LMFDB - Embedded newform 54.3.f.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.47139342755$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	54.11
Dual form			54.3.f.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909039 - 1.08335i) q^{2} +(1.54884 - 2.56926i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-1.07911 + 2.96482i) q^{5} +(-1.37545 - 4.01349i) q^{6} +(-0.250410 + 1.42015i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.20220 - 7.95874i) q^{9} +O(q^{10})$	\(q+(0.909039 - 1.08335i) q^{2} +(1.54884 - 2.56926i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-1.07911 + 2.96482i) q^{5} +(-1.37545 - 4.01349i) q^{6} +(-0.250410 + 1.42015i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.20220 - 7.95874i) q^{9} +(2.23099 + 3.86419i) q^{10} +(6.39485 + 17.5697i) q^{11} +(-5.59836 - 2.15832i) q^{12} +(10.5936 - 8.88908i) q^{13} +(1.31088 + 1.56225i) q^{14} +(5.94604 + 7.36454i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-16.3520 + 9.44086i) q^{17} +(-12.4421 - 2.68235i) q^{18} +(-1.14343 + 1.98047i) q^{19} +(6.21434 + 1.09575i) q^{20} +(3.26088 + 2.84294i) q^{21} +(24.8473 + 9.04368i) q^{22} +(-26.5788 + 4.68656i) q^{23} +(-7.42735 + 4.10299i) q^{24} +(11.5254 + 9.67096i) q^{25} -19.5571i q^{26} +(-26.9566 - 1.53026i) q^{27} +2.88411 q^{28} +(17.2495 - 20.5571i) q^{29} +(13.3836 + 0.253009i) q^{30} +(-4.55767 - 25.8478i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(55.0457 + 10.7826i) q^{33} +(-4.63689 + 26.2971i) q^{34} +(-3.94026 - 2.27491i) q^{35} +(-14.2162 + 11.0408i) q^{36} +(-33.8611 - 58.6492i) q^{37} +(1.10613 + 3.03906i) q^{38} +(-6.43059 - 40.9854i) q^{39} +(6.83616 - 5.73622i) q^{40} +(-13.0402 - 15.5407i) q^{41} +(6.04417 - 0.948327i) q^{42} +(-32.2609 + 11.7420i) q^{43} +(32.3847 - 18.6973i) q^{44} +(28.1309 - 3.87044i) q^{45} +(-19.0840 + 33.0544i) q^{46} +(46.4969 + 8.19866i) q^{47} +(-2.30677 + 11.7762i) q^{48} +(44.0908 + 16.0478i) q^{49} +(20.9541 - 3.69477i) q^{50} +(-1.07065 + 56.6350i) q^{51} +(-21.1872 - 17.7782i) q^{52} -49.0655i q^{53} +(-26.1624 + 27.8124i) q^{54} -58.9918 q^{55} +(2.62176 - 3.12450i) q^{56} +(3.31737 + 6.00520i) q^{57} +(-6.59012 - 37.3744i) q^{58} +(-13.0684 + 35.9050i) q^{59} +(12.4403 - 14.2691i) q^{60} +(-9.55898 + 54.2117i) q^{61} +(-32.1454 - 18.5591i) q^{62} +(12.3548 - 3.97479i) q^{63} +(4.00000 + 6.92820i) q^{64} +(14.9229 + 41.0004i) q^{65} +(61.7201 - 49.8320i) q^{66} +(-95.2638 + 79.9358i) q^{67} +(24.2739 + 28.9285i) q^{68} +(-29.1253 + 75.5466i) q^{69} +(-6.04638 + 2.20070i) q^{70} +(10.4669 - 6.04307i) q^{71} +(-0.962114 + 25.4377i) q^{72} +(37.3933 - 64.7671i) q^{73} +(-94.3187 - 16.6309i) q^{74} +(42.6982 - 14.6330i) q^{75} +(4.29788 + 1.56430i) q^{76} +(-26.5529 + 4.68199i) q^{77} +(-50.2472 - 30.2908i) q^{78} +(74.8249 + 62.7855i) q^{79} -12.6204i q^{80} +(-45.6831 + 66.8884i) q^{81} -28.6900 q^{82} +(81.1294 - 96.6863i) q^{83} +(4.46701 - 7.41002i) q^{84} +(-10.3449 - 58.6687i) q^{85} +(-16.6057 + 45.6238i) q^{86} +(-26.0999 - 76.1580i) q^{87} +(9.18320 - 52.0805i) q^{88} +(9.23832 + 5.33375i) q^{89} +(21.3790 - 33.9940i) q^{90} +(9.97104 + 17.2703i) q^{91} +(18.4614 + 50.7224i) q^{92} +(-73.4689 - 28.3243i) q^{93} +(51.1495 - 42.9196i) q^{94} +(-4.63788 - 5.52721i) q^{95} +(10.6608 + 13.2041i) q^{96} +(145.826 - 53.0765i) q^{97} +(57.4656 - 33.1778i) q^{98} +(112.960 - 124.726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$3$	1.54884	−	2.56926i	0.516279	−	0.856420i
$3$	1.54884	−	2.56926i	0.516279	−	0.856420i
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	−1.07911	+	2.96482i	−0.215822	+	0.592965i	−0.999606	−	0.0280680i	$-0.991064\pi$
$5$	−1.07911	+	2.96482i	−0.215822	+	0.592965i	0.783784	+	0.621033i	$0.213287\pi$
$6$	−1.37545	−	4.01349i	−0.229242	−	0.668915i
$7$	−0.250410	+	1.42015i	−0.0357728	+	0.202878i	−0.997456	−	0.0712856i	$-0.977290\pi$
$7$	−0.250410	+	1.42015i	−0.0357728	+	0.202878i	0.961683	+	0.274163i	$0.0884009\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	−4.20220	−	7.95874i	−0.466911	−	0.884304i
$10$	2.23099	+	3.86419i	0.223099	+	0.386419i
$11$	6.39485	+	17.5697i	0.581350	+	1.59725i	0.785876	+	0.618385i	$0.212213\pi$
$11$	6.39485	+	17.5697i	0.581350	+	1.59725i	−0.204526	+	0.978861i	$0.565565\pi$
$12$	−5.59836	−	2.15832i	−0.466530	−	0.179860i
$13$	10.5936	−	8.88908i	0.814891	−	0.683775i	−0.136879	−	0.990588i	$-0.543707\pi$
$13$	10.5936	−	8.88908i	0.814891	−	0.683775i	0.951770	+	0.306813i	$0.0992625\pi$
$14$	1.31088	+	1.56225i	0.0936345	+	0.111589i
$15$	5.94604	+	7.36454i	0.396403	+	0.490970i
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	−16.3520	+	9.44086i	−0.961885	+	0.555345i	−0.896753	−	0.442532i	$-0.854080\pi$
$17$	−16.3520	+	9.44086i	−0.961885	+	0.555345i	−0.0651325	+	0.997877i	$0.520747\pi$
$18$	−12.4421	−	2.68235i	−0.691226	−	0.149019i
$19$	−1.14343	+	1.98047i	−0.0601804	+	0.104236i	−0.894546	−	0.446976i	$-0.852501\pi$
$19$	−1.14343	+	1.98047i	−0.0601804	+	0.104236i	0.834366	+	0.551212i	$0.185834\pi$
$20$	6.21434	+	1.09575i	0.310717	+	0.0547877i
$21$	3.26088	+	2.84294i	0.155280	+	0.135378i
$22$	24.8473	+	9.04368i	1.12942	+	0.411077i
$23$	−26.5788	+	4.68656i	−1.15560	+	0.203763i	−0.718419	−	0.695610i	$-0.755134\pi$
$23$	−26.5788	+	4.68656i	−1.15560	+	0.203763i	−0.437181	+	0.899374i	$0.644023\pi$
$24$	−7.42735	+	4.10299i	−0.309473	+	0.170958i
$25$	11.5254	+	9.67096i	0.461016	+	0.386838i
$26$		−	19.5571i		−	0.752196i
$27$	−26.9566	−	1.53026i	−0.998393	−	0.0566762i
$28$	2.88411			0.103004
$29$	17.2495	−	20.5571i	0.594809	−	0.708865i	−0.381714	−	0.924281i	$-0.624666\pi$
$29$	17.2495	−	20.5571i	0.594809	−	0.708865i	0.976523	+	0.215415i	$0.0691105\pi$
$30$	13.3836	+	0.253009i	0.446119	+	0.00843363i
$31$	−4.55767	−	25.8478i	−0.147022	−	0.833801i	−0.965722	−	0.259580i	$-0.916416\pi$
$31$	−4.55767	−	25.8478i	−0.147022	−	0.833801i	0.818700	−	0.574221i	$-0.194695\pi$
$32$	−1.93476	+	5.31570i	−0.0604612	+	0.166116i
$33$	55.0457	+	10.7826i	1.66805	+	0.326745i
$34$	−4.63689	+	26.2971i	−0.136379	+	0.773444i
$35$	−3.94026	−	2.27491i	−0.112579	−	0.0649975i
$36$	−14.2162	+	11.0408i	−0.394896	+	0.306688i
$37$	−33.8611	−	58.6492i	−0.915166	−	1.58511i	−0.806659	−	0.591018i	$-0.798726\pi$
$37$	−33.8611	−	58.6492i	−0.915166	−	1.58511i	−0.108507	−	0.994096i	$-0.534607\pi$
$38$	1.10613	+	3.03906i	0.0291086	+	0.0799753i
$39$	−6.43059	−	40.9854i	−0.164887	−	1.05091i
$40$	6.83616	−	5.73622i	0.170904	−	0.143405i
$41$	−13.0402	−	15.5407i	−0.318053	−	0.379041i	0.583204	−	0.812326i	$-0.301799\pi$
$41$	−13.0402	−	15.5407i	−0.318053	−	0.379041i	−0.901257	+	0.433285i	$0.857354\pi$
$42$	6.04417	−	0.948327i	0.143909	−	0.0225792i
$43$	−32.2609	+	11.7420i	−0.750254	+	0.273070i	−0.688713	−	0.725034i	$-0.741824\pi$
$43$	−32.2609	+	11.7420i	−0.750254	+	0.273070i	−0.0615413	+	0.998105i	$0.519602\pi$
$44$	32.3847	−	18.6973i	0.736015	−	0.424938i
$45$	28.1309	−	3.87044i	0.625131	−	0.0860099i
$46$	−19.0840	+	33.0544i	−0.414869	+	0.718574i
$47$	46.4969	+	8.19866i	0.989296	+	0.174440i	0.644803	−	0.764349i	$-0.276940\pi$
$47$	46.4969	+	8.19866i	0.989296	+	0.174440i	0.344494	+	0.938789i	$0.388051\pi$
$48$	−2.30677	+	11.7762i	−0.0480578	+	0.245337i
$49$	44.0908	+	16.0478i	0.899813	+	0.327505i
$50$	20.9541	−	3.69477i	0.419081	−	0.0738954i
$51$	−1.07065	+	56.6350i	−0.0209932	+	1.11049i
$52$	−21.1872	−	17.7782i	−0.407446	−	0.341888i
