LMFDB - Embedded newform 253.3.c.a.208.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [253,3,Mod(208,253)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			208.7
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.88425i q^{2} +1.17107 q^{3} -4.31889 q^{4} +1.65709 q^{5} -3.37766i q^{6} -6.12044i q^{7} +0.919746i q^{8} -7.62859 q^{9} -4.77946i q^{10} +(10.8798 - 1.62150i) q^{11} -5.05772 q^{12} +3.05880i q^{13} -17.6529 q^{14} +1.94057 q^{15} -14.6228 q^{16} -25.1270i q^{17} +22.0028i q^{18} -4.90728i q^{19} -7.15678 q^{20} -7.16746i q^{21} +(-4.67681 - 31.3801i) q^{22} -4.79583 q^{23} +1.07709i q^{24} -22.2541 q^{25} +8.82234 q^{26} -19.4733 q^{27} +26.4335i q^{28} +4.85186i q^{29} -5.59708i q^{30} +31.3705 q^{31} +45.8547i q^{32} +(12.7410 - 1.89889i) q^{33} -72.4725 q^{34} -10.1421i q^{35} +32.9470 q^{36} +18.5273 q^{37} -14.1538 q^{38} +3.58207i q^{39} +1.52410i q^{40} +17.6289i q^{41} -20.6727 q^{42} +55.4511i q^{43} +(-46.9888 + 7.00308i) q^{44} -12.6413 q^{45} +13.8324i q^{46} +77.9523 q^{47} -17.1243 q^{48} +11.5402 q^{49} +64.1862i q^{50} -29.4255i q^{51} -13.2106i q^{52} +47.3539 q^{53} +56.1657i q^{54} +(18.0289 - 2.68697i) q^{55} +5.62925 q^{56} -5.74677i q^{57} +13.9940 q^{58} +25.3673 q^{59} -8.38109 q^{60} -72.9857i q^{61} -90.4804i q^{62} +46.6903i q^{63} +73.7652 q^{64} +5.06870i q^{65} +(-5.47687 - 36.7483i) q^{66} -18.1694 q^{67} +108.521i q^{68} -5.61625 q^{69} -29.2524 q^{70} -68.4310 q^{71} -7.01637i q^{72} -74.7380i q^{73} -53.4373i q^{74} -26.0611 q^{75} +21.1940i q^{76} +(-9.92429 - 66.5893i) q^{77} +10.3316 q^{78} -128.093i q^{79} -24.2312 q^{80} +45.8528 q^{81} +50.8461 q^{82} +33.0931i q^{83} +30.9554i q^{84} -41.6377i q^{85} +159.935 q^{86} +5.68186i q^{87} +(1.49137 + 10.0067i) q^{88} -76.4692 q^{89} +36.4605i q^{90} +18.7212 q^{91} +20.7126 q^{92} +36.7371 q^{93} -224.834i q^{94} -8.13181i q^{95} +53.6990i q^{96} +184.662 q^{97} -33.2849i q^{98} +(-82.9978 + 12.3698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.88425i		−	1.44212i	−0.692871	−	0.721062i	$-0.743654\pi$
$2$		−	2.88425i		−	1.44212i	0.692871	−	0.721062i	$-0.256346\pi$
$3$	1.17107			0.390357			0.195178	−	0.980768i	$-0.437471\pi$
$3$	1.17107			0.390357			0.195178	+	0.980768i	$0.437471\pi$
$4$	−4.31889			−1.07972
$5$	1.65709			0.331418			0.165709	−	0.986175i	$-0.447009\pi$
$5$	1.65709			0.331418			0.165709	+	0.986175i	$0.447009\pi$
$6$		−	3.37766i		−	0.562943i
$7$		−	6.12044i		−	0.874348i	−0.899377	−	0.437174i	$-0.855979\pi$
$7$		−	6.12044i		−	0.874348i	0.899377	−	0.437174i	$-0.144021\pi$
$8$			0.919746i			0.114968i
$9$	−7.62859			−0.847622
$10$		−	4.77946i		−	0.477946i
$11$	10.8798	−	1.62150i	0.989076	−	0.147409i
$11$	10.8798	−	1.62150i	0.989076	−	0.147409i
$12$	−5.05772			−0.421477
$13$			3.05880i			0.235292i	0.993056	+	0.117646i	$0.0375349\pi$
$13$			3.05880i			0.235292i	−0.993056	+	0.117646i	$0.962465\pi$
$14$	−17.6529			−1.26092
$15$	1.94057			0.129371
$16$	−14.6228			−0.913923
$17$		−	25.1270i		−	1.47806i	−0.673674	−	0.739029i	$-0.735285\pi$
$17$		−	25.1270i		−	1.47806i	0.673674	−	0.739029i	$-0.264715\pi$
$18$			22.0028i			1.22238i
$19$		−	4.90728i		−	0.258278i	−0.991626	−	0.129139i	$-0.958779\pi$
$19$		−	4.90728i		−	0.258278i	0.991626	−	0.129139i	$-0.0412214\pi$
$20$	−7.15678			−0.357839
$21$		−	7.16746i		−	0.341308i
$22$	−4.67681	−	31.3801i	−0.212582	−	1.42637i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$			1.07709i			0.0448786i
$25$	−22.2541			−0.890162
$26$	8.82234			0.339321
$27$	−19.4733			−0.721231
$28$			26.4335i			0.944053i
$29$			4.85186i			0.167305i	0.996495	+	0.0836527i	$0.0266586\pi$
$29$			4.85186i			0.167305i	−0.996495	+	0.0836527i	$0.973341\pi$
$30$		−	5.59708i		−	0.186569i
$31$	31.3705			1.01195			0.505976	−	0.862547i	$-0.331132\pi$
$31$	31.3705			1.01195			0.505976	+	0.862547i	$0.331132\pi$
$32$			45.8547i			1.43296i
$33$	12.7410	−	1.89889i	0.386092	−	0.0575421i
$34$	−72.4725			−2.13154
$35$		−	10.1421i		−	0.289775i
$36$	32.9470			0.915195
$37$	18.5273			0.500737			0.250369	−	0.968151i	$-0.419448\pi$
$37$	18.5273			0.500737			0.250369	+	0.968151i	$0.419448\pi$
$38$	−14.1538			−0.372469
$39$			3.58207i			0.0918479i
$40$			1.52410i			0.0381025i
$41$			17.6289i			0.429973i	0.976617	+	0.214987i	$0.0689708\pi$
$41$			17.6289i			0.429973i	−0.976617	+	0.214987i	$0.931029\pi$
$42$	−20.6727			−0.492208
$43$			55.4511i			1.28956i	0.764368	+	0.644780i	$0.223051\pi$
$43$			55.4511i			1.28956i	−0.764368	+	0.644780i	$0.776949\pi$
$44$	−46.9888	+	7.00308i	−1.06793	+	0.159161i
$45$	−12.6413			−0.280917
$46$			13.8324i			0.300704i
$47$	77.9523			1.65856			0.829280	−	0.558833i	$-0.188751\pi$
$47$	77.9523			1.65856			0.829280	+	0.558833i	$0.188751\pi$
$48$	−17.1243			−0.356756
$49$	11.5402			0.235515
$50$			64.1862i			1.28372i
$51$		−	29.4255i		−	0.576970i
$52$		−	13.2106i		−	0.254050i
$53$	47.3539			0.893470			0.446735	−	0.894666i	$-0.352587\pi$
$53$	47.3539			0.893470			0.446735	+	0.894666i	$0.352587\pi$
$54$			56.1657i			1.04011i
$55$	18.0289	−	2.68697i	0.327797	−	0.0488540i
$56$	5.62925			0.100522
$57$		−	5.74677i		−	0.100821i
$58$	13.9940			0.241275
$59$	25.3673			0.429955			0.214978	−	0.976619i	$-0.431032\pi$
$59$	25.3673			0.429955			0.214978	+	0.976619i	$0.431032\pi$
$60$	−8.38109			−0.139685
$61$		−	72.9857i		−	1.19649i	−0.801314	−	0.598244i	$-0.795866\pi$
$61$		−	72.9857i		−	1.19649i	0.801314	−	0.598244i	$-0.204134\pi$
$62$		−	90.4804i		−	1.45936i
$63$			46.6903i			0.741116i
$64$	73.7652			1.15258
$65$			5.06870i			0.0779801i
$66$	−5.47687	−	36.7483i	−0.0829829	−	0.556793i
$67$	−18.1694			−0.271185			−0.135593	−	0.990765i	$-0.543294\pi$
$67$	−18.1694			−0.271185			−0.135593	+	0.990765i	$0.543294\pi$
$68$			108.521i			1.59589i
$69$	−5.61625			−0.0813950
$70$	−29.2524			−0.417891
$71$	−68.4310			−0.963816			−0.481908	−	0.876222i	$-0.660056\pi$
$71$	−68.4310			−0.963816			−0.481908	+	0.876222i	$0.660056\pi$
$72$		−	7.01637i		−	0.0974496i
$73$		−	74.7380i		−	1.02381i	−0.859043	−	0.511904i	$-0.828940\pi$
$73$		−	74.7380i		−	1.02381i	0.859043	−	0.511904i	$-0.171060\pi$
$74$		−	53.4373i		−	0.722125i
$75$	−26.0611			−0.347481
$76$			21.1940i			0.278868i
$77$	−9.92429	−	66.5893i	−0.128887	−	0.864796i
$78$	10.3316			0.132456
$79$		−	128.093i		−	1.62144i	−0.585437	−	0.810718i	$-0.699077\pi$
$79$		−	128.093i		−	1.62144i	0.585437	−	0.810718i	$-0.300923\pi$
$80$	−24.2312			−0.302890
