LMFDB - Embedded newform 15.6.e.a.2.3

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			2.3
Root			$4.35647 + 4.35647i$ of defining polynomial
Character	$\chi$	$=$	15.2
Dual form			15.6.e.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.17835 + 3.17835i) q^{2} +(14.5679 - 5.54767i) q^{3} +11.7962i q^{4} +(11.9990 + 54.5987i) q^{5} +(-28.6694 + 63.9343i) q^{6} +(83.6967 + 83.6967i) q^{7} +(-139.200 - 139.200i) q^{8} +(181.447 - 161.636i) q^{9} +O(q^{10})$	\(q+(-3.17835 + 3.17835i) q^{2} +(14.5679 - 5.54767i) 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} +(65.4414 + 171.846i) q^{12} +(-208.475 + 208.475i) q^{13} -532.035 q^{14} +(477.697 + 728.822i) q^{15} +507.372 q^{16} +(-155.680 + 155.680i) q^{17} +(-62.9658 + 1090.44i) 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} +(1746.59 - 3361.30i) q^{27} +(-987.303 + 987.303i) q^{28} +1310.94 q^{29} +(-3834.74 - 798.162i) q^{30} +303.760 q^{31} +(2841.78 - 2841.78i) q^{32} +(-3143.87 - 8255.62i) 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} +(-7750.62 + 2951.55i) q^{42} +(-4683.92 + 4683.92i) q^{43} +6684.90 q^{44} +(11002.3 + 7967.28i) q^{45} -7593.51 q^{46} +(-13211.3 + 13211.3i) q^{47} +(7391.33 - 2814.73i) 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} +(-12792.0 - 33591.1i) q^{57} +(-4166.63 + 4166.63i) q^{58} +2080.36 q^{59} +(-8597.32 + 5635.00i) q^{60} -50807.1 q^{61} +(-965.455 + 965.455i) q^{62} +(28714.9 + 1658.10i) 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} +(-47756.9 - 2757.66i) q^{72} +(19151.6 - 19151.6i) q^{73} -17481.5 q^{74} +(-34060.8 + 34826.8i) q^{75} +27200.1 q^{76} +(47430.9 - 47430.9i) q^{77} +(-7351.84 - 19305.5i) 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} +(19097.7 - 7272.68i) q^{87} +(-78884.4 + 78884.4i) q^{88} -42602.7 q^{89} +(-60291.9 + 9646.33i) q^{90} -34897.3 q^{91} +(-14091.4 + 14091.4i) q^{92} +(4425.14 - 1685.16i) 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	−0.929835	−	0.367977i	$-0.880051\pi$
$2$	−3.17835	+	3.17835i	−0.561858	+	0.561858i	0.367977	+	0.929835i	$0.380051\pi$
$3$	14.5679	−	5.54767i	0.934530	−	0.355883i
$3$	14.5679	−	5.54767i	0.934530	−	0.355883i
$4$			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	$-0.750471\pi$
$11$		−	566.700i		−	1.41212i	0.708152	−	0.706060i	$-0.249529\pi$
$12$	65.4414	+	171.846i	0.131190	+	0.344497i
$13$	−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
$15$	477.697	+	728.822i	0.548181	+	0.836360i
$16$	507.372			0.495480
$17$	−155.680	+	155.680i	−0.130651	+	0.130651i	−0.769408	−	0.638757i	$-0.779449\pi$
$17$	−155.680	+	155.680i	−0.130651	+	0.130651i	0.638757	+	0.769408i	$0.279449\pi$
$18$	−62.9658	+	1090.44i	−0.0458061	+	0.793266i
$19$		−	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	0.902193	−	0.431333i	$-0.141957\pi$
$23$	1194.57	+	1194.57i	0.470860	+	0.470860i	−0.431333	+	0.902193i	$0.641957\pi$
$24$	−2800.08	−	1255.61i	−0.992298	−	0.444966i
$25$	−2837.05	+	1310.27i	−0.907855	+	0.419285i
$26$		−	1325.21i		−	0.384461i
$27$	1746.59	−	3361.30i	0.461086	−	0.887355i
$28$	−987.303	+	987.303i	−0.237988	+	0.237988i
$29$	1310.94			0.289460			0.144730	−	0.989471i	$-0.453769\pi$
$29$	1310.94			0.289460			0.144730	+	0.989471i	$0.453769\pi$
$30$	−3834.74	−	798.162i	−0.777915	−	0.161915i
$31$	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
$33$	−3143.87	−	8255.62i	−0.502550	−	1.31967i
$34$		−	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	$0.00125148\pi$
$41$			84.6376i			0.00786328i	−0.999992	+	0.00393164i	$0.998749\pi$
$42$	−7750.62	+	2951.55i	−0.677974	+	0.258183i
$43$	−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
$45$	11002.3	+	7967.28i	0.809938	+	0.586515i
$46$	−7593.51			−0.529112
$47$	−13211.3	+	13211.3i	−0.872369	+	0.872369i	−0.992730	−	0.120361i	$-0.961595\pi$
$47$	−13211.3	+	13211.3i	−0.872369	+	0.872369i	0.120361	+	0.992730i	$0.461595\pi$
$48$	7391.33	−	2814.73i	0.463041	−	0.176333i
$49$		−	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	0.0432812	−	0.999063i	$-0.486219\pi$
$53$	−19545.6	−	19545.6i	−0.955782	−	0.955782i	−0.999063	+	0.0432812i	$0.986219\pi$
$54$	5132.10	+	16234.7i	0.239503	+	0.757633i
$55$	30941.1	−	6799.85i	1.37921	−	0.303105i
$56$		−	23301.1i		−	0.992902i
$57$	−12792.0	−	33591.1i	−0.521497	−	1.36942i
$58$	−4166.63	+	4166.63i	−0.162636	+	0.162636i
$59$	2080.36			0.0778051			0.0389026	−	0.999243i	$-0.487614\pi$
$59$	2080.36			0.0778051			0.0389026	+	0.999243i	$0.487614\pi$
$60$	−8597.32	+	5635.00i	−0.308308	+	0.202077i
$61$	−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
$63$	28714.9	+	1658.10i	0.911497	+	0.0526332i
$64$			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	$0.346759\pi$
$71$			75296.6i			1.77268i	−0.463038	+	0.886339i	$0.653241\pi$
$72$	−47756.9	−	2757.66i	−1.08569	−	0.0626917i
$73$	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
$75$	−34060.8	+	34826.8i	−0.699201	+	0.714925i
$76$	27200.1			0.540177
$77$	47430.9	−	47430.9i	0.911664	−	0.911664i
