LMFDB - Embedded newform 405.4.e.w.271.5

Newspace parameters

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Defining polynomial:	$ x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496 $ x^12 - 2x^11 + 2x^10 + 32x^9 + 583x^8 - 624x^7 + 594x^6 + 9450x^5 + 90513x^4 - 20304x^3 + 10368x^2 + 124416*x + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.5
Root			$1.25636 - 1.25636i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.w.136.5

$q$-expansion

$f(q)$	$=$	$q+(1.78729 + 3.09567i) q^{2} +(-2.38879 + 4.13751i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.07987 - 12.2627i) q^{7} +11.5188 q^{8} +O(q^{10})$	\(q+(1.78729 + 3.09567i) q^{2} +(-2.38879 + 4.13751i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.07987 - 12.2627i) q^{7} +11.5188 q^{8} -17.8729 q^{10} +(-31.8319 - 55.1345i) q^{11} +(5.19795 - 9.00312i) q^{13} +(25.3075 - 43.8339i) q^{14} +(39.6977 + 68.7584i) q^{16} +108.605 q^{17} +18.6145 q^{19} +(-11.9440 - 20.6876i) q^{20} +(113.786 - 197.082i) q^{22} +(64.4120 - 111.565i) q^{23} +(-12.5000 - 21.6506i) q^{25} +37.1609 q^{26} +67.6494 q^{28} +(-41.8248 - 72.4426i) q^{29} +(5.23638 - 9.06967i) q^{31} +(-95.8273 + 165.978i) q^{32} +(194.109 + 336.206i) q^{34} +70.7987 q^{35} -81.8885 q^{37} +(33.2695 + 57.6245i) q^{38} +(-28.7969 + 49.8777i) q^{40} +(153.726 - 266.262i) q^{41} +(111.220 + 192.638i) q^{43} +304.159 q^{44} +460.491 q^{46} +(-180.965 - 313.441i) q^{47} +(71.2509 - 123.410i) q^{49} +(44.6822 - 77.3918i) q^{50} +(24.8337 + 43.0132i) q^{52} +562.215 q^{53} +318.319 q^{55} +(-81.5513 - 141.251i) q^{56} +(149.506 - 258.952i) q^{58} +(-231.155 + 400.372i) q^{59} +(324.533 + 562.108i) q^{61} +37.4356 q^{62} -49.9208 q^{64} +(25.9898 + 45.0156i) q^{65} +(-127.090 + 220.126i) q^{67} +(-259.435 + 449.355i) q^{68} +(126.538 + 219.170i) q^{70} -1092.93 q^{71} +1034.52 q^{73} +(-146.358 - 253.500i) q^{74} +(-44.4663 + 77.0179i) q^{76} +(-450.731 + 780.690i) q^{77} +(-575.927 - 997.534i) q^{79} -396.977 q^{80} +1099.01 q^{82} +(-262.160 - 454.075i) q^{83} +(-271.513 + 470.274i) q^{85} +(-397.563 + 688.599i) q^{86} +(-366.664 - 635.081i) q^{88} +656.485 q^{89} -147.203 q^{91} +(307.734 + 533.010i) q^{92} +(646.874 - 1120.42i) q^{94} +(-46.5363 + 80.6033i) q^{95} +(-562.755 - 974.721i) q^{97} +509.383 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8	$ 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8 + 40 * q^10 - 88 * q^11 - 20 * q^13 - 180 * q^14 - 58 * q^16 + 248 * q^17 - 92 * q^19 - 170 * q^20 + 74 * q^22 - 210 * q^23 - 150 * q^25 + 8 * q^26 + 704 * q^28 - 296 * q^29 + 104 * q^31 - 722 * q^32 + 428 * q^34 + 400 * q^35 - 408 * q^37 + 20 * q^38 - 330 * q^40 - 344 * q^41 - 512 * q^43 + 1432 * q^44 - 372 * q^46 - 238 * q^47 - 68 * q^49 - 100 * q^50 + 468 * q^52 + 1700 * q^53 + 880 * q^55 - 2316 * q^56 - 890 * q^58 - 1840 * q^59 + 364 * q^61 + 2076 * q^62 - 1980 * q^64 - 100 * q^65 - 88 * q^67 - 236 * q^68 - 900 * q^70 + 2728 * q^71 + 1672 * q^73 - 1316 * q^74 + 2106 * q^76 - 840 * q^77 + 680 * q^79 + 580 * q^80 + 3484 * q^82 - 2148 * q^83 - 620 * q^85 - 2872 * q^86 - 1296 * q^88 + 6000 * q^89 - 6116 * q^91 - 1002 * q^92 + 3662 * q^94 + 230 * q^95 + 612 * q^97 + 3964 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.78729	+	3.09567i	0.631902	+	1.09449i	0.987163	+	0.159718i	$0.0510586\pi$
$2$	1.78729	+	3.09567i	0.631902	+	1.09449i	−0.355261	+	0.934767i	$0.615608\pi$
$3$		0			0
$3$		0			0
$4$	−2.38879	+	4.13751i	−0.298599	+	0.517189i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−7.07987	−	12.2627i	−0.382277	−	0.662123i	0.609110	−	0.793086i	$-0.291527\pi$
$7$	−7.07987	−	12.2627i	−0.382277	−	0.662123i	−0.991387	+	0.130962i	$0.958193\pi$
$8$	11.5188			0.509062
$9$		0			0
$10$	−17.8729			−0.565190
$11$	−31.8319	−	55.1345i	−0.872516	−	1.51124i	−0.859385	−	0.511329i	$-0.829153\pi$
$11$	−31.8319	−	55.1345i	−0.872516	−	1.51124i	−0.0131312	−	0.999914i	$-0.504180\pi$
$12$		0			0
$13$	5.19795	−	9.00312i	0.110896	−	0.192078i	−0.805236	−	0.592955i	$-0.797961\pi$
$13$	5.19795	−	9.00312i	0.110896	−	0.192078i	0.916132	+	0.400877i	$0.131294\pi$
$14$	25.3075	−	43.8339i	0.483123	−	0.836794i
$15$		0			0
$16$	39.6977	+	68.7584i	0.620276	+	1.07435i
$17$	108.605			1.54945			0.774724	−	0.632300i	$-0.217889\pi$
$17$	108.605			1.54945			0.774724	+	0.632300i	$0.217889\pi$
$18$		0			0
$19$	18.6145			0.224761			0.112381	−	0.993665i	$-0.464152\pi$
$19$	18.6145			0.224761			0.112381	+	0.993665i	$0.464152\pi$
$20$	−11.9440	−	20.6876i	−0.133538	−	0.231294i
$21$		0			0
$22$	113.786	−	197.082i	1.10269	−	1.90991i
$23$	64.4120	−	111.565i	0.583949	−	1.01143i	−0.411057	−	0.911610i	$-0.634840\pi$
$23$	64.4120	−	111.565i	0.583949	−	1.01143i	0.995006	−	0.0998192i	$-0.0318264\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	37.1609			0.280302
$27$		0			0
$28$	67.6494			0.456590
$29$	−41.8248	−	72.4426i	−0.267816	−	0.463871i	0.700481	−	0.713671i	$-0.252969\pi$
$29$	−41.8248	−	72.4426i	−0.267816	−	0.463871i	−0.968298	+	0.249799i	$0.919635\pi$
$30$		0			0
$31$	5.23638	−	9.06967i	0.0303381	−	0.0525471i	−0.850458	−	0.526043i	$-0.823675\pi$
$31$	5.23638	−	9.06967i	0.0303381	−	0.0525471i	0.880796	+	0.473496i	$0.157008\pi$
$32$	−95.8273	+	165.978i	−0.529376	+	0.916906i
$33$		0			0
$34$	194.109	+	336.206i	0.979098	+	1.69585i
$35$	70.7987			0.341919
$36$		0			0
$37$	−81.8885			−0.363848			−0.181924	−	0.983313i	$-0.558233\pi$
$37$	−81.8885			−0.363848			−0.181924	+	0.983313i	$0.558233\pi$
$38$	33.2695	+	57.6245i	0.142027	+	0.245998i
$39$		0			0
$40$	−28.7969	+	49.8777i	−0.113830	+	0.197159i
$41$	153.726	−	266.262i	0.585562	−	1.01422i	−0.409244	−	0.912425i	$-0.634207\pi$
$41$	153.726	−	266.262i	0.585562	−	1.01422i	0.994805	−	0.101797i	$-0.0324593\pi$
$42$		0			0
