LMFDB - Embedded newform 63.6.o.a.41.5

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			41.5
Character	$\chi$	$=$	63.41
Dual form			63.6.o.a.20.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.10965 + 4.68211i) q^{2} +(-9.16477 + 12.6098i) q^{3} +(27.8443 - 48.2277i) q^{4} +(-41.6759 + 72.1848i) q^{5} +(15.2827 - 145.171i) q^{6} +(-128.575 - 16.6010i) q^{7} +221.824i q^{8} +(-75.0139 - 231.132i) q^{9} -780.524i q^{10} +(-604.787 + 349.174i) q^{11} +(352.955 + 793.106i) q^{12} +(-278.725 - 160.922i) q^{13} +(1120.42 - 467.372i) q^{14} +(-528.285 - 1187.08i) q^{15} +(-147.589 - 255.632i) q^{16} +822.097 q^{17} +(1690.52 + 1523.17i) q^{18} +2142.69i q^{19} +(2320.87 + 4019.86i) q^{20} +(1387.69 - 1469.15i) q^{21} +(3269.74 - 5663.36i) q^{22} +(3181.98 + 1837.12i) q^{23} +(-2797.16 - 2032.97i) q^{24} +(-1911.26 - 3310.40i) q^{25} +3013.82 q^{26} +(3602.01 + 1172.36i) q^{27} +(-4380.69 + 5738.61i) q^{28} +(-5243.42 + 3027.29i) q^{29} +(9842.25 + 7153.33i) q^{30} +(-2138.15 - 1234.46i) q^{31} +(-3753.58 - 2167.13i) q^{32} +(1139.72 - 10826.3i) q^{33} +(-6666.92 + 3849.15i) q^{34} +(6556.80 - 8589.26i) q^{35} +(-13235.7 - 2817.95i) q^{36} +3538.28 q^{37} +(-10032.3 - 17376.4i) q^{38} +(4583.65 - 2039.85i) q^{39} +(-16012.3 - 9244.73i) q^{40} +(-2371.75 + 4107.99i) q^{41} +(-4374.95 + 18411.6i) q^{42} +(-587.782 - 1018.07i) q^{43} +38890.0i q^{44} +(19810.5 + 4217.77i) q^{45} -34406.3 q^{46} +(1409.10 + 2440.64i) q^{47} +(4576.09 + 481.739i) q^{48} +(16255.8 + 4268.92i) q^{49} +(30999.3 + 17897.5i) q^{50} +(-7534.33 + 10366.5i) q^{51} +(-15521.8 + 8961.51i) q^{52} -12675.5i q^{53} +(-34700.2 + 7357.57i) q^{54} -58208.6i q^{55} +(3682.50 - 28521.0i) q^{56} +(-27018.8 - 19637.2i) q^{57} +(28348.2 - 49100.5i) q^{58} +(-9135.35 + 15822.9i) q^{59} +(-71959.9 - 7575.45i) q^{60} +(-2759.58 + 1593.24i) q^{61} +23119.5 q^{62} +(5807.87 + 30963.0i) q^{63} +50032.7 q^{64} +(23232.2 - 13413.1i) q^{65} +(41447.3 + 93134.1i) q^{66} +(8785.35 - 15216.7i) q^{67} +(22890.7 - 39647.8i) q^{68} +(-52327.8 + 23287.4i) q^{69} +(-12957.5 + 100356. i) q^{70} -50169.2i q^{71} +(51270.7 - 16639.9i) q^{72} -10304.5i q^{73} +(-28694.2 + 16566.6i) q^{74} +(59259.8 + 6238.47i) q^{75} +(103337. + 59661.5i) q^{76} +(83556.8 - 34854.8i) q^{77} +(-27620.9 + 38003.6i) q^{78} +(9652.48 + 16718.6i) q^{79} +24603.7 q^{80} +(-47794.8 + 34676.2i) q^{81} -44419.1i q^{82} +(23241.4 + 40255.3i) q^{83} +(-32214.7 - 107833. i) q^{84} +(-34261.6 + 59342.9i) q^{85} +(9533.41 + 5504.11i) q^{86} +(9881.24 - 93862.8i) q^{87} +(-77455.3 - 134156. i) q^{88} -124345. q^{89} +(-180404. + 58550.2i) q^{90} +(33165.5 + 25317.6i) q^{91} +(177200. - 102306. i) q^{92} +(35162.0 - 15648.1i) q^{93} +(-22854.7 - 13195.2i) q^{94} +(-154669. - 89298.4i) q^{95} +(61727.8 - 27470.7i) q^{96} +(68609.1 - 39611.5i) q^{97} +(-151816. + 41492.0i) q^{98} +(126073. + 113593. i) 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 $

$2$	−8.10965	+	4.68211i	−1.43360	+	0.827687i	−0.997393	−	0.0721605i	$-0.977011\pi$
$2$	−8.10965	+	4.68211i	−1.43360	+	0.827687i	−0.436204	+	0.899848i	$0.643677\pi$
$3$	−9.16477	+	12.6098i	−0.587920	+	0.808919i
$3$	−9.16477	+	12.6098i	−0.587920	+	0.808919i
$4$	27.8443	−	48.2277i	0.870133	−	1.50711i
$5$	−41.6759	+	72.1848i	−0.745521	+	1.29128i	0.204429	+	0.978881i	$0.434466\pi$
$5$	−41.6759	+	72.1848i	−0.745521	+	1.29128i	−0.949951	+	0.312400i	$0.898867\pi$
$6$	15.2827	−	145.171i	0.173309	−	1.64628i
$7$	−128.575	−	16.6010i	−0.991767	−	0.128053i
$7$	−128.575	−	16.6010i	−0.991767	−	0.128053i
$8$			221.824i			1.22542i
$9$	−75.0139	−	231.132i	−0.308699	−	0.951160i
$10$		−	780.524i		−	2.46823i
$11$	−604.787	+	349.174i	−1.50703	+	0.870082i	−0.507059	+	0.861911i	$0.669268\pi$
$11$	−604.787	+	349.174i	−1.50703	+	0.870082i	−0.999967	+	0.00817081i	$0.997399\pi$
$12$	352.955	+	793.106i	0.707564	+	1.58993i
$13$	−278.725	−	160.922i	−0.457423	−	0.264093i	0.253537	−	0.967326i	$-0.418406\pi$
$13$	−278.725	−	160.922i	−0.457423	−	0.264093i	−0.710960	+	0.703232i	$0.751739\pi$
$14$	1120.42	−	467.372i	1.52778	−	0.637298i
$15$	−528.285	−	1187.08i	−0.606234	−	1.36224i
$16$	−147.589	−	255.632i	−0.144130	−	0.249641i
$17$	822.097			0.689923			0.344962	−	0.938617i	$-0.387892\pi$
$17$	822.097			0.689923			0.344962	+	0.938617i	$0.387892\pi$
$18$	1690.52	+	1523.17i	1.22981	+	1.10807i
$19$			2142.69i			1.36168i	0.732433	+	0.680839i	$0.238385\pi$
$19$			2142.69i			1.36168i	−0.732433	+	0.680839i	$0.761615\pi$
$20$	2320.87	+	4019.86i	1.29741	+	2.24717i
$21$	1387.69	−	1469.15i	0.686664	−	0.726975i
$22$	3269.74	−	5663.36i	1.44031	−	2.49469i
$23$	3181.98	+	1837.12i	1.25423	+	0.724131i	0.971947	−	0.235200i	$-0.0755745\pi$
$23$	3181.98	+	1837.12i	1.25423	+	0.724131i	0.282284	+	0.959331i	$0.408908\pi$
$24$	−2797.16	−	2032.97i	−0.991264	−	0.720448i
$25$	−1911.26	−	3310.40i	−0.611604	−	1.05933i
$26$	3013.82			0.874346
$27$	3602.01	+	1172.36i	0.950902	+	0.309494i
$28$	−4380.69	+	5738.61i	−1.05596	+	1.38328i
$29$	−5243.42	+	3027.29i	−1.15776	+	0.668434i	−0.950767	−	0.309907i	$-0.899702\pi$
$29$	−5243.42	+	3027.29i	−1.15776	+	0.668434i	−0.206996	+	0.978342i	$0.566369\pi$
$30$	9842.25	+	7153.33i	1.99660	+	1.45113i
$31$	−2138.15	−	1234.46i	−0.399608	−	0.230714i	0.286707	−	0.958018i	$-0.407439\pi$
$31$	−2138.15	−	1234.46i	−0.399608	−	0.230714i	−0.686315	+	0.727305i	$0.740773\pi$
$32$	−3753.58	−	2167.13i	−0.647994	−	0.374120i
$33$	1139.72	−	10826.3i	0.182186	−	1.73060i
$34$	−6666.92	+	3849.15i	−0.989072	+	0.571041i
$35$	6556.80	−	8589.26i	0.904736	−	1.18518i
$36$	−13235.7	−	2817.95i	−1.70212	−	0.362390i
$37$	3538.28			0.424902			0.212451	−	0.977172i	$-0.431855\pi$
$37$	3538.28			0.424902			0.212451	+	0.977172i	$0.431855\pi$
$38$	−10032.3	−	17376.4i	−1.12704	−	1.95210i
$39$	4583.65	−	2039.85i	0.482558	−	0.214752i
$40$	−16012.3	−	9244.73i	−1.58236	−	0.913575i
$41$	−2371.75	+	4107.99i	−0.220348	+	0.381654i	−0.954914	−	0.296884i	$-0.904053\pi$
$41$	−2371.75	+	4107.99i	−0.220348	+	0.381654i	0.734566	+	0.678538i	$0.237386\pi$
$42$	−4374.95	+	18411.6i	−0.382692	+	1.61053i
$43$	−587.782	−	1018.07i	−0.0484780	−	0.0839664i	0.840768	−	0.541395i	$-0.182104\pi$
$43$	−587.782	−	1018.07i	−0.0484780	−	0.0839664i	−0.889246	+	0.457429i	$0.848770\pi$
$44$			38890.0i			3.02835i
$45$	19810.5	+	4217.77i	1.45836	+	0.310493i
$46$	−34406.3			−2.39742
$47$	1409.10	+	2440.64i	0.0930461	+	0.161161i	0.908791	−	0.417251i	$-0.137006\pi$
$47$	1409.10	+	2440.64i	0.0930461	+	0.161161i	−0.815745	+	0.578411i	$0.803673\pi$
$48$	4576.09	+	481.739i	0.286676	+	0.0301793i
$49$	16255.8	+	4268.92i	0.967205	+	0.253997i
$50$	30999.3	+	17897.5i	1.75359	+	1.01243i
$51$	−7534.33	+	10366.5i	−0.405620	+	0.558092i
$52$	−15521.8	+	8961.51i	−0.796037	+	0.459592i
$53$		−	12675.5i		−	0.619833i	−0.950764	−	0.309917i	$-0.899699\pi$
$53$		−	12675.5i		−	0.619833i	0.950764	−	0.309917i	$-0.100301\pi$
$54$	−34700.2	+	7357.57i	−1.61937	+	0.343360i
$55$		−	58208.6i		−	2.59466i
$56$	3682.50	−	28521.0i	0.156918	−	1.21533i
$57$	−27018.8	−	19637.2i	−1.10149	−	0.800558i
$58$	28348.2	−	49100.5i	1.10651	−	1.91653i
$59$	−9135.35	+	15822.9i	−0.341661	+	0.591774i	−0.984741	−	0.174025i	$-0.944323\pi$
$59$	−9135.35	+	15822.9i	−0.341661	+	0.591774i	0.643080	+	0.765799i	$0.277656\pi$
$60$	−71959.9	−	7575.45i	−2.58055	−	0.271663i
$61$	−2759.58	+	1593.24i	−0.0949550	+	0.0548223i	−0.546726	−	0.837312i	$-0.684126\pi$
$61$	−2759.58	+	1593.24i	−0.0949550	+	0.0548223i	0.451771	+	0.892134i	$0.350793\pi$
$62$	23119.5			0.763836
$63$	5807.87	+	30963.0i	0.184359	+	0.982859i
$64$	50032.7			1.52688
$65$	23232.2	−	13413.1i	0.682037	−	0.393774i
$66$	41447.3	+	93134.1i	1.17122	+	2.63178i
$67$	8785.35	−	15216.7i	0.239096	−	0.414126i	−0.721359	−	0.692561i	$-0.756482\pi$
$67$	8785.35	−	15216.7i	0.239096	−	0.414126i	0.960455	+	0.278435i	$0.0898157\pi$
$68$	22890.7	−	39647.8i	0.600325	−	1.03979i
$69$	−52327.8	+	23287.4i	−1.32315	+	0.588840i
$70$	−12957.5	+	100356.i	−0.316064	+	2.44791i
$71$		−	50169.2i		−	1.18111i	−0.806997	−	0.590556i	$-0.798909\pi$
$71$		−	50169.2i		−	1.18111i	0.806997	−	0.590556i	$-0.201091\pi$
$72$	51270.7	−	16639.9i	1.16557	−	0.378286i
$73$		−	10304.5i		−	0.226318i	−0.993577	−	0.113159i	$-0.963903\pi$
$73$		−	10304.5i		−	0.226318i	0.993577	−	0.113159i	$-0.0360969\pi$
$74$	−28694.2	+	16566.6i	−0.609138	+	0.351686i
$75$	59259.8	+	6238.47i	1.21649	+	0.128063i
$76$	103337.	+	59661.5i	2.05220	+	1.18484i
$77$	83556.8	−	34854.8i	1.60604	−	0.669940i
$78$	−27620.9	+	38003.6i	−0.514046	+	0.707275i
$79$	9652.48	+	16718.6i	0.174009	+	0.301392i	0.939818	−	0.341676i	$-0.110995\pi$
$79$	9652.48	+	16718.6i	0.174009	+	0.301392i	−0.765809	+	0.643068i	$0.777661\pi$
$80$	24603.7			0.429808
$81$	−47794.8	+	34676.2i	−0.809410	+	0.587244i
$82$		−	44419.1i		−	0.729517i
$83$	23241.4	+	40255.3i	0.370311	+	0.641398i	0.989613	−	0.143755i	$-0.0459177\pi$
$83$	23241.4	+	40255.3i	0.370311	+	0.641398i	−0.619302	+	0.785153i	$0.712584\pi$
$84$	−32214.7	−	107833.i	−0.498145	−	1.66745i
