LMFDB - Embedded newform 490.4.e.i.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.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:	$28.9109359028$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.4.e.i.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -16.0000 q^{6} +8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -16.0000 q^{6} +8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(-5.00000 - 8.66025i) q^{10} +(-6.00000 - 10.3923i) q^{11} +(16.0000 - 27.7128i) q^{12} -58.0000 q^{13} -40.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-33.0000 - 57.1577i) q^{17} +(-37.0000 - 64.0859i) q^{18} +(50.0000 - 86.6025i) q^{19} +20.0000 q^{20} +24.0000 q^{22} +(-66.0000 + 114.315i) q^{23} +(32.0000 + 55.4256i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(58.0000 - 100.459i) q^{26} -80.0000 q^{27} -90.0000 q^{29} +(40.0000 - 69.2820i) q^{30} +(-76.0000 - 131.636i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(48.0000 - 83.1384i) q^{33} +132.000 q^{34} +148.000 q^{36} +(17.0000 - 29.4449i) q^{37} +(100.000 + 173.205i) q^{38} +(-232.000 - 401.836i) q^{39} +(-20.0000 + 34.6410i) q^{40} -438.000 q^{41} +32.0000 q^{43} +(-24.0000 + 41.5692i) q^{44} +(-92.5000 - 160.215i) q^{45} +(-132.000 - 228.631i) q^{46} +(102.000 - 176.669i) q^{47} -128.000 q^{48} +50.0000 q^{50} +(264.000 - 457.261i) q^{51} +(116.000 + 200.918i) q^{52} +(-111.000 - 192.258i) q^{53} +(80.0000 - 138.564i) q^{54} +60.0000 q^{55} +800.000 q^{57} +(90.0000 - 155.885i) q^{58} +(-210.000 - 363.731i) q^{59} +(80.0000 + 138.564i) q^{60} +(-451.000 + 781.155i) q^{61} +304.000 q^{62} +64.0000 q^{64} +(145.000 - 251.147i) q^{65} +(96.0000 + 166.277i) q^{66} +(512.000 + 886.810i) q^{67} +(-132.000 + 228.631i) q^{68} -1056.00 q^{69} +432.000 q^{71} +(-148.000 + 256.344i) q^{72} +(-181.000 - 313.501i) q^{73} +(34.0000 + 58.8897i) q^{74} +(100.000 - 173.205i) q^{75} -400.000 q^{76} +928.000 q^{78} +(80.0000 - 138.564i) q^{79} +(-40.0000 - 69.2820i) q^{80} +(179.500 + 310.903i) q^{81} +(438.000 - 758.638i) q^{82} +72.0000 q^{83} +330.000 q^{85} +(-32.0000 + 55.4256i) q^{86} +(-360.000 - 623.538i) q^{87} +(-48.0000 - 83.1384i) q^{88} +(-405.000 + 701.481i) q^{89} +370.000 q^{90} +528.000 q^{92} +(608.000 - 1053.09i) q^{93} +(204.000 + 353.338i) q^{94} +(250.000 + 433.013i) q^{95} +(128.000 - 221.703i) q^{96} +1106.00 q^{97} +444.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 8 q^{3} - 4 q^{4} - 5 q^{5} - 32 q^{6} + 16 q^{8} - 37 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 8 * q^3 - 4 * q^4 - 5 * q^5 - 32 * q^6 + 16 * q^8 - 37 * q^9	\( 2 q - 2 q^{2} + 8 q^{3} - 4 q^{4} - 5 q^{5} - 32 q^{6} + 16 q^{8} - 37 q^{9} - 10 q^{10} - 12 q^{11} + 32 q^{12} - 116 q^{13} - 80 q^{15} - 16 q^{16} - 66 q^{17} - 74 q^{18} + 100 q^{19} + 40 q^{20} + 48 q^{22} - 132 q^{23} + 64 q^{24} - 25 q^{25} + 116 q^{26} - 160 q^{27} - 180 q^{29} + 80 q^{30} - 152 q^{31} - 32 q^{32} + 96 q^{33} + 264 q^{34} + 296 q^{36} + 34 q^{37} + 200 q^{38} - 464 q^{39} - 40 q^{40} - 876 q^{41} + 64 q^{43} - 48 q^{44} - 185 q^{45} - 264 q^{46} + 204 q^{47} - 256 q^{48} + 100 q^{50} + 528 q^{51} + 232 q^{52} - 222 q^{53} + 160 q^{54} + 120 q^{55} + 1600 q^{57} + 180 q^{58} - 420 q^{59} + 160 q^{60} - 902 q^{61} + 608 q^{62} + 128 q^{64} + 290 q^{65} + 192 q^{66} + 1024 q^{67} - 264 q^{68} - 2112 q^{69} + 864 q^{71} - 296 q^{72} - 362 q^{73} + 68 q^{74} + 200 q^{75} - 800 q^{76} + 1856 q^{78} + 160 q^{79} - 80 q^{80} + 359 q^{81} + 876 q^{82} + 144 q^{83} + 660 q^{85} - 64 q^{86} - 720 q^{87} - 96 q^{88} - 810 q^{89} + 740 q^{90} + 1056 q^{92} + 1216 q^{93} + 408 q^{94} + 500 q^{95} + 256 q^{96} + 2212 q^{97} + 888 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 8 * q^3 - 4 * q^4 - 5 * q^5 - 32 * q^6 + 16 * q^8 - 37 * q^9 - 10 * q^10 - 12 * q^11 + 32 * q^12 - 116 * q^13 - 80 * q^15 - 16 * q^16 - 66 * q^17 - 74 * q^18 + 100 * q^19 + 40 * q^20 + 48 * q^22 - 132 * q^23 + 64 * q^24 - 25 * q^25 + 116 * q^26 - 160 * q^27 - 180 * q^29 + 80 * q^30 - 152 * q^31 - 32 * q^32 + 96 * q^33 + 264 * q^34 + 296 * q^36 + 34 * q^37 + 200 * q^38 - 464 * q^39 - 40 * q^40 - 876 * q^41 + 64 * q^43 - 48 * q^44 - 185 * q^45 - 264 * q^46 + 204 * q^47 - 256 * q^48 + 100 * q^50 + 528 * q^51 + 232 * q^52 - 222 * q^53 + 160 * q^54 + 120 * q^55 + 1600 * q^57 + 180 * q^58 - 420 * q^59 + 160 * q^60 - 902 * q^61 + 608 * q^62 + 128 * q^64 + 290 * q^65 + 192 * q^66 + 1024 * q^67 - 264 * q^68 - 2112 * q^69 + 864 * q^71 - 296 * q^72 - 362 * q^73 + 68 * q^74 + 200 * q^75 - 800 * q^76 + 1856 * q^78 + 160 * q^79 - 80 * q^80 + 359 * q^81 + 876 * q^82 + 144 * q^83 + 660 * q^85 - 64 * q^86 - 720 * q^87 - 96 * q^88 - 810 * q^89 + 740 * q^90 + 1056 * q^92 + 1216 * q^93 + 408 * q^94 + 500 * q^95 + 256 * q^96 + 2212 * q^97 + 888 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	4.00000	+	6.92820i	0.769800	+	1.33333i	0.937671	+	0.347524i	$0.112978\pi$
$3$	4.00000	+	6.92820i	0.769800	+	1.33333i	−0.167871	+	0.985809i	$0.553689\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	−16.0000			−1.08866
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−18.5000	+	32.0429i	−0.685185	+	1.18678i
$10$	−5.00000	−	8.66025i	−0.158114	−	0.273861i
$11$	−6.00000	−	10.3923i	−0.164461	−	0.284854i	0.772003	−	0.635619i	$-0.219255\pi$
$11$	−6.00000	−	10.3923i	−0.164461	−	0.284854i	−0.936464	+	0.350765i	$0.885922\pi$
$12$	16.0000	−	27.7128i	0.384900	−	0.666667i
$13$	−58.0000			−1.23741			−0.618704	−	0.785624i	$-0.712342\pi$
$13$	−58.0000			−1.23741			−0.618704	+	0.785624i	$0.712342\pi$
$14$		0			0
$15$	−40.0000			−0.688530
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−33.0000	−	57.1577i	−0.470804	−	0.815457i	0.528638	−	0.848847i	$-0.322703\pi$
$17$	−33.0000	−	57.1577i	−0.470804	−	0.815457i	−0.999442	+	0.0333902i	$0.989370\pi$
$18$	−37.0000	−	64.0859i	−0.484499	−	0.839177i
$19$	50.0000	−	86.6025i	0.603726	−	1.04568i	−0.388526	−	0.921438i	$-0.627016\pi$
$19$	50.0000	−	86.6025i	0.603726	−	1.04568i	0.992251	−	0.124246i	$-0.0396511\pi$
$20$	20.0000			0.223607
$21$		0			0
$22$	24.0000			0.232583
$23$	−66.0000	+	114.315i	−0.598346	+	1.03637i	0.394720	+	0.918802i	$0.370842\pi$
$23$	−66.0000	+	114.315i	−0.598346	+	1.03637i	−0.993065	+	0.117564i	$0.962492\pi$
$24$	32.0000	+	55.4256i	0.272166	+	0.471405i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	58.0000	−	100.459i	0.437490	−	0.757755i
$27$	−80.0000			−0.570222
$28$		0			0
$29$	−90.0000			−0.576296			−0.288148	−	0.957586i	$-0.593039\pi$
$29$	−90.0000			−0.576296			−0.288148	+	0.957586i	$0.593039\pi$
$30$	40.0000	−	69.2820i	0.243432	−	0.421637i
$31$	−76.0000	−	131.636i	−0.440323	−	0.762661i	0.557391	−	0.830250i	$-0.311803\pi$
$31$	−76.0000	−	131.636i	−0.440323	−	0.762661i	−0.997713	+	0.0675892i	$0.978469\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	48.0000	−	83.1384i	0.253204	−	0.438562i
$34$	132.000			0.665818
$35$		0			0
$36$	148.000			0.685185
$37$	17.0000	−	29.4449i	0.0755347	−	0.130830i	−0.825784	−	0.563987i	$-0.809267\pi$
$37$	17.0000	−	29.4449i	0.0755347	−	0.130830i	0.901319	+	0.433157i	$0.142600\pi$
$38$	100.000	+	173.205i	0.426898	+	0.739410i
$39$	−232.000	−	401.836i	−0.952557	−	1.64988i
$40$	−20.0000	+	34.6410i	−0.0790569	+	0.136931i
$41$	−438.000			−1.66839			−0.834196	−	0.551467i	$-0.814068\pi$
$41$	−438.000			−1.66839			−0.834196	+	0.551467i	$0.814068\pi$
$42$		0			0
$43$	32.0000			0.113487			0.0567437	−	0.998389i	$-0.481928\pi$
$43$	32.0000			0.113487			0.0567437	+	0.998389i	$0.481928\pi$
$44$	−24.0000	+	41.5692i	−0.0822304	+	0.142427i
$45$	−92.5000	−	160.215i	−0.306424	−	0.530742i
$46$	−132.000	−	228.631i	−0.423094	−	0.732821i
$47$	102.000	−	176.669i	0.316558	−	0.548295i	−0.663209	−	0.748434i	$-0.730806\pi$
$47$	102.000	−	176.669i	0.316558	−	0.548295i	0.979767	+	0.200139i	$0.0641395\pi$
$48$	−128.000			−0.384900
$49$		0			0
$50$	50.0000			0.141421
$51$	264.000	−	457.261i	0.724851	−	1.25548i
$52$	116.000	+	200.918i	0.309352	+	0.535813i
$53$	−111.000	−	192.258i	−0.287680	−	0.498276i	0.685576	−	0.728001i	$-0.259551\pi$
$53$	−111.000	−	192.258i	−0.287680	−	0.498276i	−0.973255	+	0.229725i	$0.926217\pi$
$54$	80.0000	−	138.564i	0.201604	−	0.349189i
$55$	60.0000			0.147098
$56$		0			0
$57$	800.000			1.85899
$58$	90.0000	−	155.885i	0.203751	−	0.352908i
$59$	−210.000	−	363.731i	−0.463384	−	0.802605i	0.535743	−	0.844381i	$-0.320032\pi$
