LMFDB - Embedded newform 54.3.f.a.23.1

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			23.1
Character	$\chi$	$=$	54.23
Dual form			54.3.f.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483690 + 1.32893i) q^{2} +(-2.93655 - 0.613727i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-7.71206 - 1.35984i) q^{5} +(2.23598 - 3.60561i) q^{6} +(-0.690206 + 0.579152i) q^{7} +(2.44949 - 1.41421i) q^{8} +(8.24668 + 3.60448i) q^{9} +O(q^{10})$	\(q+(-0.483690 + 1.32893i) q^{2} +(-2.93655 - 0.613727i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-7.71206 - 1.35984i) q^{5} +(2.23598 - 3.60561i) q^{6} +(-0.690206 + 0.579152i) q^{7} +(2.44949 - 1.41421i) q^{8} +(8.24668 + 3.60448i) q^{9} +(5.53738 - 9.59102i) q^{10} +(-15.2420 + 2.68757i) q^{11} +(3.71007 + 4.71544i) q^{12} +(-0.854187 + 0.310899i) q^{13} +(-0.435804 - 1.19736i) q^{14} +(21.8123 + 8.72635i) q^{15} +(0.694593 + 3.93923i) q^{16} +(10.6672 + 6.15869i) q^{17} +(-8.77892 + 9.21578i) q^{18} +(-5.40619 - 9.36379i) q^{19} +(10.0674 + 11.9978i) q^{20} +(2.38227 - 1.27711i) q^{21} +(3.80080 - 21.5554i) q^{22} +(-21.0966 + 25.1419i) q^{23} +(-8.06100 + 2.64959i) q^{24} +(34.1344 + 12.4239i) q^{25} -1.28553i q^{26} +(-22.0046 - 15.6460i) q^{27} +1.80200 q^{28} +(19.3495 - 53.1622i) q^{29} +(-22.1471 + 24.7661i) q^{30} +(-37.9518 - 31.8453i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(46.4083 + 1.46222i) q^{33} +(-13.3440 + 11.1970i) q^{34} +(6.11047 - 3.52788i) q^{35} +(-8.00081 - 16.1241i) q^{36} +(-17.4417 + 30.2099i) q^{37} +(15.0587 - 2.65526i) q^{38} +(2.69917 - 0.388733i) q^{39} +(-20.8137 + 7.57558i) q^{40} +(-12.2490 - 33.6538i) q^{41} +(0.544909 + 3.78358i) q^{42} +(7.20864 + 40.8822i) q^{43} +(26.8072 + 15.4771i) q^{44} +(-58.6974 - 39.0122i) q^{45} +(-23.2075 - 40.1966i) q^{46} +(-15.9152 - 18.9670i) q^{47} +(0.377904 - 11.9940i) q^{48} +(-8.36779 + 47.4561i) q^{49} +(-33.0209 + 39.3528i) q^{50} +(-27.5449 - 24.6320i) q^{51} +(1.70837 + 0.621797i) q^{52} +50.3340i q^{53} +(31.4357 - 21.6747i) q^{54} +121.202 q^{55} +(-0.871609 + 2.39472i) q^{56} +(10.1287 + 30.8152i) q^{57} +(61.2895 + 51.4280i) q^{58} +(65.7126 + 11.5869i) q^{59} +(-22.2000 - 41.4109i) q^{60} +(-18.7893 + 15.7661i) q^{61} +(60.6770 - 35.0319i) q^{62} +(-7.77945 + 2.28824i) q^{63} +(4.00000 - 6.92820i) q^{64} +(7.01032 - 1.23611i) q^{65} +(-24.3904 + 60.9660i) q^{66} +(-61.2882 + 22.3071i) q^{67} +(-8.42558 - 23.1491i) q^{68} +(77.3814 - 60.8830i) q^{69} +(1.73272 + 9.82676i) q^{70} +(24.4496 + 14.1160i) q^{71} +(25.2977 - 2.83342i) q^{72} +(-10.7760 - 18.6646i) q^{73} +(-31.7104 - 37.7910i) q^{74} +(-92.6126 - 57.4327i) q^{75} +(-3.75510 + 21.2962i) q^{76} +(8.96360 - 10.6824i) q^{77} +(-0.788964 + 3.77503i) q^{78} +(-27.2240 - 9.90872i) q^{79} -31.3241i q^{80} +(55.0154 + 59.4500i) q^{81} +50.6481 q^{82} +(-0.0509121 + 0.139880i) q^{83} +(-5.29167 - 1.10594i) q^{84} +(-73.8910 - 62.0019i) q^{85} +(-57.8162 - 10.1946i) q^{86} +(-89.4477 + 144.238i) q^{87} +(-33.5343 + 28.1386i) q^{88} +(-79.3008 + 45.7843i) q^{89} +(80.2356 - 59.1347i) q^{90} +(0.409508 - 0.709288i) q^{91} +(64.6436 - 11.3984i) q^{92} +(91.9031 + 116.807i) q^{93} +(32.9038 - 11.9760i) q^{94} +(28.9595 + 79.5657i) q^{95} +(15.7564 + 6.30360i) q^{96} +(-17.4501 - 98.9646i) q^{97} +(-59.0182 - 34.0742i) q^{98} +(-135.383 - 32.7759i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$3$	−2.93655	−	0.613727i	−0.978851	−	0.204576i
$3$	−2.93655	−	0.613727i	−0.978851	−	0.204576i
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	−7.71206	−	1.35984i	−1.54241	−	0.271969i	−0.663216	−	0.748428i	$-0.730809\pi$
$5$	−7.71206	−	1.35984i	−1.54241	−	0.271969i	−0.879197	+	0.476459i	$0.841920\pi$
$6$	2.23598	−	3.60561i	0.372663	−	0.600935i
$7$	−0.690206	+	0.579152i	−0.0986009	+	0.0827360i	−0.690756	−	0.723088i	$-0.742722\pi$
$7$	−0.690206	+	0.579152i	−0.0986009	+	0.0827360i	0.592155	+	0.805824i	$0.298277\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$	8.24668	+	3.60448i	0.916298	+	0.400498i
$10$	5.53738	−	9.59102i	0.553738	−	0.959102i
$11$	−15.2420	+	2.68757i	−1.38564	+	0.244325i	−0.816228	−	0.577730i	$-0.803938\pi$
$11$	−15.2420	+	2.68757i	−1.38564	+	0.244325i	−0.569408	+	0.822055i	$0.692827\pi$
$12$	3.71007	+	4.71544i	0.309172	+	0.392954i
$13$	−0.854187	+	0.310899i	−0.0657067	+	0.0239153i	−0.374664	−	0.927160i	$-0.622242\pi$
$13$	−0.854187	+	0.310899i	−0.0657067	+	0.0239153i	0.308958	+	0.951076i	$0.400020\pi$
$14$	−0.435804	−	1.19736i	−0.0311289	−	0.0855259i
$15$	21.8123	+	8.72635i	1.45415	+	0.581757i
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	10.6672	+	6.15869i	0.627480	+	0.362276i	0.779776	−	0.626059i	$-0.215333\pi$
$17$	10.6672	+	6.15869i	0.627480	+	0.362276i	−0.152295	+	0.988335i	$0.548666\pi$
$18$	−8.77892	+	9.21578i	−0.487718	+	0.511988i
$19$	−5.40619	−	9.36379i	−0.284536	−	0.492831i	0.687960	−	0.725748i	$-0.258506\pi$
$19$	−5.40619	−	9.36379i	−0.284536	−	0.492831i	−0.972497	+	0.232917i	$0.925173\pi$
$20$	10.0674	+	11.9978i	0.503369	+	0.599892i
$21$	2.38227	−	1.27711i	0.113441	−	0.0608148i
$22$	3.80080	−	21.5554i	0.172764	−	0.979792i
$23$	−21.0966	+	25.1419i	−0.917241	+	1.09313i	0.0781224	+	0.996944i	$0.475108\pi$
$23$	−21.0966	+	25.1419i	−0.917241	+	1.09313i	−0.995364	+	0.0961819i	$0.969337\pi$
$24$	−8.06100	+	2.64959i	−0.335875	+	0.110400i
$25$	34.1344	+	12.4239i	1.36538	+	0.496956i
$26$		−	1.28553i		−	0.0494435i
$27$	−22.0046	−	15.6460i	−0.814987	−	0.579480i
$28$	1.80200			0.0643571
$29$	19.3495	−	53.1622i	0.667222	−	1.83318i	0.126521	−	0.991964i	$-0.459619\pi$
$29$	19.3495	−	53.1622i	0.667222	−	1.83318i	0.540701	−	0.841215i	$-0.318159\pi$
$30$	−22.1471	+	24.7661i	−0.738235	+	0.825536i
$31$	−37.9518	−	31.8453i	−1.22425	−	1.02727i	−0.998591	−	0.0530624i	$-0.983102\pi$
$31$	−37.9518	−	31.8453i	−1.22425	−	1.02727i	−0.225660	−	0.974206i	$-0.572454\pi$
$32$	−5.57091	−	0.982302i	−0.174091	−	0.0306970i
$33$	46.4083	+	1.46222i	1.40631	+	0.0443096i
$34$	−13.3440	+	11.1970i	−0.392472	+	0.329323i
$35$	6.11047	−	3.52788i	0.174585	−	0.100797i
$36$	−8.00081	−	16.1241i	−0.222245	−	0.447892i
$37$	−17.4417	+	30.2099i	−0.471398	+	0.816485i	−0.999465	−	0.0327181i	$-0.989584\pi$
$37$	−17.4417	+	30.2099i	−0.471398	+	0.816485i	0.528067	+	0.849203i	$0.322917\pi$
$38$	15.0587	−	2.65526i	0.396282	−	0.0698751i
$39$	2.69917	−	0.388733i	0.0692095	−	0.00996751i
$40$	−20.8137	+	7.57558i	−0.520343	+	0.189389i
$41$	−12.2490	−	33.6538i	−0.298756	−	0.820824i	−0.994709	−	0.102737i	$-0.967240\pi$
$41$	−12.2490	−	33.6538i	−0.298756	−	0.820824i	0.695953	−	0.718087i	$-0.254982\pi$
$42$	0.544909	+	3.78358i	0.0129740	+	0.0900853i
$43$	7.20864	+	40.8822i	0.167643	+	0.950750i	0.946298	+	0.323297i	$0.104791\pi$
$43$	7.20864	+	40.8822i	0.167643	+	0.950750i	−0.778655	+	0.627453i	$0.784098\pi$
$44$	26.8072	+	15.4771i	0.609254	+	0.351753i
$45$	−58.6974	−	39.0122i	−1.30439	−	0.866938i
$46$	−23.2075	−	40.1966i	−0.504512	−	0.873840i
$47$	−15.9152	−	18.9670i	−0.338622	−	0.403554i	0.569682	−	0.821865i	$-0.307067\pi$
$47$	−15.9152	−	18.9670i	−0.338622	−	0.403554i	−0.908304	+	0.418311i	$0.862622\pi$
$48$	0.377904	−	11.9940i	0.00787300	−	0.249876i
$49$	−8.36779	+	47.4561i	−0.170771	+	0.968492i
$50$	−33.0209	+	39.3528i	−0.660418	+	0.787056i
$51$	−27.5449	−	24.6320i	−0.540097	−	0.482981i
