LMFDB - Embedded newform 294.6.e.u.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.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:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.6.e.u.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5355 + 52.8891i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5355 + 52.8891i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(122.142 - 211.556i) q^{10} +(18.2721 - 31.6482i) q^{11} +(-72.0000 - 124.708i) q^{12} +34.5656 q^{13} -549.640 q^{15} +(-128.000 - 221.703i) q^{16} +(1030.52 - 1784.91i) q^{17} +(-162.000 + 280.592i) q^{18} +(-226.119 - 391.650i) q^{19} -977.137 q^{20} -146.177 q^{22} +(-842.124 - 1458.60i) q^{23} +(-288.000 + 498.831i) q^{24} +(-302.338 + 523.664i) q^{25} +(-69.1312 - 119.739i) q^{26} +729.000 q^{27} -4765.22 q^{29} +(1099.28 + 1904.01i) q^{30} +(2630.43 - 4556.04i) q^{31} +(-512.000 + 886.810i) q^{32} +(164.449 + 284.834i) q^{33} -8244.16 q^{34} +1296.00 q^{36} +(6410.98 + 11104.1i) q^{37} +(-904.476 + 1566.60i) q^{38} +(-155.545 + 269.412i) q^{39} +(1954.27 + 3384.90i) q^{40} -7126.74 q^{41} +11141.7 q^{43} +(292.353 + 506.371i) q^{44} +(2473.38 - 4284.02i) q^{45} +(-3368.50 + 5834.41i) q^{46} +(11721.6 + 20302.4i) q^{47} +2304.00 q^{48} +2418.70 q^{50} +(9274.68 + 16064.2i) q^{51} +(-276.525 + 478.955i) q^{52} +(3515.15 - 6088.42i) q^{53} +(-1458.00 - 2525.33i) q^{54} +2231.79 q^{55} +4070.14 q^{57} +(9530.43 + 16507.2i) q^{58} +(22111.4 - 38298.1i) q^{59} +(4397.12 - 7616.03i) q^{60} +(-9690.24 - 16784.0i) q^{61} -21043.5 q^{62} +4096.00 q^{64} +(1055.48 + 1828.14i) q^{65} +(657.795 - 1139.33i) q^{66} +(-10472.0 + 18138.1i) q^{67} +(16488.3 + 28558.6i) q^{68} +15158.2 q^{69} +79843.4 q^{71} +(-2592.00 - 4489.48i) q^{72} +(18532.9 - 32099.9i) q^{73} +(25643.9 - 44416.6i) q^{74} +(-2721.04 - 4712.98i) q^{75} +7235.81 q^{76} +1244.36 q^{78} +(-21036.0 - 36435.4i) q^{79} +(7817.10 - 13539.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(14253.5 + 24687.7i) q^{82} -6311.34 q^{83} +125870. q^{85} +(-22283.4 - 38595.9i) q^{86} +(21443.5 - 37141.2i) q^{87} +(1169.41 - 2025.48i) q^{88} +(25747.9 + 44596.7i) q^{89} -19787.0 q^{90} +26948.0 q^{92} +(23673.9 + 41004.4i) q^{93} +(46886.4 - 81209.6i) q^{94} +(13809.3 - 23918.5i) q^{95} +(-4608.00 - 7981.29i) q^{96} -127357. q^{97} -2960.08 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 1440 q^{13} - 1944 q^{15} - 512 q^{16} + 612 q^{17} - 648 q^{18} + 2088 q^{19} - 3456 q^{20} - 992 q^{22} - 772 q^{23} - 1152 q^{24} + 318 q^{25} + 2880 q^{26} + 2916 q^{27} - 9184 q^{29} + 3888 q^{30} + 9792 q^{31} - 2048 q^{32} + 1116 q^{33} - 4896 q^{34} + 5184 q^{36} + 5992 q^{37} + 8352 q^{38} + 6480 q^{39} + 6912 q^{40} - 40392 q^{41} - 2272 q^{43} + 1984 q^{44} + 8748 q^{45} - 3088 q^{46} + 36936 q^{47} + 9216 q^{48} - 2544 q^{50} + 5508 q^{51} + 11520 q^{52} + 16708 q^{53} - 5832 q^{54} + 12672 q^{55} - 37584 q^{57} + 18368 q^{58} + 74592 q^{59} + 15552 q^{60} - 18648 q^{61} - 78336 q^{62} + 16384 q^{64} - 33300 q^{65} + 4464 q^{66} - 67344 q^{67} + 9792 q^{68} + 13896 q^{69} + 153096 q^{71} - 10368 q^{72} + 47304 q^{73} + 23968 q^{74} + 2862 q^{75} - 66816 q^{76} - 51840 q^{78} - 140656 q^{79} + 27648 q^{80} - 13122 q^{81} + 80784 q^{82} - 188208 q^{83} + 115736 q^{85} + 4544 q^{86} + 41328 q^{87} + 7936 q^{88} - 17604 q^{89} - 69984 q^{90} + 24704 q^{92} + 88128 q^{93} + 147744 q^{94} - 91592 q^{95} - 18432 q^{96} - 170352 q^{97} - 20088 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 1440 * q^13 - 1944 * q^15 - 512 * q^16 + 612 * q^17 - 648 * q^18 + 2088 * q^19 - 3456 * q^20 - 992 * q^22 - 772 * q^23 - 1152 * q^24 + 318 * q^25 + 2880 * q^26 + 2916 * q^27 - 9184 * q^29 + 3888 * q^30 + 9792 * q^31 - 2048 * q^32 + 1116 * q^33 - 4896 * q^34 + 5184 * q^36 + 5992 * q^37 + 8352 * q^38 + 6480 * q^39 + 6912 * q^40 - 40392 * q^41 - 2272 * q^43 + 1984 * q^44 + 8748 * q^45 - 3088 * q^46 + 36936 * q^47 + 9216 * q^48 - 2544 * q^50 + 5508 * q^51 + 11520 * q^52 + 16708 * q^53 - 5832 * q^54 + 12672 * q^55 - 37584 * q^57 + 18368 * q^58 + 74592 * q^59 + 15552 * q^60 - 18648 * q^61 - 78336 * q^62 + 16384 * q^64 - 33300 * q^65 + 4464 * q^66 - 67344 * q^67 + 9792 * q^68 + 13896 * q^69 + 153096 * q^71 - 10368 * q^72 + 47304 * q^73 + 23968 * q^74 + 2862 * q^75 - 66816 * q^76 - 51840 * q^78 - 140656 * q^79 + 27648 * q^80 - 13122 * q^81 + 80784 * q^82 - 188208 * q^83 + 115736 * q^85 + 4544 * q^86 + 41328 * q^87 + 7936 * q^88 - 17604 * q^89 - 69984 * q^90 + 24704 * q^92 + 88128 * q^93 + 147744 * q^94 - 91592 * q^95 - 18432 * q^96 - 170352 * q^97 - 20088 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	30.5355	+	52.8891i	0.546236	+	0.946109i	0.998528	+	0.0542389i	$0.0172732\pi$
$5$	30.5355	+	52.8891i	0.546236	+	0.946109i	−0.452292	+	0.891870i	$0.649393\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	122.142	−	211.556i	0.386247	−	0.669000i
$11$	18.2721	−	31.6482i	0.0455309	−	0.0788618i	−0.842362	−	0.538912i	$-0.818835\pi$
$11$	18.2721	−	31.6482i	0.0455309	−	0.0788618i	0.887893	+	0.460051i	$0.152169\pi$
$12$	−72.0000	−	124.708i	−0.144338	−	0.250000i
$13$	34.5656			0.0567264			0.0283632	−	0.999598i	$-0.490970\pi$
$13$	34.5656			0.0567264			0.0283632	+	0.999598i	$0.490970\pi$
$14$		0			0
$15$	−549.640			−0.630739
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	1030.52	−	1784.91i	0.864836	−	1.49794i	−0.00237330	−	0.999997i	$-0.500755\pi$
$17$	1030.52	−	1784.91i	0.864836	−	1.49794i	0.867210	−	0.497943i	$-0.165911\pi$
$18$	−162.000	+	280.592i	−0.117851	+	0.204124i
$19$	−226.119	−	391.650i	−0.143699	−	0.248894i	0.785188	−	0.619258i	$-0.212566\pi$
$19$	−226.119	−	391.650i	−0.143699	−	0.248894i	−0.928887	+	0.370364i	$0.879233\pi$
$20$	−977.137			−0.546236
$21$		0			0
$22$	−146.177			−0.0643904
$23$	−842.124	−	1458.60i	−0.331938	−	0.574933i	0.650954	−	0.759117i	$-0.274369\pi$
$23$	−842.124	−	1458.60i	−0.331938	−	0.574933i	−0.982892	+	0.184184i	$0.941036\pi$
$24$	−288.000	+	498.831i	−0.102062	+	0.176777i
$25$	−302.338	+	523.664i	−0.0967481	+	0.167573i
$26$	−69.1312	−	119.739i	−0.0200558	−	0.0347377i
$27$	729.000			0.192450
$28$		0			0
$29$	−4765.22			−1.05217			−0.526087	−	0.850431i	$-0.676341\pi$
$29$	−4765.22			−1.05217			−0.526087	+	0.850431i	$0.676341\pi$
$30$	1099.28	+	1904.01i	0.223000	+	0.386247i
$31$	2630.43	−	4556.04i	0.491613	−	0.851498i	−0.508341	−	0.861156i	$-0.669741\pi$
$31$	2630.43	−	4556.04i	0.491613	−	0.851498i	0.999953	+	0.00965788i	$0.00307425\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	164.449	+	284.834i	0.0262873	+	0.0455309i
$34$	−8244.16			−1.22306
$35$		0			0
$36$	1296.00			0.166667
