LMFDB - Embedded newform 180.9.c.a.91.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,9,Mod(91,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.91"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$73.3281498110$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15630052 x^{14} + 100431843210026 x^{12} + \cdots + 41\!\cdots\!25 $ x^16 + 15630052x^14 + 100431843210026x^12 + 340815019972466359600x^10 + 649371842679456980126645875x^8 + 673266389314517670870339888950000x^6 + 325232066696204458027621996847496406250x^4 + 40989992790937256917294995464570014826562500*x^2 + 414509653712510017117723543124903397237712890625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{58}\cdot 3^{4}\cdot 5^{16} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.10
Root			$1316.60i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.9.c.a.91.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41320 + 15.9375i) q^{2} +(-252.006 + 45.0455i) q^{4} -279.508 q^{5} +2633.20i q^{7} +(-1074.04 - 3952.68i) q^{8} +(-395.000 - 4454.66i) q^{10} +2484.31i q^{11} +41319.8 q^{13} +(-41966.5 + 3721.22i) q^{14} +(61477.8 - 22703.5i) q^{16} +48625.0 q^{17} +241516. i q^{19} +(70437.8 - 12590.6i) q^{20} +(-39593.7 + 3510.82i) q^{22} -57735.4i q^{23} +78125.0 q^{25} +(58392.9 + 658533. i) q^{26} +(-118614. - 663581. i) q^{28} +729286. q^{29} +134865. i q^{31} +(448716. + 947716. i) q^{32} +(68716.6 + 774960. i) q^{34} -736001. i q^{35} +1.68171e6 q^{37} +(-3.84915e6 + 341309. i) q^{38} +(300205. + 1.10481e6i) q^{40} +761790. q^{41} -2.54364e6i q^{43} +(-111907. - 626061. i) q^{44} +(920156. - 81591.4i) q^{46} +5.65990e6i q^{47} -1.16893e6 q^{49} +(110406. + 1.24511e6i) q^{50} +(-1.04128e7 + 1.86127e6i) q^{52} -1.14302e7 q^{53} -694387. i q^{55} +(1.04082e7 - 2.82817e6i) q^{56} +(1.03062e6 + 1.16230e7i) q^{58} +2.12902e7i q^{59} -2.63701e7 q^{61} +(-2.14940e6 + 190590. i) q^{62} +(-1.44701e7 + 8.49070e6i) q^{64} -1.15492e7 q^{65} -1.53982e6i q^{67} +(-1.22538e7 + 2.19034e6i) q^{68} +(1.17300e7 - 1.04011e6i) q^{70} -2.06597e7i q^{71} +2.51296e7 q^{73} +(2.37658e6 + 2.68022e7i) q^{74} +(-1.08792e7 - 6.08634e7i) q^{76} -6.54169e6 q^{77} +1.95344e7i q^{79} +(-1.71836e7 + 6.34581e6i) q^{80} +(1.07656e6 + 1.21410e7i) q^{82} -2.37076e7i q^{83} -1.35911e7 q^{85} +(4.05392e7 - 3.59466e6i) q^{86} +(9.81968e6 - 2.66826e6i) q^{88} -3.86749e7 q^{89} +1.08803e8i q^{91} +(2.60072e6 + 1.45497e7i) q^{92} +(-9.02045e7 + 7.99855e6i) q^{94} -6.75057e7i q^{95} -9.46443e7 q^{97} +(-1.65192e6 - 1.86298e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.41320	+	15.9375i	0.0883247	+	0.996092i
$2$	1.41320	+	15.9375i	0.0883247	+	0.996092i
$3$		0			0
$3$		0			0
$4$	−252.006	+	45.0455i	−0.984397	+	0.175959i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$		0			0
$7$			2633.20i			1.09671i	0.836246	+	0.548354i	$0.184745\pi$
$7$			2633.20i			1.09671i	−0.836246	+	0.548354i	$0.815255\pi$
$8$	−1074.04	−	3952.68i	−0.262218	−	0.965009i
$9$		0			0
$10$	−395.000	−	4454.66i	−0.0395000	−	0.445466i
$11$			2484.31i			0.169682i	0.996395	+	0.0848410i	$0.0270382\pi$
$11$			2484.31i			0.169682i	−0.996395	+	0.0848410i	$0.972962\pi$
$12$		0			0
$13$	41319.8			1.44672			0.723360	−	0.690471i	$-0.242597\pi$
$13$	41319.8			1.44672			0.723360	+	0.690471i	$0.242597\pi$
$14$	−41966.5	+	3721.22i	−1.09242	+	0.0968665i
$15$		0			0
$16$	61477.8	−	22703.5i	0.938077	−	0.346427i
$17$	48625.0			0.582189			0.291095	−	0.956694i	$-0.405981\pi$
$17$	48625.0			0.582189			0.291095	+	0.956694i	$0.405981\pi$
$18$		0			0
$19$			241516.i			1.85324i	0.376002	+	0.926619i	$0.377299\pi$
$19$			241516.i			1.85324i	−0.376002	+	0.926619i	$0.622701\pi$
$20$	70437.8	−	12590.6i	0.440236	−	0.0786913i
$21$		0			0
$22$	−39593.7	+	3510.82i	−0.169019	+	0.0149871i
$23$		−	57735.4i		−	0.206315i	−0.994665	−	0.103158i	$-0.967105\pi$
$23$		−	57735.4i		−	0.206315i	0.994665	−	0.103158i	$-0.0328946\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	58392.9	+	658533.i	0.127781	+	1.44107i
$27$		0			0
$28$	−118614.	−	663581.i	−0.192976	−	1.07960i
$29$	729286.			1.03111			0.515556	−	0.856856i	$-0.327585\pi$
$29$	729286.			1.03111			0.515556	+	0.856856i	$0.327585\pi$
$30$		0			0
$31$			134865.i			0.146033i	0.997331	+	0.0730165i	$0.0232626\pi$
$31$			134865.i			0.146033i	−0.997331	+	0.0730165i	$0.976737\pi$
$32$	448716.	+	947716.i	0.427929	+	0.903813i
$33$		0			0
$34$	68716.6	+	774960.i	0.0514217	+	0.579914i
$35$		−	736001.i		−	0.490463i
$36$		0			0
$37$	1.68171e6			0.897313			0.448656	−	0.893704i	$-0.351903\pi$
$37$	1.68171e6			0.897313			0.448656	+	0.893704i	$0.351903\pi$
$38$	−3.84915e6	+	341309.i	−1.84599	+	0.163687i
$39$		0			0
$40$	300205.	+	1.10481e6i	0.117267	+	0.431565i
$41$	761790.			0.269588			0.134794	−	0.990874i	$-0.456963\pi$
$41$	761790.			0.269588			0.134794	+	0.990874i	$0.456963\pi$
$42$		0			0
$43$		−	2.54364e6i		−	0.744016i	−0.928230	−	0.372008i	$-0.878669\pi$
$43$		−	2.54364e6i		−	0.744016i	0.928230	−	0.372008i	$-0.121331\pi$
$44$	−111907.	−	626061.i	−0.0298571	−	0.167034i
$45$		0			0
$46$	920156.	−	81591.4i	0.205509	−	0.0182227i
$47$			5.65990e6i			1.15989i	0.814655	+	0.579946i	$0.196926\pi$
$47$			5.65990e6i			1.15989i	−0.814655	+	0.579946i	$0.803074\pi$
$48$		0			0
$49$	−1.16893e6			−0.202770
$50$	110406.	+	1.24511e6i	0.0176649	+	0.199218i
$51$		0			0
$52$	−1.04128e7	+	1.86127e6i	−1.42415	+	0.254564i
$53$	−1.14302e7			−1.44861			−0.724305	−	0.689480i	$-0.757839\pi$
$53$	−1.14302e7			−1.44861			−0.724305	+	0.689480i	$0.757839\pi$
$54$		0			0
$55$		−	694387.i		−	0.0758841i
$56$	1.04082e7	−	2.82817e6i	1.05833	−	0.287577i
$57$		0			0
$58$	1.03062e6	+	1.16230e7i	0.0910727	+	1.02708i
$59$			2.12902e7i			1.75700i	0.477740	+	0.878501i	$0.341456\pi$
$59$			2.12902e7i			1.75700i	−0.477740	+	0.878501i	$0.658544\pi$
$60$		0			0
$61$	−2.63701e7			−1.90455			−0.952276	−	0.305238i	$-0.901264\pi$
$61$	−2.63701e7			−1.90455			−0.952276	+	0.305238i	$0.901264\pi$
$62$	−2.14940e6	+	190590.i	−0.145462	+	0.0128983i
$63$		0			0
$64$	−1.44701e7	+	8.49070e6i	−0.862483	+	0.506085i
$65$	−1.15492e7			−0.646993
$66$		0			0
$67$		−	1.53982e6i		−	0.0764137i	−0.999270	−	0.0382068i	$-0.987835\pi$
$67$		−	1.53982e6i		−	0.0764137i	0.999270	−	0.0382068i	$-0.0121646\pi$
$68$	−1.22538e7	+	2.19034e6i	−0.573105	+	0.102441i
$69$		0			0
$70$	1.17300e7	−	1.04011e6i	0.488546	−	0.0433200i
$71$		−	2.06597e7i		−	0.813002i	−0.913650	−	0.406501i	$-0.866749\pi$
$71$		−	2.06597e7i		−	0.813002i	0.913650	−	0.406501i	$-0.133251\pi$
$72$		0			0
$73$	2.51296e7			0.884899			0.442449	−	0.896793i	$-0.354110\pi$
$73$	2.51296e7			0.884899			0.442449	+	0.896793i	$0.354110\pi$
$74$	2.37658e6	+	2.68022e7i	0.0792549	+	0.893806i
$75$		0			0
$76$	−1.08792e7	−	6.08634e7i	−0.326094	−	1.82432i
$77$	−6.54169e6			−0.186092
$78$		0			0
$79$			1.95344e7i			0.501525i	0.968049	+	0.250762i	$0.0806812\pi$
