LMFDB - Embedded newform 63.6.o.a.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.o (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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	63.41
Dual form			63.6.o.a.20.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.40544 + 4.85288i) q^{2} +(6.76084 + 14.0460i) q^{3} +(31.1009 - 53.8683i) q^{4} +(32.8857 - 56.9596i) q^{5} +(-124.992 - 85.2535i) q^{6} +(-3.05564 + 129.606i) q^{7} +293.131i q^{8} +(-151.582 + 189.926i) q^{9} +638.361i q^{10} +(-298.785 + 172.504i) q^{11} +(966.905 + 72.6490i) q^{12} +(14.0132 + 8.09053i) q^{13} +(-603.277 - 1104.22i) q^{14} +(1022.39 + 76.8181i) q^{15} +(-427.303 - 740.110i) q^{16} -1129.50 q^{17} +(352.425 - 2332.02i) q^{18} +1621.87i q^{19} +(-2045.55 - 3542.99i) q^{20} +(-1841.11 + 833.325i) q^{21} +(1674.28 - 2899.93i) q^{22} +(-3737.69 - 2157.95i) q^{23} +(-4117.33 + 1981.81i) q^{24} +(-600.433 - 1039.98i) q^{25} -157.050 q^{26} +(-3692.53 - 845.068i) q^{27} +(6886.61 + 4195.46i) q^{28} +(3445.90 - 1989.49i) q^{29} +(-8966.43 + 4315.85i) q^{30} +(5813.45 + 3356.40i) q^{31} +(-940.164 - 542.804i) q^{32} +(-4443.03 - 3030.47i) q^{33} +(9493.94 - 5481.33i) q^{34} +(7281.81 + 4436.22i) q^{35} +(5516.66 + 14072.3i) q^{36} -12392.6 q^{37} +(-7870.73 - 13632.5i) q^{38} +(-18.8988 + 251.529i) q^{39} +(16696.7 + 9639.82i) q^{40} +(-5829.95 + 10097.8i) q^{41} +(11431.3 - 15939.1i) q^{42} +(-5962.62 - 10327.6i) q^{43} +21460.1i q^{44} +(5833.24 + 14879.9i) q^{45} +41889.2 q^{46} +(5039.23 + 8728.21i) q^{47} +(7506.68 - 11005.7i) q^{48} +(-16788.3 - 792.057i) q^{49} +(10093.8 + 5827.65i) q^{50} +(-7636.37 - 15865.0i) q^{51} +(871.647 - 503.246i) q^{52} +6140.70i q^{53} +(35138.3 - 10816.2i) q^{54} +22691.6i q^{55} +(-37991.5 - 895.704i) q^{56} +(-22780.8 + 10965.2i) q^{57} +(-19309.5 + 33445.1i) q^{58} +(10009.5 - 17337.0i) q^{59} +(35935.3 - 52685.4i) q^{60} +(-42680.8 + 24641.8i) q^{61} -65152.8 q^{62} +(-24152.3 - 20226.3i) q^{63} +37884.0 q^{64} +(921.668 - 532.125i) q^{65} +(52052.1 + 3910.97i) q^{66} +(8329.89 - 14427.8i) q^{67} +(-35128.5 + 60844.3i) q^{68} +(5040.79 - 67089.2i) q^{69} +(-82735.2 - 1950.60i) q^{70} -8769.01i q^{71} +(-55673.3 - 44433.5i) q^{72} -25373.2i q^{73} +(104165. - 60139.6i) q^{74} +(10548.2 - 15464.8i) q^{75} +(87367.3 + 50441.5i) q^{76} +(-21444.5 - 39251.4i) q^{77} +(-1061.79 - 2205.92i) q^{78} +(28435.6 + 49251.9i) q^{79} -56208.5 q^{80} +(-13094.7 - 57578.7i) q^{81} -113168. i q^{82} +(60102.0 + 104100. i) q^{83} +(-12370.2 + 125094. i) q^{84} +(-37144.3 + 64335.9i) q^{85} +(100237. + 57871.7i) q^{86} +(51241.7 + 34950.6i) q^{87} +(-50566.2 - 87583.2i) q^{88} -72575.9 q^{89} +(-121241. - 96764.0i) q^{90} +(-1091.40 + 1791.47i) q^{91} +(-232491. + 134229. i) q^{92} +(-7840.25 + 104348. i) q^{93} +(-84713.9 - 48909.6i) q^{94} +(92380.9 + 53336.2i) q^{95} +(1267.94 - 16875.4i) q^{96} +(78010.1 - 45039.1i) q^{97} +(144957. - 74814.2i) q^{98} +(12527.5 - 82895.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} + 574 q^{4} - 30 q^{7} + 156 q^{9} - 576 q^{11} + 1392 q^{14} - 666 q^{15} - 8130 q^{16} + 3798 q^{18} + 4194 q^{21} - 130 q^{22} - 8112 q^{23} - 18752 q^{25} - 1732 q^{28} - 35826 q^{29}+ \cdots + 325080 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 + 574 * q^4 - 30 * q^7 + 156 * q^9 - 576 * q^11 + 1392 * q^14 - 666 * q^15 - 8130 * q^16 + 3798 * q^18 + 4194 * q^21 - 130 * q^22 - 8112 * q^23 - 18752 * q^25 - 1732 * q^28 - 35826 * q^29 + 19104 * q^30 - 1092 * q^32 + 71190 * q^36 + 10308 * q^37 - 5016 * q^39 + 51450 * q^42 + 18486 * q^43 - 38056 * q^46 + 7948 * q^49 + 76104 * q^50 - 2346 * q^51 + 164652 * q^56 - 150102 * q^57 + 9902 * q^58 - 115356 * q^60 - 168468 * q^63 - 192648 * q^64 + 12666 * q^65 + 1244 * q^67 + 33024 * q^70 - 17364 * q^72 + 356496 * q^74 - 16458 * q^77 - 412764 * q^78 + 168074 * q^79 - 148872 * q^81 + 162282 * q^84 + 2598 * q^85 + 543300 * q^86 + 69694 * q^88 + 139368 * q^91 - 211794 * q^92 - 196818 * q^93 - 950328 * q^95 + 325080 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−8.40544	+	4.85288i	−1.48589	+	0.857876i	−0.999871	−	0.0160747i	$-0.994883\pi$
$2$	−8.40544	+	4.85288i	−1.48589	+	0.857876i	−0.486014	+	0.873951i	$0.661550\pi$
$3$	6.76084	+	14.0460i	0.433708	+	0.901053i
$3$	6.76084	+	14.0460i	0.433708	+	0.901053i
$4$	31.1009	−	53.8683i	0.971903	−	1.68339i
$5$	32.8857	−	56.9596i	0.588276	−	1.01892i	−0.406182	−	0.913792i	$-0.633140\pi$
$5$	32.8857	−	56.9596i	0.588276	−	1.01892i	0.994458	−	0.105132i	$-0.0335266\pi$
$6$	−124.992	−	85.2535i	−1.41743	−	0.966794i
$7$	−3.05564	+	129.606i	−0.0235699	+	0.999722i
$7$	−3.05564	+	129.606i	−0.0235699	+	0.999722i
$8$			293.131i			1.61934i
$9$	−151.582	+	189.926i	−0.623795	+	0.781588i
$10$			638.361i			2.01867i
$11$	−298.785	+	172.504i	−0.744521	+	0.429849i	−0.823711	−	0.567010i	$-0.808100\pi$
$11$	−298.785	+	172.504i	−0.744521	+	0.429849i	0.0791899	+	0.996860i	$0.474767\pi$
$12$	966.905	+	72.6490i	1.93834	+	0.145639i
$13$	14.0132	+	8.09053i	0.0229974	+	0.0132776i	0.511455	−	0.859310i	$-0.329107\pi$
$13$	14.0132	+	8.09053i	0.0229974	+	0.0132776i	−0.488457	+	0.872588i	$0.662440\pi$
$14$	−603.277	−	1104.22i	−0.822616	−	1.50569i
$15$	1022.39	+	76.8181i	1.17325	+	0.0881526i
$16$	−427.303	−	740.110i	−0.417288	−	0.722764i
$17$	−1129.50			−0.947903			−0.473951	−	0.880551i	$-0.657173\pi$
$17$	−1129.50			−0.947903			−0.473951	+	0.880551i	$0.657173\pi$
$18$	352.425	−	2332.02i	0.256381	−	1.69649i
$19$			1621.87i			1.03070i	0.856981	+	0.515349i	$0.172338\pi$
$19$			1621.87i			1.03070i	−0.856981	+	0.515349i	$0.827662\pi$
$20$	−2045.55	−	3542.99i	−1.14350	−	1.98059i
$21$	−1841.11	+	833.325i	−0.911026	+	0.412350i
$22$	1674.28	−	2899.93i	0.737515	−	1.27741i
$23$	−3737.69	−	2157.95i	−1.47327	−	0.850594i	−0.473725	−	0.880673i	$-0.657091\pi$
$23$	−3737.69	−	2157.95i	−1.47327	−	0.850594i	−0.999548	+	0.0300784i	$0.990424\pi$
$24$	−4117.33	+	1981.81i	−1.45911	+	0.702320i
$25$	−600.433	−	1039.98i	−0.192138	−	0.332794i
$26$	−157.050			−0.0455621
$27$	−3692.53	−	845.068i	−0.974798	−	0.223091i
$28$	6886.61	+	4195.46i	1.66001	+	1.01131i
$29$	3445.90	−	1989.49i	0.760866	−	0.439286i	−0.0687408	−	0.997635i	$-0.521898\pi$
$29$	3445.90	−	1989.49i	0.760866	−	0.439286i	0.829606	+	0.558349i	$0.188565\pi$
$30$	−8966.43	+	4315.85i	−1.81893	+	0.875515i
$31$	5813.45	+	3356.40i	1.08650	+	0.627291i	0.932642	−	0.360802i	$-0.117497\pi$
$31$	5813.45	+	3356.40i	1.08650	+	0.627291i	0.153857	+	0.988093i	$0.450830\pi$
$32$	−940.164	−	542.804i	−0.162304	−	0.0937061i
$33$	−4443.03	−	3030.47i	−0.710222	−	0.484424i
$34$	9493.94	−	5481.33i	1.40847	−	0.813183i
$35$	7281.81	+	4436.22i	1.00478	+	0.612129i
$36$	5516.66	+	14072.3i	0.709447	+	1.80971i
$37$	−12392.6			−1.48819			−0.744093	−	0.668077i	$-0.767118\pi$
$37$	−12392.6			−1.48819			−0.744093	+	0.668077i	$0.767118\pi$
$38$	−7870.73	−	13632.5i	−0.884211	−	1.53150i
$39$	−18.8988	+	251.529i	−0.00198963	+	0.0264805i
$40$	16696.7	+	9639.82i	1.64998	+	0.952618i
$41$	−5829.95	+	10097.8i	−0.541633	+	0.938135i	0.457178	+	0.889375i	$0.348860\pi$
$41$	−5829.95	+	10097.8i	−0.541633	+	0.938135i	−0.998811	+	0.0487601i	$0.984473\pi$
$42$	11431.3	−	15939.1i	0.999934	−	1.39425i
$43$	−5962.62	−	10327.6i	−0.491774	−	0.851778i	0.508181	−	0.861250i	$-0.330318\pi$
$43$	−5962.62	−	10327.6i	−0.491774	−	0.851778i	−0.999955	+	0.00947224i	$0.996985\pi$
$44$			21460.1i			1.67109i
$45$	5833.24	+	14879.9i	0.429416	+	1.09539i
$46$	41889.2			2.91882
$47$	5039.23	+	8728.21i	0.332751	+	0.576342i	0.983050	−	0.183336i	$-0.0586897\pi$
$47$	5039.23	+	8728.21i	0.332751	+	0.576342i	−0.650299	+	0.759678i	$0.725356\pi$
$48$	7506.68	−	11005.7i	0.470268	−	0.689467i
$49$	−16788.3	−	792.057i	−0.998889	−	0.0471266i
$50$	10093.8	+	5827.65i	0.570991	+	0.329662i
$51$	−7636.37	−	15865.0i	−0.411113	−	0.854111i
$52$	871.647	−	503.246i	0.0447026	−	0.0258090i
$53$			6140.70i			0.300281i	0.988665	+	0.150141i	$0.0479726\pi$
$53$			6140.70i			0.300281i	−0.988665	+	0.150141i	$0.952027\pi$
$54$	35138.3	−	10816.2i	1.63982	−	0.504768i
$55$			22691.6i			1.01148i
$56$	−37991.5	−	895.704i	−1.61889	−	0.0381675i
$57$	−22780.8	+	10965.2i	−0.928713	+	0.447022i
$58$	−19309.5	+	33445.1i	−0.753706	+	1.30546i
$59$	10009.5	−	17337.0i	0.374354	−	0.648400i	−0.615876	−	0.787843i	$-0.711198\pi$
$59$	10009.5	−	17337.0i	0.374354	−	0.648400i	0.990230	+	0.139443i	$0.0445312\pi$
$60$	35935.3	−	52685.4i	1.28868	−	1.88935i
$61$	−42680.8	+	24641.8i	−1.46862	+	0.847906i	−0.999381	−	0.0351680i	$-0.988803\pi$
$61$	−42680.8	+	24641.8i	−1.46862	+	0.847906i	−0.469234	+	0.883074i	$0.655470\pi$
$62$	−65152.8			−2.15255
$63$	−24152.3	−	20226.3i	−0.766668	−	0.642043i
$64$	37884.0			1.15613
$65$	921.668	−	532.125i	0.0270577	−	0.0156218i
$66$	52052.1	+	3910.97i	1.47088	+	0.110516i
$67$	8329.89	−	14427.8i	0.226700	−	0.392656i	−0.730128	−	0.683310i	$-0.760540\pi$
$67$	8329.89	−	14427.8i	0.226700	−	0.392656i	0.956828	+	0.290654i	$0.0938729\pi$
$68$	−35128.5	+	60844.3i	−0.921270	+	1.59569i
$69$	5040.79	−	67089.2i	0.127461	−	1.69641i
$70$	−82735.2	−	1950.60i	−2.01811	−	0.0475798i
$71$		−	8769.01i		−	0.206445i	−0.994658	−	0.103223i	$-0.967085\pi$
$71$		−	8769.01i		−	0.206445i	0.994658	−	0.103223i	$-0.0329154\pi$
