LMFDB - Embedded newform 490.4.c.g.99.11

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 438 x^{18} + 80439 x^{16} + 8097428 x^{14} + 488971671 x^{12} + 18162509334 x^{10} + \cdots + 9871083181584 $ x^20 + 438x^18 + 80439x^16 + 8097428x^14 + 488971671x^12 + 18162509334x^10 + 407198911753x^8 + 5129420990112x^6 + 30509282328120x^4 + 52488428698656*x^2 + 9871083181584
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{23}\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.11
Root			$10.7468i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.g.99.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -9.74678i q^{3} -4.00000 q^{4} +(4.75591 - 10.1184i) q^{5} +19.4936 q^{6} -8.00000i q^{8} -67.9997 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -9.74678i q^{3} -4.00000 q^{4} +(4.75591 - 10.1184i) q^{5} +19.4936 q^{6} -8.00000i q^{8} -67.9997 q^{9} +(20.2367 + 9.51182i) q^{10} +6.52280 q^{11} +38.9871i q^{12} +41.6565i q^{13} +(-98.6215 - 46.3548i) q^{15} +16.0000 q^{16} -109.689i q^{17} -135.999i q^{18} -29.7403 q^{19} +(-19.0236 + 40.4735i) q^{20} +13.0456i q^{22} -180.661i q^{23} -77.9742 q^{24} +(-79.7627 - 96.2440i) q^{25} -83.3131 q^{26} +399.615i q^{27} -183.754 q^{29} +(92.7096 - 197.243i) q^{30} -116.518 q^{31} +32.0000i q^{32} -63.5763i q^{33} +219.379 q^{34} +271.999 q^{36} +396.605i q^{37} -59.4806i q^{38} +406.017 q^{39} +(-80.9469 - 38.0473i) q^{40} +197.275 q^{41} +302.257i q^{43} -26.0912 q^{44} +(-323.400 + 688.046i) q^{45} +361.322 q^{46} +277.408i q^{47} -155.948i q^{48} +(192.488 - 159.525i) q^{50} -1069.12 q^{51} -166.626i q^{52} -405.896i q^{53} -799.231 q^{54} +(31.0218 - 66.0001i) q^{55} +289.872i q^{57} -367.508i q^{58} +67.8911 q^{59} +(394.486 + 185.419i) q^{60} +510.023 q^{61} -233.036i q^{62} -64.0000 q^{64} +(421.496 + 198.115i) q^{65} +127.153 q^{66} +1026.25i q^{67} +438.758i q^{68} -1760.86 q^{69} -352.582 q^{71} +543.998i q^{72} -59.7536i q^{73} -793.210 q^{74} +(-938.070 + 777.429i) q^{75} +118.961 q^{76} +812.034i q^{78} +133.868 q^{79} +(76.0945 - 161.894i) q^{80} +2058.97 q^{81} +394.549i q^{82} -571.708i q^{83} +(-1109.88 - 521.673i) q^{85} -604.514 q^{86} +1791.01i q^{87} -52.1824i q^{88} -547.534 q^{89} +(-1376.09 - 646.801i) q^{90} +722.644i q^{92} +1135.68i q^{93} -554.815 q^{94} +(-141.442 + 300.923i) q^{95} +311.897 q^{96} -783.724i q^{97} -443.549 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) $ 20 * q - 80 * q^4 - 316 * q^9	$ 20 q - 80 q^{4} - 316 q^{9} + 104 q^{11} - 360 q^{15} + 320 q^{16} - 440 q^{25} - 216 q^{29} + 224 q^{30} + 1264 q^{36} - 504 q^{39} - 416 q^{44} + 1600 q^{46} + 952 q^{50} - 296 q^{51} + 1440 q^{60} - 1280 q^{64} + 2732 q^{65} - 1872 q^{71} - 5968 q^{74} - 6424 q^{79} + 2020 q^{81} + 428 q^{85} + 3616 q^{86} + 3568 q^{95} + 624 q^{99}+O(q^{100}) $ 20 * q - 80 * q^4 - 316 * q^9 + 104 * q^11 - 360 * q^15 + 320 * q^16 - 440 * q^25 - 216 * q^29 + 224 * q^30 + 1264 * q^36 - 504 * q^39 - 416 * q^44 + 1600 * q^46 + 952 * q^50 - 296 * q^51 + 1440 * q^60 - 1280 * q^64 + 2732 * q^65 - 1872 * q^71 - 5968 * q^74 - 6424 * q^79 + 2020 * q^81 + 428 * q^85 + 3616 * q^86 + 3568 * q^95 + 624 * 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
$3$		−	9.74678i		−	1.87577i	−0.346948	−	0.937884i	$-0.612782\pi$
$3$		−	9.74678i		−	1.87577i	0.346948	−	0.937884i	$-0.387218\pi$
$4$	−4.00000			−0.500000
$5$	4.75591	−	10.1184i	0.425381	−	0.905014i
$5$	4.75591	−	10.1184i	0.425381	−	0.905014i
$6$	19.4936			1.32637
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	−67.9997			−2.51851
$10$	20.2367	+	9.51182i	0.639942	+	0.300790i
$11$	6.52280			0.178791			0.0893954	−	0.995996i	$-0.471507\pi$
$11$	6.52280			0.178791			0.0893954	+	0.995996i	$0.471507\pi$
$12$			38.9871i			0.937884i
$13$			41.6565i			0.888726i	0.895847	+	0.444363i	$0.146570\pi$
$13$			41.6565i			0.888726i	−0.895847	+	0.444363i	$0.853430\pi$
$14$		0			0
$15$	−98.6215	−	46.3548i	−1.69760	−	0.797917i
$16$	16.0000			0.250000
$17$		−	109.689i		−	1.56492i	−0.622702	−	0.782459i	$-0.713965\pi$
$17$		−	109.689i		−	1.56492i	0.622702	−	0.782459i	$-0.286035\pi$
$18$		−	135.999i		−	1.78085i
$19$	−29.7403			−0.359100			−0.179550	−	0.983749i	$-0.557464\pi$
$19$	−29.7403			−0.359100			−0.179550	+	0.983749i	$0.557464\pi$
$20$	−19.0236	+	40.4735i	−0.212691	+	0.452507i
$21$		0			0
$22$			13.0456i			0.126424i
$23$		−	180.661i		−	1.63784i	−0.573904	−	0.818922i	$-0.694572\pi$
$23$		−	180.661i		−	1.63784i	0.573904	−	0.818922i	$-0.305428\pi$
$24$	−77.9742			−0.663184
$25$	−79.7627	−	96.2440i	−0.638101	−	0.769952i
$26$	−83.3131			−0.628425
$27$			399.615i			2.84837i
$28$		0			0
$29$	−183.754			−1.17663			−0.588315	−	0.808632i	$-0.700209\pi$
$29$	−183.754			−1.17663			−0.588315	+	0.808632i	$0.700209\pi$
$30$	92.7096	−	197.243i	0.564213	−	1.20038i
$31$	−116.518			−0.675074			−0.337537	−	0.941312i	$-0.609594\pi$
$31$	−116.518			−0.675074			−0.337537	+	0.941312i	$0.609594\pi$
$32$			32.0000i			0.176777i
$33$		−	63.5763i		−	0.335370i
$34$	219.379			1.10656
$35$		0			0
$36$	271.999			1.25925
$37$			396.605i			1.76220i	0.472928	+	0.881101i	$0.343197\pi$
$37$			396.605i			1.76220i	−0.472928	+	0.881101i	$0.656803\pi$
$38$		−	59.4806i		−	0.253922i
$39$	406.017			1.66705
$40$	−80.9469	−	38.0473i	−0.319971	−	0.150395i
$41$	197.275			0.751442			0.375721	−	0.926733i	$-0.377395\pi$
$41$	197.275			0.751442			0.375721	+	0.926733i	$0.377395\pi$
$42$		0			0
$43$			302.257i			1.07195i	0.844235	+	0.535974i	$0.180055\pi$
$43$			302.257i			1.07195i	−0.844235	+	0.535974i	$0.819945\pi$
$44$	−26.0912			−0.0893954
$45$	−323.400	+	688.046i	−1.07133	+	2.27929i
$46$	361.322			1.15813
$47$			277.408i			0.860937i	0.902606	+	0.430469i	$0.141652\pi$
$47$			277.408i			0.860937i	−0.902606	+	0.430469i	$0.858348\pi$
$48$		−	155.948i		−	0.468942i
$49$		0			0
$50$	192.488	−	159.525i	0.544438	−	0.451206i
$51$	−1069.12			−2.93542
$52$		−	166.626i		−	0.444363i
$53$		−	405.896i		−	1.05196i	−0.850496	−	0.525982i	$-0.823698\pi$
$53$		−	405.896i		−	1.05196i	0.850496	−	0.525982i	$-0.176302\pi$
$54$	−799.231			−2.01410
$55$	31.0218	−	66.0001i	0.0760542	−	0.161808i
$56$		0			0
$57$			289.872i			0.673588i
$58$		−	367.508i		−	0.832004i
$59$	67.8911			0.149808			0.0749040	−	0.997191i	$-0.476135\pi$
$59$	67.8911			0.149808			0.0749040	+	0.997191i	$0.476135\pi$
$60$	394.486	+	185.419i	0.848799	+	0.398959i
$61$	510.023			1.07052			0.535260	−	0.844687i	$-0.320214\pi$
$61$	510.023			1.07052			0.535260	+	0.844687i	$0.320214\pi$
$62$		−	233.036i		−	0.477349i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	421.496	+	198.115i	0.804310	+	0.378048i
