LMFDB - Embedded newform 253.3.c.a.208.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(208,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("253.208"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.8
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.86502i q^{2} +5.21944 q^{3} -4.20834 q^{4} +3.21069 q^{5} -14.9538i q^{6} -5.03509i q^{7} +0.596911i q^{8} +18.2426 q^{9} -9.19869i q^{10} +(-3.77449 + 10.3321i) q^{11} -21.9652 q^{12} +15.9623i q^{13} -14.4256 q^{14} +16.7580 q^{15} -15.1232 q^{16} -2.07725i q^{17} -52.2654i q^{18} -2.99343i q^{19} -13.5117 q^{20} -26.2803i q^{21} +(29.6018 + 10.8140i) q^{22} +4.79583 q^{23} +3.11554i q^{24} -14.6915 q^{25} +45.7323 q^{26} +48.2412 q^{27} +21.1894i q^{28} -19.2645i q^{29} -48.0120i q^{30} -53.4474 q^{31} +45.7160i q^{32} +(-19.7007 + 53.9280i) q^{33} -5.95137 q^{34} -16.1661i q^{35} -76.7711 q^{36} +35.6340 q^{37} -8.57624 q^{38} +83.3142i q^{39} +1.91649i q^{40} +64.1419i q^{41} -75.2937 q^{42} -48.4215i q^{43} +(15.8844 - 43.4812i) q^{44} +58.5713 q^{45} -13.7402i q^{46} -29.4086 q^{47} -78.9348 q^{48} +23.6479 q^{49} +42.0914i q^{50} -10.8421i q^{51} -67.1748i q^{52} -23.6910 q^{53} -138.212i q^{54} +(-12.1187 + 33.1733i) q^{55} +3.00550 q^{56} -15.6240i q^{57} -55.1933 q^{58} -74.5141 q^{59} -70.5235 q^{60} +36.0105i q^{61} +153.128i q^{62} -91.8530i q^{63} +70.4843 q^{64} +51.2499i q^{65} +(154.505 + 56.4430i) q^{66} +133.886 q^{67} +8.74180i q^{68} +25.0316 q^{69} -46.3162 q^{70} +30.5895 q^{71} +10.8892i q^{72} -52.3969i q^{73} -102.092i q^{74} -76.6814 q^{75} +12.5974i q^{76} +(52.0232 + 19.0049i) q^{77} +238.697 q^{78} +75.9222i q^{79} -48.5559 q^{80} +87.6087 q^{81} +183.768 q^{82} -16.6444i q^{83} +110.597i q^{84} -6.66941i q^{85} -138.728 q^{86} -100.550i q^{87} +(-6.16737 - 2.25303i) q^{88} +56.5773 q^{89} -167.808i q^{90} +80.3715 q^{91} -20.1825 q^{92} -278.966 q^{93} +84.2563i q^{94} -9.61097i q^{95} +238.612i q^{96} +168.076 q^{97} -67.7517i q^{98} +(-68.8565 + 188.485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) $ 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.86502i		−	1.43251i	−0.697838	−	0.716255i	$-0.745855\pi$
$2$		−	2.86502i		−	1.43251i	0.697838	−	0.716255i	$-0.254145\pi$
$3$	5.21944			1.73981			0.869907	−	0.493215i	$-0.164179\pi$
$3$	5.21944			1.73981			0.869907	+	0.493215i	$0.164179\pi$
$4$	−4.20834			−1.05209
$5$	3.21069			0.642138			0.321069	−	0.947056i	$-0.395958\pi$
$5$	3.21069			0.642138			0.321069	+	0.947056i	$0.395958\pi$
$6$		−	14.9538i		−	2.49230i
$7$		−	5.03509i		−	0.719298i	−0.933088	−	0.359649i	$-0.882896\pi$
$7$		−	5.03509i		−	0.719298i	0.933088	−	0.359649i	$-0.117104\pi$
$8$			0.596911i			0.0746138i
$9$	18.2426			2.02695
$10$		−	9.19869i		−	0.919869i
$11$	−3.77449	+	10.3321i	−0.343136	+	0.939286i
$11$	−3.77449	+	10.3321i	−0.343136	+	0.939286i
$12$	−21.9652			−1.83043
$13$			15.9623i			1.22787i	0.789357	+	0.613934i	$0.210414\pi$
$13$			15.9623i			1.22787i	−0.789357	+	0.613934i	$0.789586\pi$
$14$	−14.4256			−1.03040
$15$	16.7580			1.11720
$16$	−15.1232			−0.945201
$17$		−	2.07725i		−	0.122191i	−0.998132	−	0.0610957i	$-0.980541\pi$
$17$		−	2.07725i		−	0.122191i	0.998132	−	0.0610957i	$-0.0194595\pi$
$18$		−	52.2654i		−	2.90363i
$19$		−	2.99343i		−	0.157549i	−0.996892	−	0.0787745i	$-0.974899\pi$
$19$		−	2.99343i		−	0.157549i	0.996892	−	0.0787745i	$-0.0251007\pi$
$20$	−13.5117			−0.675584
$21$		−	26.2803i		−	1.25145i
$22$	29.6018	+	10.8140i	1.34554	+	0.491545i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$			3.11554i			0.129814i
$25$	−14.6915			−0.587659
$26$	45.7323			1.75893
$27$	48.2412			1.78671
$28$			21.1894i			0.756763i
$29$		−	19.2645i		−	0.664294i	−0.943228	−	0.332147i	$-0.892227\pi$
$29$		−	19.2645i		−	0.664294i	0.943228	−	0.332147i	$-0.107773\pi$
$30$		−	48.0120i		−	1.60040i
$31$	−53.4474			−1.72411			−0.862055	−	0.506816i	$-0.830823\pi$
$31$	−53.4474			−1.72411			−0.862055	+	0.506816i	$0.830823\pi$
$32$			45.7160i			1.42862i
$33$	−19.7007	+	53.9280i	−0.596992	+	1.63418i
$34$	−5.95137			−0.175040
$35$		−	16.1661i		−	0.461888i
$36$	−76.7711			−2.13253
$37$	35.6340			0.963082			0.481541	−	0.876424i	$-0.340077\pi$
$37$	35.6340			0.963082			0.481541	+	0.876424i	$0.340077\pi$
$38$	−8.57624			−0.225691
$39$			83.3142i			2.13626i
$40$			1.91649i			0.0479123i
$41$			64.1419i			1.56444i	0.623005	+	0.782218i	$0.285912\pi$
$41$			64.1419i			1.56444i	−0.623005	+	0.782218i	$0.714088\pi$
$42$	−75.2937			−1.79271
$43$		−	48.4215i		−	1.12608i	−0.826429	−	0.563040i	$-0.809632\pi$
$43$		−	48.4215i		−	1.12608i	0.826429	−	0.563040i	$-0.190368\pi$
$44$	15.8844	−	43.4812i	0.361008	−	0.988210i
$45$	58.5713			1.30158
$46$		−	13.7402i		−	0.298699i
$47$	−29.4086			−0.625715			−0.312858	−	0.949800i	$-0.601286\pi$
$47$	−29.4086			−0.625715			−0.312858	+	0.949800i	$0.601286\pi$
$48$	−78.9348			−1.64447
$49$	23.6479			0.482610
$50$			42.0914i			0.841828i
$51$		−	10.8421i		−	0.212590i
$52$		−	67.1748i		−	1.29182i
$53$	−23.6910			−0.446999			−0.223500	−	0.974704i	$-0.571748\pi$
$53$	−23.6910			−0.446999			−0.223500	+	0.974704i	$0.571748\pi$
$54$		−	138.212i		−	2.55948i
$55$	−12.1187	+	33.1733i	−0.220340	+	0.603151i
$56$	3.00550			0.0536696
$57$		−	15.6240i		−	0.274106i
$58$	−55.1933			−0.951608
$59$	−74.5141			−1.26295			−0.631475	−	0.775396i	$-0.717550\pi$
$59$	−74.5141			−1.26295			−0.631475	+	0.775396i	$0.717550\pi$
$60$	−70.5235			−1.17539
$61$			36.0105i			0.590336i	0.955445	+	0.295168i	$0.0953755\pi$
$61$			36.0105i			0.590336i	−0.955445	+	0.295168i	$0.904624\pi$
$62$			153.128i			2.46980i
$63$		−	91.8530i		−	1.45798i
$64$	70.4843			1.10132
$65$			51.2499i			0.788460i
$66$	154.505	+	56.4430i	2.34098	+	0.855197i
$67$	133.886			1.99830			0.999151	−	0.0411946i	$-0.0131164\pi$
$67$	133.886			1.99830			0.999151	+	0.0411946i	$0.0131164\pi$
$68$			8.74180i			0.128556i
$69$	25.0316			0.362776
$70$	−46.3162			−0.661660
$71$	30.5895			0.430837			0.215419	−	0.976522i	$-0.430888\pi$
$71$	30.5895			0.430837			0.215419	+	0.976522i	$0.430888\pi$
$72$			10.8892i			0.151239i
$73$		−	52.3969i		−	0.717765i	−0.933383	−	0.358883i	$-0.883158\pi$
$73$		−	52.3969i		−	0.717765i	0.933383	−	0.358883i	$-0.116842\pi$
$74$		−	102.092i		−	1.37962i
$75$	−76.6814			−1.02242
$76$			12.5974i			0.165755i
$77$	52.0232	+	19.0049i	0.675627	+	0.246817i
$78$	238.697			3.06022
$79$			75.9222i			0.961041i	0.876984	+	0.480520i	$0.159552\pi$
