LMFDB - Embedded newform 171.4.u.b.82.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			82.4
Character	$\chi$	$=$	171.82
Dual form			171.4.u.b.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.26193 - 1.89799i) q^{2} +(0.124797 - 0.707761i) q^{4} +(0.0925462 + 0.524856i) q^{5} +(-11.8949 + 20.6025i) q^{7} +(10.7499 + 18.6194i) q^{8} +O(q^{10})$	\(q+(2.26193 - 1.89799i) q^{2} +(0.124797 - 0.707761i) q^{4} +(0.0925462 + 0.524856i) q^{5} +(-11.8949 + 20.6025i) q^{7} +(10.7499 + 18.6194i) q^{8} +(1.20550 + 1.01154i) q^{10} +(18.5849 + 32.1900i) q^{11} +(-14.9925 + 5.45682i) q^{13} +(12.1979 + 69.1778i) q^{14} +(65.0577 + 23.6791i) q^{16} +(47.7006 - 40.0256i) q^{17} +(-57.8848 + 59.2314i) q^{19} +0.383022 q^{20} +(103.134 + 37.5376i) q^{22} +(3.18128 - 18.0420i) q^{23} +(117.195 - 42.6554i) q^{25} +(-23.5550 + 40.7984i) q^{26} +(13.0972 + 10.9899i) q^{28} +(-13.6165 - 11.4256i) q^{29} +(-76.5514 + 132.591i) q^{31} +(30.4725 - 11.0911i) q^{32} +(31.9276 - 181.070i) q^{34} +(-11.9142 - 4.33641i) q^{35} -41.5560 q^{37} +(-18.5110 + 243.842i) q^{38} +(-8.77764 + 7.36532i) q^{40} +(314.270 + 114.385i) q^{41} +(-53.2608 - 302.057i) q^{43} +(25.1022 - 9.13644i) q^{44} +(-27.0475 - 46.8477i) q^{46} +(-37.2512 - 31.2575i) q^{47} +(-111.476 - 193.082i) q^{49} +(184.127 - 318.917i) q^{50} +(1.99110 + 11.2921i) q^{52} +(84.6010 - 479.796i) q^{53} +(-15.1751 + 12.7334i) q^{55} -511.476 q^{56} -52.4854 q^{58} +(-160.725 + 134.865i) q^{59} +(-36.3671 + 206.248i) q^{61} +(78.5016 + 445.205i) q^{62} +(-229.056 + 396.736i) q^{64} +(-4.25154 - 7.36388i) q^{65} +(327.060 + 274.436i) q^{67} +(-22.3756 - 38.7557i) q^{68} +(-35.1795 + 12.8043i) q^{70} +(-105.727 - 599.609i) q^{71} +(-299.014 - 108.832i) q^{73} +(-93.9969 + 78.8728i) q^{74} +(34.6978 + 48.3605i) q^{76} -884.260 q^{77} +(-245.166 - 89.2331i) q^{79} +(-6.40725 + 36.3373i) q^{80} +(927.958 - 337.749i) q^{82} +(-328.838 + 569.565i) q^{83} +(25.4222 + 21.3317i) q^{85} +(-693.772 - 582.144i) q^{86} +(-399.572 + 692.080i) q^{88} +(1246.08 - 453.535i) q^{89} +(65.9094 - 373.791i) q^{91} +(-12.3724 - 4.50318i) q^{92} -143.586 q^{94} +(-36.4449 - 24.8995i) q^{95} +(245.942 - 206.370i) q^{97} +(-618.618 - 225.159i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	2.26193	−	1.89799i	0.799713	−	0.671039i	−0.148416	−	0.988925i	$-0.547417\pi$
$2$	2.26193	−	1.89799i	0.799713	−	0.671039i	0.948129	+	0.317886i	$0.102973\pi$
$3$		0			0
$3$		0			0
$4$	0.124797	−	0.707761i	0.0155997	−	0.0884702i
$5$	0.0925462	+	0.524856i	0.00827759	+	0.0469445i	0.988667	−	0.150127i	$-0.0479681\pi$
$5$	0.0925462	+	0.524856i	0.00827759	+	0.0469445i	−0.980389	+	0.197071i	$0.936857\pi$
$6$		0			0
$7$	−11.8949	+	20.6025i	−0.642263	+	1.11243i	0.342664	+	0.939458i	$0.388671\pi$
$7$	−11.8949	+	20.6025i	−0.642263	+	1.11243i	−0.984926	+	0.172974i	$0.944662\pi$
$8$	10.7499	+	18.6194i	0.475084	+	0.822870i
$9$		0			0
$10$	1.20550	+	1.01154i	0.0381213	+	0.0319876i
$11$	18.5849	+	32.1900i	0.509414	+	0.882331i	0.999941	+	0.0109047i	$0.00347115\pi$
$11$	18.5849	+	32.1900i	0.509414	+	0.882331i	−0.490527	+	0.871426i	$0.663196\pi$
$12$		0			0
$13$	−14.9925	+	5.45682i	−0.319859	+	0.116419i	−0.496960	−	0.867774i	$-0.665550\pi$
$13$	−14.9925	+	5.45682i	−0.319859	+	0.116419i	0.177101	+	0.984193i	$0.443328\pi$
$14$	12.1979	+	69.1778i	0.232859	+	1.32061i
$15$		0			0
$16$	65.0577	+	23.6791i	1.01653	+	0.369985i
$17$	47.7006	−	40.0256i	0.680535	−	0.571037i	−0.235627	−	0.971843i	$-0.575715\pi$
$17$	47.7006	−	40.0256i	0.680535	−	0.571037i	0.916163	+	0.400807i	$0.131270\pi$
$18$		0			0
$19$	−57.8848	+	59.2314i	−0.698930	+	0.715190i
$19$	−57.8848	+	59.2314i	−0.698930	+	0.715190i
$20$	0.383022			0.00428232
$21$		0			0
$22$	103.134	+	37.5376i	0.999464	+	0.363775i
$23$	3.18128	−	18.0420i	0.0288410	−	0.163566i	−0.966986	−	0.254831i	$-0.917980\pi$
$23$	3.18128	−	18.0420i	0.0288410	−	0.163566i	0.995827	+	0.0912656i	$0.0290912\pi$
$24$		0			0
$25$	117.195	−	42.6554i	0.937557	−	0.341243i
$26$	−23.5550	+	40.7984i	−0.177674	+	0.307740i
$27$		0			0
$28$	13.0972	+	10.9899i	0.0883979	+	0.0741747i
$29$	−13.6165	−	11.4256i	−0.0871906	−	0.0731616i	0.598151	−	0.801384i	$-0.295902\pi$
$29$	−13.6165	−	11.4256i	−0.0871906	−	0.0731616i	−0.685341	+	0.728222i	$0.740347\pi$
$30$		0			0
$31$	−76.5514	+	132.591i	−0.443517	+	0.768195i	−0.997948	−	0.0640356i	$-0.979603\pi$
$31$	−76.5514	+	132.591i	−0.443517	+	0.768195i	0.554430	+	0.832230i	$0.312936\pi$
$32$	30.4725	−	11.0911i	0.168338	−	0.0612701i
$33$		0			0
$34$	31.9276	−	181.070i	0.161045	−	0.913332i
$35$	−11.9142	−	4.33641i	−0.0575390	−	0.0209425i
$36$		0			0
$37$	−41.5560			−0.184642			−0.0923212	−	0.995729i	$-0.529429\pi$
$37$	−41.5560			−0.184642			−0.0923212	+	0.995729i	$0.529429\pi$
$38$	−18.5110	+	243.842i	−0.0790234	+	1.04096i
$39$		0			0
$40$	−8.77764	+	7.36532i	−0.0346967	+	0.0291140i
$41$	314.270	+	114.385i	1.19709	+	0.435706i	0.862208	−	0.506554i	$-0.169081\pi$
$41$	314.270	+	114.385i	1.19709	+	0.435706i	0.334883	+	0.942260i	$0.391303\pi$
$42$		0			0
$43$	−53.2608	−	302.057i	−0.188888	−	1.07124i	−0.920857	−	0.389901i	$-0.872509\pi$
$43$	−53.2608	−	302.057i	−0.188888	−	1.07124i	0.731969	−	0.681338i	$-0.238602\pi$
$44$	25.1022	−	9.13644i	0.0860067	−	0.0313039i
$45$		0			0
$46$	−27.0475	−	46.8477i	−0.0866944	−	0.150159i
$47$	−37.2512	−	31.2575i	−0.115610	−	0.0970080i	0.583150	−	0.812364i	$-0.301820\pi$
$47$	−37.2512	−	31.2575i	−0.115610	−	0.0970080i	−0.698760	+	0.715356i	$0.746264\pi$
$48$		0			0
$49$	−111.476	−	193.082i	−0.325003	−	0.562922i
$50$	184.127	−	318.917i	0.520790	−	0.902034i
$51$		0			0
$52$	1.99110	+	11.2921i	0.00530992	+	0.0301141i
$53$	84.6010	−	479.796i	0.219261	−	1.24349i	−0.654096	−	0.756412i	$-0.726951\pi$
$53$	84.6010	−	479.796i	0.219261	−	1.24349i	0.873357	−	0.487080i	$-0.161938\pi$
$54$		0			0
$55$	−15.1751	+	12.7334i	−0.0372039	+	0.0312178i
$56$	−511.476			−1.22052
$57$		0			0
$58$	−52.4854			−0.118822
$59$	−160.725	+	134.865i	−0.354655	+	0.297591i	−0.802656	−	0.596442i	$-0.796581\pi$
$59$	−160.725	+	134.865i	−0.354655	+	0.297591i	0.448001	+	0.894033i	$0.352136\pi$
$60$		0			0
$61$	−36.3671	+	206.248i	−0.0763332	+	0.432907i	0.922559	+	0.385855i	$0.126094\pi$
$61$	−36.3671	+	206.248i	−0.0763332	+	0.432907i	−0.998892	+	0.0470516i	$0.985017\pi$
$62$	78.5016	+	445.205i	0.160802	+	0.911953i
$63$		0			0
$64$	−229.056	+	396.736i	−0.447375	+	0.774876i
$65$	−4.25154	−	7.36388i	−0.00811290	−	0.0140520i
$66$		0			0
$67$	327.060	+	274.436i	0.596369	+	0.500413i	0.890276	−	0.455421i	$-0.150511\pi$
$67$	327.060	+	274.436i	0.596369	+	0.500413i	−0.293907	+	0.955834i	$0.594956\pi$
$68$	−22.3756	−	38.7557i	−0.0399036	−	0.0691151i
$69$		0			0
$70$	−35.1795	+	12.8043i	−0.0600679	+	0.0218629i
$71$	−105.727	−	599.609i	−0.176726	−	1.00226i	−0.936133	−	0.351646i	$-0.885622\pi$
$71$	−105.727	−	599.609i	−0.176726	−	1.00226i	0.759407	−	0.650615i	$-0.225489\pi$
$72$		0			0
$73$	−299.014	−	108.832i	−0.479411	−	0.174491i	0.0909999	−	0.995851i	$-0.470994\pi$
$73$	−299.014	−	108.832i	−0.479411	−	0.174491i	−0.570411	+	0.821360i	$0.693216\pi$
$74$	−93.9969	+	78.8728i	−0.147661	+	0.123902i
$75$		0			0
$76$	34.6978	+	48.3605i	0.0523699	+	0.0729912i
$77$	−884.260			−1.30871
$78$		0			0
$79$	−245.166	−	89.2331i	−0.349156	−	0.127082i	0.161488	−	0.986875i	$-0.448371\pi$
$79$	−245.166	−	89.2331i	−0.349156	−	0.127082i	−0.510644	+	0.859792i	$0.670593\pi$
$80$	−6.40725	+	36.3373i	−0.00895440	+	0.0507829i
$81$		0			0
