LMFDB - Embedded newform 171.4.u.b.28.4

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			28.4
Character	$\chi$	$=$	171.28
Dual form			171.4.u.b.55.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.851642 + 4.82990i) q^{2} +(-15.0851 + 5.49052i) q^{4} +(-6.94640 - 2.52828i) q^{5} +(14.5751 - 25.2448i) q^{7} +(-19.7481 - 34.2048i) q^{8} +O(q^{10})$	\(q+(0.851642 + 4.82990i) q^{2} +(-15.0851 + 5.49052i) q^{4} +(-6.94640 - 2.52828i) q^{5} +(14.5751 - 25.2448i) q^{7} +(-19.7481 - 34.2048i) q^{8} +(6.29551 - 35.7036i) q^{10} +(-26.3895 - 45.7080i) q^{11} +(-30.9868 - 26.0010i) q^{13} +(134.343 + 48.8967i) q^{14} +(50.0074 - 41.9612i) q^{16} +(0.0277382 + 0.157311i) q^{17} +(-13.4549 + 81.7188i) q^{19} +118.669 q^{20} +(198.291 - 166.386i) q^{22} +(39.4491 - 14.3583i) q^{23} +(-53.8953 - 45.2235i) q^{25} +(99.1927 - 171.807i) q^{26} +(-81.2594 + 460.845i) q^{28} +(-11.8095 + 66.9751i) q^{29} +(108.113 - 187.257i) q^{31} +(3.20963 + 2.69320i) q^{32} +(-0.736175 + 0.267946i) q^{34} +(-165.071 + 138.511i) q^{35} -288.898 q^{37} +(-406.152 + 4.60942i) q^{38} +(50.6991 + 287.529i) q^{40} +(24.4278 - 20.4974i) q^{41} +(128.653 + 46.8260i) q^{43} +(649.050 + 544.617i) q^{44} +(102.946 + 178.307i) q^{46} +(32.7846 - 185.931i) q^{47} +(-253.367 - 438.844i) q^{49} +(172.526 - 298.823i) q^{50} +(610.199 + 222.094i) q^{52} +(31.5953 - 11.4998i) q^{53} +(67.7495 + 384.227i) q^{55} -1151.32 q^{56} -333.540 q^{58} +(-50.5342 - 286.594i) q^{59} +(-10.9927 + 4.00101i) q^{61} +(996.508 + 362.699i) q^{62} +(250.846 - 434.478i) q^{64} +(149.509 + 258.957i) q^{65} +(61.8269 - 350.638i) q^{67} +(-1.28216 - 2.22076i) q^{68} +(-809.573 - 679.313i) q^{70} +(237.468 + 86.4315i) q^{71} +(-619.706 + 519.995i) q^{73} +(-246.037 - 1395.35i) q^{74} +(-245.711 - 1306.61i) q^{76} -1538.52 q^{77} +(540.834 - 453.814i) q^{79} +(-453.461 + 165.046i) q^{80} +(119.804 + 100.528i) q^{82} +(-608.912 + 1054.67i) q^{83} +(0.205047 - 1.16288i) q^{85} +(-116.598 + 661.261i) q^{86} +(-1042.29 + 1805.30i) q^{88} +(-895.877 - 751.730i) q^{89} +(-1108.03 + 403.289i) q^{91} +(-516.259 + 433.193i) q^{92} +925.947 q^{94} +(300.071 - 533.634i) q^{95} +(-69.0328 - 391.505i) q^{97} +(1903.80 - 1597.48i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.851642	+	4.82990i	0.301101	+	1.70763i	0.641314	+	0.767279i	$0.278390\pi$
$2$	0.851642	+	4.82990i	0.301101	+	1.70763i	−0.340213	+	0.940348i	$0.610499\pi$
$3$		0			0
$3$		0			0
$4$	−15.0851	+	5.49052i	−1.88564	+	0.686315i
$5$	−6.94640	−	2.52828i	−0.621305	−	0.226137i	0.0121374	−	0.999926i	$-0.496136\pi$
$5$	−6.94640	−	2.52828i	−0.621305	−	0.226137i	−0.633442	+	0.773790i	$0.718359\pi$
$6$		0			0
$7$	14.5751	−	25.2448i	0.786981	−	1.36309i	−0.140827	−	0.990034i	$-0.544976\pi$
$7$	14.5751	−	25.2448i	0.786981	−	1.36309i	0.927808	−	0.373057i	$-0.121691\pi$
$8$	−19.7481	−	34.2048i	−0.872752	−	1.51165i
$9$		0			0
$10$	6.29551	−	35.7036i	0.199081	−	1.12905i
$11$	−26.3895	−	45.7080i	−0.723341	−	1.25286i	−0.959653	−	0.281186i	$-0.909272\pi$
$11$	−26.3895	−	45.7080i	−0.723341	−	1.25286i	0.236313	−	0.971677i	$-0.424061\pi$
$12$		0			0
$13$	−30.9868	−	26.0010i	−0.661092	−	0.554722i	0.249322	−	0.968421i	$-0.419792\pi$
$13$	−30.9868	−	26.0010i	−0.661092	−	0.554722i	−0.910414	+	0.413698i	$0.864237\pi$
$14$	134.343	+	48.8967i	2.56461	+	0.933443i
$15$		0			0
$16$	50.0074	−	41.9612i	0.781366	−	0.655644i
$17$	0.0277382	+	0.157311i	0.000395736	+	0.00224433i	0.985005	−	0.172526i	$-0.0551928\pi$
$17$	0.0277382	+	0.157311i	0.000395736	+	0.00224433i	−0.984609	+	0.174770i	$0.944082\pi$
$18$		0			0
$19$	−13.4549	+	81.7188i	−0.162461	+	0.986715i
$19$	−13.4549	+	81.7188i	−0.162461	+	0.986715i
$20$	118.669			1.32676
$21$		0			0
$22$	198.291	−	166.386i	1.92162	−	1.61243i
$23$	39.4491	−	14.3583i	0.357640	−	0.130170i	−0.156950	−	0.987606i	$-0.550166\pi$
$23$	39.4491	−	14.3583i	0.357640	−	0.130170i	0.514590	+	0.857436i	$0.327944\pi$
$24$		0			0
$25$	−53.8953	−	45.2235i	−0.431162	−	0.361788i
$26$	99.1927	−	171.807i	0.748204	−	1.29593i
$27$		0			0
$28$	−81.2594	+	460.845i	−0.548450	+	3.11041i
$29$	−11.8095	+	66.9751i	−0.0756197	+	0.428861i	0.923370	+	0.383912i	$0.125423\pi$
$29$	−11.8095	+	66.9751i	−0.0756197	+	0.428861i	−0.998989	+	0.0449484i	$0.985688\pi$
$30$		0			0
$31$	108.113	−	187.257i	0.626377	−	1.08492i	−0.361896	−	0.932219i	$-0.617870\pi$
$31$	108.113	−	187.257i	0.626377	−	1.08492i	0.988273	−	0.152698i	$-0.0487963\pi$
$32$	3.20963	+	2.69320i	0.0177309	+	0.0148780i
$33$		0			0
$34$	−0.736175	+	0.267946i	−0.00371332	+	0.00135154i
$35$	−165.071	+	138.511i	−0.797200	+	0.668930i
$36$		0			0
$37$	−288.898			−1.28363			−0.641817	−	0.766858i	$-0.721819\pi$
$37$	−288.898			−1.28363			−0.641817	+	0.766858i	$0.721819\pi$
$38$	−406.152	+	4.60942i	−1.73386	+	0.0196775i
$39$		0			0
$40$	50.6991	+	287.529i	0.200406	+	1.13656i
$41$	24.4278	−	20.4974i	0.0930485	−	0.0780769i	−0.595077	−	0.803669i	$-0.702878\pi$
$41$	24.4278	−	20.4974i	0.0930485	−	0.0780769i	0.688125	+	0.725592i	$0.258434\pi$
$42$		0			0
$43$	128.653	+	46.8260i	0.456266	+	0.166067i	0.559921	−	0.828546i	$-0.310831\pi$
$43$	128.653	+	46.8260i	0.456266	+	0.166067i	−0.103655	+	0.994613i	$0.533054\pi$
$44$	649.050	+	544.617i	2.22382	+	1.86600i
$45$		0			0
$46$	102.946	+	178.307i	0.329968	+	0.571521i
$47$	32.7846	−	185.931i	0.101747	−	0.577038i	−0.890722	−	0.454548i	$-0.849801\pi$
$47$	32.7846	−	185.931i	0.101747	−	0.577038i	0.992470	−	0.122490i	$-0.0390880\pi$
$48$		0			0
$49$	−253.367	−	438.844i	−0.738679	−	1.27943i
$50$	172.526	−	298.823i	0.487976	−	0.845199i
$51$		0			0
$52$	610.199	+	222.094i	1.62729	+	0.592287i
$53$	31.5953	−	11.4998i	0.0818859	−	0.0298040i	−0.300752	−	0.953702i	$-0.597238\pi$
$53$	31.5953	−	11.4998i	0.0818859	−	0.0298040i	0.382638	+	0.923898i	$0.375016\pi$
$54$		0			0
$55$	67.7495	+	384.227i	0.166097	+	0.941984i
$56$	−1151.32			−2.74736
$57$		0			0
$58$	−333.540			−0.755103
$59$	−50.5342	−	286.594i	−0.111508	−	0.632395i	−0.988420	−	0.151743i	$-0.951511\pi$
$59$	−50.5342	−	286.594i	−0.111508	−	0.632395i	0.876912	−	0.480652i	$-0.159600\pi$
$60$		0			0
$61$	−10.9927	+	4.00101i	−0.0230732	+	0.00839798i	−0.353531	−	0.935423i	$-0.615019\pi$
$61$	−10.9927	+	4.00101i	−0.0230732	+	0.00839798i	0.330458	+	0.943821i	$0.392797\pi$
$62$	996.508	+	362.699i	2.04124	+	0.742949i
$63$		0			0
$64$	250.846	−	434.478i	0.489933	−	0.848589i
$65$	149.509	+	258.957i	0.285297	+	0.494149i
$66$		0			0
$67$	61.8269	−	350.638i	0.112737	−	0.639362i	−0.875109	−	0.483926i	$-0.839211\pi$
$67$	61.8269	−	350.638i	0.112737	−	0.639362i	0.987846	−	0.155436i	$-0.0496784\pi$
$68$	−1.28216	−	2.22076i	−0.00228653	−	0.00396039i
$69$		0			0
$70$	−809.573	−	679.313i	−1.38232	−	1.15991i
$71$	237.468	+	86.4315i	0.396934	+	0.144472i	0.532772	−	0.846259i	$-0.321150\pi$
$71$	237.468	+	86.4315i	0.396934	+	0.144472i	−0.135838	+	0.990731i	$0.543373\pi$
$72$		0			0
$73$	−619.706	+	519.995i	−0.993577	+	0.833710i	−0.986082	−	0.166262i	$-0.946830\pi$
$73$	−619.706	+	519.995i	−0.993577	+	0.833710i	−0.00749546	+	0.999972i	$0.502386\pi$
$74$	−246.037	−	1395.35i	−0.386503	−	2.19197i
$75$		0			0
$76$	−245.711	−	1306.61i	−0.370855	−	1.97209i
$77$	−1538.52			−2.27702
$78$		0			0
$79$	540.834	−	453.814i	0.770235	−	0.646304i	−0.170534	−	0.985352i	$-0.554549\pi$
$79$	540.834	−	453.814i	0.770235	−	0.646304i	0.940769	+	0.339048i	$0.110105\pi$
$80$	−453.461	+	165.046i	−0.633732	+	0.230659i
$81$		0			0
