LMFDB - Embedded newform 98.5.d.c.31.2

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			31.2
Root			$1.60021 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	98.31
Dual form			98.5.d.c.19.2

$q$-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 $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

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
$3$	1.76104	+	1.01673i	0.195671	+	0.112970i	0.594634	−	0.803996i	$-0.297297\pi$
$3$	1.76104	+	1.01673i	0.195671	+	0.112970i	−0.398964	+	0.916967i	$0.630630\pi$
$4$	−4.00000	+	6.92820i	−0.250000	+	0.433013i
$5$	−0.615721	+	0.355487i	−0.0246289	+	0.0142195i	−0.512264	−	0.858828i	$-0.671193\pi$
$5$	−0.615721	+	0.355487i	−0.0246289	+	0.0142195i	0.487635	+	0.873048i	$0.337860\pi$
$6$		−	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	0.361497	+	0.932373i	$0.382266\pi$
$11$	−75.8320	+	131.345i	−0.626711	+	1.08549i	−0.988207	+	0.153121i	$0.951067\pi$
$12$	−14.0883	+	8.13387i	−0.0978353	+	0.0564852i
$13$		−	260.864i		−	1.54358i	−0.635880	−	0.771788i	$-0.719363\pi$
$13$		−	260.864i		−	1.54358i	0.635880	−	0.771788i	$-0.280637\pi$
$14$		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	−0.205274	−	0.978705i	$-0.565809\pi$
$17$	−333.938	−	192.799i	−1.15549	−	0.667125i	−0.950220	+	0.311580i	$0.899142\pi$
$18$	−108.704	+	188.280i	−0.335505	+	0.581111i
$19$	−337.871	+	195.070i	−0.935931	+	0.540360i	−0.888682	−	0.458523i	$-0.848379\pi$
$19$	−337.871	+	195.070i	−0.935931	+	0.540360i	−0.0472483	+	0.998883i	$0.515045\pi$
$20$		−	5.68779i		−	0.0142195i
$21$		0			0
$22$	428.971			0.886303
$23$	88.8234	+	153.847i	0.167908	+	0.290825i	0.937684	−	0.347489i	$-0.112965\pi$
$23$	88.8234	+	153.847i	0.167908	+	0.290825i	−0.769776	+	0.638314i	$0.779632\pi$
$24$	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	−0.249833	−	0.968289i	$-0.580376\pi$
$31$	−1165.99	−	673.186i	−1.21331	−	0.700506i	−0.963479	+	0.267783i	$0.913709\pi$
$32$	−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	0.974075	−	0.226225i	$-0.0726386\pi$
$37$	398.544	+	690.299i	0.291121	+	0.504236i	−0.682954	+	0.730461i	$0.739305\pi$
$38$	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	$-0.921977\pi$
$41$		−	815.856i		−	0.485340i	0.970109	−	0.242670i	$-0.0780232\pi$
$42$		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	0.718589	−	0.695435i	$-0.244788\pi$
$47$	3711.45	−	2142.80i	1.68015	−	0.970034i	0.961559	−	0.274598i	$-0.0885449\pi$
$48$		−	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	−0.432556	−	0.901607i	$-0.642388\pi$
$53$	1585.78	−	2746.66i	0.564536	−	0.977806i	0.997093	−	0.0761987i	$-0.0242783\pi$
$54$	−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	0.953889	−	0.300160i	$-0.0970401\pi$
$59$	4075.86	+	2353.20i	1.17089	+	0.676012i	0.216998	+	0.976172i	$0.430373\pi$
$60$	5.78297	−	10.0164i	0.00160638	−	0.00278233i
$61$	2195.18	−	1267.39i	0.589944	−	0.340604i	−0.175131	−	0.984545i	$-0.556035\pi$
$61$	2195.18	−	1267.39i	0.589944	−	0.340604i	0.765075	+	0.643941i	$0.222702\pi$
$62$			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	−0.542907	−	0.839793i	$-0.682676\pi$
$67$	2046.21	−	3544.15i	0.455828	−	0.789518i	0.998735	+	0.0502748i	$0.0160097\pi$
$68$	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	0.0717308	−	0.997424i	$-0.477148\pi$
$73$	−4029.78	−	2326.60i	−0.756198	−	0.436591i	−0.827929	+	0.560833i	$0.810481\pi$
