LMFDB - Embedded newform 54.3.f.a.23.3

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			23.3
Character	$\chi$	$=$	54.23
Dual form			54.3.f.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483690 + 1.32893i) q^{2} +(-0.391734 - 2.97431i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(7.52350 + 1.32660i) q^{5} +(4.14212 + 0.918059i) q^{6} +(4.40811 - 3.69885i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.69309 + 2.33028i) q^{9} +O(q^{10})$	\(q+(-0.483690 + 1.32893i) q^{2} +(-0.391734 - 2.97431i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(7.52350 + 1.32660i) q^{5} +(4.14212 + 0.918059i) q^{6} +(4.40811 - 3.69885i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.69309 + 2.33028i) q^{9} +(-5.40199 + 9.35652i) q^{10} +(8.02644 - 1.41528i) q^{11} +(-3.22353 + 5.06052i) q^{12} +(-22.0464 + 8.02423i) q^{13} +(2.78334 + 7.64715i) q^{14} +(0.998502 - 22.8969i) q^{15} +(0.694593 + 3.93923i) q^{16} +(6.39327 + 3.69115i) q^{17} +(1.10799 - 12.6796i) q^{18} +(-7.80130 - 13.5122i) q^{19} +(-9.82124 - 11.7045i) q^{20} +(-12.7283 - 11.6622i) q^{21} +(-2.00151 + 11.3511i) q^{22} +(-19.9755 + 23.8059i) q^{23} +(-5.16586 - 6.73156i) q^{24} +(31.3510 + 11.4108i) q^{25} -33.1793i q^{26} +(10.3364 + 24.9431i) q^{27} -11.5088 q^{28} +(-9.68546 + 26.6106i) q^{29} +(29.9454 + 12.4019i) q^{30} +(12.2601 + 10.2874i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(-7.35371 - 23.3187i) q^{33} +(-7.99763 + 6.71081i) q^{34} +(38.0714 - 21.9805i) q^{35} +(16.3143 + 7.60542i) q^{36} +(5.99046 - 10.3758i) q^{37} +(21.7302 - 3.83162i) q^{38} +(32.5029 + 62.4295i) q^{39} +(20.3048 - 7.39036i) q^{40} +(2.82625 + 7.76505i) q^{41} +(21.6547 - 11.2742i) q^{42} +(-7.82854 - 44.3978i) q^{43} +(-14.1167 - 8.15026i) q^{44} +(-68.4938 + 5.99965i) q^{45} +(-21.9743 - 38.0606i) q^{46} +(-43.4592 - 51.7927i) q^{47} +(11.4444 - 3.60907i) q^{48} +(-2.75876 + 15.6457i) q^{49} +(-30.3283 + 36.1438i) q^{50} +(8.47419 - 20.4615i) q^{51} +(44.0928 + 16.0485i) q^{52} +16.4115i q^{53} +(-38.1472 + 1.67154i) q^{54} +62.2645 q^{55} +(5.56667 - 15.2943i) q^{56} +(-37.1336 + 28.4967i) q^{57} +(-30.6787 - 25.7425i) q^{58} +(57.3592 + 10.1140i) q^{59} +(-30.9655 + 33.7965i) q^{60} +(54.6605 - 45.8656i) q^{61} +(-19.6013 + 11.3168i) q^{62} +(-29.7008 + 42.4266i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-176.511 + 31.1237i) q^{65} +(34.5458 + 1.50649i) q^{66} +(-47.1688 + 17.1680i) q^{67} +(-5.04980 - 13.8742i) q^{68} +(78.6313 + 50.0879i) q^{69} +(10.7958 + 61.2257i) q^{70} +(35.4363 + 20.4592i) q^{71} +(-17.9981 + 18.0019i) q^{72} +(-49.7692 - 86.2028i) q^{73} +(10.8911 + 12.9795i) q^{74} +(21.6581 - 97.7176i) q^{75} +(-5.41873 + 30.7311i) q^{76} +(30.1466 - 35.9273i) q^{77} +(-98.6855 + 12.9974i) q^{78} +(-72.4061 - 26.3537i) q^{79} +30.5583i q^{80} +(70.1396 - 40.5147i) q^{81} -11.6862 q^{82} +(36.0769 - 99.1205i) q^{83} +(4.50838 + 34.2307i) q^{84} +(43.2031 + 36.2517i) q^{85} +(62.7880 + 11.0712i) q^{86} +(82.9423 + 18.3833i) q^{87} +(17.6592 - 14.8178i) q^{88} +(-0.302200 + 0.174475i) q^{89} +(25.1567 - 93.9252i) q^{90} +(-67.5026 + 116.918i) q^{91} +(61.2085 - 10.7927i) q^{92} +(25.7954 - 40.4953i) q^{93} +(89.8494 - 32.7025i) q^{94} +(-40.7678 - 112.009i) q^{95} +(-0.739359 + 16.9544i) q^{96} +(11.1076 + 62.9944i) q^{97} +(-19.4576 - 11.2338i) q^{98} +(-66.4766 + 31.0070i) 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
$3$	−0.391734	−	2.97431i	−0.130578	−	0.991438i
$3$	−0.391734	−	2.97431i	−0.130578	−	0.991438i
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	7.52350	+	1.32660i	1.50470	+	0.265319i	0.864400	−	0.502805i	$-0.167699\pi$
$5$	7.52350	+	1.32660i	1.50470	+	0.265319i	0.640301	+	0.768124i	$0.278810\pi$
$6$	4.14212	+	0.918059i	0.690354	+	0.153010i
$7$	4.40811	−	3.69885i	0.629731	−	0.528407i	−0.271115	−	0.962547i	$-0.587392\pi$
$7$	4.40811	−	3.69885i	0.629731	−	0.528407i	0.900845	+	0.434140i	$0.142948\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$	−8.69309	+	2.33028i	−0.965899	+	0.258920i
$10$	−5.40199	+	9.35652i	−0.540199	+	0.935652i
$11$	8.02644	−	1.41528i	0.729677	−	0.128662i	0.203546	−	0.979065i	$-0.434753\pi$
$11$	8.02644	−	1.41528i	0.729677	−	0.128662i	0.526131	+	0.850404i	$0.323642\pi$
$12$	−3.22353	+	5.06052i	−0.268628	+	0.421710i
$13$	−22.0464	+	8.02423i	−1.69588	+	0.617248i	−0.995345	−	0.0963739i	$-0.969276\pi$
$13$	−22.0464	+	8.02423i	−1.69588	+	0.617248i	−0.700531	+	0.713622i	$0.747053\pi$
$14$	2.78334	+	7.64715i	0.198810	+	0.546225i
$15$	0.998502	−	22.8969i	0.0665668	−	1.52646i
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	6.39327	+	3.69115i	0.376075	+	0.217127i	0.676109	−	0.736802i	$-0.263665\pi$
$17$	6.39327	+	3.69115i	0.376075	+	0.217127i	−0.300034	+	0.953928i	$0.596998\pi$
$18$	1.10799	−	12.6796i	0.0615547	−	0.704422i
$19$	−7.80130	−	13.5122i	−0.410595	−	0.711171i	0.584360	−	0.811494i	$-0.301346\pi$
$19$	−7.80130	−	13.5122i	−0.410595	−	0.711171i	−0.994955	+	0.100324i	$0.968012\pi$
$20$	−9.82124	−	11.7045i	−0.491062	−	0.585225i
$21$	−12.7283	−	11.6622i	−0.606112	−	0.555341i
$22$	−2.00151	+	11.3511i	−0.0909775	+	0.515959i
$23$	−19.9755	+	23.8059i	−0.868500	+	1.03504i	0.130549	+	0.991442i	$0.458326\pi$
$23$	−19.9755	+	23.8059i	−0.868500	+	1.03504i	−0.999049	+	0.0435964i	$0.986118\pi$
$24$	−5.16586	−	6.73156i	−0.215244	−	0.280482i
$25$	31.3510	+	11.4108i	1.25404	+	0.456433i
$26$		−	33.1793i		−	1.27613i
$27$	10.3364	+	24.9431i	0.382828	+	0.923819i
$28$	−11.5088			−0.411027
$29$	−9.68546	+	26.6106i	−0.333981	+	0.917606i	0.653084	+	0.757286i	$0.273475\pi$
$29$	−9.68546	+	26.6106i	−0.333981	+	0.917606i	−0.987065	+	0.160320i	$0.948747\pi$
$30$	29.9454	+	12.4019i	0.998179	+	0.413398i
$31$	12.2601	+	10.2874i	0.395487	+	0.331853i	0.818746	−	0.574156i	$-0.194670\pi$
$31$	12.2601	+	10.2874i	0.395487	+	0.331853i	−0.423259	+	0.906009i	$0.639114\pi$
$32$	−5.57091	−	0.982302i	−0.174091	−	0.0306970i
$33$	−7.35371	−	23.3187i	−0.222840	−	0.706629i
$34$	−7.99763	+	6.71081i	−0.235224	+	0.197377i
$35$	38.0714	−	21.9805i	1.08775	−	0.628014i
$36$	16.3143	+	7.60542i	0.453176	+	0.211262i
$37$	5.99046	−	10.3758i	0.161904	−	0.280427i	−0.773647	−	0.633617i	$-0.781570\pi$
$37$	5.99046	−	10.3758i	0.161904	−	0.280427i	0.935552	+	0.353190i	$0.114903\pi$
$38$	21.7302	−	3.83162i	0.571847	−	0.100832i
$39$	32.5029	+	62.4295i	0.833408	+	1.60076i
$40$	20.3048	−	7.39036i	0.507621	−	0.184759i
$41$	2.82625	+	7.76505i	0.0689329	+	0.189391i	0.969375	−	0.245583i	$-0.0789795\pi$
$41$	2.82625	+	7.76505i	0.0689329	+	0.189391i	−0.900443	+	0.434975i	$0.856757\pi$
$42$	21.6547	−	11.2742i	0.515588	−	0.268433i
$43$	−7.82854	−	44.3978i	−0.182059	−	1.03251i	−0.929676	−	0.368378i	$-0.879913\pi$
$43$	−7.82854	−	44.3978i	−0.182059	−	1.03251i	0.747617	−	0.664130i	$-0.231198\pi$
$44$	−14.1167	−	8.15026i	−0.320833	−	0.185233i
$45$	−68.4938	+	5.99965i	−1.52209	+	0.133326i
$46$	−21.9743	−	38.0606i	−0.477702	−	0.827405i
$47$	−43.4592	−	51.7927i	−0.924664	−	1.10197i	−0.994534	−	0.104416i	$-0.966703\pi$
$47$	−43.4592	−	51.7927i	−0.924664	−	1.10197i	0.0698695	−	0.997556i	$-0.477742\pi$
$48$	11.4444	−	3.60907i	0.238425	−	0.0751889i
$49$	−2.75876	+	15.6457i	−0.0563012	+	0.319300i
$50$	−30.3283	+	36.1438i	−0.606565	+	0.722876i
$51$	8.47419	−	20.4615i	0.166161	−	0.401207i
