LMFDB - Embedded newform 54.3.f.a.23.5

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			23.5
Character	$\chi$	$=$	54.23
Dual form			54.3.f.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483690 - 1.32893i) q^{2} +(0.320982 + 2.98278i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(5.90332 + 1.04091i) q^{5} +(4.11915 + 1.01618i) q^{6} +(5.59840 - 4.69762i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(-8.79394 + 1.91484i) q^{9} +O(q^{10})$	\(q+(0.483690 - 1.32893i) q^{2} +(0.320982 + 2.98278i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(5.90332 + 1.04091i) q^{5} +(4.11915 + 1.01618i) q^{6} +(5.59840 - 4.69762i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(-8.79394 + 1.91484i) q^{9} +(4.23867 - 7.34160i) q^{10} +(-20.3832 + 3.59412i) q^{11} +(3.34281 - 4.98253i) q^{12} +(6.40830 - 2.33243i) q^{13} +(-3.53490 - 9.71205i) q^{14} +(-1.20996 + 17.9424i) q^{15} +(0.694593 + 3.93923i) q^{16} +(1.96510 + 1.13455i) q^{17} +(-1.70886 + 12.6127i) q^{18} +(-12.1634 - 21.0675i) q^{19} +(-7.70624 - 9.18394i) q^{20} +(15.8089 + 15.1909i) q^{21} +(-5.08285 + 28.8263i) q^{22} +(-15.5320 + 18.5103i) q^{23} +(-5.00453 - 6.85235i) q^{24} +(10.2734 + 3.73921i) q^{25} -9.64433i q^{26} +(-8.53423 - 25.6158i) q^{27} -14.6164 q^{28} +(6.32777 - 17.3854i) q^{29} +(23.2589 + 10.2865i) q^{30} +(16.6469 + 13.9684i) q^{31} +(5.57091 + 0.982302i) q^{32} +(-17.2631 - 59.6451i) q^{33} +(2.45823 - 2.06270i) q^{34} +(37.9390 - 21.9041i) q^{35} +(15.9348 + 8.37157i) q^{36} +(22.3832 - 38.7688i) q^{37} +(-33.8805 + 5.97405i) q^{38} +(9.01408 + 18.3659i) q^{39} +(-15.9322 + 5.79885i) q^{40} +(17.5398 + 48.1902i) q^{41} +(27.8343 - 13.6612i) q^{42} +(6.41470 + 36.3796i) q^{43} +(35.8494 + 20.6977i) q^{44} +(-53.9066 + 2.15015i) q^{45} +(17.0861 + 29.5941i) q^{46} +(8.15595 + 9.71989i) q^{47} +(-11.5269 + 3.33624i) q^{48} +(0.765740 - 4.34273i) q^{49} +(9.93826 - 11.8440i) q^{50} +(-2.75335 + 6.22562i) q^{51} +(-12.8166 - 4.66486i) q^{52} -17.7730i q^{53} +(-38.1694 - 1.04871i) q^{54} -124.070 q^{55} +(-7.06980 + 19.4241i) q^{56} +(58.9356 - 43.0429i) q^{57} +(-20.0432 - 16.8183i) q^{58} +(64.9049 + 11.4445i) q^{59} +(24.9201 - 25.9339i) q^{60} +(32.3438 - 27.1396i) q^{61} +(26.6150 - 15.3662i) q^{62} +(-40.2369 + 52.0306i) q^{63} +(4.00000 - 6.92820i) q^{64} +(40.2581 - 7.09859i) q^{65} +(-87.6139 - 5.90830i) q^{66} +(-111.190 + 40.4700i) q^{67} +(-1.55216 - 4.26451i) q^{68} +(-60.1976 - 40.3870i) q^{69} +(-10.7582 - 61.0129i) q^{70} +(-46.1702 - 26.6564i) q^{71} +(18.8327 - 17.1269i) q^{72} +(33.8569 + 58.6419i) q^{73} +(-40.6944 - 48.4976i) q^{74} +(-7.85565 + 31.8434i) q^{75} +(-8.44858 + 47.9143i) q^{76} +(-97.2298 + 115.874i) q^{77} +(28.7669 - 3.09566i) q^{78} +(104.610 + 38.0750i) q^{79} +23.9776i q^{80} +(73.6668 - 33.6779i) q^{81} +72.5250 q^{82} +(8.63542 - 23.7256i) q^{83} +(-4.69160 - 43.5975i) q^{84} +(10.4196 + 8.74311i) q^{85} +(51.4485 + 9.07175i) q^{86} +(53.8879 + 13.2939i) q^{87} +(44.8457 - 37.6300i) q^{88} +(-35.4447 + 20.4640i) q^{89} +(-23.2167 + 72.6779i) q^{90} +(24.9194 - 43.1616i) q^{91} +(47.5927 - 8.39188i) q^{92} +(-36.3214 + 54.1378i) q^{93} +(16.8620 - 6.13725i) q^{94} +(-49.8747 - 137.030i) q^{95} +(-1.14183 + 16.9321i) q^{96} +(7.02010 + 39.8130i) q^{97} +(-5.40078 - 3.11814i) q^{98} +(172.367 - 70.6370i) 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
$3$	0.320982	+	2.98278i	0.106994	+	0.994260i
$3$	0.320982	+	2.98278i	0.106994	+	0.994260i
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	5.90332	+	1.04091i	1.18066	+	0.208183i	0.729324	−	0.684169i	$-0.239835\pi$
$5$	5.90332	+	1.04091i	1.18066	+	0.208183i	0.451341	+	0.892352i	$0.350946\pi$
$6$	4.11915	+	1.01618i	0.686525	+	0.169363i
$7$	5.59840	−	4.69762i	0.799772	−	0.671088i	−0.148371	−	0.988932i	$-0.547403\pi$
$7$	5.59840	−	4.69762i	0.799772	−	0.671088i	0.948143	+	0.317844i	$0.102959\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$	−8.79394	+	1.91484i	−0.977105	+	0.212760i
$10$	4.23867	−	7.34160i	0.423867	−	0.734160i
$11$	−20.3832	+	3.59412i	−1.85302	+	0.326738i	−0.985369	−	0.170433i	$-0.945483\pi$
$11$	−20.3832	+	3.59412i	−1.85302	+	0.326738i	−0.867653	+	0.497170i	$0.834372\pi$
$12$	3.34281	−	4.98253i	0.278568	−	0.415211i
$13$	6.40830	−	2.33243i	0.492946	−	0.179418i	−0.0835725	−	0.996502i	$-0.526633\pi$
$13$	6.40830	−	2.33243i	0.492946	−	0.179418i	0.576519	+	0.817084i	$0.304411\pi$
$14$	−3.53490	−	9.71205i	−0.252493	−	0.693718i
$15$	−1.20996	+	17.9424i	−0.0806639	+	1.19616i
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	1.96510	+	1.13455i	0.115594	+	0.0667382i	0.556682	−	0.830725i	$-0.312074\pi$
$17$	1.96510	+	1.13455i	0.115594	+	0.0667382i	−0.441088	+	0.897464i	$0.645407\pi$
$18$	−1.70886	+	12.6127i	−0.0949367	+	0.700705i
$19$	−12.1634	−	21.0675i	−0.640176	−	1.10882i	−0.985393	−	0.170295i	$-0.945528\pi$
$19$	−12.1634	−	21.0675i	−0.640176	−	1.10882i	0.345217	−	0.938523i	$-0.387805\pi$
$20$	−7.70624	−	9.18394i	−0.385312	−	0.459197i
$21$	15.8089	+	15.1909i	0.752807	+	0.723378i
$22$	−5.08285	+	28.8263i	−0.231039	+	1.31028i
$23$	−15.5320	+	18.5103i	−0.675303	+	0.804795i	−0.989495	−	0.144564i	$-0.953822\pi$
$23$	−15.5320	+	18.5103i	−0.675303	+	0.804795i	0.314192	+	0.949359i	$0.398266\pi$
$24$	−5.00453	−	6.85235i	−0.208522	−	0.285515i
$25$	10.2734	+	3.73921i	0.410935	+	0.149568i
$26$		−	9.64433i		−	0.370936i
$27$	−8.53423	−	25.6158i	−0.316083	−	0.948732i
$28$	−14.6164			−0.522014
$29$	6.32777	−	17.3854i	0.218199	−	0.599497i	−0.781503	−	0.623901i	$-0.785547\pi$
$29$	6.32777	−	17.3854i	0.218199	−	0.599497i	0.999702	+	0.0244045i	$0.00776896\pi$
$30$	23.2589	+	10.2865i	0.775297	+	0.342884i
$31$	16.6469	+	13.9684i	0.536998	+	0.450595i	0.870510	−	0.492151i	$-0.163789\pi$
$31$	16.6469	+	13.9684i	0.536998	+	0.450595i	−0.333512	+	0.942746i	$0.608234\pi$
$32$	5.57091	+	0.982302i	0.174091	+	0.0306970i
$33$	−17.2631	−	59.6451i	−0.523124	−	1.80743i
$34$	2.45823	−	2.06270i	0.0723009	−	0.0606677i
$35$	37.9390	−	21.9041i	1.08397	−	0.625831i
$36$	15.9348	+	8.37157i	0.442632	+	0.232544i
$37$	22.3832	−	38.7688i	0.604951	−	1.04781i	−0.387109	−	0.922034i	$-0.626526\pi$
$37$	22.3832	−	38.7688i	0.604951	−	1.04781i	0.992059	−	0.125771i	$-0.0401405\pi$
$38$	−33.8805	+	5.97405i	−0.891592	+	0.157212i
$39$	9.01408	+	18.3659i	0.231130	+	0.470920i
$40$	−15.9322	+	5.79885i	−0.398305	+	0.144971i
$41$	17.5398	+	48.1902i	0.427800	+	1.17537i	0.947145	+	0.320806i	$0.103954\pi$
$41$	17.5398	+	48.1902i	0.427800	+	1.17537i	−0.519345	+	0.854565i	$0.673824\pi$
$42$	27.8343	−	13.6612i	0.662721	−	0.325267i
$43$	6.41470	+	36.3796i	0.149179	+	0.846036i	0.963916	+	0.266206i	$0.0857701\pi$
$43$	6.41470	+	36.3796i	0.149179	+	0.846036i	−0.814737	+	0.579830i	$0.803119\pi$
$44$	35.8494	+	20.6977i	0.814760	+	0.470402i
$45$	−53.9066	+	2.15015i	−1.19793	+	0.0477812i
$46$	17.0861	+	29.5941i	0.371438	+	0.643350i
$47$	8.15595	+	9.71989i	0.173531	+	0.206806i	0.845799	−	0.533502i	$-0.179124\pi$
$47$	8.15595	+	9.71989i	0.173531	+	0.206806i	−0.672268	+	0.740308i	$0.734680\pi$
$48$	−11.5269	+	3.33624i	−0.240144	+	0.0695050i
$49$	0.765740	−	4.34273i	0.0156273	−	0.0886271i
$50$	9.93826	−	11.8440i	0.198765	−	0.236879i
$51$	−2.75335	+	6.22562i	−0.0539873	+	0.122071i
