LMFDB - Embedded newform 98.5.d.c.19.2

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			19.2
Root			$1.60021 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.5.d.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 2.44949i) q^{2} +(1.76104 - 1.01673i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-0.615721 - 0.355487i) q^{5} +5.75152i q^{6} +22.6274 q^{8} +(-38.4325 + 66.5670i) q^{9} +O(q^{10})$	\(q+(-1.41421 + 2.44949i) q^{2} +(1.76104 - 1.01673i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-0.615721 - 0.355487i) q^{5} +5.75152i q^{6} +22.6274 q^{8} +(-38.4325 + 66.5670i) q^{9} +(1.74152 - 1.00547i) q^{10} +(-75.8320 - 131.345i) q^{11} +(-14.0883 - 8.13387i) q^{12} +260.864i q^{13} -1.44574 q^{15} +(-32.0000 + 55.4256i) q^{16} +(-333.938 + 192.799i) q^{17} +(-108.704 - 188.280i) q^{18} +(-337.871 - 195.070i) q^{19} +5.68779i q^{20} +428.971 q^{22} +(88.8234 - 153.847i) q^{23} +(39.8477 - 23.0061i) q^{24} +(-312.247 - 540.828i) q^{25} +(-638.984 - 368.918i) q^{26} +321.013i q^{27} -320.887 q^{29} +(2.04459 - 3.54133i) q^{30} +(-1165.99 + 673.186i) q^{31} +(-90.5097 - 156.767i) q^{32} +(-267.086 - 154.202i) q^{33} -1090.64i q^{34} +614.920 q^{36} +(398.544 - 690.299i) q^{37} +(955.643 - 551.741i) q^{38} +(265.230 + 459.391i) q^{39} +(-13.9322 - 8.04375i) q^{40} +815.856i q^{41} -2167.70 q^{43} +(-606.656 + 1050.76i) q^{44} +(47.3274 - 27.3245i) q^{45} +(251.230 + 435.144i) q^{46} +(3711.45 + 2142.80i) q^{47} +130.142i q^{48} +1766.34 q^{50} +(-392.051 + 679.052i) q^{51} +(1807.32 - 1043.46i) q^{52} +(1585.78 + 2746.66i) q^{53} +(-786.319 - 453.982i) q^{54} +107.829i q^{55} -793.337 q^{57} +(453.803 - 786.010i) q^{58} +(4075.86 - 2353.20i) q^{59} +(5.78297 + 10.0164i) q^{60} +(2195.18 + 1267.39i) q^{61} -3808.12i q^{62} +512.000 q^{64} +(92.7338 - 160.620i) q^{65} +(755.432 - 436.149i) q^{66} +(2046.21 + 3544.15i) q^{67} +(2671.50 + 1542.39i) q^{68} -361.239i q^{69} -2255.28 q^{71} +(-869.628 + 1506.24i) q^{72} +(-4029.78 + 2326.60i) q^{73} +(1127.25 + 1952.46i) q^{74} +(-1099.76 - 634.945i) q^{75} +3121.12i q^{76} -1500.37 q^{78} +(2096.87 - 3631.88i) q^{79} +(39.4062 - 22.7512i) q^{80} +(-2786.65 - 4826.61i) q^{81} +(-1998.43 - 1153.80i) q^{82} -7799.12i q^{83} +274.150 q^{85} +(3065.59 - 5309.76i) q^{86} +(-565.094 + 326.257i) q^{87} +(-1715.88 - 2972.00i) q^{88} +(-8200.49 - 4734.55i) q^{89} +154.571i q^{90} -1421.17 q^{92} +(-1368.90 + 2371.01i) q^{93} +(-10497.6 + 6060.77i) q^{94} +(138.690 + 240.217i) q^{95} +(-318.781 - 184.049i) q^{96} +9945.39i q^{97} +11657.7 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 $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$3$	1.76104	−	1.01673i	0.195671	−	0.112970i	−0.398964	−	0.916967i	$-0.630630\pi$
$3$	1.76104	−	1.01673i	0.195671	−	0.112970i	0.594634	+	0.803996i	$0.297297\pi$
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$	−0.615721	−	0.355487i	−0.0246289	−	0.0142195i	0.487635	−	0.873048i	$-0.337860\pi$
$5$	−0.615721	−	0.355487i	−0.0246289	−	0.0142195i	−0.512264	+	0.858828i	$0.671193\pi$
$6$			5.75152i			0.159764i
$7$		0			0
$7$		0			0
$8$	22.6274			0.353553
$9$	−38.4325	+	66.5670i	−0.474475	+	0.821815i
$10$	1.74152	−	1.00547i	0.0174152	−	0.0100547i
$11$	−75.8320	−	131.345i	−0.626711	−	1.08549i	−0.988207	−	0.153121i	$-0.951067\pi$
$11$	−75.8320	−	131.345i	−0.626711	−	1.08549i	0.361497	−	0.932373i	$-0.382266\pi$
$12$	−14.0883	−	8.13387i	−0.0978353	−	0.0564852i
$13$			260.864i			1.54358i	0.635880	+	0.771788i	$0.280637\pi$
$13$			260.864i			1.54358i	−0.635880	+	0.771788i	$0.719363\pi$
$14$		0			0
$15$	−1.44574			−0.00642552
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	−333.938	+	192.799i	−1.15549	+	0.667125i	−0.950220	−	0.311580i	$-0.899142\pi$
$17$	−333.938	+	192.799i	−1.15549	+	0.667125i	−0.205274	+	0.978705i	$0.565809\pi$
$18$	−108.704	−	188.280i	−0.335505	−	0.581111i
$19$	−337.871	−	195.070i	−0.935931	−	0.540360i	−0.0472483	−	0.998883i	$-0.515045\pi$
$19$	−337.871	−	195.070i	−0.935931	−	0.540360i	−0.888682	+	0.458523i	$0.848379\pi$
$20$			5.68779i			0.0142195i
$21$		0			0
$22$	428.971			0.886303
$23$	88.8234	−	153.847i	0.167908	−	0.290825i	−0.769776	−	0.638314i	$-0.779632\pi$
$23$	88.8234	−	153.847i	0.167908	−	0.290825i	0.937684	+	0.347489i	$0.112965\pi$
$24$	39.8477	−	23.0061i	0.0691800	−	0.0399411i
$25$	−312.247	−	540.828i	−0.499596	−	0.865325i
$26$	−638.984	−	368.918i	−0.945243	−	0.545736i
$27$			321.013i			0.440348i
$28$		0			0
$29$	−320.887			−0.381554			−0.190777	−	0.981633i	$-0.561101\pi$
$29$	−320.887			−0.381554			−0.190777	+	0.981633i	$0.561101\pi$
$30$	2.04459	−	3.54133i	0.00227177	−	0.00393481i
$31$	−1165.99	+	673.186i	−1.21331	+	0.700506i	−0.963479	−	0.267783i	$-0.913709\pi$
$31$	−1165.99	+	673.186i	−1.21331	+	0.700506i	−0.249833	+	0.968289i	$0.580376\pi$
$32$	−90.5097	−	156.767i	−0.0883883	−	0.153093i
$33$	−267.086	−	154.202i	−0.245258	−	0.141600i
$34$		−	1090.64i		−	0.943457i
$35$		0			0
$36$	614.920			0.474475
$37$	398.544	−	690.299i	0.291121	−	0.504236i	−0.682954	−	0.730461i	$-0.739305\pi$
$37$	398.544	−	690.299i	0.291121	−	0.504236i	0.974075	+	0.226225i	$0.0726386\pi$
$38$	955.643	−	551.741i	0.661803	−	0.382092i
$39$	265.230	+	459.391i	0.174378	+	0.302032i
$40$	−13.9322	−	8.04375i	−0.00870762	−	0.00502734i
$41$			815.856i			0.485340i	0.970109	+	0.242670i	$0.0780232\pi$
$41$			815.856i			0.485340i	−0.970109	+	0.242670i	$0.921977\pi$
$42$		0			0
$43$	−2167.70			−1.17236			−0.586182	−	0.810179i	$-0.699370\pi$
$43$	−2167.70			−1.17236			−0.586182	+	0.810179i	$0.699370\pi$
$44$	−606.656	+	1050.76i	−0.313355	+	0.542747i
$45$	47.3274	−	27.3245i	0.0233716	−	0.0134936i
$46$	251.230	+	435.144i	0.118729	+	0.205645i
$47$	3711.45	+	2142.80i	1.68015	+	0.970034i	0.961559	+	0.274598i	$0.0885449\pi$
$47$	3711.45	+	2142.80i	1.68015	+	0.970034i	0.718589	+	0.695435i	$0.244788\pi$
$48$			130.142i			0.0564852i
$49$		0			0
$50$	1766.34			0.706535
$51$	−392.051	+	679.052i	−0.150731	+	0.261073i
$52$	1807.32	−	1043.46i	0.668388	−	0.385894i
$53$	1585.78	+	2746.66i	0.564536	+	0.977806i	0.997093	+	0.0761987i	$0.0242783\pi$
$53$	1585.78	+	2746.66i	0.564536	+	0.977806i	−0.432556	+	0.901607i	$0.642388\pi$
$54$	−786.319	−	453.982i	−0.269657	−	0.155686i
$55$			107.829i			0.0356460i
$56$		0			0
$57$	−793.337			−0.244179
$58$	453.803	−	786.010i	0.134900	−	0.233653i
$59$	4075.86	−	2353.20i	1.17089	−	0.676012i	0.216998	−	0.976172i	$-0.430373\pi$
$59$	4075.86	−	2353.20i	1.17089	−	0.676012i	0.953889	+	0.300160i	$0.0970401\pi$
$60$	5.78297	+	10.0164i	0.00160638	+	0.00278233i
$61$	2195.18	+	1267.39i	0.589944	+	0.340604i	0.765075	−	0.643941i	$-0.222702\pi$
$61$	2195.18	+	1267.39i	0.589944	+	0.340604i	−0.175131	+	0.984545i	$0.556035\pi$
$62$		−	3808.12i		−	0.990665i
$63$		0			0
$64$	512.000			0.125000
$65$	92.7338	−	160.620i	0.0219488	−	0.0380165i
$66$	755.432	−	436.149i	0.173423	−	0.100126i
$67$	2046.21	+	3544.15i	0.455828	+	0.789518i	0.998735	−	0.0502748i	$-0.0160097\pi$
$67$	2046.21	+	3544.15i	0.455828	+	0.789518i	−0.542907	+	0.839793i	$0.682676\pi$
$68$	2671.50	+	1542.39i	0.577747	+	0.333562i
$69$		−	361.239i		−	0.0758746i
$70$		0			0
$71$	−2255.28			−0.447388			−0.223694	−	0.974659i	$-0.571812\pi$
$71$	−2255.28			−0.447388			−0.223694	+	0.974659i	$0.571812\pi$
$72$	−869.628	+	1506.24i	−0.167752	+	0.290556i
$73$	−4029.78	+	2326.60i	−0.756198	+	0.436591i	−0.827929	−	0.560833i	$-0.810481\pi$
$73$	−4029.78	+	2326.60i	−0.756198	+	0.436591i	0.0717308	+	0.997424i	$0.477148\pi$
$74$	1127.25	+	1952.46i	0.205853	+	0.356549i
$75$	−1099.76	−	634.945i	−0.195512	−	0.112879i
$76$			3121.12i			0.540360i
$77$		0			0
$78$	−1500.37			−0.246608
$79$	2096.87	−	3631.88i	0.335983	−	0.581939i	−0.647690	−	0.761904i	$-0.724265\pi$
$79$	2096.87	−	3631.88i	0.335983	−	0.581939i	0.983673	+	0.179965i	$0.0575983\pi$
