LMFDB - Embedded newform 19.5.d.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,5,Mod(8,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("19.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	19.d (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:	$1.96402929859$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.2
Root			$4.58432i$ of defining polynomial
Character	$\chi$	$=$	19.8
Dual form			19.5.d.a.12.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.97014 - 2.29216i) q^{2} +(10.1306 + 5.84893i) q^{3} +(2.50801 + 4.34400i) q^{4} +(20.8352 - 36.0877i) q^{5} +(-26.8134 - 46.4422i) q^{6} +24.1856 q^{7} +50.3541i q^{8} +(27.9200 + 48.3589i) q^{9} +O(q^{10})$	\(q+(-3.97014 - 2.29216i) q^{2} +(10.1306 + 5.84893i) q^{3} +(2.50801 + 4.34400i) q^{4} +(20.8352 - 36.0877i) q^{5} +(-26.8134 - 46.4422i) q^{6} +24.1856 q^{7} +50.3541i q^{8} +(27.9200 + 48.3589i) q^{9} +(-165.438 + 95.5155i) q^{10} +62.4993 q^{11} +58.6767i q^{12} +(-250.356 + 144.543i) q^{13} +(-96.0201 - 55.4372i) q^{14} +(422.149 - 243.728i) q^{15} +(155.548 - 269.417i) q^{16} +(-12.2538 + 21.2242i) q^{17} -255.989i q^{18} +(-283.198 + 223.874i) q^{19} +209.020 q^{20} +(245.015 + 141.460i) q^{21} +(-248.131 - 143.258i) q^{22} +(302.902 + 524.641i) q^{23} +(-294.518 + 510.120i) q^{24} +(-555.715 - 962.527i) q^{25} +1325.26 q^{26} -294.318i q^{27} +(60.6576 + 105.062i) q^{28} +(249.575 - 144.092i) q^{29} -2234.65 q^{30} +418.074i q^{31} +(-537.367 + 310.249i) q^{32} +(633.158 + 365.554i) q^{33} +(97.2984 - 56.1752i) q^{34} +(503.912 - 872.801i) q^{35} +(-140.047 + 242.569i) q^{36} +2023.50i q^{37} +(1637.49 - 239.675i) q^{38} -3381.69 q^{39} +(1817.17 + 1049.14i) q^{40} +(-717.741 - 414.388i) q^{41} +(-648.497 - 1123.23i) q^{42} +(632.930 - 1096.27i) q^{43} +(156.749 + 271.497i) q^{44} +2326.88 q^{45} -2777.20i q^{46} +(-421.122 - 729.404i) q^{47} +(3151.60 - 1819.58i) q^{48} -1816.06 q^{49} +5095.15i q^{50} +(-248.277 + 143.343i) q^{51} +(-1255.79 - 725.029i) q^{52} +(3144.31 - 1815.37i) q^{53} +(-674.624 + 1168.48i) q^{54} +(1302.19 - 2255.46i) q^{55} +1217.84i q^{56} +(-4178.41 + 611.581i) q^{57} -1321.13 q^{58} +(-4625.90 - 2670.77i) q^{59} +(2117.51 + 1222.54i) q^{60} +(1471.85 + 2549.32i) q^{61} +(958.292 - 1659.81i) q^{62} +(675.261 + 1169.59i) q^{63} -2132.97 q^{64} +12046.3i q^{65} +(-1675.82 - 2902.60i) q^{66} +(4194.98 - 2421.97i) q^{67} -122.930 q^{68} +7086.61i q^{69} +(-4001.20 + 2310.10i) q^{70} +(-4788.02 - 2764.37i) q^{71} +(-2435.07 + 1405.89i) q^{72} +(792.717 - 1373.03i) q^{73} +(4638.19 - 8033.59i) q^{74} -13001.4i q^{75} +(-1682.77 - 668.735i) q^{76} +1511.58 q^{77} +(13425.8 + 7751.37i) q^{78} +(4627.33 + 2671.59i) q^{79} +(-6481.76 - 11226.7i) q^{80} +(3982.97 - 6898.70i) q^{81} +(1899.69 + 3290.36i) q^{82} -740.501 q^{83} +1419.13i q^{84} +(510.621 + 884.421i) q^{85} +(-5025.64 + 2901.56i) q^{86} +3371.14 q^{87} +3147.10i q^{88} +(4789.36 - 2765.14i) q^{89} +(-9238.05 - 5333.59i) q^{90} +(-6054.99 + 3495.85i) q^{91} +(-1519.36 + 2631.61i) q^{92} +(-2445.28 + 4235.36i) q^{93} +3861.11i q^{94} +(2178.59 + 14884.5i) q^{95} -7258.50 q^{96} +(2969.63 + 1714.52i) q^{97} +(7210.01 + 4162.70i) q^{98} +(1744.98 + 3022.40i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9} + 144 q^{10} + 50 q^{11} - 624 q^{13} - 474 q^{14} + 504 q^{15} + 285 q^{16} - 292 q^{17} + 305 q^{19} - 652 q^{20} + 1158 q^{21} + 1629 q^{22} + 98 q^{23} + 505 q^{24} - 681 q^{25} + 1524 q^{26} - 1472 q^{28} + 2598 q^{29} - 6656 q^{30} - 2745 q^{32} - 3441 q^{33} + 486 q^{34} + 694 q^{35} + 3402 q^{36} - 342 q^{38} - 5552 q^{39} + 8784 q^{40} - 1407 q^{41} + 292 q^{42} + 5424 q^{43} + 4151 q^{44} + 9572 q^{45} - 2416 q^{47} + 11481 q^{48} - 17826 q^{49} - 3342 q^{51} - 19962 q^{52} + 1122 q^{53} - 1039 q^{54} + 11424 q^{55} - 7906 q^{57} - 20236 q^{58} + 15387 q^{59} + 8886 q^{60} + 860 q^{61} + 21636 q^{62} + 5318 q^{63} + 19710 q^{64} - 13921 q^{66} + 14763 q^{67} - 48844 q^{68} - 20334 q^{70} - 27264 q^{71} + 354 q^{72} + 1561 q^{73} + 17094 q^{74} + 1955 q^{76} - 18392 q^{77} + 40266 q^{78} + 24750 q^{79} - 2002 q^{80} + 14311 q^{81} + 14479 q^{82} + 6002 q^{83} - 14944 q^{85} + 59946 q^{86} - 31996 q^{87} - 22566 q^{89} - 60630 q^{90} + 8724 q^{91} + 9572 q^{92} + 12476 q^{93} - 7312 q^{95} - 41850 q^{96} + 46287 q^{97} + 25515 q^{98} - 2048 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9 + 144 * q^10 + 50 * q^11 - 624 * q^13 - 474 * q^14 + 504 * q^15 + 285 * q^16 - 292 * q^17 + 305 * q^19 - 652 * q^20 + 1158 * q^21 + 1629 * q^22 + 98 * q^23 + 505 * q^24 - 681 * q^25 + 1524 * q^26 - 1472 * q^28 + 2598 * q^29 - 6656 * q^30 - 2745 * q^32 - 3441 * q^33 + 486 * q^34 + 694 * q^35 + 3402 * q^36 - 342 * q^38 - 5552 * q^39 + 8784 * q^40 - 1407 * q^41 + 292 * q^42 + 5424 * q^43 + 4151 * q^44 + 9572 * q^45 - 2416 * q^47 + 11481 * q^48 - 17826 * q^49 - 3342 * q^51 - 19962 * q^52 + 1122 * q^53 - 1039 * q^54 + 11424 * q^55 - 7906 * q^57 - 20236 * q^58 + 15387 * q^59 + 8886 * q^60 + 860 * q^61 + 21636 * q^62 + 5318 * q^63 + 19710 * q^64 - 13921 * q^66 + 14763 * q^67 - 48844 * q^68 - 20334 * q^70 - 27264 * q^71 + 354 * q^72 + 1561 * q^73 + 17094 * q^74 + 1955 * q^76 - 18392 * q^77 + 40266 * q^78 + 24750 * q^79 - 2002 * q^80 + 14311 * q^81 + 14479 * q^82 + 6002 * q^83 - 14944 * q^85 + 59946 * q^86 - 31996 * q^87 - 22566 * q^89 - 60630 * q^90 + 8724 * q^91 + 9572 * q^92 + 12476 * q^93 - 7312 * q^95 - 41850 * q^96 + 46287 * q^97 + 25515 * q^98 - 2048 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−3.97014	−	2.29216i	−0.992535	−	0.573040i	−0.0865039	−	0.996252i	$-0.527570\pi$
$2$	−3.97014	−	2.29216i	−0.992535	−	0.573040i	−0.906031	+	0.423211i	$0.860903\pi$
$3$	10.1306	+	5.84893i	1.12563	+	0.649881i	0.942832	−	0.333270i	$-0.108152\pi$
$3$	10.1306	+	5.84893i	1.12563	+	0.649881i	0.182796	+	0.983151i	$0.441485\pi$
$4$	2.50801	+	4.34400i	0.156750	+	0.271500i
$5$	20.8352	−	36.0877i	0.833410	−	1.44351i	−0.0619087	−	0.998082i	$-0.519719\pi$
$5$	20.8352	−	36.0877i	0.833410	−	1.44351i	0.895319	−	0.445426i	$-0.146948\pi$
$6$	−26.8134	−	46.4422i	−0.744816	−	1.29006i
$7$	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
$9$	27.9200	+	48.3589i	0.344692	+	0.597023i
$10$	−165.438	+	95.5155i	−1.65438	+	0.955155i
$11$	62.4993			0.516523			0.258261	−	0.966075i	$-0.416850\pi$
$11$	62.4993			0.516523			0.258261	+	0.966075i	$0.416850\pi$
$12$			58.6767i			0.407477i
$13$	−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
$15$	422.149	−	243.728i	1.87622	−	1.08324i
$16$	155.548	−	269.417i	0.607609	−	1.05241i
$17$	−12.2538	+	21.2242i	−0.0424006	+	0.0734400i	−0.886447	−	0.462830i	$-0.846834\pi$
$17$	−12.2538	+	21.2242i	−0.0424006	+	0.0734400i	0.844046	+	0.536270i	$0.180167\pi$
$18$		−	255.989i		−	0.790089i
$19$	−283.198	+	223.874i	−0.784483	+	0.620150i
$19$	−283.198	+	223.874i	−0.784483	+	0.620150i
$20$	209.020			0.522550
$21$	245.015	+	141.460i	0.555590	+	0.320770i
$22$	−248.131	−	143.258i	−0.512667	−	0.295988i
$23$	302.902	+	524.641i	0.572593	+	0.991760i	0.996299	+	0.0859604i	$0.0273959\pi$
$23$	302.902	+	524.641i	0.572593	+	0.991760i	−0.423705	+	0.905800i	$0.639271\pi$
$24$	−294.518	+	510.120i	−0.511316	+	0.885625i
$25$	−555.715	−	962.527i	−0.889144	−	1.54004i
$26$	1325.26			1.96045
$27$		−	294.318i		−	0.403728i
$28$	60.6576	+	105.062i	0.0773693	+	0.134008i
$29$	249.575	−	144.092i	0.296760	−	0.171334i	−0.344227	−	0.938887i	$-0.611859\pi$
$29$	249.575	−	144.092i	0.296760	−	0.171334i	0.640986	+	0.767552i	$0.278526\pi$
$30$	−2234.65			−2.48295
$31$			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
$33$	633.158	+	365.554i	0.581412	+	0.335679i
