LMFDB - Embedded newform 54.3.f.a.41.3

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			41.3
Character	$\chi$	$=$	54.41
Dual form			54.3.f.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39273 + 0.245576i) q^{2} +(2.66538 + 1.37686i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-1.49345 + 1.77982i) q^{5} +(-4.05028 - 1.26303i) q^{6} +(5.91054 + 2.15126i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.20853 + 7.33970i) q^{9} +O(q^{10})$	\(q+(-1.39273 + 0.245576i) q^{2} +(2.66538 + 1.37686i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-1.49345 + 1.77982i) q^{5} +(-4.05028 - 1.26303i) q^{6} +(5.91054 + 2.15126i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.20853 + 7.33970i) q^{9} +(1.64289 - 2.84556i) q^{10} +(1.00782 + 1.20107i) q^{11} +(5.95111 + 0.764415i) q^{12} +(1.33408 - 7.56595i) q^{13} +(-8.76008 - 1.54464i) q^{14} +(-6.43117 + 2.68764i) q^{15} +(3.06418 - 2.57115i) q^{16} +(-20.1411 - 11.6285i) q^{17} +(-9.05652 - 8.94312i) q^{18} +(-15.0781 - 26.1161i) q^{19} +(-1.58929 + 4.36655i) q^{20} +(12.7919 + 13.8719i) q^{21} +(-1.69857 - 1.42527i) q^{22} +(-7.69793 - 21.1499i) q^{23} +(-8.47600 + 0.396823i) q^{24} +(3.40383 + 19.3041i) q^{25} +10.8649i q^{26} +(3.77701 + 26.7345i) q^{27} +12.5797 q^{28} +(49.0949 - 8.65675i) q^{29} +(8.29685 - 5.32249i) q^{30} +(-27.8049 + 10.1202i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(1.03252 + 4.58892i) q^{33} +(30.9068 + 11.2492i) q^{34} +(-12.6559 + 7.30691i) q^{35} +(14.8095 + 10.2313i) q^{36} +(14.5999 - 25.2877i) q^{37} +(27.4132 + 32.6698i) q^{38} +(13.9731 - 18.3293i) q^{39} +(1.14114 - 6.47170i) q^{40} +(17.1669 + 3.02698i) q^{41} +(-21.2222 - 16.1784i) q^{42} +(-64.1027 + 53.7886i) q^{43} +(2.71565 + 1.56788i) q^{44} +(-20.8420 - 1.69120i) q^{45} +(15.9150 + 27.5656i) q^{46} +(11.3382 - 31.1513i) q^{47} +(11.7073 - 2.63417i) q^{48} +(-7.22958 - 6.06634i) q^{49} +(-9.48121 - 26.0494i) q^{50} +(-37.6730 - 58.7258i) q^{51} +(-2.66816 - 15.1319i) q^{52} +86.0360i q^{53} +(-11.8257 - 36.3064i) q^{54} -3.64280 q^{55} +(-17.5202 + 3.08928i) q^{56} +(-4.23087 - 90.3699i) q^{57} +(-66.2499 + 24.1130i) q^{58} +(29.2986 - 34.9167i) q^{59} +(-10.2482 + 9.45029i) q^{60} +(79.4407 + 28.9140i) q^{61} +(36.2395 - 20.9229i) q^{62} +(14.9956 + 54.5865i) q^{63} +(4.00000 - 6.92820i) q^{64} +(11.4736 + 13.6738i) q^{65} +(-2.56494 - 6.13756i) q^{66} +(-8.80100 + 49.9130i) q^{67} +(-45.8073 - 8.07706i) q^{68} +(8.60244 - 66.9715i) q^{69} +(15.8319 - 13.2845i) q^{70} +(-32.5457 - 18.7903i) q^{71} +(-23.1381 - 10.6125i) q^{72} +(-3.93896 - 6.82248i) q^{73} +(-14.1236 + 38.8043i) q^{74} +(-17.5064 + 56.1393i) q^{75} +(-46.2021 - 38.7682i) q^{76} +(3.37293 + 9.26704i) q^{77} +(-14.9594 + 28.9592i) q^{78} +(-12.5403 - 71.1198i) q^{79} +9.29356i q^{80} +(-26.7424 + 76.4581i) q^{81} -24.6521 q^{82} +(-25.4050 + 4.47959i) q^{83} +(33.5298 + 17.3205i) q^{84} +(50.7763 - 18.4811i) q^{85} +(76.0685 - 90.6549i) q^{86} +(142.776 + 44.5230i) q^{87} +(-4.16720 - 1.51674i) q^{88} +(-23.4923 + 13.5633i) q^{89} +(29.4426 - 2.76290i) q^{90} +(24.1615 - 41.8489i) q^{91} +(-28.9347 - 34.4831i) q^{92} +(-88.0448 - 11.3093i) q^{93} +(-8.14096 + 46.1697i) q^{94} +(69.0004 + 12.1666i) q^{95} +(-15.6582 + 6.54371i) q^{96} +(-27.0251 + 22.6768i) q^{97} +(11.5586 + 6.67336i) q^{98} +(-3.56624 + 13.6529i) 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
$3$	2.66538	+	1.37686i	0.888461	+	0.458952i
$3$	2.66538	+	1.37686i	0.888461	+	0.458952i
$4$	1.87939	−	0.684040i	0.469846	−	0.171010i
$5$	−1.49345	+	1.77982i	−0.298689	+	0.355964i	−0.894426	−	0.447216i	$-0.852416\pi$
$5$	−1.49345	+	1.77982i	−0.298689	+	0.355964i	0.595737	+	0.803180i	$0.296860\pi$
$6$	−4.05028	−	1.26303i	−0.675046	−	0.210506i
$7$	5.91054	+	2.15126i	0.844363	+	0.307323i	0.727740	−	0.685853i	$-0.240571\pi$
$7$	5.91054	+	2.15126i	0.844363	+	0.307323i	0.116623	+	0.993176i	$0.462793\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$	5.20853	+	7.33970i	0.578726	+	0.815522i
$10$	1.64289	−	2.84556i	0.164289	−	0.284556i
$11$	1.00782	+	1.20107i	0.0916196	+	0.109188i	0.809906	−	0.586559i	$-0.199518\pi$
$11$	1.00782	+	1.20107i	0.0916196	+	0.109188i	−0.718287	+	0.695747i	$0.755073\pi$
$12$	5.95111	+	0.764415i	0.495926	+	0.0637013i
$13$	1.33408	−	7.56595i	0.102622	−	0.581996i	−0.889522	−	0.456892i	$-0.848963\pi$
$13$	1.33408	−	7.56595i	0.102622	−	0.581996i	0.992144	−	0.125104i	$-0.0399264\pi$
$14$	−8.76008	−	1.54464i	−0.625720	−	0.110331i
$15$	−6.43117	+	2.68764i	−0.428744	+	0.179176i
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$	−20.1411	−	11.6285i	−1.18477	−	0.684028i	−0.227658	−	0.973741i	$-0.573107\pi$
$17$	−20.1411	−	11.6285i	−1.18477	−	0.684028i	−0.957114	+	0.289713i	$0.906440\pi$
$18$	−9.05652	−	8.94312i	−0.503140	−	0.496840i
$19$	−15.0781	−	26.1161i	−0.793586	−	1.37453i	−0.923733	−	0.383037i	$-0.874878\pi$
$19$	−15.0781	−	26.1161i	−0.793586	−	1.37453i	0.130147	−	0.991495i	$-0.458455\pi$
$20$	−1.58929	+	4.36655i	−0.0794646	+	0.218327i
$21$	12.7919	+	13.8719i	0.609137	+	0.660567i
$22$	−1.69857	−	1.42527i	−0.0772076	−	0.0647848i
$23$	−7.69793	−	21.1499i	−0.334693	−	0.919560i	−0.986873	−	0.161497i	$-0.948368\pi$
$23$	−7.69793	−	21.1499i	−0.334693	−	0.919560i	0.652181	−	0.758064i	$-0.273854\pi$
$24$	−8.47600	+	0.396823i	−0.353167	+	0.0165343i
$25$	3.40383	+	19.3041i	0.136153	+	0.772162i
$26$			10.8649i			0.417882i
$27$	3.77701	+	26.7345i	0.139889	+	0.990167i
$28$	12.5797			0.449276
$29$	49.0949	−	8.65675i	1.69293	−	0.298509i	0.757711	−	0.652590i	$-0.226318\pi$
$29$	49.0949	−	8.65675i	1.69293	−	0.298509i	0.935215	+	0.354081i	$0.115206\pi$
$30$	8.29685	−	5.32249i	0.276562	−	0.177416i
$31$	−27.8049	+	10.1202i	−0.896933	+	0.326457i	−0.749023	−	0.662544i	$-0.769477\pi$
$31$	−27.8049	+	10.1202i	−0.896933	+	0.326457i	−0.147910	+	0.989001i	$0.547255\pi$
$32$	−3.63616	+	4.33340i	−0.113630	+	0.135419i
$33$	1.03252	+	4.58892i	0.0312883	+	0.139058i
$34$	30.9068	+	11.2492i	0.909023	+	0.330857i
$35$	−12.6559	+	7.30691i	−0.361598	+	0.208769i
$36$	14.8095	+	10.2313i	0.411375	+	0.284202i
$37$	14.5999	−	25.2877i	0.394591	−	0.683452i	−0.598458	−	0.801154i	$-0.704220\pi$
$37$	14.5999	−	25.2877i	0.394591	−	0.683452i	0.993049	+	0.117702i	$0.0375529\pi$
$38$	27.4132	+	32.6698i	0.721401	+	0.859732i
$39$	13.9731	−	18.3293i	0.358284	−	0.469982i
$40$	1.14114	−	6.47170i	0.0285284	−	0.161793i
$41$	17.1669	+	3.02698i	0.418704	+	0.0738288i	0.379031	−	0.925384i	$-0.376257\pi$
$41$	17.1669	+	3.02698i	0.418704	+	0.0738288i	0.0396727	+	0.999213i	$0.487368\pi$
$42$	−21.2222	−	16.1784i	−0.505291	−	0.385201i
$43$	−64.1027	+	53.7886i	−1.49076	+	1.25090i	−0.597089	+	0.802175i	$0.703676\pi$
$43$	−64.1027	+	53.7886i	−1.49076	+	1.25090i	−0.893671	+	0.448722i	$0.851879\pi$
$44$	2.71565	+	1.56788i	0.0617194	+	0.0356337i
$45$	−20.8420	−	1.69120i	−0.463156	−	0.0375823i
$46$	15.9150	+	27.5656i	0.345979	+	0.599253i
$47$	11.3382	−	31.1513i	0.241237	−	0.662794i	−0.758698	−	0.651442i	$-0.774164\pi$
$47$	11.3382	−	31.1513i	0.241237	−	0.662794i	0.999936	−	0.0113518i	$-0.00361348\pi$
$48$	11.7073	−	2.63417i	0.243902	−	0.0548784i
$49$	−7.22958	−	6.06634i	−0.147543	−	0.123803i
$50$	−9.48121	−	26.0494i	−0.189624	−	0.520988i
$51$	−37.6730	−	58.7258i	−0.738687	−	1.15149i