$37$	6410.98	+	11104.1i	0.769875	+	1.33346i	0.937631	+	0.347633i	$0.113015\pi$
$37$	6410.98	+	11104.1i	0.769875	+	1.33346i	−0.167756	+	0.985829i	$0.553652\pi$
$38$	−904.476	+	1566.60i	−0.101610	+	0.175994i
$39$	−155.545	+	269.412i	−0.0163755	+	0.0283632i
$40$	1954.27	+	3384.90i	0.193124	+	0.334500i
$41$	−7126.74			−0.662111			−0.331056	−	0.943611i	$-0.607405\pi$
$41$	−7126.74			−0.662111			−0.331056	+	0.943611i	$0.607405\pi$
$42$		0			0
$43$	11141.7			0.918925			0.459462	−	0.888197i	$-0.348042\pi$
$43$	11141.7			0.918925			0.459462	+	0.888197i	$0.348042\pi$
$44$	292.353	+	506.371i	0.0227654	+	0.0394309i
$45$	2473.38	−	4284.02i	0.182079	−	0.315370i
$46$	−3368.50	+	5834.41i	−0.234715	+	0.406539i
$47$	11721.6	+	20302.4i	0.774002	+	1.34061i	0.935353	+	0.353714i	$0.115082\pi$
$47$	11721.6	+	20302.4i	0.774002	+	1.34061i	−0.161351	+	0.986897i	$0.551585\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	2418.70			0.136822
$51$	9274.68	+	16064.2i	0.499313	+	0.864836i
$52$	−276.525	+	478.955i	−0.0141816	+	0.0245633i
$53$	3515.15	−	6088.42i	0.171891	−	0.297725i	−0.767190	−	0.641420i	$-0.778346\pi$
$53$	3515.15	−	6088.42i	0.171891	−	0.297725i	0.939081	+	0.343696i	$0.111679\pi$
$54$	−1458.00	−	2525.33i	−0.0680414	−	0.117851i
$55$	2231.79			0.0994825
$56$		0			0
$57$	4070.14			0.165929
$58$	9530.43	+	16507.2i	0.372000	+	0.644323i
$59$	22111.4	−	38298.1i	0.826964	−	1.43234i	−0.0734457	−	0.997299i	$-0.523400\pi$
$59$	22111.4	−	38298.1i	0.826964	−	1.43234i	0.900409	−	0.435044i	$-0.143267\pi$
$60$	4397.12	−	7616.03i	0.157685	−	0.273118i
$61$	−9690.24	−	16784.0i	−0.333434	−	0.577524i	0.649749	−	0.760149i	$-0.274874\pi$
$61$	−9690.24	−	16784.0i	−0.333434	−	0.577524i	−0.983183	+	0.182624i	$0.941541\pi$
$62$	−21043.5			−0.695245
$63$		0			0
$64$	4096.00			0.125000
$65$	1055.48	+	1828.14i	0.0309860	+	0.0536694i
$66$	657.795	−	1139.33i	0.0185879	−	0.0321952i
$67$	−10472.0	+	18138.1i	−0.285000	+	0.493634i	−0.972609	−	0.232447i	$-0.925327\pi$
$67$	−10472.0	+	18138.1i	−0.285000	+	0.493634i	0.687609	+	0.726081i	$0.258660\pi$
$68$	16488.3	+	28558.6i	0.432418	+	0.748970i
$69$	15158.2			0.383289
$70$		0			0
$71$	79843.4			1.87972			0.939860	−	0.341560i	$-0.110955\pi$
$71$	79843.4			1.87972			0.939860	+	0.341560i	$0.110955\pi$
$72$	−2592.00	−	4489.48i	−0.0589256	−	0.102062i
$73$	18532.9	−	32099.9i	0.407039	−	0.705013i	−0.587517	−	0.809212i	$-0.699895\pi$
$73$	18532.9	−	32099.9i	0.407039	−	0.705013i	0.994556	+	0.104199i	$0.0332278\pi$
$74$	25643.9	−	44416.6i	0.544384	−	0.942900i
$75$	−2721.04	−	4712.98i	−0.0558575	−	0.0967481i
$76$	7235.81			0.143699
$77$		0			0
$78$	1244.36			0.0231585
$79$	−21036.0	−	36435.4i	−0.379224	−	0.656835i	0.611726	−	0.791070i	$-0.290476\pi$
$79$	−21036.0	−	36435.4i	−0.379224	−	0.656835i	−0.990950	+	0.134235i	$0.957142\pi$
$80$	7817.10	−	13539.6i	0.136559	−	0.236527i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	14253.5	+	24687.7i	0.234092	+	0.405459i
$83$	−6311.34			−0.100560			−0.0502801	−	0.998735i	$-0.516011\pi$
$83$	−6311.34			−0.100560			−0.0502801	+	0.998735i	$0.516011\pi$
$84$		0			0
$85$	125870.			1.88962
$86$	−22283.4	−	38595.9i	−0.324889	−	0.562724i
$87$	21443.5	−	37141.2i	0.303737	−	0.526087i
$88$	1169.41	−	2025.48i	0.0160976	−	0.0278819i
$89$	25747.9	+	44596.7i	0.344562	+	0.596798i	0.985274	−	0.170983i	$-0.0546942\pi$
$89$	25747.9	+	44596.7i	0.344562	+	0.596798i	−0.640712	+	0.767781i	$0.721361\pi$
$90$	−19787.0			−0.257498
$91$		0			0
$92$	26948.0			0.331938
$93$	23673.9	+	41004.4i	0.283833	+	0.491613i
$94$	46886.4	−	81209.6i	0.547302	−	0.947955i
$95$	13809.3	−	23918.5i	0.156987	−	0.271909i
$96$	−4608.00	−	7981.29i	−0.0510310	−	0.0883883i
$97$	−127357.			−1.37434			−0.687171	−	0.726496i	$-0.741148\pi$
$97$	−127357.			−1.37434			−0.687171	+	0.726496i	$0.741148\pi$
$98$		0			0
$99$	−2960.08			−0.0303539
$100$	−4837.40	−	8378.63i	−0.0483740	−	0.0837863i
$101$	−32879.0	+	56948.0i	−0.320712	+	0.555489i	−0.980635	−	0.195844i	$-0.937255\pi$
$101$	−32879.0	+	56948.0i	−0.320712	+	0.555489i	0.659923	+	0.751333i	$0.270589\pi$
$102$	37098.7	−	64256.8i	0.353068	−	0.611532i
$103$	−85005.1	−	147233.i	−0.789499	−	1.36745i	−0.926274	−	0.376851i	$-0.877007\pi$
$103$	−85005.1	−	147233.i	−0.789499	−	1.36745i	0.136774	−	0.990602i	$-0.456326\pi$
$104$	2212.20			0.0200558
$105$		0			0
$106$	−28121.2			−0.243091
$107$	53966.4	+	93472.6i	0.455685	+	0.789269i	0.998727	−	0.0504363i	$-0.0160612\pi$
$107$	53966.4	+	93472.6i	0.455685	+	0.789269i	−0.543043	+	0.839705i	$0.682728\pi$
$108$	−5832.00	+	10101.3i	−0.0481125	+	0.0833333i
$109$	111349.	−	192862.i	0.897679	−	1.55482i	0.0672244	−	0.997738i	$-0.478586\pi$
$109$	111349.	−	192862.i	0.897679	−	1.55482i	0.830454	−	0.557087i	$-0.188081\pi$
$110$	−4463.58	−	7731.15i	−0.0351724	−	0.0609203i
$111$	−115398.			−0.888975
$112$		0			0
$113$	181055.			1.33387			0.666936	−	0.745115i	$-0.267605\pi$
$113$	181055.			1.33387			0.666936	+	0.745115i	$0.267605\pi$
$114$	−8140.28	−	14099.4i	−0.0586648	−	0.101610i
$115$	51429.4	−	89078.4i	0.362633	−	0.628098i
$116$	38121.7	−	66028.8i	0.263044	−	0.455605i
$117$	−1399.91	−	2424.71i	−0.00945441	−	0.0163755i
$118$	−176891.			−1.16950
$119$		0			0
$120$	−35176.9			−0.223000
$121$	79857.8	+	138318.i	0.495854	+	0.858844i
$122$	−38760.9	+	67135.9i	−0.235773	+	0.408371i
$123$	32070.3	−	55547.4i	0.191135	−	0.331056i
$124$	42086.9	+	72896.7i	0.245806	+	0.425749i
$125$	153919.			0.881083
$126$		0			0
$127$	91474.7			0.503259			0.251630	−	0.967824i	$-0.419034\pi$
$127$	91474.7			0.503259			0.251630	+	0.967824i	$0.419034\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	−50137.6	+	86840.9i	−0.265271	+	0.459462i
$130$	4221.91	−	7312.57i	0.0219104	−	0.0379500i
$131$	9671.95	+	16752.3i	0.0492420	+	0.0852896i	0.889596	−	0.456749i	$-0.150986\pi$
$131$	9671.95	+	16752.3i	0.0492420	+	0.0852896i	−0.840354	+	0.542038i	$0.817653\pi$
$132$	−5262.36			−0.0262873
$133$		0			0
$134$	83776.3			0.403050
$135$	22260.4	+	38556.2i	0.105123	+	0.182079i
$136$	65953.2	−	114234.i	0.305766	−	0.529602i
$137$	1538.52	−	2664.79i	0.00700327	−	0.0121300i	−0.862503	−	0.506053i	$-0.831104\pi$
$137$	1538.52	−	2664.79i	0.00700327	−	0.0121300i	0.869506	+	0.493923i	$0.164437\pi$
$138$	−30316.5	−	52509.7i	−0.135513	−	0.234715i
$139$	370001.			1.62430			0.812149	−	0.583450i	$-0.198298\pi$
$139$	370001.			1.62430			0.812149	+	0.583450i	$0.198298\pi$
$140$		0			0
$141$	−210989.			−0.893741
$142$	−159687.	−	276586.i	−0.664581	−	1.15109i
$143$	631.585	−	1093.94i	0.00258281	−	0.00447355i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	−145508.	−	252028.i	−0.574736	−	0.995471i
$146$	−148263.			−0.575641
$147$		0			0
$148$	−205151.			−0.769875
