LMFDB - Embedded newform 294.6.e.x.67.1

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:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.6.e.x.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-51.7487 - 89.6314i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-51.7487 - 89.6314i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(206.995 - 358.526i) q^{10} +(-120.095 + 208.011i) q^{11} +(-72.0000 - 124.708i) q^{12} +805.477 q^{13} +931.477 q^{15} +(-128.000 - 221.703i) q^{16} +(646.633 - 1120.00i) q^{17} +(162.000 - 280.592i) q^{18} +(137.688 + 238.483i) q^{19} +1655.96 q^{20} -960.764 q^{22} +(-1898.29 - 3287.93i) q^{23} +(288.000 - 498.831i) q^{24} +(-3793.36 + 6570.30i) q^{25} +(1610.95 + 2790.26i) q^{26} +729.000 q^{27} +1227.52 q^{29} +(1862.95 + 3226.73i) q^{30} +(-2812.43 + 4871.27i) q^{31} +(512.000 - 886.810i) q^{32} +(-1080.86 - 1872.10i) q^{33} +5173.06 q^{34} +1296.00 q^{36} +(4539.25 + 7862.20i) q^{37} +(-550.754 + 953.933i) q^{38} +(-3624.65 + 6278.07i) q^{39} +(3311.92 + 5736.41i) q^{40} -18207.4 q^{41} -11708.2 q^{43} +(-1921.53 - 3328.18i) q^{44} +(-4191.65 + 7260.15i) q^{45} +(7593.15 - 13151.7i) q^{46} +(11524.3 + 19960.7i) q^{47} +2304.00 q^{48} -30346.9 q^{50} +(5819.70 + 10080.0i) q^{51} +(-6443.82 + 11161.0i) q^{52} +(-8831.40 + 15296.4i) q^{53} +(1458.00 + 2525.33i) q^{54} +24859.2 q^{55} -2478.39 q^{57} +(2455.04 + 4252.25i) q^{58} +(-9188.15 + 15914.3i) q^{59} +(-7451.82 + 12906.9i) q^{60} +(-5662.04 - 9806.95i) q^{61} -22499.5 q^{62} +4096.00 q^{64} +(-41682.4 - 72196.1i) q^{65} +(4323.44 - 7488.41i) q^{66} +(-18039.7 + 31245.6i) q^{67} +(10346.1 + 17920.0i) q^{68} +34169.2 q^{69} -63434.2 q^{71} +(2592.00 + 4489.48i) q^{72} +(26491.2 - 45884.1i) q^{73} +(-18157.0 + 31448.8i) q^{74} +(-34140.3 - 59132.7i) q^{75} -4406.03 q^{76} -28997.2 q^{78} +(24282.0 + 42057.7i) q^{79} +(-13247.7 + 22945.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-36414.8 - 63072.3i) q^{82} +113161. q^{83} -133850. q^{85} +(-23416.4 - 40558.5i) q^{86} +(-5523.83 + 9567.56i) q^{87} +(7686.11 - 13312.7i) q^{88} +(-54182.9 - 93847.6i) q^{89} -33533.2 q^{90} +60745.2 q^{92} +(-25311.9 - 43841.5i) q^{93} +(-46097.2 + 79842.7i) q^{94} +(14250.4 - 24682.4i) q^{95} +(4608.00 + 7981.29i) q^{96} +99641.2 q^{97} +19455.5 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	\( 4 q + 8 q^{2} - 18 q^{3} - 32 q^{4} - 108 q^{5} - 144 q^{6} - 256 q^{8} - 162 q^{9} + 432 q^{10} - 124 q^{11} - 288 q^{12} + 1440 q^{13} + 1944 q^{15} - 512 q^{16} + 1260 q^{17} + 648 q^{18} - 360 q^{19} + 3456 q^{20} - 992 q^{22} - 6524 q^{23} + 1152 q^{24} - 4482 q^{25} + 2880 q^{26} + 2916 q^{27} + 14176 q^{29} + 3888 q^{30} - 5904 q^{31} + 2048 q^{32} - 1116 q^{33} + 10080 q^{34} + 5184 q^{36} + 6040 q^{37} + 1440 q^{38} - 6480 q^{39} + 6912 q^{40} - 34776 q^{41} - 1216 q^{43} - 1984 q^{44} - 8748 q^{45} + 26096 q^{46} + 30456 q^{47} + 9216 q^{48} - 35856 q^{50} + 11340 q^{51} - 11520 q^{52} - 3964 q^{53} + 5832 q^{54} + 48672 q^{55} + 6480 q^{57} + 28352 q^{58} - 40752 q^{59} - 15552 q^{60} + 1368 q^{61} - 47232 q^{62} + 16384 q^{64} - 82980 q^{65} + 4464 q^{66} + 16224 q^{67} + 20160 q^{68} + 117432 q^{69} - 6408 q^{71} + 10368 q^{72} - 23976 q^{73} - 24160 q^{74} - 40338 q^{75} + 11520 q^{76} - 51840 q^{78} + 82160 q^{79} - 27648 q^{80} - 13122 q^{81} - 69552 q^{82} + 347472 q^{83} - 267400 q^{85} - 2432 q^{86} - 63792 q^{87} + 7936 q^{88} - 200556 q^{89} - 69984 q^{90} + 208768 q^{92} - 53136 q^{93} - 121824 q^{94} + 25640 q^{95} + 18432 q^{96} + 503856 q^{97} + 20088 q^{99}+O(q^{100}) \) 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 + 1260 * q^17 + 648 * q^18 - 360 * q^19 + 3456 * q^20 - 992 * q^22 - 6524 * q^23 + 1152 * q^24 - 4482 * q^25 + 2880 * q^26 + 2916 * q^27 + 14176 * q^29 + 3888 * q^30 - 5904 * q^31 + 2048 * q^32 - 1116 * q^33 + 10080 * q^34 + 5184 * q^36 + 6040 * q^37 + 1440 * q^38 - 6480 * q^39 + 6912 * q^40 - 34776 * q^41 - 1216 * q^43 - 1984 * q^44 - 8748 * q^45 + 26096 * q^46 + 30456 * q^47 + 9216 * q^48 - 35856 * q^50 + 11340 * q^51 - 11520 * q^52 - 3964 * q^53 + 5832 * q^54 + 48672 * q^55 + 6480 * q^57 + 28352 * q^58 - 40752 * q^59 - 15552 * q^60 + 1368 * q^61 - 47232 * q^62 + 16384 * q^64 - 82980 * q^65 + 4464 * q^66 + 16224 * q^67 + 20160 * q^68 + 117432 * q^69 - 6408 * q^71 + 10368 * q^72 - 23976 * q^73 - 24160 * q^74 - 40338 * q^75 + 11520 * q^76 - 51840 * q^78 + 82160 * q^79 - 27648 * q^80 - 13122 * q^81 - 69552 * q^82 + 347472 * q^83 - 267400 * q^85 - 2432 * q^86 - 63792 * q^87 + 7936 * q^88 - 200556 * q^89 - 69984 * q^90 + 208768 * q^92 - 53136 * q^93 - 121824 * q^94 + 25640 * q^95 + 18432 * q^96 + 503856 * 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
$5$	−51.7487	−	89.6314i	−0.925710	−	1.60338i	−0.790416	−	0.612570i	$-0.790136\pi$
$5$	−51.7487	−	89.6314i	−0.925710	−	1.60338i	−0.135294	−	0.990806i	$-0.543198\pi$
$6$	−36.0000			−0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	206.995	−	358.526i	0.654576	−	1.13376i
$11$	−120.095	+	208.011i	−0.299257	+	0.518329i	−0.975966	−	0.217922i	$-0.930072\pi$
$11$	−120.095	+	208.011i	−0.299257	+	0.518329i	0.676709	+	0.736251i	$0.263406\pi$
$12$	−72.0000	−	124.708i	−0.144338	−	0.250000i
$13$	805.477			1.32189			0.660944	−	0.750435i	$-0.270156\pi$
$13$	805.477			1.32189			0.660944	+	0.750435i	$0.270156\pi$
$14$		0			0
$15$	931.477			1.06892
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	646.633	−	1120.00i	0.542670	−	0.939932i	−0.456080	−	0.889939i	$-0.650747\pi$
$17$	646.633	−	1120.00i	0.542670	−	0.939932i	0.998750	−	0.0499927i	$-0.0159198\pi$
$18$	162.000	−	280.592i	0.117851	−	0.204124i
$19$	137.688	+	238.483i	0.0875011	+	0.151556i	0.906454	−	0.422304i	$-0.138779\pi$
$19$	137.688	+	238.483i	0.0875011	+	0.151556i	−0.818953	+	0.573860i	$0.805445\pi$
$20$	1655.96			0.925710
$21$		0			0
$22$	−960.764			−0.423214
$23$	−1898.29	−	3287.93i	−0.748242	−	1.29599i	−0.948665	−	0.316284i	$-0.897565\pi$
$23$	−1898.29	−	3287.93i	−0.748242	−	1.29599i	0.200423	−	0.979710i	$-0.435769\pi$
$24$	288.000	−	498.831i	0.102062	−	0.176777i
$25$	−3793.36	+	6570.30i	−1.21388	+	2.10250i
$26$	1610.95	+	2790.26i	0.467358	+	0.809488i
$27$	729.000			0.192450
$28$		0			0
$29$	1227.52			0.271040			0.135520	−	0.990775i	$-0.456730\pi$
$29$	1227.52			0.271040			0.135520	+	0.990775i	$0.456730\pi$
$30$	1862.95	+	3226.73i	0.377919	+	0.654576i
$31$	−2812.43	+	4871.27i	−0.525627	+	0.910413i	0.473927	+	0.880564i	$0.342836\pi$
$31$	−2812.43	+	4871.27i	−0.525627	+	0.910413i	−0.999554	+	0.0298489i	$0.990497\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−1080.86	−	1872.10i	−0.172776	−	0.299257i
$34$	5173.06			0.767451
$35$		0			0
$36$	1296.00			0.166667
