LMFDB - Embedded newform 490.4.c.a.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(99,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.c (of order $2$, degree $1$, 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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.a.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -7.00000i q^{3} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +14.0000 q^{6} -8.00000i q^{8} -22.0000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -7.00000i q^{3} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +14.0000 q^{6} -8.00000i q^{8} -22.0000 q^{9} +(10.0000 - 20.0000i) q^{10} -37.0000 q^{11} +28.0000i q^{12} +51.0000i q^{13} +(-35.0000 + 70.0000i) q^{15} +16.0000 q^{16} -41.0000i q^{17} -44.0000i q^{18} -108.000 q^{19} +(40.0000 + 20.0000i) q^{20} -74.0000i q^{22} +70.0000i q^{23} -56.0000 q^{24} +(75.0000 + 100.000i) q^{25} -102.000 q^{26} -35.0000i q^{27} +249.000 q^{29} +(-140.000 - 70.0000i) q^{30} +134.000 q^{31} +32.0000i q^{32} +259.000i q^{33} +82.0000 q^{34} +88.0000 q^{36} -334.000i q^{37} -216.000i q^{38} +357.000 q^{39} +(-40.0000 + 80.0000i) q^{40} -206.000 q^{41} +376.000i q^{43} +148.000 q^{44} +(220.000 + 110.000i) q^{45} -140.000 q^{46} +287.000i q^{47} -112.000i q^{48} +(-200.000 + 150.000i) q^{50} -287.000 q^{51} -204.000i q^{52} +6.00000i q^{53} +70.0000 q^{54} +(370.000 + 185.000i) q^{55} +756.000i q^{57} +498.000i q^{58} -2.00000 q^{59} +(140.000 - 280.000i) q^{60} +940.000 q^{61} +268.000i q^{62} -64.0000 q^{64} +(255.000 - 510.000i) q^{65} -518.000 q^{66} +106.000i q^{67} +164.000i q^{68} +490.000 q^{69} +456.000 q^{71} +176.000i q^{72} +650.000i q^{73} +668.000 q^{74} +(700.000 - 525.000i) q^{75} +432.000 q^{76} +714.000i q^{78} +1239.00 q^{79} +(-160.000 - 80.0000i) q^{80} -839.000 q^{81} -412.000i q^{82} +428.000i q^{83} +(-205.000 + 410.000i) q^{85} -752.000 q^{86} -1743.00i q^{87} +296.000i q^{88} -220.000 q^{89} +(-220.000 + 440.000i) q^{90} -280.000i q^{92} -938.000i q^{93} -574.000 q^{94} +(1080.00 + 540.000i) q^{95} +224.000 q^{96} +1055.00i q^{97} +814.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} - 20 q^{5} + 28 q^{6} - 44 q^{9}+O(q^{10}) $ 2 * q - 8 * q^4 - 20 * q^5 + 28 * q^6 - 44 * q^9	$ 2 q - 8 q^{4} - 20 q^{5} + 28 q^{6} - 44 q^{9} + 20 q^{10} - 74 q^{11} - 70 q^{15} + 32 q^{16} - 216 q^{19} + 80 q^{20} - 112 q^{24} + 150 q^{25} - 204 q^{26} + 498 q^{29} - 280 q^{30} + 268 q^{31} + 164 q^{34} + 176 q^{36} + 714 q^{39} - 80 q^{40} - 412 q^{41} + 296 q^{44} + 440 q^{45} - 280 q^{46} - 400 q^{50} - 574 q^{51} + 140 q^{54} + 740 q^{55} - 4 q^{59} + 280 q^{60} + 1880 q^{61} - 128 q^{64} + 510 q^{65} - 1036 q^{66} + 980 q^{69} + 912 q^{71} + 1336 q^{74} + 1400 q^{75} + 864 q^{76} + 2478 q^{79} - 320 q^{80} - 1678 q^{81} - 410 q^{85} - 1504 q^{86} - 440 q^{89} - 440 q^{90} - 1148 q^{94} + 2160 q^{95} + 448 q^{96} + 1628 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 - 20 * q^5 + 28 * q^6 - 44 * q^9 + 20 * q^10 - 74 * q^11 - 70 * q^15 + 32 * q^16 - 216 * q^19 + 80 * q^20 - 112 * q^24 + 150 * q^25 - 204 * q^26 + 498 * q^29 - 280 * q^30 + 268 * q^31 + 164 * q^34 + 176 * q^36 + 714 * q^39 - 80 * q^40 - 412 * q^41 + 296 * q^44 + 440 * q^45 - 280 * q^46 - 400 * q^50 - 574 * q^51 + 140 * q^54 + 740 * q^55 - 4 * q^59 + 280 * q^60 + 1880 * q^61 - 128 * q^64 + 510 * q^65 - 1036 * q^66 + 980 * q^69 + 912 * q^71 + 1336 * q^74 + 1400 * q^75 + 864 * q^76 + 2478 * q^79 - 320 * q^80 - 1678 * q^81 - 410 * q^85 - 1504 * q^86 - 440 * q^89 - 440 * q^90 - 1148 * q^94 + 2160 * q^95 + 448 * q^96 + 1628 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	7.00000i		−	1.34715i	−0.739119	−	0.673575i	$-0.764758\pi$
$3$		−	7.00000i		−	1.34715i	0.739119	−	0.673575i	$-0.235242\pi$
$4$	−4.00000			−0.500000
$5$	−10.0000	−	5.00000i	−0.894427	−	0.447214i
$5$	−10.0000	−	5.00000i	−0.894427	−	0.447214i
$6$	14.0000			0.952579
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	−22.0000			−0.814815
$10$	10.0000	−	20.0000i	0.316228	−	0.632456i
$11$	−37.0000			−1.01417			−0.507087	−	0.861895i	$-0.669278\pi$
$11$	−37.0000			−1.01417			−0.507087	+	0.861895i	$0.669278\pi$
$12$			28.0000i			0.673575i
$13$			51.0000i			1.08807i	0.839064	+	0.544033i	$0.183103\pi$
$13$			51.0000i			1.08807i	−0.839064	+	0.544033i	$0.816897\pi$
$14$		0			0
$15$	−35.0000	+	70.0000i	−0.602464	+	1.20493i
$16$	16.0000			0.250000
$17$		−	41.0000i		−	0.584939i	−0.956275	−	0.292469i	$-0.905523\pi$
$17$		−	41.0000i		−	0.584939i	0.956275	−	0.292469i	$-0.0944770\pi$
$18$		−	44.0000i		−	0.576161i
$19$	−108.000			−1.30405			−0.652024	−	0.758199i	$-0.726080\pi$
$19$	−108.000			−1.30405			−0.652024	+	0.758199i	$0.726080\pi$
$20$	40.0000	+	20.0000i	0.447214	+	0.223607i
$21$		0			0
$22$		−	74.0000i		−	0.717130i
$23$			70.0000i			0.634609i	0.948324	+	0.317305i	$0.102778\pi$
$23$			70.0000i			0.634609i	−0.948324	+	0.317305i	$0.897222\pi$
$24$	−56.0000			−0.476290
$25$	75.0000	+	100.000i	0.600000	+	0.800000i
$26$	−102.000			−0.769379
$27$		−	35.0000i		−	0.249472i
$28$		0			0
$29$	249.000			1.59442			0.797209	−	0.603703i	$-0.206309\pi$
$29$	249.000			1.59442			0.797209	+	0.603703i	$0.206309\pi$
$30$	−140.000	−	70.0000i	−0.852013	−	0.426006i
$31$	134.000			0.776358			0.388179	−	0.921584i	$-0.373104\pi$
$31$	134.000			0.776358			0.388179	+	0.921584i	$0.373104\pi$
$32$			32.0000i			0.176777i
$33$			259.000i			1.36625i
$34$	82.0000			0.413614
$35$		0			0
$36$	88.0000			0.407407
$37$		−	334.000i		−	1.48403i	−0.670381	−	0.742017i	$-0.733869\pi$
$37$		−	334.000i		−	1.48403i	0.670381	−	0.742017i	$-0.266131\pi$
$38$		−	216.000i		−	0.922101i
$39$	357.000			1.46579
$40$	−40.0000	+	80.0000i	−0.158114	+	0.316228i
$41$	−206.000			−0.784678			−0.392339	−	0.919821i	$-0.628334\pi$
$41$	−206.000			−0.784678			−0.392339	+	0.919821i	$0.628334\pi$
$42$		0			0
$43$			376.000i			1.33348i	0.745292	+	0.666738i	$0.232310\pi$
$43$			376.000i			1.33348i	−0.745292	+	0.666738i	$0.767690\pi$
$44$	148.000			0.507087
$45$	220.000	+	110.000i	0.728793	+	0.364396i
$46$	−140.000			−0.448736
$47$			287.000i			0.890708i	0.895355	+	0.445354i	$0.146922\pi$
$47$			287.000i			0.890708i	−0.895355	+	0.445354i	$0.853078\pi$
$48$		−	112.000i		−	0.336788i
$49$		0			0
$50$	−200.000	+	150.000i	−0.565685	+	0.424264i
$51$	−287.000			−0.788001
$52$		−	204.000i		−	0.544033i
$53$			6.00000i			0.0155503i	0.999970	+	0.00777513i	$0.00247492\pi$
$53$			6.00000i			0.0155503i	−0.999970	+	0.00777513i	$0.997525\pi$
$54$	70.0000			0.176404
$55$	370.000	+	185.000i	0.907105	+	0.453553i
$56$		0			0
$57$			756.000i			1.75675i
$58$			498.000i			1.12742i
$59$	−2.00000			−0.00441318			−0.00220659	−	0.999998i	$-0.500702\pi$
$59$	−2.00000			−0.00441318			−0.00220659	+	0.999998i	$0.500702\pi$
