LMFDB - Embedded newform 54.3.f.a.41.5

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			41.5
Character	$\chi$	$=$	54.41
Dual form			54.3.f.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39273 - 0.245576i) q^{2} +(-0.101242 + 2.99829i) q^{3} +(1.87939 - 0.684040i) q^{4} +(0.379008 - 0.451684i) q^{5} +(0.595305 + 4.20067i) q^{6} +(2.96297 + 1.07843i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.97950 - 0.607104i) q^{9} +O(q^{10})$	\(q+(1.39273 - 0.245576i) q^{2} +(-0.101242 + 2.99829i) q^{3} +(1.87939 - 0.684040i) q^{4} +(0.379008 - 0.451684i) q^{5} +(0.595305 + 4.20067i) q^{6} +(2.96297 + 1.07843i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.97950 - 0.607104i) q^{9} +(0.416932 - 0.722148i) q^{10} +(-6.03341 - 7.19034i) q^{11} +(1.86068 + 5.70420i) q^{12} +(2.11998 - 12.0230i) q^{13} +(4.39145 + 0.774332i) q^{14} +(1.31591 + 1.18210i) q^{15} +(3.06418 - 2.57115i) q^{16} +(-24.5140 - 14.1532i) q^{17} +(-12.6551 + 1.35961i) q^{18} +(11.2011 + 19.4008i) q^{19} +(0.403332 - 1.10814i) q^{20} +(-3.53344 + 8.77467i) q^{21} +(-10.1687 - 8.53254i) q^{22} +(3.44380 + 9.46175i) q^{23} +(3.99223 + 7.48746i) q^{24} +(4.28083 + 24.2778i) q^{25} -17.2654i q^{26} +(2.72938 - 26.8617i) q^{27} +6.30626 q^{28} +(-23.6767 + 4.17484i) q^{29} +(2.12300 + 1.32320i) q^{30} +(42.7251 - 15.5506i) q^{31} +(3.63616 - 4.33340i) q^{32} +(22.1696 - 17.3620i) q^{33} +(-37.6170 - 13.6915i) q^{34} +(1.61010 - 0.929592i) q^{35} +(-17.2912 + 5.00136i) q^{36} +(-15.7500 + 27.2799i) q^{37} +(20.3644 + 24.2694i) q^{38} +(35.8339 + 7.57355i) q^{39} +(0.289598 - 1.64239i) q^{40} +(69.7771 + 12.3036i) q^{41} +(-2.76627 + 13.0885i) q^{42} +(-11.1607 + 9.36490i) q^{43} +(-16.2576 - 9.38633i) q^{44} +(-3.67752 + 3.82580i) q^{45} +(7.11985 + 12.3319i) q^{46} +(-18.9216 + 51.9868i) q^{47} +(7.39884 + 9.44761i) q^{48} +(-29.9200 - 25.1059i) q^{49} +(11.9241 + 32.7611i) q^{50} +(44.9172 - 72.0672i) q^{51} +(-4.23996 - 24.0460i) q^{52} +25.4089i q^{53} +(-2.79530 - 38.0813i) q^{54} -5.53447 q^{55} +(8.78291 - 1.54866i) q^{56} +(-59.3034 + 31.6199i) q^{57} +(-31.9499 + 11.6288i) q^{58} +(18.4282 - 21.9619i) q^{59} +(3.28171 + 1.32150i) q^{60} +(-106.265 - 38.6772i) q^{61} +(55.6855 - 32.1501i) q^{62} +(-25.9513 - 11.4826i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-4.62711 - 5.51438i) q^{65} +(26.6125 - 29.6248i) q^{66} +(8.68700 - 49.2664i) q^{67} +(-55.7526 - 9.83069i) q^{68} +(-28.7178 + 9.36758i) q^{69} +(2.01415 - 1.69007i) q^{70} +(-7.59817 - 4.38680i) q^{71} +(-22.8538 + 11.2118i) q^{72} +(-11.7358 - 20.3271i) q^{73} +(-15.2363 + 41.8613i) q^{74} +(-73.2253 + 10.3773i) q^{75} +(34.3221 + 28.7997i) q^{76} +(-10.1225 - 27.8114i) q^{77} +(51.7667 + 1.74798i) q^{78} +(23.0535 + 130.743i) q^{79} -2.35853i q^{80} +(80.2628 + 10.9030i) q^{81} +100.202 q^{82} +(-66.1377 + 11.6619i) q^{83} +(-0.638457 + 18.9080i) q^{84} +(-15.6838 + 5.70842i) q^{85} +(-13.2440 + 15.7835i) q^{86} +(-10.1203 - 71.4122i) q^{87} +(-24.9475 - 9.08013i) q^{88} +(62.9935 - 36.3693i) q^{89} +(-4.18226 + 6.23141i) q^{90} +(19.2475 - 33.3376i) q^{91} +(12.9444 + 15.4266i) q^{92} +(42.2998 + 129.677i) q^{93} +(-13.5860 + 77.0502i) q^{94} +(13.0083 + 2.29372i) q^{95} +(12.6247 + 11.3410i) q^{96} +(120.419 - 101.043i) q^{97} +(-47.8358 - 27.6180i) q^{98} +(49.8117 + 68.2286i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	1.39273	−	0.245576i	0.696364	−	0.122788i
$2$	1.39273	−	0.245576i	0.696364	−	0.122788i
$3$	−0.101242	+	2.99829i	−0.0337472	+	0.999430i
$3$	−0.101242	+	2.99829i	−0.0337472	+	0.999430i
$4$	1.87939	−	0.684040i	0.469846	−	0.171010i
$5$	0.379008	−	0.451684i	0.0758015	−	0.0903368i	−0.726811	−	0.686838i	$-0.758998\pi$
$5$	0.379008	−	0.451684i	0.0758015	−	0.0903368i	0.802612	+	0.596501i	$0.203443\pi$
$6$	0.595305	+	4.20067i	0.0992175	+	0.700111i
$7$	2.96297	+	1.07843i	0.423282	+	0.154062i	0.544874	−	0.838518i	$-0.316578\pi$
$7$	2.96297	+	1.07843i	0.423282	+	0.154062i	−0.121592	+	0.992580i	$0.538800\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$	−8.97950	−	0.607104i	−0.997722	−	0.0674561i
$10$	0.416932	−	0.722148i	0.0416932	−	0.0722148i
$11$	−6.03341	−	7.19034i	−0.548492	−	0.653667i	0.418577	−	0.908181i	$-0.362529\pi$
$11$	−6.03341	−	7.19034i	−0.548492	−	0.653667i	−0.967069	+	0.254514i	$0.918085\pi$
$12$	1.86068	+	5.70420i	0.155057	+	0.475350i
$13$	2.11998	−	12.0230i	0.163076	−	0.924847i	−0.787951	−	0.615738i	$-0.788858\pi$
$13$	2.11998	−	12.0230i	0.163076	−	0.924847i	0.951027	−	0.309109i	$-0.100031\pi$
$14$	4.39145	+	0.774332i	0.313675	+	0.0553094i
$15$	1.31591	+	1.18210i	0.0877272	+	0.0788070i
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$	−24.5140	−	14.1532i	−1.44200	−	0.832539i	−0.444017	−	0.896018i	$-0.646447\pi$
$17$	−24.5140	−	14.1532i	−1.44200	−	0.832539i	−0.997983	+	0.0634789i	$0.979780\pi$
$18$	−12.6551	+	1.35961i	−0.703061	+	0.0755341i
$19$	11.2011	+	19.4008i	0.589530	+	1.02110i	0.994294	+	0.106675i	$0.0340205\pi$
$19$	11.2011	+	19.4008i	0.589530	+	1.02110i	−0.404764	+	0.914421i	$0.632646\pi$
$20$	0.403332	−	1.10814i	0.0201666	−	0.0554072i
$21$	−3.53344	+	8.77467i	−0.168259	+	0.417842i
$22$	−10.1687	−	8.53254i	−0.462213	−	0.387843i
$23$	3.44380	+	9.46175i	0.149730	+	0.411381i	0.991770	−	0.128036i	$-0.0408672\pi$
$23$	3.44380	+	9.46175i	0.149730	+	0.411381i	−0.842039	+	0.539416i	$0.818645\pi$
$24$	3.99223	+	7.48746i	0.166343	+	0.311978i
$25$	4.28083	+	24.2778i	0.171233	+	0.971112i
$26$		−	17.2654i		−	0.664054i
$27$	2.72938	−	26.8617i	0.101088	−	0.994877i
$28$	6.30626			0.225224
$29$	−23.6767	+	4.17484i	−0.816437	+	0.143960i	−0.566246	−	0.824237i	$-0.691605\pi$
$29$	−23.6767	+	4.17484i	−0.816437	+	0.143960i	−0.250191	+	0.968196i	$0.580494\pi$
$30$	2.12300	+	1.32320i	0.0707666	+	0.0441065i
$31$	42.7251	−	15.5506i	1.37823	−	0.501634i	0.456587	−	0.889679i	$-0.349072\pi$
$31$	42.7251	−	15.5506i	1.37823	−	0.501634i	0.921640	+	0.388045i	$0.126849\pi$
$32$	3.63616	−	4.33340i	0.113630	−	0.135419i
$33$	22.1696	−	17.3620i	0.671805	−	0.526120i
$34$	−37.6170	−	13.6915i	−1.10638	−	0.402691i
$35$	1.61010	−	0.929592i	0.0460029	−	0.0265598i
$36$	−17.2912	+	5.00136i	−0.480312	+	0.138927i
$37$	−15.7500	+	27.2799i	−0.425677	+	0.737293i	−0.996483	−	0.0837909i	$-0.973297\pi$
$37$	−15.7500	+	27.2799i	−0.425677	+	0.737293i	0.570807	+	0.821084i	$0.306631\pi$
$38$	20.3644	+	24.2694i	0.535906	+	0.638668i
$39$	35.8339	+	7.57355i	0.918817	+	0.194194i
$40$	0.289598	−	1.64239i	0.00723995	−	0.0410598i
$41$	69.7771	+	12.3036i	1.70188	+	0.300087i	0.938351	−	0.345685i	$-0.112354\pi$
$41$	69.7771	+	12.3036i	1.70188	+	0.300087i	0.763530	+	0.645773i	$0.223465\pi$
$42$	−2.76627	+	13.0885i	−0.0658636	+	0.311630i
$43$	−11.1607	+	9.36490i	−0.259550	+	0.217788i	−0.763272	−	0.646078i	$-0.776408\pi$
$43$	−11.1607	+	9.36490i	−0.259550	+	0.217788i	0.503722	+	0.863866i	$0.331964\pi$
$44$	−16.2576	−	9.38633i	−0.369491	−	0.213326i
$45$	−3.67752	+	3.82580i	−0.0817226	+	0.0850177i
$46$	7.11985	+	12.3319i	0.154779	+	0.268086i
$47$	−18.9216	+	51.9868i	−0.402588	+	1.10610i	0.558414	+	0.829562i	$0.311410\pi$
$47$	−18.9216	+	51.9868i	−0.402588	+	1.10610i	−0.961002	+	0.276540i	$0.910812\pi$
$48$	7.39884	+	9.44761i	0.154142	+	0.196825i
$49$	−29.9200	−	25.1059i	−0.610612	−	0.512364i
$50$	11.9241	+	32.7611i	0.238482	+	0.655223i