$37$	4539.25	+	7862.20i	0.545104	+	0.944148i	0.998600	+	0.0528897i	$0.0168432\pi$
$37$	4539.25	+	7862.20i	0.545104	+	0.944148i	−0.453496	+	0.891258i	$0.649824\pi$
$38$	−550.754	+	953.933i	−0.0618726	+	0.107166i
$39$	−3624.65	+	6278.07i	−0.381596	+	0.660944i
$40$	3311.92	+	5736.41i	0.327288	+	0.566879i
$41$	−18207.4			−1.69156			−0.845782	−	0.533528i	$-0.820866\pi$
$41$	−18207.4			−1.69156			−0.845782	+	0.533528i	$0.820866\pi$
$42$		0			0
$43$	−11708.2			−0.965650			−0.482825	−	0.875717i	$-0.660389\pi$
$43$	−11708.2			−0.965650			−0.482825	+	0.875717i	$0.660389\pi$
$44$	−1921.53	−	3328.18i	−0.149629	−	0.259164i
$45$	−4191.65	+	7260.15i	−0.308570	+	0.534459i
$46$	7593.15	−	13151.7i	0.529087	−	0.916406i
$47$	11524.3	+	19960.7i	0.760974	+	1.31805i	0.942349	+	0.334632i	$0.108612\pi$
$47$	11524.3	+	19960.7i	0.760974	+	1.31805i	−0.181375	+	0.983414i	$0.558055\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	−30346.9			−1.71668
$51$	5819.70	+	10080.0i	0.313311	+	0.542670i
$52$	−6443.82	+	11161.0i	−0.330472	+	0.572395i
$53$	−8831.40	+	15296.4i	−0.431857	+	0.747998i	−0.997033	−	0.0769720i	$-0.975475\pi$
$53$	−8831.40	+	15296.4i	−0.431857	+	0.747998i	0.565176	+	0.824970i	$0.308808\pi$
$54$	1458.00	+	2525.33i	0.0680414	+	0.117851i
$55$	24859.2			1.10810
$56$		0			0
$57$	−2478.39			−0.101038
$58$	2455.04	+	4252.25i	0.0958270	+	0.165977i
$59$	−9188.15	+	15914.3i	−0.343636	+	0.595194i	−0.985105	−	0.171954i	$-0.944992\pi$
$59$	−9188.15	+	15914.3i	−0.343636	+	0.595194i	0.641469	+	0.767149i	$0.278325\pi$
$60$	−7451.82	+	12906.9i	−0.267229	+	0.462855i
$61$	−5662.04	−	9806.95i	−0.194827	−	0.337450i	0.752017	−	0.659144i	$-0.229081\pi$
$61$	−5662.04	−	9806.95i	−0.194827	−	0.337450i	−0.946844	+	0.321694i	$0.895748\pi$
$62$	−22499.5			−0.743349
$63$		0			0
$64$	4096.00			0.125000
$65$	−41682.4	−	72196.1i	−1.22369	−	2.11948i
$66$	4323.44	−	7488.41i	0.122171	−	0.211607i
$67$	−18039.7	+	31245.6i	−0.490955	+	0.850359i	−0.999946	−	0.0104130i	$-0.996685\pi$
$67$	−18039.7	+	31245.6i	−0.490955	+	0.850359i	0.508991	+	0.860772i	$0.330019\pi$
$68$	10346.1	+	17920.0i	0.271335	+	0.469966i
$69$	34169.2			0.863996
$70$		0			0
$71$	−63434.2			−1.49341			−0.746703	−	0.665158i	$-0.768364\pi$
$71$	−63434.2			−1.49341			−0.746703	+	0.665158i	$0.768364\pi$
$72$	2592.00	+	4489.48i	0.0589256	+	0.102062i
$73$	26491.2	−	45884.1i	0.581828	−	1.00776i	−0.413435	−	0.910534i	$-0.635671\pi$
$73$	26491.2	−	45884.1i	0.581828	−	1.00776i	0.995263	−	0.0972215i	$-0.0309955\pi$
$74$	−18157.0	+	31448.8i	−0.385447	+	0.667613i
$75$	−34140.3	−	59132.7i	−0.700832	−	1.21388i
$76$	−4406.03			−0.0875011
$77$		0			0
$78$	−28997.2			−0.539659
$79$	24282.0	+	42057.7i	0.437741	+	0.758189i	0.997515	−	0.0704561i	$-0.0224455\pi$
$79$	24282.0	+	42057.7i	0.437741	+	0.758189i	−0.559774	+	0.828645i	$0.689112\pi$
$80$	−13247.7	+	22945.6i	−0.231427	+	0.400844i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−36414.8	−	63072.3i	−0.598058	−	1.03587i
$83$	113161.			1.80303			0.901513	−	0.432753i	$-0.142458\pi$
$83$	113161.			1.80303			0.901513	+	0.432753i	$0.142458\pi$
$84$		0			0
$85$	−133850.			−2.00942
$86$	−23416.4	−	40558.5i	−0.341409	−	0.591337i
$87$	−5523.83	+	9567.56i	−0.0782424	+	0.135520i
$88$	7686.11	−	13312.7i	0.105803	−	0.183257i
$89$	−54182.9	−	93847.6i	−0.725083	−	1.25588i	−0.958940	−	0.283609i	$-0.908468\pi$
$89$	−54182.9	−	93847.6i	−0.725083	−	1.25588i	0.233857	−	0.972271i	$-0.424865\pi$
$90$	−33533.2			−0.436384
$91$		0			0
$92$	60745.2			0.748242
$93$	−25311.9	−	43841.5i	−0.303471	−	0.525627i
$94$	−46097.2	+	79842.7i	−0.538090	+	0.931999i
$95$	14250.4	−	24682.4i	0.162001	−	0.280594i
$96$	4608.00	+	7981.29i	0.0510310	+	0.0883883i
$97$	99641.2			1.07525			0.537625	−	0.843184i	$-0.319321\pi$
$97$	99641.2			1.07525			0.537625	+	0.843184i	$0.319321\pi$
$98$		0			0
$99$	19455.5			0.199505
$100$	−60693.8	−	105125.i	−0.606938	−	1.05125i
$101$	−82599.9	+	143067.i	−0.805705	+	1.39552i	0.110109	+	0.993920i	$0.464880\pi$
$101$	−82599.9	+	143067.i	−0.805705	+	1.39552i	−0.915814	+	0.401603i	$0.868453\pi$
$102$	−23278.8	+	40320.0i	−0.221544	+	0.383725i
$103$	53623.6	+	92878.8i	0.498038	+	0.862628i	0.999997	−	0.00226355i	$-0.000720512\pi$
$103$	53623.6	+	92878.8i	0.498038	+	0.862628i	−0.501959	+	0.864891i	$0.667387\pi$
$104$	−51550.5			−0.467358
$105$		0			0
$106$	−70651.2			−0.610738
$107$	48711.2	+	84370.2i	0.411310	+	0.712409i	0.995033	−	0.0995431i	$-0.0317381\pi$
$107$	48711.2	+	84370.2i	0.411310	+	0.712409i	−0.583723	+	0.811953i	$0.698405\pi$
$108$	−5832.00	+	10101.3i	−0.0481125	+	0.0833333i
$109$	−29653.6	+	51361.5i	−0.239062	+	0.414068i	−0.960445	−	0.278468i	$-0.910173\pi$
$109$	−29653.6	+	51361.5i	−0.239062	+	0.414068i	0.721383	+	0.692536i	$0.243507\pi$
$110$	49718.3	+	86114.6i	0.391773	+	0.678571i
$111$	−81706.4			−0.629432
$112$		0			0
$113$	157268.			1.15863			0.579313	−	0.815105i	$-0.303321\pi$
$113$	157268.			1.15863			0.579313	+	0.815105i	$0.303321\pi$
$114$	−4956.78	−	8585.40i	−0.0357222	−	0.0618726i
$115$	−196468.	+	340292.i	−1.38531	+	2.39943i
$116$	−9820.15	+	17009.0i	−0.0677599	+	0.117364i
$117$	−32621.8	−	56502.7i	−0.220315	−	0.381596i
$118$	−73505.2			−0.485974
$119$		0			0
$120$	−59614.5			−0.377919
$121$	51679.7	+	89511.8i	0.320890	+	0.555798i
$122$	22648.2	−	39227.8i	0.137763	−	0.238613i
$123$	81933.4	−	141913.i	0.488313	−	0.845782i
$124$	−44998.9	−	77940.4i	−0.262814	−	0.455206i
$125$	461778.			2.64337
$126$		0			0
$127$	−92477.3			−0.508775			−0.254387	−	0.967102i	$-0.581874\pi$
$127$	−92477.3			−0.508775			−0.254387	+	0.967102i	$0.581874\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	52687.0	−	91256.5i	0.278759	−	0.482825i
$130$	166730.	−	288784.i	0.865276	−	1.49870i
$131$	36164.2	+	62638.2i	0.184120	+	0.318905i	0.943280	−	0.331999i	$-0.107723\pi$
$131$	36164.2	+	62638.2i	0.184120	+	0.318905i	−0.759160	+	0.650904i	$0.774390\pi$
$132$	34587.5			0.172776
$133$		0			0
$134$	−144317.			−0.694315
$135$	−37724.8	−	65341.3i	−0.178153	−	0.308570i
$136$	−41384.5	+	71680.1i	−0.191863	+	0.332316i
$137$	−112831.	+	195429.i	−0.513602	+	0.889585i	0.486273	+	0.873807i	$0.338356\pi$
$137$	−112831.	+	195429.i	−0.513602	+	0.889585i	−0.999876	+	0.0157784i	$0.994977\pi$
$138$	68338.3	+	118365.i	0.305469	+	0.529087i
$139$	−327971.			−1.43979			−0.719894	−	0.694084i	$-0.755810\pi$
$139$	−327971.			−1.43979			−0.719894	+	0.694084i	$0.755810\pi$
$140$		0			0
$141$	−207437.			−0.878697
$142$	−126868.	−	219743.i	−0.527999	−	0.914521i
$143$	−96734.2	+	167548.i	−0.395585	+	0.685173i
$144$	−10368.0	+	17957.9i	−0.0416667	+	0.0721688i
$145$	−63522.5	−	110024.i	−0.250904	−	0.434579i
$146$	211930.			0.822829
$147$		0			0
$148$	−145256.			−0.545104