$34$	97.2984	−	56.1752i	0.0841681	−	0.0485945i
$35$	503.912	−	872.801i	0.411357	−	0.712491i
$36$	−140.047	+	242.569i	−0.108061	+	0.187167i
$37$			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
$39$	−3381.69			−2.22333
$40$	1817.17	+	1049.14i	1.13573	+	0.655713i
$41$	−717.741	−	414.388i	−0.426973	−	0.246513i	0.271083	−	0.962556i	$-0.412618\pi$
$41$	−717.741	−	414.388i	−0.426973	−	0.246513i	−0.698056	+	0.716043i	$0.745951\pi$
$42$	−648.497	−	1123.23i	−0.367629	−	0.636752i
$43$	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
$45$	2326.88			1.14908
$46$		−	2777.20i		−	1.31248i
$47$	−421.122	−	729.404i	−0.190639	−	0.330196i	0.754823	−	0.655928i	$-0.227723\pi$
$47$	−421.122	−	729.404i	−0.190639	−	0.330196i	−0.945462	+	0.325732i	$0.894389\pi$
$48$	3151.60	−	1819.58i	1.36788	−	0.789748i
$49$	−1816.06			−0.756376
$50$			5095.15i			2.03806i
$51$	−248.277	+	143.343i	−0.0954545	+	0.0551107i
$52$	−1255.79	−	725.029i	−0.464418	−	0.268132i
$53$	3144.31	−	1815.37i	1.11937	−	0.646268i	0.178130	−	0.984007i	$-0.442995\pi$
$53$	3144.31	−	1815.37i	1.11937	−	0.646268i	0.941240	+	0.337739i	$0.109662\pi$
$54$	−674.624	+	1168.48i	−0.231353	+	0.400714i
$55$	1302.19	−	2255.46i	0.430475	−	0.745605i
$56$			1217.84i			0.388343i
$57$	−4178.41	+	611.581i	−1.28606	+	0.188237i
$58$	−1321.13			−0.392726
$59$	−4625.90	−	2670.77i	−1.32890	−	0.767241i	−0.343771	−	0.939053i	$-0.611704\pi$
$59$	−4625.90	−	2670.77i	−1.32890	−	0.767241i	−0.985130	+	0.171812i	$0.945038\pi$
$60$	2117.51	+	1222.54i	0.588196	+	0.339595i
$61$	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
$63$	675.261	+	1169.59i	0.170134	+	0.294680i
$64$	−2132.97			−0.520745
$65$			12046.3i			2.85121i
$66$	−1675.82	−	2902.60i	−0.384715	−	0.666346i
$67$	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
$69$			7086.61i			1.48847i
$70$	−4001.20	+	2310.10i	−0.816572	+	0.471448i
$71$	−4788.02	−	2764.37i	−0.949816	−	0.548377i	−0.0567923	−	0.998386i	$-0.518087\pi$
$71$	−4788.02	−	2764.37i	−0.949816	−	0.548377i	−0.893024	+	0.450009i	$0.851421\pi$
$72$	−2435.07	+	1405.89i	−0.469728	+	0.271198i
$73$	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
$75$		−	13001.4i		−	2.31135i
$76$	−1682.77	−	668.735i	−0.291339	−	0.115778i
$77$	1511.58			0.254947
$78$	13425.8	+	7751.37i	2.20673	+	1.27406i
$79$	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
$81$	3982.97	−	6898.70i	0.607067	−	1.05147i
$82$	1899.69	+	3290.36i	0.282524	+	0.489345i
$83$	−740.501			−0.107490			−0.0537452	−	0.998555i	$-0.517116\pi$
$83$	−740.501			−0.107490			−0.0537452	+	0.998555i	$0.517116\pi$
$84$			1419.13i			0.201124i
$85$	510.621	+	884.421i	0.0706741	+	0.122411i
$86$	−5025.64	+	2901.56i	−0.679508	+	0.392314i
$87$	3371.14			0.445388
$88$			3147.10i			0.406392i
$89$	4789.36	−	2765.14i	0.604641	−	0.349089i	−0.166224	−	0.986088i	$-0.553158\pi$
$89$	4789.36	−	2765.14i	0.604641	−	0.349089i	0.770865	+	0.636998i	$0.219824\pi$
$90$	−9238.05	−	5333.59i	−1.14050	−	0.658468i
$91$	−6054.99	+	3495.85i	−0.731191	+	0.422153i
$92$	−1519.36	+	2631.61i	−0.179509	+	0.310918i
$93$	−2445.28	+	4235.36i	−0.282725	+	0.489693i
$94$			3861.11i			0.436975i
$95$	2178.59	+	14884.5i	0.241395	+	1.64925i
$96$	−7258.50			−0.787597
$97$	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
$99$	1744.98	+	3022.40i	0.178041	+	0.308376i
$100$	2787.47	−	4828.05i	0.278747	−	0.482805i
$101$	−702.204	−	1216.25i	−0.0688368	−	0.119229i	0.829553	−	0.558428i	$-0.188595\pi$
$101$	−702.204	−	1216.25i	−0.0688368	−	0.119229i	−0.898390	+	0.439200i	$0.855262\pi$
$102$	1314.26			0.126323
$103$		−	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
$105$	10209.9	−	5894.70i	0.926069	−	0.534666i
$106$	−16644.5			−1.48135
$107$		−	8311.74i		−	0.725980i	−0.931793	−	0.362990i	$-0.881756\pi$
$107$		−	8311.74i		−	0.725980i	0.931793	−	0.362990i	$-0.118244\pi$
$108$	1278.52	−	738.151i	0.109612	−	0.0632846i
$109$	−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
$111$	−11835.3	+	20499.4i	−0.960582	+	1.66378i
$112$	3762.01	−	6516.00i	0.299905	−	0.519451i
$113$		−	4056.19i		−	0.317659i	−0.987306	−	0.158830i	$-0.949228\pi$
$113$		−	4056.19i		−	0.317659i	0.987306	−	0.158830i	$-0.0507721\pi$
$114$	17990.7	+	7149.52i	1.38433	+	0.550133i
$115$	25244.1			1.90882
$116$	1251.87	+	722.768i	0.0930344	+	0.0537134i
$117$	−13979.9	−	8071.28i	−1.02125	−	0.589618i
$118$	12243.7	+	21206.6i	0.879320	+	1.52303i
$119$	−296.364	+	513.318i	−0.0209282	+	0.0362487i
$120$	12272.7	+	21257.0i	0.852271	+	1.47618i
$121$	−10734.8			−0.733204
$122$		−	13494.9i		−	0.906668i
$123$	−4847.45	−	8396.04i	−0.320408	−	0.554963i
$124$	−1816.11	+	1048.53i	−0.118113	+	0.0681928i
$125$	−20269.8			−1.29727
$126$		−	6191.23i		−	0.389974i
$127$	−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
$129$	12824.0	−	7403.93i	0.770626	−	0.444921i
$130$	27612.2	−	47825.7i	1.63386	−	2.82992i
$131$	3002.45	−	5200.40i	0.174958	−	0.303036i	−0.765189	−	0.643806i	$-0.777354\pi$
$131$	3002.45	−	5200.40i	0.174958	−	0.303036i	0.940147	+	0.340770i	$0.110688\pi$
$132$			3667.25i			0.210471i
$133$	−6849.31	+	5414.52i	−0.387208	+	0.306095i
$134$	−22206.2			−1.23670
$135$	−10621.3	−	6132.18i	−0.582785	−	0.336471i
$136$	−1068.72	−	617.028i	−0.0577813	−	0.0333601i
$137$	8783.25	+	15213.0i	0.467966	+	0.810540i	0.999330	−	0.0366031i	$-0.0116537\pi$
$137$	8783.25	+	15213.0i	0.467966	+	0.810540i	−0.531364	+	0.847144i	$0.678320\pi$
$138$	16243.6	−	28134.8i	0.852954	−	1.47736i
$139$	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
$141$		−	9852.45i		−	0.495571i
$142$	12672.7	+	21949.8i	0.628484	+	1.08857i
$143$	−15647.0	+	9033.82i	−0.765174	+	0.441773i
$144$	17371.6			0.837751
$145$		−	12008.8i		−	0.571167i
$146$	−6294.40	+	3634.07i	−0.295290	+	0.170486i
$147$	−18397.9	−	10622.0i	−0.851398	−	0.491555i
$148$	−8790.09	+	5074.96i	−0.401301	+	0.231691i
$149$	−8963.63	+	15525.5i	−0.403749	+	0.699314i	−0.994175	−	0.107778i	$-0.965626\pi$
$149$	−8963.63	+	15525.5i	−0.403749	+	0.699314i	0.590426	+	0.807092i	$0.298960\pi$
$150$	−29801.2	+	51617.2i	−1.32450	+	2.29410i
$151$		−	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
$153$	−1368.50			−0.0584605
$154$	−6001.18	−	3464.79i	−0.253044	−	0.146095i
$155$	15087.3	+	8710.67i	0.627984	+	0.362567i
$156$	−8481.29	−	14690.0i	−0.348508	−	0.603634i
$157$	−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
$159$	42471.9			1.67999
$160$			25856.4i			1.01002i
$161$	7325.85	+	12688.7i	0.282622	+	0.489516i
$162$	−31625.9	+	18259.2i	−1.20507	+	0.695748i
$163$	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
$165$	26384.0	−	15232.8i	0.969110	−	0.559516i
$166$	2939.89	+	1697.35i	0.106688	+	0.0615963i
$167$	25860.0	−	14930.3i	0.927246	−	0.535346i	0.0413065	−	0.999147i	$-0.486848\pi$
$167$	25860.0	−	14930.3i	0.927246	−	0.535346i	0.885940	+	0.463801i	$0.153515\pi$
$168$	−7123.08	+	12337.5i	−0.252377	+	0.437129i
$169$	27504.8	−	47639.7i	0.963019	−	1.66800i
$170$		−	4681.70i		−	0.161997i
$171$	−18733.2	−	7444.59i	−0.640649	−	0.254594i
$172$	6349.58			0.214629
$173$	12746.0	+	7358.89i	0.425874	+	0.245878i	0.697587	−	0.716500i	$-0.254257\pi$
$173$	12746.0	+	7358.89i	0.425874	+	0.245878i	−0.271713	+	0.962378i	$0.587590\pi$
$174$	−13383.9	−	7727.20i	−0.442063	−	0.255225i
$175$	−13440.3	−	23279.2i	−0.438866	−	0.760139i
$176$	9721.63	−	16838.4i	0.313844	−	0.543594i
$177$	−31242.3	−	54113.2i	−0.997232	−	1.72726i
$178$	−25352.6			−0.800169
$179$			16538.4i			0.516163i	0.966123	+	0.258082i	$0.0830903\pi$
$179$			16538.4i			0.516163i	−0.966123	+	0.258082i	$0.916910\pi$
$180$	5835.84	+	10108.0i	0.180118	+	0.311974i
$181$	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
