LMFDB - Embedded newform 98.5.d.c.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,5,Mod(19,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not 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:	$10.1302563822$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$0.662827 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	98.31
Dual form			98.5.d.c.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 + 2.44949i) q^{2} +(13.8528 + 7.99789i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(24.1168 - 13.9239i) q^{5} +45.2429i q^{6} -22.6274 q^{8} +(87.4325 + 151.438i) q^{9} +O(q^{10})$	\(q+(1.41421 + 2.44949i) q^{2} +(13.8528 + 7.99789i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(24.1168 - 13.9239i) q^{5} +45.2429i q^{6} -22.6274 q^{8} +(87.4325 + 151.438i) q^{9} +(68.2127 + 39.3826i) q^{10} +(69.8320 - 120.953i) q^{11} +(-110.822 + 63.9831i) q^{12} +101.931i q^{13} +445.446 q^{15} +(-32.0000 - 55.4256i) q^{16} +(-470.154 - 271.443i) q^{17} +(-247.296 + 428.330i) q^{18} +(-121.203 + 69.9767i) q^{19} +222.782i q^{20} +395.029 q^{22} +(-114.823 - 198.880i) q^{23} +(-313.452 - 180.972i) q^{24} +(75.2473 - 130.332i) q^{25} +(-249.678 + 144.152i) q^{26} +1501.44i q^{27} -383.113 q^{29} +(629.955 + 1091.11i) q^{30} +(-344.238 - 198.746i) q^{31} +(90.5097 - 156.767i) q^{32} +(1934.73 - 1117.02i) q^{33} -1535.52i q^{34} -1398.92 q^{36} +(449.456 + 778.480i) q^{37} +(-342.814 - 197.924i) q^{38} +(-815.230 + 1412.02i) q^{39} +(-545.701 + 315.061i) q^{40} +657.862i q^{41} +1155.70 q^{43} +(558.656 + 967.621i) q^{44} +(4217.19 + 2434.79i) q^{45} +(324.770 - 562.517i) q^{46} +(-1121.08 + 647.253i) q^{47} -1023.73i q^{48} +425.663 q^{50} +(-4341.95 - 7520.48i) q^{51} +(-706.196 - 407.722i) q^{52} +(2584.22 - 4476.00i) q^{53} +(-3677.77 + 2123.36i) q^{54} -3889.32i q^{55} -2238.66 q^{57} +(-541.803 - 938.431i) q^{58} +(-3598.54 - 2077.62i) q^{59} +(-1781.78 + 3086.14i) q^{60} +(1593.56 - 920.043i) q^{61} -1124.28i q^{62} +512.000 q^{64} +(1419.27 + 2458.24i) q^{65} +(5472.25 + 3159.40i) q^{66} +(3157.79 - 5469.45i) q^{67} +(3761.23 - 2171.55i) q^{68} -3673.38i q^{69} +1263.28 q^{71} +(-1978.37 - 3426.64i) q^{72} +(3460.15 + 1997.72i) q^{73} +(-1271.25 + 2201.87i) q^{74} +(2084.76 - 1203.64i) q^{75} -1119.63i q^{76} -4611.63 q^{78} +(5307.13 + 9192.22i) q^{79} +(-1543.48 - 891.126i) q^{80} +(-4926.35 + 8532.69i) q^{81} +(-1611.43 + 930.357i) q^{82} +5750.31i q^{83} -15118.2 q^{85} +(1634.41 + 2830.88i) q^{86} +(-5307.17 - 3064.09i) q^{87} +(-1580.12 + 2736.84i) q^{88} +(3626.09 - 2093.52i) q^{89} +13773.3i q^{90} +1837.17 q^{92} +(-3179.10 - 5506.36i) q^{93} +(-3170.88 - 1830.71i) q^{94} +(-1948.69 + 3375.23i) q^{95} +(2507.62 - 1447.77i) q^{96} -3814.28i q^{97} +24422.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 196 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 + 196 * q^9	$ 8 q - 32 q^{4} + 196 q^{9} - 24 q^{11} + 1776 q^{15} - 256 q^{16} - 1424 q^{18} + 3296 q^{22} - 104 q^{23} - 948 q^{25} - 2816 q^{29} + 2528 q^{30} - 3136 q^{36} + 3392 q^{37} - 2200 q^{39} - 4048 q^{43} - 192 q^{44} + 2304 q^{46} + 8768 q^{50} - 18936 q^{51} + 16680 q^{53} - 12128 q^{57} - 352 q^{58} - 7104 q^{60} + 4096 q^{64} + 6048 q^{65} + 20816 q^{67} - 3968 q^{71} - 11392 q^{72} - 576 q^{74} - 24448 q^{78} + 29616 q^{79} - 30852 q^{81} - 59376 q^{85} + 18800 q^{86} - 13184 q^{88} + 1664 q^{92} - 18192 q^{93} - 7240 q^{95} + 144320 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 196 * q^9 - 24 * q^11 + 1776 * q^15 - 256 * q^16 - 1424 * q^18 + 3296 * q^22 - 104 * q^23 - 948 * q^25 - 2816 * q^29 + 2528 * q^30 - 3136 * q^36 + 3392 * q^37 - 2200 * q^39 - 4048 * q^43 - 192 * q^44 + 2304 * q^46 + 8768 * q^50 - 18936 * q^51 + 16680 * q^53 - 12128 * q^57 - 352 * q^58 - 7104 * q^60 + 4096 * q^64 + 6048 * q^65 + 20816 * q^67 - 3968 * q^71 - 11392 * q^72 - 576 * q^74 - 24448 * q^78 + 29616 * q^79 - 30852 * q^81 - 59376 * q^85 + 18800 * q^86 - 13184 * q^88 + 1664 * q^92 - 18192 * q^93 - 7240 * q^95 + 144320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$3$	13.8528	+	7.99789i	1.53919	+	0.888654i	0.998886	+	0.0471876i	$0.0150259\pi$
$3$	13.8528	+	7.99789i	1.53919	+	0.888654i	0.540309	+	0.841467i	$0.318307\pi$
$4$	−4.00000	+	6.92820i	−0.250000	+	0.433013i
$5$	24.1168	−	13.9239i	0.964673	−	0.556954i	0.0670647	−	0.997749i	$-0.478637\pi$
$5$	24.1168	−	13.9239i	0.964673	−	0.556954i	0.897608	+	0.440795i	$0.145303\pi$
$6$			45.2429i			1.25675i
$7$		0			0
$7$		0			0
$8$	−22.6274			−0.353553
$9$	87.4325	+	151.438i	1.07941	+	1.86960i
$10$	68.2127	+	39.3826i	0.682127	+	0.393826i
$11$	69.8320	−	120.953i	0.577124	−	0.999608i	−0.418683	−	0.908132i	$-0.637508\pi$
$11$	69.8320	−	120.953i	0.577124	−	0.999608i	0.995807	−	0.0914757i	$-0.0291584\pi$
$12$	−110.822	+	63.9831i	−0.769597	+	0.444327i
$13$			101.931i			0.603140i	0.953444	+	0.301570i	$0.0975106\pi$
$13$			101.931i			0.603140i	−0.953444	+	0.301570i	$0.902489\pi$
$14$		0			0
$15$	445.446			1.97976
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−470.154	−	271.443i	−1.62683	−	0.939251i	−0.985031	−	0.172377i	$-0.944855\pi$
$17$	−470.154	−	271.443i	−1.62683	−	0.939251i	−0.641799	−	0.766873i	$-0.721812\pi$
$18$	−247.296	+	428.330i	−0.763261	+	1.32201i
$19$	−121.203	+	69.9767i	−0.335743	+	0.193841i	−0.658388	−	0.752679i	$-0.728761\pi$
$19$	−121.203	+	69.9767i	−0.335743	+	0.193841i	0.322645	+	0.946520i	$0.395428\pi$
$20$			222.782i			0.556954i
$21$		0			0
$22$	395.029			0.816177
$23$	−114.823	−	198.880i	−0.217057	−	0.375954i	0.736850	−	0.676057i	$-0.236313\pi$
$23$	−114.823	−	198.880i	−0.217057	−	0.375954i	−0.953907	+	0.300102i	$0.902979\pi$
$24$	−313.452	−	180.972i	−0.544188	−	0.314187i
$25$	75.2473	−	130.332i	0.120396	−	0.208531i
$26$	−249.678	+	144.152i	−0.369346	+	0.213242i
$27$			1501.44i			2.05959i
$28$		0			0
$29$	−383.113			−0.455544			−0.227772	−	0.973714i	$-0.573144\pi$
$29$	−383.113			−0.455544			−0.227772	+	0.973714i	$0.573144\pi$
$30$	629.955	+	1091.11i	0.699950	+	1.21235i
$31$	−344.238	−	198.746i	−0.358208	−	0.206812i	0.310086	−	0.950708i	$-0.399642\pi$
$31$	−344.238	−	198.746i	−0.358208	−	0.206812i	−0.668294	+	0.743897i	$0.732975\pi$
$32$	90.5097	−	156.767i	0.0883883	−	0.153093i
$33$	1934.73	−	1117.02i	1.77661	−	1.02573i
$34$		−	1535.52i		−	1.32830i
$35$		0			0
$36$	−1398.92			−1.07941
$37$	449.456	+	778.480i	0.328310	+	0.568649i	0.982177	−	0.187961i	$-0.0601877\pi$
$37$	449.456	+	778.480i	0.328310	+	0.568649i	−0.653867	+	0.756610i	$0.726854\pi$
$38$	−342.814	−	197.924i	−0.237406	−	0.137066i
$39$	−815.230	+	1412.02i	−0.535983	+	0.928349i
$40$	−545.701	+	315.061i	−0.341063	+	0.196913i
$41$			657.862i			0.391352i	0.980669	+	0.195676i	$0.0626900\pi$
$41$			657.862i			0.391352i	−0.980669	+	0.195676i	$0.937310\pi$
$42$		0			0
$43$	1155.70			0.625041			0.312521	−	0.949911i	$-0.398827\pi$
$43$	1155.70			0.625041			0.312521	+	0.949911i	$0.398827\pi$
$44$	558.656	+	967.621i	0.288562	+	0.499804i
$45$	4217.19	+	2434.79i	2.08256	+	1.20237i
$46$	324.770	−	562.517i	0.153483	−	0.265840i
$47$	−1121.08	+	647.253i	−0.507504	+	0.293007i	−0.731807	−	0.681512i	$-0.761323\pi$
$47$	−1121.08	+	647.253i	−0.507504	+	0.293007i	0.224303	+	0.974519i	$0.427989\pi$
$48$		−	1023.73i		−	0.444327i
$49$		0			0
$50$	425.663			0.170265
$51$	−4341.95	−	7520.48i	−1.66934	−	2.89138i
$52$	−706.196	−	407.722i	−0.261167	−	0.150785i
$53$	2584.22	−	4476.00i	0.919978	−	1.59345i	0.120532	−	0.992709i	$-0.461540\pi$
$53$	2584.22	−	4476.00i	0.919978	−	1.59345i	0.799445	−	0.600739i	$-0.205127\pi$
$54$	−3677.77	+	2123.36i	−1.26124	+	0.728176i
$55$		−	3889.32i		−	1.28573i
$56$		0			0
$57$	−2238.66			−0.689031
$58$	−541.803	−	938.431i	−0.161059	−	0.278963i
$59$	−3598.54	−	2077.62i	−1.03377	−	0.596846i	−0.115706	−	0.993284i	$-0.536913\pi$
$59$	−3598.54	−	2077.62i	−1.03377	−	0.596846i	−0.918062	+	0.396438i	$0.870246\pi$
$60$	−1781.78	+	3086.14i	−0.494940	+	0.857261i
$61$	1593.56	−	920.043i	0.428262	−	0.247257i	−0.270344	−	0.962764i	$-0.587138\pi$
$61$	1593.56	−	920.043i	0.428262	−	0.247257i	0.698606	+	0.715507i	$0.253804\pi$
