LMFDB - Embedded newform 18.7.d.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,7,Mod(5,18)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, 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:	$4.14097350516$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.6
Root			$3.87527i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.7.d.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +10.4362 q^{10} +(-49.8080 - 28.7567i) q^{11} +(176.609 + 845.757i) q^{12} +(-1411.17 - 2444.23i) q^{13} +(62.1593 - 35.8877i) q^{14} +(48.7599 - 10.1820i) q^{15} +(-512.000 + 886.810i) q^{16} -7221.17i q^{17} +(1650.31 + 3779.23i) q^{18} -10648.3 q^{19} +(51.1267 + 29.5180i) q^{20} +(255.407 - 228.319i) q^{21} +(-162.672 - 281.757i) q^{22} +(11573.9 - 6682.21i) q^{23} +(-1526.96 + 4642.87i) q^{24} +(-7810.80 + 13528.7i) q^{25} -15965.6i q^{26} +(11397.7 + 16047.2i) q^{27} +406.023 q^{28} +(30795.1 + 17779.6i) q^{29} +(267.673 + 88.0326i) q^{30} +(8657.84 + 14995.8i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-1034.93 - 1157.71i) q^{33} +(20424.5 - 35376.3i) q^{34} -23.4082i q^{35} +(-2604.46 + 23182.2i) q^{36} -60441.2 q^{37} +(-52166.0 - 30118.0i) q^{38} +(-15576.7 - 74594.4i) q^{39} +(166.979 + 289.216i) q^{40} +(-75436.3 + 43553.2i) q^{41} +(1897.02 - 396.132i) q^{42} +(37932.2 - 65700.4i) q^{43} -1840.43i q^{44} +(1336.51 + 150.153i) q^{45} +75600.6 q^{46} +(61896.5 + 35736.0i) q^{47} +(-20612.6 + 18426.5i) q^{48} +(58744.0 + 101748. i) q^{49} +(-76529.9 + 44184.5i) q^{50} +(60912.8 - 185212. i) q^{51} +(45157.6 - 78215.2i) q^{52} +147761. i q^{53} +(10448.9 + 110853. i) q^{54} -106.105 q^{55} +(1989.10 + 1148.41i) q^{56} +(-273114. - 89822.1i) q^{57} +(100576. + 174203. i) q^{58} +(100224. - 57864.1i) q^{59} +(1062.33 + 1188.36i) q^{60} +(20138.6 - 34881.1i) q^{61} +97952.2i q^{62} +(8476.74 - 3701.61i) q^{63} -32768.0 q^{64} +(-4509.29 - 2603.44i) q^{65} +(-1795.59 - 8598.83i) q^{66} +(90883.7 + 157415. i) q^{67} +(200119. - 115539. i) q^{68} +(353221. - 73758.9i) q^{69} +(66.2083 - 114.676i) q^{70} -301066. i q^{71} +(-78328.3 + 106202. i) q^{72} -612635. q^{73} +(-296100. - 170954. i) q^{74} +(-314454. + 281104. i) q^{75} +(-170373. - 295095. i) q^{76} +(-631.975 + 364.871i) q^{77} +(134675. - 409494. i) q^{78} +(171651. - 297308. i) q^{79} +1889.15i q^{80} +(156971. + 507730. i) q^{81} -492748. q^{82} +(-131581. - 75968.6i) q^{83} +(10413.9 + 3424.93i) q^{84} +(-6661.07 - 11537.3i) q^{85} +(371658. - 214577. i) q^{86} +(639872. + 715786. i) q^{87} +(5205.52 - 9016.22i) q^{88} -102435. i q^{89} +(6122.82 + 4515.81i) q^{90} -35810.6 q^{91} +(370366. + 213831. i) q^{92} +(95566.0 + 457652. i) q^{93} +(202153. + 350140. i) q^{94} +(-17012.9 + 9822.43i) q^{95} +(-153098. + 31969.7i) q^{96} +(247882. - 429345. i) q^{97} +664613. i q^{98} +(-16778.7 - 38423.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) $ 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$3$	25.6485	+	8.43532i	0.949944	+	0.312419i
$3$	25.6485	+	8.43532i	0.949944	+	0.312419i
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	1.59771	−	0.922438i	0.0127817	−	0.00737950i	−0.493596	−	0.869692i	$-0.664318\pi$
$5$	1.59771	−	0.922438i	0.0127817	−	0.00737950i	0.506377	+	0.862312i	$0.330984\pi$
$6$	101.793	+	113.869i	0.471263	+	0.527173i
$7$	6.34411	−	10.9883i	0.0184959	−	0.0320359i	−0.856629	−	0.515932i	$-0.827446\pi$
$7$	6.34411	−	10.9883i	0.0184959	−	0.0320359i	0.875125	+	0.483897i	$0.160779\pi$
$8$			181.019i			0.353553i
$9$	586.691	+	432.707i	0.804788	+	0.593562i
$10$	10.4362			0.0104362
$11$	−49.8080	−	28.7567i	−0.0374215	−	0.0216053i	0.481173	−	0.876626i	$-0.340211\pi$
$11$	−49.8080	−	28.7567i	−0.0374215	−	0.0216053i	−0.518594	+	0.855021i	$0.673544\pi$
$12$	176.609	+	845.757i	0.102205	+	0.489443i
$13$	−1411.17	−	2444.23i	−0.642319	−	1.11253i	−0.984914	−	0.173046i	$-0.944639\pi$
$13$	−1411.17	−	2444.23i	−0.642319	−	1.11253i	0.342595	−	0.939483i	$-0.388694\pi$
$14$	62.1593	−	35.8877i	0.0226528	−	0.0130786i
$15$	48.7599	−	10.1820i	0.0144474	−	0.00301687i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$		−	7221.17i		−	1.46981i	−0.678171	−	0.734904i	$-0.737227\pi$
$17$		−	7221.17i		−	1.46981i	0.678171	−	0.734904i	$-0.262773\pi$
$18$	1650.31	+	3779.23i	0.282974	+	0.648017i
$19$	−10648.3			−1.55246			−0.776231	−	0.630449i	$-0.782871\pi$
$19$	−10648.3			−1.55246			−0.776231	+	0.630449i	$0.782871\pi$
$20$	51.1267	+	29.5180i	0.00639084	+	0.00368975i
$21$	255.407	−	228.319i	0.0275787	−	0.0246538i
$22$	−162.672	−	281.757i	−0.0152773	−	0.0264610i
$23$	11573.9	−	6682.21i	0.951256	−	0.549208i	0.0577851	−	0.998329i	$-0.481596\pi$
$23$	11573.9	−	6682.21i	0.951256	−	0.549208i	0.893471	+	0.449121i	$0.148263\pi$
$24$	−1526.96	+	4642.87i	−0.110457	+	0.335856i
$25$	−7810.80	+	13528.7i	−0.499891	+	0.865837i
$26$		−	15965.6i		−	0.908376i
$27$	11397.7	+	16047.2i	0.579064	+	0.815282i
$28$	406.023			0.0184959
$29$	30795.1	+	17779.6i	1.26266	+	0.729000i	0.973589	−	0.228307i	$-0.0733190\pi$
$29$	30795.1	+	17779.6i	1.26266	+	0.729000i	0.289075	+	0.957306i	$0.406652\pi$
$30$	267.673	+	88.0326i	0.00991380	+	0.00326047i
$31$	8657.84	+	14995.8i	0.290619	+	0.503367i	0.973956	−	0.226736i	$-0.0728054\pi$
$31$	8657.84	+	14995.8i	0.290619	+	0.503367i	−0.683337	+	0.730103i	$0.739472\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$	−1034.93	−	1157.71i	−0.0287984	−	0.0322151i
$34$	20424.5	−	35376.3i	0.519656	−	0.900070i
$35$		−	23.4082i		−	0.000545963i
$36$	−2604.46	+	23182.2i	−0.0558227	+	0.496874i
$37$	−60441.2			−1.19324			−0.596620	−	0.802524i	$-0.703490\pi$
$37$	−60441.2			−1.19324			−0.596620	+	0.802524i	$0.703490\pi$
$38$	−52166.0	−	30118.0i	−0.950685	−	0.548878i
$39$	−15576.7	−	74594.4i	−0.262592	−	1.25751i
$40$	166.979	+	289.216i	0.00260905	+	0.00451900i
$41$	−75436.3	+	43553.2i	−1.09453	+	0.631929i	−0.934780	−	0.355228i	$-0.884403\pi$
$41$	−75436.3	+	43553.2i	−1.09453	+	0.631929i	−0.159754	+	0.987157i	$0.551070\pi$
$42$	1897.02	−	396.132i	0.0256049	−	0.00534677i
$43$	37932.2	−	65700.4i	0.477092	−	0.826348i	−0.522563	−	0.852601i	$-0.675024\pi$
$43$	37932.2	−	65700.4i	0.477092	−	0.826348i	0.999655	+	0.0262527i	$0.00835745\pi$
$44$		−	1840.43i		−	0.0216053i
$45$	1336.51	+	150.153i	0.0146667	+	0.00164777i
$46$	75600.6			0.776697
$47$	61896.5	+	35736.0i	0.596174	+	0.344201i	0.767535	−	0.641007i	$-0.221483\pi$
$47$	61896.5	+	35736.0i	0.596174	+	0.344201i	−0.171361	+	0.985208i	$0.554817\pi$
$48$	−20612.6	+	18426.5i	−0.186384	+	0.166617i
$49$	58744.0	+	101748.i	0.499316	+	0.864840i
$50$	−76529.9	+	44184.5i	−0.612239	+	0.353476i
$51$	60912.8	−	185212.i	0.459196	−	1.39624i
$52$	45157.6	−	78215.2i	0.321159	−	0.556265i
$53$			147761.i			0.992505i	0.868178	+	0.496252i	$0.165291\pi$
$53$			147761.i			0.992505i	−0.868178	+	0.496252i	$0.834709\pi$
$54$	10448.9	+	110853.i	0.0663571	+	0.703986i
$55$	−106.105			−0.000637746
$56$	1989.10	+	1148.41i	0.0113264	+	0.00653930i
$57$	−273114.	−	89822.1i	−1.47475	−	0.485019i
$58$	100576.	+	174203.i	0.515481	+	0.892838i