$52$	−2.66816	−	15.1319i	−0.0513108	−	0.290998i
$53$			86.0360i			1.62332i	0.584130	+	0.811660i	$0.301436\pi$
$53$			86.0360i			1.62332i	−0.584130	+	0.811660i	$0.698564\pi$
$54$	−11.8257	−	36.3064i	−0.218994	−	0.672340i
$55$	−3.64280			−0.0662328
$56$	−17.5202	+	3.08928i	−0.312860	+	0.0551657i
$57$	−4.23087	−	90.3699i	−0.0742259	−	1.58544i
$58$	−66.2499	+	24.1130i	−1.14224	+	0.415741i
$59$	29.2986	−	34.9167i	0.496586	−	0.591809i	−0.458294	−	0.888801i	$-0.651539\pi$
$59$	29.2986	−	34.9167i	0.496586	−	0.591809i	0.954880	+	0.296992i	$0.0959836\pi$
$60$	−10.2482	+	9.45029i	−0.170803	+	0.157505i
$61$	79.4407	+	28.9140i	1.30231	+	0.474001i	0.897747	−	0.440511i	$-0.145203\pi$
$61$	79.4407	+	28.9140i	1.30231	+	0.474001i	0.404559	+	0.914512i	$0.367425\pi$
$62$	36.2395	−	20.9229i	0.584507	−	0.337465i
$63$	14.9956	+	54.5865i	0.238026	+	0.866453i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	11.4736	+	13.6738i	0.176518	+	0.210366i
$66$	−2.56494	−	6.13756i	−0.0388627	−	0.0929934i
$67$	−8.80100	+	49.9130i	−0.131358	+	0.744969i	0.845969	+	0.533233i	$0.179023\pi$
$67$	−8.80100	+	49.9130i	−0.131358	+	0.744969i	−0.977327	+	0.211737i	$0.932088\pi$
$68$	−45.8073	−	8.07706i	−0.673636	−	0.118780i
$69$	8.60244	−	66.9715i	0.124673	−	0.970601i
$70$	15.8319	−	13.2845i	0.226170	−	0.189779i
$71$	−32.5457	−	18.7903i	−0.458391	−	0.264652i	0.252977	−	0.967472i	$-0.418590\pi$
$71$	−32.5457	−	18.7903i	−0.458391	−	0.264652i	−0.711367	+	0.702820i	$0.751924\pi$
$72$	−23.1381	−	10.6125i	−0.321363	−	0.147397i
$73$	−3.93896	−	6.82248i	−0.0539584	−	0.0934587i	0.837785	−	0.546001i	$-0.183850\pi$
$73$	−3.93896	−	6.82248i	−0.0539584	−	0.0934587i	−0.891743	+	0.452542i	$0.850517\pi$
$74$	−14.1236	+	38.8043i	−0.190860	+	0.524383i
$75$	−17.5064	+	56.1393i	−0.233419	+	0.748524i
$76$	−46.2021	−	38.7682i	−0.607922	−	0.510107i
$77$	3.37293	+	9.26704i	0.0438042	+	0.120351i
$78$	−14.9594	+	28.9592i	−0.191788	+	0.371272i
$79$	−12.5403	−	71.1198i	−0.158738	−	0.900250i	−0.955288	−	0.295677i	$-0.904455\pi$
$79$	−12.5403	−	71.1198i	−0.158738	−	0.900250i	0.796550	−	0.604573i	$-0.206656\pi$
$80$			9.29356i			0.116170i
$81$	−26.7424	+	76.4581i	−0.330153	+	0.943927i
$82$	−24.6521			−0.300636
$83$	−25.4050	+	4.47959i	−0.306084	+	0.0539709i	−0.324581	−	0.945858i	$-0.605223\pi$
$83$	−25.4050	+	4.47959i	−0.306084	+	0.0539709i	0.0184964	+	0.999829i	$0.494112\pi$
$84$	33.5298	+	17.3205i	0.399164	+	0.206196i
$85$	50.7763	−	18.4811i	0.597368	−	0.217424i
$86$	76.0685	−	90.6549i	0.884518	−	1.05413i
$87$	142.776	+	44.5230i	1.64110	+	0.511759i
$88$	−4.16720	−	1.51674i	−0.0473545	−	0.0172356i
$89$	−23.4923	+	13.5633i	−0.263958	+	0.152396i	−0.626139	−	0.779712i	$-0.715366\pi$
$89$	−23.4923	+	13.5633i	−0.263958	+	0.152396i	0.362181	+	0.932108i	$0.382032\pi$
$90$	29.4426	−	2.76290i	0.327140	−	0.0306989i
$91$	24.1615	−	41.8489i	0.265511	−	0.459878i
$92$	−28.9347	−	34.4831i	−0.314508	−	0.374816i
$93$	−88.0448	−	11.3093i	−0.946718	−	0.121605i
$94$	−8.14096	+	46.1697i	−0.0866060	+	0.491167i
$95$	69.0004	+	12.1666i	0.726320	+	0.128070i
$96$	−15.6582	+	6.54371i	−0.163106	+	0.0681636i
$97$	−27.0251	+	22.6768i	−0.278610	+	0.233781i	−0.771375	−	0.636381i	$-0.780431\pi$
$97$	−27.0251	+	22.6768i	−0.278610	+	0.233781i	0.492765	+	0.870162i	$0.335986\pi$
$98$	11.5586	+	6.67336i	0.117945	+	0.0680955i
$99$	−3.56624	+	13.6529i	−0.0360226	+	0.137908i
$100$	19.6019	+	33.9514i	0.196019	+	0.339514i
$101$	−1.81805	+	4.99504i	−0.0180005	+	0.0494559i	−0.948367	−	0.317174i	$-0.897266\pi$
$101$	−1.81805	+	4.99504i	−0.0180005	+	0.0494559i	0.930367	+	0.366630i	$0.119488\pi$
$102$	66.8899	+	72.5375i	0.655784	+	0.711152i
$103$	51.6309	+	43.3235i	0.501271	+	0.420616i	0.858045	−	0.513574i	$-0.171679\pi$
$103$	51.6309	+	43.3235i	0.501271	+	0.420616i	−0.356774	+	0.934191i	$0.616123\pi$
$104$	7.43205	+	20.4194i	0.0714620	+	0.196340i
$105$	−43.7935	+	2.05029i	−0.417081	+	0.0195266i
$106$	−21.1283	−	119.825i	−0.199324	−	1.13042i
$107$		−	0.744883i		−	0.00696152i	−0.999994	−	0.00348076i	$-0.998892\pi$
$107$		−	0.744883i		−	0.00696152i	0.999994	−	0.00348076i	$-0.00110796\pi$
$108$	25.3859	+	47.6608i	0.235055	+	0.441304i
$109$	56.8674			0.521719			0.260859	−	0.965377i	$-0.415994\pi$
$109$	56.8674			0.521719			0.260859	+	0.965377i	$0.415994\pi$
$110$	5.07344	−	0.894584i	0.0461221	−	0.00813258i
$111$	73.7318	−	47.2995i	0.664251	−	0.426122i
$112$	23.6422	−	8.60505i	0.211091	−	0.0768308i
$113$	−137.389	+	163.733i	−1.21583	+	1.44897i	−0.359022	+	0.933329i	$0.616890\pi$
$113$	−137.389	+	163.733i	−1.21583	+	1.44897i	−0.856806	+	0.515638i	$0.827555\pi$
$114$	28.0851	+	124.822i	0.246360	+	1.09493i
$115$	49.1394	+	17.8853i	0.427300	+	0.155524i
$116$	86.3466	−	49.8522i	0.744367	−	0.429761i
$117$	62.4804	−	29.6157i	0.534020	−	0.253126i
$118$	−32.2303	+	55.8245i	−0.273138	+	0.473089i
$119$	−94.0291	−	112.059i	−0.790160	−	0.941676i
$120$	11.9522	−	15.6784i	0.0996015	−	0.130653i
$121$	20.5846	−	116.741i	0.170120	−	0.964800i
$122$	−117.740	−	20.7607i	−0.965081	−	0.170170i
$123$	41.5885	+	31.7044i	0.338118	+	0.257759i
$124$	−45.3336	+	38.0394i	−0.365593	+	0.306769i
$125$	−89.7441	−	51.8138i	−0.717953	−	0.414510i
$126$	−34.2900	−	72.3417i	−0.272142	−	0.574140i
$127$	−24.6922	−	42.7682i	−0.194427	−	0.336758i	0.752285	−	0.658837i	$-0.228951\pi$
$127$	−24.6922	−	42.7682i	−0.194427	−	0.336758i	−0.946713	+	0.322080i	$0.895618\pi$
$128$	−3.86952	+	10.6314i	−0.0302306	+	0.0830579i
$129$	−244.917	+	55.1068i	−1.89858	+	0.427185i
$130$	−19.3376	−	16.2262i	−0.148751	−	0.124817i
$131$	16.8555	+	46.3101i	0.128668	+	0.353513i	0.987253	−	0.159159i	$-0.0508782\pi$
$131$	16.8555	+	46.3101i	0.128668	+	0.353513i	−0.858585	+	0.512671i	$0.828656\pi$
$132$	5.07950	+	7.91807i	0.0384811	+	0.0599854i
$133$	−32.9374	−	186.797i	−0.247650	−	1.40449i
$134$		−	71.6765i		−	0.534899i
$135$	−53.2234	−	33.2042i	−0.394247	−	0.245957i
$136$	65.7806			0.483681
$137$	−133.137	+	23.4756i	−0.971801	+	0.171355i	−0.636940	−	0.770913i	$-0.719800\pi$
$137$	−133.137	+	23.4756i	−0.971801	+	0.171355i	−0.334860	+	0.942268i	$0.608689\pi$
$138$	4.46570	+	95.3856i	0.0323601	+	0.691200i
$139$	204.776	−	74.5324i	1.47321	−	0.536204i	0.524239	−	0.851571i	$-0.324350\pi$
$139$	204.776	−	74.5324i	1.47321	−	0.536204i	0.948970	+	0.315367i	$0.102128\pi$
$140$	−18.7872	+	22.3897i	−0.134194	+	0.159926i
$141$	73.1114	−	67.4192i	0.518521	−	0.478150i
$142$	49.9418	+	18.1773i	0.351703	+	0.128009i
$143$	10.4317	−	6.02276i	0.0729491	−	0.0421172i
$144$	34.8313	+	9.09824i	0.241884	+	0.0631822i
$145$	−57.9131	+	100.308i	−0.399401	+	0.691782i
$146$	7.16134	+	8.53455i	0.0490503	+	0.0584558i
$147$	−10.9171	−	26.1232i	−0.0742662	−	0.177709i
$148$	10.1410	−	57.5123i	0.0685201	−	0.388597i
$149$	69.7907	+	12.3060i	0.468394	+	0.0825905i	0.402864	−	0.915260i	$-0.368015\pi$
$149$	69.7907	+	12.3060i	0.468394	+	0.0825905i	0.0655305	+	0.997851i	$0.479126\pi$
$150$	10.5953	−	82.4859i	0.0706351	−	0.549906i
$151$	−202.069	+	169.556i	−1.33821	+	1.12289i	−0.356123	+	0.934439i	$0.615902\pi$
$151$	−202.069	+	169.556i	−1.33821	+	1.12289i	−0.982083	+	0.188449i	$0.939654\pi$
$152$	73.8675	+	42.6474i	0.485970	+	0.280575i
$153$	−19.5561	−	208.397i	−0.127817	−	1.36207i
$154$	−6.97333	−	12.0782i	−0.0452814	−	0.0784296i
$155$	23.5131	−	64.6017i	0.151697	−	0.416785i
