LMFDB - Embedded newform 19.6.c.a.11.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,6,Mod(7,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	19.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.04729257645$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 210 x^{14} - 467 x^{13} + 30342 x^{12} - 66627 x^{11} + 2132053 x^{10} + \cdots + 629547033600 $ x^16 - 3x^15 + 210x^14 - 467x^13 + 30342x^12 - 66627x^11 + 2132053x^10 - 4466112x^9 + 107274084x^8 - 194802192x^7 + 2730460272x^6 - 2111232960x^5 + 43674750144x^4 - 28959939072x^3 + 296503029504x^2 + 289675422720*x + 629547033600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.8
Root			$5.58024 + 9.66525i$ of defining polynomial
Character	$\chi$	$=$	19.11
Dual form			19.6.c.a.7.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.58024 - 9.66525i) q^{2} +(-4.94172 + 8.55931i) q^{3} +(-46.2781 - 80.1560i) q^{4} +(8.46093 - 14.6548i) q^{5} +(55.1519 + 95.5260i) q^{6} +176.093 q^{7} -675.836 q^{8} +(72.6588 + 125.849i) q^{9} +(-94.4280 - 163.554i) q^{10} +312.571 q^{11} +914.774 q^{12} +(3.09579 + 5.36206i) q^{13} +(982.642 - 1701.99i) q^{14} +(83.6231 + 144.839i) q^{15} +(-2290.42 + 3967.13i) q^{16} +(-34.3186 + 59.4415i) q^{17} +1621.81 q^{18} +(-1508.69 - 447.155i) q^{19} -1566.22 q^{20} +(-870.203 + 1507.24i) q^{21} +(1744.22 - 3021.07i) q^{22} +(565.409 + 979.317i) q^{23} +(3339.79 - 5784.69i) q^{24} +(1419.33 + 2458.34i) q^{25} +69.1009 q^{26} -3837.91 q^{27} +(-8149.26 - 14114.9i) q^{28} +(304.470 + 527.358i) q^{29} +1866.55 q^{30} -6352.59 q^{31} +(14748.9 + 25545.8i) q^{32} +(-1544.64 + 2675.39i) q^{33} +(383.011 + 663.395i) q^{34} +(1489.91 - 2580.60i) q^{35} +(6725.02 - 11648.1i) q^{36} +1739.63 q^{37} +(-12740.7 + 12086.7i) q^{38} -61.1940 q^{39} +(-5718.20 + 9904.21i) q^{40} +(6310.81 - 10930.6i) q^{41} +(9711.88 + 16821.5i) q^{42} +(-357.976 + 620.032i) q^{43} +(-14465.2 - 25054.4i) q^{44} +2459.04 q^{45} +12620.5 q^{46} +(1944.93 + 3368.72i) q^{47} +(-22637.3 - 39208.9i) q^{48} +14201.8 q^{49} +31680.7 q^{50} +(-339.185 - 587.486i) q^{51} +(286.534 - 496.292i) q^{52} +(7039.41 + 12192.6i) q^{53} +(-21416.5 + 37094.4i) q^{54} +(2644.64 - 4580.65i) q^{55} -119010. q^{56} +(11282.9 - 10703.7i) q^{57} +6796.07 q^{58} +(9116.48 - 15790.2i) q^{59} +(7739.84 - 13405.8i) q^{60} +(-15531.3 - 26901.1i) q^{61} +(-35449.0 + 61399.4i) q^{62} +(12794.7 + 22161.1i) q^{63} +182621. q^{64} +104.773 q^{65} +(17238.9 + 29858.6i) q^{66} +(-26564.1 - 46010.4i) q^{67} +6352.79 q^{68} -11176.4 q^{69} +(-16628.1 - 28800.8i) q^{70} +(-12200.5 + 21131.9i) q^{71} +(-49105.4 - 85053.1i) q^{72} +(-2485.94 + 4305.77i) q^{73} +(9707.57 - 16814.0i) q^{74} -28055.6 q^{75} +(33977.2 + 141624. i) q^{76} +55041.6 q^{77} +(-341.477 + 591.456i) q^{78} +(-32904.2 + 56991.7i) q^{79} +(38758.2 + 67131.3i) q^{80} +(1309.81 - 2268.66i) q^{81} +(-70431.7 - 121991. i) q^{82} -85775.4 q^{83} +161085. q^{84} +(580.734 + 1005.86i) q^{85} +(3995.18 + 6919.86i) q^{86} -6018.43 q^{87} -211246. q^{88} +(24816.8 + 42984.0i) q^{89} +(13722.0 - 23767.3i) q^{90} +(545.147 + 944.222i) q^{91} +(52332.1 - 90641.8i) q^{92} +(31392.7 - 54373.8i) q^{93} +43412.7 q^{94} +(-19317.9 + 18326.2i) q^{95} -291539. q^{96} +(37310.2 - 64623.2i) q^{97} +(79249.5 - 137264. i) q^{98} +(22711.0 + 39336.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 28 q^{3} - 155 q^{4} + 10 q^{5} + 149 q^{6} + 208 q^{7} - 78 q^{8} - 616 q^{9} + 580 q^{10} + 632 q^{11} - 2238 q^{12} + 786 q^{13} + 2054 q^{14} + 796 q^{15} - 3779 q^{16} - 746 q^{17}+ \cdots + 163952 q^{99}+O(q^{100}) $ 16 * q + 3 * q^2 + 28 * q^3 - 155 * q^4 + 10 * q^5 + 149 * q^6 + 208 * q^7 - 78 * q^8 - 616 * q^9 + 580 * q^10 + 632 * q^11 - 2238 * q^12 + 786 * q^13 + 2054 * q^14 + 796 * q^15 - 3779 * q^16 - 746 * q^17 + 8868 * q^18 - 5972 * q^19 - 7780 * q^20 - 292 * q^21 + 1841 * q^22 + 2084 * q^23 + 17913 * q^24 - 1378 * q^25 - 824 * q^26 - 28184 * q^27 - 9270 * q^28 + 5266 * q^29 + 41656 * q^30 - 15536 * q^31 + 21711 * q^32 + 14926 * q^33 - 2240 * q^34 - 7488 * q^35 - 41734 * q^36 - 3752 * q^37 - 33546 * q^38 - 36648 * q^39 + 9822 * q^40 + 21676 * q^41 + 8698 * q^42 + 9584 * q^43 - 43859 * q^44 + 69352 * q^45 + 90956 * q^46 + 29340 * q^47 - 1281 * q^48 + 16784 * q^49 - 98366 * q^50 + 23576 * q^51 + 71182 * q^52 - 30310 * q^53 + 49919 * q^54 - 36000 * q^55 - 305652 * q^56 + 107502 * q^57 - 286928 * q^58 + 101924 * q^59 + 19034 * q^60 + 36394 * q^61 - 69544 * q^62 - 44112 * q^63 + 459910 * q^64 + 106020 * q^65 + 219667 * q^66 - 50716 * q^67 + 27116 * q^68 - 110748 * q^69 + 159588 * q^70 + 116292 * q^71 - 468618 * q^72 + 36584 * q^73 - 278908 * q^74 - 518536 * q^75 + 311611 * q^76 - 446968 * q^77 + 136808 * q^78 + 110692 * q^79 + 253310 * q^80 - 99760 * q^81 - 92057 * q^82 + 229240 * q^83 + 452292 * q^84 + 113898 * q^85 - 126186 * q^86 + 342264 * q^87 - 347742 * q^88 + 356518 * q^89 + 741244 * q^90 - 337648 * q^91 + 52840 * q^92 - 368832 * q^93 - 781920 * q^94 + 265028 * q^95 - 1983074 * q^96 + 150004 * q^97 + 536843 * q^98 + 163952 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	5.58024	−	9.66525i	0.986456	−	1.70859i	0.351177	−	0.936309i	$-0.385782\pi$
$2$	5.58024	−	9.66525i	0.986456	−	1.70859i	0.635279	−	0.772282i	$-0.280885\pi$
$3$	−4.94172	+	8.55931i	−0.317012	+	0.549080i	−0.979863	−	0.199671i	$-0.936013\pi$
$3$	−4.94172	+	8.55931i	−0.317012	+	0.549080i	0.662852	+	0.748751i	$0.269346\pi$
$4$	−46.2781	−	80.1560i	−1.44619	−	2.50488i
$5$	8.46093	−	14.6548i	0.151354	−	0.262152i	−0.780372	−	0.625316i	$-0.784970\pi$
$5$	8.46093	−	14.6548i	0.151354	−	0.262152i	0.931725	+	0.363164i	$0.118303\pi$
$6$	55.1519	+	95.5260i	0.625436	+	1.08329i
$7$	176.093			1.35831			0.679153	−	0.733997i	$-0.262347\pi$
$7$	176.093			1.35831			0.679153	+	0.733997i	$0.262347\pi$
$8$	−675.836			−3.73350
$9$	72.6588	+	125.849i	0.299007	+	0.517896i
$10$	−94.4280	−	163.554i	−0.298608	−	0.517203i
$11$	312.571			0.778873			0.389436	−	0.921053i	$-0.372670\pi$
$11$	312.571			0.778873			0.389436	+	0.921053i	$0.372670\pi$
$12$	914.774			1.83384
$13$	3.09579	+	5.36206i	0.00508057	+	0.00879981i	0.868555	−	0.495594i	$-0.165049\pi$
$13$	3.09579	+	5.36206i	0.00508057	+	0.00879981i	−0.863474	+	0.504393i	$0.831716\pi$
$14$	982.642	−	1701.99i	1.33991	−	2.32079i
$15$	83.6231	+	144.839i	0.0959617	+	0.166211i
$16$	−2290.42	+	3967.13i	−2.23674	+	3.87415i
$17$	−34.3186	+	59.4415i	−0.0288009	+	0.0498847i	−0.880067	−	0.474850i	$-0.842502\pi$
$17$	−34.3186	+	59.4415i	−0.0288009	+	0.0498847i	0.851266	+	0.524735i	$0.175836\pi$
$18$	1621.81			1.17983
$19$	−1508.69	−	447.155i	−0.958775	−	0.284167i
$19$	−1508.69	−	447.155i	−0.958775	−	0.284167i
$20$	−1566.22			−0.875545
$21$	−870.203	+	1507.24i	−0.430599	+	0.745819i
$22$	1744.22	−	3021.07i	0.768324	−	1.33078i
$23$	565.409	+	979.317i	0.222866	+	0.386014i	0.955677	−	0.294417i	$-0.0951256\pi$
$23$	565.409	+	979.317i	0.222866	+	0.386014i	−0.732811	+	0.680432i	$0.761792\pi$
$24$	3339.79	−	5784.69i	1.18356	−	2.04999i
$25$	1419.33	+	2458.34i	0.454184	+	0.786670i
$26$	69.1009			0.0200470
$27$	−3837.91			−1.01318
$28$	−8149.26	−	14114.9i	−1.96437	−	3.40239i
$29$	304.470	+	527.358i	0.0672280	+	0.116442i	0.897680	−	0.440648i	$-0.145251\pi$
$29$	304.470	+	527.358i	0.0672280	+	0.116442i	−0.830452	+	0.557090i	$0.811918\pi$
$30$	1866.55			0.378648
$31$	−6352.59			−1.18726			−0.593631	−	0.804737i	$-0.702306\pi$
$31$	−6352.59			−1.18726			−0.593631	+	0.804737i	$0.702306\pi$
$32$	14748.9	+	25545.8i	2.54615	+	4.41005i
$33$	−1544.64	+	2675.39i	−0.246912	+	0.427663i
$34$	383.011	+	663.395i	0.0568217	+	0.0984181i
$35$	1489.91	−	2580.60i	0.205585	−	0.356083i
$36$	6725.02	−	11648.1i	0.864843	−	1.49795i
$37$	1739.63			0.208907			0.104454	−	0.994530i	$-0.466691\pi$
$37$	1739.63			0.208907			0.104454	+	0.994530i	$0.466691\pi$
$38$	−12740.7	+	12086.7i	−1.43131	+	1.35784i
$39$	−61.1940			−0.00644240
$40$	−5718.20	+	9904.21i	−0.565079	+	0.978746i
$41$	6310.81	−	10930.6i	0.586308	−	1.01551i	−0.408403	−	0.912802i	$-0.633914\pi$
$41$	6310.81	−	10930.6i	0.586308	−	1.01551i	0.994711	−	0.102713i	$-0.0327524\pi$
$42$	9711.88	+	16821.5i	0.849533	+	1.47143i
$43$	−357.976	+	620.032i	−0.0295245	+	0.0511379i	−0.880410	−	0.474213i	$-0.842733\pi$
$43$	−357.976	+	620.032i	−0.0295245	+	0.0511379i	0.850886	+	0.525351i	$0.176066\pi$
$44$	−14465.2	−	25054.4i	−1.12640	−	1.95098i
$45$	2459.04			0.181024
$46$	12620.5			0.879388
$47$	1944.93	+	3368.72i	0.128428	+	0.222444i	0.923068	−	0.384638i	$-0.125674\pi$
$47$	1944.93	+	3368.72i	0.128428	+	0.222444i	−0.794640	+	0.607081i	$0.792340\pi$
$48$	−22637.3	−	39208.9i	−1.41815	−	2.45630i
$49$	14201.8			0.844994
$50$	31680.7			1.79213
$51$	−339.185	−	587.486i	−0.0182605	−	0.0316280i
$52$	286.534	−	496.292i	0.0146949	−	0.0254524i
$53$	7039.41	+	12192.6i	0.344228	+	0.596221i	0.985213	−	0.171333i	$-0.0548072\pi$
$53$	7039.41	+	12192.6i	0.344228	+	0.596221i	−0.640985	+	0.767553i	$0.721474\pi$
$54$	−21416.5	+	37094.4i	−0.999456	+	1.73111i
$55$	2644.64	−	4580.65i	0.117885	−	0.204183i
