LMFDB - Embedded newform 253.3.c.a.208.36

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			208.36
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.64438i q^{2} -0.454888 q^{3} -2.99272 q^{4} -5.27954 q^{5} -1.20289i q^{6} -3.36948i q^{7} +2.66362i q^{8} -8.79308 q^{9} -13.9611i q^{10} +(4.03808 + 10.2320i) q^{11} +1.36135 q^{12} -22.4414i q^{13} +8.91017 q^{14} +2.40160 q^{15} -19.0145 q^{16} -19.8649i q^{17} -23.2522i q^{18} -10.9596i q^{19} +15.8002 q^{20} +1.53274i q^{21} +(-27.0573 + 10.6782i) q^{22} +4.79583 q^{23} -1.21165i q^{24} +2.87357 q^{25} +59.3436 q^{26} +8.09385 q^{27} +10.0839i q^{28} -7.02213i q^{29} +6.35073i q^{30} -27.2934 q^{31} -39.6270i q^{32} +(-1.83687 - 4.65441i) q^{33} +52.5303 q^{34} +17.7893i q^{35} +26.3152 q^{36} -62.0799 q^{37} +28.9813 q^{38} +10.2083i q^{39} -14.0627i q^{40} +20.1654i q^{41} -4.05313 q^{42} +79.7326i q^{43} +(-12.0849 - 30.6216i) q^{44} +46.4234 q^{45} +12.6820i q^{46} +8.66460 q^{47} +8.64946 q^{48} +37.6466 q^{49} +7.59879i q^{50} +9.03631i q^{51} +67.1610i q^{52} -67.8010 q^{53} +21.4032i q^{54} +(-21.3192 - 54.0203i) q^{55} +8.97502 q^{56} +4.98538i q^{57} +18.5691 q^{58} -8.14834 q^{59} -7.18732 q^{60} -81.2608i q^{61} -72.1740i q^{62} +29.6281i q^{63} +28.7307 q^{64} +118.480i q^{65} +(12.3080 - 4.85738i) q^{66} -37.3264 q^{67} +59.4502i q^{68} -2.18157 q^{69} -47.0416 q^{70} -48.1210 q^{71} -23.4214i q^{72} -34.8727i q^{73} -164.163i q^{74} -1.30715 q^{75} +32.7990i q^{76} +(34.4765 - 13.6062i) q^{77} -26.9947 q^{78} +75.0277i q^{79} +100.388 q^{80} +75.4559 q^{81} -53.3248 q^{82} +22.7069i q^{83} -4.58705i q^{84} +104.878i q^{85} -210.843 q^{86} +3.19428i q^{87} +(-27.2542 + 10.7559i) q^{88} -172.233 q^{89} +122.761i q^{90} -75.6160 q^{91} -14.3526 q^{92} +12.4154 q^{93} +22.9125i q^{94} +57.8616i q^{95} +18.0258i q^{96} +27.8833 q^{97} +99.5518i q^{98} +(-35.5071 - 89.9708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.64438i			1.32219i	0.750303	+	0.661094i	$0.229908\pi$
$2$			2.64438i			1.32219i	−0.750303	+	0.661094i	$0.770092\pi$
$3$	−0.454888			−0.151629			−0.0758146	−	0.997122i	$-0.524156\pi$
$3$	−0.454888			−0.151629			−0.0758146	+	0.997122i	$0.524156\pi$
$4$	−2.99272			−0.748181
$5$	−5.27954			−1.05591			−0.527954	−	0.849273i	$-0.677041\pi$
$5$	−5.27954			−1.05591			−0.527954	+	0.849273i	$0.677041\pi$
$6$		−	1.20289i		−	0.200482i
$7$		−	3.36948i		−	0.481354i	−0.970605	−	0.240677i	$-0.922630\pi$
$7$		−	3.36948i		−	0.481354i	0.970605	−	0.240677i	$-0.0773695\pi$
$8$			2.66362i			0.332952i
$9$	−8.79308			−0.977009
$10$		−	13.9611i		−	1.39611i
$11$	4.03808	+	10.2320i	0.367098	+	0.930182i
$11$	4.03808	+	10.2320i	0.367098	+	0.930182i
$12$	1.36135			0.113446
$13$		−	22.4414i		−	1.72626i	−0.504978	−	0.863132i	$-0.668500\pi$
$13$		−	22.4414i		−	1.72626i	0.504978	−	0.863132i	$-0.331500\pi$
$14$	8.91017			0.636441
$15$	2.40160			0.160107
$16$	−19.0145			−1.18841
$17$		−	19.8649i		−	1.16852i	−0.811565	−	0.584262i	$-0.801384\pi$
$17$		−	19.8649i		−	1.16852i	0.811565	−	0.584262i	$-0.198616\pi$
$18$		−	23.2522i		−	1.29179i
$19$		−	10.9596i		−	0.576820i	−0.957507	−	0.288410i	$-0.906873\pi$
$19$		−	10.9596i		−	0.576820i	0.957507	−	0.288410i	$-0.0931266\pi$
$20$	15.8002			0.790010
$21$			1.53274i			0.0729874i
$22$	−27.0573	+	10.6782i	−1.22988	+	0.485373i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$		−	1.21165i		−	0.0504853i
$25$	2.87357			0.114943
$26$	59.3436			2.28245
$27$	8.09385			0.299772
$28$			10.0839i			0.360140i
$29$		−	7.02213i		−	0.242142i	−0.992644	−	0.121071i	$-0.961367\pi$
$29$		−	7.02213i		−	0.242142i	0.992644	−	0.121071i	$-0.0386329\pi$
$30$			6.35073i			0.211691i
$31$	−27.2934			−0.880433			−0.440216	−	0.897892i	$-0.645098\pi$
$31$	−27.2934			−0.880433			−0.440216	+	0.897892i	$0.645098\pi$
$32$		−	39.6270i		−	1.23834i
$33$	−1.83687	−	4.65441i	−0.0556628	−	0.141043i
$34$	52.5303			1.54501
$35$			17.7893i			0.508266i
$36$	26.3152			0.730979
$37$	−62.0799			−1.67783			−0.838917	−	0.544259i	$-0.816811\pi$
$37$	−62.0799			−1.67783			−0.838917	+	0.544259i	$0.816811\pi$
$38$	28.9813			0.762665
$39$			10.2083i			0.261752i
$40$		−	14.0627i		−	0.351567i
$41$			20.1654i			0.491839i	0.969290	+	0.245919i	$0.0790898\pi$
$41$			20.1654i			0.491839i	−0.969290	+	0.245919i	$0.920910\pi$
$42$	−4.05313			−0.0965031
$43$			79.7326i			1.85425i	0.374756	+	0.927124i	$0.377727\pi$
$43$			79.7326i			1.85425i	−0.374756	+	0.927124i	$0.622273\pi$
$44$	−12.0849	−	30.6216i	−0.274656	−	0.695944i
$45$	46.4234			1.03163
$46$			12.6820i			0.275695i
$47$	8.66460			0.184353			0.0921766	−	0.995743i	$-0.470618\pi$
$47$	8.66460			0.184353			0.0921766	+	0.995743i	$0.470618\pi$
$48$	8.64946			0.180197
$49$	37.6466			0.768298
$50$			7.59879i			0.151976i
$51$			9.03631i			0.177183i
$52$			67.1610i			1.29156i
$53$	−67.8010			−1.27926			−0.639632	−	0.768682i	$-0.720913\pi$
$53$	−67.8010			−1.27926			−0.639632	+	0.768682i	$0.720913\pi$
$54$			21.4032i			0.396355i
$55$	−21.3192	−	54.0203i	−0.387622	−	0.982187i
$56$	8.97502			0.160268
$57$			4.98538i			0.0874628i
$58$	18.5691			0.320158
$59$	−8.14834			−0.138108			−0.0690538	−	0.997613i	$-0.521998\pi$
$59$	−8.14834			−0.138108			−0.0690538	+	0.997613i	$0.521998\pi$
$60$	−7.18732			−0.119789
$61$		−	81.2608i		−	1.33214i	−0.745888	−	0.666072i	$-0.767974\pi$
$61$		−	81.2608i		−	1.33214i	0.745888	−	0.666072i	$-0.232026\pi$
$62$		−	72.1740i		−	1.16410i
$63$			29.6281i			0.470287i
$64$	28.7307			0.448917
$65$			118.480i			1.82278i
$66$	12.3080	−	4.85738i	0.186485	−	0.0735967i
$67$	−37.3264			−0.557110			−0.278555	−	0.960420i	$-0.589855\pi$
$67$	−37.3264			−0.557110			−0.278555	+	0.960420i	$0.589855\pi$
$68$			59.4502i			0.874268i
$69$	−2.18157			−0.0316169
$70$	−47.0416			−0.672023
$71$	−48.1210			−0.677760			−0.338880	−	0.940830i	$-0.610048\pi$
$71$	−48.1210			−0.677760			−0.338880	+	0.940830i	$0.610048\pi$
$72$		−	23.4214i		−	0.325297i
$73$		−	34.8727i		−	0.477708i	−0.971055	−	0.238854i	$-0.923228\pi$
$73$		−	34.8727i		−	0.477708i	0.971055	−	0.238854i	$-0.0767718\pi$
$74$		−	164.163i		−	2.21841i
$75$	−1.30715			−0.0174287
$76$			32.7990i			0.431566i
$77$	34.4765	−	13.6062i	0.447747	−	0.176704i
$78$	−26.9947			−0.346085
$79$			75.0277i			0.949717i	0.880062	+	0.474859i	$0.157501\pi$
$79$			75.0277i			0.949717i	−0.880062	+	0.474859i	$0.842499\pi$
$80$	100.388			1.25485
$81$	75.4559			0.931554
$82$	−53.3248			−0.650303