$149$	227060.	+	393279.i	0.837866	+	1.45123i	0.891675	+	0.452676i	$0.149531\pi$
$149$	227060.	+	393279.i	0.837866	+	1.45123i	−0.0538086	+	0.998551i	$0.517136\pi$
$150$	−10884.2	+	18851.9i	−0.0394972	+	0.0684112i
$151$	−88795.9	+	153799.i	−0.316921	+	0.548923i	−0.979844	−	0.199765i	$-0.935982\pi$
$151$	−88795.9	+	153799.i	−0.316921	+	0.548923i	0.662923	+	0.748687i	$0.269316\pi$
$152$	−14471.6	−	25065.6i	−0.0508052	−	0.0879972i
$153$	−166944.			−0.576558
$154$		0			0
$155$	321287.			1.07415
$156$	−2488.72	−	4310.59i	−0.00818776	−	0.0141816i
$157$	124491.	−	215624.i	0.403076	−	0.698149i	−0.591019	−	0.806658i	$-0.701274\pi$
$157$	124491.	−	215624.i	0.403076	−	0.698149i	0.994095	+	0.108509i	$0.0346076\pi$
$158$	−84144.0	+	145742.i	−0.268152	+	0.464452i
$159$	31636.3	+	54795.7i	0.0992415	+	0.171891i
$160$	−62536.8			−0.193124
$161$		0			0
$162$	26244.0			0.0785674
$163$	−101124.	−	175152.i	−0.298116	−	0.516351i	0.677589	−	0.735441i	$-0.263025\pi$
$163$	−101124.	−	175152.i	−0.298116	−	0.516351i	−0.975705	+	0.219089i	$0.929691\pi$
$164$	57013.9	−	98751.0i	0.165528	−	0.286703i
$165$	−10043.1	+	17395.1i	−0.0287181	+	0.0497413i
$166$	12622.7	+	21863.1i	0.0355534	+	0.0615803i
$167$	475790.			1.32015			0.660076	−	0.751199i	$-0.270524\pi$
$167$	475790.			1.32015			0.660076	+	0.751199i	$0.270524\pi$
$168$		0			0
$169$	−370098.			−0.996782
$170$	−251740.	−	436026.i	−0.668081	−	1.15715i
$171$	−18315.6	+	31723.6i	−0.0478996	+	0.0829645i
$172$	−89133.5	+	154384.i	−0.229731	+	0.397906i
$173$	142352.	+	246560.i	0.361616	+	0.626337i	0.988227	−	0.152995i	$-0.0488920\pi$
$173$	142352.	+	246560.i	0.361616	+	0.626337i	−0.626611	+	0.779332i	$0.715559\pi$
$174$	−171548.			−0.429548
$175$		0			0
$176$	−9355.30			−0.0227654
$177$	199003.	+	344683.i	0.477448	+	0.826964i
$178$	102992.	−	178387.i	0.243642	−	0.422000i
$179$	−173979.	+	301341.i	−0.405849	+	0.702952i	−0.994420	−	0.105494i	$-0.966358\pi$
$179$	−173979.	+	301341.i	−0.405849	+	0.702952i	0.588571	+	0.808446i	$0.299691\pi$
$180$	39574.1	+	68544.3i	0.0910394	+	0.157685i
$181$	379706.			0.861492			0.430746	−	0.902473i	$-0.358250\pi$
$181$	379706.			0.861492			0.430746	+	0.902473i	$0.358250\pi$
$182$		0			0
$183$	174424.			0.385016
$184$	−53895.9	−	93350.5i	−0.117358	−	0.203269i
$185$	−391525.	+	678142.i	−0.841067	+	1.45677i
$186$	94695.6	−	164018.i	0.200700	−	0.347623i
$187$	−37659.5	−	65228.1i	−0.0787535	−	0.136405i
$188$	−375091.			−0.774002
$189$		0			0
$190$	−110475.			−0.222013
$191$	−97246.2	−	168435.i	−0.192881	−	0.334080i	0.753323	−	0.657651i	$-0.228450\pi$
$191$	−97246.2	−	168435.i	−0.192881	−	0.334080i	−0.946204	+	0.323571i	$0.895116\pi$
$192$	−18432.0	+	31925.2i	−0.0360844	+	0.0625000i
$193$	−438700.	+	759851.i	−0.847763	+	1.46837i	0.0354361	+	0.999372i	$0.488718\pi$
$193$	−438700.	+	759851.i	−0.847763	+	1.46837i	−0.883200	+	0.468997i	$0.844615\pi$
$194$	254715.	+	441179.i	0.485903	+	0.841609i
$195$	−18998.6			−0.0357796
$196$		0			0
$197$	−752368.			−1.38123			−0.690613	−	0.723225i	$-0.742659\pi$
$197$	−752368.			−1.38123			−0.690613	+	0.723225i	$0.742659\pi$
$198$	5920.15	+	10254.0i	0.0107317	+	0.0185879i
$199$	77726.4	−	134626.i	0.139135	−	0.240989i	−0.788035	−	0.615631i	$-0.788901\pi$
$199$	77726.4	−	134626.i	0.139135	−	0.240989i	0.927169	+	0.374642i	$0.122235\pi$
$200$	−19349.6	+	33514.5i	−0.0342056	+	0.0592458i
$201$	−94248.4	−	163243.i	−0.164545	−	0.285000i
$202$	263032.			0.453555
$203$		0			0
$204$	−296790.			−0.499313
$205$	−217619.	−	376927.i	−0.361669	−	0.626430i
$206$	−340020.	+	588932.i	−0.558260	+	0.966935i
$207$	−68212.0	+	118147.i	−0.110646	+	0.191644i
$208$	−4424.39	−	7663.28i	−0.00709080	−	0.0122816i
$209$	−16526.7			−0.0261709
$210$		0			0
$211$	3898.23			0.00602783			0.00301391	−	0.999995i	$-0.499041\pi$
$211$	3898.23			0.00602783			0.00301391	+	0.999995i	$0.499041\pi$
$212$	56242.4	+	97414.6i	0.0859457	+	0.148862i
$213$	−359295.	+	622318.i	−0.542628	+	0.939860i
$214$	215866.	−	373890.i	0.322218	−	0.558097i
$215$	340217.	+	589274.i	0.501950	+	0.869403i
$216$	46656.0			0.0680414
$217$		0			0
$218$	−890794.			−1.26951
$219$	166796.	+	288899.i	0.235004	+	0.407039i
$220$	−17854.3	+	30924.6i	−0.0248706	+	0.0430772i
$221$	35620.5	−	61696.5i	0.0490591	−	0.0849728i
$222$	230795.	+	399749.i	0.314300	+	0.544384i
$223$	782574.			1.05381			0.526906	−	0.849924i	$-0.323352\pi$
$223$	782574.			1.05381			0.526906	+	0.849924i	$0.323352\pi$
$224$		0			0
$225$	48978.7			0.0644987
$226$	−362110.	−	627193.i	−0.471595	−	0.816827i
$227$	−398271.	+	689826.i	−0.512997	+	0.888536i	0.486890	+	0.873463i	$0.338131\pi$
$227$	−398271.	+	689826.i	−0.512997	+	0.888536i	−0.999886	+	0.0150727i	$0.995202\pi$
$228$	−32561.1	+	56397.5i	−0.0414823	+	0.0718494i
$229$	−193522.	−	335191.i	−0.243861	−	0.422380i	0.717950	−	0.696095i	$-0.245081\pi$
$229$	−193522.	−	335191.i	−0.243861	−	0.422380i	−0.961811	+	0.273715i	$0.911747\pi$
$230$	−411435.			−0.512840
$231$		0			0
$232$	−304974.			−0.372000
$233$	191879.	+	332345.i	0.231547	+	0.401051i	0.958263	−	0.285887i	$-0.0922881\pi$
$233$	191879.	+	332345.i	0.231547	+	0.401051i	−0.726717	+	0.686937i	$0.758955\pi$
$234$	−5599.62	+	9698.83i	−0.00668527	+	0.0115792i
$235$	−715851.	+	1.23989e6i	−0.845576	+	1.46458i
$236$	353783.	+	612769.i	0.413482	+	0.716171i
$237$	378648.			0.437890
$238$		0			0
$239$	−465409.			−0.527036			−0.263518	−	0.964654i	$-0.584883\pi$
$239$	−465409.			−0.527036			−0.263518	+	0.964654i	$0.584883\pi$
$240$	70353.9	+	121856.i	0.0788424	+	0.136559i
$241$	174372.	−	302022.i	0.193390	−	0.334962i	−0.752981	−	0.658042i	$-0.771385\pi$
$241$	174372.	−	302022.i	0.193390	−	0.334962i	0.946372	+	0.323080i	$0.104718\pi$
$242$	319431.	−	553271.i	0.350622	−	0.607294i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	310088.			0.333434
$245$		0			0
$246$	−256563.			−0.270306
$247$	−7815.93	−	13537.6i	−0.00815152	−	0.0141188i
$248$	168348.	−	291587.i	0.173811	−	0.301050i
$249$	28401.0	−	49192.0i	0.0290292	−	0.0502801i
$250$	−307838.	−	533191.i	−0.311510	−	0.539551i
$251$	−186543.			−0.186894			−0.0934468	−	0.995624i	$-0.529789\pi$
$251$	−186543.			−0.186894			−0.0934468	+	0.995624i	$0.529789\pi$
$252$		0			0
$253$	−61549.4			−0.0604537
$254$	−182949.	−	316878.i	−0.177929	−	0.308182i
$255$	−566414.	+	981058.i	−0.545486	+	0.944810i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−776774.	−	1.34541e6i	−0.733605	−	1.27064i	−0.955333	−	0.295532i	$-0.904503\pi$
$257$	−776774.	−	1.34541e6i	−0.733605	−	1.27064i	0.221728	−	0.975109i	$-0.428830\pi$
$258$	401101.			0.375149
$259$		0			0
$260$	−33775.3			−0.0309860
$261$	192991.	+	334271.i	0.175362	+	0.303737i
$262$	38687.8	−	67009.2i	0.0348193	−	0.0603089i
