LMFDB - Embedded newform 171.5.p.a.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,5,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, 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:	$17.6762636873$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 $ x^10 + 109x^8 + 4107x^6 + 61507x^4 + 300520x^2 + 108300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.4
Root			$4.58432i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.5.p.a.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.97014 + 2.29216i) q^{2} +(2.50801 + 4.34400i) q^{4} +(-20.8352 + 36.0877i) q^{5} +24.1856 q^{7} -50.3541i q^{8} +O(q^{10})$	\(q+(3.97014 + 2.29216i) q^{2} +(2.50801 + 4.34400i) q^{4} +(-20.8352 + 36.0877i) q^{5} +24.1856 q^{7} -50.3541i q^{8} +(-165.438 + 95.5155i) q^{10} -62.4993 q^{11} +(-250.356 + 144.543i) q^{13} +(96.0201 + 55.4372i) q^{14} +(155.548 - 269.417i) q^{16} +(12.2538 - 21.2242i) q^{17} +(-283.198 + 223.874i) q^{19} -209.020 q^{20} +(-248.131 - 143.258i) q^{22} +(-302.902 - 524.641i) q^{23} +(-555.715 - 962.527i) q^{25} -1325.26 q^{26} +(60.6576 + 105.062i) q^{28} +(-249.575 + 144.092i) q^{29} +418.074i q^{31} +(537.367 - 310.249i) q^{32} +(97.2984 - 56.1752i) q^{34} +(-503.912 + 872.801i) q^{35} +2023.50i q^{37} +(-1637.49 + 239.675i) q^{38} +(1817.17 + 1049.14i) q^{40} +(717.741 + 414.388i) q^{41} +(632.930 - 1096.27i) q^{43} +(-156.749 - 271.497i) q^{44} -2777.20i q^{46} +(421.122 + 729.404i) q^{47} -1816.06 q^{49} -5095.15i q^{50} +(-1255.79 - 725.029i) q^{52} +(-3144.31 + 1815.37i) q^{53} +(1302.19 - 2255.46i) q^{55} -1217.84i q^{56} -1321.13 q^{58} +(4625.90 + 2670.77i) q^{59} +(1471.85 + 2549.32i) q^{61} +(-958.292 + 1659.81i) q^{62} -2132.97 q^{64} -12046.3i q^{65} +(4194.98 - 2421.97i) q^{67} +122.930 q^{68} +(-4001.20 + 2310.10i) q^{70} +(4788.02 + 2764.37i) q^{71} +(792.717 - 1373.03i) q^{73} +(-4638.19 + 8033.59i) q^{74} +(-1682.77 - 668.735i) q^{76} -1511.58 q^{77} +(4627.33 + 2671.59i) q^{79} +(6481.76 + 11226.7i) q^{80} +(1899.69 + 3290.36i) q^{82} +740.501 q^{83} +(510.621 + 884.421i) q^{85} +(5025.64 - 2901.56i) q^{86} +3147.10i q^{88} +(-4789.36 + 2765.14i) q^{89} +(-6054.99 + 3495.85i) q^{91} +(1519.36 - 2631.61i) q^{92} +3861.11i q^{94} +(-2178.59 - 14884.5i) q^{95} +(2969.63 + 1714.52i) q^{97} +(-7210.01 - 4162.70i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7}+O(q^{10}) $ 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7	$ 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7} + 144 q^{10} - 50 q^{11} - 624 q^{13} + 474 q^{14} + 285 q^{16} + 292 q^{17} + 305 q^{19} + 652 q^{20} + 1629 q^{22} - 98 q^{23} - 681 q^{25} - 1524 q^{26} - 1472 q^{28} - 2598 q^{29} + 2745 q^{32} + 486 q^{34} - 694 q^{35} + 342 q^{38} + 8784 q^{40} + 1407 q^{41} + 5424 q^{43} - 4151 q^{44} + 2416 q^{47} - 17826 q^{49} - 19962 q^{52} - 1122 q^{53} + 11424 q^{55} - 20236 q^{58} - 15387 q^{59} + 860 q^{61} - 21636 q^{62} + 19710 q^{64} + 14763 q^{67} + 48844 q^{68} - 20334 q^{70} + 27264 q^{71} + 1561 q^{73} - 17094 q^{74} + 1955 q^{76} + 18392 q^{77} + 24750 q^{79} + 2002 q^{80} + 14479 q^{82} - 6002 q^{83} - 14944 q^{85} - 59946 q^{86} + 22566 q^{89} + 8724 q^{91} - 9572 q^{92} + 7312 q^{95} + 46287 q^{97} - 25515 q^{98}+O(q^{100}) $ 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7 + 144 * q^10 - 50 * q^11 - 624 * q^13 + 474 * q^14 + 285 * q^16 + 292 * q^17 + 305 * q^19 + 652 * q^20 + 1629 * q^22 - 98 * q^23 - 681 * q^25 - 1524 * q^26 - 1472 * q^28 - 2598 * q^29 + 2745 * q^32 + 486 * q^34 - 694 * q^35 + 342 * q^38 + 8784 * q^40 + 1407 * q^41 + 5424 * q^43 - 4151 * q^44 + 2416 * q^47 - 17826 * q^49 - 19962 * q^52 - 1122 * q^53 + 11424 * q^55 - 20236 * q^58 - 15387 * q^59 + 860 * q^61 - 21636 * q^62 + 19710 * q^64 + 14763 * q^67 + 48844 * q^68 - 20334 * q^70 + 27264 * q^71 + 1561 * q^73 - 17094 * q^74 + 1955 * q^76 + 18392 * q^77 + 24750 * q^79 + 2002 * q^80 + 14479 * q^82 - 6002 * q^83 - 14944 * q^85 - 59946 * q^86 + 22566 * q^89 + 8724 * q^91 - 9572 * q^92 + 7312 * q^95 + 46287 * q^97 - 25515 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.97014	+	2.29216i	0.992535	+	0.573040i	0.906031	−	0.423211i	$-0.139097\pi$
$2$	3.97014	+	2.29216i	0.992535	+	0.573040i	0.0865039	+	0.996252i	$0.472430\pi$
$3$		0			0
$3$		0			0
$4$	2.50801	+	4.34400i	0.156750	+	0.271500i
$5$	−20.8352	+	36.0877i	−0.833410	+	1.44351i	0.0619087	+	0.998082i	$0.480281\pi$
$5$	−20.8352	+	36.0877i	−0.833410	+	1.44351i	−0.895319	+	0.445426i	$0.853052\pi$
$6$		0			0
$7$	24.1856			0.493583			0.246791	−	0.969069i	$-0.420624\pi$
$7$	24.1856			0.493583			0.246791	+	0.969069i	$0.420624\pi$
$8$		−	50.3541i		−	0.786783i
$9$		0			0
$10$	−165.438	+	95.5155i	−1.65438	+	0.955155i
$11$	−62.4993			−0.516523			−0.258261	−	0.966075i	$-0.583150\pi$
$11$	−62.4993			−0.516523			−0.258261	+	0.966075i	$0.583150\pi$
$12$		0			0
$13$	−250.356	+	144.543i	−1.48139	+	0.855283i	−0.999777	−	0.0210988i	$-0.993284\pi$
$13$	−250.356	+	144.543i	−1.48139	+	0.855283i	−0.481617	+	0.876382i	$0.659950\pi$
$14$	96.0201	+	55.4372i	0.489898	+	0.282843i
$15$		0			0
$16$	155.548	−	269.417i	0.607609	−	1.05241i
$17$	12.2538	−	21.2242i	0.0424006	−	0.0734400i	−0.844046	−	0.536270i	$-0.819833\pi$
$17$	12.2538	−	21.2242i	0.0424006	−	0.0734400i	0.886447	+	0.462830i	$0.153166\pi$
$18$		0			0
$19$	−283.198	+	223.874i	−0.784483	+	0.620150i
$19$	−283.198	+	223.874i	−0.784483	+	0.620150i
$20$	−209.020			−0.522550
$21$		0			0
$22$	−248.131	−	143.258i	−0.512667	−	0.295988i
$23$	−302.902	−	524.641i	−0.572593	−	0.991760i	−0.996299	−	0.0859604i	$-0.972604\pi$
$23$	−302.902	−	524.641i	−0.572593	−	0.991760i	0.423705	−	0.905800i	$-0.360729\pi$
$24$		0			0
$25$	−555.715	−	962.527i	−0.889144	−	1.54004i
$26$	−1325.26			−1.96045
$27$		0			0
$28$	60.6576	+	105.062i	0.0773693	+	0.134008i
$29$	−249.575	+	144.092i	−0.296760	+	0.171334i	−0.640986	−	0.767552i	$-0.721474\pi$
$29$	−249.575	+	144.092i	−0.296760	+	0.171334i	0.344227	+	0.938887i	$0.388141\pi$
$30$		0			0
$31$			418.074i			0.435040i	0.976056	+	0.217520i	$0.0697968\pi$
$31$			418.074i			0.435040i	−0.976056	+	0.217520i	$0.930203\pi$
$32$	537.367	−	310.249i	0.524772	−	0.302977i
$33$		0			0
$34$	97.2984	−	56.1752i	0.0841681	−	0.0485945i
$35$	−503.912	+	872.801i	−0.411357	+	0.712491i
$36$		0			0
$37$			2023.50i			1.47809i	0.673657	+	0.739044i	$0.264722\pi$
$37$			2023.50i			1.47809i	−0.673657	+	0.739044i	$0.735278\pi$
$38$	−1637.49	+	239.675i	−1.13400	+	0.165980i
$39$		0			0
$40$	1817.17	+	1049.14i	1.13573	+	0.655713i
$41$	717.741	+	414.388i	0.426973	+	0.246513i	0.698056	−	0.716043i	$-0.254049\pi$
$41$	717.741	+	414.388i	0.426973	+	0.246513i	−0.271083	+	0.962556i	$0.587382\pi$
$42$		0			0
$43$	632.930	−	1096.27i	0.342310	−	0.592898i	−0.642552	−	0.766242i	$-0.722124\pi$
$43$	632.930	−	1096.27i	0.342310	−	0.592898i	0.984861	+	0.173345i	$0.0554575\pi$
$44$	−156.749	−	271.497i	−0.0809652	−	0.140236i
$45$		0			0
$46$		−	2777.20i		−	1.31248i
$47$	421.122	+	729.404i	0.190639	+	0.330196i	0.945462	−	0.325732i	$-0.105611\pi$
$47$	421.122	+	729.404i	0.190639	+	0.330196i	−0.754823	+	0.655928i	$0.772277\pi$
$48$		0			0
$49$	−1816.06			−0.756376
$50$		−	5095.15i		−	2.03806i
$51$		0			0
$52$	−1255.79	−	725.029i	−0.464418	−	0.268132i
$53$	−3144.31	+	1815.37i	−1.11937	+	0.646268i	−0.941240	−	0.337739i	$-0.890338\pi$
$53$	−3144.31	+	1815.37i	−1.11937	+	0.646268i	−0.178130	+	0.984007i	$0.557005\pi$
$54$		0			0