$52$	−12.8166	−	4.66486i	−0.246473	−	0.0897089i
$53$		−	17.7730i		−	0.335339i	−0.985843	−	0.167670i	$-0.946376\pi$
$53$		−	17.7730i		−	0.335339i	0.985843	−	0.167670i	$-0.0536242\pi$
$54$	−38.1694	−	1.04871i	−0.706840	−	0.0194206i
$55$	−124.070			−2.25582
$56$	−7.06980	+	19.4241i	−0.126246	+	0.346859i
$57$	58.9356	−	43.0429i	1.03396	−	0.755139i
$58$	−20.0432	−	16.8183i	−0.345573	−	0.289970i
$59$	64.9049	+	11.4445i	1.10008	+	0.193974i	0.694080	−	0.719897i	$-0.255811\pi$
$59$	64.9049	+	11.4445i	1.10008	+	0.193974i	0.406003	+	0.913872i	$0.366922\pi$
$60$	24.9201	−	25.9339i	0.415335	−	0.432231i
$61$	32.3438	−	27.1396i	0.530226	−	0.444912i	−0.337954	−	0.941163i	$-0.609735\pi$
$61$	32.3438	−	27.1396i	0.530226	−	0.444912i	0.868179	+	0.496251i	$0.165290\pi$
$62$	26.6150	−	15.3662i	0.429274	−	0.247841i
$63$	−40.2369	+	52.0306i	−0.638680	+	0.825882i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	40.2581	−	7.09859i	0.619356	−	0.109209i
$66$	−87.6139	−	5.90830i	−1.32748	−	0.0895197i
$67$	−111.190	+	40.4700i	−1.65956	+	0.604030i	−0.990293	−	0.138993i	$-0.955613\pi$
$67$	−111.190	+	40.4700i	−1.65956	+	0.604030i	−0.669266	+	0.743023i	$0.733391\pi$
$68$	−1.55216	−	4.26451i	−0.0228258	−	0.0627134i
$69$	−60.1976	−	40.3870i	−0.872429	−	0.585319i
$70$	−10.7582	−	61.0129i	−0.153689	−	0.871613i
$71$	−46.1702	−	26.6564i	−0.650284	−	0.375442i	0.138281	−	0.990393i	$-0.455842\pi$
$71$	−46.1702	−	26.6564i	−0.650284	−	0.375442i	−0.788565	+	0.614951i	$0.789176\pi$
$72$	18.8327	−	17.1269i	0.261565	−	0.237873i
$73$	33.8569	+	58.6419i	0.463793	+	0.803314i	0.999146	−	0.0413148i	$-0.0131546\pi$
$73$	33.8569	+	58.6419i	0.463793	+	0.803314i	−0.535353	+	0.844629i	$0.679821\pi$
$74$	−40.6944	−	48.4976i	−0.549924	−	0.655374i
$75$	−7.85565	+	31.8434i	−0.104742	+	0.424579i
$76$	−8.44858	+	47.9143i	−0.111165	+	0.630451i
$77$	−97.2298	+	115.874i	−1.26273	+	1.50486i
$78$	28.7669	−	3.09566i	0.368807	−	0.0396879i
$79$	104.610	+	38.0750i	1.32418	+	0.481962i	0.904795	−	0.425846i	$-0.140024\pi$
$79$	104.610	+	38.0750i	1.32418	+	0.481962i	0.419385	+	0.907809i	$0.362246\pi$
$80$			23.9776i			0.299719i
$81$	73.6668	−	33.6779i	0.909467	−	0.415777i
$82$	72.5250			0.884452
$83$	8.63542	−	23.7256i	0.104041	−	0.285851i	−0.876739	−	0.480966i	$-0.840286\pi$
$83$	8.63542	−	23.7256i	0.104041	−	0.285851i	0.980780	+	0.195115i	$0.0625081\pi$
$84$	−4.69160	−	43.5975i	−0.0558524	−	0.519017i
$85$	10.4196	+	8.74311i	0.122584	+	0.102860i
$86$	51.4485	+	9.07175i	0.598238	+	0.105486i
$87$	53.8879	+	13.2939i	0.619401	+	0.152804i
$88$	44.8457	−	37.6300i	0.509610	−	0.427614i
$89$	−35.4447	+	20.4640i	−0.398254	+	0.229932i	−0.685731	−	0.727855i	$-0.740517\pi$
$89$	−35.4447	+	20.4640i	−0.398254	+	0.229932i	0.287476	+	0.957788i	$0.407184\pi$
$90$	−23.2167	+	72.6779i	−0.257963	+	0.807533i
$91$	24.9194	−	43.1616i	0.273839	−	0.474304i
$92$	47.5927	−	8.39188i	0.517312	−	0.0912161i
$93$	−36.3214	+	54.1378i	−0.390553	+	0.582127i
$94$	16.8620	−	6.13725i	0.179383	−	0.0652899i
$95$	−49.8747	−	137.030i	−0.524996	−	1.44242i
$96$	−1.14183	+	16.9321i	−0.0118940	+	0.176376i
$97$	7.02010	+	39.8130i	0.0723722	+	0.410443i	0.999374	+	0.0353855i	$0.0112659\pi$
$97$	7.02010	+	39.8130i	0.0723722	+	0.410443i	−0.927002	+	0.375057i	$0.877623\pi$
$98$	−5.40078	−	3.11814i	−0.0551100	−	0.0318178i
$99$	172.367	−	70.6370i	1.74108	−	0.713505i
$100$	−10.9327	−	18.9360i	−0.109327	−	0.189360i
$101$	7.45688	+	8.88677i	0.0738305	+	0.0879878i	0.801695	−	0.597733i	$-0.203932\pi$
$101$	7.45688	+	8.88677i	0.0738305	+	0.0879878i	−0.727865	+	0.685721i	$0.759487\pi$
$102$	6.94163	+	6.67027i	0.0680552	+	0.0653948i
$103$	21.6451	−	122.756i	0.210147	−	1.19180i	−0.678985	−	0.734152i	$-0.737580\pi$
$103$	21.6451	−	122.756i	0.210147	−	1.19180i	0.889132	−	0.457650i	$-0.151309\pi$
$104$	−12.3985	+	14.7760i	−0.119216	+	0.142077i
$105$	77.5128	+	106.133i	0.738217	+	1.01079i
$106$	−23.6190	−	8.59660i	−0.222820	−	0.0811000i
$107$		−	142.548i		−	1.33223i	−0.745850	−	0.666113i	$-0.767957\pi$
$107$		−	142.548i		−	1.33223i	0.745850	−	0.666113i	$-0.232043\pi$
$108$	−19.8558	+	50.2170i	−0.183850	+	0.464972i
$109$	−119.276			−1.09427			−0.547137	−	0.837043i	$-0.684282\pi$
$109$	−119.276			−1.09427			−0.547137	+	0.837043i	$0.684282\pi$
$110$	−60.0114	+	164.880i	−0.545558	+	1.49891i
$111$	122.823	+	54.3200i	1.10652	+	0.489369i
$112$	22.3936	+	18.7905i	0.199943	+	0.167772i
$113$	−102.092	−	18.0016i	−0.903471	−	0.159306i	−0.297434	−	0.954743i	$-0.596131\pi$
$113$	−102.092	−	18.0016i	−0.903471	−	0.159306i	−0.606037	+	0.795436i	$0.707242\pi$
$114$	−28.6943	−	99.1405i	−0.251704	−	0.869653i
$115$	−110.958	+	93.1047i	−0.964851	+	0.809606i
$116$	−32.0450	+	18.5012i	−0.276250	+	0.159493i
$117$	−51.8880	+	32.7821i	−0.443487	+	0.280189i
$118$	46.6027	−	80.7183i	0.394938	−	0.684053i
$119$	16.3311	−	2.87961i	0.137236	−	0.0241984i
$120$	−22.4106	−	45.6609i	−0.186755	−	0.380508i
$121$	288.856	−	105.135i	2.38724	−	0.868885i
$122$	−20.4222	−	56.1096i	−0.167395	−	0.459915i
$123$	−138.111	+	67.7855i	−1.12285	+	0.551102i
$124$	−7.54711	−	42.8018i	−0.0608638	−	0.345176i
$125$	−73.0275	−	42.1624i	−0.584220	−	0.337299i
$126$	49.6827	+	78.6385i	0.394307	+	0.624115i
$127$	109.770	+	190.127i	0.864329	+	1.49706i	0.867712	+	0.497067i	$0.165590\pi$
$127$	109.770	+	190.127i	0.864329	+	1.49706i	−0.00338367	+	0.999994i	$0.501077\pi$
$128$	−7.27231	−	8.66680i	−0.0568149	−	0.0677094i
$129$	−106.453	+	30.8108i	−0.825219	+	0.238844i
$130$	10.0389	−	56.9336i	0.0772225	−	0.437951i
$131$	83.9745	−	100.077i	0.641027	−	0.763946i	−0.343505	−	0.939151i	$-0.611614\pi$
$131$	83.9745	−	100.077i	0.641027	−	0.763946i	0.984532	+	0.175205i	$0.0560587\pi$
$132$	−50.2296	+	113.575i	−0.380527	+	0.860413i
$133$	−167.063	−	60.8058i	−1.25611	−	0.457187i
$134$			167.339i			1.24880i
$135$	−23.7165	−	160.101i	−0.175678	−	1.18594i
$136$	−6.41798			−0.0471911
$137$	26.4097	−	72.5602i	0.192772	−	0.529636i	−0.805220	−	0.592976i	$-0.797953\pi$
$137$	26.4097	−	72.5602i	0.192772	−	0.529636i	0.997992	+	0.0633396i	$0.0201751\pi$
$138$	−82.7882	+	60.4634i	−0.599915	+	0.438140i
$139$	−81.8517	−	68.6818i	−0.588861	−	0.494113i	0.298982	−	0.954259i	$-0.403353\pi$
$139$	−81.8517	−	68.6818i	−0.588861	−	0.494113i	−0.887844	+	0.460145i	$0.847797\pi$
$140$	−86.2852	−	15.2144i	−0.616323	−	0.108674i
$141$	−26.3744	+	27.4473i	−0.187052	+	0.194662i
$142$	−57.7564	+	48.4633i	−0.406735	+	0.341291i
$143$	−122.239	+	70.5747i	−0.854818	+	0.493529i
$144$	−13.6512	−	33.3113i	−0.0947999	−	0.231329i
$145$	55.4516	−	96.0450i	0.382425	−	0.662379i
$146$	94.3070	−	16.6289i	0.645938	−	0.113896i
$147$	13.1992	+	0.890096i	0.0897903	+	0.00605507i
$148$	−84.1332	+	30.6220i	−0.568468	+	0.206905i
$149$	53.0524	+	145.760i	0.356056	+	0.978257i	0.980384	+	0.197095i	$0.0631506\pi$
$149$	53.0524	+	145.760i	0.356056	+	0.978257i	−0.624328	+	0.781162i	$0.714627\pi$
$150$	38.5179	+	25.8419i	0.256786	+	0.172279i
$151$	−26.9250	−	152.699i	−0.178311	−	1.01125i	−0.934252	−	0.356614i	$-0.883931\pi$
$151$	−26.9250	−	152.699i	−0.178311	−	1.01125i	0.755940	−	0.654641i	$-0.227180\pi$
$152$	59.5880	+	34.4032i	0.392026	+	0.226337i
$153$	−19.4534	−	6.21432i	−0.127147	−	0.0406165i
$154$	106.959	+	185.258i	0.694538	+	1.20298i
$155$	83.7323	+	99.7883i	0.540208	+	0.643795i