$79$			1.95344e7i			0.501525i	−0.968049	+	0.250762i	$0.919319\pi$
$80$	−1.71836e7	+	6.34581e6i	−0.419521	+	0.154927i
$81$		0			0
$82$	1.07656e6	+	1.21410e7i	0.0238113	+	0.268534i
$83$		−	2.37076e7i		−	0.499547i	−0.968304	−	0.249773i	$-0.919644\pi$
$83$		−	2.37076e7i		−	0.499547i	0.968304	−	0.249773i	$-0.0803561\pi$
$84$		0			0
$85$	−1.35911e7			−0.260363
$86$	4.05392e7	−	3.59466e6i	0.741108	−	0.0657150i
$87$		0			0
$88$	9.81968e6	−	2.66826e6i	0.163745	−	0.0444937i
$89$	−3.86749e7			−0.616410			−0.308205	−	0.951320i	$-0.599728\pi$
$89$	−3.86749e7			−0.616410			−0.308205	+	0.951320i	$0.599728\pi$
$90$		0			0
$91$			1.08803e8i			1.58663i
$92$	2.60072e6	+	1.45497e7i	0.0363030	+	0.203096i
$93$		0			0
$94$	−9.02045e7	+	7.99855e6i	−1.15536	+	0.102447i
$95$		−	6.75057e7i		−	0.828793i
$96$		0			0
$97$	−9.46443e7			−1.06907			−0.534537	−	0.845145i	$-0.679514\pi$
$97$	−9.46443e7			−1.06907			−0.534537	+	0.845145i	$0.679514\pi$
$98$	−1.65192e6	−	1.86298e7i	−0.0179096	−	0.201978i
$99$		0			0
$100$	−1.96879e7	+	3.51918e6i	−0.196879	+	0.0351918i
$101$	6.52649e7			0.627183			0.313591	−	0.949558i	$-0.398468\pi$
$101$	6.52649e7			0.627183			0.313591	+	0.949558i	$0.398468\pi$
$102$		0			0
$103$		−	1.47000e8i		−	1.30607i	−0.757326	−	0.653037i	$-0.773495\pi$
$103$		−	1.47000e8i		−	1.30607i	0.757326	−	0.653037i	$-0.226505\pi$
$104$	−4.43793e7	−	1.63324e8i	−0.379356	−	1.39610i
$105$		0			0
$106$	−1.61531e7	−	1.82169e8i	−0.127948	−	1.44295i
$107$			2.42429e8i			1.84948i	0.380603	+	0.924739i	$0.375716\pi$
$107$			2.42429e8i			1.84948i	−0.380603	+	0.924739i	$0.624284\pi$
$108$		0			0
$109$	−5.93486e7			−0.420440			−0.210220	−	0.977654i	$-0.567418\pi$
$109$	−5.93486e7			−0.420440			−0.210220	+	0.977654i	$0.567418\pi$
$110$	1.10668e7	−	981304.i	0.0755875	−	0.00670244i
$111$		0			0
$112$	5.97827e7	+	1.61883e8i	0.379930	+	1.02880i
$113$	−5.46199e7			−0.334994			−0.167497	−	0.985873i	$-0.553568\pi$
$113$	−5.46199e7			−0.334994			−0.167497	+	0.985873i	$0.553568\pi$
$114$		0			0
$115$			1.61375e7i			0.0922669i
$116$	−1.83784e8	+	3.28511e7i	−1.01502	+	0.181434i
$117$		0			0
$118$	−3.39312e8	+	3.00873e7i	−1.75014	+	0.155187i
$119$			1.28039e8i			0.638492i
$120$		0			0
$121$	2.08187e8			0.971208
$122$	−3.72661e7	−	4.20273e8i	−0.168219	−	1.89711i
$123$		0			0
$124$	−6.07505e6	−	3.39867e7i	−0.0256958	−	0.143755i
$125$	−2.18366e7			−0.0894427
$126$		0			0
$127$		−	2.01099e8i		−	0.773026i	−0.922284	−	0.386513i	$-0.873679\pi$
$127$		−	2.01099e8i		−	0.773026i	0.922284	−	0.386513i	$-0.126321\pi$
$128$	−1.55769e8	−	2.18617e8i	−0.580286	−	0.814413i
$129$		0			0
$130$	−1.63213e7	−	1.84065e8i	−0.0571455	−	0.644464i
$131$		−	4.36365e8i		−	1.48172i	−0.671662	−	0.740858i	$-0.734419\pi$
$131$		−	4.36365e8i		−	1.48172i	0.671662	−	0.740858i	$-0.265581\pi$
$132$		0			0
$133$	−6.35959e8			−2.03246
$134$	2.45409e7	−	2.17607e6i	0.0761151	−	0.00674922i
$135$		0			0
$136$	−5.22254e7	−	1.92199e8i	−0.152660	−	0.561818i
$137$	−4.48301e8			−1.27259			−0.636293	−	0.771447i	$-0.719533\pi$
$137$	−4.48301e8			−1.27259			−0.636293	+	0.771447i	$0.719533\pi$
$138$		0			0
$139$		−	4.73879e8i		−	1.26943i	−0.772747	−	0.634714i	$-0.781118\pi$
$139$		−	4.73879e8i		−	1.26943i	0.772747	−	0.634714i	$-0.218882\pi$
$140$	3.31535e7	+	1.85477e8i	0.0863014	+	0.482811i
$141$		0			0
$142$	3.29264e8	−	2.91963e7i	0.809825	−	0.0718082i
$143$			1.02651e8i			0.245482i
$144$		0			0
$145$	−2.03842e8			−0.461128
$146$	3.55130e7	+	4.00502e8i	0.0781584	+	0.881440i
$147$		0			0
$148$	−4.23800e8	+	7.57534e7i	−0.883312	+	0.157890i
$149$	2.98504e8			0.605627			0.302814	−	0.953050i	$-0.402074\pi$
$149$	2.98504e8			0.605627			0.302814	+	0.953050i	$0.402074\pi$
$150$		0			0
$151$			7.25032e8i			1.39460i	0.716780	+	0.697299i	$0.245615\pi$
$151$			7.25032e8i			1.39460i	−0.716780	+	0.697299i	$0.754385\pi$
$152$	9.54634e8	−	2.59399e8i	1.78839	−	0.485952i
$153$		0			0
$154$	−9.24468e6	−	1.04258e8i	−0.0164365	−	0.185364i
$155$		−	3.76958e7i		−	0.0653080i
$156$		0			0
$157$	−6.70288e8			−1.10322			−0.551611	−	0.834101i	$-0.685987\pi$
$157$	−6.70288e8			−1.10322			−0.551611	+	0.834101i	$0.685987\pi$
$158$	−3.11329e8	+	2.76060e7i	−0.499564	+	0.0442970i
$159$		0			0
$160$	−1.25420e8	−	2.64895e8i	−0.191376	−	0.404197i
$161$	1.52029e8			0.226268
$162$		0			0
$163$			9.70735e8i			1.37515i	0.726113	+	0.687575i	$0.241325\pi$
$163$			9.70735e8i			1.37515i	−0.726113	+	0.687575i	$0.758675\pi$
$164$	−1.91976e8	+	3.43152e7i	−0.265381	+	0.0474364i
$165$		0			0
$166$	3.77840e8	−	3.35035e7i	0.497594	−	0.0441223i
$167$			7.98683e8i			1.02685i	0.858133	+	0.513427i	$0.171624\pi$
$167$			7.98683e8i			1.02685i	−0.858133	+	0.513427i	$0.828376\pi$
$168$		0			0
$169$	8.91594e8			1.09300
$170$	−1.92069e7	−	2.16608e8i	−0.0229965	−	0.259345i
$171$		0			0
$172$	1.14580e8	+	6.41013e8i	0.130916	+	0.732408i
$173$	−6.00425e8			−0.670308			−0.335154	−	0.942163i	$-0.608788\pi$
$173$	−6.00425e8			−0.670308			−0.335154	+	0.942163i	$0.608788\pi$
$174$		0			0
$175$			2.05719e8i			0.219342i
$176$	5.64025e7	+	1.52730e8i	0.0587824	+	0.159175i
$177$		0			0
$178$	−5.46552e7	−	6.16380e8i	−0.0544442	−	0.614001i
$179$			1.15845e9i			1.12840i	0.825637	+	0.564202i	$0.190816\pi$
$179$			1.15845e9i			1.12840i	−0.825637	+	0.564202i	$0.809184\pi$
$180$		0			0
$181$	−7.96493e8			−0.742109			−0.371055	−	0.928611i	$-0.621004\pi$
$181$	−7.96493e8			−0.742109			−0.371055	+	0.928611i	$0.621004\pi$
$182$	−1.73405e9	+	1.53760e8i	−1.58043	+	0.140139i
$183$		0			0
$184$	−2.28209e8	+	6.20104e7i	−0.199096	+	0.0540995i
$185$	−4.70052e8			−0.401290
$186$		0			0
$187$			1.20800e8i			0.0987870i
$188$	−2.54953e8	−	1.42633e9i	−0.204094	−	1.14180i
$189$		0			0
$190$	1.07587e9	−	9.53988e7i	0.825554	−	0.0732029i
$191$			1.84245e9i			1.38440i	0.721706	+	0.692200i	$0.243358\pi$
$191$			1.84245e9i			1.38440i	−0.721706	+	0.692200i	$0.756642\pi$
$192$		0			0
$193$	2.34201e9			1.68795			0.843975	−	0.536382i	$-0.180209\pi$
$193$	2.34201e9			1.68795			0.843975	+	0.536382i	$0.180209\pi$
$194$	−1.33751e8	−	1.50839e9i	−0.0944256	−	1.06490i
$195$		0			0
$196$	2.94577e8	−	5.26550e7i	0.199606	−	0.0356792i
$197$	1.86381e9			1.23747			0.618737	−	0.785598i	$-0.287644\pi$
$197$	1.86381e9			1.23747			0.618737	+	0.785598i	$0.287644\pi$
$198$		0			0
$199$			1.82005e9i			1.16057i	0.814413	+	0.580286i	$0.197059\pi$
$199$			1.82005e9i			1.16057i	−0.814413	+	0.580286i	$0.802941\pi$
$200$	−8.39097e7	−	3.08803e8i	−0.0524436	−	0.193002i
$201$		0			0
$202$	9.22320e7	+	1.04016e9i	0.0553957	+	0.624732i
$203$			1.92035e9i			1.13083i
$204$		0			0
$205$	−2.12927e8			−0.120563
$206$	2.34280e9	−	2.07739e8i	1.30097	−	0.115359i
$207$		0			0
$208$	2.54025e9	−	9.38102e8i	1.35713	−	0.501183i
$209$	−6.00001e8			−0.314461
$210$		0			0
$211$		−	2.89129e9i		−	1.45869i	−0.684148	−	0.729344i	$-0.739826\pi$
$211$		−	2.89129e9i		−	1.45869i	0.684148	−	0.729344i	$-0.260174\pi$