$82$	119.804	+	100.528i	0.161343	+	0.135383i
$83$	−608.912	+	1054.67i	−0.805263	+	1.39476i	0.110851	+	0.993837i	$0.464642\pi$
$83$	−608.912	+	1054.67i	−0.805263	+	1.39476i	−0.916113	+	0.400919i	$0.868691\pi$
$84$		0			0
$85$	0.205047	−	1.16288i	0.000261652	−	0.00148390i
$86$	−116.598	+	661.261i	−0.146199	+	0.829136i
$87$		0			0
$88$	−1042.29	+	1805.30i	−1.26259	+	2.18688i
$89$	−895.877	−	751.730i	−1.06700	−	0.895318i	−0.0722208	−	0.997389i	$-0.523009\pi$
$89$	−895.877	−	751.730i	−1.06700	−	0.895318i	−0.994777	+	0.102071i	$0.967453\pi$
$90$		0			0
$91$	−1108.03	+	403.289i	−1.27640	+	0.464573i
$92$	−516.259	+	433.193i	−0.585041	+	0.490907i
$93$		0			0
$94$	925.947			1.01600
$95$	300.071	−	533.634i	0.324070	−	0.576313i
$96$		0			0
$97$	−69.0328	−	391.505i	−0.0722600	−	0.409807i	−0.999385	−	0.0350556i	$-0.988839\pi$
$97$	−69.0328	−	391.505i	−0.0722600	−	0.409807i	0.927125	−	0.374751i	$-0.122272\pi$
$98$	1903.80	−	1597.48i	1.96237	−	1.64663i
$99$		0			0
$100$	1061.32	+	386.287i	1.06132	+	0.386287i
$101$	264.263	+	221.743i	0.260348	+	0.218458i	0.763613	−	0.645674i	$-0.223424\pi$
$101$	264.263	+	221.743i	0.260348	+	0.218458i	−0.503265	+	0.864132i	$0.667868\pi$
$102$		0			0
$103$	−412.120	−	713.813i	−0.394247	−	0.682855i	0.598758	−	0.800930i	$-0.295661\pi$
$103$	−412.120	−	713.813i	−0.394247	−	0.682855i	−0.993005	+	0.118075i	$0.962328\pi$
$104$	−277.427	+	1573.37i	−0.261577	+	1.48348i
$105$		0			0
$106$	82.4506	+	142.809i	0.0755501	+	0.130857i
$107$	−166.554	+	288.479i	−0.150480	+	0.260639i	−0.931404	−	0.363987i	$-0.881415\pi$
$107$	−166.554	+	288.479i	−0.150480	+	0.260639i	0.780924	+	0.624626i	$0.214749\pi$
$108$		0			0
$109$	1381.61	+	502.866i	1.21408	+	0.441889i	0.868117	−	0.496360i	$-0.165330\pi$
$109$	1381.61	+	502.866i	1.21408	+	0.441889i	0.345962	+	0.938248i	$0.387553\pi$
$110$	−1798.08	+	654.447i	−1.55855	+	0.567264i
$111$		0			0
$112$	−330.440	−	1874.02i	−0.278782	−	1.58105i
$113$	2149.63			1.78956			0.894778	−	0.446511i	$-0.147334\pi$
$113$	2149.63			1.78956			0.894778	+	0.446511i	$0.147334\pi$
$114$		0			0
$115$	−310.331			−0.251640
$116$	−189.581	−	1075.17i	−0.151742	−	0.860574i
$117$		0			0
$118$	1341.18	−	488.150i	1.04632	−	0.380829i
$119$	4.37558	+	1.59258i	0.00337066	+	0.00122682i
$120$		0			0
$121$	−727.316	+	1259.75i	−0.546444	+	0.946468i
$122$	−28.6863	−	49.6861i	−0.0212880	−	0.0368719i
$123$		0			0
$124$	−602.755	+	3418.39i	−0.436524	+	2.47565i
$125$	722.053	+	1250.63i	0.516659	+	0.894880i
$126$		0			0
$127$	−581.035	−	487.547i	−0.405973	−	0.340652i	0.416824	−	0.908987i	$-0.363143\pi$
$127$	−581.035	−	487.547i	−0.405973	−	0.340652i	−0.822797	+	0.568336i	$0.807588\pi$
$128$	2343.61	+	853.005i	1.61834	+	0.589029i
$129$		0			0
$130$	−1123.41	+	942.652i	−0.757919	+	0.635970i
$131$	−0.740327	−	4.19860i	−0.000493761	−	0.00280026i	0.984560	−	0.175048i	$-0.0560081\pi$
$131$	−0.740327	−	4.19860i	−0.000493761	−	0.00280026i	−0.985054	+	0.172248i	$0.944897\pi$
$132$		0			0
$133$	1866.87	+	1530.73i	1.21713	+	0.997976i
$134$	1746.20			1.12574
$135$		0			0
$136$	4.83302	−	4.05538i	0.00304726	−	0.00255696i
$137$	−826.086	+	300.671i	−0.515163	+	0.187504i	−0.586501	−	0.809948i	$-0.699495\pi$
$137$	−826.086	+	300.671i	−0.515163	+	0.187504i	0.0713386	+	0.997452i	$0.477273\pi$
$138$		0			0
$139$	1508.17	+	1265.50i	0.920295	+	0.772219i	0.974049	−	0.226335i	$-0.0726745\pi$
$139$	1508.17	+	1265.50i	0.920295	+	0.772219i	−0.0537547	+	0.998554i	$0.517119\pi$
$140$	1729.61	−	2995.77i	1.04413	−	1.80849i
$141$		0			0
$142$	−215.217	+	1220.56i	−0.127188	+	0.721316i
$143$	−370.728	+	2102.50i	−0.216796	+	1.22951i
$144$		0			0
$145$	251.365	−	435.378i	0.143964	−	0.249353i
$146$	−3039.29	−	2550.27i	−1.72283	−	1.44563i
$147$		0			0
$148$	4358.05	−	1586.20i	2.42047	−	0.880978i
$149$	−1153.19	+	967.640i	−0.634046	+	0.532028i	−0.902183	−	0.431353i	$-0.858036\pi$
$149$	−1153.19	+	967.640i	−0.634046	+	0.532028i	0.268137	+	0.963381i	$0.413592\pi$
$150$		0			0
$151$	−2394.72			−1.29059			−0.645296	−	0.763933i	$-0.723266\pi$
$151$	−2394.72			−1.29059			−0.645296	+	0.763933i	$0.723266\pi$
$152$	3060.88	−	1153.57i	1.63336	−	0.615573i
$153$		0			0
$154$	−1310.27	−	7430.90i	−0.685613	−	3.88831i
$155$	−1224.44	+	1027.42i	−0.634511	+	0.532418i
$156$		0			0
$157$	2541.54	+	925.045i	1.29196	+	0.470233i	0.894368	−	0.447331i	$-0.147625\pi$
$157$	2541.54	+	925.045i	1.29196	+	0.470233i	0.397587	+	0.917564i	$0.369848\pi$
$158$	2652.47	+	2225.69i	1.33556	+	1.12067i
$159$		0			0
$160$	−15.4862	−	26.8229i	−0.00765183	−	0.0132534i
$161$	212.502	−	1205.16i	0.104022	−	0.589937i
$162$		0			0
$163$	927.459	+	1606.41i	0.445670	+	0.771923i	0.998099	−	0.0616373i	$-0.0196322\pi$
$163$	927.459	+	1606.41i	0.445670	+	0.771923i	−0.552429	+	0.833560i	$0.686299\pi$
$164$	−255.955	+	443.327i	−0.121870	+	0.211085i
$165$		0			0
$166$	−5612.51	−	2042.79i	−2.62419	−	0.955127i
$167$	835.550	−	304.115i	0.387166	−	0.140917i	−0.141101	−	0.989995i	$-0.545064\pi$
$167$	835.550	−	304.115i	0.387166	−	0.140917i	0.528267	+	0.849078i	$0.322842\pi$
$168$		0			0
$169$	−97.3753	−	552.243i	−0.0443219	−	0.251362i
$170$	5.79121			0.00261274
$171$		0			0
$172$	−2197.85			−0.974327
$173$	−604.938	−	3430.77i	−0.265853	−	1.50773i	−0.766595	−	0.642130i	$-0.778051\pi$
$173$	−604.938	−	3430.77i	−0.265853	−	1.50773i	0.500743	−	0.865596i	$-0.333060\pi$
$174$		0			0
$175$	−1927.19	+	701.439i	−0.832467	+	0.302993i
$176$	−3237.64	−	1178.40i	−1.38663	−	0.504690i
$177$		0			0
$178$	2867.82	−	4967.20i	1.20759	−	2.09162i
$179$	−52.0088	−	90.0818i	−0.0217169	−	0.0376147i	0.854963	−	0.518689i	$-0.173580\pi$
$179$	−52.0088	−	90.0818i	−0.0217169	−	0.0376147i	−0.876680	+	0.481075i	$0.840247\pi$
$180$		0			0
$181$	191.556	−	1086.37i	0.0786642	−	0.446127i	−0.919881	−	0.392199i	$-0.871715\pi$
$181$	191.556	−	1086.37i	0.0786642	−	0.446127i	0.998545	−	0.0539284i	$-0.0171743\pi$
$182$	−2891.49	−	5008.20i	−1.17764	−	2.03974i
$183$		0			0
$184$	−1270.17	−	1065.80i	−0.508903	−	0.427020i
$185$	2006.80	+	730.415i	0.797529	+	0.290277i
$186$		0			0
$187$	6.45839	−	5.41924i	0.00252559	−	0.00211922i
$188$	526.298	+	2984.79i	0.204172	+	1.15791i
$189$		0			0
$190$	2832.95	+	994.849i	1.08170	+	0.379863i
$191$	−2275.97			−0.862216			−0.431108	−	0.902300i	$-0.641877\pi$
$191$	−2275.97			−0.862216			−0.431108	+	0.902300i	$0.641877\pi$
$192$		0			0
$193$	−444.200	+	372.728i	−0.165669	+	0.139013i	−0.721853	−	0.692046i	$-0.756709\pi$
$193$	−444.200	+	372.728i	−0.165669	+	0.139013i	0.556184	+	0.831059i	$0.312265\pi$
$194$	1832.14	−	666.843i	0.678040	−	0.246786i
$195$		0			0
$196$	6231.55	+	5228.89i	2.27097	+	1.90557i
$197$	−300.114	+	519.812i	−0.108539	+	0.187995i	−0.915179	−	0.403048i	$-0.867951\pi$
$197$	−300.114	+	519.812i	−0.108539	+	0.187995i	0.806639	+	0.591044i	$0.201284\pi$
$198$		0			0
$199$	−193.396	+	1096.81i	−0.0688920	+	0.390706i	0.930792	+	0.365550i	$0.119119\pi$
$199$	−193.396	+	1096.81i	−0.0688920	+	0.390706i	−0.999684	+	0.0251556i	$0.991992\pi$
$200$	−482.529	+	2736.56i	−0.170600	+	0.967518i
$201$		0			0
$202$	−845.940	+	1465.21i	−0.294654	+	0.510356i
$203$	1518.65	+	1274.30i	0.525065	+	0.440582i
$204$		0			0
$205$	−221.509	+	80.6226i	−0.0754675	+	0.0274679i
$206$	3096.67	−	2598.41i	1.04735	−	0.878834i
$207$		0			0
$208$	−2640.61			−0.880255
$209$	4090.28	−	1541.53i	1.35373	−	0.510190i
$210$		0			0
$211$	−151.430	−	858.804i	−0.0494071	−	0.280201i	0.950088	−	0.311983i	$-0.100993\pi$