$78$	−7351.84	−	19305.5i	−0.136823	−	0.359290i
$79$		−	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	0.880969	−	0.473174i	$-0.156892\pi$
$83$	25593.9	+	25593.9i	0.407794	+	0.407794i	−0.473174	+	0.880969i	$0.656892\pi$
$84$	−8905.68	+	19860.1i	−0.137711	+	0.307103i
$85$	−10368.0	−	6631.94i	−0.155649	−	0.0995620i
$86$		−	29774.3i		−	0.434105i
$87$	19097.7	−	7272.68i	0.270509	−	0.103014i
$88$	−78884.4	+	78884.4i	−1.08589	+	1.08589i
$89$	−42602.7			−0.570114			−0.285057	−	0.958511i	$-0.592013\pi$
$89$	−42602.7			−0.570114			−0.285057	+	0.958511i	$0.592013\pi$
$90$	−60291.9	+	9646.33i	−0.784609	+	0.125532i
$91$	−34897.3			−0.441762
$92$	−14091.4	+	14091.4i	−0.173573	+	0.173573i
$93$	4425.14	−	1685.16i	0.0530542	−	0.0202038i
$94$		−	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	$0.0119718\pi$
$101$			7709.74i			0.0752032i	−0.999293	+	0.0376016i	$0.988028\pi$
$102$	−5490.05	−	14416.6i	−0.0522488	−	0.137202i
$103$	−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
$105$	−21018.3	+	100982.i	−0.186048	+	0.893859i
$106$	124245.			1.07403
$107$	−86698.6	+	86698.6i	−0.732070	+	0.732070i	−0.971030	−	0.238959i	$-0.923194\pi$
$107$	−86698.6	+	86698.6i	−0.732070	+	0.732070i	0.238959	+	0.971030i	$0.423194\pi$
$108$	39650.5	+	20603.1i	0.327107	+	0.169971i
$109$		−	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	0.360634	−	0.932707i	$-0.382560\pi$
$113$	−77651.2	−	77651.2i	−0.572074	−	0.572074i	−0.932707	+	0.360634i	$0.882560\pi$
$114$	147422.	+	66106.9i	1.06243	+	0.476414i
$115$	−50888.3	+	79555.6i	−0.358817	+	0.560953i
$116$			15464.1i			0.106704i
$117$	−4130.06	+	71524.0i	−0.0278928	+	0.483045i
$118$	−6612.10	+	6612.10i	−0.0437154	+	0.0437154i
$119$	−26059.9			−0.168696
$120$	34956.5	−	167947.i	0.221602	−	1.06468i
$121$	−160098.			−0.994081
$122$	161483.	−	161483.i	0.982259	−	0.982259i
$123$	469.542	+	1232.99i	0.00279841	+	0.00734847i
$124$			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	$-0.802174\pi$
$131$		−	228726.i		−	1.16449i	0.813012	−	0.582247i	$-0.197826\pi$
$132$	97384.9	−	37085.7i	0.486471	−	0.185256i
$133$	192991.	−	192991.i	0.946035	−	0.946035i
$134$	−194827.			−0.937320
$135$	204480.	+	55029.3i	0.965643	+	0.259872i
$136$	43341.3			0.200935
$137$	−17998.3	+	17998.3i	−0.0819275	+	0.0819275i	−0.746883	−	0.664956i	$-0.768450\pi$
$137$	−17998.3	+	17998.3i	−0.0819275	+	0.0819275i	0.664956	+	0.746883i	$0.268450\pi$
$138$	−110621.	+	42126.3i	−0.494472	+	0.188302i
$139$			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
$147$	−15515.3	−	40742.4i	−0.0592199	−	0.155508i
$148$	−32440.6	+	32440.6i	−0.121740	+	0.121740i
$149$	434636.			1.60384			0.801919	−	0.597433i	$-0.203813\pi$
$149$	434636.			1.60384			0.801919	+	0.597433i	$0.203813\pi$
$150$	−2434.48	−	218949.i	−0.00883442	−	0.794538i
$151$	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
$153$	−3084.16	+	53411.2i	−0.0106515	+	0.184461i
$154$			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
$162$	164828.	+	208033.i	0.493452	+	0.622796i
$163$	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
$165$	413023.	−	270711.i	1.18104	−	0.774097i
$166$	−162693.			−0.458245
$167$	132460.	−	132460.i	0.367532	−	0.367532i	−0.499044	−	0.866576i	$-0.666316\pi$
$167$	132460.	−	132460.i	0.367532	−	0.367532i	0.866576	+	0.499044i	$0.166316\pi$
$168$	−129267.	−	339448.i	−0.353357	−	0.927897i
$169$			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	0.485794	−	0.874074i	$-0.338531\pi$
$173$	−152848.	−	152848.i	−0.388280	−	0.388280i	−0.874074	+	0.485794i	$0.838531\pi$
$174$	−37583.9	+	83814.2i	−0.0941085	+	0.209867i
$175$	−347116.	−	127787.i	−0.856801	−	0.315421i
$176$		−	287527.i		−	0.699677i
$177$	30306.4	−	11541.1i	0.0727112	−	0.0276895i
$178$	135406.	−	135406.i	0.320323	−	0.320323i
$179$	480813.			1.12162			0.560808	−	0.827946i	$-0.310491\pi$
$179$	480813.			1.12162			0.560808	+	0.827946i	$0.310491\pi$
$180$	−93983.6	+	129785.i	−0.216208	+	0.298569i
$181$	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
$183$	−740152.	+	281861.i	−1.63378	+	0.622168i
$184$		−	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	$0.0384743\pi$
$191$			121584.i			0.241153i	−0.992704	+	0.120576i	$0.961526\pi$
$192$	190287.	+	499682.i	0.372525	+	0.978229i
$193$	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
$195$	−251529.	−	52353.2i	−0.473697	−	0.0985954i
$196$	32990.7			0.0613411
$197$	−144403.	+	144403.i	−0.265100	+	0.265100i	−0.827122	−	0.562022i	$-0.810024\pi$
$197$	−144403.	+	144403.i	−0.265100	+	0.265100i	0.562022	+	0.827122i	$0.310024\pi$
$198$	617950.	+	35682.7i	1.12019	+	0.0646837i
$199$		−	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
$207$	409835.	+	23665.4i	0.664789	+	0.0383874i
$208$	−105774.	+	105774.i	−0.169520	+	0.169520i
$209$	−1.30672e6			−2.06926
$210$	−254151.	−	387758.i	−0.397689	−	0.606754i
$211$	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
$213$	417721.	+	1.09691e6i	0.630866	+	1.65662i
$214$		−	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
