LMFDB - Embedded newform 20.11.b.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,11,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, 11, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
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:	$12.7071450535$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 84 x^{18} - 86 x^{17} - 51565 x^{16} + 188134 x^{15} - 12946328 x^{14} + \cdots + 11\!\cdots\!25 $ x^20 - x^19 + 84x^18 - 86x^17 - 51565x^16 + 188134x^15 - 12946328x^14 + 95990512x^13 + 5401091173x^12 - 59241975423x^11 + 1752287752812x^10 - 13855072435862x^9 + 53025624411849x^8 + 4768661862568058x^7 - 71663288570646432x^6 + 1087383280946073208x^5 - 9530913414031332129x^4 - 22591082233500222765x^3 + 1758197001700115583660x^2 - 51913151006968686718150x + 1126337396992659918451525
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{94}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.15
Root			$10.5132 - 10.4323i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.11.b.a.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(24.2624 - 20.8647i) q^{2} +208.777i q^{3} +(153.329 - 1012.46i) q^{4} -1397.54 q^{5} +(4356.06 + 5065.43i) q^{6} -17557.3i q^{7} +(-17404.4 - 27763.8i) q^{8} +15461.2 q^{9} +O(q^{10})$	\(q+(24.2624 - 20.8647i) q^{2} +208.777i q^{3} +(153.329 - 1012.46i) q^{4} -1397.54 q^{5} +(4356.06 + 5065.43i) q^{6} -17557.3i q^{7} +(-17404.4 - 27763.8i) q^{8} +15461.2 q^{9} +(-33907.8 + 29159.3i) q^{10} -265895. i q^{11} +(211377. + 32011.6i) q^{12} +647096. q^{13} +(-366328. - 425983. i) q^{14} -291775. i q^{15} +(-1.00156e6 - 310478. i) q^{16} -2.51402e6 q^{17} +(375126. - 322594. i) q^{18} +170501. i q^{19} +(-214284. + 1.41495e6i) q^{20} +3.66556e6 q^{21} +(-5.54781e6 - 6.45125e6i) q^{22} -5.21076e6i q^{23} +(5.79644e6 - 3.63364e6i) q^{24} +1.95312e6 q^{25} +(1.57001e7 - 1.35015e7i) q^{26} +1.55560e7i q^{27} +(-1.77760e7 - 2.69205e6i) q^{28} +6.80100e6 q^{29} +(-6.08779e6 - 7.07915e6i) q^{30} +2.47062e7i q^{31} +(-3.07782e7 + 1.33642e7i) q^{32} +5.55127e7 q^{33} +(-6.09962e7 + 5.24543e7i) q^{34} +2.45371e7i q^{35} +(2.37066e6 - 1.56538e7i) q^{36} +9.23131e6 q^{37} +(3.55745e6 + 4.13676e6i) q^{38} +1.35099e8i q^{39} +(2.43234e7 + 3.88011e7i) q^{40} +1.44940e8 q^{41} +(8.89354e7 - 7.64809e7i) q^{42} +2.79512e7i q^{43} +(-2.69207e8 - 4.07695e7i) q^{44} -2.16077e7 q^{45} +(-1.08721e8 - 1.26426e8i) q^{46} +1.10913e8i q^{47} +(6.48207e7 - 2.09102e8i) q^{48} -2.57846e7 q^{49} +(4.73875e7 - 4.07514e7i) q^{50} -5.24869e8i q^{51} +(9.92188e7 - 6.55156e8i) q^{52} +1.09572e8 q^{53} +(3.24571e8 + 3.77426e8i) q^{54} +3.71599e8i q^{55} +(-4.87458e8 + 3.05575e8i) q^{56} -3.55966e7 q^{57} +(1.65009e8 - 1.41901e8i) q^{58} -6.65268e8i q^{59} +(-2.95409e8 - 4.47376e7i) q^{60} -7.40208e8 q^{61} +(5.15487e8 + 5.99431e8i) q^{62} -2.71458e8i q^{63} +(-4.67913e8 + 9.66426e8i) q^{64} -9.04344e8 q^{65} +(1.34687e9 - 1.15826e9i) q^{66} -4.17577e7i q^{67} +(-3.85473e8 + 2.54533e9i) q^{68} +1.08789e9 q^{69} +(5.11959e8 + 5.95330e8i) q^{70} -6.30071e8i q^{71} +(-2.69094e8 - 4.29262e8i) q^{72} +9.52604e8 q^{73} +(2.23974e8 - 1.92608e8i) q^{74} +4.07767e8i q^{75} +(1.72624e8 + 2.61428e7i) q^{76} -4.66840e9 q^{77} +(2.81879e9 + 3.27782e9i) q^{78} -2.24561e9i q^{79} +(1.39972e9 + 4.33906e8i) q^{80} -2.33477e9 q^{81} +(3.51659e9 - 3.02413e9i) q^{82} +6.38664e9i q^{83} +(5.62038e8 - 3.71122e9i) q^{84} +3.51345e9 q^{85} +(5.83192e8 + 6.78162e8i) q^{86} +1.41989e9i q^{87} +(-7.38225e9 + 4.62775e9i) q^{88} -1.29920e9 q^{89} +(-5.24255e8 + 4.50838e8i) q^{90} -1.13613e10i q^{91} +(-5.27567e9 - 7.98963e8i) q^{92} -5.15808e9 q^{93} +(2.31416e9 + 2.69101e9i) q^{94} -2.38282e8i q^{95} +(-2.79014e9 - 6.42578e9i) q^{96} +1.43562e10 q^{97} +(-6.25596e8 + 5.37987e8i) q^{98} -4.11106e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9} - 31250 q^{10} + 1329640 q^{12} - 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} - 1921656 q^{17} - 3556082 q^{18} - 1187500 q^{20} + 4157512 q^{21} - 5811280 q^{22} - 19112144 q^{24} + 39062500 q^{25} + 25066884 q^{26} - 87415400 q^{28} - 66014888 q^{29} + 39875000 q^{30} - 33171328 q^{32} + 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} - 153620656 q^{37} + 250352720 q^{38} - 112375000 q^{40} + 477406160 q^{41} - 570662040 q^{42} + 339141040 q^{44} - 140125000 q^{45} - 897549304 q^{46} - 479727360 q^{48} + 333772012 q^{49} + 42968750 q^{50} - 110465096 q^{52} - 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} + 3973032960 q^{57} + 2075027916 q^{58} - 677375000 q^{60} - 4283166080 q^{61} + 1664032240 q^{62} + 340459456 q^{64} + 290125000 q^{65} + 1884031760 q^{66} + 3042411896 q^{68} - 5321669928 q^{69} - 2070000000 q^{70} + 1632326712 q^{72} + 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} + 410885040 q^{77} - 19914223760 q^{78} + 3604750000 q^{80} + 9939722652 q^{81} - 3197757116 q^{82} + 2383099552 q^{84} + 4799500000 q^{85} + 19648321456 q^{86} + 2774318240 q^{88} + 3011851592 q^{89} - 2849906250 q^{90} - 27349072440 q^{92} - 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} - 39984502056 q^{97} + 38416891998 q^{98}+O(q^{100}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9 - 31250 * q^10 + 1329640 * q^12 - 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 - 1921656 * q^17 - 3556082 * q^18 - 1187500 * q^20 + 4157512 * q^21 - 5811280 * q^22 - 19112144 * q^24 + 39062500 * q^25 + 25066884 * q^26 - 87415400 * q^28 - 66014888 * q^29 + 39875000 * q^30 - 33171328 * q^32 + 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 - 153620656 * q^37 + 250352720 * q^38 - 112375000 * q^40 + 477406160 * q^41 - 570662040 * q^42 + 339141040 * q^44 - 140125000 * q^45 - 897549304 * q^46 - 479727360 * q^48 + 333772012 * q^49 + 42968750 * q^50 - 110465096 * q^52 - 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 + 3973032960 * q^57 + 2075027916 * q^58 - 677375000 * q^60 - 4283166080 * q^61 + 1664032240 * q^62 + 340459456 * q^64 + 290125000 * q^65 + 1884031760 * q^66 + 3042411896 * q^68 - 5321669928 * q^69 - 2070000000 * q^70 + 1632326712 * q^72 + 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 + 410885040 * q^77 - 19914223760 * q^78 + 3604750000 * q^80 + 9939722652 * q^81 - 3197757116 * q^82 + 2383099552 * q^84 + 4799500000 * q^85 + 19648321456 * q^86 + 2774318240 * q^88 + 3011851592 * q^89 - 2849906250 * q^90 - 27349072440 * q^92 - 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 - 39984502056 * q^97 + 38416891998 * 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 $

$2$	24.2624	−	20.8647i	0.758200	−	0.652022i
$2$	24.2624	−	20.8647i	0.758200	−	0.652022i
$3$			208.777i			0.859164i	0.903028	+	0.429582i	$0.141339\pi$
$3$			208.777i			0.859164i	−0.903028	+	0.429582i	$0.858661\pi$
$4$	153.329	−	1012.46i	0.149736	−	0.988726i
$5$	−1397.54			−0.447214
$5$	−1397.54			−0.447214
$6$	4356.06	+	5065.43i	0.560194	+	0.651419i
$7$		−	17557.3i		−	1.04464i	−0.852748	−	0.522322i	$-0.825066\pi$
$7$		−	17557.3i		−	1.04464i	0.852748	−	0.522322i	$-0.174934\pi$
$8$	−17404.4	−	27763.8i	−0.531141	−	0.847283i
$9$	15461.2			0.261837
$10$	−33907.8	+	29159.3i	−0.339078	+	0.291593i
$11$		−	265895.i		−	1.65100i	−0.564404	−	0.825499i	$-0.690894\pi$
$11$		−	265895.i		−	1.65100i	0.564404	−	0.825499i	$-0.309106\pi$
$12$	211377.	+	32011.6i	0.849478	+	0.128647i
$13$	647096.			1.74282			0.871409	−	0.490558i	$-0.163207\pi$
$13$	647096.			1.74282			0.871409	+	0.490558i	$0.163207\pi$
$14$	−366328.	−	425983.i	−0.681130	−	0.792049i
$15$		−	291775.i		−	0.384230i
$16$	−1.00156e6	−	310478.i	−0.955158	−	0.296095i
$17$	−2.51402e6			−1.77062			−0.885308	−	0.465006i	$-0.846052\pi$
$17$	−2.51402e6			−1.77062			−0.885308	+	0.465006i	$0.846052\pi$
$18$	375126.	−	322594.i	0.198525	−	0.170723i
$19$			170501.i			0.0688586i	0.999407	+	0.0344293i	$0.0109614\pi$
$19$			170501.i			0.0688586i	−0.999407	+	0.0344293i	$0.989039\pi$
$20$	−214284.	+	1.41495e6i	−0.0669638	+	0.442172i
$21$	3.66556e6			0.897520
$22$	−5.54781e6	−	6.45125e6i	−1.07649	−	1.25179i
$23$		−	5.21076e6i		−	0.809585i	−0.914409	−	0.404792i	$-0.867344\pi$
$23$		−	5.21076e6i		−	0.809585i	0.914409	−	0.404792i	$-0.132656\pi$
$24$	5.79644e6	−	3.63364e6i	0.727955	−	0.456337i
$25$	1.95312e6			0.200000
$26$	1.57001e7	−	1.35015e7i	1.32140	−	1.13635i
$27$			1.55560e7i			1.08413i
$28$	−1.77760e7	−	2.69205e6i	−1.03287	−	0.156420i
$29$	6.80100e6			0.331576			0.165788	−	0.986161i	$-0.446983\pi$
$29$	6.80100e6			0.331576			0.165788	+	0.986161i	$0.446983\pi$
$30$	−6.08779e6	−	7.07915e6i	−0.250526	−	0.291323i
$31$			2.47062e7i			0.862973i	0.902120	+	0.431486i	$0.142011\pi$
$31$			2.47062e7i			0.862973i	−0.902120	+	0.431486i	$0.857989\pi$
$32$	−3.07782e7	+	1.33642e7i	−0.917262	+	0.398285i
$33$	5.55127e7			1.41848
$34$	−6.09962e7	+	5.24543e7i	−1.34248	+	1.15448i
$35$			2.45371e7i			0.467179i
$36$	2.37066e6	−	1.56538e7i	0.0392063	−	0.258885i
$37$	9.23131e6			0.133124			0.0665618	−	0.997782i	$-0.478797\pi$
$37$	9.23131e6			0.133124			0.0665618	+	0.997782i	$0.478797\pi$
$38$	3.55745e6	+	4.13676e6i	0.0448973	+	0.0522086i
$39$			1.35099e8i			1.49737i
