LMFDB - Embedded newform 81.9.f.a.8.11

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			8.11
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99728 - 0.352174i) q^{2} +(-236.696 - 86.1504i) q^{4} +(-67.5893 - 80.5497i) q^{5} +(3385.55 - 1232.24i) q^{7} +(892.041 + 515.020i) q^{8} +(106.627 + 184.683i) q^{10} +(-5656.92 + 6741.66i) q^{11} +(4915.16 + 27875.3i) q^{13} +(-7195.84 + 1268.82i) q^{14} +(47796.6 + 40106.1i) q^{16} +(-115312. + 66575.1i) q^{17} +(56477.6 - 97822.1i) q^{19} +(9058.73 + 24888.7i) q^{20} +(13672.7 - 11472.7i) q^{22} +(141378. - 388433. i) q^{23} +(65911.4 - 373802. i) q^{25} -57405.7i q^{26} -907504. q^{28} +(970128. + 171060. i) q^{29} +(-23816.5 - 8668.51i) q^{31} +(-250836. - 298934. i) q^{32} +(253755. - 92359.3i) q^{34} +(-328083. - 189419. i) q^{35} +(-54478.7 - 94360.0i) q^{37} +(-147252. + 175488. i) q^{38} +(-18807.6 - 106663. i) q^{40} +(4.20215e6 - 740952. i) q^{41} +(-3.87489e6 - 3.25142e6i) q^{43} +(1.91977e6 - 1.10838e6i) q^{44} +(-419167. + 726019. i) q^{46} +(-917770. - 2.52155e6i) q^{47} +(5.52741e6 - 4.63805e6i) q^{49} +(-263287. + 723374. i) q^{50} +(1.23806e6 - 7.02141e6i) q^{52} -4.76381e6i q^{53} +925386. q^{55} +(3.65467e6 + 644417. i) q^{56} +(-1.87737e6 - 683308. i) q^{58} +(-1.05864e7 - 1.26163e7i) q^{59} +(-1.05057e6 + 382376. i) q^{61} +(44515.4 + 25701.0i) q^{62} +(-7.59072e6 - 1.31475e7i) q^{64} +(1.91313e6 - 2.27998e6i) q^{65} +(-1.51350e6 - 8.58350e6i) q^{67} +(3.30293e7 - 5.82395e6i) q^{68} +(588565. + 493864. i) q^{70} +(9.87592e6 - 5.70186e6i) q^{71} +(1.01458e7 - 1.75731e7i) q^{73} +(75578.1 + 207649. i) q^{74} +(-2.17954e7 + 1.82886e7i) q^{76} +(-1.08444e7 + 2.97949e7i) q^{77} +(-3.73057e6 + 2.11571e7i) q^{79} -6.56074e6i q^{80} -8.65380e6 q^{82} +(-8.64355e6 - 1.52409e6i) q^{83} +(1.31564e7 + 4.78855e6i) q^{85} +(6.59417e6 + 7.85863e6i) q^{86} +(-8.51829e6 + 3.10040e6i) q^{88} +(1.19561e7 + 6.90285e6i) q^{89} +(5.09895e7 + 8.83163e7i) q^{91} +(-6.69273e7 + 7.97608e7i) q^{92} +(945017. + 5.35946e6i) q^{94} +(-1.16968e7 + 2.06247e6i) q^{95} +(-5.38212e7 - 4.51614e7i) q^{97} +(-1.26732e7 + 7.31687e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.99728	−	0.352174i	−0.124830	−	0.0220109i	0.110884	−	0.993833i	$-0.464632\pi$
$2$	−1.99728	−	0.352174i	−0.124830	−	0.0220109i	−0.235714	+	0.971822i	$0.575743\pi$
$3$		0			0
$3$		0			0
$4$	−236.696	−	86.1504i	−0.924595	−	0.336525i
$5$	−67.5893	−	80.5497i	−0.108143	−	0.128880i	0.709258	−	0.704949i	$-0.249030\pi$
$5$	−67.5893	−	80.5497i	−0.108143	−	0.128880i	−0.817401	+	0.576070i	$0.804586\pi$
$6$		0			0
$7$	3385.55	−	1232.24i	1.41006	−	0.513219i	0.478910	−	0.877864i	$-0.341032\pi$
$7$	3385.55	−	1232.24i	1.41006	−	0.513219i	0.931146	+	0.364645i	$0.118810\pi$
$8$	892.041	+	515.020i	0.217783	+	0.125737i
$9$		0			0
$10$	106.627	+	184.683i	0.0106627	+	0.0184683i
$11$	−5656.92	+	6741.66i	−0.386375	+	0.460464i	−0.923816	−	0.382838i	$-0.874947\pi$
$11$	−5656.92	+	6741.66i	−0.386375	+	0.460464i	0.537440	+	0.843302i	$0.319391\pi$
$12$		0			0
$13$	4915.16	+	27875.3i	0.172093	+	0.975991i	0.941445	+	0.337165i	$0.109468\pi$
$13$	4915.16	+	27875.3i	0.172093	+	0.975991i	−0.769352	+	0.638825i	$0.779421\pi$
$14$	−7195.84	+	1268.82i	−0.187314	+	0.0330284i
$15$		0			0
$16$	47796.6	+	40106.1i	0.729318	+	0.611971i
$17$	−115312.	+	66575.1i	−1.38063	+	0.797106i	−0.992234	−	0.124386i	$-0.960304\pi$
$17$	−115312.	+	66575.1i	−1.38063	+	0.797106i	−0.388395	+	0.921493i	$0.626970\pi$
$18$		0			0
$19$	56477.6	−	97822.1i	0.433373	−	0.750624i	−0.563788	−	0.825919i	$-0.690657\pi$
$19$	56477.6	−	97822.1i	0.433373	−	0.750624i	0.997161	+	0.0752952i	$0.0239899\pi$
$20$	9058.73	+	24888.7i	0.0566171	+	0.155554i
$21$		0			0
$22$	13672.7	−	11472.7i	0.0583664	−	0.0489752i
$23$	141378.	−	388433.i	0.505208	−	1.38805i	−0.380920	−	0.924608i	$-0.624393\pi$
$23$	141378.	−	388433.i	0.505208	−	1.38805i	0.886128	−	0.463440i	$-0.153385\pi$
$24$		0			0
$25$	65911.4	−	373802.i	0.168733	−	0.956933i
$26$		−	57405.7i		−	0.125621i
$27$		0			0
$28$	−907504.			−1.47644
$29$	970128.	+	171060.i	1.37163	+	0.241855i	0.810435	−	0.585828i	$-0.199231\pi$
$29$	970128.	+	171060.i	1.37163	+	0.241855i	0.561195	+	0.827684i	$0.310342\pi$
$30$		0			0
$31$	−23816.5	−	8668.51i	−0.0257888	−	0.00938637i	0.329094	−	0.944297i	$-0.393257\pi$
$31$	−23816.5	−	8668.51i	−0.0257888	−	0.00938637i	−0.354882	+	0.934911i	$0.615479\pi$
$32$	−250836.	−	298934.i	−0.239215	−	0.285086i
$33$		0			0
$34$	253755.	−	92359.3i	0.189889	−	0.0691139i
$35$	−328083.	−	189419.i	−0.218631	−	0.126227i
$36$		0			0
$37$	−54478.7	−	94360.0i	−0.0290683	−	0.0503478i	0.851125	−	0.524963i	$-0.175921\pi$
$37$	−54478.7	−	94360.0i	−0.0290683	−	0.0503478i	−0.880194	+	0.474615i	$0.842587\pi$
$38$	−147252.	+	175488.i	−0.0706198	+	0.0841614i
$39$		0			0
$40$	−18807.6	−	106663.i	−0.00734674	−	0.0416654i
$41$	4.20215e6	−	740952.i	1.48708	−	0.262213i	0.629679	−	0.776855i	$-0.283186\pi$
$41$	4.20215e6	−	740952.i	1.48708	−	0.262213i	0.857405	+	0.514642i	$0.172075\pi$
$42$		0			0
$43$	−3.87489e6	−	3.25142e6i	−1.13341	−	0.951041i	−0.134204	−	0.990954i	$-0.542848\pi$
$43$	−3.87489e6	−	3.25142e6i	−1.13341	−	0.951041i	−0.999203	+	0.0399123i	$0.987292\pi$
$44$	1.91977e6	−	1.10838e6i	0.512198	−	0.295718i
$45$		0			0
$46$	−419167.	+	726019.i	−0.0936172	+	0.162150i
$47$	−917770.	−	2.52155e6i	−0.188080	−	0.516745i	0.809434	−	0.587210i	$-0.199774\pi$
$47$	−917770.	−	2.52155e6i	−0.188080	−	0.516745i	−0.997514	+	0.0704651i	$0.977552\pi$
$48$		0			0
$49$	5.52741e6	−	4.63805e6i	0.958821	−	0.804547i
$50$	−263287.	+	723374.i	−0.0421259	+	0.115740i
$51$		0			0
$52$	1.23806e6	−	7.02141e6i	0.169328	−	0.960309i
$53$		−	4.76381e6i		−	0.603742i	−0.953349	−	0.301871i	$-0.902389\pi$
$53$		−	4.76381e6i		−	0.603742i	0.953349	−	0.301871i	$-0.0976111\pi$
$54$		0			0
$55$	925386.			0.101128
$56$	3.65467e6	+	644417.i	0.371618	+	0.0655262i
$57$		0			0
$58$	−1.87737e6	−	683308.i	−0.165897	−	0.0603816i
$59$	−1.05864e7	−	1.26163e7i	−0.873652	−	1.04118i	−0.998797	−	0.0490398i	$-0.984384\pi$
$59$	−1.05864e7	−	1.26163e7i	−0.873652	−	1.04118i	0.125144	−	0.992139i	$-0.460061\pi$
$60$		0			0
$61$	−1.05057e6	+	382376.i	−0.0758761	+	0.0276166i	−0.379679	−	0.925118i	$-0.623966\pi$
$61$	−1.05057e6	+	382376.i	−0.0758761	+	0.0276166i	0.303803	+	0.952735i	$0.401743\pi$
$62$	44515.4	+	25701.0i	0.00301262	+	0.00173933i
$63$		0			0
$64$	−7.59072e6	−	1.31475e7i	−0.452442	−	0.783653i
$65$	1.91313e6	−	2.27998e6i	0.107175	−	0.127726i
$66$		0			0
$67$	−1.51350e6	−	8.58350e6i	−0.0751076	−	0.425956i	−0.999056	−	0.0434394i	$-0.986168\pi$
$67$	−1.51350e6	−	8.58350e6i	−0.0751076	−	0.425956i	0.923948	−	0.382517i	$-0.124943\pi$
$68$	3.30293e7	−	5.82395e6i	1.54477	−	0.272384i
$69$		0			0
$70$	588565.	+	493864.i	0.0245133	+	0.0205691i
$71$	9.87592e6	−	5.70186e6i	0.388637	−	0.224380i	−0.292932	−	0.956133i	$-0.594631\pi$
$71$	9.87592e6	−	5.70186e6i	0.388637	−	0.224380i	0.681569	+	0.731754i	$0.261298\pi$
$72$		0			0
$73$	1.01458e7	−	1.75731e7i	0.357270	−	0.618810i	−0.630234	−	0.776406i	$-0.717041\pi$
$73$	1.01458e7	−	1.75731e7i	0.357270	−	0.618810i	0.987504	+	0.157595i	$0.0503742\pi$
$74$	75578.1	+	207649.i	0.00252040	+	0.00692474i
$75$		0			0
$76$	−2.17954e7	+	1.82886e7i	−0.653298	+	0.548182i
$77$	−1.08444e7	+	2.97949e7i	−0.308492	+	0.847575i
$78$		0			0
$79$	−3.73057e6	+	2.11571e7i	−0.0957782	+	0.543185i	0.898728	+	0.438507i	$0.144492\pi$
$79$	−3.73057e6	+	2.11571e7i	−0.0957782	+	0.543185i	−0.994506	+	0.104678i	$0.966619\pi$
$80$		−	6.56074e6i		−	0.160174i
$81$		0			0
$82$	−8.65380e6			−0.191404
$83$	−8.64355e6	−	1.52409e6i	−0.182129	−	0.0321143i	0.0818395	−	0.996646i	$-0.473921\pi$
$83$	−8.64355e6	−	1.52409e6i	−0.182129	−	0.0321143i	−0.263969	+	0.964531i	$0.585032\pi$
$84$		0			0
$85$	1.31564e7	+	4.78855e6i	0.252036	+	0.0917335i
$86$	6.59417e6	+	7.85863e6i	0.120550	+	0.143666i
$87$		0			0
$88$	−8.51829e6	+	3.10040e6i	−0.142044	+	0.0516997i
