LMFDB - Embedded newform 81.9.f.a.8.9

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			8.9
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-13.3375 - 2.35175i) q^{2} +(-68.2042 - 24.8243i) q^{4} +(636.805 + 758.914i) q^{5} +(-2502.00 + 910.653i) q^{7} +(3853.85 + 2225.02i) q^{8} +(-6708.58 - 11619.6i) q^{10} +(-15349.9 + 18293.3i) q^{11} +(4780.28 + 27110.3i) q^{13} +(35511.9 - 6261.71i) q^{14} +(-31934.2 - 26796.0i) q^{16} +(105956. - 61173.5i) q^{17} +(-547.495 + 948.289i) q^{19} +(-24593.2 - 67569.4i) q^{20} +(247750. - 207887. i) q^{22} +(-50471.0 + 138668. i) q^{23} +(-102599. + 581870. i) q^{25} -372825. i q^{26} +193253. q^{28} +(924074. + 162939. i) q^{29} +(131238. + 47766.6i) q^{31} +(-369368. - 440196. i) q^{32} +(-1.55704e6 + 566717. i) q^{34} +(-2.28439e6 - 1.31889e6i) q^{35} +(-379045. - 656525. i) q^{37} +(9532.34 - 11360.2i) q^{38} +(765550. + 4.34165e6i) q^{40} +(-4.60079e6 + 811243. i) q^{41} +(-1.82392e6 - 1.53045e6i) q^{43} +(1.50104e6 - 866629. i) q^{44} +(999268. - 1.73078e6i) q^{46} +(-425686. - 1.16956e6i) q^{47} +(1.01461e6 - 851361. i) q^{49} +(2.73683e6 - 7.51938e6i) q^{50} +(346960. - 1.96771e6i) q^{52} +6.96711e6i q^{53} -2.36579e7 q^{55} +(-1.16686e7 - 2.05748e6i) q^{56} +(-1.19416e7 - 4.34639e6i) q^{58} +(-4.48304e6 - 5.34268e6i) q^{59} +(-2.36882e7 + 8.62179e6i) q^{61} +(-1.63804e6 - 945725. i) q^{62} +(9.22715e6 + 1.59819e7i) q^{64} +(-1.75303e7 + 2.08918e7i) q^{65} +(-3.60777e6 - 2.04607e7i) q^{67} +(-8.74520e6 + 1.54201e6i) q^{68} +(2.73663e7 + 2.29630e7i) q^{70} +(1.06620e7 - 6.15572e6i) q^{71} +(3.50114e6 - 6.06416e6i) q^{73} +(3.51151e6 + 9.64780e6i) q^{74} +(60882.1 - 51086.1i) q^{76} +(2.17466e7 - 5.97482e7i) q^{77} +(2.79249e6 - 1.58370e7i) q^{79} -4.12991e7i q^{80} +6.32706e7 q^{82} +(-4.48356e6 - 790573. i) q^{83} +(1.13898e8 + 4.14556e7i) q^{85} +(2.07272e7 + 2.47018e7i) q^{86} +(-9.98592e7 + 3.63458e7i) q^{88} +(3.86601e7 + 2.23204e7i) q^{89} +(-3.66484e7 - 6.34768e7i) q^{91} +(6.88467e6 - 8.20483e6i) q^{92} +(2.92705e6 + 1.66001e7i) q^{94} +(-1.06832e6 + 188373. i) q^{95} +(1.19186e7 + 1.00009e7i) q^{97} +(-1.55345e7 + 8.96887e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−13.3375	−	2.35175i	−0.833591	−	0.146985i	−0.259466	−	0.965752i	$-0.583547\pi$
$2$	−13.3375	−	2.35175i	−0.833591	−	0.146985i	−0.574125	+	0.818768i	$0.694658\pi$
$3$		0			0
$3$		0			0
$4$	−68.2042	−	24.8243i	−0.266423	−	0.0969699i
$5$	636.805	+	758.914i	1.01889	+	1.21426i	0.976579	+	0.215158i	$0.0690267\pi$
$5$	636.805	+	758.914i	1.01889	+	1.21426i	0.0423083	+	0.999105i	$0.486529\pi$
$6$		0			0
$7$	−2502.00	+	910.653i	−1.04207	+	0.379281i	−0.805663	−	0.592375i	$-0.798191\pi$
$7$	−2502.00	+	910.653i	−1.04207	+	0.379281i	−0.236402	+	0.971655i	$0.575968\pi$
$8$	3853.85	+	2225.02i	0.940882	+	0.543219i
$9$		0			0
$10$	−6708.58	−	11619.6i	−0.670858	−	1.16196i
$11$	−15349.9	+	18293.3i	−1.04842	+	1.24946i	−0.0808814	+	0.996724i	$0.525773\pi$
$11$	−15349.9	+	18293.3i	−1.04842	+	1.24946i	−0.967536	+	0.252732i	$0.918671\pi$
$12$		0			0
$13$	4780.28	+	27110.3i	0.167371	+	0.949208i	0.946586	+	0.322451i	$0.104507\pi$
$13$	4780.28	+	27110.3i	0.167371	+	0.949208i	−0.779215	+	0.626757i	$0.784382\pi$
$14$	35511.9	−	6261.71i	0.924405	−	0.162997i
$15$		0			0
$16$	−31934.2	−	26796.0i	−0.487277	−	0.408874i
$17$	105956.	−	61173.5i	1.26861	−	0.732432i	0.293885	−	0.955841i	$-0.405052\pi$
$17$	105956.	−	61173.5i	1.26861	−	0.732432i	0.974725	+	0.223409i	$0.0717185\pi$
$18$		0			0
$19$	−547.495	+	948.289i	−0.00420113	+	0.00727656i	−0.868118	−	0.496357i	$-0.834671\pi$
$19$	−547.495	+	948.289i	−0.00420113	+	0.00727656i	0.863917	+	0.503634i	$0.168004\pi$
$20$	−24593.2	−	67569.4i	−0.153708	−	0.422309i
$21$		0			0
$22$	247750.	−	207887.i	1.05760	−	0.887434i
$23$	−50471.0	+	138668.i	−0.180356	+	0.495524i	−0.996619	−	0.0821558i	$-0.973819\pi$
$23$	−50471.0	+	138668.i	−0.180356	+	0.495524i	0.816264	+	0.577680i	$0.196042\pi$
$24$		0			0
$25$	−102599.	+	581870.i	−0.262654	+	1.48959i
$26$		−	372825.i		−	0.815853i
$27$		0			0
$28$	193253.			0.314409
$29$	924074.	+	162939.i	1.30652	+	0.230374i	0.783203	−	0.621766i	$-0.213585\pi$
$29$	924074.	+	162939.i	1.30652	+	0.230374i	0.523313	+	0.852140i	$0.324696\pi$
$30$		0			0
$31$	131238.	+	47766.6i	0.142106	+	0.0517223i	0.412094	−	0.911141i	$-0.364798\pi$
$31$	131238.	+	47766.6i	0.142106	+	0.0517223i	−0.269988	+	0.962864i	$0.587020\pi$
$32$	−369368.	−	440196.i	−0.352257	−	0.419804i
$33$		0			0
$34$	−1.55704e6	+	566717.i	−1.16516	+	0.424083i
$35$	−2.28439e6	−	1.31889e6i	−1.52229	−	0.878897i
$36$		0			0
$37$	−379045.	−	656525.i	−0.202248	−	0.350303i	0.747005	−	0.664819i	$-0.231491\pi$
$37$	−379045.	−	656525.i	−0.202248	−	0.350303i	−0.949252	+	0.314515i	$0.898158\pi$
$38$	9532.34	−	11360.2i	0.00457157	−	0.00544818i
$39$		0			0
$40$	765550.	+	4.34165e6i	0.299043	+	1.69596i
$41$	−4.60079e6	+	811243.i	−1.62816	+	0.287088i	−0.911797	−	0.410641i	$-0.865305\pi$
$41$	−4.60079e6	+	811243.i	−1.62816	+	0.287088i	−0.716361	+	0.697730i	$0.754194\pi$
$42$		0			0
$43$	−1.82392e6	−	1.53045e6i	−0.533498	−	0.447658i	0.335810	−	0.941930i	$-0.390990\pi$
$43$	−1.82392e6	−	1.53045e6i	−0.533498	−	0.447658i	−0.869307	+	0.494272i	$0.835435\pi$
$44$	1.50104e6	−	866629.i	0.400482	−	0.231218i
$45$		0			0
$46$	999268.	−	1.73078e6i	0.223178	−	0.386555i
$47$	−425686.	−	1.16956e6i	−0.0872365	−	0.239680i	0.888401	−	0.459068i	$-0.151816\pi$
$47$	−425686.	−	1.16956e6i	−0.0872365	−	0.239680i	−0.975638	+	0.219387i	$0.929594\pi$
$48$		0			0
$49$	1.01461e6	−	851361.i	0.176001	−	0.147683i
$50$	2.73683e6	−	7.51938e6i	0.437893	−	1.20310i
$51$		0			0
$52$	346960.	−	1.96771e6i	0.0474532	−	0.269121i
$53$			6.96711e6i			0.882977i	0.897267	+	0.441489i	$0.145549\pi$
$53$			6.96711e6i			0.882977i	−0.897267	+	0.441489i	$0.854451\pi$
$54$		0			0
$55$	−2.36579e7			−2.58539
$56$	−1.16686e7	−	2.05748e6i	−1.18649	−	0.209211i
$57$		0			0
$58$	−1.19416e7	−	4.34639e6i	−1.05524	−	0.384076i
$59$	−4.48304e6	−	5.34268e6i	−0.369968	−	0.440911i	0.548653	−	0.836050i	$-0.315141\pi$
$59$	−4.48304e6	−	5.34268e6i	−0.369968	−	0.440911i	−0.918621	+	0.395139i	$0.870696\pi$
$60$		0			0
$61$	−2.36882e7	+	8.62179e6i	−1.71085	+	0.622699i	−0.996986	−	0.0775852i	$-0.975279\pi$
$61$	−2.36882e7	+	8.62179e6i	−1.71085	+	0.622699i	−0.713865	+	0.700284i	$0.753057\pi$
$62$	−1.63804e6	−	945725.i	−0.110856	−	0.0640026i
$63$		0			0
$64$	9.22715e6	+	1.59819e7i	0.549981	+	0.952595i
$65$	−1.75303e7	+	2.08918e7i	−0.982056	+	1.17037i
$66$		0			0
$67$	−3.60777e6	−	2.04607e7i	−0.179036	−	1.01536i	−0.933382	−	0.358885i	$-0.883157\pi$
$67$	−3.60777e6	−	2.04607e7i	−0.179036	−	1.01536i	0.754346	−	0.656477i	$-0.227954\pi$
$68$	−8.74520e6	+	1.54201e6i	−0.409010	+	0.0721195i
$69$		0			0
$70$	2.73663e7	+	2.29630e7i	1.13979	+	0.956394i
$71$	1.06620e7	−	6.15572e6i	0.419571	−	0.242240i	−0.275323	−	0.961352i	$-0.588785\pi$
$71$	1.06620e7	−	6.15572e6i	0.419571	−	0.242240i	0.694894	+	0.719112i	$0.255451\pi$
$72$		0			0
$73$	3.50114e6	−	6.06416e6i	0.123287	−	0.213540i	−0.797775	−	0.602956i	$-0.793990\pi$
$73$	3.50114e6	−	6.06416e6i	0.123287	−	0.213540i	0.921062	+	0.389415i	$0.127323\pi$
$74$	3.51151e6	+	9.64780e6i	0.117103	+	0.321737i
$75$		0			0
$76$	60882.1	−	51086.1i	0.00182488	−	0.00153126i
$77$	2.17466e7	−	5.97482e7i	0.618625	−	1.69966i
$78$		0			0
$79$	2.79249e6	−	1.58370e7i	0.0716941	−	0.406598i	−0.927748	−	0.373207i	$-0.878258\pi$
$79$	2.79249e6	−	1.58370e7i	0.0716941	−	0.406598i	0.999442	−	0.0333910i	$-0.0106306\pi$
$80$		−	4.12991e7i		−	1.00828i
$81$		0			0
$82$	6.32706e7			1.39942
$83$	−4.48356e6	−	790573.i	−0.0944737	−	0.0166583i	0.126211	−	0.992003i	$-0.459718\pi$
$83$	−4.48356e6	−	790573.i	−0.0944737	−	0.0166583i	−0.220685	+	0.975345i	$0.570829\pi$
$84$		0			0
$85$	1.13898e8	+	4.14556e7i	2.18194	+	0.794159i
$86$	2.07272e7	+	2.47018e7i	0.378920	+	0.451579i
$87$		0			0
