LMFDB - Embedded newform 180.9.c.a.91.5

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			91.5
Root			$-1970.29i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.9.c.a.91.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.3498 - 11.2775i) q^{2} +(1.63618 + 255.995i) q^{4} +279.508 q^{5} -3940.57i q^{7} +(2868.41 - 2923.94i) q^{8} +(-3172.37 - 3152.16i) q^{10} +17097.0i q^{11} +10938.7 q^{13} +(-44439.8 + 44724.8i) q^{14} +(-65530.6 + 837.705i) q^{16} -101666. q^{17} +93432.1i q^{19} +(457.325 + 71552.7i) q^{20} +(192811. - 194047. i) q^{22} -147346. i q^{23} +78125.0 q^{25} +(-124152. - 123361. i) q^{26} +(1.00877e6 - 6447.48i) q^{28} -41637.4 q^{29} -138577. i q^{31} +(753207. + 729514. i) q^{32} +(1.15389e6 + 1.14653e6i) q^{34} -1.10142e6i q^{35} +1.14978e6 q^{37} +(1.05368e6 - 1.06044e6i) q^{38} +(801745. - 817267. i) q^{40} -3.83906e6 q^{41} -3.18959e6i q^{43} +(-4.37673e6 + 27973.6i) q^{44} +(-1.66170e6 + 1.67235e6i) q^{46} -3.51218e6i q^{47} -9.76332e6 q^{49} +(-886704. - 881054. i) q^{50} +(17897.6 + 2.80024e6i) q^{52} -5.66612e6 q^{53} +4.77874e6i q^{55} +(-1.15220e7 - 1.13032e7i) q^{56} +(472576. + 469565. i) q^{58} +1.69068e7i q^{59} -5.16010e6 q^{61} +(-1.56280e6 + 1.57282e6i) q^{62} +(-321668. - 1.67741e7i) q^{64} +3.05745e6 q^{65} -1.05358e7i q^{67} +(-166343. - 2.60259e7i) q^{68} +(-1.24213e7 + 1.25009e7i) q^{70} +1.85971e7i q^{71} +2.38535e6 q^{73} +(-1.30498e7 - 1.29666e7i) q^{74} +(-2.39181e7 + 152871. i) q^{76} +6.73718e7 q^{77} +4.42560e7i q^{79} +(-1.83164e7 + 234146. i) q^{80} +(4.35726e7 + 4.32950e7i) q^{82} +1.51824e7i q^{83} -2.84164e7 q^{85} +(-3.59706e7 + 3.62013e7i) q^{86} +(4.99905e7 + 4.90411e7i) q^{88} +5.42739e7 q^{89} -4.31047e7i q^{91} +(3.77199e7 - 241085. i) q^{92} +(-3.96086e7 + 3.98625e7i) q^{94} +2.61151e7i q^{95} -1.24798e8 q^{97} +(1.10812e8 + 1.10106e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.3498	−	11.2775i	−0.709363	−	0.704843i
$2$	−11.3498	−	11.2775i	−0.709363	−	0.704843i
$3$		0			0
$3$		0			0
$4$	1.63618	+	255.995i	0.00639132	+	0.999980i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$		0			0
$7$		−	3940.57i		−	1.64122i	−0.571487	−	0.820611i	$-0.693633\pi$
$7$		−	3940.57i		−	1.64122i	0.571487	−	0.820611i	$-0.306367\pi$
$8$	2868.41	−	2923.94i	0.700295	−	0.713853i
$9$		0			0
$10$	−3172.37	−	3152.16i	−0.317237	−	0.315216i
$11$			17097.0i			1.16775i	0.811845	+	0.583873i	$0.198463\pi$
$11$			17097.0i			1.16775i	−0.811845	+	0.583873i	$0.801537\pi$
$12$		0			0
$13$	10938.7			0.382994			0.191497	−	0.981493i	$-0.438666\pi$
$13$	10938.7			0.382994			0.191497	+	0.981493i	$0.438666\pi$
$14$	−44439.8	+	44724.8i	−1.15680	+	1.16422i
$15$		0			0
$16$	−65530.6	+	837.705i	−0.999918	+	0.0127824i
$17$	−101666.			−1.21725			−0.608624	−	0.793459i	$-0.708278\pi$
$17$	−101666.			−1.21725			−0.608624	+	0.793459i	$0.708278\pi$
$18$		0			0
$19$			93432.1i			0.716938i	0.933542	+	0.358469i	$0.116701\pi$
$19$			93432.1i			0.716938i	−0.933542	+	0.358469i	$0.883299\pi$
$20$	457.325	+	71552.7i	0.00285828	+	0.447204i
$21$		0			0
$22$	192811.	−	194047.i	0.823078	−	0.828355i
$23$		−	147346.i		−	0.526536i	−0.964723	−	0.263268i	$-0.915200\pi$
$23$		−	147346.i		−	0.526536i	0.964723	−	0.263268i	$-0.0848003\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	−124152.	−	123361.i	−0.271681	−	0.269951i
$27$		0			0
$28$	1.00877e6	−	6447.48i	1.64119	−	0.0104896i
$29$	−41637.4			−0.0588696			−0.0294348	−	0.999567i	$-0.509371\pi$
$29$	−41637.4			−0.0588696			−0.0294348	+	0.999567i	$0.509371\pi$
$30$		0			0
$31$		−	138577.i		−	0.150052i	−0.997182	−	0.0750262i	$-0.976096\pi$
$31$		−	138577.i		−	0.150052i	0.997182	−	0.0750262i	$-0.0239040\pi$
$32$	753207.	+	729514.i	0.718314	+	0.695719i
$33$		0			0
$34$	1.15389e6	+	1.14653e6i	0.863470	+	0.857969i
$35$		−	1.10142e6i		−	0.733977i
$36$		0			0
$37$	1.14978e6			0.613489			0.306745	−	0.951792i	$-0.400760\pi$
$37$	1.14978e6			0.613489			0.306745	+	0.951792i	$0.400760\pi$
$38$	1.05368e6	−	1.06044e6i	0.505329	−	0.508569i
$39$		0			0
$40$	801745.	−	817267.i	0.313182	−	0.319245i
$41$	−3.83906e6			−1.35859			−0.679297	−	0.733864i	$-0.737715\pi$
$41$	−3.83906e6			−1.35859			−0.679297	+	0.733864i	$0.737715\pi$
$42$		0			0
$43$		−	3.18959e6i		−	0.932956i	−0.884533	−	0.466478i	$-0.845523\pi$
$43$		−	3.18959e6i		−	0.932956i	0.884533	−	0.466478i	$-0.154477\pi$
$44$	−4.37673e6	+	27973.6i	−1.16772	+	0.00746343i
$45$		0			0
$46$	−1.66170e6	+	1.67235e6i	−0.371125	+	0.373505i
$47$		−	3.51218e6i		−	0.719756i	−0.932999	−	0.359878i	$-0.882818\pi$
$47$		−	3.51218e6i		−	0.719756i	0.932999	−	0.359878i	$-0.117182\pi$
$48$		0			0
$49$	−9.76332e6			−1.69361
$50$	−886704.	−	881054.i	−0.141873	−	0.140969i
$51$		0			0
$52$	17897.6	+	2.80024e6i	0.00244783	+	0.382986i
$53$	−5.66612e6			−0.718096			−0.359048	−	0.933319i	$-0.616899\pi$
$53$	−5.66612e6			−0.718096			−0.359048	+	0.933319i	$0.616899\pi$
$54$		0			0
$55$			4.77874e6i			0.522231i
$56$	−1.15220e7	−	1.13032e7i	−1.17159	−	1.14934i
$57$		0			0
$58$	472576.	+	469565.i	0.0417599	+	0.0414939i
$59$			1.69068e7i			1.39525i	0.716461	+	0.697627i	$0.245761\pi$
$59$			1.69068e7i			1.39525i	−0.716461	+	0.697627i	$0.754239\pi$
$60$		0			0
$61$	−5.16010e6			−0.372682			−0.186341	−	0.982485i	$-0.559663\pi$
$61$	−5.16010e6			−0.372682			−0.186341	+	0.982485i	$0.559663\pi$
$62$	−1.56280e6	+	1.57282e6i	−0.105763	+	0.106442i
$63$		0			0
$64$	−321668.	−	1.67741e7i	−0.0191729	−	0.999816i
$65$	3.05745e6			0.171280
$66$		0			0
$67$		−	1.05358e7i		−	0.522838i	−0.965225	−	0.261419i	$-0.915810\pi$
$67$		−	1.05358e7i		−	0.522838i	0.965225	−	0.261419i	$-0.0841904\pi$
$68$	−166343.	−	2.60259e7i	−0.00777981	−	1.21722i
$69$		0			0
$70$	−1.24213e7	+	1.25009e7i	−0.517339	+	0.520656i
$71$			1.85971e7i			0.731833i	0.930648	+	0.365916i	$0.119244\pi$
$71$			1.85971e7i			0.731833i	−0.930648	+	0.365916i	$0.880756\pi$
$72$		0			0
$73$	2.38535e6			0.0839964			0.0419982	−	0.999118i	$-0.486628\pi$
$73$	2.38535e6			0.0839964			0.0419982	+	0.999118i	$0.486628\pi$
$74$	−1.30498e7	−	1.29666e7i	−0.435186	−	0.432414i
$75$		0			0
$76$	−2.39181e7	+	152871.i	−0.716923	+	0.00458218i
$77$	6.73718e7			1.91653
$78$		0			0
$79$			4.42560e7i			1.13622i	0.822951	+	0.568112i	$0.192326\pi$
$79$			4.42560e7i			1.13622i	−0.822951	+	0.568112i	$0.807674\pi$
$80$	−1.83164e7	+	234146.i	−0.447177	+	0.00571645i
$81$		0			0
$82$	4.35726e7	+	4.32950e7i	0.963736	+	0.957596i
$83$			1.51824e7i			0.319910i	0.987124	+	0.159955i	$0.0511349\pi$
$83$			1.51824e7i			0.319910i	−0.987124	+	0.159955i	$0.948865\pi$
$84$		0			0
$85$	−2.84164e7			−0.544369
$86$	−3.59706e7	+	3.62013e7i	−0.657588	+	0.661805i
$87$		0			0
$88$	4.99905e7	+	4.90411e7i	0.833599	+	0.817766i
$89$	5.42739e7			0.865030			0.432515	−	0.901627i	$-0.357626\pi$
$89$	5.42739e7			0.865030			0.432515	+	0.901627i	$0.357626\pi$