$55$	1302.19	−	2255.46i	0.430475	−	0.745605i
$56$		−	1217.84i		−	0.388343i
$57$		0			0
$58$	−1321.13			−0.392726
$59$	4625.90	+	2670.77i	1.32890	+	0.767241i	0.985130	−	0.171812i	$-0.0549622\pi$
$59$	4625.90	+	2670.77i	1.32890	+	0.767241i	0.343771	+	0.939053i	$0.388296\pi$
$60$		0			0
$61$	1471.85	+	2549.32i	0.395552	+	0.685116i	0.993171	−	0.116664i	$-0.0372201\pi$
$61$	1471.85	+	2549.32i	0.395552	+	0.685116i	−0.597620	+	0.801780i	$0.703887\pi$
$62$	−958.292	+	1659.81i	−0.249296	+	0.431793i
$63$		0			0
$64$	−2132.97			−0.520745
$65$		−	12046.3i		−	2.85121i
$66$		0			0
$67$	4194.98	−	2421.97i	0.934501	−	0.539534i	0.0462688	−	0.998929i	$-0.485267\pi$
$67$	4194.98	−	2421.97i	0.934501	−	0.539534i	0.888232	+	0.459395i	$0.151934\pi$
$68$	122.930			0.0265853
$69$		0			0
$70$	−4001.20	+	2310.10i	−0.816572	+	0.471448i
$71$	4788.02	+	2764.37i	0.949816	+	0.548377i	0.893024	−	0.450009i	$-0.148579\pi$
$71$	4788.02	+	2764.37i	0.949816	+	0.548377i	0.0567923	+	0.998386i	$0.481913\pi$
$72$		0			0
$73$	792.717	−	1373.03i	0.148755	−	0.257652i	−0.782012	−	0.623263i	$-0.785807\pi$
$73$	792.717	−	1373.03i	0.148755	−	0.257652i	0.930768	+	0.365611i	$0.119140\pi$
$74$	−4638.19	+	8033.59i	−0.847004	+	1.46705i
$75$		0			0
$76$	−1682.77	−	668.735i	−0.291339	−	0.115778i
$77$	−1511.58			−0.254947
$78$		0			0
$79$	4627.33	+	2671.59i	0.741440	+	0.428071i	0.822593	−	0.568631i	$-0.192527\pi$
$79$	4627.33	+	2671.59i	0.741440	+	0.428071i	−0.0811524	+	0.996702i	$0.525860\pi$
$80$	6481.76	+	11226.7i	1.01277	+	1.75418i
$81$		0			0
$82$	1899.69	+	3290.36i	0.282524	+	0.489345i
$83$	740.501			0.107490			0.0537452	−	0.998555i	$-0.482884\pi$
$83$	740.501			0.107490			0.0537452	+	0.998555i	$0.482884\pi$
$84$		0			0
$85$	510.621	+	884.421i	0.0706741	+	0.122411i
$86$	5025.64	−	2901.56i	0.679508	−	0.392314i
$87$		0			0
$88$			3147.10i			0.406392i
$89$	−4789.36	+	2765.14i	−0.604641	+	0.349089i	−0.770865	−	0.636998i	$-0.780176\pi$
$89$	−4789.36	+	2765.14i	−0.604641	+	0.349089i	0.166224	+	0.986088i	$0.446842\pi$
$90$		0			0
$91$	−6054.99	+	3495.85i	−0.731191	+	0.422153i
$92$	1519.36	−	2631.61i	0.179509	−	0.310918i
$93$		0			0
$94$			3861.11i			0.436975i
$95$	−2178.59	−	14884.5i	−0.241395	−	1.64925i
$96$		0			0
$97$	2969.63	+	1714.52i	0.315616	+	0.182221i	0.649437	−	0.760415i	$-0.275005\pi$
$97$	2969.63	+	1714.52i	0.315616	+	0.182221i	−0.333821	+	0.942637i	$0.608338\pi$
$98$	−7210.01	−	4162.70i	−0.750730	−	0.433434i
$99$		0			0
$100$	2787.47	−	4828.05i	0.278747	−	0.482805i
$101$	702.204	+	1216.25i	0.0688368	+	0.119229i	0.898390	−	0.439200i	$-0.144738\pi$
$101$	702.204	+	1216.25i	0.0688368	+	0.119229i	−0.829553	+	0.558428i	$0.811405\pi$
$102$		0			0
$103$		−	8424.53i		−	0.794093i	−0.917798	−	0.397047i	$-0.870035\pi$
$103$		−	8424.53i		−	0.794093i	0.917798	−	0.397047i	$-0.129965\pi$
$104$	7278.33	+	12606.4i	0.672923	+	1.16554i
$105$		0			0
$106$	−16644.5			−1.48135
$107$			8311.74i			0.725980i	0.931793	+	0.362990i	$0.118244\pi$
$107$			8311.74i			0.725980i	−0.931793	+	0.362990i	$0.881756\pi$
$108$		0			0
$109$	−8045.29	−	4644.95i	−0.677156	−	0.390956i	0.121627	−	0.992576i	$-0.461189\pi$
$109$	−8045.29	−	4644.95i	−0.677156	−	0.390956i	−0.798783	+	0.601620i	$0.794522\pi$
$110$	10339.7	−	5969.65i	0.854524	−	0.493359i
$111$		0			0
$112$	3762.01	−	6516.00i	0.299905	−	0.519451i
$113$			4056.19i			0.317659i	0.987306	+	0.158830i	$0.0507721\pi$
$113$			4056.19i			0.317659i	−0.987306	+	0.158830i	$0.949228\pi$
$114$		0			0
$115$	25244.1			1.90882
$116$	−1251.87	−	722.768i	−0.0930344	−	0.0537134i
$117$		0			0
$118$	12243.7	+	21206.6i	0.879320	+	1.52303i
$119$	296.364	−	513.318i	0.0209282	−	0.0362487i
$120$		0			0
$121$	−10734.8			−0.733204
$122$			13494.9i			0.906668i
$123$		0			0
$124$	−1816.11	+	1048.53i	−0.118113	+	0.0681928i
$125$	20269.8			1.29727
$126$		0			0
$127$	−9729.41	+	5617.28i	−0.603225	+	0.348272i	−0.770309	−	0.637671i	$-0.779898\pi$
$127$	−9729.41	+	5617.28i	−0.603225	+	0.348272i	0.167084	+	0.985943i	$0.446565\pi$
$128$	−17066.1	−	9853.10i	−1.04163	−	0.601385i
$129$		0			0
$130$	27612.2	−	47825.7i	1.63386	−	2.82992i
$131$	−3002.45	+	5200.40i	−0.174958	+	0.303036i	−0.940147	−	0.340770i	$-0.889312\pi$
$131$	−3002.45	+	5200.40i	−0.174958	+	0.303036i	0.765189	+	0.643806i	$0.222646\pi$
$132$		0			0
$133$	−6849.31	+	5414.52i	−0.387208	+	0.306095i
$134$	22206.2			1.23670
$135$		0			0
$136$	−1068.72	−	617.028i	−0.0577813	−	0.0333601i
$137$	−8783.25	−	15213.0i	−0.467966	−	0.810540i	0.531364	−	0.847144i	$-0.321680\pi$
$137$	−8783.25	−	15213.0i	−0.467966	−	0.810540i	−0.999330	+	0.0366031i	$0.988346\pi$
$138$		0			0
$139$	5697.89	+	9869.03i	0.294906	+	0.510793i	0.974963	−	0.222367i	$-0.0713782\pi$
$139$	5697.89	+	9869.03i	0.294906	+	0.510793i	−0.680057	+	0.733160i	$0.738045\pi$
$140$	−5055.26			−0.257922
$141$		0			0
$142$	12672.7	+	21949.8i	0.628484	+	1.08857i
$143$	15647.0	−	9033.82i	0.765174	−	0.441773i
$144$		0			0
$145$		−	12008.8i		−	0.571167i
$146$	6294.40	−	3634.07i	0.295290	−	0.170486i
$147$		0			0
$148$	−8790.09	+	5074.96i	−0.401301	+	0.231691i
$149$	8963.63	−	15525.5i	0.403749	−	0.699314i	−0.590426	−	0.807092i	$-0.701040\pi$
$149$	8963.63	−	15525.5i	0.403749	−	0.699314i	0.994175	+	0.107778i	$0.0343736\pi$
$150$		0			0
$151$		−	2550.85i		−	0.111874i	−0.998434	−	0.0559372i	$-0.982185\pi$
$151$		−	2550.85i		−	0.111874i	0.998434	−	0.0559372i	$-0.0178147\pi$
$152$	11273.0	+	14260.2i	0.487924	+	0.617218i
$153$		0			0
$154$	−6001.18	−	3464.79i	−0.253044	−	0.146095i
$155$	−15087.3	−	8710.67i	−0.627984	−	0.362567i
$156$		0			0
$157$	−20083.8	+	34786.2i	−0.814793	+	1.41126i	0.0946826	+	0.995508i	$0.469816\pi$
$157$	−20083.8	+	34786.2i	−0.814793	+	1.41126i	−0.909476	+	0.415756i	$0.863517\pi$
$158$	12247.4	+	21213.2i	0.490604	+	0.849751i
$159$		0			0
$160$			25856.4i			1.01002i
$161$	−7325.85	−	12688.7i	−0.282622	−	0.489516i
$162$		0			0
$163$	8363.32			0.314777			0.157389	−	0.987537i	$-0.449692\pi$
$163$	8363.32			0.314777			0.157389	+	0.987537i	$0.449692\pi$
$164$			4157.15i			0.154564i
$165$		0			0
$166$	2939.89	+	1697.35i	0.106688	+	0.0615963i
$167$	−25860.0	+	14930.3i	−0.927246	+	0.535346i	−0.885940	−	0.463801i	$-0.846485\pi$
$167$	−25860.0	+	14930.3i	−0.927246	+	0.535346i	−0.0413065	+	0.999147i	$0.513152\pi$
$168$		0			0
$169$	27504.8	−	47639.7i	0.963019	−	1.66800i
$170$			4681.70i			0.161997i
$171$		0			0
$172$	6349.58			0.214629
$173$	−12746.0	−	7358.89i	−0.425874	−	0.245878i	0.271713	−	0.962378i	$-0.412410\pi$
$173$	−12746.0	−	7358.89i	−0.425874	−	0.245878i	−0.697587	+	0.716500i	$0.745743\pi$
$174$		0			0
$175$	−13440.3	−	23279.2i	−0.438866	−	0.760139i
$176$	−9721.63	+	16838.4i	−0.313844	+	0.543594i
$177$		0			0
$178$	−25352.6			−0.800169
$179$		−	16538.4i		−	0.516163i	−0.966123	−	0.258082i	$-0.916910\pi$
$179$		−	16538.4i		−	0.516163i	0.966123	−	0.258082i	$-0.0830903\pi$
$180$		0			0
$181$	10274.9	−	5932.22i	0.313632	−	0.181076i	−0.334919	−	0.942247i	$-0.608709\pi$
$181$	10274.9	−	5932.22i	0.313632	−	0.181076i	0.648551	+	0.761171i	$0.275375\pi$
$182$	−32052.2			−0.967643
$183$		0			0
$184$	−26417.9	+	15252.4i	−0.780301	+	0.450507i
$185$	−73023.6	−	42160.2i	−2.13363	−	1.23185i
$186$		0			0
$187$	−765.852	+	1326.49i	−0.0219009	+	0.0379334i
$188$	−2112.35	+	3658.70i	−0.0597655	+	0.103517i
$189$		0			0
$190$	25468.3	−	64087.1i	0.705492	−	1.77526i
$191$	−50556.6			−1.38583			−0.692917	−	0.721017i	$-0.743675\pi$
