LMFDB - Embedded newform 208.8.i.d.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,8,Mod(81,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.81"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 8, names="a")

Level:	$N$	$=$	$208 = 2^{4} \cdot 13$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	208.i (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$64.9760853007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - x^{15} + 796 x^{14} - 475 x^{13} + 449889 x^{12} - 92038 x^{11} + 116806037 x^{10} + \cdots + 11\!\cdots\!00$ x^16 - x^15 + 796x^14 - 475x^13 + 449889x^12 - 92038x^11 + 116806037x^10 + 198490961x^9 + 21546318357x^8 + 32373621530x^7 + 2116860322049x^6 + 2147931692741x^5 + 148294262896076x^4 + 71847528967407x^3 + 4924011367741489x^2 - 2411116235274240x + 113340278793830400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$2^{30}\cdot 3\cdot 13^{2}$
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$-5.55707 + 9.62513i$ of defining polynomial
Character	$\chi$	$=$	208.81
Dual form			208.8.i.d.113.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-35.2053 - 60.9774i) q^{3} -163.930 q^{5} +(123.469 - 213.855i) q^{7} +(-1385.33 + 2399.46i) q^{9} +(1015.56 + 1759.01i) q^{11} +(7174.32 - 3358.22i) q^{13} +(5771.21 + 9996.02i) q^{15} +(17484.9 - 30284.8i) q^{17} +(10739.1 - 18600.7i) q^{19} -17387.1 q^{21} +(-35146.7 - 60875.8i) q^{23} -51252.0 q^{25} +41095.4 q^{27} +(-103098. - 178571. i) q^{29} +304382. q^{31} +(71506.5 - 123853. i) q^{33} +(-20240.3 + 35057.2i) q^{35} +(61327.8 + 106223. i) q^{37} +(-457349. - 319244. i) q^{39} +(-117759. - 203964. i) q^{41} +(45675.1 - 79111.6i) q^{43} +(227097. - 393343. i) q^{45} +967683. q^{47} +(381282. + 660400. i) q^{49} -2.46225e6 q^{51} +28768.9 q^{53} +(-166482. - 288354. i) q^{55} -1.51229e6 q^{57} +(38248.5 - 66248.4i) q^{59} +(296556. - 513650. i) q^{61} +(342090. + 592517. i) q^{63} +(-1.17609e6 + 550512. i) q^{65} +(-915012. - 1.58485e6i) q^{67} +(-2.47470e6 + 4.28630e6i) q^{69} +(-1.41939e6 + 2.45845e6i) q^{71} +1.74309e6 q^{73} +(1.80434e6 + 3.12521e6i) q^{75} +501563. q^{77} -3.23539e6 q^{79} +(1.58293e6 + 2.74172e6i) q^{81} +4.95198e6 q^{83} +(-2.86630e6 + 4.96458e6i) q^{85} +(-7.25920e6 + 1.25733e7i) q^{87} +(2.54255e6 + 4.40382e6i) q^{89} +(167636. - 1.94890e6i) q^{91} +(-1.07159e7 - 1.85604e7i) q^{93} +(-1.76046e6 + 3.04920e6i) q^{95} +(-7.53784e6 + 1.30559e7i) q^{97} -5.62756e6 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 28 q^{3} + 384 q^{5} - 196 q^{7} - 5988 q^{9} - 5052 q^{11} + 17064 q^{13} + 184 q^{15} - 22824 q^{17} - 63692 q^{19} - 271240 q^{21} + 72468 q^{23} + 58488 q^{25} - 358616 q^{27} - 221772 q^{29}+ \cdots - 27386736 q^{99}+O(q^{100})$ 16 * q + 28 * q^3 + 384 * q^5 - 196 * q^7 - 5988 * q^9 - 5052 * q^11 + 17064 * q^13 + 184 * q^15 - 22824 * q^17 - 63692 * q^19 - 271240 * q^21 + 72468 * q^23 + 58488 * q^25 - 358616 * q^27 - 221772 * q^29 - 58432 * q^31 - 352372 * q^33 - 31560 * q^35 - 368884 * q^37 + 672996 * q^39 - 385824 * q^41 - 391492 * q^43 + 232096 * q^45 - 1089984 * q^47 - 1108780 * q^49 - 8040712 * q^51 + 3329328 * q^53 + 418216 * q^55 - 12068664 * q^57 + 6318924 * q^59 + 1763548 * q^61 - 6641128 * q^63 + 9500508 * q^65 + 8607964 * q^67 - 4618492 * q^69 - 9473220 * q^71 + 5020888 * q^73 + 21834988 * q^75 + 35263992 * q^77 - 12644416 * q^79 - 9316272 * q^81 + 22158432 * q^83 - 36911824 * q^85 - 5199988 * q^87 + 18469860 * q^89 + 9614540 * q^91 - 26340696 * q^93 + 16267080 * q^95 + 19660916 * q^97 - 27386736 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$ .

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		0			0
$2$		0			0
$3$	−35.2053	−	60.9774i	−0.752807	−	1.30390i	−0.946457	−	0.322830i	$-0.895366\pi$
$3$	−35.2053	−	60.9774i	−0.752807	−	1.30390i	0.193650	−	0.981071i	$-0.437967\pi$
$4$		0			0
$5$	−163.930			−0.586494			−0.293247	−	0.956037i	$-0.594736\pi$
$5$	−163.930			−0.586494			−0.293247	+	0.956037i	$0.594736\pi$
$6$		0			0
$7$	123.469	−	213.855i	0.136055	−	0.235654i	−0.789945	−	0.613178i	$-0.789891\pi$
$7$	123.469	−	213.855i	0.136055	−	0.235654i	0.926000	+	0.377524i	$0.123224\pi$
$8$		0			0
$9$	−1385.33	+	2399.46i	−0.633437	+	1.09715i
$10$		0			0
$11$	1015.56	+	1759.01i	0.230056	+	0.398468i	0.957824	−	0.287355i	$-0.0927758\pi$
$11$	1015.56	+	1759.01i	0.230056	+	0.398468i	−0.727768	+	0.685823i	$0.759442\pi$
$12$		0			0
$13$	7174.32	−	3358.22i	0.905689	−	0.423943i
$13$	7174.32	−	3358.22i	0.905689	−	0.423943i
$14$		0			0
$15$	5771.21	+	9996.02i	0.441517	+	0.764729i
$16$		0			0
$17$	17484.9	−	30284.8i	0.863162	−	1.49504i	−0.00569886	−	0.999984i	$-0.501814\pi$
$17$	17484.9	−	30284.8i	0.863162	−	1.49504i	0.868861	−	0.495057i	$-0.164853\pi$
$18$		0			0
$19$	10739.1	−	18600.7i	0.359195	−	0.622144i	−0.628632	−	0.777703i	$-0.716385\pi$
$19$	10739.1	−	18600.7i	0.359195	−	0.622144i	0.987827	+	0.155560i	$0.0497181\pi$
$20$		0			0
$21$	−17387.1			−0.409693
$22$		0			0
$23$	−35146.7	−	60875.8i	−0.602333	−	1.04327i	−0.992467	−	0.122513i	$-0.960905\pi$
$23$	−35146.7	−	60875.8i	−0.602333	−	1.04327i	0.390134	−	0.920758i	$-0.372429\pi$
$24$		0			0
$25$	−51252.0			−0.656025
$26$		0			0
$27$	41095.4			0.401810
$28$		0			0
$29$	−103098.	−	178571.i	−0.784979	−	1.35962i	−0.929012	−	0.370050i	$-0.879341\pi$
$29$	−103098.	−	178571.i	−0.784979	−	1.35962i	0.144033	−	0.989573i	$-0.453993\pi$
$30$		0			0
$31$	304382.			1.83507			0.917537	−	0.397651i	$-0.130175\pi$
$31$	304382.			1.83507			0.917537	+	0.397651i	$0.130175\pi$
$32$		0			0
$33$	71506.5	−	123853.i	0.346375	−	0.599940i
$34$		0			0
$35$	−20240.3	+	35057.2i	−0.0797954	+	0.138210i
$36$		0			0
$37$	61327.8	+	106223.i	0.199045	+	0.344756i	0.948219	−	0.317617i	$-0.102883\pi$
$37$	61327.8	+	106223.i	0.199045	+	0.344756i	−0.749174	+	0.662373i	$0.769549\pi$
$38$		0			0
$39$	−457349.	−	319244.i	−1.23459	−	0.861781i
$40$		0			0
$41$	−117759.	−	203964.i	−0.266839	−	0.462179i	0.701205	−	0.712960i	$-0.252646\pi$
$41$	−117759.	−	203964.i	−0.266839	−	0.462179i	−0.968044	+	0.250781i	$0.919313\pi$
$42$		0			0
$43$	45675.1	−	79111.6i	0.0876072	−	0.151740i	−0.818892	−	0.573948i	$-0.805411\pi$
$43$	45675.1	−	79111.6i	0.0876072	−	0.151740i	0.906499	+	0.422207i	$0.138745\pi$
$44$		0			0
$45$	227097.	−	393343.i	0.371507	−	0.643469i
$46$		0			0
$47$	967683.			1.35954			0.679768	−	0.733427i	$-0.262081\pi$
$47$	967683.			1.35954			0.679768	+	0.733427i	$0.262081\pi$
$48$		0			0
$49$	381282.	+	660400.i	0.462978	+	0.801901i
$50$		0			0
$51$	−2.46225e6			−2.59918
$52$		0			0
$53$	28768.9			0.0265435			0.0132717	−	0.999912i	$-0.495775\pi$
$53$	28768.9			0.0265435			0.0132717	+	0.999912i	$0.495775\pi$