$79$			75.9222i			0.961041i	−0.876984	+	0.480520i	$0.840448\pi$
$80$	−48.5559			−0.606949
$81$	87.6087			1.08159
$82$	183.768			2.24107
$83$		−	16.6444i		−	0.200535i	−0.994961	−	0.100267i	$-0.968030\pi$
$83$		−	16.6444i		−	0.200535i	0.994961	−	0.100267i	$-0.0319698\pi$
$84$			110.597i			1.31663i
$85$		−	6.66941i		−	0.0784637i
$86$	−138.728			−1.61312
$87$		−	100.550i		−	1.15575i
$88$	−6.16737	−	2.25303i	−0.0700837	−	0.0256027i
$89$	56.5773			0.635700			0.317850	−	0.948141i	$-0.397039\pi$
$89$	56.5773			0.635700			0.317850	+	0.948141i	$0.397039\pi$
$90$		−	167.808i		−	1.86453i
$91$	80.3715			0.883203
$92$	−20.1825			−0.219375
$93$	−278.966			−2.99963
$94$			84.2563i			0.896343i
$95$		−	9.61097i		−	0.101168i
$96$			238.612i			2.48554i
$97$	168.076			1.73274			0.866371	−	0.499401i	$-0.166447\pi$
$97$	168.076			1.73274			0.866371	+	0.499401i	$0.166447\pi$
$98$		−	67.7517i		−	0.691344i
$99$	−68.8565	+	188.485i	−0.695520	+	1.90389i
$100$	61.8268			0.618268
$101$		−	106.258i		−	1.05206i	−0.850466	−	0.526031i	$-0.823680\pi$
$101$		−	106.258i		−	1.05206i	0.850466	−	0.526031i	$-0.176320\pi$
$102$	−31.0629			−0.304538
$103$	5.04786			0.0490084			0.0245042	−	0.999700i	$-0.492199\pi$
$103$	5.04786			0.0490084			0.0245042	+	0.999700i	$0.492199\pi$
$104$	−9.52805			−0.0916159
$105$		−	84.3780i		−	0.803600i
$106$			67.8751i			0.640331i
$107$			132.268i			1.23615i	0.786119	+	0.618075i	$0.212087\pi$
$107$			132.268i			1.23615i	−0.786119	+	0.618075i	$0.787913\pi$
$108$	−203.015			−1.87977
$109$		−	38.8789i		−	0.356687i	−0.983968	−	0.178344i	$-0.942926\pi$
$109$		−	38.8789i		−	0.356687i	0.983968	−	0.178344i	$-0.0570739\pi$
$110$	95.0422	+	34.7204i	0.864020	+	0.315640i
$111$	185.990			1.67558
$112$			76.1467i			0.679881i
$113$	−65.0290			−0.575478			−0.287739	−	0.957709i	$-0.592904\pi$
$113$	−65.0290			−0.575478			−0.287739	+	0.957709i	$0.592904\pi$
$114$	−44.7632			−0.392660
$115$	15.3979			0.133895
$116$			81.0717i			0.698894i
$117$			291.193i			2.48883i
$118$			213.484i			1.80919i
$119$	−10.4592			−0.0878920
$120$			10.0030i			0.0833586i
$121$	−92.5064	−	77.9972i	−0.764516	−	0.644605i
$122$	103.171			0.845662
$123$			334.785i			2.72183i
$124$	224.925			1.81391
$125$	−127.437			−1.01950
$126$	−263.161			−2.08858
$127$		−	92.9376i		−	0.731792i	−0.930656	−	0.365896i	$-0.880763\pi$
$127$		−	92.9376i		−	0.731792i	0.930656	−	0.365896i	$-0.119237\pi$
$128$		−	19.0752i		−	0.149025i
$129$		−	252.733i		−	1.95917i
$130$	146.832			1.12948
$131$		−	23.7233i		−	0.181094i	−0.995892	−	0.0905468i	$-0.971139\pi$
$131$		−	23.7233i		−	0.181094i	0.995892	−	0.0905468i	$-0.0288615\pi$
$132$	82.9075	−	226.948i	0.628087	−	1.71930i
$133$	−15.0722			−0.113325
$134$		−	383.587i		−	2.86259i
$135$	154.887			1.14731
$136$	1.23993			0.00911717
$137$	79.0137			0.576742			0.288371	−	0.957519i	$-0.406886\pi$
$137$	79.0137			0.576742			0.288371	+	0.957519i	$0.406886\pi$
$138$		−	71.7160i		−	0.519681i
$139$			61.7697i			0.444386i	0.975003	+	0.222193i	$0.0713215\pi$
$139$			61.7697i			0.444386i	−0.975003	+	0.222193i	$0.928678\pi$
$140$			68.0325i			0.485946i
$141$	−153.497			−1.08863
$142$		−	87.6394i		−	0.617179i
$143$	−164.925	−	60.2495i	−1.15332	−	0.421325i
$144$	−275.887			−1.91588
$145$		−	61.8524i		−	0.426568i
$146$	−150.118			−1.02821
$147$	123.429			0.839652
$148$	−149.960			−1.01324
$149$		−	214.994i		−	1.44292i	−0.692458	−	0.721458i	$-0.743472\pi$
$149$		−	214.994i		−	1.44292i	0.692458	−	0.721458i	$-0.256528\pi$
$150$			219.694i			1.46462i
$151$		−	227.647i		−	1.50760i	−0.657104	−	0.753800i	$-0.728219\pi$
$151$		−	227.647i		−	1.50760i	0.657104	−	0.753800i	$-0.271781\pi$
$152$	1.78681			0.0117553
$153$		−	37.8945i		−	0.247676i
$154$	54.4494	−	149.048i	0.353568	−	0.967842i
$155$	−171.603			−1.10712
$156$		−	350.615i		−	2.24753i
$157$	−5.83540			−0.0371682			−0.0185841	−	0.999827i	$-0.505916\pi$
$157$	−5.83540			−0.0371682			−0.0185841	+	0.999827i	$0.505916\pi$
$158$	217.519			1.37670
$159$	−123.654			−0.777696
$160$			146.780i			0.917373i
$161$		−	24.1474i		−	0.149984i
$162$		−	251.001i		−	1.54939i
$163$	71.6551			0.439602			0.219801	−	0.975545i	$-0.429459\pi$
$163$	71.6551			0.439602			0.219801	+	0.975545i	$0.429459\pi$
$164$		−	269.931i		−	1.64592i
$165$	−63.2529	+	173.146i	−0.383351	+	1.04937i
$166$	−47.6865			−0.287268
$167$		−	35.4817i		−	0.212465i	−0.994341	−	0.106233i	$-0.966121\pi$
$167$		−	35.4817i		−	0.212465i	0.994341	−	0.106233i	$-0.0338789\pi$
$168$	15.6870			0.0933751
$169$	−85.7944			−0.507659
$170$	−19.1080			−0.112400
$171$		−	54.6079i		−	0.319345i
$172$			203.774i			1.18473i
$173$			126.163i			0.729265i	0.931152	+	0.364632i	$0.118805\pi$
$173$			126.163i			0.729265i	−0.931152	+	0.364632i	$0.881195\pi$
$174$	−288.078			−1.65562
$175$			73.9729i			0.422702i
$176$	57.0824	−	156.255i	0.324332	−	0.887814i
$177$	−388.922			−2.19730
$178$		−	162.095i		−	0.910647i
$179$	−333.353			−1.86231			−0.931153	−	0.364628i	$-0.881196\pi$
$179$	−333.353			−1.86231			−0.931153	+	0.364628i	$0.881196\pi$
$180$	−246.488			−1.36938
$181$	−99.1014			−0.547522			−0.273761	−	0.961798i	$-0.588268\pi$
$181$	−99.1014			−0.547522			−0.273761	+	0.961798i	$0.588268\pi$
$182$		−	230.266i		−	1.26520i
$183$			187.955i			1.02707i
$184$			2.86268i			0.0155581i
$185$	114.410			0.618431
$186$			799.242i			4.29700i
$187$	21.4625	+	7.84057i	0.114773	+	0.0419282i
$188$	123.762			0.658306
$189$		−	242.898i		−	1.28518i
$190$	−27.5356			−0.144924
$191$	−78.4796			−0.410888			−0.205444	−	0.978669i	$-0.565864\pi$
$191$	−78.4796			−0.410888			−0.205444	+	0.978669i	$0.565864\pi$
$192$	367.889			1.91609
$193$			233.573i			1.21022i	0.796141	+	0.605112i	$0.206871\pi$
$193$			233.573i			1.21022i	−0.796141	+	0.605112i	$0.793129\pi$
$194$		−	481.541i		−	2.48217i
$195$			267.496i			1.37177i
$196$	−99.5185			−0.507748
$197$		−	196.368i		−	0.996791i	−0.866950	−	0.498395i	$-0.833923\pi$
$197$		−	196.368i		−	0.996791i	0.866950	−	0.498395i	$-0.166077\pi$
$198$	540.014	+	197.275i	2.72734	+	0.996340i
$199$	320.558			1.61085			0.805423	−	0.592700i	$-0.201938\pi$
$199$	320.558			1.61085			0.805423	+	0.592700i	$0.201938\pi$
$200$		−	8.76950i		−	0.0438475i
$201$	698.812			3.47668
$202$	−304.432			−1.50709
$203$	−96.9985			−0.477825
$204$			45.6273i			0.223663i
$205$			205.940i			1.00458i
$206$		−	14.4622i		−	0.0702050i
$207$	87.4884			0.422649
$208$		−	241.401i		−	1.16058i
