LMFDB - Embedded newform 20.9.b.a.11.12

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			11.12
Root			$-6.29294 - 5.63875i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.9.b.a.11.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.3498 + 11.2775i) q^{2} -137.297i q^{3} +(1.63618 + 255.995i) q^{4} -279.508 q^{5} +(1548.37 - 1558.29i) q^{6} -3940.57i q^{7} +(-2868.41 + 2923.94i) q^{8} -12289.4 q^{9} +O(q^{10})$	\(q+(11.3498 + 11.2775i) q^{2} -137.297i q^{3} +(1.63618 + 255.995i) q^{4} -279.508 q^{5} +(1548.37 - 1558.29i) q^{6} -3940.57i q^{7} +(-2868.41 + 2923.94i) q^{8} -12289.4 q^{9} +(-3172.37 - 3152.16i) q^{10} -17097.0i q^{11} +(35147.3 - 224.642i) q^{12} +10938.7 q^{13} +(44439.8 - 44724.8i) q^{14} +38375.6i q^{15} +(-65530.6 + 837.705i) q^{16} +101666. q^{17} +(-139483. - 138594. i) q^{18} +93432.1i q^{19} +(-457.325 - 71552.7i) q^{20} -541029. q^{21} +(192811. - 194047. i) q^{22} +147346. i q^{23} +(401448. + 393824. i) q^{24} +78125.0 q^{25} +(124152. + 123361. i) q^{26} +786497. i q^{27} +(1.00877e6 - 6447.48i) q^{28} +41637.4 q^{29} +(-432781. + 435556. i) q^{30} -138577. i q^{31} +(-753207. - 729514. i) q^{32} -2.34736e6 q^{33} +(1.15389e6 + 1.14653e6i) q^{34} +1.10142e6i q^{35} +(-20107.7 - 3.14603e6i) q^{36} +1.14978e6 q^{37} +(-1.05368e6 + 1.06044e6i) q^{38} -1.50185e6i q^{39} +(801745. - 817267. i) q^{40} +3.83906e6 q^{41} +(-6.14057e6 - 6.10145e6i) q^{42} -3.18959e6i q^{43} +(4.37673e6 - 27973.6i) q^{44} +3.43500e6 q^{45} +(-1.66170e6 + 1.67235e6i) q^{46} +3.51218e6i q^{47} +(115014. + 8.99715e6i) q^{48} -9.76332e6 q^{49} +(886704. + 881054. i) q^{50} -1.39584e7i q^{51} +(17897.6 + 2.80024e6i) q^{52} +5.66612e6 q^{53} +(-8.86971e6 + 8.92658e6i) q^{54} +4.77874e6i q^{55} +(1.15220e7 + 1.13032e7i) q^{56} +1.28279e7 q^{57} +(472576. + 469565. i) q^{58} -1.69068e7i q^{59} +(-9.82397e6 + 62789.3i) q^{60} -5.16010e6 q^{61} +(1.56280e6 - 1.57282e6i) q^{62} +4.84274e7i q^{63} +(-321668. - 1.67741e7i) q^{64} -3.05745e6 q^{65} +(-2.66421e7 - 2.64723e7i) q^{66} -1.05358e7i q^{67} +(166343. + 2.60259e7i) q^{68} +2.02302e7 q^{69} +(-1.24213e7 + 1.25009e7i) q^{70} -1.85971e7i q^{71} +(3.52511e7 - 3.59336e7i) q^{72} +2.38535e6 q^{73} +(1.30498e7 + 1.29666e7i) q^{74} -1.07263e7i q^{75} +(-2.39181e7 + 152871. i) q^{76} -6.73718e7 q^{77} +(1.69371e7 - 1.70457e7i) q^{78} +4.42560e7i q^{79} +(1.83164e7 - 234146. i) q^{80} +2.73525e7 q^{81} +(4.35726e7 + 4.32950e7i) q^{82} -1.51824e7i q^{83} +(-885218. - 1.38500e8i) q^{84} -2.84164e7 q^{85} +(3.59706e7 - 3.62013e7i) q^{86} -5.71668e6i q^{87} +(4.99905e7 + 4.90411e7i) q^{88} -5.42739e7 q^{89} +(3.89866e7 + 3.87382e7i) q^{90} -4.31047e7i q^{91} +(-3.77199e7 + 241085. i) q^{92} -1.90261e7 q^{93} +(-3.96086e7 + 3.98625e7i) q^{94} -2.61151e7i q^{95} +(-1.00160e8 + 1.03413e8i) q^{96} -1.24798e8 q^{97} +(-1.10812e8 - 1.10106e8i) q^{98} +2.10112e8i 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 $

$2$	11.3498	+	11.2775i	0.709363	+	0.704843i
$2$	11.3498	+	11.2775i	0.709363	+	0.704843i
$3$		−	137.297i		−	1.69502i	−0.530777	−	0.847512i	$-0.678100\pi$
$3$		−	137.297i		−	1.69502i	0.530777	−	0.847512i	$-0.321900\pi$
$4$	1.63618	+	255.995i	0.00639132	+	0.999980i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$	1548.37	−	1558.29i	1.19473	−	1.20239i
$7$		−	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
$9$	−12289.4			−1.87310
$10$	−3172.37	−	3152.16i	−0.317237	−	0.315216i
$11$		−	17097.0i		−	1.16775i	−0.811845	−	0.583873i	$-0.801537\pi$
$11$		−	17097.0i		−	1.16775i	0.811845	−	0.583873i	$-0.198463\pi$
$12$	35147.3	−	224.642i	1.69499	−	0.0108334i
$13$	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
$15$			38375.6i			0.758037i
$16$	−65530.6	+	837.705i	−0.999918	+	0.0127824i
$17$	101666.			1.21725			0.608624	−	0.793459i	$-0.291722\pi$
$17$	101666.			1.21725			0.608624	+	0.793459i	$0.291722\pi$
$18$	−139483.	−	138594.i	−1.32871	−	1.32025i
$19$			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
$21$	−541029.			−2.78191
$22$	192811.	−	194047.i	0.823078	−	0.828355i
$23$			147346.i			0.526536i	0.964723	+	0.263268i	$0.0848003\pi$
$23$			147346.i			0.526536i	−0.964723	+	0.263268i	$0.915200\pi$
$24$	401448.	+	393824.i	1.21000	+	1.18702i
$25$	78125.0			0.200000
$26$	124152.	+	123361.i	0.271681	+	0.269951i
$27$			786497.i			1.47993i
$28$	1.00877e6	−	6447.48i	1.64119	−	0.0104896i
$29$	41637.4			0.0588696			0.0294348	−	0.999567i	$-0.490629\pi$
$29$	41637.4			0.0588696			0.0294348	+	0.999567i	$0.490629\pi$
$30$	−432781.	+	435556.i	−0.534298	+	0.537724i
$31$		−	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
$33$	−2.34736e6			−1.97936
$34$	1.15389e6	+	1.14653e6i	0.863470	+	0.857969i
$35$			1.10142e6i			0.733977i
$36$	−20107.7	−	3.14603e6i	−0.0119716	−	1.87307i
$37$	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
$39$		−	1.50185e6i		−	0.649183i
$40$	801745.	−	817267.i	0.313182	−	0.319245i
$41$	3.83906e6			1.35859			0.679297	−	0.733864i	$-0.262285\pi$
$41$	3.83906e6			1.35859			0.679297	+	0.733864i	$0.262285\pi$
$42$	−6.14057e6	−	6.10145e6i	−1.97338	−	1.96081i
$43$		−	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
$45$	3.43500e6			0.837678
$46$	−1.66170e6	+	1.67235e6i	−0.371125	+	0.373505i
$47$			3.51218e6i			0.719756i	0.932999	+	0.359878i	$0.117182\pi$
$47$			3.51218e6i			0.719756i	−0.932999	+	0.359878i	$0.882818\pi$
$48$	115014.	+	8.99715e6i	0.0216664	+	1.69488i
$49$	−9.76332e6			−1.69361
$50$	886704.	+	881054.i	0.141873	+	0.140969i
$51$		−	1.39584e7i		−	2.06326i
$52$	17897.6	+	2.80024e6i	0.00244783	+	0.382986i
$53$	5.66612e6			0.718096			0.359048	−	0.933319i	$-0.383101\pi$
$53$	5.66612e6			0.718096			0.359048	+	0.933319i	$0.383101\pi$
$54$	−8.86971e6	+	8.92658e6i	−1.04312	+	1.04981i
$55$			4.77874e6i			0.522231i
$56$	1.15220e7	+	1.13032e7i	1.17159	+	1.14934i
$57$	1.28279e7			1.21523
$58$	472576.	+	469565.i	0.0417599	+	0.0414939i
$59$		−	1.69068e7i		−	1.39525i	−0.716461	−	0.697627i	$-0.754239\pi$
$59$		−	1.69068e7i		−	1.39525i	0.716461	−	0.697627i	$-0.245761\pi$
$60$	−9.82397e6	+	62789.3i	−0.758022	+	0.00484486i
$61$	−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
$63$			4.84274e7i			3.07418i
$64$	−321668.	−	1.67741e7i	−0.0191729	−	0.999816i
$65$	−3.05745e6			−0.171280
$66$	−2.66421e7	−	2.64723e7i	−1.40408	−	1.39514i
$67$		−	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
$69$	2.02302e7			0.892490
$70$	−1.24213e7	+	1.25009e7i	−0.517339	+	0.520656i
$71$		−	1.85971e7i		−	0.731833i	−0.930648	−	0.365916i	$-0.880756\pi$
$71$		−	1.85971e7i		−	0.731833i	0.930648	−	0.365916i	$-0.119244\pi$
$72$	3.52511e7	−	3.59336e7i	1.31173	−	1.33712i
$73$	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
$75$		−	1.07263e7i		−	0.339005i
$76$	−2.39181e7	+	152871.i	−0.716923	+	0.00458218i
$77$	−6.73718e7			−1.91653
$78$	1.69371e7	−	1.70457e7i	0.457572	−	0.460506i
$79$			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
$81$	2.73525e7			0.635415