$89$	1.19561e7	+	6.90285e6i	0.190559	+	0.110019i	0.592244	−	0.805759i	$-0.298242\pi$
$89$	1.19561e7	+	6.90285e6i	0.190559	+	0.110019i	−0.401685	+	0.915778i	$0.631575\pi$
$90$		0			0
$91$	5.09895e7	+	8.83163e7i	0.743558	+	1.28788i
$92$	−6.69273e7	+	7.97608e7i	−0.934225	+	1.11337i
$93$		0			0
$94$	945017.	+	5.35946e6i	0.0121040	+	0.0686451i
$95$	−1.16968e7	+	2.06247e6i	−0.143606	+	0.0253217i
$96$		0			0
$97$	−5.38212e7	−	4.51614e7i	−0.607948	−	0.510129i	0.286041	−	0.958217i	$-0.407661\pi$
$97$	−5.38212e7	−	4.51614e7i	−0.607948	−	0.510129i	−0.893989	+	0.448088i	$0.852105\pi$
$98$	−1.26732e7	+	7.31687e6i	−0.137398	+	0.0793270i
$99$		0			0
$100$	−4.78041e7	+	8.27992e7i	−0.478041	+	0.827992i
$101$	−3.11081e7	−	8.54689e7i	−0.298943	−	0.821340i	−0.994677	−	0.103040i	$-0.967143\pi$
$101$	−3.11081e7	−	8.54689e7i	−0.298943	−	0.821340i	0.695734	−	0.718299i	$-0.255079\pi$
$102$		0			0
$103$	9.97579e7	−	8.37069e7i	0.886336	−	0.743725i	−0.0811355	−	0.996703i	$-0.525855\pi$
$103$	9.97579e7	−	8.37069e7i	0.886336	−	0.743725i	0.967472	+	0.252979i	$0.0814102\pi$
$104$	−9.97179e6	+	2.73973e7i	−0.0852393	+	0.234193i
$105$		0			0
$106$	−1.67769e6	+	9.51466e6i	−0.0132889	+	0.0753650i
$107$		−	5.29085e7i		−	0.403637i	−0.979423	−	0.201818i	$-0.935315\pi$
$107$		−	5.29085e7i		−	0.403637i	0.979423	−	0.201818i	$-0.0646850\pi$
$108$		0			0
$109$	1.60893e7			0.113981			0.0569903	−	0.998375i	$-0.481850\pi$
$109$	1.60893e7			0.113981			0.0569903	+	0.998375i	$0.481850\pi$
$110$	−1.84825e6	−	325897.i	−0.0126238	−	0.00222592i
$111$		0			0
$112$	2.11238e8	+	7.68843e7i	1.34245	+	0.488613i
$113$	1.27906e8	+	1.52432e8i	0.784469	+	0.934894i	0.999126	−	0.0417953i	$-0.0133077\pi$
$113$	1.27906e8	+	1.52432e8i	0.784469	+	0.934894i	−0.214657	+	0.976690i	$0.568863\pi$
$114$		0			0
$115$	−4.08438e7	+	1.48659e7i	−0.233526	+	0.0849964i
$116$	−2.14889e8	−	1.24066e8i	−1.18681	−	0.685206i
$117$		0			0
$118$	1.67008e7	+	2.89266e7i	0.0861407	+	0.149200i
$119$	−3.08356e8	+	3.67484e8i	−1.53767	+	1.83253i
$120$		0			0
$121$	2.37739e7	+	1.34828e8i	0.110907	+	0.628984i
$122$	2.23294e6	−	393728.i	0.0100795	−	0.00177728i
$123$		0			0
$124$	4.89049e6	+	4.10361e6i	0.0206855	+	0.0173572i
$125$	−7.01359e7	+	4.04930e7i	−0.287277	+	0.165859i
$126$		0			0
$127$	−2.28221e8	+	3.95290e8i	−0.877285	+	1.51950i	−0.0229765	+	0.999736i	$0.507314\pi$
$127$	−2.28221e8	+	3.95290e8i	−0.877285	+	1.51950i	−0.854309	+	0.519766i	$0.826019\pi$
$128$	4.46981e7	+	1.22807e8i	0.166513	+	0.457492i
$129$		0			0
$130$	−4.62401e6	+	3.88001e6i	−0.0161899	+	0.0135850i
$131$	1.50031e8	−	4.12206e8i	0.509442	−	1.39968i	−0.372373	−	0.928083i	$-0.621456\pi$
$131$	1.50031e8	−	4.12206e8i	0.509442	−	1.39968i	0.881814	−	0.471597i	$-0.156322\pi$
$132$		0			0
$133$	7.06674e7	−	4.00775e8i	0.225846	−	1.28084i
$134$			1.76766e7i			0.0548253i
$135$		0			0
$136$	−1.37150e8			−0.400904
$137$	5.04185e8	+	8.89014e7i	1.43122	+	0.252363i	0.834909	−	0.550388i	$-0.185520\pi$
$137$	5.04185e8	+	8.89014e7i	1.43122	+	0.252363i	0.596314	+	0.802751i	$0.296631\pi$
$138$		0			0
$139$	1.27574e8	+	4.64331e7i	0.341745	+	0.124385i	0.507191	−	0.861834i	$-0.330684\pi$
$139$	1.27574e8	+	4.64331e7i	0.341745	+	0.124385i	−0.165445	+	0.986219i	$0.552906\pi$
$140$	6.13375e7	+	7.30992e7i	0.159667	+	0.190283i
$141$		0			0
$142$	−2.17330e7	+	7.91016e6i	−0.0534523	+	0.0194550i
$143$	−2.15730e8	−	1.24552e8i	−0.515901	−	0.297856i
$144$		0			0
$145$	−5.17914e7	−	8.97054e7i	−0.117162	−	0.202930i
$146$	−2.64529e7	+	3.15253e7i	−0.0582186	+	0.0693822i
$147$		0			0
$148$	4.76577e6	+	2.70280e7i	0.00993313	+	0.0563336i
$149$	5.85971e8	−	1.03322e8i	1.18886	−	0.209628i	0.455983	−	0.889989i	$-0.349288\pi$
$149$	5.85971e8	−	1.03322e8i	1.18886	−	0.209628i	0.732877	+	0.680361i	$0.238177\pi$
$150$		0			0
$151$	−7.38513e8	−	6.19686e8i	−1.42053	−	1.19197i	−0.951056	−	0.309018i	$-0.899999\pi$
$151$	−7.38513e8	−	6.19686e8i	−1.42053	−	1.19197i	−0.469473	−	0.882947i	$-0.655556\pi$
$152$	1.00761e8	−	5.81742e7i	0.188763	−	0.108982i
$153$		0			0
$154$	3.21523e7	−	5.56895e7i	0.0571649	−	0.0990126i
$155$	911496.	+	2.50431e6i	0.00157917	+	0.00433872i
$156$		0			0
$157$	6.15909e8	−	5.16809e8i	1.01372	−	0.850611i	0.0248938	−	0.999690i	$-0.492075\pi$
$157$	6.15909e8	−	5.16809e8i	1.01372	−	0.850611i	0.988825	+	0.149079i	$0.0476308\pi$
$158$	1.49020e7	−	4.09428e7i	0.0239120	−	0.0656976i
$159$		0			0
$160$	−7.12528e6	+	4.04095e7i	−0.0108723	+	0.0616600i
$161$		−	1.48927e9i		−	2.21651i
$162$		0			0
$163$	−3.83046e8			−0.542626			−0.271313	−	0.962491i	$-0.587458\pi$
$163$	−3.83046e8			−0.542626			−0.271313	+	0.962491i	$0.587458\pi$
$164$	−1.05847e9	−	1.86636e8i	−1.46319	−	0.258000i
$165$		0			0
$166$	1.67268e7	+	6.08807e6i	0.0220283	+	0.00801765i
$167$	8.19824e8	+	9.77028e8i	1.05403	+	1.25615i	0.965590	+	0.260068i	$0.0837449\pi$
$167$	8.19824e8	+	9.77028e8i	1.05403	+	1.25615i	0.0884438	+	0.996081i	$0.471811\pi$
$168$		0			0
$169$	1.36645e7	−	4.97349e6i	0.0167513	−	0.00609697i
$170$	−2.45906e7	−	1.41974e7i	−0.0294425	−	0.0169986i
$171$		0			0
$172$	6.37061e8	+	1.10342e9i	0.727893	+	1.26075i
$173$	−2.82308e8	+	3.36442e8i	−0.315166	+	0.375600i	−0.900251	−	0.435372i	$-0.856617\pi$
$173$	−2.82308e8	+	3.36442e8i	−0.315166	+	0.375600i	0.585085	+	0.810972i	$0.301061\pi$
$174$		0			0
$175$	−2.37467e8	−	1.34674e9i	−0.253193	−	1.43593i
$176$	−5.40763e8	+	9.53511e7i	−0.563581	+	0.0993745i
$177$		0			0
$178$	−2.14486e7	−	1.79975e7i	−0.0213658	−	0.0179280i
$179$	1.38419e9	−	7.99161e8i	1.34829	−	0.778435i	0.360281	−	0.932844i	$-0.382681\pi$
$179$	1.38419e9	−	7.99161e8i	1.34829	−	0.778435i	0.988007	+	0.154409i	$0.0493474\pi$
$180$		0			0
$181$	9.08248e6	−	1.57313e7i	0.00846233	−	0.0146572i	−0.861763	−	0.507311i	$-0.830640\pi$
$181$	9.08248e6	−	1.57313e7i	0.00846233	−	0.0146572i	0.870226	+	0.492654i	$0.163973\pi$
$182$	−7.07374e7	−	1.94349e8i	−0.0644709	−	0.177132i
$183$		0			0
$184$	3.26166e8	−	2.73685e8i	0.284555	−	0.238770i
$185$	−3.91849e6	+	1.07660e7i	−0.00334528	+	0.00919107i
$186$		0			0
$187$	2.03481e8	−	1.15400e9i	0.166402	−	0.943712i
$188$			6.75908e8i			0.541073i
$189$		0			0
$190$	2.40882e7			0.0184837
$191$	−2.92953e8	−	5.16555e7i	−0.220122	−	0.0388135i	0.0624992	−	0.998045i	$-0.480093\pi$
$191$	−2.92953e8	−	5.16555e7i	−0.220122	−	0.0388135i	−0.282621	+	0.959232i	$0.591204\pi$
$192$		0			0
$193$	1.23554e9	+	4.49699e8i	0.890485	+	0.324110i	0.746433	−	0.665460i	$-0.231765\pi$
$193$	1.23554e9	+	4.49699e8i	0.890485	+	0.324110i	0.144052	+	0.989570i	$0.453987\pi$
$194$	9.15913e7	+	1.09154e8i	0.0646617	+	0.0770608i
$195$		0			0
$196$	−1.70789e9	+	6.21620e8i	−1.15727	+	0.421212i
$197$	−1.12925e9	−	6.51972e8i	−0.749765	−	0.432877i	0.0758442	−	0.997120i	$-0.475835\pi$
$197$	−1.12925e9	−	6.51972e8i	−0.749765	−	0.432877i	−0.825609	+	0.564243i	$0.809168\pi$
$198$		0			0
$199$	−3.99362e8	−	6.91715e8i	−0.254656	−	0.441077i	0.710146	−	0.704054i	$-0.248629\pi$
$199$	−3.99362e8	−	6.91715e8i	−0.254656	−	0.441077i	−0.964802	+	0.262977i	$0.915296\pi$
$200$	2.51311e8	−	2.99501e8i	0.157069	−	0.187188i
$201$		0			0
$202$	3.20317e7	+	1.81661e8i	0.0192386	+	0.109108i
$203$	3.49520e9	−	6.16298e8i	2.05820	−	0.362916i
$204$		0			0
$205$	−3.43703e8	−	2.88401e8i	−0.194611	−	0.163298i
$206$	−2.28724e8	+	1.32054e8i	−0.127011	+	0.0733300i
$207$		0			0
$208$	−8.83040e8	+	1.52947e9i	−0.471767	+	0.817124i
$209$	3.39993e8	+	9.34124e8i	0.178191	+	0.489575i
$210$		0			0
$211$	−1.03228e9	+	8.66188e8i	−0.520797	+	0.437001i	−0.864910	−	0.501928i	$-0.832624\pi$
$211$	−1.03228e9	+	8.66188e8i	−0.520797	+	0.437001i	0.344112	+	0.938928i	$0.388180\pi$
$212$	−4.10404e8	+	1.12758e9i	−0.203174	+	0.558216i
$213$		0			0
$214$	−1.86330e7	+	1.05673e8i	−0.00888439	+	0.0503859i
$215$			5.31883e8i			0.248921i
$216$		0			0
$217$	−9.13136e7			−0.0411810
$218$	−3.21348e7	−	5.66623e6i	−0.0142282	−	0.00250881i
$219$		0			0
$220$	−2.19035e8	−	7.97223e7i	−0.0935025	−	0.0340321i