$80$	39.4062	−	22.7512i	0.00615721	−	0.00355487i
$81$	−2786.65	−	4826.61i	−0.424729	−	0.735652i
$82$	−1998.43	−	1153.80i	−0.297209	−	0.171594i
$83$		−	7799.12i		−	1.13211i	−0.824367	−	0.566056i	$-0.808468\pi$
$83$		−	7799.12i		−	1.13211i	0.824367	−	0.566056i	$-0.191532\pi$
$84$		0			0
$85$	274.150			0.0379447
$86$	3065.59	−	5309.76i	0.414493	−	0.717923i
$87$	−565.094	+	326.257i	−0.0746590	+	0.0431044i
$88$	−1715.88	−	2972.00i	−0.221576	−	0.383780i
$89$	−8200.49	−	4734.55i	−1.03528	−	0.597722i	−0.116790	−	0.993157i	$-0.537261\pi$
$89$	−8200.49	−	4734.55i	−1.03528	−	0.597722i	−0.918494	+	0.395435i	$0.870594\pi$
$90$			154.571i			0.0190828i
$91$		0			0
$92$	−1421.17			−0.167908
$93$	−1368.90	+	2371.01i	−0.158273	+	0.274137i
$94$	−10497.6	+	6060.77i	−1.18804	+	0.685917i
$95$	138.690	+	240.217i	0.0153673	+	0.0266169i
$96$	−318.781	−	184.049i	−0.0345900	−	0.0199705i
$97$			9945.39i			1.05701i	0.848931	+	0.528504i	$0.177247\pi$
$97$			9945.39i			1.05701i	−0.848931	+	0.528504i	$0.822753\pi$
$98$		0			0
$99$	11657.7			1.18944
$100$	−2497.98	+	4326.62i	−0.249798	+	0.432662i
$101$	1791.21	−	1034.16i	0.175592	−	0.101378i	−0.409628	−	0.912253i	$-0.634341\pi$
$101$	1791.21	−	1034.16i	0.175592	−	0.101378i	0.585220	+	0.810875i	$0.301008\pi$
$102$	−1108.89	−	1920.65i	−0.106583	−	0.184607i
$103$	−2169.19	−	1252.38i	−0.204467	−	0.118049i	0.394271	−	0.918994i	$-0.370997\pi$
$103$	−2169.19	−	1252.38i	−0.204467	−	0.118049i	−0.598737	+	0.800946i	$0.704331\pi$
$104$			5902.68i			0.545736i
$105$		0			0
$106$	−8970.54			−0.798375
$107$	−3221.70	+	5580.14i	−0.281395	+	0.487391i	−0.971729	−	0.236100i	$-0.924131\pi$
$107$	−3221.70	+	5580.14i	−0.281395	+	0.487391i	0.690333	+	0.723491i	$0.257464\pi$
$108$	2224.05	−	1284.05i	0.190676	−	0.110087i
$109$	−11773.0	−	20391.5i	−0.990912	−	1.71631i	−0.611949	−	0.790897i	$-0.709614\pi$
$109$	−11773.0	−	20391.5i	−0.990912	−	1.71631i	−0.378962	−	0.925412i	$-0.623719\pi$
$110$	−264.126	−	152.493i	−0.0218286	−	0.0126028i
$111$		−	1620.85i		−	0.131552i
$112$		0			0
$113$	19692.2			1.54219			0.771096	−	0.636719i	$-0.219709\pi$
$113$	19692.2			1.54219			0.771096	+	0.636719i	$0.219709\pi$
$114$	1121.95	−	1943.27i	0.0863302	−	0.149528i
$115$	−109.381	+	63.1511i	−0.00827077	+	0.00477513i
$116$	1283.55	+	2223.17i	0.0953886	+	0.165218i
$117$	−17365.0	−	10025.7i	−1.26853	−	0.732389i
$118$			13311.7i			0.956025i
$119$		0			0
$120$	−32.7134			−0.00227177
$121$	−4180.48	+	7240.81i	−0.285533	+	0.494557i
$122$	−6208.91	+	3584.72i	−0.417154	+	0.240844i
$123$	829.509	+	1436.75i	0.0548291	+	0.0949667i
$124$	9327.95	+	5385.49i	0.606656	+	0.350253i
$125$			888.358i			0.0568549i
$126$		0			0
$127$	−12550.5			−0.778135			−0.389067	−	0.921209i	$-0.627203\pi$
$127$	−12550.5			−0.778135			−0.389067	+	0.921209i	$0.627203\pi$
$128$	−724.077	+	1254.14i	−0.0441942	+	0.0765466i
$129$	−3817.40	+	2203.98i	−0.229397	+	0.132442i
$130$	262.291	+	454.301i	0.0155202	+	0.0268817i
$131$	16734.4	+	9661.63i	0.975143	+	0.562999i	0.900800	−	0.434234i	$-0.142981\pi$
$131$	16734.4	+	9661.63i	0.975143	+	0.562999i	0.0743429	+	0.997233i	$0.476314\pi$
$132$			2467.23i			0.141600i
$133$		0			0
$134$	−11575.1			−0.644639
$135$	114.116	−	197.655i	0.00626151	−	0.0108453i
$136$	−7556.15	+	4362.54i	−0.408529	+	0.235864i
$137$	−1854.29	−	3211.73i	−0.0987955	−	0.171119i	0.812391	−	0.583113i	$-0.198166\pi$
$137$	−1854.29	−	3211.73i	−0.0987955	−	0.171119i	−0.911186	+	0.411994i	$0.864832\pi$
$138$	884.851	+	510.869i	0.0464635	+	0.0268257i
$139$			1096.09i			0.0567307i	0.999598	+	0.0283653i	$0.00903018\pi$
$139$			1096.09i			0.0567307i	−0.999598	+	0.0283653i	$0.990970\pi$
$140$		0			0
$141$	8714.65			0.438341
$142$	3189.45	−	5524.29i	0.158175	−	0.273968i
$143$	34263.2	−	19781.9i	1.67554	−	0.967375i
$144$	−2459.68	−	4260.29i	−0.118619	−	0.205454i
$145$	197.577	+	114.071i	0.00939725	+	0.00542551i
$146$		−	13161.2i		−	0.617433i
$147$		0			0
$148$	−6376.71			−0.291121
$149$	616.908	−	1068.52i	0.0277874	−	0.0481291i	−0.851797	−	0.523872i	$-0.824487\pi$
$149$	616.908	−	1068.52i	0.0277874	−	0.0481291i	0.879585	+	0.475742i	$0.157821\pi$
$150$	3110.58	−	1795.90i	0.138248	−	0.0798176i
$151$	21336.4	+	36955.7i	0.935766	+	1.62079i	0.773262	+	0.634086i	$0.218624\pi$
$151$	21336.4	+	36955.7i	0.935766	+	1.62079i	0.162503	+	0.986708i	$0.448043\pi$
$152$	−7645.15	−	4413.93i	−0.330901	−	0.191046i
$153$		−	29639.0i		−	1.26614i
$154$		0			0
$155$	957.236			0.0398433
$156$	2121.84	−	3675.13i	0.0871892	−	0.151016i
$157$	−25881.1	+	14942.5i	−1.04999	+	0.606209i	−0.922645	−	0.385650i	$-0.873977\pi$
$157$	−25881.1	+	14942.5i	−1.04999	+	0.606209i	−0.127340	+	0.991859i	$0.540644\pi$
$158$	5930.84	+	10272.5i	0.237576	+	0.411493i
$159$	5585.24	+	3224.64i	0.220926	+	0.127552i
$160$			128.700i			0.00502734i
$161$		0			0
$162$	15763.7			0.600658
$163$	13102.6	−	22694.4i	0.493154	−	0.854168i	−0.506815	−	0.862055i	$-0.669177\pi$
$163$	13102.6	−	22694.4i	0.493154	−	0.854168i	0.999969	+	0.00788711i	$0.00251057\pi$
$164$	5652.42	−	3263.43i	0.210158	−	0.121335i
$165$	109.634	+	189.891i	0.00402694	+	0.00697487i
$166$	19103.9	+	11029.6i	0.693275	+	0.400262i
$167$		−	35887.5i		−	1.28680i	−0.765532	−	0.643398i	$-0.777524\pi$
$167$		−	35887.5i		−	1.28680i	0.765532	−	0.643398i	$-0.222476\pi$
$168$		0			0
$169$	−39489.2			−1.38263
$170$	−387.707	+	671.528i	−0.0134155	+	0.0232363i
$171$	25970.5	−	14994.0i	0.888152	−	0.512775i
$172$	8670.80	+	15018.3i	0.293091	+	0.507648i
$173$	−9502.65	−	5486.36i	−0.317506	−	0.183312i	0.332774	−	0.943007i	$-0.392015\pi$
$173$	−9502.65	−	5486.36i	−0.317506	−	0.183312i	−0.650281	+	0.759694i	$0.725349\pi$
$174$		−	1845.59i		−	0.0609588i
$175$		0			0
$176$	9706.50			0.313355
$177$	4785.15	−	8288.13i	0.152739	−	0.264551i
$178$	23194.5	−	13391.3i	0.732057	−	0.422653i
$179$	16922.1	+	29309.9i	0.528138	+	0.914761i	0.999462	+	0.0328012i	$0.0104428\pi$
$179$	16922.1	+	29309.9i	0.528138	+	0.914761i	−0.471324	+	0.881960i	$0.656224\pi$
$180$	−378.619	−	218.596i	−0.0116858	−	0.00674679i
$181$			50094.5i			1.52909i	0.644571	+	0.764545i	$0.277036\pi$
$181$			50094.5i			1.52909i	−0.644571	+	0.764545i	$0.722964\pi$
$182$		0			0
$183$	5154.39			0.153913
$184$	2009.84	−	3481.15i	0.0593645	−	0.102822i
$185$	−490.784	+	283.354i	−0.0143399	+	0.00827917i
$186$	−3871.84	−	6706.23i	−0.111916	−	0.193844i
$187$	50646.3	+	29240.7i	1.44832	+	0.836189i
$188$		−	34284.9i		−	0.970034i
$189$		0			0
$190$	−784.547			−0.0217326
$191$	−8806.47	+	15253.3i	−0.241399	+	0.418115i	−0.961113	−	0.276155i	$-0.910940\pi$
$191$	−8806.47	+	15253.3i	−0.241399	+	0.418115i	0.719714	+	0.694271i	$0.244273\pi$
$192$	901.650	−	520.568i	0.0244588	−	0.0141213i
$193$	−6632.12	−	11487.2i	−0.178048	−	0.308389i	0.763164	−	0.646205i	$-0.223645\pi$
$193$	−6632.12	−	11487.2i	−0.178048	−	0.308389i	−0.941212	+	0.337817i	$0.890312\pi$
$194$	−24361.1	−	14064.9i	−0.647282	−	0.373709i
$195$		−	377.143i		−	0.00991828i
$196$		0			0
$197$	5362.20			0.138169			0.0690844	−	0.997611i	$-0.477992\pi$
$197$	5362.20			0.138169			0.0690844	+	0.997611i	$0.477992\pi$
$198$	−16486.4	+	28555.3i	−0.420529	+	0.728377i
$199$	−36572.8	+	21115.3i	−0.923532	+	0.533202i	−0.884760	−	0.466047i	$-0.845678\pi$
$199$	−36572.8	+	21115.3i	−0.923532	+	0.533202i	−0.0387720	+	0.999248i	$0.512345\pi$
$200$	−7065.35	−	12237.5i	−0.176634	−	0.305939i
$201$	7206.91	+	4160.91i	0.178384	+	0.102990i
$202$			5850.08i			0.143370i
$203$		0			0
$204$	6272.81			0.150731
$205$	290.026	−	502.340i	0.00690128	−	0.0119534i
$206$	6135.38	−	3542.27i	0.144580	−	0.0834731i
$207$	6827.41	+	11825.4i	0.159336	+	0.275979i
$208$	−14458.6	−	8347.66i	−0.334194	−	0.192947i
$209$			59170.2i			1.35460i
$210$		0			0
$211$	−77049.0			−1.73062			−0.865311	−	0.501236i	$-0.832879\pi$
$211$	−77049.0			−1.73062			−0.865311	+	0.501236i	$0.832879\pi$
$212$	12686.3	−	21973.2i	0.282268	−	0.488903i