$83$			22.7069i			0.273577i	0.990600	+	0.136789i	$0.0436781\pi$
$83$			22.7069i			0.273577i	−0.990600	+	0.136789i	$0.956322\pi$
$84$		−	4.58705i		−	0.0546078i
$85$			104.878i			1.23386i
$86$	−210.843			−2.45166
$87$			3.19428i			0.0367159i
$88$	−27.2542	+	10.7559i	−0.309706	+	0.122226i
$89$	−172.233			−1.93520			−0.967598	−	0.252494i	$-0.918749\pi$
$89$	−172.233			−1.93520			−0.967598	+	0.252494i	$0.918749\pi$
$90$			122.761i			1.36401i
$91$	−75.6160			−0.830945
$92$	−14.3526			−0.156006
$93$	12.4154			0.133499
$94$			22.9125i			0.243750i
$95$			57.8616i			0.609069i
$96$			18.0258i			0.187769i
$97$	27.8833			0.287457			0.143728	−	0.989617i	$-0.454091\pi$
$97$	27.8833			0.287457			0.143728	+	0.989617i	$0.454091\pi$
$98$			99.5518i			1.01583i
$99$	−35.5071	−	89.9708i	−0.358658	−	0.908796i
$100$	−8.59979			−0.0859979
$101$			103.827i			1.02799i	0.857794	+	0.513994i	$0.171835\pi$
$101$			103.827i			1.02799i	−0.857794	+	0.513994i	$0.828165\pi$
$102$	−23.8954			−0.234269
$103$	−67.1661			−0.652098			−0.326049	−	0.945353i	$-0.605717\pi$
$103$	−67.1661			−0.652098			−0.326049	+	0.945353i	$0.605717\pi$
$104$	59.7754			0.574764
$105$		−	8.09214i		−	0.0770680i
$106$		−	179.291i		−	1.69143i
$107$		−	143.527i		−	1.34138i	−0.741739	−	0.670689i	$-0.765998\pi$
$107$		−	143.527i		−	1.34138i	0.741739	−	0.670689i	$-0.234002\pi$
$108$	−24.2227			−0.224284
$109$		−	20.0854i		−	0.184270i	−0.995747	−	0.0921348i	$-0.970631\pi$
$109$		−	20.0854i		−	0.184270i	0.995747	−	0.0921348i	$-0.0293691\pi$
$110$	142.850	−	56.3760i	1.29864	−	0.512509i
$111$	28.2394			0.254409
$112$			64.0690i			0.572045i
$113$	61.9410			0.548151			0.274075	−	0.961708i	$-0.411628\pi$
$113$	61.9410			0.548151			0.274075	+	0.961708i	$0.411628\pi$
$114$	−13.1832			−0.115642
$115$	−25.3198			−0.220172
$116$			21.0153i			0.181166i
$117$			197.329i			1.68657i
$118$		−	21.5473i		−	0.182604i
$119$	−66.9345			−0.562474
$120$			6.39695i			0.0533079i
$121$	−88.3878	+	82.6353i	−0.730478	+	0.682936i
$122$	214.884			1.76134
$123$		−	9.17299i		−	0.0745771i
$124$	81.6816			0.658723
$125$	116.817			0.934539
$126$	−78.3478			−0.621808
$127$		−	91.0968i		−	0.717298i	−0.933473	−	0.358649i	$-0.883238\pi$
$127$		−	91.0968i		−	0.717298i	0.933473	−	0.358649i	$-0.116762\pi$
$128$		−	82.5333i		−	0.644791i
$129$		−	36.2694i		−	0.281158i
$130$	−313.307			−2.41005
$131$			162.629i			1.24145i	0.784030	+	0.620723i	$0.213161\pi$
$131$			162.629i			1.24145i	−0.784030	+	0.620723i	$0.786839\pi$
$132$	5.49725	+	13.9294i	0.0416458	+	0.105526i
$133$	−36.9281			−0.277655
$134$		−	98.7050i		−	0.736604i
$135$	−42.7318			−0.316532
$136$	52.9126			0.389063
$137$	238.747			1.74268			0.871339	−	0.490681i	$-0.163252\pi$
$137$	238.747			1.74268			0.871339	+	0.490681i	$0.163252\pi$
$138$		−	5.76888i		−	0.0418035i
$139$		−	140.887i		−	1.01357i	−0.862071	−	0.506787i	$-0.830833\pi$
$139$		−	140.887i		−	1.01357i	0.862071	−	0.506787i	$-0.169167\pi$
$140$		−	53.2385i		−	0.380275i
$141$	−3.94142			−0.0279533
$142$		−	127.250i		−	0.896126i
$143$	229.621	−	90.6203i	1.60574	−	0.633708i
$144$	167.196			1.16108
$145$			37.0736i			0.255680i
$146$	92.2165			0.631620
$147$	−17.1250			−0.116496
$148$	185.788			1.25532
$149$		−	158.479i		−	1.06362i	−0.846864	−	0.531810i	$-0.821512\pi$
$149$		−	158.479i		−	1.06362i	0.846864	−	0.531810i	$-0.178488\pi$
$150$		−	3.45660i		−	0.0230440i
$151$			37.9137i			0.251084i	0.992088	+	0.125542i	$0.0400670\pi$
$151$			37.9137i			0.251084i	−0.992088	+	0.125542i	$0.959933\pi$
$152$	29.1922			0.192054
$153$			174.674i			1.14166i
$154$	35.9800	+	91.1689i	0.233636	+	0.592006i
$155$	144.097			0.929656
$156$		−	30.5507i		−	0.195838i
$157$	100.149			0.637891			0.318946	−	0.947773i	$-0.396671\pi$
$157$	100.149			0.637891			0.318946	+	0.947773i	$0.396671\pi$
$158$	−198.401			−1.25570
$159$	30.8418			0.193974
$160$			209.212i			1.30758i
$161$		−	16.1595i		−	0.100369i
$162$			199.534i			1.23169i
$163$	309.680			1.89988			0.949940	−	0.312433i	$-0.101144\pi$
$163$	309.680			1.89988			0.949940	+	0.312433i	$0.101144\pi$
$164$		−	60.3494i		−	0.367984i
$165$	9.69785	+	24.5732i	0.0587748	+	0.148928i
$166$	−60.0456			−0.361720
$167$		−	136.995i		−	0.820331i	−0.912011	−	0.410166i	$-0.865471\pi$
$167$		−	136.995i		−	0.820331i	0.912011	−	0.410166i	$-0.134529\pi$
$168$	−4.08262			−0.0243013
$169$	−334.618			−1.97999
$170$	−277.336			−1.63139
$171$			96.3685i			0.563558i
$172$		−	238.618i		−	1.38731i
$173$			240.397i			1.38958i	0.719212	+	0.694790i	$0.244503\pi$
$173$			240.397i			1.38958i	−0.719212	+	0.694790i	$0.755497\pi$
$174$	−8.44687			−0.0485453
$175$		−	9.68243i		−	0.0553282i
$176$	−76.7821	−	194.556i	−0.436262	−	1.10543i
$177$	3.70658			0.0209411
$178$		−	455.447i		−	2.55869i
$179$	256.995			1.43572			0.717862	−	0.696185i	$-0.245121\pi$
$179$	256.995			1.43572			0.717862	+	0.696185i	$0.245121\pi$
$180$	−138.932			−0.771847
$181$	−329.196			−1.81876			−0.909382	−	0.415961i	$-0.863445\pi$
$181$	−329.196			−1.81876			−0.909382	+	0.415961i	$0.863445\pi$
$182$		−	199.957i		−	1.09866i
$183$			36.9645i			0.201992i
$184$			12.7743i			0.0694254i
$185$	327.753			1.77164
$186$			32.8311i			0.176511i
$187$	203.258	−	80.2161i	1.08694	−	0.428963i
$188$	−25.9307			−0.137929
$189$		−	27.2721i		−	0.144297i
$190$	−153.008			−0.805304
$191$	−95.0930			−0.497869			−0.248935	−	0.968520i	$-0.580080\pi$
$191$	−95.0930			−0.497869			−0.248935	+	0.968520i	$0.580080\pi$
$192$	−13.0692			−0.0680689
$193$			3.95422i			0.0204882i	0.999948	+	0.0102441i	$0.00326086\pi$
$193$			3.95422i			0.0204882i	−0.999948	+	0.0102441i	$0.996739\pi$
$194$			73.7340i			0.380072i
$195$		−	53.8953i		−	0.276386i
$196$	−112.666			−0.574826
$197$		−	82.2187i		−	0.417354i	−0.977985	−	0.208677i	$-0.933084\pi$
$197$		−	82.2187i		−	0.417354i	0.977985	−	0.208677i	$-0.0669157\pi$
$198$	237.917	−	93.8942i	1.20160	−	0.474213i
$199$	60.0739			0.301879			0.150939	−	0.988543i	$-0.451770\pi$
$199$	60.0739			0.301879			0.150939	+	0.988543i	$0.451770\pi$
$200$			7.65409i			0.0382705i
$201$	16.9793			0.0844742
$202$	−274.557			−1.35919
$203$	−23.6609			−0.116556
$204$		−	27.0432i		−	0.132565i
$205$		−	106.464i		−	0.519337i
$206$		−	177.612i		−	0.862196i
$207$	−42.1701			−0.203720
$208$			426.713i			2.05150i
$209$	112.138	−	44.2557i	0.536548	−	0.211750i
$210$	21.3987			0.101898
$211$			165.026i			0.782112i	0.920367	+	0.391056i	$0.127890\pi$
$211$			165.026i			0.782112i	−0.920367	+	0.391056i	$0.872110\pi$