$40$	2.43234e7	+	3.88011e7i	0.237534	+	0.378917i
$41$	1.44940e8			1.25103			0.625516	−	0.780211i	$-0.284888\pi$
$41$	1.44940e8			1.25103			0.625516	+	0.780211i	$0.284888\pi$
$42$	8.89354e7	−	7.64809e7i	0.680500	−	0.585203i
$43$			2.79512e7i			0.190133i	0.995471	+	0.0950665i	$0.0303064\pi$
$43$			2.79512e7i			0.190133i	−0.995471	+	0.0950665i	$0.969694\pi$
$44$	−2.69207e8	−	4.07695e7i	−1.63238	−	0.247213i
$45$	−2.16077e7			−0.117097
$46$	−1.08721e8	−	1.26426e8i	−0.527867	−	0.613827i
$47$			1.10913e8i			0.483607i	0.970325	+	0.241804i	$0.0777389\pi$
$47$			1.10913e8i			0.483607i	−0.970325	+	0.241804i	$0.922261\pi$
$48$	6.48207e7	−	2.09102e8i	0.254394	−	0.820638i
$49$	−2.57846e7			−0.0912808
$50$	4.73875e7	−	4.07514e7i	0.151640	−	0.130404i
$51$		−	5.24869e8i		−	1.52125i
$52$	9.92188e7	−	6.55156e8i	0.260962	−	1.72317i
$53$	1.09572e8			0.262011			0.131006	−	0.991382i	$-0.458179\pi$
$53$	1.09572e8			0.262011			0.131006	+	0.991382i	$0.458179\pi$
$54$	3.24571e8	+	3.77426e8i	0.706873	+	0.821984i
$55$			3.71599e8i			0.738349i
$56$	−4.87458e8	+	3.05575e8i	−0.885109	+	0.554853i
$57$	−3.55966e7			−0.0591609
$58$	1.65009e8	−	1.41901e8i	0.251401	−	0.216194i
$59$		−	6.65268e8i		−	0.930543i	−0.885168	−	0.465271i	$-0.845957\pi$
$59$		−	6.65268e8i		−	0.930543i	0.885168	−	0.465271i	$-0.154043\pi$
$60$	−2.95409e8	−	4.47376e7i	−0.379898	−	0.0575329i
$61$	−7.40208e8			−0.876405			−0.438202	−	0.898876i	$-0.644385\pi$
$61$	−7.40208e8			−0.876405			−0.438202	+	0.898876i	$0.644385\pi$
$62$	5.15487e8	+	5.99431e8i	0.562677	+	0.654306i
$63$		−	2.71458e8i		−	0.273527i
$64$	−4.67913e8	+	9.66426e8i	−0.435778	+	0.900054i
$65$	−9.04344e8			−0.779412
$66$	1.34687e9	−	1.15826e9i	1.07549	−	0.924878i
$67$		−	4.17577e7i		−	0.0309287i	−0.999880	−	0.0154644i	$-0.995077\pi$
$67$		−	4.17577e7i		−	0.0309287i	0.999880	−	0.0154644i	$-0.00492266\pi$
$68$	−3.85473e8	+	2.54533e9i	−0.265124	+	1.75065i
$69$	1.08789e9			0.695566
$70$	5.11959e8	+	5.95330e8i	0.304611	+	0.354215i
$71$		−	6.30071e8i		−	0.349219i	−0.984638	−	0.174609i	$-0.944134\pi$
$71$		−	6.30071e8i		−	0.349219i	0.984638	−	0.174609i	$-0.0558663\pi$
$72$	−2.69094e8	−	4.29262e8i	−0.139072	−	0.221850i
$73$	9.52604e8			0.459513			0.229757	−	0.973248i	$-0.426207\pi$
$73$	9.52604e8			0.459513			0.229757	+	0.973248i	$0.426207\pi$
$74$	2.23974e8	−	1.92608e8i	0.100934	−	0.0867994i
$75$			4.07767e8i			0.171833i
$76$	1.72624e8	+	2.61428e7i	0.0680823	+	0.0103106i
$77$	−4.66840e9			−1.72470
$78$	2.81879e9	+	3.27782e9i	0.976315	+	1.13530i
$79$		−	2.24561e9i		−	0.729793i	−0.931048	−	0.364896i	$-0.881104\pi$
$79$		−	2.24561e9i		−	0.729793i	0.931048	−	0.364896i	$-0.118896\pi$
$80$	1.39972e9	+	4.33906e8i	0.427160	+	0.132418i
$81$	−2.33477e9			−0.669604
$82$	3.51659e9	−	3.02413e9i	0.948533	−	0.815700i
$83$			6.38664e9i			1.62137i	0.585483	+	0.810685i	$0.300905\pi$
$83$			6.38664e9i			1.62137i	−0.585483	+	0.810685i	$0.699095\pi$
$84$	5.62038e8	−	3.71122e9i	0.134391	−	0.887402i
$85$	3.51345e9			0.791843
$86$	5.83192e8	+	6.78162e8i	0.123971	+	0.144159i
$87$			1.41989e9i			0.284878i
$88$	−7.38225e9	+	4.62775e9i	−1.39886	+	0.876913i
$89$	−1.29920e9			−0.232663			−0.116332	−	0.993210i	$-0.537114\pi$
$89$	−1.29920e9			−0.232663			−0.116332	+	0.993210i	$0.537114\pi$
$90$	−5.24255e8	+	4.50838e8i	−0.0887831	+	0.0763498i
$91$		−	1.13613e10i		−	1.82062i
$92$	−5.27567e9	−	7.98963e8i	−0.800457	−	0.121224i
$93$	−5.15808e9			−0.741435
$94$	2.31416e9	+	2.69101e9i	0.315322	+	0.366671i
$95$		−	2.38282e8i		−	0.0307945i
$96$	−2.79014e9	−	6.42578e9i	−0.342192	−	0.788078i
$97$	1.43562e10			1.67178			0.835892	−	0.548894i	$-0.184951\pi$
$97$	1.43562e10			1.67178			0.835892	+	0.548894i	$0.184951\pi$
$98$	−6.25596e8	+	5.37987e8i	−0.0692091	+	0.0595170i
$99$		−	4.11106e9i		−	0.432292i
$100$	2.99471e8	−	1.97745e9i	0.0299471	−	0.197745i
$101$	7.00408e9			0.666414			0.333207	−	0.942854i	$-0.391869\pi$
$101$	7.00408e9			0.666414			0.333207	+	0.942854i	$0.391869\pi$
$102$	−1.09512e10	−	1.27346e10i	−0.991887	−	1.15341i
$103$			1.99613e10i			1.72188i	0.508711	+	0.860938i	$0.330122\pi$
$103$			1.99613e10i			1.72188i	−0.508711	+	0.860938i	$0.669878\pi$
$104$	−1.12623e10	−	1.79658e10i	−0.925682	−	1.47666i
$105$	−5.12278e9			−0.401383
$106$	2.65848e9	−	2.28618e9i	0.198657	−	0.170837i
$107$		−	1.47384e10i		−	1.05083i	−0.850846	−	0.525414i	$-0.823910\pi$
$107$		−	1.47384e10i		−	1.05083i	0.850846	−	0.525414i	$-0.176090\pi$
$108$	1.57498e10	+	2.38519e9i	1.07190	+	0.162332i
$109$	1.01363e10			0.658787			0.329394	−	0.944193i	$-0.393156\pi$
$109$	1.01363e10			0.658787			0.329394	+	0.944193i	$0.393156\pi$
$110$	7.75330e9	+	9.01590e9i	0.481419	+	0.559816i
$111$			1.92728e9i			0.114375i
$112$	−5.45117e9	+	1.75847e10i	−0.309314	+	0.997800i
$113$	1.71783e10			0.932367			0.466184	−	0.884688i	$-0.345629\pi$
$113$	1.71783e10			0.932367			0.466184	+	0.884688i	$0.345629\pi$
$114$	−8.63660e8	+	7.42712e8i	−0.0448558	+	0.0385742i
$115$			7.28226e9i			0.362057i
$116$	1.04279e9	−	6.88571e9i	0.0496487	−	0.327837i
$117$	1.00049e10			0.456334
$118$	−1.38806e10	−	1.61410e10i	−0.606734	−	0.705538i
$119$			4.41395e10i			1.84966i
$120$	−8.10076e9	+	5.07817e9i	−0.325552	+	0.204080i
$121$	−4.47626e10			−1.72579
$122$	−1.79592e10	+	1.54442e10i	−0.664491	+	0.571435i
$123$			3.02601e10i			1.07484i
$124$	2.50139e10	+	3.78818e9i	0.853243	+	0.129218i
$125$	−2.72958e9			−0.0894427
$126$	−5.66388e9	−	6.58622e9i	−0.178345	−	0.207388i
$127$			2.47585e10i			0.749385i	0.927149	+	0.374693i	$0.122252\pi$
$127$			2.47585e10i			0.749385i	−0.927149	+	0.374693i	$0.877748\pi$
$128$	8.81147e9	+	3.32107e10i	0.256448	+	0.966558i
$129$	−5.83555e9			−0.163355
$130$	−2.19416e10	+	1.88689e10i	−0.590950	+	0.508193i
$131$		−	6.21126e10i		−	1.60999i	−0.593282	−	0.804995i	$-0.702168\pi$
$131$		−	6.21126e10i		−	1.60999i	0.593282	−	0.804995i	$-0.297832\pi$
$132$	8.51172e9	−	5.62041e10i	0.212397	−	1.40249i
$133$	2.99354e9			0.0719327
$134$	−8.71261e8	−	1.01314e9i	−0.0201662	−	0.0234502i
$135$		−	2.17402e10i		−	0.484835i
$136$	4.37551e10	+	6.97987e10i	0.940447	+	1.50021i
$137$	5.40807e10			1.12057			0.560285	−	0.828300i	$-0.310691\pi$
$137$	5.40807e10			1.12057			0.560285	+	0.828300i	$0.310691\pi$
$138$	2.63948e10	−	2.26984e10i	0.527378	−	0.453524i
$139$		−	1.71319e9i		−	0.0330166i	−0.999864	−	0.0165083i	$-0.994745\pi$
$139$		−	1.71319e9i		−	0.0330166i	0.999864	−	0.0165083i	$-0.00525499\pi$
$140$	2.48427e10	+	3.76226e9i	0.461912	+	0.0699533i
$141$	−2.31560e10			−0.415498
$142$	−1.31462e10	−	1.52870e10i	−0.227698	−	0.264778i
$143$		−	1.72059e11i		−	2.87739i
$144$	−1.54853e10	−	4.80037e9i	−0.250096	−	0.0775287i
$145$	−9.50468e9			−0.148285
$146$	2.31125e10	−	1.98758e10i	0.348403	−	0.299613i
$147$		−	5.38322e9i		−	0.0784252i
$148$	1.41543e9	−	9.34629e9i	0.0199333	−	0.131623i
$149$	−9.21894e10			−1.25531			−0.627653	−	0.778493i	$-0.715984\pi$
$149$	−9.21894e10			−1.25531			−0.627653	+	0.778493i	$0.715984\pi$
$150$	8.50794e9	+	9.89342e9i	0.112039	+	0.130284i
$151$		−	1.62044e10i		−	0.206418i	−0.994660	−	0.103209i	$-0.967089\pi$
$151$		−	1.62044e10i		−	0.206418i	0.994660	−	0.103209i	$-0.0329110\pi$
$152$	4.73375e9	−	2.96747e9i	0.0583428	−	0.0365737i
$153$	−3.88698e10			−0.463613
$154$	−1.13267e11	+	9.74048e10i	−1.30767	+	1.12454i
$155$		−	3.45279e10i		−	0.385933i
$156$	1.36781e11	+	2.07146e10i	1.48048	+	0.224209i
$157$	−3.25976e10			−0.341733			−0.170867	−	0.985294i	$-0.554657\pi$
$157$	−3.25976e10			−0.341733			−0.170867	+	0.985294i	$0.554657\pi$
$158$	−4.68540e10	−	5.44840e10i	−0.475841	−	0.553329i
$159$			2.28761e10i			0.225110i
$160$	4.30138e10	−	1.86771e10i	0.410212	−	0.178118i
$161$	−9.14871e10			−0.845728
$162$	−5.66470e10	+	4.87142e10i	−0.507694	+	0.436596i
$163$			1.38371e11i			1.20256i	0.799037	+	0.601282i	$0.205343\pi$
$163$			1.38371e11i			1.20256i	−0.799037	+	0.601282i	$0.794657\pi$
$164$	2.22235e10	−	1.46745e11i	0.187324	−	1.23693i
$165$	−7.75813e10			−0.634363
$166$	1.33255e11	+	1.54955e11i	1.05717	+	1.22932i
$167$			1.45798e11i			1.12246i	0.827660	+	0.561229i	$0.189671\pi$
$167$			1.45798e11i			1.12246i	−0.827660	+	0.561229i	$0.810329\pi$
$168$	−6.37971e10	−	1.01770e11i	−0.476710	−	0.760454i
$169$	2.80875e11			2.03741
$170$	8.52448e10	−	7.33071e10i	0.600376	−	0.516299i
$171$			2.63615e9i			0.0180297i
$172$	2.82993e10	+	4.28573e9i	0.187989	+	0.0284697i
$173$	1.82593e10			0.117830			0.0589148	−	0.998263i	$-0.481236\pi$
$173$	1.82593e10			0.117830			0.0589148	+	0.998263i	$0.481236\pi$
$174$	2.96256e10	+	3.44500e10i	0.185747	+	0.215994i
$175$		−	3.42917e10i		−	0.208929i
$176$	−8.25545e10	+	2.66309e11i	−0.488852	+	1.57696i
$177$	1.38892e11			0.799489
$178$	−3.15218e10	+	2.71075e10i	−0.176405	+	0.151701i
$179$		−	1.18186e11i		−	0.643134i	−0.946887	−	0.321567i	$-0.895791\pi$
$179$		−	1.18186e11i		−	0.643134i	0.946887	−	0.321567i	$-0.104209\pi$
$180$	−3.31309e9	+	2.18768e10i	−0.0175336	+	0.115777i
$181$	−1.26493e11			−0.651138			−0.325569	−	0.945518i	$-0.605556\pi$
$181$	−1.26493e11			−0.651138			−0.325569	+	0.945518i	$0.605556\pi$
$182$	−2.37050e11	−	2.75652e11i	−1.18709	−	1.38040i
$183$		−	1.54538e11i		−	0.752976i