$62$		−	1124.28i		−	0.292476i
$63$		0			0
$64$	512.000			0.125000
$65$	1419.27	+	2458.24i	0.335921	+	0.581832i
$66$	5472.25	+	3159.40i	1.25625	+	0.725299i
$67$	3157.79	−	5469.45i	0.703450	−	1.21841i	−0.263798	−	0.964578i	$-0.584975\pi$
$67$	3157.79	−	5469.45i	0.703450	−	1.21841i	0.967248	−	0.253833i	$-0.0816913\pi$
$68$	3761.23	−	2171.55i	0.813415	−	0.469625i
$69$		−	3673.38i		−	0.771556i
$70$		0			0
$71$	1263.28			0.250601			0.125301	−	0.992119i	$-0.460010\pi$
$71$	1263.28			0.250601			0.125301	+	0.992119i	$0.460010\pi$
$72$	−1978.37	−	3426.64i	−0.381630	−	0.661003i
$73$	3460.15	+	1997.72i	0.649305	+	0.374877i	0.788190	−	0.615432i	$-0.211018\pi$
$73$	3460.15	+	1997.72i	0.649305	+	0.374877i	−0.138885	+	0.990309i	$0.544352\pi$
$74$	−1271.25	+	2201.87i	−0.232150	+	0.402096i
$75$	2084.76	−	1203.64i	0.370625	−	0.213980i
$76$		−	1119.63i		−	0.193841i
$77$		0			0
$78$	−4611.63			−0.757994
$79$	5307.13	+	9192.22i	0.850366	+	1.47288i	0.880879	+	0.473342i	$0.156953\pi$
$79$	5307.13	+	9192.22i	0.850366	+	1.47288i	−0.0305129	+	0.999534i	$0.509714\pi$
$80$	−1543.48	−	891.126i	−0.241168	−	0.139239i
$81$	−4926.35	+	8532.69i	−0.750854	+	1.30052i
$82$	−1611.43	+	930.357i	−0.239653	+	0.138364i
$83$			5750.31i			0.834709i	0.908744	+	0.417355i	$0.137043\pi$
$83$			5750.31i			0.834709i	−0.908744	+	0.417355i	$0.862957\pi$
$84$		0			0
$85$	−15118.2			−2.09248
$86$	1634.41	+	2830.88i	0.220985	+	0.382758i
$87$	−5307.17	−	3064.09i	−0.701171	−	0.404821i
$88$	−1580.12	+	2736.84i	−0.204044	+	0.353415i
$89$	3626.09	−	2093.52i	0.457782	−	0.264301i	−0.253329	−	0.967380i	$-0.581526\pi$
$89$	3626.09	−	2093.52i	0.457782	−	0.264301i	0.711111	+	0.703080i	$0.248192\pi$
$90$			13773.3i			1.70040i
$91$		0			0
$92$	1837.17			0.217057
$93$	−3179.10	−	5506.36i	−0.367568	−	0.636647i
$94$	−3170.88	−	1830.71i	−0.358859	−	0.207188i
$95$	−1948.69	+	3375.23i	−0.215921	+	0.373987i
$96$	2507.62	−	1447.77i	0.272094	−	0.157093i
$97$		−	3814.28i		−	0.405386i	−0.979242	−	0.202693i	$-0.935031\pi$
$97$		−	3814.28i		−	0.405386i	0.979242	−	0.202693i	$-0.0649694\pi$
$98$		0			0
$99$	24422.3			2.49182
$100$	601.978	+	1042.66i	0.0601978	+	0.104266i
$101$	−4265.53	−	2462.71i	−0.418149	−	0.241418i	0.276136	−	0.961118i	$-0.410946\pi$
$101$	−4265.53	−	2462.71i	−0.418149	−	0.241418i	−0.694285	+	0.719700i	$0.744279\pi$
$102$	12280.9	−	21271.1i	1.18040	−	2.04451i
$103$	−16361.5	+	9446.32i	−1.54223	+	0.890407i	−0.543532	+	0.839389i	$0.682913\pi$
$103$	−16361.5	+	9446.32i	−1.54223	+	0.890407i	−0.998698	+	0.0510180i	$0.983753\pi$
$104$		−	2306.43i		−	0.213242i
$105$		0			0
$106$	14618.5			1.30104
$107$	4239.70	+	7343.37i	0.370311	+	0.641398i	0.989613	−	0.143755i	$-0.0459176\pi$
$107$	4239.70	+	7343.37i	0.370311	+	0.641398i	−0.619302	+	0.785153i	$0.712584\pi$
$108$	−10402.3	−	6005.78i	−0.891830	−	0.514899i
$109$	−5838.98	+	10113.4i	−0.491455	+	0.851225i	−0.999952	−	0.00983867i	$-0.996868\pi$
$109$	−5838.98	+	10113.4i	−0.491455	+	0.851225i	0.508496	+	0.861064i	$0.330202\pi$
$110$	9526.85	−	5500.33i	0.787343	−	0.454573i
$111$			14378.8i			1.16702i
$112$		0			0
$113$	19683.8			1.54153			0.770763	−	0.637121i	$-0.219875\pi$
$113$	19683.8			1.54153			0.770763	+	0.637121i	$0.219875\pi$
$114$	−3165.95	−	5483.58i	−0.243609	−	0.421944i
$115$	−5538.35	−	3197.57i	−0.418779	−	0.241782i
$116$	1532.45	−	2654.28i	0.113886	−	0.197256i
$117$	−15436.1	+	8912.05i	−1.12763	+	0.651037i
$118$		−	11752.8i		−	0.844067i
$119$		0			0
$120$	−10079.3			−0.699950
$121$	−2432.52	−	4213.24i	−0.166144	−	0.287770i
$122$	4507.27	+	2602.27i	0.302827	+	0.174837i
$123$	−5261.51	+	9113.20i	−0.347776	+	0.602366i
$124$	2753.90	−	1589.97i	0.179104	−	0.103406i
$125$			13213.9i			0.845689i
$126$		0			0
$127$	−27965.5			−1.73386			−0.866931	−	0.498428i	$-0.833911\pi$
$127$	−27965.5			−1.73386			−0.866931	+	0.498428i	$0.833911\pi$
$128$	724.077	+	1254.14i	0.0441942	+	0.0765466i
$129$	16009.6	+	9243.17i	0.962060	+	0.555446i
$130$	−4014.29	+	6952.96i	−0.237532	+	0.411418i
$131$	1013.02	−	584.866i	0.0590302	−	0.0340811i	−0.470194	−	0.882563i	$-0.655816\pi$
$131$	1013.02	−	584.866i	0.0590302	−	0.0340811i	0.529225	+	0.848482i	$0.322483\pi$
$132$			17872.3i			1.02573i
$133$		0			0
$134$	17863.1			0.994828
$135$	20905.9	+	36210.1i	1.14710	+	1.98683i
$136$	10638.4	+	6142.06i	0.575171	+	0.332075i
$137$	10442.3	−	18086.6i	0.556359	−	0.963641i	−0.441438	−	0.897292i	$-0.645531\pi$
$137$	10442.3	−	18086.6i	0.556359	−	0.963641i	0.997796	−	0.0663495i	$-0.0211352\pi$
$138$	8997.90	−	5194.94i	0.472480	−	0.272786i
$139$		−	3499.87i		−	0.181143i	−0.995890	−	0.0905716i	$-0.971131\pi$
$139$		−	3499.87i		−	0.181143i	0.995890	−	0.0905716i	$-0.0288694\pi$
$140$		0			0
$141$	−20706.6			−1.04153
$142$	1786.55	+	3094.40i	0.0886010	+	0.153461i
$143$	12328.8	+	7118.02i	0.602903	+	0.348086i
$144$	5595.68	−	9692.00i	0.269853	−	0.467400i
$145$	−9239.46	+	5334.40i	−0.439451	+	0.253717i
$146$			11300.8i			0.530156i
$147$		0			0
$148$	−7191.29			−0.328310
$149$	−14766.9	−	25577.0i	−0.665146	−	1.15207i	−0.979246	−	0.202677i	$-0.935036\pi$
$149$	−14766.9	−	25577.0i	−0.665146	−	1.15207i	0.314100	−	0.949390i	$-0.398297\pi$
$150$	5896.60	+	3404.40i	0.262071	+	0.151307i
$151$	−12890.4	+	22326.8i	−0.565344	+	0.979204i	0.431674	+	0.902030i	$0.357923\pi$
$151$	−12890.4	+	22326.8i	−0.565344	+	0.979204i	−0.997018	+	0.0771741i	$0.975410\pi$
$152$	2742.51	−	1583.39i	0.118703	−	0.0685332i
$153$		−	94931.9i		−	4.05536i
$154$		0			0
$155$	−11069.2			−0.460738
$156$	−6521.84	−	11296.2i	−0.267991	−	0.464175i
$157$	−22195.7	−	12814.7i	−0.900470	−	0.519887i	−0.0231177	−	0.999733i	$-0.507359\pi$
$157$	−22195.7	−	12814.7i	−0.900470	−	0.519887i	−0.877353	+	0.479846i	$0.840693\pi$
$158$	−15010.8	+	25999.5i	−0.601299	+	1.04148i
$159$	71597.0	−	41336.6i	2.83205	−	1.63508i
$160$		−	5040.97i		−	0.196913i
$161$		0			0
$162$	−27867.7			−1.06187
$163$	3091.39	+	5354.45i	0.116353	+	0.201530i	0.918320	−	0.395839i	$-0.129546\pi$
$163$	3091.39	+	5354.45i	0.116353	+	0.201530i	−0.801967	+	0.597369i	$0.796213\pi$
$164$	−4557.80	−	2631.45i	−0.169460	−	0.0978379i
$165$	31106.4	−	53877.8i	1.14257	−	1.97898i
$166$	−14085.3	+	8132.17i	−0.511153	+	0.295114i
$167$			39270.9i			1.40811i	0.710144	+	0.704056i	$0.248630\pi$
$167$			39270.9i			1.40811i	−0.710144	+	0.704056i	$0.751370\pi$
$168$		0			0
$169$	18171.2			0.636223
$170$	−21380.3	−	37031.8i	−0.739803	−	1.28138i
$171$	−21194.2	−	12236.5i	−0.724811	−	0.418470i
$172$	−4622.80	+	8006.93i	−0.156260	+	0.270651i
$173$	−28497.3	+	16452.9i	−0.952165	+	0.549732i	−0.893753	−	0.448560i	$-0.851937\pi$
$173$	−28497.3	+	16452.9i	−0.952165	+	0.549732i	−0.0584119	+	0.998293i	$0.518604\pi$
$174$		−	17333.1i		−	0.572504i
$175$		0			0
$176$	−8938.50			−0.288562
$177$	−33233.2	−	57561.5i	−1.06078	−	1.83732i
$178$	10256.1	+	5921.38i	0.323701	+	0.186889i
$179$	2383.94	−	4129.11i	0.0744029	−	0.128870i	−0.826424	−	0.563049i	$-0.809628\pi$
$179$	2383.94	−	4129.11i	0.0744029	−	0.128870i	0.900826	+	0.434179i	$0.142962\pi$
$180$	−33737.5	+	19478.4i	−1.04128	+	0.601184i
$181$		−	35195.4i		−	1.07431i	−0.843484	−	0.537154i	$-0.819499\pi$
$181$		−	35195.4i		−	1.07431i	0.843484	−	0.537154i	$-0.180501\pi$
$182$		0			0
$183$	29433.6			0.878904
$184$	2598.16	+	4500.14i	0.0767414	+	0.132920i
$185$	21678.9	+	12516.3i	0.633423	+	0.365707i
$186$	8991.84	−	15574.3i	0.259910	−	0.450177i
$187$	−65663.6	+	37910.9i	−1.87776	+	1.08413i
$188$		−	10356.1i		−	0.293007i
$189$		0			0
$190$	−11023.5			−0.305359
$191$	−11657.5	−	20191.4i	−0.319551	−	0.553478i	0.660844	−	0.750524i	$-0.270199\pi$
$191$	−11657.5	−	20191.4i	−0.319551	−	0.553478i	−0.980394	+	0.197046i	$0.936865\pi$
$192$	7092.61	+	4094.92i	0.192399	+	0.111082i
$193$	−29591.9	+	51254.6i	−0.794434	+	1.37600i	0.128764	+	0.991675i	$0.458899\pi$
$193$	−29591.9	+	51254.6i	−0.794434	+	1.37600i	−0.923198	+	0.384325i	$0.874434\pi$
$194$	9343.04	−	5394.21i	0.248247	−	0.143326i
$195$			45404.5i			1.19407i
$196$		0			0
$197$	−60902.2			−1.56928			−0.784640	−	0.619952i	$-0.787152\pi$
$197$	−60902.2			−1.56928			−0.784640	+	0.619952i	$0.787152\pi$