$209$	30.9286	+	11.2987i	0.147984	+	0.0540607i
$210$	−241.745			−1.15117
$211$			360.599i			1.70900i	0.519450	+	0.854501i	$0.326137\pi$
$211$			360.599i			1.70900i	−0.519450	+	0.854501i	$0.673863\pi$
$212$	99.6997			0.470282
$213$	159.660			0.749577
$214$	378.951			1.77080
$215$		−	155.466i		−	0.723099i
$216$			28.7957i			0.133313i
$217$			269.112i			1.24015i
$218$	−111.389			−0.510959
$219$		−	273.482i		−	1.24878i
$220$	50.9997	−	139.605i	0.231817	−	0.634567i
$221$	33.1577			0.150035
$222$		−	532.864i		−	2.40029i
$223$	−166.162			−0.745122			−0.372561	−	0.928008i	$-0.621520\pi$
$223$	−166.162			−0.745122			−0.372561	+	0.928008i	$0.621520\pi$
$224$	230.184			1.02761
$225$	−268.011			−1.19116
$226$			186.309i			0.824378i
$227$			42.3260i			0.186458i	0.995645	+	0.0932290i	$0.0297189\pi$
$227$			42.3260i			0.186458i	−0.995645	+	0.0932290i	$0.970281\pi$
$228$			65.7513i			0.288383i
$229$	−163.446			−0.713739			−0.356870	−	0.934154i	$-0.616156\pi$
$229$	−163.446			−0.713739			−0.356870	+	0.934154i	$0.616156\pi$
$230$		−	44.1154i		−	0.191806i
$231$	271.532	+	99.1949i	1.17546	+	0.429415i
$232$	11.4992			0.0495655
$233$			344.958i			1.48051i	0.672328	+	0.740254i	$0.265295\pi$
$233$			344.958i			1.48051i	−0.672328	+	0.740254i	$0.734705\pi$
$234$	834.275			3.56528
$235$	−94.4219			−0.401795
$236$	313.581			1.32873
$237$			396.272i			1.67203i
$238$			29.9657i			0.125906i
$239$			31.9150i			0.133536i	0.997769	+	0.0667678i	$0.0212687\pi$
$239$			31.9150i			0.133536i	−0.997769	+	0.0667678i	$0.978731\pi$
$240$	−253.435			−1.05598
$241$		−	434.350i		−	1.80228i	−0.433526	−	0.901141i	$-0.642731\pi$
$241$		−	434.350i		−	1.80228i	0.433526	−	0.901141i	$-0.357269\pi$
$242$	−223.464	+	265.033i	−0.923403	+	1.09518i
$243$	23.0981			0.0950541
$244$		−	151.544i		−	0.621084i
$245$	75.9260			0.309902
$246$	959.166			3.89905
$247$	47.7820			0.193449
$248$		−	31.9033i		−	0.128642i
$249$		−	86.8744i		−	0.348893i
$250$			365.110i			1.46044i
$251$	−381.453			−1.51973			−0.759867	−	0.650079i	$-0.774736\pi$
$251$	−381.453			−1.51973			−0.759867	+	0.650079i	$0.774736\pi$
$252$			386.549i			1.53392i
$253$	−18.1018	+	49.5512i	−0.0715487	+	0.195855i
$254$	−266.268			−1.04830
$255$		−	34.8106i		−	0.136512i
$256$	227.286			0.887838
$257$	−217.809			−0.847506			−0.423753	−	0.905778i	$-0.639288\pi$
$257$	−217.809			−0.847506			−0.423753	+	0.905778i	$0.639288\pi$
$258$	−724.085			−2.80653
$259$		−	179.420i		−	0.692743i
$260$		−	215.677i		−	0.829528i
$261$		−	351.435i		−	1.34649i
$262$	−67.9676			−0.259418
$263$		−	72.0649i		−	0.274011i	−0.990570	−	0.137005i	$-0.956252\pi$
$263$		−	72.0649i		−	0.274011i	0.990570	−	0.137005i	$-0.0437478\pi$
$264$	−32.1902	−	11.7596i	−0.121933	−	0.0445439i
$265$	−76.0643			−0.287035
$266$			43.1821i			0.162339i
$267$	295.302			1.10600
$268$	−563.439			−2.10239
$269$	88.1182			0.327577			0.163788	−	0.986495i	$-0.447629\pi$
$269$	88.1182			0.327577			0.163788	+	0.986495i	$0.447629\pi$
$270$		−	443.755i		−	1.64354i
$271$		−	420.838i		−	1.55291i	−0.630175	−	0.776454i	$-0.717017\pi$
$271$		−	420.838i		−	1.55291i	0.630175	−	0.776454i	$-0.282983\pi$
$272$			31.4148i			0.115495i
$273$	419.494			1.53661
$274$		−	226.376i		−	0.826189i
$275$	55.4529	−	151.795i	0.201647	−	0.551980i
$276$	−105.341			−0.381672
$277$			224.180i			0.809316i	0.914468	+	0.404658i	$0.132609\pi$
$277$			224.180i			0.809316i	−0.914468	+	0.404658i	$0.867391\pi$
$278$	176.971			0.636588
$279$	−975.018			−3.49469
$280$	9.64971			0.0344633
$281$			382.501i			1.36121i	0.732650	+	0.680606i	$0.238283\pi$
$281$			382.501i			1.36121i	−0.732650	+	0.680606i	$0.761717\pi$
$282$			439.771i			1.55947i
$283$		−	543.305i		−	1.91980i	−0.280336	−	0.959902i	$-0.590446\pi$
$283$		−	543.305i		−	1.91980i	0.280336	−	0.959902i	$-0.409554\pi$
$284$	−128.731			−0.453278
$285$		−	50.1639i		−	0.176014i
$286$	−172.616	+	472.512i	−0.603553	+	1.65214i
$287$	322.960			1.12530
$288$			833.978i			2.89576i
$289$	284.685			0.985069
$290$	−177.208			−0.611063
$291$	877.263			3.01465
$292$			220.504i			0.755151i
$293$		−	576.181i		−	1.96649i	−0.182293	−	0.983244i	$-0.558352\pi$
$293$		−	576.181i		−	1.96649i	0.182293	−	0.983244i	$-0.441648\pi$
$294$		−	353.626i		−	1.20281i
$295$	−239.241			−0.810988
$296$			21.2703i			0.0718592i
$297$	−182.086	+	498.435i	−0.613083	+	1.67823i
$298$	−615.964			−2.06699
$299$			76.5524i			0.256028i
$300$	322.702			1.07567
$301$	−243.806			−0.809988
$302$	−652.215			−2.15965
$303$		−	554.609i		−	1.83039i
$304$			45.2703i			0.148915i
$305$			115.618i			0.379077i
$306$	−108.568			−0.354799
$307$		−	380.988i		−	1.24100i	−0.784205	−	0.620502i	$-0.786929\pi$
$307$		−	380.988i		−	1.24100i	0.784205	−	0.620502i	$-0.213071\pi$
$308$	−218.932	−	79.9791i	−0.710817	−	0.259672i
$309$	26.3470			0.0852654
$310$			491.646i			1.58595i
$311$	−331.228			−1.06504			−0.532520	−	0.846417i	$-0.678755\pi$
$311$	−331.228			−1.06504			−0.532520	+	0.846417i	$0.678755\pi$
$312$	−49.7311			−0.159395
$313$	−86.7825			−0.277260			−0.138630	−	0.990344i	$-0.544270\pi$
$313$	−86.7825			−0.277260			−0.138630	+	0.990344i	$0.544270\pi$
$314$			16.7186i			0.0532438i
$315$		−	294.911i		−	0.936226i
$316$		−	319.507i		−	1.01110i
$317$	−18.9429			−0.0597567			−0.0298784	−	0.999554i	$-0.509512\pi$
$317$	−18.9429			−0.0597567			−0.0298784	+	0.999554i	$0.509512\pi$
$318$			354.270i			1.11406i
$319$	199.044	+	72.7138i	0.623962	+	0.227943i
$320$	226.303			0.707198
$321$			690.366i			2.15067i
$322$	−69.1829			−0.214854
$323$	−6.21811			−0.0192511
$324$	−368.687			−1.13792
$325$		−	234.510i		−	0.721568i
$326$		−	205.293i		−	0.629735i
$327$		−	202.926i		−	0.620570i
$328$	−38.2870			−0.116729
$329$			148.075i			0.450076i
$330$	496.067	+	181.221i	1.50323	+	0.549154i
$331$	563.364			1.70200			0.851002	−	0.525162i	$-0.175995\pi$
$331$	563.364			1.70200			0.851002	+	0.525162i	$0.175995\pi$
$332$			70.0452i			0.210980i
$333$	650.057			1.95212
$334$	−101.656			−0.304359
$335$	429.867			1.28319
$336$			397.443i			1.18287i
$337$			318.523i			0.945172i	0.881285	+	0.472586i	$0.156679\pi$
$337$			318.523i			0.945172i	−0.881285	+	0.472586i	$0.843321\pi$
$338$			245.803i			0.727227i
$339$	−339.415			−1.00122
$340$			28.0672i			0.0825506i
$341$	201.737	−	552.226i	0.591603	−	1.61943i
$342$	−156.453			−0.457464
$343$		−	365.788i		−	1.06644i
$344$	28.9033			0.0840212
$345$	80.3686			0.232952
$346$	361.459			1.04468