$183$			34435.0i			1.02825i
$184$	−26417.9	+	15252.4i	−0.780301	+	0.450507i
$185$	73023.6	+	42160.2i	2.13363	+	1.23185i
$186$	19416.2	−	11210.0i	0.561228	−	0.324025i
$187$	−765.852	+	1326.49i	−0.0219009	+	0.0379334i
$188$	2112.35	−	3658.70i	0.0597655	−	0.103517i
$189$		−	7118.24i		−	0.199273i
$190$	25468.3	−	64087.1i	0.705492	−	1.77526i
$191$	50556.6			1.38583			0.692917	−	0.721017i	$-0.256325\pi$
$191$	50556.6			1.38583			0.692917	+	0.721017i	$0.256325\pi$
$192$	−21608.4	−	12475.6i	−0.586165	−	0.338423i
$193$	−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
$195$	−70458.3	+	122037.i	−1.85295	+	3.20940i
$196$	−4554.69	−	7888.95i	−0.118562	−	0.205356i
$197$	−39065.4			−1.00661			−0.503303	−	0.864110i	$-0.667882\pi$
$197$	−39065.4			−1.00661			−0.503303	+	0.864110i	$0.667882\pi$
$198$		−	15999.1i		−	0.408099i
$199$	−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
$201$	56663.8			1.40253
$202$			6438.26i			0.157785i
$203$	6036.11	−	3484.95i	0.146475	−	0.0845676i
$204$	−1245.36	−	719.010i	−0.0299251	−	0.0172773i
$205$	−29908.6	+	17267.7i	−0.711686	+	0.410892i
$206$	−19310.4	+	33446.6i	−0.455047	+	0.788165i
$207$	−16914.0	+	29296.0i	−0.394736	+	0.683703i
$208$			89933.4i			2.07871i
$209$	−17699.7	+	13992.0i	−0.405204	+	0.320322i
$210$	−54046.4			−1.22554
$211$	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
$213$	−32337.2	−	56009.6i	−0.712759	−	1.23454i
$214$	−19051.9	+	32998.8i	−0.416016	+	0.720560i
$215$	−26374.5	−	45682.0i	−0.570568	−	0.988253i
$216$	14820.1			0.317647
$217$			10111.3i			0.214728i
$218$	21293.9	+	36882.2i	0.448067	+	0.776075i
$219$	16061.5	−	9273.10i	0.334886	−	0.193347i
$220$	13063.6			0.269909
$221$		−	7084.78i		−	0.145058i
$222$	93975.8	−	54257.0i	1.90682	−	1.10090i
$223$	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
$225$	31031.1	−	53747.5i	0.612961	−	1.06168i
$226$	−9297.45	+	16103.7i	−0.182032	+	0.315288i
$227$			32899.8i			0.638472i	0.947675	+	0.319236i	$0.103426\pi$
$227$			32899.8i			0.638472i	−0.947675	+	0.319236i	$0.896574\pi$
$228$	−13136.2	−	16617.1i	−0.252697	−	0.319659i
$229$	−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
$231$	15313.3	+	8841.13i	0.286975	+	0.165685i
$232$	7255.63	+	12567.1i	0.134803	+	0.233485i
$233$	45770.7	−	79277.2i	0.843094	−	1.46028i	−0.0441722	−	0.999024i	$-0.514065\pi$
$233$	45770.7	−	79277.2i	0.843094	−	1.46028i	0.887266	−	0.461258i	$-0.152602\pi$
$234$	37001.3	+	64088.2i	0.675750	+	1.17043i
$235$	−35096.7			−0.635522
$236$		−	26793.2i		−	0.481062i
$237$	31251.9	+	54129.9i	0.556391	+	0.963697i
$238$	2353.22	−	1358.63i	0.0415440	−	0.0239854i
$239$	−4322.59			−0.0756742			−0.0378371	−	0.999284i	$-0.512047\pi$
$239$	−4322.59			−0.0756742			−0.0378371	+	0.999284i	$0.512047\pi$
$240$		−	151645.i		−	2.63273i
$241$	−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
$243$	60054.2	−	34672.3i	1.01702	−	0.587179i
$244$	−7382.81	+	12787.4i	−0.124006	+	0.214784i
$245$	−37838.0	+	65537.4i	−0.630371	+	1.09183i
$246$			44444.6i			0.734427i
$247$	38540.9	−	96982.5i	0.631725	−	1.58964i
$248$	−21051.7			−0.342282
$249$	−7501.75	−	4331.14i	−0.120994	−	0.0698560i
$250$	80473.8	+	46461.6i	1.28758	+	0.743385i
$251$	31250.4	+	54127.2i	0.496030	+	0.859149i	0.999990	−	0.00457824i	$-0.00145730\pi$
$251$	31250.4	+	54127.2i	0.496030	+	0.859149i	−0.503960	+	0.863727i	$0.668124\pi$
$252$	−3387.12	+	5866.67i	−0.0533371	+	0.0923826i
$253$	18931.1	+	32789.7i	0.295757	+	0.512267i
$254$	51502.8			0.798296
$255$			11946.3i			0.183719i
$256$	−28106.0	−	48681.0i	−0.428864	−	0.742813i
$257$	−64690.3	+	37349.0i	−0.979429	+	0.565474i	−0.902098	−	0.431532i	$-0.857973\pi$
$257$	−64690.3	+	37349.0i	−0.979429	+	0.565474i	−0.0773313	+	0.997005i	$0.524640\pi$
$258$	−67884.1			−1.01983
$259$			48939.5i			0.729559i
$260$	−52329.3	+	30212.3i	−0.774102	+	0.446928i
$261$	13936.3	+	8046.11i	0.204581	+	0.118115i
$262$	−23840.3	+	13764.2i	−0.347304	+	0.200516i
$263$	12657.9	−	21924.1i	0.182999	−	0.316964i	−0.759901	−	0.650038i	$-0.774753\pi$
$263$	12657.9	−	21924.1i	0.182999	−	0.316964i	0.942900	+	0.333075i	$0.108086\pi$
$264$	−18407.2	+	31882.1i	−0.264106	+	0.457446i
$265$		−	151295.i		−	2.15443i
$266$	39603.7	−	5796.68i	0.559722	−	0.0819249i
$267$	64692.4			0.907467
$268$	21042.1	+	12148.6i	0.292967	+	0.169145i
$269$	−115616.	−	66751.1i	−1.59777	−	0.922474i	−0.991916	−	0.126900i	$-0.959497\pi$
$269$	−115616.	−	66751.1i	−1.59777	−	0.922474i	−0.605856	−	0.795574i	$-0.707169\pi$
$270$	28111.9	+	48691.3i	0.385623	+	0.667919i
$271$	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
$273$	−81788.0			−1.09740
$274$		−	80530.5i		−	1.07265i
$275$	−34731.8	−	60157.2i	−0.459263	−	0.795467i
$276$	−30784.2	+	17773.3i	−0.404119	+	0.233318i
$277$	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
$279$	−20217.6	+	11672.6i	−0.259729	+	0.149955i
$280$	43949.2	+	25374.1i	0.560576	+	0.323649i
$281$	−71334.5	+	41185.0i	−0.903414	+	0.521586i	−0.878306	−	0.478098i	$-0.841326\pi$
$281$	−71334.5	+	41185.0i	−0.903414	+	0.521586i	−0.0251079	+	0.999685i	$0.507993\pi$
$282$	−22583.4	+	39115.6i	−0.283982	+	0.491871i
$283$	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
$285$	−64987.6	+	163532.i	−0.800094	+	2.01332i
$286$	82827.9			1.01262
$287$	−17359.0	−	10022.2i	−0.210746	−	0.121674i
$288$	−30006.6	−	17324.3i	−0.361769	−	0.208867i
$289$	41460.2	+	71811.2i	0.496404	+	0.859798i
$290$	−27526.1	+	47676.5i	−0.327301	+	0.566903i
$291$	20056.2	+	34738.4i	0.236844	+	0.410226i
$292$	7952.56			0.0932699
$293$			97102.9i			1.13109i	0.824717	+	0.565545i	$0.191334\pi$
$293$			97102.9i			1.13109i	−0.824717	+	0.565545i	$0.808666\pi$
$294$	48694.7	+	84341.7i	0.563361	+	0.975770i
$295$	−192764.	+	111292.i	−2.21504	+	1.27885i
$296$	−101892.			−1.16294
$297$		−	18394.6i		−	0.208535i
$298$	71173.8	−	41092.2i	0.801470	−	0.462729i
$299$	−151666.	−	87564.6i	−1.69647	−	0.979459i
$300$	56477.8	−	32607.5i	0.627532	−	0.362306i
$301$	15307.8	−	26513.8i	0.168958	−	0.292644i
$302$	−5846.96	+	10127.2i	−0.0641085	+	0.111039i
$303$		−	16428.6i		−	0.178943i
$304$	16264.5	+	111122.i	0.175993	+	1.20241i
$305$	122665.			1.31863
$306$	5433.14	+	3136.83i	0.0580241	+	0.0335002i
$307$	−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
$309$	49274.5	−	85346.0i	0.516066	−	0.893853i
$310$	−39932.5	−	69165.1i	−0.415531	−	0.719721i
$311$	157167.			1.62495			0.812476	−	0.582994i	$-0.198119\pi$
$311$	157167.			1.62495			0.812476	+	0.582994i	$0.198119\pi$
$312$		−	170282.i		−	1.74928i
$313$	−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
$315$	56276.9			0.567165
$316$			26801.5i			0.268401i
$317$	11437.7	−	6603.57i	0.113821	−	0.0657144i	−0.442009	−	0.897011i	$-0.645734\pi$
$317$	11437.7	−	6603.57i	0.113821	−	0.0657144i	0.555830	+	0.831296i	$0.312401\pi$
$318$	−168619.	−	97352.3i	−1.66745	−	0.962703i
$319$	15598.2	−	9005.65i	0.153283	−	0.0884981i
$320$	−44441.0	+	76974.1i	−0.433994	+	0.751700i
$321$	48614.8	−	84203.3i	0.471801	−	0.817183i
$322$		−	67168.1i		−	0.647816i
$323$	−1281.29	−	8753.95i	−0.0122812	−	0.0839072i
$324$	39957.2			0.380632
$325$	278253.	+	160649.i	2.63434	+	1.52094i
$326$	−33203.5	−	19170.1i	−0.312428	−	0.180380i
$327$	−54336.0	−	94112.7i	−0.508150	−	0.880142i
$328$	20866.1	−	36141.2i	0.193952	−	0.335935i
$329$	−10185.1	−	17641.0i	−0.0940961	−	0.162979i
$330$	−139664.			−1.28250
$331$			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
$333$	−97854.3	+	56496.2i	−0.882453	+	0.509485i
$334$	−136890.			−1.22710
$335$		−	201849.i		−	1.79861i
$336$	76223.3	−	44007.5i	0.675164	−	0.389806i
$337$	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
