LMFDB - Embedded newform 20.11.b.a.11.6

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			11.6
Root			$-7.66078 + 13.6916i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.11.b.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.5576 + 27.3833i) q^{2} +17.1314i q^{3} +(-475.690 - 906.805i) q^{4} +1397.54 q^{5} +(-469.114 - 283.655i) q^{6} +2883.30i q^{7} +(32707.6 + 1988.60i) q^{8} +58755.5 q^{9} +O(q^{10})$	\(q+(-16.5576 + 27.3833i) q^{2} +17.1314i q^{3} +(-475.690 - 906.805i) q^{4} +1397.54 q^{5} +(-469.114 - 283.655i) q^{6} +2883.30i q^{7} +(32707.6 + 1988.60i) q^{8} +58755.5 q^{9} +(-23140.0 + 38269.3i) q^{10} +104916. i q^{11} +(15534.8 - 8149.23i) q^{12} -145317. q^{13} +(-78954.1 - 47740.6i) q^{14} +23941.9i q^{15} +(-596015. + 862715. i) q^{16} -1.16784e6 q^{17} +(-972852. + 1.60892e6i) q^{18} +4.52473e6i q^{19} +(-664796. - 1.26730e6i) q^{20} -49394.9 q^{21} +(-2.87295e6 - 1.73716e6i) q^{22} +3.50848e6i q^{23} +(-34067.5 + 560327. i) q^{24} +1.95312e6 q^{25} +(2.40611e6 - 3.97926e6i) q^{26} +2.01816e6i q^{27} +(2.61459e6 - 1.37155e6i) q^{28} +2.68714e7 q^{29} +(-655607. - 396420. i) q^{30} +2.04707e7i q^{31} +(-1.37554e7 - 3.06054e7i) q^{32} -1.79736e6 q^{33} +(1.93367e7 - 3.19793e7i) q^{34} +4.02953e6i q^{35} +(-2.79494e7 - 5.32798e7i) q^{36} +4.45179e7 q^{37} +(-1.23902e8 - 7.49188e7i) q^{38} -2.48949e6i q^{39} +(4.57103e7 + 2.77915e6i) q^{40} +2.94019e7 q^{41} +(817862. - 1.35259e6i) q^{42} +1.50220e8i q^{43} +(9.51385e7 - 4.99075e7i) q^{44} +8.21133e7 q^{45} +(-9.60736e7 - 5.80921e7i) q^{46} +1.88353e8i q^{47} +(-1.47795e7 - 1.02106e7i) q^{48} +2.74162e8 q^{49} +(-3.23391e7 + 5.34830e7i) q^{50} -2.00067e7i q^{51} +(6.91259e7 + 1.31774e8i) q^{52} -5.81398e8 q^{53} +(-5.52638e7 - 3.34159e7i) q^{54} +1.46625e8i q^{55} +(-5.73372e6 + 9.43057e7i) q^{56} -7.75150e7 q^{57} +(-4.44926e8 + 7.35826e8i) q^{58} +1.80702e8i q^{59} +(2.17106e7 - 1.13889e7i) q^{60} -2.75462e8 q^{61} +(-5.60556e8 - 3.38947e8i) q^{62} +1.69410e8i q^{63} +(1.06583e9 + 1.30085e8i) q^{64} -2.03087e8 q^{65} +(2.97600e7 - 4.92177e7i) q^{66} -2.41173e9i q^{67} +(5.55529e8 + 1.05900e9i) q^{68} -6.01051e7 q^{69} +(-1.10342e8 - 6.67195e7i) q^{70} -2.50764e9i q^{71} +(1.92175e9 + 1.16841e8i) q^{72} -2.32959e8 q^{73} +(-7.37111e8 + 1.21905e9i) q^{74} +3.34598e7i q^{75} +(4.10305e9 - 2.15237e9i) q^{76} -3.02504e8 q^{77} +(6.81703e7 + 4.12200e7i) q^{78} -3.56415e9i q^{79} +(-8.32956e8 + 1.20568e9i) q^{80} +3.43488e9 q^{81} +(-4.86827e8 + 8.05122e8i) q^{82} +3.50970e9i q^{83} +(2.34966e7 + 4.47915e7i) q^{84} -1.63211e9 q^{85} +(-4.11353e9 - 2.48730e9i) q^{86} +4.60344e8i q^{87} +(-2.08636e8 + 3.43156e9i) q^{88} -9.00063e9 q^{89} +(-1.35960e9 + 2.24853e9i) q^{90} -4.18992e8i q^{91} +(3.18150e9 - 1.66895e9i) q^{92} -3.50692e8 q^{93} +(-5.15772e9 - 3.11868e9i) q^{94} +6.32350e9i q^{95} +(5.24313e8 - 2.35649e8i) q^{96} +4.72381e9 q^{97} +(-4.53947e9 + 7.50745e9i) q^{98} +6.16440e9i 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 $

$2$	−16.5576	+	27.3833i	−0.517426	+	0.855728i
$2$	−16.5576	+	27.3833i	−0.517426	+	0.855728i
$3$			17.1314i			0.0704996i	0.999379	+	0.0352498i	$0.0112227\pi$
$3$			17.1314i			0.0704996i	−0.999379	+	0.0352498i	$0.988777\pi$
$4$	−475.690	−	906.805i	−0.464541	−	0.885552i
$5$	1397.54			0.447214
$5$	1397.54			0.447214
$6$	−469.114	−	283.655i	−0.0603285	−	0.0364783i
$7$			2883.30i			0.171553i	0.996314	+	0.0857766i	$0.0273371\pi$
$7$			2883.30i			0.171553i	−0.996314	+	0.0857766i	$0.972663\pi$
$8$	32707.6	+	1988.60i	0.998157	+	0.0606872i
$9$	58755.5			0.995030
$10$	−23140.0	+	38269.3i	−0.231400	+	0.382693i
$11$			104916.i			0.651447i	0.945465	+	0.325723i	$0.105608\pi$
$11$			104916.i			0.651447i	−0.945465	+	0.325723i	$0.894392\pi$
$12$	15534.8	−	8149.23i	0.0624310	−	0.0327499i
$13$	−145317.			−0.391381			−0.195691	−	0.980666i	$-0.562695\pi$
$13$	−145317.			−0.391381			−0.195691	+	0.980666i	$0.562695\pi$
$14$	−78954.1	−	47740.6i	−0.146803	−	0.0887661i
$15$			23941.9i			0.0315284i
$16$	−596015.	+	862715.i	−0.568404	+	0.822750i
$17$	−1.16784e6			−0.822506			−0.411253	−	0.911521i	$-0.634909\pi$
$17$	−1.16784e6			−0.822506			−0.411253	+	0.911521i	$0.634909\pi$
$18$	−972852.	+	1.60892e6i	−0.514854	+	0.851475i
$19$			4.52473e6i			1.82736i	0.406431	+	0.913681i	$0.366773\pi$
$19$			4.52473e6i			1.82736i	−0.406431	+	0.913681i	$0.633227\pi$
$20$	−664796.	−	1.26730e6i	−0.207749	−	0.396031i
$21$	−49394.9			−0.0120944
$22$	−2.87295e6	−	1.73716e6i	−0.557461	−	0.337076i
$23$			3.50848e6i			0.545104i	0.962141	+	0.272552i	$0.0878677\pi$
$23$			3.50848e6i			0.545104i	−0.962141	+	0.272552i	$0.912132\pi$
$24$	−34067.5	+	560327.i	−0.00427842	+	0.0703696i
$25$	1.95312e6			0.200000
$26$	2.40611e6	−	3.97926e6i	0.202511	−	0.334916i
$27$			2.01816e6i			0.140649i
$28$	2.61459e6	−	1.37155e6i	0.151919	−	0.0796935i
$29$	2.68714e7			1.31009			0.655043	−	0.755592i	$-0.272651\pi$
$29$	2.68714e7			1.31009			0.655043	+	0.755592i	$0.272651\pi$
$30$	−655607.	−	396420.i	−0.0269797	−	0.0163136i
$31$			2.04707e7i			0.715031i	0.933907	+	0.357516i	$0.116376\pi$
$31$			2.04707e7i			0.715031i	−0.933907	+	0.357516i	$0.883624\pi$
$32$	−1.37554e7	−	3.06054e7i	−0.409943	−	0.912111i
$33$	−1.79736e6			−0.0459267
$34$	1.93367e7	−	3.19793e7i	0.425586	−	0.703841i
$35$			4.02953e6i			0.0767210i
$36$	−2.79494e7	−	5.32798e7i	−0.462232	−	0.881150i
$37$	4.45179e7			0.641987			0.320993	−	0.947081i	$-0.395983\pi$
$37$	4.45179e7			0.641987			0.320993	+	0.947081i	$0.395983\pi$
$38$	−1.23902e8	−	7.49188e7i	−1.56373	−	0.945525i
$39$		−	2.48949e6i		−	0.0275922i
$40$	4.57103e7	+	2.77915e6i	0.446389	+	0.0271402i
$41$	2.94019e7			0.253780			0.126890	−	0.991917i	$-0.459501\pi$
$41$	2.94019e7			0.253780			0.126890	+	0.991917i	$0.459501\pi$
$42$	817862.	−	1.35259e6i	0.00625797	−	0.0103495i
$43$			1.50220e8i			1.02185i	0.859625	+	0.510925i	$0.170697\pi$
$43$			1.50220e8i			1.02185i	−0.859625	+	0.510925i	$0.829303\pi$
$44$	9.51385e7	−	4.99075e7i	0.576890	−	0.302624i
$45$	8.21133e7			0.444991
$46$	−9.60736e7	−	5.80921e7i	−0.466461	−	0.282051i
$47$			1.88353e8i			0.821264i	0.911801	+	0.410632i	$0.134692\pi$
$47$			1.88353e8i			0.821264i	−0.911801	+	0.410632i	$0.865308\pi$
$48$	−1.47795e7	−	1.02106e7i	−0.0580035	−	0.0400723i
$49$	2.74162e8			0.970569
$50$	−3.23391e7	+	5.34830e7i	−0.103485	+	0.171146i
$51$		−	2.00067e7i		−	0.0579863i
$52$	6.91259e7	+	1.31774e8i	0.181813	+	0.346588i
$53$	−5.81398e8			−1.39025			−0.695127	−	0.718887i	$-0.744652\pi$
$53$	−5.81398e8			−1.39025			−0.695127	+	0.718887i	$0.744652\pi$
$54$	−5.52638e7	−	3.34159e7i	−0.120357	−	0.0727753i
$55$			1.46625e8i			0.291336i
$56$	−5.73372e6	+	9.43057e7i	−0.0104111	+	0.171237i
$57$	−7.75150e7			−0.128828
$58$	−4.44926e8	+	7.35826e8i	−0.677872	+	1.12108i
$59$			1.80702e8i			0.252757i	0.991982	+	0.126379i	$0.0403355\pi$
$59$			1.80702e8i			0.252757i	−0.991982	+	0.126379i	$0.959665\pi$
$60$	2.17106e7	−	1.13889e7i	0.0279200	−	0.0146462i
$61$	−2.75462e8			−0.326146			−0.163073	−	0.986614i	$-0.552141\pi$
$61$	−2.75462e8			−0.326146			−0.163073	+	0.986614i	$0.552141\pi$
$62$	−5.60556e8	−	3.38947e8i	−0.611872	−	0.369976i
$63$			1.69410e8i			0.170701i
$64$	1.06583e9	+	1.30085e8i	0.992634	+	0.121151i
$65$	−2.03087e8			−0.175031
$66$	2.97600e7	−	4.92177e7i	0.0237637	−	0.0393008i
$67$		−	2.41173e9i		−	1.78630i	−0.449758	−	0.893150i	$-0.648490\pi$
$67$		−	2.41173e9i		−	1.78630i	0.449758	−	0.893150i	$-0.351510\pi$
$68$	5.55529e8	+	1.05900e9i	0.382087	+	0.728371i
$69$	−6.01051e7			−0.0384296
$70$	−1.10342e8	−	6.67195e7i	−0.0656523	−	0.0396974i
