LMFDB - Embedded newform 15.6.e.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,6,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, 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:	$2.40575729719$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10768x^{12} + 16341006x^{8} + 4217167600x^{4} + 50906640625 $ x^16 + 10768x^12 + 16341006x^8 + 4217167600*x^4 + 50906640625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{10}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.6
Root			$-4.35647 - 4.35647i$ of defining polynomial
Character	$\chi$	$=$	15.2
Dual form			15.6.e.a.8.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.17835 - 3.17835i) q^{2} +(5.54767 - 14.5679i) q^{3} +11.7962i q^{4} +(-11.9990 - 54.5987i) q^{5} +(-28.6694 - 63.9343i) q^{6} +(83.6967 + 83.6967i) q^{7} +(139.200 + 139.200i) q^{8} +(-181.447 - 161.636i) q^{9} +O(q^{10})$	\(q+(3.17835 - 3.17835i) q^{2} +(5.54767 - 14.5679i) q^{3} +11.7962i q^{4} +(-11.9990 - 54.5987i) q^{5} +(-28.6694 - 63.9343i) q^{6} +(83.6967 + 83.6967i) q^{7} +(139.200 + 139.200i) q^{8} +(-181.447 - 161.636i) q^{9} +(-211.671 - 135.397i) q^{10} +566.700i q^{11} +(171.846 + 65.4414i) q^{12} +(-208.475 + 208.475i) q^{13} +532.035 q^{14} +(-861.955 - 128.095i) q^{15} +507.372 q^{16} +(155.680 - 155.680i) q^{17} +(-1090.44 + 62.9658i) q^{18} -2305.83i q^{19} +(644.057 - 141.543i) q^{20} +(1683.61 - 754.962i) q^{21} +(1801.17 + 1801.17i) q^{22} +(-1194.57 - 1194.57i) q^{23} +(2800.08 - 1255.61i) q^{24} +(-2837.05 + 1310.27i) q^{25} +1325.21i q^{26} +(-3361.30 + 1746.59i) q^{27} +(-987.303 + 987.303i) q^{28} -1310.94 q^{29} +(-3146.73 + 2332.46i) q^{30} +303.760 q^{31} +(-2841.78 + 2841.78i) q^{32} +(8255.62 + 3143.87i) q^{33} -989.614i q^{34} +(3565.45 - 5574.01i) q^{35} +(1906.69 - 2140.38i) q^{36} +(2750.09 + 2750.09i) q^{37} +(-7328.75 - 7328.75i) q^{38} +(1880.49 + 4193.59i) q^{39} +(5929.86 - 9270.38i) q^{40} -84.6376i q^{41} +(2951.55 - 7750.62i) q^{42} +(-4683.92 + 4683.92i) q^{43} -6684.90 q^{44} +(-6647.93 + 11846.2i) q^{45} -7593.51 q^{46} +(13211.3 - 13211.3i) q^{47} +(2814.73 - 7391.33i) q^{48} -2796.73i q^{49} +(-4852.64 + 13181.6i) q^{50} +(-1404.27 - 3131.60i) q^{51} +(-2459.21 - 2459.21i) q^{52} +(19545.6 + 19545.6i) q^{53} +(-5132.10 + 16234.7i) q^{54} +(30941.1 - 6799.85i) q^{55} +23301.1i q^{56} +(-33591.1 - 12792.0i) q^{57} +(-4166.63 + 4166.63i) q^{58} -2080.36 q^{59} +(1511.04 - 10167.8i) q^{60} -50807.1 q^{61} +(965.455 - 965.455i) q^{62} +(-1658.10 - 28714.9i) q^{63} +34300.2i q^{64} +(13884.0 + 8880.97i) q^{65} +(36231.5 - 16246.9i) q^{66} +(30649.1 + 30649.1i) q^{67} +(1836.44 + 1836.44i) q^{68} +(-24029.4 + 10775.3i) q^{69} +(-6383.90 - 29048.4i) q^{70} -75296.6i q^{71} +(-2757.66 - 47756.9i) q^{72} +(19151.6 - 19151.6i) q^{73} +17481.5 q^{74} +(3348.78 + 48598.7i) q^{75} +27200.1 q^{76} +(-47430.9 + 47430.9i) q^{77} +(19305.5 + 7351.84i) q^{78} -56900.8i q^{79} +(-6087.97 - 27701.8i) q^{80} +(6796.76 + 58656.5i) q^{81} +(-269.008 - 269.008i) q^{82} +(-25593.9 - 25593.9i) q^{83} +(8905.68 + 19860.1i) q^{84} +(-10368.0 - 6631.94i) q^{85} +29774.3i q^{86} +(-7272.68 + 19097.7i) q^{87} +(-78884.4 + 78884.4i) q^{88} +42602.7 q^{89} +(16522.0 + 58780.9i) q^{90} -34897.3 q^{91} +(14091.4 - 14091.4i) q^{92} +(1685.16 - 4425.14i) q^{93} -83980.1i q^{94} +(-125896. + 27667.8i) q^{95} +(25633.5 + 57164.1i) q^{96} +(78017.6 + 78017.6i) q^{97} +(-8888.97 - 8888.97i) q^{98} +(91599.0 - 102826. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 84 q^{6} - 80 q^{7}+O(q^{10}) $ 16 * q - 84 * q^6 - 80 * q^7	$ 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31} + 5760 q^{33} + 61932 q^{36} + 55720 q^{37} + 21480 q^{40} - 103020 q^{42} - 23360 q^{43} - 21240 q^{45} - 151168 q^{46} + 74820 q^{48} + 138816 q^{51} + 204160 q^{52} + 89120 q^{55} - 163800 q^{57} - 163500 q^{58} - 217380 q^{60} - 175168 q^{61} + 143040 q^{63} + 263400 q^{66} + 140320 q^{67} + 385260 q^{70} - 328680 q^{72} - 240320 q^{73} - 199920 q^{75} - 271536 q^{76} + 429960 q^{78} + 326016 q^{81} + 431120 q^{82} + 2440 q^{85} - 331680 q^{87} - 401700 q^{88} - 348360 q^{90} - 487168 q^{91} - 22320 q^{93} + 311748 q^{96} + 440800 q^{97}+O(q^{100}) $ 16 * q - 84 * q^6 - 80 * q^7 + 1060 * q^10 + 420 * q^12 - 2120 * q^13 - 3000 * q^15 - 452 * q^16 + 6000 * q^18 + 1416 * q^21 + 3380 * q^22 + 9160 * q^25 - 12960 * q^27 - 10900 * q^28 - 13380 * q^30 - 21568 * q^31 + 5760 * q^33 + 61932 * q^36 + 55720 * q^37 + 21480 * q^40 - 103020 * q^42 - 23360 * q^43 - 21240 * q^45 - 151168 * q^46 + 74820 * q^48 + 138816 * q^51 + 204160 * q^52 + 89120 * q^55 - 163800 * q^57 - 163500 * q^58 - 217380 * q^60 - 175168 * q^61 + 143040 * q^63 + 263400 * q^66 + 140320 * q^67 + 385260 * q^70 - 328680 * q^72 - 240320 * q^73 - 199920 * q^75 - 271536 * q^76 + 429960 * q^78 + 326016 * q^81 + 431120 * q^82 + 2440 * q^85 - 331680 * q^87 - 401700 * q^88 - 348360 * q^90 - 487168 * q^91 - 22320 * q^93 + 311748 * q^96 + 440800 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	3.17835	−	3.17835i	0.561858	−	0.561858i	−0.367977	−	0.929835i	$-0.619949\pi$
$2$	3.17835	−	3.17835i	0.561858	−	0.561858i	0.929835	+	0.367977i	$0.119949\pi$
$3$	5.54767	−	14.5679i	0.355883	−	0.934530i
$3$	5.54767	−	14.5679i	0.355883	−	0.934530i
$4$			11.7962i			0.368631i
$5$	−11.9990	−	54.5987i	−0.214645	−	0.976692i
$5$	−11.9990	−	54.5987i	−0.214645	−	0.976692i
$6$	−28.6694	−	63.9343i	−0.325117	−	0.725029i
$7$	83.6967	+	83.6967i	0.645600	+	0.645600i	0.951926	−	0.306327i	$-0.0991000\pi$
$7$	83.6967	+	83.6967i	0.645600	+	0.645600i	−0.306327	+	0.951926i	$0.599100\pi$
$8$	139.200	+	139.200i	0.768976	+	0.768976i
$9$	−181.447	−	161.636i	−0.746694	−	0.665168i
$10$	−211.671	−	135.397i	−0.669362	−	0.428162i
$11$			566.700i			1.41212i	0.708152	+	0.706060i	$0.249529\pi$
$11$			566.700i			1.41212i	−0.708152	+	0.706060i	$0.750471\pi$
$12$	171.846	+	65.4414i	0.344497	+	0.131190i
$13$	−208.475	+	208.475i	−0.342133	+	0.342133i	−0.857169	−	0.515036i	$-0.827779\pi$
$13$	−208.475	+	208.475i	−0.342133	+	0.342133i	0.515036	+	0.857169i	$0.327779\pi$
$14$	532.035			0.725471
$15$	−861.955	−	128.095i	−0.989137	−	0.146996i
$16$	507.372			0.495480
$17$	155.680	−	155.680i	0.130651	−	0.130651i	−0.638757	−	0.769408i	$-0.720551\pi$
$17$	155.680	−	155.680i	0.130651	−	0.130651i	0.769408	+	0.638757i	$0.220551\pi$
$18$	−1090.44	+	62.9658i	−0.793266	+	0.0458061i
$19$		−	2305.83i		−	1.46536i	−0.680574	−	0.732680i	$-0.738269\pi$
$19$		−	2305.83i		−	1.46536i	0.680574	−	0.732680i	$-0.261731\pi$
$20$	644.057	−	141.543i	0.360039	−	0.0791250i
$21$	1683.61	−	754.962i	0.833091	−	0.373574i
$22$	1801.17	+	1801.17i	0.793411	+	0.793411i
$23$	−1194.57	−	1194.57i	−0.470860	−	0.470860i	0.431333	−	0.902193i	$-0.358043\pi$
$23$	−1194.57	−	1194.57i	−0.470860	−	0.470860i	−0.902193	+	0.431333i	$0.858043\pi$
$24$	2800.08	−	1255.61i	0.992298	−	0.444966i
$25$	−2837.05	+	1310.27i	−0.907855	+	0.419285i
$26$			1325.21i			0.384461i
$27$	−3361.30	+	1746.59i	−0.887355	+	0.461086i
$28$	−987.303	+	987.303i	−0.237988	+	0.237988i
$29$	−1310.94			−0.289460			−0.144730	−	0.989471i	$-0.546231\pi$
$29$	−1310.94			−0.289460			−0.144730	+	0.989471i	$0.546231\pi$
$30$	−3146.73	+	2332.46i	−0.638345	+	0.473164i
$31$	303.760			0.0567709			0.0283855	−	0.999597i	$-0.490963\pi$
$31$	303.760			0.0567709			0.0283855	+	0.999597i	$0.490963\pi$
$32$	−2841.78	+	2841.78i	−0.490587	+	0.490587i
$33$	8255.62	+	3143.87i	1.31967	+	0.502550i
$34$		−	989.614i		−	0.146814i
$35$	3565.45	−	5574.01i	0.491977	−	0.769127i
$36$	1906.69	−	2140.38i	0.245202	−	0.275255i
$37$	2750.09	+	2750.09i	0.330250	+	0.330250i	0.852681	−	0.522432i	$-0.174975\pi$
$37$	2750.09	+	2750.09i	0.330250	+	0.330250i	−0.522432	+	0.852681i	$0.674975\pi$
$38$	−7328.75	−	7328.75i	−0.823324	−	0.823324i
$39$	1880.49	+	4193.59i	0.197974	+	0.441493i
$40$	5929.86	−	9270.38i	0.585996	−	0.916110i
$41$		−	84.6376i		−	0.00786328i	−0.999992	−	0.00393164i	$-0.998749\pi$
$41$		−	84.6376i		−	0.00786328i	0.999992	−	0.00393164i	$-0.00125148\pi$
$42$	2951.55	−	7750.62i	0.258183	−	0.677974i
$43$	−4683.92	+	4683.92i	−0.386312	+	0.386312i	−0.873370	−	0.487057i	$-0.838070\pi$
$43$	−4683.92	+	4683.92i	−0.386312	+	0.386312i	0.487057	+	0.873370i	$0.338070\pi$
$44$	−6684.90			−0.520551
$45$	−6647.93	+	11846.2i	−0.489390	+	0.872065i
$46$	−7593.51			−0.529112
$47$	13211.3	−	13211.3i	0.872369	−	0.872369i	−0.120361	−	0.992730i	$-0.538405\pi$
$47$	13211.3	−	13211.3i	0.872369	−	0.872369i	0.992730	+	0.120361i	$0.0384053\pi$
$48$	2814.73	−	7391.33i	0.176333	−	0.463041i
$49$		−	2796.73i		−	0.166402i
$50$	−4852.64	+	13181.6i	−0.274507	+	0.745664i
$51$	−1404.27	−	3131.60i	−0.0756006	−	0.168594i
$52$	−2459.21	−	2459.21i	−0.126121	−	0.126121i
$53$	19545.6	+	19545.6i	0.955782	+	0.955782i	0.999063	−	0.0432812i	$-0.0137811\pi$
$53$	19545.6	+	19545.6i	0.955782	+	0.955782i	−0.0432812	+	0.999063i	$0.513781\pi$
$54$	−5132.10	+	16234.7i	−0.239503	+	0.757633i
$55$	30941.1	−	6799.85i	1.37921	−	0.303105i
$56$			23301.1i			0.992902i
$57$	−33591.1	−	12792.0i	−1.36942	−	0.521497i
$58$	−4166.63	+	4166.63i	−0.162636	+	0.162636i
$59$	−2080.36			−0.0778051			−0.0389026	−	0.999243i	$-0.512386\pi$
$59$	−2080.36			−0.0778051			−0.0389026	+	0.999243i	$0.512386\pi$