$52$	1.70837	+	0.621797i	0.0328533	+	0.0119576i
$53$			50.3340i			0.949699i	0.880067	+	0.474850i	$0.157498\pi$
$53$			50.3340i			0.949699i	−0.880067	+	0.474850i	$0.842502\pi$
$54$	31.4357	−	21.6747i	0.582143	−	0.401384i
$55$	121.202			2.20367
$56$	−0.871609	+	2.39472i	−0.0155644	+	0.0427629i
$57$	10.1287	+	30.8152i	0.177697	+	0.540617i
$58$	61.2895	+	51.4280i	1.05672	+	0.886689i
$59$	65.7126	+	11.5869i	1.11377	+	0.196388i	0.700105	−	0.714040i	$-0.253137\pi$
$59$	65.7126	+	11.5869i	1.11377	+	0.196388i	0.413667	+	0.910428i	$0.364248\pi$
$60$	−22.2000	−	41.4109i	−0.370000	−	0.690182i
$61$	−18.7893	+	15.7661i	−0.308021	+	0.258460i	−0.783673	−	0.621173i	$-0.786656\pi$
$61$	−18.7893	+	15.7661i	−0.308021	+	0.258460i	0.475653	+	0.879633i	$0.342212\pi$
$62$	60.6770	−	35.0319i	0.978661	−	0.565030i
$63$	−7.77945	+	2.28824i	−0.123483	+	0.0363213i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	7.01032	−	1.23611i	0.107851	−	0.0190170i
$66$	−24.3904	+	60.9660i	−0.369551	+	0.923727i
$67$	−61.2882	+	22.3071i	−0.914750	+	0.332942i	−0.756148	−	0.654401i	$-0.772921\pi$
$67$	−61.2882	+	22.3071i	−0.914750	+	0.332942i	−0.158602	+	0.987343i	$0.550699\pi$
$68$	−8.42558	−	23.1491i	−0.123906	−	0.340428i
$69$	77.3814	−	60.8830i	1.12147	−	0.882362i
$70$	1.73272	+	9.82676i	0.0247532	+	0.140382i
$71$	24.4496	+	14.1160i	0.344361	+	0.198817i	0.662199	−	0.749328i	$-0.269623\pi$
$71$	24.4496	+	14.1160i	0.344361	+	0.198817i	−0.317838	+	0.948145i	$0.602957\pi$
$72$	25.2977	−	2.83342i	0.351356	−	0.0393531i
$73$	−10.7760	−	18.6646i	−0.147617	−	0.255680i	0.782729	−	0.622362i	$-0.213827\pi$
$73$	−10.7760	−	18.6646i	−0.147617	−	0.255680i	−0.930346	+	0.366682i	$0.880494\pi$
$74$	−31.7104	−	37.7910i	−0.428519	−	0.510689i
$75$	−92.6126	−	57.4327i	−1.23483	−	0.765769i
$76$	−3.75510	+	21.2962i	−0.0494092	+	0.280213i
$77$	8.96360	−	10.6824i	0.116410	−	0.138732i
$78$	−0.788964	+	3.77503i	−0.0101149	+	0.0483978i
$79$	−27.2240	−	9.90872i	−0.344608	−	0.125427i	0.163918	−	0.986474i	$-0.447587\pi$
$79$	−27.2240	−	9.90872i	−0.344608	−	0.125427i	−0.508525	+	0.861047i	$0.669809\pi$
$80$		−	31.3241i		−	0.391552i
$81$	55.0154	+	59.4500i	0.679203	+	0.733951i
$82$	50.6481			0.617660
$83$	−0.0509121	+	0.139880i	−0.000613399	+	0.00168530i	−0.939999	−	0.341177i	$-0.889174\pi$
$83$	−0.0509121	+	0.139880i	−0.000613399	+	0.00168530i	0.939386	+	0.342863i	$0.111397\pi$
$84$	−5.29167	−	1.10594i	−0.0629960	−	0.0131659i
$85$	−73.8910	−	62.0019i	−0.869306	−	0.729434i
$86$	−57.8162	−	10.1946i	−0.672282	−	0.118541i
$87$	−89.4477	+	144.238i	−1.02813	+	1.65791i
$88$	−33.5343	+	28.1386i	−0.381071	+	0.319757i
$89$	−79.3008	+	45.7843i	−0.891020	+	0.514431i	−0.874276	−	0.485429i	$-0.838663\pi$
$89$	−79.3008	+	45.7843i	−0.891020	+	0.514431i	−0.0167439	+	0.999860i	$0.505330\pi$
$90$	80.2356	−	59.1347i	0.891507	−	0.657052i
$91$	0.409508	−	0.709288i	0.00450008	−	0.00779437i
$92$	64.6436	−	11.3984i	0.702648	−	0.123896i
$93$	91.9031	+	116.807i	0.988205	+	1.25599i
$94$	32.9038	−	11.9760i	0.350041	−	0.127404i
$95$	28.9595	+	79.5657i	0.304837	+	0.837534i
$96$	15.7564	+	6.30360i	0.164129	+	0.0656625i
$97$	−17.4501	−	98.9646i	−0.179898	−	1.02025i	−0.932337	−	0.361591i	$-0.882234\pi$
$97$	−17.4501	−	98.9646i	−0.179898	−	1.02025i	0.752439	−	0.658662i	$-0.228877\pi$
$98$	−59.0182	−	34.0742i	−0.602227	−	0.347696i
$99$	−135.383	−	32.7759i	−1.36751	−	0.331070i
$100$	−36.3251	−	62.9169i	−0.363251	−	0.629169i
$101$	−67.8785	−	80.8944i	−0.672064	−	0.800935i	0.316999	−	0.948426i	$-0.397325\pi$
$101$	−67.8785	−	80.8944i	−0.672064	−	0.800935i	−0.989063	+	0.147491i	$0.952880\pi$
$102$	46.0574	−	24.6909i	0.451543	−	0.242068i
$103$	15.1042	−	85.6604i	0.146643	−	0.831654i	−0.819390	−	0.573236i	$-0.805688\pi$
$103$	15.1042	−	85.6604i	0.146643	−	0.831654i	0.966033	−	0.258418i	$-0.0832011\pi$
$104$	−1.65265	+	1.96955i	−0.0158908	+	0.0189379i
$105$	−20.1089	+	6.60965i	−0.191513	+	0.0629490i
$106$	−66.8902	−	24.3461i	−0.631040	−	0.229680i
$107$			24.5062i			0.229030i	0.993422	+	0.114515i	$0.0365313\pi$
$107$			24.5062i			0.229030i	−0.993422	+	0.114515i	$0.963469\pi$
$108$	13.5990	+	52.2596i	0.125917	+	0.483885i
$109$	−33.5716			−0.307996			−0.153998	−	0.988071i	$-0.549215\pi$
$109$	−33.5716			−0.307996			−0.153998	+	0.988071i	$0.549215\pi$
$110$	−58.6241	+	161.068i	−0.532946	+	1.46426i
$111$	69.7591	−	78.0086i	0.628461	−	0.702780i
$112$	−2.76082	−	2.31661i	−0.0246502	−	0.0206840i
$113$	120.158	+	21.1870i	1.06334	+	0.187496i	0.677839	−	0.735211i	$-0.262917\pi$
$113$	120.158	+	21.1870i	1.06334	+	0.187496i	0.385503	+	0.922707i	$0.374028\pi$
$114$	−45.8503	−	1.44463i	−0.402195	−	0.0126722i
$115$	196.887	−	165.208i	1.71206	−	1.43659i
$116$	−97.9891	+	56.5740i	−0.844733	+	0.487707i
$117$	−8.16484	−	0.515020i	−0.0697849	−	0.00440188i
$118$	−47.1826	+	81.7227i	−0.399853	+	0.692565i
$119$	−10.9294	+	1.92714i	−0.0918433	+	0.0161945i
$120$	65.7699	−	9.47214i	0.548083	−	0.0789345i
$121$	111.392	−	40.5435i	0.920598	−	0.335070i
$122$	−11.8638	−	32.5954i	−0.0972440	−	0.267176i
$123$	15.3155	+	106.344i	0.124517	+	0.864583i
$124$	17.2059	+	97.5797i	0.138758	+	0.786933i
$125$	−76.8053	−	44.3435i	−0.614442	−	0.354748i
$126$	0.721933	−	11.4451i	0.00572963	−	0.0908342i
$127$	−52.2314	−	90.4674i	−0.411271	−	0.712342i	0.583758	−	0.811927i	$-0.301582\pi$
$127$	−52.2314	−	90.4674i	−0.411271	−	0.712342i	−0.995029	+	0.0995859i	$0.968248\pi$
$128$	7.27231	+	8.66680i	0.0568149	+	0.0677094i
$129$	3.92197	−	124.477i	0.0304029	−	0.964938i
$130$	−1.74812	+	9.91409i	−0.0134471	+	0.0762622i
$131$	−0.587532	+	0.700193i	−0.00448497	+	0.00534498i	−0.768282	−	0.640111i	$-0.778888\pi$
$131$	−0.587532	+	0.700193i	−0.00448497	+	0.00534498i	0.763797	+	0.645456i	$0.223333\pi$
$132$	−69.2219	−	61.9016i	−0.524408	−	0.468952i
$133$	9.15444	+	3.33194i	0.0688304	+	0.0250522i
$134$		−	92.2372i		−	0.688337i
$135$	148.425	+	150.585i	1.09944	+	1.11545i
$136$	34.8388			0.256168
$137$	4.80632	−	13.2053i	0.0350826	−	0.0963887i	−0.920915	−	0.389764i	$-0.872556\pi$
$137$	4.80632	−	13.2053i	0.0350826	−	0.0963887i	0.955997	+	0.293376i	$0.0947787\pi$
$138$	43.4804	+	132.283i	0.315075	+	0.958569i
$139$	142.580	+	119.639i	1.02576	+	0.860714i	0.990340	−	0.138659i	$-0.0442792\pi$
$139$	142.580	+	119.639i	1.02576	+	0.860714i	0.0354184	+	0.999373i	$0.488724\pi$
$140$	−13.8971	−	2.45044i	−0.0992653	−	0.0175031i
$141$	35.0953	+	65.4653i	0.248903	+	0.464293i
$142$	−30.5851	+	25.6640i	−0.215388	+	0.180732i
$143$	12.1839	−	7.03440i	0.0852024	−	0.0491916i
$144$	−8.47080	+	34.9892i	−0.0588250	+	0.242981i
$145$	−221.516	+	383.678i	−1.52770	+	2.64605i
$146$	30.0162	−	5.29267i	0.205590	−	0.0362511i
$147$	53.6975	−	134.222i	0.365289	−	0.913074i
$148$	65.5594	−	23.8617i	0.442969	−	0.161227i
$149$	−43.3633	−	119.140i	−0.291029	−	0.799595i	−0.995917	−	0.0902764i	$-0.971225\pi$
$149$	−43.3633	−	119.140i	−0.291029	−	0.799595i	0.704888	−	0.709319i	$-0.250997\pi$
$150$	121.120	−	95.2957i	0.807463	−	0.635305i
$151$	−23.8651	−	135.346i	−0.158047	−	0.896331i	−0.955947	−	0.293540i	$-0.905167\pi$
$151$	−23.8651	−	135.346i	−0.158047	−	0.896331i	0.797899	−	0.602791i	$-0.205945\pi$
$152$	−26.4848	−	15.2910i	−0.174242	−	0.100599i
$153$	65.7698	+	89.2383i	0.429868	+	0.583257i
$154$	9.86052	+	17.0789i	0.0640294	+	0.110902i