$71$		−	2.50764e9i		−	1.38987i	−0.719074	−	0.694933i	$-0.755434\pi$
$71$		−	2.50764e9i		−	1.38987i	0.719074	−	0.694933i	$-0.244566\pi$
$72$	1.92175e9	+	1.16841e8i	0.993196	+	0.0603856i
$73$	−2.32959e8			−0.112374			−0.0561870	−	0.998420i	$-0.517894\pi$
$73$	−2.32959e8			−0.112374			−0.0561870	+	0.998420i	$0.517894\pi$
$74$	−7.37111e8	+	1.21905e9i	−0.332181	+	0.549366i
$75$			3.34598e7i			0.0140999i
$76$	4.10305e9	−	2.15237e9i	1.61822	−	0.848884i
$77$	−3.02504e8			−0.111758
$78$	6.81703e7	+	4.12200e7i	0.0236114	+	0.0142769i
$79$		−	3.56415e9i		−	1.15830i	−0.815221	−	0.579150i	$-0.803385\pi$
$79$		−	3.56415e9i		−	1.15830i	0.815221	−	0.579150i	$-0.196615\pi$
$80$	−8.32956e8	+	1.20568e9i	−0.254198	+	0.367945i
$81$	3.43488e9			0.985114
$82$	−4.86827e8	+	8.05122e8i	−0.131312	+	0.217166i
$83$			3.50970e9i			0.891004i	0.895281	+	0.445502i	$0.146975\pi$
$83$			3.50970e9i			0.891004i	−0.895281	+	0.445502i	$0.853025\pi$
$84$	2.34966e7	+	4.47915e7i	0.00561836	+	0.0107102i
$85$	−1.63211e9			−0.367836
$86$	−4.11353e9	−	2.48730e9i	−0.874425	−	0.528731i
$87$			4.60344e8i			0.0923605i
$88$	−2.08636e8	+	3.43156e9i	−0.0395345	+	0.650246i
$89$	−9.00063e9			−1.61184			−0.805922	−	0.592022i	$-0.798330\pi$
$89$	−9.00063e9			−1.61184			−0.805922	+	0.592022i	$0.798330\pi$
$90$	−1.35960e9	+	2.24853e9i	−0.230250	+	0.380791i
$91$		−	4.18992e8i		−	0.0671428i
$92$	3.18150e9	−	1.66895e9i	0.482718	−	0.253223i
$93$	−3.50692e8			−0.0504094
$94$	−5.15772e9	−	3.11868e9i	−0.702779	−	0.424944i
$95$			6.32350e9i			0.817221i
$96$	5.24313e8	−	2.35649e8i	0.0643035	−	0.0289008i
$97$	4.72381e9			0.550090			0.275045	−	0.961431i	$-0.411307\pi$
$97$	4.72381e9			0.550090			0.275045	+	0.961431i	$0.411307\pi$
$98$	−4.53947e9	+	7.50745e9i	−0.502198	+	0.830543i
$99$			6.16440e9i			0.648209i
$100$	−9.29081e8	−	1.77110e9i	−0.0929081	−	0.177110i
$101$	9.24631e9			0.879755			0.439878	−	0.898058i	$-0.355022\pi$
$101$	9.24631e9			0.879755			0.439878	+	0.898058i	$0.355022\pi$
$102$	5.47850e8	+	3.31264e8i	0.0496205	+	0.0300036i
$103$			1.66575e10i			1.43689i	0.695584	+	0.718445i	$0.255146\pi$
$103$			1.66575e10i			1.43689i	−0.695584	+	0.718445i	$0.744854\pi$
$104$	−4.75298e9	−	2.88978e8i	−0.390660	−	0.0237519i
$105$	−6.90315e7			−0.00540880
$106$	9.62657e9	−	1.59206e10i	0.719353	−	1.18968i
$107$		−	5.83294e9i		−	0.415881i	−0.978142	−	0.207940i	$-0.933324\pi$
$107$		−	5.83294e9i		−	0.415881i	0.978142	−	0.207940i	$-0.0666760\pi$
$108$	1.83007e9	−	9.60016e8i	0.124552	−	0.0653371i
$109$	1.91747e10			1.24622			0.623110	−	0.782134i	$-0.285869\pi$
$109$	1.91747e10			1.24622			0.623110	+	0.782134i	$0.285869\pi$
$110$	−4.01507e9	−	2.42776e9i	−0.249304	−	0.150745i
$111$			7.62654e8i			0.0452598i
$112$	−2.48746e9	−	1.71849e9i	−0.141145	−	0.0975116i
$113$	−8.31679e9			−0.451402			−0.225701	−	0.974197i	$-0.572467\pi$
$113$	−8.31679e9			−0.451402			−0.225701	+	0.974197i	$0.572467\pi$
$114$	1.28346e9	−	2.12261e9i	0.0666591	−	0.110242i
$115$			4.90325e9i			0.243778i
$116$	−1.27824e10	−	2.43671e10i	−0.608588	−	1.16015i
$117$	−8.53818e9			−0.389436
$118$	−4.94823e9	−	2.99201e9i	−0.216292	−	0.130783i
$119$		−	3.36723e9i		−	0.141104i
$120$	−4.76108e7	+	7.83081e8i	−0.00191337	+	0.0314703i
$121$	1.49300e10			0.575617
$122$	4.56100e9	−	7.54305e9i	0.168757	−	0.279092i
$123$			5.03696e8i			0.0178914i
$124$	1.85630e10	−	9.73772e9i	0.633197	−	0.332161i
$125$	2.72958e9			0.0894427
$126$	−4.63899e9	−	2.80502e9i	−0.146073	−	0.0883249i
$127$		−	4.40429e10i		−	1.33308i	−0.745468	−	0.666541i	$-0.767774\pi$
$127$		−	4.40429e10i		−	1.33308i	0.745468	−	0.666541i	$-0.232226\pi$
$128$	−2.12098e10	+	2.70321e10i	−0.617287	+	0.786738i
$129$	−2.57349e9			−0.0720400
$130$	3.36264e9	−	5.56119e9i	0.0905656	−	0.149779i
$131$			2.62437e10i			0.680251i	0.940380	+	0.340125i	$0.110469\pi$
$131$			2.62437e10i			0.680251i	−0.940380	+	0.340125i	$0.889531\pi$
$132$	8.54986e8	+	1.62986e9i	0.0213348	+	0.0406705i
$133$	−1.30461e10			−0.313490
$134$	6.60411e10	+	3.99325e10i	1.52859	+	0.924279i
$135$			2.82046e9i			0.0629000i
$136$	−3.81973e10	−	2.32237e9i	−0.820990	−	0.0499156i
$137$	−3.12210e10			−0.646911			−0.323455	−	0.946243i	$-0.604845\pi$
$137$	−3.12210e10			−0.646911			−0.323455	+	0.946243i	$0.604845\pi$
$138$	9.95198e8	−	1.64588e9i	0.0198845	−	0.0328853i
$139$		−	6.29964e10i		−	1.21406i	−0.794677	−	0.607032i	$-0.792360\pi$
$139$		−	6.29964e10i		−	1.21406i	0.794677	−	0.607032i	$-0.207640\pi$
$140$	3.65400e9	−	1.91680e9i	0.0679404	−	0.0356400i
$141$	−3.22675e9			−0.0578988
$142$	6.86674e10	+	4.15206e10i	1.18935	+	0.719153i
$143$		−	1.52461e10i		−	0.254964i
$144$	−3.50192e10	+	5.06893e10i	−0.565579	+	0.818660i
$145$	3.75539e10			0.585888
$146$	3.85725e9	−	6.37919e9i	0.0581452	−	0.0961615i
$147$			4.69678e9i			0.0684247i
$148$	−2.11767e10	−	4.03691e10i	−0.298229	−	0.568513i
$149$	−1.51962e10			−0.206920			−0.103460	−	0.994634i	$-0.532991\pi$
$149$	−1.51962e10			−0.206920			−0.103460	+	0.994634i	$0.532991\pi$
$150$	−9.16238e8	−	5.54014e8i	−0.0120657	−	0.00729566i
$151$			7.77577e10i			0.990509i	0.868748	+	0.495255i	$0.164925\pi$
$151$			7.77577e10i			0.990509i	−0.868748	+	0.495255i	$0.835075\pi$
$152$	−8.99788e9	+	1.47993e11i	−0.110898	+	1.82399i
$153$	−6.86171e10			−0.818418
$154$	5.00876e9	−	8.28357e9i	0.0578264	−	0.0956343i
$155$			2.86087e10i			0.319772i
$156$	−2.25748e9	+	1.18422e9i	−0.0244343	+	0.0128177i
$157$	−7.92443e10			−0.830749			−0.415375	−	0.909650i	$-0.636349\pi$
$157$	−7.92443e10			−0.830749			−0.415375	+	0.909650i	$0.636349\pi$
$158$	9.75983e10	+	5.90139e10i	0.991189	+	0.599334i
$159$		−	9.96015e9i		−	0.0980123i
$160$	−1.92237e10	−	4.27723e10i	−0.183332	−	0.407909i
$161$	−1.01160e10			−0.0935144
$162$	−5.68735e10	+	9.40583e10i	−0.509724	+	0.842990i
$163$		−	2.06315e11i		−	1.79305i	−0.442990	−	0.896527i	$-0.646082\pi$
$163$		−	2.06315e11i		−	1.79305i	0.442990	−	0.896527i	$-0.353918\pi$
$164$	−1.39862e10	−	2.66618e10i	−0.117891	−	0.224735i
$165$	−2.51189e9			−0.0205391
$166$	−9.61072e10	−	5.81123e10i	−0.762457	−	0.461029i
$167$		−	1.62954e11i		−	1.25454i	−0.778804	−	0.627268i	$-0.784173\pi$
$167$		−	1.62954e11i		−	1.25454i	0.778804	−	0.627268i	$-0.215827\pi$
$168$	−1.61559e9	−	9.82266e7i	−0.0120721	−	0.000733978i
$169$	−1.16741e11			−0.846821
$170$	2.70238e10	−	4.46925e10i	0.190328	−	0.314767i
$171$			2.65853e11i			1.81828i
$172$	1.36221e11	−	7.14583e10i	0.904901	−	0.474691i
$173$	2.50915e11			1.61918			0.809592	−	0.586993i	$-0.199688\pi$
$173$	2.50915e11			1.61918			0.809592	+	0.586993i	$0.199688\pi$
$174$	−1.26057e10	−	7.62220e9i	−0.0790354	−	0.0477897i
$175$			5.63144e9i			0.0343107i
$176$	−9.05128e10	−	6.25316e10i	−0.535978	−	0.370285i
$177$	−3.09569e9			−0.0178193
$178$	1.49029e11	−	2.46467e11i	0.834010	−	1.37930i
$179$			2.16891e10i			0.118026i	0.998257	+	0.0590129i	$0.0187953\pi$
$179$			2.16891e10i			0.118026i	−0.998257	+	0.0590129i	$0.981205\pi$
$180$	−3.90605e10	−	7.44608e10i	−0.206716	−	0.394062i
$181$	3.01887e11			1.55400			0.777002	−	0.629498i	$-0.216740\pi$
$181$	3.01887e11			1.55400			0.777002	+	0.629498i	$0.216740\pi$
$182$	1.14734e10	+	6.93752e9i	0.0574559	+	0.0347414i
$183$		−	4.71905e9i		−	0.0229932i
$184$	−6.97695e9	+	1.14754e11i	−0.0330809	+	0.544099i
$185$	6.22157e10			0.287105
$186$	5.80664e9	−	9.60311e9i	0.0260831	−	0.0431367i
$187$		−	1.22525e11i		−	0.535819i
$188$	1.70799e11	−	8.95975e10i	0.727272	−	0.381511i
$189$	−5.81894e9			−0.0241288
$190$	−1.73158e11	−	1.04702e11i	−0.699319	−	0.422852i
$191$			4.36485e11i			1.71713i	0.512706	+	0.858564i	$0.328643\pi$
$191$			4.36485e11i			1.71713i	−0.512706	+	0.858564i	$0.671357\pi$