$60$	1511.04	−	10167.8i	0.0541873	−	0.364627i
$61$	−50807.1			−1.74823			−0.874117	−	0.485715i	$-0.838559\pi$
$61$	−50807.1			−1.74823			−0.874117	+	0.485715i	$0.838559\pi$
$62$	965.455	−	965.455i	0.0318972	−	0.0318972i
$63$	−1658.10	−	28714.9i	−0.0526332	−	0.911497i
$64$			34300.2i			1.04676i
$65$	13884.0	+	8880.97i	0.407596	+	0.260721i
$66$	36231.5	−	16246.9i	1.02383	−	0.459105i
$67$	30649.1	+	30649.1i	0.834125	+	0.834125i	0.988078	−	0.153953i	$-0.0492004\pi$
$67$	30649.1	+	30649.1i	0.834125	+	0.834125i	−0.153953	+	0.988078i	$0.549200\pi$
$68$	1836.44	+	1836.44i	0.0481619	+	0.0481619i
$69$	−24029.4	+	10775.3i	−0.607604	+	0.272461i
$70$	−6383.90	−	29048.4i	−0.155719	−	0.708561i
$71$		−	75296.6i		−	1.77268i	−0.463038	−	0.886339i	$-0.653241\pi$
$71$		−	75296.6i		−	1.77268i	0.463038	−	0.886339i	$-0.346759\pi$
$72$	−2757.66	−	47756.9i	−0.0626917	−	1.08569i
$73$	19151.6	−	19151.6i	0.420627	−	0.420627i	−0.464793	−	0.885420i	$-0.653871\pi$
$73$	19151.6	−	19151.6i	0.420627	−	0.420627i	0.885420	+	0.464793i	$0.153871\pi$
$74$	17481.5			0.371107
$75$	3348.78	+	48598.7i	0.0687439	+	0.997634i
$76$	27200.1			0.540177
$77$	−47430.9	+	47430.9i	−0.911664	+	0.911664i
$78$	19305.5	+	7351.84i	0.359290	+	0.136823i
$79$		−	56900.8i		−	1.02577i	−0.858457	−	0.512886i	$-0.828576\pi$
$79$		−	56900.8i		−	1.02577i	0.858457	−	0.512886i	$-0.171424\pi$
$80$	−6087.97	−	27701.8i	−0.106352	−	0.483931i
$81$	6796.76	+	58656.5i	0.115104	+	0.993353i
$82$	−269.008	−	269.008i	−0.00441805	−	0.00441805i
$83$	−25593.9	−	25593.9i	−0.407794	−	0.407794i	0.473174	−	0.880969i	$-0.343108\pi$
$83$	−25593.9	−	25593.9i	−0.407794	−	0.407794i	−0.880969	+	0.473174i	$0.843108\pi$
$84$	8905.68	+	19860.1i	0.137711	+	0.307103i
$85$	−10368.0	−	6631.94i	−0.155649	−	0.0995620i
$86$			29774.3i			0.434105i
$87$	−7272.68	+	19097.7i	−0.103014	+	0.270509i
$88$	−78884.4	+	78884.4i	−1.08589	+	1.08589i
$89$	42602.7			0.570114			0.285057	−	0.958511i	$-0.407987\pi$
$89$	42602.7			0.570114			0.285057	+	0.958511i	$0.407987\pi$
$90$	16522.0	+	58780.9i	0.215009	+	0.764944i
$91$	−34897.3			−0.441762
$92$	14091.4	−	14091.4i	0.173573	−	0.173573i
$93$	1685.16	−	4425.14i	0.0202038	−	0.0530542i
$94$		−	83980.1i		−	0.980295i
$95$	−125896.	+	27667.8i	−1.43121	+	0.314533i
$96$	25633.5	+	57164.1i	0.283877	+	0.633060i
$97$	78017.6	+	78017.6i	0.841906	+	0.841906i	0.989107	−	0.147201i	$-0.0470264\pi$
$97$	78017.6	+	78017.6i	0.841906	+	0.841906i	−0.147201	+	0.989107i	$0.547026\pi$
$98$	−8888.97	−	8888.97i	−0.0934945	−	0.0934945i
$99$	91599.0	−	102826.i	0.939296	−	1.05442i
$100$	−15456.1	−	33466.4i	−0.154561	−	0.334664i
$101$		−	7709.74i		−	0.0752032i	−0.999293	−	0.0376016i	$-0.988028\pi$
$101$		−	7709.74i		−	0.0752032i	0.999293	−	0.0376016i	$-0.0119718\pi$
$102$	−14416.6	−	5490.05i	−0.137202	−	0.0522488i
$103$	−14320.2	+	14320.2i	−0.133001	+	0.133001i	−0.770473	−	0.637472i	$-0.779980\pi$
$103$	−14320.2	+	14320.2i	−0.133001	+	0.133001i	0.637472	+	0.770473i	$0.279980\pi$
$104$	−58039.2			−0.526185
$105$	−61421.6	−	82864.0i	−0.543686	−	0.733487i
$106$	124245.			1.07403
$107$	86698.6	−	86698.6i	0.732070	−	0.732070i	−0.238959	−	0.971030i	$-0.576806\pi$
$107$	86698.6	−	86698.6i	0.732070	−	0.732070i	0.971030	+	0.238959i	$0.0768063\pi$
$108$	−20603.1	−	39650.5i	−0.169971	−	0.327107i
$109$		−	12001.3i		−	0.0967527i	−0.998829	−	0.0483764i	$-0.984595\pi$
$109$		−	12001.3i		−	0.0967527i	0.998829	−	0.0483764i	$-0.0154047\pi$
$110$	76729.3	−	119954.i	0.604616	−	0.945220i
$111$	55319.6	−	24806.4i	0.426159	−	0.191098i
$112$	42465.3	+	42465.3i	0.319882	+	0.319882i
$113$	77651.2	+	77651.2i	0.572074	+	0.572074i	0.932707	−	0.360634i	$-0.117440\pi$
$113$	77651.2	+	77651.2i	0.572074	+	0.572074i	−0.360634	+	0.932707i	$0.617440\pi$
$114$	−147422.	+	66106.9i	−1.06243	+	0.476414i
$115$	−50888.3	+	79555.6i	−0.358817	+	0.560953i
$116$		−	15464.1i		−	0.106704i
$117$	71524.0	−	4130.06i	0.483045	−	0.0278928i
$118$	−6612.10	+	6612.10i	−0.0437154	+	0.0437154i
$119$	26059.9			0.168696
$120$	−102153.	−	137815.i	−0.647587	−	0.873659i
$121$	−160098.			−0.994081
$122$	−161483.	+	161483.i	−0.982259	+	0.982259i
$123$	−1232.99	−	469.542i	−0.00734847	−	0.00279841i
$124$			3583.21i			0.0209275i
$125$	105581.	+	139177.i	0.604379	+	0.796697i
$126$	−96535.9	−	85995.8i	−0.541704	−	0.482560i
$127$	−108319.	−	108319.i	−0.595929	−	0.595929i	0.343297	−	0.939227i	$-0.388456\pi$
$127$	−108319.	−	108319.i	−0.595929	−	0.595929i	−0.939227	+	0.343297i	$0.888456\pi$
$128$	18081.1	+	18081.1i	0.0975438	+	0.0975438i
$129$	42250.0	+	94219.7i	0.223538	+	0.498503i
$130$	72354.9	−	15901.3i	0.375500	−	0.0825227i
$131$			228726.i			1.16449i	0.813012	+	0.582247i	$0.197826\pi$
$131$			228726.i			1.16449i	−0.813012	+	0.582247i	$0.802174\pi$
$132$	−37085.7	+	97384.9i	−0.185256	+	0.486471i
$133$	192991.	−	192991.i	0.946035	−	0.946035i
$134$	194827.			0.937320
$135$	135694.	+	162565.i	0.640806	+	0.767703i
$136$	43341.3			0.200935
$137$	17998.3	−	17998.3i	0.0819275	−	0.0819275i	−0.664956	−	0.746883i	$-0.731550\pi$
$137$	17998.3	−	17998.3i	0.0819275	−	0.0819275i	0.746883	+	0.664956i	$0.231550\pi$
$138$	−42126.3	+	110621.i	−0.188302	+	0.494472i
$139$			197969.i			0.869082i	0.900652	+	0.434541i	$0.143089\pi$
$139$			197969.i			0.869082i	−0.900652	+	0.434541i	$0.856911\pi$
$140$	65752.2	+	42058.8i	0.283524	+	0.181358i
$141$	−119169.	−	265752.i	−0.504793	−	1.12572i
$142$	−239319.	−	239319.i	−0.995993	−	0.995993i
$143$	−118143.	−	118143.i	−0.483133	−	0.483133i
$144$	−92060.8	−	82009.4i	−0.369972	−	0.329577i
$145$	15730.1	+	71575.8i	0.0621313	+	0.282713i
$146$		−	121741.i		−	0.472665i
$147$	−40742.4	−	15515.3i	−0.155508	−	0.0592199i
$148$	−32440.6	+	32440.6i	−0.121740	+	0.121740i
$149$	−434636.			−1.60384			−0.801919	−	0.597433i	$-0.796187\pi$
$149$	−434636.			−1.60384			−0.801919	+	0.597433i	$0.796187\pi$
$150$	165107.	+	143820.i	0.599153	+	0.521905i
$151$	238082.			0.849738			0.424869	−	0.905255i	$-0.360320\pi$
$151$	238082.			0.849738			0.424869	+	0.905255i	$0.360320\pi$
$152$	320971.	−	320971.i	1.12683	−	1.12683i
$153$	−53411.2	+	3084.16i	−0.184461	+	0.0106515i
$154$			301504.i			1.02445i
$155$	−3644.83	−	16584.9i	−0.0121856	−	0.0554477i
$156$	−49468.4	+	22182.6i	−0.162748	+	0.0729795i
$157$	−116365.	−	116365.i	−0.376767	−	0.376767i	0.493168	−	0.869934i	$-0.335839\pi$
$157$	−116365.	−	116365.i	−0.376767	−	0.376767i	−0.869934	+	0.493168i	$0.835839\pi$
$158$	−180851.	−	180851.i	−0.576338	−	0.576338i
$159$	393170.	−	176305.i	1.23335	−	0.553060i
$160$	189256.	+	121059.i	0.584455	+	0.373850i
$161$		−	199963.i		−	0.607973i
$162$	208033.	+	164828.i	0.622796	+	0.493452i
$163$	89054.5	−	89054.5i	0.262535	−	0.262535i	−0.563548	−	0.826083i	$-0.690564\pi$
$163$	89054.5	−	89054.5i	0.262535	−	0.262535i	0.826083	+	0.563548i	$0.190564\pi$
$164$	998.402			0.00289865
$165$	72591.6	−	488470.i	0.207576	−	1.39678i
$166$	−162693.			−0.458245
$167$	−132460.	+	132460.i	−0.367532	+	0.367532i	−0.866576	−	0.499044i	$-0.833684\pi$
$167$	−132460.	+	132460.i	−0.367532	+	0.367532i	0.499044	+	0.866576i	$0.333684\pi$
$168$	339448.	+	129267.i	0.927897	+	0.353357i
$169$			284369.i			0.765890i
$170$	−54031.7	+	11874.4i	−0.143392	+	0.0315130i
$171$	−372705.	+	418386.i	−0.974710	+	1.09418i
$172$	−55252.5	−	55252.5i	−0.142407	−	0.142407i
$173$	152848.	+	152848.i	0.388280	+	0.388280i	0.874074	−	0.485794i	$-0.161469\pi$
$173$	152848.	+	152848.i	0.388280	+	0.388280i	−0.485794	+	0.874074i	$0.661469\pi$
$174$	37583.9	+	83814.2i	0.0941085	+	0.209867i
$175$	−347116.	−	127787.i	−0.856801	−	0.315421i
$176$			287527.i			0.699677i
$177$	−11541.1	+	30306.4i	−0.0276895	+	0.0727112i
$178$	135406.	−	135406.i	0.320323	−	0.320323i
$179$	−480813.			−1.12162			−0.560808	−	0.827946i	$-0.689509\pi$
$179$	−480813.			−1.12162			−0.560808	+	0.827946i	$0.689509\pi$
$180$	−139740.	−	78420.2i	−0.321470	−	0.180404i
$181$	152370.			0.345704			0.172852	−	0.984948i	$-0.444702\pi$
$181$	152370.			0.345704			0.172852	+	0.984948i	$0.444702\pi$
$182$	−110916.	+	110916.i	−0.248208	+	0.248208i
$183$	−281861.	+	740152.i	−0.622168	+	1.63378i
$184$		−	332567.i		−	0.724160i
$185$	117153.	−	183150.i	0.251666	−	0.393439i
$186$	−8708.61	−	19420.7i	−0.0184572	−	0.0411606i
$187$	88224.1	+	88224.1i	0.184494	+	0.184494i
$188$	155843.	+	155843.i	0.321582	+	0.321582i
$189$	−427513.	−	135146.i	−0.870553	−	0.275199i
$190$	−312203.	+	488078.i	−0.627411	+	0.980857i
$191$		−	121584.i		−	0.241153i	−0.992704	−	0.120576i	$-0.961526\pi$
$191$		−	121584.i		−	0.241153i	0.992704	−	0.120576i	$-0.0384743\pi$
$192$	499682.	+	190287.i	0.978229	+	0.372525i
$193$	110399.	−	110399.i	0.213340	−	0.213340i	−0.592344	−	0.805685i	$-0.701798\pi$
$193$	110399.	−	110399.i	0.213340	−	0.213340i	0.805685	+	0.592344i	$0.201798\pi$
$194$	495935.			0.946063
$195$	206401.	−	152991.i	0.388709	−	0.288124i
$196$	32990.7			0.0613411
$197$	144403.	−	144403.i	0.265100	−	0.265100i	−0.562022	−	0.827122i	$-0.689976\pi$
$197$	144403.	−	144403.i	0.265100	−	0.265100i	0.827122	+	0.562022i	$0.189976\pi$
$198$	−35682.7	−	617950.i	−0.0646837	−	1.12019i
$199$		−	537929.i		−	0.962924i	−0.876467	−	0.481462i	$-0.840106\pi$
$199$		−	537929.i		−	0.962924i	0.876467	−	0.481462i	$-0.159894\pi$