$85$	−34261.6	+	59342.9i	−0.514353	+	0.890885i
$86$	9533.41	+	5504.11i	0.138996	+	0.0802493i
$87$	9881.24	−	93862.8i	0.139963	−	1.32952i
$88$	−77455.3	−	134156.i	−1.06621	−	1.84674i
$89$	−124345.			−1.66401			−0.832003	−	0.554771i	$-0.812806\pi$
$89$	−124345.			−1.66401			−0.832003	+	0.554771i	$0.812806\pi$
$90$	−180404.	+	58550.2i	−2.34769	+	0.761942i
$91$	33165.5	+	25317.6i	0.419839	+	0.320493i
$92$	177200.	−	102306.i	2.18270	−	1.26018i
$93$	35162.0	−	15648.1i	0.421567	−	0.187609i
$94$	−22854.7	−	13195.2i	−0.266781	−	0.154026i
$95$	−154669.	−	89298.4i	−1.75831	−	1.01516i
$96$	61727.8	−	27470.7i	0.683602	−	0.304222i
$97$	68609.1	−	39611.5i	0.740376	−	0.427456i	−0.0818299	−	0.996646i	$-0.526076\pi$
$97$	68609.1	−	39611.5i	0.740376	−	0.427456i	0.822206	+	0.569190i	$0.192743\pi$
$98$	−151816.	+	41492.0i	−1.59681	+	0.436415i
$99$	126073.	+	113593.i	1.29280	+	1.16483i
$100$	−212871.			−2.12871
$101$	−66098.2	−	114485.i	−0.644742	−	1.11673i	−0.984361	−	0.176163i	$-0.943631\pi$
$101$	−66098.2	−	114485.i	−0.644742	−	1.11673i	0.339619	−	0.940563i	$-0.389702\pi$
$102$	12563.8	−	119345.i	0.119570	−	1.13581i
$103$	15520.9	+	8961.01i	0.144153	+	0.0832269i	0.570342	−	0.821407i	$-0.306811\pi$
$103$	15520.9	+	8961.01i	0.144153	+	0.0832269i	−0.426189	+	0.904634i	$0.640144\pi$
$104$	35696.4	−	61828.0i	0.323624	−	0.560534i
$105$	48217.3	+	161399.i	0.426805	+	1.42865i
$106$	59348.0	+	102794.i	0.513028	+	0.888591i
$107$			11114.7i			0.0938508i	0.998898	+	0.0469254i	$0.0149423\pi$
$107$			11114.7i			0.0938508i	−0.998898	+	0.0469254i	$0.985058\pi$
$108$	156836.	−	141073.i	1.29385	−	1.16382i
$109$	24380.6			0.196552			0.0982762	−	0.995159i	$-0.468667\pi$
$109$	24380.6			0.196552			0.0982762	+	0.995159i	$0.468667\pi$
$110$	272539.	+	472051.i	2.14757	+	3.71969i
$111$	−32427.6	+	44617.0i	−0.249808	+	0.343711i
$112$	14732.5	+	35317.9i	0.110976	+	0.266042i
$113$	−106395.	−	61427.4i	−0.783839	−	0.452550i	0.0539502	−	0.998544i	$-0.482819\pi$
$113$	−106395.	−	61427.4i	−0.783839	−	0.452550i	−0.837789	+	0.545994i	$0.816152\pi$
$114$	311057.	+	32745.9i	2.24170	+	0.235991i
$115$	−265224.	+	153127.i	−1.87011	+	1.07971i
$116$			337170.i			2.32651i
$117$	−16285.9	+	76493.6i	−0.109989	+	0.516607i
$118$		−	171091.i		−	1.13115i
$119$	−105701.	−	13647.6i	−0.684243	−	0.0883464i
$120$	263324.	−	117187.i	1.66931	−	0.742890i
$121$	163319.	−	282878.i	1.01409	−	1.75645i
$122$	14919.5	−	25841.3i	0.0907514	−	0.157186i
$123$	−30064.4	−	67556.1i	−0.179180	−	0.402626i
$124$	−119071.	+	68745.4i	−0.695425	+	0.401504i
$125$	58140.0			0.332813
$126$	−192072.	−	223906.i	−1.07780	−	1.25643i
$127$	56281.2			0.309638			0.154819	−	0.987943i	$-0.450521\pi$
$127$	56281.2			0.309638			0.154819	+	0.987943i	$0.450521\pi$
$128$	−285633.	+	164910.i	−1.54093	+	0.889657i
$129$	18224.5	+	1918.55i	0.0964232	+	0.0101508i
$130$	−125604.	+	217552.i	−0.651844	+	1.12903i
$131$	−116483.	+	201755.i	−0.593042	+	1.02718i	0.400778	+	0.916175i	$0.368740\pi$
$131$	−116483.	+	201755.i	−0.593042	+	1.02718i	−0.993820	+	0.111003i	$0.964594\pi$
$132$	−490394.	−	356418.i	−2.44969	−	1.78043i
$133$	35570.6	−	275495.i	0.174366	−	1.35047i
$134$			164536.i			0.791586i
$135$	−234744.	+	211151.i	−1.10856	+	0.997147i
$136$			182361.i			0.845444i
$137$	90797.2	−	52421.8i	0.413305	−	0.238622i	−0.278904	−	0.960319i	$-0.589971\pi$
$137$	90797.2	−	52421.8i	0.413305	−	0.238622i	0.692209	+	0.721697i	$0.256638\pi$
$138$	315326.	−	433856.i	1.40949	−	1.93932i
$139$	123149.	+	71100.1i	0.540622	+	0.312128i	0.745331	−	0.666695i	$-0.232291\pi$
$139$	123149.	+	71100.1i	0.540622	+	0.312128i	−0.204709	+	0.978823i	$0.565625\pi$
$140$	−231671.	−	555381.i	−0.998968	−	2.39481i
$141$	−43690.1	−	4599.39i	−0.185070	−	0.0194829i
$142$	234897.	+	406854.i	0.977591	+	1.69324i
$143$	224759.			0.919131
$144$	−48013.4	+	53288.5i	−0.192955	+	0.214155i
$145$		−	504660.i		−	1.99333i
$146$	48246.7	+	83565.7i	0.187320	+	0.324448i
$147$	−202811.	+	165859.i	−0.774102	+	0.633061i
$148$	98520.9	−	170643.i	0.369721	−	0.640376i
$149$	147909.	+	85395.4i	0.545795	+	0.315115i	0.747424	−	0.664347i	$-0.231290\pi$
$149$	147909.	+	85395.4i	0.545795	+	0.315115i	−0.201630	+	0.979462i	$0.564624\pi$
$150$	−509785.	+	226869.i	−1.84995	+	0.823279i
$151$	216348.	+	374726.i	0.772166	+	1.33743i	0.936374	+	0.351005i	$0.114160\pi$
$151$	216348.	+	374726.i	0.772166	+	1.33743i	−0.164208	+	0.986426i	$0.552507\pi$
$152$	−475300.			−1.66862
$153$	−61668.7	−	190013.i	−0.212979	−	0.656227i
$154$	−514422.	+	673882.i	−1.74791	+	2.28972i
$155$	178219.	−	102895.i	0.595833	−	0.344004i
$156$	29250.9	−	277857.i	0.0962337	−	0.914133i
$157$	−45657.0	−	26360.1i	−0.147829	−	0.0853489i	0.424261	−	0.905540i	$-0.360534\pi$
$157$	−45657.0	−	26360.1i	−0.147829	−	0.0853489i	−0.572090	+	0.820191i	$0.693867\pi$
$158$	−156556.	−	90387.9i	−0.498917	−	0.288050i
$159$	159835.	+	116168.i	0.501395	+	0.364413i
$160$	312868.	−	180634.i	0.966187	−	0.557828i
$161$	−378624.	−	289030.i	−1.15118	−	0.878777i
$162$	225242.	−	504992.i	0.674312	−	1.51181i
$163$	−61314.4			−0.180756			−0.0903782	−	0.995908i	$-0.528808\pi$
$163$	−61314.4			−0.180756			−0.0903782	+	0.995908i	$0.528808\pi$
$164$	132079.	+	228768.i	0.383464	+	0.664180i
$165$	733998.	+	533468.i	2.09887	+	1.52545i
$166$	−376959.	−	217637.i	−1.06175	−	0.613004i
$167$	−41611.0	+	72072.4i	−0.115456	+	0.199976i	−0.917962	−	0.396668i	$-0.870166\pi$
$167$	−41611.0	+	72072.4i	−0.115456	+	0.199976i	0.802506	+	0.596644i	$0.203500\pi$
$168$	325894.	+	307824.i	0.890848	+	0.841451i
$169$	−133855.	−	231843.i	−0.360510	−	0.624421i
$170$		−	641667.i		−	1.70289i
$171$	495243.	−	160731.i	1.29517	−	0.420349i
$172$	−65465.4			−0.168729
$173$	9283.35	+	16079.2i	0.0235825	+	0.0408460i	0.877576	−	0.479438i	$-0.159159\pi$
$173$	9283.35	+	16079.2i	0.0235825	+	0.0408460i	−0.853993	+	0.520284i	$0.825826\pi$
$174$	359343.	+	807460.i	0.899778	+	2.02184i
$175$	190784.	+	457362.i	0.470919	+	1.12893i
$176$	178520.	+	103069.i	0.434416	+	0.250810i
$177$	−115800.	−	260208.i	−0.277828	−	0.624292i
$178$	1.00840e6	−	582199.i	2.38551	−	1.37728i
$179$		−	558033.i		−	1.30175i	−0.759185	−	0.650875i	$-0.774402\pi$
$179$		−	558033.i		−	1.30175i	0.759185	−	0.650875i	$-0.225598\pi$
$180$	755021.	−	837972.i	1.73691	−	1.92774i
$181$			470205.i			1.06682i	0.845857	+	0.533409i	$0.179089\pi$
$181$			470205.i			1.06682i	−0.845857	+	0.533409i	$0.820911\pi$
$182$	−387500.	−	50032.3i	−0.867148	−	0.111962i
$183$	5200.43	−	49399.4i	0.0114792	−	0.109042i
$184$	−407517.	+	705840.i	−0.887363	+	1.53696i
$185$	−147461.	+	255410.i	−0.316773	+	0.548667i
$186$	−211885.	+	291533.i	−0.449075	+	0.617881i
$187$	−497194.	+	287055.i	−1.03973	+	0.600290i
$188$	156942.			0.323850
$189$	−443664.	−	210533.i	−0.903442	−	0.428711i
$190$	1.67242e6			3.36094
$191$	738476.	−	426359.i	1.46471	−	0.845653i	0.465490	−	0.885053i	$-0.345878\pi$
$191$	738476.	−	426359.i	1.46471	−	0.845653i	0.999224	+	0.0394004i	$0.0125448\pi$
$192$	−458538.	+	630902.i	−0.897682	+	1.23512i
$193$	−31383.8	+	54358.3i	−0.0606474	+	0.105044i	−0.894755	−	0.446557i	$-0.852650\pi$
$193$	−31383.8	+	54358.3i	−0.0606474	+	0.105044i	0.834108	+	0.551602i	$0.185983\pi$
$194$	−370930.	+	642470.i	−0.707601	+	1.22560i
$195$	−43781.2	+	415882.i	−0.0824521	+	0.783220i
$196$	658511.	−	665115.i	1.22440	−	1.23668i
$197$			996438.i			1.82930i	0.404247	+	0.914650i	$0.367534\pi$
$197$			996438.i			1.82930i	−0.404247	+	0.914650i	$0.632466\pi$
$198$	−1.55426e6	−	330911.i	−2.81747	−	0.599857i
$199$		−	241345.i		−	0.432021i	−0.976391	−	0.216011i	$-0.930695\pi$
$199$		−	241345.i		−	0.432021i	0.976391	−	0.216011i	$-0.0693046\pi$
$200$	734328.	−	423965.i	1.29812	−	0.749471i
$201$	111363.	+	250239.i	0.194425	+	0.436882i
$202$	1.07207e6	+	618957.i	1.84860	+	1.06729i
$203$	724426.	−	302186.i	1.23383	−	0.514677i
$204$	290163.	+	652010.i	0.488165	+	1.09693i
$205$	−197690.	−	342409.i	−0.328548	−	0.569062i
$206$	−167826.			−0.275544
$207$	185923.	−	873266.i	0.301584	−	1.41651i
$208$			95001.4i			0.152255i
$209$	−748170.	−	1.29587e6i	−1.18477	−	2.05208i
$210$	−1.14671e6	−	1.08313e6i	−1.79434	−	1.69485i
$211$	−323964.	+	561122.i	−0.500945	+	0.867663i	0.499054	+	0.866571i	$0.333681\pi$
$211$	−323964.	+	561122.i	−0.500945	+	0.867663i	−0.999999	+	0.00109202i	$0.999652\pi$
$212$	−611309.	−	352939.i	−0.934160	−	0.539337i
$213$	632623.	+	459789.i	0.955423	+	0.694400i
$214$	−52040.2	−	90136.3i	−0.0776791	−	0.134544i
$215$	97985.3			0.144566
$216$	−260058.	+	799014.i	−0.379259	+	1.16525i
$217$	254419.	+	194216.i	0.366775	+	0.279985i
$218$	−197718.	+	114153.i	−0.281777	+	0.162684i
$219$	129937.	+	94438.2i	0.183073	+	0.133057i
$220$	−2.80726e6	−	1.62077e6i	−3.91045	−	2.25770i
$221$	−229139.	−	132294.i	−0.315587	−	0.182204i
$222$	54074.4	−	513658.i	0.0736392	−	0.699506i
$223$	−1.20755e6	+	697182.i	−1.62609	+	0.938823i	−0.640845	+	0.767670i	$0.721416\pi$
$223$	−1.20755e6	+	697182.i	−1.62609	+	0.938823i	−0.985244	+	0.171153i	$0.945251\pi$