$263$	629798.	−	1.09084e6i	0.561451	−	0.972462i	−0.435919	−	0.899986i	$-0.643577\pi$
$263$	629798.	−	1.09084e6i	0.561451	−	0.972462i	0.997370	−	0.0724759i	$-0.0230901\pi$
$264$	10524.7	+	18229.3i	0.00929396	+	0.0160976i
$265$	429348.			0.375573
$266$		0			0
$267$	−463462.			−0.397866
$268$	−167553.	−	290210.i	−0.142500	−	0.246817i
$269$	85230.6	−	147624.i	0.0718149	−	0.124387i	−0.827882	−	0.560903i	$-0.810454\pi$
$269$	85230.6	−	147624.i	0.0718149	−	0.124387i	0.899697	+	0.436515i	$0.143788\pi$
$270$	89041.6	−	154225.i	0.0743333	−	0.128749i
$271$	−1.11372e6	−	1.92901e6i	−0.921194	−	1.59555i	−0.797571	−	0.603225i	$-0.793882\pi$
$271$	−1.11372e6	−	1.92901e6i	−0.921194	−	1.59555i	−0.123623	−	0.992329i	$-0.539451\pi$
$272$	−527626.			−0.432418
$273$		0			0
$274$	−12308.1			−0.00990412
$275$	11048.7	+	19136.9i	0.00881005	+	0.0152595i
$276$	−121266.	+	210039.i	−0.0958221	+	0.165969i
$277$	−991697.	+	1.71767e6i	−0.776568	+	1.34506i	0.157341	+	0.987544i	$0.449708\pi$
$277$	−991697.	+	1.71767e6i	−0.776568	+	1.34506i	−0.933909	+	0.357511i	$0.883626\pi$
$278$	−740002.	−	1.28172e6i	−0.574276	−	0.994676i
$279$	−426130.			−0.327742
$280$		0			0
$281$	−1.16687e6			−0.881573			−0.440786	−	0.897612i	$-0.645300\pi$
$281$	−1.16687e6			−0.881573			−0.440786	+	0.897612i	$0.645300\pi$
$282$	421978.	+	730887.i	0.315985	+	0.547302i
$283$	950450.	−	1.64623e6i	0.705445	−	1.22187i	−0.261086	−	0.965316i	$-0.584081\pi$
$283$	950450.	−	1.64623e6i	0.705445	−	1.22187i	0.966531	−	0.256551i	$-0.0825861\pi$
$284$	−638747.	+	1.10634e6i	−0.469930	+	0.813943i
$285$	124284.	+	215266.i	0.0906364	+	0.156987i
$286$	−5052.68			−0.00365264
$287$		0			0
$288$	82944.0			0.0589256
$289$	−1.41401e6	−	2.44914e6i	−0.995884	−	1.72492i
$290$	−582034.	+	1.00811e6i	−0.406400	+	0.703905i
$291$	573108.	−	992653.i	0.396738	−	0.687171i
$292$	296527.	+	513599.i	0.203520	+	0.352506i
$293$	1.65009e6			1.12289			0.561445	−	0.827514i	$-0.310245\pi$
$293$	1.65009e6			1.12289			0.561445	+	0.827514i	$0.310245\pi$
$294$		0			0
$295$	2.70073e6			1.80687
$296$	410303.	+	710665.i	0.272192	+	0.471450i
$297$	13320.3	−	23071.5i	0.00876243	−	0.0151770i
$298$	908240.	−	1.57312e6i	0.592461	−	1.02617i
$299$	−29108.5	−	50417.4i	−0.0188296	−	0.0326139i
$300$	87073.2			0.0558575
$301$		0			0
$302$	710367.			0.448194
$303$	−295911.	−	512532.i	−0.185163	−	0.320712i
$304$	−57886.5	+	100262.i	−0.0359247	+	0.0622234i
$305$	591793.	−	1.02502e6i	0.364267	−	0.630930i
$306$	333888.	+	578312.i	0.203844	+	0.353068i
$307$	597936.			0.362084			0.181042	−	0.983475i	$-0.442053\pi$
$307$	597936.			0.362084			0.181042	+	0.983475i	$0.442053\pi$
$308$		0			0
$309$	1.53009e6			0.911635
$310$	−642574.	−	1.11297e6i	−0.379768	−	0.657778i
$311$	−115240.	+	199602.i	−0.0675620	+	0.117021i	−0.897828	−	0.440347i	$-0.854855\pi$
$311$	−115240.	+	199602.i	−0.0675620	+	0.117021i	0.830266	+	0.557368i	$0.188189\pi$
$312$	−9954.89	+	17242.4i	−0.00578962	+	0.0100279i
$313$	−221289.	−	383283.i	−0.127673	−	0.221136i	0.795102	−	0.606476i	$-0.207417\pi$
$313$	−221289.	−	383283.i	−0.127673	−	0.221136i	−0.922775	+	0.385340i	$0.874084\pi$
$314$	−995925.			−0.570036
$315$		0			0
$316$	673152.			0.379224
$317$	631238.	+	1.09334e6i	0.352813	+	0.611091i	0.986741	−	0.162302i	$-0.0518917\pi$
$317$	631238.	+	1.09334e6i	0.352813	+	0.611091i	−0.633928	+	0.773392i	$0.718558\pi$
$318$	126545.	−	219183.i	0.0701743	−	0.121546i
$319$	−87070.4	+	150810.i	−0.0479064	+	0.0829764i
$320$	125074.	+	216634.i	0.0682795	+	0.118264i
$321$	−971396.			−0.526179
$322$		0			0
$323$	−932080.			−0.497104
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	−10450.5	+	18100.8i	−0.00548817	+	0.00950579i
$326$	−404496.	+	700607.i	−0.210800	+	0.365116i
$327$	1.00214e6	+	1.73576e6i	0.518275	+	0.897679i
$328$	−456111.			−0.234092
$329$		0			0
$330$	80344.5			0.0406136
$331$	234468.	+	406110.i	0.117629	+	0.203739i	0.918827	−	0.394659i	$-0.129137\pi$
$331$	234468.	+	406110.i	0.117629	+	0.203739i	−0.801199	+	0.598398i	$0.795804\pi$
$332$	50490.7	−	87452.4i	0.0251400	−	0.0435438i
$333$	519289.	−	899435.i	0.256625	−	0.444487i
$334$	−951580.	−	1.64818e6i	−0.466744	−	0.808425i
$335$	−1.27908e6			−0.622708
$336$		0			0
$337$	−2.46798e6			−1.18377			−0.591884	−	0.806023i	$-0.701616\pi$
$337$	−2.46798e6			−1.18377			−0.591884	+	0.806023i	$0.701616\pi$
$338$	740196.	+	1.28206e6i	0.352416	+	0.610402i
$339$	−814747.	+	1.41118e6i	−0.385056	+	0.666936i
$340$	−1.00696e6	+	1.74410e6i	−0.472405	+	0.818229i
$341$	−96127.0	−	166497.i	−0.0447671	−	0.0775390i
$342$	146525.			0.0677402
$343$		0			0
$344$	713068.			0.324889
$345$	462865.	+	801705.i	0.209366	+	0.362633i
$346$	569406.	−	986241.i	0.255701	−	0.442887i
$347$	2.14125e6	−	3.70875e6i	0.954648	−	1.65350i	0.219477	−	0.975618i	$-0.429565\pi$
$347$	2.14125e6	−	3.70875e6i	0.954648	−	1.65350i	0.735171	−	0.677882i	$-0.237102\pi$
$348$	343096.	+	594259.i	0.151868	+	0.263044i
$349$	−1.84999e6			−0.813028			−0.406514	−	0.913645i	$-0.633256\pi$
$349$	−1.84999e6			−0.813028			−0.406514	+	0.913645i	$0.633256\pi$
$350$		0			0
$351$	25198.3			0.0109170
$352$	18710.6	+	32407.7i	0.00804880	+	0.0139409i
$353$	1.13690e6	−	1.96916e6i	0.485607	−	0.841095i	−0.514257	−	0.857636i	$-0.671932\pi$
$353$	1.13690e6	−	1.96916e6i	0.485607	−	0.841095i	0.999863	+	0.0165411i	$0.00526543\pi$
$354$	796011.	−	1.37873e6i	0.337606	−	0.584752i
$355$	2.43806e6	+	4.22284e6i	1.02677	+	1.77842i
$356$	−823933.			−0.344562
$357$		0			0
$358$	1.39183e6			0.573958
$359$	2.19996e6	+	3.81044e6i	0.900905	+	1.56041i	0.826322	+	0.563198i	$0.190429\pi$
$359$	2.19996e6	+	3.81044e6i	0.900905	+	1.56041i	0.0745823	+	0.997215i	$0.476238\pi$
$360$	158296.	−	274177.i	0.0643746	−	0.111500i
$361$	1.13579e6	−	1.96725e6i	0.458701	−	0.794494i
$362$	−759412.	−	1.31534e6i	−0.304583	−	0.527554i
$363$	−1.43744e6			−0.572563
$364$		0			0
$365$	2.26365e6			0.889359
$366$	−348849.	−	604223.i	−0.136124	−	0.235773i
$367$	948716.	−	1.64322e6i	0.367681	−	0.636842i	−0.621522	−	0.783397i	$-0.713485\pi$
$367$	948716.	−	1.64322e6i	0.367681	−	0.636842i	0.989203	+	0.146555i	$0.0468185\pi$
$368$	−215584.	+	373402.i	−0.0829844	+	0.143733i
$369$	288633.	+	499927.i	0.110352	+	0.191135i
$370$	3.13220e6			1.18945
$371$		0			0
$372$	−757565.			−0.283833
$373$	−2.28130e6	−	3.95133e6i	−0.849005	−	1.47052i	−0.882097	−	0.471067i	$-0.843869\pi$
$373$	−2.28130e6	−	3.95133e6i	−0.849005	−	1.47052i	0.0330929	−	0.999452i	$-0.489464\pi$
$374$	−150638.	+	260912.i	−0.0556872	+	0.0964530i
$375$	−692635.	+	1.19968e6i	−0.254347	+	0.440542i
$376$	750183.	+	1.29935e6i	0.273651	+	0.473978i
$377$	−164713.			−0.0596861
$378$		0			0
$379$	4.99400e6			1.78587			0.892936	−	0.450184i	$-0.148642\pi$
$379$	4.99400e6			1.78587			0.892936	+	0.450184i	$0.148642\pi$