$212$	2.88048e9	−	5.14880e8i	1.42601	−	0.254896i
$213$		0			0
$214$	−3.86370e9	+	3.42599e8i	−1.84225	+	0.163355i
$215$			7.10970e8i			0.332734i
$216$		0			0
$217$	−3.55125e8			−0.160156
$218$	−8.38711e7	−	9.45866e8i	−0.0371353	−	0.418797i
$219$		0			0
$220$	3.12790e7	+	1.74989e8i	0.0133525	+	0.0747001i
$221$	2.00917e9			0.842265
$222$		0			0
$223$			2.26023e9i			0.913973i	0.889474	+	0.456986i	$0.151071\pi$
$223$			2.26023e9i			0.913973i	−0.889474	+	0.456986i	$0.848929\pi$
$224$	−2.49552e9	+	1.18156e9i	−0.991219	+	0.469313i
$225$		0			0
$226$	−7.71886e7	−	8.70503e8i	−0.0295882	−	0.333685i
$227$			1.08021e9i			0.406823i	0.979093	+	0.203412i	$0.0652029\pi$
$227$			1.08021e9i			0.406823i	−0.979093	+	0.203412i	$0.934797\pi$
$228$		0			0
$229$	6.30352e8			0.229214			0.114607	−	0.993411i	$-0.463439\pi$
$229$	6.30352e8			0.229214			0.114607	+	0.993411i	$0.463439\pi$
$230$	−2.57192e8	+	2.28055e7i	−0.0919063	+	0.00814945i
$231$		0			0
$232$	−7.83286e8	−	2.88263e9i	−0.270376	−	0.995032i
$233$	−1.17430e9			−0.398435			−0.199217	−	0.979955i	$-0.563840\pi$
$233$	−1.17430e9			−0.398435			−0.199217	+	0.979955i	$0.563840\pi$
$234$		0			0
$235$		−	1.58199e9i		−	0.518720i
$236$	−9.59030e8	−	5.36526e9i	−0.309161	−	1.72959i
$237$		0			0
$238$	−2.04062e9	+	1.80944e8i	−0.635996	+	0.0563946i
$239$			3.05182e9i			0.935334i	0.883905	+	0.467667i	$0.154905\pi$
$239$			3.05182e9i			0.935334i	−0.883905	+	0.467667i	$0.845095\pi$
$240$		0			0
$241$	2.81871e9			0.835570			0.417785	−	0.908546i	$-0.362807\pi$
$241$	2.81871e9			0.835570			0.417785	+	0.908546i	$0.362807\pi$
$242$	2.94209e8	+	3.31797e9i	0.0857817	+	0.967412i
$243$		0			0
$244$	6.64542e9	−	1.18786e9i	1.87484	−	0.335123i
$245$	3.26726e8			0.0906815
$246$		0			0
$247$			9.97938e9i			2.68112i
$248$	5.33076e8	−	1.44851e8i	0.140923	−	0.0382925i
$249$		0			0
$250$	−3.08594e7	−	3.48020e8i	−0.00790000	−	0.0890932i
$251$		−	2.92571e8i		−	0.0737116i	−0.999321	−	0.0368558i	$-0.988266\pi$
$251$		−	2.92571e8i		−	0.0737116i	0.999321	−	0.0368558i	$-0.0117342\pi$
$252$		0			0
$253$	1.43433e8			0.0350079
$254$	3.20500e9	−	2.84192e8i	0.770005	−	0.0682773i
$255$		0			0
$256$	3.26407e9	−	2.79152e9i	0.759976	−	0.649951i
$257$	−3.03746e9			−0.696270			−0.348135	−	0.937444i	$-0.613185\pi$
$257$	−3.03746e9			−0.696270			−0.348135	+	0.937444i	$0.613185\pi$
$258$		0			0
$259$			4.42827e9i			0.984091i
$260$	2.91047e9	−	5.20241e8i	0.636898	−	0.113844i
$261$		0			0
$262$	6.95456e9	−	6.16669e8i	1.47593	−	0.130872i
$263$		−	1.69827e9i		−	0.354964i	−0.984124	−	0.177482i	$-0.943205\pi$
$263$		−	1.69827e9i		−	0.354964i	0.984124	−	0.177482i	$-0.0567951\pi$
$264$		0			0
$265$	3.19485e9			0.647838
$266$	−8.98734e8	−	1.01356e10i	−0.179517	−	2.02452i
$267$		0			0
$268$	6.93621e7	+	3.88044e8i	0.0134457	+	0.0752215i
$269$	8.70547e8			0.166258			0.0831291	−	0.996539i	$-0.473509\pi$
$269$	8.70547e8			0.166258			0.0831291	+	0.996539i	$0.473509\pi$
$270$		0			0
$271$		−	7.36841e9i		−	1.36614i	−0.730351	−	0.683072i	$-0.760643\pi$
$271$		−	7.36841e9i		−	1.36614i	0.730351	−	0.683072i	$-0.239357\pi$
$272$	2.98936e9	−	1.10396e9i	0.546138	−	0.201686i
$273$		0			0
$274$	−6.33537e8	−	7.14478e9i	−0.112401	−	1.26761i
$275$			1.94087e8i			0.0339364i
$276$		0			0
$277$	2.37339e9			0.403135			0.201568	−	0.979475i	$-0.435396\pi$
$277$	2.37339e9			0.403135			0.201568	+	0.979475i	$0.435396\pi$
$278$	7.55243e9	−	6.69684e8i	1.26447	−	0.112122i
$279$		0			0
$280$	−2.90917e9	+	7.90498e8i	−0.473301	+	0.128608i
$281$	−5.50733e9			−0.883315			−0.441657	−	0.897184i	$-0.645609\pi$
$281$	−5.50733e9			−0.883315			−0.441657	+	0.897184i	$0.645609\pi$
$282$		0			0
$283$		−	4.55904e9i		−	0.710768i	−0.934720	−	0.355384i	$-0.884350\pi$
$283$		−	4.55904e9i		−	0.710768i	0.934720	−	0.355384i	$-0.115650\pi$
$284$	9.30629e8	+	5.20638e9i	0.143055	+	0.800317i
$285$		0			0
$286$	−1.63600e9	+	1.45066e8i	−0.244523	+	0.0216822i
$287$			2.00594e9i			0.295659i
$288$		0			0
$289$	−4.61137e9			−0.661056
$290$	−2.88068e8	−	3.24872e9i	−0.0407290	−	0.459325i
$291$		0			0
$292$	−6.33280e9	+	1.13197e9i	−0.871092	+	0.155706i
$293$	8.27611e9			1.12294			0.561469	−	0.827498i	$-0.310237\pi$
$293$	8.27611e9			1.12294			0.561469	+	0.827498i	$0.310237\pi$
$294$		0			0
$295$		−	5.95080e9i		−	0.785756i
$296$	−1.80623e9	−	6.64725e9i	−0.235291	−	0.865914i
$297$		0			0
$298$	4.21845e8	+	4.75740e9i	0.0534918	+	0.603260i
$299$		−	2.38562e9i		−	0.298480i
$300$		0			0
$301$	6.69791e9			0.815969
$302$	−1.15552e10	+	1.02461e9i	−1.38915	+	0.123178i
$303$		0			0
$304$	5.48324e9	+	1.48479e10i	0.642012	+	1.73848i
$305$	7.37067e9			0.851742
$306$		0			0
$307$			7.73582e9i			0.870869i	0.900221	+	0.435434i	$0.143405\pi$
$307$			7.73582e9i			0.870869i	−0.900221	+	0.435434i	$0.856595\pi$
$308$	1.64854e9	−	2.94674e8i	0.183188	−	0.0327445i
$309$		0			0
$310$	6.00776e8	−	5.32715e7i	0.0650527	−	0.00576831i
$311$			1.08068e10i			1.15520i	0.816321	+	0.577599i	$0.196010\pi$
$311$			1.08068e10i			1.15520i	−0.816321	+	0.577599i	$0.803990\pi$
$312$		0			0
$313$	−4.73025e9			−0.492841			−0.246421	−	0.969163i	$-0.579254\pi$
$313$	−4.73025e9			−0.492841			−0.246421	+	0.969163i	$0.579254\pi$
$314$	−9.47248e8	−	1.06827e10i	−0.0974418	−	1.09891i
$315$		0			0
$316$	−8.79938e8	−	4.92279e9i	−0.0882478	−	0.493700i
$317$	5.44758e9			0.539469			0.269735	−	0.962935i	$-0.413064\pi$
$317$	5.44758e9			0.539469			0.269735	+	0.962935i	$0.413064\pi$
$318$		0			0
$319$			1.81178e9i			0.174961i
$320$	4.04451e9	−	2.37322e9i	0.385714	−	0.226328i
$321$		0			0
$322$	2.14846e8	+	2.42295e9i	0.0199850	+	0.225383i
$323$			1.17437e10i			1.07893i
$324$		0			0
$325$	3.22811e9			0.289344
$326$	−1.54711e10	+	1.37184e9i	−1.36978	+	0.121460i
$327$		0			0
$328$	−8.18197e8	−	3.01111e9i	−0.0706907	−	0.260154i
$329$	−1.49036e10			−1.27206
$330$		0			0
$331$		−	8.65354e8i		−	0.0720911i	−0.999350	−	0.0360456i	$-0.988524\pi$
$331$		−	8.65354e8i		−	0.0720911i	0.999350	−	0.0360456i	$-0.0114761\pi$
$332$	1.06792e9	+	5.97446e9i	0.0878997	+	0.491752i
$333$		0			0
$334$	−1.27290e10	+	1.12870e9i	−1.02284	+	0.0906966i
$335$			4.30393e8i			0.0341732i
$336$		0			0
$337$	8.64475e8			0.0670244			0.0335122	−	0.999438i	$-0.489331\pi$
$337$	8.64475e8			0.0670244			0.0335122	+	0.999438i	$0.489331\pi$
$338$	1.26000e9	+	1.42097e10i	0.0965389	+	1.08873i
$339$		0			0
$340$	3.42504e9	−	6.12218e8i	0.256301	−	0.0458132i
$341$	−3.35046e8			−0.0247792
$342$		0			0
$343$			1.21018e10i			0.874329i
$344$	−1.00542e10	+	2.73199e9i	−0.717982	+	0.195094i
$345$		0			0
$346$	−8.48518e8	−	9.56926e9i	−0.0592048	−	0.667689i
$347$			1.10077e10i			0.759239i	0.925143	+	0.379620i	$0.123945\pi$
$347$			1.10077e10i			0.759239i	−0.925143	+	0.379620i	$0.876055\pi$
$348$		0			0
$349$	−1.99631e10			−1.34563			−0.672816	−	0.739810i	$-0.734915\pi$
$349$	−1.99631e10			−1.34563			−0.672816	+	0.739810i	$0.734915\pi$
