LMFDB - Embedded newform 20.9.b.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,9,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.14757220122$
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} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{58}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.1
Root			$9.29581 + 2.24761i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.9.b.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.3556 - 4.49522i) q^{2} +98.1237i q^{3} +(215.586 + 138.053i) q^{4} +279.508 q^{5} +(441.088 - 1506.74i) q^{6} +820.952i q^{7} +(-2689.86 - 3088.99i) q^{8} -3067.27 q^{9} +O(q^{10})$	\(q+(-15.3556 - 4.49522i) q^{2} +98.1237i q^{3} +(215.586 + 138.053i) q^{4} +279.508 q^{5} +(441.088 - 1506.74i) q^{6} +820.952i q^{7} +(-2689.86 - 3088.99i) q^{8} -3067.27 q^{9} +(-4292.01 - 1256.45i) q^{10} +21147.7i q^{11} +(-13546.3 + 21154.1i) q^{12} -36649.1 q^{13} +(3690.36 - 12606.2i) q^{14} +27426.4i q^{15} +(27418.7 + 59524.7i) q^{16} -110563. q^{17} +(47099.6 + 13788.0i) q^{18} -184840. i q^{19} +(60258.1 + 38587.0i) q^{20} -80554.9 q^{21} +(95063.7 - 324735. i) q^{22} +181906. i q^{23} +(303103. - 263939. i) q^{24} +78125.0 q^{25} +(562767. + 164746. i) q^{26} +342818. i q^{27} +(-113335. + 176986. i) q^{28} -229647. q^{29} +(123288. - 421148. i) q^{30} +388118. i q^{31} +(-153452. - 1.03729e6i) q^{32} -2.07510e6 q^{33} +(1.69776e6 + 497005. i) q^{34} +229463. i q^{35} +(-661260. - 423446. i) q^{36} +1.32611e6 q^{37} +(-830894. + 2.83831e6i) q^{38} -3.59615e6i q^{39} +(-751840. - 863399. i) q^{40} -303036. q^{41} +(1.23696e6 + 362112. i) q^{42} +962361. i q^{43} +(-2.91951e6 + 4.55916e6i) q^{44} -857327. q^{45} +(817709. - 2.79327e6i) q^{46} +8.76124e6i q^{47} +(-5.84078e6 + 2.69042e6i) q^{48} +5.09084e6 q^{49} +(-1.19965e6 - 351189. i) q^{50} -1.08489e7i q^{51} +(-7.90103e6 - 5.05952e6i) q^{52} -577555. q^{53} +(1.54104e6 - 5.26416e6i) q^{54} +5.91097e6i q^{55} +(2.53591e6 - 2.20825e6i) q^{56} +1.81371e7 q^{57} +(3.52636e6 + 1.03231e6i) q^{58} -4.11725e6i q^{59} +(-3.78630e6 + 5.91275e6i) q^{60} +2.10168e7 q^{61} +(1.74467e6 - 5.95976e6i) q^{62} -2.51808e6i q^{63} +(-2.30649e6 + 1.66179e7i) q^{64} -1.02437e7 q^{65} +(3.18642e7 + 9.32801e6i) q^{66} -3.85926e7i q^{67} +(-2.38359e7 - 1.52636e7i) q^{68} -1.78493e7 q^{69} +(1.03149e6 - 3.52353e6i) q^{70} +2.07744e7i q^{71} +(8.25053e6 + 9.47475e6i) q^{72} -2.70559e7 q^{73} +(-2.03632e7 - 5.96116e6i) q^{74} +7.66592e6i q^{75} +(2.55177e7 - 3.98488e7i) q^{76} -1.73613e7 q^{77} +(-1.61655e7 + 5.52208e7i) q^{78} +5.62358e7i q^{79} +(7.66375e6 + 1.66376e7i) q^{80} -5.37629e7 q^{81} +(4.65328e6 + 1.36221e6i) q^{82} +6.22189e7i q^{83} +(-1.73665e7 - 1.11209e7i) q^{84} -3.09033e7 q^{85} +(4.32602e6 - 1.47776e7i) q^{86} -2.25338e7i q^{87} +(6.53251e7 - 5.68845e7i) q^{88} +6.04409e7 q^{89} +(1.31647e7 + 3.85387e6i) q^{90} -3.00871e7i q^{91} +(-2.51127e7 + 3.92165e7i) q^{92} -3.80836e7 q^{93} +(3.93837e7 - 1.34534e8i) q^{94} -5.16642e7i q^{95} +(1.01782e8 - 1.50573e7i) q^{96} +1.31334e8 q^{97} +(-7.81727e7 - 2.28844e7i) q^{98} -6.48658e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	−15.3556	−	4.49522i	−0.959722	−	0.280951i
$2$	−15.3556	−	4.49522i	−0.959722	−	0.280951i
$3$			98.1237i			1.21140i	0.795692	+	0.605702i	$0.207108\pi$
$3$			98.1237i			1.21140i	−0.795692	+	0.605702i	$0.792892\pi$
$4$	215.586	+	138.053i	0.842133	+	0.539270i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$	441.088	−	1506.74i	0.340345	−	1.16261i
$7$			820.952i			0.341921i	0.985278	+	0.170960i	$0.0546870\pi$
$7$			820.952i			0.341921i	−0.985278	+	0.170960i	$0.945313\pi$
$8$	−2689.86	−	3088.99i	−0.656705	−	0.754148i
$9$	−3067.27			−0.467500
$10$	−4292.01	−	1256.45i	−0.429201	−	0.125645i
$11$			21147.7i			1.44442i	0.691674	+	0.722210i	$0.256873\pi$
$11$			21147.7i			1.44442i	−0.691674	+	0.722210i	$0.743127\pi$
$12$	−13546.3	+	21154.1i	−0.653274	+	1.02016i
$13$	−36649.1			−1.28319			−0.641593	−	0.767045i	$-0.721726\pi$
$13$	−36649.1			−1.28319			−0.641593	+	0.767045i	$0.721726\pi$
$14$	3690.36	−	12606.2i	0.0960630	−	0.328149i
$15$			27426.4i			0.541756i
$16$	27418.7	+	59524.7i	0.418376	+	0.908274i
$17$	−110563.			−1.32378			−0.661888	−	0.749603i	$-0.730245\pi$
$17$	−110563.			−1.32378			−0.661888	+	0.749603i	$0.730245\pi$
$18$	47099.6	+	13788.0i	0.448670	+	0.131345i
$19$		−	184840.i		−	1.41834i	−0.705037	−	0.709170i	$-0.749070\pi$
$19$		−	184840.i		−	1.41834i	0.705037	−	0.709170i	$-0.250930\pi$
$20$	60258.1	+	38587.0i	0.376613	+	0.241169i
$21$	−80554.9			−0.414204
$22$	95063.7	−	324735.i	0.405811	−	1.38624i
$23$			181906.i			0.650035i	0.945708	+	0.325017i	$0.105370\pi$
$23$			181906.i			0.650035i	−0.945708	+	0.325017i	$0.894630\pi$
$24$	303103.	−	263939.i	0.913577	−	0.795535i
$25$	78125.0			0.200000
$26$	562767.	+	164746.i	1.23150	+	0.360513i
$27$			342818.i			0.645073i
$28$	−113335.	+	176986.i	−0.184388	+	0.287943i
$29$	−229647.			−0.324690			−0.162345	−	0.986734i	$-0.551906\pi$
$29$	−229647.			−0.324690			−0.162345	+	0.986734i	$0.551906\pi$
$30$	123288.	−	421148.i	0.152207	−	0.519936i
$31$			388118.i			0.420259i	0.977674	+	0.210129i	$0.0673885\pi$
$31$			388118.i			0.420259i	−0.977674	+	0.210129i	$0.932611\pi$
$32$	−153452.	−	1.03729e6i	−0.146344	−	0.989234i
$33$	−2.07510e6			−1.74978
$34$	1.69776e6	+	497005.i	1.27046	+	0.371916i
$35$			229463.i			0.152912i
$36$	−661260.	−	423446.i	−0.393697	−	0.252109i
$37$	1.32611e6			0.707576			0.353788	−	0.935326i	$-0.384893\pi$
$37$	1.32611e6			0.707576			0.353788	+	0.935326i	$0.384893\pi$
$38$	−830894.	+	2.83831e6i	−0.398484	+	1.36121i
$39$		−	3.59615e6i		−	1.55446i
$40$	−751840.	−	863399.i	−0.293687	−	0.337265i
$41$	−303036.			−0.107240			−0.0536202	−	0.998561i	$-0.517076\pi$
$41$	−303036.			−0.107240			−0.0536202	+	0.998561i	$0.517076\pi$
$42$	1.23696e6	+	362112.i	0.397521	+	0.116371i
$43$			962361.i			0.281491i	0.990046	+	0.140745i	$0.0449499\pi$
$43$			962361.i			0.281491i	−0.990046	+	0.140745i	$0.955050\pi$
$44$	−2.91951e6	+	4.55916e6i	−0.778932	+	1.21639i
$45$	−857327.			−0.209072
$46$	817709.	−	2.79327e6i	0.182628	−	0.623853i
$47$			8.76124e6i			1.79545i	0.440552	+	0.897727i	$0.354783\pi$
$47$			8.76124e6i			1.79545i	−0.440552	+	0.897727i	$0.645217\pi$
$48$	−5.84078e6	+	2.69042e6i	−1.10029	+	0.506822i
$49$	5.09084e6			0.883090
$50$	−1.19965e6	−	351189.i	−0.191944	−	0.0561902i
$51$		−	1.08489e7i		−	1.60363i
$52$	−7.90103e6	−	5.05952e6i	−1.08061	−	0.691984i
$53$	−577555.			−0.0731965			−0.0365982	−	0.999330i	$-0.511652\pi$
$53$	−577555.			−0.0731965			−0.0365982	+	0.999330i	$0.511652\pi$
$54$	1.54104e6	−	5.26416e6i	0.181234	−	0.619091i
$55$			5.91097e6i			0.645964i
$56$	2.53591e6	−	2.20825e6i	0.257859	−	0.224541i
$57$	1.81371e7			1.71818
$58$	3.52636e6	+	1.03231e6i	0.311612	+	0.0912220i
$59$		−	4.11725e6i		−	0.339781i	−0.985463	−	0.169891i	$-0.945659\pi$
$59$		−	4.11725e6i		−	0.339781i	0.985463	−	0.169891i	$-0.0543414\pi$
$60$	−3.78630e6	+	5.91275e6i	−0.292153	+	0.456231i
$61$	2.10168e7			1.51791			0.758956	−	0.651142i	$-0.225710\pi$
$61$	2.10168e7			1.51791			0.758956	+	0.651142i	$0.225710\pi$
$62$	1.74467e6	−	5.95976e6i	0.118072	−	0.403332i
$63$		−	2.51808e6i		−	0.159848i
$64$	−2.30649e6	+	1.66179e7i	−0.137477	+	0.990505i
$65$	−1.02437e7			−0.573858
$66$	3.18642e7	+	9.32801e6i	1.67930	+	0.491601i
$67$		−	3.85926e7i		−	1.91516i	−0.288168	−	0.957580i	$-0.593046\pi$
$67$		−	3.85926e7i		−	1.91516i	0.288168	−	0.957580i	$-0.406954\pi$
$68$	−2.38359e7	−	1.52636e7i	−1.11480	−	0.713873i
$69$	−1.78493e7			−0.787455
$70$	1.03149e6	−	3.52353e6i	0.0429607	−	0.146753i
$71$			2.07744e7i			0.817515i	0.912643	+	0.408758i	$0.134038\pi$
$71$			2.07744e7i			0.817515i	−0.912643	+	0.408758i	$0.865962\pi$
$72$	8.25053e6	+	9.47475e6i	0.307009	+	0.352564i
$73$	−2.70559e7			−0.952732			−0.476366	−	0.879247i	$-0.658046\pi$
$73$	−2.70559e7			−0.952732			−0.476366	+	0.879247i	$0.658046\pi$
$74$	−2.03632e7	−	5.96116e6i	−0.679077	−	0.198794i
$75$			7.66592e6i			0.242281i
$76$	2.55177e7	−	3.98488e7i	0.764869	−	1.19443i
$77$	−1.73613e7			−0.493877
$78$	−1.61655e7	+	5.52208e7i	−0.436727	+	1.49185i
$79$			5.62358e7i			1.44379i	0.692002	+	0.721896i	$0.256729\pi$
$79$			5.62358e7i			1.44379i	−0.692002	+	0.721896i	$0.743271\pi$