$155$	249.382	+	297.202i	1.60891	+	1.91743i
$156$	−4.63512	−	2.87442i	−0.0297123	−	0.0184257i
$157$	4.03656	−	22.8925i	0.0257106	−	0.145812i	−0.969250	−	0.246078i	$-0.920858\pi$
$157$	4.03656	−	22.8925i	0.0257106	−	0.145812i	0.994961	+	0.100266i	$0.0319693\pi$
$158$	26.3359	−	31.3859i	0.166683	−	0.198645i
$159$	30.8914	−	147.809i	0.194285	−	0.929614i
$160$	41.6275	+	15.1512i	0.260172	+	0.0946947i
$161$		−	29.5712i		−	0.183672i
$162$	−105.615	+	44.3561i	−0.651945	+	0.273803i
$163$	157.977			0.969187			0.484593	−	0.874740i	$-0.338968\pi$
$163$	157.977			0.969187			0.484593	+	0.874740i	$0.338968\pi$
$164$	−24.4980	+	67.3076i	−0.149378	+	0.410412i
$165$	−355.916	−	74.3848i	−2.15706	−	0.450817i
$166$	−0.161264	−	0.135317i	−0.000971472	−	0.000815162i
$167$	−93.0755	−	16.4117i	−0.557338	−	0.0982737i	−0.112118	−	0.993695i	$-0.535763\pi$
$167$	−93.0755	−	16.4117i	−0.557338	−	0.0982737i	−0.445220	+	0.895421i	$0.646875\pi$
$168$	4.02923	−	6.49731i	0.0239835	−	0.0386744i
$169$	−128.829	+	108.100i	−0.762299	+	0.639645i
$170$	118.136	−	68.2060i	0.694919	−	0.401212i
$171$	−10.8315	−	96.7067i	−0.0633420	−	0.565536i
$172$	41.5129	−	71.9025i	0.241354	−	0.418038i
$173$	−286.053	+	50.4388i	−1.65348	+	0.291554i	−0.921097	−	0.389334i	$-0.872705\pi$
$173$	−286.053	+	50.4388i	−1.65348	+	0.291554i	−0.732388	+	0.680888i	$0.761594\pi$
$174$	−148.417	−	188.636i	−0.852971	−	1.08411i
$175$	−30.7551	+	11.1939i	−0.175743	+	0.0639654i
$176$	−21.1739	−	58.1749i	−0.120307	−	0.330539i
$177$	−185.857	−	74.3551i	−1.05004	−	0.420085i
$178$	−22.4870	−	127.530i	−0.126332	−	0.716462i
$179$	9.64834	+	5.57047i	0.0539013	+	0.0311200i	0.526709	−	0.850046i	$-0.323426\pi$
$179$	9.64834	+	5.57047i	0.0539013	+	0.0311200i	−0.472807	+	0.881166i	$0.656759\pi$
$180$	39.7765	+	135.230i	0.220980	+	0.751278i
$181$	−95.2763	−	165.023i	−0.526389	−	0.911732i	−0.999527	−	0.0307438i	$-0.990212\pi$
$181$	−95.2763	−	165.023i	−0.526389	−	0.911732i	0.473139	−	0.880988i	$-0.343121\pi$
$182$	0.744517	+	0.887281i	0.00409075	+	0.00487517i
$183$	64.8517	−	34.7664i	0.354381	−	0.189980i
$184$	−16.1198	+	91.4198i	−0.0876075	+	0.496847i
$185$	175.592	−	209.263i	0.949148	−	1.13115i
$186$	−199.681	+	65.6338i	−1.07355	+	0.352870i
$187$	−179.141	−	65.2019i	−0.957972	−	0.348673i
$188$			49.5194i			0.263401i
$189$	24.2491	−	1.94509i	0.128302	−	0.0102915i
$190$	−119.744			−0.630233
$191$	5.86380	−	16.1107i	0.0307005	−	0.0843490i	−0.923395	−	0.383850i	$-0.874598\pi$
$191$	5.86380	−	16.1107i	0.0307005	−	0.0843490i	0.954096	+	0.299501i	$0.0968202\pi$
$192$	−15.9982	+	17.8901i	−0.0833241	+	0.0931777i
$193$	118.098	+	99.0962i	0.611908	+	0.513452i	0.895248	−	0.445568i	$-0.146998\pi$
$193$	118.098	+	99.0962i	0.611908	+	0.513452i	−0.283340	+	0.959019i	$0.591443\pi$
$194$	139.957	+	24.6782i	0.721428	+	0.127207i
$195$	−21.3448	−	0.672524i	−0.109460	−	0.00344884i
$196$	73.8286	−	61.9496i	0.376677	−	0.316069i
$197$	107.213	−	61.8996i	0.544230	−	0.314211i	−0.202561	−	0.979270i	$-0.564927\pi$
$197$	107.213	−	61.8996i	0.544230	−	0.314211i	0.746792	+	0.665058i	$0.231593\pi$
$198$	109.040	−	164.061i	0.550708	−	0.828590i
$199$	−117.239	+	203.063i	−0.589139	+	1.02042i	0.405207	+	0.914225i	$0.367200\pi$
$199$	−117.239	+	203.063i	−0.589139	+	1.02042i	−0.994345	+	0.106193i	$0.966134\pi$
$200$	101.182	−	17.8411i	0.505910	−	0.0892055i
$201$	193.667	−	27.8917i	0.963515	−	0.138765i
$202$	140.335	−	51.0777i	0.694727	−	0.252860i
$203$	17.4339	+	47.8991i	0.0858811	+	0.235956i
$204$	10.5349	+	73.1496i	0.0516419	+	0.358576i
$205$	48.7010	+	276.197i	0.237566	+	1.34730i
$206$	106.531	+	61.5054i	0.517139	+	0.298570i
$207$	−264.600	+	131.295i	−1.27826	+	0.634275i
$208$	−1.81801	−	3.14889i	−0.00874045	−	0.0151389i
$209$	107.567	+	128.193i	0.514674	+	0.613365i
$210$	0.942714	−	29.9202i	0.00448912	−	0.142477i
$211$	−9.24958	+	52.4570i	−0.0438369	+	0.248611i	−0.998850	−	0.0479537i	$-0.984730\pi$
$211$	−9.24958	+	52.4570i	−0.0438369	+	0.248611i	0.955013	+	0.296565i	$0.0958411\pi$
$212$	64.7082	−	77.1162i	0.305227	−	0.363756i
$213$	−63.1342	−	56.4577i	−0.296405	−	0.265060i
$214$	−32.5669	−	11.8534i	−0.152182	−	0.0553896i
$215$		−	325.089i		−	1.51204i
$216$	−76.0269	−	7.20535i	−0.351976	−	0.0333581i
$217$	44.6378			0.205704
$218$	16.2382	−	44.6142i	0.0744873	−	0.204652i
$219$	20.1894	+	61.4233i	0.0921891	+	0.280472i
$220$	−185.692	−	155.814i	−0.844054	−	0.708246i
$221$	−11.0265	−	1.94427i	−0.0498936	−	0.00879759i
$222$	69.9259	+	130.437i	0.314982	+	0.587553i
$223$	−45.9011	+	38.5156i	−0.205835	+	0.172716i	−0.739878	−	0.672742i	$-0.765117\pi$
$223$	−45.9011	+	38.5156i	−0.205835	+	0.172716i	0.534043	+	0.845457i	$0.320672\pi$
$224$	4.41398	−	2.54841i	0.0197053	−	0.0113768i
$225$	236.714	+	225.493i	1.05206	+	1.00219i
$226$	−86.2750	+	149.433i	−0.381748	+	0.661206i
$227$	−62.7048	+	11.0565i	−0.276232	+	0.0487072i	−0.310048	−	0.950721i	$-0.600345\pi$
$227$	−62.7048	+	11.0565i	−0.276232	+	0.0487072i	0.0338157	+	0.999428i	$0.489234\pi$
$228$	24.0971	−	60.2329i	0.105689	−	0.264179i
$229$	−201.212	+	73.2350i	−0.878653	+	0.319804i	−0.741666	−	0.670769i	$-0.765964\pi$
$229$	−201.212	+	73.2350i	−0.878653	+	0.319804i	−0.136987	+	0.990573i	$0.543742\pi$
$230$	124.317	+	341.558i	0.540508	+	1.48503i
$231$	−32.8782	+	25.8682i	−0.142330	+	0.111984i
$232$	−27.7864	−	157.584i	−0.119769	−	0.679243i
$233$	−186.691	−	107.786i	−0.801248	−	0.462601i	0.0426593	−	0.999090i	$-0.486417\pi$
$233$	−186.691	−	107.786i	−0.801248	−	0.462601i	−0.843907	+	0.536489i	$0.819750\pi$
$234$	4.63367	−	10.6014i	0.0198020	−	0.0453049i
$235$	96.9470	+	167.917i	0.412541	+	0.714541i
$236$	−85.7817	−	102.231i	−0.363482	−	0.433180i
$237$	73.8634	+	45.8056i	0.311660	+	0.193272i
$238$	2.72539	−	15.4564i	0.0114512	−	0.0649431i
$239$	26.8944	−	32.0515i	0.112529	−	0.134107i	−0.706840	−	0.707374i	$-0.749880\pi$
$239$	26.8944	−	32.0515i	0.112529	−	0.134107i	0.819369	+	0.573267i	$0.194324\pi$
$240$	−19.2245	+	91.9850i	−0.0801019	+	0.383271i
$241$	421.281	+	153.334i	1.74805	+	0.636240i	0.999636	−	0.0269874i	$-0.00859139\pi$
$241$	421.281	+	153.334i	1.74805	+	0.636240i	0.748418	+	0.663227i	$0.230814\pi$
$242$			167.643i			0.692738i
$243$	−125.070	−	208.342i	−0.514690	−	0.857376i
$244$	49.0553			0.201046
$245$	129.066	−	354.606i	0.526800	−	1.44737i
$246$	−148.731	−	31.0841i	−0.604597	−	0.126358i
$247$	7.52908	+	6.31765i	0.0304821	+	0.0255775i
$248$	−137.999	−	24.3329i	−0.556446	−	0.0981164i
$249$	0.235354	−	0.379518i	0.000945197	−	0.00152417i
$250$	96.0792	−	80.6200i	0.384317	−	0.322480i
$251$	−222.273	+	128.329i	−0.885549	+	0.511272i	−0.872484	−	0.488643i	$-0.837492\pi$
$251$	−222.273	+	128.329i	−0.885549	+	0.511272i	−0.0130650	+	0.999915i	$0.504159\pi$
$252$	14.8605	+	6.49528i	0.0589703	+	0.0257749i
$253$	253.983	−	439.911i	1.00388	−	1.73878i
$254$	145.488	−	25.6535i	0.572788	−	0.100998i
$255$	178.932	+	227.421i	0.701696	+	0.891846i
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	134.312	+	369.019i	0.522614	+	1.43587i	0.867600	+	0.497262i	$0.165661\pi$
$257$	134.312	+	369.019i	0.522614	+	1.43587i	−0.344986	+	0.938608i	$0.612116\pi$
$258$	163.524	+	65.4202i	0.633813	+	0.253567i
$259$	−5.45776	−	30.9525i	−0.0210724	−	0.119508i
$260$	−12.3295	−	7.11846i	−0.0474213	−	0.0273787i
$261$	351.191	−	368.667i	1.34556	−	1.41252i
