LMFDB - Embedded newform 490.4.c.g.99.9

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			99.9
Root			$-8.11026i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.g.99.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +7.11026i q^{3} -4.00000 q^{4} +(6.02808 + 9.41606i) q^{5} +14.2205 q^{6} +8.00000i q^{8} -23.5558 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +7.11026i q^{3} -4.00000 q^{4} +(6.02808 + 9.41606i) q^{5} +14.2205 q^{6} +8.00000i q^{8} -23.5558 q^{9} +(18.8321 - 12.0562i) q^{10} -65.2884 q^{11} -28.4410i q^{12} +55.0095i q^{13} +(-66.9506 + 42.8612i) q^{15} +16.0000 q^{16} -116.759i q^{17} +47.1115i q^{18} -98.8324 q^{19} +(-24.1123 - 37.6642i) q^{20} +130.577i q^{22} -87.1142i q^{23} -56.8821 q^{24} +(-52.3244 + 113.522i) q^{25} +110.019 q^{26} +24.4894i q^{27} +47.4747 q^{29} +(85.7225 + 133.901i) q^{30} +165.355 q^{31} -32.0000i q^{32} -464.217i q^{33} -233.518 q^{34} +94.2230 q^{36} -107.127i q^{37} +197.665i q^{38} -391.131 q^{39} +(-75.3285 + 48.2247i) q^{40} +280.281 q^{41} +236.981i q^{43} +261.154 q^{44} +(-141.996 - 221.802i) q^{45} -174.228 q^{46} -85.8061i q^{47} +113.764i q^{48} +(227.043 + 104.649i) q^{50} +830.185 q^{51} -220.038i q^{52} -473.771i q^{53} +48.9789 q^{54} +(-393.564 - 614.760i) q^{55} -702.724i q^{57} -94.9494i q^{58} -548.294 q^{59} +(267.802 - 171.445i) q^{60} -693.644 q^{61} -330.710i q^{62} -64.0000 q^{64} +(-517.973 + 331.602i) q^{65} -928.435 q^{66} -310.152i q^{67} +467.035i q^{68} +619.404 q^{69} -331.372 q^{71} -188.446i q^{72} -277.139i q^{73} -214.253 q^{74} +(-807.168 - 372.040i) q^{75} +395.330 q^{76} +782.263i q^{78} -645.756 q^{79} +(96.4493 + 150.657i) q^{80} -810.132 q^{81} -560.563i q^{82} -315.047i q^{83} +(1099.41 - 703.832i) q^{85} +473.963 q^{86} +337.557i q^{87} -522.307i q^{88} -829.630 q^{89} +(-443.605 + 283.992i) q^{90} +348.457i q^{92} +1175.72i q^{93} -171.612 q^{94} +(-595.770 - 930.612i) q^{95} +227.528 q^{96} -63.7075i q^{97} +1537.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			7.11026i			1.36837i	0.729309	+	0.684185i	$0.239842\pi$
$3$			7.11026i			1.36837i	−0.729309	+	0.684185i	$0.760158\pi$
$4$	−4.00000			−0.500000
$5$	6.02808	+	9.41606i	0.539168	+	0.842198i
$5$	6.02808	+	9.41606i	0.539168	+	0.842198i
$6$	14.2205			0.967583
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−23.5558			−0.872436
$10$	18.8321	−	12.0562i	0.595524	−	0.381250i
$11$	−65.2884			−1.78956			−0.894781	−	0.446504i	$-0.852669\pi$
$11$	−65.2884			−1.78956			−0.894781	+	0.446504i	$0.852669\pi$
$12$		−	28.4410i		−	0.684185i
$13$			55.0095i			1.17361i	0.809730	+	0.586803i	$0.199614\pi$
$13$			55.0095i			1.17361i	−0.809730	+	0.586803i	$0.800386\pi$
$14$		0			0
$15$	−66.9506	+	42.8612i	−1.15244	+	0.737781i
$16$	16.0000			0.250000
$17$		−	116.759i		−	1.66578i	−0.553442	−	0.832888i	$-0.686686\pi$
$17$		−	116.759i		−	1.66578i	0.553442	−	0.832888i	$-0.313314\pi$
$18$			47.1115i			0.616905i
$19$	−98.8324			−1.19335			−0.596677	−	0.802482i	$-0.703513\pi$
$19$	−98.8324			−1.19335			−0.596677	+	0.802482i	$0.703513\pi$
$20$	−24.1123	−	37.6642i	−0.269584	−	0.421099i
$21$		0			0
$22$			130.577i			1.26541i
$23$		−	87.1142i		−	0.789764i	−0.918732	−	0.394882i	$-0.870786\pi$
$23$		−	87.1142i		−	0.789764i	0.918732	−	0.394882i	$-0.129214\pi$
$24$	−56.8821			−0.483792
$25$	−52.3244	+	113.522i	−0.418595	+	0.908173i
$26$	110.019			0.829865
$27$			24.4894i			0.174555i
$28$		0			0
$29$	47.4747			0.303994			0.151997	−	0.988381i	$-0.451430\pi$
$29$	47.4747			0.303994			0.151997	+	0.988381i	$0.451430\pi$
$30$	85.7225	+	133.901i	0.521690	+	0.814897i
$31$	165.355			0.958021			0.479010	−	0.877809i	$-0.340996\pi$
$31$	165.355			0.958021			0.479010	+	0.877809i	$0.340996\pi$
$32$		−	32.0000i		−	0.176777i
$33$		−	464.217i		−	2.44878i
$34$	−233.518			−1.17788
$35$		0			0
$36$	94.2230			0.436218
$37$		−	107.127i		−	0.475986i	−0.971267	−	0.237993i	$-0.923510\pi$
$37$		−	107.127i		−	0.475986i	0.971267	−	0.237993i	$-0.0764896\pi$
$38$			197.665i			0.843828i
$39$	−391.131			−1.60593
$40$	−75.3285	+	48.2247i	−0.297762	+	0.190625i
$41$	280.281			1.06762			0.533812	−	0.845603i	$-0.320759\pi$
$41$	280.281			1.06762			0.533812	+	0.845603i	$0.320759\pi$
$42$		0			0
$43$			236.981i			0.840450i	0.907420	+	0.420225i	$0.138049\pi$
$43$			236.981i			0.840450i	−0.907420	+	0.420225i	$0.861951\pi$
$44$	261.154			0.894781
$45$	−141.996	−	221.802i	−0.470390	−	0.734764i
$46$	−174.228			−0.558447
$47$		−	85.8061i		−	0.266300i	−0.991096	−	0.133150i	$-0.957491\pi$
$47$		−	85.8061i		−	0.266300i	0.991096	−	0.133150i	$-0.0425092\pi$
$48$			113.764i			0.342092i
$49$		0			0
$50$	227.043	+	104.649i	0.642175	+	0.295992i
$51$	830.185			2.27940
$52$		−	220.038i		−	0.586803i
$53$		−	473.771i		−	1.22788i	−0.789354	−	0.613939i	$-0.789584\pi$
$53$		−	473.771i		−	1.22788i	0.789354	−	0.613939i	$-0.210416\pi$
$54$	48.9789			0.123429
$55$	−393.564	−	614.760i	−0.964875	−	1.50717i
$56$		0			0
$57$		−	702.724i		−	1.63295i
$58$		−	94.9494i		−	0.214956i
$59$	−548.294			−1.20986			−0.604930	−	0.796279i	$-0.706799\pi$
$59$	−548.294			−1.20986			−0.604930	+	0.796279i	$0.706799\pi$
$60$	267.802	−	171.445i	0.576219	−	0.368891i
$61$	−693.644			−1.45594			−0.727968	−	0.685612i	$-0.759535\pi$
$61$	−693.644			−1.45594			−0.727968	+	0.685612i	$0.759535\pi$
$62$		−	330.710i		−	0.677423i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−517.973	+	331.602i	−0.988409	+	0.632771i
$66$	−928.435			−1.73155
$67$		−	310.152i		−	0.565539i	−0.959188	−	0.282770i	$-0.908747\pi$
$67$		−	310.152i		−	0.565539i	0.959188	−	0.282770i	$-0.0912532\pi$
$68$			467.035i			0.832888i
$69$	619.404			1.08069
$70$		0			0
$71$	−331.372			−0.553896			−0.276948	−	0.960885i	$-0.589323\pi$
$71$	−331.372			−0.553896			−0.276948	+	0.960885i	$0.589323\pi$
$72$		−	188.446i		−	0.308453i
$73$		−	277.139i		−	0.444338i	−0.975008	−	0.222169i	$-0.928686\pi$
$73$		−	277.139i		−	0.444338i	0.975008	−	0.222169i	$-0.0713137\pi$
$74$	−214.253			−0.336573
$75$	−807.168	−	372.040i	−1.24272	−	0.572793i
$76$	395.330			0.596677
$77$		0			0
$78$			782.263i			1.13556i
$79$	−645.756			−0.919661			−0.459830	−	0.888007i	$-0.652090\pi$
$79$	−645.756			−0.919661			−0.459830	+	0.888007i	$0.652090\pi$
$80$	96.4493	+	150.657i	0.134792	+	0.210550i
$81$	−810.132			−1.11129
$82$		−	560.563i		−	0.754924i
$83$		−	315.047i		−	0.416637i	−0.978061	−	0.208319i	$-0.933201\pi$