$66$	127.153			0.237142
$67$			1026.25i			1.87129i	0.352943	+	0.935645i	$0.385181\pi$
$67$			1026.25i			1.87129i	−0.352943	+	0.935645i	$0.614819\pi$
$68$			438.758i			0.782459i
$69$	−1760.86			−3.07222
$70$		0			0
$71$	−352.582			−0.589349			−0.294674	−	0.955598i	$-0.595211\pi$
$71$	−352.582			−0.589349			−0.294674	+	0.955598i	$0.595211\pi$
$72$			543.998i			0.890427i
$73$		−	59.7536i		−	0.0958031i	−0.998852	−	0.0479016i	$-0.984747\pi$
$73$		−	59.7536i		−	0.0958031i	0.998852	−	0.0479016i	$-0.0152534\pi$
$74$	−793.210			−1.24606
$75$	−938.070	+	777.429i	−1.44425	+	1.19693i
$76$	118.961			0.179550
$77$		0			0
$78$			812.034i			1.17878i
$79$	133.868			0.190650			0.0953251	−	0.995446i	$-0.469611\pi$
$79$	133.868			0.190650			0.0953251	+	0.995446i	$0.469611\pi$
$80$	76.0945	−	161.894i	0.106345	−	0.226254i
$81$	2058.97			2.82438
$82$			394.549i			0.531350i
$83$		−	571.708i		−	0.756062i	−0.925793	−	0.378031i	$-0.876601\pi$
$83$		−	571.708i		−	0.756062i	0.925793	−	0.378031i	$-0.123399\pi$
$84$		0			0
$85$	−1109.88	−	521.673i	−1.41627	−	0.665687i
$86$	−604.514			−0.757982
$87$			1791.01i			2.20709i
$88$		−	52.1824i		−	0.0632121i
$89$	−547.534			−0.652118			−0.326059	−	0.945349i	$-0.605721\pi$
$89$	−547.534			−0.652118			−0.326059	+	0.945349i	$0.605721\pi$
$90$	−1376.09	−	646.801i	−1.61170	−	0.757542i
$91$		0			0
$92$			722.644i			0.818922i
$93$			1135.68i			1.26628i
$94$	−554.815			−0.608775
$95$	−141.442	+	300.923i	−0.152754	+	0.324990i
$96$	311.897			0.331592
$97$		−	783.724i		−	0.820362i	−0.912004	−	0.410181i	$-0.865466\pi$
$97$		−	783.724i		−	0.820362i	0.912004	−	0.410181i	$-0.134534\pi$
$98$		0			0
$99$	−443.549			−0.450286
$100$	319.051	+	384.976i	0.319051	+	0.384976i
$101$	−376.583			−0.371004			−0.185502	−	0.982644i	$-0.559391\pi$
$101$	−376.583			−0.371004			−0.185502	+	0.982644i	$0.559391\pi$
$102$		−	2138.24i		−	2.07566i
$103$			540.138i			0.516713i	0.966050	+	0.258356i	$0.0831809\pi$
$103$			540.138i			0.516713i	−0.966050	+	0.258356i	$0.916819\pi$
$104$	333.252			0.314212
$105$		0			0
$106$	811.791			0.743850
$107$		−	990.242i		−	0.894676i	−0.894365	−	0.447338i	$-0.852372\pi$
$107$		−	990.242i		−	0.894676i	0.894365	−	0.447338i	$-0.147628\pi$
$108$		−	1598.46i		−	1.42419i
$109$	630.880			0.554379			0.277189	−	0.960815i	$-0.410597\pi$
$109$	630.880			0.554379			0.277189	+	0.960815i	$0.410597\pi$
$110$	132.000	+	62.0437i	0.114416	+	0.0537785i
$111$	3865.62			3.30548
$112$		0			0
$113$		−	1527.02i		−	1.27124i	−0.772003	−	0.635619i	$-0.780745\pi$
$113$		−	1527.02i		−	1.27124i	0.772003	−	0.635619i	$-0.219255\pi$
$114$	−579.745			−0.476299
$115$	−1827.99	−	859.207i	−1.48227	−	0.696708i
$116$	735.017			0.588315
$117$		−	2832.63i		−	2.23827i
$118$			135.782i			0.105930i
$119$		0			0
$120$	−370.838	+	788.972i	−0.282106	+	0.600191i
$121$	−1288.45			−0.968034
$122$			1020.05i			0.756972i
$123$		−	1922.79i		−	1.40953i
$124$	466.073			0.337537
$125$	−1353.18	+	349.340i	−0.968254	+	0.249968i
$126$		0			0
$127$		−	2431.46i		−	1.69888i	−0.527687	−	0.849439i	$-0.676941\pi$
$127$		−	2431.46i		−	1.69888i	0.527687	−	0.849439i	$-0.323059\pi$
$128$		−	128.000i		−	0.0883883i
$129$	2946.03			2.01073
$130$	−396.229	+	842.992i	−0.267320	+	0.568733i
$131$	−433.676			−0.289240			−0.144620	−	0.989487i	$-0.546196\pi$
$131$	−433.676			−0.289240			−0.144620	+	0.989487i	$0.546196\pi$
$132$			254.305i			0.167685i
$133$		0			0
$134$	−2052.50			−1.32320
$135$	4043.46	+	1900.53i	2.57782	+	1.21164i
$136$	−877.516			−0.553282
$137$		−	844.492i		−	0.526641i	−0.964708	−	0.263320i	$-0.915182\pi$
$137$		−	844.492i		−	0.526641i	0.964708	−	0.263320i	$-0.0848176\pi$
$138$		−	3521.73i		−	2.17239i
$139$	351.476			0.214473			0.107237	−	0.994234i	$-0.465800\pi$
$139$	351.476			0.214473			0.107237	+	0.994234i	$0.465800\pi$
$140$		0			0
$141$	2703.83			1.61492
$142$		−	705.164i		−	0.416733i
$143$			271.717i			0.158896i
$144$	−1088.00			−0.629627
$145$	−873.918	+	1859.29i	−0.500517	+	1.06487i
$146$	119.507			0.0677430
$147$		0			0
$148$		−	1586.42i		−	0.881101i
$149$	743.766			0.408938			0.204469	−	0.978873i	$-0.434453\pi$
$149$	743.766			0.408938			0.204469	+	0.978873i	$0.434453\pi$
$150$	−1554.86	−	1876.14i	−0.846358	−	1.02124i
$151$	−1900.57			−1.02428			−0.512140	−	0.858902i	$-0.671147\pi$
$151$	−1900.57			−1.02428			−0.512140	+	0.858902i	$0.671147\pi$
$152$			237.922i			0.126961i
$153$			7458.85i			3.94126i
$154$		0			0
$155$	−554.150	+	1178.97i	−0.287164	+	0.610951i
$156$	−1624.07			−0.833523
$157$		−	1336.18i		−	0.679227i	−0.940565	−	0.339614i	$-0.889704\pi$
$157$		−	1336.18i		−	0.679227i	0.940565	−	0.339614i	$-0.110296\pi$
$158$			267.737i			0.134810i
$159$	−3956.18			−1.97324
$160$	323.788	+	152.189i	0.159985	+	0.0751975i
$161$		0			0
$162$			4117.94i			1.99714i
$163$			251.318i			0.120765i	0.998175	+	0.0603827i	$0.0192321\pi$
$163$			251.318i			0.120765i	−0.998175	+	0.0603827i	$0.980768\pi$
$164$	−789.099			−0.375721
$165$	−643.288	−	302.363i	−0.303515	−	0.142660i
$166$	1143.42			0.534616
$167$		−	848.924i		−	0.393364i	−0.980467	−	0.196682i	$-0.936983\pi$
$167$		−	848.924i		−	0.393364i	0.980467	−	0.196682i	$-0.0630166\pi$
$168$		0			0
$169$	461.733			0.210165
$170$	1043.35	−	2219.76i	0.470712	−	1.00146i
$171$	2022.33			0.904396
$172$		−	1209.03i		−	0.535974i
$173$			2808.67i			1.23433i	0.786833	+	0.617165i	$0.211719\pi$
$173$			2808.67i			1.23433i	−0.786833	+	0.617165i	$0.788281\pi$
$174$	−3582.02			−1.56065
$175$		0			0
$176$	104.365			0.0446977
$177$		−	661.720i		−	0.281005i
$178$		−	1095.07i		−	0.461117i
$179$	−4364.59			−1.82248			−0.911241	−	0.411873i	$-0.864875\pi$
$179$	−4364.59			−1.82248			−0.911241	+	0.411873i	$0.864875\pi$
$180$	1293.60	−	2752.19i	0.535663	−	1.13964i
$181$	1160.46			0.476555			0.238278	−	0.971197i	$-0.423417\pi$
$181$	1160.46			0.476555			0.238278	+	0.971197i	$0.423417\pi$
$182$		0			0
$183$		−	4971.08i		−	2.00805i
$184$	−1445.29			−0.579066
$185$	4013.00	+	1886.22i	1.59482	+	0.749608i
$186$	−2271.35			−0.895397
$187$		−	715.482i		−	0.279793i
$188$		−	1109.63i		−	0.430469i
$189$		0			0
$190$	−601.847	−	282.884i	−0.229803	−	0.108014i
$191$	−2943.59			−1.11513			−0.557567	−	0.830132i	$-0.688265\pi$
$191$	−2943.59			−1.11513			−0.557567	+	0.830132i	$0.688265\pi$
$192$			623.794i			0.234471i
$193$			923.536i			0.344443i	0.985058	+	0.172222i	$0.0550945\pi$
$193$			923.536i			0.344443i	−0.985058	+	0.172222i	$0.944905\pi$
$194$	1567.45			0.580084
$195$	1930.98	−	4108.23i	0.709130	−	1.50870i
$196$		0			0
$197$		−	1726.42i		−	0.624376i	−0.950020	−	0.312188i	$-0.898938\pi$
$197$		−	1726.42i		−	0.624376i	0.950020	−	0.312188i	$-0.101062\pi$