$262$	−0.646322	−	1.11946i	−0.00246688	−	0.00427276i
$263$	78.9273	+	94.0619i	0.300104	+	0.357650i	0.894932	−	0.446203i	$-0.147224\pi$
$263$	78.9273	+	94.0619i	0.300104	+	0.357650i	−0.594828	+	0.803853i	$0.702780\pi$
$264$	115.745	−	62.0496i	0.438427	−	0.235036i
$265$	68.4465	−	388.179i	0.258289	−	1.46483i
$266$	−8.85581	+	10.5539i	−0.0332925	+	0.0396765i
$267$	260.970	−	85.7790i	0.977415	−	0.321270i
$268$	122.576	+	44.6142i	0.457375	+	0.166471i
$269$			392.295i			1.45835i	0.684329	+	0.729173i	$0.260095\pi$
$269$			392.295i			1.45835i	−0.684329	+	0.729173i	$0.739905\pi$
$270$	−271.909	+	124.409i	−1.00707	+	0.460775i
$271$	−43.9569			−0.162203			−0.0811013	−	0.996706i	$-0.525844\pi$
$271$	−43.9569			−0.162203			−0.0811013	+	0.996706i	$0.525844\pi$
$272$	−16.8512	+	46.2982i	−0.0619528	+	0.170214i
$273$	−1.63785	+	1.83154i	−0.00599945	+	0.00670892i
$274$	15.2240	+	12.7745i	0.0555622	+	0.0466222i
$275$	−553.666	−	97.6263i	−2.01333	−	0.355005i
$276$	−196.825	−	6.20148i	−0.713133	−	0.0224691i
$277$	−253.346	+	212.582i	−0.914606	+	0.767446i	−0.972990	−	0.230849i	$-0.925850\pi$
$277$	−253.346	+	212.582i	−0.914606	+	0.767446i	0.0583836	+	0.998294i	$0.481405\pi$
$278$	−227.956	+	131.611i	−0.819987	+	0.473420i
$279$	−198.190	−	399.415i	−0.710359	−	1.43159i
$280$	9.97835	−	17.2830i	0.0356370	−	0.0617251i
$281$	−252.252	+	44.4788i	−0.897692	+	0.158287i	−0.603410	−	0.797431i	$-0.706192\pi$
$281$	−252.252	+	44.4788i	−0.897692	+	0.158287i	−0.294282	+	0.955719i	$0.595081\pi$
$282$	−103.974	+	14.9742i	−0.368701	+	0.0531001i
$283$	146.361	−	53.2711i	0.517177	−	0.188237i	−0.0702267	−	0.997531i	$-0.522372\pi$
$283$	146.361	−	53.2711i	0.517177	−	0.188237i	0.587404	+	0.809294i	$0.300150\pi$
$284$	−19.3118	−	53.0588i	−0.0679993	−	0.186827i
$285$	−36.2096	−	251.422i	−0.127051	−	0.882183i
$286$	3.45496	+	19.5940i	0.0120803	+	0.0685106i
$287$	27.9450	+	16.1340i	0.0973693	+	0.0562162i
$288$	−42.4008	−	28.1810i	−0.147225	−	0.0978507i
$289$	−68.6411	−	118.890i	−0.237512	−	0.411383i
$290$	−402.734	−	479.960i	−1.38874	−	1.65503i
$291$	−9.49400	+	301.324i	−0.0326254	+	1.03548i
$292$	−7.48496	+	42.4493i	−0.0256334	+	0.145374i
$293$	−131.430	+	156.632i	−0.448566	+	0.534580i	−0.942183	−	0.335100i	$-0.891230\pi$
$293$	−131.430	+	156.632i	−0.448566	+	0.534580i	0.493617	+	0.869679i	$0.335674\pi$
$294$	152.398	+	136.282i	0.518360	+	0.463543i
$295$	−491.023	−	178.718i	−1.66448	−	0.605823i
$296$			98.6652i			0.333328i
$297$	377.444	+	179.336i	1.27086	+	0.603826i
$298$	179.302			0.601685
$299$	10.2038	−	28.0348i	0.0341265	−	0.0937618i
$300$	68.0567	+	207.052i	0.226856	+	0.690175i
$301$	−28.6525	−	24.0423i	−0.0951909	−	0.0798747i
$302$	191.408	+	33.7504i	0.633801	+	0.111756i
$303$	149.682	+	279.209i	0.493999	+	0.921483i
$304$	33.1310	−	27.8002i	0.108984	−	0.0914482i
$305$	166.343	−	96.0384i	0.545388	−	0.314880i
$306$	−150.403	+	44.2395i	−0.491514	+	0.144574i
$307$	284.956	−	493.559i	0.928196	−	1.60768i	0.141857	−	0.989887i	$-0.454693\pi$
$307$	284.956	−	493.559i	0.928196	−	1.60768i	0.786339	−	0.617796i	$-0.211974\pi$
$308$	−27.4661	+	4.84301i	−0.0891755	+	0.0157241i
$309$	−96.9264	+	242.276i	−0.313678	+	0.784066i
$310$	−515.582	+	187.657i	−1.66317	+	0.605344i
$311$	−152.905	−	420.102i	−0.491654	−	1.35081i	−0.899165	−	0.437609i	$-0.855825\pi$
$311$	−152.905	−	420.102i	−0.491654	−	1.35081i	0.407511	−	0.913200i	$-0.366397\pi$
$312$	6.06184	−	4.76940i	0.0194290	−	0.0152865i
$313$	−50.5690	−	286.791i	−0.161562	−	0.916265i	−0.952538	−	0.304418i	$-0.901538\pi$
$313$	−50.5690	−	286.791i	−0.161562	−	0.916265i	0.790976	−	0.611847i	$-0.209573\pi$
$314$	28.4700	+	16.4371i	0.0906686	+	0.0523476i
$315$	63.1073	−	7.06823i	0.200340	−	0.0224388i
$316$	28.9712	+	50.1795i	0.0916809	+	0.158796i
$317$	−216.870	−	258.455i	−0.684131	−	0.815316i	0.306501	−	0.951870i	$-0.400842\pi$
$317$	−216.870	−	258.455i	−0.684131	−	0.815316i	−0.990633	+	0.136554i	$0.956397\pi$
$318$	181.485	+	112.546i	0.570707	+	0.353918i
$319$	−152.047	+	862.300i	−0.476636	+	2.70314i
$320$	−40.2695	+	47.9914i	−0.125842	+	0.149973i
$321$	15.0401	−	71.9636i	0.0468539	−	0.224186i
$322$	39.2979	+	14.3033i	0.122043	+	0.0444201i
$323$		−	133.180i		−	0.412322i
$324$	−7.86107	−	161.809i	−0.0242626	−	0.499411i
$325$	−33.0197			−0.101599
$326$	−76.4120	+	209.940i	−0.234393	+	0.643989i
$327$	98.5848	+	20.6038i	0.301482	+	0.0630085i
$328$	−77.5974	−	65.1120i	−0.236577	−	0.198512i
$329$	21.9696	+	3.87383i	0.0667768	+	0.0117746i
$330$	271.005	−	437.006i	0.821226	−	1.32426i
$331$	116.755	−	97.9694i	0.352735	−	0.295980i	−0.449152	−	0.893455i	$-0.648274\pi$
$331$	116.755	−	97.9694i	0.352735	−	0.295980i	0.801887	+	0.597475i	$0.203829\pi$
$332$	0.257828	−	0.148857i	0.000776590	−	0.000448365i
$333$	−252.727	+	186.263i	−0.758941	+	0.559349i
$334$	66.8296	−	115.752i	0.200089	−	0.346564i
$335$	502.993	−	88.6912i	1.50147	−	0.264750i
$336$	6.68554	+	8.49723i	0.0198974	+	0.0252894i
$337$	219.421	−	79.8628i	0.651102	−	0.236982i	0.00471178	−	0.999989i	$-0.498500\pi$
$337$	219.421	−	79.8628i	0.651102	−	0.236982i	0.646390	+	0.763007i	$0.276278\pi$
$338$	−81.3439	−	223.490i	−0.240662	−	0.661214i
$339$	−339.846	−	135.961i	−1.00250	−	0.401064i
$340$	33.4994	+	189.985i	0.0985278	+	0.558779i
$341$	664.047	+	383.388i	1.94735	+	1.12430i
$342$	133.755	+	32.3818i	0.391097	+	0.0946835i
$343$	−43.7833	−	75.8349i	−0.127648	−	0.221093i
$344$	75.4737	+	89.9461i	0.219400	+	0.261471i
$345$	−679.561	+	364.307i	−1.96974	+	1.05596i
$346$	71.3313	−	404.540i	0.206160	−	1.16919i
$347$	−409.259	+	487.736i	−1.17942	+	1.40558i	−0.284899	+	0.958558i	$0.591960\pi$
$347$	−409.259	+	487.736i	−1.17942	+	1.40558i	−0.894523	+	0.447022i	$0.852484\pi$
$348$	322.471	−	105.994i	0.926641	−	0.304581i
$349$	268.471	+	97.7153i	0.769257	+	0.279987i	0.696686	−	0.717377i	$-0.254657\pi$
$349$	268.471	+	97.7153i	0.769257	+	0.279987i	0.0725714	+	0.997363i	$0.476879\pi$
$350$		−	46.2857i		−	0.132245i
$351$	23.6604	+	6.52336i	0.0674085	+	0.0185851i
$352$	87.5518			0.248727
$353$	−112.137	+	308.094i	−0.317669	+	0.872788i	0.673381	+	0.739296i	$0.264841\pi$
$353$	−112.137	+	308.094i	−0.317669	+	0.872788i	−0.991050	+	0.133492i	$0.957381\pi$
$354$	188.710	−	211.026i	0.533078	−	0.596118i
$355$	−169.361	−	142.111i	−0.477074	−	0.400313i
$356$	180.355	+	31.8015i	0.506615	+	0.0893299i
$357$	33.2774	+	1.04849i	0.0932139	+	0.00293695i
$358$	−12.0695	+	10.1276i	−0.0337138	+	0.0282893i
$359$	484.455	−	279.700i	1.34946	−	0.779109i	0.361284	−	0.932456i	$-0.382339\pi$
$359$	484.455	−	279.700i	1.34946	−	0.779109i	0.988172	+	0.153347i	$0.0490053\pi$
$360$	−198.950	−	12.5493i	−0.552639	−	0.0348593i
$361$	122.046	−	211.390i	0.338078	−	0.585569i
$362$	265.388	−	46.7951i	0.733116	−	0.129268i
$363$	−351.992	+	50.6936i	−0.969675	+	0.139652i
$364$	−1.53925	+	0.560239i	−0.00422870	+	0.00153912i
$365$	57.7245	+	158.597i	0.158149	+	0.434511i
$366$	14.8339	+	102.999i	0.0405297	+	0.281419i
$367$	83.2991	+	472.413i	0.226973	+	1.28723i	0.858877	+	0.512182i	$0.171163\pi$
$367$	83.2991	+	472.413i	0.226973	+	1.28723i	−0.631904	+	0.775047i	$0.717726\pi$
$368$	−113.693	−	65.6408i	−0.308949	−	0.178372i
$369$	20.2911	−	321.683i	0.0549894	−	0.871770i
$370$	193.163	+	334.568i	0.522061	+	0.904237i
$371$	−29.1510	−	34.7409i	−0.0785743	−	0.0936411i
$372$	9.36115	−	297.108i	0.0251644	−	0.798677i