$192$	−2.22853e9	+	1.82592e10i	−0.00854108	+	0.0699803i
$193$	1.39392e11			0.520536			0.260268	−	0.965536i	$-0.416189\pi$
$193$	1.39392e11			0.520536			0.260268	+	0.965536i	$0.416189\pi$
$194$	−7.82151e10	+	1.29353e11i	−0.284631	+	0.470727i
$195$		−	3.47916e9i		−	0.0123396i
$196$	−1.30416e11	−	2.48611e11i	−0.450869	−	0.859490i
$197$	−2.77965e11			−0.936825			−0.468413	−	0.883510i	$-0.655174\pi$
$197$	−2.77965e11			−0.936825			−0.468413	+	0.883510i	$0.655174\pi$
$198$	−1.68802e11	−	1.02068e11i	−0.554691	−	0.335400i
$199$		−	9.29471e10i		−	0.297831i	−0.988850	−	0.148916i	$-0.952422\pi$
$199$		−	9.29471e10i		−	0.297831i	0.988850	−	0.148916i	$-0.0475783\pi$
$200$	6.38820e10	+	3.88398e9i	0.199631	+	0.0121374i
$201$	4.13163e10			0.125933
$202$	−1.53097e11	+	2.53195e11i	−0.455208	+	0.752831i
$203$			7.74781e10i			0.224749i
$204$	−1.81422e10	+	9.51700e9i	−0.0513499	+	0.0269370i
$205$	4.10905e10			0.113494
$206$	−4.56137e11	−	2.75809e11i	−1.22959	−	0.743484i
$207$			2.06142e11i			0.542395i
$208$	8.66112e10	−	1.25367e11i	0.222463	−	0.322009i
$209$	−4.74717e11			−1.19043
$210$	1.14300e9	−	1.89031e9i	0.00279865	−	0.00462846i
$211$			5.67215e11i			1.35624i	0.734952	+	0.678119i	$0.237205\pi$
$211$			5.67215e11i			1.35624i	−0.734952	+	0.678119i	$0.762795\pi$
$212$	2.76565e11	+	5.27214e11i	0.645829	+	1.23114i
$213$	4.29593e10			0.0979850
$214$	1.59725e11	+	9.65797e10i	0.355881	+	0.215188i
$215$			2.09940e11i			0.456985i
$216$	−4.01330e9	+	6.60090e10i	−0.00853558	+	0.140390i
$217$	−5.90232e10			−0.122666
$218$	−3.17487e11	+	5.25065e11i	−0.644827	+	1.06643i
$219$		−	3.99092e9i		−	0.00792232i
$220$	1.32960e11	−	6.97479e10i	0.257993	−	0.135337i
$221$	1.69707e11			0.321913
$222$	−2.08840e10	−	1.26277e10i	−0.0387301	−	0.0234186i
$223$		−	4.41854e11i		−	0.801224i	−0.916248	−	0.400612i	$-0.868797\pi$
$223$		−	4.41854e11i		−	0.801224i	0.916248	−	0.400612i	$-0.131203\pi$
$224$	8.82444e10	−	3.96609e10i	0.156476	−	0.0703270i
$225$	1.14757e11			0.199006
$226$	1.37706e11	−	2.27741e11i	0.233567	−	0.386277i
$227$		−	9.71516e11i		−	1.61184i	−0.592027	−	0.805918i	$-0.701672\pi$
$227$		−	9.71516e11i		−	1.61184i	0.592027	−	0.805918i	$-0.298328\pi$
$228$	3.68731e10	+	7.02910e10i	0.0598460	+	0.114084i
$229$	8.08050e11			1.28310			0.641550	−	0.767081i	$-0.278292\pi$
$229$	8.08050e11			1.28310			0.641550	+	0.767081i	$0.278292\pi$
$230$	−1.34267e11	−	8.11861e10i	−0.208608	−	0.126137i
$231$		−	5.18232e9i		−	0.00787888i
$232$	8.78898e11	+	5.34364e10i	1.30767	+	0.0795055i
$233$	−1.08018e12			−1.57295			−0.786476	−	0.617621i	$-0.788097\pi$
$233$	−1.08018e12			−1.57295			−0.786476	+	0.617621i	$0.788097\pi$
$234$	1.41372e11	−	2.33804e11i	0.201504	−	0.333251i
$235$			2.63231e11i			0.367281i
$236$	1.63862e11	−	8.59583e10i	0.223830	−	0.117416i
$237$	6.10589e10			0.0816596
$238$	9.22058e10	+	5.57533e10i	0.120746	+	0.0730106i
$239$		−	1.03615e12i		−	1.32872i	−0.747414	−	0.664358i	$-0.768705\pi$
$239$		−	1.03615e12i		−	1.32872i	0.747414	−	0.664358i	$-0.231295\pi$
$240$	−2.06550e10	−	1.42697e10i	−0.0259400	−	0.0179209i
$241$	−3.07111e11			−0.377755			−0.188877	−	0.982001i	$-0.560485\pi$
$241$	−3.07111e11			−0.377755			−0.188877	+	0.982001i	$0.560485\pi$
$242$	−2.47206e11	+	4.08833e11i	−0.297839	+	0.492571i
$243$			1.78014e11i			0.210099i
$244$	1.31034e11	+	2.49790e11i	0.151508	+	0.288819i
$245$	3.83153e11			0.434052
$246$	−1.37929e10	−	8.34002e9i	−0.0153101	−	0.00925745i
$247$		−	6.57521e11i		−	0.715196i
$248$	−4.07081e10	+	6.69549e11i	−0.0433933	+	0.713713i
$249$	−6.01261e10			−0.0628154
$250$	−4.51953e10	+	7.47448e10i	−0.0462800	+	0.0765386i
$251$		−	1.57563e12i		−	1.58156i	−0.612098	−	0.790782i	$-0.709674\pi$
$251$		−	1.57563e12i		−	1.58156i	0.612098	−	0.790782i	$-0.290326\pi$
$252$	1.53621e11	−	8.05863e10i	0.151164	−	0.0792974i
$253$	−3.68096e11			−0.355106
$254$	1.20604e12	+	7.29246e11i	1.14076	+	0.689772i
$255$		−	2.79603e10i		−	0.0259323i
$256$	−3.89044e11	−	1.02838e12i	−0.353834	−	0.935308i
$257$	−1.61149e12			−1.43735			−0.718674	−	0.695348i	$-0.755250\pi$
$257$	−1.61149e12			−1.43735			−0.718674	+	0.695348i	$0.755250\pi$
$258$	4.26109e10	−	7.04705e10i	0.0372753	−	0.0616466i
$259$			1.28358e11i			0.110135i
$260$	9.66063e10	+	1.84160e11i	0.0813090	+	0.154999i
$261$	1.57884e12			1.30357
$262$	−7.18639e11	−	4.34534e11i	−0.582109	−	0.351979i
$263$			9.26437e11i			0.736270i	0.929772	+	0.368135i	$0.120004\pi$
$263$			9.26437e11i			0.736270i	−0.929772	+	0.368135i	$0.879996\pi$
$264$	−5.87874e10	−	3.57423e9i	−0.0458421	−	0.00278717i
$265$	−8.12528e11			−0.621740
$266$	2.16013e11	−	3.57246e11i	0.162208	−	0.268262i
$267$		−	1.54193e11i		−	0.113634i
$268$	−2.18697e12	+	1.14723e12i	−1.58186	+	0.829809i
$269$	−1.77195e10			−0.0125803			−0.00629013	−	0.999980i	$-0.502002\pi$
$269$	−1.77195e10			−0.0125803			−0.00629013	+	0.999980i	$0.502002\pi$
$270$	−7.72335e10	−	4.67001e10i	−0.0538253	−	0.0325461i
$271$			8.13510e11i			0.556566i	0.960499	+	0.278283i	$0.0897652\pi$
$271$			8.13510e11i			0.556566i	−0.960499	+	0.278283i	$0.910235\pi$
$272$	6.96050e11	−	1.00751e12i	0.467516	−	0.676716i
$273$	7.17792e9			0.00473354
$274$	5.16946e11	−	8.54935e11i	0.334729	−	0.553580i
$275$			2.04914e11i			0.130289i
$276$	2.85914e10	+	5.45036e10i	0.0178521	+	0.0340314i
$277$	2.52752e12			1.54987			0.774935	−	0.632040i	$-0.217782\pi$
$277$	2.52752e12			1.54987			0.774935	+	0.632040i	$0.217782\pi$
$278$	1.72505e12	+	1.04307e12i	1.03891	+	0.628188i
$279$			1.20277e12i			0.711477i
$280$	−8.01312e9	+	1.31796e11i	−0.00465598	+	0.0765795i
$281$	−5.48736e11			−0.313208			−0.156604	−	0.987662i	$-0.550055\pi$
$281$	−5.48736e11			−0.313208			−0.156604	+	0.987662i	$0.550055\pi$
$282$	5.34273e10	−	8.83590e10i	0.0299583	−	0.0495456i
$283$			2.81384e12i			1.55013i	0.631884	+	0.775063i	$0.282282\pi$
$283$			2.81384e12i			1.55013i	−0.631884	+	0.775063i	$0.717718\pi$
$284$	−2.27394e12	+	1.19286e12i	−1.23080	+	0.645649i
$285$	−1.08330e11			−0.0576138
$286$	4.17489e11	+	2.52440e11i	0.218180	+	0.131925i
$287$			8.47745e10i			0.0435367i
$288$	−8.08205e11	−	1.79823e12i	−0.407905	−	0.907578i
$289$	−6.52143e11			−0.323484
$290$	−6.21803e11	+	1.02835e12i	−0.303154	+	0.501361i
$291$			8.09255e10i			0.0387811i
$292$	1.10816e11	+	2.11249e11i	0.0522023	+	0.0995130i
$293$	1.26769e12			0.587049			0.293524	−	0.955952i	$-0.405172\pi$
$293$	1.26769e12			0.587049			0.293524	+	0.955952i	$0.405172\pi$
$294$	−1.28613e11	−	7.77675e10i	−0.0585530	−	0.0354047i
$295$			2.52539e11i			0.113037i
$296$	1.45607e12	+	8.85283e10i	0.640803	+	0.0389604i
$297$	−2.11737e11			−0.0916252
$298$	2.51613e11	−	4.16122e11i	0.107066	−	0.177068i
$299$		−	5.09842e11i		−	0.213344i
$300$	3.03415e10	−	1.59165e10i	0.0124862	−	0.00654998i
$301$	−4.33130e11			−0.175302
$302$	−2.12926e12	−	1.28748e12i	−0.847606	−	0.512515i
$303$			1.58402e11i			0.0620224i
$304$	−3.90355e12	−	2.69681e12i	−1.50346	−	1.03868i
$305$	−3.84970e11			−0.145857
$306$	1.13614e12	−	1.87896e12i	0.423471	−	0.700343i
$307$			4.86551e12i			1.78417i	0.451867	+	0.892085i	$0.350758\pi$
$307$			4.86551e12i			1.78417i	−0.451867	+	0.892085i	$0.649242\pi$
$308$	1.43898e11	+	2.74313e11i	0.0519161	+	0.0989674i
$309$	−2.85366e11			−0.101300
$310$	−7.83401e11	−	4.73693e11i	−0.273638	−	0.165458i
$311$		−	4.12707e12i		−	1.41854i	−0.704939	−	0.709268i	$-0.749026\pi$
$311$		−	4.12707e12i		−	1.41854i	0.704939	−	0.709268i	$-0.250974\pi$
$312$	4.95059e9	−	8.14251e10i	0.00167450	−	0.0275414i
$313$	4.24950e11			0.141454			0.0707271	−	0.997496i	$-0.477468\pi$
$313$	4.24950e11			0.141454			0.0707271	+	0.997496i	$0.477468\pi$
$314$	1.31210e12	−	2.16997e12i	0.429851	−	0.710895i