$191$	−50556.6			−1.38583			−0.692917	+	0.721017i	$0.743675\pi$
$192$		0			0
$193$	−41764.2	−	24112.6i	−1.12122	−	0.647335i	−0.179506	−	0.983757i	$-0.557450\pi$
$193$	−41764.2	−	24112.6i	−1.12122	−	0.647335i	−0.941711	+	0.336422i	$0.890783\pi$
$194$	7859.91	+	13613.8i	0.208840	+	0.361722i
$195$		0			0
$196$	−4554.69	−	7888.95i	−0.118562	−	0.205356i
$197$	39065.4			1.00661			0.503303	−	0.864110i	$-0.332118\pi$
$197$	39065.4			1.00661			0.503303	+	0.864110i	$0.332118\pi$
$198$		0			0
$199$	−12907.6	−	22356.6i	−0.325941	−	0.564546i	0.655761	−	0.754968i	$-0.272348\pi$
$199$	−12907.6	−	22356.6i	−0.325941	−	0.564546i	−0.981702	+	0.190422i	$0.939014\pi$
$200$	−48467.2	+	27982.5i	−1.21168	+	0.699564i
$201$		0			0
$202$			6438.26i			0.157785i
$203$	−6036.11	+	3484.95i	−0.146475	+	0.0845676i
$204$		0			0
$205$	−29908.6	+	17267.7i	−0.711686	+	0.410892i
$206$	19310.4	−	33446.6i	0.455047	−	0.788165i
$207$		0			0
$208$			89933.4i			2.07871i
$209$	17699.7	−	13992.0i	0.405204	−	0.320322i
$210$		0			0
$211$	5877.77	+	3393.53i	0.132023	+	0.0762232i	0.564557	−	0.825394i	$-0.309047\pi$
$211$	5877.77	+	3393.53i	0.132023	+	0.0762232i	−0.432534	+	0.901618i	$0.642381\pi$
$212$	−15771.9	−	9105.91i	−0.350923	−	0.202606i
$213$		0			0
$214$	−19051.9	+	32998.8i	−0.416016	+	0.720560i
$215$	26374.5	+	45682.0i	0.570568	+	0.988253i
$216$		0			0
$217$			10111.3i			0.214728i
$218$	−21293.9	−	36882.2i	−0.448067	−	0.776075i
$219$		0			0
$220$	13063.6			0.269909
$221$			7084.78i			0.145058i
$222$		0			0
$223$	8103.55	+	4678.58i	0.162954	+	0.0940816i	0.579259	−	0.815143i	$-0.303342\pi$
$223$	8103.55	+	4678.58i	0.162954	+	0.0940816i	−0.416305	+	0.909225i	$0.636675\pi$
$224$	12996.5	−	7503.54i	0.259019	−	0.149544i
$225$		0			0
$226$	−9297.45	+	16103.7i	−0.182032	+	0.315288i
$227$		−	32899.8i		−	0.638472i	−0.947675	−	0.319236i	$-0.896574\pi$
$227$		−	32899.8i		−	0.638472i	0.947675	−	0.319236i	$-0.103426\pi$
$228$		0			0
$229$	−34126.2			−0.650753			−0.325377	−	0.945584i	$-0.605491\pi$
$229$	−34126.2			−0.650753			−0.325377	+	0.945584i	$0.605491\pi$
$230$	100223.	+	57863.6i	1.89457	+	1.09383i
$231$		0			0
$232$	7255.63	+	12567.1i	0.134803	+	0.233485i
$233$	−45770.7	+	79277.2i	−0.843094	+	1.46028i	0.0441722	+	0.999024i	$0.485935\pi$
$233$	−45770.7	+	79277.2i	−0.843094	+	1.46028i	−0.887266	+	0.461258i	$0.847398\pi$
$234$		0			0
$235$	−35096.7			−0.635522
$236$			26793.2i			0.481062i
$237$		0			0
$238$	2353.22	−	1358.63i	0.0415440	−	0.0239854i
$239$	4322.59			0.0756742			0.0378371	−	0.999284i	$-0.487953\pi$
$239$	4322.59			0.0756742			0.0378371	+	0.999284i	$0.487953\pi$
$240$		0			0
$241$	−38952.7	+	22489.4i	−0.670662	+	0.387207i	−0.796327	−	0.604866i	$-0.793227\pi$
$241$	−38952.7	+	22489.4i	−0.670662	+	0.387207i	0.125665	+	0.992073i	$0.459893\pi$
$242$	−42618.8	−	24606.0i	−0.727731	−	0.420156i
$243$		0			0
$244$	−7382.81	+	12787.4i	−0.124006	+	0.214784i
$245$	37838.0	−	65537.4i	0.630371	−	1.09183i
$246$		0			0
$247$	38540.9	−	96982.5i	0.631725	−	1.58964i
$248$	21051.7			0.342282
$249$		0			0
$250$	80473.8	+	46461.6i	1.28758	+	0.743385i
$251$	−31250.4	−	54127.2i	−0.496030	−	0.859149i	0.503960	−	0.863727i	$-0.331876\pi$
$251$	−31250.4	−	54127.2i	−0.496030	−	0.859149i	−0.999990	+	0.00457824i	$0.998543\pi$
$252$		0			0
$253$	18931.1	+	32789.7i	0.295757	+	0.512267i
$254$	−51502.8			−0.798296
$255$		0			0
$256$	−28106.0	−	48681.0i	−0.428864	−	0.742813i
$257$	64690.3	−	37349.0i	0.979429	−	0.565474i	0.0773313	−	0.997005i	$-0.475360\pi$
$257$	64690.3	−	37349.0i	0.979429	−	0.565474i	0.902098	+	0.431532i	$0.142027\pi$
$258$		0			0
$259$			48939.5i			0.729559i
$260$	52329.3	−	30212.3i	0.774102	−	0.446928i
$261$		0			0
$262$	−23840.3	+	13764.2i	−0.347304	+	0.200516i
$263$	−12657.9	+	21924.1i	−0.182999	+	0.316964i	−0.942900	−	0.333075i	$-0.891914\pi$
$263$	−12657.9	+	21924.1i	−0.182999	+	0.316964i	0.759901	+	0.650038i	$0.225247\pi$
$264$		0			0
$265$		−	151295.i		−	2.15443i
$266$	−39603.7	+	5796.68i	−0.559722	+	0.0819249i
$267$		0			0
$268$	21042.1	+	12148.6i	0.292967	+	0.169145i
$269$	115616.	+	66751.1i	1.59777	+	0.922474i	0.991916	+	0.126900i	$0.0405026\pi$
$269$	115616.	+	66751.1i	1.59777	+	0.922474i	0.605856	+	0.795574i	$0.292831\pi$
$270$		0			0
$271$	8684.87	−	15042.6i	0.118256	−	0.204826i	−0.800820	−	0.598905i	$-0.795603\pi$
$271$	8684.87	−	15042.6i	0.118256	−	0.204826i	0.919077	+	0.394079i	$0.128936\pi$
$272$	−3812.10	−	6602.75i	−0.0515260	−	0.0892456i
$273$		0			0
$274$		−	80530.5i		−	1.07265i
$275$	34731.8	+	60157.2i	0.459263	+	0.795467i
$276$		0			0
$277$	151171.			1.97020			0.985098	−	0.171996i	$-0.0550217\pi$
$277$	151171.			1.97020			0.985098	+	0.171996i	$0.0550217\pi$
$278$			52241.9i			0.675973i
$279$		0			0
$280$	43949.2	+	25374.1i	0.560576	+	0.323649i
$281$	71334.5	−	41185.0i	0.903414	−	0.521586i	0.0251079	−	0.999685i	$-0.492007\pi$
$281$	71334.5	−	41185.0i	0.903414	−	0.521586i	0.878306	+	0.478098i	$0.158674\pi$
$282$		0			0
$283$	38305.5	−	66347.1i	0.478287	−	0.828417i	−0.521403	−	0.853310i	$-0.674591\pi$
$283$	38305.5	−	66347.1i	0.478287	−	0.828417i	0.999690	+	0.0248934i	$0.00792465\pi$
$284$			27732.2i			0.343833i
$285$		0			0
$286$	82827.9			1.01262
$287$	17359.0	+	10022.2i	0.210746	+	0.121674i
$288$		0			0
$289$	41460.2	+	71811.2i	0.496404	+	0.859798i
$290$	27526.1	−	47676.5i	0.327301	−	0.566903i
$291$		0			0
$292$	7952.56			0.0932699
$293$		−	97102.9i		−	1.13109i	−0.824717	−	0.565545i	$-0.808666\pi$
$293$		−	97102.9i		−	1.13109i	0.824717	−	0.565545i	$-0.191334\pi$
$294$		0			0
$295$	−192764.	+	111292.i	−2.21504	+	1.27885i
$296$	101892.			1.16294
$297$		0			0
$298$	71173.8	−	41092.2i	0.801470	−	0.462729i
$299$	151666.	+	87564.6i	1.69647	+	0.979459i
$300$		0			0
$301$	15307.8	−	26513.8i	0.168958	−	0.292644i
$302$	5846.96	−	10127.2i	0.0641085	−	0.111039i
$303$		0			0
$304$	16264.5	+	111122.i	0.175993	+	1.20241i
$305$	−122665.			−1.31863
$306$		0			0
$307$	−32190.8	−	18585.4i	−0.341550	−	0.197194i	0.319407	−	0.947618i	$-0.396516\pi$
$307$	−32190.8	−	18585.4i	−0.341550	−	0.197194i	−0.660957	+	0.750423i	$0.729850\pi$
$308$	−3791.05	−	6566.30i	−0.0399630	−	0.0692180i
$309$		0			0
$310$	−39932.5	−	69165.1i	−0.415531	−	0.719721i
$311$	−157167.			−1.62495			−0.812476	−	0.582994i	$-0.801881\pi$
$311$	−157167.			−1.62495			−0.812476	+	0.582994i	$0.801881\pi$
$312$		0			0
$313$	−6297.21	−	10907.1i	−0.0642776	−	0.111332i	0.832096	−	0.554632i	$-0.187141\pi$
$313$	−6297.21	−	10907.1i	−0.0642776	−	0.111332i	−0.896373	+	0.443300i	$0.853808\pi$
$314$	−159471.	+	92070.8i	−1.61742	+	0.933819i
$315$		0			0
$316$			26801.5i			0.268401i
$317$	−11437.7	+	6603.57i	−0.113821	+	0.0657144i	−0.555830	−	0.831296i	$-0.687599\pi$
$317$	−11437.7	+	6603.57i	−0.113821	+	0.0657144i	0.442009	+	0.897011i	$0.354266\pi$
$318$		0			0
$319$	15598.2	−	9005.65i	0.153283	−	0.0884981i
$320$	44441.0	−	76974.1i	0.433994	−	0.751700i
$321$		0			0
$322$		−	67168.1i		−	0.647816i
$323$	1281.29	+	8753.95i	0.0122812	+	0.0839072i
$324$		0			0
$325$	278253.	+	160649.i	2.63434	+	1.52094i
$326$	33203.5	+	19170.1i	0.312428	+	0.180380i
$327$		0			0
$328$	20866.1	−	36141.2i	0.193952	−	0.335935i
$329$	10185.1	+	17641.0i	0.0940961	+	0.162979i
$330$		0			0
$331$			62057.0i			0.566415i	0.959059	+	0.283208i	$0.0913985\pi$
$331$			62057.0i			0.566415i	−0.959059	+	0.283208i	$0.908601\pi$
$332$	1857.18	+	3216.73i	0.0168492	+	0.0291836i
$333$		0			0
$334$	−136890.			−1.22710
$335$			201849.i			1.79861i
