	1.18202	−	0.682440i	0.956481	+	0.291794i	$0.0942523\pi$
$992$	−100.319	+	571.222i	−0.101128	+	0.575829i
$993$		0			0
$994$	804.541	+	628.399i	0.809398	+	0.632192i
$995$	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.199.4		204
3.2	odd	2		108.3.j.a.103.31	yes	204
4.3	odd	2	inner	324.3.j.a.199.19		204
12.11	even	2		108.3.j.a.103.16	yes	204
27.11	odd	18		108.3.j.a.43.16	✓	204
27.16	even	9	inner	324.3.j.a.127.19		204
108.11	even	18		108.3.j.a.43.31	yes	204
108.43	odd	18	inner	324.3.j.a.127.4		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.16	✓	204	27.11	odd	18
108.3.j.a.43.31	yes	204	108.11	even	18
108.3.j.a.103.16	yes	204	12.11	even	2
108.3.j.a.103.31	yes	204	3.2	odd	2
324.3.j.a.127.4		204	108.43	odd	18	inner
324.3.j.a.127.19		204	27.16	even	9	inner
324.3.j.a.199.4		204	1.1	even	1	trivial
324.3.j.a.199.19		204	4.3	odd	2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.90220 - 0.617774i) q^{2} +(3.23671 + 2.35025i) q^{4} +(5.80978 - 2.11459i) q^{5} +(7.71693 - 1.36070i) q^{7} +(-4.70494 - 6.47020i) q^{8} +O(q^{10})\)	\(q+(-1.90220 - 0.617774i) q^{2} +(3.23671 + 2.35025i) q^{4} +(5.80978 - 2.11459i) q^{5} +(7.71693 - 1.36070i) q^{7} +(-4.70494 - 6.47020i) q^{8} +(-12.3577 + 0.433234i) q^{10} +(5.58301 - 15.3392i) q^{11} +(0.501591 + 0.420885i) q^{13} +(-15.5197 - 2.17899i) q^{14} +(4.95261 + 15.2142i) q^{16} +(-16.2536 + 28.1521i) q^{17} +(22.1106 - 12.7656i) q^{19} +(23.7744 + 6.81015i) q^{20} +(-20.0961 + 25.7292i) q^{22} +(-11.4625 - 2.02115i) q^{23} +(10.1309 - 8.50086i) q^{25} +(-0.694114 - 1.11048i) q^{26} +(28.1755 + 13.7326i) q^{28} +(-0.277178 + 0.232580i) q^{29} +(-17.8485 - 3.14718i) q^{31} +(-0.0219106 - 32.0000i) q^{32} +(48.3092 - 43.5097i) q^{34} +(41.9564 - 24.2235i) q^{35} +(16.6488 - 28.8366i) q^{37} +(-49.9451 + 10.6233i) q^{38} +(-41.0165 - 27.6414i) q^{40} +(-13.6788 - 11.4779i) q^{41} +(-1.58745 + 4.36148i) q^{43} +(54.1216 - 36.5271i) q^{44} +(20.5554 + 10.9259i) q^{46} +(58.2666 - 10.2740i) q^{47} +(11.6546 - 4.24194i) q^{49} +(-24.5226 + 9.91170i) q^{50} +(0.634319 + 2.54115i) q^{52} +65.6694 q^{53} -100.923i q^{55} +(-45.1117 - 43.5281i) q^{56} +(0.670929 - 0.271180i) q^{58} +(7.73105 + 21.2409i) q^{59} +(-11.4644 - 65.0179i) q^{61} +(32.0072 + 17.0129i) q^{62} +(-19.7271 + 60.8838i) q^{64} +(3.80413 + 1.38459i) q^{65} +(-20.4878 + 24.4165i) q^{67} +(-118.773 + 52.9200i) q^{68} +(-94.7739 + 20.1584i) q^{70} +(-56.4127 - 32.5699i) q^{71} +(27.4849 + 47.6052i) q^{73} +(-49.4838 + 44.5677i) q^{74} +(101.568 + 10.6471i) q^{76} +(22.2116 - 125.968i) q^{77} +(-18.8412 - 22.4541i) q^{79} +(60.9453 + 77.9184i) q^{80} +(18.9290 + 30.2835i) q^{82} +(11.6992 + 13.9426i) q^{83} +(-34.8999 + 197.927i) q^{85} +(5.71404 - 7.31571i) q^{86} +(-125.515 + 36.0468i) q^{88} +(37.7308 + 65.3517i) q^{89} +(4.44344 + 2.56542i) q^{91} +(-32.3507 - 33.4818i) q^{92} +(-117.182 - 16.4524i) q^{94} +(101.464 - 120.920i) q^{95} +(144.082 + 52.4414i) q^{97} +(-24.7900 + 0.869083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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