$74$	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	0.983673	−	0.179965i	$-0.0575983\pi$
$79$	2096.87	+	3631.88i	0.335983	+	0.581939i	−0.647690	+	0.761904i	$0.724265\pi$
$80$	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	$0.191532\pi$
$83$			7799.12i			1.13211i	−0.824367	+	0.566056i	$0.808468\pi$
$84$		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	−0.918494	−	0.395435i	$-0.870594\pi$
$89$	−8200.49	+	4734.55i	−1.03528	+	0.597722i	−0.116790	+	0.993157i	$0.537261\pi$
$90$		−	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	$-0.822753\pi$
$97$		−	9945.39i		−	1.05701i	0.848931	−	0.528504i	$-0.177247\pi$
$98$		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	0.585220	−	0.810875i	$-0.301008\pi$
$101$	1791.21	+	1034.16i	0.175592	+	0.101378i	−0.409628	+	0.912253i	$0.634341\pi$
$102$	−1108.89	+	1920.65i	−0.106583	+	0.184607i
$103$	−2169.19	+	1252.38i	−0.204467	+	0.118049i	−0.598737	−	0.800946i	$-0.704331\pi$
$103$	−2169.19	+	1252.38i	−0.204467	+	0.118049i	0.394271	+	0.918994i	$0.370997\pi$
$104$		−	5902.68i		−	0.545736i
$105$		0			0
$106$	−8970.54			−0.798375
$107$	−3221.70	−	5580.14i	−0.281395	−	0.487391i	0.690333	−	0.723491i	$-0.257464\pi$
$107$	−3221.70	−	5580.14i	−0.281395	−	0.487391i	−0.971729	+	0.236100i	$0.924131\pi$
$108$	2224.05	+	1284.05i	0.190676	+	0.110087i
$109$	−11773.0	+	20391.5i	−0.990912	+	1.71631i	−0.378962	+	0.925412i	$0.623719\pi$
$109$	−11773.0	+	20391.5i	−0.990912	+	1.71631i	−0.611949	+	0.790897i	$0.709614\pi$
$110$	−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	0.0743429	−	0.997233i	$-0.476314\pi$
$131$	16734.4	−	9661.63i	0.975143	−	0.562999i	0.900800	+	0.434234i	$0.142981\pi$
$132$		−	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	−0.911186	−	0.411994i	$-0.864832\pi$
$137$	−1854.29	+	3211.73i	−0.0987955	+	0.171119i	0.812391	+	0.583113i	$0.198166\pi$
$138$	884.851	−	510.869i	0.0464635	−	0.0268257i
$139$		−	1096.09i		−	0.0567307i	−0.999598	−	0.0283653i	$-0.990970\pi$
$139$		−	1096.09i		−	0.0567307i	0.999598	−	0.0283653i	$-0.00903018\pi$
$140$		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	0.879585	−	0.475742i	$-0.157821\pi$
$149$	616.908	+	1068.52i	0.0277874	+	0.0481291i	−0.851797	+	0.523872i	$0.824487\pi$
$150$	3110.58	+	1795.90i	0.138248	+	0.0798176i
$151$	21336.4	−	36955.7i	0.935766	−	1.62079i	0.162503	−	0.986708i	$-0.448043\pi$
$151$	21336.4	−	36955.7i	0.935766	−	1.62079i	0.773262	−	0.634086i	$-0.218624\pi$
$152$	−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	−0.127340	−	0.991859i	$-0.540644\pi$
$157$	−25881.1	−	14942.5i	−1.04999	−	0.606209i	−0.922645	+	0.385650i	$0.873977\pi$
$158$	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	0.999969	−	0.00788711i	$-0.00251057\pi$
$163$	13102.6	+	22694.4i	0.493154	+	0.854168i	−0.506815	+	0.862055i	$0.669177\pi$
$164$	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	$0.222476\pi$
$167$			35887.5i			1.28680i	−0.765532	+	0.643398i	$0.777524\pi$
$168$		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	−0.650281	−	0.759694i	$-0.725349\pi$
$173$	−9502.65	+	5486.36i	−0.317506	+	0.183312i	0.332774	+	0.943007i	$0.392015\pi$
$174$			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	−0.471324	−	0.881960i	$-0.656224\pi$
$179$	16922.1	−	29309.9i	0.528138	−	0.914761i	0.999462	−	0.0328012i	$-0.0104428\pi$