$198$	34538.4	+	59822.3i	0.880992	+	1.52592i
$199$	34742.1	+	20058.4i	0.877304	+	0.506512i	0.869769	−	0.493460i	$-0.164268\pi$
$199$	34742.1	+	20058.4i	0.877304	+	0.506512i	0.00753551	+	0.999972i	$0.497601\pi$
$200$	−1702.65	+	2949.08i	−0.0425663	+	0.0737270i
$201$	87488.1	−	50511.3i	2.16549	−	1.25025i
$202$		−	13931.2i		−	0.341417i
$203$		0			0
$204$	69471.2			1.66934
$205$	9159.97	+	15865.5i	0.217965	+	0.377526i
$206$	−46277.3	−	26718.2i	−1.09052	−	0.629613i
$207$	20078.6	−	34777.1i	0.468589	−	0.811621i
$208$	5649.57	−	3261.78i	0.130584	−	0.0753924i
$209$			19546.4i			0.447482i
$210$		0			0
$211$	21929.0			0.492554			0.246277	−	0.969200i	$-0.420793\pi$
$211$	21929.0			0.492554			0.246277	+	0.969200i	$0.420793\pi$
$212$	20673.7	+	35808.0i	0.459989	+	0.796724i
$213$	17499.9	+	10103.6i	0.385724	+	0.222698i
$214$	−11991.7	+	20770.2i	−0.261850	+	0.453537i
$215$	27871.8	−	16091.8i	0.602960	−	0.348119i
$216$		−	33973.8i		−	0.728176i
$217$		0			0
$218$	−33030.3			−0.695023
$219$	31955.1	+	55347.8i	0.666272	+	1.15402i
$220$	26946.0	+	15557.3i	0.556736	+	0.321432i
$221$	27668.4	−	47923.0i	0.566499	−	0.981205i
$222$	−35220.7	+	20334.7i	−0.714648	+	0.412602i
$223$			64358.0i			1.29418i	0.762416	+	0.647088i	$0.224013\pi$
$223$			64358.0i			1.29418i	−0.762416	+	0.647088i	$0.775987\pi$
$224$		0			0
$225$	26316.2			0.519827
$226$	27837.0	+	48215.2i	0.545012	+	0.943989i
$227$	37910.1	+	21887.4i	0.735704	+	0.424759i	0.820505	−	0.571639i	$-0.193692\pi$
$227$	37910.1	+	21887.4i	0.735704	+	0.424759i	−0.0848015	+	0.996398i	$0.527026\pi$
$228$	8954.65	−	15509.9i	0.172258	−	0.298359i
$229$	−24687.3	+	14253.2i	−0.470763	+	0.271795i	−0.716559	−	0.697526i	$-0.754284\pi$
$229$	−24687.3	+	14253.2i	−0.470763	+	0.271795i	0.245796	+	0.969322i	$0.420951\pi$
$230$		−	18088.2i		−	0.341931i
$231$		0			0
$232$	8668.85			0.161059
$233$	1097.45	+	1900.83i	0.0202149	+	0.0350132i	0.875956	−	0.482391i	$-0.160232\pi$
$233$	1097.45	+	1900.83i	0.0202149	+	0.0350132i	−0.855741	+	0.517404i	$0.826898\pi$
$234$	−43659.9	−	25207.1i	−0.797354	−	0.460353i
$235$	−18024.5	+	31219.4i	−0.326383	+	0.565313i
$236$	28788.3	−	16621.0i	0.516884	−	0.298423i
$237$			169783.i			3.02273i
$238$		0			0
$239$	80942.6			1.41704			0.708519	−	0.705692i	$-0.249364\pi$
$239$	80942.6			1.41704			0.708519	+	0.705692i	$0.249364\pi$
$240$	−14254.3	−	24689.1i	−0.247470	−	0.428630i
$241$	−37253.5	−	21508.3i	−0.641406	−	0.370316i	0.143750	−	0.989614i	$-0.454084\pi$
$241$	−37253.5	−	21508.3i	−0.641406	−	0.370316i	−0.785156	+	0.619298i	$0.787417\pi$
$242$	6880.19	−	11916.8i	0.117482	−	0.203484i
$243$	−31163.7	+	17992.4i	−0.527760	+	0.304702i
$244$			14720.7i			0.247257i
$245$		0			0
$246$	−29763.6			−0.491830
$247$	−7132.76	−	12354.3i	−0.116913	−	0.202500i
$248$	7789.22	+	4497.11i	0.126646	+	0.0731189i
$249$	−45990.4	+	79657.6i	−0.741768	+	1.28478i
$250$	−32367.3	+	18687.3i	−0.517877	+	0.298996i
$251$		−	31568.5i		−	0.501080i	−0.968106	−	0.250540i	$-0.919392\pi$
$251$		−	31568.5i		−	0.501080i	0.968106	−	0.250540i	$-0.0806082\pi$
$252$		0			0
$253$	−32073.4			−0.501076
$254$	−39549.1	−	68501.1i	−0.613013	−	1.06177i
$255$	−209428.	−	120913.i	−3.22073	−	1.85949i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	58981.4	−	34052.9i	0.892995	−	0.515571i	0.0180739	−	0.999837i	$-0.494247\pi$
$257$	58981.4	−	34052.9i	0.892995	−	0.515571i	0.874921	+	0.484266i	$0.160913\pi$
$258$			52287.3i			0.785519i
$259$		0			0
$260$	−22708.3			−0.335921
$261$	−33496.5	−	58017.6i	−0.491721	−	0.851685i
$262$	2865.25	+	1654.25i	0.0417406	+	0.0240990i
$263$	4173.78	−	7229.20i	0.0603418	−	0.104515i	−0.834276	−	0.551346i	$-0.814114\pi$
$263$	4173.78	−	7229.20i	0.0603418	−	0.104515i	0.894618	+	0.446831i	$0.147448\pi$
$264$	−43778.0	+	25275.2i	−0.628127	+	0.362649i
$265$		−	143929.i		−	2.04954i
$266$		0			0
$267$	66975.1			0.939488
$268$	25262.3	+	43755.6i	0.351725	+	0.609205i
$269$	79605.9	+	45960.5i	1.10012	+	0.635156i	0.936253	−	0.351326i	$-0.114269\pi$
$269$	79605.9	+	45960.5i	1.10012	+	0.635156i	0.163869	+	0.986482i	$0.447603\pi$
$270$	−59130.8	+	102417.i	−0.811122	+	1.40490i
$271$	4446.49	−	2567.18i	0.0605450	−	0.0349557i	−0.469422	−	0.882974i	$-0.655538\pi$
$271$	4446.49	−	2567.18i	0.0605450	−	0.0349557i	0.529967	+	0.848018i	$0.322204\pi$
$272$			34744.8i			0.469625i
$273$		0			0
$274$	59070.5			0.786810
$275$	−10509.3	−	18202.7i	−0.138966	−	0.240697i
$276$	25449.9	+	14693.5i	0.334094	+	0.192889i
$277$	33127.1	−	57377.8i	0.431741	−	0.747798i	−0.565282	−	0.824898i	$-0.691233\pi$
$277$	33127.1	−	57377.8i	0.431741	−	0.747798i	0.997023	+	0.0770996i	$0.0245660\pi$
$278$	8572.89	−	4949.56i	0.110927	−	0.0640438i
$279$		−	69507.4i		−	0.892941i
$280$		0			0
$281$	38156.4			0.483230			0.241615	−	0.970372i	$-0.422323\pi$
$281$	38156.4			0.483230			0.241615	+	0.970372i	$0.422323\pi$
$282$	−29283.6	−	50720.7i	−0.368236	−	0.637804i
$283$	−95464.8	−	55116.6i	−1.19198	−	0.688192i	−0.233228	−	0.972422i	$-0.574929\pi$
$283$	−95464.8	−	55116.6i	−1.19198	−	0.688192i	−0.958756	+	0.284230i	$0.908262\pi$
$284$	−5053.13	+	8752.27i	−0.0626504	+	0.108514i
$285$	−53989.4	+	31170.8i	−0.664690	+	0.383759i
$286$			40265.6i			0.492268i
$287$		0			0
$288$	31653.9			0.381630
$289$	105603.	+	182909.i	1.26438	+	2.18998i
$290$	−26133.1	−	15088.0i	−0.310739	−	0.179405i
$291$	30506.2	−	52838.3i	0.360248	−	0.623968i
$292$	−27681.2	+	15981.7i	−0.324653	+	0.187438i
$293$		−	79011.7i		−	0.920357i	−0.887826	−	0.460179i	$-0.847785\pi$
$293$		−	79011.7i		−	0.920357i	0.887826	−	0.460179i	$-0.152215\pi$
$294$		0			0
$295$	−115714.			−1.32966
$296$	−10170.0	−	17615.0i	−0.116075	−	0.201048i
$297$	181604.	+	104849.i	2.05879	+	1.18864i
$298$	41767.1	−	72342.8i	0.470329	−	0.814634i
$299$	20271.9	−	11704.0i	0.226753	−	0.130916i
$300$			19258.2i			0.213980i
$301$		0			0
$302$	−72919.1			−0.799517
$303$	−39392.9	−	68230.6i	−0.429075	−	0.743179i
$304$	7757.00	+	4478.51i	0.0839357	+	0.0484603i
$305$	25621.1	−	44377.0i	0.275421	−	0.477044i
$306$	232535.	−	134254.i	2.48339	−	1.43379i
$307$			2801.57i			0.0297252i	0.999890	+	0.0148626i	$0.00473109\pi$
$307$			2801.57i			0.0297252i	−0.999890	+	0.0148626i	$0.995269\pi$
$308$		0			0
$309$	−302203.			−3.16506
$310$	−15654.3	−	27114.0i	−0.162896	−	0.282143i
$311$	17891.5	+	10329.7i	0.184981	+	0.106799i	0.589631	−	0.807673i	$-0.299273\pi$
$311$	17891.5	+	10329.7i	0.184981	+	0.106799i	−0.404650	+	0.914472i	$0.632607\pi$
$312$	18446.5	−	31950.3i	0.189498	−	0.328221i
$313$	32368.6	−	18688.0i	0.330397	−	0.190755i	−0.325620	−	0.945501i	$-0.605573\pi$
$313$	32368.6	−	18688.0i	0.330397	−	0.190755i	0.656017	+	0.754746i	$0.272240\pi$
$314$		−	72490.8i		−	0.735231i
$315$		0			0
$316$	−84914.1			−0.850366
$317$	53333.0	+	92375.5i	0.530735	+	0.919259i	0.999357	+	0.0358607i	$0.0114173\pi$
$317$	53333.0	+	92375.5i	0.530735	+	0.919259i	−0.468622	+	0.883399i	$0.655249\pi$
$318$	202507.	+	116917.i	2.00256	+	1.15618i
$319$	−26753.5	+	46338.5i	−0.262905	+	0.455366i
$320$	12347.8	−	7129.01i	0.120584	−	0.0696193i
$321$			135634.i			1.31632i
$322$		0			0
$323$	75978.8			0.728262
$324$	−39410.8	−	68261.5i	−0.375427	−	0.650259i
$325$	13284.8	+	7670.00i	0.125773	+	0.0726154i
$326$	−8743.77	+	15144.7i	−0.0822742	+	0.142503i
$327$	−161772.	+	93399.0i	−1.51289	+	0.873468i
$328$		−	14885.7i		−	0.138364i
$329$		0			0
$330$	175964.			1.61583
$331$	−54181.4	−	93844.9i	−0.494532	−	0.856554i	0.505448	−	0.862857i	$-0.331327\pi$
$331$	−54181.4	−	93844.9i	−0.494532	−	0.856554i	−0.999980	+	0.00630282i	$0.997994\pi$
$332$	−39839.3	−	23001.2i	−0.361440	−	0.208677i
$333$	−78594.1	+	136129.i	−0.708764	+	1.22761i
$334$	−96193.6	+	55537.4i	−0.862289	+	0.497843i
$335$		−	175874.i		−	1.56716i
$336$		0			0
$337$	186946.			1.64610			0.823050	−	0.567968i	$-0.192270\pi$
$337$	186946.			1.64610			0.823050	+	0.567968i	$0.192270\pi$
$338$	25697.9	+	44510.1i	0.224939	+	0.389605i
$339$	272674.	+	157429.i	2.37271	+	1.36988i
$340$	60472.6	−	104742.i	0.523119	−	0.906069i
$341$	−48077.7	+	27757.7i	−0.413461	+	0.238712i
$342$		−	69219.9i		−	0.591805i
$343$		0			0
$344$	−26150.5			−0.220985