$198$		−	887.097i		−	0.318400i
$199$	362.210			0.129027			0.0645136	−	0.997917i	$-0.479450\pi$
$199$	362.210			0.129027			0.0645136	+	0.997917i	$0.479450\pi$
$200$	−769.952	+	638.101i	−0.272219	+	0.225603i
$201$	10002.6			3.51011
$202$		−	753.167i		−	0.262340i
$203$		0			0
$204$	4276.48			1.46771
$205$	938.220	−	1996.10i	0.319649	−	0.680066i
$206$	−1080.28			−0.365371
$207$			12284.9i			4.12493i
$208$			666.505i			0.222182i
$209$	−193.990			−0.0642037
$210$		0			0
$211$	−138.041			−0.0450385			−0.0225192	−	0.999746i	$-0.507169\pi$
$211$	−138.041			−0.0450385			−0.0225192	+	0.999746i	$0.507169\pi$
$212$			1623.58i			0.525982i
$213$			3436.54i			1.10548i
$214$	1980.48			0.632631
$215$	3058.35	+	1437.51i	0.970128	+	0.455987i
$216$	3196.92			1.00705
$217$		0			0
$218$			1261.76i			0.392005i
$219$	−582.405			−0.179705
$220$	−124.087	+	264.000i	−0.0380271	+	0.0809041i
$221$	4569.28			1.39078
$222$			7731.24i			2.33733i
$223$		−	1253.85i		−	0.376520i	−0.982119	−	0.188260i	$-0.939715\pi$
$223$		−	1253.85i		−	0.376520i	0.982119	−	0.188260i	$-0.0602848\pi$
$224$		0			0
$225$	5423.84	+	6544.57i	1.60706	+	1.93913i
$226$	3054.04			0.898902
$227$		−	6575.17i		−	1.92251i	−0.275663	−	0.961254i	$-0.588897\pi$
$227$		−	6575.17i		−	1.92251i	0.275663	−	0.961254i	$-0.411103\pi$
$228$		−	1159.49i		−	0.336794i
$229$	2609.84			0.753113			0.376557	−	0.926394i	$-0.377108\pi$
$229$	2609.84			0.753113			0.376557	+	0.926394i	$0.377108\pi$
$230$	1718.41	−	3655.99i	0.492647	−	1.04813i
$231$		0			0
$232$			1470.03i			0.416002i
$233$		−	2876.02i		−	0.808646i	−0.914616	−	0.404323i	$-0.867507\pi$
$233$		−	2876.02i		−	0.808646i	0.914616	−	0.404323i	$-0.132493\pi$
$234$	5665.27			1.58269
$235$	2806.91	+	1319.32i	0.779160	+	0.366227i
$236$	−271.564			−0.0749040
$237$		−	1304.78i		−	0.357616i
$238$		0			0
$239$	−4829.24			−1.30702			−0.653509	−	0.756919i	$-0.726704\pi$
$239$	−4829.24			−1.30702			−0.653509	+	0.756919i	$0.726704\pi$
$240$	−1577.94	−	741.677i	−0.424399	−	0.199479i
$241$	−2446.51			−0.653914			−0.326957	−	0.945039i	$-0.606023\pi$
$241$	−2446.51			−0.653914			−0.326957	+	0.945039i	$0.606023\pi$
$242$		−	2576.91i		−	0.684503i
$243$		−	9278.73i		−	2.44951i
$244$	−2040.09			−0.535260
$245$		0			0
$246$	3845.59			0.996689
$247$		−	1238.88i		−	0.319141i
$248$			932.145i			0.238675i
$249$	−5572.31			−1.41820
$250$	−698.681	−	2706.35i	−0.176754	−	0.684659i
$251$	−5708.32			−1.43548			−0.717741	−	0.696311i	$-0.754824\pi$
$251$	−5708.32			−1.43548			−0.717741	+	0.696311i	$0.754824\pi$
$252$		0			0
$253$		−	1178.42i		−	0.292831i
$254$	4862.93			1.20129
$255$	−5084.63	+	10817.7i	−1.24867	+	2.65660i
$256$	256.000			0.0625000
$257$			2437.90i			0.591720i	0.955231	+	0.295860i	$0.0956061\pi$
$257$			2437.90i			0.591720i	−0.955231	+	0.295860i	$0.904394\pi$
$258$			5892.06i			1.42180i
$259$		0			0
$260$	−1685.98	−	792.459i	−0.402155	−	0.189024i
$261$	12495.2			2.96335
$262$		−	867.351i		−	0.204523i
$263$		−	2313.53i		−	0.542428i	−0.962519	−	0.271214i	$-0.912575\pi$
$263$		−	2313.53i		−	0.542428i	0.962519	−	0.271214i	$-0.0874251\pi$
$264$	−508.610			−0.118571
$265$	−4107.00	−	1930.40i	−0.952042	−	0.447486i
$266$		0			0
$267$			5336.69i			1.22322i
$268$		−	4105.00i		−	0.935645i
$269$	6561.65			1.48725			0.743626	−	0.668596i	$-0.233105\pi$
$269$	6561.65			1.48725			0.743626	+	0.668596i	$0.233105\pi$
$270$	−3801.07	+	8086.91i	−0.856762	+	1.82279i
$271$	−3738.06			−0.837901			−0.418950	−	0.908009i	$-0.637602\pi$
$271$	−3738.06			−0.837901			−0.418950	+	0.908009i	$0.637602\pi$
$272$		−	1755.03i		−	0.391229i
$273$		0			0
$274$	1688.98			0.372391
$275$	−520.276	−	627.781i	−0.114087	−	0.137660i
$276$	7043.45			1.53611
$277$			5378.86i			1.16673i	0.812210	+	0.583365i	$0.198264\pi$
$277$			5378.86i			1.16673i	−0.812210	+	0.583365i	$0.801736\pi$
$278$			702.952i			0.151656i
$279$	7923.21			1.70018
$280$		0			0
$281$	−4110.19			−0.872575			−0.436287	−	0.899807i	$-0.643707\pi$
$281$	−4110.19			−0.872575			−0.436287	+	0.899807i	$0.643707\pi$
$282$			5407.66i			1.14192i
$283$		−	5729.58i		−	1.20349i	−0.798688	−	0.601745i	$-0.794472\pi$
$283$		−	5729.58i		−	1.20349i	0.798688	−	0.601745i	$-0.205528\pi$
$284$	1410.33			0.294674
$285$	2933.03	+	1378.61i	0.609607	+	0.286532i
$286$	−543.435			−0.112356
$287$		0			0
$288$		−	2175.99i		−	0.445214i
$289$	−7118.78			−1.44897
$290$	−3718.58	−	1747.84i	−0.752975	−	0.353919i
$291$	−7638.79			−1.53881
$292$			239.014i			0.0479016i
$293$			6963.57i			1.38845i	0.719757	+	0.694226i	$0.244253\pi$
$293$			6963.57i			1.38845i	−0.719757	+	0.694226i	$0.755747\pi$
$294$		0			0
$295$	322.884	−	686.947i	0.0637255	−	0.135578i
$296$	3172.84			0.623032
$297$			2606.61i			0.509263i
$298$			1487.53i			0.289163i
$299$	7525.71			1.45560
$300$	3752.28	−	3109.72i	0.722126	−	0.598465i
$301$		0			0
$302$		−	3801.14i		−	0.724275i
$303$			3670.48i			0.695919i
$304$	−475.845			−0.0897749
$305$	2425.62	−	5160.60i	0.455379	−	0.968836i
$306$	−14917.7			−2.78689
$307$		−	3775.12i		−	0.701817i	−0.936410	−	0.350908i	$-0.885873\pi$
$307$		−	3775.12i		−	0.701817i	0.936410	−	0.350908i	$-0.114127\pi$
$308$		0			0
$309$	5264.61			0.969234
$310$	−2357.95	−	1108.30i	−0.432008	−	0.203055i
$311$	4237.62			0.772647			0.386324	−	0.922363i	$-0.373745\pi$
$311$	4237.62			0.772647			0.386324	+	0.922363i	$0.373745\pi$
$312$		−	3248.14i		−	0.589390i
$313$		−	3176.59i		−	0.573647i	−0.957983	−	0.286824i	$-0.907401\pi$
$313$		−	3176.59i		−	0.573647i	0.957983	−	0.286824i	$-0.0925994\pi$
$314$	2672.36			0.480286
$315$		0			0
$316$	−535.473			−0.0953251
$317$			1564.66i			0.277224i	0.990347	+	0.138612i	$0.0442640\pi$
$317$			1564.66i			0.277224i	−0.990347	+	0.138612i	$0.955736\pi$
$318$		−	7912.35i		−	1.39529i
$319$	−1198.59			−0.210371
$320$	−304.378	+	647.575i	−0.0531727	+	0.113127i
$321$	−9651.67			−1.67821
$322$		0			0
$323$			3262.20i			0.561962i
$324$	−8235.89			−1.41219
$325$	4009.19	−	3322.64i	0.684277	−	0.567098i
$326$	−502.636			−0.0853940
$327$		−	6149.05i		−	1.03989i
$328$		−	1578.20i		−	0.265675i
$329$		0			0
$330$	604.726	−	1286.58i	0.100876	−	0.214617i
$331$	−5238.60			−0.869907			−0.434954	−	0.900453i	$-0.643235\pi$
$331$	−5238.60			−0.869907			−0.434954	+	0.900453i	$0.643235\pi$
$332$			2286.83i			0.378031i
$333$		−	26969.0i		−	4.43812i
$334$	1697.85			0.278150
$335$	10384.0	+	4880.75i	1.69354	+	0.796012i
$336$		0			0
$337$		−	10272.8i		−	1.66051i	−0.557380	−	0.830257i	$-0.688193\pi$
$337$		−	10272.8i		−	1.66051i	0.557380	−	0.830257i	$-0.311807\pi$
$338$			923.466i			0.148609i
$339$	−14883.5			−2.38455
$340$	4439.51	+	2086.69i	0.708136	+	0.332843i