$53$		−	49.0655i		−	0.925765i	−0.886420	−	0.462882i	$-0.846815\pi$
$53$		−	49.0655i		−	0.925765i	0.886420	−	0.462882i	$-0.153185\pi$
$54$	−26.1624	+	27.8124i	−0.484489	+	0.515044i
$55$	−58.9918			−1.07258
$56$	2.62176	−	3.12450i	0.0468172	−	0.0557946i
$57$	3.31737	+	6.00520i	0.0581995	+	0.105354i
$58$	−6.59012	−	37.3744i	−0.113623	−	0.644386i
$59$	−13.0684	+	35.9050i	−0.221498	+	0.608560i	−0.999813	−	0.0193130i	$-0.993852\pi$
$59$	−13.0684	+	35.9050i	−0.221498	+	0.608560i	0.778316	+	0.627873i	$0.216074\pi$
$60$	12.4403	−	14.2691i	0.207338	−	0.237818i
$61$	−9.55898	+	54.2117i	−0.156705	+	0.888716i	0.800506	+	0.599324i	$0.204564\pi$
$61$	−9.55898	+	54.2117i	−0.156705	+	0.888716i	−0.957211	+	0.289391i	$0.906547\pi$
$62$	−32.1454	−	18.5591i	−0.518474	−	0.299341i
$63$	12.3548	−	3.97479i	0.196109	−	0.0630918i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	14.9229	+	41.0004i	0.229583	+	0.630775i
$66$	61.7201	−	49.8320i	0.935152	−	0.755031i
$67$	−95.2638	+	79.9358i	−1.42185	+	1.19307i	−0.471505	+	0.881863i	$0.656289\pi$
$67$	−95.2638	+	79.9358i	−1.42185	+	1.19307i	−0.950342	+	0.311208i	$0.899266\pi$
$68$	24.2739	+	28.9285i	0.356969	+	0.425419i
$69$	−29.1253	+	75.5466i	−0.422105	+	1.09488i
$70$	−6.04638	+	2.20070i	−0.0863768	+	0.0314386i
$71$	10.4669	−	6.04307i	0.147421	−	0.0851136i	−0.424475	−	0.905440i	$-0.639541\pi$
$71$	10.4669	−	6.04307i	0.147421	−	0.0851136i	0.571896	+	0.820326i	$0.306208\pi$
$72$	−0.962114	+	25.4377i	−0.0133627	+	0.353301i
$73$	37.3933	−	64.7671i	0.512237	−	0.887220i	−0.487663	−	0.873032i	$-0.662150\pi$
$73$	37.3933	−	64.7671i	0.512237	−	0.887220i	0.999899	−	0.0141878i	$-0.00451627\pi$
$74$	−94.3187	−	16.6309i	−1.27458	−	0.224742i
$75$	42.6982	−	14.6330i	0.569309	−	0.195107i
$76$	4.29788	+	1.56430i	0.0565511	+	0.0205829i
$77$	−26.5529	+	4.68199i	−0.344842	+	0.0608050i
$78$	−50.2472	−	30.2908i	−0.644195	−	0.388343i
$79$	74.8249	+	62.7855i	0.947151	+	0.794754i	0.978815	−	0.204745i	$-0.0656364\pi$
$79$	74.8249	+	62.7855i	0.947151	+	0.794754i	−0.0316647	+	0.999499i	$0.510081\pi$
$80$		−	12.6204i		−	0.157755i
$81$	−45.6831	+	66.8884i	−0.563988	+	0.825783i
$82$	−28.6900			−0.349879
$83$	81.1294	−	96.6863i	0.977463	−	1.16490i	−0.00884154	−	0.999961i	$-0.502814\pi$
$83$	81.1294	−	96.6863i	0.977463	−	1.16490i	0.986305	−	0.164934i	$-0.0527412\pi$
$84$	4.46701	−	7.41002i	0.0531787	−	0.0882145i
$85$	−10.3449	−	58.6687i	−0.121704	−	0.690220i
$86$	−16.6057	+	45.6238i	−0.193090	+	0.530510i
$87$	−26.0999	−	76.1580i	−0.299999	−	0.875379i
$88$	9.18320	−	52.0805i	0.104355	−	0.591824i
$89$	9.23832	+	5.33375i	0.103801	+	0.0599298i	0.551002	−	0.834504i	$-0.314246\pi$
$89$	9.23832	+	5.33375i	0.103801	+	0.0599298i	−0.447201	+	0.894434i	$0.647579\pi$
$90$	21.3790	−	33.9940i	0.237545	−	0.377711i
$91$	9.97104	+	17.2703i	0.109572	+	0.189784i
$92$	18.4614	+	50.7224i	0.200668	+	0.551330i
$93$	−73.4689	−	28.3243i	−0.789988	−	0.304562i
$94$	51.1495	−	42.9196i	0.544144	−	0.456591i
$95$	−4.63788	−	5.52721i	−0.0488198	−	0.0581811i
$96$	10.6608	+	13.2041i	0.111050	+	0.137542i
$97$	145.826	−	53.0765i	1.50337	−	0.547180i	0.546436	−	0.837501i	$-0.315984\pi$
$97$	145.826	−	53.0765i	1.50337	−	0.547180i	0.956929	+	0.290320i	$0.0937619\pi$
$98$	57.4656	−	33.1778i	0.586384	−	0.338549i
$99$	112.960	−	124.726i	1.14101	−	1.25986i
$100$	15.0453	−	26.0593i	0.150453	−	0.260593i
$101$	−98.5993	−	17.3857i	−0.976231	−	0.172136i	−0.337298	−	0.941398i	$-0.609513\pi$
$101$	−98.5993	−	17.3857i	−0.976231	−	0.172136i	−0.638933	+	0.769262i	$0.720624\pi$
$102$	60.3823	+	52.6434i	0.591984	+	0.516111i
$103$	121.218	+	44.1198i	1.17687	+	0.428347i	0.855097	−	0.518468i	$-0.173498\pi$
$103$	121.218	+	44.1198i	1.17687	+	0.428347i	0.321777	+	0.946815i	$0.395720\pi$
$104$	−38.5199	+	6.79210i	−0.370384	+	0.0653087i
$105$	−11.9477	+	6.60009i	−0.113787	+	0.0628580i
$106$	−53.1552	−	44.6025i	−0.501464	−	0.420778i
$107$			106.516i			0.995473i	0.867328	+	0.497736i	$0.165835\pi$
$107$			106.516i			0.995473i	−0.867328	+	0.497736i	$0.834165\pi$
$108$	6.34791	+	53.6256i	0.0587769	+	0.496533i
$109$	102.881			0.943865			0.471933	−	0.881635i	$-0.343557\pi$
$109$	102.881			0.943865			0.471933	+	0.881635i	$0.343557\pi$
$110$	−53.6259	+	63.9088i	−0.487508	+	0.580989i
$111$	−203.130	−	3.84007i	−1.83000	−	0.0345952i
$112$	−1.00164	−	5.68058i	−0.00894321	−	0.0507195i
$113$	30.8936	−	84.8796i	0.273395	−	0.751147i	−0.724678	−	0.689088i	$-0.758011\pi$
$113$	30.8936	−	84.8796i	0.273395	−	0.751147i	0.998073	−	0.0620584i	$-0.0197665\pi$
$114$	9.52135	+	1.86508i	0.0835207	+	0.0163604i
$115$	14.7866	−	83.8588i	0.128579	−	0.729207i
$116$	−46.4802	−	26.8354i	−0.400692	−	0.231340i
$117$	−115.262	−	46.9579i	−0.985147	−	0.401350i
$118$	27.0181	+	46.7967i	0.228967	+	0.396582i
$119$	−9.31268	−	25.5864i	−0.0782578	−	0.215011i
$120$	−4.14973	−	26.4484i	−0.0345811	−	0.220403i
$121$	−175.109	+	146.934i	−1.44718	+	1.21433i
$122$	50.0408	+	59.6362i	0.410170	+	0.488822i
$123$	−60.1252	+	9.43362i	−0.488823	+	0.0766961i
$124$	−49.3274	+	17.9537i	−0.397802	+	0.144788i
$125$	−109.420	+	63.1735i	−0.875358	+	0.505388i
$126$	6.92494	−	16.9979i	0.0549599	−	0.134904i
$127$	−20.3684	+	35.2791i	−0.160381	+	0.277788i	−0.935005	−	0.354634i	$-0.884606\pi$
$127$	−20.3684	+	35.2791i	−0.160381	+	0.277788i	0.774624	+	0.632422i	$0.217939\pi$
$128$	11.1418	+	1.96460i	0.0870455	+	0.0153485i
$129$	−19.7987	+	101.073i	−0.153478	+	0.783513i
$130$	57.9833	+	21.1042i	0.446026	+	0.162340i
$131$	48.6358	−	8.57581i	0.371266	−	0.0654642i	0.0150977	−	0.999886i	$-0.495194\pi$
$131$	48.6358	−	8.57581i	0.371266	−	0.0654642i	0.356168	+	0.934422i	$0.384083\pi$
$132$	2.12039	−	112.164i	0.0160636	−	0.849725i
$133$	−2.52624	−	2.11976i	−0.0189943	−	0.0159381i
$134$			175.869i			1.31245i
$135$	33.6260	−	78.2703i	0.249082	−	0.579780i
$136$	53.4056			0.392688
$137$	−86.7066	+	103.333i	−0.632895	+	0.754255i	−0.983230	−	0.182369i	$-0.941623\pi$
$137$	−86.7066	+	103.333i	−0.632895	+	0.754255i	0.350335	+	0.936624i	$0.386068\pi$
$138$	55.3674	+	100.228i	0.401213	+	0.726287i
$139$	−13.8192	−	78.3726i	−0.0994187	−	0.563832i	−0.993303	−	0.115535i	$-0.963142\pi$
$139$	−13.8192	−	78.3726i	−0.0994187	−	0.563832i	0.893885	−	0.448297i	$-0.147969\pi$
$140$	−3.11226	+	8.55087i	−0.0222304	+	0.0610776i
$141$	93.0807	−	106.764i	0.660147	−	0.757194i
$142$	2.96806	−	16.8327i	0.0209018	−	0.118540i
$143$	223.923	+	129.282i	1.56589	+	0.904069i
$144$	26.6833	+	24.1661i	0.185301	+	0.167820i
$145$	42.3342	+	73.3249i	0.291960	+	0.505689i
$146$	−36.1735	−	99.3858i	−0.247764	−	0.680725i
$147$	109.520	−	88.4255i	0.745037	−	0.601534i
$148$	−103.757	+	87.0621i	−0.701058	+	0.588257i
$149$	−80.7384	−	96.2203i	−0.541869	−	0.645774i	0.423737	−	0.905785i	$-0.360718\pi$
$149$	−80.7384	−	96.2203i	−0.541869	−	0.645774i	−0.965606	+	0.260011i	$0.916274\pi$
$150$	22.9617	−	59.5591i	0.153078	−	0.397060i
$151$	−106.373	+	38.7167i	−0.704459	+	0.256402i	−0.669314	−	0.742980i	$-0.733412\pi$
$151$	−106.373	+	38.7167i	−0.704459	+	0.256402i	−0.0351455	+	0.999382i	$0.511189\pi$
$152$	5.60163	−	3.23410i	0.0368528	−	0.0212770i
$153$	143.852	+	90.4693i	0.940208	+	0.591303i
$154$	−19.0654	+	33.0222i	−0.123801	+	0.214430i
$155$	81.5525	+	14.3799i	0.526145	+	0.0927736i
$156$	−78.4922	+	26.8999i	−0.503155	+	0.172435i
$157$	−48.5338	−	17.6648i	−0.309132	−	0.112515i	0.182796	−	0.983151i	$-0.441485\pi$
$157$	−48.5338	−	17.6648i	−0.309132	−	0.112515i	−0.491928	+	0.870636i	$0.663708\pi$