$90$		0			0
$91$		−	4.31047e7i		−	0.628577i
$92$	3.77199e7	−	241085.i	0.526525	−	0.00336526i
$93$		0			0
$94$	−3.96086e7	+	3.98625e7i	−0.507315	+	0.510568i
$95$			2.61151e7i			0.320624i
$96$		0			0
$97$	−1.24798e8			−1.40968			−0.704841	−	0.709365i	$-0.748982\pi$
$97$	−1.24798e8			−1.40968			−0.704841	+	0.709365i	$0.748982\pi$
$98$	1.10812e8	+	1.10106e8i	1.20138	+	1.19373i
$99$		0			0
$100$	127826.	+	1.99996e7i	0.00127826	+	0.199996i
$101$	−1.96354e8			−1.88693			−0.943463	−	0.331478i	$-0.892453\pi$
$101$	−1.96354e8			−1.88693			−0.943463	+	0.331478i	$0.892453\pi$
$102$		0			0
$103$			1.08404e8i			0.963152i	0.876404	+	0.481576i	$0.159935\pi$
$103$			1.08404e8i			0.963152i	−0.876404	+	0.481576i	$0.840065\pi$
$104$	3.13766e7	−	3.19841e7i	0.268209	−	0.273401i
$105$		0			0
$106$	6.43094e7	+	6.38996e7i	0.509390	+	0.506145i
$107$		−	5.19293e7i		−	0.396166i	−0.980185	−	0.198083i	$-0.936528\pi$
$107$		−	5.19293e7i		−	0.396166i	0.980185	−	0.198083i	$-0.0634715\pi$
$108$		0			0
$109$	2.01131e8			1.42486			0.712432	−	0.701741i	$-0.247594\pi$
$109$	2.01131e8			1.42486			0.712432	+	0.701741i	$0.247594\pi$
$110$	5.38923e7	−	5.42378e7i	0.368091	−	0.370452i
$111$		0			0
$112$	3.30104e6	+	2.58228e8i	0.0209787	+	1.64109i
$113$	6.82663e7			0.418690			0.209345	−	0.977842i	$-0.432867\pi$
$113$	6.82663e7			0.418690			0.209345	+	0.977842i	$0.432867\pi$
$114$		0			0
$115$		−	4.11845e7i		−	0.235474i
$116$	−68126.1	−	1.06590e7i	−0.000376254	−	0.0588684i
$117$		0			0
$118$	1.90666e8	−	1.91889e8i	0.983435	−	0.989741i
$119$			4.00621e8i			1.99777i
$120$		0			0
$121$	−7.79470e7			−0.363629
$122$	5.85661e7	+	5.81930e7i	0.264367	+	0.262683i
$123$		0			0
$124$	3.54749e7	−	226736.i	0.150049	−	0.000959032i
$125$	2.18366e7			0.0894427
$126$		0			0
$127$			3.48984e8i			1.34150i	0.741683	+	0.670751i	$0.234028\pi$
$127$			3.48984e8i			1.34150i	−0.741683	+	0.670751i	$0.765972\pi$
$128$	−1.85519e8	+	1.94011e8i	−0.691113	+	0.722746i
$129$		0			0
$130$	−3.47015e7	−	3.44804e7i	−0.121500	−	0.120726i
$131$			1.49192e8i			0.506596i	0.967388	+	0.253298i	$0.0815153\pi$
$131$			1.49192e8i			0.506596i	−0.967388	+	0.253298i	$0.918485\pi$
$132$		0			0
$133$	3.68176e8			1.17665
$134$	−1.18817e8	+	1.19579e8i	−0.368519	+	0.370882i
$135$		0			0
$136$	−2.91619e8	+	2.97265e8i	−0.852433	+	0.868936i
$137$	−6.05661e8			−1.71928			−0.859642	−	0.510897i	$-0.829313\pi$
$137$	−6.05661e8			−1.71928			−0.859642	+	0.510897i	$0.829313\pi$
$138$		0			0
$139$			5.19290e8i			1.39107i	0.718490	+	0.695537i	$0.244834\pi$
$139$			5.19290e8i			1.39107i	−0.718490	+	0.695537i	$0.755166\pi$
$140$	2.81959e8	−	1.80212e6i	0.733962	−	0.00469108i
$141$		0			0
$142$	2.09729e8	−	2.11074e8i	0.515828	−	0.519135i
$143$			1.87018e8i			0.447239i
$144$		0			0
$145$	−1.16380e7			−0.0263273
$146$	−2.70732e7	−	2.69008e7i	−0.0595839	−	0.0592043i
$147$		0			0
$148$	1.88124e6	+	2.94337e8i	0.00392100	+	0.613477i
$149$	6.13964e8			1.24565			0.622827	−	0.782359i	$-0.285984\pi$
$149$	6.13964e8			1.24565			0.622827	+	0.782359i	$0.285984\pi$
$150$		0			0
$151$			5.41162e8i			1.04093i	0.853884	+	0.520463i	$0.174241\pi$
$151$			5.41162e8i			1.04093i	−0.853884	+	0.520463i	$0.825759\pi$
$152$	2.73190e8	+	2.68001e8i	0.511788	+	0.502068i
$153$		0			0
$154$	−7.64657e8	−	7.59785e8i	−1.35951	−	1.35085i
$155$		−	3.87333e7i		−	0.0671055i
$156$		0			0
$157$	−6.43982e8			−1.05993			−0.529963	−	0.848021i	$-0.677794\pi$
$157$	−6.43982e8			−1.05993			−0.529963	+	0.848021i	$0.677794\pi$
$158$	4.99097e8	−	5.02297e8i	0.800860	−	0.805995i
$159$		0			0
$160$	2.10528e8	+	2.03905e8i	0.321240	+	0.311135i
$161$	−5.80629e8			−0.864162
$162$		0			0
$163$			6.74607e8i			0.955653i	0.878454	+	0.477826i	$0.158575\pi$
$163$			6.74607e8i			0.955653i	−0.878454	+	0.477826i	$0.841425\pi$
$164$	−6.28138e6	−	9.82780e8i	−0.00868320	−	1.35857i
$165$		0			0
$166$	1.71219e8	−	1.72317e8i	0.225486	−	0.226932i
$167$			4.55554e8i			0.585699i	0.956159	+	0.292849i	$0.0946035\pi$
$167$			4.55554e8i			0.585699i	−0.956159	+	0.292849i	$0.905397\pi$
$168$		0			0
$169$	−6.96076e8			−0.853316
$170$	3.22521e8	+	3.20466e8i	0.386155	+	0.383695i
$171$		0			0
$172$	8.16519e8	−	5.21874e6i	0.932937	−	0.00596282i
$173$	−9.64344e8			−1.07658			−0.538292	−	0.842759i	$-0.680930\pi$
$173$	−9.64344e8			−1.07658			−0.538292	+	0.842759i	$0.680930\pi$
$174$		0			0
$175$		−	3.07857e8i		−	0.328244i
$176$	−1.43222e7	−	1.12037e9i	−0.0149265	−	1.16765i
$177$		0			0
$178$	−6.15998e8	−	6.12074e8i	−0.613620	−	0.609711i
$179$		−	1.01365e9i		−	0.987363i	−0.869643	−	0.493682i	$-0.835651\pi$
$179$		−	1.01365e9i		−	0.987363i	0.869643	−	0.493682i	$-0.164349\pi$
$180$		0			0
$181$	1.51507e8			0.141162			0.0705812	−	0.997506i	$-0.477515\pi$
$181$	1.51507e8			0.141162			0.0705812	+	0.997506i	$0.477515\pi$
$182$	−4.86113e8	+	4.89230e8i	−0.443049	+	0.445889i
$183$		0			0
$184$	−4.30832e8	−	4.22649e8i	−0.375869	−	0.368730i
$185$	3.21373e8			0.274361
$186$		0			0
$187$		−	1.73817e9i		−	1.42143i
$188$	8.99099e8	−	5.74654e6i	0.719741	−	0.00460019i
$189$		0			0
$190$	2.94512e8	−	2.96401e8i	0.225990	−	0.227439i
$191$			5.46186e8i			0.410399i	0.978720	+	0.205200i	$0.0657844\pi$
$191$			5.46186e8i			0.410399i	−0.978720	+	0.205200i	$0.934216\pi$
$192$		0			0
$193$	1.52005e9			1.09554			0.547771	−	0.836628i	$-0.315477\pi$
$193$	1.52005e9			1.09554			0.547771	+	0.836628i	$0.315477\pi$
$194$	1.41643e9	+	1.40741e9i	0.999976	+	0.993605i
$195$		0			0
$196$	−1.59745e7	−	2.49936e9i	−0.0108244	−	1.69358i
$197$	−1.98770e9			−1.31974			−0.659868	−	0.751382i	$-0.729388\pi$
$197$	−1.98770e9			−1.31974			−0.659868	+	0.751382i	$0.729388\pi$
$198$		0			0
$199$			1.68735e9i			1.07595i	0.842960	+	0.537976i	$0.180811\pi$
$199$			1.68735e9i			1.07595i	−0.842960	+	0.537976i	$0.819189\pi$
$200$	2.24095e8	−	2.28433e8i	0.140059	−	0.142771i
$201$		0			0
$202$	2.22858e9	+	2.21438e9i	1.33852	+	1.32999i
$203$			1.64075e8i			0.0966182i
$204$		0			0
$205$	−1.07305e9			−0.607582
$206$	1.22252e9	−	1.23036e9i	0.678872	−	0.683224i
$207$		0			0
$208$	−7.16819e8	+	9.16339e6i	−0.382962	+	0.00489556i
$209$	−1.59740e9			−0.837201
$210$		0			0
$211$		−	3.55239e9i		−	1.79222i	−0.443834	−	0.896109i	$-0.646382\pi$
$211$		−	3.55239e9i		−	1.79222i	0.443834	−	0.896109i	$-0.353618\pi$
$212$	−9.27077e6	−	1.45050e9i	−0.00458958	−	0.718081i
$213$		0			0
$214$	−5.85632e8	+	5.89387e8i	−0.279235	+	0.281025i
$215$		−	8.91518e8i		−	0.417231i
$216$		0			0
$217$	−5.46071e8			−0.246269
$218$	−2.28280e9	−	2.26826e9i	−1.01075	−	1.00431i
$219$		0			0
$220$	−1.22333e9	+	7.81887e6i	−0.522221	+	0.00333775i
$221$	−1.11209e9			−0.466198
$222$		0			0
$223$			1.41187e9i			0.570920i	0.958391	+	0.285460i	$0.0921465\pi$
$223$			1.41187e9i			0.570920i	−0.958391	+	0.285460i	$0.907854\pi$
$224$	2.87470e9	−	2.96807e9i	1.14183	−	1.17891i
