LMFDB - Embedded newform 171.4.u.b.55.3

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			55.3
Character	$\chi$	$=$	171.55
Dual form			171.4.u.b.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.163781 - 0.928850i) q^{2} +(6.68160 + 2.43190i) q^{4} +(3.55727 - 1.29474i) q^{5} +(-11.7083 - 20.2794i) q^{7} +(7.12592 - 12.3424i) q^{8} +O(q^{10})$	\(q+(0.163781 - 0.928850i) q^{2} +(6.68160 + 2.43190i) q^{4} +(3.55727 - 1.29474i) q^{5} +(-11.7083 - 20.2794i) q^{7} +(7.12592 - 12.3424i) q^{8} +(-0.620006 - 3.51623i) q^{10} +(8.50109 - 14.7243i) q^{11} +(3.66005 - 3.07115i) q^{13} +(-20.7541 + 7.55387i) q^{14} +(33.2779 + 27.9235i) q^{16} +(9.73487 - 55.2092i) q^{17} +(80.5692 - 19.1731i) q^{19} +26.9170 q^{20} +(-12.2844 - 10.3078i) q^{22} +(83.8179 + 30.5072i) q^{23} +(-84.7777 + 71.1369i) q^{25} +(-2.25319 - 3.90264i) q^{26} +(-28.9127 - 163.972i) q^{28} +(-29.8807 - 169.462i) q^{29} +(-48.1783 - 83.4472i) q^{31} +(118.727 - 99.6241i) q^{32} +(-49.6867 - 18.0845i) q^{34} +(-67.9062 - 56.9800i) q^{35} +339.998 q^{37} +(-4.61325 - 77.9769i) q^{38} +(9.36855 - 53.1317i) q^{40} +(-339.942 - 285.246i) q^{41} +(-253.541 + 92.2813i) q^{43} +(92.6090 - 77.7082i) q^{44} +(42.0644 - 72.8577i) q^{46} +(84.2516 + 477.815i) q^{47} +(-102.668 + 177.827i) q^{49} +(52.1906 + 90.3967i) q^{50} +(31.9238 - 11.6193i) q^{52} +(594.726 + 216.463i) q^{53} +(11.1765 - 63.3851i) q^{55} -333.729 q^{56} -162.298 q^{58} +(-114.283 + 648.131i) q^{59} +(-135.978 - 49.4918i) q^{61} +(-85.4007 + 31.0833i) q^{62} +(100.675 + 174.373i) q^{64} +(9.04347 - 15.6638i) q^{65} +(62.4481 + 354.161i) q^{67} +(199.308 - 345.212i) q^{68} +(-64.0477 + 53.7424i) q^{70} +(-998.198 + 363.314i) q^{71} +(227.447 + 190.851i) q^{73} +(55.6853 - 315.807i) q^{74} +(584.958 + 67.8292i) q^{76} -398.133 q^{77} +(-81.3652 - 68.2735i) q^{79} +(154.533 + 56.2452i) q^{80} +(-320.627 + 269.038i) q^{82} +(332.777 + 576.387i) q^{83} +(-36.8521 - 208.998i) q^{85} +(44.1902 + 250.615i) q^{86} +(-121.156 - 209.848i) q^{88} +(252.988 - 212.282i) q^{89} +(-105.134 - 38.2656i) q^{91} +(485.847 + 407.674i) q^{92} +457.617 q^{94} +(261.782 - 172.520i) q^{95} +(4.50343 - 25.5402i) q^{97} +(148.359 + 124.488i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.163781	−	0.928850i	0.0579055	−	0.328398i	−0.942070	−	0.335417i	$-0.891123\pi$
$2$	0.163781	−	0.928850i	0.0579055	−	0.328398i	0.999975	+	0.00701838i	$0.00223404\pi$
$3$		0			0
$3$		0			0
$4$	6.68160	+	2.43190i	0.835200	+	0.303988i
$5$	3.55727	−	1.29474i	0.318172	−	0.115805i	−0.177997	−	0.984031i	$-0.556962\pi$
$5$	3.55727	−	1.29474i	0.318172	−	0.115805i	0.496169	+	0.868226i	$0.334740\pi$
$6$		0			0
$7$	−11.7083	−	20.2794i	−0.632188	−	1.09498i	−0.987103	−	0.160084i	$-0.948824\pi$
$7$	−11.7083	−	20.2794i	−0.632188	−	1.09498i	0.354915	−	0.934899i	$-0.384510\pi$
$8$	7.12592	−	12.3424i	0.314924	−	0.545464i
$9$		0			0
$10$	−0.620006	−	3.51623i	−0.0196063	−	0.111193i
$11$	8.50109	−	14.7243i	0.233016	−	0.403595i	−0.725678	−	0.688034i	$-0.758474\pi$
$11$	8.50109	−	14.7243i	0.233016	−	0.403595i	0.958694	+	0.284439i	$0.0918073\pi$
$12$		0			0
$13$	3.66005	−	3.07115i	0.0780859	−	0.0655218i	−0.602909	−	0.797810i	$-0.705992\pi$
$13$	3.66005	−	3.07115i	0.0780859	−	0.0655218i	0.680995	+	0.732288i	$0.261547\pi$
$14$	−20.7541	+	7.55387i	−0.396197	+	0.144204i
$15$		0			0
$16$	33.2779	+	27.9235i	0.519968	+	0.436305i
$17$	9.73487	−	55.2092i	0.138886	−	0.787659i	−0.833189	−	0.552988i	$-0.813488\pi$
$17$	9.73487	−	55.2092i	0.138886	−	0.787659i	0.972075	−	0.234671i	$-0.0754013\pi$
$18$		0			0
$19$	80.5692	−	19.1731i	0.972833	−	0.231506i
$19$	80.5692	−	19.1731i	0.972833	−	0.231506i
$20$	26.9170			0.300941
$21$		0			0
$22$	−12.2844	−	10.3078i	−0.119047	−	0.0998924i
$23$	83.8179	+	30.5072i	0.759880	+	0.276574i	0.692757	−	0.721171i	$-0.256396\pi$
$23$	83.8179	+	30.5072i	0.759880	+	0.276574i	0.0671227	+	0.997745i	$0.478618\pi$
$24$		0			0
$25$	−84.7777	+	71.1369i	−0.678222	+	0.569096i
$26$	−2.25319	−	3.90264i	−0.0169957	−	0.0294373i
$27$		0			0
$28$	−28.9127	−	163.972i	−0.195142	−	1.10671i
$29$	−29.8807	−	169.462i	−0.191335	−	1.08511i	−0.917543	−	0.397637i	$-0.869830\pi$
$29$	−29.8807	−	169.462i	−0.191335	−	1.08511i	0.726208	−	0.687475i	$-0.241281\pi$
$30$		0			0
$31$	−48.1783	−	83.4472i	−0.279131	−	0.483470i	0.692038	−	0.721861i	$-0.256713\pi$
$31$	−48.1783	−	83.4472i	−0.279131	−	0.483470i	−0.971169	+	0.238392i	$0.923380\pi$
$32$	118.727	−	99.6241i	0.655882	−	0.550350i
$33$		0			0
$34$	−49.6867	−	18.0845i	−0.250624	−	0.0912195i
$35$	−67.9062	−	56.9800i	−0.327950	−	0.275182i
$36$		0			0
$37$	339.998			1.51068			0.755342	−	0.655331i	$-0.227471\pi$
$37$	339.998			1.51068			0.755342	+	0.655331i	$0.227471\pi$
$38$	−4.61325	−	77.9769i	−0.0196939	−	0.332882i
$39$		0			0
$40$	9.36855	−	53.1317i	0.0370325	−	0.210021i
$41$	−339.942	−	285.246i	−1.29488	−	1.08653i	−0.991005	−	0.133822i	$-0.957275\pi$
$41$	−339.942	−	285.246i	−1.29488	−	1.08653i	−0.303875	−	0.952712i	$-0.598281\pi$
$42$		0			0
$43$	−253.541	+	92.2813i	−0.899177	+	0.327274i	−0.749923	−	0.661525i	$-0.769909\pi$
$43$	−253.541	+	92.2813i	−0.899177	+	0.327274i	−0.149254	+	0.988799i	$0.547687\pi$
$44$	92.6090	−	77.7082i	0.317303	−	0.266249i
$45$		0			0
$46$	42.0644	−	72.8577i	0.134827	−	0.233528i
$47$	84.2516	+	477.815i	0.261476	+	1.48290i	0.778886	+	0.627165i	$0.215785\pi$
$47$	84.2516	+	477.815i	0.261476	+	1.48290i	−0.517410	+	0.855737i	$0.673104\pi$
$48$		0			0
$49$	−102.668	+	177.827i	−0.299325	+	0.518445i
$50$	52.1906	+	90.3967i	0.147617	+	0.255681i
$51$		0			0
$52$	31.9238	−	11.6193i	0.0851352	−	0.0309867i
$53$	594.726	+	216.463i	1.54136	+	0.561008i	0.966370	−	0.257154i	$-0.0827848\pi$
$53$	594.726	+	216.463i	1.54136	+	0.561008i	0.574987	+	0.818162i	$0.305007\pi$
$54$		0			0
$55$	11.1765	−	63.3851i	0.0274007	−	0.155397i
$56$	−333.729			−0.796365
$57$		0			0
$58$	−162.298			−0.367428
$59$	−114.283	+	648.131i	−0.252176	+	1.43016i	0.551043	+	0.834477i	$0.314230\pi$
$59$	−114.283	+	648.131i	−0.252176	+	1.43016i	−0.803219	+	0.595684i	$0.796881\pi$
$60$		0			0
$61$	−135.978	−	49.4918i	−0.285412	−	0.103882i	0.195347	−	0.980734i	$-0.437417\pi$
$61$	−135.978	−	49.4918i	−0.285412	−	0.103882i	−0.480759	+	0.876853i	$0.659639\pi$
$62$	−85.4007	+	31.0833i	−0.174934	+	0.0636707i
$63$		0			0
$64$	100.675	+	174.373i	0.196630	+	0.340573i
$65$	9.04347	−	15.6638i	0.0172570	−	0.0298900i
$66$		0			0
$67$	62.4481	+	354.161i	0.113869	+	0.645785i	0.987304	+	0.158843i	$0.0507765\pi$
$67$	62.4481	+	354.161i	0.113869	+	0.645785i	−0.873434	+	0.486942i	$0.838112\pi$
$68$	199.308	−	345.212i	0.355436	−	0.615633i
$69$		0			0
$70$	−64.0477	+	53.7424i	−0.109359	+	0.0917635i
$71$	−998.198	+	363.314i	−1.66851	+	0.607289i	−0.991666	−	0.128836i	$-0.958876\pi$
$71$	−998.198	+	363.314i	−1.66851	+	0.607289i	−0.676846	+	0.736125i	$0.736654\pi$
$72$		0			0
$73$	227.447	+	190.851i	0.364666	+	0.305991i	0.806647	−	0.591033i	$-0.201280\pi$
$73$	227.447	+	190.851i	0.364666	+	0.305991i	−0.441981	+	0.897024i	$0.645724\pi$
$74$	55.6853	−	315.807i	0.0874768	−	0.496106i
$75$		0			0
$76$	584.958	+	67.8292i	0.882886	+	0.102376i
$77$	−398.133			−0.589240
$78$		0			0
$79$	−81.3652	−	68.2735i	−0.115877	−	0.0972325i	0.583008	−	0.812467i	$-0.301876\pi$
$79$	−81.3652	−	68.2735i	−0.115877	−	0.0972325i	−0.698885	+	0.715234i	$0.746320\pi$
$80$	154.533	+	56.2452i	0.215966	+	0.0786051i
$81$		0			0
$82$	−320.627	+	269.038i	−0.431796	+	0.362320i