$350$	−3.27863e9	+	2.90721e8i	−0.218484	+	0.0193733i
$351$		0			0
$352$	−2.35442e9	+	1.11475e9i	−0.153361	+	0.0726118i
$353$	−1.32468e10			−0.853126			−0.426563	−	0.904458i	$-0.640276\pi$
$353$	−1.32468e10			−0.853126			−0.426563	+	0.904458i	$0.640276\pi$
$354$		0			0
$355$			5.77457e9i			0.363586i
$356$	9.74630e9	−	1.74213e9i	0.606792	−	0.108463i
$357$		0			0
$358$	−1.84627e10	+	1.63711e9i	−1.12399	+	0.0996659i
$359$		−	2.59685e9i		−	0.156340i	−0.996940	−	0.0781699i	$-0.975092\pi$
$359$		−	2.59685e9i		−	0.156340i	0.996940	−	0.0781699i	$-0.0249076\pi$
$360$		0			0
$361$	−4.13463e10			−2.43449
$362$	−1.12560e9	−	1.26941e10i	−0.0655466	−	0.739209i
$363$		0			0
$364$	−4.90109e9	−	2.74190e10i	−0.279182	−	1.56188i
$365$	−7.02393e9			−0.395739
$366$		0			0
$367$			3.62330e9i			0.199728i	0.995001	+	0.0998642i	$0.0318408\pi$
$367$			3.62330e9i			0.199728i	−0.995001	+	0.0998642i	$0.968159\pi$
$368$	−1.31079e9	−	3.54945e9i	−0.0714732	−	0.193539i
$369$		0			0
$370$	−6.64275e8	−	7.49144e9i	−0.0354439	−	0.399722i
$371$		−	3.00981e10i		−	1.58870i
$372$		0			0
$373$	4.15162e9			0.214478			0.107239	−	0.994233i	$-0.465799\pi$
$373$	4.15162e9			0.214478			0.107239	+	0.994233i	$0.465799\pi$
$374$	−1.92524e9	+	1.70714e8i	−0.0984009	+	0.00872533i
$375$		0			0
$376$	2.23718e10	−	6.07899e9i	1.11931	−	0.304145i
$377$	3.01339e10			1.49173
$378$		0			0
$379$		−	1.89551e10i		−	0.918692i	−0.888257	−	0.459346i	$-0.848084\pi$
$379$		−	1.89551e10i		−	0.918692i	0.888257	−	0.459346i	$-0.151916\pi$
$380$	3.04083e9	+	1.70118e10i	0.145834	+	0.815862i
$381$		0			0
$382$	−2.93639e10	+	2.60374e9i	−1.37899	+	0.122277i
$383$		−	8.87673e9i		−	0.412532i	−0.978496	−	0.206266i	$-0.933869\pi$
$383$		−	8.87673e9i		−	0.412532i	0.978496	−	0.206266i	$-0.0661313\pi$
$384$		0			0
$385$	1.82846e9			0.0832227
$386$	3.30972e9	+	3.73257e10i	0.149088	+	1.68135i
$387$		0			0
$388$	2.38509e10	−	4.26330e9i	1.05239	−	0.188113i
$389$	−2.05595e10			−0.897872			−0.448936	−	0.893564i	$-0.648197\pi$
$389$	−2.05595e10			−0.897872			−0.448936	+	0.893564i	$0.648197\pi$
$390$		0			0
$391$		−	2.80739e9i		−	0.120114i
$392$	1.25548e9	+	4.62040e9i	0.0531699	+	0.195675i
$393$		0			0
$394$	2.63393e9	+	2.97044e10i	0.109300	+	1.23264i
$395$		−	5.46004e9i		−	0.224289i
$396$		0			0
$397$	2.04868e10			0.824733			0.412366	−	0.911018i	$-0.364702\pi$
$397$	2.04868e10			0.824733			0.412366	+	0.911018i	$0.364702\pi$
$398$	−2.90071e10	+	2.57209e9i	−1.15604	+	0.102507i
$399$		0			0
$400$	4.80295e9	−	1.77371e9i	0.187615	−	0.0692854i
$401$	7.30576e9			0.282545			0.141273	−	0.989971i	$-0.454881\pi$
$401$	7.30576e9			0.282545			0.141273	+	0.989971i	$0.454881\pi$
$402$		0			0
$403$			5.57258e9i			0.211269i
$404$	−1.64471e10	+	2.93989e9i	−0.617397	+	0.110358i
$405$		0			0
$406$	−3.06056e10	+	2.71384e9i	−1.12641	+	0.0998802i
$407$			4.17789e9i			0.152258i
$408$		0			0
$409$	−1.05889e10			−0.378406			−0.189203	−	0.981938i	$-0.560590\pi$
$409$	−1.05889e10			−0.378406			−0.189203	+	0.981938i	$0.560590\pi$
$410$	−3.00907e8	−	3.39352e9i	−0.0106487	−	0.120092i
$411$		0			0
$412$	6.62168e9	+	3.70448e10i	0.229815	+	1.28570i
$413$	−5.60614e10			−1.92692
$414$		0			0
$415$			6.62649e9i			0.223404i
$416$	1.85408e10	+	3.91594e10i	0.619093	+	1.30756i
$417$		0			0
$418$	−8.47919e8	−	9.56250e9i	−0.0277747	−	0.313232i
$419$			2.61037e9i			0.0846928i	0.999103	+	0.0423464i	$0.0134833\pi$
$419$			2.61037e9i			0.0846928i	−0.999103	+	0.0423464i	$0.986517\pi$
$420$		0			0
$421$	9.29505e9			0.295885			0.147943	−	0.988996i	$-0.452735\pi$
$421$	9.29505e9			0.295885			0.147943	+	0.988996i	$0.452735\pi$
$422$	4.60799e10	−	4.08596e9i	1.45299	−	0.128838i
$423$		0			0
$424$	1.22766e10	+	4.51800e10i	0.379852	+	1.39792i
$425$	3.79883e9			0.116438
$426$		0			0
$427$		−	6.94377e10i		−	2.08874i
$428$	−1.09203e10	−	6.10934e10i	−0.325432	−	1.82062i
$429$		0			0
$430$	−1.13311e10	+	1.00474e9i	−0.331434	+	0.0293886i
$431$		−	1.86560e10i		−	0.540642i	−0.962770	−	0.270321i	$-0.912870\pi$
$431$		−	1.86560e10i		−	0.540642i	0.962770	−	0.270321i	$-0.0871298\pi$
$432$		0			0
$433$	−1.66970e10			−0.474994			−0.237497	−	0.971388i	$-0.576327\pi$
$433$	−1.66970e10			−0.474994			−0.237497	+	0.971388i	$0.576327\pi$
$434$	−5.01861e8	−	5.65980e9i	−0.0141457	−	0.159530i
$435$		0			0
$436$	1.49562e10	−	2.67339e9i	0.413880	−	0.0739802i
$437$	1.39440e10			0.382351
$438$		0			0
$439$			5.48360e9i			0.147641i	0.997272	+	0.0738206i	$0.0235192\pi$
$439$			5.48360e9i			0.147641i	−0.997272	+	0.0738206i	$0.976481\pi$
$440$	−2.74469e9	+	7.45802e8i	−0.0732288	+	0.0198982i
$441$		0			0
$442$	2.83936e9	+	3.20212e10i	0.0743928	+	0.838973i
$443$		−	5.97812e9i		−	0.155221i	−0.996984	−	0.0776104i	$-0.975271\pi$
$443$		−	5.97812e9i		−	0.155221i	0.996984	−	0.0776104i	$-0.0247290\pi$
$444$		0			0
$445$	1.08100e10			0.275667
$446$	−3.60223e10	+	3.19415e9i	−0.910401	+	0.0807264i
$447$		0			0
$448$	−2.23577e10	−	3.81026e10i	−0.555028	−	0.945893i
$449$	3.11696e10			0.766913			0.383456	−	0.923559i	$-0.374734\pi$
$449$	3.11696e10			0.766913			0.383456	+	0.923559i	$0.374734\pi$
$450$		0			0
$451$			1.89253e9i			0.0457442i
$452$	1.37645e10	−	2.46038e9i	0.329767	−	0.0589452i
$453$		0			0
$454$	−1.72158e10	+	1.52655e9i	−0.405233	+	0.0359325i
$455$		−	3.04114e10i		−	0.709563i
$456$		0			0
$457$	−4.33966e9			−0.0994927			−0.0497463	−	0.998762i	$-0.515841\pi$
$457$	−4.33966e9			−0.0994927			−0.0497463	+	0.998762i	$0.515841\pi$
$458$	8.90810e8	+	1.00462e10i	0.0202453	+	0.228318i
$459$		0			0
$460$	−7.26924e8	−	4.06675e9i	−0.0162352	−	0.0908273i
$461$	5.16164e10			1.14284			0.571418	−	0.820659i	$-0.306393\pi$
$461$	5.16164e10			1.14284			0.571418	+	0.820659i	$0.306393\pi$
$462$		0			0
$463$		−	6.86820e10i		−	1.49458i	−0.664499	−	0.747289i	$-0.731355\pi$
$463$		−	6.86820e10i		−	1.49458i	0.664499	−	0.747289i	$-0.268645\pi$
$464$	4.48349e10	−	1.65573e10i	0.967263	−	0.357205i
$465$		0			0
$466$	−1.65952e9	−	1.87154e10i	−0.0351916	−	0.396877i
$467$		−	2.14596e10i		−	0.451185i	−0.974222	−	0.225592i	$-0.927568\pi$
$467$		−	2.14596e10i		−	0.451185i	0.974222	−	0.225592i	$-0.0724317\pi$
$468$		0			0
$469$	4.05465e9			0.0838036
$470$	2.52129e10	−	2.23566e9i	0.516692	−	0.0458158i
$471$		0			0
$472$	8.41534e10	−	2.28667e10i	1.69552	−	0.460718i
$473$	6.31921e9			0.126246
$474$		0			0
$475$			1.88684e10i			0.370648i
$476$	−5.76759e9	−	3.22666e10i	−0.112348	−	0.628530i
$477$		0			0
$478$	−4.86382e10	+	4.31281e9i	−0.931679	+	0.0826131i
$479$		−	8.24617e10i		−	1.56643i	−0.621753	−	0.783213i	$-0.713579\pi$
$479$		−	8.24617e10i		−	1.56643i	0.621753	−	0.783213i	$-0.286421\pi$
$480$		0			0
$481$	6.94878e10			1.29816
$482$	3.98339e9	+	4.49231e10i	0.0738014	+	0.832304i
$483$		0			0
$484$	−5.24643e10	+	9.37789e9i	−0.956055	+	0.170893i
$485$	2.64539e10			0.478104
$486$		0			0
$487$			2.94674e9i			0.0523874i	0.999657	+	0.0261937i	$0.00833866\pi$