$347$			98.0094i			0.282448i	0.989978	+	0.141224i	$0.0451037\pi$
$347$			98.0094i			0.282448i	−0.989978	+	0.141224i	$0.954896\pi$
$348$			423.149i			1.21595i
$349$		−	68.6741i		−	0.196774i	−0.995148	−	0.0983870i	$-0.968632\pi$
$349$		−	68.6741i		−	0.196774i	0.995148	−	0.0983870i	$-0.0313683\pi$
$350$	211.934			0.605525
$351$			770.039i			2.19384i
$352$	−472.344	−	172.555i	−1.34189	−	0.490212i
$353$	−30.7226			−0.0870328			−0.0435164	−	0.999053i	$-0.513856\pi$
$353$	−30.7226			−0.0870328			−0.0435164	+	0.999053i	$0.513856\pi$
$354$			1114.27i			3.14765i
$355$	98.2132			0.276657
$356$	−238.097			−0.668811
$357$	−54.5909			−0.152916
$358$			955.063i			2.66777i
$359$		−	448.408i		−	1.24905i	−0.781006	−	0.624524i	$-0.785293\pi$
$359$		−	448.408i		−	1.24905i	0.781006	−	0.624524i	$-0.214707\pi$
$360$			34.9618i			0.0971161i
$361$	352.039			0.975178
$362$			283.928i			0.784330i
$363$	−482.832	−	407.102i	−1.33012	−	1.12149i
$364$	−338.231			−0.929205
$365$		−	168.230i		−	0.460904i
$366$	538.494			1.47129
$367$	−485.115			−1.32184			−0.660919	−	0.750457i	$-0.729833\pi$
$367$	−485.115			−1.32184			−0.660919	+	0.750457i	$0.729833\pi$
$368$	−72.5284			−0.197088
$369$			1170.11i			3.17104i
$370$		−	327.786i		−	0.885909i
$371$			119.286i			0.321526i
$372$	1173.98			3.15587
$373$			637.189i			1.70828i	0.520041	+	0.854141i	$0.325917\pi$
$373$			637.189i			1.70828i	−0.520041	+	0.854141i	$0.674083\pi$
$374$	22.4634	−	61.4905i	0.0600626	−	0.164413i
$375$	−665.150			−1.77373
$376$		−	17.5543i		−	0.0466870i
$377$	307.506			0.815665
$378$	−695.909			−1.84103
$379$	−81.1675			−0.214162			−0.107081	−	0.994250i	$-0.534150\pi$
$379$	−81.1675			−0.214162			−0.107081	+	0.994250i	$0.534150\pi$
$380$			40.4463i			0.106438i
$381$		−	485.082i		−	1.27318i
$382$			224.846i			0.588601i
$383$	432.293			1.12870			0.564351	−	0.825535i	$-0.309126\pi$
$383$	432.293			1.12870			0.564351	+	0.825535i	$0.309126\pi$
$384$		−	99.5621i		−	0.259276i
$385$	167.030	+	61.0188i	0.433845	+	0.158490i
$386$	669.192			1.73366
$387$		−	883.333i		−	2.28251i
$388$	−707.321			−1.82299
$389$	−528.536			−1.35870			−0.679352	−	0.733812i	$-0.737739\pi$
$389$	−528.536			−1.35870			−0.679352	+	0.733812i	$0.737739\pi$
$390$	766.382			1.96508
$391$		−	9.96216i		−	0.0254787i
$392$			14.1157i			0.0360094i
$393$		−	123.822i		−	0.315069i
$394$	−562.598			−1.42791
$395$			243.763i			0.617120i
$396$	289.772	−	793.210i	0.731747	−	2.00306i
$397$	−39.0756			−0.0984273			−0.0492136	−	0.998788i	$-0.515672\pi$
$397$	−39.0756			−0.0984273			−0.0492136	+	0.998788i	$0.515672\pi$
$398$		−	918.407i		−	2.30755i
$399$	−78.6684			−0.197164
$400$	222.182			0.555456
$401$	195.864			0.488438			0.244219	−	0.969720i	$-0.421468\pi$
$401$	195.864			0.488438			0.244219	+	0.969720i	$0.421468\pi$
$402$		−	2002.11i		−	4.98037i
$403$		−	853.142i		−	2.11698i
$404$			447.171i			1.10686i
$405$	281.284			0.694529
$406$			277.903i			0.684490i
$407$	−134.500	+	368.176i	−0.330468	+	0.904609i
$408$	6.47177			0.0158622
$409$			527.157i			1.28889i	0.764649	+	0.644447i	$0.222912\pi$
$409$			527.157i			1.28889i	−0.764649	+	0.644447i	$0.777088\pi$
$410$	590.021			1.43908
$411$	412.408			1.00342
$412$	−21.2431			−0.0515610
$413$			375.185i			0.908438i
$414$		−	250.656i		−	0.605449i
$415$		−	53.4399i		−	0.128771i
$416$	−729.731			−1.75416
$417$			322.403i			0.773149i
$418$	32.3709	−	88.6110i	0.0774424	−	0.211988i
$419$	−549.419			−1.31126			−0.655631	−	0.755081i	$-0.727597\pi$
$419$	−549.419			−1.31126			−0.655631	+	0.755081i	$0.727597\pi$
$420$			355.092i			0.845456i
$421$	−50.8288			−0.120734			−0.0603668	−	0.998176i	$-0.519227\pi$
$421$	−50.8288			−0.120734			−0.0603668	+	0.998176i	$0.519227\pi$
$422$	1033.12			2.44816
$423$	−536.489			−1.26830
$424$		−	14.1414i		−	0.0333523i
$425$			30.5179i			0.0718069i
$426$		−	457.429i		−	1.07378i
$427$	181.316			0.424627
$428$		−	556.630i		−	1.30054i
$429$	−860.815	−	314.469i	−2.00656	−	0.733027i
$430$	−445.414			−1.03585
$431$		−	151.965i		−	0.352588i	−0.984338	−	0.176294i	$-0.943589\pi$
$431$		−	151.965i		−	0.352588i	0.984338	−	0.176294i	$-0.0564109\pi$
$432$	−729.561			−1.68880
$433$	17.3838			0.0401473			0.0200736	−	0.999799i	$-0.493610\pi$
$433$	17.3838			0.0401473			0.0200736	+	0.999799i	$0.493610\pi$
$434$	771.012			1.77653
$435$		−	322.835i		−	0.742149i
$436$			163.616i			0.375266i
$437$		−	14.3560i		−	0.0328512i
$438$	−783.533			−1.78889
$439$		−	491.356i		−	1.11926i	−0.828742	−	0.559631i	$-0.810943\pi$
$439$		−	491.356i		−	1.11926i	0.828742	−	0.559631i	$-0.189057\pi$
$440$	−19.8015	−	7.23379i	−0.0450034	−	0.0164404i
$441$	431.399			0.978229
$442$		−	94.9975i		−	0.214927i
$443$	−287.338			−0.648618			−0.324309	−	0.945951i	$-0.605132\pi$
$443$	−287.338			−0.648618			−0.324309	+	0.945951i	$0.605132\pi$
$444$	−782.709			−1.76286
$445$	181.652			0.408207
$446$			476.058i			1.06740i
$447$		−	1122.15i		−	2.51041i
$448$		−	354.895i		−	0.792176i
$449$	574.563			1.27965			0.639825	−	0.768520i	$-0.279007\pi$
$449$	574.563			1.27965			0.639825	+	0.768520i	$0.279007\pi$
$450$			767.856i			1.70635i
$451$	−662.723	−	242.103i	−1.46945	−	0.536814i
$452$	273.664			0.605452
$453$		−	1188.19i		−	2.62294i
$454$	121.265			0.267103
$455$	258.048			0.567138
$456$	9.32615			0.0204521
$457$		−	596.898i		−	1.30612i	−0.757305	−	0.653061i	$-0.773484\pi$
$457$		−	596.898i		−	1.30612i	0.757305	−	0.653061i	$-0.226516\pi$
$458$			468.277i			1.02244i
$459$		−	100.209i		−	0.218321i
$460$	−64.7997			−0.140869
$461$			405.057i			0.878649i	0.898328	+	0.439325i	$0.144782\pi$
$461$			405.057i			0.878649i	−0.898328	+	0.439325i	$0.855218\pi$
$462$	284.196	−	777.946i	0.615142	−	1.68387i
$463$	696.882			1.50514			0.752572	−	0.658510i	$-0.228813\pi$
$463$	696.882			1.50514			0.752572	+	0.658510i	$0.228813\pi$
$464$			291.342i			0.627891i
$465$	−895.671			−1.92618
$466$	988.313			2.12084
$467$	579.895			1.24175			0.620873	−	0.783911i	$-0.286778\pi$
$467$	579.895			1.24175			0.620873	+	0.783911i	$0.286778\pi$
$468$		−	1225.44i		−	2.61846i
$469$		−	674.129i		−	1.43737i
$470$			270.521i			0.575576i
$471$	−30.4576			−0.0646657
$472$		−	44.4782i		−	0.0942335i
$473$	500.298	+	182.766i	1.05771	+	0.386398i
$474$	1135.33			2.39520
$475$			43.9779i			0.0925851i
$476$	44.0157			0.0924700
$477$	−432.184			−0.906047
$478$	91.4371			0.191291
$479$			460.293i			0.960945i	0.877010	+	0.480472i	$0.159535\pi$