$83$	332.777	+	576.387i	0.440085	+	0.762249i	0.997695	−	0.0678534i	$-0.0216150\pi$
$83$	332.777	+	576.387i	0.440085	+	0.762249i	−0.557610	+	0.830103i	$0.688282\pi$
$84$		0			0
$85$	−36.8521	−	208.998i	−0.0470255	−	0.266695i
$86$	44.1902	+	250.615i	0.0554088	+	0.314239i
$87$		0			0
$88$	−121.156	−	209.848i	−0.146765	−	0.254204i
$89$	252.988	−	212.282i	0.301311	−	0.252830i	−0.479579	−	0.877499i	$-0.659211\pi$
$89$	252.988	−	212.282i	0.301311	−	0.252830i	0.780890	+	0.624669i	$0.214766\pi$
$90$		0			0
$91$	−105.134	−	38.2656i	−0.121110	−	0.0440805i
$92$	485.847	+	407.674i	0.550577	+	0.461989i
$93$		0			0
$94$	457.617			0.502124
$95$	261.782	−	172.520i	0.282719	−	0.186318i
$96$		0			0
$97$	4.50343	−	25.5402i	0.00471396	−	0.0267342i	−0.982360	−	0.186999i	$-0.940124\pi$
$97$	4.50343	−	25.5402i	0.00471396	−	0.0267342i	0.987074	+	0.160265i	$0.0512349\pi$
$98$	148.359	+	124.488i	0.152924	+	0.128318i
$99$		0			0
$100$	−739.449	+	269.137i	−0.739449	+	0.269137i
$101$	−930.836	+	781.064i	−0.917046	+	0.769493i	−0.973446	−	0.228916i	$-0.926482\pi$
$101$	−930.836	+	781.064i	−0.917046	+	0.769493i	0.0564006	+	0.998408i	$0.482038\pi$
$102$		0			0
$103$	−552.102	+	956.268i	−0.528157	+	0.914795i	0.471304	+	0.881971i	$0.343784\pi$
$103$	−552.102	+	956.268i	−0.528157	+	0.914795i	−0.999461	+	0.0328243i	$0.989550\pi$
$104$	−11.8243	−	67.0588i	−0.0111487	−	0.0632274i
$105$		0			0
$106$	298.467	−	516.959i	0.273487	−	0.473694i
$107$	−428.523	−	742.224i	−0.387167	−	0.670593i	0.604900	−	0.796301i	$-0.293213\pi$
$107$	−428.523	−	742.224i	−0.387167	−	0.670593i	−0.992067	+	0.125708i	$0.959880\pi$
$108$		0			0
$109$	−642.380	+	233.807i	−0.564484	+	0.205456i	−0.608470	−	0.793577i	$-0.708217\pi$
$109$	−642.380	+	233.807i	−0.564484	+	0.205456i	0.0439859	+	0.999032i	$0.485994\pi$
$110$	−57.0448	−	20.7626i	−0.0494455	−	0.0179967i
$111$		0			0
$112$	176.643	−	1001.79i	0.149028	−	0.845183i
$113$	51.8430			0.0431591			0.0215796	−	0.999767i	$-0.493130\pi$
$113$	51.8430			0.0431591			0.0215796	+	0.999767i	$0.493130\pi$
$114$		0			0
$115$	337.662			0.273801
$116$	212.464	−	1204.94i	0.170058	−	0.964449i
$117$		0			0
$118$	583.299	+	212.304i	0.455060	+	0.165628i
$119$	−1233.59	+	448.989i	−0.950275	+	0.345872i
$120$		0			0
$121$	520.963	+	902.334i	0.391407	+	0.677937i
$122$	−68.2411	+	118.197i	−0.0506414	+	0.0877136i
$123$		0			0
$124$	−118.972	−	674.726i	−0.0861616	−	0.488647i
$125$	−446.072	+	772.619i	−0.319183	+	0.552841i
$126$		0			0
$127$	243.730	−	204.513i	0.170295	−	0.142895i	−0.553657	−	0.832745i	$-0.686768\pi$
$127$	243.730	−	204.513i	0.170295	−	0.142895i	0.723952	+	0.689850i	$0.242324\pi$
$128$	1343.58	−	489.023i	0.927788	−	0.337687i
$129$		0			0
$130$	−13.0681	−	10.9655i	−0.00881654	−	0.00739796i
$131$	258.796	−	1467.71i	0.172604	−	0.978887i	−0.768269	−	0.640127i	$-0.778882\pi$
$131$	258.796	−	1467.71i	0.172604	−	0.978887i	0.940873	−	0.338759i	$-0.110007\pi$
$132$		0			0
$133$	−1332.15	−	1409.41i	−0.868509	−	0.918880i
$134$	339.190			0.218668
$135$		0			0
$136$	−612.047	−	513.568i	−0.385901	−	0.323810i
$137$	1502.61	+	546.904i	0.937054	+	0.341060i	0.765002	−	0.644028i	$-0.222738\pi$
$137$	1502.61	+	546.904i	0.937054	+	0.341060i	0.172052	+	0.985088i	$0.444960\pi$
$138$		0			0
$139$	905.282	−	759.622i	0.552410	−	0.463527i	−0.323346	−	0.946281i	$-0.604808\pi$
$139$	905.282	−	759.622i	0.552410	−	0.463527i	0.875756	+	0.482754i	$0.160363\pi$
$140$	−315.152	−	545.859i	−0.190251	−	0.329525i
$141$		0			0
$142$	173.978	+	986.681i	0.102817	+	0.583102i
$143$	−14.1061	−	79.9999i	−0.00824905	−	0.0467827i
$144$		0			0
$145$	−325.703	−	564.134i	−0.186539	−	0.323095i
$146$	214.523	−	180.006i	0.121603	−	0.102037i
$147$		0			0
$148$	2271.73	+	826.842i	1.26172	+	0.459230i
$149$	1677.96	+	1407.98i	0.922576	+	0.774133i	0.974470	−	0.224519i	$-0.0720812\pi$
$149$	1677.96	+	1407.98i	0.922576	+	0.774133i	−0.0518935	+	0.998653i	$0.516526\pi$
$150$		0			0
$151$	−3644.97			−1.96439			−0.982196	−	0.187857i	$-0.939846\pi$
$151$	−3644.97			−1.96439			−0.982196	+	0.187857i	$0.939846\pi$
$152$	337.486	−	1131.05i	0.180090	−	0.603553i
$153$		0			0
$154$	−65.2068	+	369.806i	−0.0341202	+	0.193505i
$155$	−279.426	−	234.466i	−0.144800	−	0.121502i
$156$		0			0
$157$	3119.81	−	1135.52i	1.58591	−	0.577224i	0.609431	−	0.792839i	$-0.291398\pi$
$157$	3119.81	−	1135.52i	1.58591	−	0.577224i	0.976478	+	0.215615i	$0.0691756\pi$
$158$	−76.7420	+	64.3942i	−0.0386409	+	0.0324236i
$159$		0			0
$160$	293.358	−	508.112i	0.144950	−	0.251061i
$161$	−362.698	−	2056.96i	−0.177544	−	1.00690i
$162$		0			0
$163$	51.8896	−	89.8755i	0.0249344	−	0.0431877i	−0.853289	−	0.521438i	$-0.825396\pi$
$163$	51.8896	−	89.8755i	0.0249344	−	0.0431877i	0.878223	+	0.478251i	$0.158729\pi$
$164$	−1577.67	−	2732.61i	−0.751191	−	1.30110i
$165$		0			0
$166$	589.880	−	214.699i	0.275805	−	0.100385i
$167$	−1548.96	−	563.774i	−0.717736	−	0.261234i	−0.0427714	−	0.999085i	$-0.513619\pi$
$167$	−1548.96	−	563.774i	−0.717736	−	0.261234i	−0.674964	+	0.737851i	$0.735841\pi$
$168$		0			0
$169$	−377.541	+	2141.14i	−0.171844	+	0.974575i
$170$	−200.164			−0.0903052
$171$		0			0
$172$	−1918.48			−0.850480
$173$	104.162	−	590.734i	0.0457764	−	0.259611i	−0.953327	−	0.301938i	$-0.902366\pi$
$173$	104.162	−	590.734i	0.0457764	−	0.259611i	0.999104	+	0.0423278i	$0.0134774\pi$
$174$		0			0
$175$	2435.21	+	886.345i	1.05191	+	0.382865i
$176$	694.053	−	252.615i	0.297251	−	0.108191i
$177$		0			0
$178$	−155.744	−	269.756i	−0.0655814	−	0.113590i
$179$	1194.03	−	2068.13i	0.498582	−	0.863570i	−0.501416	−	0.865206i	$-0.667187\pi$
$179$	1194.03	−	2068.13i	0.498582	−	0.863570i	0.999999	+	0.00163610i	$0.000520788\pi$
$180$		0			0
$181$	−522.855	−	2965.26i	−0.214715	−	1.21771i	−0.881400	−	0.472371i	$-0.843398\pi$
$181$	−522.855	−	2965.26i	−0.214715	−	1.21771i	0.666685	−	0.745340i	$-0.267713\pi$
$182$	−52.7620	+	91.3865i	−0.0214889	+	0.0372199i
$183$		0			0
$184$	973.813	−	817.126i	0.390165	−	0.327388i
$185$	1209.47	−	440.209i	0.480658	−	0.174945i
$186$		0			0
$187$	−730.161	−	612.678i	−0.285533	−	0.239591i
$188$	−599.064	+	3397.46i	−0.232400	+	1.31801i
$189$		0			0
$190$	−117.371	−	271.412i	−0.0448156	−	0.103633i
$191$	885.430			0.335432			0.167716	−	0.985835i	$-0.446361\pi$
$191$	885.430			0.335432			0.167716	+	0.985835i	$0.446361\pi$
$192$		0			0
$193$	1248.09	+	1047.27i	0.465490	+	0.390593i	0.845146	−	0.534535i	$-0.179513\pi$
$193$	1248.09	+	1047.27i	0.465490	+	0.390593i	−0.379656	+	0.925128i	$0.623958\pi$
$194$	−22.9855	−	8.36603i	−0.00850650	−	0.00309611i
$195$		0			0
$196$	−1118.45	+	938.488i	−0.407597	+	0.342015i
$197$	949.709	+	1644.94i	0.343472	+	0.594911i	0.985075	−	0.172126i	$-0.0550636\pi$
$197$	949.709	+	1644.94i	0.343472	+	0.594911i	−0.641603	+	0.767037i	$0.721730\pi$
$198$		0			0
$199$	98.2858	+	557.406i	0.0350115	+	0.198560i	0.997296	−	0.0734834i	$-0.0234116\pi$
$199$	98.2858	+	557.406i	0.0350115	+	0.198560i	−0.962285	+	0.272044i	$0.912300\pi$
$200$	273.885	+	1553.28i	0.0968330	+	0.549167i
$201$		0			0
$202$	573.038	+	992.531i	0.199598	+	0.345714i
$203$	−3086.72	+	2590.07i	−1.06722	+	0.895503i
$204$		0			0
$205$	−1578.59	−	574.559i	−0.537821	−	0.195751i
$206$	797.806	+	669.439i	0.269834	+	0.226418i
$207$		0			0
$208$	207.556			0.0691896
$209$	402.614	−	1349.32i	0.133251	−	0.446576i
$210$		0			0
$211$	−128.944	+	731.279i	−0.0420705	+	0.238594i	−0.998591	−	0.0530725i	$-0.983099\pi$
$211$	−128.944	+	731.279i	−0.0420705	+	0.238594i	0.956520	+	0.291666i	$0.0942097\pi$