$82$	4.35726e7	+	4.32950e7i	0.963736	+	0.957596i
$83$		−	1.51824e7i		−	0.319910i	−0.987124	−	0.159955i	$-0.948865\pi$
$83$		−	1.51824e7i		−	0.319910i	0.987124	−	0.159955i	$-0.0511349\pi$
$84$	−885218.	−	1.38500e8i	−0.0177801	−	2.78185i
$85$	−2.84164e7			−0.544369
$86$	3.59706e7	−	3.62013e7i	0.657588	−	0.661805i
$87$		−	5.71668e6i		−	0.0997854i
$88$	4.99905e7	+	4.90411e7i	0.833599	+	0.817766i
$89$	−5.42739e7			−0.865030			−0.432515	−	0.901627i	$-0.642374\pi$
$89$	−5.42739e7			−0.865030			−0.432515	+	0.901627i	$0.642374\pi$
$90$	3.89866e7	+	3.87382e7i	0.594217	+	0.590432i
$91$		−	4.31047e7i		−	0.628577i
$92$	−3.77199e7	+	241085.i	−0.526525	+	0.00336526i
$93$	−1.90261e7			−0.254342
$94$	−3.96086e7	+	3.98625e7i	−0.507315	+	0.510568i
$95$		−	2.61151e7i		−	0.320624i
$96$	−1.00160e8	+	1.03413e8i	−1.17926	+	1.21756i
$97$	−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
$99$			2.10112e8i			2.18731i
$100$	127826.	+	1.99996e7i	0.00127826	+	0.199996i
$101$	1.96354e8			1.88693			0.943463	−	0.331478i	$-0.107547\pi$
$101$	1.96354e8			1.88693			0.943463	+	0.331478i	$0.107547\pi$
$102$	1.57416e8	−	1.58425e8i	1.45428	−	1.46360i
$103$			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
$105$	1.51222e8			1.24411
$106$	6.43094e7	+	6.38996e7i	0.509390	+	0.506145i
$107$			5.19293e7i			0.396166i	0.980185	+	0.198083i	$0.0634715\pi$
$107$			5.19293e7i			0.396166i	−0.980185	+	0.198083i	$0.936528\pi$
$108$	−2.01339e8	+	1.28685e6i	−1.47990	+	0.00945871i
$109$	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
$111$		−	1.57861e8i		−	1.03988i
$112$	3.30104e6	+	2.58228e8i	0.0209787	+	1.64109i
$113$	−6.82663e7			−0.418690			−0.209345	−	0.977842i	$-0.567133\pi$
$113$	−6.82663e7			−0.418690			−0.209345	+	0.977842i	$0.567133\pi$
$114$	1.45595e8	+	1.44667e8i	0.862037	+	0.856544i
$115$		−	4.11845e7i		−	0.235474i
$116$	68126.1	+	1.06590e7i	0.000376254	+	0.0588684i
$117$	−1.34430e8			−0.717387
$118$	1.90666e8	−	1.91889e8i	0.983435	−	0.989741i
$119$		−	4.00621e8i		−	1.99777i
$120$	−1.12208e8	−	1.10077e8i	−0.541128	−	0.530850i
$121$	−7.79470e7			−0.363629
$122$	−5.85661e7	−	5.81930e7i	−0.264367	−	0.262683i
$123$		−	5.27091e8i		−	2.30285i
$124$	3.54749e7	−	226736.i	0.150049	−	0.000959032i
$125$	−2.18366e7			−0.0894427
$126$	−5.46140e8	+	5.49642e8i	−2.16682	+	2.18071i
$127$			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
$129$	−4.37921e8			−1.58138
$130$	−3.47015e7	−	3.44804e7i	−0.121500	−	0.120726i
$131$		−	1.49192e8i		−	0.506596i	−0.967388	−	0.253298i	$-0.918485\pi$
$131$		−	1.49192e8i		−	0.506596i	0.967388	−	0.253298i	$-0.0815153\pi$
$132$	−3.84069e6	−	6.00912e8i	−0.0126507	−	1.97931i
$133$	3.68176e8			1.17665
$134$	1.18817e8	−	1.19579e8i	0.368519	−	0.370882i
$135$		−	2.19832e8i		−	0.661846i
$136$	−2.91619e8	+	2.97265e8i	−0.852433	+	0.868936i
$137$	6.05661e8			1.71928			0.859642	−	0.510897i	$-0.170687\pi$
$137$	6.05661e8			1.71928			0.859642	+	0.510897i	$0.170687\pi$
$138$	2.29609e8	+	2.28146e8i	0.633099	+	0.629066i
$139$			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
$141$	4.82211e8			1.22000
$142$	2.09729e8	−	2.11074e8i	0.515828	−	0.519135i
$143$		−	1.87018e8i		−	0.447239i
$144$	8.05335e8	−	1.02949e7i	1.87295	−	0.0239427i
$145$	−1.16380e7			−0.0263273
$146$	2.70732e7	+	2.69008e7i	0.0595839	+	0.0592043i
$147$			1.34047e9i			2.87071i
$148$	1.88124e6	+	2.94337e8i	0.00392100	+	0.613477i
$149$	−6.13964e8			−1.24565			−0.622827	−	0.782359i	$-0.714016\pi$
$149$	−6.13964e8			−1.24565			−0.622827	+	0.782359i	$0.714016\pi$
$150$	1.20966e8	−	1.21742e8i	0.238945	−	0.240477i
$151$			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
$153$	−1.24941e9			−2.28003
$154$	−7.64657e8	−	7.59785e8i	−1.35951	−	1.35085i
$155$			3.87333e7i			0.0671055i
$156$	3.84465e8	−	2.45729e6i	0.649170	−	0.00414913i
$157$	−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
$159$		−	7.77941e8i		−	1.21719i
$160$	2.10528e8	+	2.03905e8i	0.321240	+	0.311135i
$161$	5.80629e8			0.864162
$162$	3.10446e8	+	3.08468e8i	0.450740	+	0.447868i
$163$			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
$165$	6.56107e8			0.885195
$166$	1.71219e8	−	1.72317e8i	0.225486	−	0.226932i
$167$		−	4.55554e8i		−	0.585699i	−0.956159	−	0.292849i	$-0.905397\pi$
$167$		−	4.55554e8i		−	0.585699i	0.956159	−	0.292849i	$-0.0946035\pi$
$168$	1.55189e9	−	1.58194e9i	1.94816	−	1.98588i
$169$	−6.96076e8			−0.853316
$170$	−3.22521e8	−	3.20466e8i	−0.386155	−	0.383695i
$171$		−	1.14823e9i		−	1.34290i
$172$	8.16519e8	−	5.21874e6i	0.932937	−	0.00596282i
$173$	9.64344e8			1.07658			0.538292	−	0.842759i	$-0.319070\pi$
$173$	9.64344e8			1.07658			0.538292	+	0.842759i	$0.319070\pi$
$174$	6.44699e7	−	6.48832e7i	0.0703331	−	0.0707841i
$175$		−	3.07857e8i		−	0.328244i
$176$	1.43222e7	+	1.12037e9i	0.0149265	+	1.16765i
$177$	−2.32125e9			−2.36499
$178$	−6.15998e8	−	6.12074e8i	−0.613620	−	0.609711i
$179$			1.01365e9i			0.987363i	0.869643	+	0.493682i	$0.164349\pi$
$179$			1.01365e9i			0.987363i	−0.869643	+	0.493682i	$0.835651\pi$
$180$	5.62027e6	+	8.79343e8i	0.00535386	+	0.837661i
$181$	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
$183$			7.08465e8i			0.631705i
$184$	−4.30832e8	−	4.22649e8i	−0.375869	−	0.368730i
$185$	−3.21373e8			−0.274361
$186$	−2.15943e8	−	2.14567e8i	−0.180421	−	0.179272i
$187$		−	1.73817e9i		−	1.42143i
$188$	−8.99099e8	+	5.74654e6i	−0.719741	+	0.00460019i
$189$	3.09925e9			2.42890
$190$	2.94512e8	−	2.96401e8i	0.225990	−	0.227439i
$191$		−	5.46186e8i		−	0.410399i	−0.978720	−	0.205200i	$-0.934216\pi$
$191$		−	5.46186e8i		−	0.410399i	0.978720	−	0.205200i	$-0.0657844\pi$
$192$	−2.30304e9	+	4.41640e7i	−1.69471	+	0.0324985i
$193$	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
$195$			4.19779e8i			0.290323i
$196$	−1.59745e7	−	2.49936e9i	−0.0108244	−	1.69358i
$197$	1.98770e9			1.31974			0.659868	−	0.751382i	$-0.270612\pi$
$197$	1.98770e9			1.31974			0.659868	+	0.751382i	$0.270612\pi$
$198$	−2.36954e9	+	2.38473e9i	−1.54171	+	1.55160i
$199$			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
$201$	−1.44653e9			−0.886222
$202$	2.22858e9	+	2.21438e9i	1.33852	+	1.32999i
$203$		−	1.64075e8i		−	0.0966182i
$204$	3.57327e9	−	2.28384e7i	2.06322	−	0.0131870i
$205$	−1.07305e9			−0.607582
$206$	−1.22252e9	+	1.23036e9i	−0.678872	+	0.683224i
$207$		−	1.81080e9i		−	0.986256i
$208$	−7.16819e8	+	9.16339e6i	−0.382962	+	0.00489556i
$209$	1.59740e9			0.837201
$210$	1.71634e9	+	1.70541e9i	0.882524	+	0.876901i
$211$		−	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
$213$	−2.55332e9			−1.24047
$214$	−5.85632e8	+	5.89387e8i	−0.279235	+	0.281025i
$215$			8.91518e8i			0.417231i
$216$	−2.29967e9	−	2.25599e9i	−1.05645	−	1.03639i
$217$	−5.46071e8			−0.246269
$218$	2.28280e9	+	2.26826e9i	1.01075	+	1.00431i
$219$		−	3.27501e8i		−	0.142376i
$220$	−1.22333e9	+	7.81887e6i	−0.522221	+	0.00333775i
$221$	1.11209e9			0.466198
$222$	1.78028e9	−	1.79169e9i	0.732952	−	0.737651i
$223$			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