$225$		0			0
$226$	−7.74809e8	−	7.69873e8i	−0.297003	−	0.295111i
$227$			1.08981e9i			0.410438i	0.978716	+	0.205219i	$0.0657906\pi$
$227$			1.08981e9i			0.410438i	−0.978716	+	0.205219i	$0.934209\pi$
$228$		0			0
$229$	−2.25807e9			−0.821097			−0.410549	−	0.911839i	$-0.634663\pi$
$229$	−2.25807e9			−0.821097			−0.410549	+	0.911839i	$0.634663\pi$
$230$	−4.64458e8	+	4.67436e8i	−0.165972	+	0.167036i
$231$		0			0
$232$	−1.19433e8	+	1.21745e8i	−0.0412261	+	0.0420243i
$233$	−6.52483e8			−0.221384			−0.110692	−	0.993855i	$-0.535307\pi$
$233$	−6.52483e8			−0.221384			−0.110692	+	0.993855i	$0.535307\pi$
$234$		0			0
$235$		−	9.81684e8i		−	0.321885i
$236$	−4.32805e9	+	2.76625e7i	−1.39522	+	0.00891750i
$237$		0			0
$238$	4.51800e9	−	4.54697e9i	1.40812	−	1.41715i
$239$			4.79300e9i			1.46898i	0.678619	+	0.734490i	$0.262579\pi$
$239$			4.79300e9i			1.46898i	−0.678619	+	0.734490i	$0.737421\pi$
$240$		0			0
$241$	−5.18381e9			−1.53667			−0.768335	−	0.640048i	$-0.778915\pi$
$241$	−5.18381e9			−1.53667			−0.768335	+	0.640048i	$0.778915\pi$
$242$	8.84683e8	+	8.79047e8i	0.257945	+	0.256301i
$243$		0			0
$244$	−8.44283e6	−	1.32096e9i	−0.00238193	−	0.372675i
$245$	−2.72893e9			−0.757405
$246$		0			0
$247$			1.02202e9i			0.274583i
$248$	−4.05190e8	−	3.97494e8i	−0.107115	−	0.105081i
$249$		0			0
$250$	−2.47841e8	−	2.46262e8i	−0.0634473	−	0.0630431i
$251$			2.41878e9i			0.609398i	0.952449	+	0.304699i	$0.0985558\pi$
$251$			2.41878e9i			0.609398i	−0.952449	+	0.304699i	$0.901444\pi$
$252$		0			0
$253$	2.51917e9			0.614859
$254$	3.93567e9	−	3.96090e9i	0.945548	−	0.951611i
$255$		0			0
$256$	4.29356e9	−	1.09791e8i	0.999673	−	0.0255627i
$257$	5.25554e9			1.20472			0.602358	−	0.798226i	$-0.294228\pi$
$257$	5.25554e9			1.20472			0.602358	+	0.798226i	$0.294228\pi$
$258$		0			0
$259$		−	4.53078e9i		−	1.00687i
$260$	5.00253e6	+	7.82692e8i	0.00109470	+	0.171276i
$261$		0			0
$262$	1.68252e9	−	1.69331e9i	0.357071	−	0.359360i
$263$			1.24951e9i			0.261165i	0.991437	+	0.130583i	$0.0416848\pi$
$263$			1.24951e9i			0.261165i	−0.991437	+	0.130583i	$0.958315\pi$
$264$		0			0
$265$	−1.58373e9			−0.321142
$266$	−4.17873e9	−	4.15210e9i	−0.834675	−	0.829357i
$267$		0			0
$268$	2.69710e9	−	1.72384e7i	0.522827	−	0.00334162i
$269$	5.36357e9			1.02434			0.512171	−	0.858884i	$-0.328841\pi$
$269$	5.36357e9			1.02434			0.512171	+	0.858884i	$0.328841\pi$
$270$		0			0
$271$			6.72329e8i			0.124654i	0.998056	+	0.0623268i	$0.0198521\pi$
$271$			6.72329e8i			0.124654i	−0.998056	+	0.0623268i	$0.980148\pi$
$272$	6.66222e9	−	8.51659e7i	1.21715	−	0.0155593i
$273$		0			0
$274$	6.87414e9	+	6.83034e9i	1.21960	+	1.21183i
$275$			1.33570e9i			0.233549i
$276$		0			0
$277$	8.55117e9			1.45247			0.726234	−	0.687448i	$-0.241269\pi$
$277$	8.55117e9			1.45247			0.726234	+	0.687448i	$0.241269\pi$
$278$	5.85629e9	−	5.89384e9i	0.980490	−	0.986777i
$279$		0			0
$280$	−3.22050e9	−	3.15934e9i	−0.523952	−	0.514001i
$281$	8.47677e8			0.135958			0.0679791	−	0.997687i	$-0.478345\pi$
$281$	8.47677e8			0.135958			0.0679791	+	0.997687i	$0.478345\pi$
$282$		0			0
$283$		−	2.59848e9i		−	0.405111i	−0.979271	−	0.202555i	$-0.935075\pi$
$283$		−	2.59848e9i		−	0.405111i	0.979271	−	0.202555i	$-0.0649246\pi$
$284$	−4.76076e9	+	3.04282e7i	−0.731818	+	0.00467738i
$285$		0			0
$286$	2.10910e9	−	2.12262e9i	0.315233	−	0.317255i
$287$			1.51281e10i			2.22975i
$288$		0			0
$289$	3.36016e9			0.481691
$290$	1.32089e8	+	1.31248e8i	0.0186756	+	0.0185566i
$291$		0			0
$292$	3.90285e6	+	6.10637e8i	0.000536847	+	0.0839946i
$293$	−1.18893e10			−1.61319			−0.806594	−	0.591107i	$-0.798691\pi$
$293$	−1.18893e10			−1.61319			−0.806594	+	0.591107i	$0.798691\pi$
$294$		0			0
$295$			4.72559e9i			0.623976i
$296$	3.29803e9	−	3.36188e9i	0.429624	−	0.437941i
$297$		0			0
$298$	−6.96837e9	−	6.92397e9i	−0.883621	−	0.877992i
$299$		−	1.61177e9i		−	0.201660i
$300$		0			0
$301$	−1.25688e10			−1.53119
$302$	6.10296e9	−	6.14209e9i	0.733690	−	0.738394i
$303$		0			0
$304$	−7.82685e7	−	6.12266e9i	−0.00916417	−	0.716879i
$305$	−1.44229e9			−0.166669
$306$		0			0
$307$			1.74109e10i			1.96005i	0.198868	+	0.980026i	$0.436273\pi$
$307$			1.74109e10i			1.96005i	−0.198868	+	0.980026i	$0.563727\pi$
$308$	1.10232e8	+	1.72468e10i	0.0122491	+	1.91649i
$309$		0			0
$310$	−4.36815e8	+	4.39616e8i	−0.0472989	+	0.0476021i
$311$		−	8.61717e9i		−	0.921135i	−0.887625	−	0.460567i	$-0.847646\pi$
$311$		−	8.61717e9i		−	0.921135i	0.887625	−	0.460567i	$-0.152354\pi$
$312$		0			0
$313$	−9.76978e9			−1.01791			−0.508953	−	0.860794i	$-0.669967\pi$
$313$	−9.76978e9			−1.01791			−0.508953	+	0.860794i	$0.669967\pi$
$314$	7.30907e9	+	7.26250e9i	0.751871	+	0.747081i
$315$		0			0
$316$	−1.13293e10	+	7.24107e7i	−1.13620	+	0.00726197i
$317$	6.57561e9			0.651177			0.325589	−	0.945512i	$-0.394438\pi$
$317$	6.57561e9			0.651177			0.325589	+	0.945512i	$0.394438\pi$
$318$		0			0
$319$		−	7.11872e8i		−	0.0687447i
$320$	−8.99089e7	−	4.68851e9i	−0.00857438	−	0.447131i
$321$		0			0
$322$	6.59002e9	+	6.54804e9i	0.613004	+	0.609099i
$323$		−	9.49884e9i		−	0.872691i
$324$		0			0
$325$	8.54584e8			0.0765987
$326$	7.60787e9	−	7.65665e9i	0.673586	−	0.677905i
$327$		0			0
$328$	−1.10120e10	+	1.12252e10i	−0.951417	+	0.969837i
$329$	−1.38400e10			−1.18128
$330$		0			0
$331$		−	2.32794e10i		−	1.93936i	−0.244370	−	0.969682i	$-0.578581\pi$
$331$		−	2.32794e10i		−	1.93936i	0.244370	−	0.969682i	$-0.421419\pi$
$332$	−3.88661e9	+	2.48411e7i	−0.319903	+	0.00204464i
$333$		0			0
$334$	5.13751e9	−	5.17045e9i	0.412826	−	0.415473i
$335$		−	2.94484e9i		−	0.233820i
$336$		0			0
$337$	−1.99301e9			−0.154522			−0.0772610	−	0.997011i	$-0.524617\pi$
$337$	−1.99301e9			−0.154522			−0.0772610	+	0.997011i	$0.524617\pi$
$338$	7.90033e9	+	7.84999e9i	0.605311	+	0.601454i
$339$		0			0
$340$	−4.64943e7	−	7.27446e9i	−0.00347924	−	0.544358i
$341$	2.36924e9			0.175223
$342$		0			0
$343$			1.57565e10i			1.13837i
$344$	−9.32619e9	−	9.14906e9i	−0.665994	−	0.653345i
$345$		0			0
$346$	1.09451e10	+	1.08754e10i	0.763688	+	0.758823i
$347$			6.31855e9i			0.435813i	0.975970	+	0.217906i	$0.0699227\pi$
$347$			6.31855e9i			0.435813i	−0.975970	+	0.217906i	$0.930077\pi$
$348$		0			0
$349$	−1.87010e9			−0.126056			−0.0630279	−	0.998012i	$-0.520076\pi$
$349$	−1.87010e9			−0.126056			−0.0630279	+	0.998012i	$0.520076\pi$
$350$	−3.47186e9	+	3.49412e9i	−0.231361	+	0.232844i
$351$		0			0
$352$	−1.24725e10	+	1.28776e10i	−0.812422	+	0.838808i
$353$	−3.02132e10			−1.94580			−0.972900	−	0.231225i	$-0.925727\pi$
$353$	−3.02132e10			−1.94580			−0.972900	+	0.231225i	$0.925727\pi$
$354$		0			0
$355$			5.19805e9i			0.327286i
$356$	8.88017e7	+	1.38938e10i	0.00552868	+	0.865012i
$357$		0			0
$358$	−1.14315e10	+	1.15048e10i	−0.695937	+	0.700399i
$359$		−	1.82078e10i		−	1.09618i	−0.836421	−	0.548088i	$-0.815356\pi$