$479$			460.293i			0.960945i	−0.877010	+	0.480472i	$0.840465\pi$
$480$			766.108i			1.59606i
$481$			568.800i			1.18254i
$482$	−1244.42			−2.58179
$483$		−	126.036i		−	0.260944i
$484$	389.299	+	328.239i	0.804337	+	0.678180i
$485$	539.639			1.11266
$486$		−	66.1767i		−	0.136166i
$487$	−668.522			−1.37274			−0.686368	−	0.727254i	$-0.740796\pi$
$487$	−668.522			−1.37274			−0.686368	+	0.727254i	$0.740796\pi$
$488$	−21.4950			−0.0440472
$489$	374.000			0.764826
$490$		−	217.530i		−	0.443938i
$491$		−	75.5332i		−	0.153835i	−0.997037	−	0.0769177i	$-0.975492\pi$
$491$		−	75.5332i		−	0.153835i	0.997037	−	0.0769177i	$-0.0245079\pi$
$492$		−	1408.89i		−	2.86360i
$493$	−40.0173			−0.0811710
$494$		−	136.896i		−	0.277118i
$495$	−221.077	+	605.167i	−0.446620	+	1.22256i
$496$	808.296			1.62963
$497$		−	154.021i		−	0.309901i
$498$	−248.897			−0.499793
$499$	−185.124			−0.370990			−0.185495	−	0.982645i	$-0.559389\pi$
$499$	−185.124			−0.370990			−0.185495	+	0.982645i	$0.559389\pi$
$500$	536.299			1.07260
$501$		−	185.195i		−	0.369651i
$502$			1092.87i			2.17703i
$503$			125.110i			0.248729i	0.992237	+	0.124364i	$0.0396891\pi$
$503$			125.110i			0.248729i	−0.992237	+	0.124364i	$0.960311\pi$
$504$	54.8280			0.108786
$505$		−	341.162i		−	0.675568i
$506$	141.965	+	51.8621i	0.280564	+	0.102494i
$507$	−447.799			−0.883233
$508$			391.113i			0.769908i
$509$	755.706			1.48469			0.742344	−	0.670019i	$-0.233714\pi$
$509$	755.706			1.48469			0.742344	+	0.670019i	$0.233714\pi$
$510$	−99.7332			−0.195555
$511$	−263.823			−0.516287
$512$		−	727.481i		−	1.42086i
$513$		−	144.407i		−	0.281494i
$514$			624.028i			1.21406i
$515$	16.2071			0.0314701
$516$			1063.59i			2.06122i
$517$	111.003	−	303.854i	0.214705	−	0.587725i
$518$	−514.043			−0.992361
$519$			658.500i			1.26879i
$520$	−30.5916			−0.0588300
$521$	791.446			1.51909			0.759545	−	0.650455i	$-0.225422\pi$
$521$	791.446			1.51909			0.759545	+	0.650455i	$0.225422\pi$
$522$	−1006.87			−1.92887
$523$			652.320i			1.24727i	0.781717	+	0.623633i	$0.214344\pi$
$523$			652.320i			1.24727i	−0.781717	+	0.623633i	$0.785656\pi$
$524$			99.8356i			0.190526i
$525$			386.097i			0.735423i
$526$	−206.467			−0.392523
$527$			111.024i			0.210671i
$528$	297.939	−	815.565i	0.564278	−	1.54463i
$529$	23.0000			0.0434783
$530$			217.926i			0.411181i
$531$	−1359.33			−2.55994
$532$	63.4289			0.119227
$533$	−1023.85			−1.92092
$534$		−	846.046i		−	1.58436i
$535$			424.672i			0.793779i
$536$			79.9181i			0.149101i
$537$	−1739.92			−3.24007
$538$		−	252.460i		−	0.469257i
$539$	−89.2588	+	244.334i	−0.165601	+	0.453309i
$540$	−651.819			−1.20707
$541$			339.679i			0.627872i	0.949444	+	0.313936i	$0.101648\pi$
$541$			339.679i			0.627872i	−0.949444	+	0.313936i	$0.898352\pi$
$542$	−1205.71			−2.22456
$543$	−517.254			−0.952586
$544$	94.9637			0.174566
$545$		−	124.828i		−	0.229042i
$546$		−	1201.86i		−	2.20121i
$547$			531.120i			0.970969i	0.874245	+	0.485485i	$0.161357\pi$
$547$			531.120i			0.970969i	−0.874245	+	0.485485i	$0.838643\pi$
$548$	−332.517			−0.606783
$549$			656.924i			1.19658i
$550$	−434.894	−	158.874i	−0.790717	−	0.288861i
$551$	−57.6670			−0.104659
$552$			14.9416i			0.0270681i
$553$	382.275			0.691275
$554$	642.282			1.15935
$555$	597.155			1.07596
$556$		−	259.948i		−	0.467532i
$557$			741.975i			1.33209i	0.745911	+	0.666046i	$0.232015\pi$
$557$			741.975i			1.33209i	−0.745911	+	0.666046i	$0.767985\pi$
$558$			2793.45i			5.00618i
$559$	772.917			1.38268
$560$			244.483i			0.436577i
$561$	112.022	+	40.9234i	0.199683	+	0.0729473i
$562$	1095.87			1.94995
$563$		−	775.491i		−	1.37743i	−0.725034	−	0.688713i	$-0.758176\pi$
$563$		−	775.491i		−	1.37743i	0.725034	−	0.688713i	$-0.241824\pi$
$564$	645.966			1.14533
$565$	−208.788			−0.369536
$566$	−1556.58			−2.75014
$567$		−	441.117i		−	0.777985i
$568$			18.2592i			0.0321464i
$569$			690.359i			1.21328i	0.794975	+	0.606642i	$0.207484\pi$
$569$			690.359i			1.21328i	−0.794975	+	0.606642i	$0.792516\pi$
$570$	−143.721			−0.252142
$571$			88.0692i			0.154237i	0.997022	+	0.0771184i	$0.0245719\pi$
$571$			88.0692i			0.154237i	−0.997022	+	0.0771184i	$0.975428\pi$
$572$	694.059	+	253.551i	1.21339	+	0.443270i
$573$	−409.620			−0.714869
$574$		−	925.287i		−	1.61200i
$575$	−70.4579			−0.122535
$576$	1285.82			2.23232
$577$	−59.9277			−0.103861			−0.0519304	−	0.998651i	$-0.516537\pi$
$577$	−59.9277			−0.103861			−0.0519304	+	0.998651i	$0.516537\pi$
$578$		−	815.628i		−	1.41112i
$579$			1219.12i			2.10556i
$580$			260.296i			0.448786i
$581$	−83.8059			−0.144244
$582$		−	2513.38i		−	4.31852i
$583$	89.4213	−	244.778i	0.153381	−	0.419860i
$584$	31.2762			0.0535552
$585$			934.931i			1.59817i
$586$	−1650.77			−2.81702
$587$	−65.2446			−0.111149			−0.0555746	−	0.998455i	$-0.517699\pi$
$587$	−65.2446			−0.111149			−0.0555746	+	0.998455i	$0.517699\pi$
$588$	−519.431			−0.883386
$589$			159.991i			0.271632i
$590$			685.432i			1.16175i
$591$		−	1024.93i		−	1.73423i
$592$	−538.901			−0.910306
$593$			269.648i			0.454718i	0.973811	+	0.227359i	$0.0730090\pi$
$593$			269.648i			0.454718i	−0.973811	+	0.227359i	$0.926991\pi$
$594$	1428.03	+	521.680i	2.40408	+	0.878248i
$595$	−33.5811			−0.0564388
$596$			904.771i			1.51807i
$597$	1673.14			2.80257
$598$	219.324			0.366763
$599$	344.884			0.575767			0.287883	−	0.957665i	$-0.407048\pi$
$599$	344.884			0.575767			0.287883	+	0.957665i	$0.407048\pi$
$600$		−	45.7719i		−	0.0762865i
$601$			766.012i			1.27456i	0.770631	+	0.637282i	$0.219941\pi$
$601$			766.012i			1.27456i	−0.770631	+	0.637282i	$0.780059\pi$
$602$			698.510i			1.16032i
$603$	2442.43			4.05047
$604$			958.019i			1.58612i
$605$	−297.009	−	250.425i	−0.490924	−	0.413925i
$606$	−1588.97			−2.62205
$607$		−	600.171i		−	0.988750i	−0.869249	−	0.494375i	$-0.835397\pi$
$607$		−	600.171i		−	0.988750i	0.869249	−	0.494375i	$-0.164603\pi$
$608$	136.848			0.225078
$609$	−506.278			−0.831327
$610$	331.249			0.543031
$611$		−	469.428i		−	0.768295i
$612$			159.473i			0.260577i
$613$		−	303.933i		−	0.495813i	−0.968784	−	0.247906i	$-0.920257\pi$
$613$		−	303.933i		−	0.495813i	0.968784	−	0.247906i	$-0.0797425\pi$
$614$	−1091.54			−1.77775
$615$			1074.89i			1.74779i
$616$	−11.3442	+	31.0532i	−0.0184159	+	0.0504111i
$617$	−298.795			−0.484270			−0.242135	−	0.970243i	$-0.577848\pi$
$617$	−298.795			−0.484270			−0.242135	+	0.970243i	$0.577848\pi$
$618$		−	75.4848i		−	0.122144i