$59$	100224.	−	57864.1i	0.487993	−	0.281743i	−0.235748	−	0.971814i	$-0.575754\pi$
$59$	100224.	−	57864.1i	0.487993	−	0.281743i	0.723742	+	0.690071i	$0.242421\pi$
$60$	1062.33	+	1188.36i	0.00491819	+	0.00550168i
$61$	20138.6	−	34881.1i	0.0887239	−	0.153674i	−0.818248	−	0.574865i	$-0.805054\pi$
$61$	20138.6	−	34881.1i	0.0887239	−	0.153674i	0.906972	+	0.421191i	$0.138388\pi$
$62$			97952.2i			0.410998i
$63$	8476.74	−	3701.61i	0.0339006	−	0.0148036i
$64$	−32768.0			−0.125000
$65$	−4509.29	−	2603.44i	−0.0164198	−	0.00947999i
$66$	−1795.59	−	8598.83i	−0.00624563	−	0.0299094i
$67$	90883.7	+	157415.i	0.302177	+	0.523386i	0.976629	−	0.214933i	$-0.0689533\pi$
$67$	90883.7	+	157415.i	0.302177	+	0.523386i	−0.674452	+	0.738319i	$0.735620\pi$
$68$	200119.	−	115539.i	0.636445	−	0.367452i
$69$	353221.	−	73758.9i	1.07522	−	0.224526i
$70$	66.2083	−	114.676i	0.000193027	−	0.000334333i
$71$		−	301066.i		−	0.841175i	−0.907252	−	0.420588i	$-0.861824\pi$
$71$		−	301066.i		−	0.841175i	0.907252	−	0.420588i	$-0.138176\pi$
$72$	−78328.3	+	106202.i	−0.209856	+	0.284536i
$73$	−612635.			−1.57483			−0.787415	−	0.616424i	$-0.788581\pi$
$73$	−612635.			−1.57483			−0.787415	+	0.616424i	$0.788581\pi$
$74$	−296100.	−	170954.i	−0.730707	−	0.421874i
$75$	−314454.	+	281104.i	−0.745373	+	0.666321i
$76$	−170373.	−	295095.i	−0.388116	−	0.672236i
$77$	−631.975	+	364.871i	−0.00138429	+	0.000799221i
$78$	134675.	−	409494.i	0.283794	−	0.862907i
$79$	171651.	−	297308.i	0.348149	−	0.603012i	−0.637772	−	0.770225i	$-0.720144\pi$
$79$	171651.	−	297308.i	0.348149	−	0.603012i	0.985921	+	0.167214i	$0.0534770\pi$
$80$			1889.15i			0.00368975i
$81$	156971.	+	507730.i	0.295369	+	0.955383i
$82$	−492748.			−0.893683
$83$	−131581.	−	75968.6i	−0.230123	−	0.132862i	0.380506	−	0.924779i	$-0.375750\pi$
$83$	−131581.	−	75968.6i	−0.230123	−	0.132862i	−0.610629	+	0.791917i	$0.709083\pi$
$84$	10413.9	+	3424.93i	0.0175701	+	0.00577849i
$85$	−6661.07	−	11537.3i	−0.0108464	−	0.0187866i
$86$	371658.	−	214577.i	0.584316	−	0.337355i
$87$	639872.	+	715786.i	0.971707	+	1.08699i
$88$	5205.52	−	9016.22i	0.00763864	−	0.0132305i
$89$		−	102435.i		−	0.145304i	−0.997357	−	0.0726520i	$-0.976854\pi$
$89$		−	102435.i		−	0.145304i	0.997357	−	0.0726520i	$-0.0231462\pi$
$90$	6122.82	+	4515.81i	0.00839893	+	0.00619452i
$91$	−35810.6			−0.0475212
$92$	370366.	+	213831.i	0.475628	+	0.274604i
$93$	95566.0	+	457652.i	0.118810	+	0.568966i
$94$	202153.	+	350140.i	0.243387	+	0.421558i
$95$	−17012.9	+	9822.43i	−0.0198431	+	0.0114564i
$96$	−153098.	+	31969.7i	−0.173044	+	0.0361348i
$97$	247882.	−	429345.i	0.271600	−	0.470425i	−0.697672	−	0.716418i	$-0.745780\pi$
$97$	247882.	−	429345.i	0.271600	−	0.470425i	0.969272	+	0.245992i	$0.0791138\pi$
$98$			664613.i			0.706139i
$99$	−16778.7	−	38423.5i	−0.0172923	−	0.0395997i
$100$	−499891.			−0.499891
$101$	68156.2	+	39350.0i	0.0661517	+	0.0381927i	0.532711	−	0.846297i	$-0.321173\pi$
$101$	68156.2	+	39350.0i	0.0661517	+	0.0381927i	−0.466559	+	0.884490i	$0.654507\pi$
$102$	822270.	−	735062.i	0.774843	−	0.692666i
$103$	326814.	+	566059.i	0.299081	+	0.518024i	0.975926	−	0.218102i	$-0.0699865\pi$
$103$	326814.	+	566059.i	0.299081	+	0.518024i	−0.676845	+	0.736126i	$0.736653\pi$
$104$	442452.	−	255450.i	0.393338	−	0.227094i
$105$	197.455	−	600.384i	0.000170569	−	0.000518634i
$106$	−417932.	+	723879.i	−0.350903	+	0.607783i
$107$		−	1.53176e6i		−	1.25037i	−0.780476	−	0.625186i	$-0.785023\pi$
$107$		−	1.53176e6i		−	1.25037i	0.780476	−	0.625186i	$-0.214977\pi$
$108$	−262349.	+	572618.i	−0.208261	+	0.454563i
$109$	863246.			0.666584			0.333292	−	0.942824i	$-0.391840\pi$
$109$	863246.			0.666584			0.333292	+	0.942824i	$0.391840\pi$
$110$	−519.806	−	300.110i	−0.000390538	−	0.000225477i
$111$	−1.55023e6	−	509841.i	−1.13351	−	0.372791i
$112$	6496.36	+	11252.0i	0.00462398	+	0.00800897i
$113$	−1.51141e6	+	872613.i	−1.04748	+	0.604765i	−0.921944	−	0.387324i	$-0.873400\pi$
$113$	−1.51141e6	+	872613.i	−1.04748	+	0.604765i	−0.125540	+	0.992089i	$0.540066\pi$
$114$	−1.08392e6	−	1.21252e6i	−0.731618	−	0.818416i
$115$	12327.8	−	21352.5i	0.00810576	−	0.0140396i
$116$			1.13789e6i			0.729000i
$117$	229710.	−	2.04463e6i	0.143424	−	1.27661i
$118$	654658.			0.398445
$119$	−79348.4	−	45811.8i	−0.0470866	−	0.0271855i
$120$	1843.13	+	8826.48i	0.00106663	+	0.00510792i
$121$	−884127.	−	1.53135e6i	−0.499066	−	0.864408i
$122$	197318.	−	113921.i	0.108664	−	0.0627373i
$123$	−2.30221e6	+	480744.i	−1.23717	+	0.258344i
$124$	−277051.	+	479866.i	−0.145310	+	0.251684i
$125$			57646.1i			0.0295148i
$126$	51997.1	+	5841.76i	0.0259937	+	0.00292033i
$127$	3.20463e6			1.56447			0.782234	−	0.622985i	$-0.214080\pi$
$127$	3.20463e6			1.56447			0.782234	+	0.622985i	$0.214080\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$	1.52711e6	−	1.36515e6i	0.711378	−	0.635932i
$130$	−14727.3	−	25508.4i	−0.00670336	−	0.0116106i
$131$	−2.63987e6	+	1.52413e6i	−1.17427	+	0.677967i	−0.954683	−	0.297625i	$-0.903805\pi$
$131$	−2.63987e6	+	1.52413e6i	−1.17427	+	0.677967i	−0.219590	+	0.975592i	$0.570472\pi$
$132$	15524.6	−	47204.2i	0.00674992	−	0.0205239i
$133$	−67554.2	+	117007.i	−0.0287142	+	0.0497345i
$134$			1.02823e6i			0.427343i
$135$	33012.8	+	15125.1i	0.0134178	+	0.00614746i
$136$	1.30717e6			0.519656
$137$	3.54873e6	+	2.04886e6i	1.38010	+	0.796802i	0.992171	−	0.124887i	$-0.0398567\pi$
$137$	3.54873e6	+	2.04886e6i	1.38010	+	0.796802i	0.387931	+	0.921689i	$0.373190\pi$
$138$	1.93904e6	+	637715.i	0.737819	+	0.242655i
$139$	556460.	+	963816.i	0.207200	+	0.358881i	0.950831	−	0.309709i	$-0.100232\pi$
$139$	556460.	+	963816.i	0.207200	+	0.358881i	−0.743632	+	0.668590i	$0.766898\pi$
$140$	648.706	−	374.531i	0.000236409	−	0.000136491i
$141$	1.28611e6	+	1.43869e6i	0.458797	+	0.513228i
$142$	851543.	−	1.47492e6i	0.297400	−	0.515112i
$143$			162323.i			0.0555100i
$144$	−684114.	+	298737.i	−0.229108	+	0.100047i
$145$	65602.2			0.0215186
$146$	−3.00129e6	−	1.73279e6i	−0.964382	−	0.556786i
$147$	648422.	+	3.10520e6i	0.204129	+	0.977546i
$148$	−967059.	−	1.67500e6i	−0.298310	−	0.516688i
$149$	−440188.	+	254142.i	−0.133070	+	0.0768278i	−0.565057	−	0.825052i	$-0.691146\pi$
$149$	−440188.	+	254142.i	−0.133070	+	0.0768278i	0.431987	+	0.901880i	$0.357812\pi$
$150$	−2.33559e6	+	487713.i	−0.692026	+	0.144508i
$151$	−2.81751e6	+	4.88007e6i	−0.818341	+	1.41741i	0.0885624	+	0.996071i	$0.471773\pi$
$151$	−2.81751e6	+	4.88007e6i	−0.818341	+	1.41741i	−0.906904	+	0.421338i	$0.861561\pi$
$152$		−	1.92756e6i		−	0.548878i
$153$	3.12465e6	−	4.23659e6i	0.872422	−	1.18288i
$154$	−4128.04			−0.00113027
$155$	27665.4	+	15972.6i	0.00742920	+	0.00428925i
$156$	1.81799e6	−	1.62518e6i	0.478871	−	0.428084i
$157$	−2.68126e6	−	4.64408e6i	−0.692852	−	1.20005i	−0.970900	−	0.239487i	$-0.923021\pi$
$157$	−2.68126e6	−	4.64408e6i	−0.692852	−	1.20005i	0.278048	−	0.960567i	$-0.410313\pi$
$158$	1.68183e6	−	971005.i	0.426394	−	0.246179i
$159$	−1.24641e6	+	3.78985e6i	−0.310078	+	0.942824i
$160$	−5343.33	+	9254.92i	−0.00130452	+	0.00225950i