$180$	−378.619	+	218.596i	−0.0116858	+	0.00674679i
$181$		−	50094.5i		−	1.52909i	−0.644571	−	0.764545i	$-0.722964\pi$
$181$		−	50094.5i		−	1.52909i	0.644571	−	0.764545i	$-0.277036\pi$
$182$		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	0.719714	−	0.694271i	$-0.244273\pi$
$191$	−8806.47	−	15253.3i	−0.241399	−	0.418115i	−0.961113	+	0.276155i	$0.910940\pi$
$192$	901.650	+	520.568i	0.0244588	+	0.0141213i
$193$	−6632.12	+	11487.2i	−0.178048	+	0.308389i	−0.941212	−	0.337817i	$-0.890312\pi$
$193$	−6632.12	+	11487.2i	−0.178048	+	0.308389i	0.763164	+	0.646205i	$0.223645\pi$
$194$	−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	−0.0387720	−	0.999248i	$-0.512345\pi$
$199$	−36572.8	−	21115.3i	−0.923532	−	0.533202i	−0.884760	+	0.466047i	$0.845678\pi$
$200$	−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	$-0.988147\pi$
$223$		−	3702.60i		−	0.0744555i	0.999307	−	0.0372278i	$-0.0118527\pi$
$224$		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	0.395591	−	0.918427i	$-0.370540\pi$
$227$	−10408.5	−	6009.38i	−0.201994	−	0.116621i	−0.597585	+	0.801805i	$0.703873\pi$
$228$	3173.35	−	5496.40i	0.0610447	−	0.105733i
$229$	−28891.0	+	16680.2i	−0.550924	+	0.318076i	−0.749495	−	0.662010i	$-0.769703\pi$
$229$	−28891.0	+	16680.2i	−0.550924	+	0.318076i	0.198570	+	0.980087i	$0.436370\pi$
$230$			357.237i			0.00675305i
$231$		0			0
$232$	−7260.85			−0.134900
$233$	−27069.4	−	46885.7i	−0.498618	−	0.863631i	0.501381	−	0.865226i	$-0.332825\pi$
$233$	−27069.4	−	46885.7i	−0.498618	−	0.863631i	−0.999999	+	0.00159563i	$0.999492\pi$
$234$	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	−0.493039	−	0.870007i	$-0.664114\pi$
$241$	−86715.3	−	50065.1i	−1.49301	−	0.861988i	−0.999968	+	0.00801977i	$0.997447\pi$
$242$	−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	$-0.774480\pi$
$251$		−	81988.2i		−	1.30138i	0.759344	−	0.650690i	$-0.225520\pi$
$252$		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	−0.898420	−	0.439138i	$-0.855284\pi$
$257$	−63890.8	+	36887.4i	−0.967324	+	0.558485i	−0.0689050	+	0.997623i	$0.521951\pi$
$258$			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	−0.972288	−	0.233787i	$-0.924888\pi$
$263$	−19621.8	+	33985.9i	−0.283679	+	0.491346i	0.688609	+	0.725133i	$0.258222\pi$
$264$	−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	0.437024	−	0.899450i	$-0.356032\pi$
$269$	−8930.08	−	5155.78i	−0.123410	−	0.0712509i	−0.560434	+	0.828199i	$0.689366\pi$
$270$	322.769	−	559.052i	0.00442756	−	0.00766876i
$271$	32016.3	−	18484.6i	0.435946	−	0.251694i	−0.265930	−	0.963992i	$-0.585679\pi$
$271$	32016.3	−	18484.6i	0.435946	−	0.251694i	0.701877	+	0.712299i	$0.252346\pi$
$272$			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	−0.390337	−	0.920672i	$-0.627641\pi$
$277$	46202.9	−	80025.8i	0.602157	−	1.04297i	0.992494	−	0.122294i	$-0.0390252\pi$
$278$	−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	0.736829	−	0.676079i	$-0.236322\pi$
$283$	41625.7	+	24032.6i	0.519743	+	0.300074i	−0.217087	+	0.976152i	$0.569655\pi$
$284$	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	$0.0498528\pi$
$293$			26781.1i			0.311956i	−0.987761	+	0.155978i	$0.950147\pi$
$294$		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	$0.121100\pi$
$307$			69996.0i			0.742671i	−0.928499	+	0.371336i	$0.878900\pi$