$43$	111.220	+	192.638i	0.394438	+	0.683187i	0.993029	−	0.117868i	$-0.0376059\pi$
$43$	111.220	+	192.638i	0.394438	+	0.683187i	−0.598591	+	0.801055i	$0.704273\pi$
$44$	304.159			1.04213
$45$		0			0
$46$	460.491			1.47599
$47$	−180.965	−	313.441i	−0.561628	−	0.972768i	−0.997355	−	0.0726889i	$-0.976842\pi$
$47$	−180.965	−	313.441i	−0.561628	−	0.972768i	0.435727	−	0.900079i	$-0.356491\pi$
$48$		0			0
$49$	71.2509	−	123.410i	0.207728	−	0.359796i
$50$	44.6822	−	77.3918i	0.126380	−	0.218897i
$51$		0			0
$52$	24.8337	+	43.0132i	0.0662271	+	0.114709i
$53$	562.215			1.45710			0.728548	−	0.684994i	$-0.240195\pi$
$53$	562.215			1.45710			0.728548	+	0.684994i	$0.240195\pi$
$54$		0			0
$55$	318.319			0.780402
$56$	−81.5513	−	141.251i	−0.194603	−	0.337062i
$57$		0			0
$58$	149.506	−	258.952i	0.338467	−	0.586242i
$59$	−231.155	+	400.372i	−0.510065	+	0.883458i	0.489867	+	0.871797i	$0.337045\pi$
$59$	−231.155	+	400.372i	−0.510065	+	0.883458i	−0.999932	+	0.0116608i	$0.996288\pi$
$60$		0			0
$61$	324.533	+	562.108i	0.681184	+	1.17985i	0.974620	+	0.223867i	$0.0718682\pi$
$61$	324.533	+	562.108i	0.681184	+	1.17985i	−0.293435	+	0.955979i	$0.594799\pi$
$62$	37.4356			0.0766827
$63$		0			0
$64$	−49.9208			−0.0975015
$65$	25.9898	+	45.0156i	0.0495944	+	0.0859000i
$66$		0			0
$67$	−127.090	+	220.126i	−0.231739	+	0.401384i	−0.958320	−	0.285697i	$-0.907775\pi$
$67$	−127.090	+	220.126i	−0.231739	+	0.401384i	0.726581	+	0.687081i	$0.241108\pi$
$68$	−259.435	+	449.355i	−0.462664	+	0.801357i
$69$		0			0
$70$	126.538	+	219.170i	0.216059	+	0.374225i
$71$	−1092.93			−1.82685			−0.913426	−	0.407006i	$-0.866573\pi$
$71$	−1092.93			−1.82685			−0.913426	+	0.407006i	$0.866573\pi$
$72$		0			0
$73$	1034.52			1.65865			0.829324	−	0.558769i	$-0.188726\pi$
$73$	1034.52			1.65865			0.829324	+	0.558769i	$0.188726\pi$
$74$	−146.358	−	253.500i	−0.229916	−	0.398227i
$75$		0			0
$76$	−44.4663	+	77.0179i	−0.0671136	+	0.116244i
$77$	−450.731	+	780.690i	−0.667086	+	1.15543i
$78$		0			0
$79$	−575.927	−	997.534i	−0.820213	−	1.42065i	−0.905524	−	0.424296i	$-0.860522\pi$
$79$	−575.927	−	997.534i	−0.820213	−	1.42065i	0.0853111	−	0.996354i	$-0.472812\pi$
$80$	−396.977			−0.554792
$81$		0			0
$82$	1099.01			1.48007
$83$	−262.160	−	454.075i	−0.346697	−	0.600496i	0.638964	−	0.769237i	$-0.279363\pi$
$83$	−262.160	−	454.075i	−0.346697	−	0.600496i	−0.985660	+	0.168741i	$0.946030\pi$
$84$		0			0
$85$	−271.513	+	470.274i	−0.346467	+	0.600099i
$86$	−397.563	+	688.599i	−0.498492	+	0.863414i
$87$		0			0
$88$	−366.664	−	635.081i	−0.444165	−	0.769316i
$89$	656.485			0.781879			0.390940	−	0.920416i	$-0.372150\pi$
$89$	656.485			0.781879			0.390940	+	0.920416i	$0.372150\pi$
$90$		0			0
$91$	−147.203			−0.169573
$92$	307.734	+	533.010i	0.348733	+	0.604024i
$93$		0			0
$94$	646.874	−	1120.42i	0.709787	−	1.22939i
$95$	−46.5363	+	80.6033i	−0.0502582	+	0.0870497i
$96$		0			0
$97$	−562.755	−	974.721i	−0.589063	−	1.02029i	−0.994355	−	0.106100i	$-0.966163\pi$
$97$	−562.755	−	974.721i	−0.589063	−	1.02029i	0.405292	−	0.914187i	$-0.367170\pi$
$98$	509.383			0.525056
$99$		0			0
$100$	119.440			0.119440
$101$	190.162	+	329.371i	0.187345	+	0.324491i	0.944364	−	0.328902i	$-0.106678\pi$
$101$	190.162	+	329.371i	0.187345	+	0.324491i	−0.757019	+	0.653393i	$0.773345\pi$
$102$		0			0
$103$	−382.139	+	661.884i	−0.365566	+	0.633178i	−0.988867	−	0.148804i	$-0.952458\pi$
$103$	−382.139	+	661.884i	−0.365566	+	0.633178i	0.623301	+	0.781982i	$0.285791\pi$
$104$	59.8740	−	103.705i	0.0564531	−	0.0977797i
$105$		0			0
$106$	1004.84	+	1740.43i	0.920742	+	1.59477i
$107$	−816.083			−0.737325			−0.368662	−	0.929563i	$-0.620184\pi$
$107$	−816.083			−0.737325			−0.368662	+	0.929563i	$0.620184\pi$
$108$		0			0
$109$	606.775			0.533198			0.266599	−	0.963808i	$-0.414100\pi$
$109$	606.775			0.533198			0.266599	+	0.963808i	$0.414100\pi$
$110$	568.928	+	985.412i	0.493137	+	0.854139i
$111$		0			0
$112$	562.109	−	973.601i	0.474235	−	0.821399i
$113$	13.6613	−	23.6621i	0.0113730	−	0.0196986i	−0.860283	−	0.509817i	$-0.829713\pi$
$113$	13.6613	−	23.6621i	0.0113730	−	0.0196986i	0.871656	+	0.490118i	$0.163046\pi$
$114$		0			0
$115$	322.060	+	557.824i	0.261150	+	0.452325i
$116$	399.643			0.319879
$117$		0			0
$118$	−1652.56			−1.28924
$119$	−768.910	−	1331.79i	−0.592318	−	1.02593i
$120$		0			0
$121$	−1361.04	+	2357.39i	−1.02257	+	1.77114i
$122$	−1160.07	+	2009.30i	−0.860883	+	1.49109i
$123$		0			0
$124$	25.0172	+	43.3311i	0.0181179	+	0.0313810i
$125$	125.000			0.0894427
$126$		0			0
$127$	−1206.22			−0.842794			−0.421397	−	0.906876i	$-0.638460\pi$
$127$	−1206.22			−0.842794			−0.421397	+	0.906876i	$0.638460\pi$
$128$	677.396	+	1173.28i	0.467765	+	0.810192i
$129$		0			0
$130$	−92.9024	+	160.912i	−0.0626775	+	0.108561i
$131$	766.002	−	1326.75i	0.510885	−	0.884878i	−0.489036	−	0.872264i	$-0.662651\pi$
$131$	766.002	−	1326.75i	0.510885	−	0.884878i	0.999920	−	0.0126146i	$-0.00401547\pi$
$132$		0			0
$133$	−131.789	−	228.264i	−0.0859212	−	0.148820i
$134$	−908.585			−0.585745
$135$		0			0
$136$	1251.00			0.788765
$137$	−1236.06	−	2140.92i	−0.770830	−	1.33512i	−0.937109	−	0.349038i	$-0.886509\pi$
$137$	−1236.06	−	2140.92i	−0.770830	−	1.33512i	0.166279	−	0.986079i	$-0.446825\pi$
$138$		0			0
$139$	−6.06336	+	10.5020i	−0.00369991	+	0.00640843i	−0.867869	−	0.496792i	$-0.834511\pi$
$139$	−6.06336	+	10.5020i	−0.00369991	+	0.00640843i	0.864170	+	0.503201i	$0.167844\pi$
$140$	−169.123	+	292.930i	−0.102097	+	0.176837i
$141$		0			0
$142$	−1953.37	−	3383.34i	−1.15439	−	1.99946i
$143$	−661.843			−0.387036
$144$		0			0
$145$	418.248			0.239542
$146$	1848.98	+	3202.53i	1.04810	+	1.81537i
$147$		0			0
$148$	195.615	−	338.815i	0.108645	−	0.188178i
$149$	1568.26	−	2716.30i	0.862258	−	1.49348i	−0.00748582	−	0.999972i	$-0.502383\pi$