$373$	59.7262	−	338.724i	0.160124	−	0.908107i	−0.793827	−	0.608144i	$-0.791914\pi$
$373$	59.7262	−	338.724i	0.160124	−	0.908107i	0.953951	−	0.299964i	$-0.0969745\pi$
$374$	173.297	−	206.527i	0.463361	−	0.552212i
$375$	198.328	+	177.355i	0.528874	+	0.472946i
$376$	−65.8076	−	23.9520i	−0.175020	−	0.0637022i
$377$			51.4262i			0.136409i
$378$	−9.14417	+	33.1661i	−0.0241909	+	0.0877410i
$379$	−104.156			−0.274817			−0.137408	−	0.990514i	$-0.543877\pi$
$379$	−104.156			−0.274817			−0.137408	+	0.990514i	$0.543877\pi$
$380$	57.9191	−	159.131i	0.152419	−	0.418767i
$381$	97.8579	+	297.718i	0.256845	+	0.781412i
$382$	18.5736	+	15.5851i	0.0486220	+	0.0407987i
$383$	−63.8855	−	11.2647i	−0.166803	−	0.0294118i	0.0896229	−	0.995976i	$-0.471434\pi$
$383$	−63.8855	−	11.2647i	−0.166803	−	0.0294118i	−0.256426	+	0.966564i	$0.582545\pi$
$384$	−16.0365	−	29.9137i	−0.0417617	−	0.0779003i
$385$	−83.6542	+	70.1942i	−0.217284	+	0.182323i
$386$	−188.814	+	109.012i	−0.489156	+	0.282415i
$387$	−87.9119	+	363.126i	−0.227163	+	0.938310i
$388$	−100.491	+	174.056i	−0.258998	+	0.448598i
$389$	232.365	−	40.9722i	0.597339	−	0.105327i	0.133200	−	0.991089i	$-0.457475\pi$
$389$	232.365	−	40.9722i	0.597339	−	0.105327i	0.464139	+	0.885762i	$0.346364\pi$
$390$	11.2180	−	28.0404i	0.0287641	−	0.0718984i
$391$	−379.882	+	138.266i	−0.971564	+	0.353620i
$392$	46.6163	+	128.077i	0.118919	+	0.326727i
$393$	2.15504	−	1.69557i	0.00548357	−	0.00431443i
$394$	30.4021	+	172.419i	0.0771627	+	0.437611i
$395$	196.479	+	113.437i	0.497415	+	0.287183i
$396$	165.283	+	224.261i	0.417381	+	0.566315i
$397$	−2.59349	−	4.49206i	−0.00653272	−	0.0113150i	0.862741	−	0.505647i	$-0.168746\pi$
$397$	−2.59349	−	4.49206i	−0.00653272	−	0.0113150i	−0.869273	+	0.494332i	$0.835413\pi$
$398$	−213.149	−	254.021i	−0.535550	−	0.638244i
$399$	−24.8376	−	15.4027i	−0.0622496	−	0.0386034i
$400$	−25.2311	+	143.093i	−0.0630778	+	0.357732i
$401$	103.381	−	123.205i	0.257808	−	0.307244i	−0.621579	−	0.783352i	$-0.713508\pi$
$401$	103.381	−	123.205i	0.257808	−	0.307244i	0.879387	+	0.476108i	$0.157953\pi$
$402$	−56.6085	+	270.859i	−0.140817	+	0.673780i
$403$	42.3186	+	15.4027i	0.105009	+	0.0382201i
$404$			211.200i			0.522773i
$405$	−343.440	−	533.295i	−0.847999	−	1.31678i
$406$	−72.0870			−0.177554
$407$	184.655	−	507.335i	0.453698	−	1.24652i
$408$	−102.306	−	21.3815i	−0.250750	−	0.0524057i
$409$	−132.217	−	110.943i	−0.323269	−	0.271255i	0.466682	−	0.884425i	$-0.345449\pi$
$409$	−132.217	−	110.943i	−0.323269	−	0.271255i	−0.789950	+	0.613171i	$0.789894\pi$
$410$	−390.601	−	68.8736i	−0.952686	−	0.167984i
$411$	−22.2184	+	35.8282i	−0.0540594	+	0.0871731i
$412$	−133.264	+	111.822i	−0.323456	+	0.271412i
$413$	−52.0658	+	30.0602i	−0.126067	+	0.0727850i
$414$	−46.4971	−	415.140i	−0.112312	−	1.00275i
$415$	0.582852	−	1.00953i	0.00140446	−	0.00243260i
$416$	5.06400	−	0.892920i	0.0121731	−	0.00214644i
$417$	−345.269	−	438.832i	−0.827984	−	1.05236i
$418$	−222.388	+	80.9427i	−0.532029	+	0.193643i
$419$	97.9330	+	269.069i	0.233730	+	0.642169i	1.00000		0.000350278i	$-0.000111497\pi$
$419$	97.9330	+	269.069i	0.233730	+	0.642169i	−0.766270	+	0.642519i	$0.777889\pi$
$420$	39.3058	+	15.7249i	0.0935852	+	0.0374402i
$421$	117.029	+	663.704i	0.277979	+	1.57649i	0.729339	+	0.684153i	$0.239828\pi$
$421$	117.029	+	663.704i	0.277979	+	1.57649i	−0.451360	+	0.892342i	$0.649061\pi$
$422$	−65.2375	−	37.6649i	−0.154591	−	0.0892533i
$423$	−62.8815	−	213.781i	−0.148656	−	0.505393i
$424$	71.1831	+	123.293i	0.167885	+	0.290785i
$425$	287.602	+	342.751i	0.676711	+	0.806473i
$426$	105.566	−	56.5927i	0.247806	−	0.132847i
$427$	3.83752	−	21.7637i	0.00898717	−	0.0509688i
$428$	31.5045	−	37.5456i	0.0736087	−	0.0877234i
$429$	−40.0960	+	13.1793i	−0.0934639	+	0.0307209i
$430$	432.019	+	157.242i	1.00470	+	0.365679i
$431$		−	539.138i		−	1.25090i	−0.780264	−	0.625450i	$-0.784915\pi$
$431$		−	539.138i		−	1.25090i	0.780264	−	0.625450i	$-0.215085\pi$
$432$	46.3488	−	97.5489i	0.107289	−	0.225808i
$433$	−802.991			−1.85448			−0.927241	−	0.374466i	$-0.877826\pi$
$433$	−802.991			−1.85448			−0.927241	+	0.374466i	$0.877826\pi$
$434$	−21.5908	+	59.3204i	−0.0497485	+	0.136683i
$435$	885.968	−	990.739i	2.03671	−	2.27756i
$436$	51.4347	+	43.1588i	0.117969	+	0.0989881i
$437$	349.475	+	61.6219i	0.799715	+	0.141011i
$438$	−91.3924	−	2.87956i	−0.208658	−	0.00657433i
$439$	−59.9232	+	50.2816i	−0.136499	+	0.114537i	−0.708481	−	0.705730i	$-0.750619\pi$
$439$	−59.9232	+	50.2816i	−0.136499	+	0.114537i	0.571982	+	0.820266i	$0.306175\pi$
$440$	296.883	−	171.405i	0.674733	−	0.389557i
$441$	−240.061	+	361.194i	−0.544356	+	0.819033i
$442$	7.91718	−	13.7130i	0.0179122	−	0.0310248i
$443$	−537.994	+	94.8628i	−1.21443	+	0.214137i	−0.743928	−	0.668260i	$-0.767039\pi$
$443$	−537.994	+	94.8628i	−1.21443	+	0.214137i	−0.470505	+	0.882397i	$0.655928\pi$
$444$	−207.163	+	29.8355i	−0.466584	+	0.0671970i
$445$	673.832	−	245.255i	1.51423	−	0.551134i
$446$	−28.9825	−	79.6288i	−0.0649832	−	0.178540i
$447$	54.2194	+	376.473i	0.121296	+	0.842222i
$448$	1.25166	+	7.09849i	0.00279388	+	0.0158449i
$449$	−592.342	−	341.989i	−1.31925	−	0.761667i	−0.335639	−	0.941991i	$-0.608952\pi$
$449$	−592.342	−	341.989i	−1.31925	−	0.761667i	−0.983607	+	0.180323i	$0.942286\pi$
$450$	−414.159	+	205.507i	−0.920354	+	0.456681i
$451$	277.146	+	480.031i	0.614514	+	1.06437i
$452$	−156.855	−	186.932i	−0.347024	−	0.413567i
$453$	−12.9842	+	412.097i	−0.0286627	+	0.909707i
$454$	15.6363	−	88.6779i	0.0344412	−	0.195326i
$455$	−4.12267	+	4.91321i	−0.00906081	+	0.0107983i
$456$	68.3895	+	61.1573i	0.149977	+	0.134117i
$457$	−80.6475	−	29.3533i	−0.176472	−	0.0642304i	0.252273	−	0.967656i	$-0.418822\pi$
$457$	−80.6475	−	29.3533i	−0.176472	−	0.0642304i	−0.428745	+	0.903426i	$0.641044\pi$
$458$		−	302.818i		−	0.661175i
$459$	−138.368	−	302.418i	−0.301456	−	0.658862i
$460$	−514.035			−1.11747
$461$	1.94941	−	5.35597i	0.00422866	−	0.0116181i	−0.937560	−	0.347823i	$-0.886921\pi$
$461$	1.94941	−	5.35597i	0.00422866	−	0.0116181i	0.941789	+	0.336205i	$0.109143\pi$
$462$	−18.4741	−	56.2048i	−0.0399873	−	0.121655i
$463$	−247.066	−	207.313i	−0.533620	−	0.447760i	0.335729	−	0.941959i	$-0.391017\pi$
$463$	−247.066	−	207.313i	−0.533620	−	0.447760i	−0.869349	+	0.494198i	$0.835462\pi$
$464$	222.858	+	39.2959i	0.480298	+	0.0846894i
$465$	−549.922	−	1025.80i	−1.18263	−	2.20602i
$466$	233.540	−	195.963i	0.501159	−	0.420522i
$467$	32.7859	−	18.9290i	0.0702054	−	0.0405331i	−0.464486	−	0.885580i	$-0.653761\pi$
$467$	32.7859	−	18.9290i	0.0702054	−	0.0405331i	0.534692	+	0.845047i	$0.320428\pi$
$468$	11.8472	+	11.2856i	0.0253144	+	0.0241145i
$469$	29.3823	−	50.8917i	0.0626489	−	0.108511i
$470$	−270.042	+	47.6157i	−0.574557	+	0.101310i
$471$	−25.9033	+	64.7476i	−0.0549964	+	0.137468i
$472$	177.349	−	64.5496i	0.375739	−	0.136758i
$473$	−219.748	−	603.753i	−0.464584	−	1.27643i
$474$	−96.5992	+	76.0034i	−0.203796	+	0.160345i
$475$	−68.2021	−	386.793i	−0.143583	−	0.814302i
$476$	19.2222	+	11.0980i	0.0403828	+	0.0233150i
$477$	−181.428	+	415.089i	−0.380353	+	0.870207i
$478$	29.5855	+	51.2436i	0.0618944	+	0.107204i
$479$	461.346	+	549.811i	0.963145	+	1.14783i	0.988963	+	0.148164i	$0.0473365\pi$
$479$	461.346	+	549.811i	0.963145	+	1.14783i	−0.0258182	+	0.999667i	$0.508219\pi$