$161$		−	169571.i		−	0.0406324i
$162$	−667079.	+	2.93134e6i	−0.156903	+	0.689479i
$163$	−2.42021e6			−0.558844			−0.279422	−	0.960168i	$-0.590143\pi$
$163$	−2.42021e6			−0.558844			−0.279422	+	0.960168i	$0.590143\pi$
$164$	−2.41396e6	−	1.39370e6i	−0.547267	−	0.315965i
$165$	−2721.43	−	895.030i	−0.000605823	−	0.000199244i
$166$	−429743.	−	744337.i	−0.0939474	−	0.162722i
$167$	7.16092e6	−	4.13436e6i	1.53751	−	0.887685i	0.538532	−	0.842605i	$-0.318979\pi$
$167$	7.16092e6	−	4.13436e6i	1.53751	−	0.887685i	0.998983	−	0.0450793i	$-0.0143541\pi$
$168$	41330.2	+	46233.5i	0.00871645	+	0.00975056i
$169$	−1.56942e6	+	2.71832e6i	−0.325147	+	0.563171i
$170$		−	75361.5i		−	0.0153392i
$171$	−6.24728e6	−	4.60761e6i	−1.24940	−	0.921482i
$172$	2.42766e6			0.477092
$173$	2.27322e6	+	1.31244e6i	0.439039	+	0.253479i	0.703190	−	0.711002i	$-0.251758\pi$
$173$	2.27322e6	+	1.31244e6i	0.439039	+	0.253479i	−0.264151	+	0.964481i	$0.585092\pi$
$174$	1.11017e6	+	5.31645e6i	0.210738	+	1.00919i
$175$	99105.0	+	171655.i	0.0184919	+	0.0320289i
$176$	51003.4	−	29446.8i	0.00935538	−	0.00540133i
$177$	3.05869e6	−	638709.i	0.551588	−	0.115182i
$178$	289729.	−	501826.i	0.0513727	−	0.0889802i
$179$		−	7.60442e6i		−	1.32589i	−0.748669	−	0.662944i	$-0.769307\pi$
$179$		−	7.60442e6i		−	1.32589i	0.748669	−	0.662944i	$-0.230693\pi$
$180$	17222.9	+	39440.8i	0.00295318	+	0.00676282i
$181$	−9.89440e6			−1.66861			−0.834303	−	0.551306i	$-0.814130\pi$
$181$	−9.89440e6			−1.66861			−0.834303	+	0.551306i	$0.814130\pi$
$182$	−175435.	−	101288.i	−0.0291006	−	0.0168013i
$183$	810759.	−	724773.i	0.132294	−	0.118263i
$184$	1.20961e6	+	2.09511e6i	0.194174	+	0.336320i
$185$	−96567.4	+	55753.2i	−0.0152516	+	0.00880552i
$186$	−826258.	+	2.51233e6i	−0.128404	+	0.390425i
$187$	−207657.	+	359672.i	−0.0317557	+	0.0550024i
$188$			2.28710e6i			0.344201i
$189$	248640.	−	23436.6i	0.0368286	−	0.00347143i
$190$	−111128.			−0.0162018
$191$	−1.09559e6	−	632537.i	−0.157234	−	0.0907791i	0.419319	−	0.907839i	$-0.362269\pi$
$191$	−1.09559e6	−	632537.i	−0.157234	−	0.0907791i	−0.576553	+	0.817060i	$0.695602\pi$
$192$	−840450.	−	276409.i	−0.118743	−	0.0390524i
$193$	−654987.	−	1.13447e6i	−0.0911089	−	0.157805i	0.816869	−	0.576823i	$-0.195708\pi$
$193$	−654987.	−	1.13447e6i	−0.0911089	−	0.157805i	−0.907978	+	0.419018i	$0.862374\pi$
$194$	2.42874e6	−	1.40223e6i	0.332641	−	0.192050i
$195$	−93695.7	−	104812.i	−0.0126362	−	0.0141353i
$196$	−1.87981e6	+	3.25592e6i	−0.249658	+	0.432420i
$197$			9.83234e6i			1.28605i	0.765845	+	0.643025i	$0.222321\pi$
$197$			9.83234e6i			1.28605i	−0.765845	+	0.643025i	$0.777679\pi$
$198$	26479.6	−	235694.i	0.00341127	−	0.0303635i
$199$	1.36283e7			1.72934			0.864672	−	0.502336i	$-0.167526\pi$
$199$	1.36283e7			1.72934			0.864672	+	0.502336i	$0.167526\pi$
$200$	−2.44896e6	−	1.41391e6i	−0.306120	−	0.176738i
$201$	1.00318e6	+	4.80410e6i	0.123536	+	0.591594i
$202$	222597.	+	385549.i	0.0270063	+	0.0467763i
$203$	390735.	−	225591.i	0.0467083	−	0.0269671i
$204$	6.10735e6	−	1.27533e6i	0.719387	−	0.150221i
$205$	−80350.2	+	139171.i	−0.00932664	+	0.0161542i
$206$			3.69748e6i			0.422965i
$207$	9.68176e6	+	1.08772e6i	1.09155	+	0.122633i
$208$	2.89009e6			0.321159
$209$	530373.	+	306211.i	0.0580955	+	0.0335414i
$210$	2665.47	−	2382.78i	0.000287817	−	0.000257292i
$211$	1.55640e6	+	2.69577e6i	0.165682	+	0.286969i	0.936897	−	0.349605i	$-0.113684\pi$
$211$	1.55640e6	+	2.69577e6i	0.165682	+	0.286969i	−0.771216	+	0.636574i	$0.780351\pi$
$212$	−4.09488e6	+	2.36418e6i	−0.429767	+	0.248126i
$213$	2.53959e6	−	7.72189e6i	0.262799	−	0.799070i
$214$	4.33247e6	−	7.50405e6i	0.442073	−	0.765693i
$215$		−	139960.i		−	0.0140828i
$216$	−2.90485e6	+	2.06321e6i	−0.288246	+	0.204730i
$217$	219705.			0.0215011
$218$	4.22902e6	+	2.44163e6i	0.408198	+	0.235673i
$219$	−1.57132e7	−	5.16778e6i	−1.49600	−	0.492007i
$220$	−1697.68	−	2940.47i	−0.000159437	−	0.000276152i
$221$	−1.76502e7	+	1.01903e7i	−1.63520	+	0.944085i
$222$	−6.15248e6	−	6.88240e6i	−0.562330	−	0.629044i
$223$	1.00499e7	−	1.74069e7i	0.906248	−	1.56967i	0.0870139	−	0.996207i	$-0.472268\pi$
$223$	1.00499e7	−	1.74069e7i	0.906248	−	1.56967i	0.819234	−	0.573460i	$-0.194399\pi$
$224$			73498.0i			0.00653930i
$225$	−1.04365e7	+	4.55738e6i	−0.916234	+	0.400099i
$226$	−9.87249e6			−0.855267
$227$	−1.03090e7	−	5.95188e6i	−0.881328	−	0.508835i	−0.0102317	−	0.999948i	$-0.503257\pi$
$227$	−1.03090e7	−	5.95188e6i	−0.881328	−	0.508835i	−0.871096	+	0.491113i	$0.836590\pi$
$228$	−1.88060e6	−	9.00591e6i	−0.158669	−	0.759841i
$229$	1.55174e6	+	2.68769e6i	0.129215	+	0.223807i	0.923373	−	0.383905i	$-0.125421\pi$
$229$	1.55174e6	+	2.68769e6i	0.129215	+	0.223807i	−0.794158	+	0.607712i	$0.792088\pi$
$230$	120788.	−	69736.8i	0.00992749	−	0.00573164i
$231$	−19287.0	+	4027.48i	−0.00156469	+	0.000326736i
$232$	−3.21845e6	+	5.57451e6i	−0.257740	+	0.446419i
$233$			9.36024e6i			0.739979i	0.929036	+	0.369989i	$0.120639\pi$
$233$			9.36024e6i			0.739979i	−0.929036	+	0.369989i	$0.879361\pi$
$234$	6.90843e6	−	9.36688e6i	0.539177	−	0.731051i
$235$	131857.			0.0101601
$236$	3.20715e6	+	1.85165e6i	0.243997	+	0.140872i
$237$	6.91048e6	−	6.17758e6i	0.519115	−	0.464059i
$238$	−259151.	−	448862.i	−0.0192230	−	0.0332953i
$239$	6.05702e6	−	3.49702e6i	0.443676	−	0.256156i	−0.261480	−	0.965209i	$-0.584211\pi$
$239$	6.05702e6	−	3.49702e6i	0.443676	−	0.256156i	0.705156	+	0.709053i	$0.250877\pi$
$240$	−15935.6	+	48453.9i	−0.00115275	+	0.00350506i
$241$	2.06773e6	−	3.58141e6i	0.147721	−	0.255860i	−0.782664	−	0.622445i	$-0.786140\pi$
$241$	2.06773e6	−	3.58141e6i	0.147721	−	0.255860i	0.930385	+	0.366585i	$0.119473\pi$
$242$		−	1.00028e7i		−	0.705786i
$243$	−256792.	+	1.43466e7i	−0.0178963	+	0.999840i
$244$	1.28887e6			0.0887239
$245$	187712.	+	108375.i	0.0127642	+	0.00736940i
$246$	−1.26382e7	−	4.15649e6i	−0.848949	−	0.279204i
$247$	1.50267e7	+	2.60269e7i	0.997176	+	1.72716i
$248$	−2.71453e6	+	1.56724e6i	−0.177967	+	0.102749i
$249$	−2.73405e6	−	3.05841e6i	−0.177096	−	0.198106i
$250$	−163048.	+	282407.i	−0.0104351	+	0.0180740i
$251$		−	6.15130e6i		−	0.388997i	−0.980903	−	0.194498i	$-0.937692\pi$
$251$		−	6.15130e6i		−	0.388997i	0.980903	−	0.194498i	$-0.0623079\pi$
$252$	238210.	+	175689.i	0.0148853	+	0.0109785i
$253$	−768633.			−0.0474633
$254$	1.56994e7	+	9.06406e6i	0.958037	+	0.553123i
$255$	−73525.6	−	352103.i	−0.00443423	−	0.0212349i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	6.62383e6	−	3.82427e6i	0.390220	−	0.225294i	−0.292035	−	0.956408i	$-0.594332\pi$
$257$	6.62383e6	−	3.82427e6i	0.390220	−	0.225294i	0.682256	+	0.731114i	$0.260999\pi$
$258$	1.13425e7	−	2.36852e6i	0.660464	−	0.137917i
$259$	−383445.	+	664147.i	−0.0220701	+	0.0382265i
$260$		−	166620.i		−	0.00947999i
$261$	1.03739e7	+	2.37564e7i	0.583471	+	1.33616i
$262$	−1.72436e7			−0.958790
$263$	7.24714e6	+	4.18414e6i	0.398382	+	0.230006i	0.685786	−	0.727804i	$-0.259459\pi$
$263$	7.24714e6	+	4.18414e6i	0.398382	+	0.230006i	−0.287404	+	0.957810i	$0.592792\pi$
$264$	209568.	−	187342.i	0.0113897	−	0.0101818i