$200$	−577304.	−	212527.i	−1.02054	−	0.375699i
$201$	616525.	−	276462.i	1.07637	−	0.482664i
$202$	−24504.2	−	24504.2i	−0.0422535	−	0.0422535i
$203$	−109722.	−	109722.i	−0.186875	−	0.186875i
$204$	36941.0	−	16565.1i	0.0621488	−	0.0278687i
$205$	−4621.11	+	1015.57i	−0.00768000	+	0.00168782i
$206$			91029.1i			0.149456i
$207$	23665.4	+	409835.i	0.0383874	+	0.664789i
$208$	−105774.	+	105774.i	−0.169520	+	0.169520i
$209$	1.30672e6			2.06926
$210$	−458590.	−	68151.2i	−0.717590	−	0.106641i
$211$	727241.			1.12453			0.562266	−	0.826956i	$-0.309930\pi$
$211$	727241.			1.12453			0.562266	+	0.826956i	$0.309930\pi$
$212$	−230563.	+	230563.i	−0.352331	+	0.352331i
$213$	−1.09691e6	−	417721.i	−1.65662	−	0.630866i
$214$		−	551117.i		−	0.822639i
$215$	311939.	+	199534.i	0.460228	+	0.294388i
$216$	−711016.	−	224767.i	−1.03692	−	0.327791i
$217$	25423.7	+	25423.7i	0.0366513	+	0.0366513i
$218$	−38144.4	−	38144.4i	−0.0543613	−	0.0543613i
$219$	−172751.	−	385245.i	−0.243395	−	0.542783i
$220$	80212.4	+	364987.i	0.111734	+	0.508418i
$221$			64910.9i			0.0893999i
$222$	96981.5	−	254668.i	0.132071	−	0.346810i
$223$	−682808.	+	682808.i	−0.919468	+	0.919468i	−0.996991	−	0.0775229i	$-0.975299\pi$
$223$	−682808.	+	682808.i	−0.919468	+	0.919468i	0.0775229	+	0.996991i	$0.475299\pi$
$224$	−475696.			−0.633445
$225$	726558.	+	220825.i	0.956784	+	0.290798i
$226$	493605.			0.642848
$227$	−354384.	+	354384.i	−0.456467	+	0.456467i	−0.897494	−	0.441027i	$-0.854614\pi$
$227$	−354384.	+	354384.i	−0.456467	+	0.456467i	0.441027	+	0.897494i	$0.354614\pi$
$228$	150897.	−	396248.i	0.192240	−	0.504812i
$229$			1.01934e6i			1.28449i	0.766499	+	0.642246i	$0.221997\pi$
$229$			1.01934e6i			1.28449i	−0.766499	+	0.642246i	$0.778003\pi$
$230$	91114.8	+	414596.i	0.113572	+	0.516780i
$231$	427837.	+	954099.i	0.527531	+	1.17642i
$232$	−182483.	−	182483.i	−0.222588	−	0.222588i
$233$	483742.	+	483742.i	0.583746	+	0.583746i	0.935930	−	0.352185i	$-0.114561\pi$
$233$	483742.	+	483742.i	0.583746	+	0.583746i	−0.352185	+	0.935930i	$0.614561\pi$
$234$	214202.	−	240455.i	0.255731	−	0.287074i
$235$	−879842.	−	562796.i	−1.03929	−	0.664786i
$236$		−	24540.3i		−	0.0286814i
$237$	−828925.	−	315667.i	−0.958615	−	0.365055i
$238$	82827.4	−	82827.4i	0.0947833	−	0.0947833i
$239$	445259.			0.504218			0.252109	−	0.967699i	$-0.418876\pi$
$239$	445259.			0.504218			0.252109	+	0.967699i	$0.418876\pi$
$240$	−437331.	−	64992.0i	−0.490098	−	0.0728336i
$241$	−616510.			−0.683750			−0.341875	−	0.939745i	$-0.611062\pi$
$241$	−616510.			−0.683750			−0.341875	+	0.939745i	$0.611062\pi$
$242$	−508846.	+	508846.i	−0.558532	+	0.558532i
$243$	892208.	+	226393.i	0.969282	+	0.245950i
$244$		−	599330.i		−	0.644454i
$245$	−152698.	+	33558.0i	−0.162524	+	0.0357175i
$246$	−5411.24	+	2426.51i	−0.00570111	+	0.00255649i
$247$	480709.	+	480709.i	0.501348	+	0.501348i
$248$	42283.2	+	42283.2i	0.0436555	+	0.0436555i
$249$	−514836.	+	230862.i	−0.526223	+	0.235969i
$250$	777926.	+	106782.i	0.787206	+	0.108055i
$251$		−	1.07551e6i		−	1.07754i	−0.842454	−	0.538768i	$-0.818890\pi$
$251$		−	1.07551e6i		−	1.07754i	0.842454	−	0.538768i	$-0.181110\pi$
$252$	338726.	−	19559.3i	0.336006	−	0.0194023i
$253$	676962.	−	676962.i	0.664910	−	0.664910i
$254$	−688550.			−0.669655
$255$	−154132.	+	114248.i	−0.148437	+	0.110026i
$256$	−982672.			−0.937149
$257$	1.24679e6	−	1.24679e6i	1.17750	−	1.17750i	0.197118	−	0.980380i	$-0.436842\pi$
$257$	1.24679e6	−	1.24679e6i	1.17750	−	1.17750i	0.980380	−	0.197118i	$-0.0631581\pi$
$258$	433748.	+	165178.i	0.405685	+	0.154491i
$259$			460347.i			0.426418i
$260$	−104762.	+	163778.i	−0.0961101	+	0.150253i
$261$	237866.	+	211895.i	0.216138	+	0.192540i
$262$	726971.	+	726971.i	0.654280	+	0.654280i
$263$	−769745.	−	769745.i	−0.686211	−	0.686211i	0.275181	−	0.961392i	$-0.411262\pi$
$263$	−769745.	−	769745.i	−0.686211	−	0.686211i	−0.961392	+	0.275181i	$0.911262\pi$
$264$	711554.	+	1.58680e6i	0.628345	+	1.40124i
$265$	832636.	−	1.30169e6i	0.728350	−	1.13866i
$266$		−	1.22678e6i		−	1.06308i
$267$	236346.	−	620631.i	0.202894	−	0.532789i
$268$	−361543.	+	361543.i	−0.307485	+	0.307485i
$269$	−2.10012e6			−1.76955			−0.884776	−	0.466017i	$-0.845689\pi$
$269$	−2.10012e6			−1.76955			−0.884776	+	0.466017i	$0.845689\pi$
$270$	947972.	+	85406.1i	0.791382	+	0.0712983i
$271$	−982155.			−0.812376			−0.406188	−	0.913790i	$-0.633142\pi$
$271$	−982155.			−0.812376			−0.406188	+	0.913790i	$0.633142\pi$
$272$	78987.8	−	78987.8i	0.0647348	−	0.0647348i
$273$	−193599.	+	508380.i	−0.157216	+	0.412840i
$274$		−	114410.i		−	0.0920632i
$275$	−742527.	−	1.60775e6i	−0.592080	−	1.28200i
$276$	−127107.	−	283456.i	−0.100438	−	0.223982i
$277$	−907548.	−	907548.i	−0.710673	−	0.710673i	0.256003	−	0.966676i	$-0.417594\pi$
$277$	−907548.	−	907548.i	−0.710673	−	0.710673i	−0.966676	+	0.256003i	$0.917594\pi$
$278$	629215.	+	629215.i	0.488300	+	0.488300i
$279$	−55116.2	−	49098.5i	−0.0423905	−	0.0377622i
$280$	1.27221e6	−	279591.i	0.969759	−	0.213122i
$281$			2.43616e6i			1.84052i	0.391308	+	0.920260i	$0.372023\pi$
$281$			2.43616e6i			1.84052i	−0.391308	+	0.920260i	$0.627977\pi$
$282$	−1.22341e6	−	465894.i	−0.916115	−	0.348871i
$283$	828841.	−	828841.i	0.615184	−	0.615184i	−0.329108	−	0.944292i	$-0.606748\pi$
$283$	828841.	−	828841.i	0.615184	−	0.615184i	0.944292	+	0.329108i	$0.106748\pi$
$284$	888214.			0.653464
$285$	−295367.	+	1.98753e6i	−0.215402	+	1.44944i
$286$	−750997.			−0.542904
$287$	7083.89	−	7083.89i	0.00507653	−	0.00507653i
$288$	974966.	−	56298.2i	0.692641	−	0.0399957i
$289$			1.37138e6i			0.965861i
$290$	277489.	+	177497.i	0.193754	+	0.123936i
$291$	1.56937e6	−	703736.i	1.08641	−	0.487166i
$292$	225916.	+	225916.i	0.155056	+	0.155056i
$293$	−284240.	−	284240.i	−0.193426	−	0.193426i	0.603748	−	0.797175i	$-0.293673\pi$
$293$	−284240.	−	284240.i	−0.193426	−	0.193426i	−0.797175	+	0.603748i	$0.793673\pi$
$294$	−178807.	+	80180.4i	−0.120647	+	0.0541003i
$295$	24962.3	+	113585.i	0.0167005	+	0.0759916i
$296$			765622.i			0.507908i
$297$	−989793.	−	1.90485e6i	−0.651108	−	1.25305i
$298$	−1.38143e6	+	1.38143e6i	−0.901129	+	0.901129i
$299$	498075.			0.322193
$300$	−573280.	+	39502.9i	−0.367759	+	0.0253411i
$301$	−784058.			−0.498806
$302$	756709.	−	756709.i	0.477432	−	0.477432i
$303$	−112315.	−	42771.1i	−0.0702797	−	0.0267636i
$304$		−	1.16991e6i		−	0.726056i
$305$	609636.	+	2.77400e6i	0.375250	+	1.70749i
$306$	−159957.	+	179562.i	−0.0976562	+	0.109625i
$307$	1.28579e6	+	1.28579e6i	0.778617	+	0.778617i	0.979596	−	0.200978i	$-0.0644121\pi$
$307$	1.28579e6	+	1.28579e6i	0.778617	+	0.778617i	−0.200978	+	0.979596i	$0.564412\pi$
$308$	−559504.	−	559504.i	−0.336068	−	0.336068i
$309$	129171.	+	288059.i	0.0769608	+	0.171627i
$310$	−64297.2	−	41128.1i	−0.0380003	−	0.0243072i
$311$		−	361008.i		−	0.211649i	−0.994385	−	0.105824i	$-0.966252\pi$
$311$		−	361008.i		−	0.211649i	0.994385	−	0.105824i	$-0.0337482\pi$
$312$	−321983.	+	845509.i	−0.187260	+	0.491736i
$313$	−1.01609e6	+	1.01609e6i	−0.586232	+	0.586232i	−0.936609	−	0.350377i	$-0.886054\pi$
$313$	−1.01609e6	+	1.01609e6i	−0.586232	+	0.586232i	0.350377	+	0.936609i	$0.386054\pi$
$314$	−739696.			−0.423379
$315$	−1.54790e6	+	435081.i	−0.878955	+	0.247055i
$316$	671213.			0.378131
$317$	−1.40830e6	+	1.40830e6i	−0.787133	+	0.787133i	−0.981023	−	0.193890i	$-0.937890\pi$
$317$	−1.40830e6	+	1.40830e6i	−0.787133	+	0.787133i	0.193890	+	0.981023i	$0.437890\pi$
$318$	689272.	−	1.80999e6i	0.382229	−	1.00371i
$319$		−	742911.i		−	0.408752i
$320$	1.87275e6	−	411570.i	1.02236	−	0.224682i
$321$	−782040.	−	1.74399e6i	−0.423610	−	0.944673i
$322$	−635552.	−	635552.i	−0.341595	−	0.341595i
$323$	−358973.	−	358973.i	−0.191450	−	0.191450i
$324$	−691924.	+	80175.9i	−0.366181	+	0.0424308i
$325$	318295.	−	864610.i	0.167156	−	0.454059i
$326$		−	566092.i		−	0.295015i
$327$	−174834.	−	66579.5i	−0.0904184	−	0.0344327i
$328$	11781.5	−	11781.5i	0.00604668	−	0.00604668i
$329$	2.21148e6			1.12640
$330$	−1.32181e6	−	1.78325e6i	−0.668164	−	0.901420i
$331$	1.29322e6			0.648786			0.324393	−	0.945922i	$-0.394840\pi$
$331$	1.29322e6			0.648786			0.324393	+	0.945922i	$0.394840\pi$
$332$	301911.	−	301911.i	0.150326	−	0.150326i
$333$	−54481.6	−	943507.i	−0.0269240	−	0.466267i
$334$			842011.i			0.413001i
$335$	1.30564e6	−	2.04116e6i	0.635642	−	0.993725i
$336$	854214.	−	383046.i	0.412780	−	0.185099i
$337$	1.56646e6	+	1.56646e6i	0.751352	+	0.751352i	0.974731	−	0.223380i	$-0.0717090\pi$
$337$	1.56646e6	+	1.56646e6i	0.751352	+	0.751352i	−0.223380	+	0.974731i	$0.571709\pi$
$338$	903826.	+	903826.i	0.430321	+	0.430321i
$339$	1.56200e6	−	700430.i	0.738212	−	0.331029i
$340$	78231.7	−	122303.i	0.0367016	−	0.0573771i
$341$			172141.i			0.0801673i
$342$	145189.	+	2.51436e6i	0.0671224	+	1.16242i
$343$	1.64077e6	−	1.64077e6i	0.753029	−	0.753029i
$344$	−1.30400e6			−0.594130
$345$	876646.	+	1.18268e6i	0.396530	+	0.534959i
$346$	971610.			0.436316
$347$	−629702.	+	629702.i	−0.280745	+	0.280745i	−0.833406	−	0.552661i	$-0.813612\pi$
$347$	−629702.	+	629702.i	−0.280745	+	0.280745i	0.552661	+	0.833406i	$0.313612\pi$
$348$	−225280.	−	85790.0i	−0.0997181	−	0.0379742i
$349$		−	2.65405e6i		−	1.16639i	−0.812331	−	0.583197i	$-0.801801\pi$
$349$		−	2.65405e6i		−	1.16639i	0.812331	−	0.583197i	$-0.198199\pi$