$158$	136.038	−	23.9871i	0.860997	−	0.151817i
$159$	−126.062	−	75.9946i	−0.792843	−	0.477953i
$160$	−13.6723	−	11.4724i	−0.0854520	−	0.0717027i
$161$		−	38.9193i		−	0.241735i
$162$	30.9359	+	110.295i	0.190962	+	0.680833i
$163$	1.04117			0.00638756			0.00319378	−	0.999995i	$-0.498983\pi$
$163$	1.04117			0.00638756			0.00319378	+	0.999995i	$0.498983\pi$
$164$	−26.0804	+	31.0814i	−0.159027	+	0.189521i
$165$	−91.3688	+	151.565i	−0.553750	+	0.918578i
$166$	−30.9953	−	175.783i	−0.186719	−	1.05894i
$167$	79.8469	−	219.378i	0.478125	−	1.31364i	−0.432957	−	0.901414i	$-0.642530\pi$
$167$	79.8469	−	219.378i	0.478125	−	1.31364i	0.911083	−	0.412224i	$-0.135248\pi$
$168$	−3.96696	−	11.5753i	−0.0236128	−	0.0689008i
$169$	3.86190	−	21.9019i	0.0228515	−	0.129597i
$170$	−72.9626	−	42.1250i	−0.429192	−	0.247794i
$171$	20.5670	+	0.777893i	0.120275	+	0.00454908i
$172$	34.3313	+	59.4636i	0.199601	+	0.345719i
$173$	−39.2036	−	107.711i	−0.226611	−	0.622607i	0.773324	−	0.634011i	$-0.218592\pi$
$173$	−39.2036	−	107.711i	−0.226611	−	0.622607i	−0.999935	+	0.0114031i	$0.996370\pi$
$174$	−106.232	−	40.9552i	−0.610526	−	0.235375i
$175$	−16.6202	+	13.9460i	−0.0949728	+	0.0796916i
$176$	−48.0735	−	57.2918i	−0.273145	−	0.325522i
$177$	72.0086	+	89.1872i	0.406828	+	0.503882i
$178$	14.1763	−	5.15976i	0.0796422	−	0.0289874i
$179$	−156.103	+	90.1263i	−0.872086	+	0.503499i	−0.868041	−	0.496493i	$-0.834621\pi$
$179$	−156.103	+	90.1263i	−0.872086	+	0.503499i	−0.00404482	+	0.999992i	$0.501288\pi$
$180$	−17.3930	−	54.0629i	−0.0966280	−	0.300349i
$181$	17.6283	−	30.5332i	0.0973941	−	0.168691i	−0.813211	−	0.581969i	$-0.802283\pi$
$181$	17.6283	−	30.5332i	0.0973941	−	0.168691i	0.910605	+	0.413277i	$0.135616\pi$
$182$	27.7739	+	4.89729i	0.152604	+	0.0269082i
$183$	124.479	+	108.525i	0.680211	+	0.593031i
$184$	71.7323	+	26.1084i	0.389849	+	0.141894i
$185$	210.424	−	37.1035i	1.13743	−	0.200559i
$186$	−97.4712	+	53.8447i	−0.524039	+	0.289488i
$187$	−270.442	−	226.928i	−1.44621	−	1.21352i
$188$		−	94.4284i		−	0.502279i
$189$	8.92339	−	37.8991i	0.0472137	−	0.200524i
$190$	−10.2039			−0.0537048
$191$	−13.7198	+	16.3506i	−0.0718313	+	0.0856053i	−0.800763	−	0.598981i	$-0.795573\pi$
$191$	−13.7198	+	16.3506i	−0.0718313	+	0.0856053i	0.728932	+	0.684586i	$0.240017\pi$
$192$	23.9957	+	0.453626i	0.124978	+	0.00236263i
$193$	−22.8734	−	129.722i	−0.118515	−	0.672133i	−0.984950	−	0.172842i	$-0.944705\pi$
$193$	−22.8734	−	129.722i	−0.118515	−	0.672133i	0.866434	−	0.499291i	$-0.166406\pi$
$194$	75.0615	−	206.230i	0.386915	−	1.06304i
$195$	128.454	+	25.1621i	0.658738	+	0.129037i
$196$	16.2953	−	92.4153i	0.0831394	−	0.471507i
$197$	−26.6300	−	15.3748i	−0.135177	−	0.0780447i	0.430886	−	0.902406i	$-0.358201\pi$
$197$	−26.6300	−	15.3748i	−0.135177	−	0.0780447i	−0.566064	+	0.824362i	$0.691534\pi$
$198$	−32.4370	−	235.757i	−0.163823	−	1.19069i
$199$	122.692	+	212.509i	0.616545	+	1.06789i	0.990111	+	0.140283i	$0.0448013\pi$
$199$	122.692	+	212.509i	0.616545	+	1.06789i	−0.373567	+	0.927603i	$0.621865\pi$
$200$	−14.5545	−	39.9883i	−0.0727727	−	0.199941i
$201$	57.8277	+	368.565i	0.287700	+	1.83366i
$202$	−108.465	+	91.0133i	−0.536958	+	0.450561i
$203$	24.8746	+	29.6444i	0.122535	+	0.146032i
$204$	111.921	−	17.5604i	0.548633	−	0.0860802i
$205$	60.1472	−	21.8918i	0.293401	−	0.106789i
$206$	157.989	−	91.2150i	0.766937	−	0.442791i
$207$	148.988	+	191.840i	0.719751	+	0.926763i
$208$	−27.6579	+	47.9049i	−0.132971	+	0.230312i
$209$	−42.1084	−	7.42485i	−0.201476	−	0.0355256i
$210$	−3.71069	+	18.9433i	−0.0176699	+	0.0902060i
$211$	−43.4786	−	15.8249i	−0.206059	−	0.0749995i	0.236928	−	0.971527i	$-0.423859\pi$
$211$	−43.4786	−	15.8249i	−0.206059	−	0.0749995i	−0.442988	+	0.896528i	$0.646082\pi$
$212$	−96.6402	+	17.0403i	−0.455850	+	0.0803787i
$213$	0.685323	−	36.2519i	0.00321748	−	0.170197i
$214$	115.394	+	96.8268i	0.539223	+	0.452462i
$215$		−	108.319i		−	0.503809i
$216$	63.8658	+	41.8707i	0.295675	+	0.193846i
$217$	37.8490			0.174419
$218$	93.5231	−	111.457i	0.429005	−	0.511269i
$219$	−108.487	−	196.387i	−0.495376	−	0.896743i
$220$	20.4876	+	116.191i	0.0931257	+	0.528142i
$221$	−89.3063	+	245.367i	−0.404101	+	1.11026i
$222$	−188.814	+	216.571i	−0.850512	+	0.975544i
$223$	9.89164	−	56.0983i	0.0443571	−	0.251562i	−0.954564	−	0.298007i	$-0.903678\pi$
$223$	9.89164	−	56.0983i	0.0443571	−	0.251562i	0.998921	+	0.0464451i	$0.0147893\pi$
$224$	−7.06459	−	4.07874i	−0.0315383	−	0.0182087i
$225$	28.5366	−	132.367i	0.126829	−	0.588297i
$226$	−63.8708	−	110.627i	−0.282614	−	0.489502i
$227$	−29.6402	−	81.4359i	−0.130574	−	0.358748i	0.857127	−	0.515105i	$-0.172247\pi$
$227$	−29.6402	−	81.4359i	−0.130574	−	0.358748i	−0.987701	+	0.156357i	$0.950025\pi$
$228$	10.6758	−	8.61953i	0.0468238	−	0.0378050i
$229$	−99.4359	+	83.4366i	−0.434218	+	0.364352i	−0.833540	−	0.552458i	$-0.813690\pi$
$229$	−99.4359	+	83.4366i	−0.434218	+	0.364352i	0.399322	+	0.916811i	$0.369245\pi$
$230$	−77.4069	−	92.2499i	−0.336552	−	0.401087i
$231$	−29.0969	+	75.4729i	−0.125960	+	0.326722i
$232$	−71.3245	+	25.9600i	−0.307433	+	0.111897i
$233$	−98.9330	+	57.1190i	−0.424605	+	0.245146i	−0.697046	−	0.717027i	$-0.745503\pi$
$233$	−98.9330	+	57.1190i	−0.424605	+	0.245146i	0.272441	+	0.962173i	$0.412169\pi$
$234$	−155.650	+	82.1828i	−0.665170	+	0.351208i
$235$	−74.4828	+	129.008i	−0.316948	+	0.548970i
$236$	75.2577	+	13.2700i	0.318889	+	0.0562287i
$237$	277.204	−	95.0000i	1.16964	−	0.400844i
$238$	−36.1846	−	13.1701i	−0.152036	−	0.0553366i
$239$	−300.307	+	52.9523i	−1.25652	+	0.221558i	−0.761980	−	0.647600i	$-0.775773\pi$
$239$	−300.307	+	52.9523i	−1.25652	+	0.221558i	−0.494535	+	0.869158i	$0.664662\pi$
$240$	−32.4251	−	19.5470i	−0.135105	−	0.0814457i
$241$	103.761	+	87.0654i	0.430542	+	0.361267i	0.832156	−	0.554542i	$-0.187106\pi$
$241$	103.761	+	87.0654i	0.430542	+	0.361267i	−0.401614	+	0.915809i	$0.631551\pi$
$242$			323.273i			1.33584i
$243$	101.098	+	220.971i	0.416041	+	0.909346i
$244$	110.096			0.451213
$245$	−95.1575	+	113.404i	−0.388398	+	0.462875i
$246$	−44.4363	+	73.7122i	−0.180635	+	0.299643i
$247$	5.49159	+	31.1443i	0.0222332	+	0.126090i
$248$	−25.3904	+	69.7595i	−0.102381	+	0.281288i
$249$	−122.756	−	358.194i	−0.492996	−	1.43853i
$250$	−31.0278	+	175.967i	−0.124111	+	0.703869i
$251$	218.202	+	125.979i	0.869331	+	0.501909i	0.867126	−	0.498089i	$-0.165965\pi$
$251$	218.202	+	125.979i	0.869331	+	0.501909i	0.00220530	+	0.999998i	$0.499298\pi$
$252$	−12.1196	−	22.9538i	−0.0480936	−	0.0910867i
$253$	−252.309	−	437.012i	−0.997268	−	1.72732i
$254$	19.7040	+	54.1362i	0.0775746	+	0.213135i
$255$	−166.758	−	64.2896i	−0.653951	−	0.252116i
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	208.414	+	248.378i	0.810948	+	0.966450i	0.999879	−	0.0155401i	$-0.00494676\pi$
$257$	208.414	+	248.378i	0.810948	+	0.966450i	−0.188931	+	0.981990i	$0.560502\pi$
$258$	91.4999	+	113.328i	0.354651	+	0.439257i
$259$	91.7695	−	33.4014i	0.354323	−	0.128963i
$260$	75.5724	−	43.6317i	0.290663	−	0.167814i
$261$	−236.094	−	50.8989i	−0.904575	−	0.195015i
$262$	34.9213	−	60.4854i	0.133287	−	0.230860i
$263$	−26.0438	−	4.59223i	−0.0990259	−	0.0174609i	0.123916	−	0.992293i	$-0.460455\pi$
$263$	−26.0438	−	4.59223i	−0.0990259	−	0.0174609i	−0.222942	+	0.974832i	$0.571566\pi$
$264$	−119.585	−	104.258i	−0.452974	−	0.394918i
$265$	145.471	+	52.9470i	0.548946	+	0.199800i