$212$	202.909			0.957120
$213$	21.8896			0.102768
$214$	379.541			1.77355
$215$		−	420.952i		−	1.95792i
$216$			21.5589i			0.0998099i
$217$			91.9646i			0.423800i
$218$	53.1133			0.243639
$219$			15.8632i			0.0724346i
$220$	63.8025	+	161.668i	0.290011	+	0.734854i
$221$	−445.797			−2.01718
$222$			74.6755i			0.336376i
$223$	319.714			1.43370			0.716848	−	0.697229i	$-0.245584\pi$
$223$	319.714			1.43370			0.716848	+	0.697229i	$0.245584\pi$
$224$	−133.522			−0.596082
$225$	−25.2675			−0.112300
$226$			163.795i			0.724758i
$227$			63.1393i			0.278147i	0.990282	+	0.139073i	$0.0444124\pi$
$227$			63.1393i			0.278147i	−0.990282	+	0.139073i	$0.955588\pi$
$228$		−	14.9199i		−	0.0654380i
$229$	−317.443			−1.38621			−0.693107	−	0.720834i	$-0.743759\pi$
$229$	−317.443			−1.38621			−0.693107	+	0.720834i	$0.743759\pi$
$230$		−	66.9551i		−	0.291109i
$231$	−15.6830	+	6.18931i	−0.0678916	+	0.0267935i
$232$	18.7043			0.0806219
$233$			356.067i			1.52818i	0.645108	+	0.764091i	$0.276812\pi$
$233$			356.067i			1.52818i	−0.645108	+	0.764091i	$0.723188\pi$
$234$	−521.813			−2.22997
$235$	−45.7451			−0.194660
$236$	24.3857			0.103329
$237$		−	34.1292i		−	0.144005i
$238$		−	177.000i		−	0.743697i
$239$		−	348.412i		−	1.45779i	−0.684624	−	0.728896i	$-0.740034\pi$
$239$		−	348.412i		−	1.45779i	0.684624	−	0.728896i	$-0.259966\pi$
$240$	−45.6652			−0.190272
$241$		−	294.330i		−	1.22129i	−0.791905	−	0.610644i	$-0.790911\pi$
$241$		−	294.330i		−	1.22129i	0.791905	−	0.610644i	$-0.209089\pi$
$242$	−218.519	−	233.731i	−0.902970	−	0.965829i
$243$	−107.169			−0.441023
$244$			243.191i			0.996684i
$245$	−198.757			−0.811252
$246$	24.2568			0.0986050
$247$	−245.949			−0.995744
$248$		−	72.6993i		−	0.293142i
$249$		−	10.3291i		−	0.0414823i
$250$			308.909i			1.23564i
$251$	−280.050			−1.11574			−0.557869	−	0.829929i	$-0.688381\pi$
$251$	−280.050			−1.11574			−0.557869	+	0.829929i	$0.688381\pi$
$252$		−	88.6687i		−	0.351860i
$253$	19.3660	+	49.0710i	0.0765453	+	0.193956i
$254$	240.894			0.948402
$255$		−	47.7076i		−	0.187089i
$256$	333.172			1.30145
$257$	−419.365			−1.63177			−0.815885	−	0.578215i	$-0.803750\pi$
$257$	−419.365			−1.63177			−0.815885	+	0.578215i	$0.803750\pi$
$258$	95.9099			0.371744
$259$			209.177i			0.807633i
$260$		−	354.579i		−	1.36377i
$261$			61.7461i			0.236575i
$262$	−430.053			−1.64143
$263$		−	14.6952i		−	0.0558752i	−0.999610	−	0.0279376i	$-0.991106\pi$
$263$		−	14.6952i		−	0.0558752i	0.999610	−	0.0279376i	$-0.00889397\pi$
$264$	12.3976	−	4.89273i	0.0469606	−	0.0185331i
$265$	357.958			1.35079
$266$		−	97.6518i		−	0.367112i
$267$	78.3465			0.293432
$268$	111.707			0.416819
$269$	−61.4090			−0.228286			−0.114143	−	0.993464i	$-0.536412\pi$
$269$	−61.4090			−0.228286			−0.114143	+	0.993464i	$0.536412\pi$
$270$		−	112.999i		−	0.418515i
$271$		−	106.118i		−	0.391579i	−0.980646	−	0.195789i	$-0.937273\pi$
$271$		−	106.118i		−	0.391579i	0.980646	−	0.195789i	$-0.0627269\pi$
$272$			377.722i			1.38868i
$273$	34.3968			0.125996
$274$			631.337i			2.30415i
$275$	11.6037	+	29.4024i	0.0421953	+	0.106918i
$276$	6.52882			0.0236551
$277$		−	6.81722i		−	0.0246109i	−0.999924	−	0.0123054i	$-0.996083\pi$
$277$		−	6.81722i		−	0.0246109i	0.999924	−	0.0123054i	$-0.00391704\pi$
$278$	372.558			1.34014
$279$	239.993			0.860190
$280$	−47.3840			−0.169228
$281$			39.3407i			0.140003i	0.997547	+	0.0700013i	$0.0223003\pi$
$281$			39.3407i			0.140003i	−0.997547	+	0.0700013i	$0.977700\pi$
$282$		−	10.4226i		−	0.0369596i
$283$		−	242.404i		−	0.856550i	−0.903648	−	0.428275i	$-0.859121\pi$
$283$		−	242.404i		−	0.856550i	0.903648	−	0.428275i	$-0.140879\pi$
$284$	144.013			0.507087
$285$		−	26.3205i		−	0.0923527i
$286$	239.634	+	607.204i	0.837881	+	2.12309i
$287$	67.9469			0.236749
$288$			348.443i			1.20987i
$289$	−105.615			−0.365450
$290$	−98.0366			−0.338057
$291$	−12.6838			−0.0435869
$292$			104.364i			0.357412i
$293$			314.967i			1.07497i	0.843273	+	0.537486i	$0.180626\pi$
$293$			314.967i			1.07497i	−0.843273	+	0.537486i	$0.819374\pi$
$294$		−	45.2849i		−	0.154030i
$295$	43.0195			0.145829
$296$		−	165.357i		−	0.558639i
$297$	32.6836	+	82.8163i	0.110046	+	0.278843i
$298$	419.079			1.40630
$299$		−	107.625i		−	0.359951i
$300$	3.91194			0.0130398
$301$	268.658			0.892550
$302$	−100.258			−0.331981
$303$		−	47.2295i		−	0.155873i
$304$			208.391i			0.685497i
$305$			429.020i			1.40662i
$306$	−461.903			−1.50949
$307$		−	248.876i		−	0.810670i	−0.914168	−	0.405335i	$-0.867155\pi$
$307$		−	248.876i		−	0.810670i	0.914168	−	0.405335i	$-0.132845\pi$
$308$	−103.179	+	40.7197i	−0.334996	+	0.132207i
$309$	30.5530			0.0988771
$310$			381.046i			1.22918i
$311$	413.852			1.33071			0.665357	−	0.746525i	$-0.268279\pi$
$311$	413.852			1.33071			0.665357	+	0.746525i	$0.268279\pi$
$312$	−27.1911			−0.0871510
$313$	−216.030			−0.690191			−0.345095	−	0.938568i	$-0.612153\pi$
$313$	−216.030			−0.690191			−0.345095	+	0.938568i	$0.612153\pi$
$314$			264.831i			0.843412i
$315$		−	156.423i		−	0.496580i
$316$		−	224.537i		−	0.710560i
$317$	106.613			0.336318			0.168159	−	0.985760i	$-0.446218\pi$
$317$	106.613			0.336318			0.168159	+	0.985760i	$0.446218\pi$
$318$			81.5574i			0.256470i
$319$	71.8504	−	28.3559i	0.225236	−	0.0888900i
$320$	−151.685			−0.474015
$321$			65.2889i			0.203392i
$322$	42.7317			0.132707
$323$	−217.711			−0.674029
$324$	−225.819			−0.696971
$325$		−	64.4870i		−	0.198422i
$326$			818.911i			2.51200i
$327$			9.13659i			0.0279407i
$328$	−53.7129			−0.163759
$329$		−	29.1952i		−	0.0887392i
$330$	−64.9807	+	25.6448i	−0.196911	+	0.0777114i
$331$	−487.825			−1.47379			−0.736895	−	0.676007i	$-0.763709\pi$
$331$	−487.825			−1.47379			−0.736895	+	0.676007i	$0.763709\pi$
$332$		−	67.9554i		−	0.204685i
$333$	545.873			1.63926
$334$	362.267			1.08463
$335$	197.066			0.588257
$336$		−	29.1442i		−	0.0867387i
$337$		−	2.71785i		−	0.00806483i	−0.999992	−	0.00403242i	$-0.998716\pi$
$337$		−	2.71785i		−	0.00806483i	0.999992	−	0.00403242i	$-0.00128356\pi$
$338$		−	884.855i		−	2.61791i
$339$	−28.1762			−0.0831157
$340$		−	313.870i		−	0.923147i
$341$	−110.213	−	279.266i	−0.323205	−	0.818963i
$342$	−254.834			−0.745130
$343$		−	291.954i		−	0.851178i
$344$	−212.377			−0.617376
$345$	11.5177			0.0333845
$346$	−635.701			−1.83729
$347$			486.217i			1.40120i	0.713553	+	0.700601i	$0.247085\pi$
$347$			486.217i			1.40120i	−0.713553	+	0.700601i	$0.752915\pi$