$60$	140.000	−	280.000i	0.301232	−	0.602464i
$61$	940.000			1.97303			0.986514	−	0.163679i	$-0.0523361\pi$
$61$	940.000			1.97303			0.986514	+	0.163679i	$0.0523361\pi$
$62$			268.000i			0.548968i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	255.000	−	510.000i	0.486598	−	0.973196i
$66$	−518.000			−0.966082
$67$			106.000i			0.193283i	0.995319	+	0.0966415i	$0.0308100\pi$
$67$			106.000i			0.193283i	−0.995319	+	0.0966415i	$0.969190\pi$
$68$			164.000i			0.292469i
$69$	490.000			0.854914
$70$		0			0
$71$	456.000			0.762215			0.381107	−	0.924531i	$-0.375543\pi$
$71$	456.000			0.762215			0.381107	+	0.924531i	$0.375543\pi$
$72$			176.000i			0.288081i
$73$			650.000i			1.04215i	0.853512	+	0.521074i	$0.174468\pi$
$73$			650.000i			1.04215i	−0.853512	+	0.521074i	$0.825532\pi$
$74$	668.000			1.04937
$75$	700.000	−	525.000i	1.07772	−	0.808290i
$76$	432.000			0.652024
$77$		0			0
$78$			714.000i			1.03647i
$79$	1239.00			1.76454			0.882268	−	0.470747i	$-0.156016\pi$
$79$	1239.00			1.76454			0.882268	+	0.470747i	$0.156016\pi$
$80$	−160.000	−	80.0000i	−0.223607	−	0.111803i
$81$	−839.000			−1.15089
$82$		−	412.000i		−	0.554851i
$83$			428.000i			0.566013i	0.959118	+	0.283007i	$0.0913319\pi$
$83$			428.000i			0.566013i	−0.959118	+	0.283007i	$0.908668\pi$
$84$		0			0
$85$	−205.000	+	410.000i	−0.261593	+	0.523185i
$86$	−752.000			−0.942910
$87$		−	1743.00i		−	2.14792i
$88$			296.000i			0.358565i
$89$	−220.000			−0.262022			−0.131011	−	0.991381i	$-0.541822\pi$
$89$	−220.000			−0.262022			−0.131011	+	0.991381i	$0.541822\pi$
$90$	−220.000	+	440.000i	−0.257667	+	0.515334i
$91$		0			0
$92$		−	280.000i		−	0.317305i
$93$		−	938.000i		−	1.04587i
$94$	−574.000			−0.629825
$95$	1080.00	+	540.000i	1.16638	+	0.583188i
$96$	224.000			0.238145
$97$			1055.00i			1.10432i	0.833738	+	0.552160i	$0.186196\pi$
$97$			1055.00i			1.10432i	−0.833738	+	0.552160i	$0.813804\pi$
$98$		0			0
$99$	814.000			0.826364
$100$	−300.000	−	400.000i	−0.300000	−	0.400000i
$101$	−1960.00			−1.93096			−0.965482	−	0.260471i	$-0.916122\pi$
$101$	−1960.00			−1.93096			−0.965482	+	0.260471i	$0.916122\pi$
$102$		−	574.000i		−	0.557201i
$103$			1825.00i			1.74585i	0.487854	+	0.872925i	$0.337780\pi$
$103$			1825.00i			1.74585i	−0.487854	+	0.872925i	$0.662220\pi$
$104$	408.000			0.384689
$105$		0			0
$106$	−12.0000			−0.0109957
$107$		−	144.000i		−	0.130103i	−0.997882	−	0.0650514i	$-0.979279\pi$
$107$		−	144.000i		−	0.130103i	0.997882	−	0.0650514i	$-0.0207211\pi$
$108$			140.000i			0.124736i
$109$	−1681.00			−1.47716			−0.738581	−	0.674165i	$-0.764504\pi$
$109$	−1681.00			−1.47716			−0.738581	+	0.674165i	$0.764504\pi$
$110$	−370.000	+	740.000i	−0.320710	+	0.641420i
$111$	−2338.00			−1.99922
$112$		0			0
$113$		−	798.000i		−	0.664332i	−0.943221	−	0.332166i	$-0.892221\pi$
$113$		−	798.000i		−	0.664332i	0.943221	−	0.332166i	$-0.107779\pi$
$114$	−1512.00			−1.24221
$115$	350.000	−	700.000i	0.283806	−	0.567612i
$116$	−996.000			−0.797209
$117$		−	1122.00i		−	0.886572i
$118$		−	4.00000i		−	0.00312059i
$119$		0			0
$120$	560.000	+	280.000i	0.426006	+	0.213003i
$121$	38.0000			0.0285500
$122$			1880.00i			1.39514i
$123$			1442.00i			1.05708i
$124$	−536.000			−0.388179
$125$	−250.000	−	1375.00i	−0.178885	−	0.983870i
$126$		0			0
$127$			434.000i			0.303238i	0.988439	+	0.151619i	$0.0484487\pi$
$127$			434.000i			0.303238i	−0.988439	+	0.151619i	$0.951551\pi$
$128$		−	128.000i		−	0.0883883i
$129$	2632.00			1.79639
$130$	1020.00	+	510.000i	0.688153	+	0.344077i
$131$	1290.00			0.860365			0.430183	−	0.902742i	$-0.358449\pi$
$131$	1290.00			0.860365			0.430183	+	0.902742i	$0.358449\pi$
$132$		−	1036.00i		−	0.683123i
$133$		0			0
$134$	−212.000			−0.136672
$135$	−175.000	+	350.000i	−0.111567	+	0.223135i
$136$	−328.000			−0.206807
$137$			192.000i			0.119735i	0.998206	+	0.0598674i	$0.0190678\pi$
$137$			192.000i			0.119735i	−0.998206	+	0.0598674i	$0.980932\pi$
$138$			980.000i			0.604516i
$139$	1402.00			0.855511			0.427756	−	0.903894i	$-0.359304\pi$
$139$	1402.00			0.855511			0.427756	+	0.903894i	$0.359304\pi$
$140$		0			0
$141$	2009.00			1.19992
$142$			912.000i			0.538967i
$143$		−	1887.00i		−	1.10349i
$144$	−352.000			−0.203704
$145$	−2490.00	−	1245.00i	−1.42609	−	0.713046i
$146$	−1300.00			−0.736909
$147$		0			0
$148$			1336.00i			0.742017i
$149$	302.000			0.166046			0.0830228	−	0.996548i	$-0.473543\pi$
$149$	302.000			0.166046			0.0830228	+	0.996548i	$0.473543\pi$
$150$	1050.00	+	1400.00i	0.571548	+	0.762063i
$151$	−3167.00			−1.70680			−0.853400	−	0.521257i	$-0.825463\pi$
$151$	−3167.00			−1.70680			−0.853400	+	0.521257i	$0.825463\pi$
$152$			864.000i			0.461050i
$153$			902.000i			0.476617i
$154$		0			0
$155$	−1340.00	−	670.000i	−0.694396	−	0.347198i
$156$	−1428.00			−0.732894
$157$			470.000i			0.238918i	0.992839	+	0.119459i	$0.0381160\pi$
$157$			470.000i			0.238918i	−0.992839	+	0.119459i	$0.961884\pi$
$158$			2478.00i			1.24772i
$159$	42.0000			0.0209485
$160$	160.000	−	320.000i	0.0790569	−	0.158114i
$161$		0			0
$162$		−	1678.00i		−	0.813803i
$163$			2390.00i			1.14846i	0.818693	+	0.574231i	$0.194699\pi$
$163$			2390.00i			1.14846i	−0.818693	+	0.574231i	$0.805301\pi$
$164$	824.000			0.392339
$165$	1295.00	−	2590.00i	0.611004	−	1.22201i
$166$	−856.000			−0.400232
$167$			2631.00i			1.21912i	0.792740	+	0.609560i	$0.208654\pi$
$167$			2631.00i			1.21912i	−0.792740	+	0.609560i	$0.791346\pi$
$168$		0			0
$169$	−404.000			−0.183887
$170$	−820.000	−	410.000i	−0.369948	−	0.184974i
$171$	2376.00			1.06256
$172$		−	1504.00i		−	0.666738i
$173$		−	2243.00i		−	0.985735i	−0.870104	−	0.492867i	$-0.835949\pi$
$173$		−	2243.00i		−	0.985735i	0.870104	−	0.492867i	$-0.164051\pi$
$174$	3486.00			1.51881
$175$		0			0
$176$	−592.000			−0.253544
$177$			14.0000i			0.00594522i
$178$		−	440.000i		−	0.185277i
$179$	−52.0000			−0.0217132			−0.0108566	−	0.999941i	$-0.503456\pi$
$179$	−52.0000			−0.0217132			−0.0108566	+	0.999941i	$0.503456\pi$
$180$	−880.000	−	440.000i	−0.364396	−	0.182198i
$181$	−2462.00			−1.01104			−0.505522	−	0.862814i	$-0.668700\pi$
$181$	−2462.00			−1.01104			−0.505522	+	0.862814i	$0.668700\pi$
$182$		0			0
$183$		−	6580.00i		−	2.65797i
$184$	560.000			0.224368
$185$	−1670.00	+	3340.00i	−0.663680	+	1.32736i
$186$	1876.00			0.739543
$187$			1517.00i			0.593230i
$188$		−	1148.00i		−	0.445354i
$189$		0			0
$190$	−1080.00	+	2160.00i	−0.412376	+	0.824752i
$191$	3159.00			1.19674			0.598370	−	0.801220i	$-0.295815\pi$
$191$	3159.00			1.19674			0.598370	+	0.801220i	$0.295815\pi$
$192$			448.000i			0.168394i
$193$		−	2060.00i		−	0.768301i	−0.923271	−	0.384150i	$-0.874494\pi$
$193$		−	2060.00i		−	0.768301i	0.923271	−	0.384150i	$-0.125506\pi$
$194$	−2110.00			−0.780872
$195$	−3570.00	−	1785.00i	−1.31104	−	0.655521i
$196$		0			0