$308$		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	0.835948	−	0.548808i	$-0.184918\pi$
$311$	75310.9	+	43480.8i	0.778641	+	0.449549i	−0.0573075	+	0.998357i	$0.518252\pi$
$312$	6001.46	−	10394.8i	0.0616521	−	0.106785i
$313$	28720.2	−	16581.6i	0.293156	−	0.169253i	−0.346208	−	0.938158i	$-0.612531\pi$
$313$	28720.2	−	16581.6i	0.293156	−	0.169253i	0.639364	+	0.768904i	$0.279198\pi$
$314$			84527.3i			0.857310i
$315$		0			0
$316$	−33549.9			−0.335983
$317$	−14603.0	−	25293.1i	−0.145319	−	0.251700i	0.784173	−	0.620543i	$-0.213088\pi$
$317$	−14603.0	−	25293.1i	−0.145319	−	0.251700i	−0.929492	+	0.368842i	$0.879754\pi$
$318$	−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	−0.941765	−	0.336271i	$-0.890834\pi$
$331$	−83496.6	−	144620.i	−0.762102	−	1.32000i	0.179664	−	0.983728i	$-0.442499\pi$
$332$	−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	−0.886178	−	0.463344i	$-0.846649\pi$
$347$	−5035.67	+	8722.04i	−0.0418214	+	0.0724368i	0.844357	+	0.535781i	$0.179983\pi$
$348$	4520.75	−	2610.06i	0.0373295	−	0.0215522i
$349$			97674.1i			0.801915i	0.916097	+	0.400958i	$0.131323\pi$
$349$			97674.1i			0.801915i	−0.916097	+	0.400958i	$0.868677\pi$
$350$		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	0.766093	−	0.642730i	$-0.222198\pi$
$353$	73833.2	+	42627.6i	0.592519	+	0.342091i	−0.173574	+	0.984821i	$0.555532\pi$
$354$	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	0.998143	+	0.0609162i	$0.0194022\pi$
$359$	71119.9	+	123183.i	0.551826	+	0.955791i	−0.446316	+	0.894875i	$0.647264\pi$
$360$	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	−0.196193	−	0.980565i	$-0.562858\pi$
$367$	−154015.	−	88920.4i	−1.14348	−	0.660191i	−0.947291	+	0.320375i	$0.896191\pi$
$368$	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	0.902335	−	0.431035i	$-0.141851\pi$
$373$	10835.4	+	18767.5i	0.0778803	+	0.134893i	−0.824455	+	0.565928i	$0.808518\pi$
$374$	−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	−0.970735	−	0.240152i	$-0.922803\pi$
$383$	−183086.	+	105705.i	−1.24813	+	0.720605i	−0.277390	+	0.960757i	$0.589469\pi$
$384$		−	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	−0.794047	−	0.607857i	$-0.792029\pi$
$389$	19580.4	−	33914.2i	0.129396	−	0.224121i	0.923443	+	0.383736i	$0.125363\pi$
$390$	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	−0.930858	−	0.365381i	$-0.880939\pi$
$397$	−170195.	+	98262.3i	−1.07986	+	0.623456i	−0.149000	+	0.988837i	$0.547605\pi$
$398$			119446.i			0.754061i
$399$		0			0
$400$	39967.6			0.249798
$401$	−106825.	−	185026.i	−0.664330	−	1.15065i	−0.979466	−	0.201608i	$-0.935383\pi$
$401$	−106825.	−	185026.i	−0.664330	−	1.15065i	0.315136	−	0.949047i	$-0.397950\pi$
$402$	−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	0.404998	−	0.914317i	$-0.367272\pi$
$409$	−30834.0	−	17802.0i	−0.184325	−	0.106420i	−0.589323	+	0.807898i	$0.700605\pi$
$410$	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	$-0.741334\pi$
$419$		−	254947.i		−	1.45219i	0.687597	−	0.726093i	$-0.258666\pi$
$420$		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	−0.981082	−	0.193594i	$-0.937986\pi$
$431$	−59979.2	+	103887.i	−0.322884	+	0.559251i	0.658198	+	0.752845i	$0.271319\pi$
$432$	−17792.4	+	10272.4i	−0.0953381	+	0.0550435i
$433$			110159.i			0.587547i	0.955875	+	0.293773i	$0.0949111\pi$
$433$			110159.i			0.587547i	−0.955875	+	0.293773i	$0.905089\pi$
