LMFDB - Embedded newform 81.9.f.a.8.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not 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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.17
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(18.1654 + 3.20306i) q^{2} +(79.1620 + 28.8126i) q^{4} +(-462.775 - 551.514i) q^{5} +(1642.82 - 597.939i) q^{7} +(-2743.73 - 1584.09i) q^{8} +(-6639.98 - 11500.8i) q^{10} +(-9016.87 + 10745.9i) q^{11} +(9043.29 + 51287.0i) q^{13} +(31757.8 - 5599.76i) q^{14} +(-61287.6 - 51426.4i) q^{16} +(49707.0 - 28698.4i) q^{17} +(-116884. + 202450. i) q^{19} +(-20743.7 - 56992.7i) q^{20} +(-198215. + 166322. i) q^{22} +(-79587.0 + 218664. i) q^{23} +(-22175.6 + 125764. i) q^{25} +960617. i q^{26} +147277. q^{28} +(-147697. - 26043.0i) q^{29} +(-1.38587e6 - 504414. i) q^{31} +(-427258. - 509186. i) q^{32} +(994872. - 362104. i) q^{34} +(-1.09003e6 - 629329. i) q^{35} +(697113. + 1.20744e6i) q^{37} +(-2.77171e6 + 3.30320e6i) q^{38} +(396080. + 2.24628e6i) q^{40} +(1.41044e6 - 248698. i) q^{41} +(-69449.3 - 58274.9i) q^{43} +(-1.02341e6 + 590866. i) q^{44} +(-2.14612e6 + 3.71720e6i) q^{46} +(-2.27848e6 - 6.26006e6i) q^{47} +(-2.07476e6 + 1.74093e6i) q^{49} +(-805657. + 2.21352e6i) q^{50} +(-761828. + 4.32054e6i) q^{52} +396154. i q^{53} +1.00993e7 q^{55} +(-5.45465e6 - 961801. i) q^{56} +(-2.59957e6 - 946165. i) q^{58} +(3.41825e6 + 4.07371e6i) q^{59} +(1.58012e6 - 575117. i) q^{61} +(-2.35592e7 - 1.36019e7i) q^{62} +(4.11030e6 + 7.11925e6i) q^{64} +(2.41005e7 - 2.87219e7i) q^{65} +(1.88303e6 + 1.06792e7i) q^{67} +(4.76178e6 - 839630. i) q^{68} +(-1.77851e7 - 1.49235e7i) q^{70} +(-3.79332e7 + 2.19007e7i) q^{71} +(-9.39455e6 + 1.62718e7i) q^{73} +(8.79588e6 + 2.41665e7i) q^{74} +(-1.50859e7 + 1.26586e7i) q^{76} +(-8.38774e6 + 2.30451e7i) q^{77} +(171845. - 974580. i) q^{79} +5.75999e7i q^{80} +2.64178e7 q^{82} +(-2.50236e7 - 4.41234e6i) q^{83} +(-3.88307e7 - 1.41332e7i) q^{85} +(-1.07492e6 - 1.28104e6i) q^{86} +(4.17623e7 - 1.52002e7i) q^{88} +(3.33894e7 + 1.92774e7i) q^{89} +(4.55230e7 + 7.88482e7i) q^{91} +(-1.26005e7 + 1.50167e7i) q^{92} +(-2.13382e7 - 1.21015e8i) q^{94} +(1.65745e8 - 2.92253e7i) q^{95} +(-1.11208e8 - 9.33146e7i) q^{97} +(-4.32651e7 + 2.49791e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	18.1654	+	3.20306i	1.13534	+	0.200191i	0.709566	−	0.704639i	$-0.248891\pi$
$2$	18.1654	+	3.20306i	1.13534	+	0.200191i	0.425773	+	0.904830i	$0.360002\pi$
$3$		0			0
$3$		0			0
$4$	79.1620	+	28.8126i	0.309227	+	0.112549i
$5$	−462.775	−	551.514i	−0.740441	−	0.882423i	0.256004	−	0.966676i	$-0.417594\pi$
$5$	−462.775	−	551.514i	−0.740441	−	0.882423i	−0.996444	+	0.0842531i	$0.973150\pi$
$6$		0			0
$7$	1642.82	−	597.939i	0.684225	−	0.249037i	0.0235642	−	0.999722i	$-0.492499\pi$
$7$	1642.82	−	597.939i	0.684225	−	0.249037i	0.660660	+	0.750685i	$0.270276\pi$
$8$	−2743.73	−	1584.09i	−0.669855	−	0.386741i
$9$		0			0
$10$	−6639.98	−	11500.8i	−0.663998	−	1.15008i
$11$	−9016.87	+	10745.9i	−0.615864	+	0.733958i	−0.980353	−	0.197249i	$-0.936799\pi$
$11$	−9016.87	+	10745.9i	−0.615864	+	0.733958i	0.364489	+	0.931208i	$0.381244\pi$
$12$		0			0
$13$	9043.29	+	51287.0i	0.316631	+	1.79570i	0.562927	+	0.826507i	$0.309675\pi$
$13$	9043.29	+	51287.0i	0.316631	+	1.79570i	−0.246296	+	0.969195i	$0.579214\pi$
$14$	31757.8	−	5599.76i	0.826682	−	0.145766i
$15$		0			0
$16$	−61287.6	−	51426.4i	−0.935175	−	0.784705i
$17$	49707.0	−	28698.4i	0.595144	−	0.343606i	−0.171985	−	0.985100i	$-0.555018\pi$
$17$	49707.0	−	28698.4i	0.595144	−	0.343606i	0.767129	+	0.641493i	$0.221685\pi$
$18$		0			0
$19$	−116884.	+	202450.i	−0.896896	+	1.55347i	−0.0654550	+	0.997856i	$0.520850\pi$
$19$	−116884.	+	202450.i	−0.896896	+	1.55347i	−0.831441	+	0.555613i	$0.812483\pi$
$20$	−20743.7	−	56992.7i	−0.129648	−	0.356205i
$21$		0			0
$22$	−198215.	+	166322.i	−0.846147	+	0.710001i
$23$	−79587.0	+	218664.i	−0.284401	+	0.781385i	0.712423	+	0.701750i	$0.247598\pi$
$23$	−79587.0	+	218664.i	−0.284401	+	0.781385i	−0.996824	+	0.0796349i	$0.974625\pi$
$24$		0			0
$25$	−22175.6	+	125764.i	−0.0567694	+	0.321955i
$26$			960617.i			2.10212i
$27$		0			0
$28$	147277.			0.239609
$29$	−147697.	−	26043.0i	−0.208824	−	0.0368213i	0.0682575	−	0.997668i	$-0.478256\pi$
$29$	−147697.	−	26043.0i	−0.208824	−	0.0368213i	−0.277081	+	0.960846i	$0.589367\pi$
$30$		0			0
$31$	−1.38587e6	−	504414.i	−1.50063	−	0.546186i	−0.544409	−	0.838820i	$-0.683246\pi$
$31$	−1.38587e6	−	504414.i	−1.50063	−	0.546186i	−0.956225	+	0.292633i	$0.905468\pi$
$32$	−427258.	−	509186.i	−0.407465	−	0.485598i
$33$		0			0
$34$	994872.	−	362104.i	0.744477	−	0.270968i
$35$	−1.09003e6	−	629329.i	−0.726384	−	0.419378i
$36$		0			0
$37$	697113.	+	1.20744e6i	0.371960	+	0.644254i	0.989867	−	0.141998i	$-0.0453525\pi$
$37$	697113.	+	1.20744e6i	0.371960	+	0.644254i	−0.617907	+	0.786251i	$0.712019\pi$
$38$	−2.77171e6	+	3.30320e6i	−1.32927	+	1.58416i
$39$		0			0
$40$	396080.	+	2.24628e6i	0.154719	+	0.877454i
$41$	1.41044e6	−	248698.i	0.499136	−	0.0880111i	0.0815882	−	0.996666i	$-0.474001\pi$
$41$	1.41044e6	−	248698.i	0.499136	−	0.0880111i	0.417548	+	0.908655i	$0.362890\pi$
$42$		0			0
$43$	−69449.3	−	58274.9i	−0.0203139	−	0.0170454i	0.632574	−	0.774500i	$-0.281998\pi$
$43$	−69449.3	−	58274.9i	−0.0203139	−	0.0170454i	−0.652888	+	0.757454i	$0.726443\pi$
$44$	−1.02341e6	+	590866.i	−0.273048	+	0.157644i
$45$		0			0
$46$	−2.14612e6	+	3.71720e6i	−0.479318	+	0.830203i
$47$	−2.27848e6	−	6.26006e6i	−0.466931	−	1.28288i	−0.920179	−	0.391498i	$-0.871957\pi$
$47$	−2.27848e6	−	6.26006e6i	−0.466931	−	1.28288i	0.453248	−	0.891385i	$-0.350265\pi$
$48$		0			0
$49$	−2.07476e6	+	1.74093e6i	−0.359901	+	0.301993i
$50$	−805657.	+	2.21352e6i	−0.128905	+	0.354164i
$51$		0			0
$52$	−761828.	+	4.32054e6i	−0.104194	+	0.590915i
$53$			396154.i			0.0502065i	0.999685	+	0.0251033i	$0.00799146\pi$
$53$			396154.i			0.0502065i	−0.999685	+	0.0251033i	$0.992009\pi$
$54$		0			0
$55$	1.00993e7			1.10367
$56$	−5.45465e6	−	961801.i	−0.554644	−	0.0977987i
$57$		0			0
$58$	−2.59957e6	−	946165.i	−0.229715	−	0.0836093i
$59$	3.41825e6	+	4.07371e6i	0.282095	+	0.336188i	0.888422	−	0.459028i	$-0.151802\pi$
$59$	3.41825e6	+	4.07371e6i	0.282095	+	0.336188i	−0.606327	+	0.795216i	$0.707358\pi$
$60$		0			0
$61$	1.58012e6	−	575117.i	0.114123	−	0.0415372i	−0.284328	−	0.958727i	$-0.591770\pi$
$61$	1.58012e6	−	575117.i	0.114123	−	0.0415372i	0.398450	+	0.917190i	$0.369548\pi$
$62$	−2.35592e7	−	1.36019e7i	−1.59439	−	0.920520i
$63$		0			0
$64$	4.11030e6	+	7.11925e6i	0.244993	+	0.424340i
$65$	2.41005e7	−	2.87219e7i	1.35012	−	1.60901i
$66$		0			0
$67$	1.88303e6	+	1.06792e7i	0.0934456	+	0.529956i	0.995213	+	0.0977338i	$0.0311594\pi$
$67$	1.88303e6	+	1.06792e7i	0.0934456	+	0.529956i	−0.901767	+	0.432222i	$0.857730\pi$
$68$	4.76178e6	−	839630.i	0.222707	−	0.0392692i
$69$		0			0
$70$	−1.77851e7	−	1.49235e7i	−0.740737	−	0.621552i
$71$	−3.79332e7	+	2.19007e7i	−1.49275	+	0.861837i	−0.999965	−	0.00831631i	$-0.997353\pi$
$71$	−3.79332e7	+	2.19007e7i	−1.49275	+	0.861837i	−0.492781	+	0.870154i	$0.664019\pi$
$72$		0			0
$73$	−9.39455e6	+	1.62718e7i	−0.330815	+	0.572988i	−0.982672	−	0.185354i	$-0.940657\pi$
$73$	−9.39455e6	+	1.62718e7i	−0.330815	+	0.572988i	0.651857	+	0.758342i	$0.273990\pi$
$74$	8.79588e6	+	2.41665e7i	0.293327	+	0.805910i
$75$		0			0
$76$	−1.50859e7	+	1.26586e7i	−0.452186	+	0.379429i
$77$	−8.38774e6	+	2.30451e7i	−0.238606	+	0.655565i
$78$		0			0
$79$	171845.	−	974580.i	0.00441192	−	0.0250213i	−0.982522	−	0.186145i	$-0.940401\pi$
$79$	171845.	−	974580.i	0.00441192	−	0.0250213i	0.986934	+	0.161124i	$0.0515118\pi$
$80$			5.75999e7i			1.40625i
$81$		0			0
$82$	2.64178e7			0.584308
$83$	−2.50236e7	−	4.41234e6i	−0.527276	−	0.0929730i	−0.0963279	−	0.995350i	$-0.530710\pi$
$83$	−2.50236e7	−	4.41234e6i	−0.527276	−	0.0929730i	−0.430948	+	0.902377i	$0.641821\pi$
$84$		0			0