$350$	−1.50941e6	+	697106.i	−0.658622	+	0.304179i
$351$	336626.	−	1.06487e6i	0.145841	−	0.461347i
$352$	−1.61044e6	−	1.61044e6i	−0.692767	−	0.692767i
$353$	749916.	+	749916.i	0.320314	+	0.320314i	0.848887	−	0.528574i	$-0.177273\pi$
$353$	749916.	+	749916.i	0.320314	+	0.320314i	−0.528574	+	0.848887i	$0.677273\pi$
$354$	59642.6	+	133006.i	0.0252958	+	0.0564110i
$355$	−4.11110e6	+	903487.i	−1.73136	+	0.380497i
$356$			502550.i			0.210162i
$357$	144572.	−	379637.i	0.0600362	−	0.157652i
$358$	−1.52819e6	+	1.52819e6i	−0.630189	+	0.630189i
$359$	−403932.			−0.165414			−0.0827069	−	0.996574i	$-0.526357\pi$
$359$	−403932.			−0.165414			−0.0827069	+	0.996574i	$0.526357\pi$
$360$	−2.57438e6	+	723602.i	−1.04693	+	0.294268i
$361$	−2.84078e6			−1.14728
$362$	484286.	−	484286.i	0.194236	−	0.194236i
$363$	−888170.	+	2.33229e6i	−0.353777	+	0.928999i
$364$		−	411655.i		−	0.162847i
$365$	−1.27545e6	−	815851.i	−0.501109	−	0.320537i
$366$	1.45661e6	+	3.24831e6i	0.568381	+	1.26752i
$367$	2.79218e6	+	2.79218e6i	1.08213	+	1.08213i	0.996311	+	0.0858143i	$0.0273492\pi$
$367$	2.79218e6	+	2.79218e6i	1.08213	+	1.08213i	0.0858143	+	0.996311i	$0.472651\pi$
$368$	−606090.	−	606090.i	−0.233302	−	0.233302i
$369$	−13680.5	+	15357.2i	−0.00523040	+	0.00587146i
$370$	−209761.	−	954467.i	−0.0796563	−	0.362457i
$371$			3.27180e6i			1.23410i
$372$	52199.8	+	19878.5i	0.0195574	+	0.00744776i
$373$	−244300.	+	244300.i	−0.0909184	+	0.0909184i	−0.751103	−	0.660185i	$-0.770478\pi$
$373$	−244300.	+	244300.i	−0.0909184	+	0.0909184i	0.660185	+	0.751103i	$0.270478\pi$
$374$	560814.			0.207319
$375$	2.61325e6	−	765977.i	0.959626	−	0.281279i
$376$	3.67801e6			1.34166
$377$	273299.	−	273299.i	0.0990339	−	0.0990339i
$378$	−1.78833e6	+	929247.i	−0.643750	+	0.334504i
$379$		−	2.36429e6i		−	0.845480i	−0.906251	−	0.422740i	$-0.861068\pi$
$379$		−	2.36429e6i		−	0.845480i	0.906251	−	0.422740i	$-0.138932\pi$
$380$	−326375.	−	1.48509e6i	−0.115947	−	0.527587i
$381$	−2.17889e6	+	977059.i	−0.768995	+	0.344833i
$382$	−386436.	−	386436.i	−0.135494	−	0.135494i
$383$	−699669.	−	699669.i	−0.243722	−	0.243722i	0.574666	−	0.818388i	$-0.305132\pi$
$383$	−699669.	−	699669.i	−0.243722	−	0.243722i	−0.818388	+	0.574666i	$0.805132\pi$
$384$	363711.	−	163095.i	0.125872	−	0.0564434i
$385$	3.15879e6	+	2.02054e6i	1.08610	+	0.694730i
$386$		−	701775.i		−	0.239734i
$387$	1.60697e6	−	92792.5i	0.545420	−	0.0314946i
$388$	−920311.	+	920311.i	−0.310353	+	0.310353i
$389$	1.08294e6			0.362852			0.181426	−	0.983405i	$-0.441929\pi$
$389$	1.08294e6			0.362852			0.181426	+	0.983405i	$0.441929\pi$
$390$	169754.	−	1.14227e6i	0.0565142	−	0.380284i
$391$	−371942.			−0.123036
$392$	389303.	−	389303.i	0.127960	−	0.127960i
$393$	3.33205e6	+	1.26890e6i	1.08825	+	0.414424i
$394$		−	917925.i		−	0.297897i
$395$	−3.10671e6	+	682755.i	−1.00186	+	0.220177i
$396$	1.21295e6	+	1.08052e6i	0.388692	+	0.346254i
$397$	−1.24433e6	−	1.24433e6i	−0.396242	−	0.396242i	0.480663	−	0.876905i	$-0.340396\pi$
$397$	−1.24433e6	−	1.24433e6i	−0.396242	−	0.396242i	−0.876905	+	0.480663i	$0.840396\pi$
$398$	−1.70973e6	−	1.70973e6i	−0.541027	−	0.541027i
$399$	−1.74082e6	−	3.88212e6i	−0.547420	−	1.22078i
$400$	−1.43944e6	+	664791.i	−0.449824	+	0.207747i
$401$		−	5.24320e6i		−	1.62830i	−0.580652	−	0.814152i	$-0.697202\pi$
$401$		−	5.24320e6i		−	1.62830i	0.580652	−	0.814152i	$-0.302798\pi$
$402$	1.08084e6	−	2.83822e6i	0.333577	−	0.875954i
$403$	−63326.3	+	63326.3i	−0.0194232	+	0.0194232i
$404$	90945.6			0.0277222
$405$	3.12102e6	−	1.07492e6i	0.945494	−	0.325640i
$406$	−697467.			−0.209995
$407$	−1.55847e6	+	1.55847e6i	−0.466352	+	0.466352i
$408$	240444.	−	631391.i	0.0715093	−	0.187780i
$409$			6.02331e6i			1.78044i	0.455533	+	0.890219i	$0.349449\pi$
$409$			6.02331e6i			1.78044i	−0.455533	+	0.890219i	$0.650551\pi$
$410$	−11459.7	+	17915.3i	−0.00336676	+	0.00526339i
$411$	−162348.	−	362045.i	−0.0474071	−	0.105720i
$412$	−168924.	−	168924.i	−0.0490284	−	0.0490284i
$413$	−174119.	−	174119.i	−0.0502309	−	0.0502309i
$414$	1.37782e6	+	1.22738e6i	0.395085	+	0.351949i
$415$	−1.09029e6	+	1.70450e6i	−0.310758	+	0.485821i
$416$		−	1.18488e6i		−	0.335692i
$417$	2.88399e6	+	1.09827e6i	0.812183	+	0.309292i
$418$	4.15320e6	−	4.15320e6i	1.16263	−	1.16263i
$419$	−268063.			−0.0745937			−0.0372969	−	0.999304i	$-0.511875\pi$
$419$	−268063.			−0.0745937			−0.0372969	+	0.999304i	$0.511875\pi$
$420$	977479.	−	724542.i	0.270386	−	0.200420i
$421$	569052.			0.156476			0.0782378	−	0.996935i	$-0.475071\pi$
$421$	569052.			0.156476			0.0782378	+	0.996935i	$0.475071\pi$
$422$	2.31143e6	−	2.31143e6i	0.631828	−	0.631828i
$423$	−4.53256e6	+	261727.i	−1.23166	+	0.0711209i
$424$			5.44147e6i			1.46995i
$425$	−237690.	+	645655.i	−0.0638320	+	0.173392i
$426$	−4.81403e6	+	2.15871e6i	−1.28524	+	0.576328i
$427$	−4.25238e6	−	4.25238e6i	−1.12866	−	1.12866i
$428$	1.02271e6	+	1.02271e6i	0.269864	+	0.269864i
$429$	−2.37651e6	+	1.06567e6i	−0.623441	+	0.279563i
$430$	1.62564e6	−	357263.i	0.423987	−	0.0931787i
$431$		−	2.65898e6i		−	0.689480i	−0.938698	−	0.344740i	$-0.887967\pi$
$431$		−	2.65898e6i		−	0.689480i	0.938698	−	0.344740i	$-0.112033\pi$
$432$	−1.70543e6	+	886171.i	−0.439667	+	0.228459i
$433$	3.76956e6	−	3.76956e6i	0.966209	−	0.966209i	−0.0332380	−	0.999447i	$-0.510582\pi$
$433$	3.76956e6	−	3.76956e6i	0.966209	−	0.966209i	0.999447	+	0.0332380i	$0.0105819\pi$
$434$	161611.			0.0411857
$435$	1.12997e6	+	167926.i	0.286316	+	0.0425495i
$436$	141570.			0.0356661
$437$	−2.75448e6	+	2.75448e6i	−0.689979	+	0.689979i
$438$	−1.77351e6	−	675378.i	−0.441720	−	0.168214i
$439$		−	2.74484e6i		−	0.679760i	−0.940469	−	0.339880i	$-0.889613\pi$
$439$		−	2.74484e6i		−	0.679760i	0.940469	−	0.339880i	$-0.110387\pi$
$440$	5.25353e6	+	3.36045e6i	1.29366	+	0.827496i
$441$	−452051.	+	507456.i	−0.110686	+	0.124252i
$442$	206310.	+	206310.i	0.0502301	+	0.0502301i
$443$	5.61400e6	+	5.61400e6i	1.35914	+	1.35914i	0.874982	+	0.484156i	$0.160873\pi$
$443$	5.61400e6	+	5.61400e6i	1.35914	+	1.35914i	0.484156	+	0.874982i	$0.339127\pi$
$444$	292621.	+	652560.i	0.0704446	+	0.157095i
$445$	−511191.	−	2.32605e6i	−0.122372	−	0.556826i
$446$			4.34040e6i			1.03322i
$447$	−2.41122e6	+	6.33173e6i	−0.570779	+	1.49883i
$448$	−2.87082e6	+	2.87082e6i	−0.675788	+	0.675788i
$449$	−4.10120e6			−0.960054			−0.480027	−	0.877254i	$-0.659373\pi$
$449$	−4.10120e6			−0.960054			−0.480027	+	0.877254i	$0.659373\pi$
$450$	3.01111e6	−	1.60740e6i	0.700964	−	0.374190i
$451$	47964.1			0.0111039
$452$	−915988.	+	915988.i	−0.210884	+	0.210884i
$453$	1.32080e6	−	3.46836e6i	0.302408	−	0.794106i
$454$			2.25271e6i			0.512939i
$455$	418734.	+	1.90535e6i	0.0948222	+	0.431466i
$456$	−2.89523e6	−	6.45652e6i	−0.652035	−	1.45407i
$457$	−6.11240e6	−	6.11240e6i	−1.36906	−	1.36906i	−0.861790	−	0.507266i	$-0.830656\pi$
$457$	−6.11240e6	−	6.11240e6i	−1.36906	−	1.36906i	−0.507266	−	0.861790i	$-0.669344\pi$
$458$	3.23983e6	+	3.23983e6i	0.721702	+	0.721702i
$459$	−251378.	+	795199.i	−0.0556924	+	0.176175i
$460$	−938454.	−	600288.i	−0.206785	−	0.132271i
$461$		−	3.40793e6i		−	0.746859i	−0.927659	−	0.373430i	$-0.878182\pi$
$461$		−	3.40793e6i		−	0.746859i	0.927659	−	0.373430i	$-0.121818\pi$
$462$	4.39228e6	+	1.67265e6i	0.957381	+	0.364585i
$463$	565359.	−	565359.i	0.122566	−	0.122566i	−0.643163	−	0.765729i	$-0.722378\pi$
$463$	565359.	−	565359.i	0.122566	−	0.122566i	0.765729	+	0.643163i	$0.222378\pi$
$464$	−665135.			−0.143422
$465$	−261827.	−	38910.2i	−0.0561542	−	0.00834510i
$466$	3.07500e6			0.655964
$467$	2.53896e6	−	2.53896e6i	0.538721	−	0.538721i	−0.384432	−	0.923153i	$-0.625603\pi$
$467$	2.53896e6	−	2.53896e6i	0.538721	−	0.538721i	0.923153	+	0.384432i	$0.125603\pi$
$468$	48719.0	+	843712.i	0.0102822	+	0.178065i
$469$			5.13046e6i			1.07702i
$470$	−4.58521e6	+	1.00768e6i	−0.957446	+	0.210416i
$471$	−2.34074e6	+	1.04964e6i	−0.486185	+	0.218015i
$472$	−289585.	−	289585.i	−0.0598303	−	0.0598303i
$473$	−2.65438e6	−	2.65438e6i	−0.545519	−	0.545519i
$474$	−3.63791e6	+	1.63131e6i	−0.743715	+	0.333496i
$475$	3.02125e6	+	6.54176e6i	0.614403	+	1.33033i
$476$			307407.i			0.0621866i
$477$	−387214.	−	6.70574e6i	−0.0779212	−	1.34943i
$478$	1.41519e6	−	1.41519e6i	0.283299	−	0.283299i
$479$	8.45014e6			1.68277			0.841385	−	0.540436i	$-0.181741\pi$
$479$	8.45014e6			1.68277			0.841385	+	0.540436i	$0.181741\pi$
$480$	2.81351e6	−	2.08547e6i	0.557372	−	0.413143i
$481$	−1.14665e6			−0.225979
$482$	−1.95948e6	+	1.95948e6i	−0.384171	+	0.384171i
$483$	−2.91304e6	−	1.10933e6i	−0.568170	−	0.216368i
$484$		−	1.88854e6i		−	0.366449i
$485$	3.32353e6	−	5.19580e6i	0.641571	−	1.00299i
$486$	3.55530e6	−	2.11619e6i	0.682788	−	0.406410i
$487$	2.98007e6	+	2.98007e6i	0.569383	+	0.569383i	0.931955	−	0.362573i	$-0.118102\pi$
$487$	2.98007e6	+	2.98007e6i	0.569383	+	0.569383i	−0.362573	+	0.931955i	$0.618102\pi$
$488$	−7.07232e6	−	7.07232e6i	−1.34435	−	1.34435i
$489$	−803290.	−	1.79138e6i	−0.151915	−	0.338778i
$490$	−378667.	+	591986.i	−0.0712472	+	0.111384i
$491$			8.65624e6i			1.62041i	0.586145	+	0.810206i	$0.300645\pi$
$491$			8.65624e6i			1.62041i	−0.586145	+	0.810206i	$0.699355\pi$
$492$	5538.81	−	14544.6i	0.00103158	−	0.00270888i
$493$	−204088.	+	204088.i	−0.0378182	+	0.0378182i
$494$	3.05572e6			0.563373