$266$	−4.59289	+	0.809851i	−0.0172665	+	0.00304455i
$267$	28.0125	−	15.4745i	0.104916	−	0.0579571i
$268$	190.528	+	159.872i	0.710924	+	0.596536i
$269$		−	499.973i		−	1.85864i	−0.369280	−	0.929318i	$-0.620396\pi$
$269$		−	499.973i		−	1.85864i	0.369280	−	0.929318i	$-0.379604\pi$
$270$	−54.2268	−	107.580i	−0.200840	−	0.398443i
$271$	−101.367			−0.374047			−0.187024	−	0.982355i	$-0.559884\pi$
$271$	−101.367			−0.374047			−0.187024	+	0.982355i	$0.559884\pi$
$272$	48.5477	−	57.8569i	0.178484	−	0.212709i
$273$	59.8155	+	1.13078i	0.219105	+	0.00414205i
$274$	33.1261	+	187.867i	0.120898	+	0.685647i
$275$	−96.2127	+	264.342i	−0.349864	+	0.961244i
$276$	158.913	+	31.1285i	0.575771	+	0.112785i
$277$	−9.93895	+	56.3666i	−0.0358807	+	0.203489i	−0.997478	−	0.0709742i	$-0.977389\pi$
$277$	−9.93895	+	56.3666i	−0.0358807	+	0.203489i	0.961597	+	0.274464i	$0.0885003\pi$
$278$	−97.4672	−	56.2727i	−0.350601	−	0.202420i
$279$	−186.564	+	144.891i	−0.668688	+	0.519323i
$280$	6.43442	+	11.1447i	0.0229801	+	0.0398027i
$281$	41.8819	+	115.069i	0.149046	+	0.409500i	0.991638	−	0.129053i	$-0.0411936\pi$
$281$	41.8819	+	115.069i	0.149046	+	0.409500i	−0.842592	+	0.538552i	$0.818971\pi$
$282$	−31.0492	−	197.892i	−0.110103	−	0.701745i
$283$	360.147	−	302.199i	1.27260	−	1.06784i	0.278384	−	0.960470i	$-0.410201\pi$
$283$	360.147	−	302.199i	1.27260	−	1.06784i	0.994219	−	0.107371i	$-0.0342432\pi$
$284$	−15.5376	−	18.5170i	−0.0547100	−	0.0652008i
$285$	−21.3842	+	3.35517i	−0.0750322	+	0.0117725i
$286$	343.612	−	125.065i	1.20144	−	0.437289i
$287$	25.3354	−	14.6274i	0.0882767	−	0.0509666i
$288$	50.4365	−	6.93941i	0.175127	−	0.0240952i
$289$	33.7597	−	58.4734i	0.116815	−	0.202330i
$290$	117.920	+	20.7925i	0.406621	+	0.0716982i
$291$	89.4943	−	456.873i	0.307541	−	1.57001i
$292$	−140.553	−	51.1570i	−0.481345	−	0.175195i
$293$	201.841	−	35.5901i	0.688879	−	0.121468i	0.181758	−	0.983343i	$-0.441821\pi$
$293$	201.841	−	35.5901i	0.688879	−	0.121468i	0.507120	+	0.861875i	$0.330710\pi$
$294$	3.76258	−	199.031i	0.0127979	−	0.676977i
$295$	−92.3500	−	77.4908i	−0.313051	−	0.262681i
$296$			191.547i			0.647120i
$297$	−145.497	−	483.405i	−0.489890	−	1.62763i
$298$	−177.635			−0.596090
$299$	−239.906	+	285.908i	−0.802360	+	0.956215i
$300$	−43.6503	−	79.0170i	−0.145501	−	0.263390i
$301$	−8.59691	−	48.7555i	−0.0285612	−	0.161978i
$302$	−54.7537	+	150.435i	−0.181304	+	0.498128i
$303$	−197.383	+	226.400i	−0.651428	+	0.747193i
$304$	1.58843	−	9.00845i	0.00522511	−	0.0296331i
$305$	−150.413	−	86.8409i	−0.493157	−	0.284724i
$306$	228.777	−	73.6019i	0.747637	−	0.240529i
$307$	−28.8883	−	50.0359i	−0.0940986	−	0.162984i	0.815133	−	0.579273i	$-0.196664\pi$
$307$	−28.8883	−	50.0359i	−0.0940986	−	0.162984i	−0.909232	+	0.416290i	$0.863330\pi$
$308$	18.4434	+	50.6729i	0.0598813	+	0.164522i
$309$	301.102	−	243.106i	0.974441	−	0.786752i
$310$	89.7129	−	75.2780i	0.289396	−	0.242832i
$311$	−11.1131	−	13.2441i	−0.0357336	−	0.0425856i	0.747882	−	0.663832i	$-0.231071\pi$
$311$	−11.1131	−	13.2441i	−0.0357336	−	0.0425856i	−0.783615	+	0.621246i	$0.786627\pi$
$312$	−42.2105	+	109.488i	−0.135290	+	0.350922i
$313$	−327.046	+	119.035i	−1.04488	+	0.380304i	−0.806727	−	0.590925i	$-0.798763\pi$
$313$	−327.046	+	119.035i	−1.04488	+	0.380304i	−0.238149	+	0.971229i	$0.576541\pi$
$314$	−63.2563	+	36.5210i	−0.201453	+	0.116309i
$315$	−1.54766	+	40.9191i	−0.00491321	+	0.129902i
$316$	97.6770	−	169.181i	0.309104	−	0.535384i
$317$	255.079	+	44.9772i	0.804664	+	0.141884i	0.560828	−	0.827932i	$-0.310483\pi$
$317$	255.079	+	44.9772i	0.804664	+	0.141884i	0.243836	+	0.969816i	$0.421594\pi$
$318$	−196.924	+	67.4874i	−0.619258	+	0.212225i
$319$	471.490	+	171.608i	1.47802	+	0.537957i
$320$	−24.8573	+	4.38302i	−0.0776792	+	0.0136969i
$321$	273.666	+	164.975i	0.852543	+	0.513942i
$322$	−42.1633	−	35.3792i	−0.130942	−	0.109873i
$323$		−	43.1798i		−	0.133683i
$324$	147.610	+	66.7479i	0.455586	+	0.206012i
$325$	208.061			0.640188
$326$	0.946467	−	1.12796i	0.00290327	−	0.00345998i
$327$	159.347	−	264.329i	0.487298	−	0.808345i
$328$	9.96395	+	56.5084i	0.0303779	+	0.172282i
$329$	−23.2866	+	63.9794i	−0.0707799	+	0.194466i
$330$	81.1406	+	236.763i	0.245881	+	0.717464i
$331$	−57.9326	+	328.552i	−0.175023	+	0.992605i	0.763094	+	0.646287i	$0.223679\pi$
$331$	−57.9326	+	328.552i	−0.175023	+	0.992605i	−0.938117	+	0.346318i	$0.887432\pi$
$332$	−218.611	−	126.215i	−0.658466	−	0.380166i
$333$	−324.482	+	515.947i	−0.974422	+	1.54939i
$334$	−165.079	−	285.925i	−0.494248	−	0.856063i
$335$	−134.196	−	368.700i	−0.400584	−	1.10060i
$336$	−16.1463	−	6.22483i	−0.0480544	−	0.0185263i
$337$	192.673	−	161.672i	0.571731	−	0.479739i	−0.310489	−	0.950577i	$-0.600493\pi$
$337$	192.673	−	161.672i	0.571731	−	0.479739i	0.882220	+	0.470838i	$0.156048\pi$
$338$	−20.2168	−	24.0935i	−0.0598131	−	0.0712825i
$339$	−170.228	−	210.839i	−0.502149	−	0.621943i
$340$	−111.962	+	40.7508i	−0.329300	+	0.119855i
$341$	424.993	−	245.370i	1.24631	−	0.719560i
$342$	19.5389	−	21.5741i	0.0571314	−	0.0630822i
$343$	−69.1612	+	119.791i	−0.201636	+	0.349244i
$344$	95.6285	+	16.8619i	0.277990	+	0.0490171i
$345$	−192.553	−	167.874i	−0.558125	−	0.486592i
$346$	−152.326	−	55.4423i	−0.440250	−	0.160238i
$347$	−532.939	+	93.9715i	−1.53585	+	0.270811i	−0.876638	−	0.481150i	$-0.840219\pi$
$347$	−532.939	+	93.9715i	−1.53585	+	0.270811i	−0.659208	+	0.751961i	$0.729108\pi$
$348$	−140.937	+	77.8562i	−0.404993	+	0.223725i
$349$	473.306	+	397.151i	1.35618	+	1.13797i	0.977142	+	0.212586i	$0.0681886\pi$
$349$	473.306	+	397.151i	1.35618	+	1.13797i	0.379036	+	0.925382i	$0.376256\pi$
$350$			30.6830i			0.0876658i
$351$	−299.170	+	223.408i	−0.852335	+	0.636491i
$352$	−105.768			−0.300477
$353$	−84.7293	+	100.976i	−0.240026	+	0.286052i	−0.872587	−	0.488458i	$-0.837559\pi$
$353$	−84.7293	+	100.976i	−0.240026	+	0.286052i	0.632561	+	0.774511i	$0.282004\pi$
$354$	162.080	+	3.06403i	0.457852	+	0.00865544i
$355$	6.62172	+	37.5537i	0.0186527	+	0.105785i
$356$	7.29700	−	20.0483i	0.0204972	−	0.0563156i
$357$	−80.1619	−	15.7025i	−0.224543	−	0.0439845i
$358$	−44.2656	+	251.043i	−0.123647	+	0.701237i
$359$	−114.766	−	66.2604i	−0.319683	−	0.184569i	0.331568	−	0.943431i	$-0.392422\pi$
$359$	−114.766	−	66.2604i	−0.319683	−	0.184569i	−0.651251	+	0.758862i	$0.725756\pi$
$360$	−74.3800	−	30.3025i	−0.206611	−	0.0841735i
$361$	177.885	+	308.106i	0.492757	+	0.853480i
$362$	−17.0533	−	46.8535i	−0.0471085	−	0.129429i
$363$	106.296	+	677.478i	0.292826	+	1.86633i
$364$	30.5530	−	25.6370i	0.0839369	−	0.0704314i
$365$	151.672	+	180.755i	0.415539	+	0.495220i
$366$	230.726	−	36.2008i	0.630399	−	0.0989093i
$367$	−74.9103	+	27.2651i	−0.204115	+	0.0742919i	−0.442055	−	0.896988i	$-0.645750\pi$
$367$	−74.9103	+	27.2651i	−0.204115	+	0.0742919i	0.237939	+	0.971280i	$0.423528\pi$
$368$	93.4920	−	53.9776i	0.254054	−	0.146678i
$369$	−68.8868	+	169.088i	−0.186685	+	0.458234i
$370$	151.088	−	261.692i	0.408346	−	0.707275i
$371$	69.6802	+	12.2865i	0.187817	+	0.0331172i
$372$	−30.2724	+	154.542i	−0.0813775	+	0.415437i
$373$	−526.327	−	191.567i	−1.41106	−	0.513586i	−0.479623	−	0.877475i	$-0.659226\pi$
$373$	−526.327	−	191.567i	−1.41106	−	0.513586i	−0.931442	+	0.363889i	$0.881449\pi$
$374$	−491.685	+	86.6973i	−1.31466	+	0.231811i
$375$	−7.16429	+	378.974i	−0.0191048	+	1.01060i
$376$	−102.299	−	85.8391i	−0.272072	−	0.228296i
$377$		−	371.105i		−	0.984364i