$359$		−	1.82078e10i		−	1.09618i	0.836421	−	0.548088i	$-0.184644\pi$
$360$		0			0
$361$	8.25401e9			0.486000
$362$	−1.71958e9	−	1.70862e9i	−0.100135	−	0.0994974i
$363$		0			0
$364$	1.10346e10	−	7.05269e7i	0.628565	−	0.00401744i
$365$	6.66725e8			0.0375643
$366$		0			0
$367$			1.46648e10i			0.808372i	0.914677	+	0.404186i	$0.132445\pi$
$367$			1.46648e10i			0.808372i	−0.914677	+	0.404186i	$0.867555\pi$
$368$	1.23433e8	+	9.65570e9i	0.00673037	+	0.526493i
$369$		0			0
$370$	−3.64752e9	−	3.62428e9i	−0.194621	−	0.193381i
$371$			2.23278e10i			1.17855i
$372$		0			0
$373$	1.41277e10			0.729857			0.364928	−	0.931036i	$-0.381094\pi$
$373$	1.41277e10			0.729857			0.364928	+	0.931036i	$0.381094\pi$
$374$	−1.96022e10	+	1.97279e10i	−1.00189	+	1.00831i
$375$		0			0
$376$	−1.02694e10	−	1.00744e10i	−0.513800	−	0.504042i
$377$	−4.55458e8			−0.0225467
$378$		0			0
$379$			3.94069e9i			0.190992i	0.995430	+	0.0954960i	$0.0304437\pi$
$379$			3.94069e9i			0.190992i	−0.995430	+	0.0954960i	$0.969556\pi$
$380$	−6.68532e9	+	4.27288e7i	−0.320618	+	0.00204921i
$381$		0			0
$382$	6.15961e9	−	6.19910e9i	0.289267	−	0.291122i
$383$		−	3.43063e10i		−	1.59433i	−0.603760	−	0.797166i	$-0.706332\pi$
$383$		−	3.43063e10i		−	1.59433i	0.603760	−	0.797166i	$-0.293668\pi$
$384$		0			0
$385$	1.88310e10			0.857098
$386$	−1.72523e10	−	1.71424e10i	−0.777137	−	0.772185i
$387$		0			0
$388$	−2.04192e8	−	3.19477e10i	−0.00900972	−	1.40965i
$389$	−4.14309e8			−0.0180936			−0.00904681	−	0.999959i	$-0.502880\pi$
$389$	−4.14309e8			−0.0180936			−0.00904681	+	0.999959i	$0.502880\pi$
$390$		0			0
$391$			1.49801e10i			0.640924i
$392$	−2.80052e10	+	2.85474e10i	−1.18603	+	1.20899i
$393$		0			0
$394$	2.25601e10	+	2.24163e10i	0.936171	+	0.930207i
$395$			1.23699e10i			0.508135i
$396$		0			0
$397$	2.25453e10			0.907598			0.453799	−	0.891104i	$-0.350068\pi$
$397$	2.25453e10			0.907598			0.453799	+	0.891104i	$0.350068\pi$
$398$	1.90291e10	−	1.91511e10i	0.758377	−	0.763240i
$399$		0			0
$400$	−5.11958e9	+	6.54457e7i	−0.199984	+	0.00255647i
$401$	2.53666e10			0.981037			0.490519	−	0.871431i	$-0.336807\pi$
$401$	2.53666e10			0.981037			0.490519	+	0.871431i	$0.336807\pi$
$402$		0			0
$403$		−	1.51584e9i		−	0.0574691i
$404$	−3.21270e8	−	5.02657e10i	−0.0120599	−	1.88689i
$405$		0			0
$406$	1.85036e9	−	1.86222e9i	0.0681007	−	0.0685373i
$407$			1.96577e10i			0.716399i
$408$		0			0
$409$	1.47057e10			0.525523			0.262761	−	0.964861i	$-0.415367\pi$
$409$	1.47057e10			0.525523			0.262761	+	0.964861i	$0.415367\pi$
$410$	1.21789e10	+	1.21013e10i	0.430996	+	0.428250i
$411$		0			0
$412$	−2.77508e10	+	1.77367e8i	−0.963132	+	0.00615581i
$413$	6.66225e10			2.28992
$414$		0			0
$415$			4.24361e9i			0.143068i
$416$	8.23909e9	+	7.97992e9i	0.275110	+	0.266456i
$417$		0			0
$418$	1.81302e10	+	1.80147e10i	0.593879	+	0.590095i
$419$			7.30915e9i			0.237143i	0.992946	+	0.118572i	$0.0378315\pi$
$419$			7.30915e9i			0.237143i	−0.992946	+	0.118572i	$0.962168\pi$
$420$		0			0
$421$	−4.09140e10			−1.30240			−0.651199	−	0.758907i	$-0.725734\pi$
$421$	−4.09140e10			−1.30240			−0.651199	+	0.758907i	$0.725734\pi$
$422$	−4.00621e10	+	4.03189e10i	−1.26323	+	1.27133i
$423$		0			0
$424$	−1.62528e10	+	1.65674e10i	−0.502879	+	0.512615i
$425$	−7.94263e9			−0.243449
$426$		0			0
$427$			2.03337e10i			0.611654i
$428$	1.32936e10	−	8.49655e7i	0.396158	−	0.00253202i
$429$		0			0
$430$	−1.00541e10	+	1.01186e10i	−0.294082	+	0.295968i
$431$		−	3.95128e9i		−	0.114506i	−0.998360	−	0.0572531i	$-0.981766\pi$
$431$		−	3.95128e9i		−	0.114506i	0.998360	−	0.0572531i	$-0.0182342\pi$
$432$		0			0
$433$	2.88725e10			0.821358			0.410679	−	0.911780i	$-0.365292\pi$
$433$	2.88725e10			0.821358			0.410679	+	0.911780i	$0.365292\pi$
$434$	6.19780e9	+	6.15831e9i	0.174694	+	0.173581i
$435$		0			0
$436$	3.29086e8	+	5.14885e10i	0.00910676	+	1.42484i
$437$	1.37669e10			0.377493
$438$		0			0
$439$		−	1.66340e10i		−	0.447857i	−0.974606	−	0.223929i	$-0.928112\pi$
$439$		−	1.66340e10i		−	0.447857i	0.974606	−	0.223929i	$-0.0718883\pi$
$440$	1.39728e10	+	1.37074e10i	0.372797	+	0.365716i
$441$		0			0
$442$	1.26220e10	+	1.25416e10i	0.330703	+	0.328596i
$443$		−	1.61256e10i		−	0.418699i	−0.977841	−	0.209350i	$-0.932865\pi$
$443$		−	1.61256e10i		−	0.418699i	0.977841	−	0.209350i	$-0.0671346\pi$
$444$		0			0
$445$	1.51700e10			0.386853
$446$	1.59224e10	−	1.60245e10i	0.402410	−	0.404990i
$447$		0			0
$448$	−6.60997e10	+	1.26756e9i	−1.64092	+	0.0314670i
$449$	−1.31471e10			−0.323478			−0.161739	−	0.986834i	$-0.551710\pi$
$449$	−1.31471e10			−0.323478			−0.161739	+	0.986834i	$0.551710\pi$
$450$		0			0
$451$		−	6.56363e10i		−	1.58649i
$452$	1.11696e8	+	1.74758e10i	0.00267598	+	0.418682i
$453$		0			0
$454$	1.22903e10	−	1.23691e10i	0.289294	−	0.291149i
$455$		−	1.20481e10i		−	0.281108i
$456$		0			0
$457$	−6.79985e10			−1.55896			−0.779480	−	0.626427i	$-0.784516\pi$
$457$	−6.79985e10			−1.55896			−0.779480	+	0.626427i	$0.784516\pi$
$458$	2.56286e10	+	2.54653e10i	0.582456	+	0.578745i
$459$		0			0
$460$	1.05430e10	−	6.73852e7i	0.235469	−	0.00150499i
$461$	2.86783e10			0.634966			0.317483	−	0.948264i	$-0.397162\pi$
$461$	2.86783e10			0.634966			0.317483	+	0.948264i	$0.397162\pi$
$462$		0			0
$463$			4.22729e9i			0.0919894i	0.998942	+	0.0459947i	$0.0146457\pi$
$463$			4.22729e9i			0.0919894i	−0.998942	+	0.0459947i	$0.985354\pi$
$464$	2.72852e9	−	3.48799e7i	0.0588648	−	0.000752494i
$465$		0			0
$466$	7.40556e9	+	7.35838e9i	0.157041	+	0.156041i
$467$			4.27269e10i			0.898325i	0.893450	+	0.449163i	$0.148278\pi$
$467$			4.27269e10i			0.898325i	−0.893450	+	0.449163i	$0.851722\pi$
$468$		0			0
$469$	−4.15170e10			−0.858093
$470$	−1.10709e10	+	1.11419e10i	−0.226878	+	0.228333i
$471$		0			0
$472$	4.94345e10	+	4.84956e10i	0.996006	+	0.977089i
$473$	5.45323e10			1.08946
$474$		0			0
$475$			7.29938e9i			0.143388i
$476$	−1.02557e11	+	6.55487e8i	−1.99773	+	0.0127684i
$477$		0			0
$478$	5.40531e10	−	5.43996e10i	1.03540	−	1.04204i
$479$		−	6.73017e10i		−	1.27845i	−0.769020	−	0.639225i	$-0.779255\pi$
$479$		−	6.73017e10i		−	1.27845i	0.769020	−	0.639225i	$-0.220745\pi$
$480$		0			0
$481$	1.25770e10			0.234962
$482$	5.88352e10	+	5.84604e10i	1.09006	+	1.08311i
$483$		0			0
$484$	−1.27535e8	−	1.99540e10i	−0.00232406	−	0.363621i
$485$	−3.48821e10			−0.630429
$486$		0			0
$487$		−	9.69928e10i		−	1.72434i	−0.506616	−	0.862172i	$-0.669104\pi$
$487$		−	9.69928e10i		−	1.72434i	0.506616	−	0.862172i	$-0.330896\pi$
$488$	−1.48013e10	+	1.50878e10i	−0.260988	+	0.266040i
$489$		0			0
$490$	3.09728e10	+	3.07755e10i	0.537275	+	0.533852i
$491$		−	1.73575e10i		−	0.298648i	−0.988788	−	0.149324i	$-0.952290\pi$
$491$		−	1.73575e10i		−	0.298648i	0.988788	−	0.149324i	$-0.0477098\pi$
$492$		0			0
$493$	4.23309e9			0.0716589
$494$	1.15259e10	−	1.15998e10i	0.193538	−	0.194779i
$495$		0			0