$211$	−151.430	−	858.804i	−0.0494071	−	0.280201i	−0.999495	+	0.0317813i	$0.989882\pi$
$212$	−413.479	+	346.950i	−0.133952	+	0.112399i
$213$		0			0
$214$	−1535.17	−	558.756i	−0.490384	−	0.178485i
$215$	−775.288	−	650.544i	−0.245927	−	0.206357i
$216$		0			0
$217$	−3151.52	−	5458.59i	−0.985894	−	1.70762i
$218$	−1252.15	+	7101.32i	−0.389021	+	2.20625i
$219$		0			0
$220$	−3131.61	−	5424.11i	−0.959697	−	1.66224i
$221$	3.23074	−	5.59580i	0.000983362	−	0.00170323i
$222$		0			0
$223$	4308.68	+	1568.23i	1.29386	+	0.470926i	0.894992	−	0.446082i	$-0.147181\pi$
$223$	4308.68	+	1568.23i	1.29386	+	0.470926i	0.398867	+	0.917009i	$0.369403\pi$
$224$	114.770	−	41.7729i	0.0342339	−	0.0124601i
$225$		0			0
$226$	1830.71	+	10382.5i	0.538837	+	3.05589i
$227$	−2444.50			−0.714744			−0.357372	−	0.933962i	$-0.616327\pi$
$227$	−2444.50			−0.714744			−0.357372	+	0.933962i	$0.616327\pi$
$228$		0			0
$229$	225.313			0.0650178			0.0325089	−	0.999471i	$-0.489650\pi$
$229$	225.313			0.0650178			0.0325089	+	0.999471i	$0.489650\pi$
$230$	−264.291	−	1498.87i	−0.0757689	−	0.429707i
$231$		0			0
$232$	2524.08	−	918.691i	0.714285	−	0.259978i
$233$	−1158.16	−	421.534i	−0.325636	−	0.118522i	0.174029	−	0.984741i	$-0.444321\pi$
$233$	−1158.16	−	421.534i	−0.325636	−	0.118522i	−0.499665	+	0.866219i	$0.666544\pi$
$234$		0			0
$235$	−697.820	+	1208.66i	−0.193705	+	0.335508i
$236$	2335.86	+	4045.83i	0.644287	+	1.11594i
$237$		0			0
$238$	−3.96558	+	22.4899i	−0.00108004	+	0.00612523i
$239$	1193.70	+	2067.54i	0.323070	+	0.559574i	0.981120	−	0.193400i	$-0.0619516\pi$
$239$	1193.70	+	2067.54i	0.323070	+	0.559574i	−0.658050	+	0.752975i	$0.728618\pi$
$240$		0			0
$241$	−1170.63	−	982.276i	−0.312892	−	0.262548i	0.472794	−	0.881173i	$-0.343245\pi$
$241$	−1170.63	−	982.276i	−0.312892	−	0.262548i	−0.785686	+	0.618625i	$0.787690\pi$
$242$	−6703.87	−	2440.01i	−1.78075	−	0.648140i
$243$		0			0
$244$	143.858	−	120.711i	0.0377441	−	0.0316711i
$245$	650.466	+	3688.97i	0.169619	+	0.961959i
$246$		0			0
$247$	2541.70	−	2182.37i	0.654755	−	0.562189i
$248$	−8540.13			−2.18669
$249$		0			0
$250$	−5425.50	+	4552.54i	−1.37256	+	1.15171i
$251$	−5132.44	+	1868.06i	−1.29067	+	0.469764i	−0.893945	−	0.448176i	$-0.852074\pi$
$251$	−5132.44	+	1868.06i	−1.29067	+	0.469764i	−0.396720	+	0.917940i	$0.629852\pi$
$252$		0			0
$253$	−1697.33	−	1424.23i	−0.421781	−	0.353916i
$254$	1859.97	−	3221.56i	0.459467	−	0.795821i
$255$		0			0
$256$	−1427.07	+	8093.30i	−0.348405	+	1.97590i
$257$	893.499	−	5067.29i	0.216867	−	1.22992i	−0.660769	−	0.750589i	$-0.729770\pi$
$257$	893.499	−	5067.29i	0.216867	−	1.22992i	0.877636	−	0.479327i	$-0.159119\pi$
$258$		0			0
$259$	−4210.71	+	7293.17i	−1.01020	+	1.74971i
$260$	−3677.17	−	3085.51i	−0.877108	−	0.735981i
$261$		0			0
$262$	19.6483	−	7.15141i	0.00463312	−	0.00168632i
$263$	2709.39	−	2273.45i	0.635241	−	0.533030i	−0.267312	−	0.963610i	$-0.586135\pi$
$263$	2709.39	−	2273.45i	0.635241	−	0.533030i	0.902553	+	0.430580i	$0.141691\pi$
$264$		0			0
$265$	−248.548			−0.0576159
$266$	−5803.35	+	10320.4i	−1.33769	+	2.37889i
$267$		0			0
$268$	992.521	+	5628.87i	0.226223	+	1.28298i
$269$	3470.12	−	2911.78i	0.786532	−	0.659979i	−0.158352	−	0.987383i	$-0.550618\pi$
$269$	3470.12	−	2911.78i	0.786532	−	0.659979i	0.944884	+	0.327404i	$0.106174\pi$
$270$		0			0
$271$	2619.55	+	953.438i	0.587182	+	0.213717i	0.618490	−	0.785793i	$-0.287745\pi$
$271$	2619.55	+	953.438i	0.587182	+	0.213717i	−0.0313075	+	0.999510i	$0.509967\pi$
$272$	7.98809	+	6.70280i	0.00178070	+	0.00149418i
$273$		0			0
$274$	−2155.74	−	3733.85i	−0.475303	−	0.823248i
$275$	−644.806	+	3656.88i	−0.141394	+	0.801883i
$276$		0			0
$277$	−715.482	−	1239.25i	−0.155196	−	0.268807i	0.777935	−	0.628345i	$-0.216267\pi$
$277$	−715.482	−	1239.25i	−0.155196	−	0.268807i	−0.933130	+	0.359539i	$0.882934\pi$
$278$	−4827.83	+	8362.04i	−1.04156	+	1.80404i
$279$		0			0
$280$	7997.56	+	2910.87i	1.70695	+	0.621278i
$281$	7973.14	−	2901.99i	1.69266	−	0.616078i	0.697704	−	0.716386i	$-0.254205\pi$
$281$	7973.14	−	2901.99i	1.69266	−	0.616078i	0.994956	+	0.100308i	$0.0319829\pi$
$282$		0			0
$283$	−1171.22	−	6642.33i	−0.246014	−	1.39521i	−0.818126	−	0.575039i	$-0.804987\pi$
$283$	−1171.22	−	6642.33i	−0.246014	−	1.39521i	0.572112	−	0.820176i	$-0.306124\pi$
$284$	−4056.79			−0.847627
$285$		0			0
$286$	−10470.6			−2.16482
$287$	−161.415	−	915.428i	−0.0331986	−	0.188279i
$288$		0			0
$289$	4616.69	−	1680.34i	0.939688	−	0.342018i
$290$	2316.90	+	843.284i	0.469149	+	0.170756i
$291$		0			0
$292$	6493.28	−	11246.7i	1.30134	−	2.25398i
$293$	−3990.52	−	6911.78i	−0.795660	−	1.37812i	−0.922419	−	0.386190i	$-0.873791\pi$
$293$	−3990.52	−	6911.78i	−0.795660	−	1.37812i	0.126759	−	0.991934i	$-0.459542\pi$
$294$		0			0
$295$	−373.559	+	2118.56i	−0.0737270	+	0.418126i
$296$	5705.19	+	9881.68i	1.12030	+	1.94041i
$297$		0			0
$298$	−5655.71	−	4745.70i	−1.09942	−	0.922521i
$299$	−1595.73	−	580.800i	−0.308641	−	0.112336i
$300$		0			0
$301$	3057.25	−	2565.34i	0.585438	−	0.491241i
$302$	−2039.44	−	11566.2i	−0.388598	−	2.20385i
$303$		0			0
$304$	2756.18	+	4651.13i	0.519992	+	0.877502i
$305$	86.4752			0.0162346
$306$		0			0
$307$	3138.81	−	2633.77i	0.583522	−	0.489633i	−0.302580	−	0.953124i	$-0.597848\pi$
$307$	3138.81	−	2633.77i	0.583522	−	0.489633i	0.886102	+	0.463491i	$0.153403\pi$
$308$	23208.7	−	8447.29i	4.29364	−	1.56276i
$309$		0			0
$310$	−6005.14	−	5038.91i	−1.10022	−	0.923196i
$311$	4343.64	−	7523.40i	0.791978	−	1.37175i	−0.132763	−	0.991148i	$-0.542385\pi$
$311$	4343.64	−	7523.40i	0.791978	−	1.37175i	0.924741	−	0.380598i	$-0.124282\pi$
$312$		0			0
$313$	1160.01	−	6578.73i	0.209481	−	1.18803i	−0.680750	−	0.732516i	$-0.738346\pi$
$313$	1160.01	−	6578.73i	0.209481	−	1.18803i	0.890231	−	0.455510i	$-0.150543\pi$
$314$	−2303.39	+	13063.2i	−0.413974	+	2.34777i
$315$		0			0
$316$	−5666.85	+	9815.28i	−1.00881	+	1.74732i
$317$	7872.02	+	6605.41i	1.39475	+	1.17034i	0.963373	+	0.268166i	$0.0864175\pi$
$317$	7872.02	+	6605.41i	1.39475	+	1.17034i	0.431380	+	0.902170i	$0.358027\pi$
$318$		0			0
$319$	3372.95	−	1227.65i	0.592002	−	0.215471i
$320$	−2840.96	+	2383.85i	−0.496295	+	0.416441i
$321$		0			0
$322$	6001.78			1.03871
$323$	−13.2285	+	0.150130i	−0.00227881	+	2.58621e-5i
$324$		0			0
$325$	494.186	+	2802.67i	0.0843461	+	0.478351i
$326$	−6968.92	+	5847.61i	−1.18396	+	0.993464i
$327$		0			0
$328$	−1183.51	−	430.763i	−0.199233	−	0.0725150i
$329$	−4215.95	−	3537.60i	−0.706482	−	0.592809i
$330$		0			0
$331$	867.289	+	1502.19i	0.144020	+	0.249449i	0.929007	−	0.370063i	$-0.120664\pi$
$331$	867.289	+	1502.19i	0.144020	+	0.249449i	−0.784987	+	0.619512i	$0.787330\pi$
$332$	3394.82	−	19253.0i	0.561190	−	3.18267i
$333$		0			0
$334$	2180.43	+	3776.62i	0.357210	+	0.618705i
$335$	−1315.99	+	2279.36i	−0.214627	+	0.371745i
$336$		0			0
$337$	−7972.22	−	2901.65i	−1.28865	−	0.469029i	−0.395365	−	0.918524i	$-0.629382\pi$
$337$	−7972.22	−	2901.65i	−1.28865	−	0.469029i	−0.893283	+	0.449495i	$0.851604\pi$
$338$	2584.35	−	940.626i	0.415888	−	0.151371i
$339$		0			0
$340$	3.29166	+	18.6679i	0.000525045	+	0.00297768i
$341$	−11412.2			−1.81234
$342$		0			0
$343$	−4772.88			−0.751344
$344$	−938.991	−	5325.28i	−0.147171	−	0.834651i
$345$		0			0
$346$	16055.1	−	5843.57i	2.49459	−	0.907955i
$347$	−1475.13	−	536.902i	−0.228210	−	0.0830618i	0.225384	−	0.974270i	$-0.427636\pi$
$347$	−1475.13	−	536.902i	−0.228210	−	0.0830618i	−0.453594	+	0.891208i	$0.649859\pi$
$348$		0			0