$222$	−254668.	+	96981.5i	−0.346810	+	0.132071i
$223$	−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
$225$	−302987.	+	696311.i	−0.398995	+	0.916953i
$226$	493605.			0.642848
$227$	354384.	−	354384.i	0.456467	−	0.456467i	−0.441027	−	0.897494i	$-0.645386\pi$
$227$	354384.	−	354384.i	0.456467	−	0.456467i	0.897494	+	0.441027i	$0.145386\pi$
$228$	396248.	−	150897.i	0.504812	−	0.192240i
$229$			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	0.352185	−	0.935930i	$-0.385439\pi$
$233$	−483742.	−	483742.i	−0.583746	−	0.583746i	−0.935930	+	0.352185i	$0.885439\pi$
$234$	−214202.	−	240455.i	−0.255731	−	0.287074i
$235$	−879842.	−	562796.i	−1.03929	−	0.664786i
$236$			24540.3i			0.0286814i
$237$	−315667.	−	828925.i	−0.365055	−	0.958615i
$238$	82827.4	−	82827.4i	0.0947833	−	0.0947833i
$239$	−445259.			−0.504218			−0.252109	−	0.967699i	$-0.581124\pi$
$239$	−445259.			−0.504218			−0.252109	+	0.967699i	$0.581124\pi$
$240$	242370.	+	369783.i	0.271613	+	0.414399i
$241$	−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
$243$	−226393.	−	892208.i	−0.245950	−	0.969282i
$244$		−	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	$0.181110\pi$
$251$			1.07551e6i			1.07754i	−0.842454	+	0.538768i	$0.818890\pi$
$252$	−19559.3	+	338726.i	−0.0194023	+	0.336006i
$253$	676962.	−	676962.i	0.664910	−	0.664910i
$254$	688550.			0.669655
$255$	−187831.	−	39095.2i	−0.180891	−	0.0376507i
$256$	−982672.			−0.937149
$257$	−1.24679e6	+	1.24679e6i	−1.17750	+	1.17750i	−0.197118	+	0.980380i	$0.563158\pi$
$257$	−1.24679e6	+	1.24679e6i	−1.17750	+	1.17750i	−0.980380	+	0.197118i	$0.936842\pi$
$258$	−165178.	−	433748.i	−0.154491	−	0.405685i
$259$			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	0.961392	−	0.275181i	$-0.0887379\pi$
$263$	769745.	+	769745.i	0.686211	+	0.686211i	−0.275181	+	0.961392i	$0.588738\pi$
$264$	−711554.	+	1.58680e6i	−0.628345	+	1.40124i
$265$	832636.	−	1.30169e6i	0.728350	−	1.13866i
$266$			1.22678e6i			1.06308i
$267$	−620631.	+	236346.i	−0.532789	+	0.202894i
$268$	−361543.	+	361543.i	−0.307485	+	0.307485i
$269$	2.10012e6			1.76955			0.884776	−	0.466017i	$-0.154311\pi$
$269$	2.10012e6			1.76955			0.884776	+	0.466017i	$0.154311\pi$
$270$	−824812.	+	475007.i	−0.688566	+	0.396543i
$271$	−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
$273$	−508380.	+	193599.i	−0.412840	+	0.157216i
$274$		−	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	$-0.627977\pi$
$281$		−	2.43616e6i		−	1.84052i	0.391308	−	0.920260i	$-0.372023\pi$
$282$	−465894.	−	1.22341e6i	−0.348871	−	0.916115i
$283$	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
$285$	1.68054e6	−	1.10149e6i	1.22557	−	0.803282i
$286$	−750997.			−0.542904
$287$	−7083.89	+	7083.89i	−0.00507653	+	0.00507653i
$288$	56298.2	−	974966.i	0.0399957	−	0.692641i
$289$			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	0.797175	−	0.603748i	$-0.206327\pi$
$293$	284240.	+	284240.i	0.193426	+	0.193426i	−0.603748	+	0.797175i	$0.706327\pi$
$294$	178807.	+	80180.4i	0.120647	+	0.0541003i
$295$	24962.3	+	113585.i	0.0167005	+	0.0759916i
$296$		−	765622.i		−	0.507908i
$297$	−1.90485e6	−	989793.i	−1.25305	−	0.651108i
$298$	−1.38143e6	+	1.38143e6i	−0.901129	+	0.901129i
$299$	−498075.			−0.322193
$300$	−410824.	−	401788.i	−0.263544	−	0.257747i
$301$	−784058.			−0.498806
$302$	−756709.	+	756709.i	−0.477432	+	0.477432i
$303$	42771.1	+	112315.i	0.0267636	+	0.0702797i
$304$		−	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	$0.0337482\pi$
$311$			361008.i			0.211649i	−0.994385	+	0.105824i	$0.966252\pi$
$312$	845509.	−	321983.i	0.491736	−	0.187260i
$313$	−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
$315$	254020.	+	1.58769e6i	0.144242	+	0.901550i
$316$	671213.			0.378131
$317$	1.40830e6	−	1.40830e6i	0.787133	−	0.787133i	−0.193890	−	0.981023i	$-0.562110\pi$
$317$	1.40830e6	−	1.40830e6i	0.787133	−	0.787133i	0.981023	+	0.193890i	$0.0621104\pi$
$318$	1.80999e6	−	689272.i	1.00371	−	0.382229i
$319$		−	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
$327$	−66579.5	−	174834.i	−0.0344327	−	0.0904184i
$328$	11781.5	−	11781.5i	0.00604668	−	0.00604668i
$329$	−2.21148e6			−1.12640
$330$	−452319.	+	2.17314e6i	−0.228644	+	1.09851i
$331$	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
$333$	943507.	+	54481.6i	0.466267	+	0.0269240i
$334$			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
$342$	2.51436e6	+	145189.i	1.16242	+	0.0671224i
$343$	1.64077e6	−	1.64077e6i	0.753029	−	0.753029i
$344$	1.30400e6			0.594130
$345$	−299986.	+	1.44127e6i	−0.135692	+	0.651924i
$346$	971610.			0.436316
$347$	629702.	−	629702.i	0.280745	−	0.280745i	−0.552661	−	0.833406i	$-0.686388\pi$
$347$	629702.	−	629702.i	0.280745	−	0.280745i	0.833406	+	0.552661i	$0.186388\pi$
$348$	85790.0	+	225280.i	0.0379742	+	0.0997181i
$349$		−	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	0.528574	−	0.848887i	$-0.322727\pi$
$353$	−749916.	−	749916.i	−0.320314	−	0.320314i	−0.848887	+	0.528574i	$0.822727\pi$