$88$	−9.98592e7	+	3.63458e7i	−1.66517	+	0.606071i
$89$	3.86601e7	+	2.23204e7i	0.616174	+	0.355748i	0.775378	−	0.631497i	$-0.217559\pi$
$89$	3.86601e7	+	2.23204e7i	0.616174	+	0.355748i	−0.159204	+	0.987246i	$0.550893\pi$
$90$		0			0
$91$	−3.66484e7	−	6.34768e7i	−0.534428	−	0.925656i
$92$	6.88467e6	−	8.20483e6i	0.0961018	−	0.114530i
$93$		0			0
$94$	2.92705e6	+	1.66001e7i	0.0374903	+	0.212618i
$95$	−1.06832e6	+	188373.i	−0.0131161	+	0.00231273i
$96$		0			0
$97$	1.19186e7	+	1.00009e7i	0.134629	+	0.112967i	0.707616	−	0.706598i	$-0.249771\pi$
$97$	1.19186e7	+	1.00009e7i	0.134629	+	0.112967i	−0.572987	+	0.819565i	$0.694215\pi$
$98$	−1.55345e7	+	8.96887e6i	−0.168420	+	0.0972374i
$99$		0			0
$100$	2.14422e7	−	3.71390e7i	0.214422	−	0.371390i
$101$	5.97338e7	+	1.64117e8i	0.574030	+	1.57714i	0.798076	+	0.602557i	$0.205851\pi$
$101$	5.97338e7	+	1.64117e8i	0.574030	+	1.57714i	−0.224046	+	0.974579i	$0.571927\pi$
$102$		0			0
$103$	6.03092e7	−	5.06054e7i	0.535839	−	0.449623i	−0.334273	−	0.942476i	$-0.608491\pi$
$103$	6.03092e7	−	5.06054e7i	0.535839	−	0.449623i	0.870112	+	0.492854i	$0.164046\pi$
$104$	−4.18986e7	+	1.15116e8i	−0.358151	+	0.984012i
$105$		0			0
$106$	1.63849e7	−	9.29236e7i	0.129784	−	0.736042i
$107$		−	6.15134e7i		−	0.469283i	−0.972082	−	0.234641i	$-0.924608\pi$
$107$		−	6.15134e7i		−	0.469283i	0.972082	−	0.234641i	$-0.0753916\pi$
$108$		0			0
$109$	−2.02005e7			−0.143105			−0.0715526	−	0.997437i	$-0.522795\pi$
$109$	−2.02005e7			−0.143105			−0.0715526	+	0.997437i	$0.522795\pi$
$110$	3.15536e8	+	5.56376e7i	2.15516	+	0.380012i
$111$		0			0
$112$	1.04301e8	+	3.79625e7i	0.662852	+	0.241258i
$113$	−7.22019e7	−	8.60469e7i	−0.442828	−	0.527742i	0.497750	−	0.867321i	$-0.334160\pi$
$113$	−7.22019e7	−	8.60469e7i	−0.442828	−	0.527742i	−0.940578	+	0.339579i	$0.889715\pi$
$114$		0			0
$115$	−1.37377e8	+	5.00012e7i	−0.785459	+	0.285884i
$116$	−5.89809e7	−	3.40526e7i	−0.325746	−	0.188070i
$117$		0			0
$118$	4.72277e7	+	8.18007e7i	0.243595	+	0.421919i
$119$	−2.09393e8	+	2.49545e8i	−1.04418	+	1.24440i
$120$		0			0
$121$	−6.18021e7	−	3.50497e8i	−0.288311	−	1.63510i
$122$	3.36216e8	−	5.92840e7i	1.51768	−	0.267607i
$123$		0			0
$124$	−7.76519e6	−	6.51577e6i	−0.0328447	−	0.0275600i
$125$	−1.71783e8	+	9.91787e7i	−0.703622	+	0.406236i
$126$		0			0
$127$	−1.22668e8	+	2.12467e8i	−0.471536	+	0.816725i	−0.999470	−	0.0325610i	$-0.989634\pi$
$127$	−1.22668e8	+	2.12467e8i	−0.471536	+	0.816725i	0.527934	+	0.849286i	$0.322967\pi$
$128$	−3.51679e7	−	9.66229e7i	−0.131011	−	0.359948i
$129$		0			0
$130$	2.82942e8	−	2.37417e8i	0.990660	−	0.831262i
$131$	1.43812e8	−	3.95121e8i	0.488327	−	1.34167i	−0.413867	−	0.910337i	$-0.635822\pi$
$131$	1.43812e8	−	3.95121e8i	0.488327	−	1.34167i	0.902194	−	0.431330i	$-0.141955\pi$
$132$		0			0
$133$	506269.	−	2.87120e6i	0.00161799	−	0.00917606i
$134$			2.81378e8i			0.872713i
$135$		0			0
$136$	5.44450e8			1.59148
$137$	−3.65675e8	−	6.44783e7i	−1.03804	−	0.183034i	−0.371444	−	0.928456i	$-0.621137\pi$
$137$	−3.65675e8	−	6.44783e7i	−1.03804	−	0.183034i	−0.666593	+	0.745422i	$0.732248\pi$
$138$		0			0
$139$	−3.96654e8	−	1.44370e8i	−1.06256	−	0.386739i	−0.249169	−	0.968460i	$-0.580158\pi$
$139$	−3.96654e8	−	1.44370e8i	−1.06256	−	0.386739i	−0.813389	+	0.581721i	$0.802380\pi$
$140$	1.23064e8	+	1.46663e8i	0.320347	+	0.381775i
$141$		0			0
$142$	−1.56681e8	+	5.70272e7i	−0.385357	+	0.140258i
$143$	−5.69314e8	−	3.28693e8i	−1.36147	−	0.786044i
$144$		0			0
$145$	4.64798e8	+	8.05053e8i	1.05146	+	1.82118i
$146$	−6.09578e7	+	7.26467e7i	−0.134158	+	0.159884i
$147$		0			0
$148$	9.55468e6	+	5.41873e7i	0.0199145	+	0.112941i
$149$	4.73599e8	−	8.35083e7i	0.960873	−	0.169428i	0.328854	−	0.944381i	$-0.393338\pi$
$149$	4.73599e8	−	8.35083e7i	0.960873	−	0.169428i	0.632019	+	0.774953i	$0.282227\pi$
$150$		0			0
$151$	−3.88229e8	−	3.25763e8i	−0.746758	−	0.626605i	0.187885	−	0.982191i	$-0.439837\pi$
$151$	−3.88229e8	−	3.25763e8i	−0.746758	−	0.626605i	−0.934643	+	0.355586i	$0.884281\pi$
$152$	−4.21993e6	+	2.43638e6i	−0.00790553	+	0.00456426i
$153$		0			0
$154$	−4.30557e8	+	7.45746e8i	−0.765504	+	1.32589i
$155$	4.73220e7	+	1.30016e8i	0.0819854	+	0.225253i
$156$		0			0
$157$	−3.53896e8	+	2.96954e8i	−0.582475	+	0.488755i	−0.885759	−	0.464146i	$-0.846361\pi$
$157$	−3.53896e8	+	2.96954e8i	−0.582475	+	0.488755i	0.303284	+	0.952900i	$0.401917\pi$
$158$	−7.44895e7	+	2.04658e8i	−0.119527	+	0.328398i
$159$		0			0
$160$	9.88555e7	−	5.60638e8i	0.150842	−	0.855465i
$161$		−	3.92908e8i		−	0.584774i
$162$		0			0
$163$	−4.56114e8			−0.646134			−0.323067	−	0.946376i	$-0.604714\pi$
$163$	−4.56114e8			−0.646134			−0.323067	+	0.946376i	$0.604714\pi$
$164$	3.33932e8	+	5.88811e7i	0.461617	+	0.0813956i
$165$		0			0
$166$	5.79401e7	+	2.10885e7i	0.0763040	+	0.0277724i
$167$	−1.61471e8	−	1.92434e8i	−0.207601	−	0.247409i	0.652190	−	0.758056i	$-0.273850\pi$
$167$	−1.61471e8	−	1.92434e8i	−0.207601	−	0.247409i	−0.859791	+	0.510647i	$0.829406\pi$
$168$		0			0
$169$	5.44170e7	−	1.98062e7i	0.0667095	−	0.0242803i
$170$	−1.42162e9	−	8.20774e8i	−1.70211	−	0.982715i
$171$		0			0
$172$	8.64068e7	+	1.49661e8i	0.0987265	+	0.170999i
$173$	7.42345e8	−	8.84693e8i	0.828746	−	0.987661i	−0.171251	−	0.985227i	$-0.554781\pi$
$173$	7.42345e8	−	8.84693e8i	0.828746	−	0.987661i	0.999997	−	0.00243395i	$-0.000774751\pi$
$174$		0			0
$175$	−2.73178e8	−	1.54927e9i	−0.291269	−	1.65187i
$176$	9.80372e8	−	1.72866e8i	1.02174	−	0.180160i
$177$		0			0
$178$	−4.63136e8	−	3.88617e8i	−0.461348	−	0.387117i
$179$	−6.53835e8	+	3.77492e8i	−0.636878	+	0.367702i	−0.783411	−	0.621504i	$-0.786522\pi$
$179$	−6.53835e8	+	3.77492e8i	−0.636878	+	0.367702i	0.146533	+	0.989206i	$0.453189\pi$
$180$		0			0
$181$	1.14593e8	−	1.98480e8i	0.106768	−	0.184928i	−0.807691	−	0.589606i	$-0.799283\pi$
$181$	1.14593e8	−	1.98480e8i	0.106768	−	0.184928i	0.914459	+	0.404678i	$0.132616\pi$
$182$	3.39514e8	+	9.32808e8i	0.309437	+	0.850171i
$183$		0			0
$184$	−5.03047e8	+	4.22107e8i	−0.438872	+	0.368257i
$185$	2.56869e8	−	7.05741e8i	0.219293	−	0.602502i
$186$		0			0
$187$	−5.07342e8	+	2.87728e9i	−0.414891	+	2.35297i
$188$			9.03366e7i			0.0723156i
$189$		0			0
$190$	1.46916e7			0.0112734
$191$	9.71028e7	+	1.71218e7i	0.0729623	+	0.0128652i	0.210010	−	0.977699i	$-0.432650\pi$
$191$	9.71028e7	+	1.71218e7i	0.0729623	+	0.0128652i	−0.137048	+	0.990564i	$0.543761\pi$
$192$		0			0
$193$	2.38182e9	+	8.66911e8i	1.71664	+	0.624806i	0.997540	−	0.0700985i	$-0.0223314\pi$
$193$	2.38182e9	+	8.66911e8i	1.71664	+	0.624806i	0.719102	+	0.694905i	$0.244554\pi$
$194$	−1.35444e8	−	1.61416e8i	−0.0956211	−	0.113957i
$195$		0			0
$196$	−9.03352e7	+	3.28793e7i	−0.0612115	+	0.0222792i
$197$	−3.70754e8	−	2.14055e8i	−0.246162	−	0.142122i	0.371843	−	0.928295i	$-0.378726\pi$
$197$	−3.70754e8	−	2.14055e8i	−0.246162	−	0.142122i	−0.618006	+	0.786174i	$0.712059\pi$
$198$		0			0
$199$	4.87197e8	+	8.43850e8i	0.310665	+	0.538088i	0.978507	−	0.206216i	$-0.0661149\pi$
$199$	4.87197e8	+	8.43850e8i	0.310665	+	0.538088i	−0.667842	+	0.744303i	$0.732782\pi$
$200$	−1.69008e9	+	2.01416e9i	−1.05630	+	1.25885i
$201$		0			0
$202$	−4.10734e8	−	2.32939e9i	−0.246692	−	1.39906i
$203$	−2.46041e9	+	4.33837e8i	−1.44885	+	0.255472i
$204$		0			0
$205$	−3.54547e9	−	2.97500e9i	−2.00751	−	1.68450i
$206$	−9.23383e8	+	5.33115e8i	−0.512759	+	0.296041i
$207$		0			0
$208$	5.73793e8	−	9.93838e8i	0.306550	−	0.530961i
$209$	−8.94333e6	−	2.45716e7i	−0.00468721	−	0.0128780i
$210$		0			0
$211$	−1.10978e9	+	9.31219e8i	−0.559897	+	0.469809i	−0.878276	−	0.478154i	$-0.841306\pi$
$211$	−1.10978e9	+	9.31219e8i	−0.559897	+	0.469809i	0.318379	+	0.947964i	$0.396862\pi$
$212$	1.72954e8	−	4.75187e8i	0.0856222	−	0.235245i
$213$		0			0
$214$	−1.44664e8	+	8.20432e8i	−0.0689773	+	0.391190i
$215$		−	2.35880e9i		−	1.10392i
$216$		0			0
$217$	−3.71855e8			−0.167701
$218$	2.69423e8	+	4.75066e7i	0.119291	+	0.0210343i
$219$		0			0