$56$	−119010.			−5.07123
$57$	11282.9	−	10703.7i	0.459973	−	0.436360i
$58$	6796.07			0.265270
$59$	9116.48	−	15790.2i	0.340955	−	0.590551i	−0.643655	−	0.765316i	$-0.722583\pi$
$59$	9116.48	−	15790.2i	0.340955	−	0.590551i	0.984610	+	0.174764i	$0.0559163\pi$
$60$	7739.84	−	13405.8i	0.277558	−	0.480744i
$61$	−15531.3	−	26901.1i	−0.534422	−	0.925646i	−0.999191	−	0.0402142i	$-0.987196\pi$
$61$	−15531.3	−	26901.1i	−0.534422	−	0.925646i	0.464769	−	0.885432i	$-0.346137\pi$
$62$	−35449.0	+	61399.4i	−1.17118	+	2.02855i
$63$	12794.7	+	22161.1i	0.406143	+	0.703461i
$64$	182621.			5.57316
$65$	104.773			0.00307585
$66$	17238.9	+	29858.6i	0.487135	+	0.843742i
$67$	−26564.1	−	46010.4i	−0.722950	−	1.25219i	−0.959812	−	0.280643i	$-0.909452\pi$
$67$	−26564.1	−	46010.4i	−0.722950	−	1.25219i	0.236862	−	0.971543i	$-0.423881\pi$
$68$	6352.79			0.166607
$69$	−11176.4			−0.282604
$70$	−16628.1	−	28800.8i	−0.405600	−	0.702520i
$71$	−12200.5	+	21131.9i	−0.287231	+	0.497499i	−0.973148	−	0.230181i	$-0.926068\pi$
$71$	−12200.5	+	21131.9i	−0.287231	+	0.497499i	0.685917	+	0.727680i	$0.259401\pi$
$72$	−49105.4	−	85053.1i	−1.11634	−	1.93356i
$73$	−2485.94	+	4305.77i	−0.0545988	+	0.0945679i	−0.892033	−	0.451970i	$-0.850721\pi$
$73$	−2485.94	+	4305.77i	−0.0545988	+	0.0945679i	0.837434	+	0.546538i	$0.184055\pi$
$74$	9707.57	−	16814.0i	0.206078	−	0.356937i
$75$	−28055.6			−0.575926
$76$	33977.2	+	141624.i	0.674768	+	2.81257i
$77$	55041.6			1.05795
$78$	−341.477	+	591.456i	−0.00635514	+	0.0110074i
$79$	−32904.2	+	56991.7i	−0.593176	+	1.02741i	0.400626	+	0.916242i	$0.368793\pi$
$79$	−32904.2	+	56991.7i	−0.593176	+	1.02741i	−0.993802	+	0.111169i	$0.964541\pi$
$80$	38758.2	+	67131.3i	0.677079	+	1.17273i
$81$	1309.81	−	2268.66i	0.0221817	−	0.0384199i
$82$	−70431.7	−	121991.i	−1.15673	−	2.00352i
$83$	−85775.4			−1.36668			−0.683341	−	0.730100i	$-0.739474\pi$
$83$	−85775.4			−1.36668			−0.683341	+	0.730100i	$0.739474\pi$
$84$	161085.			2.49091
$85$	580.734	+	1005.86i	0.00871826	+	0.0151005i
$86$	3995.18	+	6919.86i	0.0582492	+	0.100891i
$87$	−6018.43			−0.0852482
$88$	−211246.			−2.90792
$89$	24816.8	+	42984.0i	0.332102	+	0.575217i	0.982924	−	0.184013i	$-0.0589089\pi$
$89$	24816.8	+	42984.0i	0.332102	+	0.575217i	−0.650822	+	0.759230i	$0.725576\pi$
$90$	13722.0	−	23767.3i	0.178572	−	0.309295i
$91$	545.147	+	944.222i	0.00690097	+	0.0119528i
$92$	52332.1	−	90641.8i	0.644612	−	1.11650i
$93$	31392.7	−	54373.8i	0.376376	−	0.651902i
$94$	43412.7			0.506754
$95$	−19317.9	+	18326.2i	−0.219609	+	0.208335i
$96$	−291539.			−3.22863
$97$	37310.2	−	64623.2i	0.402623	−	0.697363i	−0.591419	−	0.806365i	$-0.701432\pi$
$97$	37310.2	−	64623.2i	0.402623	−	0.697363i	0.994042	+	0.109001i	$0.0347653\pi$
$98$	79249.5	−	137264.i	0.833549	−	1.44375i
$99$	22711.0	+	39336.6i	0.232889	+	0.403375i
$100$	131367.	−	227535.i	1.31367	−	2.27535i
$101$	74477.7	+	128999.i	0.726479	+	1.25830i	0.958362	+	0.285555i	$0.0921779\pi$
$101$	74477.7	+	128999.i	0.726479	+	1.25830i	−0.231883	+	0.972744i	$0.574489\pi$
$102$	−7570.94			−0.0720526
$103$	−109510.			−1.01709			−0.508546	−	0.861035i	$-0.669817\pi$
$103$	−109510.			−1.01709			−0.508546	+	0.861035i	$0.669817\pi$
$104$	−2092.24	−	3623.87i	−0.0189683	−	0.0328541i
$105$	14725.5	+	25505.2i	0.130345	+	0.225765i
$106$	157126.			1.35826
$107$	42265.2			0.356881			0.178441	−	0.983951i	$-0.442895\pi$
$107$	42265.2			0.356881			0.178441	+	0.983951i	$0.442895\pi$
$108$	177611.	+	307632.i	1.46525	+	2.53788i
$109$	16089.5	−	27867.9i	0.129711	−	0.224666i	−0.793854	−	0.608109i	$-0.791928\pi$
$109$	16089.5	−	27867.9i	0.129711	−	0.224666i	0.923565	+	0.383443i	$0.125262\pi$
$110$	−29515.4	−	51122.2i	−0.232577	−	0.402836i
$111$	−8596.78	+	14890.1i	−0.0662260	+	0.114707i
$112$	−403328.	+	698585.i	−3.03818	+	5.26228i
$113$	83859.3			0.617811			0.308905	−	0.951093i	$-0.400037\pi$
$113$	83859.3			0.617811			0.308905	+	0.951093i	$0.400037\pi$
$114$	−40492.4	−	168781.i	−0.291818	−	1.21636i
$115$	19135.5			0.134926
$116$	28180.6	−	48810.3i	0.194449	−	0.336795i
$117$	−449.872	+	779.201i	−0.00303826	+	0.00526241i
$118$	−101744.	−	176226.i	−0.672674	−	1.16511i
$119$	−6043.26	+	10467.2i	−0.0391205	+	0.0677587i
$120$	−56515.5	−	97887.7i	−0.358273	−	0.620547i
$121$	−63350.6			−0.393357
$122$	−346674.			−2.10874
$123$	62372.5	+	108032.i	0.371733	+	0.643860i
$124$	293986.	+	509198.i	1.71701	+	2.97394i
$125$	100916.			0.577677
$126$	285590.			1.60257
$127$	−132790.	−	230000.i	−0.730563	−	1.26537i	−0.956643	−	0.291264i	$-0.905924\pi$
$127$	−132790.	−	230000.i	−0.730563	−	1.26537i	0.226080	−	0.974109i	$-0.427409\pi$
$128$	547106.	−	947616.i	2.95153	−	5.11220i
$129$	−3538.03	−	6128.05i	−0.0187192	−	0.0324226i
$130$	584.658	−	1012.66i	0.00303419	−	0.00525538i
$131$	82351.0	−	142636.i	0.419267	−	0.726191i	−0.576599	−	0.817027i	$-0.695621\pi$
$131$	82351.0	−	142636.i	0.419267	−	0.726191i	0.995866	+	0.0908358i	$0.0289539\pi$
$132$	285931.			1.42832
$133$	−265670.	−	78740.9i	−1.30231	−	0.385986i
$134$	−592936.			−2.85263
$135$	−32472.3	+	56243.7i	−0.153348	+	0.265607i
$136$	23193.7	−	40172.7i	0.107528	−	0.186245i
$137$	106269.	+	184063.i	0.483731	+	0.837847i	0.999825	−	0.0186845i	$-0.00594781\pi$
$137$	106269.	+	184063.i	0.483731	+	0.837847i	−0.516094	+	0.856532i	$0.672614\pi$
$138$	−62366.8	+	108022.i	−0.278776	+	0.482854i
$139$	−64495.3	−	111709.i	−0.283133	−	0.490402i	0.689021	−	0.724741i	$-0.258041\pi$
$139$	−64495.3	−	111709.i	−0.283133	−	0.490402i	−0.972155	+	0.234339i	$0.924707\pi$
$140$	−275801.			−1.18926
$141$	−38445.2			−0.162852
$142$	136163.	+	235842.i	0.566681	+	0.981521i
$143$	967.652	+	1676.02i	0.00395712	+	0.00685393i
$144$	−665678.			−2.67521
$145$	10304.4			0.0407008
$146$	27744.2	+	48054.4i	0.107719	+	0.186574i
$147$	−70181.4	+	121558.i	−0.267873	+	0.463969i
$148$	−80506.9	−	139442.i	−0.302120	−	0.523286i
$149$	−11453.0	+	19837.2i	−0.0422623	+	0.0732005i	−0.886383	−	0.462953i	$-0.846790\pi$
$149$	−11453.0	+	19837.2i	−0.0422623	+	0.0732005i	0.844120	+	0.536154i	$0.180123\pi$
$150$	−156557.	+	271165.i	−0.568126	+	0.984023i
$151$	−159683.			−0.569924			−0.284962	−	0.958539i	$-0.591981\pi$
$151$	−159683.			−0.569924			−0.284962	+	0.958539i	$0.591981\pi$
$152$	1.01963e6	+	302203.i	3.57959	+	1.06094i
$153$	−9974.18			−0.0344468
$154$	307145.	−	531991.i	1.04362	−	1.80760i
$155$	−53748.8	+	93095.7i	−0.179697	+	0.311244i
$156$	2831.94	+	4905.07i	0.00931693	+	0.0161374i
$157$	217385.	−	376522.i	0.703851	−	1.21911i	−0.263254	−	0.964727i	$-0.584796\pi$
$157$	217385.	−	376522.i	0.703851	−	1.21911i	0.967105	−	0.254379i	$-0.0818711\pi$
$158$	367226.	+	636055.i	1.17028	+	2.02699i
$159$	−139147.			−0.436497
$160$	499156.			1.54147
$161$	99564.6	+	172451.i	0.302719	+	0.524326i
$162$	−14618.1	−	25319.3i	−0.0437626	−	0.0757991i
$163$	70626.9			0.208210			0.104105	−	0.994566i	$-0.466802\pi$
$163$	70626.9			0.208210			0.104105	+	0.994566i	$0.466802\pi$
$164$	−1.16821e6			−3.39165
$165$	26138.1	+	45272.6i	0.0747420	+	0.129457i
$166$	−478647.	+	829041.i	−1.34817	+	2.33510i
$167$	−272239.	−	471532.i	−0.755369	−	1.30834i	−0.945191	−	0.326519i	$-0.894124\pi$
$167$	−272239.	−	471532.i	−0.755369	−	1.30834i	0.189822	−	0.981819i	$-0.439209\pi$
$168$	588115.	−	1.01864e6i	1.60764	−	2.78451i
$169$	185627.	−	321516.i	0.499948	−	0.865936i
$170$	12962.5			0.0344007
$171$	−53345.9	−	222357.i	−0.139512	−	0.581514i
$172$	66265.8			0.170792
$173$	172303.	−	298438.i	0.437701	−	0.758121i	−0.559810	−	0.828621i	$-0.689126\pi$
$173$	172303.	−	298438.i	0.437701	−	0.758121i	0.997512	+	0.0704997i	$0.0224594\pi$
$174$	−33584.3	+	58169.7i	−0.0840936	+	0.145654i
$175$	249934.	+	432898.i	0.616921	+	1.06854i
$176$	−715920.	+	1.24001e6i	−1.74214	+	3.01747i
$177$	90102.2	+	156062.i	0.216173	+	0.374423i
$178$	553935.			1.31042
$179$	557728.			1.30104			0.650519	−	0.759490i	$-0.274552\pi$
$179$	557728.			1.30104			0.650519	+	0.759490i	$0.274552\pi$
$180$	−113800.	−	197107.i	−0.261794	−	0.453441i
$181$	130459.	+	225961.i	0.295990	+	0.512669i	0.975215	−	0.221261i	$-0.0710173\pi$
$181$	130459.	+	225961.i	0.295990	+	0.512669i	−0.679225	+	0.733930i	$0.737684\pi$
$182$	12168.2			0.0272300
$183$	307006.			0.677672
$184$	−382123.	−	661857.i	−0.832068	−	1.44118i
$185$	14718.9	−	25493.9i	0.0316189	−	0.0547655i
$186$	−350358.	−	606838.i	−0.742556	−	1.28615i
$187$	−10727.0	+	18579.7i	−0.0224323	+	0.0388538i
$188$	180015.	−	311796.i	0.371462	−	0.643391i
$189$	−675831.			−1.37621
$190$	69328.8	+	288977.i	0.139325	+	0.580736i
$191$	692437.			1.37340			0.686700	−	0.726941i	$-0.259059\pi$
$191$	692437.			1.37340			0.686700	+	0.726941i	$0.259059\pi$
$192$	−902463.	+	1.56311e6i	−1.76676	+	3.06011i
$193$	−415707.	+	720026.i	−0.803331	+	1.39141i	0.114081	+	0.993471i	$0.463608\pi$
$193$	−415707.	+	720026.i	−0.803331	+	1.39141i	−0.917412	+	0.397939i	$0.869726\pi$
$194$	−416400.	−	721225.i	−0.794339	−	1.37584i
$195$	−517.758	+	896.784i	−0.000975081	+	0.00168889i
$196$	−657233.	−	1.13836e6i	−1.22202	−	2.11660i
$197$	−760180.			−1.39557			−0.697784	−	0.716308i	$-0.745830\pi$