$149$	−82005.4	−	142038.i	−0.302606	−	0.524128i	0.674120	−	0.738622i	$-0.264523\pi$
$149$	−82005.4	−	142038.i	−0.302606	−	0.524128i	−0.976725	+	0.214494i	$0.931190\pi$
$150$	136561.	−	236531.i	0.495563	−	0.858340i
$151$	−31154.4	+	53961.0i	−0.111193	+	0.192592i	−0.916251	−	0.400604i	$-0.868800\pi$
$151$	−31154.4	+	53961.0i	−0.111193	+	0.192592i	0.805059	+	0.593195i	$0.202134\pi$
$152$	−8812.06	−	15262.9i	−0.0309363	−	0.0535832i
$153$	−104755.			−0.361780
$154$		0			0
$155$	582159.			1.94631
$156$	−57994.4	−	100449.i	−0.190798	−	0.330472i
$157$	119903.	−	207679.i	0.388224	−	0.672423i	−0.603987	−	0.796994i	$-0.706422\pi$
$157$	119903.	−	207679.i	0.388224	−	0.672423i	0.992211	+	0.124571i	$0.0397555\pi$
$158$	−97128.0	+	168231.i	−0.309529	+	0.536121i
$159$	−79482.6	−	137668.i	−0.249333	−	0.431857i
$160$	−105981.			−0.327288
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	218397.	+	378275.i	0.643841	+	1.11516i	0.984568	+	0.175002i	$0.0559933\pi$
$163$	218397.	+	378275.i	0.643841	+	1.11516i	−0.340727	+	0.940162i	$0.610673\pi$
$164$	145659.	−	252289.i	0.422891	−	0.732469i
$165$	−111866.	+	193758.i	−0.319881	+	0.554051i
$166$	226322.	+	392001.i	0.637466	+	1.10412i
$167$	38846.7			0.107786			0.0538931	−	0.998547i	$-0.482837\pi$
$167$	38846.7			0.107786			0.0538931	+	0.998547i	$0.482837\pi$
$168$		0			0
$169$	277501.			0.747390
$170$	−267700.	−	463669.i	−0.710437	−	1.23051i
$171$	11152.8	−	19317.1i	0.0291670	−	0.0505188i
$172$	93665.7	−	162234.i	0.241412	−	0.418139i
$173$	−198139.	−	343186.i	−0.503331	−	0.871795i	−0.999993	−	0.00385097i	$-0.998774\pi$
$173$	−198139.	−	343186.i	−0.503331	−	0.871795i	0.496661	−	0.867944i	$-0.334559\pi$
$174$	−44190.7			−0.110652
$175$		0			0
$176$	61488.9			0.149629
$177$	−82693.4	−	143229.i	−0.198398	−	0.343636i
$178$	216732.	−	375390.i	0.512711	−	0.888041i
$179$	−121942.	+	211209.i	−0.284459	+	0.492698i	−0.972478	−	0.232995i	$-0.925147\pi$
$179$	−121942.	+	211209.i	−0.284459	+	0.492698i	0.688019	+	0.725693i	$0.258481\pi$
$180$	−67066.4	−	116162.i	−0.154285	−	0.267229i
$181$	−299273.			−0.679002			−0.339501	−	0.940606i	$-0.610258\pi$
$181$	−299273.			−0.679002			−0.339501	+	0.940606i	$0.610258\pi$
$182$		0			0
$183$	101917.			0.224967
$184$	121490.	+	210427.i	0.264544	+	0.458203i
$185$	469800.	−	813718.i	1.00922	−	1.74801i
$186$	101248.	−	175366.i	0.214586	−	0.371675i
$187$	155315.	+	269014.i	0.324796	+	0.562563i
$188$	−368778.			−0.760974
$189$		0			0
$190$	114003.			0.229104
$191$	388498.	+	672899.i	0.770558	+	1.33465i	0.937257	+	0.348639i	$0.113356\pi$
$191$	388498.	+	672899.i	0.770558	+	1.33465i	−0.166699	+	0.986008i	$0.553311\pi$
$192$	−18432.0	+	31925.2i	−0.0360844	+	0.0625000i
$193$	−138211.	+	239388.i	−0.267084	+	0.462603i	−0.968108	−	0.250535i	$-0.919393\pi$
$193$	−138211.	+	239388.i	−0.267084	+	0.462603i	0.701023	+	0.713138i	$0.252727\pi$
$194$	199282.	+	345167.i	0.380159	+	0.658454i
$195$	750284.			1.41299
$196$		0			0
$197$	−131615.			−0.241624			−0.120812	−	0.992675i	$-0.538550\pi$
$197$	−131615.			−0.241624			−0.120812	+	0.992675i	$0.538550\pi$
$198$	38910.9	+	67395.7i	0.0705356	+	0.122171i
$199$	−282480.	+	489270.i	−0.505656	+	0.875822i	0.494322	+	0.869279i	$0.335416\pi$
$199$	−282480.	+	489270.i	−0.505656	+	0.875822i	−0.999979	+	0.00654355i	$0.997917\pi$
$200$	242775.	−	420499.i	0.429170	−	0.743344i
$201$	−162357.	−	281211.i	−0.283453	−	0.490955i
$202$	−660799.			−1.13944
$203$		0			0
$204$	−186230.			−0.313311
$205$	942211.	+	1.63196e6i	1.56590	+	2.71221i
$206$	−214494.	+	371515.i	−0.352166	+	0.609970i
$207$	−153761.	+	266322.i	−0.249414	+	0.431998i
$208$	−103101.	−	178576.i	−0.165236	−	0.286197i
$209$	−66143.0			−0.104741
$210$		0			0
$211$	313637.			0.484977			0.242489	−	0.970154i	$-0.422036\pi$
$211$	313637.			0.484977			0.242489	+	0.970154i	$0.422036\pi$
$212$	−141302.	−	244743.i	−0.215928	−	0.373999i
$213$	285454.	−	494421.i	0.431109	−	0.746703i
$214$	−194845.	+	337481.i	−0.290840	+	0.503750i
$215$	605886.	+	1.04942e6i	0.893911	+	1.54830i
$216$	−46656.0			−0.0680414
$217$		0			0
$218$	−237229.			−0.338085
$219$	238421.	+	412957.i	0.335918	+	0.581828i
$220$	−198873.	+	344459.i	−0.277025	+	0.479822i
$221$	520848.	−	902136.i	0.717349	−	1.24248i
$222$	−163413.	−	283039.i	−0.222538	−	0.385447i
$223$	−279483.			−0.376351			−0.188176	−	0.982135i	$-0.560257\pi$
$223$	−279483.			−0.376351			−0.188176	+	0.982135i	$0.560257\pi$
$224$		0			0
$225$	614525.			0.809251
$226$	314535.	+	544791.i	0.409636	+	0.709511i
$227$	611754.	−	1.05959e6i	0.787974	−	1.36481i	−0.139232	−	0.990260i	$-0.544463\pi$
$227$	611754.	−	1.05959e6i	0.787974	−	1.36481i	0.927206	−	0.374551i	$-0.122203\pi$
$228$	19827.1	−	34341.6i	0.0252594	−	0.0437505i
$229$	−127387.	−	220641.i	−0.160523	−	0.278034i	0.774533	−	0.632533i	$-0.217985\pi$
$229$	−127387.	−	220641.i	−0.160523	−	0.278034i	−0.935056	+	0.354499i	$0.884651\pi$
$230$	−1.57174e6			−1.95912
$231$		0			0
$232$	−78561.2			−0.0958270
$233$	−373086.	−	646204.i	−0.450215	−	0.779794i	0.548184	−	0.836357i	$-0.315319\pi$
$233$	−373086.	−	646204.i	−0.450215	−	0.779794i	−0.998399	+	0.0565630i	$0.981986\pi$
$234$	130487.	−	226011.i	0.155786	−	0.269829i
$235$	1.19274e6	−	2.06588e6i	1.40888	−	2.44026i
$236$	−147010.	−	254630.i	−0.171818	−	0.297597i
$237$	−437076.			−0.505459
$238$		0			0
$239$	321036.			0.363546			0.181773	−	0.983341i	$-0.441816\pi$
$239$	321036.			0.363546			0.181773	+	0.983341i	$0.441816\pi$
$240$	−119229.	−	206511.i	−0.133615	−	0.231427i
$241$	−621268.	+	1.07607e6i	−0.689027	+	1.19343i	0.283125	+	0.959083i	$0.408629\pi$
$241$	−621268.	+	1.07607e6i	−0.689027	+	1.19343i	−0.972153	+	0.234348i	$0.924705\pi$
$242$	−206719.	+	358047.i	−0.226904	+	0.393008i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	181185.			0.194827
$245$		0			0
$246$	655467.			0.690578
$247$	110905.	+	192093.i	0.115667	+	0.200341i
$248$	179996.	−	311762.i	0.185837	−	0.321880i
$249$	−509225.	+	882003.i	−0.520489	+	0.901513i
$250$	923555.	+	1.59964e6i	0.934572	+	1.61873i
$251$	690235.			0.691532			0.345766	−	0.938321i	$-0.387619\pi$
$251$	690235.			0.691532			0.345766	+	0.938321i	$0.387619\pi$
$252$		0			0
$253$	911902.			0.895668
$254$	−184955.	−	320351.i	−0.179879	−	0.311560i
$255$	602324.	−	1.04326e6i	0.580069	−	1.00471i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−6893.35	−	11939.6i	−0.00651024	−	0.0112761i	0.862752	−	0.505627i	$-0.168739\pi$
$257$	−6893.35	−	11939.6i	−0.00651024	−	0.0112761i	−0.869262	+	0.494351i	$0.835406\pi$
$258$	421496.			0.394225
$259$		0			0
$260$	1.33384e6			1.22369
$261$	−49714.5	−	86108.0i	−0.0451733	−	0.0782424i
$262$	−144657.	+	250553.i	−0.130192	+	0.225500i
$263$	−287417.	+	497820.i	−0.256226	+	0.443796i	−0.965228	−	0.261411i	$-0.915812\pi$