$336$		0			0
$337$	128238.	+	74038.1i	1.12916	+	0.651922i	0.943724	−	0.330734i	$-0.107296\pi$
$337$	128238.	+	74038.1i	1.12916	+	0.651922i	0.185438	+	0.982656i	$0.440630\pi$
$338$	218396.	−	126091.i	1.91166	−	1.10370i
$339$		0			0
$340$	−2561.28	+	4436.27i	−0.0221564	+	0.0383760i
$341$		−	26129.3i		−	0.224708i
$342$		0			0
$343$	−101992.			−0.866917
$344$	−55201.6	−	31870.7i	−0.466482	−	0.269323i
$345$		0			0
$346$	−33735.5	−	58431.7i	−0.281796	−	0.488086i
$347$	12650.7	−	21911.7i	0.105064	−	0.181977i	−0.808700	−	0.588221i	$-0.799828\pi$
$347$	12650.7	−	21911.7i	0.105064	−	0.181977i	0.913765	+	0.406244i	$0.133162\pi$
$348$		0			0
$349$	−155086.			−1.27327			−0.636637	−	0.771164i	$-0.719675\pi$
$349$	−155086.			−1.27327			−0.636637	+	0.771164i	$0.719675\pi$
$350$		−	123229.i		−	1.00595i
$351$		0			0
$352$	−33585.0	+	19390.3i	−0.271057	+	0.156495i
$353$	119944.			0.962561			0.481280	−	0.876567i	$-0.340172\pi$
$353$	119944.			0.962561			0.481280	+	0.876567i	$0.340172\pi$
$354$		0			0
$355$	−199519.	+	115192.i	−1.58317	+	0.914045i
$356$	−24023.5	−	13870.0i	−0.189555	−	0.109440i
$357$		0			0
$358$	37908.6	−	65659.7i	0.295782	−	0.512310i
$359$	−93344.7	+	161678.i	−0.724270	+	1.25447i	0.235004	+	0.971995i	$0.424490\pi$
$359$	−93344.7	+	161678.i	−0.724270	+	1.25447i	−0.959274	+	0.282478i	$0.908843\pi$
$360$		0			0
$361$	30081.7	−	126802.i	0.230828	−	0.972995i
$362$	54390.4			0.415055
$363$		0			0
$364$	−30371.9	−	17535.2i	−0.229229	−	0.132345i
$365$	33032.9	+	57214.7i	0.247948	+	0.429459i
$366$		0			0
$367$	113839.	+	197175.i	0.845200	+	1.46393i	0.885447	+	0.464740i	$0.153852\pi$
$367$	113839.	+	197175.i	0.845200	+	1.46393i	−0.0402473	+	0.999190i	$0.512815\pi$
$368$	−188463.			−1.39165
$369$		0			0
$370$	−193276.	−	334764.i	−1.41180	−	2.44531i
$371$	−76046.9	+	43905.7i	−0.552502	+	0.318987i
$372$		0			0
$373$			248937.i			1.78925i	0.446814	+	0.894627i	$0.352558\pi$
$373$			248937.i			1.78925i	−0.446814	+	0.894627i	$0.647442\pi$
$374$	−6081.08	+	3510.91i	−0.0434748	+	0.0251002i
$375$		0			0
$376$	36728.5	−	21205.2i	0.259793	−	0.149992i
$377$	41655.0	−	72148.5i	0.293079	−	0.507627i
$378$		0			0
$379$		−	236451.i		−	1.64612i	−0.567952	−	0.823061i	$-0.692264\pi$
$379$		−	236451.i		−	1.64612i	0.567952	−	0.823061i	$-0.307736\pi$
$380$	59194.1	−	46794.1i	0.409931	−	0.324059i
$381$		0			0
$382$	−200717.	−	115884.i	−1.37549	−	0.794139i
$383$	−199085.	−	114942.i	−1.35719	−	0.783576i	−0.367949	−	0.929846i	$-0.619940\pi$
$383$	−199085.	−	114942.i	−1.35719	−	0.783576i	−0.989245	+	0.146270i	$0.953273\pi$
$384$		0			0
$385$	31494.1	−	54549.4i	0.212475	−	0.368018i
$386$	−110540.	−	191461.i	−0.741898	−	1.28501i
$387$		0			0
$388$			17200.1i			0.114253i
$389$	12134.5	+	21017.5i	0.0801904	+	0.138894i	0.903332	−	0.428943i	$-0.141114\pi$
$389$	12134.5	+	21017.5i	0.0801904	+	0.138894i	−0.823141	+	0.567837i	$0.807781\pi$
$390$		0			0
$391$	−14846.8			−0.0971132
$392$			91446.1i			0.595104i
$393$		0			0
$394$	155095.	+	89544.2i	0.999092	+	0.576826i
$395$	−192823.	+	111326.i	−1.23585	+	0.713517i
$396$		0			0
$397$	−144488.	+	250260.i	−0.916748	+	1.58785i	−0.112425	+	0.993660i	$0.535862\pi$
$397$	−144488.	+	250260.i	−0.916748	+	1.58785i	−0.804322	+	0.594193i	$0.797471\pi$
$398$		−	118345.i		−	0.747109i
$399$		0			0
$400$	−345761.			−2.16101
$401$	−8555.46	−	4939.50i	−0.0532052	−	0.0307181i	0.473161	−	0.880976i	$-0.343113\pi$
$401$	−8555.46	−	4939.50i	−0.0532052	−	0.0307181i	−0.526367	+	0.850258i	$0.676446\pi$
$402$		0			0
$403$	−60429.6	−	104667.i	−0.372083	−	0.644466i
$404$	−3522.27	+	6100.75i	−0.0215804	+	0.0373784i
$405$		0			0
$406$	−31952.3			−0.193843
$407$		−	126467.i		−	0.763466i
$408$		0			0
$409$	154121.	−	88981.9i	0.921331	−	0.531931i	0.0372718	−	0.999305i	$-0.488133\pi$
$409$	154121.	−	88981.9i	0.921331	−	0.531931i	0.884060	+	0.467374i	$0.154800\pi$
$410$	−158322.			−0.941832
$411$		0			0
$412$	36596.2	−	21128.8i	0.215596	−	0.124474i
$413$	111880.	+	64594.0i	0.655923	+	0.378697i
$414$		0			0
$415$	−15428.5	+	26723.0i	−0.0895835	+	0.155163i
$416$	−89688.5	+	155345.i	−0.518263	+	0.897658i
$417$		0			0
$418$	102342.	−	14979.5i	0.585736	−	0.0857325i
$419$	−28240.8			−0.160860			−0.0804301	−	0.996760i	$-0.525629\pi$
$419$	−28240.8			−0.160860			−0.0804301	+	0.996760i	$0.525629\pi$
$420$		0			0
$421$	−54520.9	−	31477.6i	−0.307609	−	0.177598i	0.338247	−	0.941057i	$-0.390166\pi$
$421$	−54520.9	−	31477.6i	−0.307609	−	0.177598i	−0.645856	+	0.763459i	$0.723499\pi$
$422$	15557.1	+	26945.6i	0.0873580	+	0.151308i
$423$		0			0
$424$	91411.3	+	158329.i	0.508473	+	0.880701i
$425$	−27238.4			−0.150801
$426$		0			0
$427$	35597.5	+	61656.6i	0.195238	+	0.338161i
$428$	−36106.2	+	20845.9i	−0.197103	+	0.113798i
$429$		0			0
$430$			241819.i			1.30783i
$431$	144786.	−	83592.1i	0.779420	−	0.449998i	−0.0568047	−	0.998385i	$-0.518091\pi$
$431$	144786.	−	83592.1i	0.779420	−	0.449998i	0.836225	+	0.548387i	$0.184758\pi$
$432$		0			0
$433$	30557.5	−	17642.4i	0.162983	−	0.0940982i	−0.416290	−	0.909232i	$-0.636670\pi$
$433$	30557.5	−	17642.4i	0.162983	−	0.0940982i	0.579273	+	0.815134i	$0.303337\pi$
$434$	−23176.8	+	40143.5i	−0.123048	+	0.213125i
$435$		0			0
$436$		−	46598.3i		−	0.245130i
$437$	203235.	+	80765.7i	1.06423	+	0.422926i
$438$		0			0
$439$	163512.	+	94403.8i	0.848440	+	0.489847i	0.860124	−	0.510085i	$-0.170386\pi$
$439$	163512.	+	94403.8i	0.848440	+	0.489847i	−0.0116842	+	0.999932i	$0.503719\pi$
$440$	−113571.	−	65570.5i	−0.586630	−	0.338691i
$441$		0			0
$442$	−16239.5	+	28127.6i	−0.0831241	+	0.143975i
$443$	101510.	+	175820.i	0.517249	+	0.895901i	0.999799	+	0.0200330i	$0.00637714\pi$
$443$	101510.	+	175820.i	0.517249	+	0.895901i	−0.482551	+	0.875868i	$0.660290\pi$
$444$		0			0
$445$		−	230449.i		−	1.16374i
$446$	21448.1	+	37149.3i	0.107825	+	0.186759i
$447$		0			0
$448$	−51587.1			−0.257031
$449$		−	182146.i		−	0.903497i	−0.892145	−	0.451748i	$-0.850801\pi$
$449$		−	182146.i		−	0.903497i	0.892145	−	0.451748i	$-0.149199\pi$
$450$		0			0
$451$	−44858.3	−	25898.9i	−0.220541	−	0.127329i
$452$	−17620.1	+	10173.0i	−0.0862445	+	0.0497933i
$453$		0			0
$454$	75411.8	−	130617.i	0.365870	−	0.633706i
$455$		−	291348.i		−	1.40731i
$456$		0			0
$457$	66790.2			0.319801			0.159901	−	0.987133i	$-0.448883\pi$
$457$	66790.2			0.319801			0.159901	+	0.987133i	$0.448883\pi$
$458$	−135486.	−	78222.6i	−0.645895	−	0.372908i
$459$		0			0
$460$	63312.5	+	109660.i	0.299208	+	0.518244i
$461$	−34244.2	+	59312.7i	−0.161133	+	0.279091i	−0.935275	−	0.353921i	$-0.884848\pi$
$461$	−34244.2	+	59312.7i	−0.161133	+	0.279091i	0.774142	+	0.633012i	$0.218182\pi$
$462$		0			0
$463$	390746.			1.82277			0.911386	−	0.411552i	$-0.135013\pi$
$463$	390746.			1.82277			0.911386	+	0.411552i	$0.135013\pi$
$464$			89652.9i			0.416417i
$465$		0			0
$466$	−363432.	+	209828.i	−1.67360	+	0.966254i
$467$	−72245.4			−0.331266			−0.165633	−	0.986187i	$-0.552967\pi$
$467$	−72245.4			−0.331266			−0.165633	+	0.986187i	$0.552967\pi$
$468$		0			0
$469$	101458.	−	58576.7i	0.461254	−	0.266305i
$470$	−139339.	−	80447.3i	−0.630777	−	0.364180i
$471$		0			0
$472$	134484.	−	232933.i	0.603653	−	1.04556i
$473$	−39557.7	+	68515.9i	−0.176811	+	0.306245i
$474$		0			0
$475$	372862.	+	148176.i	1.65258	+	0.656735i
$476$	2973.14			0.0131220
$477$		0			0
$478$	17161.3	+	9908.07i	0.0751093	+	0.0433644i
$479$	157819.	+	273351.i	0.687843	+	1.19138i	0.972534	+	0.232760i	$0.0747755\pi$