$345$	−51147.6	−	88590.2i	−0.429721	−	0.744299i
$346$	−80602.6	−	46536.0i	−0.673282	−	0.388720i
$347$	31613.7	−	54756.5i	0.262552	−	0.454754i	−0.704367	−	0.709836i	$-0.748769\pi$
$347$	31613.7	−	54756.5i	0.262552	−	0.454754i	0.966919	+	0.255082i	$0.0821024\pi$
$348$	42457.3	−	24512.7i	0.350586	−	0.202411i
$349$		−	93605.0i		−	0.768508i	−0.923227	−	0.384254i	$-0.874459\pi$
$349$		−	93605.0i		−	0.768508i	0.923227	−	0.384254i	$-0.125541\pi$
$350$		0			0
$351$	−153043.			−1.24222
$352$	−12640.9	−	21894.8i	−0.102022	−	0.176707i
$353$	−124059.	−	71625.3i	−0.995583	−	0.574800i	−0.0886445	−	0.996063i	$-0.528254\pi$
$353$	−124059.	−	71625.3i	−0.995583	−	0.574800i	−0.906938	+	0.421263i	$0.861587\pi$
$354$	93997.5	−	162809.i	0.750084	−	1.29918i
$355$	30466.3	−	17589.7i	0.241748	−	0.139573i
$356$			33496.4i			0.264301i
$357$		0			0
$358$	13485.6			0.105222
$359$	−51169.9	−	88628.9i	−0.397032	−	0.687680i	0.596326	−	0.802742i	$-0.296627\pi$
$359$	−51169.9	−	88628.9i	−0.397032	−	0.687680i	−0.993358	+	0.115062i	$0.963293\pi$
$360$	−95424.1	−	55093.1i	−0.736297	−	0.425101i
$361$	−55367.0	+	95898.5i	−0.424851	+	0.735864i
$362$	86210.8	−	49773.9i	0.657877	−	0.379826i
$363$		−	77820.0i		−	0.590579i
$364$		0			0
$365$	111264.			0.835156
$366$	41625.4	+	72097.3i	0.310739	+	0.538216i
$367$	−13307.7	−	7683.22i	−0.0988034	−	0.0570442i	0.449784	−	0.893137i	$-0.351501\pi$
$367$	−13307.7	−	7683.22i	−0.0988034	−	0.0570442i	−0.548588	+	0.836093i	$0.684834\pi$
$368$	−7348.70	+	12728.3i	−0.0542644	+	0.0939886i
$369$	−99625.0	+	57518.5i	−0.731671	+	0.422430i
$370$			70803.0i			0.517187i
$371$		0			0
$372$	50865.5			0.367568
$373$	−48745.4	−	84429.5i	−0.350361	−	0.606843i	0.635951	−	0.771729i	$-0.280608\pi$
$373$	−48745.4	−	84429.5i	−0.350361	−	0.606843i	−0.986313	+	0.164886i	$0.947275\pi$
$374$	−185725.	−	107228.i	−1.32778	−	0.766594i
$375$	−105683.	+	183049.i	−0.751525	+	1.30168i
$376$	25367.1	−	14645.7i	0.179430	−	0.103594i
$377$		−	39050.9i		−	0.274757i
$378$		0			0
$379$	−66090.7			−0.460110			−0.230055	−	0.973178i	$-0.573891\pi$
$379$	−66090.7			−0.460110			−0.230055	+	0.973178i	$0.573891\pi$
$380$	−15589.5	−	27001.8i	−0.107961	−	0.186993i
$381$	−387399.	−	223665.i	−2.66875	−	1.54080i
$382$	32972.5	−	57110.0i	0.225956	−	0.391368i
$383$	−180913.	+	104450.i	−1.23331	+	0.712053i	−0.967719	−	0.252032i	$-0.918901\pi$
$383$	−180913.	+	104450.i	−1.23331	+	0.712053i	−0.265593	+	0.964085i	$0.585568\pi$
$384$			23164.4i			0.157093i
$385$		0			0
$386$	−167397.			−1.12350
$387$	101046.	+	175017.i	0.674678	+	1.16858i
$388$	26426.1	+	15257.1i	0.175537	+	0.101347i
$389$	71999.6	−	124707.i	0.475807	−	0.824122i	−0.523809	−	0.851836i	$-0.675489\pi$
$389$	71999.6	−	124707.i	0.475807	−	0.824122i	0.999616	+	0.0277137i	$0.00882267\pi$
$390$	−111218.	+	64211.7i	−0.731216	+	0.422168i
$391$			124672.i			0.815485i
$392$		0			0
$393$	18710.8			0.121145
$394$	−86128.7	−	149179.i	−0.554824	−	0.960984i
$395$	255982.	+	147791.i	1.64065	+	0.947229i
$396$	−97689.4	+	169203.i	−0.622955	+	1.07899i
$397$	246451.	−	142289.i	1.56369	−	0.902796i	0.566809	−	0.823849i	$-0.308178\pi$
$397$	246451.	−	142289.i	1.56369	−	0.902796i	0.996879	−	0.0789466i	$-0.0251556\pi$
$398$			113467.i			0.716316i
$399$		0			0
$400$	−9631.65			−0.0601978
$401$	53923.0	+	93397.4i	0.335340	+	0.580826i	0.983550	−	0.180636i	$-0.0578155\pi$
$401$	53923.0	+	93397.4i	0.335340	+	0.580826i	−0.648210	+	0.761462i	$0.724482\pi$
$402$	247454.	+	142867.i	1.53123	+	0.884059i
$403$	20258.3	−	35088.4i	0.124736	−	0.216050i
$404$	34124.3	−	19701.7i	0.209074	−	0.120709i
$405$			274375.i			1.67276i
$406$		0			0
$407$	125546.			0.757901
$408$	98247.1	+	170169.i	0.590200	+	1.02226i
$409$	−73553.4	−	42466.1i	−0.439700	−	0.253861i	0.263771	−	0.964585i	$-0.415034\pi$
$409$	−73553.4	−	42466.1i	−0.439700	−	0.253861i	−0.703470	+	0.710725i	$0.748367\pi$
$410$	−25908.3	+	44874.5i	−0.154124	+	0.266951i
$411$	289309.	−	167033.i	1.71269	−	0.988821i
$412$		−	151141.i		−	0.890407i
$413$		0			0
$414$	113582.			0.662686
$415$	80066.5	+	138679.i	0.464895	+	0.805221i
$416$	15979.4	+	9225.70i	0.0923365	+	0.0533105i
$417$	27991.6	−	48482.8i	0.160974	−	0.278815i
$418$	−47878.8	+	27642.8i	−0.274025	+	0.158209i
$419$			331905.i			1.89054i	0.326292	+	0.945269i	$0.394201\pi$
$419$			331905.i			1.89054i	−0.326292	+	0.945269i	$0.605799\pi$
$420$		0			0
$421$	101490.			0.572609			0.286304	−	0.958139i	$-0.407573\pi$
$421$	101490.			0.572609			0.286304	+	0.958139i	$0.407573\pi$
$422$	31012.3	+	53714.8i	0.174144	+	0.301626i
$423$	−196037.	−	113182.i	−1.09561	−	0.632552i
$424$	−58474.2	+	101280.i	−0.325261	+	0.563369i
$425$	−70755.6	+	40850.7i	−0.391726	+	0.226163i
$426$			57154.5i			0.314943i
$427$		0			0
$428$	−67835.1			−0.370311
$429$	113858.	+	197208.i	0.618657	+	1.07155i
$430$	78833.4	+	45514.5i	0.426357	+	0.246157i
$431$	−114899.	+	199011.i	−0.618530	+	1.07133i	0.371224	+	0.928543i	$0.378938\pi$
$431$	−114899.	+	199011.i	−0.618530	+	1.07133i	−0.989754	+	0.142782i	$0.954395\pi$
$432$	83218.5	−	48046.2i	0.445915	−	0.257449i
$433$			114264.i			0.609442i	0.952442	+	0.304721i	$0.0985632\pi$
$433$			114264.i			0.609442i	−0.952442	+	0.304721i	$0.901437\pi$
$434$		0			0
$435$	−170656.			−0.901868
$436$	−46711.8	−	80907.3i	−0.245728	−	0.425613i
$437$	27833.9	+	16069.9i	0.145751	+	0.0841493i
$438$	−90382.6	+	156547.i	−0.471125	+	0.816013i
$439$	305134.	−	176169.i	1.58330	−	0.914116i	0.588921	−	0.808190i	$-0.299553\pi$
$439$	305134.	−	176169.i	1.58330	−	0.914116i	0.994374	−	0.105926i	$-0.0337806\pi$
$440$			88005.3i			0.454573i
$441$		0			0
$442$	156516.			0.801151
$443$	98158.2	+	170015.i	0.500172	+	0.866323i	1.00000		0.000198349i	$6.31363e-5\pi$
$443$	98158.2	+	170015.i	0.500172	+	0.866323i	−0.499828	+	0.866125i	$0.666604\pi$
$444$	−99619.2	−	57515.2i	−0.505332	−	0.291754i
$445$	58299.9	−	100978.i	0.294407	−	0.509927i
$446$	−157644.	+	91016.0i	−0.792517	+	0.457560i
$447$		−	472416.i		−	2.36434i
$448$		0			0
$449$	77520.3			0.384523			0.192262	−	0.981344i	$-0.438418\pi$
$449$	77520.3			0.384523			0.192262	+	0.981344i	$0.438418\pi$
$450$	37216.8	+	64461.3i	0.183786	+	0.318328i
$451$	79570.1	+	45939.8i	0.391198	+	0.225858i
$452$	−78735.0	+	136373.i	−0.385382	+	0.667501i
$453$	−357135.	+	206192.i	−1.74035	+	1.00479i
$454$			123814.i			0.600699i
$455$		0			0
$456$	50655.2			0.243609
$457$	−94936.1	−	164434.i	−0.454568	−	0.787335i	0.544095	−	0.839024i	$-0.316873\pi$
$457$	−94936.1	−	164434.i	−0.454568	−	0.787335i	−0.998663	+	0.0516882i	$0.983540\pi$
$458$	−69826.2	−	40314.2i	−0.332880	−	0.192188i
$459$	407557.	−	705910.i	1.93447	−	3.35061i
$460$	44306.8	−	25580.5i	0.209389	−	0.120891i
$461$			52599.9i			0.247505i	0.992313	+	0.123752i	$0.0394928\pi$
$461$			52599.9i			0.247505i	−0.992313	+	0.123752i	$0.960507\pi$
$462$		0			0
$463$	−244268.			−1.13947			−0.569736	−	0.821828i	$-0.692955\pi$
$463$	−244268.			−1.13947			−0.569736	+	0.821828i	$0.692955\pi$
$464$	12259.6	+	21234.3i	0.0569430	+	0.0986282i
$465$	−153339.	−	88530.5i	−0.709166	−	0.409437i
$466$	−3104.05	+	5376.36i	−0.0142941	+	0.0247581i
$467$	−257742.	+	148807.i	−1.18182	+	0.682324i	−0.956435	−	0.291946i	$-0.905697\pi$
$467$	−257742.	+	148807.i	−1.18182	+	0.682324i	−0.225385	+	0.974270i	$0.572364\pi$
$468$		−	142593.i		−	0.651037i
$469$		0			0
$470$	−101962.			−0.461576
$471$	−204981.	−	355037.i	−0.924000	−	1.60041i
$472$	81425.7	+	47011.2i	0.365492	+	0.211017i
$473$	80704.9	−	139785.i	0.360726	−	0.624796i
$474$	−415883.	+	240110.i	−1.85103	+	1.06869i
$475$			21062.2i			0.0933505i
$476$		0			0
$477$	903778.			3.97215
$478$	114470.	+	198268.i	0.500998	+	0.867755i
$479$	40591.3	+	23435.4i	0.176914	+	0.102141i	0.585842	−	0.810425i	$-0.300764\pi$
$479$	40591.3	+	23435.4i	0.176914	+	0.102141i	−0.408928	+	0.912567i	$0.634097\pi$
$480$	40317.1	−	69831.3i	0.174988	−	0.303087i
$481$	−79351.0	+	45813.3i	−0.342975	+	0.198016i
$482$		−	121669.i		−	0.523706i
$483$		0			0
$484$	38920.3			0.166144
$485$	−53109.5	−	91988.3i	−0.225782	−	0.391065i
$486$	−88144.3	−	50890.1i	−0.373183	−	0.215457i