$225$	−9.60112e8			−0.374621
$226$	−7.74809e8	−	7.69873e8i	−0.297003	−	0.295111i
$227$		−	1.08981e9i		−	0.410438i	−0.978716	−	0.205219i	$-0.934209\pi$
$227$		−	1.08981e9i		−	0.410438i	0.978716	−	0.205219i	$-0.0657906\pi$
$228$	2.09888e7	+	3.28388e9i	0.00776690	+	1.21520i
$229$	−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
$231$			9.24994e9i			3.24856i
$232$	−1.19433e8	+	1.21745e8i	−0.0412261	+	0.0420243i
$233$	6.52483e8			0.221384			0.110692	−	0.993855i	$-0.464693\pi$
$233$	6.52483e8			0.221384			0.110692	+	0.993855i	$0.464693\pi$
$234$	−1.52576e9	−	1.51604e9i	−0.508888	−	0.505645i
$235$		−	9.81684e8i		−	0.321885i
$236$	4.32805e9	−	2.76625e7i	1.39522	−	0.00891750i
$237$	6.07622e9			1.92593
$238$	4.51800e9	−	4.54697e9i	1.40812	−	1.41715i
$239$		−	4.79300e9i		−	1.46898i	−0.678619	−	0.734490i	$-0.737421\pi$
$239$		−	4.79300e9i		−	1.46898i	0.678619	−	0.734490i	$-0.262579\pi$
$240$	−3.21475e7	−	2.51478e9i	−0.00968952	−	0.757976i
$241$	−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
$243$			1.40479e9i			0.402889i
$244$	−8.44283e6	−	1.32096e9i	−0.00238193	−	0.372675i
$245$	2.72893e9			0.757405
$246$	5.94427e9	−	5.98238e9i	1.62315	−	1.63355i
$247$			1.02202e9i			0.274583i
$248$	4.05190e8	+	3.97494e8i	0.107115	+	0.105081i
$249$	−2.08449e9			−0.542255
$250$	−2.47841e8	−	2.46262e8i	−0.0634473	−	0.0630431i
$251$		−	2.41878e9i		−	0.609398i	−0.952449	−	0.304699i	$-0.901444\pi$
$251$		−	2.41878e9i		−	0.609398i	0.952449	−	0.304699i	$-0.0985558\pi$
$252$	−1.23972e10	+	7.92358e7i	−3.07412	+	0.0196481i
$253$	2.51917e9			0.614859
$254$	−3.93567e9	+	3.96090e9i	−0.945548	+	0.951611i
$255$			3.90149e9i			0.922719i
$256$	4.29356e9	−	1.09791e8i	0.999673	−	0.0255627i
$257$	−5.25554e9			−1.20472			−0.602358	−	0.798226i	$-0.705772\pi$
$257$	−5.25554e9			−1.20472			−0.602358	+	0.798226i	$0.705772\pi$
$258$	−4.97032e9	−	4.93865e9i	−1.12177	−	1.11463i
$259$		−	4.53078e9i		−	1.00687i
$260$	−5.00253e6	−	7.82692e8i	−0.00109470	−	0.171276i
$261$	−5.11700e8			−0.110269
$262$	1.68252e9	−	1.69331e9i	0.357071	−	0.359360i
$263$		−	1.24951e9i		−	0.261165i	−0.991437	−	0.130583i	$-0.958315\pi$
$263$		−	1.24951e9i		−	0.261165i	0.991437	−	0.130583i	$-0.0416848\pi$
$264$	6.73319e9	−	6.86354e9i	1.38613	−	1.41297i
$265$	−1.58373e9			−0.321142
$266$	4.17873e9	+	4.15210e9i	0.834675	+	0.829357i
$267$			7.45164e9i			1.46625i
$268$	2.69710e9	−	1.72384e7i	0.522827	−	0.00334162i
$269$	−5.36357e9			−1.02434			−0.512171	−	0.858884i	$-0.671159\pi$
$269$	−5.36357e9			−1.02434			−0.512171	+	0.858884i	$0.671159\pi$
$270$	2.47916e9	−	2.49506e9i	0.466498	−	0.469489i
$271$			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
$273$	−5.91814e9			−1.06545
$274$	6.87414e9	+	6.83034e9i	1.21960	+	1.21183i
$275$		−	1.33570e9i		−	0.233549i
$276$	3.31002e7	+	5.17882e9i	0.00570419	+	0.892472i
$277$	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
$279$			1.70303e9i			0.281064i
$280$	−3.22050e9	−	3.15934e9i	−0.523952	−	0.514001i
$281$	−8.47677e8			−0.135958			−0.0679791	−	0.997687i	$-0.521655\pi$
$281$	−8.47677e8			−0.135958			−0.0679791	+	0.997687i	$0.521655\pi$
$282$	5.47300e9	+	5.43813e9i	0.865425	+	0.859911i
$283$		−	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
$285$	−3.58552e9			−0.543466
$286$	2.10910e9	−	2.12262e9i	0.315233	−	0.317255i
$287$		−	1.51281e10i		−	2.22975i
$288$	9.25649e9	+	8.96531e9i	1.34548	+	1.30315i
$289$	3.36016e9			0.481691
$290$	−1.32089e8	−	1.31248e8i	−0.0186756	−	0.0185566i
$291$			1.71344e10i			2.38944i
$292$	3.90285e6	+	6.10637e8i	0.000536847	+	0.0839946i
$293$	1.18893e10			1.61319			0.806594	−	0.591107i	$-0.201309\pi$
$293$	1.18893e10			1.61319			0.806594	+	0.591107i	$0.201309\pi$
$294$	−1.51172e10	+	1.52141e10i	−2.02340	+	2.03637i
$295$			4.72559e9i			0.623976i
$296$	−3.29803e9	+	3.36188e9i	−0.429624	+	0.437941i
$297$	1.34467e10			1.72818
$298$	−6.96837e9	−	6.92397e9i	−0.883621	−	0.877992i
$299$			1.61177e9i			0.201660i
$300$	2.74588e9	−	1.75502e7i	0.338998	−	0.00216669i
$301$	−1.25688e10			−1.53119
$302$	−6.10296e9	+	6.14209e9i	−0.733690	+	0.738394i
$303$		−	2.69588e10i		−	3.19838i
$304$	−7.82685e7	−	6.12266e9i	−0.00916417	−	0.716879i
$305$	1.44229e9			0.166669
$306$	−1.41806e10	−	1.40903e10i	−1.61737	−	1.60706i
$307$			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
$309$	1.48835e10			1.63257
$310$	−4.36815e8	+	4.39616e8i	−0.0472989	+	0.0476021i
$311$			8.61717e9i			0.921135i	0.887625	+	0.460567i	$0.152354\pi$
$311$			8.61717e9i			0.921135i	−0.887625	+	0.460567i	$0.847646\pi$
$312$	4.39131e9	+	4.30791e9i	0.463421	+	0.454620i
$313$	−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
$315$		−	1.35359e10i		−	1.37482i
$316$	−1.13293e10	+	7.24107e7i	−1.13620	+	0.00726197i
$317$	−6.57561e9			−0.651177			−0.325589	−	0.945512i	$-0.605562\pi$
$317$	−6.57561e9			−0.651177			−0.325589	+	0.945512i	$0.605562\pi$
$318$	8.77322e9	−	8.82948e9i	0.857928	−	0.863429i
$319$		−	7.11872e8i		−	0.0687447i
$320$	8.99089e7	+	4.68851e9i	0.00857438	+	0.447131i
$321$	7.12973e9			0.671510
$322$	6.59002e9	+	6.54804e9i	0.613004	+	0.609099i
$323$			9.49884e9i			0.872691i
$324$	4.47536e7	+	7.00211e9i	0.00406114	+	0.635402i
$325$	8.54584e8			0.0765987
$326$	−7.60787e9	+	7.65665e9i	−0.673586	+	0.677905i
$327$		−	2.76147e10i		−	2.41518i
$328$	−1.10120e10	+	1.12252e10i	−0.951417	+	0.969837i
$329$	1.38400e10			1.18128
$330$	7.44668e9	+	7.39924e9i	0.627924	+	0.623924i
$331$		−	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
$333$	−1.41301e10			−1.14913
$334$	5.13751e9	−	5.17045e9i	0.412826	−	0.415473i
$335$			2.94484e9i			0.233820i
$336$	3.54540e10	−	4.53223e8i	2.78168	−	0.0355594i
$337$	−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
$339$			9.37275e9i			0.709690i
$340$	−4.64943e7	−	7.27446e9i	−0.00347924	−	0.544358i
$341$	−2.36924e9			−0.175223
$342$	1.29491e10	−	1.30322e10i	0.946534	−	0.952603i
$343$			1.57565e10i			1.13837i
$344$	9.32619e9	+	9.14906e9i	0.665994	+	0.653345i
$345$	−5.65451e9			−0.399134
$346$	1.09451e10	+	1.08754e10i	0.763688	+	0.758823i
$347$		−	6.31855e9i		−	0.435813i	−0.975970	−	0.217906i	$-0.930077\pi$
$347$		−	6.31855e9i		−	0.435813i	0.975970	−	0.217906i	$-0.0699227\pi$
$348$	1.46344e9	−	9.35350e6i	0.0997834	−	0.000637760i
$349$	−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
$351$			8.60323e9i			0.566804i
$352$	−1.24725e10	+	1.28776e10i	−0.812422	+	0.838808i
$353$	3.02132e10			1.94580			0.972900	−	0.231225i	$-0.0742734\pi$
$353$	3.02132e10			1.94580			0.972900	+	0.231225i	$0.0742734\pi$
$354$	−2.63457e10	−	2.61779e10i	−1.67763	−	1.66695i
$355$			5.19805e9i			0.327286i
$356$	−8.88017e7	−	1.38938e10i	−0.00552868	−	0.865012i
$357$	−5.50041e10			−3.38627
$358$	−1.14315e10	+	1.15048e10i	−0.695937	+	0.700399i
$359$			1.82078e10i			1.09618i	0.836421	+	0.548088i	$0.184644\pi$
$359$			1.82078e10i			1.09618i	−0.836421	+	0.548088i	$0.815356\pi$
$360$	−9.85299e9	+	1.00437e10i	−0.586622	+	0.597979i
$361$	8.25401e9			0.486000