$224$	446639.	+	340951.i	0.594753	+	0.454017i
$225$	−621768.	+	690080.i	−0.818790	+	0.908747i
$226$	1.15044e6			1.49828
$227$	604943.	+	1.04779e6i	0.779202	+	1.34962i	0.932402	+	0.361422i	$0.117709\pi$
$227$	604943.	+	1.04779e6i	0.779202	+	1.34962i	−0.153200	+	0.988195i	$0.548958\pi$
$228$	−1.69938e6	+	756271.i	−2.16497	+	0.963475i
$229$	−1.03340e6	−	596636.i	−1.30221	−	0.751832i	−0.321428	−	0.946934i	$-0.604163\pi$
$229$	−1.03340e6	−	596636.i	−1.30221	−	0.751832i	−0.980783	+	0.195102i	$0.937496\pi$
$230$	1.43391e6	−	2.48361e6i	1.78732	−	3.09574i
$231$	−326267.	+	1.37307e6i	−0.402294	+	1.69302i
$232$	−671526.	−	1.16312e6i	−0.819112	−	1.41874i
$233$			39880.5i			0.0481250i	0.999710	+	0.0240625i	$0.00766007\pi$
$233$			39880.5i			0.0481250i	−0.999710	+	0.0240625i	$0.992340\pi$
$234$	−226078.	−	696589.i	−0.269910	−	0.831643i
$235$	−234903.			−0.277472
$236$	508734.	+	881154.i	0.594581	+	1.02984i
$237$	−299281.	−	31506.2i	−0.346105	−	0.0364356i
$238$	921095.	−	384225.i	1.05405	−	0.439687i
$239$	217181.	+	125389.i	0.245939	+	0.141993i	0.617903	−	0.786254i	$-0.287982\pi$
$239$	217181.	+	125389.i	0.245939	+	0.141993i	−0.371964	+	0.928247i	$0.621316\pi$
$240$	−225487.	+	310247.i	−0.252693	+	0.347680i
$241$	301883.	−	174292.i	0.334808	−	0.193301i	−0.323166	−	0.946342i	$-0.604747\pi$
$241$	301883.	−	174292.i	0.334808	−	0.193301i	0.657974	+	0.753041i	$0.271414\pi$
$242$			3.05872e6i			3.35738i
$243$	768.943	−	920482.i	0.000835369	−	1.00000i
$244$			177451.i			0.190811i
$245$	−985627.	+	995511.i	−1.04905	+	1.05957i
$246$	560116.	+	407091.i	0.590120	+	0.428898i
$247$	344805.	−	597220.i	0.359610	−	0.622862i
$248$	273834.	−	474294.i	0.282721	−	0.489687i
$249$	−720613.	−	75861.2i	−0.736552	−	0.0775392i
$250$	−471495.	+	272218.i	−0.477120	+	0.275465i
$251$	−1.53416e6			−1.53705			−0.768523	−	0.639822i	$-0.779008\pi$
$251$	−1.53416e6			−1.53705			−0.768523	+	0.639822i	$0.779008\pi$
$252$	1.65499e6	+	582041.i	1.64170	+	0.577367i
$253$	−2.56589e6			−2.52021
$254$	−456421.	+	263515.i	−0.443896	+	0.256283i
$255$	−434302.	−	975897.i	−0.418255	−	0.939839i
$256$	743732.	−	1.28818e6i	0.709278	−	1.22851i
$257$	−131448.	+	227675.i	−0.124143	+	0.215022i	−0.921398	−	0.388621i	$-0.872951\pi$
$257$	−131448.	+	227675.i	−0.124143	+	0.215022i	0.797255	+	0.603643i	$0.206285\pi$
$258$	−156777.	+	69770.3i	−0.146634	+	0.0652562i
$259$	−454933.	−	58738.9i	−0.421404	−	0.0544097i
$260$		−	1.49392e6i		−	1.37054i
$261$	1.09303e6	+	984832.i	0.993188	+	0.894872i
$262$		−	2.18155e6i		−	1.96341i
$263$	897591.	−	518224.i	0.800182	−	0.461986i	−0.0433525	−	0.999060i	$-0.513804\pi$
$263$	897591.	−	518224.i	0.800182	−	0.461986i	0.843535	+	0.537074i	$0.180471\pi$
$264$	2.40155e6	+	252818.i	2.12071	+	0.223254i
$265$	914977.	+	528262.i	0.800379	+	0.462099i
$266$	1.00143e6	+	2.40071e6i	0.867794	+	2.08035i
$267$	1.13960e6	−	1.56797e6i	0.978303	−	1.34605i
$268$	−489243.	−	847394.i	−0.416090	−	0.720690i
$269$	1.18519e6			0.998634			0.499317	−	0.866419i	$-0.333584\pi$
$269$	1.18519e6			0.998634			0.499317	+	0.866419i	$0.333584\pi$
$270$	915056.	−	2.81146e6i	0.763903	−	2.34705i
$271$			2.07151e6i			1.71342i	0.515800	+	0.856709i	$0.327495\pi$
$271$			2.07151e6i			1.71342i	−0.515800	+	0.856709i	$0.672505\pi$
$272$	−121333.	−	210154.i	−0.0994387	−	0.172233i
$273$	−623204.	+	186180.i	−0.506085	+	0.151191i
$274$	−490889.	+	850245.i	−0.395009	+	0.684175i
$275$	2.31181e6	+	1.33473e6i	1.84341	+	1.06429i
$276$	−333933.	+	3.17207e6i	−0.263868	+	2.50651i
$277$	−57621.6	−	99803.5i	−0.0451217	−	0.0781531i	0.842583	−	0.538567i	$-0.181034\pi$
$277$	−57621.6	−	99803.5i	−0.0451217	−	0.0781531i	−0.887704	+	0.460414i	$0.847701\pi$
$278$	−1.33159e6			−1.03338
$279$	−124932.	+	586797.i	−0.0960870	+	0.451312i
$280$	1.90531e6	+	1.45446e6i	1.45235	+	1.10868i
$281$	388942.	−	224556.i	0.293846	−	0.169652i	−0.345829	−	0.938297i	$-0.612402\pi$
$281$	388942.	−	224556.i	0.293846	−	0.169652i	0.639675	+	0.768646i	$0.279069\pi$
$282$	375846.	−	167262.i	0.281441	−	0.125249i
$283$	498351.	+	287723.i	0.369887	+	0.213554i	0.673409	−	0.739270i	$-0.264829\pi$
$283$	498351.	+	287723.i	0.369887	+	0.213554i	−0.303522	+	0.952824i	$0.598163\pi$
$284$	−2.41954e6	−	1.39692e6i	−1.78007	−	1.02772i
$285$	2.54354e6	−	1.13195e6i	1.85493	−	0.825496i
$286$	−1.82272e6	+	1.05235e6i	−1.31766	+	0.760753i
$287$	373143.	−	488810.i	0.267406	−	0.350296i
$288$	−219322.	+	1.03014e6i	−0.155812	+	0.731837i
$289$	−744013.			−0.524006
$290$	2.36287e6	+	4.09261e6i	1.64985	+	2.85763i
$291$	−129294.	+	1.22818e6i	−0.0895048	+	0.850214i
$292$	−496961.	−	286920.i	−0.341087	−	0.196927i
$293$	1.31228e6	−	2.27293e6i	0.893011	−	1.54674i	0.0567629	−	0.998388i	$-0.481922\pi$
$293$	1.31228e6	−	2.27293e6i	0.893011	−	1.54674i	0.836248	−	0.548352i	$-0.184745\pi$
$294$	868158.	−	2.29464e6i	0.585774	−	1.54827i
$295$	−761448.	−	1.31887e6i	−0.509431	−	0.882360i
$296$			784878.i			0.520682i
$297$	−2.58781e6	+	548700.i	−1.70232	+	0.360947i
$298$	−1.59932e6			−1.04327
$299$	−591265.	−	1.02410e6i	−0.382476	−	0.662468i
$300$	1.95091e6	−	2.68426e6i	1.25151	−	1.72195i
$301$	58672.8	+	140655.i	0.0373268	+	0.0894829i
$302$	−3.50901e6	−	2.02593e6i	−2.21395	−	1.27822i
$303$	2.04941e6	+	215748.i	1.28240	+	0.135002i
$304$	547739.	−	316237.i	0.339930	−	0.196259i
$305$		−	265599.i		−	0.163485i
$306$	1.38977e6	+	1.25220e6i	0.848477	+	0.764485i
$307$		−	1.24176e6i		−	0.751954i	−0.926629	−	0.375977i	$-0.877307\pi$
$307$		−	1.24176e6i		−	0.751954i	0.926629	−	0.375977i	$-0.122693\pi$
$308$	645611.	−	5.00026e6i	0.387788	−	3.00342i
$309$	−255242.	+	113590.i	−0.152074	+	0.0676775i
$310$	−963528.	+	1.66888e6i	−0.569456	+	0.986327i
$311$	845642.	−	1.46470e6i	0.495776	−	0.858710i	−0.504212	−	0.863580i	$-0.668217\pi$
$311$	845642.	−	1.46470e6i	0.495776	−	0.858710i	0.999988	+	0.00487030i	$0.00155027\pi$
$312$	452489.	+	1.01676e6i	0.263161	+	0.591335i
$313$	532241.	−	307289.i	0.307077	−	0.177291i	−0.338541	−	0.940952i	$-0.609933\pi$
$313$	532241.	−	307289.i	0.307077	−	0.177291i	0.645618	+	0.763661i	$0.276600\pi$
$314$	493683.			0.282569
$315$	−2.47710e6	−	871170.i	−1.40659	−	0.494683i
$316$	1.07506e6			0.605643
$317$	−1.54129e6	+	889863.i	−0.861461	+	0.497365i	−0.864501	−	0.502631i	$-0.832366\pi$
$317$	−1.54129e6	+	889863.i	−0.861461	+	0.497365i	0.00304037	+	0.999995i	$0.499032\pi$
$318$	−1.84012e6	−	193715.i	−1.02042	−	0.107423i
$319$	2.11410e6	−	3.66173e6i	1.16319	−	2.01470i
$320$	−2.08516e6	+	3.61160e6i	−1.13832	+	1.97163i
$321$	−140154.	−	101864.i	−0.0759177	−	0.0551768i
$322$	4.42377e6	+	571178.i	2.37768	+	0.306995i
$323$			1.76150e6i			0.939453i
$324$	341541.	+	3.27057e6i	0.180751	+	1.73085i
$325$			1.23026e6i			0.646082i
$326$	497238.	−	287081.i	0.259132	−	0.149610i
$327$	−223443.	+	307434.i	−0.115557	+	0.158995i
$328$	−911253.	−	526112.i	−0.467686	−	0.270018i
$329$	−140658.	−	337197.i	−0.0716431	−	0.171749i
$330$	−8.45022e6	−	889582.i	−4.27153	−	0.449677i
$331$	725671.	+	1.25690e6i	0.364057	+	0.630565i	0.988624	−	0.150406i	$-0.0480580\pi$
$331$	725671.	+	1.25690e6i	0.364057	+	0.630565i	−0.624567	+	0.780971i	$0.714725\pi$
$332$	2.58856e6			1.28888
$333$	−265421.	−	817810.i	−0.131167	−	0.404149i
$334$		−	779309.i		−	0.382246i
$335$	732275.	+	1.26834e6i	0.356502	+	0.617480i
$336$	−580371.	−	137907.i	−0.280451	−	0.0666404i
$337$	−238695.	+	413432.i	−0.114490	+	0.198303i	−0.917576	−	0.397561i	$-0.869857\pi$
$337$	−238695.	+	413432.i	−0.114490	+	0.198303i	0.803086	+	0.595864i	$0.203190\pi$
$338$	2.17103e6	+	1.25344e6i	1.03365	+	0.596779i
$339$	1.74968e6	−	778656.i	0.826911	−	0.367999i
$340$	1.90798e6	+	3.30472e6i	0.895110	+	1.55038i
$341$	1.72417e6			0.802960
$342$	−3.26368e6	+	3.62225e6i	−1.50884	+	1.67461i
$343$	−2.01922e6	−	818737.i	−0.926718	−	0.375759i
$344$	225832.	−	130384.i	0.102894	−	0.0594058i
$345$	499815.	−	4.74779e6i	0.226080	−	2.14755i
$346$	−150569.	−	86931.2i	−0.0676155	−	0.0390378i
$347$	−496332.	−	286557.i	−0.221283	−	0.127758i	0.385261	−	0.922808i	$-0.374111\pi$
$347$	−496332.	−	286557.i	−0.221283	−	0.127758i	−0.606544	+	0.795050i	$0.707445\pi$
$348$	−4.25165e6	−	3.09009e6i	−1.88196	−	1.36780i
$349$	1.36991e6	−	790918.i	0.602045	−	0.347591i	−0.167801	−	0.985821i	$-0.553667\pi$
$349$	1.36991e6	−	790918.i	0.602045	−	0.347591i	0.769846	+	0.638230i	$0.220333\pi$
$350$	−3.68861e6	−	2.81578e6i	−1.60951	−	1.22865i
$351$	−815312.	−	906409.i	−0.353229	−	0.392696i
$352$	3.02683e6			1.30206
$353$	−1.93522e6	−	3.35190e6i	−0.826597	−	1.43171i	−0.900693	−	0.434457i	$-0.856940\pi$
$353$	−1.93522e6	−	3.35190e6i	−0.826597	−	1.43171i	0.0740958	−	0.997251i	$-0.476393\pi$
$354$	2.15742e6	+	1.56801e6i	0.915012	+	0.665029i
$355$	3.62145e6	+	2.09085e6i	1.52515	+	0.880544i
$356$	−3.46231e6	+	5.99689e6i	−1.44791	+	2.50785i
$357$	1.14082e6	−	1.20779e6i	0.473746	−	0.501557i
$358$	2.61277e6	+	4.52545e6i	1.07744	+	1.86618i
$359$		−	4.28975e6i		−	1.75669i	−0.478026	−	0.878346i	$-0.658647\pi$
$359$		−	4.28975e6i		−	1.75669i	0.478026	−	0.878346i	$-0.341353\pi$