$221$	−2.42257e9	−	2.88711e9i	−1.01557	−	1.21030i
$222$		0			0
$223$	2.22382e9	−	8.09406e8i	0.899251	−	0.327301i	0.149298	−	0.988792i	$-0.452298\pi$
$223$	2.22382e9	−	8.09406e8i	0.899251	−	0.327301i	0.749953	+	0.661492i	$0.230076\pi$
$224$	−1.21757e9	−	7.02966e8i	−0.483619	−	0.279217i
$225$		0			0
$226$	−2.01781e8	−	3.49494e8i	−0.0773474	−	0.133970i
$227$	−9.99253e8	+	1.19086e9i	−0.376333	+	0.448496i	−0.920653	−	0.390382i	$-0.872343\pi$
$227$	−9.99253e8	+	1.19086e9i	−0.376333	+	0.448496i	0.544320	+	0.838877i	$0.316788\pi$
$228$		0			0
$229$	3.39844e8	+	1.92735e9i	0.123577	+	0.700841i	0.982143	+	0.188137i	$0.0602449\pi$
$229$	3.39844e8	+	1.92735e9i	0.123577	+	0.700841i	−0.858566	+	0.512704i	$0.828644\pi$
$230$	8.68118e7	−	1.53073e7i	0.0310218	−	0.00546999i
$231$		0			0
$232$	7.77295e8	+	6.52228e8i	0.268308	+	0.225137i
$233$	−1.94723e9	+	1.12424e9i	−0.660685	+	0.381447i	−0.792538	−	0.609823i	$-0.791241\pi$
$233$	−1.94723e9	+	1.12424e9i	−0.660685	+	0.381447i	0.131853	+	0.991269i	$0.457907\pi$
$234$		0			0
$235$	−1.41079e8	+	2.44356e8i	−0.0462584	+	0.0801219i
$236$	1.41885e9	+	3.89826e9i	0.457392	+	1.25667i
$237$		0			0
$238$	7.45291e8	−	6.25373e8i	0.232283	−	0.194909i
$239$	−6.06245e8	+	1.66565e9i	−0.185805	+	0.510494i	−0.997265	−	0.0739138i	$-0.976451\pi$
$239$	−6.06245e8	+	1.66565e9i	−0.185805	+	0.510494i	0.811460	+	0.584408i	$0.198673\pi$
$240$		0			0
$241$	−1.62275e8	+	9.20306e8i	−0.0481042	+	0.272813i	−0.999367	−	0.0355681i	$-0.988676\pi$
$241$	−1.62275e8	+	9.20306e8i	−0.0481042	+	0.272813i	0.951263	+	0.308381i	$0.0997870\pi$
$242$		−	2.77662e8i		−	0.0809571i
$243$		0			0
$244$	2.81607e8			0.0794483
$245$	−7.47188e8	−	1.31749e8i	−0.207379	−	0.0365666i
$246$		0			0
$247$	3.00441e9	+	1.09352e9i	0.807183	+	0.293791i
$248$	−1.67809e7	−	1.99987e7i	−0.00443616	−	0.00528681i
$249$		0			0
$250$	1.54342e8	−	5.61757e7i	0.0395114	−	0.0143810i
$251$	5.42483e7	+	3.13203e7i	0.0136676	+	0.00789097i	0.506818	−	0.862053i	$-0.330822\pi$
$251$	5.42483e7	+	3.13203e7i	0.0136676	+	0.00789097i	−0.493151	+	0.869944i	$0.664155\pi$
$252$		0			0
$253$	1.81892e9	+	3.15045e9i	0.443946	+	0.768938i
$254$	5.95032e8	−	7.09131e8i	0.142957	−	0.170369i
$255$		0			0
$256$	6.28850e8	+	3.56639e9i	0.146416	+	0.830364i
$257$	−4.07519e9	+	7.18565e8i	−0.934146	+	0.164715i	−0.619949	−	0.784642i	$-0.712847\pi$
$257$	−4.07519e9	+	7.18565e8i	−0.934146	+	0.164715i	−0.314198	+	0.949358i	$0.601735\pi$
$258$		0			0
$259$	−3.00714e8	−	2.52329e8i	−0.0668274	−	0.0560749i
$260$	−6.49253e8	+	3.74846e8i	−0.142076	+	0.0820276i
$261$		0			0
$262$	−4.44821e8	+	7.70452e8i	−0.0944018	+	0.163509i
$263$	−4.28068e8	−	1.17611e9i	−0.0894726	−	0.245824i	0.886883	−	0.461994i	$-0.152866\pi$
$263$	−4.28068e8	−	1.17611e9i	−0.0894726	−	0.245824i	−0.976356	+	0.216170i	$0.930644\pi$
$264$		0			0
$265$	−3.83724e8	+	3.21982e8i	−0.0778100	+	0.0652903i
$266$	−2.82285e8	+	7.75572e8i	−0.0563847	+	0.154916i
$267$		0			0
$268$	−3.81231e8	+	2.16207e9i	−0.0739008	+	0.419112i
$269$			9.92958e9i			1.89636i	0.317728	+	0.948182i	$0.397080\pi$
$269$			9.92958e9i			1.89636i	−0.317728	+	0.948182i	$0.602920\pi$
$270$		0			0
$271$	8.78328e8			0.162847			0.0814235	−	0.996680i	$-0.474053\pi$
$271$	8.78328e8			0.162847			0.0814235	+	0.996680i	$0.474053\pi$
$272$	−8.18157e9	−	1.44263e9i	−1.49472	−	0.263560i
$273$		0			0
$274$	−9.75689e8	−	3.55122e8i	−0.173105	−	0.0630050i
$275$	2.14719e9	+	2.55892e9i	0.375439	+	0.447431i
$276$		0			0
$277$	−4.06954e9	+	1.48119e9i	−0.691236	+	0.251589i	−0.663664	−	0.748030i	$-0.731000\pi$
$277$	−4.06954e9	+	1.48119e9i	−0.691236	+	0.251589i	−0.0275717	+	0.999620i	$0.508777\pi$
$278$	−2.38448e8	−	1.37668e8i	−0.0399222	−	0.0230491i
$279$		0			0
$280$	−1.95109e8	−	3.37939e8i	−0.0317428	−	0.0549801i
$281$	6.16482e9	−	7.34695e9i	0.988770	−	1.17837i	0.00480818	−	0.999988i	$-0.498470\pi$
$281$	6.16482e9	−	7.34695e9i	0.988770	−	1.17837i	0.983961	−	0.178381i	$-0.0570861\pi$
$282$		0			0
$283$	−1.44765e9	−	8.21005e9i	−0.225693	−	1.27997i	−0.861355	−	0.508003i	$-0.830384\pi$
$283$	−1.44765e9	−	8.21005e9i	−0.225693	−	1.27997i	0.635662	−	0.771968i	$-0.280727\pi$
$284$	−2.82881e9	+	4.98795e8i	−0.434841	+	0.0766742i
$285$		0			0
$286$	3.87009e8	+	3.24739e8i	0.0578438	+	0.0485367i
$287$	1.33135e10	−	7.68657e9i	1.96230	−	1.13293i
$288$		0			0
$289$	5.37662e9	−	9.31257e9i	0.770758	−	1.33499i
$290$	7.18500e7	+	1.97406e8i	0.0101586	+	0.0279106i
$291$		0			0
$292$	−3.91541e9	+	3.28542e9i	−0.538575	+	0.451918i
$293$	3.69863e9	−	1.01619e10i	0.501845	−	1.37881i	−0.387626	−	0.921817i	$-0.626705\pi$
$293$	3.69863e9	−	1.01619e10i	0.501845	−	1.37881i	0.889471	−	0.456992i	$-0.151073\pi$
$294$		0			0
$295$	−3.00718e8	+	1.70546e9i	−0.0397074	+	0.225192i
$296$		−	1.12231e8i		−	0.0146199i
$297$		0			0
$298$	−1.20673e9			−0.153019
$299$	1.15226e10	+	2.03174e9i	1.44166	+	0.254204i
$300$		0			0
$301$	−1.71252e10	−	6.23305e9i	−2.08626	−	0.759337i
$302$	1.25678e9	+	1.49777e9i	0.151088	+	0.180060i
$303$		0			0
$304$	6.62270e9	−	2.41047e9i	0.775427	−	0.282232i
$305$	1.01807e8	+	5.87785e7i	0.0117647	+	0.00679234i
$306$		0			0
$307$	−8.84641e9	−	1.53224e10i	−0.995895	−	1.72494i	−0.576339	−	0.817211i	$-0.695519\pi$
$307$	−8.84641e9	−	1.53224e10i	−0.995895	−	1.72494i	−0.419556	−	0.907730i	$-0.637814\pi$
$308$	5.13368e9	−	6.11808e9i	0.570460	−	0.679848i
$309$		0			0
$310$	−938556.	−	5.32282e6i	−0.000101628	−	0.000576361i
$311$	−1.20968e10	+	2.13299e9i	−1.29309	+	0.228007i	−0.777530	−	0.628846i	$-0.783527\pi$
$311$	−1.20968e10	+	2.13299e9i	−1.29309	+	0.228007i	−0.515561	+	0.856853i	$0.672416\pi$
$312$		0			0
$313$	1.15186e10	+	9.66527e9i	1.20012	+	1.00702i	0.999627	+	0.0273201i	$0.00869734\pi$
$313$	1.15186e10	+	9.66527e9i	1.20012	+	1.00702i	0.200488	+	0.979696i	$0.435747\pi$
$314$	−1.41215e9	+	8.15304e8i	−0.145265	+	0.0838689i
$315$		0			0
$316$	2.70570e9	−	4.68642e9i	0.271351	−	0.469994i
$317$	−3.85001e9	−	1.05778e10i	−0.381263	−	1.04751i	−0.970825	−	0.239789i	$-0.922922\pi$
$317$	−3.85001e9	−	1.05778e10i	−0.381263	−	1.04751i	0.589562	−	0.807723i	$-0.299301\pi$
$318$		0			0
$319$	−6.64116e9	+	5.57260e9i	−0.641330	+	0.538140i
$320$	−5.45978e8	+	1.50006e9i	−0.0520685	+	0.143057i
$321$		0			0
$322$	−5.24481e8	+	2.97448e9i	−0.0487873	+	0.276686i
$323$			1.50400e10i			1.38178i
$324$		0			0
$325$	1.07438e10			0.962995
$326$	7.65049e8	+	1.34899e8i	0.0677359	+	0.0119437i
$327$		0			0
$328$	4.13009e9	+	1.50323e9i	0.356832	+	0.129876i
$329$	−6.21430e9	−	7.40592e9i	−0.530407	−	0.632114i
$330$		0			0
$331$	6.63184e9	−	2.41379e9i	0.552487	−	0.201089i	−0.0506641	−	0.998716i	$-0.516134\pi$
$331$	6.63184e9	−	2.41379e9i	0.552487	−	0.201089i	0.603151	+	0.797627i	$0.293912\pi$
$332$	1.91460e9	+	1.10539e9i	0.157589	+	0.0909838i
$333$		0			0
$334$	−1.29333e9	−	2.24012e9i	−0.103926	−	0.180005i
$335$	−5.89102e8	+	7.02064e8i	−0.0467747	+	0.0557439i
$336$		0			0
$337$	3.94099e7	+	2.23505e8i	0.00305553	+	0.0173287i	0.986297	−	0.164977i	$-0.0527550\pi$
$337$	3.94099e7	+	2.23505e8i	0.00305553	+	0.0173287i	−0.983242	+	0.182306i	$0.941644\pi$
$338$	−2.90434e7	+	5.12114e6i	−0.00222526	+	0.000392374i
$339$		0			0
$340$	−2.70154e9	−	2.26686e9i	−0.202160	−	0.169633i
$341$	1.93168e8	−	1.11526e8i	0.0142863	−	0.00824817i
$342$		0			0
$343$	2.61335e9	−	4.52646e9i	0.188809	−	0.327026i
$344$	−1.78202e9	−	4.89605e9i	−0.127256	−	0.349633i
$345$		0			0
$346$	6.82334e8	−	5.72546e8i	0.0476094	−	0.0399490i
$347$	−8.18317e8	+	2.24831e9i	−0.0564421	+	0.155074i	−0.964709	−	0.263317i	$-0.915183\pi$
$347$	−8.18317e8	+	2.24831e9i	−0.0564421	+	0.155074i	0.908267	+	0.418391i	$0.137406\pi$
$348$		0			0
$349$	−7.45944e8	+	4.23046e9i	−0.0502811	+	0.285158i	−0.999572	−	0.0292395i	$-0.990691\pi$
$349$	−7.45944e8	+	4.23046e9i	−0.0502811	+	0.285158i	0.949291	+	0.314398i	$0.101803\pi$
$350$			2.77345e9i			0.184820i
$351$		0			0
$352$	3.43427e9			0.223699
$353$	2.16757e10	+	3.82200e9i	1.39596	+	0.246146i	0.820483	−	0.571671i	$-0.193705\pi$