$378$	−32.9463	−	44.1189i	−0.0871595	−	0.116717i
$379$	−485.129			−1.28002			−0.640012	−	0.768365i	$-0.721071\pi$
$379$	−485.129			−1.28002			−0.640012	+	0.768365i	$0.721071\pi$
$380$	−9.27576	+	11.0544i	−0.0244099	+	0.0290906i
$381$	59.0938	+	106.973i	0.155102	+	0.280770i
$382$	5.24161	+	29.7267i	0.0137215	+	0.0778185i
$383$	60.5772	−	166.434i	0.158165	−	0.434555i	−0.835145	−	0.550029i	$-0.814617\pi$
$383$	60.5772	−	166.434i	0.158165	−	0.434555i	0.993310	+	0.115474i	$0.0368388\pi$
$384$	22.3045	−	25.5834i	0.0580846	−	0.0666234i
$385$	14.7721	−	83.7770i	0.0383692	−	0.217602i
$386$	−161.327	−	93.1422i	−0.417945	−	0.241301i
$387$	229.018	+	207.414i	0.591779	+	0.535953i
$388$	−155.185	−	268.789i	−0.399962	−	0.692755i
$389$	200.042	+	549.610i	0.514246	+	1.41288i	0.876773	+	0.480905i	$0.159692\pi$
$389$	200.042	+	549.610i	0.514246	+	1.41288i	−0.362527	+	0.931973i	$0.618086\pi$
$390$	144.029	−	116.287i	0.369305	−	0.298172i
$391$	390.373	−	327.562i	0.998396	−	0.837753i
$392$	−85.3051	−	101.663i	−0.217615	−	0.259343i
$393$	53.2956	−	138.241i	0.135612	−	0.351757i
$394$	−40.8640	+	14.8733i	−0.103716	+	0.0377494i
$395$	−266.892	+	154.090i	−0.675677	+	0.390102i
$396$	−284.894	−	179.171i	−0.719428	−	0.452453i
$397$	−167.855	+	290.734i	−0.422810	+	0.732328i	−0.996213	−	0.0869453i	$-0.972289\pi$
$397$	−167.855	+	290.734i	−0.422810	+	0.732328i	0.573403	+	0.819273i	$0.305623\pi$
$398$	341.754	+	60.2605i	0.858679	+	0.151408i
$399$	−9.35896	+	3.20739i	−0.0234560	+	0.00803856i
$400$	−56.5520	−	20.5832i	−0.141380	−	0.0514581i
$401$	656.528	−	115.764i	1.63723	−	0.288687i	0.722080	−	0.691810i	$-0.243186\pi$
$401$	656.528	−	115.764i	1.63723	−	0.288687i	0.915146	+	0.403123i	$0.132075\pi$
$402$	451.853	+	272.392i	1.12401	+	0.677593i
$403$	−278.045	−	233.308i	−0.689939	−	0.578928i
$404$			200.241i			0.495645i
$405$	−149.015	−	207.622i	−0.367939	−	0.512647i
$406$	54.7273			0.134796
$407$	813.912	−	969.983i	1.99978	−	2.38325i
$408$	82.7166	−	137.213i	0.202737	−	0.336306i
$409$	83.1381	+	471.500i	0.203272	+	1.15281i	0.900136	+	0.435608i	$0.143467\pi$
$409$	83.1381	+	471.500i	0.203272	+	1.15281i	−0.696865	+	0.717203i	$0.745422\pi$
$410$	30.9597	−	85.0610i	0.0755114	−	0.207466i
$411$	131.195	+	382.818i	0.319208	+	0.931431i
$412$	44.8004	−	254.076i	0.108739	−	0.616688i
$413$	−47.7179	−	27.5500i	−0.115540	−	0.0667069i
$414$	343.266	+	12.9832i	0.829145	+	0.0313603i
$415$	199.110	+	344.869i	0.479784	+	0.831011i
$416$	26.7557	+	73.5106i	0.0643165	+	0.176708i
$417$	−222.763	−	85.8813i	−0.534205	−	0.205950i
$418$	−46.3219	+	38.8687i	−0.110818	+	0.0929873i
$419$	−111.219	−	132.545i	−0.265438	−	0.316337i	0.616819	−	0.787105i	$-0.288421\pi$
$419$	−111.219	−	132.545i	−0.265438	−	0.316337i	−0.882257	+	0.470769i	$0.843977\pi$
$420$	17.1490	+	21.2401i	0.0408310	+	0.0505717i
$421$	−252.806	+	92.0139i	−0.600490	+	0.218560i	−0.624337	−	0.781155i	$-0.714631\pi$
$421$	−252.806	+	92.0139i	−0.600490	+	0.218560i	0.0238471	+	0.999716i	$0.492409\pi$
$422$	−56.6676	+	32.7171i	−0.134283	+	0.0775286i
$423$	−130.138	−	404.509i	−0.307656	−	0.956287i
$424$	−69.3891	+	120.185i	−0.163654	+	0.283456i
$425$	−279.766	−	49.3303i	−0.658273	−	0.116071i
$426$	−38.6506	−	33.6969i	−0.0907290	−	0.0791006i
$427$	−74.5948	−	27.1503i	−0.174695	−	0.0635838i
$428$	209.795	−	36.9925i	0.490175	−	0.0864310i
$429$	678.979	−	375.079i	1.58270	−	0.874311i
$430$	−117.347	−	98.4661i	−0.272901	−	0.228991i
$431$		−	457.490i		−	1.06146i	−0.847540	−	0.530731i	$-0.821918\pi$
$431$		−	457.490i		−	1.06146i	0.847540	−	0.530731i	$-0.178082\pi$
$432$	103.417	−	31.1269i	0.239392	−	0.0720530i
$433$	−541.733			−1.25112			−0.625558	−	0.780178i	$-0.715129\pi$
$433$	−541.733			−1.25112			−0.625558	+	0.780178i	$0.715129\pi$
$434$	34.4062	−	41.0037i	0.0792769	−	0.0944785i
$435$	253.960	+	4.80097i	0.583815	+	0.0110367i
$436$	−35.7303	−	202.637i	−0.0819503	−	0.464763i
$437$	21.1093	−	57.9974i	0.0483051	−	0.132717i
$438$	−311.375	−	60.9935i	−0.710902	−	0.139255i
$439$	48.5394	−	275.280i	0.110568	−	0.627062i	−0.878281	−	0.478144i	$-0.841310\pi$
$439$	48.5394	−	275.280i	0.110568	−	0.627062i	0.988849	−	0.148918i	$-0.0475792\pi$
$440$	144.500	+	83.4270i	0.328409	+	0.189607i
$441$	−57.5586	−	418.343i	−0.130518	−	0.948624i
$442$	184.636	+	319.798i	0.417728	+	0.723526i
$443$	80.1232	+	220.137i	0.180865	+	0.496923i	0.996683	−	0.0813867i	$-0.0259349\pi$
$443$	80.1232	+	220.137i	0.180865	+	0.496923i	−0.815818	+	0.578309i	$0.803713\pi$
$444$	62.9830	+	401.423i	0.141854	+	0.904105i
$445$	−25.7828	+	21.6343i	−0.0579388	+	0.0486165i
$446$	−51.7822	−	61.7116i	−0.116104	−	0.138367i
$447$	−372.266	+	58.4083i	−0.832809	+	0.130667i
$448$	−10.8407	+	3.94569i	−0.0241980	+	0.00880734i
$449$	−26.8989	+	15.5301i	−0.0599085	+	0.0345882i	−0.529655	−	0.848213i	$-0.677679\pi$
$449$	−26.8989	+	15.5301i	−0.0599085	+	0.0345882i	0.469747	+	0.882801i	$0.344345\pi$
$450$	−117.459	−	151.242i	−0.261020	−	0.336093i
$451$	189.655	−	328.493i	0.420522	−	0.728365i
$452$	−177.909	−	31.3702i	−0.393605	−	0.0694031i
$453$	−65.2817	+	333.267i	−0.144110	+	0.735688i
$454$	−115.168	−	41.9176i	−0.253673	−	0.0923296i
$455$	−61.9634	+	10.9258i	−0.136183	+	0.0240128i
$456$	0.366768	−	19.4011i	0.000804316	−	0.0425464i
$457$	−299.624	−	251.414i	−0.655632	−	0.550140i	0.253142	−	0.967429i	$-0.418536\pi$
$457$	−299.624	−	251.414i	−0.655632	−	0.550140i	−0.908774	+	0.417289i	$0.862980\pi$
$458$			183.571i			0.400810i
$459$	455.243	−	229.471i	0.991814	−	0.499936i
$460$	−170.305			−0.370228
$461$	−29.1528	+	34.7429i	−0.0632381	+	0.0753642i	−0.796736	−	0.604327i	$-0.793442\pi$
$461$	−29.1528	+	34.7429i	−0.0632381	+	0.0753642i	0.733498	+	0.679692i	$0.237886\pi$
$462$	55.3134	+	100.130i	0.119726	+	0.216731i
$463$	37.4481	+	212.379i	0.0808815	+	0.458702i	0.998170	+	0.0604774i	$0.0192623\pi$
$463$	37.4481	+	212.379i	0.0808815	+	0.458702i	−0.917288	+	0.398224i	$0.869627\pi$
$464$	−36.7130	+	100.868i	−0.0791228	+	0.217388i
$465$	163.257	−	187.257i	0.351091	−	0.402704i
$466$	−28.0541	+	159.102i	−0.0602018	+	0.341422i
$467$	336.385	+	194.212i	0.720312	+	0.415872i	0.814867	−	0.579648i	$-0.196810\pi$
$467$	336.385	+	194.212i	0.720312	+	0.415872i	−0.0945558	+	0.995520i	$0.530143\pi$
$468$	−52.4589	+	243.331i	−0.112092	+	0.519937i
$469$	−89.6654	−	155.305i	−0.191184	−	0.331141i
$470$	72.0531	+	197.964i	0.153304	+	0.421201i
$471$	−120.557	+	97.3359i	−0.255959	+	0.206658i
$472$	82.7882	−	69.4676i	0.175399	−	0.147177i
$473$	−412.607	−	491.726i	−0.872320	−	1.03959i
$474$	149.071	−	386.668i	0.314496	−	0.815755i
$475$	−32.3315	+	11.7677i	−0.0680664	+	0.0247742i
$476$	−47.1610	+	27.2284i	−0.0990778	+	0.0572026i
$477$	−390.500	+	206.183i	−0.818658	+	0.432250i
$478$	−215.625	+	373.474i	−0.451099	+	0.781326i
$479$	−301.385	−	53.1423i	−0.629196	−	0.110944i	−0.150048	−	0.988679i	$-0.547943\pi$
$479$	−301.385	−	53.1423i	−0.629196	−	0.110944i	−0.479147	+	0.877734i	$0.659054\pi$
$480$	−50.6519	+	17.3588i	−0.105525	+	0.0361642i
$481$	−880.048	−	320.311i	−1.82962	−	0.665928i
$482$	188.645	−	33.2632i	0.391379	−	0.0690107i
$483$	−99.9938	−	60.2797i	−0.207027	−	0.124803i
$484$	350.218	+	293.868i	0.723591	+	0.607165i
$485$			489.625i			1.00954i
$486$	331.291	+	91.3466i	0.681669	+	0.187956i
$487$	947.316			1.94521			0.972604	−	0.232469i	$-0.0746805\pi$
$487$	947.316			1.94521			0.972604	+	0.232469i	$0.0746805\pi$
$488$	100.082	−	119.272i	0.205085	−	0.244411i