$54$		0			0
$55$	−166482.	−	288354.i	−0.134926	−	0.233699i
$56$		0			0
$57$	−1.51229e6			−1.08162
$58$		0			0
$59$	38248.5	−	66248.4i	0.0242456	−	0.0419946i	−0.853648	−	0.520850i	$-0.825615\pi$
$59$	38248.5	−	66248.4i	0.0242456	−	0.0419946i	0.877894	+	0.478856i	$0.158948\pi$
$60$		0			0
$61$	296556.	−	513650.i	0.167283	−	0.289743i	−0.770180	−	0.637826i	$-0.779834\pi$
$61$	296556.	−	513650.i	0.167283	−	0.289743i	0.937464	+	0.348083i	$0.113167\pi$
$62$		0			0
$63$	342090.	+	592517.i	0.172365	+	0.298544i
$64$		0			0
$65$	−1.17609e6	+	550512.i	−0.531181	+	0.248640i
$66$		0			0
$67$	−915012.	−	1.58485e6i	−0.371676	−	0.643762i	0.618147	−	0.786062i	$-0.287884\pi$
$67$	−915012.	−	1.58485e6i	−0.371676	−	0.643762i	−0.989824	+	0.142300i	$0.954550\pi$
$68$		0			0
$69$	−2.47470e6	+	4.28630e6i	−0.906881	+	1.57076i
$70$		0			0
$71$	−1.41939e6	+	2.45845e6i	−0.470649	+	0.815188i	−0.999436	−	0.0335663i	$-0.989314\pi$
$71$	−1.41939e6	+	2.45845e6i	−0.470649	+	0.815188i	0.528788	+	0.848754i	$0.322647\pi$
$72$		0			0
$73$	1.74309e6			0.524434			0.262217	−	0.965009i	$-0.415546\pi$
$73$	1.74309e6			0.524434			0.262217	+	0.965009i	$0.415546\pi$
$74$		0			0
$75$	1.80434e6	+	3.12521e6i	0.493860	+	0.855391i
$76$		0			0
$77$	501563.			0.125201
$78$		0			0
$79$	−3.23539e6			−0.738298			−0.369149	−	0.929370i	$-0.620351\pi$
$79$	−3.23539e6			−0.738298			−0.369149	+	0.929370i	$0.620351\pi$
$80$		0			0
$81$	1.58293e6	+	2.74172e6i	0.330952	+	0.573226i
$82$		0			0
$83$	4.95198e6			0.950617			0.475309	−	0.879819i	$-0.342336\pi$
$83$	4.95198e6			0.950617			0.475309	+	0.879819i	$0.342336\pi$
$84$		0			0
$85$	−2.86630e6	+	4.96458e6i	−0.506239	+	0.876832i
$86$		0			0
$87$	−7.25920e6	+	1.25733e7i	−1.18188	+	2.04707i
$88$		0			0
$89$	2.54255e6	+	4.40382e6i	0.382300	+	0.662163i	0.991391	−	0.130938i	$-0.0417988\pi$
$89$	2.54255e6	+	4.40382e6i	0.382300	+	0.662163i	−0.609091	+	0.793101i	$0.708465\pi$
$90$		0			0
$91$	167636.	−	1.94890e6i	0.0233197	−	0.271109i
$92$		0			0
$93$	−1.07159e7	−	1.85604e7i	−1.38146	−	2.39275i
$94$		0			0
$95$	−1.76046e6	+	3.04920e6i	−0.210665	+	0.364883i
$96$		0			0
$97$	−7.53784e6	+	1.30559e7i	−0.838583	+	1.45247i	0.0524965	+	0.998621i	$0.483282\pi$
$97$	−7.53784e6	+	1.30559e7i	−0.838583	+	1.45247i	−0.891080	+	0.453847i	$0.850051\pi$
$98$		0			0
$99$	−5.62756e6			−0.582904
$100$		0			0
$101$	−5.83275e6	−	1.01026e7i	−0.563312	−	0.975685i	−0.997205	−	0.0747201i	$-0.976194\pi$
$101$	−5.83275e6	−	1.01026e7i	−0.563312	−	0.975685i	0.433893	−	0.900965i	$-0.357140\pi$
$102$		0			0
$103$	−6.15835e6			−0.555308			−0.277654	−	0.960681i	$-0.589557\pi$
$103$	−6.15835e6			−0.555308			−0.277654	+	0.960681i	$0.589557\pi$
$104$		0			0
$105$	2.85026e6			0.240282
$106$		0			0
$107$	−8.05811e6	−	1.39571e7i	−0.635902	−	1.10141i	−0.986323	−	0.164822i	$-0.947295\pi$
$107$	−8.05811e6	−	1.39571e7i	−0.635902	−	1.10141i	0.350422	−	0.936592i	$-0.386038\pi$
$108$		0			0
$109$	−2.48704e7			−1.83946			−0.919729	−	0.392553i	$-0.871592\pi$
$109$	−2.48704e7			−1.83946			−0.919729	+	0.392553i	$0.871592\pi$
$110$		0			0
$111$	4.31813e6	−	7.47921e6i	0.299685	−	0.519070i
$112$		0			0
$113$	727777.	−	1.26055e6i	0.0474486	−	0.0821834i	−0.841326	−	0.540529i	$-0.818224\pi$
$113$	727777.	−	1.26055e6i	0.0474486	−	0.0821834i	0.888774	+	0.458345i	$0.151558\pi$
$114$		0			0
$115$	5.76159e6	+	9.97937e6i	0.353264	+	0.611872i
$116$		0			0
$117$	−1.88089e6	+	2.18667e7i	−0.108571	+	1.26221i
$118$		0			0
$119$	−4.31769e6	−	7.47846e6i	−0.234875	−	0.406816i
$120$		0			0
$121$	7.68084e6	−	1.33036e7i	0.394149	−	0.682685i
$122$		0			0
$123$	−8.29146e6	+	1.43612e7i	−0.401757	+	0.695863i
$124$		0			0
$125$	2.12088e7			0.971248
$126$		0			0
$127$	−6.95145e6	−	1.20403e7i	−0.301136	−	0.521582i	0.675258	−	0.737582i	$-0.264032\pi$
$127$	−6.95145e6	−	1.20403e7i	−0.301136	−	0.521582i	−0.976393	+	0.216000i	$0.930699\pi$
$128$		0			0
$129$	−6.43202e6			−0.263805
$130$		0			0
$131$	−2.68014e7			−1.04162			−0.520809	−	0.853673i	$-0.674369\pi$
$131$	−2.68014e7			−1.04162			−0.520809	+	0.853673i	$0.674369\pi$
$132$		0			0
$133$	−2.65189e6	−	4.59321e6i	−0.0977405	−	0.169292i
$134$		0			0
$135$	−6.73678e6			−0.235659
$136$		0			0
$137$	3.59209e6	−	6.22169e6i	0.119351	−	0.206722i	−0.800160	−	0.599787i	$-0.795252\pi$
$137$	3.59209e6	−	6.22169e6i	0.119351	−	0.206722i	0.919511	+	0.393065i	$0.128585\pi$
$138$		0			0
$139$	9.16798e6	−	1.58794e7i	0.289549	−	0.501514i	−0.684153	−	0.729338i	$-0.739828\pi$
$139$	9.16798e6	−	1.58794e7i	0.289549	−	0.501514i	0.973702	+	0.227825i	$0.0731614\pi$
$140$		0			0
$141$	−3.40676e7	−	5.90068e7i	−1.02347	−	1.77270i
$142$		0			0
$143$	1.31931e7	+	9.20921e6i	0.377287	+	0.263358i
$144$		0			0
$145$	1.69009e7	+	2.92732e7i	0.460385	+	0.797410i
$146$		0			0
$147$	2.68463e7	−	4.64992e7i	0.697066	−	1.20735i
$148$		0			0
$149$	−5.10856e6	+	8.84829e6i	−0.126516	+	0.219133i	−0.922325	−	0.386416i	$-0.873713\pi$
$149$	−5.10856e6	+	8.84829e6i	−0.126516	+	0.219133i	0.795808	+	0.605549i	$0.207046\pi$
$150$		0			0
$151$	−1.08524e7			−0.256512			−0.128256	−	0.991741i	$-0.540938\pi$
$151$	−1.08524e7			−0.256512			−0.128256	+	0.991741i	$0.540938\pi$
$152$		0			0
$153$	4.84446e7	+	8.39086e7i	1.09352	+	1.89403i
$154$		0			0
$155$	−4.98974e7			−1.07626
$156$		0			0
$157$	−3.58959e7			−0.740280			−0.370140	−	0.928976i	$-0.620690\pi$
$157$	−3.58959e7			−0.740280			−0.370140	+	0.928976i	$0.620690\pi$
$158$		0			0
$159$	−1.01282e6	−	1.75425e6i	−0.0199821	−	0.0346100i
$160$		0			0
$161$	−1.73581e7			−0.327802
$162$		0			0
$163$	−2.59182e7	+	4.48917e7i	−0.468758	+	0.811912i	−0.999362	−	0.0357073i	$-0.988632\pi$
$163$	−2.59182e7	+	4.48917e7i	−0.468758	+	0.811912i	0.530605	+	0.847619i	$0.321965\pi$
$164$		0			0
$165$	−1.17221e7	+	2.03032e7i	−0.203147	+	0.351861i
$166$		0			0
$167$	3.48738e7	+	6.04031e7i	0.579417	+	1.00358i	0.995546	+	0.0942740i	$0.0300530\pi$
$167$	3.48738e7	+	6.04031e7i	0.579417	+	1.00358i	−0.416129	+	0.909305i	$0.636614\pi$
$168$		0			0
$169$	4.01933e7	−	4.81859e7i	0.640545	−	0.767920i
$170$		0			0
$171$	2.97543e7	+	5.15360e7i	0.455055	+	0.788178i
$172$		0			0
$173$	2.17440e7	−	3.76617e7i	0.319285	−	0.553018i	−0.661054	−	0.750338i	$-0.729891\pi$
$173$	2.17440e7	−	3.76617e7i	0.319285	−	0.553018i	0.980339	+	0.197320i	$0.0632239\pi$
$174$		0			0
$175$	−6.32803e6	+	1.09605e7i	−0.0892555	+	0.154595i
$176$		0			0
$177$	−5.38620e6			−0.0730090
$178$		0			0
$179$	−1.54367e7	−	2.67372e7i	−0.201173	−	0.348441i	0.747734	−	0.663999i	$-0.231142\pi$
$179$	−1.54367e7	−	2.67372e7i	−0.201173	−	0.348441i	−0.948907	+	0.315557i	$0.897809\pi$
$180$		0			0