$51$	44.9172	−	72.0672i	0.880729	−	1.41308i
$52$	−4.23996	−	24.0460i	−0.0815378	−	0.462424i
$53$			25.4089i			0.479412i	0.970845	+	0.239706i	$0.0770511\pi$
$53$			25.4089i			0.479412i	−0.970845	+	0.239706i	$0.922949\pi$
$54$	−2.79530	−	38.0813i	−0.0517647	−	0.705209i
$55$	−5.53447			−0.100627
$56$	8.78291	−	1.54866i	0.156838	−	0.0276547i
$57$	−59.3034	+	31.6199i	−1.04041	+	0.554735i
$58$	−31.9499	+	11.6288i	−0.550861	+	0.200497i
$59$	18.4282	−	21.9619i	0.312343	−	0.372236i	−0.586919	−	0.809645i	$-0.699659\pi$
$59$	18.4282	−	21.9619i	0.312343	−	0.372236i	0.899263	+	0.437409i	$0.144104\pi$
$60$	3.28171	+	1.32150i	0.0546951	+	0.0220249i
$61$	−106.265	−	38.6772i	−1.74205	−	0.634053i	−0.742680	−	0.669646i	$-0.766446\pi$
$61$	−106.265	−	38.6772i	−1.74205	−	0.634053i	−0.999366	+	0.0355933i	$0.988668\pi$
$62$	55.6855	−	32.1501i	0.898154	−	0.518549i
$63$	−25.9513	−	11.4826i	−0.411925	−	0.182264i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	−4.62711	−	5.51438i	−0.0711863	−	0.0848365i
$66$	26.6125	−	29.6248i	0.403220	−	0.448861i
$67$	8.68700	−	49.2664i	0.129657	−	0.735320i	−0.848776	−	0.528753i	$-0.822660\pi$
$67$	8.68700	−	49.2664i	0.129657	−	0.735320i	0.978432	−	0.206567i	$-0.0662291\pi$
$68$	−55.7526	−	9.83069i	−0.819891	−	0.144569i
$69$	−28.7178	+	9.36758i	−0.416199	+	0.135762i
$70$	2.01415	−	1.69007i	0.0287735	−	0.0241439i
$71$	−7.59817	−	4.38680i	−0.107016	−	0.0617860i	0.445536	−	0.895264i	$-0.353013\pi$
$71$	−7.59817	−	4.38680i	−0.107016	−	0.0617860i	−0.552553	+	0.833478i	$0.686346\pi$
$72$	−22.8538	+	11.2118i	−0.317413	+	0.155720i
$73$	−11.7358	−	20.3271i	−0.160765	−	0.278453i	0.774378	−	0.632723i	$-0.218063\pi$
$73$	−11.7358	−	20.3271i	−0.160765	−	0.278453i	−0.935143	+	0.354270i	$0.884729\pi$
$74$	−15.2363	+	41.8613i	−0.205895	+	0.565693i
$75$	−73.2253	+	10.3773i	−0.976338	+	0.138363i
$76$	34.3221	+	28.7997i	0.451606	+	0.378943i
$77$	−10.1225	−	27.8114i	−0.131461	−	0.361187i
$78$	51.7667	+	1.74798i	0.663676	+	0.0224100i
$79$	23.0535	+	130.743i	0.291816	+	1.65497i	0.679869	+	0.733334i	$0.262037\pi$
$79$	23.0535	+	130.743i	0.291816	+	1.65497i	−0.388053	+	0.921637i	$0.626852\pi$
$80$		−	2.35853i		−	0.0294816i
$81$	80.2628	+	10.9030i	0.990899	+	0.134605i
$82$	100.202			1.22198
$83$	−66.1377	+	11.6619i	−0.796839	+	0.140504i	−0.557223	−	0.830363i	$-0.688133\pi$
$83$	−66.1377	+	11.6619i	−0.796839	+	0.140504i	−0.239617	+	0.970868i	$0.577022\pi$
$84$	−0.638457	+	18.9080i	−0.00760068	+	0.225095i
$85$	−15.6838	+	5.70842i	−0.184515	+	0.0671579i
$86$	−13.2440	+	15.7835i	−0.154000	+	0.183530i
$87$	−10.1203	−	71.4122i	−0.116325	−	0.820830i
$88$	−24.9475	−	9.08013i	−0.283494	−	0.103183i
$89$	62.9935	−	36.3693i	0.707792	−	0.408644i	−0.102451	−	0.994738i	$-0.532668\pi$
$89$	62.9935	−	36.3693i	0.707792	−	0.408644i	0.810243	+	0.586094i	$0.199335\pi$
$90$	−4.18226	+	6.23141i	−0.0464696	+	0.0692378i
$91$	19.2475	−	33.3376i	0.211511	−	0.366347i
$92$	12.9444	+	15.4266i	0.140700	+	0.167680i
$93$	42.2998	+	129.677i	0.454837	+	1.39437i
$94$	−13.5860	+	77.0502i	−0.144532	+	0.819683i
$95$	13.0083	+	2.29372i	0.136930	+	0.0241444i
$96$	12.6247	+	11.3410i	0.131507	+	0.118135i
$97$	120.419	−	101.043i	1.24143	−	1.04168i	0.244021	−	0.969770i	$-0.421534\pi$
$97$	120.419	−	101.043i	1.24143	−	1.04168i	0.997411	−	0.0719147i	$-0.0229109\pi$
$98$	−47.8358	−	27.6180i	−0.488120	−	0.281816i
$99$	49.8117	+	68.2286i	0.503149	+	0.689178i
$100$	24.6523	+	42.6991i	0.246523	+	0.426991i
$101$	42.9450	−	117.991i	0.425198	−	1.16822i	−0.523496	−	0.852028i	$-0.675372\pi$
$101$	42.9450	−	117.991i	0.425198	−	1.16822i	0.948694	−	0.316195i	$-0.102405\pi$
$102$	44.8595	−	111.401i	0.439799	−	1.09216i
$103$	72.1665	+	60.5548i	0.700645	+	0.587911i	0.921957	−	0.387292i	$-0.126589\pi$
$103$	72.1665	+	60.5548i	0.700645	+	0.587911i	−0.221312	+	0.975203i	$0.571034\pi$
$104$	−11.8102	−	32.4484i	−0.113560	−	0.312003i
$105$	2.62418	+	4.92166i	0.0249922	+	0.0468730i
$106$	6.23979	+	35.3876i	0.0588660	+	0.333846i
$107$			107.896i			1.00838i	0.863594	+	0.504188i	$0.168208\pi$
$107$			107.896i			1.00838i	−0.863594	+	0.504188i	$0.831792\pi$
$108$	−13.2449	−	52.3505i	−0.122638	−	0.484727i
$109$	−42.9667			−0.394190			−0.197095	−	0.980384i	$-0.563151\pi$
$109$	−42.9667			−0.394190			−0.197095	+	0.980384i	$0.563151\pi$
$110$	−7.70802	+	1.35913i	−0.0700729	+	0.0123557i
$111$	−80.1984	−	49.9850i	−0.722508	−	0.450316i
$112$	11.8519	−	4.31374i	0.105820	−	0.0385155i
$113$	6.89768	−	8.22034i	0.0610414	−	0.0727463i	−0.734660	−	0.678436i	$-0.762658\pi$
$113$	6.89768	−	8.22034i	0.0610414	−	0.0727463i	0.795701	+	0.605689i	$0.207103\pi$
$114$	−74.8284	+	58.6014i	−0.656390	+	0.514048i
$115$	5.57895	+	2.03057i	0.0485126	+	0.0176571i
$116$	−41.6418	+	24.0419i	−0.358981	+	0.207258i
$117$	−26.3356	+	106.674i	−0.225091	+	0.911740i
$118$	20.2722	−	35.1125i	0.171799	−	0.297564i
$119$	−57.3711	−	68.3722i	−0.482110	−	0.574556i
$120$	4.89505	+	1.03458i	0.0407921	+	0.00862148i
$121$	5.71249	−	32.3971i	0.0472106	−	0.267745i
$122$	−157.496	−	27.7708i	−1.29095	−	0.227630i
$123$	−43.9541	+	207.966i	−0.357350	+	1.69078i
$124$	69.6596	−	58.4513i	0.561771	−	0.471382i
$125$	25.3543	+	14.6383i	0.202834	+	0.117106i
$126$	−38.9630	−	9.61918i	−0.309230	−	0.0763427i
$127$	−49.1507	−	85.1315i	−0.387013	−	0.670327i	0.605033	−	0.796200i	$-0.293160\pi$
$127$	−49.1507	−	85.1315i	−0.387013	−	0.670327i	−0.992046	+	0.125874i	$0.959827\pi$
$128$	3.86952	−	10.6314i	0.0302306	−	0.0830579i
$129$	−26.9488	−	34.4110i	−0.208905	−	0.266752i
$130$	−7.79850	−	6.54372i	−0.0599885	−	0.0503363i
$131$	−46.8665	−	128.765i	−0.357760	−	0.982937i	−0.979805	−	0.199956i	$-0.935920\pi$
$131$	−46.8665	−	128.765i	−0.357760	−	0.982937i	0.622045	−	0.782981i	$-0.286302\pi$
$132$	29.7889	−	47.7947i	0.225673	−	0.362081i
$133$	12.2660	+	69.5638i	0.0922253	+	0.523036i
$134$		−	70.7481i		−	0.527971i
$135$	−11.0985	−	11.4136i	−0.0822114	−	0.0845452i
$136$	−80.0624			−0.588694
$137$	197.146	−	34.7622i	1.43902	−	0.253739i	0.600947	−	0.799289i	$-0.294790\pi$
$137$	197.146	−	34.7622i	1.43902	−	0.253739i	0.838078	+	0.545550i	$0.183679\pi$
$138$	−37.6956	+	20.0989i	−0.273156	+	0.145644i
$139$	−6.69802	+	2.43788i	−0.0481872	+	0.0175387i	−0.366001	−	0.930614i	$-0.619273\pi$
$139$	−6.69802	+	2.43788i	−0.0481872	+	0.0175387i	0.317814	+	0.948153i	$0.397051\pi$
$140$	2.39012	−	2.84844i	0.0170723	−	0.0203460i
$141$	−153.956	−	61.9958i	−1.09189	−	0.439687i
$142$	−11.6595	−	4.24370i	−0.0821090	−	0.0298852i
$143$	−99.2403	+	57.2964i	−0.693988	+	0.400674i
$144$	−29.0757	+	21.2274i	−0.201915	+	0.147412i
$145$	−7.08794	+	12.2767i	−0.0488823	+	0.0846666i
$146$	−21.3367	−	25.4281i	−0.146142	−	0.174165i
$147$	78.3038	−	87.1671i	0.532679	−	0.592973i
$148$	−10.9399	+	62.0430i	−0.0739180	+	0.419210i
$149$	92.3284	+	16.2800i	0.619654	+	0.109262i	0.474658	−	0.880171i	$-0.342572\pi$
$149$	92.3284	+	16.2800i	0.619654	+	0.109262i	0.144996	+	0.989432i	$0.453683\pi$
$150$	−99.4346	+	32.4351i	−0.662897	+	0.216234i
$151$	154.567	−	129.697i	1.02362	−	0.858921i	0.0335439	−	0.999437i	$-0.489321\pi$
$151$	154.567	−	129.697i	1.02362	−	0.858921i	0.990078	+	0.140516i	$0.0448762\pi$
$152$	54.8738	+	31.6814i	0.361012	+	0.208430i
$153$	211.531	+	141.971i	1.38256	+	0.927915i
$154$	−20.9277	−	36.2479i	−0.135894	−	0.235376i