$213$	−3971.63	+	2293.02i	−0.0875406	+	0.0505416i
$214$	−9112.33	−	15783.0i	−0.198977	−	0.344638i
$215$	1334.70	+	770.589i	0.0288740	+	0.0166704i
$216$			7263.71i			0.155686i
$217$		0			0
$218$	66598.3			1.40136
$219$	−4731.06	+	8194.43i	−0.0986438	+	0.170856i
$220$	747.062	−	431.317i	0.0154352	−	0.00891150i
$221$	−50294.4	−	87112.4i	−1.02976	−	1.78359i
$222$	3970.26	+	2292.23i	0.0805589	+	0.0465107i
$223$			3702.60i			0.0744555i	0.999307	+	0.0372278i	$0.0118527\pi$
$223$			3702.60i			0.0744555i	−0.999307	+	0.0372278i	$0.988147\pi$
$224$		0			0
$225$	48001.8			0.948183
$226$	−27849.0	+	48235.9i	−0.545247	+	0.944396i
$227$	−10408.5	+	6009.38i	−0.201994	+	0.116621i	−0.597585	−	0.801805i	$-0.703873\pi$
$227$	−10408.5	+	6009.38i	−0.201994	+	0.116621i	0.395591	+	0.918427i	$0.370540\pi$
$228$	3173.35	+	5496.40i	0.0610447	+	0.105733i
$229$	−28891.0	−	16680.2i	−0.550924	−	0.318076i	0.198570	−	0.980087i	$-0.436370\pi$
$229$	−28891.0	−	16680.2i	−0.550924	−	0.318076i	−0.749495	+	0.662010i	$0.769703\pi$
$230$		−	357.237i		−	0.00675305i
$231$		0			0
$232$	−7260.85			−0.134900
$233$	−27069.4	+	46885.7i	−0.498618	+	0.863631i	−0.999999	−	0.00159563i	$-0.999492\pi$
$233$	−27069.4	+	46885.7i	−0.498618	+	0.863631i	0.501381	+	0.865226i	$0.332825\pi$
$234$	49115.5	−	28356.9i	0.896989	−	0.517877i
$235$	−1523.48	−	2638.74i	−0.0275867	−	0.0477816i
$236$	−32606.9	−	18825.6i	−0.585443	−	0.338006i
$237$		−	8527.83i		−	0.151824i
$238$		0			0
$239$	29165.4			0.510590			0.255295	−	0.966863i	$-0.417827\pi$
$239$	29165.4			0.510590			0.255295	+	0.966863i	$0.417827\pi$
$240$	46.2638	−	80.1312i	0.000803190	−	0.00139117i
$241$	−86715.3	+	50065.1i	−1.49301	+	0.861988i	−0.999968	−	0.00801977i	$-0.997447\pi$
$241$	−86715.3	+	50065.1i	−1.49301	+	0.861988i	−0.493039	+	0.870007i	$0.664114\pi$
$242$	−11824.2	−	20480.1i	−0.201902	−	0.349705i
$243$	−32333.2	−	18667.6i	−0.547566	−	0.316138i
$244$		−	20278.2i		−	0.340604i
$245$		0			0
$246$	−4692.41			−0.0775400
$247$	50886.8	−	88138.5i	0.834086	−	1.44468i
$248$	−26383.4	+	15232.5i	−0.428971	+	0.247666i
$249$	−7929.64	−	13734.5i	−0.127895	−	0.221521i
$250$	−2176.02	−	1256.33i	−0.0348164	−	0.0201012i
$251$			81988.2i			1.30138i	0.759344	+	0.650690i	$0.225520\pi$
$251$			81988.2i			1.30138i	−0.759344	+	0.650690i	$0.774480\pi$
$252$		0			0
$253$	−26942.6			−0.420919
$254$	17749.1	−	30742.4i	0.275112	−	0.476508i
$255$	482.788	−	278.738i	0.00742465	−	0.00428663i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−63890.8	−	36887.4i	−0.967324	−	0.558485i	−0.0689050	−	0.997623i	$-0.521951\pi$
$257$	−63890.8	−	36887.4i	−0.967324	−	0.558485i	−0.898420	+	0.439138i	$0.855284\pi$
$258$		−	12467.6i		−	0.187302i
$259$		0			0
$260$	−1483.74			−0.0219488
$261$	12332.5	−	21360.5i	0.181038	−	0.313567i
$262$	−47332.1	+	27327.2i	−0.689530	+	0.398101i
$263$	−19621.8	−	33985.9i	−0.283679	−	0.491346i	0.688609	−	0.725133i	$-0.258222\pi$
$263$	−19621.8	−	33985.9i	−0.283679	−	0.491346i	−0.972288	+	0.233787i	$0.924888\pi$
$264$	−6043.46	−	3489.19i	−0.0867117	−	0.0500630i
$265$		−	2254.90i		−	0.0321096i
$266$		0			0
$267$	−19255.1			−0.270100
$268$	16369.7	−	28353.2i	0.227914	−	0.394759i
$269$	−8930.08	+	5155.78i	−0.123410	+	0.0712509i	−0.560434	−	0.828199i	$-0.689366\pi$
$269$	−8930.08	+	5155.78i	−0.123410	+	0.0712509i	0.437024	+	0.899450i	$0.356032\pi$
$270$	322.769	+	559.052i	0.00442756	+	0.00766876i
$271$	32016.3	+	18484.6i	0.435946	+	0.251694i	0.701877	−	0.712299i	$-0.252346\pi$
$271$	32016.3	+	18484.6i	0.435946	+	0.251694i	−0.265930	+	0.963992i	$0.585679\pi$
$272$		−	24678.3i		−	0.333562i
$273$		0			0
$274$	10489.5			0.139718
$275$	−47356.7	+	82024.2i	−0.626204	+	1.08462i
$276$	−2502.74	+	1444.96i	−0.0328547	+	0.0189687i
$277$	46202.9	+	80025.8i	0.602157	+	1.04297i	0.992494	+	0.122294i	$0.0390252\pi$
$277$	46202.9	+	80025.8i	0.602157	+	1.04297i	−0.390337	+	0.920672i	$0.627641\pi$
$278$	−2684.87	−	1550.11i	−0.0347403	−	0.0200573i
$279$		−	103489.i		−	1.32949i
$280$		0			0
$281$	21171.6			0.268128			0.134064	−	0.990973i	$-0.457197\pi$
$281$	21171.6			0.268128			0.134064	+	0.990973i	$0.457197\pi$
$282$	−12324.4	+	21346.4i	−0.154977	+	0.268428i
$283$	41625.7	−	24032.6i	0.519743	−	0.300074i	−0.217087	−	0.976152i	$-0.569655\pi$
$283$	41625.7	−	24032.6i	0.519743	−	0.300074i	0.736829	+	0.676079i	$0.236322\pi$
$284$	9021.13	+	15625.0i	0.111847	+	0.193725i
$285$	488.475	+	282.021i	0.00601384	+	0.00347209i
$286$			111903.i			1.36808i
$287$		0			0
$288$	13914.1			0.167752
$289$	32582.5	−	56434.5i	0.390111	−	0.675692i
$290$	−558.833	+	322.642i	−0.00664486	+	0.00383641i
$291$	10111.8	+	17514.2i	0.119411	+	0.206825i
$292$	32238.2	+	18612.8i	0.378099	+	0.218296i
$293$		−	26781.1i		−	0.311956i	−0.987761	−	0.155978i	$-0.950147\pi$
$293$		−	26781.1i		−	0.311956i	0.987761	−	0.155978i	$-0.0498528\pi$
$294$		0			0
$295$	−3346.12			−0.0384501
$296$	9018.02	−	15619.7i	0.102927	−	0.178274i
$297$	42163.5	−	24343.1i	0.477995	−	0.275971i
$298$	1744.88	+	3022.22i	0.0196486	+	0.0340324i
$299$	40133.1	+	23170.8i	0.448911	+	0.259179i
$300$			10159.1i			0.112879i
$301$		0			0
$302$	−120697.			−1.32337
$303$	2102.93	−	3642.38i	0.0229055	−	0.0396734i
$304$	21623.7	−	12484.5i	0.233983	−	0.135090i
$305$	−901.081	−	1560.72i	−0.00968643	−	0.0167774i
$306$	72600.4	+	41915.9i	0.775347	+	0.447647i
$307$		−	69996.0i		−	0.742671i	−0.928499	−	0.371336i	$-0.878900\pi$
$307$		−	69996.0i		−	0.742671i	0.928499	−	0.371336i	$-0.121100\pi$
$308$		0			0
$309$	−5093.35			−0.0533441
$310$	−1353.74	+	2344.74i	−0.0140867	+	0.0243990i
$311$	75310.9	−	43480.8i	0.778641	−	0.449549i	−0.0573075	−	0.998357i	$-0.518252\pi$
$311$	75310.9	−	43480.8i	0.778641	−	0.449549i	0.835948	+	0.548808i	$0.184918\pi$
$312$	6001.46	+	10394.8i	0.0616521	+	0.106785i
$313$	28720.2	+	16581.6i	0.293156	+	0.169253i	0.639364	−	0.768904i	$-0.279198\pi$
$313$	28720.2	+	16581.6i	0.293156	+	0.169253i	−0.346208	+	0.938158i	$0.612531\pi$
$314$		−	84527.3i		−	0.857310i
$315$		0			0
$316$	−33549.9			−0.335983
$317$	−14603.0	+	25293.1i	−0.145319	+	0.251700i	−0.929492	−	0.368842i	$-0.879754\pi$
$317$	−14603.0	+	25293.1i	−0.145319	+	0.251700i	0.784173	+	0.620543i	$0.213088\pi$
$318$	−15797.4	+	9120.66i	−0.156218	+	0.0901928i
$319$	24333.5	+	42146.9i	0.239124	+	0.414175i
$320$	−315.249	−	182.009i	−0.00307861	−	0.00177743i
$321$			13102.4i			0.127157i
$322$		0			0
$323$	150437.			1.44195
$324$	−22293.2	+	38612.9i	−0.212365	+	0.367826i
$325$	141083.	−	81454.1i	1.33569	−	0.771164i
$326$	37059.8	+	64189.4i	0.348713	+	0.603988i
$327$	−41465.4	−	23940.1i	−0.387784	−	0.223887i
$328$			18460.7i			0.171594i
$329$		0			0
$330$	−620.181			−0.00569496
$331$	−83496.6	+	144620.i	−0.762102	+	1.32000i	0.179664	+	0.983728i	$0.442499\pi$
$331$	−83496.6	+	144620.i	−0.762102	+	1.32000i	−0.941765	+	0.336271i	$0.890834\pi$
$332$	−54033.9	+	31196.5i	−0.490219	+	0.283028i
$333$	30634.1	+	53059.8i	0.276259	+	0.478495i
$334$	87906.0	+	50752.5i	0.787999	+	0.454951i
$335$		−	2909.61i		−	0.0259266i
$336$		0			0
$337$	16126.0			0.141993			0.0709964	−	0.997477i	$-0.477382\pi$
$337$	16126.0			0.141993			0.0709964	+	0.997477i	$0.477382\pi$
$338$	55846.1	−	96728.3i	0.488832	−	0.846682i
$339$	34678.7	−	20021.8i	0.301761	−	0.174222i
$340$	−1096.60	−	1899.37i	−0.00948617	−	0.0164305i
$341$	176839.	+	102098.i	1.52079	+	0.878030i
$342$			84819.2i			0.725173i
$343$		0			0
$344$	−49049.5			−0.414493
$345$	−128.416	+	222.423i	−0.00107890	+	0.00186871i
$346$	26877.5	−	15517.8i	0.224511	−	0.129621i
$347$	−5035.67	−	8722.04i	−0.0418214	−	0.0724368i	0.844357	−	0.535781i	$-0.179983\pi$
$347$	−5035.67	−	8722.04i	−0.0418214	−	0.0724368i	−0.886178	+	0.463344i	$0.846649\pi$
$348$	4520.75	+	2610.06i	0.0373295	+	0.0215522i
$349$		−	97674.1i		−	0.801915i	−0.916097	−	0.400958i	$-0.868677\pi$
$349$		−	97674.1i		−	0.801915i	0.916097	−	0.400958i	$-0.131323\pi$