$85$	−3.88307e7	−	1.41332e7i	−0.743875	−	0.270748i
$86$	−1.07492e6	−	1.28104e6i	−0.0196509	−	0.0234190i
$87$		0			0
$88$	4.17623e7	−	1.52002e7i	0.696391	−	0.253466i
$89$	3.33894e7	+	1.92774e7i	0.532168	+	0.307247i	0.741899	−	0.670512i	$-0.233925\pi$
$89$	3.33894e7	+	1.92774e7i	0.532168	+	0.307247i	−0.209731	+	0.977759i	$0.567259\pi$
$90$		0			0
$91$	4.55230e7	+	7.88482e7i	0.663843	+	1.14981i
$92$	−1.26005e7	+	1.50167e7i	−0.175889	+	0.209616i
$93$		0			0
$94$	−2.13382e7	−	1.21015e8i	−0.273304	−	1.54998i
$95$	1.65745e8	−	2.92253e7i	2.03491	−	0.358810i
$96$		0			0
$97$	−1.11208e8	−	9.33146e7i	−1.25617	−	1.05405i	−0.996079	−	0.0884697i	$-0.971802\pi$
$97$	−1.11208e8	−	9.33146e7i	−1.25617	−	1.05405i	−0.260093	−	0.965584i	$-0.583753\pi$
$98$	−4.32651e7	+	2.49791e7i	−0.469066	+	0.270815i
$99$		0			0
$100$	−5.37905e6	+	9.31678e6i	−0.0537905	+	0.0931678i
$101$	−1.89584e7	−	5.20877e7i	−0.182186	−	0.500552i	0.814658	−	0.579942i	$-0.196925\pi$
$101$	−1.89584e7	−	5.20877e7i	−0.182186	−	0.500552i	−0.996844	+	0.0793901i	$0.974703\pi$
$102$		0			0
$103$	3.52430e6	−	2.95724e6i	0.0313130	−	0.0262747i	−0.626997	−	0.779022i	$-0.715716\pi$
$103$	3.52430e6	−	2.95724e6i	0.0313130	−	0.0262747i	0.658310	+	0.752747i	$0.271272\pi$
$104$	5.64310e7	−	1.55043e8i	0.482375	−	1.32531i
$105$		0			0
$106$	−1.26890e6	+	7.19630e6i	−0.0100509	+	0.0570015i
$107$		−	1.83233e8i		−	1.39788i	−0.715182	−	0.698938i	$-0.753656\pi$
$107$		−	1.83233e8i		−	1.39788i	0.715182	−	0.698938i	$-0.246344\pi$
$108$		0			0
$109$	1.67490e8			1.18654			0.593269	−	0.805004i	$-0.297837\pi$
$109$	1.67490e8			1.18654			0.593269	+	0.805004i	$0.297837\pi$
$110$	1.83458e8	+	3.23486e7i	1.25304	+	0.220945i
$111$		0			0
$112$	−1.31435e8	−	4.78383e7i	−0.835290	−	0.304021i
$113$	2.59179e7	+	3.08878e7i	0.158959	+	0.189440i	0.839646	−	0.543135i	$-0.182763\pi$
$113$	2.59179e7	+	3.08878e7i	0.158959	+	0.189440i	−0.680686	+	0.732575i	$0.738318\pi$
$114$		0			0
$115$	1.57427e8	−	5.72987e7i	0.900094	−	0.327607i
$116$	−1.09416e7	−	6.31716e6i	−0.0604297	−	0.0348891i
$117$		0			0
$118$	4.90456e7	+	8.49495e7i	0.252972	+	0.438160i
$119$	6.45000e7	−	7.68681e7i	0.321641	−	0.383317i
$120$		0			0
$121$	3.05291e6	+	1.73139e7i	0.0142420	+	0.0807707i
$122$	3.05457e7	−	5.38604e6i	0.137883	−	0.0243125i
$123$		0			0
$124$	−9.51745e7	−	7.98609e7i	−0.402563	−	0.337791i
$125$	−1.63930e8	+	9.46451e7i	−0.671458	+	0.387666i
$126$		0			0
$127$	2.01391e8	−	3.48820e8i	0.774151	−	1.34087i	−0.161119	−	0.986935i	$-0.551510\pi$
$127$	2.01391e8	−	3.48820e8i	0.774151	−	1.34087i	0.935270	−	0.353935i	$-0.115156\pi$
$128$	1.10061e8	+	3.02390e8i	0.410009	+	1.12649i
$129$		0			0
$130$	5.29794e8	−	4.44550e8i	1.85496	−	1.55649i
$131$	1.26817e8	−	3.48427e8i	0.430618	−	1.18311i	−0.514816	−	0.857301i	$-0.672140\pi$
$131$	1.26817e8	−	3.48427e8i	0.430618	−	1.18311i	0.945434	−	0.325813i	$-0.105638\pi$
$132$		0			0
$133$	−7.09678e7	+	4.02479e8i	−0.226806	+	1.28628i
$134$			2.00024e8i			0.620387i
$135$		0			0
$136$	−1.81843e8			−0.531547
$137$	8.60399e7	+	1.51711e7i	0.244240	+	0.0430662i	0.294428	−	0.955674i	$-0.404871\pi$
$137$	8.60399e7	+	1.51711e7i	0.244240	+	0.0430662i	−0.0501877	+	0.998740i	$0.515982\pi$
$138$		0			0
$139$	2.71609e7	+	9.88575e6i	0.0727587	+	0.0264820i	0.378143	−	0.925747i	$-0.376563\pi$
$139$	2.71609e7	+	9.88575e6i	0.0727587	+	0.0264820i	−0.305384	+	0.952229i	$0.598785\pi$
$140$	−6.81563e7	−	8.12255e7i	−0.177417	−	0.211437i
$141$		0			0
$142$	−7.59222e8	+	2.76334e8i	−1.86731	+	0.679644i
$143$	−6.32666e8	−	3.65270e8i	−1.51297	−	0.873514i
$144$		0			0
$145$	5.39875e7	+	9.35092e7i	0.122130	+	0.211535i
$146$	−2.22776e8	+	2.65494e8i	−0.490294	+	0.584309i
$147$		0			0
$148$	2.03955e7	+	1.15669e8i	0.0425096	+	0.241084i
$149$	−7.98721e8	+	1.40836e8i	−1.62050	+	0.285739i	−0.908954	−	0.416896i	$-0.863118\pi$
$149$	−7.98721e8	+	1.40836e8i	−1.62050	+	0.285739i	−0.711550	+	0.702635i	$0.752007\pi$
$150$		0			0
$151$	2.02568e8	+	1.69974e8i	0.389639	+	0.326946i	0.816472	−	0.577384i	$-0.195927\pi$
$151$	2.02568e8	+	1.69974e8i	0.389639	+	0.326946i	−0.426834	+	0.904330i	$0.640371\pi$
$152$	6.41397e8	−	3.70311e8i	1.20158	−	0.693733i
$153$		0			0
$154$	−2.26182e8	+	3.91758e8i	−0.402137	+	0.696522i
$155$	3.63153e8	+	9.97756e8i	0.629163	+	1.72861i
$156$		0			0
$157$	5.05526e8	−	4.24187e8i	0.832041	−	0.698165i	−0.123718	−	0.992317i	$-0.539482\pi$
$157$	5.05526e8	−	4.24187e8i	0.832041	−	0.698165i	0.955759	+	0.294152i	$0.0950372\pi$
$158$	6.24327e6	−	1.71532e7i	0.0100181	−	0.0275244i
$159$		0			0
$160$	−8.30990e7	+	4.71278e8i	−0.126799	+	0.719113i
$161$			4.06814e8i			0.605469i
$162$		0			0
$163$	−1.96394e8			−0.278213			−0.139106	−	0.990277i	$-0.544423\pi$
$163$	−1.96394e8			−0.278213			−0.139106	+	0.990277i	$0.544423\pi$
$164$	1.18819e8	+	2.09510e7i	0.164252	+	0.0289620i
$165$		0			0
$166$	−4.40432e8	−	1.60304e8i	−0.580025	−	0.211112i
$167$	−3.42930e8	−	4.08688e8i	−0.440900	−	0.525444i	0.499134	−	0.866525i	$-0.333651\pi$
$167$	−3.42930e8	−	4.08688e8i	−0.440900	−	0.525444i	−0.940034	+	0.341081i	$0.889207\pi$
$168$		0			0
$169$	−1.78204e9	+	6.48610e8i	−2.18460	+	0.795128i
$170$	−6.60107e8	−	3.81113e8i	−0.790349	−	0.456308i
$171$		0			0
$172$	−3.81869e6	−	6.61417e6i	−0.00436316	−	0.00755721i
$173$	−4.07106e8	+	4.85170e8i	−0.454489	+	0.541638i	−0.943820	−	0.330459i	$-0.892796\pi$
$173$	−4.07106e8	+	4.85170e8i	−0.454489	+	0.541638i	0.489332	+	0.872098i	$0.337241\pi$
$174$		0			0
$175$	3.87685e7	+	2.19867e8i	0.0413359	+	0.234427i
$176$	1.10524e9	−	1.94884e8i	1.15188	−	0.203108i
$177$		0			0
$178$	5.44786e8	+	4.57130e8i	0.542683	+	0.455365i
$179$	−1.48872e9	+	8.59512e8i	−1.45011	+	0.837221i	−0.998487	−	0.0549884i	$-0.982488\pi$
$179$	−1.48872e9	+	8.59512e8i	−1.45011	+	0.837221i	−0.451622	+	0.892209i	$0.649154\pi$
$180$		0			0
$181$	−9.45427e8	+	1.63753e9i	−0.880874	+	1.52572i	−0.0305022	+	0.999535i	$0.509711\pi$
$181$	−9.45427e8	+	1.63753e9i	−0.880874	+	1.52572i	−0.850371	+	0.526183i	$0.823623\pi$
$182$	5.74390e8	+	1.57812e9i	0.523506	+	1.43832i
$183$		0			0
$184$	5.64748e8	−	4.73880e8i	0.492701	−	0.413425i
$185$	3.43311e8	−	9.43239e8i	0.293090	−	0.805258i
$186$		0			0
$187$	−1.39812e8	+	7.92915e8i	−0.114335	+	0.648426i
$188$		−	5.61208e8i		−	0.449254i
$189$		0			0
$190$	3.10444e9			2.38215
$191$	−4.60832e8	−	8.12572e7i	−0.346266	−	0.0610560i	−0.00218915	−	0.999998i	$-0.500697\pi$
$191$	−4.60832e8	−	8.12572e7i	−0.346266	−	0.0610560i	−0.344076	+	0.938942i	$0.611808\pi$
$192$		0			0
$193$	−1.24219e9	−	4.52119e8i	−0.895278	−	0.325854i	−0.146919	−	0.989149i	$-0.546936\pi$
$193$	−1.24219e9	−	4.52119e8i	−0.895278	−	0.325854i	−0.748359	+	0.663294i	$0.769158\pi$
$194$	−1.72125e9	−	2.05130e9i	−1.21517	−	1.44818i
$195$		0			0
$196$	−2.14403e8	+	7.80362e7i	−0.145280	+	0.0528776i
$197$	1.03606e9	+	5.98170e8i	0.687892	+	0.397155i	0.802822	−	0.596219i	$-0.203331\pi$
$197$	1.03606e9	+	5.98170e8i	0.687892	+	0.397155i	−0.114930	+	0.993374i	$0.536664\pi$
$198$		0			0
$199$	5.77895e8	+	1.00094e9i	0.368499	+	0.638259i	0.989331	−	0.145684i	$-0.0465384\pi$
$199$	5.77895e8	+	1.00094e9i	0.368499	+	0.638259i	−0.620832	+	0.783944i	$0.713205\pi$
$200$	2.60065e8	−	3.09933e8i	0.162541	−	0.193708i
$201$		0			0
$202$	−1.77547e8	−	1.00692e9i	−0.106637	−	0.604769i
$203$	−2.58213e8	+	4.55298e7i	−0.152052	+	0.0268109i
$204$		0			0
$205$	−7.89877e8	−	6.62786e8i	−0.447244	−	0.375282i
$206$	7.34927e7	−	4.24310e7i	0.0408108	−	0.0235621i
$207$		0			0
$208$	2.08327e9	−	3.60832e9i	1.11299	−	1.92776i
$209$	−1.12157e9	−	3.08149e9i	−0.587816	−	1.61501i
$210$		0			0
$211$	1.94143e9	−	1.62906e9i	0.979474	−	0.821876i	−0.00453579	−	0.999990i	$-0.501444\pi$
$211$	1.94143e9	−	1.62906e9i	0.979474	−	0.821876i	0.984010	+	0.178113i	$0.0569993\pi$
$212$	−1.14142e7	+	3.13603e7i	−0.00565071	+	0.0155252i
$213$		0			0
$214$	5.86906e8	−	3.32851e9i	0.279842	−	1.58706i
$215$			6.52705e7i			0.0305466i
$216$		0			0
$217$	−2.57834e9			−1.16279