$220$	1.61357e9	+	5.87291e8i	0.688806	+	0.250705i
$221$	2.16493e9	+	2.58006e9i	0.907559	+	1.08159i
$222$		0			0
$223$	9.28127e8	−	3.37811e8i	0.375308	−	0.136601i	−0.147477	−	0.989065i	$-0.547115\pi$
$223$	9.28127e8	−	3.37811e8i	0.375308	−	0.136601i	0.522785	+	0.852464i	$0.324893\pi$
$224$	1.32502e9	+	7.65003e8i	0.526298	+	0.303858i
$225$		0			0
$226$	7.60629e8	+	1.31745e9i	0.291568	+	0.505010i
$227$	−4.10560e8	+	4.89286e8i	−0.154623	+	0.184272i	−0.837795	−	0.545985i	$-0.816155\pi$
$227$	−4.10560e8	+	4.89286e8i	−0.154623	+	0.184272i	0.683172	+	0.730257i	$0.260600\pi$
$228$		0			0
$229$	1.06279e8	+	6.02738e8i	0.0386460	+	0.219173i	0.998015	−	0.0629834i	$-0.0200615\pi$
$229$	1.06279e8	+	6.02738e8i	0.0386460	+	0.219173i	−0.959369	+	0.282156i	$0.908950\pi$
$230$	1.94985e9	−	3.43812e8i	0.696772	−	0.122860i
$231$		0			0
$232$	3.19870e9	+	2.68403e9i	1.10413	+	0.926479i
$233$	3.04859e9	−	1.76010e9i	1.03437	−	0.597192i	0.116134	−	0.993234i	$-0.462950\pi$
$233$	3.04859e9	−	1.76010e9i	1.03437	−	0.597192i	0.918233	+	0.396041i	$0.129616\pi$
$234$		0			0
$235$	6.16520e8	−	1.06784e9i	0.202151	−	0.350135i
$236$	1.73134e8	+	4.75681e8i	0.0558128	+	0.153344i
$237$		0			0
$238$	3.37963e9	−	2.83585e9i	1.05332	−	0.883844i
$239$	1.07538e9	−	2.95458e9i	0.329587	−	0.905533i	−0.658629	−	0.752468i	$-0.728863\pi$
$239$	1.07538e9	−	2.95458e9i	0.329587	−	0.905533i	0.988216	−	0.153065i	$-0.0489144\pi$
$240$		0			0
$241$	6.25199e8	−	3.54568e9i	0.185332	−	1.05107i	−0.740196	−	0.672391i	$-0.765267\pi$
$241$	6.25199e8	−	3.54568e9i	0.185332	−	1.05107i	0.925528	−	0.378679i	$-0.123622\pi$
$242$			4.82009e9i			1.40538i
$243$		0			0
$244$	1.82966e9			0.516192
$245$	1.29222e9	+	2.27853e8i	0.358651	+	0.0632398i
$246$		0			0
$247$	−2.83256e7	−	1.03097e7i	−0.00761012	−	0.00276986i
$248$	3.99489e8	+	4.76093e8i	0.105608	+	0.125859i
$249$		0			0
$250$	2.52439e9	−	9.18802e8i	0.646243	−	0.235213i
$251$	1.40741e9	+	8.12567e8i	0.354589	+	0.204722i	0.666705	−	0.745322i	$-0.267704\pi$
$251$	1.40741e9	+	8.12567e8i	0.354589	+	0.204722i	−0.312116	+	0.950044i	$0.601038\pi$
$252$		0			0
$253$	−1.76197e9	−	3.05182e9i	−0.430047	−	0.744863i
$254$	2.13574e9	−	2.54528e9i	0.513114	−	0.611506i
$255$		0			0
$256$	−5.78550e8	−	3.28112e9i	−0.134704	−	0.763945i
$257$	−5.64879e8	+	9.96034e7i	−0.129486	+	0.0228319i	−0.238016	−	0.971261i	$-0.576497\pi$
$257$	−5.64879e8	+	9.96034e7i	−0.129486	+	0.0228319i	0.108530	+	0.994093i	$0.465386\pi$
$258$		0			0
$259$	1.54624e9	+	1.29745e9i	0.343619	+	0.288330i
$260$	1.71427e9	−	9.89732e8i	0.375133	−	0.216583i
$261$		0			0
$262$	−2.84732e9	+	4.93170e9i	−0.604269	+	1.04663i
$263$	2.40422e9	+	6.60554e9i	0.502517	+	1.38065i	0.888809	+	0.458278i	$0.151534\pi$
$263$	2.40422e9	+	6.60554e9i	0.502517	+	1.38065i	−0.386292	+	0.922377i	$0.626244\pi$
$264$		0			0
$265$	−5.28744e9	+	4.43669e9i	−1.07217	+	0.899654i
$266$	−1.35047e7	+	3.71038e7i	−0.00269748	+	0.00741126i
$267$		0			0
$268$	−2.61857e8	+	1.48507e9i	−0.0507604	+	0.287877i
$269$			8.50405e9i			1.62411i	0.583578	+	0.812057i	$0.301652\pi$
$269$			8.50405e9i			1.62411i	−0.583578	+	0.812057i	$0.698348\pi$
$270$		0			0
$271$	3.66496e9			0.679504			0.339752	−	0.940515i	$-0.389657\pi$
$271$	3.66496e9			0.679504			0.339752	+	0.940515i	$0.389657\pi$
$272$	−5.02280e9	−	8.85656e8i	−0.917636	−	0.161804i
$273$		0			0
$274$	4.72554e9	+	1.71995e9i	0.838395	+	0.305151i
$275$	−9.06942e9	−	1.08085e10i	−1.58580	−	1.88988i
$276$		0			0
$277$	−7.34026e9	+	2.67163e9i	−1.24679	+	0.453793i	−0.879315	−	0.476241i	$-0.841999\pi$
$277$	−7.34026e9	+	2.67163e9i	−1.24679	+	0.453793i	−0.367472	+	0.930035i	$0.619777\pi$
$278$	4.95083e9	+	2.85836e9i	0.828894	+	0.478562i
$279$		0			0
$280$	−5.86914e9	−	1.01657e10i	−0.954866	−	1.65388i
$281$	1.00634e9	−	1.19931e9i	0.161405	−	0.192356i	−0.679280	−	0.733879i	$-0.737708\pi$
$281$	1.00634e9	−	1.19931e9i	0.161405	−	0.192356i	0.840686	+	0.541524i	$0.182152\pi$
$282$		0			0
$283$	1.38681e9	+	7.86497e9i	0.216207	+	1.22617i	0.878799	+	0.477192i	$0.158345\pi$
$283$	1.38681e9	+	7.86497e9i	0.216207	+	1.22617i	−0.662592	+	0.748980i	$0.730544\pi$
$284$	−8.80006e8	+	1.55169e8i	−0.135273	+	0.0238523i
$285$		0			0
$286$	6.82019e9	+	5.72282e9i	1.01937	+	0.855354i
$287$	1.07724e10	−	6.21945e9i	1.58776	−	0.916693i
$288$		0			0
$289$	3.99650e9	−	6.92215e9i	0.572913	−	0.992315i
$290$	−4.30593e9	−	1.18305e10i	−0.608801	−	1.67267i
$291$		0			0
$292$	−3.89331e8	+	3.26688e8i	−0.0535535	+	0.0449367i
$293$	−3.64627e9	+	1.00180e10i	−0.494741	+	1.35929i	0.401555	+	0.915835i	$0.368470\pi$
$293$	−3.64627e9	+	1.00180e10i	−0.494741	+	1.35929i	−0.896296	+	0.443456i	$0.853752\pi$
$294$		0			0
$295$	1.19981e9	−	6.80448e9i	0.158426	−	0.898477i
$296$		−	3.37354e9i		−	0.439459i
$297$		0			0
$298$	−6.51300e9			−0.825878
$299$	−4.00060e9	−	7.05414e8i	−0.500542	−	0.0882590i
$300$		0			0
$301$	5.95716e9	+	2.16823e9i	0.725727	+	0.264143i
$302$	4.41187e9	+	5.25787e9i	0.530390	+	0.632094i
$303$		0			0
$304$	4.28941e7	−	1.56122e7i	0.00502231	−	0.00182797i
$305$	−2.16279e10	−	1.24869e10i	−2.49928	−	1.44296i
$306$		0			0
$307$	−1.42521e9	−	2.46854e9i	−0.160445	−	0.277899i	0.774583	−	0.632472i	$-0.217960\pi$
$307$	−1.42521e9	−	2.46854e9i	−0.160445	−	0.277899i	−0.935028	+	0.354573i	$0.884626\pi$
$308$	−2.96641e9	+	3.53523e9i	−0.329632	+	0.392840i
$309$		0			0
$310$	−3.25390e8	−	1.84538e9i	−0.0352336	−	0.199820i
$311$	−1.12462e10	+	1.98300e9i	−1.20216	+	0.211974i	−0.738633	−	0.674108i	$-0.764528\pi$
$311$	−1.12462e10	+	1.98300e9i	−1.20216	+	0.211974i	−0.463529	+	0.886082i	$0.653417\pi$
$312$		0			0
$313$	3.45161e9	+	2.89625e9i	0.359621	+	0.301758i	0.804639	−	0.593764i	$-0.202359\pi$
$313$	3.45161e9	+	2.89625e9i	0.359621	+	0.301758i	−0.445019	+	0.895521i	$0.646803\pi$
$314$	5.41844e9	−	3.12834e9i	0.557386	−	0.321807i
$315$		0			0
$316$	−5.83602e8	+	1.01083e9i	−0.0585287	+	0.101375i
$317$	−1.83180e9	−	5.03284e9i	−0.181402	−	0.498398i	0.815347	−	0.578973i	$-0.196546\pi$
$317$	−1.83180e9	−	5.03284e9i	−0.181402	−	0.498398i	−0.996749	+	0.0805754i	$0.974324\pi$
$318$		0			0
$319$	−1.71651e10	+	1.44032e10i	−1.65762	+	1.39091i
$320$	−6.25299e9	+	1.71800e10i	−0.596332	+	1.63841i
$321$		0			0
$322$	−9.24024e8	+	5.24040e9i	−0.0859527	+	0.487462i
$323$			1.33969e8i			0.0123082i
$324$		0			0
$325$	−1.62651e10			−1.45789
$326$	6.08340e9	+	1.07267e9i	0.538612	+	0.0949718i
$327$		0			0
$328$	−1.95358e10	−	7.11045e9i	−1.68786	−	0.614330i
$329$	2.13013e9	+	2.53859e9i	0.181812	+	0.216675i
$330$		0			0
$331$	−3.90947e9	+	1.42293e9i	−0.325691	+	0.118542i	−0.499691	−	0.866204i	$-0.666553\pi$
$331$	−3.90947e9	+	1.42293e9i	−0.325691	+	0.118542i	0.174000	+	0.984746i	$0.444331\pi$
$332$	2.86173e8	+	1.65222e8i	0.0235546	+	0.0135992i
$333$		0			0
$334$	1.70106e9	+	2.94632e9i	0.136689	+	0.236752i
$335$	1.32305e10	−	1.57675e10i	1.05050	−	1.25194i
$336$		0			0
$337$	−1.67135e9	−	9.47871e9i	−0.129583	−	0.734902i	−0.978480	−	0.206343i	$-0.933844\pi$
$337$	−1.67135e9	−	9.47871e9i	−0.129583	−	0.734902i	0.848897	−	0.528559i	$-0.177267\pi$
$338$	−7.72364e8	+	1.36189e8i	−0.0591773	+	0.0104346i
$339$		0			0
$340$	−6.73924e9	−	5.65490e9i	−0.504307	−	0.423164i
$341$	−2.88829e9	+	1.66756e9i	−0.213611	+	0.123328i
$342$		0			0
$343$	5.91133e9	−	1.02387e10i	0.427080	−	0.739724i
$344$	−3.62384e9	−	9.95641e9i	−0.258782	−	0.710999i
$345$		0			0
$346$	−1.19816e10	+	1.00537e10i	−0.836007	+	0.701493i
$347$	6.87957e7	−	1.89015e8i	0.00474508	−	0.0130370i	−0.937297	−	0.348530i	$-0.886681\pi$
$347$	6.87957e7	−	1.89015e8i	0.00474508	−	0.0130370i	0.942043	+	0.335493i	$0.108903\pi$
$348$		0			0
$349$	2.82255e9	−	1.60075e10i	0.190257	−	1.07900i	−0.728756	−	0.684773i	$-0.759901\pi$
$349$	2.82255e9	−	1.60075e10i	0.190257	−	1.07900i	0.919013	−	0.394227i	$-0.128988\pi$
$350$			2.13058e10i			1.41979i
$351$		0			0
$352$	1.37224e10			0.893838
$353$	−5.10574e9	−	9.00279e8i	−0.328821	−	0.0579800i	0.00680064	−	0.999977i	$-0.497835\pi$