$362$	1.71958e9	+	1.70862e9i	0.100135	+	0.0994974i
$363$			1.07019e10i			0.616359i
$364$	1.10346e10	−	7.05269e7i	0.628565	−	0.00401744i
$365$	−6.66725e8			−0.0375643
$366$	−7.98972e9	+	8.04094e9i	−0.445253	+	0.448108i
$367$			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
$369$	−4.71799e10			−2.54479
$370$	−3.64752e9	−	3.62428e9i	−0.194621	−	0.193381i
$371$		−	2.23278e10i		−	1.17855i
$372$	−3.11301e7	−	4.87059e9i	−0.00162558	−	0.254337i
$373$	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
$375$			2.99810e9i			0.151607i
$376$	−1.02694e10	−	1.00744e10i	−0.513800	−	0.504042i
$377$	4.55458e8			0.0225467
$378$	3.51759e10	+	3.49518e10i	1.72297	+	1.71199i
$379$			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
$381$	4.79145e10			2.27388
$382$	6.15961e9	−	6.19910e9i	0.289267	−	0.291122i
$383$			3.43063e10i			1.59433i	0.603760	+	0.797166i	$0.293668\pi$
$383$			3.43063e10i			1.59433i	−0.603760	+	0.797166i	$0.706332\pi$
$384$	−2.66371e10	−	2.54712e10i	−1.22507	−	1.17145i
$385$	1.88310e10			0.857098
$386$	1.72523e10	+	1.71424e10i	0.777137	+	0.772185i
$387$			3.91983e10i			1.74752i
$388$	−2.04192e8	−	3.19477e10i	−0.00900972	−	1.40965i
$389$	4.14309e8			0.0180936			0.00904681	−	0.999959i	$-0.497120\pi$
$389$	4.14309e8			0.0180936			0.00904681	+	0.999959i	$0.497120\pi$
$390$	−4.73405e9	+	4.76441e9i	−0.204633	+	0.205945i
$391$			1.49801e10i			0.640924i
$392$	2.80052e10	−	2.85474e10i	1.18603	−	1.20899i
$393$	−2.04837e10			−0.858692
$394$	2.25601e10	+	2.24163e10i	0.936171	+	0.930207i
$395$		−	1.23699e10i		−	0.508135i
$396$	−5.37876e10	+	3.43780e8i	−2.18726	+	0.0139798i
$397$	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
$399$		−	5.05494e10i		−	1.99446i
$400$	−5.11958e9	+	6.54457e7i	−0.199984	+	0.00255647i
$401$	−2.53666e10			−0.981037			−0.490519	−	0.871431i	$-0.663193\pi$
$401$	−2.53666e10			−0.981037			−0.490519	+	0.871431i	$0.663193\pi$
$402$	−1.64178e10	−	1.63132e10i	−0.628653	−	0.624648i
$403$		−	1.51584e9i		−	0.0574691i
$404$	3.21270e8	+	5.02657e10i	0.0120599	+	1.88689i
$405$	−7.64527e9			−0.284166
$406$	1.85036e9	−	1.86222e9i	0.0681007	−	0.0685373i
$407$		−	1.96577e10i		−	0.716399i
$408$	4.08135e10	+	4.00384e10i	1.47287	+	1.44489i
$409$	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
$411$		−	8.31554e10i		−	2.91423i
$412$	−2.77508e10	+	1.77367e8i	−0.963132	+	0.00615581i
$413$	−6.66225e10			−2.28992
$414$	2.04213e10	−	2.05523e10i	0.695156	−	0.699613i
$415$			4.24361e9i			0.143068i
$416$	−8.23909e9	−	7.97992e9i	−0.275110	−	0.266456i
$417$	7.12968e10			2.35790
$418$	1.81302e10	+	1.80147e10i	0.593879	+	0.590095i
$419$		−	7.30915e9i		−	0.237143i	−0.992946	−	0.118572i	$-0.962168\pi$
$419$		−	7.30915e9i		−	0.237143i	0.992946	−	0.118572i	$-0.0378315\pi$
$420$	2.47426e8	+	3.87121e10i	0.00795149	+	1.24408i
$421$	−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
$423$		−	4.31627e10i		−	1.34818i
$424$	−1.62528e10	+	1.65674e10i	−0.502879	+	0.512615i
$425$	7.94263e9			0.243449
$426$	−2.89797e10	−	2.87951e10i	−0.879946	−	0.874340i
$427$			2.03337e10i			0.611654i
$428$	−1.32936e10	+	8.49655e7i	−0.396158	+	0.00253202i
$429$	−2.56770e10			−0.758080
$430$	−1.00541e10	+	1.01186e10i	−0.294082	+	0.295968i
$431$			3.95128e9i			0.114506i	0.998360	+	0.0572531i	$0.0182342\pi$
$431$			3.95128e9i			0.114506i	−0.998360	+	0.0572531i	$0.981766\pi$
$432$	−6.58852e8	−	5.15396e10i	−0.0189170	−	1.47981i
$433$	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
$435$			1.59786e9i			0.0446254i
$436$	3.29086e8	+	5.14885e10i	0.00910676	+	1.42484i
$437$	−1.37669e10			−0.377493
$438$	3.69339e9	−	3.71707e9i	0.100353	−	0.100996i
$439$		−	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
$441$	1.19986e11			3.17231
$442$	1.26220e10	+	1.25416e10i	0.330703	+	0.328596i
$443$			1.61256e10i			0.418699i	0.977841	+	0.209350i	$0.0671346\pi$
$443$			1.61256e10i			0.418699i	−0.977841	+	0.209350i	$0.932865\pi$
$444$	4.04116e10	−	2.58288e8i	1.03986	−	0.00664619i
$445$	1.51700e10			0.386853
$446$	−1.59224e10	+	1.60245e10i	−0.402410	+	0.404990i
$447$			8.42953e10i			2.11141i
$448$	−6.60997e10	+	1.26756e9i	−1.64092	+	0.0314670i
$449$	1.31471e10			0.323478			0.161739	−	0.986834i	$-0.448290\pi$
$449$	1.31471e10			0.323478			0.161739	+	0.986834i	$0.448290\pi$
$450$	−1.08971e10	−	1.08277e10i	−0.265742	−	0.264049i
$451$		−	6.56363e10i		−	1.58649i
$452$	−1.11696e8	−	1.74758e10i	−0.00267598	−	0.418682i
$453$	7.42999e10			1.76439
$454$	1.22903e10	−	1.23691e10i	0.289294	−	0.291149i
$455$			1.20481e10i			0.281108i
$456$	−3.67958e10	+	3.75081e10i	−0.851017	+	0.867493i
$457$	−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
$459$			7.99597e10i			1.80144i
$460$	1.05430e10	−	6.73852e7i	0.235469	−	0.00150499i
$461$	−2.86783e10			−0.634966			−0.317483	−	0.948264i	$-0.602838\pi$
$461$	−2.86783e10			−0.634966			−0.317483	+	0.948264i	$0.602838\pi$
$462$	−1.04316e11	+	1.04985e11i	−2.28973	+	2.30441i
$463$			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
$465$	5.31796e9			0.113745
$466$	7.40556e9	+	7.35838e9i	0.157041	+	0.156041i
$467$		−	4.27269e10i		−	0.898325i	−0.893450	−	0.449163i	$-0.851722\pi$
$467$		−	4.27269e10i		−	0.898325i	0.893450	−	0.449163i	$-0.148278\pi$
$468$	−2.19952e8	−	3.44134e10i	−0.00458505	−	0.717372i
$469$	−4.15170e10			−0.858093
$470$	1.10709e10	−	1.11419e10i	0.226878	−	0.228333i
$471$			8.84167e10i			1.79660i
$472$	4.94345e10	+	4.84956e10i	0.996006	+	0.977089i
$473$	−5.45323e10			−1.08946
$474$	6.89639e10	+	6.85245e10i	1.36618	+	1.35748i
$475$			7.29938e9i			0.143388i
$476$	1.02557e11	−	6.55487e8i	1.99773	−	0.0127684i
$477$	−6.96334e10			−1.34507
$478$	5.40531e10	−	5.43996e10i	1.03540	−	1.04204i
$479$			6.73017e10i			1.27845i	0.769020	+	0.639225i	$0.220745\pi$
$479$			6.73017e10i			1.27845i	−0.769020	+	0.639225i	$0.779255\pi$
$480$	2.79956e10	−	2.89048e10i	0.527381	−	0.544509i
$481$	1.25770e10			0.234962
$482$	−5.88352e10	−	5.84604e10i	−1.09006	−	1.08311i
$483$		−	7.97185e10i		−	1.46477i
$484$	−1.27535e8	−	1.99540e10i	−0.00232406	−	0.363621i
$485$	3.48821e10			0.630429
$486$	−1.58425e10	+	1.59440e10i	−0.283973	+	0.285794i
$487$		−	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
$489$	9.26214e10			1.61985
$490$	3.09728e10	+	3.07755e10i	0.537275	+	0.533852i
$491$			1.73575e10i			0.298648i	0.988788	+	0.149324i	$0.0477098\pi$
$491$			1.73575e10i			0.298648i	−0.988788	+	0.149324i	$0.952290\pi$
$492$	1.34933e11	−	8.62414e8i	2.30280	−	0.0147182i
$493$	4.23309e9			0.0716589
$494$	−1.15259e10	+	1.15998e10i	−0.193538	+	0.194779i
$495$		−	5.87281e10i		−	0.978194i
$496$	1.16086e8	+	9.08101e9i	0.00191803	+	0.150040i
$497$	−7.32833e10			−1.20110
$498$	−2.36586e10	−	2.35079e10i	−0.384655	−	0.382205i
$499$		−	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
$501$	−6.25462e10			−0.992773
$502$	2.72777e10	−	2.74526e10i	0.429530	−	0.432284i
$503$			6.90584e10i			1.07881i	0.842047	+	0.539404i	$0.181351\pi$
$503$			6.90584e10i			1.07881i	−0.842047	+	0.539404i	$0.818649\pi$