$263$	−287417.	+	497820.i	−0.256226	+	0.443796i	0.709002	+	0.705206i	$0.249146\pi$
$264$	69175.0	+	119815.i	0.0610857	+	0.105803i
$265$	1.82806e6			1.59910
$266$		0			0
$267$	975293.			0.837253
$268$	−288635.	−	499930.i	−0.245477	−	0.425179i
$269$	559464.	−	969020.i	0.471402	−	0.816492i	−0.528063	−	0.849205i	$-0.677081\pi$
$269$	559464.	−	969020.i	0.471402	−	0.816492i	0.999465	+	0.0327131i	$0.0104147\pi$
$270$	150899.	−	261365.i	0.125973	−	0.218192i
$271$	−347435.	−	601775.i	−0.287376	−	0.497749i	0.685807	−	0.727784i	$-0.259449\pi$
$271$	−347435.	−	601775.i	−0.287376	−	0.497749i	−0.973183	+	0.230034i	$0.926116\pi$
$272$	−331076.			−0.271335
$273$		0			0
$274$	−902648.			−0.726343
$275$	−911131.	−	1.57813e6i	−0.726523	−	1.25837i
$276$	−273353.	+	473462.i	−0.215999	+	0.374121i
$277$	418827.	−	725429.i	0.327971	−	0.568062i	−0.654138	−	0.756375i	$-0.726969\pi$
$277$	418827.	−	725429.i	0.327971	−	0.568062i	0.982109	+	0.188313i	$0.0603019\pi$
$278$	−655942.	−	1.13613e6i	−0.509042	−	0.881687i
$279$	455614.			0.350418
$280$		0			0
$281$	−917687.			−0.693312			−0.346656	−	0.937992i	$-0.612683\pi$
$281$	−917687.			−0.693312			−0.346656	+	0.937992i	$0.612683\pi$
$282$	−414875.	−	718584.i	−0.310666	−	0.538090i
$283$	207632.	−	359629.i	0.154109	−	0.266924i	−0.778625	−	0.627489i	$-0.784083\pi$
$283$	207632.	−	359629.i	0.154109	−	0.266924i	0.932734	+	0.360565i	$0.117416\pi$
$284$	507474.	−	878971.i	0.373352	−	0.646664i
$285$	128254.	+	222142.i	0.0935314	+	0.162001i
$286$	−773873.			−0.559442
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	−126340.	−	218828.i	−0.0889809	−	0.154119i
$290$	254090.	−	440097.i	0.177416	−	0.307293i
$291$	−448386.	+	776627.i	−0.310398	+	0.537625i
$292$	423859.	+	734145.i	0.290914	+	0.503878i
$293$	−1.21491e6			−0.826752			−0.413376	−	0.910561i	$-0.635650\pi$
$293$	−1.21491e6			−0.826752			−0.413376	+	0.910561i	$0.635650\pi$
$294$		0			0
$295$	1.90190e6			1.27243
$296$	−290512.	−	503181.i	−0.192723	−	0.333807i
$297$	−87549.6	+	151640.i	−0.0575921	+	0.0997525i
$298$	328022.	−	568150.i	0.213974	−	0.370615i
$299$	−1.52903e6	−	2.64835e6i	−0.989093	−	1.71316i
$300$	1.09249e6			0.700832
$301$		0			0
$302$	−249235.			−0.157250
$303$	−743399.	−	1.28761e6i	−0.465174	−	0.805705i
$304$	35248.2	−	61051.7i	0.0218753	−	0.0378891i
$305$	−586007.	+	1.01499e6i	−0.360706	+	0.624761i
$306$	−209509.	−	362880.i	−0.127908	−	0.221544i
$307$	−2.60119e6			−1.57517			−0.787584	−	0.616207i	$-0.788668\pi$
$307$	−2.60119e6			−1.57517			−0.787584	+	0.616207i	$0.788668\pi$
$308$		0			0
$309$	−965225.			−0.575085
$310$	1.16432e6	+	2.01666e6i	0.688125	+	1.19187i
$311$	409582.	−	709417.i	0.240126	−	0.415911i	−0.720624	−	0.693326i	$-0.756144\pi$
$311$	409582.	−	709417.i	0.240126	−	0.415911i	0.960750	+	0.277415i	$0.0894778\pi$
$312$	231977.	−	401797.i	0.134915	−	0.233679i
$313$	440970.	+	763782.i	0.254418	+	0.440665i	0.964737	−	0.263215i	$-0.0847828\pi$
$313$	440970.	+	763782.i	0.254418	+	0.440665i	−0.710319	+	0.703880i	$0.751449\pi$
$314$	959226.			0.549031
$315$		0			0
$316$	−777024.			−0.437741
$317$	802191.	+	1.38944e6i	0.448363	+	0.776587i	0.998280	−	0.0586323i	$-0.0186740\pi$
$317$	802191.	+	1.38944e6i	0.448363	+	0.776587i	−0.549917	+	0.835219i	$0.685341\pi$
$318$	317930.	−	550672.i	0.176305	−	0.305369i
$319$	−147419.	+	255338.i	−0.0811106	+	0.140488i
$320$	−211963.	−	367130.i	−0.115714	−	0.200422i
$321$	−876801.			−0.474940
$322$		0			0
$323$	356135.			0.189937
$324$	−52488.0	−	90911.9i	−0.0277778	−	0.0481125i
$325$	−3.05547e6	+	5.29223e6i	−1.60461	+	2.77927i
$326$	−873589.	+	1.51310e6i	−0.455264	+	0.788540i
$327$	−266882.	−	462254.i	−0.138023	−	0.239062i
$328$	1.16527e6			0.598058
$329$		0			0
$330$	−894929.			−0.452381
$331$	−501540.	−	868693.i	−0.251614	−	0.435809i	0.712356	−	0.701818i	$-0.247628\pi$
$331$	−501540.	−	868693.i	−0.251614	−	0.435809i	−0.963970	+	0.266009i	$0.914295\pi$
$332$	−905288.	+	1.56801e6i	−0.450756	+	0.780733i
$333$	367679.	−	636839.i	0.181701	−	0.314716i
$334$	77693.4	+	134569.i	0.0381082	+	0.0660053i
$335$	3.73412e6			1.81793
$336$		0			0
$337$	−2.62317e6			−1.25821			−0.629103	−	0.777322i	$-0.716578\pi$
$337$	−2.62317e6			−1.25821			−0.629103	+	0.777322i	$0.716578\pi$
$338$	555001.	+	961290.i	0.264242	+	0.457681i
$339$	−707705.	+	1.22578e6i	−0.334467	+	0.579313i
$340$	1.07080e6	−	1.85468e6i	0.502355	−	0.870104i
$341$	−675521.	−	1.17004e6i	−0.314596	−	0.544896i
$342$	89222.1			0.0412484
$343$		0			0
$344$	749326.			0.341409
$345$	−1.76821e6	−	3.06263e6i	−0.799809	−	1.38531i
$346$	792555.	−	1.37274e6i	0.355909	−	0.616452i
$347$	−113117.	+	195924.i	−0.0504317	+	0.0873503i	−0.890139	−	0.455689i	$-0.849393\pi$
$347$	−113117.	+	195924.i	−0.0504317	+	0.0873503i	0.839708	+	0.543039i	$0.182726\pi$
$348$	−88381.3	−	153081.i	−0.0391212	−	0.0677599i
$349$	−1.46280e6			−0.642866			−0.321433	−	0.946932i	$-0.604165\pi$
$349$	−1.46280e6			−0.642866			−0.321433	+	0.946932i	$0.604165\pi$
$350$		0			0
$351$	587193.			0.254398
$352$	122978.	+	213004.i	0.0529017	+	0.0916285i
$353$	−1.40479e6	+	2.43316e6i	−0.600031	+	1.03928i	0.392785	+	0.919630i	$0.371512\pi$
$353$	−1.40479e6	+	2.43316e6i	−0.600031	+	1.03928i	−0.992816	+	0.119653i	$0.961822\pi$
$354$	330773.	−	572916.i	0.140289	−	0.242987i
$355$	3.28264e6	+	5.68570e6i	1.38246	+	2.39449i
$356$	1.73385e6			0.725083
$357$		0			0
$358$	−975534.			−0.402286
$359$	1.84950e6	+	3.20343e6i	0.757388	+	1.31183i	0.944178	+	0.329435i	$0.106858\pi$
$359$	1.84950e6	+	3.20343e6i	0.757388	+	1.31183i	−0.186790	+	0.982400i	$0.559808\pi$
$360$	268265.	−	464649.i	0.109096	−	0.188960i
$361$	1.20013e6	−	2.07869e6i	0.484687	−	0.839503i
$362$	−598546.	−	1.03671e6i	−0.240063	−	0.415802i
$363$	−930234.			−0.370532
$364$		0			0
$365$	−5.48354e6			−2.15441
$366$	203834.	+	353050.i	0.0795377	+	0.137763i
$367$	−584623.	+	1.01260e6i	−0.226574	+	0.392438i	−0.956791	−	0.290778i	$-0.906086\pi$
$367$	−584623.	+	1.01260e6i	−0.226574	+	0.392438i	0.730216	+	0.683216i	$0.239419\pi$
$368$	−485961.	+	841710.i	−0.187061	+	0.323998i
$369$	737400.	+	1.27721e6i	0.281927	+	0.488313i
$370$	3.75840e6			1.42725
$371$		0			0
$372$	809980.			0.303471
$373$	2.28845e6	+	3.96371e6i	0.851666	+	1.47513i	0.879704	+	0.475523i	$0.157741\pi$
$373$	2.28845e6	+	3.96371e6i	0.851666	+	1.47513i	−0.0280372	+	0.999607i	$0.508926\pi$
$374$	−621262.	+	1.07606e6i	−0.229665	+	0.397792i
$375$	−2.07800e6	+	3.59920e6i	−0.763075	+	1.32168i
$376$	−737555.	−	1.27748e6i	−0.269045	−	0.466000i
$377$	988738.			0.358284
$378$		0			0
$379$	−2.35520e6			−0.842229			−0.421114	−	0.907007i	$-0.638361\pi$
$379$	−2.35520e6			−0.842229			−0.421114	+	0.907007i	$0.638361\pi$
$380$	228006.	+	394919.i	0.0810006	+	0.140297i
$381$	416148.	−	720789.i	0.146871	−	0.254387i