$155$	9.16915	−	25.1920i	0.0591558	−	0.162529i
$156$	72.5263	−	10.2782i	0.464912	−	0.0658858i
$157$	−56.2262	−	47.1794i	−0.358128	−	0.300505i	0.445916	−	0.895075i	$-0.352878\pi$
$157$	−56.2262	−	47.1794i	−0.358128	−	0.300505i	−0.804044	+	0.594569i	$0.797323\pi$
$158$	64.2144	+	176.428i	0.406420	+	1.11663i
$159$	−76.1831	−	2.57244i	−0.479139	−	0.0161788i
$160$	−0.579196	−	3.28479i	−0.00361998	−	0.0205299i
$161$			31.7488i			0.197198i
$162$	114.462	−	4.52569i	0.706555	−	0.0279364i
$163$	−217.128			−1.33208			−0.666038	−	0.745918i	$-0.732011\pi$
$163$	−217.128			−1.33208			−0.666038	+	0.745918i	$0.732011\pi$
$164$	139.554	−	24.6072i	0.850940	−	0.150044i
$165$	0.560319	−	16.5940i	0.00339588	−	0.100569i
$166$	−89.2480	+	32.4836i	−0.537638	+	0.195684i
$167$	−138.533	+	165.098i	−0.829541	+	0.988609i	0.170454	+	0.985366i	$0.445477\pi$
$167$	−138.533	+	165.098i	−0.829541	+	0.988609i	−0.999995	+	0.00324290i	$0.998968\pi$
$168$	3.75415	+	26.4905i	0.0223461	+	0.157682i
$169$	18.7495	+	6.82427i	0.110944	+	0.0403803i
$170$	−20.4414	+	11.8018i	−0.120243	+	0.0694225i
$171$	−88.8017	−	181.010i	−0.519308	−	1.05854i
$172$	−14.5692	+	25.2346i	−0.0847046	+	0.146713i
$173$	40.5261	+	48.2971i	0.234255	+	0.279174i	0.870347	−	0.492439i	$-0.163895\pi$
$173$	40.5261	+	48.2971i	0.234255	+	0.279174i	−0.636092	+	0.771613i	$0.719450\pi$
$174$	−31.6319	−	96.9725i	−0.181793	−	0.557313i
$175$	−13.4980	+	76.5511i	−0.0771316	+	0.437435i
$176$	−36.9749	−	6.51967i	−0.210085	−	0.0370436i
$177$	63.9825	+	57.4767i	0.361483	+	0.324727i
$178$	78.8015	−	66.1223i	0.442705	−	0.371473i
$179$	172.225	+	99.4340i	0.962150	+	0.555497i	0.896834	−	0.442367i	$-0.145861\pi$
$179$	172.225	+	99.4340i	0.962150	+	0.555497i	0.0653157	+	0.997865i	$0.479195\pi$
$180$	−4.29448	+	9.70572i	−0.0238582	+	0.0539207i
$181$	−35.6490	−	61.7458i	−0.196956	−	0.341137i	0.750584	−	0.660775i	$-0.229772\pi$
$181$	−35.6490	−	61.7458i	−0.196956	−	0.341137i	−0.947540	+	0.319638i	$0.896439\pi$
$182$	18.6196	−	51.1569i	0.102306	−	0.281082i
$183$	126.724	−	314.697i	0.692481	−	1.71966i
$184$	21.8165	+	18.3062i	0.118568	+	0.0994902i
$185$	6.35249	+	17.4533i	0.0343378	+	0.0943422i
$186$	90.7575	+	170.216i	0.487944	+	0.915142i
$187$	46.1370	+	261.656i	0.246722	+	1.39923i
$188$			110.646i			0.588545i
$189$	37.0556	−	76.6470i	0.196062	−	0.405540i
$190$	18.6804			0.0983177
$191$	−98.1741	+	17.3107i	−0.514000	+	0.0906322i	−0.424631	−	0.905366i	$-0.639596\pi$
$191$	−98.1741	+	17.3107i	−0.514000	+	0.0906322i	−0.0893693	+	0.995999i	$0.528485\pi$
$192$	20.3678	+	12.6946i	0.106082	+	0.0661176i
$193$	−178.750	+	65.0595i	−0.926164	+	0.337096i	−0.760688	−	0.649118i	$-0.775138\pi$
$193$	−178.750	+	65.0595i	−0.926164	+	0.337096i	−0.165476	+	0.986214i	$0.552916\pi$
$194$	142.897	−	170.298i	0.736582	−	0.877825i
$195$	17.0022	−	13.3151i	0.0871906	−	0.0682828i
$196$	−73.4046	−	26.7171i	−0.374513	−	0.136312i
$197$	−159.929	+	92.3348i	−0.811820	+	0.468705i	−0.847588	−	0.530656i	$-0.821946\pi$
$197$	−159.929	+	92.3348i	−0.811820	+	0.468705i	0.0357675	+	0.999360i	$0.488612\pi$
$198$	86.1295	+	82.7914i	0.434998	+	0.418138i
$199$	−31.0944	+	53.8571i	−0.156253	+	0.270639i	−0.933515	−	0.358539i	$-0.883275\pi$
$199$	−31.0944	+	53.8571i	−0.156253	+	0.270639i	0.777261	+	0.629178i	$0.216608\pi$
$200$	44.8199	+	53.4142i	0.224099	+	0.267071i
$201$	146.836	+	31.0340i	0.730525	+	0.154398i
$202$	30.8352	−	174.875i	0.152649	−	0.865718i
$203$	−74.6556	−	13.1638i	−0.367762	−	0.0648463i
$204$	35.1198	−	166.167i	0.172156	−	0.814545i
$205$	32.0034	−	26.8540i	0.156114	−	0.130995i
$206$	115.379	+	66.6141i	0.560093	+	0.323370i
$207$	−25.1793	−	87.0526i	−0.121639	−	0.420544i
$208$	−24.4170	−	42.2914i	−0.117389	−	0.203324i
$209$	71.9179	−	197.593i	0.344105	−	0.945420i
$210$	4.86341	+	6.21011i	0.0231591	+	0.0295719i
$211$	5.60018	+	4.69911i	0.0265411	+	0.0222706i	0.655962	−	0.754794i	$-0.272263\pi$
$211$	5.60018	+	4.69911i	0.0265411	+	0.0222706i	−0.629421	+	0.777065i	$0.716708\pi$
$212$	17.3807	+	47.7530i	0.0819843	+	0.225250i
$213$	13.9222	−	22.3374i	0.0653623	−	0.104870i
$214$	26.4967	+	150.270i	0.123816	+	0.702197i
$215$			8.59045i			0.0399556i
$216$	−31.3026	−	69.6574i	−0.144919	−	0.322488i
$217$	143.364			0.660661
$218$	−59.8410	+	10.5516i	−0.274500	+	0.0484017i
$219$	62.1346	−	33.1295i	0.283720	−	0.151276i
$220$	−10.4014	+	3.78580i	−0.0472791	+	0.0172082i
$221$	−222.133	+	264.728i	−1.00513	+	1.19786i
$222$	−123.970	−	49.9208i	−0.558422	−	0.224869i
$223$	−80.8775	−	29.4370i	−0.362679	−	0.132004i	0.154252	−	0.988032i	$-0.450703\pi$
$223$	−80.8775	−	29.4370i	−0.362679	−	0.132004i	−0.516931	+	0.856027i	$0.672926\pi$
$224$	15.4471	−	8.91840i	0.0689604	−	0.0398143i
$225$	−23.7006	−	220.602i	−0.105336	−	0.980451i
$226$	7.58788	−	13.1426i	0.0335747	−	0.0581531i
$227$	42.0709	+	50.1382i	0.185335	+	0.220873i	0.850709	−	0.525636i	$-0.176173\pi$
$227$	42.0709	+	50.1382i	0.185335	+	0.220873i	−0.665375	+	0.746509i	$0.731728\pi$
$228$	−89.8246	+	99.9919i	−0.393967	+	0.438561i
$229$	−57.3799	+	325.418i	−0.250567	+	1.42104i	0.556632	+	0.830759i	$0.312093\pi$
$229$	−57.3799	+	325.418i	−0.250567	+	1.42104i	−0.807199	+	0.590279i	$0.799018\pi$
$230$	8.26862	+	1.45798i	0.0359505	+	0.00633904i
$231$	84.4116	−	27.5346i	0.365418	−	0.119197i
$232$	−52.0917	+	43.7101i	−0.224533	+	0.188406i
$233$	−123.820	−	71.4877i	−0.531418	−	0.306814i	0.210176	−	0.977664i	$-0.432596\pi$
$233$	−123.820	−	71.4877i	−0.531418	−	0.306814i	−0.741594	+	0.670849i	$0.765930\pi$
$234$	−10.4819	+	155.035i	−0.0447945	+	0.662542i
$235$	16.3101	+	28.2500i	0.0694049	+	0.120213i
$236$	19.6109	−	53.8806i	0.0830971	−	0.228308i
$237$	−394.339	+	55.8844i	−1.66388	+	0.235799i
$238$	−96.6929	−	81.1350i	−0.406273	−	0.340903i
$239$	−103.746	−	285.040i	−0.434084	−	1.19264i	−0.943284	−	0.331988i	$-0.892281\pi$
$239$	−103.746	−	285.040i	−0.434084	−	1.19264i	0.509200	−	0.860649i	$-0.329942\pi$
$240$	7.07154	+	0.238781i	0.0294648	+	0.000994922i
$241$	−54.3108	−	308.012i	−0.225356	−	1.27806i	−0.862003	−	0.506903i	$-0.830790\pi$
$241$	−54.3108	−	308.012i	−0.225356	−	1.27806i	0.636647	−	0.771155i	$-0.280321\pi$
$242$		−	46.5232i		−	0.192245i
$243$	−40.8163	+	239.548i	−0.167968	+	0.985792i
$244$	−226.169			−0.926924
$245$	−22.6798	+	3.99906i	−0.0925707	+	0.0163227i
$246$	−10.1446	+	300.435i	−0.0412383	+	1.22128i
$247$	257.003	−	93.5413i	1.04050	−	0.378710i
$248$	82.6626	−	98.5135i	0.333317	−	0.397232i
$249$	−28.2697	−	199.481i	−0.113533	−	0.801127i
$250$	38.9064	+	14.1608i	0.155626	+	0.0566431i
$251$	116.446	−	67.2298i	0.463926	−	0.267848i	−0.249767	−	0.968306i	$-0.580354\pi$
$251$	116.446	−	67.2298i	0.463926	−	0.267848i	0.713694	+	0.700458i	$0.247021\pi$
$252$	−56.6271	−	3.82856i	−0.224711	−	0.0151927i
$253$	47.2554	−	81.8488i	0.186780	−	0.323513i
$254$	−89.3598	−	106.495i	−0.351810	−	0.419271i
$255$	−15.5277	−	47.6024i	−0.0608928	−	0.186676i
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	46.8542	+	8.26166i	0.182312	+	0.0321465i	0.264059	−	0.964507i	$-0.414939\pi$
$257$	46.8542	+	8.26166i	0.182312	+	0.0321465i	−0.0817466	+	0.996653i	$0.526050\pi$
$258$	−45.9828	−	41.3072i	−0.178228	−	0.160106i
$259$	−76.0865	+	63.8441i	−0.293770	+	0.246502i
$260$	−12.4682	−	7.19851i	−0.0479545	−	0.0276866i
$261$	215.139	−	23.1137i	0.824288	−	0.0885584i