$218$	3.04252e9	+	5.36479e8i	1.34712	+	0.237534i
$219$		0			0
$220$	7.99480e8	+	2.90987e8i	0.341285	+	0.124217i
$221$	1.92137e9	+	2.28980e9i	0.805455	+	0.959904i
$222$		0			0
$223$	2.25559e9	−	8.20967e8i	0.912096	−	0.331976i	0.157006	−	0.987598i	$-0.449816\pi$
$223$	2.25559e9	−	8.20967e8i	0.912096	−	0.331976i	0.755089	+	0.655622i	$0.227593\pi$
$224$	−1.00637e9	−	5.81029e8i	−0.399730	−	0.230784i
$225$		0			0
$226$	3.71875e8	+	6.44106e8i	0.142549	+	0.246901i
$227$	−1.60366e9	+	1.91116e9i	−0.603959	+	0.719770i	−0.978224	−	0.207551i	$-0.933451\pi$
$227$	−1.60366e9	+	1.91116e9i	−0.603959	+	0.719770i	0.374265	+	0.927322i	$0.377895\pi$
$228$		0			0
$229$	6.89136e8	+	3.90829e9i	0.250590	+	1.42116i	0.807145	+	0.590354i	$0.201012\pi$
$229$	6.89136e8	+	3.90829e9i	0.250590	+	1.42116i	−0.556555	+	0.830811i	$0.687877\pi$
$230$	3.04326e9	−	5.36609e8i	1.08750	−	0.191755i
$231$		0			0
$232$	3.63986e8	+	3.05421e8i	0.125641	+	0.105426i
$233$	4.22219e8	−	2.43768e8i	0.143256	−	0.0827091i	−0.426659	−	0.904413i	$-0.640309\pi$
$233$	4.22219e8	−	2.43768e8i	0.143256	−	0.0827091i	0.569915	+	0.821704i	$0.306976\pi$
$234$		0			0
$235$	−2.39809e9	+	4.15361e9i	−0.786310	+	1.36193i
$236$	1.53221e8	+	4.20972e8i	0.0493936	+	0.135708i
$237$		0			0
$238$	1.41788e9	−	1.18974e9i	0.441908	−	0.370805i
$239$	4.06551e8	−	1.11699e9i	0.124602	−	0.342340i	−0.861670	−	0.507468i	$-0.830581\pi$
$239$	4.06551e8	−	1.11699e9i	0.124602	−	0.342340i	0.986272	+	0.165128i	$0.0528037\pi$
$240$		0			0
$241$	2.13497e8	−	1.21080e9i	0.0632883	−	0.358926i	−0.936674	−	0.350203i	$-0.886112\pi$
$241$	2.13497e8	−	1.21080e9i	0.0632883	−	0.358926i	0.999962	−	0.00872222i	$-0.00277640\pi$
$242$			3.24293e8i			0.0945533i
$243$		0			0
$244$	1.41656e8			0.0399647
$245$	1.92029e9	+	3.38599e8i	0.532970	+	0.0939771i
$246$		0			0
$247$	−1.14401e10	−	4.16384e9i	−3.07355	−	1.11868i
$248$	3.00340e9	+	3.57931e9i	0.793975	+	0.946222i
$249$		0			0
$250$	−3.28101e9	+	1.19419e9i	−0.839940	+	0.305713i
$251$	−3.54220e9	−	2.04509e9i	−0.892437	−	0.515249i	−0.0176984	−	0.999843i	$-0.505634\pi$
$251$	−3.54220e9	−	2.04509e9i	−0.892437	−	0.515249i	−0.874739	+	0.484594i	$0.838967\pi$
$252$		0			0
$253$	−1.63211e9	−	2.82689e9i	−0.398352	−	0.689965i
$254$	4.77565e9	−	5.69140e9i	1.14735	−	1.36736i
$255$		0			0
$256$	6.65294e8	+	3.77307e9i	0.154901	+	0.878486i
$257$	1.63864e9	−	2.88936e8i	0.375622	−	0.0662322i	0.0173497	−	0.999849i	$-0.494477\pi$
$257$	1.63864e9	−	2.88936e8i	0.375622	−	0.0662322i	0.358272	+	0.933617i	$0.383366\pi$
$258$		0			0
$259$	1.86721e9	+	1.56677e9i	0.414947	+	0.348182i
$260$	2.73540e9	−	1.57928e9i	0.598587	−	0.345594i
$261$		0			0
$262$	3.41972e9	−	5.92313e9i	0.725747	−	1.25703i
$263$	−1.77101e9	−	4.86581e9i	−0.370167	−	1.01703i	−0.975297	−	0.220899i	$-0.929101\pi$
$263$	−1.77101e9	−	4.86581e9i	−0.370167	−	1.01703i	0.605129	−	0.796127i	$-0.293121\pi$
$264$		0			0
$265$	2.18484e8	−	1.83330e8i	0.0443034	−	0.0371750i
$266$	−2.57832e9	+	7.08388e9i	−0.515004	+	1.41496i
$267$		0			0
$268$	−1.58631e8	+	8.99643e8i	−0.0307503	+	0.174394i
$269$			1.03009e10i			1.96728i	0.180134	+	0.983642i	$0.442347\pi$
$269$			1.03009e10i			1.96728i	−0.180134	+	0.983642i	$0.557653\pi$
$270$		0			0
$271$	6.13223e9			1.13695			0.568474	−	0.822701i	$-0.307534\pi$
$271$	6.13223e9			1.13695			0.568474	+	0.822701i	$0.307534\pi$
$272$	−4.52228e9	−	7.97399e8i	−0.826193	−	0.145680i
$273$		0			0
$274$	1.51436e9	+	5.51181e8i	0.268674	+	0.0977894i
$275$	−1.15149e9	−	1.37229e9i	−0.201340	−	0.239947i
$276$		0			0
$277$	6.01341e9	−	2.18870e9i	1.02141	−	0.371764i	0.223608	−	0.974679i	$-0.428216\pi$
$277$	6.01341e9	−	2.18870e9i	1.02141	−	0.371764i	0.797805	+	0.602915i	$0.205994\pi$
$278$	4.61725e8	+	2.66577e8i	0.0773043	+	0.0446317i
$279$		0			0
$280$	1.99383e9	+	3.45341e9i	0.324381	+	0.561845i
$281$	−8.46391e8	+	1.00869e9i	−0.135752	+	0.161783i	−0.829638	−	0.558302i	$-0.811453\pi$
$281$	−8.46391e8	+	1.00869e9i	−0.135752	+	0.161783i	0.693886	+	0.720085i	$0.255897\pi$
$282$		0			0
$283$	6.64649e8	+	3.76941e9i	0.103621	+	0.587662i	0.991762	+	0.128092i	$0.0408854\pi$
$283$	6.64649e8	+	3.76941e9i	0.103621	+	0.587662i	−0.888142	+	0.459570i	$0.848004\pi$
$284$	−3.63388e9	+	6.40752e8i	−0.558596	+	0.0984955i
$285$		0			0
$286$	−1.03227e10	−	8.66176e9i	−1.54287	−	1.29462i
$287$	2.16840e9	−	1.25192e9i	0.319603	−	0.184523i
$288$		0			0
$289$	−1.84069e9	+	3.18816e9i	−0.263869	+	0.457035i
$290$	6.81192e8	+	1.87156e9i	0.0963114	+	0.264613i
$291$		0			0
$292$	−1.21253e9	+	1.01743e9i	−0.166786	+	0.139950i
$293$	−1.60626e7	+	4.41317e7i	−0.00217944	+	0.00598797i	−0.940778	−	0.339024i	$-0.889903\pi$
$293$	−1.60626e7	+	4.41317e7i	−0.00217944	+	0.00598797i	0.938598	+	0.345012i	$0.112125\pi$
$294$		0			0
$295$	6.64828e8	−	3.77043e9i	0.0877851	−	0.497854i
$296$		−	4.41716e9i		−	0.575409i
$297$		0			0
$298$	−1.49602e10			−1.89702
$299$	−1.19343e10	−	2.10434e9i	−1.49318	−	0.263289i
$300$		0			0
$301$	−1.48938e8	−	5.42089e7i	−0.0181442	−	0.00660396i
$302$	3.13529e9	+	3.73649e9i	0.376921	+	0.449197i
$303$		0			0
$304$	1.75748e10	−	6.39671e9i	2.05777	−	0.748966i
$305$	−1.04843e9	−	6.05310e8i	−0.121154	−	0.0699485i
$306$		0			0
$307$	1.01998e9	+	1.76665e9i	0.114825	+	0.198883i	0.917710	−	0.397251i	$-0.130036\pi$
$307$	1.01998e9	+	1.76665e9i	0.114825	+	0.198883i	−0.802885	+	0.596134i	$0.796703\pi$
$308$	−1.32798e9	+	1.58263e9i	−0.147567	+	0.175863i
$309$		0			0
$310$	3.40097e9	+	1.92879e10i	0.368261	+	2.08851i
$311$	−2.45554e9	+	4.32978e8i	−0.262485	+	0.0462833i	−0.303342	−	0.952882i	$-0.598102\pi$
$311$	−2.45554e9	+	4.32978e8i	−0.262485	+	0.0462833i	0.0408565	+	0.999165i	$0.486991\pi$
$312$		0			0
$313$	1.11051e10	+	9.31825e9i	1.15703	+	0.970861i	0.999860	−	0.0167116i	$-0.00531970\pi$
$313$	1.11051e10	+	9.31825e9i	1.15703	+	0.970861i	0.157166	+	0.987572i	$0.449764\pi$
$314$	1.05418e10	−	6.08630e9i	1.08442	−	0.626088i
$315$		0			0
$316$	4.16838e7	−	7.21984e7i	0.00418041	−	0.00724068i
$317$	−3.46689e9	−	9.52521e9i	−0.343323	−	0.943273i	−0.984423	−	0.175816i	$-0.943744\pi$
$317$	−3.46689e9	−	9.52521e9i	−0.343323	−	0.943273i	0.641100	−	0.767458i	$-0.278478\pi$
$318$		0			0
$319$	1.61162e9	−	1.35231e9i	0.155632	−	0.130591i
$320$	2.02422e9	−	5.56150e9i	0.193045	−	0.530386i
$321$		0			0
$322$	−1.30305e9	+	7.38995e9i	−0.121209	+	0.687413i
$323$			1.34176e10i			1.23272i
$324$		0			0
$325$	−6.65059e9			−0.596111
$326$	−3.56758e9	−	6.29060e8i	−0.315866	−	0.0556957i
$327$		0			0
$328$	−4.26382e9	−	1.55190e9i	−0.368386	−	0.134082i
$329$	−7.48626e9	−	8.92178e9i	−0.638972	−	0.761497i
$330$		0			0
$331$	5.31002e9	−	1.93269e9i	0.442369	−	0.161009i	−0.111226	−	0.993795i	$-0.535478\pi$
$331$	5.31002e9	−	1.93269e9i	0.442369	−	0.161009i	0.553595	+	0.832786i	$0.313256\pi$
$332$	−1.85379e9	−	1.07029e9i	−0.152584	−	0.0880943i
$333$		0			0
$334$	−4.92042e9	−	8.52242e9i	−0.395382	−	0.684821i
$335$	5.01832e9	−	5.98060e9i	0.398455	−	0.474860i
$336$		0			0
$337$	−1.87667e9	−	1.06431e10i	−0.145502	−	0.825183i	−0.966963	−	0.254918i	$-0.917951\pi$
$337$	−1.87667e9	−	1.06431e10i	−0.145502	−	0.825183i	0.821461	−	0.570265i	$-0.193160\pi$
$338$	−3.44491e10	+	6.07430e9i	−2.63943	+	0.465404i
$339$		0			0
$340$	−2.66670e9	−	2.23763e9i	−0.199553	−	0.167445i
$341$	1.79166e10	−	1.03441e10i	1.32506	−	0.765026i
$342$		0			0
$343$	−7.40666e9	+	1.28287e10i	−0.535114	+	0.926844i
$344$	9.82371e7	+	2.69904e8i	0.00701523	+	0.0192742i
$345$		0			0
$346$	−8.94928e9	+	7.50934e9i	−0.624430	+	0.523959i
$347$	−4.55820e9	+	1.25235e10i	−0.314395	+	0.863792i	0.677361	+	0.735651i	$0.263123\pi$
$347$	−4.55820e9	+	1.25235e10i	−0.314395	+	0.863792i	−0.991756	+	0.128142i	$0.959099\pi$
$348$		0			0
$349$	−2.30095e9	+	1.30494e10i	−0.155098	+	0.879605i	0.803598	+	0.595172i	$0.202916\pi$
$349$	−2.30095e9	+	1.30494e10i	−0.155098	+	0.879605i	−0.958696	+	0.284432i	$0.908195\pi$
$350$			4.11816e9i			0.274430i
$351$		0			0
$352$	9.32419e9			0.607352