$181$	−1.39507e8			−1.74872			−0.874360	−	0.485278i	$-0.838718\pi$
$181$	−1.39507e8			−1.74872			−0.874360	+	0.485278i	$0.838718\pi$
$182$		0			0
$183$	−4.17614e7			−0.503728
$184$		0			0
$185$	−1.00535e7	−	1.74131e7i	−0.116739	−	0.202197i
$186$		0			0
$187$	7.10282e7			0.794302
$188$		0			0
$189$	5.07401e6	−	8.78845e6i	0.0546682	−	0.0946882i
$190$		0			0
$191$	−2.06193e7	+	3.57136e7i	−0.214120	+	0.370866i	−0.953000	−	0.302971i	$-0.902022\pi$
$191$	−2.06193e7	+	3.57136e7i	−0.214120	+	0.370866i	0.738880	+	0.673837i	$0.235355\pi$
$192$		0			0
$193$	6.94001e7	+	1.20204e8i	0.694879	+	1.20357i	0.970221	+	0.242220i	$0.0778754\pi$
$193$	6.94001e7	+	1.20204e8i	0.694879	+	1.20357i	−0.275342	+	0.961346i	$0.588791\pi$
$194$		0			0
$195$	7.49733e7	+	5.23337e7i	0.724078	+	0.505429i
$196$		0			0
$197$	−2.56717e6	−	4.44647e6i	−0.0239234	−	0.0414366i	0.853816	−	0.520575i	$-0.174282\pi$
$197$	−2.56717e6	−	4.44647e6i	−0.0239234	−	0.0414366i	−0.877739	+	0.479139i	$0.840949\pi$
$198$		0			0
$199$	4.81377e7	−	8.33770e7i	0.433012	−	0.749999i	−0.564119	−	0.825693i	$-0.690784\pi$
$199$	4.81377e7	−	8.33770e7i	0.433012	−	0.749999i	0.997131	+	0.0756947i	$0.0241174\pi$
$200$		0			0
$201$	−6.44265e7	+	1.11590e8i	−0.559601	+	0.969258i
$202$		0			0
$203$	−5.09177e7			−0.427201
$204$		0			0
$205$	1.93042e7	+	3.34358e7i	0.156499	+	0.271065i
$206$		0			0
$207$	1.94758e8			1.52616
$208$		0			0
$209$	4.36250e7			0.330539
$210$		0			0
$211$	5.38980e7	+	9.33541e7i	0.394988	+	0.684140i	0.993100	−	0.117273i	$-0.0374154\pi$
$211$	5.38980e7	+	9.33541e7i	0.394988	+	0.684140i	−0.598112	+	0.801413i	$0.704082\pi$
$212$		0			0
$213$	1.99880e8			1.41723
$214$		0			0
$215$	−7.48752e6	+	1.29688e7i	−0.0513811	+	0.0889946i
$216$		0			0
$217$	3.75818e7	−	6.50935e7i	0.249671	−	0.432443i
$218$		0			0
$219$	−6.13662e7	−	1.06289e8i	−0.394798	−	0.683810i
$220$		0			0
$221$	2.37396e7	−	2.75991e8i	0.147945	−	1.71997i
$222$		0			0
$223$	3.77450e6	+	6.53762e6i	0.0227925	+	0.0394778i	0.877197	−	0.480131i	$-0.159411\pi$
$223$	3.77450e6	+	6.53762e6i	0.0227925	+	0.0394778i	−0.854404	+	0.519609i	$0.826078\pi$
$224$		0			0
$225$	7.10007e7	−	1.22977e8i	0.415551	−	0.719755i
$226$		0			0
$227$	8.05895e7	−	1.39585e8i	0.457286	−	0.792043i	−0.541530	−	0.840681i	$-0.682155\pi$
$227$	8.05895e7	−	1.39585e8i	0.457286	−	0.792043i	0.998816	+	0.0486385i	$0.0154882\pi$
$228$		0			0
$229$	4.77059e7			0.262511			0.131256	−	0.991349i	$-0.458099\pi$
$229$	4.77059e7			0.262511			0.131256	+	0.991349i	$0.458099\pi$
$230$		0			0
$231$	−1.76577e7	−	3.05840e7i	−0.0942522	−	0.163250i
$232$		0			0
$233$	1.71967e8			0.890632			0.445316	−	0.895373i	$-0.353091\pi$
$233$	1.71967e8			0.890632			0.445316	+	0.895373i	$0.353091\pi$
$234$		0			0
$235$	−1.58632e8			−0.797359
$236$		0			0
$237$	1.13903e8	+	1.97286e8i	0.555796	+	0.962667i
$238$		0			0
$239$	−2.50000e8			−1.18453			−0.592266	−	0.805743i	$-0.701766\pi$
$239$	−2.50000e8			−1.18453			−0.592266	+	0.805743i	$0.701766\pi$
$240$		0			0
$241$	3.56126e7	−	6.16829e7i	0.163887	−	0.283861i	−0.772373	−	0.635170i	$-0.780930\pi$
$241$	3.56126e7	−	6.16829e7i	0.163887	−	0.283861i	0.936259	+	0.351309i	$0.114263\pi$
$242$		0			0
$243$	1.56393e8	−	2.70881e8i	0.699191	−	1.21103i
$244$		0			0
$245$	−6.25036e7	−	1.08259e8i	−0.271534	−	0.470310i
$246$		0			0
$247$	1.45807e7	−	1.69511e8i	0.0615656	−	0.715747i
$248$		0			0
$249$	−1.74336e8	−	3.01959e8i	−0.715632	−	1.23951i
$250$		0			0
$251$	1.90407e8	−	3.29795e8i	0.760022	−	1.31640i	−0.182817	−	0.983147i	$-0.558522\pi$
$251$	1.90407e8	−	3.29795e8i	0.760022	−	1.31640i	0.942839	−	0.333249i	$-0.108145\pi$
$252$		0			0
$253$	7.13874e7	−	1.23647e8i	0.277140	−	0.480021i
$254$		0			0
$255$	4.03636e8			1.52440
$256$		0			0
$257$	−2.42914e7	−	4.20740e7i	−0.0892662	−	0.154614i	0.817935	−	0.575311i	$-0.195119\pi$
$257$	−2.42914e7	−	4.20740e7i	−0.0892662	−	0.154614i	−0.907201	+	0.420697i	$0.861786\pi$
$258$		0			0
$259$	3.02883e7			0.108324
$260$		0			0
$261$	5.71299e8			1.98894
$262$		0			0
$263$	1.24702e8	+	2.15990e8i	0.422697	+	0.732132i	0.996202	−	0.0870697i	$-0.0277503\pi$
$263$	1.24702e8	+	2.15990e8i	0.422697	+	0.732132i	−0.573506	+	0.819202i	$0.694417\pi$
$264$		0			0
$265$	−4.71609e6			−0.0155676
$266$		0			0
$267$	1.79022e8	−	3.10076e8i	0.575596	−	0.996962i
$268$		0			0
$269$	−2.36778e8	+	4.10112e8i	−0.741667	+	1.28460i	0.210069	+	0.977687i	$0.432631\pi$
$269$	−2.36778e8	+	4.10112e8i	−0.741667	+	1.28460i	−0.951736	+	0.306918i	$0.900702\pi$
$270$		0			0
$271$	−7.22227e7	−	1.25093e8i	−0.220435	−	0.381805i	0.734505	−	0.678603i	$-0.237415\pi$
$271$	−7.22227e7	−	1.25093e8i	−0.220435	−	0.381805i	−0.954940	+	0.296798i	$0.904081\pi$
$272$		0			0
$273$	−1.24740e8	+	5.83895e7i	−0.371054	+	0.173686i
$274$		0			0
$275$	−5.20497e7	−	9.01527e7i	−0.150922	−	0.261405i
$276$		0			0
$277$	−2.26085e8	+	3.91590e8i	−0.639134	+	1.10701i	0.346489	+	0.938054i	$0.387374\pi$
$277$	−2.26085e8	+	3.91590e8i	−0.639134	+	1.10701i	−0.985623	+	0.168959i	$0.945959\pi$
$278$		0			0
$279$	−4.21669e8	+	7.30352e8i	−1.16240	+	2.01334i
$280$		0			0
$281$	1.80819e8			0.486151			0.243075	−	0.970007i	$-0.421844\pi$
$281$	1.80819e8			0.486151			0.243075	+	0.970007i	$0.421844\pi$
$282$		0			0
$283$	2.79735e8	+	4.84514e8i	0.733658	+	1.27073i	0.955310	+	0.295607i	$0.0955218\pi$
$283$	2.79735e8	+	4.84514e8i	0.733658	+	1.27073i	−0.221652	+	0.975126i	$0.571145\pi$
$284$		0			0
$285$	2.47910e8			0.634362
$286$		0			0
$287$	−5.81582e7			−0.145219
$288$		0			0
$289$	−4.06275e8	−	7.03689e8i	−0.990097	−	1.71490i
$290$		0			0
$291$	1.06149e9			2.52517
$292$		0			0
$293$	1.89521e8	−	3.28260e8i	0.440170	−	0.762397i	−0.557532	−	0.830156i	$-0.688251\pi$
$293$	1.89521e8	−	3.28260e8i	0.440170	−	0.762397i	0.997702	+	0.0677587i	$0.0215848\pi$
$294$		0			0
$295$	−6.27008e6	+	1.08601e7i	−0.0142199	+	0.0246296i
$296$		0			0
$297$	4.17351e7	+	7.22873e7i	0.0924387	+	0.160108i
$298$		0			0
$299$	−4.56588e8	−	3.18712e8i	−0.987813	−	0.689525i
$300$		0			0
$301$	−1.12789e7	−	1.95357e7i	−0.0238388	−	0.0412900i
$302$		0			0
$303$	−4.10688e8	+	7.11332e8i	−0.848130	+	1.46900i
$304$		0			0
$305$	−4.86145e7	+	8.42027e7i	−0.0981106	+	0.169933i
$306$		0			0
$307$	−1.00446e9			−1.98130			−0.990649	−	0.136433i	$-0.956436\pi$
$307$	−1.00446e9			−1.98130			−0.990649	+	0.136433i	$0.956436\pi$
$308$		0			0
$309$	2.16807e8	+	3.75520e8i	0.418040	+	0.724066i
$310$		0			0
$311$	−4.57084e8			−0.861658			−0.430829	−	0.902434i	$-0.641779\pi$
$311$	−4.57084e8			−0.861658			−0.430829	+	0.902434i	$0.641779\pi$
$312$		0			0
$313$	−6.79628e8			−1.25275			−0.626377	−	0.779520i	$-0.715463\pi$
$313$	−6.79628e8			−1.25275			−0.626377	+	0.779520i	$0.715463\pi$