$52$	44.0928	+	16.0485i	0.847938	+	0.308624i
$53$			16.4115i			0.309652i	0.987942	+	0.154826i	$0.0494816\pi$
$53$			16.4115i			0.309652i	−0.987942	+	0.154826i	$0.950518\pi$
$54$	−38.1472	+	1.67154i	−0.706429	+	0.0309544i
$55$	62.2645			1.13208
$56$	5.56667	−	15.2943i	0.0994048	−	0.273113i
$57$	−37.1336	+	28.4967i	−0.651467	+	0.499943i
$58$	−30.6787	−	25.7425i	−0.528944	−	0.443836i
$59$	57.3592	+	10.1140i	0.972190	+	0.171423i	0.637115	−	0.770768i	$-0.280127\pi$
$59$	57.3592	+	10.1140i	0.972190	+	0.171423i	0.335074	+	0.942192i	$0.391239\pi$
$60$	−30.9655	+	33.7965i	−0.516092	+	0.563275i
$61$	54.6605	−	45.8656i	0.896073	−	0.751895i	−0.0733455	−	0.997307i	$-0.523368\pi$
$61$	54.6605	−	45.8656i	0.896073	−	0.751895i	0.969419	+	0.245412i	$0.0789231\pi$
$62$	−19.6013	+	11.3168i	−0.316151	+	0.182530i
$63$	−29.7008	+	42.4266i	−0.471441	+	0.673437i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	−176.511	+	31.1237i	−2.71555	+	0.478825i
$66$	34.5458	+	1.50649i	0.523421	+	0.0228256i
$67$	−47.1688	+	17.1680i	−0.704012	+	0.256239i	−0.669123	−	0.743152i	$-0.733330\pi$
$67$	−47.1688	+	17.1680i	−0.704012	+	0.256239i	−0.0348888	+	0.999391i	$0.511108\pi$
$68$	−5.04980	−	13.8742i	−0.0742617	−	0.204032i
$69$	78.6313	+	50.0879i	1.13958	+	0.725911i
$70$	10.7958	+	61.2257i	0.154225	+	0.874654i
$71$	35.4363	+	20.4592i	0.499103	+	0.288157i	0.728343	−	0.685213i	$-0.240291\pi$
$71$	35.4363	+	20.4592i	0.499103	+	0.288157i	−0.229240	+	0.973370i	$0.573624\pi$
$72$	−17.9981	+	18.0019i	−0.249974	+	0.250026i
$73$	−49.7692	−	86.2028i	−0.681770	−	1.18086i	−0.974440	−	0.224647i	$-0.927877\pi$
$73$	−49.7692	−	86.2028i	−0.681770	−	1.18086i	0.292670	−	0.956213i	$-0.405456\pi$
$74$	10.8911	+	12.9795i	0.147177	+	0.175399i
$75$	21.6581	−	97.7176i	0.288775	−	1.30290i
$76$	−5.41873	+	30.7311i	−0.0712990	+	0.404357i
$77$	30.1466	−	35.9273i	0.391514	−	0.466588i
$78$	−98.6855	+	12.9974i	−1.26520	+	0.166634i
$79$	−72.4061	−	26.3537i	−0.916533	−	0.333591i	−0.159674	−	0.987170i	$-0.551044\pi$
$79$	−72.4061	−	26.3537i	−0.916533	−	0.333591i	−0.756858	+	0.653579i	$0.773267\pi$
$80$			30.5583i			0.381978i
$81$	70.1396	−	40.5147i	0.865921	−	0.500181i
$82$	−11.6862			−0.142515
$83$	36.0769	−	99.1205i	0.434662	−	1.19422i	−0.508259	−	0.861204i	$-0.669711\pi$
$83$	36.0769	−	99.1205i	0.434662	−	1.19422i	0.942920	−	0.333018i	$-0.108067\pi$
$84$	4.50838	+	34.2307i	0.0536712	+	0.407508i
$85$	43.2031	+	36.2517i	0.508272	+	0.426491i
$86$	62.7880	+	11.0712i	0.730093	+	0.128735i
$87$	82.9423	+	18.3833i	0.953360	+	0.211303i
$88$	17.6592	−	14.8178i	0.200673	−	0.168384i
$89$	−0.302200	+	0.174475i	−0.00339551	+	0.00196040i	−0.501697	−	0.865044i	$-0.667291\pi$
$89$	−0.302200	+	0.174475i	−0.00339551	+	0.00196040i	0.498301	+	0.867004i	$0.333957\pi$
$90$	25.1567	−	93.9252i	0.279518	−	1.04361i
$91$	−67.5026	+	116.918i	−0.741787	+	1.28481i
$92$	61.2085	−	10.7927i	0.665310	−	0.117312i
$93$	25.7954	−	40.4953i	0.277370	−	0.435434i
$94$	89.8494	−	32.7025i	0.955845	−	0.347899i
$95$	−40.7678	−	112.009i	−0.429135	−	1.17904i
$96$	−0.739359	+	16.9544i	−0.00770165	+	0.176609i
$97$	11.1076	+	62.9944i	0.114511	+	0.649427i	0.986991	+	0.160776i	$0.0513997\pi$
$97$	11.1076	+	62.9944i	0.114511	+	0.649427i	−0.872479	+	0.488651i	$0.837489\pi$
$98$	−19.4576	−	11.2338i	−0.198547	−	0.114631i
$99$	−66.4766	+	31.0070i	−0.671481	+	0.313202i
$100$	−33.3630	−	57.7864i	−0.333630	−	0.577864i
$101$	107.169	+	127.719i	1.06107	+	1.26454i	0.963040	+	0.269357i	$0.0868111\pi$
$101$	107.169	+	127.719i	1.06107	+	1.26454i	0.0980344	+	0.995183i	$0.468744\pi$
$102$	23.0930	+	21.1586i	0.226402	+	0.207437i
$103$	−17.4708	+	99.0819i	−0.169620	+	0.961960i	0.774553	+	0.632509i	$0.217975\pi$
$103$	−17.4708	+	99.0819i	−0.169620	+	0.961960i	−0.944173	+	0.329451i	$0.893136\pi$
$104$	−42.6544	+	50.8336i	−0.410139	+	0.488784i
$105$	−80.2908	−	104.626i	−0.764674	−	0.996435i
$106$	−21.8097	−	7.93809i	−0.205752	−	0.0748876i
$107$		−	6.57806i		−	0.0614772i	−0.999527	−	0.0307386i	$-0.990214\pi$
$107$		−	6.57806i		−	0.0614772i	0.999527	−	0.0307386i	$-0.00978594\pi$
$108$	16.2300	−	51.5033i	0.150278	−	0.476882i
$109$	198.876			1.82455			0.912276	−	0.409576i	$-0.134323\pi$
$109$	198.876			1.82455			0.912276	+	0.409576i	$0.134323\pi$
$110$	−30.1167	+	82.7449i	−0.273788	+	0.752226i
$111$	−33.2075	−	13.7530i	−0.299167	−	0.123901i
$112$	17.6325	+	14.7954i	0.157433	+	0.132102i
$113$	−5.16749	−	0.911168i	−0.0457300	−	0.00806344i	0.150736	−	0.988574i	$-0.451836\pi$
$113$	−5.16749	−	0.911168i	−0.0457300	−	0.00806344i	−0.196466	+	0.980511i	$0.562947\pi$
$114$	−19.9089	−	63.1314i	−0.174639	−	0.553784i
$115$	−181.867	+	152.604i	−1.58145	+	1.32699i
$116$	49.0489	−	28.3184i	0.422835	−	0.244124i
$117$	172.952	−	121.130i	1.47823	−	1.03530i
$118$	−41.1848	+	71.3341i	−0.349023	+	0.604526i
$119$	41.8353	−	7.37669i	0.351557	−	0.0619890i
$120$	−29.9353	−	57.4979i	−0.249461	−	0.479149i
$121$	−51.2820	+	18.6651i	−0.423819	+	0.154257i
$122$	34.5133	+	94.8244i	0.282896	+	0.777250i
$123$	21.9886	−	11.4480i	0.178769	−	0.0930730i
$124$	−5.55828	−	31.5226i	−0.0448248	−	0.254214i
$125$	55.3300	+	31.9448i	0.442640	+	0.255558i
$126$	−42.0158	−	59.9914i	−0.333459	−	0.476122i
$127$	−22.2191	−	38.4846i	−0.174954	−	0.303029i	0.765192	−	0.643803i	$-0.222644\pi$
$127$	−22.2191	−	38.4846i	−0.174954	−	0.303029i	−0.940145	+	0.340774i	$0.889311\pi$
$128$	7.27231	+	8.66680i	0.0568149	+	0.0677094i
$129$	−128.986	+	40.6767i	−0.999895	+	0.315323i
$130$	44.0155	−	249.624i	0.338581	−	1.92019i
$131$	25.8274	−	30.7798i	0.197155	−	0.234961i	−0.658405	−	0.752664i	$-0.728768\pi$
$131$	25.8274	−	30.7798i	0.197155	−	0.234961i	0.855560	+	0.517703i	$0.173213\pi$
$132$	−18.7115	+	45.1801i	−0.141753	+	0.342274i
$133$	−84.3688	−	30.7077i	−0.634352	−	0.230885i
$134$		−	70.9878i		−	0.529760i
$135$	44.6762	+	201.372i	0.330935	+	1.49164i
$136$	20.8803			0.153532
$137$	17.6267	−	48.4289i	0.128662	−	0.353495i	−0.858590	−	0.512663i	$-0.828659\pi$
$137$	17.6267	−	48.4289i	0.128662	−	0.353495i	0.987252	+	0.159168i	$0.0508811\pi$
$138$	−104.596	+	80.2682i	−0.757943	+	0.581653i
$139$	−82.4641	−	69.1956i	−0.593267	−	0.497810i	0.296006	−	0.955186i	$-0.404345\pi$
$139$	−82.4641	−	69.1956i	−0.593267	−	0.497810i	−0.889274	+	0.457376i	$0.848789\pi$
$140$	−86.5863	−	15.2675i	−0.618473	−	0.109054i
$141$	−137.023	+	149.550i	−0.971796	+	1.06064i
$142$	−44.3289	+	37.1964i	−0.312175	+	0.261946i
$143$	−165.598	+	95.6078i	−1.15802	+	0.668586i
$144$	−15.2177	−	32.6255i	−0.105678	−	0.226566i
$145$	−108.170	+	187.356i	−0.746001	+	1.29211i
$146$	138.630	−	24.4442i	0.949520	−	0.167426i
$147$	47.6159	+	2.07646i	0.323918	+	0.0141256i
$148$	−22.5168	+	8.19544i	−0.152140	+	0.0553746i
$149$	−48.2594	−	132.592i	−0.323888	−	0.889876i	−0.989623	−	0.143688i	$-0.954104\pi$
$149$	−48.2594	−	132.592i	−0.323888	−	0.889876i	0.665735	−	0.746189i	$-0.268118\pi$
$150$	119.384	+	76.0470i	0.795891	+	0.506980i
$151$	−22.7795	−	129.189i	−0.150858	−	0.855557i	−0.962476	−	0.271368i	$-0.912524\pi$
$151$	−22.7795	−	129.189i	−0.150858	−	0.855557i	0.811618	−	0.584189i	$-0.198587\pi$
$152$	−38.2184	−	22.0654i	−0.251437	−	0.145167i
$153$	−64.1787	−	17.1894i	−0.419468	−	0.112349i
$154$	33.1631	+	57.4402i	0.215345	+	0.372988i
$155$	78.5916	+	93.6618i	0.507043	+	0.604270i
