LMFDB - Embedded newform 147.6.e.p.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not 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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 $ x^12 - 2x^11 + 63x^10 - 126x^9 + 2784x^8 - 5290x^7 + 62015x^6 - 99530x^5 + 973971x^4 - 1176024x^3 + 5644794x^2 + 4339328*x + 5466244
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$2.79840 - 4.84697i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.p.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.00445 - 8.66795i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-34.0890 + 59.0438i) q^{4} +(-35.1756 - 60.9260i) q^{5} +90.0800 q^{6} +362.101 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-5.00445 - 8.66795i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-34.0890 + 59.0438i) q^{4} +(-35.1756 - 60.9260i) q^{5} +90.0800 q^{6} +362.101 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-352.069 + 609.801i) q^{10} +(365.698 - 633.408i) q^{11} +(-306.801 - 531.394i) q^{12} +899.645 q^{13} +633.161 q^{15} +(-721.267 - 1249.27i) q^{16} +(696.195 - 1205.84i) q^{17} +(-405.360 + 702.104i) q^{18} +(95.0989 + 164.716i) q^{19} +4796.40 q^{20} -7320.46 q^{22} +(-21.4885 - 37.2192i) q^{23} +(-1629.45 + 2822.30i) q^{24} +(-912.148 + 1579.89i) q^{25} +(-4502.22 - 7798.08i) q^{26} +729.000 q^{27} -7746.59 q^{29} +(-3168.62 - 5488.21i) q^{30} +(-589.611 + 1021.24i) q^{31} +(-1425.47 + 2468.99i) q^{32} +(3291.28 + 5700.67i) q^{33} -13936.3 q^{34} +5522.41 q^{36} +(-4644.34 - 8044.23i) q^{37} +(951.835 - 1648.63i) q^{38} +(-4048.40 + 7012.04i) q^{39} +(-12737.1 - 22061.3i) q^{40} +13453.4 q^{41} +6033.68 q^{43} +(24932.5 + 43184.4i) q^{44} +(-2849.22 + 4935.00i) q^{45} +(-215.076 + 372.523i) q^{46} +(1622.47 + 2810.20i) q^{47} +12982.8 q^{48} +18259.2 q^{50} +(6265.75 + 10852.6i) q^{51} +(-30668.0 + 53118.5i) q^{52} +(-12837.9 + 22235.9i) q^{53} +(-3648.24 - 6318.94i) q^{54} -51454.6 q^{55} -1711.78 q^{57} +(38767.4 + 67147.1i) q^{58} +(13225.2 - 22906.8i) q^{59} +(-21583.8 + 37384.2i) q^{60} +(3216.38 + 5570.94i) q^{61} +11802.7 q^{62} -17626.3 q^{64} +(-31645.6 - 54811.7i) q^{65} +(32942.1 - 57057.4i) q^{66} +(11907.8 - 20625.0i) q^{67} +(47465.1 + 82212.0i) q^{68} +386.793 q^{69} -44680.7 q^{71} +(-14665.1 - 25400.7i) q^{72} +(19800.6 - 34295.7i) q^{73} +(-46484.7 + 80513.8i) q^{74} +(-8209.33 - 14219.0i) q^{75} -12967.3 q^{76} +81040.0 q^{78} +(-11561.5 - 20025.1i) q^{79} +(-50742.0 + 87887.7i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-67326.8 - 116613. i) q^{82} -17267.2 q^{83} -97956.3 q^{85} +(-30195.2 - 52299.6i) q^{86} +(34859.7 - 60378.7i) q^{87} +(132420. - 229357. i) q^{88} +(-24964.9 - 43240.4i) q^{89} +57035.2 q^{90} +2930.08 q^{92} +(-5306.50 - 9191.13i) q^{93} +(16239.1 - 28127.0i) q^{94} +(6690.33 - 11588.0i) q^{95} +(-12829.2 - 22220.9i) q^{96} -16865.0 q^{97} -59243.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−5.00445	−	8.66795i	−0.884669	−	1.53229i	−0.846092	−	0.533037i	$-0.821051\pi$
$2$	−5.00445	−	8.66795i	−0.884669	−	1.53229i	−0.0385772	−	0.999256i	$-0.512283\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	−34.0890	+	59.0438i	−1.06528	+	1.84512i
$5$	−35.1756	−	60.9260i	−0.629241	−	1.08988i	−0.987704	−	0.156333i	$-0.950033\pi$
$5$	−35.1756	−	60.9260i	−0.629241	−	1.08988i	0.358464	−	0.933544i	$-0.383301\pi$
$6$	90.0800			1.02153
$7$		0			0
$7$		0			0
$8$	362.101			2.00034
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	−352.069	+	609.801i	−1.11334	+	1.92836i
$11$	365.698	−	633.408i	0.911257	−	1.57834i	0.0989661	−	0.995091i	$-0.468446\pi$
$11$	365.698	−	633.408i	0.911257	−	1.57834i	0.812291	−	0.583253i	$-0.198220\pi$
$12$	−306.801	−	531.394i	−0.615040	−	1.06528i
$13$	899.645			1.47643			0.738215	−	0.674566i	$-0.235669\pi$
$13$	899.645			1.47643			0.738215	+	0.674566i	$0.235669\pi$
$14$		0			0
$15$	633.161			0.726584
$16$	−721.267	−	1249.27i	−0.704362	−	1.21999i
$17$	696.195	−	1205.84i	0.584263	−	1.01197i	−0.410704	−	0.911769i	$-0.634717\pi$
$17$	696.195	−	1205.84i	0.584263	−	1.01197i	0.994967	−	0.100204i	$-0.0319497\pi$
$18$	−405.360	+	702.104i	−0.294890	+	0.510764i
$19$	95.0989	+	164.716i	0.0604354	+	0.104677i	0.894660	−	0.446747i	$-0.147418\pi$
$19$	95.0989	+	164.716i	0.0604354	+	0.104677i	−0.834225	+	0.551425i	$0.814084\pi$
$20$	4796.40			2.68127
$21$		0			0
$22$	−7320.46			−3.22464
$23$	−21.4885	−	37.2192i	−0.00847006	−	0.0146706i	0.861759	−	0.507317i	$-0.169363\pi$
$23$	−21.4885	−	37.2192i	−0.00847006	−	0.0146706i	−0.870229	+	0.492647i	$0.836029\pi$
$24$	−1629.45	+	2822.30i	−0.577449	+	1.00017i
$25$	−912.148	+	1579.89i	−0.291887	+	0.505564i
$26$	−4502.22	−	7798.08i	−1.30615	−	2.26232i
$27$	729.000			0.192450
$28$		0			0
$29$	−7746.59			−1.71047			−0.855236	−	0.518239i	$-0.826588\pi$
$29$	−7746.59			−1.71047			−0.855236	+	0.518239i	$0.826588\pi$
$30$	−3168.62	−	5488.21i	−0.642787	−	1.11334i
$31$	−589.611	+	1021.24i	−0.110195	+	0.190863i	−0.915849	−	0.401523i	$-0.868481\pi$
$31$	−589.611	+	1021.24i	−0.110195	+	0.190863i	0.805654	+	0.592387i	$0.201814\pi$
$32$	−1425.47	+	2468.99i	−0.246084	+	0.426230i
$33$	3291.28	+	5700.67i	0.526114	+	0.911257i
$34$	−13936.3			−2.06752
$35$		0			0
$36$	5522.41			0.710187
$37$	−4644.34	−	8044.23i	−0.557724	−	0.966007i	−0.997686	−	0.0679904i	$-0.978341\pi$
$37$	−4644.34	−	8044.23i	−0.557724	−	0.966007i	0.439962	−	0.898017i	$-0.354992\pi$
$38$	951.835	−	1648.63i	0.106931	−	0.185209i
$39$	−4048.40	+	7012.04i	−0.426209	+	0.738215i
$40$	−12737.1	−	22061.3i	−1.25870	−	2.18013i
$41$	13453.4			1.24989			0.624945	−	0.780668i	$-0.285121\pi$
$41$	13453.4			1.24989			0.624945	+	0.780668i	$0.285121\pi$
$42$		0			0
$43$	6033.68			0.497635			0.248818	−	0.968550i	$-0.419958\pi$
$43$	6033.68			0.497635			0.248818	+	0.968550i	$0.419958\pi$
$44$	24932.5	+	43184.4i	1.94149	+	3.36275i
$45$	−2849.22	+	4935.00i	−0.209747	+	0.363292i
$46$	−215.076	+	372.523i	−0.0149864	+	0.0259572i
$47$	1622.47	+	2810.20i	0.107135	+	0.185564i	0.914609	−	0.404340i	$-0.132499\pi$
$47$	1622.47	+	2810.20i	0.107135	+	0.185564i	−0.807473	+	0.589904i	$0.799166\pi$
$48$	12982.8			0.813327
$49$		0			0
$50$	18259.2			1.03289
$51$	6265.75	+	10852.6i	0.337324	+	0.584263i
$52$	−30668.0	+	53118.5i	−1.57281	+	2.72419i
$53$	−12837.9	+	22235.9i	−0.627775	+	1.08734i	0.360222	+	0.932867i	$0.382701\pi$
$53$	−12837.9	+	22235.9i	−0.627775	+	1.08734i	−0.987997	+	0.154472i	$0.950632\pi$
$54$	−3648.24	−	6318.94i	−0.170255	−	0.294890i
$55$	−51454.6			−2.29360
$56$		0			0
$57$	−1711.78			−0.0697848
$58$	38767.4	+	67147.1i	1.51320	+	2.62094i
$59$	13225.2	−	22906.8i	0.494622	−	0.856711i	−0.505359	−	0.862909i	$-0.668640\pi$
$59$	13225.2	−	22906.8i	0.494622	−	0.856711i	0.999981	+	0.00619873i	$0.00197313\pi$
$60$	−21583.8	+	37384.2i	−0.774016	+	1.34063i
$61$	3216.38	+	5570.94i	0.110673	+	0.191692i	0.916042	−	0.401082i	$-0.131366\pi$
$61$	3216.38	+	5570.94i	0.110673	+	0.191692i	−0.805369	+	0.592774i	$0.798033\pi$
$62$	11802.7			0.389944
$63$		0			0
$64$	−17626.3			−0.537913
$65$	−31645.6	−	54811.7i	−0.929029	−	1.60913i
$66$	32942.1	−	57057.4i	0.930875	−	1.61232i
$67$	11907.8	−	20625.0i	0.324075	−	0.561315i	−0.657250	−	0.753673i	$-0.728280\pi$
$67$	11907.8	−	20625.0i	0.324075	−	0.561315i	0.981325	+	0.192358i	$0.0616136\pi$
$68$	47465.1	+	82212.0i	1.24481	+	2.15607i
$69$	386.793			0.00978039
$70$		0			0
$71$	−44680.7			−1.05190			−0.525949	−	0.850516i	$-0.676290\pi$
$71$	−44680.7			−1.05190			−0.525949	+	0.850516i	$0.676290\pi$
$72$	−14665.1	−	25400.7i	−0.333390	−	0.577449i
$73$	19800.6	−	34295.7i	0.434882	−	0.753238i	−0.562404	−	0.826863i	$-0.690123\pi$
$73$	19800.6	−	34295.7i	0.434882	−	0.753238i	0.997286	+	0.0736245i	$0.0234566\pi$
$74$	−46484.7	+	80513.8i	−0.986803	+	1.70919i
$75$	−8209.33	−	14219.0i	−0.168521	−	0.291887i
$76$	−12967.3			−0.257523
$77$		0			0
$78$	81040.0			1.50821
$79$	−11561.5	−	20025.1i	−0.208423	−	0.360999i	0.742795	−	0.669519i	$-0.233500\pi$
$79$	−11561.5	−	20025.1i	−0.208423	−	0.360999i	−0.951218	+	0.308520i	$0.900166\pi$