$212$	3447.31	+	2892.64i	1.11680	+	0.937108i
$213$		0			0
$214$	−759.599	+	276.472i	−0.242641	+	0.0883140i
$215$	−782.433	+	656.540i	−0.248193	+	0.208259i
$216$		0			0
$217$	−1128.17	+	1954.05i	−0.352927	+	0.611288i
$218$	111.962	+	634.968i	0.0347845	+	0.197273i
$219$		0			0
$220$	228.824	−	396.334i	0.0701240	−	0.121458i
$221$	−133.926	−	231.966i	−0.0407639	−	0.0706051i
$222$		0			0
$223$	1784.05	−	649.340i	0.535734	−	0.194991i	−0.0599629	−	0.998201i	$-0.519098\pi$
$223$	1784.05	−	649.340i	0.535734	−	0.194991i	0.595697	+	0.803209i	$0.296876\pi$
$224$	−3410.41	−	1241.29i	−1.01727	−	0.370254i
$225$		0			0
$226$	8.49092	−	48.1544i	0.00249915	−	0.0141734i
$227$	−2033.08			−0.594451			−0.297226	−	0.954807i	$-0.596061\pi$
$227$	−2033.08			−0.594451			−0.297226	+	0.954807i	$0.596061\pi$
$228$		0			0
$229$	2816.38			0.812715			0.406357	−	0.913714i	$-0.366799\pi$
$229$	2816.38			0.812715			0.406357	+	0.913714i	$0.366799\pi$
$230$	55.3028	−	313.638i	0.0158546	−	0.0899159i
$231$		0			0
$232$	−2304.50	−	838.769i	−0.652146	−	0.237362i
$233$	−2189.83	+	797.031i	−0.615709	+	0.224100i	−0.630999	−	0.775783i	$-0.717355\pi$
$233$	−2189.83	+	797.031i	−0.615709	+	0.224100i	0.0152902	+	0.999883i	$0.495133\pi$
$234$		0			0
$235$	918.353	+	1590.63i	0.254922	+	0.441538i
$236$	−2339.79	+	4052.63i	−0.645369	+	1.11781i
$237$		0			0
$238$	215.005	+	1219.35i	0.0585575	+	0.332096i
$239$	−262.887	+	455.333i	−0.0711495	+	0.123234i	−0.899405	−	0.437116i	$-0.856000\pi$
$239$	−262.887	+	455.333i	−0.0711495	+	0.123234i	0.828256	+	0.560350i	$0.189333\pi$
$240$		0			0
$241$	−4726.11	+	3965.68i	−1.26322	+	1.05997i	−0.267887	+	0.963450i	$0.586326\pi$
$241$	−4726.11	+	3965.68i	−1.26322	+	1.05997i	−0.995331	+	0.0965162i	$0.969230\pi$
$242$	923.458	−	336.111i	0.245298	−	0.0892812i
$243$		0			0
$244$	−788.189	−	661.369i	−0.206798	−	0.173524i
$245$	−134.980	+	765.508i	−0.0351981	+	0.199618i
$246$		0			0
$247$	236.004	−	317.615i	0.0607958	−	0.0818192i
$248$	−1373.26			−0.351621
$249$		0			0
$250$	644.589	+	540.875i	0.163070	+	0.136832i
$251$	3983.36	+	1449.82i	1.00170	+	0.364590i	0.790241	−	0.612796i	$-0.209955\pi$
$251$	3983.36	+	1449.82i	1.00170	+	0.364590i	0.211462	+	0.977386i	$0.432178\pi$
$252$		0			0
$253$	1161.74	−	974.816i	0.288688	−	0.242238i
$254$	−150.044	−	259.884i	−0.0370654	−	0.0641991i
$255$		0			0
$256$	45.5351	+	258.243i	0.0111170	+	0.0630475i
$257$	−1148.40	−	6512.88i	−0.278735	−	1.58079i	−0.726840	−	0.686806i	$-0.759012\pi$
$257$	−1148.40	−	6512.88i	−0.278735	−	1.58079i	0.448105	−	0.893981i	$-0.352099\pi$
$258$		0			0
$259$	−3980.79	−	6894.94i	−0.955037	−	1.65417i
$260$	98.5176	−	82.6661i	0.0234992	−	0.0197182i
$261$		0			0
$262$	−1320.89	−	480.766i	−0.311470	−	0.113366i
$263$	413.975	+	347.367i	0.0970601	+	0.0814431i	0.690026	−	0.723784i	$-0.257599\pi$
$263$	413.975	+	347.367i	0.0970601	+	0.0814431i	−0.592966	+	0.805227i	$0.702043\pi$
$264$		0			0
$265$	2395.87			0.555385
$266$	−1527.31	+	1006.53i	−0.352050	+	0.232009i
$267$		0			0
$268$	−444.032	+	2518.23i	−0.101207	+	0.573975i
$269$	1331.16	+	1116.97i	0.301718	+	0.253171i	0.781059	−	0.624457i	$-0.214680\pi$
$269$	1331.16	+	1116.97i	0.301718	+	0.253171i	−0.479341	+	0.877629i	$0.659124\pi$
$270$		0			0
$271$	−2574.72	+	937.122i	−0.577133	+	0.210059i	−0.614061	−	0.789259i	$-0.710465\pi$
$271$	−2574.72	+	937.122i	−0.577133	+	0.210059i	0.0369276	+	0.999318i	$0.488243\pi$
$272$	1865.59	−	1565.42i	0.415875	−	0.348961i
$273$		0			0
$274$	754.091	−	1306.12i	0.166264	−	0.287978i
$275$	326.740	+	1853.03i	0.0716479	+	0.406335i
$276$		0			0
$277$	−659.907	+	1142.99i	−0.143141	+	0.247927i	−0.928678	−	0.370888i	$-0.879053\pi$
$277$	−659.907	+	1142.99i	−0.143141	+	0.247927i	0.785537	+	0.618815i	$0.212387\pi$
$278$	−557.307	−	965.284i	−0.120234	−	0.208251i
$279$		0			0
$280$	−1187.17	+	432.093i	−0.253381	+	0.0922233i
$281$	3029.69	+	1102.72i	0.643189	+	0.234102i	0.642962	−	0.765898i	$-0.277705\pi$
$281$	3029.69	+	1102.72i	0.643189	+	0.234102i	0.000227570		1.00000i	$0.499928\pi$
$282$		0			0
$283$	−71.3067	+	404.400i	−0.0149779	+	0.0849439i	−0.991380	−	0.131015i	$-0.958176\pi$
$283$	−71.3067	+	404.400i	−0.0149779	+	0.0849439i	0.976403	+	0.215959i	$0.0692876\pi$
$284$	−7553.11			−1.57815
$285$		0			0
$286$	−76.6183			−0.0158410
$287$	−1804.45	+	10233.6i	−0.371127	+	2.10477i
$288$		0			0
$289$	1663.42	+	605.436i	0.338575	+	0.123231i
$290$	−577.340	+	210.135i	−0.116905	+	0.0425501i
$291$		0			0
$292$	1055.58	+	1828.32i	0.211552	+	0.366418i
$293$	2885.13	−	4997.20i	0.575260	−	0.996380i	−0.420753	−	0.907175i	$-0.638234\pi$
$293$	2885.13	−	4997.20i	0.575260	−	0.996380i	0.996013	−	0.0892050i	$-0.0284326\pi$
$294$		0			0
$295$	432.626	+	2453.55i	0.0853847	+	0.484241i
$296$	2422.80	−	4196.40i	0.475750	−	0.824024i
$297$		0			0
$298$	1582.62	−	1327.97i	0.307646	−	0.258146i
$299$	400.470	−	145.759i	0.0774575	−	0.0281922i
$300$		0			0
$301$	4839.93	+	4061.19i	0.926808	+	0.777684i
$302$	−596.978	+	3385.63i	−0.113749	+	0.645103i
$303$		0			0
$304$	3216.56	+	1611.73i	0.606849	+	0.304076i
$305$	−547.789			−0.102840
$306$		0			0
$307$	3846.67	+	3227.74i	0.715118	+	0.600055i	0.926030	−	0.377450i	$-0.123199\pi$
$307$	3846.67	+	3227.74i	0.715118	+	0.600055i	−0.210912	+	0.977505i	$0.567643\pi$
$308$	−2660.17	−	968.221i	−0.492133	−	0.179122i
$309$		0			0
$310$	−263.549	+	221.144i	−0.0482857	+	0.0405165i
$311$	1420.47	+	2460.33i	0.258996	+	0.448593i	0.965973	−	0.258643i	$-0.0832752\pi$
$311$	1420.47	+	2460.33i	0.258996	+	0.448593i	−0.706978	+	0.707236i	$0.749942\pi$
$312$		0			0
$313$	−1853.30	−	10510.6i	−0.334680	−	1.89806i	−0.430370	−	0.902653i	$-0.641617\pi$
$313$	−1853.30	−	10510.6i	−0.334680	−	1.89806i	0.0956900	−	0.995411i	$-0.469494\pi$
$314$	−543.759	−	3083.81i	−0.0977265	−	0.554234i
$315$		0			0
$316$	−377.615	−	654.049i	−0.0672232	−	0.116434i
$317$	814.617	−	683.545i	0.144333	−	0.121109i	−0.567763	−	0.823192i	$-0.692191\pi$
$317$	814.617	−	683.545i	0.144333	−	0.121109i	0.712095	+	0.702083i	$0.247746\pi$
$318$		0			0
$319$	−2749.23	−	1000.64i	−0.482530	−	0.175627i
$320$	583.896	+	489.947i	0.102002	+	0.0855901i
$321$		0			0
$322$	−1970.01			−0.340945
$323$	−274.203	−	4634.81i	−0.0472356	−	0.798414i
$324$		0			0
$325$	−91.8188	+	520.730i	−0.0156714	+	0.0888767i
$326$	−74.9823	−	62.9176i	−0.0127389	−	0.0106892i
$327$		0			0
$328$	−5943.03	+	2163.09i	−1.00045	+	0.364136i
$329$	8703.33	−	7302.96i	1.45845	−	1.22379i
$330$		0			0
$331$	2675.39	−	4633.90i	0.444267	−	0.769494i	−0.553734	−	0.832694i	$-0.686797\pi$
$331$	2675.39	−	4633.90i	0.444267	−	0.769494i	0.998001	+	0.0632003i	$0.0201307\pi$
$332$	821.767	+	4660.47i	0.135844	+	0.770411i
$333$		0			0
$334$	−777.352	+	1346.41i	−0.127350	+	0.220576i
$335$	680.692	+	1178.99i	0.111015	+	0.192284i
$336$		0			0
$337$	7998.78	−	2911.32i	1.29294	−	0.470592i	0.398250	−	0.917277i	$-0.369618\pi$
$337$	7998.78	−	2911.32i	1.29294	−	0.470592i	0.894691	+	0.446685i	$0.147395\pi$
$338$	1926.97	+	701.358i	0.310098	+	0.112866i
$339$		0			0
$340$	262.033	−	1486.07i	0.0417963	−	0.237039i
$341$	−1638.27			−0.260168
$342$		0			0
$343$	−3223.61			−0.507459
$344$	−667.733	+	3786.90i	−0.104656	+	0.593535i
$345$		0			0
$346$	−531.643	−	193.502i	−0.0826050	−	0.0300658i
$347$	−5063.32	+	1842.90i	−0.783324	+	0.285107i	−0.702558	−	0.711626i	$-0.747959\pi$
$347$	−5063.32	+	1842.90i	−0.783324	+	0.285107i	−0.0807660	+	0.996733i	$0.525737\pi$
$348$		0			0