$339$	23724.4	−	41091.9i	0.206441	−	0.357566i
$340$	−2561.28	+	4436.27i	−0.0221564	+	0.0383760i
$341$			26129.3i			0.224708i
$342$	57309.3	+	72495.6i	0.489974	+	0.619811i
$343$	−101992.			−0.866917
$344$	55201.6	+	31870.7i	0.466482	+	0.269323i
$345$	255739.	+	147651.i	2.14862	+	1.24051i
$346$	−33735.5	−	58431.7i	−0.281796	−	0.488086i
$347$	−12650.7	+	21911.7i	−0.105064	+	0.181977i	−0.913765	−	0.406244i	$-0.866838\pi$
$347$	−12650.7	+	21911.7i	−0.105064	+	0.181977i	0.808700	+	0.588221i	$0.200172\pi$
$348$	8454.84	+	14644.2i	0.0698147	+	0.120923i
$349$	−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
$351$	42541.5	+	73684.1i	0.345302	+	0.598080i
$352$	−33585.0	+	19390.3i	−0.271057	+	0.156495i
$353$	−119944.			−0.962561			−0.481280	−	0.876567i	$-0.659828\pi$
$353$	−119944.			−0.962561			−0.481280	+	0.876567i	$0.659828\pi$
$354$			286449.i			2.28582i
$355$	−199519.	+	115192.i	−1.58317	+	0.914045i
$356$	24023.5	+	13870.0i	0.189555	+	0.109440i
$357$	−6004.73	+	3466.83i	−0.0471147	+	0.0272017i
$358$	37908.6	−	65659.7i	0.295782	−	0.512310i
$359$	93344.7	−	161678.i	0.724270	−	1.25447i	−0.235004	−	0.971995i	$-0.575510\pi$
$359$	93344.7	−	161678.i	0.724270	−	1.25447i	0.959274	−	0.282478i	$-0.0911565\pi$
$360$			117168.i			0.904075i
$361$	30081.7	−	126802.i	0.230828	−	0.972995i
$362$	−54390.4			−0.415055
$363$	−108751.	−	62787.4i	−0.825315	−	0.476496i
$364$	−30371.9	−	17535.2i	−0.229229	−	0.132345i
$365$	−33032.9	−	57214.7i	−0.247948	−	0.429459i
$366$	78930.5	−	136712.i	0.589227	−	1.02057i
$367$	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
$369$		−	46278.9i		−	0.339884i
$370$	−193276.	−	334764.i	−1.41180	−	2.44531i
$371$	76046.9	−	43905.7i	0.552502	−	0.318987i
$372$	−24531.2			−0.177269
$373$			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
$375$	−205346.	−	118557.i	−1.46024	−	0.843069i
$376$	36728.5	−	21205.2i	0.259793	−	0.149992i
$377$	−41655.0	+	72148.5i	−0.293079	+	0.507627i
$378$	−16316.2	+	28260.4i	−0.114192	+	0.197786i
$379$		−	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
$381$	−131420.			−0.905342
$382$	−200717.	−	115884.i	−1.37549	−	0.794139i
$383$	199085.	+	114942.i	1.35719	+	0.783576i	0.989245	−	0.146270i	$-0.0467267\pi$
$383$	199085.	+	114942.i	1.35719	+	0.783576i	0.367949	+	0.929846i	$0.380060\pi$
$384$	115260.	+	199637.i	0.781658	+	1.35387i
$385$	31494.1	−	54549.4i	0.212475	−	0.368018i
$386$	110540.	+	191461.i	0.741898	+	1.28501i
$387$	70685.7			0.471965
$388$			17200.1i			0.114253i
$389$	−12134.5	−	21017.5i	−0.0801904	−	0.138894i	0.823141	−	0.567837i	$-0.192219\pi$
$389$	−12134.5	−	21017.5i	−0.0801904	−	0.138894i	−0.903332	+	0.428943i	$0.858886\pi$
$390$	559458.	−	323003.i	3.67823	−	2.12363i
$391$	−14846.8			−0.0971132
$392$		−	91446.1i		−	0.595104i
$393$	60833.6	−	35122.3i	0.393875	−	0.227404i
$394$	155095.	+	89544.2i	0.999092	+	0.576826i
$395$	192823.	−	111326.i	1.23585	−	0.713517i
$396$	−8752.85	+	15160.4i	−0.0558161	+	0.0966762i
$397$	−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
$399$	−101057.	+	14791.4i	−0.634777	+	0.0929105i
$400$	−345761.			−2.16101
$401$	8555.46	+	4939.50i	0.0532052	+	0.0307181i	0.526367	−	0.850258i	$-0.323554\pi$
$401$	8555.46	+	4939.50i	0.0532052	+	0.0307181i	−0.473161	+	0.880976i	$0.656887\pi$
$402$	−224963.	−	129882.i	−1.39206	−	0.803708i
$403$	−60429.6	−	104667.i	−0.372083	−	0.644466i
$404$	3522.27	−	6100.75i	0.0215804	−	0.0373784i
$405$	−165972.	−	287472.i	−1.01187	−	1.75261i
$406$	−31952.3			−0.193843
$407$			126467.i			0.763466i
$408$	−7217.91	−	12501.8i	−0.0433602	−	0.0751020i
$409$	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
$411$			205491.i			1.21649i
$412$	36596.2	−	21128.8i	0.215596	−	0.124474i
$413$	−111880.	−	64594.0i	−0.655923	−	0.378697i
$414$	134302.	−	77539.5i	0.783579	−	0.452399i
$415$	−15428.5	+	26723.0i	−0.0895835	+	0.155163i
$416$	89688.5	−	155345.i	0.518263	−	0.897658i
$417$			133306.i			0.766617i
$418$	102342.	−	14979.5i	0.585736	−	0.0857325i
$419$	28240.8			0.160860			0.0804301	−	0.996760i	$-0.474371\pi$
$419$	28240.8			0.160860			0.0804301	+	0.996760i	$0.474371\pi$
$420$	51213.1	+	29567.9i	0.290324	+	0.167618i
$421$	−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
$423$	23515.4	−	40729.9i	0.131423	−	0.227632i
$424$	91411.3	+	158329.i	0.508473	+	0.880701i
$425$	27238.4			0.150801
$426$			296488.i			1.63376i
$427$	35597.5	+	61656.6i	0.195238	+	0.338161i
$428$	36106.2	−	20845.9i	0.197103	−	0.113798i
$429$	−211353.			−1.14840
$430$			241819.i			1.30783i
$431$	−144786.	+	83592.1i	−0.779420	+	0.449998i	−0.836225	−	0.548387i	$-0.815242\pi$
$431$	−144786.	+	83592.1i	−0.779420	+	0.449998i	0.0568047	+	0.998385i	$0.481909\pi$
$432$	−79294.2	−	45780.5i	−0.424887	−	0.245309i
$433$	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
$435$	70238.5	−	121657.i	0.371190	−	0.642921i
$436$		−	46598.3i		−	0.245130i
$437$	−203235.	−	80765.7i	−1.06423	−	0.422926i
$438$	−85021.8			−0.443182
$439$	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
$441$	−50704.4	−	87822.6i	−0.260716	−	0.451574i
$442$	−16239.5	+	28127.6i	−0.0831241	+	0.143975i
$443$	−101510.	−	175820.i	−0.517249	−	0.895901i	−0.999799	−	0.0200330i	$-0.993623\pi$
$443$	−101510.	−	175820.i	−0.517249	−	0.895901i	0.482551	−	0.875868i	$-0.339710\pi$
$444$	−118732.			−0.602287
$445$		−	230449.i		−	1.16374i
$446$	−21448.1	−	37149.3i	−0.107825	−	0.186759i
$447$	−181615.	+	104855.i	−0.908942	+	0.524778i
$448$	−51587.1			−0.257031
$449$			182146.i			0.903497i	0.892145	+	0.451748i	$0.149199\pi$
$449$			182146.i			0.903497i	−0.892145	+	0.451748i	$0.850801\pi$
$450$	−246396.	+	142257.i	−1.21677	+	0.702503i
$451$	−44858.3	−	25898.9i	−0.220541	−	0.127329i
$452$	17620.1	−	10173.0i	0.0862445	−	0.0497933i
$453$	14919.7	−	25841.7i	0.0727051	−	0.125929i
$454$	75411.8	−	130617.i	0.365870	−	0.633706i
$455$			291348.i			1.40731i
$456$	−30795.7	−	210400.i	−0.148102	−	1.01185i
$457$	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
$459$	6246.65	+	3606.50i	0.0296498	+	0.0171183i
$460$	63312.5	+	109660.i	0.299208	+	0.518244i
$461$	34244.2	−	59312.7i	0.161133	−	0.279091i	−0.774142	−	0.633012i	$-0.781818\pi$
$461$	34244.2	−	59312.7i	0.161133	−	0.279091i	0.935275	+	0.353921i	$0.115152\pi$
$462$	−40530.6	−	70201.0i	−0.189889	−	0.328897i
$463$	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
$465$	101896.	+	176489.i	0.471251	+	0.816230i
$466$	−363432.	+	209828.i	−1.67360	+	0.966254i
$467$	72245.4			0.331266			0.165633	−	0.986187i	$-0.447033\pi$
$467$	72245.4			0.331266			0.165633	+	0.986187i	$0.447033\pi$
$468$		−	80971.3i		−	0.369692i
$469$	101458.	−	58576.7i	0.461254	−	0.266305i
$470$	139339.	+	80447.3i	0.630777	+	0.364180i
$471$	−406925.	+	234938.i	−1.83431	+	1.05904i
$472$	134484.	−	232933.i	0.603653	−	1.04556i
$473$	39557.7	−	68515.9i	0.176811	−	0.306245i
$474$		−	286538.i		−	1.27534i
$475$	372862.	+	148176.i	1.65258	+	0.656735i
$476$	−2973.14			−0.0131220
$477$	175578.	+	101370.i	0.771675	+	0.445527i
$478$	17161.3	+	9908.07i	0.0751093	+	0.0433644i
$479$	−157819.	−	273351.i	−0.687843	−	1.19138i	−0.972534	−	0.232760i	$-0.925224\pi$
$479$	−157819.	−	273351.i	−0.687843	−	1.19138i	0.284691	−	0.958619i	$-0.408109\pi$
$480$	−151233.	+	261943.i	−0.656391	+	1.13690i
$481$	−292483.	−	506595.i	−1.26418	−	2.18963i
$482$	206197.			0.887541
$483$			171394.i			0.734684i
$484$	−26923.1	−	46632.1i	−0.114930	−	0.199065i
$485$	123746.	−	71444.8i	0.526075	−	0.303730i
$486$	−317898.			−1.34591
$487$			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
$489$	84725.8	+	48916.5i	0.354322	+	0.204568i
$490$	300445.	−	173462.i	1.25133	−	0.722456i