$83$		−	315.047i		−	0.416637i	0.978061	−	0.208319i	$-0.0667991\pi$
$84$		0			0
$85$	1099.41	−	703.832i	1.40291	−	0.898133i
$86$	473.963			0.594288
$87$			337.557i			0.415976i
$88$		−	522.307i		−	0.632706i
$89$	−829.630			−0.988097			−0.494049	−	0.869434i	$-0.664484\pi$
$89$	−829.630			−0.988097			−0.494049	+	0.869434i	$0.664484\pi$
$90$	−443.605	+	283.992i	−0.519556	+	0.332616i
$91$		0			0
$92$			348.457i			0.394882i
$93$			1175.72i			1.31093i
$94$	−171.612			−0.188303
$95$	−595.770	−	930.612i	−0.643418	−	1.00504i
$96$	227.528			0.241896
$97$		−	63.7075i		−	0.0666858i	−0.999444	−	0.0333429i	$-0.989385\pi$
$97$		−	63.7075i		−	0.0666858i	0.999444	−	0.0333429i	$-0.0106153\pi$
$98$		0			0
$99$	1537.92			1.56128
$100$	209.298	−	454.086i	0.209298	−	0.454086i
$101$	857.505			0.844801			0.422400	−	0.906409i	$-0.361188\pi$
$101$	857.505			0.844801			0.422400	+	0.906409i	$0.361188\pi$
$102$		−	1660.37i		−	1.61178i
$103$			1042.61i			0.997394i	0.866776	+	0.498697i	$0.166188\pi$
$103$			1042.61i			0.997394i	−0.866776	+	0.498697i	$0.833812\pi$
$104$	−440.076			−0.414932
$105$		0			0
$106$	−947.543			−0.868241
$107$			1143.29i			1.03295i	0.856302	+	0.516476i	$0.172756\pi$
$107$			1143.29i			1.03295i	−0.856302	+	0.516476i	$0.827244\pi$
$108$		−	97.9577i		−	0.0872776i
$109$	151.498			0.133128			0.0665638	−	0.997782i	$-0.478796\pi$
$109$	151.498			0.133128			0.0665638	+	0.997782i	$0.478796\pi$
$110$	−1229.52	+	787.128i	−1.06573	+	0.682270i
$111$	761.697			0.651325
$112$		0			0
$113$			1135.03i			0.944912i	0.881354	+	0.472456i	$0.156632\pi$
$113$			1135.03i			0.944912i	−0.881354	+	0.472456i	$0.843368\pi$
$114$	−1405.45			−1.15467
$115$	820.273	−	525.132i	0.665137	−	0.425815i
$116$	−189.899			−0.151997
$117$		−	1295.79i		−	1.02390i
$118$			1096.59i			0.855500i
$119$		0			0
$120$	−342.890	−	535.605i	−0.260845	−	0.407448i
$121$	2931.57			2.20254
$122$			1387.29i			1.02950i
$123$			1992.87i			1.46090i
$124$	−661.420			−0.479010
$125$	−1384.34	+	191.628i	−0.990555	+	0.137118i
$126$		0			0
$127$		−	1638.75i		−	1.14500i	−0.819904	−	0.572501i	$-0.805973\pi$
$127$		−	1638.75i		−	1.14500i	0.819904	−	0.572501i	$-0.194027\pi$
$128$			128.000i			0.0883883i
$129$	−1685.00			−1.15005
$130$	663.203	+	1035.95i	0.447437	+	0.698911i
$131$	2320.41			1.54760			0.773799	−	0.633432i	$-0.218354\pi$
$131$	2320.41			1.54760			0.773799	+	0.633432i	$0.218354\pi$
$132$			1856.87i			1.22439i
$133$		0			0
$134$	−620.304			−0.399896
$135$	−230.594	+	147.624i	−0.147010	+	0.0941147i
$136$	934.071			0.588941
$137$			2319.27i			1.44634i	0.690669	+	0.723171i	$0.257316\pi$
$137$			2319.27i			1.44634i	−0.690669	+	0.723171i	$0.742684\pi$
$138$		−	1238.81i		−	0.764162i
$139$	−2549.97			−1.55601			−0.778007	−	0.628256i	$-0.783769\pi$
$139$	−2549.97			−1.55601			−0.778007	+	0.628256i	$0.783769\pi$
$140$		0			0
$141$	610.104			0.364397
$142$			662.744i			0.391664i
$143$		−	3591.48i		−	2.10024i
$144$	−376.892			−0.218109
$145$	286.182	+	447.025i	0.163904	+	0.256023i
$146$	−554.279			−0.314195
$147$		0			0
$148$			428.506i			0.237993i
$149$	−3286.67			−1.80708			−0.903538	−	0.428508i	$-0.859039\pi$
$149$	−3286.67			−1.80708			−0.903538	+	0.428508i	$0.859039\pi$
$150$	−744.080	+	1614.34i	−0.405026	+	0.878733i
$151$	−2501.03			−1.34789			−0.673944	−	0.738782i	$-0.735401\pi$
$151$	−2501.03			−1.34789			−0.673944	+	0.738782i	$0.735401\pi$
$152$		−	790.660i		−	0.421914i
$153$			2750.34i			1.45328i
$154$		0			0
$155$	996.774	+	1556.99i	0.516534	+	0.806843i
$156$	1564.53			0.802964
$157$		−	450.666i		−	0.229090i	−0.993418	−	0.114545i	$-0.963459\pi$
$157$		−	450.666i		−	0.229090i	0.993418	−	0.114545i	$-0.0365410\pi$
$158$			1291.51i			0.650298i
$159$	3368.64			1.68019
$160$	301.314	−	192.899i	0.148881	−	0.0953124i
$161$		0			0
$162$			1620.26i			0.785802i
$163$			939.794i			0.451597i	0.974174	+	0.225799i	$0.0724991\pi$
$163$			939.794i			0.451597i	−0.974174	+	0.225799i	$0.927501\pi$
$164$	−1121.13			−0.533812
$165$	4371.10	−	2798.34i	2.06236	−	1.32031i
$166$	−630.094			−0.294607
$167$		−	1783.15i		−	0.826252i	−0.910674	−	0.413126i	$-0.864437\pi$
$167$		−	1783.15i		−	0.826252i	0.910674	−	0.413126i	$-0.135563\pi$
$168$		0			0
$169$	−829.042			−0.377352
$170$	−1407.66	−	2198.82i	−0.635076	−	0.992009i
$171$	2328.07			1.04112
$172$		−	947.926i		−	0.420225i
$173$		−	3267.58i		−	1.43601i	−0.696039	−	0.718004i	$-0.745056\pi$
$173$		−	3267.58i		−	1.43601i	0.696039	−	0.718004i	$-0.254944\pi$
$174$	675.115			0.294140
$175$		0			0
$176$	−1044.61			−0.447391
$177$		−	3898.51i		−	1.65554i
$178$			1659.26i			0.698690i
$179$	−1604.72			−0.670068			−0.335034	−	0.942206i	$-0.608748\pi$
$179$	−1604.72			−0.670068			−0.335034	+	0.942206i	$0.608748\pi$
$180$	567.984	+	887.210i	0.235195	+	0.367382i
$181$	3709.52			1.52335			0.761676	−	0.647959i	$-0.224377\pi$
$181$	3709.52			1.52335			0.761676	+	0.647959i	$0.224377\pi$
$182$		0			0
$183$		−	4931.99i		−	1.99226i
$184$	696.914			0.279224
$185$	1008.71	−	645.768i	0.400875	−	0.256637i
$186$	2351.43			0.926965
$187$			7623.00i			2.98101i
$188$			343.225i			0.133150i
$189$		0			0
$190$	−1861.22	+	1191.54i	−0.710671	+	0.454965i
$191$	−3869.37			−1.46585			−0.732926	−	0.680308i	$-0.761846\pi$
$191$	−3869.37			−1.46585			−0.732926	+	0.680308i	$0.761846\pi$
$192$		−	455.056i		−	0.171046i
$193$			4309.95i			1.60744i	0.595005	+	0.803722i	$0.297150\pi$
$193$			4309.95i			1.60744i	−0.595005	+	0.803722i	$0.702850\pi$
$194$	−127.415			−0.0471540
$195$	−2357.77	−	3682.92i	−0.865865	−	1.35251i
$196$		0			0
$197$			707.884i			0.256013i	0.991773	+	0.128007i	$0.0408579\pi$
$197$			707.884i			0.256013i	−0.991773	+	0.128007i	$0.959142\pi$
$198$		−	3075.84i		−	1.10399i
$199$	36.9243			0.0131532			0.00657662	−	0.999978i	$-0.497907\pi$
$199$	36.9243			0.0131532			0.00657662	+	0.999978i	$0.497907\pi$
$200$	−908.173	−	418.595i	−0.321088	−	0.147996i
$201$	2205.26			0.773866
$202$		−	1715.01i		−	0.597364i
$203$		0			0
$204$	−3320.74			−1.13970
$205$	1689.56	+	2639.15i	0.575629	+	0.899151i
$206$	2085.22			0.705264
$207$			2052.04i			0.689018i
$208$			880.152i			0.293402i
$209$	6452.61			2.13558
$210$		0			0
$211$	−4656.12			−1.51915			−0.759575	−	0.650420i	$-0.774593\pi$
$211$	−4656.12			−1.51915			−0.759575	+	0.650420i	$0.774593\pi$
$212$			1895.09i			0.613939i
$213$		−	2356.14i		−	0.757935i
$214$	2286.58			0.730407