$197$			1738.00i			0.628565i	0.949329	+	0.314283i	$0.101764\pi$
$197$			1738.00i			0.628565i	−0.949329	+	0.314283i	$0.898236\pi$
$198$			1628.00i			0.584328i
$199$	−894.000			−0.318462			−0.159231	−	0.987241i	$-0.550901\pi$
$199$	−894.000			−0.318462			−0.159231	+	0.987241i	$0.550901\pi$
$200$	800.000	−	600.000i	0.282843	−	0.212132i
$201$	742.000			0.260381
$202$		−	3920.00i		−	1.36540i
$203$		0			0
$204$	1148.00			0.394000
$205$	2060.00	+	1030.00i	0.701837	+	0.350919i
$206$	−3650.00			−1.23450
$207$		−	1540.00i		−	0.517089i
$208$			816.000i			0.272016i
$209$	3996.00			1.32253
$210$		0			0
$211$	−4083.00			−1.33216			−0.666079	−	0.745881i	$-0.732029\pi$
$211$	−4083.00			−1.33216			−0.666079	+	0.745881i	$0.732029\pi$
$212$		−	24.0000i		−	0.00777513i
$213$		−	3192.00i		−	1.02682i
$214$	288.000			0.0919966
$215$	1880.00	−	3760.00i	0.596349	−	1.19270i
$216$	−280.000			−0.0882018
$217$		0			0
$218$		−	3362.00i		−	1.04451i
$219$	4550.00			1.40393
$220$	−1480.00	−	740.000i	−0.453553	−	0.226776i
$221$	2091.00			0.636452
$222$		−	4676.00i		−	1.41366i
$223$			377.000i			0.113210i	0.998397	+	0.0566049i	$0.0180275\pi$
$223$			377.000i			0.113210i	−0.998397	+	0.0566049i	$0.981972\pi$
$224$		0			0
$225$	−1650.00	−	2200.00i	−0.488889	−	0.651852i
$226$	1596.00			0.469754
$227$			2551.00i			0.745885i	0.927855	+	0.372942i	$0.121651\pi$
$227$			2551.00i			0.745885i	−0.927855	+	0.372942i	$0.878349\pi$
$228$		−	3024.00i		−	0.878374i
$229$	74.0000			0.0213540			0.0106770	−	0.999943i	$-0.496601\pi$
$229$	74.0000			0.0213540			0.0106770	+	0.999943i	$0.496601\pi$
$230$	1400.00	+	700.000i	0.401362	+	0.200681i
$231$		0			0
$232$		−	1992.00i		−	0.563712i
$233$		−	1888.00i		−	0.530845i	−0.964132	−	0.265423i	$-0.914488\pi$
$233$		−	1888.00i		−	0.530845i	0.964132	−	0.265423i	$-0.0855115\pi$
$234$	2244.00			0.626901
$235$	1435.00	−	2870.00i	0.398337	−	0.796673i
$236$	8.00000			0.00220659
$237$		−	8673.00i		−	2.37710i
$238$		0			0
$239$	−4997.00			−1.35242			−0.676211	−	0.736708i	$-0.736379\pi$
$239$	−4997.00			−1.35242			−0.676211	+	0.736708i	$0.736379\pi$
$240$	−560.000	+	1120.00i	−0.150616	+	0.301232i
$241$	3830.00			1.02370			0.511851	−	0.859074i	$-0.328960\pi$
$241$	3830.00			1.02370			0.511851	+	0.859074i	$0.328960\pi$
$242$			76.0000i			0.0201879i
$243$			4928.00i			1.30095i
$244$	−3760.00			−0.986514
$245$		0			0
$246$	−2884.00			−0.747468
$247$		−	5508.00i		−	1.41889i
$248$		−	1072.00i		−	0.274484i
$249$	2996.00			0.762505
$250$	2750.00	−	500.000i	0.695701	−	0.126491i
$251$	3390.00			0.852490			0.426245	−	0.904608i	$-0.359836\pi$
$251$	3390.00			0.852490			0.426245	+	0.904608i	$0.359836\pi$
$252$		0			0
$253$		−	2590.00i		−	0.643604i
$254$	−868.000			−0.214422
$255$	2870.00	+	1435.00i	0.704809	+	0.352405i
$256$	256.000			0.0625000
$257$		−	7170.00i		−	1.74028i	−0.492803	−	0.870141i	$-0.664028\pi$
$257$		−	7170.00i		−	1.74028i	0.492803	−	0.870141i	$-0.335972\pi$
$258$			5264.00i			1.27024i
$259$		0			0
$260$	−1020.00	+	2040.00i	−0.243299	+	0.486598i
$261$	−5478.00			−1.29916
$262$			2580.00i			0.608370i
$263$			7672.00i			1.79877i	0.437160	+	0.899384i	$0.355984\pi$
$263$			7672.00i			1.79877i	−0.437160	+	0.899384i	$0.644016\pi$
$264$	2072.00			0.483041
$265$	30.0000	−	60.0000i	0.00695428	−	0.0139086i
$266$		0			0
$267$			1540.00i			0.352983i
$268$		−	424.000i		−	0.0966415i
$269$	−54.0000			−0.0122395			−0.00611977	−	0.999981i	$-0.501948\pi$
$269$	−54.0000			−0.0122395			−0.00611977	+	0.999981i	$0.501948\pi$
$270$	−700.000	−	350.000i	−0.157780	−	0.0788901i
$271$	−2932.00			−0.657219			−0.328609	−	0.944466i	$-0.606580\pi$
$271$	−2932.00			−0.657219			−0.328609	+	0.944466i	$0.606580\pi$
$272$		−	656.000i		−	0.146235i
$273$		0			0
$274$	−384.000			−0.0846653
$275$	−2775.00	−	3700.00i	−0.608505	−	0.811340i
$276$	−1960.00			−0.427457
$277$			3254.00i			0.705826i	0.935656	+	0.352913i	$0.114809\pi$
$277$			3254.00i			0.705826i	−0.935656	+	0.352913i	$0.885191\pi$
$278$			2804.00i			0.604938i
$279$	−2948.00			−0.632588
$280$		0			0
$281$	3327.00			0.706307			0.353153	−	0.935565i	$-0.385109\pi$
$281$	3327.00			0.706307			0.353153	+	0.935565i	$0.385109\pi$
$282$			4018.00i			0.848470i
$283$			4627.00i			0.971896i	0.873988	+	0.485948i	$0.161526\pi$
$283$			4627.00i			0.971896i	−0.873988	+	0.485948i	$0.838474\pi$
$284$	−1824.00			−0.381107
$285$	3780.00	−	7560.00i	0.785642	−	1.57128i
$286$	3774.00			0.780284
$287$		0			0
$288$		−	704.000i		−	0.144040i
$289$	3232.00			0.657847
$290$	2490.00	−	4980.00i	0.504199	−	1.00840i
$291$	7385.00			1.48769
$292$		−	2600.00i		−	0.521074i
$293$		−	4083.00i		−	0.814100i	−0.913406	−	0.407050i	$-0.866557\pi$
$293$		−	4083.00i		−	0.814100i	0.913406	−	0.407050i	$-0.133443\pi$
$294$		0			0
$295$	20.0000	+	10.0000i	0.00394727	+	0.00197364i
$296$	−2672.00			−0.524685
$297$			1295.00i			0.253008i
$298$			604.000i			0.117412i
$299$	−3570.00			−0.690496
$300$	−2800.00	+	2100.00i	−0.538860	+	0.404145i
$301$		0			0
$302$		−	6334.00i		−	1.20689i
$303$			13720.0i			2.60130i
$304$	−1728.00			−0.326012
$305$	−9400.00	−	4700.00i	−1.76473	−	0.882365i
$306$	−1804.00			−0.337019
$307$			4089.00i			0.760168i	0.924952	+	0.380084i	$0.124105\pi$
$307$			4089.00i			0.760168i	−0.924952	+	0.380084i	$0.875895\pi$
$308$		0			0
$309$	12775.0			2.35192
$310$	1340.00	−	2680.00i	0.245506	−	0.491012i
$311$	4008.00			0.730781			0.365390	−	0.930854i	$-0.380935\pi$
$311$	4008.00			0.730781			0.365390	+	0.930854i	$0.380935\pi$
$312$		−	2856.00i		−	0.518234i
$313$			7355.00i			1.32821i	0.747640	+	0.664104i	$0.231187\pi$
$313$			7355.00i			1.32821i	−0.747640	+	0.664104i	$0.768813\pi$
$314$	−940.000			−0.168940
$315$		0			0
$316$	−4956.00			−0.882268
$317$		−	1684.00i		−	0.298369i	−0.988809	−	0.149184i	$-0.952335\pi$
$317$		−	1684.00i		−	0.298369i	0.988809	−	0.149184i	$-0.0476648\pi$
$318$			84.0000i			0.0148128i
$319$	−9213.00			−1.61702
$320$	640.000	+	320.000i	0.111803	+	0.0559017i
$321$	−1008.00			−0.175268
$322$		0			0
$323$			4428.00i			0.762788i
$324$	3356.00			0.575446
$325$	−5100.00	+	3825.00i	−0.870453	+	0.652839i
$326$	−4780.00			−0.812085
$327$			11767.0i			1.98996i
$328$			1648.00i			0.277426i
$329$		0			0
$330$	5180.00	+	2590.00i	0.864090	+	0.432045i
$331$	−1460.00			−0.242444			−0.121222	−	0.992625i	$-0.538681\pi$
$331$	−1460.00			−0.242444			−0.121222	+	0.992625i	$0.538681\pi$
$332$		−	1712.00i		−	0.283007i
$333$			7348.00i			1.20921i
$334$	−5262.00			−0.862047
$335$	530.000	−	1060.00i	0.0864388	−	0.172878i
$336$		0			0
$337$			7514.00i			1.21458i	0.794480	+	0.607290i	$0.207744\pi$
$337$			7514.00i			1.21458i	−0.794480	+	0.607290i	$0.792256\pi$
$338$		−	808.000i		−	0.130028i
$339$	−5586.00			−0.894955
$340$	820.000	−	1640.00i	0.130796	−	0.261593i
$341$	−4958.00			−0.787363
$342$			4752.00i			0.751341i
$343$		0			0