$491$	−72237.5	+	125119.i	−0.299640	+	0.518992i	−0.976054	−	0.217530i	$-0.930200\pi$
$491$	−72237.5	+	125119.i	−0.299640	+	0.518992i	0.676414	+	0.736522i	$0.263533\pi$
$492$	24314.9	−	42114.6i	0.100448	−	0.173981i
$493$			7062.69i			0.0290587i
$494$	−375312.	+	296692.i	−1.53794	+	1.21577i
$495$	145428.			0.593525
$496$	112636.	+	65030.5i	0.457841	+	0.264334i
$497$	−115801.	−	66857.7i	−0.468813	−	0.270669i
$498$	19855.3	+	34390.5i	0.0800606	+	0.138669i
$499$	−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
$501$	349304.			1.39164
$502$		−	286524.i		−	1.13698i
$503$	166366.	+	288154.i	0.657548	+	1.13891i	0.981248	+	0.192747i	$0.0617398\pi$
$503$	166366.	+	288154.i	0.657548	+	1.13891i	−0.323700	+	0.946160i	$0.604927\pi$
$504$	−58893.5	+	34002.2i	−0.231850	+	0.133858i
$505$	−58522.4			−0.229477
$506$		−	173573.i		−	0.677924i
$507$	557282.	−	321747.i	2.16800	−	1.25170i
$508$	−48802.9	−	28176.4i	−0.189112	−	0.109184i
$509$	189141.	−	109200.i	0.730044	−	0.421491i	−0.0883942	−	0.996086i	$-0.528174\pi$
$509$	189141.	−	109200.i	0.730044	−	0.421491i	0.818438	+	0.574594i	$0.194840\pi$
$510$	27382.9	−	47428.7i	0.105279	−	0.182348i
$511$	19172.3	−	33207.4i	0.0734231	−	0.127173i
$512$		−	57605.1i		−	0.219746i
$513$	65890.2	+	83350.4i	0.250372	+	0.316718i
$514$	342439.			1.29616
$515$	−304022.	−	175527.i	−1.14628	−	0.661805i
$516$	64325.3	+	37138.2i	0.241592	+	0.139483i
$517$	−26319.8	−	45587.2i	−0.0984694	−	0.170554i
$518$	112177.	−	194297.i	0.418067	−	0.724113i
$519$	86083.3	+	149101.i	0.319584	+	0.553535i
$520$	−606583.			−2.24328
$521$		−	199162.i		−	0.733722i	−0.930276	−	0.366861i	$-0.880432\pi$
$521$		−	199162.i		−	0.733722i	0.930276	−	0.366861i	$-0.119568\pi$
$522$	−36886.0	−	63888.3i	−0.135369	−	0.234466i
$523$	−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
$525$		−	314445.i		−	1.14084i
$526$	−100507.	+	58027.8i	−0.363266	+	0.209732i
$527$	−8873.26	−	5122.98i	−0.0319493	−	0.0184460i
$528$	196973.	−	113722.i	0.706543	−	0.407923i
$529$	−43578.5	+	75480.1i	−0.155726	+	0.269725i
$530$	−346791.	+	600660.i	−1.23457	+	2.13834i
$531$		−	298271.i		−	1.05785i
$532$	−40698.8	−	16173.7i	−0.143800	−	0.0571462i
$533$	239587.			0.843353
$534$	−256838.	−	148285.i	−0.900693	−	0.520015i
$535$	−299952.	−	173177.i	−1.04796	−	0.605039i
$536$	121956.	+	211234.i	0.424497	+	0.735250i
$537$	−96731.9	+	167545.i	−0.335445	+	0.581007i
$538$	306009.	+	530023.i	1.05723	+	1.83118i
$539$	−113502.			−0.390685
$540$		−	61518.3i		−	0.210968i
$541$	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
$543$	138789.			0.470711
$544$		−	15206.9i		−	0.0513857i
$545$	−335251.	+	193557.i	−1.12870	+	0.651653i
$546$	324710.	+	187471.i	1.08921	+	0.628853i
$547$	−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
$549$	−82188.0	+	142354.i	−0.272687	+	0.472307i
$550$			318443.i			1.05271i
$551$	−38420.7	+	96680.0i	−0.126550	+	0.318444i
$552$	−356840.			−1.17110
$553$	111915.	+	64613.9i	0.365962	+	0.211288i
$554$	−600170.	−	346509.i	−1.95549	−	1.12900i
$555$	493184.	+	854220.i	1.60112	+	2.77322i
$556$	−28580.7	+	49503.2i	−0.0924535	+	0.160134i
$557$	140576.	+	243485.i	0.453107	+	0.784805i	0.998577	−	0.0533254i	$-0.0169821\pi$
$557$	140576.	+	243485.i	0.453107	+	0.784805i	−0.545470	+	0.838131i	$0.683649\pi$
$558$	107022.			0.343720
$559$			365942.i			1.17109i
$560$	−156765.	−	271525.i	−0.499888	−	0.865832i
$561$	−15517.1	+	8958.83i	−0.0493045	+	0.0284659i
$562$	377611.			1.19556
$563$		−	559461.i		−	1.76503i	−0.470282	−	0.882516i	$-0.655848\pi$
$563$		−	559461.i		−	1.76503i	0.470282	−	0.882516i	$-0.344152\pi$
$564$	42799.0	−	24710.0i	0.134547	−	0.0776810i
$565$	−146379.	−	84511.8i	−0.458544	−	0.264741i
$566$	−304156.	+	175605.i	−0.949433	+	0.548155i
$567$	96330.3	−	166849.i	0.299638	−	0.518988i
$568$	139197.	−	241097.i	0.431454	−	0.747299i
$569$			95700.7i			0.295590i	0.989018	+	0.147795i	$0.0472177\pi$
$569$			95700.7i			0.295590i	−0.989018	+	0.147795i	$0.952782\pi$
$570$	632851.	−	500281.i	1.94783	−	1.53980i
$571$	−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
$573$	512172.	+	295702.i	1.55993	+	0.900628i
$574$	45945.0	+	79579.1i	0.139449	+	0.241532i
$575$	336654.	−	583102.i	1.01824	−	1.76364i
$576$	−59552.6	−	103148.i	−0.179496	−	0.310897i
$577$	−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
$579$	−282066.	−	488552.i	−0.841382	−	1.45732i
$580$	52166.1	−	30118.1i	0.155072	−	0.0895306i
$581$	−17909.4			−0.0530554
$582$		−	183888.i		−	0.542885i
$583$	196517.	−	113459.i	0.578180	−	0.333812i
$584$	69137.6	+	39916.6i	0.202716	+	0.117038i
$585$	−582548.	+	336334.i	−1.70224	+	0.982787i
$586$	222576.	−	385512.i	0.648160	−	1.12265i
$587$	−176824.	+	306269.i	−0.513176	+	0.888846i	0.486708	+	0.873565i	$0.338198\pi$
$587$	−176824.	+	306269.i	−0.513176	+	0.888846i	−0.999883	+	0.0152813i	$0.995136\pi$
$588$		−	106560.i		−	0.308206i
$589$	−93595.9	−	118398.i	−0.269790	−	0.341282i
$590$	1.02040e6			2.93134
$591$	−395758.	−	228491.i	−1.13306	−	0.654175i
$592$	545166.	+	314752.i	1.55555	+	0.898100i
$593$	−316633.	−	548424.i	−0.900423	−	1.55958i	−0.826946	−	0.562282i	$-0.809924\pi$
$593$	−316633.	−	548424.i	−0.900423	−	1.55958i	−0.0734773	−	0.997297i	$-0.523410\pi$
$594$	−42163.5	+	73029.3i	−0.119499	+	0.206978i
$595$	12349.6	+	21390.2i	0.0348835	+	0.0604201i
$596$	−89923.4			−0.253151
$597$		−	301982.i		−	0.847292i
$598$	401424.	+	695287.i	1.12254	+	1.94429i
$599$	126946.	−	73292.3i	0.353806	−	0.204270i	−0.312554	−	0.949900i	$-0.601185\pi$
$599$	126946.	−	73292.3i	0.353806	−	0.204270i	0.666360	+	0.745630i	$0.267851\pi$
$600$	654672.			1.81853
$601$		−	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
$603$	234248.	+	135243.i	0.644229	+	0.371946i
$604$	11080.9	−	6397.55i	0.0303739	−	0.0175364i
$605$	−223663.	+	387396.i	−0.611060	+	1.05839i
$606$	−37657.0	+	65223.8i	−0.102542	+	0.177607i
$607$			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
$609$	81532.9			0.219836
$610$	−486998.	−	281169.i	−1.30878	−	0.755626i
$611$	210860.	+	121740.i	0.564823	+	0.326101i
$612$	−3432.21	−	5944.77i	−0.00916371	−	0.0158720i
$613$	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
$615$	−403992.			−1.06813
$616$			76114.3i			0.200588i
$617$	169457.	+	293507.i	0.445131	+	0.770990i	0.998061	−	0.0622378i	$-0.0198237\pi$
$617$	169457.	+	293507.i	0.445131	+	0.770990i	−0.552930	+	0.833228i	$0.686490\pi$
$618$	−391254.	+	225890.i	−1.02443	+	0.591454i
$619$	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
$621$	154411.	−	89149.4i	0.400402	−	0.231172i
$622$	−623975.	−	360252.i	−1.61282	−	0.931163i
$623$	115833.	−	66876.4i	0.298440	−	0.172305i
$624$	−526014.	+	911083.i	−1.35092	+	2.33985i
$625$	−75003.9	+	129911.i	−0.192010	+	0.332571i
$626$			57736.9i			0.147335i
$627$	−261147.	+	38223.4i	−0.664279	+	0.0972286i
$628$	−201482.			−0.510877
$629$	−42947.1	−	24795.5i	−0.108551	−	0.0626718i
$630$	−223427.	−	128996.i	−0.562931	−	0.325008i
$631$	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
$633$	39697.1	+	68757.4i	0.0990721	+	0.171598i
$634$	−60545.8			−0.150628
$635$			468150.i			1.16101i
$636$	106520.	+	184498.i	0.263339	+	0.456117i
$637$	454660.	−	262498.i	1.12049	−	0.646916i
$638$	−82569.6			−0.202852
$639$		−	308725.i		−	0.756083i
$640$	711151.	−	410583.i	1.73621	−	1.00240i
$641$	474195.	+	273776.i	1.15409	+	0.666316i	0.949881	−	0.312611i	$-0.101204\pi$
$641$	474195.	+	273776.i	1.15409	+	0.666316i	0.204211	+	0.978927i	$0.434537\pi$
$642$	−386015.	+	222866.i	−0.936557	+	0.540722i
$643$	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
$645$		−	617051.i		−	1.48321i
$646$	−14978.6	+	37691.3i	−0.0358926	+	0.0903184i
$647$	−140129.			−0.334749			−0.167375	−	0.985893i	$-0.553529\pi$