$353$	9.35744e9	+	1.64997e9i	0.602640	+	0.106262i	0.466641	−	0.884447i	$-0.345464\pi$
$353$	9.35744e9	+	1.64997e9i	0.602640	+	0.106262i	0.136000	+	0.990709i	$0.456575\pi$
$354$		0			0
$355$	2.96331e10	+	1.07856e10i	1.86579	+	0.679094i
$356$	2.08774e9	+	2.48807e9i	0.129980	+	0.154904i
$357$		0			0
$358$	−2.97963e10	+	1.08450e10i	−1.81397	+	0.660231i
$359$	4.24744e9	+	2.45226e9i	0.255711	+	0.147635i	0.622376	−	0.782718i	$-0.286167\pi$
$359$	4.24744e9	+	2.45226e9i	0.255711	+	0.147635i	−0.366666	+	0.930353i	$0.619501\pi$
$360$		0			0
$361$	−1.88321e10	−	3.26182e10i	−1.10884	−	1.92057i
$362$	−2.24192e10	+	2.67181e10i	−1.30553	+	1.55586i
$363$		0			0
$364$	1.33187e9	+	7.55342e9i	0.0758677	+	0.430267i
$365$	1.33217e10	−	2.34898e9i	0.750566	−	0.132345i
$366$		0			0
$367$	1.40786e9	+	1.18134e9i	0.0776061	+	0.0651193i	0.680765	−	0.732501i	$-0.261647\pi$
$367$	1.40786e9	+	1.18134e9i	0.0776061	+	0.0651193i	−0.603159	+	0.797621i	$0.706092\pi$
$368$	1.61228e10	−	9.30849e9i	0.879121	−	0.507561i
$369$		0			0
$370$	9.25764e9	−	1.60347e10i	0.493962	−	0.855567i
$371$	2.36876e8	+	6.50811e8i	0.0125033	+	0.0343526i
$372$		0			0
$373$	3.52175e9	−	2.95510e9i	0.181938	−	0.152664i	−0.547270	−	0.836956i	$-0.684333\pi$
$373$	3.52175e9	−	2.95510e9i	0.181938	−	0.152664i	0.729208	+	0.684292i	$0.239889\pi$
$374$	−5.07950e9	+	1.39558e10i	−0.259618	+	0.713294i
$375$		0			0
$376$	−3.66499e9	+	2.07852e10i	−0.183367	+	1.03993i
$377$		−	7.81046e9i		−	0.386644i
$378$		0			0
$379$	−2.22539e10			−1.07857			−0.539286	−	0.842123i	$-0.681306\pi$
$379$	−2.22539e10			−1.07857			−0.539286	+	0.842123i	$0.681306\pi$
$380$	1.39628e10	+	2.46201e9i	0.669633	+	0.118074i
$381$		0			0
$382$	−8.11094e9	−	2.95214e9i	−0.380906	−	0.138638i
$383$	1.36042e10	+	1.62128e10i	0.632233	+	0.753466i	0.983122	−	0.182951i	$-0.0585649\pi$
$383$	1.36042e10	+	1.62128e10i	0.632233	+	0.753466i	−0.350889	+	0.936417i	$0.614120\pi$
$384$		0			0
$385$	1.65913e10	−	6.03876e9i	0.755160	−	0.274856i
$386$	−2.11167e10	−	1.21917e10i	−0.951211	−	0.549182i
$387$		0			0
$388$	−6.11481e9	−	1.05912e10i	−0.269809	−	0.467322i
$389$	9.00357e9	−	1.07300e10i	0.393203	−	0.468601i	−0.532732	−	0.846284i	$-0.678835\pi$
$389$	9.00357e9	−	1.07300e10i	0.393203	−	0.468601i	0.925935	+	0.377683i	$0.123279\pi$
$390$		0			0
$391$	2.31925e9	+	1.31531e10i	0.0992295	+	0.562758i
$392$	8.45035e9	−	1.49002e9i	0.357874	−	0.0631029i
$393$		0			0
$394$	1.69045e10	+	1.41846e10i	0.701484	+	0.588615i
$395$	−6.17021e8	+	3.56237e8i	−0.0253461	+	0.0146336i
$396$		0			0
$397$	5.43453e9	−	9.41289e9i	0.218776	−	0.378932i	−0.735658	−	0.677353i	$-0.763127\pi$
$397$	5.43453e9	−	9.41289e9i	0.218776	−	0.378932i	0.954434	+	0.298422i	$0.0964602\pi$
$398$	7.29163e9	+	2.00336e10i	0.290598	+	0.798411i
$399$		0			0
$400$	7.82667e9	−	6.56735e9i	0.305729	−	0.256537i
$401$	−2.85037e9	+	7.83132e9i	−0.110236	+	0.302871i	−0.982528	−	0.186114i	$-0.940411\pi$
$401$	−2.85037e9	+	7.83132e9i	−0.110236	+	0.302871i	0.872292	+	0.488985i	$0.162633\pi$
$402$		0			0
$403$	1.33371e10	−	7.56386e10i	0.505640	−	2.86763i
$404$		−	4.66960e9i		−	0.175289i
$405$		0			0
$406$	−4.83638e9			−0.177998
$407$	−1.92607e10	−	3.39619e9i	−0.701932	−	0.123770i
$408$		0			0
$409$	9.00316e9	+	3.27688e9i	0.321737	+	0.117103i	0.497840	−	0.867269i	$-0.334127\pi$
$409$	9.00316e9	+	3.27688e9i	0.321737	+	0.117103i	−0.176102	+	0.984372i	$0.556349\pi$
$410$	−1.22255e10	−	1.45698e10i	−0.432645	−	0.515606i
$411$		0			0
$412$	3.64197e8	−	1.32557e8i	0.0126400	−	0.00460059i
$413$	8.05141e9	+	4.64848e9i	0.276740	+	0.159776i
$414$		0			0
$415$	9.14685e9	+	1.58428e10i	0.308375	+	0.534121i
$416$	2.22508e10	−	2.65175e10i	0.742973	−	0.885441i
$417$		0			0
$418$	−1.05036e10	−	5.95690e10i	−0.344060	−	1.95126i
$419$	1.91013e10	−	3.36808e9i	0.619737	−	0.109276i	0.145040	−	0.989426i	$-0.453669\pi$
$419$	1.91013e10	−	3.36808e9i	0.619737	−	0.109276i	0.474697	+	0.880149i	$0.342558\pi$
$420$		0			0
$421$	−1.62543e9	−	1.36390e9i	−0.0517416	−	0.0434164i	0.616550	−	0.787316i	$-0.288530\pi$
$421$	−1.62543e9	−	1.36390e9i	−0.0517416	−	0.0434164i	−0.668292	+	0.743899i	$0.732974\pi$
$422$	4.04850e10	−	2.33740e10i	1.27657	−	0.737027i
$423$		0			0
$424$	6.27544e8	−	1.08694e9i	0.0194169	−	0.0336311i
$425$	2.50693e9	+	6.88774e9i	0.0768400	+	0.211116i
$426$		0			0
$427$	2.25198e9	−	1.88963e9i	0.0677411	−	0.0568415i
$428$	5.27942e9	−	1.45051e10i	0.157330	−	0.432260i
$429$		0			0
$430$	−2.09065e8	+	1.18567e9i	−0.00611515	+	0.0346808i
$431$			5.48147e10i			1.58850i	0.607589	+	0.794251i	$0.292137\pi$
$431$			5.48147e10i			1.58850i	−0.607589	+	0.794251i	$0.707863\pi$
$432$		0			0
$433$	4.47196e10			1.27217			0.636087	−	0.771617i	$-0.280552\pi$
$433$	4.47196e10			1.27217			0.636087	+	0.771617i	$0.280552\pi$
$434$	−4.68367e10	−	8.25858e9i	−1.32016	−	0.232780i
$435$		0			0
$436$	1.32588e10	+	4.82581e9i	0.366909	+	0.133544i
$437$	−3.49659e10	−	4.16707e10i	−0.958779	−	1.14263i
$438$		0			0
$439$	−3.39413e10	+	1.23536e10i	−0.913841	+	0.332611i	−0.755785	−	0.654820i	$-0.772745\pi$
$439$	−3.39413e10	+	1.23536e10i	−0.913841	+	0.332611i	−0.158055	+	0.987430i	$0.550522\pi$
$440$	−2.77097e10	−	1.59982e10i	−0.739300	−	0.426835i
$441$		0			0
$442$	2.75681e10	+	4.77494e10i	0.722301	+	1.25106i
$443$	4.43162e10	−	5.28140e10i	1.15066	−	1.37131i	0.233710	−	0.972306i	$-0.424913\pi$
$443$	4.43162e10	−	5.28140e10i	1.15066	−	1.37131i	0.916951	−	0.398999i	$-0.130642\pi$
$444$		0			0
$445$	−4.82004e9	−	2.73358e10i	−0.122917	−	0.697095i
$446$	4.36033e10	−	7.68845e9i	1.10200	−	0.194312i
$447$		0			0
$448$	1.10094e10	+	9.23796e9i	0.273307	+	0.229332i
$449$	1.65666e10	−	9.56473e9i	0.407613	−	0.235335i	−0.282151	−	0.959370i	$-0.591048\pi$
$449$	1.65666e10	−	9.56473e9i	0.407613	−	0.235335i	0.689764	+	0.724035i	$0.257714\pi$
$450$		0			0
$451$	−1.00453e10	+	1.73989e10i	−0.242803	+	0.420548i
$452$	1.16176e9	+	3.19190e9i	0.0278331	+	0.0764708i
$453$		0			0
$454$	−3.52526e10	+	2.95805e10i	−0.829790	+	0.696277i
$455$	2.24190e10	−	6.15956e10i	0.523082	−	1.43716i
$456$		0			0
$457$	2.24574e9	−	1.27362e10i	0.0514867	−	0.291996i	−0.948182	−	0.317727i	$-0.897080\pi$
$457$	2.24574e9	−	1.27362e10i	0.0514867	−	0.291996i	0.999669	+	0.0257316i	$0.00819152\pi$
$458$			7.32030e10i			1.66367i
$459$		0			0
$460$	1.41132e10			0.315205
$461$	8.59007e10	+	1.51466e10i	1.90192	+	0.335360i	0.996095	−	0.0882848i	$-0.0281386\pi$
$461$	8.59007e10	+	1.51466e10i	1.90192	+	0.335360i	0.905828	+	0.423645i	$0.139250\pi$
$462$		0			0
$463$	−3.39370e10	−	1.23521e10i	−0.738498	−	0.268791i	−0.0547406	−	0.998501i	$-0.517433\pi$
$463$	−3.39370e10	−	1.23521e10i	−0.738498	−	0.268791i	−0.683758	+	0.729709i	$0.739655\pi$
$464$	7.71271e9	+	9.19165e9i	0.166393	+	0.198299i
$465$		0			0
$466$	8.45059e9	−	3.07576e9i	0.179202	−	0.0652243i
$467$	−6.28492e10	−	3.62860e10i	−1.32139	−	0.762907i	−0.337442	−	0.941346i	$-0.609562\pi$
$467$	−6.28492e10	−	3.62860e10i	−1.32139	−	0.762907i	−0.983951	+	0.178439i	$0.942895\pi$
$468$		0			0
$469$	9.47900e9	+	1.64181e10i	0.195917	+	0.339338i
$470$	−5.68666e10	+	6.77710e10i	−1.16537	+	1.38884i
$471$		0			0
$472$	−2.92561e9	−	1.65920e10i	−0.0589452	−	0.334295i
$473$	1.25243e9	−	2.20837e8i	0.0250212	−	0.00441192i
$474$		0			0
$475$	−2.28689e10	−	1.91893e10i	−0.449231	−	0.376950i
$476$	7.32072e9	−	4.22662e9i	0.142602	−	0.0823313i
$477$		0			0
$478$	1.09630e10	−	1.89884e10i	0.209999	−	0.363728i
$479$	−5.00005e9	−	1.37375e10i	−0.0949800	−	0.260955i	0.883100	−	0.469185i	$-0.155452\pi$
$479$	−5.00005e9	−	1.37375e10i	−0.0949800	−	0.260955i	−0.978080	+	0.208229i	$0.933230\pi$
$480$		0			0
$481$	−5.56216e10	+	4.66720e10i	−1.03911	+	0.871919i
$482$	7.75652e9	−	2.13109e10i	0.143707	−	0.394833i
$483$		0			0
$484$	−2.57185e8	+	1.45857e9i	−0.00468666	+	0.0265794i
$485$			1.04516e11i			1.88894i
$486$		0			0
$487$	5.04287e9			0.0896523			0.0448262	−	0.998995i	$-0.485727\pi$
$487$	5.04287e9			0.0896523			0.0448262	+	0.998995i	$0.485727\pi$