$487$			2.94674e9i			0.0523874i	−0.999657	+	0.0261937i	$0.991661\pi$
$488$	2.83227e10	+	1.04233e11i	0.499408	+	1.83791i
$489$		0			0
$490$	4.61727e8	+	5.20718e9i	0.00800942	+	0.0903271i
$491$		−	8.17812e10i		−	1.40711i	−0.710642	−	0.703554i	$-0.751595\pi$
$491$		−	8.17812e10i		−	1.40711i	0.710642	−	0.703554i	$-0.248405\pi$
$492$		0			0
$493$	3.54616e10			0.600302
$494$	−1.59046e11	+	1.41028e10i	−2.67064	+	0.236809i
$495$		0			0
$496$	3.06189e9	+	8.29118e9i	0.0505898	+	0.136990i
$497$	5.44012e10			0.891626
$498$		0			0
$499$		−	4.69562e10i		−	0.757340i	−0.925532	−	0.378670i	$-0.876382\pi$
$499$		−	4.69562e10i		−	0.757340i	0.925532	−	0.378670i	$-0.123618\pi$
$500$	5.50295e9	−	9.83641e8i	0.0880472	−	0.0157383i
$501$		0			0
$502$	4.66284e9	−	4.13460e8i	0.0734236	−	0.00651056i
$503$		−	8.89245e10i		−	1.38915i	−0.719420	−	0.694575i	$-0.755592\pi$
$503$		−	8.89245e10i		−	1.38915i	0.719420	−	0.694575i	$-0.244408\pi$
$504$		0			0
$505$	−1.82421e10			−0.280485
$506$	2.02699e8	+	2.28596e9i	0.00309207	+	0.0348711i
$507$		0			0
$508$	9.05859e9	+	5.06780e10i	0.136021	+	0.760965i
$509$	−1.30873e11			−1.94975			−0.974877	−	0.222745i	$-0.928498\pi$
$509$	−1.30873e11			−1.94975			−0.974877	+	0.222745i	$0.928498\pi$
$510$		0			0
$511$			6.61711e10i			0.970476i
$512$	4.91025e10	+	4.80761e10i	0.714535	+	0.699599i
$513$		0			0
$514$	−4.29252e9	−	4.84094e10i	−0.0614978	−	0.693549i
$515$			4.10877e10i			0.584094i
$516$		0			0
$517$	−1.40610e10			−0.196813
$518$	−7.05754e10	+	6.25801e9i	−0.980245	+	0.0869195i
$519$		0			0
$520$	1.24044e10	+	4.56504e10i	0.169653	+	0.624354i
$521$	−7.03085e10			−0.954238			−0.477119	−	0.878839i	$-0.658319\pi$
$521$	−7.03085e10			−0.954238			−0.477119	+	0.878839i	$0.658319\pi$
$522$		0			0
$523$			7.40744e10i			0.990060i	0.868876	+	0.495030i	$0.164843\pi$
$523$			7.40744e10i			0.990060i	−0.868876	+	0.495030i	$0.835157\pi$
$524$	1.96563e10	+	1.09967e11i	0.260721	+	1.45860i
$525$		0			0
$526$	2.70661e10	−	2.39999e9i	0.353577	−	0.0313521i
$527$			6.55779e9i			0.0850189i
$528$		0			0
$529$	7.49776e10			0.957434
$530$	4.51494e9	+	5.09178e10i	0.0572201	+	0.645306i
$531$		0			0
$532$	1.60265e11	−	2.86471e10i	2.00075	−	0.357630i
$533$	3.14770e10			0.390018
$534$		0			0
$535$		−	6.77609e10i		−	0.827111i
$536$	−6.08642e9	+	1.65384e9i	−0.0737399	+	0.0200370i
$537$		0			0
$538$	1.23025e9	+	1.38743e10i	0.0146847	+	0.165608i
$539$		−	2.90399e9i		−	0.0344064i
$540$		0			0
$541$	3.35458e9			0.0391605			0.0195803	−	0.999808i	$-0.493767\pi$
$541$	3.35458e9			0.0391605			0.0195803	+	0.999808i	$0.493767\pi$
$542$	1.17434e11	−	1.04130e10i	1.36081	−	0.120664i
$543$		0			0
$544$	2.18188e10	+	4.60827e10i	0.249135	+	0.526190i
$545$	1.65884e10			0.188027
$546$		0			0
$547$			1.13812e11i			1.27128i	0.771987	+	0.635638i	$0.219263\pi$
$547$			1.13812e11i			1.27128i	−0.771987	+	0.635638i	$0.780737\pi$
$548$	1.12974e11	−	2.01939e10i	1.25273	−	0.223923i
$549$		0			0
$550$	−3.09325e9	+	2.74283e8i	−0.0338038	+	0.00299742i
$551$			1.76134e11i			1.91090i
$552$		0			0
$553$	−5.14380e10			−0.550026
$554$	3.35407e9	+	3.78259e10i	0.0356068	+	0.401560i
$555$		0			0
$556$	2.13461e10	+	1.19420e11i	0.223367	+	1.24962i
$557$	1.05403e11			1.09505			0.547524	−	0.836790i	$-0.315570\pi$
$557$	1.05403e11			1.09505			0.547524	+	0.836790i	$0.315570\pi$
$558$		0			0
$559$		−	1.05103e11i		−	1.07638i
$560$	−1.67098e10	−	4.52477e10i	−0.169910	−	0.460092i
$561$		0			0
$562$	−7.78293e9	−	8.77728e10i	−0.0780185	−	0.879862i
$563$			7.97945e10i			0.794217i	0.917772	+	0.397108i	$0.129986\pi$
$563$			7.97945e10i			0.794217i	−0.917772	+	0.397108i	$0.870014\pi$
$564$		0			0
$565$	1.52667e10			0.149814
$566$	7.26596e10	−	6.44282e9i	0.707990	−	0.0627784i
$567$		0			0
$568$	−8.16613e10	+	2.21895e10i	−0.784554	+	0.213184i
$569$	4.57243e10			0.436212			0.218106	−	0.975925i	$-0.430012\pi$
$569$	4.57243e10			0.436212			0.218106	+	0.975925i	$0.430012\pi$
$570$		0			0
$571$		−	2.16780e10i		−	0.203927i	−0.994788	−	0.101964i	$-0.967487\pi$
$571$		−	2.16780e10i		−	0.203927i	0.994788	−	0.101964i	$-0.0325126\pi$
$572$	−4.62398e9	−	2.58687e10i	−0.0431948	−	0.241652i
$573$		0			0
$574$	−3.19697e10	+	2.83479e9i	−0.294504	+	0.0261140i
$575$		−	4.51058e9i		−	0.0412630i
$576$		0			0
$577$	1.69273e11			1.52716			0.763579	−	0.645715i	$-0.223440\pi$
$577$	1.69273e11			1.52716			0.763579	+	0.645715i	$0.223440\pi$
$578$	−6.51676e9	−	7.34935e10i	−0.0583876	−	0.658472i
$579$		0			0
$580$	5.13693e10	−	9.18215e9i	0.453933	−	0.0811395i
$581$	6.24269e10			0.547857
$582$		0			0
$583$		−	2.83963e10i		−	0.245803i
$584$	−2.69903e10	−	9.93290e10i	−0.232036	−	0.853935i
$585$		0			0
$586$	1.16958e10	+	1.31900e11i	0.0991831	+	1.11855i
$587$		−	3.75401e10i		−	0.316187i	−0.987424	−	0.158093i	$-0.949465\pi$
$587$		−	3.75401e10i		−	0.316187i	0.987424	−	0.158093i	$-0.0505347\pi$
$588$		0			0
$589$	−3.25719e10			−0.270634
$590$	9.48407e10	−	8.40965e9i	0.782685	−	0.0694016i
$591$		0			0
$592$	1.03388e11	−	3.81806e10i	0.841748	−	0.310854i
$593$	−1.04118e11			−0.841994			−0.420997	−	0.907062i	$-0.638320\pi$
$593$	−1.04118e11			−0.841994			−0.420997	+	0.907062i	$0.638320\pi$
$594$		0			0
$595$		−	3.57881e10i		−	0.285542i
$596$	−7.52248e10	+	1.34463e10i	−0.596178	+	0.106566i
$597$		0			0
$598$	3.80207e10	−	3.37134e9i	0.297314	−	0.0263632i
$599$		−	4.81442e10i		−	0.373970i	−0.982363	−	0.186985i	$-0.940128\pi$
$599$		−	4.81442e10i		−	0.373970i	0.982363	−	0.186985i	$-0.0598716\pi$
$600$		0			0
$601$	−1.48443e11			−1.13779			−0.568896	−	0.822410i	$-0.692629\pi$
$601$	−1.48443e11			−1.13779			−0.568896	+	0.822410i	$0.692629\pi$
$602$	9.46546e9	+	1.06748e11i	0.0720702	+	0.812780i
$603$		0			0
$604$	−3.26594e10	−	1.82712e11i	−0.245392	−	1.37284i
$605$	−5.81901e10			−0.434337
$606$		0			0
$607$		−	5.44460e10i		−	0.401062i	−0.979687	−	0.200531i	$-0.935733\pi$
$607$		−	5.44460e10i		−	0.401062i	0.979687	−	0.200531i	$-0.0642667\pi$
$608$	−2.28888e11	+	1.08372e11i	−1.67498	+	0.793054i
$609$		0			0
$610$	1.04162e10	+	1.17470e11i	0.0752298	+	0.848413i
$611$			2.33866e11i			1.67804i
$612$		0			0
$613$	1.16278e11			0.823484			0.411742	−	0.911301i	$-0.364921\pi$
$613$	1.16278e11			0.823484			0.411742	+	0.911301i	$0.364921\pi$
$614$	−1.23289e11	+	1.09322e10i	−0.867465	+	0.0769192i
$615$		0			0
$616$	7.02607e9	+	2.58572e10i	0.0487966	+	0.179580i
$617$	4.87411e10			0.336321			0.168161	−	0.985760i	$-0.446217\pi$
$617$	4.87411e10			0.336321			0.168161	+	0.985760i	$0.446217\pi$
$618$		0			0
$619$			4.92280e10i			0.335312i	0.985846	+	0.167656i	$0.0536198\pi$
$619$			4.92280e10i			0.335312i	−0.985846	+	0.167656i	$0.946380\pi$
$620$	1.69803e9	+	9.49956e9i	0.0114915	+	0.0642890i
$621$		0			0
$622$	−1.72233e11	+	1.52721e10i	−1.15068	+	0.102033i
$623$		−	1.01839e11i		−	0.676022i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	−6.68477e9	−	7.53882e10i	−0.0435300	−	0.490915i