$315$			2.36757e11i			0.0763396i
$316$	−3.23199e12	+	1.69543e12i	−1.02573	+	0.538077i
$317$	3.83351e12			1.19757			0.598785	−	0.800910i	$-0.295651\pi$
$317$	3.83351e12			1.19757			0.598785	+	0.800910i	$0.295651\pi$
$318$	2.72742e11	+	1.64917e11i	0.0838718	+	0.0507141i
$319$			2.81924e12i			0.853451i
$320$	1.48955e12	+	1.81799e11i	0.443919	+	0.0541803i
$321$	9.99265e10			0.0293194
$322$	1.67497e11	−	2.77009e11i	0.0483868	−	0.0800229i
$323$		−	5.28416e12i		−	1.50302i
$324$	−1.63394e12	−	3.11477e12i	−0.457625	−	0.872370i
$325$	−2.83823e11			−0.0782763
$326$	5.64959e12	+	3.41609e12i	1.53437	+	0.927772i
$327$			3.28489e11i			0.0878581i
$328$	9.61667e11	+	5.84687e10i	0.253312	+	0.0154012i
$329$	−5.43077e11			−0.140891
$330$	4.15909e10	−	6.87838e10i	0.0106274	−	0.0175758i
$331$		−	2.14151e12i		−	0.538990i	−0.963002	−	0.269495i	$-0.913143\pi$
$331$		−	2.14151e12i		−	0.538990i	0.963002	−	0.269495i	$-0.0868568\pi$
$332$	3.18261e12	−	1.66953e12i	0.789030	−	0.413907i
$333$	2.61567e12			0.638796
$334$	4.46222e12	+	2.69813e12i	1.07354	+	0.649129i
$335$		−	3.37049e12i		−	0.798858i
$336$	2.94401e10	−	4.26137e10i	0.00687453	−	0.00995069i
$337$	−2.14379e12			−0.493210			−0.246605	−	0.969116i	$-0.579315\pi$
$337$	−2.14379e12			−0.493210			−0.246605	+	0.969116i	$0.579315\pi$
$338$	1.93296e12	−	3.19676e12i	0.438167	−	0.724648i
$339$		−	1.42478e11i		−	0.0318236i
$340$	7.76376e11	+	1.48000e12i	0.170875	+	0.325738i
$341$	−2.14771e12			−0.465805
$342$	−7.27993e12	−	4.40189e12i	−1.55595	−	0.940826i
$343$			1.60495e12i			0.338058i
$344$	−2.98728e11	+	4.91335e12i	−0.0620132	+	1.01997i
$345$	−8.39994e10			−0.0171862
$346$	−4.15456e12	+	6.87088e12i	−0.837808	+	1.38558i
$347$		−	1.75806e12i		−	0.349452i	−0.984617	−	0.174726i	$-0.944096\pi$
$347$		−	1.75806e12i		−	0.349452i	0.984617	−	0.174726i	$-0.0559039\pi$
$348$	4.17442e11	−	2.18981e11i	0.0817900	−	0.0429052i
$349$	3.75815e12			0.725849			0.362925	−	0.931818i	$-0.381778\pi$
$349$	3.75815e12			0.725849			0.362925	+	0.931818i	$0.381778\pi$
$350$	−1.54207e11	−	9.32433e10i	−0.0293606	−	0.0177532i
$351$		−	2.93273e11i		−	0.0550473i
$352$	3.21100e12	−	1.44316e12i	0.594192	−	0.267056i
$353$	−5.37546e12			−0.980713			−0.490357	−	0.871522i	$-0.663133\pi$
$353$	−5.37546e12			−0.980713			−0.490357	+	0.871522i	$0.663133\pi$
$354$	5.12572e10	−	8.47701e10i	0.00922017	−	0.0152485i
$355$		−	3.50453e12i		−	0.621567i
$356$	4.28151e12	+	8.16182e12i	0.748767	+	1.42737i
$357$	5.76853e10			0.00994774
$358$	−5.93920e11	−	3.59121e11i	−0.100998	−	0.0610696i
$359$		−	1.35676e12i		−	0.227526i	−0.993508	−	0.113763i	$-0.963710\pi$
$359$		−	1.35676e12i		−	0.227526i	0.993508	−	0.113763i	$-0.0362905\pi$
$360$	2.68573e12	+	1.63291e11i	0.444171	+	0.0270053i
$361$	−1.43421e13			−2.33925
$362$	−4.99854e12	+	8.26667e12i	−0.804082	+	1.32980i
$363$			2.55772e11i			0.0405808i
$364$	−3.79944e11	+	1.99310e11i	−0.0594584	+	0.0311905i
$365$	−3.25571e11			−0.0502552
$366$	1.29223e11	+	7.81363e10i	0.0196759	+	0.0118973i
$367$			7.99180e12i			1.20037i	0.799862	+	0.600184i	$0.204906\pi$
$367$			7.99180e12i			1.20037i	−0.799862	+	0.600184i	$0.795094\pi$
$368$	−3.02682e12	−	2.09110e12i	−0.448484	−	0.309839i
$369$	1.72753e12			0.252518
$370$	−1.03014e12	+	1.70367e12i	−0.148556	+	0.245684i
$371$		−	1.67634e12i		−	0.238502i
$372$	1.66821e11	+	3.18010e11i	0.0234172	+	0.0446401i
$373$	4.04467e12			0.560195			0.280097	−	0.959972i	$-0.409633\pi$
$373$	4.04467e12			0.560195			0.280097	+	0.959972i	$0.409633\pi$
$374$	3.35515e12	+	2.02873e12i	0.458515	+	0.277247i
$375$			4.67614e10i			0.00630567i
$376$	−3.74558e11	+	6.16057e12i	−0.0498403	+	0.819751i
$377$	−3.90487e12			−0.512743
$378$	9.63479e10	−	1.59342e11i	0.0124848	−	0.0206476i
$379$			5.15915e12i			0.659754i	0.944024	+	0.329877i	$0.107007\pi$
$379$			5.15915e12i			0.659754i	−0.944024	+	0.329877i	$0.892993\pi$
$380$	5.73418e12	−	3.00802e12i	0.723692	−	0.379632i
$381$	7.54516e11			0.0939818
$382$	−1.19524e13	−	7.22716e12i	−1.46939	−	0.888487i
$383$		−	1.12386e13i		−	1.36369i	−0.731495	−	0.681846i	$-0.761177\pi$
$383$		−	1.12386e13i		−	1.36369i	0.731495	−	0.681846i	$-0.238823\pi$
$384$	−4.63098e11	−	3.63354e11i	−0.0554647	−	0.0435185i
$385$	−4.22763e11			−0.0499796
$386$	−2.30800e12	+	3.81701e12i	−0.269339	+	0.445438i
$387$			8.82628e12i			1.01677i
$388$	−2.24707e12	−	4.28357e12i	−0.255539	−	0.487133i
$389$	1.75648e12			0.197195			0.0985975	−	0.995127i	$-0.468564\pi$
$389$	1.75648e12			0.197195			0.0985975	+	0.995127i	$0.468564\pi$
$390$	9.52709e10	+	5.76067e10i	0.0105594	+	0.00638484i
$391$		−	4.09734e12i		−	0.448351i
$392$	8.96718e12	+	5.45198e11i	0.968781	+	0.0589012i
$393$	−4.49592e11			−0.0479574
$394$	4.60244e12	−	7.61159e12i	0.484738	−	0.801668i
$395$		−	4.98106e12i		−	0.518007i
$396$	5.58991e12	−	2.93234e12i	0.574023	−	0.301119i
$397$	1.50680e13			1.52793			0.763965	−	0.645258i	$-0.223250\pi$
$397$	1.50680e13			1.52793			0.763965	+	0.645258i	$0.223250\pi$
$398$	2.54520e12	+	1.53898e12i	0.254863	+	0.154106i
$399$		−	2.23499e11i		−	0.0221009i
$400$	−1.16409e12	+	1.68499e12i	−0.113681	+	0.164550i
$401$	−1.56037e11			−0.0150489			−0.00752446	−	0.999972i	$-0.502395\pi$
$401$	−1.56037e11			−0.0150489			−0.00752446	+	0.999972i	$0.502395\pi$
$402$	−6.84100e11	+	1.13138e12i	−0.0651612	+	0.107765i
$403$		−	2.97475e12i		−	0.279850i
$404$	−4.39837e12	−	8.38460e12i	−0.408682	−	0.779069i
$405$	4.80039e12			0.440556
$406$	−2.12160e12	−	1.28285e12i	−0.192324	−	0.116291i
$407$			4.67065e12i			0.418220i
$408$	3.97854e10	−	6.54372e11i	0.00351903	−	0.0578794i
$409$	5.89025e12			0.514656			0.257328	−	0.966324i	$-0.417158\pi$
$409$	5.89025e12			0.514656			0.257328	+	0.966324i	$0.417158\pi$
$410$	−6.80361e11	+	1.12519e12i	−0.0587246	+	0.0971197i
$411$		−	5.34860e11i		−	0.0456069i
$412$	1.51051e13	−	7.92379e12i	1.27244	−	0.667494i
$413$	−5.21019e11			−0.0433614
$414$	−5.64486e12	−	3.41323e12i	−0.464142	−	0.280649i
$415$			4.90496e12i			0.398469i
$416$	1.99889e12	+	4.44749e12i	0.160444	+	0.356983i
$417$	1.07922e12			0.0855910
$418$	7.86020e12	−	1.29993e13i	0.615959	−	1.01868i
$419$			6.30332e12i			0.488089i	0.969764	+	0.244045i	$0.0784744\pi$
$419$			6.30332e12i			0.488089i	−0.969764	+	0.244045i	$0.921526\pi$
$420$	3.28375e10	+	6.25981e10i	0.00251260	+	0.00478977i
$421$	−3.74730e12			−0.283340			−0.141670	−	0.989914i	$-0.545247\pi$
$421$	−3.74730e12			−0.283340			−0.141670	+	0.989914i	$0.545247\pi$
$422$	−1.55322e13	−	9.39175e12i	−1.16057	−	0.701753i
$423$			1.10668e13i			0.817182i
$424$	−1.90161e13	−	1.15617e12i	−1.38769	−	0.0843706i
$425$	−2.28094e12			−0.164501
$426$	−7.11305e11	+	1.17637e12i	−0.0507000	+	0.0838485i
$427$		−	7.94238e11i		−	0.0559515i
$428$	−5.28934e12	+	2.77467e12i	−0.368284	+	0.193193i
$429$	2.61187e11			0.0179749
$430$	−5.74884e12	−	3.47610e12i	−0.391055	−	0.236456i
$431$		−	2.91174e11i		−	0.0195779i	−0.999952	−	0.00978895i	$-0.996884\pi$
$431$		−	2.91174e11i		−	0.0195779i	0.999952	−	0.00978895i	$-0.00311597\pi$
$432$	−1.74109e12	−	1.20285e12i	−0.115719	−	0.0799453i
$433$	1.67455e13			1.10017			0.550084	−	0.835109i	$-0.314596\pi$
$433$	1.67455e13			1.10017			0.550084	+	0.835109i	$0.314596\pi$
$434$	9.77284e11	−	1.61625e12i	0.0634706	−	0.104969i
$435$			6.43350e11i			0.0413049i
$436$	−9.12118e12	−	1.73877e13i	−0.578920	−	1.10359i
$437$	−1.58749e13			−0.996103
$438$	1.09284e11	+	6.60802e10i	0.00677935	+	0.00409921i
$439$			5.15587e11i			0.0316213i	0.999875	+	0.0158106i	$0.00503289\pi$
$439$			5.15587e11i			0.0316213i	−0.999875	+	0.0158106i	$0.994967\pi$
$440$	−2.91578e11	+	4.79575e12i	−0.0176804	+	0.290799i