$488$	−5.24646e9	−	9.25093e8i	−0.0925097	−	0.0163120i
$489$		0			0
$490$	3.37984e10	+	1.23016e10i	0.586289	+	0.213392i
$491$	6.98310e10	+	8.32214e10i	1.20150	+	1.43189i	0.873234	+	0.487301i	$0.162019\pi$
$491$	6.98310e10	+	8.32214e10i	1.20150	+	1.43189i	0.328263	+	0.944587i	$0.393537\pi$
$492$		0			0
$493$	−8.08898e9	+	2.94415e9i	−0.136932	+	0.0498393i
$494$	−1.94477e11	−	1.12281e11i	−3.26557	−	1.88538i
$495$		0			0
$496$	5.89962e10	+	1.02185e11i	0.974760	+	1.68833i
$497$	−4.92222e10	+	5.86608e10i	−0.806744	+	0.961440i
$498$		0			0
$499$	−1.09560e10	−	6.21345e10i	−0.176705	−	1.00215i	−0.936157	−	0.351582i	$-0.885644\pi$
$499$	−1.09560e10	−	6.21345e10i	−0.176705	−	1.00215i	0.759452	−	0.650564i	$-0.225467\pi$
$500$	−1.57040e10	+	2.76904e9i	−0.251264	+	0.0443046i
$501$		0			0
$502$	−5.77950e10	−	4.84958e10i	−0.910071	−	0.763640i
$503$	−8.47129e10	+	4.89090e10i	−1.32336	+	0.764042i	−0.984263	−	0.176710i	$-0.943454\pi$
$503$	−8.47129e10	+	4.89090e10i	−1.32336	+	0.764042i	−0.339096	+	0.940752i	$0.610121\pi$
$504$		0			0
$505$	−1.99536e10	+	3.45607e10i	−0.306801	+	0.531394i
$506$	−2.05932e10	−	5.65795e10i	−0.314139	−	0.863091i
$507$		0			0
$508$	2.59930e10	−	2.18107e10i	0.390302	−	0.327502i
$509$	−2.69504e10	+	7.40456e10i	−0.401508	+	1.10313i	0.560033	+	0.828471i	$0.310789\pi$
$509$	−2.69504e10	+	7.40456e10i	−0.401508	+	1.10313i	−0.961540	+	0.274663i	$0.911434\pi$
$510$		0			0
$511$	−5.70402e9	+	3.23491e10i	−0.0836561	+	0.474437i
$512$		−	1.17095e10i		−	0.170395i
$513$		0			0
$514$	3.06921e10			0.439717
$515$	−3.26192e9	−	5.75165e8i	−0.0463708	−	0.00817643i
$516$		0			0
$517$	8.78146e10	+	3.19619e10i	1.22915	+	0.447374i
$518$	2.89001e10	+	3.44418e10i	0.401403	+	0.478374i
$519$		0			0
$520$	−1.11623e11	+	4.06275e10i	−1.52666	+	0.555657i
$521$	3.76198e10	+	2.17198e10i	0.510582	+	0.294785i	0.733073	−	0.680150i	$-0.238085\pi$
$521$	3.76198e10	+	2.17198e10i	0.510582	+	0.294785i	−0.222491	+	0.974935i	$0.571419\pi$
$522$		0			0
$523$	−2.11930e9	−	3.67073e9i	−0.0283260	−	0.0490621i	0.851515	−	0.524330i	$-0.175684\pi$
$523$	−2.11930e9	−	3.67073e9i	−0.0283260	−	0.0490621i	−0.879841	+	0.475268i	$0.842351\pi$
$524$	2.00782e10	−	2.39283e10i	0.266317	−	0.317385i
$525$		0			0
$526$	−1.65857e10	−	9.40622e10i	−0.216666	−	1.22877i
$527$	−8.33632e10	+	1.46992e10i	−1.08077	+	0.190568i
$528$		0			0
$529$	1.85100e10	+	1.55318e10i	0.236366	+	0.198335i
$530$	4.55608e9	−	2.63045e9i	0.0577415	−	0.0333371i
$531$		0			0
$532$	−1.72144e10	+	2.98162e10i	−0.214905	+	0.372226i
$533$	2.55100e10	+	7.00882e10i	0.316083	+	0.868432i
$534$		0			0
$535$	−1.01056e11	+	8.47957e10i	−1.23352	+	1.03504i
$536$	1.17503e10	−	3.22837e10i	0.142361	−	0.391133i
$537$		0			0
$538$	−3.29944e10	+	1.87121e11i	−0.393833	+	2.23354i
$539$		−	3.79928e10i		−	0.450139i
$540$		0			0
$541$	−2.11172e10			−0.246517			−0.123258	−	0.992375i	$-0.539334\pi$
$541$	−2.11172e10			−0.246517			−0.123258	+	0.992375i	$0.539334\pi$
$542$	1.11395e11	+	1.96419e10i	1.29082	+	0.227607i
$543$		0			0
$544$	−3.58505e10	−	1.30485e10i	−0.409355	−	0.148993i
$545$	−7.75101e10	−	9.23729e10i	−0.878561	−	1.04703i
$546$		0			0
$547$	2.43115e10	−	8.84865e9i	0.271557	−	0.0988388i	−0.202652	−	0.979251i	$-0.564956\pi$
$547$	2.43115e10	−	8.84865e9i	0.271557	−	0.0988388i	0.474210	+	0.880412i	$0.342734\pi$
$548$	6.37397e9	+	3.68001e9i	0.0706785	+	0.0408063i
$549$		0			0
$550$	−1.65218e10	−	2.86166e10i	−0.180553	−	0.312728i
$551$	2.25359e10	−	2.68572e10i	0.244494	−	0.291377i
$552$		0			0
$553$	−3.00429e8	−	1.70382e9i	−0.00321248	−	0.0182189i
$554$	1.16247e11	−	2.04974e10i	1.23407	−	0.217601i
$555$		0			0
$556$	1.86528e9	+	1.56515e9i	0.0195184	+	0.0163779i
$557$	1.96099e10	−	1.13218e10i	0.203730	−	0.117623i	−0.394664	−	0.918825i	$-0.629139\pi$
$557$	1.96099e10	−	1.13218e10i	0.203730	−	0.117623i	0.598394	+	0.801202i	$0.295806\pi$
$558$		0			0
$559$	2.36070e9	−	4.08884e9i	0.0241765	−	0.0418749i
$560$	3.44412e10	+	9.46264e10i	0.350208	+	0.962188i
$561$		0			0
$562$	−1.86060e10	+	1.56122e10i	−0.186512	+	0.156502i
$563$	4.81783e10	−	1.32369e11i	0.479532	−	1.31750i	−0.430359	−	0.902658i	$-0.641613\pi$
$563$	4.81783e10	−	1.32369e11i	0.479532	−	1.31750i	0.909891	−	0.414847i	$-0.136165\pi$
$564$		0			0
$565$	5.04087e9	−	2.85882e10i	0.0494665	−	0.280539i
$566$			7.06019e10i			0.687940i
$567$		0			0
$568$	1.38771e11			1.33323
$569$	−3.65522e10	−	6.44514e9i	−0.348710	−	0.0614870i	−0.00344997	−	0.999994i	$-0.501098\pi$
$569$	−3.65522e10	−	6.44514e9i	−0.348710	−	0.0614870i	−0.345260	+	0.938507i	$0.612209\pi$
$570$		0			0
$571$	1.26055e11	+	4.58802e10i	1.18581	+	0.431599i	0.858250	−	0.513231i	$-0.171552\pi$
$571$	1.26055e11	+	4.58802e10i	1.18581	+	0.431599i	0.327559	+	0.944831i	$0.393774\pi$
$572$	−3.95588e10	−	4.71443e10i	−0.369537	−	0.440398i
$573$		0			0
$574$	4.33998e10	−	1.57962e10i	0.399798	−	0.145514i
$575$	−2.57351e10	−	1.48582e10i	−0.235426	−	0.135923i
$576$		0			0
$577$	−8.40995e10	−	1.45665e11i	−0.758735	−	1.31417i	−0.943496	−	0.331384i	$-0.892484\pi$
$577$	−8.40995e10	−	1.45665e11i	−0.758735	−	1.31417i	0.184761	−	0.982784i	$-0.440849\pi$
$578$	−4.36488e10	+	5.20186e10i	−0.391075	+	0.466066i
$579$		0			0
$580$	1.57952e9	+	8.95789e9i	0.0139577	+	0.0791578i
$581$	−4.37477e10	+	7.71390e9i	−0.383929	+	0.0676970i
$582$		0			0
$583$	−4.25702e9	−	3.57207e9i	−0.0368495	−	0.0309204i
$584$	5.15521e10	−	2.97636e10i	0.443196	−	0.255879i
$585$		0			0
$586$	−4.33140e8	+	7.50221e8i	−0.00367315	+	0.00636208i
$587$	−2.12822e10	−	5.84723e10i	−0.179252	−	0.492490i	0.817229	−	0.576313i	$-0.195509\pi$
$587$	−2.12822e10	−	5.84723e10i	−0.179252	−	0.492490i	−0.996481	+	0.0838232i	$0.973287\pi$
$588$		0			0
$589$	2.64105e11	−	2.21610e11i	2.19440	−	1.84132i
$590$	2.41538e10	−	6.63619e10i	0.199332	−	0.547660i
$591$		0			0
$592$	1.93697e10	−	1.09851e11i	0.157701	−	0.894368i
$593$		−	1.16087e11i		−	0.938783i	−0.882990	−	0.469391i	$-0.844473\pi$
$593$		−	1.16087e11i		−	0.938783i	0.882990	−	0.469391i	$-0.155527\pi$
$594$		0			0
$595$	−7.22428e10			−0.576404
$596$	−6.72862e10	−	1.18644e10i	−0.533263	−	0.0940286i
$597$		0			0
$598$	−2.10052e11	−	7.64526e10i	−1.64256	−	0.597844i
$599$	−1.03477e11	−	1.23319e11i	−0.803779	−	0.957906i	0.195963	−	0.980611i	$-0.437217\pi$
$599$	−1.03477e11	−	1.23319e11i	−0.803779	−	0.957906i	−0.999742	+	0.0227048i	$0.992772\pi$
$600$		0			0
$601$	1.36871e11	−	4.98170e10i	1.04909	−	0.381838i	0.240772	−	0.970582i	$-0.422599\pi$
$601$	1.36871e11	−	4.98170e10i	1.04909	−	0.381838i	0.808320	+	0.588743i	$0.200377\pi$
$602$	−2.53188e9	−	1.46178e9i	−0.0192778	−	0.0111301i
$603$		0			0
$604$	1.11383e10	+	1.92920e10i	0.0836892	+	0.144954i
$605$	8.13606e9	−	9.69617e9i	0.0607285	−	0.0723734i
$606$		0			0
$607$	9.73305e9	+	5.51989e10i	0.0716959	+	0.406608i	0.999442	+	0.0333962i	$0.0106323\pi$
$607$	9.73305e9	+	5.51989e10i	0.0716959	+	0.406608i	−0.927746	+	0.373212i	$0.878257\pi$
$608$	1.53024e11	−	2.69823e10i	1.11982	−	0.197454i
$609$		0			0
$610$	−1.71063e10	−	1.43539e10i	−0.123548	−	0.103669i
$611$	3.00455e11	−	1.73468e11i	2.15583	−	1.24467i
$612$		0			0
$613$	−4.20804e7	+	7.28855e7i	−0.000298015	+	0.000516177i	−0.866174	−	0.499742i	$-0.833428\pi$
$613$	−4.20804e7	+	7.28855e7i	−0.000298015	+	0.000516177i	0.865876	+	0.500258i	$0.166762\pi$
$614$	1.28696e10	+	3.53591e10i	0.0905510	+	0.248787i
$615$		0			0
$616$	5.95192e10	−	4.99426e10i	0.413366	−	0.346855i
$617$	−5.97309e10	+	1.64109e11i	−0.412153	+	1.13238i	0.543890	+	0.839156i	$0.316951\pi$
$617$	−5.97309e10	+	1.64109e11i	−0.412153	+	1.13238i	−0.956043	+	0.293225i	$0.905271\pi$
$618$		0			0
$619$	−1.84903e9	+	1.04864e10i	−0.0125945	+	0.0714269i	−0.990457	−	0.137820i	$-0.955990\pi$
$619$	−1.84903e9	+	1.04864e10i	−0.0125945	+	0.0714269i	0.977863	+	0.209247i	$0.0671014\pi$
$620$			8.94478e10i			0.605345i
$621$		0			0
$622$	−4.59928e10			−0.307276
$623$	6.63796e10	+	1.17045e10i	0.440638	+	0.0776964i
$624$		0			0