$149$	1568.26	−	2716.30i	0.862258	−	1.49348i	0.869744	−	0.493503i	$-0.164284\pi$
$150$		0			0
$151$	1350.04	+	2338.33i	0.727580	+	1.26020i	0.957903	+	0.287091i	$0.0926881\pi$
$151$	1350.04	+	2338.33i	0.727580	+	1.26020i	−0.230324	+	0.973114i	$0.573979\pi$
$152$	214.416			0.114418
$153$		0			0
$154$	−3222.35			−1.68613
$155$	26.1819	+	45.3483i	0.0135676	+	0.0234998i
$156$		0			0
$157$	−221.314	+	383.326i	−0.112502	+	0.194858i	−0.916778	−	0.399397i	$-0.869220\pi$
$157$	−221.314	+	383.326i	−0.112502	+	0.194858i	0.804277	+	0.594255i	$0.202553\pi$
$158$	2058.69	−	3565.76i	1.03659	−	1.79542i
$159$		0			0
$160$	−479.136	−	829.889i	−0.236744	−	0.410053i
$161$	−1824.11			−0.892921
$162$		0			0
$163$	−2116.29			−1.01694			−0.508469	−	0.861080i	$-0.669788\pi$
$163$	−2116.29			−1.01694			−0.508469	+	0.861080i	$0.669788\pi$
$164$	734.441	+	1272.09i	0.349696	+	0.605692i
$165$		0			0
$166$	937.111	−	1623.12i	0.438156	−	0.758909i
$167$	−647.312	+	1121.18i	−0.299943	+	0.519517i	−0.976123	−	0.217220i	$-0.930301\pi$
$167$	−647.312	+	1121.18i	−0.299943	+	0.519517i	0.676180	+	0.736737i	$0.263634\pi$
$168$		0			0
$169$	1044.46	+	1809.06i	0.475404	+	0.823424i
$170$	−1941.09			−0.875732
$171$		0			0
$172$	−1062.72			−0.471116
$173$	−1461.09	−	2530.67i	−0.642106	−	1.11216i	−0.984962	−	0.172772i	$-0.944728\pi$
$173$	−1461.09	−	2530.67i	−0.642106	−	1.11216i	0.342856	−	0.939388i	$-0.388606\pi$
$174$		0			0
$175$	−176.997	+	306.567i	−0.0764554	+	0.132425i
$176$	2527.31	−	4377.42i	1.08240	−	1.87478i
$177$		0			0
$178$	1173.33	+	2032.26i	0.494071	+	0.855756i
$179$	3955.51			1.65167			0.825834	−	0.563913i	$-0.190705\pi$
$179$	3955.51			1.65167			0.825834	+	0.563913i	$0.190705\pi$
$180$		0			0
$181$	−2694.00			−1.10632			−0.553159	−	0.833076i	$-0.686578\pi$
$181$	−2694.00			−1.10632			−0.553159	+	0.833076i	$0.686578\pi$
$182$	−263.095	−	455.693i	−0.107153	−	0.185595i
$183$		0			0
$184$	741.946	−	1285.09i	0.297266	−	0.514880i
$185$	204.721	−	354.588i	0.0813590	−	0.140918i
$186$		0			0
$187$	−3457.11	−	5987.89i	−1.35192	−	2.34159i
$188$	1729.15			0.670806
$189$		0			0
$190$	−332.695			−0.127033
$191$	428.173	+	741.618i	0.162207	+	0.280951i	0.935660	−	0.352903i	$-0.114805\pi$
$191$	428.173	+	741.618i	0.162207	+	0.280951i	−0.773453	+	0.633854i	$0.781472\pi$
$192$		0			0
$193$	867.607	−	1502.74i	0.323584	−	0.560464i	−0.657641	−	0.753332i	$-0.728446\pi$
$193$	867.607	−	1502.74i	0.323584	−	0.560464i	0.981225	+	0.192868i	$0.0617789\pi$
$194$	2011.61	−	3484.21i	0.744460	−	1.28944i
$195$		0			0
$196$	340.407	+	589.602i	0.124055	+	0.214870i
$197$	2943.95			1.06471			0.532354	−	0.846522i	$-0.321308\pi$
$197$	2943.95			1.06471			0.532354	+	0.846522i	$0.321308\pi$
$198$		0			0
$199$	−4172.06			−1.48618			−0.743088	−	0.669193i	$-0.766640\pi$
$199$	−4172.06			−1.48618			−0.743088	+	0.669193i	$0.766640\pi$
$200$	−143.985	−	249.388i	−0.0509062	−	0.0881721i
$201$		0			0
$202$	−679.749	+	1177.36i	−0.236767	+	0.410093i
$203$	−592.228	+	1025.77i	−0.204760	+	0.354655i
$204$		0			0
$205$	768.632	+	1331.31i	0.261871	+	0.453574i
$206$	−2731.97			−0.924006
$207$		0			0
$208$	825.387			0.275146
$209$	−592.536	−	1026.30i	−0.196108	−	0.339669i
$210$		0			0
$211$	−1925.52	+	3335.10i	−0.628239	+	1.08814i	0.359666	+	0.933081i	$0.382891\pi$
$211$	−1925.52	+	3335.10i	−0.628239	+	1.08814i	−0.987905	+	0.155060i	$0.950443\pi$
$212$	−1343.01	+	2326.17i	−0.435088	+	0.753594i
$213$		0			0
$214$	−1458.58	−	2526.33i	−0.465917	−	0.806991i
$215$	−1112.20			−0.352796
$216$		0			0
$217$	−148.291			−0.0463902
$218$	1084.48	+	1878.38i	0.336928	+	0.583577i
$219$		0			0
$220$	−760.398	+	1317.05i	−0.233027	+	0.403615i
$221$	564.524	−	977.785i	0.171828	−	0.297615i
$222$		0			0
$223$	−410.357	−	710.759i	−0.123227	−	0.213435i	0.797812	−	0.602907i	$-0.205991\pi$
$223$	−410.357	−	710.759i	−0.123227	−	0.213435i	−0.921038	+	0.389472i	$0.872658\pi$
$224$	2713.78			0.809473
$225$		0			0
$226$	97.6667			0.0287464
$227$	2630.61	+	4556.36i	0.769163	+	1.33223i	0.938018	+	0.346588i	$0.112660\pi$
$227$	2630.61	+	4556.36i	0.769163	+	1.33223i	−0.168855	+	0.985641i	$0.554007\pi$
$228$		0			0
$229$	−9.79945	+	16.9731i	−0.00282780	+	0.00489789i	−0.867436	−	0.497549i	$-0.834233\pi$
$229$	−9.79945	+	16.9731i	−0.00282780	+	0.00489789i	0.864608	+	0.502447i	$0.167567\pi$
$230$	−1151.23	+	1993.98i	−0.330042	+	0.571649i
$231$		0			0
$232$	−481.770	−	834.449i	−0.136335	−	0.236139i
$233$	−3181.79			−0.894619			−0.447309	−	0.894379i	$-0.647618\pi$
$233$	−3181.79			−0.894619			−0.447309	+	0.894379i	$0.647618\pi$
$234$		0			0
$235$	1809.65			0.502335
$236$	−1104.36	−	1912.81i	−0.304610	−	0.527599i
$237$		0			0
$238$	2748.53	−	4760.59i	0.748574	−	1.29657i
$239$	−817.052	+	1415.18i	−0.221133	+	0.383013i	−0.955152	−	0.296115i	$-0.904309\pi$
$239$	−817.052	+	1415.18i	−0.221133	+	0.383013i	0.734019	+	0.679128i	$0.237642\pi$
$240$		0			0
$241$	−707.355	−	1225.17i	−0.189065	−	0.327471i	0.755874	−	0.654718i	$-0.227212\pi$
$241$	−707.355	−	1225.17i	−0.189065	−	0.327471i	−0.944939	+	0.327247i	$0.893879\pi$
$242$	−9730.28			−2.58465
$243$		0			0
$244$	−3100.97			−0.813604
$245$	356.254	+	617.051i	0.0928990	+	0.160906i
$246$		0			0
$247$	96.7575	−	167.589i	0.0249252	−	0.0431718i
$248$	60.3166	−	104.471i	0.0154440	−	0.0267497i
$249$		0			0
$250$	223.411	+	386.959i	0.0565190	+	0.0978938i
$251$	5932.53			1.49186			0.745932	−	0.666022i	$-0.232005\pi$
$251$	5932.53			1.49186			0.745932	+	0.666022i	$0.232005\pi$
$252$		0			0
$253$	−8201.42			−2.03802
$254$	−2155.86	−	3734.07i	−0.532563	−	0.922426i
$255$		0			0
$256$	−2621.08	+	4539.85i	−0.639913	+	1.10836i
$257$	−3500.65	+	6063.30i	−0.849666	+	1.47167i	0.0318400	+	0.999493i	$0.489863\pi$
$257$	−3500.65	+	6063.30i	−0.849666	+	1.47167i	−0.881506	+	0.472172i	$0.843470\pi$
$258$		0			0