$59$	−210.000	−	363.731i	−0.463384	−	0.802605i	−0.999127	+	0.0417762i	$0.986698\pi$
$60$	80.0000	+	138.564i	0.172133	+	0.298142i
$61$	−451.000	+	781.155i	−0.946633	+	1.63962i	−0.194186	+	0.980965i	$0.562206\pi$
$61$	−451.000	+	781.155i	−0.946633	+	1.63962i	−0.752447	+	0.658652i	$0.771127\pi$
$62$	304.000			0.622710
$63$		0			0
$64$	64.0000			0.125000
$65$	145.000	−	251.147i	0.276693	−	0.479246i
$66$	96.0000	+	166.277i	0.179042	+	0.310110i
$67$	512.000	+	886.810i	0.933593	+	1.61703i	0.777123	+	0.629348i	$0.216678\pi$
$67$	512.000	+	886.810i	0.933593	+	1.61703i	0.156470	+	0.987683i	$0.449989\pi$
$68$	−132.000	+	228.631i	−0.235402	+	0.407729i
$69$	−1056.00			−1.84243
$70$		0			0
$71$	432.000			0.722098			0.361049	−	0.932547i	$-0.382419\pi$
$71$	432.000			0.722098			0.361049	+	0.932547i	$0.382419\pi$
$72$	−148.000	+	256.344i	−0.242250	+	0.419589i
$73$	−181.000	−	313.501i	−0.290198	−	0.502638i	0.683658	−	0.729802i	$-0.260388\pi$
$73$	−181.000	−	313.501i	−0.290198	−	0.502638i	−0.973856	+	0.227165i	$0.927054\pi$
$74$	34.0000	+	58.8897i	0.0534111	+	0.0925107i
$75$	100.000	−	173.205i	0.153960	−	0.266667i
$76$	−400.000			−0.603726
$77$		0			0
$78$	928.000			1.34712
$79$	80.0000	−	138.564i	0.113933	−	0.197338i	−0.803420	−	0.595413i	$-0.796988\pi$
$79$	80.0000	−	138.564i	0.113933	−	0.197338i	0.917353	+	0.398075i	$0.130322\pi$
$80$	−40.0000	−	69.2820i	−0.0559017	−	0.0968246i
$81$	179.500	+	310.903i	0.246228	+	0.426479i
$82$	438.000	−	758.638i	0.589866	−	1.02168i
$83$	72.0000			0.0952172			0.0476086	−	0.998866i	$-0.484840\pi$
$83$	72.0000			0.0952172			0.0476086	+	0.998866i	$0.484840\pi$
$84$		0			0
$85$	330.000			0.421100
$86$	−32.0000	+	55.4256i	−0.0401238	+	0.0694965i
$87$	−360.000	−	623.538i	−0.443633	−	0.768395i
$88$	−48.0000	−	83.1384i	−0.0581456	−	0.100711i
$89$	−405.000	+	701.481i	−0.482359	+	0.835470i	−0.999795	−	0.0202521i	$-0.993553\pi$
$89$	−405.000	+	701.481i	−0.482359	+	0.835470i	0.517436	+	0.855722i	$0.326886\pi$
$90$	370.000			0.433349
$91$		0			0
$92$	528.000			0.598346
$93$	608.000	−	1053.09i	0.677921	−	1.17419i
$94$	204.000	+	353.338i	0.223840	+	0.387703i
$95$	250.000	+	433.013i	0.269994	+	0.467644i
$96$	128.000	−	221.703i	0.136083	−	0.235702i
$97$	1106.00			1.15770			0.578852	−	0.815433i	$-0.303501\pi$
$97$	1106.00			1.15770			0.578852	+	0.815433i	$0.303501\pi$
$98$		0			0
$99$	444.000			0.450744
$100$	−50.0000	+	86.6025i	−0.0500000	+	0.0866025i
$101$	129.000	+	223.435i	0.127089	+	0.220124i	0.922548	−	0.385883i	$-0.126103\pi$
$101$	129.000	+	223.435i	0.127089	+	0.220124i	−0.795459	+	0.606008i	$0.792770\pi$
$102$	528.000	+	914.523i	0.512547	+	0.887757i
$103$	494.000	−	855.633i	0.472575	−	0.818525i	−0.526932	−	0.849907i	$-0.676658\pi$
$103$	494.000	−	855.633i	0.472575	−	0.818525i	0.999507	+	0.0313828i	$0.00999110\pi$
$104$	−464.000			−0.437490
$105$		0			0
$106$	444.000			0.406840
$107$	12.0000	−	20.7846i	0.0108419	−	0.0187787i	−0.860554	−	0.509360i	$-0.829882\pi$
$107$	12.0000	−	20.7846i	0.0108419	−	0.0187787i	0.871395	+	0.490581i	$0.163216\pi$
$108$	160.000	+	277.128i	0.142556	+	0.246914i
$109$	−475.000	−	822.724i	−0.417401	−	0.722960i	0.578276	−	0.815841i	$-0.303726\pi$
$109$	−475.000	−	822.724i	−0.417401	−	0.722960i	−0.995677	+	0.0928809i	$0.970392\pi$
$110$	−60.0000	+	103.923i	−0.0520071	+	0.0900789i
$111$	272.000			0.232586
$112$		0			0
$113$	−1038.00			−0.864131			−0.432066	−	0.901842i	$-0.642215\pi$
$113$	−1038.00			−0.864131			−0.432066	+	0.901842i	$0.642215\pi$
$114$	−800.000	+	1385.64i	−0.657253	+	1.13840i
$115$	−330.000	−	571.577i	−0.267588	−	0.463477i
$116$	180.000	+	311.769i	0.144074	+	0.249543i
$117$	1073.00	−	1858.49i	0.847854	−	1.46853i
$118$	840.000			0.655324
$119$		0			0
$120$	−320.000			−0.243432
$121$	593.500	−	1027.97i	0.445905	−	0.772331i
$122$	−902.000	−	1562.31i	−0.669371	−	1.15938i
$123$	−1752.00	−	3034.55i	−1.28433	−	2.22452i
$124$	−304.000	+	526.543i	−0.220161	+	0.381331i
$125$	125.000			0.0894427
$126$		0			0
$127$	−124.000			−0.0866395			−0.0433198	−	0.999061i	$-0.513793\pi$
$127$	−124.000			−0.0866395			−0.0433198	+	0.999061i	$0.513793\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	128.000	+	221.703i	0.0873626	+	0.151316i
$130$	290.000	+	502.295i	0.195651	+	0.338878i
$131$	−66.0000	+	114.315i	−0.0440187	+	0.0762426i	−0.887195	−	0.461394i	$-0.847349\pi$
$131$	−66.0000	+	114.315i	−0.0440187	+	0.0762426i	0.843177	+	0.537637i	$0.180683\pi$
$132$	−384.000			−0.253204
$133$		0			0
$134$	−2048.00			−1.32030
$135$	200.000	−	346.410i	0.127506	−	0.220846i
$136$	−264.000	−	457.261i	−0.166455	−	0.288308i
$137$	627.000	+	1086.00i	0.391009	+	0.677247i	0.992583	−	0.121570i	$-0.0387928\pi$
$137$	627.000	+	1086.00i	0.391009	+	0.677247i	−0.601574	+	0.798817i	$0.705459\pi$
$138$	1056.00	−	1829.05i	0.651396	−	1.12825i
$139$	−2860.00			−1.74519			−0.872597	−	0.488440i	$-0.837566\pi$
$139$	−2860.00			−1.74519			−0.872597	+	0.488440i	$0.837566\pi$
$140$		0			0
$141$	1632.00			0.974746
$142$	−432.000	+	748.246i	−0.255300	+	0.442193i
$143$	348.000	+	602.754i	0.203505	+	0.352481i
$144$	−296.000	−	512.687i	−0.171296	−	0.296694i
$145$	225.000	−	389.711i	0.128864	−	0.223198i
$146$	724.000			0.410402
$147$		0			0
$148$	−136.000			−0.0755347
$149$	−375.000	+	649.519i	−0.206183	+	0.357119i	−0.950509	−	0.310697i	$-0.899437\pi$
$149$	−375.000	+	649.519i	−0.206183	+	0.357119i	0.744326	+	0.667816i	$0.232771\pi$
$150$	200.000	+	346.410i	0.108866	+	0.188562i
$151$	224.000	+	387.979i	0.120721	+	0.209095i	0.920052	−	0.391796i	$-0.128146\pi$
$151$	224.000	+	387.979i	0.120721	+	0.209095i	−0.799331	+	0.600891i	$0.794813\pi$
$152$	400.000	−	692.820i	0.213449	−	0.369705i
$153$	2442.00			1.29035
$154$		0			0
$155$	760.000			0.393837
$156$	−928.000	+	1607.34i	−0.476279	+	0.824939i
$157$	−1123.00	−	1945.09i	−0.570861	−	0.988760i	−0.996478	−	0.0838566i	$-0.973276\pi$
$157$	−1123.00	−	1945.09i	−0.570861	−	0.988760i	0.425617	−	0.904903i	$-0.360057\pi$
$158$	160.000	+	277.128i	0.0805628	+	0.139539i
$159$	888.000	−	1538.06i	0.442912	−	0.767146i
$160$	160.000			0.0790569
$161$		0			0
$162$	−718.000			−0.348219
$163$	284.000	−	491.902i	0.136470	−	0.236373i	−0.789688	−	0.613509i	$-0.789758\pi$
$163$	284.000	−	491.902i	0.136470	−	0.236373i	0.926158	+	0.377136i	$0.123091\pi$
$164$	876.000	+	1517.28i	0.417098	+	0.722435i
$165$	240.000	+	415.692i	0.113236	+	0.196131i
$166$	−72.0000	+	124.708i	−0.0336644	+	0.0583084i
$167$	−1524.00			−0.706172			−0.353086	−	0.935591i	$-0.614868\pi$
$167$	−1524.00			−0.706172			−0.353086	+	0.935591i	$0.614868\pi$
$168$		0			0
$169$	1167.00			0.531179
$170$	−330.000	+	571.577i	−0.148881	+	0.257870i
$171$	1850.00	+	3204.29i	0.827328	+	1.43297i
$172$	−64.0000	−	110.851i	−0.0283718	−	0.0491414i
$173$	−1851.00	+	3206.03i	−0.813462	+	1.40896i	0.0969650	+	0.995288i	$0.469086\pi$
$173$	−1851.00	+	3206.03i	−0.813462	+	1.40896i	−0.910427	+	0.413670i	$0.864247\pi$
$174$	1440.00			0.627391
$175$		0			0
$176$	192.000			0.0822304
$177$	1680.00	−	2909.85i	0.713427	−	1.23569i
$178$	−810.000	−	1402.96i	−0.341079	−	0.590766i
$179$	−1590.00	−	2753.96i	−0.663923	−	1.14995i	−0.979576	−	0.201073i	$-0.935557\pi$
$179$	−1590.00	−	2753.96i	−0.663923	−	1.14995i	0.315653	−	0.948875i	$-0.397776\pi$
$180$	−370.000	+	640.859i	−0.153212	+	0.265371i
$181$	−2098.00			−0.861564			−0.430782	−	0.902456i	$-0.641762\pi$
$181$	−2098.00			−0.861564			−0.430782	+	0.902456i	$0.641762\pi$
$182$		0			0
$183$	−7216.00			−2.91487
$184$	−528.000	+	914.523i	−0.211547	+	0.366410i
$185$	85.0000	+	147.224i	0.0337801	+	0.0585089i
$186$	1216.00	+	2106.17i	0.479363	+	0.830280i
$187$	−396.000	+	685.892i	−0.154858	+	0.268221i
$188$	−816.000			−0.316558
$189$		0			0
$190$	−1000.00			−0.381830
$191$	−2196.00	+	3803.58i	−0.831921	+	1.44093i	0.0645912	+	0.997912i	$0.479426\pi$
$191$	−2196.00	+	3803.58i	−0.831921	+	1.44093i	−0.896513	+	0.443018i	$0.853908\pi$
$192$	256.000	+	443.405i	0.0962250	+	0.166667i
$193$	1079.00	+	1868.88i	0.402425	+	0.697021i	0.994018	−	0.109216i	$-0.0348339\pi$
$193$	1079.00	+	1868.88i	0.402425	+	0.697021i	−0.591593	+	0.806237i	$0.701501\pi$
$194$	−1106.00	+	1915.65i	−0.409310	+	0.708946i
$195$	2320.00			0.851993
$196$		0			0
$197$	−1074.00			−0.388423			−0.194212	−	0.980960i	$-0.562215\pi$
$197$	−1074.00			−0.388423			−0.194212	+	0.980960i	$0.562215\pi$
$198$	−444.000	+	769.031i	−0.159362	+	0.276023i
$199$	−1420.00	−	2459.51i	−0.505835	−	0.876132i	−0.999977	−	0.00675064i	$-0.997851\pi$