$353$	−5.10574e9	−	9.00279e8i	−0.328821	−	0.0579800i	−0.335622	+	0.941997i	$0.608946\pi$
$354$		0			0
$355$	1.14613e10	+	4.17157e9i	0.721639	+	0.262655i
$356$	−2.08270e9	−	2.48206e9i	−0.129666	−	0.154530i
$357$		0			0
$358$	9.60827e9	−	3.49712e9i	0.584942	−	0.212902i
$359$	2.29627e10	+	1.32575e10i	1.38244	+	0.798151i	0.992448	−	0.122668i	$-0.0391449\pi$
$359$	2.29627e10	+	1.32575e10i	1.38244	+	0.798151i	0.389991	+	0.920819i	$0.372478\pi$
$360$		0			0
$361$	8.49118e9	+	1.47072e10i	0.499965	+	0.865964i
$362$	−1.99515e9	+	2.37773e9i	−0.116183	+	0.138461i
$363$		0			0
$364$	9.23805e8	+	5.23916e9i	0.0526229	+	0.298439i
$365$	6.83172e9	−	1.20462e9i	0.384910	−	0.0678700i
$366$		0			0
$367$	2.18128e10	+	1.83031e10i	1.20239	+	1.00893i	0.999558	+	0.0297143i	$0.00945975\pi$
$367$	2.18128e10	+	1.83031e10i	1.20239	+	1.00893i	0.202834	+	0.979213i	$0.434985\pi$
$368$	5.32749e9	−	3.07583e9i	0.290490	−	0.167714i
$369$		0			0
$370$	−5.08570e9	+	8.80870e9i	−0.271359	+	0.470007i
$371$	−6.34462e9	−	1.74317e10i	−0.334896	−	0.920120i
$372$		0			0
$373$	2.43295e9	−	2.04149e9i	0.125689	−	0.105466i	−0.577776	−	0.816195i	$-0.696079\pi$
$373$	2.43295e9	−	2.04149e9i	0.125689	−	0.105466i	0.703465	+	0.710729i	$0.251635\pi$
$374$	1.35333e10	−	3.71825e10i	0.691700	−	1.90043i
$375$		0			0
$376$	9.61774e8	−	5.45449e9i	0.0481196	−	0.272900i
$377$			2.58308e10i			1.27871i
$378$		0			0
$379$	−2.63613e10			−1.27764			−0.638822	−	0.769354i	$-0.720578\pi$
$379$	−2.63613e10			−1.27764			−0.638822	+	0.769354i	$0.720578\pi$
$380$	7.75400e7	+	1.36724e7i	0.00371870	+	0.000655707i
$381$		0			0
$382$	−1.25484e9	−	4.56724e8i	−0.0589297	−	0.0214487i
$383$	−5.71089e9	−	6.80598e9i	−0.265405	−	0.316297i	0.616839	−	0.787089i	$-0.288413\pi$
$383$	−5.71089e9	−	6.80598e9i	−0.265405	−	0.316297i	−0.882244	+	0.470792i	$0.843968\pi$
$384$		0			0
$385$	5.91920e10	−	2.15441e10i	2.69414	−	0.980587i
$386$	−2.97287e10	−	1.71639e10i	−1.33914	−	0.773153i
$387$		0			0
$388$	−5.64634e8	−	9.77975e8i	−0.0249138	−	0.0431520i
$389$	−3.83291e9	+	4.56788e9i	−0.167390	+	0.199488i	−0.843218	−	0.537572i	$-0.819342\pi$
$389$	−3.83291e9	+	4.56788e9i	−0.167390	+	0.199488i	0.675828	+	0.737059i	$0.263786\pi$
$390$		0			0
$391$	3.13511e9	+	1.77801e10i	0.134136	+	0.760725i
$392$	5.80446e9	−	1.02348e9i	0.245820	−	0.0433448i
$393$		0			0
$394$	4.44152e9	+	3.72688e9i	0.184309	+	0.154654i
$395$	1.37972e10	−	7.96582e9i	0.566765	−	0.327222i
$396$		0			0
$397$	−1.60190e9	+	2.77457e9i	−0.0644871	+	0.111695i	−0.896466	−	0.443112i	$-0.853874\pi$
$397$	−1.60190e9	+	2.77457e9i	−0.0644871	+	0.111695i	0.831979	+	0.554807i	$0.187208\pi$
$398$	−4.51344e9	−	1.24006e10i	−0.179877	−	0.494208i
$399$		0			0
$400$	1.88682e10	−	1.58323e10i	0.737038	−	0.618449i
$401$	−1.33575e10	+	3.66996e10i	−0.516594	+	1.41933i	0.357656	+	0.933853i	$0.383576\pi$
$401$	−1.33575e10	+	3.66996e10i	−0.516594	+	1.41933i	−0.874250	+	0.485477i	$0.838646\pi$
$402$		0			0
$403$	−6.67616e8	+	3.78624e9i	−0.0253108	+	0.143545i
$404$		−	1.26763e10i		−	0.475848i
$405$		0			0
$406$	3.38359e10			1.24530
$407$	1.78283e10	+	3.14361e9i	0.649729	+	0.114565i
$408$		0			0
$409$	−3.94804e10	−	1.43697e10i	−1.41087	−	0.513516i	−0.479488	−	0.877548i	$-0.659178\pi$
$409$	−3.94804e10	−	1.43697e10i	−1.41087	−	0.513516i	−0.931386	+	0.364032i	$0.881400\pi$
$410$	4.02910e10	+	4.80170e10i	1.42585	+	1.69926i
$411$		0			0
$412$	−5.36959e9	+	1.95437e9i	−0.186360	+	0.0678294i
$413$	1.60819e10	+	9.28487e9i	0.552760	+	0.319136i
$414$		0			0
$415$	−2.25518e9	−	3.90608e9i	−0.0760306	−	0.131689i
$416$	1.01682e10	−	1.21180e10i	0.339523	−	0.404628i
$417$		0			0
$418$	6.14950e7	+	3.48755e8i	0.00201435	+	0.0114239i
$419$	−2.44273e10	+	4.30720e9i	−0.792538	+	0.139746i	−0.555239	−	0.831691i	$-0.687373\pi$
$419$	−2.44273e10	+	4.30720e9i	−0.792538	+	0.139746i	−0.237299	+	0.971437i	$0.576262\pi$
$420$		0			0
$421$	−4.34557e10	−	3.64636e10i	−1.38331	−	1.16073i	−0.967971	−	0.251062i	$-0.919220\pi$
$421$	−4.34557e10	−	3.64636e10i	−1.38331	−	1.16073i	−0.415335	−	0.909669i	$-0.636335\pi$
$422$	1.69917e10	−	9.81015e9i	0.535780	−	0.309333i
$423$		0			0
$424$	−1.55020e10	+	2.68502e10i	−0.479650	+	0.830778i
$425$	2.47240e10	+	6.79287e10i	0.757815	+	2.08208i
$426$		0			0
$427$	5.14163e10	−	4.31434e10i	1.54664	−	1.29778i
$428$	−1.52703e9	+	4.19547e9i	−0.0455063	+	0.125028i
$429$		0			0
$430$	−5.54732e9	+	3.14604e10i	−0.162259	+	0.920217i
$431$			6.46311e10i			1.87298i	0.350698	+	0.936489i	$0.385945\pi$
$431$			6.46311e10i			1.87298i	−0.350698	+	0.936489i	$0.614055\pi$
$432$		0			0
$433$	2.65628e10			0.755653			0.377826	−	0.925876i	$-0.376672\pi$
$433$	2.65628e10			0.755653			0.377826	+	0.925876i	$0.376672\pi$
$434$	4.95961e9	+	8.74513e8i	0.139794	+	0.0246494i
$435$		0			0
$436$	1.37776e9	+	5.01463e8i	0.0381265	+	0.0138769i
$437$	−1.03865e8	−	1.23781e8i	−0.00284801	−	0.00339413i
$438$		0			0
$439$	−5.28937e10	+	1.92517e10i	−1.42412	+	0.518337i	−0.935240	−	0.354015i	$-0.884816\pi$
$439$	−5.28937e10	+	1.92517e10i	−1.42412	+	0.518337i	−0.488878	+	0.872352i	$0.662594\pi$
$440$	−9.11741e10	−	5.26394e10i	−2.43255	−	1.40443i
$441$		0			0
$442$	−2.28070e10	−	3.95029e10i	−0.597557	−	1.03500i
$443$	−2.12742e10	+	2.53536e10i	−0.552381	+	0.658302i	−0.967916	−	0.251275i	$-0.919150\pi$
$443$	−2.12742e10	+	2.53536e10i	−0.552381	+	0.658302i	0.415534	+	0.909577i	$0.363595\pi$
$444$		0			0
$445$	7.67966e9	+	4.35535e10i	0.195840	+	1.11066i
$446$	−1.31733e10	+	2.32281e9i	−0.332932	+	0.0587049i
$447$		0			0
$448$	−3.76403e10	−	3.15839e10i	−0.934417	−	0.784069i
$449$	6.27975e10	−	3.62562e10i	1.54510	−	0.892065i	0.546597	−	0.837396i	$-0.315923\pi$
$449$	6.27975e10	−	3.62562e10i	1.54510	−	0.892065i	0.998505	−	0.0546691i	$-0.0174104\pi$
$450$		0			0
$451$	5.57812e10	−	9.66159e10i	1.34829	−	2.33530i
$452$	2.78842e9	+	7.66113e9i	0.0668043	+	0.183543i
$453$		0			0
$454$	6.62650e9	−	5.56030e9i	0.155977	−	0.130880i
$455$	2.48356e10	−	6.82353e10i	0.579468	−	1.59208i
$456$		0			0
$457$	−9.23518e9	+	5.23753e10i	−0.211729	+	1.20078i	0.674764	+	0.738033i	$0.264245\pi$
$457$	−9.23518e9	+	5.23753e10i	−0.211729	+	1.20078i	−0.886493	+	0.462742i	$0.846866\pi$
$458$		−	8.28893e9i		−	0.188381i
$459$		0			0
$460$	1.06110e10			0.236986
$461$	3.01751e10	+	5.32068e9i	0.668104	+	0.117805i	0.497405	−	0.867518i	$-0.334286\pi$
$461$	3.01751e10	+	5.32068e9i	0.668104	+	0.117805i	0.170699	+	0.985323i	$0.445397\pi$
$462$		0			0
$463$	3.02920e10	+	1.10254e10i	0.659181	+	0.239922i	0.649883	−	0.760035i	$-0.274818\pi$
$463$	3.02920e10	+	1.10254e10i	0.659181	+	0.239922i	0.00929829	+	0.999957i	$0.497040\pi$
$464$	−2.51434e10	−	2.99648e10i	−0.542441	−	0.646456i
$465$		0			0
$466$	−4.47997e10	+	1.63058e10i	−0.950017	+	0.345778i
$467$	−4.49907e10	−	2.59754e10i	−0.945922	−	0.546129i	−0.0541106	−	0.998535i	$-0.517232\pi$
$467$	−4.49907e10	−	2.59754e10i	−0.945922	−	0.546129i	−0.891812	+	0.452406i	$0.850566\pi$
$468$		0			0
$469$	2.76592e10	+	4.79072e10i	0.571674	+	0.990169i
$470$	−1.07341e10	+	1.27924e10i	−0.219976	+	0.262157i
$471$		0			0
$472$	−5.38939e9	−	3.05648e10i	−0.108585	−	0.615819i
$473$	5.59940e10	−	9.87325e9i	1.11866	−	0.197249i
$474$		0			0
$475$	−4.95608e8	−	4.15865e8i	−0.00973563	−	0.00816916i
$476$	2.04762e10	−	1.18220e10i	0.398862	−	0.230283i
$477$		0			0
$478$	−2.12913e10	+	3.68776e10i	−0.407840	+	0.706400i
$479$	7.77313e9	+	2.13565e10i	0.147657	+	0.405684i	0.991367	−	0.131115i	$-0.0418556\pi$
$479$	7.77313e9	+	2.13565e10i	0.147657	+	0.405684i	−0.843710	+	0.536799i	$0.819633\pi$
$480$		0			0
$481$	1.59867e10	−	1.34144e10i	0.298660	−	0.250606i
$482$	−1.66771e10	+	4.58201e10i	−0.308982	+	0.848922i
$483$		0			0
$484$	−4.48568e9	+	2.54396e10i	−0.0817424	+	0.463584i
$485$			1.54138e10i			0.278576i
$486$		0			0
$487$	−6.87683e10			−1.22257			−0.611283	−	0.791412i	$-0.709346\pi$
$487$	−6.87683e10			−1.22257			−0.611283	+	0.791412i	$0.709346\pi$