$496$	1.16086e8	+	9.08101e9i	0.00191803	+	0.150040i
$497$	7.32833e10			1.20110
$498$		0			0
$499$		−	1.42959e10i		−	0.230573i	−0.993332	−	0.115287i	$-0.963221\pi$
$499$		−	1.42959e10i		−	0.230573i	0.993332	−	0.115287i	$-0.0367787\pi$
$500$	3.57285e7	+	5.59006e9i	0.000571657	+	0.0894409i
$501$		0			0
$502$	2.72777e10	−	2.74526e10i	0.429530	−	0.432284i
$503$		−	6.90584e10i		−	1.07881i	−0.842047	−	0.539404i	$-0.818649\pi$
$503$		−	6.90584e10i		−	1.07881i	0.842047	−	0.539404i	$-0.181351\pi$
$504$		0			0
$505$	−5.48827e10			−0.843859
$506$	−2.85921e10	−	2.84100e10i	−0.436158	−	0.433380i
$507$		0			0
$508$	−8.93382e10	+	5.71000e8i	−1.34147	+	0.00857396i
$509$	5.98939e10			0.892302			0.446151	−	0.894958i	$-0.352794\pi$
$509$	5.98939e10			0.892302			0.446151	+	0.894958i	$0.352794\pi$
$510$		0			0
$511$		−	9.39964e9i		−	0.137857i
$512$	−4.99693e10	−	4.71745e10i	−0.727149	−	0.686480i
$513$		0			0
$514$	−5.96493e10	−	5.92693e10i	−0.854581	−	0.849136i
$515$			3.02997e10i			0.430735i
$516$		0			0
$517$	6.00476e10			0.840491
$518$	−5.10959e10	+	5.14235e10i	−0.709687	+	0.714238i
$519$		0			0
$520$	8.77003e9	−	8.93982e9i	0.119947	−	0.122269i
$521$	−2.97388e10			−0.403620			−0.201810	−	0.979425i	$-0.564682\pi$
$521$	−2.97388e10			−0.403620			−0.201810	+	0.979425i	$0.564682\pi$
$522$		0			0
$523$		−	3.20935e10i		−	0.428954i	−0.976729	−	0.214477i	$-0.931195\pi$
$523$		−	3.20935e10i		−	0.428954i	0.976729	−	0.214477i	$-0.0688047\pi$
$524$	−3.81925e10	+	2.44105e8i	−0.506586	+	0.00323781i
$525$		0			0
$526$	1.40913e10	−	1.41817e10i	0.184081	−	0.185261i
$527$			1.40885e10i			0.182651i
$528$		0			0
$529$	5.66001e10			0.722760
$530$	1.79750e10	+	1.78605e10i	0.227806	+	0.226355i
$531$		0			0
$532$	6.02401e8	+	9.42511e10i	0.00752037	+	1.17663i
$533$	−4.19943e10			−0.520333
$534$		0			0
$535$		−	1.45147e10i		−	0.177171i
$536$	−3.08060e10	−	3.02209e10i	−0.373229	−	0.366141i
$537$		0			0
$538$	−6.08755e10	−	6.04876e10i	−0.726630	−	0.722000i
$539$		−	1.66923e11i		−	1.97770i
$540$		0			0
$541$	3.92268e10			0.457924			0.228962	−	0.973435i	$-0.426467\pi$
$541$	3.92268e10			0.457924			0.228962	+	0.973435i	$0.426467\pi$
$542$	7.58219e9	−	7.63081e9i	0.0878613	−	0.0884247i
$543$		0			0
$544$	−7.65753e10	−	7.41665e10i	−0.874366	−	0.846861i
$545$	5.62179e10			0.637219
$546$		0			0
$547$		−	9.39638e10i		−	1.04957i	−0.851235	−	0.524785i	$-0.824146\pi$
$547$		−	9.39638e10i		−	1.04957i	0.851235	−	0.524785i	$-0.175854\pi$
$548$	−9.90969e8	−	1.55046e11i	−0.0109885	−	1.71925i
$549$		0			0
$550$	1.50633e10	−	1.51599e10i	0.164616	−	0.165671i
$551$		−	3.89027e9i		−	0.0422059i
$552$		0			0
$553$	1.74394e11			1.86480
$554$	−9.70541e10	−	9.64358e10i	−1.03033	−	1.02376i
$555$		0			0
$556$	−1.32935e11	+	8.49650e8i	−1.39105	+	0.00889080i
$557$	−8.98122e10			−0.933071			−0.466535	−	0.884503i	$-0.654498\pi$
$557$	−8.98122e10			−0.933071			−0.466535	+	0.884503i	$0.654498\pi$
$558$		0			0
$559$		−	3.48899e10i		−	0.357316i
$560$	9.22669e8	+	7.21770e10i	0.00938196	+	0.733917i
$561$		0			0
$562$	−9.62097e9	−	9.55967e9i	−0.0964436	−	0.0958292i
$563$			1.80533e10i			0.179689i	0.995956	+	0.0898446i	$0.0286371\pi$
$563$			1.80533e10i			0.179689i	−0.995956	+	0.0898446i	$0.971363\pi$
$564$		0			0
$565$	1.90810e10			0.187244
$566$	−2.93043e10	+	2.94922e10i	−0.285540	+	0.287370i
$567$		0			0
$568$	5.43769e10	+	5.33441e10i	0.522421	+	0.512499i
$569$	6.90947e10			0.659167			0.329584	−	0.944126i	$-0.393092\pi$
$569$	6.90947e10			0.659167			0.329584	+	0.944126i	$0.393092\pi$
$570$		0			0
$571$			7.86073e10i			0.739467i	0.929138	+	0.369733i	$0.120551\pi$
$571$			7.86073e10i			0.739467i	−0.929138	+	0.369733i	$0.879449\pi$
$572$	−4.78757e10	+	3.05995e8i	−0.447230	+	0.00285844i
$573$		0			0
$574$	1.70607e11	−	1.71701e11i	1.57163	−	1.58170i
$575$		−	1.15114e10i		−	0.105307i
$576$		0			0
$577$	−1.80277e11			−1.62643			−0.813216	−	0.581962i	$-0.802285\pi$
$577$	−1.80277e11			−1.62643			−0.813216	+	0.581962i	$0.802285\pi$
$578$	−3.81371e10	−	3.78942e10i	−0.341693	−	0.339517i
$579$		0			0
$580$	−1.90418e7	−	2.97927e9i	−0.000168266	−	0.0263268i
$581$	5.98273e10			0.525043
$582$		0			0
$583$		−	9.68734e10i		−	0.838553i
$584$	6.84216e9	−	6.97462e9i	0.0588223	−	0.0599611i
$585$		0			0
$586$	1.34941e11	+	1.34081e11i	1.14433	+	1.13704i
$587$			3.62809e9i			0.0305581i	0.999883	+	0.0152790i	$0.00486366\pi$
$587$			3.62809e9i			0.0305581i	−0.999883	+	0.0152790i	$0.995136\pi$
$588$		0			0
$589$	1.29475e10			0.107578
$590$	5.32928e10	−	5.36345e10i	0.439806	−	0.442626i
$591$		0			0
$592$	−7.53457e10	+	9.63175e8i	−0.613439	+	0.00784185i
$593$	−8.72511e10			−0.705589			−0.352795	−	0.935701i	$-0.614769\pi$
$593$	−8.72511e10			−0.705589			−0.352795	+	0.935701i	$0.614769\pi$
$594$		0			0
$595$			1.11977e11i			0.893431i
$596$	1.00455e9	+	1.57172e11i	0.00796137	+	1.24563i
$597$		0			0
$598$	−1.81768e10	+	1.82933e10i	−0.142139	+	0.143050i
$599$			1.90496e10i			0.147972i	0.997259	+	0.0739858i	$0.0235720\pi$
$599$			1.90496e10i			0.147972i	−0.997259	+	0.0739858i	$0.976428\pi$
$600$		0			0
$601$	1.75085e11			1.34200			0.670998	−	0.741459i	$-0.265866\pi$
$601$	1.75085e11			1.34200			0.670998	+	0.741459i	$0.265866\pi$
$602$	1.42654e11	+	1.41745e11i	1.08617	+	1.07925i
$603$		0			0
$604$	−1.38535e11	+	8.85437e8i	−1.04090	+	0.00665289i
$605$	−2.17869e10			−0.162620
$606$		0			0
$607$			1.75308e11i			1.29136i	0.763608	+	0.645680i	$0.223426\pi$
$607$			1.75308e11i			1.29136i	−0.763608	+	0.645680i	$0.776574\pi$
$608$	−6.81600e10	+	7.03737e10i	−0.498787	+	0.514987i
$609$		0			0
$610$	1.63697e10	+	1.62654e10i	0.118228	+	0.117475i
$611$		−	3.84186e10i		−	0.275662i
$612$		0			0
$613$	1.26999e10			0.0899412			0.0449706	−	0.998988i	$-0.485681\pi$
$613$	1.26999e10			0.0899412			0.0449706	+	0.998988i	$0.485681\pi$
$614$	1.96351e11	−	1.97610e11i	1.38153	−	1.39039i
$615$		0			0
$616$	1.93250e11	−	1.96991e11i	1.34214	−	1.36812i
$617$	−2.29769e11			−1.58544			−0.792720	−	0.609586i	$-0.791336\pi$
$617$	−2.29769e11			−1.58544			−0.792720	+	0.609586i	$0.791336\pi$
$618$		0			0
$619$		−	1.67400e11i		−	1.14023i	−0.821564	−	0.570116i	$-0.806898\pi$
$619$		−	1.67400e11i		−	1.14023i	0.821564	−	0.570116i	$-0.193102\pi$
$620$	9.91553e9	−	6.33746e7i	0.0671041	−	0.000428892i
$621$		0			0
$622$	−9.71801e10	+	9.78032e10i	−0.649256	+	0.653419i
$623$		−	2.13870e11i		−	1.41971i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	1.10885e11	+	1.10179e11i	0.722065	+	0.717464i
$627$		0			0
$628$	−1.05367e9	−	1.64856e11i	−0.00677432	−	1.05990i
$629$	−1.16893e11			−0.746768
$630$		0			0
$631$			2.92637e9i			0.0184591i	0.999957	+	0.00922957i	$0.00293791\pi$
$631$			2.92637e9i			0.0184591i	−0.999957	+	0.00922957i	$0.997062\pi$
$632$	1.29402e11	+	1.26944e11i	0.811098	+	0.795693i
$633$		0			0
$634$	−7.46319e10	−	7.41564e10i	−0.461921	−	0.458978i