$480$	−112.943	−	70.0400i	−0.235297	−	0.145917i
$481$	5.50626	−	31.2275i	0.0114475	−	0.0649221i
$482$	−407.538	+	485.685i	−0.845515	+	1.00765i
$483$	−18.1486	+	86.8373i	−0.0375748	+	0.179787i
$484$	−222.785	−	81.0870i	−0.460299	−	0.167535i
$485$			786.950i			1.62258i
$486$	337.367	−	65.4352i	0.694170	−	0.134640i
$487$	52.1558			0.107096			0.0535480	−	0.998565i	$-0.482947\pi$
$487$	52.1558			0.107096			0.0535480	+	0.998565i	$0.482947\pi$
$488$	−23.7275	+	65.1909i	−0.0486220	+	0.133588i
$489$	−463.909	−	96.9550i	−0.948689	−	0.198272i
$490$	408.817	+	343.038i	0.834320	+	0.700078i
$491$	77.8114	+	13.7202i	0.158475	+	0.0279435i	0.252323	−	0.967643i	$-0.418806\pi$
$491$	77.8114	+	13.7202i	0.158475	+	0.0279435i	−0.0938475	+	0.995587i	$0.529917\pi$
$492$	113.248	−	182.617i	0.230179	−	0.371173i
$493$	533.813	−	447.922i	1.08279	−	0.908565i
$494$	−12.0374	+	6.94981i	−0.0243673	+	0.0140685i
$495$	999.513	+	436.870i	2.01922	+	0.882565i
$496$	99.0851	−	171.620i	0.199768	−	0.346009i
$497$	−25.0506	+	4.41709i	−0.0504036	+	0.00888751i
$498$	0.390514	+	0.496337i	0.000784164	+	0.000996661i
$499$	27.9915	−	10.1881i	0.0560952	−	0.0204170i	−0.313820	−	0.949482i	$-0.601609\pi$
$499$	27.9915	−	10.1881i	0.0560952	−	0.0204170i	0.369915	+	0.929065i	$0.379387\pi$
$500$	60.6655	+	166.677i	0.121331	+	0.333354i
$501$	263.249	+	105.317i	0.525446	+	0.210213i
$502$	−63.0291	−	357.456i	−0.125556	−	0.712063i
$503$	−146.080	−	84.3394i	−0.290418	−	0.167673i	0.347713	−	0.937601i	$-0.386959\pi$
$503$	−146.080	−	84.3394i	−0.290418	−	0.167673i	−0.638130	+	0.769928i	$0.720292\pi$
$504$	−15.8196	+	16.6068i	−0.0313881	+	0.0329501i
$505$	413.479	+	716.167i	0.818771	+	1.41815i
$506$	461.760	+	550.305i	0.912570	+	1.08756i
$507$	444.656	−	238.376i	0.877033	−	0.470169i
$508$	−36.2795	+	205.751i	−0.0714164	+	0.405022i
$509$	223.993	−	266.945i	0.440066	−	0.524450i	−0.499733	−	0.866180i	$-0.666568\pi$
$509$	223.993	−	266.945i	0.440066	−	0.524450i	0.939798	+	0.341730i	$0.111013\pi$
$510$	−388.773	+	127.787i	−0.762300	+	0.250563i
$511$	18.2474	+	6.64149i	0.0357091	+	0.0129971i
$512$		−	22.6274i		−	0.0441942i
$513$	−27.5443	+	290.632i	−0.0536925	+	0.566534i
$514$	−555.364			−1.08047
$515$	−232.970	+	640.079i	−0.452368	+	1.24287i
$516$	−166.033	+	185.668i	−0.321770	+	0.359821i
$517$	293.555	+	246.322i	0.567805	+	0.476445i
$518$	43.7734	+	7.71843i	0.0845047	+	0.0149005i
$519$	870.965	+	27.4420i	1.67816	+	0.0528748i
$520$	15.4236	−	12.9419i	0.0296607	−	0.0248883i
$521$	−95.9710	+	55.4089i	−0.184205	+	0.106351i	−0.589267	−	0.807938i	$-0.700583\pi$
$521$	−95.9710	+	55.4089i	−0.184205	+	0.106351i	0.405062	+	0.914289i	$0.367250\pi$
$522$	320.063	+	645.027i	0.613148	+	1.23568i
$523$	280.197	−	485.316i	0.535750	−	0.927946i	−0.463377	−	0.886161i	$-0.653362\pi$
$523$	280.197	−	485.316i	0.535750	−	0.927946i	0.999127	−	0.0417848i	$-0.0133044\pi$
$524$	1.80030	−	0.317442i	0.00343569	−	0.000605805i
$525$	97.1840	−	13.9964i	0.185112	−	0.0266597i
$526$	−163.178	+	59.3918i	−0.310224	+	0.112912i
$527$	−208.712	−	573.433i	−0.396039	−	1.08811i
$528$	26.4749	+	183.829i	0.0501418	+	0.348161i
$529$	−95.1903	−	539.851i	−0.179944	−	1.02051i
$530$	482.755	+	278.719i	0.910858	+	0.525884i
$531$	500.146	+	332.413i	0.941894	+	0.626013i
$532$	−9.74195	−	16.8736i	−0.0183119	−	0.0317172i
$533$	20.9258	+	24.9384i	0.0392605	+	0.0467888i
$534$	−12.2344	+	388.300i	−0.0229109	+	0.727154i
$535$	33.3246	−	188.993i	0.0622889	−	0.353258i
$536$	−118.578	+	141.316i	−0.221227	+	0.263649i
$537$	−24.9141	−	22.2794i	−0.0463950	−	0.0414887i
$538$	−521.331	−	189.749i	−0.969018	−	0.352694i
$539$		−	745.814i		−	1.38370i
$540$	−33.8114	−	421.522i	−0.0626137	−	0.780596i
$541$	−313.055			−0.578660			−0.289330	−	0.957229i	$-0.593433\pi$
$541$	−313.055			−0.578660			−0.289330	+	0.957229i	$0.593433\pi$
$542$	21.2615	−	58.4155i	0.0392279	−	0.107778i
$543$	178.505	+	543.074i	0.328738	+	1.00014i
$544$	−53.3762	−	44.7879i	−0.0981179	−	0.0823307i
$545$	258.906	+	45.6522i	0.475057	+	0.0837654i
$546$	−1.64176	−	3.06248i	−0.00300689	−	0.00560893i
$547$	−564.255	+	473.466i	−1.03155	+	0.865569i	−0.991034	−	0.133610i	$-0.957343\pi$
$547$	−564.255	+	473.466i	−1.03155	+	0.865569i	−0.0405113	+	0.999179i	$0.512899\pi$
$548$	−24.3401	+	14.0527i	−0.0444162	+	0.0256437i
$549$	−211.778	+	62.2921i	−0.385751	+	0.113465i
$550$	397.541	−	688.561i	0.722801	−	1.25193i
$551$	−602.406	+	106.220i	−1.09330	+	0.192778i
$552$	103.443	−	258.566i	0.187397	−	0.468417i
$553$	24.5288	−	8.92776i	0.0443559	−	0.0161442i
$554$	−159.966	−	439.502i	−0.288747	−	0.793325i
$555$	−644.066	+	506.746i	−1.16048	+	0.913055i
$556$	−64.6407	−	366.596i	−0.116260	−	0.659345i
$557$	−552.604	−	319.046i	−0.992108	−	0.572794i	−0.0862045	−	0.996277i	$-0.527474\pi$
$557$	−552.604	−	319.046i	−0.992108	−	0.572794i	−0.905904	+	0.423483i	$0.860807\pi$
$558$	626.655	−	70.1875i	1.12304	−	0.125784i
$559$	−18.8678	−	32.6799i	−0.0337527	−	0.0584614i
$560$	18.1414	+	21.6201i	0.0323954	+	0.0386073i
$561$	486.040	+	301.412i	0.866381	+	0.537277i
$562$	62.9025	−	356.738i	0.111926	−	0.634764i
$563$	224.179	−	267.166i	0.398187	−	0.474541i	−0.529279	−	0.848448i	$-0.677538\pi$
$563$	224.179	−	267.166i	0.398187	−	0.474541i	0.927466	+	0.373907i	$0.121982\pi$
$564$	30.3914	−	145.416i	0.0538854	−	0.257830i
$565$	−897.852	−	326.791i	−1.58912	−	0.578392i
$566$			220.270i			0.389169i
$567$	−72.4026	−	9.17048i	−0.127694	−	0.0161737i
$568$	79.8521			0.140585
$569$	187.157	−	514.209i	0.328922	−	0.903707i	−0.659463	−	0.751737i	$-0.729216\pi$
$569$	187.157	−	514.209i	0.328922	−	0.903707i	0.988385	−	0.151970i	$-0.0485616\pi$
$570$	351.636	+	73.4903i	0.616905	+	0.128930i
$571$	534.384	+	448.402i	0.935874	+	0.785292i	0.976863	−	0.213868i	$-0.0686062\pi$
$571$	534.384	+	448.402i	0.935874	+	0.785292i	−0.0409882	+	0.999160i	$0.513051\pi$
$572$	−27.7101	−	4.88605i	−0.0484443	−	0.00854204i
$573$	−27.1069	+	43.7110i	−0.0473070	+	0.0762845i
$574$	−34.9576	+	29.3329i	−0.0609018	+	0.0511027i
$575$	−1032.48	+	596.102i	−1.79562	+	1.03670i
$576$	57.9593	−	42.7167i	0.100624	−	0.0741610i
$577$	−193.884	+	335.816i	−0.336020	+	0.582004i	−0.983680	−	0.179925i	$-0.942414\pi$
$577$	−193.884	+	335.816i	−0.336020	+	0.582004i	0.647660	+	0.761929i	$0.275748\pi$
$578$	191.197	−	33.7131i	0.330790	−	0.0583272i
$579$	−285.984	−	363.481i	−0.493927	−	0.627774i
$580$	832.630	−	303.052i	1.43557	−	0.522504i
$581$	−0.0458718	−	0.126032i	−7.89532e−5	−	0.000216922i
$582$	−395.845	−	158.364i	−0.680147	−	0.272103i
$583$	−135.276	−	767.191i	−0.232035	−	1.31594i
$584$	−52.7916	−	30.4792i	−0.0903966	−	0.0521905i
$585$	62.2674	+	15.0748i	0.106440	+	0.0257688i
$586$	−144.581	−	250.422i	−0.246725	−	0.427341i
$587$	−229.618	−	273.648i	−0.391173	−	0.466181i	0.534135	−	0.845399i	$-0.320637\pi$
$587$	−229.618	−	273.648i	−0.391173	−	0.466181i	−0.925307	+	0.379218i	$0.876193\pi$
$588$	−254.822	+	136.608i	−0.433370	+	0.232326i
$589$	−93.0185	+	527.534i	−0.157926	+	0.895644i
$590$	475.005	−	566.089i	0.805094	−	0.959473i
$591$	−352.827	+	115.972i	−0.597000	+	0.196230i
$592$	−131.119	−	47.7233i	−0.221484	−	0.0806137i
$593$			828.411i			1.39698i	0.715618	+	0.698492i	$0.246145\pi$
$593$			828.411i			1.39698i	−0.715618	+	0.698492i	$0.753855\pi$
$594$	−420.891	+	414.852i	−0.708570	+	0.698404i