$488$	−1.10474e11	−	1.94796e10i	−1.94797	−	0.343480i
$489$		0			0
$490$	−1.66991e10	−	6.07796e9i	−0.289673	−	0.105432i
$491$	−4.69265e10	−	5.59248e10i	−0.807406	−	0.962229i	0.192412	−	0.981314i	$-0.438369\pi$
$491$	−4.69265e10	−	5.59248e10i	−0.807406	−	0.962229i	−0.999818	+	0.0190855i	$0.993925\pi$
$492$		0			0
$493$	1.07878e11	−	3.92645e10i	1.82619	−	0.664679i
$494$	3.53546e8	+	2.04120e8i	0.00593660	+	0.00342750i
$495$		0			0
$496$	−2.91102e9	−	5.04203e9i	−0.0480970	−	0.0833064i
$497$	−2.10706e10	+	2.51110e10i	−0.345344	+	0.411565i
$498$		0			0
$499$	6.66714e9	+	3.78112e10i	0.107532	+	0.609844i	0.990179	+	0.139807i	$0.0446482\pi$
$499$	6.66714e9	+	3.78112e10i	0.107532	+	0.609844i	−0.882647	+	0.470037i	$0.844241\pi$
$500$	1.41783e10	−	2.50002e9i	0.226853	−	0.0400004i
$501$		0			0
$502$	−1.68603e10	−	1.41475e10i	−0.265491	−	0.222774i
$503$	−1.37684e9	+	7.94918e8i	−0.0215085	+	0.0124180i	−0.510716	−	0.859750i	$-0.670620\pi$
$503$	−1.37684e9	+	7.94918e8i	−0.0215085	+	0.0124180i	0.489207	+	0.872168i	$0.337286\pi$
$504$		0			0
$505$	−8.65122e10	+	1.49844e11i	−1.33018	+	2.30395i
$506$	1.63230e10	+	4.48472e10i	0.249000	+	0.684121i
$507$		0			0
$508$	1.36408e10	−	1.14460e10i	0.204826	−	0.171869i
$509$	2.97231e10	−	8.16637e10i	0.442816	−	1.21663i	−0.494816	−	0.868998i	$-0.664764\pi$
$509$	2.97231e10	−	8.16637e10i	0.442816	−	1.21663i	0.937632	−	0.347630i	$-0.113013\pi$
$510$		0			0
$511$	−3.23751e9	+	1.83608e10i	−0.0474819	+	0.269283i
$512$			7.14453e10i			1.03967i
$513$		0			0
$514$	7.76829e9			0.111294
$515$	7.68104e10	+	1.35437e10i	1.09192	+	0.192535i
$516$		0			0
$517$	2.79294e10	+	1.01655e10i	0.390930	+	0.142287i
$518$	−1.75716e10	−	2.09410e10i	−0.244057	−	0.290856i
$519$		0			0
$520$	−1.14044e11	+	4.15086e10i	−1.55977	+	0.567708i
$521$	−1.18023e11	−	6.81406e10i	−1.60183	−	0.924815i	−0.991122	−	0.132956i	$-0.957553\pi$
$521$	−1.18023e11	−	6.81406e10i	−1.60183	−	0.924815i	−0.610704	−	0.791859i	$-0.709114\pi$
$522$		0			0
$523$	−1.68568e10	−	2.91969e10i	−0.225304	−	0.390238i	0.731107	−	0.682263i	$-0.239004\pi$
$523$	−1.68568e10	−	2.91969e10i	−0.225304	−	0.390238i	−0.956411	+	0.292025i	$0.905671\pi$
$524$	−1.96172e10	+	2.33789e10i	−0.260203	+	0.310098i
$525$		0			0
$526$	−1.65316e10	−	9.37552e10i	−0.215959	−	1.22476i
$527$	1.68274e10	−	2.96713e9i	0.218160	−	0.0384675i
$528$		0			0
$529$	4.33082e10	+	3.63399e10i	0.553029	+	0.464046i
$530$	8.09551e10	−	4.67394e10i	1.02598	−	0.592352i
$531$		0			0
$532$	−1.05805e8	+	1.83260e8i	−0.00132087	+	0.00228781i
$533$	−4.39861e10	−	1.20851e11i	−0.545013	−	1.49741i
$534$		0			0
$535$	4.66834e10	−	3.91720e10i	0.569832	−	0.478146i
$536$	3.16217e10	−	8.68799e10i	0.383112	−	1.05259i
$537$		0			0
$538$	1.99994e10	−	1.13422e11i	0.238720	−	1.35385i
$539$			3.16289e10i			0.374739i
$540$		0			0
$541$	1.02849e11			1.20064			0.600319	−	0.799760i	$-0.295040\pi$
$541$	1.02849e11			1.20064			0.600319	+	0.799760i	$0.295040\pi$
$542$	−4.88813e10	−	8.61908e9i	−0.566429	−	0.0998767i
$543$		0			0
$544$	−6.60649e10	−	2.40457e10i	−0.754354	−	0.274562i
$545$	−1.28638e10	−	1.53304e10i	−0.145808	−	0.173767i
$546$		0			0
$547$	−1.29316e11	+	4.70673e10i	−1.44446	+	0.525739i	−0.941037	−	0.338304i	$-0.890147\pi$
$547$	−1.29316e11	+	4.70673e10i	−1.44446	+	0.525739i	−0.503418	+	0.864043i	$0.667925\pi$
$548$	2.33399e10	+	1.34753e10i	0.258808	+	0.149423i
$549$		0			0
$550$	9.55441e10	+	1.65487e11i	1.04413	+	1.80848i
$551$	−6.60439e8	+	7.87081e8i	−0.00716517	+	0.00853912i
$552$		0			0
$553$	7.43521e9	+	4.21672e10i	0.0795047	+	0.450893i
$554$	1.04183e11	−	1.83703e10i	1.10601	−	0.195020i
$555$		0			0
$556$	2.34696e10	+	1.96933e10i	0.245587	+	0.206072i
$557$	−1.34913e11	+	7.78922e10i	−1.40163	+	0.809232i	−0.994560	−	0.104165i	$-0.966783\pi$
$557$	−1.34913e11	+	7.78922e10i	−1.40163	+	0.809232i	−0.407071	+	0.913397i	$0.633450\pi$
$558$		0			0
$559$	3.27722e10	−	5.67631e10i	0.335628	−	0.581325i
$560$	3.76091e10	+	1.03330e11i	0.382421	+	1.05069i
$561$		0			0
$562$	−1.62425e10	+	1.36290e10i	−0.162820	+	0.136622i
$563$	−3.49849e10	+	9.61202e10i	−0.348214	+	0.956711i	0.634718	+	0.772744i	$0.281116\pi$
$563$	−3.49849e10	+	9.61202e10i	−0.348214	+	0.956711i	−0.982932	+	0.183967i	$0.941106\pi$
$564$		0			0
$565$	1.93237e10	−	1.09590e11i	0.189625	−	1.07542i
$566$		−	1.08160e11i		−	1.05391i
$567$		0			0
$568$	5.47865e10			0.526356
$569$	8.94456e10	+	1.57717e10i	0.853316	+	0.150463i	0.583163	−	0.812355i	$-0.301815\pi$
$569$	8.94456e10	+	1.57717e10i	0.853316	+	0.150463i	0.270152	+	0.962818i	$0.412926\pi$
$570$		0			0
$571$	−1.14927e11	−	4.18298e10i	−1.08113	−	0.393497i	−0.260799	−	0.965393i	$-0.583986\pi$
$571$	−1.14927e11	−	4.18298e10i	−1.08113	−	0.393497i	−0.820326	+	0.571896i	$0.806208\pi$
$572$	3.06700e10	+	3.65511e10i	0.286503	+	0.341441i
$573$		0			0
$574$	−1.58303e11	+	5.76176e10i	−1.45828	+	0.530771i
$575$	−7.55084e10	−	4.35948e10i	−0.690755	−	0.398807i
$576$		0			0
$577$	−1.35572e9	−	2.34817e9i	−0.0122311	−	0.0211849i	0.859845	−	0.510555i	$-0.170560\pi$
$577$	−1.35572e9	−	2.34817e9i	−0.0122311	−	0.0211849i	−0.872076	+	0.489370i	$0.837227\pi$
$578$	−6.95824e10	+	8.29251e10i	−0.623431	+	0.742976i
$579$		0			0
$580$	−1.17163e10	−	6.64463e10i	−0.103533	−	0.587163i
$581$	1.19378e10	−	2.10496e9i	0.104766	−	0.0184731i
$582$		0			0
$583$	−1.27451e11	−	1.06944e11i	−1.10324	−	0.925729i
$584$	2.69858e10	−	1.55803e10i	0.231998	−	0.133944i
$585$		0			0
$586$	7.21919e10	−	1.25040e11i	0.612207	−	1.06037i
$587$	4.01800e10	+	1.10394e11i	0.338421	+	0.929805i	0.985843	+	0.167673i	$0.0536253\pi$
$587$	4.01800e10	+	1.10394e11i	0.338421	+	0.929805i	−0.647421	+	0.762132i	$0.724153\pi$
$588$		0			0
$589$	−1.17149e8	+	9.82993e7i	−0.000973365	+	0.000816751i
$590$	−3.20049e10	+	8.79328e10i	−0.264125	+	0.725677i
$591$		0			0
$592$	−5.48773e9	+	3.11224e10i	−0.0446792	+	0.253389i
$593$			1.69673e11i			1.37212i	0.727544	+	0.686061i	$0.240662\pi$
$593$			1.69673e11i			1.37212i	−0.727544	+	0.686061i	$0.759338\pi$
$594$		0			0
$595$	−3.22725e11			−2.57493
$596$	−3.43745e10	−	6.06115e9i	−0.272428	−	0.0480364i
$597$		0			0
$598$	5.16989e10	+	1.88168e10i	0.404274	+	0.147144i
$599$	1.03440e11	+	1.23275e11i	0.803493	+	0.957566i	0.999736	−	0.0229897i	$-0.00731850\pi$
$599$	1.03440e11	+	1.23275e11i	0.803493	+	0.957566i	−0.196243	+	0.980555i	$0.562874\pi$
$600$		0			0
$601$	1.59242e11	−	5.79593e10i	1.22056	−	0.444248i	0.350206	−	0.936673i	$-0.386112\pi$
$601$	1.59242e11	−	5.79593e10i	1.22056	−	0.444248i	0.870355	+	0.492425i	$0.163889\pi$
$602$	−7.43542e10	−	4.29284e10i	−0.566135	−	0.326858i
$603$		0			0
$604$	1.83920e10	+	3.18559e10i	0.138192	+	0.239355i
$605$	2.26641e11	−	2.70101e11i	1.69168	−	2.01606i
$606$		0			0
$607$	3.08833e10	+	1.75148e11i	0.227494	+	1.29018i	0.857860	+	0.513883i	$0.171794\pi$
$607$	3.08833e10	+	1.75148e11i	0.227494	+	1.29018i	−0.630366	+	0.776298i	$0.717095\pi$
$608$	6.19660e8	−	1.09263e8i	0.00453460	−	0.000799573i
$609$		0			0
$610$	2.59096e11	+	2.17407e11i	1.87129	+	1.57020i
$611$	2.96724e10	−	1.71314e10i	0.212906	−	0.122921i
$612$		0			0
$613$	−2.91010e10	+	5.04044e10i	−0.206094	+	0.356966i	−0.950481	−	0.310783i	$-0.899409\pi$
$613$	−2.91010e10	+	5.04044e10i	−0.206094	+	0.356966i	0.744387	+	0.667749i	$0.232742\pi$
$614$	1.32033e10	+	3.62758e10i	0.0928987	+	0.255237i
$615$		0			0
$616$	2.16749e11	−	1.81874e11i	1.50534	−	1.26313i
$617$	−4.57298e10	+	1.25641e11i	−0.315543	+	0.866947i	0.675969	+	0.736930i	$0.263725\pi$
$617$	−4.57298e10	+	1.25641e11i	−0.315543	+	0.866947i	−0.991512	+	0.130017i	$0.958497\pi$
$618$		0			0
$619$	2.33487e10	−	1.32417e11i	0.159038	−	0.901948i	−0.795963	−	0.605345i	$-0.793035\pi$
$619$	2.33487e10	−	1.32417e11i	0.159038	−	0.901948i	0.955001	−	0.296603i	$-0.0958538\pi$
$620$		−	1.00424e10i		−	0.0679627i
$621$		0			0
$622$	1.54659e11			1.03327
$623$	−1.17054e11	−	2.06397e10i	−0.777022	−	0.137010i
$624$		0			0