$262$	−96.8939	−	167.825i	−0.369824	−	0.640554i
$263$	−162.251	+	445.781i	−0.616924	+	1.69498i	0.0974685	+	0.995239i	$0.468925\pi$
$263$	−162.251	+	445.781i	−0.616924	+	1.69498i	−0.714392	+	0.699745i	$0.753297\pi$
$264$	29.7506	−	73.8805i	0.112692	−	0.279850i
$265$	11.4768	+	9.63015i	0.0433085	+	0.0363402i
$266$	34.1663	+	93.8712i	0.128445	+	0.352899i
$267$	102.668	+	192.555i	0.384525	+	0.721180i
$268$	−17.3740	−	98.5329i	−0.0648284	−	0.367660i
$269$		−	455.081i		−	1.69175i	−0.533380	−	0.845876i	$-0.679078\pi$
$269$		−	455.081i		−	1.69175i	0.533380	−	0.845876i	$-0.320922\pi$
$270$	−18.2601	−	13.1705i	−0.0676302	−	0.0487797i
$271$	440.939			1.62708			0.813541	−	0.581508i	$-0.197537\pi$
$271$	440.939			1.62708			0.813541	+	0.581508i	$0.197537\pi$
$272$	−111.505	+	19.6614i	−0.409946	+	0.0722845i
$273$	98.0072	+	61.0847i	0.359001	+	0.223753i
$274$	266.035	−	96.8287i	0.970929	−	0.353389i
$275$	148.738	−	177.259i	0.540864	−	0.644577i
$276$	−47.5639	+	37.2494i	−0.172333	+	0.134962i
$277$	−70.8393	−	25.7834i	−0.255738	−	0.0930808i	0.210970	−	0.977493i	$-0.432338\pi$
$277$	−70.8393	−	25.7834i	−0.255738	−	0.0930808i	−0.466708	+	0.884412i	$0.654560\pi$
$278$	−8.72984	+	5.04017i	−0.0314023	+	0.0181301i
$279$	−393.091	+	113.698i	−1.40893	+	0.407521i
$280$	2.62928	−	4.55405i	0.00939030	−	0.0162645i
$281$	4.98848	+	5.94504i	0.0177526	+	0.0211567i	0.774848	−	0.632148i	$-0.217827\pi$
$281$	4.98848	+	5.94504i	0.0177526	+	0.0211567i	−0.757095	+	0.653305i	$0.773382\pi$
$282$	−229.643	−	48.5356i	−0.814339	−	0.172112i
$283$	28.3852	−	160.981i	0.100301	−	0.568836i	−0.892692	−	0.450667i	$-0.851186\pi$
$283$	28.3852	−	160.981i	0.100301	−	0.568836i	0.992993	−	0.118169i	$-0.0377026\pi$
$284$	−17.2806	−	3.04704i	−0.0608473	−	0.0107290i
$285$	−8.19423	+	38.7706i	−0.0287517	+	0.136037i
$286$	−124.144	+	104.169i	−0.434071	+	0.364229i
$287$	193.479	+	111.705i	0.674143	+	0.389217i
$288$	−35.2817	+	36.7043i	−0.122506	+	0.127445i
$289$	256.124	+	443.620i	0.886244	+	1.53502i
$290$	−6.85672	+	18.8387i	−0.0236439	+	0.0649610i
$291$	290.766	+	371.281i	0.999196	+	1.27588i
$292$	−35.9607	−	30.1746i	−0.123153	−	0.103338i
$293$	18.4986	+	50.8246i	0.0631353	+	0.173463i	0.967249	−	0.253829i	$-0.0816900\pi$
$293$	18.4986	+	50.8246i	0.0631353	+	0.173463i	−0.904114	+	0.427292i	$0.859468\pi$
$294$	87.6498	−	140.630i	0.298129	−	0.478332i
$295$	−2.93540	−	16.6475i	−0.00995051	−	0.0564321i
$296$			89.0956i			0.300999i
$297$	−209.612	+	142.443i	−0.705765	+	0.479605i
$298$	132.586			0.444921
$299$	121.060	−	21.3461i	0.404882	−	0.0713915i
$300$	−130.520	+	69.5919i	−0.435067	+	0.231973i
$301$	−43.1681	+	15.7119i	−0.143416	+	0.0521991i
$302$	183.419	−	218.591i	0.607349	−	0.723810i
$303$	349.422	+	140.707i	1.15321	+	0.464381i
$304$	84.2046	+	30.6480i	0.276989	+	0.100816i
$305$	−57.7451	+	33.3391i	−0.189328	+	0.109309i
$306$	329.470	+	145.780i	1.07670	+	0.476406i
$307$	73.1993	−	126.785i	0.238434	−	0.412980i	−0.721831	−	0.692069i	$-0.756699\pi$
$307$	73.1993	−	126.785i	0.238434	−	0.412980i	0.960265	+	0.279089i	$0.0900325\pi$
$308$	−38.0483	−	45.3442i	−0.123533	−	0.147221i
$309$	−188.867	+	210.245i	−0.611221	+	0.680406i
$310$	6.58359	−	37.3374i	0.0212374	−	0.120443i
$311$	272.335	+	48.0200i	0.875676	+	0.154405i	0.593380	−	0.804922i	$-0.297793\pi$
$311$	272.335	+	48.0200i	0.875676	+	0.154405i	0.282295	+	0.959328i	$0.408904\pi$
$312$	98.4853	−	32.1254i	0.315658	−	0.102966i
$313$	−22.9780	+	19.2809i	−0.0734123	+	0.0616002i	−0.678755	−	0.734364i	$-0.737480\pi$
$313$	−22.9780	+	19.2809i	−0.0734123	+	0.0616002i	0.605343	+	0.795965i	$0.293036\pi$
$314$	−89.8939	−	51.9003i	−0.286286	−	0.165287i
$315$	−15.0223	+	7.36977i	−0.0476897	+	0.0233961i
$316$	132.760	+	229.946i	0.420125	+	0.727678i
$317$	−91.5339	+	251.487i	−0.288750	+	0.793335i	0.707492	+	0.706722i	$0.249827\pi$
$317$	−91.5339	+	251.487i	−0.288750	+	0.793335i	−0.996242	+	0.0866133i	$0.972396\pi$
$318$	−106.734	+	15.1260i	−0.335642	+	0.0475661i
$319$	172.870	+	145.055i	0.541911	+	0.454717i
$320$	−1.61333	−	4.43258i	−0.00504164	−	0.0138518i
$321$	−323.504	−	10.9236i	−1.00780	−	0.0340299i
$322$	7.79674	+	44.2175i	0.0242135	+	0.137321i
$323$		−	634.123i		−	1.96323i
$324$	158.303	−	34.4121i	0.488589	−	0.106210i
$325$	300.968			0.926055
$326$	−302.401	+	53.3214i	−0.927610	+	0.163563i
$327$	4.35002	−	128.827i	0.0133028	−	0.393965i
$328$	188.318	−	68.5422i	0.574141	−	0.208970i
$329$	−112.129	+	133.630i	−0.340817	+	0.406169i
$330$	−3.29470	−	23.2485i	−0.00998393	−	0.0704499i
$331$	−358.351	−	130.429i	−1.08263	−	0.394045i	−0.261744	−	0.965137i	$-0.584298\pi$
$331$	−358.351	−	130.429i	−1.08263	−	0.394045i	−0.820886	+	0.571092i	$0.806520\pi$
$332$	−116.321	+	67.1580i	−0.350364	+	0.202283i
$333$	157.989	−	235.398i	0.474442	−	0.706900i
$334$	−152.395	+	263.957i	−0.456274	+	0.790289i
$335$	−18.9604	−	22.5961i	−0.0565982	−	0.0674511i
$336$	11.7339	+	35.9722i	0.0349224	+	0.107060i
$337$	20.7953	−	117.936i	0.0617071	−	0.349958i	−0.938285	−	0.345864i	$-0.887586\pi$
$337$	20.7953	−	117.936i	0.0617071	−	0.349958i	0.999992	−	0.00409401i	$-0.00130317\pi$
$338$	27.7889	+	4.89993i	0.0822156	+	0.0144968i
$339$	23.9486	+	21.5135i	0.0706449	+	0.0634616i
$340$	−25.5710	+	21.4566i	−0.0752089	+	0.0631078i
$341$	−369.592	−	213.384i	−1.08385	−	0.625760i
$342$	−168.128	−	230.290i	−0.491603	−	0.673363i
$343$	−138.829	−	240.459i	−0.404749	−	0.701045i
$344$	−14.0939	+	38.7228i	−0.0409707	+	0.112566i
$345$	−6.65306	+	16.5217i	−0.0192842	+	0.0478891i
$346$	68.3024	+	57.3125i	0.197406	+	0.165643i
$347$	−85.0851	−	233.769i	−0.245202	−	0.673687i	−0.999846	−	0.0175526i	$-0.994413\pi$
$347$	−85.0851	−	233.769i	−0.245202	−	0.673687i	0.754644	−	0.656135i	$-0.227810\pi$
$348$	−67.8688	−	127.288i	−0.195025	−	0.365771i
$349$	−55.5583	−	315.087i	−0.159193	−	0.902827i	−0.954852	−	0.297082i	$-0.903986\pi$
$349$	−55.5583	−	315.087i	−0.159193	−	0.902827i	0.795659	−	0.605745i	$-0.207125\pi$
$350$			109.930i			0.314085i
$351$	−317.172	−	89.7616i	−0.903625	−	0.255731i
$352$	−53.0971			−0.150844
$353$	−326.236	+	57.5243i	−0.924182	+	0.162958i	−0.615437	−	0.788186i	$-0.711020\pi$
$353$	−326.236	+	57.5243i	−0.924182	+	0.162958i	−0.308746	+	0.951145i	$0.599909\pi$
$354$	103.225	+	64.3369i	0.291597	+	0.181743i
$355$	−4.86121	+	1.76934i	−0.0136936	+	0.00498405i
$356$	93.5110	−	111.442i	0.262671	−	0.313040i
$357$	210.808	−	165.093i	0.590499	−	0.462446i
$358$	264.281	+	96.1904i	0.738215	+	0.268688i
$359$	277.930	−	160.463i	0.774178	−	0.446972i	−0.0601853	−	0.998187i	$-0.519169\pi$
$359$	277.930	−	160.463i	0.774178	−	0.446972i	0.834363	+	0.551216i	$0.185836\pi$
$360$	−3.59755	+	14.5720i	−0.00999319	+	0.0404779i
$361$	−70.4283	+	121.985i	−0.195092	+	0.337910i
$362$	−64.8126	−	77.2407i	−0.179040	−	0.213372i
$363$	96.5577	+	20.4076i	0.265999	+	0.0562194i
$364$	13.3692	−	75.8202i	0.0367284	−	0.208297i
$365$	−13.6294	−	2.40323i	−0.0373408	−	0.00658419i
$366$	99.2103	−	469.408i	0.271066	−	1.28254i
$367$	−558.217	+	468.400i	−1.52103	+	1.27629i	−0.683410	+	0.730035i	$0.739504\pi$
$367$	−558.217	+	468.400i	−1.52103	+	1.27629i	−0.837617	+	0.546258i	$0.816052\pi$
$368$	34.8800	+	20.1380i	0.0947826	+	0.0547228i
$369$	−619.094	−	152.842i	−1.67776	−	0.414206i
$370$	13.1334	+	22.7477i	0.0354957	+	0.0614803i