$434$		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	−0.588696	+	0.808355i	$0.700358\pi$
$439$	−305096.	+	176148.i	−1.58310	+	0.914003i	−0.994404	+	0.105648i	$0.966308\pi$
$440$		−	2439.90i		−	0.0126028i
$441$		0			0
$442$	284508.			1.45630
$443$	−142866.	−	247452.i	−0.727984	−	1.26091i	−0.957734	−	0.287656i	$-0.907124\pi$
$443$	−142866.	−	247452.i	−0.727984	−	1.26091i	0.229749	−	0.973250i	$-0.426209\pi$
$444$	−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	0.979379	+	0.202030i	$0.0647540\pi$
$457$	138812.	+	240430.i	0.664653	+	1.15121i	−0.314726	+	0.949183i	$0.601913\pi$
$458$	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	$-0.675678\pi$
$461$		−	361934.i		−	1.70305i	0.524315	−	0.851524i	$-0.324322\pi$
$462$		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	0.138803	−	0.990320i	$-0.455674\pi$
$467$	232450.	−	134205.i	1.06585	−	0.615367i	0.927044	+	0.374953i	$0.122341\pi$
$468$		−	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	0.177440	−	0.984132i	$-0.443219\pi$
$479$	−134481.	−	77642.5i	−0.586124	−	0.338399i	−0.763563	+	0.645733i	$0.776552\pi$
$480$	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	−0.654039	−	0.756461i	$-0.726927\pi$
$487$	77813.9	−	134778.i	0.328095	−	0.568277i	0.982134	+	0.188184i	$0.0602601\pi$
$488$	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	0.646877	−	0.762594i	$-0.276075\pi$
$499$	−83910.2	−	145337.i	−0.336987	−	0.583679i	−0.983865	+	0.178915i	$0.942741\pi$
$500$	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	$0.0846806\pi$
$503$			133035.i			0.525810i	−0.964822	+	0.262905i	$0.915319\pi$
$504$		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	−0.0679416	−	0.997689i	$-0.521643\pi$
$509$	197449.	−	113997.i	0.762112	−	0.440005i	0.830053	+	0.557684i	$0.188310\pi$
$510$		−	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	0.933380	−	0.358890i	$-0.116845\pi$
$521$	295670.	+	170705.i	1.08926	+	0.628885i	0.155882	+	0.987776i	$0.450178\pi$
$522$	34881.6	−	60416.7i	0.128013	−	0.221726i
$523$	−54483.4	+	31456.0i	−0.199187	+	0.115001i	−0.596276	−	0.802779i	$-0.703354\pi$
$523$	−54483.4	+	31456.0i	−0.199187	+	0.115001i	0.397089	+	0.917780i	$0.370020\pi$
$524$			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	0.567656	−	0.823266i	$-0.307850\pi$
$541$	−125601.	−	217548.i	−0.429141	−	0.743294i	−0.996797	+	0.0799715i	$0.974517\pi$
$542$	−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	−0.174087	−	0.984730i	$-0.555697\pi$
$557$	237576.	−	411493.i	0.765758	−	1.32633i	0.939845	−	0.341601i	$-0.110969\pi$
$558$	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	0.445086	−	0.895488i	$-0.353173\pi$
$563$	−34196.7	−	19743.5i	−0.107887	−	0.0622884i	−0.552972	+	0.833200i	$0.686507\pi$
$564$	−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	0.924349	−	0.381547i	$-0.124609\pi$
$569$	42653.8	+	73878.6i	0.131745	+	0.228189i	−0.792604	+	0.609736i	$0.791275\pi$
$570$	−1381.61	−	797.676i	−0.00425243	−	0.00245514i
$571$	−44549.5	+	77162.0i	−0.136638	+	0.236664i	−0.926222	−	0.376979i	$-0.876963\pi$
$571$	−44549.5	+	77162.0i	−0.136638	+	0.236664i	0.789584	+	0.613642i	$0.210296\pi$
$572$	−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	0.846671	−	0.532116i	$-0.178603\pi$
$577$	269400.	+	155538.i	0.809181	+	0.467181i	−0.0374905	+	0.999297i	$0.511936\pi$