$479$	157819.	+	273351.i	0.687843	+	1.19138i	−0.284691	+	0.958619i	$0.591891\pi$
$480$		0			0
$481$	−292483.	−	506595.i	−1.26418	−	2.18963i
$482$	−206197.			−0.887541
$483$		0			0
$484$	−26923.1	−	46632.1i	−0.114930	−	0.199065i
$485$	−123746.	+	71444.8i	−0.526075	+	0.303730i
$486$		0			0
$487$			15586.3i			0.0657182i	0.999460	+	0.0328591i	$0.0104613\pi$
$487$			15586.3i			0.0657182i	−0.999460	+	0.0328591i	$0.989539\pi$
$488$	128369.	−	74113.6i	0.539038	−	0.311213i
$489$		0			0
$490$	300445.	−	173462.i	1.25133	−	0.722456i
$491$	72237.5	−	125119.i	0.299640	−	0.518992i	−0.676414	−	0.736522i	$-0.736467\pi$
$491$	72237.5	−	125119.i	0.299640	−	0.518992i	0.976054	+	0.217530i	$0.0698001\pi$
$492$		0			0
$493$			7062.69i			0.0290587i
$494$	375312.	−	296692.i	1.53794	−	1.21577i
$495$		0			0
$496$	112636.	+	65030.5i	0.457841	+	0.264334i
$497$	115801.	+	66857.7i	0.468813	+	0.270669i
$498$		0			0
$499$	−127001.	+	219972.i	−0.510042	+	0.883419i	0.489890	+	0.871784i	$0.337037\pi$
$499$	−127001.	+	219972.i	−0.510042	+	0.883419i	−0.999932	+	0.0116348i	$0.996296\pi$
$500$	50836.7	+	88051.8i	0.203347	+	0.352207i
$501$		0			0
$502$		−	286524.i		−	1.13698i
$503$	−166366.	−	288154.i	−0.657548	−	1.13891i	−0.981248	−	0.192747i	$-0.938260\pi$
$503$	−166366.	−	288154.i	−0.657548	−	1.13891i	0.323700	−	0.946160i	$-0.395073\pi$
$504$		0			0
$505$	−58522.4			−0.229477
$506$			173573.i			0.677924i
$507$		0			0
$508$	−48802.9	−	28176.4i	−0.189112	−	0.109184i
$509$	−189141.	+	109200.i	−0.730044	+	0.421491i	−0.818438	−	0.574594i	$-0.805160\pi$
$509$	−189141.	+	109200.i	−0.730044	+	0.421491i	0.0883942	+	0.996086i	$0.471826\pi$
$510$		0			0
$511$	19172.3	−	33207.4i	0.0734231	−	0.127173i
$512$			57605.1i			0.219746i
$513$		0			0
$514$	342439.			1.29616
$515$	304022.	+	175527.i	1.14628	+	0.661805i
$516$		0			0
$517$	−26319.8	−	45587.2i	−0.0984694	−	0.170554i
$518$	−112177.	+	194297.i	−0.418067	+	0.724113i
$519$		0			0
$520$	−606583.			−2.24328
$521$			199162.i			0.733722i	0.930276	+	0.366861i	$0.119568\pi$
$521$			199162.i			0.733722i	−0.930276	+	0.366861i	$0.880432\pi$
$522$		0			0
$523$	−317690.	+	183419.i	−1.16145	+	0.670564i	−0.951651	−	0.307181i	$-0.900614\pi$
$523$	−317690.	+	183419.i	−1.16145	+	0.670564i	−0.209799	+	0.977744i	$0.567281\pi$
$524$	−30120.7			−0.109699
$525$		0			0
$526$	−100507.	+	58027.8i	−0.363266	+	0.209732i
$527$	8873.26	+	5122.98i	0.0319493	+	0.0184460i
$528$		0			0
$529$	−43578.5	+	75480.1i	−0.155726	+	0.269725i
$530$	346791.	−	600660.i	1.23457	−	2.13834i
$531$		0			0
$532$	−40698.8	−	16173.7i	−0.143800	−	0.0571462i
$533$	−239587.			−0.843353
$534$		0			0
$535$	−299952.	−	173177.i	−1.04796	−	0.605039i
$536$	−121956.	−	211234.i	−0.424497	−	0.735250i
$537$		0			0
$538$	306009.	+	530023.i	1.05723	+	1.83118i
$539$	113502.			0.390685
$540$		0			0
$541$	20782.0	+	35995.5i	0.0710058	+	0.122986i	0.899342	−	0.437245i	$-0.144046\pi$
$541$	20782.0	+	35995.5i	0.0710058	+	0.122986i	−0.828337	+	0.560231i	$0.810712\pi$
$542$	68960.3	−	39814.2i	0.234747	−	0.135531i
$543$		0			0
$544$		−	15206.9i		−	0.0513857i
$545$	335251.	−	193557.i	1.12870	−	0.651653i
$546$		0			0
$547$	−58247.7	+	33629.4i	−0.194672	+	0.112394i	−0.594168	−	0.804341i	$-0.702519\pi$
$547$	−58247.7	+	33629.4i	−0.194672	+	0.112394i	0.399496	+	0.916735i	$0.369185\pi$
$548$	44056.9	−	76308.8i	0.146708	−	0.254105i
$549$		0			0
$550$			318443.i			1.05271i
$551$	38420.7	−	96680.0i	0.126550	−	0.318444i
$552$		0			0
$553$	111915.	+	64613.9i	0.365962	+	0.211288i
$554$	600170.	+	346509.i	1.95549	+	1.12900i
$555$		0			0
$556$	−28580.7	+	49503.2i	−0.0924535	+	0.160134i
$557$	−140576.	−	243485.i	−0.453107	−	0.784805i	0.545470	−	0.838131i	$-0.316351\pi$
$557$	−140576.	−	243485.i	−0.453107	−	0.784805i	−0.998577	+	0.0533254i	$0.983018\pi$
$558$		0			0
$559$			365942.i			1.17109i
$560$	156765.	+	271525.i	0.499888	+	0.865832i
$561$		0			0
$562$	377611.			1.19556
$563$			559461.i			1.76503i	0.470282	+	0.882516i	$0.344152\pi$
$563$			559461.i			1.76503i	−0.470282	+	0.882516i	$0.655848\pi$
$564$		0			0
$565$	−146379.	−	84511.8i	−0.458544	−	0.264741i
$566$	304156.	−	175605.i	0.949433	−	0.548155i
$567$		0			0
$568$	139197.	−	241097.i	0.431454	−	0.747299i
$569$		−	95700.7i		−	0.295590i	−0.989018	−	0.147795i	$-0.952782\pi$
$569$		−	95700.7i		−	0.295590i	0.989018	−	0.147795i	$-0.0472177\pi$
$570$		0			0
$571$	−562671.			−1.72577			−0.862883	−	0.505403i	$-0.831344\pi$
$571$	−562671.			−1.72577			−0.862883	+	0.505403i	$0.831344\pi$
$572$	78485.8	+	45313.8i	0.239883	+	0.138496i
$573$		0			0
$574$	45945.0	+	79579.1i	0.139449	+	0.241532i
$575$	−336654.	+	583102.i	−1.01824	+	1.76364i
$576$		0			0
$577$	−384557.			−1.15507			−0.577536	−	0.816365i	$-0.695986\pi$
$577$	−384557.			−1.15507			−0.577536	+	0.816365i	$0.695986\pi$
$578$			380134.i			1.13784i
$579$		0			0
$580$	52166.1	−	30118.1i	0.155072	−	0.0895306i
$581$	17909.4			0.0530554
$582$		0			0
$583$	196517.	−	113459.i	0.578180	−	0.333812i
$584$	−69137.6	−	39916.6i	−0.202716	−	0.117038i
$585$		0			0
$586$	222576.	−	385512.i	0.648160	−	1.12265i
$587$	176824.	−	306269.i	0.513176	−	0.888846i	−0.486708	−	0.873565i	$-0.661802\pi$
$587$	176824.	−	306269.i	0.513176	−	0.888846i	0.999883	−	0.0152813i	$-0.00486437\pi$
$588$		0			0
$589$	−93595.9	−	118398.i	−0.269790	−	0.341282i
$590$	−1.02040e6			−2.93134
$591$		0			0
$592$	545166.	+	314752.i	1.55555	+	0.898100i
$593$	316633.	+	548424.i	0.900423	+	1.55958i	0.826946	+	0.562282i	$0.190076\pi$
$593$	316633.	+	548424.i	0.900423	+	1.55958i	0.0734773	+	0.997297i	$0.476590\pi$
$594$		0			0
$595$	12349.6	+	21390.2i	0.0348835	+	0.0604201i
$596$	89923.4			0.253151
$597$		0			0
$598$	401424.	+	695287.i	1.12254	+	1.94429i
$599$	−126946.	+	73292.3i	−0.353806	+	0.204270i	−0.666360	−	0.745630i	$-0.732149\pi$
$599$	−126946.	+	73292.3i	−0.353806	+	0.204270i	0.312554	+	0.949900i	$0.398815\pi$
$600$		0			0
$601$		−	565825.i		−	1.56651i	−0.621701	−	0.783255i	$-0.713558\pi$
$601$		−	565825.i		−	1.56651i	0.621701	−	0.783255i	$-0.286442\pi$
$602$	121548.	−	70175.8i	0.335394	−	0.193640i
$603$		0			0
$604$	11080.9	−	6397.55i	0.0303739	−	0.0175364i
$605$	223663.	−	387396.i	0.611060	−	1.05839i
$606$		0			0
$607$			360850.i			0.979376i	0.871898	+	0.489688i	$0.162889\pi$
$607$			360850.i			0.979376i	−0.871898	+	0.489688i	$0.837111\pi$
$608$	−82724.7	+	208164.i	−0.223784	+	0.563118i
$609$		0			0
$610$	−486998.	−	281169.i	−1.30878	−	0.755626i
$611$	−210860.	−	121740.i	−0.564823	−	0.326101i
$612$		0			0
$613$	19524.2	−	33816.9i	0.0519580	−	0.0899938i	−0.838877	−	0.544322i	$-0.816787\pi$
$613$	19524.2	−	33816.9i	0.0519580	−	0.0899938i	0.890835	+	0.454328i	$0.150120\pi$
$614$	−85201.3	−	147573.i	−0.226001	−	0.391444i
$615$		0			0
$616$			76114.3i			0.200588i
$617$	−169457.	−	293507.i	−0.445131	−	0.770990i	0.552930	−	0.833228i	$-0.313510\pi$
$617$	−169457.	−	293507.i	−0.445131	−	0.770990i	−0.998061	+	0.0622378i	$0.980176\pi$
$618$		0			0
$619$	308686.			0.805631			0.402815	−	0.915281i	$-0.368032\pi$
$619$	308686.			0.805631			0.402815	+	0.915281i	$0.368032\pi$
$620$		−	87385.7i		−	0.227330i
$621$		0			0
$622$	−623975.	−	360252.i	−1.61282	−	0.931163i
$623$	−115833.	+	66876.4i	−0.298440	+	0.172305i
$624$		0			0
$625$	−75003.9	+	129911.i	−0.192010	+	0.332571i
$626$		−	57736.9i		−	0.147335i
$627$		0			0
$628$	−201482.			−0.510877
$629$	42947.1	+	24795.5i	0.108551	+	0.0626718i
$630$		0			0