$259$	579.760	+	1004.17i	0.139091	+	0.240913i
$260$	−248.337			−0.0592353
$261$		0			0
$262$	5476.26			1.29132
$263$	−1827.27	−	3164.93i	−0.428420	−	0.742045i	0.568313	−	0.822812i	$-0.307596\pi$
$263$	−1827.27	−	3164.93i	−0.428420	−	0.742045i	−0.996733	+	0.0807677i	$0.974263\pi$
$264$		0			0
$265$	−1405.54	+	2434.46i	−0.325817	+	0.564331i
$266$	471.088	−	815.948i	0.108587	−	0.188079i
$267$		0			0
$268$	−607.183	−	1051.67i	−0.138394	−	0.239706i
$269$	2589.46			0.586922			0.293461	−	0.955971i	$-0.405193\pi$
$269$	2589.46			0.586922			0.293461	+	0.955971i	$0.405193\pi$
$270$		0			0
$271$	4854.10			1.08806			0.544032	−	0.839064i	$-0.316897\pi$
$271$	4854.10			1.08806			0.544032	+	0.839064i	$0.316897\pi$
$272$	4311.37	+	7467.52i	0.961086	+	1.66465i
$273$		0			0
$274$	4418.39	−	7652.87i	0.974177	−	1.68732i
$275$	−795.798	+	1378.36i	−0.174503	+	0.302249i
$276$		0			0
$277$	3757.58	+	6508.31i	0.815058	+	1.41172i	0.909287	+	0.416170i	$0.136628\pi$
$277$	3757.58	+	6508.31i	0.815058	+	1.41172i	−0.0942291	+	0.995551i	$0.530039\pi$
$278$	−43.3478			−0.00935191
$279$		0			0
$280$	815.513			0.174058
$281$	1806.03	+	3128.14i	0.383412	+	0.664090i	0.991548	−	0.129744i	$-0.0414154\pi$
$281$	1806.03	+	3128.14i	0.383412	+	0.664090i	−0.608135	+	0.793834i	$0.708082\pi$
$282$		0			0
$283$	−2583.45	+	4474.67i	−0.542652	+	0.939900i	0.456099	+	0.889929i	$0.349246\pi$
$283$	−2583.45	+	4474.67i	−0.542652	+	0.939900i	−0.998751	+	0.0499712i	$0.984087\pi$
$284$	2610.77	−	4521.99i	0.545496	−	0.944827i
$285$		0			0
$286$	−1182.90	−	2048.85i	−0.244568	−	0.423605i
$287$	−4353.45			−0.895387
$288$		0			0
$289$	6882.07			1.40079
$290$	747.529	+	1294.76i	0.151367	+	0.262175i
$291$		0			0
$292$	−2471.25	+	4280.33i	−0.495271	+	0.857834i
$293$	2113.18	−	3660.13i	0.421342	−	0.729785i	−0.574729	−	0.818344i	$-0.694893\pi$
$293$	2113.18	−	3660.13i	0.421342	−	0.729785i	0.996071	+	0.0885584i	$0.0282260\pi$
$294$		0			0
$295$	−1155.77	−	2001.86i	−0.228108	−	0.395094i
$296$	−943.255			−0.185221
$297$		0			0
$298$	11211.7			2.17945
$299$	−669.621	−	1159.82i	−0.129516	−	0.224328i
$300$		0			0
$301$	1574.84	−	2727.71i	0.301569	−	0.522333i
$302$	−4825.81	+	8358.55i	−0.919517	+	1.59265i
$303$		0			0
$304$	738.954	+	1279.91i	0.139414	+	0.241472i
$305$	−3245.33			−0.609270
$306$		0			0
$307$	5734.25			1.06603			0.533015	−	0.846106i	$-0.321059\pi$
$307$	5734.25			1.06603			0.533015	+	0.846106i	$0.321059\pi$
$308$	−2153.41	−	3729.81i	−0.398383	−	0.690019i
$309$		0			0
$310$	−93.5891	+	162.101i	−0.0171468	+	0.0296991i
$311$	−3310.19	+	5733.42i	−0.603549	+	1.04538i	0.388730	+	0.921352i	$0.372914\pi$
$311$	−3310.19	+	5733.42i	−0.603549	+	1.04538i	−0.992279	+	0.124026i	$0.960419\pi$
$312$		0			0
$313$	−46.7155	−	80.9136i	−0.00843615	−	0.0146118i	0.861777	−	0.507288i	$-0.169352\pi$
$313$	−46.7155	−	80.9136i	−0.00843615	−	0.0146118i	−0.870213	+	0.492676i	$0.836019\pi$
$314$	−1582.20			−0.284360
$315$		0			0
$316$	5503.08			0.979659
$317$	−996.584	−	1726.13i	−0.176573	−	0.305834i	0.764131	−	0.645061i	$-0.223168\pi$
$317$	−996.584	−	1726.13i	−0.176573	−	0.305834i	−0.940705	+	0.339227i	$0.889835\pi$
$318$		0			0
$319$	−2662.72	+	4611.97i	−0.467348	+	0.809470i
$320$	124.802	−	216.163i	0.0218020	−	0.0377622i
$321$		0			0
$322$	−3260.21	−	5646.86i	−0.564238	−	0.977289i
$323$	2021.63			0.348256
$324$		0			0
$325$	−259.898			−0.0443586
$326$	−3782.42	−	6551.35i	−0.642605	−	1.11302i
$327$		0			0
$328$	1770.74	−	3067.01i	0.298087	−	0.516302i
$329$	−2562.42	+	4438.25i	−0.429395	+	0.743734i
$330$		0			0
$331$	1194.59	+	2069.09i	0.198370	+	0.343587i	0.948000	−	0.318270i	$-0.103102\pi$
$331$	1194.59	+	2069.09i	0.198370	+	0.343587i	−0.749630	+	0.661857i	$0.769769\pi$
$332$	2504.99			0.414093
$333$		0			0
$334$	−4627.73			−0.758138
$335$	−635.450	−	1100.63i	−0.103637	−	0.179504i
$336$		0			0
$337$	−5142.75	+	8907.50i	−0.831286	+	1.43983i	0.0657327	+	0.997837i	$0.479062\pi$
$337$	−5142.75	+	8907.50i	−0.831286	+	1.43983i	−0.897019	+	0.441992i	$0.854272\pi$
$338$	−3733.51	+	6466.63i	−0.600817	+	1.04065i
$339$		0			0
$340$	−1297.18	−	2246.77i	−0.206910	−	0.358378i
$341$	−666.735			−0.105882
$342$		0			0
$343$	−6874.58			−1.08219
$344$	1281.11	+	2218.95i	0.200794	+	0.347785i
$345$		0			0
$346$	5222.76	−	9046.09i	0.811495	−	1.40555i
$347$	−2115.10	+	3663.47i	−0.327218	+	0.566758i	−0.981959	−	0.189095i	$-0.939445\pi$
$347$	−2115.10	+	3663.47i	−0.327218	+	0.566758i	0.654741	+	0.755854i	$0.272778\pi$
$348$		0			0
$349$	5605.46	+	9708.94i	0.859752	+	1.48913i	0.872166	+	0.489211i	$0.162715\pi$
$349$	5605.46	+	9708.94i	0.859752	+	1.48913i	−0.0124138	+	0.999923i	$0.503952\pi$
$350$	−1265.38			−0.193249
$351$		0			0
$352$	12201.5			1.84756
$353$	5691.50	+	9857.98i	0.858154	+	1.48637i	0.873688	+	0.486486i	$0.161722\pi$
$353$	5691.50	+	9857.98i	0.858154	+	1.48637i	−0.0155346	+	0.999879i	$0.504945\pi$
$354$		0			0
$355$	2732.31	−	4732.51i	0.408496	−	0.707536i
$356$	−1568.21	+	2716.21i	−0.233468	+	0.404379i
$357$		0			0
$358$	7069.63	+	12245.0i	1.04369	+	1.80773i
$359$	8942.57			1.31468			0.657341	−	0.753593i	$-0.271681\pi$
$359$	8942.57			1.31468			0.657341	+	0.753593i	$0.271681\pi$
$360$		0			0
$361$	−6512.50			−0.949482
$362$	−4814.95	−	8339.74i	−0.699084	−	1.21085i
$363$		0			0
$364$	351.638	−	609.055i	0.0506342	−	0.0877010i
$365$	−2586.30	+	4479.60i	−0.370885	+	0.642391i
$366$		0			0
$367$	222.085	+	384.662i	0.0315878	+	0.0547118i	0.881387	−	0.472395i	$-0.156610\pi$
$367$	222.085	+	384.662i	0.0315878	+	0.0547118i	−0.849799	+	0.527106i	$0.823277\pi$
$368$	10228.0			1.44884
$369$		0			0
$370$	1463.58			0.205643
$371$	−3980.41	−	6894.27i	−0.557015	−	0.964778i
$372$		0			0
$373$	−1708.05	+	2958.42i	−0.237103	+	0.410674i	−0.959882	−	0.280405i	$-0.909531\pi$