$156$	9.80035	−	39.7264i	0.0628228	−	0.254657i
$157$	−21.0948	+	119.634i	−0.134362	+	0.762003i	0.840941	+	0.541128i	$0.182002\pi$
$157$	−21.0948	+	119.634i	−0.134362	+	0.762003i	−0.975302	+	0.220875i	$0.929109\pi$
$158$	101.198	−	120.603i	0.640492	−	0.763309i
$159$	53.0128	−	5.70480i	0.333414	−	0.0358793i
$160$	31.8644	+	11.5977i	0.199153	+	0.0724856i
$161$			176.591i			1.09684i
$162$	−9.12361	−	114.187i	−0.0563186	−	0.704860i
$163$	−66.9033			−0.410450			−0.205225	−	0.978715i	$-0.565793\pi$
$163$	−66.9033			−0.410450			−0.205225	+	0.978715i	$0.565793\pi$
$164$	35.0796	−	96.3804i	0.213900	−	0.587685i
$165$	−39.8242	−	370.073i	−0.241359	−	2.24287i
$166$	−27.3527	−	22.9517i	−0.164776	−	0.138263i
$167$	−7.14238	−	1.25939i	−0.0427687	−	0.00754128i	0.152223	−	0.988346i	$-0.451357\pi$
$167$	−7.14238	−	1.25939i	−0.0427687	−	0.00754128i	−0.194992	+	0.980805i	$0.562468\pi$
$168$	−60.2071	−	14.8528i	−0.358375	−	0.0884098i
$169$	−93.8354	+	78.7373i	−0.555239	+	0.465901i
$170$	16.6588	−	9.61798i	0.0979931	−	0.0565763i
$171$	147.305	+	161.976i	0.861431	+	0.947228i
$172$	36.9408	−	63.9833i	0.214772	−	0.371996i
$173$	−71.4004	+	12.5898i	−0.412719	+	0.0727735i	−0.376153	−	0.926558i	$-0.622753\pi$
$173$	−71.4004	+	12.5898i	−0.412719	+	0.0727735i	−0.0365665	+	0.999331i	$0.511642\pi$
$174$	43.7317	−	65.1829i	0.251332	−	0.374615i
$175$	75.0799	−	27.3268i	0.429028	−	0.156153i
$176$	−28.3161	−	77.7979i	−0.160887	−	0.442033i
$177$	−13.3031	+	197.270i	−0.0751586	+	1.11452i
$178$	10.0509	+	57.0015i	0.0564658	+	0.320233i
$179$	219.366	+	126.651i	1.22551	+	0.707547i	0.966087	−	0.258218i	$-0.0831352\pi$
$179$	219.366	+	126.651i	1.22551	+	0.707547i	0.259420	+	0.965765i	$0.416469\pi$
$180$	85.3539	+	66.0068i	0.474189	+	0.366705i
$181$	19.4150	+	33.6278i	0.107265	+	0.185789i	0.914662	−	0.404221i	$-0.132457\pi$
$181$	19.4150	+	33.6278i	0.107265	+	0.185789i	−0.807396	+	0.590010i	$0.799124\pi$
$182$	−45.3054	−	53.9928i	−0.248931	−	0.296664i
$183$	91.3333	+	87.7630i	0.499089	+	0.479579i
$184$	11.8679	−	67.3063i	0.0644995	−	0.365795i
$185$	172.490	−	205.566i	0.932379	−	1.11117i
$186$	54.3768	+	74.4544i	0.292348	+	0.400292i
$187$	−44.1328	−	16.0630i	−0.236004	−	0.0858985i
$188$		−	25.3768i		−	0.134983i
$189$	−168.111	−	103.317i	−0.889477	−	0.546649i
$190$	−206.226			−1.08540
$191$	67.8767	−	186.490i	0.355375	−	0.976385i	−0.625238	−	0.780434i	$-0.714998\pi$
$191$	67.8767	−	186.490i	0.355375	−	0.976385i	0.980614	−	0.195951i	$-0.0627795\pi$
$192$	21.9492	+	9.70729i	0.114319	+	0.0505588i
$193$	43.6611	+	36.6360i	0.226223	+	0.189824i	0.748853	−	0.662736i	$-0.230605\pi$
$193$	43.6611	+	36.6360i	0.226223	+	0.189824i	−0.522630	+	0.852560i	$0.675049\pi$
$194$	56.3040	+	9.92792i	0.290227	+	0.0511748i
$195$	34.0957	+	117.803i	0.174850	+	0.604116i
$196$	−6.75608	+	5.66903i	−0.0344698	+	0.0289236i
$197$	−64.8251	+	37.4268i	−0.329061	+	0.189984i	−0.655424	−	0.755261i	$-0.727510\pi$
$197$	−64.8251	+	37.4268i	−0.329061	+	0.189984i	0.326363	+	0.945245i	$0.394177\pi$
$198$	−10.4993	−	263.229i	−0.0530269	−	1.32944i
$199$	−65.2158	+	112.957i	−0.327717	+	0.567623i	−0.982059	−	0.188576i	$-0.939613\pi$
$199$	−65.2158	+	112.957i	−0.327717	+	0.567623i	0.654341	+	0.756200i	$0.272946\pi$
$200$	−30.4526	+	5.36961i	−0.152263	+	0.0268481i
$201$	−156.403	−	318.666i	−0.778126	−	1.58540i
$202$	15.4167	−	5.61121i	0.0763201	−	0.0277783i
$203$	−46.2446	−	127.056i	−0.227806	−	0.625891i
$204$	12.2219	−	5.99857i	0.0599112	−	0.0294048i
$205$	53.3812	+	302.740i	0.260396	+	1.47678i
$206$	−152.664	−	88.1404i	−0.741085	−	0.427866i
$207$	101.143	−	192.520i	0.488614	−	0.930046i
$208$	13.6391	+	23.6237i	0.0655728	+	0.113575i
$209$	323.648	+	385.708i	1.54855	+	1.84549i
$210$	178.535	−	51.6734i	0.850166	−	0.246064i
$211$	5.49032	−	31.1372i	0.0260205	−	0.147570i	−0.969030	−	0.246945i	$-0.920573\pi$
$211$	5.49032	−	31.1372i	0.0260205	−	0.147570i	0.995050	+	0.0993753i	$0.0316844\pi$
$212$	−22.8485	+	27.2298i	−0.107776	+	0.128442i
$213$	64.6902	−	146.272i	0.303710	−	0.686721i
$214$	−189.436	−	68.9491i	−0.885215	−	0.322192i
$215$			221.437i			1.02994i
$216$	57.1307	+	50.6763i	0.264494	+	0.234613i
$217$	158.815			0.731865
$218$	−57.6925	+	158.509i	−0.264644	+	0.727105i
$219$	−164.048	+	119.811i	−0.749079	+	0.547081i
$220$	190.086	+	159.501i	0.864029	+	0.725006i
$221$	15.2392	+	2.68708i	0.0689557	+	0.0121587i
$222$	131.596	−	136.949i	0.592773	−	0.616888i
$223$	78.1769	−	65.5982i	0.350569	−	0.294162i	−0.450449	−	0.892802i	$-0.648736\pi$
$223$	78.1769	−	65.5982i	0.350569	−	0.294162i	0.801019	+	0.598639i	$0.204292\pi$
$224$	35.8027	−	20.6707i	0.159833	−	0.0922799i
$225$	−97.5035	−	13.2105i	−0.433349	−	0.0587133i
$226$	−73.3037	+	126.966i	−0.324353	+	0.561796i
$227$	−253.309	+	44.6652i	−1.11590	+	0.196763i	−0.701039	−	0.713123i	$-0.747280\pi$
$227$	−253.309	+	44.6652i	−1.11590	+	0.196763i	−0.414859	+	0.909886i	$0.636169\pi$
$228$	−145.629	−	9.82062i	−0.638726	−	0.0430729i
$229$	−258.391	+	94.0468i	−1.12835	+	0.410685i	−0.837692	−	0.546143i	$-0.816095\pi$
$229$	−258.391	+	94.0468i	−1.12835	+	0.410685i	−0.290655	+	0.956828i	$0.593873\pi$
$230$	70.0601	+	192.489i	0.304609	+	0.836907i
$231$	−376.836	−	252.822i	−1.63132	−	1.09447i
$232$	9.08687	+	51.5342i	0.0391675	+	0.222130i
$233$	−223.311	−	128.928i	−0.958414	−	0.553341i	−0.0627296	−	0.998031i	$-0.519981\pi$
$233$	−223.311	−	128.928i	−0.958414	−	0.553341i	−0.895685	+	0.444690i	$0.853314\pi$
$234$	18.4673	+	84.8117i	0.0789202	+	0.362443i
$235$	38.0296	+	65.8693i	0.161828	+	0.280295i
$236$	−84.7273	−	100.974i	−0.359014	−	0.427856i
$237$	−79.9913	+	324.251i	−0.337516	+	1.36815i
$238$	4.07239	−	23.0957i	0.0171109	−	0.0970406i
$239$	−80.0566	+	95.4078i	−0.334965	+	0.399196i	−0.907067	−	0.420987i	$-0.861684\pi$
$239$	−80.0566	+	95.4078i	−0.334965	+	0.399196i	0.572102	+	0.820183i	$0.306128\pi$
$240$	−71.5198	+	7.69636i	−0.297999	+	0.0320682i
$241$	−61.5004	−	22.3843i	−0.255188	−	0.0928809i	0.211258	−	0.977430i	$-0.432244\pi$
$241$	−61.5004	−	22.3843i	−0.255188	−	0.0928809i	−0.466447	+	0.884549i	$0.654466\pi$
$242$		−	434.721i		−	1.79637i
$243$	124.100	+	208.922i	0.510698	+	0.859760i
$244$	−84.4436			−0.346080
$245$	9.04081	−	24.8394i	0.0369013	−	0.101385i
$246$	23.2792	+	216.326i	0.0946310	+	0.879375i
$247$	−127.085	−	106.637i	−0.514514	−	0.431729i
$248$	−60.5309	−	10.6732i	−0.244076	−	0.0430372i
$249$	73.5401	+	18.1421i	0.295342	+	0.0728597i
$250$	−91.3534	+	76.6546i	−0.365413	+	0.306618i
$251$	202.528	−	116.930i	0.806884	−	0.465855i	−0.0389884	−	0.999240i	$-0.512414\pi$
$251$	202.528	−	116.930i	0.806884	−	0.465855i	0.845873	+	0.533385i	$0.179080\pi$
$252$	128.536	−	27.9880i	0.510062	−	0.111063i
$253$	250.064	−	433.123i	0.988395	−	1.71195i
$254$	305.759	−	53.9135i	1.20378	−	0.212258i
$255$	−22.7343	+	33.8859i	−0.0891540	+	0.132886i
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	25.7075	+	70.6309i	0.100029	+	0.274828i	0.979606	−	0.200929i	$-0.0643962\pi$
$257$	25.7075	+	70.6309i	0.100029	+	0.274828i	−0.879576	+	0.475758i	$0.842174\pi$
$258$	−10.5450	+	156.371i	−0.0408721	+	0.606090i
$259$	−56.8110	−	322.191i	−0.219347	−	1.24398i
$260$	−70.8048	−	40.8792i	−0.272326	−	0.157228i
$261$	−22.3558	+	165.003i	−0.0856545	+	0.632195i