$353$	2.16757e10	+	3.82200e9i	1.39596	+	0.246146i	0.575479	+	0.817817i	$0.304816\pi$
$354$		0			0
$355$	−1.12679e9	−	4.10118e8i	−0.0709462	−	0.0258223i
$356$	−2.23528e9	−	2.66390e9i	−0.139165	−	0.165851i
$357$		0			0
$358$	−3.04605e9	+	1.10867e9i	−0.185441	+	0.0674949i
$359$	−1.28604e10	−	7.42496e9i	−0.774242	−	0.447009i	0.0601437	−	0.998190i	$-0.480844\pi$
$359$	−1.28604e10	−	7.42496e9i	−0.774242	−	0.447009i	−0.834386	+	0.551181i	$0.814177\pi$
$360$		0			0
$361$	2.11234e9	+	3.65868e9i	0.124376	+	0.215425i
$362$	−2.36804e7	+	2.82212e7i	−0.00137897	+	0.00164339i
$363$		0			0
$364$	−4.46053e9	−	2.52969e10i	−0.254086	−	1.44099i
$365$	−2.10126e9	+	3.70509e8i	−0.118388	+	0.0208750i
$366$		0			0
$367$	−4.22342e9	−	3.54387e9i	−0.232809	−	0.195350i	0.518919	−	0.854824i	$-0.326335\pi$
$367$	−4.22342e9	−	3.54387e9i	−0.232809	−	0.195350i	−0.751728	+	0.659474i	$0.770779\pi$
$368$	2.23359e10	−	1.28956e10i	1.21790	−	0.703156i
$369$		0			0
$370$	1.16178e7	−	2.01226e7i	0.000619894	−	0.00107369i
$371$	−5.87015e9	−	1.61281e10i	−0.309851	−	0.851310i
$372$		0			0
$373$	−9.87507e9	+	8.28617e9i	−0.510158	+	0.428074i	−0.861185	−	0.508292i	$-0.830277\pi$
$373$	−9.87507e9	+	8.28617e9i	−0.510158	+	0.428074i	0.351027	+	0.936365i	$0.385833\pi$
$374$	−8.12818e8	+	2.23320e9i	−0.0415439	+	0.114141i
$375$		0			0
$376$	4.79962e8	−	2.72200e9i	0.0240135	−	0.136187i
$377$			2.78834e10i			1.38032i
$378$		0			0
$379$	−2.46521e10			−1.19481			−0.597403	−	0.801941i	$-0.703801\pi$
$379$	−2.46521e10			−1.19481			−0.597403	+	0.801941i	$0.703801\pi$
$380$	2.94628e9	+	5.19508e8i	0.141299	+	0.0249148i
$381$		0			0
$382$	5.66916e8	+	2.06341e8i	0.0266235	+	0.00969017i
$383$	−3.85665e9	−	4.59618e9i	−0.179232	−	0.213600i	0.668947	−	0.743310i	$-0.266745\pi$
$383$	−3.85665e9	−	4.59618e9i	−0.179232	−	0.213600i	−0.848179	+	0.529710i	$0.822301\pi$
$384$		0			0
$385$	3.13293e9	−	1.14030e9i	0.142596	−	0.0519008i
$386$	−2.30934e9	−	1.33330e9i	−0.104025	−	0.0600590i
$387$		0			0
$388$	8.84861e9	+	1.53262e10i	0.390434	+	0.676252i
$389$	−1.83348e10	+	2.18505e10i	−0.800714	+	0.954254i	−0.999668	−	0.0257550i	$-0.991801\pi$
$389$	−1.83348e10	+	2.18505e10i	−0.800714	+	0.954254i	0.198954	+	0.980009i	$0.436245\pi$
$390$		0			0
$391$	9.55745e9	+	5.42030e10i	0.408917	+	2.31908i
$392$	7.31937e9	−	1.29060e9i	0.309977	−	0.0546573i
$393$		0			0
$394$	2.02582e9	+	1.69986e9i	0.0840650	+	0.0705389i
$395$	1.95635e9	−	1.12950e9i	0.0803632	−	0.0463977i
$396$		0			0
$397$	−4.82759e9	+	8.36163e9i	−0.194343	+	0.336611i	−0.946685	−	0.322161i	$-0.895591\pi$
$397$	−4.82759e9	+	8.36163e9i	−0.194343	+	0.336611i	0.752342	+	0.658773i	$0.228924\pi$
$398$	5.54032e8	+	1.52219e9i	0.0220802	+	0.0606648i
$399$		0			0
$400$	1.81421e10	−	1.52230e10i	0.708675	−	0.594649i
$401$	−7.24584e9	+	1.99078e10i	−0.280228	+	0.769920i	0.717107	+	0.696963i	$0.245466\pi$
$401$	−7.24584e9	+	1.99078e10i	−0.280228	+	0.769920i	−0.997335	+	0.0729567i	$0.976756\pi$
$402$		0			0
$403$	1.24575e8	−	7.06499e8i	0.00472292	−	0.0267850i
$404$			2.29101e10i			0.860008i
$405$		0			0
$406$	−7.19793e9			−0.264913
$407$	9.44324e8	+	1.66510e8i	0.0344147	+	0.00606823i
$408$		0			0
$409$	2.74242e9	+	9.98159e8i	0.0980032	+	0.0356703i	0.390556	−	0.920579i	$-0.372283\pi$
$409$	2.74242e9	+	9.98159e8i	0.0980032	+	0.0356703i	−0.292553	+	0.956249i	$0.594505\pi$
$410$	5.84904e8	+	6.97061e8i	0.0206990	+	0.0246681i
$411$		0			0
$412$	−3.08237e10	+	1.12189e10i	−1.06978	+	0.389369i
$413$	−5.13869e10	−	2.96683e10i	−1.76625	−	1.01975i
$414$		0			0
$415$	4.61446e8	+	7.99248e8i	0.0155571	+	0.0269457i
$416$	7.09997e9	−	8.46142e9i	0.237074	−	0.282533i
$417$		0			0
$418$	−3.50087e8	−	1.98544e9i	−0.0114676	−	0.0650358i
$419$	1.09072e10	−	1.92323e9i	0.353880	−	0.0623985i	0.00611745	−	0.999981i	$-0.498053\pi$
$419$	1.09072e10	−	1.92323e9i	0.353880	−	0.0623985i	0.347762	+	0.937583i	$0.386942\pi$
$420$		0			0
$421$	3.98726e10	+	3.34571e10i	1.26925	+	1.06502i	0.994633	+	0.103469i	$0.0329943\pi$
$421$	3.98726e10	+	3.34571e10i	1.26925	+	1.06502i	0.274613	+	0.961555i	$0.411450\pi$
$422$	2.36680e9	−	1.36647e9i	0.0746298	−	0.0430876i
$423$		0			0
$424$	2.45346e9	−	4.24951e9i	0.0759128	−	0.131485i
$425$	1.72856e10	+	4.74917e10i	0.529820	+	1.45567i
$426$		0			0
$427$	−3.08557e9	+	2.58910e9i	−0.0928162	+	0.0778820i
$428$	−4.55809e9	+	1.25232e10i	−0.135834	+	0.373200i
$429$		0			0
$430$	1.87315e8	−	1.06232e9i	0.00547898	−	0.0310728i
$431$			2.63476e10i			0.763540i	0.924257	+	0.381770i	$0.124685\pi$
$431$			2.63476e10i			0.763540i	−0.924257	+	0.381770i	$0.875315\pi$
$432$		0			0
$433$	3.69739e10			1.05183			0.525913	−	0.850539i	$-0.323724\pi$
$433$	3.69739e10			1.05183			0.525913	+	0.850539i	$0.323724\pi$
$434$	1.82379e8	+	3.21583e7i	0.00514062	+	0.000906429i
$435$		0			0
$436$	−3.80828e9	−	1.38610e9i	−0.105386	−	0.0383573i
$437$	−3.00126e10	−	3.57676e10i	−0.822959	−	0.980764i
$438$		0			0
$439$	4.82865e10	−	1.75748e10i	1.30007	−	0.473188i	0.403052	−	0.915177i	$-0.367949\pi$
$439$	4.82865e10	−	1.75748e10i	1.30007	−	0.473188i	0.897020	+	0.441989i	$0.145727\pi$
$440$	8.25482e8	+	4.76592e8i	0.0220240	+	0.0127156i
$441$		0			0
$442$	3.82179e9	+	6.61953e9i	0.100133	+	0.173436i
$443$	−2.10019e10	+	2.50291e10i	−0.545311	+	0.649876i	−0.966370	−	0.257157i	$-0.917214\pi$
$443$	−2.10019e10	+	2.50291e10i	−0.545311	+	0.649876i	0.421059	+	0.907033i	$0.361659\pi$
$444$		0			0
$445$	−2.52080e8	−	1.42962e9i	−0.00642834	−	0.0364569i
$446$	−4.72665e9	+	8.33435e8i	−0.119458	+	0.0210636i
$447$		0			0
$448$	−4.18996e10	−	3.51579e10i	−1.04015	−	0.872793i
$449$	4.98804e9	−	2.87985e9i	0.122728	−	0.0708572i	−0.437379	−	0.899277i	$-0.644093\pi$
$449$	4.98804e9	−	2.87985e9i	0.122728	−	0.0708572i	0.560107	+	0.828420i	$0.310760\pi$
$450$		0			0
$451$	−1.87760e10	+	3.25209e10i	−0.453833	+	0.786062i
$452$	−1.71427e10	−	4.70992e10i	−0.410701	−	1.12839i
$453$		0			0
$454$	2.41518e9	−	2.02657e9i	0.0568494	−	0.0477023i
$455$	3.66752e9	−	1.00764e10i	0.0855710	−	0.235104i
$456$		0			0
$457$	−3.51560e9	+	1.99380e10i	−0.0806000	+	0.457105i	0.917620	+	0.397460i	$0.130108\pi$
$457$	−3.51560e9	+	1.99380e10i	−0.0806000	+	0.457105i	−0.998220	+	0.0596455i	$0.981003\pi$
$458$		−	3.96914e9i		−	0.0902059i
$459$		0			0
$460$	1.09483e10			0.244520
$461$	−6.14335e10	−	1.08324e10i	−1.36020	−	0.239839i	−0.554507	−	0.832179i	$-0.687093\pi$
$461$	−6.14335e10	−	1.08324e10i	−1.36020	−	0.239839i	−0.805688	+	0.592340i	$0.798204\pi$
$462$		0			0
$463$	1.91395e10	+	6.96622e9i	0.416493	+	0.151591i	0.541762	−	0.840532i	$-0.317757\pi$
$463$	1.91395e10	+	6.96622e9i	0.416493	+	0.151591i	−0.125270	+	0.992123i	$0.539980\pi$
$464$	3.95083e10	+	4.70841e10i	0.852347	+	1.01579i
$465$		0			0
$466$	4.28509e9	−	1.55965e9i	0.0908692	−	0.0330737i
$467$	−5.46491e10	−	3.15517e10i	−1.14899	−	0.663369i	−0.200348	−	0.979725i	$-0.564207\pi$
$467$	−5.46491e10	−	3.15517e10i	−1.14899	−	0.663369i	−0.948641	+	0.316356i	$0.897541\pi$
$468$		0			0
$469$	−1.57009e10	−	2.71948e10i	−0.324515	−	0.562076i
$470$	3.67830e8	−	4.38362e8i	0.00753799	−	0.00898342i
$471$		0			0
$472$	−2.94580e9	−	1.67065e10i	−0.0593520	−	0.336602i
$473$	4.38399e10	−	7.73016e9i	0.875841	−	0.154434i
$474$		0			0
$475$	−3.28436e10	−	2.75590e10i	−0.645173	−	0.541364i
$476$	1.04646e11	−	6.04172e10i	2.03842	−	1.17688i
$477$		0			0
$478$	1.79744e9	−	3.11325e9i	0.0344304	−	0.0596352i
$479$	7.35383e9	+	2.02045e10i	0.139692	+	0.383801i	0.989735	−	0.142912i	$-0.0456466\pi$
$479$	7.35383e9	+	2.02045e10i	0.139692	+	0.383801i	−0.850043	+	0.526713i	$0.823424\pi$
$480$		0			0
$481$	2.36254e9	−	1.98240e9i	0.0441365	−	0.0370350i
$482$	6.48216e8	−	1.78096e9i	0.0120097	−	0.0329963i
$483$		0			0
$484$	5.98832e9	−	3.39615e10i	0.109125	−	0.618878i
$485$			7.38771e9i			0.133519i
$486$		0			0
$487$	−2.63994e10			−0.469330			−0.234665	−	0.972076i	$-0.575399\pi$
$487$	−2.63994e10			−0.469330			−0.234665	+	0.972076i	$0.575399\pi$
$488$	−1.13408e9	−	1.99969e8i	−0.0199970	−	0.00352601i