$72$	−55673.3	−	44433.5i	−1.26566	−	1.01013i
$73$		−	25373.2i		−	0.557273i	−0.960397	−	0.278636i	$-0.910118\pi$
$73$		−	25373.2i		−	0.557273i	0.960397	−	0.278636i	$-0.0898825\pi$
$74$	104165.	−	60139.6i	2.21127	−	1.27668i
$75$	10548.2	−	15464.8i	0.216533	−	0.317462i
$76$	87367.3	+	50441.5i	1.73506	+	1.00174i
$77$	−21444.5	−	39251.4i	−0.412182	−	0.754446i
$78$	−1061.79	−	2205.92i	−0.0197606	−	0.0410539i
$79$	28435.6	+	49251.9i	0.512619	+	0.887882i	0.999893	+	0.0146326i	$0.00465787\pi$
$79$	28435.6	+	49251.9i	0.512619	+	0.887882i	−0.487274	+	0.873249i	$0.662009\pi$
$80$	−56208.5			−0.981922
$81$	−13094.7	−	57578.7i	−0.221761	−	0.975101i
$82$		−	113168.i		−	1.85862i
$83$	60102.0	+	104100.i	0.957621	+	1.65865i	0.728252	+	0.685309i	$0.240333\pi$
$83$	60102.0	+	104100.i	0.957621	+	1.65865i	0.229369	+	0.973340i	$0.426334\pi$
$84$	−12370.2	+	125094.i	−0.191285	+	1.93437i
$85$	−37144.3	+	64335.9i	−0.557629	+	0.965842i
$86$	100237.	+	57871.7i	1.46144	+	0.843763i
$87$	51241.7	+	34950.6i	0.725814	+	0.495059i
$88$	−50566.2	−	87583.2i	−0.696071	−	1.20563i
$89$	−72575.9			−0.971219			−0.485610	−	0.874176i	$-0.661402\pi$
$89$	−72575.9			−0.971219			−0.485610	+	0.874176i	$0.661402\pi$
$90$	−121241.	−	96764.0i	−1.57777	−	1.25924i
$91$	−1091.40	+	1791.47i	−0.0138159	+	0.0226781i
$92$	−232491.	+	134229.i	−2.86376	+	1.65339i
$93$	−7840.25	+	104348.i	−0.0939989	+	1.25106i
$94$	−84713.9	−	48909.6i	−0.988860	−	0.570919i
$95$	92380.9	+	53336.2i	1.05020	+	0.606335i
$96$	1267.94	−	16875.4i	0.0140418	−	0.186885i
$97$	78010.1	−	45039.1i	0.841824	−	0.486027i	−0.0160597	−	0.999871i	$-0.505112\pi$
$97$	78010.1	−	45039.1i	0.841824	−	0.486027i	0.857884	+	0.513844i	$0.171779\pi$
$98$	144957.	−	74814.2i	1.52466	−	0.786898i
$99$	12527.5	−	82895.4i	0.128463	−	0.850046i
$100$	−74696.0			−0.746960
$101$	75246.2	+	130330.i	0.733975	+	1.27128i	0.955172	+	0.296053i	$0.0956704\pi$
$101$	75246.2	+	130330.i	0.733975	+	1.27128i	−0.221197	+	0.975229i	$0.570996\pi$
$102$	141178.	+	96293.8i	1.34359	+	0.916427i
$103$	59960.7	+	34618.3i	0.556896	+	0.321524i	0.751899	−	0.659279i	$-0.229138\pi$
$103$	59960.7	+	34618.3i	0.556896	+	0.321524i	−0.195003	+	0.980803i	$0.562472\pi$
$104$	−2371.59	+	4107.71i	−0.0215009	+	0.0372406i
$105$	−13080.1	+	132273.i	−0.115781	+	1.17084i
$106$	−29800.1	−	51615.2i	−0.257604	−	0.446183i
$107$		−	109784.i		−	0.927004i	−0.886096	−	0.463502i	$-0.846593\pi$
$107$		−	109784.i		−	0.927004i	0.886096	−	0.463502i	$-0.153407\pi$
$108$	−160363.	+	172628.i	−1.32296	+	1.42414i
$109$	94345.2			0.760595			0.380297	−	0.924864i	$-0.375822\pi$
$109$	94345.2			0.760595			0.380297	+	0.924864i	$0.375822\pi$
$110$	−110119.	−	190732.i	−0.867725	−	1.50294i
$111$	−83784.2	−	174066.i	−0.645438	−	1.34093i
$112$	97228.2	−	53119.4i	0.732398	−	0.400136i
$113$	−52826.5	−	30499.4i	−0.389185	−	0.224696i	0.292622	−	0.956228i	$-0.405472\pi$
$113$	−52826.5	−	30499.4i	−0.389185	−	0.224696i	−0.681807	+	0.731532i	$0.738806\pi$
$114$	138270.	−	202720.i	0.996472	−	1.46094i
$115$	−245832.	+	141931.i	−1.73338	+	1.00077i
$116$		−	247500.i		−	1.70777i
$117$	−3660.76	+	1435.09i	−0.0247233	+	0.00969205i
$118$			194300.i			1.28460i
$119$	3451.34	−	146390.i	0.0223419	−	0.947639i
$120$	−22517.8	+	299695.i	−0.142749	+	1.89988i
$121$	−21010.6	+	36391.4i	−0.130459	+	0.225962i
$122$	239167.	−	414250.i	1.45480	−	2.51978i
$123$	−181249.	−	13618.3i	−1.08022	−	0.0811631i
$124$	361607.	−	208774.i	2.11194	−	1.21933i
$125$	126553.			0.724431
$126$	301166.	+	52802.2i	1.68997	+	0.296296i
$127$	247481.			1.36155			0.680774	−	0.732493i	$-0.261644\pi$
$127$	247481.			1.36155			0.680774	+	0.732493i	$0.261644\pi$
$128$	−288346.	+	166477.i	−1.55557	+	0.898109i
$129$	104749.	−	153574.i	0.554211	−	0.812538i
$130$	−5164.68	+	8945.49i	−0.0268031	+	0.0464243i
$131$	−93216.0	+	161455.i	−0.474583	+	0.822002i	−0.999576	−	0.0291044i	$-0.990734\pi$
$131$	−93216.0	+	161455.i	−0.474583	+	0.822002i	0.524993	+	0.851106i	$0.324068\pi$
$132$	−301429.	+	145088.i	−1.50574	+	0.724764i
$133$	−210203.	−	4955.84i	−1.03041	−	0.0242934i
$134$			161696.i			0.777923i
$135$	−169566.	+	182534.i	−0.800763	+	0.862006i
$136$		−	331092.i		−	1.53497i
$137$	−172340.	+	99500.6i	−0.784485	+	0.452923i	−0.838017	−	0.545643i	$-0.816285\pi$
$137$	−172340.	+	99500.6i	−0.784485	+	0.452923i	0.0535323	+	0.998566i	$0.482952\pi$
$138$	283206.	+	588377.i	1.26592	+	2.63001i
$139$	256366.	+	148013.i	1.12544	+	0.649774i	0.942785	−	0.333403i	$-0.108197\pi$
$139$	256366.	+	148013.i	1.12544	+	0.649774i	0.182657	+	0.983177i	$0.441530\pi$
$140$	465443.	−	254289.i	2.00699	−	1.09650i
$141$	−88527.2	+	129791.i	−0.374998	+	0.549791i
$142$	42554.9	+	73707.3i	0.177104	+	0.306754i
$143$	−5582.58			−0.0228294
$144$	205338.	+	31031.5i	0.825206	+	0.124709i
$145$		−	261703.i		−	1.03369i
$146$	123133.	+	213273.i	0.478071	+	0.828044i
$147$	−102378.	−	241164.i	−0.390763	−	0.920491i
$148$	−385420.	+	667567.i	−1.44637	+	2.50519i
$149$	157150.	+	90730.9i	0.579896	+	0.334803i	0.761092	−	0.648644i	$-0.224664\pi$
$149$	157150.	+	90730.9i	0.579896	+	0.334803i	−0.181196	+	0.983447i	$0.557997\pi$
$150$	−13612.9	+	181178.i	−0.0493995	+	0.657471i
$151$	17230.7	+	29844.5i	0.0614980	+	0.106518i	0.895135	−	0.445795i	$-0.147079\pi$
$151$	17230.7	+	29844.5i	0.0614980	+	0.106518i	−0.833637	+	0.552312i	$0.813746\pi$
$152$	−475420.			−1.66905
$153$	171212.	−	214521.i	0.591297	−	0.740870i
$154$	370732.	+	225857.i	1.25968	+	0.767419i
$155$	382358.	−	220755.i	1.27832	−	0.738041i
$156$	12961.7	+	8840.82i	0.0426432	+	0.0290858i
$157$	−128045.	−	73926.7i	−0.414584	−	0.239360i	0.278173	−	0.960531i	$-0.410271\pi$
$157$	−128045.	−	73926.7i	−0.414584	−	0.239360i	−0.692757	+	0.721171i	$0.743604\pi$
$158$	−478027.	−	275989.i	−1.52338	−	0.879527i
$159$	−86252.4	+	41516.3i	−0.270569	+	0.130234i
$160$	−61835.8	+	35700.9i	−0.190959	+	0.110250i
$161$	291104.	−	477832.i	0.885083	−	1.45281i
$162$	389490.	+	420427.i	1.16603	+	1.25864i
$163$	−358664.			−1.05735			−0.528675	−	0.848824i	$-0.677311\pi$
$163$	−358664.			−1.05735			−0.528675	+	0.848824i	$0.677311\pi$
$164$	362633.	+	628099.i	1.05283	+	1.82355i
$165$	−318726.	+	153414.i	−0.911398	+	0.438687i
$166$	−1.01037e6	−	583336.i	−2.84583	−	1.64304i
$167$	69945.8	−	121150.i	0.194075	−	0.336148i	−0.752522	−	0.658567i	$-0.771163\pi$
$167$	69945.8	−	121150.i	0.194075	−	0.336148i	0.946597	+	0.322419i	$0.104496\pi$
$168$	−244274.	−	539686.i	−0.667734	−	1.47526i
$169$	−185516.	−	321322.i	−0.499647	−	0.865415i
$170$		−	721028.i		−	1.91351i
$171$	−308035.	−	245846.i	−0.805581	−	0.642943i
$172$	−741771.			−1.91183
$173$	171808.	+	297580.i	0.436443	+	0.755942i	0.997412	−	0.0718951i	$-0.0229047\pi$
$173$	171808.	+	297580.i	0.436443	+	0.755942i	−0.560969	+	0.827837i	$0.689571\pi$
$174$	−600320.	−	45105.4i	−1.50317	−	0.112942i
$175$	136622.	−	74641.7i	0.337230	−	0.184241i
$176$	255343.	+	147422.i	0.621359	+	0.358742i
$177$	311188.	+	23381.3i	0.746603	+	0.0560965i
$178$	610032.	−	352202.i	1.44312	−	0.833186i
$179$			726867.i			1.69560i	0.530320	+	0.847798i	$0.322072\pi$
$179$			726867.i			1.69560i	−0.530320	+	0.847798i	$0.677928\pi$
$180$	982974.	+	148551.i	2.26131	+	0.341740i
$181$			238798.i			0.541793i	0.962608	+	0.270897i	$0.0873201\pi$
$181$			238798.i			0.541793i	−0.962608	+	0.270897i	$0.912680\pi$
$182$	479.887	−	20354.5i	0.00107389	−	0.0455494i
$183$	−634678.	−	432897.i	−1.40096	−	0.955558i
$184$	632564.	−	1.09563e6i	1.37740	−	2.38573i
$185$	−407538.	+	705876.i	−0.875464	+	1.51635i
$186$	−440487.	−	915138.i	−0.933579	−	1.93956i
$187$	337477.	−	194843.i	0.705733	−	0.407455i
$188$	626898.			1.29361
$189$	120809.	−	475991.i	0.246005	−	0.969269i
$190$	−1.03534e6			−2.08064
$191$	131564.	−	75958.3i	0.260947	−	0.150658i	−0.363819	−	0.931470i	$-0.618527\pi$
$191$	131564.	−	75958.3i	0.260947	−	0.150658i	0.624767	+	0.780812i	$0.285194\pi$
$192$	256128.	+	532120.i	0.501422	+	1.04173i
$193$	138137.	−	239260.i	0.266942	−	0.462357i	−0.701129	−	0.713035i	$-0.747320\pi$
$193$	138137.	−	239260.i	0.266942	−	0.462357i	0.968071	+	0.250678i	$0.0806535\pi$
$194$	−437139.	+	757147.i	−0.833903	+	1.44436i
$195$	13705.5	+	9348.16i	0.0258112	+	0.0176051i
$196$	−564799.	+	879725.i	−1.05016	+	1.63571i
$197$			148825.i			0.273219i	0.990625	+	0.136609i	$0.0436205\pi$
$197$			148825.i			0.273219i	−0.990625	+	0.136609i	$0.956379\pi$
$198$	296982.	+	757567.i	0.538354	+	1.37328i
$199$		−	507404.i		−	0.908282i	−0.890930	−	0.454141i	$-0.849946\pi$
$199$		−	507404.i		−	0.908282i	0.890930	−	0.454141i	$-0.150054\pi$
$200$	304851.	−	176006.i	0.538905	−	0.311137i
$201$	258970.	+	19457.9i	0.452126	+	0.0339708i
$202$	−1.26495e6	−	730322.i	−2.18120	−	1.25932i
$203$	247320.	+	452688.i	0.421230	+	0.771008i
$204$	−1.09212e6	−	82057.0i	−1.83736	−	0.138051i
$205$	383443.	+	664143.i	0.637260	+	1.10377i
$206$	−671995.			−1.10331
$207$	976418.	−	382776.i	1.58383	−	0.620897i
$208$		−	13828.4i		−	0.0221623i
$209$	−279778.	−	484589.i	−0.443045	−	0.767376i
$210$	−531962.	−	1.17529e6i	−0.832400	−	1.83906i
$211$	15175.5	−	26284.7i	0.0234658	−	0.0406440i	−0.854054	−	0.520184i	$-0.825863\pi$
$211$	15175.5	−	26284.7i	0.0234658	−	0.0406440i	0.877520	+	0.479540i	$0.159197\pi$
$212$	330789.	+	190981.i	0.505489	+	0.291844i
$213$	123170.	−	59285.9i	0.186018	−	0.0895369i