$156$	30.4605	−	137.432i	0.195260	−	0.880978i
$157$	33.4745	−	189.844i	0.213214	−	1.20919i	−0.670766	−	0.741669i	$-0.734034\pi$
$157$	33.4745	−	189.844i	0.213214	−	1.20919i	0.883980	−	0.467526i	$-0.154854\pi$
$158$	70.0441	−	83.4753i	0.443317	−	0.528325i
$159$	48.8131	−	6.42896i	0.307000	−	0.0404337i
$160$	−40.6097	−	14.7807i	−0.253810	−	0.0923795i
$161$			178.825i			1.11072i
$162$	19.9152	+	112.807i	0.122934	+	0.696339i
$163$	80.4819			0.493754			0.246877	−	0.969047i	$-0.420596\pi$
$163$	80.4819			0.493754			0.246877	+	0.969047i	$0.420596\pi$
$164$	5.65249	−	15.5301i	0.0344664	−	0.0946957i
$165$	−24.3911	−	185.194i	−0.147825	−	1.12239i
$166$	114.274	+	95.8871i	0.688396	+	0.577633i
$167$	−106.625	−	18.8008i	−0.638472	−	0.112580i	−0.154964	−	0.987920i	$-0.549526\pi$
$167$	−106.625	−	18.8008i	−0.638472	−	0.112580i	−0.483508	+	0.875340i	$0.660637\pi$
$168$	−47.6707	−	10.5657i	−0.283754	−	0.0628912i
$169$	292.193	−	245.179i	1.72896	−	1.45077i
$170$	−69.0727	+	39.8792i	−0.406310	+	0.234583i
$171$	99.3047	+	99.2839i	0.580729	+	0.580608i
$172$	−45.0827	+	78.0856i	−0.262109	+	0.453986i
$173$	83.3770	−	14.7016i	0.481948	−	0.0849804i	0.0726044	−	0.997361i	$-0.476869\pi$
$173$	83.3770	−	14.7016i	0.481948	−	0.0849804i	0.409343	+	0.912380i	$0.365758\pi$
$174$	−64.5484	+	101.332i	−0.370968	+	0.582370i
$175$	180.405	−	65.6622i	1.03089	−	0.375213i
$176$	11.1502	+	30.6350i	0.0633535	+	0.174062i
$177$	7.61258	−	174.566i	0.0430089	−	0.986250i
$178$	−0.0856938	−	0.485994i	−0.000481426	−	0.00273030i
$179$	−145.291	−	83.8837i	−0.811681	−	0.468624i	0.0358583	−	0.999357i	$-0.488583\pi$
$179$	−145.291	−	83.8837i	−0.811681	−	0.468624i	−0.847539	+	0.530733i	$0.821917\pi$
$180$	112.652	+	78.8620i	0.625843	+	0.438122i
$181$	144.733	+	250.684i	0.799627	+	1.38500i	0.919859	+	0.392249i	$0.128303\pi$
$181$	144.733	+	250.684i	0.799627	+	1.38500i	−0.120232	+	0.992746i	$0.538364\pi$
$182$	−122.725	−	146.258i	−0.674313	−	0.803615i
$183$	−157.831	−	144.610i	−0.862465	−	0.790220i
$184$	−15.2632	+	86.5619i	−0.0829522	+	0.470445i
$185$	58.8338	−	70.1154i	0.318020	−	0.379002i
$186$	41.3383	+	53.8673i	0.222249	+	0.289609i
$187$	56.5392	+	20.5786i	0.302349	+	0.110046i
$188$			135.221i			0.719261i
$189$	137.825	+	71.7195i	0.729231	+	0.379468i
$190$	168.570			0.887211
$191$	−13.7963	+	37.9051i	−0.0722320	+	0.198456i	−0.970555	−	0.240880i	$-0.922564\pi$
$191$	−13.7963	+	37.9051i	−0.0722320	+	0.198456i	0.898323	+	0.439336i	$0.144786\pi$
$192$	−22.1736	−	9.18324i	−0.115487	−	0.0478294i
$193$	−185.784	−	155.891i	−0.962610	−	0.807726i	0.0187656	−	0.999824i	$-0.494026\pi$
$193$	−185.784	−	155.891i	−0.962610	−	0.807726i	−0.981376	+	0.192098i	$0.938471\pi$
$194$	−89.0875	−	15.7085i	−0.459214	−	0.0809718i
$195$	161.717	+	512.807i	0.829318	+	2.62978i
$196$	24.3404	−	20.4240i	0.124186	−	0.104204i
$197$	−4.72432	+	2.72758i	−0.0239813	+	0.0138456i	−0.511943	−	0.859020i	$-0.671074\pi$
$197$	−4.72432	+	2.72758i	−0.0239813	+	0.0138456i	0.487961	+	0.872865i	$0.337741\pi$
$198$	−9.05199	−	103.340i	−0.0457171	−	0.521920i
$199$	71.5073	−	123.854i	0.359333	−	0.622383i	−0.628516	−	0.777796i	$-0.716337\pi$
$199$	71.5073	−	123.854i	0.359333	−	0.622383i	0.987850	+	0.155413i	$0.0496708\pi$
$200$	92.9312	−	16.3863i	0.464656	−	0.0819314i
$201$	69.5407	+	133.569i	0.345974	+	0.664525i
$202$	−221.565	+	80.6430i	−1.09686	+	0.399223i
$203$	55.7339	+	153.127i	0.274551	+	0.754323i
$204$	−39.2881	+	20.4547i	−0.192589	+	0.100268i
$205$	10.9622	+	62.1697i	0.0534741	+	0.303267i
$206$	−123.222	−	71.1423i	−0.598165	−	0.345351i
$207$	118.174	−	253.495i	0.570891	−	1.22461i
$208$	−46.9226	−	81.2722i	−0.225589	−	0.390732i
$209$	−81.7403	−	97.4143i	−0.391102	−	0.466097i
$210$	177.876	−	56.0942i	0.847026	−	0.267115i
$211$	−1.49994	+	8.50659i	−0.00710873	+	0.0403156i	−0.988156	−	0.153454i	$-0.950960\pi$
$211$	−1.49994	+	8.50659i	−0.00710873	+	0.0403156i	0.981047	+	0.193770i	$0.0620714\pi$
$212$	21.0983	−	25.1439i	0.0995201	−	0.118603i
$213$	46.9704	−	113.413i	0.220518	−	0.532457i
$214$	8.74176	+	3.18174i	0.0408493	+	0.0148679i
$215$		−	344.413i		−	1.60192i
$216$	60.5937	+	46.4801i	0.280527	+	0.215186i
$217$	92.0956			0.424404
$218$	−96.1943	+	264.292i	−0.441258	+	1.21235i
$219$	−236.898	+	181.798i	−1.08173	+	0.830127i
$220$	−95.3947	−	80.0457i	−0.433612	−	0.363844i
$221$	−170.567	−	30.0756i	−0.771797	−	0.136089i
$222$	34.3388	−	37.4782i	0.154679	−	0.168821i
$223$	−235.030	+	197.214i	−1.05395	+	0.884367i	−0.993503	−	0.113805i	$-0.963696\pi$
$223$	−235.030	+	197.214i	−1.05395	+	0.884367i	−0.0604441	+	0.998172i	$0.519252\pi$
$224$	−28.1906	+	16.2759i	−0.125851	+	0.0726601i
$225$	−299.127	−	26.1387i	−1.32945	−	0.116172i
$226$	3.71034	−	6.42649i	0.0164174	−	0.0284358i
$227$	11.7174	−	2.06609i	0.0516185	−	0.00910173i	−0.147779	−	0.989020i	$-0.547213\pi$
$227$	11.7174	−	2.06609i	0.0516185	−	0.00910173i	0.199398	+	0.979919i	$0.436101\pi$
$228$	93.5267	+	4.07856i	0.410205	+	0.0178884i
$229$	362.125	−	131.803i	1.58133	−	0.575558i	0.605839	−	0.795587i	$-0.292837\pi$
$229$	362.125	−	131.803i	1.58133	−	0.575558i	0.975493	+	0.220029i	$0.0706153\pi$
$230$	−114.833	−	315.500i	−0.499273	−	1.37174i
$231$	−118.668	−	75.5914i	−0.513716	−	0.327236i
$232$	13.9086	+	78.8796i	0.0599509	+	0.339998i
$233$	−8.31951	−	4.80327i	−0.0357060	−	0.0206149i	0.482041	−	0.876149i	$-0.339896\pi$
$233$	−8.31951	−	4.80327i	−0.0357060	−	0.0206149i	−0.517747	+	0.855534i	$0.673229\pi$
$234$	77.3170	+	288.430i	0.330414	+	1.23261i
$235$	−258.258	−	447.315i	−1.09897	−	1.90347i
$236$	−74.8771	−	89.2351i	−0.317276	−	0.378115i
$237$	−50.0201	+	225.682i	−0.211055	+	0.952245i
$238$	−10.4322	+	59.1640i	−0.0438328	+	0.248588i
$239$	−66.1793	+	78.8695i	−0.276901	+	0.329998i	−0.886514	−	0.462701i	$-0.846880\pi$
$239$	−66.1793	+	78.8695i	−0.276901	+	0.329998i	0.609613	+	0.792699i	$0.291325\pi$
$240$	90.8899	−	11.9707i	0.378708	−	0.0498780i
$241$	−100.052	−	36.4160i	−0.415154	−	0.151104i	0.125994	−	0.992031i	$-0.459788\pi$
$241$	−100.052	−	36.4160i	−0.415154	−	0.151104i	−0.541148	+	0.840927i	$0.682010\pi$
$242$		−	77.1782i		−	0.318918i
$243$	−147.979	−	192.746i	−0.608969	−	0.793194i
$244$	−142.708			−0.584870
$245$	−41.5111	+	114.051i	−0.169433	+	0.465513i
$246$	4.57789	+	34.7584i	0.0186093	+	0.141294i
$247$	280.416	+	235.297i	1.13529	+	0.952619i
$248$	44.5796	+	7.86059i	0.179757	+	0.0316959i
$249$	−308.948	−	68.4752i	−1.24076	−	0.275001i
$250$	−69.2148	+	58.0781i	−0.276859	+	0.232312i
$251$	70.6683	−	40.8004i	0.281547	−	0.162551i	−0.352577	−	0.935783i	$-0.614694\pi$
$251$	70.6683	−	40.8004i	0.281547	−	0.162551i	0.634124	+	0.773232i	$0.281361\pi$
$252$	100.047	−	26.8187i	0.397011	−	0.106423i
$253$	−126.640	+	219.347i	−0.500555	+	0.866986i
$254$	61.8904	−	10.9129i	0.243663	−	0.0429643i
$255$	90.8998	−	142.701i	0.356470	−	0.559610i
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	150.247	+	412.801i	0.584620	+	1.60623i	0.780192	+	0.625541i	$0.215122\pi$
$257$	150.247	+	412.801i	0.584620	+	1.60623i	−0.195572	+	0.980689i	$0.562656\pi$
$258$	8.33308	−	191.088i	0.0322988	−	0.740652i
$259$	−11.9718	−	67.8955i	−0.0462232	−	0.262145i
$260$	310.442	+	179.234i	1.19401	+	0.689361i
$261$	22.1864	−	253.898i	0.0850055	−	0.972789i
$262$	28.4117	+	49.2105i	0.108442	+	0.187826i