$487$	−53591.9	+	92824.0i	−0.225965	+	0.391383i	−0.956609	−	0.291376i	$-0.905887\pi$
$487$	−53591.9	+	92824.0i	−0.225965	+	0.391383i	0.730643	+	0.682759i	$0.239220\pi$
$488$	−36058.2	+	20818.2i	−0.151413	+	0.0874185i
$489$			98898.4i			0.413592i
$490$		0			0
$491$	−116367.			−0.482687			−0.241344	−	0.970440i	$-0.577588\pi$
$491$	−116367.			−0.482687			−0.241344	+	0.970440i	$0.577588\pi$
$492$	−42092.1	−	72905.6i	−0.173888	−	0.301183i
$493$	180122.	+	103993.i	0.741093	+	0.427870i
$494$	20174.5	−	34943.3i	0.0826702	−	0.143189i
$495$	588989.	−	340053.i	2.40379	−	1.38783i
$496$			25439.5i			0.103406i
$497$		0			0
$498$	−260161.			−1.04902
$499$	−221454.	−	383569.i	−0.889369	−	1.54043i	−0.840623	−	0.541621i	$-0.817811\pi$
$499$	−221454.	−	383569.i	−0.889369	−	1.54043i	−0.0487464	−	0.998811i	$-0.515523\pi$
$500$	−91548.5	−	52855.5i	−0.366194	−	0.211422i
$501$	−314084.	+	544009.i	−1.25133	+	2.16736i
$502$	77326.8	−	44644.7i	0.306848	−	0.177159i
$503$			68955.1i			0.272540i	0.990672	+	0.136270i	$0.0435115\pi$
$503$			68955.1i			0.272540i	−0.990672	+	0.136270i	$0.956489\pi$
$504$		0			0
$505$	−137161.			−0.537835
$506$	−45358.6	−	78563.4i	−0.177157	−	0.306845i
$507$	251721.	+	145331.i	0.979271	+	0.565382i
$508$	111862.	−	193750.i	0.433466	−	0.750784i
$509$	80344.2	−	46386.8i	0.310112	−	0.179044i	−0.336864	−	0.941553i	$-0.609366\pi$
$509$	80344.2	−	46386.8i	0.310112	−	0.179044i	0.646977	+	0.762510i	$0.276033\pi$
$510$		−	683989.i		−	2.62972i
$511$		0			0
$512$	−11585.2			−0.0441942
$513$	−105066.	−	181980.i	−0.399234	−	0.691494i
$514$	166825.	+	96316.2i	0.631443	+	0.364564i
$515$	−263058.	+	455631.i	−0.991831	+	1.71790i
$516$	−128077.	+	73945.4i	−0.481030	+	0.277723i
$517$			180796.i			0.676406i
$518$		0			0
$519$	−526355.			−1.95409
$520$	−32114.3	−	55623.6i	−0.118766	−	0.205709i
$521$	−123766.	−	71456.2i	−0.455958	−	0.263248i	0.254385	−	0.967103i	$-0.418127\pi$
$521$	−123766.	−	71456.2i	−0.455958	−	0.263248i	−0.710343	+	0.703855i	$0.751460\pi$
$522$	94742.4	−	164099.i	0.347699	−	0.602232i
$523$	−19228.8	+	11101.8i	−0.0702990	+	0.0405871i	−0.534737	−	0.845018i	$-0.679589\pi$
$523$	−19228.8	+	11101.8i	−0.0702990	+	0.0405871i	0.464439	+	0.885605i	$0.346256\pi$
$524$			9357.85i			0.0340811i
$525$		0			0
$526$	23610.5			0.0853361
$527$	107897.	+	186882.i	0.388496	+	0.672894i
$528$	−123823.	−	71489.1i	−0.444153	−	0.256432i
$529$	113552.	−	196677.i	0.405772	−	0.702818i
$530$	352553.	−	203546.i	1.25508	−	0.724622i
$531$		−	726606.i		−	2.57697i
$532$		0			0
$533$	−67056.3			−0.236040
$534$	94717.1	+	164055.i	0.332159	+	0.575316i
$535$	204496.	+	118066.i	0.714459	+	0.412493i
$536$	−71452.5	+	123759.i	−0.248707	+	0.430773i
$537$	66048.3	−	38133.0i	0.229041	−	0.132237i
$538$			259992.i			0.898246i
$539$		0			0
$540$	−334494.			−1.14710
$541$	−105605.	−	182912.i	−0.360818	−	0.624955i	0.627278	−	0.778796i	$-0.284169\pi$
$541$	−105605.	−	182912.i	−0.360818	−	0.624955i	−0.988096	+	0.153841i	$0.950836\pi$
$542$	12576.6	+	7261.09i	0.0428118	+	0.0247174i
$543$	281489.	−	487554.i	0.954689	−	1.65357i
$544$	−85106.9	+	49136.5i	−0.287586	+	0.166038i
$545$			325204.i			1.09487i
$546$		0			0
$547$	254227.			0.849664			0.424832	−	0.905272i	$-0.360333\pi$
$547$	254227.			0.849664			0.424832	+	0.905272i	$0.360333\pi$
$548$	83538.3	+	144693.i	0.278179	+	0.481821i
$549$	278658.	+	160883.i	0.924543	+	0.533785i
$550$	29724.9	−	51485.0i	0.0982641	−	0.170198i
$551$	46434.5	−	26809.0i	0.152946	−	0.0883032i
$552$			83119.1i			0.272786i
$553$		0			0
$554$	187395.			0.610575
$555$	200208.	+	346771.i	0.649974	+	1.12579i
$556$	24247.8	+	13999.5i	0.0784373	+	0.0452858i
$557$	−23069.6	+	39957.7i	−0.0743584	+	0.128792i	−0.900807	−	0.434220i	$-0.857024\pi$
$557$	−23069.6	+	39957.7i	−0.0743584	+	0.128792i	0.826449	+	0.563012i	$0.190358\pi$
$558$	170258.	−	98298.3i	0.546812	−	0.315702i
$559$			117801.i			0.376987i
$560$		0			0
$561$	−1.21283e6			−3.85366
$562$	53961.2	+	93463.6i	0.170848	+	0.295917i
$563$	302788.	+	174814.i	0.955259	+	0.551519i	0.894711	−	0.446646i	$-0.147382\pi$
$563$	302788.	+	174814.i	0.955259	+	0.551519i	0.0605484	+	0.998165i	$0.480715\pi$
$564$	82826.6	−	143460.i	0.260382	−	0.450996i
$565$	474710.	−	274074.i	1.48707	−	0.858560i
$566$		−	311787.i		−	0.973251i
$567$		0			0
$568$	−28584.8			−0.0886010
$569$	88098.2	+	152591.i	0.272109	+	0.471306i	0.969402	−	0.245480i	$-0.0789457\pi$
$569$	88098.2	+	152591.i	0.272109	+	0.471306i	−0.697293	+	0.716786i	$0.745612\pi$
$570$	−152705.	−	88164.4i	−0.470007	−	0.271358i
$571$	88263.5	−	152877.i	0.270713	−	0.468889i	−0.698332	−	0.715774i	$-0.746074\pi$
$571$	88263.5	−	152877.i	0.270713	−	0.468889i	0.969045	+	0.246886i	$0.0794072\pi$
$572$	−98630.1	+	56944.1i	−0.301452	+	0.174043i
$573$		−	372943.i		−	1.13588i
$574$		0			0
$575$	−34560.6			−0.104531
$576$	44765.4	+	77536.0i	0.134927	+	0.233700i
$577$	−196469.	−	113432.i	−0.590124	−	0.340708i	0.175023	−	0.984564i	$-0.444000\pi$
$577$	−196469.	−	113432.i	−0.590124	−	0.340708i	−0.765147	+	0.643856i	$0.777333\pi$
$578$	−298689.	+	517345.i	−0.894054	+	1.54855i
$579$	−819858.	+	473345.i	−2.44558	+	1.41196i
$580$		−	85350.5i		−	0.253717i
$581$		0			0
$582$	172569.			0.509468
$583$	−360922.	−	625135.i	−1.06188	−	1.83923i
$584$	−78294.2	−	45203.2i	−0.229564	−	0.132539i
$585$	−248180.	+	429860.i	−0.725195	+	1.25608i
$586$	193538.	−	111739.i	0.563601	−	0.325395i
$587$		−	349659.i		−	1.01477i	−0.861719	−	0.507386i	$-0.830612\pi$
$587$		−	349659.i		−	1.01477i	0.861719	−	0.507386i	$-0.169388\pi$
$588$		0			0
$589$	55630.3			0.160354
$590$	−163644.	−	283440.i	−0.470107	−	0.814249i
$591$	−843663.	−	487089.i	−2.41543	−	1.39455i
$592$	28765.2	−	49822.7i	0.0820774	−	0.142162i
$593$	−119299.	+	68877.4i	−0.339256	+	0.195870i	−0.659943	−	0.751316i	$-0.729420\pi$
$593$	−119299.	+	68877.4i	−0.339256	+	0.195870i	0.320687	+	0.947185i	$0.396086\pi$
$594$			593115.i			1.68099i
$595$		0			0
$596$	236271.			0.665146
$597$	320849.	+	555727.i	0.900228	+	1.55924i
$598$	57337.7	+	33103.9i	0.160339	+	0.0925715i
$599$	−40438.6	+	70041.7i	−0.112705	+	0.195210i	−0.916860	−	0.399209i	$-0.869285\pi$
$599$	−40438.6	+	70041.7i	−0.112705	+	0.195210i	0.804155	+	0.594420i	$0.202618\pi$
$600$	−47172.8	+	27235.2i	−0.131036	+	0.0756534i
$601$			228798.i			0.633438i	0.948519	+	0.316719i	$0.102581\pi$
$601$			228798.i			0.633438i	−0.948519	+	0.316719i	$0.897419\pi$
$602$		0			0
$603$	1.10437e6			3.03725
$604$	−103123.	−	178615.i	−0.282672	−	0.489602i
$605$	−117329.	−	67740.0i	−0.320549	−	0.185069i
$606$	111420.	−	192985.i	0.303402	−	0.525507i
$607$	−230320.	+	132975.i	−0.625107	+	0.360906i	−0.778855	−	0.627204i	$-0.784199\pi$
$607$	−230320.	+	132975.i	−0.625107	+	0.360906i	0.153748	+	0.988110i	$0.450866\pi$
$608$			25334.3i			0.0685332i
$609$		0			0
$610$	144935.			0.389505
$611$	−65974.9	−	114272.i	−0.176724	−	0.306096i
$612$	657708.	+	379728.i	1.75602	+	1.01384i
$613$	153261.	−	265456.i	0.407859	−	0.706433i	−0.586790	−	0.809739i	$-0.699609\pi$
$613$	153261.	−	265456.i	0.407859	−	0.706433i	0.994650	+	0.103306i	$0.0329421\pi$
$614$	−6862.42	+	3962.02i	−0.0182029	+	0.0105095i
$615$			293042.i			0.774782i
$616$		0			0
$617$	491906.			1.29215			0.646074	−	0.763275i	$-0.276410\pi$
$617$	491906.			1.29215			0.646074	+	0.763275i	$0.276410\pi$
$618$	−427379.	−	740242.i	−1.11902	−	1.93819i
$619$	−99792.1	−	57615.0i	−0.260444	−	0.150368i	0.364093	−	0.931363i	$-0.381379\pi$
$619$	−99792.1	−	57615.0i	−0.260444	−	0.150368i	−0.624537	+	0.780995i	$0.714712\pi$
$620$	44276.9	−	76689.9i	0.115185	−	0.199506i
$621$	298607.	−	172401.i	0.774314	−	0.447050i
$622$			58433.5i			0.151036i
$623$		0			0
$624$	104349.			0.267991
$625$	231018.	+	400134.i	0.591405	+	1.02434i
$626$	91552.3	+	52857.8i	0.233626	+	0.134884i
$627$	−156330.	+	270772.i	−0.397657	+	0.688761i
$628$	177566.	−	102518.i	0.450235	−	0.259943i
$629$		−	488007.i		−	1.23346i
$630$		0			0
$631$	72815.9			0.182880			0.0914402	−	0.995811i	$-0.470853\pi$
$631$	72815.9			0.182880			0.0914402	+	0.995811i	$0.470853\pi$
$632$	−120087.	−	207996.i	−0.300650	−	0.520741i
$633$	303777.	+	175386.i	0.758136	+	0.437710i