$350$		0			0
$351$	−83740.9			−0.679710
$352$	−13727.1	+	23776.0i	−0.110788	+	0.191890i
$353$	73833.2	−	42627.6i	0.592519	−	0.342091i	−0.173574	−	0.984821i	$-0.555532\pi$
$353$	73833.2	−	42627.6i	0.592519	−	0.342091i	0.766093	+	0.642730i	$0.222198\pi$
$354$	13534.5	+	23442.4i	0.108003	+	0.187066i
$355$	1388.63	+	801.723i	0.0110186	+	0.00636162i
$356$			75752.9i			0.597722i
$357$		0			0
$358$	−95725.6			−0.746899
$359$	71119.9	−	123183.i	0.551826	−	0.955791i	−0.446316	−	0.894875i	$-0.647264\pi$
$359$	71119.9	−	123183.i	0.551826	−	0.955791i	0.998143	−	0.0609162i	$-0.0194022\pi$
$360$	1070.90	−	618.283i	0.00826310	−	0.00477070i
$361$	10944.0	+	18955.6i	0.0839775	+	0.145453i
$362$	−122706.	−	70844.3i	−0.936372	−	0.540615i
$363$			17001.8i			0.129027i
$364$		0			0
$365$	3308.30			0.0248324
$366$	−7289.41	+	12625.6i	−0.0544164	+	0.0942520i
$367$	−154015.	+	88920.4i	−1.14348	+	0.660191i	−0.947291	−	0.320375i	$-0.896191\pi$
$367$	−154015.	+	88920.4i	−1.14348	+	0.660191i	−0.196193	+	0.980565i	$0.562858\pi$
$368$	5684.70	+	9846.18i	0.0419770	+	0.0727063i
$369$	−54309.1	−	31355.4i	−0.398860	−	0.230282i
$370$		−	1602.90i		−	0.0117085i
$371$		0			0
$372$	21902.5			0.158273
$373$	10835.4	−	18767.5i	0.0778803	−	0.134893i	−0.824455	−	0.565928i	$-0.808518\pi$
$373$	10835.4	−	18767.5i	0.0778803	−	0.134893i	0.902335	+	0.431035i	$0.141851\pi$
$374$	−143249.	+	82705.1i	−1.02412	+	0.591275i
$375$	903.224	+	1564.43i	0.00642293	+	0.0111248i
$376$	83980.4	+	48486.1i	0.594022	+	0.342959i
$377$		−	83708.0i		−	0.588958i
$378$		0			0
$379$	125199.			0.871608			0.435804	−	0.900042i	$-0.356464\pi$
$379$	125199.			0.871608			0.435804	+	0.900042i	$0.356464\pi$
$380$	1109.52	−	1921.74i	0.00768363	−	0.0133084i
$381$	−22101.9	+	12760.6i	−0.152258	+	0.0879062i
$382$	−24908.5	−	43142.7i	−0.170695	−	0.295652i
$383$	−183086.	−	105705.i	−1.24813	−	0.720605i	−0.277390	−	0.960757i	$-0.589469\pi$
$383$	−183086.	−	105705.i	−1.24813	−	0.720605i	−0.970735	+	0.240152i	$0.922803\pi$
$384$			2944.78i			0.0199705i
$385$		0			0
$386$	37516.9			0.251798
$387$	83310.2	−	144297.i	0.556258	−	0.963467i
$388$	68903.7	−	39781.5i	0.457698	−	0.264252i
$389$	19580.4	+	33914.2i	0.129396	+	0.224121i	0.923443	−	0.383736i	$-0.125363\pi$
$389$	19580.4	+	33914.2i	0.129396	+	0.224121i	−0.794047	+	0.607857i	$0.792029\pi$
$390$	923.807	+	533.360i	0.00607368	+	0.00350664i
$391$			68500.3i			0.448063i
$392$		0			0
$393$	39293.2			0.254409
$394$	−7583.29	+	13134.6i	−0.0488501	+	0.0846108i
$395$	−2582.17	+	1490.82i	−0.0165497	+	0.00955500i
$396$	−46630.6	−	80766.6i	−0.297359	−	0.515041i
$397$	−170195.	−	98262.3i	−1.07986	−	0.623456i	−0.149000	−	0.988837i	$-0.547605\pi$
$397$	−170195.	−	98262.3i	−1.07986	−	0.623456i	−0.930858	+	0.365381i	$0.880939\pi$
$398$		−	119446.i		−	0.754061i
$399$		0			0
$400$	39967.6			0.249798
$401$	−106825.	+	185026.i	−0.664330	+	1.15065i	0.315136	+	0.949047i	$0.397950\pi$
$401$	−106825.	+	185026.i	−0.664330	+	1.15065i	−0.979466	+	0.201608i	$0.935383\pi$
$402$	−20384.2	+	11768.8i	−0.126137	+	0.0728251i
$403$	−175610.	−	304166.i	−1.08128	−	1.87284i
$404$	−14329.7	−	8273.26i	−0.0877960	−	0.0506890i
$405$			3962.47i			0.0241577i
$406$		0			0
$407$	−120890.			−0.729794
$408$	−8871.10	+	15365.2i	−0.0532914	+	0.0923034i
$409$	−30834.0	+	17802.0i	−0.184325	+	0.106420i	−0.589323	−	0.807898i	$-0.700605\pi$
$409$	−30834.0	+	17802.0i	−0.184325	+	0.106420i	0.404998	+	0.914317i	$0.367272\pi$
$410$	820.318	+	1420.83i	0.00487994	+	0.00845231i
$411$	−6530.95	−	3770.65i	−0.0386628	−	0.0223220i
$412$			20038.1i			0.118049i
$413$		0			0
$414$	−38621.7			−0.225336
$415$	−2772.49	+	4802.09i	−0.0160981	+	0.0278826i
$416$	40895.0	−	23610.7i	0.236311	−	0.136434i
$417$	1114.44	+	1930.26i	0.00640889	+	0.0111005i
$418$	−144937.	−	83679.2i	−0.829518	−	0.478922i
$419$			254947.i			1.45219i	0.687597	+	0.726093i	$0.258666\pi$
$419$			254947.i			1.45219i	−0.687597	+	0.726093i	$0.741334\pi$
$420$		0			0
$421$	107186.			0.604748			0.302374	−	0.953189i	$-0.402221\pi$
$421$	107186.			0.604748			0.302374	+	0.953189i	$0.402221\pi$
$422$	108964.	−	188731.i	0.611867	−	1.05978i
$423$	−285280.	+	164707.i	−1.59438	+	0.920514i
$424$	35882.2	+	62149.7i	0.199594	+	0.345707i
$425$	208542.	+	120402.i	1.15456	+	0.666585i
$426$		−	12971.3i		−	0.0714766i
$427$		0			0
$428$	51547.1			0.281395
$429$	40225.8	−	69673.1i	0.218570	−	0.378574i
$430$	−3775.10	+	2179.56i	−0.0204170	+	0.0117878i
$431$	−59979.2	−	103887.i	−0.322884	−	0.559251i	0.658198	−	0.752845i	$-0.271319\pi$
$431$	−59979.2	−	103887.i	−0.322884	−	0.559251i	−0.981082	+	0.193594i	$0.937986\pi$
$432$	−17792.4	−	10272.4i	−0.0953381	−	0.0550435i
$433$		−	110159.i		−	0.587547i	−0.955875	−	0.293773i	$-0.905089\pi$
$433$		−	110159.i		−	0.587547i	0.955875	−	0.293773i	$-0.0949111\pi$
$434$		0			0
$435$	463.921			0.00245169
$436$	−94184.2	+	163132.i	−0.495456	+	0.858155i
$437$	−60021.7	+	34653.5i	−0.314301	+	0.181462i
$438$	−13381.4	−	23177.4i	−0.0697517	−	0.120814i
$439$	−305096.	−	176148.i	−1.58310	−	0.914003i	−0.994404	−	0.105648i	$-0.966308\pi$
$439$	−305096.	−	176148.i	−1.58310	−	0.914003i	−0.588696	−	0.808355i	$-0.700358\pi$
$440$			2439.90i			0.0126028i
$441$		0			0
$442$	284508.			1.45630
$443$	−142866.	+	247452.i	−0.727984	+	1.26091i	0.229749	+	0.973250i	$0.426209\pi$
$443$	−142866.	+	247452.i	−0.727984	+	1.26091i	−0.957734	+	0.287656i	$0.907124\pi$
$444$	−11229.6	+	6483.41i	−0.0569637	+	0.0328880i
$445$	3366.14	+	5830.33i	0.0169986	+	0.0294424i
$446$	−9069.48	−	5236.27i	−0.0455945	−	0.0263240i
$447$		−	2508.92i		−	0.0125566i
$448$		0			0
$449$	−342184.			−1.69733			−0.848667	−	0.528927i	$-0.822594\pi$
$449$	−342184.			−1.69733			−0.848667	+	0.528927i	$0.822594\pi$
$450$	−67884.8	+	117580.i	−0.335233	+	0.580641i
$451$	107159.	−	61868.0i	0.526834	−	0.304168i
$452$	−78769.0	−	136432.i	−0.385548	−	0.667788i
$453$	75148.3	+	43386.9i	0.366204	+	0.211428i
$454$		−	33994.2i		−	0.164927i
$455$		0			0
$456$	−17951.2			−0.0863302
$457$	138812.	−	240430.i	0.664653	−	1.15121i	−0.314726	−	0.949183i	$-0.601913\pi$
$457$	138812.	−	240430.i	0.664653	−	1.15121i	0.979379	−	0.202030i	$-0.0647540\pi$
$458$	81716.2	−	47178.8i	0.389562	−	0.224914i
$459$	−61891.1	−	107199.i	−0.293767	−	0.508819i
$460$	875.047	+	505.209i	0.00413538	+	0.00238757i
$461$			361934.i			1.70305i	0.524315	+	0.851524i	$0.324322\pi$
$461$			361934.i			1.70305i	−0.524315	+	0.851524i	$0.675678\pi$
$462$		0			0
$463$	146876.			0.685153			0.342577	−	0.939490i	$-0.388700\pi$
$463$	146876.			0.685153			0.342577	+	0.939490i	$0.388700\pi$
$464$	10268.4	−	17785.4i	0.0476943	−	0.0826090i
$465$	1685.73	−	973.255i	0.00779617	−	0.00450112i
$466$	−76564.0	−	132613.i	−0.352576	−	0.610679i
$467$	232450.	+	134205.i	1.06585	+	0.615367i	0.927044	−	0.374953i	$-0.122341\pi$
$467$	232450.	+	134205.i	1.06585	+	0.615367i	0.138803	+	0.990320i	$0.455674\pi$
$468$			160411.i			0.732389i
$469$		0			0
$470$	8618.09			0.0390136
$471$	−30385.0	+	52628.4i	−0.136968	+	0.237235i
$472$	92226.1	−	53246.8i	0.413971	−	0.239006i
$473$	164381.	+	284716.i	0.734733	+	1.27259i
$474$	20888.8	+	12060.2i	0.0929731	+	0.0536780i
$475$			243640.i			1.07985i
$476$		0			0
$477$	−243782.			−1.07143
$478$	−41246.1	+	71440.4i	−0.180521	+	0.312671i
$479$	−134481.	+	77642.5i	−0.586124	+	0.338399i	−0.763563	−	0.645733i	$-0.776552\pi$
$479$	−134481.	+	77642.5i	−0.586124	+	0.338399i	0.177440	+	0.984132i	$0.443219\pi$
$480$	130.854	+	226.645i	0.000567941	+	0.000983703i
$481$	180074.	+	103966.i	0.778326	+	0.449367i
$482$		−	283211.i		−	1.21903i
$483$		0			0
$484$	66887.7			0.285533
$485$	3535.46	−	6123.59i	0.0150301	−	0.0260329i
$486$	91452.2	−	52800.0i	0.387188	−	0.223543i
$487$	77813.9	+	134778.i	0.328095	+	0.568277i	0.982134	−	0.188184i	$-0.0602601\pi$
$487$	77813.9	+	134778.i	0.328095	+	0.568277i	−0.654039	+	0.756461i	$0.726927\pi$