$199$	−1420.00	−	2459.51i	−0.505835	−	0.876132i	0.494142	−	0.869381i	$-0.335482\pi$
$200$	−100.000	−	173.205i	−0.0353553	−	0.0612372i
$201$	−4096.00	+	7094.48i	−1.43736	+	2.48958i
$202$	−516.000			−0.179731
$203$		0			0
$204$	−2112.00			−0.724851
$205$	1095.00	−	1896.60i	0.373064	−	0.646166i
$206$	988.000	+	1711.27i	0.334161	+	0.578784i
$207$	−2442.00	−	4229.67i	−0.819955	−	1.42020i
$208$	464.000	−	803.672i	0.154676	−	0.267907i
$209$	−1200.00			−0.397157
$210$		0			0
$211$	−2668.00			−0.870487			−0.435243	−	0.900313i	$-0.643338\pi$
$211$	−2668.00			−0.870487			−0.435243	+	0.900313i	$0.643338\pi$
$212$	−444.000	+	769.031i	−0.143840	+	0.249138i
$213$	1728.00	+	2992.98i	0.555871	+	0.962798i
$214$	24.0000	+	41.5692i	0.00766638	+	0.0132786i
$215$	−80.0000	+	138.564i	−0.0253765	+	0.0439534i
$216$	−640.000			−0.201604
$217$		0			0
$218$	1900.00			0.590295
$219$	1448.00	−	2508.01i	0.446789	−	0.773861i
$220$	−120.000	−	207.846i	−0.0367745	−	0.0636954i
$221$	1914.00	+	3315.15i	0.582577	+	1.00905i
$222$	−272.000	+	471.118i	−0.0822317	+	0.142430i
$223$	1772.00			0.532116			0.266058	−	0.963957i	$-0.414279\pi$
$223$	1772.00			0.532116			0.266058	+	0.963957i	$0.414279\pi$
$224$		0			0
$225$	925.000			0.274074
$226$	1038.00	−	1797.87i	0.305517	−	0.529170i
$227$	1392.00	+	2411.01i	0.407006	+	0.704954i	0.994553	−	0.104236i	$-0.0332396\pi$
$227$	1392.00	+	2411.01i	0.407006	+	0.704954i	−0.587547	+	0.809190i	$0.699906\pi$
$228$	−1600.00	−	2771.28i	−0.464748	−	0.804967i
$229$	−175.000	+	303.109i	−0.0504992	+	0.0874672i	−0.890170	−	0.455628i	$-0.849415\pi$
$229$	−175.000	+	303.109i	−0.0504992	+	0.0874672i	0.839671	+	0.543096i	$0.182748\pi$
$230$	1320.00			0.378427
$231$		0			0
$232$	−720.000			−0.203751
$233$	−981.000	+	1699.14i	−0.275826	+	0.477745i	−0.970343	−	0.241732i	$-0.922285\pi$
$233$	−981.000	+	1699.14i	−0.275826	+	0.477745i	0.694517	+	0.719476i	$0.255618\pi$
$234$	2146.00	+	3716.98i	0.599523	+	1.03840i
$235$	510.000	+	883.346i	0.141569	+	0.245205i
$236$	−840.000	+	1454.92i	−0.231692	+	0.401303i
$237$	1280.00			0.350823
$238$		0			0
$239$	−4320.00			−1.16919			−0.584597	−	0.811324i	$-0.698748\pi$
$239$	−4320.00			−1.16919			−0.584597	+	0.811324i	$0.698748\pi$
$240$	320.000	−	554.256i	0.0860663	−	0.149071i
$241$	239.000	+	413.960i	0.0638811	+	0.110645i	0.896197	−	0.443656i	$-0.146319\pi$
$241$	239.000	+	413.960i	0.0638811	+	0.110645i	−0.832316	+	0.554301i	$0.812985\pi$
$242$	1187.00	+	2055.94i	0.315303	+	0.546120i
$243$	−2516.00	+	4357.84i	−0.664204	+	1.15043i
$244$	3608.00			0.946633
$245$		0			0
$246$	7008.00			1.81632
$247$	−2900.00	+	5022.95i	−0.747055	+	1.29394i
$248$	−608.000	−	1053.09i	−0.155678	−	0.269641i
$249$	288.000	+	498.831i	0.0732982	+	0.126956i
$250$	−125.000	+	216.506i	−0.0316228	+	0.0547723i
$251$	2652.00			0.666903			0.333452	−	0.942767i	$-0.391787\pi$
$251$	2652.00			0.666903			0.333452	+	0.942767i	$0.391787\pi$
$252$		0			0
$253$	1584.00			0.393617
$254$	124.000	−	214.774i	0.0306317	−	0.0530557i
$255$	1320.00	+	2286.31i	0.324163	+	0.561467i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1167.00	−	2021.30i	0.283251	−	0.490605i	−0.688933	−	0.724825i	$-0.741920\pi$
$257$	1167.00	−	2021.30i	0.283251	−	0.490605i	0.972183	+	0.234221i	$0.0752538\pi$
$258$	−512.000			−0.123549
$259$		0			0
$260$	−1160.00			−0.276693
$261$	1665.00	−	2883.86i	0.394869	−	0.683934i
$262$	−132.000	−	228.631i	−0.0311259	−	0.0539116i
$263$	1974.00	+	3419.07i	0.462822	+	0.801630i	0.999100	−	0.0424106i	$-0.0135038\pi$
$263$	1974.00	+	3419.07i	0.462822	+	0.801630i	−0.536279	+	0.844041i	$0.680170\pi$
$264$	384.000	−	665.108i	0.0895211	−	0.155055i
$265$	1110.00			0.257309
$266$		0			0
$267$	−6480.00			−1.48528
$268$	2048.00	−	3547.24i	0.466797	−	0.808516i
$269$	−795.000	−	1376.98i	−0.180193	−	0.312104i	0.761753	−	0.647868i	$-0.224339\pi$
$269$	−795.000	−	1376.98i	−0.180193	−	0.312104i	−0.941946	+	0.335764i	$0.891006\pi$
$270$	400.000	+	692.820i	0.0901601	+	0.156162i
$271$	−2476.00	+	4288.56i	−0.555005	+	0.961296i	0.442898	+	0.896572i	$0.353950\pi$
$271$	−2476.00	+	4288.56i	−0.555005	+	0.961296i	−0.997903	+	0.0647246i	$0.979383\pi$
$272$	1056.00			0.235402
$273$		0			0
$274$	−2508.00			−0.552970
$275$	−150.000	+	259.808i	−0.0328921	+	0.0569709i
$276$	2112.00	+	3658.09i	0.460607	+	0.797794i
$277$	−823.000	−	1425.48i	−0.178517	−	0.309201i	0.762856	−	0.646569i	$-0.223797\pi$
$277$	−823.000	−	1425.48i	−0.178517	−	0.309201i	−0.941373	+	0.337368i	$0.890463\pi$
$278$	2860.00	−	4953.67i	0.617019	−	1.06871i
$279$	5624.00			1.20681
$280$		0			0
$281$	−1158.00			−0.245838			−0.122919	−	0.992417i	$-0.539226\pi$
$281$	−1158.00			−0.245838			−0.122919	+	0.992417i	$0.539226\pi$
$282$	−1632.00	+	2826.71i	−0.344625	+	0.596908i
$283$	−3496.00	−	6055.25i	−0.734331	−	1.27190i	−0.955016	−	0.296553i	$-0.904163\pi$
$283$	−3496.00	−	6055.25i	−0.734331	−	1.27190i	0.220685	−	0.975345i	$-0.429171\pi$
$284$	−864.000	−	1496.49i	−0.180525	−	0.312678i
$285$	−2000.00	+	3464.10i	−0.415683	+	0.719985i
$286$	−1392.00			−0.287800
$287$		0			0
$288$	1184.00			0.242250
$289$	278.500	−	482.376i	0.0566863	−	0.0981836i
$290$	450.000	+	779.423i	0.0911204	+	0.157825i
$291$	4424.00	+	7662.59i	0.891201	+	1.54361i
$292$	−724.000	+	1254.00i	−0.145099	+	0.251319i
$293$	−258.000			−0.0514421			−0.0257210	−	0.999669i	$-0.508188\pi$
$293$	−258.000			−0.0514421			−0.0257210	+	0.999669i	$0.508188\pi$
$294$		0			0
$295$	2100.00			0.414463
$296$	136.000	−	235.559i	0.0267055	−	0.0462553i
$297$	480.000	+	831.384i	0.0937792	+	0.162430i
$298$	−750.000	−	1299.04i	−0.145793	−	0.252521i
$299$	3828.00	−	6630.29i	0.740398	−	1.28241i
$300$	−800.000			−0.153960
$301$		0			0
$302$	−896.000			−0.170725
$303$	−1032.00	+	1787.48i	−0.195666	+	0.338904i
$304$	800.000	+	1385.64i	0.150931	+	0.261421i
$305$	−2255.00	−	3905.77i	−0.423347	−	0.733259i
$306$	−2442.00	+	4229.67i	−0.456209	+	0.790177i
$307$	−8944.00			−1.66274			−0.831370	−	0.555720i	$-0.812443\pi$
$307$	−8944.00			−1.66274			−0.831370	+	0.555720i	$0.812443\pi$
$308$		0			0
$309$	7904.00			1.45515
$310$	−760.000	+	1316.36i	−0.139242	+	0.241175i
$311$	−696.000	−	1205.51i	−0.126902	−	0.219801i	0.795573	−	0.605858i	$-0.207170\pi$
$311$	−696.000	−	1205.51i	−0.126902	−	0.219801i	−0.922475	+	0.386057i	$0.873837\pi$
$312$	−1856.00	−	3214.69i	−0.336780	−	0.583320i
$313$	2939.00	−	5090.50i	0.530742	−	0.919271i	−0.468615	−	0.883403i	$-0.655247\pi$
$313$	2939.00	−	5090.50i	0.530742	−	0.919271i	0.999357	−	0.0358688i	$-0.0114198\pi$
$314$	4492.00			0.807319
$315$		0			0
$316$	−640.000			−0.113933
$317$	−5163.00	+	8942.58i	−0.914773	+	1.58443i	−0.107539	+	0.994201i	$0.534297\pi$
$317$	−5163.00	+	8942.58i	−0.914773	+	1.58443i	−0.807234	+	0.590232i	$0.799036\pi$
$318$	1776.00	+	3076.12i	0.313186	+	0.542454i
$319$	540.000	+	935.307i	0.0947780	+	0.164160i
$320$	−160.000	+	277.128i	−0.0279508	+	0.0484123i
$321$	192.000			0.0333844
$322$		0			0
$323$	−6600.00			−1.13695
$324$	718.000	−	1243.61i	0.123114	−	0.213239i
$325$	725.000	+	1255.74i	0.123741	+	0.214325i
$326$	568.000	+	983.805i	0.0964988	+	0.167141i
$327$	3800.00	−	6581.79i	0.642631	−	1.11307i
$328$	−3504.00			−0.589866
$329$		0			0
$330$	−960.000			−0.160140
$331$	2114.00	−	3661.56i	0.351045	−	0.608028i	−0.635388	−	0.772193i	$-0.719160\pi$
$331$	2114.00	−	3661.56i	0.351045	−	0.608028i	0.986433	+	0.164165i	$0.0524930\pi$
$332$	−144.000	−	249.415i	−0.0238043	−	0.0412303i
$333$	629.000	+	1089.46i	0.103510	+	0.179285i
$334$	1524.00	−	2639.65i	0.249669	−	0.432440i
$335$	−5120.00			−0.835031
$336$		0			0
$337$	1106.00			0.178776			0.0893882	−	0.995997i	$-0.471509\pi$
$337$	1106.00			0.178776			0.0893882	+	0.995997i	$0.471509\pi$
$338$	−1167.00	+	2021.30i	−0.187800	+	0.325279i
$339$	−4152.00	−	7191.47i	−0.665209	−	1.15217i
$340$	−660.000	−	1143.15i	−0.105275	−	0.182342i
$341$	−912.000	+	1579.63i	−0.144832	+	0.250856i
$342$	−7400.00			−1.17002
$343$		0			0
$344$	256.000			0.0401238
$345$	2640.00	−	4572.61i	0.411979	−	0.713569i
$346$	−3702.00	−	6412.05i	−0.575204	−	0.996283i
$347$	−4668.00	−	8085.21i	−0.722165	−	1.25083i	−0.960130	−	0.279553i	$-0.909814\pi$
$347$	−4668.00	−	8085.21i	−0.722165	−	1.25083i	0.237965	−	0.971274i	$-0.423520\pi$
$348$	−1440.00	+	2494.15i	−0.221816	+	0.384197i
$349$	−11770.0			−1.80525			−0.902627	−	0.430424i	$-0.858364\pi$
$349$	−11770.0			−1.80525			−0.902627	+	0.430424i	$0.858364\pi$
$350$		0			0