$80$	7.66375e6	+	1.66376e7i	0.187103	+	0.406193i
$81$	−5.37629e7			−1.24894
$82$	4.65328e6	+	1.36221e6i	0.102921	+	0.0301293i
$83$			6.22189e7i			1.31102i	0.755186	+	0.655511i	$0.227547\pi$
$83$			6.22189e7i			1.31102i	−0.755186	+	0.655511i	$0.772453\pi$
$84$	−1.73665e7	−	1.11209e7i	−0.348815	−	0.223368i
$85$	−3.09033e7			−0.592011
$86$	4.32602e6	−	1.47776e7i	0.0790852	−	0.270153i
$87$		−	2.25338e7i		−	0.393331i
$88$	6.53251e7	−	5.68845e7i	1.08931	−	0.948557i
$89$	6.04409e7			0.963321			0.481661	−	0.876358i	$-0.340034\pi$
$89$	6.04409e7			0.963321			0.481661	+	0.876358i	$0.340034\pi$
$90$	1.31647e7	+	3.85387e6i	0.200651	+	0.0587391i
$91$		−	3.00871e7i		−	0.438748i
$92$	−2.51127e7	+	3.92165e7i	−0.350544	+	0.547416i
$93$	−3.80836e7			−0.509103
$94$	3.93837e7	−	1.34534e8i	0.504435	−	1.72314i
$95$		−	5.16642e7i		−	0.634301i
$96$	1.01782e8	−	1.50573e7i	1.19836	−	0.177281i
$97$	1.31334e8			1.48351			0.741755	−	0.670671i	$-0.233994\pi$
$97$	1.31334e8			1.48351			0.741755	+	0.670671i	$0.233994\pi$
$98$	−7.81727e7	−	2.28844e7i	−0.847521	−	0.248105i
$99$		−	6.48658e7i		−	0.675266i
$100$	1.68427e7	+	1.07854e7i	0.168427	+	0.107854i
$101$	−1.55397e8			−1.49333			−0.746665	−	0.665200i	$-0.768346\pi$
$101$	−1.55397e8			−1.49333			−0.746665	+	0.665200i	$0.768346\pi$
$102$	−4.87680e7	+	1.66590e8i	−0.450541	+	1.53904i
$103$		−	3.83213e7i		−	0.340480i	−0.985403	−	0.170240i	$-0.945546\pi$
$103$		−	3.83213e7i		−	0.340480i	0.985403	−	0.170240i	$-0.0544543\pi$
$104$	9.85810e7	+	1.13209e8i	0.842675	+	0.967712i
$105$	−2.25158e7			−0.185238
$106$	8.86868e6	+	2.59624e6i	0.0702483	+	0.0205646i
$107$		−	3.36904e7i		−	0.257022i	−0.991708	−	0.128511i	$-0.958980\pi$
$107$		−	3.36904e7i		−	0.257022i	0.991708	−	0.128511i	$-0.0410198\pi$
$108$	−4.73271e7	+	7.39068e7i	−0.347869	+	0.543237i
$109$	1.87899e8			1.33112			0.665562	−	0.746343i	$-0.268192\pi$
$109$	1.87899e8			1.33112			0.665562	+	0.746343i	$0.268192\pi$
$110$	2.65711e7	−	9.07663e7i	0.181484	−	0.619946i
$111$			1.30123e8i			0.857161i
$112$	−4.88669e7	+	2.25094e7i	−0.310558	+	0.143051i
$113$	2.44191e8			1.49767			0.748835	−	0.662757i	$-0.230614\pi$
$113$	2.44191e8			1.49767			0.748835	+	0.662757i	$0.230614\pi$
$114$	−2.78506e8	−	8.15304e7i	−1.64898	−	0.482726i
$115$			5.08444e7i			0.290704i
$116$	−4.95087e7	−	3.17035e7i	−0.273432	−	0.175096i
$117$	1.12413e8			0.599889
$118$	−1.85079e7	+	6.32226e7i	−0.0954619	+	0.326095i
$119$		−	9.07670e7i		−	0.452627i
$120$	8.47199e7	−	7.37733e7i	0.408564	−	0.355774i
$121$	−2.32868e8			−1.08635
$122$	−3.22724e8	−	9.44749e7i	−1.45677	−	0.426459i
$123$		−	2.97350e7i		−	0.129911i
$124$	−5.35809e7	+	8.36728e7i	−0.226633	+	0.353914i
$125$	2.18366e7			0.0894427
$126$	−1.13193e7	+	3.86665e7i	−0.0449095	+	0.153410i
$127$		−	4.32402e7i		−	0.166216i	−0.996541	−	0.0831080i	$-0.973515\pi$
$127$		−	4.32402e7i		−	0.166216i	0.996541	−	0.0831080i	$-0.0264846\pi$
$128$	1.10119e8	−	2.44809e8i	0.410223	−	0.911985i
$129$	−9.44304e7			−0.340999
$130$	1.57298e8	+	4.60478e7i	0.550745	+	0.161226i
$131$			3.46986e8i			1.17822i	0.808052	+	0.589111i	$0.200522\pi$
$131$			3.46986e8i			1.17822i	−0.808052	+	0.589111i	$0.799478\pi$
$132$	−4.47362e8	−	2.86473e8i	−1.47354	−	0.943602i
$133$	1.51744e8			0.484960
$134$	−1.73482e8	+	5.92611e8i	−0.538066	+	1.83802i
$135$			9.58206e7i			0.288485i
$136$	2.97400e8	+	3.41528e8i	0.869330	+	0.998323i
$137$	4.54595e8			1.29045			0.645227	−	0.763991i	$-0.276763\pi$
$137$	4.54595e8			1.29045			0.645227	+	0.763991i	$0.276763\pi$
$138$	2.74086e8	+	8.02366e7i	0.755738	+	0.221236i
$139$		−	1.24500e8i		−	0.333511i	−0.985998	−	0.166755i	$-0.946671\pi$
$139$		−	1.24500e8i		−	0.333511i	0.985998	−	0.166755i	$-0.0533290\pi$
$140$	−3.16781e7	+	4.94690e7i	−0.0824607	+	0.128772i
$141$	−8.59686e8			−2.17502
$142$	9.33856e7	−	3.19003e8i	0.229682	−	0.784587i
$143$		−	7.75046e8i		−	1.85346i
$144$	−8.41003e7	−	1.82578e8i	−0.195590	−	0.424618i
$145$	−6.41883e7			−0.145206
$146$	4.15459e8	+	1.21622e8i	0.914358	+	0.267671i
$147$			4.99532e8i			1.06978i
$148$	2.85891e8	+	1.83074e8i	0.595873	+	0.381575i
$149$	−2.17967e8			−0.442228			−0.221114	−	0.975248i	$-0.570969\pi$
$149$	−2.17967e8			−0.442228			−0.221114	+	0.975248i	$0.570969\pi$
$150$	3.44600e7	−	1.17714e8i	0.0680691	−	0.232522i
$151$		−	2.00315e8i		−	0.385306i	−0.981267	−	0.192653i	$-0.938291\pi$
$151$		−	2.00315e8i		−	0.385306i	0.981267	−	0.192653i	$-0.0617091\pi$
$152$	−5.70967e8	+	4.97193e8i	−1.06964	+	0.931431i
$153$	3.39126e8			0.618865
$154$	2.66592e8	+	7.80427e7i	0.473985	+	0.138755i
$155$			1.08482e8i			0.187945i
$156$	4.96459e8	−	7.75279e8i	0.838272	−	1.30906i
$157$	−2.01644e7			−0.0331885			−0.0165942	−	0.999862i	$-0.505282\pi$
$157$	−2.01644e7			−0.0331885			−0.0165942	+	0.999862i	$0.505282\pi$
$158$	2.52792e8	−	8.63532e8i	0.405635	−	1.38564i
$159$		−	5.66719e7i		−	0.0886705i
$160$	−4.28912e7	−	2.89930e8i	−0.0654468	−	0.442399i
$161$	−1.49336e8			−0.222260
$162$	8.25560e8	+	2.41676e8i	1.19864	+	0.350892i
$163$			1.92932e7i			0.0273309i	0.999907	+	0.0136654i	$0.00434998\pi$
$163$			1.92932e7i			0.0273309i	−0.999907	+	0.0136654i	$0.995650\pi$
$164$	−6.53303e7	−	4.18350e7i	−0.0903107	−	0.0578315i
$165$	−5.80007e8			−0.782523
$166$	2.79687e8	−	9.55405e8i	0.368333	−	1.25822i
$167$			2.03394e8i			0.261500i	0.991415	+	0.130750i	$0.0417385\pi$
$167$			2.03394e8i			0.261500i	−0.991415	+	0.130750i	$0.958261\pi$
$168$	2.16682e8	+	2.48833e8i	0.272010	+	0.312371i
$169$	5.27425e8			0.646567
$170$	4.74538e8	+	1.38917e8i	0.568166	+	0.166326i
$171$			5.66952e8i			0.663074i
$172$	−1.32857e8	+	2.07472e8i	−0.151800	+	0.237053i
$173$	−4.16190e8			−0.464630			−0.232315	−	0.972641i	$-0.574630\pi$
$173$	−4.16190e8			−0.464630			−0.232315	+	0.972641i	$0.574630\pi$
$174$	−1.01294e8	+	3.46019e8i	−0.110507	+	0.377488i
$175$			6.41369e7i			0.0683842i
$176$	−1.25881e9	+	5.79843e8i	−1.31193	+	0.604310i
$177$	4.04000e8			0.411612
$178$	−9.28104e8	−	2.71695e8i	−0.924521	−	0.270646i
$179$			5.41911e8i			0.527856i	0.964542	+	0.263928i	$0.0850182\pi$
$179$			5.41911e8i			0.527856i	−0.964542	+	0.263928i	$0.914982\pi$
$180$	−1.84828e8	−	1.18357e8i	−0.176067	−	0.112746i
$181$	−1.43210e9			−1.33432			−0.667159	−	0.744915i	$-0.732490\pi$
$181$	−1.43210e9			−1.33432			−0.667159	+	0.744915i	$0.732490\pi$
$182$	−1.35248e8	+	4.62005e8i	−0.123267	+	0.421076i
$183$			2.06224e9i			1.83880i
$184$	5.61907e8	−	4.89303e8i	0.490222	−	0.426881i
$185$	3.70660e8			0.316438
$186$	5.84794e8	+	1.71194e8i	0.488598	+	0.143033i
$187$		−	2.33816e9i		−	1.91209i
$188$	−1.20952e9	+	1.88880e9i	−0.968235	+	1.51201i
$189$	−2.81437e8			−0.220564
$190$	−2.32242e8	+	7.93333e8i	−0.178208	+	0.608753i
$191$		−	1.75647e9i		−	1.31980i	−0.751355	−	0.659898i	$-0.770600\pi$
$191$		−	1.75647e9i		−	1.31980i	0.751355	−	0.659898i	$-0.229400\pi$
$192$	−1.63061e9	−	2.26321e8i	−1.19990	−	0.166540i
$193$	−6.79519e8			−0.489748			−0.244874	−	0.969555i	$-0.578747\pi$
$193$	−6.79519e8			−0.489748			−0.244874	+	0.969555i	$0.578747\pi$
$194$	−2.01671e9	−	5.90376e8i	−1.42376	−	0.416794i
$195$		−	1.00515e9i		−	0.695174i
$196$	1.09751e9	+	7.02806e8i	0.743679	+	0.476224i
$197$	4.80726e8			0.319178			0.159589	−	0.987184i	$-0.448983\pi$
$197$	4.80726e8			0.319178			0.159589	+	0.987184i	$0.448983\pi$
$198$	−2.91586e8	+	9.96050e8i	−0.189717	+	0.648067i
$199$			6.20901e8i			0.395922i	0.980210	+	0.197961i	$0.0634320\pi$
$199$			6.20901e8i			0.395922i	−0.980210	+	0.197961i	$0.936568\pi$
$200$	−2.10146e8	−	2.41327e8i	−0.131341	−	0.150830i
$201$	3.78685e9			2.32003
$202$	2.38620e9	+	6.98541e8i	1.43318	+	0.419553i
$203$		−	1.88529e8i		−	0.111018i
$204$	1.49772e9	−	2.33886e9i	0.864788	−	1.35047i
$205$	−8.47011e7			−0.0479594
$206$	−1.72263e8	+	5.88445e8i	−0.0956582	+	0.326766i
$207$		−	5.57955e8i		−	0.303891i
$208$	−1.00487e9	−	2.18152e9i	−0.536854	−	1.16549i
$209$	3.90894e9			2.04868
$210$	3.45742e8	+	1.01213e8i	0.177777	+	0.0520428i
$211$			2.32298e9i			1.17197i	0.810322	+	0.585984i	$0.199292\pi$
$211$			2.32298e9i			1.17197i	−0.810322	+	0.585984i	$0.800708\pi$
$212$	−1.24513e8	−	7.97333e7i	−0.0616411	−	0.0394727i
$213$	−2.03846e9			−0.990341
$214$	−1.51446e8	+	5.17334e8i	−0.0722107	+	0.246670i
$215$			2.68988e8i			0.125886i
$216$	1.05896e9	−	9.22134e8i	0.486480	−	0.423623i