$488$	49671.3	+	28677.7i	0.208577	+	0.120422i
$489$		−	53287.5i		−	0.222847i
$490$		0			0
$491$	37550.7			0.155760			0.0778798	−	0.996963i	$-0.475185\pi$
$491$	37550.7			0.155760			0.0778798	+	0.996963i	$0.475185\pi$
$492$	6636.07	−	11494.0i	0.0274145	−	0.0474834i
$493$	107156.	−	61866.8i	0.440884	−	0.254544i
$494$	143930.	+	249293.i	0.589788	+	1.02154i
$495$	−7177.87	−	4144.14i	−0.0292944	−	0.0169131i
$496$		−	86167.9i		−	0.350253i
$497$		0			0
$498$	44856.8			0.180871
$499$	−83910.2	+	145337.i	−0.336987	+	0.583679i	−0.983865	−	0.178915i	$-0.942741\pi$
$499$	−83910.2	+	145337.i	−0.336987	+	0.583679i	0.646877	+	0.762594i	$0.276075\pi$
$500$	6154.72	−	3553.43i	0.0246189	−	0.0142137i
$501$	−36488.0	−	63199.1i	−0.145370	−	0.251788i
$502$	−200829.	−	115949.i	−0.796929	−	0.460107i
$503$		−	133035.i		−	0.525810i	−0.964822	−	0.262905i	$-0.915319\pi$
$503$		−	133035.i		−	0.525810i	0.964822	−	0.262905i	$-0.0846806\pi$
$504$		0			0
$505$	−1470.52			−0.00576617
$506$	38102.6	−	65995.7i	0.148817	−	0.257759i
$507$	−69541.8	+	40150.0i	−0.270539	+	0.156196i
$508$	50202.1	+	86952.7i	0.194534	+	0.336942i
$509$	197449.	+	113997.i	0.762112	+	0.440005i	0.830053	−	0.557684i	$-0.188310\pi$
$509$	197449.	+	113997.i	0.762112	+	0.440005i	−0.0679416	+	0.997689i	$0.521643\pi$
$510$			1576.78i			0.00606220i
$511$		0			0
$512$	11585.2			0.0441942
$513$	62620.1	−	108461.i	0.237946	−	0.412135i
$514$	180711.	−	104333.i	0.684002	−	0.394909i
$515$	890.410	+	1542.23i	0.00335719	+	0.00581482i
$516$	30539.2	+	17631.8i	0.114699	+	0.0662212i
$517$		−	649973.i		−	2.43172i
$518$		0			0
$519$	−22312.7			−0.0828355
$520$	2098.33	−	3634.41i	0.00776009	−	0.0134409i
$521$	295670.	−	170705.i	1.08926	−	0.628885i	0.155882	−	0.987776i	$-0.450178\pi$
$521$	295670.	−	170705.i	1.08926	−	0.628885i	0.933380	+	0.358890i	$0.116845\pi$
$522$	34881.6	+	60416.7i	0.128013	+	0.221726i
$523$	−54483.4	−	31456.0i	−0.199187	−	0.115001i	0.397089	−	0.917780i	$-0.370020\pi$
$523$	−54483.4	−	31456.0i	−0.199187	−	0.115001i	−0.596276	+	0.802779i	$0.703354\pi$
$524$		−	154586.i		−	0.562999i
$525$		0			0
$526$	110998.			0.401182
$527$	259579.	−	449605.i	0.934650	−	1.61886i
$528$	17093.5	−	9868.93i	0.0613144	−	0.0353999i
$529$	124141.	+	215019.i	0.443614	+	0.768362i
$530$	5523.35	+	3188.91i	0.0196631	+	0.0113525i
$531$			361757.i			1.28300i
$532$		0			0
$533$	−212828.			−0.749159
$534$	27230.9	−	47165.2i	0.0954946	−	0.165402i
$535$	3967.33	−	2290.54i	0.0138609	−	0.00800259i
$536$	46300.5	+	80194.9i	0.161160	+	0.279137i
$537$	59600.7	+	34410.5i	0.206682	+	0.119328i
$538$		−	29165.5i		−	0.100764i
$539$		0			0
$540$	−1825.86			−0.00626151
$541$	−125601.	+	217548.i	−0.429141	+	0.743294i	−0.996797	−	0.0799715i	$-0.974517\pi$
$541$	−125601.	+	217548.i	−0.429141	+	0.743294i	0.567656	+	0.823266i	$0.307850\pi$
$542$	−90555.9	+	52282.5i	−0.308261	+	0.177974i
$543$	50932.8	+	88218.2i	0.172742	+	0.299198i
$544$	60449.2	+	34900.4i	0.204264	+	0.117932i
$545$			16740.6i			0.0563610i
$546$		0			0
$547$	−153431.			−0.512789			−0.256395	−	0.966572i	$-0.582535\pi$
$547$	−153431.			−0.512789			−0.256395	+	0.966572i	$0.582535\pi$
$548$	−14834.3	+	25693.8i	−0.0493978	+	0.0855594i
$549$	−168733.	+	97417.9i	−0.559828	+	0.323217i
$550$	−133945.	−	231999.i	−0.442793	−	0.766940i
$551$	108419.	+	62595.5i	0.357109	+	0.206177i
$552$		−	8173.91i		−	0.0268257i
$553$		0			0
$554$	−261363.			−0.851579
$555$	−576.192	+	997.994i	−0.00187060	+	0.00323998i
$556$	7593.96	−	4384.37i	0.0245651	−	0.0141827i
$557$	237576.	+	411493.i	0.765758	+	1.32633i	0.939845	+	0.341601i	$0.110969\pi$
$557$	237576.	+	411493.i	0.765758	+	1.32633i	−0.174087	+	0.984730i	$0.555697\pi$
$558$	253495.	+	146356.i	0.814144	+	0.470046i
$559$		−	565476.i		−	1.80963i
$560$		0			0
$561$	118920.			0.377858
$562$	−29941.2	+	51859.7i	−0.0947975	+	0.164194i
$563$	−34196.7	+	19743.5i	−0.107887	+	0.0622884i	−0.552972	−	0.833200i	$-0.686507\pi$
$563$	−34196.7	+	19743.5i	−0.107887	+	0.0622884i	0.445086	+	0.895488i	$0.353173\pi$
$564$	−34858.6	−	60376.9i	−0.109585	−	0.189807i
$565$	−12124.9	−	7000.34i	−0.0379824	−	0.0219292i
$566$			135949.i			0.424368i
$567$		0			0
$568$	−51031.2			−0.158175
$569$	42653.8	−	73878.6i	0.131745	−	0.228189i	−0.792604	−	0.609736i	$-0.791275\pi$
$569$	42653.8	−	73878.6i	0.131745	−	0.228189i	0.924349	+	0.381547i	$0.124609\pi$
$570$	−1381.61	+	797.676i	−0.00425243	+	0.00245514i
$571$	−44549.5	−	77162.0i	−0.136638	−	0.236664i	0.789584	−	0.613642i	$-0.210296\pi$
$571$	−44549.5	−	77162.0i	−0.136638	−	0.236664i	−0.926222	+	0.376979i	$0.876963\pi$
$572$	−274105.	−	158255.i	−0.837772	−	0.483688i
$573$			35815.4i			0.109084i
$574$		0			0
$575$	−110939.			−0.335545
$576$	−19677.4	+	34082.3i	−0.0593094	+	0.102727i
$577$	269400.	−	155538.i	0.809181	−	0.467181i	−0.0374905	−	0.999297i	$-0.511936\pi$
$577$	269400.	−	155538.i	0.809181	−	0.467181i	0.846671	+	0.532116i	$0.178603\pi$
$578$	92157.1	+	159621.i	0.275850	+	0.477786i
$579$	−23358.8	−	13486.2i	−0.0696776	−	0.0402284i
$580$		−	1825.14i		−	0.00542551i
$581$		0			0
$582$	−57201.1			−0.168872
$583$	240506.	−	416569.i	0.707602	−	1.22560i
$584$	−91183.5	+	52644.8i	−0.267356	+	0.154358i
$585$	7127.99	+	12346.0i	0.0208284	+	0.0360758i
$586$	65600.0	+	37874.2i	0.191033	+	0.110293i
$587$			62466.3i			0.181288i	0.995883	+	0.0906440i	$0.0288926\pi$
$587$			62466.3i			0.181288i	−0.995883	+	0.0906440i	$0.971107\pi$
$588$		0			0
$589$	525274.			1.51410
$590$	4732.13	−	8196.30i	0.0135942	−	0.0235458i
$591$	9443.01	−	5451.93i	0.0270356	−	0.0156090i
$592$	25506.8	+	44179.1i	0.0727802	+	0.126059i
$593$	41194.5	+	23783.7i	0.117147	+	0.0676346i	0.557428	−	0.830225i	$-0.311788\pi$
$593$	41194.5	+	23783.7i	0.117147	+	0.0676346i	−0.440282	+	0.897860i	$0.645121\pi$
$594$			137705.i			0.390281i
$595$		0			0
$596$	−9870.52			−0.0277874
$597$	−42937.3	+	74369.6i	−0.120472	+	0.208664i
$598$	−113513.	+	65537.0i	−0.317428	+	0.183267i
$599$	−282017.	−	488468.i	−0.785999	−	1.36139i	−0.928400	−	0.371582i	$-0.878815\pi$
$599$	−282017.	−	488468.i	−0.785999	−	1.36139i	0.142401	−	0.989809i	$-0.454518\pi$
$600$	−24884.7	−	14367.2i	−0.0691240	−	0.0399088i
$601$			255637.i			0.707740i	0.935295	+	0.353870i	$0.115135\pi$
$601$			255637.i			0.707740i	−0.935295	+	0.353870i	$0.884865\pi$
$602$		0			0
$603$	−314565.			−0.865118
$604$	170691.	−	295646.i	0.467883	−	0.810397i
$605$	5148.03	−	2972.22i	0.0140647	−	0.00812025i
$606$	5947.98	+	10302.2i	0.0161966	+	0.0280533i
$607$	−495972.	−	286350.i	−1.34611	−	0.777176i	−0.358412	−	0.933564i	$-0.616682\pi$
$607$	−495972.	−	286350.i	−1.34611	−	0.777176i	−0.987696	+	0.156388i	$0.950015\pi$
$608$			70622.8i			0.191046i
$609$		0			0
$610$	5097.28			0.0136987
$611$	−558981.	+	968184.i	−1.49732	+	2.59343i
$612$	−205345.	+	118556.i	−0.548253	+	0.316534i
$613$	−141501.	−	245087.i	−0.376563	−	0.652227i	0.613996	−	0.789309i	$-0.289561\pi$
$613$	−141501.	−	245087.i	−0.376563	−	0.652227i	−0.990560	+	0.137082i	$0.956228\pi$
$614$	171455.	+	98989.3i	0.454791	+	0.262574i
$615$		−	1179.52i		−	0.00311856i
$616$		0			0
$617$	248170.			0.651896			0.325948	−	0.945388i	$-0.394317\pi$
$617$	248170.			0.651896			0.325948	+	0.945388i	$0.394317\pi$
$618$	7203.09	−	12476.1i	0.0188600	−	0.0326665i
$619$	49006.8	−	28294.1i	0.127901	−	0.0738438i	−0.434684	−	0.900583i	$-0.643140\pi$
$619$	49006.8	−	28294.1i	0.127901	−	0.0738438i	0.562586	+	0.826739i	$0.309807\pi$
$620$	−3828.94	−	6631.93i	−0.00996083	−	0.0172527i
$621$	49386.8	+	28513.5i	0.128064	+	0.0739379i
$622$			245964.i			0.635758i
$623$		0			0
$624$	−33949.4			−0.0871892
$625$	−194839.	+	337471.i	−0.498787	+	0.863925i
$626$	−81232.9	+	46899.8i	−0.207292	+	0.119680i
$627$	60160.3	+	104201.i	0.153029	+	0.265055i
$628$	207049.	+	119540.i	0.524993	+	0.303105i
$629$			307356.i			0.776855i
$630$		0			0