$341$	−760.025			−0.120697
$342$			4044.67i			0.639504i
$343$		0			0
$344$	2418.06			0.378991
$345$	−8374.50	+	17817.1i	−1.30686	+	2.78040i
$346$	−5617.34			−0.872804
$347$		−	3465.53i		−	0.536137i	−0.963400	−	0.268069i	$-0.913615\pi$
$347$		−	3465.53i		−	0.536137i	0.963400	−	0.268069i	$-0.0863854\pi$
$348$		−	7164.05i		−	1.10354i
$349$	542.927			0.0832729			0.0416364	−	0.999133i	$-0.486743\pi$
$349$	542.927			0.0832729			0.0416364	+	0.999133i	$0.486743\pi$
$350$		0			0
$351$	−16646.6			−2.53142
$352$			208.730i			0.0316060i
$353$		−	12470.2i		−	1.88024i	−0.340848	−	0.940118i	$-0.610714\pi$
$353$		−	12470.2i		−	1.88024i	0.340848	−	0.940118i	$-0.389286\pi$
$354$	1323.44			0.198701
$355$	−1676.85	+	3567.55i	−0.250698	+	0.533369i
$356$	2190.14			0.326059
$357$		0			0
$358$		−	8729.17i		−	1.28869i
$359$	−153.039			−0.0224988			−0.0112494	−	0.999937i	$-0.503581\pi$
$359$	−153.039			−0.0224988			−0.0112494	+	0.999937i	$0.503581\pi$
$360$	5504.37	+	2587.20i	0.805849	+	0.378771i
$361$	−5974.51			−0.871047
$362$			2320.92i			0.336975i
$363$			12558.3i			1.81581i
$364$		0			0
$365$	−604.609	−	284.183i	−0.0867032	−	0.0407529i
$366$	9942.16			1.41990
$367$			4349.29i			0.618614i	0.950962	+	0.309307i	$0.100097\pi$
$367$			4349.29i			0.618614i	−0.950962	+	0.309307i	$0.899903\pi$
$368$		−	2890.58i		−	0.409461i
$369$	−13414.6			−1.89251
$370$	−3772.43	+	8025.99i	−0.530053	+	1.12771i
$371$		0			0
$372$		−	4542.71i		−	0.633141i
$373$		−	4765.57i		−	0.661533i	−0.943713	−	0.330767i	$-0.892693\pi$
$373$		−	4765.57i		−	0.661533i	0.943713	−	0.330767i	$-0.107307\pi$
$374$	1430.96			0.197843
$375$	3404.94	+	13189.1i	0.468881	+	1.81622i
$376$	2219.26			0.304387
$377$		−	7654.56i		−	1.04570i
$378$		0			0
$379$	5358.54			0.726252			0.363126	−	0.931740i	$-0.381709\pi$
$379$	5358.54			0.726252			0.363126	+	0.931740i	$0.381709\pi$
$380$	565.769	−	1203.69i	0.0763772	−	0.162495i
$381$	−23698.9			−3.18670
$382$		−	5887.17i		−	0.788518i
$383$		−	191.833i		−	0.0255933i	−0.999918	−	0.0127966i	$-0.995927\pi$
$383$		−	191.833i		−	0.0255933i	0.999918	−	0.0127966i	$-0.00407341\pi$
$384$	−1247.59			−0.165796
$385$		0			0
$386$	−1847.07			−0.243558
$387$		−	20553.4i		−	2.69971i
$388$			3134.90i			0.410181i
$389$	8698.90			1.13381			0.566904	−	0.823784i	$-0.308141\pi$
$389$	8698.90			1.13381			0.566904	+	0.823784i	$0.308141\pi$
$390$	8216.46	+	3861.96i	1.06681	+	0.501431i
$391$	−19816.6			−2.56309
$392$		0			0
$393$			4226.94i			0.542547i
$394$	3452.83			0.441500
$395$	636.665	−	1354.53i	0.0810990	−	0.172541i
$396$	1774.19			0.225143
$397$		−	2982.58i		−	0.377056i	−0.982068	−	0.188528i	$-0.939628\pi$
$397$		−	2982.58i		−	0.377056i	0.982068	−	0.188528i	$-0.0603716\pi$
$398$			724.420i			0.0912360i
$399$		0			0
$400$	−1276.20	−	1539.90i	−0.159525	−	0.192488i
$401$	11128.1			1.38582			0.692909	−	0.721025i	$-0.256329\pi$
$401$	11128.1			1.38582			0.692909	+	0.721025i	$0.256329\pi$
$402$			20005.3i			2.48202i
$403$		−	4853.74i		−	0.599956i
$404$	1506.33			0.185502
$405$	9792.28	−	20833.4i	1.20144	−	2.55610i
$406$		0			0
$407$			2586.98i			0.315065i
$408$			8552.95i			1.03783i
$409$	4404.28			0.532464			0.266232	−	0.963909i	$-0.414221\pi$
$409$	4404.28			0.532464			0.266232	+	0.963909i	$0.414221\pi$
$410$	3992.19	+	1876.44i	0.480879	+	0.226026i
$411$	−8231.08			−0.987857
$412$		−	2160.55i		−	0.258356i
$413$		0			0
$414$	−24569.8			−2.91676
$415$	−5784.75	−	2718.99i	−0.684247	−	0.321614i
$416$	−1333.01			−0.157106
$417$		−	3425.76i		−	0.402302i
$418$		−	387.980i		−	0.0453989i
$419$	−6613.48			−0.771097			−0.385548	−	0.922688i	$-0.625988\pi$
$419$	−6613.48			−0.771097			−0.385548	+	0.922688i	$0.625988\pi$
$420$		0			0
$421$	−1465.77			−0.169685			−0.0848425	−	0.996394i	$-0.527039\pi$
$421$	−1465.77			−0.169685			−0.0848425	+	0.996394i	$0.527039\pi$
$422$		−	276.081i		−	0.0318470i
$423$		−	18863.6i		−	2.16828i
$424$	−3247.17			−0.371925
$425$	−10557.0	+	8749.13i	−1.20491	+	0.998576i
$426$	−6873.08			−0.781694
$427$		0			0
$428$			3960.97i			0.447338i
$429$	2648.37			0.298052
$430$	−2875.01	+	6116.69i	−0.322431	+	0.685984i
$431$	2508.55			0.280354			0.140177	−	0.990126i	$-0.455233\pi$
$431$	2508.55			0.280354			0.140177	+	0.990126i	$0.455233\pi$
$432$			6393.85i			0.712093i
$433$			771.874i			0.0856672i	0.999082	+	0.0428336i	$0.0136385\pi$
$433$			771.874i			0.0856672i	−0.999082	+	0.0428336i	$0.986361\pi$
$434$		0			0
$435$	18122.1	+	8517.89i	1.99745	+	0.938854i
$436$	−2523.52			−0.277189
$437$			5372.91i			0.588150i
$438$		−	1164.81i		−	0.127070i
$439$	−7613.29			−0.827705			−0.413852	−	0.910344i	$-0.635817\pi$
$439$	−7613.29			−0.827705			−0.413852	+	0.910344i	$0.635817\pi$
$440$	−528.001	−	248.175i	−0.0572078	−	0.0268892i
$441$		0			0
$442$			9138.57i			0.983433i
$443$			3896.21i			0.417865i	0.977930	+	0.208933i	$0.0669989\pi$
$443$			3896.21i			0.417865i	−0.977930	+	0.208933i	$0.933001\pi$
$444$	−15462.5			−1.65274
$445$	−2604.02	+	5540.15i	−0.277399	+	0.590176i
$446$	2507.70			0.266240
$447$		−	7249.33i		−	0.767073i
$448$		0			0
$449$	940.538			0.0988569			0.0494285	−	0.998778i	$-0.484260\pi$
$449$	940.538			0.0988569			0.0494285	+	0.998778i	$0.484260\pi$
$450$	−13089.1	+	10847.7i	−1.37117	+	1.13637i
$451$	1286.78			0.134351
$452$			6108.08i			0.635619i
$453$			18524.5i			1.92131i
$454$	13150.3			1.35942
$455$		0			0
$456$	2318.98			0.238149
$457$			15441.7i			1.58059i	0.612724	+	0.790297i	$0.290074\pi$
$457$			15441.7i			1.58059i	−0.612724	+	0.790297i	$0.709926\pi$
$458$			5219.67i			0.532531i
$459$	43833.6			4.45747
$460$	7311.98	+	3436.83i	0.741136	+	0.348354i
$461$	10448.7			1.05563			0.527814	−	0.849360i	$-0.323012\pi$
$461$	10448.7			1.05563			0.527814	+	0.849360i	$0.323012\pi$
$462$		0			0
$463$		−	3706.21i		−	0.372014i	−0.982548	−	0.186007i	$-0.940445\pi$
$463$		−	3706.21i		−	0.372014i	0.982548	−	0.186007i	$-0.0595547\pi$
$464$	−2940.07			−0.294158
$465$	11491.2	+	5401.18i	1.14600	+	0.538653i
$466$	5752.05			0.571799
$467$		−	3776.68i		−	0.374227i	−0.982338	−	0.187113i	$-0.940087\pi$
$467$		−	3776.68i		−	0.374227i	0.982338	−	0.187113i	$-0.0599132\pi$
$468$			11330.5i			1.11913i
$469$		0			0
$470$	−2638.65	+	5613.82i	−0.258961	+	0.550950i
$471$	−13023.4			−1.27407
$472$		−	543.129i		−	0.0529651i
$473$			1971.56i			0.191654i
$474$	2609.57			0.252872
$475$	2372.17	+	2862.33i	0.229142	+	0.276490i
$476$		0			0
$477$			27600.8i			2.64938i
$478$		−	9658.47i		−	0.924201i
$479$	13515.6			1.28924			0.644619	−	0.764504i	$-0.277016\pi$
$479$	13515.6			1.28924			0.644619	+	0.764504i	$0.277016\pi$
$480$	1483.35	−	3155.89i	0.141053	−	0.300096i