$373$	−1708.05	+	2958.42i	−0.237103	+	0.410674i	0.722779	+	0.691079i	$0.242864\pi$
$374$	12357.7	−	21404.1i	1.70856	−	2.95931i
$375$		0			0
$376$	−2084.50	−	3610.45i	−0.285903	−	0.495199i
$377$	−869.613			−0.118799
$378$		0			0
$379$	598.277			0.0810855			0.0405428	−	0.999178i	$-0.487091\pi$
$379$	598.277			0.0810855			0.0405428	+	0.999178i	$0.487091\pi$
$380$	−222.331	−	385.089i	−0.0300141	−	0.0519860i
$381$		0			0
$382$	−1530.54	+	2650.97i	−0.204998	+	0.355066i
$383$	4528.59	−	7843.74i	0.604178	−	1.04647i	−0.388003	−	0.921658i	$-0.626835\pi$
$383$	4528.59	−	7843.74i	0.604178	−	1.04647i	0.992181	−	0.124808i	$-0.0398316\pi$
$384$		0			0
$385$	−2253.66	−	3903.45i	−0.298330	−	0.516723i
$386$	6202.65			0.817893
$387$		0			0
$388$	5377.22			0.703575
$389$	−315.703	−	546.814i	−0.0411485	−	0.0712714i	0.844718	−	0.535212i	$-0.179768\pi$
$389$	−315.703	−	546.814i	−0.0411485	−	0.0712714i	−0.885866	+	0.463941i	$0.846435\pi$
$390$		0			0
$391$	6995.47	−	12116.5i	0.904798	−	1.56716i
$392$	820.722	−	1421.53i	0.105747	−	0.183159i
$393$		0			0
$394$	5261.68	+	9113.49i	0.672791	+	1.16531i
$395$	5759.27			0.733620
$396$		0			0
$397$	−4615.39			−0.583475			−0.291738	−	0.956498i	$-0.594233\pi$
$397$	−4615.39			−0.583475			−0.291738	+	0.956498i	$0.594233\pi$
$398$	−7456.66	−	12915.3i	−0.939118	−	1.62660i
$399$		0			0
$400$	992.442	−	1718.96i	0.124055	−	0.214870i
$401$	−2345.60	+	4062.69i	−0.292104	+	0.505938i	−0.974307	−	0.225224i	$-0.927689\pi$
$401$	−2345.60	+	4062.69i	−0.292104	+	0.505938i	0.682203	+	0.731163i	$0.261022\pi$
$402$		0			0
$403$	−54.4369	−	94.2874i	−0.00672877	−	0.0116546i
$404$	−1817.03			−0.223764
$405$		0			0
$406$	−4233.93			−0.517552
$407$	2606.67	+	4514.88i	0.317464	+	0.549863i
$408$		0			0
$409$	7781.64	−	13478.2i	0.940776	−	1.62947i	0.176781	−	0.984250i	$-0.443432\pi$
$409$	7781.64	−	13478.2i	0.940776	−	1.62947i	0.763995	−	0.645222i	$-0.223235\pi$
$410$	−2747.53	+	4758.86i	−0.330953	+	0.573228i
$411$		0			0
$412$	−1825.70	−	3162.21i	−0.218315	−	0.378133i
$413$	6546.19			0.779944
$414$		0			0
$415$	2621.60			0.310095
$416$	996.212	+	1725.49i	0.117412	+	0.203363i
$417$		0			0
$418$	2118.06	−	3668.60i	0.247842	−	0.429275i
$419$	−2139.22	+	3705.23i	−0.249422	+	0.432011i	−0.963365	−	0.268192i	$-0.913574\pi$
$419$	−2139.22	+	3705.23i	−0.249422	+	0.432011i	0.713944	+	0.700203i	$0.246907\pi$
$420$		0			0
$421$	48.8531	+	84.6161i	0.00565548	+	0.00979558i	0.868839	−	0.495094i	$-0.164866\pi$
$421$	48.8531	+	84.6161i	0.00565548	+	0.00979558i	−0.863184	+	0.504890i	$0.831533\pi$
$422$	−13765.8			−1.58794
$423$		0			0
$424$	6476.02			0.741753
$425$	−1357.56	−	2351.37i	−0.154945	−	0.268372i
$426$		0			0
$427$	4595.31	−	7959.31i	0.520802	−	0.902056i
$428$	1949.45	−	3376.55i	0.220164	−	0.381336i
$429$		0			0
$430$	−1987.82	−	3443.00i	−0.222932	−	0.386130i
$431$	11932.9			1.33361			0.666806	−	0.745231i	$-0.267661\pi$
$431$	11932.9			1.33361			0.666806	+	0.745231i	$0.267661\pi$
$432$		0			0
$433$	6304.32			0.699691			0.349845	−	0.936807i	$-0.386234\pi$
$433$	6304.32			0.699691			0.349845	+	0.936807i	$0.386234\pi$
$434$	−265.039	−	459.062i	−0.0293141	−	0.0507734i
$435$		0			0
$436$	−1449.46	+	2510.54i	−0.159212	+	0.275764i
$437$	1199.00	−	2076.73i	0.131249	−	0.227330i
$438$		0			0
$439$	6461.34	+	11191.4i	0.702466	+	1.21671i	0.967598	+	0.252495i	$0.0812512\pi$
$439$	6461.34	+	11191.4i	0.702466	+	1.21671i	−0.265132	+	0.964212i	$0.585415\pi$
$440$	3666.64			0.397273
$441$		0			0
$442$	4035.87			0.434314
$443$	1912.21	+	3312.04i	0.205083	+	0.355214i	0.950159	−	0.311765i	$-0.100920\pi$
$443$	1912.21	+	3312.04i	0.205083	+	0.355214i	−0.745076	+	0.666979i	$0.767587\pi$
$444$		0			0
$445$	−1641.21	+	2842.66i	−0.174834	+	0.302821i
$446$	1466.85	−	2540.66i	0.155734	−	0.269740i
$447$		0			0
$448$	353.433	+	612.163i	0.0372726	+	0.0645580i
$449$	−530.656			−0.0557756			−0.0278878	−	0.999611i	$-0.508878\pi$
$449$	−530.656			−0.0557756			−0.0278878	+	0.999611i	$0.508878\pi$
$450$		0			0
$451$	−19573.6			−2.04365
$452$	65.2680	+	113.048i	0.00679193	+	0.0117640i
$453$		0			0
$454$	−9403.32	+	16287.0i	−0.972070	+	1.68367i
$455$	368.008	−	637.409i	0.0379176	−	0.0656752i
$456$		0			0
$457$	7796.80	+	13504.5i	0.798072	+	1.38230i	0.920870	+	0.389870i	$0.127480\pi$
$457$	7796.80	+	13504.5i	0.798072	+	1.38230i	−0.122798	+	0.992432i	$0.539187\pi$
$458$	−70.0577			−0.00714756
$459$		0			0
$460$	−3077.34			−0.311916
$461$	3637.30	+	6300.00i	0.367475	+	0.636486i	0.989170	−	0.146774i	$-0.0468889\pi$
$461$	3637.30	+	6300.00i	0.367475	+	0.636486i	−0.621695	+	0.783260i	$0.713556\pi$
$462$		0			0
$463$	−1342.57	+	2325.40i	−0.134761	+	0.233413i	−0.925506	−	0.378732i	$-0.876360\pi$
$463$	−1342.57	+	2325.40i	−0.134761	+	0.233413i	0.790745	+	0.612146i	$0.209693\pi$
$464$	3320.69	−	5751.61i	0.332240	−	0.575456i
$465$		0			0
$466$	−5686.78	−	9849.79i	−0.565311	−	0.979147i
$467$	−8844.77			−0.876418			−0.438209	−	0.898873i	$-0.644387\pi$
$467$	−8844.77			−0.876418			−0.438209	+	0.898873i	$0.644387\pi$
$468$		0			0
$469$	3599.12			0.354354
$470$	3234.37	+	5602.09i	0.317426	+	0.549799i
$471$		0			0
$472$	−2662.62	+	4611.79i	−0.259655	+	0.449735i
$473$	7080.67	−	12264.1i	0.688308	−	1.19218i
$474$		0			0
$475$	−232.682	−	403.017i	−0.0224761	−	0.0389298i
$476$	7347.07			0.707463
$477$		0			0
$478$	−5841.23			−0.558936
$479$	−6167.17	−	10681.9i	−0.588278	−	1.01893i	−0.994458	−	0.105134i	$-0.966473\pi$
$479$	−6167.17	−	10681.9i	−0.588278	−	1.01893i	0.406180	−	0.913793i	$-0.366861\pi$
$480$		0			0
$481$	−425.653	+	737.252i	−0.0403495	+	0.0698873i
$482$	2528.49	−	4379.48i	0.238941	−	0.413858i
$483$		0			0
$484$	−6502.49	−	11262.6i	−0.610677	−	1.05772i
$485$	5627.55			0.526874
$486$		0			0
$487$	3540.31			0.329419			0.164709	−	0.986342i	$-0.447331\pi$