$634$	−150848.	+	261277.i	−0.375286	+	0.650015i
$635$	−674438.	+	389387.i	−1.67261	+	0.965682i
$636$			661385.i			1.63508i
$637$		0			0
$638$	−151341.			−0.371805
$639$	110452.	+	191308.i	0.270503	+	0.468524i
$640$	34924.9	+	20163.9i	0.0852658	+	0.0492282i
$641$	378897.	−	656269.i	0.922157	−	1.59722i	0.126087	−	0.992019i	$-0.459758\pi$
$641$	378897.	−	656269.i	0.922157	−	1.59722i	0.796070	−	0.605204i	$-0.206908\pi$
$642$	−332235.	+	191816.i	−0.806075	+	0.465388i
$643$			353082.i			0.853992i	0.904254	+	0.426996i	$0.140428\pi$
$643$			353082.i			0.853992i	−0.904254	+	0.426996i	$0.859572\pi$
$644$		0			0
$645$	514802.			1.23743
$646$	107450.	+	186109.i	0.257479	+	0.445967i
$647$	−185815.	−	107281.i	−0.443888	−	0.256279i	0.261358	−	0.965242i	$-0.415830\pi$
$647$	−185815.	−	107281.i	−0.443888	−	0.256279i	−0.705245	+	0.708963i	$0.749163\pi$
$648$	111471.	−	193073.i	0.265467	−	0.459802i
$649$	−502587.	+	290169.i	−1.19322	+	0.688908i
$650$			43388.1i			0.102694i
$651$		0			0
$652$	−49462.3			−0.116353
$653$	248796.	+	430927.i	0.583467	+	1.01059i	0.995065	+	0.0992289i	$0.0316376\pi$
$653$	248796.	+	430927.i	0.583467	+	1.01059i	−0.411598	+	0.911366i	$0.635029\pi$
$654$	−457560.	−	264172.i	−1.06978	−	0.617635i
$655$	16287.2	−	28210.2i	0.0379632	−	0.0657542i
$656$	36462.4	−	21051.6i	0.0847301	−	0.0489190i
$657$			698662.i			1.61859i
$658$		0			0
$659$	−197464.			−0.454692			−0.227346	−	0.973814i	$-0.573005\pi$
$659$	−197464.			−0.454692			−0.227346	+	0.973814i	$0.573005\pi$
$660$	248851.	+	431022.i	0.571283	+	0.989491i
$661$	−578871.	−	334211.i	−1.32489	−	0.764924i	−0.340383	−	0.940287i	$-0.610557\pi$
$661$	−578871.	−	334211.i	−1.32489	−	0.764924i	−0.984504	+	0.175363i	$0.943890\pi$
$662$	153248.	−	265433.i	0.349687	−	0.605675i
$663$	766567.	−	442577.i	1.74390	−	1.00684i
$664$		−	130115.i		−	0.295114i
$665$		0			0
$666$	−444595.			−1.00234
$667$	43990.3	+	76193.4i	0.0988793	+	0.171264i
$668$	−272076.	−	157083.i	−0.609731	−	0.352028i
$669$	−514729.	+	891536.i	−1.15007	+	1.99199i
$670$	430802.	−	248724.i	0.959684	−	0.554074i
$671$		−	256994.i		−	0.570792i
$672$		0			0
$673$	−404534.			−0.893151			−0.446575	−	0.894746i	$-0.647357\pi$
$673$	−404534.			−0.893151			−0.446575	+	0.894746i	$0.647357\pi$
$674$	264382.	+	457922.i	0.581984	+	1.00803i
$675$	195686.	+	112980.i	0.429490	+	0.247966i
$676$	−72684.6	+	125893.i	−0.159056	+	0.275493i
$677$	182878.	−	105585.i	0.399010	−	0.230369i	−0.287047	−	0.957917i	$-0.592673\pi$
$677$	182878.	−	105585.i	0.399010	−	0.230369i	0.686057	+	0.727548i	$0.259340\pi$
$678$			890550.i			1.93731i
$679$		0			0
$680$	342085.			0.739803
$681$	350106.	+	606401.i	0.754927	+	1.30757i
$682$	−135984.	−	78510.5i	−0.292361	−	0.168795i
$683$	85054.3	−	147318.i	0.182329	−	0.315802i	−0.760345	−	0.649520i	$-0.774970\pi$
$683$	85054.3	−	147318.i	0.182329	−	0.315802i	0.942673	+	0.333718i	$0.108303\pi$
$684$	169554.	−	97891.8i	0.362405	−	0.209235i
$685$		−	581588.i		−	1.23946i
$686$		0			0
$687$	−455983.			−0.966128
$688$	−36982.4	−	64055.4i	−0.0781301	−	0.135325i
$689$	456241.	+	263411.i	0.961072	+	0.554875i
$690$	144667.	−	250571.i	0.303859	−	0.526299i
$691$	146038.	−	84315.2i	0.305851	−	0.176583i	−0.339217	−	0.940708i	$-0.610162\pi$
$691$	146038.	−	84315.2i	0.305851	−	0.176583i	0.645068	+	0.764125i	$0.276829\pi$
$692$		−	263247.i		−	0.549732i
$693$		0			0
$694$	178834.			0.371305
$695$	−48731.6	−	84405.7i	−0.100888	−	0.174744i
$696$	120087.	+	69332.5i	0.247901	+	0.143126i
$697$	178572.	−	309296.i	0.367577	−	0.636662i
$698$	229284.	−	132377.i	0.470613	−	0.271708i
$699$			35109.0i			0.0718562i
$700$		0			0
$701$	−487646.			−0.992359			−0.496179	−	0.868220i	$-0.665264\pi$
$701$	−487646.			−0.992359			−0.496179	+	0.868220i	$0.665264\pi$
$702$	−216436.	−	374877.i	−0.439192	−	0.760703i
$703$	−108951.	−	62902.9i	−0.220455	−	0.127280i
$704$	35754.0	−	61927.7i	0.0721405	−	0.124951i
$705$	−499378.	+	288316.i	−1.00474	+	0.580084i
$706$		−	405174.i		−	0.812890i
$707$		0			0
$708$	531730.			1.06078
$709$	193465.	+	335090.i	0.384865	+	0.666606i	0.991751	−	0.128183i	$-0.0409145\pi$
$709$	193465.	+	335090.i	0.384865	+	0.666606i	−0.606885	+	0.794790i	$0.707581\pi$
$710$	86171.8	+	49751.3i	0.170942	+	0.0986933i
$711$	−928032.	+	1.60740e6i	−1.83579	+	3.17969i
$712$	−82049.1	+	47371.1i	−0.161850	+	0.0934444i
$713$			91282.7i			0.179560i
$714$		0			0
$715$	396441.			0.775472
$716$	19071.5	+	33032.9i	0.0372014	+	0.0644348i
$717$	1.12128e6	+	647370.i	2.18110	+	1.25926i
$718$	144730.	−	250680.i	0.280744	−	0.486263i
$719$	163137.	−	94187.2i	0.315569	−	0.182194i	−0.333847	−	0.942627i	$-0.608347\pi$
$719$	163137.	−	94187.2i	0.315569	−	0.182194i	0.649416	+	0.760433i	$0.275013\pi$
$720$		−	311654.i		−	0.601184i
$721$		0			0
$722$	−313203.			−0.600830
$723$	−344042.	−	595899.i	−0.658166	−	1.13998i
$724$	243841.	+	140782.i	0.465189	+	0.268577i
$725$	−28828.2	+	49931.9i	−0.0548455	+	0.0949952i
$726$	190619.	−	110054.i	0.361654	−	0.208801i
$727$			901538.i			1.70575i	0.522115	+	0.852875i	$0.325143\pi$
$727$			901538.i			1.70575i	−0.522115	+	0.852875i	$0.674857\pi$
$728$		0			0
$729$	222465.			0.418607
$730$	157351.	+	272539.i	0.295272	+	0.511427i
$731$	−543357.	−	313707.i	−1.01684	−	0.587070i
$732$	−117734.	+	203922.i	−0.219726	+	0.380577i
$733$	348560.	−	201241.i	0.648738	−	0.374549i	−0.139235	−	0.990259i	$-0.544464\pi$
$733$	348560.	−	201241.i	0.648738	−	0.374549i	0.787972	+	0.615710i	$0.211131\pi$
$734$		−	43462.9i		−	0.0806726i
$735$		0			0
$736$	−41570.5			−0.0767414
$737$	−441029.	−	763885.i	−0.811955	−	1.40635i
$738$	−281782.	−	162687.i	−0.517369	−	0.298703i
$739$	18650.6	−	32303.7i	0.0341510	−	0.0591513i	−0.848445	−	0.529284i	$-0.822461\pi$
$739$	18650.6	−	32303.7i	0.0341510	−	0.0591513i	0.882596	+	0.470133i	$0.155794\pi$
$740$	−173431.	+	100130.i	−0.316711	+	0.182853i
$741$		−	228188.i		−	0.415582i
$742$		0			0
$743$	−831221.			−1.50570			−0.752851	−	0.658191i	$-0.771322\pi$
$743$	−831221.			−1.50570			−0.752851	+	0.658191i	$0.771322\pi$
$744$	71934.7	+	124595.i	0.129955	+	0.225089i
$745$	−712262.	−	411224.i	−1.28330	−	0.740912i
$746$	137873.	−	238803.i	0.247743	−	0.429103i
$747$	−870813.	+	502764.i	−1.56057	+	0.900997i
$748$		−	606574.i		−	1.08413i
$749$		0			0
$750$	−597835.			−1.06282
$751$	125549.	+	217458.i	0.222605	+	0.385562i	0.955598	−	0.294673i	$-0.0952108\pi$
$751$	125549.	+	217458.i	0.222605	+	0.385562i	−0.732994	+	0.680236i	$0.761877\pi$
$752$	71748.9	+	41424.2i	0.126876	+	0.0732519i
$753$	252482.	−	437311.i	0.445287	−	0.771260i
$754$	95654.8	−	55226.3i	0.168253	−	0.0971412i
$755$			717936.i			1.25948i
$756$		0			0
$757$	−422399.			−0.737108			−0.368554	−	0.929606i	$-0.620147\pi$
$757$	−422399.			−0.737108			−0.368554	+	0.929606i	$0.620147\pi$
$758$	−93466.3	−	161888.i	−0.162673	−	0.281759i
$759$	−444305.	−	256519.i	−0.771254	−	0.445284i
$760$	44093.8	−	76372.7i	0.0763397	−	0.132224i
$761$	214084.	−	123602.i	0.369671	−	0.213430i	−0.303644	−	0.952786i	$-0.598203\pi$
$761$	214084.	−	123602.i	0.369671	−	0.213430i	0.673315	+	0.739356i	$0.264870\pi$
$762$		−	1.26524e6i		−	2.17903i
$763$		0			0
$764$	186520.			0.319551
$765$	−1.32182e6	−	2.28946e6i	−2.25865	−	3.91209i
$766$	−511700.	−	295430.i	−0.872083	−	0.503497i
$767$	211773.	−	366802.i	0.359981	−	0.623506i
$768$	−56740.9	+	32759.4i	−0.0961997	+	0.0555409i
$769$		−	903767.i		−	1.52828i	−0.645049	−	0.764141i	$-0.723163\pi$
$769$		−	903767.i		−	1.52828i	0.645049	−	0.764141i	$-0.276837\pi$
$770$		0			0
$771$	1.08941e6			1.83266
$772$	−236735.	−	410037.i	−0.397217	−	0.688000i
$773$	211888.	+	122333.i	0.354606	+	0.204732i	0.666712	−	0.745315i	$-0.267701\pi$
$773$	211888.	+	122333.i	0.354606	+	0.204732i	−0.312106	+	0.950047i	$0.601034\pi$
$774$	−285801.	+	495021.i	−0.477069	+	0.826308i
$775$	−51805.9	+	29910.2i	−0.0862534	+	0.0497984i
$776$			86307.3i			0.143326i
$777$		0			0
$778$	407291.			0.672893
$779$	−46035.0	−	79735.0i	−0.0758601	−	0.131393i
$780$	−314572.	−	181618.i	−0.517048	−	0.298518i
$781$	88217.5	−	152797.i	0.144628	−	0.250503i
$782$	−305383.	+	176313.i	−0.499381	+	0.288318i