$349$	−1466.84	−	2540.64i	−0.224980	−	0.389677i	0.731334	−	0.682020i	$-0.238898\pi$
$349$	−1466.84	−	2540.64i	−0.224980	−	0.389677i	−0.956313	+	0.292343i	$0.905565\pi$
$350$	1222.13	−	2116.78i	0.186644	−	0.323277i
$351$		0			0
$352$	−457.585	−	2595.09i	−0.0692879	−	0.392951i
$353$	4641.05	−	8038.53i	0.699767	−	1.21203i	−0.268779	−	0.963202i	$-0.586620\pi$
$353$	4641.05	−	8038.53i	0.699767	−	1.21203i	0.968547	−	0.248831i	$-0.0800464\pi$
$354$		0			0
$355$	−3080.47	+	2584.82i	−0.460547	+	0.386445i
$356$	2206.62	−	803.142i	0.328512	−	0.119569i
$357$		0			0
$358$	−1725.42	−	1447.80i	−0.254724	−	0.213739i
$359$	826.688	−	4688.38i	0.121535	−	0.689257i	−0.861771	−	0.507297i	$-0.830645\pi$
$359$	826.688	−	4688.38i	0.121535	−	0.689257i	0.983306	−	0.181960i	$-0.0582442\pi$
$360$		0			0
$361$	6123.78	−	3089.53i	0.892810	−	0.450434i
$362$	−2839.91			−0.412327
$363$		0			0
$364$	−609.405	−	511.351i	−0.0877514	−	0.0736321i
$365$	1056.19	+	384.423i	0.151462	+	0.0551277i
$366$		0			0
$367$	−1956.31	+	1641.54i	−0.278253	+	0.233482i	−0.771224	−	0.636564i	$-0.780355\pi$
$367$	−1956.31	+	1641.54i	−0.278253	+	0.233482i	0.492971	+	0.870046i	$0.335911\pi$
$368$	1937.42	+	3355.71i	0.274443	+	0.475349i
$369$		0			0
$370$	−210.801	−	1195.51i	−0.0296189	−	0.167977i
$371$	−2573.51	−	14595.1i	−0.360134	−	2.04242i
$372$		0			0
$373$	2414.57	+	4182.17i	0.335179	+	0.580548i	0.983519	−	0.180803i	$-0.0578697\pi$
$373$	2414.57	+	4182.17i	0.335179	+	0.580548i	−0.648340	+	0.761351i	$0.724536\pi$
$374$	−688.673	+	577.865i	−0.0952150	+	0.0798949i
$375$		0			0
$376$	6497.77	+	2365.00i	0.891215	+	0.324376i
$377$	−629.807	−	528.471i	−0.0860390	−	0.0721953i
$378$		0			0
$379$	1850.42			0.250791			0.125395	−	0.992107i	$-0.459980\pi$
$379$	1850.42			0.250791			0.125395	+	0.992107i	$0.459980\pi$
$380$	2168.68	−	516.083i	0.292765	−	0.0696698i
$381$		0			0
$382$	145.017	−	822.432i	0.0194233	−	0.110155i
$383$	−3338.66	−	2801.47i	−0.445424	−	0.373755i	0.392311	−	0.919833i	$-0.371676\pi$
$383$	−3338.66	−	2801.47i	−0.445424	−	0.373755i	−0.837734	+	0.546078i	$0.816120\pi$
$384$		0			0
$385$	−1416.27	+	515.479i	−0.187480	+	0.0682370i
$386$	1177.17	−	987.767i	0.155224	−	0.130249i
$387$		0			0
$388$	92.2016	−	159.698i	0.0120640	−	0.0208954i
$389$	−828.971	−	4701.33i	−0.108048	−	0.612768i	−0.989959	−	0.141353i	$-0.954855\pi$
$389$	−828.971	−	4701.33i	−0.108048	−	0.612768i	0.881912	−	0.471415i	$-0.156256\pi$
$390$		0			0
$391$	2500.24	−	4330.53i	0.323382	−	0.560114i
$392$	1463.21	+	2534.36i	0.188529	+	0.326542i
$393$		0			0
$394$	1683.45	−	612.727i	0.215257	−	0.0783470i
$395$	−377.835	−	137.521i	−0.0481290	−	0.0175175i
$396$		0			0
$397$	−186.308	+	1056.60i	−0.0235529	+	0.133575i	−0.994317	−	0.106461i	$-0.966048\pi$
$397$	−186.308	+	1056.60i	−0.0235529	+	0.133575i	0.970764	+	0.240036i	$0.0771592\pi$
$398$	533.844			0.0672342
$399$		0			0
$400$	−4807.62			−0.600953
$401$	−1715.93	+	9731.54i	−0.213690	+	1.21190i	0.669476	+	0.742834i	$0.266519\pi$
$401$	−1715.93	+	9731.54i	−0.213690	+	1.21190i	−0.883166	+	0.469061i	$0.844592\pi$
$402$		0			0
$403$	−432.614	−	157.459i	−0.0534741	−	0.0194630i
$404$	−8118.95	+	2955.05i	−0.999833	+	0.363910i
$405$		0			0
$406$	1900.24	+	3291.31i	0.232284	+	0.402327i
$407$	2890.35	−	5006.23i	0.352013	−	0.609705i
$408$		0			0
$409$	−1971.95	−	11183.5i	−0.238403	−	1.35205i	−0.835328	−	0.549752i	$-0.814722\pi$
$409$	−1971.95	−	11183.5i	−0.238403	−	1.35205i	0.596925	−	0.802297i	$-0.296389\pi$
$410$	−792.223	+	1372.17i	−0.0954271	+	0.165285i
$411$		0			0
$412$	−6014.48	+	5046.75i	−0.719204	+	0.603484i
$413$	14481.7	−	5270.92i	1.72542	−	0.628003i
$414$		0			0
$415$	1930.05	+	1619.51i	0.228295	+	0.191563i
$416$	128.588	−	729.259i	0.0151552	−	0.0859492i
$417$		0			0
$418$	−1187.37	−	594.962i	−0.138939	−	0.0696185i
$419$	38.5998			0.00450053			0.00225027	−	0.999997i	$-0.499284\pi$
$419$	38.5998			0.00450053			0.00225027	+	0.999997i	$0.499284\pi$
$420$		0			0
$421$	−3814.96	−	3201.13i	−0.441638	−	0.370579i	0.394684	−	0.918817i	$-0.370854\pi$
$421$	−3814.96	−	3201.13i	−0.441638	−	0.370579i	−0.836322	+	0.548238i	$0.815299\pi$
$422$	658.130	+	239.540i	0.0759177	+	0.0276318i
$423$		0			0
$424$	6909.65	−	5797.88i	0.791420	−	0.664080i
$425$	3102.11	+	5373.02i	0.354058	+	0.613246i
$426$		0			0
$427$	588.404	+	3337.00i	0.0666858	+	0.378194i
$428$	−1058.20	−	6001.37i	−0.119510	−	0.677774i
$429$		0			0
$430$	481.679	+	834.293i	0.0540201	+	0.0935655i
$431$	−10524.9	+	8831.41i	−1.17625	+	0.986993i	−0.176256	+	0.984344i	$0.556399\pi$
$431$	−10524.9	+	8831.41i	−1.17625	+	0.986993i	−0.999996	+	0.00264876i	$0.999157\pi$
$432$		0			0
$433$	−7727.14	−	2812.45i	−0.857605	−	0.312143i	−0.124468	−	0.992224i	$-0.539722\pi$
$433$	−7727.14	−	2812.45i	−0.857605	−	0.312143i	−0.733137	+	0.680081i	$0.761945\pi$
$434$	1630.25	+	1367.94i	0.180309	+	0.151298i
$435$		0			0
$436$	−4860.72			−0.533914
$437$	7338.05	+	850.888i	0.803265	+	0.0931431i
$438$		0			0
$439$	−2744.45	+	15564.5i	−0.298372	+	1.69215i	0.354800	+	0.934942i	$0.384549\pi$
$439$	−2744.45	+	15564.5i	−0.298372	+	1.69215i	−0.653172	+	0.757209i	$0.726562\pi$
$440$	−702.685	−	589.623i	−0.0761345	−	0.0638844i
$441$		0			0
$442$	−237.396	+	86.4052i	−0.0255470	+	0.00929836i
$443$	−9716.94	+	8153.48i	−1.04213	+	0.874455i	−0.992245	−	0.124300i	$-0.960332\pi$
$443$	−9716.94	+	8153.48i	−1.04213	+	0.874455i	−0.0498902	+	0.998755i	$0.515887\pi$
$444$		0			0
$445$	625.097	−	1082.70i	0.0665898	−	0.115337i
$446$	−310.946	−	1763.46i	−0.0330128	−	0.187225i
$447$		0			0
$448$	2357.45	−	4083.23i	0.248614	−	0.430613i
$449$	−506.466	−	877.224i	−0.0532329	−	0.0922022i	0.838181	−	0.545392i	$-0.183619\pi$
$449$	−506.466	−	877.224i	−0.0532329	−	0.0922022i	−0.891414	+	0.453190i	$0.850286\pi$
$450$		0			0
$451$	−7089.93	+	2580.52i	−0.740247	+	0.269428i
$452$	346.394	+	126.077i	0.0360465	+	0.0131199i
$453$		0			0
$454$	−332.981	+	1888.43i	−0.0344220	+	0.195217i
$455$	−423.534			−0.0436387
$456$		0			0
$457$	6259.48			0.640713			0.320357	−	0.947297i	$-0.396197\pi$
$457$	6259.48			0.640713			0.320357	+	0.947297i	$0.396197\pi$
$458$	461.271	−	2616.00i	0.0470606	−	0.266894i
$459$		0			0
$460$	2256.12	+	821.162i	0.228679	+	0.0832323i
$461$	−14661.8	+	5336.47i	−1.48128	+	0.539142i	−0.951138	−	0.308767i	$-0.900084\pi$
$461$	−14661.8	+	5336.47i	−1.48128	+	0.539142i	−0.530142	+	0.847909i	$0.677861\pi$
$462$		0			0
$463$	681.454	+	1180.31i	0.0684014	+	0.118475i	0.898198	−	0.439592i	$-0.144877\pi$
$463$	681.454	+	1180.31i	0.0684014	+	0.118475i	−0.829796	+	0.558066i	$0.811543\pi$
$464$	3737.60	−	6473.71i	0.373952	−	0.647703i
$465$		0			0
$466$	381.670	+	2164.56i	0.0379411	+	0.215174i
$467$	−5920.04	+	10253.8i	−0.586610	+	1.01604i	0.408062	+	0.912954i	$0.366205\pi$
$467$	−5920.04	+	10253.8i	−0.586610	+	1.01604i	−0.994673	+	0.103085i	$0.967129\pi$
$468$		0			0
$469$	6450.99	−	5413.02i	0.635137	−	0.532943i
$470$	1627.87	−	592.496i	0.159762	−	0.0581485i
$471$		0			0
$472$	7185.15	+	6029.06i	0.700685	+	0.587945i
$473$	−796.593	+	4517.70i	−0.0774363	+	0.439163i
$474$		0			0
$475$	−5466.55	+	7356.90i	−0.528047	+	0.710648i
$476$	−9334.23			−0.898810
$477$		0			0
$478$	379.880	+	318.757i	0.0363500	+	0.0305013i
$479$	2848.93	+	1036.93i	0.271756	+	0.0989110i	0.474304	−	0.880361i	$-0.342700\pi$
$479$	2848.93	+	1036.93i	0.271756	+	0.0989110i	−0.202548	+	0.979272i	$0.564922\pi$
$480$		0			0
$481$	1244.41	−	1044.18i	0.117963	−	0.0989828i