$263$	289.840	+	345.418i	1.10205	+	1.31338i	0.945469	+	0.325711i	$0.105604\pi$
$263$	289.840	+	345.418i	1.10205	+	1.31338i	0.156584	+	0.987665i	$0.449952\pi$
$264$	−50.9905	−	46.7193i	−0.193146	−	0.176967i
$265$	−21.7715	+	123.472i	−0.0821566	+	0.465933i
$266$	81.6166	−	97.2668i	0.306829	−	0.365665i
$267$	0.637327	+	0.830491i	0.00238699	+	0.00311045i
$268$	94.3375	+	34.3361i	0.352006	+	0.128120i
$269$			363.566i			1.35155i	0.737110	+	0.675773i	$0.236190\pi$
$269$			363.566i			1.35155i	−0.737110	+	0.675773i	$0.763810\pi$
$270$	−289.218	−	38.0301i	−1.07118	−	0.140852i
$271$	−70.6655			−0.260758			−0.130379	−	0.991464i	$-0.541619\pi$
$271$	−70.6655			−0.260758			−0.130379	+	0.991464i	$0.541619\pi$
$272$	−10.0996	+	27.7484i	−0.0371309	+	0.102016i
$273$	374.194	+	154.973i	1.37067	+	0.567667i
$274$	55.8326	+	46.8491i	0.203768	+	0.170982i
$275$	267.786	+	47.2179i	0.973768	+	0.171701i
$276$	−56.0784	−	177.825i	−0.203182	−	0.644295i
$277$	−178.872	+	150.091i	−0.645746	+	0.541845i	−0.905777	−	0.423755i	$-0.860712\pi$
$277$	−178.872	+	150.091i	−0.645746	+	0.541845i	0.260031	+	0.965600i	$0.416267\pi$
$278$	131.843	−	76.1195i	0.474255	−	0.273811i
$279$	−130.551	−	60.8602i	−0.467924	−	0.218137i
$280$	62.1703	−	107.682i	0.222037	−	0.384579i
$281$	−284.922	+	50.2394i	−1.01396	+	0.178788i	−0.655849	−	0.754892i	$-0.727689\pi$
$281$	−284.922	+	50.2394i	−1.01396	+	0.178788i	−0.358108	+	0.933680i	$0.616578\pi$
$282$	−132.465	−	254.430i	−0.469733	−	0.902233i
$283$	−144.152	+	52.4669i	−0.509370	+	0.185395i	−0.583903	−	0.811823i	$-0.698475\pi$
$283$	−144.152	+	52.4669i	−0.509370	+	0.185395i	0.0745339	+	0.997218i	$0.476253\pi$
$284$	−27.9898	−	76.9013i	−0.0985556	−	0.270779i
$285$	−317.179	+	165.134i	−1.11291	+	0.579417i
$286$	−46.9579	−	266.311i	−0.164188	−	0.931159i
$287$	41.1802	+	23.7754i	0.143485	+	0.0828410i
$288$	50.7175	−	4.44255i	0.176102	−	0.0154255i
$289$	−117.251	−	203.084i	−0.405712	−	0.702714i
$290$	−196.662	−	234.372i	−0.678144	−	0.808180i
$291$	183.014	−	57.7146i	0.628914	−	0.198332i
$292$	−34.5693	+	196.052i	−0.118388	+	0.671412i
$293$	104.985	−	125.117i	0.358311	−	0.427019i	−0.556533	−	0.830826i	$-0.687869\pi$
$293$	104.985	−	125.117i	0.358311	−	0.427019i	0.914844	+	0.403807i	$0.132313\pi$
$294$	−25.7908	+	62.2737i	−0.0877237	+	0.211815i
$295$	418.125	+	152.185i	1.41737	+	0.515882i
$296$		−	33.8872i		−	0.114484i
$297$	118.266	+	185.576i	0.398201	+	0.624834i
$298$	199.547			0.669621
$299$	249.364	−	685.122i	0.833993	−	2.29138i
$300$	−158.805	+	121.869i	−0.529351	+	0.406230i
$301$	−198.730	−	166.754i	−0.660232	−	0.554001i
$302$	182.701	+	32.2151i	0.604970	+	0.106673i
$303$	337.893	−	368.785i	1.11516	−	1.21711i
$304$	47.8091	−	40.1166i	0.157267	−	0.131963i
$305$	472.084	−	272.558i	1.54781	−	0.893631i
$306$	53.8860	−	76.9744i	0.176098	−	0.251550i
$307$	163.324	−	282.886i	0.532000	−	0.921452i	−0.467302	−	0.884098i	$-0.654774\pi$
$307$	163.324	−	282.886i	0.532000	−	0.921452i	0.999302	−	0.0373539i	$-0.0118929\pi$
$308$	−92.3745	+	16.2881i	−0.299917	+	0.0528835i
$309$	301.545	+	13.1499i	0.975873	+	0.0425564i
$310$	−162.484	+	59.1392i	−0.524141	+	0.190772i
$311$	159.228	+	437.476i	0.511988	+	1.40668i	0.879162	+	0.476524i	$0.158103\pi$
$311$	159.228	+	437.476i	0.511988	+	1.40668i	−0.367173	+	0.930152i	$0.619674\pi$
$312$	167.904	+	106.954i	0.538154	+	0.342803i
$313$	38.0827	+	215.978i	0.121670	+	0.690025i	0.983230	+	0.182369i	$0.0583766\pi$
$313$	38.0827	+	215.978i	0.121670	+	0.690025i	−0.861560	+	0.507655i	$0.830512\pi$
$314$	236.097	+	136.311i	0.751901	+	0.434110i
$315$	−279.737	+	279.795i	−0.888054	+	0.888239i
$316$	77.0529	+	133.460i	0.243838	+	0.422341i
$317$	−81.8800	−	97.5807i	−0.258296	−	0.307826i	0.621275	−	0.783593i	$-0.286615\pi$
$317$	−81.8800	−	97.5807i	−0.258296	−	0.307826i	−0.879571	+	0.475767i	$0.842171\pi$
$318$	−15.0668	+	67.9786i	−0.0473797	+	0.213769i
$319$	−40.0784	+	227.296i	−0.125638	+	0.712526i
$320$	39.2850	−	46.8180i	0.122765	−	0.146306i
$321$	−19.5652	+	2.57685i	−0.0609508	+	0.00802757i
$322$	−237.646	−	86.4960i	−0.738030	−	0.268621i
$323$		−	115.183i		−	0.356604i
$324$	−159.545	−	28.0976i	−0.492422	−	0.0867211i
$325$	−782.738			−2.40843
$326$	−38.9282	+	106.954i	−0.119412	+	0.328081i
$327$	−77.9066	−	591.520i	−0.238246	−	1.80893i
$328$	17.9043	+	15.0235i	0.0545863	+	0.0458033i
$329$	−383.146	−	67.5591i	−1.16458	−	0.205347i
$330$	257.907	+	57.1625i	0.781536	+	0.173220i
$331$	208.107	−	174.623i	0.628723	−	0.527561i	−0.271809	−	0.962351i	$-0.587622\pi$
$331$	208.107	−	174.623i	0.628723	−	0.527561i	0.900532	+	0.434790i	$0.143177\pi$
$332$	−182.700	+	105.482i	−0.550301	+	0.317716i
$333$	−27.8971	+	104.157i	−0.0837752	+	0.312784i
$334$	76.5582	−	132.603i	0.229216	−	0.397014i
$335$	−377.650	+	66.5898i	−1.12731	+	0.198776i
$336$	37.0989	−	58.2403i	0.110413	−	0.173334i
$337$	−482.379	+	175.572i	−1.43139	+	0.520984i	−0.937330	−	0.348443i	$-0.886710\pi$
$337$	−482.379	+	175.572i	−1.43139	+	0.520984i	−0.494061	+	0.869427i	$0.664488\pi$
$338$	184.494	+	506.894i	0.545841	+	1.49969i
$339$	−0.685818	+	15.7267i	−0.00202306	+	0.0463914i
$340$	−19.5867	−	111.082i	−0.0576079	−	0.326711i
$341$	112.965	+	65.2201i	0.331274	+	0.191261i
$342$	−179.974	+	83.9460i	−0.526239	+	0.245456i
$343$	186.693	+	323.361i	0.544293	+	0.942743i
$344$	−81.9639	−	97.6808i	−0.238267	−	0.283956i
$345$	525.136	+	481.148i	1.52213	+	1.39463i
$346$	−20.7912	+	117.913i	−0.0600902	+	0.340789i
$347$	−115.155	+	137.237i	−0.331859	+	0.395494i	−0.906011	−	0.423255i	$-0.860888\pi$
$347$	−115.155	+	137.237i	−0.331859	+	0.395494i	0.574152	+	0.818749i	$0.305332\pi$
$348$	−103.442	−	134.793i	−0.297247	−	0.387338i
$349$	324.668	+	118.170i	0.930281	+	0.338595i	0.762321	−	0.647199i	$-0.224060\pi$
$349$	324.668	+	118.170i	0.930281	+	0.338595i	0.167960	+	0.985794i	$0.446282\pi$
$350$			271.506i			0.775730i
$351$	−428.029	−	466.964i	−1.21946	−	1.33038i
$352$	−46.1048			−0.130980
$353$	84.0412	−	230.901i	0.238077	−	0.654112i	−0.761902	−	0.647692i	$-0.775734\pi$
$353$	84.0412	−	230.901i	0.238077	−	0.654112i	0.999979	−	0.00641959i	$-0.00204343\pi$
$354$	228.304	+	94.5524i	0.644925	+	0.267097i
$355$	239.464	+	200.934i	0.674547	+	0.566012i
$356$	0.687299	+	0.121189i	0.00193062	+	0.000340420i
$357$	−38.3289	−	121.542i	−0.107364	−	0.340452i
$358$	181.751	−	152.507i	0.507684	−	0.425998i
$359$	−481.215	+	277.830i	−1.34043	+	0.773899i	−0.986871	−	0.161512i	$-0.948363\pi$
$359$	−481.215	+	277.830i	−1.34043	+	0.773899i	−0.353562	+	0.935411i	$0.615030\pi$
$360$	−159.290	+	111.561i	−0.442473	+	0.309892i
$361$	58.7794	−	101.809i	0.162824	−	0.282019i
$362$	−403.146	+	71.0856i	−1.11366	+	0.196369i
$363$	75.6049	+	145.217i	0.208278	+	0.400047i
$364$	253.727	−	92.3490i	0.697052	−	0.253706i
$365$	−260.082	−	714.571i	−0.712555	−	1.95773i
$366$	268.518	−	139.799i	0.733655	−	0.381965i
$367$	69.2101	+	392.510i	0.188583	+	1.06951i	0.921264	+	0.388937i	$0.127158\pi$
$367$	69.2101	+	392.510i	0.188583	+	1.06951i	−0.732681	+	0.680572i	$0.761731\pi$
$368$	−107.652	−	62.1527i	−0.292532	−	0.168893i
$369$	−42.6636	−	60.9163i	−0.115619	−	0.165085i
$370$	64.7209	+	112.100i	0.174921	+	0.302972i
$371$	60.7038	+	72.3439i	0.163622	+	0.194997i
$372$	−91.5806	+	28.8805i	−0.246184	+	0.0776358i