$647$	−140129.			−0.334749			−0.167375	+	0.985893i	$0.553529\pi$
$648$	347378.	+	200559.i	0.827280	+	0.477630i
$649$	−289116.	−	166921.i	−0.686408	−	0.396298i
$650$	−736468.	−	1.27560e6i	−1.74312	−	3.01917i
$651$	−59140.6	+	102434.i	−0.139548	+	0.241704i
$652$	20975.3	+	36330.2i	0.0493415	+	0.0854620i
$653$	−457094.			−1.07196			−0.535980	−	0.844231i	$-0.680058\pi$
$653$	−457094.			−1.07196			−0.535980	+	0.844231i	$0.680058\pi$
$654$			498187.i			1.16476i
$655$	−125114.	−	216703.i	−0.291623	−	0.505106i
$656$	−223286.	+	128914.i	−0.518865	+	0.299567i
$657$	88530.7			0.205099
$658$			93383.2i			0.215684i
$659$	357061.	−	206149.i	0.822188	−	0.474691i	−0.0289821	−	0.999580i	$-0.509227\pi$
$659$	357061.	−	206149.i	0.822188	−	0.474691i	0.851171	+	0.524889i	$0.175893\pi$
$660$	132343.	+	76408.0i	0.303817	+	0.175409i
$661$	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
$663$	41438.4	−	71773.4i	0.0942705	−	0.163281i
$664$		−	37287.3i		−	0.0845716i
$665$	52690.5	+	359989.i	0.119149	+	0.814040i
$666$	517994.			1.16782
$667$	151193.	+	87291.5i	0.339845	+	0.196210i
$668$	129714.	+	74890.4i	0.290693	+	0.167831i
$669$	54729.5	+	94794.2i	0.122284	+	0.211802i
$670$	−462671.	+	801370.i	−1.03068	+	1.78519i
$671$	91989.4	+	159330.i	0.204312	+	0.353878i
$672$	−175551.			−0.388745
$673$		−	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
$675$	−283289.	+	163557.i	−0.621759	+	0.358972i
$676$	275929.			0.603815
$677$			391079.i			0.853272i	0.904423	+	0.426636i	$0.140301\pi$
$677$			391079.i			0.853272i	−0.904423	+	0.426636i	$0.859699\pi$
$678$	−188378.	+	108760.i	−0.409800	+	0.236598i
$679$	71822.2	+	41466.6i	0.155783	+	0.0899412i
$680$	−44534.2	+	25711.9i	−0.0963111	+	0.0556052i
$681$	−192429.	+	333297.i	−0.414931	+	0.718682i
$682$	59892.6	−	103737.i	0.128767	−	0.223031i
$683$			416919.i			0.893739i	0.894599	+	0.446869i	$0.147461\pi$
$683$			416919.i			0.893739i	−0.894599	+	0.446869i	$0.852539\pi$
$684$	−14643.7	−	100048.i	−0.0312997	−	0.213844i
$685$	732005.			1.56003
$686$	404922.	+	233782.i	0.860446	+	0.496778i
$687$	−345720.	−	199602.i	−0.732506	−	0.422912i
$688$	−196902.	−	341044.i	−0.415981	−	0.720500i
$689$	−524797.	+	908975.i	−1.10548	+	1.91476i
$690$	−676881.	−	1.17239e6i	−1.42172	−	2.46249i
$691$	−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
$693$	42203.3	+	73098.3i	0.0878780	+	0.152209i
$694$	100450.	−	57994.9i	0.208560	−	0.120412i
$695$	474868.			0.983112
$696$			169751.i			0.350424i
$697$	17590.1	−	10155.6i	0.0362078	−	0.0209046i
$698$	615713.	+	355482.i	1.26377	+	0.729637i
$699$	927374.	−	535420.i	1.89802	−	1.09582i
$700$	67416.6	−	116769.i	0.137585	−	0.238304i
$701$	432212.	−	748612.i	0.879550	−	1.52342i	0.0277137	−	0.999616i	$-0.491177\pi$
$701$	432212.	−	748612.i	0.879550	−	1.52342i	0.851836	−	0.523809i	$-0.175489\pi$
$702$		−	390048.i		−	0.791488i
$703$	−453010.	−	573053.i	−0.916636	−	1.15954i
$704$	−133309.			−0.268977
$705$	−355552.	−	205278.i	−0.715361	−	0.413014i
$706$	476193.	+	274930.i	0.955375	+	0.551586i
$707$	−16983.2	−	29415.8i	−0.0339767	−	0.0588493i
$708$	156712.	−	271433.i	0.312633	−	0.541496i
$709$	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
$711$			298363.i			0.590210i
$712$	139236.	+	241164.i	0.274658	+	0.475721i
$713$	−219339.	+	126635.i	−0.431456	+	0.249101i
$714$	31786.1			0.0623507
$715$			752888.i			1.47271i
$716$	−71842.7	+	41478.4i	−0.140138	+	0.0809088i
$717$	−43790.6	−	25282.5i	−0.0851810	−	0.0491793i
$718$	−741183.	+	427922.i	−1.43773	+	0.830072i
$719$	263310.	−	456066.i	0.509341	−	0.882205i	−0.490600	−	0.871385i	$-0.663222\pi$
$719$	263310.	−	456066.i	0.509341	−	0.882205i	0.999941	−	0.0108204i	$-0.00344430\pi$
$720$	361942.	−	626901.i	0.698190	−	1.20930i
$721$		−	203752.i		−	0.391951i
$722$	−410079.	+	434468.i	−0.786670	+	0.833457i
$723$	−526155.			−1.00655
$724$	51539.1	+	29756.1i	0.0983240	+	0.0567674i
$725$	−277385.	−	160148.i	−0.527724	−	0.304682i
$726$	287838.	+	498549.i	0.546103	+	0.945877i
$727$	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
$729$	165944.			0.312253
$730$			302867.i			0.568338i
$731$	15511.6	+	26866.8i	0.0290283	+	0.0502784i
$732$	−149585.	+	86363.1i	−0.279169	+	0.161178i
$733$	−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
$735$	−766648.	+	442624.i	−1.41913	+	0.819333i
$736$	−325539.	−	187950.i	−0.600962	−	0.346966i
$737$	262183.	−	151371.i	0.482691	−	0.278682i
$738$	−106079.	+	183734.i	−0.194767	+	0.337346i
$739$	−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
$741$	957688.	−	757072.i	1.74417	−	1.37880i
$742$	−402556.			−0.731170
$743$	−602317.	−	347748.i	−1.09106	−	0.629922i	−0.157199	−	0.987567i	$-0.550247\pi$
$743$	−602317.	−	347748.i	−1.09106	−	0.629922i	−0.933858	+	0.357645i	$0.883580\pi$
$744$	−213268.	−	123130.i	−0.385282	−	0.222443i
$745$	373519.	+	646954.i	0.672977	+	1.16563i
$746$	570604.	−	988315.i	1.02531	−	1.77590i
$747$	−20674.8	−	35809.8i	−0.0370510	−	0.0641742i
$748$	−7683.05			−0.0137319
$749$		−	201024.i		−	0.358331i
$750$	543501.	+	941372.i	0.966225	+	1.67355i
$751$	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
$753$			731125.i			1.28944i
$754$	330752.	−	190960.i	0.581782	−	0.335892i
$755$	−92054.3	−	53147.5i	−0.161492	−	0.0932372i
$756$	30921.6	−	17852.6i	0.0541027	−	0.0312362i
$757$	−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
$759$			442908.i			0.768829i
$760$	−749494.	+	109701.i	−1.29760	+	0.189926i
$761$	−319277.			−0.551313			−0.275657	−	0.961256i	$-0.588895\pi$
$761$	−319277.			−0.551313			−0.275657	+	0.961256i	$0.588895\pi$
$762$	521757.	+	301237.i	0.898584	+	0.518798i
$763$	−194580.	−	112341.i	−0.334233	−	0.192969i
$764$	126796.	+	219618.i	0.217230	+	0.376254i
$765$	−28513.1	+	49386.1i	−0.0487216	+	0.0843882i
$766$	−526931.	−	912672.i	−0.898042	−	1.55545i
$767$	1.54416e6			2.62483
$768$		−	657560.i		−	1.11484i
$769$	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
$771$	−873806.			−1.46996
$772$		−	241898.i		−	0.405880i
$773$	−785095.	+	453275.i	−1.31390	+	0.758583i	−0.982740	−	0.184991i	$-0.940774\pi$
$773$	−785095.	+	453275.i	−1.31390	+	0.758583i	−0.331163	+	0.943573i	$0.607441\pi$
$774$	−280632.	−	162023.i	−0.468442	−	0.270455i
$775$	402407.	−	232330.i	0.669980	−	0.386813i
$776$	−86333.1	+	149533.i	−0.143369	+	0.248322i
$777$	−286244.	+	495789.i	−0.474127	+	0.821212i
$778$			111257.i			0.183809i
$779$	296034.	−	43329.6i	0.487828	−	0.0714019i
$780$	−706839.			−1.16180
$781$	−299248.	−	172771.i	−0.490602	−	0.283249i
$782$	58943.7	+	34031.2i	0.0963882	+	0.0556498i
$783$	−42408.9	−	73454.3i	−0.0691725	−	0.119810i
$784$	−282484.	+	489277.i	−0.459581	+	0.796017i
$785$	836904.	+	1.44956e6i	1.35811	+	2.35232i
$786$	−322024.			−0.521246
$787$		−	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
$789$	256465.	−	148070.i	0.411978	−	0.237855i
$790$	−1.02071e6			−1.63550
$791$		−	98101.3i		−	0.156791i
$792$	−152190.	+	87867.0i	−0.242625	+	0.140080i
$793$	−736971.	−	425490.i	−1.17194	−	0.676617i
$794$	1.14727e6	−	662378.i	1.81981	−	1.05067i
$795$	884911.	−	1.53271e6i	1.40012	−	2.42508i
$796$	64744.7	−	112141.i	0.102183	−	0.176986i
$797$			936748.i			1.47471i	0.675506	+	0.737354i	$0.263925\pi$
$797$			936748.i			1.47471i	−0.675506	+	0.737354i	$0.736075\pi$
$798$	435115.	+	172915.i	0.683280	+	0.271536i
$799$	20641.3			0.0323328
$800$	597245.	+	344820.i	0.933196	+	0.538781i
$801$	267438.	+	154405.i	0.416829	+	0.240656i
$802$	−22644.2	−	39221.0i	−0.0352054	−	0.0609775i
$803$	49544.2	−	85813.2i	0.0768355	−	0.133083i
$804$	142113.	+	246147.i	0.219848	+	0.380788i
$805$	610544.			0.942160
$806$			554057.i			0.852873i