$349$	3113.45	−	5392.65i	0.477533	−	0.827112i	−0.522135	−	0.852863i	$-0.674864\pi$
$349$	3113.45	−	5392.65i	0.477533	−	0.827112i	0.999668	+	0.0257507i	$0.00819762\pi$
$350$	−5029.15	−	8710.75i	−0.768056	−	1.33031i
$351$		0			0
$352$	38.4002	−	217.778i	0.00581459	−	0.0329762i
$353$	−3022.18	−	5234.56i	−0.455678	−	0.789257i	0.543049	−	0.839701i	$-0.317270\pi$
$353$	−3022.18	−	5234.56i	−0.455678	−	0.789257i	−0.998727	+	0.0504440i	$0.983936\pi$
$354$		0			0
$355$	−1431.03	−	1200.78i	−0.213947	−	0.179523i
$356$	17641.8	+	6421.08i	2.62644	+	0.955946i
$357$		0			0
$358$	390.793	−	327.914i	0.0576929	−	0.0484101i
$359$	1718.83	+	9747.95i	0.252691	+	1.43308i	0.801930	+	0.597418i	$0.203807\pi$
$359$	1718.83	+	9747.95i	0.252691	+	1.43308i	−0.549239	+	0.835665i	$0.685082\pi$
$360$		0			0
$361$	−6496.93	−	2199.03i	−0.947213	−	0.320606i
$362$	5410.18			0.785505
$363$		0			0
$364$	14500.4	−	12167.3i	2.08799	−	1.75203i
$365$	5619.42	−	2045.30i	0.805847	−	0.293304i
$366$		0			0
$367$	−6820.82	−	5723.35i	−0.970147	−	0.814050i	0.0124266	−	0.999923i	$-0.496044\pi$
$367$	−6820.82	−	5723.35i	−0.970147	−	0.814050i	−0.982574	+	0.185873i	$0.940489\pi$
$368$	1370.26	−	2373.36i	0.194102	−	0.336195i
$369$		0			0
$370$	−1818.76	+	10314.7i	−0.255548	+	1.44928i
$371$	170.196	−	965.228i	0.0238170	−	0.135073i
$372$		0			0
$373$	−3961.67	+	6861.81i	−0.549939	+	0.952523i	0.448339	+	0.893864i	$0.352016\pi$
$373$	−3961.67	+	6861.81i	−0.549939	+	0.952523i	−0.998278	+	0.0586591i	$0.981318\pi$
$374$	31.6746	+	26.5781i	0.00437929	+	0.00367466i
$375$		0			0
$376$	−7007.15	+	2550.39i	−0.961080	+	0.349805i
$377$	2107.36	−	1768.29i	0.287890	−	0.241569i
$378$		0			0
$379$	566.318			0.0767541			0.0383771	−	0.999263i	$-0.487781\pi$
$379$	566.318			0.0767541			0.0383771	+	0.999263i	$0.487781\pi$
$380$	−1596.67	+	9697.47i	−0.215546	+	1.30913i
$381$		0			0
$382$	−1938.31	−	10992.7i	−0.259614	−	1.47234i
$383$	1836.22	−	1540.78i	0.244978	−	0.205561i	−0.512028	−	0.858969i	$-0.671106\pi$
$383$	1836.22	−	1540.78i	0.244978	−	0.205561i	0.757006	+	0.653408i	$0.226661\pi$
$384$		0			0
$385$	10687.2	+	3889.82i	1.41473	+	0.514918i
$386$	−2178.54	−	1828.01i	−0.287266	−	0.241045i
$387$		0			0
$388$	3190.93	+	5526.86i	0.417513	+	0.723154i
$389$	1961.56	−	11124.5i	0.255668	−	1.44997i	−0.538684	−	0.842508i	$-0.681078\pi$
$389$	1961.56	−	11124.5i	0.255668	−	1.44997i	0.794352	−	0.607458i	$-0.207811\pi$
$390$		0			0
$391$	3.35297	+	5.80752i	0.000433676	+	0.000751148i
$392$	−10007.0	+	17332.7i	−1.28937	+	2.23325i
$393$		0			0
$394$	−2766.23	−	1006.83i	−0.353707	−	0.128739i
$395$	−4904.22	+	1784.99i	−0.624704	+	0.227374i
$396$		0			0
$397$	297.045	+	1684.63i	0.0375523	+	0.212970i	0.997810	−	0.0661451i	$-0.0210700\pi$
$397$	297.045	+	1684.63i	0.0375523	+	0.212970i	−0.960258	+	0.279115i	$0.909959\pi$
$398$	−5462.16			−0.687924
$399$		0			0
$400$	−4592.80			−0.574100
$401$	1599.12	+	9069.07i	0.199143	+	1.12940i	0.906394	+	0.422434i	$0.138824\pi$
$401$	1599.12	+	9069.07i	0.199143	+	1.12940i	−0.707251	+	0.706963i	$0.750065\pi$
$402$		0			0
$403$	−8218.97	+	2991.46i	−1.01592	+	0.369765i
$404$	−5203.92	−	1894.07i	−0.640854	−	0.233252i
$405$		0			0
$406$	−4861.38	+	8420.16i	−0.594252	+	1.02927i
$407$	7623.88	+	13204.9i	0.928505	+	1.60822i
$408$		0			0
$409$	−1876.27	+	10640.9i	−0.226835	+	1.28645i	0.632310	+	0.774715i	$0.282107\pi$
$409$	−1876.27	+	10640.9i	−0.226835	+	1.28645i	−0.859146	+	0.511731i	$0.829004\pi$
$410$	−578.045	−	1001.20i	−0.0696283	−	0.120600i
$411$		0			0
$412$	10136.1	+	8505.18i	1.21206	+	1.01704i
$413$	−7971.54	−	2901.40i	−0.949768	−	0.345687i
$414$		0			0
$415$	6896.25	−	5786.64i	0.815719	−	0.684470i
$416$	−29.4303	−	166.907i	−0.00346860	−	0.0196714i
$417$		0			0
$418$	10928.9	+	18442.8i	1.27882	+	2.15805i
$419$	15330.6			1.78747			0.893735	−	0.448596i	$-0.148076\pi$
$419$	15330.6			1.78747			0.893735	+	0.448596i	$0.148076\pi$
$420$		0			0
$421$	−126.027	+	105.750i	−0.0145896	+	0.0122421i	−0.650053	−	0.759889i	$-0.725253\pi$
$421$	−126.027	+	105.750i	−0.0145896	+	0.0122421i	0.635464	+	0.772131i	$0.280809\pi$
$422$	4018.97	−	1462.79i	0.463603	−	0.168738i
$423$		0			0
$424$	−1017.30	−	853.612i	−0.116519	−	0.0977714i
$425$	5.61921	−	9.73276i	0.000641345	−	0.00111084i
$426$		0			0
$427$	−59.2147	+	335.823i	−0.00671101	+	0.0380600i
$428$	928.574	−	5266.20i	0.104870	−	0.594747i
$429$		0			0
$430$	2481.79	−	4298.59i	0.278332	−	0.482085i
$431$	−9869.95	−	8281.87i	−1.10306	−	0.925577i	−0.105433	−	0.994426i	$-0.533623\pi$
$431$	−9869.95	−	8281.87i	−1.10306	−	0.925577i	−0.997627	+	0.0688493i	$0.978067\pi$
$432$		0			0
$433$	9951.14	−	3621.92i	1.10444	−	0.401982i	0.275487	−	0.961305i	$-0.411161\pi$
$433$	9951.14	−	3621.92i	1.10444	−	0.401982i	0.828950	+	0.559323i	$0.188939\pi$
$434$	23680.5	−	19870.3i	2.61912	−	2.19771i
$435$		0			0
$436$	−23602.8			−2.59259
$437$	642.561	+	3416.93i	0.0703383	+	0.374036i
$438$		0			0
$439$	2617.95	+	14847.1i	0.284619	+	1.61415i	0.706643	+	0.707570i	$0.250209\pi$
$439$	2617.95	+	14847.1i	0.284619	+	1.61415i	−0.422024	+	0.906584i	$0.638680\pi$
$440$	11804.5	−	9905.11i	1.27899	−	1.07320i
$441$		0			0
$442$	29.7786	+	10.8385i	0.00320458	+	0.00116637i
$443$	277.823	+	233.122i	0.0297964	+	0.0250021i	0.657564	−	0.753398i	$-0.271587\pi$
$443$	277.823	+	233.122i	0.0297964	+	0.0250021i	−0.627768	+	0.778401i	$0.716031\pi$
$444$		0			0
$445$	4322.54	+	7486.85i	0.460467	+	0.797552i
$446$	−3904.95	+	22146.1i	−0.414584	+	2.35123i
$447$		0			0
$448$	−7312.20	−	12665.1i	−0.771136	−	1.33565i
$449$	−6292.87	+	10899.6i	−0.661423	+	1.14562i	0.318819	+	0.947816i	$0.396714\pi$
$449$	−6292.87	+	10899.6i	−0.661423	+	1.14562i	−0.980242	+	0.197802i	$0.936620\pi$
$450$		0			0
$451$	−1581.53	−	575.632i	−0.165125	−	0.0601007i
$452$	−32427.3	+	11802.6i	−3.37445	+	1.22820i
$453$		0			0
$454$	−2081.83	−	11806.7i	−0.215210	−	1.22052i
$455$	8716.43			0.898094
$456$		0			0
$457$	19220.1			1.96735			0.983673	−	0.179965i	$-0.0575984\pi$
$457$	19220.1			1.96735			0.983673	+	0.179965i	$0.0575984\pi$
$458$	191.886	+	1088.24i	0.0195769	+	0.111026i
$459$		0			0
$460$	4681.38	−	1703.88i	0.474501	−	0.172704i
$461$	5961.69	+	2169.88i	0.602307	+	0.219222i	0.625134	−	0.780518i	$-0.285044\pi$
$461$	5961.69	+	2169.88i	0.602307	+	0.219222i	−0.0228268	+	0.999739i	$0.507267\pi$
$462$		0			0
$463$	−2665.67	+	4617.07i	−0.267568	+	0.463442i	−0.968233	−	0.250049i	$-0.919553\pi$
$463$	−2665.67	+	4617.07i	−0.267568	+	0.463442i	0.700665	+	0.713490i	$0.252887\pi$
$464$	2219.79	+	3844.79i	0.222093	+	0.384677i
$465$		0			0
$466$	1049.63	−	5952.77i	0.104342	−	0.591752i
$467$	−2903.91	−	5029.71i	−0.287745	−	0.498388i	0.685526	−	0.728048i	$-0.259572\pi$
$467$	−2903.91	−	5029.71i	−0.287745	−	0.498388i	−0.973271	+	0.229659i	$0.926239\pi$
$468$		0			0
$469$	−7950.66	−	6671.39i	−0.782787	−	0.656836i
$470$	−6432.00	−	2341.06i	−0.631247	−	0.229755i
$471$		0			0
$472$	−8804.91	+	7388.20i	−0.858642	+	0.720486i
$473$	−1254.78	−	7116.21i	−0.121976	−	0.691762i
$474$		0			0
$475$	4420.77	−	3795.78i	0.427029	−	0.366658i
$476$	−74.7502			−0.00719783
$477$		0			0
$478$	−8969.42	+	7526.24i	−0.858268	+	0.720172i
$479$	−7365.10	+	2680.68i	−0.702547	+	0.255706i	−0.668498	−	0.743714i	$-0.733063\pi$
$479$	−7365.10	+	2680.68i	−0.702547	+	0.255706i	−0.0340492	+	0.999420i	$0.510840\pi$
$480$		0			0
$481$	8952.02	+	7511.64i	0.848601	+	0.712061i
$482$	3747.34	−	6490.58i	0.354121	−	0.613356i
$483$		0			0