$578$	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	$-0.971107\pi$
$587$		−	62466.3i		−	0.181288i	0.995883	−	0.0906440i	$-0.0288926\pi$
$588$		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	−0.440282	−	0.897860i	$-0.645121\pi$
$593$	41194.5	−	23783.7i	0.117147	−	0.0676346i	0.557428	+	0.830225i	$0.311788\pi$
$594$		−	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	0.142401	+	0.989809i	$0.454518\pi$
$599$	−282017.	+	488468.i	−0.785999	+	1.36139i	−0.928400	+	0.371582i	$0.878815\pi$
$600$	−24884.7	+	14367.2i	−0.0691240	+	0.0399088i
$601$		−	255637.i		−	0.707740i	−0.935295	−	0.353870i	$-0.884865\pi$
$601$		−	255637.i		−	0.707740i	0.935295	−	0.353870i	$-0.115135\pi$
$602$		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	−0.987696	−	0.156388i	$-0.950015\pi$
$607$	−495972.	+	286350.i	−1.34611	+	0.777176i	−0.358412	+	0.933564i	$0.616682\pi$
$608$		−	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	−0.990560	−	0.137082i	$-0.956228\pi$
$613$	−141501.	+	245087.i	−0.376563	+	0.652227i	0.613996	+	0.789309i	$0.289561\pi$
$614$	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	0.562586	−	0.826739i	$-0.309807\pi$
$619$	49006.8	+	28294.1i	0.127901	+	0.0738438i	−0.434684	+	0.900583i	$0.643140\pi$
$620$	−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	0.0765754	+	0.997064i	$0.475601\pi$
$641$	−339057.	+	587264.i	−0.825195	+	1.42928i	−0.901770	+	0.432216i	$0.857732\pi$
$642$	−32094.3	+	18529.6i	−0.0778677	+	0.0449569i
$643$		−	345520.i		−	0.835701i	−0.908516	−	0.417851i	$-0.862784\pi$
$643$		−	345520.i		−	0.835701i	0.908516	−	0.417851i	$-0.137216\pi$
$644$		0			0
$645$	3133.94			0.00753305
$646$	−212750.	−	368494.i	−0.509806	−	0.883010i
$647$	−6718.19	−	3878.75i	−0.0160489	−	0.00926581i	0.491954	−	0.870621i	$-0.336283\pi$
$647$	−6718.19	−	3878.75i	−0.0160489	−	0.00926581i	−0.508003	+	0.861355i	$0.669616\pi$
$648$	−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	0.999546	+	0.0301362i	$0.00959410\pi$
$653$	224236.	+	388389.i	0.525872	+	0.910836i	−0.473674	+	0.880700i	$0.657073\pi$
$654$	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	0.828908	−	0.559384i	$-0.188962\pi$
$661$	331589.	+	191443.i	0.758922	+	0.438164i	−0.0699869	+	0.997548i	$0.522296\pi$
$662$	−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	−0.810395	−	0.585884i	$-0.800747\pi$
$677$	−324589.	+	187402.i	−0.708201	+	0.408880i	0.102194	+	0.994765i	$0.467414\pi$
$678$		−	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	−0.913476	−	0.406892i	$-0.866612\pi$
$683$	−48682.3	+	84320.1i	−0.104359	+	0.180755i	0.809117	+	0.587647i	$0.199946\pi$
$684$	−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	0.430689	−	0.902501i	$-0.358271\pi$
$691$	681662.	−	393558.i	1.42762	−	0.824238i	0.996933	+	0.0782630i	$0.0249374\pi$
$692$		−	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	0.781073	−	0.624439i	$-0.214672\pi$
$709$	−75524.5	−	130812.i	−0.150243	−	0.260229i	−0.931317	+	0.364210i	$0.881339\pi$
$710$	−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	−0.958973	−	0.283497i	$-0.908505\pi$
$719$	−616705.	+	356055.i	−1.19294	+	0.688746i	−0.233971	+	0.972244i	$0.575172\pi$
$720$		−	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	$0.227645\pi$
$727$			693160.i			1.31149i	−0.754983	+	0.655744i	$0.772355\pi$