$265$	136300.	+	236079.i	0.00732419	+	0.0126859i
$266$	−661893.	+	382144.i	−0.0351676	+	0.0203040i
$267$	864071.	−	2.62730e6i	0.0453958	−	0.138031i
$268$	−2.90828e6	+	5.03729e6i	−0.151089	+	0.261693i
$269$		−	2.26505e7i		−	1.16364i	−0.813316	−	0.581822i	$-0.802340\pi$
$269$		−	2.26505e7i		−	1.16364i	0.813316	−	0.581822i	$-0.197660\pi$
$270$	118949.	+	167472.i	0.00604322	+	0.00850844i
$271$	−1.56983e7			−0.788758			−0.394379	−	0.918948i	$-0.629040\pi$
$271$	−1.56983e7			−0.788758			−0.394379	+	0.918948i	$0.629040\pi$
$272$	6.40380e6	+	3.69724e6i	0.318223	+	0.183726i
$273$	−918487.	−	302074.i	−0.0451424	−	0.0148465i
$274$	1.15901e7	+	2.00746e7i	0.563424	+	0.975879i
$275$	778081.	−	449225.i	0.0374134	−	0.0216006i
$276$	7.69559e6	+	8.60859e6i	0.366029	+	0.409454i
$277$	9.51658e6	−	1.64832e7i	0.447756	−	0.775537i	−0.550483	−	0.834846i	$-0.685557\pi$
$277$	9.51658e6	−	1.64832e7i	0.447756	−	0.775537i	0.998240	+	0.0593095i	$0.0188899\pi$
$278$			6.29562e6i			0.293025i
$279$	−1.40931e6	+	1.25442e7i	−0.0648926	+	0.577605i
$280$	4237.33			0.000193027
$281$	−1.12171e7	−	6.47622e6i	−0.505549	−	0.291879i	0.225453	−	0.974254i	$-0.427614\pi$
$281$	−1.12171e7	−	6.47622e6i	−0.505549	−	0.291879i	−0.731002	+	0.682375i	$0.760947\pi$
$282$	2.23139e6	+	1.06858e7i	0.0995010	+	0.476496i
$283$	−1.67469e7	−	2.90065e7i	−0.738883	−	1.27978i	−0.952999	−	0.302974i	$-0.902020\pi$
$283$	−1.67469e7	−	2.90065e7i	−0.738883	−	1.27978i	0.214116	−	0.976808i	$-0.431313\pi$
$284$	8.34338e6	−	4.81705e6i	0.364240	−	0.210294i
$285$	−519212.	+	108421.i	−0.0224290	+	0.00468358i
$286$	−459118.	+	795216.i	−0.0196258	+	0.0339928i
$287$			1.10522e6i			0.0467525i
$288$	−4.19642e6	−	471458.i	−0.175672	−	0.0197363i
$289$	−2.80077e7			−1.16033
$290$	321384.	+	185551.i	0.0131774	+	0.00760798i
$291$	9.97946e6	−	8.92108e6i	0.404975	−	0.362025i
$292$	−9.80217e6	−	1.69779e7i	−0.393707	−	0.681921i
$293$	1.31069e7	−	7.56728e6i	0.521072	−	0.300841i	−0.216301	−	0.976327i	$-0.569399\pi$
$293$	1.31069e7	−	7.56728e6i	0.521072	−	0.300841i	0.737373	+	0.675486i	$0.236066\pi$
$294$	−5.60622e6	+	1.70463e7i	−0.220611	+	0.670793i
$295$	106752.	−	184900.i	0.00415825	−	0.00720229i
$296$		−	1.09410e7i		−	0.421874i
$297$	−106234.	−	1.12704e6i	−0.00405502	−	0.0430200i
$298$	−2.87529e6			−0.108651
$299$	−3.26657e7	−	1.88595e7i	−1.22202	−	0.705533i
$300$	−1.28215e7	−	4.21674e6i	−0.474869	−	0.156176i
$301$	−481291.	−	833621.i	−0.0176485	−	0.0305682i
$302$	−2.76058e7	+	1.59382e7i	−1.00226	+	0.578655i
$303$	1.41617e6	+	1.58419e6i	0.0509083	+	0.0569480i
$304$	5.45195e6	−	9.44305e6i	0.194058	−	0.336118i
$305$		−	74306.5i		−	0.00261895i
$306$	2.72905e7	−	1.19171e7i	0.952460	−	0.415918i
$307$	−5.41823e6			−0.187259			−0.0936294	−	0.995607i	$-0.529847\pi$
$307$	−5.41823e6			−0.187259			−0.0936294	+	0.995607i	$0.529847\pi$
$308$	−20223.2	−	11675.9i	−0.000692146	−	0.000399611i
$309$	3.60741e6	+	1.72753e7i	0.122270	+	0.585533i
$310$	90354.8	+	156499.i	0.00303296	+	0.00525324i
$311$	2.36986e7	−	1.36824e7i	0.787848	−	0.454864i	−0.0513567	−	0.998680i	$-0.516355\pi$
$311$	2.36986e7	−	1.36824e7i	0.787848	−	0.454864i	0.839204	+	0.543816i	$0.183021\pi$
$312$	1.35030e7	−	2.81968e6i	0.444598	−	0.0928402i
$313$	−1.13895e7	+	1.97272e7i	−0.371426	+	0.643328i	−0.989785	−	0.142567i	$-0.954464\pi$
$313$	−1.13895e7	+	1.97272e7i	−0.371426	+	0.643328i	0.618360	+	0.785895i	$0.287798\pi$
$314$		−	3.03350e7i		−	0.979840i
$315$	10128.9	−	13733.4i	0.000324063	−	0.000439385i
$316$	1.09857e7			0.348149
$317$	2.29031e7	+	1.32231e7i	0.718979	+	0.415103i	0.814377	−	0.580337i	$-0.197079\pi$
$317$	2.29031e7	+	1.32231e7i	0.718979	+	0.415103i	−0.0953979	+	0.995439i	$0.530412\pi$
$318$	−1.68255e7	+	1.50410e7i	−0.523222	+	0.467731i
$319$	−1.02256e6	−	1.77113e6i	−0.0315005	−	0.0545605i
$320$	−52353.7	+	30226.4i	−0.00159771	+	0.000922438i
$321$	1.29209e7	−	3.92873e7i	0.390640	−	1.18778i
$322$	479618.	−	830723.i	0.0143657	−	0.0248822i
$323$			7.68934e7i			2.28182i
$324$	−1.15591e7	+	1.24738e7i	−0.339851	+	0.366744i
$325$	4.40896e7			1.28436
$326$	−1.18566e7	−	6.84539e6i	−0.342221	−	0.197581i
$327$	2.21410e7	+	7.28176e6i	0.633218	+	0.208254i
$328$	−7.88397e6	−	1.36554e7i	−0.223421	−	0.386976i
$329$	785356.	−	453426.i	0.0220536	−	0.0127326i
$330$	−10800.7	−	12082.1i	−0.000300546	−	0.000336203i
$331$	−2.25635e7	+	3.90812e7i	−0.622190	+	1.07766i	0.366887	+	0.930265i	$0.380424\pi$
$331$	−2.25635e7	+	3.90812e7i	−0.622190	+	1.07766i	−0.989077	+	0.147399i	$0.952910\pi$
$332$		−	4.86199e6i		−	0.132862i
$333$	−3.54603e7	−	2.61533e7i	−0.960306	−	0.708262i
$334$	4.67749e7			1.25538
$335$	290411.	+	167669.i	0.00772466	+	0.00445983i
$336$	71707.5	+	343397.i	0.00189037	+	0.00905270i
$337$	1.56916e7	+	2.71787e7i	0.409994	+	0.710131i	0.994889	−	0.100978i	$-0.0321973\pi$
$337$	1.56916e7	+	2.71787e7i	0.409994	+	0.710131i	−0.584894	+	0.811110i	$0.698864\pi$
$338$	−1.53771e7	+	8.87800e6i	−0.398222	+	0.229914i
$339$	−4.61262e7	+	9.63199e6i	−1.18399	+	0.247239i
$340$	213154.	−	369194.i	0.00542322	−	0.00939330i
$341$		−	995883.i		−	0.0251157i
$342$	−1.75730e7	−	4.02425e7i	−0.439307	−	1.00602i
$343$	2.98347e6			0.0739331
$344$	1.18931e7	+	6.86646e6i	0.292158	+	0.168678i
$345$	496306.	−	443669.i	0.0120863	−	0.0108044i
$346$	7.42430e6	+	1.28593e7i	0.179237	+	0.310447i
$347$	9.52685e6	−	5.50033e6i	0.228014	−	0.131644i	−0.381642	−	0.924310i	$-0.624641\pi$
$347$	9.52685e6	−	5.50033e6i	0.228014	−	0.131644i	0.609655	+	0.792667i	$0.291308\pi$
$348$	−9.59849e6	+	2.91852e7i	−0.227753	+	0.692509i
$349$	1.73905e6	−	3.01213e6i	0.0409107	−	0.0708594i	−0.844845	−	0.535011i	$-0.820307\pi$
$349$	1.73905e6	−	3.01213e6i	0.0409107	−	0.0708594i	0.885756	+	0.464152i	$0.153641\pi$
$350$			1.12125e6i			0.0261515i
$351$	2.31388e7	−	5.05040e7i	0.535081	−	1.16790i
$352$	333153.			0.00763864
$353$	2.33541e7	+	1.34835e7i	0.530932	+	0.306534i	0.741396	−	0.671068i	$-0.234164\pi$
$353$	2.33541e7	+	1.34835e7i	0.530932	+	0.306534i	−0.210464	+	0.977602i	$0.567497\pi$
$354$	1.67910e7	+	5.52225e6i	0.378500	+	0.124482i
$355$	−277714.	−	481016.i	−0.00620745	−	0.0107516i
$356$	2.83876e6	−	1.63896e6i	0.0629185	−	0.0363260i
$357$	−1.64873e6	−	1.84433e6i	−0.0362364	−	0.0405354i
$358$	2.15086e7	−	3.72539e7i	0.468773	−	0.811938i
$359$			8.82517e7i			1.90739i	0.300775	+	0.953695i	$0.402755\pi$
$359$			8.82517e7i			1.90739i	−0.300775	+	0.953695i	$0.597245\pi$
$360$	−27180.7	+	241933.i	−0.000582576	+	0.00518547i
$361$	6.63412e7			1.41014
$362$	−4.84725e7	−	2.79856e7i	−1.02181	−	0.589941i
$363$	−9.75907e6	−	4.67348e7i	−0.204027	−	0.977058i
$364$	−572969.	−	992411.i	−0.0118803	−	0.0205773i
$365$	−978813.	+	565118.i	−0.0201290	+	0.0116215i
$366$	6.02186e6	−	1.25747e6i	0.122825	−	0.0256481i
$367$	−1.50282e7	+	2.60296e7i	−0.304024	+	0.526585i	−0.977044	−	0.213040i	$-0.931664\pi$
$367$	−1.50282e7	+	2.60296e7i	−0.304024	+	0.526585i	0.673019	+	0.739625i	$0.264997\pi$
$368$			1.36852e7i			0.274604i
$369$	−6.31036e7	−	7.08954e6i	−1.25596	−	0.141104i
$370$	−630776.			−0.0124529