$314$		0			0
$315$	−5.60788e7	−	9.71313e7i	−0.101091	−	0.175094i
$316$		0			0
$317$	1.42499e8			0.251249			0.125625	−	0.992078i	$-0.459907\pi$
$317$	1.42499e8			0.251249			0.125625	+	0.992078i	$0.459907\pi$
$318$		0			0
$319$	2.09406e8	−	3.62701e8i	0.361178	−	0.625578i
$320$		0			0
$321$	−5.67377e8	+	9.82725e8i	−0.957423	+	1.65830i
$322$		0			0
$323$	−3.75544e8	−	6.50462e8i	−0.620086	−	1.07402i
$324$		0			0
$325$	−3.67698e8	+	1.72115e8i	−0.594155	+	0.278117i
$326$		0			0
$327$	8.75570e8	+	1.51653e9i	1.38476	+	2.39847i
$328$		0			0
$329$	1.19479e8	−	2.06943e8i	0.184972	−	0.320380i
$330$		0			0
$331$	5.95525e7	−	1.03148e8i	0.0902614	−	0.156337i	−0.817360	−	0.576128i	$-0.804563\pi$
$331$	5.95525e7	−	1.03148e8i	0.0902614	−	0.156337i	0.907621	+	0.419790i	$0.137896\pi$
$332$		0			0
$333$	−3.39836e8			−0.504330
$334$		0			0
$335$	1.49998e8	+	2.59804e8i	0.217986	+	0.377563i
$336$		0			0
$337$	−3.15254e8			−0.448700			−0.224350	−	0.974509i	$-0.572026\pi$
$337$	−3.15254e8			−0.448700			−0.224350	+	0.974509i	$0.572026\pi$
$338$		0			0
$339$	−1.02486e8			−0.142879
$340$		0			0
$341$	3.09120e8	+	5.35411e8i	0.422169	+	0.731219i
$342$		0			0
$343$	3.91670e8			0.524072
$344$		0			0
$345$	4.05677e8	−	7.02653e8i	0.531880	−	0.921243i
$346$		0			0
$347$	−2.70320e8	+	4.68208e8i	−0.347316	+	0.601569i	−0.985772	−	0.168089i	$-0.946240\pi$
$347$	−2.70320e8	+	4.68208e8i	−0.347316	+	0.601569i	0.638456	+	0.769659i	$0.279574\pi$
$348$		0			0
$349$	1.38744e8	+	2.40312e8i	0.174713	+	0.302612i	0.940062	−	0.341004i	$-0.110767\pi$
$349$	1.38744e8	+	2.40312e8i	0.174713	+	0.302612i	−0.765349	+	0.643616i	$0.777434\pi$
$350$		0			0
$351$	2.94832e8	−	1.38007e8i	0.363915	−	0.170344i
$352$		0			0
$353$	−3.29885e6	−	5.71377e6i	−0.00399163	−	0.00691371i	0.864023	−	0.503453i	$-0.167937\pi$
$353$	−3.29885e6	−	5.71377e6i	−0.00399163	−	0.00691371i	−0.868014	+	0.496539i	$0.834604\pi$
$354$		0			0
$355$	2.32680e8	−	4.03014e8i	0.276033	−	0.478103i
$356$		0			0
$357$	−3.04011e8	+	5.26563e8i	−0.353631	+	0.612507i
$358$		0			0
$359$	−6.67727e8			−0.761672			−0.380836	−	0.924643i	$-0.624364\pi$
$359$	−6.67727e8			−0.761672			−0.380836	+	0.924643i	$0.624364\pi$
$360$		0			0
$361$	2.16280e8	+	3.74607e8i	0.241958	+	0.419084i
$362$		0			0
$363$	−1.08163e9			−1.18687
$364$		0			0
$365$	−2.85745e8			−0.307577
$366$		0			0
$367$	4.05024e8	+	7.01522e8i	0.427710	+	0.740816i	0.996669	−	0.0815499i	$-0.0259870\pi$
$367$	4.05024e8	+	7.01522e8i	0.427710	+	0.740816i	−0.568959	+	0.822366i	$0.692654\pi$
$368$		0			0
$369$	6.52537e8			0.676103
$370$		0			0
$371$	3.55207e6	−	6.15236e6i	0.00361137	−	0.00625508i
$372$		0			0
$373$	3.26424e8	−	5.65382e8i	0.325687	−	0.564107i	−0.655964	−	0.754792i	$-0.727738\pi$
$373$	3.26424e8	−	5.65382e8i	0.325687	−	0.564107i	0.981651	+	0.190685i	$0.0610711\pi$
$374$		0			0
$375$	−7.46661e8	−	1.29325e9i	−0.731163	−	1.26641i
$376$		0			0
$377$	−1.33934e9	−	9.34902e8i	−1.28735	−	0.898610i
$378$		0			0
$379$	−7.44867e8	−	1.29015e9i	−0.702816	−	1.21731i	−0.967474	−	0.252971i	$-0.918592\pi$
$379$	−7.44867e8	−	1.29015e9i	−0.702816	−	1.21731i	0.264658	−	0.964342i	$-0.414741\pi$
$380$		0			0
$381$	−4.89456e8	+	8.47762e8i	−0.453394	+	0.785302i
$382$		0			0
$383$	−2.20288e7	+	3.81550e7i	−0.0200353	+	0.0347021i	−0.875869	−	0.482549i	$-0.839711\pi$
$383$	−2.20288e7	+	3.81550e7i	−0.0200353	+	0.0347021i	0.855834	+	0.517251i	$0.173045\pi$
$384$		0			0
$385$	−8.22212e7			−0.0734296
$386$		0			0
$387$	1.26550e8	+	2.19191e8i	0.110987	+	0.192236i
$388$		0			0
$389$	−742221.			−0.000639307			−0.000319654	−	1.00000i	$-0.500102\pi$
$389$	−742221.			−0.000639307			−0.000319654		1.00000i	$0.500102\pi$
$390$		0			0
$391$	−2.45814e9			−2.07964
$392$		0			0
$393$	9.43552e8	+	1.63428e9i	0.784137	+	1.35816i
$394$		0			0
$395$	5.30377e8			0.433007
$396$		0			0
$397$	6.46952e8	−	1.12055e9i	0.518926	−	0.898806i	−0.480832	−	0.876813i	$-0.659665\pi$
$397$	6.46952e8	−	1.12055e9i	0.518926	−	0.898806i	0.999758	−	0.0219932i	$-0.00700121\pi$
$398$		0			0
$399$	−1.86721e8	+	3.23410e8i	−0.147160	+	0.254888i
$400$		0			0
$401$	−1.13847e9	−	1.97188e9i	−0.881688	−	1.52713i	−0.849464	−	0.527647i	$-0.823074\pi$
$401$	−1.13847e9	−	1.97188e9i	−0.881688	−	1.52713i	−0.0322237	−	0.999481i	$-0.510259\pi$
$402$		0			0
$403$	2.18374e9	−	1.02218e9i	1.66201	−	0.777966i
$404$		0			0
$405$	−2.59490e8	−	4.49450e8i	−0.194101	−	0.336193i
$406$		0			0
$407$	−1.24565e8	+	2.15752e8i	−0.0915829	+	0.158626i
$408$		0			0
$409$	−1.21746e8	+	2.10871e8i	−0.0879882	+	0.152400i	−0.906661	−	0.421861i	$-0.861377\pi$
$409$	−1.21746e8	+	2.10871e8i	−0.0879882	+	0.152400i	0.818672	+	0.574261i	$0.194710\pi$
$410$		0			0
$411$	−5.05843e8			−0.359393
$412$		0			0
$413$	−9.44501e6	−	1.63592e7i	−0.00659747	−	0.0114271i
$414$		0			0
$415$	−8.11778e8			−0.557531
$416$		0			0
$417$	−1.29105e9			−0.871898
$418$		0			0
$419$	−4.30530e8	−	7.45700e8i	−0.285926	−	0.495239i	0.686907	−	0.726745i	$-0.258968\pi$
$419$	−4.30530e8	−	7.45700e8i	−0.285926	−	0.495239i	−0.972833	+	0.231506i	$0.925635\pi$
$420$		0			0
$421$	3.23521e8			0.211308			0.105654	−	0.994403i	$-0.466306\pi$
$421$	3.23521e8			0.211308			0.105654	+	0.994403i	$0.466306\pi$
$422$		0			0
$423$	−1.34056e9	+	2.32191e9i	−0.861180	+	1.49161i
$424$		0			0
$425$	−8.96136e8	+	1.55215e9i	−0.566256	+	0.980784i
$426$		0			0
$427$	−7.32310e7	−	1.26840e8i	−0.0455195	−	0.0788421i
$428$		0			0
$429$	9.70858e7	−	1.12870e9i	0.0593684	−	0.690202i
$430$		0			0
$431$	1.11143e9	+	1.92505e9i	0.668667	+	1.15817i	0.978277	+	0.207302i	$0.0664682\pi$
$431$	1.11143e9	+	1.92505e9i	0.668667	+	1.15817i	−0.309610	+	0.950864i	$0.600198\pi$
$432$		0			0
$433$	1.02721e9	−	1.77918e9i	0.608066	−	1.05320i	−0.383493	−	0.923544i	$-0.625279\pi$
$433$	1.02721e9	−	1.77918e9i	0.608066	−	1.05320i	0.991559	−	0.129657i	$-0.0413876\pi$
$434$		0			0
$435$	1.19000e9	−	2.06114e9i	0.693162	−	1.20059i
$436$		0			0
$437$	−1.50977e9			−0.865419
$438$		0			0
$439$	−1.17568e8	−	2.03634e8i	−0.0663229	−	0.114875i	0.830957	−	0.556336i	$-0.187793\pi$
$439$	−1.17568e8	−	2.03634e8i	−0.0663229	−	0.114875i	−0.897280	+	0.441462i	$0.854460\pi$
$440$		0			0
$441$	−2.11280e9			−1.17307
$442$		0			0
$443$	1.35426e9			0.740100			0.370050	−	0.929012i	$-0.379341\pi$
$443$	1.35426e9			0.740100			0.370050	+	0.929012i	$0.379341\pi$
$444$		0			0
$445$	−4.16800e8	−	7.21919e8i	−0.224217	−	0.388354i
$446$		0			0
$447$	7.19394e8			0.380970
$448$		0			0
$449$	9.56886e8	−	1.65738e9i	0.498882	−	0.864089i	−0.501117	−	0.865380i	$-0.667077\pi$
$449$	9.56886e8	−	1.65738e9i	0.498882	−	0.864089i	0.999999	+	0.00129025i	$0.000410699\pi$
$450$		0			0