$380$	220949.	+	382695.i	0.0784935	+	0.135955i
$381$	−411636.	+	712975.i	−0.145278	+	0.251630i
$382$	−388985.	+	673742.i	−0.136387	+	0.236230i
$383$	1.83954e6	+	3.18617e6i	0.640783	+	1.10987i	0.985258	+	0.171074i	$0.0547236\pi$
$383$	1.83954e6	+	3.18617e6i	0.640783	+	1.10987i	−0.344475	+	0.938796i	$0.611943\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	3.50960e6			1.19892
$387$	−451238.	−	781568.i	−0.153154	−	0.265271i
$388$	1.01886e6	−	1.76472e6i	0.343585	−	0.595107i
$389$	−128617.	+	222771.i	−0.0430947	+	0.0746422i	−0.886768	−	0.462214i	$-0.847055\pi$
$389$	−128617.	+	222771.i	−0.0430947	+	0.0746422i	0.843673	+	0.536857i	$0.180388\pi$
$390$	37997.2	+	65813.1i	0.0126500	+	0.0219104i
$391$	−3.47130e6			−1.14829
$392$		0			0
$393$	−174095.			−0.0568598
$394$	1.50474e6	+	2.60628e6i	0.488337	+	0.845825i
$395$	1.28469e6	−	2.22515e6i	0.414292	−	0.717574i
$396$	23680.6	−	41016.0i	0.00758848	−	0.0131436i
$397$	−216640.	−	375232.i	−0.0689862	−	0.119488i	0.829469	−	0.558553i	$-0.188643\pi$
$397$	−216640.	−	375232.i	−0.0689862	−	0.119488i	−0.898455	+	0.439065i	$0.855310\pi$
$398$	−621811.			−0.196766
$399$		0			0
$400$	154797.			0.0483740
$401$	569122.	+	985748.i	0.176744	+	0.306129i	0.940763	−	0.339064i	$-0.110110\pi$
$401$	569122.	+	985748.i	0.176744	+	0.306129i	−0.764020	+	0.645193i	$0.776777\pi$
$402$	−376993.	+	652972.i	−0.116351	+	0.201525i
$403$	90922.5	−	157482.i	0.0278874	−	0.0483025i
$404$	−526063.	−	911169.i	−0.160356	−	0.277744i
$405$	−400687.			−0.121386
$406$		0			0
$407$	468568.			0.140212
$408$	593579.	+	1.02811e6i	0.176534	+	0.305766i
$409$	2.51219e6	−	4.35124e6i	0.742581	−	1.28619i	−0.208735	−	0.977972i	$-0.566935\pi$
$409$	2.51219e6	−	4.35124e6i	0.742581	−	1.28619i	0.951316	−	0.308216i	$-0.0997320\pi$
$410$	−870475.	+	1.50771e6i	−0.255739	+	0.442953i
$411$	13846.7	+	23983.1i	0.00404334	+	0.00700327i
$412$	2.72016e6			0.789499
$413$		0			0
$414$	545696.			0.156477
$415$	−192720.	−	333801.i	−0.0549296	−	0.0951409i
$416$	−17697.6	+	30653.1i	−0.00501396	+	0.00868443i
$417$	−1.66500e6	+	2.88387e6i	−0.468895	+	0.812149i
$418$	33053.3	+	57250.0i	0.00925282	+	0.0160264i
$419$	−2.57295e6			−0.715974			−0.357987	−	0.933727i	$-0.616537\pi$
$419$	−2.57295e6			−0.715974			−0.357987	+	0.933727i	$0.616537\pi$
$420$		0			0
$421$	336425.			0.0925089			0.0462545	−	0.998930i	$-0.485271\pi$
$421$	336425.			0.0925089			0.0462545	+	0.998930i	$0.485271\pi$
$422$	−7796.45	−	13503.9i	−0.00213116	−	0.00369128i
$423$	949450.	−	1.64450e6i	0.258001	−	0.446871i
$424$	224969.	−	389659.i	0.0607728	−	0.105262i
$425$	623130.	+	1.07929e6i	0.167342	+	0.289846i
$426$	2.87436e6			0.767392
$427$		0			0
$428$	−1.72693e6			−0.455685
$429$	5684.27	+	9845.44i	0.00149118	+	0.00258281i
$430$	1.36087e6	−	2.35710e6i	0.354932	−	0.614761i
$431$	−118205.	+	204737.i	−0.0306509	+	0.0530889i	−0.880944	−	0.473221i	$-0.843091\pi$
$431$	−118205.	+	204737.i	−0.0306509	+	0.0530889i	0.850293	+	0.526310i	$0.176425\pi$
$432$	−93312.0	−	161621.i	−0.0240563	−	0.0416667i
$433$	−2.33004e6			−0.597232			−0.298616	−	0.954373i	$-0.596525\pi$
$433$	−2.33004e6			−0.597232			−0.298616	+	0.954373i	$0.596525\pi$
$434$		0			0
$435$	2.61915e6			0.663648
$436$	1.78159e6	+	3.08580e6i	0.448839	+	0.777412i
$437$	−380840.	+	659635.i	−0.0953980	+	0.165234i
$438$	667185.	−	1.15560e6i	0.166173	−	0.287820i
$439$	−1.59981e6	−	2.77095e6i	−0.396193	−	0.686227i	0.597059	−	0.802197i	$-0.296336\pi$
$439$	−1.59981e6	−	2.77095e6i	−0.396193	−	0.686227i	−0.993253	+	0.115970i	$0.963002\pi$
$440$	142835.			0.0351724
$441$		0			0
$442$	−284964.			−0.0693800
$443$	−566202.	−	980690.i	−0.137076	−	0.237423i	0.789313	−	0.613992i	$-0.210437\pi$
$443$	−566202.	−	980690.i	−0.137076	−	0.237423i	−0.926389	+	0.376569i	$0.877104\pi$
$444$	923181.	−	1.59900e6i	0.222244	−	0.384937i
$445$	−1.57245e6	+	2.72357e6i	−0.376424	+	0.651986i
$446$	−1.56515e6	−	2.71091e6i	−0.372579	−	0.645325i
$447$	−4.08708e6			−0.967485
$448$		0			0
$449$	−8.23687e6			−1.92817			−0.964087	−	0.265585i	$-0.914435\pi$
$449$	−8.23687e6			−1.92817			−0.964087	+	0.265585i	$0.914435\pi$
$450$	−97957.4	−	169667.i	−0.0228037	−	0.0394972i
$451$	−130220.	+	225548.i	−0.0301465	+	0.0522153i
$452$	−1.44844e6	+	2.50877e6i	−0.333468	+	0.577584i
$453$	−799163.	−	1.38419e6i	−0.182974	−	0.316921i
$454$	3.18617e6			0.725487
$455$		0			0
$456$	260489.			0.0586648
$457$	182566.	+	316214.i	0.0408912	+	0.0708256i	0.885747	−	0.464169i	$-0.153647\pi$
$457$	182566.	+	316214.i	0.0408912	+	0.0708256i	−0.844855	+	0.534995i	$0.820314\pi$
$458$	−774090.	+	1.34076e6i	−0.172436	+	0.298668i
$459$	751249.	−	1.30120e6i	0.166438	−	0.288279i
$460$	822871.	+	1.42525e6i	0.181316	+	0.314049i
$461$	332567.			0.0728832			0.0364416	−	0.999336i	$-0.488398\pi$
$461$	332567.			0.0728832			0.0364416	+	0.999336i	$0.488398\pi$
$462$		0			0
$463$	1.69992e6			0.368533			0.184266	−	0.982876i	$-0.441009\pi$
$463$	1.69992e6			0.368533			0.184266	+	0.982876i	$0.441009\pi$
$464$	609948.	+	1.05646e6i	0.131522	+	0.227802i
$465$	−1.44579e6	+	2.50418e6i	−0.310079	+	0.537073i
$466$	767518.	−	1.32938e6i	0.163728	−	0.283586i
$467$	495233.	+	857768.i	0.105079	+	0.182003i	0.913771	−	0.406231i	$-0.133157\pi$
$467$	495233.	+	857768.i	0.105079	+	0.182003i	−0.808691	+	0.588233i	$0.799824\pi$
$468$	44797.0			0.00945441
$469$		0			0
$470$	5.72681e6			1.19583
$471$	1.12042e6	+	1.94062e6i	0.232716	+	0.403076i
$472$	1.41513e6	−	2.45108e6i	0.292376	−	0.506410i
$473$	203582.	−	352614.i	0.0418395	−	0.0724681i
$474$	−757296.	−	1.31168e6i	−0.154817	−	0.268152i
$475$	273457.			0.0556103
$476$		0			0
$477$	−569454.			−0.114594
$478$	930819.	+	1.61223e6i	0.186335	+	0.322742i
$479$	3.04033e6	−	5.26600e6i	0.605454	−	1.04868i	−0.386525	−	0.922279i	$-0.626325\pi$
$479$	3.04033e6	−	5.26600e6i	0.605454	−	1.04868i	0.991980	−	0.126399i	$-0.0403419\pi$
$480$	281415.	−	487426.i	0.0557500	−	0.0965618i
$481$	221599.	+	383821.i	0.0436722	+	0.0756425i
$482$	−1.39498e6			−0.273495
$483$		0			0
$484$	−2.55545e6			−0.495854
$485$	−3.88893e6	−	6.73582e6i	−0.750715	−	1.30028i
$486$	−118098.	+	204552.i	−0.0226805	+	0.0392837i
$487$	3.35549e6	−	5.81188e6i	0.641112	−	1.11044i	−0.344073	−	0.938943i	$-0.611807\pi$
$487$	3.35549e6	−	5.81188e6i	0.641112	−	1.11044i	0.985185	−	0.171495i	$-0.0548598\pi$
$488$	−620175.	−	1.07417e6i	−0.117887	−	0.204186i
$489$	1.82023e6			0.344234
$490$		0			0
$491$	−914042.			−0.171105			−0.0855525	−	0.996334i	$-0.527266\pi$
$491$	−914042.			−0.171105			−0.0855525	+	0.996334i	$0.527266\pi$
$492$	513125.	+	888759.i	0.0955676	+	0.165528i
$493$	−4.91065e6	+	8.50549e6i	−0.909959	+	1.57609i
$494$	−31263.7	+	54150.4i	−0.00576399	+	0.00998353i