$82$	927.958	−	337.749i	1.24971	−	0.454856i
$83$	−328.838	+	569.565i	−0.434876	+	0.753227i	−0.997286	−	0.0736316i	$-0.976541\pi$
$83$	−328.838	+	569.565i	−0.434876	+	0.753227i	0.562410	+	0.826859i	$0.309874\pi$
$84$		0			0
$85$	25.4222	+	21.3317i	0.0324402	+	0.0272206i
$86$	−693.772	−	582.144i	−0.869900	−	0.729933i
$87$		0			0
$88$	−399.572	+	692.080i	−0.484029	+	0.838363i
$89$	1246.08	−	453.535i	1.48409	−	0.540165i	0.532204	−	0.846616i	$-0.321364\pi$
$89$	1246.08	−	453.535i	1.48409	−	0.540165i	0.951886	+	0.306452i	$0.0991418\pi$
$90$		0			0
$91$	65.9094	−	373.791i	0.0759251	−	0.430593i
$92$	−12.3724	−	4.50318i	−0.0140208	−	0.00510314i
$93$		0			0
$94$	−143.586			−0.157551
$95$	−36.4449	−	24.8995i	−0.0393597	−	0.0268909i
$96$		0			0
$97$	245.942	−	206.370i	0.257440	−	0.216018i	−0.504928	−	0.863161i	$-0.668481\pi$
$97$	245.942	−	206.370i	0.257440	−	0.216018i	0.762368	+	0.647144i	$0.224037\pi$
$98$	−618.618	−	225.159i	−0.637652	−	0.232086i
$99$		0			0
$100$	−15.5642	−	88.2691i	−0.0155642	−	0.0882691i
$101$	−224.491	+	81.7080i	−0.221165	+	0.0804975i	−0.450226	−	0.892915i	$-0.648657\pi$
$101$	−224.491	+	81.7080i	−0.221165	+	0.0804975i	0.229061	+	0.973412i	$0.426434\pi$
$102$		0			0
$103$	710.612	+	1230.82i	0.679793	+	1.17744i	0.975043	+	0.222016i	$0.0712637\pi$
$103$	710.612	+	1230.82i	0.679793	+	1.17744i	−0.295250	+	0.955420i	$0.595403\pi$
$104$	−262.771	−	220.491i	−0.247758	−	0.207893i
$105$		0			0
$106$	−719.284	−	1245.84i	−0.659086	−	1.14157i
$107$	586.706	−	1016.20i	0.530084	−	0.918133i	−0.469300	−	0.883039i	$-0.655494\pi$
$107$	586.706	−	1016.20i	0.530084	−	0.918133i	0.999384	−	0.0350939i	$-0.0111730\pi$
$108$		0			0
$109$	−361.469	−	2049.99i	−0.317637	−	1.80141i	−0.557036	−	0.830488i	$-0.688061\pi$
$109$	−361.469	−	2049.99i	−0.317637	−	1.80141i	0.239399	−	0.970921i	$-0.423050\pi$
$110$	−10.1572	+	57.6043i	−0.00880410	+	0.0499305i
$111$		0			0
$112$	−1261.70	+	1058.69i	−1.06446	+	0.893188i
$113$	286.831			0.238786			0.119393	−	0.992847i	$-0.461905\pi$
$113$	286.831			0.238786			0.119393	+	0.992847i	$0.461905\pi$
$114$		0			0
$115$	9.76384			0.00791724
$116$	−9.78593	+	8.21137i	−0.00783277	+	0.00657247i
$117$		0			0
$118$	−107.579	+	610.109i	−0.0839273	+	0.475975i
$119$	257.235	+	1458.85i	0.198157	+	1.12380i
$120$		0			0
$121$	−25.2961	+	43.8141i	−0.0190053	+	0.0329182i
$122$	309.196	+	535.542i	0.229453	+	0.397424i
$123$		0			0
$124$	84.2893	+	70.7271i	0.0610436	+	0.0512216i
$125$	66.5434	+	115.256i	0.0476146	+	0.0824708i
$126$		0			0
$127$	687.962	−	250.398i	0.480683	−	0.174954i	−0.0903027	−	0.995914i	$-0.528783\pi$
$127$	687.962	−	250.398i	0.480683	−	0.174954i	0.570986	+	0.820960i	$0.306561\pi$
$128$	279.940	+	1587.62i	0.193308	+	1.09630i
$129$		0			0
$130$	−23.5932	−	8.58723i	−0.0159174	−	0.00579346i
$131$	1633.37	−	1370.56i	1.08938	−	0.914095i	0.0927101	−	0.995693i	$-0.470447\pi$
$131$	1633.37	−	1370.56i	1.08938	−	0.914095i	0.996665	+	0.0815986i	$0.0260026\pi$
$132$		0			0
$133$	−531.784	−	1897.12i	−0.346703	−	1.23685i
$134$	1260.66			0.812722
$135$		0			0
$136$	1258.03	+	457.886i	0.793201	+	0.288701i
$137$	−50.9993	+	289.231i	−0.0318041	+	0.180370i	−0.996572	−	0.0827335i	$-0.973635\pi$
$137$	−50.9993	+	289.231i	−0.0318041	+	0.180370i	0.964768	+	0.263104i	$0.0847461\pi$
$138$		0			0
$139$	1318.52	−	479.902i	0.804572	−	0.292840i	0.0931922	−	0.995648i	$-0.470293\pi$
$139$	1318.52	−	479.902i	0.804572	−	0.292840i	0.711380	+	0.702808i	$0.248071\pi$
$140$	−4.55600	+	7.89122i	−0.00275037	+	0.00476379i
$141$		0			0
$142$	−1377.20	−	1155.61i	−0.813886	−	0.682932i
$143$	−454.288	−	381.193i	−0.265661	−	0.222916i
$144$		0			0
$145$	4.73665	−	8.20412i	0.00271281	−	0.00469872i
$146$	−882.912	+	321.354i	−0.500482	+	0.182160i
$147$		0			0
$148$	−5.18609	+	29.4118i	−0.00288036	+	0.0163353i
$149$	2677.37	+	974.482i	1.47207	+	0.535790i	0.948662	−	0.316292i	$-0.102438\pi$
$149$	2677.37	+	974.482i	1.47207	+	0.535790i	0.523409	+	0.852082i	$0.324660\pi$
$150$		0			0
$151$	2865.57			1.54435			0.772175	−	0.635409i	$-0.219169\pi$
$151$	2865.57			1.54435			0.772175	+	0.635409i	$0.219169\pi$
$152$	−1725.11	−	441.048i	−0.920559	−	0.235353i
$153$		0			0
$154$	−2000.13	+	1678.31i	−1.04659	+	0.878196i
$155$	−76.6756	−	27.9077i	−0.0397338	−	0.0144619i
$156$		0			0
$157$	302.676	+	1716.56i	0.153861	+	0.872590i	0.959820	+	0.280618i	$0.0905393\pi$
$157$	302.676	+	1716.56i	0.153861	+	0.872590i	−0.805958	+	0.591972i	$0.798350\pi$
$158$	−723.911	+	263.482i	−0.364502	+	0.132668i
$159$		0			0
$160$	8.64132	+	14.9672i	0.00426973	+	0.00739538i
$161$	333.869	+	280.149i	0.163432	+	0.137136i
$162$		0			0
$163$	904.362	+	1566.40i	0.434571	+	0.752699i	0.997261	−	0.0739692i	$-0.0235666\pi$
$163$	904.362	+	1566.40i	0.434571	+	0.752699i	−0.562689	+	0.826668i	$0.690233\pi$
$164$	120.177	−	208.153i	0.0572212	−	0.0991100i
$165$		0			0
$166$	337.216	+	1912.45i	0.157669	+	0.894185i
$167$	−105.553	+	598.619i	−0.0489097	+	0.277381i	−0.999448	−	0.0332273i	$-0.989421\pi$
$167$	−105.553	+	598.619i	−0.0489097	+	0.277381i	0.950538	+	0.310608i	$0.100533\pi$
$168$		0			0
$169$	−1488.00	+	1248.58i	−0.677288	+	0.568312i
$170$	97.9905			0.0442090
$171$		0			0
$172$	−220.431			−0.0977193
$173$	−712.191	+	597.599i	−0.312988	+	0.262628i	−0.785726	−	0.618575i	$-0.787710\pi$
$173$	−712.191	+	597.599i	−0.312988	+	0.262628i	0.472738	+	0.881203i	$0.343266\pi$
$174$		0			0
$175$	−515.207	+	2921.89i	−0.222549	+	1.26214i
$176$	446.861	+	2534.28i	0.191383	+	1.08539i
$177$		0			0
$178$	1957.74	−	3390.90i	0.824375	−	1.42786i
$179$	182.925	+	316.836i	0.0763825	+	0.132298i	0.901687	−	0.432390i	$-0.142330\pi$
$179$	182.925	+	316.836i	0.0763825	+	0.132298i	−0.825304	+	0.564688i	$0.808996\pi$
$180$		0			0
$181$	1410.33	+	1183.41i	0.579167	+	0.485978i	0.884673	−	0.466211i	$-0.154381\pi$
$181$	1410.33	+	1183.41i	0.579167	+	0.485978i	−0.305507	+	0.952190i	$0.598826\pi$
$182$	−560.367	−	970.585i	−0.228226	−	0.395300i
$183$		0			0
$184$	370.129	−	134.716i	0.148295	−	0.0539750i
$185$	−3.84585	−	21.8109i	−0.00152839	−	0.00866795i
$186$		0			0
$187$	2174.93	+	791.611i	0.850518	+	0.309563i
$188$	−26.7717	+	22.4641i	−0.0103858	+	0.00871471i
$189$		0			0
$190$	−129.695	+	12.8510i	−0.0495213	+	0.00490689i
$191$	−1134.23			−0.429687			−0.214844	−	0.976648i	$-0.568924\pi$
$191$	−1134.23			−0.429687			−0.214844	+	0.976648i	$0.568924\pi$
$192$		0			0
$193$	2216.37	+	806.694i	0.826622	+	0.300866i	0.720472	−	0.693484i	$-0.243925\pi$
$193$	2216.37	+	806.694i	0.826622	+	0.300866i	0.106150	+	0.994350i	$0.466148\pi$
$194$	164.617	−	933.590i	0.0609218	−	0.345505i
$195$		0			0
$196$	−150.568	+	54.8023i	−0.0548717	+	0.0199717i
$197$	575.656	−	997.066i	0.208192	−	0.360599i	−0.742953	−	0.669343i	$-0.766575\pi$
$197$	575.656	−	997.066i	0.208192	−	0.360599i	0.951145	+	0.308745i	$0.0999088\pi$
$198$		0			0
$199$	−3637.30	−	3052.06i	−1.29569	−	1.08721i	−0.990873	−	0.134797i	$-0.956962\pi$
$199$	−3637.30	−	3052.06i	−1.29569	−	1.08721i	−0.304813	−	0.952412i	$-0.598594\pi$
$200$	2054.05	+	1723.55i	0.726217	+	0.609369i
$201$		0			0
$202$	−352.702	+	610.898i	−0.122852	+	0.212785i
$203$	397.364	−	144.629i	0.137387	−	0.0500046i
$204$		0			0
$205$	−30.9511	+	175.532i	−0.0105450	+	0.0598035i
$206$	3943.43	+	1435.29i	1.33375	+	0.485444i
$207$		0			0
$208$	−1104.59			−0.368218
$209$	−2982.44	−	762.500i	−0.987079	−	0.252360i
$210$		0			0
$211$	−3640.50	+	3054.74i	−1.18778	+	0.996669i	−0.187888	+	0.982190i	$0.560164\pi$
$211$	−3640.50	+	3054.74i	−1.18778	+	0.996669i	−0.999895	+	0.0144784i	$0.995391\pi$