$783$		−	575222.i		−	0.938236i
$784$		0			0
$785$	−713719.			−1.15821
$786$	26461.0	+	45831.8i	0.0428313	+	0.0741860i
$787$	823098.	+	475216.i	1.32893	+	0.767258i	0.985134	−	0.171787i	$-0.0549541\pi$
$787$	823098.	+	475216.i	1.32893	+	0.767258i	0.343795	+	0.939045i	$0.388287\pi$
$788$	243609.	−	421943.i	0.392320	−	0.679518i
$789$	115637.	−	66762.8i	0.185755	−	0.107246i
$790$			836035.i			1.33958i
$791$		0			0
$792$	−552615.			−0.880992
$793$	93780.5	+	162433.i	0.149130	+	0.258301i
$794$	697070.	+	402453.i	1.10569	+	0.638373i
$795$	1.15113e6	−	1.99381e6i	1.82133	−	3.15464i
$796$	−277937.	+	160467.i	−0.438652	+	0.253256i
$797$		−	560412.i		−	0.882248i	−0.897446	−	0.441124i	$-0.854580\pi$
$797$		−	560412.i		−	0.882248i	0.897446	−	0.441124i	$-0.145420\pi$
$798$		0			0
$799$	702771.			1.10083
$800$	−13621.2	−	23592.6i	−0.0212831	−	0.0368635i
$801$	634076.	+	366084.i	0.988272	+	0.570579i
$802$	−152517.	+	264168.i	−0.237121	+	0.410706i
$803$	483258.	−	279009.i	0.749459	−	0.432701i
$804$			808180.i			1.25025i
$805$		0			0
$806$	114598.			0.176404
$807$	735174.	+	1.27336e6i	1.12887	+	1.95526i
$808$	96518.0	+	55724.7i	0.147838	+	0.0853542i
$809$	25932.1	−	44915.7i	0.0396224	−	0.0686279i	−0.845534	−	0.533921i	$-0.820718\pi$
$809$	25932.1	−	44915.7i	0.0396224	−	0.0686279i	0.885157	+	0.465293i	$0.154051\pi$
$810$	−672079.	+	388025.i	−1.02435	+	0.591412i
$811$		−	978879.i		−	1.48829i	−0.668019	−	0.744145i	$-0.732857\pi$
$811$		−	978879.i		−	1.48829i	0.668019	−	0.744145i	$-0.267143\pi$
$812$		0			0
$813$	82128.1			0.124254
$814$	177548.	+	307523.i	0.267959	+	0.464118i
$815$	149109.	+	86088.1i	0.224486	+	0.129607i
$816$	−277885.	+	481311.i	−0.417335	+	0.722845i
$817$	−140075.	+	80872.1i	−0.209853	+	0.121159i
$818$		−	240224.i		−	0.359013i
$819$		0			0
$820$	−146560.			−0.217965
$821$	−74399.0	−	128863.i	−0.110377	−	0.191179i	0.805545	−	0.592535i	$-0.201873\pi$
$821$	−74399.0	−	128863.i	−0.110377	−	0.191179i	−0.915923	+	0.401355i	$0.868539\pi$
$822$	818289.	+	472440.i	1.21105	+	0.699202i
$823$	−669533.	+	1.15966e6i	−0.988490	+	1.71211i	−0.363227	+	0.931701i	$0.618325\pi$
$823$	−669533.	+	1.15966e6i	−0.988490	+	1.71211i	−0.625263	+	0.780414i	$0.715008\pi$
$824$	370219.	−	213746.i	0.545260	−	0.314806i
$825$		−	336210.i		−	0.493972i
$826$		0			0
$827$	−127284.			−0.186108			−0.0930538	−	0.995661i	$-0.529663\pi$
$827$	−127284.			−0.186108			−0.0930538	+	0.995661i	$0.529663\pi$
$828$	160629.	+	278217.i	0.234295	+	0.405810i
$829$	385899.	+	222799.i	0.561519	+	0.324193i	0.753755	−	0.657156i	$-0.228241\pi$
$829$	385899.	+	222799.i	0.561519	+	0.324193i	−0.192236	+	0.981349i	$0.561574\pi$
$830$	−226462.	+	392244.i	−0.328730	+	0.569377i
$831$	917803.	−	529894.i	1.32907	−	0.767338i
$832$			52188.5i			0.0753924i
$833$		0			0
$834$	158344.			0.227651
$835$	546802.	+	947088.i	0.784254	+	1.35837i
$836$	−135422.	−	78185.8i	−0.193765	−	0.111870i
$837$	298406.	−	516854.i	0.425948	−	0.737763i
$838$	−812997.	+	469384.i	−1.15771	+	0.668406i
$839$		−	552232.i		−	0.784509i	−0.919857	−	0.392254i	$-0.871695\pi$
$839$		−	552232.i		−	0.784509i	0.919857	−	0.392254i	$-0.128305\pi$
$840$		0			0
$841$	−560506.			−0.792479
$842$	143528.	+	248598.i	0.202448	+	0.350650i
$843$	528571.	+	305170.i	0.743786	+	0.429425i
$844$	−87716.0	+	151928.i	−0.123138	+	0.213282i
$845$	438230.	−	253012.i	0.613747	−	0.354347i
$846$		−	640254.i		−	0.894564i
$847$		0			0
$848$	−330780.			−0.459989
$849$	−881634.	−	1.52703e6i	−1.22313	−	2.11852i
$850$	−200127.	−	115543.i	−0.276992	−	0.159922i
$851$	103216.	−	178775.i	0.142524	−	0.246859i
$852$	−139999.	+	80828.7i	−0.192862	+	0.111349i
$853$			753308.i			1.03532i	0.855586	+	0.517660i	$0.173197\pi$
$853$			753308.i			1.03532i	−0.855586	+	0.517660i	$0.826803\pi$
$854$		0			0
$855$	−681515.			−0.932274
$856$	−95933.4	−	166161.i	−0.130925	−	0.226769i
$857$	−1.12685e6	−	650586.i	−1.53428	−	0.885816i	−0.999158	−	0.0410399i	$-0.986933\pi$
$857$	−1.12685e6	−	650586.i	−1.53428	−	0.885816i	−0.535120	−	0.844776i	$-0.679734\pi$
$858$	−322040.	+	557789.i	−0.437456	+	0.757697i
$859$	850759.	−	491186.i	1.15298	−	0.665671i	0.203366	−	0.979103i	$-0.434812\pi$
$859$	850759.	−	491186.i	1.15298	−	0.665671i	0.949611	+	0.313432i	$0.101479\pi$
$860$			257469.i			0.348119i
$861$		0			0
$862$	−649966.			−0.874734
$863$	360718.	+	624781.i	0.484335	+	0.838893i	0.999838	−	0.0179949i	$-0.00572826\pi$
$863$	360718.	+	624781.i	0.484335	+	0.838893i	−0.515503	+	0.856888i	$0.672395\pi$
$864$	235377.	+	135895.i	0.315310	+	0.182044i
$865$	−458177.	+	793585.i	−0.612351	+	1.06062i
$866$	−279888.	+	161593.i	−0.373205	+	0.215470i
$867$			3.37839e6i			4.49440i
$868$		0			0
$869$	1.48243e6			1.96307
$870$	−241344.	−	418020.i	−0.318858	−	0.552279i
$871$	557504.	+	321875.i	0.734872	+	0.424278i
$872$	132121.	−	228840.i	0.173756	−	0.300954i
$873$	577625.	−	333492.i	0.757910	−	0.437579i
$874$			90905.2i			0.119005i
$875$		0			0
$876$	−511281.			−0.666272
$877$	358504.	+	620947.i	0.466117	+	0.807338i	0.999251	−	0.0386923i	$-0.0123192\pi$
$877$	358504.	+	620947.i	0.466117	+	0.807338i	−0.533134	+	0.846031i	$0.678986\pi$
$878$	863050.	+	498282.i	1.11956	+	0.646378i
$879$	631927.	−	1.09453e6i	0.817879	−	1.41661i
$880$	−215568.	+	124458.i	−0.278368	+	0.160716i
$881$			79128.9i			0.101949i	0.998700	+	0.0509745i	$0.0162327\pi$
$881$			79128.9i			0.101949i	−0.998700	+	0.0509745i	$0.983767\pi$
$882$		0			0
$883$	−286591.			−0.367571			−0.183786	−	0.982966i	$-0.558835\pi$
$883$	−286591.			−0.367571			−0.183786	+	0.982966i	$0.558835\pi$
$884$	221347.	+	383384.i	0.283250	+	0.490603i
$885$	−1.60296e6	−	925467.i	−2.04661	−	1.18161i
$886$	−277633.	+	480875.i	−0.353675	+	0.612583i
$887$	−725266.	+	418733.i	−0.921829	+	0.532218i	−0.884218	−	0.467074i	$-0.845308\pi$
$887$	−725266.	+	418733.i	−0.921829	+	0.532218i	−0.0376108	+	0.999292i	$0.511975\pi$
$888$		−	325355.i		−	0.412602i
$889$		0			0
$890$	329794.			0.416354
$891$	688034.	+	1.19171e6i	0.866672	+	1.50112i
$892$	−445886.	−	257432.i	−0.560394	−	0.323544i
$893$	90585.3	−	156898.i	0.113594	−	0.196750i
$894$	1.15718e6	−	668098.i	1.44786	−	0.835920i
$895$		−	132775.i		−	0.165756i
$896$		0			0
$897$	374430.			0.465356
$898$	109630.	+	189885.i	0.135950	+	0.235472i
$899$	131882.	+	76142.1i	0.163180	+	0.0942118i
$900$	−105265.	+	182324.i	−0.129957	+	0.225092i
$901$	−2.42996e6	+	1.40294e6i	−2.99329	+	1.72818i
$902$			259875.i			0.319412i
$903$		0			0
$904$	−445393.			−0.545012
$905$	−490056.	−	848802.i	−0.598341	−	1.03636i
$906$	−1.01013e6	−	583199.i	−1.23061	−	0.710494i
$907$	423285.	−	733150.i	0.514538	−	0.891207i	−0.485319	−	0.874337i	$-0.661297\pi$
$907$	423285.	−	733150.i	0.514538	−	0.891207i	0.999858	−	0.0168697i	$-0.00537006\pi$
$908$	−303281.	+	175099.i	−0.367852	+	0.212379i
$909$		−	861283.i		−	1.04236i
$910$		0			0
$911$	167017.			0.201244			0.100622	−	0.994925i	$-0.467917\pi$
$911$	167017.			0.201244			0.100622	+	0.994925i	$0.467917\pi$
$912$	71637.2	+	124079.i	0.0861289	+	0.149180i
$913$	695515.	+	401556.i	0.834382	+	0.481731i
$914$	268520.	−	465090.i	0.321428	−	0.556730i
$915$	709845.	−	409829.i	0.847854	−	0.489509i
$916$		−	228051.i		−	0.271795i
$917$		0			0
$918$	2.30549e6			2.73576
$919$	−561015.	−	971707.i	−0.664268	−	1.15055i	−0.979483	−	0.201526i	$-0.935410\pi$
$919$	−561015.	−	971707.i	−0.664268	−	1.15055i	0.315215	−	0.949020i	$-0.397923\pi$
$920$	125319.	+	72352.7i	0.148061	+	0.0854829i
$921$	−22406.7	+	38809.5i	−0.0264154	+	0.0457529i
$922$	−128843.	+	74387.5i	−0.151565	+	0.0875061i
$923$			128767.i			0.151148i
$924$		0			0
$925$	135281.			0.158108
$926$	−345447.	−	598331.i	−0.402864	−	0.697782i
$927$	−2.86106e6	−	1.65183e6i	−3.32941	−	1.92223i
$928$	−34675.4	+	60059.6i	−0.0402648	+	0.0697407i
$929$	1.23549e6	−	713313.i	1.43156	−	0.826511i	0.434319	−	0.900759i	$-0.356989\pi$
$929$	1.23549e6	−	713313.i	1.43156	−	0.826511i	0.997240	+	0.0742487i	$0.0236559\pi$
$930$		−	500804.i		−	0.579032i
$931$		0			0
$932$	−17559.1			−0.0202149
$933$	165231.	+	286189.i	0.189814	+	0.328768i
$934$	−729004.	−	420891.i	−0.835673	−	0.482476i