$217$	−3.18626e8			−0.143695
$218$	−2.88529e9	−	8.44647e8i	−1.27751	−	0.373981i
$219$		−	2.65483e9i		−	1.15414i
$220$	−8.16029e8	+	1.27432e9i	−0.348349	+	0.543987i
$221$	4.05204e9			1.69865
$222$	5.84932e8	−	1.99811e9i	0.240820	−	0.822636i
$223$			1.52445e9i			0.616446i	0.951314	+	0.308223i	$0.0997343\pi$
$223$			1.52445e9i			0.616446i	−0.951314	+	0.308223i	$0.900266\pi$
$224$	8.51563e8	−	1.25977e8i	0.338240	−	0.0500379i
$225$	−2.39630e8			−0.0935000
$226$	−3.74969e9	−	1.09769e9i	−1.43735	−	0.420772i
$227$		−	7.14722e8i		−	0.269174i	−0.990902	−	0.134587i	$-0.957029\pi$
$227$		−	7.14722e8i		−	0.269174i	0.990902	−	0.134587i	$-0.0429708\pi$
$228$	3.91012e9	+	2.50389e9i	1.44694	+	0.926565i
$229$	−4.05044e9			−1.47286			−0.736428	−	0.676516i	$-0.763489\pi$
$229$	−4.05044e9			−1.47286			−0.736428	+	0.676516i	$0.763489\pi$
$230$	2.28557e8	−	7.80743e8i	0.0816737	−	0.278995i
$231$		−	1.70355e9i		−	0.598285i
$232$	6.17719e8	+	7.09377e8i	0.213226	+	0.244864i
$233$	1.91668e9			0.650318			0.325159	−	0.945659i	$-0.394582\pi$
$233$	1.91668e9			0.650318			0.325159	+	0.945659i	$0.394582\pi$
$234$	−1.72616e9	−	5.05319e8i	−0.575727	−	0.168540i
$235$			2.44884e9i			0.802952i
$236$	5.68399e8	−	8.87622e8i	0.183234	−	0.286141i
$237$	−5.51807e9			−1.74901
$238$	−4.08017e8	+	1.39378e9i	−0.127166	+	0.434396i
$239$			3.09701e9i			0.949186i	0.880205	+	0.474593i	$0.157405\pi$
$239$			3.09701e9i			0.949186i	−0.880205	+	0.474593i	$0.842595\pi$
$240$	−1.63255e9	+	7.51996e8i	−0.492063	+	0.226658i
$241$	−1.93463e9			−0.573496			−0.286748	−	0.958006i	$-0.592574\pi$
$241$	−1.93463e9			−0.573496			−0.286748	+	0.958006i	$0.592574\pi$
$242$	3.57582e9	+	1.04679e9i	1.04259	+	0.305211i
$243$		−	3.02619e9i		−	0.867903i
$244$	4.53092e9	+	2.90143e9i	1.27828	+	0.818564i
$245$	1.42293e9			0.394930
$246$	−1.33665e8	+	4.56597e8i	−0.0364988	+	0.124679i
$247$			6.77420e9i			1.82000i
$248$	1.19889e9	−	1.04398e9i	0.316937	−	0.275986i
$249$	−6.10515e9			−1.58818
$250$	−3.35313e8	−	9.81603e7i	−0.0858402	−	0.0251290i
$251$		−	5.70277e9i		−	1.43678i	−0.695639	−	0.718391i	$-0.744879\pi$
$251$		−	5.70277e9i		−	1.43678i	0.695639	−	0.718391i	$-0.255121\pi$
$252$	3.47629e8	−	5.42862e8i	0.0862012	−	0.134613i
$253$	−3.84691e9			−0.938923
$254$	−1.94374e8	+	6.63977e8i	−0.0466986	+	0.159521i
$255$		−	3.03235e9i		−	0.717164i
$256$	−2.79140e9	+	3.26417e9i	−0.649924	+	0.759999i
$257$	1.76094e9			0.403656			0.201828	−	0.979421i	$-0.435312\pi$
$257$	1.76094e9			0.403656			0.201828	+	0.979421i	$0.435312\pi$
$258$	1.45003e9	+	4.24485e8i	0.327264	+	0.0958041i
$259$			1.08867e9i			0.241935i
$260$	−2.20841e9	−	1.41418e9i	−0.483265	−	0.309465i
$261$	7.04389e8			0.151793
$262$	1.55978e9	−	5.32816e9i	0.331023	−	1.13076i
$263$		−	2.58682e8i		−	0.0540683i	−0.999635	−	0.0270342i	$-0.991394\pi$
$263$		−	2.58682e8i		−	0.0540683i	0.999635	−	0.0270342i	$-0.00860629\pi$
$264$	5.58172e9	+	6.40995e9i	1.14909	+	1.31959i
$265$	−1.61432e8			−0.0327345
$266$	−2.33012e9	−	6.82124e8i	−0.465427	−	0.136250i
$267$			5.93069e9i			1.16697i
$268$	5.32783e9	−	8.32003e9i	1.03279	−	1.61282i
$269$	−3.03788e9			−0.580178			−0.290089	−	0.957000i	$-0.593685\pi$
$269$	−3.03788e9			−0.580178			−0.290089	+	0.957000i	$0.593685\pi$
$270$	4.30735e8	−	1.47138e9i	0.0810503	−	0.276866i
$271$		−	1.65010e9i		−	0.305937i	−0.988231	−	0.152968i	$-0.951117\pi$
$271$		−	1.65010e9i		−	0.305937i	0.988231	−	0.152968i	$-0.0488833\pi$
$272$	−3.03149e9	−	6.58123e9i	−0.553836	−	1.20235i
$273$	2.95226e9			0.531501
$274$	−6.98056e9	−	2.04350e9i	−1.23848	−	0.362554i
$275$			1.65217e9i			0.288884i
$276$	−3.84807e9	−	2.46416e9i	−0.663141	−	0.424651i
$277$	−5.17850e9			−0.879599			−0.439800	−	0.898096i	$-0.644951\pi$
$277$	−5.17850e9			−0.879599			−0.439800	+	0.898096i	$0.644951\pi$
$278$	−5.59654e8	+	1.91176e9i	−0.0937002	+	0.320078i
$279$		−	1.19046e9i		−	0.196471i
$280$	7.08809e8	−	6.17224e8i	0.115318	−	0.100418i
$281$	8.47832e9			1.35983			0.679915	−	0.733291i	$-0.262017\pi$
$281$	8.47832e9			1.35983			0.679915	+	0.733291i	$0.262017\pi$
$282$	1.32010e10	+	3.86448e9i	2.08742	+	0.611075i
$283$		−	3.20005e8i		−	0.0498898i	−0.999689	−	0.0249449i	$-0.992059\pi$
$283$		−	3.20005e8i		−	0.0498898i	0.999689	−	0.0249449i	$-0.00794102\pi$
$284$	−2.86798e9	+	4.47868e9i	−0.440861	+	0.688456i
$285$	5.06949e9			0.768395
$286$	−3.48400e9	+	1.19013e10i	−0.520732	+	1.77881i
$287$		−	2.48778e8i		−	0.0366677i
$288$	4.70679e8	+	3.18163e9i	0.0684156	+	0.462467i
$289$	5.24844e9			0.752383
$290$	9.85647e8	+	2.88540e8i	0.139357	+	0.0407957i
$291$			1.28870e10i			1.79713i
$292$	−5.83288e9	−	3.73516e9i	−0.802327	−	0.513780i
$293$	7.87248e9			1.06817			0.534086	−	0.845430i	$-0.320656\pi$
$293$	7.87248e9			1.06817			0.534086	+	0.845430i	$0.320656\pi$
$294$	2.24551e9	−	7.67059e9i	0.300556	−	1.02669i
$295$		−	1.15081e9i		−	0.151955i
$296$	−3.56706e9	−	4.09634e9i	−0.464669	−	0.533617i
$297$	−7.24983e9			−0.931756
$298$	3.34701e9	+	9.79811e8i	0.424416	+	0.124245i
$299$		−	6.66670e9i		−	0.834116i
$300$	−1.05830e9	+	1.65266e9i	−0.130655	+	0.204033i
$301$	−7.90052e8			−0.0962475
$302$	−9.00459e8	+	3.07595e9i	−0.108252	+	0.369786i
$303$		−	1.52481e10i		−	1.80903i
$304$	1.10025e10	−	5.06805e9i	1.28824	−	0.593399i
$305$	5.87436e9			0.678831
$306$	−5.20747e9	−	1.52445e9i	−0.593938	−	0.173871i
$307$		−	1.47434e10i		−	1.65976i	−0.557941	−	0.829881i	$-0.688408\pi$
$307$		−	1.47434e10i		−	1.65976i	0.557941	−	0.829881i	$-0.311592\pi$
$308$	−3.74285e9	−	2.39678e9i	−0.415910	−	0.266333i
$309$	3.76023e9			0.412459
$310$	4.87651e8	−	1.66580e9i	0.0528035	−	0.180375i
$311$		−	6.36308e9i		−	0.680184i	−0.940392	−	0.340092i	$-0.889542\pi$
$311$		−	6.36308e9i		−	0.680184i	0.940392	−	0.340092i	$-0.110458\pi$
$312$	−1.11085e10	+	9.67314e9i	−1.17229	+	1.02082i
$313$	4.35717e9			0.453970			0.226985	−	0.973898i	$-0.427113\pi$
$313$	4.35717e9			0.453970			0.226985	+	0.973898i	$0.427113\pi$
$314$	3.09636e8	+	9.06435e7i	0.0318517	+	0.00932434i
$315$		−	7.03824e8i		−	0.0714862i
$316$	−7.76353e9	+	1.21237e10i	−0.778594	+	1.21586i
$317$	−1.02074e9			−0.101083			−0.0505413	−	0.998722i	$-0.516095\pi$
$317$	−1.02074e9			−0.101083			−0.0505413	+	0.998722i	$0.516095\pi$
$318$	−2.54752e8	+	8.70228e8i	−0.0249121	+	0.0850990i
$319$		−	4.85652e9i		−	0.468989i
$320$	−6.44682e8	+	4.64485e9i	−0.0614817	+	0.442967i
$321$	3.30583e9			0.311358
$322$	2.29314e9	+	6.71299e8i	0.213308	+	0.0624443i
$323$			2.04364e10i			1.87757i
$324$	−1.15905e10	−	7.42214e9i	−1.05178	−	0.673518i
$325$	−2.86321e9			−0.256637
$326$	8.67271e7	−	2.96258e8i	0.00767865	−	0.0262301i
$327$			1.84373e10i			1.61253i
$328$	8.15125e8	+	9.36074e8i	0.0704253	+	0.0808751i
$329$	−7.19256e9			−0.613903
$330$	8.90633e9	+	2.60726e9i	0.751005	+	0.219851i
$331$			1.01219e10i			0.843235i	0.906774	+	0.421617i	$0.138537\pi$
$331$			1.01219e10i			0.843235i	−0.906774	+	0.421617i	$0.861463\pi$
$332$	−8.58951e9	+	1.34135e10i	−0.706995	+	1.10405i
$333$	−4.06754e9			−0.330792
$334$	9.14299e8	−	3.12322e9i	0.0734687	−	0.250967i
$335$		−	1.07870e10i		−	0.856485i
$336$	−2.20871e9	−	4.79500e9i	−0.173293	−	0.376211i
$337$	−1.94388e9			−0.150713			−0.0753563	−	0.997157i	$-0.524009\pi$
$337$	−1.94388e9			−0.150713			−0.0753563	+	0.997157i	$0.524009\pi$
$338$	−8.09890e9	−	2.37089e9i	−0.620525	−	0.181654i
$339$			2.39609e10i			1.81428i
$340$	−6.66233e9	−	4.26630e9i	−0.498552	−	0.319254i
$341$	−8.20782e9			−0.607030
$342$	2.54857e9	−	8.70586e9i	0.186291	−	0.636367i
$343$			8.91196e9i			0.643868i
$344$	2.97272e9	−	2.58862e9i	0.212286	−	0.184856i
$345$	−4.98904e9			−0.352160
$346$	6.39083e9	+	1.87087e9i	0.445916	+	0.130538i
$347$		−	2.15696e10i		−	1.48773i	−0.668330	−	0.743865i	$-0.732991\pi$
$347$		−	2.15696e10i		−	1.48773i	0.668330	−	0.743865i	$-0.267009\pi$
$348$	3.11087e9	−	4.85798e9i	0.212112	−	0.331237i
$349$	1.37934e10			0.929760			0.464880	−	0.885374i	$-0.346097\pi$
$349$	1.37934e10			0.929760			0.464880	+	0.885374i	$0.346097\pi$
$350$	2.88309e8	−	9.84857e8i	0.0192126	−	0.0656298i
$351$		−	1.25640e10i		−	0.827749i
$352$	2.19363e10	−	3.24517e9i	1.42887	−	0.211382i
$353$	−1.69884e10			−1.09409			−0.547047	−	0.837102i	$-0.684248\pi$
$353$	−1.69884e10			−1.09409			−0.547047	+	0.837102i	$0.684248\pi$
$354$	−6.20364e9	−	1.81607e9i	−0.395033	−	0.115643i
$355$			5.80663e9i			0.365604i