$504$	−1.41599e11	−	1.38910e11i	−2.19451	−	2.15283i
$505$	−5.48827e10			−0.843859
$506$	2.85921e10	+	2.84100e10i	0.436158	+	0.433380i
$507$			9.55691e10i			1.44639i
$508$	−8.93382e10	+	5.71000e8i	−1.34147	+	0.00857396i
$509$	−5.98939e10			−0.892302			−0.446151	−	0.894958i	$-0.647206\pi$
$509$	−5.98939e10			−0.892302			−0.446151	+	0.894958i	$0.647206\pi$
$510$	−4.39990e10	+	4.42811e10i	−0.650372	+	0.654543i
$511$		−	9.39964e9i		−	0.137857i
$512$	4.99693e10	+	4.71745e10i	0.727149	+	0.686480i
$513$	−7.34840e10			−1.06102
$514$	−5.96493e10	−	5.92693e10i	−0.854581	−	0.849136i
$515$		−	3.02997e10i		−	0.430735i
$516$	−7.16516e8	−	1.12106e11i	−0.0101071	−	1.58135i
$517$	6.00476e10			0.840491
$518$	5.10959e10	−	5.14235e10i	0.709687	−	0.714238i
$519$		−	1.32401e11i		−	1.82483i
$520$	8.77003e9	−	8.93982e9i	0.119947	−	0.122269i
$521$	2.97388e10			0.403620			0.201810	−	0.979425i	$-0.435318\pi$
$521$	2.97388e10			0.403620			0.201810	+	0.979425i	$0.435318\pi$
$522$	−5.80770e9	−	5.77069e9i	−0.0782207	−	0.0777224i
$523$		−	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
$525$	−4.22679e10			−0.556382
$526$	1.40913e10	−	1.41817e10i	0.184081	−	0.185261i
$527$		−	1.40885e10i		−	0.182651i
$528$	1.53824e11	−	1.96640e9i	1.97919	−	0.0253008i
$529$	5.66001e10			0.722760
$530$	−1.79750e10	−	1.78605e10i	−0.227806	−	0.226355i
$531$			2.07775e11i			2.61345i
$532$	6.02401e8	+	9.42511e10i	0.00752037	+	1.17663i
$533$	4.19943e10			0.520333
$534$	−8.40358e10	+	8.45746e10i	−1.03347	+	1.04010i
$535$		−	1.45147e10i		−	0.177171i
$536$	3.08060e10	+	3.02209e10i	0.373229	+	0.366141i
$537$	1.39171e11			1.67360
$538$	−6.08755e10	−	6.04876e10i	−0.726630	−	0.722000i
$539$			1.66923e11i			1.97770i
$540$	5.62760e10	−	3.59685e8i	0.661832	−	0.00423006i
$541$	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
$543$		−	2.08015e10i		−	0.239274i
$544$	−7.65753e10	−	7.41665e10i	−0.874366	−	0.846861i
$545$	−5.62179e10			−0.637219
$546$	−6.71697e10	−	6.67418e10i	−0.755793	−	0.750978i
$547$		−	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
$549$	6.34147e10			0.698073
$550$	1.50633e10	−	1.51599e10i	0.164616	−	0.165671i
$551$			3.89027e9i			0.0422059i
$552$	−5.80285e10	+	5.91519e10i	−0.625007	+	0.637107i
$553$	1.74394e11			1.86480
$554$	9.70541e10	+	9.64358e10i	1.03033	+	1.02376i
$555$			4.41235e10i			0.465048i
$556$	−1.32935e11	+	8.49650e8i	−1.39105	+	0.00889080i
$557$	8.98122e10			0.933071			0.466535	−	0.884503i	$-0.345502\pi$
$557$	8.98122e10			0.933071			0.466535	+	0.884503i	$0.345502\pi$
$558$	−1.92059e10	+	1.93290e10i	−0.198106	+	0.199376i
$559$		−	3.48899e10i		−	0.357316i
$560$	−9.22669e8	−	7.21770e10i	−0.00938196	−	0.733917i
$561$	−2.38646e11			−2.40936
$562$	−9.62097e9	−	9.55967e9i	−0.0964436	−	0.0958292i
$563$		−	1.80533e10i		−	0.179689i	−0.995956	−	0.0898446i	$-0.971363\pi$
$563$		−	1.80533e10i		−	0.179689i	0.995956	−	0.0898446i	$-0.0286371\pi$
$564$	7.88983e8	+	1.23444e11i	0.00779742	+	1.21998i
$565$	1.90810e10			0.187244
$566$	2.93043e10	−	2.94922e10i	0.285540	−	0.287370i
$567$		−	1.07785e11i		−	1.04286i
$568$	5.43769e10	+	5.33441e10i	0.522421	+	0.512499i
$569$	−6.90947e10			−0.659167			−0.329584	−	0.944126i	$-0.606908\pi$
$569$	−6.90947e10			−0.659167			−0.329584	+	0.944126i	$0.606908\pi$
$570$	−4.06949e10	−	4.04356e10i	−0.385514	−	0.383058i
$571$			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
$573$	−7.49896e10			−0.695637
$574$	1.70607e11	−	1.71701e11i	1.57163	−	1.58170i
$575$			1.15114e10i			0.105307i
$576$	3.95312e9	+	2.06145e11i	0.0359128	+	1.87276i
$577$	−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
$579$		−	2.08698e11i		−	1.85697i
$580$	−1.90418e7	−	2.97927e9i	−0.000168266	−	0.0263268i
$581$	−5.98273e10			−0.525043
$582$	−1.93233e11	+	1.94472e11i	−1.68418	+	1.69498i
$583$		−	9.68734e10i		−	0.838553i
$584$	−6.84216e9	+	6.97462e9i	−0.0588223	+	0.0599611i
$585$	3.75744e10			0.320825
$586$	1.34941e11	+	1.34081e11i	1.14433	+	1.13704i
$587$		−	3.62809e9i		−	0.0305581i	−0.999883	−	0.0152790i	$-0.995136\pi$
$587$		−	3.62809e9i		−	0.0305581i	0.999883	−	0.0152790i	$-0.00486366\pi$
$588$	−3.43154e11	+	2.19325e9i	−2.87065	+	0.0183476i
$589$	1.29475e10			0.107578
$590$	−5.32928e10	+	5.36345e10i	−0.439806	+	0.442626i
$591$		−	2.72906e11i		−	2.23698i
$592$	−7.53457e10	+	9.63175e8i	−0.613439	+	0.00784185i
$593$	8.72511e10			0.705589			0.352795	−	0.935701i	$-0.385231\pi$
$593$	8.72511e10			0.705589			0.352795	+	0.935701i	$0.385231\pi$
$594$	1.52617e11	+	1.51645e11i	1.22591	+	1.21810i
$595$			1.11977e11i			0.893431i
$596$	−1.00455e9	−	1.57172e11i	−0.00796137	−	1.24563i
$597$	2.31668e11			1.82376
$598$	−1.81768e10	+	1.82933e10i	−0.142139	+	0.143050i
$599$		−	1.90496e10i		−	0.147972i	−0.997259	−	0.0739858i	$-0.976428\pi$
$599$		−	1.90496e10i		−	0.147972i	0.997259	−	0.0739858i	$-0.0235720\pi$
$600$	3.13631e10	+	3.07675e10i	0.242000	+	0.237403i
$601$	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
$603$			1.29479e11i			0.979329i
$604$	−1.38535e11	+	8.85437e8i	−1.04090	+	0.00665289i
$605$	2.17869e10			0.162620
$606$	3.04028e11	−	3.05977e11i	2.25436	−	2.26881i
$607$			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
$609$	−2.25270e10			−0.163770
$610$	1.63697e10	+	1.62654e10i	0.118228	+	0.117475i
$611$			3.84186e10i			0.275662i
$612$	−2.04426e9	−	3.19843e11i	−0.0145724	−	2.27998i
$613$	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
$615$			1.47326e11i			1.02987i
$616$	1.93250e11	−	1.96991e11i	1.34214	−	1.36812i
$617$	2.29769e11			1.58544			0.792720	−	0.609586i	$-0.208664\pi$
$617$	2.29769e11			1.58544			0.792720	+	0.609586i	$0.208664\pi$
$618$	1.68925e11	+	1.67848e11i	1.15808	+	1.15070i
$619$		−	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
$621$	−1.15887e11			−0.779237
$622$	−9.71801e10	+	9.78032e10i	−0.649256	+	0.653419i
$623$			2.13870e11i			1.41971i
$624$	1.25810e9	+	9.84170e10i	0.00829810	+	0.649130i
$625$	6.10352e9			0.0400000
$626$	−1.10885e11	−	1.10179e11i	−0.722065	−	0.717464i
$627$		−	2.19319e11i		−	1.41907i
$628$	−1.05367e9	−	1.64856e11i	−0.00677432	−	1.05990i
$629$	1.16893e11			0.746768
$630$	1.52651e11	−	1.53630e11i	0.969029	−	0.975243i
$631$			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
$633$	−4.87732e11			−3.03785
$634$	−7.46319e10	−	7.41564e10i	−0.461921	−	0.458978i
$635$		−	9.75441e10i		−	0.599938i
$636$	1.99149e11	−	1.27285e9i	1.21716	−	0.00777944i
$637$	−1.06798e11			−0.648642
$638$	8.02814e9	−	8.07961e9i	0.0484543	−	0.0487650i
$639$			2.28548e11i			1.37080i
$640$	−5.18542e10	+	5.42277e10i	−0.309075	+	0.323222i
$641$	−1.15318e11			−0.683071			−0.341535	−	0.939869i	$-0.610947\pi$
$641$	−1.15318e11			−0.683071			−0.341535	+	0.939869i	$0.610947\pi$
$642$	8.09210e10	+	8.04055e10i	0.476345	+	0.473310i
$643$		−	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
$645$	1.22403e11			0.707216
$646$	−1.07123e11	+	1.07810e11i	−0.615110	+	0.619054i
$647$			5.43112e10i			0.309936i	0.987919	+	0.154968i	$0.0495275\pi$