$484$	4054.95	−	22996.8i	0.380818	−	2.15973i
$485$	−510.305	+	2894.08i	−0.0477768	+	0.270956i
$486$		0			0
$487$	453.583	−	785.629i	0.0422049	−	0.0731011i	−0.844151	−	0.536105i	$-0.819895\pi$
$487$	453.583	−	785.629i	0.0422049	−	0.0731011i	0.886356	+	0.463004i	$0.153228\pi$
$488$	353.938	+	296.990i	0.0328320	+	0.0275494i
$489$		0			0
$490$	−17263.4	+	6283.37i	−1.59159	+	0.579293i
$491$	−9362.55	+	7856.11i	−0.860542	+	0.722080i	−0.962085	−	0.272751i	$-0.912067\pi$
$491$	−9362.55	+	7856.11i	−0.860542	+	0.722080i	0.101543	+	0.994831i	$0.467622\pi$
$492$		0			0
$493$	−10.8635			−0.000992430
$494$	12705.2	+	10417.6i	1.15716	+	0.948801i
$495$		0			0
$496$	−2451.09	−	13900.8i	−0.221889	−	1.25840i
$497$	5643.07	−	4735.10i	0.509309	−	0.427361i
$498$		0			0
$499$	−16468.4	−	5994.00i	−1.47741	−	0.537732i	−0.527307	−	0.849675i	$-0.676798\pi$
$499$	−16468.4	−	5994.00i	−1.47741	−	0.537732i	−0.950101	+	0.311943i	$0.899020\pi$
$500$	−17758.9	−	14901.5i	−1.58840	−	1.33283i
$501$		0			0
$502$	−13393.5	−	23198.3i	−1.19080	−	2.06253i
$503$	−1352.90	+	7672.65i	−0.119926	+	0.680133i	0.864267	+	0.503033i	$0.167783\pi$
$503$	−1352.90	+	7672.65i	−0.119926	+	0.680133i	−0.984193	+	0.177100i	$0.943329\pi$
$504$		0			0
$505$	−1275.05	−	2208.45i	−0.112354	−	0.194603i
$506$	5433.38	−	9410.89i	0.477358	−	0.826809i
$507$		0			0
$508$	11441.9	+	4164.49i	0.999311	+	0.363720i
$509$	17576.7	−	6397.40i	1.53060	−	0.557092i	0.566830	−	0.823835i	$-0.308170\pi$
$509$	17576.7	−	6397.40i	1.53060	−	0.557092i	0.963768	+	0.266743i	$0.0859474\pi$
$510$		0			0
$511$	4094.90	+	23223.3i	0.354497	+	2.01045i
$512$	−20353.0			−1.75681
$513$		0			0
$514$	25235.4			2.16554
$515$	1058.03	+	6000.39i	0.0905289	+	0.513415i
$516$		0			0
$517$	−9363.70	+	3408.11i	−0.796547	+	0.289920i
$518$	−38811.3	−	14126.2i	−3.29203	−	1.19820i
$519$		0			0
$520$	5905.05	−	10227.8i	0.497987	−	0.862539i
$521$	−7347.85	−	12726.8i	−0.617879	−	1.07020i	−0.989872	−	0.141963i	$-0.954659\pi$
$521$	−7347.85	−	12726.8i	−0.617879	−	1.07020i	0.371993	−	0.928236i	$-0.378675\pi$
$522$		0			0
$523$	580.974	−	3294.87i	0.0485741	−	0.275477i	−0.950841	−	0.309680i	$-0.899778\pi$
$523$	580.974	−	3294.87i	0.0485741	−	0.275477i	0.999415	+	0.0342028i	$0.0108892\pi$
$524$	34.2204	+	59.2715i	0.00285291	+	0.00494139i
$525$		0			0
$526$	13288.0	+	11149.9i	1.10149	+	0.924259i
$527$	32.4566	+	11.8132i	0.00268279	+	0.000976456i
$528$		0			0
$529$	−7970.39	+	6687.95i	−0.655083	+	0.549680i
$530$	−211.674	−	1200.46i	−0.0173482	−	0.0983865i
$531$		0			0
$532$	−36566.4	−	12841.0i	−2.97999	−	1.04648i
$533$	−1289.89			−0.104825
$534$		0			0
$535$	1886.31	−	1582.80i	0.152434	−	0.127907i
$536$	−13214.5	+	4809.67i	−1.06488	+	0.387586i
$537$		0			0
$538$	17018.9	+	14280.5i	1.36382	+	1.14438i
$539$	−13372.5	+	23161.8i	−1.06863	+	1.85093i
$540$		0			0
$541$	276.383	−	1567.44i	0.0219642	−	0.124565i	−0.971854	−	0.235583i	$-0.924300\pi$
$541$	276.383	−	1567.44i	0.0219642	−	0.124565i	0.993818	+	0.111018i	$0.0354111\pi$
$542$	−2374.09	+	13464.2i	−0.188148	+	1.06704i
$543$		0			0
$544$	−0.334641	+	0.579616i	−2.63743e−5	+	4.56817e-5i
$545$	−8325.86	−	6986.22i	−0.654386	−	0.549095i
$546$		0			0
$547$	−3803.34	+	1384.30i	−0.297293	+	0.108206i	−0.486360	−	0.873758i	$-0.661676\pi$
$547$	−3803.34	+	1384.30i	−0.297293	+	0.108206i	0.189068	+	0.981964i	$0.439453\pi$
$548$	10810.7	−	9071.29i	0.842723	−	0.707128i
$549$		0			0
$550$	−18211.5			−1.41189
$551$	−5314.23	−	1866.20i	−0.410878	−	0.144288i
$552$		0			0
$553$	−3573.73	−	20267.6i	−0.274811	−	1.55853i
$554$	5376.13	−	4511.11i	0.412292	−	0.345954i
$555$		0			0
$556$	−29699.1	−	10809.6i	−2.26533	−	0.824512i
$557$	6337.57	+	5317.86i	0.482103	+	0.404533i	0.851186	−	0.524864i	$-0.175884\pi$
$557$	6337.57	+	5317.86i	0.482103	+	0.404533i	−0.369083	+	0.929397i	$0.620328\pi$
$558$		0			0
$559$	−2769.03	−	4796.11i	−0.209513	−	0.362887i
$560$	−2442.68	+	13853.1i	−0.184325	+	1.04536i
$561$		0			0
$562$	20806.6	+	36038.0i	1.56169	+	2.70493i
$563$	6349.65	−	10997.9i	0.475321	−	0.823281i	−0.524279	−	0.851546i	$-0.675665\pi$
$563$	6349.65	−	10997.9i	0.475321	−	0.823281i	0.999600	+	0.0282659i	$0.00899850\pi$
$564$		0			0
$565$	−14932.2	−	5434.86i	−1.11186	−	0.404684i
$566$	31084.3	−	11313.8i	2.30843	−	0.840200i
$567$		0			0
$568$	−1733.19	−	9829.41i	−0.128034	−	0.726114i
$569$	−2775.56			−0.204495			−0.102247	−	0.994759i	$-0.532603\pi$
$569$	−2775.56			−0.204495			−0.102247	+	0.994759i	$0.532603\pi$
$570$		0			0
$571$	12723.9			0.932537			0.466269	−	0.884643i	$-0.345598\pi$
$571$	12723.9			0.932537			0.466269	+	0.884643i	$0.345598\pi$
$572$	−5951.38	−	33751.9i	−0.435034	−	2.46720i
$573$		0			0
$574$	4283.96	−	1559.23i	0.311514	−	0.113382i
$575$	−2775.46	−	1010.18i	−0.201295	−	0.0732653i
$576$		0			0
$577$	2815.52	−	4876.63i	0.203140	−	0.351849i	−0.746399	−	0.665499i	$-0.768219\pi$
$577$	2815.52	−	4876.63i	0.203140	−	0.351849i	0.949538	+	0.313651i	$0.101552\pi$
$578$	12047.6	+	20867.1i	0.866981	+	1.50165i
$579$		0			0
$580$	−1401.42	+	7947.84i	−0.100329	+	0.568993i
$581$	17749.9	+	30743.8i	1.26745	+	2.19529i
$582$		0			0
$583$	−1359.42	−	1140.69i	−0.0965718	−	0.0810333i
$584$	30024.4	+	10928.0i	2.12743	+	0.774320i
$585$		0			0
$586$	29984.7	−	25160.1i	2.11375	−	1.77364i
$587$	−3296.82	−	18697.2i	−0.231813	−	1.31468i	−0.849222	−	0.528036i	$-0.822929\pi$
$587$	−3296.82	−	18697.2i	−0.231813	−	1.31468i	0.617409	−	0.786642i	$-0.288182\pi$
$588$		0			0
$589$	13847.8	+	11354.4i	0.968742	+	0.794313i
$590$	−10550.6			−0.736203
$591$		0			0
$592$	−14447.0	+	12122.5i	−1.00299	+	0.841607i
$593$	2738.32	−	996.668i	0.189628	−	0.0690190i	−0.245461	−	0.969407i	$-0.578939\pi$
$593$	2738.32	−	996.668i	0.189628	−	0.0690190i	0.435089	+	0.900388i	$0.356717\pi$
$594$		0			0
$595$	−26.3681	−	22.1254i	−0.00181678	−	0.00152446i
$596$	12083.1	−	20928.5i	0.830442	−	1.43837i
$597$		0			0
$598$	1446.21	−	8201.87i	0.0988963	−	0.560869i
$599$	−3247.07	+	18415.0i	−0.221488	+	1.25612i	0.647797	+	0.761813i	$0.275690\pi$
$599$	−3247.07	+	18415.0i	−0.221488	+	1.25612i	−0.869286	+	0.494310i	$0.835421\pi$
$600$		0			0
$601$	12297.4	−	21299.7i	0.834645	−	1.44565i	−0.0596744	−	0.998218i	$-0.519006\pi$
$601$	12297.4	−	21299.7i	0.834645	−	1.44565i	0.894319	−	0.447429i	$-0.147660\pi$
$602$	14994.0	+	12581.5i	1.01513	+	0.851797i
$603$		0			0
$604$	36124.5	−	13148.3i	2.43359	−	0.885753i
$605$	8237.23	−	6911.86i	0.553539	−	0.464475i
$606$		0			0
$607$	8927.76			0.596980			0.298490	−	0.954413i	$-0.403517\pi$
$607$	8927.76			0.596980			0.298490	+	0.954413i	$0.403517\pi$
$608$	−263.270	+	226.051i	−0.0175609	+	0.0150782i
$609$		0			0
$610$	73.6459	+	417.667i	0.00488825	+	0.0277227i
$611$	−5850.28	+	4908.97i	−0.387360	+	0.325034i
$612$		0			0
$613$	−6800.54	−	2475.19i	−0.448077	−	0.163087i	0.108119	−	0.994138i	$-0.465517\pi$
$613$	−6800.54	−	2475.19i	−0.448077	−	0.163087i	−0.556196	+	0.831051i	$0.687740\pi$
$614$	15394.0	+	12917.1i	1.01181	+	0.849009i
$615$		0			0
$616$	30382.9	+	52624.8i	1.98728	+	3.44206i
$617$	1209.90	−	6861.70i	0.0789447	−	0.447718i	−0.919555	−	0.392961i	$-0.871451\pi$
$617$	1209.90	−	6861.70i	0.0789447	−	0.447718i	0.998500	−	0.0547564i	$-0.0174382\pi$
$618$		0			0
$619$	10772.8	+	18659.0i	0.699508	+	1.21158i	0.968637	+	0.248479i	$0.0799307\pi$
$619$	10772.8	+	18659.0i	0.699508	+	1.21158i	−0.269130	+	0.963104i	$0.586736\pi$
$620$	12829.6	−	22221.6i	0.831050	−	1.43942i
$621$		0			0
$622$	40036.5	+	14572.1i	2.58090	+	0.939369i