$356$	1.30302e10	+	8.34406e9i	0.811244	+	0.519490i
$357$	8.90639e9			0.548314
$358$	2.43601e9	−	8.32134e9i	0.148302	−	0.506595i
$359$			1.35600e10i			0.816358i	0.912902	+	0.408179i	$0.133836\pi$
$359$			1.35600e10i			0.816358i	−0.912902	+	0.408179i	$0.866164\pi$
$360$	2.30609e9	+	2.64827e9i	0.137299	+	0.157671i
$361$	−1.71821e10			−1.01169
$362$	2.19907e10	+	6.43761e9i	1.28057	+	0.374878i
$363$		−	2.28499e10i		−	1.31601i
$364$	4.15362e9	−	6.48637e9i	0.236604	−	0.369484i
$365$	−7.56236e9			−0.426075
$366$	9.27023e9	−	3.16669e10i	0.516614	−	1.76474i
$367$		−	9.93203e9i		−	0.547487i	−0.961803	−	0.273743i	$-0.911738\pi$
$367$		−	9.93203e9i		−	0.547487i	0.961803	−	0.273743i	$-0.0882619\pi$
$368$	−1.08279e10	+	4.98763e9i	−0.590410	+	0.271959i
$369$	9.29491e8			0.0501349
$370$	−5.69168e9	−	1.66620e9i	−0.303692	−	0.0889036i
$371$		−	4.74145e8i		−	0.0250274i
$372$	−8.21028e9	−	5.25756e9i	−0.428733	−	0.274544i
$373$	2.08933e10			1.07937			0.539686	−	0.841867i	$-0.318543\pi$
$373$	2.08933e10			1.07937			0.539686	+	0.841867i	$0.318543\pi$
$374$	−1.05105e10	+	3.59037e10i	−0.537203	+	1.83507i
$375$			2.14269e9i			0.108351i
$376$	2.70634e10	−	2.35666e10i	1.35404	−	1.17908i
$377$	8.41636e9			0.416638
$378$	4.32162e9	+	1.26512e9i	0.211680	+	0.0619677i
$379$		−	2.78733e10i		−	1.35093i	−0.737394	−	0.675463i	$-0.763944\pi$
$379$		−	2.78733e10i		−	1.35093i	0.737394	−	0.675463i	$-0.236056\pi$
$380$	7.13241e9	−	1.11381e10i	0.342060	−	0.534166i
$381$	4.24289e9			0.201355
$382$	−7.89571e9	+	2.69715e10i	−0.370798	+	1.26664i
$383$			3.14260e10i			1.46048i	0.683193	+	0.730238i	$0.260591\pi$
$383$			3.14260e10i			1.46048i	−0.683193	+	0.730238i	$0.739409\pi$
$384$	2.40216e10	+	1.08052e10i	1.10478	+	0.496946i
$385$	−4.85262e9			−0.220869
$386$	1.04344e10	+	3.05459e9i	0.470022	+	0.137595i
$387$		−	2.95182e9i		−	0.131597i
$388$	2.83138e10	+	1.81311e10i	1.24931	+	0.800013i
$389$	−2.45574e10			−1.07247			−0.536233	−	0.844070i	$-0.680153\pi$
$389$	−2.45574e10			−1.07247			−0.536233	+	0.844070i	$0.680153\pi$
$390$	−4.51838e9	+	1.54347e10i	−0.195310	+	0.667174i
$391$		−	2.01121e10i		−	0.860500i
$392$	−1.36937e10	−	1.57255e10i	−0.579930	−	0.665980i
$393$	−3.40476e10			−1.42730
$394$	−7.38181e9	−	2.16097e9i	−0.306322	−	0.0896733i
$395$			1.57184e10i			0.645683i
$396$	8.95492e9	−	1.39842e10i	0.364151	−	0.568663i
$397$	3.64363e10			1.46681			0.733403	−	0.679794i	$-0.237931\pi$
$397$	3.64363e10			1.46681			0.733403	+	0.679794i	$0.237931\pi$
$398$	2.79109e9	−	9.53428e9i	0.111235	−	0.379975i
$399$			1.48897e10i			0.587483i
$400$	2.14208e9	+	4.65036e9i	0.0836751	+	0.181655i
$401$	−1.07267e10			−0.414847			−0.207423	−	0.978251i	$-0.566508\pi$
$401$	−1.07267e10			−0.414847			−0.207423	+	0.978251i	$0.566508\pi$
$402$	−5.81492e10	−	1.70227e10i	−2.22659	−	0.651816i
$403$		−	1.42242e10i		−	0.539270i
$404$	−3.35013e10	−	2.14530e10i	−1.25758	−	0.805308i
$405$	−1.50272e10			−0.558545
$406$	−8.47480e8	+	2.89497e9i	−0.0311907	+	0.106547i
$407$			2.80443e10i			1.02204i
$408$	−3.35120e10	+	2.91820e10i	−1.20937	+	1.05311i
$409$	−3.91731e7			−0.00139989			−0.000699947	−	1.00000i	$-0.500223\pi$
$409$	−3.91731e7			−0.00139989			−0.000699947		1.00000i	$0.500223\pi$
$410$	1.30063e9	+	3.80750e8i	0.0460277	+	0.0134742i
$411$			4.46066e10i			1.56326i
$412$	5.29038e9	−	8.26154e9i	0.183611	−	0.286729i
$413$	3.38006e9			0.116178
$414$	−2.50813e9	+	8.56771e9i	−0.0853785	+	0.291651i
$415$			1.73907e10i			0.586307i
$416$	5.62389e9	+	3.80156e10i	0.187786	+	1.26937i
$417$	1.22164e10			0.404016
$418$	−6.00239e10	−	1.75715e10i	−1.96616	−	0.575579i
$419$		−	3.53613e10i		−	1.14729i	−0.819105	−	0.573644i	$-0.805529\pi$
$419$		−	3.53613e10i		−	1.14729i	0.819105	−	0.573644i	$-0.194471\pi$
$420$	−4.85408e9	−	3.10837e9i	−0.155995	−	0.0998932i
$421$	9.81579e9			0.312462			0.156231	−	0.987721i	$-0.450066\pi$
$421$	9.81579e9			0.312462			0.156231	+	0.987721i	$0.450066\pi$
$422$	1.04423e10	−	3.56707e10i	0.329266	−	1.12476i
$423$		−	2.68731e10i		−	0.839375i
$424$	1.55354e9	+	1.78406e9i	0.0480685	+	0.0552009i
$425$	−8.63774e9			−0.264755
$426$	3.13018e10	+	9.16334e9i	0.950452	+	0.278237i
$427$			1.72537e10i			0.519005i
$428$	4.65106e9	−	7.26317e9i	0.138604	−	0.216447i
$429$	7.60504e10			2.24529
$430$	1.20916e9	−	4.13046e9i	0.0353680	−	0.120816i
$431$		−	9.11726e9i		−	0.264214i	−0.991235	−	0.132107i	$-0.957826\pi$
$431$		−	9.11726e9i		−	0.264214i	0.991235	−	0.132107i	$-0.0421742\pi$
$432$	−2.04061e10	+	9.39962e9i	−0.585903	+	0.269883i
$433$	4.67005e9			0.132852			0.0664262	−	0.997791i	$-0.478840\pi$
$433$	4.67005e9			0.132852			0.0664262	+	0.997791i	$0.478840\pi$
$434$	4.89268e9	+	1.43229e9i	0.137907	+	0.0403713i
$435$		−	6.29840e9i		−	0.175903i
$436$	4.05084e10	+	2.59400e10i	1.12098	+	0.717835i
$437$	3.36235e10			0.921970
$438$	−1.19340e10	+	4.07664e10i	−0.324258	+	1.10766i
$439$		−	3.39406e10i		−	0.913822i	−0.889512	−	0.456911i	$-0.848956\pi$
$439$		−	3.39406e10i		−	0.913822i	0.889512	−	0.456911i	$-0.151044\pi$
$440$	1.82589e10	−	1.58997e10i	0.487152	−	0.424208i
$441$	−1.56150e10			−0.412844
$442$	−6.22213e10	−	1.82148e10i	−1.63023	−	0.477238i
$443$		−	7.20845e9i		−	0.187166i	−0.995611	−	0.0935830i	$-0.970168\pi$
$443$		−	7.20845e9i		−	0.187166i	0.995611	−	0.0935830i	$-0.0298320\pi$
$444$	−1.79639e10	+	2.80527e10i	−0.462241	+	0.721843i
$445$	1.68938e10			0.430810
$446$	6.85276e9	−	2.34088e10i	0.173191	−	0.591617i
$447$		−	2.13878e10i		−	0.535717i
$448$	−1.36425e10	−	1.89351e9i	−0.338674	−	0.0470063i
$449$	−2.32977e10			−0.573229			−0.286614	−	0.958046i	$-0.592530\pi$
$449$	−2.32977e10			−0.573229			−0.286614	+	0.958046i	$0.592530\pi$
$450$	3.67965e9	+	1.07719e9i	0.0897340	+	0.0262689i
$451$		−	6.40852e9i		−	0.154900i
$452$	5.26442e10	+	3.37113e10i	1.26124	+	0.807648i
$453$	1.96556e10			0.466761
$454$	−3.21283e9	+	1.09749e10i	−0.0756248	+	0.258333i
$455$		−	8.40961e9i		−	0.196214i
$456$	−4.87864e10	−	5.60254e10i	−1.12834	−	1.29576i
$457$	1.72652e10			0.395829			0.197915	−	0.980219i	$-0.436583\pi$
$457$	1.72652e10			0.395829			0.197915	+	0.980219i	$0.436583\pi$
$458$	6.21967e10	+	1.82076e10i	1.41353	+	0.413800i
$459$		−	3.79030e10i		−	0.853932i
$460$	−7.01922e9	+	1.09613e10i	−0.156768	+	0.244812i
$461$	−5.65725e10			−1.25257			−0.626285	−	0.779594i	$-0.715425\pi$
$461$	−5.65725e10			−1.25257			−0.626285	+	0.779594i	$0.715425\pi$
$462$	−7.65785e9	+	2.61590e10i	−0.168089	+	0.574187i
$463$			7.57511e10i			1.64841i	0.566292	+	0.824205i	$0.308377\pi$
$463$			7.57511e10i			1.64841i	−0.566292	+	0.824205i	$0.691623\pi$
$464$	−6.29662e9	−	1.36697e10i	−0.135842	−	0.294908i
$465$	−1.06447e10			−0.227678
$466$	−2.94317e10	−	8.61589e9i	−0.624124	−	0.182708i
$467$		−	5.63076e10i		−	1.18386i	−0.805990	−	0.591929i	$-0.798367\pi$
$467$		−	5.63076e10i		−	1.18386i	0.805990	−	0.591929i	$-0.201633\pi$
$468$	2.42346e10	+	1.55189e10i	0.505187	+	0.323502i
$469$	3.16827e10			0.654833
$470$	1.10081e10	−	3.76033e10i	0.225590	−	0.770610i
$471$		−	1.97861e9i		−	0.0402046i
$472$	−1.27181e10	+	1.10748e10i	−0.256245	+	0.223136i
$473$	−2.03518e10			−0.406591
$474$	8.47330e10	+	2.48049e10i	1.67857	+	0.491388i
$475$		−	1.44406e10i		−	0.283668i
$476$	1.25307e10	−	1.95681e10i	0.244088	−	0.381172i
$477$	1.77152e9			0.0342193
$478$	1.39218e10	−	4.75563e10i	0.266675	−	0.910955i
$479$			8.37112e10i			1.59016i	0.606502	+	0.795082i	$0.292572\pi$
$479$			8.37112e10i			1.59016i	−0.606502	+	0.795082i	$0.707428\pi$
$480$	2.84491e10	−	4.20865e9i	0.535924	−	0.0792826i
$481$	−4.86008e10			−0.907952
$482$	2.97073e10	+	8.69659e9i	0.550397	+	0.161124i
$483$		−	1.46534e10i		−	0.269247i
$484$	−5.02031e10	−	3.21482e10i	−0.914849	−	0.585835i
$485$	3.67090e10			0.663446
$486$	−1.36034e10	+	4.64688e10i	−0.243838	+	0.832945i
$487$			3.58034e10i			0.636514i	0.948004	+	0.318257i	$0.103098\pi$
$487$			3.58034e10i			0.636514i	−0.948004	+	0.318257i	$0.896902\pi$
$488$	−5.65322e10	−	6.49205e10i	−0.996820	−	1.14473i
$489$	−1.89312e9			−0.0331088
$490$	−2.18499e10	−	6.39639e9i	−0.379023	−	0.110956i
$491$			5.45993e10i			0.939423i	0.882820	+	0.469712i	$0.155642\pi$
$491$			5.45993e10i			0.939423i	−0.882820	+	0.469712i	$0.844358\pi$
$492$	4.10501e9	−	6.41045e9i	0.0700574	−	0.109403i
$493$	2.53905e10			0.429817
$494$	3.04515e10	−	1.04022e11i	0.511330	−	1.74669i