$262$	−92.3773	−	160.002i	−0.352585	−	0.610695i
$263$	−97.3609	−	116.030i	−0.370194	−	0.441180i	0.548500	−	0.836151i	$-0.315199\pi$
$263$	−97.3609	−	116.030i	−0.370194	−	0.441180i	−0.918694	+	0.394971i	$0.870755\pi$
$264$	126.637	+	121.686i	0.479684	+	0.460933i
$265$	18.5001	−	104.920i	0.0698119	−	0.395923i
$266$	−161.613	+	192.603i	−0.607567	+	0.724070i
$267$	−72.4166	−	99.1550i	−0.271223	−	0.371367i
$268$	222.381	+	80.9400i	0.829780	+	0.302015i
$269$		−	170.868i		−	0.635198i	−0.948225	−	0.317599i	$-0.897123\pi$
$269$		−	170.868i		−	0.635198i	0.948225	−	0.317599i	$-0.102877\pi$
$270$	−224.234	−	45.9219i	−0.830498	−	0.170081i
$271$	−8.46530			−0.0312373			−0.0156186	−	0.999878i	$-0.504972\pi$
$271$	−8.46530			−0.0312373			−0.0156186	+	0.999878i	$0.504972\pi$
$272$	−3.10431	+	8.52903i	−0.0114129	+	0.0313567i
$273$	136.740	+	60.4749i	0.500880	+	0.221520i
$274$	−83.6530	−	70.1932i	−0.305303	−	0.256180i
$275$	−222.844	−	39.2934i	−0.810342	−	0.142885i
$276$	40.3075	+	139.265i	0.146042	+	0.504583i
$277$	382.880	−	321.274i	1.38224	−	1.15984i	0.413862	−	0.910340i	$-0.364180\pi$
$277$	382.880	−	321.274i	1.38224	−	1.15984i	0.968376	−	0.249496i	$-0.0802649\pi$
$278$	−130.864	+	75.5542i	−0.470733	+	0.271778i
$279$	−173.140	−	90.9615i	−0.620572	−	0.326027i
$280$	−61.9541	+	107.308i	−0.221265	+	0.383242i
$281$	−68.9552	+	12.1587i	−0.245392	+	0.0432693i	−0.294991	−	0.955500i	$-0.595317\pi$
$281$	−68.9552	+	12.1587i	−0.245392	+	0.0432693i	0.0495990	+	0.998769i	$0.484206\pi$
$282$	23.7185	+	48.3256i	0.0841080	+	0.171367i
$283$	33.6840	−	12.2600i	0.119025	−	0.0433214i	−0.281821	−	0.959467i	$-0.590939\pi$
$283$	33.6840	−	12.2600i	0.119025	−	0.0433214i	0.400846	+	0.916145i	$0.368716\pi$
$284$	36.4680	+	100.195i	0.128409	+	0.352800i
$285$	392.720	−	192.749i	1.37796	−	0.676313i
$286$	34.6628	+	196.583i	0.121199	+	0.687352i
$287$	324.574	+	187.393i	1.13092	+	0.652937i
$288$	−50.8712	+	2.02908i	−0.176636	+	0.00704542i
$289$	−141.926	−	245.822i	−0.491092	−	0.850596i
$290$	−100.815	−	120.147i	−0.347639	−	0.414300i
$291$	−116.500	+	33.7187i	−0.400343	+	0.115872i
$292$	23.5168	−	133.370i	0.0805369	−	0.456747i
$293$	−21.9392	+	26.1461i	−0.0748779	+	0.0892360i	−0.802183	−	0.597078i	$-0.796328\pi$
$293$	−21.9392	+	26.1461i	−0.0748779	+	0.0892360i	0.727305	+	0.686314i	$0.240773\pi$
$294$	7.56718	−	17.1102i	0.0257387	−	0.0581980i
$295$	371.242	+	135.121i	1.25845	+	0.458037i
$296$			126.618i			0.427765i
$297$	266.021	+	491.459i	0.895695	+	1.65474i
$298$	219.366			0.736126
$299$	−56.3596	+	154.847i	−0.188494	+	0.517882i
$300$	52.9727	−	38.6880i	0.176576	−	0.128960i
$301$	206.809	+	173.534i	0.687074	+	0.576524i
$302$	−215.950	−	38.0777i	−0.715065	−	0.126085i
$303$	−24.1137	+	25.0947i	−0.0795833	+	0.0828209i
$304$	74.5414	−	62.5476i	0.245202	−	0.205749i
$305$	219.186	−	126.547i	0.718642	−	0.414908i
$306$	−17.6678	+	22.8464i	−0.0577379	+	0.0746614i
$307$	−165.305	+	286.316i	−0.538452	+	0.932627i	0.460535	+	0.887641i	$0.347657\pi$
$307$	−165.305	+	286.316i	−0.538452	+	0.932627i	−0.998988	+	0.0449854i	$0.985676\pi$
$308$	297.929	−	52.5330i	0.967303	−	0.170562i
$309$	373.101	+	25.1603i	1.20745	+	0.0814249i
$310$	173.112	−	63.0075i	0.558425	−	0.203250i
$311$	82.6437	+	227.062i	0.265735	+	0.730102i	0.998755	+	0.0498938i	$0.0158883\pi$
$311$	82.6437	+	227.062i	0.265735	+	0.730102i	−0.733019	+	0.680208i	$0.761889\pi$
$312$	−48.0532	−	32.2392i	−0.154017	−	0.103331i
$313$	−54.4006	−	308.521i	−0.173804	−	0.985691i	−0.939515	−	0.342507i	$-0.888724\pi$
$313$	−54.4006	−	308.521i	−0.173804	−	0.985691i	0.765712	−	0.643184i	$-0.222387\pi$
$314$	148.782	+	85.8993i	0.473828	+	0.273565i
$315$	−291.690	+	265.270i	−0.926002	+	0.842128i
$316$	−111.324	−	192.819i	−0.352291	−	0.610186i
$317$	−317.348	−	378.201i	−1.00110	−	1.19306i	−0.981147	−	0.193262i	$-0.938093\pi$
$317$	−317.348	−	378.201i	−1.00110	−	1.19306i	−0.0199518	−	0.999801i	$-0.506351\pi$
$318$	18.0605	−	73.2095i	0.0567940	−	0.230219i
$319$	−66.4953	+	377.114i	−0.208449	+	1.18217i
$320$	30.8250	−	36.7358i	0.0963280	−	0.114799i
$321$	425.190	−	45.7554i	1.32458	−	0.142540i
$322$	234.677	+	85.4154i	0.728810	+	0.265265i
$323$		−	55.1997i		−	0.170897i
$324$	−156.160	−	43.1066i	−0.481974	−	0.133045i
$325$	74.5564			0.229404
$326$	−32.3604	+	88.9096i	−0.0992651	+	0.272729i
$327$	−38.2854	−	355.774i	−0.117081	−	1.08799i
$328$	−111.115	−	93.2364i	−0.338765	−	0.284257i
$329$	91.3206	+	16.1023i	0.277570	+	0.0489431i
$330$	−511.063	−	126.077i	−1.54868	−	0.382052i
$331$	198.545	−	166.599i	0.599833	−	0.503320i	−0.291559	−	0.956553i	$-0.594174\pi$
$331$	198.545	−	166.599i	0.599833	−	0.503320i	0.891392	+	0.453233i	$0.149730\pi$
$332$	−43.7313	+	25.2483i	−0.131721	+	0.0760491i
$333$	−122.600	+	383.791i	−0.368169	+	1.15252i
$334$	−5.12833	+	8.88254i	−0.0153543	+	0.0265944i
$335$	−698.519	+	123.168i	−2.08513	+	0.367665i
$336$	−48.8599	+	72.8266i	−0.145416	+	0.216746i
$337$	−431.168	+	156.932i	−1.27943	+	0.465675i	−0.890244	−	0.455484i	$-0.849466\pi$
$337$	−431.168	+	156.932i	−1.27943	+	0.465675i	−0.389187	+	0.921159i	$0.627244\pi$
$338$	59.2488	+	162.785i	0.175292	+	0.481612i
$339$	20.9251	−	310.297i	0.0617259	−	0.915329i
$340$	−4.72388	−	26.7905i	−0.0138938	−	0.0787955i
$341$	−389.523	−	224.891i	−1.14230	−	0.659505i
$342$	286.504	−	117.411i	0.837730	−	0.343307i
$343$	162.937	+	282.216i	0.475036	+	0.822786i
$344$	−67.1612	−	80.0396i	−0.195236	−	0.232673i
$345$	−313.326	−	301.078i	−0.908192	−	0.872689i
$346$	−17.8047	+	100.975i	−0.0514587	+	0.291837i
$347$	173.848	−	207.184i	0.501002	−	0.597071i	−0.454978	−	0.890503i	$-0.650353\pi$
$347$	173.848	−	207.184i	0.501002	−	0.597071i	0.955980	+	0.293432i	$0.0947973\pi$
$348$	−65.4707	−	89.6445i	−0.188134	−	0.257599i
$349$	−314.152	−	114.342i	−0.900148	−	0.327627i	−0.149836	−	0.988711i	$-0.547875\pi$
$349$	−314.152	−	114.342i	−0.900148	−	0.327627i	−0.750312	+	0.661084i	$0.770097\pi$
$350$		−	112.993i		−	0.322838i
$351$	−114.437	−	144.248i	−0.326031	−	0.410963i
$352$	−117.084			−0.332624
$353$	179.081	−	492.021i	0.507312	−	1.39383i	−0.376688	−	0.926340i	$-0.622937\pi$
$353$	179.081	−	492.021i	0.507312	−	1.39383i	0.884000	−	0.467487i	$-0.154841\pi$
$354$	255.723	+	113.096i	0.722382	+	0.319482i
$355$	−244.810	−	205.420i	−0.689607	−	0.578649i
$356$	80.6123	+	14.2141i	0.226439	+	0.0399273i
$357$	13.8312	+	47.7877i	0.0387430	+	0.133859i
$358$	274.415	−	230.261i	0.766521	−	0.643188i
$359$	−46.0527	+	26.5885i	−0.128280	+	0.0740627i	−0.562767	−	0.826616i	$-0.690263\pi$
$359$	−46.0527	+	26.5885i	−0.128280	+	0.0740627i	0.434487	+	0.900678i	$0.356930\pi$
$360$	129.003	−	81.5023i	0.358342	−	0.226395i
$361$	−115.394	+	199.869i	−0.319652	+	0.553653i
$362$	54.0798	−	9.53572i	0.149392	−	0.0263418i
$363$	406.312	+	827.848i	1.11932	+	2.28057i
$364$	−93.6662	+	34.0917i	−0.257325	+	0.0936586i
$365$	138.827	+	381.424i	0.380348	+	1.04500i
$366$	160.807	−	78.9252i	0.439365	−	0.215643i
$367$	76.2686	+	432.541i	0.207816	+	1.17859i	0.892946	+	0.450164i	$0.148635\pi$
$367$	76.2686	+	432.541i	0.207816	+	1.17859i	−0.685129	+	0.728421i	$0.740254\pi$
$368$	−83.7047	−	48.3269i	−0.227458	−	0.131323i
$369$	−246.520	−	390.196i	−0.668077	−	1.05744i
$370$	−189.750	−	328.657i	−0.512838	−	0.888261i
$371$	−83.4906	−	99.5002i	−0.225042	−	0.268195i