$623$	−32034.8	+	11659.7i	−2.06011	+	0.749818i
$624$		0			0
$625$	−326.584	−	1852.15i	−0.0209014	−	0.118537i
$626$	32762.5			2.09178
$627$		0			0
$628$	−43418.3			−2.75889
$629$	−8.01351	−	45.4469i	−0.000507980	−	0.00288090i
$630$		0			0
$631$	−24103.4	+	8772.92i	−1.52067	+	0.553478i	−0.961315	−	0.275451i	$-0.911173\pi$
$631$	−24103.4	+	8772.92i	−1.52067	+	0.553478i	−0.559353	+	0.828929i	$0.688950\pi$
$632$	−26203.0	−	9537.13i	−1.64921	−	0.600264i
$633$		0			0
$634$	−25199.3	+	43646.5i	−1.57854	+	2.73411i
$635$	2803.45	+	4855.72i	0.175199	+	0.303454i
$636$		0			0
$637$	−3559.37	+	20186.2i	−0.221393	+	1.25558i
$638$	8801.98	+	15245.5i	0.546197	+	0.946041i
$639$		0			0
$640$	−14123.0	−	11850.6i	−0.872284	−	0.731933i
$641$	3534.42	+	1286.42i	0.217786	+	0.0792678i	0.448609	−	0.893728i	$-0.351920\pi$
$641$	3534.42	+	1286.42i	0.217786	+	0.0792678i	−0.230823	+	0.972996i	$0.574142\pi$
$642$		0			0
$643$	−4012.59	+	3366.96i	−0.246098	+	0.206501i	−0.757490	−	0.652847i	$-0.773574\pi$
$643$	−4012.59	+	3366.96i	−0.246098	+	0.206501i	0.511392	+	0.859348i	$0.329130\pi$
$644$	3411.34	+	19346.7i	0.208736	+	1.18380i
$645$		0			0
$646$	−11.9911	−	63.7645i	−0.000730313	−	0.00388356i
$647$	−1791.60			−0.108864			−0.0544320	−	0.998517i	$-0.517335\pi$
$647$	−1791.60			−0.108864			−0.0544320	+	0.998517i	$0.517335\pi$
$648$		0			0
$649$	−11766.1	+	9872.90i	−0.711646	+	0.597142i
$650$	−13115.7	+	4773.73i	−0.791448	+	0.288064i
$651$		0			0
$652$	−22810.8	−	19140.5i	−1.37015	−	1.14970i
$653$	3041.86	−	5268.66i	0.182293	−	0.315741i	−0.760368	−	0.649492i	$-0.774981\pi$
$653$	3041.86	−	5268.66i	0.182293	−	0.315741i	0.942661	+	0.333752i	$0.108315\pi$
$654$		0			0
$655$	−5.47265	+	31.0369i	−0.000326464	+	0.00185147i
$656$	361.478	−	2050.04i	0.0215142	−	0.122013i
$657$		0			0
$658$	13495.8	−	23375.4i	0.799574	−	1.38490i
$659$	−23608.8	−	19810.1i	−1.39555	−	1.17101i	−0.963034	−	0.269379i	$-0.913182\pi$
$659$	−23608.8	−	19810.1i	−1.39555	−	1.17101i	−0.432515	−	0.901627i	$-0.642374\pi$
$660$		0			0
$661$	−7588.81	+	2762.10i	−0.446551	+	0.162531i	−0.555501	−	0.831516i	$-0.687474\pi$
$661$	−7588.81	+	2762.10i	−0.446551	+	0.162531i	0.108950	+	0.994047i	$0.465251\pi$
$662$	−6516.80	+	5468.24i	−0.382602	+	0.321041i
$663$		0			0
$664$	48099.5			2.81118
$665$	−9097.92	−	15353.0i	−0.530530	−	0.895285i
$666$		0			0
$667$	495.774	+	2811.67i	0.0287803	+	0.163221i
$668$	−10934.6	+	9175.21i	−0.633341	+	0.531436i
$669$		0			0
$670$	−12129.8	−	4414.89i	−0.699426	−	0.254570i
$671$	472.970	+	396.869i	0.0272113	+	0.0228330i
$672$		0			0
$673$	4863.53	+	8423.89i	0.278567	+	0.482492i	0.971029	−	0.238963i	$-0.0768073\pi$
$673$	4863.53	+	8423.89i	0.278567	+	0.482492i	−0.692462	+	0.721454i	$0.743474\pi$
$674$	7225.20	−	40976.2i	0.412915	−	2.34175i
$675$		0			0
$676$	4501.02	+	7795.99i	0.256089	+	0.443559i
$677$	−13853.0	+	23994.0i	−0.786429	+	1.36214i	0.141712	+	0.989908i	$0.454739\pi$
$677$	−13853.0	+	23994.0i	−0.786429	+	1.36214i	−0.928142	+	0.372227i	$0.878594\pi$
$678$		0			0
$679$	−10889.6	−	3963.50i	−0.615472	−	0.224013i
$680$	−43.8253	+	15.9511i	−0.00247150	+	0.000899553i
$681$		0			0
$682$	−9719.13	−	55119.9i	−0.545696	−	3.09479i
$683$	18109.8			1.01457			0.507285	−	0.861778i	$-0.330649\pi$
$683$	18109.8			1.01457			0.507285	+	0.861778i	$0.330649\pi$
$684$		0			0
$685$	6498.51			0.362475
$686$	−4064.78	−	23052.5i	−0.226230	−	1.28302i
$687$		0			0
$688$	8398.49	−	3056.80i	0.465392	−	0.169389i
$689$	−1278.04	−	465.170i	−0.0706671	−	0.0257207i
$690$		0			0
$691$	−1319.21	+	2284.94i	−0.0726267	+	0.125793i	−0.900052	−	0.435783i	$-0.856471\pi$
$691$	−1319.21	+	2284.94i	−0.0726267	+	0.125793i	0.827425	+	0.561576i	$0.189805\pi$
$692$	27962.3	+	48432.1i	1.53608	+	2.66057i
$693$		0			0
$694$	1336.90	−	7581.96i	0.0731242	−	0.414708i
$695$	−7276.78	−	12603.8i	−0.397157	−	0.687896i
$696$		0			0
$697$	3.90206	+	3.27421i	0.000212053	+	0.000177934i
$698$	28697.5	+	10445.0i	1.55618	+	0.566405i
$699$		0			0
$700$	25220.5	−	21162.5i	1.36178	−	1.14267i
$701$	−1096.82	−	6220.39i	−0.0590962	−	0.335151i	0.940898	−	0.338691i	$-0.109984\pi$
$701$	−1096.82	−	6220.39i	−0.0590962	−	0.335151i	−0.999994	+	0.00354027i	$0.998873\pi$
$702$		0			0
$703$	3887.08	−	23608.4i	0.208541	−	1.26658i
$704$	−26478.8			−1.41755
$705$		0			0
$706$	22708.6	−	19054.8i	1.21055	−	1.01577i
$707$	9449.53	−	3439.35i	0.502668	−	0.182956i
$708$		0			0
$709$	−16129.5	−	13534.3i	−0.854382	−	0.716911i	0.106368	−	0.994327i	$-0.466078\pi$
$709$	−16129.5	−	13534.3i	−0.854382	−	0.716911i	−0.960750	+	0.277416i	$0.910522\pi$
$710$	4580.90	−	7934.35i	0.242138	−	0.419396i
$711$		0			0
$712$	−8020.86	+	45488.5i	−0.422183	+	2.39432i
$713$	1576.27	−	8939.47i	0.0827935	−	0.469545i
$714$		0			0
$715$	7890.95	−	13667.5i	0.412734	−	0.714876i
$716$	1279.15	+	1073.34i	0.0667656	+	0.0560230i
$717$		0			0
$718$	−45617.8	+	16603.5i	−2.37109	+	0.863005i
$719$	−10752.4	+	9022.34i	−0.557715	+	0.467978i	−0.877543	−	0.479497i	$-0.840819\pi$
$719$	−10752.4	+	9022.34i	−0.557715	+	0.467978i	0.319829	+	0.947475i	$0.396375\pi$
$720$		0			0
$721$	−24026.8			−1.24106
$722$	5088.06	−	33252.3i	0.262268	−	1.71402i
$723$		0			0
$724$	3075.09	+	17439.7i	0.157852	+	0.895222i
$725$	3665.32	−	3075.57i	0.187761	−	0.157550i
$726$		0			0
$727$	−3622.30	−	1318.41i	−0.184792	−	0.0672587i	0.247967	−	0.968769i	$-0.420238\pi$
$727$	−3622.30	−	1318.41i	−0.184792	−	0.0672587i	−0.432759	+	0.901510i	$0.642460\pi$
$728$	35675.9	+	29935.6i	1.81626	+	1.52402i
$729$		0			0
$730$	14664.3	+	25399.4i	0.743495	+	1.28777i
$731$	−3.79764	+	21.5375i	−0.000192149	+	0.00108973i
$732$		0			0
$733$	−6023.55	−	10433.1i	−0.303526	−	0.525723i	0.673406	−	0.739273i	$-0.264831\pi$
$733$	−6023.55	−	10433.1i	−0.303526	−	0.525723i	−0.976932	+	0.213550i	$0.931497\pi$
$734$	21834.3	−	37818.1i	1.09798	−	1.90176i
$735$		0			0
$736$	165.287	+	60.1595i	0.00827793	+	0.00301292i
$737$	−17658.6	+	6427.19i	−0.882580	+	0.321233i
$738$		0			0
$739$	4354.89	+	24697.8i	0.216776	+	1.22940i	0.877798	+	0.479030i	$0.159012\pi$
$739$	4354.89	+	24697.8i	0.216776	+	1.22940i	−0.661023	+	0.750366i	$0.729877\pi$
$740$	−34283.1			−1.70307
$741$		0			0
$742$	4806.90			0.237826
$743$	34.8023	+	197.374i	0.00171840	+	0.00974554i	0.985655	−	0.168773i	$-0.0539806\pi$
$743$	34.8023	+	197.374i	0.00171840	+	0.00974554i	−0.983936	+	0.178519i	$0.942869\pi$
$744$		0			0
$745$	10457.0	−	3806.03i	0.514247	−	0.187171i
$746$	−36515.8	−	13290.7i	−1.79214	−	0.652286i
$747$		0			0
$748$	−67.6710	+	117.210i	−0.00330788	+	0.00572942i
$749$	4855.07	+	8409.23i	0.236850	+	0.410236i
$750$		0			0
$751$	3146.09	−	17842.4i	0.152866	−	0.866947i	−0.807845	−	0.589396i	$-0.799366\pi$
$751$	3146.09	−	17842.4i	0.152866	−	0.866947i	0.960711	−	0.277552i	$-0.0895229\pi$
$752$	−6162.40	−	10673.6i	−0.298829	−	0.517588i
$753$		0			0
$754$	10335.4	+	8672.39i	0.499193	+	0.418873i
$755$	16634.7	+	6054.52i	0.801851	+	0.291850i
$756$		0			0
$757$	15248.9	−	12795.4i	0.732143	−	0.614341i	−0.198572	−	0.980086i	$-0.563630\pi$
$757$	15248.9	−	12795.4i	0.732143	−	0.614341i	0.930715	+	0.365745i	$0.119186\pi$
$758$	482.300	+	2735.26i	0.0231107	+	0.131067i
$759$		0			0
$760$	−24178.7	+	274.404i	−1.15402	+	0.0130969i
$761$	34118.1			1.62520			0.812602	−	0.582819i	$-0.198050\pi$
$761$	34118.1			1.62520			0.812602	+	0.582819i	$0.198050\pi$
$762$		0			0
$763$	32831.9	−	27549.3i	1.55779	−	1.30714i
$764$	34333.2	−	12496.2i	1.62582	−	0.591752i