$80$	−50742.0	+	87887.7i	−0.886426	+	1.53534i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−67326.8	−	116613.i	−1.10574	−	1.91520i
$83$	−17267.2			−0.275122			−0.137561	−	0.990493i	$-0.543926\pi$
$83$	−17267.2			−0.275122			−0.137561	+	0.990493i	$0.543926\pi$
$84$		0			0
$85$	−97956.3			−1.47057
$86$	−30195.2	−	52299.6i	−0.440242	−	0.762522i
$87$	34859.7	−	60378.7i	0.493771	−	0.855236i
$88$	132420.	−	229357.i	1.82283	−	3.15723i
$89$	−24964.9	−	43240.4i	−0.334083	−	0.578649i	0.649225	−	0.760596i	$-0.275093\pi$
$89$	−24964.9	−	43240.4i	−0.334083	−	0.578649i	−0.983308	+	0.181947i	$0.941760\pi$
$90$	57035.2			0.742226
$91$		0			0
$92$	2930.08			0.0360920
$93$	−5306.50	−	9191.13i	−0.0636211	−	0.110195i
$94$	16239.1	−	28127.0i	0.189558	−	0.328325i
$95$	6690.33	−	11588.0i	0.0760568	−	0.131734i
$96$	−12829.2	−	22220.9i	−0.142077	−	0.246084i
$97$	−16865.0			−0.181994			−0.0909970	−	0.995851i	$-0.529005\pi$
$97$	−16865.0			−0.181994			−0.0909970	+	0.995851i	$0.529005\pi$
$98$		0			0
$99$	−59243.1			−0.607505
$100$	−62188.3	−	107713.i	−0.621883	−	1.07713i
$101$	−52724.4	+	91321.3i	−0.514290	+	0.890776i	0.485573	+	0.874196i	$0.338611\pi$
$101$	−52724.4	+	91321.3i	−0.514290	+	0.890776i	−0.999863	+	0.0165797i	$0.994722\pi$
$102$	62713.2	−	108623.i	0.596841	−	1.03376i
$103$	10177.9	+	17628.6i	0.0945290	+	0.163729i	0.909412	−	0.415897i	$-0.136532\pi$
$103$	10177.9	+	17628.6i	0.0945290	+	0.163729i	−0.814883	+	0.579626i	$0.803199\pi$
$104$	325762.			2.95337
$105$		0			0
$106$	256986.			2.22149
$107$	1887.72	+	3269.62i	0.0159396	+	0.0276082i	0.873885	−	0.486132i	$-0.161593\pi$
$107$	1887.72	+	3269.62i	0.0159396	+	0.0276082i	−0.857946	+	0.513741i	$0.828259\pi$
$108$	−24850.8	+	43042.9i	−0.205013	+	0.355093i
$109$	−4268.49	+	7393.24i	−0.0344118	+	0.0596031i	−0.882718	−	0.469902i	$-0.844289\pi$
$109$	−4268.49	+	7393.24i	−0.0344118	+	0.0596031i	0.848307	+	0.529505i	$0.177622\pi$
$110$	257502.	+	446006.i	2.02908	+	3.51446i
$111$	83598.1			0.644005
$112$		0			0
$113$	−100869.			−0.743125			−0.371562	−	0.928408i	$-0.621178\pi$
$113$	−100869.			−0.743125			−0.371562	+	0.928408i	$0.621178\pi$
$114$	8566.51	+	14837.6i	0.0617365	+	0.106931i
$115$	−1511.74	+	2618.42i	−0.0106594	+	0.0184626i
$116$	264073.	−	457388.i	1.82213	−	3.15602i
$117$	−36435.6	−	63108.3i	−0.246072	−	0.426209i
$118$	−264740.			−1.75031
$119$		0			0
$120$	229268.			1.45342
$121$	−186945.	−	323797.i	−1.16078	−	2.01053i
$122$	32192.4	−	55758.9i	0.195819	−	0.339168i
$123$	−60540.3	+	104859.i	−0.360812	+	0.624945i
$124$	−40198.5	−	69625.8i	−0.234777	−	0.406646i
$125$	−91506.2			−0.523812
$126$		0			0
$127$	−185451.			−1.02028			−0.510142	−	0.860090i	$-0.670407\pi$
$127$	−185451.			−1.02028			−0.510142	+	0.860090i	$0.670407\pi$
$128$	133825.	+	231792.i	0.721959	+	1.25047i
$129$	−27151.5	+	47027.9i	−0.143655	+	0.248818i
$130$	−316737.	+	548605.i	−1.64377	+	2.84709i
$131$	−62023.0	−	107427.i	−0.315773	−	0.546934i	0.663829	−	0.747885i	$-0.268930\pi$
$131$	−62023.0	−	107427.i	−0.315773	−	0.546934i	−0.979601	+	0.200950i	$0.935597\pi$
$132$	−448785.			−2.24184
$133$		0			0
$134$	−238368.			−1.14680
$135$	−25643.0	−	44415.0i	−0.121097	−	0.209747i
$136$	252093.	−	436637.i	1.16873	−	2.02429i
$137$	−49760.2	+	86187.3i	−0.226507	+	0.392321i	−0.956770	−	0.290844i	$-0.906064\pi$
$137$	−49760.2	+	86187.3i	−0.226507	+	0.392321i	0.730264	+	0.683165i	$0.239397\pi$
$138$	−1935.69	−	3352.71i	−0.00865241	−	0.0149864i
$139$	254481.			1.11717			0.558583	−	0.829449i	$-0.311345\pi$
$139$	254481.			1.11717			0.558583	+	0.829449i	$0.311345\pi$
$140$		0			0
$141$	−29204.5			−0.123709
$142$	223602.	+	387290.i	0.930582	+	1.61182i
$143$	328998.	−	569842.i	1.34541	−	2.33031i
$144$	−58422.6	+	101191.i	−0.234787	+	0.406664i
$145$	272491.	+	471969.i	1.07630	+	1.86420i
$146$	−396365.			−1.53891
$147$		0			0
$148$	633283.			2.37653
$149$	213630.	+	370018.i	0.788309	+	1.36539i	0.927002	+	0.375056i	$0.122377\pi$
$149$	213630.	+	370018.i	0.788309	+	1.36539i	−0.138693	+	0.990335i	$0.544290\pi$
$150$	−82166.3	+	142316.i	−0.298171	+	0.516447i
$151$	75235.8	−	130312.i	0.268523	−	0.465096i	−0.699957	−	0.714185i	$-0.746798\pi$
$151$	75235.8	−	130312.i	0.268523	−	0.465096i	0.968481	+	0.249089i	$0.0801310\pi$
$152$	34435.4	+	59643.8i	0.120892	+	0.209390i
$153$	−112784.			−0.389509
$154$		0			0
$155$	82959.8			0.277357
$156$	−276012.	−	478066.i	−0.908063	−	1.57281i
$157$	−82915.6	+	143614.i	−0.268465	+	0.464995i	−0.968466	−	0.249147i	$-0.919850\pi$
$157$	−82915.6	+	143614.i	−0.268465	+	0.464995i	0.700001	+	0.714142i	$0.253183\pi$
$158$	−115718.	+	200429.i	−0.368771	+	0.638730i
$159$	−115541.	−	200123.i	−0.362446	−	0.627775i
$160$	200567.			0.619384
$161$		0			0
$162$	65668.3			0.196593
$163$	−47859.1	−	82894.4i	−0.141090	−	0.244375i	0.786818	−	0.617186i	$-0.211727\pi$
$163$	−47859.1	−	82894.4i	−0.141090	−	0.244375i	−0.927907	+	0.372811i	$0.878394\pi$
$164$	−458612.	+	794339.i	−1.33148	+	2.30620i
$165$	231546.	−	401049.i	0.662105	−	1.14680i
$166$	86412.5	+	149671.i	0.243392	+	0.421568i
$167$	474209.			1.31577			0.657883	−	0.753120i	$-0.271452\pi$
$167$	474209.			1.31577			0.657883	+	0.753120i	$0.271452\pi$
$168$		0			0
$169$	438068.			1.17984
$170$	490217.	+	849081.i	1.30097	+	2.25334i
$171$	7703.01	−	13342.0i	0.0201451	−	0.0348924i
$172$	−205682.	+	356251.i	−0.530121	+	0.918196i
$173$	−129438.	−	224194.i	−0.328812	−	0.569519i	0.653465	−	0.756957i	$-0.273315\pi$
$173$	−129438.	−	224194.i	−0.328812	−	0.569519i	−0.982276	+	0.187438i	$0.939981\pi$
$174$	−697813.			−1.74729
$175$		0			0
$176$	−1.05506e6			−2.56742
$177$	119027.	+	206161.i	0.285570	+	0.494622i
$178$	−249871.	+	432789.i	−0.591106	+	1.02383i
$179$	271089.	−	469540.i	0.632381	−	1.09532i	−0.354682	−	0.934987i	$-0.615411\pi$
$179$	271089.	−	469540.i	0.632381	−	1.09532i	0.987064	−	0.160330i	$-0.0512557\pi$
$180$	−194254.	−	336458.i	−0.446878	−	0.774016i
$181$	653930.			1.48366			0.741831	−	0.670587i	$-0.233958\pi$
$181$	653930.			1.48366			0.741831	+	0.670587i	$0.233958\pi$
$182$		0			0
$183$	−57894.9			−0.127795
$184$	−7781.01	−	13477.1i	−0.0169430	−	0.0293462i
$185$	−326735.	+	565922.i	−0.701886	+	1.21570i
$186$	−53112.2	+	91993.1i	−0.112567	+	0.194972i
$187$	−509194.	−	881950.i	−1.06483	−	1.84434i
$188$	−221233.			−0.456516
$189$		0			0
$190$	−133925.			−0.269141
$191$	−384768.	−	666437.i	−0.763159	−	1.32183i	−0.941214	−	0.337810i	$-0.890314\pi$
$191$	−384768.	−	666437.i	−0.763159	−	1.32183i	0.178055	−	0.984021i	$-0.443020\pi$
$192$	79318.5	−	137384.i	0.155282	−	0.268956i
$193$	−407115.	+	705144.i	−0.786727	+	1.36265i	0.141235	+	0.989976i	$0.454893\pi$
$193$	−407115.	+	705144.i	−0.786727	+	1.36265i	−0.927962	+	0.372675i	$0.878441\pi$
$194$	84400.0	+	146185.i	0.161004	+	0.278868i
$195$	569620.			1.07275
$196$		0			0
$197$	−443688.			−0.814539			−0.407269	−	0.913308i	$-0.633519\pi$
$197$	−443688.			−0.814539			−0.407269	+	0.913308i	$0.633519\pi$
$198$	296479.	+	513516.i	0.537441	+	0.930875i
$199$	−309470.	+	536019.i	−0.553970	+	0.959505i	0.444012	+	0.896021i	$0.353555\pi$
$199$	−309470.	+	536019.i	−0.553970	+	0.959505i	−0.997983	+	0.0634842i	$0.979779\pi$
$200$	−330289.	+	572078.i	−0.583875	+	1.01130i
$201$	107171.	+	185625.i	0.187105	+	0.324075i
$202$	1.05542e6			1.81991
$203$		0			0
$204$	−854372.			−1.43738
$205$	−473231.	−	819661.i	−0.786482	−	1.36223i
$206$	101870.	−	176443.i	0.167254	−	0.289692i
$207$	−1740.57	+	3014.75i	−0.00282335	+	0.00489019i
$208$	−648884.	−	1.12390e6i	−1.03994	−	1.80123i
$209$	139110.			0.220289
$210$		0			0
$211$	769805.			1.19035			0.595175	−	0.803596i	$-0.297083\pi$
$211$	769805.			1.19035			0.595175	+	0.803596i	$0.297083\pi$
$212$	−875261.	−	1.51600e6i	−1.33751	−	2.31664i
$213$	201063.	−	348251.i	0.303657	−	0.525949i
$214$	18893.9	−	32725.3i	0.0282025	−	0.0488482i
$215$	−212238.	−	367608.i	−0.313132	−	0.542361i
$216$	263971.			0.384966
$217$		0			0
$218$	85445.7			0.121772
$219$	178206.	+	308661.i	0.251079	+	0.434882i
$220$	1.75403e6	−	3.03808e6i	2.44332	−	4.23196i
$221$	626328.	−	1.08483e6i	0.862623	−	1.49411i
$222$	−418362.	−	724625.i	−0.569731	−	0.986803i
$223$	−1.45664e6			−1.96151			−0.980755	−	0.195244i	$-0.937450\pi$