$371$	1.62365e6	+	937412.i	0.0317958	+	0.0183573i
$372$	−1.11538e7	+	9.97083e6i	−0.216667	+	0.193688i
$373$	−1.95923e7	−	3.39349e7i	−0.377537	−	0.653913i	0.613166	−	0.789954i	$-0.289896\pi$
$373$	−1.95923e7	−	3.39349e7i	−0.377537	−	0.653913i	−0.990703	+	0.136041i	$0.956562\pi$
$374$	−2.03461e6	+	1.17468e6i	−0.0388926	+	0.0224547i
$375$	−486263.	+	1.47854e6i	−0.00922099	+	0.0280374i
$376$	−6.46890e6	+	1.12045e7i	−0.121693	+	0.210779i
$377$		−	1.00360e8i		−	1.87300i
$378$	1.28437e6	+	588445.i	0.0237802	+	0.0108951i
$379$	−3.94927e7			−0.725436			−0.362718	−	0.931899i	$-0.618151\pi$
$379$	−3.94927e7			−0.725436			−0.362718	+	0.931899i	$0.618151\pi$
$380$	−544414.	−	314318.i	−0.00992153	−	0.00572820i
$381$	8.21939e7	+	2.70321e7i	1.48616	+	0.488770i
$382$	−3.57817e6	−	6.19757e6i	−0.0641905	−	0.111181i
$383$	−5.89496e7	+	3.40346e7i	−1.04926	+	0.605793i	−0.922443	−	0.386133i	$-0.873811\pi$
$383$	−5.89496e7	+	3.40346e7i	−1.04926	+	0.605793i	−0.126821	+	0.991926i	$0.540477\pi$
$384$	−3.33555e6	−	3.73127e6i	−0.0589079	−	0.0658966i
$385$	−673.141	+	1165.91i	−1.17957e−5	+	2.04308e-5i
$386$		−	7.41034e6i		−	0.128847i
$387$	5.06835e7	−	2.21323e7i	0.874447	−	0.381852i
$388$	1.58645e7			0.271600
$389$	−6.88443e7	−	3.97473e7i	−1.16955	−	0.675241i	−0.215977	−	0.976398i	$-0.569294\pi$
$389$	−6.88443e7	−	3.97473e7i	−1.16955	−	0.675241i	−0.953574	+	0.301157i	$0.902627\pi$
$390$	−162561.	−	778482.i	−0.00274046	−	0.0131236i
$391$	−4.82534e7	−	8.35773e7i	−0.807230	−	1.39816i
$392$	−1.84183e7	+	1.06338e7i	−0.305767	+	0.176535i
$393$	−8.05653e7	+	1.68235e7i	−1.32730	+	0.277165i
$394$	−2.78101e7	+	4.81684e7i	−0.454688	+	0.787542i
$395$		−	633349.i		−	0.0102767i
$396$	796365.	−	1.07976e6i	0.0128241	−	0.0173877i
$397$	−4.50639e6			−0.0720206			−0.0360103	−	0.999351i	$-0.511465\pi$
$397$	−4.50639e6			−0.0720206			−0.0360103	+	0.999351i	$0.511465\pi$
$398$	6.67646e7	+	3.85466e7i	1.05900	+	0.611416i
$399$	−2.71966e6	+	2.43122e6i	−0.0428149	+	0.0382741i
$400$	−7.99826e6	−	1.38534e7i	−0.124973	−	0.216459i
$401$	3.46331e7	−	1.99954e7i	0.537104	−	0.310097i	−0.206801	−	0.978383i	$-0.566305\pi$
$401$	3.46331e7	−	1.99954e7i	0.537104	−	0.310097i	0.743904	+	0.668286i	$0.232972\pi$
$402$	−8.67346e6	+	2.63726e7i	−0.133510	+	0.405952i
$403$	2.44354e7	−	4.23234e7i	0.373340	−	0.646645i
$404$			2.51840e6i			0.0381927i
$405$	719143.	+	666409.i	0.0108256	+	0.0100317i
$406$	2.55227e6			0.0381372
$407$	3.01046e6	+	1.73809e6i	0.0446529	+	0.0257803i
$408$	3.35270e7	+	1.10264e7i	0.493644	+	0.162350i
$409$	2.00563e7	+	3.47385e7i	0.293144	+	0.507740i	0.974551	−	0.224164i	$-0.0719653\pi$
$409$	2.00563e7	+	3.47385e7i	0.293144	+	0.507740i	−0.681408	+	0.731904i	$0.738632\pi$
$410$	−787268.	+	454529.i	−0.0114228	+	0.00659493i
$411$	7.37368e7	+	8.24848e7i	1.06208	+	1.18809i
$412$	−1.04581e7	+	1.81139e7i	−0.149541	+	0.259012i
$413$		−	1.46838e6i		−	0.0208444i
$414$	4.43542e7	+	3.27129e7i	0.625077	+	0.461018i
$415$	−280305.			−0.00392181
$416$	1.41585e7	+	8.17440e6i	0.196669	+	0.113547i
$417$	6.14225e6	+	2.94144e7i	0.0847071	+	0.405650i
$418$	1.73219e6	+	3.00024e6i	0.0237174	+	0.0410797i
$419$	7.70293e7	−	4.44729e7i	1.04716	−	0.604579i	0.125309	−	0.992118i	$-0.460008\pi$
$419$	7.70293e7	−	4.44729e7i	1.04716	−	0.604579i	0.921854	+	0.387538i	$0.126675\pi$
$420$	19797.6	−	4134.10i	0.000267218	−	5.57999e-5i
$421$	−2.31687e7	+	4.01293e7i	−0.310495	+	0.537793i	−0.978470	−	0.206391i	$-0.933828\pi$
$421$	−2.31687e7	+	4.01293e7i	−0.310495	+	0.537793i	0.667975	+	0.744184i	$0.267161\pi$
$422$			1.76087e7i			0.234309i
$423$	2.08509e7	+	4.77490e7i	0.275489	+	0.630875i
$424$	−2.67476e7			−0.350903
$425$	9.76930e7	+	5.64031e7i	1.27261	+	0.734744i
$426$	3.42822e7	−	3.06463e7i	0.443445	−	0.396415i
$427$	−255523.	−	442579.i	−0.00328206	−	0.00568470i
$428$	4.24493e7	−	2.45081e7i	0.541427	−	0.312593i
$429$	−1.36925e6	+	4.16334e6i	−0.0173424	+	0.0527314i
$430$	395867.	−	685662.i	0.00497902	−	0.00862392i
$431$		−	1.17075e8i		−	1.46228i	−0.682227	−	0.731140i	$-0.738988\pi$
$431$		−	1.17075e8i		−	1.46228i	0.682227	−	0.731140i	$-0.261012\pi$
$432$	−2.00664e7	+	1.89144e6i	−0.248897	+	0.0234608i
$433$	1.81236e7			0.223244			0.111622	−	0.993751i	$-0.464395\pi$
$433$	1.81236e7			0.223244			0.111622	+	0.993751i	$0.464395\pi$
$434$	1.07633e6	+	621419.i	0.0131667	+	0.00760178i
$435$	1.68260e6	+	553375.i	0.0204415	+	0.00672283i
$436$	1.38119e7	+	2.39230e7i	0.166646	+	0.288639i
$437$	−1.23243e8	+	7.11545e7i	−1.47679	+	0.852624i
$438$	−6.23619e7	−	6.97604e7i	−0.742159	−	0.830208i
$439$	−3.02641e6	+	5.24189e6i	−0.0357712	+	0.0619576i	−0.883357	−	0.468701i	$-0.844722\pi$
$439$	−3.02641e6	+	5.24189e6i	−0.0357712	+	0.0619576i	0.847586	+	0.530659i	$0.178055\pi$
$440$		−	19207.1i		−	0.000225477i
$441$	−9.56229e6	+	8.51133e7i	−0.111493	+	0.992388i
$442$	−1.15290e8			−1.33514
$443$	4.21347e6	+	2.43265e6i	0.0484651	+	0.0279813i	0.524037	−	0.851696i	$-0.324425\pi$
$443$	4.21347e6	+	2.43265e6i	0.0484651	+	0.0279813i	−0.475572	+	0.879677i	$0.657759\pi$
$444$	−1.06745e7	−	5.11186e7i	−0.121955	−	0.584023i
$445$	−94489.7	−	163661.i	−0.00107227	−	0.00185723i
$446$	9.84684e7	−	5.68508e7i	1.10992	−	0.640814i
$447$	−1.34339e7	+	2.80525e6i	−0.150411	+	0.0314086i
$448$	−207884.	+	360065.i	−0.00231199	+	0.00400449i
$449$		−	1.43332e8i		−	1.58345i	−0.610877	−	0.791725i	$-0.709183\pi$
$449$		−	1.43332e8i		−	1.58345i	0.610877	−	0.791725i	$-0.290817\pi$
$450$	−6.40183e7	−	7.19232e6i	−0.702533	−	0.0789280i
$451$	5.00978e6			0.0546121
$452$	−4.83651e7	−	2.79236e7i	−0.523742	−	0.302382i
$453$	−1.13430e8	+	1.01400e8i	−1.22020	+	1.09079i
$454$	−3.36689e7	−	5.83163e7i	−0.359800	−	0.623193i
$455$	−57214.9	+	33033.0i	−0.000607400	+	0.000350682i
$456$	1.62595e7	−	4.94389e7i	0.171480	−	0.521404i
$457$	−4.87353e7	+	8.44121e7i	−0.510617	+	0.884415i	0.489307	+	0.872111i	$0.337250\pi$
$457$	−4.87353e7	+	8.44121e7i	−0.510617	+	0.884415i	−0.999924	+	0.0123031i	$0.996084\pi$
$458$			1.75559e7i			0.182738i
$459$	1.15879e8	−	8.23048e7i	1.19831	−	0.851113i
$460$	788982.			0.00810576
$461$	−4.63065e7	−	2.67351e7i	−0.472650	−	0.272884i	0.244699	−	0.969599i	$-0.421311\pi$
$461$	−4.63065e7	−	2.67351e7i	−0.472650	−	0.272884i	−0.717348	+	0.696715i	$0.754644\pi$
$462$	−105878.	−	34821.4i	−0.00107369	−	0.000353118i
$463$	−1.53890e7	−	2.66545e7i	−0.155048	−	0.268552i	0.778028	−	0.628229i	$-0.216220\pi$
$463$	−1.53890e7	−	2.66545e7i	−0.155048	−	0.268552i	−0.933077	+	0.359678i	$0.882887\pi$
$464$	−3.15342e7	+	1.82063e7i	−0.315666	+	0.182250i
$465$	574842.	+	643040.i	0.00571728	+	0.00639557i
$466$	−2.64748e7	+	4.58556e7i	−0.261622	+	0.453142i
$467$			1.10305e8i			1.08304i	0.840688	+	0.541519i	$0.182151\pi$
$467$			1.10305e8i			1.08304i	−0.840688	+	0.541519i	$0.817849\pi$
$468$	6.03378e7	−	2.63482e7i	0.588643	−	0.257047i
$469$	2.30630e6			0.0223562
$470$	645964.	+	372947.i	0.00622178	+	0.00359215i
$471$	−2.95960e7	−	1.41731e8i	−0.283250	−	1.35644i
$472$	1.04745e7	+	1.81424e7i	0.0996112	+	0.172532i
$473$	−3.77865e6	+	2.18161e6i	−0.0357070	+	0.0206155i