$451$	2.39183e8	−	4.14277e8i	0.122776	−	0.212654i
$452$		0			0
$453$	3.82063e8	+	6.61753e8i	0.193104	+	0.334466i
$454$		0			0
$455$	−2.74806e7	+	3.19483e8i	−0.0136769	+	0.159004i
$456$		0			0
$457$	1.64555e9	+	2.85018e9i	0.806500	+	1.39690i	0.915274	+	0.402832i	$0.131974\pi$
$457$	1.64555e9	+	2.85018e9i	0.806500	+	1.39690i	−0.108774	+	0.994067i	$0.534692\pi$
$458$		0			0
$459$	7.18550e8	−	1.24457e9i	0.346827	−	0.600722i
$460$		0			0
$461$	−8.70376e8	+	1.50754e9i	−0.413765	+	0.716662i	−0.995298	−	0.0968608i	$-0.969120\pi$
$461$	−8.70376e8	+	1.50754e9i	−0.413765	+	0.716662i	0.581533	+	0.813523i	$0.302453\pi$
$462$		0			0
$463$	−5.88177e7			−0.0275407			−0.0137703	−	0.999905i	$-0.504383\pi$
$463$	−5.88177e7			−0.0275407			−0.0137703	+	0.999905i	$0.504383\pi$
$464$		0			0
$465$	1.75665e9	+	3.04261e9i	0.810215	+	1.40333i
$466$		0			0
$467$	−1.47573e9			−0.670499			−0.335249	−	0.942129i	$-0.608821\pi$
$467$	−1.47573e9			−0.670499			−0.335249	+	0.942129i	$0.608821\pi$
$468$		0			0
$469$	−4.51902e8			−0.202274
$470$		0			0
$471$	1.26373e9	+	2.18884e9i	0.557288	+	0.965252i
$472$		0			0
$473$	1.85544e8			0.0806182
$474$		0			0
$475$	−5.50399e8	+	9.53320e8i	−0.235641	+	0.408142i
$476$		0			0
$477$	−3.98543e7	+	6.90297e7i	−0.0168136	+	0.0291220i
$478$		0			0
$479$	5.75573e8	+	9.96921e8i	0.239291	+	0.414464i	0.960511	−	0.278242i	$-0.0897518\pi$
$479$	5.75573e8	+	9.96921e8i	0.239291	+	0.414464i	−0.721220	+	0.692706i	$0.756418\pi$
$480$		0			0
$481$	7.96705e8	+	5.56125e8i	0.326430	+	0.227858i
$482$		0			0
$483$	6.11097e8	+	1.05845e9i	0.246771	+	0.427421i
$484$		0			0
$485$	1.23568e9	−	2.14026e9i	0.491824	−	0.851864i
$486$		0			0
$487$	−2.44105e9	+	4.22803e9i	−0.957692	+	1.65877i	−0.229607	+	0.973283i	$0.573744\pi$
$487$	−2.44105e9	+	4.22803e9i	−0.957692	+	1.65877i	−0.728084	+	0.685487i	$0.759589\pi$
$488$		0			0
$489$	3.64983e9			1.41154
$490$		0			0
$491$	−6.01834e8	−	1.04241e9i	−0.229452	−	0.397422i	0.728194	−	0.685371i	$-0.240360\pi$
$491$	−6.01834e8	−	1.04241e9i	−0.229452	−	0.397422i	−0.957646	+	0.287949i	$0.907027\pi$
$492$		0			0
$493$	−7.21065e9			−2.71025
$494$		0			0
$495$	9.22525e8			0.341869
$496$		0			0
$497$	3.50501e8	+	6.07085e8i	0.128068	+	0.221821i
$498$		0			0
$499$	3.64043e9			1.31160			0.655799	−	0.754935i	$-0.272332\pi$
$499$	3.64043e9			1.31160			0.655799	+	0.754935i	$0.272332\pi$
$500$		0			0
$501$	2.45548e9	−	4.25302e9i	0.872378	−	1.51100i
$502$		0			0
$503$	1.65318e9	−	2.86340e9i	0.579206	−	1.00321i	−0.416365	−	0.909198i	$-0.636696\pi$
$503$	1.65318e9	−	2.86340e9i	0.579206	−	1.00321i	0.995571	−	0.0940160i	$-0.0299705\pi$
$504$		0			0
$505$	9.56163e8	+	1.65612e9i	0.330379	+	0.572233i
$506$		0			0
$507$	−4.35326e9	−	7.54483e8i	−1.48350	−	0.257111i
$508$		0			0
$509$	5.50673e8	+	9.53794e8i	0.185089	+	0.320584i	0.943607	−	0.331069i	$-0.107409\pi$
$509$	5.50673e8	+	9.53794e8i	0.185089	+	0.320584i	−0.758517	+	0.651653i	$0.774076\pi$
$510$		0			0
$511$	2.15218e8	−	3.72769e8i	0.0713519	−	0.123585i
$512$		0			0
$513$	4.41328e8	−	7.64402e8i	0.144328	−	0.249983i
$514$		0			0
$515$	1.00954e9			0.325685
$516$		0			0
$517$	9.82745e8	+	1.70216e9i	0.312769	+	0.541732i
$518$		0			0
$519$	−3.06202e9			−0.961440
$520$		0			0
$521$	4.27358e9			1.32391			0.661957	−	0.749541i	$-0.269726\pi$
$521$	4.27358e9			1.32391			0.661957	+	0.749541i	$0.269726\pi$
$522$		0			0
$523$	−1.50948e9	−	2.61450e9i	−0.461395	−	0.799159i	0.537636	−	0.843177i	$-0.319318\pi$
$523$	−1.50948e9	−	2.61450e9i	−0.461395	−	0.799159i	−0.999031	+	0.0440177i	$0.985984\pi$
$524$		0			0
$525$	8.91120e8			0.268769
$526$		0			0
$527$	5.32210e9	−	9.21814e9i	1.58397	−	2.74351i
$528$		0			0
$529$	−7.68162e8	+	1.33050e9i	−0.225610	+	0.390768i
$530$		0			0
$531$	1.05973e8	+	1.83551e8i	0.0307161	+	0.0532019i
$532$		0			0
$533$	−1.52979e9	−	1.06784e9i	−0.437611	−	0.305466i
$534$		0			0
$535$	1.32097e9	+	2.28798e9i	0.372952	+	0.645973i
$536$		0			0
$537$	−1.08691e9	+	1.88258e9i	−0.302888	+	0.524618i
$538$		0			0
$539$	−7.74434e8	+	1.34136e9i	−0.213022	+	0.368964i
$540$		0			0
$541$	2.08205e9			0.565329			0.282664	−	0.959219i	$-0.408782\pi$
$541$	2.08205e9			0.565329			0.282664	+	0.959219i	$0.408782\pi$
$542$		0			0
$543$	4.91138e9	+	8.50675e9i	1.31645	+	2.28016i
$544$		0			0
$545$	4.07700e9			1.07883
$546$		0			0
$547$	1.26947e9			0.331641			0.165820	−	0.986156i	$-0.446973\pi$
$547$	1.26947e9			0.331641			0.165820	+	0.986156i	$0.446973\pi$
$548$		0			0
$549$	8.21655e8	+	1.42315e9i	0.211927	+	0.367068i
$550$		0			0
$551$	−4.42872e9			−1.12784
$552$		0			0
$553$	−3.99470e8	+	6.91903e8i	−0.100449	+	0.173983i
$554$		0			0
$555$	−7.07870e8	+	1.22607e9i	−0.175763	+	0.304431i
$556$		0			0
$557$	−1.46286e9	−	2.53375e9i	−0.358682	−	0.621256i	0.629059	−	0.777358i	$-0.283441\pi$
$557$	−1.46286e9	−	2.53375e9i	−0.358682	−	0.621256i	−0.987741	+	0.156102i	$0.950107\pi$
$558$		0			0
$559$	6.20140e7	−	7.20959e8i	0.0150158	−	0.174570i
$560$		0			0
$561$	−2.50057e9	−	4.33112e9i	−0.597956	−	1.03569i
$562$		0			0
$563$	4.08319e9	−	7.07229e9i	0.964318	−	1.67025i	0.252882	−	0.967497i	$-0.418621\pi$
$563$	4.08319e9	−	7.07229e9i	0.964318	−	1.67025i	0.711436	−	0.702751i	$-0.248045\pi$
$564$		0			0
$565$	−1.19304e8	+	2.06641e8i	−0.0278283	+	0.0482001i
$566$		0			0
$567$	7.81772e8			0.180111
$568$		0			0
$569$	1.01027e9	+	1.74984e9i	0.229903	+	0.398203i	0.957779	−	0.287505i	$-0.0928259\pi$
$569$	1.01027e9	+	1.74984e9i	0.229903	+	0.398203i	−0.727876	+	0.685708i	$0.759493\pi$
$570$		0			0
$571$	−4.65062e9			−1.04540			−0.522702	−	0.852515i	$-0.675076\pi$
$571$	−4.65062e9			−1.04540			−0.522702	+	0.852515i	$0.675076\pi$
$572$		0			0
$573$	2.90363e9			0.644764
$574$		0			0
$575$	1.80133e9	+	3.12000e9i	0.395145	+	0.684412i
$576$		0			0
$577$	5.94249e9			1.28781			0.643907	−	0.765104i	$-0.277312\pi$
$577$	5.94249e9			1.28781			0.643907	+	0.765104i	$0.277312\pi$
$578$		0			0
$579$	4.88650e9	−	8.46367e9i	1.04622	−	1.81211i
$580$		0			0
$581$	6.11416e8	−	1.05900e9i	0.129336	−	0.224017i
$582$		0			0
$583$	2.92167e7	+	5.06048e7i	0.00610648	+	0.0105767i
$584$		0			0
$585$	3.08334e8	−	3.58461e9i	0.0636759	−	0.740280i
$586$		0			0
$587$	−3.98257e8	−	6.89802e8i	−0.0812700	−	0.140764i	0.822526	−	0.568728i	$-0.192564\pi$
$587$	−3.98257e8	−	6.89802e8i	−0.0812700	−	0.140764i	−0.903796	+	0.427964i	$0.859231\pi$
$588$		0			0
$589$	3.26879e9	−	5.66171e9i	0.659149	−	1.14168i
$590$		0			0
$591$	−1.80756e8	+	3.13079e8i	−0.0360194	+	0.0623875i
$592$		0			0
$593$	−6.11768e9			−1.20475			−0.602373	−	0.798215i	$-0.705778\pi$
$593$	−6.11768e9			−1.20475			−0.602373	+	0.798215i	$0.705778\pi$
$594$		0			0
$595$	7.07799e8	+	1.22594e9i	0.137753	+	0.238595i