$351$	4640.00			0.705598
$352$	−192.000	+	332.554i	−0.0290728	+	0.0503556i
$353$	−4161.00	−	7207.06i	−0.627387	−	1.08667i	−0.988074	−	0.153980i	$-0.950791\pi$
$353$	−4161.00	−	7207.06i	−0.627387	−	1.08667i	0.360687	−	0.932687i	$-0.382542\pi$
$354$	3360.00	+	5819.69i	0.504469	+	0.873766i
$355$	−1080.00	+	1870.61i	−0.161466	+	0.279667i
$356$	3240.00			0.482359
$357$		0			0
$358$	6360.00			0.938929
$359$	−5340.00	+	9249.15i	−0.785054	+	1.35975i	0.143913	+	0.989590i	$0.454032\pi$
$359$	−5340.00	+	9249.15i	−0.785054	+	1.35975i	−0.928967	+	0.370163i	$0.879302\pi$
$360$	−740.000	−	1281.72i	−0.108337	−	0.187646i
$361$	−1570.50	−	2720.19i	−0.228969	−	0.396586i
$362$	2098.00	−	3633.84i	0.304609	−	0.527598i
$363$	9496.00			1.37303
$364$		0			0
$365$	1810.00			0.259561
$366$	7216.00	−	12498.5i	1.03056	−	1.78499i
$367$	2942.00	+	5095.69i	0.418450	+	0.724777i	0.995784	−	0.0917316i	$-0.0292402\pi$
$367$	2942.00	+	5095.69i	0.418450	+	0.724777i	−0.577334	+	0.816508i	$0.695907\pi$
$368$	−1056.00	−	1829.05i	−0.149586	−	0.259091i
$369$	8103.00	−	14034.8i	1.14316	−	1.98001i
$370$	−340.000			−0.0477723
$371$		0			0
$372$	−4864.00			−0.677921
$373$	1049.00	−	1816.92i	0.145617	−	0.252216i	−0.783986	−	0.620779i	$-0.786817\pi$
$373$	1049.00	−	1816.92i	0.145617	−	0.252216i	0.929603	+	0.368562i	$0.120150\pi$
$374$	−792.000	−	1371.78i	−0.109501	−	0.189661i
$375$	500.000	+	866.025i	0.0688530	+	0.119257i
$376$	816.000	−	1413.35i	0.111920	−	0.193851i
$377$	5220.00			0.713113
$378$		0			0
$379$	3860.00			0.523153			0.261576	−	0.965183i	$-0.415758\pi$
$379$	3860.00			0.523153			0.261576	+	0.965183i	$0.415758\pi$
$380$	1000.00	−	1732.05i	0.134997	−	0.233822i
$381$	−496.000	−	859.097i	−0.0666951	−	0.115519i
$382$	−4392.00	−	7607.17i	−0.588257	−	1.01889i
$383$	4794.00	−	8303.45i	0.639587	−	1.10780i	−0.345936	−	0.938258i	$-0.612439\pi$
$383$	4794.00	−	8303.45i	0.639587	−	1.10780i	0.985523	−	0.169540i	$-0.0542281\pi$
$384$	−1024.00			−0.136083
$385$		0			0
$386$	−4316.00			−0.569116
$387$	−592.000	+	1025.37i	−0.0777598	+	0.134684i
$388$	−2212.00	−	3831.30i	−0.289426	−	0.501301i
$389$	6705.00	+	11613.4i	0.873925	+	1.51368i	0.857903	+	0.513812i	$0.171767\pi$
$389$	6705.00	+	11613.4i	0.873925	+	1.51368i	0.0160224	+	0.999872i	$0.494900\pi$
$390$	−2320.00	+	4018.36i	−0.301225	+	0.521737i
$391$	8712.00			1.12682
$392$		0			0
$393$	−1056.00			−0.135542
$394$	1074.00	−	1860.22i	0.137328	−	0.237860i
$395$	400.000	+	692.820i	0.0509524	+	0.0882521i
$396$	−888.000	−	1538.06i	−0.112686	−	0.195178i
$397$	6557.00	−	11357.1i	0.828933	−	1.43575i	−0.0699430	−	0.997551i	$-0.522282\pi$
$397$	6557.00	−	11357.1i	0.828933	−	1.43575i	0.898876	−	0.438203i	$-0.144385\pi$
$398$	5680.00			0.715358
$399$		0			0
$400$	400.000			0.0500000
$401$	2919.00	−	5055.86i	0.363511	−	0.629619i	−0.625025	−	0.780605i	$-0.714911\pi$
$401$	2919.00	−	5055.86i	0.363511	−	0.629619i	0.988536	+	0.150985i	$0.0482446\pi$
$402$	−8192.00	−	14189.0i	−1.01637	−	1.76040i
$403$	4408.00	+	7634.88i	0.544859	+	0.943723i
$404$	516.000	−	893.738i	0.0635445	−	0.110062i
$405$	−1795.00			−0.220233
$406$		0			0
$407$	−408.000			−0.0496899
$408$	2112.00	−	3658.09i	0.256273	−	0.443879i
$409$	−4765.00	−	8253.22i	−0.576074	−	0.997789i	−0.995924	−	0.0901954i	$-0.971251\pi$
$409$	−4765.00	−	8253.22i	−0.576074	−	0.997789i	0.419851	−	0.907593i	$-0.362082\pi$
$410$	2190.00	+	3793.19i	0.263796	+	0.456908i
$411$	−5016.00	+	8687.97i	−0.601998	+	1.04269i
$412$	−3952.00			−0.472575
$413$		0			0
$414$	9768.00			1.15959
$415$	−180.000	+	311.769i	−0.0212912	+	0.0368775i
$416$	928.000	+	1607.34i	0.109372	+	0.189439i
$417$	−11440.0	−	19814.7i	−1.34345	−	2.32693i
$418$	1200.00	−	2078.46i	0.140416	−	0.243208i
$419$	7260.00			0.846478			0.423239	−	0.906018i	$-0.360893\pi$
$419$	7260.00			0.846478			0.423239	+	0.906018i	$0.360893\pi$
$420$		0			0
$421$	12062.0			1.39636			0.698178	−	0.715924i	$-0.253994\pi$
$421$	12062.0			1.39636			0.698178	+	0.715924i	$0.253994\pi$
$422$	2668.00	−	4621.11i	0.307764	−	0.533062i
$423$	3774.00	+	6536.76i	0.433802	+	0.751367i
$424$	−888.000	−	1538.06i	−0.101710	−	0.176167i
$425$	−825.000	+	1428.94i	−0.0941609	+	0.163091i
$426$	−6912.00			−0.786121
$427$		0			0
$428$	−96.0000			−0.0108419
$429$	−2784.00	+	4822.03i	−0.313317	+	0.542680i
$430$	−160.000	−	277.128i	−0.0179439	−	0.0310798i
$431$	6804.00	+	11784.9i	0.760411	+	1.31707i	0.942639	+	0.333814i	$0.108336\pi$
$431$	6804.00	+	11784.9i	0.760411	+	1.31707i	−0.182228	+	0.983256i	$0.558331\pi$
$432$	640.000	−	1108.51i	0.0712778	−	0.123457i
$433$	−3838.00			−0.425964			−0.212982	−	0.977056i	$-0.568318\pi$
$433$	−3838.00			−0.425964			−0.212982	+	0.977056i	$0.568318\pi$
$434$		0			0
$435$	3600.00			0.396797
$436$	−1900.00	+	3290.90i	−0.208701	+	0.361480i
$437$	6600.00	+	11431.5i	0.722473	+	1.25136i
$438$	2896.00	+	5016.02i	0.315927	+	0.547202i
$439$	−3700.00	+	6408.59i	−0.402258	+	0.696732i	−0.993998	−	0.109397i	$-0.965108\pi$
$439$	−3700.00	+	6408.59i	−0.402258	+	0.696732i	0.591740	+	0.806129i	$0.298441\pi$
$440$	480.000			0.0520071
$441$		0			0
$442$	−7656.00			−0.823889
$443$	−4176.00	+	7233.04i	−0.447873	+	0.775739i	−0.998247	−	0.0591792i	$-0.981152\pi$
$443$	−4176.00	+	7233.04i	−0.447873	+	0.775739i	0.550374	+	0.834918i	$0.314485\pi$
$444$	−544.000	−	942.236i	−0.0581466	−	0.100713i
$445$	−2025.00	−	3507.40i	−0.215717	−	0.373633i
$446$	−1772.00	+	3069.19i	−0.188131	+	0.325853i
$447$	−6000.00			−0.634878
$448$		0			0
$449$	10770.0			1.13200			0.566000	−	0.824405i	$-0.308490\pi$
$449$	10770.0			1.13200			0.566000	+	0.824405i	$0.308490\pi$
$450$	−925.000	+	1602.15i	−0.0968998	+	0.167835i
$451$	2628.00	+	4551.83i	0.274385	+	0.475249i
$452$	2076.00	+	3595.74i	0.216033	+	0.374180i
$453$	−1792.00	+	3103.84i	−0.185862	+	0.321922i
$454$	−5568.00			−0.575593
$455$		0			0
$456$	6400.00			0.657253
$457$	3347.00	−	5797.17i	0.342595	−	0.593392i	−0.642319	−	0.766438i	$-0.722027\pi$
$457$	3347.00	−	5797.17i	0.342595	−	0.593392i	0.984914	+	0.173045i	$0.0553607\pi$
$458$	−350.000	−	606.218i	−0.0357084	−	0.0618487i
$459$	2640.00	+	4572.61i	0.268463	+	0.464992i
$460$	−1320.00	+	2286.31i	−0.133794	+	0.231738i
$461$	−3018.00			−0.304907			−0.152454	−	0.988311i	$-0.548717\pi$
$461$	−3018.00			−0.304907			−0.152454	+	0.988311i	$0.548717\pi$
$462$		0			0
$463$	14492.0			1.45464			0.727322	−	0.686296i	$-0.240765\pi$
$463$	14492.0			1.45464			0.727322	+	0.686296i	$0.240765\pi$
$464$	720.000	−	1247.08i	0.0720370	−	0.124772i
$465$	3040.00	+	5265.43i	0.303176	+	0.525115i
$466$	−1962.00	−	3398.28i	−0.195038	−	0.337816i
$467$	−3888.00	+	6734.21i	−0.385257	+	0.667285i	−0.991805	−	0.127762i	$-0.959221\pi$
$467$	−3888.00	+	6734.21i	−0.385257	+	0.667285i	0.606548	+	0.795047i	$0.292554\pi$
$468$	−8584.00			−0.847854
$469$		0			0
$470$	−2040.00			−0.200209
$471$	8984.00	−	15560.7i	0.878898	−	1.52230i
$472$	−1680.00	−	2909.85i	−0.163831	−	0.283764i
$473$	−192.000	−	332.554i	−0.0186642	−	0.0323274i
$474$	−1280.00	+	2217.03i	−0.124034	+	0.214834i
$475$	−2500.00			−0.241490
$476$		0			0
$477$	8214.00			0.788455
$478$	4320.00	−	7482.46i	0.413373	−	0.715983i
$479$	6840.00	+	11847.2i	0.652458	+	1.13009i	0.982525	+	0.186133i	$0.0595956\pi$
$479$	6840.00	+	11847.2i	0.652458	+	1.13009i	−0.330066	+	0.943958i	$0.607071\pi$
$480$	640.000	+	1108.51i	0.0608581	+	0.105409i
$481$	−986.000	+	1707.80i	−0.0934672	+	0.161890i
$482$	−956.000			−0.0903415
$483$		0			0
$484$	−4748.00			−0.445905
$485$	−2765.00	+	4789.12i	−0.258870	+	0.448377i
$486$	−5032.00	−	8715.68i	−0.469663	−	0.813480i
$487$	−3958.00	−	6855.46i	−0.368284	−	0.637886i	0.621014	−	0.783800i	$-0.286721\pi$
$487$	−3958.00	−	6855.46i	−0.368284	−	0.637886i	−0.989297	+	0.145914i	$0.953388\pi$
$488$	−3608.00	+	6249.24i	−0.334685	+	0.579692i
$489$	4544.00			0.420218
$490$		0			0
$491$	13932.0			1.28053			0.640267	−	0.768152i	$-0.278824\pi$
$491$	13932.0			1.28053			0.640267	+	0.768152i	$0.278824\pi$
$492$	−7008.00	+	12138.2i	−0.642165	+	1.11226i
$493$	2970.00	+	5144.19i	0.271323	+	0.469945i
$494$	−5800.00	−	10045.9i	−0.528248	−	0.914952i
$495$	−1110.00	+	1922.58i	−0.100789	+	0.174572i
$496$	2432.00			0.220161
$497$		0			0
$498$	−1152.00			−0.103659
$499$	4130.00	−	7153.37i	0.370509	−	0.641741i	−0.619135	−	0.785285i	$-0.712516\pi$
$499$	4130.00	−	7153.37i	0.370509	−	0.641741i	0.989644	+	0.143544i	$0.0458498\pi$
$500$	−250.000	−	433.013i	−0.0223607	−	0.0387298i
$501$	−6096.00	−	10558.6i	−0.543611	−	0.941562i