$214$	532771.	+	922786.i	0.795254	+	1.37742i
$215$	−784338.			−1.15720
$216$	247716.	−	1.08240e6i	0.361260	−	1.57853i
$217$	−452772.	+	743201.i	−0.652725	+	1.07141i
$218$	−793012.	+	457846.i	−1.13016	+	0.652496i
$219$	356393.	−	171544.i	0.502133	−	0.241694i
$220$	1.22236e6	+	705728.i	1.70271	+	0.983061i
$221$	−15827.9	−	9138.26i	−0.0217993	−	0.0125859i
$222$	1.54897e6	+	1.05651e6i	2.10940	+	1.43877i
$223$	−208301.	+	120262.i	−0.280497	+	0.161945i	−0.633648	−	0.773621i	$-0.718443\pi$
$223$	−208301.	+	120262.i	−0.280497	+	0.161945i	0.353151	+	0.935566i	$0.385110\pi$
$224$	73223.3	−	120192.i	0.0975055	−	0.160050i
$225$	288534.	+	43604.5i	0.379962	+	0.0574216i
$226$	592039.			0.771045
$227$	−415474.	−	719621.i	−0.535154	−	0.926914i	−0.999156	−	0.0410797i	$-0.986920\pi$
$227$	−415474.	−	719621.i	−0.535154	−	0.926914i	0.464002	−	0.885834i	$-0.346413\pi$
$228$	−117827.	+	1.56819e6i	−0.150109	+	1.99784i
$229$	666915.	+	385043.i	0.840391	+	0.485200i	0.857397	−	0.514655i	$-0.172080\pi$
$229$	666915.	+	385043.i	0.840391	+	0.485200i	−0.0170059	+	0.999855i	$0.505413\pi$
$230$	1.37755e6	−	2.38599e6i	1.71707	−	2.97406i
$231$	406343.	−	566582.i	0.501029	−	0.698607i
$232$	583183.	+	1.01010e6i	0.711352	+	1.23210i
$233$			793987.i			0.958128i	0.877780	+	0.479064i	$0.159024\pi$
$233$			793987.i			0.958128i	−0.877780	+	0.479064i	$0.840976\pi$
$234$	23805.9	−	29827.8i	0.0284214	−	0.0356108i
$235$	662874.			0.782999
$236$	−622609.	−	1.07839e6i	−0.727671	−	1.26036i
$237$	−499545.	+	732391.i	−0.577702	+	0.846978i
$238$	681402.	+	1.24722e6i	0.779760	+	1.42725i
$239$	−75094.8	−	43356.0i	−0.0850384	−	0.0490969i	0.456878	−	0.889529i	$-0.348968\pi$
$239$	−75094.8	−	43356.0i	−0.0850384	−	0.0490969i	−0.541916	+	0.840433i	$0.682301\pi$
$240$	−380017.	−	789507.i	−0.425868	−	0.884765i
$241$	1.15078e6	−	664401.i	1.27629	−	0.736865i	0.300124	−	0.953900i	$-0.402972\pi$
$241$	1.15078e6	−	664401.i	1.27629	−	0.736865i	0.976164	+	0.217035i	$0.0696386\pi$
$242$		−	407847.i		−	0.447671i
$243$	720221.	−	573210.i	0.782439	−	0.622728i
$244$			3.06553e6i			3.29633i
$245$	−597210.	+	930209.i	−0.635641	+	0.990069i
$246$	1.58956e6	−	765112.i	1.67471	−	0.806096i
$247$	−13121.8	+	22727.6i	−0.0136852	+	0.0237034i
$248$	−983865.	+	1.70410e6i	−1.01580	+	1.75941i
$249$	−1.05585e6	+	1.54800e6i	−1.07920	+	1.58224i
$250$	−1.06373e6	+	614146.i	−1.07642	+	0.621472i
$251$	861013.			0.862631			0.431316	−	0.902201i	$-0.358050\pi$
$251$	861013.			0.862631			0.431316	+	0.902201i	$0.358050\pi$
$252$	−1.84071e6	+	671991.i	−1.82593	+	0.666595i
$253$	1.48902e6			1.46251
$254$	−2.08019e6	+	1.20100e6i	−2.02310	+	1.16804i
$255$	−1.15479e6	−	86766.0i	−1.11212	−	0.0835601i
$256$	1.00964e6	−	1.74875e6i	0.962868	−	1.66774i
$257$	390545.	−	676444.i	0.368840	−	0.638850i	−0.620544	−	0.784171i	$-0.713088\pi$
$257$	390545.	−	676444.i	0.368840	−	0.638850i	0.989384	+	0.145322i	$0.0464217\pi$
$258$	−135183.	+	1.79919e6i	−0.126437	+	1.68278i
$259$	37867.2	−	1.60615e6i	0.0350763	−	1.48777i
$260$		−	66198.3i		−	0.0607314i
$261$	−144481.	+	956038.i	−0.131283	+	0.868708i
$262$		−	1.80946e6i		−	1.62853i
$263$	944052.	−	545049.i	0.841602	−	0.485899i	−0.0162067	−	0.999869i	$-0.505159\pi$
$263$	944052.	−	545049.i	0.841602	−	0.485899i	0.857808	+	0.513970i	$0.171826\pi$
$264$	888327.	−	1.30239e6i	0.784446	−	1.15009i
$265$	349772.	+	201941.i	0.305964	+	0.176648i
$266$	1.79090e6	−	978436.i	1.55191	−	0.847868i
$267$	−490674.	−	1.01940e6i	−0.421226	−	0.875121i
$268$	−518134.	−	897434.i	−0.440661	−	0.763248i
$269$	−1.23916e6			−1.04411			−0.522057	−	0.852911i	$-0.674835\pi$
$269$	−1.23916e6			−1.04411			−0.522057	+	0.852911i	$0.674835\pi$
$270$	539458.	−	2.35716e6i	0.450348	−	1.96780i
$271$		−	1.50729e6i		−	1.24673i	−0.781931	−	0.623365i	$-0.785765\pi$
$271$		−	1.50729e6i		−	1.24673i	0.781931	−	0.623365i	$-0.214235\pi$
$272$	482638.	+	835954.i	0.395548	+	0.685110i
$273$	−32541.9	−	3217.97i	−0.0264263	−	0.00261322i
$274$	965729.	−	1.67269e6i	0.777103	−	1.34598i
$275$	358800.	+	207153.i	0.286102	+	0.165181i
$276$	−3.45721e6	−	2.35807e6i	−2.73183	−	1.86331i
$277$	−612568.	−	1.06100e6i	−0.479683	−	0.830836i	0.520045	−	0.854139i	$-0.325915\pi$
$277$	−612568.	−	1.06100e6i	−0.479683	−	0.830836i	−0.999728	+	0.0233029i	$0.992582\pi$
$278$	−2.87315e6			−2.22970
$279$	−1.51868e6	+	595355.i	−1.16804	+	0.457895i
$280$	−1.30040e6	+	2.13453e6i	−0.991243	+	1.62707i
$281$	825466.	−	476583.i	0.623639	−	0.360058i	−0.154645	−	0.987970i	$-0.549424\pi$
$281$	825466.	−	476583.i	0.623639	−	0.360058i	0.778284	+	0.627912i	$0.216090\pi$
$282$	114249.	−	1.52056e6i	0.0855516	−	1.13863i
$283$	1.21115e6	+	699259.i	0.898944	+	0.519005i	0.876857	−	0.480751i	$-0.159636\pi$
$283$	1.21115e6	+	699259.i	0.898944	+	0.519005i	0.0220864	+	0.999756i	$0.492969\pi$
$284$	−472372.	−	272724.i	−0.347527	−	0.200645i
$285$	−124589.	+	1.65818e6i	−0.0908587	+	1.20926i
$286$	46924.0	−	27091.6i	0.0339219	−	0.0195848i
$287$	−1.29091e6	−	786450.i	−0.925109	−	0.563594i
$288$	245604.	−	96282.2i	0.174484	−	0.0684013i
$289$	−144087.			−0.101480
$290$	1.27001e6	+	2.19973e6i	0.886775	+	1.53594i
$291$	1.16003e6	+	791230.i	0.803043	+	0.547735i
$292$	−1.36681e6	−	789129.i	−0.938105	−	0.541615i
$293$	−50755.0	+	87910.3i	−0.0345390	+	0.0598234i	−0.882778	−	0.469790i	$-0.844330\pi$
$293$	−50755.0	+	87910.3i	−0.0345390	+	0.0598234i	0.848239	+	0.529613i	$0.177663\pi$
$294$	2.03087e6	+	1.53026e6i	1.37030	+	1.03252i
$295$	−658338.	−	1.14027e6i	−0.440447	−	0.762877i
$296$		−	3.63265e6i		−	2.40987i
$297$	1.24905e6	−	384481.i	0.821653	−	0.252920i
$298$	−1.76122e6			−1.14888
$299$	−34918.0	−	60479.7i	−0.0225877	−	0.0391230i
$300$	−505007.	−	1.04918e6i	−0.323962	−	0.673051i
$301$	1.35673e6	−	741233.i	0.863133	−	0.471561i
$302$	−289663.	−	167237.i	−0.182758	−	0.105515i
$303$	−1.32190e6	+	1.93805e6i	−0.827162	+	1.21272i
$304$	1.20036e6	−	693028.i	0.744951	−	0.430097i
$305$			3.24144e6i			1.99521i
$306$	−398064.	+	2.63402e6i	−0.243024	+	1.60811i
$307$			402643.i			0.243823i	0.992541	+	0.121911i	$0.0389024\pi$
$307$			402643.i			0.243823i	−0.992541	+	0.121911i	$0.961098\pi$
$308$	−2.78135e6	−	65574.2i	−1.67062	−	0.0393873i
$309$	−80865.5	+	1.07626e6i	−0.0481800	+	0.641240i
$310$	−2.14259e6	+	3.71108e6i	−1.26630	+	2.19329i
$311$	−788811.	+	1.36626e6i	−0.462458	+	0.801000i	−0.999083	−	0.0428205i	$-0.986366\pi$
$311$	−788811.	+	1.36626e6i	−0.462458	+	0.801000i	0.536625	+	0.843821i	$0.319699\pi$
$312$	−73731.0	−	5539.83i	−0.0428809	−	0.00322188i
$313$	649509.	−	374994.i	0.374735	−	0.216353i	−0.300790	−	0.953690i	$-0.597250\pi$
$313$	649509.	−	374994.i	0.374735	−	0.216353i	0.675525	+	0.737337i	$0.263917\pi$
$314$	1.43503e6			0.821366
$315$	−1.94635e6	+	710554.i	−1.10521	+	0.403479i
$316$	3.53749e6			1.99286
$317$	−2.01695e6	+	1.16449e6i	−1.12732	+	0.650859i	−0.943260	−	0.332056i	$-0.892258\pi$
$317$	−2.01695e6	+	1.16449e6i	−1.12732	+	0.650859i	−0.184061	+	0.982915i	$0.558924\pi$
$318$	523516.	−	767535.i	0.290310	−	0.425628i
$319$	−686389.	+	1.18886e6i	−0.377654	+	0.654115i
$320$	1.24584e6	−	2.15786e6i	0.680123	−	1.17801i
$321$	1.54204e6	−	742235.i	0.835280	−	0.402049i
$322$	−127998.	+	5.42908e6i	−0.0687961	+	2.91801i
$323$		−	1.83190e6i		−	0.977001i
$324$	−3.50893e6	−	1.08536e6i	−1.85700	−	0.574395i
$325$		−	19431.3i		−	0.0102045i
$326$	3.01473e6	−	1.74055e6i	1.57110	−	0.907076i
$327$	637853.	+	1.32518e6i	0.329876	+	0.685337i
$328$	−2.95997e6	−	1.70894e6i	−1.51916	−	0.877086i
$329$	−1.14662e6	+	626443.i	−0.584025	+	0.319075i
$330$	1.93453e6	−	2.83625e6i	0.977894	−	1.43371i
$331$	−1.42556e6	−	2.46914e6i	−0.715180	−	1.23873i	−0.962890	−	0.269894i	$-0.913011\pi$
$331$	−1.42556e6	−	2.46914e6i	−0.715180	−	1.23873i	0.247710	−	0.968834i	$-0.420322\pi$
$332$	7.47690e6			3.72286
$333$	1.87849e6	−	2.35367e6i	0.928322	−	1.16315i
$334$			1.35775e6i			0.665970i
$335$	−547868.	−	948934.i	−0.266725	−	0.461981i
$336$	1.40346e6	+	1.00654e6i	0.678191	+	0.486388i
$337$	−1.11190e6	+	1.92586e6i	−0.533322	+	0.923741i	0.465920	+	0.884827i	$0.345723\pi$
$337$	−1.11190e6	+	1.92586e6i	−0.533322	+	0.923741i	−0.999243	+	0.0389145i	$0.987610\pi$
$338$	3.11868e6	+	1.80057e6i	1.48484	+	0.857271i
$339$	71243.9	−	948204.i	0.0336704	−	0.448128i
$340$	2.31044e6	+	4.00181e6i	1.08392	+	1.87741i
$341$	−2.31596e6			−1.07856
$342$	3.78223e6	+	571587.i	1.74857	+	0.264251i
$343$	153954.	−	2.17344e6i	0.0706572	−	0.997501i
$344$	3.02733e6	−	1.74783e6i	1.37932	−	0.796349i
$345$	−3.65561e6	−	2.49339e6i	−1.65353	−	1.12783i
$346$	−2.88824e6	−	1.66753e6i	−1.29701	−	0.748828i
$347$	−2.34080e6	−	1.35146e6i	−1.04361	−	0.602531i	−0.122759	−	0.992436i	$-0.539174\pi$
$347$	−2.34080e6	−	1.35146e6i	−1.04361	−	0.602531i	−0.920855	+	0.389906i	$0.872508\pi$
$348$	3.47639e6	−	1.67331e6i	1.53880	−	0.740675i
$349$	922979.	−	532882.i	0.405628	−	0.234190i	−0.283281	−	0.959037i	$-0.591423\pi$
$349$	922979.	−	532882.i	0.405628	−	0.234190i	0.688910	+	0.724847i	$0.258090\pi$
$350$	−786141.	+	1.29041e6i	−0.343029	+	0.563063i
$351$	−44907.2	−	41716.6i	−0.0194557	−	0.0180735i
$352$	374542.			0.161118
$353$	925198.	+	1.60249e6i	0.395183	+	0.684476i	0.993124	−	0.117063i	$-0.0373480\pi$
$353$	925198.	+	1.60249e6i	0.395183	+	0.684476i	−0.597942	+	0.801540i	$0.704015\pi$