$489$	1.61261	−	2.67504i	0.00329777	−	0.00547044i
$490$	36.3547	+	206.178i	0.0741933	+	0.420771i
$491$	49.4422	−	135.841i	0.100697	−	0.276663i	−0.879107	−	0.476625i	$-0.841860\pi$
$491$	49.4422	−	135.841i	0.100697	−	0.276663i	0.979804	+	0.199963i	$0.0640821\pi$
$492$	39.4619	+	115.147i	0.0802071	+	0.234039i
$493$	−87.9872	+	499.000i	−0.178473	+	1.01217i
$494$	38.7323	+	22.3621i	0.0784055	+	0.0452674i
$495$	247.895	+	469.501i	0.500799	+	0.948486i
$496$	52.4932	+	90.9208i	0.105833	+	0.183308i
$497$	5.96102	+	16.3778i	0.0119940	+	0.0329532i
$498$	−499.640	−	192.625i	−1.00329	−	0.386797i
$499$	636.655	−	534.217i	1.27586	−	1.07058i	0.282062	−	0.959396i	$-0.408982\pi$
$499$	636.655	−	534.217i	1.27586	−	1.07058i	0.993800	−	0.111179i	$-0.0354628\pi$
$500$	162.429	+	193.575i	0.324857	+	0.387150i
$501$	−439.968	−	544.928i	−0.878180	−	1.08768i
$502$	334.834	−	121.870i	0.666999	−	0.242768i
$503$	−252.425	+	145.738i	−0.501840	+	0.289737i	−0.729473	−	0.684010i	$-0.760235\pi$
$503$	−252.425	+	145.738i	−0.501840	+	0.289737i	0.227633	+	0.973747i	$0.426901\pi$
$504$	−35.8842	−	7.73618i	−0.0711989	−	0.0153496i
$505$	157.945	−	273.569i	0.312762	−	0.541720i
$506$	−702.796	−	123.922i	−1.38892	−	0.244905i
$507$	−50.2902	−	43.8447i	−0.0991918	−	0.0864788i
$508$	76.5601	+	27.8656i	0.150709	+	0.0548536i
$509$	50.9622	−	8.98602i	0.100122	−	0.0176543i	−0.123363	−	0.992362i	$-0.539368\pi$
$509$	50.9622	−	8.98602i	0.100122	−	0.0176543i	0.223485	+	0.974707i	$0.428257\pi$
$510$	−221.237	+	122.215i	−0.433799	+	0.239638i
$511$	82.6150	+	69.3222i	0.161673	+	0.135660i
$512$		−	22.6274i		−	0.0441942i
$513$	33.8536	−	51.6371i	0.0659913	−	0.100657i
$514$	458.536			0.892094
$515$	−261.615	+	311.780i	−0.507990	+	0.605399i
$516$	205.951	+	3.89340i	0.399130	+	0.00754534i
$517$	153.293	+	869.366i	0.296504	+	1.68156i
$518$	47.2367	−	129.782i	0.0911905	−	0.250544i
$519$	−337.458	−	66.1027i	−0.650208	−	0.127366i
$520$	21.4298	−	121.534i	0.0412111	−	0.233720i
$521$	230.062	+	132.827i	0.441578	+	0.254945i	0.704267	−	0.709935i	$-0.251276\pi$
$521$	230.062	+	132.827i	0.441578	+	0.254945i	−0.262689	+	0.964881i	$0.584609\pi$
$522$	−269.760	+	209.504i	−0.516782	+	0.401348i
$523$	−9.24084	−	16.0056i	−0.0176689	−	0.0306035i	0.857056	−	0.515224i	$-0.172291\pi$
$523$	−9.24084	−	16.0056i	−0.0176689	−	0.0306035i	−0.874725	+	0.484620i	$0.838958\pi$
$524$	−33.7821	−	92.8156i	−0.0644697	−	0.177129i
$525$	10.0889	+	64.3019i	0.0192170	+	0.122480i
$526$	−28.6498	+	24.0401i	−0.0544673	+	0.0457035i
$527$	318.553	+	379.637i	0.604465	+	0.720373i
$528$	−221.656	+	34.7777i	−0.419803	+	0.0658668i
$529$	187.371	−	68.1976i	0.354199	−	0.128918i
$530$	189.599	−	109.465i	0.357733	−	0.206537i
$531$	340.675	−	46.8724i	0.641572	−	0.0882720i
$532$	−3.29777	+	5.71190i	−0.00619881	+	0.0107367i
$533$	−276.285	−	48.7165i	−0.518358	−	0.0914005i
$534$	8.70006	−	44.4143i	0.0162923	−	0.0831728i
$535$	−315.800	−	114.942i	−0.590280	−	0.214845i
$536$	346.394	−	61.0786i	0.646257	−	0.113953i
$537$	−10.2209	+	540.661i	−0.0190333	+	1.00682i
$538$	−541.646	−	454.495i	−1.00678	−	0.844786i
$539$			877.286i			1.62762i
$540$	−165.841	−	39.0474i	−0.307112	−	0.0723099i
$541$	469.047			0.867000			0.433500	−	0.901154i	$-0.357278\pi$
$541$	469.047			0.867000			0.433500	+	0.901154i	$0.357278\pi$
$542$	−92.1464	+	109.816i	−0.170012	+	0.202612i
$543$	−51.1442	−	92.5827i	−0.0941882	−	0.170502i
$544$	−18.5476	−	105.188i	−0.0340948	−	0.193361i
$545$	−111.020	+	305.025i	−0.203707	+	0.559679i
$546$	55.5997	−	63.7733i	0.101831	−	0.116801i
$547$	172.475	−	978.152i	0.315310	−	1.78821i	−0.255166	−	0.966897i	$-0.582130\pi$
$547$	172.475	−	978.152i	0.315310	−	1.78821i	0.570476	−	0.821314i	$-0.306759\pi$
$548$	233.639	+	134.892i	0.426349	+	0.246152i
$549$	471.625	−	151.731i	0.859062	−	0.276377i
$550$	198.914	+	344.529i	0.361662	+	0.626417i
$551$	20.9893	+	57.6677i	0.0380931	+	0.104660i
$552$	178.181	−	143.861i	0.322792	−	0.260618i
$553$	−107.901	+	90.5401i	−0.195120	+	0.163725i
$554$	52.0299	+	62.0068i	0.0939167	+	0.111926i
$555$	230.585	−	598.102i	0.415468	−	1.07766i
$556$	−149.564	+	54.4370i	−0.269001	+	0.0979083i
$557$	−743.009	+	428.977i	−1.33395	+	0.770155i	−0.985902	−	0.167322i	$-0.946488\pi$
$557$	−743.009	+	428.977i	−1.33395	+	0.770155i	−0.348046	+	0.937477i	$0.613155\pi$
$558$	−12.6261	+	333.826i	−0.0226274	+	0.598254i
$559$	−237.383	+	411.160i	−0.424657	+	0.735527i
$560$	17.9228	+	3.16027i	0.0320050	+	0.00564335i
$561$	−1001.91	+	343.361i	−1.78593	+	0.612053i
$562$	162.733	+	59.2299i	0.289560	+	0.105391i
$563$	−367.498	+	64.7999i	−0.652750	+	0.115097i	−0.490210	−	0.871604i	$-0.663080\pi$
$563$	−367.498	+	64.7999i	−0.652750	+	0.115097i	−0.162540	+	0.986702i	$0.551969\pi$
$564$	−242.611	−	146.254i	−0.430162	−	0.259316i
$565$	218.315	+	183.188i	0.386399	+	0.324227i
$566$		−	664.876i		−	1.17469i
$567$	−83.5518	−	81.6261i	−0.147358	−	0.143961i
$568$	−34.1848			−0.0601844
$569$	−392.267	+	467.485i	−0.689396	+	0.821591i	−0.991283	−	0.131753i	$-0.957939\pi$
$569$	−392.267	+	467.485i	−0.689396	+	0.821591i	0.301886	+	0.953344i	$0.402384\pi$
$570$	−15.8042	+	26.2165i	−0.0277267	+	0.0459939i
$571$	−18.1196	−	102.761i	−0.0317331	−	0.179967i	0.964822	−	0.262905i	$-0.0846807\pi$
$571$	−18.1196	−	102.761i	−0.0317331	−	0.179967i	−0.996555	+	0.0829382i	$0.973570\pi$
$572$	176.868	−	485.941i	0.309210	−	0.849547i
$573$	20.7592	+	60.5741i	0.0362290	+	0.105714i
$574$	7.18427	−	40.7440i	0.0125162	−	0.0709826i
$575$	−351.655	−	203.028i	−0.611574	−	0.353092i
$576$	38.3310	−	60.9486i	0.0665468	−	0.105814i
$577$	−53.6060	−	92.8483i	−0.0929046	−	0.160916i	0.815828	−	0.578295i	$-0.196282\pi$
$577$	−53.6060	−	92.8483i	−0.0929046	−	0.160916i	−0.908732	+	0.417380i	$0.862949\pi$
$578$	−32.6584	−	89.7282i	−0.0565024	−	0.155239i
$579$	−368.716	−	142.150i	−0.636816	−	0.245510i
$580$	129.719	−	108.848i	0.223654	−	0.187668i
$581$	116.993	+	139.427i	0.201365	+	0.239977i
$582$	−413.600	−	512.269i	−0.710653	−	0.880188i
$583$	862.067	−	313.767i	1.47867	−	0.538193i
$584$	−183.189	+	105.764i	−0.313680	+	0.181103i
$585$	263.602	−	291.060i	0.450602	−	0.497538i
$586$	144.925	−	251.018i	0.247313	−	0.428358i
$587$	−272.582	−	48.0636i	−0.464365	−	0.0818801i	−0.0634293	−	0.997986i	$-0.520204\pi$
$587$	−272.582	−	48.0636i	−0.464365	−	0.0818801i	−0.400936	+	0.916106i	$0.631315\pi$
$588$	−212.200	−	185.003i	−0.360885	−	0.314631i
$589$	56.4023	+	20.5288i	0.0957595	+	0.0348536i
$590$	−167.899	+	29.6052i	−0.284575	+	0.0501783i
$591$	−80.7474	+	44.6062i	−0.136628	+	0.0754758i
$592$	207.513	+	174.124i	0.350529	+	0.294129i
$593$			44.7982i			0.0755451i	0.999286	+	0.0377725i	$0.0120262\pi$
$593$			44.7982i			0.0755451i	−0.999286	+	0.0377725i	$0.987974\pi$
$594$	−655.960	−	281.810i	−1.10431	−	0.474427i
$595$	85.9085			0.144384
$596$	−161.477	+	192.441i	−0.270934	+	0.322887i
$597$	736.023	+	13.9141i	1.23287	+	0.0233067i
$598$	91.6554	+	519.804i	0.153270	+	0.869237i
$599$	318.570	−	875.264i	0.531836	−	1.46121i	−0.325047	−	0.945698i	$-0.605380\pi$
$599$	318.570	−	875.264i	0.531836	−	1.46121i	0.856883	−	0.515511i	$-0.172398\pi$
$600$	−125.283	−	24.5410i	−0.208805	−	0.0409016i
$601$	59.0610	−	334.951i	0.0982712	−	0.557323i	−0.895425	−	0.445213i	$-0.853128\pi$
$601$	59.0610	−	334.951i	0.0982712	−	0.557323i	0.993696	−	0.112110i	$-0.0357610\pi$
$602$	−60.6342	−	35.0072i	−0.100721	−	0.0581515i
$603$	1036.51	+	422.273i	1.71891	+	0.700287i