$223$	−1.45664e6			−1.96151			−0.980755	+	0.195244i	$0.937450\pi$
$224$		0			0
$225$	147768.			0.194592
$226$	504794.	+	874328.i	0.657420	+	1.13868i
$227$	−474953.	+	822642.i	−0.611767	+	1.05961i	0.379176	+	0.925325i	$0.376207\pi$
$227$	−474953.	+	822642.i	−0.611767	+	1.05961i	−0.990943	+	0.134286i	$0.957126\pi$
$228$	58352.8	−	101070.i	0.0743404	−	0.128761i
$229$	156141.	+	270445.i	0.196757	+	0.340793i	0.947475	−	0.319830i	$-0.103626\pi$
$229$	156141.	+	270445.i	0.196757	+	0.340793i	−0.750718	+	0.660622i	$0.770292\pi$
$230$	30261.7			0.0377202
$231$		0			0
$232$	−2.80505e6			−3.42153
$233$	−198453.	−	343730.i	−0.239479	−	0.414789i	0.721086	−	0.692845i	$-0.243643\pi$
$233$	−198453.	−	343730.i	−0.239479	−	0.414789i	−0.960565	+	0.278056i	$0.910310\pi$
$234$	−364680.	+	631645.i	−0.435384	+	0.754107i
$235$	114143.	−	197701.i	0.134828	−	0.233528i
$236$	901669.	+	1.56174e6i	1.05382	+	1.82527i
$237$	208107.			0.240666
$238$		0			0
$239$	−87033.3			−0.0985578			−0.0492789	−	0.998785i	$-0.515692\pi$
$239$	−87033.3			−0.0985578			−0.0492789	+	0.998785i	$0.515692\pi$
$240$	−456678.	−	790990.i	−0.511779	−	0.886426i
$241$	−785865.	+	1.36116e6i	−0.871576	+	1.50961i	−0.0112105	+	0.999937i	$0.503569\pi$
$241$	−785865.	+	1.36116e6i	−0.871576	+	1.50961i	−0.860366	+	0.509677i	$0.829765\pi$
$242$	−1.87111e6	+	3.24085e6i	−2.05381	+	3.55730i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	−438573.			−0.471593
$245$		0			0
$246$	1.21188e6			1.27680
$247$	85555.3	+	148186.i	0.0892286	+	0.154549i
$248$	−213499.	+	369791.i	−0.220428	+	0.381792i
$249$	77702.2	−	134584.i	0.0794209	−	0.137561i
$250$	457938.	+	793171.i	0.463400	+	0.802633i
$251$	385591.			0.386316			0.193158	−	0.981168i	$-0.438127\pi$
$251$	385591.			0.386316			0.193158	+	0.981168i	$0.438127\pi$
$252$		0			0
$253$	−31433.2			−0.0308736
$254$	928081.	+	1.60748e6i	0.902613	+	1.56337i
$255$	440803.	−	763494.i	0.424516	−	0.735284i
$256$	1.05742e6	−	1.83150e6i	1.00843	−	1.74666i
$257$	−220904.	−	382618.i	−0.208627	−	0.361353i	0.742655	−	0.669674i	$-0.233566\pi$
$257$	−220904.	−	382618.i	−0.208627	−	0.361353i	−0.951282	+	0.308321i	$0.900233\pi$
$258$	543514.			0.508348
$259$		0			0
$260$	4.31506e6			3.95870
$261$	313737.	+	543409.i	0.285079	+	0.493771i
$262$	−620781.	+	1.07522e6i	−0.558709	+	0.967712i
$263$	300132.	−	519844.i	0.267561	−	0.463429i	−0.700670	−	0.713485i	$-0.747116\pi$
$263$	300132.	−	519844.i	0.267561	−	0.463429i	0.968231	+	0.250056i	$0.0804490\pi$
$264$	1.19178e6	+	2.06422e6i	1.05241	+	1.82283i
$265$	1.80632e6			1.58009
$266$		0			0
$267$	449368.			0.385766
$268$	811851.	+	1.40617e6i	0.690462	+	1.19591i
$269$	162804.	−	281985.i	0.137178	−	0.237600i	−0.789249	−	0.614073i	$-0.789530\pi$
$269$	162804.	−	281985.i	0.137178	−	0.237600i	0.926427	+	0.376473i	$0.122863\pi$
$270$	−256658.	+	444545.i	−0.214262	+	0.371113i
$271$	877961.	+	1.52067e6i	0.726193	+	1.25780i	0.958481	+	0.285156i	$0.0920454\pi$
$271$	877961.	+	1.52067e6i	0.726193	+	1.25780i	−0.232288	+	0.972647i	$0.574621\pi$
$272$	−2.00857e6			−1.64613
$273$		0			0
$274$	996090.			0.801534
$275$	667141.	+	1.15552e6i	0.531969	+	0.921397i
$276$	−13185.4	+	22837.7i	−0.0104188	+	0.0180460i
$277$	171182.	−	296495.i	0.134047	−	0.232177i	−0.791186	−	0.611576i	$-0.790536\pi$
$277$	171182.	−	296495.i	0.134047	−	0.232177i	0.925233	+	0.379399i	$0.123869\pi$
$278$	−1.27353e6	−	2.20583e6i	−0.988322	−	1.71182i
$279$	95517.1			0.0734633
$280$		0			0
$281$	930671.			0.703122			0.351561	−	0.936165i	$-0.385651\pi$
$281$	930671.			0.703122			0.351561	+	0.936165i	$0.385651\pi$
$282$	146152.	+	253143.i	0.109442	+	0.189558i
$283$	−823799.	+	1.42686e6i	−0.611442	+	1.05905i	0.379556	+	0.925169i	$0.376077\pi$
$283$	−823799.	+	1.42686e6i	−0.611442	+	1.05905i	−0.990998	+	0.133879i	$0.957257\pi$
$284$	1.52312e6	−	2.63812e6i	1.12057	−	1.94088i
$285$	60212.9	+	104292.i	0.0439114	+	0.0760568i
$286$	−6.58582e6			−4.76096
$287$		0			0
$288$	230926.			0.164056
$289$	−259446.	−	449373.i	−0.182727	−	0.316492i
$290$	2.72733e6	−	4.72388e6i	1.90434	−	3.29841i
$291$	75892.5	−	131450.i	0.0525371	−	0.0909970i
$292$	1.34997e6	+	2.33821e6i	0.926543	+	1.60482i
$293$	1.14378e6			0.778347			0.389174	−	0.921164i	$-0.372761\pi$
$293$	1.14378e6			0.778347			0.389174	+	0.921164i	$0.372761\pi$
$294$		0			0
$295$	−1.86082e6			−1.24495
$296$	−1.68172e6	−	2.91282e6i	−1.11564	−	1.93235i
$297$	266594.	−	461754.i	0.175371	−	0.303752i
$298$	2.13820e6	−	3.70347e6i	1.39479	−	2.41584i
$299$	−19332.0	−	33484.1i	−0.0125055	−	0.0216601i
$300$	1.11939e6			0.718089
$301$		0			0
$302$	−1.50605e6			−0.950218
$303$	−474519.	−	821891.i	−0.296925	−	0.514290i
$304$	137183.	−	237609.i	0.0851369	−	0.147461i
$305$	226277.	−	391923.i	0.139280	−	0.241241i
$306$	564419.	+	977603.i	0.344586	+	0.596841i
$307$	−2.98831e6			−1.80959			−0.904795	−	0.425848i	$-0.859976\pi$
$307$	−2.98831e6			−1.80959			−0.904795	+	0.425848i	$0.859976\pi$
$308$		0			0
$309$	−183202.			−0.109153
$310$	−415168.	−	719092.i	−0.245369	−	0.424991i
$311$	1.41875e6	−	2.45735e6i	0.831775	−	1.44068i	−0.0648544	−	0.997895i	$-0.520658\pi$
$311$	1.41875e6	−	2.45735e6i	0.831775	−	1.44068i	0.896629	−	0.442782i	$-0.146008\pi$
$312$	−1.46593e6	+	2.53906e6i	−0.852563	+	1.47668i
$313$	−1.07374e6	−	1.85978e6i	−0.619497	−	1.07300i	−0.989578	−	0.144001i	$-0.954003\pi$
$313$	−1.07374e6	−	1.85978e6i	−0.619497	−	1.07300i	0.370080	−	0.929000i	$-0.379330\pi$
$314$	1.65979e6			0.950010
$315$		0			0
$316$	1.57648e6			0.888116
$317$	1.31679e6	+	2.28074e6i	0.735982	+	1.27476i	0.954291	+	0.298878i	$0.0966125\pi$
$317$	1.31679e6	+	2.28074e6i	0.735982	+	1.27476i	−0.218309	+	0.975880i	$0.570054\pi$
$318$	−1.15644e6	+	2.00301e6i	−0.641290	+	1.11075i
$319$	−2.83291e6	+	4.90675e6i	−1.55868	+	2.69971i
$320$	620017.	+	1.07390e6i	0.338477	+	0.586259i
$321$	−33978.9			−0.0184054
$322$		0			0
$323$	264829.			0.141241
$324$	−223658.	−	387386.i	−0.118364	−	0.205013i
$325$	−820609.	+	1.42134e6i	−0.430951	+	0.746429i
$326$	−479017.	+	829681.i	−0.249636	+	0.432382i
$327$	−38416.4	−	66539.2i	−0.0198677	−	0.0344118i
$328$	4.87148e6			2.50021
$329$		0			0
$330$	−4.63503e6			−2.34298
$331$	−1.64217e6	−	2.84432e6i	−0.823849	−	1.42695i	−0.902795	−	0.430070i	$-0.858489\pi$
$331$	−1.64217e6	−	2.84432e6i	−0.823849	−	1.42695i	0.0789461	−	0.996879i	$-0.474845\pi$
$332$	588619.	−	1.01952e6i	0.293082	−	0.507633i
$333$	−376191.	+	651583.i	−0.185908	+	0.322002i
$334$	−2.37315e6	−	4.11042e6i	−1.16402	−	2.01614i
$335$	−1.67546e6			−0.815685
$336$		0			0
$337$	−238202.			−0.114254			−0.0571270	−	0.998367i	$-0.518194\pi$
$337$	−238202.			−0.114254			−0.0571270	+	0.998367i	$0.518194\pi$
$338$	−2.19229e6	−	3.79715e6i	−1.04377	−	1.80787i
$339$	453911.	−	786196.i	0.214522	−	0.371562i
$340$	3.33923e6	−	5.78371e6i	1.56657	−	2.71337i
$341$	431239.	+	746929.i	0.200832	+	0.347851i
$342$	−154197.			−0.0712872
$343$		0			0
$344$	2.18480e6			0.995441
$345$	−13605.7	−	23565.7i	−0.00615422	−	0.0106594i
$346$	−1.29553e6	+	2.24393e6i	−0.581779	+	1.00767i
$347$	−532180.	+	921763.i	−0.237266	+	0.410956i	−0.959929	−	0.280244i	$-0.909585\pi$
$347$	−532180.	+	921763.i	−0.237266	+	0.410956i	0.722663	+	0.691201i	$0.242918\pi$
$348$	2.37666e6	+	4.11649e6i	1.05201	+	1.82213i
$349$	1.85940e6			0.817163			0.408582	−	0.912722i	$-0.366023\pi$
$349$	1.85940e6			0.817163			0.408582	+	0.912722i	$0.366023\pi$
$350$		0			0
$351$	655841.			0.284139
$352$	1.04258e6	+	1.80581e6i	0.448491	+	0.776810i
$353$	832437.	−	1.44182e6i	0.355561	−	0.615850i	−0.631653	−	0.775252i	$-0.717623\pi$
$353$	832437.	−	1.44182e6i	0.355561	−	0.615850i	0.987214	+	0.159401i	$0.0509564\pi$
$354$	1.19133e6	−	2.06344e6i	0.505270	−	0.875154i
$355$	1.57167e6	+	2.72221e6i	0.661897	+	1.14644i
$356$	3.40411e6			1.42357
$357$		0			0
$358$	−5.42660e6			−2.23779
$359$	−1.33729e6	−	2.31625e6i	−0.547632	−	0.948526i	−0.998436	−	0.0559031i	$-0.982196\pi$
$359$	−1.33729e6	−	2.31625e6i	−0.547632	−	0.948526i	0.450805	−	0.892623i	$-0.351137\pi$
$360$	−1.03171e6	+	1.78697e6i	−0.419566	+	0.726709i
$361$	1.21996e6	−	2.11304e6i	0.492695	−	0.853373i
$362$	−3.27256e6	−	5.66823e6i	−1.31255	−	2.27340i