$631$	132924.	+	230231.i	0.333845	+	0.578237i	0.983262	−	0.182195i	$-0.0583204\pi$
$631$	132924.	+	230231.i	0.333845	+	0.578237i	−0.649417	+	0.760432i	$0.724987\pi$
$632$	134526.	−	233005.i	0.336799	−	0.583353i
$633$		0			0
$634$	−60545.8			−0.150628
$635$		−	468150.i		−	1.16101i
$636$		0			0
$637$	454660.	−	262498.i	1.12049	−	0.646916i
$638$	82569.6			0.202852
$639$		0			0
$640$	711151.	−	410583.i	1.73621	−	1.00240i
$641$	−474195.	−	273776.i	−1.15409	−	0.666316i	−0.204211	−	0.978927i	$-0.565463\pi$
$641$	−474195.	−	273776.i	−1.15409	−	0.666316i	−0.949881	+	0.312611i	$0.898796\pi$
$642$		0			0
$643$	123976.	−	214732.i	0.299857	−	0.519368i	−0.676246	−	0.736676i	$-0.736394\pi$
$643$	123976.	−	214732.i	0.299857	−	0.519368i	0.976103	+	0.217308i	$0.0697276\pi$
$644$	36746.6	−	63646.9i	0.0886023	−	0.153464i
$645$		0			0
$646$	−14978.6	+	37691.3i	−0.0358926	+	0.0903184i
$647$	140129.			0.334749			0.167375	−	0.985893i	$-0.446471\pi$
$647$	140129.			0.334749			0.167375	+	0.985893i	$0.446471\pi$
$648$		0			0
$649$	−289116.	−	166921.i	−0.686408	−	0.396298i
$650$	736468.	+	1.27560e6i	1.74312	+	3.01917i
$651$		0			0
$652$	20975.3	+	36330.2i	0.0493415	+	0.0854620i
$653$	457094.			1.07196			0.535980	−	0.844231i	$-0.319942\pi$
$653$	457094.			1.07196			0.535980	+	0.844231i	$0.319942\pi$
$654$		0			0
$655$	−125114.	−	216703.i	−0.291623	−	0.505106i
$656$	223286.	−	128914.i	0.518865	−	0.299567i
$657$		0			0
$658$			93383.2i			0.215684i
$659$	−357061.	+	206149.i	−0.822188	+	0.474691i	−0.851171	−	0.524889i	$-0.824107\pi$
$659$	−357061.	+	206149.i	−0.822188	+	0.474691i	0.0289821	+	0.999580i	$0.490773\pi$
$660$		0			0
$661$	26307.5	−	15188.7i	0.0602111	−	0.0347629i	−0.469592	−	0.882883i	$-0.655599\pi$
$661$	26307.5	−	15188.7i	0.0602111	−	0.0347629i	0.529803	+	0.848121i	$0.322266\pi$
$662$	−142245.	+	246375.i	−0.324579	+	0.562187i
$663$		0			0
$664$		−	37287.3i		−	0.0845716i
$665$	−52690.5	−	359989.i	−0.119149	−	0.814040i
$666$		0			0
$667$	151193.	+	87291.5i	0.339845	+	0.196210i
$668$	−129714.	−	74890.4i	−0.290693	−	0.167831i
$669$		0			0
$670$	−462671.	+	801370.i	−1.03068	+	1.78519i
$671$	−91989.4	−	159330.i	−0.204312	−	0.353878i
$672$		0			0
$673$		−	517440.i		−	1.14243i	−0.820801	−	0.571215i	$-0.806472\pi$
$673$		−	517440.i		−	1.14243i	0.820801	−	0.571215i	$-0.193528\pi$
$674$	339415.	+	587883.i	0.747155	+	1.29411i
$675$		0			0
$676$	275929.			0.603815
$677$		−	391079.i		−	0.853272i	−0.904423	−	0.426636i	$-0.859699\pi$
$677$		−	391079.i		−	0.853272i	0.904423	−	0.426636i	$-0.140301\pi$
$678$		0			0
$679$	71822.2	+	41466.6i	0.155783	+	0.0899412i
$680$	44534.2	−	25711.9i	0.0963111	−	0.0556052i
$681$		0			0
$682$	59892.6	−	103737.i	0.128767	−	0.223031i
$683$		−	416919.i		−	0.893739i	−0.894599	−	0.446869i	$-0.852539\pi$
$683$		−	416919.i		−	0.893739i	0.894599	−	0.446869i	$-0.147461\pi$
$684$		0			0
$685$	732005.			1.56003
$686$	−404922.	−	233782.i	−0.860446	−	0.496778i
$687$		0			0
$688$	−196902.	−	341044.i	−0.415981	−	0.720500i
$689$	524797.	−	908975.i	1.10548	−	1.91476i
$690$		0			0
$691$	−430225.			−0.901031			−0.450516	−	0.892769i	$-0.648760\pi$
$691$	−430225.			−0.901031			−0.450516	+	0.892769i	$0.648760\pi$
$692$		−	73824.6i		−	0.154166i
$693$		0			0
$694$	100450.	−	57994.9i	0.208560	−	0.120412i
$695$	−474868.			−0.983112
$696$		0			0
$697$	17590.1	−	10155.6i	0.0362078	−	0.0209046i
$698$	−615713.	−	355482.i	−1.26377	−	0.729637i
$699$		0			0
$700$	67416.6	−	116769.i	0.137585	−	0.238304i
$701$	−432212.	+	748612.i	−0.879550	+	1.52342i	−0.0277137	+	0.999616i	$0.508823\pi$
$701$	−432212.	+	748612.i	−0.879550	+	1.52342i	−0.851836	+	0.523809i	$0.824511\pi$
$702$		0			0
$703$	−453010.	−	573053.i	−0.916636	−	1.15954i
$704$	133309.			0.268977
$705$		0			0
$706$	476193.	+	274930.i	0.955375	+	0.551586i
$707$	16983.2	+	29415.8i	0.0339767	+	0.0588493i
$708$		0			0
$709$	162798.	+	281974.i	0.323859	+	0.560941i	0.981281	−	0.192582i	$-0.0616863\pi$
$709$	162798.	+	281974.i	0.323859	+	0.560941i	−0.657422	+	0.753523i	$0.728353\pi$
$710$	−1.05616e6			−2.09514
$711$		0			0
$712$	139236.	+	241164.i	0.274658	+	0.475721i
$713$	219339.	−	126635.i	0.431456	−	0.249101i
$714$		0			0
$715$			752888.i			1.47271i
$716$	71842.7	−	41478.4i	0.140138	−	0.0809088i
$717$		0			0
$718$	−741183.	+	427922.i	−1.43773	+	0.830072i
$719$	−263310.	+	456066.i	−0.509341	+	0.882205i	0.490600	+	0.871385i	$0.336778\pi$
$719$	−263310.	+	456066.i	−0.509341	+	0.882205i	−0.999941	+	0.0108204i	$0.996556\pi$
$720$		0			0
$721$		−	203752.i		−	0.391951i
$722$	410079.	−	434468.i	0.786670	−	0.833457i
$723$		0			0
$724$	51539.1	+	29756.1i	0.0983240	+	0.0567674i
$725$	277385.	+	160148.i	0.527724	+	0.304682i
$726$		0			0
$727$	345843.	−	599018.i	0.654351	−	1.13337i	−0.327706	−	0.944780i	$-0.606275\pi$
$727$	345843.	−	599018.i	0.654351	−	1.13337i	0.982056	−	0.188589i	$-0.0603913\pi$
$728$	176030.	+	304894.i	0.332143	+	0.575289i
$729$		0			0
$730$			302867.i			0.568338i
$731$	−15511.6	−	26866.8i	−0.0290283	−	0.0502784i
$732$		0			0
$733$	−248355.			−0.462238			−0.231119	−	0.972926i	$-0.574239\pi$
$733$	−248355.			−0.462238			−0.231119	+	0.972926i	$0.574239\pi$
$734$			1.04375e6i			1.93733i
$735$		0			0
$736$	−325539.	−	187950.i	−0.600962	−	0.346966i
$737$	−262183.	+	151371.i	−0.482691	+	0.278682i
$738$		0			0
$739$	−363794.	+	630109.i	−0.666141	+	1.15379i	0.312833	+	0.949808i	$0.398722\pi$
$739$	−363794.	+	630109.i	−0.666141	+	1.15379i	−0.978975	+	0.203982i	$0.934612\pi$
$740$		−	422952.i		−	0.772374i
$741$		0			0
$742$	−402556.			−0.731170
$743$	602317.	+	347748.i	1.09106	+	0.629922i	0.933858	−	0.357645i	$-0.116420\pi$
$743$	602317.	+	347748.i	1.09106	+	0.629922i	0.157199	+	0.987567i	$0.449753\pi$
$744$		0			0
$745$	373519.	+	646954.i	0.672977	+	1.16563i
$746$	−570604.	+	988315.i	−1.02531	+	1.77590i
$747$		0			0
$748$	−7683.05			−0.0137319
$749$			201024.i			0.358331i
$750$		0			0
$751$	631954.	−	364859.i	1.12048	−	0.646912i	0.178960	−	0.983856i	$-0.442727\pi$
$751$	631954.	−	364859.i	1.12048	−	0.646912i	0.941524	+	0.336945i	$0.109393\pi$
$752$	262018.			0.463336
$753$		0			0
$754$	330752.	−	190960.i	0.581782	−	0.335892i
$755$	92054.3	+	53147.5i	0.161492	+	0.0932372i
$756$		0			0
$757$	−141571.	+	245208.i	−0.247049	+	0.427901i	−0.962706	−	0.270551i	$-0.912794\pi$
$757$	−141571.	+	245208.i	−0.247049	+	0.427901i	0.715657	+	0.698452i	$0.246128\pi$
$758$	541983.	−	938743.i	0.943295	−	1.63383i
$759$		0			0
$760$	−749494.	+	109701.i	−1.29760	+	0.189926i
$761$	319277.			0.551313			0.275657	−	0.961256i	$-0.411105\pi$
$761$	319277.			0.551313			0.275657	+	0.961256i	$0.411105\pi$
$762$		0			0
$763$	−194580.	−	112341.i	−0.334233	−	0.192969i
$764$	−126796.	−	219618.i	−0.217230	−	0.376254i
$765$		0			0
$766$	−526931.	−	912672.i	−0.898042	−	1.55545i
$767$	−1.54416e6			−2.62483
$768$		0			0
$769$	219721.	+	380569.i	0.371552	+	0.643547i	0.989805	−	0.142432i	$-0.0454924\pi$
$769$	219721.	+	380569.i	0.371552	+	0.643547i	−0.618252	+	0.785980i	$0.712159\pi$
$770$	250072.	−	144379.i	0.421778	−	0.243514i
$771$		0			0
$772$		−	241898.i		−	0.405880i
$773$	785095.	−	453275.i	1.31390	−	0.758583i	0.331163	−	0.943573i	$-0.392559\pi$
$773$	785095.	−	453275.i	1.31390	−	0.758583i	0.982740	+	0.184991i	$0.0592256\pi$
$774$		0			0
$775$	402407.	−	232330.i	0.669980	−	0.386813i
$776$	86333.1	−	149533.i	0.143369	−	0.248322i
$777$		0			0
$778$			111257.i			0.183809i
$779$	−296034.	+	43329.6i	−0.487828	+	0.0714019i
$780$		0			0