$495$	−6.71326e6	−	3.76738e6i	−1.23146	−	0.691077i
$496$	154119.			0.0281289
$497$	6.30208e6	−	6.30208e6i	1.14444	−	1.14444i
$498$	−902566.	+	2.37009e6i	−0.163082	+	0.428244i
$499$		−	583551.i		−	0.104912i	−0.998623	−	0.0524562i	$-0.983295\pi$
$499$		−	583551.i		−	0.104912i	0.998623	−	0.0524562i	$-0.0167050\pi$
$500$	−1.64176e6	+	1.24545e6i	−0.293687	+	0.222793i
$501$	1.19482e6	+	2.66452e6i	0.212671	+	0.474268i
$502$	−3.41836e6	−	3.41836e6i	−0.605422	−	0.605422i
$503$	229863.	+	229863.i	0.0405088	+	0.0405088i	0.727071	−	0.686562i	$-0.240881\pi$
$503$	229863.	+	229863.i	0.0405088	+	0.0405088i	−0.686562	+	0.727071i	$0.740881\pi$
$504$	3.76629e6	−	4.22790e6i	0.660446	−	0.741394i
$505$	−420942.	+	92509.5i	−0.0734504	+	0.0161420i
$506$		−	4.30324e6i		−	0.747170i
$507$	4.14266e6	+	1.57759e6i	0.715747	+	0.272567i
$508$	1.27775e6	−	1.27775e6i	0.219678	−	0.219678i
$509$	−8.34113e6			−1.42702			−0.713511	−	0.700644i	$-0.752896\pi$
$509$	−8.34113e6			−1.42702			−0.713511	+	0.700644i	$0.752896\pi$
$510$	−126765.	+	853003.i	−0.0215811	+	0.145220i
$511$	3.20585e6			0.543113
$512$	−3.70187e6	+	3.70187e6i	−0.624088	+	0.624088i
$513$	4.02735e6	+	7.75060e6i	0.675657	+	1.30029i
$514$		−	7.92546e6i		−	1.32317i
$515$	953693.	+	610036.i	0.158449	+	0.101353i
$516$	−1.11143e6	+	498389.i	−0.183764	+	0.0824032i
$517$	7.48683e6	+	7.48683e6i	1.23189	+	1.23189i
$518$	1.46314e6	+	1.46314e6i	0.239586	+	0.239586i
$519$	3.07463e6	−	1.37872e6i	0.501042	−	0.224677i
$520$	696415.	+	3.16887e6i	0.112943	+	0.513920i
$521$		−	1.63560e6i		−	0.263986i	−0.991251	−	0.131993i	$-0.957862\pi$
$521$		−	1.63560e6i		−	0.263986i	0.991251	−	0.131993i	$-0.0421377\pi$
$522$	1.42950e6	−	82544.6i	0.229619	−	0.0132590i
$523$	−4.53453e6	+	4.53453e6i	−0.724901	+	0.724901i	−0.969599	−	0.244699i	$-0.921311\pi$
$523$	−4.53453e6	+	4.53453e6i	−0.724901	+	0.724901i	0.244699	+	0.969599i	$0.421311\pi$
$524$	−2.69810e6			−0.429269
$525$	−3.78727e6	+	4.34783e6i	−0.599691	+	0.688453i
$526$	−4.89304e6			−0.771106
$527$	47289.5	−	47289.5i	0.00741717	−	0.00741717i
$528$	4.18867e6	+	1.59511e6i	0.653869	+	0.249003i
$529$		−	3.58236e6i		−	0.556582i
$530$	−1.49082e6	−	6.78364e6i	−0.230535	−	1.04899i
$531$	377474.	+	336260.i	0.0580966	+	0.0517534i
$532$	2.27656e6	+	2.27656e6i	0.348738	+	0.348738i
$533$	17644.8	+	17644.8i	0.00269029	+	0.00269029i
$534$	−1.22139e6	−	2.72377e6i	−0.185354	−	0.413350i
$535$	−5.77394e6	−	3.69334e6i	−0.872143	−	0.557872i
$536$			8.53269e6i			1.28285i
$537$	−2.66740e6	+	7.00443e6i	−0.399164	+	1.04818i
$538$	−6.67491e6	+	6.67491e6i	−0.994237	+	0.994237i
$539$	1.58490e6			0.234980
$540$	−1.91765e6	+	1.60067e6i	−0.282999	+	0.236221i
$541$	4.13526e6			0.607449			0.303725	−	0.952760i	$-0.401770\pi$
$541$	4.13526e6			0.607449			0.303725	+	0.952760i	$0.401770\pi$
$542$	−3.12163e6	+	3.12163e6i	−0.456440	+	0.456440i
$543$	845301.	−	2.21972e6i	0.123030	−	0.323071i
$544$			884820.i			0.128191i
$545$	−655258.	+	144004.i	−0.0944976	+	0.0207675i
$546$	1.00048e6	+	2.23113e6i	0.143625	+	0.320290i
$547$	−6.14982e6	−	6.14982e6i	−0.878808	−	0.878808i	0.114603	−	0.993411i	$-0.463440\pi$
$547$	−6.14982e6	−	6.14982e6i	−0.878808	−	0.878808i	−0.993411	+	0.114603i	$0.963440\pi$
$548$	212311.	+	212311.i	0.0302010	+	0.0302010i
$549$	9.21877e6	+	8.21224e6i	1.30540	+	1.16287i
$550$	−7.47001e6	−	2.74999e6i	−1.05297	−	0.387637i
$551$			3.02282e6i			0.424163i
$552$	−4.84480e6	−	1.84497e6i	−0.676749	−	0.257716i
$553$	4.76241e6	−	4.76241e6i	0.662238	−	0.662238i
$554$	−5.76901e6			−0.798595
$555$	−2.01818e6	−	2.72273e6i	−0.278117	−	0.375207i
$556$	−2.33528e6			−0.320371
$557$	3.86658e6	−	3.86658e6i	0.528067	−	0.528067i	−0.391929	−	0.919996i	$-0.628192\pi$
$557$	3.86658e6	−	3.86658e6i	0.528067	−	0.528067i	0.919996	+	0.391929i	$0.128192\pi$
$558$	−331231.	+	19126.5i	−0.0450345	+	0.00260046i
$559$		−	1.95296e6i		−	0.264341i
$560$	1.80901e6	−	2.82810e6i	0.243765	−	0.381087i
$561$	1.77468e6	−	795800.i	0.238074	−	0.106757i
$562$	7.74298e6	+	7.74298e6i	1.03411	+	1.03411i
$563$	−7.46303e6	−	7.46303e6i	−0.992303	−	0.992303i	0.00766747	−	0.999971i	$-0.497559\pi$
$563$	−7.46303e6	−	7.46303e6i	−0.992303	−	0.992303i	−0.999971	+	0.00766747i	$0.997559\pi$
$564$	3.13487e6	−	1.40574e6i	0.414974	−	0.186083i
$565$	3.30792e6	−	5.17140e6i	0.435947	−	0.681533i
$566$		−	5.26869e6i		−	0.691292i
$567$	−4.34049e6	+	5.47822e6i	−0.566998	+	0.715619i
$568$	1.04813e7	−	1.04813e7i	1.36315	−	1.36315i
$569$	−562233.			−0.0728008			−0.0364004	−	0.999337i	$-0.511589\pi$
$569$	−562233.			−0.0728008			−0.0364004	+	0.999337i	$0.511589\pi$
$570$	5.37827e6	+	7.25583e6i	0.693355	+	0.935406i
$571$	9.36133e6			1.20157			0.600783	−	0.799412i	$-0.294856\pi$
$571$	9.36133e6			1.20157			0.600783	+	0.799412i	$0.294856\pi$
$572$	1.39363e6	−	1.39363e6i	0.178098	−	0.178098i
$573$	−1.77122e6	−	674508.i	−0.225365	−	0.0858223i
$574$		−	45030.1i		−	0.00570458i
$575$	4.95425e6	+	1.82384e6i	0.624896	+	0.230048i
$576$	5.54415e6	−	6.22366e6i	0.696271	−	0.781610i
$577$	2.52643e6	+	2.52643e6i	0.315913	+	0.315913i	0.847195	−	0.531282i	$-0.178289\pi$
$577$	2.52643e6	+	2.52643e6i	0.315913	+	0.315913i	−0.531282	+	0.847195i	$0.678289\pi$
$578$	4.35874e6	+	4.35874e6i	0.542677	+	0.542677i
$579$	−995826.	−	2.22074e6i	−0.123449	−	0.275297i
$580$	−844323.	+	185555.i	−0.104217	+	0.0229035i
$581$		−	4.28425e6i		−	0.526544i
$582$	2.75128e6	−	7.22472e6i	0.336688	−	0.884125i
$583$	−1.10765e7	+	1.10765e7i	−1.34968	+	1.34968i
$584$	5.33178e6			0.646904
$585$	−1.08372e6	−	3.85557e6i	−0.130926	−	0.465799i
$586$	−1.80683e6			−0.217356
$587$	−1.64460e6	+	1.64460e6i	−0.196999	+	0.196999i	−0.798712	−	0.601713i	$-0.794485\pi$
$587$	−1.64460e6	+	1.64460e6i	−0.196999	+	0.196999i	0.601713	+	0.798712i	$0.294485\pi$
$588$	183022.	−	480605.i	0.0218303	−	0.0573251i
$589$		−	700420.i		−	0.0831898i
$590$	440351.	+	281674.i	0.0520798	+	0.0333132i
$591$	−1.30254e6	−	2.90474e6i	−0.153399	−	0.342089i
$592$	1.39532e6	+	1.39532e6i	0.163632	+	0.163632i
$593$	−5.38412e6	−	5.38412e6i	−0.628750	−	0.628750i	0.319003	−	0.947754i	$-0.396652\pi$
$593$	−5.38412e6	−	5.38412e6i	−0.628750	−	0.628750i	−0.947754	+	0.319003i	$0.896652\pi$
$594$	−9.20018e6	−	2.90836e6i	−1.06987	−	0.338207i
$595$	−312694.	−	1.42284e6i	−0.0362098	−	0.164764i
$596$		−	5.12705e6i		−	0.591224i
$597$	−7.83649e6	−	2.98425e6i	−0.899882	−	0.342689i
$598$	1.58306e6	−	1.58306e6i	0.181027	−	0.181027i
$599$	4.06152e6			0.462510			0.231255	−	0.972893i	$-0.425717\pi$
$599$	4.06152e6			0.462510			0.231255	+	0.972893i	$0.425717\pi$
$600$	−6.29877e6	+	7.23107e6i	−0.714295	+	0.820020i
$601$	−6.61384e6			−0.746908			−0.373454	−	0.927649i	$-0.621827\pi$
$601$	−6.61384e6			−0.746908			−0.373454	+	0.927649i	$0.621827\pi$
$602$	−2.49201e6	+	2.49201e6i	−0.280258	+	0.280258i
$603$	−607186.	−	1.05152e7i	−0.0680030	−	1.17767i
$604$			2.80847e6i			0.313240i
$605$	1.92102e6	+	8.74113e6i	0.213375	+	0.970911i
$606$	−492917.	+	221034.i	−0.0545245	+	0.0244499i
$607$	−707385.	−	707385.i	−0.0779263	−	0.0779263i	0.667069	−	0.744996i	$-0.267548\pi$
$607$	−707385.	−	707385.i	−0.0779263	−	0.0779263i	−0.744996	+	0.667069i	$0.767548\pi$
$608$	6.55268e6	+	6.55268e6i	0.718886	+	0.718886i
$609$	−2.20711e6	+	989712.i	−0.241147	+	0.108135i
$610$	1.07544e7	+	6.87911e6i	1.17020	+	0.748528i
$611$			5.50844e6i			0.596933i
$612$	−36381.4	−	630049.i	−0.00392646	−	0.0679980i
$613$	−1.14619e7	+	1.14619e7i	−1.23198	+	1.23198i	−0.268781	+	0.963201i	$0.586621\pi$
$613$	−1.14619e7	+	1.14619e7i	−1.23198	+	1.23198i	−0.963201	+	0.268781i	$0.913379\pi$
$614$	8.17338e6			0.874945
$615$	−10841.7	+	72953.8i	−0.00115587	+	0.00777786i
$616$	−1.32047e7			−1.40210
$617$	−9.62794e6	+	9.62794e6i	−1.01817	+	1.01817i	−0.0183386	+	0.999832i	$0.505838\pi$
$617$	−9.62794e6	+	9.62794e6i	−1.01817	+	1.01817i	−0.999832	+	0.0183386i	$0.994162\pi$
$618$	1.32610e6	+	505000.i	0.139671	+	0.0531888i
$619$		−	3.89290e6i		−	0.408363i	−0.978933	−	0.204181i	$-0.934547\pi$
$619$		−	3.89290e6i		−	0.408363i	0.978933	−	0.204181i	$-0.0654532\pi$
$620$	195639.	−	42995.1i	0.0204398	−	0.00449200i
$621$	6.10172e6	+	1.92888e6i	0.634927	+	0.200713i
$622$	−1.14741e6	−	1.14741e6i	−0.118917	−	0.118917i
$623$	3.56570e6	+	3.56570e6i	0.368066	+	0.368066i
$624$	954106.	+	2.12771e6i	0.0980923	+	0.218751i
$625$	6.33204e6	−	7.43456e6i	0.648401	−	0.761299i
$626$			6.45895e6i			0.658759i
$627$	7.24924e6	−	1.90361e7i	0.736416	−	1.93379i
$628$	1.37266e6	−	1.37266e6i	0.138888	−	0.138888i
$629$	856270.			0.0862947
$630$	−3.53693e6	+	6.30261e6i	−0.355038	+	0.632658i
$631$	721341.			0.0721219			0.0360610	−	0.999350i	$-0.488519\pi$
$631$	721341.			0.0721219			0.0360610	+	0.999350i	$0.488519\pi$
$632$	7.92057e6	−	7.92057e6i	0.788794	−	0.788794i
$633$	4.03450e6	−	1.05944e7i	0.400203	−	1.05091i
$634$			8.95217e6i			0.884514i
$635$	−4.61435e6	+	7.21380e6i	−0.454126	+	0.709953i
$636$	2.07973e6	+	4.63791e6i	0.203875	+	0.454653i
$637$	583047.	+	583047.i	0.0569318	+	0.0569318i
$638$	−2.36123e6	−	2.36123e6i	−0.229661	−	0.229661i
$639$	−1.21706e7	+	1.36623e7i	−1.17913	+	1.32365i
$640$	770249.	−	1.20416e6i	0.0743329	−	0.116208i
$641$			6.96826e6i			0.669853i	0.942244	+	0.334926i	$0.108711\pi$
$641$			6.96826e6i			0.669853i	−0.942244	+	0.334926i	$0.891289\pi$