$372$	125.246	−	36.2500i	0.336682	−	0.0974462i
$373$	−102.738	+	582.657i	−0.275438	+	1.56208i	0.462131	+	0.886812i	$0.347085\pi$
$373$	−102.738	+	582.657i	−0.275438	+	1.56208i	−0.737568	+	0.675272i	$0.764026\pi$
$374$	−42.6931	+	50.8797i	−0.114153	+	0.136042i
$375$	102.321	−	231.358i	0.272855	−	0.616955i
$376$	−33.7239	−	12.2745i	−0.0896913	−	0.0326450i
$377$		−	126.170i		−	0.334668i
$378$	−218.614	+	173.434i	−0.578344	+	0.458820i
$379$	198.665			0.524183			0.262092	−	0.965043i	$-0.415588\pi$
$379$	198.665			0.524183			0.262092	+	0.965043i	$0.415588\pi$
$380$	−99.7493	+	274.059i	−0.262498	+	0.721208i
$381$	−531.872	+	388.446i	−1.39599	+	1.01954i
$382$	−215.000	−	180.406i	−0.562826	−	0.472267i
$383$	31.8457	+	5.61525i	0.0831479	+	0.0146612i	0.215067	−	0.976599i	$-0.431003\pi$
$383$	31.8457	+	5.61525i	0.0831479	+	0.0146612i	−0.131919	+	0.991260i	$0.542114\pi$
$384$	23.5169	−	24.4736i	0.0612419	−	0.0637333i
$385$	−694.594	+	582.833i	−1.80414	+	1.51385i
$386$	69.8050	−	40.3019i	0.180842	−	0.104409i
$387$	−126.071	−	307.637i	−0.325766	−	0.794927i
$388$	40.4271	−	70.0219i	0.104194	−	0.180469i
$389$	215.378	−	37.9769i	0.553671	−	0.0976271i	0.110189	−	0.993911i	$-0.464854\pi$
$389$	215.378	−	37.9769i	0.553671	−	0.0976271i	0.443482	+	0.896284i	$0.353743\pi$
$390$	173.043	+	11.6692i	0.443699	+	0.0299211i
$391$	−51.5227	+	18.7527i	−0.131772	+	0.0479610i
$392$	4.26587	+	11.7204i	0.0108823	+	0.0298989i
$393$	325.462	+	218.355i	0.828147	+	0.555610i
$394$	18.3822	+	104.251i	0.0466553	+	0.264596i
$395$	577.915	+	333.659i	1.46308	+	0.844707i
$396$	−354.891	−	113.368i	−0.896188	−	0.286284i
$397$	−264.698	−	458.471i	−0.666746	−	1.15484i	−0.978809	−	0.204777i	$-0.934353\pi$
$397$	−264.698	−	458.471i	−0.666746	−	1.15484i	0.312062	−	0.950062i	$-0.398980\pi$
$398$	118.567	+	141.303i	0.297908	+	0.355033i
$399$	127.746	−	517.828i	0.320166	−	1.29782i
$400$	−7.59378	+	43.0665i	−0.0189844	+	0.107666i
$401$	−167.829	+	200.011i	−0.418526	+	0.498780i	−0.933576	−	0.358380i	$-0.883329\pi$
$401$	−167.829	+	200.011i	−0.418526	+	0.498780i	0.515049	+	0.857161i	$0.327774\pi$
$402$	−499.135	+	53.7127i	−1.24163	+	0.133614i
$403$	139.259	+	50.6862i	0.345556	+	0.125772i
$404$		−	23.2017i		−	0.0574299i
$405$	469.935	−	122.131i	1.16033	−	0.301557i
$406$	−191.216			−0.470975
$407$	−316.902	+	870.682i	−0.778629	+	2.13927i
$408$	−2.06006	−	19.1434i	−0.00504916	−	0.0469202i
$409$	489.930	+	411.100i	1.19787	+	1.00513i	0.999688	+	0.0249695i	$0.00794888\pi$
$409$	489.930	+	411.100i	1.19787	+	1.00513i	0.198184	+	0.980165i	$0.436496\pi$
$410$	428.139	+	75.4924i	1.04424	+	0.184128i
$411$	224.908	+	55.4839i	0.547221	+	0.134997i
$412$	−190.974	+	160.246i	−0.463529	+	0.388947i
$413$	417.126	−	240.828i	1.00999	−	0.583118i
$414$	−206.922	−	227.531i	−0.499813	−	0.549593i
$415$	75.6740	−	131.071i	0.182347	−	0.315834i
$416$	37.9912	−	6.69888i	0.0913251	−	0.0161031i
$417$	178.590	−	266.191i	0.428272	−	0.638348i
$418$	669.123	−	243.541i	1.60077	−	0.582634i
$419$	−244.237	−	671.034i	−0.582904	−	1.60151i	−0.783194	−	0.621778i	$-0.786411\pi$
$419$	−244.237	−	671.034i	−0.582904	−	1.60151i	0.200290	−	0.979737i	$-0.435811\pi$
$420$	17.6852	−	262.253i	0.0421077	−	0.624413i
$421$	−12.1583	−	68.9530i	−0.0288795	−	0.163784i	0.966957	−	0.254939i	$-0.0820553\pi$
$421$	−12.1583	−	68.9530i	−0.0288795	−	0.163784i	−0.995837	+	0.0911549i	$0.970944\pi$
$422$	−38.7234	−	22.3570i	−0.0917616	−	0.0529786i
$423$	−90.3350	−	69.8588i	−0.213558	−	0.165151i
$424$	25.1348	+	43.5347i	0.0592801	+	0.102676i
$425$	15.9459	+	19.0036i	0.0375197	+	0.0447143i
$426$	−163.094	−	156.719i	−0.382850	−	0.367884i
$427$	53.5818	−	303.877i	0.125484	−	0.711656i
$428$	−183.257	+	218.397i	−0.428169	+	0.510272i
$429$	−249.745	−	341.959i	−0.582157	−	0.797106i
$430$	294.274	+	107.107i	0.684358	+	0.249086i
$431$			76.1177i			0.176607i	0.996094	+	0.0883036i	$0.0281446\pi$
$431$			76.1177i			0.176607i	−0.996094	+	0.0883036i	$0.971855\pi$
$432$	94.9786	−	51.4108i	0.219858	−	0.119007i
$433$	109.713			0.253380			0.126690	−	0.991942i	$-0.459565\pi$
$433$	109.713			0.253380			0.126690	+	0.991942i	$0.459565\pi$
$434$	76.8170	−	211.053i	0.176998	−	0.486297i
$435$	304.280	+	134.571i	0.699494	+	0.309359i
$436$	182.741	+	153.338i	0.419131	+	0.351693i
$437$	578.887	+	102.073i	1.32468	+	0.233578i
$438$	79.8711	+	275.959i	0.182354	+	0.630044i
$439$	87.3258	−	73.2751i	0.198920	−	0.166914i	−0.537887	−	0.843017i	$-0.680777\pi$
$439$	87.3258	−	73.2751i	0.198920	−	0.166914i	0.736807	+	0.676103i	$0.236333\pi$
$440$	303.908	−	175.461i	0.690701	−	0.398776i
$441$	1.58174	+	39.6559i	0.00358671	+	0.0899228i
$442$	10.9420	−	18.9521i	0.0247556	−	0.0428780i
$443$	170.087	−	29.9909i	0.383944	−	0.0676996i	0.0216549	−	0.999766i	$-0.493107\pi$
$443$	170.087	−	29.9909i	0.383944	−	0.0676996i	0.362289	+	0.932066i	$0.381995\pi$
$444$	−118.344	−	241.122i	−0.266540	−	0.543067i
$445$	−230.542	+	83.9106i	−0.518073	+	0.188563i
$446$	−49.3618	−	135.621i	−0.110677	−	0.304082i
$447$	−417.742	+	205.030i	−0.934545	+	0.458680i
$448$	−10.1524	−	57.5773i	−0.0226617	−	0.128521i
$449$	164.941	+	95.2288i	0.367352	+	0.212091i	0.672301	−	0.740278i	$-0.265306\pi$
$449$	164.941	+	95.2288i	0.367352	+	0.212091i	−0.304949	+	0.952369i	$0.598639\pi$
$450$	−64.7172	+	123.185i	−0.143816	+	0.273745i
$451$	−530.719	−	919.233i	−1.17676	−	2.03821i
$452$	133.272	+	158.827i	0.294849	+	0.351388i
$453$	446.826	−	129.325i	0.986371	−	0.285486i
$454$	−63.1661	+	358.233i	−0.139132	+	0.789059i
$455$	192.035	−	228.858i	0.422054	−	0.502985i
$456$	−83.4903	+	188.781i	−0.183093	+	0.413993i
$457$	−135.071	−	49.1618i	−0.295560	−	0.107575i	0.189984	−	0.981787i	$-0.439156\pi$
$457$	−135.071	−	49.1618i	−0.295560	−	0.107575i	−0.485544	+	0.874212i	$0.661379\pi$
$458$			388.872i			0.849066i
$459$	12.2918	−	60.0200i	0.0267794	−	0.130763i
$460$	289.690			0.629762
$461$	223.385	−	613.745i	0.484566	−	1.33133i	−0.420974	−	0.907073i	$-0.638312\pi$
$461$	223.385	−	613.745i	0.484566	−	1.33133i	0.905540	−	0.424261i	$-0.139466\pi$
$462$	−518.253	+	378.499i	−1.12176	+	0.819263i
$463$	17.1769	+	14.4132i	0.0370992	+	0.0311299i	0.661149	−	0.750255i	$-0.270069\pi$
$463$	17.1769	+	14.4132i	0.0370992	+	0.0311299i	−0.624050	+	0.781385i	$0.714514\pi$
$464$	72.8804	+	12.8508i	0.157070	+	0.0276956i
$465$	−270.770	+	281.785i	−0.582301	+	0.605990i
$466$	−279.349	+	234.402i	−0.599462	+	0.503008i
$467$	−413.326	+	238.634i	−0.885065	+	0.510993i	−0.872325	−	0.488926i	$-0.837389\pi$
$467$	−413.326	+	238.634i	−0.885065	+	0.510993i	−0.0127402	+	0.999919i	$0.504055\pi$
$468$	121.641	+	16.4808i	0.259916	+	0.0352154i
$469$	−432.376	+	748.898i	−0.921911	+	1.59680i
$470$	105.930	−	18.6783i	0.225383	−	0.0397411i
$471$	−363.614	−	24.5206i	−0.772004	−	0.0520606i
$472$	−175.169	+	63.7563i	−0.371120	+	0.135077i
$473$	−261.505	−	718.478i	−0.552864	−	1.51898i
$474$	392.214	+	263.139i	0.827456	+	0.555146i
$475$	−46.1829	−	261.916i	−0.0972272	−	0.551403i
$476$	−28.7226	−	16.5830i	−0.0603417	−	0.0348383i
$477$	34.0323	+	156.294i	0.0713466	+	0.327661i
$478$	88.0673	+	152.537i	0.184241	+	0.319115i
$479$	383.849	+	457.454i	0.801356	+	0.955019i	0.999685	−	0.0251168i	$-0.00799577\pi$
$479$	383.849	+	457.454i	0.801356	+	0.955019i	−0.198329	+	0.980136i	$0.563551\pi$