$474$	5.13271e7	−	1.07180e7i	0.481961	−	0.100642i
$475$	8.31720e7	−	1.44058e8i	0.776062	−	1.34418i
$476$		−	2.93196e6i		−	0.0271855i
$477$	−6.39372e7	+	8.66901e7i	−0.589113	+	0.798756i
$478$	3.95643e7			0.362260
$479$	−7.31282e6	−	4.22206e6i	−0.0665393	−	0.0384165i	0.466361	−	0.884594i	$-0.345565\pi$
$479$	−7.31282e6	−	4.22206e6i	−0.0665393	−	0.0384165i	−0.532901	+	0.846178i	$0.678898\pi$
$480$	−215117.	+	192302.i	−0.00194514	+	0.00173884i
$481$	8.52931e7	+	1.47732e8i	0.766441	+	1.32751i
$482$	2.02595e7	−	1.16968e7i	0.180920	−	0.104454i
$483$	1.43038e6	−	4.34923e6i	0.0126944	−	0.0385986i
$484$	2.82921e7	−	4.90033e7i	0.249533	−	0.432204i
$485$		−	914623.i		−	0.00801710i
$486$	−4.18364e7	+	6.95574e7i	−0.364456	+	0.605947i
$487$	−3.58999e7			−0.310818			−0.155409	−	0.987850i	$-0.549669\pi$
$487$	−3.58999e7			−0.310818			−0.155409	+	0.987850i	$0.549669\pi$
$488$	6.31416e6	+	3.64548e6i	0.0543321	+	0.0313686i
$489$	−6.20748e7	−	2.04153e7i	−0.530871	−	0.174594i
$490$	613064.	+	1.06186e6i	0.00521095	+	0.00902564i
$491$	−6.98926e7	+	4.03525e7i	−0.590455	+	0.340899i	−0.765277	−	0.643701i	$-0.777398\pi$
$491$	−6.98926e7	+	4.03525e7i	−0.590455	+	0.340899i	0.174823	+	0.984600i	$0.444065\pi$
$492$	−5.01582e7	−	5.61089e7i	−0.421159	−	0.471125i
$493$	1.28389e8	−	2.22377e8i	1.07149	−	1.85587i
$494$			1.70007e8i			1.41022i
$495$	−62250.8	−	45912.3i	−0.000513251	−	0.000378542i
$496$	−1.77312e7			−0.145310
$497$	−3.30821e6	−	1.90999e6i	−0.0269478	−	0.0155583i
$498$	−4.74355e6	−	2.27162e7i	−0.0384074	−	0.183928i
$499$	4.86033e7	+	8.41833e7i	0.391169	+	0.677524i	0.992604	−	0.121398i	$-0.0387376\pi$
$499$	4.86033e7	+	8.41833e7i	0.391169	+	0.677524i	−0.601435	+	0.798921i	$0.705404\pi$
$500$	−1.59753e6	+	922337.i	−0.0127803	+	0.00737870i
$501$	2.18541e8	−	4.56354e7i	1.73788	−	0.362902i
$502$	1.73985e7	−	3.01351e7i	0.137531	−	0.238211i
$503$			1.31021e8i			1.02952i	0.857333	+	0.514762i	$0.172120\pi$
$503$			1.31021e8i			1.02952i	−0.857333	+	0.514762i	$0.827880\pi$
$504$	670062.	+	1.53445e6i	0.00523388	+	0.0119857i
$505$	145192.			0.00112737
$506$	−3.76552e6	−	2.17402e6i	−0.0290652	−	0.0167808i
$507$	−6.31833e7	+	5.64823e7i	−0.484817	+	0.433399i
$508$	5.12741e7	+	8.88093e7i	0.391117	+	0.677435i
$509$	−1.64280e8	+	9.48472e7i	−1.24575	+	0.719236i	−0.970260	−	0.242067i	$-0.922175\pi$
$509$	−1.64280e8	+	9.48472e7i	−1.24575	+	0.719236i	−0.275493	+	0.961303i	$0.588841\pi$
$510$	635698.	−	1.93291e6i	0.00479226	−	0.0145714i
$511$	−3.88662e6	+	6.73183e6i	−0.0291279	+	0.0504511i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−1.21367e8	−	1.70876e8i	−0.898975	−	1.26569i
$514$	4.32667e7			0.318614
$515$	1.04431e6	+	602931.i	0.00764552	+	0.00441414i
$516$	6.22658e7	+	2.04781e7i	0.453211	+	0.149053i
$517$	−2.05530e6	−	3.55988e6i	−0.0148731	−	0.0257610i
$518$	−3.75698e6	+	2.16909e6i	−0.0270302	+	0.0156059i
$519$	4.72337e7	+	5.28375e7i	0.337871	+	0.377955i
$520$	471273.	−	816269.i	0.00335168	−	0.00580528i
$521$			3.24426e7i			0.229405i	0.993400	+	0.114702i	$0.0365914\pi$
$521$			3.24426e7i			0.229405i	−0.993400	+	0.114702i	$0.963409\pi$
$522$	−1.63717e7	+	1.45724e8i	−0.115102	+	1.02452i
$523$	8.16094e7			0.570473			0.285237	−	0.958457i	$-0.407928\pi$
$523$	8.16094e7			0.570473			0.285237	+	0.958457i	$0.407928\pi$
$524$	−8.44759e7	−	4.87722e7i	−0.587137	−	0.338983i
$525$	1.09393e6	+	5.23868e6i	0.00755983	+	0.0362029i
$526$	2.36691e7	+	4.09960e7i	0.162639	+	0.281699i
$527$	1.08287e8	−	6.25197e7i	0.739853	−	0.427154i
$528$	1.55656e6	−	325037.i	0.0105746	−	0.00220816i
$529$	1.52860e7	−	2.64761e7i	0.103259	−	0.178849i
$530$			1.54206e6i			0.0103580i
$531$	8.38384e7	+	9.41906e6i	0.559963	+	0.0629106i
$532$	−4.32347e6			−0.0287142
$533$	2.12908e8	+	1.22922e8i	1.40608	+	0.811800i
$534$	1.16642e7	−	1.04271e7i	0.0766004	−	0.0684764i
$535$	−1.41295e6	−	2.44730e6i	−0.00922712	−	0.0159818i
$536$	−2.84952e7	+	1.64517e7i	−0.185045	+	0.106836i
$537$	6.41457e7	−	1.95042e8i	0.414233	−	1.25952i
$538$	6.40652e7	−	1.10964e8i	0.411410	−	0.712584i
$539$		−	6.75713e6i		−	0.0431515i
$540$	109046.	+	1.15688e6i	0.000692515	+	0.00734694i
$541$	−1.52147e8			−0.960884			−0.480442	−	0.877027i	$-0.659524\pi$
$541$	−1.52147e8			−0.960884			−0.480442	+	0.877027i	$0.659524\pi$
$542$	−7.69055e7	−	4.44014e7i	−0.483014	−	0.278868i
$543$	−2.53777e8	−	8.34625e7i	−1.58508	−	0.521305i
$544$	2.09147e7	+	3.62254e7i	0.129914	+	0.225017i
$545$	1.37922e6	−	796291.i	0.00852006	−	0.00491906i
$546$	−3.64526e6	−	4.07773e6i	−0.0223950	−	0.0250519i
$547$	−8.56437e7	+	1.48339e8i	−0.523279	+	0.906346i	0.476354	+	0.879254i	$0.341958\pi$
$547$	−8.56437e7	+	1.48339e8i	−0.523279	+	0.906346i	−0.999633	+	0.0270921i	$0.991375\pi$
$548$			1.31127e8i			0.796802i
$549$	2.69084e7	−	1.17503e7i	0.162619	−	0.0710122i
$550$	5.08240e6			0.0305479
$551$	−3.27917e8	−	1.89323e8i	−1.96024	−	1.13174i
$552$	1.33518e7	+	6.39397e7i	0.0793820	+	0.380149i
$553$	−2.17794e6	−	3.77231e6i	−0.0128787	−	0.0223065i
$554$	9.32431e7	−	5.38339e7i	0.548387	−	0.316612i
$555$	−2.94711e6	+	615409.i	−0.0172392	+	0.00359986i
$556$	−1.78067e7	+	3.08421e7i	−0.103600	+	0.179440i
$557$		−	2.71640e8i		−	1.57191i	−0.618283	−	0.785956i	$-0.712171\pi$
$557$		−	2.71640e8i		−	1.57191i	0.618283	−	0.785956i	$-0.287829\pi$
$558$	−4.23846e7	+	5.74677e7i	−0.243952	+	0.330766i
$559$	−2.14116e8			−1.22578
$560$	20758.6	+	11985.0i	0.000118204	+	6.82454e-5i
$561$	−8.36003e6	+	7.47340e6i	−0.0473499	+	0.0423282i
$562$	−3.66351e7	−	6.34538e7i	−0.206390	−	0.357477i
$563$	2.27013e8	−	1.31066e8i	1.27211	−	0.734454i	0.296727	−	0.954962i	$-0.404105\pi$
$563$	2.27013e8	−	1.31066e8i	1.27211	−	0.734454i	0.975385	+	0.220508i	$0.0707715\pi$
$564$	−1.92924e7	+	5.86607e7i	−0.107535	+	0.326972i
$565$	−1.60986e6	+	2.78836e6i	−0.00892573	+	0.0154598i
$566$		−	1.89470e8i		−	1.04494i
$567$	6.57494e6	+	1.49624e6i	0.0360697	+	0.00820830i
$568$	5.44987e7			0.297400
$569$	2.40050e8	+	1.38593e8i	1.30306	+	0.752324i	0.980928	−	0.194370i	$-0.0622662\pi$
$569$	2.40050e8	+	1.38593e8i	1.30306	+	0.752324i	0.322135	+	0.946694i	$0.395600\pi$
$570$	−2.85027e6	−	937401.i	−0.0153908	−	0.00506175i
$571$	3.53749e7	+	6.12712e7i	0.190015	+	0.329115i	0.945255	−	0.326333i	$-0.105813\pi$
$571$	3.53749e7	+	6.12712e7i	0.190015	+	0.329115i	−0.755240	+	0.655448i	$0.772480\pi$
$572$	−4.49842e6	+	2.59717e6i	−0.0240366	+	0.0138775i
$573$	−2.27645e7	−	2.54652e7i	−0.121002	−	0.135358i
$574$	−3.12605e6	+	5.41447e6i	−0.0165295	+	0.0286299i
$575$			2.08774e8i			1.09818i
$576$	−1.92247e7	−	1.41789e7i	−0.100599	−	0.0741952i
$577$	−1.69497e8			−0.882336			−0.441168	−	0.897425i	$-0.645436\pi$
$577$	−1.69497e8			−0.882336			−0.441168	+	0.897425i	$0.645436\pi$
$578$	−1.37209e8	−	7.92176e7i	−0.710557	−	0.410240i
$579$	−7.22981e6	−	3.46225e7i	−0.0372470	−	0.178370i
$580$	1.04963e6	+	1.81802e6i	0.00537965	+	0.00931783i
$581$	−1.66953e6	+	963906.i	−0.00851269	+	0.00491480i
$582$	7.41218e7	−	1.54780e7i	0.375991	−	0.0785137i
$583$	4.24912e6	−	7.35969e6i	0.0214434	−	0.0371410i
$584$		−	1.10899e8i		−	0.556786i