$631$	681448.			1.71149			0.855744	−	0.517399i	$-0.173100\pi$
$631$	681448.			1.71149			0.855744	+	0.517399i	$0.173100\pi$
$632$	47446.7	−	82180.1i	0.118788	−	0.205747i
$633$	−135686.	+	78338.3i	−0.338632	+	0.195509i
$634$	−41303.5	−	71539.8i	−0.102756	−	0.177979i
$635$	7727.63	+	4461.55i	0.0191646	+	0.0110647i
$636$		−	51594.2i		−	0.127552i
$637$		0			0
$638$	−137651.			−0.338173
$639$	86676.1	−	150127.i	0.212274	−	0.367670i
$640$	891.660	−	514.800i	0.00217690	−	0.00125684i
$641$	−339057.	−	587264.i	−0.825195	−	1.42928i	−0.901770	−	0.432216i	$-0.857732\pi$
$641$	−339057.	−	587264.i	−0.825195	−	1.42928i	0.0765754	−	0.997064i	$-0.475601\pi$
$642$	−32094.3	−	18529.6i	−0.0778677	−	0.0449569i
$643$			345520.i			0.835701i	0.908516	+	0.417851i	$0.137216\pi$
$643$			345520.i			0.835701i	−0.908516	+	0.417851i	$0.862784\pi$
$644$		0			0
$645$	3133.94			0.00753305
$646$	−212750.	+	368494.i	−0.509806	+	0.883010i
$647$	−6718.19	+	3878.75i	−0.0160489	+	0.00926581i	−0.508003	−	0.861355i	$-0.669616\pi$
$647$	−6718.19	+	3878.75i	−0.0160489	+	0.00926581i	0.491954	+	0.870621i	$0.336283\pi$
$648$	−63054.6	−	109214.i	−0.150164	−	0.260092i
$649$	−618161.	−	356895.i	−1.46761	−	0.847328i
$650$			460774.i			1.09059i
$651$		0			0
$652$	−209642.			−0.493154
$653$	224236.	−	388389.i	0.525872	−	0.910836i	−0.473674	−	0.880700i	$-0.657073\pi$
$653$	224236.	−	388389.i	0.525872	−	0.910836i	0.999546	−	0.0301362i	$-0.00959410\pi$
$654$	117282.	−	67712.7i	0.274205	−	0.158312i
$655$	−6869.17	−	11897.7i	−0.0160111	−	0.0277321i
$656$	−45219.3	−	26107.4i	−0.105079	−	0.0606675i
$657$		−	357667.i		−	0.828607i
$658$		0			0
$659$	583660.			1.34397			0.671984	−	0.740565i	$-0.265442\pi$
$659$	583660.			1.34397			0.671984	+	0.740565i	$0.265442\pi$
$660$	877.069	−	1519.13i	0.00201347	−	0.00348744i
$661$	331589.	−	191443.i	0.758922	−	0.438164i	−0.0699869	−	0.997548i	$-0.522296\pi$
$661$	331589.	−	191443.i	0.758922	−	0.438164i	0.828908	+	0.559384i	$0.188962\pi$
$662$	−236164.	−	409048.i	−0.538887	−	0.933380i
$663$	−177140.	−	102272.i	−0.402986	−	0.232664i
$664$		−	176474.i		−	0.400262i
$665$		0			0
$666$	−173293.			−0.390689
$667$	−28502.3	+	49367.4i	−0.0640661	+	0.110966i
$668$	−248636.	+	143550.i	−0.557199	+	0.321699i
$669$	3764.56	+	6520.41i	0.00841128	+	0.0145688i
$670$	7127.06	+	4114.81i	0.0158767	+	0.00916643i
$671$		−	384435.i		−	0.853842i
$672$		0			0
$673$	−323802.			−0.714907			−0.357453	−	0.933931i	$-0.616355\pi$
$673$	−323802.			−0.714907			−0.357453	+	0.933931i	$0.616355\pi$
$674$	−22805.6	+	39500.4i	−0.0502021	+	0.0869525i
$675$	173613.	−	100236.i	0.381044	−	0.219996i
$676$	157957.	+	273589.i	0.345656	+	0.598694i
$677$	−324589.	−	187402.i	−0.708201	−	0.408880i	0.102194	−	0.994765i	$-0.467414\pi$
$677$	−324589.	−	187402.i	−0.708201	−	0.408880i	−0.810395	+	0.585884i	$0.800747\pi$
$678$			113260.i			0.246387i
$679$		0			0
$680$	6203.31			0.0134155
$681$	−12219.9	+	21165.5i	−0.0263495	+	0.0456387i
$682$	−500177.	+	288777.i	−1.07536	+	0.620861i
$683$	−48682.3	−	84320.1i	−0.104359	−	0.180755i	0.809117	−	0.587647i	$-0.199946\pi$
$683$	−48682.3	−	84320.1i	−0.104359	−	0.180755i	−0.913476	+	0.406892i	$0.866612\pi$
$684$	−207764.	−	119952.i	−0.444076	−	0.256387i
$685$			2636.71i			0.00561928i
$686$		0			0
$687$	−67837.5			−0.143733
$688$	69366.4	−	120146.i	0.146545	−	0.253824i
$689$	−716504.	+	413674.i	−1.50932	+	0.871404i
$690$	−363.215	−	629.106i	−0.000762896	−	0.00132137i
$691$	681662.	+	393558.i	1.42762	+	0.824238i	0.996933	−	0.0782630i	$-0.0249374\pi$
$691$	681662.	+	393558.i	1.42762	+	0.824238i	0.430689	+	0.902501i	$0.358271\pi$
$692$			87781.7i			0.183312i
$693$		0			0
$694$	28486.1			0.0591444
$695$	389.647	−	674.888i	0.000806681	−	0.00139721i
$696$	−12786.6	+	7382.35i	−0.0263959	+	0.0152397i
$697$	−157296.	−	272445.i	−0.323782	−	0.560807i
$698$	239252.	+	138132.i	0.491071	+	0.283520i
$699$			110090.i			0.225316i
$700$		0			0
$701$	−232522.			−0.473182			−0.236591	−	0.971609i	$-0.576030\pi$
$701$	−232522.			−0.473182			−0.236591	+	0.971609i	$0.576030\pi$
$702$	118428.	−	205123.i	0.240314	−	0.416236i
$703$	−269313.	+	155488.i	−0.544937	+	0.314620i
$704$	−38826.0	−	67248.6i	−0.0783388	−	0.135687i
$705$	−5365.80	−	3097.94i	−0.0107958	−	0.00623297i
$706$			241138.i			0.483790i
$707$		0			0
$708$	−76562.4			−0.152739
$709$	−75524.5	+	130812.i	−0.150243	+	0.260229i	−0.931317	−	0.364210i	$-0.881339\pi$
$709$	−75524.5	+	130812.i	−0.150243	+	0.260229i	0.781073	+	0.624439i	$0.214672\pi$
$710$	−3927.63	+	2267.62i	−0.00779136	+	0.00449834i
$711$	161176.	+	279165.i	0.318831	+	0.552231i
$712$	−185556.	−	107131.i	−0.366028	−	0.211327i
$713$			239179.i			0.470483i
$714$		0			0
$715$	−28128.8			−0.0550223
$716$	135376.	−	234479.i	0.264069	−	0.457381i
$717$	51361.3	−	29653.5i	0.0999074	−	0.0576816i
$718$	201158.	+	348415.i	0.390200	+	0.675847i
$719$	−616705.	−	356055.i	−1.19294	−	0.688746i	−0.233971	−	0.972244i	$-0.575172\pi$
$719$	−616705.	−	356055.i	−1.19294	−	0.688746i	−0.958973	+	0.283497i	$0.908505\pi$
$720$			3497.54i			0.00674679i
$721$		0			0
$722$	−61908.8			−0.118762
$723$	−101806.	+	176333.i	−0.194758	+	0.337331i
$724$	347065.	−	200378.i	0.662115	−	0.382272i
$725$	100196.	+	173545.i	0.190623	+	0.330169i
$726$	−41645.6	−	24044.1i	−0.0790126	−	0.0456179i
$727$		−	693160.i		−	1.31149i	−0.754983	−	0.655744i	$-0.772355\pi$
$727$		−	693160.i		−	1.31149i	0.754983	−	0.655744i	$-0.227645\pi$
$728$		0			0
$729$	375517.			0.706601
$730$	−4678.64	+	8103.64i	−0.00877958	+	0.0152067i
$731$	723877.	−	417931.i	1.35466	−	0.782113i
$732$	−20617.6	−	35710.7i	−0.0384782	−	0.0666463i
$733$	233054.	+	134554.i	0.433759	+	0.250431i	0.700947	−	0.713214i	$-0.252761\pi$
$733$	233054.	+	134554.i	0.433759	+	0.250431i	−0.267188	+	0.963644i	$0.586094\pi$
$734$		−	503010.i		−	0.933651i
$735$		0			0
$736$	−32157.5			−0.0593645
$737$	310337.	−	537519.i	0.571345	−	0.989599i
$738$	153609.	−	88686.5i	0.282036	−	0.162834i
$739$	−43092.6	−	74638.5i	−0.0789066	−	0.136670i	0.823872	−	0.566776i	$-0.191810\pi$
$739$	−43092.6	−	74638.5i	−0.0789066	−	0.136670i	−0.902778	+	0.430106i	$0.858476\pi$
$740$	3926.28	+	2266.84i	0.00716997	+	0.00413958i
$741$		−	206953.i		−	0.376908i
$742$		0			0
$743$	−457439.			−0.828620			−0.414310	−	0.910136i	$-0.635977\pi$
$743$	−457439.			−0.828620			−0.414310	+	0.910136i	$0.635977\pi$
$744$	−30974.7	+	53649.8i	−0.0559580	+	0.0969220i
$745$	−759.686	+	438.605i	−0.00136874	+	0.000790244i
$746$	30647.2	+	53082.4i	0.0550697	+	0.0953835i
$747$	519165.	+	299740.i	0.930388	+	0.537160i
$748$		−	467851.i		−	0.836189i
$749$		0			0
$750$	−5109.41			−0.00908339
$751$	290721.	−	503543.i	0.515462	−	0.892806i	−0.484377	−	0.874859i	$-0.660954\pi$
$751$	290721.	−	503543.i	0.515462	−	0.892806i	0.999839	−	0.0179464i	$-0.00571284\pi$
$752$	−237533.	+	137139.i	−0.420037	+	0.242508i
$753$	83360.2	+	144384.i	0.147017	+	0.254642i
$754$	205042.	+	118381.i	0.360662	+	0.208228i
$755$		−	30339.2i		−	0.0532244i
$756$		0			0
$757$	398071.			0.694655			0.347327	−	0.937744i	$-0.387089\pi$
$757$	398071.			0.694655			0.347327	+	0.937744i	$0.387089\pi$
$758$	−177058.	+	306673.i	−0.308160	+	0.533749i
$759$	−47446.9	+	27393.5i	−0.0823615	+	0.0475514i
$760$	3138.19	+	5435.50i	0.00543315	+	0.00941049i
$761$	−280562.	−	161982.i	−0.484462	−	0.279704i	0.237812	−	0.971311i	$-0.423570\pi$
$761$	−280562.	−	161982.i	−0.484462	−	0.279704i	−0.722274	+	0.691607i	$0.756903\pi$
$762$		−	72184.6i		−	0.124318i
$763$		0			0
$764$	140904.			0.241399
$765$	−10536.3	+	18249.4i	−0.0180038	+	0.0311835i
$766$	517846.	−	298979.i	0.882558	−	0.509545i
$767$	613865.	+	1.06325e6i	1.04348	+	1.80735i
$768$	−7213.20	−	4164.54i	−0.0122294	−	0.00706065i
$769$			318602.i			0.538760i	0.963034	+	0.269380i	$0.0868187\pi$
$769$			318602.i			0.538760i	−0.963034	+	0.269380i	$0.913181\pi$
$770$		0			0
$771$	−150019.			−0.252369