$212$	−329.023	−	119.755i	−0.106592	−	0.0387961i
$213$		0			0
$214$	−601.653	−	3412.14i	−0.192188	−	1.08995i
$215$	153.607	−	55.9085i	0.0487253	−	0.0177345i
$216$		0			0
$217$	−1821.14	−	3154.30i	−0.569709	−	0.986766i
$218$	−4708.47	−	3950.88i	−1.46284	−	1.22746i
$219$		0			0
$220$	7.11842	+	12.3295i	0.00218147	+	0.00377842i
$221$	−496.738	+	860.376i	−0.151196	+	0.261879i
$222$		0			0
$223$	−1018.45	−	5775.91i	−0.305831	−	1.73446i	−0.619566	−	0.784945i	$-0.712691\pi$
$223$	−1018.45	−	5775.91i	−0.305831	−	1.73446i	0.313734	−	0.949511i	$-0.398420\pi$
$224$	−133.962	+	759.736i	−0.0399585	+	0.226616i
$225$		0			0
$226$	648.793	−	544.402i	0.190960	−	0.160235i
$227$	4739.12			1.38567			0.692834	−	0.721097i	$-0.256362\pi$
$227$	4739.12			1.38567			0.692834	+	0.721097i	$0.256362\pi$
$228$		0			0
$229$	−4075.09			−1.17594			−0.587968	−	0.808884i	$-0.700072\pi$
$229$	−4075.09			−1.17594			−0.587968	+	0.808884i	$0.700072\pi$
$230$	22.0851	−	18.5316i	0.00633152	−	0.00531278i
$231$		0			0
$232$	66.3619	−	376.357i	0.0187796	−	0.106504i
$233$	−576.213	−	3267.86i	−0.162013	−	0.918819i	−0.952091	−	0.305814i	$-0.901071\pi$
$233$	−576.213	−	3267.86i	−0.162013	−	0.918819i	0.790079	−	0.613005i	$-0.210040\pi$
$234$		0			0
$235$	12.9582	−	22.4443i	0.00359702	−	0.00623023i
$236$	75.3938	+	130.586i	0.0207954	+	0.0360187i
$237$		0			0
$238$	3350.73	+	2811.59i	0.912586	+	0.765750i
$239$	−3195.57	−	5534.90i	−0.864873	−	1.49800i	−0.867174	−	0.498006i	$-0.834066\pi$
$239$	−3195.57	−	5534.90i	−0.864873	−	1.49800i	0.00230119	−	0.999997i	$-0.499268\pi$
$240$		0			0
$241$	76.3532	−	27.7903i	0.0204081	−	0.00742792i	−0.331796	−	0.943351i	$-0.607655\pi$
$241$	76.3532	−	27.7903i	0.0204081	−	0.00742792i	0.352204	+	0.935923i	$0.385432\pi$
$242$	25.9405	+	147.116i	0.00689058	+	0.0390784i
$243$		0			0
$244$	141.436	+	51.4784i	0.0371086	+	0.0135064i
$245$	91.0236	−	76.3779i	0.0237359	−	0.0199167i
$246$		0			0
$247$	544.621	−	1203.89i	0.140297	−	0.310129i
$248$	−3291.69			−0.842832
$249$		0			0
$250$	369.272	+	134.404i	0.0934192	+	0.0340018i
$251$	−682.235	+	3869.15i	−0.171563	+	0.972982i	0.770474	+	0.637472i	$0.220020\pi$
$251$	−682.235	+	3869.15i	−0.171563	+	0.972982i	−0.942037	+	0.335510i	$0.891091\pi$
$252$		0			0
$253$	639.894	−	232.902i	0.159011	−	0.0578753i
$254$	1080.87	−	1872.12i	0.267007	−	0.462470i
$255$		0			0
$256$	839.010	+	704.013i	0.204836	+	0.171878i
$257$	−1404.52	−	1178.53i	−0.340900	−	0.286049i	0.456223	−	0.889865i	$-0.349202\pi$
$257$	−1404.52	−	1178.53i	−0.340900	−	0.286049i	−0.797124	+	0.603816i	$0.793646\pi$
$258$		0			0
$259$	494.304	−	856.159i	0.118589	−	0.205402i
$260$	−5.74245	+	2.09008i	−0.00136974	+	0.000498544i
$261$		0			0
$262$	1093.27	−	6200.22i	0.257795	−	1.46203i
$263$	213.532	+	77.7194i	0.0500645	+	0.0182220i	0.366931	−	0.930248i	$-0.380409\pi$
$263$	213.532	+	77.7194i	0.0500645	+	0.0182220i	−0.316867	+	0.948470i	$0.602631\pi$
$264$		0			0
$265$	259.653			0.0601901
$266$	−4803.57	−	3281.84i	−1.10724	−	0.756476i
$267$		0			0
$268$	235.051	−	197.232i	0.0535748	−	0.0449546i
$269$	−8023.95	−	2920.48i	−1.81869	−	0.661951i	−0.995563	−	0.0941002i	$-0.970003\pi$
$269$	−8023.95	−	2920.48i	−1.81869	−	0.661951i	−0.823132	−	0.567850i	$-0.807775\pi$
$270$		0			0
$271$	1353.50	+	7676.06i	0.303392	+	1.72062i	0.630981	+	0.775799i	$0.282653\pi$
$271$	1353.50	+	7676.06i	0.303392	+	1.72062i	−0.327589	+	0.944820i	$0.606236\pi$
$272$	4051.06	−	1474.47i	0.903057	−	0.328686i
$273$		0			0
$274$	433.600	+	751.017i	0.0956012	+	0.165586i
$275$	3551.12	+	2979.75i	0.778694	+	0.653402i
$276$		0			0
$277$	−4140.21	−	7171.06i	−0.898055	−	1.55548i	−0.829977	−	0.557797i	$-0.811647\pi$
$277$	−4140.21	−	7171.06i	−0.898055	−	1.55548i	−0.0680775	−	0.997680i	$-0.521687\pi$
$278$	2071.56	−	3588.04i	0.446920	−	0.774087i
$279$		0			0
$280$	−47.3352	−	268.451i	−0.0101029	−	0.0572965i
$281$	−20.6644	+	117.193i	−0.00438695	+	0.0248796i	−0.986923	−	0.161195i	$-0.948465\pi$
$281$	−20.6644	+	117.193i	−0.00438695	+	0.0248796i	0.982536	+	0.186074i	$0.0595765\pi$
$282$		0			0
$283$	−3142.94	+	2637.24i	−0.660171	+	0.553950i	−0.910138	−	0.414305i	$-0.864025\pi$
$283$	−3142.94	+	2637.24i	−0.660171	+	0.553950i	0.249967	+	0.968254i	$0.419580\pi$
$284$	−437.575			−0.0914271
$285$		0			0
$286$	−1751.07			−0.362038
$287$	−6094.82	+	5114.16i	−1.25354	+	1.05185i
$288$		0			0
$289$	−179.831	+	1019.87i	−0.0366031	+	0.207586i
$290$	−4.85732	−	27.5472i	−0.000983558	−	0.00557803i
$291$		0			0
$292$	−114.344	+	198.049i	−0.0229159	+	0.0396915i
$293$	544.911	+	943.814i	0.108649	+	0.188185i	0.915223	−	0.402948i	$-0.132014\pi$
$293$	544.911	+	943.814i	0.108649	+	0.188185i	−0.806574	+	0.591133i	$0.798681\pi$
$294$		0			0
$295$	−85.6590	−	71.8764i	−0.0169060	−	0.0141858i
$296$	−446.724	−	773.749i	−0.0877207	−	0.151937i
$297$		0			0
$298$	7905.58	−	2877.39i	1.53677	−	0.559339i
$299$	50.7563	+	287.853i	0.00981710	+	0.0556756i
$300$		0			0
$301$	6856.67	+	2495.62i	1.31300	+	0.477892i
$302$	6481.73	−	5438.81i	1.23504	−	1.03632i
$303$		0			0
$304$	−5168.39	+	2482.80i	−0.975091	+	0.468415i
$305$	−111.616			−0.0209545
$306$		0			0
$307$	−1695.91	−	617.259i	−0.315278	−	0.114752i	0.179534	−	0.983752i	$-0.442541\pi$
$307$	−1695.91	−	617.259i	−0.315278	−	0.114752i	−0.494812	+	0.869000i	$0.664763\pi$
$308$	−110.353	+	625.845i	−0.0204155	+	0.115782i
$309$		0			0
$310$	−226.403	+	82.4041i	−0.0414801	+	0.0150975i
$311$	−4126.79	+	7147.81i	−0.752440	+	1.30326i	0.194197	+	0.980962i	$0.437790\pi$
$311$	−4126.79	+	7147.81i	−0.752440	+	1.30326i	−0.946637	+	0.322301i	$0.895544\pi$
$312$		0			0
$313$	−1435.12	−	1204.21i	−0.259162	−	0.217463i	0.503944	−	0.863737i	$-0.331882\pi$
$313$	−1435.12	−	1204.21i	−0.259162	−	0.217463i	−0.763106	+	0.646274i	$0.776326\pi$
$314$	3942.64	+	3308.27i	0.708587	+	0.594575i
$315$		0			0
$316$	−93.7518	+	162.383i	−0.0166897	+	0.0289074i
$317$	6607.38	−	2404.89i	1.17069	−	0.426095i	0.317782	−	0.948164i	$-0.397062\pi$
$317$	6607.38	−	2404.89i	1.17069	−	0.426095i	0.852903	+	0.522069i	$0.174840\pi$
$318$		0			0
$319$	114.729	−	650.660i	0.0201366	−	0.114201i
$320$	−229.428	−	83.5048i	−0.0400794	−	0.0145877i
$321$		0			0
$322$	1286.91			0.222722
$323$	−390.369	+	5142.24i	−0.0672468	+	0.885827i
$324$		0			0
$325$	−1524.28	+	1279.02i	−0.260159	+	0.218299i
$326$	5018.61	+	1826.62i	0.852623	+	0.310329i
$327$		0			0
$328$	1248.60	+	7081.16i	0.210190	+	1.19205i
$329$	1087.08	−	395.666i	0.182167	−	0.0663032i
$330$		0			0
$331$	3066.16	+	5310.75i	0.509159	+	0.881889i	0.999944	+	0.0106083i	$0.00337678\pi$
$331$	3066.16	+	5310.75i	0.509159	+	0.881889i	−0.490785	+	0.871281i	$0.663290\pi$
$332$	362.078	+	303.819i	0.0598542	+	0.0502236i
$333$		0			0
$334$	897.418	+	1554.37i	0.147019	+	0.254645i
$335$	−113.771	+	197.057i	−0.0185552	+	0.0321385i
$336$		0			0
$337$	291.349	+	1652.32i	0.0470943	+	0.267085i	0.999259	−	0.0385017i	$-0.0122585\pi$
$337$	291.349	+	1652.32i	0.0470943	+	0.267085i	−0.952164	+	0.305587i	$0.901147\pi$
$338$	−995.967	+	5648.41i	−0.160277	+	0.908974i
$339$		0			0
$340$	18.2704	−	15.3307i	0.00291427	−	0.00244536i
$341$	−5690.80			−0.903736
$342$		0			0
$343$	−2855.91			−0.449576
$344$	5051.58	−	4238.78i	0.791753	−	0.664359i
$345$		0			0
$346$	−476.692	+	2703.46i	−0.0740669	+	0.420054i
$347$	1274.06	+	7225.54i	0.197104	+	1.11783i	0.909391	+	0.415942i	$0.136548\pi$
$347$	1274.06	+	7225.54i	0.197104	+	1.11783i	−0.712287	+	0.701888i	$0.752341\pi$
$348$		0			0