$373$	71.1393	−	403.451i	0.190722	−	1.08164i	−0.727659	−	0.685939i	$-0.759392\pi$
$373$	71.1393	−	403.451i	0.190722	−	1.08164i	0.918381	−	0.395698i	$-0.129497\pi$
$374$	−54.6948	+	65.1828i	−0.146243	+	0.174285i
$375$	73.3392	−	177.083i	0.195571	−	0.472220i
$376$	−179.699	−	65.4050i	−0.477922	−	0.173950i
$377$		−	664.385i		−	1.76230i
$378$	−161.974	+	148.469i	−0.428503	+	0.392775i
$379$	−61.5139			−0.162306			−0.0811529	−	0.996702i	$-0.525860\pi$
$379$	−61.5139			−0.162306			−0.0811529	+	0.996702i	$0.525860\pi$
$380$	−81.5356	+	224.017i	−0.214567	+	0.589519i
$381$	−105.761	+	81.1623i	−0.277589	+	0.213025i
$382$	−43.6999	−	36.6686i	−0.114398	−	0.0959910i
$383$	200.252	+	35.3098i	0.522851	+	0.0921927i	0.428844	−	0.903379i	$-0.358921\pi$
$383$	200.252	+	35.3098i	0.522851	+	0.0921927i	0.0940074	+	0.995572i	$0.470032\pi$
$384$	22.9290	−	25.0252i	0.0597109	−	0.0651698i
$385$	274.469	−	230.307i	0.712906	−	0.598199i
$386$	297.029	−	171.490i	0.769506	−	0.444275i
$387$	171.514	+	367.712i	0.443188	+	0.950159i
$388$	63.9662	−	110.793i	0.164861	−	0.285548i
$389$	−251.130	+	44.2810i	−0.645579	+	0.113833i	−0.486845	−	0.873488i	$-0.661852\pi$
$389$	−251.130	+	44.2810i	−0.645579	+	0.113833i	−0.158734	+	0.987321i	$0.550741\pi$
$390$	−759.703	−	33.1296i	−1.94796	−	0.0849476i
$391$	−215.580	+	78.4647i	−0.551355	+	0.200677i
$392$	15.3688	+	42.2254i	0.0392061	+	0.107718i
$393$	−101.666	−	64.7612i	−0.258693	−	0.164787i
$394$	−1.33966	−	7.59757i	−0.00340014	−	0.0192832i
$395$	−509.787	−	294.326i	−1.29060	−	0.745128i
$396$	141.710	+	37.9552i	0.357853	+	0.0958463i
$397$	13.8139	+	23.9264i	0.0347957	+	0.0602679i	0.882899	−	0.469563i	$-0.155589\pi$
$397$	13.8139	+	23.9264i	0.0347957	+	0.0602679i	−0.848103	+	0.529831i	$0.822255\pi$
$398$	130.006	+	154.935i	0.326648	+	0.389284i
$399$	−58.2843	+	262.968i	−0.146076	+	0.659069i
$400$	−23.1737	+	131.425i	−0.0579342	+	0.328561i
$401$	−240.702	+	286.857i	−0.600254	+	0.715354i	−0.977542	−	0.210741i	$-0.932412\pi$
$401$	−240.702	+	286.857i	−0.600254	+	0.715354i	0.377288	+	0.926096i	$0.376857\pi$
$402$	−211.140	+	27.8083i	−0.525224	+	0.0691750i
$403$	−352.840	−	128.423i	−0.875533	−	0.318668i
$404$		−	333.449i		−	0.825370i
$405$	581.442	−	211.765i	1.43566	−	0.522878i
$406$	−230.453			−0.567618
$407$	33.3975	−	91.7588i	0.0820577	−	0.225452i
$408$	−8.17954	−	62.1046i	−0.0200479	−	0.152217i
$409$	156.992	+	131.732i	0.383843	+	0.322082i	0.814209	−	0.580572i	$-0.197171\pi$
$409$	156.992	+	131.732i	0.383843	+	0.322082i	−0.430366	+	0.902654i	$0.641616\pi$
$410$	−87.9212	−	15.5029i	−0.214442	−	0.0378119i
$411$	−150.948	−	33.4560i	−0.367269	−	0.0814015i
$412$	154.144	−	129.342i	0.374136	−	0.313937i
$413$	290.256	−	167.579i	0.702799	−	0.405761i
$414$	279.717	+	279.658i	0.675644	+	0.675503i
$415$	402.918	−	697.874i	0.970886	−	1.68162i
$416$	130.701	−	23.0461i	0.314184	−	0.0553992i
$417$	−173.505	+	272.380i	−0.416080	+	0.653191i
$418$	168.993	−	61.5085i	0.404290	−	0.147150i
$419$	81.7427	+	224.586i	0.195090	+	0.536005i	0.998210	−	0.0598126i	$-0.0190503\pi$
$419$	81.7427	+	224.586i	0.195090	+	0.536005i	−0.803120	+	0.595818i	$0.796828\pi$
$420$	−11.4915	+	263.516i	−0.0273608	+	0.627418i
$421$	34.6408	+	196.458i	0.0822821	+	0.466645i	0.997910	+	0.0646183i	$0.0205830\pi$
$421$	34.6408	+	196.458i	0.0822821	+	0.466645i	−0.915628	+	0.402027i	$0.868306\pi$
$422$	−10.5791	−	6.10786i	−0.0250690	−	0.0144736i
$423$	498.486	+	348.966i	1.17845	+	0.824979i
$424$	23.2094	+	40.1999i	0.0547392	+	0.0948111i
$425$	158.316	+	188.674i	0.372508	+	0.443938i
$426$	127.999	+	117.277i	0.300467	+	0.275298i
$427$	71.2998	−	404.362i	0.166979	−	0.946983i
$428$	−8.45659	+	10.0782i	−0.0197584	+	0.0235471i
$429$	349.238	+	455.086i	0.814074	+	1.06081i
$430$	457.699	+	166.589i	1.06442	+	0.387416i
$431$		−	235.094i		−	0.545461i	−0.962090	−	0.272731i	$-0.912073\pi$
$431$		−	235.094i		−	0.545461i	0.962090	−	0.272731i	$-0.0879267\pi$
$432$	−91.0772	+	58.0427i	−0.210827	+	0.134358i
$433$	−391.650			−0.904504			−0.452252	−	0.891890i	$-0.649379\pi$
$433$	−391.650			−0.904504			−0.452252	+	0.891890i	$0.649379\pi$
$434$	−44.5457	+	122.388i	−0.102640	+	0.282001i
$435$	599.630	+	248.338i	1.37846	+	0.570892i
$436$	−304.696	−	255.670i	−0.698844	−	0.586400i
$437$	477.506	+	84.1972i	1.09269	+	0.192671i
$438$	−127.011	−	402.753i	−0.289979	−	0.919528i
$439$	62.2561	−	52.2391i	0.141813	−	0.118996i	−0.569121	−	0.822254i	$-0.692717\pi$
$439$	62.2561	−	52.2391i	0.141813	−	0.118996i	0.710935	+	0.703258i	$0.248272\pi$
$440$	152.516	−	88.0553i	0.346628	−	0.200126i
$441$	−12.4767	−	142.438i	−0.0282919	−	0.322989i
$442$	122.470	−	212.124i	0.277081	−	0.479918i
$443$	519.689	−	91.6352i	1.17311	−	0.206851i	0.447069	−	0.894500i	$-0.352468\pi$
$443$	519.689	−	91.6352i	1.17311	−	0.206851i	0.726044	+	0.687648i	$0.241357\pi$
$444$	33.1964	+	63.7615i	0.0747667	+	0.143607i
$445$	−2.50506	+	0.911769i	−0.00562936	+	0.00204892i
$446$	−148.401	−	407.728i	−0.332737	−	0.914188i
$447$	−375.464	+	195.479i	−0.839965	+	0.437314i
$448$	−7.99391	−	45.3357i	−0.0178435	−	0.101196i
$449$	−104.119	−	60.1132i	−0.231891	−	0.133882i	0.379553	−	0.925170i	$-0.376078\pi$
$449$	−104.119	−	60.1132i	−0.231891	−	0.133882i	−0.611444	+	0.791288i	$0.709411\pi$
$450$	179.421	−	384.875i	0.398713	−	0.855277i
$451$	33.6744	+	58.3258i	0.0746661	+	0.129326i
$452$	6.74568	+	8.03919i	0.0149241	+	0.0177858i
$453$	−375.325	+	118.361i	−0.828533	+	0.261283i
$454$	−2.92190	+	16.5709i	−0.00643590	+	0.0364998i
$455$	−662.959	+	790.084i	−1.45705	+	1.73645i
$456$	−50.6580	+	122.317i	−0.111092	+	0.268240i
$457$	134.507	+	48.9566i	0.294326	+	0.107126i	0.484963	−	0.874535i	$-0.338833\pi$
$457$	134.507	+	48.9566i	0.294326	+	0.107126i	−0.190637	+	0.981661i	$0.561055\pi$
$458$			544.989i			1.18993i
$459$	−25.9858	+	197.621i	−0.0566139	+	0.430547i
$460$	474.820			1.03222
$461$	−80.7643	+	221.898i	−0.175194	+	0.481341i	−0.995947	−	0.0899422i	$-0.971332\pi$
$461$	−80.7643	+	221.898i	−0.175194	+	0.481341i	0.820753	+	0.571283i	$0.193554\pi$
$462$	157.854	−	121.139i	0.341676	−	0.262205i
$463$	113.622	+	95.3405i	0.245405	+	0.205919i	0.757191	−	0.653194i	$-0.226571\pi$
$463$	113.622	+	95.3405i	0.245405	+	0.205919i	−0.511786	+	0.859113i	$0.671016\pi$
$464$	−111.553	−	19.6697i	−0.240415	−	0.0423917i
$465$	247.793	−	270.447i	0.532888	−	0.581606i
$466$	10.4073	−	8.73272i	0.0223332	−	0.0187397i
$467$	−78.1166	+	45.1006i	−0.167273	+	0.0965752i	−0.581299	−	0.813690i	$-0.697456\pi$
$467$	−78.1166	+	45.1006i	−0.167273	+	0.0965752i	0.414026	+	0.910265i	$0.364122\pi$
$468$	−420.700	−	36.7621i	−0.898931	−	0.0785515i
$469$	−144.423	+	250.149i	−0.307939	+	0.533366i
$470$	719.366	−	126.844i	1.53056	−	0.269880i
$471$	−577.767	−	25.1956i	−1.22668	−	0.0534938i
$472$	154.804	−	56.3441i	0.327975	−	0.119373i
$473$	−125.671	−	345.277i	−0.265688	−	0.729973i
$474$	−275.721	−	175.633i	−0.581689	−	0.370534i
$475$	−90.3924	−	512.641i	−0.190300	−	1.07924i
$476$	−73.5786	−	42.4806i	−0.154577	−	0.0892451i
$477$	−38.2435	−	142.667i	−0.0801750	−	0.299092i
$478$	−72.8014	−	126.096i	−0.152304	−	0.263799i
$479$	−165.915	−	197.730i	−0.346378	−	0.412797i	0.564526	−	0.825415i	$-0.309059\pi$
$479$	−165.915	−	197.730i	−0.346378	−	0.412797i	−0.910904	+	0.412618i	$0.864614\pi$
$480$	−28.0543	+	126.576i	−0.0584464	+	0.263700i