$480$	−24.3655	+	98.7671i	−0.0507614	+	0.205765i
$481$	53.0126	−	300.649i	0.110213	−	0.625051i
$482$	−59.4942	+	70.9024i	−0.123432	+	0.147100i
$483$	−526.733	+	56.6826i	−1.09054	+	0.117355i
$484$	−577.712	−	210.270i	−1.19362	−	0.434442i
$485$			242.336i			0.499662i
$486$	337.667	−	63.8658i	0.694789	−	0.131411i
$487$	758.948			1.55842			0.779208	−	0.626766i	$-0.215622\pi$
$487$	758.948			1.55842			0.779208	+	0.626766i	$0.215622\pi$
$488$	−40.8445	+	112.219i	−0.0836977	+	0.229957i
$489$	−21.4748	−	199.558i	−0.0439157	−	0.408094i
$490$	−28.6368	−	24.0291i	−0.0584425	−	0.0490391i
$491$	258.651	+	45.6071i	0.526783	+	0.0928861i	0.430714	−	0.902489i	$-0.358262\pi$
$491$	258.651	+	45.6071i	0.526783	+	0.0928861i	0.0960694	+	0.995375i	$0.469373\pi$
$492$	298.741	+	73.6983i	0.607198	+	0.149793i
$493$	32.1593	−	26.9849i	0.0652319	−	0.0547360i
$494$	−203.182	+	117.307i	−0.411300	+	0.237464i
$495$	1091.06	−	237.574i	2.20417	−	0.479947i
$496$	−43.4621	+	75.2785i	−0.0876252	+	0.151771i
$497$	−383.701	+	67.6568i	−0.772033	+	0.136130i
$498$	59.6800	−	88.9543i	0.119839	−	0.178623i
$499$	85.4398	−	31.0975i	0.171222	−	0.0623197i	−0.254987	−	0.966945i	$-0.582071\pi$
$499$	85.4398	−	31.0975i	0.171222	−	0.0623197i	0.426209	+	0.904625i	$0.359849\pi$
$500$	57.6816	+	158.479i	0.115363	+	0.316958i
$501$	1.46392	−	21.7084i	0.00292199	−	0.0433301i
$502$	−57.4301	−	325.702i	−0.114403	−	0.648809i
$503$	−368.263	−	212.617i	−0.732134	−	0.422698i	0.0870685	−	0.996202i	$-0.472250\pi$
$503$	−368.263	−	212.617i	−0.732134	−	0.422698i	−0.819202	+	0.573505i	$0.805583\pi$
$504$	24.9774	−	184.352i	0.0495583	−	0.365778i
$505$	34.7700	+	60.2234i	0.0688515	+	0.119254i
$506$	−454.636	−	541.814i	−0.898490	−	1.07078i
$507$	−264.975	−	254.617i	−0.522634	−	0.502203i
$508$	76.2453	−	432.408i	0.150089	−	0.851198i
$509$	−434.422	+	517.724i	−0.853481	+	1.01714i	0.146130	+	0.989265i	$0.453318\pi$
$509$	−434.422	+	517.724i	−0.853481	+	1.01714i	−0.999611	+	0.0278737i	$0.991126\pi$
$510$	34.0355	+	46.6024i	0.0667362	+	0.0913772i
$511$	465.022	+	169.254i	0.910023	+	0.331221i
$512$			22.6274i			0.0441942i
$513$	−435.856	+	491.369i	−0.849622	+	0.957834i
$514$	106.298			0.206805
$515$	255.556	−	702.135i	0.496226	−	1.36337i
$516$	202.705	+	89.6487i	0.392840	+	0.173738i
$517$	−201.179	−	168.809i	−0.389128	−	0.326517i
$518$	−455.647	−	80.3428i	−0.879627	−	0.155102i
$519$	−60.4709	−	208.931i	−0.116514	−	0.402564i
$520$	−88.5729	+	74.3215i	−0.170333	+	0.142926i
$521$	−677.597	+	391.211i	−1.30057	+	0.750885i	−0.980502	−	0.196509i	$-0.937039\pi$
$521$	−677.597	+	391.211i	−1.30057	+	0.750885i	−0.320069	+	0.947394i	$0.603706\pi$
$522$	208.463	+	109.519i	0.399355	+	0.209807i
$523$	−342.909	+	593.936i	−0.655658	+	1.13563i	0.326071	+	0.945345i	$0.394275\pi$
$523$	−342.909	+	593.936i	−0.655658	+	1.13563i	−0.981729	+	0.190287i	$0.939058\pi$
$524$	−257.313	+	45.3712i	−0.491055	+	0.0865863i
$525$	105.609	+	215.175i	0.201160	+	0.409858i
$526$	−201.288	+	73.2629i	−0.382677	+	0.139283i
$527$	16.8650	+	46.3362i	0.0320019	+	0.0879244i
$528$	222.965	−	109.432i	0.422282	−	0.207258i
$529$	−9.52859	−	54.0393i	−0.0180124	−	0.102154i
$530$	−130.482	−	75.3338i	−0.246192	−	0.142139i
$531$	−592.684	+	23.6402i	−1.11617	+	0.0445201i
$532$	177.784	+	307.931i	0.334181	+	0.578819i
$533$	224.801	+	267.907i	0.421765	+	0.502640i
$534$	−166.797	+	48.2761i	−0.312354	+	0.0904047i
$535$	148.381	−	841.508i	0.277347	−	1.57291i
$536$	215.127	−	256.378i	0.401356	−	0.478317i
$537$	−307.359	+	694.972i	−0.572363	+	1.29418i
$538$	−227.071	−	82.6472i	−0.422066	−	0.153619i
$539$			91.2710i			0.169334i
$540$	−169.487	+	275.779i	−0.313864	+	0.510702i
$541$	884.789			1.63547			0.817735	−	0.575595i	$-0.195229\pi$
$541$	884.789			1.63547			0.817735	+	0.575595i	$0.195229\pi$
$542$	−4.09458	+	11.2498i	−0.00755457	+	0.0207560i
$543$	−94.0725	+	68.7047i	−0.173246	+	0.126528i
$544$	9.83292	+	8.25080i	0.0180752	+	0.0151669i
$545$	−704.124	−	124.156i	−1.29197	−	0.227809i
$546$	146.507	−	152.467i	0.268327	−	0.279243i
$547$	263.600	−	221.186i	0.481901	−	0.404363i	−0.369212	−	0.929345i	$-0.620373\pi$
$547$	263.600	−	221.186i	0.481901	−	0.404363i	0.851113	+	0.524982i	$0.175928\pi$
$548$	−133.744	+	77.2169i	−0.244058	+	0.140907i
$549$	−232.461	+	300.597i	−0.423427	+	0.547536i
$550$	−160.005	+	277.137i	−0.290919	+	0.503886i
$551$	−443.235	+	78.1542i	−0.804419	+	0.141841i
$552$	204.569	+	13.7953i	0.370596	+	0.0249914i
$553$	764.512	−	278.260i	1.38248	−	0.503182i
$554$	−241.755	−	664.216i	−0.436381	−	1.19895i
$555$	668.523	+	448.517i	1.20455	+	0.808139i
$556$	37.1086	+	210.453i	0.0667420	+	0.378513i
$557$	−274.575	−	158.526i	−0.492953	−	0.284606i	0.232846	−	0.972514i	$-0.425196\pi$
$557$	−274.575	−	158.526i	−0.492953	−	0.284606i	−0.725799	+	0.687907i	$0.758530\pi$
$558$	−204.627	+	186.093i	−0.366715	+	0.333499i
$559$	125.960	+	218.169i	0.225331	+	0.390285i
$560$	112.637	+	134.236i	0.201138	+	0.239707i
$561$	33.7466	−	136.794i	0.0601544	−	0.243840i
$562$	−17.1950	+	97.5174i	−0.0305960	+	0.173519i
$563$	130.488	−	155.510i	0.231773	−	0.276216i	−0.637605	−	0.770363i	$-0.720075\pi$
$563$	130.488	−	155.510i	0.231773	−	0.276216i	0.869379	+	0.494147i	$0.164519\pi$
$564$	75.6935	−	8.14550i	0.134208	−	0.0144424i
$565$	−583.945	−	212.539i	−1.03353	−	0.376174i
$566$		−	50.6935i		−	0.0895646i
$567$	254.210	−	534.601i	0.448343	−	0.942859i
$568$	150.791			0.265477
$569$	−80.4994	+	221.170i	−0.141475	+	0.388700i	−0.990113	−	0.140275i	$-0.955201\pi$
$569$	−80.4994	+	221.170i	−0.141475	+	0.388700i	0.848637	+	0.528975i	$0.177424\pi$
$570$	−66.1948	−	615.126i	−0.116131	−	1.07917i
$571$	50.2848	+	42.1940i	0.0880645	+	0.0738949i	0.685757	−	0.727830i	$-0.259471\pi$
$571$	50.2848	+	42.1940i	0.0880645	+	0.0738949i	−0.597693	+	0.801725i	$0.703916\pi$
$572$	278.010	+	49.0207i	0.486031	+	0.0857005i
$573$	578.044	+	142.601i	1.00880	+	0.248868i
$574$	406.024	−	340.695i	0.707359	−	0.593545i
$575$	−228.780	+	132.086i	−0.397878	+	0.229715i
$576$	−21.9094	+	68.5856i	−0.0380371	+	0.119072i
$577$	72.1281	−	124.930i	0.125005	−	0.216516i	−0.796730	−	0.604336i	$-0.793439\pi$
$577$	72.1281	−	124.930i	0.125005	−	0.216516i	0.921735	+	0.387820i	$0.126772\pi$
$578$	−395.328	+	69.7069i	−0.683958	+	0.120600i
$579$	−95.2627	+	141.991i	−0.164530	+	0.245235i
$580$	−208.430	+	75.8622i	−0.359362	+	0.130797i
$581$	−63.1094	−	173.392i	−0.108622	−	0.298436i
$582$	−11.5402	+	171.129i	−0.0198285	+	0.294036i
$583$	63.8781	+	362.271i	0.109568	+	0.621391i
$584$	−165.864	−	95.7618i	−0.284014	−	0.163976i
$585$	−340.435	+	139.512i	−0.581940	+	0.238483i
$586$	24.1345	+	41.8022i	0.0411852	+	0.0713348i
$587$	364.747	+	434.688i	0.621375	+	0.740526i	0.981306	−	0.192453i	$-0.0616444\pi$
$587$	364.747	+	434.688i	0.621375	+	0.740526i	−0.359931	+	0.932979i	$0.617200\pi$
$588$	−19.0780	−	18.3322i	−0.0324456	−	0.0311773i
$589$	91.7982	−	520.613i	0.155854	−	0.883894i
$590$	359.132	−	427.996i	0.608698	−	0.725418i
$591$	−132.443	−	181.346i	−0.224101	−	0.306845i
$592$	168.266	+	61.2440i	0.284234	+	0.103453i
$593$			174.635i			0.294494i	0.989100	+	0.147247i	$0.0470412\pi$
$593$			174.635i			0.294494i	−0.989100	+	0.147247i	$0.952959\pi$
$594$	781.785	−	115.809i	1.31614	−	0.194965i
$595$	99.4051			0.167067