$184$	−1.44671e11	+	9.06904e10i	−0.685947	+	0.430004i
$185$	−1.29011e10			−0.0595346
$186$	−1.25147e11	+	1.07622e11i	−0.562156	+	0.483432i
$187$			6.68465e11i			2.92328i
$188$	1.12294e11	+	1.70062e10i	0.478155	+	0.0724132i
$189$	2.73122e11			1.13252
$190$	−4.97168e9	−	5.78130e9i	−0.0200787	−	0.0233484i
$191$		−	5.22919e10i		−	0.205716i	−0.994696	−	0.102858i	$-0.967201\pi$
$191$		−	5.22919e10i		−	0.205716i	0.994696	−	0.102858i	$-0.0327987\pi$
$192$	−2.01767e11	−	9.76895e10i	−0.773294	−	0.374405i
$193$	5.76304e10			0.215211			0.107606	−	0.994194i	$-0.465682\pi$
$193$	5.76304e10			0.215211			0.107606	+	0.994194i	$0.465682\pi$
$194$	3.48315e11	−	2.99537e11i	1.26755	−	1.09004i
$195$		−	1.88806e11i		−	0.669643i
$196$	−3.95353e9	+	2.61057e10i	−0.0136680	+	0.0902517i
$197$	2.43700e11			0.821344			0.410672	−	0.911783i	$-0.365294\pi$
$197$	2.43700e11			0.821344			0.410672	+	0.911783i	$0.365294\pi$
$198$	−8.57760e10	−	9.97442e10i	−0.281864	−	0.327764i
$199$			1.54373e11i			0.494658i	0.968932	+	0.247329i	$0.0795528\pi$
$199$			1.54373e11i			0.494658i	−0.968932	+	0.247329i	$0.920447\pi$
$200$	−3.39930e10	−	5.42261e10i	−0.106228	−	0.169457i
$201$	8.71804e9			0.0265729
$202$	1.69936e11	−	1.46138e11i	0.505275	−	0.434516i
$203$		−	1.19407e11i		−	0.346378i
$204$	−5.31407e11	−	8.04778e10i	−1.50410	−	0.227785i
$205$	−2.02560e11			−0.559479
$206$	4.16485e11	+	4.84308e11i	1.12270	+	1.30553i
$207$		−	8.05648e10i		−	0.211979i
$208$	−6.48103e11	−	2.00909e11i	−1.66467	−	0.516040i
$209$	4.53353e10			0.113685
$210$	−1.24291e11	+	1.06885e11i	−0.304329	+	0.261711i
$211$			8.84929e10i			0.211591i	0.994388	+	0.105795i	$0.0337388\pi$
$211$			8.84929e10i			0.211591i	−0.994388	+	0.105795i	$0.966261\pi$
$212$	1.68006e10	−	1.10937e11i	0.0392324	−	0.259057i
$213$	1.31544e11			0.300036
$214$	−3.07513e11	−	3.57590e11i	−0.685163	−	0.796739i
$215$		−	3.90629e10i		−	0.0850301i
$216$	4.31894e11	−	2.70744e11i	0.918561	−	0.575823i
$217$	4.33774e11			0.901499
$218$	2.45930e11	−	2.11490e11i	0.499493	−	0.429544i
$219$			1.98882e11i			0.394797i
$220$	3.76228e11	+	5.69771e10i	0.730024	+	0.110557i
$221$	−1.62681e12			−3.08586
$222$	4.02122e10	+	4.67606e10i	0.0745749	+	0.0867191i
$223$		−	1.09819e11i		−	0.199137i	−0.995031	−	0.0995685i	$-0.968254\pi$
$223$		−	1.09819e11i		−	0.199137i	0.995031	−	0.0995685i	$-0.0317462\pi$
$224$	2.34640e11	+	5.40383e11i	0.416066	+	0.958212i
$225$	3.01977e10			0.0523674
$226$	4.16786e11	−	3.58419e11i	0.706921	−	0.607923i
$227$		−	4.71593e11i		−	0.782417i	−0.920302	−	0.391208i	$-0.872057\pi$
$227$		−	4.71593e11i		−	0.782417i	0.920302	−	0.391208i	$-0.127943\pi$
$228$	−5.45800e9	+	3.60400e10i	−0.00885849	+	0.0584939i
$229$	−2.85211e11			−0.452885			−0.226443	−	0.974025i	$-0.572710\pi$
$229$	−2.85211e11			−0.452885			−0.226443	+	0.974025i	$0.572710\pi$
$230$	1.51942e11	+	1.76685e11i	0.236069	+	0.274512i
$231$		−	9.74654e11i		−	1.48180i
$232$	−1.18367e11	−	1.88821e11i	−0.176113	−	0.280938i
$233$	1.71346e11			0.249514			0.124757	−	0.992187i	$-0.460185\pi$
$233$	1.71346e11			0.249514			0.124757	+	0.992187i	$0.460185\pi$
$234$	2.42743e11	−	2.08749e11i	0.345993	−	0.297540i
$235$		−	1.55005e11i		−	0.216276i
$236$	−6.73554e11	−	1.02005e11i	−0.920052	−	0.139335i
$237$	4.68832e11			0.627012
$238$	9.20957e11	+	1.07093e12i	1.20602	+	1.40241i
$239$			7.55431e11i			0.968735i	0.874865	+	0.484368i	$0.160950\pi$
$239$			7.55431e11i			0.968735i	−0.874865	+	0.484368i	$0.839050\pi$
$240$	−9.05896e10	+	2.92229e11i	−0.113769	+	0.367000i
$241$	1.27312e12			1.56598			0.782989	−	0.622036i	$-0.213694\pi$
$241$	1.27312e12			1.56598			0.782989	+	0.622036i	$0.213694\pi$
$242$	−1.08605e12	+	9.33958e11i	−1.30850	+	1.12525i
$243$			4.31122e11i			0.508825i
$244$	−1.13496e11	+	7.49428e11i	−0.131229	+	0.866524i
$245$	3.60350e10			0.0408220
$246$	6.31367e11	+	7.34183e11i	0.700820	+	0.814946i
$247$			1.10330e11i			0.120008i
$248$	6.85937e11	−	4.29997e11i	0.731182	−	0.458360i
$249$	−1.33338e12			−1.39302
$250$	−6.62261e10	+	5.69517e10i	−0.0678155	+	0.0583186i
$251$		−	1.13923e12i		−	1.14351i	−0.820423	−	0.571757i	$-0.806262\pi$
$251$		−	1.13923e12i		−	1.14351i	0.820423	−	0.571757i	$-0.193738\pi$
$252$	−2.74839e11	−	4.16224e10i	−0.270443	−	0.0409567i
$253$	−1.38552e12			−1.33662
$254$	5.16578e11	+	6.00700e11i	0.488615	+	0.568184i
$255$			7.33527e11i			0.680323i
$256$	9.06718e11	+	6.21923e11i	0.824655	+	0.565635i
$257$	−5.10456e11			−0.455294			−0.227647	−	0.973744i	$-0.573103\pi$
$257$	−5.10456e11			−0.455294			−0.227647	+	0.973744i	$0.573103\pi$
$258$	−1.41585e11	+	1.21757e11i	−0.123856	+	0.106511i
$259$		−	1.62077e11i		−	0.139067i
$260$	−1.38662e11	+	9.15608e11i	−0.116706	+	0.770625i
$261$	1.05152e11			0.0868188
$262$	−1.29596e12	−	1.50700e12i	−1.04975	−	1.22069i
$263$			1.69927e12i			1.35047i	0.737603	+	0.675235i	$0.235958\pi$
$263$			1.69927e12i			1.35047i	−0.737603	+	0.675235i	$0.764042\pi$
$264$	−9.66167e11	−	1.54124e12i	−0.753412	−	1.20185i
$265$	−1.53131e11			−0.117175
$266$	7.26305e10	−	6.24593e10i	0.0545394	−	0.0469017i
$267$		−	2.71244e11i		−	0.199896i
$268$	−4.22778e10	−	6.40267e9i	−0.0305801	−	0.00463114i
$269$	3.81904e11			0.271140			0.135570	−	0.990768i	$-0.456713\pi$
$269$	3.81904e11			0.271140			0.135570	+	0.990768i	$0.456713\pi$
$270$	−4.53602e11	−	5.27469e11i	−0.316123	−	0.367602i
$271$		−	1.61226e12i		−	1.10304i	−0.834163	−	0.551518i	$-0.814049\pi$
$271$		−	1.61226e12i		−	1.10304i	0.834163	−	0.551518i	$-0.185951\pi$
$272$	2.51793e12	+	7.80549e11i	1.69122	+	0.524270i
$273$	2.37197e12			1.56421
$274$	1.31213e12	−	1.12838e12i	0.849617	−	0.730637i
$275$		−	5.19326e11i		−	0.330200i
$276$	1.66805e11	−	1.10144e12i	0.104151	−	0.687724i
$277$	−1.26749e12			−0.777225			−0.388613	−	0.921401i	$-0.627046\pi$
$277$	−1.26749e12			−0.777225			−0.388613	+	0.921401i	$0.627046\pi$
$278$	−3.57452e10	−	4.15662e10i	−0.0215275	−	0.0250332i
$279$			3.81988e11i			0.225958i
$280$	6.81243e11	−	4.27055e11i	0.395833	−	0.248138i
$281$	−1.44692e12			−0.825875			−0.412938	−	0.910759i	$-0.635497\pi$
$281$	−1.44692e12			−0.825875			−0.412938	+	0.910759i	$0.635497\pi$
$282$	−5.61821e11	+	4.83144e11i	−0.315031	+	0.270914i
$283$			1.60428e11i			0.0883788i	0.999023	+	0.0441894i	$0.0140705\pi$
$283$			1.60428e11i			0.0883788i	−0.999023	+	0.0441894i	$0.985929\pi$
$284$	−6.37919e11	−	9.66083e10i	−0.345282	−	0.0522905i
$285$	4.97478e10			0.0264575
$286$	−3.58997e12	−	4.17458e12i	−1.87612	−	2.18164i
$287$		−	2.54476e12i		−	1.30688i
$288$	−4.75869e11	+	2.06627e11i	−0.240173	+	0.104286i
$289$	4.30431e12			2.13508
$290$	−2.30606e11	+	1.98312e11i	−0.112430	+	0.0966851i
$291$			2.99724e12i			1.43634i
$292$	1.46062e11	−	9.64469e11i	0.0688055	−	0.454333i
$293$	−1.75525e12			−0.812831			−0.406416	−	0.913688i	$-0.633222\pi$
$293$	−1.75525e12			−0.812831			−0.406416	+	0.913688i	$0.633222\pi$
$294$	−1.12319e11	−	1.30610e11i	−0.0511349	−	0.0594620i
$295$			9.29740e11i			0.416151i
$296$	−1.60666e11	−	2.56296e11i	−0.0707074	−	0.112793i
$297$	4.13626e12			1.78989
$298$	−2.23674e12	+	1.92350e12i	−0.951774	+	0.818487i
$299$		−	3.37186e12i		−	1.41096i
$300$	4.12846e11	+	6.25227e10i	0.169896	+	0.0257295i
$301$	4.90748e11			0.198621
$302$	−3.38099e11	−	3.93157e11i	−0.134589	−	0.156506i
$303$			1.46229e12i			0.572559i
$304$	5.29368e10	−	1.70766e11i	0.0203887	−	0.0657709i
$305$	1.03447e12			0.391940
$306$	−9.43076e11	+	8.11007e11i	−0.351511	+	0.302286i
$307$			3.35291e12i			1.22950i	0.788720	+	0.614752i	$0.210744\pi$
$307$			3.35291e12i			1.22950i	−0.788720	+	0.614752i	$0.789256\pi$
$308$	−7.15803e11	+	4.72655e12i	−0.258250	+	1.70526i
$309$	−4.16745e12			−1.47937
$310$	−7.20414e11	−	8.37731e11i	−0.251637	−	0.292615i
$311$			4.30452e12i			1.47953i	0.672867	+	0.739763i	$0.265062\pi$
$311$			4.30452e12i			1.47953i	−0.672867	+	0.739763i	$0.734938\pi$
$312$	3.75085e12	−	2.35132e12i	1.26869	−	0.795313i
$313$	2.31790e12			0.771566			0.385783	−	0.922589i	$-0.373931\pi$
$313$	2.31790e12			0.771566			0.385783	+	0.922589i	$0.373931\pi$
$314$	−7.90896e11	+	6.80138e11i	−0.259102	+	0.222817i
$315$			3.79374e11i			0.122325i
$316$	−2.27358e12	−	3.44318e11i	−0.721565	−	0.109276i
$317$	−5.00628e12			−1.56394			−0.781968	−	0.623319i	$-0.785784\pi$
$317$	−5.00628e12			−1.56394			−0.781968	+	0.623319i	$0.785784\pi$
$318$	4.77302e11	+	5.55028e11i	0.146777	+	0.170679i
$319$		−	1.80835e12i		−	0.547430i
$320$	6.53929e11	−	1.35062e12i	0.194886	−	0.402516i
$321$	3.07704e12			0.902835
$322$	−2.21970e12	+	1.90885e12i	−0.641231	+	0.551433i
$323$		−	4.28643e11i		−	0.121922i
$324$	−3.57988e11	+	2.36385e12i	−0.100264	+	0.662055i
$325$	1.26386e12			0.348564
$326$	2.88707e12	+	3.35722e12i	0.784097	+	0.911784i
$327$			2.11622e12i			0.566006i
$328$	−2.52260e12	−	4.02408e12i	−0.664475	−	1.05998i
$329$	1.94733e12			0.505197
$330$	−1.88231e12	+	1.61871e12i	−0.480974	+	0.413618i
$331$		−	4.10802e12i		−	1.03393i	−0.856005	−	0.516967i	$-0.827061\pi$
$331$		−	4.10802e12i		−	1.03393i	0.856005	−	0.516967i	$-0.172939\pi$
$332$	6.46619e12	+	9.79259e11i	1.60309	+	0.242777i
$333$	1.42727e11			0.0348567
$334$	3.04204e12	+	3.53742e12i	0.731867	+	0.851048i
$335$			5.83581e10i			0.0138318i