$481$	−48.8104	+	276.818i	−0.101477	+	0.575504i
$482$	96.7883	−	115.348i	0.200806	−	0.239311i
$483$	531.883	−	70.0520i	1.10121	−	0.145035i
$484$	102.564	+	37.3303i	0.211909	+	0.0771287i
$485$			488.674i			1.00758i
$486$	327.722	−	103.424i	0.674324	−	0.212807i
$487$	−103.107			−0.211718			−0.105859	−	0.994381i	$-0.533759\pi$
$487$	−103.107			−0.211718			−0.105859	+	0.994381i	$0.533759\pi$
$488$	69.0265	−	189.649i	0.141448	−	0.388625i
$489$	−31.5275	−	239.378i	−0.0644734	−	0.489526i
$490$	−131.486	−	110.330i	−0.268340	−	0.225164i
$491$	−753.133	−	132.798i	−1.53388	−	0.270464i	−0.658007	−	0.753012i	$-0.728600\pi$
$491$	−753.133	−	132.798i	−1.53388	−	0.270464i	−0.875870	+	0.482548i	$0.839711\pi$
$492$	−48.4057	−	10.7286i	−0.0983855	−	0.0218061i
$493$	−160.145	+	134.378i	−0.324839	+	0.272572i
$494$	−448.326	+	258.841i	−0.907543	+	0.523970i
$495$	−541.271	+	145.094i	−1.09348	+	0.293119i
$496$	−32.0088	+	55.4409i	−0.0645340	+	0.111776i
$497$	231.883	−	40.8872i	0.466565	−	0.0822679i
$498$	240.433	−	377.448i	0.482798	−	0.757928i
$499$	675.618	−	245.905i	1.35394	−	0.492795i	0.439767	−	0.898112i	$-0.355061\pi$
$499$	675.618	−	245.905i	1.35394	−	0.492795i	0.914176	+	0.405317i	$0.132839\pi$
$500$	−43.7030	−	120.073i	−0.0874061	−	0.240146i
$501$	−14.1510	+	324.501i	−0.0282455	+	0.647706i
$502$	20.0391	+	113.648i	0.0399186	+	0.226390i
$503$	506.649	+	292.514i	1.00725	+	0.581538i	0.910386	−	0.413759i	$-0.135784\pi$
$503$	506.649	+	292.514i	1.00725	+	0.581538i	0.0968675	+	0.995297i	$0.469118\pi$
$504$	−12.7515	+	145.927i	−0.0253007	+	0.289537i
$505$	636.852	+	1103.06i	1.26109	+	2.18428i
$506$	−230.242	−	274.392i	−0.455024	−	0.542276i
$507$	−843.703	−	773.030i	−1.66411	−	1.52471i
$508$	−15.4332	+	87.5262i	−0.0303804	+	0.172296i
$509$	567.862	−	676.751i	1.11564	−	1.32957i	0.177184	−	0.984178i	$-0.443301\pi$
$509$	567.862	−	676.751i	1.11564	−	1.32957i	0.938458	−	0.345393i	$-0.112254\pi$
$510$	145.671	+	189.822i	0.285630	+	0.372200i
$511$	−538.239	−	195.903i	−1.05331	−	0.383372i
$512$		−	22.6274i		−	0.0441942i
$513$	256.401	−	334.256i	0.499806	−	0.651572i
$514$	−621.255			−1.20867
$515$	−262.884	+	722.266i	−0.510453	+	1.40246i
$516$	249.912	+	103.501i	0.484325	+	0.200584i
$517$	−422.124	−	354.204i	−0.816487	−	0.685114i
$518$	96.0187	+	16.9307i	0.185364	+	0.0326847i
$519$	−76.3888	−	242.230i	−0.147185	−	0.466725i
$520$	−388.346	+	325.861i	−0.746820	+	0.626656i
$521$	22.5511	−	13.0199i	0.0432843	−	0.0249902i	−0.478202	−	0.878250i	$-0.658711\pi$
$521$	22.5511	−	13.0199i	0.0432843	−	0.0249902i	0.521486	+	0.853260i	$0.325378\pi$
$522$	326.680	+	152.292i	0.625824	+	0.291747i
$523$	−289.411	+	501.274i	−0.553366	+	0.958458i	0.444662	+	0.895698i	$0.353324\pi$
$523$	−289.411	+	501.274i	−0.553366	+	0.958458i	−0.998029	+	0.0627602i	$0.980010\pi$
$524$	−79.1396	+	13.9545i	−0.151030	+	0.0266306i
$525$	−265.971	−	510.860i	−0.506611	−	0.973067i
$526$	−599.227	+	218.101i	−1.13922	+	0.414641i
$527$	40.4095	+	111.024i	0.0766784	+	0.210672i
$528$	86.7501	−	45.1650i	0.164299	−	0.0855398i
$529$	−75.8392	−	430.106i	−0.143363	−	0.813054i
$530$	−153.555	−	88.6550i	−0.289726	−	0.167274i
$531$	−522.197	+	45.7414i	−0.983422	+	0.0861419i
$532$	89.7834	+	155.509i	0.168766	+	0.292311i
$533$	−124.617	−	148.513i	−0.233803	−	0.278636i
$534$	−1.41193	+	0.445261i	−0.00264406	+	0.000833822i
$535$	8.72643	−	49.4901i	0.0163111	−	0.0925048i
$536$	−91.2602	+	108.760i	−0.170262	+	0.202910i
$537$	−192.581	+	465.001i	−0.358624	+	0.865923i
$538$	−483.152	−	175.853i	−0.898053	−	0.326864i
$539$			129.484i			0.240229i
$540$	190.431	−	365.954i	0.352650	−	0.677693i
$541$	−84.9565			−0.157036			−0.0785180	−	0.996913i	$-0.525019\pi$
$541$	−84.9565			−0.157036			−0.0785180	+	0.996913i	$0.525019\pi$
$542$	34.1801	−	93.9092i	0.0630630	−	0.173264i
$543$	688.917	−	528.682i	1.26872	−	0.973631i
$544$	−31.9905	−	26.8432i	−0.0588061	−	0.0493442i
$545$	1496.25	+	263.828i	2.74540	+	0.484089i
$546$	−386.942	+	422.317i	−0.708684	+	0.773474i
$547$	−662.004	+	555.487i	−1.21025	+	1.01552i	−0.210968	+	0.977493i	$0.567662\pi$
$547$	−662.004	+	555.487i	−1.21025	+	1.01552i	−0.999277	+	0.0380234i	$0.987894\pi$
$548$	−89.2646	+	51.5369i	−0.162892	+	0.0940455i
$549$	−368.289	+	526.088i	−0.670836	+	0.958266i
$550$	−192.274	+	333.029i	−0.349590	+	0.605507i
$551$	435.128	−	76.7248i	0.789706	−	0.139246i
$552$	263.441	+	11.4883i	0.477249	+	0.0208121i
$553$	−416.652	+	151.649i	−0.753440	+	0.274230i
$554$	−112.942	−	310.305i	−0.203866	−	0.560117i
$555$	−231.592	−	147.524i	−0.417283	−	0.265808i
$556$	37.3862	+	212.028i	0.0672414	+	0.381345i
$557$	−226.376	−	130.698i	−0.406420	−	0.234647i	0.282830	−	0.959170i	$-0.408727\pi$
$557$	−226.376	−	130.698i	−0.406420	−	0.234647i	−0.689250	+	0.724523i	$0.742060\pi$
$558$	144.025	−	144.055i	0.258109	−	0.258163i
$559$	528.849	+	915.994i	0.946063	+	1.63863i
$560$	113.030	+	134.704i	0.201840	+	0.240543i
$561$	39.0588	−	176.227i	0.0696236	−	0.314130i
$562$	71.0493	−	402.940i	0.126422	−	0.716976i
$563$	505.895	−	602.902i	0.898570	−	1.07087i	−0.0985575	−	0.995131i	$-0.531423\pi$
$563$	505.895	−	602.902i	0.898570	−	1.07087i	0.997127	−	0.0757425i	$-0.0241327\pi$
$564$	402.190	−	52.9707i	0.713103	−	0.0939197i
$565$	−37.6689	−	13.7104i	−0.0666706	−	0.0242661i
$566$		−	216.944i		−	0.383294i
$567$	159.326	−	438.029i	0.280998	−	0.772538i
$568$	115.735			0.203758
$569$	90.4364	−	248.472i	0.158939	−	0.436682i	−0.834505	−	0.551001i	$-0.814246\pi$
$569$	90.4364	−	248.472i	0.158939	−	0.436682i	0.993444	+	0.114319i	$0.0364684\pi$
$570$	−66.0347	−	501.381i	−0.115850	−	0.879615i
$571$	−48.7960	−	40.9447i	−0.0854572	−	0.0717071i	0.599058	−	0.800705i	$-0.295542\pi$
$571$	−48.7960	−	40.9447i	−0.0854572	−	0.0717071i	−0.684515	+	0.728998i	$0.739986\pi$
$572$	376.621	+	66.4085i	0.658429	+	0.116099i
$573$	118.146	+	26.1859i	0.206189	+	0.0456996i
$574$	−51.5141	+	43.2255i	−0.0897459	+	0.0753057i
$575$	−897.896	+	518.400i	−1.56156	+	0.901566i
$576$	−18.6277	+	69.5486i	−0.0323397	+	0.120744i
$577$	485.361	−	840.670i	0.841180	−	1.45697i	−0.0477175	−	0.998861i	$-0.515195\pi$
$577$	485.361	−	840.670i	0.841180	−	1.45697i	0.888898	−	0.458106i	$-0.151472\pi$
$578$	326.597	−	57.5879i	0.565047	−	0.0996330i
$579$	−390.891	+	613.647i	−0.675114	+	1.05984i
$580$	406.587	−	147.985i	0.701011	−	0.255147i
$581$	−207.600	−	570.377i	−0.357316	−	0.981717i
$582$	−11.8235	+	271.128i	−0.0203153	+	0.465856i
$583$	23.2269	+	131.726i	0.0398403	+	0.225946i
$584$	−243.818	−	140.769i	−0.417497	−	0.241042i
$585$	1461.90	−	681.881i	2.49897	−	1.16561i
$586$	115.490	+	200.035i	0.197083	+	0.341357i
$587$	65.3472	+	77.8778i	0.111324	+	0.132671i	0.818829	−	0.574038i	$-0.194624\pi$
$587$	65.3472	+	77.8778i	0.111324	+	0.132671i	−0.707505	+	0.706708i	$0.750179\pi$
$588$	−70.2824	−	64.3952i	−0.119528	−	0.109516i
$589$	43.3618	−	245.917i	0.0736193	−	0.417516i
$590$	−404.485	+	482.047i	−0.685568	+	0.817029i
$591$	9.96337	+	12.9831i	0.0168585	+	0.0219680i
$592$	45.0336	+	16.3909i	0.0760702	+	0.0276873i
$593$			926.755i			1.56282i	0.624016	+	0.781412i	$0.285500\pi$
$593$			926.755i			1.56282i	−0.624016	+	0.781412i	$0.714500\pi$
$594$	−303.820	+	67.4054i	−0.511482	+	0.113477i
$595$	324.534			0.545435
$596$	−96.5188	+	265.183i	−0.161944	+	0.444938i