$619$	898.772			1.45197			0.725987	−	0.687709i	$-0.241383\pi$
$619$	898.772			1.45197			0.725987	+	0.687709i	$0.241383\pi$
$620$	722.164			1.16478
$621$	231.356			0.372555
$622$			948.974i			1.52568i
$623$		−	284.872i		−	0.457258i
$624$		−	1259.98i		−	2.01920i
$625$	−41.8733			−0.0669973
$626$			248.634i			0.397178i
$627$	161.430	+	58.9728i	0.257464	+	0.0940555i
$628$	24.5574			0.0391041
$629$		−	74.0209i		−	0.117680i
$630$	−844.927			−1.34115
$631$	−288.733			−0.457580			−0.228790	−	0.973476i	$-0.573477\pi$
$631$	−288.733			−0.457580			−0.228790	+	0.973476i	$0.573477\pi$
$632$	−45.3188			−0.0717069
$633$			1882.13i			2.97335i
$634$			54.2718i			0.0856021i
$635$		−	298.394i		−	0.469911i
$636$	520.377			0.818203
$637$			377.474i			0.592582i
$638$	208.326	−	570.265i	0.326531	−	0.893832i
$639$	558.031			0.873288
$640$		−	61.2446i		−	0.0956947i
$641$	−90.8999			−0.141810			−0.0709048	−	0.997483i	$-0.522589\pi$
$641$	−90.8999			−0.141810			−0.0709048	+	0.997483i	$0.522589\pi$
$642$	1977.91			3.08086
$643$	256.597			0.399063			0.199531	−	0.979891i	$-0.436058\pi$
$643$	256.597			0.399063			0.199531	+	0.979891i	$0.436058\pi$
$644$			101.621i			0.157796i
$645$		−	811.447i		−	1.25806i
$646$			17.8150i			0.0275774i
$647$	−482.348			−0.745515			−0.372758	−	0.927929i	$-0.621588\pi$
$647$	−482.348			−0.745515			−0.372758	+	0.927929i	$0.621588\pi$
$648$			52.2945i			0.0807015i
$649$	281.253	−	769.890i	0.433363	−	1.18627i
$650$	−671.875			−1.03365
$651$			1404.62i			2.15763i
$652$	−301.549			−0.462499
$653$	717.322			1.09850			0.549251	−	0.835657i	$-0.314913\pi$
$653$	717.322			1.09850			0.549251	+	0.835657i	$0.314913\pi$
$654$	−581.388			−0.888973
$655$		−	76.1680i		−	0.116287i
$656$		−	970.032i		−	1.47871i
$657$		−	955.854i		−	1.45488i
$658$	424.238			0.644738
$659$			265.092i			0.402264i	0.979564	+	0.201132i	$0.0644620\pi$
$659$			265.092i			0.402264i	−0.979564	+	0.201132i	$0.935538\pi$
$660$	266.190	−	728.659i	0.403318	−	1.10403i
$661$	229.692			0.347492			0.173746	−	0.984790i	$-0.444413\pi$
$661$	229.692			0.347492			0.173746	+	0.984790i	$0.444413\pi$
$662$		−	1614.05i		−	2.43814i
$663$	173.065			0.261033
$664$	9.93520			0.0149627
$665$	−48.3921			−0.0727700
$666$		−	1862.43i		−	2.79644i
$667$		−	92.3894i		−	0.138515i
$668$			149.319i			0.223532i
$669$	−867.275			−1.29637
$670$		−	1231.58i		−	1.83818i
$671$	−372.065	−	135.921i	−0.554494	−	0.202565i
$672$	1201.43			1.78784
$673$			300.834i			0.447004i	0.974703	+	0.223502i	$0.0717490\pi$
$673$			300.834i			0.447004i	−0.974703	+	0.223502i	$0.928251\pi$
$674$	912.574			1.35397
$675$	−708.734			−1.04998
$676$	361.052			0.534101
$677$			1097.42i			1.62100i	0.585740	+	0.810499i	$0.300804\pi$
$677$			1097.42i			1.62100i	−0.585740	+	0.810499i	$0.699196\pi$
$678$			972.431i			1.43426i
$679$		−	846.277i		−	1.24636i
$680$	3.98104			0.00585448
$681$			220.918i			0.324402i
$682$	−1582.14	−	577.980i	−2.31985	−	0.847478i
$683$	−944.682			−1.38314			−0.691568	−	0.722311i	$-0.743080\pi$
$683$	−944.682			−1.38314			−0.691568	+	0.722311i	$0.743080\pi$
$684$			229.809i			0.335978i
$685$	253.688			0.370348
$686$	−1047.99			−1.52768
$687$	−853.099			−1.24177
$688$			732.288i			1.06437i
$689$		−	378.162i		−	0.548856i
$690$		−	230.258i		−	0.333707i
$691$	−536.710			−0.776714			−0.388357	−	0.921509i	$-0.626957\pi$
$691$	−536.710			−0.776714			−0.388357	+	0.921509i	$0.626957\pi$
$692$		−	530.937i		−	0.767249i
$693$	949.039	+	346.698i	1.36946	+	0.500286i
$694$	280.799			0.404609
$695$			198.323i			0.285357i
$696$	60.0194			0.0862348
$697$	133.239			0.191161
$698$	−196.753			−0.281881
$699$			1800.49i			2.57581i
$700$		−	311.303i		−	0.444719i
$701$			1306.89i			1.86433i	0.362040	+	0.932163i	$0.382080\pi$
$701$			1306.89i			1.86433i	−0.362040	+	0.932163i	$0.617920\pi$
$702$	2206.18			3.14270
$703$		−	106.668i		−	0.151733i
$704$	−266.043	+	728.254i	−0.377901	+	1.03445i
$705$	−492.830			−0.699049
$706$			88.0208i			0.124675i
$707$	−535.019			−0.756746
$708$	1636.72			2.31175
$709$	14.1130			0.0199055			0.00995275	−	0.999950i	$-0.496832\pi$
$709$	14.1130			0.0199055			0.00995275	+	0.999950i	$0.496832\pi$
$710$		−	281.383i		−	0.396314i
$711$			1385.02i			1.94799i
$712$			33.7716i			0.0474320i
$713$	−256.325			−0.359502
$714$			156.404i			0.219054i
$715$	−529.521	−	193.442i	−0.740589	−	0.270549i
$716$	1402.86			1.95931
$717$			166.579i			0.232327i
$718$	−1284.70			−1.78927
$719$	669.154			0.930673			0.465337	−	0.885134i	$-0.345933\pi$
$719$	669.154			0.930673			0.465337	+	0.885134i	$0.345933\pi$
$720$	−885.786			−1.23026
$721$		−	25.4164i		−	0.0352516i
$722$		−	1008.60i		−	1.39695i
$723$		−	2267.06i		−	3.13564i
$724$	417.053			0.576040
$725$			283.024i			0.390378i
$726$	−1166.36	+	1383.32i	−1.60655	+	1.90540i
$727$	1298.54			1.78616			0.893080	−	0.449897i	$-0.148539\pi$
$727$	1298.54			1.78616			0.893080	+	0.449897i	$0.148539\pi$
$728$			47.9746i			0.0658991i
$729$	−667.919			−0.916212
$730$	−481.982			−0.660250
$731$	−100.584			−0.137597
$732$		−	790.978i		−	1.08057i
$733$		−	157.669i		−	0.215101i	−0.994200	−	0.107550i	$-0.965699\pi$
$733$		−	157.669i		−	0.215101i	0.994200	−	0.107550i	$-0.0343007\pi$
$734$			1389.86i			1.89355i
$735$	396.292			0.539172
$736$			219.246i			0.297889i
$737$	−505.352	+	1383.33i	−0.685689	+	1.87698i
$738$	3352.40			4.54255
$739$		−	1360.20i		−	1.84060i	−0.391212	−	0.920301i	$-0.627944\pi$
$739$		−	1360.20i		−	1.84060i	0.391212	−	0.920301i	$-0.372056\pi$
$740$	−481.476			−0.650643
$741$	249.395			0.336566
$742$	341.757			0.460589
$743$			798.694i			1.07496i	0.843277	+	0.537479i	$0.180623\pi$
$743$			798.694i			1.07496i	−0.843277	+	0.537479i	$0.819377\pi$
$744$		−	166.517i		−	0.223814i
$745$		−	690.280i		−	0.926551i
$746$	1825.56			2.44713
$747$		−	303.636i		−	0.406474i
$748$	−90.3215	−	32.9958i	−0.120751	−	0.0441121i
$749$	665.982			0.889161
$750$			1905.67i			2.54089i
$751$	227.333			0.302707			0.151354	−	0.988480i	$-0.451637\pi$
$751$	227.333			0.302707			0.151354	+	0.988480i	$0.451637\pi$
$752$	444.753			0.591426
$753$	−1990.97			−2.64405
$754$		−	881.010i		−	1.16845i
$755$		−	730.905i		−	0.968086i
$756$			1022.20i			1.35212i
$757$	981.114			1.29605			0.648027	−	0.761617i	$-0.275594\pi$
$757$	981.114			1.29605			0.648027	+	0.761617i	$0.275594\pi$
$758$			232.547i			0.306790i
$759$	−94.4814	+	258.630i	−0.124481	+	0.340751i
$760$	5.73689			0.00754854