$156$	13.7228	−	44.0060i	0.0879665	−	0.282089i
$157$	74.3308	+	62.3709i	0.473444	+	0.397267i	0.848049	−	0.529918i	$-0.177777\pi$
$157$	74.3308	+	62.3709i	0.473444	+	0.397267i	−0.374605	+	0.927185i	$0.622222\pi$
$158$	34.9306	+	95.9709i	0.221079	+	0.607411i
$159$	−118.459	+	229.319i	−0.745027	+	1.44226i
$160$	−2.28227	−	12.9434i	−0.0142642	−	0.0808963i
$161$		−	141.568i		−	0.879302i
$162$	18.4687	−	113.053i	0.114004	−	0.697856i
$163$	−166.799			−1.02331			−0.511654	−	0.859191i	$-0.670967\pi$
$163$	−166.799			−1.02331			−0.511654	+	0.859191i	$0.670967\pi$
$164$	34.3337	−	6.05396i	0.209352	−	0.0369144i
$165$	−9.70947	−	5.01562i	−0.0588452	−	0.0303977i
$166$	34.2822	−	12.4777i	0.206519	−	0.0751668i
$167$	−13.4784	+	16.0630i	−0.0807092	+	0.0961855i	−0.804888	−	0.593427i	$-0.797775\pi$
$167$	−13.4784	+	16.0630i	−0.0807092	+	0.0961855i	0.724179	+	0.689612i	$0.242219\pi$
$168$	−50.9514	−	15.8886i	−0.303282	−	0.0945753i
$169$	103.344	+	37.6142i	0.611505	+	0.222569i
$170$	−66.1791	+	38.2085i	−0.389289	+	0.224756i
$171$	113.149	−	246.696i	0.661693	−	1.44266i
$172$	−83.6801	+	144.938i	−0.486512	+	0.842664i
$173$	115.925	+	138.154i	0.670088	+	0.798580i	0.988796	−	0.149273i	$-0.0476934\pi$
$173$	115.925	+	138.154i	0.670088	+	0.798580i	−0.318708	+	0.947853i	$0.603249\pi$
$174$	−209.782	−	26.9463i	−1.20564	−	0.154864i
$175$	−21.4096	+	121.420i	−0.122341	+	0.693829i
$176$	6.17625	+	1.08904i	0.0350923	+	0.00618773i
$177$	126.167	−	52.7264i	0.712809	−	0.297889i
$178$	29.3876	−	24.6591i	0.165099	−	0.138534i
$179$	200.580	+	115.805i	1.12056	+	0.646955i	0.941544	−	0.336891i	$-0.109375\pi$
$179$	200.580	+	115.805i	1.12056	+	0.646955i	0.179016	+	0.983846i	$0.442709\pi$
$180$	−40.3270	+	11.0784i	−0.224039	+	0.0615464i
$181$	48.1236	+	83.3525i	0.265876	+	0.460511i	0.967793	−	0.251748i	$-0.0810054\pi$
$181$	48.1236	+	83.3525i	0.265876	+	0.460511i	−0.701917	+	0.712259i	$0.747672\pi$
$182$	−23.3733	+	64.2176i	−0.128425	+	0.352844i
$183$	171.929	+	186.445i	0.939505	+	1.01883i
$184$	48.7665	+	40.9199i	0.265035	+	0.222391i
$185$	23.2035	+	63.7510i	0.125424	+	0.344600i
$186$	125.400	−	5.87088i	0.674192	−	0.0315639i
$187$	−6.33194	−	35.9102i	−0.0338606	−	0.192033i
$188$		−	66.3011i		−	0.352665i
$189$	−35.1888	+	166.141i	−0.186184	+	0.879052i
$190$	−99.0866			−0.521509
$191$	95.7785	−	16.8883i	0.501458	−	0.0884206i	0.0828031	−	0.996566i	$-0.473613\pi$
$191$	95.7785	−	16.8883i	0.501458	−	0.0884206i	0.418655	+	0.908145i	$0.362502\pi$
$192$	20.2007	−	12.9589i	0.105212	−	0.0674942i
$193$	−46.9759	+	17.0978i	−0.243398	+	0.0885897i	−0.460839	−	0.887484i	$-0.652451\pi$
$193$	−46.9759	+	17.0978i	−0.243398	+	0.0885897i	0.217441	+	0.976074i	$0.430229\pi$
$194$	32.0698	−	38.2193i	0.165308	−	0.197007i
$195$	11.7549	+	52.2434i	0.0602813	+	0.267915i
$196$	−17.7368	−	6.45567i	−0.0904939	−	0.0329371i
$197$	229.122	−	132.284i	1.16306	−	0.671491i	0.211022	−	0.977481i	$-0.432321\pi$
$197$	229.122	−	132.284i	1.16306	−	0.671491i	0.952035	+	0.305991i	$0.0989876\pi$
$198$	1.61400	−	19.8905i	0.00815149	−	0.100457i
$199$	−66.9711	+	115.997i	−0.336538	+	0.582901i	−0.983779	−	0.179384i	$-0.942589\pi$
$199$	−66.9711	+	115.997i	−0.336538	+	0.582901i	0.647241	+	0.762285i	$0.275923\pi$
$200$	−35.6377	−	42.4714i	−0.178189	−	0.212357i
$201$	−92.1810	+	120.919i	−0.458612	+	0.601589i
$202$	1.30539	−	7.40321i	0.00646230	−	0.0366495i
$203$	308.800	+	54.4498i	1.52118	+	0.268226i
$204$	−110.973	−	84.5985i	−0.543985	−	0.414699i
$205$	−31.0253	+	26.0333i	−0.151343	+	0.126992i
$206$	−82.5471	−	47.6586i	−0.400714	−	0.231352i
$207$	115.139	−	166.660i	0.556227	−	0.805122i
$208$	−15.3653	−	26.6135i	−0.0738718	−	0.127950i
$209$	16.1712	−	44.4301i	0.0773743	−	0.212584i
$210$	60.4889	−	13.6101i	0.288043	−	0.0648101i
$211$	−51.7595	−	43.4314i	−0.245306	−	0.205836i	0.511842	−	0.859080i	$-0.328963\pi$
$211$	−51.7595	−	43.4314i	−0.245306	−	0.205836i	−0.757148	+	0.653244i	$0.773408\pi$
$212$	58.8521	+	161.695i	0.277604	+	0.762711i
$213$	−60.8753	−	94.8941i	−0.285800	−	0.445512i
$214$	0.182925	+	1.03742i	0.000854790	+	0.00484776i
$215$		−	194.422i		−	0.904287i
$216$	−47.0601	−	60.1444i	−0.217871	−	0.278446i
$217$	−186.113			−0.857665
$218$	−79.2008	+	13.9652i	−0.363306	+	0.0640607i
$219$	−1.10526	−	23.6079i	−0.00504685	−	0.107799i
$220$	−6.84623	+	2.49182i	−0.0311192	+	0.0113265i
$221$	−114.850	+	136.873i	−0.519685	+	0.619336i
$222$	−91.0728	+	83.9822i	−0.410238	+	0.378298i
$223$	−212.711	−	77.4206i	−0.953863	−	0.347178i	−0.182237	−	0.983255i	$-0.558334\pi$
$223$	−212.711	−	77.4206i	−0.953863	−	0.347178i	−0.771626	+	0.636077i	$0.780556\pi$
$224$	−30.8139	+	17.7904i	−0.137562	+	0.0794216i
$225$	−123.957	+	125.529i	−0.550920	+	0.557906i
$226$	151.136	−	261.775i	0.668744	−	1.15830i
$227$	−166.065	−	197.909i	−0.731565	−	0.871845i	0.264135	−	0.964486i	$-0.414914\pi$
$227$	−166.065	−	197.909i	−0.731565	−	0.871845i	−0.995700	+	0.0926409i	$0.970469\pi$
$228$	−69.7681	−	166.946i	−0.306000	−	0.732218i
$229$	9.32712	−	52.8967i	0.0407298	−	0.230990i	−0.957647	−	0.287945i	$-0.907028\pi$
$229$	9.32712	−	52.8967i	0.0407298	−	0.230990i	0.998377	+	0.0569548i	$0.0181391\pi$
$230$	−72.8301	−	12.8419i	−0.316653	−	0.0558344i
$231$	−3.76925	+	29.3442i	−0.0163171	+	0.127031i
$232$	−108.015	+	90.6352i	−0.465581	+	0.390669i
$233$	93.1740	+	53.7940i	0.399888	+	0.230876i	0.686436	−	0.727190i	$-0.259174\pi$
$233$	93.1740	+	53.7940i	0.399888	+	0.230876i	−0.286547	+	0.958066i	$0.592508\pi$
$234$	−79.7453	+	56.5903i	−0.340792	+	0.241839i
$235$	38.5108	+	66.7027i	0.163876	+	0.283841i
$236$	31.1789	−	85.6634i	0.132114	−	0.362980i
$237$	64.4969	−	206.828i	0.272139	−	0.872690i
$238$	158.476	+	132.977i	0.665866	+	0.558728i
$239$	−152.119	−	417.943i	−0.636480	−	1.74872i	−0.662509	−	0.749054i	$-0.730508\pi$
$239$	−152.119	−	417.943i	−0.636480	−	1.74872i	0.0260287	−	0.999661i	$-0.491714\pi$
$240$	−12.7959	+	24.7709i	−0.0533163	+	0.103212i
$241$	−35.4521	−	201.059i	−0.147104	−	0.834269i	−0.965654	−	0.259833i	$-0.916333\pi$
$241$	−35.4521	−	201.059i	−0.147104	−	0.834269i	0.818549	−	0.574436i	$-0.194779\pi$
$242$			167.643i			0.692741i
$243$	−176.551	+	166.970i	−0.726546	+	0.687118i
$244$	169.078			0.692943
$245$	21.5940	−	3.80760i	0.0881388	−	0.0155412i
$246$	−65.7073	−	33.9424i	−0.267103	−	0.137977i
$247$	−217.709	+	79.2394i	−0.881411	+	0.320807i
$248$	53.7958	−	64.1114i	0.216919	−	0.258514i
$249$	−73.8818	−	23.0392i	−0.296714	−	0.0925270i
$250$	137.713	+	50.1236i	0.550853	+	0.200494i
$251$	−298.670	+	172.437i	−1.18992	+	0.687000i	−0.958288	−	0.285803i	$-0.907740\pi$
$251$	−298.670	+	172.437i	−1.18992	+	0.687000i	−0.231631	+	0.972804i	$0.574406\pi$
$252$	65.5219	+	92.3315i	0.260008	+	0.366395i
$253$	17.6444	−	30.5609i	0.0697405	−	0.120794i
$254$	44.8924	+	53.5007i	0.176742	+	0.210633i
$255$	160.784	+	20.6526i	0.630526	+	0.0809906i
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	−179.971	−	31.7338i	−0.700278	−	0.123478i	−0.187837	−	0.982200i	$-0.560148\pi$
$257$	−179.971	−	31.7338i	−0.700278	−	0.123478i	−0.512441	+	0.858722i	$0.671259\pi$
$258$	327.571	−	136.895i	1.26965	−	0.530599i
$259$	140.694	−	118.056i	0.543219	−	0.455815i
$260$	30.9168	+	17.8498i	0.118911	+	0.0686532i
$261$	319.250	+	315.253i	1.22318	+	1.20786i
$262$	−34.8478	−	60.3582i	−0.133007	−	0.230375i