$489$		0			0
$490$	1.44594e9	+	5.26280e8i	0.0250823	+	0.00912920i
$491$	5.15419e10	+	6.14253e10i	0.886818	+	1.05687i	0.998009	+	0.0630696i	$0.0200890\pi$
$491$	5.15419e10	+	6.14253e10i	0.886818	+	1.05687i	−0.111191	+	0.993799i	$0.535467\pi$
$492$		0			0
$493$	−1.23255e11	+	4.48613e10i	−2.08650	+	0.759423i
$494$	−5.61554e9	−	3.24213e9i	−0.0942940	−	0.0544406i
$495$		0			0
$496$	−7.90689e8	−	1.36951e9i	−0.0130641	−	0.0226277i
$497$	2.64093e10	−	3.14734e10i	0.432844	−	0.515844i
$498$		0			0
$499$	−8.53818e9	−	4.84224e10i	−0.137709	−	0.780988i	−0.972935	−	0.231080i	$-0.925774\pi$
$499$	−8.53818e9	−	4.84224e10i	−0.137709	−	0.780988i	0.835225	−	0.549908i	$-0.185337\pi$
$500$	2.00894e10	−	3.54230e9i	0.321430	−	0.0566768i
$501$		0			0
$502$	−9.73187e7	−	8.16601e7i	−0.00153243	−	0.00128586i
$503$	7.47465e10	−	4.31549e10i	1.16767	−	0.674153i	0.214538	−	0.976716i	$-0.431176\pi$
$503$	7.47465e10	−	4.31549e10i	1.16767	−	0.674153i	0.953129	+	0.302563i	$0.0978422\pi$
$504$		0			0
$505$	−4.78192e9	+	8.28253e9i	−0.0735253	+	0.127350i
$506$	−2.52337e9	−	6.93291e9i	−0.0384928	−	0.105758i
$507$		0			0
$508$	8.80735e10	−	7.39024e10i	1.32248	−	1.10970i
$509$	2.04132e10	−	5.60848e10i	0.304116	−	0.835553i	−0.689658	−	0.724136i	$-0.742239\pi$
$509$	2.04132e10	−	5.60848e10i	0.304116	−	0.835553i	0.993774	−	0.111417i	$-0.0355389\pi$
$510$		0			0
$511$	1.26950e10	−	7.19967e10i	0.186186	−	1.05591i
$512$		−	4.08008e10i		−	0.593729i
$513$		0			0
$514$	8.39234e9			0.120235
$515$	−1.34851e10	−	2.37779e9i	−0.191702	−	0.0338022i
$516$		0			0
$517$	2.21912e10	+	8.07693e9i	0.310612	+	0.113054i
$518$	5.11746e8	+	6.09875e8i	0.00710781	+	0.00847075i
$519$		0			0
$520$	2.88083e9	−	1.04854e9i	0.0394007	−	0.0143407i
$521$	−4.74442e10	−	2.73919e10i	−0.643921	−	0.371768i	0.142203	−	0.989838i	$-0.454582\pi$
$521$	−4.74442e10	−	2.73919e10i	−0.643921	−	0.371768i	−0.786123	+	0.618070i	$0.787915\pi$
$522$		0			0
$523$	5.33114e10	+	9.23381e10i	0.712547	+	1.23417i	0.963898	+	0.266272i	$0.0857918\pi$
$523$	5.33114e10	+	9.23381e10i	0.712547	+	1.23417i	−0.251351	+	0.967896i	$0.580875\pi$
$524$	−7.10233e10	+	8.46423e10i	−0.942054	+	1.12270i
$525$		0			0
$526$	4.40777e8	+	2.49977e9i	0.00575805	+	0.0326555i
$527$	3.32343e9	−	5.86010e8i	0.0430868	−	0.00759736i
$528$		0			0
$529$	−7.09026e10	−	5.94943e10i	−0.905397	−	0.759719i
$530$	8.79797e8	−	5.07951e8i	0.0111501	−	0.00643752i
$531$		0			0
$532$	−5.12536e10	+	8.87739e10i	−0.639850	+	1.10825i
$533$	4.13084e10	+	1.13494e11i	0.511835	+	1.40626i
$534$		0			0
$535$	−4.26177e9	+	3.57605e9i	−0.0520205	+	0.0436504i
$536$	3.07057e9	−	8.43631e9i	0.0372014	−	0.102210i
$537$		0			0
$538$	3.49694e9	−	1.98321e10i	0.0417406	−	0.236723i
$539$			6.35010e10i			0.752360i
$540$		0			0
$541$	−1.25068e11			−1.46001			−0.730007	−	0.683440i	$-0.760483\pi$
$541$	−1.25068e11			−1.46001			−0.730007	+	0.683440i	$0.760483\pi$
$542$	−1.75427e9	−	3.09324e8i	−0.0203282	−	0.00358440i
$543$		0			0
$544$	4.88258e10	+	1.77711e10i	0.557512	+	0.202918i
$545$	−1.08746e9	−	1.29599e9i	−0.0123262	−	0.0146898i
$546$		0			0
$547$	1.19145e11	−	4.33652e10i	1.33084	−	0.484387i	0.423926	−	0.905697i	$-0.360652\pi$
$547$	1.19145e11	−	4.33652e10i	1.33084	−	0.484387i	0.906917	+	0.421310i	$0.138430\pi$
$548$	−1.11680e11	−	6.44783e10i	−1.23838	−	0.714976i
$549$		0			0
$550$	−3.38735e9	−	5.86706e9i	−0.0370177	−	0.0641165i
$551$	7.15240e10	−	8.52389e10i	0.775970	−	0.924765i
$552$		0			0
$553$	1.34406e10	+	7.62253e10i	0.143720	+	0.815077i
$554$	8.64964e9	−	1.52517e9i	0.0918246	−	0.0161912i
$555$		0			0
$556$	−2.61960e10	−	2.19811e10i	−0.274117	−	0.230012i
$557$	−1.23761e10	+	7.14536e9i	−0.128577	+	0.0742340i	−0.562909	−	0.826519i	$-0.690318\pi$
$557$	−1.23761e10	+	7.14536e9i	−0.128577	+	0.0742340i	0.434332	+	0.900753i	$0.356985\pi$
$558$		0			0
$559$	7.15885e10	−	1.23995e11i	0.733156	−	1.26986i
$560$	−8.08440e9	−	2.22117e10i	−0.0822045	−	0.225855i
$561$		0			0
$562$	−1.49003e10	+	1.25028e10i	−0.149365	+	0.125332i
$563$	5.56583e10	−	1.52920e11i	0.553983	−	1.52206i	−0.274243	−	0.961660i	$-0.588427\pi$
$563$	5.56583e10	−	1.52920e11i	0.553983	−	1.52206i	0.828226	−	0.560395i	$-0.189351\pi$
$564$		0			0
$565$	3.63331e9	−	2.06055e10i	0.0356541	−	0.202204i
$566$			1.69076e10i			0.164746i
$567$		0			0
$568$	1.17463e10			0.112852
$569$	6.79582e9	+	1.19829e9i	0.0648325	+	0.0114317i	0.205970	−	0.978558i	$-0.433965\pi$
$569$	6.79582e9	+	1.19829e9i	0.0648325	+	0.0114317i	−0.141138	+	0.989990i	$0.545076\pi$
$570$		0			0
$571$	3.97562e10	+	1.44701e10i	0.373991	+	0.136121i	0.522175	−	0.852838i	$-0.325121\pi$
$571$	3.97562e10	+	1.44701e10i	0.373991	+	0.136121i	−0.148185	+	0.988960i	$0.547343\pi$
$572$	4.03323e10	+	4.80662e10i	0.376764	+	0.449009i
$573$		0			0
$574$	−2.92978e10	+	1.06635e10i	−0.269891	+	0.0982322i
$575$	−1.35878e11	−	7.84495e10i	−1.24302	−	0.717660i
$576$		0			0
$577$	−6.78404e10	−	1.17503e11i	−0.612047	−	1.06010i	−0.990895	−	0.134638i	$-0.957013\pi$
$577$	−6.78404e10	−	1.17503e11i	−0.612047	−	1.06010i	0.378848	−	0.925459i	$-0.376320\pi$
$578$	−1.40182e10	+	1.67063e10i	−0.125598	+	0.149682i
$579$		0			0
$580$	4.53068e9	+	2.56948e10i	0.0400361	+	0.227056i
$581$	−3.11412e10	+	5.49103e9i	−0.273294	+	0.0481892i
$582$		0			0
$583$	3.21160e10	+	2.69485e10i	0.278001	+	0.233271i
$584$	1.81010e10	−	1.04506e10i	0.155615	−	0.0898444i
$585$		0			0
$586$	−1.09659e10	+	1.89936e10i	−0.0929941	+	0.161070i
$587$	4.72536e10	+	1.29828e11i	0.398000	+	1.09350i	0.963257	+	0.268581i	$0.0865546\pi$
$587$	4.72536e10	+	1.29828e11i	0.398000	+	1.09350i	−0.565257	+	0.824915i	$0.691223\pi$
$588$		0			0
$589$	−2.19307e9	+	1.84021e9i	−0.0182218	+	0.0152899i
$590$	1.20124e9	−	3.30037e9i	0.00991334	−	0.0272367i
$591$		0			0
$592$	1.18051e9	−	6.69502e9i	0.00961133	−	0.0545086i
$593$			1.47786e11i			1.19513i	0.801821	+	0.597564i	$0.203865\pi$
$593$			1.47786e11i			1.19513i	−0.801821	+	0.597564i	$0.796135\pi$
$594$		0			0
$595$	5.04423e10			0.402464
$596$	−1.47598e11	−	2.60256e10i	−1.16976	−	0.206260i
$597$		0			0
$598$	−2.22982e10	−	8.11589e9i	−0.174368	−	0.0634646i
$599$	−2.98197e9	−	3.55377e9i	−0.0231630	−	0.0276046i	0.754339	−	0.656486i	$-0.227958\pi$
$599$	−2.98197e9	−	3.55377e9i	−0.0231630	−	0.0276046i	−0.777502	+	0.628881i	$0.783513\pi$
$600$		0			0
$601$	1.14595e11	−	4.17093e10i	0.878354	−	0.319695i	0.136809	−	0.990598i	$-0.456315\pi$
$601$	1.14595e11	−	4.17093e10i	0.878354	−	0.319695i	0.741545	+	0.670903i	$0.234093\pi$
$602$	3.20086e10	+	1.84802e10i	0.243714	+	0.140708i
$603$		0			0
$604$	1.21417e11	+	2.10300e11i	0.912287	+	1.58013i
$605$	9.25352e9	−	1.10279e10i	0.0690694	−	0.0823137i
$606$		0			0
$607$	−6.96919e9	−	3.95242e10i	−0.0513367	−	0.291145i	0.948321	−	0.317313i	$-0.102781\pi$
$607$	−6.96919e9	−	3.95242e10i	−0.0513367	−	0.291145i	−0.999658	+	0.0261682i	$0.991669\pi$
$608$	−4.34090e10	+	7.65417e9i	−0.317662	+	0.0560124i
$609$		0			0
$610$	−1.82637e8	−	1.53251e8i	−0.00131908	−	0.00110684i
$611$	6.57779e10	−	3.79769e10i	0.471971	−	0.272493i
$612$		0			0
$613$	−1.34667e11	+	2.33249e11i	−0.953714	+	1.65188i	−0.216430	+	0.976298i	$0.569441\pi$
$613$	−1.34667e11	+	2.33249e11i	−0.953714	+	1.65188i	−0.737284	+	0.675583i	$0.763892\pi$
$614$	1.22726e10	+	3.37186e10i	0.0863500	+	0.237245i
$615$		0			0
$616$	−2.50186e10	+	2.09931e10i	−0.173756	+	0.145799i
$617$	−7.45509e10	+	2.04827e11i	−0.514413	+	1.41334i	0.362180	+	0.932108i	$0.382032\pi$
$617$	−7.45509e10	+	2.04827e11i	−0.514413	+	1.41334i	−0.876594	+	0.481231i	$0.840190\pi$
$618$		0			0
$619$	−4.72166e10	+	2.67779e11i	−0.321612	+	1.82395i	0.210875	+	0.977513i	$0.432369\pi$
$619$	−4.72166e10	+	2.67779e11i	−0.321612	+	1.82395i	−0.532487	+	0.846438i	$0.678742\pi$
$620$		−	6.71287e8i		−	0.00454299i
$621$		0			0
$622$	2.49119e10			0.166435
$623$	4.89838e10	+	8.63717e9i	0.325162	+	0.0573349i
$624$		0			0
$625$	−1.31325e11	−	4.77984e10i	−0.860652	−	0.313252i
$626$	−1.96020e10	−	2.33608e10i	−0.127645	−	0.152121i