$349$	−3668.58	+	6354.17i	−0.562678	+	0.974586i	0.434584	+	0.900631i	$0.356895\pi$
$349$	−3668.58	+	6354.17i	−0.562678	+	0.974586i	−0.997262	+	0.0739550i	$0.976438\pi$
$350$	4380.33	+	7586.96i	0.668968	+	1.15869i
$351$		0			0
$352$	923.348	+	774.781i	0.139814	+	0.117318i
$353$	−4073.90	−	7056.20i	−0.614254	−	1.06392i	−0.990515	−	0.137406i	$-0.956124\pi$
$353$	−4073.90	−	7056.20i	−0.614254	−	1.06392i	0.376260	−	0.926514i	$-0.377210\pi$
$354$		0			0
$355$	304.924	−	110.983i	0.0455878	−	0.0165926i
$356$	−165.487	−	938.526i	−0.0246371	−	0.139724i
$357$		0			0
$358$	1015.11	+	369.471i	0.149862	+	0.0545451i
$359$	−5314.20	+	4459.15i	−0.781262	+	0.655556i	−0.943566	−	0.331184i	$-0.892552\pi$
$359$	−5314.20	+	4459.15i	−0.781262	+	0.655556i	0.162304	+	0.986741i	$0.448107\pi$
$360$		0			0
$361$	−157.710	−	6857.19i	−0.0229932	−	0.999736i
$362$	5436.17			0.789278
$363$		0			0
$364$	−256.330	−	93.2963i	−0.0369102	−	0.0134342i
$365$	29.4486	−	167.011i	0.00422304	−	0.0239501i
$366$		0			0
$367$	4609.00	−	1677.54i	0.655552	−	0.238602i	0.00723736	−	0.999974i	$-0.497696\pi$
$367$	4609.00	−	1677.54i	0.655552	−	0.238602i	0.648315	+	0.761372i	$0.275474\pi$
$368$	634.184	−	1098.44i	0.0898345	−	0.155598i
$369$		0			0
$370$	−50.0959	−	42.0354i	−0.00703881	−	0.00590626i
$371$	8878.69	+	7450.11i	1.24248	+	1.04256i
$372$		0			0
$373$	2502.34	−	4334.17i	0.347362	−	0.601649i	−0.638418	−	0.769690i	$-0.720411\pi$
$373$	2502.34	−	4334.17i	0.347362	−	0.601649i	0.985780	+	0.168041i	$0.0537442\pi$
$374$	6422.01	−	2337.42i	0.887899	−	0.323169i
$375$		0			0
$376$	181.548	−	1029.61i	0.0249007	−	0.141219i
$377$	266.493	+	96.9956i	0.0364061	+	0.0132507i
$378$		0			0
$379$	−5592.63			−0.757979			−0.378990	−	0.925401i	$-0.623728\pi$
$379$	−5592.63			−0.757979			−0.378990	+	0.925401i	$0.623728\pi$
$380$	−22.1711	+	22.6869i	−0.00299304	+	0.00306267i
$381$		0			0
$382$	−2565.56	+	2152.76i	−0.343627	+	0.288337i
$383$	8979.44	+	3268.25i	1.19798	+	0.436031i	0.862520	−	0.506022i	$-0.168885\pi$
$383$	8979.44	+	3268.25i	1.19798	+	0.436031i	0.335464	+	0.942053i	$0.391107\pi$
$384$		0			0
$385$	−81.8349	−	464.109i	−0.0108330	−	0.0614368i
$386$	6544.37	−	2381.96i	0.862953	−	0.314089i
$387$		0			0
$388$	−115.368	−	199.823i	−0.0150951	−	0.0261456i
$389$	−10041.0	−	8425.44i	−1.30874	−	1.09817i	−0.988563	−	0.150810i	$-0.951812\pi$
$389$	−10041.0	−	8425.44i	−1.30874	−	1.09817i	−0.320181	−	0.947357i	$-0.603744\pi$
$390$		0			0
$391$	−570.390	−	987.945i	−0.0737746	−	0.127781i
$392$	2396.72	−	4151.24i	0.308808	−	0.534870i
$393$		0			0
$394$	−590.322	−	3347.88i	−0.0754822	−	0.428081i
$395$	24.1453	−	136.935i	0.00307565	−	0.0174429i
$396$		0			0
$397$	2660.92	−	2232.77i	0.336392	−	0.282266i	−0.458906	−	0.888485i	$-0.651759\pi$
$397$	2660.92	−	2232.77i	0.336392	−	0.282266i	0.795298	+	0.606218i	$0.207314\pi$
$398$	−14020.1			−1.76574
$399$		0			0
$400$	8634.45			1.07931
$401$	−6382.68	+	5355.71i	−0.794853	+	0.666961i	−0.946941	−	0.321406i	$-0.895844\pi$
$401$	−6382.68	+	5355.71i	−0.794853	+	0.666961i	0.152089	+	0.988367i	$0.451400\pi$
$402$		0			0
$403$	424.171	−	2405.59i	0.0524304	−	0.297348i
$404$	29.8139	+	169.083i	0.00367152	+	0.0208222i
$405$		0			0
$406$	624.307	−	1081.33i	0.0763148	−	0.132181i
$407$	−772.314	−	1337.69i	−0.0940595	−	0.162916i
$408$		0			0
$409$	−3563.12	−	2989.81i	−0.430770	−	0.361459i	0.401472	−	0.915871i	$-0.368499\pi$
$409$	−3563.12	−	2989.81i	−0.430770	−	0.361459i	−0.832242	+	0.554412i	$0.812943\pi$
$410$	263.149	+	455.787i	0.0316975	+	0.0549017i
$411$		0			0
$412$	959.807	−	349.341i	0.114773	−	0.0417738i
$413$	−866.743	−	4915.55i	−0.103268	−	0.585661i
$414$		0			0
$415$	−329.372	−	119.882i	−0.0389596	−	0.0141801i
$416$	−396.336	+	332.565i	−0.0467114	+	0.0391955i
$417$		0			0
$418$	−8193.28	+	3935.90i	−0.958724	+	0.460553i
$419$	−4285.78			−0.499700			−0.249850	−	0.968285i	$-0.580381\pi$
$419$	−4285.78			−0.499700			−0.249850	+	0.968285i	$0.580381\pi$
$420$		0			0
$421$	5616.05	+	2044.08i	0.650142	+	0.236632i	0.645974	−	0.763359i	$-0.276451\pi$
$421$	5616.05	+	2044.08i	0.650142	+	0.236632i	0.00416721	+	0.999991i	$0.498674\pi$
$422$	−2436.70	+	13819.2i	−0.281083	+	1.59410i
$423$		0			0
$424$	9842.98	−	3582.55i	1.12740	−	0.410340i
$425$	3882.95	−	6725.47i	0.443178	−	0.767608i
$426$		0			0
$427$	−3816.64	−	3202.54i	−0.432553	−	0.362955i
$428$	−646.011	−	542.068i	−0.0729582	−	0.0612192i
$429$		0			0
$430$	241.336	−	418.006i	0.0270657	−	0.0468791i
$431$	13212.4	−	4808.91i	1.47661	−	0.537441i	0.526722	−	0.850038i	$-0.323421\pi$
$431$	13212.4	−	4808.91i	1.47661	−	0.537441i	0.949886	+	0.312596i	$0.101199\pi$
$432$		0			0
$433$	−1523.85	+	8642.18i	−0.169126	+	0.959160i	0.775582	+	0.631247i	$0.217457\pi$
$433$	−1523.85	+	8642.18i	−0.169126	+	0.959160i	−0.944708	+	0.327913i	$0.893655\pi$
$434$	−10106.1	−	3678.32i	−1.11776	−	0.406832i
$435$		0			0
$436$	−1496.02			−0.164326
$437$	884.502	+	1232.79i	0.0968226	+	0.134948i
$438$		0			0
$439$	9383.14	−	7873.39i	1.02012	−	0.855983i	0.0304779	−	0.999535i	$-0.490297\pi$
$439$	9383.14	−	7873.39i	1.02012	−	0.855983i	0.989643	+	0.143553i	$0.0458526\pi$
$440$	−400.221	−	145.668i	−0.0433631	−	0.0157829i
$441$		0			0
$442$	509.393	+	2888.91i	0.0548176	+	0.310886i
$443$	6351.80	−	2311.87i	0.681227	−	0.247946i	0.0218525	−	0.999761i	$-0.493044\pi$
$443$	6351.80	−	2311.87i	0.681227	−	0.247946i	0.659374	+	0.751815i	$0.270821\pi$
$444$		0			0
$445$	353.360	+	612.038i	0.0376425	+	0.0651986i
$446$	−13266.3	−	11131.7i	−1.40846	−	1.18184i
$447$		0			0
$448$	−5449.18	−	9438.26i	−0.574664	−	0.995348i
$449$	−343.589	+	595.114i	−0.0361135	+	0.0625505i	−0.883517	−	0.468399i	$-0.844831\pi$
$449$	−343.589	+	595.114i	−0.0361135	+	0.0625505i	0.847404	+	0.530949i	$0.178164\pi$
$450$		0			0
$451$	2158.63	+	12242.2i	0.225379	+	1.27819i
$452$	35.7958	−	203.008i	0.00372499	−	0.0211255i
$453$		0			0
$454$	10719.6	−	8994.78i	1.10814	−	0.929837i
$455$	202.286			0.0208425
$456$		0			0
$457$	4568.51			0.467628			0.233814	−	0.972281i	$-0.424879\pi$
$457$	4568.51			0.467628			0.233814	+	0.972281i	$0.424879\pi$
$458$	−9217.56	+	7734.45i	−0.940411	+	0.789099i
$459$		0			0
$460$	1.21850	−	6.91047i	0.000123506	−	0.000700440i
$461$	−916.750	−	5199.15i	−0.0926189	−	0.525268i	−0.995451	−	0.0952748i	$-0.969627\pi$
$461$	−916.750	−	5199.15i	−0.0926189	−	0.525268i	0.902832	−	0.429993i	$-0.141484\pi$
$462$		0			0
$463$	−4899.30	+	8485.84i	−0.491771	+	0.851772i	−0.999955	−	0.00947662i	$-0.996983\pi$
$463$	−4899.30	+	8485.84i	−0.491771	+	0.851772i	0.508185	+	0.861248i	$0.330317\pi$
$464$	−615.312	−	1065.75i	−0.0615628	−	0.106630i
$465$		0			0
$466$	−7505.71	−	6298.04i	−0.746127	−	0.626075i
$467$	−6591.67	−	11417.1i	−0.653161	−	1.13131i	−0.982351	−	0.187044i	$-0.940109\pi$
$467$	−6591.67	−	11417.1i	−0.653161	−	1.13131i	0.329191	−	0.944264i	$-0.393224\pi$
$468$		0			0
$469$	−9544.41	+	3473.88i	−0.939702	+	0.342023i
$470$	−13.2883	−	75.3619i	−0.00130414	−	0.00739614i
$471$		0			0
$472$	−4238.89	−	1542.83i	−0.413370	−	0.150454i
$473$	8733.36	−	7328.16i	0.848965	−	0.712366i
$474$		0			0
$475$	−4257.25	+	9410.70i	−0.411234	+	0.909037i
$476$	1064.62			0.102514
$477$		0			0
$478$	−17733.3	−	6454.40i	−1.69687	−	0.617610i
$479$	−1719.35	+	9750.94i	−0.164007	+	0.930129i	0.786076	+	0.618130i	$0.212110\pi$
$479$	−1719.35	+	9750.94i	−0.164007	+	0.930129i	−0.950083	+	0.311999i	$0.899002\pi$
$480$		0			0
$481$	623.028	−	226.764i	0.0590595	−	0.0214959i
$482$	119.960	−	207.777i	0.0113362	−	0.0196348i
$483$		0			0