$354$	−2.72914e6	+	1.31363e6i	−1.15749	+	0.557140i
$355$	−499479.	−	288375.i	−0.210352	−	0.121447i
$356$	−2.25718e6	+	3.90954e6i	−0.943931	+	1.63494i
$357$	2.07953e6	−	941240.i	0.863564	−	0.390868i
$358$	−3.52740e6	−	6.10963e6i	−1.45461	−	2.51946i
$359$		−	55649.4i		−	0.0227889i	−0.999935	−	0.0113945i	$-0.996373\pi$
$359$		−	55649.4i		−	0.0227889i	0.999935	−	0.0113945i	$-0.00362705\pi$
$360$	−4.36176e6	+	1.70990e6i	−1.77381	+	0.695369i
$361$	−154353.			−0.0623371
$362$	−1.15886e6	−	2.00720e6i	−0.464791	−	0.805042i
$363$	−653204.	−	49078.9i	−0.260185	−	0.0195492i
$364$	62560.1	+	114508.i	0.0247482	+	0.0452985i
$365$	−1.44525e6	−	834414.i	−0.567819	−	0.327831i
$366$	7.43554e6	+	558674.i	2.90141	+	0.218000i
$367$	−2.31805e6	+	1.33833e6i	−0.898377	+	0.518678i	−0.876673	−	0.481086i	$-0.840242\pi$
$367$	−2.31805e6	+	1.33833e6i	−0.898377	+	0.518678i	−0.0217036	+	0.999764i	$0.506909\pi$
$368$			3.68840e6i			1.41977i
$369$	−1.03411e6	−	2.63790e6i	−0.395368	−	1.00854i
$370$		−	7.91093e6i		−	3.00416i
$371$	−795870.	−	18763.8i	−0.300198	−	0.00707758i
$372$	5.37721e6	+	3.66766e6i	2.01465	+	1.37414i
$373$	−2.23379e6	+	3.86904e6i	−0.831325	+	1.43990i	0.0656625	+	0.997842i	$0.479084\pi$
$373$	−2.23379e6	+	3.86904e6i	−0.831325	+	1.43990i	−0.896988	+	0.442056i	$0.854249\pi$
$374$	−1.89110e6	+	3.27547e6i	−0.699092	+	1.21086i
$375$	855604.	+	1.77757e6i	0.314192	+	0.652751i
$376$	−2.55851e6	+	1.47716e6i	−0.933292	+	0.538836i
$377$	64384.2			0.0233306
$378$	1.29448e6	+	4.58718e6i	0.465977	+	1.65126i
$379$	−215079.			−0.0769130			−0.0384565	−	0.999260i	$-0.512244\pi$
$379$	−215079.			−0.0769130			−0.0384565	+	0.999260i	$0.512244\pi$
$380$	5.74626e6	−	3.31760e6i	2.04139	−	1.17860i
$381$	1.67318e6	+	3.47613e6i	0.590514	+	1.22683i
$382$	−737233.	+	1.27693e6i	−0.258492	+	0.447721i
$383$	−348342.	+	603346.i	−0.121341	+	0.210170i	−0.920297	−	0.391221i	$-0.872053\pi$
$383$	−348342.	+	603346.i	−0.121341	+	0.210170i	0.798955	+	0.601390i	$0.205386\pi$
$384$	−4.28780e6	−	2.92460e6i	−1.48391	−	1.01213i
$385$	−2.94096e6	−	69337.2i	−1.01120	−	0.0238405i
$386$			2.68145e6i			0.916012i
$387$	2.86530e6	+	433017.i	0.972506	+	0.146969i
$388$		−	5.60303e6i		−	1.88949i
$389$	234067.	−	135138.i	0.0784270	−	0.0452798i	−0.460274	−	0.887777i	$-0.652249\pi$
$389$	234067.	−	135138.i	0.0784270	−	0.0452798i	0.538701	+	0.842497i	$0.318915\pi$
$390$	−160566.	−	12064.2i	−0.0534555	−	0.00401642i
$391$	4.22171e6	+	2.43741e6i	1.39652	+	0.806281i
$392$	232177.	−	4.92118e6i	0.0763139	−	1.61754i
$393$	−2.89802e6	−	217745.i	−0.946498	−	0.0711158i
$394$	−722231.	−	1.25094e6i	−0.234388	−	0.405972i
$395$	3.74049e6			1.20625
$396$	−4.07582e6	−	3.25296e6i	−1.30610	−	1.04242i
$397$			3.22623e6i			1.02735i	0.857985	+	0.513675i	$0.171716\pi$
$397$			3.22623e6i			1.02735i	−0.857985	+	0.513675i	$0.828284\pi$
$398$	2.46237e6	+	4.26495e6i	0.779194	+	1.34960i
$399$	−1.35154e6	−	2.98603e6i	−0.425008	−	0.938992i
$400$	−513133.	+	888772.i	−0.160354	+	0.277741i
$401$	1.85817e6	+	1.07281e6i	0.577064	+	0.333168i	0.759966	−	0.649963i	$-0.225216\pi$
$401$	1.85817e6	+	1.07281e6i	0.577064	+	0.333168i	−0.182902	+	0.983131i	$0.558549\pi$
$402$	−2.27118e6	+	1.09320e6i	−0.700950	+	0.337392i
$403$	54310.1	+	94067.8i	0.0166578	+	0.0288522i
$404$	9.36090e6			2.85341
$405$	−3.71029e6	−	1.14764e6i	−1.12401	−	0.347672i
$406$	−4.27568e6	−	2.60482e6i	−1.28733	−	0.784266i
$407$	3.70271e6	−	2.13776e6i	1.10798	−	0.639695i
$408$	4.65053e6	−	2.23846e6i	1.38309	−	0.665731i
$409$	−63844.0	−	36860.4i	−0.0188717	−	0.0108956i	0.490534	−	0.871422i	$-0.336802\pi$
$409$	−63844.0	−	36860.4i	−0.0188717	−	0.0108956i	−0.509406	+	0.860526i	$0.670135\pi$
$410$	−6.44601e6	−	3.72161e6i	−1.89379	−	1.09338i
$411$	−2.56275e6	−	1.74799e6i	−0.748345	−	0.510427i
$412$	3.72967e6	−	2.15332e6i	1.08250	−	0.624980i
$413$	2.21638e6	+	1.35026e6i	0.639396	+	0.389532i
$414$	−6.34965e6	+	7.95584e6i	−1.82074	+	2.28131i
$415$	7.90598e6			2.25338
$416$	−8783.14	−	15212.9i	−0.00248838	−	0.00431000i
$417$	−345745.	+	4.60161e6i	−0.0973679	+	1.29590i
$418$	4.70331e6	+	2.71546e6i	1.31663	+	0.760155i
$419$	−1.84563e6	+	3.19672e6i	−0.513581	+	0.889548i	0.486295	+	0.873795i	$0.338348\pi$
$419$	−1.84563e6	+	3.19672e6i	−0.513581	+	0.889548i	−0.999876	+	0.0157535i	$0.994985\pi$
$420$	6.71853e6	+	4.81842e6i	1.85845	+	1.33285i
$421$	−361478.	−	626099.i	−0.0993979	−	0.172162i	0.812038	−	0.583605i	$-0.198358\pi$
$421$	−361478.	−	626099.i	−0.0993979	−	0.172162i	−0.911436	+	0.411443i	$0.865025\pi$
$422$			294579.i			0.0805230i
$423$	−2.42157e6	−	365959.i	−0.658031	−	0.0994445i
$424$	−1.80003e6			−0.486256
$425$	678188.	+	1.17466e6i	0.182129	+	0.315456i
$426$	−747588.	+	1.09605e6i	−0.199590	+	0.292622i
$427$	−3.06330e6	−	5.60698e6i	−0.813055	−	1.48819i
$428$	−5.91390e6	−	3.41439e6i	−1.56050	−	0.900957i
$429$	−37742.9	−	78413.1i	−0.00990131	−	0.0205705i
$430$	6.59271e6	−	3.80630e6i	1.71946	−	0.992732i
$431$			2.43942e6i			0.632548i	0.948668	+	0.316274i	$0.102432\pi$
$431$			2.43942e6i			0.632548i	−0.948668	+	0.316274i	$0.897568\pi$
$432$	952384.	+	3.09398e6i	0.245529	+	0.797641i
$433$			105036.i			0.0269227i	0.999909	+	0.0134614i	$0.00428501\pi$
$433$			105036.i			0.0269227i	−0.999909	+	0.0134614i	$0.995715\pi$
$434$	199083.	−	8.44417e6i	0.0507353	−	2.15195i
$435$	3.67589e6	−	1.76933e6i	0.931407	−	0.448318i
$436$	2.93422e6	−	5.08222e6i	0.739224	−	1.28037i
$437$	3.49991e6	−	6.06203e6i	0.876705	−	1.51850i
$438$	−2.16315e6	+	3.17143e6i	−0.538768	+	0.789897i
$439$	−3.99365e6	+	2.30573e6i	−0.989028	+	0.571015i	−0.904983	−	0.425447i	$-0.860117\pi$
$439$	−3.99365e6	+	2.30573e6i	−0.989028	+	0.571015i	−0.0840441	+	0.996462i	$0.526784\pi$
$440$	−6.65161e6			−1.63793
$441$	2.69524e6	−	3.06848e6i	0.659935	−	0.751323i
$442$	177387.			0.0431884
$443$	417658.	−	241135.i	0.101114	−	0.0583782i	−0.448590	−	0.893738i	$-0.648074\pi$
$443$	417658.	−	241135.i	0.101114	−	0.0583782i	0.549704	+	0.835359i	$0.314740\pi$
$444$	−1.19824e7	−	900308.i	−2.88461	−	0.216737i
$445$	−2.38671e6	+	4.13390e6i	−0.571346	+	0.989600i
$446$	1.16724e6	−	2.02171e6i	0.277858	−	0.481263i
$447$	−211939.	+	2.82076e6i	−0.0501699	+	0.667724i
$448$	−115760.	+	4.90999e6i	−0.0272498	+	1.15581i
$449$			1.59561e6i			0.373516i	0.982406	+	0.186758i	$0.0597981\pi$
$449$			1.59561e6i			0.373516i	−0.982406	+	0.186758i	$0.940202\pi$
$450$	−2.63686e6	+	1.03371e6i	−0.613841	+	0.240639i
$451$		−	4.02274e6i		−	0.931282i
$452$	−3.28590e6	+	1.89712e6i	−0.756499	+	0.436765i
$453$	−302702.	+	443797.i	−0.0693059	+	0.101610i
$454$	6.98447e6	+	4.03249e6i	1.59035	+	0.918192i
$455$	66150.2	+	121079.i	0.0149797	+	0.0274184i
$456$	−3.21424e6	−	6.67776e6i	−0.723879	−	1.50390i
$457$	189929.	+	328967.i	0.0425404	+	0.0736821i	0.886512	−	0.462706i	$-0.153122\pi$
$457$	189929.	+	328967.i	0.0425404	+	0.0736821i	−0.843971	+	0.536388i	$0.819788\pi$
$458$	−7.47428e6			−1.66497
$459$	4.17071e6	+	954504.i	0.924013	+	0.211469i
$460$			1.76568e7i			3.89060i
$461$	−4.27982e6	−	7.41287e6i	−0.937937	−	1.62455i	−0.769311	−	0.638874i	$-0.779400\pi$
$461$	−4.27982e6	−	7.41287e6i	−0.937937	−	1.62455i	−0.168626	−	0.985680i	$-0.553933\pi$
$462$	−665937.	+	6.73430e6i	−0.145154	+	1.46787i
$463$	−1.99695e6	+	3.45882e6i	−0.432927	+	0.749851i	−0.997124	−	0.0757888i	$-0.975853\pi$
$463$	−1.99695e6	+	3.45882e6i	−0.432927	+	0.749851i	0.564197	+	0.825640i	$0.309186\pi$
$464$	−2.94489e6	−	1.70023e6i	−0.635000	−	0.366617i
$465$	5.68579e6	+	3.87813e6i	1.21943	+	0.831744i
$466$	−3.85313e6	−	6.67381e6i	−0.821956	−	1.42367i
$467$	7.96510e6			1.69005			0.845024	−	0.534729i	$-0.179586\pi$
$467$	7.96510e6			1.69005			0.845024	+	0.534729i	$0.179586\pi$
$468$	−36546.7	+	241831.i	−0.00771317	+	0.0510385i
$469$	1.84447e6	+	1.12369e6i	0.387204	+	0.235892i
$470$	−5.57174e6	+	3.21685e6i	−1.16345	+	0.671716i
$471$	172686.	−	2.29833e6i	0.0358679	−	0.477375i
$472$	5.08201e6	+	2.93410e6i	1.04998	+	0.606205i
$473$	3.56308e6	+	2.05715e6i	0.732273	+	0.422778i
$474$	644687.	−	8.58030e6i	0.131796	−	1.75411i
$475$	1.68671e6	−	973822.i	0.343009	−	0.198037i
$476$	−7.77843e6	−	4.73877e6i	−1.57353	−	0.958624i
$477$	−1.16628e6	−	930820.i	−0.234696	−	0.187314i
$478$	841606.			0.168476
$479$	1.65799e6	+	2.87173e6i	0.330175	+	0.571879i	0.982546	−	0.186020i	$-0.0595590\pi$
$479$	1.65799e6	+	2.87173e6i	0.330175	+	0.571879i	−0.652371	+	0.757900i	$0.726226\pi$
$480$	−919518.	−	627179.i	−0.182162	−	0.124248i
$481$	−173660.	−	100262.i	−0.0342244	−	0.0197595i
$482$	−6.44852e6	+	1.11692e7i	−1.26428	+	2.18979i
$483$	8.67975e6	+	858317.i	1.69293	+	0.167409i
$484$	1.30690e6	+	2.26361e6i	0.253587	+	0.439226i
$485$		−	5.92457e6i		−	1.14367i
$486$	−3.27206e6	+	8.31323e6i	−0.628391	+	1.59654i
$487$	−5.66667e6			−1.08269			−0.541347	−	0.840799i	$-0.682085\pi$
$487$	−5.66667e6			−1.08269			−0.541347	+	0.840799i	$0.682085\pi$
$488$	−7.22328e6	−	1.25111e7i	−1.37305	−	2.37818i
$489$	−2.42487e6	−	5.03781e6i	−0.458582	−	0.952730i
$490$	505618.	−	1.07170e7i	0.0951332	−	2.01643i
$491$	492580.	+	284391.i	0.0922089	+	0.0532368i	0.545395	−	0.838179i	$-0.316380\pi$
$491$	492580.	+	284391.i	0.0922089	+	0.0532368i	−0.453187	+	0.891416i	$0.649713\pi$
$492$	−6.37059e6	+	9.34003e6i	−1.18650	+	1.73954i
$493$	−3.89215e6	+	2.24713e6i	−0.721227	+	0.416400i