$807$	−780846.	−	1.35246e6i	−1.19900	−	2.07672i
$808$	61243.4	−	35358.9i	0.0938073	−	0.0541597i
$809$	−55778.3			−0.0852252			−0.0426126	−	0.999092i	$-0.513568\pi$
$809$	−55778.3			−0.0852252			−0.0426126	+	0.999092i	$0.513568\pi$
$810$			1.52174e6i			2.31937i
$811$	−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
$813$	175967.	−	101594.i	0.266225	−	0.153705i
$814$	289884.	−	502093.i	0.437497	−	0.757767i
$815$	174252.	−	301813.i	0.262339	−	0.454384i
$816$			89186.8i			0.133943i
$817$	66181.1	+	452158.i	0.0991493	+	0.677402i
$818$	−815844.			−1.21927
$819$	−338111.	−	195208.i	−0.504071	−	0.291025i
$820$	−150022.	−	86615.3i	−0.223114	−	0.128815i
$821$	160712.	+	278361.i	0.238431	+	0.412974i	0.960264	−	0.279093i	$-0.0900337\pi$
$821$	160712.	+	278361.i	0.238431	+	0.412974i	−0.721834	+	0.692067i	$0.756700\pi$
$822$	471017.	−	815826.i	0.697097	−	1.20741i
$823$	−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
$825$		−	812575.i		−	1.19387i
$826$	296120.	+	512894.i	0.434017	+	0.751740i
$827$	650685.	−	375673.i	0.951393	−	0.549287i	0.0578795	−	0.998324i	$-0.481566\pi$
$827$	650685.	−	375673.i	0.951393	−	0.549287i	0.893513	+	0.449037i	$0.148233\pi$
$828$	−169682.			−0.247500
$829$			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
$831$	1.53146e6	+	884190.i	2.21771	+	1.28039i
$832$	534001.	−	308306.i	0.771429	−	0.445385i
$833$	22253.6	−	38544.3i	0.0320708	−	0.0555482i
$834$	305559.	−	529244.i	0.439302	−	0.760894i
$835$		−	1.24430e6i		−	1.78465i
$836$	−105172.	−	41795.5i	−0.150483	−	0.0598021i
$837$	123047.			0.175638
$838$	−112120.	−	64732.5i	−0.159659	−	0.0921794i
$839$	−1.05400e6	−	608525.i	−1.49732	−	0.864479i	−0.497326	−	0.867563i	$-0.665685\pi$
$839$	−1.05400e6	−	608525.i	−1.49732	−	0.864479i	−0.999995	+	0.00308436i	$0.999018\pi$
$840$	296822.	+	514111.i	0.420666	+	0.728616i
$841$	−312115.	+	540600.i	−0.441289	+	0.764335i
$842$	144304.	+	249941.i	0.203542	+	0.352544i
$843$	−963553.			−1.35588
$844$			34044.0i			0.0477921i
$845$	−1.14614e6	−	1.98517e6i	−1.60518	−	2.78025i
$846$	−186719.	+	107802.i	−0.260884	+	0.150622i
$847$	−259628.			−0.361897
$848$		−	1.12951e6i		−	1.57071i
$849$	776119.	−	448093.i	1.07675	−	0.621659i
$850$	−108140.	−	62434.8i	−0.149675	−	0.0864150i
$851$	−1.06161e6	+	612923.i	−1.46591	+	0.846343i
$852$	162204.	−	280945.i	0.223451	−	0.387028i
$853$	−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
$855$	−658969.	+	520929.i	−0.901432	+	0.712600i
$856$	418531.			0.571189
$857$	1.00185e6	+	578418.i	1.36408	+	0.787553i	0.990164	−	0.139908i	$-0.0446808\pi$
$857$	1.00185e6	+	578418.i	1.36408	+	0.787553i	0.373918	+	0.927462i	$0.378014\pi$
$858$	839101.	+	484455.i	1.13983	+	0.658080i
$859$	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
$861$	−117238.	−	203063.i	−0.158148	−	0.273920i
$862$	766427.			1.03147
$863$			38746.3i			0.0520246i	0.999662	+	0.0260123i	$0.00828090\pi$
$863$			38746.3i			0.0520246i	−0.999662	+	0.0260123i	$0.991719\pi$
$864$	91311.8	+	158157.i	0.122320	+	0.211865i
$865$	531131.	−	306649.i	0.709855	−	0.409835i
$866$	−161757.			−0.215688
$867$			969991.i			1.29042i
$868$	−43923.7	+	25359.3i	−0.0582987	+	0.0336588i
$869$	289205.	+	166972.i	0.382971	+	0.221108i
$870$	−557714.	+	321996.i	−0.736839	+	0.425414i
$871$	−700157.	+	1.21271e6i	−0.922910	+	1.59853i
$872$	233892.	−	405114.i	0.307598	−	0.532775i
$873$			191478.i			0.251240i
$874$	621743.	+	786499.i	0.813932	+	1.02962i
$875$	−490236.			−0.640308
$876$	80564.6	+	46514.0i	0.104987	+	0.0606144i
$877$	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
$879$	−567949.	+	983716.i	−0.735074	+	1.27319i
$880$	−405105.	−	701663.i	−0.523121	−	0.906073i
$881$	−243497.			−0.313720			−0.156860	−	0.987621i	$-0.550137\pi$
$881$	−243497.			−0.313720			−0.156860	+	0.987621i	$0.550137\pi$
$882$			464891.i			0.597604i
$883$	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
$885$	−2.60376e6			−3.32441
$886$			930705.i			1.18562i
$887$	−963132.	+	556064.i	−1.22416	+	0.706769i	−0.965802	−	0.259280i	$-0.916515\pi$
$887$	−963132.	+	556064.i	−1.22416	+	0.706769i	−0.258358	+	0.966049i	$0.583182\pi$
$888$	−1.03223e6	−	595958.i	−1.30903	−	0.755770i
$889$	−235311.	+	135857.i	−0.297741	+	0.171901i
$890$	−528227.	+	914916.i	−0.666869	+	1.15505i
$891$	248933.	−	431164.i	0.313564	−	0.543109i
$892$			46935.7i			0.0589894i
$893$	282556.	+	112288.i	0.354324	+	0.140809i
$894$	961382.			1.20288
$895$	596832.	+	344581.i	0.745086	+	0.430175i
$896$	412752.	+	238303.i	0.514131	+	0.296833i
$897$	−1.02432e6	−	1.77417e6i	−1.27306	−	2.20501i
$898$	417508.	−	723144.i	0.517740	−	0.896752i
$899$	60241.1	+	104341.i	0.0745373	+	0.129102i
$900$	311305.			0.384328
$901$			88980.4i			0.109609i
$902$	118729.	+	205645.i	0.145930	+	0.252758i
$903$	310155.	−	179068.i	0.380368	−	0.219606i
$904$	204246.			0.249929
$905$		−	494397.i		−	0.603641i
$906$	−118467.	+	68396.9i	−0.144325	+	0.0833259i
$907$	−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
$909$	39211.1	−	67915.6i	0.0474549	−	0.0821944i
$910$	667816.	−	1.15669e6i	0.806443	−	1.39680i
$911$		−	298558.i		−	0.359743i	−0.983690	−	0.179871i	$-0.942432\pi$
$911$		−	298558.i		−	0.359743i	0.983690	−	0.179871i	$-0.0575682\pi$
$912$	−485172.	+	1.22086e6i	−0.583319	+	1.46784i
$913$	−46280.8			−0.0555212
$914$	−265166.	−	153094.i	−0.317414	−	0.183259i
$915$	1.24268e6	+	717461.i	1.48428	+	0.856951i
$916$	−85588.6	−	148244.i	−0.102006	−	0.176679i
$917$	72616.0	−	125775.i	0.0863562	−	0.149573i
$918$	−16533.4	−	28636.6i	−0.0196190	−	0.0339811i
$919$	−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
$921$	−217409.	−	376564.i	−0.256306	−	0.443935i
$922$	−271908.	+	156986.i	−0.319861	+	0.184672i
$923$	1.59828e6			1.87607
$924$			88694.5i			0.103885i
$925$	1.94767e6	−	1.12449e6i	2.27632	−	1.31423i
$926$	−1.55132e6	−	895653.i	−1.80917	−	1.04452i
$927$	407401.	−	235213.i	0.474092	−	0.273717i
$928$	−89408.8	+	154861.i	−0.103821	+	0.179823i
$929$	234694.	−	406501.i	0.271938	−	0.471010i	−0.697420	−	0.716662i	$-0.745669\pi$
$929$	234694.	−	406501.i	0.271938	−	0.471010i	0.969358	+	0.245652i	$0.0790022\pi$
$930$		−	934250.i		−	1.08018i
$931$	514305.	−	406569.i	0.593364	−	0.469067i
$932$	459173.			0.528622
$933$	1.59220e6	+	919259.i	1.82909	+	1.05603i
$934$	−286824.	−	165598.i	−0.328793	−	0.189829i
$935$	31913.4	+	55275.7i	0.0365048	+	0.0632282i
$936$	406422.	−	703944.i	0.463901	−	0.803501i
$937$	−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
$939$		−	147328.i		−	0.167091i
$940$	−88022.7	−	152460.i	−0.0996183	−	0.172544i
$941$	−253995.	+	146644.i	−0.286844	+	0.165609i	−0.636518	−	0.771262i	$-0.719626\pi$
$941$	−253995.	+	146644.i	−0.286844	+	0.165609i	0.349674	+	0.936872i	$0.386292\pi$
$942$	2.15406e6			2.42749
$943$		−	502075.i		−	0.564606i
$944$	−1.43910e6	+	830864.i	−1.61490	+	0.932365i
$945$	−256881.	−	148310.i	−0.287653	−	0.166076i
$946$	−314099.	+	181345.i	−0.350982	+	0.202639i
$947$	273771.	−	474186.i	0.305273	−	0.528748i	−0.672049	−	0.740506i	$-0.734586\pi$
$947$	273771.	−	474186.i	0.305273	−	0.528748i	0.977322	+	0.211759i	$0.0679190\pi$
$948$	−156760.	+	271516.i	−0.174429	+	0.302120i
$949$			458326.i			0.508912i
$950$	−1.14067e6	−	1.44294e6i	−1.26390	−	1.59883i
$951$	154495.			0.170826
$952$	−25847.7	−	14923.2i	−0.0285199	−	0.0164660i
$953$	−978151.	−	564736.i	−1.07701	−	0.621812i	−0.146922	−	0.989148i	$-0.546937\pi$
$953$	−978151.	−	564736.i	−1.07701	−	0.621812i	−0.930088	+	0.367336i	$0.880270\pi$
$954$	−464714.	−	804908.i	−0.510609	−	0.884401i
$955$	1.05336e6	−	1.82447e6i	1.15497	−	2.00046i
$956$	−10841.1	−	18777.3i	−0.0118620	−	0.0205455i
$957$	210694.			0.230053