$635$			9.75441e10i			0.599938i
$636$		0			0
$637$	−1.06798e11			−0.648642
$638$	−8.02814e9	+	8.07961e9i	−0.0484543	+	0.0487650i
$639$		0			0
$640$	−5.18542e10	+	5.42277e10i	−0.309075	+	0.323222i
$641$	1.15318e11			0.683071			0.341535	−	0.939869i	$-0.389053\pi$
$641$	1.15318e11			0.683071			0.341535	+	0.939869i	$0.389053\pi$
$642$		0			0
$643$		−	4.99010e10i		−	0.291921i	−0.989290	−	0.145961i	$-0.953373\pi$
$643$		−	4.99010e10i		−	0.291921i	0.989290	−	0.145961i	$-0.0466273\pi$
$644$	−9.50011e8	−	1.48638e11i	−0.00552313	−	0.864144i
$645$		0			0
$646$	−1.07123e11	+	1.07810e11i	−0.615110	+	0.619054i
$647$		−	5.43112e10i		−	0.309936i	−0.987919	−	0.154968i	$-0.950473\pi$
$647$		−	5.43112e10i		−	0.309936i	0.987919	−	0.154968i	$-0.0495275\pi$
$648$		0			0
$649$	−2.89055e11			−1.62930
$650$	−9.69937e9	−	9.63757e9i	−0.0543363	−	0.0539901i
$651$		0			0
$652$	−1.72696e11	+	1.10378e9i	−0.955633	+	0.00610788i
$653$	−1.40265e11			−0.771433			−0.385716	−	0.922617i	$-0.626046\pi$
$653$	−1.40265e11			−0.771433			−0.385716	+	0.922617i	$0.626046\pi$
$654$		0			0
$655$			4.17006e10i			0.226557i
$656$	2.51576e11	−	3.21600e9i	1.35848	−	0.0173660i
$657$		0			0
$658$	1.57081e11	+	1.56081e11i	0.837955	+	0.832617i
$659$			2.51334e11i			1.33263i	0.745670	+	0.666315i	$0.232129\pi$
$659$			2.51334e11i			1.33263i	−0.745670	+	0.666315i	$0.767871\pi$
$660$		0			0
$661$	1.18006e10			0.0618155			0.0309077	−	0.999522i	$-0.490160\pi$
$661$	1.18006e10			0.0618155			0.0309077	+	0.999522i	$0.490160\pi$
$662$	−2.62533e11	+	2.64216e11i	−1.36695	+	1.37571i
$663$		0			0
$664$	4.43924e10	+	4.35493e10i	0.228369	+	0.224031i
$665$	1.02908e11			0.526216
$666$		0			0
$667$			6.13511e9i			0.0309970i
$668$	−1.16620e11	+	7.45368e8i	−0.585687	+	0.00374339i
$669$		0			0
$670$	−3.32104e10	+	3.34233e10i	−0.164807	+	0.165863i
$671$		−	8.82220e10i		−	0.435198i
$672$		0			0
$673$	−3.32886e11			−1.62269			−0.811345	−	0.584567i	$-0.801264\pi$
$673$	−3.32886e11			−1.62269			−0.811345	+	0.584567i	$0.801264\pi$
$674$	2.26203e10	+	2.24762e10i	0.109612	+	0.108914i
$675$		0			0
$676$	−1.13890e9	−	1.78192e11i	−0.00545381	−	0.853299i
$677$	1.55980e11			0.742530			0.371265	−	0.928527i	$-0.378924\pi$
$677$	1.55980e11			0.742530			0.371265	+	0.928527i	$0.378924\pi$
$678$		0			0
$679$			4.91776e11i			2.31360i
$680$	−8.15100e10	+	8.30880e10i	−0.381219	+	0.388600i
$681$		0			0
$682$	−2.68904e10	−	2.67191e10i	−0.124297	−	0.123505i
$683$			2.38756e10i			0.109716i	0.998494	+	0.0548581i	$0.0174707\pi$
$683$			2.38756e10i			0.109716i	−0.998494	+	0.0548581i	$0.982529\pi$
$684$		0			0
$685$	−1.69287e11			−0.768887
$686$	1.77694e11	−	1.78833e11i	0.802371	−	0.807516i
$687$		0			0
$688$	2.67194e9	+	2.09016e11i	0.0119254	+	0.932880i
$689$	−6.19799e10			−0.275026
$690$		0			0
$691$			3.49556e11i			1.53322i	0.642113	+	0.766610i	$0.278058\pi$
$691$			3.49556e11i			1.53322i	−0.642113	+	0.766610i	$0.721942\pi$
$692$	−1.57784e9	−	2.46867e11i	−0.00688078	−	1.07656i
$693$		0			0
$694$	7.12574e10	−	7.17143e10i	0.307180	−	0.309149i
$695$			1.45146e11i			0.622107i
$696$		0			0
$697$	3.90301e11			1.65374
$698$	2.12253e10	+	2.10900e10i	0.0894193	+	0.0888496i
$699$		0			0
$700$	7.88099e10	−	5.03709e8i	0.328238	−	0.00209791i
$701$	2.57887e10			0.106796			0.0533982	−	0.998573i	$-0.482995\pi$
$701$	2.57887e10			0.106796			0.0533982	+	0.998573i	$0.482995\pi$
$702$		0			0
$703$			1.07426e11i			0.439834i
$704$	2.86787e11	−	5.49954e9i	1.16753	−	0.0223891i
$705$		0			0
$706$	3.42914e11	+	3.40730e11i	1.38028	+	1.37148i
$707$			7.73749e11i			3.09686i
$708$		0			0
$709$	−1.18322e11			−0.468251			−0.234126	−	0.972206i	$-0.575223\pi$
$709$	−1.18322e11			−0.468251			−0.234126	+	0.972206i	$0.575223\pi$
$710$	5.86210e10	−	5.89968e10i	0.230685	−	0.232164i
$711$		0			0
$712$	1.55680e11	−	1.58694e11i	0.605776	−	0.617504i
$713$	−2.04187e10			−0.0790079
$714$		0			0
$715$			5.22731e10i			0.200011i
$716$	2.59490e11	−	1.65851e9i	0.987343	−	0.00631055i
$717$		0			0
$718$	−2.05339e11	+	2.06655e11i	−0.772632	+	0.777587i
$719$		−	1.28179e11i		−	0.479624i	−0.970819	−	0.239812i	$-0.922914\pi$
$719$		−	1.28179e11i		−	0.479624i	0.970819	−	0.239812i	$-0.0770858\pi$
$720$		0			0
$721$	4.27173e11			1.58075
$722$	−9.36814e10	−	9.30846e10i	−0.344750	−	0.342554i
$723$		0			0
$724$	2.47893e8	+	3.87850e10i	0.000902213	+	0.141159i
$725$	−3.25292e9			−0.0117739
$726$		0			0
$727$			2.11824e11i			0.758295i	0.925336	+	0.379148i	$0.123783\pi$
$727$			2.11824e11i			0.758295i	−0.925336	+	0.379148i	$0.876217\pi$
$728$	−1.26036e11	−	1.23642e11i	−0.448712	−	0.440190i
$729$		0			0
$730$	−7.56720e9	−	7.51899e9i	−0.0266467	−	0.0264770i
$731$			3.24272e11i			1.13564i
$732$		0			0
$733$	2.18401e11			0.756552			0.378276	−	0.925693i	$-0.376517\pi$
$733$	2.18401e11			0.756552			0.378276	+	0.925693i	$0.376517\pi$
$734$	1.65382e11	−	1.66442e11i	0.569776	−	0.573429i
$735$		0			0
$736$	1.07491e11	−	1.10982e11i	0.366321	−	0.378218i
$737$	1.80129e11			0.610541
$738$		0			0
$739$		−	1.87281e11i		−	0.627936i	−0.949433	−	0.313968i	$-0.898341\pi$
$739$		−	1.87281e11i		−	0.627936i	0.949433	−	0.313968i	$-0.101659\pi$
$740$	5.25822e8	+	8.22697e10i	0.00175353	+	0.274355i
$741$		0			0
$742$	2.51801e11	−	2.53416e11i	0.830696	−	0.836023i
$743$			4.43366e11i			1.45481i	0.686207	+	0.727406i	$0.259274\pi$
$743$			4.43366e11i			1.45481i	−0.686207	+	0.727406i	$0.740726\pi$
$744$		0			0
$745$	1.71608e11			0.557074
$746$	−1.60347e11	−	1.59326e11i	−0.517733	−	0.514435i
$747$		0			0
$748$	4.44963e11	−	2.84396e9i	1.42141	−	0.00908484i
$749$	−2.04631e11			−0.650196
$750$		0			0
$751$		−	1.63129e11i		−	0.512827i	−0.966567	−	0.256414i	$-0.917459\pi$
$751$		−	1.63129e11i		−	0.512827i	0.966567	−	0.256414i	$-0.0825409\pi$
$752$	2.94217e9	+	2.30155e11i	0.00920018	+	0.719697i
$753$		0			0
$754$	5.16936e9	+	5.13643e9i	0.0159938	+	0.0158919i
$755$			1.51260e11i			0.465516i
$756$		0			0
$757$	8.66867e10			0.263979			0.131989	−	0.991251i	$-0.457864\pi$
$757$	8.66867e10			0.263979			0.131989	+	0.991251i	$0.457864\pi$
$758$	4.44411e10	−	4.47260e10i	0.134619	−	0.135483i
$759$		0			0
$760$	7.63589e10	+	7.49087e10i	0.228879	+	0.224532i
$761$	−3.59912e11			−1.07314			−0.536571	−	0.843855i	$-0.680281\pi$
$761$	−3.59912e11			−1.07314			−0.536571	+	0.843855i	$0.680281\pi$
$762$		0			0
$763$		−	7.92573e11i		−	2.33852i
$764$	−1.39821e11	+	8.93656e8i	−0.410391	+	0.00262299i
$765$		0			0
$766$	−3.86889e11	+	3.89370e11i	−1.12375	+	1.13096i
$767$			1.84938e11i			0.534373i
$768$		0			0
$769$	−6.61724e11			−1.89222			−0.946110	−	0.323845i	$-0.895024\pi$
$769$	−6.61724e11			−1.89222			−0.946110	+	0.323845i	$0.895024\pi$
$770$	−2.13728e11	−	2.12366e11i	−0.607993	−	0.604120i
$771$		0			0
$772$	2.48707e9	+	3.89125e11i	0.00700195	+	1.09552i
$773$	2.24564e11			0.628958			0.314479	−	0.949264i	$-0.398170\pi$