$371$	−27.4018	+	75.2857i	−0.0738592	+	0.202927i
$372$	168.202	+	214.777i	0.452155	+	0.577359i
$373$	−262.562	−	220.316i	−0.703920	−	0.590659i	0.218966	−	0.975733i	$-0.429732\pi$
$373$	−262.562	−	220.316i	−0.703920	−	0.590659i	−0.922886	+	0.385073i	$0.874176\pi$
$374$	128.513	+	353.086i	0.343617	+	0.944079i
$375$	−46.4567	+	74.5374i	−0.123885	+	0.198766i
$376$	27.1721	+	154.100i	0.0722661	+	0.409841i
$377$			293.516i			0.778556i
$378$	32.7858	−	115.848i	0.0867349	−	0.306477i
$379$	−607.166			−1.60202			−0.801011	−	0.598650i	$-0.795704\pi$
$379$	−607.166			−1.60202			−0.801011	+	0.598650i	$0.795704\pi$
$380$	26.0167	−	4.58744i	0.0684649	−	0.0120722i
$381$	260.225	−	138.749i	0.683006	−	0.364171i
$382$	−132.479	+	48.2183i	−0.346803	+	0.126226i
$383$	−97.3839	+	116.058i	−0.254266	+	0.303023i	−0.878045	−	0.478578i	$-0.841152\pi$
$383$	−97.3839	+	116.058i	−0.254266	+	0.303023i	0.623779	+	0.781601i	$0.285597\pi$
$384$	31.4843	+	12.6783i	0.0819904	+	0.0330164i
$385$	−16.3985	−	5.96856i	−0.0425935	−	0.0155028i
$386$	−232.973	+	134.507i	−0.603556	+	0.348463i
$387$	105.903	−	77.3164i	0.273650	−	0.199784i
$388$	157.196	−	272.271i	0.405143	−	0.701729i
$389$	389.211	+	463.844i	1.00054	+	1.19240i	0.981280	+	0.192587i	$0.0616876\pi$
$389$	389.211	+	463.844i	1.00054	+	1.19240i	0.0192633	+	0.999814i	$0.493868\pi$
$390$	20.4095	−	22.7197i	0.0523321	−	0.0582556i
$391$	49.4925	−	280.686i	0.126579	−	0.717867i
$392$	−108.794	−	19.1833i	−0.277535	−	0.0489369i
$393$	390.819	−	127.483i	0.994451	−	0.324385i
$394$	−200.062	+	167.872i	−0.507771	+	0.426071i
$395$	67.7918	+	39.1396i	0.171625	+	0.0990876i
$396$	140.287	+	94.1546i	0.354259	+	0.237764i
$397$	301.433	+	522.097i	0.759277	+	1.31511i	0.943220	+	0.332170i	$0.107781\pi$
$397$	301.433	+	522.097i	0.759277	+	1.31511i	−0.183942	+	0.982937i	$0.558886\pi$
$398$	−30.0801	+	82.6444i	−0.0755782	+	0.207649i
$399$	−209.814	+	29.7342i	−0.525850	+	0.0745218i
$400$	75.5391	+	63.3849i	0.188848	+	0.158462i
$401$	151.840	+	417.177i	0.378653	+	1.04034i	0.971915	+	0.235332i	$0.0756177\pi$
$401$	151.840	+	417.177i	0.378653	+	1.04034i	−0.593262	+	0.805010i	$0.702160\pi$
$402$	212.123	+	7.16266i	0.527670	+	0.0178176i
$403$	−96.3893	−	546.651i	−0.239179	−	1.35645i
$404$		−	251.126i		−	0.621599i
$405$	35.3449	−	32.1211i	0.0872715	−	0.0793114i
$406$	−107.208			−0.264058
$407$	291.178	−	51.3425i	0.715425	−	0.126149i
$408$	8.10566	−	240.050i	0.0198668	−	0.588359i
$409$	−388.673	+	141.465i	−0.950300	+	0.345881i	−0.770225	−	0.637772i	$-0.779856\pi$
$409$	−388.673	+	141.465i	−0.950300	+	0.345881i	−0.180075	+	0.983653i	$0.557634\pi$
$410$	37.9773	−	45.2596i	0.0926276	−	0.110389i
$411$	84.2678	+	594.622i	0.205031	+	1.44677i
$412$	177.051	+	64.4411i	0.429734	+	0.156410i
$413$	78.2869	−	45.1989i	0.189557	−	0.109441i
$414$	−56.4459	−	115.057i	−0.136343	−	0.277916i
$415$	−19.7992	+	34.2932i	−0.0477090	+	0.0826343i
$416$	−44.3920	−	52.9043i	−0.106711	−	0.127174i
$417$	−6.63135	−	20.3294i	−0.0159025	−	0.0487516i
$418$	51.6381	−	292.854i	0.123536	−	0.700609i
$419$	606.886	+	107.010i	1.44842	+	0.255395i	0.841881	−	0.539662i	$-0.181448\pi$
$419$	606.886	+	107.010i	1.44842	+	0.255395i	0.606534	+	0.795057i	$0.292559\pi$
$420$	8.29846	+	7.45466i	0.0197582	+	0.0177492i
$421$	2.88941	−	2.42451i	0.00686322	−	0.00575892i	−0.639350	−	0.768916i	$-0.720796\pi$
$421$	2.88941	−	2.42451i	0.00686322	−	0.00575892i	0.646213	+	0.763157i	$0.276352\pi$
$422$	8.95351	+	5.16931i	0.0212169	+	0.0122496i
$423$	201.468	−	455.328i	0.476285	−	1.07643i
$424$	35.9335	+	62.2387i	0.0847489	+	0.146789i
$425$	238.668	−	655.734i	0.561571	−	1.54290i
$426$	13.9043	−	34.5289i	0.0326392	−	0.0810537i
$427$	−273.149	−	229.199i	−0.639693	−	0.536766i
$428$	73.8054	+	202.779i	0.172442	+	0.473782i
$429$	−161.744	−	303.352i	−0.377026	−	0.707115i
$430$	2.10961	+	11.9642i	0.00490606	+	0.0278237i
$431$			658.872i			1.52871i	0.644798	+	0.764353i	$0.276941\pi$
$431$			658.872i			1.52871i	−0.644798	+	0.764353i	$0.723059\pi$
$432$	−60.7022	−	89.3266i	−0.140514	−	0.206775i
$433$	170.484			0.393728			0.196864	−	0.980431i	$-0.436924\pi$
$433$	170.484			0.393728			0.196864	+	0.980431i	$0.436924\pi$
$434$	199.666	−	35.2066i	0.460061	−	0.0811212i
$435$	−36.0914	−	22.4946i	−0.0829688	−	0.0517117i
$436$	−80.7510	+	29.3910i	−0.185209	+	0.0674105i
$437$	−144.992	+	172.794i	−0.331789	+	0.395410i
$438$	78.4009	−	61.3992i	0.178997	−	0.140181i
$439$	805.882	+	293.317i	1.83572	+	0.668148i	0.991157	+	0.132697i	$0.0423636\pi$
$439$	805.882	+	293.317i	1.83572	+	0.668148i	0.844566	+	0.535452i	$0.179859\pi$
$440$	−13.5566	+	7.82692i	−0.0308105	+	0.0177885i
$441$	253.425	+	243.603i	0.574659	+	0.552387i
$442$	−244.360	+	423.244i	−0.552851	+	0.957566i
$443$	−160.598	−	191.394i	−0.362524	−	0.432040i	0.553693	−	0.832721i	$-0.313218\pi$
$443$	−160.598	−	191.394i	−0.362524	−	0.432040i	−0.916218	+	0.400681i	$0.868774\pi$
$444$	−184.915	−	39.0822i	−0.416476	−	0.0880230i
$445$	7.44759	−	42.2374i	0.0167362	−	0.0949155i
$446$	−119.869	−	21.1362i	−0.268765	−	0.0473906i
$447$	−58.1596	+	275.179i	−0.130111	+	0.615614i
$448$	19.3235	−	16.2143i	0.0431328	−	0.0361927i
$449$	−208.642	−	120.460i	−0.464682	−	0.268284i	0.249329	−	0.968419i	$-0.419790\pi$
$449$	−208.642	−	120.460i	−0.464682	−	0.268284i	−0.714011	+	0.700135i	$0.753123\pi$
$450$	−87.1828	−	301.418i	−0.193740	−	0.669817i
$451$	−332.527	−	575.954i	−0.737311	−	1.27706i
$452$	7.34036	−	20.1675i	0.0162397	−	0.0446183i
$453$	373.221	+	476.568i	0.823887	+	1.05203i
$454$	70.9061	+	59.4973i	0.156181	+	0.131051i
$455$	−7.76311	−	21.3290i	−0.0170618	−	0.0468769i
$456$	−100.546	+	161.320i	−0.220495	+	0.353773i
$457$	−33.0420	−	187.391i	−0.0723020	−	0.410045i	−0.999381	−	0.0351791i	$-0.988800\pi$
$457$	−33.0420	−	187.391i	−0.0723020	−	0.410045i	0.927079	−	0.374866i	$-0.122311\pi$
$458$			467.310i			1.02033i
$459$	−447.086	+	619.858i	−0.974044	+	1.35045i
$460$	11.8740			0.0258130
$461$	282.999	−	49.9003i	0.613880	−	0.108244i	0.141941	−	0.989875i	$-0.454666\pi$
$461$	282.999	−	49.9003i	0.613880	−	0.108244i	0.471938	+	0.881632i	$0.343554\pi$
$462$	110.801	−	59.0777i	0.239828	−	0.127874i
$463$	15.8899	−	5.78346i	0.0343195	−	0.0124913i	−0.324803	−	0.945782i	$-0.605298\pi$
$463$	15.8899	−	5.78346i	0.0343195	−	0.0124913i	0.359123	+	0.933290i	$0.383076\pi$
$464$	−61.8154	+	73.6687i	−0.133223	+	0.158769i
$465$	74.6047	+	30.0423i	0.160440	+	0.0646070i
$466$	−190.004	−	69.1557i	−0.407734	−	0.148403i
$467$	590.760	−	341.075i	1.26501	−	0.730354i	0.290971	−	0.956732i	$-0.406022\pi$
$467$	590.760	−	341.075i	1.26501	−	0.730354i	0.974040	+	0.226378i	$0.0726883\pi$
$468$	23.4743	+	218.495i	0.0501588	+	0.466871i
$469$	78.8699	−	136.607i	0.168166	−	0.291272i
$470$	29.6531	+	35.3392i	0.0630917	+	0.0751898i
$471$	147.150	−	163.806i	0.312420	−	0.347783i
$472$	14.0809	−	79.8570i	0.0298325	−	0.169189i
$473$	134.674	+	23.7466i	0.284722	+	0.0502042i
$474$	−535.483	+	174.672i	−1.12971	+	0.368506i
$475$	−423.060	+	354.989i	−0.890652	+	0.747346i
$476$	−154.592	−	89.2536i	−0.324772	−	0.187507i
$477$	15.4258	−	228.159i	0.0323393	−	0.478320i
$478$	−214.489	−	371.506i	−0.448722	−	0.777209i
$479$	−191.036	+	524.867i	−0.398822	+	1.09576i	0.564037	+	0.825750i	$0.309248\pi$
$479$	−191.036	+	524.867i	−0.398822	+	1.09576i	−0.962859	+	0.270005i	$0.912975\pi$