$495$		−	1.81305e10i		−	0.301988i
$496$	−2.31026e10	+	1.06417e10i	−0.381710	+	0.175826i
$497$	−1.70548e10			−0.279525
$498$	9.37479e10	+	2.74440e10i	1.52421	+	0.446200i
$499$			6.97805e10i			1.12547i	0.826639	+	0.562733i	$0.190250\pi$
$499$			6.97805e10i			1.12547i	−0.826639	+	0.562733i	$0.809750\pi$
$500$	4.70767e9	+	3.01461e9i	0.0753227	+	0.0482338i
$501$	−1.99578e10			−0.316782
$502$	−2.56352e10	+	8.75692e10i	−0.403666	+	1.37891i
$503$		−	6.40878e10i		−	1.00116i	−0.865691	−	0.500580i	$-0.833120\pi$
$503$		−	6.40878e10i		−	1.00116i	0.865691	−	0.500580i	$-0.166880\pi$
$504$	−7.77831e9	+	6.77329e9i	−0.120549	+	0.104973i
$505$	−4.34347e10			−0.667838
$506$	5.90714e10	+	1.72927e10i	0.901105	+	0.263791i
$507$			5.17529e10i			0.783254i
$508$	5.96944e9	−	9.32198e9i	0.0896353	−	0.139976i
$509$	−1.03640e11			−1.54402			−0.772012	−	0.635608i	$-0.780750\pi$
$509$	−1.03640e11			−1.54402			−0.772012	+	0.635608i	$0.780750\pi$
$510$	−1.36311e10	+	4.65634e10i	−0.201488	+	0.688278i
$511$		−	2.22116e10i		−	0.325759i
$512$	5.75367e10	−	3.75752e10i	0.837269	−	0.546791i
$513$	6.33664e10			0.914933
$514$	−2.70402e10	−	7.91580e9i	−0.387398	−	0.113408i
$515$		−	1.07111e10i		−	0.152267i
$516$	−2.03579e10	−	1.30364e10i	−0.287166	−	0.183891i
$517$	−1.85281e11			−2.59339
$518$	4.89383e9	−	1.67172e10i	0.0679719	−	0.232190i
$519$		−	4.08382e10i		−	0.562855i
$520$	2.75542e10	+	3.16428e10i	0.376856	+	0.432774i
$521$	−3.35410e10			−0.455225			−0.227612	−	0.973752i	$-0.573092\pi$
$521$	−3.35410e10			−0.455225			−0.227612	+	0.973752i	$0.573092\pi$
$522$	−1.08163e10	−	3.16638e9i	−0.145679	−	0.0426463i
$523$			3.32143e10i			0.443934i	0.975054	+	0.221967i	$0.0712477\pi$
$523$			3.32143e10i			0.443934i	−0.975054	+	0.221967i	$0.928752\pi$
$524$	−4.79025e10	+	7.48053e10i	−0.635379	+	0.992219i
$525$	−6.29335e9			−0.0828408
$526$	−1.16283e9	+	3.97220e9i	−0.0151906	+	0.0518906i
$527$		−	4.29115e10i		−	0.556329i
$528$	−5.68963e10	−	1.23519e11i	−0.732063	−	1.58928i
$529$	4.52211e10			0.577455
$530$	2.47887e9	+	7.25670e8i	0.0314160	+	0.00919678i
$531$			1.26287e10i			0.158848i
$532$	3.27140e10	+	2.09488e10i	0.408401	+	0.261524i
$533$	1.11060e10			0.137609
$534$	2.66597e10	−	9.10690e10i	0.327862	−	1.11997i
$535$		−	9.41675e9i		−	0.114944i
$536$	−1.19212e11	+	1.03809e11i	−1.44431	+	1.25769i
$537$	−5.31743e10			−0.639447
$538$	4.66483e10	+	1.36559e10i	0.556810	+	0.163002i
$539$			1.07660e11i			1.27555i
$540$	−1.32283e10	+	2.06576e10i	−0.155572	+	0.242943i
$541$	1.39040e11			1.62312			0.811562	−	0.584266i	$-0.198618\pi$
$541$	1.39040e11			1.62312			0.811562	+	0.584266i	$0.198618\pi$
$542$	−7.41754e9	+	2.53381e10i	−0.0859533	+	0.293614i
$543$		−	1.40523e11i		−	1.61640i
$544$	1.69662e10	+	1.14686e11i	0.193726	+	1.30952i
$545$	5.25193e10			0.595296
$546$	−4.53336e10	−	1.32711e10i	−0.510093	−	0.149326i
$547$		−	7.05870e10i		−	0.788452i	−0.919013	−	0.394226i	$-0.871013\pi$
$547$		−	7.05870e10i		−	0.788452i	0.919013	−	0.394226i	$-0.128987\pi$
$548$	9.80043e10	+	6.27583e10i	1.08673	+	0.695903i
$549$	−6.44640e10			−0.709623
$550$	7.42685e9	−	2.53699e10i	0.0811623	−	0.277248i
$551$			4.24479e10i			0.460521i
$552$	4.80123e10	+	5.51364e10i	0.517125	+	0.593857i
$553$	−4.61669e10			−0.493662
$554$	7.95187e10	+	2.32785e10i	0.844171	+	0.247124i
$555$			3.63705e10i			0.383334i
$556$	1.71876e10	−	2.68404e10i	0.179852	−	0.280860i
$557$	1.36274e11			1.41577			0.707884	−	0.706328i	$-0.249650\pi$
$557$	1.36274e11			1.41577			0.707884	+	0.706328i	$0.249650\pi$
$558$	−5.35138e9	+	1.82802e10i	−0.0551987	+	0.188557i
$559$		−	3.52696e10i		−	0.361205i
$560$	−1.36587e10	+	6.29157e9i	−0.138886	+	0.0639745i
$561$	2.29429e11			2.31631
$562$	−1.30189e11	−	3.81119e10i	−1.30506	−	0.382046i
$563$			9.28198e10i			0.923862i	0.886916	+	0.461931i	$0.152843\pi$
$563$			9.28198e10i			0.923862i	−0.886916	+	0.461931i	$0.847157\pi$
$564$	−1.85336e11	−	1.18682e11i	−1.83166	−	1.17292i
$565$	6.82535e10			0.669778
$566$	−1.43849e9	+	4.91386e9i	−0.0140166	+	0.0478803i
$567$		−	4.41368e10i		−	0.427040i
$568$	6.41720e10	−	5.58804e10i	0.616527	−	0.536866i
$569$	−3.45537e10			−0.329644			−0.164822	−	0.986323i	$-0.552705\pi$
$569$	−3.45537e10			−0.329644			−0.164822	+	0.986323i	$0.552705\pi$
$570$	−7.78448e10	−	2.27885e10i	−0.737446	−	0.215881i
$571$		−	9.27891e10i		−	0.872876i	−0.899734	−	0.436438i	$-0.856240\pi$
$571$		−	9.27891e10i		−	0.872876i	0.899734	−	0.436438i	$-0.143760\pi$
$572$	1.06997e11	−	1.67089e11i	0.999515	−	1.56086i
$573$	1.72351e11			1.59881
$574$	−1.11831e9	+	3.82012e9i	−0.0103018	+	0.0351908i
$575$			1.42114e10i			0.130007i
$576$	7.07460e9	−	5.09716e10i	0.0642706	−	0.463061i
$577$	−3.75444e10			−0.338721			−0.169361	−	0.985554i	$-0.554170\pi$
$577$	−3.75444e10			−0.338721			−0.169361	+	0.985554i	$0.554170\pi$
$578$	−8.05927e10	−	2.35929e10i	−0.722079	−	0.211383i
$579$		−	6.66770e10i		−	0.593282i
$580$	−1.38381e10	−	8.86140e9i	−0.122283	−	0.0783051i
$581$	−5.10787e10			−0.448266
$582$	5.79299e10	−	1.97887e11i	0.504906	−	1.72475i
$583$		−	1.22140e10i		−	0.105726i
$584$	7.27767e10	+	8.35754e10i	0.625664	+	0.718501i
$585$	3.14203e10			0.268279
$586$	−1.20886e11	−	3.53885e10i	−1.02515	−	0.300104i
$587$			2.66542e10i			0.224498i	0.993680	+	0.112249i	$0.0358054\pi$
$587$			2.66542e10i			0.224498i	−0.993680	+	0.112249i	$0.964195\pi$
$588$	−6.89620e10	+	1.07692e11i	−0.576900	+	0.900896i
$589$	7.17395e10			0.596070
$590$	−5.17313e9	+	1.76713e10i	−0.0426919	+	0.145834i
$591$			4.71706e10i			0.386653i
$592$	3.63602e10	+	7.89363e10i	0.296033	+	0.642673i
$593$	−1.07542e11			−0.869681			−0.434840	−	0.900508i	$-0.643195\pi$
$593$	−1.07542e11			−0.869681			−0.434840	+	0.900508i	$0.643195\pi$
$594$	1.11325e11	+	3.25896e10i	0.894227	+	0.261778i
$595$		−	2.53701e10i		−	0.202421i
$596$	−4.69907e10	−	3.00911e10i	−0.372415	−	0.238480i
$597$	−6.09251e10			−0.479622
$598$	−2.99683e10	+	1.02371e11i	−0.234346	+	0.800519i
$599$		−	5.10104e10i		−	0.396234i	−0.980178	−	0.198117i	$-0.936517\pi$
$599$		−	5.10104e10i		−	0.396234i	0.980178	−	0.198117i	$-0.0634825\pi$
$600$	2.36799e10	−	2.06203e10i	0.182715	−	0.159107i
$601$	1.64304e11			1.25936			0.629681	−	0.776854i	$-0.283186\pi$
$601$	1.64304e11			1.25936			0.629681	+	0.776854i	$0.283186\pi$
$602$	1.21317e10	+	3.55146e9i	0.0923709	+	0.0270409i
$603$			1.18374e11i			0.895337i
$604$	2.76541e10	−	4.31851e10i	0.207784	−	0.324479i
$605$	−6.50886e10			−0.485829
$606$	−6.85435e10	+	2.34143e11i	−0.508248	+	1.73616i
$607$			2.64985e11i			1.95194i	0.217909	+	0.975969i	$0.430077\pi$
$607$			2.64985e11i			1.95194i	−0.217909	+	0.975969i	$0.569923\pi$
$608$	−1.91732e11	+	2.83641e10i	−1.40307	+	0.207565i
$609$	1.84992e10			0.134488
$610$	−9.02041e10	−	2.64065e10i	−0.651489	−	0.190718i
$611$		−	3.21092e11i		−	2.30390i
$612$	7.31109e10	+	4.68175e10i	0.521167	+	0.333735i
$613$	−2.58975e11			−1.83407			−0.917036	−	0.398804i	$-0.869425\pi$
$613$	−2.58975e11			−1.83407			−0.917036	+	0.398804i	$0.869425\pi$
$614$	−6.62750e10	+	2.26394e11i	−0.466312	+	1.59291i
$615$		−	8.31118e9i		−	0.0580982i
$616$	4.66995e10	+	5.36288e10i	0.324331	+	0.372456i
$617$	2.43563e10			0.168063			0.0840313	−	0.996463i	$-0.473220\pi$
$617$	2.43563e10			0.168063			0.0840313	+	0.996463i	$0.473220\pi$
$618$	−5.77404e10	−	1.69031e10i	−0.395846	−	0.115881i
$619$		−	6.16901e10i		−	0.420197i	−0.977680	−	0.210098i	$-0.932622\pi$
$619$		−	6.16901e10i		−	0.420197i	0.977680	−	0.210098i	$-0.0673784\pi$
$620$	−1.49763e10	+	2.33873e10i	−0.101353	+	0.158275i
$621$	−6.23608e10			−0.419320
$622$	−2.86035e10	+	9.77087e10i	−0.191098	+	0.652787i
$623$			4.96191e10i			0.329380i
$624$	2.14059e11	−	9.86015e10i	1.41187	−	0.650347i
$625$	6.10352e9			0.0400000
$626$	−6.69068e10	−	1.95864e10i	−0.435685	−	0.127543i
$627$			3.83560e11i			2.48178i
$628$	−4.34717e9	−	2.78376e9i	−0.0279491	−	0.0178975i
$629$	−1.46619e11			−0.936673
$630$	−3.16384e9	+	1.08076e10i	−0.0200841	+	0.0686068i
$631$		−	2.91259e10i		−	0.183722i	−0.995772	−	0.0918611i	$-0.970718\pi$
$631$		−	2.91259e10i		−	0.183722i	0.995772	−	0.0918611i	$-0.0292816\pi$
$632$	1.73712e11	−	1.51267e11i	1.08883	−	0.948145i
$633$	−2.27940e11			−1.41973
$634$	1.56740e10	+	4.58844e9i	0.0970113	+	0.0283993i
$635$		−	1.20860e10i		−	0.0743340i