$495$	−90387.5	−	156556.i	−0.0165804	−	0.0287181i
$496$	−1.34678e6			−0.245806
$497$		0			0
$498$	−227208.			−0.0410535
$499$	3.87746e6	+	6.71596e6i	0.697101	+	1.20742i	0.969467	+	0.245221i	$0.0788606\pi$
$499$	3.87746e6	+	6.71596e6i	0.697101	+	1.20742i	−0.272366	+	0.962194i	$0.587806\pi$
$500$	−1.23135e6	+	2.13276e6i	−0.220271	+	0.381520i
$501$	−2.14106e6	+	3.70842e6i	−0.381095	+	0.660076i
$502$	373086.	+	646204.i	0.0660769	+	0.114449i
$503$	−3.79381e6			−0.668584			−0.334292	−	0.942470i	$-0.608497\pi$
$503$	−3.79381e6			−0.668584			−0.334292	+	0.942470i	$0.608497\pi$
$504$		0			0
$505$	−4.01591e6			−0.700737
$506$	123099.	+	213213.i	0.0213736	+	0.0370202i
$507$	1.66544e6	−	2.88463e6i	0.287746	−	0.498391i
$508$	−731798.	+	1.26751e6i	−0.125815	+	0.217918i
$509$	4.26580e6	+	7.38858e6i	0.729804	+	1.26406i	0.956966	+	0.290200i	$0.0937220\pi$
$509$	4.26580e6	+	7.38858e6i	0.729804	+	1.26406i	−0.227162	+	0.973857i	$0.572945\pi$
$510$	4.53131e6			0.771434
$511$		0			0
$512$	262144.			0.0441942
$513$	−164841.	−	285513.i	−0.0276548	−	0.0478996i
$514$	−3.10710e6	+	5.38165e6i	−0.518737	+	0.898478i
$515$	5.19135e6	−	8.99168e6i	0.862506	−	1.49390i
$516$	−802202.	−	1.38945e6i	−0.132635	−	0.229731i
$517$	856712.			0.140964
$518$		0			0
$519$	−2.56233e6			−0.417558
$520$	67550.6	+	117001.i	0.0109552	+	0.0189750i
$521$	−1.59533e6	+	2.76320e6i	−0.257488	+	0.445982i	−0.965568	−	0.260150i	$-0.916228\pi$
$521$	−1.59533e6	+	2.76320e6i	−0.257488	+	0.445982i	0.708080	+	0.706132i	$0.249561\pi$
$522$	771965.	−	1.33708e6i	0.124000	−	0.214774i
$523$	−4.80339e6	−	8.31971e6i	−0.767880	−	1.33001i	−0.938710	−	0.344707i	$-0.887978\pi$
$523$	−4.80339e6	−	8.31971e6i	−0.767880	−	1.33001i	0.170830	−	0.985301i	$-0.445355\pi$
$524$	−309502.			−0.0492420
$525$		0			0
$526$	−5.03838e6			−0.794012
$527$	−5.42143e6	−	9.39019e6i	−0.850329	−	1.47281i
$528$	42098.9	−	72917.4i	0.00657182	−	0.0113827i
$529$	1.79983e6	−	3.11739e6i	0.279635	−	0.484342i
$530$	−858695.	−	1.48730e6i	−0.132785	−	0.229991i
$531$	−3.58205e6			−0.551309
$532$		0			0
$533$	−246340.			−0.0375592
$534$	926925.	+	1.60548e6i	0.140667	+	0.243642i
$535$	−3.29579e6	+	5.70847e6i	−0.497823	+	0.862254i
$536$	−670210.	+	1.16084e6i	−0.100763	+	0.174526i
$537$	−1.56581e6	−	2.71207e6i	−0.234317	−	0.405849i
$538$	−681844.			−0.101562
$539$		0			0
$540$	−712333.			−0.105123
$541$	−5.11832e6	−	8.86519e6i	−0.751855	−	1.30225i	−0.946923	−	0.321462i	$-0.895826\pi$
$541$	−5.11832e6	−	8.86519e6i	−0.751855	−	1.30225i	0.195067	−	0.980790i	$-0.437508\pi$
$542$	−4.45486e6	+	7.71605e6i	−0.651382	+	1.12823i
$543$	−1.70868e6	+	2.95952e6i	−0.248691	+	0.430746i
$544$	1.05525e6	+	1.82775e6i	0.152883	+	0.264801i
$545$	1.36004e7			1.96138
$546$		0			0
$547$	−9.27757e6			−1.32576			−0.662882	−	0.748724i	$-0.730667\pi$
$547$	−9.27757e6			−1.32576			−0.662882	+	0.748724i	$0.730667\pi$
$548$	24616.3	+	42636.7i	0.00350164	+	0.00606501i
$549$	−784909.	+	1.35950e6i	−0.111145	+	0.192508i
$550$	44194.7	−	76547.5i	0.00622965	−	0.0107901i
$551$	1.07751e6	+	1.86630e6i	0.151196	+	0.261879i
$552$	970127.			0.135513
$553$		0			0
$554$	7.93357e6			1.09823
$555$	−3.52373e6	−	6.10327e6i	−0.485590	−	0.841067i
$556$	−2.96001e6	+	5.12688e6i	−0.406075	+	0.703342i
$557$	−310049.	+	537021.i	−0.0423441	+	0.0733421i	−0.886421	−	0.462881i	$-0.846816\pi$
$557$	−310049.	+	537021.i	−0.0423441	+	0.0733421i	0.844077	+	0.536223i	$0.180149\pi$
$558$	852260.	+	1.47616e6i	0.115874	+	0.200700i
$559$	385119.			0.0521273
$560$		0			0
$561$	677870.			0.0909368
$562$	2.33375e6	+	4.04217e6i	0.311683	+	0.539851i
$563$	3.68332e6	−	6.37970e6i	0.489744	−	0.848261i	−0.510187	−	0.860064i	$-0.670424\pi$
$563$	3.68332e6	−	6.37970e6i	0.489744	−	0.848261i	0.999930	+	0.0118029i	$0.00375708\pi$
$564$	1.68791e6	−	2.92355e6i	0.223435	−	0.387001i
$565$	5.52861e6	+	9.57583e6i	0.728610	+	1.26199i
$566$	−7.60360e6			−0.997650
$567$		0			0
$568$	5.10998e6			0.664581
$569$	−1.84111e6	−	3.18890e6i	−0.238396	−	0.412914i	0.721858	−	0.692041i	$-0.243288\pi$
$569$	−1.84111e6	−	3.18890e6i	−0.238396	−	0.412914i	−0.960254	+	0.279127i	$0.909955\pi$
$570$	497136.	−	861064.i	0.0640896	−	0.111007i
$571$	−5.16600e6	+	8.94777e6i	−0.663077	+	1.14848i	0.316726	+	0.948517i	$0.397416\pi$
$571$	−5.16600e6	+	8.94777e6i	−0.663077	+	1.14848i	−0.979803	+	0.199966i	$0.935917\pi$
$572$	10105.4	+	17503.0i	0.00129140	+	0.00223678i
$573$	1.75043e6			0.222720
$574$		0			0
$575$	1.01842e6			0.128457
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	−6.25617e6	+	1.08360e7i	−0.782292	+	1.35497i	0.148311	+	0.988941i	$0.452616\pi$
$577$	−6.25617e6	+	1.08360e7i	−0.782292	+	1.35497i	−0.930603	+	0.366029i	$0.880717\pi$
$578$	−5.65605e6	+	9.79657e6i	−0.704196	+	1.21970i
$579$	−3.94830e6	−	6.83866e6i	−0.489456	−	0.847763i
$580$	4.65627e6			0.574736
$581$		0			0
$582$	−4.58487e6			−0.561073
$583$	−128458.	−	222496.i	−0.0156527	−	0.0271113i
$584$	1.18611e6	−	2.05440e6i	0.143910	−	0.249260i
$585$	85493.8	−	148080.i	0.0103287	−	0.0178898i
$586$	−3.30017e6	−	5.71607e6i	−0.397002	−	0.687627i
$587$	1.60865e7			1.92694			0.963468	−	0.267823i	$-0.0863042\pi$
$587$	1.60865e7			1.92694			0.963468	+	0.267823i	$0.0863042\pi$
$588$		0			0
$589$	−2.37916e6			−0.282577
$590$	−5.40147e6	−	9.35562e6i	−0.638825	−	1.10648i
$591$	3.38566e6	−	5.86413e6i	0.398726	−	0.690613i
$592$	1.64121e6	−	2.84266e6i	0.192469	−	0.333365i
$593$	−4.73165e6	−	8.19546e6i	−0.552556	−	0.957054i	−0.998089	−	0.0617892i	$-0.980319\pi$
$593$	−4.73165e6	−	8.19546e6i	−0.552556	−	0.957054i	0.445534	−	0.895265i	$-0.353014\pi$
$594$	−106563.			−0.0123919
$595$		0			0
$596$	−7.26592e6			−0.837866
$597$	699538.	+	1.21163e6i	0.0803295	+	0.139135i
$598$	−116434.	+	201670.i	−0.0133146	+	0.0230615i
$599$	−2.50749e6	+	4.34310e6i	−0.285544	+	0.494576i	−0.972741	−	0.231895i	$-0.925507\pi$
$599$	−2.50749e6	+	4.34310e6i	−0.285544	+	0.494576i	0.687197	+	0.726471i	$0.258841\pi$
$600$	−174146.	−	301631.i	−0.0197486	−	0.0342056i
$601$	−1.26473e7			−1.42828			−0.714139	−	0.700004i	$-0.753182\pi$
$601$	−1.26473e7			−1.42828			−0.714139	+	0.700004i	$0.753182\pi$
$602$		0			0
$603$	1.69647e6			0.190000
$604$	−1.42073e6	−	2.46078e6i	−0.158460	−	0.274461i
$605$	−4.87700e6	+	8.44721e6i	−0.541707	+	0.938264i
$606$	−1.18364e6	+	2.05013e6i	−0.130930	+	0.226777i
$607$	−1.43851e6	−	2.49157e6i	−0.158468	−	0.274475i	0.775848	−	0.630919i	$-0.217322\pi$
$607$	−1.43851e6	−	2.49157e6i	−0.158468	−	0.274475i	−0.934316	+	0.356445i	$0.883989\pi$
$608$	463092.			0.0508052
$609$		0			0
$610$	−4.73434e6			−0.515152
$611$	405164.	+	701765.i	0.0439064	+	0.0760481i
$612$	1.33555e6	−	2.31325e6i	0.144139	−	0.249657i