$480$	9.90738	−	1.40404i	0.0206404	−	0.00292509i
$481$	294.596	+	247.196i	0.612466	+	0.513920i
$482$	−151.280	−	415.640i	−0.313860	−	0.862323i
$483$	−95.1922	−	3.21431i	−0.197085	−	0.00665488i
$484$	−11.4250	−	64.7942i	−0.0236053	−	0.133872i
$485$		−	92.6875i		−	0.191108i
$486$	1.98103	+	343.648i	0.00407619	+	0.707095i
$487$	−115.842			−0.237869			−0.118935	−	0.992902i	$-0.537948\pi$
$487$	−115.842			−0.237869			−0.118935	+	0.992902i	$0.537948\pi$
$488$	−314.992	+	55.5417i	−0.645476	+	0.113815i
$489$	21.9825	−	651.014i	0.0449539	−	1.33132i
$490$	−30.6047	+	11.1392i	−0.0624587	+	0.0227331i
$491$	79.5701	−	94.8280i	0.162057	−	0.193132i	−0.678905	−	0.734226i	$-0.737545\pi$
$491$	79.5701	−	94.8280i	0.162057	−	0.193132i	0.840962	+	0.541094i	$0.181990\pi$
$492$	59.6507	+	420.915i	0.121241	+	0.855519i
$493$	639.497	+	232.758i	1.29715	+	0.472126i
$494$	334.963	−	193.391i	0.678063	−	0.391480i
$495$	49.6968	+	3.36000i	0.100398	+	0.00678788i
$496$	90.9341	−	157.502i	0.183335	−	0.317545i
$497$	−17.7823	−	21.1921i	−0.0357793	−	0.0426401i
$498$	−88.3597	−	270.880i	−0.177429	−	0.543936i
$499$	−65.4282	+	371.062i	−0.131119	+	0.743610i	0.846366	+	0.532602i	$0.178786\pi$
$499$	−65.4282	+	371.062i	−0.131119	+	0.743610i	−0.977484	+	0.211008i	$0.932325\pi$
$500$	57.6636	+	10.1676i	0.115327	+	0.0203353i
$501$	−480.985	−	432.078i	−0.960051	−	0.862431i
$502$	145.667	−	122.229i	0.290173	−	0.243484i
$503$	−363.520	−	209.878i	−0.722704	−	0.417253i	0.0930432	−	0.995662i	$-0.470341\pi$
$503$	−363.520	−	209.878i	−0.722704	−	0.417253i	−0.815747	+	0.578409i	$0.803674\pi$
$504$	−79.8063	+	8.57408i	−0.158346	+	0.0170121i
$505$	−37.0179	−	64.1169i	−0.0733028	−	0.126964i
$506$	45.7139	−	125.598i	0.0903436	−	0.248217i
$507$	−22.3594	+	55.5256i	−0.0441013	+	0.109518i
$508$	−150.606	−	126.374i	−0.296469	−	0.248767i
$509$	−41.8155	−	114.887i	−0.0821523	−	0.225712i	0.891815	−	0.452400i	$-0.149432\pi$
$509$	−41.8155	−	114.887i	−0.0821523	−	0.225712i	−0.973967	+	0.226689i	$0.927210\pi$
$510$	−33.3158	−	62.4840i	−0.0653251	−	0.122518i
$511$	−12.8516	−	72.8849i	−0.0251498	−	0.142632i
$512$		−	22.6274i		−	0.0441942i
$513$	551.711	−	247.928i	1.07546	−	0.483290i
$514$	67.2841			0.130903
$515$	54.7033	−	9.64566i	0.106220	−	0.0187294i
$516$	−74.1856	−	46.2375i	−0.143771	−	0.0896075i
$517$	487.965	−	177.605i	0.943840	−	0.343530i
$518$	−90.2892	+	107.602i	−0.174303	+	0.207727i
$519$	−148.912	+	116.619i	−0.286920	+	0.224700i
$520$	−19.1326	−	6.96368i	−0.0367934	−	0.0133917i
$521$	−891.453	+	514.680i	−1.71104	+	0.987870i	−0.777880	+	0.628412i	$0.783705\pi$
$521$	−891.453	+	514.680i	−1.71104	+	0.987870i	−0.933161	+	0.359458i	$0.882962\pi$
$522$	293.954	−	85.0241i	0.563131	−	0.162881i
$523$	−131.269	+	227.364i	−0.250992	+	0.434731i	−0.963799	−	0.266629i	$-0.914090\pi$
$523$	−131.269	+	227.364i	−0.250992	+	0.434731i	0.712807	+	0.701360i	$0.247423\pi$
$524$	−176.161	−	209.940i	−0.336184	−	0.400649i
$525$	−228.156	−	48.2212i	−0.434583	−	0.0918498i
$526$	−116.499	+	660.697i	−0.221480	+	1.25608i
$527$	−1267.45	−	223.486i	−2.40503	−	0.424072i
$528$	23.2913	−	110.201i	0.0441123	−	0.208715i
$529$	327.572	−	274.866i	0.619230	−	0.519595i
$530$	18.3489	+	10.5938i	0.0346207	+	0.0199882i
$531$	−178.810	+	186.019i	−0.336741	+	0.350319i
$532$	70.6369	+	122.347i	0.132776	+	0.229975i
$533$	295.852	−	812.848i	0.555070	−	1.52504i
$534$	190.276	+	242.964i	0.356322	+	0.454989i
$535$	48.7350	+	40.8935i	0.0910934	+	0.0764364i
$536$	−48.3945	−	132.963i	−0.0902883	−	0.248065i
$537$	−315.569	+	506.313i	−0.587651	+	0.942855i
$538$	−111.757	−	633.804i	−0.207726	−	1.17808i
$539$			366.609i			0.680165i
$540$	−28.6658	−	13.8587i	−0.0530848	−	0.0256643i
$541$	14.7044			0.0271800			0.0135900	−	0.999908i	$-0.495674\pi$
$541$	14.7044			0.0271800			0.0135900	+	0.999908i	$0.495674\pi$
$542$	614.109	−	108.284i	1.13304	−	0.199786i
$543$	188.741	−	100.635i	0.347590	−	0.185331i
$544$	−150.468	+	54.7659i	−0.276596	+	0.100673i
$545$	−16.2847	+	19.4074i	−0.0298802	+	0.0356098i
$546$	151.498	+	61.0062i	0.277469	+	0.111733i
$547$	353.812	+	128.777i	0.646823	+	0.235424i	0.644537	−	0.764573i	$-0.277050\pi$
$547$	353.812	+	128.777i	0.646823	+	0.235424i	0.00228579	+	0.999997i	$0.499272\pi$
$548$	346.735	−	200.188i	0.632729	−	0.365306i
$549$	930.724	+	411.816i	1.69531	+	0.750120i
$550$	163.621	−	283.400i	0.297492	−	0.515272i
$551$	−346.200	−	412.585i	−0.628311	−	0.748792i
$552$	−57.0961	+	63.5588i	−0.103435	+	0.115143i
$553$	−72.6906	+	412.249i	−0.131448	+	0.745477i
$554$	−104.992	−	18.5129i	−0.189516	−	0.0334167i
$555$	−52.9732	+	17.2796i	−0.0954473	+	0.0311344i
$556$	−10.9205	+	9.16343i	−0.0196413	+	0.0164810i
$557$	339.531	+	196.028i	0.609571	+	0.351936i	0.772798	−	0.634653i	$-0.218857\pi$
$557$	339.531	+	196.028i	0.609571	+	0.351936i	−0.163226	+	0.986589i	$0.552190\pi$
$558$	−519.547	+	254.885i	−0.931087	+	0.456782i
$559$	88.9339	+	154.038i	0.159095	+	0.275560i
$560$	2.54351	−	6.98825i	0.00454199	−	0.0124790i
$561$	−789.192	+	111.842i	−1.40676	+	0.199361i
$562$	8.40755	+	7.05477i	0.0149601	+	0.0125530i
$563$	−282.488	−	776.129i	−0.501754	−	1.37856i	−0.889560	−	0.456818i	$-0.848989\pi$
$563$	−282.488	−	776.129i	−0.501754	−	1.37856i	0.387806	−	0.921741i	$-0.373233\pi$
$564$	−331.750	−	11.2020i	−0.588209	−	0.0198618i
$565$	−1.09872	−	6.23114i	−0.00194463	−	0.0110286i
$566$		−	231.173i		−	0.408433i
$567$	226.058	+	118.863i	0.398692	+	0.209636i
$568$	−24.8155			−0.0436893
$569$	−820.292	+	144.640i	−1.44164	+	0.254200i	−0.839138	−	0.543919i	$-0.816940\pi$
$569$	−820.292	+	144.640i	−1.44164	+	0.254200i	−0.602501	+	0.798118i	$0.705829\pi$
$570$	−1.89123	+	56.0092i	−0.00331795	+	0.0982617i
$571$	−171.024	+	62.2478i	−0.299517	+	0.109015i	−0.487407	−	0.873175i	$-0.662057\pi$
$571$	−171.024	+	62.2478i	−0.299517	+	0.109015i	0.187890	+	0.982190i	$0.439835\pi$
$572$	−147.318	+	175.566i	−0.257548	+	0.306934i
$573$	−41.9633	−	296.107i	−0.0732344	−	0.516766i
$574$	296.896	+	108.061i	0.517240	+	0.188260i
$575$	−214.968	+	124.112i	−0.373858	+	0.215847i
$576$	−40.1241	+	59.7834i	−0.0696600	+	0.103791i
$577$	−25.3860	+	43.9699i	−0.0439966	+	0.0762043i	−0.887185	−	0.461414i	$-0.847342\pi$
$577$	−25.3860	+	43.9699i	−0.0439966	+	0.0762043i	0.843189	+	0.537618i	$0.180676\pi$
$578$	465.654	+	554.945i	0.805630	+	0.960112i
$579$	−176.971	−	542.530i	−0.305649	−	0.937012i
$580$	−4.92323	+	27.9210i	−0.00848832	+	0.0481397i
$581$	−208.541	−	36.7713i	−0.358934	−	0.0632898i
$582$	496.136	+	445.688i	0.852467	+	0.765787i
$583$	182.698	−	153.302i	0.313376	−	0.262954i
$584$	−57.4936	−	33.1940i	−0.0984480	−	0.0568390i
$585$	38.2013	+	52.3255i	0.0653014	+	0.0894453i
$586$	38.2449	+	66.2421i	0.0652643	+	0.113041i
$587$	29.4058	−	80.7919i	0.0500951	−	0.137635i	−0.912122	−	0.409919i	$-0.865557\pi$
$587$	29.4058	−	80.7919i	0.0500951	−	0.137635i	0.962217	+	0.272284i	$0.0877791\pi$
$588$	87.5372	−	217.383i	0.148873	−	0.369700i
$589$	780.262	+	654.718i	1.32472	+	1.11158i
$590$	−8.17643	−	22.4646i	−0.0138584	−	0.0380755i
$591$	−260.655	−	488.860i	−0.441041	−	0.827175i
$592$	21.8797	+	124.086i	0.0369590	+	0.209605i
$593$			333.051i			0.561638i	0.959761	+	0.280819i	$0.0906060\pi$
$593$			333.051i			0.561638i	−0.959761	+	0.280819i	$0.909394\pi$
$594$	−256.952	+	249.859i	−0.432580	+	0.420639i