$636$	7.82373e9	−	1.22177e10i	0.0478173	−	0.0746723i
$637$	−1.86575e11			−1.13317
$638$	−2.18311e10	+	7.45745e10i	−0.131763	+	0.450099i
$639$		−	6.37207e10i		−	0.382188i
$640$	3.07791e10	−	6.84262e10i	0.183458	−	0.407852i
$641$	2.97316e11			1.76111			0.880555	−	0.473943i	$-0.157170\pi$
$641$	2.97316e11			1.76111			0.880555	+	0.473943i	$0.157170\pi$
$642$	−5.07628e10	−	1.48604e10i	−0.298817	−	0.0874764i
$643$		−	2.02204e11i		−	1.18289i	−0.806344	−	0.591447i	$-0.798557\pi$
$643$		−	2.02204e11i		−	1.18289i	0.806344	−	0.591447i	$-0.201443\pi$
$644$	−3.21948e10	−	2.06163e10i	−0.187173	−	0.119858i
$645$	−2.63941e10			−0.152499
$646$	9.18663e10	−	3.13813e11i	0.527504	−	1.80194i
$647$		−	2.98562e11i		−	1.70380i	−0.523708	−	0.851898i	$-0.675452\pi$
$647$		−	2.98562e11i		−	1.70380i	0.523708	−	0.851898i	$-0.324548\pi$
$648$	1.44615e11	+	1.66073e11i	0.820188	+	0.941888i
$649$	8.70705e10			0.490786
$650$	4.39662e10	+	1.28708e10i	0.246300	+	0.0721025i
$651$		−	3.12648e10i		−	0.174073i
$652$	−2.66349e9	+	4.15934e9i	−0.0147387	+	0.0230162i
$653$	3.34280e10			0.183847			0.0919237	−	0.995766i	$-0.470698\pi$
$653$	3.34280e10			0.183847			0.0919237	+	0.995766i	$0.470698\pi$
$654$	8.28799e10	−	2.83116e11i	0.453042	−	1.54758i
$655$			9.69855e10i			0.526916i
$656$	−8.30883e9	−	1.80381e10i	−0.0448668	−	0.0974037i
$657$	8.29877e10			0.445402
$658$	1.10446e11	+	3.23321e10i	0.589176	+	0.172477i
$659$		−	7.70116e10i		−	0.408333i	−0.978936	−	0.204166i	$-0.934552\pi$
$659$		−	7.70116e10i		−	0.408333i	0.978936	−	0.204166i	$-0.0654484\pi$
$660$	−1.25041e11	−	8.00718e10i	−0.658989	−	0.421991i
$661$	−2.47987e11			−1.29904			−0.649520	−	0.760344i	$-0.725030\pi$
$661$	−2.47987e11			−1.29904			−0.649520	+	0.760344i	$0.725030\pi$
$662$	4.55000e10	−	1.55427e11i	0.236908	−	0.809271i
$663$			3.97601e11i			2.05775i
$664$	1.92193e11	−	1.67360e11i	0.988704	−	0.860954i
$665$	4.24138e10			0.216881
$666$	6.24593e10	+	1.82845e10i	0.317468	+	0.0929363i
$667$		−	4.17743e10i		−	0.211060i
$668$	−2.80791e10	+	4.38488e10i	−0.141019	+	0.220218i
$669$	−1.49585e11			−0.746765
$670$	−4.84898e10	+	1.65640e11i	−0.240631	+	0.821988i
$671$			4.44457e11i			2.19250i
$672$	1.23613e10	+	8.35585e10i	0.0606161	+	0.409745i
$673$	1.03219e11			0.503151			0.251576	−	0.967838i	$-0.419051\pi$
$673$	1.03219e11			0.503151			0.251576	+	0.967838i	$0.419051\pi$
$674$	2.98493e10	+	8.73816e9i	0.144642	+	0.0423429i
$675$			2.67827e10i			0.129015i
$676$	1.13705e11	+	7.28127e10i	0.544496	+	0.348674i
$677$	−3.83549e10			−0.182585			−0.0912926	−	0.995824i	$-0.529100\pi$
$677$	−3.83549e10			−0.182585			−0.0912926	+	0.995824i	$0.529100\pi$
$678$	1.07710e11	−	3.67933e11i	0.509725	−	1.74121i
$679$			1.07819e11i			0.507243i
$680$	8.31257e10	+	9.54600e10i	0.388776	+	0.446463i
$681$	7.01312e10			0.326079
$682$	1.26036e11	+	3.68959e10i	0.582580	+	0.170546i
$683$		−	2.47284e10i		−	0.113635i	−0.998385	−	0.0568177i	$-0.981905\pi$
$683$		−	2.47284e10i		−	0.113635i	0.998385	−	0.0568177i	$-0.0180954\pi$
$684$	−7.82695e10	+	1.22227e11i	−0.357576	+	0.558396i
$685$	1.27063e11			0.577108
$686$	4.00612e10	−	1.36848e11i	0.180895	−	0.617934i
$687$		−	3.97444e11i		−	1.78422i
$688$	−5.72842e10	+	2.63866e10i	−0.255671	+	0.117769i
$689$	2.11669e10			0.0939247
$690$	7.66094e10	+	2.24268e10i	0.337976	+	0.0989399i
$691$		−	3.63864e10i		−	0.159598i	−0.996811	−	0.0797988i	$-0.974572\pi$
$691$		−	3.63864e10i		−	0.159598i	0.996811	−	0.0797988i	$-0.0254278\pi$
$692$	−8.97248e10	−	5.74564e10i	−0.391281	−	0.250561i
$693$	5.32517e10			0.230887
$694$	−9.69601e10	+	3.31213e11i	−0.417979	+	1.42781i
$695$		−	3.47988e10i		−	0.149151i
$696$	−6.96067e10	+	6.06129e10i	−0.296629	+	0.258302i
$697$	3.35046e10			0.141962
$698$	−2.11806e11	−	6.20045e10i	−0.892311	−	0.261217i
$699$			1.88072e11i			0.787797i
$700$	−8.85429e9	+	1.38270e10i	−0.0368775	+	0.0575885i
$701$	1.36852e11			0.566732			0.283366	−	0.959012i	$-0.408549\pi$
$701$	1.36852e11			0.566732			0.283366	+	0.959012i	$0.408549\pi$
$702$	−5.64778e10	+	1.92927e11i	−0.232557	+	0.794409i
$703$		−	2.45118e11i		−	1.00358i
$704$	−3.51431e11	−	4.87770e10i	−1.43070	−	0.198575i
$705$	−2.40290e11			−0.972699
$706$	2.60867e11	+	7.63667e10i	1.05003	+	0.307387i
$707$		−	1.27573e11i		−	0.510601i
$708$	8.70967e10	+	5.57735e10i	0.346632	+	0.221970i
$709$	1.84677e11			0.730848			0.365424	−	0.930841i	$-0.380924\pi$
$709$	1.84677e11			0.730848			0.365424	+	0.930841i	$0.380924\pi$
$710$	2.61021e10	−	8.91640e10i	0.102717	−	0.350878i
$711$		−	1.72490e11i		−	0.674972i
$712$	−1.62578e11	−	1.86701e11i	−0.632618	−	0.726486i
$713$	−7.06011e10			−0.273183
$714$	−1.36763e11	−	4.00362e10i	−0.526229	−	0.154049i
$715$		−	2.16632e11i		−	0.828892i
$716$	−7.48125e10	+	1.16828e11i	−0.284657	+	0.444525i
$717$	−3.03890e11			−1.14985
$718$	6.09550e10	−	2.08221e11i	0.229357	−	0.783477i
$719$			2.26289e11i			0.846735i	0.905958	+	0.423368i	$0.139152\pi$
$719$			2.26289e11i			0.846735i	−0.905958	+	0.423368i	$0.860848\pi$
$720$	−2.35068e10	−	5.10321e10i	−0.0874707	−	0.189895i
$721$	3.14600e10			0.116417
$722$	2.63841e11	+	7.72373e10i	0.970941	+	0.284235i
$723$		−	1.89833e11i		−	0.694735i
$724$	−3.08741e11	−	1.97706e11i	−1.12367	−	0.719558i
$725$	−1.79412e10			−0.0649380
$726$	−1.02715e11	+	3.50873e11i	−0.369733	+	1.26300i
$727$			6.89485e10i			0.246824i	0.992356	+	0.123412i	$0.0393837\pi$
$727$			6.89485e10i			0.246824i	−0.992356	+	0.123412i	$0.960616\pi$
$728$	−9.29388e10	+	8.09303e10i	−0.330881	+	0.288128i
$729$	−5.57976e10			−0.197563
$730$	1.16124e11	+	3.39945e10i	0.408913	+	0.119706i
$731$		−	1.06402e11i		−	0.372631i
$732$	−2.84699e11	+	4.44591e11i	−0.991612	+	1.54852i
$733$	3.05441e11			1.05806			0.529031	−	0.848603i	$-0.322556\pi$
$733$	3.05441e11			1.05806			0.529031	+	0.848603i	$0.322556\pi$
$734$	−4.46466e10	+	1.52512e11i	−0.153817	+	0.525435i
$735$			1.39623e11i			0.478420i
$736$	1.88689e11	−	2.79140e10i	0.643036	−	0.0951284i
$737$	8.16147e11			2.76629
$738$	−1.42729e10	−	4.17827e9i	−0.0481155	−	0.0140854i
$739$			3.94495e11i			1.32271i	0.750074	+	0.661354i	$0.230018\pi$
$739$			3.94495e11i			1.32271i	−0.750074	+	0.661354i	$0.769982\pi$
$740$	7.99090e10	+	5.11707e10i	0.266483	+	0.170645i
$741$	−6.64710e11			−2.20475
$742$	−2.13139e9	+	7.28076e9i	−0.00703147	+	0.0240193i
$743$			5.69341e10i			0.186817i	0.995628	+	0.0934086i	$0.0297763\pi$
$743$			5.69341e10i			0.186817i	−0.995628	+	0.0934086i	$0.970224\pi$
$744$	1.02440e11	+	1.17640e11i	0.334331	+	0.383939i
$745$	−6.09237e10			−0.197770
$746$	−3.20828e11	−	9.39198e10i	−1.03590	−	0.303251i
$747$		−	1.90842e11i		−	0.612902i
$748$	3.22790e11	−	5.04075e11i	1.03113	−	1.61023i
$749$	2.76582e10			0.0878813
$750$	9.63185e9	−	3.29022e10i	0.0304414	−	0.103987i
$751$			2.12038e11i			0.666583i	0.942824	+	0.333292i	$0.108159\pi$
$751$			2.12038e11i			0.666583i	−0.942824	+	0.333292i	$0.891841\pi$
$752$	−5.21510e11	+	2.40222e11i	−1.63076	+	0.751174i
$753$	5.59577e11			1.74052
$754$	−1.29238e11	−	3.78334e10i	−0.399856	−	0.117055i
$755$		−	5.59897e10i		−	0.172314i
$756$	−6.06739e10	−	3.88533e10i	−0.185744	−	0.118943i
$757$	−6.46697e10			−0.196933			−0.0984663	−	0.995140i	$-0.531394\pi$
$757$	−6.46697e10			−0.196933			−0.0984663	+	0.995140i	$0.531394\pi$
$758$	−1.25297e11	+	4.28010e11i	−0.379544	+	1.29651i
$759$		−	3.77473e11i		−	1.13741i
$760$	−1.59590e11	+	1.38970e11i	−0.478357	+	0.416549i
$761$	−2.88384e11			−0.859869			−0.429935	−	0.902860i	$-0.641463\pi$
$761$	−2.88384e11			−0.859869			−0.429935	+	0.902860i	$0.641463\pi$
$762$	−6.51519e10	−	1.90727e10i	−0.193245	−	0.0565708i
$763$			1.54256e11i			0.455139i
$764$	2.42486e11	−	3.78670e11i	0.711726	−	1.11144i
$765$	9.47887e10			0.276765
$766$	1.41267e11	−	4.82564e11i	0.410322	−	1.40165i
$767$			1.50893e11i			0.436002i
$768$	−3.20293e11	−	2.73903e11i	−0.920666	−	0.787320i
$769$	3.09585e11			0.885267			0.442633	−	0.896703i	$-0.354044\pi$
$769$	3.09585e11			0.885267			0.442633	+	0.896703i	$0.354044\pi$
$770$	7.45147e10	+	2.18136e10i	0.211972	+	0.0620533i
$771$			1.72790e11i			0.488991i
$772$	−1.46495e11	−	9.38097e10i	−0.412433	−	0.264106i
$773$	5.21097e11			1.45949			0.729744	−	0.683721i	$-0.239639\pi$
$773$	5.21097e11			1.45949			0.729744	+	0.683721i	$0.239639\pi$
$774$	−1.32691e10	+	4.53268e10i	−0.0369723	+	0.126296i