$197$	−760180.			−1.39557			−0.697784	+	0.716308i	$0.745830\pi$
$198$	506931.			0.918938
$199$	407611.	+	706003.i	0.729648	+	1.26379i	0.957032	+	0.289982i	$0.0936494\pi$
$199$	407611.	+	706003.i	0.729648	+	1.26379i	−0.227384	+	0.973805i	$0.573017\pi$
$200$	−959231.	−	1.66144e6i	−1.69570	−	2.93703i
$201$	525090.			0.916734
$202$	1.66241e6			2.86656
$203$	53615.2	+	92864.2i	0.0913162	+	0.158164i
$204$	−31393.7	+	54375.5i	−0.0528162	+	0.0914804i
$205$	−106791.	−	184967.i	−0.177480	−	0.307404i
$206$	−611092.	+	1.05844e6i	−1.00332	+	1.73780i
$207$	−82163.8	+	142312.i	−0.133277	+	0.230842i
$208$	−28362.7			−0.0454557
$209$	−471573.	−	139767.i	−0.746764	−	0.221330i
$210$	328686.			0.514320
$211$	290891.	−	503838.i	0.449805	−	0.779085i	−0.548568	−	0.836106i	$-0.684827\pi$
$211$	290891.	−	503838.i	0.449805	−	0.779085i	0.998373	+	0.0570211i	$0.0181602\pi$
$212$	651541.	−	1.12850e6i	0.995639	−	1.72450i
$213$	−120583.	−	208855.i	−0.182111	−	0.315426i
$214$	235850.	−	408504.i	0.352047	−	0.609764i
$215$	6057.62	+	10492.1i	0.00893729	+	0.0154798i
$216$	2.59380e6			3.78270
$217$	−1.11865e6			−1.61267
$218$	−179567.	−	311019.i	−0.255909	−	0.443247i
$219$	−24569.6	−	42555.8i	−0.0346169	−	0.0599582i
$220$	−489555.			−0.681938
$221$	−424.972			−0.000585301
$222$	95944.2	+	166180.i	0.130658	+	0.226306i
$223$	−157553.	+	272890.i	−0.212161	+	0.367473i	−0.952390	−	0.304881i	$-0.901383\pi$
$223$	−157553.	+	272890.i	−0.212161	+	0.367473i	0.740230	+	0.672354i	$0.234717\pi$
$224$	2.59717e6	+	4.49844e6i	3.45844	+	5.99020i
$225$	−206253.	+	357241.i	−0.271609	+	0.470440i
$226$	467955.	−	810522.i	0.609443	−	1.05559i
$227$	−951914.			−1.22612			−0.613060	−	0.790036i	$-0.710062\pi$
$227$	−951914.			−1.22612			−0.613060	+	0.790036i	$0.710062\pi$
$228$	−1.38011e6	−	409045.i	−1.75824	−	0.521116i
$229$	−1.11908e6			−1.41017			−0.705084	−	0.709124i	$-0.749091\pi$
$229$	−1.11908e6			−1.41017			−0.705084	+	0.709124i	$0.749091\pi$
$230$	106781.	−	184950.i	0.133099	−	0.230534i
$231$	−272000.	+	471118.i	−0.335381	+	0.580898i
$232$	−205772.	−	356408.i	−0.250996	−	0.434737i
$233$	126616.	−	219305.i	0.152791	−	0.264642i	−0.779461	−	0.626450i	$-0.784507\pi$
$233$	126616.	−	219305.i	0.152791	−	0.264642i	0.932253	+	0.361808i	$0.117840\pi$
$234$	5020.79	+	8696.26i	0.00599421	+	0.0103823i
$235$	65823.6			0.0777521
$236$	−1.68757e6			−1.97234
$237$	−325207.	−	563274.i	−0.376087	−	0.651402i
$238$	67445.7	+	116819.i	0.0771813	+	0.133682i
$239$	1.24520e6			1.41009			0.705043	−	0.709164i	$-0.250928\pi$
$239$	1.24520e6			1.41009			0.705043	+	0.709164i	$0.250928\pi$
$240$	−766130.			−0.858567
$241$	770112.	+	1.33387e6i	0.854105	+	1.47935i	0.877473	+	0.479626i	$0.159228\pi$
$241$	770112.	+	1.33387e6i	0.854105	+	1.47935i	−0.0233682	+	0.999727i	$0.507439\pi$
$242$	−353511.	+	612299.i	−0.388030	+	0.672087i
$243$	−453361.	−	785244.i	−0.492525	−	0.853079i
$244$	−1.43752e6	+	2.48986e6i	−1.54575	+	2.67732i
$245$	120161.	−	208124.i	0.127893	−	0.221517i
$246$	1.39221e6			1.46679
$247$	−2272.92	−	9473.99i	−0.00237051	−	0.00988076i
$248$	4.29331e6			4.43264
$249$	423878.	−	734178.i	0.433254	−	0.750418i
$250$	563136.	−	975379.i	0.569853	−	0.987015i
$251$	608564.	+	1.05406e6i	0.609708	+	1.05605i	0.991288	+	0.131710i	$0.0420467\pi$
$251$	608564.	+	1.05406e6i	0.609708	+	1.05605i	−0.381580	+	0.924336i	$0.624620\pi$
$252$	1.18423e6	−	2.05115e6i	1.17472	−	2.03468i
$253$	176730.	+	306106.i	0.173584	+	0.300656i
$254$	−2.96401e6			−2.88267
$255$	−11479.3			−0.0110552
$256$	−3.18403e6	−	5.51490e6i	−3.03653	−	5.25942i
$257$	119881.	+	207640.i	0.113219	+	0.196100i	0.917066	−	0.398735i	$-0.130551\pi$
$257$	119881.	+	207640.i	0.113219	+	0.196100i	−0.803848	+	0.594835i	$0.797217\pi$
$258$	−78972.3			−0.0738627
$259$	306338.			0.283760
$260$	−4848.69	−	8398.18i	−0.00444827	−	0.00770463i
$261$	−44244.9	+	76634.4i	−0.0402033	+	0.0696342i
$262$	−919076.	−	1.59189e6i	−0.827176	−	1.43271i
$263$	670861.	−	1.16197e6i	0.598058	−	1.03587i	−0.395050	−	0.918660i	$-0.629273\pi$
$263$	670861.	−	1.16197e6i	0.598058	−	1.03587i	0.993108	−	0.117207i	$-0.0373941\pi$
$264$	1.04392e6	−	1.80812e6i	0.921845	−	1.59668i
$265$	238240.			0.208401
$266$	−2.24355e6	+	2.12838e6i	−1.94416	+	1.84436i
$267$	−490551.			−0.421120
$268$	−2.45867e6	+	4.25855e6i	−2.09105	+	3.62180i
$269$	763317.	−	1.32210e6i	0.643168	−	1.11400i	−0.341554	−	0.939862i	$-0.610953\pi$
$269$	763317.	−	1.32210e6i	0.643168	−	1.11400i	0.984721	−	0.174137i	$-0.0557135\pi$
$270$	362407.	+	627707.i	0.302543	+	0.524019i
$271$	−73514.8	+	127331.i	−0.0608067	+	0.105320i	−0.894826	−	0.446415i	$-0.852701\pi$
$271$	−73514.8	+	127331.i	−0.0608067	+	0.105320i	0.834020	+	0.551735i	$0.186034\pi$
$272$	−157208.	−	272292.i	−0.128841	−	0.223158i
$273$	−10775.9			−0.00875074
$274$	2.37202e6			1.90872
$275$	443639.	+	768406.i	0.353752	+	0.612716i
$276$	517221.	+	895853.i	0.408699	+	0.707887i
$277$	902793.			0.706950			0.353475	−	0.935444i	$-0.385000\pi$
$277$	902793.			0.706950			0.353475	+	0.935444i	$0.385000\pi$
$278$	−1.43960e6			−1.11719
$279$	−461572.	−	799466.i	−0.355000	−	0.614878i
$280$	−1.00694e6	+	1.74406e6i	−0.767550	+	1.32944i
$281$	386886.	+	670106.i	0.292292	+	0.506265i	0.974351	−	0.225032i	$-0.0722488\pi$
$281$	386886.	+	670106.i	0.292292	+	0.506265i	−0.682059	+	0.731297i	$0.738915\pi$
$282$	−214533.	+	371582.i	−0.160647	+	0.278248i
$283$	980147.	−	1.69766e6i	0.727487	−	1.26004i	−0.230455	−	0.973083i	$-0.574022\pi$
$283$	980147.	−	1.69766e6i	0.727487	−	1.26004i	0.957942	−	0.286961i	$-0.0926451\pi$
$284$	2.25846e6			1.66156
$285$	−61395.8	−	255911.i	−0.0447741	−	0.186628i
$286$	21598.9			0.0156141
$287$	1.11129e6	−	1.92481e6i	0.796385	−	1.37938i
$288$	−2.14327e6	+	3.71225e6i	−1.52263	+	2.63728i
$289$	707573.	+	1.22555e6i	0.498341	+	0.863152i
$290$	57501.1	−	99594.8i	0.0401496	−	0.0695411i
$291$	368753.	+	638699.i	0.255272	+	0.442144i
$292$	460178.			0.315841
$293$	−1.89185e6			−1.28741			−0.643707	−	0.765272i	$-0.722605\pi$
$293$	−1.89185e6			−1.28741			−0.643707	+	0.765272i	$0.722605\pi$
$294$	783258.	+	1.35664e6i	0.528490	+	0.915371i
$295$	−154268.	−	267200.i	−0.103210	−	0.178764i
$296$	−1.17571e6			−0.779955
$297$	−1.19962e6			−0.789137
$298$	127821.	+	221392.i	0.0833799	+	0.144418i
$299$	−3500.77	+	6063.51i	−0.00226457	+	0.00392235i
$300$	1.29836e6	+	2.24883e6i	0.832899	+	1.44262i
$301$	−63037.1	+	109183.i	−0.0401033	+	0.0694610i
$302$	−891070.	+	1.54338e6i	−0.562205	+	0.973767i
$303$	−1.47219e6			−0.921209
$304$	5.22947e6	−	4.96101e6i	3.24544	−	3.07883i
$305$	−525638.			−0.323547
$306$	−55658.3	+	96403.0i	−0.0339802	+	0.0588555i
$307$	−532070.	+	921571.i	−0.322198	+	0.558063i	−0.980941	−	0.194305i	$-0.937755\pi$
$307$	−532070.	+	921571.i	−0.322198	+	0.558063i	0.658743	+	0.752368i	$0.271088\pi$
$308$	−2.54722e6	−	4.41191e6i	−1.52999	−	2.65003i
$309$	541168.	−	937330.i	0.322430	−	0.558465i
$310$	599863.	+	1.03899e6i	0.354526	+	0.614056i
$311$	112927.			0.0662062			0.0331031	−	0.999452i	$-0.489461\pi$
$311$	112927.			0.0662062			0.0331031	+	0.999452i	$0.489461\pi$
$312$	41357.1			0.0240527
$313$	648415.	+	1.12309e6i	0.374104	+	0.647967i	0.990192	−	0.139710i	$-0.0446170\pi$
$313$	648415.	+	1.12309e6i	0.374104	+	0.647967i	−0.616088	+	0.787677i	$0.711284\pi$
$314$	−2.42612e6	−	4.20217e6i	−1.38864	−	2.40519i
$315$	433021.			0.245885
$316$	6.09097e6			3.43138
$317$	−700591.	−	1.21346e6i	−0.391576	−	0.678230i	0.601081	−	0.799188i	$-0.294737\pi$
$317$	−700591.	−	1.21346e6i	−0.391576	−	0.678230i	−0.992658	+	0.120958i	$0.961403\pi$
$318$	−776474.	+	1.34489e6i	−0.430585	+	0.745796i
$319$	95168.5	+	164837.i	0.0523620	+	0.0906937i
$320$	1.54515e6	−	2.67627e6i	0.843518	−	1.46102i
$321$	−208863.	+	361761.i	−0.113135	+	0.195956i
$322$	2.22238e6			1.19448
$323$	78355.7	−	74333.2i	0.0417892	−	0.0396439i
$324$	−242462.			−0.128316
$325$	−8787.85	+	15221.0i	−0.00461503	+	0.00799346i
$326$	394115.	−	682627.i	0.205390	−	0.355745i
$327$	159020.	+	275431.i	0.0822398	+	0.142444i
$328$	−4.26507e6	+	7.38732e6i	−2.18898	+	3.79142i
$329$	342489.	+	593208.i	0.174444	+	0.302146i
$330$	583428.			0.294919
$331$	−1.32026e6			−0.662353			−0.331177	−	0.943569i	$-0.607446\pi$
$331$	−1.32026e6			−0.662353			−0.331177	+	0.943569i	$0.607446\pi$
$332$	3.96952e6	+	6.87541e6i	1.97648	+	3.42337i
$333$	126400.	+	218931.i	0.0624648	+	0.108192i
$334$	−6.07663e6			−2.98055
$335$	−899028.			−0.437685
$336$	−3.98627e6	−	6.90442e6i	−1.92628	−	3.33641i
$337$	772353.	−	1.33776e6i	0.370460	−	0.641655i	−0.619176	−	0.785252i	$-0.712533\pi$
$337$	772353.	−	1.33776e6i	0.370460	−	0.641655i	0.989636	+	0.143597i	$0.0458667\pi$
$338$	−2.07169e6	−	3.58827e6i	−0.986354	−	1.70842i
$339$	−414409.	+	717778.i	−0.195853	+	0.339227i
$340$	53750.5	−	93098.6i	0.0252165	−	0.0436763i
$341$	−1.98563e6			−0.924726
$342$	−2.44682e6	−	725202.i	−1.13119	−	0.335269i
$343$	−458755.			−0.210545
$344$	241933.	−	419040.i	0.110230	−	0.190924i
$345$	−94562.5	+	163787.i	−0.0427731	+	0.0740852i
$346$	−1.92298e6	−	3.33071e6i	−0.863546	−	1.49571i