$354$	−59642.6	+	133006.i	−0.0252958	+	0.0564110i
$355$	−4.11110e6	+	903487.i	−1.73136	+	0.380497i
$356$		−	502550.i		−	0.210162i
$357$	−379637.	+	144572.i	−0.157652	+	0.0600362i
$358$	−1.52819e6	+	1.52819e6i	−0.630189	+	0.630189i
$359$	403932.			0.165414			0.0827069	−	0.996574i	$-0.473643\pi$
$359$	403932.			0.165414			0.0827069	+	0.996574i	$0.473643\pi$
$360$	−422472.	−	2.64056e6i	−0.171807	−	1.07384i
$361$	−2.84078e6			−1.14728
$362$	−484286.	+	484286.i	−0.194236	+	0.194236i
$363$	−2.33229e6	+	888170.i	−0.928999	+	0.353777i
$364$		−	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
$372$	19878.5	+	52199.8i	0.00744776	+	0.0195574i
$373$	−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
$375$	−2.31020e6	−	1.44179e6i	−0.848342	−	0.529449i
$376$	3.67801e6			1.34166
$377$	−273299.	+	273299.i	−0.0990339	+	0.0990339i
$378$	−929247.	+	1.78833e6i	−0.334504	+	0.643750i
$379$		−	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	0.818388	−	0.574666i	$-0.194868\pi$
$383$	699669.	+	699669.i	0.243722	+	0.243722i	−0.574666	+	0.818388i	$0.694868\pi$
$384$	−363711.	−	163095.i	−0.125872	−	0.0564434i
$385$	3.15879e6	+	2.02054e6i	1.08610	+	0.694730i
$386$			701775.i			0.239734i
$387$	−92792.5	+	1.60697e6i	−0.0314946	+	0.545420i
$388$	−920311.	+	920311.i	−0.310353	+	0.310353i
$389$	−1.08294e6			−0.362852			−0.181426	−	0.983405i	$-0.558071\pi$
$389$	−1.08294e6			−0.362852			−0.181426	+	0.983405i	$0.558071\pi$
$390$	965843.	−	633049.i	0.321547	−	0.210754i
$391$	−371942.			−0.123036
$392$	−389303.	+	389303.i	−0.127960	+	0.127960i
$393$	−1.26890e6	−	3.33205e6i	−0.414424	−	1.08825i
$394$		−	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	$0.302798\pi$
$401$			5.24320e6i			1.62830i	−0.580652	+	0.814152i	$0.697202\pi$
$402$	−2.83822e6	+	1.08084e6i	−0.875954	+	0.333577i
$403$	−63326.3	+	63326.3i	−0.0194232	+	0.0194232i
$404$	−90945.6			−0.0277222
$405$	3.28413e6	−	332728.i	0.994907	−	0.100798i
$406$	−697467.			−0.209995
$407$	1.55847e6	−	1.55847e6i	0.466352	−	0.466352i
$408$	631391.	−	240444.i	0.187780	−	0.0715093i
$409$			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
$417$	1.09827e6	+	2.88399e6i	0.309292	+	0.812183i
$418$	4.15320e6	−	4.15320e6i	1.16263	−	1.16263i
$419$	268063.			0.0745937			0.0372969	−	0.999304i	$-0.488125\pi$
$419$	268063.			0.0745937			0.0372969	+	0.999304i	$0.488125\pi$
$420$	−1.19120e6	−	247936.i	−0.329504	−	0.0685830i
$421$	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
$423$	−261727.	+	4.53256e6i	−0.0711209	+	1.23166i
$424$			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	$0.112033\pi$
$431$			2.65898e6i			0.689480i	−0.938698	+	0.344740i	$0.887967\pi$
$432$	886171.	−	1.70543e6i	0.228459	−	0.439667i
$433$	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
$435$	626233.	+	955443.i	0.158677	+	0.242093i
$436$	141570.			0.0356661
$437$	2.75448e6	−	2.75448e6i	0.689979	−	0.689979i
$438$	675378.	+	1.77351e6i	0.168214	+	0.441720i
$439$		−	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	$-0.839127\pi$
$443$	−5.61400e6	−	5.61400e6i	−1.35914	−	1.35914i	−0.484156	−	0.874982i	$-0.660873\pi$
$444$	−292621.	+	652560.i	−0.0704446	+	0.157095i
$445$	−511191.	−	2.32605e6i	−0.122372	−	0.556826i
$446$		−	4.34040e6i		−	1.03322i
$447$	6.33173e6	−	2.41122e6i	1.49883	−	0.570779i
$448$	−2.87082e6	+	2.87082e6i	−0.675788	+	0.675788i
$449$	4.10120e6			0.960054			0.480027	−	0.877254i	$-0.340627\pi$
$449$	4.10120e6			0.960054			0.480027	+	0.877254i	$0.340627\pi$
$450$	−1.25012e6	−	3.17612e6i	−0.291019	−	0.739376i
$451$	47964.1			0.0111039
$452$	915988.	−	915988.i	0.210884	−	0.210884i
$453$	3.46836e6	−	1.32080e6i	0.794106	−	0.302408i
$454$			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	$0.121818\pi$
$461$			3.40793e6i			0.746859i	−0.927659	+	0.373430i	$0.878182\pi$
$462$	1.67265e6	+	4.39228e6i	0.364585	+	0.957381i
$463$	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
$465$	145105.	+	221387.i	0.0311208	+	0.0474809i
$466$	3.07500e6			0.655964
$467$	−2.53896e6	+	2.53896e6i	−0.538721	+	0.538721i	−0.923153	−	0.384432i	$-0.874397\pi$
$467$	−2.53896e6	+	2.53896e6i	−0.538721	+	0.538721i	0.384432	+	0.923153i	$0.374397\pi$
$468$	−843712.	−	48719.0i	−0.178065	−	0.0102822i
$469$			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
$477$	−6.70574e6	−	387214.i	−1.34943	−	0.0779212i
$478$	1.41519e6	−	1.41519e6i	0.283299	−	0.283299i
$479$	−8.45014e6			−1.68277			−0.841385	−	0.540436i	$-0.818259\pi$
$479$	−8.45014e6			−1.68277			−0.841385	+	0.540436i	$0.818259\pi$
$480$	3.42866e6	+	713642.i	0.679238	+	0.141377i
$481$	−1.14665e6			−0.225979
$482$	1.95948e6	−	1.95948e6i	0.384171	−	0.384171i
$483$	1.10933e6	+	2.91304e6i	0.216368	+	0.568170i
$484$		−	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	$-0.699355\pi$
$491$		−	8.65624e6i		−	1.62041i	0.586145	−	0.810206i	$-0.300645\pi$
$492$	−14544.6	+	5538.81i	−0.00270888	+	0.00103158i
$493$	−204088.	+	204088.i	−0.0378182	+	0.0378182i
$494$	−3.05572e6			−0.563373