$344$	3008.00			0.471455
$345$	−4900.00	−	2450.00i	−0.764658	−	0.382329i
$346$	4486.00			0.697020
$347$		−	2862.00i		−	0.442767i	−0.975187	−	0.221384i	$-0.928943\pi$
$347$		−	2862.00i		−	0.442767i	0.975187	−	0.221384i	$-0.0710573\pi$
$348$			6972.00i			1.07396i
$349$	−6368.00			−0.976708			−0.488354	−	0.872646i	$-0.662403\pi$
$349$	−6368.00			−0.976708			−0.488354	+	0.872646i	$0.662403\pi$
$350$		0			0
$351$	1785.00			0.271442
$352$		−	1184.00i		−	0.179282i
$353$		−	3635.00i		−	0.548078i	−0.961719	−	0.274039i	$-0.911640\pi$
$353$		−	3635.00i		−	0.548078i	0.961719	−	0.274039i	$-0.0883597\pi$
$354$	−28.0000			−0.00420391
$355$	−4560.00	−	2280.00i	−0.681746	−	0.340873i
$356$	880.000			0.131011
$357$		0			0
$358$		−	104.000i		−	0.0153535i
$359$	−7116.00			−1.04615			−0.523075	−	0.852286i	$-0.675215\pi$
$359$	−7116.00			−1.04615			−0.523075	+	0.852286i	$0.675215\pi$
$360$	880.000	−	1760.00i	0.128834	−	0.257667i
$361$	4805.00			0.700539
$362$		−	4924.00i		−	0.714916i
$363$		−	266.000i		−	0.0384611i
$364$		0			0
$365$	3250.00	−	6500.00i	0.466062	−	0.932125i
$366$	13160.0			1.87947
$367$			319.000i			0.0453724i	0.999743	+	0.0226862i	$0.00722186\pi$
$367$			319.000i			0.0453724i	−0.999743	+	0.0226862i	$0.992778\pi$
$368$			1120.00i			0.158652i
$369$	4532.00			0.639367
$370$	−6680.00	−	3340.00i	−0.938586	−	0.469293i
$371$		0			0
$372$			3752.00i			0.522936i
$373$			11652.0i			1.61747i	0.588171	+	0.808737i	$0.299848\pi$
$373$			11652.0i			1.61747i	−0.588171	+	0.808737i	$0.700152\pi$
$374$	−3034.00			−0.419477
$375$	−9625.00	+	1750.00i	−1.32542	+	0.240986i
$376$	2296.00			0.314913
$377$			12699.0i			1.73483i
$378$		0			0
$379$	−7748.00			−1.05010			−0.525050	−	0.851071i	$-0.675953\pi$
$379$	−7748.00			−1.05010			−0.525050	+	0.851071i	$0.675953\pi$
$380$	−4320.00	−	2160.00i	−0.583188	−	0.291594i
$381$	3038.00			0.408508
$382$			6318.00i			0.846223i
$383$			8680.00i			1.15803i	0.815315	+	0.579017i	$0.196564\pi$
$383$			8680.00i			1.15803i	−0.815315	+	0.579017i	$0.803436\pi$
$384$	−896.000			−0.119072
$385$		0			0
$386$	4120.00			0.543271
$387$		−	8272.00i		−	1.08654i
$388$		−	4220.00i		−	0.552160i
$389$	1711.00			0.223011			0.111505	−	0.993764i	$-0.464433\pi$
$389$	1711.00			0.223011			0.111505	+	0.993764i	$0.464433\pi$
$390$	3570.00	−	7140.00i	0.463523	−	0.927046i
$391$	2870.00			0.371208
$392$		0			0
$393$		−	9030.00i		−	1.15904i
$394$	−3476.00			−0.444463
$395$	−12390.0	−	6195.00i	−1.57825	−	0.789125i
$396$	−3256.00			−0.413182
$397$		−	1589.00i		−	0.200881i	−0.994943	−	0.100440i	$-0.967975\pi$
$397$		−	1589.00i		−	0.200881i	0.994943	−	0.100440i	$-0.0320252\pi$
$398$		−	1788.00i		−	0.225187i
$399$		0			0
$400$	1200.00	+	1600.00i	0.150000	+	0.200000i
$401$	−5147.00			−0.640970			−0.320485	−	0.947254i	$-0.603846\pi$
$401$	−5147.00			−0.640970			−0.320485	+	0.947254i	$0.603846\pi$
$402$			1484.00i			0.184117i
$403$			6834.00i			0.844729i
$404$	7840.00			0.965482
$405$	8390.00	+	4195.00i	1.02939	+	0.514694i
$406$		0			0
$407$			12358.0i			1.50507i
$408$			2296.00i			0.278600i
$409$	−9100.00			−1.10016			−0.550081	−	0.835111i	$-0.685403\pi$
$409$	−9100.00			−1.10016			−0.550081	+	0.835111i	$0.685403\pi$
$410$	−2060.00	+	4120.00i	−0.248137	+	0.496274i
$411$	1344.00			0.161301
$412$		−	7300.00i		−	0.872925i
$413$		0			0
$414$	3080.00			0.365637
$415$	2140.00	−	4280.00i	0.253129	−	0.506258i
$416$	−1632.00			−0.192345
$417$		−	9814.00i		−	1.15250i
$418$			7992.00i			0.935171i
$419$	2618.00			0.305245			0.152623	−	0.988285i	$-0.451228\pi$
$419$	2618.00			0.305245			0.152623	+	0.988285i	$0.451228\pi$
$420$		0			0
$421$	−3695.00			−0.427751			−0.213876	−	0.976861i	$-0.568609\pi$
$421$	−3695.00			−0.427751			−0.213876	+	0.976861i	$0.568609\pi$
$422$		−	8166.00i		−	0.941978i
$423$		−	6314.00i		−	0.725762i
$424$	48.0000			0.00549784
$425$	4100.00	−	3075.00i	0.467951	−	0.350963i
$426$	6384.00			0.726070
$427$		0			0
$428$			576.000i			0.0650514i
$429$	−13209.0			−1.48657
$430$	7520.00	+	3760.00i	0.843364	+	0.421682i
$431$	15779.0			1.76345			0.881726	−	0.471762i	$-0.156382\pi$
$431$	15779.0			1.76345			0.881726	+	0.471762i	$0.156382\pi$
$432$		−	560.000i		−	0.0623681i
$433$			7238.00i			0.803317i	0.915790	+	0.401658i	$0.131566\pi$
$433$			7238.00i			0.803317i	−0.915790	+	0.401658i	$0.868434\pi$
$434$		0			0
$435$	−8715.00	+	17430.0i	−0.960580	+	1.92116i
$436$	6724.00			0.738581
$437$		−	7560.00i		−	0.827560i
$438$			9100.00i			0.992728i
$439$	−2646.00			−0.287669			−0.143834	−	0.989602i	$-0.545943\pi$
$439$	−2646.00			−0.287669			−0.143834	+	0.989602i	$0.545943\pi$
$440$	1480.00	−	2960.00i	0.160355	−	0.320710i
$441$		0			0
$442$			4182.00i			0.450039i
$443$		−	5688.00i		−	0.610034i	−0.952347	−	0.305017i	$-0.901338\pi$
$443$		−	5688.00i		−	0.610034i	0.952347	−	0.305017i	$-0.0986621\pi$
$444$	9352.00			0.999609
$445$	2200.00	+	1100.00i	0.234360	+	0.117180i
$446$	−754.000			−0.0800514
$447$		−	2114.00i		−	0.223689i
$448$		0			0
$449$	3285.00			0.345276			0.172638	−	0.984985i	$-0.444771\pi$
$449$	3285.00			0.345276			0.172638	+	0.984985i	$0.444771\pi$
$450$	4400.00	−	3300.00i	0.460929	−	0.345697i
$451$	7622.00			0.795800
$452$			3192.00i			0.332166i
$453$			22169.0i			2.29932i
$454$	−5102.00			−0.527420
$455$		0			0
$456$	6048.00			0.621104
$457$			14834.0i			1.51839i	0.650862	+	0.759196i	$0.274408\pi$
$457$			14834.0i			1.51839i	−0.650862	+	0.759196i	$0.725592\pi$
$458$			148.000i			0.0150995i
$459$	−1435.00			−0.145926
$460$	−1400.00	+	2800.00i	−0.141903	+	0.283806i
$461$	9972.00			1.00747			0.503734	−	0.863859i	$-0.331959\pi$
$461$	9972.00			1.00747			0.503734	+	0.863859i	$0.331959\pi$
$462$		0			0
$463$			9096.00i			0.913017i	0.889719	+	0.456509i	$0.150900\pi$
$463$			9096.00i			0.913017i	−0.889719	+	0.456509i	$0.849100\pi$
$464$	3984.00			0.398605
$465$	−4690.00	+	9380.00i	−0.467728	+	0.935456i
$466$	3776.00			0.375364
$467$		−	15867.0i		−	1.57224i	−0.618072	−	0.786121i	$-0.712086\pi$
$467$		−	15867.0i		−	1.57224i	0.618072	−	0.786121i	$-0.287914\pi$
$468$			4488.00i			0.443286i
$469$		0			0
$470$	5740.00	+	2870.00i	0.563333	+	0.281666i
$471$	3290.00			0.321858
$472$			16.0000i			0.00156030i
$473$		−	13912.0i		−	1.35238i
$474$	17346.0			1.68086
$475$	−8100.00	−	10800.0i	−0.782428	−	1.04324i
$476$		0			0
$477$		−	132.000i		−	0.0126706i
$478$		−	9994.00i		−	0.956307i
$479$	242.000			0.0230841			0.0115420	−	0.999933i	$-0.496326\pi$
$479$	242.000			0.0230841			0.0115420	+	0.999933i	$0.496326\pi$
$480$	−2240.00	−	1120.00i	−0.213003	−	0.106502i
$481$	17034.0			1.61473
$482$			7660.00i			0.723866i
$483$		0			0
$484$	−152.000			−0.0142750
$485$	5275.00	−	10550.0i	0.493867	−	0.987734i
$486$	−9856.00			−0.919912
$487$		−	3558.00i		−	0.331064i	−0.986204	−	0.165532i	$-0.947066\pi$