$935$	−1.05573e6	+	1.82858e6i	−1.20762	+	2.09166i
$936$	349279.	−	201657.i	0.398677	−	0.230176i
$937$		−	265587.i		−	0.302502i	−0.988495	−	0.151251i	$-0.951670\pi$
$937$		−	265587.i		−	0.302502i	0.988495	−	0.151251i	$-0.0483301\pi$
$938$		0			0
$939$	597860.			0.678060
$940$	−144196.	−	249755.i	−0.163192	−	0.282656i
$941$	518395.	+	299295.i	0.585439	+	0.338003i	0.763292	−	0.646054i	$-0.223582\pi$
$941$	518395.	+	299295.i	0.585439	+	0.338003i	−0.177853	+	0.984057i	$0.556915\pi$
$942$	579774.	−	1.00420e6i	0.653366	−	1.13166i
$943$	130836.	−	75537.9i	0.147130	−	0.0849458i
$944$			265935.i			0.298423i
$945$		0			0
$946$	456536.			0.510144
$947$	−575427.	−	996669.i	−0.641639	−	1.11135i	−0.985067	−	0.172172i	$-0.944922\pi$
$947$	−575427.	−	996669.i	−0.641639	−	1.11135i	0.343428	−	0.939179i	$-0.388412\pi$
$948$	−1.17629e6	−	679134.i	−1.30888	−	0.755681i
$949$	−203629.	+	352695.i	−0.226103	+	0.391622i
$950$	−51591.7	+	29786.5i	−0.0571653	+	0.0330044i
$951$			1.70621e6i			1.88656i
$952$		0			0
$953$	464604.			0.511561			0.255781	−	0.966735i	$-0.417668\pi$
$953$	464604.			0.511561			0.255781	+	0.966735i	$0.417668\pi$
$954$	1.27814e6	+	2.21380e6i	1.40437	+	2.43243i
$955$	−562285.	−	324635.i	−0.616524	−	0.355950i
$956$	−323770.	+	560787.i	−0.354259	+	0.613595i
$957$	−741220.	+	427944.i	−0.809325	+	0.467264i
$958$			132571.i			0.144450i
$959$		0			0
$960$	228068.			0.247470
$961$	−382761.	−	662961.i	−0.414458	−	0.717862i
$962$	−224438.	−	129580.i	−0.242520	−	0.140019i
$963$	−741374.	+	1.28410e6i	−0.799438	+	1.38467i
$964$	298028.	−	172066.i	0.320703	−	0.185158i
$965$			1.64813e6i			1.76985i
$966$		0			0
$967$	101298.			0.108330			0.0541648	−	0.998532i	$-0.482750\pi$
$967$	101298.			0.108330			0.0541648	+	0.998532i	$0.482750\pi$
$968$	55041.6	+	95334.8i	0.0587408	+	0.101742i
$969$	1.05252e6	+	607670.i	1.12094	+	0.647173i
$970$	150216.	−	260182.i	0.159652	−	0.276525i
$971$	282567.	−	163140.i	0.299697	−	0.173030i	−0.342610	−	0.939478i	$-0.611311\pi$
$971$	282567.	−	163140.i	0.299697	−	0.173030i	0.642307	+	0.766448i	$0.277978\pi$
$972$		−	287878.i		−	0.304702i
$973$		0			0
$974$	−303162.			−0.319563
$975$	122688.	+	212501.i	0.129060	+	0.223538i
$976$	−101988.	−	58882.7i	−0.107065	−	0.0618142i
$977$	−370964.	+	642529.i	−0.388636	+	0.673137i	−0.992266	−	0.124127i	$-0.960387\pi$
$977$	−370964.	+	642529.i	−0.388636	+	0.673137i	0.603630	+	0.797264i	$0.293720\pi$
$978$	−242251.	+	139864.i	−0.253272	+	0.146227i
$979$		−	584780.i		−	0.610137i
$980$		0			0
$981$	−2.04207e6			−2.12193
$982$	−164567.	−	285039.i	−0.170656	−	0.295584i
$983$	−506189.	−	292248.i	−0.523849	−	0.302444i	0.214659	−	0.976689i	$-0.431136\pi$
$983$	−506189.	−	292248.i	−0.523849	−	0.302444i	−0.738508	+	0.674245i	$0.764469\pi$
$984$	119054.	−	206208.i	0.122958	−	0.212969i
$985$	−1.46877e6	+	847993.i	−1.51384	+	0.874017i
$986$			588276.i			0.605100i
$987$		0			0
$988$	114124.			0.116913
$989$	−132701.	−	229846.i	−0.135670	−	0.234987i
$990$	1.66591e6	+	961815.i	1.69974	+	0.981344i
$991$	−291172.	+	504324.i	−0.296484	+	0.513526i	−0.975329	−	0.220756i	$-0.929148\pi$
$991$	−291172.	+	504324.i	−0.296484	+	0.513526i	0.678845	+	0.734282i	$0.262481\pi$
$992$	−62313.7	+	35976.9i	−0.0633229	+	0.0365595i
$993$		−	1.73335e6i		−	1.75787i
$994$		0			0
$995$	1.11716e6			1.12842
$996$	−367923.	−	637261.i	−0.370884	−	0.642390i
$997$	1.18588e6	+	684671.i	1.19303	+	0.688797i	0.958993	−	0.283430i	$-0.0914723\pi$
$997$	1.18588e6	+	684671.i	1.19303	+	0.688797i	0.234039	+	0.972227i	$0.424806\pi$
$998$	626366.	−	1.08490e6i	0.628879	−	1.08925i
$999$	−1.16884e6	+	674833.i	−1.17119	+	0.676185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.5.d.c.31.4		8
7.2	even	3	inner	98.5.d.c.19.3		8
7.3	odd	6		98.5.b.a.97.2	yes	4
7.4	even	3		98.5.b.a.97.1	✓	4
7.5	odd	6	inner	98.5.d.c.19.4		8
7.6	odd	2	inner	98.5.d.c.31.3		8
21.11	odd	6		882.5.c.c.685.3		4
21.17	even	6		882.5.c.c.685.4		4
28.3	even	6		784.5.c.a.97.1		4
28.11	odd	6		784.5.c.a.97.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.5.b.a.97.1	✓	4	7.4	even	3
98.5.b.a.97.2	yes	4	7.3	odd	6
98.5.d.c.19.3		8	7.2	even	3	inner
98.5.d.c.19.4		8	7.5	odd	6	inner
98.5.d.c.31.3		8	7.6	odd	2	inner
98.5.d.c.31.4		8	1.1	even	1	trivial
784.5.c.a.97.1		4	28.3	even	6
784.5.c.a.97.4		4	28.11	odd	6
882.5.c.c.685.3		4	21.11	odd	6
882.5.c.c.685.4		4	21.17	even	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 2.44949i) q^{2} +(13.8528 + 7.99789i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(24.1168 - 13.9239i) q^{5} +45.2429i q^{6} -22.6274 q^{8} +(87.4325 + 151.438i) q^{9} +O(q^{10})\)	\(q+(1.41421 + 2.44949i) q^{2} +(13.8528 + 7.99789i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(24.1168 - 13.9239i) q^{5} +45.2429i q^{6} -22.6274 q^{8} +(87.4325 + 151.438i) q^{9} +(68.2127 + 39.3826i) q^{10} +(69.8320 - 120.953i) q^{11} +(-110.822 + 63.9831i) q^{12} +101.931i q^{13} +445.446 q^{15} +(-32.0000 - 55.4256i) q^{16} +(-470.154 - 271.443i) q^{17} +(-247.296 + 428.330i) q^{18} +(-121.203 + 69.9767i) q^{19} +222.782i q^{20} +395.029 q^{22} +(-114.823 - 198.880i) q^{23} +(-313.452 - 180.972i) q^{24} +(75.2473 - 130.332i) q^{25} +(-249.678 + 144.152i) q^{26} +1501.44i q^{27} -383.113 q^{29} +(629.955 + 1091.11i) q^{30} +(-344.238 - 198.746i) q^{31} +(90.5097 - 156.767i) q^{32} +(1934.73 - 1117.02i) q^{33} -1535.52i q^{34} -1398.92 q^{36} +(449.456 + 778.480i) q^{37} +(-342.814 - 197.924i) q^{38} +(-815.230 + 1412.02i) q^{39} +(-545.701 + 315.061i) q^{40} +657.862i q^{41} +1155.70 q^{43} +(558.656 + 967.621i) q^{44} +(4217.19 + 2434.79i) q^{45} +(324.770 - 562.517i) q^{46} +(-1121.08 + 647.253i) q^{47} -1023.73i q^{48} +425.663 q^{50} +(-4341.95 - 7520.48i) q^{51} +(-706.196 - 407.722i) q^{52} +(2584.22 - 4476.00i) q^{53} +(-3677.77 + 2123.36i) q^{54} -3889.32i q^{55} -2238.66 q^{57} +(-541.803 - 938.431i) q^{58} +(-3598.54 - 2077.62i) q^{59} +(-1781.78 + 3086.14i) q^{60} +(1593.56 - 920.043i) q^{61} -1124.28i q^{62} +512.000 q^{64} +(1419.27 + 2458.24i) q^{65} +(5472.25 + 3159.40i) q^{66} +(3157.79 - 5469.45i) q^{67} +(3761.23 - 2171.55i) q^{68} -3673.38i q^{69} +1263.28 q^{71} +(-1978.37 - 3426.64i) q^{72} +(3460.15 + 1997.72i) q^{73} +(-1271.25 + 2201.87i) q^{74} +(2084.76 - 1203.64i) q^{75} -1119.63i q^{76} -4611.63 q^{78} +(5307.13 + 9192.22i) q^{79} +(-1543.48 - 891.126i) q^{80} +(-4926.35 + 8532.69i) q^{81} +(-1611.43 + 930.357i) q^{82} +5750.31i q^{83} -15118.2 q^{85} +(1634.41 + 2830.88i) q^{86} +(-5307.17 - 3064.09i) q^{87} +(-1580.12 + 2736.84i) q^{88} +(3626.09 - 2093.52i) q^{89} +13773.3i q^{90} +1837.17 q^{92} +(-3179.10 - 5506.36i) q^{93} +(-3170.88 - 1830.71i) q^{94} +(-1948.69 + 3375.23i) q^{95} +(2507.62 - 1447.77i) q^{96} -3814.28i q^{97} +24422.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 196 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 + 196 * q^9	\( 8 q - 32 q^{4} + 196 q^{9} - 24 q^{11} + 1776 q^{15} - 256 q^{16} - 1424 q^{18} + 3296 q^{22} - 104 q^{23} - 948 q^{25} - 2816 q^{29} + 2528 q^{30} - 3136 q^{36} + 3392 q^{37} - 2200 q^{39} - 4048 q^{43} - 192 q^{44} + 2304 q^{46} + 8768 q^{50} - 18936 q^{51} + 16680 q^{53} - 12128 q^{57} - 352 q^{58} - 7104 q^{60} + 4096 q^{64} + 6048 q^{65} + 20816 q^{67} - 3968 q^{71} - 11392 q^{72} - 576 q^{74} - 24448 q^{78} + 29616 q^{79} - 30852 q^{81} - 59376 q^{85} + 18800 q^{86} - 13184 q^{88} + 1664 q^{92} - 18192 q^{93} - 7240 q^{95} + 144320 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 196 * q^9 - 24 * q^11 + 1776 * q^15 - 256 * q^16 - 1424 * q^18 + 3296 * q^22 - 104 * q^23 - 948 * q^25 - 2816 * q^29 + 2528 * q^30 - 3136 * q^36 + 3392 * q^37 - 2200 * q^39 - 4048 * q^43 - 192 * q^44 + 2304 * q^46 + 8768 * q^50 - 18936 * q^51 + 16680 * q^53 - 12128 * q^57 - 352 * q^58 - 7104 * q^60 + 4096 * q^64 + 6048 * q^65 + 20816 * q^67 - 3968 * q^71 - 11392 * q^72 - 576 * q^74 - 24448 * q^78 + 29616 * q^79 - 30852 * q^81 - 59376 * q^85 + 18800 * q^86 - 13184 * q^88 + 1664 * q^92 - 18192 * q^93 - 7240 * q^95 + 144320 * q^99

Introduction

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