$502$	−2652.00	+	4593.40i	−0.235786	+	0.408393i
$503$	−11148.0			−0.988200			−0.494100	−	0.869405i	$-0.664502\pi$
$503$	−11148.0			−0.988200			−0.494100	+	0.869405i	$0.664502\pi$
$504$		0			0
$505$	−1290.00			−0.113672
$506$	−1584.00	+	2743.57i	−0.139165	+	0.241041i
$507$	4668.00	+	8085.21i	0.408902	+	0.708239i
$508$	248.000	+	429.549i	0.0216599	+	0.0375160i
$509$	4845.00	−	8391.79i	0.421907	−	0.730765i	−0.574219	−	0.818702i	$-0.694694\pi$
$509$	4845.00	−	8391.79i	0.421907	−	0.730765i	0.996126	+	0.0879370i	$0.0280274\pi$
$510$	−5280.00			−0.458436
$511$		0			0
$512$	512.000			0.0441942
$513$	−4000.00	+	6928.20i	−0.344258	+	0.596272i
$514$	2334.00	+	4042.61i	0.200289	+	0.346910i
$515$	2470.00	+	4278.17i	0.211342	+	0.366055i
$516$	512.000	−	886.810i	0.0436813	−	0.0756582i
$517$	−2448.00			−0.208245
$518$		0			0
$519$	−29616.0			−2.50481
$520$	1160.00	−	2009.18i	0.0978257	−	0.169439i
$521$	8019.00	+	13889.3i	0.674316	+	1.16795i	0.976668	+	0.214754i	$0.0688949\pi$
$521$	8019.00	+	13889.3i	0.674316	+	1.16795i	−0.302352	+	0.953196i	$0.597772\pi$
$522$	3330.00	+	5767.73i	0.279215	+	0.483614i
$523$	−496.000	+	859.097i	−0.0414695	+	0.0718273i	−0.886015	−	0.463656i	$-0.846537\pi$
$523$	−496.000	+	859.097i	−0.0414695	+	0.0718273i	0.844546	+	0.535484i	$0.179871\pi$
$524$	528.000			0.0440187
$525$		0			0
$526$	−7896.00			−0.654528
$527$	−5016.00	+	8687.97i	−0.414612	+	0.718129i
$528$	768.000	+	1330.22i	0.0633010	+	0.109640i
$529$	−2628.50	−	4552.70i	−0.216035	−	0.374184i
$530$	−1110.00	+	1922.58i	−0.0909723	+	0.157569i
$531$	15540.0			1.27002
$532$		0			0
$533$	25404.0			2.06448
$534$	6480.00	−	11223.7i	0.525126	−	0.909544i
$535$	60.0000	+	103.923i	0.00484865	+	0.00839810i
$536$	4096.00	+	7094.48i	0.330075	+	0.571707i
$537$	12720.0	−	22031.7i	1.02218	−	1.77046i
$538$	3180.00			0.254832
$539$		0			0
$540$	−1600.00			−0.127506
$541$	−3571.00	+	6185.15i	−0.283788	+	0.491535i	−0.972315	−	0.233676i	$-0.924925\pi$
$541$	−3571.00	+	6185.15i	−0.283788	+	0.491535i	0.688527	+	0.725211i	$0.258258\pi$
$542$	−4952.00	−	8577.12i	−0.392448	−	0.679739i
$543$	−8392.00	−	14535.4i	−0.663232	−	1.14875i
$544$	−1056.00	+	1829.05i	−0.0832273	+	0.144154i
$545$	4750.00			0.373335
$546$		0			0
$547$	7616.00			0.595314			0.297657	−	0.954673i	$-0.403795\pi$
$547$	7616.00			0.595314			0.297657	+	0.954673i	$0.403795\pi$
$548$	2508.00	−	4343.98i	0.195504	−	0.338624i
$549$	−16687.0	−	28902.7i	−1.29724	−	2.24688i
$550$	−300.000	−	519.615i	−0.0232583	−	0.0402845i
$551$	−4500.00	+	7794.23i	−0.347925	+	0.602623i
$552$	−8448.00			−0.651396
$553$		0			0
$554$	3292.00			0.252462
$555$	−680.000	+	1177.79i	−0.0520079	+	0.0900804i
$556$	5720.00	+	9907.33i	0.436299	+	0.755691i
$557$	5157.00	+	8932.19i	0.392296	+	0.679477i	0.992752	−	0.120181i	$-0.0383474\pi$
$557$	5157.00	+	8932.19i	0.392296	+	0.679477i	−0.600456	+	0.799658i	$0.705014\pi$
$558$	−5624.00	+	9741.05i	−0.426672	+	0.739017i
$559$	−1856.00			−0.140430
$560$		0			0
$561$	−6336.00			−0.476838
$562$	1158.00	−	2005.71i	0.0869169	−	0.150544i
$563$	3564.00	+	6173.03i	0.266793	+	0.462100i	0.968032	−	0.250827i	$-0.0807025\pi$
$563$	3564.00	+	6173.03i	0.266793	+	0.462100i	−0.701239	+	0.712927i	$0.747369\pi$
$564$	−3264.00	−	5653.41i	−0.243687	−	0.422077i
$565$	2595.00	−	4494.67i	0.193226	−	0.334677i
$566$	13984.0			1.03850
$567$		0			0
$568$	3456.00			0.255300
$569$	−1005.00	+	1740.71i	−0.0740453	+	0.128250i	−0.900671	−	0.434502i	$-0.856924\pi$
$569$	−1005.00	+	1740.71i	−0.0740453	+	0.128250i	0.826625	+	0.562753i	$0.190258\pi$
$570$	−4000.00	−	6928.20i	−0.293933	−	0.509106i
$571$	11594.0	+	20081.4i	0.849726	+	1.47177i	0.881452	+	0.472273i	$0.156566\pi$
$571$	11594.0	+	20081.4i	0.849726	+	1.47177i	−0.0317260	+	0.999497i	$0.510100\pi$
$572$	1392.00	−	2411.01i	0.101753	−	0.176241i
$573$	−35136.0			−2.56165
$574$		0			0
$575$	3300.00			0.239338
$576$	−1184.00	+	2050.75i	−0.0856481	+	0.148347i
$577$	−11233.0	−	19456.1i	−0.810461	−	1.40376i	−0.912542	−	0.408983i	$-0.865883\pi$
$577$	−11233.0	−	19456.1i	−0.810461	−	1.40376i	0.102081	−	0.994776i	$-0.467450\pi$
$578$	557.000	+	964.752i	0.0400833	+	0.0694263i
$579$	−8632.00	+	14951.1i	−0.619575	+	1.07313i
$580$	−1800.00			−0.128864
$581$		0			0
$582$	−17696.0			−1.26035
$583$	−1332.00	+	2307.09i	−0.0946240	+	0.163894i
$584$	−1448.00	−	2508.01i	−0.102600	−	0.177709i
$585$	5365.00	+	9292.45i	0.379172	+	0.656745i
$586$	258.000	−	446.869i	0.0181875	−	0.0315017i
$587$	22776.0			1.60148			0.800738	−	0.599015i	$-0.204441\pi$
$587$	22776.0			1.60148			0.800738	+	0.599015i	$0.204441\pi$
$588$		0			0
$589$	−15200.0			−1.06334
$590$	−2100.00	+	3637.31i	−0.146535	+	0.253806i
$591$	−4296.00	−	7440.89i	−0.299008	−	0.517897i
$592$	272.000	+	471.118i	0.0188837	+	0.0327075i
$593$	10599.0	−	18358.0i	0.733978	−	1.27129i	−0.221193	−	0.975230i	$-0.570995\pi$
$593$	10599.0	−	18358.0i	0.733978	−	1.27129i	0.955170	−	0.296057i	$-0.0956717\pi$
$594$	−1920.00			−0.132624
$595$		0			0
$596$	3000.00			0.206183
$597$	11360.0	−	19676.1i	0.778784	−	1.34889i
$598$	7656.00	+	13260.6i	0.523540	+	0.906798i
$599$	−7980.00	−	13821.8i	−0.544330	−	0.942808i	−0.998649	−	0.0519686i	$-0.983450\pi$
$599$	−7980.00	−	13821.8i	−0.544330	−	0.942808i	0.454318	−	0.890839i	$-0.349883\pi$
$600$	800.000	−	1385.64i	0.0544331	−	0.0942809i
$601$	5882.00			0.399221			0.199610	−	0.979875i	$-0.436032\pi$
$601$	5882.00			0.399221			0.199610	+	0.979875i	$0.436032\pi$
$602$		0			0
$603$	−37888.0			−2.55874
$604$	896.000	−	1551.92i	0.0603605	−	0.104547i
$605$	2967.50	+	5139.86i	0.199415	+	0.345397i
$606$	−2064.00	−	3574.95i	−0.138357	−	0.239641i
$607$	−4258.00	+	7375.07i	−0.284723	+	0.493155i	−0.972542	−	0.232728i	$-0.925235\pi$
$607$	−4258.00	+	7375.07i	−0.284723	+	0.493155i	0.687819	+	0.725882i	$0.258568\pi$
$608$	−3200.00			−0.213449
$609$		0			0
$610$	9020.00			0.598703
$611$	−5916.00	+	10246.8i	−0.391712	+	0.678464i
$612$	−4884.00	−	8459.34i	−0.322588	−	0.558739i
$613$	−4231.00	−	7328.31i	−0.278774	−	0.482851i	0.692306	−	0.721604i	$-0.256595\pi$
$613$	−4231.00	−	7328.31i	−0.278774	−	0.482851i	−0.971080	+	0.238753i	$0.923261\pi$
$614$	8944.00	−	15491.5i	0.587867	−	1.01822i
$615$	17520.0			1.14874
$616$		0			0
$617$	−11094.0			−0.723870			−0.361935	−	0.932203i	$-0.617884\pi$
$617$	−11094.0			−0.723870			−0.361935	+	0.932203i	$0.617884\pi$
$618$	−7904.00	+	13690.1i	−0.514475	+	0.891097i
$619$	−1090.00	−	1887.94i	−0.0707767	−	0.122589i	0.828465	−	0.560041i	$-0.189214\pi$
$619$	−1090.00	−	1887.94i	−0.0707767	−	0.122589i	−0.899242	+	0.437452i	$0.855881\pi$
$620$	−1520.00	−	2632.72i	−0.0984591	−	0.170536i
$621$	5280.00	−	9145.23i	0.341190	−	0.590959i
$622$	2784.00			0.179467
$623$		0			0
$624$	7424.00			0.476279
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	5878.00	+	10181.0i	0.375291	+	0.650023i
$627$	−4800.00	−	8313.84i	−0.305731	−	0.529542i
$628$	−4492.00	+	7780.37i	−0.285430	+	0.494380i
$629$	−2244.00			−0.142248
$630$		0			0
$631$	−26848.0			−1.69382			−0.846911	−	0.531734i	$-0.821541\pi$
$631$	−26848.0			−1.69382			−0.846911	+	0.531734i	$0.821541\pi$
$632$	640.000	−	1108.51i	0.0402814	−	0.0697694i
$633$	−10672.0	−	18484.4i	−0.670101	−	1.16065i
$634$	−10326.0	−	17885.2i	−0.646842	−	1.12036i
$635$	310.000	−	536.936i	0.0193732	−	0.0335553i
$636$	−7104.00			−0.442912
$637$		0			0
$638$	−2160.00			−0.134036
$639$	−7992.00	+	13842.6i	−0.494771	+	0.856968i
$640$	−320.000	−	554.256i	−0.0197642	−	0.0342327i
$641$	−13161.0	−	22795.5i	−0.810965	−	1.40463i	−0.912190	−	0.409768i	$-0.865610\pi$
$641$	−13161.0	−	22795.5i	−0.810965	−	1.40463i	0.101225	−	0.994864i	$-0.467724\pi$
$642$	−192.000	+	332.554i	−0.0118032	+	0.0204437i
$643$	−10168.0			−0.623619			−0.311809	−	0.950145i	$-0.600935\pi$
$643$	−10168.0			−0.623619			−0.311809	+	0.950145i	$0.600935\pi$
$644$		0			0
$645$	−1280.00			−0.0781395
$646$	6600.00	−	11431.5i	0.401971	−	0.696235i
$647$	11802.0	+	20441.7i	0.717132	+	1.24211i	0.962131	+	0.272586i	$0.0878789\pi$
$647$	11802.0	+	20441.7i	0.717132	+	1.24211i	−0.244999	+	0.969523i	$0.578788\pi$
$648$	1436.00	+	2487.22i	0.0870546	+	0.150783i
$649$	−2520.00	+	4364.77i	−0.152417	+	0.263994i
$650$	−2900.00			−0.174996
$651$		0			0
$652$	−2272.00			−0.136470
$653$	−8211.00	+	14221.9i	−0.492069	+	0.852289i	−0.999958	−	0.00913349i	$-0.997093\pi$
$653$	−8211.00	+	14221.9i	−0.492069	+	0.852289i	0.507889	+	0.861423i	$0.330426\pi$