$215$	−2231.43	+	1428.54i	−0.707825	+	0.453144i
$216$	−195.915			−0.0617146
$217$		0			0
$218$		−	302.997i		−	0.0941354i
$219$	1970.53			0.608019
$220$	1574.26	+	2459.04i	0.482438	+	0.753583i
$221$	6422.84			1.95496
$222$		−	1523.39i		−	0.460556i
$223$		−	45.2935i		−	0.0136012i	−0.999977	−	0.00680062i	$-0.997835\pi$
$223$		−	45.2935i		−	0.0136012i	0.999977	−	0.00680062i	$-0.00216472\pi$
$224$		0			0
$225$	1232.54	−	2674.09i	0.365197	−	0.792322i
$226$	2270.07			0.668153
$227$			5323.46i			1.55652i	0.627942	+	0.778260i	$0.283898\pi$
$227$			5323.46i			1.55652i	−0.627942	+	0.778260i	$0.716102\pi$
$228$			2810.90i			0.816474i
$229$	1909.39			0.550987			0.275493	−	0.961303i	$-0.411159\pi$
$229$	1909.39			0.550987			0.275493	+	0.961303i	$0.411159\pi$
$230$	−1050.26	−	1640.55i	−0.301097	−	0.470323i
$231$		0			0
$232$			379.798i			0.107478i
$233$		−	1505.25i		−	0.423228i	−0.977353	−	0.211614i	$-0.932128\pi$
$233$		−	1505.25i		−	0.423228i	0.977353	−	0.211614i	$-0.0678720\pi$
$234$	−2591.58			−0.724004
$235$	807.956	−	517.247i	0.224278	−	0.143581i
$236$	2193.17			0.604930
$237$		−	4591.49i		−	1.25844i
$238$		0			0
$239$	1353.19			0.366238			0.183119	−	0.983091i	$-0.441381\pi$
$239$	1353.19			0.366238			0.183119	+	0.983091i	$0.441381\pi$
$240$	−1071.21	+	685.780i	−0.288110	+	0.184445i
$241$	−1230.08			−0.328781			−0.164390	−	0.986395i	$-0.552566\pi$
$241$	−1230.08			−0.328781			−0.164390	+	0.986395i	$0.552566\pi$
$242$		−	5863.15i		−	1.55743i
$243$		−	5099.03i		−	1.34610i
$244$	2774.58			0.727968
$245$		0			0
$246$	3985.74			1.03302
$247$		−	5436.72i		−	1.40053i
$248$			1322.84i			0.338711i
$249$	2240.06			0.570114
$250$	383.256	+	2768.68i	0.0969570	+	0.700428i
$251$	1289.55			0.324286			0.162143	−	0.986767i	$-0.448159\pi$
$251$	1289.55			0.324286			0.162143	+	0.986767i	$0.448159\pi$
$252$		0			0
$253$			5687.55i			1.41333i
$254$	−3277.49			−0.809639
$255$	5004.43	+	7817.08i	1.22898	+	1.91970i
$256$	256.000			0.0625000
$257$			3323.54i			0.806679i	0.915050	+	0.403339i	$0.132151\pi$
$257$			3323.54i			0.806679i	−0.915050	+	0.403339i	$0.867849\pi$
$258$			3370.00i			0.813205i
$259$		0			0
$260$	2071.89	−	1326.41i	0.494204	−	0.316386i
$261$	−1118.30			−0.265215
$262$		−	4640.82i		−	1.09432i
$263$			1918.96i			0.449916i	0.974368	+	0.224958i	$0.0722245\pi$
$263$			1918.96i			0.449916i	−0.974368	+	0.224958i	$0.927776\pi$
$264$	3713.74			0.865776
$265$	4461.06	−	2855.93i	1.03412	−	0.662033i
$266$		0			0
$267$		−	5898.89i		−	1.35208i
$268$			1240.61i			0.282770i
$269$	5928.46			1.34373			0.671867	−	0.740672i	$-0.265493\pi$
$269$	5928.46			1.34373			0.671867	+	0.740672i	$0.265493\pi$
$270$	295.249	+	461.188i	0.0665491	+	0.103952i
$271$	−6970.50			−1.56246			−0.781232	−	0.624240i	$-0.785409\pi$
$271$	−6970.50			−1.56246			−0.781232	+	0.624240i	$0.785409\pi$
$272$		−	1868.14i		−	0.416444i
$273$		0			0
$274$	4638.55			1.02272
$275$	3416.18	−	7411.64i	0.749102	−	1.62523i
$276$	−2477.62			−0.540344
$277$			94.1940i			0.0204317i	0.999948	+	0.0102158i	$0.00325186\pi$
$277$			94.1940i			0.0204317i	−0.999948	+	0.0102158i	$0.996748\pi$
$278$			5099.95i			1.10027i
$279$	−3895.06			−0.835811
$280$		0			0
$281$	2164.99			0.459618			0.229809	−	0.973236i	$-0.426190\pi$
$281$	2164.99			0.459618			0.229809	+	0.973236i	$0.426190\pi$
$282$		−	1220.21i		−	0.257668i
$283$			629.446i			0.132214i	0.997813	+	0.0661072i	$0.0210579\pi$
$283$			629.446i			0.132214i	−0.997813	+	0.0661072i	$0.978942\pi$
$284$	1325.49			0.276948
$285$	6616.89	−	4236.08i	1.37527	−	0.880434i
$286$	−7182.96			−1.48510
$287$		0			0
$288$			753.784i			0.154226i
$289$	−8719.63			−1.77481
$290$	894.050	−	572.363i	0.181036	−	0.115898i
$291$	452.977			0.0912508
$292$			1108.56i			0.222169i
$293$			7714.43i			1.53816i	0.639151	+	0.769081i	$0.279286\pi$
$293$			7714.43i			1.53816i	−0.639151	+	0.769081i	$0.720714\pi$
$294$		0			0
$295$	−3305.16	−	5162.77i	−0.652318	−	1.01894i
$296$	857.012			0.168287
$297$		−	1598.88i		−	0.312378i
$298$			6573.33i			1.27780i
$299$	4792.11			0.926872
$300$	3228.67	+	1488.16i	0.621358	+	0.286397i
$301$		0			0
$302$			5002.07i			0.953101i
$303$			6097.08i			1.15600i
$304$	−1581.32			−0.298338
$305$	−4181.35	−	6531.40i	−0.784994	−	1.22619i
$306$	5500.69			1.02763
$307$			5840.05i			1.08570i	0.839830	+	0.542849i	$0.182654\pi$
$307$			5840.05i			1.08570i	−0.839830	+	0.542849i	$0.817346\pi$
$308$		0			0
$309$	−7413.24			−1.36480
$310$	3113.99	−	1993.55i	0.570524	−	0.365245i
$311$	−561.246			−0.102332			−0.0511661	−	0.998690i	$-0.516294\pi$
$311$	−561.246			−0.102332			−0.0511661	+	0.998690i	$0.516294\pi$
$312$		−	3129.05i		−	0.567781i
$313$		−	1728.20i		−	0.312087i	−0.987750	−	0.156044i	$-0.950126\pi$
$313$		−	1728.20i		−	0.312087i	0.987750	−	0.156044i	$-0.0498741\pi$
$314$	−901.332			−0.161991
$315$		0			0
$316$	2583.02			0.459830
$317$			10338.4i			1.83174i	0.401479	+	0.915868i	$0.368496\pi$
$317$			10338.4i			1.83174i	−0.401479	+	0.915868i	$0.631504\pi$
$318$		−	6737.27i		−	1.18807i
$319$	−3099.55			−0.544017
$320$	−385.797	−	602.628i	−0.0673960	−	0.105275i
$321$	−8129.07			−1.41346
$322$		0			0
$323$			11539.6i			1.98786i
$324$	3240.53			0.555646
$325$	−6244.76	−	2878.34i	−1.06584	−	0.491266i
$326$	1879.59			0.319327
$327$			1077.19i			0.182168i
$328$			2242.25i			0.377462i
$329$		0			0
$330$	−5596.68	−	8742.20i	−0.933598	−	1.45831i
$331$	−6957.25			−1.15530			−0.577651	−	0.816284i	$-0.696031\pi$
$331$	−6957.25			−1.15530			−0.577651	+	0.816284i	$0.696031\pi$
$332$			1260.19i			0.208319i
$333$			2523.45i			0.415267i
$334$	−3566.30			−0.584249
$335$	2920.41	−	1869.62i	0.476296	−	0.304921i
$336$		0			0
$337$		−	4191.83i		−	0.677577i	−0.940862	−	0.338789i	$-0.889983\pi$
$337$		−	4191.83i		−	0.677577i	0.940862	−	0.338789i	$-0.110017\pi$
$338$			1658.08i			0.266828i
$339$	−8070.38			−1.29299
$340$	−4397.63	+	2815.33i	−0.701456	+	0.449067i
$341$	−10795.8			−1.71444
$342$		−	4656.15i		−	0.736186i
$343$		0			0
$344$	−1895.85			−0.297144
$345$	3733.82	+	5832.35i	0.582673	+	0.910154i
$346$	−6535.16			−1.01541
$347$			4547.62i			0.703542i	0.936086	+	0.351771i	$0.114420\pi$
$347$			4547.62i			0.703542i	−0.936086	+	0.351771i	$0.885580\pi$
$348$		−	1350.23i		−	0.207988i
$349$	−4773.11			−0.732088			−0.366044	−	0.930598i	$-0.619288\pi$
$349$	−4773.11			−0.732088			−0.366044	+	0.930598i	$0.619288\pi$
$350$		0			0
$351$	−1347.15			−0.204859