$604$	113.200	+	196.068i	0.187417	+	0.324616i
$605$	−246.672	−	677.725i	−0.407722	−	1.12021i
$606$	65.8414	+	419.641i	0.108649	+	0.692477i
$607$	−857.856	+	719.827i	−1.41327	+	1.18588i	−0.458441	+	0.888725i	$0.651592\pi$
$607$	−857.856	+	719.827i	−1.41327	+	1.18588i	−0.954830	+	0.297151i	$0.903963\pi$
$608$	−8.31536	−	9.90986i	−0.0136766	−	0.0162991i
$609$	114.691	−	17.9950i	0.188327	−	0.0295484i
$610$	−230.810	+	84.0081i	−0.378378	+	0.137718i
$611$	565.448	−	326.461i	0.925446	−	0.534307i
$612$	128.231	−	314.753i	0.209527	−	0.514302i
$613$	503.975	−	872.910i	0.822144	−	1.42400i	−0.0819377	−	0.996637i	$-0.526111\pi$
$613$	503.975	−	872.910i	0.822144	−	1.42400i	0.904082	−	0.427359i	$-0.140556\pi$
$614$	−80.4670	−	14.1885i	−0.131054	−	0.0231083i
$615$	36.9126	−	188.441i	0.0600205	−	0.306408i
$616$	71.6623	+	26.0829i	0.116335	+	0.0423424i
$617$	811.213	−	143.039i	1.31477	−	0.231830i	0.528089	−	0.849189i	$-0.322909\pi$
$617$	811.213	−	143.039i	1.31477	−	0.231830i	0.786681	+	0.617359i	$0.211798\pi$
$618$	10.3444	−	547.193i	0.0167385	−	0.885425i
$619$	101.667	+	85.3084i	0.164243	+	0.137817i	0.721205	−	0.692722i	$-0.243589\pi$
$619$	101.667	+	85.3084i	0.164243	+	0.137817i	−0.556962	+	0.830538i	$0.688033\pi$
$620$		−	165.621i		−	0.267131i
$621$	723.646	−	85.6613i	1.16529	−	0.137941i
$622$	−24.4503			−0.0393092
$623$	−9.88807	+	11.7841i	−0.0158717	+	0.0189151i
$624$	80.2425	+	145.257i	0.128594	+	0.232784i
$625$	−3.90782	−	22.1623i	−0.00625251	−	0.0354598i
$626$	−168.341	+	462.513i	−0.268915	+	0.738839i
$627$	−84.2955	+	96.6876i	−0.134443	+	0.154207i
$628$	−17.9374	+	101.728i	−0.0285627	+	0.161987i
$629$	1107.40	+	639.356i	1.76057	+	1.01646i
$630$	42.9229	+	38.8738i	0.0681316	+	0.0617044i
$631$	−52.2617	−	90.5198i	−0.0828235	−	0.143455i	0.821638	−	0.570009i	$-0.193060\pi$
$631$	−52.2617	−	90.5198i	−0.0828235	−	0.143455i	−0.904462	+	0.426555i	$0.859727\pi$
$632$	−94.4907	−	259.611i	−0.149511	−	0.410777i
$633$	−108.000	+	87.1975i	−0.170615	+	0.137753i
$634$	280.602	−	235.453i	0.442591	−	0.371378i
$635$	−82.6166	−	98.4587i	−0.130105	−	0.155053i
$636$	−105.899	+	274.687i	−0.166508	+	0.431897i
$637$	609.730	−	221.923i	0.957190	−	0.348389i
$638$	614.514	−	354.790i	0.963189	−	0.556097i
$639$	−92.0792	−	57.9092i	−0.144099	−	0.0906247i
$640$	−17.8479	+	30.9135i	−0.0278874	+	0.0483024i
$641$	144.994	+	25.5664i	0.226200	+	0.0398852i	0.285599	−	0.958349i	$-0.407807\pi$
$641$	144.994	+	25.5664i	0.226200	+	0.0398852i	−0.0593990	+	0.998234i	$0.518918\pi$
$642$	427.500	−	146.507i	0.665887	−	0.228205i
$643$	−986.208	−	358.950i	−1.53376	−	0.558243i	−0.569221	−	0.822184i	$-0.692755\pi$
$643$	−986.208	−	358.950i	−1.53376	−	0.558243i	−0.964539	+	0.263941i	$0.914977\pi$
$644$	−76.6561	+	13.5165i	−0.119031	+	0.0209884i
$645$	−278.299	−	167.768i	−0.431472	−	0.260106i
$646$	−46.7788	−	39.2521i	−0.0724130	−	0.0607617i
$647$			828.962i			1.28124i	0.767858	+	0.640620i	$0.221323\pi$
$647$			828.962i			1.28124i	−0.767858	+	0.640620i	$0.778677\pi$
$648$	206.495	−	99.2369i	0.318665	−	0.153143i
$649$	−714.411			−1.10079
$650$	189.136	−	225.403i	0.290978	−	0.346774i
$651$	58.6219	−	97.2438i	0.0900490	−	0.149376i
$652$	−0.361596	−	2.05071i	−0.000554594	−	0.00314526i
$653$	−244.816	+	672.626i	−0.374910	+	1.03006i	0.598528	+	0.801102i	$0.295753\pi$
$653$	−244.816	+	672.626i	−0.374910	+	1.03006i	−0.973437	+	0.228953i	$0.926470\pi$
$654$	−141.509	−	412.913i	−0.216374	−	0.631366i
$655$	−27.0575	+	153.451i	−0.0413092	+	0.234276i
$656$	70.2760	+	40.5739i	0.107128	+	0.0618504i
$657$	−672.598	−	25.4393i	−1.02374	−	0.0387204i
$658$	48.1437	+	83.3873i	0.0731666	+	0.126728i
$659$	−77.5795	−	213.148i	−0.117723	−	0.323442i	0.866810	−	0.498638i	$-0.166166\pi$
$659$	−77.5795	−	213.148i	−0.117723	−	0.323442i	−0.984534	+	0.175196i	$0.943944\pi$
$660$	330.258	+	127.323i	0.500390	+	0.192914i
$661$	−494.893	+	415.264i	−0.748703	+	0.628237i	−0.935160	−	0.354227i	$-0.884744\pi$
$661$	−494.893	+	415.264i	−0.748703	+	0.628237i	0.186456	+	0.982463i	$0.440300\pi$
$662$	303.274	+	361.428i	0.458118	+	0.545964i
$663$	492.091	+	609.485i	0.742219	+	0.919284i
$664$	−335.461	+	122.098i	−0.505212	+	0.183882i
$665$	9.01081	−	5.20239i	0.0135501	−	0.00782315i
$666$	263.985	+	820.545i	0.396373	+	1.23205i
$667$	−362.128	+	627.223i	−0.542920	+	0.940365i
$668$	−459.820	−	81.0787i	−0.688353	−	0.121375i
$669$	−128.811	−	112.301i	−0.192542	−	0.167865i
$670$	−521.420	−	189.781i	−0.778239	−	0.283256i
$671$	−1013.61	+	178.727i	−1.51060	+	0.266359i
$672$	−21.4213	+	11.8335i	−0.0318769	+	0.0176093i
$673$	−322.666	−	270.749i	−0.479444	−	0.402301i	0.370781	−	0.928720i	$-0.379090\pi$
$673$	−322.666	−	270.749i	−0.479444	−	0.402301i	−0.850225	+	0.526419i	$0.823534\pi$
$674$		−	355.699i		−	0.527743i
$675$	−295.887	−	278.333i	−0.438350	−	0.412345i
$676$	−44.4796			−0.0657982
$677$	568.791	−	677.859i	0.840164	−	1.00127i	−0.159736	−	0.987160i	$-0.551064\pi$
$677$	568.791	−	677.859i	0.840164	−	1.00127i	0.999900	−	0.0141088i	$-0.00449111\pi$
$678$	−383.156	−	7.24336i	−0.565127	−	0.0106834i
$679$	38.8599	+	220.386i	0.0572311	+	0.324574i
$680$	−57.6304	+	158.338i	−0.0847505	+	0.232850i
$681$	−255.138	−	49.9775i	−0.374652	−	0.0733884i
$682$	120.514	−	683.467i	0.176706	−	1.00215i
$683$	−179.989	−	103.917i	−0.263527	−	0.152148i	0.362415	−	0.932017i	$-0.381952\pi$
$683$	−179.989	−	103.917i	−0.263527	−	0.152148i	−0.625943	+	0.779869i	$0.715286\pi$
$684$	−5.61069	−	40.7792i	−0.00820276	−	0.0596188i
$685$	−212.798	−	368.577i	−0.310654	−	0.538069i
$686$	66.9051	+	183.820i	0.0975293	+	0.267960i
$687$	60.3603	+	384.707i	0.0878607	+	0.559981i
$688$	105.197	−	88.2711i	0.152903	−	0.128301i
$689$	−436.147	−	519.780i	−0.633015	−	0.754398i
$690$	−356.905	+	55.9982i	−0.517253	+	0.0811568i
$691$	−688.491	+	250.590i	−0.996370	+	0.362649i	−0.788184	−	0.615440i	$-0.788978\pi$
$691$	−688.491	+	250.590i	−0.996370	+	0.362649i	−0.208186	+	0.978089i	$0.566756\pi$
$692$	−198.534	+	114.624i	−0.286899	+	0.165641i
$693$	148.843	+	191.653i	0.214781	+	0.276555i
$694$	−382.658	+	662.783i	−0.551380	+	0.955019i
$695$	247.273	+	43.6010i	0.355789	+	0.0627352i
$696$	−43.7721	+	223.459i	−0.0628910	+	0.321062i
$697$	359.951	+	131.012i	0.516429	+	0.187965i
$698$	860.507	−	151.731i	1.23282	−	0.217379i
$699$	−6.47766	+	342.653i	−0.00926704	+	0.490204i
$700$	33.2405	+	27.8921i	0.0474864	+	0.0398458i
$701$			176.592i			0.251915i	0.992036	+	0.125957i	$0.0402002\pi$
$701$			176.592i			0.251915i	−0.992036	+	0.125957i	$0.959800\pi$
$702$	−29.9274	+	527.193i	−0.0426316	+	0.750986i
$703$	154.871			0.220300
$704$	−96.1471	+	114.584i	−0.136573	+	0.162761i
$705$	216.093	+	391.178i	0.306515	+	0.554863i
$706$	32.3707	+	183.583i	0.0458508	+	0.260033i
$707$	49.3805	−	135.672i	0.0698451	−	0.191898i
$708$	150.656	−	172.804i	0.212791	−	0.244073i
$709$	−158.919	+	901.273i	−0.224145	+	1.27119i	0.640168	+	0.768235i	$0.278865\pi$
$709$	−158.919	+	901.273i	−0.224145	+	1.27119i	−0.864313	+	0.502954i	$0.832247\pi$
$710$	46.7032	+	26.9641i	0.0657791	+	0.0379776i
$711$	185.265	−	859.349i	0.260569	−	1.20865i
$712$	−15.0861	−	26.1299i	−0.0211884	−	0.0366993i
$713$	242.275	+	665.644i	0.339796	+	0.933583i
$714$	−89.8815	+	72.5693i	−0.125884	+	0.101638i
$715$	−624.935	+	524.383i	−0.874035	+	0.733403i
$716$	231.728	+	276.163i	0.323643	+	0.385702i
$717$	−329.079	+	853.582i	−0.458967	+	1.19049i
$718$	−176.110	+	64.0989i	−0.245279	+	0.0892742i