$481$	−16521.2			−1.56612
$482$		−	4893.01i		−	0.462387i
$483$		0			0
$484$	5153.81			0.484017
$485$	−7930.01	−	3727.32i	−0.742439	−	0.348967i
$486$	18557.5			1.73206
$487$			7262.21i			0.675733i	0.941194	+	0.337867i	$0.109705\pi$
$487$			7262.21i			0.675733i	−0.941194	+	0.337867i	$0.890295\pi$
$488$		−	4080.18i		−	0.378486i
$489$	2449.54			0.226528
$490$		0			0
$491$	−1732.41			−0.159231			−0.0796157	−	0.996826i	$-0.525369\pi$
$491$	−1732.41			−0.159231			−0.0796157	+	0.996826i	$0.525369\pi$
$492$			7691.17i			0.704766i
$493$			20155.9i			1.84133i
$494$	2477.76			0.225667
$495$	−2109.48	+	4487.99i	−0.191543	+	0.407515i
$496$	−1864.29			−0.168768
$497$		0			0
$498$		−	11144.6i		−	1.00282i
$499$	2283.04			0.204816			0.102408	−	0.994742i	$-0.467345\pi$
$499$	2283.04			0.204816			0.102408	+	0.994742i	$0.467345\pi$
$500$	5412.71	−	1397.36i	0.484127	−	0.124984i
$501$	−8274.28			−0.737859
$502$		−	11416.6i		−	1.01504i
$503$		−	12133.3i		−	1.07554i	−0.843091	−	0.537771i	$-0.819267\pi$
$503$		−	12133.3i		−	1.07554i	0.843091	−	0.537771i	$-0.180733\pi$
$504$		0			0
$505$	−1791.00	+	3810.41i	−0.157818	+	0.335764i
$506$	2356.83			0.207063
$507$		−	4500.41i		−	0.394222i
$508$			9725.85i			0.849439i
$509$	14159.2			1.23299			0.616497	−	0.787358i	$-0.288551\pi$
$509$	14159.2			1.23299			0.616497	+	0.787358i	$0.288551\pi$
$510$	−21635.5	−	10169.3i	−1.87850	−	0.882946i
$511$		0			0
$512$			512.000i			0.0441942i
$513$		−	11884.7i		−	1.02285i
$514$	−4875.80			−0.418409
$515$	5465.32	+	2568.85i	0.467632	+	0.219800i
$516$	−11784.1			−1.00536
$517$			1809.47i			0.153928i
$518$		0			0
$519$	27375.5			2.31532
$520$	1584.92	−	3371.97i	0.133660	−	0.284367i
$521$	19447.0			1.63530			0.817648	−	0.575719i	$-0.195278\pi$
$521$	19447.0			1.63530			0.817648	+	0.575719i	$0.195278\pi$
$522$			24990.5i			2.09541i
$523$		−	17829.3i		−	1.49067i	−0.666689	−	0.745336i	$-0.732289\pi$
$523$		−	17829.3i		−	1.49067i	0.666689	−	0.745336i	$-0.267711\pi$
$524$	1734.70			0.144620
$525$		0			0
$526$	4627.07			0.383555
$527$			12780.8i			1.05643i
$528$		−	1017.22i		−	0.0838425i
$529$	−20471.4			−1.68253
$530$	3860.80	−	8214.00i	0.316420	−	0.673195i
$531$	−4616.58			−0.377293
$532$		0			0
$533$			8217.78i			0.667826i
$534$	−10673.4			−0.864948
$535$	−10019.6	−	4709.50i	−0.809694	−	0.380578i
$536$	8210.00			0.661601
$537$			42540.7i			3.41856i
$538$			13123.3i			1.05165i
$539$		0			0
$540$	−16173.8	−	7602.14i	−1.28891	−	0.605822i
$541$	−4620.93			−0.367226			−0.183613	−	0.982999i	$-0.558779\pi$
$541$	−4620.93			−0.367226			−0.183613	+	0.982999i	$0.558779\pi$
$542$		−	7476.12i		−	0.592485i
$543$		−	11310.8i		−	0.893907i
$544$	3510.06			0.276641
$545$	3000.41	−	6383.47i	0.235822	−	0.501721i
$546$		0			0
$547$		−	1958.37i		−	0.153078i	−0.997067	−	0.0765392i	$-0.975613\pi$
$547$		−	1958.37i		−	0.153078i	0.997067	−	0.0765392i	$-0.0243870\pi$
$548$			3377.97i			0.263320i
$549$	−34681.4			−2.69611
$550$	1255.56	−	1040.55i	0.0973406	−	0.0806714i
$551$	5464.91			0.422528
$552$			14086.9i			1.08619i
$553$		0			0
$554$	−10757.7			−0.825003
$555$	18384.5	−	39113.8i	1.40609	−	2.99151i
$556$	−1405.90			−0.107237
$557$		−	13362.8i		−	1.01652i	−0.861204	−	0.508259i	$-0.830289\pi$
$557$		−	13362.8i		−	1.01652i	0.861204	−	0.508259i	$-0.169711\pi$
$558$			15846.4i			1.20221i
$559$	−12591.0			−0.952668
$560$		0			0
$561$	−6973.65			−0.524827
$562$		−	8220.38i		−	0.617004i
$563$		−	4126.24i		−	0.308882i	−0.988002	−	0.154441i	$-0.950642\pi$
$563$		−	4126.24i		−	0.308882i	0.988002	−	0.154441i	$-0.0493576\pi$
$564$	−10815.3			−0.807460
$565$	−15450.9	−	7262.37i	−1.15049	−	0.540761i
$566$	11459.2			0.850997
$567$		0			0
$568$			2820.66i			0.208366i
$569$	10707.3			0.788881			0.394440	−	0.918922i	$-0.370938\pi$
$569$	10707.3			0.788881			0.394440	+	0.918922i	$0.370938\pi$
$570$	−2757.21	+	5866.07i	−0.202609	+	0.431057i
$571$	12298.8			0.901383			0.450692	−	0.892680i	$-0.351177\pi$
$571$	12298.8			0.901383			0.450692	+	0.892680i	$0.351177\pi$
$572$		−	1086.87i		−	0.0794480i
$573$			28690.5i			2.09173i
$574$		0			0
$575$	−17387.5	+	14410.0i	−1.26106	+	1.04511i
$576$	4351.98			0.314814
$577$		−	11643.7i		−	0.840095i	−0.907502	−	0.420047i	$-0.862013\pi$
$577$		−	11643.7i		−	0.840095i	0.907502	−	0.420047i	$-0.137987\pi$
$578$		−	14237.6i		−	1.02457i
$579$	9001.50			0.646096
$580$	3495.67	−	7437.17i	0.250258	−	0.532434i
$581$		0			0
$582$		−	15277.6i		−	1.08810i
$583$		−	2647.58i		−	0.188081i
$584$	−478.029			−0.0338715
$585$	−28661.6	−	13471.7i	−2.02566	−	0.952116i
$586$	−13927.1			−0.981783
$587$			10661.8i			0.749676i	0.927090	+	0.374838i	$0.122302\pi$
$587$			10661.8i			0.749676i	−0.927090	+	0.374838i	$0.877698\pi$
$588$		0			0
$589$	3465.29			0.242419
$590$	1373.89	+	645.768i	0.0958683	+	0.0450607i
$591$	−16827.0			−1.17118
$592$			6345.68i			0.440550i
$593$		−	6638.45i		−	0.459711i	−0.973225	−	0.229855i	$-0.926175\pi$
$593$		−	6638.45i		−	0.459711i	0.973225	−	0.229855i	$-0.0738253\pi$
$594$	−5213.22			−0.360103
$595$		0			0
$596$	−2975.07			−0.204469
$597$		−	3530.38i		−	0.242025i
$598$			15051.4i			1.02926i
$599$	−6461.72			−0.440766			−0.220383	−	0.975413i	$-0.570731\pi$
$599$	−6461.72			−0.440766			−0.220383	+	0.975413i	$0.570731\pi$
$600$	6219.44	+	7504.56i	0.423179	+	0.510620i
$601$	11580.8			0.786010			0.393005	−	0.919536i	$-0.371436\pi$
$601$	11580.8			0.786010			0.393005	+	0.919536i	$0.371436\pi$
$602$		0			0
$603$		−	69784.7i		−	4.71286i
$604$	7602.28			0.512140
$605$	−6127.76	+	13037.0i	−0.411784	+	0.876084i
$606$	−7340.95			−0.492089
$607$		−	18619.2i		−	1.24503i	−0.782610	−	0.622513i	$-0.786112\pi$
$607$		−	18619.2i		−	1.24503i	0.782610	−	0.622513i	$-0.213888\pi$
$608$		−	951.690i		−	0.0634805i
$609$		0			0
$610$	10321.2	+	4851.24i	0.685071	+	0.322002i
$611$	−11555.8			−0.765138
$612$		−	29835.4i		−	1.97063i
$613$			5600.84i			0.369031i	0.982830	+	0.184515i	$0.0590716\pi$
$613$			5600.84i			0.369031i	−0.982830	+	0.184515i	$0.940928\pi$
$614$	7550.25			0.496259
$615$	−19455.5	−	9144.63i	−1.27565	−	0.599588i
$616$		0			0
$617$			26313.7i			1.71694i	0.512865	+	0.858469i	$0.328584\pi$
$617$			26313.7i			1.71694i	−0.512865	+	0.858469i	$0.671416\pi$
$618$			10529.2i			0.685352i
$619$	4736.19			0.307534			0.153767	−	0.988107i	$-0.450860\pi$
$619$	4736.19			0.307534			0.153767	+	0.988107i	$0.450860\pi$
$620$	2216.60	−	4715.89i	0.143582	−	0.305476i
$621$	72194.9			4.66519
$622$			8475.24i			0.546344i
$623$		0			0
$624$	6496.27			0.416761
$625$	−2900.83	+	15353.4i	−0.185653	+	0.982615i
$626$	6353.18			0.405630
$627$			1890.78i			0.120431i
$628$			5344.72i			0.339614i