$761$			969.838i			1.27443i	0.770688	+	0.637213i	$0.219913\pi$
$761$			969.838i			1.27443i	−0.770688	+	0.637213i	$0.780087\pi$
$762$	−1389.77			−1.82385
$763$	−195.759			−0.256565
$764$	330.269			0.432290
$765$		−	121.667i		−	0.159042i
$766$		−	1238.53i		−	1.61688i
$767$		−	1189.41i		−	1.55074i
$768$	1186.31			1.54467
$769$			244.258i			0.317630i	0.987308	+	0.158815i	$0.0507674\pi$
$769$			244.258i			0.317630i	−0.987308	+	0.158815i	$0.949233\pi$
$770$	174.820	−	478.546i	0.227039	−	0.621488i
$771$	−1136.84			−1.47450
$772$		−	982.956i		−	1.27326i
$773$	−465.031			−0.601593			−0.300796	−	0.953688i	$-0.597252\pi$
$773$	−465.031			−0.601593			−0.300796	+	0.953688i	$0.597252\pi$
$774$	−2530.77			−3.26972
$775$	785.221			1.01319
$776$			100.326i			0.129286i
$777$		−	936.474i		−	1.20524i
$778$			1514.27i			1.94636i
$779$	192.004			0.246475
$780$		−	1125.72i		−	1.44322i
$781$	−115.460	+	316.055i	−0.147836	+	0.404680i
$782$	−28.5418			−0.0364985
$783$		−	929.343i		−	1.18690i
$784$	−357.632			−0.456164
$785$	−18.7357			−0.0238671
$786$	−354.753			−0.451340
$787$		−	825.123i		−	1.04844i	−0.851583	−	0.524220i	$-0.824357\pi$
$787$		−	825.123i		−	1.04844i	0.851583	−	0.524220i	$-0.175643\pi$
$788$			826.383i			1.04871i
$789$		−	376.138i		−	0.476728i
$790$	698.385			0.884031
$791$			327.427i			0.413940i
$792$	−112.509	−	41.1012i	−0.142056	−	0.0518954i
$793$	−574.809			−0.724854
$794$			111.952i			0.140998i
$795$	−397.013			−0.499388
$796$	−1349.02			−1.69475
$797$	−703.098			−0.882181			−0.441091	−	0.897463i	$-0.645408\pi$
$797$	−703.098			−0.882181			−0.441091	+	0.897463i	$0.645408\pi$
$798$			225.387i			0.282439i
$799$			61.0891i			0.0764570i
$800$		−	671.635i		−	0.839544i
$801$	1032.12			1.28853
$802$		−	561.154i		−	0.699693i
$803$	541.372	+	197.771i	0.674187	+	0.246291i
$804$	−2940.84			−3.65776
$805$		−	77.5299i		−	0.0963104i
$806$	−2444.27			−3.03259
$807$	459.928			0.569923
$808$	63.4266			0.0784983
$809$			93.4751i			0.115544i	0.998330	+	0.0577720i	$0.0183996\pi$
$809$			93.4751i			0.115544i	−0.998330	+	0.0577720i	$0.981600\pi$
$810$		−	805.885i		−	0.994920i
$811$			1264.96i			1.55975i	0.625936	+	0.779875i	$0.284717\pi$
$811$			1264.96i			1.55975i	−0.625936	+	0.779875i	$0.715283\pi$
$812$	408.203			0.502713
$813$		−	2196.54i		−	2.70177i
$814$	1054.83	+	385.346i	1.29586	+	0.473398i
$815$	230.062			0.282285
$816$			163.968i			0.200941i
$817$	−144.946			−0.177413
$818$	1510.32			1.84635
$819$	1466.18			1.79021
$820$		−	866.665i		−	1.05691i
$821$			139.850i			0.170342i	0.996366	+	0.0851708i	$0.0271436\pi$
$821$			139.850i			0.170342i	−0.996366	+	0.0851708i	$0.972856\pi$
$822$		−	1181.56i		−	1.43742i
$823$	−1032.07			−1.25403			−0.627015	−	0.779008i	$-0.715723\pi$
$823$	−1032.07			−1.25403			−0.627015	+	0.779008i	$0.715723\pi$
$824$			3.01312i			0.00365670i
$825$	289.433	−	792.283i	0.350828	−	0.960343i
$826$	1074.91			1.30135
$827$			676.580i			0.818113i	0.912509	+	0.409057i	$0.134142\pi$
$827$			676.580i			0.818113i	−0.912509	+	0.409057i	$0.865858\pi$
$828$	−368.181			−0.444663
$829$	267.827			0.323072			0.161536	−	0.986867i	$-0.448355\pi$
$829$	267.827			0.323072			0.161536	+	0.986867i	$0.448355\pi$
$830$	−153.106			−0.184466
$831$			1170.10i			1.40806i
$832$			1125.09i			1.35227i
$833$		−	49.1227i		−	0.0589708i
$834$	923.692			1.10754
$835$		−	113.921i		−	0.136432i
$836$	−130.158	−	47.5487i	−0.155691	−	0.0568765i
$837$	−2578.36			−3.08048
$838$			1574.10i			1.87840i
$839$	1336.74			1.59326			0.796629	−	0.604469i	$-0.206615\pi$
$839$	1336.74			1.59326			0.796629	+	0.604469i	$0.206615\pi$
$840$	50.3661			0.0599597
$841$	469.878			0.558714
$842$			145.626i			0.172952i
$843$			1996.44i			2.36826i
$844$		−	1517.53i		−	1.79802i
$845$	−275.459			−0.325987
$846$			1537.05i			1.81685i
$847$	−392.723	+	465.778i	−0.463663	+	0.549915i
$848$	358.284			0.422504
$849$		−	2835.75i		−	3.34010i
$850$	87.4345			0.102864
$851$	170.895			0.200816
$852$	−671.904			−0.788620
$853$		−	1612.02i		−	1.88982i	−0.327327	−	0.944911i	$-0.606148\pi$
$853$		−	1612.02i		−	1.88982i	0.327327	−	0.944911i	$-0.393852\pi$
$854$		−	519.474i		−	0.608283i
$855$		−	175.329i		−	0.205063i
$856$	−78.9523			−0.0922339
$857$		−	237.693i		−	0.277355i	−0.990338	−	0.138677i	$-0.955715\pi$
$857$		−	237.693i		−	0.277355i	0.990338	−	0.138677i	$-0.0442851\pi$
$858$	−900.960	+	2466.25i	−1.05007	+	2.87442i
$859$	248.510			0.289302			0.144651	−	0.989483i	$-0.453794\pi$
$859$	248.510			0.289302			0.144651	+	0.989483i	$0.453794\pi$
$860$			654.255i			0.760762i
$861$	1685.67			1.95781
$862$	−435.384			−0.505086
$863$	316.222			0.366421			0.183211	−	0.983074i	$-0.441351\pi$
$863$	316.222			0.366421			0.183211	+	0.983074i	$0.441351\pi$
$864$			2205.39i			2.55254i
$865$			405.069i			0.468288i
$866$		−	49.8049i		−	0.0575114i
$867$	1485.90			1.71384
$868$		−	1132.52i		−	1.30474i
$869$	−784.439	−	286.568i	−0.902692	−	0.329767i
$870$	−924.929			−1.06314
$871$			2137.13i			2.45365i
$872$	23.2072			0.0266138
$873$	3066.14			3.51219
$874$	−41.1302			−0.0470597
$875$			641.656i			0.733321i
$876$			1150.91i			1.31382i
$877$		−	44.4435i		−	0.0506767i	−0.999679	−	0.0253384i	$-0.991934\pi$
$877$		−	44.4435i		−	0.0506767i	0.999679	−	0.0253384i	$-0.00806632\pi$
$878$	−1407.75			−1.60335
$879$		−	3007.34i		−	3.42132i
$880$	183.274	−	501.687i	0.208266	−	0.570099i
$881$	−1009.34			−1.14568			−0.572838	−	0.819668i	$-0.694158\pi$
$881$	−1009.34			−1.14568			−0.572838	+	0.819668i	$0.694158\pi$
$882$		−	1235.97i		−	1.40132i
$883$	961.842			1.08929			0.544645	−	0.838667i	$-0.316665\pi$
$883$	961.842			1.08929			0.544645	+	0.838667i	$0.316665\pi$
$884$	−139.539			−0.157850
$885$	−1248.71			−1.41097
$886$			823.229i			0.929152i
$887$		−	497.564i		−	0.560952i	−0.959861	−	0.280476i	$-0.909508\pi$
$887$		−	497.564i		−	0.560952i	0.959861	−	0.280476i	$-0.0904922\pi$
$888$			111.019i			0.125022i
$889$	−467.949			−0.526377
$890$		−	520.437i		−	0.584761i
$891$	−330.678	+	905.186i	−0.371132	+	1.01592i
$892$	699.268			0.783933
$893$			88.0326i			0.0985808i
$894$	−3214.99			−3.59618
$895$	−1070.29			−1.19586
$896$	−96.0454			−0.107194
$897$			399.561i			0.445441i
$898$		−	1646.14i		−	1.83311i
$899$			1029.64i			1.14532i
$900$	1127.88			1.25320
$901$			49.2121i			0.0546195i
$902$	−693.630	+	1898.72i	−0.768991	+	2.10501i
$903$	−1272.53			−1.40923
$904$		−	38.8165i		−	0.0429386i
$905$	−318.184			−0.351584