$336$	−3.67127e12	−	1.13808e12i	−0.857274	−	0.265751i
$337$	−5.62079e12			−1.29315			−0.646573	−	0.762852i	$-0.723799\pi$
$337$	−5.62079e12			−1.29315			−0.646573	+	0.762852i	$0.723799\pi$
$338$	6.81470e12	−	5.86036e12i	1.54477	−	1.32844i
$339$			3.58642e12i			0.801056i
$340$	5.38715e11	−	3.55721e12i	0.118567	−	0.782916i
$341$	6.56924e12			1.42477
$342$	5.50025e10	+	6.39594e10i	0.0117558	+	0.0136702i
$343$		−	4.50680e12i		−	0.949288i
$344$	7.76030e11	−	4.86474e11i	0.161097	−	0.100987i
$345$	−1.52037e12			−0.311067
$346$	4.43015e11	−	3.80975e11i	0.0893384	−	0.0768274i
$347$		−	5.58470e12i		−	1.11008i	−0.831825	−	0.555038i	$-0.812704\pi$
$347$		−	5.58470e12i		−	1.11008i	0.831825	−	0.555038i	$-0.187296\pi$
$348$	1.43758e12	+	2.17711e11i	0.281666	+	0.0426564i
$349$	−4.24215e12			−0.819331			−0.409665	−	0.912236i	$-0.634355\pi$
$349$	−4.24215e12			−0.819331			−0.409665	+	0.912236i	$0.634355\pi$
$350$	−7.15485e11	−	8.31998e11i	−0.136226	−	0.158410i
$351$			1.00662e13i			1.88943i
$352$	3.55348e12	+	8.18376e12i	0.657567	+	1.51440i
$353$	−9.65096e12			−1.76075			−0.880374	−	0.474280i	$-0.842708\pi$
$353$	−9.65096e12			−1.76075			−0.880374	+	0.474280i	$0.842708\pi$
$354$	3.36987e12	−	2.89795e12i	0.606173	−	0.521284i
$355$			8.80551e11i			0.156175i
$356$	−1.99206e11	+	1.31539e12i	−0.0348380	+	0.230040i
$357$	−9.21531e12			−1.58916
$358$	−2.46592e12	−	2.86748e12i	−0.419337	−	0.487624i
$359$		−	7.95043e12i		−	1.33327i	−0.745384	−	0.666635i	$-0.767734\pi$
$359$		−	7.95043e12i		−	1.33327i	0.745384	−	0.666635i	$-0.232266\pi$
$360$	3.76070e11	+	5.99912e11i	0.0621951	+	0.0992144i
$361$	6.10200e12			0.995258
$362$	−3.06902e12	+	2.63923e12i	−0.493693	+	0.424556i
$363$		−	9.34540e12i		−	1.48274i
$364$	−1.15028e13	−	1.74202e12i	−1.80010	−	0.272612i
$365$	−1.33130e12			−0.205501
$366$	−3.22440e12	−	3.74947e12i	−0.490956	−	0.570906i
$367$		−	7.78220e12i		−	1.16889i	−0.811435	−	0.584443i	$-0.801313\pi$
$367$		−	7.78220e12i		−	1.16889i	0.811435	−	0.584443i	$-0.198687\pi$
$368$	−1.61783e12	+	5.21887e12i	−0.239714	+	0.773282i
$369$	2.24095e12			0.327567
$370$	−3.13013e11	+	2.69178e11i	−0.0451392	+	0.0388179i
$371$		−	1.92379e12i		−	0.273708i
$372$	−7.90884e11	+	5.22232e12i	−0.111019	+	0.733076i
$373$	2.12996e12			0.295003			0.147502	−	0.989062i	$-0.452877\pi$
$373$	2.12996e12			0.295003			0.147502	+	0.989062i	$0.452877\pi$
$374$	1.39473e13	+	1.62186e13i	1.90604	+	2.21643i
$375$		−	5.69872e11i		−	0.0768460i
$376$	3.07936e12	−	1.93038e12i	0.409752	−	0.256864i
$377$	4.40090e12			0.577876
$378$	6.62660e12	−	5.69861e12i	0.858681	−	0.738431i
$379$			7.90603e12i			1.01103i	0.862819	+	0.505513i	$0.168697\pi$
$379$			7.90603e12i			1.01103i	−0.862819	+	0.505513i	$0.831303\pi$
$380$	−2.41250e11	−	3.65356e10i	−0.0304473	−	0.00461104i
$381$	−5.16900e12			−0.643845
$382$	−1.09105e12	−	1.26873e12i	−0.134131	−	0.155974i
$383$		−	1.22242e13i		−	1.48329i	−0.670793	−	0.741645i	$-0.734046\pi$
$383$		−	1.22242e13i		−	1.48329i	0.670793	−	0.741645i	$-0.265954\pi$
$384$	−6.93362e12	+	1.83963e12i	−0.830432	+	0.220331i
$385$	6.52429e12			0.771311
$386$	1.39825e12	−	1.20244e12i	0.163173	−	0.140322i
$387$			4.32159e11i			0.0497839i
$388$	2.20122e12	−	1.45350e13i	0.250326	−	1.65294i
$389$	−1.56498e13			−1.75695			−0.878476	−	0.477787i	$-0.841439\pi$
$389$	−1.56498e13			−1.75695			−0.878476	+	0.477787i	$0.841439\pi$
$390$	−3.93938e12	−	4.58089e12i	−0.436621	−	0.507723i
$391$			1.31000e13i			1.43346i
$392$	4.48766e11	+	7.15877e11i	0.0484830	+	0.0773407i
$393$	1.29677e13			1.38325
$394$	5.91276e12	−	5.08473e12i	0.622743	−	0.535534i
$395$			3.13834e12i			0.326373i
$396$	−4.16226e12	−	6.30346e11i	−0.427419	−	0.0647296i
$397$	1.02802e13			1.04244			0.521219	−	0.853423i	$-0.325477\pi$
$397$	1.02802e13			1.04244			0.521219	+	0.853423i	$0.325477\pi$
$398$	3.22094e12	+	3.74545e12i	0.322528	+	0.375050i
$399$			6.24982e11i			0.0618020i
$400$	−1.95616e12	−	6.06403e11i	−0.191032	−	0.0592190i
$401$	5.11831e12			0.493633			0.246817	−	0.969062i	$-0.420615\pi$
$401$	5.11831e12			0.493633			0.246817	+	0.969062i	$0.420615\pi$
$402$	2.11521e11	−	1.81899e11i	0.0201476	−	0.0173261i
$403$			1.59873e13i			1.50400i
$404$	1.07393e12	−	7.09132e12i	0.0997859	−	0.658901i
$405$	3.26293e12			0.299456
$406$	−2.49140e12	−	2.89711e12i	−0.225846	−	0.262624i
$407$		−	2.45456e12i		−	0.219787i
$408$	−1.45724e13	+	9.13505e12i	−1.28893	+	0.807998i
$409$	−9.36298e12			−0.818083			−0.409042	−	0.912516i	$-0.634137\pi$
$409$	−9.36298e12			−0.818083			−0.409042	+	0.912516i	$0.634137\pi$
$410$	−4.91458e12	+	4.22634e12i	−0.424197	+	0.364792i
$411$			1.12908e13i			0.962754i
$412$	2.02099e13	+	3.06064e12i	1.70246	+	0.257826i
$413$	−1.16803e13			−0.972086
$414$	−1.68096e12	−	1.95470e12i	−0.138215	−	0.160723i
$415$		−	8.92560e12i		−	0.725098i
$416$	−1.99164e13	+	8.64793e12i	−1.59862	+	0.694137i
$417$	3.57675e11			0.0283667
$418$	1.09994e12	−	9.45906e11i	0.0861963	−	0.0741254i
$419$			1.70814e13i			1.32267i	0.750089	+	0.661337i	$0.230011\pi$
$419$			1.70814e13i			1.32267i	−0.750089	+	0.661337i	$0.769989\pi$
$420$	−7.85472e11	+	5.18659e12i	−0.0601014	+	0.396858i
$421$	7.59949e12			0.574611			0.287306	−	0.957839i	$-0.407240\pi$
$421$	7.59949e12			0.574611			0.287306	+	0.957839i	$0.407240\pi$
$422$	1.84638e12	+	2.14705e12i	0.137962	+	0.160428i
$423$			1.71485e12i			0.126626i
$424$	−1.90704e12	−	3.04213e12i	−0.139165	−	0.221998i
$425$	−4.91020e12			−0.354123
$426$	3.19158e12	−	2.74463e12i	0.227488	−	0.195630i
$427$			1.29961e13i			0.915531i
$428$	−1.49220e13	−	2.25983e12i	−1.03898	−	0.157347i
$429$	3.59220e13			2.47215
$430$	−8.15036e11	−	9.47761e11i	−0.0554414	−	0.0644698i
$431$			6.00283e12i			0.403617i	0.979425	+	0.201809i	$0.0646819\pi$
$431$			6.00283e12i			0.403617i	−0.979425	+	0.201809i	$0.935318\pi$
$432$	4.82980e12	−	1.55802e13i	0.321004	−	1.03551i
$433$	−2.69188e12			−0.176855			−0.0884273	−	0.996083i	$-0.528184\pi$
$433$	−2.69188e12			−0.176855			−0.0884273	+	0.996083i	$0.528184\pi$
$434$	1.05244e13	−	9.05057e12i	0.683517	−	0.587797i
$435$		−	1.98436e12i		−	0.127401i
$436$	1.55419e12	−	1.02625e13i	0.0986439	−	0.651360i
$437$	8.88439e11			0.0557469
$438$	4.14960e12	+	4.82535e12i	0.257416	+	0.299335i
$439$		−	1.14520e13i		−	0.702360i	−0.936308	−	0.351180i	$-0.885781\pi$
$439$		−	1.14520e13i		−	0.702360i	0.936308	−	0.351180i	$-0.114219\pi$
$440$	1.03170e13	−	6.46748e12i	0.625590	−	0.392167i
$441$	−3.98661e11			−0.0239007
$442$	−3.94704e13	+	3.39429e13i	−2.33970	+	2.01205i
$443$			8.63257e12i			0.505966i	0.967471	+	0.252983i	$0.0814117\pi$
$443$			8.63257e12i			0.505966i	−0.967471	+	0.252983i	$0.918588\pi$
$444$	1.95129e12	+	2.95509e11i	0.113085	+	0.0171260i
$445$	1.81569e12			0.104050
$446$	−2.29133e12	−	2.66447e12i	−0.129842	−	0.150986i
$447$		−	1.92470e13i		−	1.07851i
$448$	1.69679e13	+	8.21531e12i	0.940236	+	0.455233i
$449$	−4.62556e11			−0.0253474			−0.0126737	−	0.999920i	$-0.504034\pi$
$449$	−4.62556e11			−0.0253474			−0.0126737	+	0.999920i	$0.504034\pi$
$450$	7.32669e11	−	6.30066e11i	0.0397050	−	0.0341447i
$451$		−	3.85388e13i		−	2.06545i
$452$	2.63393e12	−	1.73922e13i	0.139609	−	0.921856i
$453$	3.38310e12			0.177347
$454$	−9.83965e12	−	1.14420e13i	−0.510153	−	0.593229i
$455$			1.58779e13i			0.814208i
$456$	6.19539e11	+	9.88297e11i	0.0314228	+	0.0501260i
$457$	−1.39645e13			−0.700561			−0.350280	−	0.936645i	$-0.613914\pi$
$457$	−1.39645e13			−0.700561			−0.350280	+	0.936645i	$0.613914\pi$
$458$	−6.91990e12	+	5.95083e12i	−0.343378	+	0.295291i
$459$		−	3.91081e13i		−	1.91957i
$460$	7.37297e12	+	1.11658e12i	0.357975	+	0.0542129i
$461$	−2.08164e13			−0.999772			−0.499886	−	0.866091i	$-0.666625\pi$
$461$	−2.08164e13			−0.999772			−0.499886	+	0.866091i	$0.666625\pi$
$462$	−2.03359e13	−	2.36475e13i	−0.966168	−	1.12350i
$463$			3.42763e13i			1.61098i	0.592612	+	0.805488i	$0.298097\pi$
$463$			3.42763e13i			1.61098i	−0.592612	+	0.805488i	$0.701903\pi$
$464$	−6.81158e12	−	2.11156e12i	−0.316707	−	0.0981779i
$465$	7.20863e12			0.331580
$466$	4.15727e12	−	3.57509e12i	0.189182	−	0.162688i
$467$		−	1.38159e13i		−	0.622007i	−0.950409	−	0.311004i	$-0.899335\pi$
$467$		−	1.38159e13i		−	0.622007i	0.950409	−	0.311004i	$-0.100665\pi$
$468$	1.53404e12	−	1.01295e13i	0.0683295	−	0.451190i
$469$	−7.33153e11			−0.0323095
$470$	−3.23414e12	−	3.76081e12i	−0.141016	−	0.163980i
$471$		−	6.80562e12i		−	0.293605i
$472$	−1.84703e13	+	1.15786e13i	−0.788433	+	0.494250i
$473$	7.43207e12			0.313909
$474$	1.13750e13	−	9.78204e12i	0.475400	−	0.408825i
$475$			3.33009e11i			0.0137717i
$476$	4.46893e13	+	6.76788e12i	1.82881	+	0.276960i
$477$	1.69411e12			0.0686042
$478$	1.57618e13	+	1.83286e13i	0.631636	+	0.734495i
$479$		−	1.01623e13i		−	0.403007i	−0.979488	−	0.201504i	$-0.935417\pi$
$479$		−	1.01623e13i		−	0.403007i	0.979488	−	0.201504i	$-0.0645828\pi$
$480$	3.89934e12	+	8.98030e12i	0.153033	+	0.352439i
$481$	5.97354e12			0.232010
$482$	3.08891e13	−	2.65633e13i	1.18732	−	1.02105i
$483$		−	1.91004e13i		−	0.726619i
$484$	−6.86342e12	+	4.53202e13i	−0.258413	+	1.70634i
$485$	−2.00634e13			−0.747644
$486$	8.99522e12	+	1.04601e13i	0.331765	+	0.385791i