$382$	−1.55399e6	+	2.69159e6i	−0.544867	+	0.943738i
$383$	−1.51973e6	−	2.63225e6i	−0.529382	−	0.916916i	−0.999413	−	0.0342662i	$-0.989091\pi$
$383$	−1.51973e6	−	2.63225e6i	−0.529382	−	0.916916i	0.470031	−	0.882650i	$-0.344243\pi$
$384$	−147456.			−0.0510310
$385$		0			0
$386$	−1.10568e6			−0.377714
$387$	474183.	+	821309.i	0.160942	+	0.278759i
$388$	−797130.	+	1.38067e6i	−0.268813	+	0.465597i
$389$	229637.	−	397742.i	0.0769426	−	0.133269i	−0.824987	−	0.565152i	$-0.808818\pi$
$389$	229637.	−	397742.i	0.0769426	−	0.133269i	0.901929	+	0.431883i	$0.142151\pi$
$390$	1.50057e6	+	2.59906e6i	0.499567	+	0.865276i
$391$	−4.90998e6			−1.62419
$392$		0			0
$393$	−650956.			−0.212603
$394$	−263231.	−	455929.i	−0.0854272	−	0.147964i
$395$	2.51313e6	−	4.35286e6i	0.810441	−	1.40373i
$396$	−155644.	+	269583.i	−0.0498762	+	0.0863882i
$397$	−2.71250e6	−	4.69819e6i	−0.863761	−	1.49608i	−0.868272	−	0.496089i	$-0.834769\pi$
$397$	−2.71250e6	−	4.69819e6i	−0.863761	−	1.49608i	0.00451026	−	0.999990i	$-0.498564\pi$
$398$	−2.25984e6			−0.715106
$399$		0			0
$400$	1.94220e6			0.606938
$401$	−1.05564e6	−	1.82841e6i	−0.327833	−	0.567824i	0.654248	−	0.756280i	$-0.272985\pi$
$401$	−1.05564e6	−	1.82841e6i	−0.327833	−	0.567824i	−0.982082	+	0.188456i	$0.939652\pi$
$402$	649428.	−	1.12484e6i	0.200432	−	0.347158i
$403$	−2.26535e6	+	3.92370e6i	−0.694821	+	1.20346i
$404$	−1.32160e6	−	2.28908e6i	−0.402853	−	0.697761i
$405$	679047.			0.205713
$406$		0			0
$407$	−2.18057e6			−0.652506
$408$	−372461.	−	645121.i	−0.110772	−	0.191863i
$409$	−1.27872e6	+	2.21481e6i	−0.377980	+	0.654680i	−0.990768	−	0.135567i	$-0.956714\pi$
$409$	−1.27872e6	+	2.21481e6i	−0.377980	+	0.654680i	0.612788	+	0.790247i	$0.290048\pi$
$410$	−3.76884e6	+	6.52783e6i	−1.10726	+	1.91783i
$411$	−1.01548e6	−	1.75886e6i	−0.296528	−	0.513602i
$412$	−1.71595e6			−0.498038
$413$		0			0
$414$	−1.23009e6			−0.352725
$415$	−5.85594e6	−	1.01428e7i	−1.66908	−	2.89093i
$416$	412404.	−	714305.i	0.116840	−	0.202372i
$417$	1.47587e6	−	2.55628e6i	0.415631	−	0.719894i
$418$	−132286.	−	229126.i	−0.0370317	−	0.0641407i
$419$	2.17401e6			0.604959			0.302480	−	0.953156i	$-0.402186\pi$
$419$	2.17401e6			0.604959			0.302480	+	0.953156i	$0.402186\pi$
$420$		0			0
$421$	−5.47930e6			−1.50668			−0.753338	−	0.657633i	$-0.771558\pi$
$421$	−5.47930e6			−1.50668			−0.753338	+	0.657633i	$0.771558\pi$
$422$	627274.	+	1.08647e6i	0.171465	+	0.296987i
$423$	933468.	−	1.61681e6i	0.253658	−	0.439349i
$424$	565210.	−	978972.i	0.152684	−	0.264457i
$425$	4.90583e6	+	8.49714e6i	1.31747	+	2.28192i
$426$	2.28363e6			0.609680
$427$		0			0
$428$	−1.55876e6			−0.411310
$429$	−870607.	−	1.50794e6i	−0.228391	−	0.395585i
$430$	−2.42354e6	+	4.19770e6i	−0.632091	+	1.09481i
$431$	3.08437e6	−	5.34229e6i	0.799785	−	1.38527i	−0.119971	−	0.992777i	$-0.538280\pi$
$431$	3.08437e6	−	5.34229e6i	0.799785	−	1.38527i	0.919756	−	0.392491i	$-0.128387\pi$
$432$	−93312.0	−	161621.i	−0.0240563	−	0.0416667i
$433$	4.89596e6			1.25493			0.627463	−	0.778647i	$-0.284093\pi$
$433$	4.89596e6			1.25493			0.627463	+	0.778647i	$0.284093\pi$
$434$		0			0
$435$	1.14341e6			0.289719
$436$	−474458.	−	821785.i	−0.119531	−	0.207034i
$437$	522744.	−	905419.i	0.130944	−	0.226802i
$438$	−953683.	+	1.65183e6i	−0.237530	+	0.411414i
$439$	1.77294e6	+	3.07082e6i	0.439069	+	0.760489i	0.997618	−	0.0689822i	$-0.0219752\pi$
$439$	1.77294e6	+	3.07082e6i	0.439069	+	0.760489i	−0.558549	+	0.829471i	$0.688642\pi$
$440$	−1.59099e6			−0.391773
$441$		0			0
$442$	4.16679e6			1.01448
$443$	−3.02826e6	−	5.24510e6i	−0.733134	−	1.26983i	−0.955537	−	0.294871i	$-0.904723\pi$
$443$	−3.02826e6	−	5.24510e6i	−0.733134	−	1.26983i	0.222403	−	0.974955i	$-0.428610\pi$
$444$	653651.	−	1.13216e6i	0.157358	−	0.272552i
$445$	−5.60780e6	+	9.71299e6i	−1.34243	+	2.32516i
$446$	−558966.	−	968158.i	−0.133060	−	0.230467i
$447$	1.47610e6			0.349419
$448$		0			0
$449$	−1.20801e6			−0.282783			−0.141392	−	0.989954i	$-0.545158\pi$
$449$	−1.20801e6			−0.282783			−0.141392	+	0.989954i	$0.545158\pi$
$450$	1.22905e6	+	2.12878e6i	0.286113	+	0.495563i
$451$	2.18663e6	−	3.78735e6i	0.506213	−	0.876787i
$452$	−1.25814e6	+	2.17917e6i	−0.289657	+	0.501700i
$453$	−280390.	−	485649.i	−0.0641972	−	0.111193i
$454$	4.89403e6			1.11436
$455$		0			0
$456$	158617.			0.0357222
$457$	2.73275e6	+	4.73326e6i	0.612082	+	1.06016i	0.990889	+	0.134681i	$0.0430011\pi$
$457$	2.73275e6	+	4.73326e6i	0.612082	+	1.06016i	−0.378807	+	0.925476i	$0.623666\pi$
$458$	509549.	−	882565.i	0.113507	−	0.196600i
$459$	471396.	−	816481.i	0.104437	−	0.180890i
$460$	−3.14349e6	−	5.44468e6i	−0.692655	−	1.19971i
$461$	1.15956e6			0.254121			0.127061	−	0.991895i	$-0.459446\pi$
$461$	1.15956e6			0.254121			0.127061	+	0.991895i	$0.459446\pi$
$462$		0			0
$463$	−4.31335e6			−0.935108			−0.467554	−	0.883964i	$-0.654865\pi$
$463$	−4.31335e6			−0.935108			−0.467554	+	0.883964i	$0.654865\pi$
$464$	−157122.	−	272144.i	−0.0338800	−	0.0586818i
$465$	−2.61972e6	+	4.53748e6i	−0.561852	+	0.973156i
$466$	1.49235e6	−	2.58482e6i	0.318350	−	0.551398i
$467$	2.99462e6	+	5.18683e6i	0.635403	+	1.10055i	0.986430	+	0.164184i	$0.0524992\pi$
$467$	2.99462e6	+	5.18683e6i	0.635403	+	1.10055i	−0.351027	+	0.936365i	$0.614167\pi$
$468$	1.04390e6			0.220315
$469$		0			0
$470$	9.54189e6			1.99246
$471$	1.07913e6	+	1.86911e6i	0.224141	+	0.388224i
$472$	588042.	−	1.01852e6i	0.121494	−	0.210433i
$473$	1.40610e6	−	2.43544e6i	0.288978	−	0.500524i
$474$	−874152.	−	1.51408e6i	−0.178707	−	0.309529i
$475$	−2.08921e6			−0.424862
$476$		0			0
$477$	1.43069e6			0.287905
$478$	642073.	+	1.11210e6i	0.128533	+	0.222626i
$479$	−1.77326e6	+	3.07138e6i	−0.353129	+	0.611638i	−0.986796	−	0.161968i	$-0.948216\pi$
$479$	−1.77326e6	+	3.07138e6i	−0.353129	+	0.611638i	0.633667	+	0.773606i	$0.281549\pi$
$480$	476916.	−	826043.i	0.0944798	−	0.163644i
$481$	3.65626e6	+	6.33283e6i	0.720567	+	1.24806i
$482$	−4.97015e6			−0.974432
$483$		0			0
$484$	−1.65375e6			−0.320890
$485$	−5.15631e6	−	8.93099e6i	−0.995370	−	1.72403i
$486$	118098.	−	204552.i	0.0226805	−	0.0392837i
$487$	4.39160e6	−	7.60648e6i	0.839074	−	1.45332i	−0.0515950	−	0.998668i	$-0.516430\pi$
$487$	4.39160e6	−	7.60648e6i	0.839074	−	1.45332i	0.890669	−	0.454651i	$-0.150236\pi$
$488$	362371.	+	627645.i	0.0688817	+	0.119307i
$489$	−3.93115e6			−0.743443
$490$		0			0
$491$	−586608.			−0.109811			−0.0549053	−	0.998492i	$-0.517486\pi$
$491$	−586608.			−0.109811			−0.0549053	+	0.998492i	$0.517486\pi$
$492$	1.31093e6	+	2.27060e6i	0.244156	+	0.422891i
$493$	793754.	−	1.37482e6i	0.147085	−	0.254759i
$494$	−443619.	+	768371.i	−0.0817887	+	0.141662i
$495$	−1.00680e6	−	1.74382e6i	−0.184684	−	0.319881i
$496$	1.43997e6			0.262814
$497$		0			0
$498$	−4.07380e6			−0.736082