$765$		0			0
$766$	9005.60	+	7556.59i	0.424785	+	0.356437i
$767$	−5885.84	+	10194.6i	−0.277086	+	0.479928i
$768$		0			0
$769$	4352.49	−	24684.2i	0.204103	−	1.15752i	−0.694743	−	0.719258i	$-0.744482\pi$
$769$	4352.49	−	24684.2i	0.204103	−	1.15752i	0.898846	−	0.438265i	$-0.144407\pi$
$770$	−9685.77	+	54930.7i	−0.453313	+	2.57087i
$771$		0			0
$772$	4654.32	−	8061.52i	0.216985	−	0.375830i
$773$	5471.15	+	4590.84i	0.254571	+	0.213611i	0.761138	−	0.648590i	$-0.224641\pi$
$773$	5471.15	+	4590.84i	0.254571	+	0.213611i	−0.506566	+	0.862201i	$0.669085\pi$
$774$		0			0
$775$	−14295.2	+	5203.04i	−0.662580	+	0.241159i
$776$	−12028.1	+	10092.7i	−0.556420	+	0.466892i
$777$		0			0
$778$	55401.0			2.55298
$779$	1346.35	+	2272.00i	0.0619229	+	0.104497i
$780$		0			0
$781$	−2316.07	−	13135.1i	−0.106115	−	0.601807i
$782$	−25.1942	+	21.1405i	−0.00115210	+	0.000966728i
$783$		0			0
$784$	−31084.7	−	11313.9i	−1.41603	−	0.515392i
$785$	−15315.8	−	12851.5i	−0.696361	−	0.584317i
$786$		0			0
$787$	2634.37	+	4562.86i	0.119320	+	0.206669i	0.919499	−	0.393093i	$-0.128595\pi$
$787$	2634.37	+	4562.86i	0.119320	+	0.206669i	−0.800178	+	0.599762i	$0.795262\pi$
$788$	1673.20	−	9489.20i	0.0756413	−	0.428983i
$789$		0			0
$790$	−12798.0	−	22166.7i	−0.576368	−	0.998299i
$791$	31331.0	−	54266.9i	1.40835	−	2.43933i
$792$		0			0
$793$	444.659	+	161.843i	0.0199121	+	0.00724741i
$794$	−7883.61	+	2869.40i	−0.352366	+	0.128251i
$795$		0			0
$796$	−3104.63	−	17607.3i	−0.138242	−	0.784011i
$797$	−25762.7			−1.14500			−0.572498	−	0.819906i	$-0.694026\pi$
$797$	−25762.7			−1.14500			−0.572498	+	0.819906i	$0.694026\pi$
$798$		0			0
$799$	30.1584			0.00133533
$800$	−51.1880	−	290.302i	−0.00226221	−	0.0128296i
$801$		0			0
$802$	−42440.8	+	15447.2i	−1.86863	+	0.680124i
$803$	40121.7	+	14603.1i	1.76322	+	0.641759i
$804$		0			0
$805$	−4523.11	+	7834.26i	−0.198036	+	0.343008i
$806$	−21448.1	−	37149.1i	−0.937315	−	1.62348i
$807$		0			0
$808$	2365.97	−	13418.1i	0.103013	−	0.584216i
$809$	740.433	+	1282.47i	0.0321783	+	0.0557344i	0.881666	−	0.471874i	$-0.156422\pi$
$809$	740.433	+	1282.47i	0.0321783	+	0.0557344i	−0.849488	+	0.527608i	$0.823089\pi$
$810$		0			0
$811$	−27059.9	−	22705.9i	−1.17164	−	0.983124i	−0.171644	−	0.985159i	$-0.554908\pi$
$811$	−27059.9	−	22705.9i	−1.17164	−	0.983124i	−0.999998	+	0.00203518i	$0.999352\pi$
$812$	−29905.5	−	10884.7i	−1.29246	−	0.470417i
$813$		0			0
$814$	−57285.7	+	48068.4i	−2.46666	+	2.06978i
$815$	−2381.05	−	13503.6i	−0.102337	−	0.580382i
$816$		0			0
$817$	−5557.58	+	9883.36i	−0.237987	+	0.423225i
$818$	−52992.2			−2.26507
$819$		0			0
$820$	2898.82	−	2432.40i	0.123453	−	0.103589i
$821$	−25174.3	+	9162.69i	−1.07014	+	0.389501i	−0.816230	−	0.577726i	$-0.803940\pi$
$821$	−25174.3	+	9162.69i	−1.07014	+	0.389501i	−0.253913	+	0.967227i	$0.581718\pi$
$822$		0			0
$823$	−18047.9	−	15144.0i	−0.764413	−	0.641418i	0.174859	−	0.984594i	$-0.444053\pi$
$823$	−18047.9	−	15144.0i	−0.764413	−	0.641418i	−0.939271	+	0.343175i	$0.888498\pi$
$824$	−16277.2	+	28192.9i	−0.688159	+	1.19193i
$825$		0			0
$826$	7224.59	−	40972.7i	0.304329	−	1.72594i
$827$	−2209.39	+	12530.1i	−0.0928997	+	0.526860i	0.902471	+	0.430750i	$0.141751\pi$
$827$	−2209.39	+	12530.1i	−0.0928997	+	0.526860i	−0.995371	+	0.0961097i	$0.969360\pi$
$828$		0			0
$829$	11425.4	−	19789.4i	0.478675	−	0.829089i	−0.521026	−	0.853541i	$-0.674451\pi$
$829$	11425.4	−	19789.4i	0.478675	−	0.829089i	0.999701	+	0.0244514i	$0.00778390\pi$
$830$	33822.0	+	28380.0i	1.41443	+	1.18685i
$831$		0			0
$832$	−19069.8	+	6940.83i	−0.794622	+	0.289219i
$833$	62.0073	−	52.0303i	0.00257914	−	0.00216416i
$834$		0			0
$835$	−6572.95			−0.272415
$836$	−53238.4	+	45711.8i	−2.20250	+	1.89112i
$837$		0			0
$838$	13056.2	+	74045.3i	0.538208	+	3.05233i
$839$	−5552.00	+	4658.68i	−0.228458	+	0.191699i	−0.749830	−	0.661630i	$-0.769865\pi$
$839$	−5552.00	+	4658.68i	−0.228458	+	0.191699i	0.521372	+	0.853329i	$0.325420\pi$
$840$		0			0
$841$	18572.0	+	6759.64i	0.761490	+	0.277160i
$842$	−618.090	−	518.639i	−0.0252979	−	0.0212274i
$843$		0			0
$844$	6999.62	+	12123.7i	0.285470	+	0.494449i
$845$	−719.818	+	4082.29i	−0.0293047	+	0.166195i
$846$		0			0
$847$	21201.4	+	36721.9i	0.860082	+	1.48971i
$848$	1097.46	−	1900.85i	0.0444420	−	0.0769758i
$849$		0			0
$850$	51.7938	+	18.8514i	0.00209001	+	0.000760703i
$851$	−11396.8	+	4148.08i	−0.459079	+	0.167091i
$852$		0			0
$853$	6179.49	+	35045.6i	0.248044	+	1.40673i	0.813315	+	0.581823i	$0.197660\pi$
$853$	6179.49	+	35045.6i	0.248044	+	1.40673i	−0.565271	+	0.824905i	$0.691229\pi$
$854$	−1672.42			−0.0670130
$855$		0			0
$856$	13156.5			0.525327
$857$	−6165.17	−	34964.4i	−0.245739	−	1.39365i	−0.818771	−	0.574121i	$-0.805344\pi$
$857$	−6165.17	−	34964.4i	−0.245739	−	1.39365i	0.573032	−	0.819533i	$-0.305767\pi$
$858$		0			0
$859$	−25869.5	+	9415.74i	−1.02754	+	0.373994i	−0.800144	−	0.599808i	$-0.795244\pi$
$859$	−25869.5	+	9415.74i	−1.02754	+	0.373994i	−0.227397	+	0.973802i	$0.573021\pi$
$860$	15267.1	+	5556.78i	0.605354	+	0.220331i
$861$		0			0
$862$	31594.9	−	54724.0i	1.24841	−	2.16231i
$863$	13821.9	+	23940.2i	0.545195	+	0.944305i	0.998595	+	0.0529979i	$0.0168777\pi$
$863$	13821.9	+	23940.2i	0.545195	+	0.944305i	−0.453400	+	0.891307i	$0.649789\pi$
$864$		0			0
$865$	−4471.82	+	25361.0i	−0.175776	+	0.996877i
$866$	25968.3	+	44978.4i	1.01898	+	1.76493i
$867$		0			0
$868$	77511.5	+	65039.8i	3.03100	+	2.54331i
$869$	−35015.3	−	12744.5i	−1.36687	−	0.497501i
$870$		0			0
$871$	−11032.8	+	9257.60i	−0.429198	+	0.360140i
$872$	−10083.9	−	57188.5i	−0.391609	−	2.22092i
$873$		0			0
$874$	−15956.2	+	6013.50i	−0.617535	+	0.232734i
$875$	42096.0			1.62640
$876$		0			0
$877$	−23394.5	+	19630.3i	−0.900770	+	0.755836i	−0.970341	−	0.241741i	$-0.922282\pi$
$877$	−23394.5	+	19630.3i	−0.900770	+	0.755836i	0.0695706	+	0.997577i	$0.477837\pi$
$878$	−69480.5	+	25288.8i	−2.67067	+	0.972046i
$879$		0			0
$880$	19510.6	+	16371.3i	0.747388	+	0.627133i
$881$	−4483.15	+	7765.04i	−0.171443	+	0.296948i	−0.938925	−	0.344123i	$-0.888176\pi$
$881$	−4483.15	+	7765.04i	−0.171443	+	0.296948i	0.767482	+	0.641071i	$0.221510\pi$
$882$		0			0
$883$	2935.50	−	16648.0i	0.111877	−	0.634486i	−0.876372	−	0.481635i	$-0.840043\pi$
$883$	2935.50	−	16648.0i	0.111877	−	0.634486i	0.988249	−	0.152851i	$-0.0488456\pi$
$884$	−18.0121	+	102.152i	−0.000685308	+	0.00388657i
$885$		0			0
$886$	−889.348	+	1540.40i	−0.0337226	+	0.0584093i
$887$	−25811.5	−	21658.4i	−0.977075	−	0.819863i	0.00657087	−	0.999978i	$-0.497908\pi$
$887$	−25811.5	−	21658.4i	−0.977075	−	0.819863i	−0.983645	+	0.180115i	$0.942353\pi$
$888$		0			0
$889$	−20776.7	+	7562.09i	−0.783832	+	0.285292i
$890$	−32479.5	+	27253.5i	−1.22328	+	1.02645i
$891$		0			0
$892$	−73607.2			−2.76295
$893$	14752.9	+	5180.79i	0.552842	+	0.194142i
$894$		0			0
$895$	133.521	+	757.237i	0.00498673	+	0.0282812i
$896$	55692.3	−	46731.4i	2.07651	−	1.74240i
$897$		0			0
$898$	−58003.1	−	21111.4i	−2.15544	−	0.784517i
$899$	11264.8	+	9452.30i	0.417912	+	0.350669i
$900$		0			0
$901$	2.68544	+	4.65132i	9.92953e−5	+	0.000171984i
$902$	1433.34	−	8128.89i	0.0529103	−	0.300069i
$903$		0			0
$904$	−42451.1	−	73527.5i	−1.56184	−	2.70518i
$905$	−4077.27	+	7062.03i	−0.149760	+	0.259392i
$906$		0			0
$907$	40322.1	+	14676.1i	1.47616	+	0.537277i	0.949765	−	0.312965i	$-0.101322\pi$
$907$	40322.1	+	14676.1i	1.47616	+	0.537277i	0.526392	+	0.850242i	$0.323544\pi$