$484$	27.8530	+	23.3715i	0.00261580	+	0.00219492i
$485$	131.076	+	109.986i	0.0122718	+	0.0102973i
$486$		0			0
$487$	5509.38	−	9542.53i	0.512636	−	0.887912i	−0.487256	−	0.873259i	$-0.662002\pi$
$487$	5509.38	−	9542.53i	0.512636	−	0.887912i	0.999893	−	0.0146531i	$-0.00466438\pi$
$488$	−4231.16	+	1540.02i	−0.392491	+	0.142855i
$489$		0			0
$490$	60.9250	−	345.523i	0.00561696	−	0.0318554i
$491$	3275.87	+	1192.32i	0.301096	+	0.109590i	0.488150	−	0.872760i	$-0.337672\pi$
$491$	3275.87	+	1192.32i	0.301096	+	0.109590i	−0.187054	+	0.982350i	$0.559894\pi$
$492$		0			0
$493$	−1106.83			−0.101114
$494$	−1053.07	−	3756.80i	−0.0959109	−	0.342159i
$495$		0			0
$496$	−8119.88	+	6813.39i	−0.735068	+	0.616795i
$497$	13611.1	+	4954.03i	1.22845	+	0.447120i
$498$		0			0
$499$	−2543.12	−	14422.7i	−0.228148	−	1.29389i	−0.856576	−	0.516021i	$-0.827412\pi$
$499$	−2543.12	−	14422.7i	−0.228148	−	1.29389i	0.628428	−	0.777868i	$-0.283699\pi$
$500$	89.8785	−	32.7131i	0.00803898	−	0.00292595i
$501$		0			0
$502$	5800.42	+	10046.6i	0.515708	+	0.893232i
$503$	486.565	+	408.277i	0.0431309	+	0.0361912i	0.664098	−	0.747645i	$-0.268816\pi$
$503$	486.565	+	408.277i	0.0431309	+	0.0361912i	−0.620967	+	0.783836i	$0.713260\pi$
$504$		0			0
$505$	−63.6607	−	110.264i	−0.00560963	−	0.00971616i
$506$	1005.35	−	1741.32i	0.0883266	−	0.152986i
$507$		0			0
$508$	−91.3659	−	518.162i	−0.00797973	−	0.0452553i
$509$	−1146.37	+	6501.36i	−0.0998266	+	0.566145i	0.893334	+	0.449392i	$0.148360\pi$
$509$	−1146.37	+	6501.36i	−0.0998266	+	0.566145i	−0.993161	+	0.116752i	$0.962752\pi$
$510$		0			0
$511$	5798.96	−	4865.90i	0.502017	−	0.421243i
$512$	−9662.89			−0.834069
$513$		0			0
$514$	−5413.76			−0.464573
$515$	−580.236	+	486.876i	−0.0496471	+	0.0416589i
$516$		0			0
$517$	313.868	−	1780.03i	0.0267000	−	0.151423i
$518$	−506.897	−	2874.75i	−0.0429957	−	0.243841i
$519$		0			0
$520$	91.4075	−	158.322i	0.00770862	−	0.0133517i
$521$	−5186.24	−	8982.83i	−0.436110	−	0.755364i	0.561276	−	0.827629i	$-0.310311\pi$
$521$	−5186.24	−	8982.83i	−0.436110	−	0.755364i	−0.997386	+	0.0722645i	$0.976977\pi$
$522$		0			0
$523$	1920.55	+	1611.53i	0.160573	+	0.134737i	0.719534	−	0.694457i	$-0.244355\pi$
$523$	1920.55	+	1611.53i	0.160573	+	0.134737i	−0.558961	+	0.829194i	$0.688800\pi$
$524$	−766.189	−	1327.08i	−0.0638762	−	0.110637i
$525$		0			0
$526$	630.506	−	229.485i	0.0522649	−	0.0190229i
$527$	1655.48	+	9388.68i	0.136838	+	0.776048i
$528$		0			0
$529$	11117.8	+	4046.57i	0.913771	+	0.332585i
$530$	587.318	−	492.818i	0.0481348	−	0.0403899i
$531$		0			0
$532$	−1409.07	+	139.620i	−0.114833	+	0.0113784i
$533$	−5335.87			−0.433625
$534$		0			0
$535$	587.658	+	213.890i	0.0474891	+	0.0172846i
$536$	−1593.97	+	9039.84i	−0.128449	+	0.728473i
$537$		0			0
$538$	−23692.6	+	8623.42i	−1.89863	+	0.691044i
$539$	4143.54	−	7176.82i	0.331122	−	0.573520i
$540$		0			0
$541$	706.569	+	592.882i	0.0561512	+	0.0471164i	0.670431	−	0.741972i	$-0.266109\pi$
$541$	706.569	+	592.882i	0.0561512	+	0.0471164i	−0.614280	+	0.789088i	$0.710554\pi$
$542$	17630.6	+	14793.8i	1.39723	+	1.17241i
$543$		0			0
$544$	1009.63	−	1748.73i	0.0795726	−	0.137824i
$545$	1042.50	−	379.438i	0.0819370	−	0.0298226i
$546$		0			0
$547$	−3202.35	+	18161.4i	−0.250315	+	1.41961i	0.557502	+	0.830175i	$0.311760\pi$
$547$	−3202.35	+	18161.4i	−0.250315	+	1.41961i	−0.807817	+	0.589433i	$0.799351\pi$
$548$	198.342	+	72.1907i	0.0154612	+	0.00562743i
$549$		0			0
$550$	13687.9			1.06119
$551$	1464.95	−	145.156i	0.113265	−	0.0112230i
$552$		0			0
$553$	4754.64	−	3989.62i	0.365620	−	0.306792i
$554$	−22975.4	−	8362.38i	−1.76197	−	0.641306i
$555$		0			0
$556$	−175.108	−	993.089i	−0.0133566	−	0.0757488i
$557$	−4539.76	+	1652.34i	−0.345342	+	0.125694i	−0.508868	−	0.860845i	$-0.669936\pi$
$557$	−4539.76	+	1652.34i	−0.345342	+	0.125694i	0.163525	+	0.986539i	$0.447713\pi$
$558$		0			0
$559$	2446.78	+	4237.95i	0.185130	+	0.320655i
$560$	−672.427	−	564.233i	−0.0507415	−	0.0425771i
$561$		0			0
$562$	175.690	+	304.304i	0.0131869	+	0.0228404i
$563$	7152.85	−	12389.1i	0.535447	−	0.927421i	−0.463695	−	0.885995i	$-0.653477\pi$
$563$	7152.85	−	12389.1i	0.535447	−	0.927421i	0.999142	−	0.0414262i	$-0.0131901\pi$
$564$		0			0
$565$	26.5452	+	150.545i	0.00197657	+	0.0112097i
$566$	−2103.67	+	11930.5i	−0.156226	+	0.886002i
$567$		0			0
$568$	10027.8	−	8414.34i	0.740771	−	0.621581i
$569$	−13558.5			−0.998948			−0.499474	−	0.866329i	$-0.666473\pi$
$569$	−13558.5			−0.998948			−0.499474	+	0.866329i	$0.666473\pi$
$570$		0			0
$571$	−10459.4			−0.766569			−0.383284	−	0.923630i	$-0.625207\pi$
$571$	−10459.4			−0.766569			−0.383284	+	0.923630i	$0.625207\pi$
$572$	−326.488	+	273.956i	−0.0238656	+	0.0200256i
$573$		0			0
$574$	−4079.46	+	23135.8i	−0.296644	+	1.68235i
$575$	−396.757	−	2250.12i	−0.0287755	−	0.163194i
$576$		0			0
$577$	2448.85	−	4241.53i	0.176685	−	0.306027i	−0.764058	−	0.645147i	$-0.776796\pi$
$577$	2448.85	−	4241.53i	0.176685	−	0.306027i	0.940743	+	0.339120i	$0.110129\pi$
$578$	1528.94	+	2648.20i	0.110027	+	0.190572i
$579$		0			0
$580$	−5.21544	−	4.37627i	−0.000373378	−	0.000313301i
$581$	−7822.98	−	13549.8i	−0.558609	−	0.967540i
$582$		0			0
$583$	17016.9	−	6193.65i	1.20887	−	0.439991i
$584$	−1187.99	−	6737.41i	−0.0841769	−	0.477391i
$585$		0			0
$586$	3023.90	+	1100.61i	0.213167	+	0.0775866i
$587$	3929.55	−	3297.28i	0.276303	−	0.231846i	−0.494097	−	0.869407i	$-0.664501\pi$
$587$	3929.55	−	3297.28i	0.276303	−	0.231846i	0.770400	+	0.637561i	$0.220057\pi$
$588$		0			0
$589$	−3422.38	−	12209.2i	−0.239417	−	0.854114i
$590$	−330.175			−0.0230391
$591$		0			0
$592$	−2703.54	−	984.008i	−0.187694	−	0.0683150i
$593$	1954.89	−	11086.7i	0.135376	−	0.767753i	−0.839222	−	0.543789i	$-0.816989\pi$
$593$	1954.89	−	11086.7i	0.135376	−	0.767753i	0.974597	−	0.223964i	$-0.0718998\pi$
$594$		0			0
$595$	−741.881	+	270.023i	−0.0511162	+	0.0186048i
$596$	1023.83	−	1773.32i	0.0703653	−	0.121876i
$597$		0			0
$598$	661.149	+	554.770i	0.0452113	+	0.0379368i
$599$	3063.51	+	2570.59i	0.208967	+	0.175344i	0.741264	−	0.671213i	$-0.234227\pi$
$599$	3063.51	+	2570.59i	0.208967	+	0.175344i	−0.532297	+	0.846558i	$0.678671\pi$
$600$		0			0
$601$	−157.943	+	273.565i	−0.0107198	+	0.0185673i	−0.871336	−	0.490688i	$-0.836746\pi$
$601$	−157.943	+	273.565i	−0.0107198	+	0.0185673i	0.860616	+	0.509255i	$0.170079\pi$
$602$	20246.0	−	7368.93i	1.37070	−	0.498896i
$603$		0			0
$604$	357.616	−	2028.14i	0.0240914	−	0.136629i
$605$	−25.3371	−	9.22196i	−0.00170265	−	0.000619713i
$606$		0			0
$607$	4289.71			0.286844			0.143422	−	0.989662i	$-0.454189\pi$
$607$	4289.71			0.286844			0.143422	+	0.989662i	$0.454189\pi$
$608$	−1106.95	+	2446.93i	−0.0738369	+	0.163217i
$609$		0			0
$610$	−252.468	+	211.845i	−0.0167576	+	0.0140613i
$611$	729.055	+	265.354i	0.0482723	+	0.0175697i
$612$		0			0
$613$	−394.023	−	2234.62i	−0.0259616	−	0.147235i	0.969072	−	0.246780i	$-0.0793725\pi$
$613$	−394.023	−	2234.62i	−0.0259616	−	0.147235i	−0.995033	+	0.0995446i	$0.968261\pi$
$614$	−5007.57	+	1822.61i	−0.329135	+	0.119795i
$615$		0			0
$616$	−9505.73	−	16464.4i	−0.621748	−	1.07690i
$617$	12411.8	+	10414.7i	0.809854	+	0.679548i	0.950573	−	0.310501i	$-0.100497\pi$
$617$	12411.8	+	10414.7i	0.809854	+	0.679548i	−0.140719	+	0.990050i	$0.544941\pi$
$618$		0			0
$619$	657.660	+	1139.10i	0.0427037	+	0.0739649i	0.886587	−	0.462561i	$-0.153070\pi$
$619$	657.660	+	1139.10i	0.0427037	+	0.0739649i	−0.843884	+	0.536526i	$0.819736\pi$
$620$	−29.3209	+	50.7853i	−0.00189928	+	0.00328965i