$775$			3.03217e10i			0.0840518i
$776$	−3.53271e11	−	4.05690e11i	−0.974229	−	1.11879i
$777$	−1.06825e11			−0.293081
$778$	3.77092e11	+	1.10391e11i	1.02927	+	0.301311i
$779$			5.60130e10i			0.152103i
$780$	1.38765e11	−	2.16697e11i	0.374887	−	0.585429i
$781$	−4.39332e11			−1.18083
$782$	−9.04084e10	+	3.08833e11i	−0.241759	+	0.825841i
$783$		−	7.87272e10i		−	0.209449i
$784$	1.39584e11	+	3.03030e11i	0.369463	+	0.802088i
$785$	−5.63613e9			−0.0148423
$786$	5.22819e11	+	1.53051e11i	1.36981	+	0.401002i
$787$			5.00687e11i			1.30517i	0.757715	+	0.652585i	$0.226316\pi$
$787$			5.00687e11i			1.30517i	−0.757715	+	0.652585i	$0.773684\pi$
$788$	1.03638e11	+	6.63657e10i	0.268790	+	0.172123i
$789$	2.53828e10			0.0654986
$790$	7.06576e10	−	2.41364e11i	0.181405	−	0.619676i
$791$			2.00469e11i			0.512084i
$792$	−2.00370e11	+	1.74480e11i	−0.509250	+	0.443450i
$793$	−7.70245e11			−1.94776
$794$	−5.59500e11	−	1.63789e11i	−1.40773	−	0.412101i
$795$		−	1.58403e10i		−	0.0396546i
$796$	−8.57173e10	+	1.33858e11i	−0.213509	+	0.333419i
$797$	4.22774e11			1.04779			0.523896	−	0.851783i	$-0.324478\pi$
$797$	4.22774e11			1.04779			0.523896	+	0.851783i	$0.324478\pi$
$798$	6.69326e10	−	2.28640e11i	0.165054	−	0.563820i
$799$		−	9.68670e11i		−	2.37678i
$800$	−1.19885e10	−	8.10380e10i	−0.0292687	−	0.197847i
$801$	−1.85388e11			−0.450352
$802$	1.64714e11	+	4.82187e10i	0.398137	+	0.116552i
$803$		−	5.72172e11i		−	1.37615i
$804$	8.16392e11	+	5.22787e11i	1.95378	+	1.25112i
$805$	−4.17408e10			−0.0993978
$806$	−6.39407e10	+	2.18420e11i	−0.151509	+	0.517550i
$807$		−	2.98088e11i		−	0.702830i
$808$	4.17996e11	+	4.80018e11i	0.980677	+	1.12619i
$809$	1.06326e9			0.00248226			0.00124113	−	0.999999i	$-0.499605\pi$
$809$	1.06326e9			0.00248226			0.00124113	+	0.999999i	$0.499605\pi$
$810$	2.30751e11	+	6.75505e10i	0.536048	+	0.156924i
$811$			2.59999e11i			0.601020i	0.953779	+	0.300510i	$0.0971569\pi$
$811$			2.59999e11i			0.601020i	−0.953779	+	0.300510i	$0.902843\pi$
$812$	2.60270e10	−	4.06443e10i	0.0598688	−	0.0934921i
$813$	1.61913e11			0.370613
$814$	1.26065e11	−	4.30635e11i	0.287142	−	0.980871i
$815$			5.39261e9i			0.0122227i
$816$	6.45775e11	−	2.97461e11i	1.45653	−	0.670919i
$817$	1.77882e11			0.399250
$818$	6.01525e8	+	1.76092e8i	0.00134351	+	0.000393302i
$819$			9.22853e10i			0.205115i
$820$	−1.82604e10	−	1.16932e10i	−0.0403882	−	0.0258630i
$821$	−2.68005e11			−0.589889			−0.294944	−	0.955514i	$-0.595301\pi$
$821$	−2.68005e11			−0.589889			−0.294944	+	0.955514i	$0.595301\pi$
$822$	2.00516e11	−	6.84958e11i	0.439200	−	1.50030i
$823$		−	8.13596e10i		−	0.177341i	−0.996061	−	0.0886705i	$-0.971738\pi$
$823$		−	8.13596e10i		−	0.177341i	0.996061	−	0.0886705i	$-0.0282618\pi$
$824$	−1.18374e11	+	1.03079e11i	−0.256772	+	0.223595i
$825$	−1.62117e11			−0.349955
$826$	−5.19027e10	−	1.51941e10i	−0.111499	−	0.0326404i
$827$			3.60895e11i			0.771540i	0.922595	+	0.385770i	$0.126064\pi$
$827$			3.60895e11i			0.771540i	−0.922595	+	0.385770i	$0.873936\pi$
$828$	7.70275e10	−	1.20287e11i	0.163879	−	0.255917i
$829$	3.75987e11			0.796077			0.398038	−	0.917369i	$-0.369691\pi$
$829$	3.75987e11			0.796077			0.398038	+	0.917369i	$0.369691\pi$
$830$	7.81750e10	−	2.67044e11i	0.164724	−	0.562691i
$831$		−	5.08134e11i		−	1.06555i
$832$	8.45306e10	−	6.09031e11i	0.176409	−	1.27100i
$833$	−5.62859e11			−1.16901
$834$	−1.87589e11	−	5.49154e10i	−0.387743	−	0.113509i
$835$			5.68503e10i			0.116946i
$836$	8.42713e11	+	5.39641e11i	1.72526	+	1.10479i
$837$	−1.33054e11			−0.271098
$838$	−1.58957e11	+	5.42993e11i	−0.322332	+	1.10108i
$839$			3.78533e11i			0.763935i	0.924176	+	0.381967i	$0.124753\pi$
$839$			3.78533e11i			0.763935i	−0.924176	+	0.381967i	$0.875247\pi$
$840$	6.05643e10	+	6.95509e10i	0.121647	+	0.139697i
$841$	−4.47509e11			−0.894576
$842$	−1.50727e11	−	4.41241e10i	−0.299876	−	0.0877865i
$843$			8.31925e11i			1.64730i
$844$	−3.20695e11	+	5.00802e11i	−0.632008	+	0.986953i
$845$	1.47420e11			0.289154
$846$	−1.20800e11	+	4.12651e11i	−0.235823	+	0.805566i
$847$		−	1.91174e11i		−	0.371445i
$848$	−1.58358e10	−	3.43788e10i	−0.0306236	−	0.0664825i
$849$	3.14001e10			0.0604366
$850$	1.32637e11	+	3.88285e10i	0.254091	+	0.0743833i
$851$			2.41228e11i			0.459949i
$852$	−4.39464e11	−	2.81416e11i	−0.833999	−	0.534061i
$853$	−3.42638e11			−0.647202			−0.323601	−	0.946194i	$-0.604894\pi$
$853$	−3.42638e11			−0.647202			−0.323601	+	0.946194i	$0.604894\pi$
$854$	7.75594e10	−	2.64941e11i	0.145815	−	0.498101i
$855$			1.58468e11i			0.296536i
$856$	−1.04069e11	+	9.06225e10i	−0.193833	+	0.168788i
$857$	−3.33508e11			−0.618277			−0.309138	−	0.951017i	$-0.600041\pi$
$857$	−3.33508e11			−0.618277			−0.309138	+	0.951017i	$0.600041\pi$
$858$	−1.16780e12	−	3.41863e11i	−2.15485	−	0.630816i
$859$		−	1.00496e12i		−	1.84576i	−0.385084	−	0.922881i	$-0.625828\pi$
$859$		−	1.00496e12i		−	1.84576i	0.385084	−	0.922881i	$-0.374172\pi$
$860$	−3.71346e10	+	5.79901e10i	−0.0678868	+	0.106013i
$861$	2.44110e10			0.0444194
$862$	−4.09841e10	+	1.40001e11i	−0.0742312	+	0.253572i
$863$		−	4.79204e11i		−	0.863928i	−0.901891	−	0.431964i	$-0.857821\pi$
$863$		−	4.79204e11i		−	0.863928i	0.901891	−	0.431964i	$-0.142179\pi$
$864$	3.55601e11	−	5.26063e10i	0.638128	−	0.0944023i
$865$	−1.16329e11			−0.207789
$866$	−7.17111e10	−	2.09929e10i	−0.127501	−	0.0373251i
$867$			5.14997e11i			0.911440i
$868$	−6.86913e10	−	4.39873e10i	−0.121010	−	0.0774905i
$869$	−1.18926e12			−2.08544
$870$	−2.83127e10	+	9.67154e10i	−0.0494201	+	0.168818i
$871$			1.41438e12i			2.45751i
$872$	−5.05422e11	−	5.80418e11i	−0.874155	−	1.00386i
$873$	−4.02837e11			−0.693541
$874$	−5.16307e11	−	1.51145e11i	−0.884835	−	0.259029i
$875$			1.79268e10i			0.0305823i
$876$	3.66507e11	−	5.72344e11i	0.622395	−	0.971943i
$877$	4.59890e11			0.777420			0.388710	−	0.921360i	$-0.372921\pi$
$877$	4.59890e11			0.777420			0.388710	+	0.921360i	$0.372921\pi$
$878$	−1.52570e11	+	5.21177e11i	−0.256739	+	0.877015i
$879$			7.72477e11i			1.29399i
$880$	−3.51849e11	+	1.62071e11i	−0.586712	+	0.270256i
$881$	7.20232e11			1.19555			0.597777	−	0.801663i	$-0.296051\pi$
$881$	7.20232e11			1.19555			0.597777	+	0.801663i	$0.296051\pi$
$882$	2.39776e11	+	7.01927e10i	0.396216	+	0.115989i
$883$			8.35891e11i			1.37501i	0.726178	+	0.687507i	$0.241295\pi$
$883$			8.35891e11i			1.37501i	−0.726178	+	0.687507i	$0.758705\pi$
$884$	8.73563e11	+	5.59396e11i	1.43049	+	0.916032i
$885$	1.12921e11			0.184079
$886$	−3.24036e10	+	1.10690e11i	−0.0525845	+	0.179627i
$887$		−	2.07019e11i		−	0.334439i	−0.985920	−	0.167219i	$-0.946521\pi$
$887$		−	2.07019e11i		−	0.334439i	0.985920	−	0.167219i	$-0.0534788\pi$
$888$	4.01949e11	−	3.50013e11i	0.646426	−	0.562902i
$889$	3.54981e10			0.0568327
$890$	−2.59413e11	−	7.59411e10i	−0.413458	−	0.121037i
$891$		−	1.13696e12i		−	1.80400i
$892$	−2.10456e11	+	3.28651e11i	−0.332431	+	0.519129i
$893$	1.61942e12			2.54657
$894$	−9.61427e10	+	3.28421e11i	−0.150510	+	0.514140i
$895$			1.51469e11i			0.236064i
$896$	2.00976e11	+	9.04020e10i	0.311827	+	0.140264i
$897$	6.54162e11			1.01045
$898$	3.57749e11	+	1.04728e11i	0.550140	+	0.161049i
$899$		−	8.91301e10i		−	0.136454i
$900$	−5.16609e10	−	3.30817e10i	−0.0787394	−	0.0504217i
$901$	6.38563e10			0.0968957
$902$	−2.88077e10	+	9.84064e10i	−0.0435194	+	0.148661i
$903$		−	7.75228e10i		−	0.116595i
$904$	−6.56841e11	−	7.54303e11i	−0.983527	−	1.12946i
$905$	−4.00284e11			−0.596725
$906$	−3.01823e11	−	8.83564e10i	−0.447961	−	0.131137i
$907$		−	1.16689e12i		−	1.72426i	−0.506690	−	0.862128i	$-0.669131\pi$
$907$		−	1.16689e12i		−	1.72426i	0.506690	−	0.862128i	$-0.330869\pi$
$908$	9.86696e10	−	1.54084e11i	0.145158	−	0.226681i
$909$	4.76643e11			0.698132
$910$	−3.78030e10	+	1.29134e11i	−0.0551266	+	0.188311i
$911$		−	1.15580e12i		−	1.67806i	−0.544084	−	0.839031i	$-0.683123\pi$
$911$		−	1.15580e12i		−	1.67806i	0.544084	−	0.839031i	$-0.316877\pi$
$912$	4.97296e11	+	1.07961e12i	0.718846	+	1.56058i
$913$	−1.31579e12			−1.89366
$914$	−2.65117e11	−	7.76110e10i	−0.379886	−	0.111209i
$915$			5.76414e11i			0.822338i
$916$	−8.73218e11	−	5.59176e11i	−1.24034	−	0.794267i
$917$	−2.84859e11			−0.402858
$918$	−1.70382e11	+	5.82022e11i	−0.239913	+	0.819537i
$919$			1.20572e11i			0.169038i	0.996422	+	0.0845192i	$0.0269354\pi$
$919$			1.20572e11i			0.169038i	−0.996422	+	0.0845192i	$0.973065\pi$