$629$	43503.4			2.75770
$630$		0			0
$631$	2681.60			0.169180			0.0845902	−	0.996416i	$-0.473042\pi$
$631$	2681.60			0.169180			0.0845902	+	0.996416i	$0.473042\pi$
$632$		−	1070.95i		−	0.0674050i
$633$			1345.45i			0.0844817i
$634$	−3129.31			−0.196027
$635$	−24602.4	−	11563.8i	−1.53751	−	0.722671i
$636$	15824.7			0.986620
$637$		0			0
$638$		−	2397.18i		−	0.148755i
$639$	23975.5			1.48428
$640$	−1295.15	−	608.756i	−0.0799927	−	0.0375988i
$641$	−9799.52			−0.603834			−0.301917	−	0.953334i	$-0.597627\pi$
$641$	−9799.52			−0.603834			−0.301917	+	0.953334i	$0.597627\pi$
$642$		−	19303.3i		−	1.18667i
$643$			3697.53i			0.226775i	0.993551	+	0.113388i	$0.0361702\pi$
$643$			3697.53i			0.226775i	−0.993551	+	0.113388i	$0.963830\pi$
$644$		0			0
$645$	14011.1	−	29809.0i	0.855325	−	1.81974i
$646$	−6524.40			−0.397367
$647$		−	15270.7i		−	0.927903i	−0.885861	−	0.463951i	$-0.846431\pi$
$647$		−	15270.7i		−	0.927903i	0.885861	−	0.463951i	$-0.153569\pi$
$648$		−	16471.8i		−	0.998568i
$649$	442.840			0.0267843
$650$	6645.27	+	8018.39i	0.400999	+	0.483857i
$651$		0			0
$652$		−	1005.27i		−	0.0603827i
$653$		−	20504.5i		−	1.22880i	−0.788996	−	0.614399i	$-0.789399\pi$
$653$		−	20504.5i		−	1.22880i	0.788996	−	0.614399i	$-0.210601\pi$
$654$	12298.1			0.735311
$655$	−2062.52	+	4388.09i	−0.123037	+	0.261766i
$656$	3156.39			0.187861
$657$			4063.23i			0.241281i
$658$		0			0
$659$	−24774.9			−1.46448			−0.732241	−	0.681046i	$-0.761525\pi$
$659$	−24774.9			−1.46448			−0.732241	+	0.681046i	$0.761525\pi$
$660$	2573.15	+	1209.45i	0.151757	+	0.0713301i
$661$	−15616.3			−0.918914			−0.459457	−	0.888200i	$-0.651956\pi$
$661$	−15616.3			−0.918914			−0.459457	+	0.888200i	$0.651956\pi$
$662$		−	10477.2i		−	0.615117i
$663$		−	44535.8i		−	2.60879i
$664$	−4573.66			−0.267308
$665$		0			0
$666$	53938.1			3.13823
$667$			33197.2i			1.92714i
$668$			3395.70i			0.196682i
$669$	−12221.0			−0.706265
$670$	−9761.50	+	20768.0i	−0.562865	+	1.19752i
$671$	3326.78			0.191399
$672$		0			0
$673$			20453.3i			1.17150i	0.810493	+	0.585748i	$0.199199\pi$
$673$			20453.3i			1.17150i	−0.810493	+	0.585748i	$0.800801\pi$
$674$	20545.5			1.17416
$675$	38460.6	−	31874.4i	2.19311	−	1.81755i
$676$	−1846.93			−0.105083
$677$		−	20322.5i		−	1.15370i	−0.816850	−	0.576851i	$-0.804281\pi$
$677$		−	20322.5i		−	1.15370i	0.816850	−	0.576851i	$-0.195719\pi$
$678$		−	29767.1i		−	1.68613i
$679$		0			0
$680$	−4173.38	+	8879.03i	−0.235356	+	0.500728i
$681$	−64086.8			−3.60618
$682$		−	1520.05i		−	0.0853456i
$683$			20503.2i			1.14866i	0.818625	+	0.574329i	$0.194737\pi$
$683$			20503.2i			1.14866i	−0.818625	+	0.574329i	$0.805263\pi$
$684$	−8089.33			−0.452198
$685$	−8544.88	−	4016.32i	−0.476617	−	0.224023i
$686$		0			0
$687$		−	25437.5i		−	1.41267i
$688$			4836.11i			0.267987i
$689$	16908.2			0.934908
$690$	−35634.1	−	16749.0i	−1.96604	−	0.924092i
$691$	25278.2			1.39165			0.695825	−	0.718212i	$-0.255039\pi$
$691$	25278.2			1.39165			0.695825	+	0.718212i	$0.255039\pi$
$692$		−	11234.7i		−	0.617165i
$693$		0			0
$694$	6931.07			0.379106
$695$	1671.59	−	3556.36i	0.0912330	−	0.194101i
$696$	14328.1			0.780323
$697$		−	21639.0i		−	1.17595i
$698$			1085.85i			0.0588828i
$699$	−28032.0			−1.51683
$700$		0			0
$701$	−9908.61			−0.533870			−0.266935	−	0.963715i	$-0.586011\pi$
$701$	−9908.61			−0.533870			−0.266935	+	0.963715i	$0.586011\pi$
$702$		−	33293.2i		−	1.78999i
$703$		−	11795.2i		−	0.632806i
$704$	−417.459			−0.0223488
$705$	12859.2	−	27358.4i	0.686957	−	1.46153i
$706$	24940.5			1.32953
$707$		0			0
$708$			2646.88i			0.140503i
$709$	36431.3			1.92977			0.964884	−	0.262677i	$-0.0846054\pi$
$709$	36431.3			1.92977			0.964884	+	0.262677i	$0.0846054\pi$
$710$	−7135.11	−	3353.69i	−0.377149	−	0.177270i
$711$	−9103.01			−0.480154
$712$			4380.27i			0.230558i
$713$			21050.3i			1.10567i
$714$		0			0
$715$	2749.33	+	1292.26i	0.143803	+	0.0675914i
$716$	17458.3			0.911241
$717$			47069.5i			2.45166i
$718$		−	306.078i		−	0.0159091i
$719$	−15780.2			−0.818500			−0.409250	−	0.912422i	$-0.634210\pi$
$719$	−15780.2			−0.818500			−0.409250	+	0.912422i	$0.634210\pi$
$720$	−5174.41	+	11008.7i	−0.267832	+	0.569822i
$721$		0			0
$722$		−	11949.0i		−	0.615924i
$723$			23845.6i			1.22659i
$724$	−4641.85			−0.238278
$725$	14656.7	+	17685.2i	0.750810	+	0.905949i
$726$	−25116.5			−1.28397
$727$			77.3767i			0.00394738i	0.999998	+	0.00197369i	$0.000628245\pi$
$727$			77.3767i			0.00394738i	−0.999998	+	0.00197369i	$0.999372\pi$
$728$		0			0
$729$	−34845.5			−1.77033
$730$	568.365	−	1209.22i	0.0288166	−	0.0613084i
$731$	33154.4			1.67751
$732$			19884.3i			1.00402i
$733$			33094.1i			1.66761i	0.552061	+	0.833804i	$0.313842\pi$
$733$			33094.1i			1.66761i	−0.552061	+	0.833804i	$0.686158\pi$
$734$	−8698.59			−0.437426
$735$		0			0
$736$	5781.15			0.289533
$737$			6694.02i			0.334569i
$738$		−	26829.2i		−	1.33821i
$739$	−31464.3			−1.56621			−0.783107	−	0.621888i	$-0.786366\pi$
$739$	−31464.3			−1.56621			−0.783107	+	0.621888i	$0.786366\pi$
$740$	−16052.0	−	7544.87i	−0.797409	−	0.374804i
$741$	−12075.1			−0.598636
$742$		0			0
$743$			27497.1i			1.35770i	0.734277	+	0.678850i	$0.237522\pi$
$743$			27497.1i			1.35770i	−0.734277	+	0.678850i	$0.762478\pi$
$744$	9085.42			0.447698
$745$	3537.28	−	7525.70i	0.173954	−	0.370094i
$746$	9531.14			0.467775
$747$			38876.0i			1.90415i
$748$			2861.93i			0.139896i
$749$		0			0
$750$	−26378.2	+	6809.89i	−1.28426	+	0.331549i
$751$	145.407			0.00706524			0.00353262	−	0.999994i	$-0.498876\pi$
$751$	145.407			0.00706524			0.00353262	+	0.999994i	$0.498876\pi$
$752$			4438.52i			0.215234i
$753$			55637.7i			2.69263i
$754$	15309.1			0.739424
$755$	−9038.94	+	19230.7i	−0.435710	+	0.926988i
$756$		0			0
$757$		−	3458.16i		−	0.166036i	−0.996548	−	0.0830179i	$-0.973544\pi$
$757$		−	3458.16i		−	0.166036i	0.996548	−	0.0830179i	$-0.0264559\pi$
$758$			10717.1i			0.513538i
$759$	−11485.8			−0.549284
$760$	2407.39	+	1131.54i	0.114901	+	0.0540068i
$761$	8901.33			0.424012			0.212006	−	0.977268i	$-0.432000\pi$
$761$	8901.33			0.424012			0.212006	+	0.977268i	$0.432000\pi$
$762$		−	47397.9i		−	2.25334i
$763$		0			0
$764$	11774.3			0.557567
$765$	75471.4	+	35473.6i	3.56690	+	1.67654i
$766$	383.667			0.0180972
$767$			2828.11i			0.133138i
$768$		−	2495.18i		−	0.117236i
$769$	−16746.3			−0.785289			−0.392645	−	0.919690i	$-0.628440\pi$
$769$	−16746.3			−0.785289			−0.392645	+	0.919690i	$0.628440\pi$
$770$		0			0
$771$	23761.7			1.10993
$772$		−	3694.14i		−	0.172222i
$773$		−	11592.0i		−	0.539375i	−0.962948	−	0.269687i	$-0.913080\pi$
$773$		−	11592.0i		−	0.539375i	0.962948	−	0.269687i	$-0.0869204\pi$
