LMFDB - Embedded newform 29.10.b.a.28.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,Mod(28,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.28");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	29.b (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:	$14.9360392488$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			28.3
Character	$\chi$	$=$	29.28
Dual form			29.10.b.a.28.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-37.8978i q^{2} -104.304i q^{3} -924.245 q^{4} -2682.94 q^{5} -3952.89 q^{6} +4793.67 q^{7} +15623.2i q^{8} +8803.72 q^{9} +O(q^{10})$	\(q-37.8978i q^{2} -104.304i q^{3} -924.245 q^{4} -2682.94 q^{5} -3952.89 q^{6} +4793.67 q^{7} +15623.2i q^{8} +8803.72 q^{9} +101678. i q^{10} -53533.4i q^{11} +96402.2i q^{12} -65912.0 q^{13} -181670. i q^{14} +279841. i q^{15} +118871. q^{16} -91109.1i q^{17} -333642. i q^{18} +562353. i q^{19} +2.47970e6 q^{20} -499998. i q^{21} -2.02880e6 q^{22} -22800.0 q^{23} +1.62956e6 q^{24} +5.24507e6 q^{25} +2.49792e6i q^{26} -2.97127e6i q^{27} -4.43052e6 q^{28} +(-3.34566e6 + 1.82036e6i) q^{29} +1.06054e7 q^{30} +771940. i q^{31} +3.49412e6i q^{32} -5.58374e6 q^{33} -3.45283e6 q^{34} -1.28612e7 q^{35} -8.13679e6 q^{36} +1.39331e7i q^{37} +2.13120e7 q^{38} +6.87487e6i q^{39} -4.19161e7i q^{40} +1.80833e7i q^{41} -1.89488e7 q^{42} -1.71895e7i q^{43} +4.94780e7i q^{44} -2.36199e7 q^{45} +864068. i q^{46} -4.69934e7i q^{47} -1.23987e7i q^{48} -1.73743e7 q^{49} -1.98777e8i q^{50} -9.50302e6 q^{51} +6.09188e7 q^{52} +4.76701e7 q^{53} -1.12605e8 q^{54} +1.43627e8i q^{55} +7.48923e7i q^{56} +5.86556e7 q^{57} +(6.89877e7 + 1.26793e8i) q^{58} -1.64817e8 q^{59} -2.58642e8i q^{60} +1.71039e8i q^{61} +2.92548e7 q^{62} +4.22021e7 q^{63} +1.93281e8 q^{64} +1.76838e8 q^{65} +2.11612e8i q^{66} -3.13045e8 q^{67} +8.42071e7i q^{68} +2.37812e6i q^{69} +4.87410e8i q^{70} -1.66663e8 q^{71} +1.37542e8i q^{72} -2.67257e7i q^{73} +5.28035e8 q^{74} -5.47080e8i q^{75} -5.19752e8i q^{76} -2.56622e8i q^{77} +2.60543e8 q^{78} -5.08030e8i q^{79} -3.18924e8 q^{80} -1.36631e8 q^{81} +6.85318e8 q^{82} -4.73692e7 q^{83} +4.62120e8i q^{84} +2.44441e8i q^{85} -6.51446e8 q^{86} +(1.89870e8 + 3.48965e8i) q^{87} +8.36362e8 q^{88} -8.92144e8i q^{89} +8.95142e8i q^{90} -3.15960e8 q^{91} +2.10727e7 q^{92} +8.05163e7 q^{93} -1.78095e9 q^{94} -1.50876e9i q^{95} +3.64450e8 q^{96} +6.96072e8i q^{97} +6.58449e8i q^{98} -4.71293e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) $ 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9	$ 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) $ 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9 - 244222 * q^13 + 1246804 * q^16 - 1658748 * q^20 + 822328 * q^22 - 874956 * q^23 + 8668172 * q^24 + 5307748 * q^25 - 620352 * q^28 - 2425374 * q^29 - 8942448 * q^30 + 10134274 * q^33 - 37785784 * q^34 - 20790348 * q^35 + 34550680 * q^36 - 30663552 * q^38 + 56872008 * q^42 - 43877176 * q^45 - 131743922 * q^49 - 6194732 * q^51 + 342496580 * q^52 + 34886610 * q^53 + 116488784 * q^54 - 308361676 * q^57 + 342193888 * q^58 + 175799052 * q^59 - 484313328 * q^62 - 190643424 * q^63 - 419498924 * q^64 - 149739966 * q^65 - 508277640 * q^67 + 263144256 * q^71 + 435201408 * q^74 + 1065897336 * q^78 + 2990464236 * q^80 - 129895134 * q^81 - 527065064 * q^82 + 1555989756 * q^83 - 3422424120 * q^86 + 2176720604 * q^87 - 387386068 * q^88 - 1493579244 * q^91 - 1262849472 * q^92 + 2042413382 * q^93 + 166226488 * q^94 - 6686432820 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	37.8978i		−	1.67486i	−0.546543	−	0.837431i	$-0.684056\pi$
$2$		−	37.8978i		−	1.67486i	0.546543	−	0.837431i	$-0.315944\pi$
$3$		−	104.304i		−	0.743455i	−0.928342	−	0.371727i	$-0.878766\pi$
$3$		−	104.304i		−	0.743455i	0.928342	−	0.371727i	$-0.121234\pi$
$4$	−924.245			−1.80517
$5$	−2682.94			−1.91976			−0.959879	−	0.280413i	$-0.909528\pi$
$5$	−2682.94			−1.91976			−0.959879	+	0.280413i	$0.909528\pi$
$6$	−3952.89			−1.24518
$7$	4793.67			0.754618			0.377309	−	0.926087i	$-0.376850\pi$
$7$	4793.67			0.754618			0.377309	+	0.926087i	$0.376850\pi$
$8$			15623.2i			1.34854i
$9$	8803.72			0.447275
$10$			101678.i			3.21533i
$11$		−	53533.4i		−	1.10245i	−0.834357	−	0.551224i	$-0.814161\pi$
$11$		−	53533.4i		−	1.10245i	0.834357	−	0.551224i	$-0.185839\pi$
$12$			96402.2i			1.34206i
$13$	−65912.0			−0.640058			−0.320029	−	0.947408i	$-0.603693\pi$
$13$	−65912.0			−0.640058			−0.320029	+	0.947408i	$0.603693\pi$
$14$		−	181670.i		−	1.26388i
$15$			279841.i			1.42725i
$16$	118871.			0.453456
$17$		−	91109.1i		−	0.264571i	−0.991212	−	0.132285i	$-0.957769\pi$
$17$		−	91109.1i		−	0.264571i	0.991212	−	0.132285i	$-0.0422315\pi$
$18$		−	333642.i		−	0.749125i
$19$			562353.i			0.989961i	0.868904	+	0.494980i	$0.164825\pi$
$19$			562353.i			0.989961i	−0.868904	+	0.494980i	$0.835175\pi$
$20$	2.47970e6			3.46548
$21$		−	499998.i		−	0.561024i
$22$	−2.02880e6			−1.84645
$23$	−22800.0			−0.0169886			−0.00849432	−	0.999964i	$-0.502704\pi$
$23$	−22800.0			−0.0169886			−0.00849432	+	0.999964i	$0.502704\pi$
$24$	1.62956e6			1.00258
$25$	5.24507e6			2.68547
$26$			2.49792e6i			1.07201i
$27$		−	2.97127e6i		−	1.07598i
$28$	−4.43052e6			−1.36221
$29$	−3.34566e6	+	1.82036e6i	−0.878397	+	0.477932i
$29$	−3.34566e6	+	1.82036e6i	−0.878397	+	0.477932i
$30$	1.06054e7			2.39045
$31$			771940.i			0.150126i	0.997179	+	0.0750630i	$0.0239158\pi$
$31$			771940.i			0.150126i	−0.997179	+	0.0750630i	$0.976084\pi$
$32$			3.49412e6i			0.589065i
$33$	−5.58374e6			−0.819620
$34$	−3.45283e6			−0.443119
$35$	−1.28612e7			−1.44868
$36$	−8.13679e6			−0.807406
$37$			1.39331e7i			1.22220i	0.791555	+	0.611098i	$0.209272\pi$
$37$			1.39331e7i			1.22220i	−0.791555	+	0.611098i	$0.790728\pi$
$38$	2.13120e7			1.65805
$39$			6.87487e6i			0.475854i
$40$		−	4.19161e7i		−	2.58887i
$41$			1.80833e7i			0.999426i	0.866191	+	0.499713i	$0.166561\pi$
$41$			1.80833e7i			0.999426i	−0.866191	+	0.499713i	$0.833439\pi$
$42$	−1.89488e7			−0.939638
$43$		−	1.71895e7i		−	0.766754i	−0.923592	−	0.383377i	$-0.874761\pi$
$43$		−	1.71895e7i		−	0.766754i	0.923592	−	0.383377i	$-0.125239\pi$
$44$			4.94780e7i			1.99010i
$45$	−2.36199e7			−0.858661
$46$			864068.i			0.0284536i
$47$		−	4.69934e7i		−	1.40474i	−0.711812	−	0.702371i	$-0.752125\pi$
$47$		−	4.69934e7i		−	1.40474i	0.711812	−	0.702371i	$-0.247875\pi$
$48$		−	1.23987e7i		−	0.337124i
$49$	−1.73743e7			−0.430552
$50$		−	1.98777e8i		−	4.49780i
$51$	−9.50302e6			−0.196696
$52$	6.09188e7			1.15541
$53$	4.76701e7			0.829859			0.414930	−	0.909854i	$-0.363806\pi$
$53$	4.76701e7			0.829859			0.414930	+	0.909854i	$0.363806\pi$
$54$	−1.12605e8			−1.80212
$55$			1.43627e8i			2.11643i
$56$			7.48923e7i			1.01763i
$57$	5.86556e7			0.735991
$58$	6.89877e7	+	1.26793e8i	0.800471	+	1.47119i
$59$	−1.64817e8			−1.77080			−0.885399	−	0.464832i	$-0.846115\pi$
$59$	−1.64817e8			−1.77080			−0.885399	+	0.464832i	$0.846115\pi$
$60$		−	2.58642e8i		−	2.57643i
$61$			1.71039e8i			1.58165i	0.612043	+	0.790825i	$0.290348\pi$