$441$	1.61085e13			0.965746
$442$	−2.80995e12	+	4.64714e12i	−0.166566	+	0.275470i
$443$			1.40692e13i			0.824615i	0.911045	+	0.412308i	$0.135277\pi$
$443$			1.40692e13i			0.824615i	−0.911045	+	0.412308i	$0.864723\pi$
$444$	6.91578e11	−	3.62786e11i	0.0400799	−	0.0210250i
$445$	−1.25788e13			−0.720839
$446$	1.20994e13	+	7.31605e12i	0.685630	+	0.414574i
$447$		−	2.60332e11i		−	0.0145878i
$448$	−3.75072e11	+	3.07311e12i	−0.0207838	+	0.170290i
$449$	−2.96504e13			−1.62479			−0.812397	−	0.583105i	$-0.801838\pi$
$449$	−2.96504e13			−1.62479			−0.812397	+	0.583105i	$0.801838\pi$
$450$	−1.90010e12	+	3.14242e12i	−0.102971	+	0.170295i
$451$			3.08474e12i			0.165324i
$452$	3.95621e12	+	7.54171e12i	0.209695	+	0.399740i
$453$	−1.33210e12			−0.0698305
$454$	2.66033e13	+	1.60860e13i	1.37929	+	0.834006i
$455$		−	5.85560e11i		−	0.0300272i
$456$	−2.53533e12	−	1.54146e11i	−0.128591	−	0.00781823i
$457$	2.63964e13			1.32423			0.662114	−	0.749403i	$-0.269659\pi$
$457$	2.63964e13			1.32423			0.662114	+	0.749403i	$0.269659\pi$
$458$	−1.33794e13	+	2.21271e13i	−0.663910	+	1.09798i
$459$		−	2.35688e12i		−	0.115684i
$460$	4.44629e12	−	2.33242e12i	0.215878	−	0.113245i
$461$	1.53323e13			0.736379			0.368190	−	0.929751i	$-0.379978\pi$
$461$	1.53323e13			0.736379			0.368190	+	0.929751i	$0.379978\pi$
$462$	1.41909e11	+	8.58070e10i	0.00674218	+	0.00407674i
$463$			1.25359e13i			0.589182i	0.955623	+	0.294591i	$0.0951834\pi$
$463$			1.25359e13i			0.589182i	−0.955623	+	0.294591i	$0.904817\pi$
$464$	−1.60157e13	+	2.31823e13i	−0.744658	+	1.07787i
$465$	−4.90107e11			−0.0225438
$466$	1.78852e13	−	2.95788e13i	0.813887	−	1.34602i
$467$		−	1.92800e13i		−	0.868005i	−0.900912	−	0.434003i	$-0.857101\pi$
$467$		−	1.92800e13i		−	0.868005i	0.900912	−	0.434003i	$-0.142899\pi$
$468$	4.06153e12	+	7.74247e12i	0.180909	+	0.344866i
$469$	6.95373e12			0.306446
$470$	−7.20814e12	−	4.35848e12i	−0.314292	−	0.190041i
$471$		−	1.35757e12i		−	0.0585675i
$472$	−3.59345e11	+	5.91034e12i	−0.0153392	+	0.252292i
$473$	−1.57606e13			−0.665681
$474$	−1.01099e12	+	1.67199e12i	−0.0422528	+	0.0698784i
$475$			8.83736e12i			0.365473i
$476$	−3.05342e12	+	1.60176e12i	−0.124954	+	0.0655483i
$477$	−3.41603e13			−1.38334
$478$	2.83731e13	+	1.71562e13i	1.13702	+	0.687513i
$479$		−	3.77999e12i		−	0.149904i	−0.997187	−	0.0749519i	$-0.976120\pi$
$479$		−	3.77999e12i		−	0.149904i	0.997187	−	0.0749519i	$-0.0238803\pi$
$480$	7.32750e11	−	3.29330e11i	0.0287574	−	0.0129248i
$481$	−6.46922e12			−0.251262
$482$	5.08503e12	−	8.40971e12i	0.195460	−	0.323255i
$483$		−	1.73301e11i		−	0.00659272i
$484$	−7.10205e12	−	1.35386e13i	−0.267397	−	0.509739i
$485$	6.60172e12			0.246008
$486$	−4.87462e12	−	2.94750e12i	−0.179787	−	0.108711i
$487$		−	4.52315e13i		−	1.65119i	−0.564264	−	0.825594i	$-0.690840\pi$
$487$		−	4.52315e13i		−	1.65119i	0.564264	−	0.825594i	$-0.309160\pi$
$488$	−9.00970e12	−	5.47783e11i	−0.325545	−	0.0197929i
$489$	3.53447e12			0.126410
$490$	−6.34410e12	+	1.04920e13i	−0.224590	+	0.371430i
$491$		−	1.05502e13i		−	0.369703i	−0.982766	−	0.184852i	$-0.940820\pi$
$491$		−	1.05502e13i		−	0.369703i	0.982766	−	0.184852i	$-0.0591805\pi$
$492$	4.56754e11	−	2.39603e11i	0.0158437	−	0.00831126i
$493$	−3.13815e13			−1.07755
$494$	1.80051e13	+	1.08870e13i	0.612013	+	0.370061i
$495$			8.61502e12i			0.289888i
$496$	−1.76604e13	−	1.22009e13i	−0.588292	−	0.406427i
$497$	7.23026e12			0.238436
$498$	9.95546e11	−	1.64645e12i	0.0325023	−	0.0537529i
$499$		−	5.20288e13i		−	1.68167i	−0.541291	−	0.840835i	$-0.682064\pi$
$499$		−	5.20288e13i		−	1.68167i	0.541291	−	0.840835i	$-0.317936\pi$
$500$	−1.29843e12	−	2.47519e12i	−0.0415498	−	0.0792062i
$501$	2.79163e12			0.0884442
$502$	4.31461e13	+	2.60888e13i	1.35339	+	0.818342i
$503$		−	1.10018e13i		−	0.341684i	−0.985298	−	0.170842i	$-0.945351\pi$
$503$		−	1.10018e13i		−	0.341684i	0.985298	−	0.170842i	$-0.0546487\pi$
$504$	−3.36888e11	+	5.54098e12i	−0.0103593	+	0.170386i
$505$	1.29221e13			0.393438
$506$	6.09480e12	−	1.00797e13i	0.183741	−	0.303874i
$507$		−	1.99994e12i		−	0.0597005i
$508$	−3.99383e13	+	2.09507e13i	−1.18051	+	0.619271i
$509$	−6.20936e12			−0.181743			−0.0908716	−	0.995863i	$-0.528965\pi$
$509$	−6.20936e12			−0.181743			−0.0908716	+	0.995863i	$0.528965\pi$
$510$	7.65644e11	+	4.62956e11i	0.0221910	+	0.0134180i
$511$		−	6.71691e11i		−	0.0192781i
$512$	3.46021e13	+	6.37427e12i	0.983452	+	0.181168i
$513$	−9.13161e12			−0.257016
$514$	2.66824e13	−	4.41279e13i	0.743721	−	1.22998i
$515$			2.32796e13i			0.642597i
$516$	1.22418e12	+	2.33365e12i	0.0334655	+	0.0637951i
$517$	−1.97613e13			−0.535010
$518$	−3.51487e12	−	2.12531e12i	−0.0942455	−	0.0569867i
$519$			4.29853e12i			0.114152i
$520$	−6.64249e12	−	4.03858e11i	−0.174708	−	0.0106222i
$521$	4.37932e13			1.14082			0.570411	−	0.821359i	$-0.306784\pi$
$521$	4.37932e13			1.14082			0.570411	+	0.821359i	$0.306784\pi$
$522$	−2.61419e13	+	4.32338e13i	−0.674503	+	1.11550i
$523$		−	1.76636e13i		−	0.451409i	−0.974196	−	0.225705i	$-0.927532\pi$
$523$		−	1.76636e13i		−	0.451409i	0.974196	−	0.225705i	$-0.0724684\pi$
$524$	2.37979e13	−	1.24839e13i	0.602397	−	0.316004i
$525$	−9.64744e10			−0.00241889
$526$	−2.53689e13	−	1.53396e13i	−0.630047	−	0.380965i
$527$		−	2.39066e13i		−	0.588117i
$528$	1.07125e12	−	1.55061e12i	0.0261049	−	0.0377862i
$529$	2.91171e13			0.702862
$530$	1.34535e13	−	2.22497e13i	0.321704	−	0.532040i
$531$			1.06173e13i			0.251501i
$532$	6.20591e12	+	1.18303e13i	0.145629	+	0.277612i
$533$	−4.27261e12			−0.0993246
$534$	4.22232e12	+	2.55308e12i	0.0972401	+	0.0587974i
$535$		−	8.15179e12i		−	0.185988i
$536$	4.79596e12	−	7.88819e13i	0.108406	−	1.78301i
$537$	−3.71565e11			−0.00832077
$538$	2.93393e11	−	4.85218e11i	0.00650936	−	0.0107653i
$539$			2.87640e13i			0.632274i
$540$	2.55761e12	−	1.34166e12i	0.0557012	−	0.0292196i
$541$	−6.28472e12			−0.135612			−0.0678062	−	0.997699i	$-0.521600\pi$
$541$	−6.28472e12			−0.135612			−0.0678062	+	0.997699i	$0.521600\pi$
$542$	−2.22766e13	−	1.34698e13i	−0.476269	−	0.287981i
$543$			5.17175e12i			0.109557i
$544$	1.60641e13	+	3.57422e13i	0.337180	+	0.750217i
$545$	2.67974e13			0.557327
$546$	−1.18849e11	+	1.96555e11i	−0.00244925	+	0.00405062i
$547$			6.05379e12i			0.123621i	0.998088	+	0.0618103i	$0.0196874\pi$
$547$			6.05379e12i			0.123621i	−0.998088	+	0.0618103i	$0.980313\pi$
$548$	1.48515e13	+	2.83114e13i	0.300516	+	0.572873i
$549$	−1.61849e13			−0.324525
$550$	−5.61123e12	−	3.39290e12i	−0.111492	−	0.0674151i
$551$			1.21586e14i			2.39400i
$552$	−1.96589e12	−	1.19525e11i	−0.0383588	−	0.00233219i
$553$	1.02765e13			0.198710
$554$	−4.18497e13	+	6.92118e13i	−0.801944	+	1.32627i
$555$			1.06584e12i			0.0202408i
$556$	−5.71254e13	+	2.99667e13i	−1.07512	+	0.563982i
$557$	−4.39378e12			−0.0819525			−0.0409763	−	0.999160i	$-0.513047\pi$
$557$	−4.39378e12			−0.0819525			−0.0409763	+	0.999160i	$0.513047\pi$
$558$	−3.29358e13	−	1.99150e13i	−0.608831	−	0.368137i
$559$		−	2.18296e13i		−	0.399933i
$560$	−3.47634e12	−	2.40166e12i	−0.0631221	−	0.0436085i
$561$	2.09903e12			0.0377750
$562$	9.08578e12	−	1.50262e13i	0.162062	−	0.268020i
$563$			8.43480e13i			1.49119i	0.666400	+	0.745594i	$0.267834\pi$
$563$			8.43480e13i			1.49119i	−0.666400	+	0.745594i	$0.732166\pi$
$564$	1.53493e12	+	2.92603e12i	0.0268963	+	0.0512724i
$565$	−1.16231e13			−0.201873
$566$	−7.70522e13	−	4.65905e13i	−1.32649	−	0.802076i
$567$			9.90378e12i			0.169000i
$568$	4.98669e12	−	8.20188e13i	0.0843472	−	1.38730i
$569$	4.41694e13			0.740559			0.370280	−	0.928920i	$-0.379262\pi$
$569$	4.41694e13			0.740559			0.370280	+	0.928920i	$0.379262\pi$