$772$	−53057.0	+	91897.4i	−0.0890242	+	0.154194i
$773$	−443418.	+	256007.i	−0.742086	+	0.428443i	−0.822827	−	0.568292i	$-0.807605\pi$
$773$	−443418.	+	256007.i	−0.742086	+	0.428443i	0.0807415	+	0.996735i	$0.474271\pi$
$774$	235637.	+	408135.i	0.393334	+	0.681274i
$775$	728156.	+	420401.i	1.21233	+	0.699940i
$776$			225038.i			0.373709i
$777$		0			0
$778$	−110763.			−0.182994
$779$	159149.	−	275654.i	0.262258	−	0.454244i
$780$	−2612.92	+	1508.57i	−0.00429474	+	0.00247957i
$781$	171023.	+	296220.i	0.280383	+	0.485637i
$782$	−167791.	−	96874.0i	−0.274381	−	0.158414i
$783$		−	103009.i		−	0.168017i
$784$		0			0
$785$	21247.4			0.0344799
$786$	−55569.0	+	96248.4i	−0.0899472	+	0.155793i
$787$	558516.	−	322460.i	0.901751	−	0.520626i	0.0239830	−	0.999712i	$-0.492365\pi$
$787$	558516.	−	322460.i	0.901751	−	0.520626i	0.877768	+	0.479086i	$0.159032\pi$
$788$	−21448.8	−	37150.4i	−0.0345422	−	0.0598289i
$789$	−69109.3	−	39900.3i	−0.111015	−	0.0640946i
$790$		−	8433.34i		−	0.0135128i
$791$		0			0
$792$	263783.			0.420529
$793$	−330617.	+	572645.i	−0.525749	+	0.910623i
$794$	481385.	−	277928.i	0.763575	−	0.440850i
$795$	−2292.63	−	3970.96i	−0.00362744	−	0.00628291i
$796$	292582.	+	168923.i	0.461766	+	0.266601i
$797$		−	278844.i		−	0.438980i	−0.975615	−	0.219490i	$-0.929561\pi$
$797$		−	278844.i		−	0.438980i	0.975615	−	0.219490i	$-0.0704393\pi$
$798$		0			0
$799$	−1.65252e6			−2.58853
$800$	−56522.8	+	97900.3i	−0.0883169	+	0.152969i
$801$	630331.	−	363922.i	0.982434	−	0.567208i
$802$	−302147.	−	523333.i	−0.469753	−	0.813635i
$803$	611173.	+	352861.i	0.947835	+	0.547233i
$804$		−	66574.6i		−	0.102990i
$805$		0			0
$806$	993402.			1.52917
$807$	−10484.1	+	18159.0i	−0.0160985	+	0.0278834i
$808$	40530.5	−	23400.3i	0.0620811	−	0.0358426i
$809$	−331260.	−	573759.i	−0.506142	−	0.876663i	−0.999975	−	0.00710632i	$-0.997738\pi$
$809$	−331260.	−	573759.i	−0.506142	−	0.876663i	0.493833	−	0.869557i	$-0.335595\pi$
$810$	−9706.02	−	5603.77i	−0.0147935	−	0.00854104i
$811$			586078.i			0.891073i	0.895264	+	0.445537i	$0.146987\pi$
$811$			586078.i			0.891073i	−0.895264	+	0.445537i	$0.853013\pi$
$812$		0			0
$813$	75175.9			0.113736
$814$	170964.	−	296118.i	0.258021	−	0.446906i
$815$	−16135.1	+	9315.61i	−0.0242916	+	0.0140248i
$816$	−25091.2	−	43459.3i	−0.0376827	−	0.0652683i
$817$	732403.	+	422853.i	1.09725	+	0.633498i
$818$		−	100704.i		−	0.150501i
$819$		0			0
$820$	−4640.42			−0.00690128
$821$	−395267.	+	684623.i	−0.586414	+	1.01570i	0.408284	+	0.912855i	$0.366127\pi$
$821$	−395267.	+	684623.i	−0.586414	+	1.01570i	−0.994698	+	0.102844i	$0.967206\pi$
$822$	18472.3	−	10665.0i	0.0273387	−	0.0157840i
$823$	578225.	+	1.00151e6i	0.853684	+	1.47862i	0.877861	+	0.478916i	$0.158970\pi$
$823$	578225.	+	1.00151e6i	0.853684	+	1.47862i	−0.0241766	+	0.999708i	$0.507696\pi$
$824$	−49083.1	−	28338.1i	−0.0722899	−	0.0417366i
$825$			192597.i			0.282970i
$826$		0			0
$827$	390408.			0.570832			0.285416	−	0.958404i	$-0.407868\pi$
$827$	390408.			0.570832			0.285416	+	0.958404i	$0.407868\pi$
$828$	54619.3	−	94603.4i	0.0796682	−	0.137989i
$829$	−460055.	+	265613.i	−0.669423	+	0.386492i	−0.795858	−	0.605483i	$-0.792980\pi$
$829$	−460055.	+	265613.i	−0.669423	+	0.386492i	0.126435	+	0.991975i	$0.459647\pi$
$830$	−7841.78	−	13582.4i	−0.0113830	−	0.0197160i
$831$	162730.	+	93952.1i	0.235649	+	0.136052i
$832$			133562.i			0.192947i
$833$		0			0
$834$	−6304.20			−0.00906354
$835$	−12757.5	+	22096.7i	−0.0182976	+	0.0316923i
$836$	409943.	−	236681.i	0.586558	−	0.338649i
$837$	−216102.	−	374300.i	−0.308466	−	0.534279i
$838$	−624490.	−	360550.i	−0.889278	−	0.513425i
$839$		−	263842.i		−	0.374817i	−0.982282	−	0.187409i	$-0.939991\pi$
$839$		−	263842.i		−	0.374817i	0.982282	−	0.187409i	$-0.0600089\pi$
$840$		0			0
$841$	−604312.			−0.854416
$842$	−151584.	+	262552.i	−0.213811	+	0.370331i
$843$	37284.0	−	21525.9i	0.0524647	−	0.0302905i
$844$	308196.	+	533811.i	0.432655	+	0.749381i
$845$	24314.3	+	14037.9i	0.0340525	+	0.0196602i
$846$		−	931722.i		−	1.30180i
$847$		0			0
$848$	−202980.			−0.282268
$849$	48869.5	−	84644.5i	0.0677989	−	0.117431i
$850$	−589847.	+	340548.i	−0.816397	+	0.471347i
$851$	−70800.1	−	122629.i	−0.0977630	−	0.169331i
$852$	31773.0	+	18344.2i	0.0437703	+	0.0252708i
$853$			1.17089e6i			1.60923i	0.593798	+	0.804614i	$0.297628\pi$
$853$			1.17089e6i			1.60923i	−0.593798	+	0.804614i	$0.702372\pi$
$854$		0			0
$855$	−21320.8			−0.0291656
$856$	−72898.6	+	126264.i	−0.0994883	+	0.172319i
$857$	−367922.	+	212420.i	−0.500950	+	0.289223i	−0.729106	−	0.684401i	$-0.760064\pi$
$857$	−367922.	+	212420.i	−0.500950	+	0.289223i	0.228156	+	0.973625i	$0.426730\pi$
$858$	113776.	+	197065.i	0.154552	+	0.267692i
$859$	353490.	+	204087.i	0.479061	+	0.276586i	0.720025	−	0.693948i	$-0.244130\pi$
$859$	353490.	+	204087.i	0.479061	+	0.276586i	−0.240964	+	0.970534i	$0.577464\pi$
$860$		−	12329.4i		−	0.0166704i
$861$		0			0
$862$	339294.			0.456627
$863$	441370.	−	764476.i	0.592627	−	1.02646i	−0.401250	−	0.915969i	$-0.631424\pi$
$863$	441370.	−	764476.i	0.592627	−	1.02646i	0.993877	−	0.110492i	$-0.0352425\pi$
$864$	50324.4	−	29054.8i	0.0674142	−	0.0389216i
$865$	3900.66	+	6756.13i	0.00521321	+	0.00902955i
$866$	269832.	+	155788.i	0.359797	+	0.207729i
$867$		−	132511.i		−	0.176284i
$868$		0			0
$869$	−636039.			−0.842256
$870$	−656.083	+	1136.37i	−0.000866802	+	0.00150135i
$871$	−924541.	+	533784.i	−1.21868	+	0.703606i
$872$	−266393.	−	461406.i	−0.350340	−	0.606807i
$873$	−662035.	−	382226.i	−0.868665	−	0.501524i
$874$		−	196030.i		−	0.256625i
$875$		0			0
$876$	75696.9			0.0986438
$877$	297696.	−	515624.i	0.387056	−	0.670400i	−0.604996	−	0.796228i	$-0.706825\pi$
$877$	297696.	−	515624.i	0.387056	−	0.670400i	0.992052	+	0.125828i	$0.0401588\pi$
$878$	862943.	−	498220.i	1.11942	−	0.646298i
$879$	−27229.2	−	47162.4i	−0.0352418	−	0.0610405i
$880$	−5976.50	−	3450.53i	−0.00771759	−	0.00445575i
$881$			238444.i			0.307209i	0.988132	+	0.153605i	$0.0490882\pi$
$881$			238444.i			0.307209i	−0.988132	+	0.153605i	$0.950912\pi$
$882$		0			0
$883$	189523.			0.243076			0.121538	−	0.992587i	$-0.461217\pi$
$883$	189523.			0.243076			0.121538	+	0.992587i	$0.461217\pi$
$884$	−402355.	+	696899.i	−0.514879	+	0.891796i
$885$	−5892.64	+	3402.12i	−0.00752356	+	0.00434373i
$886$	−404087.	−	699899.i	−0.514763	−	0.891595i
$887$	−709753.	−	409776.i	−0.902111	−	0.520834i	−0.0242268	−	0.999706i	$-0.507712\pi$
$887$	−709753.	−	409776.i	−0.902111	−	0.520834i	−0.877885	+	0.478872i	$0.841046\pi$
$888$		−	36675.7i		−	0.0465107i
$889$		0			0
$890$	−19041.8			−0.0240396
$891$	−422634.	+	732024.i	−0.532365	+	0.922082i
$892$	25652.4	−	14810.4i	0.0322402	−	0.0186139i
$893$	−835993.	−	1.44798e6i	−1.04833	−	1.81577i
$894$	6145.58	+	3548.15i	0.00768932	+	0.00443943i
$895$		−	24062.3i		−	0.0300394i
$896$		0			0
$897$	94234.3			0.117118
$898$	483922.	−	838177.i	0.600098	−	1.03940i
$899$	374152.	−	216017.i	0.462945	−	0.267281i
$900$	−192007.	−	332566.i	−0.237046	−	0.410575i
$901$	−1.05911e6	−	611475.i	−1.30464	−	0.753232i
$902$			349978.i			0.430158i
$903$		0			0
$904$	445585.			0.545247
$905$	17807.9	−	30844.3i	0.0217429	−	0.0376597i
$906$	−212551.	+	122717.i	−0.258945	+	0.149502i
$907$	328809.	+	569515.i	0.399696	+	0.692294i	0.993688	−	0.112177i	$-0.0357824\pi$
$907$	328809.	+	569515.i	0.399696	+	0.692294i	−0.593992	+	0.804471i	$0.702449\pi$
$908$	83268.4	+	48075.0i	0.100997	+	0.0583106i
$909$			158981.i			0.192406i
$910$		0			0
$911$	1.32632e6			1.59812			0.799061	−	0.601250i	$-0.205330\pi$
$911$	1.32632e6			1.59812			0.799061	+	0.601250i	$0.205330\pi$
$912$	25386.8	−	43971.2i	0.0305223	−	0.0528663i
$913$	−1.02437e6	+	591423.i	−1.22890	+	0.709507i
$914$	392620.	+	680038.i	0.469981	+	0.814031i
$915$	−3173.67	−	1832.32i	−0.00379070	−	0.00218856i
$916$			266884.i			0.318076i
$917$		0			0