$773$	2.24564e11			0.628958			0.314479	+	0.949264i	$0.398170\pi$
$774$		0			0
$775$		−	1.08263e10i		−	0.0300105i
$776$	−3.57972e11	+	3.64903e11i	−0.987194	+	1.00631i
$777$		0			0
$778$	4.70232e9	+	4.67236e9i	0.0128349	+	0.0127532i
$779$		−	3.58691e11i		−	0.974027i
$780$		0			0
$781$	−3.17954e11			−0.854594
$782$	1.68938e11	−	1.70021e11i	0.451751	−	0.454648i
$783$		0			0
$784$	6.39797e11	−	8.17879e9i	1.69347	−	0.0216483i
$785$	−1.79998e11			−0.474013
$786$		0			0
$787$			6.78642e11i			1.76906i	0.466486	+	0.884528i	$0.345520\pi$
$787$			6.78642e11i			1.76906i	−0.466486	+	0.884528i	$0.654480\pi$
$788$	−3.25224e9	−	5.08842e11i	−0.00843485	−	1.31971i
$789$		0			0
$790$	1.39502e11	−	1.40396e11i	0.358156	−	0.360452i
$791$		−	2.69008e11i		−	0.687163i
$792$		0			0
$793$	−5.64447e10			−0.142735
$794$	−2.55884e11	−	2.54254e11i	−0.643816	−	0.639714i
$795$		0			0
$796$	−4.31952e11	+	2.76080e9i	−1.07593	+	0.00687674i
$797$	−2.55700e11			−0.633720			−0.316860	−	0.948472i	$-0.602628\pi$
$797$	−2.55700e11			−0.633720			−0.316860	+	0.948472i	$0.602628\pi$
$798$		0			0
$799$			3.57068e11i			0.876121i
$800$	5.88443e10	+	5.69933e10i	0.143663	+	0.139144i
$801$		0			0
$802$	−2.87906e11	−	2.86072e11i	−0.695911	−	0.691478i
$803$			4.07822e10i			0.0980863i
$804$		0			0
$805$	−1.62291e11			−0.386465
$806$	−1.70949e10	+	1.72045e10i	−0.0405067	+	0.0407664i
$807$		0			0
$808$	−5.63224e11	+	5.74129e11i	−1.32141	+	1.34699i
$809$	−4.12911e10			−0.0963968			−0.0481984	−	0.998838i	$-0.515348\pi$
$809$	−4.12911e10			−0.0963968			−0.0481984	+	0.998838i	$0.515348\pi$
$810$		0			0
$811$		−	2.06089e11i		−	0.476399i	−0.971216	−	0.238200i	$-0.923443\pi$
$811$		−	2.06089e11i		−	0.476399i	0.971216	−	0.238200i	$-0.0765573\pi$
$812$	−4.20024e10	+	2.68456e8i	−0.0966162	+	0.000617517i
$813$		0			0
$814$	2.21690e11	−	2.23111e11i	0.504949	−	0.508187i
$815$			1.88558e11i			0.427381i
$816$		0			0
$817$	2.98010e11			0.668872
$818$	−1.66907e11	−	1.65843e11i	−0.372786	−	0.370411i
$819$		0			0
$820$	−1.75570e9	−	2.74695e11i	−0.00388325	−	0.607569i
$821$	−8.40243e11			−1.84941			−0.924703	−	0.380688i	$-0.875687\pi$
$821$	−8.40243e11			−1.84941			−0.924703	+	0.380688i	$0.875687\pi$
$822$		0			0
$823$		−	3.94949e11i		−	0.860878i	−0.902620	−	0.430439i	$-0.858359\pi$
$823$		−	3.94949e11i		−	0.860878i	0.902620	−	0.430439i	$-0.141641\pi$
$824$	3.16966e11	+	3.10946e11i	0.687549	+	0.674491i
$825$		0			0
$826$	−7.56152e11	−	7.51334e11i	−1.62438	−	1.61404i
$827$		−	3.63473e11i		−	0.777051i	−0.921438	−	0.388526i	$-0.872984\pi$
$827$		−	3.63473e11i		−	0.777051i	0.921438	−	0.388526i	$-0.127016\pi$
$828$		0			0
$829$	−4.62310e11			−0.978847			−0.489424	−	0.872046i	$-0.662793\pi$
$829$	−4.62310e11			−0.978847			−0.489424	+	0.872046i	$0.662793\pi$
$830$	4.78572e10	−	4.81641e10i	0.100841	−	0.101487i
$831$		0			0
$832$	−3.51862e9	−	1.83487e11i	−0.00734310	−	0.382923i
$833$	9.92595e11			2.06154
$834$		0			0
$835$			1.27331e11i			0.261933i
$836$	−2.61364e9	−	4.08927e11i	−0.00535081	−	0.837184i
$837$		0			0
$838$	8.24289e10	−	8.29574e10i	0.167149	−	0.168221i
$839$		−	1.39033e11i		−	0.280588i	−0.990110	−	0.140294i	$-0.955195\pi$
$839$		−	1.39033e11i		−	0.280588i	0.990110	−	0.140294i	$-0.0448049\pi$
$840$		0			0
$841$	−4.98513e11			−0.996534
$842$	4.64366e11	+	4.61407e11i	0.923872	+	0.917986i
$843$		0			0
$844$	9.09393e11	−	5.81234e9i	1.79218	−	0.0114546i
$845$	−1.94559e11			−0.381614
$846$		0			0
$847$			3.07156e11i			0.596795i
$848$	3.71305e11	−	4.74654e9i	0.718037	−	0.00917896i
$849$		0			0
$850$	9.01473e10	+	8.95730e10i	0.172694	+	0.171594i
$851$		−	1.69415e11i		−	0.323024i
$852$		0			0
$853$	−2.95120e11			−0.557446			−0.278723	−	0.960372i	$-0.589911\pi$
$853$	−2.95120e11			−0.557446			−0.278723	+	0.960372i	$0.589911\pi$
$854$	2.29314e11	−	2.30784e11i	0.431120	−	0.433885i
$855$		0			0
$856$	−1.51838e11	−	1.48954e11i	−0.282804	−	0.277433i
$857$	−2.93094e11			−0.543355			−0.271678	−	0.962388i	$-0.587578\pi$
$857$	−2.93094e11			−0.543355			−0.271678	+	0.962388i	$0.587578\pi$
$858$		0			0
$859$		−	5.58133e11i		−	1.02510i	−0.858658	−	0.512549i	$-0.828701\pi$
$859$		−	5.58133e11i		−	1.02510i	0.858658	−	0.512549i	$-0.171299\pi$
$860$	2.28224e11	−	1.45868e9i	0.417222	−	0.00266665i
$861$		0			0
$862$	−4.45605e10	+	4.48463e10i	−0.0807089	+	0.0812264i
$863$		−	3.25698e11i		−	0.587181i	−0.955931	−	0.293590i	$-0.905150\pi$
$863$		−	3.25698e11i		−	0.587181i	0.955931	−	0.293590i	$-0.0948502\pi$
$864$		0			0
$865$	−2.69542e11			−0.481463
$866$	−3.27697e11	−	3.25609e11i	−0.582641	−	0.578929i
$867$		0			0
$868$	−8.93469e8	−	1.39791e11i	−0.00157398	−	0.246264i
$869$	−7.56643e11			−1.32682
$870$		0			0
$871$		−	1.15247e11i		−	0.200243i
$872$	5.76927e11	−	5.88096e11i	0.997826	−	1.01714i
$873$		0			0
$874$	−1.56251e11	−	1.55256e11i	−0.267780	−	0.266074i
$875$		−	8.60487e10i		−	0.146795i
$876$		0			0
$877$	−2.02891e11			−0.342976			−0.171488	−	0.985186i	$-0.554857\pi$
$877$	−2.02891e11			−0.342976			−0.171488	+	0.985186i	$0.554857\pi$
$878$	−1.87590e11	+	1.88793e11i	−0.315669	+	0.317693i
$879$		0			0
$880$	−4.00318e9	−	3.13154e11i	−0.00667536	−	0.522189i
$881$	6.22197e10			0.103282			0.0516409	−	0.998666i	$-0.483555\pi$
$881$	6.22197e10			0.103282			0.0516409	+	0.998666i	$0.483555\pi$
$882$		0			0
$883$			7.69290e10i			0.126546i	0.997996	+	0.0632729i	$0.0201538\pi$
$883$			7.69290e10i			0.126546i	−0.997996	+	0.0632729i	$0.979846\pi$
$884$	−1.81957e9	−	2.84689e11i	−0.00297962	−	0.466188i
$885$		0			0
$886$	−1.81857e11	+	1.83023e11i	−0.295117	+	0.297010i
$887$			7.30650e10i			0.118036i	0.998257	+	0.0590180i	$0.0187969\pi$
$887$			7.30650e10i			0.118036i	−0.998257	+	0.0590180i	$0.981203\pi$
$888$		0			0
$889$	1.37520e12			2.20170
$890$	−1.72177e11	−	1.71080e11i	−0.274419	−	0.272671i
$891$		0			0
$892$	−3.61432e11	+	2.31007e9i	−0.570909	+	0.00364893i
$893$	3.28150e11			0.516020
$894$		0			0
$895$		−	2.83324e11i		−	0.441562i
$896$	7.64514e11	+	7.31053e11i	1.18619	+	1.13427i
$897$		0			0
$898$	1.49217e11	+	1.48266e11i	0.229463	+	0.228001i
$899$			5.76996e9i			0.00883353i
$900$		0			0
$901$	5.76050e11			0.874100
$902$	−7.40213e11	+	7.44959e11i	−1.11823	+	1.12540i
$903$		0			0
$904$	1.95816e11	−	1.99607e11i	0.293207	−	0.298883i
$905$	4.23475e10			0.0631297
$906$		0			0
$907$		−	7.63733e11i		−	1.12853i	−0.825594	−	0.564264i	$-0.809160\pi$
$907$		−	7.63733e11i		−	1.12853i	0.825594	−	0.564264i	$-0.190840\pi$
$908$	−2.78985e11	+	1.78312e9i	−0.410429	+	0.00262324i
$909$		0			0
$910$	−1.35873e11	+	1.36744e11i	−0.198137	+	0.199408i
$911$		−	6.04985e11i		−	0.878357i	−0.898400	−	0.439178i	$-0.855270\pi$
$911$		−	6.04985e11i		−	0.878357i	0.898400	−	0.439178i	$-0.144730\pi$
$912$		0			0
$913$	−2.59573e11			−0.373573
$914$	7.71770e11	+	7.66853e11i	1.10587	+	1.09882i
$915$		0			0