$263$	−88.5587	+	243.313i	−0.336725	+	0.925144i	0.649592	+	0.760283i	$0.274940\pi$
$263$	−88.5587	+	243.313i	−0.336725	+	0.925144i	−0.986317	+	0.164861i	$0.947282\pi$
$264$	−9.01885	−	9.78032i	−0.0341623	−	0.0370467i
$265$	−153.129	−	128.490i	−0.577844	−	0.484869i
$266$	91.7458	+	252.069i	0.344909	+	0.947629i
$267$	−81.2906	+	3.80581i	−0.304459	+	0.0142540i
$268$	17.6020	+	99.8259i	0.0656791	+	0.372485i
$269$		−	152.516i		−	0.566974i	−0.958976	−	0.283487i	$-0.908509\pi$
$269$		−	152.516i		−	0.566974i	0.958976	−	0.283487i	$-0.0914913\pi$
$270$	82.2799	+	33.1740i	0.304740	+	0.122867i
$271$	352.593			1.30108			0.650541	−	0.759471i	$-0.274542\pi$
$271$	352.593			1.30108			0.650541	+	0.759471i	$0.274542\pi$
$272$	−91.6146	+	16.1541i	−0.336818	+	0.0593901i
$273$	122.020	−	78.2764i	0.446958	−	0.286727i
$274$	179.658	−	65.3903i	0.655687	−	0.238651i
$275$	−19.7551	+	23.5432i	−0.0718366	+	0.0856115i
$276$	−29.6439	−	131.750i	−0.107405	−	0.477354i
$277$	318.950	+	116.088i	1.15145	+	0.419092i	0.846034	−	0.533129i	$-0.178984\pi$
$277$	318.950	+	116.088i	1.15145	+	0.419092i	0.305411	+	0.952221i	$0.401206\pi$
$278$	−266.894	+	154.091i	−0.960051	+	0.554286i
$279$	−219.102	−	151.369i	−0.785311	−	0.542540i
$280$	20.6671	−	35.7964i	0.0738109	−	0.127844i
$281$	184.637	+	220.042i	0.657072	+	0.783067i	0.986962	−	0.160952i	$-0.0514563\pi$
$281$	184.637	+	220.042i	0.657072	+	0.783067i	−0.329891	+	0.944019i	$0.607012\pi$
$282$	−85.2679	+	111.851i	−0.302368	+	0.396635i
$283$	21.4854	−	121.850i	0.0759202	−	0.430565i	−0.923029	−	0.384731i	$-0.874294\pi$
$283$	21.4854	−	121.850i	0.0759202	−	0.430565i	0.998949	−	0.0458341i	$-0.0145946\pi$
$284$	−74.0193	−	13.0516i	−0.260631	−	0.0459563i
$285$	167.161	+	127.432i	0.586529	+	0.447131i
$286$	−13.0495	+	10.9498i	−0.0456277	+	0.0382862i
$287$	94.9536	+	54.8215i	0.330849	+	0.191016i
$288$	−50.7449	−	4.11764i	−0.176198	−	0.0142974i
$289$	125.943	+	218.140i	0.435790	+	0.754810i
$290$	56.0239	−	153.924i	0.193186	−	0.530774i
$291$	−103.255	+	23.2326i	−0.354828	+	0.0798370i
$292$	−12.0697	−	10.1277i	−0.0413345	−	0.0346838i
$293$	−172.243	−	473.234i	−0.587861	−	1.61513i	−0.774407	−	0.632688i	$-0.781952\pi$
$293$	−172.243	−	473.234i	−0.587861	−	1.61513i	0.186547	−	0.982446i	$-0.440270\pi$
$294$	21.6198	+	33.7016i	0.0735368	+	0.114631i
$295$	18.3896	+	104.292i	0.0623376	+	0.353534i
$296$			82.5894i			0.279018i
$297$	−28.3034	+	31.4799i	−0.0952978	+	0.105993i
$298$	−100.222			−0.336314
$299$	−170.289	+	30.0265i	−0.569527	+	0.100423i
$300$	5.50021	+	117.482i	0.0183340	+	0.391608i
$301$	−494.595	+	180.018i	−1.64317	+	0.598066i
$302$	239.789	−	285.769i	0.794002	−	0.946255i
$303$	−11.7233	+	10.8105i	−0.0386906	+	0.0356783i
$304$	−113.351	−	41.2562i	−0.372864	−	0.135711i
$305$	−170.102	+	98.2086i	−0.557712	+	0.321995i
$306$	78.4135	+	285.438i	0.256253	+	0.932804i
$307$	303.015	−	524.837i	0.987018	−	1.70957i	0.354417	−	0.935087i	$-0.384679\pi$
$307$	303.015	−	524.837i	0.987018	−	1.70957i	0.632601	−	0.774478i	$-0.281987\pi$
$308$	12.6781	+	15.1091i	0.0411625	+	0.0490556i
$309$	77.9659	+	186.562i	0.252317	+	0.603761i
$310$	−16.8828	+	95.7469i	−0.0544605	+	0.308861i
$311$	−112.127	−	19.7711i	−0.360538	−	0.0635725i	−0.00955468	−	0.999954i	$-0.503041\pi$
$311$	−112.127	−	19.7711i	−0.360538	−	0.0635725i	−0.350983	+	0.936382i	$0.614153\pi$
$312$	−8.30532	+	64.6583i	−0.0266196	+	0.207238i
$313$	391.591	−	328.584i	1.25109	−	1.04979i	0.254516	−	0.967069i	$-0.418084\pi$
$313$	391.591	−	328.584i	1.25109	−	1.04979i	0.996573	−	0.0827197i	$-0.0263606\pi$
$314$	−118.839	−	68.6119i	−0.378469	−	0.218509i
$315$	−119.549	−	54.8326i	−0.379522	−	0.174072i
$316$	−72.2169	−	125.083i	−0.228534	−	0.395833i
$317$	−13.2129	+	36.3021i	−0.0416810	+	0.114518i	−0.958787	−	0.284126i	$-0.908297\pi$
$317$	−13.2129	+	36.3021i	−0.0416810	+	0.114518i	0.917106	+	0.398643i	$0.130519\pi$
$318$	108.666	−	348.470i	0.341718	−	1.09582i
$319$	59.8759	+	50.2418i	0.187699	+	0.157498i
$320$	6.35717	+	17.4662i	0.0198662	+	0.0545818i
$321$	1.02560	−	1.98540i	0.00319501	−	0.00618504i
$322$	34.7655	+	197.165i	0.107968	+	0.612314i
$323$			701.344i			2.17134i
$324$	2.04110	+	161.987i	0.00629969	+	0.499960i
$325$	150.594			0.463368
$326$	232.306	−	40.9618i	0.712595	−	0.125650i
$327$	151.573	+	78.2982i	0.463527	+	0.239444i
$328$	−46.3308	+	16.8630i	−0.141253	+	0.0514117i
$329$	134.029	−	159.730i	0.407384	−	0.485501i
$330$	14.7544	+	4.60099i	0.0447102	+	0.0139424i
$331$	−99.6998	−	36.2878i	−0.301208	−	0.109631i	0.186995	−	0.982361i	$-0.440125\pi$
$331$	−99.6998	−	36.2878i	−0.301208	−	0.109631i	−0.488203	+	0.872730i	$0.662347\pi$
$332$	−44.6815	+	25.7969i	−0.134583	+	0.0777015i
$333$	261.648	−	24.5532i	0.785731	−	0.0737332i
$334$	14.8271	−	25.6814i	0.0443926	−	0.0768903i
$335$	−75.6923	−	90.2065i	−0.225947	−	0.269273i
$336$	74.8634	+	9.61615i	0.222808	+	0.0286195i
$337$	−0.873000	+	4.95103i	−0.00259051	+	0.0146915i	−0.986076	−	0.166298i	$-0.946819\pi$
$337$	−0.873000	+	4.95103i	−0.00259051	+	0.0146915i	0.983485	+	0.180989i	$0.0579299\pi$
$338$	−153.168	−	27.0076i	−0.453159	−	0.0799041i
$339$	−591.630	+	247.248i	−1.74522	+	0.729344i
$340$	82.7864	−	69.4661i	0.243490	−	0.204312i
$341$	−40.1772	−	23.1963i	−0.117822	−	0.0680245i
$342$	−97.0041	+	371.367i	−0.283638	+	1.08587i
$343$	−183.782	−	318.320i	−0.535808	−	0.928047i
$344$	80.9504	−	222.409i	0.235321	−	0.646539i
$345$	106.350	+	115.329i	0.308261	+	0.334287i
$346$	−195.380	−	163.943i	−0.564681	−	0.473824i
$347$	−77.4742	−	212.859i	−0.223268	−	0.613425i	0.776594	−	0.630001i	$-0.216946\pi$
$347$	−77.4742	−	212.859i	−0.223268	−	0.613425i	−0.999863	+	0.0165761i	$0.994723\pi$
$348$	298.786	−	13.9884i	0.858581	−	0.0401964i
$349$	85.4880	+	484.827i	0.244951	+	1.38919i	0.820606	+	0.571495i	$0.193636\pi$
$349$	85.4880	+	484.827i	0.244951	+	1.38919i	−0.575655	+	0.817693i	$0.695253\pi$
$350$		−	174.363i		−	0.498179i
$351$	207.311	+	7.08936i	0.590629	+	0.0201976i
$352$	−8.86928			−0.0251968
$353$	440.404	−	77.6551i	1.24760	−	0.219986i	0.489432	−	0.872042i	$-0.337204\pi$
$353$	440.404	−	77.6551i	1.24760	−	0.219986i	0.758171	+	0.652056i	$0.226093\pi$
$354$	−162.768	+	104.417i	−0.459798	+	0.294964i
$355$	82.0487	−	29.8633i	0.231123	−	0.0841219i
$356$	−34.8732	+	41.5603i	−0.0979585	+	0.116742i
$357$	−96.3336	−	428.146i	−0.269842	−	1.19929i
$358$	−307.793	−	112.027i	−0.859756	−	0.312926i
$359$	62.2367	−	35.9324i	0.173361	−	0.100090i	−0.410809	−	0.911722i	$-0.634754\pi$
$359$	62.2367	−	35.9324i	0.173361	−	0.100090i	0.584170	+	0.811631i	$0.301420\pi$
$360$	53.4440	−	25.3325i	0.148456	−	0.0703680i
$361$	−274.201	+	474.930i	−0.759559	+	1.31559i
$362$	−87.4925	−	104.269i	−0.241692	−	0.288037i
$363$	215.601	−	282.817i	0.593943	−	0.779110i
$364$	16.7824	−	95.1776i	0.0461054	−	0.261477i
$365$	18.0254	+	3.17837i	0.0493847	+	0.00870786i
$366$	−285.237	−	217.446i	−0.779337	−	0.594115i
$367$	−106.401	+	89.2809i	−0.289920	+	0.243272i	−0.776134	−	0.630568i	$-0.782822\pi$
$367$	−106.401	+	89.2809i	−0.289920	+	0.243272i	0.486214	+	0.873840i	$0.338378\pi$
$368$	−77.9674	−	45.0145i	−0.211868	−	0.122322i
$369$	67.1970	+	141.766i	0.182106	+	0.384189i
$370$	−47.9718	−	83.0897i	−0.129654	−	0.224567i
$371$	−185.086	+	508.519i	−0.498884	+	1.37067i