$625$	1.74937e11	+	6.36718e10i	1.14647	+	0.417280i
$626$	1.71881e11	+	2.04840e11i	1.11926	+	1.33388i
$627$		0			0
$628$	5.22404e10	−	1.90139e10i	0.335867	−	0.122246i
$629$	6.93028e10	+	4.00120e10i	0.442739	+	0.255616i
$630$		0			0
$631$	4.31131e10	+	7.46741e10i	0.271952	+	0.471035i	0.969362	−	0.245638i	$-0.0789975\pi$
$631$	4.31131e10	+	7.46741e10i	0.271952	+	0.471035i	−0.697410	+	0.716673i	$0.745664\pi$
$632$	−2.01532e9	+	2.40176e9i	−0.0126321	+	0.0150543i
$633$		0			0
$634$	−3.24678e10	−	1.84134e11i	−0.200954	−	1.13967i
$635$	−2.85578e11	+	5.03551e10i	−1.75643	+	0.309705i
$636$		0			0
$637$	−1.08050e11	−	9.06644e10i	−0.656244	−	0.550654i
$638$	3.36073e10	−	1.94032e10i	0.202839	−	0.117109i
$639$		0			0
$640$	1.15839e11	−	2.00639e11i	0.690453	−	1.19590i
$641$	4.73143e10	+	1.29995e11i	0.280260	+	0.770007i	0.997331	+	0.0730075i	$0.0232597\pi$
$641$	4.73143e10	+	1.29995e11i	0.280260	+	0.770007i	−0.717072	+	0.696999i	$0.754518\pi$
$642$		0			0
$643$	−1.87441e11	+	1.57282e11i	−1.09653	+	0.920099i	−0.997187	−	0.0749536i	$-0.976119\pi$
$643$	−1.87441e11	+	1.57282e11i	−1.09653	+	0.920099i	−0.0993448	+	0.995053i	$0.531675\pi$
$644$	−1.17214e10	+	3.22042e10i	−0.0681451	+	0.187227i
$645$		0			0
$646$	−4.29772e10	+	2.43736e11i	−0.246779	+	1.39955i
$647$			3.44674e11i			1.96694i	0.181068	+	0.983471i	$0.442045\pi$
$647$			3.44674e11i			1.96694i	−0.181068	+	0.983471i	$0.557955\pi$
$648$		0			0
$649$	−7.45975e10			−0.420480
$650$	−1.20811e11	−	2.13022e10i	−0.676788	−	0.119336i
$651$		0			0
$652$	−1.55469e10	−	5.65862e9i	−0.0860308	−	0.0313127i
$653$	−1.09007e11	−	1.29909e11i	−0.599515	−	0.714474i	0.377890	−	0.925850i	$-0.376650\pi$
$653$	−1.09007e11	−	1.29909e11i	−0.599515	−	0.714474i	−0.977405	+	0.211377i	$0.932205\pi$
$654$		0			0
$655$	−2.50850e11	+	9.13020e10i	−1.36285	+	0.496038i
$656$	−9.92321e10	−	5.72917e10i	−0.535842	−	0.309368i
$657$		0			0
$658$	−1.07414e11	−	1.86047e11i	−0.573005	−	0.992474i
$659$	9.46900e10	−	1.12847e11i	0.502068	−	0.598341i	−0.454176	−	0.890912i	$-0.650066\pi$
$659$	9.46900e10	−	1.12847e11i	0.502068	−	0.598341i	0.956244	+	0.292571i	$0.0945107\pi$
$660$		0			0
$661$	6.13448e10	+	3.47903e11i	0.321345	+	1.82244i	0.534204	+	0.845356i	$0.320611\pi$
$661$	6.13448e10	+	3.47903e11i	0.321345	+	1.82244i	−0.212859	+	0.977083i	$0.568277\pi$
$662$	1.02649e11	−	1.80999e10i	0.534471	−	0.0942417i
$663$		0			0
$664$	6.16685e10	+	5.17460e10i	0.317242	+	0.266198i
$665$	2.54815e11	−	1.47117e11i	1.30298	−	0.752277i
$666$		0			0
$667$	1.74494e10	−	3.02233e10i	0.0881613	−	0.152700i
$668$	−1.53717e10	−	4.22333e10i	−0.0771996	−	0.212104i
$669$		0			0
$670$	1.10316e11	−	9.25662e10i	0.547444	−	0.459360i
$671$	−8.06761e9	+	2.21656e10i	−0.0397974	+	0.109342i
$672$		0			0
$673$	2.30661e10	−	1.30814e11i	0.112438	−	0.637669i	−0.875549	−	0.483130i	$-0.839500\pi$
$673$	2.30661e10	−	1.30814e11i	0.112438	−	0.637669i	0.987987	−	0.154539i	$-0.0493891\pi$
$674$		−	1.99348e11i		−	0.965992i
$675$		0			0
$676$	−1.59758e11			−0.765026
$677$	1.36374e11	+	2.40464e10i	0.649198	+	0.114471i	0.488543	−	0.872540i	$-0.337528\pi$
$677$	1.36374e11	+	2.40464e10i	0.649198	+	0.114471i	0.160655	+	0.987011i	$0.448640\pi$
$678$		0			0
$679$	−2.38491e11	−	8.68038e10i	−1.12200	−	0.408375i
$680$	8.41526e10	+	1.00289e11i	0.393579	+	0.469049i
$681$		0			0
$682$	3.58595e11	−	1.30518e11i	1.65755	−	0.603299i
$683$	−1.73204e11	−	9.99994e10i	−0.795931	−	0.459531i	0.0461155	−	0.998936i	$-0.485316\pi$
$683$	−1.73204e11	−	9.99994e10i	−0.795931	−	0.459531i	−0.842046	+	0.539405i	$0.818649\pi$
$684$		0			0
$685$	−3.14500e10	−	5.44730e10i	−0.142843	−	0.247411i
$686$	−1.75636e11	+	2.09315e11i	−0.793082	+	0.945158i
$687$		0			0
$688$	1.25951e9	+	7.14306e9i	0.00562146	+	0.0318809i
$689$	−2.03175e10	+	3.58253e9i	−0.0901560	+	0.0158969i
$690$		0			0
$691$	1.31119e11	+	1.10022e11i	0.575114	+	0.482578i	0.883339	−	0.468736i	$-0.155290\pi$
$691$	1.31119e11	+	1.10022e11i	0.575114	+	0.482578i	−0.308224	+	0.951314i	$0.599735\pi$
$692$	−4.62063e10	+	2.66772e10i	−0.201501	+	0.116337i
$693$		0			0
$694$	−1.22915e11	+	2.12895e11i	−0.529868	+	0.917759i
$695$	−7.11726e9	−	1.95545e10i	−0.0305052	−	0.0838122i
$696$		0			0
$697$	6.29715e10	−	5.28393e10i	0.266816	−	0.223886i
$698$	−8.35957e10	+	2.29677e11i	−0.352178	+	0.967601i
$699$		0			0
$700$	−3.26596e9	+	1.85222e10i	−0.0136025	+	0.0771435i
$701$			1.25718e11i			0.520627i	0.965524	+	0.260313i	$0.0838259\pi$
$701$			1.25718e11i			0.520627i	−0.965524	+	0.260313i	$0.916174\pi$
$702$		0			0
$703$	−3.25926e11			−1.33444
$704$	−1.13565e11	−	2.00245e10i	−0.462330	−	0.0815213i
$705$		0			0
$706$	1.64697e11	+	5.99448e10i	0.662929	+	0.241286i
$707$	−6.22905e10	−	7.42349e10i	−0.249312	−	0.297119i
$708$		0			0
$709$	−3.45306e11	+	1.25681e11i	−1.36653	+	0.497377i	−0.918068	−	0.396424i	$-0.870251\pi$
$709$	−3.45306e11	+	1.25681e11i	−1.36653	+	0.497377i	−0.448464	+	0.893801i	$0.648029\pi$
$710$	5.03751e11	+	2.90841e11i	1.98236	+	1.14452i
$711$		0			0
$712$	−6.10742e10	−	1.05784e11i	−0.237650	−	0.411622i
$713$	2.20594e11	−	2.62894e11i	0.853563	−	1.01724i
$714$		0			0
$715$	9.13308e10	+	5.17963e11i	0.349456	+	1.98187i
$716$	−1.42615e11	+	2.51468e10i	−0.542641	+	0.0956822i
$717$		0			0
$718$	6.93018e10	+	5.81511e10i	0.260763	+	0.218807i
$719$	−3.16014e11	+	1.82451e11i	−1.18247	+	0.682701i	−0.956585	−	0.291453i	$-0.905861\pi$
$719$	−3.16014e11	+	1.82451e11i	−1.18247	+	0.682701i	−0.225887	+	0.974153i	$0.572528\pi$
$720$		0			0
$721$	4.02156e9	−	6.96555e9i	0.0148817	−	0.0257759i
$722$	−2.37616e11	−	6.52844e11i	−0.874433	−	2.40248i
$723$		0			0
$724$	−1.22023e11	+	1.02390e11i	−0.444108	+	0.372651i
$725$	6.55054e9	−	1.79974e10i	0.0237096	−	0.0651417i
$726$		0			0
$727$	8.91683e10	−	5.05698e11i	0.319207	−	1.81031i	−0.228387	−	0.973570i	$-0.573345\pi$
$727$	8.91683e10	−	5.05698e11i	0.319207	−	1.81031i	0.547594	−	0.836744i	$-0.315544\pi$
$728$		−	2.88450e11i		−	1.02694i
$729$		0			0
$730$	2.49519e11			0.878641
$731$	−5.12451e9	−	9.03589e8i	−0.0179466	−	0.00316447i
$732$		0			0
$733$	4.03939e10	+	1.47022e10i	0.139927	+	0.0509291i	0.411034	−	0.911620i	$-0.365168\pi$
$733$	4.03939e10	+	1.47022e10i	0.139927	+	0.0509291i	−0.271108	+	0.962549i	$0.587390\pi$
$734$	2.17905e10	+	2.59689e10i	0.0750730	+	0.0894685i
$735$		0			0
$736$	1.45345e11	−	5.29012e10i	0.495322	−	0.180283i
$737$	−1.31737e11	−	7.60582e10i	−0.446516	−	0.257796i
$738$		0			0
$739$	3.58339e10	+	6.20661e10i	0.120148	+	0.208102i	0.919826	−	0.392327i	$-0.128330\pi$
$739$	3.58339e10	+	6.20661e10i	0.120148	+	0.208102i	−0.799678	+	0.600429i	$0.794996\pi$
$740$	5.43544e10	−	6.47770e10i	0.181262	−	0.216020i
$741$		0			0
$742$	2.21837e9	+	1.25810e10i	0.00731843	+	0.0415049i
$743$	−2.19616e11	+	3.87242e10i	−0.720623	+	0.127065i	−0.521920	−	0.852994i	$-0.674784\pi$
$743$	−2.19616e11	+	3.87242e10i	−0.720623	+	0.127065i	−0.198703	+	0.980060i	$0.563673\pi$
$744$		0			0
$745$	4.47302e11	+	3.75331e11i	1.45203	+	1.21840i
$746$	7.34394e10	−	4.24003e10i	0.237123	−	0.136903i
$747$		0			0
$748$	−3.39138e10	+	5.87404e10i	−0.108335	+	0.187642i
$749$	−1.09562e11	−	3.01020e11i	−0.348123	−	0.956461i
$750$		0			0
$751$	−2.85366e11	+	2.39451e11i	−0.897103	+	0.752759i	−0.969622	−	0.244608i	$-0.921341\pi$
$751$	−2.85366e11	+	2.39451e11i	−0.897103	+	0.752759i	0.0725187	+	0.997367i	$0.476896\pi$
$752$	−1.82290e11	+	5.00838e11i	−0.570022	+	1.56612i
$753$		0			0
$754$	2.50174e10	−	1.41880e11i	0.0774027	−	0.438972i
$755$		−	1.90379e11i		−	0.585910i
$756$		0			0
$757$	8.96073e10			0.272873			0.136436	−	0.990649i	$-0.456435\pi$
$757$	8.96073e10			0.272873			0.136436	+	0.990649i	$0.456435\pi$
$758$	−4.04252e11	−	7.12805e10i	−1.22455	−	0.215920i
$759$		0			0
$760$	−5.01055e11	−	1.82369e11i	−1.50186	−	0.546634i
$761$	2.51712e11	+	2.99978e11i	0.750524	+	0.894439i	0.997209	−	0.0746562i	$-0.0237859\pi$
$761$	2.51712e11	+	2.99978e11i	0.750524	+	0.894439i	−0.246686	+	0.969096i	$0.579341\pi$