$621$		0			0
$622$	4231.92	+	24000.4i	0.272805	+	1.54715i
$623$	−5477.97	+	31067.1i	−0.352280	+	1.99788i
$624$		0			0
$625$	11887.9	−	9975.14i	0.760826	−	0.638409i
$626$	−5531.71			−0.353181
$627$		0			0
$628$	1252.69			0.0795983
$629$	−1982.25	+	1663.30i	−0.125656	+	0.105438i
$630$		0			0
$631$	3236.28	−	18353.9i	0.204175	−	1.15793i	−0.694558	−	0.719437i	$-0.744400\pi$
$631$	3236.28	−	18353.9i	0.204175	−	1.15793i	0.898733	−	0.438497i	$-0.144489\pi$
$632$	−974.047	−	5524.09i	−0.0613062	−	0.347685i
$633$		0			0
$634$	10381.0	−	17980.4i	0.650287	−	1.12633i
$635$	195.091	+	337.907i	0.0121920	+	0.0211172i
$636$		0			0
$637$	2724.92	+	2286.48i	0.169490	+	0.142219i
$638$	−975.434	−	1689.50i	−0.0605295	−	0.104840i
$639$		0			0
$640$	−807.363	+	293.856i	−0.0498654	+	0.0181495i
$641$	−266.985	−	1514.15i	−0.0164513	−	0.0932998i	0.975477	−	0.220103i	$-0.0706394\pi$
$641$	−266.985	−	1514.15i	−0.0164513	−	0.0932998i	−0.991928	+	0.126803i	$0.959528\pi$
$642$		0			0
$643$	−15553.9	−	5661.16i	−0.953945	−	0.347208i	−0.182287	−	0.983245i	$-0.558350\pi$
$643$	−15553.9	−	5661.16i	−0.953945	−	0.347208i	−0.771658	+	0.636038i	$0.780572\pi$
$644$	239.945	−	201.338i	0.0146819	−	0.0123196i
$645$		0			0
$646$	8876.91	+	12372.3i	0.540646	+	0.753533i
$647$	16597.6			1.00853			0.504265	−	0.863549i	$-0.331763\pi$
$647$	16597.6			1.00853			0.504265	+	0.863549i	$0.331763\pi$
$648$		0			0
$649$	−7328.35	−	2667.30i	−0.443240	−	0.161326i
$650$	−1020.25	+	5786.11i	−0.0615652	+	0.349154i
$651$		0			0
$652$	1221.50	−	444.590i	0.0733706	−	0.0267047i
$653$	9083.08	−	15732.4i	0.544331	−	0.942810i	−0.454317	−	0.890840i	$-0.650117\pi$
$653$	9083.08	−	15732.4i	0.544331	−	0.942810i	0.998649	−	0.0519697i	$-0.0165499\pi$
$654$		0			0
$655$	870.508	+	730.443i	0.0519291	+	0.0435737i
$656$	17737.2	+	14883.2i	1.05567	+	0.885812i
$657$		0			0
$658$	1707.94	−	2958.23i	0.101189	−	0.175264i
$659$	1019.58	−	371.097i	0.0602689	−	0.0219361i	−0.311710	−	0.950177i	$-0.600902\pi$
$659$	1019.58	−	371.097i	0.0602689	−	0.0219361i	0.371979	+	0.928241i	$0.378679\pi$
$660$		0			0
$661$	−1901.74	+	10785.3i	−0.111905	+	0.634645i	0.876331	+	0.481709i	$0.159984\pi$
$661$	−1901.74	+	10785.3i	−0.111905	+	0.634645i	−0.988236	+	0.152936i	$0.951127\pi$
$662$	17015.2	+	6193.02i	0.998963	+	0.363593i
$663$		0			0
$664$	−14140.0			−0.826411
$665$	946.501	−	454.681i	0.0551936	−	0.0265140i
$666$		0			0
$667$	−249.459	+	209.321i	−0.0144814	+	0.0121513i
$668$	410.507	+	149.412i	0.0237769	+	0.00865409i
$669$		0			0
$670$	116.670	+	661.666i	0.00672737	+	0.0381528i
$671$	−7314.99	+	2662.44i	−0.420852	+	0.153178i
$672$		0			0
$673$	−621.618	−	1076.67i	−0.0356042	−	0.0616683i	0.847674	−	0.530517i	$-0.178002\pi$
$673$	−621.618	−	1076.67i	−0.0356042	−	0.0616683i	−0.883278	+	0.468849i	$0.844669\pi$
$674$	3795.09	+	3184.46i	0.216887	+	0.181989i
$675$		0			0
$676$	697.999	+	1208.97i	0.0397132	+	0.0687853i
$677$	−14539.8	+	25183.7i	−0.825420	+	1.42967i	0.0761771	+	0.997094i	$0.475729\pi$
$677$	−14539.8	+	25183.7i	−0.825420	+	1.42967i	−0.901598	+	0.432576i	$0.857605\pi$
$678$		0			0
$679$	1326.29	+	7521.78i	0.0749609	+	0.425125i
$680$	−123.898	+	702.660i	−0.00698716	+	0.0396262i
$681$		0			0
$682$	−12872.2	+	10801.0i	−0.722730	+	0.606442i
$683$	24075.7			1.34880			0.674399	−	0.738367i	$-0.264403\pi$
$683$	24075.7			1.34880			0.674399	+	0.738367i	$0.264403\pi$
$684$		0			0
$685$	−156.525			−0.00873065
$686$	−6459.87	+	5420.48i	−0.359532	+	0.301683i
$687$		0			0
$688$	3687.40	−	20912.3i	0.204333	−	1.15883i
$689$	1349.78	+	7654.99i	0.0746336	+	0.423268i
$690$		0			0
$691$	−1398.33	+	2421.99i	−0.0769828	+	0.133338i	−0.901947	−	0.431847i	$-0.857862\pi$
$691$	−1398.33	+	2421.99i	−0.0769828	+	0.133338i	0.824964	+	0.565185i	$0.191195\pi$
$692$	334.078	+	578.640i	0.0183522	+	0.0317870i
$693$		0			0
$694$	16595.8	+	13925.5i	0.907734	+	0.761679i
$695$	373.904	+	647.620i	0.0204072	+	0.0353462i
$696$		0			0
$697$	19569.2	−	7122.61i	1.06347	−	0.387070i
$698$	3762.04	+	21335.6i	0.204005	+	1.15697i
$699$		0			0
$700$	2003.70	+	729.288i	0.108190	+	0.0393778i
$701$	25133.3	−	21089.3i	1.35417	−	1.13628i	0.376430	−	0.926445i	$-0.377152\pi$
$701$	25133.3	−	21089.3i	1.35417	−	1.13628i	0.977737	−	0.209836i	$-0.0672929\pi$
$702$		0			0
$703$	2405.46	−	2461.42i	0.129052	−	0.132054i
$704$	−17027.9			−0.911596
$705$		0			0
$706$	−22607.4	−	8228.44i	−1.20516	−	0.438642i
$707$	986.899	−	5596.98i	0.0524981	−	0.297732i
$708$		0			0
$709$	−32273.3	+	11746.5i	−1.70952	+	0.622214i	−0.996852	−	0.0792896i	$-0.974735\pi$
$709$	−32273.3	+	11746.5i	−1.70952	+	0.622214i	−0.712666	+	0.701503i	$0.752513\pi$
$710$	479.072	−	829.777i	0.0253229	−	0.0438605i
$711$		0			0
$712$	21839.8	+	18325.8i	1.14955	+	0.964589i
$713$	2148.67	+	1802.95i	0.112859	+	0.0946997i
$714$		0			0
$715$	158.029	−	273.714i	0.00826565	−	0.0143165i
$716$	247.073	−	89.9271i	0.0128960	−	0.00469376i
$717$		0			0
$718$	−3556.97	+	20172.6i	−0.184881	+	1.04851i
$719$	−21066.3	−	7667.51i	−1.09269	−	0.397705i	−0.268071	−	0.963399i	$-0.586386\pi$
$719$	−21066.3	−	7667.51i	−1.09269	−	0.397705i	−0.824615	+	0.565694i	$0.808608\pi$
$720$		0			0
$721$	−33810.6			−1.74642
$722$	−13371.6	−	15211.2i	−0.689250	−	0.784073i
$723$		0			0
$724$	1013.58	−	850.492i	0.0520294	−	0.0436579i
$725$	−2083.15	−	758.205i	−0.106712	−	0.0388400i
$726$		0			0
$727$	2677.06	+	15182.4i	0.136570	+	0.774529i	0.973753	+	0.227606i	$0.0730899\pi$
$727$	2677.06	+	15182.4i	0.136570	+	0.774529i	−0.837183	+	0.546923i	$0.815799\pi$
$728$	7668.29	−	2791.03i	0.390393	−	0.142091i
$729$		0			0
$730$	−250.374	−	433.661i	−0.0126942	−	0.0219870i
$731$	−14630.6	−	12276.5i	−0.740262	−	0.621154i
$732$		0			0
$733$	−3913.18	−	6777.82i	−0.197185	−	0.341534i	0.750430	−	0.660950i	$-0.229847\pi$
$733$	−3913.18	−	6777.82i	−0.197185	−	0.341534i	−0.947615	+	0.319416i	$0.896513\pi$
$734$	7241.29	−	12542.3i	0.364143	−	0.630714i
$735$		0			0
$736$	−103.163	−	585.067i	−0.00516663	−	0.0293014i
$737$	−2755.71	+	15628.4i	−0.137731	+	0.781113i
$738$		0			0
$739$	10722.3	−	8997.07i	0.533729	−	0.447852i	−0.335658	−	0.941984i	$-0.608959\pi$
$739$	10722.3	−	8997.07i	0.533729	−	0.447852i	0.869387	+	0.494132i	$0.164514\pi$
$740$	−15.9169			−0.000790698
$741$		0			0
$742$	34223.2			1.69322
$743$	6394.17	−	5365.34i	0.315719	−	0.264920i	−0.471132	−	0.882063i	$-0.656154\pi$
$743$	6394.17	−	5365.34i	0.315719	−	0.264920i	0.786851	+	0.617143i	$0.211710\pi$
$744$		0			0
$745$	−263.682	+	1495.42i	−0.0129672	+	0.0735407i
$746$	−2566.09	−	14553.0i	−0.125940	−	0.714240i
$747$		0			0
$748$	831.697	−	1440.54i	0.0406549	−	0.0704164i
$749$	13957.6	+	24175.3i	0.680907	+	1.17937i
$750$		0			0
$751$	8087.93	+	6786.58i	0.392987	+	0.329755i	0.817775	−	0.575538i	$-0.195207\pi$
$751$	8087.93	+	6786.58i	0.392987	+	0.329755i	−0.424789	+	0.905292i	$0.639652\pi$
$752$	−1683.33	−	2915.61i	−0.0816287	−	0.141385i
$753$		0			0
$754$	786.886	−	286.403i	0.0380062	−	0.0138331i
$755$	265.198	+	1504.01i	0.0127835	+	0.0724988i
$756$		0			0
$757$	−24046.0	−	8752.02i	−1.15451	−	0.420208i	−0.307378	−	0.951587i	$-0.599452\pi$
$757$	−24046.0	−	8752.02i	−1.15451	−	0.420208i	−0.847134	+	0.531379i	$0.821674\pi$
$758$	−12650.1	+	10614.7i	−0.606166	+	0.508634i
$759$		0			0
$760$	71.8339	−	946.251i	0.00342854	−	0.0451634i
$761$	33366.8			1.58942			0.794708	−	0.606992i	$-0.207624\pi$
$761$	33366.8			1.58942			0.794708	+	0.606992i	$0.207624\pi$
$762$		0			0
$763$	46534.6	+	16937.2i	2.20795	+	0.803629i