$372$	−173.206	+	38.9717i	−0.465608	+	0.104763i
$373$	−498.940	−	418.661i	−1.33764	−	1.12241i	−0.982225	−	0.187706i	$-0.939895\pi$
$373$	−498.940	−	418.661i	−1.33764	−	1.12241i	−0.355416	−	0.934708i	$-0.615661\pi$
$374$	17.6373	+	48.4582i	0.0471587	+	0.129567i
$375$	−167.862	−	261.668i	−0.447632	−	0.697782i
$376$	16.2819	+	92.3394i	0.0433030	+	0.245584i
$377$		−	382.998i		−	1.01591i
$378$	8.20827	−	240.031i	0.0217150	−	0.635001i
$379$	379.153			1.00040			0.500202	−	0.865909i	$-0.333259\pi$
$379$	379.153			1.00040			0.500202	+	0.865909i	$0.333259\pi$
$380$	138.001	−	24.3333i	0.363160	−	0.0640349i
$381$	−6.92856	−	147.991i	−0.0181852	−	0.388429i
$382$	−129.246	+	47.0417i	−0.338341	+	0.123146i
$383$	103.347	−	123.164i	0.269835	−	0.321577i	−0.614062	−	0.789258i	$-0.710466\pi$
$383$	103.347	−	123.164i	0.269835	−	0.321577i	0.883898	+	0.467680i	$0.154910\pi$
$384$	−24.9517	+	23.0090i	−0.0649783	+	0.0599193i
$385$	−21.5309	−	7.83662i	−0.0559245	−	0.0203549i
$386$	61.2258	−	35.3487i	0.158616	−	0.0915771i
$387$	−728.673	−	190.335i	−1.88288	−	0.491823i
$388$	−35.2788	+	61.1047i	−0.0909248	+	0.157486i
$389$	255.119	+	304.040i	0.655834	+	0.781593i	0.986781	−	0.162057i	$-0.0518127\pi$
$389$	255.119	+	304.040i	0.655834	+	0.781593i	−0.330947	+	0.943649i	$0.607368\pi$
$390$	−29.2010	−	69.8741i	−0.0748744	−	0.179164i
$391$	−90.8961	+	515.498i	−0.232471	+	1.31841i
$392$	26.2879	+	4.63527i	0.0670610	+	0.0118247i
$393$	−18.8360	+	146.642i	−0.0479289	+	0.373135i
$394$	−286.619	+	240.502i	−0.727460	+	0.610411i
$395$	145.309	+	83.8940i	0.367870	+	0.212390i
$396$	2.63677	+	28.0984i	0.00665850	+	0.0709557i
$397$	−19.8819	−	34.4365i	−0.0500804	−	0.0867418i	0.839898	−	0.542744i	$-0.182614\pi$
$397$	−19.8819	−	34.4365i	−0.0500804	−	0.0867418i	−0.889979	+	0.456002i	$0.849281\pi$
$398$	64.7864	−	177.999i	0.162780	−	0.447234i
$399$	169.402	−	543.237i	0.424568	−	1.36150i
$400$	60.0636	+	50.3993i	0.150159	+	0.125998i
$401$	151.169	+	415.334i	0.376981	+	1.03575i	0.972601	+	0.232480i	$0.0746842\pi$
$401$	151.169	+	415.334i	0.376981	+	1.03575i	−0.595620	+	0.803266i	$0.703094\pi$
$402$	98.6883	−	191.045i	0.245493	−	0.475237i
$403$	39.4746	+	223.872i	0.0979519	+	0.555513i
$404$			10.6312i			0.0263149i
$405$	−96.1433	−	161.783i	−0.237391	−	0.399464i
$406$	−443.446			−1.09223
$407$	45.0863	−	7.94992i	0.110777	−	0.0195330i
$408$	175.331	+	90.5705i	0.429732	+	0.221987i
$409$	130.597	−	47.5333i	0.319307	−	0.116218i	−0.177394	−	0.984140i	$-0.556767\pi$
$409$	130.597	−	47.5333i	0.319307	−	0.116218i	0.496701	+	0.867922i	$0.334544\pi$
$410$	36.8166	−	43.8764i	0.0897967	−	0.107015i
$411$	−387.183	−	120.739i	−0.942051	−	0.293768i
$412$	126.669	+	46.1039i	0.307450	+	0.111903i
$413$	248.286	−	143.348i	0.601176	−	0.347089i
$414$	−119.430	+	260.388i	−0.288477	+	0.628956i
$415$	29.9681	−	51.9063i	0.0722124	−	0.125076i
$416$	27.9354	+	33.2921i	0.0671523	+	0.0800290i
$417$	648.427	+	83.2900i	1.55498	+	0.199736i
$418$	−11.6112	+	65.8503i	−0.0277780	+	0.157537i
$419$	67.2764	+	11.8626i	0.160564	+	0.0283118i	0.253352	−	0.967374i	$-0.418467\pi$
$419$	67.2764	+	11.8626i	0.160564	+	0.0283118i	−0.0927881	+	0.995686i	$0.529578\pi$
$420$	−80.9024	+	33.8098i	−0.192625	+	0.0804995i
$421$	266.680	−	223.771i	0.633444	−	0.531522i	−0.268553	−	0.963265i	$-0.586546\pi$
$421$	266.680	−	223.771i	0.633444	−	0.531522i	0.901997	+	0.431742i	$0.142101\pi$
$422$	82.7527	+	47.7773i	0.196096	+	0.113216i
$423$	287.696	−	79.0339i	0.680134	−	0.186841i
$424$	−121.673	−	210.744i	−0.286965	−	0.497038i
$425$	155.920	−	428.387i	0.366871	−	1.00797i
$426$	108.086	+	117.212i	0.253724	+	0.275146i
$427$	407.336	+	341.795i	0.953948	+	0.800458i
$428$	−0.509530	−	1.39992i	−0.00119049	−	0.00327085i
$429$	36.0970	−	1.68996i	0.0841422	−	0.00393931i
$430$	47.7452	+	270.777i	0.111035	+	0.629713i
$431$			350.668i			0.813615i	0.913514	+	0.406807i	$0.133358\pi$
$431$			350.668i			0.813615i	−0.913514	+	0.406807i	$0.866642\pi$
$432$	80.3119	+	72.2080i	0.185907	+	0.167148i
$433$	−177.240			−0.409330			−0.204665	−	0.978832i	$-0.565610\pi$
$433$	−177.240			−0.409330			−0.204665	+	0.978832i	$0.565610\pi$
$434$	259.205	−	45.7049i	0.597247	−	0.105311i
$435$	−292.471	+	187.622i	−0.672347	+	0.431316i
$436$	106.876	−	38.8996i	0.245128	−	0.0892192i
$437$	−436.282	+	519.941i	−0.998357	+	1.18980i
$438$	7.33685	+	32.6080i	0.0167508	+	0.0744475i
$439$	2.67961	+	0.975298i	0.00610389	+	0.00222163i	0.345070	−	0.938577i	$-0.387855\pi$
$439$	2.67961	+	0.975298i	0.00610389	+	0.00222163i	−0.338966	+	0.940798i	$0.610077\pi$
$440$	8.92301	−	5.15170i	0.0202796	−	0.0117084i
$441$	6.86963	−	84.6597i	0.0155774	−	0.191972i
$442$	126.343	−	218.832i	0.285843	−	0.495095i
$443$	343.331	+	409.166i	0.775014	+	0.923626i	0.998697	−	0.0510363i	$-0.0162524\pi$
$443$	343.331	+	409.166i	0.775014	+	0.923626i	−0.223683	+	0.974662i	$0.571808\pi$
$444$	106.216	−	139.330i	0.239225	−	0.313805i
$445$	10.9443	−	62.0681i	0.0245939	−	0.139479i
$446$	315.262	+	55.5892i	0.706865	+	0.124639i
$447$	169.075	+	128.892i	0.378245	+	0.288349i
$448$	38.5466	−	32.3444i	0.0860414	−	0.0721973i
$449$	−573.148	−	330.907i	−1.27650	−	0.736987i	−0.300296	−	0.953846i	$-0.597085\pi$
$449$	−573.148	−	330.907i	−1.27650	−	0.736987i	−0.976203	+	0.216859i	$0.930419\pi$
$450$	141.812	−	205.268i	0.315137	−	0.456152i
$451$	13.6654	+	23.6692i	0.0303003	+	0.0524816i
$452$	−146.206	+	401.697i	−0.323464	+	0.888711i
$453$	−772.046	+	173.712i	−1.70430	+	0.383470i
$454$	279.885	+	234.852i	0.616487	+	0.517294i
$455$	38.3997	+	105.502i	0.0843948	+	0.231873i
$456$	138.166	+	215.377i	0.302995	+	0.472317i
$457$	106.695	+	605.098i	0.233468	+	1.32407i	0.845815	+	0.533476i	$0.179115\pi$
$457$	106.695	+	605.098i	0.233468	+	1.32407i	−0.612347	+	0.790589i	$0.709774\pi$
$458$			75.9613i			0.165854i
$459$	234.809	−	582.384i	0.511566	−	1.26881i
$460$	104.586			0.227361
$461$	−397.986	+	70.1756i	−0.863310	+	0.152225i	−0.587734	−	0.809054i	$-0.699980\pi$
$461$	−397.986	+	70.1756i	−0.863310	+	0.152225i	−0.275576	+	0.961279i	$0.588869\pi$
$462$	−1.95669	−	41.7942i	−0.00423526	−	0.0904636i
$463$	390.527	−	142.140i	0.843470	−	0.306998i	0.116095	−	0.993238i	$-0.462962\pi$
$463$	390.527	−	142.140i	0.843470	−	0.306998i	0.727375	+	0.686240i	$0.240740\pi$
$464$	128.178	−	152.756i	0.276245	−	0.329216i
$465$	151.619	−	139.814i	0.326062	−	0.300676i
$466$	−142.977	−	52.0392i	−0.306817	−	0.111672i
$467$	161.324	−	93.1404i	0.345448	−	0.199444i	−0.317231	−	0.948348i	$-0.602753\pi$
$467$	161.324	−	93.1404i	0.345448	−	0.199444i	0.662678	+	0.748904i	$0.269420\pi$
$468$	97.1664	−	98.3984i	0.207620	−	0.210253i
$469$	−159.395	+	276.079i	−0.339860	+	0.588655i
$470$	−70.0157	−	83.4414i	−0.148970	−	0.177535i
$471$	112.244	+	268.585i	0.238310	+	0.570245i
$472$	−22.3869	+	126.963i	−0.0474299	+	0.268989i
$473$	−129.207	−	22.7828i	−0.273166	−	0.0481665i
$474$	−39.0349	+	303.894i	−0.0823521	+	0.641126i
$475$	452.824	−	379.964i	0.953313	−	0.799924i
$476$	−253.370	−	146.283i	−0.532290	−	0.307318i
$477$	−631.478	+	448.121i	−1.32385	+	0.939457i
$478$	314.497	+	544.724i	0.657943	+	1.13959i
$479$	117.100	−	321.729i	0.244467	−	0.671668i	−0.755398	−	0.655266i	$-0.772557\pi$
$479$	117.100	−	321.729i	0.244467	−	0.671668i	0.999865	−	0.0164023i	$-0.00522124\pi$
$480$	11.7381	−	37.6415i	0.0244544	−	0.0784198i