$81$	45.8528			0.566084
$82$	50.8461			0.620074
$83$			33.0931i			0.398712i	0.979927	+	0.199356i	$0.0638850\pi$
$83$			33.0931i			0.398712i	−0.979927	+	0.199356i	$0.936115\pi$
$84$			30.9554i			0.368517i
$85$		−	41.6377i		−	0.489855i
$86$	159.935			1.85970
$87$			5.68186i			0.0653088i
$88$	1.49137	+	10.0067i	0.0169474	+	0.113712i
$89$	−76.4692			−0.859205			−0.429603	−	0.903018i	$-0.641346\pi$
$89$	−76.4692			−0.859205			−0.429603	+	0.903018i	$0.641346\pi$
$90$			36.4605i			0.405117i
$91$	18.7212			0.205727
$92$	20.7126			0.225137
$93$	36.7371			0.395022
$94$		−	224.834i		−	2.39185i
$95$		−	8.13181i		−	0.0855980i
$96$			53.6990i			0.559365i
$97$	184.662			1.90373			0.951866	−	0.306515i	$-0.0991630\pi$
$97$	184.662			1.90373			0.951866	+	0.306515i	$0.0991630\pi$
$98$		−	33.2849i		−	0.339642i
$99$	−82.9978	+	12.3698i	−0.838362	+	0.124947i
$100$	96.1127			0.961127
$101$			189.829i			1.87949i	0.341874	+	0.939746i	$0.388938\pi$
$101$			189.829i			1.87949i	−0.341874	+	0.939746i	$0.611062\pi$
$102$	−84.8703			−0.832062
$103$	142.657			1.38502			0.692510	−	0.721408i	$-0.256505\pi$
$103$	142.657			1.38502			0.692510	+	0.721408i	$0.256505\pi$
$104$	−2.81332			−0.0270511
$105$		−	11.8771i		−	0.113115i
$106$		−	136.580i		−	1.28849i
$107$			184.160i			1.72112i	0.509348	+	0.860560i	$0.329886\pi$
$107$			184.160i			1.72112i	−0.509348	+	0.860560i	$0.670114\pi$
$108$	84.1027			0.778729
$109$			132.961i			1.21983i	0.792468	+	0.609914i	$0.208796\pi$
$109$			132.961i			1.21983i	−0.792468	+	0.609914i	$0.791204\pi$
$110$	−7.74989	−	51.9997i	−0.0704536	−	0.472724i
$111$	21.6967			0.195466
$112$			89.4977i			0.799087i
$113$	146.598			1.29733			0.648666	−	0.761074i	$-0.275327\pi$
$113$	146.598			1.29733			0.648666	+	0.761074i	$0.275327\pi$
$114$	−16.5751			−0.145396
$115$	−7.94712			−0.0691054
$116$		−	20.9546i		−	0.180643i
$117$		−	23.3343i		−	0.199439i
$118$		−	73.1657i		−	0.620048i
$119$	−153.788			−1.29234
$120$			1.78483i			0.0148736i
$121$	115.741	−	35.2833i	0.956541	−	0.291598i
$122$	−210.509			−1.72548
$123$			20.6447i			0.167843i
$124$	−135.486			−1.09263
$125$	−78.3042			−0.626434
$126$	134.667			1.06878
$127$		−	160.042i		−	1.26017i	−0.776524	−	0.630087i	$-0.783019\pi$
$127$		−	160.042i		−	1.26017i	0.776524	−	0.630087i	$-0.216981\pi$
$128$		−	29.3383i		−	0.229206i
$129$			64.9371i			0.503388i
$130$	14.6194			0.112457
$131$		−	68.7645i		−	0.524919i	−0.964943	−	0.262460i	$-0.915466\pi$
$131$		−	68.7645i		−	0.524919i	0.964943	−	0.262460i	$-0.0845337\pi$
$132$	−55.0271	+	8.20109i	−0.416872	+	0.0621295i
$133$	−30.0347			−0.225825
$134$			52.4051i			0.391083i
$135$	−32.2689			−0.239029
$136$	23.1104			0.169930
$137$	−36.0747			−0.263319			−0.131659	−	0.991295i	$-0.542031\pi$
$137$	−36.0747			−0.263319			−0.131659	+	0.991295i	$0.542031\pi$
$138$			16.1987i			0.117382i
$139$		−	51.1973i		−	0.368326i	−0.982896	−	0.184163i	$-0.941043\pi$
$139$		−	51.1973i		−	0.368326i	0.982896	−	0.184163i	$-0.0589574\pi$
$140$			43.8026i			0.312876i
$141$	91.2876			0.647430
$142$			197.372i			1.38994i
$143$	4.95984	+	33.2792i	0.0346842	+	0.232722i
$144$	111.551			0.774661
$145$			8.03996i			0.0554480i
$146$	−215.563			−1.47646
$147$	13.5144			0.0919350
$148$	−80.0172			−0.540657
$149$			62.5029i			0.419482i	0.977757	+	0.209741i	$0.0672622\pi$
$149$			62.5029i			0.419482i	−0.977757	+	0.209741i	$0.932738\pi$
$150$			75.1666i			0.501110i
$151$			69.5586i			0.460653i	0.973113	+	0.230326i	$0.0739794\pi$
$151$			69.5586i			0.460653i	−0.973113	+	0.230326i	$0.926021\pi$
$152$	4.51346			0.0296938
$153$			191.684i			1.25283i
$154$	−192.060	+	28.6241i	−1.24714	+	0.185871i
$155$	51.9838			0.335379
$156$		−	15.4705i		−	0.0991702i
$157$	−154.166			−0.981951			−0.490975	−	0.871174i	$-0.663359\pi$
$157$	−154.166			−0.981951			−0.490975	+	0.871174i	$0.663359\pi$
$158$	−369.453			−2.33831
$159$	55.4547			0.348772
$160$			75.9853i			0.474908i
$161$			29.3526i			0.182314i
$162$		−	132.251i		−	0.816363i
$163$	−169.087			−1.03734			−0.518672	−	0.854973i	$-0.673574\pi$
$163$	−169.087			−1.03734			−0.518672	+	0.854973i	$0.673574\pi$
$164$		−	76.1372i		−	0.464251i
$165$	21.1131	−	3.14663i	0.127958	−	0.0190705i
$166$	95.4486			0.574992
$167$			78.1926i			0.468219i	0.972210	+	0.234110i	$0.0752175\pi$
$167$			78.1926i			0.468219i	−0.972210	+	0.234110i	$0.924783\pi$
$168$	6.59224			0.0392395
$169$	159.644			0.944638
$170$	−120.093			−0.706431
$171$			37.4357i			0.218922i
$172$		−	239.487i		−	1.39237i
$173$		−	13.0030i		−	0.0751618i	−0.999294	−	0.0375809i	$-0.988035\pi$
$173$		−	13.0030i		−	0.0751618i	0.999294	−	0.0375809i	$-0.0119652\pi$
$174$	16.3879			0.0941833
$175$			136.205i			0.778312i
$176$	−159.093	+	23.7108i	−0.903939	+	0.134721i
$177$	29.7069			0.167836
$178$			220.556i			1.23908i
$179$	−246.728			−1.37837			−0.689184	−	0.724586i	$-0.742031\pi$
$179$	−246.728			−1.37837			−0.689184	+	0.724586i	$0.742031\pi$
$180$	54.5962			0.303312
$181$	−74.5087			−0.411650			−0.205825	−	0.978589i	$-0.565988\pi$
$181$	−74.5087			−0.411650			−0.205825	+	0.978589i	$0.565988\pi$
$182$		−	53.9966i		−	0.296684i
$183$		−	85.4714i		−	0.467057i
$184$		−	4.41095i		−	0.0239725i
$185$	30.7014			0.165953
$186$		−	105.959i		−	0.569671i
$187$	−40.7434	−	273.377i	−0.217879	−	1.46191i
$188$	−336.667			−1.79078
$189$			119.185i			0.630607i
$190$	−23.4542			−0.123443
$191$	15.5185			0.0812487			0.0406244	−	0.999174i	$-0.487065\pi$
$191$	15.5185			0.0812487			0.0406244	+	0.999174i	$0.487065\pi$
$192$	86.3842			0.449918
$193$			265.577i			1.37605i	0.725688	+	0.688024i	$0.241521\pi$
$193$			265.577i			1.37605i	−0.725688	+	0.688024i	$0.758479\pi$
$194$		−	532.611i		−	2.74542i
$195$			5.93581i			0.0304400i
$196$	−49.8410			−0.254291
$197$			84.8175i			0.430546i	0.976554	+	0.215273i	$0.0690641\pi$
$197$			84.8175i			0.430546i	−0.976554	+	0.215273i	$0.930936\pi$
$198$	35.6775	+	239.386i	0.180189	+	1.20902i
$199$	−150.874			−0.758159			−0.379079	−	0.925364i	$-0.623759\pi$
$199$	−150.874			−0.758159			−0.379079	+	0.925364i	$0.623759\pi$
$200$		−	20.4681i		−	0.102340i
$201$	−21.2776			−0.105859
$202$	547.513			2.71046
$203$	29.6955			0.146283
$204$			127.085i			0.622967i
$205$			29.2127i			0.142501i
$206$		−	411.459i		−	1.99737i
$207$	36.5855			0.176741
$208$		−	44.7281i		−	0.215039i
$209$	−7.95716	−	53.3904i	−0.0380726	−	0.255457i
$210$	−34.2566			−0.163127
$211$		−	181.466i		−	0.860028i	−0.902822	−	0.430014i	$-0.858509\pi$