$642$	−8.02861e6	−	3.05742e6i	−0.768781	−	0.292764i
$643$	9.45414e6	−	9.45414e6i	0.901768	−	0.901768i	−0.0938213	−	0.995589i	$-0.529908\pi$
$643$	9.45414e6	−	9.45414e6i	0.901768	−	0.901768i	0.995589	+	0.0938213i	$0.0299082\pi$
$644$	2.35880e6			0.224118
$645$	4.63732e6	−	3.43734e6i	0.438902	−	0.325330i
$646$	−2.28189e6			−0.215136
$647$	3.79202e6	−	3.79202e6i	0.356131	−	0.356131i	−0.506254	−	0.862385i	$-0.668970\pi$
$647$	3.79202e6	−	3.79202e6i	0.356131	−	0.356131i	0.862385	+	0.506254i	$0.168970\pi$
$648$	−7.21886e6	+	9.11107e6i	−0.675353	+	0.852377i
$649$		−	1.17894e6i		−	0.109870i
$650$	−1.73638e6	−	3.75969e6i	−0.161198	−	0.349034i
$651$	511412.	−	229327.i	0.0472953	−	0.0212082i
$652$	1.05050e6	+	1.05050e6i	0.0967785	+	0.0967785i
$653$	1.20802e7	+	1.20802e7i	1.10864	+	1.10864i	0.993330	+	0.115310i	$0.0367862\pi$
$653$	1.20802e7	+	1.20802e7i	1.10864	+	1.10864i	0.115310	+	0.993330i	$0.463214\pi$
$654$	−767296.	+	344071.i	−0.0701486	+	0.0314560i
$655$	1.24881e7	−	2.74449e6i	1.13735	−	0.249953i
$656$		−	42942.7i		−	0.00389610i
$657$	−6.57057e6	+	379409.i	−0.593867	+	0.0342921i
$658$	7.02886e6	−	7.02886e6i	0.632878	−	0.632878i
$659$	−2.17065e7			−1.94705			−0.973524	−	0.228585i	$-0.926590\pi$
$659$	−2.17065e7			−1.94705			−0.973524	+	0.228585i	$0.926590\pi$
$660$	5.76209e6	+	856305.i	0.514896	+	0.0765189i
$661$	−1.61371e7			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$661$	−1.61371e7			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$662$	4.11029e6	−	4.11029e6i	0.364525	−	0.364525i
$663$	945615.	+	360105.i	0.0835469	+	0.0318159i
$664$		−	7.12532e6i		−	0.627168i
$665$	−1.28528e7	−	8.22135e6i	−1.12705	−	0.720923i
$666$	−3.17196e6	−	2.82563e6i	−0.277103	−	0.246848i
$667$	1.56601e6	+	1.56601e6i	0.136295	+	0.136295i
$668$	−1.56253e6	−	1.56253e6i	−0.135484	−	0.135484i
$669$	6.15907e6	+	1.37351e7i	0.532047	+	1.18649i
$670$	−2.33774e6	−	1.06373e7i	−0.201191	−	0.915473i
$671$		−	2.87924e7i		−	2.46872i
$672$	−2.63900e6	+	6.92988e6i	−0.225433	+	0.591974i
$673$	−1.23106e7	+	1.23106e7i	−1.04771	+	1.04771i	−0.0489118	+	0.998803i	$0.515575\pi$
$673$	−1.23106e7	+	1.23106e7i	−1.04771	+	1.04771i	−0.998803	+	0.0489118i	$0.984425\pi$
$674$	9.95748e6			0.844306
$675$	7.24766e6	−	9.35935e6i	0.612264	−	0.790654i
$676$	−3.35448e6			−0.282331
$677$	4.28005e6	−	4.28005e6i	0.358903	−	0.358903i	−0.504505	−	0.863408i	$-0.668325\pi$
$677$	4.28005e6	−	4.28005e6i	0.358903	−	0.358903i	0.863408	+	0.504505i	$0.168325\pi$
$678$	2.73836e6	−	7.19078e6i	0.228779	−	0.600761i
$679$			1.30596e7i			1.08707i
$680$	−520054.	−	2.36638e6i	−0.0431297	−	0.196251i
$681$	3.19662e6	+	7.12863e6i	0.264133	+	0.589031i
$682$	547123.	+	547123.i	0.0450427	+	0.0450427i
$683$	2.81149e6	+	2.81149e6i	0.230614	+	0.230614i	0.812949	−	0.582335i	$-0.197861\pi$
$683$	2.81149e6	+	2.81149e6i	0.230614	+	0.230614i	−0.582335	+	0.812949i	$0.697861\pi$
$684$	−4.93536e6	−	4.39651e6i	−0.403347	−	0.359308i
$685$	−1.19865e6	−	766721.i	−0.0976032	−	0.0624325i
$686$		−	1.04299e7i		−	0.846191i
$687$	1.48497e7	+	5.65498e6i	1.20040	+	0.457129i
$688$	−2.37649e6	+	2.37649e6i	−0.191410	+	0.191410i
$689$	−8.14952e6			−0.654009
$690$	6.54526e6	+	972694.i	0.523365	+	0.0777774i
$691$	1.44868e7			1.15419			0.577097	−	0.816676i	$-0.304185\pi$
$691$	1.44868e7			1.15419			0.577097	+	0.816676i	$0.304185\pi$
$692$	−1.80303e6	+	1.80303e6i	−0.143132	+	0.143132i
$693$	1.62727e7	−	939647.i	1.28714	−	0.0743244i
$694$			4.00283e6i			0.315477i
$695$	1.08089e7	−	2.37544e6i	0.848825	−	0.186544i
$696$	−3.67074e6	+	1.64603e6i	−0.287231	+	0.128800i
$697$	−13176.4	−	13176.4i	−0.00102734	−	0.00102734i
$698$	−8.43550e6	−	8.43550e6i	−0.655348	−	0.655348i
$699$	9.73073e6	−	4.36345e6i	0.753273	−	0.337783i
$700$	1.50739e6	−	4.09465e6i	0.116274	−	0.315843i
$701$			1.46858e7i			1.12876i	0.825515	+	0.564381i	$0.190885\pi$
$701$			1.46858e7i			1.12876i	−0.825515	+	0.564381i	$0.809115\pi$
$702$	−2.31460e6	−	4.45443e6i	−0.177269	−	0.341153i
$703$	6.34125e6	−	6.34125e6i	0.483934	−	0.483934i
$704$	−1.94379e7			−1.47815
$705$	−1.30798e7	+	9.69522e6i	−0.991127	+	0.734658i
$706$	4.76699e6			0.359942
$707$	645280.	−	645280.i	0.0485512	−	0.0485512i
$708$	−357500.	−	136142.i	−0.0268036	−	0.0102072i
$709$		−	1.99808e7i		−	1.49278i	−0.665506	−	0.746392i	$-0.731784\pi$
$709$		−	1.99808e7i		−	1.49278i	0.665506	−	0.746392i	$-0.268216\pi$
$710$	−1.01949e7	+	1.59381e7i	−0.758993	+	1.18656i
$711$	−9.19721e6	+	1.03245e7i	−0.682310	+	0.765938i
$712$	5.93028e6	+	5.93028e6i	0.438404	+	0.438404i
$713$	−362862.	−	362862.i	−0.0267311	−	0.0267311i
$714$	−747121.	−	1.66612e6i	−0.0548460	−	0.122310i
$715$	−5.03284e6	+	7.86804e6i	−0.368170	+	0.575574i
$716$		−	5.67177e6i		−	0.413462i
$717$	2.47015e6	−	6.48649e6i	0.179443	−	0.471207i
$718$	−1.28384e6	+	1.28384e6i	−0.0929391	+	0.0929391i
$719$	1.26151e7			0.910058			0.455029	−	0.890477i	$-0.349629\pi$
$719$	1.26151e7			0.910058			0.455029	+	0.890477i	$0.349629\pi$
$720$	−3.37297e6	+	6.01044e6i	−0.242483	+	0.432091i
$721$	−2.39711e6			−0.171731
$722$	−9.02898e6	+	9.02898e6i	−0.644608	+	0.644608i
$723$	−3.42020e6	+	8.98125e6i	−0.243335	+	0.638985i
$724$			1.79739e6i			0.127437i
$725$	3.71921e6	−	1.71768e6i	0.262788	−	0.121366i
$726$	4.58990e6	+	1.02357e7i	0.323193	+	0.720738i
$727$	−1.72884e7	−	1.72884e7i	−1.21316	−	1.21316i	−0.969982	−	0.243177i	$-0.921810\pi$
$727$	−1.72884e7	−	1.72884e7i	−1.21316	−	1.21316i	−0.243177	−	0.969982i	$-0.578190\pi$
$728$	−4.85769e6	−	4.85769e6i	−0.339705	−	0.339705i
$729$	8.24775e6	−	1.17416e7i	0.574800	−	0.818294i
$730$	−6.64689e6	+	1.46077e6i	−0.461648	+	0.101455i
$731$			1.45839e6i			0.100944i
$732$	−8.73097e6	−	3.32489e6i	−0.602261	−	0.229350i
$733$	−7.89945e6	+	7.89945e6i	−0.543046	+	0.543046i	−0.924421	−	0.381374i	$-0.875451\pi$
$733$	−7.89945e6	+	7.89945e6i	−0.543046	+	0.543046i	0.381374	+	0.924421i	$0.375451\pi$
$734$	1.77490e7			1.21600
$735$	−358248.	+	2.41065e6i	−0.0244605	+	0.164595i
$736$	6.78941e6			0.461995
$737$	−1.73689e7	+	1.73689e7i	−1.17788	+	1.17788i
$738$	5329.28	+	92291.9i	0.000360186	+	0.00623767i
$739$			1.57456e7i			1.06059i	0.847812	+	0.530296i	$0.177919\pi$
$739$			1.57456e7i			1.06059i	−0.847812	+	0.530296i	$0.822081\pi$
$740$	2.16047e6	+	1.38196e6i	0.145034	+	0.0927718i
$741$	9.66972e6	−	4.33609e6i	0.646947	−	0.290104i
$742$	1.03989e7	+	1.03989e7i	0.693392	+	0.693392i
$743$	835548.	+	835548.i	0.0555264	+	0.0555264i	0.734325	−	0.678798i	$-0.237499\pi$
$743$	835548.	+	835548.i	0.0555264	+	0.0555264i	−0.678798	+	0.734325i	$0.737499\pi$
$744$	850551.	−	381404.i	0.0563337	−	0.0252611i
$745$	5.21522e6	+	2.37306e7i	0.344256	+	1.56646i
$746$			1.55294e6i			0.102167i
$747$	507037.	+	8.78081e6i	0.0332459	+	0.575749i
$748$	−1.04071e6	+	1.04071e6i	−0.0680104	+	0.0680104i
$749$	1.45128e7			0.945248
$750$	5.87126e6	−	1.07403e7i	0.381135	−	0.697213i
$751$	−1.08728e6			−0.0703466			−0.0351733	−	0.999381i	$-0.511198\pi$
$751$	−1.08728e6			−0.0703466			−0.0351733	+	0.999381i	$0.511198\pi$
$752$	6.70302e6	−	6.70302e6i	0.432241	−	0.432241i
$753$	−1.56680e7	−	5.96660e6i	−1.00699	−	0.383477i
$754$		−	1.73728e6i		−	0.111286i
$755$	−2.85676e6	−	1.29990e7i	−0.182392	−	0.829932i
$756$	1.59420e6	−	5.04303e6i	0.101447	−	0.320913i
$757$	3.23275e6	+	3.23275e6i	0.205037	+	0.205037i	0.802154	−	0.597117i	$-0.203687\pi$
$757$	3.23275e6	+	3.23275e6i	0.205037	+	0.205037i	−0.597117	+	0.802154i	$0.703687\pi$
$758$	−7.51455e6	−	7.51455e6i	−0.475040	−	0.475040i
$759$	−6.10634e6	−	1.36175e7i	−0.384748	−	0.858009i
$760$	−2.13760e7	−	1.36733e7i	−1.34243	−	0.858695i
$761$		−	3.27238e6i		−	0.204834i	−0.994742	−	0.102417i	$-0.967342\pi$
$761$		−	3.27238e6i		−	0.204834i	0.994742	−	0.102417i	$-0.0326577\pi$
$762$	−3.81985e6	+	1.00307e7i	−0.238319	+	0.625813i
$763$	1.00447e6	−	1.00447e6i	0.0624635	−	0.0624635i
$764$	1.43423e6			0.0888965
$765$	809275.	+	2.87918e6i	0.0499968	+	0.177875i
$766$	−4.44758e6			−0.273875
$767$	433702.	−	433702.i	0.0266197	−	0.0266197i
$768$	−5.45154e6	+	1.43155e7i	−0.333516	+	0.875794i
$769$		−	2.90881e7i		−	1.77378i	−0.461979	−	0.886891i	$-0.652860\pi$
$769$		−	2.90881e7i		−	1.77378i	0.461979	−	0.886891i	$-0.347140\pi$
$770$	1.64617e7	−	3.61776e6i	1.00057	−	0.219894i
$771$	−1.12463e7	−	2.50799e7i	−0.681355	−	1.51946i
$772$	1.30229e6	+	1.30229e6i	0.0786439	+	0.0786439i
$773$	−8.11096e6	−	8.11096e6i	−0.488229	−	0.488229i	0.419518	−	0.907747i	$-0.362199\pi$
$773$	−8.11096e6	−	8.11096e6i	−0.488229	−	0.488229i	−0.907747	+	0.419518i	$0.862199\pi$
$774$	4.81259e6	−	5.40244e6i	0.288753	−	0.324144i
$775$	−861781.	+	398006.i	−0.0515398	+	0.0238032i
$776$			2.17200e7i			1.29481i
$777$	6.70628e6	+	2.55385e6i	0.398501	+	0.151755i
$778$	3.44195e6	−	3.44195e6i	0.203871	−	0.203871i
$779$	−195160.			−0.0115225
$780$	1.80471e6	+	2.43474e6i	0.106212	+	0.143290i
$781$	4.26706e7			2.50323
$782$	−1.18216e6	+	1.18216e6i	−0.0691289	+	0.0691289i
$783$	4.40647e6	−	2.28968e6i	0.256854	−	0.133466i
$784$		−	1.41898e6i		−	0.0824491i
$785$	−4.95711e6	+	7.74964e6i	−0.287114	+	0.448856i
$786$	1.46234e7	−	6.55743e6i	0.844292	−	0.378597i
$787$	2.82266e6	+	2.82266e6i	0.162451	+	0.162451i	0.783652	−	0.621201i	$-0.213355\pi$
$787$	2.82266e6	+	2.82266e6i	0.162451	+	0.162451i	−0.621201	+	0.783652i	$0.713355\pi$