$647$			5.43112e10i			0.309936i	−0.987919	+	0.154968i	$0.950473\pi$
$648$	−7.84583e10	+	7.99773e10i	−0.444978	+	0.453593i
$649$	−2.89055e11			−1.62930
$650$	9.69937e9	+	9.63757e9i	0.0543363	+	0.0539901i
$651$			7.49739e10i			0.417432i
$652$	−1.72696e11	+	1.10378e9i	−0.955633	+	0.00610788i
$653$	1.40265e11			0.771433			0.385716	−	0.922617i	$-0.373954\pi$
$653$	1.40265e11			0.771433			0.385716	+	0.922617i	$0.373954\pi$
$654$	3.11425e11	−	3.13421e11i	1.70232	−	1.71324i
$655$			4.17006e10i			0.226557i
$656$	−2.51576e11	+	3.21600e9i	−1.35848	+	0.0173660i
$657$	−2.93146e10			−0.157334
$658$	1.57081e11	+	1.56081e11i	0.837955	+	0.832617i
$659$		−	2.51334e11i		−	1.33263i	−0.745670	−	0.666315i	$-0.767871\pi$
$659$		−	2.51334e11i		−	1.33263i	0.745670	−	0.666315i	$-0.232129\pi$
$660$	1.07351e9	+	1.67960e11i	0.00565756	+	0.885176i
$661$	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
$663$		−	1.52686e11i		−	0.790216i
$664$	4.43924e10	+	4.35493e10i	0.228369	+	0.224031i
$665$	−1.02908e11			−0.526216
$666$	−1.60374e11	−	1.59352e11i	−0.815150	−	0.809956i
$667$			6.13511e9i			0.0309970i
$668$	1.16620e11	−	7.45368e8i	0.585687	−	0.00374339i
$669$	1.93846e11			0.967724
$670$	−3.32104e10	+	3.34233e10i	−0.164807	+	0.165863i
$671$			8.82220e10i			0.435198i
$672$	4.07507e11	+	3.94688e11i	1.99829	+	1.93543i
$673$	−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
$675$			6.14450e10i			0.295986i
$676$	−1.13890e9	−	1.78192e11i	−0.00545381	−	0.853299i
$677$	−1.55980e11			−0.742530			−0.371265	−	0.928527i	$-0.621076\pi$
$677$	−1.55980e11			−0.742530			−0.371265	+	0.928527i	$0.621076\pi$
$678$	−1.05701e11	+	1.06379e11i	−0.500220	+	0.503427i
$679$			4.91776e11i			2.31360i
$680$	8.15100e10	−	8.30880e10i	0.381219	−	0.388600i
$681$	−1.49627e11			−0.695701
$682$	−2.68904e10	−	2.67191e10i	−0.124297	−	0.123505i
$683$		−	2.38756e10i		−	0.109716i	−0.998494	−	0.0548581i	$-0.982529\pi$
$683$		−	2.38756e10i		−	0.109716i	0.998494	−	0.0548581i	$-0.0174707\pi$
$684$	2.93940e11	−	1.87870e9i	1.34287	−	0.00858289i
$685$	−1.69287e11			−0.768887
$686$	−1.77694e11	+	1.78833e11i	−0.802371	+	0.807516i
$687$			3.10025e11i			1.39178i
$688$	2.67194e9	+	2.09016e11i	0.0119254	+	0.932880i
$689$	6.19799e10			0.275026
$690$	−6.41776e10	−	6.37687e10i	−0.283131	−	0.281327i
$691$			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
$693$	8.27962e11			3.58986
$694$	7.12574e10	−	7.17143e10i	0.307180	−	0.309149i
$695$		−	1.45146e11i		−	0.622107i
$696$	1.67153e10	+	1.63978e10i	0.0712322	+	0.0698793i
$697$	3.90301e11			1.65374
$698$	−2.12253e10	−	2.10900e10i	−0.0894193	−	0.0888496i
$699$		−	8.95839e10i		−	0.375250i
$700$	7.88099e10	−	5.03709e8i	0.328238	−	0.00209791i
$701$	−2.57887e10			−0.106796			−0.0533982	−	0.998573i	$-0.517005\pi$
$701$	−2.57887e10			−0.106796			−0.0533982	+	0.998573i	$0.517005\pi$
$702$	−9.70229e10	+	9.76450e10i	−0.399508	+	0.402070i
$703$			1.07426e11i			0.439834i
$704$	−2.86787e11	+	5.49954e9i	−1.16753	+	0.0223891i
$705$	−1.34782e11			−0.545602
$706$	3.42914e11	+	3.40730e11i	1.38028	+	1.37148i
$707$		−	7.73749e11i		−	3.09686i
$708$	−3.79797e9	−	5.94228e11i	−0.0151154	−	2.36494i
$709$	−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
$711$		−	5.43882e11i		−	2.12827i
$712$	1.55680e11	−	1.58694e11i	0.605776	−	0.617504i
$713$	2.04187e10			0.0790079
$714$	−6.24285e11	−	6.20308e11i	−2.40210	−	2.38679i
$715$			5.22731e10i			0.200011i
$716$	−2.59490e11	+	1.65851e9i	−0.987343	+	0.00631055i
$717$	−6.58064e11			−2.48996
$718$	−2.05339e11	+	2.06655e11i	−0.772632	+	0.777587i
$719$			1.28179e11i			0.479624i	0.970819	+	0.239812i	$0.0770858\pi$
$719$			1.28179e11i			0.479624i	−0.970819	+	0.239812i	$0.922914\pi$
$720$	−2.25098e11	+	2.87752e9i	−0.837609	+	0.0107075i
$721$	4.27173e11			1.58075
$722$	9.36814e10	+	9.30846e10i	0.344750	+	0.342554i
$723$			7.11721e11i			2.60469i
$724$	2.47893e8	+	3.87850e10i	0.000902213	+	0.141159i
$725$	3.25292e9			0.0117739
$726$	−1.20690e11	+	1.21464e11i	−0.434437	+	0.437222i
$727$			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
$729$	3.72333e11			1.31832
$730$	−7.56720e9	−	7.51899e9i	−0.0266467	−	0.0264770i
$731$		−	3.24272e11i		−	1.13564i
$732$	−1.81363e11	+	1.15917e9i	−0.631692	+	0.00403743i
$733$	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
$735$		−	3.74674e11i		−	1.28382i
$736$	1.07491e11	−	1.10982e11i	0.366321	−	0.378218i
$737$	−1.80129e11			−0.610541
$738$	−5.35483e11	−	5.32071e11i	−1.80518	−	1.79368i
$739$		−	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
$741$	1.40321e11			0.465424
$742$	2.51801e11	−	2.53416e11i	0.830696	−	0.836023i
$743$		−	4.43366e11i		−	1.45481i	−0.686207	−	0.727406i	$-0.740726\pi$
$743$		−	4.43366e11i		−	1.45481i	0.686207	−	0.727406i	$-0.259274\pi$
$744$	5.45747e10	−	5.56313e10i	0.178115	−	0.181563i
$745$	1.71608e11			0.557074
$746$	1.60347e11	+	1.59326e11i	0.517733	+	0.514435i
$747$			1.86583e11i			0.599224i
$748$	4.44963e11	−	2.84396e9i	1.42141	−	0.00908484i
$749$	2.04631e11			0.650196
$750$	−3.38110e10	+	3.40278e10i	−0.106860	+	0.107545i
$751$		−	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
$753$	−3.32090e11			−1.03294
$754$	5.16936e9	+	5.13643e9i	0.0159938	+	0.0158919i
$755$		−	1.51260e11i		−	0.465516i
$756$	5.07092e9	+	7.93391e11i	0.0155238	+	2.42885i
$757$	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
$759$		−	3.45875e11i		−	1.04220i
$760$	7.63589e10	+	7.49087e10i	0.228879	+	0.224532i
$761$	3.59912e11			1.07314			0.536571	−	0.843855i	$-0.319719\pi$
$761$	3.59912e11			1.07314			0.536571	+	0.843855i	$0.319719\pi$
$762$	5.43820e11	+	5.40355e11i	1.61300	+	1.60273i
$763$		−	7.92573e11i		−	2.33852i
$764$	1.39821e11	−	8.93656e8i	0.410391	−	0.00262299i
$765$	3.49222e11			1.01966
$766$	−3.86889e11	+	3.89370e11i	−1.12375	+	1.13096i
$767$		−	1.84938e11i		−	0.534373i
$768$	−1.50739e10	−	5.89493e11i	−0.0433293	−	1.69447i
$769$	−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
$771$			7.21569e11i			2.04202i
$772$	2.48707e9	+	3.89125e11i	0.00700195	+	1.09552i
$773$	−2.24564e11			−0.628958			−0.314479	−	0.949264i	$-0.601830\pi$
$773$	−2.24564e11			−0.628958			−0.314479	+	0.949264i	$0.601830\pi$
$774$	−4.42059e11	+	4.44893e11i	−1.23173	+	1.23963i
$775$		−	1.08263e10i		−	0.0300105i
$776$	3.57972e11	−	3.64903e11i	0.987194	−	1.00631i
$777$	−6.22063e11			−1.70667
$778$	4.70232e9	+	4.67236e9i	0.0128349	+	0.0127532i
$779$			3.58691e11i			0.974027i
$780$	−1.07461e11	+	6.86832e8i	−0.290318	+	0.00185555i
$781$	−3.17954e11			−0.854594
$782$	−1.68938e11	+	1.70021e11i	−0.451751	+	0.454648i
$783$			3.27477e10i			0.0871231i
$784$	6.39797e11	−	8.17879e9i	1.69347	−	0.0216483i
$785$	1.79998e11			0.474013
$786$	−2.32486e11	−	2.31004e11i	−0.609124	−	0.605243i
$787$			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
$789$	−1.71553e11			−0.442682
$790$	1.39502e11	−	1.40396e11i	0.358156	−	0.360452i
$791$			2.69008e11i			0.687163i
$792$	−6.14355e11	−	6.02687e11i	−1.56142	−	1.53176i