$654$	7600.00	+	13163.6i	0.454409	+	0.787060i
$655$	−330.000	−	571.577i	−0.0196858	−	0.0340967i
$656$	3504.00	−	6069.11i	0.208549	−	0.361218i
$657$	13394.0			0.795357
$658$		0			0
$659$	−26100.0			−1.54281			−0.771405	−	0.636345i	$-0.780446\pi$
$659$	−26100.0			−1.54281			−0.771405	+	0.636345i	$0.780446\pi$
$660$	960.000	−	1662.77i	0.0566181	−	0.0980654i
$661$	1529.00	+	2648.31i	0.0899716	+	0.155835i	0.907499	−	0.420055i	$-0.137989\pi$
$661$	1529.00	+	2648.31i	0.0899716	+	0.155835i	−0.817527	+	0.575890i	$0.804656\pi$
$662$	4228.00	+	7323.11i	0.248226	+	0.429941i
$663$	−15312.0	+	26521.2i	−0.896936	+	1.55354i
$664$	576.000			0.0336644
$665$		0			0
$666$	−2516.00			−0.146386
$667$	5940.00	−	10288.4i	0.344824	−	0.597253i
$668$	3048.00	+	5279.29i	0.176543	+	0.305781i
$669$	7088.00	+	12276.8i	0.409623	+	0.709488i
$670$	5120.00	−	8868.10i	0.295228	−	0.511350i
$671$	10824.0			0.622736
$672$		0			0
$673$	10802.0			0.618702			0.309351	−	0.950948i	$-0.399888\pi$
$673$	10802.0			0.618702			0.309351	+	0.950948i	$0.399888\pi$
$674$	−1106.00	+	1915.65i	−0.0632070	+	0.109478i
$675$	1000.00	+	1732.05i	0.0570222	+	0.0987654i
$676$	−2334.00	−	4042.61i	−0.132795	−	0.230007i
$677$	5337.00	−	9243.96i	0.302980	−	0.524777i	−0.673829	−	0.738887i	$-0.735352\pi$
$677$	5337.00	−	9243.96i	0.302980	−	0.524777i	0.976810	+	0.214110i	$0.0686851\pi$
$678$	16608.0			0.940747
$679$		0			0
$680$	2640.00			0.148881
$681$	−11136.0	+	19288.1i	−0.626626	+	1.08535i
$682$	−1824.00	−	3159.26i	−0.102411	−	0.177382i
$683$	14304.0	+	24775.3i	0.801358	+	1.38799i	0.918723	+	0.394903i	$0.129222\pi$
$683$	14304.0	+	24775.3i	0.801358	+	1.38799i	−0.117365	+	0.993089i	$0.537445\pi$
$684$	7400.00	−	12817.2i	0.413664	−	0.716487i
$685$	−6270.00			−0.349729
$686$		0			0
$687$	−2800.00			−0.155497
$688$	−256.000	+	443.405i	−0.0141859	+	0.0245707i
$689$	6438.00	+	11150.9i	0.355977	+	0.616571i
$690$	5280.00	+	9145.23i	0.291313	+	0.504569i
$691$	1214.00	−	2102.71i	0.0668346	−	0.115761i	−0.830672	−	0.556763i	$-0.812043\pi$
$691$	1214.00	−	2102.71i	0.0668346	−	0.115761i	0.897506	+	0.441002i	$0.145377\pi$
$692$	14808.0			0.813462
$693$		0			0
$694$	18672.0			1.02130
$695$	7150.00	−	12384.2i	0.390237	−	0.675911i
$696$	−2880.00	−	4988.31i	−0.156848	−	0.271668i
$697$	14454.0	+	25035.1i	0.785487	+	1.36050i
$698$	11770.0	−	20386.2i	0.638254	−	1.10549i
$699$	−15696.0			−0.849324
$700$		0			0
$701$	−6618.00			−0.356574			−0.178287	−	0.983979i	$-0.557056\pi$
$701$	−6618.00			−0.356574			−0.178287	+	0.983979i	$0.557056\pi$
$702$	−4640.00	+	8036.72i	−0.249467	+	0.432089i
$703$	−1700.00	−	2944.49i	−0.0912044	−	0.157971i
$704$	−384.000	−	665.108i	−0.0205576	−	0.0356068i
$705$	−4080.00	+	7066.77i	−0.217960	+	0.377518i
$706$	16644.0			0.887259
$707$		0			0
$708$	−13440.0			−0.713427
$709$	−10255.0	+	17762.2i	−0.543208	+	0.940864i	0.455509	+	0.890231i	$0.349457\pi$
$709$	−10255.0	+	17762.2i	−0.543208	+	0.940864i	−0.998717	+	0.0506331i	$0.983876\pi$
$710$	−2160.00	−	3741.23i	−0.114174	−	0.197755i
$711$	2960.00	+	5126.87i	0.156130	+	0.270426i
$712$	−3240.00	+	5611.84i	−0.170540	+	0.295383i
$713$	20064.0			1.05386
$714$		0			0
$715$	−3480.00			−0.182020
$716$	−6360.00	+	11015.8i	−0.331961	+	0.574974i
$717$	−17280.0	−	29929.8i	−0.900047	−	1.55893i
$718$	−10680.0	−	18498.3i	−0.555117	−	0.961491i
$719$	−15840.0	+	27435.7i	−0.821603	+	1.42306i	0.0828856	+	0.996559i	$0.473586\pi$
$719$	−15840.0	+	27435.7i	−0.821603	+	1.42306i	−0.904488	+	0.426498i	$0.859747\pi$
$720$	2960.00			0.153212
$721$		0			0
$722$	6282.00			0.323811
$723$	−1912.00	+	3311.68i	−0.0983514	+	0.170350i
$724$	4196.00	+	7267.69i	0.215391	+	0.373068i
$725$	1125.00	+	1948.56i	0.0576296	+	0.0998174i
$726$	−9496.00	+	16447.6i	−0.485440	+	0.840807i
$727$	13196.0			0.673195			0.336597	−	0.941649i	$-0.390724\pi$
$727$	13196.0			0.673195			0.336597	+	0.941649i	$0.390724\pi$
$728$		0			0
$729$	−30563.0			−1.55276
$730$	−1810.00	+	3135.01i	−0.0917686	+	0.158948i
$731$	−1056.00	−	1829.05i	−0.0534303	−	0.0925440i
$732$	14432.0	+	24997.0i	0.728719	+	1.26218i
$733$	−4051.00	+	7016.54i	−0.204130	+	0.353563i	−0.949855	−	0.312690i	$-0.898770\pi$
$733$	−4051.00	+	7016.54i	−0.204130	+	0.353563i	0.745725	+	0.666253i	$0.232103\pi$
$734$	−11768.0			−0.591778
$735$		0			0
$736$	4224.00			0.211547
$737$	6144.00	−	10641.7i	0.307079	−	0.531876i
$738$	16206.0	+	28069.6i	0.808335	+	1.40008i
$739$	6290.00	+	10894.6i	0.313101	+	0.542306i	0.979032	−	0.203707i	$-0.0652989\pi$
$739$	6290.00	+	10894.6i	0.313101	+	0.542306i	−0.665931	+	0.746013i	$0.731966\pi$
$740$	340.000	−	588.897i	0.0168901	−	0.0292545i
$741$	−46400.0			−2.30033
$742$		0			0
$743$	29892.0			1.47595			0.737975	−	0.674828i	$-0.235782\pi$
$743$	29892.0			1.47595			0.737975	+	0.674828i	$0.235782\pi$
$744$	4864.00	−	8424.70i	0.239681	−	0.415140i
$745$	−1875.00	−	3247.60i	−0.0922076	−	0.159708i
$746$	2098.00	+	3633.84i	0.102967	+	0.178344i
$747$	−1332.00	+	2307.09i	−0.0652414	+	0.113001i
$748$	3168.00			0.154858
$749$		0			0
$750$	−2000.00			−0.0973729
$751$	20204.0	−	34994.4i	0.981697	−	1.70035i	0.325914	−	0.945399i	$-0.394328\pi$
$751$	20204.0	−	34994.4i	0.981697	−	1.70035i	0.655783	−	0.754950i	$-0.272339\pi$
$752$	1632.00	+	2826.71i	0.0791395	+	0.137074i
$753$	10608.0	+	18373.6i	0.513382	+	0.889205i
$754$	−5220.00	+	9041.31i	−0.252124	+	0.436691i
$755$	−2240.00			−0.107976
$756$		0			0
$757$	32366.0			1.55398			0.776990	−	0.629513i	$-0.216746\pi$
$757$	32366.0			1.55398			0.776990	+	0.629513i	$0.216746\pi$
$758$	−3860.00	+	6685.72i	−0.184962	+	0.320364i
$759$	6336.00	+	10974.3i	0.303007	+	0.524823i
$760$	2000.00	+	3464.10i	0.0954574	+	0.165337i
$761$	8619.00	−	14928.5i	0.410563	−	0.711116i	−0.584388	−	0.811474i	$-0.698665\pi$
$761$	8619.00	−	14928.5i	0.410563	−	0.711116i	0.994951	+	0.100358i	$0.0319988\pi$
$762$	1984.00			0.0943212
$763$		0			0
$764$	17568.0			0.831921
$765$	−6105.00	+	10574.2i	−0.288532	+	0.499752i
$766$	9588.00	+	16606.9i	0.452257	+	0.783331i
$767$	12180.0	+	21096.4i	0.573395	+	0.993150i
$768$	1024.00	−	1773.62i	0.0481125	−	0.0833333i
$769$	10850.0			0.508792			0.254396	−	0.967100i	$-0.418123\pi$
$769$	10850.0			0.508792			0.254396	+	0.967100i	$0.418123\pi$
$770$		0			0
$771$	18672.0			0.872186
$772$	4316.00	−	7475.53i	0.201213	−	0.348511i
$773$	−4551.00	−	7882.56i	−0.211757	−	0.366774i	0.740508	−	0.672048i	$-0.234585\pi$
$773$	−4551.00	−	7882.56i	−0.211757	−	0.366774i	−0.952264	+	0.305274i	$0.901252\pi$
$774$	−1184.00	−	2050.75i	−0.0549845	−	0.0952359i
$775$	−1900.00	+	3290.90i	−0.0880645	+	0.152532i
$776$	8848.00			0.409310
$777$		0			0
$778$	−26820.0			−1.23592
$779$	−21900.0	+	37931.9i	−1.00725	+	1.74461i
$780$	−4640.00	−	8036.72i	−0.212998	−	0.368924i
$781$	−2592.00	−	4489.48i	−0.118757	−	0.205693i
$782$	−8712.00	+	15089.6i	−0.398389	+	0.690031i
$783$	7200.00			0.328617
$784$		0			0
$785$	11230.0			0.510593
$786$	1056.00	−	1829.05i	0.0479215	−	0.0830024i
$787$	12752.0	+	22087.1i	0.577585	+	1.00041i	0.995755	+	0.0920385i	$0.0293383\pi$
$787$	12752.0	+	22087.1i	0.577585	+	1.00041i	−0.418170	+	0.908369i	$0.637328\pi$
$788$	2148.00	+	3720.45i	0.0971058	+	0.168192i
$789$	−15792.0	+	27352.5i	−0.712560	+	1.23419i
$790$	−1600.00			−0.0720575
$791$		0			0
$792$	3552.00			0.159362
$793$	26158.0	−	45307.0i	1.17137	−	2.02888i
$794$	13114.0	+	22714.1i	0.586144	+	1.01523i
$795$	4440.00	+	7690.31i	0.198076	+	0.343078i
$796$	−5680.00	+	9838.05i	−0.252917	+	0.438066i
$797$	14166.0			0.629593			0.314796	−	0.949159i	$-0.398064\pi$
$797$	14166.0			0.629593			0.314796	+	0.949159i	$0.398064\pi$
$798$		0			0
$799$	−13464.0			−0.596148
$800$	−400.000	+	692.820i	−0.0176777	+	0.0306186i
$801$	−14985.0	−	25954.8i	−0.661010	−	1.14490i
$802$	5838.00	+	10111.7i	0.257041	+	0.445208i
$803$	−2172.00	+	3762.01i	−0.0954523	+	0.165328i
$804$	32768.0			1.43736
$805$		0			0
$806$	−17632.0			−0.770547
$807$	6360.00	−	11015.8i	0.277426	−	0.480516i
$808$	1032.00	+	1787.48i	0.0449327	+	0.0778257i
$809$	−16605.0	−	28760.7i	−0.721633	−	1.24990i	−0.960345	−	0.278814i	$-0.910059\pi$
$809$	−16605.0	−	28760.7i	−0.721633	−	1.24990i	0.238713	−	0.971090i	$-0.423275\pi$
$810$	1795.00	−	3109.03i	0.0778640	−	0.134864i
$811$	39212.0			1.69780			0.848902	−	0.528550i	$-0.177264\pi$
$811$	39212.0			1.69780			0.848902	+	0.528550i	$0.177264\pi$
$812$		0			0
$813$	−39616.0			−1.70897
$814$	408.000	−	706.677i	0.0175680	−	0.0304288i
$815$	1420.00	+	2459.51i	0.0610312	+	0.105709i