$495$	4.51506e6	−	6.23500e6i	0.828229	−	1.14373i
$496$	154119.			0.0281289
$497$	−6.30208e6	+	6.30208e6i	−1.14444	+	1.14444i
$498$	−2.37009e6	+	902566.i	−0.428244	+	0.163082i
$499$		−	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	0.686562	−	0.727071i	$-0.259119\pi$
$503$	−229863.	−	229863.i	−0.0405088	−	0.0405088i	−0.727071	+	0.686562i	$0.759119\pi$
$504$	−3.76629e6	−	4.22790e6i	−0.660446	−	0.741394i
$505$	−420942.	+	92509.5i	−0.0734504	+	0.0161420i
$506$			4.30324e6i			0.747170i
$507$	1.57759e6	+	4.14266e6i	0.272567	+	0.715747i
$508$	1.27775e6	−	1.27775e6i	0.219678	−	0.219678i
$509$	8.34113e6			1.42702			0.713511	−	0.700644i	$-0.247104\pi$
$509$	8.34113e6			1.42702			0.713511	+	0.700644i	$0.247104\pi$
$510$	721252.	−	472735.i	0.122790	−	0.0804808i
$511$	3.20585e6			0.543113
$512$	3.70187e6	−	3.70187e6i	0.624088	−	0.624088i
$513$	−7.75060e6	−	4.02735e6i	−1.30029	−	0.675657i
$514$		−	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	$0.0421377\pi$
$521$			1.63560e6i			0.263986i	−0.991251	+	0.131993i	$0.957862\pi$
$522$	−82544.6	+	1.42950e6i	−0.0132590	+	0.229619i
$523$	−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
$525$	−5.76567e6	+	64108.1i	−0.912959	+	0.0101511i
$526$	−4.89304e6			−0.771106
$527$	−47289.5	+	47289.5i	−0.00741717	+	0.00741717i
$528$	−1.59511e6	−	4.18867e6i	−0.249003	−	0.653869i
$529$		−	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
$537$	7.00443e6	−	2.66740e6i	1.04818	−	0.399164i
$538$	−6.67491e6	+	6.67491e6i	−0.994237	+	0.994237i
$539$	−1.58490e6			−0.234980
$540$	−649137.	+	2.41209e6i	−0.0957970	+	0.355966i
$541$	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
$543$	2.21972e6	−	845301.i	0.323071	−	0.123030i
$544$			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
$552$	−1.84497e6	−	4.84480e6i	−0.257716	−	0.676749i
$553$	4.76241e6	−	4.76241e6i	0.662238	−	0.662238i
$554$	5.76901e6			0.798595
$555$	−690615.	+	3.31803e6i	−0.0951708	+	0.457244i
$556$	−2.33528e6			−0.320371
$557$	−3.86658e6	+	3.86658e6i	−0.528067	+	0.528067i	−0.919996	−	0.391929i	$-0.871808\pi$
$557$	−3.86658e6	+	3.86658e6i	−0.528067	+	0.528067i	0.391929	+	0.919996i	$0.371808\pi$
$558$	−19126.5	+	331231.i	−0.00260046	+	0.0450345i
$559$		−	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	0.999971	−	0.00766747i	$-0.00244065\pi$
$563$	7.46303e6	+	7.46303e6i	0.992303	+	0.992303i	−0.00766747	+	0.999971i	$0.502441\pi$
$564$	−3.13487e6	−	1.40574e6i	−0.414974	−	0.186083i
$565$	3.30792e6	−	5.17140e6i	0.435947	−	0.681533i
$566$			5.26869e6i			0.691292i
$567$	5.47822e6	−	4.34049e6i	0.715619	−	0.566998i
$568$	1.04813e7	−	1.04813e7i	1.36315	−	1.36315i
$569$	562233.			0.0728008			0.0364004	−	0.999337i	$-0.488411\pi$
$569$	562233.			0.0728008			0.0364004	+	0.999337i	$0.488411\pi$
$570$	−1.84043e6	+	8.84227e6i	−0.237264	+	1.13993i
$571$	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
$573$	674508.	+	1.77122e6i	0.0858223	+	0.225365i
$574$		−	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
$582$	−7.22472e6	+	2.75128e6i	−0.884125	+	0.336688i
$583$	−1.10765e7	+	1.10765e7i	−1.34968	+	1.34968i
$584$	−5.33178e6			−0.646904
$585$	−3.95468e6	+	632723.i	−0.477773	+	0.0764406i
$586$	−1.80683e6			−0.217356
$587$	1.64460e6	−	1.64460e6i	0.196999	−	0.196999i	−0.601713	−	0.798712i	$-0.705515\pi$
$587$	1.64460e6	−	1.64460e6i	0.196999	−	0.196999i	0.798712	+	0.601713i	$0.205515\pi$
$588$	480605.	−	183022.i	0.0573251	−	0.0218303i
$589$		−	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	0.947754	−	0.319003i	$-0.103348\pi$
$593$	5.38412e6	+	5.38412e6i	0.628750	+	0.628750i	−0.319003	+	0.947754i	$0.603348\pi$
$594$	9.20018e6	−	2.90836e6i	1.06987	−	0.338207i
$595$	−312694.	−	1.42284e6i	−0.0362098	−	0.164764i
$596$			5.12705e6i			0.591224i
$597$	−2.98425e6	−	7.83649e6i	−0.342689	−	0.899882i
$598$	1.58306e6	−	1.58306e6i	0.181027	−	0.181027i
$599$	−4.06152e6			−0.462510			−0.231255	−	0.972893i	$-0.574283\pi$
$599$	−4.06152e6			−0.462510			−0.231255	+	0.972893i	$0.574283\pi$
$600$	9.58913e6	−	106621.i	1.08743	−	0.0120911i
$601$	−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
$603$	1.05152e7	+	607186.i	1.17767	+	0.0680030i
$604$			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
$612$	−630049.	−	36381.4i	−0.0679980	−	0.00392646i
$613$	−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
$615$	−61685.7	+	40431.1i	−0.00657653	+	0.00431050i
$616$	−1.32047e7			−1.40210
$617$	9.62794e6	−	9.62794e6i	1.01817	−	1.01817i	0.0183386	−	0.999832i	$-0.494162\pi$
$617$	9.62794e6	−	9.62794e6i	1.01817	−	1.01817i	0.999832	−	0.0183386i	$-0.00583769\pi$
$618$	−505000.	−	1.32610e6i	−0.0531888	−	0.139671i
$619$		−	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
$627$	−1.90361e7	+	7.24924e6i	−1.93379	+	0.736416i
$628$	1.37266e6	−	1.37266e6i	0.138888	−	0.138888i
$629$	−856270.			−0.0862947
$630$	−5.85360e6	−	4.23887e6i	−0.587587	−	0.425499i
$631$	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
$633$	1.05944e7	−	4.03450e6i	1.05091	−	0.400203i