$920$	1.57058e11	−	1.36764e11i	0.219234	−	0.190907i
$921$	1.44668e12			2.01064
$922$	8.68702e11	+	2.54306e11i	1.20212	+	0.351911i
$923$		−	7.61364e11i		−	1.04902i
$924$	2.35181e11	−	3.67262e11i	0.322637	−	0.503835i
$925$	1.03602e11			0.141515
$926$	3.40518e11	−	1.16320e12i	0.463123	−	1.58201i
$927$			1.17542e11i			0.159174i
$928$	3.52399e10	+	2.38210e11i	0.0475163	+	0.321194i
$929$	7.85328e11			1.05436			0.527179	−	0.849754i	$-0.323250\pi$
$929$	7.85328e11			1.05436			0.527179	+	0.849754i	$0.323250\pi$
$930$	1.63455e11	+	4.78502e10i	0.218507	+	0.0639664i
$931$		−	9.40988e11i		−	1.25252i
$932$	4.13209e11	+	2.64603e11i	0.547654	+	0.350697i
$933$	6.24370e11			0.823977
$934$	−2.53115e11	+	8.64635e11i	−0.332606	+	1.13617i
$935$		−	6.53536e11i		−	0.855112i
$936$	−3.02374e11	−	3.47241e11i	−0.393950	−	0.452405i
$937$	−4.90137e11			−0.635856			−0.317928	−	0.948115i	$-0.602987\pi$
$937$	−4.90137e11			−0.635856			−0.317928	+	0.948115i	$0.602987\pi$
$938$	−4.86505e11	−	1.42421e11i	−0.628458	−	0.183976i
$939$			4.27542e11i			0.549941i
$940$	−3.38070e11	+	5.27936e11i	−0.433008	+	0.676192i
$941$	5.66225e11			0.722155			0.361077	−	0.932536i	$-0.382409\pi$
$941$	5.66225e11			0.722155			0.361077	+	0.932536i	$0.382409\pi$
$942$	−8.89428e9	+	3.03826e10i	−0.0112955	+	0.0385853i
$943$		−	5.51241e10i		−	0.0697100i
$944$	2.45078e11	−	1.12889e11i	0.308614	−	0.142156i
$945$	−7.86641e10			−0.0986391
$946$	3.12513e11	+	9.14856e10i	0.390214	+	0.114232i
$947$		−	3.38620e10i		−	0.0421029i	−0.999778	−	0.0210515i	$-0.993299\pi$
$947$		−	3.38620e10i		−	0.0421029i	0.999778	−	0.0210515i	$-0.00670139\pi$
$948$	−1.18962e12	−	7.61786e11i	−1.47290	−	0.943191i
$949$	9.91575e11			1.22253
$950$	−6.49136e10	+	2.21743e11i	−0.0796969	+	0.272243i
$951$		−	1.00159e11i		−	0.122452i
$952$	−2.80378e11	+	2.44151e11i	−0.341347	+	0.297242i
$953$	−2.54903e11			−0.309032			−0.154516	−	0.987990i	$-0.549382\pi$
$953$	−2.54903e11			−0.309032			−0.154516	+	0.987990i	$0.549382\pi$
$954$	−2.72026e10	−	7.96335e9i	−0.0328410	−	0.00961396i
$955$		−	4.90948e11i		−	0.590231i
$956$	−4.27552e11	+	6.67673e11i	−0.511868	+	0.799341i
$957$	4.76540e11			0.568135
$958$	3.76300e11	−	1.28543e12i	0.446758	−	1.52611i
$959$			3.73201e11i			0.441233i
$960$	−4.55770e11	−	6.32586e10i	−0.536612	−	0.0744792i
$961$	7.02256e11			0.823383
$962$	7.46292e11	+	2.18471e11i	0.871382	+	0.255090i
$963$			1.03337e11i			0.120158i
$964$	−4.17080e11	−	2.67082e11i	−0.482960	−	0.309269i
$965$	−1.89931e11			−0.219022
$966$	−6.58704e10	+	2.25012e11i	−0.0756453	+	0.258402i
$967$			9.19624e11i			1.05173i	0.850568	+	0.525865i	$0.176258\pi$
$967$			9.19624e11i			1.05173i	−0.850568	+	0.525865i	$0.823742\pi$
$968$	6.26384e11	+	7.19327e11i	0.713410	+	0.819266i
$969$	−2.00530e12			−2.27449
$970$	−5.63687e11	−	1.65015e11i	−0.636724	−	0.186396i
$971$			1.35436e12i			1.52355i	0.647840	+	0.761776i	$0.275672\pi$
$971$			1.35436e12i			1.52355i	−0.647840	+	0.761776i	$0.724328\pi$
$972$	4.17775e11	−	6.52404e11i	0.468034	−	0.730889i
$973$	1.02208e11			0.114034
$974$	1.60944e11	−	5.49781e11i	0.178829	−	0.610877i
$975$		−	2.80949e11i		−	0.310891i
$976$	5.76251e11	+	1.25102e12i	0.635057	+	1.37868i
$977$	−1.38499e12			−1.52008			−0.760042	−	0.649874i	$-0.774822\pi$
$977$	−1.38499e12			−1.52008			−0.760042	+	0.649874i	$0.774822\pi$
$978$	2.90699e10	+	8.50999e9i	0.0317752	+	0.00930194i
$979$			1.27819e12i			1.39144i
$980$	3.06764e11	+	1.96440e11i	0.332583	+	0.212974i
$981$	−5.76336e11			−0.622300
$982$	2.45436e11	−	8.38403e11i	0.263932	−	0.901585i
$983$			1.57780e12i			1.68981i	0.534916	+	0.844905i	$0.320343\pi$
$983$			1.57780e12i			1.68981i	−0.534916	+	0.844905i	$0.679657\pi$
$984$	−9.18511e10	+	7.99831e10i	−0.0979724	+	0.0853135i
$985$	1.34367e11			0.142741
$986$	−3.89885e11	−	1.14136e11i	−0.412505	−	0.120758i
$987$		−	7.05761e11i		−	0.743685i
$988$	−9.35200e11	+	1.46042e12i	−0.981469	+	1.53268i
$989$	−1.75060e11			−0.182979
$990$	−8.15007e10	+	2.78404e11i	−0.0848439	+	0.289825i
$991$		−	1.83814e11i		−	0.190583i	−0.995449	−	0.0952917i	$-0.969622\pi$
$991$		−	1.83814e11i		−	0.190583i	0.995449	−	0.0952917i	$-0.0303784\pi$
$992$	4.02590e11	−	5.95576e10i	0.415734	−	0.0615022i
$993$	−9.93195e11			−1.02150
$994$	2.61886e11	+	7.66651e10i	0.268267	+	0.0785330i
$995$			1.73547e11i			0.177062i
$996$	−1.31618e12	−	8.42835e11i	−1.33746	−	0.856456i
$997$	−2.34014e11			−0.236844			−0.118422	−	0.992963i	$-0.537783\pi$
$997$	−2.34014e11			−0.236844			−0.118422	+	0.992963i	$0.537783\pi$
$998$	3.13679e11	−	1.07152e12i	0.316201	−	1.08013i
$999$			4.54615e11i			0.456438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.b.a.11.1	✓	16
3.2	odd	2		180.9.c.a.91.16		16
4.3	odd	2	inner	20.9.b.a.11.2	yes	16
5.2	odd	4		100.9.d.c.99.17		32
5.3	odd	4		100.9.d.c.99.16		32
5.4	even	2		100.9.b.d.51.16		16
8.3	odd	2		320.9.b.d.191.13		16
8.5	even	2		320.9.b.d.191.4		16
12.11	even	2		180.9.c.a.91.15		16
20.3	even	4		100.9.d.c.99.18		32
20.7	even	4		100.9.d.c.99.15		32
20.19	odd	2		100.9.b.d.51.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.1	✓	16	1.1	even	1	trivial
20.9.b.a.11.2	yes	16	4.3	odd	2	inner
100.9.b.d.51.15		16	20.19	odd	2
100.9.b.d.51.16		16	5.4	even	2
100.9.d.c.99.15		32	20.7	even	4
100.9.d.c.99.16		32	5.3	odd	4
100.9.d.c.99.17		32	5.2	odd	4
100.9.d.c.99.18		32	20.3	even	4
180.9.c.a.91.15		16	12.11	even	2
180.9.c.a.91.16		16	3.2	odd	2
320.9.b.d.191.4		16	8.5	even	2
320.9.b.d.191.13		16	8.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.3556 - 4.49522i) q^{2} +98.1237i q^{3} +(215.586 + 138.053i) q^{4} +279.508 q^{5} +(441.088 - 1506.74i) q^{6} +820.952i q^{7} +(-2689.86 - 3088.99i) q^{8} -3067.27 q^{9} +O(q^{10})\)	\(q+(-15.3556 - 4.49522i) q^{2} +98.1237i q^{3} +(215.586 + 138.053i) q^{4} +279.508 q^{5} +(441.088 - 1506.74i) q^{6} +820.952i q^{7} +(-2689.86 - 3088.99i) q^{8} -3067.27 q^{9} +(-4292.01 - 1256.45i) q^{10} +21147.7i q^{11} +(-13546.3 + 21154.1i) q^{12} -36649.1 q^{13} +(3690.36 - 12606.2i) q^{14} +27426.4i q^{15} +(27418.7 + 59524.7i) q^{16} -110563. q^{17} +(47099.6 + 13788.0i) q^{18} -184840. i q^{19} +(60258.1 + 38587.0i) q^{20} -80554.9 q^{21} +(95063.7 - 324735. i) q^{22} +181906. i q^{23} +(303103. - 263939. i) q^{24} +78125.0 q^{25} +(562767. + 164746. i) q^{26} +342818. i q^{27} +(-113335. + 176986. i) q^{28} -229647. q^{29} +(123288. - 421148. i) q^{30} +388118. i q^{31} +(-153452. - 1.03729e6i) q^{32} -2.07510e6 q^{33} +(1.69776e6 + 497005. i) q^{34} +229463. i q^{35} +(-661260. - 423446. i) q^{36} +1.32611e6 q^{37} +(-830894. + 2.83831e6i) q^{38} -3.59615e6i q^{39} +(-751840. - 863399. i) q^{40} -303036. q^{41} +(1.23696e6 + 362112. i) q^{42} +962361. i q^{43} +(-2.91951e6 + 4.55916e6i) q^{44} -857327. q^{45} +(817709. - 2.79327e6i) q^{46} +8.76124e6i q^{47} +(-5.84078e6 + 2.69042e6i) q^{48} +5.09084e6 q^{49} +(-1.19965e6 - 351189. i) q^{50} -1.08489e7i q^{51} +(-7.90103e6 - 5.05952e6i) q^{52} -577555. q^{53} +(1.54104e6 - 5.26416e6i) q^{54} +5.91097e6i q^{55} +(2.53591e6 - 2.20825e6i) q^{56} +1.81371e7 q^{57} +(3.52636e6 + 1.03231e6i) q^{58} -4.11725e6i q^{59} +(-3.78630e6 + 5.91275e6i) q^{60} +2.10168e7 q^{61} +(1.74467e6 - 5.95976e6i) q^{62} -2.51808e6i q^{63} +(-2.30649e6 + 1.66179e7i) q^{64} -1.02437e7 q^{65} +(3.18642e7 + 9.32801e6i) q^{66} -3.85926e7i q^{67} +(-2.38359e7 - 1.52636e7i) q^{68} -1.78493e7 q^{69} +(1.03149e6 - 3.52353e6i) q^{70} +2.07744e7i q^{71} +(8.25053e6 + 9.47475e6i) q^{72} -2.70559e7 q^{73} +(-2.03632e7 - 5.96116e6i) q^{74} +7.66592e6i q^{75} +(2.55177e7 - 3.98488e7i) q^{76} -1.73613e7 q^{77} +(-1.61655e7 + 5.52208e7i) q^{78} +5.62358e7i q^{79} +(7.66375e6 + 1.66376e7i) q^{80} -5.37629e7 q^{81} +(4.65328e6 + 1.36221e6i) q^{82} +6.22189e7i q^{83} +(-1.73665e7 - 1.11209e7i) q^{84} -3.09033e7 q^{85} +(4.32602e6 - 1.47776e7i) q^{86} -2.25338e7i q^{87} +(6.53251e7 - 5.68845e7i) q^{88} +6.04409e7 q^{89} +(1.31647e7 + 3.85387e6i) q^{90} -3.00871e7i q^{91} +(-2.51127e7 + 3.92165e7i) q^{92} -3.80836e7 q^{93} +(3.93837e7 - 1.34534e8i) q^{94} -5.16642e7i q^{95} +(1.01782e8 - 1.50573e7i) q^{96} +1.31334e8 q^{97} +(-7.81727e7 - 2.28844e7i) q^{98} -6.48658e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

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