$360$	−935603.	+	4.39445e6i	−0.380483	+	1.78710i
$361$	−2.11500e6			−0.854167
$362$	−2.20155e6	−	3.81320e6i	−0.882992	−	1.52939i
$363$	2.07024e6	+	4.65193e6i	0.824622	+	1.85296i
$364$	2.14448e6	−	894545.i	0.848336	−	0.353874i
$365$	743826.	+	429448.i	0.292240	+	0.168725i
$366$	189120.	+	424961.i	0.0737962	+	0.165823i
$367$	−1.19292e6	+	688735.i	−0.462325	+	0.266923i	−0.713021	−	0.701142i	$-0.752674\pi$
$367$	−1.19292e6	+	688735.i	−0.462325	+	0.266923i	0.250696	+	0.968066i	$0.419340\pi$
$368$		−	1.08455e6i		−	0.417476i
$369$	1.12740e6	+	240030.i	0.431035	+	0.0917699i
$370$		−	2.76172e6i		−	1.04876i
$371$	−210425.	+	1.62974e6i	−0.0793712	+	0.614730i
$372$	224389.	−	2.13149e6i	0.0840705	−	0.798594i
$373$	−217620.	+	376929.i	−0.0809892	+	0.140277i	−0.903675	−	0.428219i	$-0.859141\pi$
$373$	−217620.	+	376929.i	−0.0809892	+	0.140277i	0.822686	+	0.568496i	$0.192475\pi$
$374$	2.68804e6	−	4.65583e6i	0.993705	−	1.72115i
$375$	−532840.	+	733134.i	−0.195668	+	0.269219i
$376$	−541393.	+	312574.i	−0.197489	+	0.114020i
$377$	1.94863e6			0.706116
$378$	4.58370e6	−	369940.i	1.65001	−	0.133169i
$379$	260275.			0.0930752			0.0465376	−	0.998917i	$-0.485181\pi$
$379$	260275.			0.0930752			0.0465376	+	0.998917i	$0.485181\pi$
$380$	−8.61330e6	+	4.97289e6i	−3.05992	+	1.76665i
$381$	−515804.	+	709694.i	−0.182042	+	0.250472i
$382$	−3.99252e6	+	6.91524e6i	−1.39987	+	2.42465i
$383$	−1.12319e6	+	1.94542e6i	−0.391252	+	0.677668i	−0.992615	−	0.121308i	$-0.961291\pi$
$383$	−1.12319e6	+	1.94542e6i	−0.391252	+	0.677668i	0.601363	+	0.798976i	$0.294625\pi$
$384$	538276.	−	5.11314e6i	0.186285	−	1.76954i
$385$	−966319.	+	7.48414e6i	−0.332253	+	2.57330i
$386$		−	587769.i		−	0.200788i
$387$	−191216.	+	212224.i	−0.0649003	+	0.0720307i
$388$		−	4.41181e6i		−	1.48778i
$389$	4.73348e6	−	2.73288e6i	1.58601	−	0.915685i	0.592058	−	0.805895i	$-0.298315\pi$
$389$	4.73348e6	−	2.73288e6i	1.58601	−	0.915685i	0.993955	−	0.109790i	$-0.0350179\pi$
$390$	−1.59216e6	−	3.57765e6i	−0.530059	−	1.19107i
$391$	2.61590e6	+	1.51029e6i	0.865324	+	0.499595i
$392$	−946951.	+	3.60594e6i	−0.311252	+	1.18523i
$393$	−1.47655e6	−	3.31787e6i	−0.482243	−	1.08362i
$394$	−4.66543e6	−	8.08076e6i	−1.51409	−	2.62248i
$395$	−1.60910e6			−0.518909
$396$	8.98871e6	−	2.91729e6i	2.88044	−	0.934849i
$397$		−	4.80477e6i		−	1.53002i	−0.644020	−	0.765008i	$-0.722735\pi$
$397$		−	4.80477e6i		−	1.53002i	0.644020	−	0.765008i	$-0.277265\pi$
$398$	1.13000e6	+	1.95722e6i	0.357579	+	0.619344i
$399$	3.14794e6	+	2.97339e6i	0.989905	+	0.935016i
$400$	−564164.	+	977160.i	−0.176301	+	0.305362i
$401$	−1.46911e6	−	848190.i	−0.456239	−	0.263410i	0.254222	−	0.967146i	$-0.418181\pi$
$401$	−1.46911e6	−	848190.i	−0.456239	−	0.263410i	−0.710462	+	0.703736i	$0.751514\pi$
$402$	−2.07476e6	−	1.50793e6i	−0.640329	−	0.465390i
$403$	397304.	+	688151.i	0.121860	+	0.211068i
$404$	−7.36182e6			−2.24405
$405$	−511201.	−	4.89522e6i	−0.154865	−	1.48298i
$406$	−4.45997e6	+	5.84246e6i	−1.34282	+	1.75906i
$407$	−2.13991e6	+	1.23548e6i	−0.640338	+	0.369699i
$408$	−2.29954e6	−	1.67130e6i	−0.683896	−	0.497054i
$409$	−3.08436e6	−	1.78076e6i	−0.911710	−	0.526376i	−0.0307288	−	0.999528i	$-0.509783\pi$
$409$	−3.08436e6	−	1.78076e6i	−0.911710	−	0.526376i	−0.880981	+	0.473152i	$0.843116\pi$
$410$	3.20639e6	+	1.85121e6i	0.942012	+	0.543871i
$411$	−171108.	+	1.62537e6i	−0.0499649	+	0.474621i
$412$	864337.	−	499025.i	0.250865	−	0.144837i
$413$	1.43725e6	−	1.88277e6i	0.414626	−	0.543152i
$414$	2.58095e6	+	7.95239e6i	0.740080	+	2.28033i
$415$	−3.87442e6			−1.10430
$416$	697479.	+	1.20807e6i	0.197605	+	0.342262i
$417$	−2.02519e6	+	901267.i	−0.570329	+	0.253813i
$418$	1.21348e7	+	7.00602e6i	3.39697	+	1.96124i
$419$	−2.48168e6	+	4.29839e6i	−0.690574	+	1.19611i	0.281076	+	0.959686i	$0.409309\pi$
$419$	−2.48168e6	+	4.29839e6i	−0.690574	+	1.19611i	−0.971650	+	0.236424i	$0.924025\pi$
$420$	9.12645e6	+	2.16861e6i	2.52452	+	0.599872i
$421$	−899225.	−	1.55750e6i	−0.247265	−	0.428276i	0.715501	−	0.698612i	$-0.246199\pi$
$421$	−899225.	−	1.55750e6i	−0.247265	−	0.428276i	−0.962766	+	0.270336i	$0.912865\pi$
$422$		−	6.06733e6i		−	1.65850i
$423$	458407.	−	508771.i	0.124566	−	0.138252i
$424$	2.81173e6			0.759555
$425$	−1.57124e6	−	2.72147e6i	−0.421960	−	0.730856i
$426$	−7.28313e6	−	766718.i	−1.94444	−	0.204697i
$427$	381260.	−	159039.i	0.101193	−	0.0422117i
$428$	536036.	+	309480.i	0.141444	+	0.0816627i
$429$	−2.05987e6	+	2.83417e6i	−0.540376	+	0.743502i
$430$	−794627.	+	458778.i	−0.207249	+	0.119655i
$431$			1.40393e6i			0.364042i	0.983295	+	0.182021i	$0.0582638\pi$
$431$			1.40393e6i			0.364042i	−0.983295	+	0.182021i	$0.941736\pi$
$432$	−231925.	−	1.09382e6i	−0.0597913	−	0.281991i
$433$		−	5.83425e6i		−	1.49543i	−0.664021	−	0.747714i	$-0.731151\pi$
$433$		−	5.83425e6i		−	1.49543i	0.664021	−	0.747714i	$-0.268849\pi$
$434$	−2.97258e6	−	383807.i	−0.757548	−	0.0978111i
$435$	6.36366e6	+	4.62509e6i	1.61244	+	1.17192i
$436$	678860.	−	1.17582e6i	0.171027	−	0.296227i
$437$	−3.93636e6	+	6.81798e6i	−0.986033	+	1.70786i
$438$	−1.49592e6	−	157480.i	−0.372582	−	0.0392229i
$439$	−4.31084e6	+	2.48886e6i	−1.06758	+	0.616368i	−0.927519	−	0.373775i	$-0.878063\pi$
$439$	−4.31084e6	+	2.48886e6i	−1.06758	+	0.616368i	−0.140061	+	0.990143i	$0.544730\pi$
$440$	1.29121e7			3.17954
$441$	−232728.	−	4.07746e6i	−0.0569840	−	0.998375i
$442$	2.47765e6			0.603232
$443$	−1.85851e6	+	1.07301e6i	−0.449941	+	0.259774i	−0.707805	−	0.706408i	$-0.750315\pi$
$443$	−1.85851e6	+	1.07301e6i	−0.449941	+	0.259774i	0.257864	+	0.966181i	$0.416981\pi$
$444$	1.24885e6	+	2.80623e6i	0.300645	+	0.675564i
$445$	5.18221e6	−	8.97585e6i	1.24055	−	2.14870i
$446$	6.52856e6	−	1.13078e7i	1.55410	−	2.69179i
$447$	−2.43237e6	+	1.08247e6i	−0.575786	+	0.256241i
$448$	−6.43293e6	−	830591.i	−1.51431	−	0.195521i
$449$			20173.9i			0.00472252i	0.999997	+	0.00236126i	$0.000751613\pi$
$449$			20173.9i			0.00472252i	−0.999997	+	0.00236126i	$0.999248\pi$
$450$	1.81129e6	−	8.50749e6i	0.421656	−	1.98048i
$451$		−	3.31261e6i		−	0.766883i
$452$	−5.92500e6	+	3.42080e6i	−1.36409	+	0.787557i
$453$	−6.70800e6	−	706172.i	−1.53585	−	0.161683i
$454$	−9.81175e6	−	5.66482e6i	−2.23412	−	1.28987i
$455$	−3.20975e6	+	1.33891e6i	−0.726846	+	0.303196i
$456$	4.35601e6	−	5.99343e6i	0.981018	−	1.34978i
$457$	2.41976e6	+	4.19115e6i	0.541978	+	0.938733i	0.998790	+	0.0491703i	$0.0156577\pi$
$457$	2.41976e6	+	4.19115e6i	0.541978	+	0.938733i	−0.456813	+	0.889563i	$0.651009\pi$
$458$	1.11741e7			2.48913
$459$	2.96120e6	+	963794.i	0.656049	+	0.213527i
$460$			1.70548e7i			3.75797i
$461$	379817.	+	657862.i	0.0832380	+	0.144173i	0.904639	−	0.426179i	$-0.140140\pi$
$461$	379817.	+	657862.i	0.0832380	+	0.144173i	−0.821401	+	0.570351i	$0.806807\pi$
$462$	−3.78296e6	−	1.26627e7i	−0.824568	−	2.76009i
$463$	−3.28987e6	+	5.69822e6i	−0.713224	+	1.23534i	0.250416	+	0.968138i	$0.419433\pi$
$463$	−3.28987e6	+	5.69822e6i	−0.713224	+	1.23534i	−0.963640	+	0.267203i	$0.913901\pi$
$464$	1.54774e6	+	893590.i	0.333737	+	0.192683i
$465$	−335854.	+	3.19031e6i	−0.0720308	+	0.684227i
$466$	−186725.	−	323417.i	−0.0398325	−	0.0689919i
$467$	7.08675e6			1.50368			0.751839	−	0.659346i	$-0.229167\pi$
$467$	7.08675e6			1.50368			0.751839	+	0.659346i	$0.229167\pi$
$468$	3.23564e6	+	2.91534e6i	0.682882	+	0.615283i
$469$	−1.38218e6	+	1.81063e6i	−0.290157	+	0.380100i
$470$	1.90498e6	−	1.09984e6i	0.397782	−	0.229660i
$471$	750832.	−	334142.i	0.155952	−	0.0694030i
$472$	−3.50990e6	−	2.02644e6i	−0.725171	−	0.418678i
$473$	710966.	+	410476.i	0.146115	+	0.0843597i
$474$	2.57458e6	−	1.14576e6i	0.526332	−	0.234233i
$475$	7.09315e6	−	4.09523e6i	1.44247	−	0.832808i
$476$	−3.60135e6	+	4.71769e6i	−0.728531	+	0.954360i
$477$	−2.92971e6	+	950838.i	−0.589560	+	0.191342i
$478$	−2.34835e6			−0.470103
$479$	−1.55520e6	−	2.69369e6i	−0.309705	−	0.536424i	0.668593	−	0.743628i	$-0.266897\pi$
$479$	−1.55520e6	−	2.69369e6i	−0.309705	−	0.536424i	−0.978298	+	0.207204i	$0.933563\pi$
$480$	−589601.	+	5.60068e6i	−0.116803	+	1.10953i
$481$	−986209.	−	569388.i	−0.194360	−	0.112214i
$482$	−1.63211e6	+	2.82690e6i	−0.319986	+	0.554233i
$483$	7.11461e6	−	2.12547e6i	1.38766	−	0.414559i
$484$	−9.09502e6	−	1.57530e7i	−1.76478	−	3.05668i
$485$			6.60338e6i			1.27471i
$486$	4.30356e6	+	7.46839e6i	0.826490	+	1.43429i
$487$	9.38314e6			1.79278			0.896388	−	0.443271i	$-0.146182\pi$
$487$	9.38314e6			1.79278			0.896388	+	0.443271i	$0.146182\pi$
$488$	−353420.	−	612141.i	−0.0671802	−	0.116360i
$489$	561933.	−	773162.i	0.106270	−	0.146217i
$490$	3.33200e6	−	1.26881e7i	0.626923	−	2.38729i
$491$	1.76716e6	+	1.02027e6i	0.330806	+	0.190991i	0.656199	−	0.754588i	$-0.272163\pi$
$491$	1.76716e6	+	1.02027e6i	0.330806	+	0.190991i	−0.325393	+	0.945579i	$0.605497\pi$
$492$	−4.09519e6	−	431114.i	−0.762714	−	0.0802933i
$493$	−4.31060e6	+	2.48872e6i	−0.798767	+	0.461168i
$494$			6.45766e6i			1.19058i
$495$	−1.34539e7	+	4.36645e6i	−2.46793	+	0.800969i
$496$			728773.i			0.133011i
$497$	−832857.	+	6.45048e6i	−0.151244	+	1.17139i