$347$	−2.11590e6	+	3.66484e6i	−0.943346	+	1.63392i	−0.184316	+	0.982867i	$0.559007\pi$
$347$	−2.11590e6	+	3.66484e6i	−0.943346	+	1.63392i	−0.759029	+	0.651056i	$0.774326\pi$
$348$	278521.	+	482413.i	0.123285	+	0.213536i
$349$	−2.90552e6			−1.27691			−0.638456	−	0.769658i	$-0.720427\pi$
$349$	−2.90552e6			−1.27691			−0.638456	+	0.769658i	$0.720427\pi$
$350$	5.57875e6			2.43426
$351$	−11881.4	−	20579.1i	−0.00514752	−	0.00891577i
$352$	4.61006e6	+	7.98486e6i	1.98312	+	3.43487i
$353$	4.08408e6			1.74445			0.872223	−	0.489109i	$-0.162678\pi$
$353$	4.08408e6			1.74445			0.872223	+	0.489109i	$0.162678\pi$
$354$	2.01117e6			0.852982
$355$	206455.	+	357590.i	0.0869469	+	0.150597i
$356$	2.29695e6	−	3.97844e6i	0.960565	−	1.66375i
$357$	−59728.2	−	103452.i	−0.0248033	−	0.0429606i
$358$	3.11225e6	−	5.39058e6i	1.28342	−	2.22294i
$359$	−235532.	+	407954.i	−0.0964527	+	0.167061i	−0.910214	−	0.414138i	$-0.864083\pi$
$359$	−235532.	+	407954.i	−0.0964527	+	0.167061i	0.813761	+	0.581199i	$0.197416\pi$
$360$	−1.66191e6			−0.675851
$361$	2.07620e6	+	1.34924e6i	0.838498	+	0.544905i
$362$	2.91196e6			1.16792
$363$	313061.	−	542237.i	0.124699	−	0.215985i
$364$	50456.7	−	87393.6i	0.0199602	−	0.0345721i
$365$	42066.7	+	72861.6i	0.0165275	+	0.0286264i
$366$	1.71317e6	−	2.96729e6i	0.668493	−	1.15786i
$367$	−2.09969e6	−	3.63678e6i	−0.813750	−	1.40946i	−0.910222	−	0.414121i	$-0.864089\pi$
$367$	−2.09969e6	−	3.63678e6i	−0.813750	−	1.40946i	0.0964721	−	0.995336i	$-0.469244\pi$
$368$	−5.18010e6			−1.99397
$369$	1.83414e6			0.701241
$370$	−164270.	−	284524.i	−0.0623813	−	0.108048i
$371$	1.23959e6	+	2.14704e6i	0.467567	+	0.809850i
$372$	−5.81118e6			−2.17724
$373$	956752.			0.356064			0.178032	−	0.984025i	$-0.443027\pi$
$373$	956752.			0.356064			0.178032	+	0.984025i	$0.443027\pi$
$374$	119718.	+	207358.i	0.0442569	+	0.0766552i
$375$	−498699.	+	863772.i	−0.183130	+	0.317191i
$376$	−1.31445e6	−	2.27670e6i	−0.479485	−	0.830493i
$377$	−1885.15	+	3265.18i	−0.000683113	+	0.00118319i
$378$	−3.77129e6	+	6.53207e6i	−1.35757	+	2.35137i
$379$	406038.			0.145201			0.0726003	−	0.997361i	$-0.476870\pi$
$379$	406038.			0.145201			0.0726003	+	0.997361i	$0.476870\pi$
$380$	2.36295e6	+	700344.i	0.839451	+	0.248801i
$381$	2.62485e6			0.926388
$382$	3.86396e6	−	6.69258e6i	1.35480	−	2.34658i
$383$	−1.26069e6	+	2.18357e6i	−0.439148	+	0.760626i	−0.997624	−	0.0688945i	$-0.978053\pi$
$383$	−1.26069e6	+	2.18357e6i	−0.439148	+	0.760626i	0.558476	+	0.829520i	$0.311386\pi$
$384$	5.40729e6	+	9.36571e6i	1.87134	+	3.24125i
$385$	465703.	−	806621.i	0.160124	−	0.277343i
$386$	4.63949e6	+	8.03584e6i	1.58490	+	2.74513i
$387$	−104040.			−0.0353122
$388$	−6.90658e6			−2.32908
$389$	−2.04526e6	−	3.54249e6i	−0.685290	−	1.18696i	−0.973346	−	0.229343i	$-0.926342\pi$
$389$	−2.04526e6	−	3.54249e6i	−0.685290	−	1.18696i	0.288055	−	0.957614i	$-0.406991\pi$
$390$	5778.43	+	10008.5i	0.00192375	+	0.00333203i
$391$	−77616.0			−0.0256749
$392$	−9.59809e6			−3.15479
$393$	813911.	+	1.40974e6i	0.265825	+	0.460422i
$394$	−4.24198e6	+	7.34733e6i	−1.37667	+	2.38446i
$395$	556800.	+	964406.i	0.179559	+	0.311005i
$396$	2.10204e6	−	3.64085e6i	0.673603	−	1.16671i
$397$	1.28312e6	−	2.22244e6i	0.408594	−	0.707706i	−0.586138	−	0.810211i	$-0.699352\pi$
$397$	1.28312e6	−	2.22244e6i	0.408594	−	0.707706i	0.994732	+	0.102505i	$0.0326858\pi$
$398$	9.09827e6			2.87906
$399$	1.98684e6	−	1.88484e6i	0.624784	−	0.592710i
$400$	−1.30034e7			−4.06357
$401$	−1.85727e6	+	3.21689e6i	−0.576785	+	0.999021i	0.419060	+	0.907958i	$0.362360\pi$
$401$	−1.85727e6	+	3.21689e6i	−0.576785	+	0.999021i	−0.995845	+	0.0910626i	$0.970974\pi$
$402$	2.93012e6	−	5.07512e6i	0.904318	−	1.56632i
$403$	−19666.3	−	34063.0i	−0.00603197	−	0.0104477i
$404$	6.89337e6	−	1.19397e7i	2.10125	−	3.63948i
$405$	−22164.4	−	38389.9i	−0.00671458	−	0.0116300i
$406$	1.19674e6			0.360317
$407$	543758.			0.162712
$408$	229234.	+	397044.i	0.0681754	+	0.118083i
$409$	969815.	+	1.67977e6i	0.286669	+	0.496525i	0.973013	−	0.230752i	$-0.0741187\pi$
$409$	969815.	+	1.67977e6i	0.286669	+	0.496525i	−0.686344	+	0.727277i	$0.740785\pi$
$410$	−2.38367e6			−0.700304
$411$	−2.10060e6			−0.613394
$412$	5.06791e6	+	8.77788e6i	1.47091	+	2.54769i
$413$	1.60535e6	−	2.78055e6i	0.463121	−	0.802149i
$414$	916987.	+	1.58827e6i	0.262944	+	0.455432i
$415$	−725739.	+	1.25702e6i	−0.206852	+	0.358279i
$416$	−91318.6	+	158168.i	−0.0258718	+	0.0448112i
$417$	1.27487e6			0.359026
$418$	−3.98238e6	+	3.77794e6i	−1.11481	+	1.05758i
$419$	−268276.			−0.0746530			−0.0373265	−	0.999303i	$-0.511884\pi$
$419$	−268276.			−0.0746530			−0.0373265	+	0.999303i	$0.511884\pi$
$420$	1.36293e6	−	2.36067e6i	0.377008	−	0.652998i
$421$	−462360.	+	800831.i	−0.127138	+	0.220209i	−0.922567	−	0.385838i	$-0.873912\pi$
$421$	−462360.	+	800831.i	−0.127138	+	0.220209i	0.795429	+	0.606047i	$0.207246\pi$
$422$	−3.24648e6	−	5.62307e6i	−0.887425	−	1.53707i
$423$	−282632.	+	489534.i	−0.0768017	+	0.133025i
$424$	−4.75749e6	−	8.24021e6i	−1.28518	−	2.22599i
$425$	−194837.			−0.0523237
$426$	−2.69152e6			−0.718578
$427$	−2.73496e6	−	4.73710e6i	−0.725908	−	1.25731i
$428$	−1.95595e6	−	3.38781e6i	−0.516118	−	0.893943i
$429$	−19127.5			−0.00501781
$430$	135212.			0.0352650
$431$	−700139.	−	1.21268e6i	−0.181548	−	0.314450i	0.760860	−	0.648916i	$-0.224777\pi$
$431$	−700139.	−	1.21268e6i	−0.181548	−	0.314450i	−0.942408	+	0.334466i	$0.891444\pi$
$432$	8.79045e6	−	1.52255e7i	2.26622	−	3.92521i
$433$	884515.	+	1.53202e6i	0.226718	+	0.392686i	0.956833	−	0.290637i	$-0.0938672\pi$
$433$	884515.	+	1.53202e6i	0.226718	+	0.392686i	−0.730116	+	0.683323i	$0.760534\pi$
$434$	−6.24232e6	+	1.08120e7i	−1.59082	+	2.75539i
$435$	−50921.5	+	88198.7i	−0.0129026	+	0.0223480i
$436$	−2.97837e6			−0.750348
$437$	−415121.	−	1.73031e6i	−0.103985	−	0.433432i
$438$	−548417.			−0.136592
$439$	−2.20550e6	+	3.82004e6i	−0.546193	+	0.946033i	0.452338	+	0.891846i	$0.350590\pi$
$439$	−2.20550e6	+	3.82004e6i	−0.546193	+	0.946033i	−0.998531	+	0.0541868i	$0.982743\pi$
$440$	−1.78734e6	+	3.09577e6i	−0.440125	+	0.762318i
$441$	1.03189e6	+	1.78728e6i	0.252659	+	0.437619i
$442$	−2371.44	+	4107.46i	−0.000577374	+	0.00100004i
$443$	−1.67901e6	−	2.90814e6i	−0.406485	−	0.704053i	0.588008	−	0.808855i	$-0.299912\pi$
$443$	−1.67901e6	−	2.90814e6i	−0.406485	−	0.704053i	−0.994493	+	0.104802i	$0.966579\pi$
$444$	1.59137e6			0.383102
$445$	839894.			0.201059
$446$	1.75837e6	+	3.04558e6i	0.418574	+	0.724992i
$447$	−113195.	−	196060.i	−0.0267953	−	0.0464108i
$448$	3.21584e7			7.57005
$449$	4.89289e6			1.14538			0.572691	−	0.819772i	$-0.305900\pi$
$449$	4.89289e6			1.14538			0.572691	+	0.819772i	$0.305900\pi$
$450$	2.30188e6	+	3.98697e6i	0.535860	+	0.928137i
$451$	1.97257e6	−	3.41660e6i	0.456659	−	0.790957i
$452$	−3.88085e6	−	6.72183e6i	−0.893472	−	1.54754i
$453$	789110.	−	1.36678e6i	0.180672	−	0.312934i
$454$	−5.31191e6	+	9.20049e6i	−1.20951	+	2.09494i
$455$	18449.8			0.00417795
$456$	−7.62537e6	+	7.23391e6i	−1.71731	+	1.62915i
$457$	−3.61785e6			−0.810327			−0.405164	−	0.914244i	$-0.632785\pi$
$457$	−3.61785e6			−0.810327			−0.405164	+	0.914244i	$0.632785\pi$
$458$	−6.24471e6	+	1.08161e7i	−1.39107	+	2.40940i
$459$	131712.	−	228131.i	0.0291805	−	0.0505421i
$460$	−885556.	−	1.53383e6i	−0.195129	−	0.337973i
$461$	−1.19709e6	+	2.07341e6i	−0.262345	+	0.454395i	−0.966865	−	0.255290i	$-0.917829\pi$
$461$	−1.19709e6	+	2.07341e6i	−0.262345	+	0.454395i	0.704520	+	0.709685i	$0.251163\pi$
$462$	3.03565e6	+	5.25790e6i	0.661678	+	1.14606i
$463$	3.90876e6			0.847397			0.423699	−	0.905803i	$-0.360732\pi$
$463$	3.90876e6			0.847397			0.423699	+	0.905803i	$0.360732\pi$
$464$	−2.78947e6			−0.601487
$465$	−531223.	−	920106.i	−0.113932	−	0.197336i
$466$	−1.41310e6	−	2.44755e6i	−0.301444	−	0.522116i
$467$	−4.66071e6			−0.988918			−0.494459	−	0.869201i	$-0.664634\pi$
$467$	−4.66071e6			−0.988918			−0.494459	+	0.869201i	$0.664634\pi$
$468$	83276.9			0.0175756
$469$	−4.67776e6	−	8.10212e6i	−0.981987	−	1.70085i
$470$	367312.	−	636202.i	0.0766990	−	0.132847i
$471$	2.14851e6	+	3.72133e6i	0.446258	+	0.772941i
$472$	−6.16124e6	+	1.06716e7i	−1.27296	+	2.20482i
$473$	−111893.	+	193804.i	−0.0229958	+	0.0398300i
$474$	−7.25892e6			−1.48397
$475$	−1.04206e6	−	4.34354e6i	−0.211914	−	0.883303i
$476$	1.11868e6			0.226303
$477$	−1.02295e6	+	1.77180e6i	−0.205854	+	0.356549i
$478$	6.94853e6	−	1.20352e7i	1.39099	−	2.40926i
$479$	2.05866e6	+	3.56571e6i	0.409965	+	0.710080i	0.994885	−	0.101011i	$-0.0322077\pi$
$479$	2.05866e6	+	3.56571e6i	0.409965	+	0.710080i	−0.584921	+	0.811091i	$0.698874\pi$
$480$	−2.46669e6	+	4.27243e6i	−0.488665	+	0.846393i
$481$	5385.53	+	9328.01i	0.00106137	+	0.00183834i
$482$	1.71896e7			3.37015
$483$	−1.96808e6			−0.383862
$484$	2.93174e6	+	5.07793e6i	0.568869	+	0.985311i
$485$	−631358.	−	1.09354e6i	−0.121877	−	0.211097i
$486$	−1.01195e7			−1.94342
$487$	−4.37614e6			−0.836120			−0.418060	−	0.908419i	$-0.637290\pi$
$487$	−4.37614e6			−0.836120			−0.418060	+	0.908419i	$0.637290\pi$
$488$	1.04966e7	+	1.81807e7i	1.99526	+	3.45590i
$489$	−349018.	+	604517.i	−0.0660049	+	0.114324i