$487$			3.58386e13i			1.30830i	0.756367	+	0.654148i	$0.226973\pi$
$487$			3.58386e13i			1.30830i	−0.756367	+	0.654148i	$0.773027\pi$
$488$	1.28829e13	+	2.05510e13i	0.465495	+	0.742563i
$489$	−2.88887e13			−1.03320
$490$	8.74297e11	−	7.51860e11i	0.0309513	−	0.0266168i
$491$		−	4.60633e13i		−	1.61416i	−0.590440	−	0.807082i	$-0.701046\pi$
$491$		−	4.60633e13i		−	1.61416i	0.590440	−	0.807082i	$-0.298954\pi$
$492$	3.06370e13	+	4.63976e12i	1.06272	+	0.160942i
$493$	−1.70978e13			−0.587093
$494$	2.30201e12	+	2.67688e12i	0.0782478	+	0.0909901i
$495$			5.74538e12i			0.193327i
$496$	7.67073e12	−	2.47446e13i	0.255522	−	0.824276i
$497$	−1.10624e13			−0.364809
$498$	−3.23511e13	+	2.78206e13i	−1.05619	+	0.908280i
$499$			5.33675e13i			1.72494i	0.506106	+	0.862471i	$0.331084\pi$
$499$			5.33675e13i			1.72494i	−0.506106	+	0.862471i	$0.668916\pi$
$500$	−4.18524e11	+	2.76357e12i	−0.0133928	+	0.0884343i
$501$	−3.04393e13			−0.964376
$502$	−2.37696e13	−	2.76404e13i	−0.745595	−	0.867012i
$503$			2.57488e13i			0.799683i	0.916584	+	0.399841i	$0.130935\pi$
$503$			2.57488e13i			0.799683i	−0.916584	+	0.399841i	$0.869065\pi$
$504$	−7.53669e12	+	4.72457e12i	−0.231754	+	0.145281i
$505$	−9.78850e12			−0.298029
$506$	−3.36159e13	+	2.89083e13i	−1.01343	+	0.871506i
$507$			5.86401e13i			1.75047i
$508$	2.50669e13	+	3.79620e12i	0.740937	+	0.112210i
$509$	3.08784e13			0.903787			0.451893	−	0.892072i	$-0.350749\pi$
$509$	3.08784e13			0.903787			0.451893	+	0.892072i	$0.350749\pi$
$510$	1.53048e13	+	1.77971e13i	0.443586	+	0.515821i
$511$		−	1.67252e13i		−	0.480028i
$512$	3.49754e13	−	3.82905e12i	0.994061	−	0.108828i
$513$	−2.65231e12			−0.0746514
$514$	−1.23849e13	+	1.06505e13i	−0.345204	+	0.296862i
$515$		−	2.78967e13i		−	0.770046i
$516$	−8.94761e11	+	5.90824e12i	−0.0244601	+	0.161514i
$517$	2.94912e13			0.798434
$518$	−3.38169e12	−	3.93238e12i	−0.0906745	−	0.105440i
$519$			3.81213e12i			0.101235i
$520$	1.57396e13	+	2.51080e13i	0.413978	+	0.660383i
$521$	−4.01792e13			−1.04668			−0.523339	−	0.852125i	$-0.675314\pi$
$521$	−4.01792e13			−1.04668			−0.523339	+	0.852125i	$0.675314\pi$
$522$	2.55123e12	−	2.19396e12i	0.0658260	−	0.0566077i
$523$		−	3.84465e13i		−	0.982536i	−0.871008	−	0.491268i	$-0.836534\pi$
$523$		−	3.84465e13i		−	0.982536i	0.871008	−	0.491268i	$-0.163466\pi$
$524$	−6.28862e13	−	9.52368e12i	−1.59184	−	0.241073i
$525$	7.15931e12			0.179504
$526$	3.54548e13	+	4.12285e13i	0.880535	+	1.02393i
$527$		−	6.21118e13i		−	1.52799i
$528$	−5.55991e13	−	1.72355e13i	−1.35487	−	0.420004i
$529$	1.42745e13			0.344573
$530$	−3.71533e12	+	3.19504e12i	−0.0888420	+	0.0764006i
$531$		−	1.02858e13i		−	0.243651i
$532$	4.58997e11	−	3.03082e12i	0.0107709	−	0.0711218i
$533$	9.37900e13			2.18032
$534$	−5.65942e12	−	6.58103e12i	−0.130336	−	0.151561i
$535$			2.05976e13i			0.469945i
$536$	−1.15935e12	+	7.26769e11i	−0.0262054	+	0.0164275i
$537$	2.46745e13			0.552557
$538$	9.26592e12	−	7.96831e12i	0.205578	−	0.176789i
$539$			6.85598e12i			0.150704i
$540$	−2.20110e13	−	3.33341e12i	−0.479369	−	0.0725971i
$541$	2.05539e13			0.443514			0.221757	−	0.975102i	$-0.428821\pi$
$541$	2.05539e13			0.443514			0.221757	+	0.975102i	$0.428821\pi$
$542$	−3.36394e13	−	3.91174e13i	−0.719203	−	0.836322i
$543$		−	2.64088e13i		−	0.559434i
$544$	7.73770e13	−	3.35979e13i	1.62412	−	0.705209i
$545$	−1.41659e13			−0.294619
$546$	5.75498e13	−	4.94905e13i	1.18599	−	1.01990i
$547$			3.41477e13i			0.697307i	0.937252	+	0.348654i	$0.113361\pi$
$547$			3.41477e13i			0.697307i	−0.937252	+	0.348654i	$0.886639\pi$
$548$	8.29215e12	−	5.47543e13i	0.167789	−	1.10794i
$549$	−1.14445e13			−0.229475
$550$	−1.08356e13	−	1.26001e13i	−0.215297	−	0.250357i
$551$			1.15958e12i			0.0228318i
$552$	−1.89341e13	−	3.02039e13i	−0.369444	−	0.589341i
$553$	−3.94270e13			−0.762373
$554$	−3.07524e13	+	2.64459e13i	−0.589292	+	0.506768i
$555$		−	2.69346e12i		−	0.0511500i
$556$	−1.73453e12	−	2.62683e11i	−0.0326444	−	0.00494376i
$557$	7.49932e13			1.39877			0.699384	−	0.714746i	$-0.253458\pi$
$557$	7.49932e13			1.39877			0.699384	+	0.714746i	$0.253458\pi$
$558$	7.97005e12	+	9.26794e12i	0.147330	+	0.171322i
$559$			1.80871e13i			0.331367i
$560$	7.61824e12	−	2.45753e13i	0.138329	−	0.446230i
$561$	−1.39560e14			−2.51158
$562$	−3.51059e13	+	3.01896e13i	−0.626179	+	0.538488i
$563$			4.72984e13i			0.836190i	0.908403	+	0.418095i	$0.137302\pi$
$563$			4.72984e13i			0.836190i	−0.908403	+	0.418095i	$0.862698\pi$
$564$	−3.55050e12	+	2.34445e13i	−0.0622148	+	0.410813i
$565$	−2.40073e13			−0.416967
$566$	3.34728e12	+	3.89237e12i	0.0576249	+	0.0670089i
$567$			4.09922e13i			0.699498i
$568$	−1.74931e13	+	1.09660e13i	−0.295887	+	0.185484i
$569$	4.38722e13			0.735576			0.367788	−	0.929910i	$-0.380115\pi$
$569$	4.38722e13			0.735576			0.367788	+	0.929910i	$0.380115\pi$
$570$	1.20700e12	−	1.03797e12i	0.0200601	−	0.0172509i
$571$		−	1.82529e13i		−	0.300712i	−0.988632	−	0.150356i	$-0.951958\pi$
$571$		−	1.82529e13i		−	0.300712i	0.988632	−	0.150356i	$-0.0480420\pi$
$572$	−1.74203e14	−	2.63818e13i	−2.84495	−	0.430847i
$573$	1.09173e13			0.176744
$574$	−5.30956e13	−	6.17419e13i	−0.852116	−	0.990879i
$575$		−	1.01773e13i		−	0.161917i
$576$	−7.23451e12	+	1.49421e13i	−0.114103	+	0.235668i
$577$	5.14350e13			0.804229			0.402114	−	0.915589i	$-0.368275\pi$
$577$	5.14350e13			0.804229			0.402114	+	0.915589i	$0.368275\pi$
$578$	1.04433e14	−	8.98080e13i	1.61882	−	1.39212i
$579$			1.20319e13i			0.184902i
$580$	−1.45735e12	+	9.62307e12i	−0.0222036	+	0.146613i
$581$	1.12132e14			1.69375
$582$	6.25364e13	+	7.27202e13i	0.936522	+	1.08903i
$583$		−	2.91346e13i		−	0.432580i
$584$	−1.65795e13	−	2.64479e13i	−0.244066	−	0.389338i
$585$	−1.39823e13			−0.204079
$586$	−4.25866e13	+	3.66227e13i	−0.616289	+	0.529984i
$587$			5.34075e13i			0.766323i	0.923681	+	0.383161i	$0.125165\pi$
$587$			5.34075e13i			0.766323i	−0.923681	+	0.383161i	$0.874835\pi$
$588$	−5.45027e12	−	8.25405e11i	−0.0775410	−	0.0117430i
$589$	−4.21242e12			−0.0594231
$590$	1.93987e13	+	2.25577e13i	0.271340	+	0.315526i
$591$			5.08790e13i			0.705669i
$592$	−9.24568e12	−	2.86612e12i	−0.127154	−	0.0394172i
$593$	−6.93655e13			−0.945954			−0.472977	−	0.881075i	$-0.656821\pi$
$593$	−6.93655e13			−0.945954			−0.472977	+	0.881075i	$0.656821\pi$
$594$	1.00356e14	−	8.63018e13i	1.35709	−	1.16705i
$595$		−	6.16868e13i		−	0.827194i
$596$	−1.41353e13	+	9.33377e13i	−0.187964	+	1.24115i
$597$	−3.22294e13			−0.424992
$598$	−7.03529e13	−	8.18096e13i	−0.919975	−	1.06979i
$599$			8.80310e13i			1.14157i	0.821100	+	0.570784i	$0.193361\pi$
$599$			8.80310e13i			1.14157i	−0.821100	+	0.570784i	$0.806639\pi$
$600$	1.13212e13	−	7.09696e12i	0.145591	−	0.0912675i
$601$	1.72426e13			0.219902			0.109951	−	0.993937i	$-0.464931\pi$
$601$	1.72426e13			0.219902			0.109951	+	0.993937i	$0.464931\pi$
$602$	1.19067e13	−	1.02393e13i	0.150595	−	0.129505i
$603$		−	6.45625e11i		−	0.00809829i
$604$	−1.64062e13	−	2.48460e12i	−0.204091	−	0.0309081i
$605$	6.25577e13			0.771798
$606$	3.05102e13	+	3.54787e13i	0.373321	+	0.434114i
$607$		−	6.87730e13i		−	0.834593i	−0.908770	−	0.417297i	$-0.862978\pi$
$607$		−	6.87730e13i		−	0.834593i	0.908770	−	0.417297i	$-0.137022\pi$
$608$	−2.27861e12	−	5.24771e12i	−0.0274253	−	0.0631614i
$609$	2.49295e13			0.297596
$610$	2.50988e13	−	2.15840e13i	0.297169	−	0.255553i
$611$			7.17713e13i			0.842839i
$612$	−5.95988e12	+	3.93540e13i	−0.0694194	+	0.458386i
$613$	−4.11211e13			−0.475075			−0.237537	−	0.971378i	$-0.576340\pi$
$613$	−4.11211e13			−0.475075			−0.237537	+	0.971378i	$0.576340\pi$
$614$	6.99574e13	+	8.13497e13i	0.801663	+	0.932210i
$615$		−	4.22898e13i		−	0.480684i
$616$	8.12509e13	+	1.29613e14i	0.916062	+	1.46131i
$617$	−4.43629e13			−0.496128			−0.248064	−	0.968744i	$-0.579794\pi$
$617$	−4.43629e13			−0.496128			−0.248064	+	0.968744i	$0.579794\pi$
$618$	−1.01112e14	+	8.69525e13i	−1.12166	+	0.964583i
$619$		−	1.10379e14i		−	1.21460i	−0.794473	−	0.607300i	$-0.792253\pi$
$619$		−	1.10379e14i		−	1.21460i	0.794473	−	0.607300i	$-0.207747\pi$
$620$	−3.49580e13	−	5.29414e12i	−0.381582	−	0.0577879i
$621$	8.10587e13			0.877691
$622$	8.98125e13	+	1.04438e14i	0.964683	+	1.12178i
$623$			2.28106e13i			0.243050i
$624$	4.19452e13	−	1.35309e14i	0.443363	−	1.43022i
$625$	3.81470e12			0.0400000
$626$	5.62379e13	−	4.83623e13i	0.585002	−	0.503078i
$627$			9.46496e12i			0.0976744i
$628$	−4.99816e12	+	3.30036e13i	−0.0511696	+	0.337880i
$629$	−2.32077e13			−0.235711
$630$	7.91552e12	+	9.20452e12i	0.0797584	+	0.0927467i
$631$		−	7.39612e13i		−	0.739362i	−0.929159	−	0.369681i	$-0.879467\pi$
$631$		−	7.39612e13i		−	0.739362i	0.929159	−	0.369681i	$-0.120533\pi$
$632$	−6.23467e13	+	3.90836e13i	−0.618341	+	0.387623i
$633$	−1.84753e13			−0.181791
$634$	−1.21464e14	+	1.04454e14i	−1.18578	+	1.01972i
$635$		−	3.46010e13i		−	0.335135i
$636$	2.31610e13	+	3.50757e12i	0.222573	+	0.0337071i
$637$	−1.66851e13			−0.159086
$638$	−3.77307e13	−	4.38749e13i	−0.356937	−	0.415062i
$639$		−	9.74166e12i		−	0.0914384i
$640$	−1.23144e13	−	4.64133e13i	−0.114687	−	0.432258i
$641$	−1.00231e14			−0.926219			−0.463109	−	0.886301i	$-0.653266\pi$