$634$			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	$-0.891289\pi$
$641$		−	6.96826e6i		−	0.669853i	0.942244	−	0.334926i	$-0.108711\pi$
$642$	−3.05742e6	−	8.02861e6i	−0.292764	−	0.768781i
$643$	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
$645$	−5.65124e6	−	1.17625e6i	−0.534865	−	0.111327i
$646$	−2.28189e6			−0.215136
$647$	−3.79202e6	+	3.79202e6i	−0.356131	+	0.356131i	−0.862385	−	0.506254i	$-0.831030\pi$
$647$	−3.79202e6	+	3.79202e6i	−0.356131	+	0.356131i	0.506254	+	0.862385i	$0.331030\pi$
$648$	−9.11107e6	+	7.21886e6i	−0.852377	+	0.675353i
$649$		−	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	$-0.963214\pi$
$653$	−1.20802e7	−	1.20802e7i	−1.10864	−	1.10864i	−0.115310	−	0.993330i	$-0.536786\pi$
$654$	767296.	+	344071.i	0.0701486	+	0.0314560i
$655$	1.24881e7	−	2.74449e6i	1.13735	−	0.249953i
$656$			42942.7i			0.00389610i
$657$	379409.	−	6.57057e6i	0.0342921	−	0.593867i
$658$	7.02886e6	−	7.02886e6i	0.632878	−	0.632878i
$659$	2.17065e7			1.94705			0.973524	−	0.228585i	$-0.0734098\pi$
$659$	2.17065e7			1.94705			0.973524	+	0.228585i	$0.0734098\pi$
$660$	3.19336e6	+	4.87210e6i	0.285356	+	0.435368i
$661$	−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
$663$	−360105.	−	945615.i	−0.0318159	−	0.0835469i
$664$		−	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
$672$	6.92988e6	−	2.63900e6i	0.591974	−	0.225433i
$673$	−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
$675$	−550968.	+	1.18247e7i	−0.0465444	+	0.998916i
$676$	−3.35448e6			−0.282331
$677$	−4.28005e6	+	4.28005e6i	−0.358903	+	0.358903i	−0.863408	−	0.504505i	$-0.831675\pi$
$677$	−4.28005e6	+	4.28005e6i	−0.358903	+	0.358903i	0.504505	+	0.863408i	$0.331675\pi$
$678$	7.19078e6	−	2.73836e6i	0.600761	−	0.228779i
$679$			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	0.582335	−	0.812949i	$-0.302139\pi$
$683$	−2.81149e6	−	2.81149e6i	−0.230614	−	0.230614i	−0.812949	+	0.582335i	$0.802139\pi$
$684$	4.93536e6	−	4.39651e6i	0.403347	−	0.359308i
$685$	−1.19865e6	−	766721.i	−0.0976032	−	0.0624325i
$686$			1.04299e7i			0.846191i
$687$	5.65498e6	+	1.48497e7i	0.457129	+	1.20040i
$688$	−2.37649e6	+	2.37649e6i	−0.191410	+	0.191410i
$689$	8.14952e6			0.654009
$690$	−3.62739e6	−	5.53431e6i	−0.290049	−	0.442528i
$691$	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
$693$	939647.	−	1.62727e7i	0.0743244	−	1.28714i
$694$			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	$-0.809115\pi$
$701$		−	1.46858e7i		−	1.12876i	0.825515	−	0.564381i	$-0.190885\pi$
$702$	−4.45443e6	−	2.31460e6i	−0.341153	−	0.177269i
$703$	6.34125e6	−	6.34125e6i	0.483934	−	0.483934i
$704$	1.94379e7			1.47815
$705$	−1.59396e7	−	3.31768e6i	−1.20783	−	0.251398i
$706$	4.76699e6			0.359942
$707$	−645280.	+	645280.i	−0.0485512	+	0.0485512i
$708$	136142.	+	357500.i	0.0102072	+	0.0268036i
$709$		−	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
$717$	−6.48649e6	+	2.47015e6i	−0.471207	+	0.179443i
$718$	−1.28384e6	+	1.28384e6i	−0.0929391	+	0.0929391i
$719$	−1.26151e7			−0.910058			−0.455029	−	0.890477i	$-0.650371\pi$
$719$	−1.26151e7			−0.910058			−0.455029	+	0.890477i	$0.650371\pi$
$720$	5.58225e6	+	4.04237e6i	0.401308	+	0.290606i
$721$	−2.39711e6			−0.171731
$722$	9.02898e6	−	9.02898e6i	0.644608	−	0.644608i
$723$	−8.98125e6	+	3.42020e6i	−0.638985	+	0.243335i
$724$			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
$732$	−3.32489e6	−	8.73097e6i	−0.229350	−	0.602261i
$733$	−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
$735$	2.03831e6	−	1.33599e6i	0.139172	−	0.0912187i
$736$	6.78941e6			0.461995
$737$	1.73689e7	−	1.73689e7i	1.17788	−	1.17788i
$738$	−92291.9	−	5329.28i	−0.00623767	−	0.000360186i
$739$			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	0.678798	−	0.734325i	$-0.262501\pi$
$743$	−835548.	−	835548.i	−0.0555264	−	0.0555264i	−0.734325	+	0.678798i	$0.762501\pi$
$744$	−850551.	−	381404.i	−0.0563337	−	0.0252611i
$745$	5.21522e6	+	2.37306e7i	0.344256	+	1.56646i
$746$		−	1.55294e6i		−	0.102167i
$747$	8.78081e6	+	507037.i	0.575749	+	0.0332459i
$748$	−1.04071e6	+	1.04071e6i	−0.0680104	+	0.0680104i
$749$	−1.45128e7			−0.945248
$750$	1.19251e7	−	2.76010e6i	0.774123	−	0.179172i
$751$	−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
$753$	5.96660e6	+	1.56680e7i	0.383477	+	1.00699i
$754$		−	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	$0.0326577\pi$
$761$			3.27238e6i			0.204834i	−0.994742	+	0.102417i	$0.967342\pi$
$762$	1.00307e7	−	3.81985e6i	0.625813	−	0.238319i
$763$	1.00447e6	−	1.00447e6i	0.0624635	−	0.0624635i
$764$	−1.43423e6			−0.0888965
$765$	−2.95319e6	+	472492.i	−0.182448	+	0.0291905i
$766$	−4.44758e6			−0.273875
$767$	−433702.	+	433702.i	−0.0266197	+	0.0266197i
$768$	−1.43155e7	+	5.45154e6i	−0.875794	+	0.333516i
$769$		−	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	0.907747	−	0.419518i	$-0.137801\pi$
$773$	8.11096e6	+	8.11096e6i	0.488229	+	0.488229i	−0.419518	+	0.907747i	$0.637801\pi$
$774$	−4.81259e6	−	5.40244e6i	−0.288753	−	0.324144i