$61$			1.71039e8i			1.58165i	−0.612043	+	0.790825i	$0.709652\pi$
$62$	2.92548e7			0.251440
$63$	4.22021e7			0.337522
$64$	1.93281e8			1.44006
$65$	1.76838e8			1.22876
$66$			2.11612e8i			1.37275i
$67$	−3.13045e8			−1.89788			−0.948942	−	0.315450i	$-0.897845\pi$
$67$	−3.13045e8			−1.89788			−0.948942	+	0.315450i	$0.897845\pi$
$68$			8.42071e7i			0.477593i
$69$			2.37812e6i			0.0126303i
$70$			4.87410e8i			2.42635i
$71$	−1.66663e8			−0.778355			−0.389178	−	0.921163i	$-0.627241\pi$
$71$	−1.66663e8			−0.778355			−0.389178	+	0.921163i	$0.627241\pi$
$72$			1.37542e8i			0.603169i
$73$		−	2.67257e7i		−	0.110148i	−0.998482	−	0.0550739i	$-0.982461\pi$
$73$		−	2.67257e7i		−	0.110148i	0.998482	−	0.0550739i	$-0.0175395\pi$
$74$	5.28035e8			2.04701
$75$		−	5.47080e8i		−	1.99653i
$76$		−	5.19752e8i		−	1.78704i
$77$		−	2.56622e8i		−	0.831927i
$78$	2.60543e8			0.796990
$79$		−	5.08030e8i		−	1.46746i	−0.679440	−	0.733731i	$-0.737777\pi$
$79$		−	5.08030e8i		−	1.46746i	0.679440	−	0.733731i	$-0.262223\pi$
$80$	−3.18924e8			−0.870526
$81$	−1.36631e8			−0.352669
$82$	6.85318e8			1.67390
$83$	−4.73692e7			−0.109558			−0.0547791	−	0.998498i	$-0.517445\pi$
$83$	−4.73692e7			−0.109558			−0.0547791	+	0.998498i	$0.517445\pi$
$84$			4.62120e8i			1.01274i
$85$			2.44441e8i			0.507912i
$86$	−6.51446e8			−1.28421
$87$	1.89870e8	+	3.48965e8i	0.355321	+	0.653048i
$88$	8.36362e8			1.48670
$89$		−	8.92144e8i		−	1.50723i	−0.657316	−	0.753615i	$-0.728308\pi$
$89$		−	8.92144e8i		−	1.50723i	0.657316	−	0.753615i	$-0.271692\pi$
$90$			8.95142e8i			1.43814i
$91$	−3.15960e8			−0.482999
$92$	2.10727e7			0.0306673
$93$	8.05163e7			0.111612
$94$	−1.78095e9			−2.35275
$95$		−	1.50876e9i		−	1.90049i
$96$	3.64450e8			0.437943
$97$			6.96072e8i			0.798328i	0.916880	+	0.399164i	$0.130700\pi$
$97$			6.96072e8i			0.798328i	−0.916880	+	0.399164i	$0.869300\pi$
$98$			6.58449e8i			0.721116i
$99$		−	4.71293e8i		−	0.493098i
$100$	−4.84772e9			−4.84772
$101$			1.06718e9i			1.02045i	0.860040	+	0.510227i	$0.170439\pi$
$101$			1.06718e9i			1.02045i	−0.860040	+	0.510227i	$0.829561\pi$
$102$			3.60144e8i			0.329439i
$103$	−7.55529e8			−0.661429			−0.330715	−	0.943731i	$-0.607290\pi$
$103$	−7.55529e8			−0.661429			−0.330715	+	0.943731i	$0.607290\pi$
$104$		−	1.02975e9i		−	0.863145i
$105$			1.34147e9i			1.07703i
$106$		−	1.80659e9i		−	1.38990i
$107$	8.63192e8			0.636621			0.318310	−	0.947987i	$-0.396885\pi$
$107$	8.63192e8			0.636621			0.318310	+	0.947987i	$0.396885\pi$
$108$			2.74618e9i			1.94233i
$109$	−4.28219e7			−0.0290567			−0.0145284	−	0.999894i	$-0.504625\pi$
$109$	−4.28219e7			−0.0290567			−0.0145284	+	0.999894i	$0.504625\pi$
$110$	5.44316e9			3.54474
$111$	1.45328e9			0.908647
$112$	5.69827e8			0.342186
$113$		−	3.33207e9i		−	1.92248i	−0.275714	−	0.961240i	$-0.588914\pi$
$113$		−	3.33207e9i		−	1.92248i	0.275714	−	0.961240i	$-0.411086\pi$
$114$		−	2.22292e9i		−	1.23268i
$115$	6.11710e7			0.0326141
$116$	3.09221e9	−	1.68246e9i	1.58565	−	0.862746i
$117$	−5.80271e8			−0.286282
$118$			6.24622e9i			2.96584i
$119$		−	4.36747e8i		−	0.199650i
$120$	−4.37201e9			−1.92471
$121$	−5.07881e8			−0.215391
$122$	6.48199e9			2.64905
$123$	1.88616e9			0.743028
$124$		−	7.13461e8i		−	0.271002i
$125$	−8.83209e9			−3.23570
$126$		−	1.59937e9i		−	0.565303i
$127$			2.30665e8i			0.0786802i	0.999226	+	0.0393401i	$0.0125256\pi$
$127$			2.30665e8i			0.0786802i	−0.999226	+	0.0393401i	$0.987474\pi$
$128$		−	5.53595e9i		−	1.82284i
$129$	−1.79293e9			−0.570047
$130$		−	6.70178e9i		−	2.05800i
$131$		−	8.68012e7i		−	0.0257516i	−0.999917	−	0.0128758i	$-0.995901\pi$
$131$		−	8.68012e7i		−	0.0257516i	0.999917	−	0.0128758i	$-0.00409861\pi$
$132$	5.16074e9			1.47955
$133$			2.69574e9i			0.747042i
$134$			1.18637e10i			3.17870i
$135$			7.97176e9i			2.06563i
$136$	1.42341e9			0.356784
$137$			1.78653e9i			0.433279i	0.976252	+	0.216640i	$0.0695096\pi$
$137$			1.78653e9i			0.433279i	−0.976252	+	0.216640i	$0.930490\pi$
$138$	9.01256e7			0.0211540
$139$	−2.25449e9			−0.512249			−0.256124	−	0.966644i	$-0.582446\pi$
$139$	−2.25449e9			−0.512249			−0.256124	+	0.966644i	$0.582446\pi$
$140$	1.18868e10			2.61511
$141$	−4.90159e9			−1.04436
$142$			6.31618e9i			1.30364i
$143$			3.52850e9i			0.705631i
$144$	1.04650e9			0.202820
$145$	8.97622e9	−	4.88392e9i	1.68631	−	0.917514i
$146$	−1.01285e9			−0.184483
$147$			1.81221e9i			0.320096i
$148$		−	1.28776e10i		−	2.20627i
$149$	2.47169e9			0.410823			0.205412	−	0.978676i	$-0.434147\pi$
$149$	2.47169e9			0.410823			0.205412	+	0.978676i	$0.434147\pi$
$150$	−2.07331e10			−3.34391
$151$	5.04614e9			0.789884			0.394942	−	0.918706i	$-0.370765\pi$
$151$	5.04614e9			0.789884			0.394942	+	0.918706i	$0.370765\pi$
$152$	−8.78574e9			−1.33500
$153$		−	8.02099e8i		−	0.118336i
$154$	−9.72540e9			−1.39336
$155$		−	2.07107e9i		−	0.288206i
$156$		−	6.35406e9i		−	0.858995i
$157$			9.57722e9i			1.25803i	0.777393	+	0.629015i	$0.216542\pi$
$157$			9.57722e9i			1.25803i	−0.777393	+	0.629015i	$0.783458\pi$
$158$	−1.92532e10			−2.45780
$159$		−	4.97217e9i		−	0.616963i
$160$		−	9.37453e9i		−	1.13086i
$161$	−1.09295e8			−0.0128199
$162$			5.17803e9i			0.590673i
$163$		−	9.89194e9i		−	1.09758i	−0.835960	−	0.548791i	$-0.815088\pi$
$163$		−	9.89194e9i		−	1.09758i	0.835960	−	0.548791i	$-0.184912\pi$
$164$		−	1.67134e10i		−	1.80413i
$165$	1.49809e10			1.57347
$166$			1.79519e9i			0.183495i
$167$	9.15965e9			0.911286			0.455643	−	0.890163i	$-0.349409\pi$
$167$	9.15965e9			0.911286			0.455643	+	0.890163i	$0.349409\pi$
$168$	7.81155e9			0.756564
$169$	−6.26011e9			−0.590326
$170$	9.26376e9			0.850682
$171$			4.95080e9i			0.442785i
$172$			1.58873e10i			1.38412i
$173$	−1.28288e10			−1.08888			−0.544440	−	0.838800i	$-0.683258\pi$
$173$	−1.28288e10			−1.08888			−0.544440	+	0.838800i	$0.683258\pi$
$174$	1.32250e10	−	7.19567e9i	1.09377	−	0.595114i
$175$	2.51431e10			2.02651
$176$		−	6.36356e9i		−	0.499911i
$177$			1.71911e10i			1.31651i
$178$	−3.38103e10			−2.52440
$179$	−1.86413e10			−1.35718			−0.678588	−	0.734519i	$-0.737408\pi$
$179$	−1.86413e10			−1.35718			−0.678588	+	0.734519i	$0.737408\pi$
$180$	2.18306e10			1.55002
$181$	−2.69935e9			−0.186942			−0.0934708	−	0.995622i	$-0.529796\pi$
$181$	−2.69935e9			−0.186942			−0.0934708	+	0.995622i	$0.529796\pi$
$182$			1.19742e10i			0.808957i
$183$	1.78400e10			1.17588
$184$		−	3.56207e8i		−	0.0229099i
$185$		−	3.73818e10i		−	2.34632i
$186$		−	3.05139e9i		−	0.186935i
$187$	−4.87738e9			−0.291675
$188$			4.34334e10i			2.53579i
$189$		−	1.42433e10i		−	0.811956i
$190$	−5.71788e10			−3.18305
$191$			2.46163e9i			0.133836i	0.997758	+	0.0669181i	$0.0213166\pi$
$191$			2.46163e9i			0.133836i	−0.997758	+	0.0669181i	$0.978683\pi$
$192$		−	2.01600e10i		−	1.07062i
$193$			1.82202e10i			0.945246i	0.881265	+	0.472623i	$0.156693\pi$
$193$			1.82202e10i			0.945246i	−0.881265	+	0.472623i	$0.843307\pi$
$194$	2.63796e10			1.33709
$195$		−	1.84449e10i		−	0.913525i
$196$	1.60581e10			0.777218
$197$	1.14606e10			0.542135			0.271068	−	0.962560i	$-0.412623\pi$