$211$		−	181.466i		−	0.860028i	0.902822	−	0.430014i	$-0.141491\pi$
$212$	−204.516			−0.964698
$213$	−80.1374			−0.376232
$214$	531.163			2.48207
$215$			91.8874i			0.427383i
$216$		−	17.9104i		−	0.0829187i
$217$		−	192.001i		−	0.884799i
$218$	383.493			1.75914
$219$		−	87.5234i		−	0.399650i
$220$	−77.8646	+	11.6047i	−0.353930	+	0.0527487i
$221$	76.8584			0.347776
$222$		−	62.5788i		−	0.281886i
$223$	−88.9586			−0.398918			−0.199459	−	0.979906i	$-0.563918\pi$
$223$	−88.9586			−0.398918			−0.199459	+	0.979906i	$0.563918\pi$
$224$	280.651			1.25290
$225$	169.767			0.754521
$226$		−	422.826i		−	1.87091i
$227$			346.885i			1.52813i	0.645140	+	0.764064i	$0.276799\pi$
$227$			346.885i			1.52813i	−0.645140	+	0.764064i	$0.723201\pi$
$228$			24.8197i			0.108858i
$229$	−50.4113			−0.220137			−0.110068	−	0.993924i	$-0.535107\pi$
$229$	−50.4113			−0.220137			−0.110068	+	0.993924i	$0.535107\pi$
$230$			22.9215i			0.0996586i
$231$	−11.6220	−	77.9808i	−0.0503119	−	0.337579i
$232$	−4.46247			−0.0192348
$233$		−	335.414i		−	1.43955i	−0.694209	−	0.719773i	$-0.744246\pi$
$233$		−	335.414i		−	1.43955i	0.694209	−	0.719773i	$-0.255754\pi$
$234$	−67.3020			−0.287615
$235$	129.174			0.549676
$236$	−109.559			−0.464232
$237$		−	150.006i		−	0.632938i
$238$			443.563i			1.86371i
$239$		−	3.34310i		−	0.0139879i	−0.999976	−	0.00699393i	$-0.997774\pi$
$239$		−	3.34310i		−	0.0139879i	0.999976	−	0.00699393i	$-0.00222625\pi$
$240$	−28.3765			−0.118235
$241$			62.8963i			0.260980i	0.991450	+	0.130490i	$0.0416551\pi$
$241$			62.8963i			0.260980i	−0.991450	+	0.130490i	$0.958345\pi$
$242$	−101.766	−	333.827i	−0.420520	−	1.37945i
$243$	228.956			0.942206
$244$			315.217i			1.29187i
$245$	19.1232			0.0780540
$246$	59.5444			0.242050
$247$	15.0104			0.0607708
$248$			28.8529i			0.116342i
$249$			38.7543i			0.155640i
$250$			225.849i			0.903395i
$251$	−74.2813			−0.295941			−0.147971	−	0.988992i	$-0.547274\pi$
$251$	−74.2813			−0.295941			−0.147971	+	0.988992i	$0.547274\pi$
$252$		−	201.650i		−	0.800199i
$253$	−52.1778	+	7.77644i	−0.206237	+	0.0307369i
$254$	−461.601			−1.81733
$255$		−	48.7606i		−	0.191218i
$256$	210.442			0.822038
$257$	−16.6453			−0.0647677			−0.0323839	−	0.999476i	$-0.510310\pi$
$257$	−16.6453			−0.0647677			−0.0323839	+	0.999476i	$0.510310\pi$
$258$	187.295			0.725948
$259$		−	113.395i		−	0.437819i
$260$		−	21.8912i		−	0.0841967i
$261$		−	37.0128i		−	0.141812i
$262$	−198.334			−0.756999
$263$			250.180i			0.951254i	0.879647	+	0.475627i	$0.157779\pi$
$263$			250.180i			0.951254i	−0.879647	+	0.475627i	$0.842221\pi$
$264$	1.74650	+	11.7185i	0.00661552	+	0.0443884i
$265$	78.4696			0.296112
$266$			86.6276i			0.325668i
$267$	−89.5509			−0.335396
$268$	78.4716			0.292804
$269$	−114.723			−0.426481			−0.213240	−	0.977000i	$-0.568402\pi$
$269$	−114.723			−0.426481			−0.213240	+	0.977000i	$0.568402\pi$
$270$			93.0715i			0.344709i
$271$		−	316.028i		−	1.16616i	−0.812416	−	0.583078i	$-0.801848\pi$
$271$		−	316.028i		−	1.16616i	0.812416	−	0.583078i	$-0.198152\pi$
$272$			367.426i			1.35083i
$273$	21.9238			0.0803071
$274$			104.048i			0.379738i
$275$	−242.120	+	36.0850i	−0.880438	+	0.131218i
$276$	24.2560			0.0878839
$277$		−	41.2805i		−	0.149027i	−0.997220	−	0.0745135i	$-0.976260\pi$
$277$		−	41.2805i		−	0.149027i	0.997220	−	0.0745135i	$-0.0237404\pi$
$278$	−147.666			−0.531172
$279$	−239.313			−0.857753
$280$	9.32817			0.0333149
$281$		−	477.815i		−	1.70041i	−0.526453	−	0.850204i	$-0.676478\pi$
$281$		−	477.815i		−	1.70041i	0.526453	−	0.850204i	$-0.323522\pi$
$282$		−	263.296i		−	0.933674i
$283$			132.022i			0.466510i	0.972416	+	0.233255i	$0.0749377\pi$
$283$			132.022i			0.466510i	−0.972416	+	0.233255i	$0.925062\pi$
$284$	295.545			1.04065
$285$		−	9.52292i		−	0.0334137i
$286$	95.9855	−	14.3054i	0.335614	−	0.0500190i
$287$	107.897			0.375946
$288$		−	349.807i		−	1.21461i
$289$	−342.365			−1.18466
$290$	23.1892			0.0799629
$291$	216.252			0.743134
$292$			322.785i			1.10543i
$293$			467.296i			1.59487i	0.603406	+	0.797434i	$0.293810\pi$
$293$			467.296i			1.59487i	−0.603406	+	0.797434i	$0.706190\pi$
$294$		−	38.9790i		−	0.132582i
$295$	42.0360			0.142495
$296$			17.0404i			0.0575689i
$297$	−211.866	+	31.5759i	−0.713352	+	0.106316i
$298$	180.274			0.604946
$299$		−	14.6695i		−	0.0490618i
$300$	112.555			0.375182
$301$	339.385			1.12752
$302$	200.624			0.664319
$303$			222.303i			0.733672i
$304$			71.7581i			0.236046i
$305$		−	120.944i		−	0.396537i
$306$	552.863			1.80674
$307$			85.4545i			0.278353i	0.990268	+	0.139177i	$0.0444456\pi$
$307$			85.4545i			0.278353i	−0.990268	+	0.139177i	$0.955554\pi$
$308$	42.8619	+	287.592i	0.139162	+	0.933739i
$309$	167.061			0.540652
$310$		−	149.934i		−	0.483658i
$311$	−233.259			−0.750030			−0.375015	−	0.927019i	$-0.622362\pi$
$311$	−233.259			−0.750030			−0.375015	+	0.927019i	$0.622362\pi$
$312$	−3.29459			−0.0105596
$313$	−156.269			−0.499263			−0.249631	−	0.968341i	$-0.580309\pi$
$313$	−156.269			−0.499263			−0.249631	+	0.968341i	$0.580309\pi$
$314$			444.654i			1.41609i
$315$			77.3701i			0.245619i
$316$			553.221i			1.75070i
$317$	146.873			0.463320			0.231660	−	0.972797i	$-0.425584\pi$
$317$	146.873			0.463320			0.231660	+	0.972797i	$0.425584\pi$
$318$		−	159.945i		−	0.502972i
$319$	7.86729	+	52.7874i	0.0246623	+	0.165478i
$320$	122.235			0.381986
$321$			215.664i			0.671851i
$322$	84.6601			0.262920
$323$	−123.305			−0.381750
$324$	−198.033			−0.611213
$325$		−	68.0707i		−	0.209448i
$326$			487.689i			1.49598i
$327$			155.707i			0.476168i
$328$	−16.2141			−0.0494333
$329$		−	477.102i		−	1.45016i
$330$	−9.07567	−	60.8953i	−0.0275020	−	0.184531i
$331$	−183.093			−0.553152			−0.276576	−	0.960992i	$-0.589200\pi$
$331$	−183.093			−0.553152			−0.276576	+	0.960992i	$0.589200\pi$
$332$		−	142.925i		−	0.430498i
$333$	−141.337			−0.424436
$334$	225.527			0.675230
$335$	−30.1083			−0.0898756
$336$			104.808i			0.311929i
$337$			411.849i			1.22210i	0.791591	+	0.611051i	$0.209253\pi$
$337$			411.849i			1.22210i	−0.791591	+	0.611051i	$0.790747\pi$
$338$		−	460.452i		−	1.36228i
$339$	171.677			0.506422
$340$			179.828i			0.528907i
$341$	341.306	−	50.8673i	1.00090	−	0.149171i
$342$	107.974			0.315713
$343$		−	370.533i		−	1.08027i
$344$	−51.0009			−0.148258
$345$	−9.30664			−0.0269758
$346$	−37.5038			−0.108393
$347$		−	558.900i		−	1.61066i	−0.592824	−	0.805332i	$-0.701987\pi$