$762$		0			0
$763$	2.75156e11	−	1.00149e11i	0.811859	−	0.295492i
$764$	−3.41392e10	−	1.97103e10i	−0.100203	−	0.0578521i
$765$		0			0
$766$	1.95195e11	+	3.38088e11i	0.566962	+	0.982007i
$767$	−1.78016e11	+	2.12152e11i	−0.514373	+	0.613006i
$768$		0			0
$769$	9.04648e10	+	5.13051e11i	0.258687	+	1.46709i	0.786429	+	0.617681i	$0.211928\pi$
$769$	9.04648e10	+	5.13051e11i	0.258687	+	1.46709i	−0.527742	+	0.849405i	$0.676961\pi$
$770$	3.20731e11	−	5.65536e10i	0.912386	−	0.160878i
$771$		0			0
$772$	−8.53073e10	−	7.15813e10i	−0.240169	−	0.201526i
$773$	−3.85204e11	+	2.22398e11i	−1.07888	+	0.622891i	−0.930594	−	0.366053i	$-0.880709\pi$
$773$	−3.85204e11	+	2.22398e11i	−1.07888	+	0.622891i	−0.148286	+	0.988945i	$0.547376\pi$
$774$		0			0
$775$	9.41695e10	−	1.63106e11i	0.261038	−	0.452131i
$776$	1.57305e11	+	4.32193e11i	0.433807	+	1.19188i
$777$		0			0
$778$	1.97923e11	−	1.66077e11i	0.540228	−	0.453305i
$779$	−1.14509e11	+	3.14612e11i	−0.310950	+	0.854329i
$780$		0			0
$781$	1.06696e11	−	6.05102e11i	0.286776	−	1.62639i
$782$			2.46361e11i			0.658787i
$783$		0			0
$784$	2.16686e11			0.573545
$785$	−4.67890e11	−	8.25016e10i	−1.23215	−	0.217262i
$786$		0			0
$787$	−2.60751e11	−	9.49055e10i	−0.679715	−	0.247396i	−0.0209896	−	0.999780i	$-0.506682\pi$
$787$	−2.60751e11	−	9.49055e10i	−0.679715	−	0.247396i	−0.658725	+	0.752384i	$0.728904\pi$
$788$	6.47818e10	+	7.72040e10i	0.168015	+	0.200233i
$789$		0			0
$790$	−1.23495e10	+	4.49485e9i	−0.0317059	+	0.0115400i
$791$	6.10475e10	+	3.52458e10i	0.155942	+	0.0900329i
$792$		0			0
$793$	4.37856e10	+	7.58388e10i	0.110723	+	0.191778i
$794$	1.28871e11	−	1.53582e11i	0.324244	−	0.386419i
$795$		0			0
$796$	1.69075e10	+	9.58873e10i	0.0421141	+	0.238841i
$797$	1.40117e11	−	2.47064e10i	0.347262	−	0.0612317i	0.00270314	−	0.999996i	$-0.499140\pi$
$797$	1.40117e11	−	2.47064e10i	0.347262	−	0.0612317i	0.344559	+	0.938765i	$0.388028\pi$
$798$		0			0
$799$	−2.92910e11	−	2.45780e11i	−0.718698	−	0.603059i
$800$	7.35119e10	−	4.24421e10i	0.179472	−	0.103618i
$801$		0			0
$802$	−7.68623e10	+	1.33129e11i	−0.185787	+	0.321793i
$803$	−9.01459e10	−	2.47674e11i	−0.216812	−	0.595687i
$804$		0			0
$805$	2.24364e11	−	1.88263e11i	0.534280	−	0.448314i
$806$	4.84549e11	−	1.33129e12i	1.14815	−	3.15451i
$807$		0			0
$808$	−3.04951e10	+	1.72946e11i	−0.0715458	+	0.405756i
$809$		−	2.00653e10i		−	0.0468437i	−0.999726	−	0.0234218i	$-0.992544\pi$
$809$		−	2.00653e10i		−	0.0468437i	0.999726	−	0.0234218i	$-0.00745608\pi$
$810$		0			0
$811$	−5.31469e11			−1.22855			−0.614277	−	0.789091i	$-0.710552\pi$
$811$	−5.31469e11			−1.22855			−0.614277	+	0.789091i	$0.710552\pi$
$812$	−2.17525e10	−	3.83554e9i	−0.0500362	−	0.00882273i
$813$		0			0
$814$	−3.39001e11	−	1.23386e11i	−0.772154	−	0.281041i
$815$	9.08862e10	+	1.08314e11i	0.206000	+	0.245501i
$816$		0			0
$817$	1.99153e10	−	7.24856e9i	0.0446990	−	0.0162691i
$818$	1.53050e11	+	8.83636e10i	0.341838	+	0.197360i
$819$		0			0
$820$	−4.34317e10	−	7.52259e10i	−0.0960619	−	0.166384i
$821$	3.02377e11	−	3.60358e11i	0.665542	−	0.793162i	−0.322628	−	0.946526i	$-0.604566\pi$
$821$	3.02377e11	−	3.60358e11i	0.665542	−	0.793162i	0.988170	+	0.153364i	$0.0490107\pi$
$822$		0			0
$823$	1.54464e10	+	8.76008e10i	0.0336688	+	0.190945i	0.997003	−	0.0773576i	$-0.0246483\pi$
$823$	1.54464e10	+	8.76008e10i	0.0336688	+	0.190945i	−0.963335	+	0.268303i	$0.913537\pi$
$824$	−1.43543e10	+	2.53104e9i	−0.0311367	+	0.00549024i
$825$		0			0
$826$	1.31368e11	+	1.10231e11i	0.282208	+	0.236801i
$827$	−3.15470e11	+	1.82137e11i	−0.674429	+	0.389381i	−0.797753	−	0.602985i	$-0.793978\pi$
$827$	−3.15470e11	+	1.82137e11i	−0.674429	+	0.389381i	0.123324	+	0.992366i	$0.460645\pi$
$828$		0			0
$829$	1.27431e11	−	2.20717e11i	0.269810	−	0.467324i	−0.699003	−	0.715119i	$-0.746373\pi$
$829$	1.27431e11	−	2.20717e11i	0.269810	−	0.467324i	0.968813	+	0.247795i	$0.0797059\pi$
$830$	1.15411e11	+	3.17089e11i	0.243184	+	0.668143i
$831$		0			0
$832$	−3.27954e11	+	2.75186e11i	−0.684416	+	0.574293i
$833$	−5.31682e10	+	1.46078e11i	−0.110426	+	0.303393i
$834$		0			0
$835$	−6.66978e10	+	3.78262e11i	−0.137204	+	0.778120i
$836$		−	2.76252e11i		−	0.565562i
$837$		0			0
$838$	3.57772e11			0.725488
$839$	−7.22478e10	−	1.27392e10i	−0.145806	−	0.0257096i	0.100269	−	0.994960i	$-0.468030\pi$
$839$	−7.22478e10	−	1.27392e10i	−0.145806	−	0.0257096i	−0.246075	+	0.969251i	$0.579141\pi$
$840$		0			0
$841$	−4.48942e11	−	1.63401e11i	−0.897441	−	0.326642i
$842$	−2.51580e10	−	2.99822e10i	−0.0500528	−	0.0596506i
$843$		0			0
$844$	2.00625e11	−	7.30216e10i	0.395381	−	0.143907i
$845$	1.18240e12	+	6.82660e11i	2.31920	+	1.33899i
$846$		0			0
$847$	1.53680e10	+	2.66182e10i	0.0298597	+	0.0517185i
$848$	2.03728e10	−	2.42793e10i	0.0393973	−	0.0469519i
$849$		0			0
$850$	2.34777e10	+	1.33149e11i	0.0449759	+	0.255071i
$851$	−3.19503e11	+	5.63370e10i	−0.609196	+	0.107418i
$852$		0			0
$853$	−3.00375e11	−	2.52045e11i	−0.567372	−	0.476081i	0.313401	−	0.949621i	$-0.398532\pi$
$853$	−3.00375e11	−	2.52045e11i	−0.567372	−	0.476081i	−0.880773	+	0.473539i	$0.842976\pi$
$854$	4.69607e10	−	2.71128e10i	0.0882883	−	0.0509733i
$855$		0			0
$856$	−2.90258e11	+	5.02741e11i	−0.540616	+	0.936374i
$857$	1.62312e11	+	4.45949e11i	0.300904	+	0.826726i	0.994344	+	0.106211i	$0.0338720\pi$
$857$	1.62312e11	+	4.45949e11i	0.300904	+	0.826726i	−0.693440	+	0.720514i	$0.743906\pi$
$858$		0			0
$859$	4.56874e11	−	3.83363e11i	0.839120	−	0.704105i	−0.118246	−	0.992984i	$-0.537727\pi$
$859$	4.56874e11	−	3.83363e11i	0.839120	−	0.704105i	0.957366	+	0.288879i	$0.0932826\pi$
$860$	−1.88061e9	+	5.16694e9i	−0.00343800	+	0.00944582i
$861$		0			0
$862$	−1.75575e11	+	9.95733e11i	−0.318004	+	1.80349i
$863$		−	3.12216e11i		−	0.562875i	−0.959580	−	0.281438i	$-0.909189\pi$
$863$		−	3.12216e11i		−	0.562875i	0.959580	−	0.281438i	$-0.0908112\pi$
$864$		0			0
$865$	4.55977e11			0.814476
$866$	8.12352e11	+	1.43239e11i	1.44435	+	0.254678i
$867$		0			0
$868$	−2.04107e11	−	7.42888e10i	−0.359566	−	0.130871i
$869$	8.92323e9	+	1.06343e10i	0.0156474	+	0.0186479i
$870$		0			0
$871$	−5.30676e11	+	1.93150e11i	−0.922055	+	0.335601i
$872$	−4.59546e11	−	2.65319e11i	−0.794809	−	0.458883i
$873$		0			0
$874$	−5.01697e11	−	8.68964e11i	−0.859796	−	1.48921i
$875$	−2.12716e11	+	2.53505e11i	−0.362884	+	0.432469i
$876$		0			0
$877$	−1.36932e11	−	7.76578e11i	−0.231476	−	1.31276i	−0.849910	−	0.526927i	$-0.823344\pi$
$877$	−1.36932e11	−	7.76578e11i	−0.231476	−	1.31276i	0.618435	−	0.785836i	$-0.287767\pi$
$878$	−6.56128e11	+	1.15693e11i	−1.10410	+	0.194683i
$879$		0			0
$880$	−6.18961e11	−	5.19370e11i	−1.03213	−	0.866057i
$881$	−4.17051e11	+	2.40784e11i	−0.692285	+	0.399691i	−0.804468	−	0.593997i	$-0.797549\pi$
$881$	−4.17051e11	+	2.40784e11i	−0.692285	+	0.399691i	0.112182	+	0.993688i	$0.464216\pi$
$882$		0			0
$883$	−3.71364e11	+	6.43221e11i	−0.610881	+	1.05808i	0.380211	+	0.924900i	$0.375851\pi$
$883$	−3.71364e11	+	6.43221e11i	−0.610881	+	1.05808i	−0.991092	+	0.133178i	$0.957482\pi$
$884$	8.61243e10	+	2.36625e11i	0.141032	+	0.387481i
$885$		0			0
$886$	9.74189e11	−	8.17442e11i	1.58091	−	1.32654i
$887$	−1.36860e11	+	3.76021e11i	−0.221097	+	0.607460i	−0.999801	−	0.0199316i	$-0.993655\pi$
$887$	−1.36860e11	+	3.76021e11i	−0.221097	+	0.607460i	0.778704	+	0.627391i	$0.215877\pi$
$888$		0			0
$889$	1.22277e11	−	6.93469e11i	0.195767	−	1.11025i
$890$		−	5.12006e11i		−	0.816047i
$891$		0			0
$892$	2.02211e11			0.319408
$893$	1.53366e12	+	2.70427e11i	2.41171	+	0.425249i
$894$		0			0
$895$	1.16298e12	+	4.23289e11i	1.81250	+	0.659697i
$896$	3.61621e11	+	4.30963e11i	0.561076	+	0.668664i
$897$		0			0
$898$	3.31576e11	−	1.20684e11i	0.509891	−	0.185585i
$899$	1.91552e11	+	1.10593e11i	0.293257	+	0.169312i
$900$		0			0
$901$	1.13690e10	+	1.96916e10i	0.0172513	+	0.0298801i
$902$	−2.38206e11	+	2.83883e11i	−0.359854	+	0.428857i
$903$		0			0
$904$	−2.21826e10	−	1.25804e11i	−0.0332154	−	0.188374i