$197$	1.14606e10			0.542135			0.271068	+	0.962560i	$0.412623\pi$
$198$	−1.78610e10			−0.825871
$199$	3.12553e9			0.141281			0.0706406	−	0.997502i	$-0.477496\pi$
$199$	3.12553e9			0.141281			0.0706406	+	0.997502i	$0.477496\pi$
$200$			8.19445e10i			3.62147i
$201$			3.26518e10i			1.41099i
$202$	4.04440e10			1.70912
$203$	−1.60380e10	+	8.72620e9i	−0.662854	+	0.360656i
$204$	8.78312e9			0.355069
$205$		−	4.85165e10i		−	1.91866i
$206$			2.86329e10i			1.10780i
$207$	−2.00724e8			−0.00759860
$208$	−7.83501e9			−0.290238
$209$	3.01047e10			1.09138
$210$	5.08387e10			1.80388
$211$		−	2.09832e10i		−	0.728789i	−0.931245	−	0.364394i	$-0.881276\pi$
$211$		−	2.09832e10i		−	0.728789i	0.931245	−	0.364394i	$-0.118724\pi$
$212$	−4.40588e10			−1.49803
$213$			1.73836e10i			0.578672i
$214$		−	3.27131e10i		−	1.06625i
$215$			4.61186e10i			1.47198i
$216$	4.64207e10			1.45101
$217$			3.70043e9i			0.113288i
$218$			1.62286e9i			0.0486660i
$219$	−2.78759e9			−0.0818899
$220$		−	1.32747e11i		−	3.82051i
$221$			6.00518e9i			0.169341i
$222$		−	5.50761e10i		−	1.52186i
$223$	−4.21485e9			−0.114133			−0.0570664	−	0.998370i	$-0.518175\pi$
$223$	−4.21485e9			−0.114133			−0.0570664	+	0.998370i	$0.518175\pi$
$224$			1.67497e10i			0.444519i
$225$	4.61761e10			1.20115
$226$	−1.26278e11			−3.21989
$227$	2.42992e10			0.607402			0.303701	−	0.952767i	$-0.401778\pi$
$227$	2.42992e10			0.607402			0.303701	+	0.952767i	$0.401778\pi$
$228$	−5.42121e10			−1.32859
$229$		−	4.53493e10i		−	1.08971i	−0.838530	−	0.544855i	$-0.816585\pi$
$229$		−	4.53493e10i		−	1.08971i	0.838530	−	0.544855i	$-0.183415\pi$
$230$		−	2.31825e9i		−	0.0546241i
$231$	−2.67666e10			−0.618500
$232$	−2.84398e10	−	5.22698e10i	−0.644511	−	1.18455i
$233$	−1.18024e10			−0.262344			−0.131172	−	0.991360i	$-0.541874\pi$
$233$	−1.18024e10			−0.262344			−0.131172	+	0.991360i	$0.541874\pi$
$234$			2.19910e10i			0.479483i
$235$			1.26081e11i			2.69676i
$236$	1.52332e11			3.19658
$237$	−5.29894e10			−1.09099
$238$	−1.65518e10			−0.334386
$239$	−2.03587e10			−0.403607			−0.201804	−	0.979426i	$-0.564680\pi$
$239$	−2.03587e10			−0.403607			−0.201804	+	0.979426i	$0.564680\pi$
$240$			3.32649e10i			0.647196i
$241$	−4.91678e10			−0.938867			−0.469434	−	0.882968i	$-0.655542\pi$
$241$	−4.91678e10			−0.938867			−0.469434	+	0.882968i	$0.655542\pi$
$242$			1.92476e10i			0.360751i
$243$		−	4.42324e10i		−	0.813790i
$244$		−	1.58082e11i		−	2.85514i
$245$	4.66144e10			0.826556
$246$		−	7.14813e10i		−	1.24447i
$247$		−	3.70658e10i		−	0.633633i
$248$	−1.20601e10			−0.202451
$249$			4.94079e9i			0.0814516i
$250$			3.34717e11i			5.41936i
$251$		−	1.81902e9i		−	0.0289272i	−0.999895	−	0.0144636i	$-0.995396\pi$
$251$		−	1.81902e9i		−	0.0289272i	0.999895	−	0.0144636i	$-0.00460407\pi$
$252$	−3.90051e10			−0.609283
$253$			1.22056e9i			0.0187291i
$254$	8.74171e9			0.131779
$255$	2.54961e10			0.377609
$256$	−1.10840e11			−1.61294
$257$	−1.75025e10			−0.250266			−0.125133	−	0.992140i	$-0.539936\pi$
$257$	−1.75025e10			−0.250266			−0.125133	+	0.992140i	$0.539936\pi$
$258$			6.79483e10i			0.954751i
$259$			6.67908e10i			0.922291i
$260$	−1.63442e11			−2.21811
$261$	−2.94542e10	+	1.60259e10i	−0.392885	+	0.213767i
$262$	−3.28958e9			−0.0431304
$263$			6.19778e10i			0.798795i	0.916778	+	0.399398i	$0.130781\pi$
$263$			6.19778e10i			0.798795i	−0.916778	+	0.399398i	$0.869219\pi$
$264$		−	8.72357e10i		−	1.10529i
$265$	−1.27896e11			−1.59313
$266$	1.02163e11			1.25119
$267$	−9.30540e10			−1.12056
$268$	2.89330e11			3.42599
$269$		−	1.49608e11i		−	1.74208i	−0.491211	−	0.871040i	$-0.663446\pi$
$269$		−	1.49608e11i		−	1.74208i	0.491211	−	0.871040i	$-0.336554\pi$
$270$	3.02112e11			3.45964
$271$			5.16998e10i			0.582274i	0.956681	+	0.291137i	$0.0940335\pi$
$271$			5.16998e10i			0.582274i	−0.956681	+	0.291137i	$0.905966\pi$
$272$		−	1.08302e10i		−	0.119971i
$273$			3.29559e10i			0.359088i
$274$	6.77056e10			0.725683
$275$		−	2.80786e11i		−	2.96059i
$276$		−	2.19797e9i		−	0.0227997i
$277$	−5.77205e10			−0.589076			−0.294538	−	0.955640i	$-0.595166\pi$
$277$	−5.77205e10			−0.589076			−0.294538	+	0.955640i	$0.595166\pi$
$278$			8.54401e10i			0.857946i
$279$			6.79594e9i			0.0671476i
$280$		−	2.00932e11i		−	1.95361i
$281$	7.15486e10			0.684577			0.342289	−	0.939595i	$-0.388798\pi$
$281$	7.15486e10			0.684577			0.342289	+	0.939595i	$0.388798\pi$
$282$			1.85759e11i			1.74916i
$283$	−1.28813e11			−1.19377			−0.596884	−	0.802328i	$-0.703595\pi$
$283$	−1.28813e11			−1.19377			−0.596884	+	0.802328i	$0.703595\pi$
$284$	1.54038e11			1.40506
$285$	−1.57370e11			−1.41293
$286$	1.33722e11			1.18183
$287$			8.66855e10i			0.754185i
$288$			3.07613e10i			0.263474i
$289$	1.10287e11			0.930002
$290$	−1.85090e11	−	3.40179e11i	−1.53671	−	2.82434i
$291$	7.26029e10			0.593520
$292$			2.47011e10i			0.198835i
$293$			1.84976e11i			1.46626i	0.680090	+	0.733128i	$0.261941\pi$
$293$			1.84976e11i			1.46626i	−0.680090	+	0.733128i	$0.738059\pi$
$294$	6.86788e10			0.536117
$295$	4.42196e11			3.39950
$296$	−2.17680e11			−1.64818
$297$	−1.59062e11			−1.18622
$298$		−	9.36715e10i		−	0.688072i
$299$	1.50279e9			0.0108737
$300$			5.05636e11i			3.60406i
$301$		−	8.24010e10i		−	0.578606i
$302$		−	1.91238e11i		−	1.32295i
$303$	1.11311e11			0.758661
$304$			6.68473e10i			0.448904i
$305$		−	4.58887e11i		−	3.03639i
$306$	−3.03978e10			−0.198196
$307$			9.05584e10i			0.581843i	0.956747	+	0.290922i	$0.0939619\pi$
$307$			9.05584e10i			0.581843i	−0.956747	+	0.290922i	$0.906038\pi$
$308$			2.37181e11i			1.50176i
$309$			7.88045e10i			0.491743i
$310$	−7.84891e10			−0.482705
$311$			1.41145e11i			0.855545i	0.903886	+	0.427773i	$0.140702\pi$
$311$			1.41145e11i			0.855545i	−0.903886	+	0.427773i	$0.859298\pi$
$312$	−1.07407e11			−0.641709
$313$	−7.41145e10			−0.436470			−0.218235	−	0.975896i	$-0.570030\pi$
$313$	−7.41145e10			−0.436470			−0.218235	+	0.975896i	$0.570030\pi$
$314$	3.62956e11			2.10703
$315$	−1.13226e11			−0.647961
$316$			4.69543e11i			2.64901i
$317$			3.77794e10i			0.210130i	0.994465	+	0.105065i	$0.0335051\pi$
$317$			3.77794e10i			0.210130i	−0.994465	+	0.105065i	$0.966495\pi$
$318$	−1.88434e11			−1.03333
$319$	9.74501e10	+	1.79105e11i	0.526895	+	0.968387i
$320$	−5.18563e11			−2.76456
$321$		−	9.00342e10i		−	0.473298i
$322$			4.14206e9i			0.0214716i
$323$	5.12355e10			0.261915
$324$	1.26281e11			0.636627
$325$	−3.45713e11			−1.71886
$326$	−3.74883e11			−1.83830
$327$			4.46648e9i			0.0216023i
$328$	−2.82519e11			−1.34777
$329$		−	2.25271e11i		−	1.06004i
$330$		−	5.67742e11i		−	2.63535i
$331$		−	1.62074e11i		−	0.742143i	−0.928604	−	0.371071i	$-0.878991\pi$
$331$		−	1.62074e11i		−	0.742143i	0.928604	−	0.371071i	$-0.121009\pi$
$332$	4.37808e10			0.197771
$333$			1.22663e11i			0.546658i
$334$		−	3.47131e11i		−	1.52628i
$335$	8.39882e11			3.64348
$336$		−	5.94351e10i		−	0.254400i
$337$		−	8.78925e10i		−	0.371208i	−0.982625	−	0.185604i	$-0.940576\pi$
$337$		−	8.78925e10i		−	0.371208i	0.982625	−	0.185604i	$-0.0594241\pi$
$338$			2.37244e11i			0.988714i
$339$	−3.47548e11			−1.42928