$596$		0			0
$597$	−6.77881e9			−1.30390
$598$		0			0
$599$	−4.08018e9			−0.775685			−0.387843	−	0.921726i	$-0.626780\pi$
$599$	−4.08018e9			−0.775685			−0.387843	+	0.921726i	$0.626780\pi$
$600$		0			0
$601$	−5.06656e9	−	8.77554e9i	−0.952035	−	1.64897i	−0.741013	−	0.671491i	$-0.765654\pi$
$601$	−5.06656e9	−	8.77554e9i	−0.952035	−	1.64897i	−0.211022	−	0.977481i	$-0.567679\pi$
$602$		0			0
$603$	5.07036e9			0.941734
$604$		0			0
$605$	−1.25912e9	+	2.18086e9i	−0.231166	+	0.400391i
$606$		0			0
$607$	−2.26264e9	+	3.91901e9i	−0.410635	+	0.711240i	−0.994959	−	0.100280i	$-0.968026\pi$
$607$	−2.26264e9	+	3.91901e9i	−0.410635	+	0.711240i	0.584325	+	0.811520i	$0.301360\pi$
$608$		0			0
$609$	1.79257e9	+	3.10483e9i	0.321600	+	0.557028i
$610$		0			0
$611$	6.94247e9	−	3.24969e9i	1.23132	−	0.576365i
$612$		0			0
$613$	−4.12211e7	−	7.13970e7i	−0.00722783	−	0.0125190i	0.862389	−	0.506246i	$-0.168967\pi$
$613$	−4.12211e7	−	7.13970e7i	−0.00722783	−	0.0125190i	−0.869617	+	0.493727i	$0.835634\pi$
$614$		0			0
$615$	1.35922e9	−	2.35424e9i	0.235628	−	0.408119i
$616$		0			0
$617$	5.32900e8	−	9.23010e8i	0.0913372	−	0.158201i	−0.816737	−	0.577010i	$-0.804219\pi$
$617$	5.32900e8	−	9.23010e8i	0.0913372	−	0.158201i	0.908074	+	0.418810i	$0.137553\pi$
$618$		0			0
$619$	7.35459e8			0.124635			0.0623177	−	0.998056i	$-0.480151\pi$
$619$	7.35459e8			0.124635			0.0623177	+	0.998056i	$0.480151\pi$
$620$		0			0
$621$	−1.44437e9	−	2.50172e9i	−0.242023	−	0.419197i
$622$		0			0
$623$	1.25570e9			0.208055
$624$		0			0
$625$	5.27307e8			0.0863940
$626$		0			0
$627$	−1.53583e9	−	2.66014e9i	−0.248832	−	0.430990i
$628$		0			0
$629$	4.28924e9			0.687232
$630$		0			0
$631$	2.07991e8	−	3.60252e8i	0.0329566	−	0.0570825i	−0.849077	−	0.528270i	$-0.822841\pi$
$631$	2.07991e8	−	3.60252e8i	0.0329566	−	0.0570825i	0.882033	+	0.471187i	$0.156174\pi$
$632$		0			0
$633$	3.79499e9	−	6.57312e9i	0.594700	−	1.03005i
$634$		0			0
$635$	1.13955e9	+	1.97376e9i	0.176614	+	0.305905i
$636$		0			0
$637$	4.95321e9	+	3.45750e9i	0.759274	+	0.529997i
$638$		0			0
$639$	−3.93264e9	−	6.81152e9i	−0.596253	−	1.03274i
$640$		0			0
$641$	−2.81157e9	+	4.86978e9i	−0.421644	+	0.730309i	−0.996100	−	0.0882264i	$-0.971880\pi$
$641$	−2.81157e9	+	4.86978e9i	−0.421644	+	0.730309i	0.574457	+	0.818535i	$0.305213\pi$
$642$		0			0
$643$	4.47709e9	−	7.75455e9i	0.664137	−	1.15032i	−0.315382	−	0.948965i	$-0.602133\pi$
$643$	4.47709e9	−	7.75455e9i	0.664137	−	1.15032i	0.979519	−	0.201354i	$-0.0645342\pi$
$644$		0			0
$645$	1.05440e9			0.154720
$646$		0			0
$647$	4.36397e9	+	7.55861e9i	0.633456	+	1.09718i	0.986840	+	0.161699i	$0.0516975\pi$
$647$	4.36397e9	+	7.55861e9i	0.633456	+	1.09718i	−0.353384	+	0.935478i	$0.614969\pi$
$648$		0			0
$649$	1.55375e8			0.0223113
$650$		0			0
$651$	−5.29231e9			−0.751816
$652$		0			0
$653$	−2.01742e9	−	3.49427e9i	−0.283531	−	0.491090i	0.688721	−	0.725026i	$-0.258172\pi$
$653$	−2.01742e9	−	3.49427e9i	−0.283531	−	0.491090i	−0.972252	+	0.233937i	$0.924839\pi$
$654$		0			0
$655$	4.39355e9			0.610902
$656$		0			0
$657$	−2.41476e9	+	4.18248e9i	−0.332196	+	0.575380i
$658$		0			0
$659$	−2.23633e9	+	3.87343e9i	−0.304394	+	0.527226i	−0.977126	−	0.212660i	$-0.931787\pi$
$659$	−2.23633e9	+	3.87343e9i	−0.304394	+	0.527226i	0.672732	+	0.739886i	$0.265121\pi$
$660$		0			0
$661$	4.53934e9	+	7.86236e9i	0.611346	+	1.05888i	0.991014	+	0.133760i	$0.0427050\pi$
$661$	4.53934e9	+	7.86236e9i	0.611346	+	1.05888i	−0.379668	+	0.925123i	$0.623962\pi$
$662$		0			0
$663$	−1.76650e10	+	8.26876e9i	−2.35405	+	1.10190i
$664$		0			0
$665$	4.34724e8	+	7.52964e8i	0.0573242	+	0.0992884i
$666$		0			0
$667$	−7.24711e9	+	1.25524e10i	−0.945637	+	1.63789i
$668$		0			0
$669$	2.65765e8	−	4.60318e8i	0.0343167	−	0.0594383i
$670$		0			0
$671$	1.20469e9			0.153938
$672$		0			0
$673$	4.13568e9	+	7.16321e9i	0.522991	+	0.905848i	0.999642	+	0.0267549i	$0.00851736\pi$
$673$	4.13568e9	+	7.16321e9i	0.522991	+	0.905848i	−0.476651	+	0.879093i	$0.658149\pi$
$674$		0			0
$675$	−2.10622e9			−0.263597
$676$		0			0
$677$	−7.18333e9			−0.889744			−0.444872	−	0.895594i	$-0.646751\pi$
$677$	−7.18333e9			−0.889744			−0.444872	+	0.895594i	$0.646751\pi$
$678$		0			0
$679$	1.86138e9	+	3.22400e9i	0.228187	+	0.395231i
$680$		0			0
$681$	−1.13487e10			−1.37699
$682$		0			0
$683$	−2.09930e9	+	3.63609e9i	−0.252117	+	0.436679i	−0.964108	−	0.265509i	$-0.914460\pi$
$683$	−2.09930e9	+	3.63609e9i	−0.252117	+	0.436679i	0.711992	+	0.702188i	$0.247793\pi$
$684$		0			0
$685$	−5.88852e8	+	1.01992e9i	−0.0699986	+	0.121241i
$686$		0			0
$687$	−1.67950e9	−	2.90898e9i	−0.197620	−	0.342289i
$688$		0			0
$689$	2.06397e8	−	9.66122e7i	0.0240401	−	0.0112529i
$690$		0			0
$691$	6.95215e9	+	1.20415e10i	0.801579	+	1.38837i	0.918577	+	0.395243i	$0.129339\pi$
$691$	6.95215e9	+	1.20415e10i	0.801579	+	1.38837i	−0.116998	+	0.993132i	$0.537327\pi$
$692$		0			0
$693$	−6.94829e8	+	1.20348e9i	−0.0793070	+	0.137364i
$694$		0			0
$695$	−1.50291e9	+	2.60311e9i	−0.169819	+	0.294135i
$696$		0			0
$697$	−8.23600e9			−0.921302
$698$		0			0
$699$	−6.05414e9	−	1.04861e10i	−0.670474	−	1.16130i
$700$		0			0
$701$	9.20624e9			1.00941			0.504707	−	0.863291i	$-0.331601\pi$
$701$	9.20624e9			1.00941			0.504707	+	0.863291i	$0.331601\pi$
$702$		0			0
$703$	2.63442e9			0.285984
$704$		0			0
$705$	5.58470e9	+	9.67298e9i	0.600258	+	1.03968i
$706$		0			0
$707$	−2.88066e9			−0.306566
$708$		0			0
$709$	−7.85494e9	+	1.36052e10i	−0.827716	+	1.43365i	0.0721104	+	0.997397i	$0.477027\pi$
$709$	−7.85494e9	+	1.36052e10i	−0.827716	+	1.43365i	−0.899826	+	0.436249i	$0.856307\pi$
$710$		0			0
$711$	4.48207e9	−	7.76318e9i	0.467665	−	0.810020i
$712$		0			0
$713$	−1.06980e10	−	1.85295e10i	−1.10532	−	1.91448i
$714$		0			0
$715$	−2.16275e9	−	1.50967e9i	−0.221276	−	0.154458i
$716$		0			0
$717$	8.80131e9	+	1.52443e10i	0.891724	+	1.54451i
$718$		0			0
$719$	2.92888e9	−	5.07296e9i	0.293866	−	0.508992i	−0.680854	−	0.732419i	$-0.738391\pi$
$719$	2.92888e9	−	5.07296e9i	0.293866	−	0.508992i	0.974721	+	0.223427i	$0.0717246\pi$
$720$		0			0
$721$	−7.60365e8	+	1.31699e9i	−0.0755525	+	0.130861i
$722$		0			0
$723$	−5.01501e9			−0.493501
$724$		0			0
$725$	5.28398e9	+	9.15213e9i	0.514966	+	0.891947i
$726$		0			0
$727$	−7.95539e8			−0.0767876			−0.0383938	−	0.999263i	$-0.512224\pi$
$727$	−7.95539e8			−0.0767876			−0.0383938	+	0.999263i	$0.512224\pi$
$728$		0			0
$729$	−1.50997e10			−1.44352
$730$		0			0
$731$	−1.59725e9	−	2.76652e9i	−0.151238	−	0.261953i
$732$		0			0
$733$	5.89067e9			0.552460			0.276230	−	0.961092i	$-0.410915\pi$
$733$	5.89067e9			0.552460			0.276230	+	0.961092i	$0.410915\pi$
$734$		0			0