$499$	4.79886e6	+	8.31187e6i	0.862753	+	1.49433i	0.869261	+	0.494353i	$0.164595\pi$
$499$	4.79886e6	+	8.31187e6i	0.862753	+	1.49433i	−0.00650801	+	0.999979i	$0.502072\pi$
$500$	−3.69422e6	+	6.39858e6i	−0.660842	+	1.14461i
$501$	−174810.	+	302780.i	−0.0311152	+	0.0538931i
$502$	1.38047e6	+	2.39104e6i	0.244494	+	0.423475i
$503$	−7.21481e6			−1.27147			−0.635733	−	0.771909i	$-0.719302\pi$
$503$	−7.21481e6			−1.27147			−0.635733	+	0.771909i	$0.719302\pi$
$504$		0			0
$505$	1.70978e7			2.98340
$506$	1.82380e6	+	3.15892e6i	0.316666	+	0.548482i
$507$	−1.24875e6	+	2.16290e6i	−0.215753	+	0.373695i
$508$	739818.	−	1.28140e6i	0.127194	−	0.220306i
$509$	−2.19210e6	−	3.79682e6i	−0.375029	−	0.649569i	0.615302	−	0.788291i	$-0.289034\pi$
$509$	−2.19210e6	−	3.79682e6i	−0.375029	−	0.649569i	−0.990331	+	0.138722i	$0.955701\pi$
$510$	4.81859e6			0.820342
$511$		0			0
$512$	−262144.			−0.0441942
$513$	100375.	+	173854.i	0.0168396	+	0.0291670i
$514$	27573.4	−	47758.5i	0.00460344	−	0.00797339i
$515$	5.54991e6	−	9.61272e6i	0.922078	−	1.59709i
$516$	842992.	+	1.46010e6i	0.139380	+	0.241412i
$517$	−5.53606e6			−0.910909
$518$		0			0
$519$	3.56650e6			0.581197
$520$	2.66768e6	+	4.62055e6i	0.432638	+	0.749351i
$521$	−1.03291e6	+	1.78905e6i	−0.166712	+	0.288753i	−0.937262	−	0.348626i	$-0.886648\pi$
$521$	−1.03291e6	+	1.78905e6i	−0.166712	+	0.288753i	0.770550	+	0.637380i	$0.219982\pi$
$522$	198858.	−	344432.i	0.0319423	−	0.0553258i
$523$	−3.98285e6	−	6.89850e6i	−0.636707	−	1.10281i	−0.986151	−	0.165852i	$-0.946963\pi$
$523$	−3.98285e6	−	6.89850e6i	−0.636707	−	1.10281i	0.349444	−	0.936957i	$-0.386371\pi$
$524$	−1.15725e6			−0.184120
$525$		0			0
$526$	−2.29933e6			−0.362358
$527$	3.63722e6	+	6.29985e6i	0.570484	+	0.988107i
$528$	−276700.	+	479258.i	−0.0431941	+	0.0748143i
$529$	−3.98881e6	+	6.90882e6i	−0.619732	+	1.07341i
$530$	3.65611e6	+	6.33257e6i	0.565366	+	0.979242i
$531$	1.48848e6			0.229090
$532$		0			0
$533$	−1.46657e7			−2.23606
$534$	1.95059e6	+	3.37851e6i	0.296014	+	0.512711i
$535$	5.04148e6	−	8.73210e6i	0.761507	−	1.31897i
$536$	1.15454e6	−	1.99972e6i	0.173579	−	0.300647i
$537$	−1.09748e6	−	1.90088e6i	−0.164233	−	0.284459i
$538$	4.47571e6			0.666663
$539$		0			0
$540$	1.20719e6			0.178153
$541$	−4.11712e6	−	7.13105e6i	−0.604784	−	1.04752i	−0.992086	−	0.125563i	$-0.959926\pi$
$541$	−4.11712e6	−	7.13105e6i	−0.604784	−	1.04752i	0.387302	−	0.921953i	$-0.373407\pi$
$542$	1.38974e6	−	2.40710e6i	0.203205	−	0.351962i
$543$	1.34673e6	−	2.33260e6i	0.196011	−	0.339501i
$544$	−662152.	−	1.14688e6i	−0.0959314	−	0.166158i
$545$	6.13815e6			0.885209
$546$		0			0
$547$	5.20365e6			0.743601			0.371800	−	0.928313i	$-0.378741\pi$
$547$	5.20365e6			0.743601			0.371800	+	0.928313i	$0.378741\pi$
$548$	−1.80530e6	−	3.12686e6i	−0.256801	−	0.444793i
$549$	−458626.	+	794363.i	−0.0649423	+	0.112483i
$550$	3.64453e6	−	6.31250e6i	0.513729	−	0.889805i
$551$	169015.	+	292743.i	0.0237163	+	0.0410778i
$552$	−2.18683e6			−0.305469
$553$		0			0
$554$	3.35061e6			0.463821
$555$	4.22820e6	+	7.32346e6i	0.582671	+	1.00922i
$556$	2.62377e6	−	4.54450e6i	0.359947	−	0.623447i
$557$	2.04583e6	−	3.54347e6i	0.279403	−	0.483940i	−0.691834	−	0.722057i	$-0.743197\pi$
$557$	2.04583e6	−	3.54347e6i	0.279403	−	0.483940i	0.971236	+	0.238117i	$0.0765302\pi$
$558$	911228.	+	1.57829e6i	0.123892	+	0.214586i
$559$	−9.43070e6			−1.27648
$560$		0			0
$561$	−2.79568e6			−0.375042
$562$	−1.83537e6	−	3.17896e6i	−0.245123	−	0.424565i
$563$	1.79526e6	−	3.10948e6i	0.238702	−	0.413444i	−0.721640	−	0.692269i	$-0.756611\pi$
$563$	1.79526e6	−	3.10948e6i	0.238702	−	0.413444i	0.960342	+	0.278824i	$0.0899447\pi$
$564$	1.65950e6	−	2.87434e6i	0.219674	−	0.380487i
$565$	−8.13841e6	−	1.40961e7i	−1.07255	−	1.85771i
$566$	1.66105e6			0.217943
$567$		0			0
$568$	4.05979e6			0.527999
$569$	−4.89858e6	−	8.48459e6i	−0.634293	−	1.09863i	−0.986665	−	0.162767i	$-0.947958\pi$
$569$	−4.89858e6	−	8.48459e6i	−0.634293	−	1.09863i	0.352372	−	0.935860i	$-0.385375\pi$
$570$	−513014.	+	888567.i	−0.0661367	+	0.114552i
$571$	1.10902e6	−	1.92088e6i	0.142347	−	0.246552i	−0.786033	−	0.618185i	$-0.787868\pi$
$571$	1.10902e6	−	1.92088e6i	0.142347	−	0.246552i	0.928380	+	0.371632i	$0.121202\pi$
$572$	−1.54775e6	−	2.68078e6i	−0.197792	−	0.342587i
$573$	−6.99297e6			−0.889764
$574$		0			0
$575$	2.88036e7			3.63309
$576$	−165888.	−	287326.i	−0.0208333	−	0.0360844i
$577$	1.32767e6	−	2.29959e6i	0.166016	−	0.287548i	−0.771000	−	0.636836i	$-0.780243\pi$
$577$	1.32767e6	−	2.29959e6i	0.166016	−	0.287548i	0.937016	+	0.349288i	$0.113576\pi$
$578$	505361.	−	875310.i	0.0629190	−	0.108979i
$579$	−1.24390e6	−	2.15449e6i	−0.154201	−	0.267084i
$580$	2.03272e6			0.250904
$581$		0			0
$582$	−3.58708e6			−0.438969
$583$	−2.12122e6	−	3.67406e6i	−0.258473	−	0.447688i
$584$	−1.69544e6	+	2.93658e6i	−0.205707	+	0.356295i
$585$	−3.37628e6	+	5.84788e6i	−0.407895	+	0.706495i
$586$	−2.42982e6	−	4.20857e6i	−0.292301	−	0.506280i
$587$	−2.62690e6			−0.314665			−0.157332	−	0.987546i	$-0.550289\pi$
$587$	−2.62690e6			−0.314665			−0.157332	+	0.987546i	$0.550289\pi$
$588$		0			0
$589$	−1.54896e6			−0.183972
$590$	3.80380e6	+	6.58838e6i	0.449871	+	0.779199i
$591$	592269.	−	1.02584e6i	0.0697510	−	0.120812i
$592$	1.16205e6	−	2.01272e6i	0.136276	−	0.236037i
$593$	5.75310e6	+	9.96467e6i	0.671839	+	1.16366i	0.977382	+	0.211481i	$0.0678287\pi$
$593$	5.75310e6	+	9.96467e6i	0.671839	+	1.16366i	−0.305543	+	0.952178i	$0.598838\pi$
$594$	−700397.			−0.0814475
$595$		0			0
$596$	2.62417e6			0.302606
$597$	−2.54232e6	−	4.40343e6i	−0.291941	−	0.505656i
$598$	6.11611e6	−	1.05934e7i	0.699394	−	1.21139i
$599$	−3.23132e6	+	5.59681e6i	−0.367970	+	0.637343i	−0.989248	−	0.146247i	$-0.953281\pi$
$599$	−3.23132e6	+	5.59681e6i	−0.367970	+	0.637343i	0.621278	+	0.783590i	$0.286614\pi$
$600$	2.18498e6	+	3.78449e6i	0.247781	+	0.429170i
$601$	8.55332e6			0.965937			0.482968	−	0.875638i	$-0.339559\pi$
$601$	8.55332e6			0.965937			0.482968	+	0.875638i	$0.339559\pi$
$602$		0			0
$603$	2.92243e6			0.327303
$604$	−498470.	−	863376.i	−0.0555964	−	0.0962958i
$605$	5.34871e6	−	9.26425e6i	0.594102	−	1.02901i
$606$	2.97360e6	−	5.15042e6i	0.328928	−	0.569720i
$607$	−1.49521e6	−	2.58978e6i	−0.164714	−	0.285293i	0.771840	−	0.635817i	$-0.219337\pi$
$607$	−1.49521e6	−	2.58978e6i	−0.164714	−	0.285293i	−0.936554	+	0.350524i	$0.886003\pi$
$608$	281986.			0.0309363
$609$		0			0
$610$	−4.68806e6			−0.510115
$611$	9.28256e6	+	1.60779e7i	1.00592	+	1.74231i
$612$	838036.	−	1.45152e6i	0.0904450	−	0.156655i
$613$	885724.	−	1.53412e6i	0.0952023	−	0.164895i	−0.814491	−	0.580177i	$-0.802984\pi$
$613$	885724.	−	1.53412e6i	0.0952023	−	0.164895i	0.909693	+	0.415281i	$0.136317\pi$
$614$	−5.20239e6	−	9.01080e6i	−0.556906	−	0.964589i