$363$	3.36500e6			1.34035
$364$		0			0
$365$	−2.78600e6			−1.09458
$366$	289732.	+	501830.i	0.113056	+	0.195819i
$367$	1.07192e6	−	1.85662e6i	0.415430	−	0.719546i	−0.580043	−	0.814586i	$-0.696964\pi$
$367$	1.07192e6	−	1.85662e6i	0.415430	−	0.719546i	0.995473	+	0.0950395i	$0.0302978\pi$
$368$	−30997.9	+	53689.9i	−0.0119320	+	0.0206668i
$369$	−544862.	−	943729.i	−0.208315	−	0.360812i
$370$	6.54051e6			2.48375
$371$		0			0
$372$	723573.			0.271097
$373$	379933.	+	658064.i	0.141395	+	0.244904i	0.928022	−	0.372525i	$-0.121508\pi$
$373$	379933.	+	658064.i	0.141395	+	0.244904i	−0.786627	+	0.617429i	$0.788174\pi$
$374$	−5.09647e6	+	8.82734e6i	−1.88404	+	3.26325i
$375$	411778.	−	713220.i	0.151211	−	0.261906i
$376$	587498.	+	1.01758e6i	0.214307	+	0.371191i
$377$	−6.96918e6			−2.52539
$378$		0			0
$379$	3.03679e6			1.08597			0.542984	−	0.839743i	$-0.317294\pi$
$379$	3.03679e6			1.08597			0.542984	+	0.839743i	$0.317294\pi$
$380$	456132.	+	790044.i	0.162044	+	0.280668i
$381$	834531.	−	1.44545e6i	0.294530	−	0.510142i
$382$	−3.85110e6	+	6.67030e6i	−1.35029	+	2.33877i
$383$	−1.25465e6	−	2.17311e6i	−0.437043	−	0.756980i	0.560417	−	0.828211i	$-0.310641\pi$
$383$	−1.25465e6	−	2.17311e6i	−0.437043	−	0.756980i	−0.997460	+	0.0712302i	$0.977308\pi$
$384$	−2.40885e6			−0.833646
$385$		0			0
$386$	8.14954e6			2.78397
$387$	−244364.	−	423251.i	−0.0829392	−	0.143655i
$388$	574910.	−	995774.i	0.193874	−	0.335800i
$389$	492568.	−	853153.i	0.165041	−	0.285860i	−0.771629	−	0.636073i	$-0.780558\pi$
$389$	492568.	−	853153.i	0.165041	−	0.285860i	0.936670	+	0.350213i	$0.113891\pi$
$390$	−2.85063e6	−	4.93744e6i	−0.949030	−	1.64377i
$391$	−59840.7			−0.0197950
$392$		0			0
$393$	1.11641e6			0.364623
$394$	2.22041e6	+	3.84586e6i	0.720597	+	1.24811i
$395$	−813365.	+	1.40879e6i	−0.262296	+	0.454311i
$396$	2.01953e6	−	3.49794e6i	0.647162	−	1.12092i
$397$	1.45255e6	+	2.51589e6i	0.462546	+	0.801153i	0.999087	−	0.0427211i	$-0.0136027\pi$
$397$	1.45255e6	+	2.51589e6i	0.462546	+	0.801153i	−0.536541	+	0.843874i	$0.680269\pi$
$398$	6.19491e6			1.96032
$399$		0			0
$400$	2.63161e6			0.822377
$401$	2.11562e6	+	3.66437e6i	0.657018	+	1.13799i	0.981384	+	0.192057i	$0.0615158\pi$
$401$	2.11562e6	+	3.66437e6i	0.657018	+	1.13799i	−0.324366	+	0.945932i	$0.605151\pi$
$402$	1.07266e6	−	1.85790e6i	0.331052	−	0.573399i
$403$	−530441.	+	918751.i	−0.162695	+	0.281796i
$404$	−3.59464e6	−	6.22609e6i	−1.09572	−	1.89785i
$405$	461574.			0.139831
$406$		0			0
$407$	−6.79370e6			−2.03292
$408$	2.26883e6	+	3.92973e6i	0.674764	+	1.16873i
$409$	2.06945e6	−	3.58439e6i	0.611711	−	1.05951i	−0.379241	−	0.925298i	$-0.623815\pi$
$409$	2.06945e6	−	3.58439e6i	0.611711	−	1.05951i	0.990952	−	0.134216i	$-0.0428517\pi$
$410$	−4.73652e6	+	8.20389e6i	−1.39155	+	2.41024i
$411$	−447842.	−	775685.i	−0.130774	−	0.226507i
$412$	−1.38782e6			−0.402799
$413$		0			0
$414$	34842.3			0.00999094
$415$	607383.	+	1.05202e6i	0.173118	+	0.299849i
$416$	−1.28242e6	+	2.22121e6i	−0.363326	+	0.629298i
$417$	−1.14516e6	+	1.98348e6i	−0.322498	+	0.558583i
$418$	−696168.	−	1.20580e6i	−0.194883	−	0.337547i
$419$	−5.99852e6			−1.66920			−0.834601	−	0.550855i	$-0.814302\pi$
$419$	−5.99852e6			−1.66920			−0.834601	+	0.550855i	$0.814302\pi$
$420$		0			0
$421$	−1.00759e6			−0.277062			−0.138531	−	0.990358i	$-0.544238\pi$
$421$	−1.00759e6			−0.277062			−0.138531	+	0.990358i	$0.544238\pi$
$422$	−3.85244e6	−	6.67263e6i	−1.05307	−	1.82396i
$423$	131420.	−	227626.i	0.0357117	−	0.0618545i
$424$	−4.64861e6	+	8.05163e6i	−1.25577	+	2.17505i
$425$	1.27006e6	+	2.19982e6i	0.341078	+	0.590764i
$426$	−4.02484e6			−1.07454
$427$		0			0
$428$	−257401.			−0.0679205
$429$	2.96099e6	+	5.12858e6i	0.776771	+	1.34541i
$430$	−2.12427e6	+	3.67934e6i	−0.554037	+	0.959620i
$431$	−151575.	+	262535.i	−0.0393037	+	0.0680759i	−0.885008	−	0.465576i	$-0.845847\pi$
$431$	−151575.	+	262535.i	−0.0393037	+	0.0680759i	0.845704	+	0.533652i	$0.179181\pi$
$432$	−525804.	−	910718.i	−0.135555	−	0.234787i
$433$	−3.97130e6			−1.01792			−0.508960	−	0.860790i	$-0.669970\pi$
$433$	−3.97130e6			−1.01792			−0.508960	+	0.860790i	$0.669970\pi$
$434$		0			0
$435$	−4.90484e6			−1.24280
$436$	−291017.	−	504056.i	−0.0733165	−	0.126988i
$437$	4087.07	−	7079.01i	0.00102378	−	0.00177325i
$438$	1.78364e6	−	3.08936e6i	0.444245	−	0.769454i
$439$	1.87400e6	+	3.24586e6i	0.464096	+	0.803838i	0.999160	−	0.0409737i	$-0.0130460\pi$
$439$	1.87400e6	+	3.24586e6i	0.464096	+	0.803838i	−0.535064	+	0.844811i	$0.679713\pi$
$440$	−1.86318e7			−4.58798
$441$		0			0
$442$	−1.25377e7			−3.05255
$443$	655384.	+	1.13516e6i	0.158667	+	0.274819i	0.934388	−	0.356256i	$-0.115947\pi$
$443$	655384.	+	1.13516e6i	0.158667	+	0.274819i	−0.775721	+	0.631076i	$0.782614\pi$
$444$	−2.84977e6	+	4.93595e6i	−0.686045	+	1.18826i
$445$	−1.75631e6	+	3.04202e6i	−0.420437	+	0.728218i
$446$	7.28968e6	+	1.26261e7i	1.73529	+	3.00561i
$447$	−3.84534e6			−0.910261
$448$		0			0
$449$	6.31311e6			1.47784			0.738920	−	0.673793i	$-0.235336\pi$
$449$	6.31311e6			1.47784			0.738920	+	0.673793i	$0.235336\pi$
$450$	−739497.	−	1.28085e6i	−0.172149	−	0.298171i
$451$	4.91988e6	−	8.52148e6i	1.13897	−	1.97276i
$452$	3.43852e6	−	5.95569e6i	0.791636	−	1.37115i
$453$	677122.	+	1.17281e6i	0.155032	+	0.268523i
$454$	9.50750e6			2.16484
$455$		0			0
$456$	−619837.			−0.139594
$457$	291738.	+	505305.i	0.0653435	+	0.113178i	0.896846	−	0.442342i	$-0.145852\pi$
$457$	291738.	+	505305.i	0.0653435	+	0.113178i	−0.831503	+	0.555521i	$0.812519\pi$
$458$	1.56280e6	−	2.70685e6i	0.348129	−	0.602978i
$459$	507526.	−	879061.i	0.112441	−	0.194754i
$460$	−103067.	−	178518.i	−0.0227105	−	0.0393358i
$461$	2.93381e6			0.642953			0.321476	−	0.946918i	$-0.395821\pi$
$461$	2.93381e6			0.642953			0.321476	+	0.946918i	$0.395821\pi$
$462$		0			0
$463$	3.76716e6			0.816699			0.408349	−	0.912826i	$-0.366105\pi$
$463$	3.76716e6			0.816699			0.408349	+	0.912826i	$0.366105\pi$
$464$	5.58736e6	+	9.67759e6i	1.20479	+	2.08676i
$465$	−373319.	+	646608.i	−0.0800659	+	0.138678i
$466$	−1.98629e6	+	3.44036e6i	−0.423719	+	0.733903i
$467$	−1.45298e6	−	2.51664e6i	−0.308296	−	0.533984i	0.669694	−	0.742637i	$-0.266425\pi$
$467$	−1.45298e6	−	2.51664e6i	−0.308296	−	0.533984i	−0.977990	+	0.208653i	$0.933092\pi$
$468$	4.96821e6			1.04854
$469$		0			0
$470$	−2.28489e6			−0.477111
$471$	−746241.	−	1.29253e6i	−0.154998	−	0.268465i
$472$	4.78887e6	−	8.29456e6i	0.989414	−	1.71371i
$473$	2.20650e6	−	3.82178e6i	0.453473	−	0.785439i
$474$	−1.04146e6	−	1.80386e6i	−0.212910	−	0.368771i
$475$	−346977.			−0.0705613
$476$		0			0
$477$	2.07974e6			0.418517
$478$	435554.	+	754401.i	0.0871910	+	0.151019i
$479$	−3.53311e6	+	6.11952e6i	−0.703588	+	1.21865i	0.263611	+	0.964629i	$0.415086\pi$
$479$	−3.53311e6	+	6.11952e6i	−0.703588	+	1.21865i	−0.967199	+	0.254021i	$0.918247\pi$
$480$	−902552.	+	1.56327e6i	−0.178801	+	0.309692i
$481$	−4.17826e6	−	7.23695e6i	−0.823441	−	1.42624i
$482$	1.57313e7			3.08423
$483$		0			0
$484$	2.54910e7			4.94622
$485$	593237.	+	1.02752e6i	0.114518	+	0.198351i
$486$	−295508.	+	511834.i	−0.0567516	+	0.0982966i
$487$	−1.36490e6	+	2.36408e6i	−0.260783	+	0.451689i	−0.966450	−	0.256854i	$-0.917314\pi$
$487$	−1.36490e6	+	2.36408e6i	−0.260783	+	0.451689i	0.705667	+	0.708543i	$0.250647\pi$
$488$	1.16466e6	+	2.01724e6i	0.221385	+	0.383450i
$489$	861464.			0.162916
$490$		0			0
$491$	−1.02859e7			−1.92548			−0.962740	−	0.270428i	$-0.912835\pi$
$491$	−1.02859e7			−1.92548			−0.962740	+	0.270428i	$0.912835\pi$
$492$	−4.12751e6	−	7.14905e6i	−0.768732	−	1.33148i
$493$	−5.39314e6	+	9.34119e6i	−0.999365	+	1.73095i
$494$	856313.	−	1.48318e6i	0.157876	−	0.273449i
$495$	2.08391e6	+	3.60944e6i	0.382267	+	0.662105i
$496$	1.70107e6			0.310469
$497$		0			0
$498$	−1.55543e6			−0.281045
$499$	1.81795e6	+	3.14879e6i	0.326837	+	0.566099i	0.981882	−	0.189491i	$-0.0606838\pi$
$499$	1.81795e6	+	3.14879e6i	0.326837	+	0.566099i	−0.655045	+	0.755590i	$0.727350\pi$
$500$	3.11935e6	−	5.40287e6i	0.558006	−	0.966495i
$501$	−2.13394e6	+	3.69609e6i	−0.379829	+	0.657883i
$502$	−1.92967e6	−	3.34228e6i	−0.341762	−	0.591949i