$918$	350109.			0.415449
$919$	118155.	−	204651.i	0.139901	−	0.242316i	−0.787558	−	0.616241i	$-0.788655\pi$
$919$	118155.	−	204651.i	0.139901	−	0.242316i	0.927459	+	0.373925i	$0.121988\pi$
$920$	−2475.01	+	1428.95i	−0.00292416	+	0.00168826i
$921$	−71167.3	−	123265.i	−0.0838999	−	0.145319i
$922$	−886553.	−	511852.i	−1.04290	−	0.602119i
$923$		−	588322.i		−	0.690577i
$924$		0			0
$925$	−497777.			−0.581770
$926$	−207713.	+	359770.i	−0.242238	+	0.419569i
$927$	166735.	−	96264.2i	0.194029	−	0.112023i
$928$	29043.4	+	50304.6i	0.0337250	+	0.0584134i
$929$	−305501.	−	176381.i	−0.353982	−	0.204372i	0.312456	−	0.949932i	$-0.398848\pi$
$929$	−305501.	−	176381.i	−0.353982	−	0.204372i	−0.666438	+	0.745561i	$0.732182\pi$
$930$			5505.56i			0.00636554i
$931$		0			0
$932$	433111.			0.498618
$933$	88416.8	−	153142.i	0.101571	−	0.175927i
$934$	−657467.	+	379589.i	−0.753668	+	0.435130i
$935$	−20789.4	−	36008.2i	−0.0237803	−	0.0411887i
$936$	−392924.	−	226855.i	−0.448495	−	0.258938i
$937$		−	113445.i		−	0.129213i	−0.997911	−	0.0646066i	$-0.979421\pi$
$937$		−	113445.i		−	0.129213i	0.997911	−	0.0646066i	$-0.0205793\pi$
$938$		0			0
$939$	67436.3			0.0764826
$940$	−12187.8	+	21109.9i	−0.0137934	+	0.0238908i
$941$	−1.01629e6	+	586757.i	−1.14773	+	0.662642i	−0.948333	−	0.317277i	$-0.897231\pi$
$941$	−1.01629e6	+	586757.i	−1.14773	+	0.662642i	−0.199396	+	0.979919i	$0.563898\pi$
$942$	−85941.8	−	148856.i	−0.0968507	−	0.167750i
$943$	125517.	+	72467.1i	0.141149	+	0.0814925i
$944$			301209.i			0.338006i
$945$		0			0
$946$	−929880.			−1.03907
$947$	−135979.	+	235522.i	−0.151625	+	0.262622i	−0.931825	−	0.362908i	$-0.881784\pi$
$947$	−135979.	+	235522.i	−0.151625	+	0.262622i	0.780200	+	0.625530i	$0.215117\pi$
$948$	−59082.5	+	34111.3i	−0.0657419	+	0.0379561i
$949$	−606925.	−	1.05123e6i	−0.673912	−	1.16725i
$950$	−596794.	−	344559.i	−0.661268	−	0.381783i
$951$			59389.5i			0.0656672i
$952$		0			0
$953$	465476.			0.512520			0.256260	−	0.966608i	$-0.417510\pi$
$953$	465476.			0.512520			0.256260	+	0.966608i	$0.417510\pi$
$954$	344760.	−	597142.i	0.378809	−	0.656117i
$955$	10844.7	−	6261.17i	0.0118908	−	0.00686513i
$956$	−116662.	−	202064.i	−0.127647	−	0.221092i
$957$	85704.4	+	49481.5i	0.0935792	+	0.0540280i
$958$		−	439212.i		−	0.478568i
$959$		0			0
$960$	−740.220			−0.000803190
$961$	444600.	−	770069.i	0.481418	−	0.833840i
$962$	−509327.	+	294060.i	−0.550360	+	0.317750i
$963$	−247636.	−	428918.i	−0.267030	−	0.462510i
$964$	693722.	+	400521.i	0.746503	+	0.430994i
$965$			9430.53i			0.0101270i
$966$		0			0
$967$	−1.49573e6			−1.59956			−0.799782	−	0.600291i	$-0.795051\pi$
$967$	−1.49573e6			−1.59956			−0.799782	+	0.600291i	$0.795051\pi$
$968$	−94593.6	+	163841.i	−0.100951	+	0.174852i
$969$	264925.	−	152955.i	0.282147	−	0.162898i
$970$	9999.78	+	17320.1i	0.0106279	+	0.0184080i
$971$	−350328.	−	202262.i	−0.371567	−	0.214524i	0.302576	−	0.953125i	$-0.402153\pi$
$971$	−350328.	−	202262.i	−0.371567	−	0.214524i	−0.674143	+	0.738601i	$0.735487\pi$
$972$			298682.i			0.316138i
$973$		0			0
$974$	−440182.			−0.463996
$975$	165634.	−	286887.i	0.174237	−	0.301788i
$976$	−140492.	+	81112.9i	−0.147486	+	0.0851511i
$977$	825968.	+	1.43062e6i	0.865315	+	1.49877i	0.866734	+	0.498770i	$0.166215\pi$
$977$	825968.	+	1.43062e6i	0.865315	+	1.49877i	−0.00141922	+	0.999999i	$0.500452\pi$
$978$	130527.	+	75359.9i	0.136466	+	0.0787884i
$979$			1.43612e6i			1.49839i
$980$		0			0
$981$	1.80987e6			1.88065
$982$	−53104.7	+	91980.0i	−0.0550693	+	0.0953829i
$983$	847459.	−	489281.i	0.877025	−	0.506350i	0.00734850	−	0.999973i	$-0.497661\pi$
$983$	847459.	−	489281.i	0.877025	−	0.506350i	0.869676	+	0.493623i	$0.164328\pi$
$984$	18769.6	+	32510.0i	0.0193850	+	0.0335758i
$985$	−3301.62	−	1906.19i	−0.00340294	−	0.00196469i
$986$			349971.i			0.359980i
$987$		0			0
$988$	−814188.			−0.834086
$989$	−192543.	+	333493.i	−0.196849	+	0.340953i
$990$	20302.1	−	11721.4i	0.0207143	−	0.0119594i
$991$	−634268.	−	1.09859e6i	−0.645841	−	1.11863i	−0.984107	−	0.177579i	$-0.943173\pi$
$991$	−634268.	−	1.09859e6i	−0.645841	−	1.11863i	0.338265	−	0.941051i	$-0.390160\pi$
$992$	211067.	+	121860.i	0.214485	+	0.123833i
$993$			339575.i			0.344380i
$994$		0			0
$995$	30024.9			0.0303274
$996$	−63437.1	+	109876.i	−0.0639476	+	0.110761i
$997$	1793.83	−	1035.67i	0.00180464	−	0.00104191i	−0.499097	−	0.866546i	$-0.666335\pi$
$997$	1793.83	−	1035.67i	0.00180464	−	0.00104191i	0.500902	+	0.865504i	$0.333002\pi$
$998$	−237334.	−	411074.i	−0.238286	−	0.412724i
$999$	221595.	+	127938.i	0.222039	+	0.128194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.5.d.c.19.2		8
7.2	even	3		98.5.b.a.97.4	yes	4
7.3	odd	6	inner	98.5.d.c.31.2		8
7.4	even	3	inner	98.5.d.c.31.1		8
7.5	odd	6		98.5.b.a.97.3	✓	4
7.6	odd	2	inner	98.5.d.c.19.1		8
21.2	odd	6		882.5.c.c.685.1		4
21.5	even	6		882.5.c.c.685.2		4
28.19	even	6		784.5.c.a.97.3		4
28.23	odd	6		784.5.c.a.97.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.5.b.a.97.3	✓	4	7.5	odd	6
98.5.b.a.97.4	yes	4	7.2	even	3
98.5.d.c.19.1		8	7.6	odd	2	inner
98.5.d.c.19.2		8	1.1	even	1	trivial
98.5.d.c.31.1		8	7.4	even	3	inner
98.5.d.c.31.2		8	7.3	odd	6	inner
784.5.c.a.97.2		4	28.23	odd	6
784.5.c.a.97.3		4	28.19	even	6
882.5.c.c.685.1		4	21.2	odd	6
882.5.c.c.685.2		4	21.5	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)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 2.44949i) q^{2} +(1.76104 - 1.01673i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-0.615721 - 0.355487i) q^{5} +5.75152i q^{6} +22.6274 q^{8} +(-38.4325 + 66.5670i) q^{9} +O(q^{10})\)	\(q+(-1.41421 + 2.44949i) q^{2} +(1.76104 - 1.01673i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(-0.615721 - 0.355487i) q^{5} +5.75152i q^{6} +22.6274 q^{8} +(-38.4325 + 66.5670i) q^{9} +(1.74152 - 1.00547i) q^{10} +(-75.8320 - 131.345i) q^{11} +(-14.0883 - 8.13387i) q^{12} +260.864i q^{13} -1.44574 q^{15} +(-32.0000 + 55.4256i) q^{16} +(-333.938 + 192.799i) q^{17} +(-108.704 - 188.280i) q^{18} +(-337.871 - 195.070i) q^{19} +5.68779i q^{20} +428.971 q^{22} +(88.8234 - 153.847i) q^{23} +(39.8477 - 23.0061i) q^{24} +(-312.247 - 540.828i) q^{25} +(-638.984 - 368.918i) q^{26} +321.013i q^{27} -320.887 q^{29} +(2.04459 - 3.54133i) q^{30} +(-1165.99 + 673.186i) q^{31} +(-90.5097 - 156.767i) q^{32} +(-267.086 - 154.202i) q^{33} -1090.64i q^{34} +614.920 q^{36} +(398.544 - 690.299i) q^{37} +(955.643 - 551.741i) q^{38} +(265.230 + 459.391i) q^{39} +(-13.9322 - 8.04375i) q^{40} +815.856i q^{41} -2167.70 q^{43} +(-606.656 + 1050.76i) q^{44} +(47.3274 - 27.3245i) q^{45} +(251.230 + 435.144i) q^{46} +(3711.45 + 2142.80i) q^{47} +130.142i q^{48} +1766.34 q^{50} +(-392.051 + 679.052i) q^{51} +(1807.32 - 1043.46i) q^{52} +(1585.78 + 2746.66i) q^{53} +(-786.319 - 453.982i) q^{54} +107.829i q^{55} -793.337 q^{57} +(453.803 - 786.010i) q^{58} +(4075.86 - 2353.20i) q^{59} +(5.78297 + 10.0164i) q^{60} +(2195.18 + 1267.39i) q^{61} -3808.12i q^{62} +512.000 q^{64} +(92.7338 - 160.620i) q^{65} +(755.432 - 436.149i) q^{66} +(2046.21 + 3544.15i) q^{67} +(2671.50 + 1542.39i) q^{68} -361.239i q^{69} -2255.28 q^{71} +(-869.628 + 1506.24i) q^{72} +(-4029.78 + 2326.60i) q^{73} +(1127.25 + 1952.46i) q^{74} +(-1099.76 - 634.945i) q^{75} +3121.12i q^{76} -1500.37 q^{78} +(2096.87 - 3631.88i) q^{79} +(39.4062 - 22.7512i) q^{80} +(-2786.65 - 4826.61i) q^{81} +(-1998.43 - 1153.80i) q^{82} -7799.12i q^{83} +274.150 q^{85} +(3065.59 - 5309.76i) q^{86} +(-565.094 + 326.257i) q^{87} +(-1715.88 - 2972.00i) q^{88} +(-8200.49 - 4734.55i) q^{89} +154.571i q^{90} -1421.17 q^{92} +(-1368.90 + 2371.01i) q^{93} +(-10497.6 + 6060.77i) q^{94} +(138.690 + 240.217i) q^{95} +(-318.781 - 184.049i) q^{96} +9945.39i q^{97} +11657.7 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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