$627$		0			0
$628$	1.68916e11	−	3.01935e10i	1.08601	−	0.194122i
$629$	8.17731e10			0.522406
$630$		0			0
$631$			1.10376e11i			0.696240i	0.937450	+	0.348120i	$0.113180\pi$
$631$			1.10376e11i			0.696240i	−0.937450	+	0.348120i	$0.886820\pi$
$632$	7.72132e10	−	2.09808e10i	0.483976	−	0.131509i
$633$		0			0
$634$	7.69850e9	+	8.68207e10i	0.0476485	+	0.537361i
$635$			5.62088e10i			0.345708i
$636$		0			0
$637$	−4.82999e10			−0.293352
$638$	−2.88751e10	+	2.56039e9i	−0.174277	+	0.0154534i
$639$		0			0
$640$	4.35388e10	+	6.11054e10i	0.259512	+	0.364217i
$641$	−2.15342e11			−1.27554			−0.637772	−	0.770225i	$-0.720144\pi$
$641$	−2.15342e11			−1.27554			−0.637772	+	0.770225i	$0.720144\pi$
$642$		0			0
$643$			1.22051e11i			0.713996i	0.934105	+	0.356998i	$0.116200\pi$
$643$			1.22051e11i			0.713996i	−0.934105	+	0.356998i	$0.883800\pi$
$644$	−3.83121e10	+	6.84821e9i	−0.222737	+	0.0398138i
$645$		0			0
$646$	−1.87165e11	+	1.65962e10i	−1.07472	+	0.0952966i
$647$		−	2.92452e11i		−	1.66893i	−0.551064	−	0.834463i	$-0.685778\pi$
$647$		−	2.92452e11i		−	1.66893i	0.551064	−	0.834463i	$-0.314222\pi$
$648$		0			0
$649$	−5.28916e10			−0.298132
$650$	4.56195e9	+	5.14479e10i	0.0255562	+	0.288213i
$651$		0			0
$652$	−4.37272e10	−	2.44631e11i	−0.241970	−	1.35369i
$653$	2.80990e10			0.154539			0.0772696	−	0.997010i	$-0.475380\pi$
$653$	2.80990e10			0.154539			0.0772696	+	0.997010i	$0.475380\pi$
$654$		0			0
$655$			1.21968e11i			0.662644i
$656$	4.68332e10	−	1.72953e10i	0.252894	−	0.0933925i
$657$		0			0
$658$	−2.10618e10	−	2.37526e11i	−0.112355	−	1.26709i
$659$		−	2.51394e11i		−	1.33295i	−0.745529	−	0.666473i	$-0.767803\pi$
$659$		−	2.51394e11i		−	1.33295i	0.745529	−	0.666473i	$-0.232197\pi$
$660$		0			0
$661$	−2.53415e11			−1.32748			−0.663738	−	0.747965i	$-0.731031\pi$
$661$	−2.53415e11			−1.32748			−0.663738	+	0.747965i	$0.731031\pi$
$662$	1.37915e10	−	1.22291e9i	0.0718094	−	0.00636743i
$663$		0			0
$664$	−9.37086e10	+	2.54631e10i	−0.482067	+	0.130990i
$665$	1.77756e11			0.908945
$666$		0			0
$667$		−	4.21056e10i		−	0.212734i
$668$	−3.59771e10	−	2.01273e11i	−0.180684	−	1.01083i
$669$		0			0
$670$	−6.85938e9	+	6.08230e8i	−0.0340397	+	0.00301834i
$671$		−	6.55116e10i		−	0.323168i
$672$		0			0
$673$	−1.77857e11			−0.866981			−0.433491	−	0.901158i	$-0.642718\pi$
$673$	−1.77857e11			−0.866981			−0.433491	+	0.901158i	$0.642718\pi$
$674$	1.22167e9	+	1.37775e10i	0.00591991	+	0.0667624i
$675$		0			0
$676$	−2.24687e11	+	4.01623e10i	−1.07595	+	0.192323i
$677$	2.43910e11			1.16111			0.580556	−	0.814220i	$-0.302835\pi$
$677$	2.43910e11			1.16111			0.580556	+	0.814220i	$0.302835\pi$
$678$		0			0
$679$		−	2.49217e11i		−	1.17246i
$680$	1.45975e10	+	5.37212e10i	0.0682718	+	0.251252i
$681$		0			0
$682$	−4.73485e8	−	5.33978e9i	−0.00218861	−	0.0246823i
$683$			2.74209e11i			1.26008i	0.776562	+	0.630041i	$0.216962\pi$
$683$			2.74209e11i			1.26008i	−0.776562	+	0.630041i	$0.783038\pi$
$684$		0			0
$685$	1.25304e11			0.569118
$686$	−1.92873e11	+	1.71023e10i	−0.870912	+	0.0772249i
$687$		0			0
$688$	−5.77495e10	−	1.56378e11i	−0.257747	−	0.697944i
$689$	−4.72295e11			−2.09573
$690$		0			0
$691$		−	1.07912e11i		−	0.473323i	−0.971592	−	0.236661i	$-0.923947\pi$
$691$		−	1.07912e11i		−	0.473323i	0.971592	−	0.236661i	$-0.0760532\pi$
$692$	1.51311e11	−	2.70465e10i	0.659850	−	0.117947i
$693$		0			0
$694$	−1.75435e11	+	1.55560e10i	−0.756272	+	0.0670596i
$695$			1.32453e11i			0.567706i
$696$		0			0
$697$	3.70421e10			0.156951
$698$	−2.82118e10	−	3.18161e11i	−0.118853	−	1.34037i
$699$		0			0
$700$	−9.26670e9	−	5.18423e10i	−0.0385952	−	0.215919i
$701$	1.00364e11			0.415630			0.207815	−	0.978168i	$-0.433365\pi$
$701$	1.00364e11			0.415630			0.207815	+	0.978168i	$0.433365\pi$
$702$		0			0
$703$			4.06159e11i			1.66293i
$704$	−2.10936e10	−	3.59482e10i	−0.0858735	−	0.146348i
$705$		0			0
$706$	−1.87204e10	−	2.11121e11i	−0.0753521	−	0.849791i
$707$			1.71855e11i			0.687837i
$708$		0			0
$709$	−4.36108e11			−1.72587			−0.862937	−	0.505311i	$-0.831378\pi$
$709$	−4.36108e11			−1.72587			−0.862937	+	0.505311i	$0.831378\pi$
$710$	−9.20321e10	+	8.16060e9i	−0.362165	+	0.0321136i
$711$		0			0
$712$	4.15386e10	+	1.52869e11i	0.161634	+	0.594841i
$713$	7.78647e9			0.0301288
$714$		0			0
$715$		−	2.86919e10i		−	0.109783i
$716$	−5.21829e10	−	2.91936e11i	−0.198553	−	1.11080i
$717$		0			0
$718$	4.13872e10	−	3.66986e9i	0.155729	−	0.0138087i
$719$			3.29910e11i			1.23447i	0.786780	+	0.617234i	$0.211747\pi$
$719$			3.29910e11i			1.23447i	−0.786780	+	0.617234i	$0.788253\pi$
$720$		0			0
$721$	3.87079e11			1.43238
$722$	−5.84304e10	−	6.58956e11i	−0.215026	−	2.42498i
$723$		0			0
$724$	2.00721e11	−	3.58784e10i	0.730531	−	0.130581i
$725$	5.69755e10			0.206222
$726$		0			0
$727$		−	2.87638e11i		−	1.02969i	−0.857282	−	0.514847i	$-0.827849\pi$
$727$		−	2.87638e11i		−	1.02969i	0.857282	−	0.514847i	$-0.172151\pi$
$728$	4.30064e11	−	1.16859e11i	1.53111	−	0.416043i
$729$		0			0
$730$	−9.92618e9	−	1.11944e11i	−0.0349535	−	0.394192i
$731$		−	1.23685e11i		−	0.433158i
$732$		0			0
$733$	7.34639e10			0.254483			0.127241	−	0.991872i	$-0.459388\pi$
$733$	7.34639e10			0.254483			0.127241	+	0.991872i	$0.459388\pi$
$734$	−5.77462e10	+	5.12043e9i	−0.198948	+	0.0176410i
$735$		0			0
$736$	5.47168e10	−	2.59068e10i	0.186470	−	0.0882881i
$737$	3.82540e9			0.0129660
$738$		0			0
$739$		−	3.53166e11i		−	1.18413i	−0.805889	−	0.592067i	$-0.798312\pi$
$739$		−	3.53166e11i		−	1.18413i	0.805889	−	0.592067i	$-0.201688\pi$
$740$	1.18456e11	−	2.11737e10i	0.395029	−	0.0706107i
$741$		0			0
$742$	4.79687e11	−	4.25344e10i	1.58249	−	0.140322i
$743$			2.51184e11i			0.824208i	0.911137	+	0.412104i	$0.135206\pi$
$743$			2.51184e11i			0.824208i	−0.911137	+	0.412104i	$0.864794\pi$
$744$		0			0
$745$	−8.34345e10			−0.270845
$746$	5.86705e9	+	6.61663e10i	0.0189437	+	0.213639i
$747$		0			0
$748$	−5.44149e9	−	3.04422e10i	−0.0173825	−	0.0972456i
$749$	−6.38363e11			−2.02834
$750$		0			0
$751$			5.06685e11i			1.59286i	0.604729	+	0.796431i	$0.293281\pi$
$751$			5.06685e11i			1.59286i	−0.604729	+	0.796431i	$0.706719\pi$
$752$	1.28499e11	+	3.47958e11i	0.401818	+	1.08807i
$753$		0			0
$754$	4.25852e10	+	4.80259e11i	0.131757	+	1.48590i
$755$		−	2.02653e11i		−	0.623684i
$756$		0			0
$757$	9.66712e10			0.294384			0.147192	−	0.989108i	$-0.452977\pi$
$757$	9.66712e10			0.294384			0.147192	+	0.989108i	$0.452977\pi$
$758$	3.02097e11	−	2.67873e10i	0.915102	−	0.0811432i
$759$		0			0
$760$	−2.66828e11	+	7.25042e10i	−0.799793	+	0.217324i
$761$	−5.18752e11			−1.54675			−0.773376	−	0.633947i	$-0.781434\pi$
$761$	−5.18752e11			−1.54675			−0.773376	+	0.633947i	$0.781434\pi$
$762$		0			0
$763$		−	1.56276e11i		−	0.461100i
$764$	−8.29940e10	−	4.64307e11i	−0.243598	−	1.36280i
$765$		0			0
$766$	1.41473e11	−	1.25446e10i	0.410920	−	0.0364368i
$767$			8.79708e11i			2.54189i
$768$		0			0