$490$	−1.34105e6	−	2.32277e6i	−0.252322	−	0.437034i
$491$	2.40784e6	−	4.17050e6i	0.450737	−	0.780699i	−0.547695	−	0.836678i	$-0.684495\pi$
$491$	2.40784e6	−	4.17050e6i	0.450737	−	0.780699i	0.998432	+	0.0559787i	$0.0178279\pi$
$492$	5.77296e6	−	9.99907e6i	1.07519	−	1.86229i
$493$	−41795.9			−0.00774492
$494$	−104252.	−	30898.8i	−0.0192206	−	0.00569671i
$495$	768625.			0.140994
$496$	1.45501e7	−	2.52016e7i	2.65560	−	4.59964i
$497$	−2.14842e6	+	3.72118e6i	−0.390147	+	0.675755i
$498$	−4.73068e6	−	8.19377e6i	−0.854772	−	1.48051i
$499$	1.06630e6	−	1.84688e6i	0.191703	−	0.332038i	−0.754112	−	0.656746i	$-0.771932\pi$
$499$	1.06630e6	−	1.84688e6i	0.191703	−	0.332038i	0.945815	+	0.324707i	$0.105266\pi$
$500$	−4.67020e6	−	8.08903e6i	−0.835431	−	1.44701i
$501$	5.38132e6			0.957843
$502$	1.35837e7			2.40580
$503$	−2.27977e6	−	3.94869e6i	−0.401765	−	0.695877i	0.592174	−	0.805810i	$-0.298270\pi$
$503$	−2.27977e6	−	3.94869e6i	−0.401765	−	0.695877i	−0.993939	+	0.109933i	$0.964936\pi$
$504$	−8.64713e6	−	1.49773e7i	−1.51634	−	2.62637i
$505$	2.52060e6			0.439821
$506$	3.94478e6			0.684931
$507$	1.83464e6	+	3.17768e6i	0.316979	+	0.549023i
$508$	−1.22906e7	+	2.12879e7i	−2.11307	+	3.65994i
$509$	3.77680e6	+	6.54161e6i	0.646145	+	1.11916i	0.984036	+	0.177970i	$0.0569531\pi$
$509$	3.77680e6	+	6.54161e6i	0.646145	+	1.11916i	−0.337891	+	0.941185i	$0.609714\pi$
$510$	−64057.2	+	110950.i	−0.0109054	+	0.0188887i
$511$	−437757.	+	758217.i	−0.0741618	+	0.128452i
$512$	−3.60557e7			−6.07854
$513$	5.79023e6	+	1.71614e6i	0.971410	+	0.287912i
$514$	2.67586e6			0.446741
$515$	−926556.	+	1.60484e6i	−0.153941	+	0.266633i
$516$	−327467.	+	567189.i	−0.0541431	+	0.0937786i
$517$	607928.	+	1.05296e6i	0.100029	+	0.173255i
$518$	1.70944e6	−	2.96083e6i	0.279917	−	0.484830i
$519$	1.70295e6	+	2.94959e6i	0.277513	+	0.480666i
$520$	−70809.3			−0.0114837
$521$	2.19611e6			0.354453			0.177227	−	0.984170i	$-0.443287\pi$
$521$	2.19611e6			0.354453			0.177227	+	0.984170i	$0.443287\pi$
$522$	493794.	+	855277.i	0.0793176	+	0.137382i
$523$	622106.	+	1.07752e6i	0.0994513	+	0.172255i	0.911458	−	0.411394i	$-0.134958\pi$
$523$	622106.	+	1.07752e6i	0.0994513	+	0.172255i	−0.812006	+	0.583649i	$0.801625\pi$
$524$	−1.52442e7			−2.42536
$525$	−4.94041e6			−0.782284
$526$	−7.48713e6	−	1.29681e7i	−1.17992	−	2.04367i
$527$	218012.	−	377608.i	0.0341943	−	0.0592262i
$528$	−7.07575e6	−	1.22556e7i	−1.10456	−	1.91315i
$529$	2.57880e6	−	4.46661e6i	0.400662	−	0.693967i
$530$	1.32943e6	−	2.30265e6i	0.205578	−	0.356072i
$531$	2.64957e6			0.407792
$532$	5.98316e6	+	2.49391e7i	0.916541	+	3.82033i
$533$	78147.7			0.0119151
$534$	−2.73739e6	+	4.74130e6i	−0.415417	+	0.719523i
$535$	357603.	−	619386.i	0.0540153	−	0.0935572i
$536$	1.79530e7	+	3.10955e7i	2.69913	+	4.67504i
$537$	−2.75614e6	+	4.77377e6i	−0.412444	+	0.714374i
$538$	−8.51898e6	−	1.47553e7i	−1.26891	−	2.19782i
$539$	4.43907e6			0.658143
$540$	6.01103e6			0.887083
$541$	−2.30502e6	−	3.99241e6i	−0.338595	−	0.586464i	0.645573	−	0.763698i	$-0.276618\pi$
$541$	−2.30502e6	−	3.99241e6i	−0.338595	−	0.586464i	−0.984169	+	0.177234i	$0.943285\pi$
$542$	820460.	+	1.42108e6i	0.119966	+	0.207788i
$543$	−2.57876e6			−0.375328
$544$	−2.02464e6			−0.293326
$545$	−272265.	−	471576.i	−0.0392645	−	0.0680081i
$546$	−60131.8	+	104151.i	−0.00863222	+	0.0149515i
$547$	3.71337e6	+	6.43174e6i	0.530639	+	0.919095i	0.999361	+	0.0357485i	$0.0113815\pi$
$547$	3.71337e6	+	6.43174e6i	0.530639	+	0.919095i	−0.468721	+	0.883346i	$0.655285\pi$
$548$	9.83583e6	−	1.70362e7i	1.39914	−	2.42337i
$549$	2.25698e6	−	3.90920e6i	0.319592	−	0.553550i
$550$	9.90245e6			1.39584
$551$	−223541.	−	931767.i	−0.0313674	−	0.130746i
$552$	7.55339e6			1.05510
$553$	−5.79420e6	+	1.00359e7i	−0.805714	+	1.39554i
$554$	5.03780e6	−	8.72573e6i	0.697375	−	1.20789i
$555$	145474.	+	251968.i	0.0200471	+	0.0347226i
$556$	−5.96944e6	+	1.03394e7i	−0.818930	+	1.41843i
$557$	−3.57629e6	−	6.19432e6i	−0.488422	−	0.845971i	0.511490	−	0.859289i	$-0.329094\pi$
$557$	−3.57629e6	−	6.19432e6i	−0.488422	−	0.845971i	−0.999911	+	0.0133185i	$0.995760\pi$
$558$	−1.03027e7			−1.40077
$559$	−4432.87			−0.000600005
$560$	6.82506e6	+	1.18214e7i	0.919680	+	1.59293i
$561$	−106019.	−	183631.i	−0.0142226	−	0.0246342i
$562$	8.63566e6			1.15333
$563$	3.48106e6			0.462850			0.231425	−	0.972853i	$-0.425661\pi$
$563$	3.48106e6			0.462850			0.231425	+	0.972853i	$0.425661\pi$
$564$	1.77917e6	+	3.08161e6i	0.235516	+	0.407925i
$565$	709528.	−	1.22894e6i	0.0935079	−	0.161960i
$566$	−1.09389e7	−	1.89467e7i	−1.43527	−	2.48596i
$567$	230649.	−	399495.i	0.0301296	−	0.0521860i
$568$	8.24552e6	−	1.42817e7i	1.07238	−	1.85741i
$569$	−1.19166e7			−1.54302			−0.771508	−	0.636219i	$-0.780497\pi$
$569$	−1.19166e7			−1.54302			−0.771508	+	0.636219i	$0.780497\pi$
$570$	−2.81604e6	−	834635.i	−0.363038	−	0.107599i
$571$	6.13068e6			0.786898			0.393449	−	0.919346i	$-0.371282\pi$
$571$	6.13068e6			0.786898			0.393449	+	0.919346i	$0.371282\pi$
$572$	89562.2	−	155126.i	0.0114455	−	0.0198242i
$573$	−3.42183e6	+	5.92679e6i	−0.435384	+	0.754106i
$574$	−1.24025e7	−	2.14818e7i	−1.57120	−	2.72139i
$575$	−1.60500e6	+	2.77994e6i	−0.202444	+	0.350643i
$576$	1.32690e7	+	2.29826e7i	1.66642	+	2.88632i
$577$	3.40578e6			0.425871			0.212935	−	0.977066i	$-0.431698\pi$
$577$	3.40578e6			0.425871			0.212935	+	0.977066i	$0.431698\pi$
$578$	1.57937e7			1.96637
$579$	−4.10862e6	−	7.11634e6i	−0.509330	−	0.882186i
$580$	−476869.	−	825961.i	−0.0588611	−	0.101950i
$581$	−1.51045e7			−1.85637
$582$	8.23092e6			1.00726
$583$	2.20031e6	+	3.81105e6i	0.268110	+	0.464380i
$584$	1.68008e6	−	2.90999e6i	0.203845	−	0.353069i
$585$	7612.67	+	13185.5i	0.000919703	+	0.00159297i
$586$	−1.05570e7	+	1.82852e7i	−1.26998	+	2.19967i
$587$	−6.76416e6	+	1.17159e7i	−0.810250	+	1.40339i	0.102440	+	0.994739i	$0.467335\pi$
$587$	−6.76416e6	+	1.17159e7i	−0.810250	+	1.40339i	−0.912689	+	0.408654i	$0.865998\pi$
$588$	1.29914e7			1.54958
$589$	9.58410e6	+	2.84059e6i	1.13832	+	0.337381i
$590$	−3.44340e6			−0.407247
$591$	3.75660e6	−	6.50662e6i	0.442411	−	0.766278i
$592$	−3.98450e6	+	6.90135e6i	−0.467272	+	0.809338i
$593$	−5.66888e6	−	9.81879e6i	−0.662004	−	1.14662i	−0.980088	−	0.198562i	$-0.936373\pi$
$593$	−5.66888e6	−	9.81879e6i	−0.662004	−	1.14662i	0.318085	−	0.948062i	$-0.396960\pi$
$594$	−6.69416e6	+	1.15946e7i	−0.778449	+	1.34831i
$595$	102263.	+	177125.i	0.0118421	+	0.0205111i
$596$	2.12009e6			0.244478
$597$	−8.05720e6			−0.925227
$598$	39070.2	+	67671.6i	0.00446779	+	0.00773844i
$599$	1.21645e6	+	2.10696e6i	0.138525	+	0.239932i	0.926939	−	0.375213i	$-0.122431\pi$
$599$	1.21645e6	+	2.10696e6i	0.138525	+	0.239932i	−0.788413	+	0.615146i	$0.789097\pi$
$600$	1.89610e7			2.15022
$601$	−9.54225e6			−1.07762			−0.538809	−	0.842428i	$-0.681125\pi$
$601$	−9.54225e6			−1.07762			−0.538809	+	0.842428i	$0.681125\pi$
$602$	703524.	+	1.21854e6i	0.0791203	+	0.137040i
$603$	3.86023e6	−	6.68612e6i	0.432335	−	0.748826i
$604$	7.38983e6	+	1.27996e7i	0.824218	+	1.42759i
$605$	−536005.	+	928388.i	−0.0595361	+	0.103120i
$606$	−8.21518e6	+	1.42291e7i	−0.908732	+	1.57397i
$607$	1.52336e6			0.167815			0.0839077	−	0.996474i	$-0.473260\pi$
$607$	1.52336e6			0.167815			0.0839077	+	0.996474i	$0.473260\pi$
$608$	−1.08286e7	−	4.51357e7i	−1.18799	−	4.95178i
$609$	−1.05980e6			−0.115793
$610$	−2.93319e6	+	5.08043e6i	−0.319165	+	0.552810i
$611$	−12042.2	+	20857.6i	−0.00130497	+	0.00226028i
$612$	461586.	+	799490.i	0.0498166	+	0.0862849i
$613$	−472665.	+	818680.i	−0.0508045	+	0.0879960i	−0.890309	−	0.455356i	$-0.849512\pi$
$613$	−472665.	+	818680.i	−0.0508045	+	0.0879960i	0.839505	+	0.543352i	$0.182845\pi$
$614$	5.93815e6	+	1.02852e7i	0.635668	+	1.10101i
$615$	2.11092e6			0.225052
$616$	−3.71991e7			−3.94985
$617$	−333050.	−	576860.i	−0.0352206	−	0.0610039i	0.847878	−	0.530192i	$-0.177880\pi$
$617$	−333050.	−	576860.i	−0.0352206	−	0.0610039i	−0.883098	+	0.469188i	$0.844547\pi$
$618$	−6.03969e6	−	1.04610e7i	−0.636126	−	1.10180i
$619$	1.10975e7			1.16413			0.582063	−	0.813144i	$-0.302246\pi$
$619$	1.10975e7			1.16413			0.582063	+	0.813144i	$0.302246\pi$
$620$	9.94957e6			1.03950
$621$	−2.16999e6	−	3.75853e6i	−0.225802	−	0.391101i
$622$	630162.	−	1.09147e6i	0.0653095	−	0.113119i
$623$	4.37008e6	+	7.56919e6i	0.451096	+	0.781321i
$624$	140160.	−	242765.i	0.0144100	−	0.0249588i
$625$	−3.58155e6	+	6.20342e6i	−0.366750	+	0.635230i
$626$	1.44732e7			1.47615
$627$	3.52669e6	−	3.34565e6i	0.358261	−	0.339869i
$628$	−4.02407e7			−4.07161
$629$	−59701.7	+	103406.i	−0.00601672	+	0.0104213i
$630$	2.41636e6	−	4.18526e6i	0.242555	−	0.420118i
$631$	−175691.	−	304305.i	−0.0175661	−	0.0304254i	0.857109	−	0.515136i	$-0.172258\pi$
$631$	−175691.	−	304305.i	−0.0175661	−	0.0304254i	−0.874675	+	0.484710i	$0.838925\pi$
$632$	2.22378e7	−	3.85170e7i	2.21462	−	3.83584i
$633$	2.87500e6	+	4.97965e6i	0.285187	+	0.493958i
$634$	−1.56379e7			−1.54509
$635$	−4.49412e6			−0.442294
$636$	6.43947e6	+	1.11535e7i	0.631258	+	1.09337i
$637$	43965.8	+	76151.0i	0.00429305	+	0.00743578i
$638$	2.12425e6			0.206611