$788$	1.70340e6	+	1.70340e6i	0.0977242	+	0.0977242i
$789$	−1.54839e7	+	6.94327e6i	−0.885496	+	0.397074i
$790$	−7.70418e6	+	1.20443e7i	−0.439197	+	0.686613i
$791$			1.29983e7i			0.738661i
$792$	2.70638e7	−	1.56277e6i	1.53312	−	0.0885281i
$793$	1.05920e7	−	1.05920e7i	0.598129	−	0.598129i
$794$	−7.90986e6			−0.445264
$795$	−1.43437e7	−	1.93511e7i	−0.804903	−	1.08590i
$796$	6.34551e6			0.354964
$797$	2.40749e7	−	2.40749e7i	1.34252	−	1.34252i	0.448968	−	0.893548i	$-0.351792\pi$
$797$	2.40749e7	−	2.40749e7i	1.34252	−	1.34252i	0.893548	−	0.448968i	$-0.148208\pi$
$798$	−1.78716e7	−	6.80580e6i	−0.993476	−	0.378331i
$799$		−	4.11348e6i		−	0.227951i
$800$	4.33878e6	−	1.17858e7i	0.239686	−	0.651077i
$801$	−7.73011e6	−	6.88612e6i	−0.425701	−	0.379222i
$802$	−1.66647e7	−	1.66647e7i	−0.914876	−	0.914876i
$803$	1.08532e7	+	1.08532e7i	0.593976	+	0.593976i
$804$	3.26120e6	+	7.27264e6i	0.177925	+	0.396782i
$805$	−1.09177e7	+	2.39936e6i	−0.593803	+	0.130499i
$806$			402546.i			0.0218262i
$807$	−1.16508e7	+	3.05943e7i	−0.629754	+	1.65370i
$808$	1.07319e6	−	1.07319e6i	0.0578295	−	0.0578295i
$809$	2.33910e6			0.125654			0.0628271	−	0.998024i	$-0.479988\pi$
$809$	2.33910e6			0.125654			0.0628271	+	0.998024i	$0.479988\pi$
$810$	6.50323e6	−	1.33361e7i	0.348270	−	0.714197i
$811$	−2.56963e7			−1.37189			−0.685945	−	0.727654i	$-0.740611\pi$
$811$	−2.56963e7			−1.37189			−0.685945	+	0.727654i	$0.740611\pi$
$812$	1.29430e6	−	1.29430e6i	0.0688881	−	0.0688881i
$813$	−5.44868e6	+	1.43079e7i	−0.289111	+	0.759190i
$814$			9.90675e6i			0.524047i
$815$	−5.93083e6	−	3.79370e6i	−0.312767	−	0.200064i
$816$	−712487.	−	1.58888e6i	−0.0374586	−	0.0835347i
$817$	1.08004e7	+	1.08004e7i	0.566087	+	0.566087i
$818$	1.91442e7	+	1.91442e7i	1.00035	+	1.00035i
$819$	6.33200e6	+	5.64065e6i	0.329861	+	0.293846i
$820$	−11979.9	−	54511.5i	−0.000622182	−	0.00283109i
$821$			5.06844e6i			0.262432i	0.991354	+	0.131216i	$0.0418881\pi$
$821$			5.06844e6i			0.262432i	−0.991354	+	0.131216i	$0.958112\pi$
$822$	−1.66671e6	−	634707.i	−0.0860358	−	0.0327638i
$823$	1.27098e7	−	1.27098e7i	0.654092	−	0.654092i	−0.299883	−	0.953976i	$-0.596948\pi$
$823$	1.27098e7	−	1.27098e7i	0.654092	−	0.654092i	0.953976	+	0.299883i	$0.0969478\pi$
$824$	−3.98673e6			−0.204550
$825$	−2.75409e7	+	1.89776e6i	−1.40878	+	0.0970746i
$826$	−1.10682e6			−0.0564453
$827$	−2.01367e7	+	2.01367e7i	−1.02382	+	1.02382i	−0.0241111	+	0.999709i	$0.507676\pi$
$827$	−2.01367e7	+	2.01367e7i	−1.02382	+	1.02382i	−0.999709	+	0.0241111i	$0.992324\pi$
$828$	−4.83450e6	+	279162.i	−0.245062	+	0.0141508i
$829$			6.04072e6i			0.305283i	0.988282	+	0.152641i	$0.0487779\pi$
$829$			6.04072e6i			0.305283i	−0.988282	+	0.152641i	$0.951222\pi$
$830$	1.95216e6	+	8.88281e6i	0.0983602	+	0.447564i
$831$	−1.82558e7	+	8.18627e6i	−0.917063	+	0.411229i
$832$	−7.15074e6	−	7.15074e6i	−0.358132	−	0.358132i
$833$	−435396.	−	435396.i	−0.0217406	−	0.0217406i
$834$	1.26570e7	−	5.67565e6i	0.630110	−	0.282554i
$835$	8.82157e6	+	5.64278e6i	0.437854	+	0.280076i
$836$			1.54143e7i			0.762794i
$837$	−1.02103e6	+	530544.i	−0.0503760	+	0.0261763i
$838$	−851999.	+	851999.i	−0.0419111	+	0.0419111i
$839$	−2.17575e7			−1.06710			−0.533548	−	0.845769i	$-0.679142\pi$
$839$	−2.17575e7			−1.06710			−0.533548	+	0.845769i	$0.679142\pi$
$840$	2.98476e6	−	2.00845e7i	0.145953	−	0.982116i
$841$	−1.87926e7			−0.916213
$842$	1.80865e6	−	1.80865e6i	0.0879171	−	0.0879171i
$843$	3.54897e7	+	1.35150e7i	1.72002	+	0.655011i
$844$			8.57868e6i			0.414538i
$845$	1.55262e7	−	3.41216e6i	0.748038	−	0.164395i
$846$	−1.35742e7	+	1.52379e7i	−0.652061	+	0.731980i
$847$	−1.33996e7	−	1.33996e7i	−0.641778	−	0.641778i
$848$	9.91687e6	+	9.91687e6i	0.473571	+	0.473571i
$849$	−7.47632e6	−	1.66726e7i	−0.355974	−	0.793842i
$850$	1.29666e6	+	2.80758e6i	0.0615570	+	0.133286i
$851$		−	6.57034e6i		−	0.311002i
$852$	4.92752e6	−	1.29394e7i	0.232557	−	0.610682i
$853$	−1.18523e7	+	1.18523e7i	−0.557737	+	0.557737i	−0.928662	−	0.370926i	$-0.879040\pi$
$853$	−1.18523e7	+	1.18523e7i	−0.557737	+	0.557737i	0.370926	+	0.928662i	$0.379040\pi$
$854$	−2.70311e7			−1.26829
$855$	2.73155e7	+	1.53290e7i	1.27789	+	0.717132i
$856$	2.41368e7			1.12589
$857$	8.70826e6	−	8.70826e6i	0.405023	−	0.405023i	−0.474976	−	0.879999i	$-0.657543\pi$
$857$	8.70826e6	−	8.70826e6i	0.405023	−	0.405023i	0.879999	+	0.474976i	$0.157543\pi$
$858$	−4.16629e6	+	1.09404e7i	−0.193211	+	0.507360i
$859$			2.53846e7i			1.17378i	0.809665	+	0.586892i	$0.199649\pi$
$859$			2.53846e7i			1.17378i	−0.809665	+	0.586892i	$0.800351\pi$
$860$	−2.35374e6	+	3.67969e6i	−0.108521	+	0.169655i
$861$	−63898.2	−	142496.i	−0.00293752	−	0.00655083i
$862$	−8.45116e6	−	8.45116e6i	−0.387390	−	0.387390i
$863$	−2.22012e7	−	2.22012e7i	−1.01473	−	1.01473i	−0.999890	−	0.0148363i	$-0.995277\pi$
$863$	−2.22012e7	−	2.22012e7i	−1.01473	−	1.01473i	−0.0148363	−	0.999890i	$-0.504723\pi$
$864$	4.58865e6	−	1.45155e7i	0.209122	−	0.661528i
$865$	6.51129e6	−	1.01794e7i	0.295888	−	0.462572i
$866$		−	2.39620e7i		−	1.08575i
$867$	1.99782e7	+	7.60799e6i	0.902626	+	0.343734i
$868$	−299903.	+	299903.i	−0.0135108	+	0.0135108i
$869$	3.22457e7			1.44851
$870$	4.12518e6	−	3.05772e6i	0.184776	−	0.136962i
$871$	−1.27791e7			−0.570764
$872$	1.67058e6	−	1.67058e6i	0.0744006	−	0.0744006i
$873$	−1.54560e6	−	2.67665e7i	−0.0686373	−	1.18865i
$874$			1.75094e7i			0.775340i
$875$	−2.81192e6	+	2.04854e7i	−0.124160	+	0.904534i
$876$	4.54442e6	−	2.03781e6i	0.200087	−	0.0897228i
$877$	1.98709e6	+	1.98709e6i	0.0872404	+	0.0872404i	0.749380	−	0.662140i	$-0.230352\pi$
$877$	1.98709e6	+	1.98709e6i	0.0872404	+	0.0872404i	−0.662140	+	0.749380i	$0.730352\pi$
$878$	−8.72406e6	−	8.72406e6i	−0.381929	−	0.381929i
$879$	−5.71764e6	+	2.56390e6i	−0.249600	+	0.111926i
$880$	1.56986e7	−	3.45005e6i	0.683369	−	0.150182i
$881$		−	8.58185e6i		−	0.372513i	−0.982501	−	0.186256i	$-0.940364\pi$
$881$		−	8.58185e6i		−	0.372513i	0.982501	−	0.186256i	$-0.0596355\pi$
$882$	176098.	+	3.04965e6i	0.00762225	+	0.132001i
$883$	1.10673e7	−	1.10673e7i	0.477685	−	0.477685i	−0.426706	−	0.904390i	$-0.640326\pi$
$883$	1.10673e7	−	1.10673e7i	0.477685	−	0.477685i	0.904390	+	0.426706i	$0.140326\pi$
$884$	−765702.			−0.0329556
$885$	1.79318e6	+	266484.i	0.0769599	+	0.0114370i
$886$	3.56865e7			1.52728
$887$	2.07797e7	−	2.07797e7i	0.886809	−	0.886809i	−0.107406	−	0.994215i	$-0.534255\pi$
$887$	2.07797e7	−	2.07797e7i	0.886809	−	0.886809i	0.994215	+	0.107406i	$0.0342545\pi$
$888$	1.11535e7	+	4.24742e6i	0.474656	+	0.180756i
$889$		−	1.81319e7i		−	0.769463i
$890$	−9.01775e6	−	5.76826e6i	−0.381613	−	0.244101i
$891$	−3.32406e7	+	3.85172e6i	−1.40273	+	0.162540i
$892$	−8.05454e6	−	8.05454e6i	−0.338944	−	0.338944i
$893$	−3.04630e7	−	3.04630e7i	−1.27833	−	1.27833i
$894$	1.24608e7	+	2.77882e7i	0.521435	+	1.16283i
$895$	5.76930e6	+	2.62518e7i	0.240750	+	1.09547i
$896$			3.02666e6i			0.125948i
$897$	2.76316e6	−	7.25590e6i	0.114663	−	0.301100i
$898$	−1.30351e7	+	1.30351e7i	−0.539414	+	0.539414i
$899$	−398212.			−0.0164329
$900$	−2.60489e6	+	8.57062e6i	−0.107197	+	0.352700i
$901$	6.08573e6			0.249747
$902$	152447.	−	152447.i	0.00623881	−	0.00623881i
$903$	−4.34970e6	+	1.14221e7i	−0.177517	+	0.466150i
$904$			2.16180e7i			0.879822i
$905$	−1.82830e6	−	8.31923e6i	−0.0742037	−	0.337646i
$906$	−6.82567e6	−	1.52216e7i	−0.276264	−	0.616085i
$907$	−2.77720e7	−	2.77720e7i	−1.12096	−	1.12096i	−0.991598	−	0.129358i	$-0.958708\pi$
$907$	−2.77720e7	−	2.77720e7i	−1.12096	−	1.12096i	−0.129358	−	0.991598i	$-0.541292\pi$
$908$	−4.18038e6	−	4.18038e6i	−0.168268	−	0.168268i
$909$	−1.24617e6	+	1.39891e6i	−0.0500228	+	0.0561538i
$910$	7.38675e6	+	4.72498e6i	0.295699	+	0.189146i
$911$		−	2.08056e7i		−	0.830586i	−0.909688	−	0.415293i	$-0.863679\pi$
$911$		−	2.08056e7i		−	0.830586i	0.909688	−	0.415293i	$-0.136321\pi$
$912$	−1.70432e7	−	6.49031e6i	−0.678522	−	0.258391i
$913$	1.45041e7	−	1.45041e7i	0.575854	−	0.575854i
$914$	−3.88547e7			−1.53843
$915$	4.37934e7	+	6.50815e6i	1.72924	+	0.256983i
$916$	−1.20244e7			−0.473504
$917$	−1.91436e7	+	1.91436e7i	−0.751797	+	0.751797i
$918$	1.72845e6	+	3.32639e6i	0.0676940	+	0.130277i
$919$			2.67083e6i			0.104318i	0.998639	+	0.0521588i	$0.0166102\pi$
$919$			2.67083e6i			0.104318i	−0.998639	+	0.0521588i	$0.983390\pi$
$920$	−1.81577e7	+	3.99048e6i	−0.707281	+	0.155438i
$921$	2.58644e7	−	1.15981e7i	1.00474	−	0.450544i
$922$	−1.08316e7	−	1.08316e7i	−0.419629	−	0.419629i
$923$	1.56974e7	+	1.56974e7i	0.606492	+	0.606492i
$924$	−1.12547e7	+	5.04685e6i	−0.433666	+	0.194464i
$925$	−1.14055e7	−	4.19878e6i	−0.438287	−	0.161350i
$926$		−	3.59382e6i		−	0.137730i
$927$	4.91301e6	−	283695.i	0.187779	−	0.0108431i
$928$	3.72542e6	−	3.72542e6i	0.142005	−	0.142005i
$929$	3.48724e7			1.32569			0.662846	−	0.748756i	$-0.269349\pi$
$929$	3.48724e7			1.32569			0.662846	+	0.748756i	$0.269349\pi$
$930$	−955849.	+	708508.i	−0.0362395	+	0.0268620i
$931$	−6.44879e6			−0.243839
$932$	−5.70631e6	+	5.70631e6i	−0.215187	+	0.215187i
$933$	−5.25913e6	−	2.00276e6i	−0.197792	−	0.0753224i
$934$		−	1.61394e7i		−	0.605369i
$935$	3.75832e6	−	5.87553e6i	0.140593	−	0.219795i
$936$	1.05310e7	+	9.38121e6i	0.392899	+	0.350001i
$937$	2.07137e7	+	2.07137e7i	0.770742	+	0.770742i	0.978236	−	0.207494i	$-0.0665308\pi$