$585$	−1.51903e6	−	3.47862e6i	−0.00758752	−	0.0173756i
$586$	8.56140e7			0.425453
$587$	2.49955e8	+	1.44312e8i	1.23580	+	0.713489i	0.968233	−	0.250051i	$-0.0804474\pi$
$587$	2.49955e8	+	1.44312e8i	1.23580	+	0.713489i	0.267566	+	0.963540i	$0.413781\pi$
$588$	−7.56790e7	+	6.76528e7i	−0.372257	+	0.332777i
$589$	−9.21916e7	−	1.59680e8i	−0.451175	−	0.781458i
$590$	1.04595e6	−	603881.i	0.00509279	−	0.00294032i
$591$	−8.29389e7	+	2.52185e8i	−0.401787	+	1.22168i
$592$	3.09459e7	−	5.35999e7i	0.149155	−	0.258344i
$593$		−	1.14093e8i		−	0.547135i	−0.961853	−	0.273567i	$-0.911796\pi$
$593$		−	1.14093e8i		−	0.547135i	0.961853	−	0.273567i	$-0.0882037\pi$
$594$	2.66731e6	−	5.82182e6i	0.0127267	−	0.0277779i
$595$	−169034.			−0.000802461
$596$	−1.40860e7	−	8.13256e6i	−0.0665348	−	0.0384139i
$597$	3.49545e8	+	1.14959e8i	1.64278	+	0.540281i
$598$	−1.06686e8	−	1.84785e8i	−0.498887	−	0.864098i
$599$	−8.39663e7	+	4.84780e7i	−0.390683	+	0.225561i	−0.682456	−	0.730927i	$-0.739088\pi$
$599$	−8.39663e7	+	4.84780e7i	−0.390683	+	0.225561i	0.291773	+	0.956488i	$0.405755\pi$
$600$	−5.08853e7	−	5.69223e7i	−0.235580	−	0.263529i
$601$	−2.05589e8	+	3.56090e8i	−0.947056	+	1.64035i	−0.195475	+	0.980709i	$0.562625\pi$
$601$	−2.05589e8	+	3.56090e8i	−0.947056	+	1.64035i	−0.751581	+	0.659640i	$0.770709\pi$
$602$		−	5.44519e6i		−	0.0249588i
$603$	−1.47940e7	+	1.31680e8i	−0.0674734	+	0.600576i
$604$	−1.80321e8			−0.818341
$605$	−2.82515e6	−	1.63110e6i	−0.0127578	−	0.00736572i
$606$	2.45705e6	+	1.17664e7i	0.0110407	+	0.0528722i
$607$	5.43359e7	+	9.41126e7i	0.242952	+	0.420806i	0.961554	−	0.274616i	$-0.0885508\pi$
$607$	5.43359e7	+	9.41126e7i	0.242952	+	0.420806i	−0.718602	+	0.695422i	$0.755217\pi$
$608$	5.34180e7	−	3.08409e7i	0.237671	−	0.137220i
$609$	1.19247e7	−	2.49009e6i	0.0527953	−	0.0110246i
$610$	210171.	−	364026.i	0.000925939	−	0.00160377i
$611$		−	2.01719e8i		−	0.884347i
$612$	1.67402e8	+	1.88073e7i	0.730309	+	0.0820486i
$613$	2.58460e8			1.12205			0.561025	−	0.827799i	$-0.310407\pi$
$613$	2.58460e8			1.12205			0.561025	+	0.827799i	$0.310407\pi$
$614$	−2.65438e7	−	1.53251e7i	−0.114672	−	0.0662060i
$615$	−3.23481e6	+	2.89174e6i	−0.0139067	+	0.0124318i
$616$	−66048.7	−	114400.i	−0.000282567	−	0.000489421i
$617$	1.05483e8	−	6.09007e7i	0.449084	−	0.259278i	−0.258360	−	0.966049i	$-0.583182\pi$
$617$	1.05483e8	−	6.09007e7i	0.449084	−	0.259278i	0.707443	+	0.706770i	$0.249849\pi$
$618$	−3.11894e7	+	9.48348e7i	−0.132142	+	0.401793i
$619$	−6.31246e7	+	1.09335e8i	−0.266150	+	0.460985i	−0.967864	−	0.251473i	$-0.919085\pi$
$619$	−6.31246e7	+	1.09335e8i	−0.266150	+	0.460985i	0.701714	+	0.712459i	$0.252418\pi$
$620$			1.02225e6i			0.00428925i
$621$	2.39147e8	+	1.09567e8i	0.998597	+	0.457515i
$622$	1.54799e8			0.643275
$623$	−1.12559e6	−	649857.i	−0.00465494	−	0.00268753i
$624$	7.41264e7	+	2.43788e7i	0.305084	+	0.100336i
$625$	−1.21991e8	−	2.11294e8i	−0.499673	−	0.865460i
$626$	−1.11594e8	+	6.44288e7i	−0.454902	+	0.262638i
$627$	1.10203e7	+	1.23277e7i	0.0447085	+	0.0500127i
$628$	8.58004e7	−	1.48611e8i	0.346426	−	0.600027i
$629$			4.36456e8i			1.75383i
$630$	88464.9	−	38630.7i	0.000353793	−	0.000154494i
$631$	1.13561e6			0.00452003			0.00226002	−	0.999997i	$-0.499281\pi$
$631$	1.13561e6			0.00452003			0.00226002	+	0.999997i	$0.499281\pi$
$632$	5.38186e7	+	3.10722e7i	0.213197	+	0.123089i
$633$	1.71797e7	+	8.22711e7i	0.0677337	+	0.324367i
$634$	7.48011e7	+	1.29559e8i	0.293522	+	0.508395i
$635$	5.12007e6	−	2.95607e6i	0.0199965	−	0.0115450i
$636$	−1.24970e8	+	2.60960e7i	−0.485774	+	0.101439i
$637$	1.65796e8	−	2.87167e8i	0.641440	−	1.11101i
$638$		−	1.15690e7i		−	0.0445485i
$639$	1.30273e8	−	1.76633e8i	0.499289	−	0.676968i
$640$	−341973.			−0.00130452
$641$	−9.76272e6	−	5.63651e6i	−0.0370678	−	0.0214011i	0.481352	−	0.876528i	$-0.340146\pi$
$641$	−9.76272e6	−	5.63651e6i	−0.0370678	−	0.0214011i	−0.518419	+	0.855127i	$0.673479\pi$
$642$	1.74420e8	−	1.55922e8i	0.659162	−	0.589253i
$643$	1.61344e7	+	2.79457e7i	0.0606905	+	0.105119i	0.894774	−	0.446519i	$-0.147336\pi$
$643$	1.61344e7	+	2.79457e7i	0.0606905	+	0.105119i	−0.834084	+	0.551638i	$0.814003\pi$
$644$	4.69928e6	−	2.71313e6i	0.0175944	−	0.0101581i
$645$	1.18061e6	−	3.58977e6i	0.00439974	−	0.0133779i
$646$	−2.17487e8	+	3.76699e8i	−0.806745	+	1.39732i
$647$		−	4.30138e8i		−	1.58816i	−0.607812	−	0.794081i	$-0.707952\pi$
$647$		−	4.30138e8i		−	1.58816i	0.607812	−	0.794081i	$-0.292048\pi$
$648$	−9.19089e7	+	2.84148e7i	−0.337779	+	0.104429i
$649$	−6.65592e6			−0.0243486
$650$	2.15994e8	+	1.24704e8i	0.786505	+	0.454089i
$651$	5.63510e6	+	1.85328e6i	0.0204248	+	0.00671736i
$652$	−3.87234e7	−	6.70709e7i	−0.139711	−	0.241986i
$653$	−4.50239e8	+	2.59945e8i	−1.61697	+	0.933561i	−0.629277	+	0.777181i	$0.716649\pi$
$653$	−4.50239e8	+	2.59945e8i	−1.61697	+	0.933561i	−0.987697	+	0.156380i	$0.950018\pi$
$654$	8.78722e7	+	9.82973e7i	0.314136	+	0.351405i
$655$	−2.81183e6	+	4.87024e6i	−0.0100061	+	0.0173311i
$656$		−	8.91969e7i		−	0.315965i
$657$	−3.59428e8	−	2.65091e8i	−1.26740	−	0.934759i
$658$	5.12993e6			0.0180067
$659$	−3.59541e8	−	2.07581e8i	−1.25630	−	0.725322i	−0.283943	−	0.958841i	$-0.591643\pi$
$659$	−3.59541e8	−	2.07581e8i	−1.25630	−	0.725322i	−0.972352	+	0.233519i	$0.924976\pi$
$660$	−18739.2	−	89739.1i	−6.51806e−5	−	0.000312140i
$661$	−2.11607e8	−	3.66515e8i	−0.732700	−	1.26907i	−0.955725	−	0.294261i	$-0.904926\pi$
$661$	−2.11607e8	−	3.66515e8i	−0.732700	−	1.26907i	0.223025	−	0.974813i	$-0.428407\pi$
$662$	−2.21077e8	+	1.27639e8i	−0.762024	+	0.439955i
$663$	−5.38659e8	+	1.12482e8i	−1.84830	+	0.385959i
$664$	1.37518e7	−	2.38188e7i	0.0469737	−	0.0813609i
$665$			249258.i			0.000847587i
$666$	−9.97465e7	−	2.28421e8i	−0.337657	−	0.773239i
$667$	4.75227e8			1.60149
$668$	2.29149e8	+	1.32299e8i	0.768757	+	0.443842i
$669$	4.04598e8	−	3.61687e8i	1.35128	−	1.20797i
$670$	948480.	+	1.64281e6i	0.00315358	+	0.00546216i
$671$	−2.00613e6	+	1.15824e6i	−0.00664036	+	0.00383382i
$672$	−619979.	+	1.88511e6i	−0.00204300	+	0.00621197i
$673$	862893.	−	1.49457e6i	0.00283082	−	0.00490312i	−0.864607	−	0.502450i	$-0.832432\pi$
$673$	862893.	−	1.49457e6i	0.00283082	−	0.00490312i	0.867437	+	0.497546i	$0.165766\pi$
$674$			1.77530e8i			0.579820i
$675$	−3.06123e8	+	2.88549e7i	−0.995370	+	0.0938227i
$676$	−1.00443e8			−0.325147
$677$	−1.62390e8	−	9.37561e7i	−0.523352	−	0.302158i	0.214953	−	0.976624i	$-0.431040\pi$
$677$	−1.62390e8	−	9.37561e7i	−0.523352	−	0.302158i	−0.738305	+	0.674467i	$0.764374\pi$
$678$	−2.53215e8	−	8.32776e7i	−0.812456	−	0.267202i
$679$	−3.14518e6	−	5.44761e6i	−0.0100470	−	0.0174019i
$680$	2.08848e6	−	1.20578e6i	0.00664207	−	0.00383480i
$681$	−2.14203e8	−	2.39616e8i	−0.678242	−	0.758708i
$682$	2.81678e6	−	4.87881e6i	0.00887974	−	0.0153802i
$683$			3.29781e8i			1.03506i	0.855666	+	0.517528i	$0.173148\pi$
$683$			3.29781e8i			1.03506i	−0.855666	+	0.517528i	$0.826852\pi$
$684$	2.77332e7	−	2.46851e8i	0.0866626	−	0.771378i
$685$	7.55978e6			0.0235200
$686$	1.46159e7	+	8.43852e6i	0.0452746	+	0.0261393i