$352$			2089.23i			0.316353i
$353$		−	6826.54i		−	1.02929i	−0.857403	−	0.514646i	$-0.827923\pi$
$353$		−	6826.54i		−	1.02929i	0.857403	−	0.514646i	$-0.172077\pi$
$354$	−7797.02			−1.17064
$355$	−1997.54	−	3120.22i	−0.298643	−	0.466490i
$356$	3318.52			0.494049
$357$		0			0
$358$			3209.43i			0.473810i
$359$	8768.61			1.28911			0.644554	−	0.764559i	$-0.277043\pi$
$359$	8768.61			1.28911			0.644554	+	0.764559i	$0.277043\pi$
$360$	1774.42	−	1135.97i	0.259778	−	0.166308i
$361$	2908.85			0.424093
$362$		−	7419.04i		−	1.07717i
$363$			20844.3i			3.01388i
$364$		0			0
$365$	2609.56	−	1670.62i	0.374221	−	0.239573i
$366$	−9863.98			−1.40874
$367$			6544.18i			0.930800i	0.885101	+	0.465400i	$0.154089\pi$
$367$			6544.18i			0.930800i	−0.885101	+	0.465400i	$0.845911\pi$
$368$		−	1393.83i		−	0.197441i
$369$	−6602.24			−0.931433
$370$	−1291.54	−	2017.42i	−0.181470	−	0.283461i
$371$		0			0
$372$		−	4702.87i		−	0.655463i
$373$		−	1236.66i		−	0.171668i	−0.996309	−	0.0858339i	$-0.972645\pi$
$373$		−	1236.66i		−	0.171668i	0.996309	−	0.0858339i	$-0.0273554\pi$
$374$	15246.0			2.10789
$375$	−1362.52	−	9843.03i	−0.187628	−	1.35545i
$376$	686.449			0.0941514
$377$			2611.56i			0.356770i
$378$		0			0
$379$	604.196			0.0818878			0.0409439	−	0.999161i	$-0.486964\pi$
$379$	604.196			0.0818878			0.0409439	+	0.999161i	$0.486964\pi$
$380$	2383.08	+	3722.45i	0.321709	+	0.502520i
$381$	11651.9			1.56679
$382$			7738.74i			1.03651i
$383$			3319.36i			0.442850i	0.975177	+	0.221425i	$0.0710708\pi$
$383$			3319.36i			0.442850i	−0.975177	+	0.221425i	$0.928929\pi$
$384$	−910.113			−0.120948
$385$		0			0
$386$	8619.89			1.13663
$387$		−	5582.28i		−	0.733238i
$388$			254.830i			0.0333429i
$389$	−3702.35			−0.482562			−0.241281	−	0.970455i	$-0.577568\pi$
$389$	−3702.35			−0.482562			−0.241281	+	0.970455i	$0.577568\pi$
$390$	−7365.84	+	4715.55i	−0.956368	+	0.612259i
$391$	−10171.4			−1.31557
$392$		0			0
$393$			16498.7i			2.11769i
$394$	1415.77			0.181029
$395$	−3892.67	−	6080.48i	−0.495852	−	0.774537i
$396$	−6151.67			−0.780639
$397$			3654.19i			0.461961i	0.972958	+	0.230981i	$0.0741934\pi$
$397$			3654.19i			0.461961i	−0.972958	+	0.230981i	$0.925807\pi$
$398$		−	73.8486i		−	0.00930075i
$399$		0			0
$400$	−837.190	+	1816.35i	−0.104649	+	0.227043i
$401$	−10069.3			−1.25396			−0.626979	−	0.779036i	$-0.715709\pi$
$401$	−10069.3			−1.25396			−0.626979	+	0.779036i	$0.715709\pi$
$402$		−	4410.52i		−	0.547206i
$403$			9096.09i			1.12434i
$404$	−3430.02			−0.422400
$405$	−4883.54	−	7628.25i	−0.599173	−	0.935928i
$406$		0			0
$407$			6994.12i			0.851807i
$408$			6641.48i			0.805888i
$409$	−11596.0			−1.40192			−0.700959	−	0.713202i	$-0.747244\pi$
$409$	−11596.0			−1.40192			−0.700959	+	0.713202i	$0.747244\pi$
$410$	5278.29	−	3379.12i	0.635796	−	0.407031i
$411$	−16490.6			−1.97913
$412$		−	4170.45i		−	0.498697i
$413$		0			0
$414$	4104.08			0.487209
$415$	2966.50	−	1899.13i	0.350891	−	0.224638i
$416$	1760.30			0.207466
$417$		−	18131.0i		−	2.12920i
$418$		−	12905.2i		−	1.51008i
$419$	11167.4			1.30206			0.651032	−	0.759050i	$-0.274336\pi$
$419$	11167.4			1.30206			0.651032	+	0.759050i	$0.274336\pi$
$420$		0			0
$421$	3141.15			0.363635			0.181817	−	0.983332i	$-0.441802\pi$
$421$	3141.15			0.363635			0.181817	+	0.983332i	$0.441802\pi$
$422$			9312.24i			1.07420i
$423$			2021.23i			0.232330i
$424$	3790.17			0.434120
$425$	13254.7	+	6109.34i	1.51281	+	0.697286i
$426$	−4712.28			−0.535941
$427$		0			0
$428$		−	4573.15i		−	0.516476i
$429$	25536.3			2.87391
$430$	2857.09	+	4462.86i	0.320421	+	0.500508i
$431$	−13433.2			−1.50128			−0.750640	−	0.660711i	$-0.770255\pi$
$431$	−13433.2			−1.50128			−0.750640	+	0.660711i	$0.770255\pi$
$432$			391.831i			0.0436388i
$433$		−	1632.96i		−	0.181236i	−0.995886	−	0.0906181i	$-0.971116\pi$
$433$		−	1632.96i		−	0.181236i	0.995886	−	0.0906181i	$-0.0288842\pi$
$434$		0			0
$435$	−3178.46	+	2034.82i	−0.350335	+	0.224281i
$436$	−605.993			−0.0665638
$437$			8609.71i			0.942467i
$438$		−	3941.06i		−	0.429934i
$439$	−4192.02			−0.455750			−0.227875	−	0.973690i	$-0.573178\pi$
$439$	−4192.02			−0.455750			−0.227875	+	0.973690i	$0.573178\pi$
$440$	4918.08	−	3148.51i	0.532864	−	0.341135i
$441$		0			0
$442$		−	12845.7i		−	1.38237i
$443$		−	7998.77i		−	0.857863i	−0.903337	−	0.428931i	$-0.858890\pi$
$443$		−	7998.77i		−	0.857863i	0.903337	−	0.428931i	$-0.141110\pi$
$444$	−3046.79			−0.325663
$445$	−5001.08	−	7811.85i	−0.532751	−	0.832174i
$446$	−90.5870			−0.00961754
$447$		−	23369.1i		−	2.47275i
$448$		0			0
$449$	6912.51			0.726552			0.363276	−	0.931682i	$-0.381658\pi$
$449$	6912.51			0.726552			0.363276	+	0.931682i	$0.381658\pi$
$450$	−5348.18	−	2465.08i	−0.560257	−	0.258234i
$451$	−18299.1			−1.91058
$452$		−	4540.14i		−	0.472456i
$453$		−	17783.0i		−	1.84441i
$454$	10646.9			1.10063
$455$		0			0
$456$	5621.79			0.577335
$457$			5302.27i			0.542735i	0.962476	+	0.271368i	$0.0874759\pi$
$457$			5302.27i			0.542735i	−0.962476	+	0.271368i	$0.912524\pi$
$458$		−	3818.78i		−	0.389607i
$459$	2859.36			0.290770
$460$	−3281.09	+	2100.53i	−0.332569	+	0.212908i
$461$	−1050.36			−0.106118			−0.0530589	−	0.998591i	$-0.516897\pi$
$461$	−1050.36			−0.106118			−0.0530589	+	0.998591i	$0.516897\pi$
$462$		0			0
$463$		−	14089.9i		−	1.41428i	−0.707071	−	0.707142i	$-0.749984\pi$
$463$		−	14089.9i		−	1.41428i	0.707071	−	0.707142i	$-0.250016\pi$
$464$	759.595			0.0759986
$465$	−11070.6	+	7087.32i	−1.10406	+	0.706810i
$466$	−3010.50			−0.299268
$467$		−	2916.25i		−	0.288968i	−0.989507	−	0.144484i	$-0.953848\pi$
$467$		−	2916.25i		−	0.288968i	0.989507	−	0.144484i	$-0.0461522\pi$
$468$			5183.16i			0.511948i
$469$		0			0
$470$	−1034.49	−	1615.91i	−0.101527	−	0.158588i
$471$	3204.35			0.313479
$472$		−	4386.35i		−	0.427750i
$473$		−	15472.1i		−	1.50404i
$474$	−9182.98			−0.889849
$475$	5171.35	−	11219.6i	0.499532	−	1.08377i
$476$		0			0
$477$			11160.0i			1.07124i
$478$		−	2706.39i		−	0.258969i
$479$	3078.80			0.293683			0.146841	−	0.989160i	$-0.453089\pi$
$479$	3078.80			0.293683			0.146841	+	0.989160i	$0.453089\pi$
$480$	1371.56	+	2142.42i	0.130423	+	0.203724i
$481$	5892.97			0.558620
$482$			2460.15i			0.232483i
$483$		0			0
$484$	−11726.3			−1.10127
$485$	599.874	−	384.034i	0.0561626	−	0.0359549i
$486$	−10198.1			−0.951838
$487$		−	8829.97i		−	0.821610i	−0.911723	−	0.410805i	$-0.865248\pi$
$487$		−	8829.97i		−	0.821610i	0.911723	−	0.410805i	$-0.134752\pi$