$627$		0			0
$628$	−1.90306e11	+	6.92659e10i	−1.22353	+	0.445329i
$629$	1.25641e10	+	7.25386e9i	0.0802652	+	0.0463411i
$630$		0			0
$631$	−7.03626e10	−	1.21872e11i	−0.443838	−	0.768750i	0.554132	−	0.832428i	$-0.313050\pi$
$631$	−7.03626e10	−	1.21872e11i	−0.443838	−	0.768750i	−0.997970	+	0.0636786i	$0.979717\pi$
$632$	−1.42241e10	+	1.69517e10i	−0.0891575	+	0.106254i
$633$		0			0
$634$	3.96431e9	+	2.24827e10i	0.0245364	+	0.139153i
$635$	4.72658e10	−	8.33424e9i	0.290705	−	0.0512591i
$636$		0			0
$637$	1.56455e11	+	1.31281e11i	0.950237	+	0.797343i
$638$	1.52268e10	−	8.79118e9i	0.0919021	−	0.0530597i
$639$		0			0
$640$	6.87096e9	−	1.19008e10i	0.0409541	−	0.0709346i
$641$	−5.53171e10	−	1.51982e11i	−0.327663	−	0.900246i	−0.988702	−	0.149894i	$-0.952107\pi$
$641$	−5.53171e10	−	1.51982e11i	−0.327663	−	0.900246i	0.661039	−	0.750351i	$-0.270116\pi$
$642$		0			0
$643$	5.46145e10	−	4.58270e10i	0.319495	−	0.268088i	−0.468908	−	0.883247i	$-0.655353\pi$
$643$	5.46145e10	−	4.58270e10i	0.319495	−	0.268088i	0.788403	+	0.615159i	$0.210908\pi$
$644$	−1.28301e11	+	3.52504e11i	−0.745910	+	2.04937i
$645$		0			0
$646$	5.29670e9	−	3.00391e10i	0.0304141	−	0.172487i
$647$			1.04773e11i			0.597905i	0.954268	+	0.298952i	$0.0966372\pi$
$647$			1.04773e11i			0.597905i	−0.954268	+	0.298952i	$0.903363\pi$
$648$		0			0
$649$	1.44941e11			0.816983
$650$	−2.14583e10	−	3.78369e9i	−0.120211	−	0.0211964i
$651$		0			0
$652$	9.06655e10	+	3.29996e10i	0.501709	+	0.182607i
$653$	−1.52339e11	−	1.81551e11i	−0.837837	−	0.998495i	−0.999931	−	0.0117197i	$-0.996269\pi$
$653$	−1.52339e11	−	1.81551e11i	−0.837837	−	0.998495i	0.162095	−	0.986775i	$-0.448175\pi$
$654$		0			0
$655$	−4.33435e10	+	1.57757e10i	−0.235483	+	0.0857087i
$656$	2.30565e11	+	1.33117e11i	1.24502	+	0.718815i
$657$		0			0
$658$	9.80352e9	+	1.69802e10i	0.0522972	+	0.0905814i
$659$	2.38359e10	−	2.84065e10i	0.126383	−	0.150618i	−0.699142	−	0.714983i	$-0.746435\pi$
$659$	2.38359e10	−	2.84065e10i	0.126383	−	0.150618i	0.825525	+	0.564365i	$0.190879\pi$
$660$		0			0
$661$	2.29243e10	+	1.30010e11i	0.120085	+	0.681038i	0.984106	+	0.177582i	$0.0568274\pi$
$661$	2.29243e10	+	1.30010e11i	0.120085	+	0.681038i	−0.864021	+	0.503456i	$0.832061\pi$
$662$	−1.40957e10	+	2.48545e9i	−0.0733930	+	0.0129412i
$663$		0			0
$664$	−6.92546e9	−	5.81115e9i	−0.0356268	−	0.0298944i
$665$	−3.70587e10	+	2.13958e10i	−0.189497	+	0.109406i
$666$		0			0
$667$	2.03600e11	−	3.52645e11i	1.02867	−	1.78170i
$668$	−1.09878e11	−	3.01887e11i	−0.551829	−	1.51614i
$669$		0			0
$670$	1.42385e9	−	1.19475e9i	0.00706586	−	0.00592896i
$671$	3.36514e9	−	9.24564e9i	0.0166002	−	0.0456086i
$672$		0			0
$673$	2.55164e10	−	1.44710e11i	0.124382	−	0.705407i	−0.857291	−	0.514833i	$-0.827854\pi$
$673$	2.55164e10	−	1.44710e11i	0.124382	−	0.705407i	0.981673	−	0.190574i	$-0.0610349\pi$
$674$		−	4.60280e8i		−	0.00223040i
$675$		0			0
$676$	−3.66281e9			−0.0175399
$677$	1.14383e11	+	2.01689e10i	0.544513	+	0.0960124i	0.439137	−	0.898420i	$-0.355284\pi$
$677$	1.14383e11	+	2.01689e10i	0.544513	+	0.0960124i	0.105376	+	0.994432i	$0.466395\pi$
$678$		0			0
$679$	−2.37864e11	−	8.65753e10i	−1.11905	−	0.407300i
$680$	9.26987e9	+	1.10474e10i	0.0433549	+	0.0516683i
$681$		0			0
$682$	−4.25087e8	+	1.54719e8i	−0.00196490	+	0.000715166i
$683$	−1.13839e11	−	6.57249e10i	−0.523128	−	0.302028i	0.215086	−	0.976595i	$-0.430997\pi$
$683$	−1.13839e11	−	6.57249e10i	−0.523128	−	0.302028i	−0.738213	+	0.674567i	$0.764330\pi$
$684$		0			0
$685$	−2.69165e10	−	4.66207e10i	−0.122252	−	0.211747i
$686$	−6.81370e9	+	8.12025e9i	−0.0307671	+	0.0366668i
$687$		0			0
$688$	−5.48048e10	−	3.10814e11i	−0.244605	−	1.38722i
$689$	1.32792e11	−	2.34149e10i	0.589246	−	0.103900i
$690$		0			0
$691$	1.59975e11	+	1.34235e11i	0.701681	+	0.588780i	0.922251	−	0.386591i	$-0.126348\pi$
$691$	1.59975e11	+	1.34235e11i	0.701681	+	0.588780i	−0.220571	+	0.975371i	$0.570792\pi$
$692$	9.58058e10	−	5.53135e10i	0.417799	−	0.241216i
$693$		0			0
$694$	2.42620e9	−	4.20230e9i	0.0104590	−	0.0181155i
$695$	−4.88245e9	−	1.34144e10i	−0.0209266	−	0.0574953i
$696$		0			0
$697$	−4.35227e11	+	3.65199e11i	−1.84410	+	1.54738i
$698$	2.97972e9	−	8.18671e9i	0.0125532	−	0.0344895i
$699$		0			0
$700$	−5.98148e10	+	3.39227e11i	−0.249125	+	1.41286i
$701$			1.31996e11i			0.546626i	0.961925	+	0.273313i	$0.0881195\pi$
$701$			1.31996e11i			0.546626i	−0.961925	+	0.273313i	$0.911881\pi$
$702$		0			0
$703$	−1.23073e10			−0.0503897
$704$	1.31576e11	+	2.32004e10i	0.535657	+	0.0944507i
$705$		0			0
$706$	−4.19463e10	−	1.52672e10i	−0.168840	−	0.0614527i
$707$	−2.10636e11	−	2.51026e11i	−0.843053	−	1.00471i
$708$		0			0
$709$	4.05092e11	−	1.47441e11i	1.60313	−	0.583492i	0.623065	−	0.782170i	$-0.285887\pi$
$709$	4.05092e11	−	1.47441e11i	1.60313	−	0.583492i	0.980065	+	0.198678i	$0.0636648\pi$
$710$	2.10608e9	+	1.21595e9i	0.00828784	+	0.00478499i
$711$		0			0
$712$	7.11021e9	+	1.23152e10i	0.0276670	+	0.0479207i
$713$	−6.73427e9	+	8.02558e9i	−0.0260575	+	0.0310541i
$714$		0			0
$715$	4.54842e9	+	2.57954e10i	0.0174035	+	0.0987001i
$716$	−3.96480e11	+	6.99101e10i	−1.50858	+	0.266004i
$717$		0			0
$718$	2.30709e10	+	1.93588e10i	0.0868095	+	0.0728418i
$719$	−5.28838e10	+	3.05325e10i	−0.197882	+	0.114247i	−0.595667	−	0.803231i	$-0.703112\pi$
$719$	−5.28838e10	+	3.05325e10i	−0.197882	+	0.114247i	0.397785	+	0.917479i	$0.369779\pi$
$720$		0			0
$721$	2.34588e11	−	4.06319e11i	0.868091	−	1.50358i
$722$	−2.93044e9	−	8.05131e9i	−0.0107841	−	0.0296291i
$723$		0			0
$724$	−3.50505e9	+	2.94108e9i	−0.0127567	+	0.0107042i
$725$	1.27885e11	−	3.51361e11i	0.462879	−	1.27175i
$726$		0			0
$727$	4.11431e10	−	2.33334e11i	0.147285	−	0.835296i	−0.818219	−	0.574907i	$-0.805038\pi$
$727$	4.11431e10	−	2.33334e11i	0.147285	−	0.835296i	0.965504	−	0.260389i	$-0.0838508\pi$
$728$			1.05042e11i			0.373972i
$729$		0			0
$730$	4.32729e9			0.0152379
$731$	6.63284e11	+	1.16955e11i	2.32290	+	0.409589i
$732$		0			0
$733$	1.40249e11	+	5.10464e10i	0.485829	+	0.176827i	0.573310	−	0.819339i	$-0.305659\pi$
$733$	1.40249e11	+	5.10464e10i	0.485829	+	0.176827i	−0.0874803	+	0.996166i	$0.527881\pi$
$734$	7.18728e9	+	8.56547e9i	0.0247617	+	0.0295099i
$735$		0			0
$736$	−1.51578e11	+	5.51700e10i	−0.516566	+	0.188015i
$737$	6.64287e10	+	3.83526e10i	0.225157	+	0.129995i
$738$		0			0
$739$	−2.69209e11	−	4.66284e11i	−0.902634	−	1.56341i	−0.824062	−	0.566500i	$-0.808297\pi$
$739$	−2.69209e11	−	4.66284e11i	−0.902634	−	1.56341i	−0.0785724	−	0.996908i	$-0.525036\pi$
$740$	1.85498e9	−	2.21068e9i	0.00618605	−	0.00737225i
$741$		0			0
$742$	6.04442e9	+	3.42796e10i	0.0199406	+	0.113089i
$743$	3.59160e10	−	6.33296e9i	0.117851	−	0.0207803i	−0.114412	−	0.993433i	$-0.536498\pi$
$743$	3.59160e10	−	6.33296e9i	0.117851	−	0.0207803i	0.232263	+	0.972653i	$0.425387\pi$
$744$		0			0
$745$	−4.79279e10	−	4.02163e10i	−0.155583	−	0.130550i
$746$	2.26414e10	−	1.30720e10i	0.0731053	−	0.0422074i
$747$		0			0
$748$	−1.47581e11	+	2.55618e11i	−0.471437	+	0.816553i
$749$	−6.51959e10	−	1.79124e11i	−0.207154	−	0.569150i
$750$		0			0
$751$	1.20638e11	−	1.01227e11i	0.379248	−	0.318227i	−0.433159	−	0.901318i	$-0.642601\pi$
$751$	1.20638e11	−	1.01227e11i	0.379248	−	0.318227i	0.812407	+	0.583090i	$0.198157\pi$
$752$	5.72634e10	−	1.57330e11i	0.179063	−	0.491971i
$753$		0			0
$754$	9.81980e9	−	5.56908e10i	0.0303821	−	0.172305i
$755$			1.01371e11i			0.311980i
$756$		0			0
$757$	−3.98668e11			−1.21403			−0.607013	−	0.794692i	$-0.707632\pi$
$757$	−3.98668e11			−1.21403			−0.607013	+	0.794692i	$0.707632\pi$
$758$	4.92372e10	+	8.68184e9i	0.149148	+	0.0262987i
$759$		0			0
$760$	−1.14963e10	−	4.18429e9i	−0.0344589	−	0.0125420i
$761$	8.36046e10	+	9.96361e10i	0.249282	+	0.297083i	0.876146	−	0.482046i	$-0.160106\pi$
$761$	8.36046e10	+	9.96361e10i	0.249282	+	0.297083i	−0.626864	+	0.779129i	$0.715662\pi$
$762$		0			0
$763$	5.44711e10	−	1.98258e10i	0.160719	−	0.0584970i