$503$	1.65499e6			0.291658			0.145829	−	0.989310i	$-0.453415\pi$
$503$	1.65499e6			0.291658			0.145829	+	0.989310i	$0.453415\pi$
$504$		0			0
$505$	7.41845e6			1.29445
$506$	157306.	+	272462.i	0.0273129	+	0.0473074i
$507$	−1.97131e6	+	3.41440e6i	−0.340592	+	0.589922i
$508$	6.32184e6	−	1.09498e7i	1.08689	−	1.88254i
$509$	365555.	+	633160.i	0.0625401	+	0.108323i	0.895600	−	0.444860i	$-0.146747\pi$
$509$	365555.	+	633160.i	0.0625401	+	0.108323i	−0.833060	+	0.553183i	$0.813413\pi$
$510$	−8.82391e6			−1.50223
$511$		0			0
$512$	−1.26024e7			−2.12460
$513$	69327.1	+	120078.i	0.0116308	+	0.0201451i
$514$	−2.21101e6	+	3.82958e6i	−0.369133	+	0.639357i
$515$	716028.	−	1.24020e6i	0.118963	−	0.206050i
$516$	−1.85114e6	−	3.20626e6i	−0.306065	−	0.530121i
$517$	2.37334e6			0.390511
$518$		0			0
$519$	2.32989e6			0.379679
$520$	−1.14589e7	−	1.98474e7i	−1.85838	−	3.21880i
$521$	−2.36548e6	+	4.09712e6i	−0.381790	+	0.661279i	−0.991318	−	0.131485i	$-0.958025\pi$
$521$	−2.36548e6	+	4.09712e6i	−0.381790	+	0.661279i	0.609528	+	0.792764i	$0.291359\pi$
$522$	3.14016e6	−	5.43892e6i	0.504401	−	0.873647i
$523$	4.86281e6	+	8.42264e6i	0.777380	+	1.34646i	0.933447	+	0.358715i	$0.116785\pi$
$523$	4.86281e6	+	8.42264e6i	0.777380	+	1.34646i	−0.156067	+	0.987746i	$0.549882\pi$
$524$	8.45719e6			1.34554
$525$		0			0
$526$	−6.00798e6			−0.946812
$527$	820969.	+	1.42196e6i	0.128766	+	0.223029i
$528$	4.74779e6	−	8.22341e6i	0.741150	−	1.28371i
$529$	3.21725e6	−	5.57244e6i	0.499857	−	0.865777i
$530$	−9.03964e6	−	1.56571e7i	−1.39785	−	2.42115i
$531$	−2.14249e6			−0.329748
$532$		0			0
$533$	1.21033e7			1.84538
$534$	−2.24884e6	−	3.89510e6i	−0.341275	−	0.591106i
$535$	132803.	−	230022.i	0.0200597	−	0.0347444i
$536$	4.31184e6	−	7.46832e6i	0.648262	−	1.12282i
$537$	2.43980e6	+	4.22586e6i	0.365105	+	0.632381i
$538$	−3.25898e6			−0.485430
$539$		0			0
$540$	3.49658e6			0.516010
$541$	−4.09501e6	−	7.09277e6i	−0.601536	−	1.04189i	−0.992589	−	0.121523i	$-0.961222\pi$
$541$	−4.09501e6	−	7.09277e6i	−0.601536	−	1.04189i	0.391052	−	0.920368i	$-0.372111\pi$
$542$	8.78742e6	−	1.52202e7i	1.28488	−	2.22548i
$543$	−2.94268e6	+	5.09688e6i	−0.428296	+	0.741831i
$544$	1.98481e6	+	3.43779e6i	0.287555	+	0.498061i
$545$	600587.			0.0866133
$546$		0			0
$547$	−4.17136e6			−0.596087			−0.298043	−	0.954552i	$-0.596334\pi$
$547$	−4.17136e6			−0.596087			−0.298043	+	0.954552i	$0.596334\pi$
$548$	−3.39255e6	−	5.87607e6i	−0.482586	−	0.835863i
$549$	260527.	−	451246.i	0.0368911	−	0.0638973i
$550$	6.67734e6	−	1.15655e7i	0.941233	−	1.63026i
$551$	−736693.	−	1.27599e6i	−0.103373	−	0.179047i
$552$	140058.			0.0195641
$553$		0			0
$554$	−3.42668e6			−0.474350
$555$	−2.94061e6	−	5.09329e6i	−0.405234	−	0.701886i
$556$	−8.67498e6	+	1.50255e7i	−1.19009	+	2.06130i
$557$	633291.	−	1.09689e6i	0.0864899	−	0.149805i	−0.819535	−	0.573029i	$-0.805768\pi$
$557$	633291.	−	1.09689e6i	0.0864899	−	0.149805i	0.906025	+	0.423224i	$0.139102\pi$
$558$	−478010.	−	827937.i	−0.0649907	−	0.112567i
$559$	5.42817e6			0.734723
$560$		0			0
$561$	9.16549e6			1.22956
$562$	−4.65749e6	−	8.06702e6i	−0.622030	−	1.07739i
$563$	3.18716e6	−	5.52032e6i	0.423772	−	0.733995i	−0.572533	−	0.819882i	$-0.694039\pi$
$563$	3.18716e6	−	5.52032e6i	0.423772	−	0.733995i	0.996305	+	0.0858870i	$0.0273724\pi$
$564$	995550.	−	1.72434e6i	0.131785	−	0.228258i
$565$	3.54813e6	+	6.14554e6i	0.467604	+	0.809914i
$566$	1.64906e7			2.16369
$567$		0			0
$568$	−1.61789e7			−2.10416
$569$	−3.82020e6	−	6.61678e6i	−0.494659	−	0.856774i	0.505322	−	0.862931i	$-0.331374\pi$
$569$	−3.82020e6	−	6.61678e6i	−0.494659	−	0.856774i	−0.999981	+	0.00615660i	$0.998040\pi$
$570$	602665.	−	1.04385e6i	0.0776942	−	0.134570i
$571$	−395457.	+	684952.i	−0.0507585	+	0.0879164i	−0.890288	−	0.455397i	$-0.849497\pi$
$571$	−395457.	+	684952.i	−0.0507585	+	0.0879164i	0.839530	+	0.543314i	$0.182831\pi$
$572$	2.24304e7	+	3.88506e7i	2.86647	+	4.96487i
$573$	6.92582e6			0.881221
$574$		0			0
$575$	78402.8			0.00988922
$576$	713866.	+	1.23645e6i	0.0896521	+	0.155282i
$577$	4.27835e6	−	7.41032e6i	0.534979	−	0.926611i	−0.464185	−	0.885738i	$-0.653653\pi$
$577$	4.27835e6	−	7.41032e6i	0.534979	−	0.926611i	0.999164	−	0.0408727i	$-0.0130138\pi$
$578$	−2.59676e6	+	4.49772e6i	−0.323305	+	0.559981i
$579$	−3.66404e6	−	6.34630e6i	−0.454217	−	0.786727i
$580$	−3.71558e7			−4.58623
$581$		0			0
$582$	−1.51920e6			−0.185912
$583$	9.38958e6	+	1.62632e7i	1.14413	+	1.98169i
$584$	7.16982e6	−	1.24185e7i	0.869914	−	1.50673i
$585$	−2.56329e6	+	4.43975e6i	−0.309676	+	0.536375i
$586$	−5.72398e6	−	9.91423e6i	−0.688580	−	1.19266i
$587$	−1.17153e7			−1.40333			−0.701663	−	0.712509i	$-0.747559\pi$
$587$	−1.17153e7			−1.40333			−0.701663	+	0.712509i	$0.747559\pi$
$588$		0			0
$589$	−224286.			−0.0266387
$590$	9.31239e6	+	1.61295e7i	1.10136	+	1.90762i
$591$	1.99659e6	−	3.45820e6i	0.235137	−	0.407269i
$592$	−6.69962e6	+	1.16041e7i	−0.785680	+	1.36084i
$593$	−7.78087e6	−	1.34769e7i	−0.908639	−	1.57381i	−0.815957	−	0.578113i	$-0.803789\pi$
$593$	−7.78087e6	−	1.34769e7i	−0.908639	−	1.57381i	−0.0926818	−	0.995696i	$-0.529544\pi$
$594$	−5.33662e6			−0.620583
$595$		0			0
$596$	−2.91297e7			−3.35908
$597$	−2.78523e6	−	4.82417e6i	−0.319835	−	0.553970i
$598$	−193492.	+	335138.i	−0.0221264	+	0.0383240i
$599$	4.59465e6	−	7.95816e6i	0.523221	−	0.906245i	−0.476414	−	0.879221i	$-0.658064\pi$
$599$	4.59465e6	−	7.95816e6i	0.523221	−	0.906245i	0.999635	−	0.0270242i	$-0.00860313\pi$
$600$	−2.97260e6	−	5.14870e6i	−0.337100	−	0.583875i
$601$	1.61226e7			1.82075			0.910373	−	0.413789i	$-0.135795\pi$
$601$	1.61226e7			1.82075			0.910373	+	0.413789i	$0.135795\pi$
$602$		0			0
$603$	−1.92907e6			−0.216050
$604$	5.12942e6	+	8.88441e6i	0.572105	+	0.990915i
$605$	−1.31518e7	+	2.27795e7i	−1.46082	+	2.53021i
$606$	−4.74941e6	+	8.22622e6i	−0.525361	+	0.909953i
$607$	−5.20278e6	−	9.01148e6i	−0.573144	−	0.992714i	−0.996241	−	0.0866296i	$-0.972390\pi$
$607$	−5.20278e6	−	9.01148e6i	−0.573144	−	0.992714i	0.423097	−	0.906084i	$-0.360943\pi$
$608$	−542243.			−0.0594887
$609$		0			0
$610$	−4.52956e6			−0.492868
$611$	1.45965e6	+	2.52818e6i	0.158178	+	0.273972i
$612$	3.84467e6	−	6.65917e6i	0.414936	−	0.718690i
$613$	5.69606e6	−	9.86587e6i	0.612243	−	1.06044i	−0.378619	−	0.925553i	$-0.623601\pi$
$613$	5.69606e6	−	9.86587e6i	0.612243	−	1.06044i	0.990862	−	0.134883i	$-0.0430658\pi$
$614$	1.49548e7	+	2.59026e7i	1.60089	+	2.77282i
$615$	8.51816e6			0.908151
$616$		0			0
$617$	6.20517e6			0.656206			0.328103	−	0.944642i	$-0.393591\pi$
$617$	6.20517e6			0.656206			0.328103	+	0.944642i	$0.393591\pi$
$618$	916826.	+	1.58799e6i	0.0965641	+	0.167254i
$619$	4.92804e6	−	8.53562e6i	0.516949	−	0.895382i	−0.482857	−	0.875699i	$-0.660401\pi$
$619$	4.92804e6	−	8.53562e6i	0.516949	−	0.895382i	0.999806	−	0.0196828i	$-0.00626564\pi$
$620$	−2.82801e6	+	4.89826e6i	−0.295462	+	0.511756i
$621$	−15665.1	−	27132.8i	−0.00163006	−	0.00282335i
$622$	−2.84003e7			−2.94338
$623$		0			0
$624$	1.16799e7			1.20082
$625$	6.06925e6	+	1.05122e7i	0.621491	+	1.07645i
$626$	−1.07470e7	+	1.86143e7i	−1.09610	+	1.89850i
$627$	−625995.	+	1.08425e6i	−0.0635919	+	0.110144i
$628$	−5.65301e6	−	9.79131e6i	−0.571980	−	0.990699i
$629$	−1.29335e7			−1.30343
$630$		0			0
$631$	7.26873e6			0.726750			0.363375	−	0.931643i	$-0.381624\pi$
$631$	7.26873e6			0.726750			0.363375	+	0.931643i	$0.381624\pi$
$632$	−4.18642e6	−	7.25109e6i	−0.416918	−	0.722122i
$633$	−3.46412e6	+	6.00003e6i	−0.343624	+	0.595175i
$634$	1.31796e7	−	2.28277e7i	1.30220	−	2.25548i
$635$	6.52337e6	+	1.12988e7i	0.642004	+	1.11198i
$636$	1.57547e7			1.54443
$637$		0			0
$638$	5.67087e7			5.51566
$639$	1.80957e6	+	3.13426e6i	0.175316	+	0.303657i
$640$	9.41476e6	−	1.63068e7i	0.908572	−	1.57369i
$641$	−4.15059e6	+	7.18904e6i	−0.398993	+	0.691076i	−0.993602	−	0.112939i	$-0.963974\pi$
$641$	−4.15059e6	+	7.18904e6i	−0.398993	+	0.691076i	0.594609	+	0.804015i	$0.297307\pi$
$642$	170045.	+	294527.i	0.0162827	+	0.0282025i
$643$	−4.14322e6			−0.395194			−0.197597	−	0.980283i	$-0.563314\pi$
$643$	−4.14322e6			−0.395194			−0.197597	+	0.980283i	$0.563314\pi$
$644$		0			0