$488$		−	5549.15i		−	0.514751i
$489$	−6682.18			−0.617952
$490$		0			0
$491$	10006.5			0.919727			0.459863	−	0.887990i	$-0.347898\pi$
$491$	10006.5			0.919727			0.459863	+	0.887990i	$0.347898\pi$
$492$		−	7971.49i		−	0.730452i
$493$		−	5543.09i		−	0.506386i
$494$	−10873.4			−0.990322
$495$	9270.70	+	14481.1i	0.841792	+	1.31491i
$496$	2645.68			0.239505
$497$		0			0
$498$		−	4480.13i		−	0.403131i
$499$	9161.11			0.821859			0.410930	−	0.911667i	$-0.365204\pi$
$499$	9161.11			0.821859			0.410930	+	0.911667i	$0.365204\pi$
$500$	5537.37	−	766.512i	0.495277	−	0.0685589i
$501$	12678.6			1.13062
$502$		−	2579.10i		−	0.229305i
$503$			17579.1i			1.55828i	0.626852	+	0.779139i	$0.284343\pi$
$503$			17579.1i			1.55828i	−0.626852	+	0.779139i	$0.715657\pi$
$504$		0			0
$505$	5169.11	+	8074.32i	0.455490	+	0.711490i
$506$	11375.1			0.999376
$507$		−	5894.70i		−	0.516357i
$508$			6554.99i			0.572501i
$509$	12943.5			1.12713			0.563567	−	0.826070i	$-0.309429\pi$
$509$	12943.5			1.12713			0.563567	+	0.826070i	$0.309429\pi$
$510$	15634.2	−	10008.9i	1.35744	−	0.869019i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$		−	2420.35i		−	0.208306i
$514$	6647.07			0.570408
$515$	−9817.30	+	6284.95i	−0.840004	+	0.537763i
$516$	6740.00			0.575023
$517$			5602.14i			0.476561i
$518$		0			0
$519$	23233.3			1.96499
$520$	−2652.81	−	4143.78i	−0.223718	−	0.349455i
$521$	1154.83			0.0971091			0.0485546	−	0.998821i	$-0.484539\pi$
$521$	1154.83			0.0971091			0.0485546	+	0.998821i	$0.484539\pi$
$522$			2236.61i			0.187536i
$523$			9561.01i			0.799376i	0.916651	+	0.399688i	$0.130882\pi$
$523$			9561.01i			0.799376i	−0.916651	+	0.399688i	$0.869118\pi$
$524$	−9281.64			−0.773799
$525$		0			0
$526$	3837.91			0.318139
$527$		−	19306.7i		−	1.59585i
$528$		−	7427.48i		−	0.612196i
$529$	4578.12			0.376273
$530$	−5711.87	−	8922.12i	−0.468128	−	0.731231i
$531$	12915.5			1.05552
$532$		0			0
$533$			15418.1i			1.25297i
$534$	−11797.8			−0.956067
$535$	−10765.3	+	6891.84i	−0.869950	+	0.556935i
$536$	2481.22			0.199948
$537$		−	11410.0i		−	0.916901i
$538$		−	11856.9i		−	0.950163i
$539$		0			0
$540$	922.376	−	590.497i	0.0735051	−	0.0470573i
$541$	3152.36			0.250519			0.125259	−	0.992124i	$-0.460024\pi$
$541$	3152.36			0.250519			0.125259	+	0.992124i	$0.460024\pi$
$542$			13941.0i			1.10483i
$543$			26375.7i			2.08451i
$544$	−3736.28			−0.294470
$545$	913.244	+	1426.52i	0.0717782	+	0.112120i
$546$		0			0
$547$		−	2010.30i		−	0.157138i	−0.996909	−	0.0785688i	$-0.974965\pi$
$547$		−	2010.30i		−	0.157138i	0.996909	−	0.0785688i	$-0.0250350\pi$
$548$		−	9277.09i		−	0.723171i
$549$	16339.3			1.27021
$550$	−14823.3	−	6832.35i	−1.14921	−	0.529695i
$551$	−4692.04			−0.362773
$552$			4955.23i			0.382081i
$553$		0			0
$554$	188.388			0.0144474
$555$	4591.57	+	7172.19i	0.351174	+	0.548545i
$556$	10199.9			0.778007
$557$		−	17816.1i		−	1.35528i	−0.735393	−	0.677641i	$-0.763002\pi$
$557$		−	17816.1i		−	1.35528i	0.735393	−	0.677641i	$-0.236998\pi$
$558$			7790.13i			0.591008i
$559$	−13036.2			−0.986357
$560$		0			0
$561$	−54201.5			−4.07912
$562$		−	4329.99i		−	0.324999i
$563$			8438.73i			0.631706i	0.948808	+	0.315853i	$0.102291\pi$
$563$			8438.73i			0.631706i	−0.948808	+	0.315853i	$0.897709\pi$
$564$	−2440.41			−0.182199
$565$	−10687.5	+	6842.08i	−0.795803	+	0.509466i
$566$	1258.89			0.0934896
$567$		0			0
$568$		−	2650.98i		−	0.195832i
$569$	−19603.9			−1.44436			−0.722178	−	0.691707i	$-0.756859\pi$
$569$	−19603.9			−1.44436			−0.722178	+	0.691707i	$0.756859\pi$
$570$	−8472.16	−	13233.8i	−0.622561	−	0.972460i
$571$	−7487.34			−0.548748			−0.274374	−	0.961623i	$-0.588471\pi$
$571$	−7487.34			−0.548748			−0.274374	+	0.961623i	$0.588471\pi$
$572$			14365.9i			1.05012i
$573$		−	27512.2i		−	2.00583i
$574$		0			0
$575$	9889.34	+	4558.20i	0.717242	+	0.330591i
$576$	1507.57			0.109054
$577$		−	5396.08i		−	0.389327i	−0.980870	−	0.194663i	$-0.937639\pi$
$577$		−	5396.08i		−	0.389327i	0.980870	−	0.194663i	$-0.0623615\pi$
$578$			17439.3i			1.25498i
$579$	−30644.8			−2.19958
$580$	−1144.73	−	1788.10i	−0.0819520	−	0.128012i
$581$		0			0
$582$		−	905.954i		−	0.0645241i
$583$			30931.8i			2.19736i
$584$	2217.11			0.157097
$585$	12201.2	−	7811.13i	0.862323	−	0.552052i
$586$	15428.9			1.08765
$587$			7274.14i			0.511475i	0.966746	+	0.255738i	$0.0823183\pi$
$587$			7274.14i			0.511475i	−0.966746	+	0.255738i	$0.917682\pi$
$588$		0			0
$589$	−16342.4			−1.14326
$590$	−10325.5	+	6610.32i	−0.720501	+	0.461259i
$591$	−5033.24			−0.350321
$592$		−	1714.02i		−	0.118997i
$593$		−	21335.9i		−	1.47750i	−0.673977	−	0.738752i	$-0.735415\pi$
$593$		−	21335.9i		−	1.47750i	0.673977	−	0.738752i	$-0.264585\pi$
$594$	−3197.75			−0.220884
$595$		0			0
$596$	13146.7			0.903538
$597$			262.541i			0.0179985i
$598$		−	9584.21i		−	0.655397i
$599$	24465.1			1.66881			0.834405	−	0.551152i	$-0.185812\pi$
$599$	24465.1			1.66881			0.834405	+	0.551152i	$0.185812\pi$
$600$	2976.32	−	6457.34i	0.202513	−	0.439367i
$601$	7109.15			0.482510			0.241255	−	0.970462i	$-0.422441\pi$
$601$	7109.15			0.482510			0.241255	+	0.970462i	$0.422441\pi$
$602$		0			0
$603$			7305.87i			0.493396i
$604$	10004.1			0.673944
$605$	17671.8	+	27603.9i	1.18754	+	1.85497i
$606$	12194.2			0.817415
$607$		−	9130.66i		−	0.610547i	−0.952265	−	0.305274i	$-0.901252\pi$
$607$		−	9130.66i		−	0.610547i	0.952265	−	0.305274i	$-0.0987479\pi$
$608$			3162.64i			0.210957i
$609$		0			0
$610$	−13062.8	+	8362.69i	−0.867044	+	0.555075i
$611$	4720.15			0.312532
$612$		−	11001.4i		−	0.726641i
$613$			20367.8i			1.34200i	0.741455	+	0.671002i	$0.234136\pi$
$613$			20367.8i			1.34200i	−0.741455	+	0.671002i	$0.765864\pi$
$614$	11680.1			0.767705
$615$	−18765.0	+	12013.2i	−1.23037	+	0.787673i
$616$		0			0
$617$		−	14687.5i		−	0.958343i	−0.877721	−	0.479171i	$-0.840937\pi$
$617$		−	14687.5i		−	0.958343i	0.877721	−	0.479171i	$-0.159063\pi$
$618$			14826.5i			0.965062i
$619$	12586.5			0.817275			0.408637	−	0.912697i	$-0.366004\pi$
$619$	12586.5			0.817275			0.408637	+	0.912697i	$0.366004\pi$
$620$	−3987.10	−	6227.97i	−0.258267	−	0.403422i
$621$	2133.38			0.137857
$622$			1122.49i			0.0723598i
$623$		0			0
$624$	−6258.10			−0.401482
$625$	−10149.3	−	11879.9i	−0.649556	−	0.760314i
$626$	−3456.39			−0.220679
$627$			45879.7i			2.92226i
$628$			1802.66i			0.114545i
$629$	−12508.0			−0.792886
$630$		0			0