$597$	−396.393	−	164.167i	−0.663976	−	0.274987i
$598$	789.861	+	662.772i	1.32084	+	1.10831i
$599$	−553.736	−	97.6386i	−0.924434	−	0.163003i	−0.308883	−	0.951100i	$-0.599955\pi$
$599$	−553.736	−	97.6386i	−0.924434	−	0.163003i	−0.615551	+	0.788097i	$0.711066\pi$
$600$	−85.1422	−	269.987i	−0.141904	−	0.449979i
$601$	291.320	−	244.447i	0.484726	−	0.406733i	−0.367406	−	0.930061i	$-0.619754\pi$
$601$	291.320	−	244.447i	0.484726	−	0.406733i	0.852132	+	0.523327i	$0.175310\pi$
$602$	317.728	−	183.440i	0.527787	−	0.304718i
$603$	370.036	−	259.160i	0.613658	−	0.429784i
$604$	−131.182	+	227.214i	−0.217189	+	0.376182i
$605$	−410.582	+	72.3967i	−0.678648	+	0.119664i
$606$	326.652	+	627.413i	0.539030	+	1.03533i
$607$	1056.66	−	384.593i	1.74079	−	0.633597i	0.741492	−	0.670962i	$-0.234119\pi$
$607$	1056.66	−	384.593i	1.74079	−	0.633597i	0.999302	+	0.0373651i	$0.0118965\pi$
$608$	30.1873	+	82.9388i	0.0496501	+	0.136413i
$609$	433.616	−	225.755i	0.712014	−	0.370698i
$610$	133.867	+	759.197i	0.219454	+	1.24459i
$611$	1373.72	+	793.115i	2.24831	+	1.29806i
$612$	76.2291	+	108.842i	0.124557	+	0.177847i
$613$	−313.409	−	542.840i	−0.511270	−	0.885546i	−0.999915	−	0.0130631i	$-0.995842\pi$
$613$	−313.409	−	542.840i	−0.511270	−	0.885546i	0.488644	−	0.872483i	$-0.337492\pi$
$614$	296.936	+	353.875i	0.483609	+	0.576343i
$615$	180.618	−	56.9590i	0.293688	−	0.0926163i
$616$	23.0349	−	130.637i	0.0373943	−	0.212073i
$617$	113.319	−	135.049i	0.183662	−	0.218880i	−0.666356	−	0.745634i	$-0.732147\pi$
$617$	113.319	−	135.049i	0.183662	−	0.218880i	0.850018	+	0.526754i	$0.176591\pi$
$618$	−163.329	+	394.370i	−0.264287	+	0.638139i
$619$	−873.825	−	318.046i	−1.41167	−	0.513807i	−0.480052	−	0.877240i	$-0.659382\pi$
$619$	−873.825	−	318.046i	−1.41167	−	0.513807i	−0.931620	+	0.363434i	$0.881604\pi$
$620$		−	244.534i		−	0.394409i
$621$	−800.267	−	252.185i	−1.28868	−	0.406095i
$622$	−658.391			−1.05851
$623$	−0.686776	+	1.88690i	−0.00110237	+	0.00302873i
$624$	−223.348	+	171.400i	−0.357930	+	0.274679i
$625$	−265.041	−	222.395i	−0.424065	−	0.355833i
$626$	−305.439	−	53.8571i	−0.487921	−	0.0860337i
$627$	−257.720	+	281.282i	−0.411037	+	0.448615i
$628$	−295.344	+	247.823i	−0.470293	+	0.394623i
$629$	76.5973	−	44.2235i	0.121776	−	0.0703076i
$630$	−236.522	−	507.084i	−0.375431	−	0.804895i
$631$	327.053	−	566.473i	0.518309	−	0.897738i	−0.481464	−	0.876466i	$-0.659895\pi$
$631$	327.053	−	566.473i	0.518309	−	0.897738i	0.999774	−	0.0212724i	$-0.00677172\pi$
$632$	−214.628	+	37.8446i	−0.339601	+	0.0598808i
$633$	25.8889	+	1.12898i	0.0408987	+	0.00178353i
$634$	169.282	−	61.6136i	0.267006	−	0.0971824i
$635$	−116.112	−	319.015i	−0.182854	−	0.502386i
$636$	−83.0509	−	52.9031i	−0.130583	−	0.0831810i
$637$	−64.7240	−	367.068i	−0.101608	−	0.576245i
$638$	−282.674	−	163.202i	−0.443063	−	0.255802i
$639$	−355.727	−	95.2768i	−0.556693	−	0.149103i
$640$	43.2159	+	74.8522i	0.0675249	+	0.116957i
$641$	473.126	+	563.850i	0.738106	+	0.879641i	0.996255	−	0.0864644i	$-0.0275569\pi$
$641$	473.126	+	563.850i	0.738106	+	0.879641i	−0.258149	+	0.966105i	$0.583112\pi$
$642$	6.03905	−	27.2471i	0.00940661	−	0.0424410i
$643$	−123.683	+	701.440i	−0.192353	+	1.09089i	0.723786	+	0.690025i	$0.242400\pi$
$643$	−123.683	+	701.440i	−0.192353	+	1.09089i	−0.916139	+	0.400862i	$0.868711\pi$
$644$	229.893	−	273.976i	0.356977	−	0.425429i
$645$	−1024.39	+	134.918i	−1.58820	+	0.209176i
$646$	153.070	+	55.7129i	0.236950	+	0.0862429i
$647$			291.136i			0.449978i	0.974361	+	0.224989i	$0.0722346\pi$
$647$			291.136i			0.449978i	−0.974361	+	0.224989i	$0.927765\pi$
$648$	114.510	−	198.433i	0.176713	−	0.306223i
$649$	474.704			0.731440
$650$	378.602	−	1040.20i	0.582465	−	1.60031i
$651$	−36.0770	−	273.921i	−0.0554178	−	0.420770i
$652$	−123.305	−	103.465i	−0.189119	−	0.158689i
$653$	−1145.26	−	201.940i	−1.75384	−	0.309250i	−0.797898	−	0.602792i	$-0.794055\pi$
$653$	−1145.26	−	201.940i	−1.75384	−	0.309250i	−0.955946	+	0.293542i	$0.905166\pi$
$654$	823.769	+	182.580i	1.25959	+	0.279174i
$655$	235.145	−	197.310i	0.359000	−	0.301236i
$656$	−28.6252	+	16.5268i	−0.0436360	+	0.0251933i
$657$	633.525	+	633.392i	0.964269	+	0.964067i
$658$	275.105	−	476.496i	0.418093	−	0.724158i
$659$	521.251	−	91.9106i	0.790972	−	0.139470i	0.236455	−	0.971642i	$-0.424014\pi$
$659$	521.251	−	91.9106i	0.790972	−	0.139470i	0.554517	+	0.832173i	$0.312903\pi$
$660$	−200.712	+	315.090i	−0.304108	+	0.477410i
$661$	−3.61822	+	1.31693i	−0.00547386	+	0.00199232i	−0.344756	−	0.938692i	$-0.612038\pi$
$661$	−3.61822	+	1.31693i	−0.00547386	+	0.00199232i	0.339282	+	0.940685i	$0.389816\pi$
$662$	131.401	+	361.022i	0.198492	+	0.545351i
$663$	−22.6373	+	519.102i	−0.0341437	+	0.782959i
$664$	−51.8075	−	293.815i	−0.0780234	−	0.442493i
$665$	−594.012	−	342.953i	−0.893251	−	0.515719i
$666$	−124.924	−	87.4529i	−0.187573	−	0.131311i
$667$	−440.016	−	762.131i	−0.659695	−	1.14262i
$668$	139.189	+	165.879i	0.208366	+	0.248322i
$669$	678.645	+	621.798i	1.01442	+	0.929444i
$670$	94.1722	−	534.077i	0.140556	−	0.797130i
$671$	373.817	−	445.497i	0.557104	−	0.663930i
$672$	59.4527	+	77.4719i	0.0884713	+	0.115286i
$673$	389.797	+	141.874i	0.579193	+	0.210809i	0.614970	−	0.788551i	$-0.289168\pi$
$673$	389.797	+	141.874i	0.579193	+	0.210809i	−0.0357768	+	0.999360i	$0.511391\pi$
$674$		−	725.968i		−	1.07710i
$675$	39.4336	+	899.937i	0.0584201	+	1.33324i
$676$	−762.863			−1.12850
$677$	−406.146	+	1115.88i	−0.599921	+	1.64827i	0.151509	+	0.988456i	$0.451587\pi$
$677$	−406.146	+	1115.88i	−0.599921	+	1.64827i	−0.751430	+	0.659813i	$0.770636\pi$
$678$	−20.5679	−	8.51823i	−0.0303361	−	0.0125638i
$679$	281.970	+	236.601i	0.415273	+	0.348455i
$680$	157.093	+	27.6998i	0.231019	+	0.0407350i
$681$	−10.7353	−	34.0419i	−0.0157640	−	0.0499881i
$682$	−141.312	+	118.575i	−0.207203	+	0.173864i
$683$	444.994	−	256.917i	0.651528	−	0.376160i	−0.137513	−	0.990500i	$-0.543911\pi$
$683$	444.994	−	256.917i	0.651528	−	0.376160i	0.789041	+	0.614340i	$0.210578\pi$
$684$	−24.5067	−	279.776i	−0.0358285	−	0.409029i
$685$	196.860	−	340.971i	0.287387	−	0.497768i
$686$	−520.024	+	91.6943i	−0.758053	+	0.133665i
$687$	−533.880	−	1025.44i	−0.777117	−	1.49264i
$688$	169.456	−	61.6768i	0.246302	−	0.0896466i
$689$	−131.690	−	361.815i	−0.191132	−	0.525131i
$690$	−893.413	+	465.141i	−1.29480	+	0.674117i
$691$	91.9225	+	521.318i	0.133028	+	0.754440i	0.976213	+	0.216816i	$0.0695671\pi$
$691$	91.9225	+	521.318i	0.133028	+	0.754440i	−0.843184	+	0.537625i	$0.819322\pi$
$692$	−146.641	−	84.6632i	−0.211909	−	0.122346i
$693$	−178.346	+	382.569i	−0.257354	+	0.552048i
$694$	−126.678	−	219.413i	−0.182533	−	0.316156i
$695$	−528.625	−	629.990i	−0.760611	−	0.906461i
$696$	229.164	−	72.2684i	0.329259	−	0.103834i
$697$	−10.5930	+	60.0762i	−0.0151981	+	0.0861925i
$698$	−314.077	+	374.303i	−0.449967	+	0.536250i
$699$	−11.0274	+	26.6264i	−0.0157760	+	0.0380922i
$700$	−360.811	−	131.324i	−0.515444	−	0.187606i
$701$			13.0718i			0.0186474i	0.999957	+	0.00932369i	$0.00296787\pi$
$701$			13.0718i			0.0186474i	−0.999957	+	0.00932369i	$0.997032\pi$
$702$	827.594	−	342.953i	1.17891	−	0.488537i
$703$	−186.934			−0.265908
$704$	22.3004	−	61.2699i	0.0316768	−	0.0870312i
$705$	−1229.29	+	943.368i	−1.74367	+	1.33811i
$706$	266.201	+	223.369i	0.377055	+	0.316387i