$764$	6.48906e10	+	3.74646e10i	0.190462	+	0.109963i
$765$		0			0
$766$	6.08415e9	+	1.05381e10i	0.0176720	+	0.0306088i
$767$	2.99650e11	−	3.57109e11i	0.865830	−	1.03186i
$768$		0			0
$769$	−2.40087e10	−	1.36160e11i	−0.0686537	−	0.389354i	−0.999701	−	0.0244556i	$-0.992215\pi$
$769$	−2.40087e10	−	1.36160e11i	−0.0686537	−	0.389354i	0.931047	−	0.364899i	$-0.118896\pi$
$770$	−6.65893e9	+	1.17415e9i	−0.0189427	+	0.00334010i
$771$		0			0
$772$	−2.53705e11	−	2.12884e11i	−0.714266	−	0.599341i
$773$	−2.26195e11	+	1.30594e11i	−0.633528	+	0.365767i	−0.782117	−	0.623132i	$-0.785860\pi$
$773$	−2.26195e11	+	1.30594e11i	−0.633528	+	0.365767i	0.148589	+	0.988899i	$0.452527\pi$
$774$		0			0
$775$	−4.81009e9	+	8.33131e9i	−0.0133336	+	0.0230944i
$776$	−2.47517e10	−	6.80048e10i	−0.0682588	−	0.187539i
$777$		0			0
$778$	4.43149e10	−	3.71846e10i	0.120957	−	0.101495i
$779$	1.64846e11	−	4.52910e11i	0.447639	−	1.22988i
$780$		0			0
$781$	−1.74273e10	+	9.88350e10i	−0.0468409	+	0.265648i
$782$		−	1.11624e11i		−	0.298492i
$783$		0			0
$784$	4.50206e11			1.19164
$785$	−8.32576e10	−	1.46806e10i	−0.219253	−	0.0386602i
$786$		0			0
$787$	−3.29394e11	−	1.19889e11i	−0.858650	−	0.312523i	−0.125088	−	0.992146i	$-0.539921\pi$
$787$	−3.29394e11	−	1.19889e11i	−0.858650	−	0.312523i	−0.733562	+	0.679622i	$0.762144\pi$
$788$	2.11121e11	+	2.51605e11i	0.547555	+	0.652550i
$789$		0			0
$790$	−4.30515e9	+	1.56694e9i	−0.0110530	+	0.00402296i
$791$	6.20863e11	+	3.58455e11i	1.58595	+	0.915649i
$792$		0			0
$793$	−1.58225e10	−	2.74054e10i	−0.0400114	−	0.0693017i
$794$	1.25868e10	−	1.50003e10i	0.0316689	−	0.0377415i
$795$		0			0
$796$	3.49359e10	+	1.98131e11i	0.0870201	+	0.493516i
$797$	−4.01383e11	+	7.07747e10i	−0.994777	+	0.175406i	−0.647262	−	0.762268i	$-0.724086\pi$
$797$	−4.01383e11	+	7.07747e10i	−0.994777	+	0.175406i	−0.347516	+	0.937674i	$0.612975\pi$
$798$		0			0
$799$	2.73702e11	+	2.29663e11i	0.671570	+	0.563514i
$800$	−1.28275e11	+	7.40597e10i	−0.313172	+	0.180810i
$801$		0			0
$802$	2.14830e10	−	3.72096e10i	0.0519274	−	0.0899409i
$803$	6.10777e10	+	1.67810e11i	0.146899	+	0.403603i
$804$		0			0
$805$	−1.19960e11	+	1.00659e11i	−0.285663	+	0.239699i
$806$	−4.97621e8	+	1.36720e9i	−0.00117912	+	0.00323961i
$807$		0			0
$808$	1.62685e10	−	9.22631e10i	0.0381682	−	0.216462i
$809$		−	6.91423e11i		−	1.61417i	−0.590434	−	0.807086i	$-0.701043\pi$
$809$		−	6.91423e11i		−	1.61417i	0.590434	−	0.807086i	$-0.298957\pi$
$810$		0			0
$811$	1.41013e11			0.325968			0.162984	−	0.986629i	$-0.447888\pi$
$811$	1.41013e11			0.325968			0.162984	+	0.986629i	$0.447888\pi$
$812$	−8.80395e11	−	1.55237e11i	−2.02513	−	0.357085i
$813$		0			0
$814$	−1.82744e9	−	6.65133e8i	−0.00416241	−	0.00151499i
$815$	2.58898e10	+	3.08542e10i	0.0586811	+	0.0699334i
$816$		0			0
$817$	−5.36906e11	+	1.95418e11i	−1.20506	+	0.438607i
$818$	−5.12585e9	−	2.95941e9i	−0.0114486	−	0.00660985i
$819$		0			0
$820$	5.65074e10	+	9.78737e10i	0.124983	+	0.216476i
$821$	−3.09207e11	+	3.68498e11i	−0.680575	+	0.811078i	−0.990182	−	0.139787i	$-0.955358\pi$
$821$	−3.09207e11	+	3.68498e11i	−0.680575	+	0.811078i	0.309606	+	0.950865i	$0.399803\pi$
$822$		0			0
$823$	−2.05735e10	−	1.16678e11i	−0.0448444	−	0.254325i	0.954141	−	0.299357i	$-0.0967722\pi$
$823$	−2.05735e10	−	1.16678e11i	−0.0448444	−	0.254325i	−0.998986	+	0.0450318i	$0.985661\pi$
$824$	1.32099e11	−	2.32926e10i	0.286543	−	0.0505253i
$825$		0			0
$826$	9.21856e10	+	7.73529e10i	0.198035	+	0.166171i
$827$	−1.48258e11	+	8.55968e10i	−0.316954	+	0.182993i	−0.650034	−	0.759905i	$-0.725245\pi$
$827$	−1.48258e11	+	8.55968e10i	−0.316954	+	0.182993i	0.333080	+	0.942899i	$0.391912\pi$
$828$		0			0
$829$	−1.14122e11	+	1.97665e11i	−0.241630	+	0.418516i	−0.961179	−	0.275926i	$-0.911015\pi$
$829$	−1.14122e11	+	1.97665e11i	−0.241630	+	0.418516i	0.719549	+	0.694442i	$0.244349\pi$
$830$	−6.40162e8	−	1.75883e9i	−0.00134889	−	0.00370605i
$831$		0			0
$832$	3.29181e11	−	2.76216e11i	0.686976	−	0.576441i
$833$	−3.28596e11	+	9.02809e11i	−0.682467	+	1.87506i
$834$		0			0
$835$	2.32881e10	−	1.32073e11i	0.0479057	−	0.271687i
$836$		−	2.50394e11i		−	0.512624i
$837$		0			0
$838$	−2.24619e10			−0.0455482
$839$	2.48039e11	+	4.37360e10i	0.500579	+	0.0882655i	0.418236	−	0.908339i	$-0.362649\pi$
$839$	2.48039e11	+	4.37360e10i	0.500579	+	0.0882655i	0.0823430	+	0.996604i	$0.473760\pi$
$840$		0			0
$841$	4.41809e11	+	1.60805e11i	0.883184	+	0.321453i
$842$	−6.78539e10	−	8.08651e10i	−0.134998	−	0.160884i
$843$		0			0
$844$	3.18960e11	−	1.16092e11i	0.628588	−	0.228787i
$845$	−1.32419e9	−	7.64521e8i	−0.00259731	−	0.00149956i
$846$		0			0
$847$	2.46628e11	+	4.27172e11i	0.479191	+	0.829983i
$848$	1.91058e11	−	2.27694e11i	0.369472	−	0.440320i
$849$		0			0
$850$	−1.77987e10	−	1.00942e11i	−0.0340968	−	0.193373i
$851$	−4.43546e10	+	7.82091e9i	−0.0845708	+	0.0149121i
$852$		0			0
$853$	1.21481e11	+	1.01935e11i	0.229464	+	0.192543i	0.750269	−	0.661133i	$-0.229924\pi$
$853$	1.21481e11	+	1.01935e11i	0.229464	+	0.192543i	−0.520806	+	0.853675i	$0.674368\pi$
$854$	7.07455e9	−	4.08450e9i	0.0133005	−	0.00767904i
$855$		0			0
$856$	2.72489e10	−	4.71966e10i	0.0507522	−	0.0879053i
$857$	−4.47678e10	−	1.22999e11i	−0.0829933	−	0.228022i	0.891254	−	0.453505i	$-0.149826\pi$
$857$	−4.47678e10	−	1.22999e11i	−0.0829933	−	0.228022i	−0.974247	+	0.225482i	$0.927604\pi$
$858$		0			0
$859$	−3.75658e11	+	3.15214e11i	−0.689953	+	0.578940i	−0.918896	−	0.394500i	$-0.870918\pi$
$859$	−3.75658e11	+	3.15214e11i	−0.689953	+	0.578940i	0.228942	+	0.973440i	$0.426473\pi$
$860$	4.58219e10	−	1.25895e11i	0.0837682	−	0.230151i
$861$		0			0
$862$	9.27893e9	−	5.26234e10i	0.0168062	−	0.0953126i
$863$			5.93817e11i			1.07056i	0.844676	+	0.535278i	$0.179793\pi$
$863$			5.93817e11i			1.07056i	−0.844676	+	0.535278i	$0.820207\pi$
$864$		0			0
$865$	4.61813e10			0.0824900
$866$	−7.38472e10	−	1.30212e10i	−0.131299	−	0.0231516i
$867$		0			0
$868$	2.16136e10	+	7.86670e9i	0.0380757	+	0.0138584i
$869$	−1.21530e11	−	1.44834e11i	−0.213111	−	0.253976i
$870$		0			0
$871$	2.31828e11	−	8.43785e10i	0.402804	−	0.146609i
$872$	1.43523e10	+	8.28631e9i	0.0248231	+	0.0143316i
$873$		0			0
$874$	4.73471e10	+	8.20076e10i	0.0811424	+	0.140543i
$875$	−1.87551e11	+	2.23515e11i	−0.319954	+	0.381307i
$876$		0			0
$877$	1.12371e11	+	6.37288e11i	0.189957	+	1.07730i	0.919419	+	0.393280i	$0.128660\pi$
$877$	1.12371e11	+	6.37288e11i	0.189957	+	1.07730i	−0.729461	+	0.684022i	$0.760229\pi$
$878$	−1.02631e11	+	1.80966e10i	−0.172703	+	0.0304522i
$879$		0			0
$880$	4.42303e10	+	3.71136e10i	0.0737546	+	0.0618874i
$881$	−9.64127e11	+	5.56639e11i	−1.60041	+	0.923995i	−0.609002	+	0.793169i	$0.708430\pi$
$881$	−9.64127e11	+	5.56639e11i	−1.60041	+	0.923995i	−0.991405	+	0.130827i	$0.958237\pi$
$882$		0			0
$883$	1.81808e11	−	3.14901e11i	0.299068	−	0.518002i	−0.676855	−	0.736117i	$-0.736657\pi$
$883$	1.81808e11	−	3.14901e11i	0.299068	−	0.518002i	0.975923	+	0.218115i	$0.0699908\pi$
$884$	3.24688e11	+	8.92074e11i	0.531689	+	1.46080i
$885$		0			0
$886$	5.07613e10	−	4.25938e10i	0.0823754	−	0.0691212i
$887$	−1.03973e10	+	2.85665e10i	−0.0167968	+	0.0461490i	−0.947808	−	0.318843i	$-0.896706\pi$
$887$	−1.03973e10	+	2.85665e10i	−0.0167968	+	0.0461490i	0.931011	+	0.364991i	$0.118928\pi$
$888$		0			0
$889$	−2.85561e11	+	1.61950e12i	−0.457185	+	2.59282i
$890$			2.94412e9i			0.00469241i
$891$		0			0
$892$	−5.96101e11			−0.941588
$893$	−2.98497e11	−	5.26331e10i	−0.469390	−	0.0827662i
$894$		0			0
$895$	−1.57928e11	−	5.74812e10i	−0.246132	−	0.0895847i
$896$	3.02655e11	+	3.60690e11i	0.469586	+	0.559631i
$897$		0			0
$898$	−1.09767e10	+	3.99520e9i	−0.0168798	+	0.00614374i
$899$	−2.16223e10	−	1.24836e10i	−0.0331026	−	0.0191118i
$900$		0			0
$901$	3.17151e11	+	5.49322e11i	0.481246	+	0.833543i
$902$	4.89538e10	−	5.83409e10i	0.0739538	−	0.0881347i
$903$		0			0
$904$	3.55915e10	+	2.01850e11i	0.0532933	+	0.302242i
$905$	−1.88103e9	+	3.31676e8i	−0.00280415	+	0.000494448i
$906$		0			0