$793$	−5.64447e10			−0.142735
$794$	2.55884e11	+	2.54254e11i	0.643816	+	0.639714i
$795$			2.17441e11i			0.544343i
$796$	−4.31952e11	+	2.76080e9i	−1.07593	+	0.00687674i
$797$	2.55700e11			0.633720			0.316860	−	0.948472i	$-0.397372\pi$
$797$	2.55700e11			0.633720			0.316860	+	0.948472i	$0.397372\pi$
$798$	5.70071e11	−	5.73726e11i	1.40578	−	1.41479i
$799$			3.57068e11i			0.876121i
$800$	−5.88443e10	−	5.69933e10i	−0.143663	−	0.139144i
$801$	6.66996e11			1.62029
$802$	−2.87906e11	−	2.86072e11i	−0.695911	−	0.691478i
$803$		−	4.07822e10i		−	0.0980863i
$804$	−2.36677e9	−	3.70303e11i	−0.00566412	−	0.886204i
$805$	−1.62291e11			−0.386465
$806$	1.70949e10	−	1.72045e10i	0.0405067	−	0.0407664i
$807$			7.36401e11i			1.73628i
$808$	−5.63224e11	+	5.74129e11i	−1.32141	+	1.34699i
$809$	4.12911e10			0.0963968			0.0481984	−	0.998838i	$-0.484652\pi$
$809$	4.12911e10			0.0963968			0.0481984	+	0.998838i	$0.484652\pi$
$810$	−8.67723e10	−	8.62195e10i	−0.201577	−	0.200293i
$811$		−	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
$813$	9.23087e10			0.211291
$814$	2.21690e11	−	2.23111e11i	0.504949	−	0.508187i
$815$		−	1.88558e11i		−	0.427381i
$816$	1.16930e10	+	9.14702e11i	0.0263734	+	2.06309i
$817$	2.98010e11			0.668872
$818$	1.66907e11	+	1.65843e11i	0.372786	+	0.370411i
$819$			5.29732e11i			1.17739i
$820$	−1.75570e9	−	2.74695e11i	−0.00388325	−	0.607569i
$821$	8.40243e11			1.84941			0.924703	−	0.380688i	$-0.124313\pi$
$821$	8.40243e11			1.84941			0.924703	+	0.380688i	$0.124313\pi$
$822$	9.37785e11	−	9.43798e11i	2.05407	−	2.06724i
$823$		−	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
$825$	−1.83387e11			−0.395871
$826$	−7.56152e11	−	7.51334e11i	−1.62438	−	1.61404i
$827$			3.63473e11i			0.777051i	0.921438	+	0.388526i	$0.127016\pi$
$827$			3.63473e11i			0.777051i	−0.921438	+	0.388526i	$0.872984\pi$
$828$	4.63556e11	−	2.96279e9i	0.986236	−	0.00630347i
$829$	−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
$831$		−	1.17405e12i		−	2.46197i
$832$	−3.51862e9	−	1.83487e11i	−0.00734310	−	0.382923i
$833$	−9.92595e11			−2.06154
$834$	8.09205e11	+	8.04050e11i	1.67261	+	1.66195i
$835$			1.27331e11i			0.261933i
$836$	2.61364e9	+	4.08927e11i	0.00535081	+	0.837184i
$837$	1.08990e11			0.222067
$838$	8.24289e10	−	8.29574e10i	0.167149	−	0.168221i
$839$			1.39033e11i			0.280588i	0.990110	+	0.140294i	$0.0448049\pi$
$839$			1.39033e11i			0.280588i	−0.990110	+	0.140294i	$0.955195\pi$
$840$	−4.33767e11	+	4.42165e11i	−0.871243	+	0.888110i
$841$	−4.98513e11			−0.996534
$842$	−4.64366e11	−	4.61407e11i	−0.923872	−	0.917986i
$843$			1.16383e11i			0.230452i
$844$	9.09393e11	−	5.81234e9i	1.79218	−	0.0114546i
$845$	1.94559e11			0.381614
$846$	4.86767e11	−	4.89888e11i	0.950254	−	0.956347i
$847$			3.07156e11i			0.596795i
$848$	−3.71305e11	+	4.74654e9i	−0.718037	+	0.00917896i
$849$	−3.56763e11			−0.686672
$850$	9.01473e10	+	8.95730e10i	0.172694	+	0.171594i
$851$			1.69415e11i			0.323024i
$852$	−4.17769e9	−	6.53638e11i	−0.00792826	−	1.24045i
$853$	−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
$855$			3.20939e11i			0.600563i
$856$	−1.51838e11	−	1.48954e11i	−0.282804	−	0.277433i
$857$	2.93094e11			0.543355			0.271678	−	0.962388i	$-0.412422\pi$
$857$	2.93094e11			0.543355			0.271678	+	0.962388i	$0.412422\pi$
$858$	−2.91429e11	−	2.89572e11i	−0.537754	−	0.534328i
$859$		−	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
$861$	−2.07704e12			−3.77949
$862$	−4.45605e10	+	4.48463e10i	−0.0807089	+	0.0812264i
$863$			3.25698e11i			0.587181i	0.955931	+	0.293590i	$0.0948502\pi$
$863$			3.25698e11i			0.587181i	−0.955931	+	0.293590i	$0.905150\pi$
$864$	5.73760e11	−	5.92395e11i	1.02962	−	1.06306i
$865$	−2.69542e11			−0.481463
$866$	3.27697e11	+	3.25609e11i	0.582641	+	0.578929i
$867$		−	4.61339e11i		−	0.816477i
$868$	−8.93469e8	−	1.39791e11i	−0.00157398	−	0.246264i
$869$	7.56643e11			1.32682
$870$	−1.80199e10	+	1.81354e10i	−0.0314539	+	0.0316556i
$871$		−	1.15247e11i		−	0.200243i
$872$	−5.76927e11	+	5.88096e11i	−0.997826	+	1.01714i
$873$	1.53370e12			2.64048
$874$	−1.56251e11	−	1.55256e11i	−0.267780	−	0.266074i
$875$			8.60487e10i			0.146795i
$876$	8.38385e10	−	5.35849e8i	0.142373	−	0.000909969i
$877$	−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
$879$		−	1.63236e12i		−	2.73439i
$880$	−4.00318e9	−	3.13154e11i	−0.00667536	−	0.522189i
$881$	−6.22197e10			−0.103282			−0.0516409	−	0.998666i	$-0.516445\pi$
$881$	−6.22197e10			−0.103282			−0.0516409	+	0.998666i	$0.516445\pi$
$882$	1.36181e12	+	1.35314e12i	2.25032	+	2.23598i
$883$			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
$885$	6.48809e11			1.05765
$886$	−1.81857e11	+	1.83023e11i	−0.295117	+	0.297010i
$887$		−	7.30650e10i		−	0.118036i	−0.998257	−	0.0590180i	$-0.981203\pi$
$887$		−	7.30650e10i		−	0.118036i	0.998257	−	0.0590180i	$-0.0187969\pi$
$888$	4.61576e11	+	4.52810e11i	0.742321	+	0.728222i
$889$	1.37520e12			2.20170
$890$	1.72177e11	+	1.71080e11i	0.274419	+	0.272671i
$891$		−	4.67645e11i		−	0.742003i
$892$	−3.61432e11	+	2.31007e9i	−0.570909	+	0.00364893i
$893$	−3.28150e11			−0.516020
$894$	−9.50640e11	+	9.56736e11i	−1.48822	+	1.49776i
$895$		−	2.83324e11i		−	0.441562i
$896$	−7.64514e11	−	7.31053e11i	−1.18619	−	1.13427i
$897$	2.21291e11			0.341818
$898$	1.49217e11	+	1.48266e11i	0.229463	+	0.228001i
$899$		−	5.76996e9i		−	0.00883353i
$900$	−1.57091e9	−	2.45784e11i	−0.00239432	−	0.374613i
$901$	5.76050e11			0.874100
$902$	7.40213e11	−	7.44959e11i	1.11823	−	1.12540i
$903$			1.72566e12i			2.59540i
$904$	1.95816e11	−	1.99607e11i	0.293207	−	0.298883i
$905$	−4.23475e10			−0.0631297
$906$	8.43290e11	+	8.37917e11i	1.25160	+	1.24362i
$907$		−	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
$909$	−2.41308e12			−3.53441
$910$	−1.35873e11	+	1.36744e11i	−0.198137	+	0.199408i
$911$			6.04985e11i			0.878357i	0.898400	+	0.439178i	$0.144730\pi$
$911$			6.04985e11i			0.878357i	−0.898400	+	0.439178i	$0.855270\pi$
$912$	−8.40623e11	+	1.07460e10i	−1.21513	+	0.0155335i
$913$	−2.59573e11			−0.373573
$914$	−7.71770e11	−	7.66853e11i	−1.10587	−	1.09882i
$915$		−	1.98022e11i		−	0.282507i
$916$	−3.69459e9	−	5.78053e11i	−0.00524789	−	0.821080i
$917$	−5.87904e11			−0.831436
$918$	−9.01745e11	+	9.07527e11i	−1.26974	+	1.27788i
$919$			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
$921$	2.39046e12			3.32233
$922$	−3.25493e11	−	3.23420e11i	−0.450421	−	0.447551i
$923$		−	2.03428e11i		−	0.280287i
$924$	−2.36794e12	+	1.51345e10i	−3.24850	+	0.0207626i
$925$	8.98264e10			0.122698
$926$	−4.76732e10	+	4.79789e10i	−0.0648381	+	0.0652539i
$927$		−	1.33222e12i		−	1.80408i
$928$	−3.13616e10	−	3.03750e10i	−0.0422869	−	0.0409567i
$929$	5.68272e11			0.762945			0.381473	−	0.924380i	$-0.375417\pi$
$929$	5.68272e11			0.762945			0.381473	+	0.924380i	$0.375417\pi$
$930$	6.03579e10	+	5.99733e10i	0.0806867	+	0.0801727i
$931$		−	9.12208e11i		−	1.21421i
$932$	1.06758e9	+	1.67032e11i	0.00141493	+	0.221379i
$933$	1.18311e12			1.56135