$340$		−	2.25923e11i		−	0.916864i
$341$	4.13246e10			0.165506
$342$	1.87625e11			0.741604
$343$	−2.76729e11			−1.07952
$344$	2.68555e11			1.03400
$345$		−	6.38037e9i		−	0.0242471i
$346$			4.86185e11i			1.82372i
$347$	3.84875e10			0.142507			0.0712537	−	0.997458i	$-0.477300\pi$
$347$	3.84875e10			0.142507			0.0712537	+	0.997458i	$0.477300\pi$
$348$	−1.75487e11	−	3.22529e11i	−0.641413	−	1.17886i
$349$	−2.89105e11			−1.04314			−0.521568	−	0.853210i	$-0.674653\pi$
$349$	−2.89105e11			−1.04314			−0.521568	+	0.853210i	$0.674653\pi$
$350$		−	9.52869e11i		−	3.39412i
$351$			1.95843e11i			0.688692i
$352$	1.87052e11			0.649413
$353$	−2.17749e11			−0.746398			−0.373199	−	0.927751i	$-0.621739\pi$
$353$	−2.17749e11			−0.746398			−0.373199	+	0.927751i	$0.621739\pi$
$354$	6.51504e11			2.20497
$355$	4.47149e11			1.49425
$356$			8.24559e11i			2.72080i
$357$	−4.55544e10			−0.148430
$358$			7.06463e11i			2.27308i
$359$		−	5.05244e11i		−	1.60537i	−0.596401	−	0.802687i	$-0.703403\pi$
$359$		−	5.05244e11i		−	1.60537i	0.596401	−	0.802687i	$-0.296597\pi$
$360$		−	3.69017e11i		−	1.15794i
$361$	6.44641e9			0.0199772
$362$			1.02300e11i			0.313102i
$363$			5.29739e10i			0.160134i
$364$	2.92025e11			0.871893
$365$			7.17035e10i			0.211457i
$366$		−	6.76097e11i		−	1.96945i
$367$		−	3.17655e11i		−	0.914027i	−0.889460	−	0.457013i	$-0.848919\pi$
$367$		−	3.17655e11i		−	0.914027i	0.889460	−	0.457013i	$-0.151081\pi$
$368$	−2.71025e9			−0.00770360
$369$			1.59200e11i			0.447019i
$370$	−1.41669e12			−3.92977
$371$	2.28515e11			0.626226
$372$	−7.44167e10			−0.201478
$373$	1.32100e11			0.353357			0.176678	−	0.984269i	$-0.443465\pi$
$373$	1.32100e11			0.353357			0.176678	+	0.984269i	$0.443465\pi$
$374$			1.84842e11i			0.488516i
$375$			9.21221e11i			2.40560i
$376$	7.34185e11			1.89435
$377$	2.20519e11	−	1.19984e11i	0.562225	−	0.305904i
$378$	−5.39790e11			−1.35992
$379$		−	4.95405e11i		−	1.23334i	−0.787220	−	0.616672i	$-0.788481\pi$
$379$		−	4.95405e11i		−	1.23334i	0.787220	−	0.616672i	$-0.211519\pi$
$380$			1.39447e12i			3.43069i
$381$	2.40593e10			0.0584951
$382$	9.32906e10			0.224157
$383$	8.75133e10			0.207816			0.103908	−	0.994587i	$-0.466865\pi$
$383$	8.75133e10			0.207816			0.103908	+	0.994587i	$0.466865\pi$
$384$	−5.77421e11			−1.35520
$385$			6.88502e11i			1.59710i
$386$	6.90505e11			1.58316
$387$		−	1.51332e11i		−	0.342950i
$388$		−	6.43340e11i		−	1.44111i
$389$		−	1.83451e10i		−	0.0406207i	−0.999794	−	0.0203103i	$-0.993535\pi$
$389$		−	1.83451e10i		−	0.0406207i	0.999794	−	0.0203103i	$-0.00646542\pi$
$390$	−6.99021e11			−1.53003
$391$			2.07728e9i			0.00449469i
$392$		−	2.71442e11i		−	0.580617i
$393$	−9.05369e9			−0.0191452
$394$		−	4.34330e11i		−	0.908002i
$395$			1.36301e12i			2.81717i
$396$			4.35590e11i			0.890123i
$397$	4.93659e11			0.997401			0.498701	−	0.866774i	$-0.333811\pi$
$397$	4.93659e11			0.997401			0.498701	+	0.866774i	$0.333811\pi$
$398$		−	1.18451e11i		−	0.236627i
$399$	2.81176e11			0.555392
$400$	6.23485e11			1.21774
$401$	−7.77915e11			−1.50239			−0.751195	−	0.660080i	$-0.770522\pi$
$401$	−7.77915e11			−1.50239			−0.751195	+	0.660080i	$0.770522\pi$
$402$	1.23743e12			2.36322
$403$		−	5.08801e10i		−	0.0960894i
$404$		−	9.86340e11i		−	1.84209i
$405$	3.66574e11			0.677040
$406$	3.30704e11	+	6.07805e11i	0.604049	+	1.11019i
$407$	7.45888e11			1.34741
$408$		−	1.48467e11i		−	0.265253i
$409$			5.05154e11i			0.892624i	0.894877	+	0.446312i	$0.147263\pi$
$409$			5.05154e11i			0.892624i	−0.894877	+	0.446312i	$0.852737\pi$
$410$	−1.83867e12			−3.21349
$411$	1.86342e11			0.322123
$412$	6.98293e11			1.19399
$413$	−7.90080e11			−1.33628
$414$			7.60702e9i			0.0127266i
$415$	1.27089e11			0.210325
$416$		−	2.30304e11i		−	0.377036i
$417$			2.35151e11i			0.380834i
$418$		−	1.14090e12i		−	1.82791i
$419$	−1.34849e11			−0.213739			−0.106870	−	0.994273i	$-0.534083\pi$
$419$	−1.34849e11			−0.213739			−0.106870	+	0.994273i	$0.534083\pi$
$420$		−	1.23984e12i		−	1.94422i
$421$			1.24371e11i			0.192952i	0.995335	+	0.0964762i	$0.0307572\pi$
$421$			1.24371e11i			0.192952i	−0.995335	+	0.0964762i	$0.969243\pi$
$422$	−7.95219e11			−1.22062
$423$		−	4.13717e11i		−	0.628306i
$424$			7.44758e11i			1.11910i
$425$		−	4.77873e11i		−	0.710497i
$426$	6.58802e11			0.969196
$427$			8.19903e11i			1.19354i
$428$	−7.97801e11			−1.14921
$429$	3.68035e11			0.524604
$430$	1.74779e12			2.46537
$431$	−1.00132e12			−1.39774			−0.698869	−	0.715250i	$-0.746313\pi$
$431$	−1.00132e12			−1.39774			−0.698869	+	0.715250i	$0.746313\pi$
$432$		−	3.53197e11i		−	0.487911i
$433$		−	1.37571e12i		−	1.88075i	−0.340135	−	0.940377i	$-0.610473\pi$
$433$		−	1.37571e12i		−	1.88075i	0.340135	−	0.940377i	$-0.389527\pi$
$434$	1.40238e11			0.189741
$435$	−5.09412e11	−	9.36254e11i	−0.682130	−	1.25369i
$436$	3.95779e10			0.0524522
$437$		−	1.28216e10i		−	0.0168181i
$438$			1.05644e11i			0.137154i
$439$	−1.11975e12			−1.43891			−0.719453	−	0.694541i	$-0.755607\pi$
$439$	−1.11975e12			−1.43891			−0.719453	+	0.694541i	$0.755607\pi$
$440$	−2.24391e12			−2.85410
$441$	−1.52959e11			−0.192575
$442$	2.27583e11			0.283622
$443$		−	5.69596e11i		−	0.702668i	−0.936250	−	0.351334i	$-0.885728\pi$
$443$		−	5.69596e11i		−	0.702668i	0.936250	−	0.351334i	$-0.114272\pi$
$444$	−1.34318e12			−1.64026
$445$			2.39357e12i			2.89352i
$446$			1.59734e11i			0.191157i
$447$		−	2.57806e11i		−	0.305428i
$448$	9.26527e11			1.08669
$449$		−	1.09783e12i		−	1.27476i	−0.770550	−	0.637379i	$-0.780018\pi$
$449$		−	1.09783e12i		−	1.27476i	0.770550	−	0.637379i	$-0.219982\pi$
$450$		−	1.74997e12i		−	2.01175i
$451$	9.68062e11			1.10182
$452$			3.07965e12i			3.47039i
$453$		−	5.26332e11i		−	0.587243i
$454$		−	9.20887e11i		−	1.01731i
$455$	8.47704e11			0.927242
$456$			9.16386e11i			0.992514i
$457$	1.55960e12			1.67259			0.836297	−	0.548277i	$-0.184716\pi$
$457$	1.55960e12			1.67259			0.836297	+	0.548277i	$0.184716\pi$
$458$	−1.71864e12			−1.82512
$459$	−2.70710e11			−0.284674
$460$	−5.65370e10			−0.0588738
$461$			4.63879e11i			0.478355i	0.970976	+	0.239178i	$0.0768778\pi$
$461$			4.63879e11i			0.478355i	−0.970976	+	0.239178i	$0.923122\pi$
$462$			1.01440e12i			1.03590i
$463$	−9.44509e11			−0.955194			−0.477597	−	0.878579i	$-0.658492\pi$
$463$	−9.44509e11			−0.955194			−0.477597	+	0.878579i	$0.658492\pi$
$464$	−3.97701e11	+	2.16387e11i	−0.398314	+	0.216721i
$465$	−2.16021e11			−0.214268
$466$			4.47287e11i			0.439389i
$467$		−	1.41202e12i		−	1.37377i	−0.726766	−	0.686885i	$-0.758978\pi$
$467$		−	1.41202e12i		−	1.37377i	0.726766	−	0.686885i	$-0.241022\pi$
$468$	5.36312e11			0.516787
$469$	−1.50063e12			−1.43218
$470$	4.77818e12			4.51671
$471$	9.98941e11			0.935289
$472$		−	2.57497e12i		−	2.38799i
$473$	−9.20215e11			−0.845307
$474$			2.00818e12i			1.82726i
$475$			2.94958e12i			2.65851i
$476$			4.03661e11i			0.360400i
$477$	4.19674e11			0.371176
$478$			7.71550e11i			0.675987i
$479$			5.22956e11i			0.453895i	0.973907	+	0.226948i	$0.0728746\pi$
$479$			5.22956e11i			0.453895i	−0.973907	+	0.226948i	$0.927125\pi$