$347$		−	558.900i		−	1.61066i	0.592824	−	0.805332i	$-0.298013\pi$
$348$		−	24.5393i		−	0.0705153i
$349$			283.165i			0.811362i	0.914015	+	0.405681i	$0.132966\pi$
$349$			283.165i			0.811362i	−0.914015	+	0.405681i	$0.867034\pi$
$350$	392.848			1.12242
$351$		−	59.5648i		−	0.169700i
$352$	74.3534	+	498.891i	0.211231	+	1.41730i
$353$	487.578			1.38124			0.690621	−	0.723217i	$-0.257337\pi$
$353$	487.578			1.38124			0.690621	+	0.723217i	$0.257337\pi$
$354$		−	85.6822i		−	0.242040i
$355$	−113.396			−0.319426
$356$	330.262			0.927702
$357$	−180.097			−0.504473
$358$			711.625i			1.98778i
$359$			226.972i			0.632234i	0.948720	+	0.316117i	$0.102379\pi$
$359$			226.972i			0.632234i	−0.948720	+	0.316117i	$0.897621\pi$
$360$		−	11.6268i		−	0.0322965i
$361$	336.919			0.933292
$362$			214.902i			0.593651i
$363$	135.541	−	41.3192i	0.373392	−	0.113827i
$364$	−80.8547			−0.222128
$365$		−	123.848i		−	0.339308i
$366$	−246.521			−0.673554
$367$	−376.527			−1.02596			−0.512980	−	0.858401i	$-0.671458\pi$
$367$	−376.527			−1.02596			−0.512980	+	0.858401i	$0.671458\pi$
$368$	70.1283			0.190566
$369$		−	134.484i		−	0.364454i
$370$		−	88.5503i		−	0.239325i
$371$		−	289.827i		−	0.781204i
$372$	−158.663			−0.426514
$373$		−	292.782i		−	0.784938i	−0.919765	−	0.392469i	$-0.871621\pi$
$373$		−	292.782i		−	0.784938i	0.919765	−	0.392469i	$-0.128379\pi$
$374$	−788.488	+	117.514i	−2.10826	+	0.314209i
$375$	−91.6997			−0.244533
$376$			71.6964i			0.190682i
$377$	−14.8409			−0.0393657
$378$	343.759			0.909414
$379$	−190.332			−0.502196			−0.251098	−	0.967962i	$-0.580792\pi$
$379$	−190.332			−0.502196			−0.251098	+	0.967962i	$0.580792\pi$
$380$			35.1204i			0.0924220i
$381$		−	187.421i		−	0.491917i
$382$		−	44.7592i		−	0.117171i
$383$	−393.375			−1.02709			−0.513544	−	0.858063i	$-0.671668\pi$
$383$	−393.375			−1.02709			−0.513544	+	0.858063i	$0.671668\pi$
$384$		−	34.3573i		−	0.0894720i
$385$	−16.4454	−	110.344i	−0.0427154	−	0.286609i
$386$	765.990			1.98443
$387$		−	423.014i		−	1.09306i
$388$	−797.534			−2.05550
$389$	265.182			0.681703			0.340851	−	0.940117i	$-0.389285\pi$
$389$	265.182			0.681703			0.340851	+	0.940117i	$0.389285\pi$
$390$	17.1203			0.0438983
$391$			120.505i			0.308196i
$392$			10.6141i			0.0270768i
$393$		−	80.5280i		−	0.204906i
$394$	244.635			0.620900
$395$		−	212.262i		−	0.537373i
$396$	358.458	−	53.4236i	0.905197	−	0.134908i
$397$	−701.775			−1.76770			−0.883848	−	0.467774i	$-0.845056\pi$
$397$	−701.775			−1.76770			−0.883848	+	0.467774i	$0.845056\pi$
$398$			435.157i			1.09336i
$399$	−35.1728			−0.0881523
$400$	325.416			0.813540
$401$	249.118			0.621241			0.310621	−	0.950534i	$-0.399463\pi$
$401$	249.118			0.621241			0.310621	+	0.950534i	$0.399463\pi$
$402$			61.3700i			0.152662i
$403$			95.9562i			0.238105i
$404$		−	819.848i		−	2.02933i
$405$	75.9822			0.187610
$406$		−	85.6491i		−	0.210958i
$407$	201.574	−	30.0420i	0.495267	−	0.0738133i
$408$	27.0640			0.0663332
$409$		−	390.758i		−	0.955399i	−0.878523	−	0.477700i	$-0.841471\pi$
$409$		−	390.758i		−	0.955399i	0.878523	−	0.477700i	$-0.158529\pi$
$410$	84.2565			0.205504
$411$	−42.2460			−0.102788
$412$	−616.120			−1.49544
$413$		−	155.259i		−	0.375930i
$414$		−	105.522i		−	0.254883i
$415$			54.8382i			0.132140i
$416$	−140.260			−0.337164
$417$		−	59.9557i		−	0.143779i
$418$	−153.991	+	22.9504i	−0.368400	+	0.0549053i
$419$	−557.913			−1.33153			−0.665767	−	0.746160i	$-0.731895\pi$
$419$	−557.913			−1.33153			−0.665767	+	0.746160i	$0.731895\pi$
$420$			51.2959i			0.122133i
$421$	415.723			0.987465			0.493732	−	0.869614i	$-0.335632\pi$
$421$	415.723			0.987465			0.493732	+	0.869614i	$0.335632\pi$
$422$	−523.392			−1.24027
$423$	−594.667			−1.40583
$424$			43.5536i			0.102721i
$425$			559.177i			1.31571i
$426$			231.136i			0.542573i
$427$	−446.704			−1.04615
$428$		−	795.366i		−	1.85833i
$429$	5.80833	+	38.9723i	0.0135392	+	0.0908445i
$430$	265.026			0.616339
$431$		−	81.5222i		−	0.189147i	−0.995518	−	0.0945733i	$-0.969851\pi$
$431$		−	81.5222i		−	0.189147i	0.995518	−	0.0945733i	$-0.0301487\pi$
$432$	284.753			0.659150
$433$	−43.8177			−0.101196			−0.0505978	−	0.998719i	$-0.516113\pi$
$433$	−43.8177			−0.101196			−0.0505978	+	0.998719i	$0.516113\pi$
$434$	−553.780			−1.27599
$435$			9.41535i			0.0216445i
$436$		−	574.244i		−	1.31707i
$437$			23.5345i			0.0538547i
$438$	−252.439			−0.576345
$439$		−	525.875i		−	1.19789i	−0.800789	−	0.598946i	$-0.795586\pi$
$439$		−	525.875i		−	1.19789i	0.800789	−	0.598946i	$-0.204414\pi$
$440$	2.47133	+	16.5820i	0.00561666	+	0.0376863i
$441$	−88.0359			−0.199628
$442$		−	221.679i		−	0.501536i
$443$	−289.124			−0.652650			−0.326325	−	0.945258i	$-0.605810\pi$
$443$	−289.124			−0.652650			−0.326325	+	0.945258i	$0.605810\pi$
$444$	−93.7058			−0.211049
$445$	−126.716			−0.284756
$446$			256.579i			0.575289i
$447$			73.1953i			0.163748i
$448$		−	451.475i		−	1.00776i
$449$	362.591			0.807552			0.403776	−	0.914858i	$-0.367697\pi$
$449$	362.591			0.807552			0.403776	+	0.914858i	$0.367697\pi$
$450$		−	489.651i		−	1.08811i
$451$	28.5853	+	191.799i	0.0633820	+	0.425276i
$452$	−633.142			−1.40076
$453$			81.4580i			0.179819i
$454$	1000.50			2.20375
$455$	31.0227			0.0681817
$456$	5.28557			0.0115912
$457$		−	261.369i		−	0.571923i	−0.958241	−	0.285962i	$-0.907687\pi$
$457$		−	261.369i		−	0.571923i	0.958241	−	0.285962i	$-0.0923130\pi$
$458$			145.399i			0.317464i
$459$			489.304i			1.06602i
$460$	34.3227			0.0746146
$461$		−	441.681i		−	0.958093i	−0.877790	−	0.479046i	$-0.840983\pi$
$461$		−	441.681i		−	0.958093i	0.877790	−	0.479046i	$-0.159017\pi$
$462$	−224.916	+	33.5209i	−0.486831	+	0.0725560i
$463$	−466.499			−1.00756			−0.503779	−	0.863833i	$-0.668057\pi$
$463$	−466.499			−1.00756			−0.503779	+	0.863833i	$0.668057\pi$
$464$		−	70.9476i		−	0.152904i
$465$	60.8766			0.130918
$466$	−967.418			−2.07600
$467$	130.596			0.279648			0.139824	−	0.990176i	$-0.455346\pi$
$467$	130.596			0.279648			0.139824	+	0.990176i	$0.455346\pi$
$468$			100.778i			0.215338i
$469$			111.205i			0.237110i
$470$		−	372.570i		−	0.792702i
$471$	−180.539			−0.383311
$472$			23.3315i			0.0494312i
$473$	89.9139	+	603.298i	0.190093	+	1.27547i
$474$	−432.656			−0.912775
$475$			109.207i			0.229909i
$476$	664.193			1.39536
$477$	−361.244			−0.757324
$478$	−9.64232			−0.0201722
$479$			398.256i			0.831432i	0.909494	+	0.415716i	$0.136469\pi$