$934$	4.81852e11	−	4.84942e11i	0.633179	−	0.637238i
$935$			4.85834e11i			0.635685i
$936$	3.85601e11	−	3.93066e11i	0.502383	−	0.512109i
$937$	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
$939$			1.34136e12i			1.72537i
$940$	2.51306e11	−	1.60621e9i	0.321878	−	0.00205727i
$941$	−5.28765e11			−0.674379			−0.337190	−	0.941437i	$-0.609476\pi$
$941$	−5.28765e11			−0.674379			−0.337190	+	0.941437i	$0.609476\pi$
$942$	−9.97119e11	+	1.00351e12i	−1.26632	+	1.27444i
$943$			5.65671e11i			0.715348i
$944$	1.41629e10	+	1.10791e12i	0.0178346	+	1.39514i
$945$	−8.66266e11			−1.08624
$946$	−6.18931e11	−	6.14988e11i	−0.772819	−	0.767896i
$947$			9.04370e11i			1.12447i	0.826979	+	0.562233i	$0.190057\pi$
$947$			9.04370e11i			1.12447i	−0.826979	+	0.562233i	$0.809943\pi$
$948$	9.94176e9	+	1.55548e12i	0.0123092	+	1.92589i
$949$	2.60926e10			0.0321701
$950$	−8.23187e10	+	8.28465e10i	−0.101066	+	0.101714i
$951$			9.02811e11i			1.10376i
$952$	1.17139e12	+	1.14915e12i	1.42612	+	1.39903i
$953$	−5.71895e11			−0.693337			−0.346669	−	0.937988i	$-0.612687\pi$
$953$	−5.71895e11			−0.693337			−0.346669	+	0.937988i	$0.612687\pi$
$954$	−7.90326e11	−	7.85291e11i	−0.954141	−	0.948062i
$955$			1.52664e11i			0.183536i
$956$	1.22698e12	−	7.84220e9i	1.46895	−	0.00938872i
$957$	−9.77379e10			−0.116524
$958$	−7.58994e11	+	7.63861e11i	−0.901107	+	0.906885i
$959$		−	2.38665e12i		−	2.82173i
$960$	6.43718e11	−	1.23442e10i	0.757898	−	0.0145338i
$961$	8.33688e11			0.977484
$962$	1.42747e11	+	1.41838e11i	0.166674	+	0.165612i
$963$		−	6.38181e11i		−	0.742060i
$964$	−8.48163e9	−	1.32703e12i	−0.00982135	−	1.53664i
$965$	−4.24867e11			−0.489941
$966$	8.99025e11	−	9.04790e11i	1.03244	−	1.03906i
$967$		−	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
$969$	1.30416e12			1.47923
$970$	3.95905e11	+	3.93383e11i	0.447203	+	0.444354i
$971$			4.62553e11i			0.520336i	0.965563	+	0.260168i	$0.0837780\pi$
$971$			4.62553e11i			0.520336i	−0.965563	+	0.260168i	$0.916222\pi$
$972$	−3.59618e11	+	2.29848e9i	−0.402880	+	0.00257499i
$973$	2.04630e12			2.28306
$974$	1.09384e12	−	1.10085e12i	1.21539	−	1.22319i
$975$		−	1.17332e11i		−	0.129837i
$976$	3.38145e11	−	4.32264e9i	0.372652	−	0.00476376i
$977$	1.35557e11			0.148780			0.0743899	−	0.997229i	$-0.476299\pi$
$977$	1.35557e11			0.148780			0.0743899	+	0.997229i	$0.476299\pi$
$978$	1.05123e12	+	1.04454e12i	1.14906	+	1.14174i
$979$			9.27919e11i			1.01013i
$980$	4.46501e9	+	6.98592e11i	0.00484082	+	0.757390i
$981$	−2.47179e12			−2.66892
$982$	−1.95749e11	+	1.97004e11i	−0.210500	+	0.211850i
$983$		−	1.95656e10i		−	0.0209546i	−0.999945	−	0.0104773i	$-0.996665\pi$
$983$		−	1.95656e10i		−	0.0209546i	0.999945	−	0.0104773i	$-0.00333509\pi$
$984$	1.54118e12	+	1.51191e12i	1.64390	+	1.61267i
$985$	−5.55580e11			−0.590204
$986$	4.80448e10	+	4.77387e10i	0.0508322	+	0.0505083i
$987$		−	1.90019e12i		−	2.00230i
$988$	−2.61633e11	+	1.67221e9i	−0.274577	+	0.00175494i
$989$	4.69975e11			0.491235
$990$	6.62306e11	−	6.66552e11i	0.689474	−	0.693894i
$991$			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
$993$	−3.19619e12			−3.28727
$994$	−8.31751e11	−	8.26452e11i	−0.852016	−	0.846588i
$995$		−	4.71628e11i		−	0.481180i
$996$	−3.41060e9	−	5.33620e11i	−0.00346572	−	0.542244i
$997$	−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
$999$			9.04296e11i			0.907922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.b.a.11.12	yes	16
3.2	odd	2		180.9.c.a.91.5		16
4.3	odd	2	inner	20.9.b.a.11.11	✓	16
5.2	odd	4		100.9.d.c.99.8		32
5.3	odd	4		100.9.d.c.99.25		32
5.4	even	2		100.9.b.d.51.5		16
8.3	odd	2		320.9.b.d.191.2		16
8.5	even	2		320.9.b.d.191.15		16
12.11	even	2		180.9.c.a.91.6		16
20.3	even	4		100.9.d.c.99.7		32
20.7	even	4		100.9.d.c.99.26		32
20.19	odd	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	4.3	odd	2	inner
20.9.b.a.11.12	yes	16	1.1	even	1	trivial
100.9.b.d.51.5		16	5.4	even	2
100.9.b.d.51.6		16	20.19	odd	2
100.9.d.c.99.7		32	20.3	even	4
100.9.d.c.99.8		32	5.2	odd	4
100.9.d.c.99.25		32	5.3	odd	4
100.9.d.c.99.26		32	20.7	even	4
180.9.c.a.91.5		16	3.2	odd	2
180.9.c.a.91.6		16	12.11	even	2
320.9.b.d.191.2		16	8.3	odd	2
320.9.b.d.191.15		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(11.3498 + 11.2775i) q^{2} -137.297i q^{3} +(1.63618 + 255.995i) q^{4} -279.508 q^{5} +(1548.37 - 1558.29i) q^{6} -3940.57i q^{7} +(-2868.41 + 2923.94i) q^{8} -12289.4 q^{9} +O(q^{10})\)	\(q+(11.3498 + 11.2775i) q^{2} -137.297i q^{3} +(1.63618 + 255.995i) q^{4} -279.508 q^{5} +(1548.37 - 1558.29i) q^{6} -3940.57i q^{7} +(-2868.41 + 2923.94i) q^{8} -12289.4 q^{9} +(-3172.37 - 3152.16i) q^{10} -17097.0i q^{11} +(35147.3 - 224.642i) q^{12} +10938.7 q^{13} +(44439.8 - 44724.8i) q^{14} +38375.6i q^{15} +(-65530.6 + 837.705i) q^{16} +101666. q^{17} +(-139483. - 138594. i) q^{18} +93432.1i q^{19} +(-457.325 - 71552.7i) q^{20} -541029. q^{21} +(192811. - 194047. i) q^{22} +147346. i q^{23} +(401448. + 393824. i) q^{24} +78125.0 q^{25} +(124152. + 123361. i) q^{26} +786497. i q^{27} +(1.00877e6 - 6447.48i) q^{28} +41637.4 q^{29} +(-432781. + 435556. i) q^{30} -138577. i q^{31} +(-753207. - 729514. i) q^{32} -2.34736e6 q^{33} +(1.15389e6 + 1.14653e6i) q^{34} +1.10142e6i q^{35} +(-20107.7 - 3.14603e6i) q^{36} +1.14978e6 q^{37} +(-1.05368e6 + 1.06044e6i) q^{38} -1.50185e6i q^{39} +(801745. - 817267. i) q^{40} +3.83906e6 q^{41} +(-6.14057e6 - 6.10145e6i) q^{42} -3.18959e6i q^{43} +(4.37673e6 - 27973.6i) q^{44} +3.43500e6 q^{45} +(-1.66170e6 + 1.67235e6i) q^{46} +3.51218e6i q^{47} +(115014. + 8.99715e6i) q^{48} -9.76332e6 q^{49} +(886704. + 881054. i) q^{50} -1.39584e7i q^{51} +(17897.6 + 2.80024e6i) q^{52} +5.66612e6 q^{53} +(-8.86971e6 + 8.92658e6i) q^{54} +4.77874e6i q^{55} +(1.15220e7 + 1.13032e7i) q^{56} +1.28279e7 q^{57} +(472576. + 469565. i) q^{58} -1.69068e7i q^{59} +(-9.82397e6 + 62789.3i) q^{60} -5.16010e6 q^{61} +(1.56280e6 - 1.57282e6i) q^{62} +4.84274e7i q^{63} +(-321668. - 1.67741e7i) q^{64} -3.05745e6 q^{65} +(-2.66421e7 - 2.64723e7i) q^{66} -1.05358e7i q^{67} +(166343. + 2.60259e7i) q^{68} +2.02302e7 q^{69} +(-1.24213e7 + 1.25009e7i) q^{70} -1.85971e7i q^{71} +(3.52511e7 - 3.59336e7i) q^{72} +2.38535e6 q^{73} +(1.30498e7 + 1.29666e7i) q^{74} -1.07263e7i q^{75} +(-2.39181e7 + 152871. i) q^{76} -6.73718e7 q^{77} +(1.69371e7 - 1.70457e7i) q^{78} +4.42560e7i q^{79} +(1.83164e7 - 234146. i) q^{80} +2.73525e7 q^{81} +(4.35726e7 + 4.32950e7i) q^{82} -1.51824e7i q^{83} +(-885218. - 1.38500e8i) q^{84} -2.84164e7 q^{85} +(3.59706e7 - 3.62013e7i) q^{86} -5.71668e6i q^{87} +(4.99905e7 + 4.90411e7i) q^{88} -5.42739e7 q^{89} +(3.89866e7 + 3.87382e7i) q^{90} -4.31047e7i q^{91} +(-3.77199e7 + 241085. i) q^{92} -1.90261e7 q^{93} +(-3.96086e7 + 3.98625e7i) q^{94} -2.61151e7i q^{95} +(-1.00160e8 + 1.03413e8i) q^{96} -1.24798e8 q^{97} +(-1.10812e8 - 1.10106e8i) q^{98} +2.10112e8i 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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