$613$	1.86291e6	−	3.22666e6i	0.200236	−	0.346818i	−0.748369	−	0.663283i	$-0.769163\pi$
$613$	1.86291e6	−	3.22666e6i	0.200236	−	0.346818i	0.948604	+	0.316465i	$0.102496\pi$
$614$	−1.19587e6	−	2.07131e6i	−0.128016	−	0.221730i
$615$	3.91714e6			0.417620
$616$		0			0
$617$	−1.15861e7			−1.22525			−0.612625	−	0.790374i	$-0.709886\pi$
$617$	−1.15861e7			−1.22525			−0.612625	+	0.790374i	$0.709886\pi$
$618$	−3.06018e6	−	5.30039e6i	−0.322312	−	0.558260i
$619$	928039.	−	1.60741e6i	0.0973508	−	0.168617i	−0.813236	−	0.581933i	$-0.802296\pi$
$619$	928039.	−	1.60741e6i	0.0973508	−	0.168617i	0.910587	+	0.413317i	$0.135630\pi$
$620$	−2.57029e6	+	4.45188e6i	−0.268537	+	0.465119i
$621$	−613908.	−	1.06332e6i	−0.0638814	−	0.110646i
$622$	921921.			0.0955471
$623$		0			0
$624$	79639.1			0.00818776
$625$	5.64480e6	+	9.77708e6i	0.578028	+	1.00117i
$626$	−885155.	+	1.53313e6i	−0.0902783	+	0.156367i
$627$	74369.9	−	128813.i	0.00755490	−	0.0130855i
$628$	1.99185e6	+	3.44998e6i	0.201538	+	0.349074i
$629$	2.64266e7			2.66326
$630$		0			0
$631$	8.92135e6			0.891984			0.445992	−	0.895037i	$-0.352851\pi$
$631$	8.92135e6			0.891984			0.445992	+	0.895037i	$0.352851\pi$
$632$	−1.34630e6	−	2.33187e6i	−0.134076	−	0.232226i
$633$	−17542.0	+	30383.7i	−0.00174008	+	0.00301391i
$634$	2.52495e6	−	4.37335e6i	0.249477	−	0.432106i
$635$	2.79323e6	+	4.83802e6i	0.274898	+	0.476138i
$636$	−1.01236e6			−0.0992415
$637$		0			0
$638$	696563.			0.0677499
$639$	−3.23366e6	−	5.60086e6i	−0.313287	−	0.542628i
$640$	500294.	−	866535.i	0.0482809	−	0.0836250i
$641$	−6.59332e6	+	1.14200e7i	−0.633810	+	1.09779i	0.352956	+	0.935640i	$0.385177\pi$
$641$	−6.59332e6	+	1.14200e7i	−0.633810	+	1.09779i	−0.986766	+	0.162151i	$0.948157\pi$
$642$	1.94279e6	+	3.36501e6i	0.186032	+	0.322218i
$643$	−9.67813e6			−0.923132			−0.461566	−	0.887106i	$-0.652712\pi$
$643$	−9.67813e6			−0.923132			−0.461566	+	0.887106i	$0.652712\pi$
$644$		0			0
$645$	−6.12391e6			−0.579602
$646$	1.86416e6	+	3.22882e6i	0.175753	+	0.304413i
$647$	862455.	−	1.49382e6i	0.0809982	−	0.140293i	−0.822681	−	0.568504i	$-0.807523\pi$
$647$	862455.	−	1.49382e6i	0.0809982	−	0.140293i	0.903679	+	0.428211i	$0.140856\pi$
$648$	−209952.	+	363648.i	−0.0196419	+	0.0340207i
$649$	−808043.	−	1.39957e6i	−0.0753048	−	0.130432i
$650$	83603.8			0.00776145
$651$		0			0
$652$	3.23596e6			0.298116
$653$	−298755.	−	517459.i	−0.0274178	−	0.0474890i	0.851991	−	0.523557i	$-0.175395\pi$
$653$	−298755.	−	517459.i	−0.0274178	−	0.0474890i	−0.879409	+	0.476068i	$0.842062\pi$
$654$	4.00857e6	−	6.94305e6i	0.366476	−	0.634755i
$655$	−590676.	+	1.02308e6i	−0.0537955	+	0.0931766i
$656$	912222.	+	1.58002e6i	0.0827639	+	0.143351i
$657$	−3.00233e6			−0.271360
$658$		0			0
$659$	1.47605e7			1.32400			0.662001	−	0.749503i	$-0.269707\pi$
$659$	1.47605e7			1.32400			0.662001	+	0.749503i	$0.269707\pi$
$660$	−160689.	−	278321.i	−0.0143591	−	0.0248706i
$661$	−8.45206e6	+	1.46394e7i	−0.752418	+	1.30323i	0.194230	+	0.980956i	$0.437779\pi$
$661$	−8.45206e6	+	1.46394e7i	−0.752418	+	1.30323i	−0.946648	+	0.322270i	$0.895554\pi$
$662$	937871.	−	1.62444e6i	0.0831760	−	0.144065i
$663$	320585.	+	555269.i	0.0283243	+	0.0490591i
$664$	−403925.			−0.0355534
$665$		0			0
$666$	−4.15431e6			−0.362922
$667$	4.01290e6	+	6.95055e6i	0.349256	+	0.604930i
$668$	−3.80632e6	+	6.59274e6i	−0.330038	+	0.571643i
$669$	−3.52158e6	+	6.09956e6i	−0.304209	+	0.526906i
$670$	2.55815e6	+	4.43085e6i	0.220161	+	0.381329i
$671$	−708243.			−0.0607262
$672$		0			0
$673$	−1.58960e7			−1.35285			−0.676425	−	0.736512i	$-0.736472\pi$
$673$	−1.58960e7			−1.35285			−0.676425	+	0.736512i	$0.736472\pi$
$674$	4.93596e6	+	8.54933e6i	0.418525	+	0.724907i
$675$	−220404.	+	381751.i	−0.0186192	+	0.0322494i
$676$	2.96079e6	−	5.12823e6i	0.249196	−	0.431619i
$677$	976806.	+	1.69188e6i	0.0819099	+	0.141872i	0.904070	−	0.427384i	$-0.140565\pi$
$677$	976806.	+	1.69188e6i	0.0819099	+	0.141872i	−0.822160	+	0.569256i	$0.807231\pi$
$678$	6.51798e6			0.544551
$679$		0			0
$680$	8.05567e6			0.668081
$681$	−3.58444e6	−	6.20844e6i	−0.296179	−	0.512997i
$682$	−384508.	+	665987.i	−0.0316551	+	0.0548283i
$683$	4.61985e6	−	8.00182e6i	0.378945	−	0.656352i	−0.611964	−	0.790886i	$-0.709620\pi$
$683$	4.61985e6	−	8.00182e6i	0.378945	−	0.656352i	0.990909	+	0.134534i	$0.0429536\pi$
$684$	−293050.	−	507578.i	−0.0239498	−	0.0414823i
$685$	187918.			0.0153018
$686$		0			0
$687$	3.48340e6			0.281587
$688$	−1.42614e6	−	2.47014e6i	−0.114866	−	0.198953i
$689$	121503.	−	210450.i	0.00975078	−	0.0168889i
$690$	1.85146e6	−	3.20682e6i	0.148044	−	0.256420i
$691$	7.28490e6	+	1.26178e7i	0.580401	+	1.00528i	0.995432	+	0.0954768i	$0.0304376\pi$
$691$	7.28490e6	+	1.26178e7i	0.580401	+	1.00528i	−0.415030	+	0.909808i	$0.636229\pi$
$692$	−4.55525e6			−0.361616
$693$		0			0
$694$	−1.71300e7			−1.35008
$695$	1.12982e7	+	1.95690e7i	0.887251	+	1.53676i
$696$	1.37238e6	−	2.37704e6i	0.107387	−	0.186000i
$697$	−7.34424e6	+	1.27206e7i	−0.572618	+	0.991804i
$698$	3.69998e6	+	6.40855e6i	0.287449	+	0.497876i
$699$	−3.45383e6			−0.267367
$700$		0			0
$701$	−3.70190e6			−0.284531			−0.142266	−	0.989829i	$-0.545439\pi$
$701$	−3.70190e6			−0.284531			−0.142266	+	0.989829i	$0.545439\pi$
$702$	−50396.6	−	87289.5i	−0.00385975	−	0.00668527i
$703$	2.89929e6	−	5.02171e6i	0.221260	−	0.383234i
$704$	74842.4	−	129631.i	0.00569136	−	0.00985773i
$705$	−6.44266e6	−	1.11590e7i	−0.488194	−	0.845576i
$706$	−9.09518e6			−0.686751
$707$		0			0
$708$	−6.36809e6			−0.477448
$709$	1.26468e7	+	2.19049e7i	0.944857	+	1.63654i	0.756038	+	0.654528i	$0.227133\pi$
$709$	1.26468e7	+	2.19049e7i	0.944857	+	1.63654i	0.188819	+	0.982012i	$0.439534\pi$
$710$	9.75224e6	−	1.68914e7i	0.726037	−	1.25753i
$711$	−1.70392e6	+	2.95127e6i	−0.126408	+	0.218945i
$712$	1.64787e6	+	2.85419e6i	0.121821	+	0.211000i
$713$	−8.86061e6			−0.652739
$714$		0			0
$715$	77143.1			0.00564329
$716$	−2.78367e6	−	4.82145e6i	−0.202925	−	0.351476i
$717$	2.09434e6	−	3.62751e6i	0.152142	−	0.263518i
$718$	8.79984e6	−	1.52418e7i	0.637036	−	1.10338i
$719$	−7.25924e6	−	1.25734e7i	−0.523683	−	0.907046i	−0.999620	−	0.0275667i	$-0.991224\pi$
$719$	−7.25924e6	−	1.25734e7i	−0.523683	−	0.907046i	0.475937	−	0.879480i	$-0.342109\pi$
$720$	−1.26637e6			−0.0910394
$721$		0			0
$722$	−9.08632e6			−0.648702
$723$	1.56935e6	+	2.71819e6i	0.111654	+	0.193390i
$724$	−3.03765e6	+	5.26136e6i	−0.215373	+	0.373037i
$725$	1.44070e6	−	2.49537e6i	0.101796	−	0.176316i
$726$	2.87488e6	+	4.97944e6i	0.202431	+	0.350622i
$727$	−1.42855e7			−1.00244			−0.501222	−	0.865319i	$-0.667116\pi$
$727$	−1.42855e7			−1.00244			−0.501222	+	0.865319i	$0.667116\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−4.52730e6	−	7.84151e6i	−0.314436	−	0.544619i