$487$	3540.31			0.329419			0.164709	+	0.986342i	$0.447331\pi$
$488$	3738.22	+	6474.79i	0.346765	+	0.600615i
$489$		0			0
$490$	−1273.46	+	2205.69i	−0.117406	+	0.203353i
$491$	−3855.63	+	6678.14i	−0.354383	+	0.613809i	−0.987012	−	0.160646i	$-0.948642\pi$
$491$	−3855.63	+	6678.14i	−0.354383	+	0.613809i	0.632629	+	0.774455i	$0.281976\pi$
$492$		0			0
$493$	−4542.39	−	7867.64i	−0.414967	−	0.718744i
$494$	691.734			0.0630012
$495$		0			0
$496$	831.488			0.0752720
$497$	7737.77	+	13402.2i	0.698363	+	1.20960i
$498$		0			0
$499$	6081.29	−	10533.1i	0.545563	−	0.944943i	−0.453008	−	0.891506i	$-0.649649\pi$
$499$	6081.29	−	10533.1i	0.545563	−	0.944943i	0.998571	−	0.0534365i	$-0.0170175\pi$
$500$	−298.599	+	517.189i	−0.0267075	+	0.0462588i
$501$		0			0
$502$	10603.1	+	18365.2i	0.942711	+	1.63282i
$503$	−8796.85			−0.779786			−0.389893	−	0.920860i	$-0.627488\pi$
$503$	−8796.85			−0.779786			−0.389893	+	0.920860i	$0.627488\pi$
$504$		0			0
$505$	−1901.62			−0.167566
$506$	−14658.3	−	25388.9i	−1.28783	−	2.23058i
$507$		0			0
$508$	2881.41	−	4990.76i	0.251658	−	0.435884i
$509$	10974.1	−	19007.7i	0.955634	−	1.65521i	0.222722	−	0.974882i	$-0.428506\pi$
$509$	10974.1	−	19007.7i	0.955634	−	1.65521i	0.732911	−	0.680324i	$-0.238161\pi$
$510$		0			0
$511$	−7324.26	−	12686.0i	−0.634063	−	1.09823i
$512$	−7900.20			−0.681919
$513$		0			0
$514$	−25026.6			−2.14762
$515$	−1910.69	−	3309.42i	−0.163486	−	0.283166i
$516$		0			0
$517$	−11520.9	+	19954.9i	−0.980059	+	1.69751i
$518$	−2072.40	+	3589.50i	−0.175784	+	0.304466i
$519$		0			0
$520$	299.370	+	518.524i	0.0252466	+	0.0437284i
$521$	−11232.4			−0.944531			−0.472265	−	0.881456i	$-0.656564\pi$
$521$	−11232.4			−0.944531			−0.472265	+	0.881456i	$0.656564\pi$
$522$		0			0
$523$	−1962.88			−0.164112			−0.0820560	−	0.996628i	$-0.526149\pi$
$523$	−1962.88			−0.164112			−0.0820560	+	0.996628i	$0.526149\pi$
$524$	3659.64	+	6338.68i	0.305100	+	0.528448i
$525$		0			0
$526$	6531.72	−	11313.3i	0.541438	−	0.937798i
$527$	568.697	−	985.013i	0.0470073	−	0.0814190i
$528$		0			0
$529$	−2214.30	−	3835.28i	−0.181992	−	0.315220i
$530$	−10048.4			−0.823537
$531$		0			0
$532$	1259.26			0.102624
$533$	−1598.12	−	2768.03i	−0.129873	−	0.224947i
$534$		0			0
$535$	2040.21	−	3533.74i	0.164871	−	0.285565i
$536$	−1463.92	+	2535.58i	−0.117970	+	0.204329i
$537$		0			0
$538$	4628.11	+	8016.11i	0.370877	+	0.642378i
$539$	−9072.20			−0.724986
$540$		0			0
$541$	2816.86			0.223856			0.111928	−	0.993716i	$-0.464297\pi$
$541$	2816.86			0.223856			0.111928	+	0.993716i	$0.464297\pi$
$542$	8675.67	+	15026.7i	0.687549	+	1.19087i
$543$		0			0
$544$	−10407.3	+	18026.0i	−0.820240	+	1.42070i
$545$	−1516.94	+	2627.41i	−0.119227	+	0.206507i
$546$		0			0
$547$	−2264.45	−	3922.15i	−0.177004	−	0.306579i	0.763849	−	0.645395i	$-0.223307\pi$
$547$	−2264.45	−	3922.15i	−0.177004	−	0.306579i	−0.940853	+	0.338815i	$0.889974\pi$
$548$	11810.8			0.920676
$549$		0			0
$550$	−5689.28			−0.441076
$551$	−778.549	−	1348.49i	−0.0601947	−	0.104260i
$552$		0			0
$553$	−8154.97	+	14124.8i	−0.627097	+	1.08616i
$554$	−13431.7	+	23264.5i	−1.03007	+	1.78414i
$555$		0			0
$556$	−28.9682	−	50.1744i	−0.00220958	−	0.00382710i
$557$	−6267.47			−0.476771			−0.238385	−	0.971171i	$-0.576618\pi$
$557$	−6267.47			−0.476771			−0.238385	+	0.971171i	$0.576618\pi$
$558$		0			0
$559$	2312.46			0.174967
$560$	2810.54	+	4868.01i	0.212084	+	0.367341i
$561$		0			0
$562$	−6455.80	+	11181.8i	−0.484558	+	0.839279i
$563$	−4897.00	+	8481.86i	−0.366579	+	0.634934i	−0.989028	−	0.147727i	$-0.952804\pi$
$563$	−4897.00	+	8481.86i	−0.366579	+	0.634934i	0.622449	+	0.782660i	$0.286138\pi$
$564$		0			0
$565$	68.3065	+	118.310i	0.00508615	+	0.00880948i
$566$	−18469.5			−1.37161
$567$		0			0
$568$	−12589.2			−0.929981
$569$	3799.94	+	6581.69i	0.279968	+	0.484919i	0.971376	−	0.237545i	$-0.0763428\pi$
$569$	3799.94	+	6581.69i	0.279968	+	0.484919i	−0.691409	+	0.722464i	$0.743010\pi$
$570$		0			0
$571$	6047.07	−	10473.8i	0.443191	−	0.767630i	−0.554733	−	0.832028i	$-0.687180\pi$
$571$	6047.07	−	10473.8i	0.443191	−	0.767630i	0.997924	+	0.0643988i	$0.0205130\pi$
$572$	1581.01	−	2738.38i	0.115568	−	0.200170i
$573$		0			0
$574$	−7780.87	−	13476.9i	−0.565796	−	0.979988i
$575$	−3220.60			−0.233580
$576$		0			0
$577$	3113.85			0.224665			0.112332	−	0.993671i	$-0.464168\pi$
$577$	3113.85			0.224665			0.112332	+	0.993671i	$0.464168\pi$
$578$	12300.2	+	21304.7i	0.885161	+	1.53314i
$579$		0			0
$580$	−999.107	+	1730.50i	−0.0715270	+	0.123888i
$581$	−3712.12	+	6429.58i	−0.265068	+	0.459112i
$582$		0			0
$583$	−17896.4	−	30997.4i	−1.27134	−	2.20203i
$584$	11916.4			0.844354
$585$		0			0
$586$	15107.4			1.06499
$587$	2973.96	+	5151.04i	0.209111	+	0.362191i	0.951435	−	0.307850i	$-0.0996096\pi$
$587$	2973.96	+	5151.04i	0.209111	+	0.362191i	−0.742324	+	0.670042i	$0.766276\pi$
$588$		0			0
$589$	97.4727	−	168.828i	0.00681883	−	0.0118106i
$590$	4131.40	−	7155.80i	0.288283	−	0.499321i
$591$		0			0
$592$	−3250.79	−	5630.53i	−0.225687	−	0.390901i
$593$	−22153.0			−1.53409			−0.767043	−	0.641596i	$-0.778273\pi$
$593$	−22153.0			−1.53409			−0.767043	+	0.641596i	$0.778273\pi$
$594$		0			0
$595$	7689.10			0.529786
$596$	7492.47	+	12977.3i	0.514939	+	0.891901i
$597$		0			0
$598$	2393.61	−	4145.85i	0.163682	−	0.283506i
$599$	−13438.2	+	23275.6i	−0.916643	+	1.58767i	−0.112164	+	0.993690i	$0.535778\pi$
$599$	−13438.2	+	23275.6i	−0.916643	+	1.58767i	−0.804478	+	0.593982i	$0.797555\pi$
$600$		0			0
$601$	−12920.1	−	22378.2i	−0.876907	−	1.51885i	−0.854717	−	0.519094i	$-0.826269\pi$
$601$	−12920.1	−	22378.2i	−0.876907	−	1.51885i	−0.0221904	−	0.999754i	$-0.507064\pi$
$602$	11258.8			0.762249
$603$		0			0
$604$	−12899.8			−0.869019
$605$	−6805.20	−	11787.0i	−0.457307	−	0.792079i
$606$		0			0