$487$		−	3558.00i		−	0.331064i	0.986204	−	0.165532i	$-0.0529342\pi$
$488$		−	7520.00i		−	0.697571i
$489$	16730.0			1.54715
$490$		0			0
$491$	1473.00			0.135388			0.0676941	−	0.997706i	$-0.478436\pi$
$491$	1473.00			0.135388			0.0676941	+	0.997706i	$0.478436\pi$
$492$		−	5768.00i		−	0.528540i
$493$		−	10209.0i		−	0.932637i
$494$	11016.0			1.00331
$495$	−8140.00	−	4070.00i	−0.739123	−	0.369561i
$496$	2144.00			0.194090
$497$		0			0
$498$			5992.00i			0.539173i
$499$	−603.000			−0.0540962			−0.0270481	−	0.999634i	$-0.508611\pi$
$499$	−603.000			−0.0540962			−0.0270481	+	0.999634i	$0.508611\pi$
$500$	1000.00	+	5500.00i	0.0894427	+	0.491935i
$501$	18417.0			1.64234
$502$			6780.00i			0.602801i
$503$			18387.0i			1.62989i	0.579537	+	0.814946i	$0.303234\pi$
$503$			18387.0i			1.62989i	−0.579537	+	0.814946i	$0.696766\pi$
$504$		0			0
$505$	19600.0	+	9800.00i	1.72711	+	0.863553i
$506$	5180.00			0.455097
$507$			2828.00i			0.247724i
$508$		−	1736.00i		−	0.151619i
$509$	9018.00			0.785296			0.392648	−	0.919689i	$-0.371559\pi$
$509$	9018.00			0.785296			0.392648	+	0.919689i	$0.371559\pi$
$510$	−2870.00	+	5740.00i	−0.249188	+	0.498375i
$511$		0			0
$512$			512.000i			0.0441942i
$513$			3780.00i			0.325324i
$514$	14340.0			1.23056
$515$	9125.00	−	18250.0i	0.780768	−	1.56154i
$516$	−10528.0			−0.898196
$517$		−	10619.0i		−	0.903333i
$518$		0			0
$519$	−15701.0			−1.32793
$520$	−4080.00	−	2040.00i	−0.344077	−	0.172038i
$521$	−4624.00			−0.388831			−0.194416	−	0.980919i	$-0.562281\pi$
$521$	−4624.00			−0.388831			−0.194416	+	0.980919i	$0.562281\pi$
$522$		−	10956.0i		−	0.918642i
$523$		−	5876.00i		−	0.491280i	−0.969361	−	0.245640i	$-0.921002\pi$
$523$		−	5876.00i		−	0.491280i	0.969361	−	0.245640i	$-0.0789981\pi$
$524$	−5160.00			−0.430183
$525$		0			0
$526$	−15344.0			−1.27192
$527$		−	5494.00i		−	0.454122i
$528$			4144.00i			0.341561i
$529$	7267.00			0.597271
$530$	120.000	+	60.0000i	0.00983484	+	0.00491742i
$531$	44.0000			0.00359593
$532$		0			0
$533$		−	10506.0i		−	0.853781i
$534$	−3080.00			−0.249597
$535$	−720.000	+	1440.00i	−0.0581838	+	0.116368i
$536$	848.000			0.0683359
$537$			364.000i			0.0292509i
$538$		−	108.000i		−	0.00865467i
$539$		0			0
$540$	700.000	−	1400.00i	0.0557837	−	0.111567i
$541$	−8537.00			−0.678437			−0.339218	−	0.940708i	$-0.610163\pi$
$541$	−8537.00			−0.678437			−0.339218	+	0.940708i	$0.610163\pi$
$542$		−	5864.00i		−	0.464724i
$543$			17234.0i			1.36203i
$544$	1312.00			0.103404
$545$	16810.0	+	8405.00i	1.32121	+	0.660607i
$546$		0			0
$547$		−	13060.0i		−	1.02085i	−0.859922	−	0.510425i	$-0.829488\pi$
$547$		−	13060.0i		−	1.02085i	0.859922	−	0.510425i	$-0.170512\pi$
$548$		−	768.000i		−	0.0598674i
$549$	−20680.0			−1.60765
$550$	7400.00	−	5550.00i	0.573704	−	0.430278i
$551$	−26892.0			−2.07920
$552$		−	3920.00i		−	0.302258i
$553$		0			0
$554$	−6508.00			−0.499095
$555$	23380.0	+	11690.0i	1.78815	+	0.894077i
$556$	−5608.00			−0.427756
$557$			21372.0i			1.62578i	0.582416	+	0.812891i	$0.302108\pi$
$557$			21372.0i			1.62578i	−0.582416	+	0.812891i	$0.697892\pi$
$558$		−	5896.00i		−	0.447307i
$559$	−19176.0			−1.45091
$560$		0			0
$561$	10619.0			0.799170
$562$			6654.00i			0.499434i
$563$		−	12704.0i		−	0.950994i	−0.879717	−	0.475497i	$-0.842268\pi$
$563$		−	12704.0i		−	0.950994i	0.879717	−	0.475497i	$-0.157732\pi$
$564$	−8036.00			−0.599959
$565$	−3990.00	+	7980.00i	−0.297098	+	0.594197i
$566$	−9254.00			−0.687234
$567$		0			0
$568$		−	3648.00i		−	0.269484i
$569$	−8762.00			−0.645557			−0.322779	−	0.946474i	$-0.604617\pi$
$569$	−8762.00			−0.645557			−0.322779	+	0.946474i	$0.604617\pi$
$570$	15120.0	+	7560.00i	1.11107	+	0.555533i
$571$	−24764.0			−1.81496			−0.907479	−	0.420097i	$-0.861996\pi$
$571$	−24764.0			−1.81496			−0.907479	+	0.420097i	$0.861996\pi$
$572$			7548.00i			0.551744i
$573$		−	22113.0i		−	1.61219i
$574$		0			0
$575$	−7000.00	+	5250.00i	−0.507687	+	0.380765i
$576$	1408.00			0.101852
$577$		−	1811.00i		−	0.130664i	−0.997864	−	0.0653318i	$-0.979189\pi$
$577$		−	1811.00i		−	0.130664i	0.997864	−	0.0653318i	$-0.0208106\pi$
$578$			6464.00i			0.465168i
$579$	−14420.0			−1.03502
$580$	9960.00	+	4980.00i	0.713046	+	0.356523i
$581$		0			0
$582$			14770.0i			1.05195i
$583$		−	222.000i		−	0.0157707i
$584$	5200.00			0.368455
$585$	−5610.00	+	11220.0i	−0.396487	+	0.792974i
$586$	8166.00			0.575656
$587$		−	10548.0i		−	0.741674i	−0.928698	−	0.370837i	$-0.879071\pi$
$587$		−	10548.0i		−	0.741674i	0.928698	−	0.370837i	$-0.120929\pi$
$588$		0			0
$589$	−14472.0			−1.01241
$590$	−20.0000	+	40.0000i	−0.00139557	+	0.00279114i
$591$	12166.0			0.846772
$592$		−	5344.00i		−	0.371009i
$593$			17439.0i			1.20765i	0.797119	+	0.603823i	$0.206357\pi$
$593$			17439.0i			1.20765i	−0.797119	+	0.603823i	$0.793643\pi$
$594$	−2590.00			−0.178904
$595$		0			0
$596$	−1208.00			−0.0830228
$597$			6258.00i			0.429017i
$598$		−	7140.00i		−	0.488255i
$599$	−2451.00			−0.167187			−0.0835936	−	0.996500i	$-0.526640\pi$
$599$	−2451.00			−0.167187			−0.0835936	+	0.996500i	$0.526640\pi$
$600$	−4200.00	−	5600.00i	−0.285774	−	0.381032i
$601$	7792.00			0.528856			0.264428	−	0.964405i	$-0.414817\pi$
$601$	7792.00			0.528856			0.264428	+	0.964405i	$0.414817\pi$
$602$		0			0
$603$		−	2332.00i		−	0.157490i
$604$	12668.0			0.853400
$605$	−380.000	−	190.000i	−0.0255359	−	0.0127679i
$606$	−27440.0			−1.83940
$607$			1937.00i			0.129523i	0.997901	+	0.0647615i	$0.0206286\pi$
$607$			1937.00i			0.129523i	−0.997901	+	0.0647615i	$0.979371\pi$
$608$		−	3456.00i		−	0.230525i
$609$		0			0
$610$	9400.00	−	18800.0i	0.623926	−	1.24785i
$611$	−14637.0			−0.969148
$612$		−	3608.00i		−	0.238308i
$613$		−	5036.00i		−	0.331814i	−0.986141	−	0.165907i	$-0.946945\pi$
$613$		−	5036.00i		−	0.331814i	0.986141	−	0.165907i	$-0.0530552\pi$
$614$	−8178.00			−0.537520
$615$	7210.00	−	14420.0i	0.472740	−	0.945481i
$616$		0			0
$617$		−	27286.0i		−	1.78038i	−0.455592	−	0.890189i	$-0.650572\pi$
$617$		−	27286.0i		−	1.78038i	0.455592	−	0.890189i	$-0.349428\pi$
$618$			25550.0i			1.66306i
$619$	28538.0			1.85305			0.926526	−	0.376231i	$-0.122780\pi$
$619$	28538.0			1.85305			0.926526	+	0.376231i	$0.122780\pi$
$620$	5360.00	+	2680.00i	0.347198	+	0.173599i
$621$	2450.00			0.158317
$622$			8016.00i			0.516740i
$623$		0			0
$624$	5712.00			0.366447
$625$	−4375.00	+	15000.0i	−0.280000	+	0.960000i
$626$	−14710.0			−0.939185
$627$		−	27972.0i		−	1.78165i
$628$		−	1880.00i		−	0.119459i
$629$	−13694.0			−0.868069
$630$		0			0
$631$	25007.0			1.57768			0.788838	−	0.614602i	$-0.210683\pi$
$631$	25007.0			1.57768			0.788838	+	0.614602i	$0.210683\pi$
$632$		−	9912.00i		−	0.623858i
$633$			28581.0i			1.79462i
$634$	3368.00			0.210978
$635$	2170.00	−	4340.00i	0.135612	−	0.271225i
$636$	−168.000			−0.0104743
$637$		0			0
$638$		−	18426.0i		−	1.14340i