$625$	3.22202e10	+	1.17272e10i	0.211158	+	0.0768554i
$626$	−3.92245e10	−	4.67459e10i	−0.255423	−	0.304401i
$627$		0			0
$628$	3.15089e10	−	1.14683e10i	0.202579	−	0.0737328i
$629$	−8.03238e10	−	4.63750e10i	−0.513147	−	0.296265i
$630$		0			0
$631$	−1.52481e10	−	2.64105e10i	−0.0961831	−	0.166594i	0.813919	−	0.580979i	$-0.197330\pi$
$631$	−1.52481e10	−	2.64105e10i	−0.0961831	−	0.166594i	−0.910102	+	0.414385i	$0.863997\pi$
$632$	4.59996e10	−	5.48202e10i	0.288327	−	0.343615i
$633$		0			0
$634$	1.25956e10	+	7.14333e10i	0.0779583	+	0.442123i
$635$	−2.39359e11	+	4.22055e10i	−1.47216	+	0.259582i
$636$		0			0
$637$	2.79308e10	+	2.34367e10i	0.169639	+	0.142344i
$638$	2.62812e11	−	1.51735e11i	1.58622	−	0.915802i
$639$		0			0
$640$	5.09334e10	−	8.82193e10i	0.303587	−	0.525828i
$641$	−7.45477e10	−	2.04818e11i	−0.441572	−	1.21321i	−0.938458	−	0.345394i	$-0.887745\pi$
$641$	−7.45477e10	−	2.04818e11i	−0.441572	−	1.21321i	0.496885	−	0.867816i	$-0.334477\pi$
$642$		0			0
$643$	−1.17314e11	+	9.84380e10i	−0.686286	+	0.575863i	−0.917836	−	0.396961i	$-0.870065\pi$
$643$	−1.17314e11	+	9.84380e10i	−0.686286	+	0.575863i	0.231549	+	0.972823i	$0.425621\pi$
$644$	−9.75368e9	+	2.67980e10i	−0.0567055	+	0.155797i
$645$		0			0
$646$	3.15061e8	−	1.78680e9i	0.00180911	−	0.0102600i
$647$			1.23404e11i			0.704226i	0.935957	+	0.352113i	$0.114537\pi$
$647$			1.23404e11i			0.704226i	−0.935957	+	0.352113i	$0.885463\pi$
$648$		0			0
$649$	1.66549e11			0.938780
$650$	2.16936e11	+	3.82516e10i	1.21528	+	0.214287i
$651$		0			0
$652$	3.11089e10	+	1.13227e10i	0.172145	+	0.0626556i
$653$	4.83237e10	+	5.75899e10i	0.265771	+	0.316733i	0.882381	−	0.470535i	$-0.155939\pi$
$653$	4.83237e10	+	5.75899e10i	0.265771	+	0.316733i	−0.616610	+	0.787268i	$0.711495\pi$
$654$		0			0
$655$	3.91443e11	−	1.42474e11i	2.12669	−	0.774051i
$656$	1.68660e11	+	9.73761e10i	0.910747	+	0.525820i
$657$		0			0
$658$	−2.24404e10	−	3.88680e10i	−0.119709	−	0.207342i
$659$	−4.53931e10	+	5.40973e10i	−0.240684	+	0.286836i	−0.872842	−	0.488004i	$-0.837725\pi$
$659$	−4.53931e10	+	5.40973e10i	−0.240684	+	0.286836i	0.632157	+	0.774840i	$0.282170\pi$
$660$		0			0
$661$	−2.47641e10	−	1.40444e11i	−0.129723	−	0.735696i	−0.978390	−	0.206768i	$-0.933705\pi$
$661$	−2.47641e10	−	1.40444e11i	−0.129723	−	0.735696i	0.848667	−	0.528928i	$-0.177406\pi$
$662$	5.54888e10	−	9.78418e9i	0.288917	−	0.0509439i
$663$		0			0
$664$	−1.55200e10	−	1.30228e10i	−0.0798396	−	0.0669934i
$665$	2.50139e9	−	1.44418e9i	0.0127907	−	0.00738471i
$666$		0			0
$667$	−6.92334e10	+	1.19916e11i	−0.349794	+	0.605861i
$668$	6.23597e9	+	1.71332e10i	0.0313183	+	0.0860464i
$669$		0			0
$670$	−2.13542e11	+	1.79183e11i	−1.05970	+	0.889196i
$671$	2.05890e11	−	5.65678e11i	1.01565	−	2.79048i
$672$		0			0
$673$	−1.33595e10	+	7.57657e10i	−0.0651225	+	0.369328i	0.934778	+	0.355232i	$0.115598\pi$
$673$	−1.33595e10	+	7.57657e10i	−0.0651225	+	0.369328i	−0.999901	+	0.0140960i	$0.995513\pi$
$674$			1.30353e11i			0.631655i
$675$		0			0
$676$	−4.20314e9			−0.0201274
$677$	2.24167e11	+	3.95267e10i	1.06713	+	0.188164i	0.679518	−	0.733659i	$-0.262189\pi$
$677$	2.24167e11	+	3.95267e10i	1.06713	+	0.188164i	0.387612	+	0.921823i	$0.373300\pi$
$678$		0			0
$679$	−3.89277e10	−	1.41685e10i	−0.183138	−	0.0666569i
$680$	3.46708e11	+	4.13191e11i	1.62154	+	1.93248i
$681$		0			0
$682$	4.24442e10	−	1.54484e10i	0.196192	−	0.0714079i
$683$	6.00315e10	+	3.46592e10i	0.275865	+	0.159271i	0.631550	−	0.775335i	$-0.282419\pi$
$683$	6.00315e10	+	3.46592e10i	0.275865	+	0.159271i	−0.355685	+	0.934606i	$0.615752\pi$
$684$		0			0
$685$	−1.83930e11	−	3.18576e11i	−0.835392	−	1.44694i
$686$	−1.02921e11	+	1.22657e11i	−0.464738	+	0.553853i
$687$		0			0
$688$	1.72355e10	+	9.77475e10i	0.0769255	+	0.436266i
$689$	−1.88881e11	+	3.33048e10i	−0.838129	+	0.147785i
$690$		0			0
$691$	−6.29010e10	−	5.27802e10i	−0.275896	−	0.231504i	0.494331	−	0.869274i	$-0.335413\pi$
$691$	−6.29010e10	−	5.27802e10i	−0.275896	−	0.231504i	−0.770228	+	0.637769i	$0.779857\pi$
$692$	−7.25930e10	+	4.19116e10i	−0.316570	+	0.182772i
$693$		0			0
$694$	−1.36208e9	+	2.35919e9i	−0.00587170	+	0.0101701i
$695$	−1.43026e11	−	3.92962e11i	−0.613024	−	1.68427i
$696$		0			0
$697$	−4.37852e11	+	3.67402e11i	−1.85522	+	1.55672i
$698$	−7.52914e10	+	2.06861e11i	−0.317193	+	0.871480i
$699$		0			0
$700$	−1.98276e10	+	1.12448e11i	−0.0825808	+	0.468339i
$701$			3.67111e11i			1.52029i	0.649755	+	0.760144i	$0.274871\pi$
$701$			3.67111e11i			1.52029i	−0.649755	+	0.760144i	$0.725129\pi$
$702$		0			0
$703$	8.30101e8			0.00339867
$704$	−4.33997e11	−	7.65254e10i	−1.76684	−	0.311541i
$705$		0			0
$706$	6.59803e10	+	2.40149e10i	0.265580	+	0.0966633i
$707$	−2.98908e11	−	3.56224e11i	−1.19635	−	1.42576i
$708$		0			0
$709$	−2.03327e10	+	7.40048e9i	−0.0804654	+	0.0292870i	−0.381939	−	0.924187i	$-0.624744\pi$
$709$	−2.03327e10	+	7.40048e9i	−0.0804654	+	0.0292870i	0.301474	+	0.953474i	$0.402521\pi$
$710$	−1.43054e11	−	8.25922e10i	−0.562945	−	0.325017i
$711$		0			0
$712$	9.93270e10	+	1.72039e11i	0.386498	+	0.669435i
$713$	−1.32474e10	+	1.57876e10i	−0.0512593	+	0.0610884i
$714$		0			0
$715$	−1.13092e11	−	6.41374e11i	−0.432719	−	2.45407i
$716$	5.39653e10	−	9.51553e9i	0.205335	−	0.0362060i
$717$		0			0
$718$	−2.75086e11	−	2.30825e11i	−1.03507	−	0.868529i
$719$	2.85002e11	−	1.64546e11i	1.06643	−	0.615703i	0.139226	−	0.990261i	$-0.455539\pi$
$719$	2.85002e11	−	1.64546e11i	1.06643	−	0.615703i	0.927204	+	0.374557i	$0.122205\pi$
$720$		0			0
$721$	−1.04810e11	+	1.81535e11i	−0.387846	+	0.671770i
$722$	−7.86632e10	−	2.16125e11i	−0.289483	−	0.795347i
$723$		0			0
$724$	−1.27428e10	+	1.06925e10i	−0.0463780	+	0.0389158i
$725$	−1.89619e11	+	5.20973e11i	−0.686324	+	1.88566i
$726$		0			0
$727$	−6.75215e10	+	3.82933e11i	−0.241715	+	1.37084i	0.586283	+	0.810106i	$0.300590\pi$
$727$	−6.75215e10	+	3.82933e11i	−0.241715	+	1.37084i	−0.827999	+	0.560730i	$0.810521\pi$
$728$		−	3.26174e11i		−	1.16124i
$729$		0			0
$730$	−9.39508e10			−0.330833
$731$	−2.86878e11	−	5.05843e10i	−1.00468	−	0.177152i
$732$		0			0
$733$	2.34914e11	+	8.55016e10i	0.813753	+	0.296182i	0.715173	−	0.698947i	$-0.246348\pi$
$733$	2.34914e11	+	8.55016e10i	0.813753	+	0.296182i	0.0985795	+	0.995129i	$0.468570\pi$
$734$	−2.47882e11	−	2.95415e11i	−0.854007	−	1.01777i
$735$		0			0
$736$	7.96834e10	−	2.90024e10i	0.271554	−	0.0988377i
$737$	4.29672e11	+	2.48071e11i	1.45635	+	0.840827i
$738$		0			0
$739$	−2.59650e11	−	4.49726e11i	−0.870582	−	1.50789i	−0.861395	−	0.507935i	$-0.830409\pi$
$739$	−2.59650e11	−	4.49726e11i	−0.870582	−	1.50789i	−0.00918707	−	0.999958i	$-0.502924\pi$
$740$	−3.50390e10	+	4.17579e10i	−0.116849	+	0.139255i
$741$		0			0
$742$	4.36261e10	+	2.47416e11i	0.143923	+	0.816228i
$743$	1.13404e11	−	1.99962e10i	0.372112	−	0.0656133i	0.0155348	−	0.999879i	$-0.495055\pi$
$743$	1.13404e11	−	1.99962e10i	0.372112	−	0.0656133i	0.356577	+	0.934266i	$0.383944\pi$
$744$		0			0
$745$	3.64966e11	+	3.06243e11i	1.18475	+	0.994124i
$746$	−3.72504e10	+	2.15065e10i	−0.120275	+	0.0694409i
$747$		0			0
$748$	1.06029e11	−	1.83648e11i	0.338703	−	0.586652i
$749$	5.60173e10	+	1.53906e11i	0.177990	+	0.489023i
$750$		0			0
$751$	−2.06886e11	+	1.73598e11i	−0.650387	+	0.545740i	−0.907188	−	0.420725i	$-0.861776\pi$
$751$	−2.06886e11	+	1.73598e11i	−0.650387	+	0.545740i	0.256801	+	0.966464i	$0.417331\pi$
$752$	−1.77456e10	+	4.87557e10i	−0.0554907	+	0.152459i
$753$		0			0
$754$	6.07478e10	−	3.44518e11i	0.187951	−	1.06592i
$755$		−	5.02080e11i		−	1.54520i
$756$		0			0
$757$	−3.18441e11			−0.969719			−0.484859	−	0.874592i	$-0.661129\pi$
$757$	−3.18441e11			−0.969719			−0.484859	+	0.874592i	$0.661129\pi$
$758$	3.51593e11	+	6.19953e10i	1.06503	+	0.187794i
$759$		0			0
$760$	−4.53627e9	−	1.65107e9i	−0.0135971	−	0.00494892i
$761$	−2.11330e11	−	2.51853e11i	−0.630118	−	0.750946i	0.352656	−	0.935753i	$-0.385278\pi$
$761$	−2.11330e11	−	2.51853e11i	−0.630118	−	0.750946i	−0.982775	+	0.184807i	$0.940834\pi$