$631$	−15855.9			−1.00034			−0.500168	−	0.865928i	$-0.666729\pi$
$631$	−15855.9			−1.00034			−0.500168	+	0.865928i	$0.666729\pi$
$632$		−	5166.05i		−	0.325149i
$633$		−	33106.2i		−	2.07876i
$634$	20676.7			1.29523
$635$	15430.5	−	9878.51i	0.964319	−	0.617349i
$636$	−13474.5			−0.840095
$637$		0			0
$638$			6199.10i			0.384678i
$639$	7805.72			0.483239
$640$	−1205.26	+	771.595i	−0.0744405	+	0.0476562i
$641$	−31817.0			−1.96052			−0.980262	−	0.197702i	$-0.936652\pi$
$641$	−31817.0			−1.96052			−0.980262	+	0.197702i	$0.936652\pi$
$642$			16258.1i			0.999467i
$643$			25566.4i			1.56803i	0.620745	+	0.784013i	$0.286830\pi$
$643$			25566.4i			1.56803i	−0.620745	+	0.784013i	$0.713170\pi$
$644$		0			0
$645$	−10157.3	−	15866.1i	−0.620068	−	0.968566i
$646$	23079.1			1.40563
$647$			2994.06i			0.181930i	0.995854	+	0.0909648i	$0.0289951\pi$
$647$			2994.06i			0.181930i	−0.995854	+	0.0909648i	$0.971005\pi$
$648$		−	6481.05i		−	0.392901i
$649$	35797.2			2.16512
$650$	−5756.68	+	12489.5i	−0.347378	+	0.753661i
$651$		0			0
$652$		−	3759.18i		−	0.225799i
$653$		−	5621.73i		−	0.336899i	−0.985710	−	0.168450i	$-0.946124\pi$
$653$		−	5621.73i		−	0.336899i	0.985710	−	0.168450i	$-0.0538761\pi$
$654$	2154.38			0.128812
$655$	13987.6	+	21849.1i	0.834415	+	1.30338i
$656$	4484.50			0.266906
$657$			6528.23i			0.387657i
$658$		0			0
$659$	−8074.77			−0.477312			−0.238656	−	0.971104i	$-0.576707\pi$
$659$	−8074.77			−0.477312			−0.238656	+	0.971104i	$0.576707\pi$
$660$	−17484.4	+	11193.4i	−1.03118	+	0.660153i
$661$	8738.07			0.514178			0.257089	−	0.966388i	$-0.417237\pi$
$661$	8738.07			0.514178			0.257089	+	0.966388i	$0.417237\pi$
$662$			13914.5i			0.816922i
$663$			45668.1i			2.67511i
$664$	2520.38			0.147304
$665$		0			0
$666$	5046.89			0.293638
$667$		−	4135.72i		−	0.240084i
$668$			7132.59i			0.413126i
$669$	322.049			0.0186115
$670$	−3739.25	−	5840.82i	−0.215611	−	0.336792i
$671$	45286.9			2.60549
$672$		0			0
$673$		−	16097.3i		−	0.922002i	−0.887400	−	0.461001i	$-0.847491\pi$
$673$		−	16097.3i		−	0.922002i	0.887400	−	0.461001i	$-0.152509\pi$
$674$	−8383.66			−0.479120
$675$	−2780.08	−	1281.39i	−0.158526	−	0.0730680i
$676$	3316.17			0.188676
$677$		−	1358.88i		−	0.0771430i	−0.999256	−	0.0385715i	$-0.987719\pi$
$677$		−	1358.88i		−	0.0771430i	0.999256	−	0.0385715i	$-0.0122807\pi$
$678$			16140.8i			0.914281i
$679$		0			0
$680$	5630.66	+	8795.27i	0.317538	+	0.496005i
$681$	−37851.1			−2.12990
$682$			21591.5i			1.21229i
$683$		−	13584.6i		−	0.761056i	−0.924769	−	0.380528i	$-0.875742\pi$
$683$		−	13584.6i		−	0.761056i	0.924769	−	0.380528i	$-0.124258\pi$
$684$	−9312.29			−0.520562
$685$	−21838.4	+	13980.8i	−1.21811	+	0.779822i
$686$		0			0
$687$			13576.3i			0.753954i
$688$			3791.70i			0.210112i
$689$	26061.9			1.44104
$690$	11664.7	−	7467.64i	0.643576	−	0.412012i
$691$	1143.06			0.0629290			0.0314645	−	0.999505i	$-0.489983\pi$
$691$	1143.06			0.0629290			0.0314645	+	0.999505i	$0.489983\pi$
$692$			13070.3i			0.718004i
$693$		0			0
$694$	9095.24			0.497479
$695$	−15371.5	−	24010.7i	−0.838953	−	1.31047i
$696$	−2700.46			−0.147070
$697$		−	32725.3i		−	1.77842i
$698$			9546.22i			0.517664i
$699$	10702.7			0.579133
$700$		0			0
$701$	15804.4			0.851534			0.425767	−	0.904833i	$-0.360004\pi$
$701$	15804.4			0.851534			0.425767	+	0.904833i	$0.360004\pi$
$702$			2694.30i			0.144857i
$703$			10587.6i			0.568020i
$704$	4178.46			0.223695
$705$	3677.76	+	5744.77i	0.196471	+	0.306895i
$706$	−13653.1			−0.727820
$707$		0			0
$708$			15594.0i			0.827768i
$709$	6434.79			0.340851			0.170426	−	0.985371i	$-0.445486\pi$
$709$	6434.79			0.340851			0.170426	+	0.985371i	$0.445486\pi$
$710$	−6240.44	+	3995.08i	−0.329859	+	0.211173i
$711$	15211.3			0.802345
$712$		−	6637.04i		−	0.349345i
$713$		−	14404.8i		−	0.756610i
$714$		0			0
$715$	33817.6	−	21649.7i	1.76882	−	1.13238i
$716$	6418.87			0.335034
$717$			9621.55i			0.501148i
$718$		−	17537.2i		−	0.911537i
$719$	−2572.58			−0.133437			−0.0667185	−	0.997772i	$-0.521253\pi$
$719$	−2572.58			−0.133437			−0.0667185	+	0.997772i	$0.521253\pi$
$720$	−2271.94	−	3548.84i	−0.117597	−	0.183691i
$721$		0			0
$722$		−	5817.71i		−	0.299879i
$723$		−	8746.16i		−	0.449894i
$724$	−14838.1			−0.761676
$725$	−2484.09	+	5389.41i	−0.127251	+	0.276079i
$726$	41688.5			2.13114
$727$			20925.5i			1.06752i	0.845637	+	0.533759i	$0.179221\pi$
$727$			20925.5i			1.06752i	−0.845637	+	0.533759i	$0.820779\pi$
$728$		0			0
$729$	14381.9			0.730674
$730$	−3341.24	−	5219.12i	−0.169404	−	0.264614i
$731$	27669.7			1.40000
$732$			19728.0i			0.996129i
$733$		−	6344.82i		−	0.319715i	−0.987140	−	0.159858i	$-0.948897\pi$
$733$		−	6344.82i		−	0.319715i	0.987140	−	0.159858i	$-0.0511035\pi$
$734$	13088.4			0.658175
$735$		0			0
$736$	−2787.65			−0.139612
$737$			20249.3i			1.01207i
$738$			13204.5i			0.658623i
$739$	9871.30			0.491369			0.245685	−	0.969350i	$-0.420987\pi$
$739$	9871.30			0.491369			0.245685	+	0.969350i	$0.420987\pi$
$740$	−4034.84	+	2583.07i	−0.200437	+	0.128318i
$741$	38656.5			1.91644
$742$		0			0
$743$		−	20268.1i		−	1.00076i	−0.865806	−	0.500380i	$-0.833193\pi$
$743$		−	20268.1i		−	1.00076i	0.865806	−	0.500380i	$-0.166807\pi$
$744$	−9405.74			−0.463482
$745$	−19812.3	−	30947.5i	−0.974318	−	1.52192i
$746$	−2473.33			−0.121387
$747$			7421.17i			0.363489i
$748$		−	30492.0i		−	1.49050i
$749$		0			0
$750$	−19686.1	+	2725.05i	−0.958444	+	0.132673i
$751$	−10226.5			−0.496897			−0.248449	−	0.968645i	$-0.579921\pi$
$751$	−10226.5			−0.496897			−0.248449	+	0.968645i	$0.579921\pi$
$752$		−	1372.90i		−	0.0665751i
$753$			9169.05i			0.443743i
$754$	5223.12			0.252274
$755$	−15076.4	−	23549.9i	−0.726739	−	1.13519i
$756$		0			0
$757$		−	18533.0i		−	0.889819i	−0.895575	−	0.444910i	$-0.853236\pi$
$757$		−	18533.0i		−	0.889819i	0.895575	−	0.444910i	$-0.146764\pi$
$758$		−	1208.39i		−	0.0579034i
$759$	−40439.9			−1.93396
$760$	7444.90	−	4766.16i	0.355335	−	0.227483i
$761$	16527.6			0.787288			0.393644	−	0.919263i	$-0.371214\pi$
$761$	16527.6			0.787288			0.393644	+	0.919263i	$0.371214\pi$
$762$		−	23303.8i		−	1.10789i
$763$		0			0
$764$	15477.5			0.732926
$765$	−25897.4	+	16579.3i	−1.22395	+	0.783563i
$766$	6638.73			0.313142
$767$		−	30161.3i		−	1.41990i
$768$			1820.23i			0.0855231i
$769$	−31787.3			−1.49061			−0.745304	−	0.666724i	$-0.767696\pi$
$769$	−31787.3			−1.49061			−0.745304	+	0.666724i	$0.767696\pi$