$639$	−3.54589e6			−0.343537
$640$	−9.25806e6	−	1.60354e7i	−0.893449	−	1.54750i
$641$	8.34408e6	−	1.44524e7i	0.802109	−	1.38929i	−0.116116	−	0.993236i	$-0.537045\pi$
$641$	8.34408e6	−	1.44524e7i	0.802109	−	1.38929i	0.918225	−	0.396058i	$-0.129622\pi$
$642$	2.33101e6	+	4.03742e6i	0.223206	+	0.386604i
$643$	−2.15111e6	+	3.72582e6i	−0.205180	+	0.355382i	−0.950190	−	0.311671i	$-0.899111\pi$
$643$	−2.15111e6	+	3.72582e6i	−0.205180	+	0.355382i	0.745010	+	0.667053i	$0.232445\pi$
$644$	9.21532e6	−	1.59614e7i	0.875580	−	1.51655i
$645$	−119740.			−0.0113329
$646$	−281206.	−	1.17212e6i	−0.0265120	−	0.110508i
$647$	7.81390e6			0.733850			0.366925	−	0.930251i	$-0.380411\pi$
$647$	7.81390e6			0.733850			0.366925	+	0.930251i	$0.380411\pi$
$648$	−885216.	+	1.53324e6i	−0.0828156	+	0.143441i
$649$	2.84954e6	−	4.93556e6i	0.265561	−	0.459964i
$650$	98076.6	+	169874.i	0.00910504	+	0.0157704i
$651$	5.52805e6	−	9.57486e6i	0.511233	−	0.885482i
$652$	−3.26848e6	−	5.66117e6i	−0.301111	−	0.521539i
$653$	−4.96926e6			−0.456046			−0.228023	−	0.973656i	$-0.573226\pi$
$653$	−4.96926e6			−0.456046			−0.228023	+	0.973656i	$0.573226\pi$
$654$	3.54948e6			0.324504
$655$	−1.39353e6	−	2.41367e6i	−0.126915	−	0.219824i
$656$	2.89089e7	+	5.00717e7i	2.62284	+	4.54289i
$657$	−722501.			−0.0653018
$658$	7.64468e6			0.688326
$659$	3.77321e6	+	6.53539e6i	0.338452	+	0.586217i	0.984142	−	0.177383i	$-0.0567632\pi$
$659$	3.77321e6	+	6.53539e6i	0.338452	+	0.586217i	−0.645689	+	0.763600i	$0.723430\pi$
$660$	2.41925e6	−	4.19026e6i	0.216182	−	0.374439i
$661$	2.14695e6	+	3.71862e6i	0.191125	+	0.331039i	0.945623	−	0.325264i	$-0.105453\pi$
$661$	2.14695e6	+	3.71862e6i	0.191125	+	0.331039i	−0.754498	+	0.656302i	$0.772120\pi$
$662$	−7.36737e6	+	1.27607e7i	−0.653382	+	1.13169i
$663$	2100.09	−	3637.46i	0.000185547	−	0.000321377i
$664$	5.79701e7			5.10251
$665$	−3.40175e6	+	3.22711e6i	−0.298296	+	0.282983i
$666$	2.82136e6			0.246475
$667$	−344300.	+	596346.i	−0.0299656	+	0.0519019i
$668$	−2.51974e7	+	4.36432e7i	−2.18481	+	3.78421i
$669$	−1.55717e6	−	2.69709e6i	−0.134515	−	0.232986i
$670$	−5.01679e6	+	8.68934e6i	−0.431757	+	0.747824i
$671$	−4.85464e6	−	8.40849e6i	−0.416247	−	0.720961i
$672$	−5.13380e7			−4.38547
$673$	2.28177e7			1.94193			0.970967	−	0.239214i	$-0.0768899\pi$
$673$	2.28177e7			1.94193			0.970967	+	0.239214i	$0.0768899\pi$
$674$	−8.61983e6	−	1.49300e7i	−0.730885	−	1.26593i
$675$	−5.44725e6	−	9.43491e6i	−0.460169	−	0.797037i
$676$	−3.43619e7			−2.89208
$677$	−3.04235e6			−0.255116			−0.127558	−	0.991831i	$-0.540714\pi$
$677$	−3.04235e6			−0.255116			−0.127558	+	0.991831i	$0.540714\pi$
$678$	4.62501e6	+	8.01074e6i	0.386401	+	0.669266i
$679$	6.57007e6	−	1.13797e7i	0.546885	−	0.947232i
$680$	−392481.	−	679796.i	−0.0325496	−	0.0563776i
$681$	4.70409e6	−	8.14773e6i	0.388694	−	0.673238i
$682$	−1.10803e7	+	1.91917e7i	−0.912202	+	1.57998i
$683$	1.38261e7			1.13409			0.567047	−	0.823685i	$-0.308086\pi$
$683$	1.38261e7			1.13409			0.567047	+	0.823685i	$0.308086\pi$
$684$	−1.53545e7	+	1.45662e7i	−1.25486	+	1.19044i
$685$	3.59653e6			0.292858
$686$	−2.55996e6	+	4.43399e6i	−0.207694	+	0.359736i
$687$	5.53016e6	−	9.57851e6i	0.447039	−	0.774295i
$688$	−1.63983e6	−	2.84028e6i	−0.132077	−	0.228765i
$689$	−43585.0	+	75491.5i	−0.00349775	+	0.00605829i
$690$	1.05536e6	+	1.82794e6i	0.0843876	+	0.146164i
$691$	−1.29633e7			−1.03281			−0.516404	−	0.856345i	$-0.672730\pi$
$691$	−1.29633e7			−1.03281			−0.516404	+	0.856345i	$0.672730\pi$
$692$	−3.18954e7			−2.53200
$693$	3.99925e6	+	6.92691e6i	0.316334	+	0.547907i
$694$	2.36144e7	+	4.09014e7i	1.86114	+	3.22359i
$695$	−2.18276e6			−0.171413
$696$	4.06747e6			0.318274
$697$	433156.	+	750248.i	0.0337724	+	0.0584956i
$698$	−1.62135e7	+	2.80826e7i	−1.25962	+	2.18172i
$699$	1.25140e6	+	2.16749e6i	0.0968733	+	0.167789i
$700$	2.31329e7	−	4.00673e7i	1.78437	−	3.09062i
$701$	6.62194e6	−	1.14695e7i	0.508968	−	0.881558i	−0.490979	−	0.871172i	$-0.663361\pi$
$701$	6.62194e6	−	1.14695e7i	0.508968	−	0.881558i	0.999946	−	0.0103860i	$-0.00330601\pi$
$702$	−265203.			−0.0203112
$703$	−2.62457e6	−	777885.i	−0.200295	−	0.0593646i
$704$	5.70820e7			4.34078
$705$	−325282.	+	563405.i	−0.0246483	+	0.0426921i
$706$	2.27901e7	−	3.94737e7i	1.72082	−	2.98054i
$707$	1.31150e7	+	2.27159e7i	0.986780	+	1.70915i
$708$	8.33951e6	−	1.44445e7i	0.625256	−	1.08297i
$709$	1.11284e7	+	1.92750e7i	0.831415	+	1.44005i	0.896916	+	0.442200i	$0.145802\pi$
$709$	1.11284e7	+	1.92750e7i	0.831415	+	1.44005i	−0.0655015	+	0.997852i	$0.520865\pi$
$710$	4.60827e6			0.343077
$711$	−9.56312e6			−0.709456
$712$	−1.67721e7	−	2.90501e7i	−1.23990	−	2.14757i
$713$	−3.59181e6	−	6.22120e6i	−0.264600	−	0.458300i
$714$	−1.33319e6			−0.0978694
$715$	32748.9			0.00239570
$716$	−2.58106e7	−	4.47052e7i	−1.88155	−	3.25894i
$717$	−6.15345e6	+	1.06581e7i	−0.447014	+	0.774250i
$718$	2.62865e6	+	4.55296e6i	0.190293	+	0.329596i
$719$	5.01555e6	−	8.68719e6i	0.361823	−	0.626696i	−0.626438	−	0.779471i	$-0.715488\pi$
$719$	5.01555e6	−	8.68719e6i	0.361823	−	0.626696i	0.988261	+	0.152775i	$0.0488210\pi$
$720$	−5.63226e6	+	9.75535e6i	−0.404903	+	0.701313i
$721$	−1.92840e7			−1.38152
$722$	2.46264e7	−	1.25380e7i	1.75816	−	0.895126i
$723$	−1.52227e7			−1.08304
$724$	1.20748e7	−	2.09141e7i	0.856114	−	1.48283i
$725$	−864285.	+	1.49699e6i	−0.0610678	+	0.105772i
$726$	−3.49391e6	−	6.05163e6i	−0.246020	−	0.426119i
$727$	−1.10058e7	+	1.90626e7i	−0.772300	+	1.33766i	0.164000	+	0.986460i	$0.447560\pi$
$727$	−1.10058e7	+	1.90626e7i	−0.772300	+	1.33766i	−0.936300	+	0.351202i	$0.885773\pi$
$728$	−368430.	−	638139.i	−0.0257648	−	0.0446259i
$729$	9.59810e6			0.668908
$730$	938968.			0.0652144
$731$	−24570.4	−	42557.2i	−0.00170067	−	0.00294564i
$732$	−1.42077e7	−	2.46084e7i	−0.980042	−	1.69748i
$733$	6.67750e6			0.459044			0.229522	−	0.973303i	$-0.426284\pi$
$733$	6.67750e6			0.459044			0.229522	+	0.973303i	$0.426284\pi$
$734$	−4.68672e7			−3.21091
$735$	1.18760e6	+	2.05698e6i	0.0810871	+	0.140447i
$736$	−1.66783e7	+	2.88876e7i	−1.13490	+	1.96570i
$737$	−8.30316e6	−	1.43815e7i	−0.563086	−	0.975294i
$738$	1.02350e7	−	1.77275e7i	0.691744	−	1.19814i
$739$	−3.33247e6	+	5.77201e6i	−0.224469	+	0.388791i	−0.956160	−	0.292845i	$-0.905398\pi$
$739$	−3.33247e6	+	5.77201e6i	−0.224469	+	0.388791i	0.731691	+	0.681636i	$0.238731\pi$
$740$	−2.72465e6			−0.182908
$741$	92322.9	+	27363.2i	0.00617681	+	0.00183072i
$742$	2.76689e7			1.84494
$743$	−1.78225e6	+	3.08694e6i	−0.118439	+	0.205143i	−0.919149	−	0.393909i	$-0.871122\pi$
$743$	−1.78225e6	+	3.08694e6i	−0.118439	+	0.205143i	0.800710	+	0.599052i	$0.204456\pi$
$744$	−2.12163e7	+	3.67478e7i	−1.40520	+	2.43388i
$745$	193806.	+	335682.i	0.0127931	+	0.0221583i
$746$	5.33891e6	−	9.24726e6i	0.351241	−	0.608367i
$747$	−6.23233e6	−	1.07947e7i	−0.408648	−	0.707799i
$748$	1.98570e6			0.129765
$749$	7.44261e6			0.484754
$750$	5.56572e6	+	9.64010e6i	0.361300	+	0.625790i
$751$	783329.	+	1.35677e6i	0.0506809	+	0.0877819i	0.890253	−	0.455466i	$-0.150528\pi$
$751$	783329.	+	1.35677e6i	0.0506809	+	0.0877819i	−0.839572	+	0.543248i	$0.817194\pi$
$752$	−1.78189e7			−1.14904
$753$	−1.20294e7			−0.773138
$754$	21039.2	+	36440.9i	0.00134772	+	0.00233432i
$755$	−1.35107e6	+	2.34012e6i	−0.0862601	+	0.149407i
$756$	3.12761e7	+	5.41719e7i	1.99026	+	3.44722i
$757$	−8.33317e6	+	1.44335e7i	−0.528531	+	0.915442i	0.470916	+	0.882178i	$0.343924\pi$
$757$	−8.33317e6	+	1.44335e7i	−0.528531	+	0.915442i	−0.999447	+	0.0332642i	$0.989410\pi$
$758$	2.26579e6	−	3.92446e6i	0.143234	−	0.248088i
$759$	−3.49340e6			−0.220112
$760$	1.30557e7	−	1.23855e7i	0.819911	−	0.777820i
$761$	−2.47171e7			−1.54716			−0.773582	−	0.633696i	$-0.781537\pi$
$761$	−2.47171e7			−1.54716			−0.773582	+	0.633696i	$0.781537\pi$
$762$	1.46473e7	−	2.53699e7i	0.913840	−	1.58282i
$763$	2.83326e6	−	4.90735e6i	0.176187	−	0.305165i
$764$	−3.20447e7	−	5.55030e7i	−1.98620	−	3.44020i
$765$	−84390.8	+	146169.i	−0.00521365	+	0.00903030i
$766$	1.40699e7	+	2.43697e7i	0.866399	+	1.50065i
$767$	112891.			0.00692899
$768$	6.29383e7			3.85045
$769$	7.10153e6	+	1.23002e7i	0.433048	+	0.750061i	0.997134	−	0.0756547i	$-0.0241047\pi$
$769$	7.10153e6	+	1.23002e7i	0.433048	+	0.750061i	−0.564086	+	0.825716i	$0.690771\pi$
$770$	−5.19747e6	−	9.00227e6i	−0.315911	−	0.547174i
$771$	−2.36968e6			−0.143566
$772$	7.69526e7			4.64708
$773$	−8.15407e6	−	1.41233e7i	−0.490824	−	0.850132i	0.509120	−	0.860695i	$-0.329971\pi$
$773$	−8.15407e6	−	1.41233e7i	−0.490824	−	0.850132i	−0.999944	+	0.0105633i	$0.996638\pi$
$774$	−580570.	+	1.00558e6i	−0.0348339	+	0.0603341i
$775$	−9.01639e6	−	1.56169e7i	−0.539236	−	0.933984i
$776$	−2.52156e7	+	4.36746e7i	−1.50319	+	2.60361i
$777$	−1.51383e6	+	2.62204e6i	−0.0899551	+	0.155807i
$778$	−4.56521e7			−2.70403
$779$	−1.44088e7	+	1.36691e7i	−0.850713	+	0.807041i
$780$	95843.5			0.00564061
$781$	−3.81351e6	+	6.60520e6i	−0.223716	+	0.387488i
$782$	−433116.	+	750179.i	−0.0253272	+	0.0438680i
$783$	−1.16853e6	−	2.02396e6i	−0.0681139	−	0.117977i
$784$	−3.25282e7	+	5.63405e7i	−1.89003	+	3.27364i