$641$	−1.00231e14			−0.926219			−0.463109	+	0.886301i	$0.653266\pi$
$642$	7.46564e13	−	6.42015e13i	0.684529	−	0.588668i
$643$		−	1.21171e13i		−	0.110241i	−0.998480	−	0.0551204i	$-0.982446\pi$
$643$		−	1.21171e13i		−	0.110241i	0.998480	−	0.0551204i	$-0.0175543\pi$
$644$	−1.40277e13	+	9.26266e13i	−0.126636	+	0.836193i
$645$	8.15544e12			0.0730548
$646$	−8.94349e12	−	1.03999e13i	−0.0794959	−	0.0924414i
$647$			4.51027e12i			0.0397815i	0.999802	+	0.0198908i	$0.00633185\pi$
$647$			4.51027e12i			0.0397815i	−0.999802	+	0.0198908i	$0.993668\pi$
$648$	4.06353e13	+	6.48219e13i	0.355654	+	0.567345i
$649$	−1.76891e14			−1.53632
$650$	3.06643e13	−	2.63700e13i	0.264281	−	0.227271i
$651$			9.05621e13i			0.774536i
$652$	1.40095e14	+	2.12164e13i	1.18901	+	0.180067i
$653$	−2.71710e13			−0.228844			−0.114422	−	0.993432i	$-0.536502\pi$
$653$	−2.71710e13			−0.228844			−0.114422	+	0.993432i	$0.536502\pi$
$654$	4.41542e13	+	5.13445e13i	0.369048	+	0.429146i
$655$			8.68050e13i			0.720009i
$656$	−1.45165e14	−	4.50007e13i	−1.19493	−	0.370424i
$657$	1.47284e13			0.120318
$658$	4.72470e13	−	4.06305e13i	0.383041	−	0.329399i
$659$			3.21903e13i			0.258999i	0.991579	+	0.129500i	$0.0413371\pi$
$659$			3.21903e13i			0.258999i	−0.991579	+	0.129500i	$0.958663\pi$
$660$	−1.18955e13	+	7.85476e13i	−0.0949867	+	0.627211i
$661$	−2.23070e14			−1.76780			−0.883901	−	0.467673i	$-0.845092\pi$
$661$	−2.23070e14			−1.76780			−0.883901	+	0.467673i	$0.845092\pi$
$662$	−8.57126e13	−	9.96705e13i	−0.674147	−	0.783929i
$663$		−	3.39641e14i		−	2.65126i
$664$	1.77317e14	−	1.11156e14i	1.37376	−	0.861176i
$665$	−4.18360e12			−0.0321693
$666$	3.46291e12	−	2.97796e12i	0.0264283	−	0.0227273i
$667$		−	3.54384e13i		−	0.268438i
$668$	1.47614e14	+	2.23552e13i	1.10980	+	0.168072i
$669$	2.29276e13			0.171091
$670$	1.21762e12	+	1.41591e12i	0.00901860	+	0.0104872i
$671$			1.96818e14i			1.44694i
$672$	−1.12819e14	+	4.89874e13i	−0.823261	+	0.357469i
$673$	1.60450e14			1.16216			0.581079	−	0.813847i	$-0.302631\pi$
$673$	1.60450e14			1.16216			0.581079	+	0.813847i	$0.302631\pi$
$674$	−1.36374e14	+	1.17276e14i	−0.980464	+	0.843160i
$675$			3.03828e13i			0.216825i
$676$	4.30663e13	−	2.84373e14i	0.305073	−	2.01444i
$677$	7.42140e13			0.521846			0.260923	−	0.965360i	$-0.415973\pi$
$677$	7.42140e13			0.521846			0.260923	+	0.965360i	$0.415973\pi$
$678$	7.48296e13	+	8.70153e13i	0.522306	+	0.607361i
$679$		−	2.52056e14i		−	1.74642i
$680$	−6.11496e13	−	9.75467e13i	−0.420581	−	0.670916i
$681$	9.84577e13			0.672224
$682$	1.59386e14	−	1.37065e14i	1.08026	−	0.928978i
$683$			1.52167e14i			1.02380i	0.859044	+	0.511901i	$0.171059\pi$
$683$			1.52167e14i			1.02380i	−0.859044	+	0.511901i	$0.828941\pi$
$684$	2.66898e12	+	4.04199e11i	0.0178265	+	0.00269969i
$685$	−7.55801e13			−0.501135
$686$	−9.40331e13	−	1.09346e14i	−0.618956	−	0.719750i
$687$		−	5.95454e13i		−	0.389103i
$688$	8.67822e12	−	2.79947e13i	0.0562974	−	0.181607i
$689$	7.09035e13			0.456637
$690$	−3.68878e13	+	3.17220e13i	−0.235851	+	0.202822i
$691$		−	2.33623e14i		−	1.48295i	−0.670981	−	0.741474i	$-0.734127\pi$
$691$		−	2.33623e14i		−	1.48295i	0.670981	−	0.741474i	$-0.265873\pi$
$692$	2.79969e12	−	1.84868e13i	0.0176433	−	0.116501i
$693$	−7.21792e13			−0.451592
$694$	−1.16523e14	−	1.35498e14i	−0.723793	−	0.841660i
$695$			2.39426e12i			0.0147655i
$696$	3.94215e13	−	2.47124e13i	0.241372	−	0.151310i
$697$	−3.64382e14			−2.21510
$698$	−1.02925e14	+	8.85112e13i	−0.621217	+	0.534221i
$699$			3.57731e13i			0.214373i
$700$	−3.47188e13	−	5.25792e12i	−0.206573	−	0.0312841i
$701$	3.29351e14			1.94567			0.972835	−	0.231498i	$-0.0743628\pi$
$701$	3.29351e14			1.94567			0.972835	+	0.231498i	$0.0743628\pi$
$702$	2.10029e14	+	2.44231e14i	1.23195	+	1.43257i
$703$			1.57395e12i			0.00916670i
$704$	2.56968e14	+	1.24416e14i	1.48599	+	0.719469i
$705$	3.23615e13			0.185816
$706$	−2.34156e14	+	2.01364e14i	−1.33500	+	1.14805i
$707$		−	1.22973e14i		−	0.696165i
$708$	2.12963e13	−	1.40622e14i	0.119712	−	0.790475i
$709$	3.11783e14			1.74029			0.870146	−	0.492795i	$-0.164025\pi$
$709$	3.11783e14			1.74029			0.870146	+	0.492795i	$0.164025\pi$
$710$	1.83724e13	+	2.13643e13i	0.101830	+	0.118412i
$711$		−	3.47199e13i		−	0.191087i
$712$	2.26119e13	+	3.60708e13i	0.123577	+	0.197132i
$713$	1.28738e14			0.698649
$714$	−2.23586e14	+	1.92274e14i	−1.20490	+	1.03617i
$715$			2.40460e14i			1.28681i
$716$	−1.19658e14	−	1.81214e13i	−0.635883	−	0.0963000i
$717$	−1.57716e14			−0.832303
$718$	−1.65883e14	−	1.92897e14i	−0.869321	−	1.01089i
$719$			3.50979e14i			1.82657i	0.407319	+	0.913286i	$0.366464\pi$
$719$			3.50979e14i			1.82657i	−0.407319	+	0.913286i	$0.633536\pi$
$720$	2.16413e13	+	6.70872e12i	0.111846	+	0.0346719i
$721$	3.50466e14			1.79875
$722$	1.48049e14	−	1.27316e14i	0.754605	−	0.648930i
$723$			2.65799e14i			1.34543i
$724$	−1.93950e13	+	1.28068e14i	−0.0974985	+	0.643797i
$725$	1.32832e13			0.0663151
$726$	−1.94989e14	−	2.26742e14i	−0.966778	−	1.12421i
$727$			1.35548e14i			0.667452i	0.942670	+	0.333726i	$0.108306\pi$
$727$			1.35548e14i			0.667452i	−0.942670	+	0.333726i	$0.891694\pi$
$728$	−3.15432e14	+	1.97737e14i	−1.54258	+	0.967008i
$729$	−2.27874e14			−1.10677
$730$	−3.23007e13	+	2.77773e13i	−0.155811	+	0.133991i
$731$		−	7.02698e13i		−	0.336652i
$732$	−1.56463e14	−	2.36953e13i	−0.744487	−	0.112747i
$733$	−7.21264e13			−0.340859			−0.170429	−	0.985370i	$-0.554515\pi$
$733$	−7.21264e13			−0.340859			−0.170429	+	0.985370i	$0.554515\pi$
$734$	−1.62373e14	−	1.88815e14i	−0.762138	−	0.886249i
$735$			7.52328e12i			0.0350728i
$736$	6.96378e13	+	1.60378e14i	0.322445	+	0.742601i
$737$	−1.11031e13			−0.0510633
$738$	5.43708e13	−	4.67567e13i	0.248361	−	0.213581i
$739$		−	9.07050e13i		−	0.411537i	−0.978601	−	0.205769i	$-0.934031\pi$
$739$		−	9.07050e13i		−	0.411537i	0.978601	−	0.205769i	$-0.0659694\pi$
$740$	−1.97812e12	+	1.30618e13i	−0.00891446	+	0.0588635i
$741$	−2.30344e13			−0.103107
$742$	−4.01393e13	−	4.66758e13i	−0.178464	−	0.207526i
$743$			3.37748e14i			1.49159i	0.666177	+	0.745794i	$0.267930\pi$
$743$			3.37748e14i			1.49159i	−0.666177	+	0.745794i	$0.732070\pi$
$744$	8.97734e13	+	1.43208e14i	0.393807	+	0.628206i
$745$	1.28839e14			0.561390
$746$	5.16779e13	−	4.44409e13i	0.223672	−	0.192349i
$747$			9.87452e13i			0.424535i
$748$	6.76791e14	+	1.02495e14i	2.89033	+	0.437719i
$749$	−2.58767e14			−1.09774
$750$	−1.18902e13	−	1.38265e13i	−0.0501052	−	0.0582646i
$751$			4.16582e14i			1.74381i	0.489671	+	0.871907i	$0.337117\pi$
$751$			4.16582e14i			1.74381i	−0.489671	+	0.871907i	$0.662883\pi$
$752$	3.44360e13	−	1.11085e14i	0.143194	−	0.461921i
$753$	2.37844e14			0.982466
$754$	1.06776e14	−	9.18234e13i	0.438146	−	0.376787i
$755$			2.26463e13i			0.0923129i
$756$	4.18776e13	−	2.76524e14i	0.169579	−	1.11976i
$757$	1.87029e14			0.752366			0.376183	−	0.926545i	$-0.377236\pi$
$757$	1.87029e14			0.752366			0.376183	+	0.926545i	$0.377236\pi$
$758$	1.64957e14	+	1.91819e14i	0.659211	+	0.766561i
$759$		−	2.89263e14i		−	1.14838i
$760$	−6.61561e12	+	4.14716e12i	−0.0260917	+	0.0163562i
$761$	1.62618e14			0.637155			0.318577	−	0.947897i	$-0.396795\pi$
$761$	1.62618e14			0.637155			0.318577	+	0.947897i	$0.396795\pi$
$762$	−1.25412e14	+	1.07850e14i	−0.488164	+	0.419801i
$763$		−	1.77966e14i		−	0.688198i
$764$	−5.29432e13	−	8.01788e12i	−0.203397	−	0.0308030i
$765$	5.43222e13			0.207334
$766$	−2.55054e14	−	2.96588e14i	−0.967137	−	1.12463i
$767$		−	4.30492e14i		−	1.62177i
$768$	−1.29843e14	+	1.89302e14i	−0.485974	+	0.708514i
$769$	−2.16562e13			−0.0805286			−0.0402643	−	0.999189i	$-0.512820\pi$
$769$	−2.16562e13			−0.0805286			−0.0402643	+	0.999189i	$0.512820\pi$
$770$	1.58295e14	−	1.36127e14i	0.584808	−	0.502912i
$771$		−	1.06571e14i		−	0.391173i
$772$	8.83642e12	−	5.83482e13i	0.0322248	−	0.212785i
$773$	−1.67235e14			−0.605942			−0.302971	−	0.953000i	$-0.597979\pi$
$773$	−1.67235e14			−0.605942			−0.302971	+	0.953000i	$0.597979\pi$
$774$	9.01686e12	+	1.04852e13i	0.0324602	+	0.0377462i
$775$			4.82542e13i			0.172595i
$776$	−2.49861e14	−	3.98582e14i	−0.887953	−	1.41647i
$777$	3.38380e13			0.119481
$778$	−3.79701e14	+	3.26527e14i	−1.33212	+	1.14557i
$779$			2.47124e13i			0.0861444i
$780$	−1.91158e14	−	2.89495e13i	−0.662093	−	0.100269i
$781$	−1.67533e14			−0.576559
$782$	2.73327e14	+	3.17837e14i	0.934649	+	1.08685i
$783$			1.05796e14i			0.359469i
$784$	2.58247e13	+	8.00554e12i	0.0871876	+	0.0270278i
$785$	4.55565e13			0.152828
$786$	3.14627e14	−	2.70566e14i	1.04878	−	0.901906i
$787$		−	3.25711e14i		−	1.07885i	−0.842035	−	0.539423i	$-0.818642\pi$
$787$		−	3.25711e14i		−	1.07885i	0.842035	−	0.539423i	$-0.181358\pi$
$788$	3.73664e13	−	2.46736e14i	0.122984	−	0.812084i
$789$	−3.54769e14			−1.16027
$790$	6.54805e13	+	7.61437e13i	0.212802	+	0.247456i
$791$		−	3.01604e14i		−	0.973992i
$792$	−1.14139e14	+	7.15506e13i	−0.366274	+	0.229608i
$793$	−4.78986e14			−1.52741
$794$	2.49423e14	−	2.14494e14i	0.790377	−	0.679692i
$795$		−	3.19703e13i		−	0.100672i
$796$	1.56295e14	+	2.36698e13i	0.489081	+	0.0740679i
$797$	−3.41010e14			−1.06041			−0.530207	−	0.847868i	$-0.677886\pi$
$797$	−3.41010e14			−1.06041			−0.530207	+	0.847868i	$0.677886\pi$