$905$	1.34064e12	−	2.36391e11i	1.99856	−	0.352400i
$906$		0			0
$907$	6.75477e11	+	5.66793e11i	0.998117	+	0.837520i	0.986723	−	0.162415i	$-0.0519284\pi$
$907$	6.75477e11	+	5.66793e11i	0.998117	+	0.837520i	0.0113948	+	0.999935i	$0.496373\pi$
$908$	−1.82014e11	+	1.05086e11i	−0.267770	+	0.154597i
$909$		0			0
$910$	6.04544e11	−	1.04710e12i	0.881581	−	1.52694i
$911$	−3.16540e11	−	8.69688e11i	−0.459574	−	1.26267i	−0.925803	−	0.378006i	$-0.876610\pi$
$911$	−3.16540e11	−	8.69688e11i	−0.459574	−	1.26267i	0.466229	−	0.884664i	$-0.345612\pi$
$912$		0			0
$913$	2.73049e11	−	2.29116e11i	0.392969	−	0.329740i
$914$	8.15897e10	−	2.24166e11i	0.116910	−	0.321207i
$915$		0			0
$916$	−5.80545e10	+	3.29244e11i	−0.0824620	+	0.467666i
$917$		−	6.48233e11i		−	0.916756i
$918$		0			0
$919$	−5.89783e11			−0.826857			−0.413428	−	0.910537i	$-0.635669\pi$
$919$	−5.89783e11			−0.826857			−0.413428	+	0.910537i	$0.635669\pi$
$920$	−5.22703e11	−	9.21666e10i	−0.729631	−	0.128654i
$921$		0			0
$922$	1.51191e12	+	5.50289e11i	2.09219	+	0.761496i
$923$	−1.46626e12	−	1.74743e12i	−2.02025	−	2.40764i
$924$		0			0
$925$	−1.67311e11	+	6.08960e10i	−0.228537	+	0.0831806i
$926$	−5.76916e11	−	3.33083e11i	−0.784636	−	0.453010i
$927$		0			0
$928$	4.98441e10	+	8.63325e10i	0.0672081	+	0.116408i
$929$	−4.01390e11	+	4.78358e11i	−0.538895	+	0.642230i	−0.964939	−	0.262472i	$-0.915462\pi$
$929$	−4.01390e11	+	4.78358e11i	−0.538895	+	0.642230i	0.426045	+	0.904702i	$0.359907\pi$
$930$		0			0
$931$	−1.09944e11	−	6.23521e11i	−0.146343	−	0.829951i
$932$	4.04473e10	−	7.13195e9i	0.0536075	−	0.00945245i
$933$		0			0
$934$	−1.02546e12	−	8.60460e11i	−1.34750	−	1.13069i
$935$	5.02005e11	−	2.89833e11i	0.656844	−	0.379229i
$936$		0			0
$937$	5.31480e11	−	9.20551e11i	0.689491	−	1.19423i	−0.282511	−	0.959264i	$-0.591167\pi$
$937$	5.31480e11	−	9.20551e11i	0.689491	−	1.19423i	0.972003	−	0.234970i	$-0.0754992\pi$
$938$	1.19602e11	+	3.28604e11i	0.154500	+	0.424484i
$939$		0			0
$940$	−3.09514e11	+	2.59713e11i	−0.396432	+	0.332646i
$941$	1.57084e11	−	4.31586e11i	0.200343	−	0.550438i	−0.798314	−	0.602241i	$-0.794275\pi$
$941$	1.57084e11	−	4.31586e11i	0.200343	−	0.550438i	0.998657	+	0.0518029i	$0.0164968\pi$
$942$		0			0
$943$	−5.78713e10	+	3.28205e11i	−0.0731841	+	0.415048i
$944$		−	4.25456e11i		−	0.535756i
$945$		0			0
$946$	2.34583e10			0.0292908
$947$	7.66319e11	+	1.35123e11i	0.952818	+	0.168007i	0.628386	−	0.777902i	$-0.283716\pi$
$947$	7.66319e11	+	1.35123e11i	0.952818	+	0.168007i	0.324432	+	0.945909i	$0.394827\pi$
$948$		0			0
$949$	−9.19492e11	−	3.34668e11i	−1.13366	−	0.412619i
$950$	−3.53959e11	−	4.21831e11i	−0.434568	−	0.517898i
$951$		0			0
$952$	−2.98736e11	+	1.08731e11i	−0.363697	+	0.132375i
$953$	2.60374e11	+	1.50327e11i	0.315664	+	0.182249i	0.649458	−	0.760397i	$-0.274996\pi$
$953$	2.60374e11	+	1.50327e11i	0.315664	+	0.182249i	−0.333794	+	0.942646i	$0.608329\pi$
$954$		0			0
$955$	1.68447e11	+	2.91759e11i	0.202512	+	0.350761i
$956$	6.43668e10	−	7.67094e10i	0.0770603	−	0.0918369i
$957$		0			0
$958$	−4.68260e10	−	2.65563e11i	−0.0555936	−	0.315287i
$959$	1.50420e11	−	2.65230e10i	0.177840	−	0.0313580i
$960$		0			0
$961$	1.01284e12	+	8.49875e11i	1.18754	+	0.996464i
$962$	−1.15988e12	+	6.69659e11i	−1.35430	+	0.781903i
$963$		0			0
$964$	5.17872e10	−	8.96980e10i	0.0599672	−	0.103866i
$965$	3.25503e11	+	8.94313e11i	0.375359	+	1.03129i
$966$		0			0
$967$	2.63774e11	−	2.21332e11i	0.301665	−	0.253127i	−0.479372	−	0.877612i	$-0.659135\pi$
$967$	2.63774e11	−	2.21332e11i	0.301665	−	0.253127i	0.781037	+	0.624485i	$0.214691\pi$
$968$	1.90505e10	−	5.23407e10i	0.0216972	−	0.0596126i
$969$		0			0
$970$	−3.34772e11	+	1.89859e12i	−0.378148	+	2.14459i
$971$			4.73806e11i			0.532996i	0.963835	+	0.266498i	$0.0858666\pi$
$971$			4.73806e11i			0.532996i	−0.963835	+	0.266498i	$0.914133\pi$
$972$		0			0
$973$	5.05316e10			0.0563783
$974$	9.16058e10	+	1.61526e10i	0.101786	+	0.0179476i
$975$		0			0
$976$	−1.26418e11	−	4.60124e10i	−0.139319	−	0.0507079i
$977$	2.73124e11	+	3.25496e11i	0.299765	+	0.357246i	0.894811	−	0.446446i	$-0.147310\pi$
$977$	2.73124e11	+	3.25496e11i	0.299765	+	0.357246i	−0.595046	+	0.803692i	$0.702866\pi$
$978$		0			0
$979$	−5.08220e11	+	1.84977e11i	−0.553250	+	0.201366i
$980$	1.42258e11	+	8.21328e10i	0.154232	+	0.0890456i
$981$		0			0
$982$	1.00195e12	+	1.73543e12i	1.07746	+	1.86621i
$983$	−4.17022e11	+	4.96987e11i	−0.446627	+	0.532269i	−0.941642	−	0.336615i	$-0.890718\pi$
$983$	−4.17022e11	+	4.96987e11i	−0.446627	+	0.532269i	0.495016	+	0.868884i	$0.335162\pi$
$984$		0			0
$985$	−1.49564e11	−	8.48221e11i	−0.158885	−	0.901081i
$986$	−1.56370e11	+	2.75723e10i	−0.165442	+	0.0291719i
$987$		0			0
$988$	−7.85647e11	−	6.59236e11i	−0.824517	−	0.691852i
$989$	1.82699e10	−	1.05481e10i	0.0190963	−	0.0110253i
$990$		0			0
$991$	−2.65986e10	+	4.60702e10i	−0.0275781	+	0.0477667i	−0.879485	−	0.475926i	$-0.842113\pi$
$991$	−2.65986e10	+	4.60702e10i	−0.0275781	+	0.0477667i	0.851907	+	0.523693i	$0.175446\pi$
$992$	3.35282e11	+	9.21180e11i	0.346229	+	0.951257i
$993$		0			0
$994$	−1.08204e12	+	9.07936e11i	−1.10840	+	0.930058i
$995$	2.84599e11	−	7.81929e11i	0.290363	−	0.797765i
$996$		0			0
$997$	−1.49115e11	+	8.45675e11i	−0.150918	+	0.855899i	0.811505	+	0.584345i	$0.198649\pi$
$997$	−1.49115e11	+	8.45675e11i	−0.150918	+	0.855899i	−0.962423	+	0.271554i	$0.912462\pi$
$998$		−	1.16379e12i		−	1.17315i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.17		138
3.2	odd	2		27.9.f.a.2.7	✓	138
27.13	even	9		27.9.f.a.14.7	yes	138
27.14	odd	18	inner	81.9.f.a.71.17		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.7	✓	138	3.2	odd	2
27.9.f.a.14.7	yes	138	27.13	even	9
81.9.f.a.8.17		138	1.1	even	1	trivial
81.9.f.a.71.17		138	27.14	odd	18	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(18.1654 + 3.20306i) q^{2} +(79.1620 + 28.8126i) q^{4} +(-462.775 - 551.514i) q^{5} +(1642.82 - 597.939i) q^{7} +(-2743.73 - 1584.09i) q^{8} +(-6639.98 - 11500.8i) q^{10} +(-9016.87 + 10745.9i) q^{11} +(9043.29 + 51287.0i) q^{13} +(31757.8 - 5599.76i) q^{14} +(-61287.6 - 51426.4i) q^{16} +(49707.0 - 28698.4i) q^{17} +(-116884. + 202450. i) q^{19} +(-20743.7 - 56992.7i) q^{20} +(-198215. + 166322. i) q^{22} +(-79587.0 + 218664. i) q^{23} +(-22175.6 + 125764. i) q^{25} +960617. i q^{26} +147277. q^{28} +(-147697. - 26043.0i) q^{29} +(-1.38587e6 - 504414. i) q^{31} +(-427258. - 509186. i) q^{32} +(994872. - 362104. i) q^{34} +(-1.09003e6 - 629329. i) q^{35} +(697113. + 1.20744e6i) q^{37} +(-2.77171e6 + 3.30320e6i) q^{38} +(396080. + 2.24628e6i) q^{40} +(1.41044e6 - 248698. i) q^{41} +(-69449.3 - 58274.9i) q^{43} +(-1.02341e6 + 590866. i) q^{44} +(-2.14612e6 + 3.71720e6i) q^{46} +(-2.27848e6 - 6.26006e6i) q^{47} +(-2.07476e6 + 1.74093e6i) q^{49} +(-805657. + 2.21352e6i) q^{50} +(-761828. + 4.32054e6i) q^{52} +396154. i q^{53} +1.00993e7 q^{55} +(-5.45465e6 - 961801. i) q^{56} +(-2.59957e6 - 946165. i) q^{58} +(3.41825e6 + 4.07371e6i) q^{59} +(1.58012e6 - 575117. i) q^{61} +(-2.35592e7 - 1.36019e7i) q^{62} +(4.11030e6 + 7.11925e6i) q^{64} +(2.41005e7 - 2.87219e7i) q^{65} +(1.88303e6 + 1.06792e7i) q^{67} +(4.76178e6 - 839630. i) q^{68} +(-1.77851e7 - 1.49235e7i) q^{70} +(-3.79332e7 + 2.19007e7i) q^{71} +(-9.39455e6 + 1.62718e7i) q^{73} +(8.79588e6 + 2.41665e7i) q^{74} +(-1.50859e7 + 1.26586e7i) q^{76} +(-8.38774e6 + 2.30451e7i) q^{77} +(171845. - 974580. i) q^{79} +5.75999e7i q^{80} +2.64178e7 q^{82} +(-2.50236e7 - 4.41234e6i) q^{83} +(-3.88307e7 - 1.41332e7i) q^{85} +(-1.07492e6 - 1.28104e6i) q^{86} +(4.17623e7 - 1.52002e7i) q^{88} +(3.33894e7 + 1.92774e7i) q^{89} +(4.55230e7 + 7.88482e7i) q^{91} +(-1.26005e7 + 1.50167e7i) q^{92} +(-2.13382e7 - 1.21015e8i) q^{94} +(1.65745e8 - 2.92253e7i) q^{95} +(-1.11208e8 - 9.33146e7i) q^{97} +(-4.32651e7 + 2.49791e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

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