$595$	86.9085			0.146065
$596$	−86.7266	+	238.279i	−0.145514	+	0.399798i
$597$	468.903	−	524.353i	0.785432	−	0.878314i
$598$	32.3207	+	27.1202i	0.0540479	+	0.0453516i
$599$	863.376	+	152.237i	1.44136	+	0.254151i	0.839026	−	0.544091i	$-0.183125\pi$
$599$	863.376	+	152.237i	1.44136	+	0.254151i	0.602337	+	0.798242i	$0.294237\pi$
$600$	−308.076	−	9.70673i	−0.513459	−	0.0161779i
$601$	627.682	−	526.688i	1.04440	−	0.876353i	0.0519035	−	0.998652i	$-0.483471\pi$
$601$	627.682	−	526.688i	1.04440	−	0.876353i	0.992493	+	0.122299i	$0.0390267\pi$
$602$	45.8093	−	26.4480i	0.0760952	−	0.0439336i
$603$	−585.830	−	36.9529i	−0.971525	−	0.0612817i
$604$	−137.434	+	238.042i	−0.227540	+	0.394110i
$605$	−914.197	+	161.198i	−1.51107	+	0.266442i
$606$	−443.448	+	63.8651i	−0.731763	+	0.105388i
$607$	−544.372	+	198.135i	−0.896823	+	0.326417i	−0.748979	−	0.662594i	$-0.769456\pi$
$607$	−544.372	+	198.135i	−0.896823	+	0.326417i	−0.147844	+	0.989011i	$0.547233\pi$
$608$	20.9193	+	57.4754i	0.0344068	+	0.0945319i
$609$	−21.7985	−	151.358i	−0.0357938	−	0.248535i
$610$	47.1694	+	267.511i	0.0773268	+	0.438542i
$611$	19.4914	+	11.2534i	0.0319008	+	0.0184180i
$612$	13.9574	−	221.273i	0.0228063	−	0.361557i
$613$	−163.781	−	283.677i	−0.267179	−	0.462768i	0.700953	−	0.713207i	$-0.252758\pi$
$613$	−163.781	−	283.677i	−0.267179	−	0.462768i	−0.968132	+	0.250439i	$0.919425\pi$
$614$	518.073	+	617.415i	0.843766	+	1.00556i
$615$	26.4965	−	840.956i	0.0430837	−	1.36741i
$616$	6.84905	−	38.8429i	0.0111186	−	0.0630566i
$617$	−685.484	+	816.928i	−1.11099	+	1.32403i	−0.170064	+	0.985433i	$0.554397\pi$
$617$	−685.484	+	816.928i	−1.11099	+	1.32403i	−0.940931	+	0.338599i	$0.890047\pi$
$618$	−275.085	−	245.995i	−0.445121	−	0.398049i
$619$	835.904	+	304.244i	1.35041	+	0.491509i	0.913076	−	0.407789i	$-0.133700\pi$
$619$	835.904	+	304.244i	1.35041	+	0.491509i	0.437335	+	0.899299i	$0.355922\pi$
$620$		−	775.938i		−	1.25151i
$621$	857.591	−	223.162i	1.38098	−	0.359360i
$622$	632.242			1.01647
$623$	28.2178	−	77.5278i	0.0452934	−	0.124443i
$624$	3.40613	+	10.3627i	0.00545855	+	0.0166068i
$625$	−163.639	−	137.309i	−0.261822	−	0.219695i
$626$	405.584	+	71.5153i	0.647897	+	0.114242i
$627$	−237.200	−	442.463i	−0.378310	−	0.705682i
$628$	−35.6144	+	29.8840i	−0.0567108	+	0.0475860i
$629$	−372.107	+	214.836i	−0.591585	+	0.341552i
$630$	−21.1312	+	87.2837i	−0.0335415	+	0.138546i
$631$	−477.341	+	826.778i	−0.756483	+	1.31027i	0.188151	+	0.982140i	$0.439750\pi$
$631$	−477.341	+	826.778i	−0.756483	+	1.31027i	−0.944634	+	0.328126i	$0.893583\pi$
$632$	−80.6979	+	14.2292i	−0.127687	+	0.0225146i
$633$	59.3561	−	148.366i	0.0937695	−	0.234385i
$634$	448.365	−	163.192i	0.707201	−	0.257400i
$635$	279.790	+	768.717i	0.440614	+	1.21058i
$636$	−237.347	+	186.743i	−0.373188	+	0.293621i
$637$	−7.60638	−	43.1379i	−0.0119409	−	0.0677205i
$638$	−1072.39	−	619.145i	−1.68086	−	0.970446i
$639$	150.747	+	204.538i	0.235911	+	0.320091i
$640$	−44.2990	−	76.7281i	−0.0692172	−	0.119888i
$641$	−456.345	−	543.850i	−0.711926	−	0.848440i	0.281894	−	0.959446i	$-0.409037\pi$
$641$	−456.345	−	543.850i	−0.711926	−	0.848440i	−0.993820	+	0.111005i	$0.964593\pi$
$642$	88.3596	+	54.7952i	0.137632	+	0.0853508i
$643$	8.61807	−	48.8755i	0.0134029	−	0.0760116i	−0.977373	−	0.211525i	$-0.932157\pi$
$643$	8.61807	−	48.8755i	0.0134029	−	0.0760116i	0.990776	+	0.135513i	$0.0432683\pi$
$644$	−38.0160	+	45.3057i	−0.0590310	+	0.0703505i
$645$	−199.516	+	954.641i	−0.309327	+	1.48006i
$646$	176.987	+	64.4178i	0.273973	+	0.0997180i
$647$		−	918.622i		−	1.41982i	−0.704294	−	0.709909i	$-0.748736\pi$
$647$		−	918.622i		−	1.41982i	0.704294	−	0.709909i	$-0.251264\pi$
$648$	218.835	+	67.8186i	0.337708	+	0.104658i
$649$	−1032.73			−1.59126
$650$	15.9713	−	43.8808i	0.0245712	−	0.0675089i
$651$	−131.081	−	27.3954i	−0.201354	−	0.0420821i
$652$	−242.035	−	203.092i	−0.371220	−	0.311491i
$653$	342.395	+	60.3734i	0.524341	+	0.0924555i	0.429552	−	0.903042i	$-0.358671\pi$
$653$	342.395	+	60.3734i	0.524341	+	0.0924555i	0.0947886	+	0.995497i	$0.469782\pi$
$654$	−75.0653	+	121.046i	−0.114779	+	0.185086i
$655$	5.48323	−	4.60098i	0.00837135	−	0.00702440i
$656$	124.062	−	71.6272i	0.189119	−	0.109188i
$657$	−21.5902	−	192.763i	−0.0328617	−	0.293399i
$658$	−15.7745	+	27.3222i	−0.0239734	+	0.0415231i
$659$	1263.48	−	222.786i	1.91728	−	0.338068i	0.918873	−	0.394554i	$-0.129101\pi$
$659$	1263.48	−	222.786i	1.91728	−	0.338068i	0.998403	+	0.0564864i	$0.0179898\pi$
$660$	449.667	+	571.520i	0.681314	+	0.865940i
$661$	−126.358	+	45.9904i	−0.191161	+	0.0695770i	−0.435827	−	0.900030i	$-0.643544\pi$
$661$	−126.358	+	45.9904i	−0.191161	+	0.0695770i	0.244666	+	0.969608i	$0.421322\pi$
$662$	73.7207	+	202.546i	0.111361	+	0.305961i
$663$	31.1866	+	12.4767i	0.0470386	+	0.0188185i
$664$	0.0731113	+	0.414635i	0.000110107	+	0.000624450i
$665$	−66.0687	−	38.1448i	−0.0993514	−	0.0573605i
$666$	−125.289	−	425.950i	−0.188121	−	0.639564i
$667$	928.391	+	1608.02i	1.39189	+	2.41083i
$668$	121.501	+	144.800i	0.181888	+	0.216766i
$669$	158.429	−	84.9324i	0.236815	−	0.126954i
$670$	−125.428	+	711.339i	−0.187206	+	1.06170i
$671$	244.013	−	290.804i	0.363656	−	0.433389i
$672$	−14.5259	+	4.77457i	−0.0216159	+	0.00710501i
$673$	522.659	+	190.232i	0.776610	+	0.282663i	0.699758	−	0.714380i	$-0.253291\pi$
$673$	522.659	+	190.232i	0.776610	+	0.282663i	0.0768517	+	0.997043i	$0.475513\pi$
$674$			330.223i			0.489946i
$675$	−556.731	−	807.449i	−0.824787	−	1.19622i
$676$	336.347			0.497555
$677$	−116.809	+	320.931i	−0.172540	+	0.474049i	−0.995578	−	0.0939369i	$-0.970055\pi$
$677$	−116.809	+	320.931i	−0.172540	+	0.474049i	0.823039	+	0.567985i	$0.192277\pi$
$678$	345.062	−	385.868i	0.508941	−	0.569126i
$679$	69.3597	+	58.1997i	0.102150	+	0.0857138i
$680$	−268.679	−	47.3754i	−0.395116	−	0.0696697i
$681$	190.922	+	6.01548i	0.280355	+	0.00883331i
$682$	−830.687	+	697.029i	−1.21802	+	1.02204i
$683$	181.638	−	104.869i	0.265942	−	0.153542i	−0.361100	−	0.932527i	$-0.617599\pi$
$683$	181.638	−	104.869i	0.265942	−	0.153542i	0.627042	+	0.778985i	$0.284265\pi$
$684$	−107.729	+	162.088i	−0.157498	+	0.236971i
$685$	−55.0237	+	95.3039i	−0.0803266	+	0.139130i
$686$	121.956	−	21.5042i	0.177779	−	0.0313473i
$687$	635.815	−	91.5695i	0.925494	−	0.133289i
$688$	−156.038	+	56.7930i	−0.226799	+	0.0825480i
$689$	−15.6488	−	42.9947i	−0.0227123	−	0.0624016i
$690$	−155.440	−	1079.30i	−0.225275	−	1.56420i
$691$	−50.5894	−	286.907i	−0.0732119	−	0.415205i	−0.999283	−	0.0378567i	$-0.987947\pi$
$691$	−50.5894	−	286.907i	−0.0732119	−	0.415205i	0.926071	−	0.377349i	$-0.123164\pi$
$692$	503.101	+	290.466i	0.727025	+	0.419748i
$693$	112.424	−	55.7852i	0.162229	−	0.0804981i
$694$	−450.211	−	779.788i	−0.648719	−	1.12361i
$695$	−936.899	−	1116.55i	−1.34806	−	1.60655i
$696$	−15.1176	+	479.808i	−0.0217207	+	0.689380i
$697$	76.6014	−	434.428i	0.109902	−	0.623283i
$698$	−259.713	+	309.514i	−0.372082	+	0.443430i
$699$	482.076	+	431.096i	0.689665	+	0.616733i
$700$	61.5102	+	22.3879i	0.0878717	+	0.0319827i
$701$			445.528i			0.635560i	0.948164	+	0.317780i	$0.102937\pi$
$701$			445.528i			0.635560i	−0.948164	+	0.317780i	$0.897063\pi$
$702$	−20.1133	+	28.2876i	−0.0286515	+	0.0402958i
$703$	377.173			0.536519
$704$	−42.3479	+	116.350i	−0.0601533	+	0.165270i
$705$	−181.635	−	552.597i	−0.257638	−	0.783825i