$774$	41106.8			1.90898
$775$	9293.80	+	11214.2i	0.430765	+	0.519774i
$776$	−6269.79			−0.290042
$777$		0			0
$778$			17397.8i			0.801724i
$779$	−5867.01			−0.269843
$780$	−7723.92	+	16432.9i	−0.354565	+	0.754350i
$781$	−2299.82			−0.105370
$782$		−	39633.2i		−	1.81238i
$783$		−	73431.0i		−	3.35148i
$784$		0			0
$785$	−13520.0	−	6354.74i	−0.614710	−	0.288931i
$786$	−8453.88			−0.383639
$787$			40705.9i			1.84372i	0.387522	+	0.921861i	$0.373331\pi$
$787$			40705.9i			1.84372i	−0.387522	+	0.921861i	$0.626669\pi$
$788$			6905.66i			0.312188i
$789$	−22549.5			−1.01747
$790$	2709.06	+	1273.33i	0.122005	+	0.0573457i
$791$		0			0
$792$			3548.39i			0.159200i
$793$			21245.8i			0.951400i
$794$	5965.16			0.266619
$795$	−18815.2	+	40030.0i	−0.839380	+	1.78581i
$796$	−1448.84			−0.0645136
$797$		−	38472.5i		−	1.70987i	−0.518734	−	0.854936i	$-0.673596\pi$
$797$		−	38472.5i		−	1.70987i	0.518734	−	0.854936i	$-0.326404\pi$
$798$		0			0
$799$	30428.7			1.34730
$800$	3079.81	−	2552.41i	0.136110	−	0.112801i
$801$	37232.2			1.64236
$802$			22256.3i			0.979921i
$803$		−	389.761i		−	0.0171287i
$804$	−40010.5			−1.75505
$805$		0			0
$806$	9707.49			0.424233
$807$		−	63954.9i		−	2.78974i
$808$			3012.67i			0.131170i
$809$	−32354.5			−1.40609			−0.703044	−	0.711146i	$-0.748176\pi$
$809$	−32354.5			−1.40609			−0.703044	+	0.711146i	$0.748176\pi$
$810$	41666.9	+	19584.6i	1.80744	+	0.849545i
$811$	34184.2			1.48011			0.740055	−	0.672546i	$-0.234799\pi$
$811$	34184.2			1.48011			0.740055	+	0.672546i	$0.234799\pi$
$812$		0			0
$813$			36434.1i			1.57171i
$814$	−5173.95			−0.222785
$815$	2542.93	+	1195.25i	0.109294	+	0.0513713i
$816$	−17105.9			−0.733856
$817$		−	8989.22i		−	0.384936i
$818$			8808.56i			0.376509i
$819$		0			0
$820$	−3752.88	+	7984.39i	−0.159825	+	0.340033i
$821$	−301.498			−0.0128165			−0.00640825	−	0.999979i	$-0.502040\pi$
$821$	−301.498			−0.0128165			−0.00640825	+	0.999979i	$0.502040\pi$
$822$		−	16462.2i		−	0.698520i
$823$		−	18337.9i		−	0.776696i	−0.921513	−	0.388348i	$-0.873046\pi$
$823$		−	18337.9i		−	0.776696i	0.921513	−	0.388348i	$-0.126954\pi$
$824$	4321.11			0.182686
$825$	−6118.84	+	5071.02i	−0.258219	+	0.214000i
$826$		0			0
$827$			1984.76i			0.0834545i	0.999129	+	0.0417273i	$0.0132861\pi$
$827$			1984.76i			0.0834545i	−0.999129	+	0.0417273i	$0.986714\pi$
$828$		−	49139.6i		−	2.06246i
$829$	−13978.8			−0.585652			−0.292826	−	0.956166i	$-0.594596\pi$
$829$	−13978.8			−0.585652			−0.292826	+	0.956166i	$0.594596\pi$
$830$	5437.98	−	11569.5i	0.227416	−	0.483835i
$831$	52426.6			2.18852
$832$		−	2666.02i		−	0.111091i
$833$		0			0
$834$	6851.52			0.284471
$835$	−8589.72	−	4037.40i	−0.356000	−	0.167329i
$836$	775.960			0.0321019
$837$		−	46562.5i		−	1.92286i
$838$		−	13227.0i		−	0.545248i
$839$	39047.2			1.60675			0.803373	−	0.595477i	$-0.203037\pi$
$839$	39047.2			1.60675			0.803373	+	0.595477i	$0.203037\pi$
$840$		0			0
$841$	9376.59			0.384460
$842$		−	2931.54i		−	0.119985i
$843$			40061.1i			1.63675i
$844$	552.163			0.0225192
$845$	2195.96	−	4671.99i	0.0894004	−	0.190203i
$846$	37727.3			1.53320
$847$		0			0
$848$		−	6494.33i		−	0.262991i
$849$	−55844.9			−2.25747
$850$	−17498.3	−	21113.9i	−0.706100	−	0.852001i
$851$	71651.1			2.88621
$852$		−	13746.2i		−	0.552741i
$853$		−	26029.2i		−	1.04481i	−0.852697	−	0.522406i	$-0.825035\pi$
$853$		−	26029.2i		−	1.04481i	0.852697	−	0.522406i	$-0.174965\pi$
$854$		0			0
$855$	9618.03	−	20462.7i	0.384713	−	0.818491i
$856$	−7921.94			−0.316316
$857$			28005.7i			1.11629i	0.829745	+	0.558143i	$0.188486\pi$
$857$			28005.7i			1.11629i	−0.829745	+	0.558143i	$0.811514\pi$
$858$			5296.74i			0.210755i
$859$	26923.4			1.06940			0.534700	−	0.845042i	$-0.320424\pi$
$859$	26923.4			1.06940			0.534700	+	0.845042i	$0.320424\pi$
$860$	−12233.4	−	5750.02i	−0.485064	−	0.227993i
$861$		0			0
$862$			5017.11i			0.198241i
$863$			21827.7i			0.860977i	0.902596	+	0.430489i	$0.141659\pi$
$863$			21827.7i			0.860977i	−0.902596	+	0.430489i	$0.858341\pi$
$864$	−12787.7			−0.503526
$865$	28419.2	+	13357.8i	1.11709	+	0.525061i
$866$	−1543.75			−0.0605758
$867$			69385.2i			2.71793i
$868$		0			0
$869$	873.196			0.0340865
$870$	−17035.8	+	36244.2i	−0.663870	+	1.41241i
$871$	−42750.0			−1.66306
$872$		−	5047.04i		−	0.196003i
$873$			53293.0i			2.06609i
$874$	−10745.8			−0.415885
$875$		0			0
$876$	2329.62			0.0898523
$877$			33776.2i			1.30050i	0.759718	+	0.650252i	$0.225337\pi$
$877$			33776.2i			1.30050i	−0.759718	+	0.650252i	$0.774663\pi$
$878$		−	15226.6i		−	0.585276i
$879$	67872.4			2.60441
$880$	496.349	−	1056.00i	0.0190136	−	0.0404520i
$881$	−14856.2			−0.568124			−0.284062	−	0.958806i	$-0.591682\pi$
$881$	−14856.2			−0.568124			−0.284062	+	0.958806i	$0.591682\pi$
$882$		0			0
$883$		−	37359.7i		−	1.42384i	−0.702259	−	0.711922i	$-0.747825\pi$
$883$		−	37359.7i		−	1.42384i	0.702259	−	0.711922i	$-0.252175\pi$
$884$	−18277.1			−0.695392
$885$	−6695.52	−	3147.08i	−0.254314	−	0.119534i
$886$	−7792.41			−0.295475
$887$			41112.5i			1.55628i	0.628090	+	0.778141i	$0.283837\pi$
$887$			41112.5i			1.55628i	−0.628090	+	0.778141i	$0.716163\pi$
$888$		−	30925.0i		−	1.16866i
$889$		0			0
$890$	−11080.3	−	5208.04i	−0.417317	−	0.196150i
$891$	13430.3			0.504973
$892$			5015.40i			0.188260i
$893$		−	8250.19i		−	0.309162i
$894$	14498.7			0.542402
$895$	−20757.6	+	44162.5i	−0.775250	+	1.64937i
$896$		0			0
$897$		−	73351.5i		−	2.73036i
$898$			1881.08i			0.0699024i
$899$	21410.7			0.794312
$900$	−21695.4	−	26178.3i	−0.803532	−	0.969566i
$901$	−44522.5			−1.64624
$902$			2573.57i			0.0950004i
$903$		0			0
$904$	−12216.2			−0.449451
$905$	5519.05	−	11742.0i	0.202718	−	0.431289i
$906$	−37048.9			−1.35857
$907$			4254.97i			0.155771i	0.996962	+	0.0778854i	$0.0248168\pi$
$907$			4254.97i			0.155771i	−0.996962	+	0.0778854i	$0.975183\pi$
$908$			26300.7i			0.961254i
$909$	25607.6			0.934378
$910$		0			0
$911$	−33342.0			−1.21259			−0.606295	−	0.795240i	$-0.707345\pi$
$911$	−33342.0			−1.21259			−0.606295	+	0.795240i	$0.707345\pi$
$912$			4637.96i			0.168397i
$913$		−	3729.14i		−	0.135177i
$914$	−30883.4			−1.11765
$915$	−50299.2	−	23642.0i	−1.81731	−	0.854186i
$916$	−10439.3			−0.376557
$917$		0			0
$918$			87667.2i			3.15191i
$919$	19686.0			0.706618			0.353309	−	0.935507i	$-0.385056\pi$
$919$	19686.0			0.706618			0.353309	+	0.935507i	$0.385056\pi$
$920$	−6873.66	+	14624.0i	−0.246324	+	0.524063i
$921$	−36795.3			−1.31645
$922$			20897.4i			0.746442i
$923$		−	14687.3i		−	0.523770i
$924$		0			0
$925$	38170.9	−	31634.3i	1.35681	−	1.12446i
$926$	7412.43			0.263053
$927$		−	36729.3i		−	1.30135i
$928$		−	5880.13i		−	0.208001i