$769$	1.06291e11			0.303943			0.151972	−	0.988385i	$-0.451438\pi$
$769$	1.06291e11			0.303943			0.151972	+	0.988385i	$0.451438\pi$
$770$	2.58397e9	+	2.91410e10i	0.00735062	+	0.0828975i
$771$		0			0
$772$	−5.90200e11	+	1.05497e11i	−1.66161	+	0.297010i
$773$	9.89630e10			0.277176			0.138588	−	0.990350i	$-0.455744\pi$
$773$	9.89630e10			0.277176			0.138588	+	0.990350i	$0.455744\pi$
$774$		0			0
$775$			1.05363e10i			0.0292066i
$776$	1.01652e11	+	3.74098e11i	0.280330	+	1.03167i
$777$		0			0
$778$	−2.90546e10	−	3.27666e11i	−0.0793043	−	0.894363i
$779$			1.83984e11i			0.499610i
$780$		0			0
$781$	5.13253e10			0.137952
$782$	4.47426e10	−	3.96738e9i	0.119645	−	0.0106091i
$783$		0			0
$784$	−7.18632e10	+	2.65387e10i	−0.190214	+	0.0702451i
$785$	1.87351e11			0.493376
$786$		0			0
$787$			3.29755e11i			0.859592i	0.902926	+	0.429796i	$0.141415\pi$
$787$			3.29755e11i			0.859592i	−0.902926	+	0.429796i	$0.858585\pi$
$788$	−4.69690e11	+	8.39562e10i	−1.21817	+	0.217745i
$789$		0			0
$790$	8.70192e10	−	7.71610e9i	0.223412	−	0.0198102i
$791$		−	1.43825e11i		−	0.367391i
$792$		0			0
$793$	−1.08961e12			−2.75535
$794$	2.89519e10	+	3.26509e11i	0.0728443	+	0.821509i
$795$		0			0
$796$	−8.19853e10	−	4.58664e11i	−0.204213	−	1.14246i
$797$	−6.85369e10			−0.169860			−0.0849300	−	0.996387i	$-0.527067\pi$
$797$	−6.85369e10			−0.169860			−0.0849300	+	0.996387i	$0.527067\pi$
$798$		0			0
$799$			2.75213e11i			0.675277i
$800$	3.50559e10	+	7.40403e10i	0.0855857	+	0.180763i
$801$		0			0
$802$	1.03245e10	+	1.16435e11i	0.0249557	+	0.281441i
$803$			6.24297e10i			0.150151i
$804$		0			0
$805$	−4.24933e10			−0.101190
$806$	−8.88128e10	+	7.87514e9i	−0.210443	+	0.0186603i
$807$		0			0
$808$	−7.00974e10	−	2.57971e11i	−0.164459	−	0.605237i
$809$	7.62508e11			1.78012			0.890062	−	0.455840i	$-0.150661\pi$
$809$	7.62508e11			1.78012			0.890062	+	0.455840i	$0.150661\pi$
$810$		0			0
$811$			4.40805e11i			1.01897i	0.860478	+	0.509487i	$0.170165\pi$
$811$			4.40805e11i			1.01897i	−0.860478	+	0.509487i	$0.829835\pi$
$812$	−8.65034e10	−	4.83940e11i	−0.198980	−	1.11319i
$813$		0			0
$814$	−6.65850e10	+	5.90418e9i	−0.151663	+	0.0134481i
$815$		−	2.71329e11i		−	0.614986i
$816$		0			0
$817$	6.14330e11			1.37884
$818$	−1.49642e10	−	1.68761e11i	−0.0334226	−	0.376927i
$819$		0			0
$820$	5.36588e10	−	9.59140e9i	0.118682	−	0.0212142i
$821$	2.67657e11			0.589123			0.294562	−	0.955632i	$-0.404826\pi$
$821$	2.67657e11			0.589123			0.294562	+	0.955632i	$0.404826\pi$
$822$		0			0
$823$			3.84869e11i			0.838906i	0.907777	+	0.419453i	$0.137778\pi$
$823$			3.84869e11i			0.838906i	−0.907777	+	0.419453i	$0.862222\pi$
$824$	−5.81042e11	+	1.57884e11i	−1.26037	+	0.342476i
$825$		0			0
$826$	−7.92257e10	−	8.93477e11i	−0.170195	−	1.91939i
$827$			4.88174e11i			1.04364i	0.853054	+	0.521822i	$0.174747\pi$
$827$			4.88174e11i			1.04364i	−0.853054	+	0.521822i	$0.825253\pi$
$828$		0			0
$829$	−1.47134e11			−0.311526			−0.155763	−	0.987794i	$-0.549784\pi$
$829$	−1.47134e11			−0.311526			−0.155763	+	0.987794i	$0.549784\pi$
$830$	−1.05609e11	+	9.36452e9i	−0.222531	+	0.0197321i
$831$		0			0
$832$	−5.97900e11	+	3.50834e11i	−1.24777	+	0.732164i
$833$	−5.68392e10			−0.118050
$834$		0			0
$835$		−	2.23239e11i		−	0.459223i
$836$	1.51204e11	−	2.70273e10i	0.309555	−	0.0553323i
$837$		0			0
$838$	−4.16027e10	+	3.68896e9i	−0.0843617	+	0.00748046i
$839$		−	4.39919e11i		−	0.887821i	−0.896071	−	0.443910i	$-0.853591\pi$
$839$		−	4.39919e11i		−	0.887821i	0.896071	−	0.443910i	$-0.146409\pi$
$840$		0			0
$841$	3.16120e10			0.0631929
$842$	1.31357e10	+	1.48140e11i	0.0261340	+	0.294729i
$843$		0			0
$844$	1.30240e11	+	7.28622e11i	0.256669	+	1.43593i
$845$	−2.49208e11			−0.488804
$846$		0			0
$847$			5.48198e11i			1.06513i
$848$	−7.02705e11	+	2.59506e11i	−1.35891	+	0.501838i
$849$		0			0
$850$	5.36849e9	+	6.05437e10i	0.0102843	+	0.115983i
$851$		−	9.70941e10i		−	0.185129i
$852$		0			0
$853$	6.98819e11			1.31998			0.659992	−	0.751273i	$-0.270560\pi$
$853$	6.98819e11			1.31998			0.659992	+	0.751273i	$0.270560\pi$
$854$	1.10666e12	−	9.81291e10i	2.08058	−	0.184487i
$855$		0			0
$856$	9.58242e11	−	2.60379e11i	1.78476	−	0.484966i
$857$	−3.28226e10			−0.0608485			−0.0304242	−	0.999537i	$-0.509686\pi$
$857$	−3.28226e10			−0.0608485			−0.0304242	+	0.999537i	$0.509686\pi$
$858$		0			0
$859$		−	6.28697e11i		−	1.15470i	−0.816497	−	0.577349i	$-0.804087\pi$
$859$		−	6.28697e11i		−	1.15470i	0.816497	−	0.577349i	$-0.195913\pi$
$860$	−3.20260e10	−	1.79168e11i	−0.0585476	−	0.327543i
$861$		0			0
$862$	2.97330e11	−	2.63646e10i	0.538529	−	0.0477521i
$863$			7.90308e11i			1.42480i	0.701775	+	0.712399i	$0.252391\pi$
$863$			7.90308e11i			1.42480i	−0.701775	+	0.712399i	$0.747609\pi$
$864$		0			0
$865$	1.67824e11			0.299771
$866$	−2.35962e10	−	2.66109e11i	−0.0419537	−	0.473138i
$867$		0			0
$868$	8.94936e10	−	1.59968e10i	0.157657	−	0.0281809i
$869$	−4.85296e10			−0.0850997
$870$		0			0
$871$		−	6.36251e10i		−	0.110549i
$872$	6.37430e10	+	2.34586e11i	0.110247	+	0.405728i
$873$		0			0
$874$	1.97056e10	+	2.22232e11i	0.0337710	+	0.380857i
$875$		−	5.75001e10i		−	0.0980926i
$876$		0			0
$877$	7.21024e10			0.121885			0.0609427	−	0.998141i	$-0.480589\pi$
$877$	7.21024e10			0.121885			0.0609427	+	0.998141i	$0.480589\pi$
$878$	−8.73947e10	+	7.74940e9i	−0.147064	+	0.0130404i
$879$		0			0
$880$	−1.57650e10	−	4.26894e10i	−0.0262883	−	0.0711851i
$881$	5.33265e11			0.885196			0.442598	−	0.896720i	$-0.354057\pi$
$881$	5.33265e11			0.885196			0.442598	+	0.896720i	$0.354057\pi$
$882$		0			0
$883$			3.49301e11i			0.574589i	0.957842	+	0.287295i	$0.0927559\pi$
$883$			3.49301e11i			0.574589i	−0.957842	+	0.287295i	$0.907244\pi$
$884$	−5.06324e11	+	9.05043e10i	−0.829123	+	0.148204i
$885$		0			0
$886$	9.52761e10	−	8.44825e9i	0.154614	−	0.0137098i
$887$		−	2.17981e11i		−	0.352148i	−0.984377	−	0.176074i	$-0.943660\pi$
$887$		−	2.17981e11i		−	0.352148i	0.984377	−	0.176074i	$-0.0563398\pi$
$888$		0			0
$889$	5.29532e11			0.847784
$890$	1.52766e10	+	1.72284e11i	0.0243482	+	0.274589i
$891$		0			0
$892$	−1.01813e11	−	5.69591e11i	−0.160822	−	0.899712i
$893$	−1.36696e12			−2.14956
$894$		0			0
$895$		−	3.23796e11i		−	0.504637i
$896$	5.75663e11	−	4.10171e11i	0.893174	−	0.636405i
$897$		0			0
$898$	4.40488e10	+	4.96765e11i	0.0677374	+	0.763916i
$899$			9.83549e10i			0.150577i
$900$		0			0
$901$	−5.55795e11			−0.843365
$902$	−3.01621e10	+	2.67451e9i	−0.0455654	+	0.00404034i
$903$		0			0
$904$	5.86642e10	+	2.15895e11i	0.0878414	+	0.323272i
$905$	2.22627e11			0.331881
$906$		0			0
$907$			6.26742e9i			0.00926104i	0.999989	+	0.00463052i	$0.00147395\pi$
$907$			6.26742e9i			0.00926104i	−0.999989	+	0.00463052i	$0.998526\pi$
$908$	−4.86587e10	−	2.72220e11i	−0.0715842	−	0.400476i
$909$		0			0
$910$	4.84681e11	−	4.29773e10i	0.706790	−	0.0626719i
$911$			6.22008e11i			0.903073i	0.892253	+	0.451536i	$0.149124\pi$