$615$	−1.69598e7			−1.80814
$616$		0			0
$617$	1.40871e7			1.48974			0.744869	−	0.667210i	$-0.232512\pi$
$617$	1.40871e7			1.48974			0.744869	+	0.667210i	$0.232512\pi$
$618$	−1.93045e6	−	3.34364e6i	−0.203323	−	0.352166i
$619$	5.67152e6	−	9.82336e6i	0.594940	−	1.03047i	−0.398616	−	0.917118i	$-0.630509\pi$
$619$	5.67152e6	−	9.82336e6i	0.594940	−	1.03047i	0.993555	−	0.113348i	$-0.0361574\pi$
$620$	−4.65727e6	+	8.06663e6i	−0.486578	+	0.842778i
$621$	−1.38385e6	−	2.39690e6i	−0.143999	−	0.249414i
$622$	3.27666e6			0.339590
$623$		0			0
$624$	1.85582e6			0.190798
$625$	−1.20421e7	−	2.08576e7i	−1.23312	−	2.13582i
$626$	−1.76388e6	+	3.05513e6i	−0.179901	+	0.311597i
$627$	297643.	−	515534.i	0.0302362	−	0.0523707i
$628$	1.91845e6	+	3.32286e6i	0.194112	+	0.336211i
$629$	1.17409e7			1.18325
$630$		0			0
$631$	−2.32628e6			−0.232588			−0.116294	−	0.993215i	$-0.537102\pi$
$631$	−2.32628e6			−0.232588			−0.116294	+	0.993215i	$0.537102\pi$
$632$	−1.55405e6	−	2.69169e6i	−0.154765	−	0.268060i
$633$	−1.41137e6	+	2.44456e6i	−0.140001	+	0.242489i
$634$	−3.20876e6	+	5.55774e6i	−0.317040	+	0.549130i
$635$	4.78558e6	+	8.28887e6i	0.470978	+	0.815758i
$636$	2.54344e6			0.249333
$637$		0			0
$638$	−1.17935e6			−0.114708
$639$	2.56909e6	+	4.44979e6i	0.248901	+	0.431109i
$640$	847851.	−	1.46852e6i	0.0818219	−	0.141720i
$641$	1.28193e6	−	2.22036e6i	0.123230	−	0.213441i	−0.797809	−	0.602910i	$-0.794008\pi$
$641$	1.28193e6	−	2.22036e6i	0.123230	−	0.213441i	0.921040	+	0.389468i	$0.127341\pi$
$642$	−1.75360e6	−	3.03733e6i	−0.167917	−	0.290840i
$643$	−5.95343e6			−0.567858			−0.283929	−	0.958845i	$-0.591638\pi$
$643$	−5.95343e6			−0.567858			−0.283929	+	0.958845i	$0.591638\pi$
$644$		0			0
$645$	−1.09059e7			−1.03220
$646$	712271.	+	1.23369e6i	0.0671528	+	0.116312i
$647$	767611.	−	1.32954e6i	0.0720909	−	0.124865i	−0.827727	−	0.561132i	$-0.810366\pi$
$647$	767611.	−	1.32954e6i	0.0720909	−	0.124865i	0.899818	+	0.436266i	$0.143699\pi$
$648$	209952.	−	363648.i	0.0196419	−	0.0340207i
$649$	−2.20691e6	−	3.82248e6i	−0.205671	−	0.356233i
$650$	−2.44437e7			−2.26926
$651$		0			0
$652$	−6.98871e6			−0.643841
$653$	9.97909e6	+	1.72843e7i	0.915815	+	1.58624i	0.805703	+	0.592319i	$0.201788\pi$
$653$	9.97909e6	+	1.72843e7i	0.915815	+	1.58624i	0.110112	+	0.993919i	$0.464879\pi$
$654$	1.06753e6	−	1.84902e6i	0.0975968	−	0.169043i
$655$	3.74290e6	−	6.48290e6i	0.340883	−	0.590427i
$656$	2.33055e6	+	4.03663e6i	0.211446	+	0.366235i
$657$	−4.29157e6			−0.387885
$658$		0			0
$659$	−1.05477e7			−0.946119			−0.473060	−	0.881030i	$-0.656850\pi$
$659$	−1.05477e7			−0.946119			−0.473060	+	0.881030i	$0.656850\pi$
$660$	−1.78986e6	−	3.10013e6i	−0.159941	−	0.277025i
$661$	6.10220e6	−	1.05693e7i	0.543229	−	0.940900i	−0.455487	−	0.890242i	$-0.650535\pi$
$661$	6.10220e6	−	1.05693e7i	0.543229	−	0.940900i	0.998716	−	0.0506576i	$-0.0161317\pi$
$662$	2.00616e6	−	3.47477e6i	0.177918	−	0.308164i
$663$	4.68763e6	+	8.11922e6i	0.414162	+	0.717349i
$664$	−7.24231e6			−0.637466
$665$		0			0
$666$	2.94143e6			0.256964
$667$	−2.33018e6	−	4.03599e6i	−0.202803	−	0.351266i
$668$	−310774.	+	538276.i	−0.0269466	+	0.0466728i
$669$	1.25767e6	−	2.17836e6i	0.108643	−	0.188176i
$670$	7.46824e6	+	1.29354e7i	0.642734	+	1.11325i
$671$	2.71994e6			0.233213
$672$		0			0
$673$	−7.97959e6			−0.679114			−0.339557	−	0.940585i	$-0.610277\pi$
$673$	−7.97959e6			−0.679114			−0.339557	+	0.940585i	$0.610277\pi$
$674$	−5.24634e6	−	9.08693e6i	−0.444843	−	0.770491i
$675$	−2.76536e6	+	4.78975e6i	−0.233611	+	0.404625i
$676$	−2.22001e6	+	3.84516e6i	−0.186847	+	0.323629i
$677$	−2.54190e6	−	4.40271e6i	−0.213151	−	0.369188i	0.739548	−	0.673104i	$-0.235039\pi$
$677$	−2.54190e6	−	4.40271e6i	−0.213151	−	0.369188i	−0.952699	+	0.303915i	$0.901706\pi$
$678$	−5.66164e6			−0.473007
$679$		0			0
$680$	8.56639e6			0.710437
$681$	5.50578e6	+	9.53629e6i	0.454937	+	0.787974i
$682$	2.70208e6	−	4.68014e6i	0.222453	−	0.385299i
$683$	8.01654e6	−	1.38850e7i	0.657559	−	1.13893i	−0.323686	−	0.946165i	$-0.604922\pi$
$683$	8.01654e6	−	1.38850e7i	0.657559	−	1.13893i	0.981246	−	0.192762i	$-0.0617445\pi$
$684$	178444.	+	309074.i	0.0145835	+	0.0252594i
$685$	2.33554e7			1.90179
$686$		0			0
$687$	2.29297e6			0.185356
$688$	1.49865e6	+	2.59574e6i	0.120706	+	0.209069i
$689$	−7.11349e6	+	1.23209e7i	−0.570867	+	0.988770i
$690$	7.07284e6	−	1.22505e7i	0.565550	−	0.979562i
$691$	5.50657e6	+	9.53766e6i	0.438719	+	0.759883i	0.997591	−	0.0693705i	$-0.0220991\pi$
$691$	5.50657e6	+	9.53766e6i	0.438719	+	0.759883i	−0.558872	+	0.829254i	$0.688766\pi$
$692$	6.34044e6			0.503331
$693$		0			0
$694$	−904935.			−0.0713212
$695$	1.69721e7	+	2.93965e7i	1.33283	+	2.30852i
$696$	353525.	−	612324.i	0.0276629	−	0.0479135i
$697$	−1.17735e7	+	2.03923e7i	−0.917961	+	1.58996i
$698$	−2.92560e6	−	5.06728e6i	−0.227288	−	0.393674i
$699$	6.71555e6			0.519863
$700$		0			0
$701$	−3.10660e6			−0.238776			−0.119388	−	0.992848i	$-0.538093\pi$
$701$	−3.10660e6			−0.238776			−0.119388	+	0.992848i	$0.538093\pi$
$702$	1.17439e6	+	2.03410e6i	0.0899431	+	0.155786i
$703$	−1.25000e6	+	2.16507e6i	−0.0953943	+	0.165228i
$704$	−491911.	+	852015.i	−0.0374072	+	0.0647911i
$705$	1.07346e7	+	1.85929e7i	0.813418	+	1.40888i
$706$	−1.12383e7			−0.848571
$707$		0			0
$708$	2.64619e6			0.198398
$709$	6.90180e6	+	1.19543e7i	0.515640	+	0.893115i	0.999835	+	0.0181549i	$0.00577922\pi$
$709$	6.90180e6	+	1.19543e7i	0.515640	+	0.893115i	−0.484195	+	0.874960i	$0.660887\pi$
$710$	−1.31306e7	+	2.27428e7i	−0.977547	+	1.69316i
$711$	1.96684e6	−	3.40667e6i	0.145914	−	0.252730i
$712$	3.46771e6	+	6.00625e6i	0.256355	+	0.444021i
$713$	2.13552e7			1.57319
$714$		0			0
$715$	2.00235e7			1.46479
$716$	−1.95107e6	−	3.37935e6i	−0.142230	−	0.246349i
$717$	−1.44466e6	+	2.50223e6i	−0.104947	+	0.181773i
$718$	−7.39800e6	+	1.28137e7i	−0.535554	+	0.927607i
$719$	6.49275e6	+	1.12458e7i	0.468389	+	0.811273i	0.999347	−	0.0361248i	$-0.0115014\pi$
$719$	6.49275e6	+	1.12458e7i	0.468389	+	0.811273i	−0.530959	+	0.847398i	$0.678168\pi$
$720$	2.14612e6			0.154285
$721$		0			0
$722$	9.60107e6			0.685451
$723$	−5.59141e6	−	9.68461e6i	−0.397810	−	0.689027i
$724$	2.39418e6	−	4.14685e6i	0.169751	−	0.294017i
$725$	−4.65642e6	+	8.06516e6i	−0.329009	+	0.569860i
$726$	−1.86047e6	−	3.22242e6i	−0.131003	−	0.226904i
$727$	−8.61224e6			−0.604338			−0.302169	−	0.953254i	$-0.597711\pi$
$727$	−8.61224e6			−0.604338			−0.302169	+	0.953254i	$0.597711\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−1.09671e7	−	1.89956e7i	−0.761700	−	1.31930i
$731$	−7.57092e6	+	1.31132e7i	−0.524029	+	0.907645i
$732$	−815334.	+	1.41220e6i	−0.0562416	+	0.0974134i
$733$	−3.01000e6	−	5.21348e6i	−0.206922	−	0.358400i	0.743821	−	0.668379i	$-0.233011\pi$