$348$		−	9.55959i		−	0.0274701i
$349$			100.542i			0.288085i	0.989571	+	0.144043i	$0.0460102\pi$
$349$			100.542i			0.288085i	−0.989571	+	0.144043i	$0.953990\pi$
$350$	25.6040			0.0731543
$351$		−	181.638i		−	0.517486i
$352$	405.464	−	160.017i	1.15189	−	0.454594i
$353$	337.433			0.955902			0.477951	−	0.878387i	$-0.341380\pi$
$353$	337.433			0.955902			0.477951	+	0.878387i	$0.341380\pi$
$354$			9.80160i			0.0276881i
$355$	254.057			0.715653
$356$	515.444			1.44788
$357$	30.4477			0.0852876
$358$			679.590i			1.89830i
$359$		−	14.8353i		−	0.0413238i	−0.999787	−	0.0206619i	$-0.993423\pi$
$359$		−	14.8353i		−	0.0413238i	0.999787	−	0.0206619i	$-0.00657736\pi$
$360$			123.654i			0.343484i
$361$	240.888			0.667279
$362$		−	870.519i		−	2.40475i
$363$	40.2065	−	37.5898i	0.110762	−	0.103553i
$364$	226.298			0.621697
$365$			184.112i			0.504416i
$366$	−97.7481			−0.267071
$367$	−210.753			−0.574260			−0.287130	−	0.957892i	$-0.592701\pi$
$367$	−210.753			−0.574260			−0.287130	+	0.957892i	$0.592701\pi$
$368$	−91.1903			−0.247800
$369$		−	177.316i		−	0.480531i
$370$			866.703i			2.34244i
$371$			228.454i			0.615779i
$372$	−37.1560			−0.0998816
$373$		−	73.1502i		−	0.196113i	−0.995181	−	0.0980566i	$-0.968737\pi$
$373$		−	73.1502i		−	0.196113i	0.995181	−	0.0980566i	$-0.0312626\pi$
$374$	212.122	+	537.490i	0.567170	+	1.43714i
$375$	−53.1388			−0.141704
$376$			23.0792i			0.0613808i
$377$	−157.587			−0.418002
$378$	72.1176			0.190787
$379$	−149.197			−0.393659			−0.196830	−	0.980438i	$-0.563065\pi$
$379$	−149.197			−0.393659			−0.196830	+	0.980438i	$0.563065\pi$
$380$		−	173.164i		−	0.455694i
$381$			41.4388i			0.108763i
$382$		−	251.462i		−	0.658277i
$383$	−392.978			−1.02605			−0.513026	−	0.858373i	$-0.671476\pi$
$383$	−392.978			−1.02605			−0.513026	+	0.858373i	$0.671476\pi$
$384$			37.5434i			0.0977692i
$385$	−182.020	+	71.8347i	−0.472780	+	0.186584i
$386$	−10.4565			−0.0270893
$387$		−	701.095i		−	1.81162i
$388$	−83.4470			−0.215070
$389$	234.577			0.603027			0.301513	−	0.953462i	$-0.402508\pi$
$389$	234.577			0.603027			0.301513	+	0.953462i	$0.402508\pi$
$390$	142.519			0.365435
$391$		−	95.2688i		−	0.243654i
$392$			100.276i			0.255807i
$393$		−	73.9782i		−	0.188240i
$394$	217.417			0.551820
$395$		−	396.112i		−	1.00281i
$396$	106.263	+	269.258i	0.268341	+	0.679944i
$397$	52.5622			0.132398			0.0661992	−	0.997806i	$-0.478913\pi$
$397$	52.5622			0.132398			0.0661992	+	0.997806i	$0.478913\pi$
$398$			158.858i			0.399141i
$399$	16.7981			0.0421006
$400$	−54.6395			−0.136599
$401$	173.510			0.432693			0.216347	−	0.976317i	$-0.430586\pi$
$401$	173.510			0.432693			0.216347	+	0.976317i	$0.430586\pi$
$402$			44.8997i			0.111691i
$403$			612.503i			1.51986i
$404$		−	310.725i		−	0.769120i
$405$	−398.373			−0.983636
$406$		−	62.5684i		−	0.154109i
$407$	−250.684	−	635.202i	−0.615930	−	1.56069i
$408$	−24.0693			−0.0589934
$409$		−	760.092i		−	1.85842i	−0.369557	−	0.929208i	$-0.620491\pi$
$409$		−	760.092i		−	1.85842i	0.369557	−	0.929208i	$-0.379509\pi$
$410$	281.531			0.686660
$411$	−108.603			−0.264241
$412$	201.009			0.487887
$413$			27.4557i			0.0664787i
$414$		−	111.514i		−	0.269357i
$415$		−	119.882i		−	0.288872i
$416$	−889.287			−2.13771
$417$			64.0877i			0.153688i
$418$	117.029	+	296.536i	0.279973	+	0.709417i
$419$	−457.479			−1.09183			−0.545917	−	0.837839i	$-0.683819\pi$
$419$	−457.479			−1.09183			−0.545917	+	0.837839i	$0.683819\pi$
$420$			24.2175i			0.0576608i
$421$	−612.397			−1.45462			−0.727312	−	0.686307i	$-0.759231\pi$
$421$	−612.397			−1.45462			−0.727312	+	0.686307i	$0.759231\pi$
$422$	−436.390			−1.03410
$423$	−76.1885			−0.180115
$424$		−	180.596i		−	0.425934i
$425$		−	57.0832i		−	0.134313i
$426$			57.8844i			0.135879i
$427$	−273.807			−0.641233
$428$			429.538i			1.00359i
$429$	−104.452	+	41.2221i	−0.243477	+	0.0960887i
$430$	1113.15			2.58873
$431$		−	861.768i		−	1.99946i	−0.0231917	−	0.999731i	$-0.507383\pi$
$431$		−	861.768i		−	1.99946i	0.0231917	−	0.999731i	$-0.492617\pi$
$432$	−153.901			−0.356251
$433$	153.723			0.355019			0.177509	−	0.984119i	$-0.443196\pi$
$433$	153.723			0.355019			0.177509	+	0.984119i	$0.443196\pi$
$434$	−243.189			−0.560343
$435$		−	16.8643i		−	0.0387686i
$436$			60.1100i			0.137867i
$437$		−	52.5603i		−	0.120275i
$438$	−41.9482			−0.0957721
$439$		−	627.662i		−	1.42975i	−0.699250	−	0.714877i	$-0.746483\pi$
$439$		−	627.662i		−	1.42975i	0.699250	−	0.714877i	$-0.253517\pi$
$440$	143.890	−	56.7863i	0.327022	−	0.129060i
$441$	−331.029			−0.750634
$442$		−	1178.86i		−	2.66709i
$443$	330.907			0.746969			0.373484	−	0.927636i	$-0.378163\pi$
$443$	330.907			0.746969			0.373484	+	0.927636i	$0.378163\pi$
$444$	−84.5126			−0.190344
$445$	909.309			2.04339
$446$			845.444i			1.89562i
$447$			72.0903i			0.161276i
$448$		−	96.8075i		−	0.216088i
$449$	−563.117			−1.25416			−0.627079	−	0.778955i	$-0.715750\pi$
$449$	−563.117			−1.25416			−0.627079	+	0.778955i	$0.715750\pi$
$450$		−	66.8168i		−	0.148482i
$451$	−206.332	+	81.4294i	−0.457500	+	0.180553i
$452$	−185.372			−0.410116
$453$		−	17.2465i		−	0.0380717i
$454$	−166.964			−0.367762
$455$	399.218			0.877402
$456$	−13.2792			−0.0291210
$457$		−	309.789i		−	0.677876i	−0.940809	−	0.338938i	$-0.889932\pi$
$457$		−	309.789i		−	0.677876i	0.940809	−	0.338938i	$-0.110068\pi$
$458$		−	839.439i		−	1.83284i
$459$		−	160.784i		−	0.350291i
$460$	75.7751			0.164729
$461$			397.876i			0.863073i	0.902096	+	0.431536i	$0.142028\pi$
$461$			397.876i			0.863073i	−0.902096	+	0.431536i	$0.857972\pi$
$462$	−16.3669	−	41.4716i	−0.0354261	−	0.0897654i
$463$	383.461			0.828210			0.414105	−	0.910229i	$-0.364095\pi$
$463$	383.461			0.828210			0.414105	+	0.910229i	$0.364095\pi$
$464$			133.522i			0.287763i
$465$	−65.5478			−0.140963
$466$	−941.574			−2.02054
$467$	149.479			0.320084			0.160042	−	0.987110i	$-0.448837\pi$
$467$	149.479			0.320084			0.160042	+	0.987110i	$0.448837\pi$
$468$		−	590.552i		−	1.26186i
$469$			125.771i			0.268167i
$470$		−	120.967i		−	0.257377i
$471$	−45.5565			−0.0967230
$472$		−	21.7041i		−	0.0459832i
$473$	−815.825	+	321.967i	−1.72479	+	0.680691i
$474$	90.2503			0.190402
$475$		−	31.4931i		−	0.0663013i
$476$	200.316			0.420833
$477$	596.179			1.24985
$478$	921.333			1.92748
$479$		−	157.152i		−	0.328084i	−0.986453	−	0.164042i	$-0.947547\pi$
$479$		−	157.152i		−	0.328084i	0.986453	−	0.164042i	$-0.0524532\pi$
$480$		−	95.1682i		−	0.198267i