$479$			398.256i			0.831432i	−0.909494	+	0.415716i	$0.863531\pi$
$480$			88.9841i			0.185384i
$481$			56.6712i			0.117820i
$482$	181.408			0.376366
$483$			34.3739i			0.0711676i
$484$	−499.874	+	152.385i	−1.03280	+	0.314844i
$485$	306.001			0.630931
$486$		−	660.366i		−	1.35878i
$487$	−190.761			−0.391706			−0.195853	−	0.980633i	$-0.562748\pi$
$487$	−190.761			−0.391706			−0.195853	+	0.980633i	$0.562748\pi$
$488$	67.1283			0.137558
$489$	−198.013			−0.404934
$490$		−	55.1561i		−	0.112563i
$491$		−	48.1180i		−	0.0980000i	−0.998799	−	0.0490000i	$-0.984397\pi$
$491$		−	48.1180i		−	0.0980000i	0.998799	−	0.0490000i	$-0.0156034\pi$
$492$		−	89.1620i		−	0.181224i
$493$	121.912			0.247287
$494$		−	43.2937i		−	0.0876391i
$495$	−137.535	+	20.4978i	−0.277848	+	0.0414097i
$496$	−458.724			−0.924847
$497$			418.827i			0.842711i
$498$	111.777			0.224452
$499$	904.074			1.81177			0.905886	−	0.423523i	$-0.139207\pi$
$499$	904.074			1.81177			0.905886	+	0.423523i	$0.139207\pi$
$500$	338.187			0.676374
$501$			91.5690i			0.182772i
$502$			214.246i			0.426784i
$503$			129.317i			0.257092i	0.991704	+	0.128546i	$0.0410310\pi$
$503$			129.317i			0.257092i	−0.991704	+	0.128546i	$0.958969\pi$
$504$	−42.9433			−0.0852049
$505$			314.563i			0.622897i
$506$	22.4292	+	150.494i	0.0443265	+	0.297419i
$507$	186.954			0.368746
$508$			691.204i			1.36064i
$509$	687.922			1.35152			0.675759	−	0.737123i	$-0.263816\pi$
$509$	687.922			1.35152			0.675759	+	0.737123i	$0.263816\pi$
$510$	−140.638			−0.275760
$511$	−457.429			−0.895165
$512$		−	724.319i		−	1.41469i
$513$			95.5608i			0.186278i
$514$			48.0092i			0.0934031i
$515$	236.396			0.459021
$516$		−	280.456i		−	0.543519i
$517$	848.108	−	126.400i	1.64044	−	0.244487i
$518$	−327.060			−0.631389
$519$		−	15.2274i		−	0.0293399i
$520$	−4.66192			−0.00896523
$521$	518.046			0.994330			0.497165	−	0.867656i	$-0.334374\pi$
$521$	518.046			0.994330			0.497165	+	0.867656i	$0.334374\pi$
$522$	−106.754			−0.204510
$523$		−	574.943i		−	1.09932i	−0.835390	−	0.549658i	$-0.814758\pi$
$523$		−	574.943i		−	1.09932i	0.835390	−	0.549658i	$-0.185242\pi$
$524$			296.986i			0.566767i
$525$			159.505i			0.303819i
$526$	721.581			1.37183
$527$		−	788.247i		−	1.49572i
$528$	−186.309	+	27.7670i	−0.352859	+	0.0525891i
$529$	23.0000			0.0434783
$530$		−	226.326i		−	0.427030i
$531$	−193.517			−0.364439
$532$	129.717			0.243828
$533$	−53.9233			−0.101169
$534$			258.287i			0.483683i
$535$			305.169i			0.570410i
$536$		−	16.7112i		−	0.0311777i
$537$	−288.936			−0.538056
$538$			330.890i			0.615038i
$539$	125.556	−	18.7125i	0.232942	−	0.0347171i
$540$	139.366			0.258085
$541$			45.3505i			0.0838271i	0.999121	+	0.0419136i	$0.0133454\pi$
$541$			45.3505i			0.0838271i	−0.999121	+	0.0419136i	$0.986655\pi$
$542$	−911.505			−1.68174
$543$	−87.2549			−0.160690
$544$	1152.19			2.11800
$545$			220.329i			0.404273i
$546$		−	63.2337i		−	0.115813i
$547$			859.116i			1.57060i	0.619118	+	0.785298i	$0.287490\pi$
$547$			859.116i			1.57060i	−0.619118	+	0.785298i	$0.712510\pi$
$548$	155.802			0.284311
$549$			556.778i			1.01417i
$550$	104.078	+	698.335i	0.189233	+	1.26970i
$551$	23.8094			0.0432113
$552$		−	5.16553i		−	0.00935784i
$553$	−783.988			−1.41770
$554$	−119.063			−0.214915
$555$	35.9534			0.0647810
$556$			221.115i			0.397690i
$557$			351.075i			0.630297i	0.949042	+	0.315148i	$0.102054\pi$
$557$			351.075i			0.630297i	−0.949042	+	0.315148i	$0.897946\pi$
$558$			690.238i			1.23699i
$559$	−169.614			−0.303423
$560$			148.306i			0.264832i
$561$	−47.7134	−	320.144i	−0.0850506	−	0.570667i
$562$	−1378.14			−2.45220
$563$			747.611i			1.32791i	0.747774	+	0.663953i	$0.231123\pi$
$563$			747.611i			1.32791i	−0.747774	+	0.663953i	$0.768877\pi$
$564$	−394.261			−0.699044
$565$	242.927			0.429959
$566$	380.785			0.672765
$567$		−	280.639i		−	0.494955i
$568$		−	62.9391i		−	0.110808i
$569$		−	385.647i		−	0.677763i	−0.940829	−	0.338882i	$-0.889951\pi$
$569$		−	385.647i		−	0.677763i	0.940829	−	0.338882i	$-0.110049\pi$
$570$	−27.4665			−0.0481868
$571$		−	152.707i		−	0.267438i	−0.991019	−	0.133719i	$-0.957308\pi$
$571$		−	152.707i		−	0.267438i	0.991019	−	0.133719i	$-0.0426919\pi$
$572$	−21.4210	−	143.729i	−0.0374493	−	0.251275i
$573$	18.1733			0.0317160
$574$		−	311.200i		−	0.542161i
$575$	106.727			0.185612
$576$	−562.725			−0.976952
$577$	728.808			1.26310			0.631549	−	0.775336i	$-0.282419\pi$
$577$	728.808			1.26310			0.631549	+	0.775336i	$0.282419\pi$
$578$			987.467i			1.70842i
$579$			311.009i			0.537149i
$580$		−	34.7237i		−	0.0598684i
$581$	202.544			0.348613
$582$		−	623.725i		−	1.07169i
$583$	515.202	−	76.7844i	0.883709	−	0.131706i
$584$	68.7400			0.117705
$585$		−	38.6671i		−	0.0660976i
$586$	1347.80			2.30000
$587$	−461.419			−0.786064			−0.393032	−	0.919525i	$-0.628574\pi$
$587$	−461.419			−0.786064			−0.393032	+	0.919525i	$0.628574\pi$
$588$	−58.3673			−0.0992641
$589$		−	153.944i		−	0.261365i
$590$		−	121.242i		−	0.205495i
$591$			99.3272i			0.168066i
$592$	−270.920			−0.457635
$593$			126.494i			0.213312i	0.994296	+	0.106656i	$0.0340143\pi$
$593$			126.494i			0.213312i	−0.994296	+	0.106656i	$0.965986\pi$
$594$	91.0727	+	611.073i	0.153321	+	1.02874i
$595$	−254.841			−0.428304
$596$		−	269.943i		−	0.452924i
$597$	−176.684			−0.295952
$598$	−42.3104			−0.0707532
$599$	−756.383			−1.26274			−0.631371	−	0.775481i	$-0.717508\pi$
$599$	−756.383			−1.26274			−0.631371	+	0.775481i	$0.717508\pi$
$600$		−	23.9696i		−	0.0399493i
$601$			831.429i			1.38341i	0.722181	+	0.691704i	$0.243140\pi$
$601$			831.429i			1.38341i	−0.722181	+	0.691704i	$0.756860\pi$
$602$		−	978.870i		−	1.62603i
$603$	138.607			0.229862
$604$		−	300.416i		−	0.497377i
$605$	191.794	−	58.4676i	0.317015	−	0.0966406i
$606$	641.176			1.05805
$607$			626.145i			1.03154i	0.856727	+	0.515770i	$0.172494\pi$
$607$			626.145i			1.03154i	−0.856727	+	0.515770i	$0.827506\pi$
$608$	225.022			0.370102
$609$	34.7755			0.0571026
$610$	−348.832			−0.571856
$611$			238.441i			0.390246i
$612$		−	827.860i		−	1.35271i
$613$		−	801.151i		−	1.30693i	−0.756955	−	0.653467i	$-0.773314\pi$
$613$		−	801.151i		−	1.30693i	0.756955	−	0.653467i	$-0.226686\pi$
$614$	246.472			0.401420
$615$			34.2101i			0.0556261i
$616$	61.2453	−	9.12783i	0.0994241	−	0.0148179i
$617$	707.635			1.14690			0.573448	−	0.819242i	$-0.305605\pi$
$617$	707.635			1.14690			0.573448	+	0.819242i	$0.305605\pi$
$618$		−	481.847i		−	0.779687i