$911$			6.22008e11i			0.903073i	−0.892253	+	0.451536i	$0.850876\pi$
$912$		0			0
$913$	5.88972e10			0.0847640
$914$	−6.13279e9	−	6.91632e10i	−0.00878766	−	0.0991038i
$915$		0			0
$916$	−1.58852e11	+	2.83945e10i	−0.225638	+	0.0403323i
$917$	1.14904e12			1.62501
$918$		0			0
$919$		−	8.27760e11i		−	1.16049i	−0.814441	−	0.580246i	$-0.802956\pi$
$919$		−	8.27760e11i		−	1.16049i	0.814441	−	0.580246i	$-0.197044\pi$
$920$	6.37865e10	−	1.73324e10i	0.0890384	−	0.0241940i
$921$		0			0
$922$	7.29441e10	+	8.22635e11i	0.100941	+	1.13837i
$923$		−	8.53656e11i		−	1.17619i
$924$		0			0
$925$	1.31383e11			0.179463
$926$	1.09462e12	−	9.70610e10i	1.48874	−	0.132008i
$927$		0			0
$928$	3.27242e11	+	6.91156e11i	0.441243	+	0.931932i
$929$	6.50031e11			0.872713			0.436356	−	0.899774i	$-0.356269\pi$
$929$	6.50031e11			0.872713			0.436356	+	0.899774i	$0.356269\pi$
$930$		0			0
$931$		−	2.82315e11i		−	0.375781i
$932$	2.95931e11	−	5.28971e10i	0.392218	−	0.0701082i
$933$		0			0
$934$	3.42012e11	−	3.03266e10i	0.449421	−	0.0398508i
$935$		−	3.37646e10i		−	0.0441789i
$936$		0			0
$937$	−6.60322e11			−0.856639			−0.428319	−	0.903627i	$-0.640894\pi$
$937$	−6.60322e11			−0.856639			−0.428319	+	0.903627i	$0.640894\pi$
$938$	5.73002e9	+	6.46209e10i	0.00740193	+	0.0834760i
$939$		0			0
$940$	7.12616e10	+	3.98671e11i	0.0912734	+	0.510626i
$941$	2.13315e11			0.272059			0.136029	−	0.990705i	$-0.456566\pi$
$941$	2.13315e11			0.272059			0.136029	+	0.990705i	$0.456566\pi$
$942$		0			0
$943$		−	4.39823e10i		−	0.0556200i
$944$	4.83362e11	+	1.30888e12i	0.608674	+	1.64820i
$945$		0			0
$946$	8.93027e9	+	1.00712e11i	0.0111506	+	0.125753i
$947$			1.23955e10i			0.0154121i	0.999970	+	0.00770607i	$0.00245294\pi$
$947$			1.23955e10i			0.0154121i	−0.999970	+	0.00770607i	$0.997547\pi$
$948$		0			0
$949$	1.03835e12			1.28020
$950$	−3.00715e11	+	2.66648e10i	−0.369199	+	0.0327373i
$951$		0			0
$952$	5.06098e11	−	1.37520e11i	0.616150	−	0.167424i
$953$	1.59801e12			1.93734			0.968672	−	0.248344i	$-0.0798864\pi$
$953$	1.59801e12			1.93734			0.968672	+	0.248344i	$0.0798864\pi$
$954$		0			0
$955$		−	5.14980e11i		−	0.619122i
$956$	−1.37471e11	−	7.69076e11i	−0.164581	−	0.920741i
$957$		0			0
$958$	1.31423e12	−	1.16534e11i	1.56030	−	0.138354i
$959$		−	1.18046e12i		−	1.39566i
$960$		0			0
$961$	8.34703e11			0.978674
$962$	9.81999e10	+	1.10746e12i	0.114660	+	1.29309i
$963$		0			0
$964$	−7.10332e11	+	1.26970e11i	−0.822533	+	0.147026i
$965$	−6.54612e11			−0.754875
$966$		0			0
$967$			4.54304e11i			0.519566i	0.965667	+	0.259783i	$0.0836510\pi$
$967$			4.54304e11i			0.519566i	−0.965667	+	0.259783i	$0.916349\pi$
$968$	−2.23602e11	−	8.22896e11i	−0.254668	−	0.937224i
$969$		0			0
$970$	3.73845e10	+	4.21608e11i	0.0422284	+	0.476236i
$971$			3.98175e11i			0.447917i	0.974599	+	0.223958i	$0.0718979\pi$
$971$			3.98175e11i			0.447917i	−0.974599	+	0.223958i	$0.928102\pi$
$972$		0			0
$973$	1.24782e12			1.39219
$974$	−4.69636e10	+	4.16432e9i	−0.0521826	+	0.00462710i
$975$		0			0
$976$	−1.62118e12	+	5.98693e11i	−1.78662	+	0.659789i
$977$	−1.61846e12			−1.77633			−0.888165	−	0.459525i	$-0.848020\pi$
$977$	−1.61846e12			−1.77633			−0.888165	+	0.459525i	$0.848020\pi$
$978$		0			0
$979$		−	9.60806e10i		−	0.104594i
$980$	−8.23367e10	+	1.47175e10i	−0.0892667	+	0.0159562i
$981$		0			0
$982$	1.30339e12	−	1.15573e11i	1.40161	−	0.124282i
$983$		−	7.83368e10i		−	0.0838980i	−0.999120	−	0.0419490i	$-0.986643\pi$
$983$		−	7.83368e10i		−	0.0838980i	0.999120	−	0.0419490i	$-0.0133567\pi$
$984$		0			0
$985$	−5.20950e11			−0.553416
$986$	5.01141e10	+	5.65167e11i	0.0530215	+	0.597956i
$987$		0			0
$988$	−4.49526e11	−	2.51486e12i	−0.471767	−	2.63929i
$989$	−1.46858e11			−0.153502
$990$		0			0
$991$		−	1.11925e12i		−	1.16046i	−0.814451	−	0.580232i	$-0.802962\pi$
$991$		−	1.11925e12i		−	1.16046i	0.814451	−	0.580232i	$-0.197038\pi$
$992$	−1.27813e11	+	6.05159e10i	−0.131987	+	0.0624917i
$993$		0			0
$994$	7.68795e10	+	8.67017e11i	0.0787526	+	0.888142i
$995$		−	5.08721e11i		−	0.519023i
$996$		0			0
$997$	−8.38483e11			−0.848621			−0.424311	−	0.905517i	$-0.639483\pi$
$997$	−8.38483e11			−0.848621			−0.424311	+	0.905517i	$0.639483\pi$
$998$	7.48363e11	−	6.63583e10i	0.754380	−	0.0668918i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.a.91.10		16
3.2	odd	2		20.9.b.a.11.7	✓	16
4.3	odd	2	inner	180.9.c.a.91.9		16
12.11	even	2		20.9.b.a.11.8	yes	16
15.2	even	4		100.9.d.c.99.31		32
15.8	even	4		100.9.d.c.99.2		32
15.14	odd	2		100.9.b.d.51.10		16
24.5	odd	2		320.9.b.d.191.6		16
24.11	even	2		320.9.b.d.191.11		16
60.23	odd	4		100.9.d.c.99.32		32
60.47	odd	4		100.9.d.c.99.1		32
60.59	even	2		100.9.b.d.51.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.7	✓	16	3.2	odd	2
20.9.b.a.11.8	yes	16	12.11	even	2
100.9.b.d.51.9		16	60.59	even	2
100.9.b.d.51.10		16	15.14	odd	2
100.9.d.c.99.1		32	60.47	odd	4
100.9.d.c.99.2		32	15.8	even	4
100.9.d.c.99.31		32	15.2	even	4
100.9.d.c.99.32		32	60.23	odd	4
180.9.c.a.91.9		16	4.3	odd	2	inner
180.9.c.a.91.10		16	1.1	even	1	trivial
320.9.b.d.191.6		16	24.5	odd	2
320.9.b.d.191.11		16	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41320 + 15.9375i) q^{2} +(-252.006 + 45.0455i) q^{4} -279.508 q^{5} +2633.20i q^{7} +(-1074.04 - 3952.68i) q^{8} +(-395.000 - 4454.66i) q^{10} +2484.31i q^{11} +41319.8 q^{13} +(-41966.5 + 3721.22i) q^{14} +(61477.8 - 22703.5i) q^{16} +48625.0 q^{17} +241516. i q^{19} +(70437.8 - 12590.6i) q^{20} +(-39593.7 + 3510.82i) q^{22} -57735.4i q^{23} +78125.0 q^{25} +(58392.9 + 658533. i) q^{26} +(-118614. - 663581. i) q^{28} +729286. q^{29} +134865. i q^{31} +(448716. + 947716. i) q^{32} +(68716.6 + 774960. i) q^{34} -736001. i q^{35} +1.68171e6 q^{37} +(-3.84915e6 + 341309. i) q^{38} +(300205. + 1.10481e6i) q^{40} +761790. q^{41} -2.54364e6i q^{43} +(-111907. - 626061. i) q^{44} +(920156. - 81591.4i) q^{46} +5.65990e6i q^{47} -1.16893e6 q^{49} +(110406. + 1.24511e6i) q^{50} +(-1.04128e7 + 1.86127e6i) q^{52} -1.14302e7 q^{53} -694387. i q^{55} +(1.04082e7 - 2.82817e6i) q^{56} +(1.03062e6 + 1.16230e7i) q^{58} +2.12902e7i q^{59} -2.63701e7 q^{61} +(-2.14940e6 + 190590. i) q^{62} +(-1.44701e7 + 8.49070e6i) q^{64} -1.15492e7 q^{65} -1.53982e6i q^{67} +(-1.22538e7 + 2.19034e6i) q^{68} +(1.17300e7 - 1.04011e6i) q^{70} -2.06597e7i q^{71} +2.51296e7 q^{73} +(2.37658e6 + 2.68022e7i) q^{74} +(-1.08792e7 - 6.08634e7i) q^{76} -6.54169e6 q^{77} +1.95344e7i q^{79} +(-1.71836e7 + 6.34581e6i) q^{80} +(1.07656e6 + 1.21410e7i) q^{82} -2.37076e7i q^{83} -1.35911e7 q^{85} +(4.05392e7 - 3.59466e6i) q^{86} +(9.81968e6 - 2.66826e6i) q^{88} -3.86749e7 q^{89} +1.08803e8i q^{91} +(2.60072e6 + 1.45497e7i) q^{92} +(-9.02045e7 + 7.99855e6i) q^{94} -6.75057e7i q^{95} -9.46443e7 q^{97} +(-1.65192e6 - 1.86298e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

Introduction

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