$481$			1393.16i			2.89639i
$482$	778.320			1.61477
$483$			7.35074i			0.0152189i
$484$	264.520	−	247.305i	0.546529	−	0.510960i
$485$	−147.211			−0.303528
$486$		−	283.394i		−	0.583116i
$487$	552.835			1.13518			0.567592	−	0.823310i	$-0.307875\pi$
$487$	552.835			1.13518			0.567592	+	0.823310i	$0.307875\pi$
$488$	216.448			0.443540
$489$	−140.870			−0.288077
$490$		−	525.588i		−	1.07263i
$491$			644.523i			1.31267i	0.754468	+	0.656337i	$0.227895\pi$
$491$			644.523i			1.31267i	−0.754468	+	0.656337i	$0.772105\pi$
$492$			27.4522i			0.0557972i
$493$	−139.494			−0.282949
$494$		−	650.381i		−	1.31656i
$495$	187.461	+	475.005i	0.378710	+	0.959605i
$496$	518.971			1.04631
$497$			162.143i			0.326243i
$498$	27.3140			0.0548474
$499$	−626.170			−1.25485			−0.627425	−	0.778677i	$-0.715891\pi$
$499$	−626.170			−1.25485			−0.627425	+	0.778677i	$0.715891\pi$
$500$	−349.602			−0.699204
$501$			62.3175i			0.124386i
$502$		−	740.558i		−	1.47521i
$503$		−	163.928i		−	0.325900i	−0.986634	−	0.162950i	$-0.947899\pi$
$503$		−	163.928i		−	0.325900i	0.986634	−	0.162950i	$-0.0521010\pi$
$504$	−78.9180			−0.156583
$505$		−	548.158i		−	1.08546i
$506$	−129.762	+	51.2108i	−0.256447	+	0.101207i
$507$	152.214			0.300224
$508$			272.628i			0.536668i
$509$	−108.759			−0.213672			−0.106836	−	0.994277i	$-0.534072\pi$
$509$	−108.759			−0.213672			−0.106836	+	0.994277i	$0.534072\pi$
$510$	126.157			0.247366
$511$	−117.503			−0.229947
$512$			550.898i			1.07597i
$513$		−	88.7053i		−	0.172915i
$514$		−	1108.96i		−	2.15751i
$515$	354.606			0.688556
$516$			108.544i			0.210357i
$517$	34.9883	+	88.6562i	0.0676757	+	0.171482i
$518$	−553.143			−1.06784
$519$		−	109.354i		−	0.210701i
$520$	−315.587			−0.606898
$521$	264.615			0.507899			0.253949	−	0.967218i	$-0.418270\pi$
$521$	264.615			0.507899			0.253949	+	0.967218i	$0.418270\pi$
$522$	−163.280			−0.312797
$523$		−	163.170i		−	0.311989i	−0.987758	−	0.155994i	$-0.950142\pi$
$523$		−	163.170i		−	0.311989i	0.987758	−	0.155994i	$-0.0498582\pi$
$524$		−	486.705i		−	0.928826i
$525$			4.40442i			0.00838937i
$526$	38.8596			0.0738775
$527$			542.181i			1.02881i
$528$	34.9272	+	88.5014i	0.0661501	+	0.167616i
$529$	23.0000			0.0434783
$530$			946.576i			1.78599i
$531$	71.6490			0.134932
$532$	110.516			0.207736
$533$	452.540			0.849043
$534$			207.177i			0.387973i
$535$			757.759i			1.41637i
$536$		−	99.4233i		−	0.185491i
$537$	−116.904			−0.217698
$538$		−	162.388i		−	0.301837i
$539$	152.020	+	385.200i	0.282041	+	0.714657i
$540$	127.885			0.236823
$541$		−	37.0332i		−	0.0684532i	−0.999414	−	0.0342266i	$-0.989103\pi$
$541$		−	37.0332i		−	0.0684532i	0.999414	−	0.0342266i	$-0.0108968\pi$
$542$	280.616			0.517741
$543$	149.747			0.275778
$544$	−787.187			−1.44704
$545$			106.042i			0.194572i
$546$			90.9580i			0.166590i
$547$			617.049i			1.12806i	0.825754	+	0.564030i	$0.190750\pi$
$547$			617.049i			1.12806i	−0.825754	+	0.564030i	$0.809250\pi$
$548$	−714.504			−1.30384
$549$			714.532i			1.30152i
$550$	−77.7509	+	30.6845i	−0.141365	+	0.0557901i
$551$	−76.9596			−0.139673
$552$		−	5.81086i		−	0.0105269i
$553$	252.804			0.457151
$554$	18.0273			0.0325402
$555$	−149.091			−0.268632
$556$			421.635i			0.758337i
$557$			437.527i			0.785507i	0.919644	+	0.392753i	$0.128477\pi$
$557$			437.527i			0.785507i	−0.919644	+	0.392753i	$0.871523\pi$
$558$			634.632i			1.13733i
$559$	1789.31			3.20092
$560$		−	338.255i		−	0.604027i
$561$	−92.4595	+	36.4893i	−0.164812	+	0.0650434i
$562$	−104.032			−0.185110
$563$		−	86.5060i		−	0.153652i	−0.997045	−	0.0768260i	$-0.975521\pi$
$563$		−	86.5060i		−	0.153652i	0.997045	−	0.0768260i	$-0.0244786\pi$
$564$	11.7956			0.0209141
$565$	−327.020			−0.578797
$566$	641.007			1.13252
$567$		−	254.247i		−	0.448408i
$568$		−	128.176i		−	0.225662i
$569$		−	34.6783i		−	0.0609460i	−0.999536	−	0.0304730i	$-0.990299\pi$
$569$		−	34.6783i		−	0.0609460i	0.999536	−	0.0304730i	$-0.00970136\pi$
$570$	69.6014			0.122108
$571$			624.331i			1.09340i	0.837329	+	0.546700i	$0.184116\pi$
$571$			624.331i			1.09340i	−0.837329	+	0.546700i	$0.815884\pi$
$572$	−687.191	+	271.201i	−1.20138	+	0.474128i
$573$	43.2567			0.0754916
$574$			179.677i			0.313026i
$575$	13.7812			0.0239672
$576$	−252.631			−0.438596
$577$	914.406			1.58476			0.792380	−	0.610028i	$-0.208842\pi$
$577$	914.406			1.58476			0.792380	+	0.610028i	$0.208842\pi$
$578$		−	279.286i		−	0.483193i
$579$		−	1.79873i		−	0.00310661i
$580$		−	110.951i		−	0.191295i
$581$	76.5104			0.131688
$582$		−	33.5407i		−	0.0576300i
$583$	−273.786	−	693.740i	−0.469615	−	1.18995i
$584$	92.8876			0.159054
$585$		−	1041.81i		−	1.78087i
$586$	−832.891			−1.42131
$587$	407.276			0.693827			0.346913	−	0.937897i	$-0.387230\pi$
$587$	407.276			0.693827			0.346913	+	0.937897i	$0.387230\pi$
$588$	51.2503			0.0871604
$589$			299.124i			0.507851i
$590$			113.760i			0.192813i
$591$			37.4003i			0.0632831i
$592$	1180.42			1.99395
$593$		−	468.218i		−	0.789575i	−0.918772	−	0.394788i	$-0.870818\pi$
$593$		−	468.218i		−	0.789575i	0.918772	−	0.394788i	$-0.129182\pi$
$594$	−218.998	+	86.4278i	−0.368683	+	0.145501i
$595$	353.383			0.593922
$596$			474.284i			0.795779i
$597$	−27.3269			−0.0457737
$598$	284.602			0.475923
$599$	389.781			0.650720			0.325360	−	0.945590i	$-0.394514\pi$
$599$	389.781			0.650720			0.325360	+	0.945590i	$0.394514\pi$
$600$		−	3.48175i		−	0.00580292i
$601$		−	242.869i		−	0.404108i	−0.979374	−	0.202054i	$-0.935238\pi$
$601$		−	242.869i		−	0.404108i	0.979374	−	0.202054i	$-0.0647617\pi$
$602$			710.432i			1.18012i
$603$	328.214			0.544301
$604$		−	113.465i		−	0.187856i
$605$	466.647	−	436.277i	0.771318	−	0.721118i
$606$	124.893			0.206093
$607$			191.841i			0.316048i	0.987435	+	0.158024i	$0.0505123\pi$
$607$			191.841i			0.316048i	−0.987435	+	0.158024i	$0.949488\pi$
$608$	−434.295			−0.714302
$609$	10.7631			0.0176733
$610$	−1134.49			−1.85982
$611$		−	194.446i		−	0.318242i
$612$		−	522.750i		−	0.854167i
$613$		−	394.349i		−	0.643310i	−0.946857	−	0.321655i	$-0.895761\pi$
$613$		−	394.349i		−	0.643310i	0.946857	−	0.321655i	$-0.104239\pi$
$614$	658.121			1.07186
$615$			48.4292i			0.0787466i
$616$	36.2418	+	91.8324i	0.0588341	+	0.149079i
$617$	−395.046			−0.640269			−0.320135	−	0.947372i	$-0.603728\pi$
$617$	−395.046			−0.640269			−0.320135	+	0.947372i	$0.603728\pi$
$618$			80.7937i			0.130734i
$619$	−667.080			−1.07767			−0.538837	−	0.842410i	$-0.681136\pi$