$781$	−299248.	−	172771.i	−0.490602	−	0.283249i
$782$	−58943.7	−	34031.2i	−0.0963882	−	0.0556498i
$783$		0			0
$784$	−282484.	+	489277.i	−0.459581	+	0.796017i
$785$	−836904.	−	1.44956e6i	−1.35811	−	2.35232i
$786$		0			0
$787$		−	461769.i		−	0.745548i	−0.927922	−	0.372774i	$-0.878407\pi$
$787$		−	461769.i		−	0.745548i	0.927922	−	0.372774i	$-0.121593\pi$
$788$	97976.3	+	169700.i	0.157786	+	0.273293i
$789$		0			0
$790$	−1.02071e6			−1.63550
$791$			98101.3i			0.156791i
$792$		0			0
$793$	−736971.	−	425490.i	−1.17194	−	0.676617i
$794$	−1.14727e6	+	662378.i	−1.81981	+	1.05067i
$795$		0			0
$796$	64744.7	−	112141.i	0.102183	−	0.176986i
$797$		−	936748.i		−	1.47471i	−0.675506	−	0.737354i	$-0.736075\pi$
$797$		−	936748.i		−	1.47471i	0.675506	−	0.737354i	$-0.263925\pi$
$798$		0			0
$799$	20641.3			0.0323328
$800$	−597245.	−	344820.i	−0.933196	−	0.538781i
$801$		0			0
$802$	−22644.2	−	39221.0i	−0.0352054	−	0.0609775i
$803$	−49544.2	+	85813.2i	−0.0768355	+	0.133083i
$804$		0			0
$805$	610544.			0.942160
$806$		−	554057.i		−	0.852873i
$807$		0			0
$808$	61243.4	−	35358.9i	0.0938073	−	0.0541597i
$809$	55778.3			0.0852252			0.0426126	−	0.999092i	$-0.486432\pi$
$809$	55778.3			0.0852252			0.0426126	+	0.999092i	$0.486432\pi$
$810$		0			0
$811$	−562443.	+	324727.i	−0.855140	+	0.493715i	−0.862382	−	0.506259i	$-0.831028\pi$
$811$	−562443.	+	324727.i	−0.855140	+	0.493715i	0.00724190	+	0.999974i	$0.497695\pi$
$812$	−30277.2	−	17480.6i	−0.0459202	−	0.0265120i
$813$		0			0
$814$	289884.	−	502093.i	0.437497	−	0.757767i
$815$	−174252.	+	301813.i	−0.262339	+	0.454384i
$816$		0			0
$817$	66181.1	+	452158.i	0.0991493	+	0.677402i
$818$	815844.			1.21927
$819$		0			0
$820$	−150022.	−	86615.3i	−0.223114	−	0.128815i
$821$	−160712.	−	278361.i	−0.238431	−	0.412974i	0.721834	−	0.692067i	$-0.243300\pi$
$821$	−160712.	−	278361.i	−0.238431	−	0.412974i	−0.960264	+	0.279093i	$0.909966\pi$
$822$		0			0
$823$	−239960.	−	415622.i	−0.354273	−	0.613619i	0.632720	−	0.774381i	$-0.281938\pi$
$823$	−239960.	−	415622.i	−0.354273	−	0.613619i	−0.986993	+	0.160761i	$0.948605\pi$
$824$	−424210.			−0.624779
$825$		0			0
$826$	296120.	+	512894.i	0.434017	+	0.751740i
$827$	−650685.	+	375673.i	−0.951393	+	0.549287i	−0.893513	−	0.449037i	$-0.851767\pi$
$827$	−650685.	+	375673.i	−0.951393	+	0.549287i	−0.0578795	+	0.998324i	$0.518434\pi$
$828$		0			0
$829$			96570.8i			0.140520i	0.997529	+	0.0702598i	$0.0223828\pi$
$829$			96570.8i			0.140520i	−0.997529	+	0.0702598i	$0.977617\pi$
$830$	−122507.	+	70729.3i	−0.177830	+	0.102670i
$831$		0			0
$832$	534001.	−	308306.i	0.771429	−	0.445385i
$833$	−22253.6	+	38544.3i	−0.0320708	+	0.0555482i
$834$		0			0
$835$		−	1.24430e6i		−	1.78465i
$836$	105172.	+	41795.5i	0.150483	+	0.0598021i
$837$		0			0
$838$	−112120.	−	64732.5i	−0.159659	−	0.0921794i
$839$	1.05400e6	+	608525.i	1.49732	+	0.864479i	0.999995	−	0.00308436i	$-0.000981784\pi$
$839$	1.05400e6	+	608525.i	1.49732	+	0.864479i	0.497326	+	0.867563i	$0.334315\pi$
$840$		0			0
$841$	−312115.	+	540600.i	−0.441289	+	0.764335i
$842$	−144304.	−	249941.i	−0.203542	−	0.352544i
$843$		0			0
$844$			34044.0i			0.0477921i
$845$	1.14614e6	+	1.98517e6i	1.60518	+	2.78025i
$846$		0			0
$847$	−259628.			−0.361897
$848$			1.12951e6i			1.57071i
$849$		0			0
$850$	−108140.	−	62434.8i	−0.149675	−	0.0864150i
$851$	1.06161e6	−	612923.i	1.46591	−	0.846343i
$852$		0			0
$853$	−119586.	+	207129.i	−0.164355	+	0.284671i	−0.936426	−	0.350865i	$-0.885888\pi$
$853$	−119586.	+	207129.i	−0.164355	+	0.284671i	0.772071	+	0.635536i	$0.219221\pi$
$854$			326381.i			0.447516i
$855$		0			0
$856$	418531.			0.571189
$857$	−1.00185e6	−	578418.i	−1.36408	−	0.787553i	−0.373918	−	0.927462i	$-0.621986\pi$
$857$	−1.00185e6	−	578418.i	−1.36408	−	0.787553i	−0.990164	+	0.139908i	$0.955319\pi$
$858$		0			0
$859$	475365.	+	823357.i	0.644230	+	1.11584i	0.984479	+	0.175504i	$0.0561555\pi$
$859$	475365.	+	823357.i	0.644230	+	1.11584i	−0.340249	+	0.940336i	$0.610511\pi$
$860$	−132295.	+	229142.i	−0.178874	+	0.309818i
$861$		0			0
$862$	766427.			1.03147
$863$		−	38746.3i		−	0.0520246i	−0.999662	−	0.0260123i	$-0.991719\pi$
$863$		−	38746.3i		−	0.0520246i	0.999662	−	0.0260123i	$-0.00828090\pi$
$864$		0			0
$865$	531131.	−	306649.i	0.709855	−	0.409835i
$866$	161757.			0.215688
$867$		0			0
$868$	−43923.7	+	25359.3i	−0.0582987	+	0.0336588i
$869$	−289205.	−	166972.i	−0.382971	−	0.221108i
$870$		0			0
$871$	−700157.	+	1.21271e6i	−0.922910	+	1.59853i
$872$	−233892.	+	405114.i	−0.307598	+	0.532775i
$873$		0			0
$874$	621743.	+	786499.i	0.813932	+	1.02962i
$875$	490236.			0.640308
$876$		0			0
$877$	315242.	+	182005.i	0.409869	+	0.236638i	0.690733	−	0.723110i	$-0.257288\pi$
$877$	315242.	+	182005.i	0.409869	+	0.236638i	−0.280865	+	0.959747i	$0.590621\pi$
$878$	432778.	+	749593.i	0.561404	+	0.972381i
$879$		0			0
$880$	−405105.	−	701663.i	−0.523121	−	0.906073i
$881$	243497.			0.313720			0.156860	−	0.987621i	$-0.449863\pi$
$881$	243497.			0.313720			0.156860	+	0.987621i	$0.449863\pi$
$882$		0			0
$883$	714345.	+	1.23728e6i	0.916193	+	1.58689i	0.805146	+	0.593077i	$0.202087\pi$
$883$	714345.	+	1.23728e6i	0.916193	+	1.58689i	0.111047	+	0.993815i	$0.464580\pi$
$884$	−30776.3	+	17768.7i	−0.0393832	+	0.0227379i
$885$		0			0
$886$			930705.i			1.18562i
$887$	963132.	−	556064.i	1.22416	−	0.706769i	0.258358	−	0.966049i	$-0.416818\pi$
$887$	963132.	−	556064.i	1.22416	−	0.706769i	0.965802	+	0.259280i	$0.0834851\pi$
$888$		0			0
$889$	−235311.	+	135857.i	−0.297741	+	0.171901i
$890$	528227.	−	914916.i	0.666869	−	1.15505i
$891$		0			0
$892$			46935.7i			0.0589894i
$893$	−282556.	−	112288.i	−0.354324	−	0.140809i
$894$		0			0
$895$	596832.	+	344581.i	0.745086	+	0.430175i
$896$	−412752.	−	238303.i	−0.514131	−	0.296833i
$897$		0			0
$898$	417508.	−	723144.i	0.517740	−	0.896752i
$899$	−60241.1	−	104341.i	−0.0745373	−	0.129102i
$900$		0			0
$901$			88980.4i			0.109609i
$902$	−118729.	−	205645.i	−0.145930	−	0.252758i
$903$		0			0
$904$	204246.			0.249929
$905$			494397.i			0.603641i
$906$		0			0
$907$	−1.07643e6	−	621477.i	−1.30849	−	0.755458i	−0.326647	−	0.945146i	$-0.605919\pi$
$907$	−1.07643e6	−	621477.i	−1.30849	−	0.755458i	−0.981844	+	0.189688i	$0.939252\pi$
$908$	142917.	−	82513.1i	0.173345	−	0.100081i
$909$		0			0
$910$	667816.	−	1.15669e6i	0.806443	−	1.39680i
$911$			298558.i			0.359743i	0.983690	+	0.179871i	$0.0575682\pi$
$911$			298558.i			0.359743i	−0.983690	+	0.179871i	$0.942432\pi$
$912$		0			0
$913$	−46280.8			−0.0555212
$914$	265166.	+	153094.i	0.317414	+	0.183259i
$915$		0			0
$916$	−85588.6	−	148244.i	−0.102006	−	0.176679i
$917$	−72616.0	+	125775.i	−0.0863562	+	0.149573i
$918$		0			0
$919$	−1.19613e6			−1.41628			−0.708138	−	0.706074i	$-0.750464\pi$
$919$	−1.19613e6			−1.41628			−0.708138	+	0.706074i	$0.750464\pi$
$920$		−	1.27115e6i		−	1.50183i
$921$		0			0
$922$	−271908.	+	156986.i	−0.319861	+	0.184672i
$923$	−1.59828e6			−1.87607
$924$		0			0
$925$	1.94767e6	−	1.12449e6i	2.27632	−	1.31423i
$926$	1.55132e6	+	895653.i	1.80917	+	1.04452i
$927$		0			0
$928$	−89408.8	+	154861.i	−0.103821	+	0.179823i
$929$	−234694.	+	406501.i	−0.271938	+	0.471010i	−0.969358	−	0.245652i	$-0.920998\pi$
$929$	−234694.	+	406501.i	−0.271938	+	0.471010i	0.697420	+	0.716662i	$0.254331\pi$
$930$		0			0
$931$	514305.	−	406569.i	0.593364	−	0.469067i
$932$	−459173.			−0.528622
$933$		0			0
$934$	−286824.	−	165598.i	−0.328793	−	0.189829i