$958$			1.44699e6i			1.57665i
$959$	212428.	+	367936.i	0.230980	+	0.400069i
$960$	−900432.	+	519865.i	−0.977031	+	0.564089i
$961$	748735.			0.810740
$962$			2.68167e6i			2.89771i
$963$	401947.	−	232064.i	0.433427	−	0.250239i
$964$	−195387.	−	112807.i	−0.210253	−	0.121390i
$965$	−1.74034e6	+	1.00478e6i	−1.86887	+	1.07899i
$966$	392862.	−	680457.i	0.421003	−	0.729199i
$967$	−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
$969$	38221.0	−	96177.4i	0.0407056	−	0.102430i
$970$	−655052.			−0.696198
$971$	156634.	+	90432.6i	0.166130	+	0.0959150i	0.580760	−	0.814075i	$-0.302756\pi$
$971$	156634.	+	90432.6i	0.166130	+	0.0959150i	−0.414630	+	0.909990i	$0.636089\pi$
$972$	301233.	+	173917.i	0.318838	+	0.184081i
$973$	137807.	+	238688.i	0.145561	+	0.252119i
$974$	35726.4	−	61879.9i	0.0376592	−	0.0652276i
$975$	1.87925e6	+	3.25496e6i	1.97686	+	3.42402i
$976$	915772.			0.961363
$977$		−	962182.i		−	1.00802i	−0.863698	−	0.504009i	$-0.831858\pi$
$977$		−	962182.i		−	1.00802i	0.863698	−	0.504009i	$-0.168142\pi$
$978$	−224249.	−	388411.i	−0.234451	−	0.406082i
$979$	299331.	−	172819.i	0.312311	−	0.180313i
$980$	−379592.			−0.395244
$981$		−	518748.i		−	0.539037i
$982$	573586.	−	331160.i	0.594806	−	0.343411i
$983$	286561.	+	165446.i	0.296558	+	0.171218i	0.640896	−	0.767628i	$-0.278563\pi$
$983$	286561.	+	165446.i	0.296558	+	0.171218i	−0.344338	+	0.938846i	$0.611896\pi$
$984$	422775.	−	244089.i	0.436636	−	0.252092i
$985$	−813937.	+	1.40978e6i	−0.838915	+	1.45304i
$986$	16188.8	−	28039.9i	0.0166518	−	0.0288418i
$987$		−	238287.i		−	0.244605i
$988$	517952.	−	75811.2i	0.530611	−	0.0776639i
$989$	766863.			0.784017
$990$	−577371.	−	333345.i	−0.589094	−	0.340114i
$991$	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
$993$	−362967.	+	628678.i	−0.368103	+	0.637572i
$994$	306497.	+	530869.i	0.310209	+	0.537297i
$995$	−1.07573e6			−1.08657
$996$		−	43450.1i		−	0.0437998i
$997$	−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
$999$	595553.			0.596746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.5.d.a.8.2	✓	10
3.2	odd	2		171.5.p.a.46.4		10
4.3	odd	2		304.5.r.a.65.1		10
19.12	odd	6	inner	19.5.d.a.12.2	yes	10
57.50	even	6		171.5.p.a.145.4		10
76.31	even	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	1.1	even	1	trivial
19.5.d.a.12.2	yes	10	19.12	odd	6	inner
171.5.p.a.46.4		10	3.2	odd	2
171.5.p.a.145.4		10	57.50	even	6
304.5.r.a.65.1		10	4.3	odd	2
304.5.r.a.145.1		10	76.31	even	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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.97014 - 2.29216i) q^{2} +(10.1306 + 5.84893i) q^{3} +(2.50801 + 4.34400i) q^{4} +(20.8352 - 36.0877i) q^{5} +(-26.8134 - 46.4422i) q^{6} +24.1856 q^{7} +50.3541i q^{8} +(27.9200 + 48.3589i) q^{9} +O(q^{10})\)	\(q+(-3.97014 - 2.29216i) q^{2} +(10.1306 + 5.84893i) q^{3} +(2.50801 + 4.34400i) q^{4} +(20.8352 - 36.0877i) q^{5} +(-26.8134 - 46.4422i) q^{6} +24.1856 q^{7} +50.3541i q^{8} +(27.9200 + 48.3589i) q^{9} +(-165.438 + 95.5155i) q^{10} +62.4993 q^{11} +58.6767i q^{12} +(-250.356 + 144.543i) q^{13} +(-96.0201 - 55.4372i) q^{14} +(422.149 - 243.728i) q^{15} +(155.548 - 269.417i) q^{16} +(-12.2538 + 21.2242i) q^{17} -255.989i q^{18} +(-283.198 + 223.874i) q^{19} +209.020 q^{20} +(245.015 + 141.460i) q^{21} +(-248.131 - 143.258i) q^{22} +(302.902 + 524.641i) q^{23} +(-294.518 + 510.120i) q^{24} +(-555.715 - 962.527i) q^{25} +1325.26 q^{26} -294.318i q^{27} +(60.6576 + 105.062i) q^{28} +(249.575 - 144.092i) q^{29} -2234.65 q^{30} +418.074i q^{31} +(-537.367 + 310.249i) q^{32} +(633.158 + 365.554i) q^{33} +(97.2984 - 56.1752i) q^{34} +(503.912 - 872.801i) q^{35} +(-140.047 + 242.569i) q^{36} +2023.50i q^{37} +(1637.49 - 239.675i) q^{38} -3381.69 q^{39} +(1817.17 + 1049.14i) q^{40} +(-717.741 - 414.388i) q^{41} +(-648.497 - 1123.23i) q^{42} +(632.930 - 1096.27i) q^{43} +(156.749 + 271.497i) q^{44} +2326.88 q^{45} -2777.20i q^{46} +(-421.122 - 729.404i) q^{47} +(3151.60 - 1819.58i) q^{48} -1816.06 q^{49} +5095.15i q^{50} +(-248.277 + 143.343i) q^{51} +(-1255.79 - 725.029i) q^{52} +(3144.31 - 1815.37i) q^{53} +(-674.624 + 1168.48i) q^{54} +(1302.19 - 2255.46i) q^{55} +1217.84i q^{56} +(-4178.41 + 611.581i) q^{57} -1321.13 q^{58} +(-4625.90 - 2670.77i) q^{59} +(2117.51 + 1222.54i) q^{60} +(1471.85 + 2549.32i) q^{61} +(958.292 - 1659.81i) q^{62} +(675.261 + 1169.59i) q^{63} -2132.97 q^{64} +12046.3i q^{65} +(-1675.82 - 2902.60i) q^{66} +(4194.98 - 2421.97i) q^{67} -122.930 q^{68} +7086.61i q^{69} +(-4001.20 + 2310.10i) q^{70} +(-4788.02 - 2764.37i) q^{71} +(-2435.07 + 1405.89i) q^{72} +(792.717 - 1373.03i) q^{73} +(4638.19 - 8033.59i) q^{74} -13001.4i q^{75} +(-1682.77 - 668.735i) q^{76} +1511.58 q^{77} +(13425.8 + 7751.37i) q^{78} +(4627.33 + 2671.59i) q^{79} +(-6481.76 - 11226.7i) q^{80} +(3982.97 - 6898.70i) q^{81} +(1899.69 + 3290.36i) q^{82} -740.501 q^{83} +1419.13i q^{84} +(510.621 + 884.421i) q^{85} +(-5025.64 + 2901.56i) q^{86} +3371.14 q^{87} +3147.10i q^{88} +(4789.36 - 2765.14i) q^{89} +(-9238.05 - 5333.59i) q^{90} +(-6054.99 + 3495.85i) q^{91} +(-1519.36 + 2631.61i) q^{92} +(-2445.28 + 4235.36i) q^{93} +3861.11i q^{94} +(2178.59 + 14884.5i) q^{95} -7258.50 q^{96} +(2969.63 + 1714.52i) q^{97} +(7210.01 + 4162.70i) q^{98} +(1744.98 + 3022.40i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9} + 144 q^{10} + 50 q^{11} - 624 q^{13} - 474 q^{14} + 504 q^{15} + 285 q^{16} - 292 q^{17} + 305 q^{19} - 652 q^{20} + 1158 q^{21} + 1629 q^{22} + 98 q^{23} + 505 q^{24} - 681 q^{25} + 1524 q^{26} - 1472 q^{28} + 2598 q^{29} - 6656 q^{30} - 2745 q^{32} - 3441 q^{33} + 486 q^{34} + 694 q^{35} + 3402 q^{36} - 342 q^{38} - 5552 q^{39} + 8784 q^{40} - 1407 q^{41} + 292 q^{42} + 5424 q^{43} + 4151 q^{44} + 9572 q^{45} - 2416 q^{47} + 11481 q^{48} - 17826 q^{49} - 3342 q^{51} - 19962 q^{52} + 1122 q^{53} - 1039 q^{54} + 11424 q^{55} - 7906 q^{57} - 20236 q^{58} + 15387 q^{59} + 8886 q^{60} + 860 q^{61} + 21636 q^{62} + 5318 q^{63} + 19710 q^{64} - 13921 q^{66} + 14763 q^{67} - 48844 q^{68} - 20334 q^{70} - 27264 q^{71} + 354 q^{72} + 1561 q^{73} + 17094 q^{74} + 1955 q^{76} - 18392 q^{77} + 40266 q^{78} + 24750 q^{79} - 2002 q^{80} + 14311 q^{81} + 14479 q^{82} + 6002 q^{83} - 14944 q^{85} + 59946 q^{86} - 31996 q^{87} - 22566 q^{89} - 60630 q^{90} + 8724 q^{91} + 9572 q^{92} + 12476 q^{93} - 7312 q^{95} - 41850 q^{96} + 46287 q^{97} + 25515 q^{98} - 2048 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9 + 144 * q^10 + 50 * q^11 - 624 * q^13 - 474 * q^14 + 504 * q^15 + 285 * q^16 - 292 * q^17 + 305 * q^19 - 652 * q^20 + 1158 * q^21 + 1629 * q^22 + 98 * q^23 + 505 * q^24 - 681 * q^25 + 1524 * q^26 - 1472 * q^28 + 2598 * q^29 - 6656 * q^30 - 2745 * q^32 - 3441 * q^33 + 486 * q^34 + 694 * q^35 + 3402 * q^36 - 342 * q^38 - 5552 * q^39 + 8784 * q^40 - 1407 * q^41 + 292 * q^42 + 5424 * q^43 + 4151 * q^44 + 9572 * q^45 - 2416 * q^47 + 11481 * q^48 - 17826 * q^49 - 3342 * q^51 - 19962 * q^52 + 1122 * q^53 - 1039 * q^54 + 11424 * q^55 - 7906 * q^57 - 20236 * q^58 + 15387 * q^59 + 8886 * q^60 + 860 * q^61 + 21636 * q^62 + 5318 * q^63 + 19710 * q^64 - 13921 * q^66 + 14763 * q^67 - 48844 * q^68 - 20334 * q^70 - 27264 * q^71 + 354 * q^72 + 1561 * q^73 + 17094 * q^74 + 1955 * q^76 - 18392 * q^77 + 40266 * q^78 + 24750 * q^79 - 2002 * q^80 + 14311 * q^81 + 14479 * q^82 + 6002 * q^83 - 14944 * q^85 + 59946 * q^86 - 31996 * q^87 - 22566 * q^89 - 60630 * q^90 + 8724 * q^91 + 9572 * q^92 + 12476 * q^93 - 7312 * q^95 - 41850 * q^96 + 46287 * q^97 + 25515 * q^98 - 2048 * q^99

Introduction

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