$481$	−171.848	−	144.198i	−0.357273	−	0.299787i
$482$	98.7503	+	271.314i	0.204876	+	0.562892i
$483$	194.918	−	377.332i	0.403558	−	0.781225i
$484$	−41.1691	−	233.482i	−0.0850602	−	0.482400i
$485$		−	81.9665i		−	0.169003i
$486$	204.884	−	275.900i	0.421571	−	0.567695i
$487$	−483.112			−0.992016			−0.496008	−	0.868318i	$-0.665201\pi$
$487$	−483.112			−0.992016			−0.496008	+	0.868318i	$0.665201\pi$
$488$	−235.480	+	41.5214i	−0.482541	+	0.0850849i
$489$	−444.584	−	229.659i	−0.909169	−	0.469650i
$490$	−29.1395	+	10.6059i	−0.0594684	+	0.0216447i
$491$	−160.343	+	191.089i	−0.326564	+	0.389184i	−0.904199	−	0.427111i	$-0.859531\pi$
$491$	−160.343	+	191.089i	−0.326564	+	0.389184i	0.577635	+	0.816295i	$0.303976\pi$
$492$	99.8479	+	31.1365i	0.202943	+	0.0632855i
$493$	−1089.49	−	396.542i	−2.20992	−	0.804345i
$494$	283.750	−	163.823i	0.574392	−	0.331625i
$495$	−18.9737	−	26.7371i	−0.0383306	−	0.0540143i
$496$	−59.1788	+	102.501i	−0.119312	+	0.206655i
$497$	−151.940	−	181.075i	−0.305715	−	0.364336i
$498$	108.555	+	13.9438i	0.217982	+	0.0279997i
$499$	57.5888	−	326.602i	0.115408	−	0.654513i	−0.871139	−	0.491037i	$-0.836618\pi$
$499$	57.5888	−	326.602i	0.115408	−	0.654513i	0.986547	−	0.163476i	$-0.0522708\pi$
$500$	−204.106	−	35.9895i	−0.408213	−	0.0719789i
$501$	−58.0416	+	24.2561i	−0.115852	+	0.0484154i
$502$	373.620	−	313.504i	0.744262	−	0.624510i
$503$	−212.097	−	122.454i	−0.421664	−	0.243448i	0.274125	−	0.961694i	$-0.411612\pi$
$503$	−212.097	−	122.454i	−0.421664	−	0.243448i	−0.695789	+	0.718246i	$0.744945\pi$
$504$	−113.929	−	112.502i	−0.226049	−	0.223219i
$505$	−6.17512	−	10.6956i	−0.0122280	−	0.0211795i
$506$	−17.0688	+	46.8961i	−0.0337328	+	0.0926800i
$507$	223.663	+	242.547i	0.441149	+	0.478396i
$508$	−75.6614	−	63.4875i	−0.148940	−	0.124975i
$509$	−302.898	−	832.205i	−0.595084	−	1.63498i	−0.760934	−	0.648829i	$-0.775259\pi$
$509$	−302.898	−	832.205i	−0.595084	−	1.63498i	0.165850	−	0.986151i	$-0.446963\pi$
$510$	−229.000	+	10.7212i	−0.449020	+	0.0210219i
$511$	−8.60446	−	48.7983i	−0.0168385	−	0.0954957i
$512$			22.6274i			0.0441942i
$513$	641.251	−	501.747i	1.25000	−	0.978065i
$514$	258.444			0.502810
$515$	−154.216	+	27.1925i	−0.299449	+	0.0528009i
$516$	−422.599	+	271.100i	−0.818990	+	0.525388i
$517$	48.8416	−	17.7769i	0.0944712	−	0.0343847i
$518$	−166.956	+	198.971i	−0.322310	+	0.384114i
$519$	118.766	+	527.846i	0.228837	+	1.01705i
$520$	−47.4422	−	17.2675i	−0.0912350	−	0.0332068i
$521$	285.381	−	164.765i	0.547756	−	0.316247i	−0.200461	−	0.979702i	$-0.564244\pi$
$521$	285.381	−	164.765i	0.547756	−	0.316247i	0.748216	+	0.663455i	$0.230911\pi$
$522$	−522.047	−	360.661i	−1.00009	−	0.690922i
$523$	145.262	−	251.600i	0.277747	−	0.481071i	−0.693078	−	0.720863i	$-0.743746\pi$
$523$	145.262	−	251.600i	0.277747	−	0.481071i	0.970824	+	0.239791i	$0.0770791\pi$
$524$	63.3560	+	75.5048i	0.120908	+	0.144093i
$525$	−224.243	+	294.153i	−0.427129	+	0.560291i
$526$	63.5865	−	360.617i	0.120887	−	0.685583i
$527$	677.705	+	119.498i	1.28597	+	0.226751i
$528$	14.9626	+	11.4065i	0.0283383	+	0.0216033i
$529$	17.1780	−	14.4140i	0.0324726	−	0.0272477i
$530$	244.821	+	141.347i	0.461926	+	0.266693i
$531$	408.881	+	33.1782i	0.770020	+	0.0624825i
$532$	−189.679	−	328.534i	−0.356540	−	0.617545i
$533$	45.8039	−	125.845i	0.0859361	−	0.236107i
$534$	112.281	−	25.2634i	0.210264	−	0.0473098i
$535$	1.32576	+	1.11244i	0.00247805	+	0.00207933i
$536$	−49.0296	−	134.708i	−0.0914732	−	0.251320i
$537$	375.176	+	584.835i	0.698652	+	1.08908i
$538$	37.4542	+	212.413i	0.0696175	+	0.394820i
$539$		−	14.7970i		−	0.0274526i
$540$	−122.740	−	25.9965i	−0.227297	−	0.0481417i
$541$	−385.680			−0.712901			−0.356451	−	0.934314i	$-0.616013\pi$
$541$	−385.680			−0.712901			−0.356451	+	0.934314i	$0.616013\pi$
$542$	−491.067	+	86.5883i	−0.906027	+	0.159757i
$543$	13.5033	+	288.426i	0.0248680	+	0.531171i
$544$	123.627	−	44.9966i	0.227256	−	0.0827143i
$545$	−84.9284	+	101.214i	−0.155832	+	0.185713i
$546$	−150.717	+	138.983i	−0.276039	+	0.254547i
$547$	−621.520	−	226.215i	−1.13623	−	0.413556i	−0.295683	−	0.955286i	$-0.595547\pi$
$547$	−621.520	−	226.215i	−1.13623	−	0.413556i	−0.840552	+	0.541731i	$0.817769\pi$
$548$	−234.157	+	135.191i	−0.427294	+	0.246698i
$549$	201.549	+	733.671i	0.367120	+	1.33638i
$550$	21.7318	−	37.6406i	0.0395124	−	0.0684374i
$551$	−966.340	−	1151.64i	−1.75379	−	2.09009i
$552$	73.6404	+	176.212i	0.133407	+	0.319224i
$553$	78.8770	−	447.334i	0.142635	−	0.808922i
$554$	−472.720	−	83.3532i	−0.853285	−	0.150457i
$555$	−25.9299	+	201.869i	−0.0467205	+	0.363728i
$556$	333.870	−	280.150i	0.600485	−	0.503867i
$557$	352.046	+	203.254i	0.632040	+	0.364909i	0.781542	−	0.623853i	$-0.214434\pi$
$557$	352.046	+	203.254i	0.632040	+	0.364909i	−0.149502	+	0.988761i	$0.547767\pi$
$558$	342.322	+	157.009i	0.613480	+	0.281379i
$559$	321.443	+	556.756i	0.575033	+	0.995986i
$560$	−19.9929	+	54.9300i	−0.0357016	+	0.0980893i
$561$	32.5662	−	104.433i	0.0580502	−	0.186154i
$562$	−311.186	−	261.116i	−0.553712	−	0.464620i
$563$	338.582	+	930.245i	0.601388	+	1.65230i	0.748464	+	0.663175i	$0.230792\pi$
$563$	338.582	+	930.245i	0.601388	+	1.65230i	−0.147076	+	0.989125i	$0.546986\pi$
$564$	91.2871	−	176.718i	0.161857	−	0.313329i
$565$	−86.2334	−	489.054i	−0.152626	−	0.865582i
$566$			174.980i			0.309152i
$567$	−322.544	+	394.379i	−0.568860	+	0.695554i
$568$	106.294			0.187137
$569$	−115.486	+	20.3632i	−0.202963	+	0.0357878i	−0.274205	−	0.961671i	$-0.588415\pi$
$569$	−115.486	+	20.3632i	−0.202963	+	0.0357878i	0.0712425	+	0.997459i	$0.477304\pi$
$570$	−264.104	−	136.428i	−0.463340	−	0.239348i
$571$	399.543	−	145.422i	0.699725	−	0.254679i	0.0324316	−	0.999474i	$-0.489675\pi$
$571$	399.543	−	145.422i	0.699725	−	0.254679i	0.667294	+	0.744795i	$0.267453\pi$
$572$	15.4854	−	18.4548i	0.0270724	−	0.0322636i
$573$	278.539	+	86.8594i	0.486107	+	0.151587i
$574$	−145.707	−	53.0332i	−0.253846	−	0.0923923i
$575$	382.076	−	220.592i	0.664480	−	0.383638i
$576$	71.6851	−	6.72695i	0.124453	−	0.0116787i
$577$	−3.24056	+	5.61282i	−0.00561623	+	0.00972759i	−0.868820	−	0.495128i	$-0.835121\pi$
$577$	−3.24056	+	5.61282i	−0.00561623	+	0.00972759i	0.863204	+	0.504856i	$0.168454\pi$
$578$	−228.975	−	272.881i	−0.396150	−	0.472113i
$579$	−148.750	−	19.1068i	−0.256908	−	0.0329997i
$580$	−40.2260	+	228.133i	−0.0693552	+	0.393333i
$581$	−159.794	−	28.1760i	−0.275033	−	0.0484957i
$582$	138.101	−	57.7136i	0.237287	−	0.0991642i
$583$	−103.335	+	86.7084i	−0.177247	+	0.148728i
$584$	19.2969	+	11.1411i	0.0330426	+	0.0190772i
$585$	−40.6005	+	155.433i	−0.0694025	+	0.265698i
$586$	356.103	+	616.788i	0.607684	+	1.05254i
$587$	−149.791	+	411.548i	−0.255181	+	0.701105i	0.744267	+	0.667882i	$0.232799\pi$
$587$	−149.791	+	411.548i	−0.255181	+	0.701105i	−0.999448	+	0.0332222i	$0.989423\pi$
$588$	−38.3868	−	41.6279i	−0.0652837	−	0.0707957i
$589$	683.546	+	573.563i	1.16052	+	0.973792i
$590$	−51.2234	−	140.735i	−0.0868193	−	0.238534i
$591$	792.834	−	37.1184i	1.34151	−	0.0628060i
$592$	−20.2819	−	115.025i	−0.0342600	−	0.194298i
$593$		−	328.720i		−	0.554334i	−0.960822	−	0.277167i	$-0.910604\pi$
$593$		−	328.720i		−	0.554334i	0.960822	−	0.277167i	$-0.0893956\pi$
$594$	31.6883	−	50.7936i	0.0533473	−	0.0855111i
$595$	339.873			0.571215