$935$	−31913.4	−	55275.7i	−0.0365048	−	0.0632282i
$936$		0			0
$937$	−48982.6	−	84840.4i	−0.0557908	−	0.0966326i	0.836781	−	0.547538i	$-0.184435\pi$
$937$	−48982.6	−	84840.4i	−0.0557908	−	0.0966326i	−0.892572	+	0.450905i	$0.851101\pi$
$938$	537069.			0.610414
$939$		0			0
$940$	−88022.7	−	152460.i	−0.0996183	−	0.172544i
$941$	253995.	−	146644.i	0.286844	−	0.165609i	−0.349674	−	0.936872i	$-0.613708\pi$
$941$	253995.	−	146644.i	0.286844	−	0.165609i	0.636518	+	0.771262i	$0.280374\pi$
$942$		0			0
$943$		−	502075.i		−	0.564606i
$944$	1.43910e6	−	830864.i	1.61490	−	0.932365i
$945$		0			0
$946$	−314099.	+	181345.i	−0.350982	+	0.202639i
$947$	−273771.	+	474186.i	−0.305273	+	0.528748i	−0.977322	−	0.211759i	$-0.932081\pi$
$947$	−273771.	+	474186.i	−0.305273	+	0.528748i	0.672049	+	0.740506i	$0.265414\pi$
$948$		0			0
$949$			458326.i			0.508912i
$950$	1.14067e6	+	1.44294e6i	1.26390	+	1.59883i
$951$		0			0
$952$	−25847.7	−	14923.2i	−0.0285199	−	0.0164660i
$953$	978151.	+	564736.i	1.07701	+	0.621812i	0.930088	−	0.367336i	$-0.119730\pi$
$953$	978151.	+	564736.i	1.07701	+	0.621812i	0.146922	+	0.989148i	$0.453063\pi$
$954$		0			0
$955$	1.05336e6	−	1.82447e6i	1.15497	−	2.00046i
$956$	10841.1	+	18777.3i	0.0118620	+	0.0205455i
$957$		0			0
$958$			1.44699e6i			1.57665i
$959$	−212428.	−	367936.i	−0.230980	−	0.400069i
$960$		0			0
$961$	748735.			0.810740
$962$		−	2.68167e6i		−	2.89771i
$963$		0			0
$964$	−195387.	−	112807.i	−0.210253	−	0.121390i
$965$	1.74034e6	−	1.00478e6i	1.86887	−	1.07899i
$966$		0			0
$967$	−551522.	+	955264.i	−0.589807	+	1.02158i	0.404451	+	0.914560i	$0.367463\pi$
$967$	−551522.	+	955264.i	−0.589807	+	1.02158i	−0.994257	+	0.107015i	$0.965871\pi$
$968$			540544.i			0.576873i
$969$		0			0
$970$	−655052.			−0.696198
$971$	−156634.	−	90432.6i	−0.166130	−	0.0959150i	0.414630	−	0.909990i	$-0.363911\pi$
$971$	−156634.	−	90432.6i	−0.166130	−	0.0959150i	−0.580760	+	0.814075i	$0.697244\pi$
$972$		0			0
$973$	137807.	+	238688.i	0.145561	+	0.252119i
$974$	−35726.4	+	61879.9i	−0.0376592	+	0.0652276i
$975$		0			0
$976$	915772.			0.961363
$977$			962182.i			1.00802i	0.863698	+	0.504009i	$0.168142\pi$
$977$			962182.i			1.00802i	−0.863698	+	0.504009i	$0.831858\pi$
$978$		0			0
$979$	299331.	−	172819.i	0.312311	−	0.180313i
$980$	379592.			0.395244
$981$		0			0
$982$	573586.	−	331160.i	0.594806	−	0.343411i
$983$	−286561.	−	165446.i	−0.296558	−	0.171218i	0.344338	−	0.938846i	$-0.388104\pi$
$983$	−286561.	−	165446.i	−0.296558	−	0.171218i	−0.640896	+	0.767628i	$0.721437\pi$
$984$		0			0
$985$	−813937.	+	1.40978e6i	−0.838915	+	1.45304i
$986$	−16188.8	+	28039.9i	−0.0166518	+	0.0288418i
$987$		0			0
$988$	517952.	−	75811.2i	0.530611	−	0.0776639i
$989$	−766863.			−0.784017
$990$		0			0
$991$	1.08063e6	+	623905.i	1.10035	+	0.635288i	0.936313	−	0.351166i	$-0.114215\pi$
$991$	1.08063e6	+	623905.i	1.10035	+	0.635288i	0.164038	+	0.986454i	$0.447548\pi$
$992$	129707.	+	224659.i	0.131807	+	0.228297i
$993$		0			0
$994$	306497.	+	530869.i	0.310209	+	0.537297i
$995$	1.07573e6			1.08657
$996$		0			0
$997$	−932962.	−	1.61594e6i	−0.938585	−	1.62568i	−0.768114	−	0.640313i	$-0.778804\pi$
$997$	−932962.	−	1.61594e6i	−0.938585	−	1.62568i	−0.170471	−	0.985363i	$-0.554529\pi$
$998$	−1.00842e6	+	582214.i	−1.01247	+	0.584549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.5.p.a.46.4		10
3.2	odd	2		19.5.d.a.8.2	✓	10
12.11	even	2		304.5.r.a.65.1		10
19.12	odd	6	inner	171.5.p.a.145.4		10
57.50	even	6		19.5.d.a.12.2	yes	10
228.107	odd	6		304.5.r.a.145.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.d.a.8.2	✓	10	3.2	odd	2
19.5.d.a.12.2	yes	10	57.50	even	6
171.5.p.a.46.4		10	1.1	even	1	trivial
171.5.p.a.145.4		10	19.12	odd	6	inner
304.5.r.a.65.1		10	12.11	even	2
304.5.r.a.145.1		10	228.107	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.97014 + 2.29216i) q^{2} +(2.50801 + 4.34400i) q^{4} +(-20.8352 + 36.0877i) q^{5} +24.1856 q^{7} -50.3541i q^{8} +O(q^{10})\)	\(q+(3.97014 + 2.29216i) q^{2} +(2.50801 + 4.34400i) q^{4} +(-20.8352 + 36.0877i) q^{5} +24.1856 q^{7} -50.3541i q^{8} +(-165.438 + 95.5155i) q^{10} -62.4993 q^{11} +(-250.356 + 144.543i) q^{13} +(96.0201 + 55.4372i) q^{14} +(155.548 - 269.417i) q^{16} +(12.2538 - 21.2242i) q^{17} +(-283.198 + 223.874i) q^{19} -209.020 q^{20} +(-248.131 - 143.258i) q^{22} +(-302.902 - 524.641i) q^{23} +(-555.715 - 962.527i) q^{25} -1325.26 q^{26} +(60.6576 + 105.062i) q^{28} +(-249.575 + 144.092i) q^{29} +418.074i q^{31} +(537.367 - 310.249i) q^{32} +(97.2984 - 56.1752i) q^{34} +(-503.912 + 872.801i) q^{35} +2023.50i q^{37} +(-1637.49 + 239.675i) q^{38} +(1817.17 + 1049.14i) q^{40} +(717.741 + 414.388i) q^{41} +(632.930 - 1096.27i) q^{43} +(-156.749 - 271.497i) q^{44} -2777.20i q^{46} +(421.122 + 729.404i) q^{47} -1816.06 q^{49} -5095.15i q^{50} +(-1255.79 - 725.029i) q^{52} +(-3144.31 + 1815.37i) q^{53} +(1302.19 - 2255.46i) q^{55} -1217.84i q^{56} -1321.13 q^{58} +(4625.90 + 2670.77i) q^{59} +(1471.85 + 2549.32i) q^{61} +(-958.292 + 1659.81i) q^{62} -2132.97 q^{64} -12046.3i q^{65} +(4194.98 - 2421.97i) q^{67} +122.930 q^{68} +(-4001.20 + 2310.10i) q^{70} +(4788.02 + 2764.37i) q^{71} +(792.717 - 1373.03i) q^{73} +(-4638.19 + 8033.59i) q^{74} +(-1682.77 - 668.735i) q^{76} -1511.58 q^{77} +(4627.33 + 2671.59i) q^{79} +(6481.76 + 11226.7i) q^{80} +(1899.69 + 3290.36i) q^{82} +740.501 q^{83} +(510.621 + 884.421i) q^{85} +(5025.64 - 2901.56i) q^{86} +3147.10i q^{88} +(-4789.36 + 2765.14i) q^{89} +(-6054.99 + 3495.85i) q^{91} +(1519.36 - 2631.61i) q^{92} +3861.11i q^{94} +(-2178.59 - 14884.5i) q^{95} +(2969.63 + 1714.52i) q^{97} +(-7210.01 - 4162.70i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7}+O(q^{10}) \) 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7	\( 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7} + 144 q^{10} - 50 q^{11} - 624 q^{13} + 474 q^{14} + 285 q^{16} + 292 q^{17} + 305 q^{19} + 652 q^{20} + 1629 q^{22} - 98 q^{23} - 681 q^{25} - 1524 q^{26} - 1472 q^{28} - 2598 q^{29} + 2745 q^{32} + 486 q^{34} - 694 q^{35} + 342 q^{38} + 8784 q^{40} + 1407 q^{41} + 5424 q^{43} - 4151 q^{44} + 2416 q^{47} - 17826 q^{49} - 19962 q^{52} - 1122 q^{53} + 11424 q^{55} - 20236 q^{58} - 15387 q^{59} + 860 q^{61} - 21636 q^{62} + 19710 q^{64} + 14763 q^{67} + 48844 q^{68} - 20334 q^{70} + 27264 q^{71} + 1561 q^{73} - 17094 q^{74} + 1955 q^{76} + 18392 q^{77} + 24750 q^{79} + 2002 q^{80} + 14479 q^{82} - 6002 q^{83} - 14944 q^{85} - 59946 q^{86} + 22566 q^{89} + 8724 q^{91} - 9572 q^{92} + 7312 q^{95} + 46287 q^{97} - 25515 q^{98}+O(q^{100}) \) 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7 + 144 * q^10 - 50 * q^11 - 624 * q^13 + 474 * q^14 + 285 * q^16 + 292 * q^17 + 305 * q^19 + 652 * q^20 + 1629 * q^22 - 98 * q^23 - 681 * q^25 - 1524 * q^26 - 1472 * q^28 - 2598 * q^29 + 2745 * q^32 + 486 * q^34 - 694 * q^35 + 342 * q^38 + 8784 * q^40 + 1407 * q^41 + 5424 * q^43 - 4151 * q^44 + 2416 * q^47 - 17826 * q^49 - 19962 * q^52 - 1122 * q^53 + 11424 * q^55 - 20236 * q^58 - 15387 * q^59 + 860 * q^61 - 21636 * q^62 + 19710 * q^64 + 14763 * q^67 + 48844 * q^68 - 20334 * q^70 + 27264 * q^71 + 1561 * q^73 - 17094 * q^74 + 1955 * q^76 + 18392 * q^77 + 24750 * q^79 + 2002 * q^80 + 14479 * q^82 - 6002 * q^83 - 14944 * q^85 - 59946 * q^86 + 22566 * q^89 + 8724 * q^91 - 9572 * q^92 + 7312 * q^95 + 46287 * q^97 - 25515 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more