$908$	36875.4	−	13421.6i	1.34775	−	0.490540i
$909$		0			0
$910$	7423.28	+	42099.5i	0.270417	+	1.53361i
$911$	−11606.2			−0.422097			−0.211048	−	0.977476i	$-0.567688\pi$
$911$	−11606.2			−0.422097			−0.211048	+	0.977476i	$0.567688\pi$
$912$		0			0
$913$	64275.7			2.32992
$914$	16368.6	+	92831.0i	0.592369	+	3.35949i
$915$		0			0
$916$	−3398.86	+	1237.08i	−0.122600	+	0.0446227i
$917$	−116.783	−	42.5056i	−0.00420559	−	0.00153071i
$918$		0			0
$919$	−11281.4	+	19539.9i	−0.404938	+	0.701373i	−0.994314	−	0.106485i	$-0.966040\pi$
$919$	−11281.4	+	19539.9i	−0.404938	+	0.701373i	0.589376	+	0.807859i	$0.299374\pi$
$920$	6128.46	+	10614.8i	0.219619	+	0.380391i
$921$		0			0
$922$	−5403.07	+	30642.3i	−0.192994	+	1.09452i
$923$	−5111.09	−	8852.66i	−0.182268	−	0.315698i
$924$		0			0
$925$	15570.2	+	13065.0i	0.553455	+	0.464404i
$926$	−24570.2	−	8942.81i	−0.871951	−	0.317364i
$927$		0			0
$928$	−218.281	+	183.160i	−0.00772138	+	0.00647900i
$929$	7163.93	+	40628.7i	0.253004	+	1.43486i	0.801144	+	0.598472i	$0.204225\pi$
$929$	7163.93	+	40628.7i	0.253004	+	1.43486i	−0.548139	+	0.836387i	$0.684664\pi$
$930$		0			0
$931$	39270.9	−	14800.3i	1.38244	−	0.521008i
$932$	19785.3			0.695375
$933$		0			0
$934$	21819.9	−	18309.1i	0.764421	−	0.641426i
$935$	−58.5640	+	21.3155i	−0.00204839	+	0.000745554i
$936$		0			0
$937$	−37364.5	−	31352.5i	−1.30271	−	1.09311i	−0.989669	−	0.143369i	$-0.954206\pi$
$937$	−37364.5	−	31352.5i	−1.30271	−	1.09311i	−0.313045	−	0.949738i	$-0.601349\pi$
$938$	25451.0	−	44082.5i	0.885934	−	1.53448i
$939$		0			0
$940$	3890.51	−	22064.2i	0.134994	−	0.765589i
$941$	−592.705	+	3361.39i	−0.0205331	+	0.116449i	−0.993352	−	0.115120i	$-0.963275\pi$
$941$	−592.705	+	3361.39i	−0.0205331	+	0.116449i	0.972819	+	0.231569i	$0.0743858\pi$
$942$		0			0
$943$	669.349	−	1159.35i	0.0231145	−	0.0400355i
$944$	−14552.9	−	12211.3i	−0.501755	−	0.421022i
$945$		0			0
$946$	33301.9	−	12120.9i	1.14454	−	0.416580i
$947$	36827.9	−	30902.3i	1.26372	−	1.06039i	0.268449	−	0.963294i	$-0.413489\pi$
$947$	36827.9	−	30902.3i	1.26372	−	1.06039i	0.995275	−	0.0970969i	$-0.0309557\pi$
$948$		0			0
$949$	32723.2			1.11932
$950$	22098.2	+	18119.2i	0.754693	+	0.618805i
$951$		0			0
$952$	−31.9357	−	181.116i	−0.00108723	−	0.00616598i
$953$	16480.5	−	13828.8i	0.560184	−	0.470050i	−0.318188	−	0.948028i	$-0.603074\pi$
$953$	16480.5	−	13828.8i	0.560184	−	0.470050i	0.878372	+	0.477978i	$0.158630\pi$
$954$		0			0
$955$	15809.8	+	5754.29i	0.535699	+	0.194978i
$956$	−29358.9	−	24635.1i	−0.993238	−	0.833425i
$957$		0			0
$958$	−19219.8	−	33289.7i	−0.648189	−	1.12270i
$959$	−4449.91	+	25236.7i	−0.149838	+	0.849776i
$960$		0			0
$961$	−8481.40	−	14690.2i	−0.284697	−	0.493109i
$962$	−28656.5	+	49634.6i	−0.960420	+	1.66350i
$963$		0			0
$964$	23052.3	+	8390.35i	0.770191	+	0.280327i
$965$	4027.95	−	1466.05i	0.134367	−	0.0489056i
$966$		0			0
$967$	−7269.67	−	41228.4i	−0.241755	−	1.37106i	−0.827910	−	0.560861i	$-0.810470\pi$
$967$	−7269.67	−	41228.4i	−0.241755	−	1.37106i	0.586155	−	0.810199i	$-0.300641\pi$
$968$	57452.6			1.90764
$969$		0			0
$970$	−14412.7			−0.477077
$971$	−6597.37	−	37415.5i	−0.218043	−	1.23658i	−0.875548	−	0.483132i	$-0.839499\pi$
$971$	−6597.37	−	37415.5i	−0.218043	−	1.23658i	0.657505	−	0.753450i	$-0.271612\pi$
$972$		0			0
$973$	53929.0	−	19628.6i	1.77686	−	0.646724i
$974$	4180.80	+	1521.69i	0.137537	+	0.0500595i
$975$		0			0
$976$	−381.828	+	661.346i	−0.0125226	+	0.0216897i
$977$	−17478.5	−	30273.6i	−0.572350	−	0.991339i	−0.996324	−	0.0856649i	$-0.972699\pi$
$977$	−17478.5	−	30273.6i	−0.572350	−	0.991339i	0.423974	−	0.905674i	$-0.360635\pi$
$978$		0			0
$979$	−10718.3	+	60786.6i	−0.349907	+	1.98442i
$980$	−30066.7	−	52077.1i	−0.980047	−	1.69749i
$981$		0			0
$982$	−45917.8	−	38529.6i	−1.49215	−	1.25207i
$983$	43607.8	+	15871.9i	1.41493	+	0.514991i	0.932571	−	0.360986i	$-0.117560\pi$
$983$	43607.8	+	15871.9i	1.41493	+	0.514991i	0.482354	+	0.875976i	$0.339782\pi$
$984$		0			0
$985$	3398.94	−	2852.05i	0.109949	−	0.0922578i
$986$	−9.25182	−	52.4697i	−0.000298821	−	0.00169470i
$987$		0			0
$988$	−26359.4	+	46876.5i	−0.848790	+	1.50945i
$989$	5747.60			0.184796
$990$		0			0
$991$	8935.82	−	7498.04i	0.286434	−	0.240346i	−0.488237	−	0.872711i	$-0.662360\pi$
$991$	8935.82	−	7498.04i	0.286434	−	0.240346i	0.774671	+	0.632365i	$0.217916\pi$
$992$	851.325	−	309.857i	0.0272476	−	0.00991730i
$993$		0			0
$994$	27675.9	+	23222.9i	0.883126	+	0.741031i
$995$	4116.44	−	7129.89i	0.131156	−	0.227169i
$996$		0			0
$997$	−877.467	+	4976.36i	−0.0278733	+	0.158077i	−0.995568	−	0.0940494i	$-0.970019\pi$
$997$	−877.467	+	4976.36i	−0.0278733	+	0.158077i	0.967694	+	0.252127i	$0.0811299\pi$
$998$	14925.3	−	84645.4i	0.473398	−	2.68477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.b.28.4		24
3.2	odd	2		19.4.e.a.9.1	✓	24
19.17	even	9	inner	171.4.u.b.55.4		24
57.17	odd	18		19.4.e.a.17.1	yes	24
57.32	even	18		361.4.a.m.1.12		12
57.44	odd	18		361.4.a.n.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.9.1	✓	24	3.2	odd	2
19.4.e.a.17.1	yes	24	57.17	odd	18
171.4.u.b.28.4		24	1.1	even	1	trivial
171.4.u.b.55.4		24	19.17	even	9	inner
361.4.a.m.1.12		12	57.32	even	18
361.4.a.n.1.1		12	57.44	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)

\(f(q)\)	\(=\)	\(q+(0.851642 + 4.82990i) q^{2} +(-15.0851 + 5.49052i) q^{4} +(-6.94640 - 2.52828i) q^{5} +(14.5751 - 25.2448i) q^{7} +(-19.7481 - 34.2048i) q^{8} +O(q^{10})\)	\(q+(0.851642 + 4.82990i) q^{2} +(-15.0851 + 5.49052i) q^{4} +(-6.94640 - 2.52828i) q^{5} +(14.5751 - 25.2448i) q^{7} +(-19.7481 - 34.2048i) q^{8} +(6.29551 - 35.7036i) q^{10} +(-26.3895 - 45.7080i) q^{11} +(-30.9868 - 26.0010i) q^{13} +(134.343 + 48.8967i) q^{14} +(50.0074 - 41.9612i) q^{16} +(0.0277382 + 0.157311i) q^{17} +(-13.4549 + 81.7188i) q^{19} +118.669 q^{20} +(198.291 - 166.386i) q^{22} +(39.4491 - 14.3583i) q^{23} +(-53.8953 - 45.2235i) q^{25} +(99.1927 - 171.807i) q^{26} +(-81.2594 + 460.845i) q^{28} +(-11.8095 + 66.9751i) q^{29} +(108.113 - 187.257i) q^{31} +(3.20963 + 2.69320i) q^{32} +(-0.736175 + 0.267946i) q^{34} +(-165.071 + 138.511i) q^{35} -288.898 q^{37} +(-406.152 + 4.60942i) q^{38} +(50.6991 + 287.529i) q^{40} +(24.4278 - 20.4974i) q^{41} +(128.653 + 46.8260i) q^{43} +(649.050 + 544.617i) q^{44} +(102.946 + 178.307i) q^{46} +(32.7846 - 185.931i) q^{47} +(-253.367 - 438.844i) q^{49} +(172.526 - 298.823i) q^{50} +(610.199 + 222.094i) q^{52} +(31.5953 - 11.4998i) q^{53} +(67.7495 + 384.227i) q^{55} -1151.32 q^{56} -333.540 q^{58} +(-50.5342 - 286.594i) q^{59} +(-10.9927 + 4.00101i) q^{61} +(996.508 + 362.699i) q^{62} +(250.846 - 434.478i) q^{64} +(149.509 + 258.957i) q^{65} +(61.8269 - 350.638i) q^{67} +(-1.28216 - 2.22076i) q^{68} +(-809.573 - 679.313i) q^{70} +(237.468 + 86.4315i) q^{71} +(-619.706 + 519.995i) q^{73} +(-246.037 - 1395.35i) q^{74} +(-245.711 - 1306.61i) q^{76} -1538.52 q^{77} +(540.834 - 453.814i) q^{79} +(-453.461 + 165.046i) q^{80} +(119.804 + 100.528i) q^{82} +(-608.912 + 1054.67i) q^{83} +(0.205047 - 1.16288i) q^{85} +(-116.598 + 661.261i) q^{86} +(-1042.29 + 1805.30i) q^{88} +(-895.877 - 751.730i) q^{89} +(-1108.03 + 403.289i) q^{91} +(-516.259 + 433.193i) q^{92} +925.947 q^{94} +(300.071 - 533.634i) q^{95} +(-69.0328 - 391.505i) q^{97} +(1903.80 - 1597.48i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 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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