$480$	−9.77799e11			−0.840745
$481$		−	9.18360e11i		−	0.782276i
$482$			1.86335e12i			1.57247i
$483$			1.13999e10i			0.00953104i
$484$	4.69406e11			0.388817
$485$		−	1.86752e12i		−	1.53260i
$486$	−1.67631e12			−1.36299
$487$	9.11397e11			0.734222			0.367111	−	0.930177i	$-0.380347\pi$
$487$	9.11397e11			0.734222			0.367111	+	0.930177i	$0.380347\pi$
$488$	−2.67217e12			−2.13292
$489$	−1.03177e12			−0.816002
$490$		−	1.76658e12i		−	1.38437i
$491$		−	1.70623e12i		−	1.32486i	−0.749124	−	0.662430i	$-0.769525\pi$
$491$		−	1.70623e12i		−	1.32486i	0.749124	−	0.662430i	$-0.230475\pi$
$492$	−1.74327e12			−1.34129
$493$	1.65851e11	+	3.04820e11i	0.126447	+	0.232398i
$494$	−1.40471e12			−1.06125
$495$			1.26445e12i			0.946629i
$496$			9.17611e10i			0.0680755i
$497$	−7.98930e11			−0.587361
$498$	1.87245e11			0.136420
$499$	6.76138e11			0.488183			0.244092	−	0.969752i	$-0.421510\pi$
$499$	6.76138e11			0.488183			0.244092	+	0.969752i	$0.421510\pi$
$500$	8.16301e12			5.84098
$501$		−	9.55386e11i		−	0.677499i
$502$	−6.89370e10			−0.0484491
$503$		−	4.87781e11i		−	0.339758i	−0.985465	−	0.169879i	$-0.945662\pi$
$503$		−	4.87781e11i		−	0.339758i	0.985465	−	0.169879i	$-0.0543376\pi$
$504$			6.59331e11i			0.455162i
$505$		−	2.86320e12i		−	1.95903i
$506$	4.62566e10			0.0313687
$507$			6.52953e11i			0.438880i
$508$		−	2.13191e11i		−	0.142031i
$509$	−2.79337e11			−0.184458			−0.0922291	−	0.995738i	$-0.529399\pi$
$509$	−2.79337e11			−0.184458			−0.0922291	+	0.995738i	$0.529399\pi$
$510$		−	9.66246e11i		−	0.632444i
$511$		−	1.28114e11i		−	0.0831195i
$512$			1.36620e12i			0.878619i
$513$	1.67091e12			1.06518
$514$			6.63308e11i			0.419161i
$515$	2.02704e12			1.26978
$516$	1.65711e12			1.02903
$517$	−2.51572e12			−1.54865
$518$	2.53123e12			1.54471
$519$			1.33810e12i			0.809533i
$520$			2.76277e12i			1.65703i
$521$	1.16532e12			0.692905			0.346453	−	0.938067i	$-0.387386\pi$
$521$	1.16532e12			0.692905			0.346453	+	0.938067i	$0.387386\pi$
$522$	6.07348e11	+	1.11625e12i	0.358031	+	0.658029i
$523$	3.13918e12			1.83467			0.917337	−	0.398112i	$-0.130335\pi$
$523$	3.13918e12			1.83467			0.917337	+	0.398112i	$0.130335\pi$
$524$			8.02255e10i			0.0464859i
$525$		−	2.62252e12i		−	1.50662i
$526$	2.34882e12			1.33787
$527$	7.03307e10			0.0397189
$528$	−6.63743e11			−0.371661
$529$	−1.80063e12			−0.999711
$530$			4.84699e12i			2.66827i
$531$	−1.45101e12			−0.792034
$532$		−	2.49152e12i		−	1.34853i
$533$		−	1.19191e12i		−	0.639691i
$534$			3.52654e12i			1.87678i
$535$	−2.31590e12			−1.22216
$536$		−	4.89075e12i		−	2.55937i
$537$			1.94435e12i			1.00900i
$538$	−5.66980e12			−2.91775
$539$			9.30108e11i			0.474661i
$540$		−	7.36786e12i		−	3.72880i
$541$		−	6.00049e11i		−	0.301161i	−0.988598	−	0.150581i	$-0.951886\pi$
$541$		−	6.00049e11i		−	0.301161i	0.988598	−	0.150581i	$-0.0481143\pi$
$542$	1.95931e12			0.975229
$543$			2.81553e11i			0.138983i
$544$	3.18346e11			0.155849
$545$	1.14889e11			0.0557819
$546$	1.24896e12			0.601423
$547$	−1.83298e12			−0.875417			−0.437709	−	0.899117i	$-0.644210\pi$
$547$	−1.83298e12			−0.875417			−0.437709	+	0.899117i	$0.644210\pi$
$548$		−	1.65119e12i		−	0.782140i
$549$			1.50578e12i			0.707433i
$550$	−1.06412e13			−4.95859
$551$	−1.02369e12	−	1.88144e12i	−0.473134	−	0.869579i
$552$	−3.71538e10			−0.0170325
$553$		−	2.43533e12i		−	1.10737i
$554$			2.18748e12i			0.986621i
$555$	−3.89906e12			−1.74438
$556$	2.08370e12			0.924694
$557$	−3.46594e12			−1.52571			−0.762856	−	0.646568i	$-0.776204\pi$
$557$	−3.46594e12			−1.52571			−0.762856	+	0.646568i	$0.776204\pi$
$558$	2.57551e11			0.112463
$559$			1.13300e12i			0.490767i
$560$	−1.52881e12			−0.656914
$561$			5.08729e11i			0.216847i
$562$		−	2.71153e12i		−	1.14657i
$563$			3.56054e12i			1.49358i	0.665060	+	0.746790i	$0.268406\pi$
$563$			3.56054e12i			1.49358i	−0.665060	+	0.746790i	$0.731594\pi$
$564$	4.53026e12			1.88524
$565$			8.93977e12i			3.69070i
$566$			4.88172e12i			1.99940i
$567$	−6.54966e11			−0.266131
$568$		−	2.60381e12i		−	1.04964i
$569$		−	7.92923e11i		−	0.317122i	−0.987349	−	0.158561i	$-0.949315\pi$
$569$		−	7.92923e11i		−	0.317122i	0.987349	−	0.158561i	$-0.0506854\pi$
$570$			5.96397e12i			2.36646i
$571$	3.84707e12			1.51449			0.757247	−	0.653129i	$-0.226544\pi$
$571$	3.84707e12			1.51449			0.757247	+	0.653129i	$0.226544\pi$
$572$		−	3.26119e12i		−	1.27378i
$573$	2.56758e11			0.0995011
$574$	3.28519e12			1.26316
$575$	−1.19587e11			−0.0456226
$576$	1.70159e12			0.644103
$577$			1.22383e12i			0.459655i	0.973231	+	0.229827i	$0.0738161\pi$
$577$			1.22383e12i			0.459655i	−0.973231	+	0.229827i	$0.926184\pi$
$578$		−	4.17964e12i		−	1.55763i
$579$	1.90043e12			0.702747
$580$	−8.29622e12	+	4.51394e12i	−3.04407	+	1.65626i
$581$	−2.27072e11			−0.0826746
$582$		−	2.75149e12i		−	0.994065i
$583$		−	2.55194e12i		−	0.914876i
$584$	4.17540e11			0.148539
$585$	1.55683e12			0.549593
$586$	7.01017e12			2.45578
$587$	2.75983e12			0.959424			0.479712	−	0.877426i	$-0.340741\pi$
$587$	2.75983e12			0.959424			0.479712	+	0.877426i	$0.340741\pi$
$588$		−	1.67492e12i		−	0.577826i
$589$	−4.34103e11			−0.148619
$590$		−	1.67583e13i		−	5.69370i
$591$		−	1.19538e12i		−	0.403053i
$592$			1.65624e12i			0.554212i
$593$	−1.24835e12			−0.414563			−0.207282	−	0.978281i	$-0.566462\pi$
$593$	−1.24835e12			−0.414563			−0.207282	+	0.978281i	$0.566462\pi$
$594$			6.02812e12i			1.98675i
$595$			1.17177e12i			0.383279i
$596$	−2.28444e12			−0.741604
$597$		−	3.26004e11i		−	0.105036i
$598$		−	5.69525e10i		−	0.0182120i
$599$			1.96318e11i			0.0623074i	0.999515	+	0.0311537i	$0.00991813\pi$
$599$			1.96318e11i			0.0623074i	−0.999515	+	0.0311537i	$0.990082\pi$
$600$	8.54713e12			2.69240
$601$		−	3.14658e12i		−	0.983793i	−0.870654	−	0.491896i	$-0.836304\pi$
$601$		−	3.14658e12i		−	0.983793i	0.870654	−	0.491896i	$-0.163696\pi$
$602$	−3.12282e12			−0.969086
$603$	−2.75596e12			−0.848877
$604$	−4.66387e12			−1.42587
$605$	1.36262e12			0.413499
$606$		−	4.21846e12i		−	1.27065i
$607$		−	4.02375e12i		−	1.20305i	−0.798856	−	0.601523i	$-0.794561\pi$
$607$		−	4.02375e12i		−	1.20305i	0.798856	−	0.601523i	$-0.205439\pi$
$608$	−1.96493e12			−0.583151
$609$	9.10176e11	+	1.67282e12i	0.268131	+	0.492802i
$610$	−1.73908e13			−5.08553
$611$			3.09743e12i			0.899116i
$612$			7.41335e11i			0.213616i
$613$	5.36267e12			1.53394			0.766971	−	0.641681i	$-0.221763\pi$
$613$	5.36267e12			1.53394			0.766971	+	0.641681i	$0.221763\pi$
$614$	3.43197e12			0.974508
$615$	−5.06046e12			−1.42643
$616$	4.00924e12			1.12189
$617$			5.00018e12i			1.38900i	0.719492	+	0.694500i	$0.244375\pi$
$617$			5.00018e12i			1.38900i	−0.719492	+	0.694500i	$0.755625\pi$
$618$	2.98652e12			0.823601
$619$			8.35185e11i			0.228652i	0.993443	+	0.114326i	$0.0364708\pi$
$619$			8.35185e11i			0.228652i	−0.993443	+	0.114326i	$0.963529\pi$
$620$			1.91418e12i			0.520259i
$621$			6.77449e10i			0.0182795i
$622$	5.34908e12			1.43292
$623$		−	4.27664e12i		−	1.13738i
$624$			8.17221e11i			0.215779i
$625$	1.34517e13			3.52629
$626$			2.80878e12i			0.731027i