$482$	2909.47	+	5039.36i	0.274944	+	0.476217i
$483$		0			0
$484$	1286.48	+	7295.97i	0.120819	+	0.685196i
$485$	−17.0481	−	96.6844i	−0.00159611	−	0.00905199i
$486$		0			0
$487$	1851.71	+	3207.25i	0.172298	+	0.298428i	0.939223	−	0.343308i	$-0.111548\pi$
$487$	1851.71	+	3207.25i	0.172298	+	0.298428i	−0.766925	+	0.641737i	$0.778214\pi$
$488$	−1579.81	+	1325.62i	−0.146547	+	0.122967i
$489$		0			0
$490$	688.935	+	250.752i	0.0635161	+	0.0231180i
$491$	9832.45	+	8250.40i	0.903731	+	0.758321i	0.970916	−	0.239420i	$-0.0769572\pi$
$491$	9832.45	+	8250.40i	0.903731	+	0.758321i	−0.0671847	+	0.997741i	$0.521402\pi$
$492$		0			0
$493$	−9646.73			−0.881272
$494$	−256.364	−	271.232i	−0.0233489	−	0.0247030i
$495$		0			0
$496$	726.865	−	4122.26i	0.0658008	−	0.373175i
$497$	19055.0	+	15989.0i	1.71978	+	1.44307i
$498$		0			0
$499$	−7899.42	+	2875.15i	−0.708670	+	0.257935i	−0.671108	−	0.741359i	$-0.734181\pi$
$499$	−7899.42	+	2875.15i	−0.708670	+	0.257935i	−0.0375620	+	0.999294i	$0.511959\pi$
$500$	−4859.41	+	4077.53i	−0.434639	+	0.364705i
$501$		0			0
$502$	1999.07	−	3462.49i	0.177735	−	0.307846i
$503$	−1924.18	−	10912.5i	−0.170566	−	0.967328i	−0.943138	−	0.332401i	$-0.892141\pi$
$503$	−1924.18	−	10912.5i	−0.170566	−	0.967328i	0.772572	−	0.634927i	$-0.218970\pi$
$504$		0			0
$505$	−2299.96	+	3983.65i	−0.202667	+	0.351030i
$506$	−715.187	−	1238.74i	−0.0628339	−	0.108831i
$507$		0			0
$508$	2125.86	−	773.751i	0.185669	−	0.0675780i
$509$	−12476.9	−	4541.22i	−1.08650	−	0.395454i	−0.264177	−	0.964474i	$-0.585100\pi$
$509$	−12476.9	−	4541.22i	−1.08650	−	0.395454i	−0.822324	+	0.569020i	$0.807323\pi$
$510$		0			0
$511$	1207.31	−	6847.01i	0.104517	−	0.592748i
$512$	11685.8			1.00868
$513$		0			0
$514$	−6237.58			−0.535268
$515$	−725.857	+	4116.54i	−0.0621069	+	0.352226i
$516$		0			0
$517$	7751.72	+	2821.40i	0.659421	+	0.240009i
$518$	−7056.35	+	2568.30i	−0.598529	+	0.217847i
$519$		0			0
$520$	−128.886	−	223.237i	−0.0108693	−	0.0188261i
$521$	−1269.34	+	2198.55i	−0.106738	+	0.184876i	−0.914447	−	0.404706i	$-0.867374\pi$
$521$	−1269.34	+	2198.55i	−0.106738	+	0.184876i	0.807709	+	0.589582i	$0.200707\pi$
$522$		0			0
$523$	−1925.75	−	10921.4i	−0.161008	−	0.913119i	−0.953086	−	0.302700i	$-0.902112\pi$
$523$	−1925.75	−	10921.4i	−0.161008	−	0.913119i	0.792078	−	0.610419i	$-0.208999\pi$
$524$	5298.50	−	9177.27i	0.441729	−	0.765097i
$525$		0			0
$526$	390.453	−	327.629i	0.0323661	−	0.0271584i
$527$	−5076.07	+	1847.54i	−0.419577	+	0.152713i
$528$		0			0
$529$	−3225.72	−	2706.70i	−0.265120	−	0.222462i
$530$	392.399	−	2225.40i	0.0321598	−	0.182387i
$531$		0			0
$532$	−5473.33	−	12656.7i	−0.446051	−	1.03147i
$533$	−2120.24			−0.172304
$534$		0			0
$535$	−2485.36	−	2085.47i	−0.200844	−	0.168528i
$536$	4816.21	+	1752.96i	0.388113	+	0.141262i
$537$		0			0
$538$	1255.52	−	1053.51i	0.100612	−	0.0844235i
$539$	1745.58	+	3023.44i	0.139495	+	0.241612i
$540$		0			0
$541$	3718.51	+	21088.7i	0.295511	+	1.67592i	0.665120	+	0.746736i	$0.268380\pi$
$541$	3718.51	+	21088.7i	0.295511	+	1.67592i	−0.369610	+	0.929187i	$0.620509\pi$
$542$	448.755	+	2545.01i	0.0355639	+	0.201693i
$543$		0			0
$544$	−4344.37	−	7524.67i	−0.342396	−	0.593047i
$545$	−1982.40	+	1663.43i	−0.155810	+	0.130741i
$546$		0			0
$547$	17512.9	+	6374.16i	1.36891	+	0.498244i	0.918799	−	0.394727i	$-0.129161\pi$
$547$	17512.9	+	6374.16i	1.36891	+	0.498244i	0.450115	+	0.892971i	$0.351383\pi$
$548$	8709.80	+	7308.39i	0.678949	+	0.569706i
$549$		0			0
$550$	1774.71			0.137589
$551$	−5656.57	−	13080.5i	−0.437347	−	1.01134i
$552$		0			0
$553$	−431.895	+	2449.40i	−0.0332117	+	0.188353i
$554$	953.589	+	800.156i	0.0731301	+	0.0613635i
$555$		0			0
$556$	7896.06	−	2873.93i	0.602280	−	0.219212i
$557$	−2389.08	+	2004.67i	−0.181739	+	0.152497i	−0.729119	−	0.684387i	$-0.760070\pi$
$557$	−2389.08	+	2004.67i	−0.181739	+	0.152497i	0.547380	+	0.836884i	$0.315625\pi$
$558$		0			0
$559$	−644.563	+	1116.42i	−0.0487694	+	0.0844711i
$560$	−668.695	−	3792.36i	−0.0504598	−	0.286172i
$561$		0			0
$562$	1520.47	−	2633.53i	0.114123	−	0.197667i
$563$	−8575.18	−	14852.6i	−0.641920	−	1.11184i	−0.985004	−	0.172533i	$-0.944805\pi$
$563$	−8575.18	−	14852.6i	−0.641920	−	1.11184i	0.343084	−	0.939305i	$-0.388528\pi$
$564$		0			0
$565$	184.420	−	67.1233i	0.0137320	−	0.00499805i
$566$	363.949	+	132.467i	0.0270281	+	0.00983743i
$567$		0			0
$568$	−2628.89	+	14909.2i	−0.194200	+	1.10136i
$569$	−13225.5			−0.974412			−0.487206	−	0.873287i	$-0.661984\pi$
$569$	−13225.5			−0.974412			−0.487206	+	0.873287i	$0.661984\pi$
$570$		0			0
$571$	−14794.1			−1.08426			−0.542131	−	0.840294i	$-0.682382\pi$
$571$	−14794.1			−1.08426			−0.542131	+	0.840294i	$0.682382\pi$
$572$	100.300	−	568.832i	0.00733177	−	0.0415805i
$573$		0			0
$574$	9209.91	+	3352.13i	0.669711	+	0.243755i
$575$	−9276.08	+	3376.22i	−0.672764	+	0.244866i
$576$		0			0
$577$	7485.49	+	12965.3i	0.540078	+	0.935443i	0.998899	+	0.0469140i	$0.0149387\pi$
$577$	7485.49	+	12965.3i	0.540078	+	0.935443i	−0.458821	+	0.888529i	$0.651728\pi$
$578$	834.796	−	1445.91i	0.0600743	−	0.104052i
$579$		0			0
$580$	−804.297	−	4561.40i	−0.0575804	−	0.326555i
$581$	7792.51	−	13497.0i	0.556433	−	0.963771i
$582$		0			0
$583$	8243.08	−	6916.77i	0.585581	−	0.491361i
$584$	3976.33	−	1447.27i	0.281750	−	0.102548i
$585$		0			0
$586$	−4169.12	−	3498.31i	−0.293899	−	0.246610i
$587$	−3691.48	+	20935.4i	−0.259564	+	1.47206i	0.524518	+	0.851400i	$0.324246\pi$
$587$	−3691.48	+	20935.4i	−0.259564	+	1.47206i	−0.784081	+	0.620658i	$0.786865\pi$
$588$		0			0
$589$	−5481.63	−	5799.54i	−0.383475	−	0.405715i
$590$	2349.83			0.163968
$591$		0			0
$592$	11314.4	+	9493.93i	0.785507	+	0.659119i
$593$	−128.134	−	46.6369i	−0.00887324	−	0.00322959i	0.337580	−	0.941297i	$-0.390392\pi$
$593$	−128.134	−	46.6369i	−0.00887324	−	0.00322959i	−0.346453	+	0.938067i	$0.612614\pi$
$594$		0			0
$595$	−3806.88	+	3194.35i	−0.262297	+	0.220094i
$596$	7787.40	+	13488.2i	0.535209	+	0.927008i
$597$		0			0
$598$	−69.7989	−	395.849i	−0.00477306	−	0.0270694i
$599$	263.981	+	1497.11i	0.0180067	+	0.102121i	0.992486	−	0.122354i	$-0.0390444\pi$
$599$	263.981	+	1497.11i	0.0180067	+	0.102121i	−0.974480	+	0.224475i	$0.927933\pi$
$600$		0			0
$601$	1491.05	+	2582.57i	0.101200	+	0.175283i	0.912179	−	0.409791i	$-0.134399\pi$
$601$	1491.05	+	2582.57i	0.101200	+	0.175283i	−0.810979	+	0.585075i	$0.801065\pi$
$602$	4564.93	−	3830.43i	0.309057	−	0.259330i
$603$		0			0
$604$	−24354.2	−	8864.21i	−1.64066	−	0.597152i
$605$	3021.50	+	2535.34i	0.203044	+	0.170374i
$606$		0			0
$607$	−23046.1			−1.54104			−0.770522	−	0.637414i	$-0.780004\pi$
$607$	−23046.1			−1.54104			−0.770522	+	0.637414i	$0.780004\pi$
$608$	7655.66	−	10303.0i	0.510654	−	0.687240i
$609$		0			0
$610$	−89.7176	+	508.814i	−0.00595502	+	0.0337726i
$611$	1775.81	+	1490.08i	0.117580	+	0.0986614i
$612$		0			0
$613$	−5160.87	+	1878.40i	−0.340042	+	0.123765i	−0.506396	−	0.862301i	$-0.669023\pi$
$613$	−5160.87	+	1878.40i	−0.340042	+	0.123765i	0.166355	+	0.986066i	$0.446800\pi$
$614$	3628.10	−	3044.34i	0.238466	−	0.200097i
$615$		0			0
$616$	−2837.06	+	4913.93i	−0.185566	+	0.321409i
$617$	4064.66	+	23051.9i	0.265214	+	1.50410i	0.768424	+	0.639941i	$0.221041\pi$
$617$	4064.66	+	23051.9i	0.265214	+	1.50410i	−0.503210	+	0.864164i	$0.667848\pi$
$618$		0			0
$619$	9055.22	−	15684.1i	0.587980	−	1.01841i	−0.406516	−	0.913644i	$-0.633257\pi$
$619$	9055.22	−	15684.1i	0.587980	−	1.01841i	0.994497	−	0.104768i	$-0.0334102\pi$