$494$		−	254713.i		−	0.0469607i
$495$	−4.30972e6	−	3.43963e6i	−0.790562	−	0.630956i
$496$		−	5.73679e6i		−	1.04704i
$497$	1.13651e6	+	26794.9i	0.206388	+	0.00486588i
$498$	1.36262e6	−	1.81355e7i	0.246208	−	3.27684i
$499$	2.74494e6	−	4.75437e6i	0.493493	−	0.854755i	−0.506479	−	0.862252i	$-0.669053\pi$
$499$	2.74494e6	−	4.75437e6i	0.493493	−	0.854755i	0.999972	+	0.00749763i	$0.00238659\pi$
$500$	3.93591e6	−	6.81719e6i	0.704077	−	1.21950i
$501$	2.17456e6	+	163387.i	0.387060	+	0.0290820i
$502$	−7.23719e6	+	4.17839e6i	−1.28177	+	0.740031i
$503$	−3.39621e6			−0.598514			−0.299257	−	0.954173i	$-0.596739\pi$
$503$	−3.39621e6			−0.598514			−0.299257	+	0.954173i	$0.596739\pi$
$504$	5.92895e6	−	7.07980e6i	1.03968	−	1.24149i
$505$	9.89808e6			1.72712
$506$	−1.25158e7	+	7.22603e6i	−2.17312	+	1.25465i
$507$	3.25906e6	−	4.77817e6i	0.563084	−	0.825546i
$508$	7.69689e6	−	1.33314e7i	1.32329	−	2.29201i
$509$	3.81494e6	−	6.60767e6i	0.652669	−	1.13046i	−0.329803	−	0.944050i	$-0.606982\pi$
$509$	3.81494e6	−	6.60767e6i	0.652669	−	1.13046i	0.982473	−	0.186407i	$-0.0596843\pi$
$510$	1.01276e7	−	4.87476e6i	1.72417	−	0.829903i
$511$	3.28851e6	+	77531.3i	0.557118	+	0.0131348i
$512$			8.94414e6i			1.50787i
$513$	1.37059e6	−	5.98879e6i	0.229939	−	1.00472i
$514$			7.58107e6i			1.26568i
$515$	3.94370e6	−	2.27689e6i	0.655217	−	0.378290i
$516$	−5.01500e6	−	1.04189e7i	−0.829175	−	1.72266i
$517$	−3.01129e6	−	1.73857e6i	−0.495480	−	0.286066i
$518$	7.47616e6	+	1.36841e7i	1.22420	+	2.24075i
$519$	−3.01825e6	+	4.42511e6i	−0.491855	+	0.721117i
$520$	155983.	+	270170.i	0.0252969	+	0.0438155i
$521$	1.89954e6			0.306587			0.153293	−	0.988181i	$-0.451012\pi$
$521$	1.89954e6			0.306587			0.153293	+	0.988181i	$0.451012\pi$
$522$	−3.42511e6	−	8.73706e6i	−0.550172	−	1.40342i
$523$			362076.i			0.0578823i	0.999581	+	0.0289412i	$0.00921355\pi$
$523$			362076.i			0.0578823i	−0.999581	+	0.0289412i	$0.990786\pi$
$524$	5.79820e6	+	1.00428e7i	0.922497	+	1.59781i
$525$	1.97210e6	+	1.41436e6i	0.312270	+	0.223955i
$526$	−5.29011e6	+	9.16274e6i	−0.833682	+	1.44398i
$527$	−6.56629e6	−	3.79105e6i	−1.02990	−	0.594611i
$528$	−344366.	+	4.58326e6i	−0.0537571	+	0.715467i
$529$	6.09536e6	+	1.05575e7i	0.947022	+	1.64029i
$530$	−3.91998e6			−0.606170
$531$	1.77548e6	+	4.52904e6i	0.273262	+	0.697059i
$532$	−6.80447e6	+	1.11692e7i	−1.04235	+	1.71097i
$533$	−163393.	+	94334.8i	−0.0249123	+	0.0143831i
$534$	9.07137e6	+	6.18735e6i	1.37664	+	0.938969i
$535$	−6.25328e6	−	3.61033e6i	−0.944547	−	0.545334i
$536$	4.22924e6	+	2.44175e6i	0.635843	+	0.367104i
$537$	−1.02096e7	+	4.91423e6i	−1.52782	+	0.735393i
$538$	1.04157e7	−	6.01351e6i	1.55143	−	0.895721i
$539$	5.15273e6	−	2.65939e6i	0.763951	−	0.394285i
$540$	4.55917e6	+	1.48112e7i	0.672824	+	2.18578i
$541$	−9.79666e6			−1.43908			−0.719540	−	0.694451i	$-0.755647\pi$
$541$	−9.79666e6			−1.43908			−0.719540	+	0.694451i	$0.755647\pi$
$542$	7.31467e6	+	1.26694e7i	1.06954	+	1.85250i
$543$	−3.35416e6	+	1.61447e6i	−0.488184	+	0.234980i
$544$	1.06191e6	+	613097.i	0.153848	+	0.0888243i
$545$	3.10260e6	−	5.37386e6i	0.447440	−	0.774989i
$546$	289145.	−	130873.i	0.0415082	−	0.0187875i
$547$	2.85035e6	+	4.93695e6i	0.407314	+	0.705489i	0.994588	−	0.103900i	$-0.0331321\pi$
$547$	2.85035e6	+	4.93695e6i	0.407314	+	0.705489i	−0.587274	+	0.809388i	$0.699799\pi$
$548$			1.23782e7i			1.76079i
$549$	1.78953e6	−	1.18414e7i	0.253401	−	1.67677i
$550$	−4.02116e6			−0.566820
$551$	3.22669e6	+	5.58879e6i	0.452771	+	0.784222i
$552$	1.96660e7	+	1.47761e6i	2.74706	+	0.206402i
$553$	−6.47022e6	+	3.53492e6i	−0.899717	+	0.491549i
$554$	1.02978e7	+	5.94543e6i	1.42551	+	0.823018i
$555$	−1.26701e7	−	951973.i	−1.74601	−	0.131187i
$556$	1.59464e7	−	9.20666e6i	2.18764	−	1.26303i
$557$		−	7.01577e6i		−	0.958159i	−0.877771	−	0.479080i	$-0.840971\pi$
$557$		−	7.01577e6i		−	0.958159i	0.877771	−	0.479080i	$-0.159029\pi$
$558$	9.87599e6	−	1.23742e7i	1.34275	−	1.68241i
$559$		−	192963.i		−	0.0261183i
$560$	171753.	−	7.28495e6i	0.0231438	−	0.981650i
$561$	5.01840e6	+	3.42292e6i	0.673221	+	0.459187i
$562$	−4.62560e6	+	8.01177e6i	−0.617771	+	1.07001i
$563$	−6.83596e6	+	1.18402e7i	−0.908926	+	1.57431i	−0.0933666	+	0.995632i	$0.529763\pi$
$563$	−6.83596e6	+	1.18402e7i	−0.908926	+	1.57431i	−0.815559	+	0.578674i	$0.803570\pi$
$564$	4.23836e6	+	8.80544e6i	0.561048	+	1.16561i
$565$	−3.47447e6	+	2.00598e6i	−0.457896	+	0.264367i
$566$	−1.35737e7			−1.78097
$567$	7.50255e6	−	1.52122e6i	0.980057	−	0.198716i
$568$	2.57047e6			0.334304
$569$	5.05105e6	−	2.91623e6i	0.654035	−	0.377607i	−0.135965	−	0.990714i	$-0.543414\pi$
$569$	5.05105e6	−	2.91623e6i	0.654035	−	0.377607i	0.790000	+	0.613106i	$0.210080\pi$
$570$	−6.99974e6	−	1.45424e7i	−0.902391	−	1.87477i
$571$	5.10348e6	−	8.83948e6i	0.655052	−	1.13458i	−0.326828	−	0.945084i	$-0.605980\pi$
$571$	5.10348e6	−	8.83948e6i	0.655052	−	1.13458i	0.981881	−	0.189500i	$-0.0606867\pi$
$572$	−173623.	+	300724.i	−0.0221880	+	0.0384307i
$573$	1.95639e6	+	1.33441e6i	0.248926	+	0.169786i
$574$	1.46672e7	+	345801.i	1.85810	+	0.0438073i
$575$			5.18282e6i			0.653727i
$576$	−5.74254e6	+	7.19516e6i	−0.721187	+	0.903617i
$577$		−	1.78932e6i		−	0.223742i	−0.993723	−	0.111871i	$-0.964316\pi$
$577$		−	1.78932e6i		−	0.223742i	0.993723	−	0.111871i	$-0.0356844\pi$
$578$	1.21112e6	−	699239.i	0.150788	−	0.0870575i
$579$	4.29458e6	+	322676.i	0.532383	+	0.0400009i
$580$	−1.40975e7	−	8.13920e6i	−1.74009	−	1.00464i
$581$	−1.36756e7	+	7.47148e6i	−1.68076	+	0.918261i
$582$	−1.35903e7	−	1.02112e6i	−1.66312	−	0.124959i
$583$	−1.05929e6	−	1.83475e6i	−0.129076	−	0.223566i
$584$	7.43768e6			0.902413
$585$	−38643.9	+	255709.i	−0.00466865	+	0.0308928i
$586$		−	985233.i		−	0.118521i
$587$	−168038.	−	291050.i	−0.0201285	−	0.0348636i	0.855786	−	0.517330i	$-0.173074\pi$
$587$	−168038.	−	291050.i	−0.0201285	−	0.0348636i	−0.875914	+	0.482467i	$0.839741\pi$
$588$	−1.61752e7	−	1.98550e6i	−1.92933	−	0.236824i
$589$	−5.44363e6	+	9.42864e6i	−0.646547	+	1.11985i
$590$	1.10672e7	+	6.38967e6i	1.30891	+	0.755698i
$591$	−2.09040e6	+	1.00618e6i	−0.246185	+	0.118497i
$592$	5.29538e6	+	9.17186e6i	0.621001	+	1.07561i
$593$	−2.65006e6			−0.309470			−0.154735	−	0.987956i	$-0.549452\pi$
$593$	−2.65006e6			−0.309470			−0.154735	+	0.987956i	$0.549452\pi$
$594$	−8.63296e6	+	9.29321e6i	−1.00391	+	1.08069i
$595$	−8.22480e6	−	5.01071e6i	−0.952430	−	0.580239i
$596$	9.77504e6	−	5.64362e6i	1.12720	−	0.650792i
$597$	7.12701e6	−	3.43047e6i	0.818411	−	0.393929i
$598$	587002.	+	338906.i	0.0671253	+	0.0387548i
$599$	−707016.	−	408196.i	−0.0805123	−	0.0464838i	0.459203	−	0.888331i	$-0.348135\pi$
$599$	−707016.	−	408196.i	−0.0805123	−	0.0464838i	−0.539716	+	0.841847i	$0.681468\pi$
$600$	4.53323e6	+	3.09200e6i	0.514078	+	0.350640i
$601$	−9.60490e6	+	5.54539e6i	−1.08469	+	0.626247i	−0.932158	−	0.362051i	$-0.882077\pi$
$601$	−9.60490e6	+	5.54539e6i	−1.08469	+	0.626247i	−0.152534	+	0.988298i	$0.548743\pi$
$602$	−7.80680e6	+	1.28144e7i	−0.877975	+	1.44115i
$603$	1.47755e6	+	3.76906e6i	0.165481	+	0.422123i
$604$	2.14356e6			0.239080
$605$	1.38189e6	+	2.39351e6i	0.153492	+	0.265856i
$606$	1.70597e6	−	2.27052e7i	0.188708	−	2.51156i
$607$	2.81198e6	+	1.62350e6i	0.309771	+	0.178846i	0.646824	−	0.762639i	$-0.276097\pi$
$607$	2.81198e6	+	1.62350e6i	0.309771	+	0.178846i	−0.337053	+	0.941486i	$0.609430\pi$
$608$	880355.	−	1.52482e6i	0.0965826	−	0.167286i
$609$	−4.68638e6	+	6.53442e6i	−0.512028	+	0.713944i
$610$	−1.57303e7	−	2.72458e7i	−1.71164	−	2.96466i
$611$			163080.i			0.0176725i
$612$	−6.23106e6	−	1.58947e7i	−0.672486	−	1.71543i
$613$	1.15559e7			1.24209			0.621046	−	0.783774i	$-0.286708\pi$
$613$	1.15559e7			1.24209			0.621046	+	0.783774i	$0.286708\pi$
$614$	−1.95398e6	−	3.38439e6i	−0.209170	−	0.362293i
$615$	−6.73618e6	+	9.87602e6i	−0.718167	+	1.05292i
$616$	1.15058e7	−	6.28605e6i	1.22170	−	0.667461i
$617$	−1.42413e6	−	822219.i	−0.150604	−	0.0869510i	0.422804	−	0.906221i	$-0.361046\pi$
$617$	−1.42413e6	−	822219.i	−0.150604	−	0.0869510i	−0.573408	+	0.819270i	$0.694379\pi$
$618$	−4.54325e6	−	9.43886e6i	−0.478515	−	0.994142i
$619$	−1.02958e7	+	5.94427e6i	−1.08002	+	0.623551i	−0.930902	−	0.365268i	$-0.880977\pi$
$619$	−1.02958e7	+	5.94427e6i	−1.08002	+	0.623551i	−0.149120	+	0.988819i	$0.547644\pi$
$620$		−	2.74627e7i		−	2.86922i
$621$	1.19779e7	+	1.11269e7i	1.24638	+	1.15783i
$622$		−	1.53120e7i		−	1.58693i
$623$	221766.	−	9.40626e6i	0.0228915	−	0.970950i
$624$	194235.	−	93491.8i	0.0199694	−	0.00961196i
$625$	6.03813e6	−	1.04583e7i	0.618304	−	1.07093i
$626$	−3.63960e6	+	6.30398e6i	−0.371209	+	0.642952i
$627$	4.91502e6	−	7.20600e6i	0.499294	−	0.732024i
$628$	−7.96461e6	+	4.59837e6i	−0.805871	+	0.465270i
$629$	1.39974e7			1.41065
$630$	1.29116e7	−	1.54179e7i	1.29608	−	1.54765i
$631$	−2.68920e6			−0.268875			−0.134437	−	0.990922i	$-0.542923\pi$
$631$	−2.68920e6			−0.268875			−0.134437	+	0.990922i	$0.542923\pi$
$632$	−1.44373e7	+	8.33536e6i	−1.43778	+	0.830103i
$633$	471794.	+	35448.6i	0.0467997	+	0.00351633i
$634$	1.13022e7	−	1.95761e7i	1.11671	−	1.93420i
$635$	8.13858e6	−	1.40964e7i	0.800967	−	1.38732i
$636$	−446116.	+	5.93747e6i	−0.0437325	+	0.582048i
$637$	−228850.	−	146926.i	−0.0223462	−	0.0143466i
$638$		−	1.33239e7i		−	1.29592i
$639$	1.66546e6	+	1.32922e6i	0.161355	+	0.128779i