$762$		0			0
$763$	5.05416e10	−	1.83956e10i	0.149125	−	0.0542771i
$764$	−6.19778e9	−	3.57829e9i	−0.0181913	−	0.0105027i
$765$		0			0
$766$	6.01628e10	+	1.04205e11i	0.174748	+	0.302673i
$767$	1.23412e11	−	1.47076e11i	0.356594	−	0.424972i
$768$		0			0
$769$	5.37175e10	+	3.04647e11i	0.153607	+	0.871148i	0.960048	+	0.279834i	$0.0902794\pi$
$769$	5.37175e10	+	3.04647e11i	0.153607	+	0.871148i	−0.806442	+	0.591314i	$0.798609\pi$
$770$	−8.40138e11	+	1.48139e11i	−2.38994	+	0.421412i
$771$		0			0
$772$	−1.40930e11	−	1.18254e11i	−0.396765	−	0.332925i
$773$	−4.97453e11	+	2.87205e11i	−1.39327	+	0.804403i	−0.993675	−	0.112291i	$-0.964181\pi$
$773$	−4.97453e11	+	2.87205e11i	−1.39327	+	0.804403i	−0.399591	+	0.916694i	$0.630848\pi$
$774$		0			0
$775$	−4.12589e10	+	7.14625e10i	−0.114370	+	0.198094i
$776$	2.36803e10	+	6.50612e10i	0.0653042	+	0.179422i
$777$		0			0
$778$	6.18638e10	−	5.19099e10i	0.168857	−	0.141688i
$779$	1.74961e9	−	4.80703e9i	0.00475108	−	0.0130535i
$780$		0			0
$781$	−5.10524e10	+	2.89533e11i	−0.137218	+	0.778204i
$782$		−	2.44515e11i		−	0.653849i
$783$		0			0
$784$	−5.52138e10			−0.146145
$785$	−4.50726e11	−	7.94751e10i	−1.18695	−	0.209292i
$786$		0			0
$787$	4.88907e11	+	1.77948e11i	1.27446	+	0.463867i	0.888598	−	0.458687i	$-0.151680\pi$
$787$	4.88907e11	+	1.77948e11i	1.27446	+	0.463867i	0.385867	+	0.922555i	$0.373902\pi$
$788$	1.99732e10	+	2.38032e10i	0.0518017	+	0.0617348i
$789$		0			0
$790$	−2.02753e11	+	7.37962e10i	−0.520547	+	0.189463i
$791$	2.59008e11	+	1.49538e11i	0.661618	+	0.381985i
$792$		0			0
$793$	−3.46976e11	−	6.00979e11i	−0.877417	−	1.51973i
$794$	2.78904e10	−	3.32384e10i	0.0701733	−	0.0836293i
$795$		0			0
$796$	−1.22809e10	−	6.96484e10i	−0.0305899	−	0.173484i
$797$	2.25157e11	−	3.97012e10i	0.558023	−	0.0983945i	0.112478	−	0.993654i	$-0.464121\pi$
$797$	2.25157e11	−	3.97012e10i	0.558023	−	0.0983945i	0.445545	+	0.895260i	$0.353010\pi$
$798$		0			0
$799$	−1.16650e11	−	9.78811e10i	−0.286219	−	0.240166i
$800$	2.94034e11	−	1.69760e11i	0.717856	−	0.414454i
$801$		0			0
$802$	2.64464e11	−	4.58065e11i	0.639248	−	1.10721i
$803$	5.71912e10	+	1.57132e11i	0.137552	+	0.377921i
$804$		0			0
$805$	2.98184e11	−	2.50206e11i	0.710069	−	0.595819i
$806$	1.78086e10	−	4.89287e10i	0.0421978	−	0.115937i
$807$		0			0
$808$	−1.34960e11	+	7.65393e11i	−0.316634	+	1.79572i
$809$			2.80231e11i			0.654218i	0.944987	+	0.327109i	$0.106074\pi$
$809$			2.80231e11i			0.654218i	−0.944987	+	0.327109i	$0.893926\pi$
$810$		0			0
$811$	−6.94464e11			−1.60534			−0.802668	−	0.596426i	$-0.796587\pi$
$811$	−6.94464e11			−1.60534			−0.802668	+	0.596426i	$0.796587\pi$
$812$	1.78580e11	+	3.14885e10i	0.410780	+	0.0724316i
$813$		0			0
$814$	−2.30391e11	−	8.38555e10i	−0.524769	−	0.191000i
$815$	−2.90455e11	−	3.46151e11i	−0.658338	−	0.784577i
$816$		0			0
$817$	2.44990e9	−	8.91690e8i	0.00549870	−	0.00200136i
$818$	4.92774e11	+	2.84503e11i	1.10061	+	0.635440i
$819$		0			0
$820$	1.67963e11	+	2.90921e11i	0.371500	+	0.643458i
$821$	−9.00287e10	+	1.07292e11i	−0.198157	+	0.236154i	−0.855968	−	0.517029i	$-0.827038\pi$
$821$	−9.00287e10	+	1.07292e11i	−0.198157	+	0.236154i	0.657811	+	0.753183i	$0.271482\pi$
$822$		0			0
$823$	1.32353e11	+	7.50609e11i	0.288492	+	1.63612i	0.692540	+	0.721379i	$0.256492\pi$
$823$	1.32353e11	+	7.50609e11i	0.288492	+	1.63612i	−0.404048	+	0.914738i	$0.632397\pi$
$824$	3.45021e11	−	6.08365e10i	0.748405	−	0.131964i
$825$		0			0
$826$	−1.92656e11	−	1.61657e11i	−0.413868	−	0.347276i
$827$	−1.73429e11	+	1.00129e11i	−0.370765	+	0.214061i	−0.673793	−	0.738921i	$-0.735336\pi$
$827$	−1.73429e11	+	1.00129e11i	−0.370765	+	0.214061i	0.303028	+	0.952982i	$0.402003\pi$
$828$		0			0
$829$	3.02214e11	−	5.23449e11i	0.639876	−	1.10830i	−0.345584	−	0.938388i	$-0.612319\pi$
$829$	3.02214e11	−	5.23449e11i	0.639876	−	1.10830i	0.985460	−	0.169910i	$-0.0543476\pi$
$830$	2.08922e10	+	5.74008e10i	0.0440222	+	0.120950i
$831$		0			0
$832$	−3.89166e11	+	3.26549e11i	−0.812160	+	0.681483i
$833$	5.54231e10	−	1.52274e11i	0.115109	−	0.316260i
$834$		0			0
$835$	4.32152e10	−	2.45085e11i	0.0888976	−	0.504164i
$836$			1.89790e9i			0.00388551i
$837$		0			0
$838$	3.35928e11			0.681193
$839$	8.98602e11	+	1.58448e11i	1.81351	+	0.319771i	0.974507	−	0.224358i	$-0.0720285\pi$
$839$	8.98602e11	+	1.58448e11i	1.81351	+	0.319771i	0.839002	+	0.544129i	$0.183140\pi$
$840$		0			0
$841$	3.57286e11	+	1.30041e11i	0.714219	+	0.259955i
$842$	4.93835e11	+	5.88529e11i	0.982502	+	1.17090i
$843$		0			0
$844$	9.88087e10	−	3.59634e10i	0.194727	−	0.0708747i
$845$	4.96842e10	+	2.86852e10i	0.0974521	+	0.0562640i
$846$		0			0
$847$	4.73810e11	+	8.20663e11i	0.920599	+	1.59452i
$848$	1.86690e11	−	2.22489e11i	0.361026	−	0.430254i
$849$		0			0
$850$	−1.70004e11	−	9.64141e11i	−0.325674	−	1.84699i
$851$	1.10170e11	−	1.94259e10i	0.210060	−	0.0370393i
$852$		0			0
$853$	4.59900e10	+	3.85902e10i	0.0868695	+	0.0728922i	0.685188	−	0.728366i	$-0.259720\pi$
$853$	4.59900e10	+	3.85902e10i	0.0868695	+	0.0728922i	−0.598319	+	0.801258i	$0.704164\pi$
$854$	−7.87225e11	+	4.54505e11i	−1.48002	+	0.854490i
$855$		0			0
$856$	1.36869e11	−	2.37064e11i	0.254923	−	0.441540i
$857$	1.56719e11	+	4.30581e11i	0.290535	+	0.798237i	0.995988	+	0.0894815i	$0.0285210\pi$
$857$	1.56719e11	+	4.30581e11i	0.290535	+	0.798237i	−0.705454	+	0.708756i	$0.749257\pi$
$858$		0			0
$859$	2.76176e11	−	2.31740e11i	0.507241	−	0.425625i	−0.352916	−	0.935655i	$-0.614810\pi$
$859$	2.76176e11	−	2.31740e11i	0.507241	−	0.425625i	0.860157	+	0.510030i	$0.170366\pi$
$860$	−5.85556e10	+	1.60880e11i	−0.107047	+	0.294109i
$861$		0			0
$862$	1.51996e11	−	8.62015e11i	0.275299	−	1.56130i
$863$		−	8.65609e11i		−	1.56055i	−0.625435	−	0.780276i	$-0.715078\pi$
$863$		−	8.65609e11i		−	1.56055i	0.625435	−	0.780276i	$-0.284922\pi$
$864$		0			0
$865$	1.14414e12			2.04368
$866$	−3.54280e11	−	6.24692e10i	−0.629906	−	0.111069i
$867$		0			0
$868$	2.53621e10	+	9.23105e9i	0.0446793	+	0.0162619i
$869$	2.46846e11	+	2.94180e11i	0.432860	+	0.515863i
$870$		0			0
$871$	5.37450e11	−	1.95616e11i	0.933825	−	0.339885i
$872$	−7.78497e10	−	4.49465e10i	−0.134645	−	0.0777375i
$873$		0			0
$874$	1.09419e9	+	1.89519e9i	0.00187519	+	0.00324793i
$875$	3.39482e11	−	4.04579e11i	0.579142	−	0.690195i
$876$		0			0
$877$	−5.54872e10	−	3.14683e11i	−0.0937981	−	0.531956i	−0.995109	−	0.0987829i	$-0.968505\pi$
$877$	−5.54872e10	−	3.14683e11i	−0.0937981	−	0.531956i	0.901311	−	0.433173i	$-0.142606\pi$
$878$	7.50743e11	−	1.32376e11i	1.26332	−	0.222757i
$879$		0			0
$880$	7.55496e11	+	6.33936e11i	1.25980	+	1.05710i
$881$	7.29538e11	−	4.21199e11i	1.21100	−	0.699172i	0.248024	−	0.968754i	$-0.420219\pi$
$881$	7.29538e11	−	4.21199e11i	1.21100	−	0.699172i	0.962977	+	0.269582i	$0.0868856\pi$
$882$		0			0
$883$	−5.44619e11	+	9.43307e11i	−0.895880	+	1.55171i	−0.0631678	+	0.998003i	$0.520120\pi$
$883$	−5.44619e11	+	9.43307e11i	−0.895880	+	1.55171i	−0.832712	+	0.553706i	$0.813213\pi$
$884$	−8.36091e10	−	2.29714e11i	−0.136913	−	0.376165i
$885$		0			0
$886$	3.43370e11	−	2.88121e11i	0.557221	−	0.467564i
$887$	−1.25823e11	+	3.45697e11i	−0.203267	+	0.558471i	−0.998879	−	0.0473352i	$-0.984927\pi$
$887$	−1.25823e11	+	3.45697e11i	−0.203267	+	0.558471i	0.795612	+	0.605806i	$0.207149\pi$
$888$		0			0
$889$	1.13431e11	−	6.43299e11i	0.181604	−	1.02992i
$890$		−	5.98954e11i		−	0.954626i
$891$		0			0
$892$	−7.16881e10			−0.113237
$893$	1.34215e9	+	2.36657e8i	0.00211054	+	0.000372145i
$894$		0			0
$895$	−7.02849e11	−	2.55816e11i	−1.09539	−	0.398690i
$896$	1.75980e11	+	2.09725e11i	0.273043	+	0.325400i
$897$		0			0
$898$	−9.22825e11	+	3.35881e11i	−1.41910	+	0.516511i
$899$	1.13490e11	+	6.55237e10i	0.173748	+	0.100314i
$900$		0			0
$901$	4.26202e11	+	7.38204e11i	0.646721	+	1.12015i
$902$	−9.71197e11	+	1.15743e12i	−1.46717	+	1.74851i
$903$		0			0
$904$	−8.67993e10	−	4.92263e11i	−0.129970	−	0.737096i