$498$	6.19911e6	−	2.75878e6i	1.12010	−	0.498475i
$499$	−1.48341e6	+	2.56934e6i	−0.266691	+	0.461923i	−0.968005	−	0.250930i	$-0.919264\pi$
$499$	−1.48341e6	+	2.56934e6i	−0.266691	+	0.461923i	0.701314	+	0.712852i	$0.252597\pi$
$500$	1.61887e6	−	2.80396e6i	0.289592	−	0.501587i
$501$	−527463.	−	1.18523e6i	−0.0938853	−	0.210965i
$502$	1.24415e7	−	7.18311e6i	2.20350	−	1.27219i
$503$	−8.52980e6			−1.50321			−0.751604	−	0.659615i	$-0.770719\pi$
$503$	−8.52980e6			−1.50321			−0.751604	+	0.659615i	$0.770719\pi$
$504$	−6.86834e6	+	1.28833e6i	−1.20441	+	0.225917i
$505$	1.10188e7			1.92268
$506$	2.08085e7	−	1.20138e7i	3.61297	−	2.08595i
$507$	4.15024e6	+	436909.i	0.717057	+	0.0754868i
$508$	1.56711e6	−	2.71431e6i	0.269426	−	0.466660i
$509$	−537078.	+	930246.i	−0.0918846	+	0.159149i	−0.908304	−	0.418310i	$-0.862622\pi$
$509$	−537078.	+	930246.i	−0.0918846	+	0.159149i	0.816419	+	0.577459i	$0.195956\pi$
$510$	8.09129e6	+	5.88073e6i	1.37750	+	1.00117i
$511$	−171064.	+	1.32489e6i	−0.0289806	+	0.224455i
$512$			3.37467e6i			0.568927i
$513$	−2.51200e6	+	7.71797e6i	−0.421431	+	1.29482i
$514$		−	2.46182e6i		−	0.411006i
$515$	−1.29370e6	+	746916.i	−0.214939	+	0.124095i
$516$	599975.	−	825505.i	0.0991994	−	0.136488i
$517$	−1.70442e6	−	984045.i	−0.280446	−	0.161916i
$518$	3.96437e6	−	1.65369e6i	0.649157	−	0.270789i
$519$	−287836.	−	30301.4i	−0.0469057	−	0.00493792i
$520$	2.97536e6	+	5.15348e6i	0.482538	+	0.835780i
$521$	8.14203e6			1.31413			0.657065	−	0.753834i	$-0.271798\pi$
$521$	8.14203e6			1.31413			0.657065	+	0.753834i	$0.271798\pi$
$522$	−1.34752e7	−	2.86895e6i	−2.16451	−	0.460836i
$523$			1.40968e6i			0.225354i	0.993632	+	0.112677i	$0.0359425\pi$
$523$			1.40968e6i			0.225354i	−0.993632	+	0.112677i	$0.964057\pi$
$524$	6.48678e6	+	1.12354e7i	1.03205	+	1.78756i
$525$	−7.51574e6	−	1.78588e6i	−1.19007	−	0.282783i
$526$	−4.85276e6	+	8.40523e6i	−0.764759	+	1.32460i
$527$	−1.75777e6	−	1.01485e6i	−0.275699	−	0.159175i
$528$	−2.93577e6	+	1.30650e6i	−0.458287	+	0.203951i
$529$	3.53182e6	+	6.11729e6i	0.548731	+	0.950430i
$530$	−9.89352e6			−1.52989
$531$	4.34245e6	+	924534.i	0.668342	+	0.142294i
$532$	−1.22960e7	−	9.38644e6i	−1.88359	−	1.43788i
$533$	1.32213e6	−	763334.i	0.201584	−	0.116385i
$534$	−1.90033e6	+	1.80514e7i	−0.288387	+	2.73942i
$535$	−802312.	−	463215.i	−0.121188	−	0.0699678i
$536$	3.37543e6	+	1.94880e6i	0.507478	+	0.292992i
$537$	7.03668e6	+	5.11425e6i	1.05301	+	0.765325i
$538$	−9.61146e6	+	5.54918e6i	−1.43164	+	0.826557i
$539$	−1.13219e7	+	3.09432e6i	−1.67860	+	0.458768i
$540$	3.64707e6	+	1.72005e7i	0.538219	+	2.53838i
$541$	6.56481e6			0.964338			0.482169	−	0.876078i	$-0.339849\pi$
$541$	6.56481e6			0.964338			0.482169	+	0.876078i	$0.339849\pi$
$542$	−9.69902e6	−	1.67992e7i	−1.41817	−	2.45635i
$543$	−5.92919e6	−	4.30932e6i	−0.862970	−	0.627204i
$544$	−3.08581e6	−	1.78159e6i	−0.447066	−	0.258114i
$545$	−1.01608e6	+	1.75991e6i	−0.146534	+	0.253804i
$546$	4.18225e6	−	4.42776e6i	0.600382	−	0.635628i
$547$	−4.87537e6	−	8.44439e6i	−0.696690	−	1.20670i	−0.969608	−	0.244665i	$-0.921322\pi$
$547$	−4.87537e6	−	8.44439e6i	−0.696690	−	1.20670i	0.272918	−	0.962037i	$-0.412011\pi$
$548$		−	5.83858e6i		−	0.830532i
$549$	575255.	+	518310.i	0.0814573	+	0.0733937i
$550$	−2.49973e7			−3.52360
$551$	−6.48653e6	−	1.12350e7i	−0.910192	−	1.57650i
$552$	−5.16570e6	−	1.16076e7i	−0.721575	−	1.62141i
$553$	−963518.	−	2.30982e6i	−0.133982	−	0.321193i
$554$	934581.	+	539581.i	0.129373	+	0.0746933i
$555$	−1.86922e6	−	4.20023e6i	−0.257590	−	0.578817i
$556$	6.85798e6	−	3.95946e6i	0.940826	−	0.543186i
$557$		−	8.57714e6i		−	1.17140i	−0.810529	−	0.585699i	$-0.800820\pi$
$557$		−	8.57714e6i		−	1.17140i	0.810529	−	0.585699i	$-0.199180\pi$
$558$	−1.73429e6	−	5.34366e6i	−0.235796	−	0.726530i
$559$			378348.i			0.0512109i
$560$	−3.16340e6	−	408445.i	−0.426270	−	0.0550380i
$561$	936963.	−	8.90030e6i	0.125694	−	1.19398i
$562$	−2.10279e6	+	3.64214e6i	−0.280837	+	0.486425i
$563$	3.16434e6	−	5.48080e6i	0.420739	−	0.728741i	−0.575273	−	0.817961i	$-0.695104\pi$
$563$	3.16434e6	−	5.48080e6i	0.420739	−	0.728741i	0.996012	+	0.0892205i	$0.0284376\pi$
$564$	−1.43834e6	+	1.97900e6i	−0.190398	+	0.261968i
$565$	8.86825e6	−	5.12009e6i	1.16874	−	0.674771i
$566$	−5.38860e6			−0.707025
$567$	6.72086e6	−	3.66504e6i	0.877944	−	0.478763i
$568$	1.11287e7			1.44736
$569$	−9.83915e6	+	5.68063e6i	−1.27402	+	0.735557i	−0.975742	−	0.218922i	$-0.929746\pi$
$569$	−9.83915e6	+	5.68063e6i	−1.27402	+	0.735557i	−0.298279	+	0.954479i	$0.596413\pi$
$570$	−1.53273e7	+	2.10888e7i	−1.97597	+	2.71873i
$571$	−5.71489e6	+	9.89848e6i	−0.733529	+	1.27051i	0.221836	+	0.975084i	$0.428795\pi$
$571$	−5.71489e6	+	9.89848e6i	−0.733529	+	1.27051i	−0.955366	+	0.295426i	$0.904538\pi$
$572$	6.25825e6	−	1.08396e7i	0.799766	−	1.38524i
$573$	−1.39166e6	+	1.32195e7i	−0.177071	+	1.68201i
$574$	−737401.	+	5.71117e6i	−0.0934166	+	0.723511i
$575$		−	1.40448e7i		−	1.77153i
$576$	−3.75315e6	−	1.15641e7i	−0.471346	−	1.45230i
$577$			9.26451e6i			1.15846i	0.815163	+	0.579232i	$0.196648\pi$
$577$			9.26451e6i			1.15846i	−0.815163	+	0.579232i	$0.803352\pi$
$578$	6.03369e6	−	3.48355e6i	0.751213	−	0.433713i
$579$	−397822.	−	893925.i	−0.0493165	−	0.110817i
$580$	−2.43386e7	−	1.40519e7i	−3.00417	−	1.73446i
$581$	−2.31997e6	−	5.56163e6i	−0.285130	−	0.683537i
$582$	−4.70193e6	−	1.05655e7i	−0.575398	−	1.29295i
$583$	4.42595e6	+	7.66597e6i	0.539306	+	0.934105i
$584$	2.28578e6			0.277334
$585$	−4.84295e6	−	4.36354e6i	−0.585086	−	0.527168i
$586$			2.45769e7i			2.95653i
$587$	−2.80690e6	−	4.86168e6i	−0.336226	−	0.582360i	0.647494	−	0.762071i	$-0.275817\pi$
$587$	−2.80690e6	−	4.86168e6i	−0.336226	−	0.582360i	−0.983720	+	0.179711i	$0.942484\pi$
$588$	2.35186e6	+	1.43993e7i	0.280523	+	1.71751i
$589$	2.64506e6	−	4.58139e6i	0.314158	−	0.544138i
$590$	1.23502e7	+	7.13037e6i	1.46064	+	0.843299i
$591$	−1.25649e7	−	9.13213e6i	−1.47975	−	1.07548i
$592$	−522213.	−	904499.i	−0.0612411	−	0.106073i
$593$	−8.99164e6			−1.05003			−0.525016	−	0.851093i	$-0.675941\pi$
$593$	−8.99164e6			−1.05003			−0.525016	+	0.851093i	$0.675941\pi$
$594$	1.84171e7	−	1.65662e7i	2.14169	−	1.92644i
$595$	5.39032e6	−	7.06121e6i	0.624198	−	0.817686i
$596$	8.23684e6	−	4.75554e6i	0.949828	−	0.548383i
$597$	3.04331e6	+	2.21187e6i	0.349470	+	0.253994i
$598$	9.58990e6	+	5.53673e6i	1.09663	+	0.633141i
$599$	−8.66366e6	−	5.00197e6i	−0.986585	−	0.569605i	−0.0823334	−	0.996605i	$-0.526237\pi$
$599$	−8.66366e6	−	5.00197e6i	−0.986585	−	0.569605i	−0.904252	+	0.427000i	$0.859571\pi$
$600$	−1.38384e6	+	1.31453e7i	−0.156931	+	1.49070i
$601$	8.75648e6	−	5.05556e6i	0.988880	−	0.570930i	0.0839405	−	0.996471i	$-0.473249\pi$
$601$	8.75648e6	−	5.05556e6i	0.988880	−	0.570930i	0.904939	+	0.425541i	$0.139916\pi$
$602$	−1.13438e6	−	865953.i	−0.127575	−	0.0973874i
$603$	−4.17608e6	−	889112.i	−0.467709	−	0.0995779i
$604$	2.40962e7			2.68755
$605$	1.36130e7	+	2.35784e7i	1.51204	+	2.61894i
$606$	−1.76302e7	+	7.84593e6i	−1.95018	+	0.867886i
$607$	1.06193e7	+	6.13104e6i	1.16983	+	0.675402i	0.953640	−	0.300949i	$-0.0973033\pi$
$607$	1.06193e7	+	6.13104e6i	1.16983	+	0.675402i	0.216191	+	0.976351i	$0.430637\pi$
$608$	4.64348e6	−	8.04275e6i	0.509431	−	0.882360i
$609$	−2.82869e6	+	1.19043e7i	−0.309059	+	1.30065i
$610$	1.24356e6	+	2.15392e6i	0.135314	+	0.234371i
$611$		−	907023.i		−	0.0982914i
$612$	−1.08810e7	−	2.31663e6i	−1.17433	−	0.250022i
$613$	−8.22655e6			−0.884233			−0.442116	−	0.896958i	$-0.645772\pi$
$613$	−8.22655e6			−0.884233			−0.442116	+	0.896958i	$0.645772\pi$
$614$	5.81405e6	+	1.00702e7i	0.622383	+	1.07800i
$615$	6.12948e6	+	645270.i	0.653486	+	0.0687945i
$616$	7.73165e6	+	1.85349e7i	0.820957	+	1.96806i
$617$	6.29472e6	+	3.63426e6i	0.665677	+	0.384329i	0.794437	−	0.607347i	$-0.207766\pi$
$617$	6.29472e6	+	3.63426e6i	0.665677	+	0.384329i	−0.128760	+	0.991676i	$0.541100\pi$
$618$	1.53808e6	−	2.11625e6i	0.161998	−	0.222892i
$619$	7.22637e6	−	4.17215e6i	0.758043	−	0.437656i	−0.0705499	−	0.997508i	$-0.522475\pi$
$619$	7.22637e6	−	4.17215e6i	0.758043	−	0.437656i	0.828593	+	0.559852i	$0.189142\pi$
$620$		−	1.14601e7i		−	1.19732i
$621$	9.30776e6	+	1.03477e7i	0.968537	+	1.07675i
$622$			1.58376e7i			1.64139i
$623$	1.59877e7	+	2.06425e6i	1.65031	+	0.213080i
$624$	−1.19795e6	−	870666.i	−0.123162	−	0.0895139i
$625$	3.54966e6	−	6.14819e6i	0.363485	−	0.629574i
$626$	−2.87752e6	+	4.98401e6i	−0.293483	+	0.508327i
$627$	2.31974e7	+	2.44207e6i	2.35652	+	0.248078i
$628$	−2.54257e6	+	1.46796e6i	−0.257261	+	0.148530i
$629$	2.90881e6			0.293150
$630$	2.41673e7	−	4.53318e6i	2.42593	−	0.455042i
$631$	1.78591e7			1.78561			0.892804	−	0.450445i	$-0.148734\pi$
$631$	1.78591e7			1.78561			0.892804	+	0.450445i	$0.148734\pi$
$632$	−3.70859e6	+	2.14115e6i	−0.369331	+	0.213233i
$633$	−4.10658e6	−	9.22767e6i	−0.407353	−	0.915341i
$634$	8.33287e6	−	1.44329e7i	0.823325	−	1.42604i
$635$	−2.34557e6	+	4.06265e6i	−0.230842	+	0.399829i
$636$	1.00530e7	−	4.47387e6i	0.985492	−	0.438572i