$764$	−141.549	+	802.767i	−0.00670298	+	0.0380145i
$765$		0			0
$766$	26514.0	−	9650.30i	1.25064	−	0.455195i
$767$	1673.74	−	2899.00i	0.0787943	−	0.136476i
$768$		0			0
$769$	2837.83	+	2381.22i	0.133075	+	0.111663i	0.706896	−	0.707318i	$-0.250095\pi$
$769$	2837.83	+	2381.22i	0.133075	+	0.111663i	−0.573821	+	0.818981i	$0.694539\pi$
$770$	−1065.98	−	894.460i	−0.0498898	−	0.0418625i
$771$		0			0
$772$	847.544	−	1467.99i	0.0395127	−	0.0684380i
$773$	−28255.2	+	10284.1i	−1.31471	+	0.478515i	−0.901759	−	0.432239i	$-0.857724\pi$
$773$	−28255.2	+	10284.1i	−1.31471	+	0.478515i	−0.412950	+	0.910754i	$0.635502\pi$
$774$		0			0
$775$	−3315.70	+	18804.3i	−0.153682	+	0.871574i
$776$	6486.36	+	2360.84i	0.300060	+	0.109213i
$777$		0			0
$778$	−38703.5			−1.78353
$779$	−24966.6	+	11993.5i	−1.14830	+	0.551620i
$780$		0			0
$781$	17336.5	−	14547.0i	0.794300	−	0.666496i
$782$	−3165.29	−	1152.07i	−0.144745	−	0.0526828i
$783$		0			0
$784$	−2680.37	−	15201.1i	−0.122101	−	0.692471i
$785$	−872.936	+	317.723i	−0.0396897	+	0.0144459i
$786$		0			0
$787$	−7452.99	−	12909.0i	−0.337574	−	0.584695i	0.646402	−	0.762997i	$-0.276273\pi$
$787$	−7452.99	−	12909.0i	−0.337574	−	0.584695i	−0.983976	+	0.178302i	$0.942940\pi$
$788$	−633.844	−	531.858i	−0.0286545	−	0.0240440i
$789$		0			0
$790$	−205.285	−	355.565i	−0.00924522	−	0.0160132i
$791$	−3411.82	+	5909.45i	−0.153363	+	0.265633i
$792$		0			0
$793$	−580.224	−	3290.61i	−0.0259828	−	0.147356i
$794$	1781.04	−	10100.8i	0.0796054	−	0.451464i
$795$		0			0
$796$	−2614.06	+	2193.45i	−0.116398	+	0.0976694i
$797$	−3805.66			−0.169139			−0.0845693	−	0.996418i	$-0.526951\pi$
$797$	−3805.66			−0.169139			−0.0845693	+	0.996418i	$0.526951\pi$
$798$		0			0
$799$	−3028.01			−0.134072
$800$	3098.12	−	2599.63i	0.136919	−	0.114888i
$801$		0			0
$802$	−4272.13	+	24228.5i	−0.188098	+	1.06675i
$803$	−2053.84	−	11647.9i	−0.0902595	−	0.511887i
$804$		0			0
$805$	−116.140	+	201.160i	−0.00508495	+	0.00880739i
$806$	−3606.34	−	6246.36i	−0.157603	−	0.272976i
$807$		0			0
$808$	−3934.62	−	3301.53i	−0.171311	−	0.143747i
$809$	−16021.2	−	27749.6i	−0.696263	−	1.20596i	−0.969753	−	0.244089i	$-0.921511\pi$
$809$	−16021.2	−	27749.6i	−0.696263	−	1.20596i	0.273489	−	0.961875i	$-0.411822\pi$
$810$		0			0
$811$	−37191.5	+	13536.6i	−1.61032	+	0.586109i	−0.981504	−	0.191443i	$-0.938683\pi$
$811$	−37191.5	+	13536.6i	−1.61032	+	0.586109i	−0.628818	+	0.777552i	$0.716461\pi$
$812$	−52.7726	−	299.288i	−0.00228073	−	0.0129347i
$813$		0			0
$814$	−4285.83	−	1559.92i	−0.184543	−	0.0671683i
$815$	−738.439	+	619.624i	−0.0317379	+	0.0266313i
$816$		0			0
$817$	20974.2	+	14329.8i	0.898159	+	0.613630i
$818$	−13734.1			−0.587046
$819$		0			0
$820$	120.372	+	43.8120i	0.00512633	+	0.00186583i
$821$	−966.969	+	5483.95i	−0.0411053	+	0.233120i	−0.998438	−	0.0558677i	$-0.982207\pi$
$821$	−966.969	+	5483.95i	−0.0411053	+	0.233120i	0.957333	+	0.288987i	$0.0933186\pi$
$822$		0			0
$823$	−11087.3	+	4035.44i	−0.469597	+	0.170919i	−0.565970	−	0.824426i	$-0.691498\pi$
$823$	−11087.3	+	4035.44i	−0.469597	+	0.170919i	0.0963727	+	0.995345i	$0.469276\pi$
$824$	−15278.1	+	26462.4i	−0.645918	+	1.11876i
$825$		0			0
$826$	−11290.1	−	9473.56i	−0.475586	−	0.399064i
$827$	−26639.2	−	22352.9i	−1.12012	−	0.939888i	−0.121505	−	0.992591i	$-0.538772\pi$
$827$	−26639.2	−	22352.9i	−1.12012	−	0.939888i	−0.998610	+	0.0527026i	$0.983216\pi$
$828$		0			0
$829$	−5944.55	+	10296.3i	−0.249050	+	0.431368i	−0.963263	−	0.268561i	$-0.913452\pi$
$829$	−5944.55	+	10296.3i	−0.249050	+	0.431368i	0.714212	+	0.699929i	$0.246785\pi$
$830$	−972.551	+	353.979i	−0.0406720	+	0.0148034i
$831$		0			0
$832$	1269.20	−	7197.98i	0.0528864	−	0.299934i
$833$	−13045.7	−	4748.25i	−0.542625	−	0.197499i
$834$		0			0
$835$	−323.957			−0.0134264
$836$	−911.869	+	2015.70i	−0.0377244	+	0.0833903i
$837$		0			0
$838$	−9694.14	+	8134.35i	−0.399616	+	0.335318i
$839$	−18828.8	−	6853.13i	−0.774783	−	0.281998i	−0.0757876	−	0.997124i	$-0.524147\pi$
$839$	−18828.8	−	6853.13i	−0.774783	−	0.281998i	−0.698996	+	0.715126i	$0.746369\pi$
$840$		0			0
$841$	−4180.24	−	23707.3i	−0.171399	−	0.972050i
$842$	16582.7	−	6035.63i	0.678716	−	0.247033i
$843$		0			0
$844$	1707.70	+	2957.83i	0.0696464	+	0.120631i
$845$	−793.034	−	665.435i	−0.0322855	−	0.0270907i
$846$		0			0
$847$	−601.787	−	1042.33i	−0.0244128	−	0.0422842i
$848$	16865.1	−	29211.2i	0.682958	−	1.18292i
$849$		0			0
$850$	−3981.88	−	22582.3i	−0.160679	−	0.911256i
$851$	−132.202	+	749.752i	−0.00532528	+	0.0302011i
$852$		0			0
$853$	9821.31	−	8241.06i	0.394227	−	0.330796i	−0.424030	−	0.905648i	$-0.639385\pi$
$853$	9821.31	−	8241.06i	0.394227	−	0.330796i	0.818257	+	0.574852i	$0.194941\pi$
$854$	−14711.4			−0.589476
$855$		0			0
$856$	25228.2			1.00734
$857$	18891.4	−	15851.8i	0.752998	−	0.631841i	−0.183296	−	0.983058i	$-0.558677\pi$
$857$	18891.4	−	15851.8i	0.752998	−	0.631841i	0.936294	+	0.351217i	$0.114232\pi$
$858$		0			0
$859$	2571.37	−	14583.0i	0.102135	−	0.579237i	−0.890191	−	0.455588i	$-0.849429\pi$
$859$	2571.37	−	14583.0i	0.102135	−	0.579237i	0.992326	−	0.123649i	$-0.0394598\pi$
$860$	−20.4001	−	115.695i	−0.000808880	−	0.00458739i
$861$		0			0
$862$	20758.2	−	35954.3i	0.820219	−	1.42066i
$863$	−6803.77	−	11784.5i	−0.268370	−	0.464830i	0.700071	−	0.714073i	$-0.253152\pi$
$863$	−6803.77	−	11784.5i	−0.268370	−	0.464830i	−0.968441	+	0.249243i	$0.919818\pi$
$864$		0			0
$865$	−379.564	−	318.492i	−0.0149197	−	0.0125191i
$866$	12955.9	+	22440.2i	0.508382	+	0.880543i
$867$		0			0
$868$	−2459.77	+	895.282i	−0.0961866	+	0.0350091i
$869$	−1683.97	−	9550.27i	−0.0657362	−	0.372809i
$870$		0			0
$871$	−6400.99	−	2329.77i	−0.249012	−	0.0906329i
$872$	34283.9	−	28767.6i	1.33142	−	1.11720i
$873$		0			0
$874$	4340.49	+	1109.71i	0.167986	+	0.0429478i
$875$	−3166.10			−0.122324
$876$		0			0
$877$	7314.81	+	2662.37i	0.281646	+	0.102511i	0.478981	−	0.877825i	$-0.341006\pi$
$877$	7314.81	+	2662.37i	0.281646	+	0.102511i	−0.197335	+	0.980336i	$0.563229\pi$
$878$	6280.44	−	35618.1i	0.241406	−	1.36908i
$879$		0			0
$880$	−1288.77	+	469.076i	−0.0493688	+	0.0179688i
$881$	−2917.05	+	5052.47i	−0.111553	+	0.193215i	−0.916396	−	0.400272i	$-0.868916\pi$
$881$	−2917.05	+	5052.47i	−0.111553	+	0.193215i	0.804844	+	0.593487i	$0.202249\pi$
$882$		0			0
$883$	−25154.3	−	21107.0i	−0.958675	−	0.804424i	0.0220623	−	0.999757i	$-0.492977\pi$
$883$	−25154.3	−	21107.0i	−0.958675	−	0.804424i	−0.980737	+	0.195333i	$0.937421\pi$
$884$	546.949	+	458.945i	0.0208098	+	0.0174615i
$885$		0			0
$886$	9979.45	−	17284.9i	0.378404	−	0.655416i
$887$	5718.56	−	2081.38i	0.216472	−	0.0787893i	−0.231508	−	0.972833i	$-0.574366\pi$
$887$	5718.56	−	2081.38i	0.216472	−	0.0787893i	0.447980	+	0.894044i	$0.352144\pi$
$888$		0			0
$889$	−3024.39	+	17152.2i	−0.114100	+	0.647093i
$890$	1960.92	+	713.715i	0.0738540	+	0.0268807i
$891$		0			0
$892$	−4215.07			−0.158218
$893$	4007.70	−	397.109i	0.150182	−	0.0148810i
$894$		0			0
$895$	−149.364	+	125.331i	−0.00557842	+	0.00468085i
$896$	−36038.8	−	13117.1i	−1.34372	−	0.489074i
$897$		0			0
$898$	352.343	+	1998.23i	0.0130933	+	0.0742561i
$899$	2557.30	−	930.781i	0.0948729	−	0.0345309i
$900$		0			0
$901$	−15168.6	−	26272.8i	−0.560865	−	0.971446i
$902$	28118.1	+	23593.9i	1.03795	+	0.870944i
$903$		0			0
$904$	3083.42	+	5340.64i	0.113444	+	0.196490i
$905$	−490.598	+	849.741i	−0.0180199	+	0.0312114i
$906$		0			0
$907$	−4025.82	−	22831.6i	−0.147382	−	0.835843i	−0.965424	−	0.260685i	$-0.916052\pi$