$640$			2.18988e7i			2.11335i
$641$	−5.29002e6	+	3.05420e6i	−0.508525	+	0.293597i	−0.732227	−	0.681060i	$-0.761519\pi$
$641$	−5.29002e6	+	3.05420e6i	−0.508525	+	0.293597i	0.223702	+	0.974658i	$0.428186\pi$
$642$	−9.35951e6	+	1.37221e7i	−0.896221	+	1.31397i
$643$	8.03058e6	+	4.63646e6i	0.765984	+	0.442241i	0.831440	−	0.555614i	$-0.187517\pi$
$643$	8.03058e6	+	4.63646e6i	0.765984	+	0.442241i	−0.0654561	+	0.997855i	$0.520850\pi$
$644$	−1.66864e7	−	3.05423e7i	−1.58543	−	2.90193i
$645$	−5.30279e6	−	1.10168e7i	−0.501886	−	1.04270i
$646$	8.88998e6	+	1.53979e7i	0.838146	+	1.45171i
$647$	−7.17731e6			−0.674063			−0.337032	−	0.941493i	$-0.609423\pi$
$647$	−7.17731e6			−0.674063			−0.337032	+	0.941493i	$0.609423\pi$
$648$	1.68781e7	−	3.83848e6i	1.57902	−	0.359105i
$649$			6.90669e6i			0.643663i
$650$	94297.7	+	163328.i	0.00875422	+	0.0151628i
$651$	−1.35001e7	−	1.33499e6i	−1.24849	−	0.123460i
$652$	−1.11548e7	+	1.93206e7i	−1.02764	+	1.77993i
$653$	−1.57921e7	−	9.11758e6i	−1.44930	−	0.836751i	−0.450856	−	0.892597i	$-0.648881\pi$
$653$	−1.57921e7	−	9.11758e6i	−1.44930	−	0.836751i	−0.998439	+	0.0558452i	$0.982215\pi$
$654$	−1.17923e7	−	8.04325e6i	−1.07809	−	0.735338i
$655$	6.13094e6	+	1.06191e7i	0.558372	+	0.967129i
$656$	9.96461e6			0.904067
$657$	4.81903e6	+	3.84612e6i	0.435558	+	0.347624i
$658$	6.59782e6	−	1.08300e7i	0.594067	−	0.975129i
$659$	−1.32789e7	+	7.66658e6i	−1.19110	+	0.687683i	−0.958556	−	0.284903i	$-0.908039\pi$
$659$	−1.32789e7	+	7.66658e6i	−1.19110	+	0.687683i	−0.232545	+	0.972586i	$0.574705\pi$
$660$	−1.64852e6	+	2.19406e7i	−0.147311	+	1.96060i
$661$	−7.54042e6	−	4.35346e6i	−0.671262	−	0.387553i	0.125293	−	0.992120i	$-0.460013\pi$
$661$	−7.54042e6	−	4.35346e6i	−0.671262	−	0.387553i	−0.796555	+	0.604567i	$0.793346\pi$
$662$	2.39649e7	+	1.38361e7i	2.12535	+	1.22707i
$663$	21346.2	−	284102.i	0.00188598	−	0.0251010i
$664$	−3.05149e7	+	1.76178e7i	−2.68591	+	1.55071i
$665$	−7.19496e6	+	1.18101e7i	−0.630920	+	1.03562i
$666$	−4.36745e6	+	2.88997e7i	−0.381542	+	2.52469i
$667$	−1.71729e7			−1.49462
$668$	−4.35075e6	−	7.53572e6i	−0.377245	−	0.653407i
$669$	−3.09750e6	−	2.11272e6i	−0.267575	−	0.182506i
$670$	9.21013e6	+	5.31747e6i	0.792645	+	0.457634i
$671$	8.50159e6	−	1.47252e7i	0.728943	−	1.26257i
$672$	2.18327e6	+	215898.i	0.186503	+	0.0184427i
$673$	−8.24982e6	−	1.42891e7i	−0.702113	−	1.21610i	−0.967723	−	0.252015i	$-0.918907\pi$
$673$	−8.24982e6	−	1.42891e7i	−0.702113	−	1.21610i	0.265610	−	0.964080i	$-0.414427\pi$
$674$		−	2.15836e7i		−	1.83010i
$675$	1.33826e6	+	4.34756e6i	0.113053	+	0.367271i
$676$	−2.30788e7			−1.94244
$677$	−8.91620e6	−	1.54433e7i	−0.747667	−	1.29500i	−0.948938	−	0.315461i	$-0.897841\pi$
$677$	−8.91620e6	−	1.54433e7i	−0.747667	−	1.29500i	0.201272	−	0.979535i	$-0.435493\pi$
$678$	4.00268e6	+	8.31581e6i	0.334408	+	0.694752i
$679$	5.59896e6	+	1.02482e7i	0.466051	+	0.853046i
$680$	−1.88589e7	−	1.08882e7i	−1.56402	−	0.902989i
$681$	7.29887e6	−	1.07010e7i	0.603098	−	0.884212i
$682$	1.94667e7	−	1.12391e7i	1.60262	−	0.925273i
$683$			2.19057e7i			1.79683i	0.439151	+	0.898413i	$0.355279\pi$
$683$			2.19057e7i			1.79683i	−0.439151	+	0.898413i	$0.644721\pi$
$684$	−2.28235e7	+	8.94728e6i	−1.86527	+	0.731225i
$685$			1.30886e7i			1.06578i
$686$	9.25341e6	+	1.90159e7i	0.750744	+	1.54279i
$687$	−899428.	+	1.19707e7i	−0.0727067	+	0.967673i
$688$	−5.09569e6	+	8.82599e6i	−0.410423	+	0.710873i
$689$	−49681.5	+	86050.9i	−0.00398701	+	0.00690570i
$690$	4.28271e7	+	3.21784e6i	3.42449	+	0.257301i
$691$	1.56485e7	−	9.03467e6i	1.24675	−	0.719809i	0.276287	−	0.961075i	$-0.410896\pi$
$691$	1.56485e7	−	9.03467e6i	1.24675	−	0.719809i	0.970459	+	0.241266i	$0.0775626\pi$
$692$	2.13735e7			1.69672
$693$	1.07055e7	+	1.87694e6i	0.846782	+	0.148463i
$694$	2.62339e7			2.06759
$695$	1.68615e7	−	9.73500e6i	1.32414	−	0.764493i
$696$	−1.02451e7	+	1.50205e7i	−0.801667	+	1.17534i
$697$	6.58492e6	−	1.14054e7i	0.513415	−	0.889261i
$698$	−5.17203e6	+	8.95821e6i	−0.401811	+	0.695958i
$699$	−1.11524e7	+	5.36802e6i	−0.863325	+	0.415548i
$700$	228244.	−	9.68103e6i	0.0176057	−	0.746752i
$701$			6.25237e6i			0.480562i	0.970703	+	0.240281i	$0.0772396\pi$
$701$			6.25237e6i			0.480562i	−0.970703	+	0.240281i	$0.922760\pi$
$702$	579910.	+	132718.i	0.0444138	+	0.0101645i
$703$		−	2.00991e7i		−	1.53387i
$704$	−1.13192e7	+	6.53513e6i	−0.860762	+	0.496961i
$705$	4.48158e6	+	9.31075e6i	0.339593	+	0.705524i
$706$	−1.55534e7	−	8.97975e6i	−1.17439	−	0.678036i
$707$	−1.71215e7	+	9.35410e6i	−1.28823	+	0.703807i
$708$	1.09377e7	−	1.60360e7i	0.820058	−	1.20230i
$709$	−3.29799e6	−	5.71229e6i	−0.246396	−	0.426770i	0.716127	−	0.697970i	$-0.245913\pi$
$709$	−3.29799e6	−	5.71229e6i	−0.246396	−	0.426770i	−0.962523	+	0.271199i	$0.912580\pi$
$710$	5.59779e6			0.416745
$711$	−1.36645e7	−	2.06505e6i	−1.01373	−	0.153199i
$712$		−	2.12743e7i		−	1.57273i
$713$	−1.44859e7	−	2.50903e7i	−1.06714	−	1.84834i
$714$	−1.29116e7	+	1.80032e7i	−0.947840	+	1.32162i
$715$	−183587.	+	317982.i	−0.0134300	+	0.0232615i
$716$	3.91551e7	+	2.26062e7i	2.85434	+	1.64795i
$717$	101276.	−	1.34791e6i	0.00735713	−	0.0979179i
$718$	270060.	+	467757.i	0.0195501	+	0.0338617i
$719$	1.23687e7			0.892279			0.446140	−	0.894963i	$-0.352798\pi$
$719$	1.23687e7			0.892279			0.446140	+	0.894963i	$0.352798\pi$
$720$	8.52020e6	−	1.06755e7i	0.612518	−	0.767459i
$721$	−4.66996e6	+	7.66548e6i	−0.334561	+	0.549163i
$722$	1.29740e6	−	749056.i	0.0926257	−	0.0534775i
$723$	1.71124e7	+	1.16719e7i	1.21749	+	0.830419i
$724$	1.28636e7	+	7.42682e6i	0.912046	+	0.526570i
$725$	−4.13806e6	−	2.38911e6i	−0.292383	−	0.168807i
$726$	5.72864e6	−	2.75739e6i	0.403376	−	0.194159i
$727$	1.72901e7	−	9.98246e6i	1.21328	−	0.700489i	0.249810	−	0.968295i	$-0.419632\pi$
$727$	1.72901e7	−	9.98246e6i	1.21328	−	0.700489i	0.963473	+	0.267806i	$0.0862985\pi$
$728$	−525137.	−	319923.i	−0.0367235	−	0.0223727i
$729$	1.29206e7	+	6.24087e6i	0.900461	+	0.434937i
$730$	1.61972e7			1.12495
$731$	6.73478e6	+	1.16650e7i	0.466154	+	0.807403i
$732$	−4.30585e7	+	2.07255e7i	−2.97017	+	1.42964i
$733$	−1.49470e7	−	8.62966e6i	−1.02753	−	0.593244i	−0.111253	−	0.993792i	$-0.535487\pi$
$733$	−1.49470e7	−	8.62966e6i	−1.02753	−	0.593244i	−0.916276	+	0.400548i	$0.868820\pi$
$734$	1.29895e7	−	2.24985e7i	0.889923	−	1.54139i
$735$	−1.71034e7	−	2.09944e6i	−1.16779	−	0.143346i
$736$	2.34269e6	+	4.05766e6i	0.159412	+	0.276109i
$737$			5.74774e6i			0.389788i
$738$	2.14936e7	+	1.71543e7i	1.45267	+	1.15939i
$739$	−1.58816e7			−1.06976			−0.534878	−	0.844930i	$-0.679642\pi$
$739$	−1.58816e7			−1.06976			−0.534878	+	0.844930i	$0.679642\pi$
$740$	2.53496e7	+	4.39067e7i	1.70173	+	2.94749i
$741$	−407946.	−	30651.3i	−0.0272934	−	0.00205071i
$742$	6.78069e6	−	3.70454e6i	0.452131	−	0.247016i
$743$	1.27508e7	+	7.36165e6i	0.847352	+	0.489219i	0.859756	−	0.510704i	$-0.170615\pi$
$743$	1.27508e7	+	7.36165e6i	0.847352	+	0.489219i	−0.0124047	+	0.999923i	$0.503949\pi$
$744$	−3.05877e7	−	2.29822e6i	−2.02588	−	0.152216i
$745$	1.03360e7	−	5.96749e6i	0.682278	−	0.393913i
$746$		−	4.33613e7i		−	2.85270i
$747$	−2.88816e7	−	4.36472e6i	−1.89374	−	0.286190i
$748$		−	2.42391e7i		−	1.58403i
$749$	1.42287e7	+	335462.i	0.926746	+	0.0218493i
$750$	−1.58180e7	−	1.07891e7i	−1.02683	−	0.700375i
$751$	−5.01794e6	+	8.69132e6i	−0.324657	+	0.562323i	−0.981443	−	0.191754i	$-0.938582\pi$
$751$	−5.01794e6	+	8.69132e6i	−0.324657	+	0.562323i	0.656786	+	0.754077i	$0.271916\pi$
$752$	4.30655e6	−	7.45917e6i	0.277706	−	0.481001i
$753$	5.82117e6	+	1.20938e7i	0.374130	+	0.777277i
$754$	−541178.	+	312449.i	−0.0346666	+	0.0200148i
$755$	2.26657e6			0.144711
$756$	−2.18836e7	−	2.13115e7i	−1.39256	−	1.35616i
$757$	1.51893e7			0.963382			0.481691	−	0.876341i	$-0.340023\pi$
$757$	1.51893e7			0.963382			0.481691	+	0.876341i	$0.340023\pi$
$758$	1.80783e6	−	1.04375e6i	0.114284	−	0.0659818i
$759$	1.00670e7	+	2.09148e7i	0.634302	+	1.31780i
$760$	−1.56345e7	+	2.70797e7i	−0.981861	+	1.70063i
$761$	−2.26847e6	+	3.92910e6i	−0.141994	+	0.245941i	−0.928248	−	0.371963i	$-0.878685\pi$
$761$	−2.26847e6	+	3.92910e6i	−0.141994	+	0.245941i	0.786253	+	0.617904i	$0.212018\pi$
$762$	−3.09331e7	−	2.10986e7i	−1.92990	−	1.31634i
$763$	−288285.	+	1.22277e7i	−0.0179271	+	0.760383i
$764$		−	9.44949e6i		−	0.585699i
$765$	−6.58864e6	−	1.68068e7i	−0.407045	−	1.03832i
$766$		−	6.76185e6i		−	0.416384i
$767$	280530.	−	161964.i	0.0172184	−	0.00994102i
$768$	3.13890e7	+	2.35843e6i	1.92032	+	0.144285i
$769$	2.79698e7	+	1.61484e7i	1.70559	+	0.984721i	0.939863	+	0.341551i	$0.110952\pi$
$769$	2.79698e7	+	1.61484e7i	1.70559	+	0.984721i	0.765724	+	0.643170i	$0.222381\pi$
$770$	2.50565e7	−	1.36893e7i	1.52298	−	0.832060i
$771$	1.21418e7	+	912279.i	0.735607	+	0.0552703i
$772$	−8.59236e6	−	1.48824e7i	−0.518883	−	0.898732i
$773$	−8.86307e6			−0.533501			−0.266751	−	0.963766i	$-0.585950\pi$
$773$	−8.86307e6			−0.533501			−0.266751	+	0.963766i	$0.585950\pi$
$774$	−2.61855e7	+	1.02653e7i	−1.57111	+	0.615910i
$775$		−	8.06116e6i		−	0.482107i
$776$	1.32024e7	+	2.28672e7i	0.787042	+	1.36320i
$777$	2.28160e7	−	1.03270e7i	1.35577	−	0.613653i
$778$	−1.31162e6	+	2.27179e6i	−0.0776890	+	0.134561i
$779$	−1.63772e7	−	9.45540e6i	−0.966934	−	0.558259i
$780$	929823.	−	447556.i	0.0547222	−	0.0263397i