$719$	555.297	−	320.601i	0.772319	−	0.445898i	−0.0613824	−	0.998114i	$-0.519551\pi$
$719$	555.297	−	320.601i	0.772319	−	0.445898i	0.833701	+	0.552216i	$0.186218\pi$
$720$	−100.442	+	53.0334i	−0.139503	+	0.0736576i
$721$	−93.0107	+	161.099i	−0.129002	+	0.223439i
$722$	495.491	+	87.3685i	0.686276	+	0.121009i
$723$	384.402	−	131.738i	0.531676	−	0.182210i
$724$	−66.2608	−	24.1170i	−0.0915205	−	0.0333107i
$725$	397.614	−	70.1100i	0.548433	−	0.0967035i
$726$	830.573	+	500.698i	1.14404	+	0.689667i
$727$	140.649	+	118.019i	0.193465	+	0.162337i	0.734375	−	0.678744i	$-0.237475\pi$
$727$	140.649	+	118.019i	0.193465	+	0.162337i	−0.540910	+	0.841081i	$0.681920\pi$
$728$		−	56.4047i		−	0.0774790i
$729$	724.317	+	82.5011i	0.993576	+	0.113170i
$730$	333.697			0.457119
$731$	416.677	−	496.577i	0.570010	−	0.679312i
$732$	170.521	−	282.865i	0.232952	−	0.386428i
$733$	−224.357	−	1272.39i	−0.306081	−	1.73587i	−0.618373	−	0.785885i	$-0.712208\pi$
$733$	−224.357	−	1272.39i	−0.306081	−	1.73587i	0.312292	−	0.949986i	$-0.398903\pi$
$734$	−38.5587	+	105.939i	−0.0525323	+	0.144331i
$735$	143.982	+	420.129i	0.195893	+	0.571605i
$736$	26.5112	−	150.352i	0.0360206	−	0.204283i
$737$	−2013.65	−	1162.58i	−2.73222	−	1.57745i
$738$	120.561	+	228.337i	0.163362	+	0.309399i
$739$	−372.906	−	645.892i	−0.504609	−	0.874008i	−0.999986	−	0.00533011i	$-0.998303\pi$
$739$	−372.906	−	645.892i	−0.504609	−	0.874008i	0.495377	−	0.868678i	$-0.335030\pi$
$740$	−146.159	−	401.569i	−0.197513	−	0.542661i
$741$	88.5235	+	34.1282i	0.119465	+	0.0460570i
$742$	76.6526	−	64.3191i	0.103305	−	0.0866835i
$743$	−20.0884	−	23.9404i	−0.0270368	−	0.0322212i	0.752357	−	0.658756i	$-0.228917\pi$
$743$	−20.0884	−	23.9404i	−0.0270368	−	0.0322212i	−0.779393	+	0.626535i	$0.784473\pi$
$744$	139.905	+	173.281i	0.188044	+	0.232904i
$745$	372.402	−	135.543i	0.499868	−	0.181937i
$746$	−685.987	+	396.055i	−0.919553	+	0.530904i
$747$	−1110.42	−	239.393i	−1.48651	−	0.320472i
$748$	−353.037	+	611.478i	−0.471975	+	0.817484i
$749$	−151.268	−	26.6726i	−0.201959	−	0.0356109i
$750$	404.049	+	352.263i	0.538731	+	0.469684i
$751$	871.195	+	317.089i	1.16005	+	0.422222i	0.849114	−	0.528210i	$-0.177136\pi$
$751$	871.195	+	317.089i	1.16005	+	0.422222i	0.310932	+	0.950432i	$0.399359\pi$
$752$	−185.988	+	32.7946i	−0.247324	+	0.0436099i
$753$	661.633	−	365.497i	0.878663	−	0.485388i
$754$	−402.037	−	337.349i	−0.533205	−	0.447412i
$755$		−	357.158i		−	0.473057i
$756$	−77.7457	−	4.41343i	−0.102838	−	0.00583787i
$757$	358.777			0.473946			0.236973	−	0.971516i	$-0.423845\pi$
$757$	358.777			0.473946			0.236973	+	0.971516i	$0.423845\pi$
$758$	−441.001	+	525.565i	−0.581796	+	0.693357i
$759$	−1513.58	−	28.6135i	−1.99418	−	0.0376989i
$760$	3.54378	+	20.0978i	0.00466287	+	0.0264445i
$761$	402.928	−	1107.03i	0.529471	−	1.45471i	−0.330224	−	0.943903i	$-0.607124\pi$
$761$	402.928	−	1107.03i	0.529471	−	1.45471i	0.859695	−	0.510807i	$-0.170653\pi$
$762$	169.608	+	33.2236i	0.222583	+	0.0436005i
$763$	−25.7625	+	146.106i	−0.0337647	+	0.191489i
$764$	36.9692	+	21.3442i	0.0483891	+	0.0279374i
$765$	−423.457	+	328.870i	−0.553539	+	0.429895i
$766$	−125.240	−

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909039 - 1.08335i) q^{2} +(1.54884 - 2.56926i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-1.07911 + 2.96482i) q^{5} +(-1.37545 - 4.01349i) q^{6} +(-0.250410 + 1.42015i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.20220 - 7.95874i) q^{9} +O(q^{10})\)	\(q+(0.909039 - 1.08335i) q^{2} +(1.54884 - 2.56926i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-1.07911 + 2.96482i) q^{5} +(-1.37545 - 4.01349i) q^{6} +(-0.250410 + 1.42015i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-4.20220 - 7.95874i) q^{9} +(2.23099 + 3.86419i) q^{10} +(6.39485 + 17.5697i) q^{11} +(-5.59836 - 2.15832i) q^{12} +(10.5936 - 8.88908i) q^{13} +(1.31088 + 1.56225i) q^{14} +(5.94604 + 7.36454i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-16.3520 + 9.44086i) q^{17} +(-12.4421 - 2.68235i) q^{18} +(-1.14343 + 1.98047i) q^{19} +(6.21434 + 1.09575i) q^{20} +(3.26088 + 2.84294i) q^{21} +(24.8473 + 9.04368i) q^{22} +(-26.5788 + 4.68656i) q^{23} +(-7.42735 + 4.10299i) q^{24} +(11.5254 + 9.67096i) q^{25} -19.5571i q^{26} +(-26.9566 - 1.53026i) q^{27} +2.88411 q^{28} +(17.2495 - 20.5571i) q^{29} +(13.3836 + 0.253009i) q^{30} +(-4.55767 - 25.8478i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(55.0457 + 10.7826i) q^{33} +(-4.63689 + 26.2971i) q^{34} +(-3.94026 - 2.27491i) q^{35} +(-14.2162 + 11.0408i) q^{36} +(-33.8611 - 58.6492i) q^{37} +(1.10613 + 3.03906i) q^{38} +(-6.43059 - 40.9854i) q^{39} +(6.83616 - 5.73622i) q^{40} +(-13.0402 - 15.5407i) q^{41} +(6.04417 - 0.948327i) q^{42} +(-32.2609 + 11.7420i) q^{43} +(32.3847 - 18.6973i) q^{44} +(28.1309 - 3.87044i) q^{45} +(-19.0840 + 33.0544i) q^{46} +(46.4969 + 8.19866i) q^{47} +(-2.30677 + 11.7762i) q^{48} +(44.0908 + 16.0478i) q^{49} +(20.9541 - 3.69477i) q^{50} +(-1.07065 + 56.6350i) q^{51} +(-21.1872 - 17.7782i) q^{52} -49.0655i q^{53} +(-26.1624 + 27.8124i) q^{54} -58.9918 q^{55} +(2.62176 - 3.12450i) q^{56} +(3.31737 + 6.00520i) q^{57} +(-6.59012 - 37.3744i) q^{58} +(-13.0684 + 35.9050i) q^{59} +(12.4403 - 14.2691i) q^{60} +(-9.55898 + 54.2117i) q^{61} +(-32.1454 - 18.5591i) q^{62} +(12.3548 - 3.97479i) q^{63} +(4.00000 + 6.92820i) q^{64} +(14.9229 + 41.0004i) q^{65} +(61.7201 - 49.8320i) q^{66} +(-95.2638 + 79.9358i) q^{67} +(24.2739 + 28.9285i) q^{68} +(-29.1253 + 75.5466i) q^{69} +(-6.04638 + 2.20070i) q^{70} +(10.4669 - 6.04307i) q^{71} +(-0.962114 + 25.4377i) q^{72} +(37.3933 - 64.7671i) q^{73} +(-94.3187 - 16.6309i) q^{74} +(42.6982 - 14.6330i) q^{75} +(4.29788 + 1.56430i) q^{76} +(-26.5529 + 4.68199i) q^{77} +(-50.2472 - 30.2908i) q^{78} +(74.8249 + 62.7855i) q^{79} -12.6204i q^{80} +(-45.6831 + 66.8884i) q^{81} -28.6900 q^{82} +(81.1294 - 96.6863i) q^{83} +(4.46701 - 7.41002i) q^{84} +(-10.3449 - 58.6687i) q^{85} +(-16.6057 + 45.6238i) q^{86} +(-26.0999 - 76.1580i) q^{87} +(9.18320 - 52.0805i) q^{88} +(9.23832 + 5.33375i) q^{89} +(21.3790 - 33.9940i) q^{90} +(9.97104 + 17.2703i) q^{91} +(18.4614 + 50.7224i) q^{92} +(-73.4689 - 28.3243i) q^{93} +(51.1495 - 42.9196i) q^{94} +(-4.63788 - 5.52721i) q^{95} +(10.6608 + 13.2041i) q^{96} +(145.826 - 53.0765i) q^{97} +(57.4656 - 33.1778i) q^{98} +(112.960 - 124.726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9}+O(q^{10}) \) 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9	\( 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31} + 324 q^{33} - 72 q^{34} + 486 q^{35} + 168 q^{36} + 180 q^{38} + 102 q^{39} - 90 q^{41} + 48 q^{42} + 90 q^{43} - 378 q^{45} - 378 q^{47} - 24 q^{48} + 72 q^{49} - 54 q^{51} - 36 q^{54} - 72 q^{56} + 72 q^{57} + 252 q^{59} + 36 q^{60} - 144 q^{61} + 318 q^{63} + 144 q^{64} + 18 q^{65} - 432 q^{66} - 594 q^{67} - 180 q^{68} - 522 q^{69} - 360 q^{70} - 648 q^{71} - 192 q^{72} + 126 q^{73} - 504 q^{74} - 438 q^{75} - 72 q^{76} - 342 q^{77} - 288 q^{78} - 72 q^{79} + 324 q^{81} + 594 q^{83} + 216 q^{84} + 360 q^{85} + 540 q^{86} + 1062 q^{87} + 144 q^{88} + 648 q^{89} + 720 q^{90} - 198 q^{91} + 396 q^{92} + 462 q^{93} + 504 q^{94} + 252 q^{95} + 96 q^{96} + 702 q^{97} + 648 q^{98} + 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Introduction

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