$907$	−4025.82	−	22831.6i	−0.147382	−	0.835843i	0.818042	−	0.575158i	$-0.195059\pi$
$908$	591.430	−	3354.17i	0.0216160	−	0.122590i
$909$		0			0
$910$	457.557	−	383.936i	0.0166680	−	0.0139861i
$911$	−30702.2			−1.11658			−0.558292	−	0.829645i	$-0.688543\pi$
$911$	−30702.2			−1.11658			−0.558292	+	0.829645i	$0.688543\pi$
$912$		0			0
$913$	−24445.7			−0.886128
$914$	10333.7	−	8670.96i	0.373968	−	0.313796i
$915$		0			0
$916$	−508.560	+	2884.19i	−0.0183442	+	0.104035i
$917$	8808.27	+	49954.2i	0.317202	+	1.79894i
$918$		0			0
$919$	−19148.3	+	33165.8i	−0.687317	+	1.19047i	0.285386	+	0.958413i	$0.407878\pi$
$919$	−19148.3	+	33165.8i	−0.687317	+	1.19047i	−0.972703	+	0.232055i	$0.925455\pi$
$920$	104.961	+	181.797i	0.00376136	+	0.00651486i
$921$		0			0
$922$	−11941.5	−	10020.1i	−0.426544	−	0.357913i
$923$	4857.07	+	8412.70i	0.173210	+	0.300008i
$924$		0			0
$925$	−4870.15	+	1772.59i	−0.173113	+	0.0630079i
$926$	5024.12	+	28493.2i	0.178297	+	1.01117i
$927$		0			0
$928$	−541.652	−	197.145i	−0.0191601	−	0.00697371i
$929$	21977.8	−	18441.5i	0.776176	−	0.651289i	−0.166107	−	0.986108i	$-0.553120\pi$
$929$	21977.8	−	18441.5i	0.776176	−	0.651289i	0.942282	+	0.334819i	$0.108675\pi$
$930$		0			0
$931$	17889.3	+	4573.64i	0.629750	+	0.161004i
$932$	−2384.78			−0.0838154
$933$		0			0
$934$	−36579.4	−	13313.8i	−1.28149	−	0.466425i
$935$	−214.200	+	1214.79i	−0.00749206	+	0.0424896i
$936$		0			0
$937$	22693.3	−	8259.69i	0.791204	−	0.287975i	0.0853677	−	0.996350i	$-0.472794\pi$
$937$	22693.3	−	8259.69i	0.791204	−	0.287975i	0.705837	+	0.708375i	$0.250571\pi$
$938$	−14995.4	+	25972.8i	−0.521981	+	0.904097i
$939$		0			0
$940$	−14.2680	−	11.9723i	−0.000495077	−	0.000415419i
$941$	−25578.3	−	21462.7i	−0.886108	−	0.743533i	0.0813173	−	0.996688i	$-0.474087\pi$
$941$	−25578.3	−	21462.7i	−0.886108	−	0.743533i	−0.967426	+	0.253155i	$0.918532\pi$
$942$		0			0
$943$	3063.51	−	5306.16i	0.105792	−	0.183237i
$944$	−13649.9	+	4968.15i	−0.470621	+	0.171292i
$945$		0			0
$946$	5845.52	−	33151.6i	0.200903	−	1.13938i
$947$	17989.1	+	6547.50i	0.617284	+	0.224673i	0.631687	−	0.775223i	$-0.282363\pi$
$947$	17989.1	+	6547.50i	0.617284	+	0.224673i	−0.0144034	+	0.999896i	$0.504585\pi$
$948$		0			0
$949$	5076.84			0.173658
$950$	8231.76	+	29366.5i	0.281130	+	1.00292i
$951$		0			0
$952$	−24397.7	+	20472.1i	−0.830604	+	0.696959i
$953$	48252.8	+	17562.6i	1.64015	+	0.596965i	0.987065	−	0.160320i	$-0.0512528\pi$
$953$	48252.8	+	17562.6i	1.64015	+	0.596965i	0.653084	+	0.757286i	$0.273475\pi$
$954$		0			0
$955$	−104.969	−	595.309i	−0.00355677	−	0.0201715i
$956$	−4316.19	+	1570.96i	−0.146020	+	0.0531470i
$957$		0			0
$958$	14618.1	+	25319.3i	0.492994	+	0.853892i
$959$	−5352.27	−	4491.08i	−0.180223	−	0.151225i
$960$		0			0
$961$	3175.27	+	5499.72i	0.106585	+	0.184610i
$962$	978.852	−	1695.42i	0.0328061	−	0.0568218i
$963$		0			0
$964$	−10.1402	−	57.5080i	−0.000338791	−	0.00192138i
$965$	−218.281	+	1237.93i	−0.00728156	+	0.0412958i
$966$		0			0
$967$	−5889.89	+	4942.20i	−0.195870	+	0.164354i	−0.735448	−	0.677581i	$-0.763028\pi$
$967$	−5889.89	+	4942.20i	−0.195870	+	0.164354i	0.539578	+	0.841936i	$0.318584\pi$
$968$	−1087.72			−0.0361165
$969$		0			0
$970$	505.235			0.0167238
$971$	−7656.07	+	6424.21i	−0.253033	+	0.212320i	−0.760477	−	0.649365i	$-0.775035\pi$
$971$	−7656.07	+	6424.21i	−0.253033	+	0.212320i	0.507444	+	0.861685i	$0.330590\pi$
$972$		0			0
$973$	−5796.44	+	32873.2i	−0.190982	+	1.08311i
$974$	−5649.74	−	32041.3i	−0.185862	−	1.05407i
$975$		0			0
$976$	−7249.71	+	12556.9i	−0.237764	+	0.411819i
$977$	11968.7	+	20730.4i	0.391927	+	0.678838i	0.992704	−	0.120579i	$-0.0384751\pi$
$977$	11968.7	+	20730.4i	0.391927	+	0.678838i	−0.600776	+	0.799417i	$0.705142\pi$
$978$		0			0
$979$	37757.5	+	31682.3i	1.23262	+	1.03429i
$980$	−42.6978	−	73.9547i	−0.00139177	−	0.00241061i
$981$		0			0
$982$	9672.80	−	3520.61i	0.314329	−	0.114407i
$983$	−1442.36	−	8180.01i	−0.0467996	−	0.265414i	0.952426	−	0.304771i	$-0.0985800\pi$
$983$	−1442.36	−	8180.01i	−0.0467996	−	0.265414i	−0.999225	+	0.0393575i	$0.987469\pi$
$984$		0			0
$985$	576.590	+	209.862i	0.0186515	+	0.00678858i
$986$	−2503.58	+	2100.76i	−0.0808624	+	0.0678516i
$987$		0			0
$988$	−784.100	−	535.704i	−0.0252485	−	0.0172500i
$989$	−5619.14			−0.180666
$990$		0			0
$991$	19359.5	+	7046.28i	0.620559	+	0.225865i	0.633117	−	0.774056i	$-0.281775\pi$
$991$	19359.5	+	7046.28i	0.620559	+	0.225865i	−0.0125578	+	0.999921i	$0.503997\pi$
$992$	−862.134	+	4889.41i	−0.0275935	+	0.156491i
$993$		0			0
$994$	40190.0	−	14628.0i	1.28244	−	0.466771i
$995$	1265.27	−	2191.52i	0.0403134	−	0.0698248i
$996$		0			0
$997$	30446.2	+	25547.4i	0.967141	+	0.811528i	0.982100	−	0.188360i	$-0.0603173\pi$
$997$	30446.2	+	25547.4i	0.967141	+	0.811528i	−0.0149588	+	0.999888i	$0.504762\pi$
$998$	−33126.5	−	27796.4i	−1.05070	−	0.881644i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.b.82.4		24
3.2	odd	2		19.4.e.a.6.1	✓	24
19.16	even	9	inner	171.4.u.b.73.4		24
57.23	odd	18		361.4.a.n.1.3		12
57.35	odd	18		19.4.e.a.16.1	yes	24
57.53	even	18		361.4.a.m.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.6.1	✓	24	3.2	odd	2
19.4.e.a.16.1	yes	24	57.35	odd	18
171.4.u.b.73.4		24	19.16	even	9	inner
171.4.u.b.82.4		24	1.1	even	1	trivial
361.4.a.m.1.10		12	57.53	even	18
361.4.a.n.1.3		12	57.23	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.26193 - 1.89799i) q^{2} +(0.124797 - 0.707761i) q^{4} +(0.0925462 + 0.524856i) q^{5} +(-11.8949 + 20.6025i) q^{7} +(10.7499 + 18.6194i) q^{8} +O(q^{10})\)	\(q+(2.26193 - 1.89799i) q^{2} +(0.124797 - 0.707761i) q^{4} +(0.0925462 + 0.524856i) q^{5} +(-11.8949 + 20.6025i) q^{7} +(10.7499 + 18.6194i) q^{8} +(1.20550 + 1.01154i) q^{10} +(18.5849 + 32.1900i) q^{11} +(-14.9925 + 5.45682i) q^{13} +(12.1979 + 69.1778i) q^{14} +(65.0577 + 23.6791i) q^{16} +(47.7006 - 40.0256i) q^{17} +(-57.8848 + 59.2314i) q^{19} +0.383022 q^{20} +(103.134 + 37.5376i) q^{22} +(3.18128 - 18.0420i) q^{23} +(117.195 - 42.6554i) q^{25} +(-23.5550 + 40.7984i) q^{26} +(13.0972 + 10.9899i) q^{28} +(-13.6165 - 11.4256i) q^{29} +(-76.5514 + 132.591i) q^{31} +(30.4725 - 11.0911i) q^{32} +(31.9276 - 181.070i) q^{34} +(-11.9142 - 4.33641i) q^{35} -41.5560 q^{37} +(-18.5110 + 243.842i) q^{38} +(-8.77764 + 7.36532i) q^{40} +(314.270 + 114.385i) q^{41} +(-53.2608 - 302.057i) q^{43} +(25.1022 - 9.13644i) q^{44} +(-27.0475 - 46.8477i) q^{46} +(-37.2512 - 31.2575i) q^{47} +(-111.476 - 193.082i) q^{49} +(184.127 - 318.917i) q^{50} +(1.99110 + 11.2921i) q^{52} +(84.6010 - 479.796i) q^{53} +(-15.1751 + 12.7334i) q^{55} -511.476 q^{56} -52.4854 q^{58} +(-160.725 + 134.865i) q^{59} +(-36.3671 + 206.248i) q^{61} +(78.5016 + 445.205i) q^{62} +(-229.056 + 396.736i) q^{64} +(-4.25154 - 7.36388i) q^{65} +(327.060 + 274.436i) q^{67} +(-22.3756 - 38.7557i) q^{68} +(-35.1795 + 12.8043i) q^{70} +(-105.727 - 599.609i) q^{71} +(-299.014 - 108.832i) q^{73} +(-93.9969 + 78.8728i) q^{74} +(34.6978 + 48.3605i) q^{76} -884.260 q^{77} +(-245.166 - 89.2331i) q^{79} +(-6.40725 + 36.3373i) q^{80} +(927.958 - 337.749i) q^{82} +(-328.838 + 569.565i) q^{83} +(25.4222 + 21.3317i) q^{85} +(-693.772 - 582.144i) q^{86} +(-399.572 + 692.080i) q^{88} +(1246.08 - 453.535i) q^{89} +(65.9094 - 373.791i) q^{91} +(-12.3724 - 4.50318i) q^{92} -143.586 q^{94} +(-36.4449 - 24.8995i) q^{95} +(245.942 - 206.370i) q^{97} +(-618.618 - 225.159i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

Introduction

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