$781$	1.51268e6	+	2.62005e6i	0.0887403	+	0.153703i
$782$	−4.73138e7			−2.76676
$783$	−1.44053e7	+	4.43424e6i	−0.839691	+	0.258473i
$784$	6.58749e6	+	1.27637e7i	0.382763	+	0.741626i
$785$	−8.42167e6	+	4.86225e6i	−0.487780	+	0.281620i
$786$	2.54158e7	−	1.22335e7i	1.46740	−	0.706308i
$787$	8.48547e6	+	4.89909e6i	0.488359	+	0.281954i	0.723893	−	0.689912i	$-0.242351\pi$
$787$	8.48547e6	+	4.89909e6i	0.488359	+	0.281954i	−0.235535	+	0.971866i	$0.575684\pi$
$788$	8.01696e6	+	4.62860e6i	0.459933	+	0.265542i
$789$	1.40384e7	+	9.57520e6i	0.802830	+	0.547590i
$790$	−3.14405e7	+	1.81522e7i	−1.79234	+	1.03481i
$791$	4.11432e6	−	6.75342e6i	0.233806	−	0.383780i
$792$	2.42993e7	+	3.67221e6i	1.37651	+	0.208025i
$793$	−797461.			−0.0450325
$794$	−1.56565e7	−	2.71178e7i	−0.881340	−	1.52652i
$795$	−471716.	+	6.27820e6i	−0.0264706	+	0.352304i
$796$	−2.73330e7	−	1.57807e7i	−1.52899	−	0.882762i
$797$	59096.5	−	102358.i	0.00329546	−	0.00570791i	−0.864373	−	0.502851i	$-0.832284\pi$
$797$	59096.5	−	102358.i	0.00329546	−	0.00570791i	0.867668	+	0.497143i	$0.165618\pi$
$798$	2.58511e7	+	1.85400e7i	1.43705	+	1.03063i
$799$	−5.69181e6	−	9.85851e6i	−0.315416	−	0.546316i
$800$			1.30367e6i			0.0720182i
$801$	1.10012e7	−	1.37840e7i	0.605841	−	0.759094i
$802$	−2.08249e7			−1.14327
$803$	4.37696e6	+	7.58113e6i	0.239543	+	0.414901i
$804$	9.10237e6	−	1.33451e7i	0.496609	−	0.728086i
$805$	−1.76440e7	−	3.22950e7i	−0.959636	−	1.75649i
$806$	−913000.	−	527121.i	−0.0495032	−	0.0285807i
$807$	−8.37779e6	−	1.74053e7i	−0.452841	−	0.940803i
$808$	−3.82039e7	+	2.20570e7i	−2.05863	+	1.18855i
$809$		−	1.20598e7i		−	0.647842i	−0.946084	−	0.323921i	$-0.894999\pi$
$809$		−	1.20598e7i		−	0.647842i	0.946084	−	0.323921i	$-0.105001\pi$
$810$	3.67560e7	−	8.35917e6i	1.96841	−	0.447662i
$811$			1.31654e7i			0.702884i	0.936210	+	0.351442i	$0.114308\pi$
$811$			1.31654e7i			0.702884i	−0.936210	+	0.351442i	$0.885692\pi$
$812$	3.20774e7	+	756271.i	1.70730	+	0.0402520i
$813$	2.11714e7	−	1.01905e7i	1.12337	−	0.540717i
$814$	−2.07486e7	+	3.59376e7i	−1.09756	+	1.90103i
$815$	−1.17949e7	+	2.04294e7i	−0.622015	+	1.07736i
$816$	−8.47880e6	+	1.24309e7i	−0.445768	+	0.653548i
$817$	1.67499e7	−	9.67057e6i	0.877926	−	0.506871i
$818$	715516.			0.0373883
$819$	−174811.	−	478840.i	−0.00910663	−	0.0249448i
$820$	4.77017e7			2.47742
$821$	−1.02559e7	+	5.92125e6i	−0.531026	+	0.306588i	−0.741434	−	0.671026i	$-0.765854\pi$
$821$	−1.02559e7	+	5.92125e6i	−0.531026	+	0.306588i	0.210408	+	0.977614i	$0.432521\pi$
$822$	3.00238e7	+	2.25586e6i	1.54984	+	0.116448i
$823$	−1.19812e7	+	2.07521e7i	−0.616597	+	1.06798i	0.373505	+	0.927628i	$0.378156\pi$
$823$	−1.19812e7	+	2.07521e7i	−0.616597	+	1.06798i	−0.990102	+	0.140349i	$0.955178\pi$
$824$	−1.01477e7	+	1.75764e7i	−0.520656	+	0.901802i
$825$	−483893.	+	6.44025e6i	−0.0247522	+	0.329434i
$826$	−2.51824e7	−	593709.i	−1.28424	−	0.0302778i
$827$			1.43412e7i			0.729156i	0.931173	+	0.364578i	$0.118787\pi$
$827$			1.43412e7i			0.729156i	−0.931173	+	0.364578i	$0.881213\pi$
$828$	9.74793e6	−	6.45027e7i	0.494125	−	3.26965i
$829$			5.16778e6i			0.261167i	0.991437	+	0.130583i	$0.0416850\pi$
$829$			5.16778e6i			0.261167i	−0.991437	+	0.130583i	$0.958315\pi$
$830$	−6.64532e7	+	3.83668e7i	−3.34827	+	1.93312i
$831$	1.07613e7	−	1.57774e7i	0.540585	−	0.792561i
$832$	530877.	+	306502.i	0.0265880	+	0.0153506i
$833$	1.89624e7	+	894628.i	0.946850	+	0.0446715i
$834$	−1.94249e7	−	4.03564e7i	−0.967040	−	2.00908i
$835$	−4.60043e6	−	7.96817e6i	−0.228340	−	0.395496i
$836$	−3.48053e7			−1.72239
$837$	−1.86299e7	−	1.73063e7i	−0.919174	−	0.853870i
$838$		−	3.58264e7i		−	1.76236i
$839$	−6.44770e6	−	1.11678e7i	−0.316228	−	0.547723i	0.663470	−	0.748203i	$-0.269083\pi$
$839$	−6.44770e6	−	1.11678e7i	−0.316228	−	0.547723i	−0.979698	+	0.200480i	$0.935750\pi$
$840$	−3.87734e7	−	3.83419e6i	−1.89599	−	0.187489i
$841$	−2.33941e6	+	4.05198e6i	−0.114056	+	0.197550i
$842$	6.07677e6	+	3.50842e6i	0.295388	+	0.170542i
$843$	1.22749e7	+	8.37242e6i	0.594909	+	0.405772i
$844$	−943940.	−	1.63495e6i	−0.0456130	−	0.0790040i
$845$	−2.44032e7			−1.17572
$846$	2.21303e7	−	8.67555e6i	1.06307	−	0.416746i
$847$	−4.65233e6	−	2.83429e6i	−0.222824	−	0.135749i
$848$	4.54479e6	−	2.62394e6i	0.217032	−	0.125304i
$849$	−1.63341e6	+	2.17395e7i	−0.0777724	+	1.03509i
$850$	−1.14009e7	−	6.58233e6i	−0.541244	−	0.312487i
$851$	4.63195e7	+	2.67426e7i	2.19250	+	1.26584i
$852$	637060.	−	8.47879e6i	0.0300664	−	0.400161i
$853$	4.14857e6	−	2.39518e6i	0.195221	−	0.112711i	−0.399204	−	0.916862i	$-0.630713\pi$
$853$	4.14857e6	−	2.39518e6i	0.195221	−	0.112711i	0.594424	+	0.804152i	$0.297380\pi$
$854$	5.29584e7	+	3.22633e7i	2.48479	+	1.51378i
$855$	−2.41332e7	+	9.46073e6i	−1.12902	+	0.442598i
$856$	3.21813e7			1.50113
$857$	−1.10039e7	−	1.90593e7i	−0.511793	−	0.886451i	−0.999907	−	0.0136711i	$-0.995648\pi$
$857$	−1.10039e7	−	1.90593e7i	−0.511793	−	0.886451i	0.488114	−	0.872780i	$-0.337685\pi$
$858$	697775.	+	475935.i	0.0323592	+	0.0220714i
$859$	−1.69532e7	−	9.78795e6i	−0.783916	−	0.452594i	0.0539006	−	0.998546i	$-0.482835\pi$
$859$	−1.69532e7	−	9.78795e6i	−0.783916	−	0.452594i	−0.837816	+	0.545952i	$0.816168\pi$
$860$	−2.43936e7	+	4.22510e7i	−1.12468	+	1.94801i
$861$	2.31884e6	−	2.34493e7i	0.106601	−	1.07801i
$862$	−1.18382e7	−	2.05044e7i	−0.542648	−	0.939894i
$863$		−	1.25803e7i		−	0.574994i	−0.957782	−	0.287497i	$-0.907177\pi$
$863$		−	1.25803e7i		−	0.574994i	0.957782	−	0.287497i	$-0.0928231\pi$
$864$	3.01288e6	+	2.79882e6i	0.137308	+	0.127553i
$865$	2.26000e7			1.02700
$866$	−509727.	−	882874.i	−0.0230963	−	0.0400040i
$867$	−974152.	−	2.02386e6i	−0.0440128	−	0.0914391i
$868$	2.59534e7	+	4.75043e7i	1.16921	+	2.14010i
$869$	−1.69922e7	−	9.81048e6i	−0.763311	−	0.440698i
$870$	−2.23111e7	+	3.27107e7i	−0.999362	+	1.46518i
$871$	233457.	−	134786.i	0.0104271	−	0.00602006i
$872$			2.76555e7i			1.23166i
$873$	−3.27083e6	+	2.16433e7i	−0.145252	+	0.961141i
$874$			6.79386e7i			3.00842i
$875$	−386700.	+	1.64020e7i	−0.0170747	+	0.724230i
$876$	1.84334e6	−	2.45335e7i	0.0811605	−	1.08019i
$877$	2.11122e7	−	3.65674e7i	0.926904	−	1.60545i	0.138435	−	0.990372i	$-0.455793\pi$
$877$	2.11122e7	−	3.65674e7i	0.926904	−	1.60545i	0.788470	−	0.615074i	$-0.210874\pi$
$878$	2.23789e7	−	3.87614e7i	0.979721	−	1.69693i
$879$	−1.57794e6	−	118559.i	−0.0688839	−	0.00517564i
$880$	1.67943e7	−	9.69617e6i	0.731062	−	0.422079i
$881$	−8.46050e6			−0.367245			−0.183623	−	0.982997i	$-0.558782\pi$
$881$	−8.46050e6			−0.367245			−0.183623	+	0.982997i	$0.558782\pi$
$882$	−7.76372e6	+	3.88716e7i	−0.336046	+	1.68252i
$883$	−3.60726e7			−1.55696			−0.778478	−	0.627672i	$-0.784008\pi$
$883$	−3.60726e7			−1.55696			−0.778478	+	0.627672i	$0.784008\pi$
$884$	−984525.	+	568416.i	−0.0423737	+	0.0244645i
$885$	1.15654e7	−	1.69562e7i	0.496367	−	0.727732i
$886$	−2.34040e6	+	4.05368e6i	−0.100162	+	0.173486i
$887$	−1.40470e7	+	2.43301e7i	−0.599480	+	1.03833i	0.393418	+	0.919360i	$0.371292\pi$
$887$	−1.40470e7	+	2.43301e7i	−0.599480	+	1.03833i	−0.992898	+	0.118970i	$0.962041\pi$
$888$	5.10243e7	−	2.45598e7i	2.17142	−	1.04518i
$889$	−756213.	+	3.20750e7i	−0.0320915	+	1.36117i
$890$		−	4.63296e7i		−	1.96057i
$891$	1.38450e7	+	1.49448e7i	0.584252	+	0.630659i
$892$			1.49611e7i			0.629579i
$893$	−1.41560e7	+	8.17296e6i	−0.594034	+	0.342966i
$894$	−1.19074e7	−	2.47382e7i	−0.498278	−	1.03520i
$895$	4.14021e7	+	2.39035e7i	1.72768	+	0.997479i
$896$	−2.06953e7	−	3.78801e7i	−0.861195	−	1.57631i
$897$	613425.	−	899353.i	0.0254554	−	0.0373206i
$898$	−7.74328e6	−	1.34118e7i	−0.320431	−	0.555002i
$899$	2.67101e7			1.10224
$900$	1.13226e7	−	1.41867e7i	0.465949	−	0.583815i
$901$		−	6.93592e6i		−	0.284637i
$902$	1.95219e7	+	3.38129e7i	0.798924	+	1.38378i
$903$	1.95840e7	+	1.40453e7i	0.799250	+	0.573209i
$904$	8.94033e6	−	1.54851e7i	0.363858	−	0.630221i
$905$	1.36018e7	+	7.85301e6i	0.552046	+	0.318724i
$906$	390651.	−	5.19928e6i	0.0158113	−	0.210437i
$907$	−1.42587e7	−	2.46968e7i	−0.575521	−	0.996831i	−0.995985	−	0.0895222i	$-0.971466\pi$
$907$	−1.42587e7	−	2.46968e7i	−0.575521	−	0.996831i	0.420464	−	0.907309i	$-0.361867\pi$
$908$	−5.16864e7			−2.08047
$909$	−3.61591e7	−	5.46452e6i	−1.45147	−	0.219352i
$910$	−1.14361e6	−	696706.i	−0.0457797	−	0.0278899i
$911$	1.82419e7	−	1.05320e7i	0.728240	−	0.420450i	−0.0895379	−	0.995983i	$-0.528539\pi$
$911$	1.82419e7	−	1.05320e7i	0.728240	−	0.420450i	0.817778	+	0.575534i	$0.195206\pi$
$912$	1.78497e7	+	1.21748e7i	0.710632	+	0.484704i
$913$	−3.59151e7	−	2.07356e7i	−1.42594	−	0.823266i
$914$	−3.19288e6	−	1.84341e6i	−0.126420	−	0.0729888i
$915$	−4.55294e7	+	2.19149e7i	−1.79779	+	0.865340i
$916$	4.14833e7	−	2.39504e7i	1.63356	−	0.943135i
$917$	−2.06407e7	−	1.25747e7i	−0.810588	−	0.493826i
$918$	−3.96887e7	+	1.22169e7i	−1.55439	+	0.478471i
$919$	3.24330e7			1.26677			0.633385	−	0.773837i	$-0.281665\pi$
$919$	3.24330e7			1.26677			0.633385	+	0.773837i	$0.281665\pi$
$920$	−4.16046e7	−	7.20612e7i	−1.62058	−	2.80693i
$921$	−5.65554e6	+	2.72221e6i	−0.219697	+	0.105748i
$922$	7.19476e7	+	4.15390e7i	2.78733	+	1.60927i
$923$	70946.0	−	122882.i	0.00274109	−	0.00474771i
$924$	−1.78832e7	−	3.95102e7i	−0.689073	−	1.52240i
$925$	7.44090e6	+	1.28880e7i	0.285938	+	0.495258i
$926$		−	3.87638e7i		−	1.48559i