$707$	944.823	+	166.598i	1.33638	+	0.235640i
$708$	−236.081	+	257.664i	−0.333448	+	0.363933i
$709$	−584.480	+	490.437i	−0.824372	+	0.691730i	−0.953992	−	0.299834i	$-0.903069\pi$
$709$	−584.480	+	490.437i	−0.824372	+	0.691730i	0.129620	+	0.991564i	$0.458624\pi$
$710$	−382.853	+	221.040i	−0.539230	+	0.311325i
$711$	690.844	+	60.3682i	0.971651	+	0.0849060i
$712$	−0.493491	+	0.854752i	−0.000693105	+	0.00120049i
$713$	−489.803	+	86.3655i	−0.686961	+	0.121130i
$714$	180.059	+	7.85211i	0.252183	+	0.0109974i
$715$	−1372.71	+	499.624i	−1.91987	+	0.698775i
$716$	114.760	+	315.300i	0.160279	+	0.440363i
$717$	260.507	+	165.942i	0.363330	+	0.231440i
$718$	−136.456	−	773.883i	−0.190051	−	1.07783i
$719$	−782.468	−	451.758i	−1.08827	−	0.628315i	−0.155157	−	0.987890i	$-0.549588\pi$
$719$	−782.468	−	451.758i	−1.08827	−	0.628315i	−0.933116	+	0.359575i	$0.882922\pi$
$720$	−71.2093	−	265.646i	−0.0989019	−	0.368952i
$721$	289.476	+	501.386i	0.401492	+	0.695404i
$722$	106.866	+	127.357i	0.148013	+	0.176395i
$723$	−69.1188	+	311.852i	−0.0955999	+	0.431330i
$724$	100.530	−	570.135i	0.138854	−	0.787479i
$725$	−607.297	+	723.748i	−0.837650	+	0.998273i
$726$	−229.552	+	30.2333i	−0.316188	+	0.0416437i
$727$	906.427	+	329.912i	1.24680	+	0.453800i	0.879321	−	0.476230i	$-0.157997\pi$
$727$	906.427	+	329.912i	1.24680	+	0.453800i	0.367484	+	0.930030i	$0.380219\pi$
$728$			381.852i			0.524523i
$729$	−515.319	+	515.643i	−0.706885	+	0.707329i
$730$	1075.41			1.47317
$731$	113.829	−	312.744i	0.155717	−	0.427830i
$732$	55.9037	+	424.460i	0.0763712	+	0.579863i
$733$	421.118	+	353.360i	0.574513	+	0.482074i	0.883140	−	0.469109i	$-0.155425\pi$
$733$	421.118	+	353.360i	0.574513	+	0.482074i	−0.308627	+	0.951183i	$0.599869\pi$
$734$	−555.093	−	97.8778i	−0.756257	−	0.133349i
$735$	355.484	+	78.7894i	0.483652	+	0.107196i
$736$	134.666	−	112.999i	0.182971	−	0.153531i
$737$	−354.300	+	204.555i	−0.480733	+	0.277551i
$738$	101.589	−	27.2321i	0.137655	−	0.0368999i
$739$	−261.308	+	452.598i	−0.353596	+	0.612446i	−0.986877	−	0.161476i	$-0.948375\pi$
$739$	−261.308	+	452.598i	−0.353596	+	0.612446i	0.633281	+	0.773922i	$0.281708\pi$
$740$	−180.277	+	31.7877i	−0.243618	+	0.0429564i
$741$	589.998	−	926.219i	0.796219	−	1.24996i
$742$	−125.502	+	45.6788i	−0.169140	+	0.0615618i
$743$	−170.432	−	468.259i	−0.229384	−	0.630227i	0.770591	−	0.637330i	$-0.219961\pi$
$743$	−170.432	−	468.259i	−0.229384	−	0.630227i	−0.999975	+	0.00710282i	$0.997739\pi$
$744$	5.91650	−	135.673i	0.00795229	−	0.182356i
$745$	−187.184	−	1061.57i	−0.251254	−	1.42493i
$746$	501.747	+	289.684i	0.672583	+	0.388316i
$747$	−82.6412	+	945.733i	−0.110631	+	1.26604i
$748$	−60.1678	−	104.214i	−0.0804382	−	0.139323i
$749$	−24.3312	−	28.9968i	−0.0324850	−	0.0387141i
$750$	199.856	+	183.115i	0.266475	+	0.244154i
$751$	69.7868	−	395.781i	0.0929252	−	0.527005i	−0.902438	−	0.430819i	$-0.858225\pi$
$751$	69.7868	−	395.781i	0.0929252	−	0.527005i	0.995363	−	0.0961857i	$-0.0306643\pi$
$752$	173.837	−	207.171i	0.231166	−	0.275493i
$753$	−149.036	−	194.207i	−0.197923	−	0.257911i
$754$	882.919	+	321.356i	1.17098	+	0.426202i
$755$		−	1002.17i		−	1.32738i
$756$	−118.959	−	287.065i	−0.157353	−	0.379715i
$757$	564.958			0.746312			0.373156	−	0.927769i	$-0.378276\pi$
$757$	564.958			0.746312			0.373156	+	0.927769i	$0.378276\pi$
$758$	29.7536	−	81.7474i	0.0392528	−	0.107846i
$759$	702.017	+	290.742i	0.924924	+	0.383059i
$760$	−258.264	−	216.710i	−0.339822	−	0.285144i
$761$	−353.849	−	62.3930i	−0.464978	−	0.0819882i	−0.0637492	−	0.997966i	$-0.520306\pi$
$761$	−353.849	−	62.3930i	−0.464978	−	0.0819882i	−0.401229	+	0.915978i	$0.631417\pi$
$762$	−56.7031	−	179.806i	−0.0744135	−	0.235966i
$763$	876.669	−	735.612i	1.14898	−	0.964105i
$764$	69.8670	−	40.3377i	0.0914489	−	0.0527981i
$765$	−460.045	−	214.464i	−0.601366	−	0.280345i
$766$	−143.784	+	249.041i	−0.187707	+

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)

\(f(q)\)	\(=\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-0.391734 - 2.97431i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(7.52350 + 1.32660i) q^{5} +(4.14212 + 0.918059i) q^{6} +(4.40811 - 3.69885i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.69309 + 2.33028i) q^{9} +O(q^{10})\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-0.391734 - 2.97431i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(7.52350 + 1.32660i) q^{5} +(4.14212 + 0.918059i) q^{6} +(4.40811 - 3.69885i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.69309 + 2.33028i) q^{9} +(-5.40199 + 9.35652i) q^{10} +(8.02644 - 1.41528i) q^{11} +(-3.22353 + 5.06052i) q^{12} +(-22.0464 + 8.02423i) q^{13} +(2.78334 + 7.64715i) q^{14} +(0.998502 - 22.8969i) q^{15} +(0.694593 + 3.93923i) q^{16} +(6.39327 + 3.69115i) q^{17} +(1.10799 - 12.6796i) q^{18} +(-7.80130 - 13.5122i) q^{19} +(-9.82124 - 11.7045i) q^{20} +(-12.7283 - 11.6622i) q^{21} +(-2.00151 + 11.3511i) q^{22} +(-19.9755 + 23.8059i) q^{23} +(-5.16586 - 6.73156i) q^{24} +(31.3510 + 11.4108i) q^{25} -33.1793i q^{26} +(10.3364 + 24.9431i) q^{27} -11.5088 q^{28} +(-9.68546 + 26.6106i) q^{29} +(29.9454 + 12.4019i) q^{30} +(12.2601 + 10.2874i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(-7.35371 - 23.3187i) q^{33} +(-7.99763 + 6.71081i) q^{34} +(38.0714 - 21.9805i) q^{35} +(16.3143 + 7.60542i) q^{36} +(5.99046 - 10.3758i) q^{37} +(21.7302 - 3.83162i) q^{38} +(32.5029 + 62.4295i) q^{39} +(20.3048 - 7.39036i) q^{40} +(2.82625 + 7.76505i) q^{41} +(21.6547 - 11.2742i) q^{42} +(-7.82854 - 44.3978i) q^{43} +(-14.1167 - 8.15026i) q^{44} +(-68.4938 + 5.99965i) q^{45} +(-21.9743 - 38.0606i) q^{46} +(-43.4592 - 51.7927i) q^{47} +(11.4444 - 3.60907i) q^{48} +(-2.75876 + 15.6457i) q^{49} +(-30.3283 + 36.1438i) q^{50} +(8.47419 - 20.4615i) q^{51} +(44.0928 + 16.0485i) q^{52} +16.4115i q^{53} +(-38.1472 + 1.67154i) q^{54} +62.2645 q^{55} +(5.56667 - 15.2943i) q^{56} +(-37.1336 + 28.4967i) q^{57} +(-30.6787 - 25.7425i) q^{58} +(57.3592 + 10.1140i) q^{59} +(-30.9655 + 33.7965i) q^{60} +(54.6605 - 45.8656i) q^{61} +(-19.6013 + 11.3168i) q^{62} +(-29.7008 + 42.4266i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-176.511 + 31.1237i) q^{65} +(34.5458 + 1.50649i) q^{66} +(-47.1688 + 17.1680i) q^{67} +(-5.04980 - 13.8742i) q^{68} +(78.6313 + 50.0879i) q^{69} +(10.7958 + 61.2257i) q^{70} +(35.4363 + 20.4592i) q^{71} +(-17.9981 + 18.0019i) q^{72} +(-49.7692 - 86.2028i) q^{73} +(10.8911 + 12.9795i) q^{74} +(21.6581 - 97.7176i) q^{75} +(-5.41873 + 30.7311i) q^{76} +(30.1466 - 35.9273i) q^{77} +(-98.6855 + 12.9974i) q^{78} +(-72.4061 - 26.3537i) q^{79} +30.5583i q^{80} +(70.1396 - 40.5147i) q^{81} -11.6862 q^{82} +(36.0769 - 99.1205i) q^{83} +(4.50838 + 34.2307i) q^{84} +(43.2031 + 36.2517i) q^{85} +(62.7880 + 11.0712i) q^{86} +(82.9423 + 18.3833i) q^{87} +(17.6592 - 14.8178i) q^{88} +(-0.302200 + 0.174475i) q^{89} +(25.1567 - 93.9252i) q^{90} +(-67.5026 + 116.918i) q^{91} +(61.2085 - 10.7927i) q^{92} +(25.7954 - 40.4953i) q^{93} +(89.8494 - 32.7025i) q^{94} +(-40.7678 - 112.009i) q^{95} +(-0.739359 + 16.9544i) q^{96} +(11.1076 + 62.9944i) q^{97} +(-19.4576 - 11.2338i) q^{98} +(-66.4766 + 31.0070i) 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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