$785$	−3.67856e6	−	6.37146e6i	−0.213061	−	0.369032i
$786$	1.81673e7			1.04890
$787$	−4.44825e6			−0.256007			−0.128004	−	0.991774i	$-0.540857\pi$
$787$	−4.44825e6			−0.256007			−0.128004	+	0.991774i	$0.540857\pi$
$788$	3.51797e7	+	6.09330e7i	2.01826	+	3.49572i
$789$	6.63042e6	+	1.14842e7i	0.379183	+	0.656763i
$790$	1.24283e7			0.708507
$791$	1.47671e7			0.839175
$792$	−1.53489e7	−	2.65851e7i	−0.869490	−	1.50600i
$793$	96163.4	−	166560.i	0.00543034	−	0.00940562i
$794$	−1.43203e7	−	2.48034e7i	−0.806120	−	1.39624i
$795$	−1.17731e6	+	2.03917e6i	−0.0660655	+	0.114429i
$796$	3.77269e7	−	6.53450e7i	2.11042	−	3.65535i
$797$	2.15457e7			1.20147			0.600737	−	0.799446i	$-0.294874\pi$
$797$	2.15457e7			1.20147			0.600737	+	0.799446i	$0.294874\pi$
$798$	−7.13044e6	−	2.97211e7i	−0.396377	−	1.65218i
$799$	−266989.			−0.0147954
$800$	−4.18668e7	+	7.25155e7i	−2.31284	+	4.00595i
$801$	−3.60632e6	+	6.24633e6i	−0.198602	+	0.343988i
$802$	2.07280e7	+	3.59020e7i	1.13795	+	1.97098i
$803$	−777031.	+	1.34586e6i	−0.0425255	+	0.0736563i
$804$	−2.43001e7	−	4.20891e7i	−1.32577	−	2.29630i
$805$	3.36964e6			0.183271
$806$	−438970.			−0.0238011
$807$	7.54420e6	+	1.30669e7i	0.407783	+	0.706301i
$808$	−5.03347e7	−	8.71823e7i	−2.71231	−	4.69786i
$809$	2.16577e7			1.16343			0.581716	−	0.813392i	$-0.302382\pi$
$809$	2.16577e7			1.16343			0.581716	+	0.813392i	$0.302382\pi$
$810$	−494731.			−0.0264945
$811$	−5.06833e6	−	8.77861e6i	−0.270591	−	0.468677i	0.698423	−	0.715686i	$-0.253886\pi$
$811$	−5.06833e6	−	8.77861e6i	−0.270591	−	0.468677i	−0.969013	+	0.247009i	$0.920552\pi$
$812$	4.96242e6	−	8.59516e6i	0.264121	−	0.457471i
$813$	−726579.	−	1.25847e6i	−0.0385528	−	0.0667755i
$814$	3.03430e6	−	5.25556e6i	0.160508	−	0.278009i
$815$	597569.	−	1.03502e6i	0.0315133	−	0.0545827i
$816$	3.10751e6			0.163376
$817$	817326.	−	775367.i	0.0428391	−	0.0406399i
$818$	2.16472e7			1.13115
$819$	−79219.4	+	137212.i	−0.00412688	+	0.00714797i
$820$	−9.88414e6	+	1.71198e7i	−0.513339	+	0.889129i
$821$	2.87587e6	+	4.98116e6i	0.148906	+	0.257912i	0.930823	−	0.365469i	$-0.119092\pi$
$821$	2.87587e6	+	4.98116e6i	0.148906	+	0.257912i	−0.781918	+	0.623382i	$0.785758\pi$
$822$	−1.17219e7	+	2.03029e7i	−0.605086	+	1.04804i
$823$	−3.46671e6	−	6.00452e6i	−0.178409	−	0.309014i	0.762926	−	0.646485i	$-0.223762\pi$
$823$	−3.46671e6	−	6.00452e6i	−0.178409	−	0.309014i	−0.941336	+	0.337471i	$0.890428\pi$
$824$	7.40107e7			3.79732
$825$	−8.76937e6			−0.448573
$826$	−1.79165e7	−	3.10322e7i	−0.913697	−	1.58257i
$827$	2.22823e6	+	3.85941e6i	0.113291	+	0.196226i	0.917095	−	0.398668i	$-0.130527\pi$
$827$	2.22823e6	+	3.85941e6i	0.113291	+	0.196226i	−0.803804	+	0.594894i	$0.797194\pi$
$828$	1.52095e7			0.770975
$829$	3.50236e7			1.77000			0.885002	−	0.465587i	$-0.154157\pi$
$829$	3.50236e7			1.77000			0.885002	+	0.465587i	$0.154157\pi$
$830$	8.09960e6	+	1.40289e7i	0.408101	+	0.706852i
$831$	−4.46135e6	+	7.72729e6i	−0.224111	+	0.388172i
$832$	565356.	+	979226.i	0.0283148	+	0.0490427i
$833$	−487386.	+	844177.i	−0.0243366	+	0.0421523i
$834$	7.11408e6	−	1.23220e7i	0.354164	−	0.613429i
$835$	−9.21358e6			−0.457312
$836$	1.06203e7	+	4.42676e7i	0.525558	+	2.19063i
$837$	2.43807e7			1.20291
$838$	−1.49705e6	+	2.59296e6i	−0.0736419	+	0.127552i
$839$	−6.91864e6	+	1.19834e7i	−0.339325	+	0.587728i	−0.984306	−	0.176470i	$-0.943532\pi$
$839$	−6.91864e6	+	1.19834e7i	−0.339325	+	0.587728i	0.644981	+	0.764199i	$0.276865\pi$
$840$	−9.95199e6	−	1.72374e7i	−0.486644	−	0.842893i
$841$	1.00702e7	−	1.74420e7i	0.490961	−	0.850369i
$842$	5.16015e6	+	8.93765e6i	0.250832	+	0.434453i
$843$	−7.64752e6			−0.370640
$844$	−5.38475e7			−2.60201
$845$	−3.14116e6	−	5.44065e6i	−0.151338	−	0.262125i
$846$	3.15431e6	+	5.46343e6i	0.151523	+	0.262446i
$847$	−1.11556e7			−0.534299
$848$	−6.44930e7			−3.07980
$849$	9.68722e6	+	1.67788e7i	0.461243	+	0.798897i
$850$	−1.08724e6	+	1.88315e6i	−0.0516150	+	0.0893999i
$851$	983604.	+	1.70365e6i	0.0465582	+	0.0806412i
$852$	−1.11607e7	+	1.93309e7i	−0.526734	+	0.912331i
$853$	1.09243e7	−	1.89215e7i	0.514070	−	0.890396i	−0.485796	−	0.874072i	$-0.661470\pi$
$853$	1.09243e7	−	1.89215e7i	0.514070	−	0.890396i	0.999867	−	0.0163241i	$-0.00519635\pi$
$854$	−6.10470e7			−2.86431
$855$	−3.70994e6	−	1.09957e6i	−0.173561	−	0.0514409i
$856$	−2.85643e7			−1.33242
$857$	2.12165e7	−	3.67480e7i	0.986781	−	1.70915i	0.353042	−	0.935608i	$-0.385147\pi$
$857$	2.12165e7	−	3.67480e7i	0.986781	−	1.70915i	0.633739	−	0.773547i	$-0.281519\pi$
$858$	−106736.	+	184872.i	−0.00494985	+	0.00857339i
$859$	−1.25019e7	−	2.16539e7i	−0.578085	−	1.00127i	−0.995699	−	0.0926485i	$-0.970467\pi$
$859$	−1.25019e7	−	2.16539e7i	−0.578085	−	1.00127i	0.417613	−	0.908625i	$-0.362867\pi$
$860$	560670.	−	971109.i	0.0258500	−	0.0447736i
$861$	1.09834e7	+	1.90238e7i	0.504926	+	0.874558i
$862$	−1.56278e7			−0.716356
$863$	1.93312e7			0.883552			0.441776	−	0.897125i	$-0.354349\pi$
$863$	1.93312e7			0.883552			0.441776	+	0.897125i	$0.354349\pi$
$864$	−5.66048e7	−	9.80424e7i	−2.57970	−	4.46817i
$865$	−2.91569e6	−	5.05012e6i	−0.132495	−	0.229489i
$866$	1.97432e7			0.894588
$867$	−1.39865e7			−0.631919
$868$	5.17689e7	+	8.96664e7i	2.33222	+	4.03953i
$869$	−1.02849e7	+	1.78139e7i	−0.462009	+	0.800222i
$870$	568308.	+	984339.i	0.0254557	+	0.0440907i
$871$	164474.	−	284877.i	0.00734600	−	0.0127236i
$872$	−1.08739e7	+	1.88341e7i	−0.484276	+	0.838791i
$873$	1.08437e7			0.481549
$874$	−1.90404e7	−	5.64330e6i	−0.843135	−	0.249893i
$875$	1.77706e7			0.784662
$876$	−2.27407e6	+	3.93880e6i	−0.100125	+	0.173422i
$877$	−8.05463e6	+	1.39510e7i	−0.353628	+	0.612502i	−0.986882	−	0.161442i	$-0.948385\pi$
$877$	−8.05463e6	+	1.39510e7i	−0.353628	+	0.612502i	0.633254	+	0.773944i	$0.281719\pi$
$878$	2.46144e7	+	4.26334e7i	1.07759	+	1.86644i
$879$	9.34901e6	−	1.61930e7i	0.408125	−	0.706894i
$880$	1.21147e7	+	2.09833e7i	0.527358	+	0.913411i
$881$	−2.68864e6			−0.116706			−0.0583529	−	0.998296i	$-0.518585\pi$
$881$	−2.68864e6			−0.116706			−0.0583529	+	0.998296i	$0.518585\pi$
$882$	2.30327e7			0.996950
$883$	6.52301e6	+	1.12982e7i	0.281544	+	0.487649i	0.971765	−	0.235950i	$-0.0758201\pi$
$883$	6.52301e6	+	1.12982e7i	0.281544	+	0.487649i	−0.690221	+	0.723599i	$0.742487\pi$
$884$	19666.9	+	34064.0i	0.000846457	+	0.00146611i
$885$	3.04939e6			0.130875
$886$	−3.74772e7			−1.60392
$887$	8.90206e6	+	1.54188e7i	0.379911	+	0.658025i	0.991049	−	0.133499i	$-0.0426214\pi$
$887$	8.90206e6	+	1.54188e7i	0.379911	+	0.658025i	−0.611138	+	0.791524i	$0.709288\pi$
$888$	5.81001e6	−	1.00632e7i	0.247255	−	0.428258i
$889$	−2.33835e7	−	4.05014e7i	−0.992328	−	1.71876i
$890$	4.68681e6	−	8.11779e6i	0.198336	−	0.343528i
$891$	409408.	−	709116.i	0.0172768	−	0.0299242i
$892$	2.91650e7			1.22730
$893$	−1.42796e6	−	5.95204e6i	−0.0599222	−	0.249768i
$894$	−2.52662e6			−0.105729
$895$	4.71890e6	−	8.17337e6i	0.196917	−	0.341070i
$896$	9.63417e7	−	1.66869e8i	4.00908	−	6.94392i
$897$	−34599.6	−	59928.3i	−0.00143579	−	0.00248686i
$898$	2.73035e7	−	4.72911e7i	1.12987	−	1.95699i
$899$	−1.93418e6	−	3.35009e6i	−0.0798173	−	0.138248i
$900$	3.81800e7			1.57119
$901$	−966330.			−0.0396564
$902$	−2.20149e7	−	3.81309e7i	−0.900948	−	1.56049i
$903$	−623024.	−	1.07911e6i	−0.0254264	−	0.0440398i
$904$	−5.66751e7			−2.30660
$905$	4.41521e6			0.179196
$906$	−8.80684e6	−	1.52539e7i	−0.356451	−	0.617391i
$907$	−1.17369e7	+	2.03290e7i	−0.473736	+	0.820536i	−0.999548	−	0.0300656i	$-0.990428\pi$
$907$	−1.17369e7	+	2.03290e7i	−0.473736	+	0.820536i	0.525812	+	0.850601i	$0.323762\pi$
$908$	4.40528e7	+	7.63016e7i	1.77320	+	3.07128i
$909$	−1.08229e7	+	1.87459e7i	−0.434445	+	0.752481i
$910$	102954.	−	178322.i	0.00412136	−	0.00713841i
$911$	−1.53323e7			−0.612085			−0.306043	−	0.952018i	$-0.599005\pi$
$911$	−1.53323e7			−0.612085			−0.306043	+	0.952018i	$0.599005\pi$
$912$	1.66202e7	+	6.92765e7i	0.661683	+	2.75803i
$913$	−2.68109e7			−1.06447
$914$	−2.01885e7	+	3.49675e7i	−0.799352	+	1.38452i
$915$	2.59756e6	−	4.49910e6i	0.102568	−	0.177653i
$916$	5.17887e7	+	8.97006e7i	2.03937	+	3.53229i
$917$	1.45014e7	−	2.51172e7i	0.569492	−	0.986390i
$918$	−1.46996e6	−	2.54605e6i	−0.0575705	−	0.0997151i
$919$	−3.49528e7			−1.36519			−0.682596	−	0.730796i	$-0.739149\pi$
$919$	−3.49528e7			−1.36519			−0.682596	+	0.730796i	$0.739149\pi$
$920$	−1.29325e7			−0.503747
$921$	−5.25868e6	−	9.10830e6i	−0.204281	−	0.353825i
$922$	1.33600e7	+	2.31403e7i	0.517584	+	0.896481i
$923$	−151080.			−0.00583719
$924$	5.03506e7			1.94010
$925$	2.46911e6	+	4.27662e6i	0.0948823	+	0.164341i
$926$	2.18118e7	−	3.77792e7i	0.835920	−	1.44786i
$927$	−7.95686e6	−	1.37817e7i	−0.304118	−	0.526748i
$928$	−8.98118e6	+	1.55559e7i	−0.342345	+	0.592958i
$929$	−378019.	+	654748.i	−0.0143706	+	0.0248906i	−0.873121	−	0.487503i	$-0.837908\pi$
$929$	−378019.	+	654748.i	−0.0143706	+	0.0248906i	0.858751	+	0.512394i	$0.171241\pi$
$930$	−1.18574e7			−0.449555
$931$	−2.14262e7	−	6.35041e6i	−0.810159	−	0.240120i
$932$	−2.34382e7			−0.883862
$933$	−558056.	+	966581.i	−0.0209881	+	0.0363525i
$934$	−2.60079e7	+	4.50470e7i	−0.975524	+	1.68966i