$595$	−52.6267			−0.0884482
$596$	184.657	−	32.5600i	0.309827	−	0.0546308i
$597$	−158.331	−	98.6828i	−0.265212	−	0.165298i
$598$	163.361	−	59.4586i	0.273179	−	0.0994290i
$599$	376.276	−	448.428i	0.628173	−	0.748628i	−0.354279	−	0.935140i	$-0.615274\pi$
$599$	376.276	−	448.428i	0.628173	−	0.748628i	0.982453	+	0.186512i	$0.0597182\pi$
$600$	−164.689	+	128.975i	−0.274482	+	0.214959i
$601$	684.489	+	249.134i	1.13892	+	0.414532i	0.841522	−	0.540223i	$-0.181660\pi$
$601$	684.489	+	249.134i	1.13892	+	0.414532i	0.297395	+	0.954755i	$0.403882\pi$
$602$	−56.2630	+	32.4835i	−0.0934602	+	0.0539593i
$603$	−107.915	+	437.114i	−0.178963	+	0.724899i
$604$	201.773	−	349.481i	0.334061	−	0.578611i
$605$	−12.4682	−	14.8590i	−0.0206086	−	0.0245603i
$606$	521.205	+	110.158i	0.860073	+	0.181778i
$607$	50.2841	−	285.175i	0.0828404	−	0.469811i	−0.914961	−	0.403541i	$-0.867779\pi$
$607$	50.2841	−	285.175i	0.0828404	−	0.469811i	0.997802	−	0.0662697i	$-0.0211098\pi$
$608$	124.800	+	22.0057i	0.205264	+	0.0361936i
$609$	47.0272	−	222.507i	0.0772203	−	0.365364i
$610$	−72.2359	+	60.6131i	−0.118420	+	0.0993658i
$611$	584.925	+	337.706i	0.957323	+	0.552711i
$612$	494.662	+	122.122i	0.808272	+	0.199546i
$613$	−431.468	−	747.325i	−0.703864	−	1.21913i	−0.967100	−	0.254396i	$-0.918123\pi$
$613$	−431.468	−	747.325i	−0.703864	−	1.21913i	0.263236	−	0.964731i	$-0.415210\pi$
$614$	70.8115	−	194.553i	0.115328	−	0.316862i
$615$	77.2761	+	98.6742i	0.125652	+	0.160446i
$616$	−64.1263	−	53.8084i	−0.104101	−	0.0873513i
$617$	−37.3588	−	102.642i	−0.0605491	−	0.166357i	0.905729	−	0.423856i	$-0.139324\pi$
$617$	−37.3588	−	102.642i	−0.0605491	−	0.166357i	−0.966279	+	0.257499i	$0.917102\pi$
$618$	−211.410	+	339.196i	−0.342087	+	0.548861i
$619$	16.5748	+	94.0001i	0.0267767	+	0.151858i	0.995265	−	0.0972023i	$-0.0309894\pi$
$619$	16.5748	+	94.0001i	0.0267767	+	0.151858i	−0.968488	+	0.249060i	$0.919878\pi$
$620$		−	53.6176i		−	0.0864800i
$621$	263.558	−	66.6815i	0.424409	−	0.107378i
$622$	391.081			0.628748
$623$	225.870	−	39.8270i	0.362552	−	0.0639277i
$624$	129.274	−	68.9275i	0.207170	−	0.110461i
$625$	−562.919	+	204.886i	−0.900671	+	0.327817i
$626$	−27.2673	+	32.4959i	−0.0435579	+	0.0519103i
$627$	585.160	+	235.635i	0.933269	+	0.375814i
$628$	−137.943	−	50.2072i	−0.219655	−	0.0799478i
$629$	772.193	−	445.826i	1.22765	−	0.708785i
$630$	−19.1121	+	13.9532i	−0.0303367	+	0.0221479i
$631$	264.888	−	458.800i	0.419791	−	0.727100i	−0.576127	−	0.817360i	$-0.695437\pi$
$631$	264.888	−	458.800i	0.419791	−	0.727100i	0.995918	+	0.0902603i	$0.0287699\pi$
$632$	241.367	+	287.650i	0.381910	+	0.455143i
$633$	−14.6563	+	16.3152i	−0.0231537	+	0.0257744i
$634$	−65.7227	+	372.732i	−0.103664	+	0.587905i
$635$	−57.0810	−	10.0649i	−0.0898914	−	0.0158503i
$636$	−144.937	+	47.2777i	−0.227889	+	0.0743361i
$637$	−365.278	+	306.504i	−0.573435	+	0.481169i
$638$	276.382	+	159.569i	0.433201	+	0.250109i
$639$	65.5645	+	44.0042i	0.102605	+	0.0688642i
$640$	−3.33546	−	5.77718i	−0.00521165	−	0.00902685i
$641$	−90.7979	+	249.465i	−0.141650	+	0.389181i	−0.990149	−	0.140016i	$-0.955285\pi$
$641$	−90.7979	+	249.465i	−0.141650	+	0.389181i	0.848499	+	0.529197i	$0.177507\pi$
$642$	−453.236	+	64.2311i	−0.705975	+	0.100049i
$643$	111.106	+	93.2293i	0.172794	+	0.144991i	0.725083	−	0.688661i	$-0.241801\pi$
$643$	111.106	+	93.2293i	0.172794	+	0.144991i	−0.552290	+	0.833652i	$0.686246\pi$
$644$	21.7175	+	59.6683i	0.0337228	+	0.0926526i
$645$	−25.7567	−	0.869713i	−0.0399328	−	0.00134839i
$646$	−155.725	−	883.161i	−0.241061	−	1.36712i
$647$			578.671i			0.894391i	0.894436	+	0.447196i	$0.147577\pi$
$647$			578.671i			0.894391i	−0.894436	+	0.447196i	$0.852423\pi$
$648$	212.022	−	86.8020i	0.327195	−	0.133954i
$649$	−269.099			−0.414636
$650$	419.166	−	73.9103i	0.644871	−	0.113708i
$651$	−14.5144	+	429.846i	−0.0222955	+	0.660285i
$652$	−408.068	+	148.525i	−0.625871	+	0.227798i
$653$	−417.061	+	497.034i	−0.638684	+	0.761154i	−0.984162	−	0.177273i	$-0.943273\pi$
$653$	−417.061	+	497.034i	−0.638684	+	0.761154i	0.345477	+	0.938427i	$0.387717\pi$
$654$	−25.5783	−	180.489i	−0.0391105	−	0.275977i
$655$	−75.9237	−	27.6340i	−0.115914	−	0.0421893i
$656$	245.444	−	141.707i	0.374152	−	0.216017i
$657$	93.0413	+	189.652i	0.141615	+	0.288663i
$658$	−123.349	+	213.646i	−0.187460	+	0.324690i
$659$	−346.075	−	412.436i	−0.525151	−	0.625851i	0.436639	−	0.899637i	$-0.356169\pi$
$659$	−346.075	−	412.436i	−0.525151	−	0.625851i	−0.961791	+	0.273785i	$0.911724\pi$
$660$	−10.2979	−	31.5697i	−0.0156028	−	0.0478329i
$661$	−66.4965	+	377.120i	−0.100600	+	0.570530i	0.892287	+	0.451468i	$0.149100\pi$
$661$	−66.4965	+	377.120i	−0.100600	+	0.570530i	−0.992887	+	0.119061i	$0.962011\pi$
$662$	−531.115	−	93.6500i	−0.802289	−	0.141465i
$663$	−771.242	−	692.821i	−1.16326	−	1.04498i
$664$	−145.511	+	122.098i	−0.219143	+	0.183883i
$665$	36.0697	+	20.8249i	0.0542402	+	0.0313156i
$666$	162.228	−	366.643i	0.243586	−	0.550515i
$667$	−121.039	−	209.646i	−0.181468	−	0.314311i
$668$	−147.424	+	405.044i	−0.220695	+	0.606354i
$669$	96.4488	−	239.514i	0.144169	−	0.358018i
$670$	−31.9558	−	26.8141i	−0.0476952	−	0.0400210i
$671$	363.037	+	997.436i	0.541039	+	1.48649i
$672$	25.1761	+	47.2179i	0.0374644	+	0.0702647i
$673$	28.0045	+	158.821i	0.0416114	+	0.235990i	0.998519	−	0.0544023i	$-0.0173253\pi$
$673$	28.0045	+	158.821i	0.0416114	+	0.235990i	−0.956908	+	0.290392i	$0.906214\pi$
$674$		−	169.360i		−	0.251275i
$675$	663.827	−	48.7271i	0.983448	−	0.0721884i
$676$	39.9056			0.0590320
$677$	126.078	−	22.2310i	0.186231	−	0.0328375i	−0.0797548	−	0.996815i	$-0.525414\pi$
$677$	126.078	−	22.2310i	0.186231	−	0.0328375i	0.265986	+	0.963977i	$0.414303\pi$
$678$	38.6371	+	24.0813i	0.0569869	+	0.0355181i
$679$	465.766	−	169.525i	0.685959	−	0.249669i
$680$	−30.3443	+	36.1629i	−0.0446239	+	0.0531807i
$681$	−154.588	+	121.065i	−0.227002	+	0.177775i
$682$	−567.144	−	206.423i	−0.831589	−	0.302674i
$683$	−410.786	+	237.168i	−0.601444	+	0.347244i	−0.769609	−	0.638515i	$-0.779549\pi$
$683$	−410.786	+	237.168i	−0.601444	+	0.347244i	0.168165	+	0.985759i	$0.446216\pi$
$684$	−290.711	−	279.444i	−0.425016	−	0.408543i
$685$	59.0185	−	102.223i	0.0861583	−	0.149231i
$686$	−252.402	−	300.800i	−0.367932	−	0.438485i
$687$	−969.888	−	204.988i	−1.41177	−	0.298381i
$688$	−10.1197	+	57.3914i	−0.0147088	+	0.0834178i
$689$	305.491	+	53.8663i	0.443383	+	0.0781804i
$690$	−5.20858	+	24.6441i	−0.00754866	+	0.0357161i
$691$	−218.877	+	183.660i	−0.316754	+	0.265788i	−0.787277	−	0.616600i	$-0.788510\pi$
$691$	−218.877	+	183.660i	−0.316754	+	0.265788i	0.470523	+	0.882388i	$0.344065\pi$
$692$	109.201	+	63.0474i	0.157805	+	0.0911089i
$693$	74.0108	+	255.878i	0.106798	+	0.369233i
$694$	−175.909	−	304.683i	−0.253471	−	0.439024i
$695$	−1.43745	+	3.94936i	−0.00206827	+	0.00568253i
$696$	−125.782	−	160.611i	−0.180721	−	0.230763i
$697$	−1536.38	−	1289.18i	−2.20428	−	1.84961i
$698$	−154.755	−	425.186i	−0.221712	−	0.609149i
$699$	226.877	−	364.012i	0.324573	−	0.520761i
$700$	26.9960	+	153.102i	0.0385658	+	0.218717i
$701$			320.086i			0.456613i	0.973589	+	0.228307i	$0.0733189\pi$
$701$			320.086i			0.456613i	−0.973589	+	0.228307i	$0.926681\pi$
$702$	−463.778	−	47.1238i	−0.660653	−	0.0671279i
$703$	−705.669			−1.00380
$704$	−73.9498	+	13.0393i	−0.105042	+	0.0185218i