$620$	−1296.81	−	2246.15i	−0.0840021	−	0.145496i
$621$		0			0
$622$	2517.93	−	916.450i	0.162315	−	0.0590777i
$623$	−7267.01	−	2644.97i	−0.467330	−	0.170094i
$624$		0			0
$625$	1815.74	−	10297.5i	0.116207	−	0.659043i
$626$	−10066.3			−0.642701
$627$		0			0
$628$	23606.8			1.50002
$629$	3309.84	−	18771.0i	0.209812	−	1.18990i
$630$		0			0
$631$	−7360.46	−	2678.99i	−0.464367	−	0.169016i	0.0992320	−	0.995064i	$-0.468361\pi$
$631$	−7360.46	−	2678.99i	−0.464367	−	0.169016i	−0.563599	+	0.826049i	$0.690584\pi$
$632$	−1422.46	+	517.734i	−0.0895294	+	0.0325860i
$633$		0			0
$634$	−501.492	−	868.609i	−0.0314145	−	0.0544115i
$635$	602.221	−	1043.08i	0.0376353	−	0.0651863i
$636$		0			0
$637$	170.361	+	966.165i	0.0105965	+	0.0600955i
$638$	−1379.71	+	2389.73i	−0.0856166	+	0.148292i
$639$		0			0
$640$	4146.33	−	3479.18i	0.256091	−	0.214885i
$641$	23616.6	−	8595.75i	1.45523	−	0.529659i	0.511181	−	0.859473i	$-0.329208\pi$
$641$	23616.6	−	8595.75i	1.45523	−	0.529659i	0.944046	+	0.329813i	$0.106986\pi$
$642$		0			0
$643$	6099.27	+	5117.90i	0.374077	+	0.313888i	0.810372	−	0.585916i	$-0.199265\pi$
$643$	6099.27	+	5117.90i	0.374077	+	0.313888i	−0.436295	+	0.899804i	$0.643709\pi$
$644$	2578.93	−	14625.8i	0.157801	−	0.894936i
$645$		0			0
$646$	−4349.95	−	504.401i	−0.264933	−	0.0307204i
$647$	25846.9			1.57055			0.785274	−	0.619148i	$-0.212522\pi$
$647$	25846.9			1.57055			0.785274	+	0.619148i	$0.212522\pi$
$648$		0			0
$649$	8571.75	+	7192.56i	0.518445	+	0.435027i
$650$	468.642	+	170.572i	0.0282795	+	0.0102929i
$651$		0			0
$652$	565.274	−	474.321i	0.0339538	−	0.0284906i
$653$	−10585.2	−	18334.1i	−0.634349	−	1.09872i	−0.986653	−	0.162839i	$-0.947935\pi$
$653$	−10585.2	−	18334.1i	−0.634349	−	1.09872i	0.352304	−	0.935886i	$-0.385398\pi$
$654$		0			0
$655$	−979.692	−	5556.11i	−0.0584424	−	0.331443i
$656$	−3347.53	−	18984.8i	−0.199236	−	1.12993i
$657$		0			0
$658$	−5357.92	−	9280.18i	−0.317437	−	0.549817i
$659$	−1457.50	+	1222.99i	−0.0861553	+	0.0722928i	−0.684848	−	0.728686i	$-0.740131\pi$
$659$	−1457.50	+	1222.99i	−0.0861553	+	0.0722928i	0.598693	+	0.800979i	$0.295687\pi$
$660$		0			0
$661$	−9249.75	−	3366.63i	−0.544287	−	0.198104i	0.0552195	−	0.998474i	$-0.482414\pi$
$661$	−9249.75	−	3366.63i	−0.544287	−	0.198104i	−0.599506	+	0.800370i	$0.704636\pi$
$662$	−3866.03	−	3243.98i	−0.226975	−	0.190454i
$663$		0			0
$664$	9485.37			0.554373
$665$	−6563.63	−	3288.86i	−0.382747	−	0.191784i
$666$		0			0
$667$	2665.27	−	15115.5i	0.154722	−	0.877473i
$668$	−8978.47	−	7533.83i	−0.520041	−	0.436366i
$669$		0			0
$670$	1206.59	−	439.164i	0.0695742	−	0.0253229i
$671$	−1884.69	+	1581.44i	−0.108432	+	0.0909850i
$672$		0			0
$673$	13512.1	−	23403.6i	0.773927	−	1.34048i	−0.161469	−	0.986878i	$-0.551623\pi$
$673$	13512.1	−	23403.6i	0.773927	−	1.34048i	0.935396	−	0.353602i	$-0.115043\pi$
$674$	−1394.13	−	7906.49i	−0.0796733	−	0.451850i
$675$		0			0
$676$	−7729.63	+	13388.1i	−0.439783	+	0.761727i
$677$	−8471.72	−	14673.4i	−0.480937	−	0.833008i	0.518823	−	0.854881i	$-0.326370\pi$
$677$	−8471.72	−	14673.4i	−0.480937	−	0.833008i	−0.999761	+	0.0218734i	$0.993037\pi$
$678$		0			0
$679$	−570.667	+	207.706i	−0.0322536	+	0.0117394i
$680$	−2842.16	−	1034.46i	−0.160282	−	0.0583379i
$681$		0			0
$682$	−268.318	+	1521.71i	−0.0150652	+	0.0854388i
$683$	−24966.9			−1.39873			−0.699364	−	0.714766i	$-0.746533\pi$
$683$	−24966.9			−1.39873			−0.699364	+	0.714766i	$0.746533\pi$
$684$		0			0
$685$	6053.28			0.337641
$686$	−527.967	+	2994.25i	−0.0293846	+	0.166649i
$687$		0			0
$688$	−11014.1	−	4008.82i	−0.610334	−	0.222143i
$689$	2841.52	−	1034.23i	0.157117	−	0.0571857i
$690$		0			0
$691$	−6307.11	−	10924.2i	−0.347227	−	0.601415i	0.638529	−	0.769598i	$-0.279543\pi$
$691$	−6307.11	−	10924.2i	−0.347227	−	0.601415i	−0.985756	+	0.168183i	$0.946210\pi$
$692$	2132.58	−	3693.73i	0.117151	−	0.202911i
$693$		0			0
$694$	882.499	+	5004.90i	0.0482698	+	0.273751i
$695$	2236.82	−	3874.29i	0.122083	−	0.211454i
$696$		0			0
$697$	−19057.5	+	15991.1i	−1.03566	+	0.869020i
$698$	−2600.11	+	946.363i	−0.140997	+	0.0513186i
$699$		0			0
$700$	14115.6	+	11844.4i	0.762172	+	0.639538i
$701$	−2001.90	+	11353.3i	−0.107861	+	0.611711i	0.882178	+	0.470917i	$0.156077\pi$
$701$	−2001.90	+	11353.3i	−0.107861	+	0.611711i	−0.990039	+	0.140794i	$0.955034\pi$
$702$		0			0
$703$	27393.3	−	6518.83i	1.46964	−	0.349733i
$704$	3423.37			0.183272
$705$		0			0
$706$	−6706.47	−	5627.40i	−0.357509	−	0.299986i
$707$	26738.0	+	9731.83i	1.42233	+	0.517685i
$708$		0			0
$709$	−10556.8	+	8858.21i	−0.559195	+	0.469220i	−0.878040	−	0.478587i	$-0.841149\pi$
$709$	−10556.8	+	8858.21i	−0.559195	+	0.469220i	0.318846	+	0.947807i	$0.396705\pi$
$710$	1896.39	+	3284.64i	0.100240	+	0.173620i
$711$		0			0
$712$	−817.310	−	4635.20i	−0.0430197	−	0.243977i
$713$	−1492.46	−	8464.15i	−0.0783913	−	0.444579i
$714$		0			0
$715$	−153.759	−	266.318i	−0.00804230	−	0.0139297i
$716$	13007.5	−	10914.6i	0.678931	−	0.569691i
$717$		0			0
$718$	−4219.41	−	1535.74i	−0.219313	−	0.0798235i
$719$	14323.1	+	12018.5i	0.742923	+	0.623387i	0.933621	−	0.358262i	$-0.116631\pi$
$719$	14323.1	+	12018.5i	0.742923	+	0.623387i	−0.190698	+	0.981649i	$0.561075\pi$
$720$		0			0
$721$	25856.7			1.33558
$722$	−1866.75	−	6194.08i	−0.0962232	−	0.319280i
$723$		0			0
$724$	3717.71	−	21084.2i	0.190839	−	1.08230i
$725$	14588.2	+	12241.0i	0.747300	+	0.627059i
$726$		0			0
$727$	−26490.8	+	9641.88i	−1.35143	+	0.491881i	−0.913395	−	0.407076i	$-0.866549\pi$
$727$	−26490.8	+	9641.88i	−1.35143	+	0.491881i	−0.438038	+	0.898957i	$0.644326\pi$
$728$	−1221.47	+	1024.93i	−0.0621849	+	0.0521793i
$729$		0			0
$730$	530.056	−	918.084i	0.0268743	−	0.0465477i
$731$	2626.59	+	14896.1i	0.132897	+	0.753698i
$732$		0			0
$733$	−6923.80	+	11992.4i	−0.348890	+	0.604295i	−0.986053	−	0.166434i	$-0.946775\pi$
$733$	−6923.80	+	11992.4i	−0.348890	+	0.604295i	0.637163	+	0.770729i	$0.280108\pi$
$734$	1204.34	+	2085.98i	0.0605626	+	0.104898i
$735$		0			0
$736$	12990.7	−	4728.24i	0.650604	−	0.236800i
$737$	5745.65	+	2091.25i	0.287169	+	0.104521i
$738$		0			0
$739$	−2423.28	+	13743.1i	−0.120625	+	0.684098i	0.863186	+	0.504887i	$0.168466\pi$
$739$	−2423.28	+	13743.1i	−0.120625	+	0.684098i	−0.983811	+	0.179212i	$0.942645\pi$
$740$	9151.71			0.454627
$741$		0			0
$742$	−13978.1			−0.691582
$743$	−1170.89	+	6640.44i	−0.0578139	+	0.327879i	−0.999973	−	0.00728582i	$-0.997681\pi$
$743$	−1170.89	+	6640.44i	−0.0578139	+	0.327879i	0.942160	+	0.335165i	$0.108792\pi$
$744$		0			0
$745$	7791.93	+	2836.03i	0.383187	+	0.139469i
$746$	4280.07	−	1557.82i	0.210060	−	0.0764554i
$747$		0			0
$748$	−3388.67	−	5869.35i	−0.165644	−	0.286905i
$749$	−10034.6	+	17380.4i	−0.489525	+	0.847883i
$750$		0			0
$751$	658.592	+	3735.06i	0.0320005	+	0.181484i	0.996619	−	0.0821675i	$-0.0261843\pi$
$751$	658.592	+	3735.06i	0.0320005	+	0.181484i	−0.964618	+	0.263651i	$0.915073\pi$
$752$	−10538.5	+	18253.3i	−0.511039	+	0.885145i
$753$		0			0
$754$	−594.021	+	498.443i	−0.0286909	+	0.0240746i
$755$	−12966.2	+	4719.29i	−0.625015	+	0.227487i
$756$		0			0
$757$	13476.9	+	11308.4i	0.647061	+	0.542949i	0.906178	−	0.422897i	$-0.138987\pi$
$757$	13476.9	+	11308.4i	0.647061	+	0.542949i	−0.259117	+	0.965846i	$0.583431\pi$
$758$	303.064	−	1718.76i	0.0145222	−	0.0823592i
$759$		0			0
$760$	−263.885	−	4460.40i	−0.0125949	−	0.212889i
$761$	−3757.72			−0.178998			−0.0894988	−	0.995987i	$-0.528527\pi$
$761$	−3757.72			−0.178998			−0.0894988	+	0.995987i	$0.528527\pi$