$798$	1.30400e13	+	1.51636e13i	0.0402963	+	0.0468583i
$799$		−	2.78837e14i		−	0.856282i
$800$	−6.01137e13	+	2.61020e13i	−0.183452	+	0.0796569i
$801$	−2.00873e13			−0.0609198
$802$	1.24182e14	−	1.06792e14i	0.374273	−	0.321860i
$803$		−	2.53292e14i		−	0.758655i
$804$	1.33673e12	−	8.82662e12i	0.00397890	−	0.0262733i
$805$	1.27857e14			0.378221
$806$	3.33569e14	+	3.87890e14i	0.980643	+	1.14034i
$807$			7.97328e13i			0.232953i
$808$	−1.21902e14	−	1.94460e14i	−0.353960	−	0.564641i
$809$	4.70292e14			1.35714			0.678570	−	0.734536i	$-0.262600\pi$
$809$	4.70292e14			1.35714			0.678570	+	0.734536i	$0.262600\pi$
$810$	7.91667e13	−	6.80801e13i	0.227048	−	0.195252i
$811$			6.93252e14i			1.97600i	0.154455	+	0.988000i	$0.450638\pi$
$811$			6.93252e14i			1.97600i	−0.154455	+	0.988000i	$0.549362\pi$
$812$	−1.20895e14	−	1.83086e13i	−0.342473	−	0.0518652i
$813$	3.36603e14			0.947689
$814$	−5.12136e13	−	5.95535e13i	−0.143306	−	0.166642i
$815$		−	1.93380e14i		−	0.537803i
$816$	−1.62960e14	+	5.25686e14i	−0.450434	+	1.45303i
$817$	−4.76569e12			−0.0130923
$818$	−2.27169e14	+	1.95356e14i	−0.620271	+	0.533408i
$819$		−	1.75659e14i		−	0.476707i
$820$	−3.10583e13	+	2.05083e14i	−0.0837739	+	0.553171i
$821$	−1.68591e14			−0.451980			−0.225990	−	0.974130i	$-0.572562\pi$
$821$	−1.68591e14			−0.451980			−0.225990	+	0.974130i	$0.572562\pi$
$822$	2.35579e14	+	2.73942e14i	0.627737	+	0.729961i
$823$			2.41032e14i			0.638373i	0.947692	+	0.319187i	$0.103410\pi$
$823$			2.41032e14i			0.638373i	−0.947692	+	0.319187i	$0.896590\pi$
$824$	5.54200e14	−	3.47414e14i	1.45892	−	0.914559i
$825$	1.08423e14			0.283696
$826$	−2.83393e14	+	2.43706e14i	−0.737036	+	0.633821i
$827$		−	7.67653e14i		−	1.98444i	−0.124503	−	0.992219i	$-0.539734\pi$
$827$		−	7.67653e14i		−	1.98444i	0.124503	−	0.992219i	$-0.460266\pi$
$828$	−8.15682e13	−	1.23529e13i	−0.209589	−	0.0317408i
$829$	1.04564e14			0.267062			0.133531	−	0.991045i	$-0.457368\pi$
$829$	1.04564e14			0.267062			0.133531	+	0.991045i	$0.457368\pi$
$830$	−1.86230e14	−	2.16557e14i	−0.472780	−	0.549770i
$831$		−	2.64623e14i		−	0.667764i
$832$	−3.02785e14	+	6.25370e14i	−0.759482	+	1.56863i
$833$	6.48229e13			0.161623
$834$	8.67806e12	−	7.46278e12i	0.0215076	−	0.0184957i
$835$		−	2.03759e14i		−	0.501979i
$836$	6.95122e12	−	4.58999e13i	0.0170228	−	0.112404i
$837$	−3.84329e14			−0.935570
$838$	3.56398e14	+	4.14436e14i	0.862412	+	1.00285i
$839$			4.91176e14i			1.18148i	0.806861	+	0.590741i	$0.201165\pi$
$839$			4.91176e14i			1.18148i	−0.806861	+	0.590741i	$0.798835\pi$
$840$	8.91591e13	+	1.42228e14i	0.213191	+	0.340085i
$841$	−3.74454e14			−0.890058
$842$	1.84382e14	−	1.58561e14i	0.435670	−	0.374659i
$843$		−	3.02084e14i		−	0.709562i
$844$	8.95951e13	+	1.35686e13i	0.209205	+	0.0316826i
$845$	−3.92534e14			−0.911159
$846$	3.57798e13	+	4.16064e13i	0.0825631	+	0.0960081i
$847$			7.85912e14i			1.80284i
$848$	−1.09742e14	−	3.40197e13i	−0.250262	−	0.0775802i
$849$	−3.34937e13			−0.0759319
$850$	−1.19133e14	+	1.02450e14i	−0.268496	+	0.230896i
$851$		−	4.81022e13i		−	0.107775i
$852$	2.01696e13	−	1.33183e14i	0.0449261	−	0.296654i
$853$	−7.29444e14			−1.61528			−0.807638	−	0.589678i	$-0.799254\pi$
$853$	−7.29444e14			−1.61528			−0.807638	+	0.589678i	$0.799254\pi$
$854$	2.71159e14	+	3.15316e14i	0.596946	+	0.694156i
$855$		−	3.68413e12i		−	0.00806315i
$856$	−4.09194e14	+	2.56514e14i	−0.890350	+	0.558139i
$857$	3.90478e14			0.844680			0.422340	−	0.906438i	$-0.361209\pi$
$857$	3.90478e14			0.844680			0.422340	+	0.906438i	$0.361209\pi$
$858$	8.71555e14	−	7.49502e14i	1.87438	−	1.61189i
$859$			3.35693e14i			0.717756i	0.933384	+	0.358878i	$0.116841\pi$
$859$			3.35693e14i			0.717756i	−0.933384	+	0.358878i	$0.883159\pi$
$860$	−3.95495e13	−	5.98949e12i	−0.0840714	−	0.0127320i
$861$	5.31286e14			1.12283
$862$	1.25247e14	+	1.45643e14i	0.263167	+	0.306023i
$863$			1.64979e14i			0.344647i	0.985040	+	0.172323i	$0.0551274\pi$
$863$			1.64979e14i			0.344647i	−0.985040	+	0.172323i	$0.944873\pi$
$864$	−2.07894e14	−	4.78786e14i	−0.431790	−	0.994427i
$865$	−2.55182e13			−0.0526950
$866$	−6.53115e13	+	5.61653e13i	−0.134091	+	0.115313i
$867$			8.98640e14i			1.83438i
$868$	6.65103e13	−	4.39177e14i	0.134987	−	0.891336i
$869$	−5.97097e14			−1.20489
$870$	−4.14030e13	−	4.81453e13i	−0.0830684	−	0.0965957i
$871$		−	2.70212e13i		−	0.0539032i
$872$	−1.76416e14	−	2.81421e14i	−0.349909	−	0.558180i
$873$	2.21964e14			0.437735
$874$	2.15557e13	−	1.85370e13i	0.0422673	−	0.0363482i
$875$			4.79241e13i			0.0934358i
$876$	2.01359e14	+	3.04944e13i	0.390346	+	0.0591152i
$877$	9.67288e14			1.86448			0.932240	−	0.361841i	$-0.117852\pi$
$877$	9.67288e14			1.86448			0.932240	+	0.361841i	$0.117852\pi$
$878$	−2.38943e14	−	2.77854e14i	−0.457954	−	0.532530i
$879$		−	3.66455e14i		−	0.698356i
$880$	1.15373e14	−	3.72178e14i	0.218621	−	0.705240i
$881$	1.03943e13			0.0195846			0.00979230	−	0.999952i	$-0.496883\pi$
$881$	1.03943e13			0.0195846			0.00979230	+	0.999952i	$0.496883\pi$
$882$	−9.67247e12	+	8.31793e12i	−0.0181215	+	0.0155838i
$883$		−	6.42429e14i		−	1.19680i	−0.801198	−	0.598400i	$-0.795803\pi$
$883$		−	6.42429e14i		−	1.19680i	0.801198	−	0.598400i	$-0.204197\pi$
$884$	−2.49438e14	+	1.64708e15i	−0.462063	+	3.05107i
$885$	−1.94108e14			−0.357542
$886$	1.80116e14	+	2.09447e14i	0.329901	+	0.383624i
$887$		−	1.79852e14i		−	0.327565i	−0.986496	−	0.163783i	$-0.947630\pi$
$887$		−	1.79852e14i		−	0.327565i	0.986496	−	0.163783i	$-0.0523696\pi$
$888$	5.35087e13	−	3.35433e13i	0.0969080	−	0.0607492i
$889$	4.34693e14			0.782841
$890$	4.40531e13	−	3.78839e13i	0.0788908	−	0.0678429i
$891$			6.20802e14i			1.10551i
$892$	−1.11186e14	−	1.68384e13i	−0.196892	−	0.0298179i
$893$	−1.89107e13			−0.0333005
$894$	−4.01583e14	−	4.66979e14i	−0.703215	−	0.817730i
$895$			1.65170e14i			0.287618i
$896$	5.83091e14	−	1.54706e14i	1.00971	−	0.267896i
$897$	7.03967e14			1.21224
$898$	−1.12227e13	+	9.65110e12i	−0.0192184	+	0.0165270i
$899$			1.68027e14i			0.286141i
$900$	4.63019e12	−	3.05738e13i	0.00784127	−	0.0517770i
$901$	−2.75466e14			−0.463921
$902$	−8.04099e14	−	9.35043e14i	−1.34672	−	1.56603i
$903$			1.02457e14i			0.170648i
$904$	−2.98978e14	−	4.76933e14i	−0.495219	−	0.789979i
$905$	1.76779e14			0.291198
$906$	8.20821e13	−	7.05873e13i	0.134464	−	0.115634i
$907$		−	3.05101e14i		−	0.497059i	−0.968624	−	0.248529i	$-0.920053\pi$
$907$		−	3.05101e14i		−	0.497059i	0.968624	−	0.248529i	$-0.0799472\pi$
$908$	−4.77467e14	−	7.23090e13i	−0.773596	−	0.117156i
$909$	1.08292e14			0.174492
$910$	3.31287e14	+	3.85235e14i	0.530881	+	0.617333i
$911$		−	4.85024e14i		−	0.772985i	−0.922292	−	0.386493i	$-0.873686\pi$
$911$		−	4.85024e14i		−	0.772985i	0.922292	−	0.386493i	$-0.126314\pi$
$912$	3.56520e13	+	1.10520e13i	0.0565080	+	0.0175172i
$913$	1.69817e15			2.67688
$914$	−3.38814e14	+	2.91366e14i	−0.531165	+	0.456781i
$915$			2.15974e14i			0.336741i
$916$	−4.37311e13	+	2.88763e14i	−0.0678130	+	0.447779i
$917$	−1.09053e15			−1.68187
$918$	−8.15979e14	−	9.48858e14i	−1.25160	−	1.45542i
$919$			7.20957e14i			1.09985i	0.835215	+	0.549923i	$0.185343\pi$
$919$			7.20957e14i			1.09985i	−0.835215	+	0.549923i	$0.814657\pi$
$920$	2.02183e14	−	1.26744e14i	0.306765	−	0.192303i
$921$	−7.00010e14			−1.05635
$922$	−5.05056e14	+	4.34328e14i	−0.758027	+	0.651873i
$923$		−	4.07716e14i		−	0.608625i
$924$	−9.86794e14	−	1.49443e14i	−1.46510	−	0.221879i
$925$	1.80299e13			0.0266247
$926$	7.15165e14	+	8.31626e14i	1.05039	+	1.22144i
$927$			3.08625e14i			0.450851i
$928$	−2.09322e14	+	9.08900e13i	−0.304142	+	0.132061i
$929$	2.60027e14			0.375785			0.187893	−	0.982190i	$-0.439834\pi$
$929$	2.60027e14			0.375785			0.187893	+	0.982190i	$0.439834\pi$
$930$	1.74899e14	−	1.50406e14i	0.251404	−	0.216197i
$931$		−	4.39629e12i		−	0.00628547i
$932$	2.62724e13	−	1.73480e14i	0.0373611	−	0.246701i
$933$	−8.98684e14			−1.27116
$934$	−2.88265e14	−	3.35208e14i	−0.405562	−	0.471606i
$935$		−	9.34208e14i		−	1.30733i
$936$	−1.74129e14	−	2.77774e14i	−0.242378	−	0.386644i
$937$	2.28649e14			0.316571			0.158285	−	0.987393i	$-0.449403\pi$
$937$	2.28649e14			0.316571			0.158285	+	0.987393i	$0.449403\pi$
$938$	−1.77881e13	+	1.52970e13i	−0.0244971	+	0.0210665i
$939$			4.83924e14i			0.662902i
$940$	−1.56936e14	−	2.37669e13i	−0.213837	−	0.0323842i
$941$	4.79378e14			0.649726			0.324863	−	0.945761i	$-0.394682\pi$
$941$	4.79378e14			0.649726			0.324863	+	0.945761i	$0.394682\pi$
$942$	−1.41997e14	−	1.65121e14i	−0.191437	−	0.222611i
$943$		−	7.55247e14i		−	1.01282i
$944$	−2.06551e14	+	6.66303e14i	−0.275529	+	0.888816i
$945$	−3.81700e14			−0.506480
$946$	1.80320e14	−	1.55068e14i	0.238006	−	0.204676i
$947$			1.22091e15i			1.60300i	0.597996	+	0.801499i	$0.295964\pi$
$947$			1.22091e15i			1.60300i	−0.597996	+	0.801499i	$0.704036\pi$
$948$	7.18857e13	−	4.74672e14i	0.0938860	−	0.619943i
$949$	6.16426e14			0.800848
$950$	6.94814e12	+	8.07961e12i	0.00897946	+	0.0104417i
$951$		−	1.04520e15i		−	1.34368i
$952$	1.22548e15	−	7.68223e14i	1.56719	−	0.982432i
$953$	−1.76783e14			−0.224893			−0.112447	−	0.993658i	$-0.535869\pi$
$953$	−1.76783e14			−0.224893			−0.112447	+	0.993658i	$0.535869\pi$