$645$	3.82029e6			0.361574
$646$	−1.32532e6	−	2.29553e6i	−0.124951	−	0.216422i
$647$	7.39529e6	−	1.28090e7i	0.694535	−	1.20297i	−0.275802	−	0.961214i	$-0.588943\pi$
$647$	7.39529e6	−	1.28090e7i	0.694535	−	1.20297i	0.970337	−	0.241756i	$-0.0777233\pi$
$648$	−1.18787e6	+	2.05745e6i	−0.111130	+	0.192483i
$649$	−9.67289e6	−	1.67539e7i	−0.901456	−	1.56137i
$650$	1.64268e7			1.52500
$651$		0			0
$652$	6.52587e6			0.601200
$653$	3.04466e6	+	5.27350e6i	0.279419	+	0.483967i	0.971240	−	0.238101i	$-0.0765249\pi$
$653$	3.04466e6	+	5.27350e6i	0.279419	+	0.483967i	−0.691822	+	0.722068i	$0.743192\pi$
$654$	−384506.	+	665983.i	−0.0351527	+	0.0608862i
$655$	−4.36339e6	+	7.55762e6i	−0.397394	+	0.688306i
$656$	−9.70348e6	−	1.68069e7i	−0.880376	−	1.52486i
$657$	−3.20770e6			−0.289922
$658$		0			0
$659$	4.14447e6			0.371754			0.185877	−	0.982573i	$-0.440487\pi$
$659$	4.14447e6			0.371754			0.185877	+	0.982573i	$0.440487\pi$
$660$	1.57863e7	+	2.73427e7i	1.41065	+	2.44332i
$661$	−9.01892e6	+	1.56212e7i	−0.802881	+	1.39063i	0.114832	+	0.993385i	$0.463367\pi$
$661$	−9.01892e6	+	1.56212e7i	−0.802881	+	1.39063i	−0.917713	+	0.397245i	$0.869966\pi$
$662$	−1.64363e7	+	2.84685e7i	−1.45767	+	2.52476i
$663$	5.63695e6	+	9.76349e6i	0.498036	+	0.862623i
$664$	−6.25245e6			−0.550339
$665$		0			0
$666$	7.53052e6			0.657869
$667$	166463.	+	288322.i	0.0144878	+	0.0250936i
$668$	−1.61653e7	+	2.79991e7i	−1.40166	+	2.42774i
$669$	6.55489e6	−	1.13534e7i	0.566239	−	0.980755i
$670$	8.38476e6	+	1.45228e7i	0.721612	+	1.24987i
$671$	4.70490e6			0.403408
$672$		0			0
$673$	5.62885e6			0.479051			0.239526	−	0.970890i	$-0.423008\pi$
$673$	5.62885e6			0.479051			0.239526	+	0.970890i	$0.423008\pi$
$674$	1.19207e6	+	2.06473e6i	0.101077	+	0.175070i
$675$	−664956.	+	1.15174e6i	−0.0561737	+	0.0972958i
$676$	−1.49333e7	+	2.58652e7i	−1.25686	+	2.17695i
$677$	7.54384e6	+	1.30663e7i	0.632588	+	1.09567i	0.987021	+	0.160593i	$0.0513407\pi$
$677$	7.54384e6	+	1.30663e7i	0.632588	+	1.09567i	−0.354433	+	0.935082i	$0.615326\pi$
$678$	−9.08628e6			−0.759123
$679$		0			0
$680$	−3.54700e7			−2.94164
$681$	−4.27457e6	−	7.40378e6i	−0.353204	−	0.611767i
$682$	4.31623e6	−	7.47593e6i	0.355340	−	0.615466i
$683$	−3.60207e6	+	6.23897e6i	−0.295461	+	0.511754i	−0.975092	−	0.221801i	$-0.928807\pi$
$683$	−3.60207e6	+	6.23897e6i	−0.295461	+	0.511754i	0.679631	+	0.733554i	$0.262140\pi$
$684$	525175.	+	909630.i	0.0429204	+	0.0743404i
$685$	7.00139e6			0.570109
$686$		0			0
$687$	−2.81055e6			−0.227195
$688$	−4.35189e6	−	7.53770e6i	−0.350515	−	0.607110i
$689$	−1.15495e7	+	2.00044e7i	−0.926866	+	1.60538i
$690$	−136178.	+	235867.i	−0.0108889	+	0.0188601i
$691$	−4.54312e6	−	7.86892e6i	−0.361959	−	0.626932i	0.626324	−	0.779563i	$-0.284559\pi$
$691$	−4.54312e6	−	7.86892e6i	−0.361959	−	0.626932i	−0.988283	+	0.152631i	$0.951225\pi$
$692$	1.76497e7			1.40111
$693$		0			0
$694$	1.06531e7			0.839607
$695$	−8.95151e6	−	1.55045e7i	−0.702966	−	1.21757i
$696$	1.26227e7	−	2.18632e7i	0.987710	−	1.71076i
$697$	9.36618e6	−	1.62227e7i	0.730265	−	1.26486i
$698$	−9.30526e6	−	1.61172e7i	−0.722919	−	1.25213i
$699$	3.57215e6			0.276526
$700$		0			0
$701$	−1.41913e7			−1.09075			−0.545376	−	0.838192i	$-0.683613\pi$
$701$	−1.41913e7			−1.09075			−0.545376	+	0.838192i	$0.683613\pi$
$702$	−3.28212e6	−	5.68480e6i	−0.251369	−	0.435384i
$703$	883343.	−	1.53000e6i	0.0674126	−	0.116762i
$704$	−6.44591e6	+	1.11646e7i	−0.490177	+	0.849011i
$705$	1.02729e6	+	1.77931e6i	0.0778428	+	0.134828i
$706$	−1.66635e7			−1.25822
$707$		0			0
$708$	−1.62300e7			−1.21685
$709$	1.10535e6	+	1.91453e6i	0.0825819	+	0.143036i	0.904358	−	0.426774i	$-0.140350\pi$
$709$	1.10535e6	+	1.91453e6i	0.0825819	+	0.143036i	−0.821776	+	0.569810i	$0.807017\pi$
$710$	1.57307e7	−	2.72463e7i	1.17112	−	2.02844i
$711$	−936480.	+	1.62203e6i	−0.0694744	+	0.120333i
$712$	−9.03980e6	−	1.56574e7i	−0.668280	−	1.15750i
$713$	50679.5			0.00373343
$714$		0			0
$715$	−4.62909e7			−3.38634
$716$	1.84823e7	+	3.20122e7i	1.34733	+	2.33364i
$717$	391650.	−	678358.i	0.0284512	−	0.0492789i
$718$	−1.33848e7	+	2.31831e7i	−0.968946	+	1.67826i
$719$	1.49541e6	+	2.59012e6i	0.107879	+	0.186852i	0.914911	−	0.403656i	$-0.132261\pi$
$719$	1.49541e6	+	2.59012e6i	0.107879	+	0.186852i	−0.807032	+	0.590508i	$0.798927\pi$
$720$	8.22021e6			0.590951
$721$		0			0
$722$	−2.44209e7			−1.74349
$723$	−7.07279e6	−	1.22504e7i	−0.503205	−	0.871576i
$724$	−2.22918e7	+	3.86105e7i	−1.58051	+	2.73753i
$725$	7.06604e6	−	1.22387e7i	0.499265	−	0.864752i
$726$	−1.68400e7	−	2.91677e7i	−1.18577	−	2.05381i
$727$	8.38066e6			0.588088			0.294044	−	0.955792i	$-0.404999\pi$
$727$	8.38066e6			0.588088			0.294044	+	0.955792i	$0.404999\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	1.39424e7	+	2.41489e7i	0.968343	+	1.67722i
$731$	4.20061e6	−	7.27568e6i	0.290750	−	0.503593i
$732$	1.97358e6	−	3.41834e6i	0.136137	−	0.235796i
$733$	−3.85123e6	−	6.67052e6i	−0.264752	−	0.458564i	0.702747	−	0.711440i	$-0.251957\pi$
$733$	−3.85123e6	−	6.67052e6i	−0.264752	−	0.458564i	−0.967499	+	0.252876i	$0.918623\pi$
$734$	−2.14575e7			−1.47007
$735$		0			0
$736$	122525.			0.00833739
$737$	−8.70934e6	−	1.50850e7i	−0.590632	−	1.02300i
$738$	−5.45347e6	+	9.44568e6i	−0.368580	+	0.638399i
$739$	3.79949e6	−	6.58092e6i	0.255926	−	0.443277i	−0.709221	−	0.704987i	$-0.750953\pi$
$739$	3.79949e6	−	6.58092e6i	0.255926	−	0.443277i	0.965147	+	0.261710i	$0.0842863\pi$
$740$	−2.22761e7	−	3.85833e7i	−1.49541	−	2.59012i
$741$	−1.53999e6			−0.103032
$742$		0			0
$743$	−2.40124e7			−1.59574			−0.797871	−	0.602828i	$-0.794041\pi$
$743$	−2.40124e7			−1.59574			−0.797871	+	0.602828i	$0.794041\pi$
$744$	−1.92149e6	−	3.32812e6i	−0.127264	−	0.220428i
$745$	1.50291e7	−	2.60312e7i	0.992072	−	1.71832i
$746$	3.80271e6	−	6.58649e6i	0.250176	−	0.433318i
$747$	699320.	+	1.21126e6i	0.0458537	+	0.0794209i
$748$	6.94316e7			4.53736
$749$		0			0
$750$	−8.24288e6			−0.535089
$751$	−8.47395e6	−	1.46773e7i	−0.548259	−	0.949613i	−0.998394	−	0.0566524i	$-0.981957\pi$
$751$	−8.47395e6	−	1.46773e7i	−0.548259	−	0.949613i	0.450135	−	0.892961i	$-0.351376\pi$
$752$	2.34047e6	−	4.05381e6i	0.150924	−	0.261408i
$753$	−1.73516e6	+	3.00538e6i	−0.111520	+	0.193158i
$754$	3.48769e7	+	6.04086e7i	2.23414	+	3.86964i
$755$	−1.05859e7			−0.675863
$756$		0			0
$757$	4.56402e6			0.289473			0.144736	−	0.989470i	$-0.453767\pi$
$757$	4.56402e6			0.289473			0.144736	+	0.989470i	$0.453767\pi$
$758$	−1.51975e7	−	2.63228e7i	−0.960723	−	1.66402i
$759$	141449.	−	244998.i	0.00891245	−	0.0154368i
$760$	2.42257e6	−	4.19602e6i	0.152140	−	0.263514i
$761$	−2.37009e6	−	4.10512e6i	−0.148355	−	0.256959i	0.782264	−	0.622947i	$-0.214065\pi$
$761$	−2.37009e6	−	4.10512e6i	−0.148355	−	0.256959i	−0.930620	+	0.365987i	$0.880731\pi$
$762$	−1.67055e7			−1.04225
$763$		0			0
$764$	5.24653e7			3.25191
$765$	3.96723e6	+	6.87144e6i	0.245095	+	0.424516i
$766$	−1.25576e7	+	2.17504e7i	−0.773277	+	1.33935i
$767$	1.18980e7	−	2.06080e7i	0.730275	−	1.26487i
$768$	9.51677e6	+	1.64835e7i	0.582219	+	1.00843i
$769$	1.39469e7			0.850476			0.425238	−	0.905082i	$-0.360190\pi$
$769$	1.39469e7			0.850476			0.425238	+	0.905082i	$0.360190\pi$
$770$		0			0
$771$	3.97628e6			0.240902
$772$	−2.77563e7	−	4.80752e7i	−1.67617	−	2.90321i
$773$	7.47806e6	−	1.29524e7i	0.450132	−	0.779652i	−0.548262	−	0.836307i	$-0.684710\pi$
$773$	7.47806e6	−	1.29524e7i	0.450132	−	0.779652i	0.998394	+	0.0566552i	$0.0180436\pi$
$774$	−2.44581e6	+	4.23627e6i	−0.146747	+	0.254174i
$775$	−1.07563e6	−	1.86304e6i	−0.0643290	−	0.111421i
$776$	−6.10683e6			−0.364050
$777$		0			0
$778$	−9.86012e6			−0.584028
$779$	1.27940e6	+	2.21599e6i	0.0755377	+	0.130835i
$780$	−1.94178e7	+	3.36325e7i	−1.14278	+	1.97935i
$781$	−1.63396e7	+	2.83011e7i	−0.958550	+	1.66026i
$782$	299470.	+	518697.i	0.0175120	+	0.0303317i
$783$	−5.64727e6			−0.329180
$784$		0			0
$785$	1.16664e7			0.675716
$786$	−5.58703e6	−	9.67702e6i	−0.322571	−	0.558709i
$787$	1.09136e7	−	1.89030e7i	0.628105	−	1.08791i	−0.359826	−	0.933019i	$-0.617164\pi$
$787$	1.09136e7	−	1.89030e7i	0.628105	−	1.08791i	0.987932	−	0.154891i	$-0.0495026\pi$