$619$	−436.085			−0.704499			−0.352250	−	0.935906i	$-0.614583\pi$
$619$	−436.085			−0.704499			−0.352250	+	0.935906i	$0.614583\pi$
$620$	−224.512			−0.362116
$621$	93.3904			0.150387
$622$			672.777i			1.08164i
$623$			468.025i			0.751244i
$624$		−	52.3798i		−	0.0839419i
$625$	426.594			0.682551
$626$			450.719i			0.719999i
$627$	−9.31840	−	62.5239i	−0.0148619	−	0.0997192i
$628$	665.826			1.06023
$629$		−	465.535i		−	0.740119i
$630$	223.154			0.354213
$631$	−134.767			−0.213577			−0.106788	−	0.994282i	$-0.534057\pi$
$631$	−134.767			−0.213577			−0.106788	+	0.994282i	$0.534057\pi$
$632$	117.813			0.186414
$633$		−	212.509i		−	0.335718i
$634$		−	423.617i		−	0.668165i
$635$		−	265.204i		−	0.417644i
$636$	−239.503			−0.376577
$637$			35.2993i			0.0554149i
$638$	152.252	−	22.6912i	0.238639	−	0.0355661i
$639$	522.032			0.816952
$640$		−	48.6163i		−	0.0759629i
$641$	−385.943			−0.602096			−0.301048	−	0.953609i	$-0.597336\pi$
$641$	−385.943			−0.602096			−0.301048	+	0.953609i	$0.597336\pi$
$642$	622.029			0.968892
$643$	946.698			1.47231			0.736157	−	0.676811i	$-0.236639\pi$
$643$	946.698			1.47231			0.736157	+	0.676811i	$0.236639\pi$
$644$		−	126.770i		−	0.196849i
$645$			107.607i			0.166832i
$646$			355.643i			0.550531i
$647$	−860.117			−1.32939			−0.664697	−	0.747113i	$-0.731439\pi$
$647$	−860.117			−1.32939			−0.664697	+	0.747113i	$0.731439\pi$
$648$			42.1729i			0.0650817i
$649$	275.992	−	41.1332i	0.425258	−	0.0633793i
$650$	−196.333			−0.302050
$651$		−	224.847i		−	0.345387i
$652$	730.268			1.12004
$653$	−402.737			−0.616749			−0.308374	−	0.951265i	$-0.599785\pi$
$653$	−402.737			−0.616749			−0.308374	+	0.951265i	$0.599785\pi$
$654$	449.097			0.686693
$655$		−	113.949i		−	0.173968i
$656$		−	257.783i		−	0.392962i
$657$			570.146i			0.867802i
$658$	−1376.08			−2.09131
$659$			543.997i			0.825489i	0.910847	+	0.412744i	$0.135430\pi$
$659$			543.997i			0.825489i	−0.910847	+	0.412744i	$0.864570\pi$
$660$	−91.1849	+	13.5899i	−0.138159	+	0.0205908i
$661$	305.677			0.462446			0.231223	−	0.972901i	$-0.425727\pi$
$661$	305.677			0.462446			0.231223	+	0.972901i	$0.425727\pi$
$662$			528.086i			0.797713i
$663$	90.0066			0.135757
$664$	−30.4372			−0.0458392
$665$	−49.7702			−0.0748424
$666$			407.651i			0.612089i
$667$		−	23.2687i		−	0.0348856i
$668$		−	337.705i		−	0.505546i
$669$	−104.177			−0.155720
$670$			86.8399i			0.129612i
$671$	−118.346	−	794.072i	−0.176373	−	1.18342i
$672$	328.662			0.489080
$673$		−	1014.28i		−	1.50711i	−0.657387	−	0.753553i	$-0.728339\pi$
$673$		−	1014.28i		−	1.50711i	0.657387	−	0.753553i	$-0.271661\pi$
$674$	1187.87			1.76242
$675$	433.359			0.642013
$676$	−689.483			−1.01995
$677$			611.117i			0.902683i	0.892351	+	0.451342i	$0.149054\pi$
$677$			611.117i			0.902683i	−0.892351	+	0.451342i	$0.850946\pi$
$678$		−	495.159i		−	0.730323i
$679$		−	1130.21i		−	1.66452i
$680$	38.2961			0.0563178
$681$			406.227i			0.596515i
$682$	−146.714	−	984.411i	−0.215123	−	1.44342i
$683$	660.065			0.966420			0.483210	−	0.875504i	$-0.339471\pi$
$683$	660.065			0.966420			0.483210	+	0.875504i	$0.339471\pi$
$684$		−	161.680i		−	0.236375i
$685$	−59.7789			−0.0872685
$686$	−1068.71			−1.55788
$687$	−59.0351			−0.0859318
$688$		−	810.848i		−	1.17856i
$689$			144.846i			0.210227i
$690$			26.8426i			0.0389024i
$691$	541.449			0.783573			0.391786	−	0.920056i	$-0.371857\pi$
$691$	541.449			0.783573			0.391786	+	0.920056i	$0.371857\pi$
$692$			56.1584i			0.0811538i
$693$	75.7084	+	507.983i	0.109247	+	0.733020i
$694$	−1612.01			−2.32278
$695$		−	84.8385i		−	0.122070i
$696$	−5.22587			−0.00750843
$697$	442.961			0.635525
$698$	816.719			1.17008
$699$		−	392.794i		−	0.561937i
$700$		−	588.252i		−	0.840360i
$701$			717.893i			1.02410i	0.858956	+	0.512049i	$0.171114\pi$
$701$			717.893i			1.02410i	−0.858956	+	0.512049i	$0.828886\pi$
$702$	−171.800			−0.244729
$703$		−	90.9186i		−	0.129330i
$704$	802.553	−	119.610i	1.13999	−	0.169901i
$705$	151.272			0.214570
$706$		−	1406.30i		−	1.99192i
$707$	1161.83			1.64333
$708$	−128.301			−0.181216
$709$	−1035.02			−1.45983			−0.729915	−	0.683538i	$-0.760440\pi$
$709$	−1035.02			−1.45983			−0.729915	+	0.683538i	$0.760440\pi$
$710$			327.063i			0.460652i
$711$			977.173i			1.37436i
$712$		−	70.3323i		−	0.0987813i
$713$	−150.448			−0.211007
$714$			519.444i			0.727512i
$715$	8.21891	+	55.1466i	0.0114950	+	0.0771282i
$716$	1065.59			1.48825
$717$		−	3.91500i		−	0.00546025i
$718$	654.643			0.911760
$719$	648.422			0.901839			0.450919	−	0.892565i	$-0.351096\pi$
$719$	648.422			0.901839			0.450919	+	0.892565i	$0.351096\pi$
$720$	184.850			0.256736
$721$		−	873.124i		−	1.21099i
$722$		−	971.757i		−	1.34592i
$723$			73.6560i			0.101875i
$724$	321.795			0.444468
$725$		−	107.973i		−	0.148929i
$726$	−119.175	−	390.935i	−0.164153	−	0.538478i
$727$	708.930			0.975144			0.487572	−	0.873083i	$-0.337883\pi$
$727$	708.930			0.975144			0.487572	+	0.873083i	$0.337883\pi$
$728$			17.2187i			0.0236521i
$729$	−144.552			−0.198288
$730$	−357.207			−0.489325
$731$	1393.32			1.90604
$732$			369.141i			0.504291i
$733$		−	1341.94i		−	1.83075i	−0.402600	−	0.915376i	$-0.631893\pi$
$733$		−	1341.94i		−	1.83075i	0.402600	−	0.915376i	$-0.368107\pi$
$734$			1086.00i			1.47956i
$735$	22.3946			0.0304689
$736$		−	219.911i		−	0.298793i
$737$	−197.680	+	29.4617i	−0.268223	+	0.0399752i
$738$	−387.884			−0.525589
$739$		−	235.678i		−	0.318914i	−0.987205	−	0.159457i	$-0.949026\pi$
$739$		−	235.678i		−	0.318914i	0.987205	−	0.159457i	$-0.0509744\pi$
$740$	−132.596			−0.179183
$741$	17.5782			0.0237223
$742$	−835.932			−1.12659
$743$			399.726i			0.537989i	0.963142	+	0.268995i	$0.0866914\pi$
$743$			399.726i			0.537989i	−0.963142	+	0.268995i	$0.913309\pi$
$744$			33.7888i			0.0454150i
$745$			103.573i			0.139024i
$746$	−844.456			−1.13198
$747$		−	252.454i		−	0.337957i
$748$	175.966	+	1180.69i	0.235249	+	1.57846i
$749$	1127.14			1.50486
$750$			264.485i			0.352646i
$751$	−700.840			−0.933209			−0.466605	−	0.884466i	$-0.654523\pi$
$751$	−700.840			−0.933209			−0.466605	+	0.884466i	$0.654523\pi$
$752$	−1139.88			−1.51580
$753$	−86.9886			−0.115523
$754$			42.8047i			0.0567702i
$755$			115.265i			0.152669i
$756$		−	514.746i		−	0.680880i
$757$	−1340.58			−1.77091			−0.885456	−	0.464724i	$-0.846154\pi$
$757$	−1340.58			−1.77091			−0.885456	+	0.464724i	$0.846154\pi$
$758$			548.966i			0.724229i
$759$	−61.1039	+	9.10676i	−0.0805058	+	0.0119984i