$639$	−10032.0			−0.621064
$640$	−640.000	+	1280.00i	−0.0395285	+	0.0790569i
$641$	−12130.0			−0.747436			−0.373718	−	0.927542i	$-0.621917\pi$
$641$	−12130.0			−0.747436			−0.373718	+	0.927542i	$0.621917\pi$
$642$		−	2016.00i		−	0.123933i
$643$			14385.0i			0.882254i	0.897445	+	0.441127i	$0.145421\pi$
$643$			14385.0i			0.882254i	−0.897445	+	0.441127i	$0.854579\pi$
$644$		0			0
$645$	−26320.0	−	13160.0i	−1.60674	−	0.803371i
$646$	−8856.00			−0.539373
$647$			2208.00i			0.134166i	0.997747	+	0.0670830i	$0.0213692\pi$
$647$			2208.00i			0.134166i	−0.997747	+	0.0670830i	$0.978631\pi$
$648$			6712.00i			0.406902i
$649$	74.0000			0.00447574
$650$	−7650.00	−	10200.0i	−0.461627	−	0.615503i
$651$		0			0
$652$		−	9560.00i		−	0.574231i
$653$		−	22448.0i		−	1.34527i	−0.739977	−	0.672633i	$-0.765163\pi$
$653$		−	22448.0i		−	1.34527i	0.739977	−	0.672633i	$-0.234837\pi$
$654$	−23534.0			−1.40711
$655$	−12900.0	−	6450.00i	−0.769534	−	0.384767i
$656$	−3296.00			−0.196169
$657$		−	14300.0i		−	0.849157i
$658$		0			0
$659$	−8791.00			−0.519649			−0.259825	−	0.965656i	$-0.583665\pi$
$659$	−8791.00			−0.519649			−0.259825	+	0.965656i	$0.583665\pi$
$660$	−5180.00	+	10360.0i	−0.305502	+	0.611004i
$661$	13180.0			0.775556			0.387778	−	0.921753i	$-0.373243\pi$
$661$	13180.0			0.775556			0.387778	+	0.921753i	$0.373243\pi$
$662$		−	2920.00i		−	0.171434i
$663$		−	14637.0i		−	0.857397i
$664$	3424.00			0.200116
$665$		0			0
$666$	−14696.0			−0.855043
$667$			17430.0i			1.01183i
$668$		−	10524.0i		−	0.609560i
$669$	2639.00			0.152511
$670$	2120.00	+	1060.00i	0.122243	+	0.0611215i
$671$	−34780.0			−2.00099
$672$		0			0
$673$			7164.00i			0.410330i	0.978727	+	0.205165i	$0.0657731\pi$
$673$			7164.00i			0.410330i	−0.978727	+	0.205165i	$0.934227\pi$
$674$	−15028.0			−0.858838
$675$	3500.00	−	2625.00i	0.199578	−	0.149683i
$676$	1616.00			0.0919436
$677$		−	12335.0i		−	0.700255i	−0.936702	−	0.350127i	$-0.886138\pi$
$677$		−	12335.0i		−	0.700255i	0.936702	−	0.350127i	$-0.113862\pi$
$678$		−	11172.0i		−	0.632829i
$679$		0			0
$680$	3280.00	+	1640.00i	0.184974	+	0.0924870i
$681$	17857.0			1.00482
$682$		−	9916.00i		−	0.556750i
$683$			15436.0i			0.864776i	0.901688	+	0.432388i	$0.142329\pi$
$683$			15436.0i			0.864776i	−0.901688	+	0.432388i	$0.857671\pi$
$684$	−9504.00			−0.531279
$685$	960.000	−	1920.00i	0.0535470	−	0.107094i
$686$		0			0
$687$		−	518.000i		−	0.0287670i
$688$			6016.00i			0.333369i
$689$	−306.000			−0.0169197
$690$	4900.00	−	9800.00i	0.270348	−	0.540695i
$691$	19184.0			1.05614			0.528071	−	0.849200i	$-0.322916\pi$
$691$	19184.0			1.05614			0.528071	+	0.849200i	$0.322916\pi$
$692$			8972.00i			0.492867i
$693$		0			0
$694$	5724.00			0.313084
$695$	−14020.0	−	7010.00i	−0.765193	−	0.382596i
$696$	−13944.0			−0.759405
$697$			8446.00i			0.458989i
$698$		−	12736.0i		−	0.690637i
$699$	−13216.0			−0.715129
$700$		0			0
$701$	32975.0			1.77667			0.888337	−	0.459192i	$-0.151861\pi$
$701$	32975.0			1.77667			0.888337	+	0.459192i	$0.151861\pi$
$702$			3570.00i			0.191939i
$703$			36072.0i			1.93525i
$704$	2368.00			0.126772
$705$	−20090.0	−	10045.0i	−1.07324	−	0.536619i
$706$	7270.00			0.387550
$707$		0			0
$708$		−	56.0000i		−	0.00297261i
$709$	31497.0			1.66840			0.834199	−	0.551463i	$-0.185930\pi$
$709$	31497.0			1.66840			0.834199	+	0.551463i	$0.185930\pi$
$710$	4560.00	−	9120.00i	0.241033	−	0.482067i
$711$	−27258.0			−1.43777
$712$			1760.00i			0.0926387i
$713$			9380.00i			0.492684i
$714$		0			0
$715$	−9435.00	+	18870.0i	−0.493495	+	0.986990i
$716$	208.000			0.0108566
$717$			34979.0i			1.82192i
$718$		−	14232.0i		−	0.739740i
$719$	−18610.0			−0.965279			−0.482640	−	0.875819i	$-0.660322\pi$
$719$	−18610.0			−0.965279			−0.482640	+	0.875819i	$0.660322\pi$
$720$	3520.00	+	1760.00i	0.182198	+	0.0910991i
$721$		0			0
$722$			9610.00i			0.495356i
$723$		−	26810.0i		−	1.37908i
$724$	9848.00			0.505522
$725$	18675.0	+	24900.0i	0.956651	+	1.27553i
$726$	532.000			0.0271961
$727$			17508.0i			0.893172i	0.894741	+	0.446586i	$0.147360\pi$
$727$			17508.0i			0.893172i	−0.894741	+	0.446586i	$0.852640\pi$
$728$		0			0
$729$	11843.0			0.601687
$730$	13000.0	+	6500.00i	0.659112	+	0.329556i
$731$	15416.0			0.780002
$732$			26320.0i			1.32898i
$733$		−	4685.00i		−	0.236077i	−0.993009	−	0.118038i	$-0.962339\pi$
$733$		−	4685.00i		−	0.236077i	0.993009	−	0.118038i	$-0.0376606\pi$
$734$	−638.000			−0.0320831
$735$		0			0
$736$	−2240.00			−0.112184
$737$		−	3922.00i		−	0.196023i
$738$			9064.00i			0.452101i
$739$	25925.0			1.29048			0.645241	−	0.763979i	$-0.276757\pi$
$739$	25925.0			1.29048			0.645241	+	0.763979i	$0.276757\pi$
$740$	6680.00	−	13360.0i	0.331840	−	0.663680i
$741$	−38556.0			−1.91146
$742$		0			0
$743$		−	25578.0i		−	1.26294i	−0.775400	−	0.631471i	$-0.782452\pi$
$743$		−	25578.0i		−	1.26294i	0.775400	−	0.631471i	$-0.217548\pi$
$744$	−7504.00			−0.369771
$745$	−3020.00	−	1510.00i	−0.148516	−	0.0742579i
$746$	−23304.0			−1.14373
$747$		−	9416.00i		−	0.461196i
$748$		−	6068.00i		−	0.296615i
$749$		0			0
$750$	−3500.00	−	19250.0i	−0.170403	−	0.937214i
$751$	−4291.00			−0.208496			−0.104248	−	0.994551i	$-0.533244\pi$
$751$	−4291.00			−0.208496			−0.104248	+	0.994551i	$0.533244\pi$
$752$			4592.00i			0.222677i
$753$		−	23730.0i		−	1.14843i
$754$	−25398.0			−1.22671
$755$	31670.0	+	15835.0i	1.52661	+	0.763304i
$756$		0			0
$757$		−	31528.0i		−	1.51374i	−0.653563	−	0.756872i	$-0.726726\pi$
$757$		−	31528.0i		−	1.51374i	0.653563	−	0.756872i	$-0.273274\pi$
$758$		−	15496.0i		−	0.742533i
$759$	−18130.0			−0.867032
$760$	4320.00	−	8640.00i	0.206188	−	0.412376i
$761$	23154.0			1.10293			0.551466	−	0.834197i	$-0.314068\pi$
$761$	23154.0			1.10293			0.551466	+	0.834197i	$0.314068\pi$
$762$			6076.00i			0.288859i
$763$		0			0
$764$	−12636.0			−0.598370
$765$	4510.00	−	9020.00i	0.213150	−	0.426299i
$766$	−17360.0			−0.818854
$767$		−	102.000i		−	0.00480183i
$768$		−	1792.00i		−	0.0841969i
$769$	13992.0			0.656131			0.328065	−	0.944655i	$-0.393603\pi$
$769$	13992.0			0.656131			0.328065	+	0.944655i	$0.393603\pi$
$770$		0			0
$771$	−50190.0			−2.34442
$772$			8240.00i			0.384150i
$773$		−	21681.0i		−	1.00881i	−0.863467	−	0.504406i	$-0.831712\pi$
$773$		−	21681.0i		−	1.00881i	0.863467	−	0.504406i	$-0.168288\pi$
$774$	16544.0			0.768297
$775$	10050.0	+	13400.0i	0.465815	+	0.621087i
$776$	8440.00			0.390436
$777$		0			0
$778$			3422.00i			0.157692i
$779$	22248.0			1.02326
$780$	14280.0	+	7140.00i	0.655521	+	0.327760i
$781$	−16872.0			−0.773019
$782$			5740.00i			0.262483i
$783$		−	8715.00i		−	0.397763i
$784$		0			0
$785$	2350.00	−	4700.00i	0.106847	−	0.213695i
$786$	18060.0			0.819566
$787$			16903.0i			0.765600i	0.923831	+	0.382800i	$0.125040\pi$
$787$			16903.0i			0.765600i	−0.923831	+	0.382800i	$0.874960\pi$