$954$	4.11033e13	−	3.53472e13i	0.0520157	−	0.0447314i
$955$			7.30801e13i			0.0919989i
$956$	7.64840e14	+	1.15830e14i	0.957814	+	0.145054i
$957$	3.77542e14			0.470333
$958$	−2.12032e14	−	2.46561e14i	−0.262769	−	0.305560i
$959$		−	9.49512e14i		−	1.17060i
$960$	2.81978e14	+	1.36525e14i	0.345828	+	0.167439i
$961$	2.09233e14			0.255278
$962$	1.44933e14	−	1.24636e14i	0.175910	−	0.151276i
$963$		−	2.27874e14i		−	0.275146i
$964$	1.95207e14	−	1.28898e15i	0.234483	−	1.54832i
$965$	−8.05409e13			−0.0962454
$966$	−3.98524e14	−	4.63422e14i	−0.473771	−	0.550923i
$967$			8.92243e14i			1.05524i	0.849481	+	0.527619i	$0.176915\pi$
$967$			8.92243e14i			1.05524i	−0.849481	+	0.527619i	$0.823085\pi$
$968$	7.79068e14	+	1.24278e15i	0.916640	+	1.46224i
$969$	8.94906e13			0.104751
$970$	−4.86786e14	+	4.18616e14i	−0.566864	+	0.487480i
$971$			5.15365e14i			0.597062i	0.954400	+	0.298531i	$0.0964966\pi$
$971$			5.15365e14i			0.597062i	−0.954400	+	0.298531i	$0.903503\pi$
$972$	4.36492e14	+	6.61036e13i	0.503089	+	0.0761893i
$973$	−3.00791e13			−0.0344906
$974$	7.47761e14	+	8.69530e14i	0.853037	+	0.991950i
$975$			2.63865e14i			0.299473i
$976$	7.41360e14	+	2.29819e14i	0.837106	+	0.259499i
$977$	−3.34826e14			−0.376138			−0.188069	−	0.982156i	$-0.560223\pi$
$977$	−3.34826e14			−0.376138			−0.188069	+	0.982156i	$0.560223\pi$
$978$	−7.00910e14	+	6.02754e14i	−0.783372	+	0.673668i
$979$			3.45452e14i			0.384126i
$980$	5.52522e12	−	3.64839e13i	0.00611251	−	0.0403618i
$981$	1.56719e14			0.172495
$982$	−9.61096e14	−	1.11761e15i	−1.05247	−	1.22386i
$983$			4.72944e13i			0.0515278i	0.999668	+	0.0257639i	$0.00820182\pi$
$983$			4.72944e13i			0.0515278i	−0.999668	+	0.0257639i	$0.991798\pi$
$984$	8.40134e14	−	5.26660e14i	0.910696	−	0.570893i
$985$	−3.40581e14			−0.367316
$986$	−4.14835e14	+	3.56741e14i	−0.445134	+	0.382797i
$987$			4.06558e14i			0.434047i
$988$	1.11705e14	+	1.69169e13i	0.118655	+	0.0179695i
$989$	1.45647e14			0.153929
$990$	1.19876e14	+	1.39397e14i	0.126053	+	0.146581i
$991$		−	5.38725e14i		−	0.563637i	−0.959468	−	0.281818i	$-0.909062\pi$
$991$		−	5.38725e14i		−	0.563637i	0.959468	−	0.281818i	$-0.0909375\pi$
$992$	−3.30179e14	−	7.60412e14i	−0.343709	−	0.791572i
$993$	8.57660e14			0.888319
$994$	−2.68400e14	+	2.30813e14i	−0.276598	+	0.237864i
$995$		−	2.15742e14i		−	0.221218i
$996$	−2.04447e14	+	1.34999e15i	−0.208585	+	1.37732i
$997$	−2.09210e14			−0.212376			−0.106188	−	0.994346i	$-0.533865\pi$
$997$	−2.09210e14			−0.212376			−0.106188	+	0.994346i	$0.533865\pi$
$998$	1.11350e15	+	1.29483e15i	1.12470	+	1.30785i
$999$			1.43602e14i			0.144323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.b.a.11.15	✓	20
3.2	odd	2		180.11.c.a.91.6		20
4.3	odd	2	inner	20.11.b.a.11.16	yes	20
5.2	odd	4		100.11.d.c.99.30		40
5.3	odd	4		100.11.d.c.99.11		40
5.4	even	2		100.11.b.e.51.6		20
8.3	odd	2		320.11.b.d.191.15		20
8.5	even	2		320.11.b.d.191.6		20
12.11	even	2		180.11.c.a.91.5		20
20.3	even	4		100.11.d.c.99.29		40
20.7	even	4		100.11.d.c.99.12		40
20.19	odd	2		100.11.b.e.51.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.15	✓	20	1.1	even	1	trivial
20.11.b.a.11.16	yes	20	4.3	odd	2	inner
100.11.b.e.51.5		20	20.19	odd	2
100.11.b.e.51.6		20	5.4	even	2
100.11.d.c.99.11		40	5.3	odd	4
100.11.d.c.99.12		40	20.7	even	4
100.11.d.c.99.29		40	20.3	even	4
100.11.d.c.99.30		40	5.2	odd	4
180.11.c.a.91.5		20	12.11	even	2
180.11.c.a.91.6		20	3.2	odd	2
320.11.b.d.191.6		20	8.5	even	2
320.11.b.d.191.15		20	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(24.2624 - 20.8647i) q^{2} +208.777i q^{3} +(153.329 - 1012.46i) q^{4} -1397.54 q^{5} +(4356.06 + 5065.43i) q^{6} -17557.3i q^{7} +(-17404.4 - 27763.8i) q^{8} +15461.2 q^{9} +O(q^{10})\)	\(q+(24.2624 - 20.8647i) q^{2} +208.777i q^{3} +(153.329 - 1012.46i) q^{4} -1397.54 q^{5} +(4356.06 + 5065.43i) q^{6} -17557.3i q^{7} +(-17404.4 - 27763.8i) q^{8} +15461.2 q^{9} +(-33907.8 + 29159.3i) q^{10} -265895. i q^{11} +(211377. + 32011.6i) q^{12} +647096. q^{13} +(-366328. - 425983. i) q^{14} -291775. i q^{15} +(-1.00156e6 - 310478. i) q^{16} -2.51402e6 q^{17} +(375126. - 322594. i) q^{18} +170501. i q^{19} +(-214284. + 1.41495e6i) q^{20} +3.66556e6 q^{21} +(-5.54781e6 - 6.45125e6i) q^{22} -5.21076e6i q^{23} +(5.79644e6 - 3.63364e6i) q^{24} +1.95312e6 q^{25} +(1.57001e7 - 1.35015e7i) q^{26} +1.55560e7i q^{27} +(-1.77760e7 - 2.69205e6i) q^{28} +6.80100e6 q^{29} +(-6.08779e6 - 7.07915e6i) q^{30} +2.47062e7i q^{31} +(-3.07782e7 + 1.33642e7i) q^{32} +5.55127e7 q^{33} +(-6.09962e7 + 5.24543e7i) q^{34} +2.45371e7i q^{35} +(2.37066e6 - 1.56538e7i) q^{36} +9.23131e6 q^{37} +(3.55745e6 + 4.13676e6i) q^{38} +1.35099e8i q^{39} +(2.43234e7 + 3.88011e7i) q^{40} +1.44940e8 q^{41} +(8.89354e7 - 7.64809e7i) q^{42} +2.79512e7i q^{43} +(-2.69207e8 - 4.07695e7i) q^{44} -2.16077e7 q^{45} +(-1.08721e8 - 1.26426e8i) q^{46} +1.10913e8i q^{47} +(6.48207e7 - 2.09102e8i) q^{48} -2.57846e7 q^{49} +(4.73875e7 - 4.07514e7i) q^{50} -5.24869e8i q^{51} +(9.92188e7 - 6.55156e8i) q^{52} +1.09572e8 q^{53} +(3.24571e8 + 3.77426e8i) q^{54} +3.71599e8i q^{55} +(-4.87458e8 + 3.05575e8i) q^{56} -3.55966e7 q^{57} +(1.65009e8 - 1.41901e8i) q^{58} -6.65268e8i q^{59} +(-2.95409e8 - 4.47376e7i) q^{60} -7.40208e8 q^{61} +(5.15487e8 + 5.99431e8i) q^{62} -2.71458e8i q^{63} +(-4.67913e8 + 9.66426e8i) q^{64} -9.04344e8 q^{65} +(1.34687e9 - 1.15826e9i) q^{66} -4.17577e7i q^{67} +(-3.85473e8 + 2.54533e9i) q^{68} +1.08789e9 q^{69} +(5.11959e8 + 5.95330e8i) q^{70} -6.30071e8i q^{71} +(-2.69094e8 - 4.29262e8i) q^{72} +9.52604e8 q^{73} +(2.23974e8 - 1.92608e8i) q^{74} +4.07767e8i q^{75} +(1.72624e8 + 2.61428e7i) q^{76} -4.66840e9 q^{77} +(2.81879e9 + 3.27782e9i) q^{78} -2.24561e9i q^{79} +(1.39972e9 + 4.33906e8i) q^{80} -2.33477e9 q^{81} +(3.51659e9 - 3.02413e9i) q^{82} +6.38664e9i q^{83} +(5.62038e8 - 3.71122e9i) q^{84} +3.51345e9 q^{85} +(5.83192e8 + 6.78162e8i) q^{86} +1.41989e9i q^{87} +(-7.38225e9 + 4.62775e9i) q^{88} -1.29920e9 q^{89} +(-5.24255e8 + 4.50838e8i) q^{90} -1.13613e10i q^{91} +(-5.27567e9 - 7.98963e8i) q^{92} -5.15808e9 q^{93} +(2.31416e9 + 2.69101e9i) q^{94} -2.38282e8i q^{95} +(-2.79014e9 - 6.42578e9i) q^{96} +1.43562e10 q^{97} +(-6.25596e8 + 5.37987e8i) q^{98} -4.11106e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9	\( 20 q + 22 q^{2} - 644 q^{4} - 14784 q^{6} + 3448 q^{8} - 414868 q^{9} - 31250 q^{10} + 1329640 q^{12} - 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} - 1921656 q^{17} - 3556082 q^{18} - 1187500 q^{20} + 4157512 q^{21} - 5811280 q^{22} - 19112144 q^{24} + 39062500 q^{25} + 25066884 q^{26} - 87415400 q^{28} - 66014888 q^{29} + 39875000 q^{30} - 33171328 q^{32} + 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} - 153620656 q^{37} + 250352720 q^{38} - 112375000 q^{40} + 477406160 q^{41} - 570662040 q^{42} + 339141040 q^{44} - 140125000 q^{45} - 897549304 q^{46} - 479727360 q^{48} + 333772012 q^{49} + 42968750 q^{50} - 110465096 q^{52} - 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} + 3973032960 q^{57} + 2075027916 q^{58} - 677375000 q^{60} - 4283166080 q^{61} + 1664032240 q^{62} + 340459456 q^{64} + 290125000 q^{65} + 1884031760 q^{66} + 3042411896 q^{68} - 5321669928 q^{69} - 2070000000 q^{70} + 1632326712 q^{72} + 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} + 410885040 q^{77} - 19914223760 q^{78} + 3604750000 q^{80} + 9939722652 q^{81} - 3197757116 q^{82} + 2383099552 q^{84} + 4799500000 q^{85} + 19648321456 q^{86} + 2774318240 q^{88} + 3011851592 q^{89} - 2849906250 q^{90} - 27349072440 q^{92} - 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} - 39984502056 q^{97} + 38416891998 q^{98}+O(q^{100}) \) 20 * q + 22 * q^2 - 644 * q^4 - 14784 * q^6 + 3448 * q^8 - 414868 * q^9 - 31250 * q^10 + 1329640 * q^12 - 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 - 1921656 * q^17 - 3556082 * q^18 - 1187500 * q^20 + 4157512 * q^21 - 5811280 * q^22 - 19112144 * q^24 + 39062500 * q^25 + 25066884 * q^26 - 87415400 * q^28 - 66014888 * q^29 + 39875000 * q^30 - 33171328 * q^32 + 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 - 153620656 * q^37 + 250352720 * q^38 - 112375000 * q^40 + 477406160 * q^41 - 570662040 * q^42 + 339141040 * q^44 - 140125000 * q^45 - 897549304 * q^46 - 479727360 * q^48 + 333772012 * q^49 + 42968750 * q^50 - 110465096 * q^52 - 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 + 3973032960 * q^57 + 2075027916 * q^58 - 677375000 * q^60 - 4283166080 * q^61 + 1664032240 * q^62 + 340459456 * q^64 + 290125000 * q^65 + 1884031760 * q^66 + 3042411896 * q^68 - 5321669928 * q^69 - 2070000000 * q^70 + 1632326712 * q^72 + 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 + 410885040 * q^77 - 19914223760 * q^78 + 3604750000 * q^80 + 9939722652 * q^81 - 3197757116 * q^82 + 2383099552 * q^84 + 4799500000 * q^85 + 19648321456 * q^86 + 2774318240 * q^88 + 3011851592 * q^89 - 2849906250 * q^90 - 27349072440 * q^92 - 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 - 39984502056 * q^97 + 38416891998 * q^98

Introduction

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