$770$		0			0
$771$	−23631.2			−1.10383
$772$		−	17239.8i		−	0.803722i
$773$			35515.3i			1.65252i	0.563291	+	0.826259i	$0.309535\pi$
$773$			35515.3i			1.65252i	−0.563291	+	0.826259i	$0.690465\pi$
$774$	−11164.6			−0.518478
$775$	−8652.10	+	18771.4i	−0.401023	+	0.870048i
$776$	509.660			0.0235770
$777$		0			0
$778$			7404.71i			0.341223i
$779$	−27700.9			−1.27405
$780$	9431.09	+	14731.7i	0.432932	+	0.676254i
$781$	21634.8			0.991232
$782$			20342.7i			0.930248i
$783$			1162.63i			0.0530638i
$784$		0			0
$785$	4243.50	−	2716.65i	0.192939	−	0.123518i
$786$	32997.4			1.49743
$787$		−	12720.5i		−	0.576157i	−0.957607	−	0.288079i	$-0.906984\pi$
$787$		−	12720.5i		−	0.576157i	0.957607	−	0.288079i	$-0.0930165\pi$
$788$		−	2831.54i		−	0.128007i
$789$	−13644.3			−0.615651
$790$	−12161.0	+	7785.34i	−0.547680	+	0.350620i
$791$		0			0
$792$			12303.3i			0.551995i
$793$		−	38157.0i		−	1.70869i
$794$	7308.38			0.326656
$795$	20306.4	+	31719.3i	0.905905	+	1.41505i
$796$	−147.697			−0.00657662
$797$		−	19581.7i		−	0.870287i	−0.900361	−	0.435143i	$-0.856698\pi$
$797$		−	19581.7i		−	0.870287i	0.900361	−	0.435143i	$-0.143302\pi$
$798$		0			0
$799$	−10018.6			−0.443596
$800$	3632.69	+	1674.38i	0.160544	+	0.0739979i
$801$	19542.6			0.862051
$802$			20138.6i			0.886682i
$803$			18094.0i			0.795171i
$804$	−8821.05			−0.386933
$805$		0			0
$806$	18192.2			0.795028
$807$			42152.9i			1.83872i
$808$			6860.04i			0.298682i
$809$	9825.05			0.426984			0.213492	−	0.976945i	$-0.431516\pi$
$809$	9825.05			0.426984			0.213492	+	0.976945i	$0.431516\pi$
$810$	−15256.5	+	9767.08i	−0.661801	+	0.423679i
$811$	−4742.79			−0.205354			−0.102677	−	0.994715i	$-0.532741\pi$
$811$	−4742.79			−0.205354			−0.102677	+	0.994715i	$0.532741\pi$
$812$		0			0
$813$		−	49562.1i		−	2.13803i
$814$	13988.2			0.602319
$815$	−8849.16	+	5665.16i	−0.380334	+	0.243487i
$816$	13283.0			0.569849
$817$		−	23421.5i		−	1.00295i
$818$			23192.0i			0.991305i
$819$		0			0
$820$	−6758.24	−	10556.6i	−0.287815	−	0.449575i
$821$	29300.8			1.24556			0.622781	−	0.782396i	$-0.286003\pi$
$821$	29300.8			1.24556			0.622781	+	0.782396i	$0.286003\pi$
$822$			32981.3i			1.39946i
$823$		−	27537.3i		−	1.16633i	−0.812353	−	0.583166i	$-0.801814\pi$
$823$		−	27537.3i		−	1.16633i	0.812353	−	0.583166i	$-0.198186\pi$
$824$	−8340.90			−0.352632
$825$	52698.7	+	24289.9i	2.22392	+	1.02505i
$826$		0			0
$827$			844.574i			0.0355124i	0.999842	+	0.0177562i	$0.00565227\pi$
$827$			844.574i			0.0355124i	−0.999842	+	0.0177562i	$0.994348\pi$
$828$		−	8208.16i		−	0.344509i
$829$	16243.7			0.680538			0.340269	−	0.940328i	$-0.389482\pi$
$829$	16243.7			0.680538			0.340269	+	0.940328i	$0.389482\pi$
$830$	−3798.26	−	5933.00i	−0.158843	−	0.248118i
$831$	−669.744			−0.0279581
$832$		−	3520.61i		−	0.146701i
$833$		0			0
$834$	−36261.9			−1.50557
$835$	16790.2	−	10749.0i	0.695868	−	0.445489i
$836$	−25810.4			−1.06779
$837$			4049.45i			0.167228i
$838$		−	22334.9i		−	0.920699i
$839$	13135.2			0.540499			0.270250	−	0.962790i	$-0.412894\pi$
$839$	13135.2			0.540499			0.270250	+	0.962790i	$0.412894\pi$
$840$		0			0
$841$	−22135.2			−0.907588
$842$		−	6282.30i		−	0.257129i
$843$			15393.7i			0.628928i
$844$	18624.5			0.759575
$845$	−4997.53	−	7806.31i	−0.203456	−	0.317805i
$846$	4042.46			0.164282
$847$		0			0
$848$		−	7580.34i		−	0.306969i
$849$	−4475.52			−0.180918
$850$	12218.7	−	26509.3i	0.493055	−	1.06972i
$851$	−9332.24			−0.375917
$852$			9424.56i			0.378967i
$853$		−	24870.1i		−	0.998282i	−0.866521	−	0.499141i	$-0.833649\pi$
$853$		−	24870.1i		−	0.998282i	0.866521	−	0.499141i	$-0.166351\pi$
$854$		0			0
$855$	14033.8	+	21921.3i	0.561341	+	0.876833i
$856$	−9146.30			−0.365203
$857$		−	48576.3i		−	1.93622i	−0.250535	−	0.968108i	$-0.580606\pi$
$857$		−	48576.3i		−	1.93622i	0.250535	−	0.968108i	$-0.419394\pi$
$858$		−	51072.7i		−	2.03216i
$859$	4535.56			0.180153			0.0900765	−	0.995935i	$-0.471289\pi$
$859$	4535.56			0.180153			0.0900765	+	0.995935i	$0.471289\pi$
$860$	8925.73	−	5714.18i	0.353913	−	0.226572i
$861$		0			0
$862$			26866.3i			1.06157i
$863$		−	19685.6i		−	0.776484i	−0.921557	−	0.388242i	$-0.873082\pi$
$863$		−	19685.6i		−	0.776484i	0.921557	−	0.388242i	$-0.126918\pi$
$864$	783.662			0.0308573
$865$	30767.7	−	19697.2i	1.20940	−	0.774250i
$866$	−3265.93			−0.128153
$867$		−	61998.8i		−	2.42859i
$868$		0			0
$869$	42160.4			1.64579
$870$	4069.65	+	6356.92i	0.158591	+	0.247724i
$871$	17061.3			0.663720
$872$			1211.99i			0.0470677i
$873$			1500.68i			0.0581791i
$874$	17219.4			0.666425
$875$		0			0
$876$	−7882.13			−0.304010
$877$			47634.9i			1.83411i	0.398759	+	0.917056i	$0.369441\pi$
$877$			47634.9i			1.83411i	−0.398759	+	0.917056i	$0.630559\pi$
$878$			8384.04i			0.322264i
$879$	−54851.6			−2.10478
$880$	−6297.02	−	9836.15i	−0.241219	−	0.376792i
$881$	26891.9			1.02839			0.514195	−	0.857674i	$-0.328091\pi$
$881$	26891.9			1.02839			0.514195	+	0.857674i	$0.328091\pi$
$882$		0			0
$883$			8927.28i			0.340234i	0.985424	+	0.170117i	$0.0544146\pi$
$883$			8927.28i			0.340234i	−0.985424	+	0.170117i	$0.945585\pi$
$884$	−25691.4			−0.977482
$885$	36708.6	−	23500.5i	1.39429	−	0.892612i
$886$	−15997.5			−0.606601
$887$			20711.5i			0.784018i	0.919961	+	0.392009i	$0.128220\pi$
$887$			20711.5i			0.784018i	−0.919961	+	0.392009i	$0.871780\pi$
$888$			6093.58i			0.230278i
$889$		0			0
$890$	−15623.7	+	10002.2i	−0.588436	+	0.376712i
$891$	52892.2			1.98873
$892$			181.174i			0.00680062i
$893$			8480.43i			0.317790i
$894$	−46738.1			−1.74850
$895$	−9673.37	−	15110.1i	−0.361279	−	0.564330i
$896$		0			0
$897$			34073.1i			1.26830i
$898$		−	13825.0i		−	0.513750i
$899$	7850.18			0.291233
$900$	−4930.16	+	10696.4i	−0.182599	+	0.396161i
$901$	−55317.0			−2.04537
$902$			36598.2i			1.35098i
$903$		0			0
$904$	−9080.27			−0.334077
$905$	22361.3	+	34929.1i	0.821343	+	1.28296i
$906$	−35566.0			−1.30419
$907$			47137.0i			1.72564i	0.505509	+	0.862821i	$0.331305\pi$
$907$			47137.0i			1.72564i	−0.505509	+	0.862821i	$0.668695\pi$
$908$		−	21293.8i		−	0.778260i
$909$	−20199.2			−0.737034
$910$		0			0
$911$	6096.61			0.221723			0.110862	−	0.993836i	$-0.464639\pi$
$911$	6096.61			0.221723			0.110862	+	0.993836i	$0.464639\pi$
$912$		−	11243.6i		−	0.408237i
$913$			20568.9i			0.745599i
$914$	10604.5			0.383772
$915$	46439.9	−	29730.4i	1.67788	−	1.07416i
$916$	−7637.56			−0.275493
$917$		0			0