$775$	−861781.	+	398006.i	−0.0515398	+	0.0238032i
$776$		−	2.17200e7i		−	1.29481i
$777$	2.55385e6	+	6.70628e6i	0.151755	+	0.398501i
$778$	3.44195e6	−	3.44195e6i	0.203871	−	0.203871i
$779$	195160.			0.0115225
$780$	617569.	−	2.96708e6i	0.0363453	−	0.174620i
$781$	4.26706e7			2.50323
$782$	1.18216e6	−	1.18216e6i	0.0691289	−	0.0691289i
$783$	2.28968e6	−	4.40647e6i	0.133466	−	0.256854i
$784$		−	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
$792$	−1.56277e6	+	2.70638e7i	−0.0885281	+	1.53312i
$793$	1.05920e7	−	1.05920e7i	0.598129	−	0.598129i
$794$	7.90986e6			0.445264
$795$	4.90838e6	−	2.35821e7i	0.275436	−	1.32332i
$796$	6.34551e6			0.354964
$797$	−2.40749e7	+	2.40749e7i	−1.34252	+	1.34252i	−0.448968	+	0.893548i	$0.648208\pi$
$797$	−2.40749e7	+	2.40749e7i	−1.34252	+	1.34252i	−0.893548	+	0.448968i	$0.851792\pi$
$798$	6.80580e6	+	1.78716e7i	0.378331	+	0.993476i
$799$		−	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
$807$	3.05943e7	−	1.16508e7i	1.65370	−	0.629754i
$808$	1.07319e6	−	1.07319e6i	0.0578295	−	0.0578295i
$809$	−2.33910e6			−0.125654			−0.0628271	−	0.998024i	$-0.520012\pi$
$809$	−2.33910e6			−0.125654			−0.0628271	+	0.998024i	$0.520012\pi$
$810$	−9.38058e6	+	1.14956e7i	−0.502362	+	0.615631i
$811$	−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
$813$	−1.43079e7	+	5.44868e6i	−0.759190	+	0.289111i
$814$			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	$-0.958112\pi$
$821$		−	5.06844e6i		−	0.262432i	0.991354	−	0.131216i	$-0.0418881\pi$
$822$	−634707.	−	1.66671e6i	−0.0327638	−	0.0860358i
$823$	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
$825$	1.97363e7	+	1.93023e7i	1.00956	+	0.987356i
$826$	−1.10682e6			−0.0564453
$827$	2.01367e7	−	2.01367e7i	1.02382	−	1.02382i	0.0241111	−	0.999709i	$-0.492324\pi$
$827$	2.01367e7	−	2.01367e7i	1.02382	−	1.02382i	0.999709	−	0.0241111i	$-0.00767554\pi$
$828$	−279162.	+	4.83450e6i	−0.0141508	+	0.245062i
$829$			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
$837$	530544.	−	1.02103e6i	0.0261763	−	0.0503760i
$838$	−851999.	+	851999.i	−0.0419111	+	0.0419111i
$839$	2.17575e7			1.06710			0.533548	−	0.845769i	$-0.320858\pi$
$839$	2.17575e7			1.06710			0.533548	+	0.845769i	$0.320858\pi$
$840$	1.69823e7	−	1.11309e7i	0.830423	−	0.544290i
$841$	−1.87926e7			−0.916213
$842$	−1.80865e6	+	1.80865e6i	−0.0879171	+	0.0879171i
$843$	−1.35150e7	−	3.54897e7i	−0.655011	−	1.72002i
$844$			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
$852$	−1.29394e7	+	4.92752e6i	−0.610682	+	0.232557i
$853$	−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
$855$	1.83712e7	−	2.53695e7i	0.859455	−	1.18685i
$856$	2.41368e7			1.12589
$857$	−8.70826e6	+	8.70826e6i	−0.405023	+	0.405023i	−0.879999	−	0.474976i	$-0.842457\pi$
$857$	−8.70826e6	+	8.70826e6i	−0.405023	+	0.405023i	0.474976	+	0.879999i	$0.342457\pi$
$858$	−1.09404e7	+	4.16629e6i	−0.507360	+	0.193211i
$859$			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	$0.00472273\pi$
$863$	2.22012e7	+	2.22012e7i	1.01473	+	1.01473i	0.0148363	+	0.999890i	$0.495277\pi$
$864$	−4.58865e6	−	1.45155e7i	−0.209122	−	0.661528i
$865$	6.51129e6	−	1.01794e7i	0.295888	−	0.462572i
$866$			2.39620e7i			1.08575i
$867$	7.60799e6	+	1.99782e7i	0.343734	+	0.902626i
$868$	−299903.	+	299903.i	−0.0135108	+	0.0135108i
$869$	−3.22457e7			−1.44851
$870$	−5.02712e6	−	1.04635e6i	−0.225175	−	0.0468681i
$871$	−1.27791e7			−0.570764
$872$	−1.67058e6	+	1.67058e6i	−0.0744006	+	0.0744006i
$873$	2.67665e7	+	1.54560e6i	1.18865	+	0.0686373i
$874$			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	$0.0596355\pi$
$881$			8.58185e6i			0.372513i	−0.982501	+	0.186256i	$0.940364\pi$
$882$	3.04965e6	+	176098.i	0.132001	+	0.00762225i
$883$	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
$885$	993780.	+	1.51621e6i	0.0426513	+	0.0650730i
$886$	3.56865e7			1.52728
$887$	−2.07797e7	+	2.07797e7i	−0.886809	+	0.886809i	−0.994215	−	0.107406i	$-0.965745\pi$
$887$	−2.07797e7	+	2.07797e7i	−0.886809	+	0.886809i	0.107406	+	0.994215i	$0.465745\pi$
$888$	−4.24742e6	−	1.11535e7i	−0.180756	−	0.474656i
$889$		−	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
$897$	−7.25590e6	+	2.76316e6i	−0.301100	+	0.114663i
$898$	−1.30351e7	+	1.30351e7i	−0.539414	+	0.539414i
$899$	398212.			0.0164329
$900$	−8.21382e6	−	3.57409e6i	−0.338017	−	0.147082i
$901$	6.08573e6			0.249747
$902$	−152447.	+	152447.i	−0.00623881	+	0.00623881i
$903$	−1.14221e7	+	4.34970e6i	−0.466150	+	0.177517i
$904$			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	$0.136321\pi$
$911$			2.08056e7i			0.830586i	−0.909688	+	0.415293i	$0.863679\pi$
$912$	−6.49031e6	−	1.70432e7i	−0.258391	−	0.678522i
$913$	1.45041e7	−	1.45041e7i	0.575854	−	0.575854i
$914$	3.88547e7			1.53843
$915$	−2.42704e7	−	3.70293e7i	−0.958349	−	1.46215i
$916$	−1.20244e7			−0.473504
$917$	1.91436e7	−	1.91436e7i	0.751797	−	0.751797i
$918$	−3.32639e6	−	1.72845e6i	−0.130277	−	0.0676940i
$919$			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