$935$	181520.	+	314402.i	0.00679042	+	0.0117613i
$936$	304040.	−	526612.i	0.0113433	−	0.0196472i
$937$	−5.33759e6	−	9.24497e6i	−0.198608	−	0.343999i	0.749470	−	0.662039i	$-0.230309\pi$
$937$	−5.33759e6	−	9.24497e6i	−0.198608	−	0.343999i	−0.948077	+	0.318040i	$0.896975\pi$
$938$	−1.04412e8			−3.87475
$939$	−1.28171e7			−0.474381
$940$	−3.04619e6	−	5.27616e6i	−0.112444	−	0.194759i
$941$	818026.	+	1.41686e6i	0.0301157	+	0.0521619i	0.880690	−	0.473692i	$-0.157079\pi$
$941$	818026.	+	1.41686e6i	0.0301157	+	0.0521619i	−0.850575	+	0.525854i	$0.823746\pi$
$942$	4.79569e7			1.76085
$943$	1.42728e7			0.522671
$944$	4.17612e7	+	7.23326e7i	1.52526	+	2.64182i
$945$	−5.71816e6	+	9.90414e6i	−0.208294	+	0.360776i
$946$	1.24878e6	+	2.16294e6i	0.0453687	+	0.0785810i
$947$	−1.00232e7	+	1.73607e7i	−0.363187	+	0.629059i	−0.988484	−	0.151328i	$-0.951645\pi$
$947$	−1.00232e7	+	1.73607e7i	−0.363187	+	0.629059i	0.625296	+	0.780388i	$0.284978\pi$
$948$	−3.00999e7	+	5.21345e7i	−1.08779	+	1.88410i
$949$	−30783.7			−0.00110957
$950$	−4.77964e7	−	1.41662e7i	−1.71825	−	0.509265i
$951$	1.38485e7			0.496537
$952$	4.08425e6	−	7.07414e6i	0.146056	−	0.252977i
$953$	7.65095e6	−	1.32518e7i	0.272887	−	0.472654i	−0.696713	−	0.717350i	$-0.745355\pi$
$953$	7.65095e6	−	1.32518e7i	0.272887	−	0.472654i	0.969600	+	0.244696i	$0.0786881\pi$
$954$	1.14166e7	+	1.97741e7i	0.406131	+	0.703440i
$955$	5.85866e6	−	1.01475e7i	0.207869	−	0.360040i
$956$	−5.76257e7	−	9.98106e7i	−2.03925	−	3.53209i
$957$	−1.88118e6			−0.0663975
$958$	4.59513e7			1.61765
$959$	1.87132e7	+	3.24122e7i	0.657055	+	1.13805i
$960$	1.52714e7	+	2.64508e7i	0.534810	+	0.926318i
$961$	1.17263e7			0.409592
$962$	120210.			0.00418797
$963$	3.07094e6	+	5.31902e6i	0.106710	+	0.184827i
$964$	7.12786e7	−	1.23458e8i	2.47040	−	4.27885i
$965$	7.03454e6	+	1.21842e7i	0.243174	+	0.421190i
$966$	−1.09824e7	+	1.90220e7i	−0.378663	+	0.655864i
$967$	8.66552e6	−	1.50091e7i	0.298008	−	0.516165i	−0.677672	−	0.735364i	$-0.737011\pi$
$967$	8.66552e6	−	1.50091e7i	0.298008	−	0.516165i	0.975680	+	0.219199i	$0.0703444\pi$
$968$	4.28146e7			1.46860
$969$	249029.	+	1.03800e6i	0.00852002	+	0.0355132i
$970$	−1.40925e7			−0.480905
$971$	2.74678e7	−	4.75756e7i	0.934923	−	1.61933i	0.160151	−	0.987093i	$-0.448802\pi$
$971$	2.74678e7	−	4.75756e7i	0.934923	−	1.61933i	0.774772	−	0.632241i	$-0.217865\pi$
$972$	−4.19614e7	+	7.26792e7i	−1.42457	+	2.46743i
$973$	−1.13572e7	−	1.96712e7i	−0.384582	−	0.666115i
$974$	−2.44199e7	+	4.22965e7i	−0.824795	+	1.42859i
$975$	−86854.2	−	150436.i	−0.00292603	−	0.00506804i
$976$	1.42293e8			4.78146
$977$	−4.25937e7			−1.42761			−0.713804	−	0.700345i	$-0.753029\pi$
$977$	−4.25937e7			−1.42761			−0.713804	+	0.700345i	$0.753029\pi$
$978$	3.89521e6	+	6.74670e6i	0.130222	+	0.225551i
$979$	7.75701e6	+	1.34355e7i	0.258665	+	0.448021i
$980$	−2.22432e7			−0.739831
$981$	4.67618e6			0.155138
$982$	−2.68726e7	−	4.65447e7i	−0.889264	−	1.54025i
$983$	−2.18270e7	+	3.78055e7i	−0.720462	+	1.24788i	0.240353	+	0.970686i	$0.422737\pi$
$983$	−2.18270e7	+	3.78055e7i	−0.720462	+	1.24788i	−0.960815	+	0.277191i	$0.910596\pi$
$984$	−4.21536e7	−	7.30122e7i	−1.38786	−	2.40385i
$985$	−6.43183e6	+	1.11403e7i	−0.211224	+	0.365851i
$986$	−233231.	+	403968.i	−0.00764002	+	0.0132329i
$987$	−6.76994e6			−0.221203
$988$	−654211.	+	620626.i	−0.0213219	+	0.0202273i
$989$	−809611.			−0.0263200
$990$	4.28911e6	−	7.42896e6i	0.139085	−	0.240902i
$991$	1.31754e7	−	2.28205e7i	0.426168	−	0.738145i	−0.570360	−	0.821395i	$-0.693196\pi$
$991$	1.31754e7	−	2.28205e7i	0.426168	−	0.738145i	0.996529	+	0.0832494i	$0.0265298\pi$
$992$	−9.36934e7	−	1.62282e8i	−3.02294	−	5.23589i
$993$	6.52436e6	−	1.13005e7i	0.209974	−	0.363685i
$994$	2.39774e7	+	4.15301e7i	0.769726	+	1.33321i
$995$	1.37951e7			0.441740
$996$	−7.84650e7			−2.50627
$997$	1.11563e7	+	1.93232e7i	0.355452	+	0.615661i	0.987195	−	0.159517i	$-0.0509936\pi$
$997$	1.11563e7	+	1.93232e7i	0.355452	+	0.615661i	−0.631743	+	0.775178i	$0.717660\pi$
$998$	−1.19004e7	−	2.06121e7i	−0.378212	−	0.655083i
$999$	−6.67656e6			−0.211660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.6.c.a.11.8	yes	16
3.2	odd	2		171.6.f.b.163.1		16
4.3	odd	2		304.6.i.c.49.6		16
19.7	even	3	inner	19.6.c.a.7.8	✓	16
19.8	odd	6		361.6.a.h.1.8		8
19.11	even	3		361.6.a.g.1.1		8
57.26	odd	6		171.6.f.b.64.1		16
76.7	odd	6		304.6.i.c.273.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.6.c.a.7.8	✓	16	19.7	even	3	inner
19.6.c.a.11.8	yes	16	1.1	even	1	trivial
171.6.f.b.64.1		16	57.26	odd	6
171.6.f.b.163.1		16	3.2	odd	2
304.6.i.c.49.6		16	4.3	odd	2
304.6.i.c.273.6		16	76.7	odd	6
361.6.a.g.1.1		8	19.11	even	3
361.6.a.h.1.8		8	19.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.58024 - 9.66525i) q^{2} +(-4.94172 + 8.55931i) q^{3} +(-46.2781 - 80.1560i) q^{4} +(8.46093 - 14.6548i) q^{5} +(55.1519 + 95.5260i) q^{6} +176.093 q^{7} -675.836 q^{8} +(72.6588 + 125.849i) q^{9} +(-94.4280 - 163.554i) q^{10} +312.571 q^{11} +914.774 q^{12} +(3.09579 + 5.36206i) q^{13} +(982.642 - 1701.99i) q^{14} +(83.6231 + 144.839i) q^{15} +(-2290.42 + 3967.13i) q^{16} +(-34.3186 + 59.4415i) q^{17} +1621.81 q^{18} +(-1508.69 - 447.155i) q^{19} -1566.22 q^{20} +(-870.203 + 1507.24i) q^{21} +(1744.22 - 3021.07i) q^{22} +(565.409 + 979.317i) q^{23} +(3339.79 - 5784.69i) q^{24} +(1419.33 + 2458.34i) q^{25} +69.1009 q^{26} -3837.91 q^{27} +(-8149.26 - 14114.9i) q^{28} +(304.470 + 527.358i) q^{29} +1866.55 q^{30} -6352.59 q^{31} +(14748.9 + 25545.8i) q^{32} +(-1544.64 + 2675.39i) q^{33} +(383.011 + 663.395i) q^{34} +(1489.91 - 2580.60i) q^{35} +(6725.02 - 11648.1i) q^{36} +1739.63 q^{37} +(-12740.7 + 12086.7i) q^{38} -61.1940 q^{39} +(-5718.20 + 9904.21i) q^{40} +(6310.81 - 10930.6i) q^{41} +(9711.88 + 16821.5i) q^{42} +(-357.976 + 620.032i) q^{43} +(-14465.2 - 25054.4i) q^{44} +2459.04 q^{45} +12620.5 q^{46} +(1944.93 + 3368.72i) q^{47} +(-22637.3 - 39208.9i) q^{48} +14201.8 q^{49} +31680.7 q^{50} +(-339.185 - 587.486i) q^{51} +(286.534 - 496.292i) q^{52} +(7039.41 + 12192.6i) q^{53} +(-21416.5 + 37094.4i) q^{54} +(2644.64 - 4580.65i) q^{55} -119010. q^{56} +(11282.9 - 10703.7i) q^{57} +6796.07 q^{58} +(9116.48 - 15790.2i) q^{59} +(7739.84 - 13405.8i) q^{60} +(-15531.3 - 26901.1i) q^{61} +(-35449.0 + 61399.4i) q^{62} +(12794.7 + 22161.1i) q^{63} +182621. q^{64} +104.773 q^{65} +(17238.9 + 29858.6i) q^{66} +(-26564.1 - 46010.4i) q^{67} +6352.79 q^{68} -11176.4 q^{69} +(-16628.1 - 28800.8i) q^{70} +(-12200.5 + 21131.9i) q^{71} +(-49105.4 - 85053.1i) q^{72} +(-2485.94 + 4305.77i) q^{73} +(9707.57 - 16814.0i) q^{74} -28055.6 q^{75} +(33977.2 + 141624. i) q^{76} +55041.6 q^{77} +(-341.477 + 591.456i) q^{78} +(-32904.2 + 56991.7i) q^{79} +(38758.2 + 67131.3i) q^{80} +(1309.81 - 2268.66i) q^{81} +(-70431.7 - 121991. i) q^{82} -85775.4 q^{83} +161085. q^{84} +(580.734 + 1005.86i) q^{85} +(3995.18 + 6919.86i) q^{86} -6018.43 q^{87} -211246. q^{88} +(24816.8 + 42984.0i) q^{89} +(13722.0 - 23767.3i) q^{90} +(545.147 + 944.222i) q^{91} +(52332.1 - 90641.8i) q^{92} +(31392.7 - 54373.8i) q^{93} +43412.7 q^{94} +(-19317.9 + 18326.2i) q^{95} -291539. q^{96} +(37310.2 - 64623.2i) q^{97} +(79249.5 - 137264. i) q^{98} +(22711.0 + 39336.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 28 q^{3} - 155 q^{4} + 10 q^{5} + 149 q^{6} + 208 q^{7} - 78 q^{8} - 616 q^{9} + 580 q^{10} + 632 q^{11} - 2238 q^{12} + 786 q^{13} + 2054 q^{14} + 796 q^{15} - 3779 q^{16} - 746 q^{17}+ \cdots + 163952 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 28 * q^3 - 155 * q^4 + 10 * q^5 + 149 * q^6 + 208 * q^7 - 78 * q^8 - 616 * q^9 + 580 * q^10 + 632 * q^11 - 2238 * q^12 + 786 * q^13 + 2054 * q^14 + 796 * q^15 - 3779 * q^16 - 746 * q^17 + 8868 * q^18 - 5972 * q^19 - 7780 * q^20 - 292 * q^21 + 1841 * q^22 + 2084 * q^23 + 17913 * q^24 - 1378 * q^25 - 824 * q^26 - 28184 * q^27 - 9270 * q^28 + 5266 * q^29 + 41656 * q^30 - 15536 * q^31 + 21711 * q^32 + 14926 * q^33 - 2240 * q^34 - 7488 * q^35 - 41734 * q^36 - 3752 * q^37 - 33546 * q^38 - 36648 * q^39 + 9822 * q^40 + 21676 * q^41 + 8698 * q^42 + 9584 * q^43 - 43859 * q^44 + 69352 * q^45 + 90956 * q^46 + 29340 * q^47 - 1281 * q^48 + 16784 * q^49 - 98366 * q^50 + 23576 * q^51 + 71182 * q^52 - 30310 * q^53 + 49919 * q^54 - 36000 * q^55 - 305652 * q^56 + 107502 * q^57 - 286928 * q^58 + 101924 * q^59 + 19034 * q^60 + 36394 * q^61 - 69544 * q^62 - 44112 * q^63 + 459910 * q^64 + 106020 * q^65 + 219667 * q^66 - 50716 * q^67 + 27116 * q^68 - 110748 * q^69 + 159588 * q^70 + 116292 * q^71 - 468618 * q^72 + 36584 * q^73 - 278908 * q^74 - 518536 * q^75 + 311611 * q^76 - 446968 * q^77 + 136808 * q^78 + 110692 * q^79 + 253310 * q^80 - 99760 * q^81 - 92057 * q^82 + 229240 * q^83 + 452292 * q^84 + 113898 * q^85 - 126186 * q^86 + 342264 * q^87 - 347742 * q^88 + 356518 * q^89 + 741244 * q^90 - 337648 * q^91 + 52840 * q^92 - 368832 * q^93 - 781920 * q^94 + 265028 * q^95 - 1983074 * q^96 + 150004 * q^97 + 536843 * q^98 + 163952 * q^99

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