$918$		−	5718.71i		−	0.205605i
$919$	−23012.9			−0.826033			−0.413017	−	0.910723i	$-0.635525\pi$
$919$	−23012.9			−0.826033			−0.413017	+	0.910723i	$0.635525\pi$
$920$	4201.05	+	6562.18i	0.150549	+	0.235162i
$921$	−41524.3			−1.48564
$922$			2100.73i			0.0750366i
$923$		−	18228.6i		−	0.650056i
$924$		0			0
$925$	12161.2	+	5605.33i	0.432278	+	0.199246i
$926$	−28179.8			−1.00005
$927$		−	24559.5i		−	0.870162i
$928$		−	1519.19i		−	0.0537391i
$929$	50361.0			1.77857			0.889284	−	0.457356i	$-0.151203\pi$
$929$	50361.0			1.77857			0.889284	+	0.457356i	$0.151203\pi$
$930$	14174.6	+	22141.2i	0.499790	+	0.780688i
$931$		0			0
$932$			6021.00i			0.211614i
$933$		−	3990.60i		−	0.140028i
$934$	−5832.50			−0.204331
$935$	−71778.6	+	45952.1i	−2.51060	+	1.60727i
$936$	10366.3			0.362002
$937$			8167.89i			0.284774i	0.989811	+	0.142387i	$0.0454778\pi$
$937$			8167.89i			0.284774i	−0.989811	+	0.142387i	$0.954522\pi$
$938$		0			0
$939$	12287.9			0.427051
$940$	−3231.82	+	2068.99i	−0.112139	+	0.0717903i
$941$	−22954.2			−0.795204			−0.397602	−	0.917558i	$-0.630157\pi$
$941$	−22954.2			−0.795204			−0.397602	+	0.917558i	$0.630157\pi$
$942$		−	6408.70i		−	0.221663i
$943$		−	24416.5i		−	0.843171i
$944$	−8772.70			−0.302465
$945$		0			0
$946$	−30944.3			−1.06352
$947$		−	46759.1i		−	1.60451i	−0.596984	−	0.802253i	$-0.703634\pi$
$947$		−	46759.1i		−	1.60451i	0.596984	−	0.802253i	$-0.296366\pi$
$948$			18366.0i			0.629218i
$949$	15245.3			0.521478
$950$	−22439.2	−	10342.7i	−0.766342	−	0.353223i
$951$	−73508.4			−2.50649
$952$		0			0
$953$			44798.2i			1.52273i	0.648326	+	0.761363i	$0.275469\pi$
$953$			44798.2i			1.52273i	−0.648326	+	0.761363i	$0.724531\pi$
$954$	22320.1			0.757484
$955$	−23324.9	−	36434.2i	−0.790341	−	1.23454i
$956$	−5412.77			−0.183119
$957$		−	22038.6i		−	0.744416i
$958$		−	6157.61i		−	0.207665i
$959$		0			0
$960$	4284.84	−	2743.12i	0.144055	−	0.0922227i
$961$	−2448.71			−0.0821963
$962$		−	11785.9i		−	0.395004i
$963$		−	26931.0i		−	0.901184i
$964$	4920.31			0.164390
$965$	−40582.7	+	25980.7i	−1.35379	+	0.866683i
$966$		0			0
$967$		−	30697.4i		−	1.02085i	−0.859923	−	0.510425i	$-0.829488\pi$
$967$		−	30697.4i		−	1.02085i	0.859923	−	0.510425i	$-0.170512\pi$
$968$			23452.6i			0.778714i
$969$	−82049.3			−2.72013
$970$	−768.069	−	1199.75i	−0.0254239	−	0.0397130i
$971$	−12380.9			−0.409187			−0.204593	−	0.978847i	$-0.565587\pi$
$971$	−12380.9			−0.409187			−0.204593	+	0.978847i	$0.565587\pi$
$972$			20396.1i			0.673051i
$973$		0			0
$974$	−17659.9			−0.580966
$975$	20465.7	−	44401.9i	0.672233	−	1.45846i
$976$	−11098.3			−0.363984
$977$			38163.6i			1.24970i	0.780743	+	0.624852i	$0.214841\pi$
$977$			38163.6i			1.24970i	−0.780743	+	0.624852i	$0.785159\pi$
$978$			13364.4i			0.436958i
$979$	54165.2			1.76826
$980$		0			0
$981$	−3568.66			−0.116145
$982$		−	20013.0i		−	0.650345i
$983$		−	3079.77i		−	0.0999283i	−0.998751	−	0.0499641i	$-0.984089\pi$
$983$		−	3079.77i		−	0.0999283i	0.998751	−	0.0499641i	$-0.0159107\pi$
$984$	−15943.0			−0.516508
$985$	−6665.48	+	4267.18i	−0.215614	+	0.138034i
$986$	−11086.2			−0.358069
$987$		0			0
$988$			21746.9i			0.700264i
$989$	20644.4			0.663757
$990$	28962.3	−	18541.4i	0.929779	−	0.595237i
$991$	−11201.4			−0.359056			−0.179528	−	0.983753i	$-0.557457\pi$
$991$	−11201.4			−0.359056			−0.179528	+	0.983753i	$0.557457\pi$
$992$		−	5291.36i		−	0.169356i
$993$		−	49467.8i		−	1.58088i
$994$		0			0
$995$	222.583	+	347.682i	0.00709181	+	0.0110776i
$996$	−8960.26			−0.285057
$997$		−	25637.7i		−	0.814396i	−0.913340	−	0.407198i	$-0.866506\pi$
$997$		−	25637.7i		−	0.814396i	0.913340	−	0.407198i	$-0.133494\pi$
$998$		−	18322.2i		−	0.581142i
$999$	2623.47			0.0830859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.g.99.9	yes	20
5.2	odd	4		2450.4.a.dc.1.9		10
5.3	odd	4		2450.4.a.db.1.2		10
5.4	even	2	inner	490.4.c.g.99.12	yes	20
7.6	odd	2	inner	490.4.c.g.99.2	✓	20
35.13	even	4		2450.4.a.db.1.9		10
35.27	even	4		2450.4.a.dc.1.2		10
35.34	odd	2	inner	490.4.c.g.99.19	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.c.g.99.2	✓	20	7.6	odd	2	inner
490.4.c.g.99.9	yes	20	1.1	even	1	trivial
490.4.c.g.99.12	yes	20	5.4	even	2	inner
490.4.c.g.99.19	yes	20	35.34	odd	2	inner
2450.4.a.db.1.2		10	5.3	odd	4
2450.4.a.db.1.9		10	35.13	even	4
2450.4.a.dc.1.2		10	35.27	even	4
2450.4.a.dc.1.9		10	5.2	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)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +7.11026i q^{3} -4.00000 q^{4} +(6.02808 + 9.41606i) q^{5} +14.2205 q^{6} +8.00000i q^{8} -23.5558 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +7.11026i q^{3} -4.00000 q^{4} +(6.02808 + 9.41606i) q^{5} +14.2205 q^{6} +8.00000i q^{8} -23.5558 q^{9} +(18.8321 - 12.0562i) q^{10} -65.2884 q^{11} -28.4410i q^{12} +55.0095i q^{13} +(-66.9506 + 42.8612i) q^{15} +16.0000 q^{16} -116.759i q^{17} +47.1115i q^{18} -98.8324 q^{19} +(-24.1123 - 37.6642i) q^{20} +130.577i q^{22} -87.1142i q^{23} -56.8821 q^{24} +(-52.3244 + 113.522i) q^{25} +110.019 q^{26} +24.4894i q^{27} +47.4747 q^{29} +(85.7225 + 133.901i) q^{30} +165.355 q^{31} -32.0000i q^{32} -464.217i q^{33} -233.518 q^{34} +94.2230 q^{36} -107.127i q^{37} +197.665i q^{38} -391.131 q^{39} +(-75.3285 + 48.2247i) q^{40} +280.281 q^{41} +236.981i q^{43} +261.154 q^{44} +(-141.996 - 221.802i) q^{45} -174.228 q^{46} -85.8061i q^{47} +113.764i q^{48} +(227.043 + 104.649i) q^{50} +830.185 q^{51} -220.038i q^{52} -473.771i q^{53} +48.9789 q^{54} +(-393.564 - 614.760i) q^{55} -702.724i q^{57} -94.9494i q^{58} -548.294 q^{59} +(267.802 - 171.445i) q^{60} -693.644 q^{61} -330.710i q^{62} -64.0000 q^{64} +(-517.973 + 331.602i) q^{65} -928.435 q^{66} -310.152i q^{67} +467.035i q^{68} +619.404 q^{69} -331.372 q^{71} -188.446i q^{72} -277.139i q^{73} -214.253 q^{74} +(-807.168 - 372.040i) q^{75} +395.330 q^{76} +782.263i q^{78} -645.756 q^{79} +(96.4493 + 150.657i) q^{80} -810.132 q^{81} -560.563i q^{82} -315.047i q^{83} +(1099.41 - 703.832i) q^{85} +473.963 q^{86} +337.557i q^{87} -522.307i q^{88} -829.630 q^{89} +(-443.605 + 283.992i) q^{90} +348.457i q^{92} +1175.72i q^{93} -171.612 q^{94} +(-595.770 - 930.612i) q^{95} +227.528 q^{96} -63.7075i q^{97} +1537.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) \) 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

Modular forms

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