$570$	1.79370e12	−	2.96644e12i	0.0298109	−	0.0493017i
$571$			9.02841e13i			1.48741i	0.668508	+	0.743705i	$0.266933\pi$
$571$			9.02841e13i			1.48741i	−0.668508	+	0.743705i	$0.733067\pi$
$572$	−1.38253e13	+	7.25242e12i	−0.225784	+	0.118441i
$573$	−7.47760e12			−0.121057
$574$	−2.32141e12	−	1.40367e12i	−0.0372556	−	0.0225270i
$575$			6.85249e12i			0.109021i
$576$	6.26236e13	+	7.64319e12i	0.987701	+	0.120549i
$577$	−5.59247e13			−0.874429			−0.437215	−	0.899357i	$-0.644035\pi$
$577$	−5.59247e13			−0.874429			−0.437215	+	0.899357i	$0.644035\pi$
$578$	1.07979e13	−	1.78578e13i	0.167379	−	0.276815i
$579$			2.38798e12i			0.0366976i
$580$	−1.78640e13	−	3.40540e13i	−0.272169	−	0.518834i
$581$	−1.01195e13			−0.152855
$582$	−2.21601e12	−	1.33993e12i	−0.0331861	−	0.0200664i
$583$		−	6.09980e13i		−	0.905676i
$584$	−7.61954e12	−	4.63263e11i	−0.112167	−	0.00681967i
$585$	−1.19325e13			−0.174161
$586$	−2.09899e13	+	3.47135e13i	−0.303754	+	0.502354i
$587$		−	6.27256e13i		−	0.900025i	−0.893022	−	0.450012i	$-0.851420\pi$
$587$		−	6.27256e13i		−	0.900025i	0.893022	−	0.450012i	$-0.148580\pi$
$588$	4.25906e12	−	2.23421e12i	0.0605937	−	0.0317861i
$589$	−9.26246e13			−1.30662
$590$	−6.91536e12	−	4.18145e12i	−0.0967286	−	0.0584881i
$591$		−	4.76192e12i		−	0.0660458i
$592$	−2.65333e13	+	3.84063e13i	−0.364908	+	0.528194i
$593$	1.28414e14			1.75121			0.875607	−	0.483025i	$-0.160462\pi$
$593$	1.28414e14			1.75121			0.875607	+	0.483025i	$0.160462\pi$
$594$	3.50587e12	−	5.79806e12i	0.0474093	−	0.0784062i
$595$		−	4.70585e12i		−	0.0631034i
$596$	7.22867e12	+	1.37800e13i	0.0961230	+	0.183239i
$597$	1.59231e12			0.0209970
$598$	1.39611e13	+	8.44177e12i	0.182564	+	0.110390i
$599$			2.89362e13i			0.375238i	0.982242	+	0.187619i	$0.0600770\pi$
$599$			2.89362e13i			0.375238i	−0.982242	+	0.187619i	$0.939923\pi$
$600$	−6.65381e10	+	1.09439e12i	−0.000855685	+	0.0140739i
$601$	9.10751e13			1.16152			0.580761	−	0.814074i	$-0.302755\pi$
$601$	9.10751e13			1.16152			0.580761	+	0.814074i	$0.302755\pi$
$602$	7.17161e12	−	1.18605e13i	0.0907056	−	0.150010i
$603$		−	1.41702e14i		−	1.77742i
$604$	7.05110e13	−	3.69885e13i	0.877147	−	0.460132i
$605$	2.08653e13			0.257424
$606$	−4.33758e12	−	2.62277e12i	−0.0530743	−	0.0320920i
$607$			5.90952e13i			0.717149i	0.933501	+	0.358574i	$0.116737\pi$
$607$			5.90952e13i			0.717149i	−0.933501	+	0.358574i	$0.883263\pi$
$608$	1.38481e14	−	6.22394e13i	1.66676	−	0.749114i
$609$	−1.32731e12			−0.0158447
$610$	6.37419e12	−	1.05417e13i	0.0754702	−	0.124814i
$611$		−	2.73709e13i		−	0.321428i
$612$	3.26404e13	+	6.22223e13i	0.380188	+	0.724751i
$613$	1.73482e13			0.200425			0.100212	−	0.994966i	$-0.468048\pi$
$613$	1.73482e13			0.200425			0.100212	+	0.994966i	$0.468048\pi$
$614$	−1.33234e14	−	8.05613e13i	−1.52676	−	0.923176i
$615$			7.03937e11i			0.00800126i
$616$	−9.89419e12	−	6.01560e11i	−0.111552	−	0.00678227i
$617$	3.19918e13			0.357777			0.178889	−	0.983869i	$-0.442750\pi$
$617$	3.19918e13			0.357777			0.178889	+	0.983869i	$0.442750\pi$
$618$	4.72499e12	−	7.81426e12i	0.0524153	−	0.0866854i
$619$			1.10144e13i			0.121201i	0.998162	+	0.0606007i	$0.0193016\pi$
$619$			1.10144e13i			0.121201i	−0.998162	+	0.0606007i	$0.980698\pi$
$620$	2.59425e13	−	1.36089e13i	0.283174	−	0.148547i
$621$	−7.08065e12			−0.0766682
$622$	1.13013e14	+	6.83346e13i	1.21388	+	0.733987i
$623$		−	2.59515e13i		−	0.276517i
$624$	2.14772e12	+	1.48377e12i	0.0227015	+	0.0156835i
$625$	3.81470e12			0.0400000
$626$	−7.03617e12	+	1.16365e13i	−0.0731921	+	0.121046i
$627$		−	8.13257e12i		−	0.0839248i
$628$	3.76957e13	+	7.18591e13i	0.385917	+	0.735671i
$629$	−5.19898e13			−0.528038
$630$	−6.48319e12	−	3.92014e12i	−0.0653260	−	0.0395001i
$631$		−	2.30262e13i		−	0.230184i	−0.993355	−	0.115092i	$-0.963284\pi$
$631$		−	2.30262e13i		−	0.230184i	0.993355	−	0.115092i	$-0.0367163\pi$
$632$	7.08767e12	−	1.16575e14i	0.0702940	−	1.15616i
$633$	−9.71719e12			−0.0956142
$634$	−6.34739e13	+	1.04974e14i	−0.619654	+	1.02479i
$635$		−	6.15518e13i		−	0.596173i
$636$	−9.03192e12	+	4.73794e12i	−0.0867949	+	0.0455307i
$637$	−3.98404e13			−0.379863
$638$	−7.72001e13	−	4.66799e13i	−0.730322	−	0.441598i
$639$		−	1.47338e14i		−	1.38296i
$640$	−2.96416e13	+	3.77785e13i	−0.276059	+	0.351840i
$641$	−1.11763e14			−1.03278			−0.516388	−	0.856355i	$-0.672724\pi$
$641$	−1.11763e14			−1.03278			−0.516388	+	0.856355i	$0.672724\pi$
$642$	−1.65455e12	+	2.73632e12i	−0.0151706	+	0.0250894i
$643$		−	7.83733e13i		−	0.713039i	−0.934288	−	0.356519i	$-0.883963\pi$
$643$		−	7.83733e13i		−	0.713039i	0.934288	−	0.356519i	$-0.116037\pi$
$644$	4.81206e12	+	9.17322e12i	0.0434412	+	0.0828118i
$645$	−3.59656e12			−0.0322172
$646$	1.44698e14	+	8.74932e13i	1.28617	+	0.777700i
$647$		−	7.95467e12i		−	0.0701618i	−0.999384	−	0.0350809i	$-0.988831\pi$
$647$		−	7.95467e12i		−	0.0701618i	0.999384	−	0.0350809i	$-0.0111689\pi$
$648$	1.12347e14	+	6.83060e12i	0.983298	+	0.0597839i
$649$	−1.89586e13			−0.164658
$650$	4.69943e12	−	7.77200e12i	0.0405022	−	0.0669832i
$651$		−	1.01115e12i		−	0.00864790i
$652$	−1.87088e14	+	9.81420e13i	−1.58784	+	0.832946i
$653$	−1.11506e14			−0.939144			−0.469572	−	0.882894i	$-0.655592\pi$
$653$	−1.11506e14			−0.939144			−0.469572	+	0.882894i	$0.655592\pi$
$654$	−8.99510e12	−	5.43899e12i	−0.0751826	−	0.0454600i
$655$			3.66767e13i			0.304217i
$656$	−1.75240e13	+	2.53655e13i	−0.144249	+	0.208797i
$657$	−1.36876e13			−0.111815
$658$	8.99207e12	−	1.48712e13i	0.0729005	−	0.120564i
$659$			9.42406e13i			0.758247i	0.925346	+	0.379124i	$0.123775\pi$
$659$			9.42406e13i			0.758247i	−0.925346	+	0.379124i	$0.876225\pi$
$660$	1.19488e12	+	2.27779e12i	0.00954123	+	0.0181884i
$661$	−1.41144e14			−1.11855			−0.559276	−	0.828982i	$-0.688921\pi$
$661$	−1.41144e14			−1.11855			−0.559276	+	0.828982i	$0.688921\pi$
$662$	5.86417e13	+	3.54584e13i	0.461229	+	0.278888i
$663$			2.90732e12i			0.0226948i
$664$	−6.97939e12	+	1.14794e14i	−0.0540726	+	0.889362i
$665$	−1.82325e13			−0.140197
$666$	−4.33093e13	+	7.16257e13i	−0.330530	+	0.546636i
$667$			9.42775e13i			0.714133i
$668$	−1.47768e14	+	7.75155e13i	−1.11096	+	0.582783i
$669$	7.56957e12			0.0564860
$670$	9.22952e13	+	5.58074e13i	0.683605	+	0.413350i
$671$		−	2.89004e13i		−	0.212467i
$672$	6.79446e11	+	1.51175e12i	0.00495802	+	0.0110315i
$673$	8.43704e13			0.611103			0.305552	−	0.952175i	$-0.401159\pi$
$673$	8.43704e13			0.611103			0.305552	+	0.952175i	$0.401159\pi$
$674$	3.54960e13	−	5.87039e13i	0.255200	−	0.422054i
$675$			3.94171e12i			0.0281298i
$676$	5.55327e13	+	1.05862e14i	0.393383	+	0.749904i
$677$	1.31560e14			0.925081			0.462541	−	0.886598i	$-0.346938\pi$
$677$	1.31560e14			0.925081			0.462541	+	0.886598i	$0.346938\pi$
$678$	3.90152e12	+	2.35910e12i	0.0272324	+	0.0164664i
$679$			1.36201e13i			0.0943697i
$680$	−5.33823e13	−	3.24561e12i	−0.367158	−	0.0223229i
$681$	1.66434e13			0.113634
$682$	3.55610e13	−	5.88114e13i	0.241020	−	0.398602i
$683$			1.84062e14i			1.23840i	0.785232	+	0.619201i	$0.212543\pi$
$683$			1.84062e14i			1.23840i	−0.785232	+	0.619201i	$0.787457\pi$
$684$	2.41077e14	−	1.26463e14i	1.61018	−	0.844665i
$685$	−4.36327e13			−0.289307
$686$	−4.39488e13	−	2.65742e13i	−0.289285	−	0.174920i
$687$			1.38430e13i			0.0904580i
$688$	−1.29598e14	−	8.95336e13i	−0.840726	−	0.580823i
$689$	8.44870e13			0.544119
$690$	1.39083e12	−	2.30018e12i	0.00889261	−	0.0147067i
$691$		−	1.11016e14i		−	0.704687i	−0.935871	−	0.352344i	$-0.885385\pi$
$691$		−	1.11016e14i		−	0.704687i	0.935871	−	0.352344i	$-0.114615\pi$
$692$	−1.19358e14	−	2.27531e14i	−0.752177	−	1.43387i
$693$	−1.77738e13			−0.111202