$705$	−86.3530	+	46.0425i	−0.122487	+	0.0653085i
$706$	−440.232	+	160.231i	−0.623558	+	0.226957i
$707$	254.490	−	303.289i	0.359958	−	0.428981i
$708$	159.564	+	64.2542i	0.225373	+	0.0907546i
$709$	−796.794	−	290.009i	−1.12383	−	0.409040i	−0.287780	−	0.957697i	$-0.592917\pi$
$709$	−796.794	−	290.009i	−1.12383	−	0.409040i	−0.836048	+	0.548657i	$0.815139\pi$
$710$	−6.33584	+	3.65800i	−0.00892372	+	0.00515211i
$711$	−127.634	−	1188.00i	−0.179514	−	1.67089i
$712$	102.868	−	178.173i	0.144478	−	0.250242i
$713$	294.273	+	350.701i	0.412725	+	0.491866i
$714$	253.056	−	281.699i	0.354420	−	0.394537i
$715$	−11.7330	+	66.5410i	−0.0164098	+	0.0930644i
$716$	391.694	+	69.0662i	0.547058	+	0.0964611i
$717$	865.137	−	282.203i	1.20661	−	0.393589i
$718$	347.675	−	291.734i	0.484227	−	0.406315i
$719$	143.869	+	83.0628i	0.200096	+	0.115525i	0.596700	−	0.802464i	$-0.296478\pi$
$719$	143.869	+	83.0628i	0.200096	+	0.115525i	−0.396604	+	0.917990i	$0.629811\pi$
$720$	−1.43187	+	21.1784i	−0.00198871	+	0.0294144i
$721$	148.523	+	257.249i	0.205996	+	0.356795i
$722$	−68.1308	+	187.188i	−0.0943640	+	0.259263i
$723$	929.008	−	131.656i	1.28494	−	0.182097i
$724$	−109.235	−	91.6589i	−0.150877	−	0.126601i
$725$	−202.712	−	556.946i	−0.279602	−	0.768201i
$726$	139.490	+	4.71009i	0.192135	+	0.00648773i
$727$	136.863	+	776.190i	0.188258	+	1.06766i	0.921698	+	0.387908i	$0.126802\pi$
$727$	136.863	+	776.190i	0.188258	+	1.06766i	−0.733440	+	0.679754i	$0.762087\pi$
$728$		−	108.880i		−	0.149561i
$729$	−714.101	−	146.631i	−0.979562	−	0.201140i
$730$	−19.5722			−0.0268112
$731$	406.135	−	71.6126i	0.555589	−	0.0979653i
$732$	22.8978	−	678.122i	0.0312811	−	0.926396i
$733$	650.225	−	236.663i	0.887074	−	0.322869i	0.142013	−	0.989865i	$-0.454643\pi$
$733$	650.225	−	236.663i	0.887074	−	0.322869i	0.745061	+	0.666996i	$0.232420\pi$
$734$	−662.417	+	789.438i	−0.902475	+	1.07553i
$735$	−9.69421	−	68.4055i	−0.0131894	−	0.0930688i
$736$	53.5238	+	19.4811i	0.0727225	+	0.0264688i
$737$	−406.655	+	234.782i	−0.551770	+	0.318565i
$738$	−899.764	−	60.8331i	−1.21919	−	0.0824297i
$739$	−117.695	+	203.854i	−0.159262	+	0.275851i	−0.934603	−	0.355693i	$-0.884245\pi$
$739$	−117.695	+	203.854i	−0.159262	+	0.275851i	0.775340	+	0.631543i	$0.217578\pi$
$740$	23.8775	+	28.4561i	0.0322669	+	0.0384542i
$741$	254.445	+	780.039i	0.343380	+	1.05268i
$742$	−19.6749	+	111.582i	−0.0265160	+	0.150380i
$743$	600.536	+	105.891i	0.808259	+	0.142518i	0.562483	−	0.826809i	$-0.309846\pi$
$743$	600.536	+	105.891i	0.808259	+	0.142518i	0.245776	+	0.969327i	$0.420957\pi$
$744$	287.003	+	257.820i	0.385757	+	0.346533i
$745$	42.3466	−	35.5330i	0.0568411	−	0.0476953i
$746$	−419.782	−	242.361i	−0.562711	−	0.324881i
$747$	600.963	−	64.5652i	0.804502	−	0.0864326i
$748$	265.692	+	460.193i	0.355204	+	0.615231i
$749$	−116.359	+	319.694i	−0.155352	+	0.426827i
$750$	−46.3971	+	115.219i	−0.0618628	+	0.153625i
$751$	163.414	+	137.121i	0.217596	+	0.182585i	0.745070	−	0.666987i	$-0.232416\pi$
$751$	163.414	+	137.121i	0.217596	+	0.182585i	−0.527474	+	0.849571i	$0.676861\pi$
$752$	75.6866	+	207.947i	0.100647	+	0.276526i
$753$	189.786	+	355.944i	0.252039	+	0.472701i
$754$	72.0803	+	408.787i	0.0955972	+	0.542158i
$755$		−	118.972i		−	0.157578i
$756$	17.2122	−	169.397i	0.0227674	−	0.224070i
$757$	−212.260			−0.280397			−0.140198	−	0.990123i	$-0.544774\pi$
$757$	−212.260			−0.280397			−0.140198	+	0.990123i	$0.544774\pi$
$758$	−845.618	+	149.105i	−1.11559	+	0.196709i
$759$	240.622	+	149.972i	0.317025	+	0.197592i
$760$	35.1076	−	12.7781i	0.0461942	−	0.0168133i
$761$	934.612	−	1113.83i	1.22814	−	1.46364i	0.387649	−	0.921807i	$-0.373287\pi$
$761$	934.612	−	1113.83i	1.22814	−	1.46364i	0.840488	−	0.541830i	$-0.182268\pi$
$762$	328.350	−	257.145i	0.430905	−	0.337461i
$763$	−127.309	−	46.3368i	−0.166853	−	0.0607297i
$764$	−172.666	+	99.6886i	−0.226002	+	0.130482i
$765$	144.298	−	41.7371i	0.188625	−	0.0545583i
$766$	−107.128	+	185.552i	−0.139854

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)

\(f(q)\)	\(=\)	\(q+(1.39273 - 0.245576i) q^{2} +(-0.101242 + 2.99829i) q^{3} +(1.87939 - 0.684040i) q^{4} +(0.379008 - 0.451684i) q^{5} +(0.595305 + 4.20067i) q^{6} +(2.96297 + 1.07843i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.97950 - 0.607104i) q^{9} +O(q^{10})\)	\(q+(1.39273 - 0.245576i) q^{2} +(-0.101242 + 2.99829i) q^{3} +(1.87939 - 0.684040i) q^{4} +(0.379008 - 0.451684i) q^{5} +(0.595305 + 4.20067i) q^{6} +(2.96297 + 1.07843i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-8.97950 - 0.607104i) q^{9} +(0.416932 - 0.722148i) q^{10} +(-6.03341 - 7.19034i) q^{11} +(1.86068 + 5.70420i) q^{12} +(2.11998 - 12.0230i) q^{13} +(4.39145 + 0.774332i) q^{14} +(1.31591 + 1.18210i) q^{15} +(3.06418 - 2.57115i) q^{16} +(-24.5140 - 14.1532i) q^{17} +(-12.6551 + 1.35961i) q^{18} +(11.2011 + 19.4008i) q^{19} +(0.403332 - 1.10814i) q^{20} +(-3.53344 + 8.77467i) q^{21} +(-10.1687 - 8.53254i) q^{22} +(3.44380 + 9.46175i) q^{23} +(3.99223 + 7.48746i) q^{24} +(4.28083 + 24.2778i) q^{25} -17.2654i q^{26} +(2.72938 - 26.8617i) q^{27} +6.30626 q^{28} +(-23.6767 + 4.17484i) q^{29} +(2.12300 + 1.32320i) q^{30} +(42.7251 - 15.5506i) q^{31} +(3.63616 - 4.33340i) q^{32} +(22.1696 - 17.3620i) q^{33} +(-37.6170 - 13.6915i) q^{34} +(1.61010 - 0.929592i) q^{35} +(-17.2912 + 5.00136i) q^{36} +(-15.7500 + 27.2799i) q^{37} +(20.3644 + 24.2694i) q^{38} +(35.8339 + 7.57355i) q^{39} +(0.289598 - 1.64239i) q^{40} +(69.7771 + 12.3036i) q^{41} +(-2.76627 + 13.0885i) q^{42} +(-11.1607 + 9.36490i) q^{43} +(-16.2576 - 9.38633i) q^{44} +(-3.67752 + 3.82580i) q^{45} +(7.11985 + 12.3319i) q^{46} +(-18.9216 + 51.9868i) q^{47} +(7.39884 + 9.44761i) q^{48} +(-29.9200 - 25.1059i) q^{49} +(11.9241 + 32.7611i) q^{50} +(44.9172 - 72.0672i) q^{51} +(-4.23996 - 24.0460i) q^{52} +25.4089i q^{53} +(-2.79530 - 38.0813i) q^{54} -5.53447 q^{55} +(8.78291 - 1.54866i) q^{56} +(-59.3034 + 31.6199i) q^{57} +(-31.9499 + 11.6288i) q^{58} +(18.4282 - 21.9619i) q^{59} +(3.28171 + 1.32150i) q^{60} +(-106.265 - 38.6772i) q^{61} +(55.6855 - 32.1501i) q^{62} +(-25.9513 - 11.4826i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-4.62711 - 5.51438i) q^{65} +(26.6125 - 29.6248i) q^{66} +(8.68700 - 49.2664i) q^{67} +(-55.7526 - 9.83069i) q^{68} +(-28.7178 + 9.36758i) q^{69} +(2.01415 - 1.69007i) q^{70} +(-7.59817 - 4.38680i) q^{71} +(-22.8538 + 11.2118i) q^{72} +(-11.7358 - 20.3271i) q^{73} +(-15.2363 + 41.8613i) q^{74} +(-73.2253 + 10.3773i) q^{75} +(34.3221 + 28.7997i) q^{76} +(-10.1225 - 27.8114i) q^{77} +(51.7667 + 1.74798i) q^{78} +(23.0535 + 130.743i) q^{79} -2.35853i q^{80} +(80.2628 + 10.9030i) q^{81} +100.202 q^{82} +(-66.1377 + 11.6619i) q^{83} +(-0.638457 + 18.9080i) q^{84} +(-15.6838 + 5.70842i) q^{85} +(-13.2440 + 15.7835i) q^{86} +(-10.1203 - 71.4122i) q^{87} +(-24.9475 - 9.08013i) q^{88} +(62.9935 - 36.3693i) q^{89} +(-4.18226 + 6.23141i) q^{90} +(19.2475 - 33.3376i) q^{91} +(12.9444 + 15.4266i) q^{92} +(42.2998 + 129.677i) q^{93} +(-13.5860 + 77.0502i) q^{94} +(13.0083 + 2.29372i) q^{95} +(12.6247 + 11.3410i) q^{96} +(120.419 - 101.043i) q^{97} +(-47.8358 - 27.6180i) q^{98} +(49.8117 + 68.2286i) 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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