$788$		−	6952.00i		−	0.314283i
$789$	53704.0			2.42321
$790$	12390.0	−	24780.0i	0.557995	−	1.11599i
$791$		0			0
$792$		−	6512.00i		−	0.292164i
$793$			47940.0i			2.14678i
$794$	3178.00			0.142044
$795$	−420.000	−	210.000i	−0.0187369	−	0.00936847i
$796$	3576.00			0.159231
$797$		−	18905.0i		−	0.840213i	−0.907475	−	0.420106i	$-0.861993\pi$
$797$		−	18905.0i		−	0.840213i	0.907475	−	0.420106i	$-0.138007\pi$
$798$		0			0
$799$	11767.0			0.521009
$800$	−3200.00	+	2400.00i	−0.141421	+	0.106066i
$801$	4840.00			0.213499
$802$		−	10294.0i		−	0.453234i
$803$		−	24050.0i		−	1.05692i
$804$	−2968.00			−0.130191
$805$		0			0
$806$	−13668.0			−0.597314
$807$			378.000i			0.0164885i
$808$			15680.0i			0.682699i
$809$	5571.00			0.242109			0.121054	−	0.992646i	$-0.461372\pi$
$809$	5571.00			0.242109			0.121054	+	0.992646i	$0.461372\pi$
$810$	−8390.00	+	16780.0i	−0.363944	+	0.727888i
$811$	−10894.0			−0.471689			−0.235845	−	0.971791i	$-0.575786\pi$
$811$	−10894.0			−0.471689			−0.235845	+	0.971791i	$0.575786\pi$
$812$		0			0
$813$			20524.0i			0.885373i
$814$	−24716.0			−1.06424
$815$	11950.0	−	23900.0i	0.513608	−	1.02722i
$816$	−4592.00			−0.197000
$817$		−	40608.0i		−	1.73892i
$818$		−	18200.0i		−	0.777932i
$819$		0			0
$820$	−8240.00	−	4120.00i	−0.350919	−	0.175459i
$821$	−30731.0			−1.30636			−0.653179	−	0.757204i	$-0.726565\pi$
$821$	−30731.0			−1.30636			−0.653179	+	0.757204i	$0.726565\pi$
$822$			2688.00i			0.114057i
$823$		−	1038.00i		−	0.0439640i	−0.999758	−	0.0219820i	$-0.993002\pi$
$823$		−	1038.00i		−	0.0439640i	0.999758	−	0.0219820i	$-0.00699766\pi$
$824$	14600.0			0.617251
$825$	−25900.0	+	19425.0i	−1.09300	+	0.819748i
$826$		0			0
$827$			7958.00i			0.334615i	0.985905	+	0.167308i	$0.0535073\pi$
$827$			7958.00i			0.334615i	−0.985905	+	0.167308i	$0.946493\pi$
$828$			6160.00i			0.258544i
$829$	−30666.0			−1.28477			−0.642385	−	0.766382i	$-0.722055\pi$
$829$	−30666.0			−1.28477			−0.642385	+	0.766382i	$0.722055\pi$
$830$	8560.00	+	4280.00i	0.357978	+	0.178989i
$831$	22778.0			0.950854
$832$		−	3264.00i		−	0.136008i
$833$		0			0
$834$	19628.0			0.814943
$835$	13155.0	−	26310.0i	0.545207	−	1.09041i
$836$	−15984.0			−0.661266
$837$		−	4690.00i		−	0.193680i
$838$			5236.00i			0.215841i
$839$	−5354.00			−0.220311			−0.110155	−	0.993914i	$-0.535135\pi$
$839$	−5354.00			−0.220311			−0.110155	+	0.993914i	$0.535135\pi$
$840$		0			0
$841$	37612.0			1.54217
$842$		−	7390.00i		−	0.302466i
$843$		−	23289.0i		−	0.951502i
$844$	16332.0			0.666079
$845$	4040.00	+	2020.00i	0.164474	+	0.0822368i
$846$	12628.0			0.513191
$847$		0			0
$848$			96.0000i			0.00388756i
$849$	32389.0			1.30929
$850$	6150.00	+	8200.00i	0.248169	+	0.330891i
$851$	23380.0			0.941782
$852$			12768.0i			0.513409i
$853$		−	42890.0i		−	1.72160i	−0.508943	−	0.860800i	$-0.669963\pi$
$853$		−	42890.0i		−	1.72160i	0.508943	−	0.860800i	$-0.330037\pi$
$854$		0			0
$855$	−23760.0	−	11880.0i	−0.950380	−	0.475190i
$856$	−1152.00			−0.0459983
$857$		−	22950.0i		−	0.914769i	−0.889269	−	0.457385i	$-0.848786\pi$
$857$		−	22950.0i		−	0.914769i	0.889269	−	0.457385i	$-0.151214\pi$
$858$		−	26418.0i		−	1.05116i
$859$	−2824.00			−0.112170			−0.0560848	−	0.998426i	$-0.517862\pi$
$859$	−2824.00			−0.112170			−0.0560848	+	0.998426i	$0.517862\pi$
$860$	−7520.00	+	15040.0i	−0.298174	+	0.596349i
$861$		0			0
$862$			31558.0i			1.24695i
$863$			4866.00i			0.191936i	0.995384	+	0.0959679i	$0.0305946\pi$
$863$			4866.00i			0.191936i	−0.995384	+	0.0959679i	$0.969405\pi$
$864$	1120.00			0.0441009
$865$	−11215.0	+	22430.0i	−0.440834	+	0.881668i
$866$	−14476.0			−0.568031
$867$		−	22624.0i		−	0.886218i
$868$		0			0
$869$	−45843.0			−1.78955
$870$	−34860.0	−	17430.0i	−1.35847	−	0.679233i
$871$	−5406.00			−0.210305
$872$			13448.0i			0.522255i
$873$		−	23210.0i		−	0.899816i
$874$	15120.0			0.585173
$875$		0			0
$876$	−18200.0			−0.701965
$877$		−	10676.0i		−	0.411064i	−0.978650	−	0.205532i	$-0.934108\pi$
$877$		−	10676.0i		−	0.411064i	0.978650	−	0.205532i	$-0.0658924\pi$
$878$		−	5292.00i		−	0.203413i
$879$	−28581.0			−1.09672
$880$	5920.00	+	2960.00i	0.226776	+	0.113388i
$881$	29856.0			1.14174			0.570871	−	0.821040i	$-0.306606\pi$
$881$	29856.0			1.14174			0.570871	+	0.821040i	$0.306606\pi$
$882$		0			0
$883$			1944.00i			0.0740893i	0.999314	+	0.0370446i	$0.0117944\pi$
$883$			1944.00i			0.0740893i	−0.999314	+	0.0370446i	$0.988206\pi$
$884$	−8364.00			−0.318226
$885$	70.0000	−	140.000i	0.00265878	−	0.00531757i
$886$	11376.0			0.431359
$887$			14628.0i			0.553732i	0.960909	+	0.276866i	$0.0892958\pi$
$887$			14628.0i			0.553732i	−0.960909	+	0.276866i	$0.910704\pi$
$888$			18704.0i			0.706830i
$889$		0			0
$890$	−2200.00	+	4400.00i	−0.0828586	+	0.165717i
$891$	31043.0			1.16720
$892$		−	1508.00i		−	0.0566049i
$893$		−	30996.0i		−	1.16152i
$894$	4228.00			0.158172
$895$	520.000	+	260.000i	0.0194209	+	0.00971044i
$896$		0			0
$897$			24990.0i			0.930203i
$898$			6570.00i			0.244147i
$899$	33366.0			1.23784
$900$	6600.00	+	8800.00i	0.244444	+	0.325926i
$901$	246.000			0.00909595
$902$			15244.0i			0.562716i
$903$		0			0
$904$	−6384.00			−0.234877
$905$	24620.0	+	12310.0i	0.904306	+	0.452153i
$906$	−44338.0			−1.62586
$907$		−	12858.0i		−	0.470720i	−0.971908	−	0.235360i	$-0.924373\pi$
$907$		−	12858.0i		−	0.470720i	0.971908	−	0.235360i	$-0.0756269\pi$
$908$		−	10204.0i		−	0.372942i
$909$	43120.0			1.57338
$910$		0			0
$911$	−18324.0			−0.666412			−0.333206	−	0.942854i	$-0.608130\pi$
$911$	−18324.0			−0.666412			−0.333206	+	0.942854i	$0.608130\pi$
$912$			12096.0i			0.439187i
$913$		−	15836.0i		−	0.574036i
$914$	−29668.0			−1.07367
$915$	−32900.0	+	65800.0i	−1.18868	+	2.37736i
$916$	−296.000			−0.0106770
$917$		0			0
$918$		−	2870.00i		−	0.103185i
$919$	14751.0			0.529478			0.264739	−	0.964320i	$-0.414714\pi$
$919$	14751.0			0.529478			0.264739	+	0.964320i	$0.414714\pi$
$920$	−5600.00	−	2800.00i	−0.200681	−	0.100341i
$921$	28623.0			1.02406
$922$			19944.0i			0.712387i
$923$			23256.0i			0.829340i
$924$		0			0
$925$	33400.0	−	25050.0i	1.18723	−	0.890420i
$926$	−18192.0			−0.645601
$927$		−	40150.0i		−	1.42254i
$928$			7968.00i			0.281856i
$929$	−47922.0			−1.69243			−0.846216	−	0.532840i	$-0.821125\pi$
$929$	−47922.0			−1.69243			−0.846216	+	0.532840i	$0.821125\pi$
$930$	−18760.0	−	9380.00i	−0.661467	−	0.330734i
$931$		0			0
$932$			7552.00i			0.265423i
$933$		−	28056.0i		−	0.984472i
$934$	31734.0			1.11174
$935$	7585.00	−	15170.0i	0.265301	−	0.530601i
$936$	−8976.00			−0.313451
$937$			44987.0i			1.56848i	0.620461	+	0.784238i	$0.286946\pi$
$937$			44987.0i			1.56848i	−0.620461	+	0.784238i	$0.713054\pi$
$938$		0			0
$939$	51485.0			1.78930
$940$	−5740.00	+	11480.0i	−0.199168	+	0.398337i
$941$	20356.0			0.705193			0.352597	−	0.935775i	$-0.385299\pi$