$706$	−355.195	−	298.044i	−0.503109	−	0.422158i
$707$	93.7003	+	16.5219i	0.132532	+	0.0233690i
$708$	189.161	+	352.852i	0.267176	+	0.498379i
$709$	−112.307	+	94.2371i	−0.158402	+	0.132915i	−0.718544	−	0.695481i	$-0.755191\pi$
$709$	−112.307	+	94.2371i	−0.158402	+	0.132915i	0.560142	+	0.828397i	$0.310747\pi$
$710$	270.773	−	156.331i	0.381371	−	0.220185i
$711$	−188.792	−	179.842i	−0.265530	−	0.252943i
$712$	−129.498	+	224.296i	−0.181879	+	0.315023i
$713$	1601.30	−	282.353i	2.24587	−	0.396007i
$714$	−17.4893	+	43.7160i	−0.0244948	+	0.0612269i
$715$	−103.529	+	37.6815i	−0.144796	+	0.0527014i
$716$	−7.62086	−	20.9381i	−0.0106437	−	0.0292432i
$717$	−98.6477	+	77.6151i	−0.137584	+	0.108250i
$718$	137.375	+	779.092i	0.191330	+	1.08509i
$719$	442.793	+	255.647i	0.615845	+	0.355559i	0.775250	−	0.631655i	$-0.217624\pi$
$719$	442.793	+	255.647i	0.615845	+	0.355559i	−0.159404	+	0.987213i	$0.550957\pi$
$720$	112.907	−	258.320i	0.156816	−	0.358778i
$721$	39.1853	+	67.8710i	0.0543486	+	0.0941345i
$722$	221.890	+	264.438i	0.307326	+	0.366257i
$723$	−1143.01	−	708.824i	−1.58092	−	0.980393i
$724$	−66.1782	+	375.315i	−0.0914064	+	0.518392i
$725$	1320.96	−	1574.26i	1.82202	−	2.17140i
$726$	102.887	−	492.291i	0.141717	−	0.678087i
$727$	−233.836	−	85.1092i	−0.321644	−	0.117069i	0.176152	−	0.984363i	$-0.443635\pi$
$727$	−233.836	−	85.1092i	−0.321644	−	0.117069i	−0.497796	+	0.867294i	$0.665857\pi$
$728$		−	2.31653i		−	0.00318204i
$729$	239.408	+	688.567i	0.328406	+	0.944537i
$730$	−238.684			−0.326964
$731$	−174.885	+	480.493i	−0.239241	+	0.657310i
$732$	−144.053	−	30.1065i	−0.196794	−	0.0411292i
$733$	645.868	+	541.947i	0.881129	+	0.739355i	0.966411	−	0.257002i	$-0.0827346\pi$
$733$	645.868	+	541.947i	0.881129	+	0.739355i	−0.0852818	+	0.996357i	$0.527179\pi$
$734$	−668.092	−	117.803i	−0.910208	−	0.160494i
$735$	−596.640	+	962.107i	−0.811755	+	1.30899i
$736$	142.224	−	119.340i	0.193239	−	0.162147i
$737$	874.202	−	504.721i	1.18616	−	0.684832i
$738$	417.679	+	182.560i	0.565960	+	0.247372i
$739$	339.638	−	588.271i	0.459592	−	0.796036i	−0.539347	−	0.842083i	$-0.681329\pi$
$739$	339.638	−	588.271i	0.459592	−	0.796036i	0.998939	+	0.0460469i	$0.0146624\pi$
$740$	−538.046	+	94.8721i	−0.727090	+	0.128206i
$741$	−18.2322	−	23.1729i	−0.0246049	−	0.0312725i
$742$	60.2681	−	21.9358i	0.0812239	−	0.0295631i
$743$	215.273	+	591.458i	0.289735	+	0.796040i	0.996103	+	0.0881957i	$0.0281101\pi$
$743$	215.273	+	591.458i	0.289735	+	0.796040i	−0.706368	+	0.707845i	$0.749668\pi$
$744$	390.306	+	156.148i	0.524605	+	0.209877i
$745$	172.409	+	977.780i	0.231421	+	1.31246i
$746$	421.250	+	243.209i	0.564679	+	0.326017i
$747$	−0.924050	+	0.970033i	−0.00123701	+	0.00129857i
$748$	190.638	+	330.194i	0.254863	+	0.441436i
$749$	−14.1928	−	16.9143i	−0.0189490	−	0.0225825i
$750$	−331.620	+	177.779i	−0.442160	+	0.237038i
$751$	123.896	−	702.649i	0.164975	−	0.935618i	−0.784116	−	0.620615i	$-0.786883\pi$
$751$	123.896	−	702.649i	0.164975	−	0.935618i	0.949090	−	0.315004i	$-0.102006\pi$
$752$	63.6609	−	75.8681i	0.0846555	−	0.100888i
$753$	731.475	−	240.431i	0.971414	−	0.319297i
$754$	−68.3416	−	24.8743i	−0.0906387	−	0.0329898i
$755$			1076.25i			1.42550i
$756$	−39.6524	−	28.1940i	−0.0524502	−	0.0372937i
$757$	1327.86			1.75411			0.877055	−	0.480390i	$-0.159505\pi$
$757$	1327.86			1.75411			0.877055	+	0.480390i	$0.159505\pi$
$758$	50.3790	−	138.415i	0.0664631	−	0.182606i
$759$	−1015.82	+	1135.95i	−1.33836	+	1.49663i
$760$	183.459	+	153.940i	0.241393	+	0.202553i
$761$	−928.015	−	163.634i	−1.21947	−	0.215025i	−0.473371	−	0.880863i	$-0.656963\pi$
$761$	−928.015	−	163.634i	−1.21947	−	0.215025i	−0.746096	+	0.665838i	$0.768074\pi$
$762$	−442.978	−	13.9572i	−0.581336	−	0.0183165i
$763$	23.1713	−	19.4430i	0.0303687	−	0.0254824i
$764$	−29.6953	+	17.1446i	−0.0388682	+	0.0224406i
$765$	−385.870	−	777.648i	−0.504406	−	1.01653i
$766$	45.8707	−	79.4505i

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)

\(f(q)\)	\(=\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-2.93655 - 0.613727i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-7.71206 - 1.35984i) q^{5} +(2.23598 - 3.60561i) q^{6} +(-0.690206 + 0.579152i) q^{7} +(2.44949 - 1.41421i) q^{8} +(8.24668 + 3.60448i) q^{9} +O(q^{10})\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-2.93655 - 0.613727i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-7.71206 - 1.35984i) q^{5} +(2.23598 - 3.60561i) q^{6} +(-0.690206 + 0.579152i) q^{7} +(2.44949 - 1.41421i) q^{8} +(8.24668 + 3.60448i) q^{9} +(5.53738 - 9.59102i) q^{10} +(-15.2420 + 2.68757i) q^{11} +(3.71007 + 4.71544i) q^{12} +(-0.854187 + 0.310899i) q^{13} +(-0.435804 - 1.19736i) q^{14} +(21.8123 + 8.72635i) q^{15} +(0.694593 + 3.93923i) q^{16} +(10.6672 + 6.15869i) q^{17} +(-8.77892 + 9.21578i) q^{18} +(-5.40619 - 9.36379i) q^{19} +(10.0674 + 11.9978i) q^{20} +(2.38227 - 1.27711i) q^{21} +(3.80080 - 21.5554i) q^{22} +(-21.0966 + 25.1419i) q^{23} +(-8.06100 + 2.64959i) q^{24} +(34.1344 + 12.4239i) q^{25} -1.28553i q^{26} +(-22.0046 - 15.6460i) q^{27} +1.80200 q^{28} +(19.3495 - 53.1622i) q^{29} +(-22.1471 + 24.7661i) q^{30} +(-37.9518 - 31.8453i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(46.4083 + 1.46222i) q^{33} +(-13.3440 + 11.1970i) q^{34} +(6.11047 - 3.52788i) q^{35} +(-8.00081 - 16.1241i) q^{36} +(-17.4417 + 30.2099i) q^{37} +(15.0587 - 2.65526i) q^{38} +(2.69917 - 0.388733i) q^{39} +(-20.8137 + 7.57558i) q^{40} +(-12.2490 - 33.6538i) q^{41} +(0.544909 + 3.78358i) q^{42} +(7.20864 + 40.8822i) q^{43} +(26.8072 + 15.4771i) q^{44} +(-58.6974 - 39.0122i) q^{45} +(-23.2075 - 40.1966i) q^{46} +(-15.9152 - 18.9670i) q^{47} +(0.377904 - 11.9940i) q^{48} +(-8.36779 + 47.4561i) q^{49} +(-33.0209 + 39.3528i) q^{50} +(-27.5449 - 24.6320i) q^{51} +(1.70837 + 0.621797i) q^{52} +50.3340i q^{53} +(31.4357 - 21.6747i) q^{54} +121.202 q^{55} +(-0.871609 + 2.39472i) q^{56} +(10.1287 + 30.8152i) q^{57} +(61.2895 + 51.4280i) q^{58} +(65.7126 + 11.5869i) q^{59} +(-22.2000 - 41.4109i) q^{60} +(-18.7893 + 15.7661i) q^{61} +(60.6770 - 35.0319i) q^{62} +(-7.77945 + 2.28824i) q^{63} +(4.00000 - 6.92820i) q^{64} +(7.01032 - 1.23611i) q^{65} +(-24.3904 + 60.9660i) q^{66} +(-61.2882 + 22.3071i) q^{67} +(-8.42558 - 23.1491i) q^{68} +(77.3814 - 60.8830i) q^{69} +(1.73272 + 9.82676i) q^{70} +(24.4496 + 14.1160i) q^{71} +(25.2977 - 2.83342i) q^{72} +(-10.7760 - 18.6646i) q^{73} +(-31.7104 - 37.7910i) q^{74} +(-92.6126 - 57.4327i) q^{75} +(-3.75510 + 21.2962i) q^{76} +(8.96360 - 10.6824i) q^{77} +(-0.788964 + 3.77503i) q^{78} +(-27.2240 - 9.90872i) q^{79} -31.3241i q^{80} +(55.0154 + 59.4500i) q^{81} +50.6481 q^{82} +(-0.0509121 + 0.139880i) q^{83} +(-5.29167 - 1.10594i) q^{84} +(-73.8910 - 62.0019i) q^{85} +(-57.8162 - 10.1946i) q^{86} +(-89.4477 + 144.238i) q^{87} +(-33.5343 + 28.1386i) q^{88} +(-79.3008 + 45.7843i) q^{89} +(80.2356 - 59.1347i) q^{90} +(0.409508 - 0.709288i) q^{91} +(64.6436 - 11.3984i) q^{92} +(91.9031 + 116.807i) q^{93} +(32.9038 - 11.9760i) q^{94} +(28.9595 + 79.5657i) q^{95} +(15.7564 + 6.30360i) q^{96} +(-17.4501 - 98.9646i) q^{97} +(-59.0182 - 34.0742i) q^{98} +(-135.383 - 32.7759i) 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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