$760$	7.47920			0.00984105
$761$			1027.25i			1.34987i	0.737878	+	0.674934i	$0.235828\pi$
$761$			1027.25i			1.34987i	−0.737878	+	0.674934i	$0.764172\pi$
$762$	−540.567			−0.709406
$763$	813.781			1.06655
$764$	−67.0227			−0.0877260
$765$			317.637i			0.415212i
$766$			1134.59i			1.48119i
$767$			77.5936i			0.101165i
$768$	246.442			0.320888
$769$			1352.09i			1.75824i	0.476601	+	0.879120i	$0.341869\pi$
$769$			1352.09i			1.75824i	−0.476601	+	0.879120i	$0.658131\pi$
$770$	−318.261	+	47.4327i	−0.413326	+	0.0616009i
$771$	−19.4928			−0.0252825
$772$		−	1147.00i		−	1.48575i
$773$	−156.235			−0.202116			−0.101058	−	0.994881i	$-0.532223\pi$
$773$	−156.235			−0.202116			−0.101058	+	0.994881i	$0.532223\pi$
$774$	−1220.08			−1.57633
$775$	−698.121			−0.900802
$776$			169.842i			0.218869i
$777$		−	132.794i		−	0.170906i
$778$		−	764.852i		−	0.983100i
$779$	86.5100			0.111053
$780$		−	25.6361i		−	0.0328668i
$781$	−744.517	+	110.961i	−0.953287	+	0.142075i
$782$	347.566			0.444457
$783$		−	94.4814i		−	0.120666i
$784$	−168.750			−0.215243
$785$	−255.467			−0.325436
$786$	−232.263			−0.295500
$787$			940.332i			1.19483i	0.801932	+	0.597415i	$0.203806\pi$
$787$			940.332i			1.19483i	−0.801932	+	0.597415i	$0.796194\pi$
$788$		−	366.317i		−	0.464869i
$789$			292.978i			0.371329i
$790$	−612.217			−0.774958
$791$		−	897.246i		−	1.13432i
$792$	−11.3770	−	76.3369i	−0.0143650	−	0.0963850i
$793$	223.249			0.281524
$794$			2024.09i			2.54924i
$795$	91.8934			0.115589
$796$	651.606			0.818600
$797$	372.320			0.467151			0.233576	−	0.972339i	$-0.424957\pi$
$797$	372.320			0.467151			0.233576	+	0.972339i	$0.424957\pi$
$798$			101.447i			0.127127i
$799$		−	1958.71i		−	2.45145i
$800$		−	1020.45i		−	1.27557i
$801$	583.353			0.728281
$802$		−	718.517i		−	0.895907i
$803$	−121.188	−	813.137i	−0.150919	−	1.01262i
$804$	91.8957			0.114298
$805$			48.6399i			0.0604222i
$806$	276.761			0.343376
$807$	−134.349			−0.166480
$808$	−174.594			−0.216082
$809$		−	1092.39i		−	1.35030i	−0.737680	−	0.675150i	$-0.764079\pi$
$809$		−	1092.39i		−	1.35030i	0.737680	−	0.675150i	$-0.235921\pi$
$810$		−	219.152i		−	0.270557i
$811$			971.750i			1.19821i	0.800670	+	0.599106i	$0.204477\pi$
$811$			971.750i			1.19821i	−0.800670	+	0.599106i	$0.795523\pi$
$812$	−128.251			−0.157945
$813$		−	370.092i		−	0.455217i
$814$	−86.6486	−	581.389i	−0.106448	−	0.714237i
$815$	−280.193			−0.343795
$816$			430.282i			0.527306i
$817$	272.114			0.333065
$818$	−1127.04			−1.37780
$819$	−142.816			−0.174379
$820$		−	126.166i		−	0.153861i
$821$			1040.33i			1.26715i	0.773683	+	0.633573i	$0.218412\pi$
$821$			1040.33i			1.26715i	−0.773683	+	0.633573i	$0.781588\pi$
$822$			121.848i			0.148233i
$823$	−1485.96			−1.80554			−0.902771	−	0.430121i	$-0.858471\pi$
$823$	−1485.96			−1.80554			−0.902771	+	0.430121i	$0.858471\pi$
$824$			131.208i			0.159233i
$825$	−283.540	+	42.2580i	−0.343685	+	0.0512218i
$826$	−447.806			−0.542138
$827$			807.164i			0.976014i	0.872840	+	0.488007i	$0.162276\pi$
$827$			807.164i			0.976014i	−0.872840	+	0.488007i	$0.837724\pi$
$828$	−158.008			−0.190831
$829$	14.3542			0.0173150			0.00865751	−	0.999963i	$-0.497244\pi$
$829$	14.3542			0.0173150			0.00865751	+	0.999963i	$0.497244\pi$
$830$	158.167			0.190563
$831$		−	48.3423i		−	0.0581737i
$832$			225.633i			0.271193i
$833$		−	289.972i		−	0.348105i
$834$	−172.927			−0.207346
$835$			129.572i			0.155176i
$836$	34.3661	+	230.587i	0.0411078	+	0.275822i
$837$	−610.886			−0.729852
$838$			1609.16i			1.92024i
$839$	−199.429			−0.237698			−0.118849	−	0.992912i	$-0.537920\pi$
$839$	−199.429			−0.237698			−0.118849	+	0.992912i	$0.537920\pi$
$840$	10.9239			0.0130047
$841$	817.460			0.972009
$842$		−	1199.05i		−	1.42405i
$843$		−	559.555i		−	0.663766i
$844$			783.730i			0.928590i
$845$	264.544			0.313070
$846$			1715.17i			2.02738i
$847$	−215.949	−	708.388i	−0.254958	−	0.836350i
$848$	−692.445			−0.816563
$849$			154.607i			0.182105i
$850$	1612.81			1.89742
$851$	−88.8537			−0.104411
$852$	346.104			0.406226
$853$		−	618.754i		−	0.725386i	−0.931909	−	0.362693i	$-0.881857\pi$
$853$		−	618.754i		−	0.725386i	0.931909	−	0.362693i	$-0.118143\pi$
$854$			1288.41i			1.50867i
$855$			62.0343i			0.0725547i
$856$	−169.380			−0.197874
$857$			1278.14i			1.49141i	0.666274	+	0.745707i	$0.267888\pi$
$857$			1278.14i			1.49141i	−0.666274	+	0.745707i	$0.732112\pi$
$858$	112.406	−	16.7527i	0.131009	−	0.0195252i
$859$	1110.98			1.29334			0.646668	−	0.762772i	$-0.276162\pi$
$859$	1110.98			1.29334			0.646668	+	0.762772i	$0.276162\pi$
$860$		−	396.851i		−	0.461455i
$861$	126.354			0.146753
$862$	−235.130			−0.272773
$863$	1138.04			1.31870			0.659351	−	0.751835i	$-0.270831\pi$
$863$	1138.04			1.31870			0.659351	+	0.751835i	$0.270831\pi$
$864$		−	892.940i		−	1.03349i
$865$		−	21.5471i		−	0.0249100i
$866$			126.381i			0.145937i
$867$	−400.934			−0.462438
$868$			829.232i			0.955336i
$869$	−207.704	−	1393.63i	−0.239014	−	1.60372i
$870$	27.1562			0.0312140
$871$		−	55.5766i		−	0.0638078i
$872$	−122.291			−0.140241
$873$	−1408.71			−1.61364
$874$	67.8794			0.0776652
$875$			479.256i			0.547721i
$876$			378.004i			0.431511i
$877$			757.268i			0.863475i	0.901999	+	0.431738i	$0.142099\pi$
$877$			757.268i			0.863475i	−0.901999	+	0.431738i	$0.857901\pi$
$878$	−1516.75			−1.72751
$879$			547.237i			0.622567i
$880$	−263.632	+	39.2910i	−0.299582	+	0.0446488i
$881$	−607.629			−0.689703			−0.344852	−	0.938657i	$-0.612071\pi$
$881$	−607.629			−0.689703			−0.344852	+	0.938657i	$0.612071\pi$
$882$			253.917i			0.287888i
$883$	774.611			0.877249			0.438624	−	0.898671i	$-0.355466\pi$
$883$	774.611			0.877249			0.438624	+	0.898671i	$0.355466\pi$
$884$	−331.943			−0.375501
$885$	49.2271			0.0556238
$886$			833.906i			0.941203i
$887$			1609.17i			1.81417i	0.420948	+	0.907085i	$0.361697\pi$
$887$			1609.17i			1.81417i	−0.420948	+	0.907085i	$0.638303\pi$
$888$			19.9555i			0.0224724i
$889$	−979.528			−1.10183
$890$			365.481i			0.410653i
$891$	498.871	−	74.3504i	0.559900	−	0.0834460i
$892$	384.202			0.430720
$893$		−	382.534i		−	0.428370i
$894$	211.113			0.236145
$895$	−408.850			−0.456816
$896$	−179.564			−0.200406
$897$		−	17.1790i		−	0.0191516i
$898$		−	1045.80i		−	1.16459i
$899$			152.205i			0.169305i
$900$	−733.205			−0.814672
$901$		−	1189.86i		−	1.32060i
$902$	553.197	−	82.4470i	0.613301	−	0.0914046i
$903$	397.443			0.440137
$904$			134.833i			0.149152i