$627$		−	3.14003e12i		−	0.811392i
$628$		−	8.85170e12i		−	2.27095i
$629$	1.26943e12			0.323357
$630$			4.29102e12i			1.08524i
$631$	−4.91799e12			−1.23497			−0.617484	−	0.786583i	$-0.711848\pi$
$631$	−4.91799e12			−1.23497			−0.617484	+	0.786583i	$0.711848\pi$
$632$	7.93703e12			1.97893
$633$	−2.18863e12			−0.541821
$634$	1.43176e12			0.351939
$635$		−	6.18862e11i		−	0.151047i
$636$			4.59550e12i			1.11372i
$637$	1.14518e12			0.275578
$638$	6.78767e12	−	3.69315e12i	1.62191	−	0.882477i
$639$	−1.46726e12			−0.348139
$640$			1.48526e13i			3.49940i
$641$			4.70484e12i			1.10074i	0.834922	+	0.550369i	$0.185513\pi$
$641$			4.70484e12i			1.10074i	−0.834922	+	0.550369i	$0.814487\pi$
$642$	−3.41210e12			−0.792710
$643$	−1.03747e12			−0.239346			−0.119673	−	0.992813i	$-0.538185\pi$
$643$	−1.03747e12			−0.239346			−0.119673	+	0.992813i	$0.538185\pi$
$644$	1.01016e11			0.0231421
$645$	4.81034e12			1.09435
$646$		−	1.94171e12i		−	0.438671i
$647$	−5.53484e12			−1.24175			−0.620877	−	0.783908i	$-0.713223\pi$
$647$	−5.53484e12			−1.24175			−0.620877	+	0.783908i	$0.713223\pi$
$648$		−	2.13461e12i		−	0.475589i
$649$			8.82324e12i			1.95221i
$650$			1.31018e13i			2.87885i
$651$	3.85968e11			0.0842243
$652$			9.14257e12i			1.98132i
$653$			1.66756e12i			0.358898i	0.983767	+	0.179449i	$0.0574315\pi$
$653$			1.66756e12i			0.358898i	−0.983767	+	0.179449i	$0.942568\pi$
$654$	1.69270e11			0.0361810
$655$			2.32883e11i			0.0494369i
$656$			2.14958e12i			0.453196i
$657$		−	2.35285e11i		−	0.0492664i
$658$	−8.53727e12			−1.77543
$659$		−	1.17342e12i		−	0.242364i	−0.992630	−	0.121182i	$-0.961332\pi$
$659$		−	1.17342e12i		−	0.242364i	0.992630	−	0.121182i	$-0.0386685\pi$
$660$	−1.38460e13			−2.84038
$661$	2.45865e12			0.500946			0.250473	−	0.968124i	$-0.419414\pi$
$661$	2.45865e12			0.500946			0.250473	+	0.968124i	$0.419414\pi$
$662$	−6.14225e12			−1.24299
$663$	6.26363e11			0.125897
$664$		−	7.40057e11i		−	0.147744i
$665$		−	7.23251e12i		−	1.43414i
$666$	4.64867e12			0.915577
$667$	7.62809e10	−	4.15041e10i	0.0149228	−	0.00811942i
$668$	−8.46575e12			−1.64502
$669$			4.39625e11i			0.0848526i
$670$		−	3.18297e13i		−	6.10233i
$671$	9.15629e12			1.74369
$672$	1.74705e12			0.330479
$673$	3.83983e12			0.721513			0.360757	−	0.932660i	$-0.382519\pi$
$673$	3.83983e12			0.721513			0.360757	+	0.932660i	$0.382519\pi$
$674$	−3.33093e12			−0.621722
$675$		−	1.55845e13i		−	2.88953i
$676$	5.78587e12			1.06564
$677$		−	3.34063e12i		−	0.611194i	−0.952161	−	0.305597i	$-0.901144\pi$
$677$		−	3.34063e12i		−	0.611194i	0.952161	−	0.305597i	$-0.0988561\pi$
$678$			1.31713e13i			2.39384i
$679$			3.33674e12i			0.602432i
$680$	−3.81894e12			−0.684940
$681$		−	2.53450e12i		−	0.451576i
$682$		−	1.56611e12i		−	0.277200i
$683$	−4.84375e11			−0.0851703			−0.0425851	−	0.999093i	$-0.513559\pi$
$683$	−4.84375e11			−0.0851703			−0.0425851	+	0.999093i	$0.513559\pi$
$684$		−	4.57575e12i		−	0.799300i
$685$		−	4.79316e12i		−	0.831791i
$686$			1.04874e13i			1.80805i
$687$	−4.73011e12			−0.810150
$688$		−	2.04333e12i		−	0.347689i
$689$	−3.14203e12			−0.531158
$690$	−2.41802e11			−0.0406106
$691$	−6.75627e11			−0.112734			−0.0563671	−	0.998410i	$-0.517952\pi$
$691$	−6.75627e11			−0.112734			−0.0563671	+	0.998410i	$0.517952\pi$
$692$	1.18570e13			1.96561
$693$		−	2.25923e12i		−	0.372100i
$694$		−	1.45859e12i		−	0.238680i
$695$	6.04866e12			0.983394
$696$	−5.45194e12	+	2.96638e12i	−0.880662	+	0.479165i
$697$	1.64755e12			0.264419
$698$			1.09564e13i			1.74711i
$699$			1.23104e12i			0.195041i
$700$	−2.32384e13			−3.65818
$701$	−2.03482e12			−0.318270			−0.159135	−	0.987257i	$-0.550871\pi$
$701$	−2.03482e12			−0.318270			−0.159135	+	0.987257i	$0.550871\pi$
$702$	7.42200e12			1.15346
$703$	−7.83534e12			−1.20993
$704$		−	1.03470e13i		−	1.58759i
$705$	1.31507e13			2.00492
$706$			8.25222e12i			1.25011i
$707$			5.11573e12i			0.770053i
$708$		−	1.58888e13i		−	2.37651i
$709$	5.16026e12			0.766943			0.383472	−	0.923553i	$-0.374728\pi$
$709$	5.16026e12			0.766943			0.383472	+	0.923553i	$0.374728\pi$
$710$		−	1.69460e13i		−	2.50267i
$711$		−	4.47255e12i		−	0.656360i
$712$	1.39381e13			2.03256
$713$		−	1.76002e10i		−	0.00255044i
$714$			1.72641e12i			0.248601i
$715$		−	9.46676e12i		−	1.35464i
$716$	1.72291e13			2.44993
$717$			2.12349e12i			0.300064i
$718$	−1.91476e13			−2.68878
$719$	8.19452e12			1.14352			0.571760	−	0.820421i	$-0.306261\pi$
$719$	8.19452e12			1.14352			0.571760	+	0.820421i	$0.306261\pi$
$720$	−2.80771e12			−0.389365
$721$	−3.62176e12			−0.499126
$722$		−	2.44305e11i		−	0.0334591i
$723$			5.12839e12i			0.698005i
$724$	2.49486e12			0.337461
$725$	−1.75482e13	+	9.54791e12i	−2.35891	+	1.28347i
$726$	2.00760e12			0.268202
$727$			5.36300e12i			0.712038i	0.934479	+	0.356019i	$0.115866\pi$
$727$			5.36300e12i			0.712038i	−0.934479	+	0.356019i	$0.884134\pi$
$728$		−	4.93630e12i		−	0.651344i
$729$	−7.30292e12			−0.957685
$730$	2.71741e12			0.354162
$731$	−1.56612e12			−0.202861
$732$	−1.64885e13			−2.12267
$733$			2.69936e12i			0.345377i	0.984976	+	0.172688i	$0.0552454\pi$
$733$			2.69936e12i			0.345377i	−0.984976	+	0.172688i	$0.944755\pi$
$734$	−1.20384e13			−1.53087
$735$		−	4.86206e12i		−	0.614507i
$736$		−	7.96658e10i		−	0.0100074i
$737$			1.67584e13i			2.09232i
$738$	6.03335e12			0.748695
$739$		−	1.34727e12i		−	0.166171i	−0.996542	−	0.0830855i	$-0.973523\pi$
$739$		−	1.34727e12i		−	0.166171i	0.996542	−	0.0830855i	$-0.0264775\pi$
$740$			3.45499e13i			4.23550i
$741$	−3.86611e12			−0.471077
$742$		−	8.66021e12i		−	1.04884i
$743$			1.20853e13i			1.45481i	0.686207	+	0.727406i	$0.259274\pi$
$743$			1.20853e13i			1.45481i	−0.686207	+	0.727406i	$0.740726\pi$
$744$			1.25792e12i			0.150513i
$745$	−6.63139e12			−0.788681
$746$		−	5.00631e12i		−	0.591824i
$747$	−4.17025e11			−0.0490027
$748$	4.50789e12			0.526522
$749$	4.13786e12			0.480405
$750$	3.49123e13			4.02905
$751$		−	1.34457e13i		−	1.54242i	−0.636578	−	0.771212i	$-0.719651\pi$
$751$		−	1.34457e13i		−	1.54242i	0.636578	−	0.771212i	$-0.280349\pi$
$752$		−	5.58614e12i		−	0.636988i
$753$	−1.89731e11			−0.0215061
$754$	−4.54711e12	−	8.35719e12i	−0.512348	−	0.941650i
$755$	−1.35385e13			−1.51639
$756$			1.31643e13i			1.46571i
$757$			4.30724e12i			0.476725i	0.971176	+	0.238363i	$0.0766106\pi$
$757$			4.30724e12i			0.476725i	−0.971176	+	0.238363i	$0.923389\pi$
$758$	−1.87748e13			−2.06568
$759$	1.27309e11			0.0139242
$760$	2.35717e13			2.56288
$761$	−4.18265e12			−0.452086			−0.226043	−	0.974117i	$-0.572579\pi$
$761$	−4.18265e12			−0.452086			−0.226043	+	0.974117i	$0.572579\pi$
$762$		−	9.11793e11i		−	0.0979713i
$763$	−2.05274e11			−0.0219267
$764$		−	2.27515e12i		−	0.241596i
$765$			2.15199e12i			0.227176i
$766$		−	3.31656e12i		−	0.348064i
$767$	1.08634e13			1.13341
$768$			1.15611e13i			1.19915i
$769$			8.62518e12i			0.889405i	0.895678	+	0.444702i	$0.146691\pi$
$769$			8.62518e12i			0.889405i	−0.895678	+	0.444702i	$0.853309\pi$
$770$	2.60927e13			2.67492
$771$			1.82558e12i			0.186062i
$772$		−	1.68399e13i		−	1.70632i