$907$	−5.34610e11	−	4.48591e11i	−0.789965	−	0.662860i	0.155772	−	0.987793i	$-0.450214\pi$
$907$	−5.34610e11	−	4.48591e11i	−0.789965	−	0.662860i	−0.945737	+	0.324933i	$0.894658\pi$
$908$	3.39113e11	−	1.95787e11i	0.498885	−	0.288032i
$909$		0			0
$910$	−1.08737e10	+	1.88338e10i	−0.0158567	+	0.0274646i
$911$	4.82114e10	+	1.32460e11i	0.0699965	+	0.192314i	0.969758	−	0.244068i	$-0.0784820\pi$
$911$	4.82114e10	+	1.32460e11i	0.0699965	+	0.192314i	−0.899762	+	0.436382i	$0.856260\pi$
$912$		0			0
$913$	5.91708e10	−	4.96502e10i	0.0851578	−	0.0714559i
$914$	1.40433e10	−	3.85836e10i	0.0201226	−	0.0552863i
$915$		0			0
$916$	8.56023e10	−	4.85475e11i	0.121592	−	0.689580i
$917$		−	1.58041e12i		−	2.23508i
$918$		0			0
$919$	−1.09245e10			−0.0153158			−0.00765789	−	0.999971i	$-0.502438\pi$
$919$	−1.09245e10			−0.0153158			−0.00765789	+	0.999971i	$0.502438\pi$
$920$	−4.40906e10	−	7.77436e9i	−0.0615452	−	0.0108521i
$921$		0			0
$922$	1.18885e11	+	4.32706e10i	0.164514	+	0.0598782i
$923$	2.07483e11	+	2.47268e11i	0.285874	+	0.340692i
$924$		0			0
$925$	−3.88627e10	+	1.41449e10i	−0.0530843	+	0.0193211i
$926$	−3.57736e10	−	2.06539e10i	−0.0486541	−	0.0280904i
$927$		0			0
$928$	−1.92207e11	−	3.32912e11i	−0.259166	−	0.448888i
$929$	−4.80764e11	+	5.72952e11i	−0.645459	+	0.769229i	−0.985222	−	0.171283i	$-0.945209\pi$
$929$	−4.80764e11	+	5.72952e11i	−0.645459	+	0.769229i	0.339763	+	0.940511i	$0.389653\pi$
$930$		0			0
$931$	−1.41529e11	−	8.02649e11i	−0.188385	−	1.06838i
$932$	5.57756e11	−	9.83475e10i	0.739232	−	0.130347i
$933$		0			0
$934$	9.80378e10	+	8.22635e10i	0.128827	+	0.108099i
$935$	−1.06708e11	+	6.16077e10i	−0.139620	+	0.0806099i
$936$		0			0
$937$	−7.09425e11	+	1.22876e12i	−0.920339	+	1.59407i	−0.121449	+	0.992598i	$0.538754\pi$
$937$	−7.09425e11	+	1.22876e12i	−0.920339	+	1.59407i	−0.798890	+	0.601477i	$0.794579\pi$
$938$	2.17818e10	+	5.98451e10i	0.0281373	+	0.0773067i
$939$		0			0
$940$	5.44442e10	−	4.56841e10i	0.0697333	−	0.0585132i
$941$	−4.20534e10	+	1.15541e11i	−0.0536342	+	0.147359i	−0.963617	−	0.267288i	$-0.913873\pi$
$941$	−4.20534e10	+	1.15541e11i	−0.0536342	+	0.147359i	0.909983	+	0.414647i	$0.136095\pi$
$942$		0			0
$943$	3.06281e11	−	1.73701e12i	0.387323	−	2.19662i
$944$		−	1.02760e12i		−	1.29400i
$945$		0			0
$946$	−9.02829e10			−0.112730
$947$	−6.20520e11	−	1.09414e11i	−0.771535	−	0.136042i	−0.225996	−	0.974128i	$-0.572564\pi$
$947$	−6.20520e11	−	1.09414e11i	−0.771535	−	0.136042i	−0.545539	+	0.838086i	$0.683675\pi$
$948$		0			0
$949$	5.39724e11	+	1.96443e11i	0.665437	+	0.242199i
$950$	5.58922e10	+	6.66097e10i	0.0686209	+	0.0817792i
$951$		0			0
$952$	−4.64328e11	+	1.69002e11i	−0.565297	+	0.205751i
$953$	9.29664e11	+	5.36742e11i	1.12708	+	0.650719i	0.943199	−	0.332229i	$-0.107801\pi$
$953$	9.29664e11	+	5.36742e11i	1.12708	+	0.650719i	0.183880	+	0.982949i	$0.441134\pi$
$954$		0			0
$955$	1.56396e10	+	2.70886e10i	0.0188024	+	0.0325667i
$956$	2.86992e11	−	3.42024e11i	0.343588	−	0.409472i
$957$		0			0
$958$	−7.57215e9	−	4.29438e10i	−0.00898995	−	0.0509845i
$959$	1.81649e12	−	3.20296e11i	2.14762	−	0.378684i
$960$		0			0
$961$	−6.52860e11	−	5.47815e11i	−0.765467	−	0.642303i
$962$	−5.41680e9	+	3.12739e9i	−0.00632473	+	0.00365159i
$963$		0			0
$964$	1.17695e11	−	2.03853e11i	0.136285	−	0.236053i
$965$	−4.72859e10	−	1.29917e11i	−0.0545284	−	0.149815i
$966$		0			0
$967$	1.04835e12	−	8.79666e11i	1.19894	−	1.00603i	0.199283	−	0.979942i	$-0.436139\pi$
$967$	1.04835e12	−	8.79666e11i	1.19894	−	1.00603i	0.999660	−	0.0260903i	$-0.00830575\pi$
$968$	−4.82320e10	+	1.32516e11i	−0.0549331	+	0.150927i
$969$		0			0
$970$	2.60176e9	−	1.47553e10i	0.00293887	−	0.0166671i
$971$		−	9.79743e11i		−	1.10214i	−0.834460	−	0.551068i	$-0.814220\pi$
$971$		−	9.79743e11i		−	1.10214i	0.834460	−	0.551068i	$-0.185780\pi$
$972$		0			0
$973$	4.89124e11			0.545717
$974$	5.27269e10	+	9.29718e9i	0.0585864	+	0.0103304i
$975$		0			0
$976$	−6.55492e10	−	2.38580e10i	−0.0722384	−	0.0262926i
$977$	−5.47974e11	−	6.53049e11i	−0.601425	−	0.716750i	0.376334	−	0.926484i	$-0.377185\pi$
$977$	−5.47974e11	−	6.53049e11i	−0.601425	−	0.716750i	−0.977758	+	0.209734i	$0.932740\pi$
$978$		0			0
$979$	−1.14171e11	+	4.15549e10i	−0.124287	+	0.0452368i
$980$	1.65506e11	+	9.55551e10i	0.179436	+	0.103598i
$981$		0			0
$982$	−8.13112e10	−	1.40835e11i	−0.0874388	−	0.151448i
$983$	−3.08149e10	+	3.67237e10i	−0.0330025	+	0.0393308i	−0.782293	−	0.622910i	$-0.785950\pi$
$983$	−3.08149e10	+	3.67237e10i	−0.0330025	+	0.0393308i	0.749291	+	0.662241i	$0.230395\pi$
$984$		0			0
$985$	2.38089e10	+	1.35027e11i	0.0252927	+	0.143442i
$986$	2.61974e11	−	4.61931e10i	0.277173	−	0.0488730i
$987$		0			0
$988$	−6.16926e11	−	5.17663e11i	−0.647449	−	0.543274i
$989$	−1.81078e12	+	1.04546e12i	−1.89270	+	1.09275i
$990$		0			0
$991$	−6.84665e11	+	1.18587e12i	−0.709878	+	1.22954i	0.255025	+	0.966935i	$0.417916\pi$
$991$	−6.84665e11	+	1.18587e12i	−0.709878	+	1.22954i	−0.964902	+	0.262609i	$0.915417\pi$
$992$	3.38272e9	+	9.29395e9i	0.00349317	+	0.00959740i
$993$		0			0
$994$	−6.38309e10	+	5.35604e10i	−0.0653860	+	0.0548654i
$995$	−2.87249e10	+	7.89209e10i	−0.0293066	+	0.0805193i
$996$		0			0
$997$	3.84888e10	−	2.18281e11i	0.0389542	−	0.220920i	−0.959116	−	0.283012i	$-0.908666\pi$
$997$	3.84888e10	−	2.18281e11i	0.0389542	−	0.220920i	0.998070	+	0.0620923i	$0.0197773\pi$
$998$			9.97200e10i			0.100522i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.11		138
3.2	odd	2		27.9.f.a.2.13	✓	138
27.13	even	9		27.9.f.a.14.13	yes	138
27.14	odd	18	inner	81.9.f.a.71.11		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.13	✓	138	3.2	odd	2
27.9.f.a.14.13	yes	138	27.13	even	9
81.9.f.a.8.11		138	1.1	even	1	trivial
81.9.f.a.71.11		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)

\(f(q)\)	\(=\)	\(q+(-1.99728 - 0.352174i) q^{2} +(-236.696 - 86.1504i) q^{4} +(-67.5893 - 80.5497i) q^{5} +(3385.55 - 1232.24i) q^{7} +(892.041 + 515.020i) q^{8} +(106.627 + 184.683i) q^{10} +(-5656.92 + 6741.66i) q^{11} +(4915.16 + 27875.3i) q^{13} +(-7195.84 + 1268.82i) q^{14} +(47796.6 + 40106.1i) q^{16} +(-115312. + 66575.1i) q^{17} +(56477.6 - 97822.1i) q^{19} +(9058.73 + 24888.7i) q^{20} +(13672.7 - 11472.7i) q^{22} +(141378. - 388433. i) q^{23} +(65911.4 - 373802. i) q^{25} -57405.7i q^{26} -907504. q^{28} +(970128. + 171060. i) q^{29} +(-23816.5 - 8668.51i) q^{31} +(-250836. - 298934. i) q^{32} +(253755. - 92359.3i) q^{34} +(-328083. - 189419. i) q^{35} +(-54478.7 - 94360.0i) q^{37} +(-147252. + 175488. i) q^{38} +(-18807.6 - 106663. i) q^{40} +(4.20215e6 - 740952. i) q^{41} +(-3.87489e6 - 3.25142e6i) q^{43} +(1.91977e6 - 1.10838e6i) q^{44} +(-419167. + 726019. i) q^{46} +(-917770. - 2.52155e6i) q^{47} +(5.52741e6 - 4.63805e6i) q^{49} +(-263287. + 723374. i) q^{50} +(1.23806e6 - 7.02141e6i) q^{52} -4.76381e6i q^{53} +925386. q^{55} +(3.65467e6 + 644417. i) q^{56} +(-1.87737e6 - 683308. i) q^{58} +(-1.05864e7 - 1.26163e7i) q^{59} +(-1.05057e6 + 382376. i) q^{61} +(44515.4 + 25701.0i) q^{62} +(-7.59072e6 - 1.31475e7i) q^{64} +(1.91313e6 - 2.27998e6i) q^{65} +(-1.51350e6 - 8.58350e6i) q^{67} +(3.30293e7 - 5.82395e6i) q^{68} +(588565. + 493864. i) q^{70} +(9.87592e6 - 5.70186e6i) q^{71} +(1.01458e7 - 1.75731e7i) q^{73} +(75578.1 + 207649. i) q^{74} +(-2.17954e7 + 1.82886e7i) q^{76} +(-1.08444e7 + 2.97949e7i) q^{77} +(-3.73057e6 + 2.11571e7i) q^{79} -6.56074e6i q^{80} -8.65380e6 q^{82} +(-8.64355e6 - 1.52409e6i) q^{83} +(1.31564e7 + 4.78855e6i) q^{85} +(6.59417e6 + 7.85863e6i) q^{86} +(-8.51829e6 + 3.10040e6i) q^{88} +(1.19561e7 + 6.90285e6i) q^{89} +(5.09895e7 + 8.83163e7i) q^{91} +(-6.69273e7 + 7.97608e7i) q^{92} +(945017. + 5.35946e6i) q^{94} +(-1.16968e7 + 2.06247e6i) q^{95} +(-5.38212e7 - 4.51614e7i) q^{97} +(-1.26732e7 + 7.31687e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 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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