$816$	4224.00	+	7316.18i	0.181213	+	0.313870i
$817$	1600.00	−	2771.28i	0.0685152	−	0.118672i
$818$	19060.0			0.814691
$819$		0			0
$820$	−8760.00			−0.373064
$821$	−3111.00	+	5388.41i	−0.132247	+	0.229058i	−0.924542	−	0.381079i	$-0.875552\pi$
$821$	−3111.00	+	5388.41i	−0.132247	+	0.229058i	0.792296	+	0.610138i	$0.208886\pi$
$822$	−10032.0	−	17375.9i	−0.425677	−	0.737294i
$823$	−15586.0	−	26995.7i	−0.660138	−	1.14339i	−0.980579	−	0.196124i	$-0.937164\pi$
$823$	−15586.0	−	26995.7i	−0.660138	−	1.14339i	0.320441	−	0.947269i	$-0.396169\pi$
$824$	3952.00	−	6845.06i	0.167081	−	0.289392i
$825$	−2400.00			−0.101282
$826$		0			0
$827$	−264.000			−0.0111006			−0.00555029	−	0.999985i	$-0.501767\pi$
$827$	−264.000			−0.0111006			−0.00555029	+	0.999985i	$0.501767\pi$
$828$	−9768.00	+	16918.7i	−0.409978	+	0.710102i
$829$	14525.0	+	25158.0i	0.608533	+	1.05401i	0.991482	+	0.130241i	$0.0415751\pi$
$829$	14525.0	+	25158.0i	0.608533	+	1.05401i	−0.382949	+	0.923769i	$0.625092\pi$
$830$	−360.000	−	623.538i	−0.0150552	−	0.0260763i
$831$	6584.00	−	11403.8i	0.274845	−	0.476046i
$832$	−3712.00			−0.154676
$833$		0			0
$834$	45760.0			1.89993
$835$	3810.00	−	6599.11i	0.157905	−	0.273499i
$836$	2400.00	+	4156.92i	0.0992892	+	0.171974i
$837$	6080.00	+	10530.9i	0.251082	+	0.434887i
$838$	−7260.00	+	12574.7i	−0.299275	+	0.518360i
$839$	−21720.0			−0.893752			−0.446876	−	0.894596i	$-0.647463\pi$
$839$	−21720.0			−0.893752			−0.446876	+	0.894596i	$0.647463\pi$
$840$		0			0
$841$	−16289.0			−0.667883
$842$	−12062.0	+	20892.0i	−0.493686	+	0.855090i
$843$	−4632.00	−	8022.86i	−0.189246	−	0.327784i
$844$	5336.00	+	9242.22i	0.217622	+	0.376932i
$845$	−2917.50	+	5053.26i	−0.118775	+	0.205725i
$846$	−15096.0			−0.613488
$847$		0			0
$848$	3552.00			0.143840
$849$	27968.0	−	48442.0i	1.13058	−	1.95822i
$850$	−1650.00	−	2857.88i	−0.0665818	−	0.115323i
$851$	2244.00	+	3886.72i	0.0903917	+	0.156563i
$852$	6912.00	−	11971.9i	0.277936	−	0.481399i
$853$	−6658.00			−0.267252			−0.133626	−	0.991032i	$-0.542662\pi$
$853$	−6658.00			−0.267252			−0.133626	+	0.991032i	$0.542662\pi$
$854$		0			0
$855$	−18500.0			−0.739984
$856$	96.0000	−	166.277i	0.00383319	−	0.00663928i
$857$	6987.00	+	12101.8i	0.278496	+	0.482370i	0.971011	−	0.239034i	$-0.0768307\pi$
$857$	6987.00	+	12101.8i	0.278496	+	0.482370i	−0.692515	+	0.721404i	$0.743497\pi$
$858$	−5568.00	−	9644.06i	−0.221548	−	0.383733i
$859$	−11890.0	+	20594.1i	−0.472272	+	0.817999i	−0.999497	−	0.0317270i	$-0.989899\pi$
$859$	−11890.0	+	20594.1i	−0.472272	+	0.817999i	0.527225	+	0.849726i	$0.323233\pi$
$860$	640.000			0.0253765
$861$		0			0
$862$	−27216.0			−1.07538
$863$	6114.00	−	10589.8i	0.241162	−	0.417705i	−0.719883	−	0.694095i	$-0.755805\pi$
$863$	6114.00	−	10589.8i	0.241162	−	0.417705i	0.961046	+	0.276390i	$0.0891381\pi$
$864$	1280.00	+	2217.03i	0.0504010	+	0.0872971i
$865$	−9255.00	−	16030.1i	−0.363791	−	0.630105i
$866$	3838.00	−	6647.61i	0.150601	−	0.260849i
$867$	4456.00			0.174549
$868$		0			0
$869$	−1920.00			−0.0749500
$870$	−3600.00	+	6235.38i	−0.140289	+	0.242988i
$871$	−29696.0	−	51435.0i	−1.15524	−	2.00093i
$872$	−3800.00	−	6581.79i	−0.147574	−	0.255605i
$873$	−20461.0	+	35439.5i	−0.793242	+	1.37393i
$874$	−26400.0			−1.02173
$875$		0			0
$876$	−11584.0			−0.446789
$877$	−5803.00	+	10051.1i	−0.223436	+	0.387003i	−0.955849	−	0.293858i	$-0.905061\pi$
$877$	−5803.00	+	10051.1i	−0.223436	+	0.387003i	0.732413	+	0.680861i	$0.238394\pi$
$878$	−7400.00	−	12817.2i	−0.284440	−	0.492664i
$879$	−1032.00	−	1787.48i	−0.0396001	−	0.0685894i
$880$	−480.000	+	831.384i	−0.0183873	+	0.0318477i
$881$	−32958.0			−1.26037			−0.630183	−	0.776446i	$-0.717020\pi$
$881$	−32958.0			−1.26037			−0.630183	+	0.776446i	$0.717020\pi$
$882$		0			0
$883$	8072.00			0.307638			0.153819	−	0.988099i	$-0.450843\pi$
$883$	8072.00			0.307638			0.153819	+	0.988099i	$0.450843\pi$
$884$	7656.00	−	13260.6i	0.291289	−	0.504527i
$885$	8400.00	+	14549.2i	0.319054	+	0.552618i
$886$	−8352.00	−	14466.1i	−0.316694	−	0.548530i
$887$	−7878.00	+	13645.1i	−0.298216	+	0.516525i	−0.975728	−	0.218987i	$-0.929725\pi$
$887$	−7878.00	+	13645.1i	−0.298216	+	0.516525i	0.677512	+	0.735512i	$0.263058\pi$
$888$	2176.00			0.0822317
$889$		0			0
$890$	8100.00			0.305070
$891$	2154.00	−	3730.84i	0.0809896	−	0.140278i
$892$	−3544.00	−	6138.39i	−0.133029	−	0.230413i
$893$	−10200.0	−	17666.9i	−0.382228	−	0.662039i
$894$	6000.00	−	10392.3i	0.224463	−	0.388782i
$895$	15900.0			0.593831
$896$		0			0
$897$	61248.0			2.27983
$898$	−10770.0	+	18654.2i	−0.400222	+	0.693205i
$899$	6840.00	+	11847.2i	0.253756	+	0.439519i
$900$	−1850.00	−	3204.29i	−0.0685185	−	0.118678i
$901$	−7326.00	+	12689.0i	−0.270882	+	0.469181i
$902$	−10512.0			−0.388039
$903$		0			0
$904$	−8304.00			−0.305517
$905$	5245.00	−	9084.61i	0.192652	−	0.333682i
$906$	−3584.00	−	6207.67i	−0.131424	−	0.227634i
$907$	−9388.00	−	16260.5i	−0.343686	−	0.595282i	0.641428	−	0.767183i	$-0.278342\pi$
$907$	−9388.00	−	16260.5i	−0.343686	−	0.595282i	−0.985114	+	0.171901i	$0.945009\pi$
$908$	5568.00	−	9644.06i	0.203503	−	0.352477i
$909$	−9546.00			−0.348318
$910$		0			0
$911$	−20568.0			−0.748022			−0.374011	−	0.927424i	$-0.622018\pi$
$911$	−20568.0			−0.748022			−0.374011	+	0.927424i	$0.622018\pi$
$912$	−6400.00	+	11085.1i	−0.232374	+	0.402484i
$913$	−432.000	−	748.246i	−0.0156595	−	0.0271230i
$914$	6694.00	+	11594.3i	0.242251	+	0.419592i
$915$	18040.0	−	31246.2i	0.651786	−	1.12893i
$916$	1400.00			0.0504992
$917$		0			0
$918$	−10560.0			−0.379664
$919$	3140.00	−	5438.64i	0.112708	−	0.195217i	−0.804153	−	0.594422i	$-0.797381\pi$
$919$	3140.00	−	5438.64i	0.112708	−	0.195217i	0.916861	+	0.399206i	$0.130714\pi$
$920$	−2640.00	−	4572.61i	−0.0946068	−	0.163864i
$921$	−35776.0	−	61965.8i	−1.27998	−	2.21699i
$922$	3018.00	−	5227.33i	0.107801	−	0.186717i
$923$	−25056.0			−0.893530
$924$		0			0
$925$	−850.000			−0.0302139
$926$	−14492.0	+	25100.9i	−0.514294	+	0.890784i
$927$	18278.0	+	31658.4i	0.647603	+	1.12168i
$928$	1440.00	+	2494.15i	0.0509378	+	0.0882269i
$929$	10215.0	−	17692.9i	0.360757	−	0.624850i	−0.627329	−	0.778755i	$-0.715852\pi$
$929$	10215.0	−	17692.9i	0.360757	−	0.624850i	0.988086	+	0.153905i	$0.0491850\pi$
$930$	−12160.0			−0.428755
$931$		0			0
$932$	7848.00			0.275826
$933$	5568.00	−	9644.06i	0.195378	−	0.338405i
$934$	−7776.00	−	13468.4i	−0.272418	−	0.471842i
$935$	−1980.00	−	3429.46i	−0.0692545	−	0.119952i
$936$	8584.00	−	14867.9i	0.299762	−	0.519202i
$937$	8906.00			0.310508			0.155254	−	0.987875i	$-0.450380\pi$
$937$	8906.00			0.310508			0.155254	+	0.987875i	$0.450380\pi$
$938$		0			0
$939$	47024.0			1.63426
$940$	2040.00	−	3533.38i	0.0707845	−	0.122602i
$941$	8709.00	+	15084.4i	0.301706	+	0.522570i	0.976522	−	0.215416i	$-0.0691106\pi$
$941$	8709.00	+	15084.4i	0.301706	+	0.522570i	−0.674817	+	0.737986i	$0.735777\pi$
$942$	17968.0	+	31121.5i	0.621475	+	1.07643i
$943$	28908.0	−	50070.1i	0.998276	−	1.72906i
$944$	6720.00			0.231692
$945$		0			0
$946$	768.000			0.0263952
$947$	1272.00	−	2203.17i	0.0436478	−	0.0756002i	−0.843376	−	0.537324i	$-0.819435\pi$
$947$	1272.00	−	2203.17i	0.0436478	−	0.0756002i	0.887024	+	0.461723i	$0.152769\pi$
$948$	−2560.00	−	4434.05i	−0.0877056	−	0.151911i
$949$	10498.0	+	18183.1i	0.359093	+	0.621968i
$950$	2500.00	−	4330.13i	0.0853797	−	0.147882i
$951$	−82608.0			−2.81677
$952$		0			0
$953$	15402.0			0.523525			0.261763	−	0.965132i	$-0.415696\pi$
$953$	15402.0			0.523525			0.261763	+	0.965132i	$0.415696\pi$
$954$	−8214.00	+	14227.1i	−0.278761	+	0.482828i
$955$	−10980.0	−	19017.9i	−0.372047	−	0.644404i
$956$	8640.00	+	14964.9i	0.292299	+	0.506276i
$957$	−4320.00	+	7482.46i	−0.145920	+	0.252741i
$958$	−27360.0			−0.922716
$959$		0			0
$960$	−2560.00			−0.0860663
$961$	3343.50	−	5791.11i	0.112232	−	0.194391i
$962$	−1972.00	−	3415.60i	−0.0660913	−	0.114473i
$963$	444.000	+	769.031i	0.0148574	+	0.0257338i
$964$	956.000	−	1655.84i	0.0319405	−	0.0553226i
$965$	−10790.0			−0.359940
$966$		0			0
$967$	−49444.0			−1.64427			−0.822136	−	0.569291i	$-0.807218\pi$
$967$	−49444.0			−1.64427			−0.822136	+	0.569291i	$0.807218\pi$
$968$	4748.00	−	8223.78i	0.157651	−	0.273060i
$969$	−26400.0	−	45726.1i	−0.875222	−	1.51593i
$970$	−5530.00	−	9578.24i	−0.183049	−	0.317050i
$971$	12594.0	−	21813.4i	0.416231	−	0.720934i	−0.579325	−	0.815096i	$-0.696684\pi$
$971$	12594.0	−	21813.4i	0.416231	−	0.720934i	0.995557	+	0.0941624i	$0.0300173\pi$