$941$	20356.0			0.705193			0.352597	+	0.935775i	$0.385299\pi$
$942$			6580.00i			0.227588i
$943$		−	14420.0i		−	0.497964i
$944$	−32.0000			−0.00110330
$945$		0			0
$946$	27824.0			0.956275
$947$		−	27786.0i		−	0.953457i	−0.879051	−	0.476728i	$-0.841823\pi$
$947$		−	27786.0i		−	0.953457i	0.879051	−	0.476728i	$-0.158177\pi$
$948$			34692.0i			1.18855i
$949$	−33150.0			−1.13392
$950$	21600.0	−	16200.0i	0.737681	−	0.553260i
$951$	−11788.0			−0.401948
$952$		0			0
$953$			48674.0i			1.65447i	0.561859	+	0.827233i	$0.310086\pi$
$953$			48674.0i			1.65447i	−0.561859	+	0.827233i	$0.689914\pi$
$954$	264.000			0.00895945
$955$	−31590.0	−	15795.0i	−1.07040	−	0.535198i
$956$	19988.0			0.676211
$957$			64491.0i			2.17837i
$958$			484.000i			0.0163229i
$959$		0			0
$960$	2240.00	−	4480.00i	0.0753080	−	0.150616i
$961$	−11835.0			−0.397268
$962$			34068.0i			1.14178i
$963$			3168.00i			0.106010i
$964$	−15320.0			−0.511851
$965$	−10300.0	+	20600.0i	−0.343595	+	0.687189i
$966$		0			0
$967$		−	11168.0i		−	0.371395i	−0.982607	−	0.185697i	$-0.940546\pi$
$967$		−	11168.0i		−	0.371395i	0.982607	−	0.185697i	$-0.0594544\pi$
$968$		−	304.000i		−	0.0100939i
$969$	30996.0			1.02759
$970$	21100.0	+	10550.0i	0.698433	+	0.349217i
$971$	−20094.0			−0.664106			−0.332053	−	0.943261i	$-0.607741\pi$
$971$	−20094.0			−0.664106			−0.332053	+	0.943261i	$0.607741\pi$
$972$		−	19712.0i		−	0.650476i
$973$		0			0
$974$	7116.00			0.234098
$975$	26775.0	+	35700.0i	0.879473	+	1.17263i
$976$	15040.0			0.493257
$977$			49104.0i			1.60796i	0.594657	+	0.803980i	$0.297288\pi$
$977$			49104.0i			1.60796i	−0.594657	+	0.803980i	$0.702712\pi$
$978$			33460.0i			1.09400i
$979$	8140.00			0.265736
$980$		0			0
$981$	36982.0			1.20361
$982$			2946.00i			0.0957338i
$983$			27751.0i			0.900427i	0.892921	+	0.450213i	$0.148652\pi$
$983$			27751.0i			0.900427i	−0.892921	+	0.450213i	$0.851348\pi$
$984$	11536.0			0.373734
$985$	8690.00	−	17380.0i	0.281103	−	0.562206i
$986$	20418.0			0.659474
$987$		0			0
$988$			22032.0i			0.709445i
$989$	−26320.0			−0.846236
$990$	8140.00	−	16280.0i	0.261319	−	0.522639i
$991$	37600.0			1.20525			0.602625	−	0.798024i	$-0.294121\pi$
$991$	37600.0			1.20525			0.602625	+	0.798024i	$0.294121\pi$
$992$			4288.00i			0.137242i
$993$			10220.0i			0.326608i
$994$		0			0
$995$	8940.00	+	4470.00i	0.284841	+	0.142421i
$996$	−11984.0			−0.381253
$997$			10911.0i			0.346595i	0.984870	+	0.173297i	$0.0554422\pi$
$997$			10911.0i			0.346595i	−0.984870	+	0.173297i	$0.944558\pi$
$998$		−	1206.00i		−	0.0382518i
$999$	−11690.0			−0.370225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.a.99.2		2
5.2	odd	4		2450.4.a.c.1.1		1
5.3	odd	4		2450.4.a.bn.1.1		1
5.4	even	2	inner	490.4.c.a.99.1		2
7.6	odd	2		70.4.c.a.29.2	yes	2
21.20	even	2		630.4.g.a.379.1		2
28.27	even	2		560.4.g.c.449.1		2
35.13	even	4		350.4.a.m.1.1		1
35.27	even	4		350.4.a.i.1.1		1
35.34	odd	2		70.4.c.a.29.1	✓	2
105.104	even	2		630.4.g.a.379.2		2
140.139	even	2		560.4.g.c.449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.c.a.29.1	✓	2	35.34	odd	2
70.4.c.a.29.2	yes	2	7.6	odd	2
350.4.a.i.1.1		1	35.27	even	4
350.4.a.m.1.1		1	35.13	even	4
490.4.c.a.99.1		2	5.4	even	2	inner
490.4.c.a.99.2		2	1.1	even	1	trivial
560.4.g.c.449.1		2	28.27	even	2
560.4.g.c.449.2		2	140.139	even	2
630.4.g.a.379.1		2	21.20	even	2
630.4.g.a.379.2		2	105.104	even	2
2450.4.a.c.1.1		1	5.2	odd	4
2450.4.a.bn.1.1		1	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -7.00000i q^{3} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +14.0000 q^{6} -8.00000i q^{8} -22.0000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -7.00000i q^{3} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +14.0000 q^{6} -8.00000i q^{8} -22.0000 q^{9} +(10.0000 - 20.0000i) q^{10} -37.0000 q^{11} +28.0000i q^{12} +51.0000i q^{13} +(-35.0000 + 70.0000i) q^{15} +16.0000 q^{16} -41.0000i q^{17} -44.0000i q^{18} -108.000 q^{19} +(40.0000 + 20.0000i) q^{20} -74.0000i q^{22} +70.0000i q^{23} -56.0000 q^{24} +(75.0000 + 100.000i) q^{25} -102.000 q^{26} -35.0000i q^{27} +249.000 q^{29} +(-140.000 - 70.0000i) q^{30} +134.000 q^{31} +32.0000i q^{32} +259.000i q^{33} +82.0000 q^{34} +88.0000 q^{36} -334.000i q^{37} -216.000i q^{38} +357.000 q^{39} +(-40.0000 + 80.0000i) q^{40} -206.000 q^{41} +376.000i q^{43} +148.000 q^{44} +(220.000 + 110.000i) q^{45} -140.000 q^{46} +287.000i q^{47} -112.000i q^{48} +(-200.000 + 150.000i) q^{50} -287.000 q^{51} -204.000i q^{52} +6.00000i q^{53} +70.0000 q^{54} +(370.000 + 185.000i) q^{55} +756.000i q^{57} +498.000i q^{58} -2.00000 q^{59} +(140.000 - 280.000i) q^{60} +940.000 q^{61} +268.000i q^{62} -64.0000 q^{64} +(255.000 - 510.000i) q^{65} -518.000 q^{66} +106.000i q^{67} +164.000i q^{68} +490.000 q^{69} +456.000 q^{71} +176.000i q^{72} +650.000i q^{73} +668.000 q^{74} +(700.000 - 525.000i) q^{75} +432.000 q^{76} +714.000i q^{78} +1239.00 q^{79} +(-160.000 - 80.0000i) q^{80} -839.000 q^{81} -412.000i q^{82} +428.000i q^{83} +(-205.000 + 410.000i) q^{85} -752.000 q^{86} -1743.00i q^{87} +296.000i q^{88} -220.000 q^{89} +(-220.000 + 440.000i) q^{90} -280.000i q^{92} -938.000i q^{93} -574.000 q^{94} +(1080.00 + 540.000i) q^{95} +224.000 q^{96} +1055.00i q^{97} +814.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} - 20 q^{5} + 28 q^{6} - 44 q^{9}+O(q^{10}) \) 2 * q - 8 * q^4 - 20 * q^5 + 28 * q^6 - 44 * q^9	\( 2 q - 8 q^{4} - 20 q^{5} + 28 q^{6} - 44 q^{9} + 20 q^{10} - 74 q^{11} - 70 q^{15} + 32 q^{16} - 216 q^{19} + 80 q^{20} - 112 q^{24} + 150 q^{25} - 204 q^{26} + 498 q^{29} - 280 q^{30} + 268 q^{31} + 164 q^{34} + 176 q^{36} + 714 q^{39} - 80 q^{40} - 412 q^{41} + 296 q^{44} + 440 q^{45} - 280 q^{46} - 400 q^{50} - 574 q^{51} + 140 q^{54} + 740 q^{55} - 4 q^{59} + 280 q^{60} + 1880 q^{61} - 128 q^{64} + 510 q^{65} - 1036 q^{66} + 980 q^{69} + 912 q^{71} + 1336 q^{74} + 1400 q^{75} + 864 q^{76} + 2478 q^{79} - 320 q^{80} - 1678 q^{81} - 410 q^{85} - 1504 q^{86} - 440 q^{89} - 440 q^{90} - 1148 q^{94} + 2160 q^{95} + 448 q^{96} + 1628 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 - 20 * q^5 + 28 * q^6 - 44 * q^9 + 20 * q^10 - 74 * q^11 - 70 * q^15 + 32 * q^16 - 216 * q^19 + 80 * q^20 - 112 * q^24 + 150 * q^25 - 204 * q^26 + 498 * q^29 - 280 * q^30 + 268 * q^31 + 164 * q^34 + 176 * q^36 + 714 * q^39 - 80 * q^40 - 412 * q^41 + 296 * q^44 + 440 * q^45 - 280 * q^46 - 400 * q^50 - 574 * q^51 + 140 * q^54 + 740 * q^55 - 4 * q^59 + 280 * q^60 + 1880 * q^61 - 128 * q^64 + 510 * q^65 - 1036 * q^66 + 980 * q^69 + 912 * q^71 + 1336 * q^74 + 1400 * q^75 + 864 * q^76 + 2478 * q^79 - 320 * q^80 - 1678 * q^81 - 410 * q^85 - 1504 * q^86 - 440 * q^89 - 440 * q^90 - 1148 * q^94 + 2160 * q^95 + 448 * q^96 + 1628 * q^99

Introduction

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