$728$		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	−0.267188	−	0.963644i	$-0.586094\pi$
$733$	233054.	−	134554.i	0.433759	−	0.250431i	0.700947	+	0.713214i	$0.252761\pi$
$734$			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	−0.902778	−	0.430106i	$-0.858476\pi$
$739$	−43092.6	+	74638.5i	−0.0789066	+	0.136670i	0.823872	+	0.566776i	$0.191810\pi$
$740$	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	0.999839	+	0.0179464i	$0.00571284\pi$
$751$	290721.	+	503543.i	0.515462	+	0.892806i	−0.484377	+	0.874859i	$0.660954\pi$
$752$	−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	−0.722274	−	0.691607i	$-0.756903\pi$
$761$	−280562.	+	161982.i	−0.484462	+	0.279704i	0.237812	+	0.971311i	$0.423570\pi$
$762$			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	$-0.913181\pi$
$769$		−	318602.i		−	0.538760i	0.963034	−	0.269380i	$-0.0868187\pi$
$770$		0			0
$771$	−150019.			−0.252369
$772$	−53057.0	−	91897.4i	−0.0890242	−	0.154194i
$773$	−443418.	−	256007.i	−0.742086	−	0.428443i	0.0807415	−	0.996735i	$-0.474271\pi$
$773$	−443418.	−	256007.i	−0.742086	−	0.428443i	−0.822827	+	0.568292i	$0.807605\pi$
$774$	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	0.877768	−	0.479086i	$-0.159032\pi$
$787$	558516.	+	322460.i	0.901751	+	0.520626i	0.0239830	+	0.999712i	$0.492365\pi$
$788$	−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	$0.0704393\pi$
$797$			278844.i			0.438980i	−0.975615	+	0.219490i	$0.929561\pi$
$798$		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	0.493833	+	0.869557i	$0.335595\pi$
$809$	−331260.	+	573759.i	−0.506142	+	0.876663i	−0.999975	+	0.00710632i	$0.997738\pi$
$810$	−9706.02	+	5603.77i	−0.0147935	+	0.00854104i
$811$		−	586078.i		−	0.891073i	−0.895264	−	0.445537i	$-0.853013\pi$
$811$		−	586078.i		−	0.891073i	0.895264	−	0.445537i	$-0.146987\pi$
$812$		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	−0.994698	−	0.102844i	$-0.967206\pi$
$821$	−395267.	−	684623.i	−0.586414	−	1.01570i	0.408284	−	0.912855i	$-0.366127\pi$
$822$	18472.3	+	10665.0i	0.0273387	+	0.0157840i
$823$	578225.	−	1.00151e6i	0.853684	−	1.47862i	−0.0241766	−	0.999708i	$-0.507696\pi$
$823$	578225.	−	1.00151e6i	0.853684	−	1.47862i	0.877861	−	0.478916i	$-0.158970\pi$
$824$	−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	0.126435	−	0.991975i	$-0.459647\pi$
$829$	−460055.	−	265613.i	−0.669423	−	0.386492i	−0.795858	+	0.605483i	$0.792980\pi$
$830$	−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	$0.0600089\pi$
$839$			263842.i			0.374817i	−0.982282	+	0.187409i	$0.939991\pi$
$840$		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	$-0.702372\pi$
$853$		−	1.17089e6i		−	1.60923i	0.593798	−	0.804614i	$-0.297628\pi$
$854$		0			0
$855$	−21320.8			−0.0291656
$856$	−72898.6	−	126264.i	−0.0994883	−	0.172319i
$857$	−367922.	−	212420.i	−0.500950	−	0.289223i	0.228156	−	0.973625i	$-0.426730\pi$
$857$	−367922.	−	212420.i	−0.500950	−	0.289223i	−0.729106	+	0.684401i	$0.760064\pi$
$858$	113776.	−	197065.i	0.154552	−	0.267692i
$859$	353490.	−	204087.i	0.479061	−	0.276586i	−0.240964	−	0.970534i	$-0.577464\pi$
$859$	353490.	−	204087.i	0.479061	−	0.276586i	0.720025	+	0.693948i	$0.244130\pi$
$860$			12329.4i			0.0166704i
$861$		0			0
$862$	339294.			0.456627
$863$	441370.	+	764476.i	0.592627	+	1.02646i	0.993877	+	0.110492i	$0.0352425\pi$
$863$	441370.	+	764476.i	0.592627	+	1.02646i	−0.401250	+	0.915969i	$0.631424\pi$