$637$	−3.84394e6	−	3.80577e6i	−0.375343	−	0.371616i
$638$			3.95938e7i			3.85102i
$639$	−1.15957e7	+	3.76338e6i	−1.12343	+	0.364608i
$640$		−	2.74911e7i		−	2.65303i
$641$	−1.50779e7	+	8.70524e6i	−1.44943	+	0.836827i	−0.998447	−	0.0557070i	$-0.982259\pi$
$641$	−1.50779e7	+	8.70524e6i	−1.44943	+	0.836827i	−0.450980	+	0.892534i	$0.648925\pi$
$642$	1.61354e6	+	169862.i	0.154505	+	0.0162652i
$643$	34291.7	+	19798.3i	0.00327086	+	0.00188843i	0.501635	−	0.865080i	$-0.332732\pi$
$643$	34291.7	+	19798.3i	0.00327086	+	0.00188843i	−0.498364	+	0.866968i	$0.666066\pi$
$644$	−2.44817e7	+	1.02123e7i	−2.32610	+	0.970306i
$645$	−898013.	+	1.23558e6i	−0.0849931	+	0.116942i
$646$	−8.24751e6	−	1.42851e7i	−0.777574	−	1.34680i
$647$	1.96808e7			1.84834			0.924172	−	0.381977i	$-0.124756\pi$
$647$	1.96808e7			1.84834			0.924172	+	0.381977i	$0.124756\pi$
$648$	−7.69203e6	−	1.06021e7i	−0.719620	−	0.991865i
$649$		−	1.27593e7i		−	1.18909i
$650$	−5.76020e6	−	9.97695e6i	−0.534754	−	0.926221i
$651$	−4.78071e6	+	1.42822e6i	−0.442120	+	0.132082i
$652$	−1.70725e6	+	2.95705e6i	−0.157282	+	0.272421i
$653$	1.01319e7	+	5.84964e6i	0.929836	+	0.536841i	0.886760	−	0.462231i	$-0.152951\pi$
$653$	1.01319e7	+	5.84964e6i	0.929836	+	0.536841i	0.0430765	+	0.999072i	$0.486284\pi$
$654$	372600.	−	3.53937e6i	0.0340643	−	0.323580i
$655$	−9.70909e6	−	1.68166e7i	−0.884251	−	1.53157i
$656$	1.40018e6			0.127035
$657$	−2.38169e6	+	772979.i	−0.215264	+	0.0698641i
$658$	2.71948e6	+	2.07597e6i	0.244862	+	0.186920i
$659$	−6.05634e6	+	3.49663e6i	−0.543246	+	0.313643i	−0.746393	−	0.665505i	$-0.768216\pi$
$659$	−6.05634e6	+	3.49663e6i	−0.543246	+	0.313643i	0.203147	+	0.979148i	$0.434883\pi$
$660$	4.61656e7	−	2.05450e7i	4.12533	−	1.83589i
$661$	−8.89704e6	−	5.13671e6i	−0.792030	−	0.457279i	0.0486466	−	0.998816i	$-0.484509\pi$
$661$	−8.89704e6	−	5.13671e6i	−0.792030	−	0.457279i	−0.840677	+	0.541537i	$0.817843\pi$
$662$	−1.17699e7	−	6.79533e6i	−1.04382	−	0.602651i
$663$	3.76820e6	−	1.67696e6i	0.332928	−	0.148162i
$664$	−8.92960e6	+	5.15551e6i	−0.785981	+	0.453786i
$665$	1.84041e7	+	1.40492e7i	1.61384	+	1.23196i
$666$	5.98154e6	+	5.38942e6i	0.522550	+	0.470822i
$667$	−2.22459e7			−1.93614
$668$	2.31726e6	+	4.01360e6i	0.200924	+	0.348011i
$669$	2.27564e6	−	2.16165e7i	0.196580	−	1.86733i
$670$	−1.18770e7	−	6.85718e6i	−1.02216	−	0.590144i
$671$	1.11264e6	−	1.92714e6i	0.0953997	−	0.165237i
$672$	−8.39267e6	+	2.50728e6i	−0.716930	+	0.214181i
$673$	913043.	+	1.58144e6i	0.0777058	+	0.134590i	0.902260	−	0.431193i	$-0.141907\pi$
$673$	913043.	+	1.58144e6i	0.0777058	+	0.134590i	−0.824554	+	0.565783i	$0.808574\pi$
$674$		−	4.47038e6i		−	0.379049i
$675$	−3.00340e6	−	1.41648e7i	−0.253720	−	1.19661i
$676$	−1.49083e7			−1.25477
$677$	−8.19911e6	−	1.42013e7i	−0.687536	−	1.19085i	−0.972633	−	0.232348i	$-0.925359\pi$
$677$	−8.19911e6	−	1.42013e7i	−0.687536	−	1.19085i	0.285097	−	0.958499i	$-0.407974\pi$
$678$	−1.05435e7	+	1.45068e7i	−0.880868	+	1.21199i
$679$	−9.47897e6	+	3.95405e6i	−0.789018	+	0.329130i
$680$	−1.31637e7	−	7.60007e6i	−1.09171	−	0.630297i
$681$	−1.87566e7	−	1.97457e6i	−1.54984	−	0.163157i
$682$	−1.39824e7	+	8.07274e6i	−1.15112	+	0.664600i
$683$		−	1.44303e7i		−	1.18365i	−0.806067	−	0.591824i	$-0.798408\pi$
$683$		−	1.44303e7i		−	1.18365i	0.806067	−	0.591824i	$-0.201592\pi$
$684$	6.03798e6	−	2.83598e7i	0.493459	−	2.31773i
$685$			8.73890e6i			0.711591i
$686$	2.02085e7	−	2.81452e6i	1.63955	−	0.228346i
$687$	1.69944e7	−	7.56298e6i	1.37377	−	0.611366i
$688$	−173500.	+	300512.i	−0.0139743	+	0.0242042i
$689$	−2.03976e6	+	3.53298e6i	−0.163694	+	0.283526i
$690$	1.81763e7	+	4.08431e7i	1.45340	+	3.26585i
$691$	−1.09765e7	+	6.33728e6i	−0.874518	+	0.504903i	−0.868847	−	0.495081i	$-0.835138\pi$
$691$	−1.09765e7	+	6.33728e6i	−0.874518	+	0.504903i	−0.00567094	+	0.999984i	$0.501805\pi$
$692$	1.03395e6			0.0820796
$693$	−1.43240e7	−	1.66980e7i	−1.13300	−	1.32079i
$694$	5.36677e6			0.422974
$695$	−1.02647e7	+	5.92632e6i	−0.806090	+	0.465396i
$696$	2.08211e7	+	2.19190e6i	1.62922	+	0.171513i
$697$	−1.94981e6	+	3.37717e6i	−0.152023	+	0.263312i
$698$	−7.40633e6	+	1.28281e7i	−0.575393	+	0.996610i
$699$	−502885.	−	365496.i	−0.0389292	−	0.0282937i
$700$	2.73698e7	+	3.53386e6i	2.11118	+	0.272586i
$701$		−	1.35935e6i		−	0.104481i	−0.998635	−	0.0522403i	$-0.983364\pi$
$701$		−	1.35935e6i		−	0.104481i	0.998635	−	0.0522403i	$-0.0166362\pi$
$702$	1.08558e7	+	3.53328e6i	0.831417	+	0.270605i
$703$			7.58143e6i			0.578579i
$704$	−3.02591e7	+	1.74701e7i	−2.30104	+	1.32851i
$705$	2.15283e6	−	2.96208e6i	0.163131	−	0.224452i
$706$	3.13879e7	+	1.81218e7i	2.37001	+	1.36833i
$707$	6.59797e6	+	1.58172e7i	0.496435	+	1.19009i
$708$	−1.57736e7	−	1.66054e6i	−1.18263	−	0.124499i
$709$	−5.06868e6	−	8.77921e6i	−0.378686	−	0.655903i	0.612186	−	0.790714i	$-0.290291\pi$
$709$	−5.06868e6	−	8.77921e6i	−0.378686	−	0.655903i	−0.990871	+	0.134811i	$0.956957\pi$
$710$	−3.91583e7			−2.91526
$711$	3.14013e6	−	3.48512e6i	0.232956	−	0.258550i
$712$		−	2.75828e7i		−	2.03910i
$713$	−4.53570e6	−	7.85607e6i	−0.334134	−	0.578737i
$714$	−3.59663e6	+	1.51362e7i	−0.264028	+	1.11114i
$715$	−9.36704e6	+	1.62242e7i	−0.685231	+	1.18686i
$716$	−2.69126e7	−	1.55380e7i	−1.96189	−	1.13270i
$717$	−3.57155e6	+	1.58944e6i	−0.259453	+	0.115464i
$718$	2.00851e7	+	3.47883e7i	1.45399	+	2.51839i
$719$	2.30066e7			1.65970			0.829850	−	0.557986i	$-0.188426\pi$
$719$	2.30066e7			1.65970			0.829850	+	0.557986i	$0.188426\pi$
$720$	−1.84562e6	−	5.68669e6i	−0.132681	−	0.408816i
$721$	−1.84683e6	−	1.40982e6i	−0.132309	−	0.101001i
$722$	1.71519e7	−	9.90266e6i	1.22453	−	0.706983i
$723$	−568899.	+	5.40403e6i	−0.0404753	+	0.384478i
$724$	2.26769e7	+	1.30925e7i	1.60782	+	0.928274i
$725$	2.00431e7	+	1.15719e7i	1.41618	+	0.817634i
$726$	−3.85698e7	−	2.80324e7i	−2.71585	−	1.97387i
$727$	1.10119e6	−	635770.i	0.0772724	−	0.0446132i	−0.460866	−	0.887470i	$-0.652461\pi$
$727$	1.10119e6	−	635770.i	0.0772724	−	0.0446132i	0.538138	+	0.842857i	$0.319128\pi$
$728$	−5.61606e6	+	7.35691e6i	−0.392738	+	0.514478i
$729$	1.16000e7	+	8.44571e6i	0.808427	+	0.588596i
$730$	−8.04289e6			−0.558605
$731$	−483214.	−	836951.i	−0.0334461	−	0.0579304i
$732$	−2.23761e6	−	1.62629e6i	−0.154350	−	0.112182i
$733$	4.70985e6	+	2.71924e6i	0.323778	+	0.186933i	0.653075	−	0.757293i	$-0.273478\pi$
$733$	4.70985e6	+	2.71924e6i	0.323778	+	0.186933i	−0.329297	+	0.944226i	$0.606812\pi$
$734$	6.44946e6	−	1.11708e7i	0.441858	−	0.765321i
$735$	−3.52015e6	−	2.15522e7i	−0.240349	−	1.47154i
$736$	−7.96255e6	−	1.37915e7i	−0.541823	−	0.938465i
$737$			1.22705e7i			0.832132i
$738$	−1.02667e7	+	3.33205e6i	−0.693887	+	0.225201i
$739$	−9.99219e6			−0.673053			−0.336527	−	0.941674i	$-0.609252\pi$
$739$	−9.99219e6			−0.673053			−0.336527	+	0.941674i	$0.609252\pi$
$740$	8.21190e6	+	1.42234e7i	0.551270	+	0.954827i
$741$	4.37076e6	+	9.82131e6i	0.292423	+	0.657089i
$742$	−5.92416e6	−	1.42019e7i	−0.395018	−	0.946970i
$743$	−9.96713e6	−	5.75452e6i	−0.662366	−	0.382417i	0.130812	−	0.991407i	$-0.458242\pi$
$743$	−9.96713e6	−	5.75452e6i	−0.662366	−	0.382417i	−0.793178	+	0.608990i	$0.791575\pi$
$744$	3.47113e6	+	7.79979e6i	0.229900	+	0.516595i
$745$	−1.23285e7	+	7.11786e6i	−0.813803	+	0.469849i
$746$		−	4.07569e6i		−	0.268135i
$747$	7.56085e6	−	8.39153e6i	0.495757	−	0.550224i
$748$			3.19713e7i			2.08933i
$749$	184515.	−	1.42907e6i	0.0120178	−	0.0930782i
$750$	888534.	−	8.44027e6i	0.0576794	−	0.547903i
$751$	−7.83370e6	+	1.35684e7i	−0.506836	+	0.877865i	0.493133	+	0.869954i	$0.335852\pi$
$751$	−7.83370e6	+	1.35684e7i	−0.506836	+	0.877865i	−0.999969	+	0.00791116i	$0.997482\pi$
$752$	415937.	−	720424.i	0.0268215	−	0.0464562i
$753$	1.40602e7	−	1.93455e7i	0.903661	−	1.24335i
$754$	−1.58027e7	+	9.12369e6i	−1.01229	+	0.584443i
$755$	−3.60660e7			−2.30266
$756$	−2.25070e7	+	1.55348e7i	−1.43223	+	0.988555i
$757$	7.21355e6			0.457519			0.228760	−	0.973483i	$-0.426533\pi$
$757$	7.21355e6			0.457519			0.228760	+	0.973483i	$0.426533\pi$
$758$	−2.11074e6	+	1.21863e6i	−0.133432	+	0.0770372i
$759$	2.35158e7	−	3.23554e7i	1.48168	−	2.03865i
$760$	1.98086e7	−	3.43094e7i	1.24400	−	2.15466i
$761$	−1.15427e6	+	1.99925e6i	−0.0722512	+	0.125143i	−0.899888	−	0.436122i	$-0.856352\pi$
$761$	−1.15427e6	+	1.99925e6i	−0.0722512	+	0.125143i	0.827636	+	0.561265i	$0.189685\pi$
$762$	860126.	−	8.17042e6i	0.0536630	−	0.509750i
$763$	−3.13472e6	−	404742.i	−0.194934	−	0.0251690i
$764$		−	4.74866e7i		−	2.94332i
$765$	1.62861e7	+	3.46741e6i	1.00615	+	0.214216i
$766$		−	2.10356e7i		−	1.29534i
$767$	5.09251e6	−	2.94016e6i	0.312567	−	0.180461i
$768$	9.42757e6	+	2.11842e7i	0.576762	+	1.29601i
$769$	5.44781e6	+	3.14530e6i	0.332205	+	0.191799i	0.656820	−	0.754048i	$-0.271901\pi$
$769$	5.44781e6	+	3.14530e6i	0.332205	+	0.191799i	−0.324615	+	0.945846i	$0.605235\pi$
$770$	−2.72050e7	−	6.52181e7i	−1.65357	−	3.96407i
$771$	−1.66624e6	−	3.74412e6i	−0.100949	−	0.226837i
$772$	1.74772e6	+	3.02713e6i	0.105543	+	0.182805i