$773$		−	6.76528e12i		−	0.681519i	−0.940150	−	0.340760i	$-0.889316\pi$
$773$		−	6.76528e12i		−	0.681519i	0.940150	−	0.340760i	$-0.110684\pi$
$774$	−5.73515e12			−0.574395
$775$			4.04888e12i			0.403159i
$776$	−1.08748e13			−1.07658
$777$	6.96654e12			0.685681
$778$	−6.95239e11			−0.0680340
$779$	−1.01692e13			−0.989393
$780$			1.70476e13i			1.64906i
$781$			8.92207e12i			0.858096i
$782$	7.87245e10			0.00752800
$783$	5.40879e12	+	9.94087e12i	0.514247	+	0.945140i
$784$	−2.06530e12			−0.195236
$785$		−	2.56952e13i		−	2.41512i
$786$			3.43115e11i			0.0320655i
$787$	−6.60390e12			−0.613640			−0.306820	−	0.951767i	$-0.599265\pi$
$787$	−6.60390e12			−0.613640			−0.306820	+	0.951767i	$0.599265\pi$
$788$	−1.05924e13			−0.978643
$789$	6.46452e12			0.593868
$790$	5.16553e13			4.71838
$791$		−	1.59729e13i		−	1.45074i
$792$	7.36309e12			0.664962
$793$		−	1.12735e13i		−	1.01235i
$794$		−	1.87086e13i		−	1.67051i
$795$			1.33401e13i			1.18442i
$796$	−2.88875e12			−0.255036
$797$			4.49942e12i			0.394998i	0.980303	+	0.197499i	$0.0632819\pi$
$797$			4.49942e12i			0.394998i	−0.980303	+	0.197499i	$0.936718\pi$
$798$		−	1.06559e13i		−	0.930205i
$799$	−4.28152e12			−0.371653
$800$			1.83269e13i			1.58192i
$801$		−	7.85418e12i		−	0.674147i
$802$			2.94813e13i			2.51630i
$803$	−1.43072e12			−0.121432
$804$		−	3.01782e13i		−	2.54707i
$805$	2.93234e11			0.0246112
$806$	−1.92824e12			−0.160936
$807$	−1.56046e13			−1.29516
$808$	−1.66728e13			−1.37612
$809$		−	1.50450e12i		−	0.123487i	−0.998092	−	0.0617437i	$-0.980334\pi$
$809$		−	1.50450e12i		−	0.123487i	0.998092	−	0.0617437i	$-0.0196661\pi$
$810$		−	1.38924e13i		−	1.13395i
$811$	1.47030e13			1.19347			0.596735	−	0.802438i	$-0.296464\pi$
$811$	1.47030e13			1.19347			0.596735	+	0.802438i	$0.296464\pi$
$812$	1.48230e13	−	8.06515e12i	1.19656	−	0.651044i
$813$	5.39249e12			0.432894
$814$		−	2.82675e13i		−	2.25672i
$815$			2.65395e13i			2.10709i
$816$	−1.12963e12			−0.0891930
$817$	9.66660e12			0.759057
$818$	1.91442e13			1.49502
$819$	−2.78163e12			−0.216034
$820$			4.48411e13i			3.46349i
$821$	−9.51209e12			−0.730687			−0.365344	−	0.930873i	$-0.619049\pi$
$821$	−9.51209e12			−0.730687			−0.365344	+	0.930873i	$0.619049\pi$
$822$		−	7.06195e12i		−	0.539512i
$823$			4.52787e11i			0.0344029i	0.999852	+	0.0172014i	$0.00547565\pi$
$823$			4.52787e11i			0.0344029i	−0.999852	+	0.0172014i	$0.994524\pi$
$824$		−	1.18038e13i		−	0.891965i
$825$	−2.92871e13			−2.20107
$826$			2.99423e13i			2.23808i
$827$		−	1.84701e13i		−	1.37308i	−0.727093	−	0.686539i	$-0.759129\pi$
$827$		−	1.84701e13i		−	1.37308i	0.727093	−	0.686539i	$-0.240871\pi$
$828$	1.85518e11			0.0137167
$829$		−	1.74632e13i		−	1.28419i	−0.766626	−	0.642093i	$-0.778066\pi$
$829$		−	1.74632e13i		−	1.28419i	0.766626	−	0.642093i	$-0.221934\pi$
$830$		−	4.81640e12i		−	0.352266i
$831$			6.02047e12i			0.437951i
$832$	−1.27396e13			−0.921721
$833$			1.58296e12i			0.113911i
$834$	8.91173e12			0.637844
$835$	−2.45748e13			−1.74945
$836$	−2.78241e13			−1.97012
$837$	2.29364e12			0.161533
$838$			5.11048e12i			0.357984i
$839$			6.33361e12i			0.441288i	0.975354	+	0.220644i	$0.0708159\pi$
$839$			6.33361e12i			0.441288i	−0.975354	+	0.220644i	$0.929184\pi$
$840$	−2.09580e13			−1.45242
$841$	7.87973e12	−	1.21806e13i	0.543162	−	0.839628i
$842$	4.71339e12			0.323169
$843$		−	7.46279e12i		−	0.508952i
$844$			1.93936e13i			1.31558i
$845$	1.67955e13			1.13328
$846$	−1.56790e13			−1.05233
$847$	−2.43461e12			−0.162538
$848$	5.66658e12			0.376304
$849$			1.34357e13i			0.887512i
$850$	−1.81103e13			−1.18999
$851$		−	3.17675e11i		−	0.0207635i
$852$		−	1.60667e13i		−	1.04460i
$853$			4.39884e12i			0.284490i	0.989831	+	0.142245i	$0.0454322\pi$
$853$			4.39884e12i			0.284490i	−0.989831	+	0.142245i	$0.954568\pi$
$854$	3.10725e13			1.99902
$855$		−	1.32827e13i		−	0.850041i
$856$			1.34858e13i			0.858509i
$857$	−1.76635e13			−1.11857			−0.559283	−	0.828976i	$-0.688924\pi$
$857$	−1.76635e13			−1.11857			−0.559283	+	0.828976i	$0.688924\pi$
$858$		−	1.39477e13i		−	0.878640i
$859$		−	1.02651e13i		−	0.643274i	−0.946863	−	0.321637i	$-0.895767\pi$
$859$		−	1.02651e13i		−	0.643274i	0.946863	−	0.321637i	$-0.104233\pi$
$860$		−	4.26249e13i		−	2.65717i
$861$	9.04162e12			0.560702
$862$			3.79479e13i			2.34102i
$863$	−9.67133e12			−0.593523			−0.296762	−	0.954952i	$-0.595907\pi$
$863$	−9.67133e12			−0.593523			−0.296762	+	0.954952i	$0.595907\pi$
$864$	1.03820e13			0.633824
$865$	3.44191e13			2.09039
$866$	−5.21365e13			−3.15000
$867$		−	1.15034e13i		−	0.691415i
$868$		−	3.42010e12i		−	0.204503i
$869$	−2.71966e13			−1.61780
$870$	−3.54820e13	+	1.93056e13i	−2.09977	+	1.14247i
$871$	2.06334e13			1.21476
$872$		−	6.69013e11i		−	0.0391842i
$873$			6.12802e12i			0.357072i
$874$	−4.85912e11			−0.0281680
$875$	−4.23381e13			−2.44172
$876$	2.57642e12			0.147825
$877$	3.11553e13			1.77842			0.889209	−	0.457502i	$-0.151256\pi$
$877$	3.11553e13			1.77842			0.889209	+	0.457502i	$0.151256\pi$
$878$			4.24362e13i			2.40997i
$879$	1.92936e13			1.09010
$880$			1.70731e13i			0.959709i
$881$			1.27511e13i			0.713109i	0.934275	+	0.356554i	$0.116049\pi$
$881$			1.27511e13i			0.713109i	−0.934275	+	0.356554i	$0.883951\pi$
$882$			5.79680e12i			0.322537i
$883$	6.02313e11			0.0333425			0.0166713	−	0.999861i	$-0.494693\pi$
$883$	6.02313e11			0.0333425			0.0166713	+	0.999861i	$0.494693\pi$
$884$		−	5.55026e12i		−	0.305688i
$885$		−	4.61227e13i		−	2.52738i
$886$	−2.15864e13			−1.17687
$887$			1.27454e13i			0.691348i	0.938355	+	0.345674i	$0.112350\pi$
$887$			1.27454e13i			0.691348i	−0.938355	+	0.345674i	$0.887650\pi$
$888$			2.27048e13i			1.22535i
$889$			1.10573e12i			0.0593735i
$890$	9.07111e13			4.84625
$891$			7.31435e12i			0.388800i
$892$	3.89556e12			0.206029
$893$	2.64269e13			1.39064
$894$	−9.77029e12			−0.511551
$895$	5.00134e13			2.60545
$896$		−	2.65375e13i		−	1.37554i
$897$		−	1.56747e11i		−	0.00808412i
$898$	−4.16055e13			−2.13505
$899$	−1.40521e12	−	2.58265e12i	−0.0717500	−	0.131870i
$900$	−4.26780e13			−2.16827
$901$		−	4.34318e12i		−	0.219556i
$902$		−	3.66874e13i		−	1.84539i
$903$	−8.59474e12			−0.430168
$904$	5.20576e13			2.59254
$905$	7.24221e12			0.358883
$906$	−1.99468e13			−0.983551
$907$		−	2.99982e13i		−	1.47185i	−0.677064	−	0.735924i	$-0.736748\pi$
$907$		−	2.99982e13i		−	1.47185i	0.677064	−	0.735924i	$-0.263252\pi$
$908$	−2.24584e13			−1.09646
$909$			9.39520e12i			0.456424i
$910$		−	3.21261e13i		−	1.55300i
$911$		−	1.20731e13i		−	0.580744i	−0.956914	−	0.290372i	$-0.906221\pi$
$911$		−	1.20731e13i		−	0.580744i	0.956914	−	0.290372i	$-0.0937790\pi$
$912$	6.97243e12			0.333739
$913$			2.53584e12i			0.120782i
$914$		−	5.91054e13i		−	2.80136i
$915$	−4.78637e13			−2.25741
$916$			4.19139e13i			1.96711i
$917$		−	4.16096e11i		−	0.0194326i
$918$			1.02593e13i			0.476789i
$919$	1.51682e13			0.701479			0.350739	−	0.936473i	$-0.385930\pi$
$919$	1.51682e13			0.701479			0.350739	+	0.936473i	$0.385930\pi$
$920$			9.55685e11i			0.0439814i
$921$	9.44558e12			0.432574