$762$		0			0
$763$	12262.6	+	10289.6i	0.581831	+	0.488214i
$764$	5916.09	+	2153.28i	0.280153	+	0.101967i
$765$		0			0
$766$	−3148.95	+	2642.28i	−0.148533	+	0.124634i
$767$	1572.23	+	2723.17i	0.0740153	+	0.128198i
$768$		0			0
$769$	−5705.99	−	32360.3i	−0.267573	−	1.51748i	−0.761608	−	0.648038i	$-0.775590\pi$
$769$	−5705.99	−	32360.3i	−0.267573	−	1.51748i	0.494035	−	0.869442i	$-0.335521\pi$
$770$	246.845	+	1399.93i	0.0115528	+	0.0655193i
$771$		0			0
$772$	5792.39	+	10032.7i	0.270042	+	0.467727i
$773$	−4992.53	+	4189.23i	−0.232301	+	0.194924i	−0.751506	−	0.659726i	$-0.770672\pi$
$773$	−4992.53	+	4189.23i	−0.232301	+	0.194924i	0.519205	+	0.854650i	$0.326228\pi$
$774$		0			0
$775$	10020.6	+	3647.21i	0.464454	+	0.169047i
$776$	−283.138	−	237.581i	−0.0130980	−	0.0109905i
$777$		0			0
$778$	−4502.60			−0.207488
$779$	−32857.9	−	16464.2i	−1.51124	−	0.757243i
$780$		0			0
$781$	−3136.21	+	17786.4i	−0.143691	+	0.814911i
$782$	−3612.93	−	3031.61i	−0.165215	−	0.138632i
$783$		0			0
$784$	−8382.14	+	3050.85i	−0.381839	+	0.138978i
$785$	9627.81	−	8078.70i	0.437747	−	0.367313i
$786$		0			0
$787$	−14507.3	+	25127.3i	−0.657088	+	1.13811i	0.324278	+	0.945962i	$0.394879\pi$
$787$	−14507.3	+	25127.3i	−0.657088	+	1.13811i	−0.981366	+	0.192148i	$0.938455\pi$
$788$	2345.23	+	13300.5i	0.106022	+	0.601281i
$789$		0			0
$790$	−189.618	+	328.429i	−0.00853965	+	0.0147911i
$791$	−606.993	−	1051.34i	−0.0272847	−	0.0472585i
$792$		0			0
$793$	−649.682	+	236.465i	−0.0290932	+	0.0105890i
$794$	950.912	+	346.104i	0.0425020	+	0.0154695i
$795$		0			0
$796$	−698.852	+	3963.39i	−0.0311183	+	0.176481i
$797$	−26521.8			−1.17873			−0.589367	−	0.807865i	$-0.700623\pi$
$797$	−26521.8			−1.17873			−0.589367	+	0.807865i	$0.700623\pi$
$798$		0			0
$799$	27200.0			1.20434
$800$	−2978.48	+	16891.8i	−0.131631	+	0.746519i
$801$		0			0
$802$	8758.11	+	3187.69i	0.385610	+	0.140351i
$803$	4743.69	−	1726.56i	0.208470	−	0.0758768i
$804$		0			0
$805$	−3953.45	−	6847.57i	−0.173094	−	0.299808i
$806$	−217.110	+	376.045i	−0.00948804	+	0.0164338i
$807$		0			0
$808$	3007.18	+	17054.6i	0.130931	+	0.742547i
$809$	18672.2	−	32341.2i	0.811471	−	1.40551i	−0.100364	−	0.994951i	$-0.532001\pi$
$809$	18672.2	−	32341.2i	0.811471	−	1.40551i	0.911835	−	0.410558i	$-0.134666\pi$
$810$		0			0
$811$	23330.3	−	19576.5i	1.01016	−	0.847623i	0.0217989	−	0.999762i	$-0.493061\pi$
$811$	23330.3	−	19576.5i	1.01016	−	0.847623i	0.988359	+	0.152139i	$0.0486162\pi$
$812$	−26923.1	+	9799.19i	−1.16356	+	0.423503i
$813$		0			0
$814$	−4176.66	−	3504.63i	−0.179842	−	0.150906i
$815$	68.2201	−	386.895i	0.00293208	−	0.0166287i
$816$		0			0
$817$	−18658.2	+	12296.2i	−0.798983	+	0.526548i
$818$	−10710.8			−0.457815
$819$		0			0
$820$	−9150.23	−	7677.95i	−0.389683	−	0.326983i
$821$	−12658.5	−	4607.33i	−0.538107	−	0.195855i	0.0586477	−	0.998279i	$-0.481321\pi$
$821$	−12658.5	−	4607.33i	−0.538107	−	0.195855i	−0.596754	+	0.802424i	$0.703543\pi$
$822$		0			0
$823$	−22566.9	+	18935.9i	−0.955813	+	0.802023i	−0.980267	−	0.197678i	$-0.936660\pi$
$823$	−22566.9	+	18935.9i	−0.955813	+	0.802023i	0.0244536	+	0.999701i	$0.492215\pi$
$824$	7868.46	+	13628.6i	0.332659	+	0.576182i
$825$		0			0
$826$	−2524.06	−	14314.6i	−0.106324	−	0.602991i
$827$	1577.82	+	8948.27i	0.0663437	+	0.376254i	0.999844	+	0.0176764i	$0.00562687\pi$
$827$	1577.82	+	8948.27i	0.0663437	+	0.376254i	−0.933500	+	0.358577i	$0.883262\pi$
$828$		0			0
$829$	−3561.37	−	6168.48i	−0.149206	−	0.258432i	0.781728	−	0.623619i	$-0.214338\pi$
$829$	−3561.37	−	6168.48i	−0.149206	−	0.258432i	−0.930934	+	0.365187i	$0.881005\pi$
$830$	1820.39	−	1527.49i	0.0761283	−	0.0638793i
$831$		0			0
$832$	904.001	+	329.030i	0.0376690	+	0.0137104i
$833$	8818.21	+	7399.36i	0.366786	+	0.307770i
$834$		0			0
$835$	−6240.00			−0.258616
$836$	5971.52	−	8036.49i	0.247045	−	0.332473i
$837$		0			0
$838$	6.32193	−	35.8534i	0.000260605	−	0.00147797i
$839$	−21899.1	−	18375.5i	−0.901121	−	0.756130i	0.0692884	−	0.997597i	$-0.477927\pi$
$839$	−21899.1	−	18375.5i	−0.901121	−	0.756130i	−0.970409	+	0.241467i	$0.922372\pi$
$840$		0			0
$841$	−4906.25	+	1785.73i	−0.201166	+	0.0732186i
$842$	−3598.19	+	3019.24i	−0.147271	+	0.123575i
$843$		0			0
$844$	−2639.95	+	4572.53i	−0.107667	+	0.186485i
$845$	1429.21	+	8105.45i	0.0581849	+	0.329983i
$846$		0			0
$847$	12199.2	−	21129.6i	0.494886	−	0.857168i
$848$	13746.9	+	23810.3i	0.556686	+	0.964208i
$849$		0			0
$850$	5498.80	−	2001.40i	0.221891	−	0.0807617i
$851$	28497.9	+	10372.4i	1.14794	+	0.417815i
$852$		0			0
$853$	1238.80	−	7025.60i	0.0497254	−	0.282007i	−0.949798	−	0.312862i	$-0.898712\pi$
$853$	1238.80	−	7025.60i	0.0497254	−	0.282007i	0.999524	+	0.0308556i	$0.00982321\pi$
$854$	3195.95			0.128060
$855$		0			0
$856$	−12214.5			−0.487713
$857$	−5098.76	+	28916.5i	−0.203232	+	1.15259i	0.696965	+	0.717106i	$0.254533\pi$
$857$	−5098.76	+	28916.5i	−0.203232	+	1.15259i	−0.900197	+	0.435483i	$0.856578\pi$
$858$		0			0
$859$	−15483.8	−	5635.63i	−0.615017	−	0.223848i	0.0156799	−	0.999877i	$-0.495009\pi$
$859$	−15483.8	−	5635.63i	−0.615017	−	0.223848i	−0.630697	+	0.776029i	$0.717231\pi$
$860$	−6824.55	+	2483.93i	−0.270599	+	0.0984900i
$861$		0			0
$862$	6479.28	+	11222.4i	0.256015	+	0.443432i
$863$	3451.27	−	5977.77i	0.136133	−	0.235789i	−0.789897	−	0.613240i	$-0.789866\pi$
$863$	3451.27	−	5977.77i	0.136133	−	0.235789i	0.926030	+	0.377451i	$0.123199\pi$
$864$		0			0
$865$	−394.314	−	2236.26i	−0.0154995	−	0.0879021i
$866$	−3877.91	+	6716.73i	−0.152167	+	0.263561i
$867$		0			0
$868$	−12290.1	+	10312.6i	−0.480589	+	0.403262i
$869$	−1696.97	+	617.648i	−0.0662438	+	0.0241108i
$870$		0			0
$871$	1316.24	+	1104.46i	0.0512046	+	0.0429658i
$872$	−1691.79	+	9594.63i	−0.0657010	+	0.372609i
$873$		0			0
$874$	1992.18	−	6676.60i	0.0771014	−	0.258397i
$875$	20891.0			0.807135
$876$		0			0
$877$	−30873.6	−	25906.1i	−1.18874	−	0.997475i	−0.999880	−	0.0154719i	$-0.995075\pi$
$877$	−30873.6	−	25906.1i	−1.18874	−	0.997475i	−0.188864	−	0.982003i	$-0.560481\pi$
$878$	14007.6	+	5098.36i	0.538422	+	0.195970i
$879$		0			0
$880$	2141.87	−	1797.24i	0.0820481	−	0.0688465i
$881$	−11311.2	−	19591.5i	−0.432557	−	0.749211i	0.564536	−	0.825409i	$-0.309055\pi$
$881$	−11311.2	−	19591.5i	−0.432557	−	0.749211i	−0.997093	+	0.0761980i	$0.975722\pi$
$882$		0			0
$883$	8726.67	+	49491.4i	0.332589	+	1.88620i	0.449851	+	0.893104i	$0.351477\pi$
$883$	8726.67	+	49491.4i	0.332589	+	1.88620i	−0.117262	+	0.993101i	$0.537412\pi$
$884$	−330.719	−	1875.60i	−0.0125829	−	0.0713611i
$885$		0			0
$886$	5981.91	+	10361.0i	0.226824	+	0.392871i
$887$	15039.9	−	12620.0i	0.569325	−	0.477721i	−0.312097	−	0.950050i	$-0.601031\pi$
$887$	15039.9	−	12620.0i	0.569325	−	0.477721i	0.881422	+	0.472330i	$0.156587\pi$
$888$		0			0
$889$	−7001.06	−	2548.18i	−0.264126	−	0.0961340i
$890$	−903.287	−	757.948i	−0.0340205	−	0.0285466i
$891$		0			0
$892$	13499.4			0.506720
$893$	15949.3	+	36881.8i	0.597674	+	1.38208i
$894$		0			0
$895$	1569.81	−	8902.86i	0.0586292	−	0.332503i
$896$	−25648.1	−	21521.3i	−0.956299	−	0.802430i
$897$		0			0
$898$	−897.760	+	326.758i	−0.0333615	+	0.0121426i
$899$	−12701.5	+	10657.8i	−0.471211	+	0.395393i
$900$		0			0
$901$	17740.3	−	30727.1i	0.655955	−	1.13615i
$902$	1235.72	+	7008.12i	0.0456153	+	0.258697i
$903$		0			0
$904$	369.429	−	639.869i	0.0135918	−	0.0235417i
$905$	−5699.18	−	9871.27i	−0.209334	−	0.362577i
$906$		0			0
$907$	6967.82	−	2536.08i	0.255086	−	0.0928436i	−0.211312	−	0.977419i	$-0.567774\pi$