$607$	1384.37	−	2397.80i	0.0925697	−	0.160335i	−0.816022	−	0.578021i	$-0.803825\pi$
$607$	1384.37	−	2397.80i	0.0925697	−	0.160335i	0.908592	+	0.417685i	$0.137159\pi$
$608$	−1783.78	+	3089.60i	−0.118983	+	0.206085i
$609$		0			0
$610$	−5800.35	−	10046.5i	−0.384999	−	0.666837i
$611$	−3762.60			−0.249130
$612$		0			0
$613$	10177.3			0.670563			0.335282	−	0.942118i	$-0.391169\pi$
$613$	10177.3			0.670563			0.335282	+	0.942118i	$0.391169\pi$
$614$	10248.8	+	17751.4i	0.673626	+	1.16675i
$615$		0			0
$616$	−5191.87	+	8992.58i	−0.339588	+	0.588184i
$617$	4208.61	−	7289.53i	0.274607	−	0.475633i	−0.695429	−	0.718595i	$-0.744786\pi$
$617$	4208.61	−	7289.53i	0.274607	−	0.475633i	0.970036	+	0.242962i	$0.0781190\pi$
$618$		0			0
$619$	6640.13	+	11501.0i	0.431162	+	0.746795i	0.996974	−	0.0777399i	$-0.0247704\pi$
$619$	6640.13	+	11501.0i	0.431162	+	0.746795i	−0.565812	+	0.824535i	$0.691437\pi$
$620$	−250.172			−0.0162051
$621$		0			0
$622$	−23665.1			−1.52553
$623$	−4647.83	−	8050.27i	−0.298895	−	0.517700i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	166.988	−	289.232i	0.0106616	−	0.0184665i
$627$		0			0
$628$	−1057.34	−	1831.37i	−0.0671857	−	0.116369i
$629$	−8893.52			−0.563764
$630$		0			0
$631$	−14454.1			−0.911903			−0.455951	−	0.890005i	$-0.650701\pi$
$631$	−14454.1			−0.911903			−0.455951	+	0.890005i	$0.650701\pi$
$632$	−6633.96	−	11490.4i	−0.417539	−	0.723199i
$633$		0			0
$634$	3562.37	−	6170.20i	0.223154	−	0.386514i
$635$	3015.55	−	5223.09i	0.188455	−	0.326413i
$636$		0			0
$637$	−740.717	−	1282.96i	−0.0460727	−	0.0798002i
$638$	−19036.2			−1.18127
$639$		0			0
$640$	−6773.96			−0.418381
$641$	10532.5	+	18242.8i	0.648997	+	1.12410i	0.983363	+	0.181653i	$0.0581447\pi$
$641$	10532.5	+	18242.8i	0.648997	+	1.12410i	−0.334366	+	0.942443i	$0.608522\pi$
$642$		0			0
$643$	3564.41	−	6173.73i	0.218610	−	0.378644i	−0.735773	−	0.677228i	$-0.763181\pi$
$643$	3564.41	−	6173.73i	0.218610	−	0.378644i	0.954383	+	0.298584i	$0.0965143\pi$
$644$	4357.43	−	7547.29i	0.266625	−	0.461809i
$645$		0			0
$646$	3613.24	+	6258.32i	0.220064	+	0.381161i
$647$	−1364.92			−0.0829376			−0.0414688	−	0.999140i	$-0.513204\pi$
$647$	−1364.92			−0.0829376			−0.0414688	+	0.999140i	$0.513204\pi$
$648$		0			0
$649$	29432.4			1.78016
$650$	−464.512	−	804.558i	−0.0280302	−	0.0485498i
$651$		0			0
$652$	5055.39	−	8756.18i	0.303657	−	0.525949i
$653$	6080.31	−	10531.4i	0.364381	−	0.631127i	−0.624295	−	0.781188i	$-0.714614\pi$
$653$	6080.31	−	10531.4i	0.364381	−	0.631127i	0.988677	+	0.150061i	$0.0479471\pi$
$654$		0			0
$655$	3830.01	+	6633.77i	0.228475	+	0.395730i
$656$	24410.3			1.45284
$657$		0			0
$658$	−18319.1			−1.08534
$659$	−3084.28	−	5342.14i	−0.182317	−	0.315782i	0.760352	−	0.649511i	$-0.225026\pi$
$659$	−3084.28	−	5342.14i	−0.182317	−	0.315782i	−0.942669	+	0.333729i	$0.891693\pi$
$660$		0			0
$661$	−9068.85	+	15707.7i	−0.533642	+	0.924295i	0.465586	+	0.885003i	$0.345844\pi$
$661$	−9068.85	+	15707.7i	−0.533642	+	0.924295i	−0.999228	+	0.0392922i	$0.987490\pi$
$662$	−4270.15	+	7396.11i	−0.250701	+	0.434226i
$663$		0			0
$664$	−3019.76	−	5230.38i	−0.176490	−	0.305690i
$665$	1317.89			0.0768502
$666$		0			0
$667$	−10776.1			−0.625564
$668$	−3092.59	−	5356.52i	−0.179125	−	0.310254i
$669$		0			0
$670$	2271.46	−	3934.29i	0.130977	−	0.226858i
$671$	20661.0	−	35786.0i	1.18869	−	2.05887i
$672$		0			0
$673$	10851.1	+	18794.6i	0.621512	+	1.07649i	0.989204	+	0.146543i	$0.0468148\pi$
$673$	10851.1	+	18794.6i	0.621512	+	1.07649i	−0.367692	+	0.929948i	$0.619852\pi$
$674$	−36766.3			−2.10116
$675$		0			0
$676$	−9980.02			−0.567821
$677$	−5235.29	−	9067.79i	−0.297206	−	0.514776i	0.678290	−	0.734795i	$-0.262721\pi$
$677$	−5235.29	−	9067.79i	−0.297206	−	0.514776i	−0.975496	+	0.220019i	$0.929388\pi$
$678$		0			0
$679$	−7968.47	+	13801.8i	−0.450371	+	0.780065i
$680$	−3127.49	+	5416.97i	−0.176373	+	0.305487i
$681$		0			0
$682$	−1191.65	−	2063.99i	−0.0669070	−	0.115886i
$683$	15386.0			0.861974			0.430987	−	0.902358i	$-0.358166\pi$
$683$	15386.0			0.861974			0.430987	+	0.902358i	$0.358166\pi$
$684$		0			0
$685$	12360.6			0.689451
$686$	−12286.8	−	21281.4i	−0.683840	−	1.18445i
$687$		0			0
$688$	−8830.33	+	15294.6i	−0.489321	+	0.847529i
$689$	2922.37	−	5061.69i	0.161587	−	0.279876i
$690$		0			0
$691$	−7595.57	−	13155.9i	−0.418161	−	0.724276i	0.577594	−	0.816324i	$-0.303992\pi$
$691$	−7595.57	−	13155.9i	−0.418161	−	0.724276i	−0.995755	+	0.0920487i	$0.970658\pi$
$692$	13960.9			0.766929
$693$		0			0
$694$	−15121.2			−0.827079
$695$	−30.3168	−	52.5102i	−0.00165465	−	0.00286594i
$696$		0			0
$697$	16695.5	−	28917.4i	0.907297	−	1.57148i
$698$	−20037.1	+	34705.3i	−1.08656	+	1.88197i
$699$		0			0
$700$	−845.617	−	1464.65i	−0.0456590	−	0.0790838i
$701$	5181.93			0.279199			0.139600	−	0.990208i	$-0.455418\pi$
$701$	5181.93			0.279199			0.139600	+	0.990208i	$0.455418\pi$
$702$		0			0
$703$	−1524.32			−0.0817791
$704$	1589.07	+	2752.36i	0.0850717	+	0.147348i
$705$		0			0
$706$	−20344.7	+	35238.1i	−1.08454	+	1.87847i
$707$	2692.65	−	4663.80i	0.143235	−	0.248091i
$708$		0			0
$709$	4393.27	+	7609.36i	0.232712	+	0.403069i	0.958605	−	0.284739i	$-0.0919068\pi$
$709$	4393.27	+	7609.36i	0.232712	+	0.403069i	−0.725893	+	0.687807i	$0.758573\pi$
$710$	19533.7			1.03252
$711$		0			0
$712$	7561.89			0.398025
$713$	−674.570	−	1168.39i	−0.0354318	−	0.0613696i
$714$		0			0
$715$	1654.61	−	2865.86i	0.0865438	−	0.149898i
$716$	−9448.89	+	16366.0i	−0.493187	+	0.854224i
$717$		0			0
$718$	15983.0	+	27683.3i	0.830750	+	1.43890i
$719$	14433.0			0.748625			0.374312	−	0.927303i	$-0.377879\pi$
$719$	14433.0			0.748625			0.374312	+	0.927303i	$0.377879\pi$
$720$		0			0
$721$	10822.0			0.558989
$722$	−11639.7	−	20160.6i	−0.599979	−	1.03919i
$723$		0			0
$724$	6435.41	−	11146.5i	0.330345	−	0.572175i