$927$	−283695.	+	4.91301e6i	−0.0108431	+	0.187779i
$928$	3.72542e6	−	3.72542e6i	0.142005	−	0.142005i
$929$	−3.48724e7			−1.32569			−0.662846	−	0.748756i	$-0.730651\pi$
$929$	−3.48724e7			−1.32569			−0.662846	+	0.748756i	$0.730651\pi$
$930$	−1.16484e6	−	242450.i	−0.0441630	−	0.00919209i
$931$	−6.44879e6			−0.243839
$932$	5.70631e6	−	5.70631e6i	0.215187	−	0.215187i
$933$	2.00276e6	+	5.25913e6i	0.0753224	+	0.197792i
$934$		−	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	$-0.996788\pi$
$941$		−	548205.i		−	0.0201822i	0.999949	−	0.0100911i	$-0.00321215\pi$
$942$	1.07758e7	−	4.10359e6i	0.395660	−	0.150674i
$943$	−101105.	+	101105.i	−0.00370250	+	0.00370250i
$944$	1.05551e6			0.0385509
$945$	1.25085e7	+	2.17201e7i	0.455645	+	0.791192i
$946$	−1.68731e7			−0.613009
$947$	8.77113e6	−	8.77113e6i	0.317820	−	0.317820i	−0.530110	−	0.847929i	$-0.677849\pi$
$947$	8.77113e6	−	8.77113e6i	0.317820	−	0.317820i	0.847929	+	0.530110i	$0.177849\pi$
$948$	9.77816e6	−	3.72367e6i	0.353375	−	0.134571i
$949$			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	$-0.918142\pi$
$953$	−3.42460e7	−	3.42460e7i	−1.22145	−	1.22145i	−0.254338	−	0.967115i	$-0.581858\pi$
$954$	2.25439e7	−	2.00825e7i	0.801970	−	0.714408i
$955$	−6.63833e6	+	1.45889e6i	−0.235532	+	0.0517624i
$956$		−	5.25237e6i		−	0.185870i
$957$	−4.12143e6	−	1.08226e7i	−0.145468	−	0.381991i
$958$	2.68575e7	−	2.68575e7i	0.945478	−	0.945478i
$959$	−3.01279e6			−0.105785
$960$	−2.49988e7	+	1.63851e7i	−0.875468	+	0.573814i
$961$	−2.85369e7			−0.996777
$962$	3.64445e6	−	3.64445e6i	0.126968	−	0.126968i
$963$	−1.71757e6	+	2.97448e7i	−0.0596829	+	1.03358i
$964$		−	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	$-0.957249\pi$
$971$		−	7.86809e6i		−	0.267807i	0.990994	−	0.133903i	$-0.0427512\pi$
$972$	1.05247e7	−	2.67058e6i	0.357308	−	0.0906649i
$973$	−1.65694e7	+	1.65694e7i	−0.561079	+	0.561079i
$974$	−1.89434e7			−0.639824
$975$	−159683.	−	1.43613e7i	−0.00537956	−	0.483820i
$976$	−2.57781e7			−0.866215
$977$	2.25244e7	−	2.25244e7i	0.754947	−	0.754947i	−0.220451	−	0.975398i	$-0.570753\pi$
$977$	2.25244e7	−	2.25244e7i	0.754947	−	0.754947i	0.975398	+	0.220451i	$0.0707530\pi$
$978$	3.14050e6	+	8.24677e6i	0.104991	+	0.275700i
$979$			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	0.406680	−	0.913571i	$-0.366686\pi$
$983$	−1.53567e7	−	1.53567e7i	−0.506891	−	0.506891i	−0.913571	+	0.406680i	$0.866686\pi$
$984$	106272.	−	236992.i	0.00349889	−	0.00780272i
$985$	−9.61691e6	−	6.15152e6i	−0.315824	−	0.202019i
$986$		−	1.29733e6i		−	0.0424969i
$987$	−3.22166e7	+	1.22686e7i	−1.05266	+	0.400868i
$988$	−5.67053e6	+	5.67053e6i	−0.184813	+	0.184813i
$989$	−1.11905e7			−0.363798
$990$	5.46657e6	+	3.41674e7i	0.177267	+	1.10796i
$991$	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
$993$	1.88394e7	−	7.17434e6i	0.606310	−	0.230892i
$994$		−	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.2.3	✓	16
3.2	odd	2	inner	15.6.e.a.2.6	yes	16
5.2	odd	4		75.6.e.e.68.3		16
5.3	odd	4	inner	15.6.e.a.8.6	yes	16
5.4	even	2		75.6.e.e.32.6		16
15.2	even	4		75.6.e.e.68.6		16
15.8	even	4	inner	15.6.e.a.8.3	yes	16
15.14	odd	2		75.6.e.e.32.3		16

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

\(f(q)\)	\(=\)	\(q+(-3.17835 + 3.17835i) q^{2} +(14.5679 - 5.54767i) q^{3} +11.7962i q^{4} +(11.9990 + 54.5987i) q^{5} +(-28.6694 + 63.9343i) q^{6} +(83.6967 + 83.6967i) q^{7} +(-139.200 - 139.200i) q^{8} +(181.447 - 161.636i) q^{9} +O(q^{10})\)	\(q+(-3.17835 + 3.17835i) q^{2} +(14.5679 - 5.54767i) 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} +(65.4414 + 171.846i) q^{12} +(-208.475 + 208.475i) q^{13} -532.035 q^{14} +(477.697 + 728.822i) q^{15} +507.372 q^{16} +(-155.680 + 155.680i) q^{17} +(-62.9658 + 1090.44i) 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} +(1746.59 - 3361.30i) q^{27} +(-987.303 + 987.303i) q^{28} +1310.94 q^{29} +(-3834.74 - 798.162i) q^{30} +303.760 q^{31} +(2841.78 - 2841.78i) q^{32} +(-3143.87 - 8255.62i) 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} +(-7750.62 + 2951.55i) q^{42} +(-4683.92 + 4683.92i) q^{43} +6684.90 q^{44} +(11002.3 + 7967.28i) q^{45} -7593.51 q^{46} +(-13211.3 + 13211.3i) q^{47} +(7391.33 - 2814.73i) 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} +(-12792.0 - 33591.1i) q^{57} +(-4166.63 + 4166.63i) q^{58} +2080.36 q^{59} +(-8597.32 + 5635.00i) q^{60} -50807.1 q^{61} +(-965.455 + 965.455i) q^{62} +(28714.9 + 1658.10i) 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} +(-47756.9 - 2757.66i) q^{72} +(19151.6 - 19151.6i) q^{73} -17481.5 q^{74} +(-34060.8 + 34826.8i) q^{75} +27200.1 q^{76} +(47430.9 - 47430.9i) q^{77} +(-7351.84 - 19305.5i) 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} +(19097.7 - 7272.68i) q^{87} +(-78884.4 + 78884.4i) q^{88} -42602.7 q^{89} +(-60291.9 + 9646.33i) q^{90} -34897.3 q^{91} +(-14091.4 + 14091.4i) q^{92} +(4425.14 - 1685.16i) 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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