$906$	−3404.20			−3.75739
$907$	510.772			0.563145			0.281572	−	0.959540i	$-0.409144\pi$
$907$	510.772			0.563145			0.281572	+	0.959540i	$0.409144\pi$
$908$		−	178.122i		−	0.196170i
$909$		−	1938.42i		−	2.13248i
$910$		−	739.312i		−	0.812431i
$911$	−815.445			−0.895109			−0.447555	−	0.894257i	$-0.647705\pi$
$911$	−815.445			−0.895109			−0.447555	+	0.894257i	$0.647705\pi$
$912$			236.286i			0.259085i
$913$	171.972	+	62.8240i	0.188359	+	0.0688105i
$914$	−1710.12			−1.87103
$915$			603.464i			0.659523i
$916$	687.838			0.750915
$917$	−119.449			−0.130260
$918$	−287.101			−0.312746
$919$		−	1208.26i		−	1.31476i	−0.753560	−	0.657379i	$-0.771665\pi$
$919$		−	1208.26i		−	1.31476i	0.753560	−	0.657379i	$-0.228335\pi$
$920$			9.19118i			0.00999041i
$921$		−	1988.55i		−	2.15912i
$922$	1160.50			1.25867
$923$			488.278i			0.529011i
$924$	−1142.70	−	417.446i	−1.23669	−	0.451782i
$925$	−523.517			−0.565964
$926$		−	1996.58i		−	2.15613i
$927$	92.0860			0.0993377
$928$	880.696			0.949026
$929$	−837.070			−0.901045			−0.450522	−	0.892765i	$-0.648762\pi$
$929$	−837.070			−0.901045			−0.450522	+	0.892765i	$0.648762\pi$
$930$			2566.12i			2.75927i
$931$		−	70.7884i		−	0.0760348i
$932$		−	1451.70i		−	1.55762i
$933$	−1728.82			−1.85297
$934$		−	1661.41i		−	1.77881i
$935$	68.9093	+	25.1736i	0.0736998	+	0.0269237i
$936$	−173.816			−0.185701
$937$			358.046i			0.382119i	0.981578	+	0.191060i	$0.0611924\pi$
$937$			358.046i			0.382119i	−0.981578	+	0.191060i	$0.938808\pi$
$938$	−1931.39			−2.05905
$939$	−452.956			−0.482381
$940$	397.360			0.422723
$941$		−	753.076i		−	0.800293i	−0.916451	−	0.400147i	$-0.868959\pi$
$941$		−	753.076i		−	0.800293i	0.916451	−	0.400147i	$-0.131041\pi$
$942$			87.2616i			0.0926343i
$943$			307.614i			0.326207i
$944$	1126.89			1.19374
$945$		−	779.871i		−	0.825260i
$946$	523.629	−	1433.36i	0.553519	−	1.51518i
$947$	−135.297			−0.142869			−0.0714344	−	0.997445i	$-0.522758\pi$
$947$	−135.297			−0.142869			−0.0714344	+	0.997445i	$0.522758\pi$
$948$		−	1667.65i		−	1.75912i
$949$	836.373			0.881321
$950$	125.998			0.132629
$951$	−98.8713			−0.103966
$952$		−	6.24318i		−	0.00655796i
$953$		−	98.8279i		−	0.103702i	−0.998655	−	0.0518510i	$-0.983488\pi$
$953$		−	98.8279i		−	0.103702i	0.998655	−	0.0518510i	$-0.0165121\pi$
$954$			1238.22i			1.29792i
$955$	−251.974			−0.263847
$956$		−	134.309i		−	0.140491i
$957$	1038.90	+	379.525i	1.08558	+	0.396578i
$958$	1318.75			1.37656
$959$		−	397.841i		−	0.414850i
$960$	1181.18			1.23039
$961$	1895.62			1.97255
$962$	1629.62			1.69400
$963$			2412.91i			2.50562i
$964$			1827.89i			1.89616i
$965$			749.930i			0.777130i
$966$	−361.096			−0.373805
$967$		−	520.664i		−	0.538432i	−0.963080	−	0.269216i	$-0.913235\pi$
$967$		−	520.664i		−	0.538432i	0.963080	−	0.269216i	$-0.0867645\pi$
$968$	46.5573	−	55.2181i	0.0480964	−	0.0570435i
$969$	−32.4551			−0.0334934
$970$		−	1546.08i		−	1.59389i
$971$	1054.39			1.08588			0.542938	−	0.839773i	$-0.317312\pi$
$971$	1054.39			1.08588			0.542938	+	0.839773i	$0.317312\pi$
$972$	−97.2050			−0.100005
$973$	311.016			0.319646
$974$			1915.33i			1.96646i
$975$		−	1224.01i		−	1.25539i
$976$		−	544.594i		−	0.557986i
$977$	1914.70			1.95978			0.979888	−	0.199550i	$-0.0639480\pi$
$977$	1914.70			1.95978			0.979888	+	0.199550i	$0.0639480\pi$
$978$		−	1071.52i		−	1.09562i
$979$	−213.550	+	584.565i	−0.218131	+	0.597104i
$980$	−319.523			−0.326044
$981$		−	709.252i		−	0.722989i
$982$	−216.404			−0.220371
$983$	−450.426			−0.458216			−0.229108	−	0.973401i	$-0.573581\pi$
$983$	−450.426			−0.458216			−0.229108	+	0.973401i	$0.573581\pi$
$984$	−199.837			−0.203086
$985$		−	630.476i		−	0.640077i
$986$			114.650i			0.116278i
$987$			772.868i			0.783048i
$988$	−201.083			−0.203525
$989$		−	232.221i		−	0.234804i
$990$	1733.82	+	633.389i	1.75133	+	0.639787i
$991$	−426.496			−0.430369			−0.215184	−	0.976573i	$-0.569035\pi$
$991$	−426.496			−0.430369			−0.215184	+	0.976573i	$0.569035\pi$
$992$		−	2443.40i		−	2.46310i
$993$	2940.44			2.96117
$994$	−441.272			−0.443936
$995$	1029.21			1.03439
$996$			365.597i			0.367065i
$997$		−	17.2823i		−	0.0173343i	−0.999962	−	0.00866716i	$-0.997241\pi$
$997$		−	17.2823i		−	0.0173343i	0.999962	−	0.00866716i	$-0.00275888\pi$
$998$			530.384i			0.531447i
$999$	1719.03			1.72075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.8	✓	44
11.10	odd	2	inner	253.3.c.a.208.37	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.8	✓	44	1.1	even	1	trivial
253.3.c.a.208.37	yes	44	11.10	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.86502i q^{2} +5.21944 q^{3} -4.20834 q^{4} +3.21069 q^{5} -14.9538i q^{6} -5.03509i q^{7} +0.596911i q^{8} +18.2426 q^{9} -9.19869i q^{10} +(-3.77449 + 10.3321i) q^{11} -21.9652 q^{12} +15.9623i q^{13} -14.4256 q^{14} +16.7580 q^{15} -15.1232 q^{16} -2.07725i q^{17} -52.2654i q^{18} -2.99343i q^{19} -13.5117 q^{20} -26.2803i q^{21} +(29.6018 + 10.8140i) q^{22} +4.79583 q^{23} +3.11554i q^{24} -14.6915 q^{25} +45.7323 q^{26} +48.2412 q^{27} +21.1894i q^{28} -19.2645i q^{29} -48.0120i q^{30} -53.4474 q^{31} +45.7160i q^{32} +(-19.7007 + 53.9280i) q^{33} -5.95137 q^{34} -16.1661i q^{35} -76.7711 q^{36} +35.6340 q^{37} -8.57624 q^{38} +83.3142i q^{39} +1.91649i q^{40} +64.1419i q^{41} -75.2937 q^{42} -48.4215i q^{43} +(15.8844 - 43.4812i) q^{44} +58.5713 q^{45} -13.7402i q^{46} -29.4086 q^{47} -78.9348 q^{48} +23.6479 q^{49} +42.0914i q^{50} -10.8421i q^{51} -67.1748i q^{52} -23.6910 q^{53} -138.212i q^{54} +(-12.1187 + 33.1733i) q^{55} +3.00550 q^{56} -15.6240i q^{57} -55.1933 q^{58} -74.5141 q^{59} -70.5235 q^{60} +36.0105i q^{61} +153.128i q^{62} -91.8530i q^{63} +70.4843 q^{64} +51.2499i q^{65} +(154.505 + 56.4430i) q^{66} +133.886 q^{67} +8.74180i q^{68} +25.0316 q^{69} -46.3162 q^{70} +30.5895 q^{71} +10.8892i q^{72} -52.3969i q^{73} -102.092i q^{74} -76.6814 q^{75} +12.5974i q^{76} +(52.0232 + 19.0049i) q^{77} +238.697 q^{78} +75.9222i q^{79} -48.5559 q^{80} +87.6087 q^{81} +183.768 q^{82} -16.6444i q^{83} +110.597i q^{84} -6.66941i q^{85} -138.728 q^{86} -100.550i q^{87} +(-6.16737 - 2.25303i) q^{88} +56.5773 q^{89} -167.808i q^{90} +80.3715 q^{91} -20.1825 q^{92} -278.966 q^{93} +84.2563i q^{94} -9.61097i q^{95} +238.612i q^{96} +168.076 q^{97} -67.7517i q^{98} +(-68.8565 + 188.485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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