$687$	1.71283e7	+	8.20248e7i	0.0528254	+	0.252973i
$688$	3.88425e7	+	6.72773e7i	0.119273	+	0.206587i
$689$	3.61162e8	−	2.08517e8i	1.10419	−	0.637505i
$690$	3.68628e6	−	769762.i	0.0112212	−	0.00234320i
$691$	7.94682e7	−	1.37643e8i	0.240857	−	0.417177i	−0.720102	−	0.693869i	$-0.755905\pi$
$691$	7.94682e7	−	1.37643e8i	0.240857	−	0.417177i	0.960959	+	0.276692i	$0.0892381\pi$
$692$			8.39964e7i			0.253479i
$693$	−528656.	−	59393.3i	−0.00158845	−	0.000178459i
$694$	6.22291e7			0.186172
$695$	1.77812e6	+	1.02660e6i	0.00529672	+	0.00305806i
$696$	−1.29571e8	+	1.15829e8i	−0.384309	+	0.343550i
$697$	3.14505e8	+	5.44738e8i	0.928814	+	1.60875i
$698$	1.70392e7	−	9.83758e6i	0.0501052	−	0.0289282i
$699$	−7.89566e7	+	2.40076e8i	−0.231184	+	0.702938i
$700$	−3.17136e6	+	5.49296e6i	−0.00924595	+	0.0160145i
$701$			1.13256e8i			0.328780i	0.986395	+	0.164390i	$0.0525656\pi$
$701$			1.13256e8i			0.328780i	−0.986395	+	0.164390i	$0.947434\pi$
$702$	2.56203e8	−	1.81972e8i	0.740583	−	0.526008i
$703$	6.43598e8			1.85246
$704$	1.63211e6	+	942299.i	0.00467769	+	0.00270067i
$705$	3.38193e6	+	1.11225e6i	0.00965155	+	0.00317422i
$706$	7.62742e7	+	1.32111e8i	0.216752	+	0.375426i
$707$	864780.	−	499281.i	0.00244707	−	0.00141282i
$708$	6.66394e7	+	7.45455e7i	0.187772	+	0.210049i
$709$	−2.95239e7	+	5.11369e7i	−0.0828390	+	0.143481i	−0.904468	−	0.426541i	$-0.859732\pi$
$709$	−2.95239e7	+	5.11369e7i	−0.0828390	+	0.143481i	0.821629	+	0.570022i	$0.193065\pi$
$710$		−	3.14198e6i		−	0.00877866i
$711$	2.29353e8	−	1.00154e8i	0.638111	−	0.278649i
$712$	1.85427e7			0.0513727
$713$	2.00410e8	+	1.15707e8i	0.552906	+	0.319221i
$714$	−2.86053e6	−	1.36987e7i	−0.00785872	−	0.0376343i
$715$	149733.	+	259345.i	0.000409636	+	0.000709511i
$716$	2.10740e8	−	1.21671e8i	0.574127	−	0.331472i
$717$	1.84852e8	−	3.86005e7i	0.501495	−	0.104721i
$718$	−2.49613e8	+	4.32343e8i	−0.674364	+	1.16803i
$719$			1.17775e8i			0.316860i	0.987370	+	0.158430i	$0.0506433\pi$
$719$			1.17775e8i			0.316860i	−0.987370	+	0.158430i	$0.949357\pi$
$720$	−817449.	+	1.10835e6i	−0.00219010	+	0.00296947i
$721$	8.29337e6			0.0221272
$722$	3.25004e8	+	1.87641e8i	0.863530	+	0.498559i
$723$	8.32444e7	−	7.44157e7i	0.220262	−	0.196902i
$724$	−1.58310e8	−	2.74202e8i	−0.417152	−	0.722528i
$725$	−4.81069e8	+	2.77745e8i	−1.26239	+	0.728841i
$726$	8.43764e7	−	2.56556e8i	0.220501	−	0.670458i
$727$	−1.08321e8	+	1.87617e8i	−0.281909	+	0.488281i	−0.971855	−	0.235580i	$-0.924301\pi$
$727$	−1.08321e8	+	1.87617e8i	−0.281909	+	0.488281i	0.689946	+	0.723861i	$0.257634\pi$
$728$		−	6.48240e6i		−	0.0168013i
$729$	−1.27605e8	+	3.65803e8i	−0.329370	+	0.944201i
$730$	−6.39358e6			−0.0164352
$731$	−4.74434e8	−	2.73914e8i	−1.21457	−	0.701234i
$732$	3.30576e7	+	1.08721e7i	0.0842827	+	0.0277190i
$733$	−2.54830e8	−	4.41379e8i	−0.647052	−	1.12073i	−0.983824	−	0.179140i	$-0.942668\pi$
$733$	−2.54830e8	−	4.41379e8i	−0.647052	−	1.12073i	0.336772	−	0.941586i	$-0.390665\pi$
$734$	−1.47245e8	+	8.50122e7i	−0.372352	+	0.214978i
$735$	3.90034e6	+	4.36307e6i	0.00982292	+	0.0109883i
$736$	−3.87075e7	+	6.70434e7i	−0.0970872	+	0.168160i
$737$		−	1.04541e7i		−	0.0261145i
$738$	−2.89091e8	−	2.13215e8i	−0.719226	−	0.530456i
$739$	1.66066e8			0.411479			0.205740	−	0.978607i	$-0.434040\pi$
$739$	1.66066e8			0.411479			0.205740	+	0.978607i	$0.434040\pi$
$740$	−3.09016e6	−	1.78410e6i	−0.00762580	−	0.00440276i
$741$	1.65866e8	+	7.94307e8i	0.407664	+	1.95224i
$742$	5.30280e6	+	9.18473e6i	0.0129806	+	0.0224830i
$743$	6.45800e8	−	3.72853e8i	1.57446	−	0.909016i	0.578849	−	0.815434i	$-0.303502\pi$
$743$	6.45800e8	−	3.72853e8i	1.57446	−	0.909016i	0.995612	−	0.0935810i	$-0.0298314\pi$
$744$	−8.28438e7	+	1.72993e7i	−0.201160	+	0.0420058i
$745$	−468861.	+	812091.i	−0.00113390	+	0.00196397i
$746$		−	2.21662e8i		−	0.533918i
$747$	−4.43255e7	−	1.01506e8i	−0.106339	−	0.243518i
$748$	−1.32900e7			−0.0317557
$749$	−1.68314e7	−	9.71764e6i	−0.0400568	−	0.0231268i
$750$	−6.56412e6	+	5.86795e6i	−0.0155594	+	0.0139092i
$751$	5.23107e7	+	9.06048e7i	0.123501	+	0.213910i	0.921146	−	0.389217i	$-0.127254\pi$
$751$	5.23107e7	+	9.06048e7i	0.123501	+	0.213910i	−0.797645	+	0.603127i	$0.793921\pi$
$752$	−6.33820e7	+	3.65936e7i	−0.149043	+	0.0860502i
$753$	5.18882e7	−	1.57772e8i	0.121530	−	0.369525i
$754$	2.83862e8	−	4.91663e8i	0.662206	−	1.14697i
$755$			1.03959e7i			0.0241558i
$756$	4.62773e6	+	6.51553e6i	0.0107103	+	0.0150794i

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +10.4362 q^{10} +(-49.8080 - 28.7567i) q^{11} +(176.609 + 845.757i) q^{12} +(-1411.17 - 2444.23i) q^{13} +(62.1593 - 35.8877i) q^{14} +(48.7599 - 10.1820i) q^{15} +(-512.000 + 886.810i) q^{16} -7221.17i q^{17} +(1650.31 + 3779.23i) q^{18} -10648.3 q^{19} +(51.1267 + 29.5180i) q^{20} +(255.407 - 228.319i) q^{21} +(-162.672 - 281.757i) q^{22} +(11573.9 - 6682.21i) q^{23} +(-1526.96 + 4642.87i) q^{24} +(-7810.80 + 13528.7i) q^{25} -15965.6i q^{26} +(11397.7 + 16047.2i) q^{27} +406.023 q^{28} +(30795.1 + 17779.6i) q^{29} +(267.673 + 88.0326i) q^{30} +(8657.84 + 14995.8i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-1034.93 - 1157.71i) q^{33} +(20424.5 - 35376.3i) q^{34} -23.4082i q^{35} +(-2604.46 + 23182.2i) q^{36} -60441.2 q^{37} +(-52166.0 - 30118.0i) q^{38} +(-15576.7 - 74594.4i) q^{39} +(166.979 + 289.216i) q^{40} +(-75436.3 + 43553.2i) q^{41} +(1897.02 - 396.132i) q^{42} +(37932.2 - 65700.4i) q^{43} -1840.43i q^{44} +(1336.51 + 150.153i) q^{45} +75600.6 q^{46} +(61896.5 + 35736.0i) q^{47} +(-20612.6 + 18426.5i) q^{48} +(58744.0 + 101748. i) q^{49} +(-76529.9 + 44184.5i) q^{50} +(60912.8 - 185212. i) q^{51} +(45157.6 - 78215.2i) q^{52} +147761. i q^{53} +(10448.9 + 110853. i) q^{54} -106.105 q^{55} +(1989.10 + 1148.41i) q^{56} +(-273114. - 89822.1i) q^{57} +(100576. + 174203. i) q^{58} +(100224. - 57864.1i) q^{59} +(1062.33 + 1188.36i) q^{60} +(20138.6 - 34881.1i) q^{61} +97952.2i q^{62} +(8476.74 - 3701.61i) q^{63} -32768.0 q^{64} +(-4509.29 - 2603.44i) q^{65} +(-1795.59 - 8598.83i) q^{66} +(90883.7 + 157415. i) q^{67} +(200119. - 115539. i) q^{68} +(353221. - 73758.9i) q^{69} +(66.2083 - 114.676i) q^{70} -301066. i q^{71} +(-78328.3 + 106202. i) q^{72} -612635. q^{73} +(-296100. - 170954. i) q^{74} +(-314454. + 281104. i) q^{75} +(-170373. - 295095. i) q^{76} +(-631.975 + 364.871i) q^{77} +(134675. - 409494. i) q^{78} +(171651. - 297308. i) q^{79} +1889.15i q^{80} +(156971. + 507730. i) q^{81} -492748. q^{82} +(-131581. - 75968.6i) q^{83} +(10413.9 + 3424.93i) q^{84} +(-6661.07 - 11537.3i) q^{85} +(371658. - 214577. i) q^{86} +(639872. + 715786. i) q^{87} +(5205.52 - 9016.22i) q^{88} -102435. i q^{89} +(6122.82 + 4515.81i) q^{90} -35810.6 q^{91} +(370366. + 213831. i) q^{92} +(95566.0 + 457652. i) q^{93} +(202153. + 350140. i) q^{94} +(-17012.9 + 9822.43i) q^{95} +(-153098. + 31969.7i) q^{96} +(247882. - 429345. i) q^{97} +664613. i q^{98} +(-16778.7 - 38423.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

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