$619$	−667.080			−1.07767			−0.538837	+	0.842410i	$0.681136\pi$
$620$	−431.242			−0.695551
$621$	38.8168			0.0625069
$622$			1094.38i			1.75945i
$623$			580.334i			0.931515i
$624$		−	194.106i		−	0.311068i
$625$	−688.582			−1.10173
$626$		−	571.264i		−	0.912562i
$627$	−51.0104	+	20.1314i	−0.0813563	+	0.0321074i
$628$	−299.718			−0.477258
$629$			1233.21i			1.96059i
$630$	413.641			0.656573
$631$	−824.427			−1.30654			−0.653270	−	0.757125i	$-0.726603\pi$
$631$	−824.427			−1.30654			−0.653270	+	0.757125i	$0.726603\pi$
$632$	−199.845			−0.316211
$633$		−	75.0681i		−	0.118591i
$634$			281.924i			0.444675i
$635$			480.950i			0.757401i
$636$	−92.3010			−0.145127
$637$		−	844.844i		−	1.32629i
$638$	74.9837	+	190.000i	0.117529	+	0.297805i
$639$	423.131			0.662178
$640$			435.738i			0.680841i
$641$	327.978			0.511666			0.255833	−	0.966721i	$-0.417650\pi$
$641$	327.978			0.511666			0.255833	+	0.966721i	$0.417650\pi$
$642$	−172.648			−0.268923
$643$	−916.240			−1.42495			−0.712473	−	0.701700i	$-0.752425\pi$
$643$	−916.240			−1.42495			−0.712473	+	0.701700i	$0.752425\pi$
$644$			48.3608i			0.0750944i
$645$			191.486i			0.296877i
$646$		−	575.710i		−	0.891192i
$647$	−808.584			−1.24974			−0.624872	−	0.780727i	$-0.714849\pi$
$647$	−808.584			−1.24974			−0.624872	+	0.780727i	$0.714849\pi$
$648$			200.986i			0.310163i
$649$	−32.9037	−	83.3739i	−0.0506990	−	0.128465i
$650$	170.528			0.262350
$651$		−	41.8336i		−	0.0642605i
$652$	−926.787			−1.42145
$653$	−67.5021			−0.103372			−0.0516861	−	0.998663i	$-0.516460\pi$
$653$	−67.5021			−0.103372			−0.0516861	+	0.998663i	$0.516460\pi$
$654$	−24.1606			−0.0369428
$655$		−	858.609i		−	1.31085i
$656$		−	383.435i		−	0.584504i
$657$			306.638i			0.466725i
$658$	77.2031			0.117330
$659$			731.633i			1.11022i	0.831778	+	0.555109i	$0.187323\pi$
$659$			731.633i			1.11022i	−0.831778	+	0.555109i	$0.812677\pi$
$660$	−29.0230	−	73.5407i	−0.0439742	−	0.111425i
$661$	−99.6613			−0.150774			−0.0753868	−	0.997154i	$-0.524019\pi$
$661$	−99.6613			−0.150774			−0.0753868	+	0.997154i	$0.524019\pi$
$662$		−	1289.99i		−	1.94863i
$663$	202.788			0.305864
$664$	−60.4825			−0.0910881
$665$	194.963			0.293178
$666$			1443.49i			2.16741i
$667$		−	33.6769i		−	0.0504902i
$668$			409.989i			0.613756i
$669$	−145.434			−0.217390
$670$			521.117i			0.777787i
$671$	831.460	−	328.137i	1.23914	−	0.489027i
$672$	60.7377			0.0903835
$673$		−	711.611i		−	1.05737i	−0.848818	−	0.528685i	$-0.822685\pi$
$673$		−	711.611i		−	1.05737i	0.848818	−	0.528685i	$-0.177315\pi$
$674$	7.18701			0.0106632
$675$	23.2582			0.0344567
$676$	1001.42			1.48139
$677$			878.449i			1.29756i	0.760976	+	0.648780i	$0.224721\pi$
$677$			878.449i			1.29756i	−0.760976	+	0.648780i	$0.775279\pi$
$678$		−	74.5085i		−	0.109895i
$679$		−	93.9523i		−	0.138369i
$680$	−279.354			−0.410815
$681$		−	28.7213i		−	0.0421752i
$682$	738.485	−	291.445i	1.08282	−	0.427338i
$683$	−907.649			−1.32892			−0.664458	−	0.747326i	$-0.731337\pi$
$683$	−907.649			−1.32892			−0.664458	+	0.747326i	$0.731337\pi$
$684$		−	288.404i		−	0.421643i
$685$	−1260.47			−1.84011
$686$	772.036			1.12542
$687$	144.401			0.210191
$688$		−	1516.08i		−	2.20360i
$689$			1521.55i			2.20835i
$690$			30.4570i			0.0441406i
$691$	−571.677			−0.827318			−0.413659	−	0.910432i	$-0.635749\pi$
$691$	−571.677			−0.827318			−0.413659	+	0.910432i	$0.635749\pi$
$692$		−	719.443i		−	1.03966i
$693$	−303.155	+	119.641i	−0.437453	+	0.172642i
$694$	−1285.74			−1.85265
$695$			743.818i			1.07024i
$696$	−8.50835			−0.0122246
$697$	400.584			0.574726
$698$	−265.870			−0.380903
$699$		−	161.970i		−	0.231717i
$700$			28.9768i			0.0413955i
$701$		−	1183.80i		−	1.68874i	−0.535763	−	0.844368i	$-0.679976\pi$
$701$		−	1183.80i		−	1.68874i	0.535763	−	0.844368i	$-0.320024\pi$
$702$	480.318			0.684214
$703$			680.370i			0.967809i
$704$	116.017	+	293.973i	0.164797	+	0.417575i
$705$	20.8089			0.0295162
$706$			892.300i			1.26388i
$707$	349.842			0.494826
$708$	−11.0928			−0.0156678
$709$	21.1559			0.0298391			0.0149195	−	0.999889i	$-0.495251\pi$
$709$	21.1559			0.0298391			0.0149195	+	0.999889i	$0.495251\pi$
$710$			671.821i			0.946227i
$711$		−	659.724i		−	0.927882i
$712$		−	458.762i		−	0.644329i
$713$	−130.895			−0.183583
$714$			80.5151i			0.112766i
$715$	−1212.29	+	478.434i	−1.69551	+	0.669138i
$716$	−769.114			−1.07418
$717$			158.489i			0.221044i
$718$	39.2300			0.0546379
$719$	−869.740			−1.20965			−0.604826	−	0.796357i	$-0.706757\pi$
$719$	−869.740			−1.20965			−0.604826	+	0.796357i	$0.706757\pi$
$720$	−882.718			−1.22600
$721$			226.315i			0.313890i
$722$			636.997i			0.882268i
$723$			133.887i			0.185183i
$724$	985.193			1.36076
$725$		−	20.1786i		−	0.0278325i
$726$	99.4015	+	106.321i	0.136917	+	0.146448i
$727$	698.088			0.960231			0.480116	−	0.877205i	$-0.340595\pi$
$727$	698.088			0.960231			0.480116	+	0.877205i	$0.340595\pi$
$728$		−	201.412i		−	0.276665i
$729$	−630.353			−0.864682
$730$	−486.861			−0.666933
$731$	1583.88			2.16673
$732$		−	110.625i		−	0.151126i
$733$			1278.80i			1.74461i	0.488963	+	0.872305i	$0.337375\pi$
$733$			1278.80i			1.74461i	−0.488963	+	0.872305i	$0.662625\pi$
$734$		−	557.311i		−	0.759280i
$735$	90.4120			0.123010
$736$		−	190.044i		−	0.258213i
$737$	−150.727	−	381.924i	−0.204514	−	0.518214i
$738$	468.889			0.635352
$739$		−	4.10955i		−	0.00556096i	−0.999996	−	0.00278048i	$-0.999115\pi$
$739$		−	4.10955i		−	0.00556096i	0.999996	−	0.00278048i	$-0.000885055\pi$
$740$	−980.875			−1.32551
$741$	111.879			0.150984
$742$	−604.118			−0.814176
$743$		−	551.840i		−	0.742719i	−0.928489	−	0.371359i	$-0.878892\pi$
$743$		−	551.840i		−	0.742719i	0.928489	−	0.371359i	$-0.121108\pi$
$744$			33.0700i			0.0444489i
$745$			836.698i			1.12308i
$746$	193.437			0.259298
$747$		−	199.663i		−	0.267287i
$748$	−608.295	+	240.065i	−0.813228	+	0.320942i
$749$	−483.613			−0.645678
$750$		−	140.519i		−	0.187359i
$751$	449.725			0.598834			0.299417	−	0.954122i	$-0.403208\pi$
$751$	449.725			0.598834			0.299417	+	0.954122i	$0.403208\pi$
$752$	−164.753			−0.219086
$753$	127.391			0.169178
$754$		−	416.718i		−	0.552676i
$755$		−	200.167i		−	0.265122i
$756$			81.6178i			0.107960i
$757$	668.376			0.882928			0.441464	−	0.897279i	$-0.354459\pi$
$757$	668.376			0.882928			0.441464	+	0.897279i	$0.354459\pi$
$758$		−	394.533i		−	0.520492i
$759$	−8.80933	−	22.3218i	−0.0116065	−	0.0294095i
$760$	−154.121			−0.202791