$735$	−4.40092e9	+	7.62261e9i	−0.408825	+	0.708106i
$736$		0			0
$737$	1.85851e9	−	3.21903e9i	0.171013	−	0.296202i
$738$		0			0
$739$	4.03340e9	+	6.98606e9i	0.367634	+	0.636761i	0.989195	−	0.146605i	$-0.0468345\pi$
$739$	4.03340e9	+	6.98606e9i	0.367634	+	0.636761i	−0.621561	+	0.783366i	$0.713501\pi$
$740$		0			0
$741$	−1.08497e10	+	5.07860e9i	−0.979609	+	0.458544i
$742$		0			0
$743$	−9.23486e9	−	1.59953e10i	−0.825980	−	1.43064i	−0.901168	−	0.433470i	$-0.857289\pi$
$743$	−9.23486e9	−	1.59953e10i	−0.825980	−	1.43064i	0.0751879	−	0.997169i	$-0.476044\pi$
$744$		0			0
$745$	8.37447e8	−	1.45050e9i	0.0742011	−	0.128520i
$746$		0			0
$747$	−6.86011e9	+	1.18821e10i	−0.602156	+	1.04297i
$748$		0			0
$749$	−3.97971e9			−0.346071
$750$		0			0
$751$	2.05763e9	+	3.56392e9i	0.177267	+	0.307035i	0.940943	−	0.338564i	$-0.109941\pi$
$751$	2.05763e9	+	3.56392e9i	0.177267	+	0.307035i	−0.763677	+	0.645599i	$0.776608\pi$
$752$		0			0
$753$	−2.68134e10			−2.28860
$754$		0			0
$755$	1.77904e9			0.150443
$756$		0			0
$757$	5.00576e9	+	8.67023e9i	0.419406	+	0.726432i	0.995880	−	0.0906832i	$-0.0289051\pi$
$757$	5.00576e9	+	8.67023e9i	0.419406	+	0.726432i	−0.576474	+	0.817116i	$0.695572\pi$
$758$		0			0
$759$	−1.00529e10			−0.834533
$760$		0			0
$761$	9.42141e9	−	1.63184e10i	0.774942	−	1.34224i	−0.159884	−	0.987136i	$-0.551112\pi$
$761$	9.42141e9	−	1.63184e10i	0.774942	−	1.34224i	0.934827	−	0.355104i	$-0.115555\pi$
$762$		0			0
$763$	−3.07072e9	+	5.31865e9i	−0.250268	+	0.433476i
$764$		0			0
$765$	−7.94153e9	−	1.37551e10i	−0.641341	−	1.11084i
$766$		0			0
$767$	5.19308e7	−	6.03734e8i	0.00415567	−	0.0483128i
$768$		0			0
$769$	3.92588e9	+	6.79983e9i	0.311312	+	0.539207i	0.978647	−	0.205550i	$-0.0658984\pi$
$769$	3.92588e9	+	6.79983e9i	0.311312	+	0.539207i	−0.667335	+	0.744758i	$0.732565\pi$
$770$		0			0
$771$	−1.71037e9	+	2.96245e9i	−0.134400	+	0.232788i
$772$		0			0
$773$	9.70260e9	−	1.68054e10i	0.755544	−	1.30864i	−0.189560	−	0.981869i	$-0.560706\pi$
$773$	9.70260e9	−	1.68054e10i	0.755544	−	1.30864i	0.945103	−	0.326771i	$-0.105961\pi$
$774$		0			0
$775$	−1.56002e10			−1.20385
$776$		0			0
$777$	−1.06631e9	−	1.84690e9i	−0.0815473	−	0.141244i
$778$		0			0
$779$	−5.05849e9			−0.383389
$780$		0			0
$781$	−5.76592e9			−0.433102
$782$		0			0
$783$	−4.23686e9	−	7.33846e9i	−0.315412	−	0.546310i
$784$		0			0
$785$	5.88442e9			0.434170
$786$		0			0
$787$	−1.26249e10	+	2.18670e10i	−0.923246	+	1.59911i	−0.128887	+	0.991659i	$0.541141\pi$
$787$	−1.26249e10	+	2.18670e10i	−0.923246	+	1.59911i	−0.794359	+	0.607449i	$0.792193\pi$
$788$		0			0
$789$	8.78035e9	−	1.52080e10i	0.636418	−	1.10231i
$790$		0			0
$791$	−1.79716e8	−	3.11277e8i	−0.0129112	−	0.0223629i
$792$		0			0
$793$	4.02640e8	−	4.68099e9i	0.0286722	−	0.333336i
$794$		0			0
$795$	1.66031e8	+	2.87575e8i	0.0117194	+	0.0202986i
$796$		0			0
$797$	−1.17485e9	+	2.03490e9i	−0.0822011	+	0.142376i	−0.904195	−	0.427120i	$-0.859528\pi$
$797$	−1.17485e9	+	2.03490e9i	−0.0822011	+	0.142376i	0.821994	+	0.569496i	$0.192862\pi$
$798$		0			0
$799$	1.69199e10	−	2.93060e10i	1.17350	−	2.03256i
$800$		0			0
$801$	−1.40890e10			−0.968652
$802$		0			0
$803$	1.77023e9	+	3.06612e9i	0.120649	+	0.208970i
$804$		0			0
$805$	2.84551e9			0.192254
$806$		0			0
$807$	3.33434e10			2.23333
$808$		0			0
$809$	5.29367e9	+	9.16891e9i	0.351510	+	0.608832i	0.986514	−	0.163676i	$-0.0523351\pi$
$809$	5.29367e9	+	9.16891e9i	0.351510	+	0.608832i	−0.635005	+	0.772508i	$0.719002\pi$
$810$		0			0
$811$	8.44691e9			0.556064			0.278032	−	0.960572i	$-0.410318\pi$
$811$	8.44691e9			0.556064			0.278032	+	0.960572i	$0.410318\pi$
$812$		0			0
$813$	−5.08525e9	+	8.80791e9i	−0.331891	+	0.574852i
$814$		0			0
$815$	4.24877e9	−	7.35909e9i	0.274923	−	0.476181i
$816$		0			0
$817$	−9.81018e8	−	1.69917e9i	−0.0629361	−	0.109009i
$818$		0			0
$819$	4.44406e9	+	3.10210e9i	0.282674	+	0.197316i
$820$		0			0
$821$	4.61864e8	+	7.99972e8i	0.0291281	+	0.0504514i	0.880222	−	0.474562i	$-0.157394\pi$
$821$	4.61864e8	+	7.99972e8i	0.0291281	+	0.0504514i	−0.851094	+	0.525014i	$0.824060\pi$
$822$		0			0
$823$	−2.97774e9	+	5.15760e9i	−0.186203	+	0.322514i	−0.943981	−	0.329999i	$-0.892952\pi$
$823$	−2.97774e9	+	5.15760e9i	−0.186203	+	0.322514i	0.757778	+	0.652512i	$0.226285\pi$
$824$		0			0
$825$	−3.66485e9	+	6.34771e9i	−0.227231	+	0.393575i
$826$		0			0
$827$	7.33081e9			0.450695			0.225348	−	0.974278i	$-0.427648\pi$
$827$	7.33081e9			0.450695			0.225348	+	0.974278i	$0.427648\pi$
$828$		0			0
$829$	−1.01384e10	−	1.75603e10i	−0.618059	−	1.07051i	−0.989839	−	0.142189i	$-0.954586\pi$
$829$	−1.01384e10	−	1.75603e10i	−0.618059	−	1.07051i	0.371780	−	0.928321i	$-0.378748\pi$
$830$		0			0
$831$	3.18375e10			1.92458
$832$		0			0
$833$	2.66668e10			1.59850
$834$		0			0
$835$	−5.71685e9	−	9.90188e9i	−0.339824	−	0.588593i
$836$		0			0
$837$	1.25087e10			0.737350
$838$		0			0
$839$	5.98389e9	−	1.03644e10i	0.349798	−	0.605867i	−0.636416	−	0.771346i	$-0.719584\pi$
$839$	5.98389e9	−	1.03644e10i	0.349798	−	0.605867i	0.986213	+	0.165479i	$0.0529170\pi$
$840$		0			0
$841$	−1.26335e10	+	2.18819e10i	−0.732383	+	1.26852i
$842$		0			0
$843$	−6.36577e9	−	1.10258e10i	−0.365978	−	0.633892i
$844$		0			0
$845$	−6.58888e9	+	7.89911e9i	−0.375676	+	0.450380i
$846$		0			0
$847$	−1.89669e9	−	3.28517e9i	−0.107252	−	0.185766i
$848$		0			0
$849$	1.96963e10	−	3.41150e10i	1.10461	−	1.91323i
$850$		0			0
$851$	4.31093e9	−	7.46675e9i	0.239783	−	0.415316i
$852$		0			0
$853$	−1.44625e10			−0.797853			−0.398927	−	0.916983i	$-0.630617\pi$
$853$	−1.44625e10			−0.797853			−0.398927	+	0.916983i	$0.630617\pi$
$854$		0			0
$855$	−4.87762e9	−	8.44829e9i	−0.266887	−	0.462261i
$856$		0			0
$857$	1.74997e10			0.949723			0.474861	−	0.880061i	$-0.342498\pi$
$857$	1.74997e10			0.949723			0.474861	+	0.880061i	$0.342498\pi$
$858$		0			0
$859$	1.21484e10			0.653945			0.326973	−	0.945034i	$-0.393972\pi$
$859$	1.21484e10			0.653945			0.326973	+	0.945034i	$0.393972\pi$
$860$		0			0
$861$	2.04748e9	+	3.54633e9i	0.109322	+	0.189351i
$862$		0			0
$863$	−5.06062e9			−0.268019			−0.134010	−	0.990980i	$-0.542785\pi$
$863$	−5.06062e9			−0.268019			−0.134010	+	0.990980i	$0.542785\pi$
$864$		0			0
$865$	−3.56450e9	+	6.17389e9i	−0.187259	+	0.324341i
$866$		0			0
$867$	−2.86061e10	+	4.95472e10i	−1.49070	+	2.58198i
$868$		0			0
$869$	−3.28575e9	−	5.69108e9i	−0.169850	−	0.294188i
$870$		0			0
$871$	−1.18868e10	−	8.29739e9i	−0.609541	−	0.425479i
$872$		0			0
$873$	−2.08848e10	−	3.61735e10i	−1.06238	−	1.84009i
$874$		0			0
$875$	2.61862e9	−	4.53559e9i	0.132143	−	0.228879i
$876$		0			0
$877$	−1.14200e10	+	1.97801e10i	−0.571700	+	0.990213i	0.424692	+	0.905338i	$0.360383\pi$