$731$	1.14817e7	−	1.98869e7i	0.794719	−	1.37649i
$732$	−1.39539e6	+	2.41689e6i	−0.0962541	+	0.166717i
$733$	4.10778e6	+	7.11488e6i	0.282389	+	0.489112i	0.971973	−	0.235094i	$-0.0755399\pi$
$733$	4.10778e6	+	7.11488e6i	0.282389	+	0.489112i	−0.689584	+	0.724206i	$0.742207\pi$
$734$	−7.58973e6			−0.519979
$735$		0			0
$736$	1.72467e6			0.117358
$737$	382692.	+	662842.i	0.0259526	+	0.0449512i
$738$	1.15453e6	−	1.99971e6i	0.0780306	−	0.135153i
$739$	1.71948e6	−	2.97822e6i	0.115821	−	0.200607i	−0.802287	−	0.596939i	$-0.796384\pi$
$739$	1.71948e6	−	2.97822e6i	0.115821	−	0.200607i	0.918107	+	0.396332i	$0.129717\pi$
$740$	−6.26440e6	−	1.08503e7i	−0.420533	−	0.728385i
$741$	140687.			0.00941256
$742$		0			0
$743$	1.53588e6			0.102067			0.0510334	−	0.998697i	$-0.483748\pi$
$743$	1.53588e6			0.102067			0.0510334	+	0.998697i	$0.483748\pi$
$744$	1.51513e6	+	2.62428e6i	0.100350	+	0.173811i
$745$	−1.38668e7	+	2.40180e7i	−0.915346	+	1.58543i
$746$	−9.12519e6	+	1.58053e7i	−0.600337	+	1.03981i
$747$	255609.	+	442728.i	0.0167600	+	0.0290292i
$748$	1.20510e6			0.0787535
$749$		0			0
$750$	5.54108e6			0.359701
$751$	1.00573e7	+	1.74197e7i	0.650700	+	1.12704i	0.982953	+	0.183855i	$0.0588576\pi$
$751$	1.00573e7	+	1.74197e7i	0.650700	+	1.12704i	−0.332254	+	0.943190i	$0.607809\pi$
$752$	3.00073e6	−	5.19742e6i	0.193501	−	0.335153i
$753$	839443.	−	1.45396e6i	0.0539515	−	0.0934468i
$754$	329425.	+	570581.i	0.0211022	+	0.0365501i
$755$	−1.08457e7			−0.692454
$756$		0			0
$757$	202045.			0.0128147			0.00640733	−	0.999979i	$-0.497960\pi$
$757$	202045.			0.0128147			0.00640733	+	0.999979i	$0.497960\pi$
$758$	−9.98799e6	−	1.72997e7i	−0.631401	−	1.09362i
$759$	276972.	−	479730.i	0.0174515	−	0.0302268i
$760$	883797.	−	1.53078e6i	0.0555033	−	0.0961345i
$761$	541011.	+	937058.i	0.0338645	+	0.0586550i	0.882461	−	0.470386i	$-0.155885\pi$
$761$	541011.	+	937058.i	0.0338645	+	0.0586550i	−0.848596	+	0.529041i	$0.822552\pi$
$762$	3.29309e6			0.205455
$763$		0			0
$764$	3.11188e6			0.192881
$765$	−5.09773e6	−	8.82953e6i	−0.314937	−	0.545486i
$766$	7.35814e6	−	1.27447e7i	0.453102	−	0.784796i
$767$	764294.	−	1.32380e6i	0.0469107	−	0.0812517i
$768$	−294912.	−	510803.i	−0.0180422	−	0.0312500i
$769$	1.19305e7

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5355 + 52.8891i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5355 + 52.8891i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(122.142 - 211.556i) q^{10} +(18.2721 - 31.6482i) q^{11} +(-72.0000 - 124.708i) q^{12} +34.5656 q^{13} -549.640 q^{15} +(-128.000 - 221.703i) q^{16} +(1030.52 - 1784.91i) q^{17} +(-162.000 + 280.592i) q^{18} +(-226.119 - 391.650i) q^{19} -977.137 q^{20} -146.177 q^{22} +(-842.124 - 1458.60i) q^{23} +(-288.000 + 498.831i) q^{24} +(-302.338 + 523.664i) q^{25} +(-69.1312 - 119.739i) q^{26} +729.000 q^{27} -4765.22 q^{29} +(1099.28 + 1904.01i) q^{30} +(2630.43 - 4556.04i) q^{31} +(-512.000 + 886.810i) q^{32} +(164.449 + 284.834i) q^{33} -8244.16 q^{34} +1296.00 q^{36} +(6410.98 + 11104.1i) q^{37} +(-904.476 + 1566.60i) q^{38} +(-155.545 + 269.412i) q^{39} +(1954.27 + 3384.90i) q^{40} -7126.74 q^{41} +11141.7 q^{43} +(292.353 + 506.371i) q^{44} +(2473.38 - 4284.02i) q^{45} +(-3368.50 + 5834.41i) q^{46} +(11721.6 + 20302.4i) q^{47} +2304.00 q^{48} +2418.70 q^{50} +(9274.68 + 16064.2i) q^{51} +(-276.525 + 478.955i) q^{52} +(3515.15 - 6088.42i) q^{53} +(-1458.00 - 2525.33i) q^{54} +2231.79 q^{55} +4070.14 q^{57} +(9530.43 + 16507.2i) q^{58} +(22111.4 - 38298.1i) q^{59} +(4397.12 - 7616.03i) q^{60} +(-9690.24 - 16784.0i) q^{61} -21043.5 q^{62} +4096.00 q^{64} +(1055.48 + 1828.14i) q^{65} +(657.795 - 1139.33i) q^{66} +(-10472.0 + 18138.1i) q^{67} +(16488.3 + 28558.6i) q^{68} +15158.2 q^{69} +79843.4 q^{71} +(-2592.00 - 4489.48i) q^{72} +(18532.9 - 32099.9i) q^{73} +(25643.9 - 44416.6i) q^{74} +(-2721.04 - 4712.98i) q^{75} +7235.81 q^{76} +1244.36 q^{78} +(-21036.0 - 36435.4i) q^{79} +(7817.10 - 13539.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(14253.5 + 24687.7i) q^{82} -6311.34 q^{83} +125870. q^{85} +(-22283.4 - 38595.9i) q^{86} +(21443.5 - 37141.2i) q^{87} +(1169.41 - 2025.48i) q^{88} +(25747.9 + 44596.7i) q^{89} -19787.0 q^{90} +26948.0 q^{92} +(23673.9 + 41004.4i) q^{93} +(46886.4 - 81209.6i) q^{94} +(13809.3 - 23918.5i) q^{95} +(-4608.00 - 7981.29i) q^{96} -127357. q^{97} -2960.08 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 1440 q^{13} - 1944 q^{15} - 512 q^{16} + 612 q^{17} - 648 q^{18} + 2088 q^{19} - 3456 q^{20} - 992 q^{22} - 772 q^{23} - 1152 q^{24} + 318 q^{25} + 2880 q^{26} + 2916 q^{27} - 9184 q^{29} + 3888 q^{30} + 9792 q^{31} - 2048 q^{32} + 1116 q^{33} - 4896 q^{34} + 5184 q^{36} + 5992 q^{37} + 8352 q^{38} + 6480 q^{39} + 6912 q^{40} - 40392 q^{41} - 2272 q^{43} + 1984 q^{44} + 8748 q^{45} - 3088 q^{46} + 36936 q^{47} + 9216 q^{48} - 2544 q^{50} + 5508 q^{51} + 11520 q^{52} + 16708 q^{53} - 5832 q^{54} + 12672 q^{55} - 37584 q^{57} + 18368 q^{58} + 74592 q^{59} + 15552 q^{60} - 18648 q^{61} - 78336 q^{62} + 16384 q^{64} - 33300 q^{65} + 4464 q^{66} - 67344 q^{67} + 9792 q^{68} + 13896 q^{69} + 153096 q^{71} - 10368 q^{72} + 47304 q^{73} + 23968 q^{74} + 2862 q^{75} - 66816 q^{76} - 51840 q^{78} - 140656 q^{79} + 27648 q^{80} - 13122 q^{81} + 80784 q^{82} - 188208 q^{83} + 115736 q^{85} + 4544 q^{86} + 41328 q^{87} + 7936 q^{88} - 17604 q^{89} - 69984 q^{90} + 24704 q^{92} + 88128 q^{93} + 147744 q^{94} - 91592 q^{95} - 18432 q^{96} - 170352 q^{97} - 20088 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 1440 * q^13 - 1944 * q^15 - 512 * q^16 + 612 * q^17 - 648 * q^18 + 2088 * q^19 - 3456 * q^20 - 992 * q^22 - 772 * q^23 - 1152 * q^24 + 318 * q^25 + 2880 * q^26 + 2916 * q^27 - 9184 * q^29 + 3888 * q^30 + 9792 * q^31 - 2048 * q^32 + 1116 * q^33 - 4896 * q^34 + 5184 * q^36 + 5992 * q^37 + 8352 * q^38 + 6480 * q^39 + 6912 * q^40 - 40392 * q^41 - 2272 * q^43 + 1984 * q^44 + 8748 * q^45 - 3088 * q^46 + 36936 * q^47 + 9216 * q^48 - 2544 * q^50 + 5508 * q^51 + 11520 * q^52 + 16708 * q^53 - 5832 * q^54 + 12672 * q^55 - 37584 * q^57 + 18368 * q^58 + 74592 * q^59 + 15552 * q^60 - 18648 * q^61 - 78336 * q^62 + 16384 * q^64 - 33300 * q^65 + 4464 * q^66 - 67344 * q^67 + 9792 * q^68 + 13896 * q^69 + 153096 * q^71 - 10368 * q^72 + 47304 * q^73 + 23968 * q^74 + 2862 * q^75 - 66816 * q^76 - 51840 * q^78 - 140656 * q^79 + 27648 * q^80 - 13122 * q^81 + 80784 * q^82 - 188208 * q^83 + 115736 * q^85 + 4544 * q^86 + 41328 * q^87 + 7936 * q^88 - 17604 * q^89 - 69984 * q^90 + 24704 * q^92 + 88128 * q^93 + 147744 * q^94 - 91592 * q^95 - 18432 * q^96 - 170352 * q^97 - 20088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more