$725$	−1045.62	+	1811.07i	−0.0535632	+	0.0927742i
$726$		0			0
$727$	−13349.5	−	23121.9i	−0.681023	−	1.17957i	−0.974669	−	0.223653i	$-0.928202\pi$
$727$	−13349.5	−	23121.9i	−0.681023	−	1.17957i	0.293646	−	0.955914i	$-0.405131\pi$
$728$	−1695.60			−0.0863230
$729$		0			0
$730$	−18489.8			−0.937451
$731$	12079.0	+	20921.5i	0.611161	+	1.05856i
$732$		0			0
$733$	3866.92	−	6697.71i	0.194854	−	0.337497i	−0.751999	−	0.659165i	$-0.770910\pi$
$733$	3866.92	−	6697.71i	0.194854	−	0.337497i	0.946853	+	0.321668i	$0.104243\pi$
$734$	−793.859	+	1375.00i	−0.0399208	+	0.0691449i
$735$		0			0
$736$	12344.8	+	21381.9i	0.618257	+	1.07085i
$737$	16182.1			0.808784
$738$		0			0
$739$	28142.2			1.40085			0.700426	−	0.713725i	$-0.252994\pi$
$739$	28142.2			1.40085			0.700426	+	0.713725i	$0.252994\pi$
$740$	978.074	+	1694.07i	0.0485874	+	0.0841559i
$741$		0			0
$742$	14228.3	−	24644.1i	0.703957	−	1.21929i
$743$	11384.6	−	19718.6i	0.562125	−	0.973629i	−0.435186	−	0.900341i	$-0.643317\pi$
$743$	11384.6	−	19718.6i	0.562125	−	0.973629i	0.997311	−	0.0732884i	$-0.0233493\pi$
$744$		0			0
$745$	7841.28	+	13581.5i	0.385614	+	0.667902i
$746$	−12211.1			−0.599302
$747$		0			0
$748$	33033.3			1.61473
$749$	5777.76	+	10007.4i	0.281862	+	0.488200i
$750$		0			0
$751$	−254.918	+	441.531i	−0.0123863	+	0.0214537i	−0.872152	−	0.489235i	$-0.837276\pi$
$751$	−254.918	+	441.531i	−0.0123863	+	0.0214537i	0.859766	+	0.510688i	$0.170609\pi$
$752$	14367.8	−	24885.8i	0.696729	−	1.20677i
$753$		0			0
$754$	−1554.25	−	2692.04i	−0.0750695	−	0.130024i
$755$	−13500.4			−0.650767
$756$		0			0
$757$	−28105.6			−1.34943			−0.674713	−	0.738080i	$-0.735733\pi$
$757$	−28105.6			−1.34943			−0.674713	+	0.738080i	$0.735733\pi$
$758$	1069.29	+	1852.07i	0.0512381	+	0.0887469i
$759$		0			0
$760$	−536.041	+	928.450i	−0.0255845	+	0.0443137i
$761$	4347.82	−	7530.64i	0.207107	−	0.358720i	−0.743695	−	0.668519i	$-0.766929\pi$
$761$	4347.82	−	7530.64i	0.207107	−	0.358720i	0.950802	+	0.309799i	$0.100262\pi$
$762$		0			0
$763$	−4295.89	−	7440.70i	−0.203829	−	0.353043i
$764$	−4091.27			−0.193739
$765$		0			0
$766$	32375.5			1.52712
$767$	2403.06	+	4162.23i	0.113129	+	0.195945i
$768$		0			0
$769$	−2730.93	+	4730.12i	−0.128062	+	0.221811i	−0.922926	−	0.384978i	$-0.874209\pi$
$769$	−2730.93	+	4730.12i	−0.128062	+	0.221811i	0.794863	+	0.606788i	$0.207542\pi$
$770$	8055.87	−	13953.2i	0.377030	−	0.653036i
$771$		0			0
$772$	4145.06	+	7179.46i	0.193244	+	0.334708i
$773$	−37952.9			−1.76594			−0.882970	−	0.469430i	$-0.844459\pi$
$773$	−37952.9			−1.76594			−0.882970	+	0.469430i	$0.844459\pi$
$774$		0			0
$775$	−261.819			−0.0121352
$776$	−6482.24	−	11227.6i	−0.299870	−	0.519390i
$777$		0			0
$778$	1128.50	−	1954.63i	0.0520037	−	0.0900730i
$779$	2861.55	−	4956.34i	0.131612	−	0.227958i
$780$		0			0
$781$	34789.9	+	60257.9i	1.59396	+	2.76082i
$782$	50011.7			2.28697
$783$		0			0
$784$	11314.0			0.515396

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.78729 + 3.09567i) q^{2} +(-2.38879 + 4.13751i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.07987 - 12.2627i) q^{7} +11.5188 q^{8} +O(q^{10})\)	\(q+(1.78729 + 3.09567i) q^{2} +(-2.38879 + 4.13751i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.07987 - 12.2627i) q^{7} +11.5188 q^{8} -17.8729 q^{10} +(-31.8319 - 55.1345i) q^{11} +(5.19795 - 9.00312i) q^{13} +(25.3075 - 43.8339i) q^{14} +(39.6977 + 68.7584i) q^{16} +108.605 q^{17} +18.6145 q^{19} +(-11.9440 - 20.6876i) q^{20} +(113.786 - 197.082i) q^{22} +(64.4120 - 111.565i) q^{23} +(-12.5000 - 21.6506i) q^{25} +37.1609 q^{26} +67.6494 q^{28} +(-41.8248 - 72.4426i) q^{29} +(5.23638 - 9.06967i) q^{31} +(-95.8273 + 165.978i) q^{32} +(194.109 + 336.206i) q^{34} +70.7987 q^{35} -81.8885 q^{37} +(33.2695 + 57.6245i) q^{38} +(-28.7969 + 49.8777i) q^{40} +(153.726 - 266.262i) q^{41} +(111.220 + 192.638i) q^{43} +304.159 q^{44} +460.491 q^{46} +(-180.965 - 313.441i) q^{47} +(71.2509 - 123.410i) q^{49} +(44.6822 - 77.3918i) q^{50} +(24.8337 + 43.0132i) q^{52} +562.215 q^{53} +318.319 q^{55} +(-81.5513 - 141.251i) q^{56} +(149.506 - 258.952i) q^{58} +(-231.155 + 400.372i) q^{59} +(324.533 + 562.108i) q^{61} +37.4356 q^{62} -49.9208 q^{64} +(25.9898 + 45.0156i) q^{65} +(-127.090 + 220.126i) q^{67} +(-259.435 + 449.355i) q^{68} +(126.538 + 219.170i) q^{70} -1092.93 q^{71} +1034.52 q^{73} +(-146.358 - 253.500i) q^{74} +(-44.4663 + 77.0179i) q^{76} +(-450.731 + 780.690i) q^{77} +(-575.927 - 997.534i) q^{79} -396.977 q^{80} +1099.01 q^{82} +(-262.160 - 454.075i) q^{83} +(-271.513 + 470.274i) q^{85} +(-397.563 + 688.599i) q^{86} +(-366.664 - 635.081i) q^{88} +656.485 q^{89} -147.203 q^{91} +(307.734 + 533.010i) q^{92} +(646.874 - 1120.42i) q^{94} +(-46.5363 + 80.6033i) q^{95} +(-562.755 - 974.721i) q^{97} +509.383 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8	\( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 - 34 * q^4 - 30 * q^5 - 40 * q^7 + 132 * q^8 + 40 * q^10 - 88 * q^11 - 20 * q^13 - 180 * q^14 - 58 * q^16 + 248 * q^17 - 92 * q^19 - 170 * q^20 + 74 * q^22 - 210 * q^23 - 150 * q^25 + 8 * q^26 + 704 * q^28 - 296 * q^29 + 104 * q^31 - 722 * q^32 + 428 * q^34 + 400 * q^35 - 408 * q^37 + 20 * q^38 - 330 * q^40 - 344 * q^41 - 512 * q^43 + 1432 * q^44 - 372 * q^46 - 238 * q^47 - 68 * q^49 - 100 * q^50 + 468 * q^52 + 1700 * q^53 + 880 * q^55 - 2316 * q^56 - 890 * q^58 - 1840 * q^59 + 364 * q^61 + 2076 * q^62 - 1980 * q^64 - 100 * q^65 - 88 * q^67 - 236 * q^68 - 900 * q^70 + 2728 * q^71 + 1672 * q^73 - 1316 * q^74 + 2106 * q^76 - 840 * q^77 + 680 * q^79 + 580 * q^80 + 3484 * q^82 - 2148 * q^83 - 620 * q^85 - 2872 * q^86 - 1296 * q^88 + 6000 * q^89 - 6116 * q^91 - 1002 * q^92 + 3662 * q^94 + 230 * q^95 + 612 * q^97 + 3964 * q^98

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