$877$	−1.14200e10	+	1.97801e10i	−0.571700	+	0.990213i	−0.996392	+	0.0848754i	$0.972951\pi$
$878$		0			0
$879$	−2.66886e10			−1.32545
$880$		0			0
$881$	−1.17368e10	−	2.03287e10i	−0.578273	−	1.00160i	−0.995677	−	0.0928780i	$-0.970393\pi$
$881$	−1.17368e10	−	2.03287e10i	−0.578273	−	1.00160i	0.417404	−	0.908721i	$-0.362940\pi$
$882$		0			0
$883$	1.70477e10			0.833302			0.416651	−	0.909067i	$-0.363204\pi$
$883$	1.70477e10			0.833302			0.416651	+	0.909067i	$0.363204\pi$
$884$		0			0
$885$	8.82960e8			0.0428193
$886$		0			0
$887$	7.28432e9	+	1.26168e10i	0.350474	+	0.607039i	0.986333	−	0.164766i	$-0.0526870\pi$
$887$	7.28432e9	+	1.26168e10i	0.350474	+	0.607039i	−0.635858	+	0.771806i	$0.719354\pi$
$888$		0			0
$889$	−3.43315e9			−0.163884
$890$		0			0
$891$	−3.21514e9	+	5.56879e9i	−0.152275	+	0.263748i
$892$		0			0
$893$	1.03920e10	−	1.79995e10i	0.488338	−	0.845826i
$894$		0			0
$895$	2.53054e9	+	4.38302e9i	0.117987	+	0.204359i
$896$		0			0
$897$	−3.35994e9	+	3.90619e10i	−0.155439	+	1.80709i
$898$		0			0
$899$	−3.13812e10	−	5.43539e10i	−1.44049	−	2.49501i
$900$		0			0
$901$	5.03022e8	−	8.71259e8i	0.0229113	−	0.0396836i
$902$		0			0
$903$	−7.94155e8	+	1.37552e9i	−0.0358920	+	0.0621668i
$904$		0			0
$905$	2.28693e10			1.02561
$906$		0			0
$907$	9.66075e9	+	1.67329e10i	0.429918	+	0.744640i	0.996866	−	0.0791142i	$-0.0252092\pi$
$907$	9.66075e9	+	1.67329e10i	0.429918	+	0.744640i	−0.566948	+	0.823754i	$0.691876\pi$
$908$		0			0
$909$	3.23211e10			1.42729
$910$		0			0
$911$	−1.95446e10			−0.856471			−0.428235	−	0.903667i	$-0.640865\pi$
$911$	−1.95446e10			−0.856471			−0.428235	+	0.903667i	$0.640865\pi$
$912$		0			0
$913$	5.02906e9	+	8.71058e9i	0.218695	+	0.378791i
$914$		0			0
$915$	6.84595e9			0.295433
$916$		0			0
$917$	−3.30914e9	+	5.73160e9i	−0.141717	+	0.245462i
$918$		0			0
$919$	9.81678e9	−	1.70032e10i	0.417220	−	0.722646i	−0.578439	−	0.815726i	$-0.696338\pi$
$919$	9.81678e9	−	1.70032e10i	0.417220	−	0.722646i	0.995659	+	0.0930800i	$0.0296712\pi$
$920$		0			0
$921$	3.53625e10	+	6.12496e10i	1.49154	+	2.58342i
$922$		0			0
$923$	−1.92713e9	+	2.24044e10i	−0.0806688	+	0.937835i
$924$		0			0
$925$	−3.14317e9	−	5.44413e9i	−0.130578	−	0.226169i
$926$		0			0
$927$	8.53133e9	−	1.47767e10i	0.351753	−	0.609254i
$928$		0			0
$929$	1.33151e10	−	2.30625e10i	0.544867	−	0.943737i	−0.453748	−	0.891130i	$-0.649913\pi$
$929$	1.33151e10	−	2.30625e10i	0.544867	−	0.943737i	0.998615	−	0.0526074i	$-0.0167532\pi$
$930$		0			0
$931$	1.63785e10			0.665197
$932$		0			0
$933$	1.60918e10	+	2.78718e10i	0.648662	+	1.12352i
$934$		0			0
$935$	−1.16437e10			−0.465853
$936$		0			0
$937$	1.47566e9			0.0585999			0.0292999	−	0.999571i	$-0.490672\pi$
$937$	1.47566e9			0.0585999			0.0292999	+	0.999571i	$0.490672\pi$
$938$		0			0
$939$	2.39265e10	+	4.14419e10i	0.943083	+	1.63347i
$940$		0			0
$941$	−2.25755e10			−0.883231			−0.441616	−	0.897204i	$-0.645595\pi$
$941$	−2.25755e10			−0.883231			−0.441616	+	0.897204i	$0.645595\pi$
$942$		0			0
$943$	−8.27765e9	+	1.43373e10i	−0.321452	+	0.556771i
$944$		0			0
$945$	−8.31783e8	+	1.44069e9i	−0.0320626	+	0.0555340i
$946$		0			0
$947$	9.93974e9	+	1.72161e10i	0.380321	+	0.658735i	0.991108	−	0.133060i	$-0.0424802\pi$
$947$	9.93974e9	+	1.72161e10i	0.380321	+	0.658735i	−0.610787	+	0.791795i	$0.709147\pi$
$948$		0			0
$949$	1.25055e10	−	5.85369e9i	0.474974	−	0.222330i
$950$		0			0
$951$	−5.01673e9	−	8.68922e9i	−0.189142	−	0.327604i
$952$		0			0
$953$	−1.23018e10	+	2.13073e10i	−0.460408	+	0.797451i	−0.998981	−	0.0451281i	$-0.985630\pi$
$953$	−1.23018e10	+	2.13073e10i	−0.460408	+	0.797451i	0.538573	+	0.842579i	$0.318964\pi$
$954$		0			0
$955$	3.38012e9	−	5.85454e9i	0.125580	−	0.217511i
$956$		0			0
$957$	−2.94888e10			−1.08759
$958$		0			0
$959$	−8.87024e8	−	1.53637e9i	−0.0324766	−	0.0562511i
$960$		0			0
$961$	6.51360e10			2.36749
$962$		0			0
$963$	4.46525e10			1.61122
$964$		0			0
$965$	−1.13767e10	−	1.97051e10i	−0.407542	−	0.705884i
$966$		0			0
$967$	−1.21598e10			−0.432449			−0.216224	−	0.976344i	$-0.569374\pi$
$967$	−1.21598e10			−0.432449			−0.216224	+	0.976344i	$0.569374\pi$
$968$		0			0
$969$	−2.64423e10	+	4.57994e10i	−0.933611	+	1.61706i
$970$		0			0
$971$	1.72456e10	−	2.98703e10i	0.604522	−	1.04706i	−0.387605	−	0.921826i	$-0.626697\pi$
$971$	1.72456e10	−	2.98703e10i	0.604522	−	1.04706i	0.992127	−	0.125237i	$-0.0399693\pi$
$972$		0			0
$973$	−2.26392e9	−	3.92123e9i	−0.0787892	−	0.136467i
$974$		0			0
$975$	2.34401e10	+	1.63619e10i	0.809921	+	0.565350i
$976$		0			0
$977$	−1.64824e10	−	2.85484e10i	−0.565445	−	0.979380i	−0.997008	−	0.0772970i	$-0.975371\pi$
$977$	−1.64824e10	−	2.85484e10i	−0.565445	−	0.979380i	0.431563	−	0.902083i	$-0.357962\pi$
$978$		0			0
$979$	−5.16425e9	+	8.94474e9i	−0.175901	+	0.304669i
$980$		0			0
$981$	3.44536e10	−	5.96755e10i	1.16518	−	2.01815i
$982$		0			0
$983$	4.71393e10			1.58287			0.791435	−	0.611253i	$-0.209334\pi$
$983$	4.71393e10			1.58287			0.791435	+	0.611253i	$0.209334\pi$
$984$		0			0
$985$	4.20837e8	+	7.28910e8i	0.0140309	+	0.0243023i
$986$		0			0
$987$	−1.68252e10			−0.556992
$988$		0			0
$989$	−6.42131e9			−0.211075
$990$		0			0
$991$	−1.18660e10	−	2.05525e10i	−0.387300	−	0.670823i	0.604786	−	0.796388i	$-0.293259\pi$
$991$	−1.18660e10	−	2.05525e10i	−0.387300	−	0.670823i	−0.992085	+	0.125565i	$0.959925\pi$
$992$		0			0
$993$	−8.38626e9			−0.271798
$994$		0			0
$995$	−7.89122e9	+	1.36680e10i	−0.253959	+	0.439870i
$996$		0			0
$997$	−6.00395e9	+	1.03991e10i	−0.191869	+	0.332326i	−0.945870	−	0.324547i	$-0.894788\pi$
$997$	−6.00395e9	+	1.03991e10i	−0.191869	+	0.332326i	0.754001	+	0.656873i	$0.228121\pi$
$998$		0			0
$999$	2.52029e9	+	4.36527e9i	0.0799782	+	0.138526i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.8.i.d.81.1		16
4.3	odd	2		13.8.c.a.3.7	✓	16
12.11	even	2		117.8.g.d.55.2		16
13.9	even	3	inner	208.8.i.d.113.1		16
52.3	odd	6		169.8.a.f.1.2		8
52.11	even	12		169.8.b.e.168.5		16
52.15	even	12		169.8.b.e.168.12		16
52.23	odd	6		169.8.a.e.1.7		8
52.35	odd	6		13.8.c.a.9.7	yes	16
156.35	even	6		117.8.g.d.100.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.c.a.3.7	✓	16	4.3	odd	2
13.8.c.a.9.7	yes	16	52.35	odd	6
117.8.g.d.55.2		16	12.11	even	2
117.8.g.d.100.2		16	156.35	even	6
169.8.a.e.1.7		8	52.23	odd	6
169.8.a.f.1.2		8	52.3	odd	6
169.8.b.e.168.5		16	52.11	even	12
169.8.b.e.168.12		16	52.15	even	12
208.8.i.d.81.1		16	1.1	even	1	trivial
208.8.i.d.113.1		16	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	208.8.i.d.81.1

Level	$208$
Weight	$8$
Character	208.81
Analytic conductor	$64.976$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$