$596$	106.105	−	291.521i	0.178028	−	0.489128i
$597$	−357.859	−	158.267i	−0.599429	−	0.265104i
$598$	178.519	+	149.796i	0.298527	+	0.250494i
$599$	−424.905	−	74.9222i	−0.709357	−	0.125079i	−0.192683	−	0.981261i	$-0.561719\pi$
$599$	−424.905	−	74.9222i	−0.709357	−	0.125079i	−0.516674	+	0.856182i	$0.672830\pi$
$600$	−25.7911	−	89.1098i	−0.0429852	−	0.148516i
$601$	−636.447	+	534.042i	−1.05898	+	0.888589i	−0.994009	−	0.109298i	$-0.965140\pi$
$601$	−636.447	+	534.042i	−1.05898	+	0.888589i	−0.0649703	+	0.997887i	$0.520695\pi$
$602$	330.645	−	190.898i	0.549244	−	0.317106i
$603$	900.309	−	568.802i	1.49305	−	0.943288i
$604$	−155.055	+	268.563i	−0.256714	+	0.444641i
$605$	1814.65	−	319.971i	2.99942	−	0.528878i
$606$	21.6855	+	44.1834i	0.0357846	+	0.0729099i
$607$	352.792	−	128.406i	0.581205	−	0.211541i	−0.0346516	−	0.999399i	$-0.511032\pi$
$607$	352.792	−	128.406i	0.581205	−	0.211541i	0.615857	+	0.787858i	$0.288810\pi$
$608$	−47.0663	−	129.314i	−0.0774117	−	0.212687i
$609$	364.136	−	178.720i	0.597925	−	0.293465i
$610$	−62.1537	−	352.491i	−0.101891	−	0.577854i
$611$	74.9368	+	43.2648i	0.122646	+	0.0708098i
$612$	21.8154	+	34.5298i	0.0356461	+	0.0564212i
$613$	192.466	+	333.361i	0.313974	+	0.543820i	0.979219	−	0.202806i	$-0.0650060\pi$
$613$	192.466	+	333.361i	0.313974	+	0.543820i	−0.665245	+	0.746626i	$0.731673\pi$
$614$	300.537	+	358.166i	0.489474	+	0.583333i
$615$	−885.871	+	256.398i	−1.44044	+	0.416908i
$616$	74.2929	−	421.336i	0.120605	−	0.683987i
$617$	−106.165	+	126.523i	−0.172066	+	0.205061i	−0.845185	−	0.534474i	$-0.820510\pi$
$617$	−106.165	+	126.523i	−0.172066	+	0.205061i	0.673119	+	0.739534i	$0.264954\pi$
$618$	213.901	−	483.653i	0.346118	−	0.782610i
$619$	−449.740	−	163.692i	−0.726560	−	0.264446i	−0.0478519	−	0.998854i	$-0.515238\pi$
$619$	−449.740	−	163.692i	−0.726560	−	0.264446i	−0.678708	+	0.734408i	$0.737460\pi$
$620$		−	260.529i		−	0.420208i
$621$	606.708	+	239.892i	0.976986	+	0.386300i
$622$	341.722			0.549392
$623$	−102.301	+	281.071i	−0.164208	+	0.451157i
$624$	−66.0863	+	48.2653i	−0.105908	+	0.0773483i
$625$	−596.591	−	500.599i	−0.954545	−	0.800958i
$626$	−436.315	−	76.9341i	−0.696989	−	0.122898i
$627$	−1046.60	+	1089.18i	−1.66922	+	1.73712i
$628$	186.118	−	156.172i	0.296366	−	0.248681i
$629$	87.9703	−	50.7897i	0.139857	−	0.0807467i
$630$	211.437	+	515.943i	0.335614	+	0.818958i
$631$	124.618	−	215.844i	0.197493	−	0.342067i	−0.750222	−	0.661186i	$-0.770053\pi$
$631$	124.618	−	215.844i	0.197493	−	0.342067i	0.947715	+	0.319119i	$0.103387\pi$
$632$	−310.088	+	54.6769i	−0.490645	+	0.0865140i
$633$	94.6376	+	6.38195i	0.149506	+	0.0100821i
$634$	−656.099	+	238.801i	−1.03486	+	0.376657i
$635$	450.100	+	1236.64i	0.708819	+	1.94746i
$636$	−88.5543	−	59.4117i	−0.139236	−	0.0934147i
$637$	−5.22202	−	29.6155i	−0.00819783	−	0.0464922i
$638$	468.993	+	270.773i	0.735099	+	0.424410i
$639$	457.060	+	146.006i	0.715274	+	0.228492i
$640$	−33.9094	−	58.7328i	−0.0529834	−	0.0917700i
$641$	144.405	+	172.096i	0.225282	+	0.268480i	0.866832	−	0.498601i	$-0.166153\pi$
$641$	144.405	+	172.096i	0.225282	+	0.268480i	−0.641550	+	0.767081i	$0.721708\pi$
$642$	144.854	−	587.177i	0.225630	−	0.914607i
$643$	−63.2329	+	358.612i	−0.0983404	+	0.557716i	0.895332	+	0.445399i	$0.146938\pi$
$643$	−63.2329	+	358.612i	−0.0983404	+	0.557716i	−0.993672	+	0.112317i	$0.964173\pi$
$644$	227.021	−	270.554i	0.352518	−	0.420114i
$645$	−660.499	+	71.0774i	−1.02403	+	0.110198i
$646$	−73.3564	−	26.6995i	−0.113555	−	0.0413305i
$647$		−	1200.78i		−	1.85593i	−0.372671	−	0.927964i	$-0.621558\pi$
$647$		−	1200.78i		−	1.85593i	0.372671	−	0.927964i	$-0.378442\pi$
$648$	−132.818	+	186.674i	−0.204967	+	0.288078i
$649$	−1364.11			−2.10186
$650$	36.0621	−	99.0799i	0.0554802	−	0.152431i
$651$	50.9767	+	473.709i	0.0783052	+	0.727664i
$652$	102.502	+	86.0092i	0.157211	+	0.131916i
$653$	626.194	+	110.415i	0.958949	+	0.169089i	0.631152	−	0.775659i	$-0.282583\pi$
$653$	626.194	+	110.415i	0.958949	+	0.169089i	0.327797	+	0.944748i	$0.393694\pi$
$654$	−491.315	−	121.205i	−0.751246	−	0.185329i
$655$	599.900	−	503.376i	0.915878	−	0.768513i
$656$	−177.649	+	102.566i	−0.270807	+	0.156350i
$657$	−410.025	−	450.863i	−0.624087	−	0.686245i
$658$	65.5696	−	113.570i	0.0996498	−	0.172599i
$659$	1147.84	−	202.395i	1.74179	−	0.307125i	0.789825	−	0.613332i	$-0.210171\pi$
$659$	1147.84	−	202.395i	1.74179	−	0.307125i	0.951965	+	0.306207i	$0.0990600\pi$
$660$	−414.743	+	618.182i	−0.628398	+	0.936640i
$661$	904.893	−	329.354i	1.36898	−	0.498266i	0.450158	−	0.892949i	$-0.351368\pi$
$661$	904.893	−	329.354i	1.36898	−	0.498266i	0.918818	+	0.394683i	$0.129145\pi$
$662$	−125.363	−	344.433i	−0.189371	−	0.520292i
$663$	−3.12346	+	46.3177i	−0.00471111	+	0.0698608i
$664$	12.4007	+	70.3280i	0.0186758	+	0.105916i
$665$	−922.931	−	532.854i	−1.38787	−	0.801285i
$666$	450.729	+	348.562i	0.676770	+	0.523367i
$667$	223.526	+	387.159i	0.335122	+	0.580448i
$668$	9.32371	+	11.1116i	0.0139577	+	0.0166341i
$669$	220.758	+	212.129i	0.329983	+	0.317083i
$670$	−174.185	+	987.855i	−0.259978	+	1.47441i
$671$	−561.728	+	669.441i	−0.837150	+	0.997677i
$672$	73.1481	+	100.157i	0.108851	+	0.149043i
$673$	612.694	+	223.002i	0.910392	+	0.331355i	0.754409	−	0.656404i	$-0.227923\pi$
$673$	612.694	+	223.002i	0.910392	+	0.331355i	0.155982	+	0.987760i	$0.450146\pi$
$674$			648.897i			0.962755i
$675$	8.10715	−	295.072i	0.0120106	−	0.437143i
$676$	244.987			0.362407
$677$	−258.040	+	708.958i	−0.381152	+	1.04721i	0.589720	+	0.807608i	$0.299238\pi$
$677$	−258.040	+	708.958i	−0.381152	+	1.04721i	−0.970872	+	0.239598i	$0.922984\pi$
$678$	−402.240	−	177.895i	−0.593274	−	0.262382i
$679$	226.327	+	189.911i	0.333325	+	0.279693i
$680$	−37.8874	−	6.68058i	−0.0557168	−	0.00982438i
$681$	−214.534	−	741.228i	−0.315028	−	1.08844i
$682$	−487.272	+	408.870i	−0.714475	+	0.599516i
$683$	−405.766	+	234.269i	−0.594094	+	0.343000i	−0.766715	−	0.641988i	$-0.778110\pi$
$683$	−405.766	+	234.269i	−0.594094	+	0.343000i	0.172621	+	0.984988i	$0.444776\pi$
$684$	−17.4517	−	437.533i	−0.0255142	−	0.639668i
$685$	231.434	−	400.856i	0.337860	−	0.585191i
$686$	453.855	−	80.0268i	0.661596	−	0.116657i
$687$	−363.460	−	740.537i	−0.529053	−	1.07793i
$688$	−138.852	+	50.5380i	−0.201820	+	0.0734563i
$689$	−41.4542	−	113.895i	−0.0601658	−	0.165304i
$690$	−551.663	+	270.759i	−0.799511	+	0.392405i
$691$	37.3428	+	211.781i	0.0540416	+	0.306485i	0.999833	−	0.0182903i	$-0.00582232\pi$
$691$	37.3428	+	211.781i	0.0540416	+	0.306485i	−0.945791	+	0.324776i	$0.894711\pi$
$692$	125.577	+	72.5019i	0.181470	+	0.104772i
$693$	633.154	−	1205.17i	0.913642	−	1.73906i
$694$	−191.243	−	331.243i	−0.275567	−	0.477296i
$695$	−411.705	−	490.651i	−0.592382	−	0.705973i
$696$	−150.798	+	43.6457i	−0.216664	+	0.0627093i
$697$	−20.2068	+	114.598i	−0.0289911	+	0.164416i
$698$	−303.904	+	362.178i	−0.435392	+	0.518880i
$699$	312.886	−	707.470i	0.447620	−	1.01212i
$700$	−150.160	−	54.6537i	−0.214514	−	0.0780767i
$701$			848.227i			1.21002i	0.796216	+	0.605012i	$0.206832\pi$
$701$			848.227i			1.21002i	−0.796216	+	0.605012i	$0.793168\pi$
$702$	−247.047	+	82.3070i	−0.351919	+	0.117246i
$703$	−1089.02			−1.54910
$704$	−56.6322	+	155.596i	−0.0804435	+	0.221017i
$705$	−184.267	+	134.577i	−0.261371	+	0.190889i