$773$	−6.62984e6			−0.399075			−0.199537	−	0.979890i	$-0.563944\pi$
$773$	−6.62984e6			−0.399075			−0.199537	+	0.979890i	$0.563944\pi$
$774$	557038.	−	2.61636e6i	0.0334220	−	0.156980i
$775$			9.43753e6i			0.564422i
$776$	8.78679e6	+	1.52192e7i	0.523813	+	0.907270i
$777$	4.91005e6	−	5.19829e6i	0.291765	−	0.308893i
$778$	−2.55913e7	+	4.43253e7i	−1.51580	+	2.62545i
$779$	−8.80213e6	−	5.08191e6i	−0.519690	−	0.300043i
$780$	1.88380e7	+	1.36914e7i	1.10866	+	0.805771i
$781$	1.75178e7	+	3.03417e7i	1.02766	+	1.77997i
$782$	−2.82853e7			−1.65403
$783$	−2.24359e7	+	4.75715e6i	−1.30779	+	0.277295i
$784$	−1.30791e6	−	4.78555e6i	−0.0759955	−	0.278062i
$785$	3.80560e6	−	2.19716e6i	0.220419	−	0.127259i
$786$	2.75089e7	+	1.99934e7i	1.58824	+	1.15433i
$787$	−1.05201e7	−	6.07377e6i	−0.605455	−	0.349560i	0.165729	−	0.986171i	$-0.447002\pi$
$787$	−1.05201e7	−	6.07377e6i	−0.605455	−	0.349560i	−0.771185	+	0.636611i	$0.780336\pi$
$788$	4.80559e7	+	2.77451e7i	2.75696	+	1.59173i
$789$	−1.69151e6	+	1.60678e7i	−0.0967348	+	0.918893i
$790$	1.30493e7	−	7.53399e6i	0.743906	−	0.429494i
$791$	1.26600e7	+	9.66427e6i	0.719436	+	0.549196i
$792$	−2.51976e7	+	2.79660e7i	−1.42740	+	1.58423i
$793$	1.02555e6			0.0579127
$794$	2.24964e7	+	3.89650e7i	1.26638	+	2.19343i
$795$	−1.50468e7	+	6.69627e6i	−0.844360	+	0.375764i
$796$	−1.16395e7	−	6.72007e6i	−0.651106	−	0.375916i
$797$	5.27471e6	−	9.13606e6i	0.294139	−	0.509464i	−0.680645	−	0.732613i	$-0.738300\pi$
$797$	5.27471e6	−	9.13606e6i	0.294139	−	0.509464i	0.974784	+	0.223150i	$0.0716338\pi$
$798$	−3.94504e7	−	9.37413e6i	−2.19303	−	0.521103i
$799$	1.15842e6	+	2.00644e6i	0.0641947	+	0.111188i
$800$			1.65678e7i			0.915253i
$801$	9.32763e6	+	2.87402e7i	0.513677	+	1.58274i
$802$	1.58853e7			0.872085
$803$	3.59805e6	+	6.23201e6i	0.196915	+	0.341067i
$804$	1.51693e7	+	1.59692e6i	0.827607	+	0.0871248i
$805$	3.66431e7	−	1.52853e7i	1.99298	−	0.831349i
$806$	−6.44400e6	−	3.72044e6i	−0.349396	−	0.201724i
$807$	−1.08620e7	+	1.49450e7i	−0.587117	+	0.807814i
$808$	2.53957e7	−	1.46622e7i	1.36846	−	0.790079i
$809$			2.25477e7i			1.21124i	0.795753	+	0.605622i	$0.207076\pi$
$809$			2.25477e7i			1.21124i	−0.795753	+	0.605622i	$0.792924\pi$
$810$	2.70656e7	+	3.73050e7i	1.44946	+	1.99781i
$811$		−	1.80983e7i		−	0.966240i	−0.875554	−	0.483120i	$-0.839504\pi$
$811$		−	1.80983e7i		−	0.966240i	0.875554	−	0.483120i	$-0.160496\pi$
$812$	5.59735e6	−	4.33515e7i	0.297915	−	2.30735i
$813$	−2.61213e7	−	1.89849e7i	−1.38602	−	1.00735i
$814$	1.15693e7	−	2.00386e7i	0.611991	−	1.06000i
$815$	2.55533e6	−	4.42597e6i	0.134758	−	0.233407i
$816$	3.76199e6	+	396036.i	0.197784	+	0.0208214i
$817$	2.18140e6	−	1.25943e6i	0.114335	−	0.0660115i
$818$	3.33507e7			1.74270
$819$	3.36383e6	−	9.56477e6i	0.175236	−	0.498270i
$820$	−2.20181e7			−1.14352
$821$	1.18532e7	−	6.84346e6i	0.613731	−	0.354338i	−0.160693	−	0.987004i	$-0.551373\pi$
$821$	1.18532e7	−	6.84346e6i	0.613731	−	0.354338i	0.774424	+	0.632666i	$0.218040\pi$
$822$	−6.22253e6	−	1.39823e7i	−0.321209	−	0.721771i
$823$	6.30569e6	−	1.09218e7i	0.324514	−	0.562075i	−0.656900	−	0.753978i	$-0.728133\pi$
$823$	6.30569e6	−	1.09218e7i	0.324514	−	0.562075i	0.981414	+	0.191903i	$0.0614660\pi$
$824$	−1.98777e6	+	3.44292e6i	−0.101988	+	0.176648i
$825$	−3.80179e7	+	1.69190e7i	−1.94470	+	0.865448i
$826$	−2.84027e6	+	2.19979e7i	−0.144847	+	1.12184i
$827$		−	2.06738e7i		−	1.05113i	−0.850754	−	0.525565i	$-0.823854\pi$
$827$		−	2.06738e7i		−	1.05113i	0.850754	−	0.525565i	$-0.176146\pi$
$828$	−3.69387e7	−	3.32821e7i	−1.87243	−	1.68708i
$829$			868617.i			0.0438977i	0.999759	+	0.0219489i	$0.00698710\pi$
$829$			868617.i			0.0438977i	−0.999759	+	0.0219489i	$0.993013\pi$
$830$	3.14202e7	−	1.81405e7i	1.58312	−	0.914015i
$831$	1.78659e6	+	188080.i	0.0897475	+	0.00944800i
$832$	−1.39454e7	−	8.05136e6i	−0.698428	−	0.403238i
$833$	1.33639e7	+	3.50947e6i	0.667297	+	0.175238i
$834$	1.22037e7	−	1.67911e7i	0.607544	−	0.835919i
$835$	−3.46835e6	−	6.00736e6i	−0.172150	−	0.298173i
$836$	−8.33289e7			−4.12363
$837$	−6.25441e6	−	6.95323e6i	−0.308584	−	0.343062i
$838$		−	4.64779e7i		−	2.28632i
$839$	−1.70427e7	−	2.95187e7i	−0.835858	−	1.44775i	−0.893330	−	0.449401i	$-0.851637\pi$
$839$	−1.70427e7	−	2.95187e7i	−0.835858	−	1.44775i	0.0574723	−	0.998347i	$-0.481696\pi$
$840$	−3.58021e7	+	1.06958e7i	−1.75070	+	0.523015i
$841$	8.07338e6	−	1.39835e7i	0.393609	−	0.681751i
$842$	1.45848e7	+	8.42053e6i	0.708957	+	0.409317i
$843$	−732963.	+	6.96249e6i	−0.0355233	+	0.337439i
$844$	1.80411e7	+	3.12480e7i	0.871778	+	1.50996i
$845$	2.23141e7			1.07507
$846$	−1.33540e6	+	6.27226e6i	−0.0641484	+	0.301299i
$847$	−2.56948e7	+	3.36596e7i	−1.23065	+	1.61213i
$848$	−3.24026e6	+	1.87076e6i	−0.154736	+	0.0893366i
$849$	−8.19540e6	+	3.64719e6i	−0.390212	+	0.173656i
$850$	2.54845e7	+	1.47135e7i	1.20984	+	0.698502i
$851$	1.12587e7	+	6.50024e6i	0.532925	+	0.307684i
$852$	3.97895e7	−	1.77074e7i	1.87789	−	0.835713i
$853$	2.40599e7	−	1.38910e7i	1.13219	−	0.653673i	0.187709	−	0.982225i	$-0.439894\pi$
$853$	2.40599e7	−	1.38910e7i	1.13219	−	0.653673i	0.944486	+	0.328552i	$0.106561\pi$
$854$	−2.34725e6	+	3.07485e6i	−0.110132	+	0.144271i
$855$	−9.03734e6	+	4.24476e7i	−0.422791	+	1.98581i
$856$	−2.46551e6			−0.115006
$857$	−3.15673e6	−	5.46762e6i	−0.146820	−	0.254300i	0.783230	−	0.621732i	$-0.213571\pi$
$857$	−3.15673e6	−	5.46762e6i	−0.146820	−	0.254300i	−0.930051	+	0.367432i	$0.880237\pi$
$858$	3.43492e6	−	3.26286e7i	0.159293	−	1.51314i
$859$	−3.51003e7	−	2.02652e7i	−1.62304	−	0.937061i	−0.986102	−	0.166143i	$-0.946869\pi$
$859$	−3.51003e7	−	2.02652e7i	−1.62304	−	0.937061i	−0.636935	−	0.770917i	$-0.719798\pi$
$860$	2.72833e6	−	4.72561e6i	0.125791	−	0.217877i
$861$	2.74402e6	+	9.18509e6i	0.126148	+	0.422256i
$862$	−6.57333e6	−	1.13853e7i	−0.301313	−	0.521889i
$863$			1.09348e7i			0.499788i	0.968273	+	0.249894i	$0.0803958\pi$
$863$			1.09348e7i			0.499788i	−0.968273	+	0.249894i	$0.919604\pi$
$864$	−1.09798e7	−	1.22066e7i	−0.500391	−	0.556301i
$865$	−1.54757e6			−0.0703249
$866$	2.73166e7	+	4.73137e7i	1.23775	+	2.14384i
$867$	6.81871e6	−	9.38186e6i	0.308074	−	0.423878i
$868$	1.64507e7	−	6.86222e6i	0.741113	−	0.309147i
$869$	−1.16754e7	−	6.74079e6i	−0.524471	−	0.302804i
$870$	−7.32622e7	−	7.71255e6i	−3.28157	−	0.345461i
$871$	−4.89739e6	+	2.82751e6i	−0.218736	+	0.126287i
$872$			5.40821e6i			0.240859i
$873$	−1.43021e7	−	1.28863e7i	−0.635133	−	0.572261i
$874$		−	7.37219e7i		−	3.26451i
$875$	−7.47533e6	−	965181.i	−0.330073	−	0.0426176i
$876$	8.17254e6	−	3.63701e6i	0.359830	−	0.160134i
$877$	−5.58393e6	+	9.67166e6i	−0.245155	+	0.424621i	−0.962175	−	0.272431i	$-0.912172\pi$
$877$	−5.58393e6	+	9.67166e6i	−0.245155	+	0.424621i	0.717020	+	0.697053i	$0.245506\pi$
$878$	2.33063e7	−	4.03676e7i	1.02032	−	1.76725i
$879$	1.66345e7	+	3.73784e7i	0.726168	+	1.63173i
$880$	−1.48800e7	+	8.59096e6i	−0.647732	+	0.373968i
$881$	−1.82538e7			−0.792343			−0.396171	−	0.918177i	$-0.629661\pi$
$881$	−1.82538e7			−0.792343			−0.396171	+	0.918177i	$0.629661\pi$
$882$	2.09785e7	+	3.19771e7i	0.908035	+	1.38410i
$883$	2.59199e6			0.111875			0.0559373	−	0.998434i	$-0.482185\pi$
$883$	2.59199e6			0.111875			0.0559373	+	0.998434i	$0.482185\pi$
$884$	−1.27604e7	+	7.36723e6i	−0.549205	+	0.317083i
$885$	2.36091e7	+	2.48541e6i	1.01326	+	0.106669i
$886$	1.00479e7	−	1.74035e7i	0.430023	−	0.744821i
$887$	−3.68668e6	+	6.38551e6i	−0.157335	+	0.272513i	−0.933907	−	0.357516i	$-0.883624\pi$
$887$	−3.68668e6	+	6.38551e6i	−0.157335	+	0.272513i	0.776572	+	0.630029i	$0.216957\pi$
$888$	−9.89715e6	−	7.19322e6i	−0.421190	−	0.306120i
$889$	−7.23633e6	−	934322.i	−0.307089	−	0.0396499i
$890$			9.70546e7i			4.10716i
$891$	1.67977e7	−	3.76604e7i	0.708851	−	1.58925i
$892$			7.76500e7i			3.26761i
$893$	−5.22952e6	+	3.01927e6i	−0.219449	+	0.126699i
$894$	1.46574e7	−	2.01671e7i	0.613357	−	0.843917i
$895$	4.02815e7	+	2.32565e7i	1.68092	+	0.970482i
$896$	3.94628e7	−	1.64615e7i	1.64217	−	0.685013i
$897$	1.83325e7	+	1.92992e6i	0.760748	+	0.0800864i
$898$	−94456.3	−	163603.i	−0.00390877	−	0.00677019i
$899$	1.49483e7			0.616868
$900$	1.59683e7	+	4.92012e7i	0.657130	+	2.02474i
$901$		−	1.04205e7i		−	0.427637i
$902$	1.55100e7	+	2.68641e7i	0.634740	+	1.09940i
$903$	−2.31136e6	−	549221.i	−0.0943296	−	0.0224144i
$904$	1.36261e7	−	2.36011e7i	0.554562	−	0.960530i
$905$	−3.39416e7	−	1.95962e7i	−1.37756	−	0.795336i
$906$	5.77059e7	−	2.56808e7i	2.33561	−	1.03941i
$907$	−2.10524e7	−	3.64639e7i	−0.849736	−	1.47179i	−0.881444	−	0.472289i	$-0.843428\pi$
$907$	−2.10524e7	−	3.64639e7i	−0.849736	−	1.47179i	0.0317080	−	0.999497i	$-0.489905\pi$
$908$	6.73768e7			2.71204
$909$	−2.15029e7	+	2.38654e7i	−0.863154	+	0.957985i
$910$	1.97610e7	−	2.58865e7i	0.791052	−	1.03626i
$911$	1.71604e7	−	9.90755e6i	0.685064	−	0.395522i	−0.116696	−	0.993168i	$-0.537230\pi$
$911$	1.71604e7	−	9.90755e6i	0.685064	−	0.395522i	0.801760	+	0.597646i	$0.203897\pi$
$912$	−1.03222e6	+	9.80512e6i	−0.0410945	+	0.390360i
$913$	−2.81122e7	−	1.62306e7i	−1.11614	−	0.644402i