$864$	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	0.992052	−	0.125828i	$-0.0401588\pi$
$877$	297696.	+	515624.i	0.387056	+	0.670400i	−0.604996	+	0.796228i	$0.706825\pi$
$878$	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	$-0.950912\pi$
$881$		−	238444.i		−	0.307209i	0.988132	−	0.153605i	$-0.0490882\pi$
$882$		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	−0.877885	−	0.478872i	$-0.841046\pi$
$887$	−709753.	+	409776.i	−0.902111	+	0.520834i	−0.0242268	+	0.999706i	$0.507712\pi$
$888$			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	−0.593992	−	0.804471i	$-0.702449\pi$
$907$	328809.	−	569515.i	0.399696	−	0.692294i	0.993688	+	0.112177i	$0.0357824\pi$
$908$	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	0.927459	−	0.373925i	$-0.121988\pi$
$919$	118155.	+	204651.i	0.139901	+	0.242316i	−0.787558	+	0.616241i	$0.788655\pi$
$920$	−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	−0.666438	−	0.745561i	$-0.732182\pi$
$929$	−305501.	+	176381.i	−0.353982	+	0.204372i	0.312456	+	0.949932i	$0.398848\pi$
$930$		−	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	$0.0205793\pi$
$937$			113445.i			0.129213i	−0.997911	+	0.0646066i	$0.979421\pi$
$938$		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	−0.199396	−	0.979919i	$-0.563898\pi$
$941$	−1.01629e6	−	586757.i	−1.14773	−	0.662642i	−0.948333	+	0.317277i	$0.897231\pi$
$942$	−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	0.780200	−	0.625530i	$-0.215117\pi$
$947$	−135979.	−	235522.i	−0.151625	−	0.262622i	−0.931825	+	0.362908i	$0.881784\pi$
$948$	−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	−0.674143	−	0.738601i	$-0.735487\pi$
$971$	−350328.	+	202262.i	−0.371567	+	0.214524i	0.302576	+	0.953125i	$0.402153\pi$
$972$		−	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	−0.00141922	−	0.999999i	$-0.500452\pi$
$977$	825968.	−	1.43062e6i	0.865315	−	1.49877i	0.866734	−	0.498770i	$-0.166215\pi$
$978$	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	0.869676	−	0.493623i	$-0.164328\pi$
$983$	847459.	+	489281.i	0.877025	+	0.506350i	0.00734850	+	0.999973i	$0.497661\pi$
$984$	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	0.338265	+	0.941051i	$0.390160\pi$
$991$	−634268.	+	1.09859e6i	−0.645841	+	1.11863i	−0.984107	+	0.177579i	$0.943173\pi$
$992$	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	0.500902	−	0.865504i	$-0.333002\pi$
$997$	1793.83	+	1035.67i	0.00180464	+	0.00104191i	−0.499097	+	0.866546i	$0.666335\pi$
$998$	−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.31.2		8
7.2	even	3	inner	98.5.d.c.19.1		8
7.3	odd	6		98.5.b.a.97.4	yes	4
7.4	even	3		98.5.b.a.97.3	✓	4
7.5	odd	6	inner	98.5.d.c.19.2		8
7.6	odd	2	inner	98.5.d.c.31.1		8
21.11	odd	6		882.5.c.c.685.2		4
21.17	even	6		882.5.c.c.685.1		4
28.3	even	6		784.5.c.a.97.2		4
28.11	odd	6		784.5.c.a.97.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.5.b.a.97.3	✓	4	7.4	even	3
98.5.b.a.97.4	yes	4	7.3	odd	6
98.5.d.c.19.1		8	7.2	even	3	inner
98.5.d.c.19.2		8	7.5	odd	6	inner
98.5.d.c.31.1		8	7.6	odd	2	inner
98.5.d.c.31.2		8	1.1	even	1	trivial
784.5.c.a.97.2		4	28.3	even	6
784.5.c.a.97.3		4	28.11	odd	6
882.5.c.c.685.1		4	21.17	even	6
882.5.c.c.685.2		4	21.11	odd	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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