$694$	4.81416e13	+	2.91094e13i	0.299036	+	0.180815i
$695$		−	8.80401e13i		−	0.542946i
$696$	−9.15439e11	+	1.50567e13i	−0.00560510	+	0.0921902i
$697$	−3.43368e13			−0.208735
$698$	−6.22260e13	+	1.02910e14i	−0.375573	+	0.621130i
$699$		−	1.85050e13i		−	0.110892i
$700$	5.10662e12	−	2.67882e12i	0.0303839	−	0.0159387i
$701$	7.35378e13			0.434431			0.217215	−	0.976124i	$-0.430303\pi$
$701$	7.35378e13			0.434431			0.217215	+	0.976124i	$0.430303\pi$
$702$	8.03077e12	+	4.85590e12i	0.0471055	+	0.0284829i
$703$			2.01432e14i			1.17314i
$704$	−1.36480e13	+	1.11823e14i	−0.0789233	+	0.646648i
$705$	−4.50952e12			−0.0258931
$706$	8.90049e13	−	1.47198e14i	0.507447	−	0.839224i
$707$			2.66599e13i			0.150925i
$708$	1.47259e12	+	2.80718e12i	0.00827779	+	0.0157799i
$709$	2.00209e14			1.11751			0.558756	−	0.829332i	$-0.311279\pi$
$709$	2.00209e14			1.11751			0.558756	+	0.829332i	$0.311279\pi$
$710$	9.59656e13	+	5.80267e13i	0.531892	+	0.321615i
$711$		−	2.09414e14i		−	1.15254i
$712$	−2.94389e14	−	1.78987e13i	−1.60887	−	0.0978184i
$713$	−7.18211e13			−0.389766
$714$	−9.55133e11	+	1.57961e12i	−0.00514722	+	0.00851256i
$715$		−	2.13071e13i		−	0.114023i
$716$	1.96678e13	−	1.03173e13i	0.104518	−	0.0548278i
$717$	1.77507e13			0.0936740
$718$	3.71526e13	+	2.24648e13i	0.194700	+	0.117728i
$719$			3.53132e14i			1.83777i	0.394520	+	0.918887i	$0.370911\pi$
$719$			3.53132e14i			1.83777i	−0.394520	+	0.918887i	$0.629089\pi$
$720$	−4.89408e13	+	7.08404e13i	−0.252935	+	0.366116i
$721$	−4.80285e13			−0.246503
$722$	2.37472e14	−	3.92734e14i	1.21039	−	2.00176i
$723$		−	5.26124e12i		−	0.0266316i
$724$	−1.43605e14	−	2.73753e14i	−0.721898	−	1.37615i
$725$	5.24831e13			0.262017
$726$	−7.00388e12	−	4.23498e12i	−0.0347261	−	0.0209975i
$727$			7.30495e13i			0.359704i	0.983694	+	0.179852i	$0.0575619\pi$
$727$			7.30495e13i			0.359704i	−0.983694	+	0.179852i	$0.942438\pi$
$728$	8.33208e11	−	1.37042e13i	0.00407471	−	0.0670190i
$729$	1.99777e14			0.970302
$730$	5.39068e12	−	8.91519e12i	0.0260033	−	0.0430048i
$731$		−	1.75434e14i		−	0.840477i
$732$	−4.27926e12	+	2.24480e12i	−0.0203616	+	0.0106813i
$733$	−2.65775e14			−1.25601			−0.628007	−	0.778208i	$-0.716129\pi$
$733$	−2.65775e14			−1.25601			−0.628007	+	0.778208i	$0.716129\pi$
$734$	−2.18842e14	−	1.32325e14i	−1.02719	−	0.621102i
$735$			6.56394e12i			0.0306005i
$736$	1.07378e14	−	4.82605e13i	0.497196	−	0.223461i
$737$	2.53029e14			1.16368
$738$	−2.86037e13	+	4.73054e13i	−0.130660	+	0.216087i
$739$		−	1.35244e14i		−	0.613615i	−0.951772	−	0.306807i	$-0.900739\pi$
$739$		−	1.35244e14i		−	0.613615i	0.951772	−	0.306807i	$-0.0992607\pi$
$740$	−2.95953e13	−	5.64175e13i	−0.133372	−	0.254247i
$741$	1.12643e13			0.0504210
$742$	4.59037e13	+	2.77562e13i	0.204093	+	0.123407i
$743$			1.31232e14i			0.579555i	0.957094	+	0.289777i	$0.0935812\pi$
$743$			1.31232e14i			0.579555i	−0.957094	+	0.289777i	$0.906419\pi$
$744$	−1.14703e13	−	6.97387e11i	−0.0503165	−	0.00305921i
$745$	−2.12373e13			−0.0925377
$746$	−6.69702e13	+	1.10756e14i	−0.289859	+	0.479374i
$747$			2.06214e14i			0.886575i
$748$	−1.11107e14	+	5.82840e13i	−0.474495	+	0.248910i
$749$	1.68181e13			0.0713457
$750$	−1.28048e12	−	7.74259e11i	−0.00539594	−	0.00326272i
$751$		−	2.81917e14i		−	1.18011i	−0.807363	−	0.590054i	$-0.799106\pi$
$751$		−	2.81917e14i		−	1.18011i	0.807363	−	0.590054i	$-0.200894\pi$
$752$	−1.62495e14	−	1.12261e14i	−0.675695	−	0.466810i
$753$	2.69928e13			0.111500
$754$	6.46554e13	−	1.06928e14i	0.265307	−	0.438768i
$755$			1.08670e14i			0.442969i
$756$	2.76801e12	+	5.27665e12i	0.0112088	+	0.0213673i
$757$	1.37312e14			0.552368			0.276184	−	0.961105i	$-0.410930\pi$
$757$	1.37312e14			0.552368			0.276184	+	0.961105i	$0.410930\pi$
$758$	−1.41274e14	−	8.54233e13i	−0.564570	−	0.341374i
$759$		−	6.30600e12i		−	0.0250348i
$760$	−1.25749e13	+	2.06827e14i	−0.0495949	+	0.815715i
$761$	−1.68637e14			−0.660740			−0.330370	−	0.943851i	$-0.607174\pi$
$761$	−1.68637e14			−0.660740			−0.330370	+	0.943851i	$0.607174\pi$
$762$	−1.24930e13	+	2.06611e13i	−0.0486286	+	0.0804228i
$763$			5.52862e13i			0.213793i
$764$	3.95807e14	−	2.07631e14i	1.52061	−	0.797676i
$765$	−9.58953e13			−0.366007
$766$	3.07749e14	+	1.86084e14i	1.16695	+	0.705610i
$767$		−	2.62592e13i		−	0.0989246i
$768$	1.76176e13	−	6.66487e12i	0.0659389	−	0.0249451i
$769$	−2.57843e14			−0.958792			−0.479396	−	0.877599i	$-0.659144\pi$
$769$	−2.57843e14			−0.958792			−0.479396	+	0.877599i	$0.659144\pi$
$770$	6.99995e12	−	1.15766e13i	0.0258608	−	0.0427690i
$771$		−	2.76071e13i		−	0.101332i
$772$	−6.63073e13	−	1.26401e14i	−0.241810	−	0.460962i
$773$	2.66379e14			0.965168			0.482584	−	0.875850i	$-0.339698\pi$
$773$	2.66379e14			0.965168			0.482584	+	0.875850i	$0.339698\pi$
$774$	−2.41693e14	−	1.46142e14i	−0.870079	−	0.526104i
$775$			3.99819e13i			0.143006i
$776$	1.54504e14	+	9.39376e12i	0.549076	+	0.0333834i
$777$	−2.19896e12			−0.00776447
$778$	−2.90832e13	+	4.80983e13i	−0.102034	+	0.168745i
$779$			1.33036e14i			0.463747i
$780$	−3.15492e12	+	1.65500e12i	−0.0109274	+	0.00573225i
$781$	2.63092e14			0.905424
$782$	1.12199e14	+	6.78423e13i	0.383667	+	0.231989i
$783$			5.42306e13i			0.184262i
$784$	−1.63405e14	+	2.36524e14i	−0.551676	+	0.798536i
$785$	−1.10747e14			−0.371522
$786$	7.44417e12	−	1.23113e13i	0.0248144	−	0.0410385i
$787$			2.75307e14i			0.911893i	0.890007	+	0.455946i	$0.150699\pi$
$787$			2.75307e14i			0.911893i	−0.890007	+	0.455946i	$0.849301\pi$
$788$	1.32225e14	+	2.52060e14i	0.435193	+	0.829607i
$789$	−1.58712e13			−0.0519067
$790$	1.36398e14	+	8.24745e13i	0.443273	+	0.268030i
$791$		−	2.39798e13i		−	0.0774395i
$792$	−1.22585e13	+	2.01623e14i	−0.0393380	+	0.647014i
$793$	4.00293e13			0.127648
$794$	−2.49491e14	+	4.12612e14i	−0.790591	+	1.30749i
$795$		−	1.39197e13i		−	0.0438324i
$796$	−8.42849e13	+	4.42139e13i	−0.263745	+	0.138355i
$797$	2.84114e14			0.883487			0.441744	−	0.897141i	$-0.354360\pi$
$797$	2.84114e14			0.883487			0.441744	+	0.897141i	$0.354360\pi$
$798$	6.12013e12	+	3.70061e12i	0.0189124	+	0.0114356i
$799$		−	2.19966e14i		−	0.675495i
$800$	−2.68660e13	−	5.97761e13i	−0.0819885	−	0.182422i
$801$	−5.28837e14			−1.60383
$802$	2.58360e12	−	4.27280e12i	0.00778670	−	0.0128778i
$803$		−	2.44412e13i		−	0.0732057i
$804$	−1.96537e13	−	3.74658e13i	−0.0585012	−	0.111521i
$805$	−1.41375e13			−0.0418209
$806$	8.14584e13	+	4.92548e13i	0.239475	+	0.144802i
$807$		−	3.03560e11i		−	0.000886904i
$808$	3.02425e14	+	1.83872e13i	0.878134	+	0.0533899i
$809$	−4.11258e14			−1.18678			−0.593392	−	0.804914i	$-0.702212\pi$
$809$	−4.11258e14			−1.18678			−0.593392	+	0.804914i	$0.702212\pi$
$810$	−7.94831e13	+	1.31451e14i	−0.227955	+	0.376996i
$811$		−	2.31437e14i		−	0.659673i	−0.944038	−	0.329836i	$-0.893006\pi$
$811$		−	2.31437e14i		−	0.659673i	0.944038	−	0.329836i	$-0.106994\pi$
$812$	7.02575e13	−	3.68555e13i	0.199027	−	0.104405i
$813$	−1.39366e13			−0.0392376
$814$	−1.27898e14	−	7.73349e13i	−0.357883	−	0.216398i
$815$		−	2.88334e14i		−	0.801878i
$816$	1.72601e13	+	1.19243e13i	0.0477082	+	0.0329597i
$817$	−6.79707e14			−1.86729
$818$	−9.75286e13	+	1.61294e14i	−0.266297	+	0.440406i
$819$		−	2.46181e13i		−	0.0668090i
$820$	−1.95463e13	−	3.72610e13i	−0.0527224	−	0.100505i
$821$	1.65254e14			0.443032			0.221516	−	0.975157i	$-0.428900\pi$
$821$	1.65254e14			0.443032			0.221516	+	0.975157i	$0.428900\pi$
$822$	1.46462e13	+	8.85601e12i	0.0390271	+	0.0235982i
$823$		−	7.40931e13i		−	0.196236i	−0.995175	−	0.0981180i	$-0.968718\pi$
$823$		−	7.40931e13i		−	0.196236i	0.995175	−	0.0981180i	$-0.0312823\pi$
$824$	−3.31251e13	+	5.44827e14i	−0.0872009	+	1.43424i
$825$	−3.51047e12			−0.00918535