$914$	−3.92468e7	−	2.26591e7i	−1.55396	−	0.897177i
$915$	3.34915e6	+	2.43416e6i	0.132246	+	0.0961160i
$916$	−5.75487e7	+	3.32258e7i	−2.26619	+	1.30839i
$917$	1.83261e7	−	2.40068e7i	0.719692	−	0.942782i
$918$	−2.85269e7	+	6.04864e6i	−1.11724	+	0.236892i
$919$	6.05618e6			0.236543			0.118271	−	0.992981i	$-0.462265\pi$
$919$	6.05618e6			0.236543			0.118271	+	0.992981i	$0.462265\pi$
$920$	−3.39673e7	−	5.88331e7i	−1.32310	−	2.29167i
$921$	1.56583e7	+	1.13804e7i	0.608270	+	0.442089i
$922$	−6.16036e6	−	3.55669e6i	−0.238660	−	0.137790i
$923$	−8.07332e6	+	1.39834e7i	−0.311923	+	0.540267i
$924$	5.71354e7	+	5.39672e7i	2.20153	+	2.07946i
$925$	−6.76259e6	−	1.17132e7i	−0.259872	−	0.450111i
$926$		−	6.16141e7i		−	2.36131i
$927$	906889.	−	4.25958e6i	0.0346621	−	0.162805i
$928$	2.62421e7			1.00030
$929$	1.84922e7	+	3.20295e7i	0.702991	+	1.21762i	0.967412	+	0.253209i	$0.0814859\pi$
$929$	1.84922e7	+	3.20295e7i	0.702991	+	1.21762i	−0.264421	+	0.964407i	$0.585181\pi$
$930$	−1.22137e7	−	2.74448e7i	−0.463063	−	1.04053i
$931$	−9.14696e6	+	3.48311e7i	−0.345862	+	1.31702i
$932$	1.92334e6	+	1.11044e6i	0.0725299	+	0.0418752i
$933$	1.07194e7	+	2.40870e7i	0.403149	+	0.905896i
$934$	−5.74711e7	+	3.31809e7i	−2.15567	+	1.24458i
$935$		−	4.78531e7i		−	1.79012i
$936$	−1.69682e7	−	3.61262e6i	−0.633060	−	0.134782i
$937$			3.91278e7i			1.45592i	0.685621	+	0.727959i	$0.259531\pi$
$937$			3.91278e7i			1.45592i	−0.685621	+	0.727959i	$0.740469\pi$
$938$	2.73145e6	−	2.11551e7i	0.101365	−	0.785069i
$939$	−1.00301e6	+	9.52768e6i	−0.0371228	+	0.352633i
$940$	−6.54069e6	+	1.13288e7i	−0.241437	+	0.418181i
$941$	−2.06473e6	+	3.57622e6i	−0.0760132	+	0.131659i	−0.901526	−	0.432724i	$-0.857552\pi$
$941$	−2.06473e6	+	3.57622e6i	−0.0760132	+	0.131659i	0.825513	+	0.564383i	$0.190886\pi$
$942$	−4.52450e6	+	6.22525e6i	−0.166128	+	0.228575i
$943$	−1.50937e7	+	8.71436e6i	−0.552735	+	0.319122i
$944$	5.39312e6			0.196974
$945$	3.36874e7	−	2.32517e7i	1.22712	−	0.846984i
$946$	−7.68757e6			−0.279294
$947$	4.20015e7	−	2.42496e7i	1.52191	−	0.878676i	0.522247	−	0.852794i	$-0.325094\pi$
$947$	4.20015e7	−	2.42496e7i	1.52191	−	0.878676i	0.999665	−	0.0258817i	$-0.00823932\pi$
$948$	−9.85272e6	+	1.35563e7i	−0.356070	+	0.489916i
$949$	−1.65822e6	+	2.87212e6i	−0.0597690	+	0.103523i
$950$	−3.83487e7	+	6.64218e7i	−1.37861	+	2.38782i
$951$	2.90456e6	−	2.75907e7i	0.104143	−	0.989263i
$952$	3.02737e6	−	2.34470e7i	0.108261	−	0.838484i
$953$			3.09501e7i			1.10390i	0.833877	+	0.551950i	$0.186116\pi$
$953$			3.09501e7i			1.10390i	−0.833877	+	0.551950i	$0.813884\pi$
$954$	1.93070e7	−	2.14282e7i	0.686821	−	0.762279i
$955$			7.10756e7i			2.52181i
$956$	1.20945e7	−	6.98275e6i	0.427999	−	0.247105i
$957$	2.67984e7	+	6.02173e7i	0.945865	+	2.12540i
$958$	2.52243e7	+	1.45632e7i	0.887983	+	0.512677i
$959$	−1.25445e7	+	5.23279e6i	−0.440459	+	0.183733i
$960$	−2.64315e7	−	5.93929e7i	−0.925645	−	2.07997i
$961$	−1.12668e7	−	1.95146e7i	−0.393542	−	0.681635i
$962$	1.06637e7			0.371511
$963$	2.56896e6	−	833757.i	0.0892671	−	0.0289717i
$964$		−	1.94121e7i		−	0.672792i
$965$	−2.61590e6	−	4.53086e6i	−0.0904278	−	0.156626i
$966$	−4.77453e7	+	5.05482e7i	−1.64622	+	1.74286i
$967$	7.68653e6	−	1.33135e7i	0.264341	−	0.457852i	−0.703050	−	0.711140i	$-0.748179\pi$
$967$	7.68653e6	−	1.33135e7i	0.264341	−	0.457852i	0.967391	+	0.253289i	$0.0815123\pi$
$968$	6.27491e7	+	3.62282e7i	2.15238	+	1.24268i
$969$	−2.22121e7	−	1.61437e7i	−0.759941	−	0.552324i
$970$	−3.09177e7	−	5.35511e7i	−1.05506	−	1.82742i
$971$	−3.82677e7			−1.30252			−0.651260	−	0.758854i	$-0.725759\pi$
$971$	−3.82677e7			−1.30252			−0.651260	+	0.758854i	$0.725759\pi$
$972$	−4.43713e7	−	2.56672e7i	−1.50639	−	0.871392i
$973$	−1.46535e7	−	1.11860e7i	−0.496202	−	0.378787i
$974$	−7.60940e7	+	4.39329e7i	−2.57012	+	1.48386i
$975$	−1.55133e7	−	1.12750e7i	−0.522628	−	0.379845i
$976$	814567.	+	470291.i	0.0273717	+	0.0158031i
$977$	4.44233e7	+	2.56478e7i	1.48893	+	0.859634i	0.999920	−	0.0126451i	$-0.00402516\pi$
$977$	4.44233e7	+	2.56478e7i	1.48893	+	0.859634i	0.489009	+	0.872279i	$0.337358\pi$
$978$	−937047.	+	8.90110e6i	−0.0313267	+	0.297575i
$979$	7.52025e7	−	4.34182e7i	2.50770	−	1.44782i
$980$	2.05671e7	+	7.52538e7i	0.684083	+	2.50301i
$981$	−1.82888e6	−	5.63513e6i	−0.0606756	−	0.186953i
$982$	−1.91081e7			−0.632322
$983$	−2.27722e7	−	3.94426e7i	−0.751659	−	1.30191i	−0.947018	−	0.321179i	$-0.895921\pi$
$983$	−2.27722e7	−	3.94426e7i	−0.751659	−	1.30191i	0.195360	−	0.980732i	$-0.437412\pi$
$984$	1.49856e7	−	6.66901e6i	0.493385	−	0.219570i
$985$	−7.19277e7	−	4.15275e7i	−2.36214	−	1.36378i
$986$	2.33050e7	−	4.03654e7i	0.763407	−	1.32226i
$987$	5.54108e6	+	1.31666e6i	0.181051	+	0.0430211i
$988$	−1.92017e7	−	3.32583e7i	−0.625817	−	1.08395i
$989$		−	4.31929e6i		−	0.140418i
$990$	8.86618e7	−	9.84028e7i	2.87507	−	3.19095i
$991$	−1.00328e7			−0.324518			−0.162259	−	0.986748i	$-0.551878\pi$
$991$	−1.00328e7			−0.324518			−0.162259	+	0.986748i	$0.551878\pi$
$992$	5.35049e6	+	9.26732e6i	0.172629	+	0.299003i
$993$	−2.24998e7	−	2.36863e6i	−0.724113	−	0.0762296i
$994$	−2.34476e7	−	5.62106e7i	−0.752720	−	1.80448i
$995$	1.74214e7	+	1.00583e7i	0.557861	+	0.322081i
$996$	−2.37235e7	+	3.26412e7i	−0.757759	+	1.04260i
$997$	2.18550e7	−	1.26180e7i	0.696326	−	0.402024i	−0.109652	−	0.993970i	$-0.534974\pi$
$997$	2.18550e7	−	1.26180e7i	0.696326	−	0.402024i	0.805977	+	0.591946i	$0.201640\pi$
$998$		−	2.77819e7i		−	0.882948i
$999$	1.27449e7	+	4.14814e6i	0.404040	+	0.131504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.o.a.41.5	yes	76
3.2	odd	2		189.6.o.a.125.33		76
7.6	odd	2	inner	63.6.o.a.41.6	yes	76
9.2	odd	6	inner	63.6.o.a.20.6	yes	76
9.7	even	3		189.6.o.a.62.34		76
21.20	even	2		189.6.o.a.125.34		76
63.20	even	6	inner	63.6.o.a.20.5	✓	76
63.34	odd	6		189.6.o.a.62.33		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.o.a.20.5	✓	76	63.20	even	6	inner
63.6.o.a.20.6	yes	76	9.2	odd	6	inner
63.6.o.a.41.5	yes	76	1.1	even	1	trivial
63.6.o.a.41.6	yes	76	7.6	odd	2	inner
189.6.o.a.62.33		76	63.34	odd	6
189.6.o.a.62.34		76	9.7	even	3
189.6.o.a.125.33		76	3.2	odd	2
189.6.o.a.125.34		76	21.20	even	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+(-8.10965 + 4.68211i) q^{2} +(-9.16477 + 12.6098i) q^{3} +(27.8443 - 48.2277i) q^{4} +(-41.6759 + 72.1848i) q^{5} +(15.2827 - 145.171i) q^{6} +(-128.575 - 16.6010i) q^{7} +221.824i q^{8} +(-75.0139 - 231.132i) q^{9} -780.524i q^{10} +(-604.787 + 349.174i) q^{11} +(352.955 + 793.106i) q^{12} +(-278.725 - 160.922i) q^{13} +(1120.42 - 467.372i) q^{14} +(-528.285 - 1187.08i) q^{15} +(-147.589 - 255.632i) q^{16} +822.097 q^{17} +(1690.52 + 1523.17i) q^{18} +2142.69i q^{19} +(2320.87 + 4019.86i) q^{20} +(1387.69 - 1469.15i) q^{21} +(3269.74 - 5663.36i) q^{22} +(3181.98 + 1837.12i) q^{23} +(-2797.16 - 2032.97i) q^{24} +(-1911.26 - 3310.40i) q^{25} +3013.82 q^{26} +(3602.01 + 1172.36i) q^{27} +(-4380.69 + 5738.61i) q^{28} +(-5243.42 + 3027.29i) q^{29} +(9842.25 + 7153.33i) q^{30} +(-2138.15 - 1234.46i) q^{31} +(-3753.58 - 2167.13i) q^{32} +(1139.72 - 10826.3i) q^{33} +(-6666.92 + 3849.15i) q^{34} +(6556.80 - 8589.26i) q^{35} +(-13235.7 - 2817.95i) q^{36} +3538.28 q^{37} +(-10032.3 - 17376.4i) q^{38} +(4583.65 - 2039.85i) q^{39} +(-16012.3 - 9244.73i) q^{40} +(-2371.75 + 4107.99i) q^{41} +(-4374.95 + 18411.6i) q^{42} +(-587.782 - 1018.07i) q^{43} +38890.0i q^{44} +(19810.5 + 4217.77i) q^{45} -34406.3 q^{46} +(1409.10 + 2440.64i) q^{47} +(4576.09 + 481.739i) q^{48} +(16255.8 + 4268.92i) q^{49} +(30999.3 + 17897.5i) q^{50} +(-7534.33 + 10366.5i) q^{51} +(-15521.8 + 8961.51i) q^{52} -12675.5i q^{53} +(-34700.2 + 7357.57i) q^{54} -58208.6i q^{55} +(3682.50 - 28521.0i) q^{56} +(-27018.8 - 19637.2i) q^{57} +(28348.2 - 49100.5i) q^{58} +(-9135.35 + 15822.9i) q^{59} +(-71959.9 - 7575.45i) q^{60} +(-2759.58 + 1593.24i) q^{61} +23119.5 q^{62} +(5807.87 + 30963.0i) q^{63} +50032.7 q^{64} +(23232.2 - 13413.1i) q^{65} +(41447.3 + 93134.1i) q^{66} +(8785.35 - 15216.7i) q^{67} +(22890.7 - 39647.8i) q^{68} +(-52327.8 + 23287.4i) q^{69} +(-12957.5 + 100356. i) q^{70} -50169.2i q^{71} +(51270.7 - 16639.9i) q^{72} -10304.5i q^{73} +(-28694.2 + 16566.6i) q^{74} +(59259.8 + 6238.47i) q^{75} +(103337. + 59661.5i) q^{76} +(83556.8 - 34854.8i) q^{77} +(-27620.9 + 38003.6i) q^{78} +(9652.48 + 16718.6i) q^{79} +24603.7 q^{80} +(-47794.8 + 34676.2i) q^{81} -44419.1i q^{82} +(23241.4 + 40255.3i) q^{83} +(-32214.7 - 107833. i) q^{84} +(-34261.6 + 59342.9i) q^{85} +(9533.41 + 5504.11i) q^{86} +(9881.24 - 93862.8i) q^{87} +(-77455.3 - 134156. i) q^{88} -124345. q^{89} +(-180404. + 58550.2i) q^{90} +(33165.5 + 25317.6i) q^{91} +(177200. - 102306. i) q^{92} +(35162.0 - 15648.1i) q^{93} +(-22854.7 - 13195.2i) q^{94} +(-154669. - 89298.4i) q^{95} +(61727.8 - 27470.7i) q^{96} +(68609.1 - 39611.5i) q^{97} +(-151816. + 41492.0i) q^{98} +(126073. + 113593. i) 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

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