$761$			784.223i			1.03052i	0.857035	+	0.515258i	$0.172304\pi$
$761$			784.223i			1.03052i	−0.857035	+	0.515258i	$0.827696\pi$
$762$	−109.580			−0.143806
$763$	−67.6773			−0.0886990
$764$	284.587			0.372496
$765$		−	922.198i		−	1.20549i
$766$		−	1039.18i		−	1.35663i
$767$			182.861i			0.238410i
$768$	−151.556			−0.197338
$769$		−	802.816i		−	1.04397i	−0.852953	−	0.521987i	$-0.825191\pi$
$769$		−	802.816i		−	1.04397i	0.852953	−	0.521987i	$-0.174809\pi$
$770$	−189.958	−	481.330i	−0.246699	−	0.625104i
$771$	190.764			0.247424
$772$		−	11.8339i		−	0.0153289i
$773$	249.905			0.323292			0.161646	−	0.986849i	$-0.448320\pi$
$773$	249.905			0.323292			0.161646	+	0.986849i	$0.448320\pi$
$774$	1853.96			2.39530
$775$	−78.4295			−0.101199
$776$			74.2706i			0.0957095i
$777$		−	95.1521i		−	0.122461i
$778$			620.311i			0.797315i
$779$	221.004			0.283702
$780$			161.294i			0.206787i
$781$	−194.316	−	492.374i	−0.248805	−	0.630440i
$782$	251.927			0.322157
$783$		−	56.8361i		−	0.0725876i
$784$	−715.831			−0.913050
$785$	−528.740			−0.673555
$786$	195.626			0.248888
$787$			195.664i			0.248621i	0.992243	+	0.124310i	$0.0396718\pi$
$787$			195.664i			0.248621i	−0.992243	+	0.124310i	$0.960328\pi$
$788$			246.058i			0.312256i
$789$			6.68465i			0.00847231i
$790$	1047.47			1.32591
$791$		−	208.709i		−	0.263855i
$792$	239.648	−	94.5775i	0.302586	−	0.119416i
$793$	−1823.61			−2.29963
$794$			138.994i			0.175056i
$795$	−162.831			−0.204819
$796$	−179.785			−0.225860
$797$	724.449			0.908970			0.454485	−	0.890755i	$-0.349823\pi$
$797$	724.449			0.908970			0.454485	+	0.890755i	$0.349823\pi$
$798$			44.4206i			0.0556649i
$799$		−	172.122i		−	0.215421i
$800$		−	113.871i		−	0.142339i
$801$	1514.45			1.89070
$802$			458.826i			0.572102i
$803$	356.818	−	140.819i	0.444356	−	0.175366i
$804$	−50.8144			−0.0632020
$805$			85.3146i			0.105981i
$806$	−1619.69			−2.00954
$807$	27.9342			0.0346149
$808$	−276.555			−0.342271
$809$			127.278i			0.157327i	0.996901	+	0.0786637i	$0.0250653\pi$
$809$			127.278i			0.157327i	−0.996901	+	0.0786637i	$0.974935\pi$
$810$		−	1053.45i		−	1.30055i
$811$			193.493i			0.238586i	0.992859	+	0.119293i	$0.0380628\pi$
$811$			193.493i			0.238586i	−0.992859	+	0.119293i	$0.961937\pi$
$812$	70.8106			0.0872051
$813$			48.2717i			0.0593748i
$814$	1679.71	−	662.902i	2.06353	−	0.814375i
$815$	−1634.97			−2.00610
$816$		−	171.821i		−	0.210565i
$817$	873.836			1.06957
$818$	2009.97			2.45717
$819$	664.897			0.811840
$820$			318.617i			0.388558i
$821$			575.808i			0.701350i	0.936497	+	0.350675i	$0.114048\pi$
$821$			575.808i			0.701350i	−0.936497	+	0.350675i	$0.885952\pi$
$822$		−	287.187i		−	0.349376i
$823$	−861.354			−1.04660			−0.523301	−	0.852148i	$-0.675300\pi$
$823$	−861.354			−1.04660			−0.523301	+	0.852148i	$0.675300\pi$
$824$		−	178.905i		−	0.217118i
$825$	−5.27838	−	13.3748i	−0.00639804	−	0.0162118i
$826$	−72.6032			−0.0878973
$827$			935.136i			1.13076i	0.824831	+	0.565379i	$0.191270\pi$
$827$			935.136i			1.13076i	−0.824831	+	0.565379i	$0.808730\pi$
$828$	126.203			0.152420
$829$	77.1026			0.0930068			0.0465034	−	0.998918i	$-0.485192\pi$
$829$	77.1026			0.0930068			0.0465034	+	0.998918i	$0.485192\pi$
$830$	317.013			0.381943
$831$			3.10107i			0.00373173i
$832$		−	644.758i		−	0.774949i
$833$		−	747.847i		−	0.897775i
$834$	−169.472			−0.203204
$835$			723.273i			0.866195i
$836$	−335.599	+	132.445i	−0.401435	+	0.158427i
$837$	−220.909			−0.263929
$838$		−	1209.75i		−	1.44361i
$839$	524.474			0.625118			0.312559	−	0.949898i	$-0.398814\pi$
$839$	524.474			0.625118			0.312559	+	0.949898i	$0.398814\pi$
$840$	21.5544			0.0256600
$841$	791.690			0.941367
$842$		−	1619.41i		−	1.92329i
$843$		−	17.8956i		−	0.0212285i
$844$		−	493.876i		−	0.585161i
$845$	1766.63			2.09069
$846$		−	201.471i		−	0.238145i
$847$	278.438	+	297.821i	0.328734	+	0.351619i
$848$	1289.20			1.52028
$849$			110.266i			0.129878i
$850$	150.949			0.177588
$851$	−297.725			−0.349853
$852$	−65.5096			−0.0768892
$853$		−	1361.85i		−	1.59655i	−0.602296	−	0.798273i	$-0.705747\pi$
$853$		−	1361.85i		−	1.59655i	0.602296	−	0.798273i	$-0.294253\pi$
$854$		−	724.047i		−	0.847831i
$855$		−	508.781i		−	0.595066i
$856$	382.303			0.446615
$857$			833.610i			0.972708i	0.873762	+	0.486354i	$0.161673\pi$
$857$			833.610i			0.972708i	−0.873762	+	0.486354i	$0.838327\pi$
$858$	−109.007	−	276.210i	−0.127047	−	0.321923i
$859$	951.816			1.10805			0.554025	−	0.832500i	$-0.313091\pi$
$859$	951.816			1.10805			0.554025	+	0.832500i	$0.313091\pi$
$860$			1259.79i			1.46487i
$861$	−30.9082			−0.0358980
$862$	2278.84			2.64366
$863$	−1265.77			−1.46671			−0.733354	−	0.679847i	$-0.762046\pi$
$863$	−1265.77			−1.46671			−0.733354	+	0.679847i	$0.762046\pi$
$864$		−	320.735i		−	0.371221i
$865$		−	1269.19i		−	1.46727i
$866$			406.501i			0.469401i
$867$	48.0430			0.0554129
$868$		−	275.225i		−	0.317079i
$869$	−767.683	+	302.968i	−0.883410	+	0.348640i
$870$	44.5956			0.0512594
$871$			837.657i			0.961719i
$872$	53.4998			0.0613530
$873$	−245.180			−0.280848
$874$	138.989			0.159027
$875$		−	393.614i		−	0.449845i
$876$		−	47.4741i		−	0.0541941i
$877$		−	877.758i		−	1.00086i	−0.865776	−	0.500432i	$-0.833174\pi$
$877$		−	877.758i		−	1.00086i	0.865776	−	0.500432i	$-0.166826\pi$
$878$	1659.77			1.89040
$879$		−	143.275i		−	0.162997i
$880$	405.374	+	1027.17i	0.460653	+	1.16724i
$881$	−840.848			−0.954425			−0.477213	−	0.878788i	$-0.658353\pi$
$881$	−840.848			−0.954425			−0.477213	+	0.878788i	$0.658353\pi$
$882$		−	875.366i		−	0.992479i
$883$	−236.068			−0.267348			−0.133674	−	0.991025i	$-0.542678\pi$
$883$	−236.068			−0.267348			−0.133674	+	0.991025i	$0.542678\pi$
$884$	1334.15			1.50922
$885$	−19.5691			−0.0221119
$886$			875.043i			0.987633i
$887$		−	1676.00i		−	1.88952i	−0.327766	−	0.944759i	$-0.606296\pi$
$887$		−	1676.00i		−	1.88952i	0.327766	−	0.944759i	$-0.393704\pi$
$888$			75.2190i			0.0847061i
$889$	−306.949			−0.345274
$890$			2404.55i			2.70175i
$891$	304.697	+	772.065i	0.341972	+	0.866515i
$892$	−956.816			−1.07266
$893$		−	94.9604i		−	0.106339i
$894$	−190.634			−0.213237
$895$	−1356.81			−1.51599
$896$	−278.094			−0.310373
$897$			48.9574i			0.0545791i
$898$		−	1489.09i		−	1.65823i
$899$			191.658i			0.213190i
$900$	75.6186			0.0840207
$901$			1346.86i			1.49485i
$902$	−215.330	−	545.620i	−0.238725	−	0.604900i
$903$	−122.209			−0.135337
$904$			164.987i			0.182508i
$905$	1738.01			1.92045
$906$	45.6062			0.0503380