$788$	1.51248e7	−	2.61970e7i	0.867712	−	1.50292i
$789$	2.70119e6	+	4.67859e6i	0.154476	+	0.267561i
$790$	1.62818e7			0.928183
$791$		0			0
$792$	−2.14520e7			−1.21522
$793$	2.89360e6	+	5.01187e6i	0.163402	+	0.283020i
$794$	1.45384e7	−	2.51813e7i	0.818400	−	1.41751i
$795$	−8.12845e6	+	1.40789e7i	−0.456131	+	0.790043i
$796$	−2.10990e7	−	3.65446e7i	−1.18027	−	2.04428i
$797$	8.79229e6			0.490294			0.245147	−	0.969486i	$-0.421164\pi$
$797$	8.79229e6			0.490294			0.245147	+	0.969486i	$0.421164\pi$
$798$		0			0
$799$	4.51822e6			0.250381
$800$	−2.60048e6	−	4.50416e6i	−0.143658	−	0.248822i
$801$	−2.02215e6	+	3.50247e6i	−0.111361	+	0.192883i
$802$	2.11750e7	−	3.66762e7i	1.16249	−	2.01349i
$803$	−1.44821e7	−	2.50837e7i	−0.792579	−	1.37279i
$804$	−1.46133e7			−0.797276
$805$		0			0
$806$	1.06183e7			0.575725
$807$	1.46524e6	+	2.53787e6i	0.0791999	+	0.137178i
$808$	−1.90915e7	+	3.30675e7i	−1.02876	+	1.78186i
$809$	1.43726e6	−	2.48940e6i	0.0772081	−	0.133728i	−0.824836	−	0.565372i	$-0.808733\pi$
$809$	1.43726e6	−	2.48940e6i	0.0772081	−	0.133728i	0.902044	+	0.431643i	$0.142066\pi$
$810$	−2.30992e6	−	4.00091e6i	−0.123704	−	0.214262i
$811$	660356.			0.0352554			0.0176277	−	0.999845i	$-0.494389\pi$
$811$	660356.			0.0352554			0.0176277	+	0.999845i	$0.494389\pi$
$812$		0			0
$813$	−1.58033e7			−0.838535
$814$	3.39987e7	+	5.88875e7i	1.79846	+	3.11503i
$815$	−3.36695e6	+	5.83172e6i	−0.177559	+	0.307541i
$816$	9.03856e6	−	1.56552e7i	0.475197	−	0.823066i
$817$	573796.	+	993844.i	0.0300748	+	0.0520910i
$818$	−4.14258e7			−2.16465
$819$		0			0
$820$	6.45278e7			3.35129
$821$	1.52869e7	+	2.64777e7i	0.791519	+	1.37095i	0.925026	+	0.379904i	$0.124043\pi$
$821$	1.52869e7	+	2.64777e7i	0.791519	+	1.37095i	−0.133507	+	0.991048i	$0.542624\pi$
$822$	−4.48240e6	+	7.76375e6i	−0.231383	+	0.400767i
$823$	−5.56406e6	+	9.63723e6i	−0.286346	+	0.495967i	−0.972935	−	0.231080i	$-0.925774\pi$
$823$	−5.56406e6	+	9.63723e6i	−0.286346	+	0.495967i	0.686588	+	0.727046i	$0.259108\pi$
$824$	3.68543e6	+	6.38334e6i	0.189090	+	0.327514i
$825$	−1.20085e7			−0.614264
$826$		0			0
$827$	−2.78304e7			−1.41500			−0.707500	−	0.706714i	$-0.750177\pi$
$827$	−2.78304e7			−1.41500			−0.707500	+	0.706714i	$0.750177\pi$
$828$	−118668.	−	205540.i	−0.00601533	−	0.0104188i
$829$	3.53066e6	−	6.11529e6i	0.178431	−	0.309051i	−0.762912	−	0.646502i	$-0.776231\pi$
$829$	3.53066e6	−	6.11529e6i	0.178431	−	0.309051i	0.941343	+	0.337451i	$0.109565\pi$
$830$	6.07923e6	−	1.05295e7i	0.306304	−	0.530535i
$831$	1.54063e6	+	2.66846e6i	0.0773922	+	0.134047i
$832$	−1.58574e7			−0.794190
$833$		0			0
$834$	2.29236e7			1.14122
$835$	−1.66806e7	−	2.88916e7i	−0.827933	−	1.43402i
$836$	−4.74211e6	+	8.21358e6i	−0.234669	+	0.406459i
$837$	−429827.	+	744482.i	−0.0212070	+	0.0367316i
$838$	3.00193e7	+	5.19949e7i	1.47669	+	2.55771i
$839$	2.27299e7			1.11479			0.557395	−	0.830247i	$-0.311801\pi$
$839$	2.27299e7			1.11479			0.557395	+	0.830247i	$0.311801\pi$
$840$		0			0
$841$	3.94986e7			1.92571
$842$	5.04241e6	+	8.73371e6i	0.245108	+	0.424540i
$843$	−4.18802e6	+	7.25386e6i	−0.202974	+	0.351561i
$844$	−2.62418e7	+	4.54522e7i	−1.26805	+	2.19634i
$845$	−1.54093e7	−	2.66897e7i	−0.742406	−	1.28588i
$846$	−2.63074e6			−0.126372
$847$		0			0
$848$	3.70382e7			1.76872
$849$	−7.41419e6	−	1.28417e7i	−0.353016	−	0.611442i
$850$	1.27119e7	−	2.20177e7i	0.603482	−	1.04526i
$851$	−199600.	+	345717.i	−0.00944792	+	0.0163643i
$852$	1.37081e7	+	2.37430e7i	0.646959	+	1.12057i
$853$	7.94309e6			0.373781			0.186890	−	0.982381i	$-0.440159\pi$
$853$	7.94309e6			0.373781			0.186890	+	0.982381i	$0.440159\pi$
$854$		0			0
$855$	−1.08383e6			−0.0507046
$856$	683543.	+	1.18393e6i	0.0318846	+	0.0552258i
$857$	−4.95883e6	+	8.58894e6i	−0.230636	+	0.399473i	−0.957995	−	0.286783i	$-0.907414\pi$
$857$	−4.95883e6	+	8.58894e6i	−0.230636	+	0.399473i	0.727359	+	0.686257i	$0.240747\pi$
$858$	2.96362e7	−	5.13314e7i	1.37437	−	2.38048i
$859$	−30877.2	−	53480.9i	−0.00142776	−	0.00247295i	0.865311	−	0.501236i	$-0.167121\pi$
$859$	−30877.2	−	53480.9i	−0.00142776	−	0.00247295i	−0.866738	+	0.498763i	$0.833788\pi$
$860$	2.89399e7			1.33429
$861$		0			0
$862$	3.03419e6			0.139083
$863$	−1.99504e7	−	3.45550e7i	−0.911851	−	1.57937i	−0.811448	−	0.584425i	$-0.801320\pi$
$863$	−1.99504e7	−	3.45550e7i	−0.911851	−	1.57937i	−0.100403	−	0.994947i	$-0.532013\pi$
$864$	−1.03917e6	+	1.79989e6i	−0.0473589	+	0.0820280i
$865$	−9.10614e6	+	1.57723e7i	−0.413803	+	0.716728i
$866$	1.98742e7	+	3.44231e7i	0.900522	+	1.55975i
$867$	4.67002e6			0.210994
$868$		0			0
$869$	−1.69120e7			−0.759708
$870$	2.45460e7	+	4.25149e7i	1.09947	+	1.90434i
$871$	1.07128e7	−	1.85552e7i	0.478474	−	0.828742i
$872$	−1.54562e6	+	2.67710e6i	−0.0688355	+	0.119227i
$873$	683032.	+	1.18305e6i	0.0303323	+	0.0525371i
$874$	−81814.0			−0.00362284
$875$		0			0
$876$	−2.42994e7			−1.06988
$877$	9.45919e6	+	1.63838e7i	0.415293	+	0.719309i	0.995459	−	0.0951894i	$-0.0303457\pi$
$877$	9.45919e6	+	1.63838e7i	0.415293	+	0.719309i	−0.580166	+	0.814498i	$0.697012\pi$
$878$	1.87566e7	−	3.24874e7i	0.821143	−	1.42226i
$879$	−5.14701e6	+	8.91488e6i	−0.224689	+	0.389174i
$880$	3.71125e7	+	6.42807e7i	1.61552	+	2.79817i
$881$	−9.12061e6			−0.395899			−0.197949	−	0.980212i	$-0.563428\pi$
$881$	−9.12061e6			−0.395899			−0.197949	+	0.980212i	$0.563428\pi$
$882$		0			0
$883$	−4.49665e7			−1.94083			−0.970414	−	0.241449i	$-0.922377\pi$
$883$	−4.49665e7			−1.94083			−0.970414	+	0.241449i	$0.922377\pi$
$884$	4.27017e7	+	7.39616e7i	1.83787	+	3.18328i
$885$	8.37371e6	−	1.45037e7i	0.359385	−	0.622473i
$886$	6.55967e6	−	1.13617e7i	0.280736	−	0.486249i
$887$	1.41493e7	+	2.45073e7i	0.603845	+	1.04589i	0.992233	+	0.124394i	$0.0396986\pi$
$887$	1.41493e7	+	2.45073e7i	0.603845	+	1.04589i	−0.388388	+	0.921496i	$0.626968\pi$
$888$	3.02709e7			1.28823
$889$		0			0
$890$	3.51574e7			1.48779
$891$	2.39934e6	+	4.15579e6i	0.101251	+	0.175371i
$892$	4.96554e7	−	8.60056e7i	2.08956	−	3.61922i
$893$	−308590.	+	534494.i	−0.0129495	+	0.0224292i
$894$	1.92438e7	+	3.33312e7i	0.805280	+	1.39479i
$895$	−3.81429e7			−1.59168
$896$		0			0
$897$	347977.			0.0144401
$898$	−3.15936e7	−	5.47218e7i	−1.30740	−	2.26448i
$899$	4.56748e6	−	7.91111e6i	0.188485	−	0.326466i
$900$	−5.03725e6	+	8.72478e6i	−0.207294	+	0.359044i
$901$	1.78753e7	+	3.09610e7i	0.733571	+	1.27058i
$902$	−9.84850e7			−4.03045
$903$		0			0
$904$	−3.65247e7			−1.48650
$905$	−2.30024e7	−	3.98413e7i	−0.933580	−	1.61701i
$906$	6.77724e6	−	1.17385e7i	0.274304	−	0.475109i
$907$	384269.	−	665573.i	0.0155102	−	0.0268644i	−0.858166	−	0.513372i	$-0.828396\pi$
$907$	384269.	−	665573.i	0.0155102	−	0.0268644i	0.873676	+	0.486508i	$0.161729\pi$
$908$	−3.23813e7	−	5.60860e7i	−1.30341	−	2.25756i
$909$	8.54135e6			0.342860
$910$		0			0
$911$	3.45594e6			0.137965			0.0689827	−	0.997618i	$-0.478025\pi$
$911$	3.45594e6			0.137965			0.0689827	+	0.997618i	$0.478025\pi$
$912$	1.23465e6	+	2.13848e6i	0.0491538	+	0.0851369i
$913$	−6.31456e6	+	1.09371e7i	−0.250707	+	0.434237i
$914$	2.91997e6	−	5.05754e6i	0.115615	−	0.200251i
$915$	2.03649e6	+	3.52730e6i	0.0804136	+	0.139280i
$916$	−2.12908e7			−0.838404
$917$		0			0
$918$	−1.01595e7			−0.397894
$919$	−2.82663e6	−	4.89587e6i	−0.110403	−	0.191224i	0.805530	−	0.592555i	$-0.201881\pi$
$919$	−2.82663e6	−	4.89587e6i	−0.110403	−	0.191224i	−0.915933	+	0.401332i	$0.868547\pi$
$920$	−547403.	+	948130.i	−0.0213225	+	0.0369316i
$921$	1.34474e7	−	2.32916e7i	0.522383	−	0.904795i
$922$	−1.46821e7	−	2.54301e7i	−0.568801	−	0.985192i
$923$	−4.01967e7			−1.55305
$924$		0			0
$925$	1.69453e7			0.651171
$926$	−1.88526e7	−	3.26536e7i	−0.722508	−	1.25142i
$927$	824410.	−	1.42792e6i	0.0315097	−	0.0545764i
$928$	1.10425e7	−	1.91262e7i	0.420919	−	0.729054i
$929$	1.21127e7	+	2.09797e7i	0.460469	+	0.797555i	0.998984	−	0.0450605i	$-0.0143481\pi$
$929$	1.21127e7	+	2.09797e7i	0.460469	+	0.797555i	−0.538516	+	0.842615i	$0.681015\pi$
$930$	7.47302e6			0.283327
$931$		0			0
$932$	2.70602e7			1.02045
$933$	1.27688e7	+	2.21162e7i	0.480226	+	0.831775i
$934$	−1.45427e7	+	2.51888e7i	−0.545480	+	0.944799i
$935$	−3.58224e7	+	6.20463e7i	−1.34007	+	2.32106i