$596$	139.581	−	24.6120i	0.234197	−	0.0412953i
$597$	−338.215	+	216.968i	−0.566525	+	0.363430i
$598$	229.792	−	83.6374i	0.384267	−	0.139862i
$599$	348.296	−	415.083i	0.581463	−	0.692960i	−0.392479	−	0.919761i	$-0.628382\pi$
$599$	348.296	−	415.083i	0.581463	−	0.692960i	0.973941	+	0.226801i	$0.0728267\pi$
$600$	−36.5111	−	162.270i	−0.0608519	−	0.270451i
$601$	148.519	+	54.0563i	0.247119	+	0.0899440i	0.462610	−	0.886562i	$-0.346913\pi$
$601$	148.519	+	54.0563i	0.247119	+	0.0899440i	−0.215491	+	0.976506i	$0.569135\pi$
$602$	644.629	−	372.177i	1.07081	−	0.618233i
$603$	−412.186	+	195.376i	−0.683560	+	0.324007i
$604$	−263.783	+	456.885i	−0.436726	+	0.756432i
$605$	177.036	+	210.983i	0.292621	+	0.348732i
$606$	13.6725	−	17.9351i	0.0225619	−	0.0295958i
$607$	16.1881	−	91.8071i	0.0266690	−	0.151247i	−0.968565	−	0.248759i	$-0.919977\pi$
$607$	16.1881	−	91.8071i	0.0266690	−	0.151247i	0.995234	+	0.0975118i	$0.0310884\pi$
$608$	167.998	+	29.6226i	0.276313	+	0.0487214i
$609$	748.101	+	570.303i	1.22841	+	0.936458i
$610$	212.789	−	178.551i	0.348834	−	0.292706i
$611$	−220.563	−	127.342i	−0.360987	−	0.208416i
$612$	−179.305	−	378.281i	−0.292983	−	0.618107i
$613$	−17.1815	−	29.7593i	−0.0280286	−	0.0485469i	0.851671	−	0.524077i	$-0.175590\pi$
$613$	−17.1815	−	29.7593i	−0.0280286	−	0.0485469i	−0.879699	+	0.475530i	$0.842256\pi$
$614$	−293.130	+	805.368i	−0.477410	+	1.31167i
$615$	−118.538	+	26.6713i	−0.192745	+	0.0433680i
$616$	−21.3675	−	17.9295i	−0.0346875	−	0.0291063i
$617$	239.022	+	656.706i	0.387393	+	1.06435i	0.968171	+	0.250291i	$0.0805264\pi$
$617$	239.022	+	656.706i	0.387393	+	1.06435i	−0.580777	+	0.814062i	$0.697251\pi$
$618$	−154.400	−	240.684i	−0.249839	−	0.389456i
$619$	−17.1006	−	96.9823i	−0.0276262	−	0.156676i	0.967874	−	0.251436i	$-0.0809027\pi$
$619$	−17.1006	−	96.9823i	−0.0276262	−	0.156676i	−0.995500	+	0.0947600i	$0.969792\pi$
$620$		−	137.495i		−	0.221767i
$621$	536.357	−	285.684i	0.863698	−	0.460038i
$622$	161.018			0.258871
$623$	−168.030	+	29.6283i	−0.269711	+	0.0475574i
$624$	−4.31146	−	92.0911i	−0.00690939	−	0.147582i
$625$	−234.246	+	85.2585i	−0.374793	+	0.136414i
$626$	−464.688	+	553.793i	−0.742312	+	0.884653i
$627$	104.276	−	96.1577i	0.166310	−	0.153362i
$628$	182.360	+	66.3737i	0.290383	+	0.105691i
$629$	−588.116	+	339.549i	−0.935001	+	0.539823i
$630$	179.965	+	47.0085i	0.285659	+	0.0746166i
$631$	−167.835	+	290.699i	−0.265983	+	0.460696i	−0.967821	−	0.251641i	$-0.919030\pi$
$631$	−167.835	+	290.699i	−0.265983	+	0.460696i	0.701838	+	0.712337i	$0.252363\pi$
$632$	131.296	+	156.472i	0.207747	+	0.247583i
$633$	−78.1601	−	187.027i	−0.123476	−	0.295461i
$634$	9.48705	−	53.8037i	0.0149638	−	0.0848639i
$635$	112.996	+	19.9243i	0.177947	+	0.0313768i
$636$	−65.7672	+	512.009i	−0.103408	+	0.805046i
$637$	−55.5425	+	46.6057i	−0.0871938	+	0.0731643i
$638$	−95.7290	−	55.2692i	−0.150045	−	0.0866288i
$639$	−31.6003	−	336.746i	−0.0494528	−	0.526989i
$640$	−13.1431	−	22.7645i	−0.0205361	−	0.0355695i
$641$	341.193	−	937.419i	0.532282	−	1.46243i	−0.324067	−	0.946034i	$-0.605050\pi$
$641$	341.193	−	937.419i	0.532282	−	1.46243i	0.856349	−	0.516398i	$-0.172727\pi$
$642$	−0.940813	+	3.01698i	−0.00146544	+	0.00469935i
$643$	478.514	+	401.521i	0.744189	+	0.624449i	0.933959	−	0.357380i	$-0.116330\pi$
$643$	478.514	+	401.521i	0.744189	+	0.624449i	−0.189770	+	0.981829i	$0.560774\pi$
$644$	−96.8379	−	266.060i	−0.150369	−	0.413137i
$645$	267.691	−	518.208i	0.415025	−	0.803423i
$646$	−172.233	−	976.781i	−0.266614	−	1.51205i
$647$			550.714i			0.851181i	0.904916	+	0.425591i	$0.139934\pi$
$647$			550.714i			0.851181i	−0.904916	+	0.425591i	$0.860066\pi$
$648$	−42.6228	−	225.103i	−0.0657759	−	0.347381i
$649$	71.4649			0.110115
$650$	−209.737	+	36.9823i	−0.322673	+	0.0568959i
$651$	−496.063	−	256.251i	−0.762002	−	0.393627i
$652$	−313.480	+	114.097i	−0.480798	+	0.174996i
$653$	435.250	−	518.711i	0.666539	−	0.794350i	−0.321770	−	0.946818i	$-0.604278\pi$
$653$	435.250	−	518.711i	0.666539	−	0.794350i	0.988308	+	0.152468i	$0.0487221\pi$
$654$	−230.329	−	71.8255i	−0.352184	−	0.109825i
$655$	−107.597	−	39.1619i	−0.164270	−	0.0597892i
$656$	60.3851	−	34.8634i	0.0920505	−	0.0531454i
$657$	29.5588	−	64.4459i	0.0449905	−	0.0980912i
$658$	−147.441	+	255.375i	−0.224074	+	0.388107i
$659$	−307.922	−	366.967i	−0.467257	−	0.556855i	0.480026	−	0.877254i	$-0.340627\pi$
$659$	−307.922	−	366.967i	−0.467257	−	0.556855i	−0.947283	+	0.320399i	$0.896183\pi$
$660$	−21.6787	−	2.78462i	−0.0328465	−	0.00421911i
$661$	−166.498	+	944.257i	−0.251888	+	1.42853i	0.552048	+	0.833812i	$0.313846\pi$
$661$	−166.498	+	944.257i	−0.251888	+	1.42853i	−0.803936	+	0.594716i	$0.797265\pi$
$662$	147.766	+	26.0552i	0.223212	+	0.0393583i
$663$	−494.575	+	206.687i	−0.745966	+	0.311746i
$664$	55.8942	−	46.9008i	0.0841780	−	0.0706337i
$665$	381.656	+	220.349i	0.573919	+	0.331352i
$666$	−358.375	+	98.4503i	−0.538101	+	0.147823i
$667$	−561.018	−	971.711i	−0.841106	−	1.45684i
$668$	−14.3435	+	39.4083i	−0.0214722	+	0.0589945i
$669$	−460.360	−	499.229i	−0.688132	−	0.746231i
$670$	127.571	+	107.045i	0.190405	+	0.159769i
$671$	45.3338	+	124.554i	0.0675616	+	0.185624i
$672$	−106.626	+	4.99194i	−0.158669	+	0.00742847i
$673$	34.1556	+	193.706i	0.0507513	+	0.287825i	0.999612	−	0.0278717i	$-0.00887300\pi$
$673$	34.1556	+	193.706i	0.0507513	+	0.287825i	−0.948860	+	0.315696i	$0.897762\pi$
$674$		−	7.10983i		−	0.0105487i
$675$	−503.228	+	163.911i	−0.745524	+	0.242831i
$676$	219.953			0.325375
$677$	−705.776	+	124.447i	−1.04250	+	0.183822i	−0.668582	−	0.743638i	$-0.733098\pi$
$677$	−705.776	+	124.447i	−1.04250	+	0.183822i	−0.373922	+	0.927460i	$0.621987\pi$
$678$	763.263	−	489.639i	1.12576	−	0.722181i
$679$	−208.517	+	75.8940i	−0.307094	+	0.111773i
$680$	−98.2399	+	117.078i	−0.144470	+	0.172173i
$681$	−170.135	−	756.151i	−0.249831	−	1.11035i
$682$	61.6524	+	22.4397i	0.0903995	+	0.0329027i
$683$	223.152	−	128.837i	0.326723	−	0.188633i	−0.327662	−	0.944795i	$-0.606261\pi$
$683$	223.152	−	128.837i	0.326723	−	0.188633i	0.654385	+	0.756161i	$0.272928\pi$
$684$	43.9017	−	541.035i	0.0641838	−	0.790987i
$685$	157.050	−	272.019i	0.229270	−	0.397108i
$686$	334.130	+	398.201i	0.487071	+	0.580468i
$687$	97.6916	−	128.148i	0.142200	−	0.186533i
$688$	−58.1236	+	329.635i	−0.0844820	+	0.479121i
$689$	650.944	+	114.779i	0.944766	+	0.166588i
$690$	−176.439	−	134.505i	−0.255708	−	0.194935i
$691$	−224.575	+	188.440i	−0.324999	+	0.272707i	−0.790659	−	0.612257i	$-0.790262\pi$
$691$	−224.575	+	188.440i	−0.324999	+	0.272707i	0.465659	+	0.884964i	$0.345817\pi$
$692$	312.371	+	180.348i	0.451403	+	0.260618i
$693$	−50.4493	+	73.0239i	−0.0727984	+	0.105374i
$694$	160.173	+	277.428i	0.230797	+	0.399753i
$695$	−173.168	+	475.775i	−0.249162	+	0.684568i
$696$	−412.693	+	92.8566i	−0.592949	+	0.133415i
$697$	−310.561	−	260.591i	−0.445568	−	0.373876i
$698$	−238.123	−	654.238i	−0.341151	−	0.937304i
$699$	174.278	+	271.669i	0.249324	+	0.388654i
$700$	42.8192	+	242.840i	0.0611703	+	0.346914i
$701$		−	414.603i		−	0.591445i	−0.955274	−	0.295722i	$-0.904440\pi$
$701$		−	414.603i		−	0.591445i	0.955274	−	0.295722i	$-0.0955603\pi$
$702$	−290.469	+	41.0369i	−0.413773	+	0.0584571i
$703$	−880.556			−1.25257
$704$	12.3525	−	2.17808i	0.0175462	−	0.00309386i