$907$	−1253.85			−1.38242			−0.691209	−	0.722655i	$-0.742921\pi$
$907$	−1253.85			−1.38242			−0.691209	+	0.722655i	$0.742921\pi$
$908$		−	188.958i		−	0.208104i
$909$		−	912.957i		−	1.00435i
$910$			1055.68i			1.16009i
$911$	−556.770			−0.611163			−0.305582	−	0.952166i	$-0.598851\pi$
$911$	−556.770			−0.611163			−0.305582	+	0.952166i	$0.598851\pi$
$912$		−	94.7945i		−	0.103941i
$913$	−232.337	+	91.6923i	−0.254476	+	0.100430i
$914$	819.200			0.896280
$915$		−	195.156i		−	0.213285i
$916$	950.019			1.03714
$917$	547.977			0.597576
$918$	425.173			0.463151
$919$		−	1392.60i		−	1.51534i	−0.652637	−	0.757671i	$-0.726337\pi$
$919$		−	1392.60i		−	1.51534i	0.652637	−	0.757671i	$-0.273663\pi$
$920$		−	67.4423i		−	0.0733069i
$921$			113.211i			0.122921i
$922$	−1052.13			−1.14114
$923$			1079.90i			1.16999i
$924$	46.9347	−	18.5229i	0.0507952	−	0.0200464i
$925$	−178.391			−0.192855
$926$			1014.02i			1.09505i
$927$	590.596			0.637105
$928$	−278.266			−0.299855
$929$	−914.021			−0.983876			−0.491938	−	0.870630i	$-0.663711\pi$
$929$	−914.021			−0.983876			−0.491938	+	0.870630i	$0.663711\pi$
$930$		−	173.333i		−	0.186380i
$931$		−	412.591i		−	0.443170i
$932$		−	1065.61i		−	1.14336i
$933$	−188.256			−0.201775
$934$			395.279i			0.423211i
$935$	−1073.11	+	423.504i	−1.14771	+	0.452946i
$936$	−525.610			−0.561549
$937$		−	174.963i		−	0.186727i	−0.995632	−	0.0933635i	$-0.970238\pi$
$937$		−	174.963i		−	0.186727i	0.995632	−	0.0933635i	$-0.0297619\pi$
$938$	−332.584			−0.354568
$939$	98.2692			0.104653
$940$	136.902			0.145641
$941$			782.715i			0.831791i	0.909412	+	0.415895i	$0.136532\pi$
$941$			782.715i			0.831791i	−0.909412	+	0.415895i	$0.863468\pi$
$942$		−	120.469i		−	0.127886i
$943$			96.7098i			0.102555i
$944$	154.937			0.164128
$945$			143.984i			0.152364i
$946$	−851.401	−	2157.35i	−0.900001	−	2.28049i
$947$	918.953			0.970383			0.485192	−	0.874408i	$-0.338750\pi$
$947$	918.953			0.970383			0.485192	+	0.874408i	$0.338750\pi$
$948$			102.139i			0.107742i
$949$	−782.593			−0.824651
$950$	83.2796			0.0876628
$951$	−48.4968			−0.0509956
$952$		−	178.288i		−	0.187277i
$953$		−	68.9236i		−	0.0723228i	−0.999346	−	0.0361614i	$-0.988487\pi$
$953$		−	68.9236i		−	0.0723228i	0.999346	−	0.0361614i	$-0.0115130\pi$
$954$			1576.52i			1.65254i
$955$	502.048			0.525704
$956$			1042.70i			1.09069i
$957$	−32.6839	+	12.8988i	−0.0341524	+	0.0134783i
$958$	415.569			0.433788
$959$		−	804.453i		−	0.838846i
$960$	68.9996			0.0718746
$961$	−216.070			−0.224838
$962$	−3684.04			−3.82957
$963$			1262.05i			1.31054i
$964$			880.849i			0.913744i
$965$		−	20.8765i		−	0.0216337i
$966$	−19.4381			−0.0201223
$967$		−	190.073i		−	0.196559i	−0.995159	−	0.0982797i	$-0.968666\pi$
$967$		−	190.073i		−	0.196559i	0.995159	−	0.0982797i	$-0.0313340\pi$
$968$	−220.109	−	235.432i	−0.227385	−	0.243214i
$969$	99.0342			0.102202
$970$		−	389.282i		−	0.401321i
$971$	−74.5118			−0.0767372			−0.0383686	−	0.999264i	$-0.512216\pi$
$971$	−74.5118			−0.0767372			−0.0383686	+	0.999264i	$0.512216\pi$
$972$	320.726			0.329965
$973$	−474.716			−0.487889
$974$			1461.90i			1.50093i
$975$			29.3343i			0.0300865i
$976$			1545.13i			1.58313i
$977$	−463.833			−0.474752			−0.237376	−	0.971418i	$-0.576287\pi$
$977$	−463.833			−0.474752			−0.237376	+	0.971418i	$0.576287\pi$
$978$		−	372.513i		−	0.380892i
$979$	−695.489	−	1762.28i	−0.710407	−	1.80009i
$980$	594.824			0.606963
$981$			176.612i			0.180033i
$982$	−1704.36			−1.73560
$983$	568.136			0.577962			0.288981	−	0.957335i	$-0.406684\pi$
$983$	568.136			0.577962			0.288981	+	0.957335i	$0.406684\pi$
$984$	24.4333			0.0248306
$985$			434.077i			0.440688i
$986$		−	368.874i		−	0.374112i
$987$			13.2805i			0.0134555i
$988$	736.056			0.744996
$989$			382.384i			0.386637i
$990$	−1256.09	+	495.719i	−1.26878	+	0.500726i
$991$	51.0375			0.0515010			0.0257505	−	0.999668i	$-0.491802\pi$
$991$	51.0375			0.0515010			0.0257505	+	0.999668i	$0.491802\pi$
$992$			1081.56i			1.09028i
$993$	221.905			0.223470
$994$	−428.766			−0.431354
$995$	−317.163			−0.318756
$996$			30.9121i			0.0310362i
$997$		−	616.536i		−	0.618391i	−0.950999	−	0.309195i	$-0.899940\pi$
$997$		−	616.536i		−	0.618391i	0.950999	−	0.309195i	$-0.100060\pi$
$998$		−	1655.83i		−	1.65915i
$999$	−502.466			−0.502969

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.36	yes	44
11.10	odd	2	inner	253.3.c.a.208.9	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.9	✓	44	11.10	odd	2	inner
253.3.c.a.208.36	yes	44	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+2.64438i q^{2} -0.454888 q^{3} -2.99272 q^{4} -5.27954 q^{5} -1.20289i q^{6} -3.36948i q^{7} +2.66362i q^{8} -8.79308 q^{9} -13.9611i q^{10} +(4.03808 + 10.2320i) q^{11} +1.36135 q^{12} -22.4414i q^{13} +8.91017 q^{14} +2.40160 q^{15} -19.0145 q^{16} -19.8649i q^{17} -23.2522i q^{18} -10.9596i q^{19} +15.8002 q^{20} +1.53274i q^{21} +(-27.0573 + 10.6782i) q^{22} +4.79583 q^{23} -1.21165i q^{24} +2.87357 q^{25} +59.3436 q^{26} +8.09385 q^{27} +10.0839i q^{28} -7.02213i q^{29} +6.35073i q^{30} -27.2934 q^{31} -39.6270i q^{32} +(-1.83687 - 4.65441i) q^{33} +52.5303 q^{34} +17.7893i q^{35} +26.3152 q^{36} -62.0799 q^{37} +28.9813 q^{38} +10.2083i q^{39} -14.0627i q^{40} +20.1654i q^{41} -4.05313 q^{42} +79.7326i q^{43} +(-12.0849 - 30.6216i) q^{44} +46.4234 q^{45} +12.6820i q^{46} +8.66460 q^{47} +8.64946 q^{48} +37.6466 q^{49} +7.59879i q^{50} +9.03631i q^{51} +67.1610i q^{52} -67.8010 q^{53} +21.4032i q^{54} +(-21.3192 - 54.0203i) q^{55} +8.97502 q^{56} +4.98538i q^{57} +18.5691 q^{58} -8.14834 q^{59} -7.18732 q^{60} -81.2608i q^{61} -72.1740i q^{62} +29.6281i q^{63} +28.7307 q^{64} +118.480i q^{65} +(12.3080 - 4.85738i) q^{66} -37.3264 q^{67} +59.4502i q^{68} -2.18157 q^{69} -47.0416 q^{70} -48.1210 q^{71} -23.4214i q^{72} -34.8727i q^{73} -164.163i q^{74} -1.30715 q^{75} +32.7990i q^{76} +(34.4765 - 13.6062i) q^{77} -26.9947 q^{78} +75.0277i q^{79} +100.388 q^{80} +75.4559 q^{81} -53.3248 q^{82} +22.7069i q^{83} -4.58705i q^{84} +104.878i q^{85} -210.843 q^{86} +3.19428i q^{87} +(-27.2542 + 10.7559i) q^{88} -172.233 q^{89} +122.761i q^{90} -75.6160 q^{91} -14.3526 q^{92} +12.4154 q^{93} +22.9125i q^{94} +57.8616i q^{95} +18.0258i q^{96} +27.8833 q^{97} +99.5518i q^{98} +(-35.5071 - 89.9708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 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

Downloads

Learn more