$972$	20128.0			0.664204
$973$		0			0
$974$	15832.0			0.520832
$975$	−5800.00	+	10045.9i	−0.190511	+	0.329976i
$976$	−7216.00	−	12498.5i	−0.236658	−	0.409904i
$977$	−1473.00	−	2551.31i	−0.0482348	−	0.0835452i	0.840900	−	0.541191i	$-0.182026\pi$
$977$	−1473.00	−	2551.31i	−0.0482348	−	0.0835452i	−0.889135	+	0.457645i	$0.848693\pi$
$978$	−4544.00	+	7870.44i	−0.148570	+	0.257330i
$979$	9720.00			0.317316
$980$		0			0
$981$	35150.0			1.14399
$982$	−13932.0	+	24130.9i	−0.452737	+	0.784164i
$983$	−7506.00	−	13000.8i	−0.243544	−	0.421831i	0.718177	−	0.695861i	$-0.244977\pi$
$983$	−7506.00	−	13000.8i	−0.243544	−	0.421831i	−0.961721	+	0.274029i	$0.911644\pi$
$984$	−14016.0	−	24276.4i	−0.454079	−	0.786488i
$985$	2685.00	−	4650.56i	0.0868540	−	0.150436i
$986$	−11880.0			−0.383708
$987$		0			0
$988$	23200.0			0.747055
$989$	−2112.00	+	3658.09i	−0.0679046	+	0.117614i
$990$	−2220.00	−	3845.15i	−0.0712689	−	0.123441i
$991$	2564.00	+	4440.98i	0.0821878	+	0.142354i	0.904189	−	0.427132i	$-0.140476\pi$
$991$	2564.00	+	4440.98i	0.0821878	+	0.142354i	−0.822002	+	0.569485i	$0.807143\pi$
$992$	−2432.00	+	4212.35i	−0.0778388	+	0.134821i
$993$	33824.0			1.08094
$994$		0			0
$995$	14200.0			0.452432
$996$	1152.00	−	1995.32i	0.0366491	−	0.0634781i
$997$	24857.0	+	43053.6i	0.789598	+	1.36762i	0.926213	+	0.377000i	$0.123044\pi$
$997$	24857.0	+	43053.6i	0.789598	+	1.36762i	−0.136616	+	0.990624i	$0.543623\pi$
$998$	8260.00	+	14306.7i	0.261990	+	0.453779i
$999$	−1360.00	+	2355.59i	−0.0430716	+	0.0746021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.e.i.471.1		2
7.2	even	3		10.4.a.a.1.1	✓	1
7.3	odd	6		490.4.e.a.361.1		2
7.4	even	3	inner	490.4.e.i.361.1		2
7.5	odd	6		490.4.a.o.1.1		1
7.6	odd	2		490.4.e.a.471.1		2
21.2	odd	6		90.4.a.a.1.1		1
28.23	odd	6		80.4.a.f.1.1		1
35.2	odd	12		50.4.b.a.49.2		2
35.9	even	6		50.4.a.c.1.1		1
35.19	odd	6		2450.4.a.b.1.1		1
35.23	odd	12		50.4.b.a.49.1		2
56.37	even	6		320.4.a.m.1.1		1
56.51	odd	6		320.4.a.b.1.1		1
63.2	odd	6		810.4.e.w.271.1		2
63.16	even	3		810.4.e.c.271.1		2
63.23	odd	6		810.4.e.w.541.1		2
63.58	even	3		810.4.e.c.541.1		2
77.65	odd	6		1210.4.a.b.1.1		1
84.23	even	6		720.4.a.j.1.1		1
91.51	even	6		1690.4.a.a.1.1		1
105.2	even	12		450.4.c.d.199.1		2
105.23	even	12		450.4.c.d.199.2		2
105.44	odd	6		450.4.a.q.1.1		1
112.37	even	12		1280.4.d.j.641.2		2
112.51	odd	12		1280.4.d.g.641.2		2
112.93	even	12		1280.4.d.j.641.1		2
112.107	odd	12		1280.4.d.g.641.1		2
140.23	even	12		400.4.c.c.49.2		2
140.79	odd	6		400.4.a.b.1.1		1
140.107	even	12		400.4.c.c.49.1		2
280.149	even	6		1600.4.a.d.1.1		1
280.219	odd	6		1600.4.a.bx.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.4.a.a.1.1	✓	1	7.2	even	3
50.4.a.c.1.1		1	35.9	even	6
50.4.b.a.49.1		2	35.23	odd	12
50.4.b.a.49.2		2	35.2	odd	12
80.4.a.f.1.1		1	28.23	odd	6
90.4.a.a.1.1		1	21.2	odd	6
320.4.a.b.1.1		1	56.51	odd	6
320.4.a.m.1.1		1	56.37	even	6
400.4.a.b.1.1		1	140.79	odd	6
400.4.c.c.49.1		2	140.107	even	12
400.4.c.c.49.2		2	140.23	even	12
450.4.a.q.1.1		1	105.44	odd	6
450.4.c.d.199.1		2	105.2	even	12
450.4.c.d.199.2		2	105.23	even	12
490.4.a.o.1.1		1	7.5	odd	6
490.4.e.a.361.1		2	7.3	odd	6
490.4.e.a.471.1		2	7.6	odd	2
490.4.e.i.361.1		2	7.4	even	3	inner
490.4.e.i.471.1		2	1.1	even	1	trivial
720.4.a.j.1.1		1	84.23	even	6
810.4.e.c.271.1		2	63.16	even	3
810.4.e.c.541.1		2	63.58	even	3
810.4.e.w.271.1		2	63.2	odd	6
810.4.e.w.541.1		2	63.23	odd	6
1210.4.a.b.1.1		1	77.65	odd	6
1280.4.d.g.641.1		2	112.107	odd	12
1280.4.d.g.641.2		2	112.51	odd	12
1280.4.d.j.641.1		2	112.93	even	12
1280.4.d.j.641.2		2	112.37	even	12
1600.4.a.d.1.1		1	280.149	even	6
1600.4.a.bx.1.1		1	280.219	odd	6
1690.4.a.a.1.1		1	91.51	even	6
2450.4.a.b.1.1		1	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -16.0000 q^{6} +8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(4.00000 + 6.92820i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} -16.0000 q^{6} +8.00000 q^{8} +(-18.5000 + 32.0429i) q^{9} +(-5.00000 - 8.66025i) q^{10} +(-6.00000 - 10.3923i) q^{11} +(16.0000 - 27.7128i) q^{12} -58.0000 q^{13} -40.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-33.0000 - 57.1577i) q^{17} +(-37.0000 - 64.0859i) q^{18} +(50.0000 - 86.6025i) q^{19} +20.0000 q^{20} +24.0000 q^{22} +(-66.0000 + 114.315i) q^{23} +(32.0000 + 55.4256i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(58.0000 - 100.459i) q^{26} -80.0000 q^{27} -90.0000 q^{29} +(40.0000 - 69.2820i) q^{30} +(-76.0000 - 131.636i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(48.0000 - 83.1384i) q^{33} +132.000 q^{34} +148.000 q^{36} +(17.0000 - 29.4449i) q^{37} +(100.000 + 173.205i) q^{38} +(-232.000 - 401.836i) q^{39} +(-20.0000 + 34.6410i) q^{40} -438.000 q^{41} +32.0000 q^{43} +(-24.0000 + 41.5692i) q^{44} +(-92.5000 - 160.215i) q^{45} +(-132.000 - 228.631i) q^{46} +(102.000 - 176.669i) q^{47} -128.000 q^{48} +50.0000 q^{50} +(264.000 - 457.261i) q^{51} +(116.000 + 200.918i) q^{52} +(-111.000 - 192.258i) q^{53} +(80.0000 - 138.564i) q^{54} +60.0000 q^{55} +800.000 q^{57} +(90.0000 - 155.885i) q^{58} +(-210.000 - 363.731i) q^{59} +(80.0000 + 138.564i) q^{60} +(-451.000 + 781.155i) q^{61} +304.000 q^{62} +64.0000 q^{64} +(145.000 - 251.147i) q^{65} +(96.0000 + 166.277i) q^{66} +(512.000 + 886.810i) q^{67} +(-132.000 + 228.631i) q^{68} -1056.00 q^{69} +432.000 q^{71} +(-148.000 + 256.344i) q^{72} +(-181.000 - 313.501i) q^{73} +(34.0000 + 58.8897i) q^{74} +(100.000 - 173.205i) q^{75} -400.000 q^{76} +928.000 q^{78} +(80.0000 - 138.564i) q^{79} +(-40.0000 - 69.2820i) q^{80} +(179.500 + 310.903i) q^{81} +(438.000 - 758.638i) q^{82} +72.0000 q^{83} +330.000 q^{85} +(-32.0000 + 55.4256i) q^{86} +(-360.000 - 623.538i) q^{87} +(-48.0000 - 83.1384i) q^{88} +(-405.000 + 701.481i) q^{89} +370.000 q^{90} +528.000 q^{92} +(608.000 - 1053.09i) q^{93} +(204.000 + 353.338i) q^{94} +(250.000 + 433.013i) q^{95} +(128.000 - 221.703i) q^{96} +1106.00 q^{97} +444.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 8 q^{3} - 4 q^{4} - 5 q^{5} - 32 q^{6} + 16 q^{8} - 37 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 8 * q^3 - 4 * q^4 - 5 * q^5 - 32 * q^6 + 16 * q^8 - 37 * q^9	\( 2 q - 2 q^{2} + 8 q^{3} - 4 q^{4} - 5 q^{5} - 32 q^{6} + 16 q^{8} - 37 q^{9} - 10 q^{10} - 12 q^{11} + 32 q^{12} - 116 q^{13} - 80 q^{15} - 16 q^{16} - 66 q^{17} - 74 q^{18} + 100 q^{19} + 40 q^{20} + 48 q^{22} - 132 q^{23} + 64 q^{24} - 25 q^{25} + 116 q^{26} - 160 q^{27} - 180 q^{29} + 80 q^{30} - 152 q^{31} - 32 q^{32} + 96 q^{33} + 264 q^{34} + 296 q^{36} + 34 q^{37} + 200 q^{38} - 464 q^{39} - 40 q^{40} - 876 q^{41} + 64 q^{43} - 48 q^{44} - 185 q^{45} - 264 q^{46} + 204 q^{47} - 256 q^{48} + 100 q^{50} + 528 q^{51} + 232 q^{52} - 222 q^{53} + 160 q^{54} + 120 q^{55} + 1600 q^{57} + 180 q^{58} - 420 q^{59} + 160 q^{60} - 902 q^{61} + 608 q^{62} + 128 q^{64} + 290 q^{65} + 192 q^{66} + 1024 q^{67} - 264 q^{68} - 2112 q^{69} + 864 q^{71} - 296 q^{72} - 362 q^{73} + 68 q^{74} + 200 q^{75} - 800 q^{76} + 1856 q^{78} + 160 q^{79} - 80 q^{80} + 359 q^{81} + 876 q^{82} + 144 q^{83} + 660 q^{85} - 64 q^{86} - 720 q^{87} - 96 q^{88} - 810 q^{89} + 740 q^{90} + 1056 q^{92} + 1216 q^{93} + 408 q^{94} + 500 q^{95} + 256 q^{96} + 2212 q^{97} + 888 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 8 * q^3 - 4 * q^4 - 5 * q^5 - 32 * q^6 + 16 * q^8 - 37 * q^9 - 10 * q^10 - 12 * q^11 + 32 * q^12 - 116 * q^13 - 80 * q^15 - 16 * q^16 - 66 * q^17 - 74 * q^18 + 100 * q^19 + 40 * q^20 + 48 * q^22 - 132 * q^23 + 64 * q^24 - 25 * q^25 + 116 * q^26 - 160 * q^27 - 180 * q^29 + 80 * q^30 - 152 * q^31 - 32 * q^32 + 96 * q^33 + 264 * q^34 + 296 * q^36 + 34 * q^37 + 200 * q^38 - 464 * q^39 - 40 * q^40 - 876 * q^41 + 64 * q^43 - 48 * q^44 - 185 * q^45 - 264 * q^46 + 204 * q^47 - 256 * q^48 + 100 * q^50 + 528 * q^51 + 232 * q^52 - 222 * q^53 + 160 * q^54 + 120 * q^55 + 1600 * q^57 + 180 * q^58 - 420 * q^59 + 160 * q^60 - 902 * q^61 + 608 * q^62 + 128 * q^64 + 290 * q^65 + 192 * q^66 + 1024 * q^67 - 264 * q^68 - 2112 * q^69 + 864 * q^71 - 296 * q^72 - 362 * q^73 + 68 * q^74 + 200 * q^75 - 800 * q^76 + 1856 * q^78 + 160 * q^79 - 80 * q^80 + 359 * q^81 + 876 * q^82 + 144 * q^83 + 660 * q^85 - 64 * q^86 - 720 * q^87 - 96 * q^88 - 810 * q^89 + 740 * q^90 + 1056 * q^92 + 1216 * q^93 + 408 * q^94 + 500 * q^95 + 256 * q^96 + 2212 * q^97 + 888 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more