$916$	−3.69459e9	−	5.78053e11i	−0.00524789	−	0.821080i
$917$	5.87904e11			0.831436
$918$		0			0
$919$			1.09773e12i			1.53898i	0.638657	+	0.769492i	$0.279490\pi$
$919$			1.09773e12i			1.53898i	−0.638657	+	0.769492i	$0.720510\pi$
$920$	−1.20421e11	−	1.18134e11i	−0.168094	−	0.164901i
$921$		0			0
$922$	−3.25493e11	−	3.23420e11i	−0.450421	−	0.447551i
$923$			2.03428e11i			0.280287i
$924$		0			0
$925$	8.98264e10			0.122698
$926$	4.76732e10	−	4.79789e10i	0.0648381	−	0.0652539i
$927$		0			0
$928$	−3.13616e10	−	3.03750e10i	−0.0422869	−	0.0409567i
$929$	−5.68272e11			−0.762945			−0.381473	−	0.924380i	$-0.624583\pi$
$929$	−5.68272e11			−0.762945			−0.381473	+	0.924380i	$0.624583\pi$
$930$		0			0
$931$		−	9.12208e11i		−	1.21421i
$932$	−1.06758e9	−	1.67032e11i	−0.00141493	−	0.221379i
$933$		0			0
$934$	4.81852e11	−	4.84942e11i	0.633179	−	0.637238i
$935$		−	4.85834e11i		−	0.635685i
$936$		0			0
$937$	1.49600e11			0.194076			0.0970382	−	0.995281i	$-0.469063\pi$
$937$	1.49600e11			0.194076			0.0970382	+	0.995281i	$0.469063\pi$
$938$	4.71209e11	+	4.68207e11i	0.608699	+	0.604821i
$939$		0			0
$940$	2.51306e11	−	1.60621e9i	0.321878	−	0.00205727i
$941$	5.28765e11			0.674379			0.337190	−	0.941437i	$-0.390524\pi$
$941$	5.28765e11			0.674379			0.337190	+	0.941437i	$0.390524\pi$
$942$		0			0
$943$			5.65671e11i			0.715348i
$944$	−1.41629e10	−	1.10791e12i	−0.0178346	−	1.39514i
$945$		0			0
$946$	−6.18931e11	−	6.14988e11i	−0.772819	−	0.767896i
$947$		−	9.04370e11i		−	1.12447i	−0.826979	−	0.562233i	$-0.809943\pi$
$947$		−	9.04370e11i		−	1.12447i	0.826979	−	0.562233i	$-0.190057\pi$
$948$		0			0
$949$	2.60926e10			0.0321701
$950$	8.23187e10	−	8.28465e10i	0.101066	−	0.101714i
$951$		0			0
$952$	1.17139e12	+	1.14915e12i	1.42612	+	1.39903i
$953$	5.71895e11			0.693337			0.346669	−	0.937988i	$-0.387313\pi$
$953$	5.71895e11			0.693337			0.346669	+	0.937988i	$0.387313\pi$
$954$		0			0
$955$			1.52664e11i			0.183536i
$956$	−1.22698e12	+	7.84220e9i	−1.46895	+	0.00938872i
$957$		0			0
$958$	−7.58994e11	+	7.63861e11i	−0.901107	+	0.906885i
$959$			2.38665e12i			2.82173i
$960$		0			0
$961$	8.33688e11			0.977484
$962$	−1.42747e11	−	1.41838e11i	−0.166674	−	0.165612i
$963$		0			0
$964$	−8.48163e9	−	1.32703e12i	−0.00982135	−	1.53664i
$965$	4.24867e11			0.489941
$966$		0			0
$967$		−	9.92056e11i		−	1.13457i	−0.823522	−	0.567284i	$-0.807994\pi$
$967$		−	9.92056e11i		−	1.13457i	0.823522	−	0.567284i	$-0.192006\pi$
$968$	−2.23584e11	+	2.27913e11i	−0.254647	+	0.259577i
$969$		0			0
$970$	3.95905e11	+	3.93383e11i	0.447203	+	0.444354i
$971$		−	4.62553e11i		−	0.520336i	−0.965563	−	0.260168i	$-0.916222\pi$
$971$		−	4.62553e11i		−	0.520336i	0.965563	−	0.260168i	$-0.0837780\pi$
$972$		0			0
$973$	2.04630e12			2.28306
$974$	−1.09384e12	+	1.10085e12i	−1.21539	+	1.22319i
$975$		0			0
$976$	3.38145e11	−	4.32264e9i	0.372652	−	0.00476376i
$977$	−1.35557e11			−0.148780			−0.0743899	−	0.997229i	$-0.523701\pi$
$977$	−1.35557e11			−0.148780			−0.0743899	+	0.997229i	$0.523701\pi$
$978$		0			0
$979$			9.27919e11i			1.01013i
$980$	−4.46501e9	−	6.98592e11i	−0.00484082	−	0.757390i
$981$		0			0
$982$	−1.95749e11	+	1.97004e11i	−0.210500	+	0.211850i
$983$			1.95656e10i			0.0209546i	0.999945	+	0.0104773i	$0.00333509\pi$
$983$			1.95656e10i			0.0209546i	−0.999945	+	0.0104773i	$0.996665\pi$
$984$		0			0
$985$	−5.55580e11			−0.590204
$986$	−4.80448e10	−	4.77387e10i	−0.0508322	−	0.0505083i
$987$		0			0
$988$	−2.61633e11	+	1.67221e9i	−0.274577	+	0.00175494i
$989$	−4.69975e11			−0.491235
$990$		0			0
$991$			4.63152e11i			0.480208i	0.970747	+	0.240104i	$0.0771815\pi$
$991$			4.63152e11i			0.480208i	−0.970747	+	0.240104i	$0.922818\pi$
$992$	1.01093e11	−	1.04377e11i	0.104394	−	0.107785i
$993$		0			0
$994$	−8.31751e11	−	8.26452e11i	−0.852016	−	0.846588i
$995$			4.71628e11i			0.481180i
$996$		0			0
$997$	−5.69988e11			−0.576879			−0.288439	−	0.957498i	$-0.593136\pi$
$997$	−5.69988e11			−0.576879			−0.288439	+	0.957498i	$0.593136\pi$
$998$	−1.61222e11	+	1.62256e11i	−0.162518	+	0.163560i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.a.91.5		16
3.2	odd	2		20.9.b.a.11.12	yes	16
4.3	odd	2	inner	180.9.c.a.91.6		16
12.11	even	2		20.9.b.a.11.11	✓	16
15.2	even	4		100.9.d.c.99.8		32
15.8	even	4		100.9.d.c.99.25		32
15.14	odd	2		100.9.b.d.51.5		16
24.5	odd	2		320.9.b.d.191.15		16
24.11	even	2		320.9.b.d.191.2		16
60.23	odd	4		100.9.d.c.99.7		32
60.47	odd	4		100.9.d.c.99.26		32
60.59	even	2		100.9.b.d.51.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.11	✓	16	12.11	even	2
20.9.b.a.11.12	yes	16	3.2	odd	2
100.9.b.d.51.5		16	15.14	odd	2
100.9.b.d.51.6		16	60.59	even	2
100.9.d.c.99.7		32	60.23	odd	4
100.9.d.c.99.8		32	15.2	even	4
100.9.d.c.99.25		32	15.8	even	4
100.9.d.c.99.26		32	60.47	odd	4
180.9.c.a.91.5		16	1.1	even	1	trivial
180.9.c.a.91.6		16	4.3	odd	2	inner
320.9.b.d.191.2		16	24.11	even	2
320.9.b.d.191.15		16	24.5	odd	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)

\(f(q)\)	\(=\)	\(q+(-11.3498 - 11.2775i) q^{2} +(1.63618 + 255.995i) q^{4} +279.508 q^{5} -3940.57i q^{7} +(2868.41 - 2923.94i) q^{8} +(-3172.37 - 3152.16i) q^{10} +17097.0i q^{11} +10938.7 q^{13} +(-44439.8 + 44724.8i) q^{14} +(-65530.6 + 837.705i) q^{16} -101666. q^{17} +93432.1i q^{19} +(457.325 + 71552.7i) q^{20} +(192811. - 194047. i) q^{22} -147346. i q^{23} +78125.0 q^{25} +(-124152. - 123361. i) q^{26} +(1.00877e6 - 6447.48i) q^{28} -41637.4 q^{29} -138577. i q^{31} +(753207. + 729514. i) q^{32} +(1.15389e6 + 1.14653e6i) q^{34} -1.10142e6i q^{35} +1.14978e6 q^{37} +(1.05368e6 - 1.06044e6i) q^{38} +(801745. - 817267. i) q^{40} -3.83906e6 q^{41} -3.18959e6i q^{43} +(-4.37673e6 + 27973.6i) q^{44} +(-1.66170e6 + 1.67235e6i) q^{46} -3.51218e6i q^{47} -9.76332e6 q^{49} +(-886704. - 881054. i) q^{50} +(17897.6 + 2.80024e6i) q^{52} -5.66612e6 q^{53} +4.77874e6i q^{55} +(-1.15220e7 - 1.13032e7i) q^{56} +(472576. + 469565. i) q^{58} +1.69068e7i q^{59} -5.16010e6 q^{61} +(-1.56280e6 + 1.57282e6i) q^{62} +(-321668. - 1.67741e7i) q^{64} +3.05745e6 q^{65} -1.05358e7i q^{67} +(-166343. - 2.60259e7i) q^{68} +(-1.24213e7 + 1.25009e7i) q^{70} +1.85971e7i q^{71} +2.38535e6 q^{73} +(-1.30498e7 - 1.29666e7i) q^{74} +(-2.39181e7 + 152871. i) q^{76} +6.73718e7 q^{77} +4.42560e7i q^{79} +(-1.83164e7 + 234146. i) q^{80} +(4.35726e7 + 4.32950e7i) q^{82} +1.51824e7i q^{83} -2.84164e7 q^{85} +(-3.59706e7 + 3.62013e7i) q^{86} +(4.99905e7 + 4.90411e7i) q^{88} +5.42739e7 q^{89} -4.31047e7i q^{91} +(3.77199e7 - 241085. i) q^{92} +(-3.96086e7 + 3.98625e7i) q^{94} +2.61151e7i q^{95} -1.24798e8 q^{97} +(1.10812e8 + 1.10106e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 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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Database

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