$937$	2.07137e7	+	2.07137e7i	0.770742	+	0.770742i	−0.207494	+	0.978236i	$0.566531\pi$
$938$	1.63064e7	+	1.63064e7i	0.605133	+	0.605133i
$939$	9.16531e6	+	2.04391e7i	0.339221	+	0.756482i
$940$	6.63886e6	−	1.03788e7i	0.245061	−	0.383113i
$941$			548205.i			0.0201822i	0.999949	+	0.0100911i	$0.00321215\pi$
$941$			548205.i			0.0201822i	−0.999949	+	0.0100911i	$0.996788\pi$
$942$	−4.10359e6	+	1.07758e7i	−0.150674	+	0.395660i
$943$	−101105.	+	101105.i	−0.00370250	+	0.00370250i
$944$	−1.05551e6			−0.0385509
$945$	−2.24903e6	+	2.49633e7i	−0.0819249	+	0.909333i
$946$	−1.68731e7			−0.613009
$947$	−8.77113e6	+	8.77113e6i	−0.317820	+	0.317820i	−0.847929	−	0.530110i	$-0.822151\pi$
$947$	−8.77113e6	+	8.77113e6i	−0.317820	+	0.317820i	0.530110	+	0.847929i	$0.322151\pi$
$948$	3.72367e6	−	9.77816e6i	0.134571	−	0.353375i
$949$			7.98524e6i			0.287821i
$950$	3.03946e7	+	1.11894e7i	1.09267	+	0.402251i
$951$	1.27032e7	+	2.83288e7i	0.455472	+	1.01573i
$952$	3.62753e6	+	3.62753e6i	0.129723	+	0.129723i
$953$	3.42460e7	+	3.42460e7i	1.22145	+	1.22145i	0.967115	+	0.254338i	$0.0818577\pi$
$953$	3.42460e7	+	3.42460e7i	1.22145	+	1.22145i	0.254338	+	0.967115i	$0.418142\pi$
$954$	−2.25439e7	−	2.00825e7i	−0.801970	−	0.714408i
$955$	−6.63833e6	+	1.45889e6i	−0.235532	+	0.0517624i
$956$			5.25237e6i			0.185870i
$957$	−1.08226e7	−	4.12143e6i	−0.381991	−	0.145468i
$958$	2.68575e7	−	2.68575e7i	0.945478	−	0.945478i
$959$	3.01279e6			0.105785
$960$	4.39370e6	−	2.95653e7i	0.153870	−	1.03539i
$961$	−2.85369e7			−0.996777
$962$	−3.64445e6	+	3.64445e6i	−0.126968	+	0.126968i
$963$	−2.97448e7	+	1.71757e6i	−1.03358	+	0.0596829i
$964$		−	7.27247e6i		−	0.252052i
$965$	−7.35235e6	−	4.70298e6i	−0.254160	−	0.162575i
$966$	−1.27845e7	+	5.73281e6i	−0.440799	+	0.197663i
$967$	−3.38352e6	−	3.38352e6i	−0.116360	−	0.116360i	0.646529	−	0.762889i	$-0.276220\pi$
$967$	−3.38352e6	−	3.38352e6i	−0.116360	−	0.116360i	−0.762889	+	0.646529i	$0.776220\pi$
$968$	−2.22855e7	−	2.22855e7i	−0.764425	−	0.764425i
$969$	−7.22095e6	+	3.23802e6i	−0.247050	+	0.110782i
$970$	−5.95074e6	−	2.70774e7i	−0.203068	−	0.924012i
$971$			7.86809e6i			0.267807i	0.990994	+	0.133903i	$0.0427512\pi$
$971$			7.86809e6i			0.267807i	−0.990994	+	0.133903i	$0.957249\pi$
$972$	−2.67058e6	+	1.05247e7i	−0.0906649	+	0.357308i
$973$	−1.65694e7	+	1.65694e7i	−0.561079	+	0.561079i
$974$	1.89434e7			0.639824
$975$	−1.08297e7	−	9.43347e6i	−0.364843	−	0.317804i
$976$	−2.57781e7			−0.866215
$977$	−2.25244e7	+	2.25244e7i	−0.754947	+	0.754947i	−0.975398	−	0.220451i	$-0.929247\pi$
$977$	−2.25244e7	+	2.25244e7i	−0.754947	+	0.754947i	0.220451	+	0.975398i	$0.429247\pi$
$978$	−8.24677e6	−	3.14050e6i	−0.275700	−	0.104991i
$979$			2.41429e7i			0.805069i
$980$	−395857.	−	1.80125e6i	−0.0131666	−	0.0599114i
$981$	−1.93984e6	+	2.17760e6i	−0.0643568	+	0.0722447i
$982$	2.75126e7	+	2.75126e7i	0.910442	+	0.910442i
$983$	1.53567e7	+	1.53567e7i	0.506891	+	0.506891i	0.913571	−	0.406680i	$-0.133314\pi$
$983$	1.53567e7	+	1.53567e7i	0.506891	+	0.506891i	−0.406680	+	0.913571i	$0.633314\pi$
$984$	−106272.	−	236992.i	−0.00349889	−	0.00780272i
$985$	−9.61691e6	−	6.15152e6i	−0.315824	−	0.202019i
$986$			1.29733e6i			0.0424969i
$987$	1.22686e7	−	3.22166e7i	0.400868	−	1.05266i
$988$	−5.67053e6	+	5.67053e6i	−0.184813	+	0.184813i
$989$	1.11905e7			0.363798
$990$	−3.33111e7	+	9.36303e6i	−1.08019	+	0.303619i
$991$	4.62484e7			1.49593			0.747967	−	0.663736i	$-0.231030\pi$
$991$	4.62484e7			1.49593			0.747967	+	0.663736i	$0.231030\pi$
$992$	−863220.	+	863220.i	−0.0278511	+	0.0278511i
$993$	7.17434e6	−	1.88394e7i	0.230892	−	0.606310i
$994$		−	4.00604e7i		−	1.28603i
$995$	−2.93702e7	+	6.45463e6i	−0.940480	+	0.206687i
$996$	−2.72330e6	−	6.07310e6i	−0.0869855	−	0.193982i
$997$	2.96424e7	+	2.96424e7i	0.944443	+	0.944443i	0.998536	−	0.0540925i	$-0.0172266\pi$
$997$	2.96424e7	+	2.96424e7i	0.944443	+	0.944443i	−0.0540925	+	0.998536i	$0.517227\pi$
$998$	−1.85473e6	−	1.85473e6i	−0.0589459	−	0.0589459i
$999$	−1.40471e7	−	4.44059e6i	−0.445322	−	0.140775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.6.e.a.2.6	yes	16
3.2	odd	2	inner	15.6.e.a.2.3	✓	16
5.2	odd	4		75.6.e.e.68.6		16
5.3	odd	4	inner	15.6.e.a.8.3	yes	16
5.4	even	2		75.6.e.e.32.3		16
15.2	even	4		75.6.e.e.68.3		16
15.8	even	4	inner	15.6.e.a.8.6	yes	16
15.14	odd	2		75.6.e.e.32.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.6.e.a.2.3	✓	16	3.2	odd	2	inner
15.6.e.a.2.6	yes	16	1.1	even	1	trivial
15.6.e.a.8.3	yes	16	5.3	odd	4	inner
15.6.e.a.8.6	yes	16	15.8	even	4	inner
75.6.e.e.32.3		16	5.4	even	2
75.6.e.e.32.6		16	15.14	odd	2
75.6.e.e.68.3		16	15.2	even	4
75.6.e.e.68.6		16	5.2	odd	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.17835 - 3.17835i) q^{2} +(5.54767 - 14.5679i) q^{3} +11.7962i q^{4} +(-11.9990 - 54.5987i) q^{5} +(-28.6694 - 63.9343i) q^{6} +(83.6967 + 83.6967i) q^{7} +(139.200 + 139.200i) q^{8} +(-181.447 - 161.636i) q^{9} +O(q^{10})\)	\(q+(3.17835 - 3.17835i) q^{2} +(5.54767 - 14.5679i) q^{3} +11.7962i q^{4} +(-11.9990 - 54.5987i) q^{5} +(-28.6694 - 63.9343i) q^{6} +(83.6967 + 83.6967i) q^{7} +(139.200 + 139.200i) q^{8} +(-181.447 - 161.636i) q^{9} +(-211.671 - 135.397i) q^{10} +566.700i q^{11} +(171.846 + 65.4414i) q^{12} +(-208.475 + 208.475i) q^{13} +532.035 q^{14} +(-861.955 - 128.095i) q^{15} +507.372 q^{16} +(155.680 - 155.680i) q^{17} +(-1090.44 + 62.9658i) q^{18} -2305.83i q^{19} +(644.057 - 141.543i) q^{20} +(1683.61 - 754.962i) q^{21} +(1801.17 + 1801.17i) q^{22} +(-1194.57 - 1194.57i) q^{23} +(2800.08 - 1255.61i) q^{24} +(-2837.05 + 1310.27i) q^{25} +1325.21i q^{26} +(-3361.30 + 1746.59i) q^{27} +(-987.303 + 987.303i) q^{28} -1310.94 q^{29} +(-3146.73 + 2332.46i) q^{30} +303.760 q^{31} +(-2841.78 + 2841.78i) q^{32} +(8255.62 + 3143.87i) q^{33} -989.614i q^{34} +(3565.45 - 5574.01i) q^{35} +(1906.69 - 2140.38i) q^{36} +(2750.09 + 2750.09i) q^{37} +(-7328.75 - 7328.75i) q^{38} +(1880.49 + 4193.59i) q^{39} +(5929.86 - 9270.38i) q^{40} -84.6376i q^{41} +(2951.55 - 7750.62i) q^{42} +(-4683.92 + 4683.92i) q^{43} -6684.90 q^{44} +(-6647.93 + 11846.2i) q^{45} -7593.51 q^{46} +(13211.3 - 13211.3i) q^{47} +(2814.73 - 7391.33i) q^{48} -2796.73i q^{49} +(-4852.64 + 13181.6i) q^{50} +(-1404.27 - 3131.60i) q^{51} +(-2459.21 - 2459.21i) q^{52} +(19545.6 + 19545.6i) q^{53} +(-5132.10 + 16234.7i) q^{54} +(30941.1 - 6799.85i) q^{55} +23301.1i q^{56} +(-33591.1 - 12792.0i) q^{57} +(-4166.63 + 4166.63i) q^{58} -2080.36 q^{59} +(1511.04 - 10167.8i) q^{60} -50807.1 q^{61} +(965.455 - 965.455i) q^{62} +(-1658.10 - 28714.9i) q^{63} +34300.2i q^{64} +(13884.0 + 8880.97i) q^{65} +(36231.5 - 16246.9i) q^{66} +(30649.1 + 30649.1i) q^{67} +(1836.44 + 1836.44i) q^{68} +(-24029.4 + 10775.3i) q^{69} +(-6383.90 - 29048.4i) q^{70} -75296.6i q^{71} +(-2757.66 - 47756.9i) q^{72} +(19151.6 - 19151.6i) q^{73} +17481.5 q^{74} +(3348.78 + 48598.7i) q^{75} +27200.1 q^{76} +(-47430.9 + 47430.9i) q^{77} +(19305.5 + 7351.84i) q^{78} -56900.8i q^{79} +(-6087.97 - 27701.8i) q^{80} +(6796.76 + 58656.5i) q^{81} +(-269.008 - 269.008i) q^{82} +(-25593.9 - 25593.9i) q^{83} +(8905.68 + 19860.1i) q^{84} +(-10368.0 - 6631.94i) q^{85} +29774.3i q^{86} +(-7272.68 + 19097.7i) q^{87} +(-78884.4 + 78884.4i) q^{88} +42602.7 q^{89} +(16522.0 + 58780.9i) q^{90} -34897.3 q^{91} +(14091.4 - 14091.4i) q^{92} +(1685.16 - 4425.14i) q^{93} -83980.1i q^{94} +(-125896. + 27667.8i) q^{95} +(25633.5 + 57164.1i) q^{96} +(78017.6 + 78017.6i) q^{97} +(-8888.97 - 8888.97i) q^{98} +(91599.0 - 102826. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 84 q^{6} - 80 q^{7}+O(q^{10}) \) 16 * q - 84 * q^6 - 80 * q^7	\( 16 q - 84 q^{6} - 80 q^{7} + 1060 q^{10} + 420 q^{12} - 2120 q^{13} - 3000 q^{15} - 452 q^{16} + 6000 q^{18} + 1416 q^{21} + 3380 q^{22} + 9160 q^{25} - 12960 q^{27} - 10900 q^{28} - 13380 q^{30} - 21568 q^{31} + 5760 q^{33} + 61932 q^{36} + 55720 q^{37} + 21480 q^{40} - 103020 q^{42} - 23360 q^{43} - 21240 q^{45} - 151168 q^{46} + 74820 q^{48} + 138816 q^{51} + 204160 q^{52} + 89120 q^{55} - 163800 q^{57} - 163500 q^{58} - 217380 q^{60} - 175168 q^{61} + 143040 q^{63} + 263400 q^{66} + 140320 q^{67} + 385260 q^{70} - 328680 q^{72} - 240320 q^{73} - 199920 q^{75} - 271536 q^{76} + 429960 q^{78} + 326016 q^{81} + 431120 q^{82} + 2440 q^{85} - 331680 q^{87} - 401700 q^{88} - 348360 q^{90} - 487168 q^{91} - 22320 q^{93} + 311748 q^{96} + 440800 q^{97}+O(q^{100}) \) 16 * q - 84 * q^6 - 80 * q^7 + 1060 * q^10 + 420 * q^12 - 2120 * q^13 - 3000 * q^15 - 452 * q^16 + 6000 * q^18 + 1416 * q^21 + 3380 * q^22 + 9160 * q^25 - 12960 * q^27 - 10900 * q^28 - 13380 * q^30 - 21568 * q^31 + 5760 * q^33 + 61932 * q^36 + 55720 * q^37 + 21480 * q^40 - 103020 * q^42 - 23360 * q^43 - 21240 * q^45 - 151168 * q^46 + 74820 * q^48 + 138816 * q^51 + 204160 * q^52 + 89120 * q^55 - 163800 * q^57 - 163500 * q^58 - 217380 * q^60 - 175168 * q^61 + 143040 * q^63 + 263400 * q^66 + 140320 * q^67 + 385260 * q^70 - 328680 * q^72 - 240320 * q^73 - 199920 * q^75 - 271536 * q^76 + 429960 * q^78 + 326016 * q^81 + 431120 * q^82 + 2440 * q^85 - 331680 * q^87 - 401700 * q^88 - 348360 * q^90 - 487168 * q^91 - 22320 * q^93 + 311748 * q^96 + 440800 * q^97

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