$936$	−1.31934e7	−	2.28516e7i	−0.492228	−	0.852563i
$937$	3.02477e7			1.12549			0.562746	−	0.826630i	$-0.309745\pi$
$937$	3.02477e7			1.12549			0.562746	+	0.826630i	$0.309745\pi$
$938$		0			0
$939$	1.93274e7			0.715334
$940$	7.78202e6	+	1.34788e7i	0.287258	+	0.497546i
$941$	−6.94743e6	+	1.20333e7i	−0.255770	+	0.443007i	−0.965104	−	0.261865i	$-0.915662\pi$
$941$	−6.94743e6	+	1.20333e7i	−0.255770	+	0.443007i	0.709334	+	0.704872i	$0.248996\pi$
$942$	−7.46904e6	+	1.29368e7i	−0.274244	+	0.475005i
$943$	−289093.	−	500724.i	−0.0105867	−	0.0183366i
$944$	−3.81557e7			−1.39357
$945$		0			0
$946$	−4.41693e7			−1.60470
$947$	8.93399e6	+	1.54741e7i	0.323721	+	0.560701i	0.981253	−	0.192726i	$-0.0617329\pi$
$947$	8.93399e6	+	1.54741e7i	0.323721	+	0.560701i	−0.657532	+	0.753427i	$0.728400\pi$
$948$	−7.09414e6	+	1.22874e7i	−0.256377	+	0.444058i
$949$	1.78135e7	−	3.08539e7i	0.642073	−	1.11210i
$950$	1.73643e6	+	3.00758e6i	0.0624234	+	0.108121i
$951$	−2.37022e7			−0.849839
$952$		0			0
$953$	1.37348e7			0.489880			0.244940	−	0.969538i	$-0.421232\pi$
$953$	1.37348e7			0.489880			0.244940	+	0.969538i	$0.421232\pi$
$954$	−1.04079e7	−	1.80271e7i	−0.370249	−	0.641290i
$955$	−2.70689e7	+	4.68847e7i	−0.960422	+	1.66350i
$956$	2.96688e6	−	5.13878e6i	0.104992	−	0.181851i
$957$	−2.54962e7	−	4.41608e7i	−0.899904	−	1.55868i
$958$	7.07250e7			2.48977
$959$		0			0
$960$	−1.11603e7			−0.390839
$961$	1.36193e7	+	2.35893e7i	0.475714	+	0.823961i
$962$	−4.18197e7	+	7.24339e7i	−1.45695	+	2.52350i
$963$	152905.	−	264839.i	0.00531319	−	0.00920272i
$964$	−5.35786e7	−	9.28009e7i	−1.85695	−	3.21632i
$965$	5.72821e7			1.98016
$966$		0			0
$967$	−7.63195e6			−0.262464			−0.131232	−	0.991352i	$-0.541893\pi$
$967$	−7.63195e6			−0.262464			−0.131232	+	0.991352i	$0.541893\pi$
$968$	−6.76928e7	−	1.17247e8i	−2.32195	−	4.02174i
$969$	−1.19173e6	+	2.06414e6i	−0.0407727	+	0.0706204i
$970$	5.93764e6	−	1.02843e7i	0.202621	−	0.350950i
$971$	1.11240e7	+	1.92674e7i	0.378629	+	0.655804i	0.990863	−	0.134872i	$-0.0430624\pi$
$971$	1.11240e7	+	1.92674e7i	0.378629	+	0.655804i	−0.612234	+	0.790676i	$0.709729\pi$
$972$	4.02584e6			0.136675
$973$		0			0
$974$	2.73223e7			0.922827
$975$	−7.38548e6	−	1.27920e7i	−0.248810	−	0.430951i
$976$	4.63974e6	−	8.03627e6i	0.155908	−	0.270041i
$977$	9.11924e6	−	1.57950e7i	0.305648	−	0.529398i	−0.671757	−	0.740771i	$-0.734460\pi$
$977$	9.11924e6	−	1.57950e7i	0.305648	−	0.529398i	0.977405	+	0.211373i	$0.0677935\pi$
$978$	−4.31115e6	−	7.46713e6i	−0.144127	−	0.249636i
$979$	−3.65184e7			−1.21774
$980$		0			0
$981$	691495.			0.0229412
$982$	5.14753e7	+	8.91578e7i	1.70341	+	2.95040i
$983$	1.92230e7	−	3.32952e7i	0.634508	−	1.09900i	−0.352112	−	0.935958i	$-0.614536\pi$
$983$	1.92230e7	−	3.32952e7i	0.634508	−	1.09900i	0.986619	−	0.163041i	$-0.0521304\pi$
$984$	−2.19217e7	+	3.79694e7i	−0.721749	+	1.25011i
$985$	1.56070e7	+	2.70321e7i	0.512541	+	0.887747i
$986$	1.07959e8			3.53643
$987$		0			0
$988$	−1.16660e7			−0.380214
$989$	−129655.	−	224569.i	−0.00421500	−	0.00730060i
$990$	2.08576e7	−	3.61265e7i	0.676359	−	1.17149i
$991$	1.24829e7	−	2.16210e7i	0.403767	−	0.699345i	−0.590410	−	0.807103i	$-0.701034\pi$
$991$	1.24829e7	−	2.16210e7i	0.403767	−	0.699345i	0.994177	+	0.107759i	$0.0343674\pi$
$992$	−1.68095e6	−	2.91149e6i	−0.0542344	−	0.0939368i
$993$	2.95590e7			0.951299
$994$		0			0
$995$	4.35433e7			1.39432
$996$	5.29757e6	+	9.17567e6i	0.169211	+	0.293082i
$997$	−1.61381e7	+	2.79521e7i	−0.514181	+	0.890587i	0.485684	+	0.874134i	$0.338571\pi$
$997$	−1.61381e7	+	2.79521e7i	−0.514181	+	0.890587i	−0.999865	+	0.0164526i	$0.994763\pi$
$998$	1.81957e7	−	3.15159e7i	0.578286	−	1.00162i
$999$	−3.38572e6	−	5.86424e6i	−0.107334	−	0.185908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.p.67.1		12
7.2	even	3	inner	147.6.e.p.79.1		12
7.3	odd	6		147.6.a.n.1.6	✓	6
7.4	even	3		147.6.a.o.1.6	yes	6
7.5	odd	6		147.6.e.q.79.1		12
7.6	odd	2		147.6.e.q.67.1		12
21.11	odd	6		441.6.a.ba.1.1		6
21.17	even	6		441.6.a.bb.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.6	✓	6	7.3	odd	6
147.6.a.o.1.6	yes	6	7.4	even	3
147.6.e.p.67.1		12	1.1	even	1	trivial
147.6.e.p.79.1		12	7.2	even	3	inner
147.6.e.q.67.1		12	7.6	odd	2
147.6.e.q.79.1		12	7.5	odd	6
441.6.a.ba.1.1		6	21.11	odd	6
441.6.a.bb.1.1		6	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.00445 - 8.66795i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-34.0890 + 59.0438i) q^{4} +(-35.1756 - 60.9260i) q^{5} +90.0800 q^{6} +362.101 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-5.00445 - 8.66795i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-34.0890 + 59.0438i) q^{4} +(-35.1756 - 60.9260i) q^{5} +90.0800 q^{6} +362.101 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-352.069 + 609.801i) q^{10} +(365.698 - 633.408i) q^{11} +(-306.801 - 531.394i) q^{12} +899.645 q^{13} +633.161 q^{15} +(-721.267 - 1249.27i) q^{16} +(696.195 - 1205.84i) q^{17} +(-405.360 + 702.104i) q^{18} +(95.0989 + 164.716i) q^{19} +4796.40 q^{20} -7320.46 q^{22} +(-21.4885 - 37.2192i) q^{23} +(-1629.45 + 2822.30i) q^{24} +(-912.148 + 1579.89i) q^{25} +(-4502.22 - 7798.08i) q^{26} +729.000 q^{27} -7746.59 q^{29} +(-3168.62 - 5488.21i) q^{30} +(-589.611 + 1021.24i) q^{31} +(-1425.47 + 2468.99i) q^{32} +(3291.28 + 5700.67i) q^{33} -13936.3 q^{34} +5522.41 q^{36} +(-4644.34 - 8044.23i) q^{37} +(951.835 - 1648.63i) q^{38} +(-4048.40 + 7012.04i) q^{39} +(-12737.1 - 22061.3i) q^{40} +13453.4 q^{41} +6033.68 q^{43} +(24932.5 + 43184.4i) q^{44} +(-2849.22 + 4935.00i) q^{45} +(-215.076 + 372.523i) q^{46} +(1622.47 + 2810.20i) q^{47} +12982.8 q^{48} +18259.2 q^{50} +(6265.75 + 10852.6i) q^{51} +(-30668.0 + 53118.5i) q^{52} +(-12837.9 + 22235.9i) q^{53} +(-3648.24 - 6318.94i) q^{54} -51454.6 q^{55} -1711.78 q^{57} +(38767.4 + 67147.1i) q^{58} +(13225.2 - 22906.8i) q^{59} +(-21583.8 + 37384.2i) q^{60} +(3216.38 + 5570.94i) q^{61} +11802.7 q^{62} -17626.3 q^{64} +(-31645.6 - 54811.7i) q^{65} +(32942.1 - 57057.4i) q^{66} +(11907.8 - 20625.0i) q^{67} +(47465.1 + 82212.0i) q^{68} +386.793 q^{69} -44680.7 q^{71} +(-14665.1 - 25400.7i) q^{72} +(19800.6 - 34295.7i) q^{73} +(-46484.7 + 80513.8i) q^{74} +(-8209.33 - 14219.0i) q^{75} -12967.3 q^{76} +81040.0 q^{78} +(-11561.5 - 20025.1i) q^{79} +(-50742.0 + 87887.7i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-67326.8 - 116613. i) q^{82} -17267.2 q^{83} -97956.3 q^{85} +(-30195.2 - 52299.6i) q^{86} +(34859.7 - 60378.7i) q^{87} +(132420. - 229357. i) q^{88} +(-24964.9 - 43240.4i) q^{89} +57035.2 q^{90} +2930.08 q^{92} +(-5306.50 - 9191.13i) q^{93} +(16239.1 - 28127.0i) q^{94} +(6690.33 - 11588.0i) q^{95} +(-12829.2 - 22220.9i) q^{96} -16865.0 q^{97} -59243.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9	\( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 54 * q^3 - 150 * q^4 - 100 * q^5 + 36 * q^6 - 228 * q^8 - 486 * q^9 - 864 * q^10 - 604 * q^11 - 1350 * q^12 + 2704 * q^13 + 1800 * q^15 - 4578 * q^16 - 3028 * q^17 - 162 * q^18 - 1728 * q^19 + 904 * q^20 - 8232 * q^22 + 4484 * q^23 + 1026 * q^24 - 4806 * q^25 - 14172 * q^26 + 8748 * q^27 - 10640 * q^29 - 7776 * q^30 - 3976 * q^31 + 37326 * q^32 - 5436 * q^33 - 32672 * q^34 + 24300 * q^36 - 22680 * q^37 - 52744 * q^38 - 12168 * q^39 - 100600 * q^40 + 57512 * q^41 - 13536 * q^43 + 64940 * q^44 - 8100 * q^45 - 540 * q^46 - 51552 * q^47 + 82404 * q^48 - 81244 * q^50 - 27252 * q^51 - 119296 * q^52 - 80884 * q^53 - 1458 * q^54 + 23312 * q^55 + 31104 * q^57 + 70464 * q^58 - 8872 * q^59 - 4068 * q^60 - 50896 * q^61 + 23648 * q^62 + 399180 * q^64 - 3492 * q^65 + 37044 * q^66 - 6480 * q^67 - 37348 * q^68 - 80712 * q^69 - 221704 * q^71 + 9234 * q^72 - 64232 * q^73 + 27464 * q^74 - 43254 * q^75 - 389728 * q^76 + 255096 * q^78 - 111696 * q^79 + 308940 * q^80 - 39366 * q^81 + 189640 * q^82 + 202256 * q^83 - 46584 * q^85 - 3824 * q^86 + 47880 * q^87 + 97788 * q^88 + 35012 * q^89 + 139968 * q^90 - 898520 * q^92 - 35784 * q^93 + 121016 * q^94 + 119080 * q^95 + 335934 * q^96 + 141904 * q^97 + 97848 * q^99

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