$905$	−123.468			−0.136428
$906$	234.945			0.259321
$907$	−1777.40			−1.95965			−0.979823	−	0.199868i	$-0.935949\pi$
$907$	−1777.40			−1.95965			−0.979823	+	0.199868i	$0.935949\pi$
$908$		−	1498.16i		−	1.64995i
$909$		−	1448.13i		−	1.59310i
$910$		−	89.4771i		−	0.0983265i
$911$	93.9112			0.103086			0.0515429	−	0.998671i	$-0.483586\pi$
$911$	93.9112			0.103086			0.0515429	+	0.998671i	$0.483586\pi$
$912$			84.0337i			0.0921423i
$913$	53.6604	+	360.047i	0.0587738	+	0.394356i
$914$	−753.853			−0.824784
$915$		−	141.634i		−	0.154791i
$916$	217.721			0.237686
$917$	−420.869			−0.458962
$918$	1411.27			1.53734
$919$		−	609.231i		−	0.662928i	−0.943468	−	0.331464i	$-0.892458\pi$
$919$		−	609.231i		−	0.662928i	0.943468	−	0.331464i	$-0.107542\pi$
$920$		−	7.30933i		−	0.00794493i
$921$			100.073i			0.108657i
$922$	−1273.92			−1.38169
$923$		−	209.317i		−	0.226778i
$924$	50.1943	+	336.790i	0.0543228	+	0.364491i
$925$	−412.307			−0.445738
$926$			1345.50i			1.45302i
$927$	−1088.27			−1.17397
$928$	−222.480			−0.239742
$929$	−430.888			−0.463820			−0.231910	−	0.972737i	$-0.574497\pi$
$929$	−430.888			−0.463820			−0.231910	+	0.972737i	$0.574497\pi$
$930$		−	175.583i		−	0.188799i
$931$		−	56.6313i		−	0.0608284i
$932$			1448.62i			1.55431i
$933$	−273.163			−0.292779
$934$		−	376.671i		−	0.403288i
$935$	−67.5155	−	453.011i	−0.0722091	−	0.484503i
$936$	21.4617			0.0229291
$937$		−	256.899i		−	0.274171i	−0.990559	−	0.137086i	$-0.956226\pi$
$937$		−	256.899i		−	0.274171i	0.990559	−	0.137086i	$-0.0437736\pi$
$938$	320.742			0.341942
$939$	−183.002			−0.194891
$940$	−557.888			−0.593498
$941$		−	217.737i		−	0.231389i	−0.993285	−	0.115695i	$-0.963091\pi$
$941$		−	217.737i		−	0.231389i	0.993285	−	0.115695i	$-0.0369094\pi$
$942$			520.721i			0.552782i
$943$		−	84.5452i		−	0.0896556i
$944$	−370.941			−0.392946
$945$			197.500i			0.208995i
$946$	1740.06	−	259.334i	1.83939	−	0.274137i
$947$	1628.47			1.71961			0.859806	−	0.510620i	$-0.170584\pi$
$947$	1628.47			1.71961			0.859806	+	0.510620i	$0.170584\pi$
$948$			647.860i			0.683397i
$949$	228.609			0.240894
$950$	314.980			0.331558
$951$	171.998			0.180860
$952$		−	141.446i		−	0.148578i
$953$		−	616.501i		−	0.646906i	−0.946244	−	0.323453i	$-0.895156\pi$
$953$		−	616.501i		−	0.646906i	0.946244	−	0.323453i	$-0.104844\pi$
$954$			1041.92i			1.09216i
$955$	25.7156			0.0269273
$956$			14.4385i			0.0151030i
$957$	9.21314	+	61.8177i	0.00962711	+	0.0645953i
$958$	1148.67			1.19903
$959$			220.793i			0.230232i
$960$	143.146			0.149111
$961$	23.1101			0.0240480
$962$	163.454			0.169911
$963$		−	1404.88i		−	1.45886i
$964$		−	271.642i		−	0.281786i
$965$			440.085i			0.456047i
$966$	99.1430			0.102632
$967$			572.952i			0.592505i	0.955110	+	0.296253i	$0.0957370\pi$
$967$			572.952i			0.592505i	−0.955110	+	0.296253i	$0.904263\pi$
$968$	32.4517	+	106.453i	0.0335245	+	0.109972i
$969$	−144.399			−0.149019
$970$		−	882.584i		−	0.909880i
$971$	645.379			0.664654			0.332327	−	0.943164i	$-0.392166\pi$
$971$	645.379			0.664654			0.332327	+	0.943164i	$0.392166\pi$
$972$	−988.835			−1.01732
$973$	−313.350			−0.322045
$974$			550.201i			0.564888i
$975$		−	79.7155i		−	0.0817595i
$976$			1067.25i			1.09350i
$977$	1497.06			1.53231			0.766153	−	0.642658i	$-0.222168\pi$
$977$	1497.06			1.53231			0.766153	+	0.642658i	$0.222168\pi$
$978$			571.118i			0.583966i
$979$	−831.973	+	123.995i	−0.849819	+	0.126655i
$980$	−82.5910			−0.0842765
$981$		−	1014.31i		−	1.03395i
$982$	−138.784			−0.141328
$983$	1233.58			1.25491			0.627457	−	0.778651i	$-0.284096\pi$
$983$	1233.58			1.25491			0.627457	+	0.778651i	$0.284096\pi$
$984$	−18.9879			−0.0192966
$985$			140.550i			0.142691i
$986$		−	351.626i		−	0.356619i
$987$		−	558.720i		−	0.566079i
$988$	−64.8282			−0.0656156
$989$		−	265.934i		−	0.268892i
$990$	59.1208	+	396.684i	0.0597180	+	0.400691i
$991$	789.236			0.796403			0.398202	−	0.917298i	$-0.369634\pi$
$991$	789.236			0.796403			0.398202	+	0.917298i	$0.369634\pi$
$992$			1438.49i			1.45009i
$993$	−214.415			−0.215927
$994$	1208.00			1.21529
$995$	−250.011			−0.251267
$996$		−	167.375i		−	0.168048i
$997$		−	872.590i		−	0.875216i	−0.899166	−	0.437608i	$-0.855826\pi$
$997$		−	872.590i		−	0.875216i	0.899166	−	0.437608i	$-0.144174\pi$
$998$		−	2607.57i		−	2.61280i
$999$	−360.786			−0.361148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.7	✓	44
11.10	odd	2	inner	253.3.c.a.208.38	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.7	✓	44	1.1	even	1	trivial
253.3.c.a.208.38	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.88425i q^{2} +1.17107 q^{3} -4.31889 q^{4} +1.65709 q^{5} -3.37766i q^{6} -6.12044i q^{7} +0.919746i q^{8} -7.62859 q^{9} -4.77946i q^{10} +(10.8798 - 1.62150i) q^{11} -5.05772 q^{12} +3.05880i q^{13} -17.6529 q^{14} +1.94057 q^{15} -14.6228 q^{16} -25.1270i q^{17} +22.0028i q^{18} -4.90728i q^{19} -7.15678 q^{20} -7.16746i q^{21} +(-4.67681 - 31.3801i) q^{22} -4.79583 q^{23} +1.07709i q^{24} -22.2541 q^{25} +8.82234 q^{26} -19.4733 q^{27} +26.4335i q^{28} +4.85186i q^{29} -5.59708i q^{30} +31.3705 q^{31} +45.8547i q^{32} +(12.7410 - 1.89889i) q^{33} -72.4725 q^{34} -10.1421i q^{35} +32.9470 q^{36} +18.5273 q^{37} -14.1538 q^{38} +3.58207i q^{39} +1.52410i q^{40} +17.6289i q^{41} -20.6727 q^{42} +55.4511i q^{43} +(-46.9888 + 7.00308i) q^{44} -12.6413 q^{45} +13.8324i q^{46} +77.9523 q^{47} -17.1243 q^{48} +11.5402 q^{49} +64.1862i q^{50} -29.4255i q^{51} -13.2106i q^{52} +47.3539 q^{53} +56.1657i q^{54} +(18.0289 - 2.68697i) q^{55} +5.62925 q^{56} -5.74677i q^{57} +13.9940 q^{58} +25.3673 q^{59} -8.38109 q^{60} -72.9857i q^{61} -90.4804i q^{62} +46.6903i q^{63} +73.7652 q^{64} +5.06870i q^{65} +(-5.47687 - 36.7483i) q^{66} -18.1694 q^{67} +108.521i q^{68} -5.61625 q^{69} -29.2524 q^{70} -68.4310 q^{71} -7.01637i q^{72} -74.7380i q^{73} -53.4373i q^{74} -26.0611 q^{75} +21.1940i q^{76} +(-9.92429 - 66.5893i) q^{77} +10.3316 q^{78} -128.093i q^{79} -24.2312 q^{80} +45.8528 q^{81} +50.8461 q^{82} +33.0931i q^{83} +30.9554i q^{84} -41.6377i q^{85} +159.935 q^{86} +5.68186i q^{87} +(1.49137 + 10.0067i) q^{88} -76.4692 q^{89} +36.4605i q^{90} +18.7212 q^{91} +20.7126 q^{92} +36.7371 q^{93} -224.834i q^{94} -8.13181i q^{95} +53.6990i q^{96} +184.662 q^{97} -33.2849i q^{98} +(-82.9978 + 12.3698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 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