$706$	−567.240	−	475.971i	−0.803456	−	0.674180i
$707$	83.4932	+	14.7221i	0.118095	+	0.0208234i
$708$	273.988	−	285.134i	0.386988	−	0.402731i
$709$	−63.9344	+	53.6473i	−0.0901754	+	0.0756662i	−0.686761	−	0.726883i	$-0.740968\pi$
$709$	−63.9344	+	53.6473i	−0.0901754	+	0.0756662i	0.596586	+	0.802549i	$0.296524\pi$
$710$	−391.401	+	225.975i	−0.551268	+	0.318275i
$711$	−992.844	−	134.518i	−1.39640	−	0.189195i
$712$	57.8809	−	100.253i	0.0812934	−	0.140804i
$713$	−517.120	+	91.1822i	−0.725273	+	0.127885i
$714$	70.1964	+	4.73374i	0.0983143	+	0.00662989i
$715$	−795.078	+	289.385i	−1.11200	+	0.404734i
$716$	−173.269	−	476.052i	−0.241995	−	0.664876i
$717$	−310.277	−	208.167i	−0.432744	−	0.290331i
$718$	13.0590	+	74.0612i	0.0181880	+	0.103149i
$719$	1032.07	+	595.867i	1.43543	+	0.828744i	0.997527	−	0.0702802i	$-0.0223893\pi$
$719$	1032.07	+	595.867i	1.43543	+	0.828744i	0.437899	+	0.899024i	$0.355723\pi$
$720$	−45.9131	−	210.857i	−0.0637682	−	0.292857i
$721$	−455.481	−	788.916i	−0.631735	−	1.09420i
$722$	209.796	+	250.025i	0.290576	+	0.346295i
$723$	47.0269	−	190.627i	0.0650441	−	0.263661i
$724$	13.4855	−	76.4803i	0.0186264	−	0.105636i
$725$	130.015	−	154.946i	0.179331	−	0.213719i
$726$	1296.68	−	139.538i	1.78606	−	0.192201i
$727$	−633.829	−	230.695i	−0.871842	−	0.317325i	−0.132929	−	0.991126i	$-0.542438\pi$
$727$	−633.829	−	230.695i	−0.871842	−	0.317325i	−0.738913	+	0.673801i	$0.764661\pi$
$728$			140.965i			0.193634i
$729$	−583.334	+	437.222i	−0.800184	+	0.599755i
$730$	574.034			0.786348
$731$	−28.6689	+	78.7672i	−0.0392188	+	0.107753i
$732$	−27.1049	−	251.876i	−0.0370285	−	0.344094i
$733$	−149.604	−	125.532i	−0.204098	−	0.171259i	0.535010	−	0.844846i	$-0.320308\pi$
$733$	−149.604	−	125.532i	−0.204098	−	0.171259i	−0.739107	+	0.673588i	$0.764752\pi$
$734$	611.705	+	107.860i	0.833386	+	0.146948i
$735$	76.9925	+	18.9937i	0.104752	+	0.0258418i
$736$	−104.710	+	87.8621i	−0.142269	+	0.119378i
$737$	2120.97	−	1224.54i	2.87784	−	1.66152i
$738$	−637.781	+	138.874i	−0.864202	+	0.188176i
$739$	−718.905	+	1245.18i	−0.972807	+	1.68495i	−0.285818	+	0.958284i	$0.592265\pi$
$739$	−718.905	+	1245.18i	−0.972807	+	1.68495i	−0.686989	+	0.726668i	$0.741068\pi$
$740$	−528.540	+	93.1959i	−0.714244	+	0.125940i
$741$	277.283	−	413.295i	0.374201	−	0.557753i
$742$	−172.612	+	62.8256i	−0.232631	+	0.0846707i
$743$	−342.663	−	941.458i	−0.461188	−	1.26710i	−0.924593	−	0.380957i	$-0.875595\pi$
$743$	−342.663	−	941.458i	−0.461188	−	1.26710i	0.463405	−	0.886147i	$-0.346628\pi$
$744$	12.4066	−	183.976i	0.0166755	−	0.247280i
$745$	161.461	+	915.693i	0.216727	+	1.22912i
$746$	724.615	+	418.357i	0.971334	+	0.560800i
$747$	−30.5087	+	225.177i	−0.0408416	+	0.301442i
$748$	46.9651	+	81.3460i	0.0627876	+	0.108751i
$749$	−669.637	−	798.043i	−0.894042	−	1.06548i
$750$	−257.966	−	247.882i	−0.343955	−	0.330510i
$751$	−129.904	+	736.724i	−0.172975	+	0.980990i	0.767480	+	0.641073i	$0.221510\pi$
$751$	−129.904	+	736.724i	−0.172975	+	0.980990i	−0.940455	+	0.339918i	$0.889601\pi$
$752$	−32.6238	+	38.8795i	−0.0433827	+	0.0517015i
$753$	413.783	+	566.564i	0.549512	+	0.752409i
$754$	−167.671	−	61.0271i	−0.222375	−	0.0809378i
$755$		−	929.460i		−	1.23107i
$756$	124.740	+	374.410i	0.165000	+	0.495251i
$757$	788.946			1.04220			0.521100	−	0.853496i	$-0.325522\pi$
$757$	788.946			1.04220			0.521100	+	0.853496i	$0.325522\pi$
$758$	96.0924	−	264.012i	0.126771	−	0.348300i
$759$	1372.18	+	606.861i	1.80788	+	0.799553i
$760$	315.956	+	265.119i	0.415732	+	0.348841i
$761$	512.126	+	90.3016i	0.672965	+	0.118662i	0.499680	−	0.866210i	$-0.333451\pi$
$761$	512.126	+	90.3016i	0.672965	+	0.118662i	0.173284	+	0.984872i	$0.444562\pi$
$762$	258.955	+	894.706i	0.339836	+	1.17415i
$763$	−667.754	+	560.312i	−0.875170	+	0.734354i
$764$	−343.739	+	198.458i	−0.449921	+	0.259762i
$765$	−108.371	−	56.9345i	−0.141662	−	0.0744242i
$766$	22.8657	−	39.6045i	0.0298507	−	0.0517030i

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)

\(f(q)\)	\(=\)	\(q+(0.483690 - 1.32893i) q^{2} +(0.320982 + 2.98278i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(5.90332 + 1.04091i) q^{5} +(4.11915 + 1.01618i) q^{6} +(5.59840 - 4.69762i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(-8.79394 + 1.91484i) q^{9} +O(q^{10})\)	\(q+(0.483690 - 1.32893i) q^{2} +(0.320982 + 2.98278i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(5.90332 + 1.04091i) q^{5} +(4.11915 + 1.01618i) q^{6} +(5.59840 - 4.69762i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(-8.79394 + 1.91484i) q^{9} +(4.23867 - 7.34160i) q^{10} +(-20.3832 + 3.59412i) q^{11} +(3.34281 - 4.98253i) q^{12} +(6.40830 - 2.33243i) q^{13} +(-3.53490 - 9.71205i) q^{14} +(-1.20996 + 17.9424i) q^{15} +(0.694593 + 3.93923i) q^{16} +(1.96510 + 1.13455i) q^{17} +(-1.70886 + 12.6127i) q^{18} +(-12.1634 - 21.0675i) q^{19} +(-7.70624 - 9.18394i) q^{20} +(15.8089 + 15.1909i) q^{21} +(-5.08285 + 28.8263i) q^{22} +(-15.5320 + 18.5103i) q^{23} +(-5.00453 - 6.85235i) q^{24} +(10.2734 + 3.73921i) q^{25} -9.64433i q^{26} +(-8.53423 - 25.6158i) q^{27} -14.6164 q^{28} +(6.32777 - 17.3854i) q^{29} +(23.2589 + 10.2865i) q^{30} +(16.6469 + 13.9684i) q^{31} +(5.57091 + 0.982302i) q^{32} +(-17.2631 - 59.6451i) q^{33} +(2.45823 - 2.06270i) q^{34} +(37.9390 - 21.9041i) q^{35} +(15.9348 + 8.37157i) q^{36} +(22.3832 - 38.7688i) q^{37} +(-33.8805 + 5.97405i) q^{38} +(9.01408 + 18.3659i) q^{39} +(-15.9322 + 5.79885i) q^{40} +(17.5398 + 48.1902i) q^{41} +(27.8343 - 13.6612i) q^{42} +(6.41470 + 36.3796i) q^{43} +(35.8494 + 20.6977i) q^{44} +(-53.9066 + 2.15015i) q^{45} +(17.0861 + 29.5941i) q^{46} +(8.15595 + 9.71989i) q^{47} +(-11.5269 + 3.33624i) q^{48} +(0.765740 - 4.34273i) q^{49} +(9.93826 - 11.8440i) q^{50} +(-2.75335 + 6.22562i) q^{51} +(-12.8166 - 4.66486i) q^{52} -17.7730i q^{53} +(-38.1694 - 1.04871i) q^{54} -124.070 q^{55} +(-7.06980 + 19.4241i) q^{56} +(58.9356 - 43.0429i) q^{57} +(-20.0432 - 16.8183i) q^{58} +(64.9049 + 11.4445i) q^{59} +(24.9201 - 25.9339i) q^{60} +(32.3438 - 27.1396i) q^{61} +(26.6150 - 15.3662i) q^{62} +(-40.2369 + 52.0306i) q^{63} +(4.00000 - 6.92820i) q^{64} +(40.2581 - 7.09859i) q^{65} +(-87.6139 - 5.90830i) q^{66} +(-111.190 + 40.4700i) q^{67} +(-1.55216 - 4.26451i) q^{68} +(-60.1976 - 40.3870i) q^{69} +(-10.7582 - 61.0129i) q^{70} +(-46.1702 - 26.6564i) q^{71} +(18.8327 - 17.1269i) q^{72} +(33.8569 + 58.6419i) q^{73} +(-40.6944 - 48.4976i) q^{74} +(-7.85565 + 31.8434i) q^{75} +(-8.44858 + 47.9143i) q^{76} +(-97.2298 + 115.874i) q^{77} +(28.7669 - 3.09566i) q^{78} +(104.610 + 38.0750i) q^{79} +23.9776i q^{80} +(73.6668 - 33.6779i) q^{81} +72.5250 q^{82} +(8.63542 - 23.7256i) q^{83} +(-4.69160 - 43.5975i) q^{84} +(10.4196 + 8.74311i) q^{85} +(51.4485 + 9.07175i) q^{86} +(53.8879 + 13.2939i) q^{87} +(44.8457 - 37.6300i) q^{88} +(-35.4447 + 20.4640i) q^{89} +(-23.2167 + 72.6779i) q^{90} +(24.9194 - 43.1616i) q^{91} +(47.5927 - 8.39188i) q^{92} +(-36.3214 + 54.1378i) q^{93} +(16.8620 - 6.13725i) q^{94} +(-49.8747 - 137.030i) q^{95} +(-1.14183 + 16.9321i) q^{96} +(7.02010 + 39.8130i) q^{97} +(-5.40078 - 3.11814i) q^{98} +(172.367 - 70.6370i) 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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