$907$	6967.82	−	2536.08i	0.255086	−	0.0928436i	0.466398	+	0.884575i	$0.345551\pi$
$908$	−13584.2	−	4944.26i	−0.496486	−	0.180706i
$909$		0			0
$910$	−69.3671	+	393.400i	−0.00252692	+	0.0143309i
$911$	8879.55			0.322934			0.161467	−	0.986878i	$-0.448378\pi$
$911$	8879.55			0.322934			0.161467	+	0.986878i	$0.448378\pi$
$912$		0			0
$913$	11315.9			0.410187
$914$	1025.19	−	5814.12i	0.0371008	−	0.210409i
$915$		0			0
$916$	18817.9	+	6849.17i	0.678780	+	0.247056i
$917$	−32794.2	+	11936.1i	−1.18098	+	0.429842i
$918$		0			0
$919$	8397.87	+	14545.5i	0.301436	+	0.522103i	0.976462	−	0.215692i	$-0.0692006\pi$
$919$	8397.87	+	14545.5i	0.301436	+	0.522103i	−0.675025	+	0.737795i	$0.735867\pi$
$920$	2406.15	−	4167.58i	0.0862266	−	0.149349i
$921$		0			0
$922$	2555.45	+	14492.7i	0.0912790	+	0.517669i
$923$	−2537.67	+	4395.37i	−0.0904965	+	0.156745i
$924$		0			0
$925$	−28824.2	+	24186.4i	−1.02458	+	0.859723i
$926$	1207.94	−	439.655i	0.0428677	−	0.0156026i
$927$		0			0
$928$	−20430.1	−	17142.9i	−0.722685	−	0.606405i
$929$	5674.97	−	32184.3i	0.200419	−	1.13663i	−0.704067	−	0.710133i	$-0.748635\pi$
$929$	5674.97	−	32184.3i	0.200419	−	1.13663i	0.904487	−	0.426502i	$-0.140254\pi$
$930$		0			0
$931$	−4862.40	+	16295.8i	−0.171170	+	0.573656i
$932$	−16569.8			−0.582364
$933$		0			0
$934$	8554.67	+	7178.22i	0.299697	+	0.251476i
$935$	−3390.64	−	1234.09i	−0.118594	−	0.0431649i
$936$		0			0
$937$	11922.2	−	10003.9i	0.415668	−	0.348787i	−0.410844	−	0.911706i	$-0.634766\pi$
$937$	11922.2	−	10003.9i	0.415668	−	0.348787i	0.826512	+	0.562919i	$0.190322\pi$
$938$	−3971.34	−	6878.56i	−0.138240	−	0.239438i
$939$		0			0
$940$	2267.80	+	12861.3i	0.0786888	+	0.446266i
$941$	3370.70	+	19116.2i	0.116771	+	0.662242i	0.985858	+	0.167582i	$0.0535960\pi$
$941$	3370.70	+	19116.2i	0.116771	+	0.662242i	−0.869087	+	0.494659i	$0.835293\pi$
$942$		0			0
$943$	−19791.2	−	34279.4i	−0.683447	−	1.18376i
$944$	−21901.2	+	18377.3i	−0.755109	+	0.633612i
$945$		0			0
$946$	4065.80	+	1479.83i	0.139736	+	0.0508599i
$947$	−16509.3	−	13852.9i	−0.566504	−	0.475353i	0.313980	−	0.949430i	$-0.398338\pi$
$947$	−16509.3	−	13852.9i	−0.566504	−	0.475353i	−0.880484	+	0.474076i	$0.842782\pi$
$948$		0			0
$949$	1418.60			0.0485244
$950$	5938.14	+	6282.53i	0.202799	+	0.214560i
$951$		0			0
$952$	−3248.81	+	18424.9i	−0.110604	+	0.627264i
$953$	33109.8	+	27782.4i	1.12543	+	0.944345i	0.998866	−	0.0476140i	$-0.0151618\pi$
$953$	33109.8	+	27782.4i	1.12543	+	0.944345i	0.126561	+	0.991959i	$0.459606\pi$
$954$		0			0
$955$	3149.72	−	1146.40i	0.106725	−	0.0388448i
$956$	−2863.83	+	2403.04i	−0.0968858	+	0.0812969i
$957$		0			0
$958$	1429.75	−	2476.40i	0.0482183	−	0.0835166i
$959$	−6502.10	−	36875.2i	−0.218940	−	1.24167i
$960$		0			0
$961$	10253.2	−	17759.1i	0.344171	−	0.596122i
$962$	−766.080	−	1326.89i	−0.0256751	−	0.0444705i
$963$		0			0
$964$	−41222.2	+	15003.6i	−1.37726	+	0.501281i
$965$	5795.76	+	2109.48i	0.193339	+	0.0703696i
$966$		0			0
$967$	5417.73	−	30725.5i	0.180168	−	1.02178i	−0.751840	−	0.659345i	$-0.770834\pi$
$967$	5417.73	−	30725.5i	0.180168	−	1.02178i	0.932008	−	0.362437i	$-0.118055\pi$
$968$	14849.4			0.493054
$969$		0			0
$970$	−92.5975			−0.00306508
$971$	3728.66	−	21146.3i	0.123232	−	0.698885i	−0.859110	−	0.511791i	$-0.828982\pi$
$971$	3728.66	−	21146.3i	0.123232	−	0.698885i	0.982342	−	0.187094i	$-0.0599068\pi$
$972$		0			0
$973$	−26004.0	−	9464.66i	−0.856782	−	0.311843i
$974$	3282.33	−	1194.67i	0.107980	−	0.0393016i
$975$		0			0
$976$	−3143.07	−	5443.96i	−0.103081	−	0.178542i
$977$	18829.9	−	32614.3i	0.616603	−	1.06799i	−0.373498	−	0.927631i	$-0.621842\pi$
$977$	18829.9	−	32614.3i	0.616603	−	1.06799i	0.990101	−	0.140356i	$-0.0448248\pi$
$978$		0			0
$979$	−975.036	−	5529.71i	−0.0318307	−	0.180521i
$980$	−2763.52	+	4786.56i	−0.0900790	+	0.156021i
$981$		0			0
$982$	9273.76	−	7781.61i	0.301362	−	0.252873i
$983$	25429.5	−	9255.60i	0.825103	−	0.300313i	0.105256	−	0.994445i	$-0.466434\pi$
$983$	25429.5	−	9255.60i	0.825103	−	0.300313i	0.719848	+	0.694132i	$0.244212\pi$
$984$		0			0
$985$	5508.16	+	4621.89i	0.178177	+	0.149508i
$986$	−1579.96	+	8960.37i	−0.0510304	+	0.289408i
$987$		0			0
$988$	2349.29	−	1548.24i	0.0756488	−	0.0498542i
$989$	−24066.5			−0.773781
$990$		0			0
$991$	17283.9	+	14502.9i	0.554027	+	0.464884i	0.876302	−	0.481762i	$-0.160003\pi$
$991$	17283.9	+	14502.9i	0.554027	+	0.464884i	−0.322275	+	0.946646i	$0.604448\pi$
$992$	−14033.4	−	5107.75i	−0.449155	−	0.163479i
$993$		0			0
$994$	17972.3	−	15080.5i	0.573487	−	0.481212i
$995$	1071.33	+	1855.59i	0.0341340	+	0.0591218i
$996$		0			0
$997$	−4442.54	−	25194.9i	−0.141120	−	0.800331i	−0.970401	−	0.241499i	$-0.922361\pi$
$997$	−4442.54	−	25194.9i	−0.141120	−	0.800331i	0.829281	−	0.558832i	$-0.188750\pi$
$998$	1376.81	+	7808.27i	0.0436695	+	0.247662i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.b.55.3		24
3.2	odd	2		19.4.e.a.17.2	yes	24
19.9	even	9	inner	171.4.u.b.28.3		24
57.35	odd	18		361.4.a.n.1.5		12
57.41	even	18		361.4.a.m.1.8		12
57.47	odd	18		19.4.e.a.9.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.9.2	✓	24	57.47	odd	18
19.4.e.a.17.2	yes	24	3.2	odd	2
171.4.u.b.28.3		24	19.9	even	9	inner
171.4.u.b.55.3		24	1.1	even	1	trivial
361.4.a.m.1.8		12	57.41	even	18
361.4.a.n.1.5		12	57.35	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)

\(f(q)\)	\(=\)	\(q+(0.163781 - 0.928850i) q^{2} +(6.68160 + 2.43190i) q^{4} +(3.55727 - 1.29474i) q^{5} +(-11.7083 - 20.2794i) q^{7} +(7.12592 - 12.3424i) q^{8} +O(q^{10})\)	\(q+(0.163781 - 0.928850i) q^{2} +(6.68160 + 2.43190i) q^{4} +(3.55727 - 1.29474i) q^{5} +(-11.7083 - 20.2794i) q^{7} +(7.12592 - 12.3424i) q^{8} +(-0.620006 - 3.51623i) q^{10} +(8.50109 - 14.7243i) q^{11} +(3.66005 - 3.07115i) q^{13} +(-20.7541 + 7.55387i) q^{14} +(33.2779 + 27.9235i) q^{16} +(9.73487 - 55.2092i) q^{17} +(80.5692 - 19.1731i) q^{19} +26.9170 q^{20} +(-12.2844 - 10.3078i) q^{22} +(83.8179 + 30.5072i) q^{23} +(-84.7777 + 71.1369i) q^{25} +(-2.25319 - 3.90264i) q^{26} +(-28.9127 - 163.972i) q^{28} +(-29.8807 - 169.462i) q^{29} +(-48.1783 - 83.4472i) q^{31} +(118.727 - 99.6241i) q^{32} +(-49.6867 - 18.0845i) q^{34} +(-67.9062 - 56.9800i) q^{35} +339.998 q^{37} +(-4.61325 - 77.9769i) q^{38} +(9.36855 - 53.1317i) q^{40} +(-339.942 - 285.246i) q^{41} +(-253.541 + 92.2813i) q^{43} +(92.6090 - 77.7082i) q^{44} +(42.0644 - 72.8577i) q^{46} +(84.2516 + 477.815i) q^{47} +(-102.668 + 177.827i) q^{49} +(52.1906 + 90.3967i) q^{50} +(31.9238 - 11.6193i) q^{52} +(594.726 + 216.463i) q^{53} +(11.1765 - 63.3851i) q^{55} -333.729 q^{56} -162.298 q^{58} +(-114.283 + 648.131i) q^{59} +(-135.978 - 49.4918i) q^{61} +(-85.4007 + 31.0833i) q^{62} +(100.675 + 174.373i) q^{64} +(9.04347 - 15.6638i) q^{65} +(62.4481 + 354.161i) q^{67} +(199.308 - 345.212i) q^{68} +(-64.0477 + 53.7424i) q^{70} +(-998.198 + 363.314i) q^{71} +(227.447 + 190.851i) q^{73} +(55.6853 - 315.807i) q^{74} +(584.958 + 67.8292i) q^{76} -398.133 q^{77} +(-81.3652 - 68.2735i) q^{79} +(154.533 + 56.2452i) q^{80} +(-320.627 + 269.038i) q^{82} +(332.777 + 576.387i) q^{83} +(-36.8521 - 208.998i) q^{85} +(44.1902 + 250.615i) q^{86} +(-121.156 - 209.848i) q^{88} +(252.988 - 212.282i) q^{89} +(-105.134 - 38.2656i) q^{91} +(485.847 + 407.674i) q^{92} +457.617 q^{94} +(261.782 - 172.520i) q^{95} +(4.50343 - 25.5402i) q^{97} +(148.359 + 124.488i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more