$929$	−934.742			−0.0330117			−0.0165059	−	0.999864i	$-0.505254\pi$
$929$	−934.742			−0.0330117			−0.0165059	+	0.999864i	$0.505254\pi$
$930$	−10802.4	+	22982.4i	−0.380885	+	0.810347i
$931$		0			0
$932$			11504.1i			0.404323i
$933$		−	41303.1i		−	1.44931i
$934$	7553.36			0.264618
$935$	−7239.51	−	3402.77i	−0.253216	−	0.119019i
$936$	−22661.1			−0.791346
$937$			29911.4i			1.04286i	0.853294	+	0.521431i	$0.174602\pi$
$937$			29911.4i			1.04286i	−0.853294	+	0.521431i	$0.825398\pi$
$938$		0			0
$939$	−30961.5			−1.07603
$940$	−11227.6	−	5277.30i	−0.389580	−	0.183113i
$941$	8914.00			0.308808			0.154404	−	0.988008i	$-0.450654\pi$
$941$	8914.00			0.308808			0.154404	+	0.988008i	$0.450654\pi$
$942$		−	26046.9i		−	0.900906i
$943$		−	35639.8i		−	1.23075i
$944$	1086.26			0.0374520
$945$		0			0
$946$	−3943.12			−0.135520
$947$		−	55917.2i		−	1.91876i	−0.282120	−	0.959379i	$-0.591038\pi$
$947$		−	55917.2i		−	1.91876i	0.282120	−	0.959379i	$-0.408962\pi$
$948$			5219.14i			0.178808i
$949$	2489.13			0.0851428
$950$	−5724.65	+	4744.33i	−0.195508	+	0.162028i
$951$	15250.4			0.520007
$952$		0			0
$953$			27010.1i			0.918092i	0.888413	+	0.459046i	$0.151809\pi$
$953$			27010.1i			0.918092i	−0.888413	+	0.459046i	$0.848191\pi$
$954$	−55201.6			−1.87339
$955$	−13999.4	+	29784.3i	−0.474357	+	1.00921i
$956$	19316.9			0.653509
$957$			11682.4i			0.394607i
$958$			27031.3i			0.911630i
$959$		0			0
$960$	6311.78	+	2966.71i	0.212200	+	0.0997396i
$961$	−16214.5			−0.544276
$962$		−	33042.4i		−	1.10741i
$963$			67336.2i			2.25325i
$964$	9786.02			0.326957
$965$	9344.67	+	4392.25i	0.311726	+	0.146520i
$966$		0			0
$967$			43263.4i			1.43873i	0.694630	+	0.719367i	$0.255568\pi$
$967$			43263.4i			1.43873i	−0.694630	+	0.719367i	$0.744432\pi$
$968$			10307.6i			0.342252i
$969$	31795.9			1.05411
$970$	7454.64	−	15860.0i	0.246757	−	0.524984i
$971$	−14329.1			−0.473575			−0.236787	−	0.971561i	$-0.576095\pi$
$971$	−14329.1			−0.473575			−0.236787	+	0.971561i	$0.576095\pi$
$972$			37114.9i			1.22475i
$973$		0			0
$974$	−14524.4			−0.477816
$975$	−32385.0	−	39076.7i	−1.06374	−	1.28355i
$976$	8160.37			0.267630
$977$			18963.4i			0.620976i	0.950577	+	0.310488i	$0.100492\pi$
$977$			18963.4i			0.620976i	−0.950577	+	0.310488i	$0.899508\pi$
$978$			4899.09i			0.160179i
$979$	−3571.45			−0.116593
$980$		0			0
$981$	−42899.6			−1.39621
$982$		−	3464.82i		−	0.112594i
$983$		−	12359.7i		−	0.401032i	−0.979690	−	0.200516i	$-0.935738\pi$
$983$		−	12359.7i		−	0.401032i	0.979690	−	0.200516i	$-0.0642619\pi$
$984$	−15382.3			−0.498345
$985$	−17468.5	−	8210.67i	−0.565069	−	0.265598i
$986$	−40311.8			−1.30202
$987$		0			0
$988$			4955.51i			0.159571i
$989$	54606.1			1.75568
$990$	−8975.98	−	4218.95i	−0.288157	−	0.135442i
$991$	−17906.0			−0.573970			−0.286985	−	0.957935i	$-0.592653\pi$
$991$	−17906.0			−0.573970			−0.286985	+	0.957935i	$0.592653\pi$
$992$		−	3728.58i		−	0.119337i
$993$			51059.5i			1.63175i
$994$		0			0
$995$	1722.64	−	3664.98i	0.0548857	−	0.116771i
$996$	22289.3			0.709098
$997$		−	42472.8i		−	1.34918i	−0.738195	−	0.674588i	$-0.764321\pi$
$997$		−	42472.8i		−	1.34918i	0.738195	−	0.674588i	$-0.235679\pi$
$998$			4566.08i			0.144827i
$999$	−158490.			−5.01941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.g.99.11	yes	20
5.2	odd	4		2450.4.a.db.1.1		10
5.3	odd	4		2450.4.a.dc.1.10		10
5.4	even	2	inner	490.4.c.g.99.10	yes	20
7.6	odd	2	inner	490.4.c.g.99.20	yes	20
35.13	even	4		2450.4.a.dc.1.1		10
35.27	even	4		2450.4.a.db.1.10		10
35.34	odd	2	inner	490.4.c.g.99.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.c.g.99.1	✓	20	35.34	odd	2	inner
490.4.c.g.99.10	yes	20	5.4	even	2	inner
490.4.c.g.99.11	yes	20	1.1	even	1	trivial
490.4.c.g.99.20	yes	20	7.6	odd	2	inner
2450.4.a.db.1.1		10	5.2	odd	4
2450.4.a.db.1.10		10	35.27	even	4
2450.4.a.dc.1.1		10	35.13	even	4
2450.4.a.dc.1.10		10	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)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -9.74678i q^{3} -4.00000 q^{4} +(4.75591 - 10.1184i) q^{5} +19.4936 q^{6} -8.00000i q^{8} -67.9997 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -9.74678i q^{3} -4.00000 q^{4} +(4.75591 - 10.1184i) q^{5} +19.4936 q^{6} -8.00000i q^{8} -67.9997 q^{9} +(20.2367 + 9.51182i) q^{10} +6.52280 q^{11} +38.9871i q^{12} +41.6565i q^{13} +(-98.6215 - 46.3548i) q^{15} +16.0000 q^{16} -109.689i q^{17} -135.999i q^{18} -29.7403 q^{19} +(-19.0236 + 40.4735i) q^{20} +13.0456i q^{22} -180.661i q^{23} -77.9742 q^{24} +(-79.7627 - 96.2440i) q^{25} -83.3131 q^{26} +399.615i q^{27} -183.754 q^{29} +(92.7096 - 197.243i) q^{30} -116.518 q^{31} +32.0000i q^{32} -63.5763i q^{33} +219.379 q^{34} +271.999 q^{36} +396.605i q^{37} -59.4806i q^{38} +406.017 q^{39} +(-80.9469 - 38.0473i) q^{40} +197.275 q^{41} +302.257i q^{43} -26.0912 q^{44} +(-323.400 + 688.046i) q^{45} +361.322 q^{46} +277.408i q^{47} -155.948i q^{48} +(192.488 - 159.525i) q^{50} -1069.12 q^{51} -166.626i q^{52} -405.896i q^{53} -799.231 q^{54} +(31.0218 - 66.0001i) q^{55} +289.872i q^{57} -367.508i q^{58} +67.8911 q^{59} +(394.486 + 185.419i) q^{60} +510.023 q^{61} -233.036i q^{62} -64.0000 q^{64} +(421.496 + 198.115i) q^{65} +127.153 q^{66} +1026.25i q^{67} +438.758i q^{68} -1760.86 q^{69} -352.582 q^{71} +543.998i q^{72} -59.7536i q^{73} -793.210 q^{74} +(-938.070 + 777.429i) q^{75} +118.961 q^{76} +812.034i q^{78} +133.868 q^{79} +(76.0945 - 161.894i) q^{80} +2058.97 q^{81} +394.549i q^{82} -571.708i q^{83} +(-1109.88 - 521.673i) q^{85} -604.514 q^{86} +1791.01i q^{87} -52.1824i q^{88} -547.534 q^{89} +(-1376.09 - 646.801i) q^{90} +722.644i q^{92} +1135.68i q^{93} -554.815 q^{94} +(-141.442 + 300.923i) q^{95} +311.897 q^{96} -783.724i q^{97} -443.549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) \) 20 * q - 80 * q^4 - 316 * q^9	\( 20 q - 80 q^{4} - 316 q^{9} + 104 q^{11} - 360 q^{15} + 320 q^{16} - 440 q^{25} - 216 q^{29} + 224 q^{30} + 1264 q^{36} - 504 q^{39} - 416 q^{44} + 1600 q^{46} + 952 q^{50} - 296 q^{51} + 1440 q^{60} - 1280 q^{64} + 2732 q^{65} - 1872 q^{71} - 5968 q^{74} - 6424 q^{79} + 2020 q^{81} + 428 q^{85} + 3616 q^{86} + 3568 q^{95} + 624 q^{99}+O(q^{100}) \) 20 * q - 80 * q^4 - 316 * q^9 + 104 * q^11 - 360 * q^15 + 320 * q^16 - 440 * q^25 - 216 * q^29 + 224 * q^30 + 1264 * q^36 - 504 * q^39 - 416 * q^44 + 1600 * q^46 + 952 * q^50 - 296 * q^51 + 1440 * q^60 - 1280 * q^64 + 2732 * q^65 - 1872 * q^71 - 5968 * q^74 - 6424 * q^79 + 2020 * q^81 + 428 * q^85 + 3616 * q^86 + 3568 * q^95 + 624 * q^99

Introduction

L-functions

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