$705$	10.8060	+	230.812i	0.0153277	+	0.327393i
$706$	−594.293	+	216.305i	−0.841774	+	0.306381i
$707$	−21.4913	+	25.6123i	−0.0303979	+	0.0362268i
$708$	201.050	−	185.397i	0.283969	−	0.261860i
$709$	−502.572	−	182.921i	−0.708846	−	0.257999i	−0.0376632	−	0.999290i	$-0.511991\pi$
$709$	−502.572	−	182.921i	−0.708846	−	0.257999i	−0.671183	+	0.741291i	$0.734214\pi$
$710$	−106.938	+	61.7406i	−0.150617	+	0.0869586i
$711$	456.681	−	462.472i	0.642308	−	0.650452i
$712$	38.3627	−	66.4462i	0.0538802	−	0.0933233i
$713$	428.081	+	510.167i	0.600394	+	0.715521i
$714$	239.309	+	572.634i	0.335166	+	0.802008i
$715$	−4.85979	+	27.5613i	−0.00679691	+	0.0385472i
$716$	456.183	+	80.4373i	0.637127	+	0.112343i
$717$	169.993	−	1323.42i	0.237089	−	1.84578i
$718$	−77.8547	+	65.3279i	−0.108433	+	0.0909859i
$719$	−829.644	−	478.995i	−1.15389	−	0.666196i	−0.204055	−	0.978959i	$-0.565412\pi$
$719$	−829.644	−	478.995i	−1.15389	−	0.666196i	−0.949831	+	0.312763i	$0.898745\pi$
$720$	−68.2120	+	48.4058i	−0.0947389	+	0.0672303i
$721$	211.967	+	367.137i	0.293990	+	0.509205i
$722$	265.256	−	728.785i	0.367391	−	1.00940i
$723$	182.336	−	584.711i	0.252193	−	0.808729i
$724$	147.459	+	123.733i	0.203673	+	0.170902i
$725$	334.221	+	918.264i	0.460994	+	1.26657i
$726$	−230.821	+	446.834i	−0.317935	+	0.615473i
$727$	132.512	+	751.513i	0.182272	+	1.03372i	0.929410	+	0.369048i	$0.120316\pi$
$727$	132.512	+	751.513i	0.182272	+	1.03372i	−0.747138	+	0.664669i	$0.768573\pi$
$728$			136.678i			0.187744i
$729$	−700.468	+	201.953i	−0.960862	+	0.277027i
$730$	−25.8851			−0.0354590
$731$	1916.58	−	337.945i	2.62186	−	0.462305i
$732$	450.658	+	232.796i	0.615653	+	0.318028i
$733$	386.707	−	140.750i	0.527568	−	0.192019i	−0.0644843	−	0.997919i	$-0.520540\pi$
$733$	386.707	−	140.750i	0.527568	−	0.192019i	0.592052	+	0.805900i	$0.298318\pi$
$734$	126.262	−	150.473i	0.172019	−	0.205005i
$735$	62.7988	+	19.5831i	0.0854405	+	0.0266437i
$736$	119.642	+	43.5461i	0.162557	+	0.0591658i
$737$	−68.8186	+	39.7324i	−0.0933767	+	0.0539111i
$738$	−128.401	−	180.939i	−0.173986	−	0.245175i
$739$	−310.367	+	537.571i	−0.419982	+	0.727431i	−0.995937	−	0.0900509i	$-0.971297\pi$
$739$	−310.367	+	537.571i	−0.419982	+	0.727431i	0.575955	+	0.817481i	$0.304630\pi$
$740$	87.2166	+	103.941i	0.117860	+	0.140460i
$741$	−689.378	−	88.5501i	−0.930334	−	0.119501i
$742$	132.894	−	753.682i	0.179103	−	1.01574i
$743$	−892.676	−	157.403i	−1.20145	−	0.211848i	−0.463124	−	0.886293i	$-0.653272\pi$
$743$	−892.676	−	157.403i	−1.20145	−	0.211848i	−0.738325	+	0.674446i	$0.764383\pi$
$744$	231.659	−	96.8122i	0.311369	−	0.130124i
$745$	−126.131	+	105.837i	−0.169304	+	0.142063i
$746$	797.701	+	460.553i	1.06930	+	0.617363i
$747$	−165.201	−	163.133i	−0.221153	−	0.218384i
$748$	−36.4642	−	63.1578i	−0.0487489	−	0.0844356i
$749$	1.60244	−	4.40266i	0.00213944	−	0.00587805i
$750$	298.046	+	323.210i	0.397394	+	0.430947i
$751$	−262.258	−	220.060i	−0.349211	−	0.293023i	0.451262	−	0.892391i	$-0.350974\pi$
$751$	−262.258	−	220.060i	−0.349211	−	0.293023i	−0.800473	+	0.599369i	$0.795418\pi$
$752$	−45.3526	−	124.605i	−0.0603093	−	0.165699i
$753$	−1033.49	+	48.3853i	−1.37250	+	0.0642566i
$754$	94.0549	+	533.412i	0.124741	+	0.707443i
$755$		−	612.870i		−	0.811748i
$756$	47.5138	+	336.313i	0.0628489	+	0.444859i
$757$	546.517			0.721951			0.360975	−	0.932575i	$-0.382444\pi$
$757$	546.517			0.721951			0.360975	+	0.932575i	$0.382444\pi$
$758$	−528.057	+	93.1108i	−0.696646	+	0.122837i
$759$	89.1070	−	57.1628i	0.117400	−	0.0753133i
$760$	−186.222	+	67.7792i	−0.245029	+	0.0891832i
$761$	−48.9259	+	58.3077i	−0.0642916	+	0.0766198i	−0.797232	−	0.603673i	$-0.793703\pi$
$761$	−48.9259	+	58.3077i	−0.0642916	+	0.0766198i	0.732940	+	0.680293i	$0.238148\pi$
$762$	45.9927	+	204.410i	0.0603578	+	0.268255i
$763$	336.117	+	122.337i	0.440520	+	0.160336i
$764$	168.452	−	97.2561i	0.220487	−	0.127299i
$765$	400.115	+	276.424i	0.523027	+	0.361338i
$766$	−113.688	+	196.914i	−0.148418	+

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)

\(f(q)\)	\(=\)	\(q+(-1.39273 + 0.245576i) q^{2} +(2.66538 + 1.37686i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-1.49345 + 1.77982i) q^{5} +(-4.05028 - 1.26303i) q^{6} +(5.91054 + 2.15126i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.20853 + 7.33970i) q^{9} +O(q^{10})\)	\(q+(-1.39273 + 0.245576i) q^{2} +(2.66538 + 1.37686i) q^{3} +(1.87939 - 0.684040i) q^{4} +(-1.49345 + 1.77982i) q^{5} +(-4.05028 - 1.26303i) q^{6} +(5.91054 + 2.15126i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.20853 + 7.33970i) q^{9} +(1.64289 - 2.84556i) q^{10} +(1.00782 + 1.20107i) q^{11} +(5.95111 + 0.764415i) q^{12} +(1.33408 - 7.56595i) q^{13} +(-8.76008 - 1.54464i) q^{14} +(-6.43117 + 2.68764i) q^{15} +(3.06418 - 2.57115i) q^{16} +(-20.1411 - 11.6285i) q^{17} +(-9.05652 - 8.94312i) q^{18} +(-15.0781 - 26.1161i) q^{19} +(-1.58929 + 4.36655i) q^{20} +(12.7919 + 13.8719i) q^{21} +(-1.69857 - 1.42527i) q^{22} +(-7.69793 - 21.1499i) q^{23} +(-8.47600 + 0.396823i) q^{24} +(3.40383 + 19.3041i) q^{25} +10.8649i q^{26} +(3.77701 + 26.7345i) q^{27} +12.5797 q^{28} +(49.0949 - 8.65675i) q^{29} +(8.29685 - 5.32249i) q^{30} +(-27.8049 + 10.1202i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(1.03252 + 4.58892i) q^{33} +(30.9068 + 11.2492i) q^{34} +(-12.6559 + 7.30691i) q^{35} +(14.8095 + 10.2313i) q^{36} +(14.5999 - 25.2877i) q^{37} +(27.4132 + 32.6698i) q^{38} +(13.9731 - 18.3293i) q^{39} +(1.14114 - 6.47170i) q^{40} +(17.1669 + 3.02698i) q^{41} +(-21.2222 - 16.1784i) q^{42} +(-64.1027 + 53.7886i) q^{43} +(2.71565 + 1.56788i) q^{44} +(-20.8420 - 1.69120i) q^{45} +(15.9150 + 27.5656i) q^{46} +(11.3382 - 31.1513i) q^{47} +(11.7073 - 2.63417i) q^{48} +(-7.22958 - 6.06634i) q^{49} +(-9.48121 - 26.0494i) q^{50} +(-37.6730 - 58.7258i) q^{51} +(-2.66816 - 15.1319i) q^{52} +86.0360i q^{53} +(-11.8257 - 36.3064i) q^{54} -3.64280 q^{55} +(-17.5202 + 3.08928i) q^{56} +(-4.23087 - 90.3699i) q^{57} +(-66.2499 + 24.1130i) q^{58} +(29.2986 - 34.9167i) q^{59} +(-10.2482 + 9.45029i) q^{60} +(79.4407 + 28.9140i) q^{61} +(36.2395 - 20.9229i) q^{62} +(14.9956 + 54.5865i) q^{63} +(4.00000 - 6.92820i) q^{64} +(11.4736 + 13.6738i) q^{65} +(-2.56494 - 6.13756i) q^{66} +(-8.80100 + 49.9130i) q^{67} +(-45.8073 - 8.07706i) q^{68} +(8.60244 - 66.9715i) q^{69} +(15.8319 - 13.2845i) q^{70} +(-32.5457 - 18.7903i) q^{71} +(-23.1381 - 10.6125i) q^{72} +(-3.93896 - 6.82248i) q^{73} +(-14.1236 + 38.8043i) q^{74} +(-17.5064 + 56.1393i) q^{75} +(-46.2021 - 38.7682i) q^{76} +(3.37293 + 9.26704i) q^{77} +(-14.9594 + 28.9592i) q^{78} +(-12.5403 - 71.1198i) q^{79} +9.29356i q^{80} +(-26.7424 + 76.4581i) q^{81} -24.6521 q^{82} +(-25.4050 + 4.47959i) q^{83} +(33.5298 + 17.3205i) q^{84} +(50.7763 - 18.4811i) q^{85} +(76.0685 - 90.6549i) q^{86} +(142.776 + 44.5230i) q^{87} +(-4.16720 - 1.51674i) q^{88} +(-23.4923 + 13.5633i) q^{89} +(29.4426 - 2.76290i) q^{90} +(24.1615 - 41.8489i) q^{91} +(-28.9347 - 34.4831i) q^{92} +(-88.0448 - 11.3093i) q^{93} +(-8.14096 + 46.1697i) q^{94} +(69.0004 + 12.1666i) q^{95} +(-15.6582 + 6.54371i) q^{96} +(-27.0251 + 22.6768i) q^{97} +(11.5586 + 6.67336i) q^{98} +(-3.56624 + 13.6529i) 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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