$922$	1.75800e13			0.801179
$923$	1.09851e13			0.498193
$924$	2.47389e13			1.11649
$925$			7.30802e13i			3.28217i
$926$			3.57948e13i			1.59982i
$927$	−6.65146e12			−0.295841
$928$	−6.36056e12	−	1.16901e13i	−0.281533	−	0.517433i
$929$	1.66057e13			0.731451			0.365726	−	0.930723i	$-0.380821\pi$
$929$	1.66057e13			0.731451			0.365726	+	0.930723i	$0.380821\pi$
$930$			8.18671e12i			0.358869i
$931$		−	9.77051e12i		−	0.426230i
$932$	1.09083e13			0.473573
$933$	1.47219e13			0.636059
$934$	−5.35124e13			−2.30088
$935$	1.30857e13			0.559946
$936$		−	9.06567e12i		−	0.386063i
$937$	−2.74085e13			−1.16160			−0.580801	−	0.814045i	$-0.697261\pi$
$937$	−2.74085e13			−1.16160			−0.580801	+	0.814045i	$0.697261\pi$
$938$			5.68707e13i			2.39870i
$939$			7.73043e12i			0.324495i
$940$		−	1.16529e14i		−	4.86810i
$941$	−1.92736e13			−0.801328			−0.400664	−	0.916225i	$-0.631220\pi$
$941$	−1.92736e13			−0.801328			−0.400664	+	0.916225i	$0.631220\pi$
$942$		−	3.78577e13i		−	1.56648i
$943$		−	4.12299e11i		−	0.0169789i
$944$	−1.95920e13			−0.802978
$945$			3.82140e13i			1.55876i
$946$			3.48742e13i			1.41577i
$947$			1.74559e13i			0.705291i	0.935757	+	0.352645i	$0.114718\pi$
$947$			1.74559e13i			0.705291i	−0.935757	+	0.352645i	$0.885282\pi$
$948$	4.89752e13			1.96942
$949$			1.76154e12i			0.0705010i
$950$	1.11783e14			4.45265
$951$	3.94054e12			0.156222
$952$	6.82337e12			0.269236
$953$	−4.68001e12			−0.183793			−0.0918964	−	0.995769i	$-0.529293\pi$
$953$	−4.68001e12			−0.183793			−0.0918964	+	0.995769i	$0.529293\pi$
$954$		−	1.59047e13i		−	0.621668i
$955$		−	6.60443e12i		−	0.256933i
$956$	1.88164e13			0.728578
$957$	1.86813e13	−	1.01644e13i	0.719951	−	0.391723i
$958$	1.98189e13			0.760212
$959$			8.56404e12i			0.326960i
$960$			5.40881e13i			2.05533i
$961$	2.58437e13			0.977462
$962$	−3.48038e13			−1.31021
$963$	7.59930e12			0.284745
$964$	4.54431e13			1.69481
$965$		−	4.88837e13i		−	1.81464i
$966$	4.32032e11			0.0159632
$967$			4.94429e13i			1.81838i	0.416380	+	0.909191i	$0.363299\pi$
$967$			4.94429e13i			1.81838i	−0.416380	+	0.909191i	$0.636701\pi$
$968$		−	7.93471e12i		−	0.290464i
$969$		−	5.34406e12i		−	0.194722i
$970$	−7.07750e13			−2.56689
$971$		−	1.82402e13i		−	0.658482i	−0.944246	−	0.329241i	$-0.893207\pi$
$971$		−	1.82402e13i		−	0.658482i	0.944246	−	0.329241i	$-0.106793\pi$
$972$			4.08815e13i			1.46902i
$973$	−1.08073e13			−0.386552
$974$		−	3.45400e13i		−	1.22972i
$975$			3.60592e13i			1.27789i
$976$			2.03315e13i			0.717208i
$977$	−3.89337e13			−1.36710			−0.683549	−	0.729904i	$-0.739565\pi$
$977$	−3.89337e13			−1.36710			−0.683549	+	0.729904i	$0.739565\pi$
$978$			3.91017e13i			1.36669i
$979$	−4.77595e13			−1.66164
$980$	−4.30831e13			−1.49207
$981$	−3.76992e11			−0.0129964
$982$	−6.46623e13			−2.21896
$983$		−	1.37206e13i		−	0.468686i	−0.972154	−	0.234343i	$-0.924706\pi$
$983$		−	1.37206e13i		−	0.468686i	0.972154	−	0.234343i	$-0.0752939\pi$
$984$			2.94678e13i			1.00200i
$985$	−3.07480e13			−1.04077
$986$	1.15520e13	−	6.28540e12i	0.389235	−	0.211781i
$987$	−2.34966e13			−0.788093
$988$			3.42579e13i			1.14381i
$989$			3.91921e11i			0.0130261i
$990$	4.79200e13			1.58547
$991$	3.31744e13			1.09263			0.546313	−	0.837581i	$-0.316031\pi$
$991$	3.31744e13			1.09263			0.546313	+	0.837581i	$0.316031\pi$
$992$	−2.69725e12			−0.0884339
$993$	−1.69049e13			−0.551749
$994$			3.02777e13i			0.983748i
$995$	−8.38561e12			−0.271226
$996$		−	4.56650e12i		−	0.147034i
$997$			9.55727e12i			0.306341i	0.988200	+	0.153171i	$0.0489484\pi$
$997$			9.55727e12i			0.306341i	−0.988200	+	0.153171i	$0.951052\pi$
$998$		−	2.56242e13i		−	0.817640i
$999$	4.13991e13			1.31506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.b.a.28.3	✓	22
29.28	even	2	inner	29.10.b.a.28.20	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.b.a.28.3	✓	22	1.1	even	1	trivial
29.10.b.a.28.20	yes	22	29.28	even	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-37.8978i q^{2} -104.304i q^{3} -924.245 q^{4} -2682.94 q^{5} -3952.89 q^{6} +4793.67 q^{7} +15623.2i q^{8} +8803.72 q^{9} +O(q^{10})\)	\(q-37.8978i q^{2} -104.304i q^{3} -924.245 q^{4} -2682.94 q^{5} -3952.89 q^{6} +4793.67 q^{7} +15623.2i q^{8} +8803.72 q^{9} +101678. i q^{10} -53533.4i q^{11} +96402.2i q^{12} -65912.0 q^{13} -181670. i q^{14} +279841. i q^{15} +118871. q^{16} -91109.1i q^{17} -333642. i q^{18} +562353. i q^{19} +2.47970e6 q^{20} -499998. i q^{21} -2.02880e6 q^{22} -22800.0 q^{23} +1.62956e6 q^{24} +5.24507e6 q^{25} +2.49792e6i q^{26} -2.97127e6i q^{27} -4.43052e6 q^{28} +(-3.34566e6 + 1.82036e6i) q^{29} +1.06054e7 q^{30} +771940. i q^{31} +3.49412e6i q^{32} -5.58374e6 q^{33} -3.45283e6 q^{34} -1.28612e7 q^{35} -8.13679e6 q^{36} +1.39331e7i q^{37} +2.13120e7 q^{38} +6.87487e6i q^{39} -4.19161e7i q^{40} +1.80833e7i q^{41} -1.89488e7 q^{42} -1.71895e7i q^{43} +4.94780e7i q^{44} -2.36199e7 q^{45} +864068. i q^{46} -4.69934e7i q^{47} -1.23987e7i q^{48} -1.73743e7 q^{49} -1.98777e8i q^{50} -9.50302e6 q^{51} +6.09188e7 q^{52} +4.76701e7 q^{53} -1.12605e8 q^{54} +1.43627e8i q^{55} +7.48923e7i q^{56} +5.86556e7 q^{57} +(6.89877e7 + 1.26793e8i) q^{58} -1.64817e8 q^{59} -2.58642e8i q^{60} +1.71039e8i q^{61} +2.92548e7 q^{62} +4.22021e7 q^{63} +1.93281e8 q^{64} +1.76838e8 q^{65} +2.11612e8i q^{66} -3.13045e8 q^{67} +8.42071e7i q^{68} +2.37812e6i q^{69} +4.87410e8i q^{70} -1.66663e8 q^{71} +1.37542e8i q^{72} -2.67257e7i q^{73} +5.28035e8 q^{74} -5.47080e8i q^{75} -5.19752e8i q^{76} -2.56622e8i q^{77} +2.60543e8 q^{78} -5.08030e8i q^{79} -3.18924e8 q^{80} -1.36631e8 q^{81} +6.85318e8 q^{82} -4.73692e7 q^{83} +4.62120e8i q^{84} +2.44441e8i q^{85} -6.51446e8 q^{86} +(1.89870e8 + 3.48965e8i) q^{87} +8.36362e8 q^{88} -8.92144e8i q^{89} +8.95142e8i q^{90} -3.15960e8 q^{91} +2.10727e7 q^{92} +8.05163e7 q^{93} -1.78095e9 q^{94} -1.50876e9i q^{95} +3.64450e8 q^{96} +6.96072e8i q^{97} +6.58449e8i q^{98} -4.71293e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) \) 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) \) 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9 - 244222 * q^13 + 1246804 * q^16 - 1658748 * q^20 + 822328 * q^22 - 874956 * q^23 + 8668172 * q^24 + 5307748 * q^25 - 620352 * q^28 - 2425374 * q^29 - 8942448 * q^30 + 10134274 * q^33 - 37785784 * q^34 - 20790348 * q^35 + 34550680 * q^36 - 30663552 * q^38 + 56872008 * q^42 - 43877176 * q^45 - 131743922 * q^49 - 6194732 * q^51 + 342496580 * q^52 + 34886610 * q^53 + 116488784 * q^54 - 308361676 * q^57 + 342193888 * q^58 + 175799052 * q^59 - 484313328 * q^62 - 190643424 * q^63 - 419498924 * q^64 - 149739966 * q^65 - 508277640 * q^67 + 263144256 * q^71 + 435201408 * q^74 + 1065897336 * q^78 + 2990464236 * q^80 - 129895134 * q^81 - 527065064 * q^82 + 1555989756 * q^83 - 3422424120 * q^86 + 2176720604 * q^87 - 387386068 * q^88 - 1493579244 * q^91 - 1262849472 * q^92 + 2042413382 * q^93 + 166226488 * q^94 - 6686432820 * q^96

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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