$905$	2.23603e11	−	3.94272e10i	0.333337	−	0.0587762i
$906$		0			0
$907$	−1.47819e11	−	1.24035e11i	−0.218425	−	0.183280i	0.527009	−	0.849860i	$-0.323313\pi$
$907$	−1.47819e11	−	1.24035e11i	−0.218425	−	0.183280i	−0.745434	+	0.666579i	$0.767758\pi$
$908$	4.01481e10	−	2.31795e10i	0.0590638	−	0.0341005i
$909$		0			0
$910$	−4.91717e11	+	8.51678e11i	−0.717050	+	1.24197i
$911$	−3.85785e10	−	1.05994e11i	−0.0560109	−	0.153889i	0.908532	−	0.417816i	$-0.137204\pi$
$911$	−3.85785e10	−	1.05994e11i	−0.0560109	−	0.153889i	−0.964543	+	0.263927i	$0.914982\pi$
$912$		0			0
$913$	8.32844e10	−	6.98839e10i	0.119862	−	0.100576i
$914$	2.46348e11	−	6.76834e11i	0.352991	−	0.969835i
$915$		0			0
$916$	7.71387e9	−	4.37475e10i	0.0109570	−	0.0621401i
$917$			1.11955e12i			1.58332i
$918$		0			0
$919$	3.60073e11			0.504811			0.252405	−	0.967622i	$-0.418778\pi$
$919$	3.60073e11			0.504811			0.252405	+	0.967622i	$0.418778\pi$
$920$	−6.40686e11	−	1.12970e11i	−0.894322	−	0.157693i
$921$		0			0
$922$	−3.89946e11	−	1.41929e11i	−0.539610	−	0.196402i
$923$	2.17851e11	+	2.59625e11i	0.300160	+	0.357717i
$924$		0			0
$925$	4.20902e11	−	1.53196e11i	0.574929	−	0.209257i
$926$	−3.78090e11	−	2.18290e11i	−0.514223	−	0.296887i
$927$		0			0
$928$	−2.69598e11	−	4.66958e11i	−0.363518	−	0.629631i
$929$	4.96330e10	−	5.91503e10i	0.0666358	−	0.0794135i	−0.731697	−	0.681630i	$-0.761271\pi$
$929$	4.96330e10	−	5.91503e10i	0.0666358	−	0.0794135i	0.798333	+	0.602217i	$0.205716\pi$
$930$		0			0
$931$	2.51841e8	+	1.42826e9i	0.000335218	+	0.00190112i
$932$	−2.51620e11	+	4.43673e10i	−0.333489	+	0.0588030i
$933$		0			0
$934$	5.38974e11	+	4.52253e11i	0.708240	+	0.594284i
$935$	−2.50669e12	+	1.44724e12i	−3.27985	+	1.89362i
$936$		0			0
$937$	−5.46345e10	+	9.46298e10i	−0.0708776	+	0.122764i	−0.899286	−	0.437361i	$-0.855913\pi$
$937$	−5.46345e10	+	9.46298e10i	−0.0708776	+	0.122764i	0.828409	+	0.560124i	$0.189247\pi$
$938$	−2.56238e11	−	7.04008e11i	−0.331003	−	0.909424i
$939$		0			0
$940$	−6.85577e10	+	5.75267e10i	−0.0878102	+	0.0736815i
$941$	1.51783e11	−	4.17019e11i	0.193581	−	0.531860i	−0.804488	−	0.593969i	$-0.797560\pi$
$941$	1.51783e11	−	4.17019e11i	0.193581	−	0.531860i	0.998069	+	0.0621085i	$0.0197825\pi$
$942$		0			0
$943$	1.19713e11	−	6.78926e11i	0.151389	−	0.858569i
$944$			2.90741e11i			0.366116i
$945$		0			0
$946$	−7.70037e11			−0.961495
$947$	−5.80418e11	−	1.02343e11i	−0.721673	−	0.127250i	−0.199265	−	0.979946i	$-0.563855\pi$
$947$	−5.80418e11	−	1.02343e11i	−0.721673	−	0.127250i	−0.522409	+	0.852695i	$0.674966\pi$
$948$		0			0
$949$	1.81138e11	+	6.59288e10i	0.223329	+	0.0812850i
$950$	5.63214e9	+	6.71213e9i	0.00691479	+	0.00824073i
$951$		0			0
$952$	−1.36221e12	+	4.95805e11i	−1.65843	+	0.603619i
$953$	−1.23865e10	−	7.15133e9i	−0.0150168	−	0.00866992i	0.492473	−	0.870328i	$-0.336093\pi$
$953$	−1.23865e10	−	7.15133e9i	−0.0150168	−	0.00866992i	−0.507490	+	0.861658i	$0.669426\pi$
$954$		0			0
$955$	4.88415e10	+	8.45960e10i	0.0587186	+	0.101704i
$956$	−1.46691e11	+	1.74819e11i	−0.175619	+	0.209294i
$957$		0			0
$958$	−5.34486e10	−	3.03122e11i	−0.0634562	−	0.359878i
$959$	9.73635e11	−	1.71678e11i	1.15112	−	0.202974i
$960$		0			0
$961$	−6.38411e11	−	5.35690e11i	−0.748526	−	0.628088i
$962$	−2.44769e11	+	1.41317e11i	−0.285796	+	0.165004i
$963$		0			0
$964$	−1.30660e11	+	2.26310e11i	−0.151299	+	0.262057i
$965$	8.58842e11	+	2.35965e12i	0.990385	+	2.72106i
$966$		0			0
$967$	−1.09840e11	+	9.21663e10i	−0.125618	+	0.105406i	−0.703433	−	0.710762i	$-0.748350\pi$
$967$	−1.09840e11	+	9.21663e10i	−0.125618	+	0.105406i	0.577814	+	0.816168i	$0.303906\pi$
$968$	5.41688e11	−	1.48828e12i	0.616947	−	1.69505i
$969$		0			0
$970$	3.62495e10	−	2.05581e11i	0.0409464	−	0.232218i
$971$		−	1.68081e12i		−	1.89078i	−0.325944	−	0.945389i	$-0.605682\pi$
$971$		−	1.68081e12i		−	1.89078i	0.325944	−	0.945389i	$-0.394318\pi$
$972$		0			0
$973$	1.12390e12			1.25394
$974$	9.17194e11	+	1.61726e11i	1.01912	+	0.179698i
$975$		0			0
$976$	9.87491e11	+	3.59417e11i	1.08826	+	0.396095i
$977$	−3.78131e11	−	4.50639e11i	−0.415015	−	0.494596i	0.517522	−	0.855670i	$-0.326855\pi$
$977$	−3.78131e11	−	4.50639e11i	−0.415015	−	0.494596i	−0.932537	+	0.361074i	$0.882410\pi$
$978$		0			0
$979$	−1.00174e12	+	3.64605e11i	−1.09050	+	0.396909i
$980$	−8.24785e10	−	4.76190e10i	−0.0894204	−	0.0516269i
$981$		0			0
$982$	4.94358e11	+	8.56254e11i	0.531614	+	0.920782i
$983$	5.44055e11	−	6.48380e11i	0.582678	−	0.694409i	−0.391503	−	0.920177i	$-0.628045\pi$
$983$	5.44055e11	−	6.48380e11i	0.582678	−	0.694409i	0.974181	+	0.225768i	$0.0724891\pi$
$984$		0			0
$985$	−7.36486e10	−	4.17682e11i	−0.0782384	−	0.443712i
$986$	−1.53116e12	+	2.69985e11i	−1.62000	+	0.285649i
$987$		0			0
$988$	1.67600e9	+	1.40633e9i	0.00175892	+	0.00147591i
$989$	3.04280e11	−	1.75676e11i	0.318045	−	0.183623i
$990$		0			0
$991$	4.81519e11	−	8.34015e11i	0.499251	−	0.864728i	−0.500749	−	0.865593i	$-0.666942\pi$
$991$	4.81519e11	−	8.34015e11i	0.499251	−	0.864728i	1.00000		0.000864758i	$0.000275261\pi$
$992$	−2.74484e10	−	7.54138e10i	−0.0283446	−	0.0778761i
$993$		0			0
$994$	3.40083e11	−	2.85364e11i	0.348369	−	0.292317i
$995$	−3.30160e11	+	9.07108e11i	−0.336847	+	0.925480i
$996$		0			0
$997$	−1.22891e11	+	6.96951e11i	−0.124377	+	0.705378i	0.857299	+	0.514819i	$0.172141\pi$
$997$	−1.22891e11	+	6.96951e11i	−0.124377	+	0.705378i	−0.981676	+	0.190559i	$0.938970\pi$
$998$		−	5.19985e11i		−	0.524166i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.9		138
3.2	odd	2		27.9.f.a.2.15	✓	138
27.13	even	9		27.9.f.a.14.15	yes	138
27.14	odd	18	inner	81.9.f.a.71.9		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.15	✓	138	3.2	odd	2
27.9.f.a.14.15	yes	138	27.13	even	9
81.9.f.a.8.9		138	1.1	even	1	trivial
81.9.f.a.71.9		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)

\(f(q)\)	\(=\)	\(q+(-13.3375 - 2.35175i) q^{2} +(-68.2042 - 24.8243i) q^{4} +(636.805 + 758.914i) q^{5} +(-2502.00 + 910.653i) q^{7} +(3853.85 + 2225.02i) q^{8} +(-6708.58 - 11619.6i) q^{10} +(-15349.9 + 18293.3i) q^{11} +(4780.28 + 27110.3i) q^{13} +(35511.9 - 6261.71i) q^{14} +(-31934.2 - 26796.0i) q^{16} +(105956. - 61173.5i) q^{17} +(-547.495 + 948.289i) q^{19} +(-24593.2 - 67569.4i) q^{20} +(247750. - 207887. i) q^{22} +(-50471.0 + 138668. i) q^{23} +(-102599. + 581870. i) q^{25} -372825. i q^{26} +193253. q^{28} +(924074. + 162939. i) q^{29} +(131238. + 47766.6i) q^{31} +(-369368. - 440196. i) q^{32} +(-1.55704e6 + 566717. i) q^{34} +(-2.28439e6 - 1.31889e6i) q^{35} +(-379045. - 656525. i) q^{37} +(9532.34 - 11360.2i) q^{38} +(765550. + 4.34165e6i) q^{40} +(-4.60079e6 + 811243. i) q^{41} +(-1.82392e6 - 1.53045e6i) q^{43} +(1.50104e6 - 866629. i) q^{44} +(999268. - 1.73078e6i) q^{46} +(-425686. - 1.16956e6i) q^{47} +(1.01461e6 - 851361. i) q^{49} +(2.73683e6 - 7.51938e6i) q^{50} +(346960. - 1.96771e6i) q^{52} +6.96711e6i q^{53} -2.36579e7 q^{55} +(-1.16686e7 - 2.05748e6i) q^{56} +(-1.19416e7 - 4.34639e6i) q^{58} +(-4.48304e6 - 5.34268e6i) q^{59} +(-2.36882e7 + 8.62179e6i) q^{61} +(-1.63804e6 - 945725. i) q^{62} +(9.22715e6 + 1.59819e7i) q^{64} +(-1.75303e7 + 2.08918e7i) q^{65} +(-3.60777e6 - 2.04607e7i) q^{67} +(-8.74520e6 + 1.54201e6i) q^{68} +(2.73663e7 + 2.29630e7i) q^{70} +(1.06620e7 - 6.15572e6i) q^{71} +(3.50114e6 - 6.06416e6i) q^{73} +(3.51151e6 + 9.64780e6i) q^{74} +(60882.1 - 51086.1i) q^{76} +(2.17466e7 - 5.97482e7i) q^{77} +(2.79249e6 - 1.58370e7i) q^{79} -4.12991e7i q^{80} +6.32706e7 q^{82} +(-4.48356e6 - 790573. i) q^{83} +(1.13898e8 + 4.14556e7i) q^{85} +(2.07272e7 + 2.47018e7i) q^{86} +(-9.98592e7 + 3.63458e7i) q^{88} +(3.86601e7 + 2.23204e7i) q^{89} +(-3.66484e7 - 6.34768e7i) q^{91} +(6.88467e6 - 8.20483e6i) q^{92} +(2.92705e6 + 1.66001e7i) q^{94} +(-1.06832e6 + 188373. i) q^{95} +(1.19186e7 + 1.00009e7i) q^{97} +(-1.55345e7 + 8.96887e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more