$733$	−3.01000e6	−	5.21348e6i	−0.206922	−	0.358400i	−0.950743	+	0.309979i	$0.899678\pi$
$734$	−4.67698e6			−0.320424
$735$		0			0
$736$	−3.88769e6			−0.264544
$737$	−4.33297e6	−	7.50492e6i	−0.293844	−	0.508952i
$738$	−2.94960e6	+	5.10886e6i	−0.199353	+	0.345289i
$739$	46846.3	−	81140.1i	0.00315547	−	0.00546543i	−0.864443	−	0.502730i	$-0.832329\pi$
$739$	46846.3	−	81140.1i	0.00315547	−	0.00546543i	0.867599	+	0.497265i	$0.165662\pi$
$740$	7.51681e6	+	1.30195e7i	0.504608	+	0.874007i
$741$	−1.99629e6			−0.133560
$742$		0			0
$743$	−1.29874e7			−0.863081			−0.431541	−	0.902094i	$-0.642030\pi$
$743$	−1.29874e7			−0.863081			−0.431541	+	0.902094i	$0.642030\pi$
$744$	1.61996e6	+	2.80585e6i	0.107293	+	0.185837i
$745$	−8.48735e6	+	1.47005e7i	−0.560250	+	0.970381i
$746$	−9.15380e6	+	1.58549e7i	−0.602219	+	1.04307i
$747$	−4.58302e6	−	7.93803e6i	−0.300504	−	0.520489i
$748$	−4.97009e6			−0.324796
$749$		0			0
$750$	−1.66240e7			−1.07915
$751$	318720.	+	552040.i	0.0206210	+	0.0357166i	0.876152	−	0.482035i	$-0.160102\pi$
$751$	318720.	+	552040.i	0.0206210	+	0.0357166i	−0.855531	+	0.517752i	$0.826769\pi$
$752$	2.95022e6	−	5.10993e6i	0.190244	−	0.329511i
$753$	−3.10606e6	+	5.37985e6i	−0.199628	+	0.345766i
$754$	1.97748e6	+	3.42509e6i	0.126673	+	0.219403i
$755$	6.44880e6			0.411729
$756$		0			0
$757$	−4.86768e6			−0.308732			−0.154366	−	0.988014i	$-0.549334\pi$
$757$	−4.86768e6			−0.308732			−0.154366	+	0.988014i	$0.549334\pi$
$758$	−4.71040e6	−	8.15866e6i	−0.297773	−	0.515758i
$759$	−4.10356e6	+	7.10757e6i	−0.258557	+	0.447834i
$760$	−912026.	+	1.57967e6i	−0.0572760	+	0.0992050i
$761$	−2.90894e6	−	5.03842e6i	−0.182084	−	0.315379i	0.760506	−	0.649331i	$-0.224951\pi$
$761$	−2.90894e6	−	5.03842e6i	−0.182084	−	0.315379i	−0.942590	+	0.333952i	$0.891618\pi$
$762$	3.32918e6			0.207706
$763$		0			0
$764$	−1.24319e7			−0.770558
$765$	5.42092e6	+	9.38930e6i	0.334903	+	0.580069i
$766$	6.07891e6	−	1.05290e7i	0.374329	−	0.648358i
$767$	−7.40085e6	+	1.28186e7i	−0.454248	+	0.786781i
$768$	−294912.	−	510803.i	−0.0180422	−	0.0312500i

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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-51.7487 - 89.6314i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-51.7487 - 89.6314i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(206.995 - 358.526i) q^{10} +(-120.095 + 208.011i) q^{11} +(-72.0000 - 124.708i) q^{12} +805.477 q^{13} +931.477 q^{15} +(-128.000 - 221.703i) q^{16} +(646.633 - 1120.00i) q^{17} +(162.000 - 280.592i) q^{18} +(137.688 + 238.483i) q^{19} +1655.96 q^{20} -960.764 q^{22} +(-1898.29 - 3287.93i) q^{23} +(288.000 - 498.831i) q^{24} +(-3793.36 + 6570.30i) q^{25} +(1610.95 + 2790.26i) q^{26} +729.000 q^{27} +1227.52 q^{29} +(1862.95 + 3226.73i) q^{30} +(-2812.43 + 4871.27i) q^{31} +(512.000 - 886.810i) q^{32} +(-1080.86 - 1872.10i) q^{33} +5173.06 q^{34} +1296.00 q^{36} +(4539.25 + 7862.20i) q^{37} +(-550.754 + 953.933i) q^{38} +(-3624.65 + 6278.07i) q^{39} +(3311.92 + 5736.41i) q^{40} -18207.4 q^{41} -11708.2 q^{43} +(-1921.53 - 3328.18i) q^{44} +(-4191.65 + 7260.15i) q^{45} +(7593.15 - 13151.7i) q^{46} +(11524.3 + 19960.7i) q^{47} +2304.00 q^{48} -30346.9 q^{50} +(5819.70 + 10080.0i) q^{51} +(-6443.82 + 11161.0i) q^{52} +(-8831.40 + 15296.4i) q^{53} +(1458.00 + 2525.33i) q^{54} +24859.2 q^{55} -2478.39 q^{57} +(2455.04 + 4252.25i) q^{58} +(-9188.15 + 15914.3i) q^{59} +(-7451.82 + 12906.9i) q^{60} +(-5662.04 - 9806.95i) q^{61} -22499.5 q^{62} +4096.00 q^{64} +(-41682.4 - 72196.1i) q^{65} +(4323.44 - 7488.41i) q^{66} +(-18039.7 + 31245.6i) q^{67} +(10346.1 + 17920.0i) q^{68} +34169.2 q^{69} -63434.2 q^{71} +(2592.00 + 4489.48i) q^{72} +(26491.2 - 45884.1i) q^{73} +(-18157.0 + 31448.8i) q^{74} +(-34140.3 - 59132.7i) q^{75} -4406.03 q^{76} -28997.2 q^{78} +(24282.0 + 42057.7i) q^{79} +(-13247.7 + 22945.6i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-36414.8 - 63072.3i) q^{82} +113161. q^{83} -133850. q^{85} +(-23416.4 - 40558.5i) q^{86} +(-5523.83 + 9567.56i) q^{87} +(7686.11 - 13312.7i) q^{88} +(-54182.9 - 93847.6i) q^{89} -33533.2 q^{90} +60745.2 q^{92} +(-25311.9 - 43841.5i) q^{93} +(-46097.2 + 79842.7i) q^{94} +(14250.4 - 24682.4i) q^{95} +(4608.00 + 7981.29i) q^{96} +99641.2 q^{97} +19455.5 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	\( 4 q + 8 q^{2} - 18 q^{3} - 32 q^{4} - 108 q^{5} - 144 q^{6} - 256 q^{8} - 162 q^{9} + 432 q^{10} - 124 q^{11} - 288 q^{12} + 1440 q^{13} + 1944 q^{15} - 512 q^{16} + 1260 q^{17} + 648 q^{18} - 360 q^{19} + 3456 q^{20} - 992 q^{22} - 6524 q^{23} + 1152 q^{24} - 4482 q^{25} + 2880 q^{26} + 2916 q^{27} + 14176 q^{29} + 3888 q^{30} - 5904 q^{31} + 2048 q^{32} - 1116 q^{33} + 10080 q^{34} + 5184 q^{36} + 6040 q^{37} + 1440 q^{38} - 6480 q^{39} + 6912 q^{40} - 34776 q^{41} - 1216 q^{43} - 1984 q^{44} - 8748 q^{45} + 26096 q^{46} + 30456 q^{47} + 9216 q^{48} - 35856 q^{50} + 11340 q^{51} - 11520 q^{52} - 3964 q^{53} + 5832 q^{54} + 48672 q^{55} + 6480 q^{57} + 28352 q^{58} - 40752 q^{59} - 15552 q^{60} + 1368 q^{61} - 47232 q^{62} + 16384 q^{64} - 82980 q^{65} + 4464 q^{66} + 16224 q^{67} + 20160 q^{68} + 117432 q^{69} - 6408 q^{71} + 10368 q^{72} - 23976 q^{73} - 24160 q^{74} - 40338 q^{75} + 11520 q^{76} - 51840 q^{78} + 82160 q^{79} - 27648 q^{80} - 13122 q^{81} - 69552 q^{82} + 347472 q^{83} - 267400 q^{85} - 2432 q^{86} - 63792 q^{87} + 7936 q^{88} - 200556 q^{89} - 69984 q^{90} + 208768 q^{92} - 53136 q^{93} - 121824 q^{94} + 25640 q^{95} + 18432 q^{96} + 503856 q^{97} + 20088 q^{99}+O(q^{100}) \) 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 + 1260 * q^17 + 648 * q^18 - 360 * q^19 + 3456 * q^20 - 992 * q^22 - 6524 * q^23 + 1152 * q^24 - 4482 * q^25 + 2880 * q^26 + 2916 * q^27 + 14176 * q^29 + 3888 * q^30 - 5904 * q^31 + 2048 * q^32 - 1116 * q^33 + 10080 * q^34 + 5184 * q^36 + 6040 * q^37 + 1440 * q^38 - 6480 * q^39 + 6912 * q^40 - 34776 * q^41 - 1216 * q^43 - 1984 * q^44 - 8748 * q^45 + 26096 * q^46 + 30456 * q^47 + 9216 * q^48 - 35856 * q^50 + 11340 * q^51 - 11520 * q^52 - 3964 * q^53 + 5832 * q^54 + 48672 * q^55 + 6480 * q^57 + 28352 * q^58 - 40752 * q^59 - 15552 * q^60 + 1368 * q^61 - 47232 * q^62 + 16384 * q^64 - 82980 * q^65 + 4464 * q^66 + 16224 * q^67 + 20160 * q^68 + 117432 * q^69 - 6408 * q^71 + 10368 * q^72 - 23976 * q^73 - 24160 * q^74 - 40338 * q^75 + 11520 * q^76 - 51840 * q^78 + 82160 * q^79 - 27648 * q^80 - 13122 * q^81 - 69552 * q^82 + 347472 * q^83 - 267400 * q^85 - 2432 * q^86 - 63792 * q^87 + 7936 * q^88 - 200556 * q^89 - 69984 * q^90 + 208768 * q^92 - 53136 * q^93 - 121824 * q^94 + 25640 * q^95 + 18432 * q^96 + 503856 * q^97 + 20088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more