$927$	−1.56639e7	+	6.14058e6i	−0.598688	+	0.234698i
$928$	−4.31962e6			−0.164655
$929$	1.98727e6	+	3.44205e6i	0.0755470	+	0.130851i	0.901324	−	0.433145i	$-0.142596\pi$
$929$	1.98727e6	+	3.44205e6i	0.0755470	+	0.130851i	−0.825777	+	0.563997i	$0.809263\pi$
$930$	−6.66116e7	−	5.00491e6i	−2.52547	−	0.189753i
$931$	1.28461e6	−	2.72284e7i	0.0485733	−	1.02955i
$932$	4.27708e7	+	2.46937e7i	1.61290	+	0.931208i
$933$	−2.45236e7	−	1.84259e6i	−0.922316	−	0.0692988i
$934$	−6.69501e7	+	3.86537e7i	−2.51122	+	1.44985i
$935$		−	2.56301e7i		−	0.958786i
$936$	−420671.	−	1.07308e6i	−0.0156947	−	0.0400353i
$937$			2.79914e7i			1.04154i	0.853697	+	0.520769i	$0.174355\pi$
$937$			2.79914e7i			1.04154i	−0.853697	+	0.520769i	$0.825645\pi$
$938$	−2.09567e7	−	494084.i	−0.777707	−	0.0183355i
$939$	9.65840e6	+	6.58774e6i	0.357471	+	0.243822i
$940$	2.06160e7	−	3.57079e7i	0.760999	−	1.31809i
$941$	−1.18359e6	+	2.05004e6i	−0.0435740	+	0.0754724i	−0.886990	−	0.461789i	$-0.847208\pi$
$941$	−1.18359e6	+	2.05004e6i	−0.0435740	+	0.0754724i	0.843416	+	0.537261i	$0.180541\pi$
$942$	9.70200e6	+	2.01565e7i	0.356233	+	0.740094i
$943$	4.35810e7	−	2.51615e7i	1.59595	−	0.921419i
$944$	−1.71083e7			−0.624853
$945$	−2.31394e7	−	2.25345e7i	−0.842893	−	0.820858i
$946$	−3.99323e7			−1.45076
$947$	2.45114e7	−	1.41517e7i	0.888166	−	0.512783i	0.0148235	−	0.999890i	$-0.495281\pi$
$947$	2.45114e7	−	1.41517e7i	0.888166	−	0.512783i	0.873342	+	0.487108i	$0.161948\pi$
$948$	2.39164e7	+	4.96877e7i	0.864321	+	1.79568i
$949$	205283.	−	355560.i	0.00739923	−	0.0128158i
$950$	−9.45168e6	+	1.63708e7i	−0.339782	+	0.588519i
$951$	−2.99927e7	−	2.04573e7i	−1.07539	−	0.733493i
$952$	4.29114e7	+	1.01170e6i	1.53455	+	0.0361791i
$953$			2.23096e7i			0.795718i	0.917447	+	0.397859i	$0.130247\pi$
$953$			2.23096e7i			0.795718i	−0.917447	+	0.397859i	$0.869753\pi$
$954$	1.43202e7	+	2.16414e6i	0.509424	+	0.0769864i
$955$		−	9.99176e6i		−	0.354514i
$956$	−4.67103e6	+	2.69682e6i	−0.165298	+	0.0954349i
$957$	−2.13393e7	−	1.60335e6i	−0.753184	−	0.0565910i
$958$	−2.78723e7	−	1.60921e7i	−0.981203	−	0.566498i
$959$	−1.23692e7	−	2.26403e7i	−0.434307	−	0.794943i
$960$	3.87323e7	+	2.91018e6i	1.35642	+	0.101916i
$961$	8.21621e6	+	1.42309e7i	0.286988	+	0.497077i
$962$	1.94625e6			0.0678048
$963$	2.08509e7	+	1.66414e7i	0.724535	+	0.578260i
$964$		−	8.26539e7i		−	2.86465i
$965$	−9.08544e6	−	1.57365e7i	−0.314071	−	0.543987i
$966$	−7.71224e7	+	3.49073e7i	−2.65912	+	1.20357i
$967$	1.90396e7	−	3.29775e7i	0.654774	−	1.13410i	−0.327177	−	0.944963i	$-0.606097\pi$
$967$	1.90396e7	−	3.29775e7i	0.654774	−	1.13410i	0.981950	−	0.189138i	$-0.0605694\pi$
$968$	−1.06675e7	−	6.15886e6i	−0.365908	−	0.211257i
$969$	2.57309e7	−	1.23852e7i	0.880330	−	0.423733i
$970$	2.87512e7	+	4.97986e7i	0.981131	+	1.69937i
$971$	1.92906e7			0.656596			0.328298	−	0.944574i	$-0.393525\pi$
$971$	1.92906e7			0.656596			0.328298	+	0.944574i	$0.393525\pi$
$972$	−8.47833e6	−	5.66245e7i	−0.287836	−	1.92238i
$973$	−1.99667e7	+	3.27742e7i	−0.676120	+	1.10981i
$974$	4.76309e7	−	2.74997e7i	1.60876	−	0.928818i
$975$	272932.	−	131372.i	0.00919483	−	0.00442579i
$976$	3.64753e7	+	2.10590e7i	1.22567	+	0.707641i
$977$	−4.90079e7	−	2.82947e7i	−1.64259	−	0.948352i	−0.979907	−	0.199454i	$-0.936083\pi$
$977$	−4.90079e7	−	2.82947e7i	−1.64259	−	0.948352i	−0.662686	−	0.748897i	$-0.730584\pi$
$978$	4.48300e7	+	3.05774e7i	1.49872	+	1.02224i
$979$	2.16846e7	−	1.25196e7i	0.723093	−	0.417478i
$980$	3.15351e7	+	6.11011e7i	1.04889	+	2.03228i
$981$	−1.43010e7	+	1.79186e7i	−0.474455	+	0.594472i
$982$	−5.52046e6			−0.182682
$983$	2.60190e7	+	4.50662e7i	0.858828	+	1.48753i	0.873047	+	0.487635i	$0.162140\pi$
$983$	2.60190e7	+	4.50662e7i	0.858828	+	1.48753i	−0.0142191	+	0.999899i	$0.504526\pi$
$984$	3.99194e6	−	5.31297e7i	0.131430	−	1.74924i
$985$	8.47703e6	+	4.89421e6i	0.278390	+	0.160728i
$986$	2.18101e7	−	3.77762e7i	0.714440	−	1.23745i
$987$	−1.65512e7	−	1.18702e7i	−0.540800	−	0.387852i
$988$	816198.	+	1.41370e6i	0.0266013	+	0.0460748i
$989$			5.14682e7i			1.67320i
$990$	5.29172e7	+	7.99708e6i	1.71597	+	0.259325i
$991$	−2.61346e6			−0.0845341			−0.0422670	−	0.999106i	$-0.513458\pi$
$991$	−2.61346e6			−0.0845341			−0.0422670	+	0.999106i	$0.513458\pi$
$992$	−3.64373e6	−	6.31112e6i	−0.117562	−	0.203623i
$993$	2.50437e7	−	3.67169e7i	0.805981	−	1.18166i
$994$	−9.68293e6	+	5.29014e6i	−0.310843	+	0.169825i
$995$	−2.89015e7	−	1.66863e7i	−0.925471	−	0.534321i
$996$	5.05502e7	+	1.05021e8i	1.61463	+	3.35450i
$997$	−4.21115e7	+	2.43131e7i	−1.34172	+	0.774644i	−0.987060	−	0.160351i	$-0.948737\pi$
$997$	−4.21115e7	+	2.43131e7i	−1.34172	+	0.774644i	−0.354662	+	0.934994i	$0.615404\pi$
$998$			5.32834e7i			1.69342i
$999$	4.57599e7	+	1.04726e7i	1.45068	+	0.332001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.o.a.41.4	yes	76
3.2	odd	2		189.6.o.a.125.36		76
7.6	odd	2	inner	63.6.o.a.41.3	yes	76
9.2	odd	6	inner	63.6.o.a.20.3	✓	76
9.7	even	3		189.6.o.a.62.35		76
21.20	even	2		189.6.o.a.125.35		76
63.20	even	6	inner	63.6.o.a.20.4	yes	76
63.34	odd	6		189.6.o.a.62.36		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.o.a.20.3	✓	76	9.2	odd	6	inner
63.6.o.a.20.4	yes	76	63.20	even	6	inner
63.6.o.a.41.3	yes	76	7.6	odd	2	inner
63.6.o.a.41.4	yes	76	1.1	even	1	trivial
189.6.o.a.62.35		76	9.7	even	3
189.6.o.a.62.36		76	63.34	odd	6
189.6.o.a.125.35		76	21.20	even	2
189.6.o.a.125.36		76	3.2	odd	2

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.40544 + 4.85288i) q^{2} +(6.76084 + 14.0460i) q^{3} +(31.1009 - 53.8683i) q^{4} +(32.8857 - 56.9596i) q^{5} +(-124.992 - 85.2535i) q^{6} +(-3.05564 + 129.606i) q^{7} +293.131i q^{8} +(-151.582 + 189.926i) q^{9} +638.361i q^{10} +(-298.785 + 172.504i) q^{11} +(966.905 + 72.6490i) q^{12} +(14.0132 + 8.09053i) q^{13} +(-603.277 - 1104.22i) q^{14} +(1022.39 + 76.8181i) q^{15} +(-427.303 - 740.110i) q^{16} -1129.50 q^{17} +(352.425 - 2332.02i) q^{18} +1621.87i q^{19} +(-2045.55 - 3542.99i) q^{20} +(-1841.11 + 833.325i) q^{21} +(1674.28 - 2899.93i) q^{22} +(-3737.69 - 2157.95i) q^{23} +(-4117.33 + 1981.81i) q^{24} +(-600.433 - 1039.98i) q^{25} -157.050 q^{26} +(-3692.53 - 845.068i) q^{27} +(6886.61 + 4195.46i) q^{28} +(3445.90 - 1989.49i) q^{29} +(-8966.43 + 4315.85i) q^{30} +(5813.45 + 3356.40i) q^{31} +(-940.164 - 542.804i) q^{32} +(-4443.03 - 3030.47i) q^{33} +(9493.94 - 5481.33i) q^{34} +(7281.81 + 4436.22i) q^{35} +(5516.66 + 14072.3i) q^{36} -12392.6 q^{37} +(-7870.73 - 13632.5i) q^{38} +(-18.8988 + 251.529i) q^{39} +(16696.7 + 9639.82i) q^{40} +(-5829.95 + 10097.8i) q^{41} +(11431.3 - 15939.1i) q^{42} +(-5962.62 - 10327.6i) q^{43} +21460.1i q^{44} +(5833.24 + 14879.9i) q^{45} +41889.2 q^{46} +(5039.23 + 8728.21i) q^{47} +(7506.68 - 11005.7i) q^{48} +(-16788.3 - 792.057i) q^{49} +(10093.8 + 5827.65i) q^{50} +(-7636.37 - 15865.0i) q^{51} +(871.647 - 503.246i) q^{52} +6140.70i q^{53} +(35138.3 - 10816.2i) q^{54} +22691.6i q^{55} +(-37991.5 - 895.704i) q^{56} +(-22780.8 + 10965.2i) q^{57} +(-19309.5 + 33445.1i) q^{58} +(10009.5 - 17337.0i) q^{59} +(35935.3 - 52685.4i) q^{60} +(-42680.8 + 24641.8i) q^{61} -65152.8 q^{62} +(-24152.3 - 20226.3i) q^{63} +37884.0 q^{64} +(921.668 - 532.125i) q^{65} +(52052.1 + 3910.97i) q^{66} +(8329.89 - 14427.8i) q^{67} +(-35128.5 + 60844.3i) q^{68} +(5040.79 - 67089.2i) q^{69} +(-82735.2 - 1950.60i) q^{70} -8769.01i q^{71} +(-55673.3 - 44433.5i) q^{72} -25373.2i q^{73} +(104165. - 60139.6i) q^{74} +(10548.2 - 15464.8i) q^{75} +(87367.3 + 50441.5i) q^{76} +(-21444.5 - 39251.4i) q^{77} +(-1061.79 - 2205.92i) q^{78} +(28435.6 + 49251.9i) q^{79} -56208.5 q^{80} +(-13094.7 - 57578.7i) q^{81} -113168. i q^{82} +(60102.0 + 104100. i) q^{83} +(-12370.2 + 125094. i) q^{84} +(-37144.3 + 64335.9i) q^{85} +(100237. + 57871.7i) q^{86} +(51241.7 + 34950.6i) q^{87} +(-50566.2 - 87583.2i) q^{88} -72575.9 q^{89} +(-121241. - 96764.0i) q^{90} +(-1091.40 + 1791.47i) q^{91} +(-232491. + 134229. i) q^{92} +(-7840.25 + 104348. i) q^{93} +(-84713.9 - 48909.6i) q^{94} +(92380.9 + 53336.2i) q^{95} +(1267.94 - 16875.4i) q^{96} +(78010.1 - 45039.1i) q^{97} +(144957. - 74814.2i) q^{98} +(12527.5 - 82895.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} + 574 q^{4} - 30 q^{7} + 156 q^{9} - 576 q^{11} + 1392 q^{14} - 666 q^{15} - 8130 q^{16} + 3798 q^{18} + 4194 q^{21} - 130 q^{22} - 8112 q^{23} - 18752 q^{25} - 1732 q^{28} - 35826 q^{29}+ \cdots + 325080 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 + 574 * q^4 - 30 * q^7 + 156 * q^9 - 576 * q^11 + 1392 * q^14 - 666 * q^15 - 8130 * q^16 + 3798 * q^18 + 4194 * q^21 - 130 * q^22 - 8112 * q^23 - 18752 * q^25 - 1732 * q^28 - 35826 * q^29 + 19104 * q^30 - 1092 * q^32 + 71190 * q^36 + 10308 * q^37 - 5016 * q^39 + 51450 * q^42 + 18486 * q^43 - 38056 * q^46 + 7948 * q^49 + 76104 * q^50 - 2346 * q^51 + 164652 * q^56 - 150102 * q^57 + 9902 * q^58 - 115356 * q^60 - 168468 * q^63 - 192648 * q^64 + 12666 * q^65 + 1244 * q^67 + 33024 * q^70 - 17364 * q^72 + 356496 * q^74 - 16458 * q^77 - 412764 * q^78 + 168074 * q^79 - 148872 * q^81 + 162282 * q^84 + 2598 * q^85 + 543300 * q^86 + 69694 * q^88 + 139368 * q^91 - 211794 * q^92 - 196818 * q^93 - 950328 * q^95 + 325080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more