$826$	8.62684e12	−	1.42672e13i	0.0224363	−	0.0371055i
$827$		−	5.11220e14i		−	1.32154i	−0.750589	−	0.660770i	$-0.770230\pi$
$827$		−	5.11220e14i		−	1.32154i	0.750589	−	0.660770i	$-0.229770\pi$
$828$	1.86931e14	−	9.80598e13i	0.480319	−	0.251964i
$829$	6.77414e13			0.173014			0.0865070	−	0.996251i	$-0.472430\pi$
$829$	6.77414e13			0.173014			0.0865070	+	0.996251i	$0.472430\pi$
$830$	−1.34314e14	−	8.12145e13i	−0.340981	−	0.206178i
$831$			4.32999e13i			0.109265i
$832$	−1.54884e14	−	1.89035e13i	−0.388498	−	0.0474161i
$833$	−3.20177e14			−0.798299
$834$	−1.78693e13	+	2.95525e13i	−0.0442870	+	0.0732426i
$835$		−	2.27735e14i		−	0.561045i
$836$	2.25818e14	+	4.30476e14i	0.553003	+	1.05419i
$837$	−4.13131e13			−0.100568
$838$	−1.72606e14	−	1.04368e14i	−0.417672	−	0.252550i
$839$			1.43402e14i			0.344940i	0.985015	+	0.172470i	$0.0551748\pi$
$839$			1.43402e14i			0.344940i	−0.985015	+	0.172470i	$0.944825\pi$
$840$	−2.25785e12	−	1.37276e11i	−0.00539883	−	0.000328245i
$841$	3.01362e14			0.716323
$842$	6.20464e13	−	1.02613e14i	0.146607	−	0.242462i
$843$		−	9.40062e12i		−	0.0220810i
$844$	5.14354e14	−	2.69818e14i	1.20102	−	0.630027i
$845$	−1.63151e14			−0.378710
$846$	−3.03045e14	−	1.83240e14i	−0.699286	−	0.422832i
$847$			4.30477e13i			0.0987490i
$848$	3.46522e14	−	5.01581e14i	0.790226	−	1.14383i
$849$	−4.82050e13			−0.109283
$850$	3.77669e13	−	6.24596e13i	0.0851172	−	0.140768i
$851$			1.56190e14i			0.349950i
$852$	−2.04353e13	−	3.89558e13i	−0.0455180	−	0.0867708i
$853$	7.94871e14			1.76016			0.880079	−	0.474828i	$-0.157490\pi$
$853$	7.94871e14			1.76016			0.880079	+	0.474828i	$0.157490\pi$
$854$	2.17489e13	+	1.31507e13i	0.0478792	+	0.0289507i
$855$			3.71541e14i			0.813160i
$856$	1.15994e13	−	1.90782e14i	0.0252387	−	0.415114i
$857$	3.32899e14			0.720126			0.360063	−	0.932928i	$-0.382755\pi$
$857$	3.32899e14			0.720126			0.360063	+	0.932928i	$0.382755\pi$
$858$	−4.32464e12	+	7.15217e12i	−0.00930066	+	0.0153816i
$859$		−	2.40371e14i		−	0.513944i	−0.966419	−	0.256972i	$-0.917275\pi$
$859$		−	2.40371e14i		−	0.513944i	0.966419	−	0.256972i	$-0.0827248\pi$
$860$	1.90374e14	−	9.98660e13i	0.404684	−	0.212288i
$861$	−1.45231e12			−0.00306932
$862$	7.97330e12	+	4.82115e12i	0.0167534	+	0.0101301i
$863$		−	8.70727e14i		−	1.81898i	−0.415725	−	0.909490i	$-0.636472\pi$
$863$		−	8.70727e14i		−	1.81898i	0.415725	−	0.909490i	$-0.363528\pi$
$864$	6.17664e13	−	2.77605e13i	0.128287	−	0.0576579i
$865$	3.50664e14			0.724121
$866$	−2.77266e14	+	4.58548e14i	−0.569256	+	0.941445i
$867$		−	1.11721e13i		−	0.0228055i
$868$	2.80767e13	+	5.35225e13i	0.0569833	+	0.108627i
$869$	3.73937e14			0.754571
$870$	−1.76170e13	−	1.06524e13i	−0.0353457	−	0.0213722i
$871$			3.50466e14i			0.699125i
$872$	6.27157e14	+	3.81307e13i	1.24392	+	0.0756297i
$873$	2.77550e14			0.547356
$874$	2.62851e14	−	4.34707e14i	0.515409	−	0.852393i
$875$			7.87017e12i			0.0153442i
$876$	−3.61899e12	+	1.89844e12i	−0.00701562	+	0.00368024i
$877$	−3.23820e14			−0.624174			−0.312087	−	0.950054i	$-0.601028\pi$
$877$	−3.23820e14			−0.624174			−0.312087	+	0.950054i	$0.601028\pi$
$878$	−1.41185e13	−	8.53690e12i	−0.0270592	−	0.0163617i
$879$			2.17173e13i			0.0413867i
$880$	−1.26495e14	−	8.73906e13i	−0.239696	−	0.165597i
$881$	−7.15560e14			−1.34824			−0.674119	−	0.738623i	$-0.735476\pi$
$881$	−7.15560e14			−1.34824			−0.674119	+	0.738623i	$0.735476\pi$
$882$	−2.66719e14	+	4.41104e14i	−0.499702	+	0.826415i
$883$		−	1.35602e14i		−	0.252617i	−0.991991	−	0.126309i	$-0.959687\pi$
$883$		−	1.35602e14i		−	0.252617i	0.991991	−	0.126309i	$-0.0403129\pi$
$884$	−8.07280e13	−	1.53891e14i	−0.149542	−	0.285071i
$885$	−4.32635e12			−0.00796903
$886$	−3.85262e14	−	2.32953e14i	−0.705646	−	0.426677i
$887$		−	4.49112e13i		−	0.0817969i	−0.999163	−	0.0408984i	$-0.986978\pi$
$887$		−	4.49112e13i		−	0.0817969i	0.999163	−	0.0408984i	$-0.0130220\pi$
$888$	−1.51661e12	+	2.49446e13i	−0.00274669	+	0.0451764i
$889$	1.26989e14			0.228695
$890$	2.08275e14	−	3.44448e14i	0.372981	−	0.616842i
$891$			3.60375e14i			0.641750i
$892$	−4.00675e14	+	2.10185e14i	−0.709526	+	0.372201i
$893$	−8.52246e14			−1.50075
$894$	7.12875e12	+	4.31048e12i	0.0124832	+	0.00754811i
$895$			3.03115e13i			0.0527828i
$896$	−7.79416e13	−	6.11542e13i	−0.134968	−	0.105898i
$897$	8.73430e12			0.0150406
$898$	4.90940e14	−	8.11924e14i	0.840711	−	1.39038i
$899$			5.50076e14i			0.936752i
$900$	−5.45886e13	−	1.04062e14i	−0.0924463	−	0.176230i
$901$	6.78980e14			1.14349
$902$	−8.44703e13	−	5.10760e13i	−0.141472	−	0.0855429i
$903$		−	7.42012e12i		−	0.0123587i
$904$	−2.72022e14	−	1.65388e13i	−0.450570	−	0.0273943i
$905$	4.21900e14			0.694972
$906$	2.20564e13	−	3.64772e13i	0.0361321	−	0.0597559i
$907$			1.98146e14i			0.322812i	0.986888	+	0.161406i	$0.0516029\pi$
$907$			1.98146e14i			0.322812i	−0.986888	+	0.161406i	$0.948397\pi$
$908$	−8.80976e14	+	4.62140e14i	−1.42736	+	0.748763i
$909$	5.43272e14			0.875383
$910$	1.60346e13	+	9.69548e12i	0.0256951	+	0.0155368i
$911$			1.04700e15i			1.66861i	0.551307	+	0.834303i	$0.314129\pi$
$911$			1.04700e15i			1.66861i	−0.551307	+	0.834303i	$0.685871\pi$
$912$	4.62001e13	−	6.68734e13i	0.0732265	−	0.105993i
$913$	−3.68224e14			−0.580442
$914$	−4.37061e14	+	7.22819e14i	−0.685191	+	1.13318i
$915$		−	6.59507e12i		−	0.0102829i
$916$	−3.84381e14	−	7.32744e14i	−0.596052	−	1.13625i
$917$	−7.56684e13			−0.116699
$918$	6.45393e13	+	3.90244e13i	0.0989944	+	0.0598581i
$919$		−	4.63516e14i		−	0.707110i	−0.935414	−	0.353555i	$-0.884973\pi$
$919$		−	4.63516e14i		−	0.707110i	0.935414	−	0.353555i	$-0.115027\pi$
$920$	−9.75059e12	+	1.60373e14i	−0.0147942	+	0.243329i
$921$	−8.33530e13			−0.125783
$922$	−2.53866e14	+	4.19848e14i	−0.381022	+	0.630140i
$923$			3.64403e14i			0.543968i
$924$	−4.69936e12	+	2.46518e12i	−0.00697716	+	0.00366006i
$925$	8.69490e13			0.128397
$926$	−3.43274e14	−	2.07564e14i	−0.504180	−	0.304858i
$927$			9.78719e14i			1.42975i
$928$	−3.69626e14	−	8.22408e14i	−0.537060	−	1.19494i
$929$	−7.39635e14			−1.06890			−0.534452	−	0.845199i	$-0.679482\pi$
$929$	−7.39635e14			−1.06890			−0.534452	+	0.845199i	$0.679482\pi$
$930$	8.11502e12	−	1.34208e13i	0.0116647	−	0.0192913i
$931$			1.24051e15i			1.77358i
$932$	5.13829e14	+	9.79511e14i	0.730700	+	1.39293i
$933$	7.07025e13			0.100006
$934$	5.27950e14	+	3.19231e14i	0.742776	+	0.449129i
$935$		−	1.71234e14i		−	0.239625i
$936$	−2.79264e14	−	1.69790e13i	−0.388718	−	0.0236338i
$937$	−7.29902e13			−0.101057			−0.0505285	−	0.998723i	$-0.516091\pi$
$937$	−7.29902e13			−0.101057			−0.0505285	+	0.998723i	$0.516091\pi$
$938$	−1.15137e14	+	1.90416e14i	−0.158563	+	0.262234i
$939$			7.27999e12i			0.00997247i
$940$	2.38699e14	−	1.25216e14i	0.325246	−	0.170617i
$941$	−1.32143e13			−0.0179101			−0.00895503	−	0.999960i	$-0.502851\pi$
$941$	−1.32143e13			−0.0179101			−0.00895503	+	0.999960i	$0.502851\pi$
$942$	3.71746e13	+	2.24781e13i	0.0501178	+	0.0303043i
$943$			1.03156e14i			0.138336i
$944$	−1.55895e14	−	1.07701e14i	−0.207956	−	0.143668i
$945$	−8.13222e12			−0.0107907
$946$	2.60958e14	−	4.31576e14i	0.344440	−	0.569642i
$947$		−	1.40433e15i		−	1.84382i	−0.387401	−	0.921911i	$-0.626627\pi$
$947$		−	1.40433e15i		−	1.84382i	0.387401	−	0.921911i	$-0.373373\pi$
$948$	−2.90451e13	−	5.53685e13i	−0.0379342	−	0.0723138i
$949$	3.38530e13			0.0439811
$950$	−2.41996e14	−	1.46326e14i	−0.312745	−	0.189105i
$951$			6.56734e13i			0.0844281i
$952$	6.69607e12	−	1.10134e14i	0.00856318	−	0.140843i
$953$	9.14756e14			1.16370			0.581850	−	0.813296i	$-0.302329\pi$
$953$	9.14756e14			1.16370			0.581850	+	0.813296i	$0.302329\pi$
$954$	5.65614e14	−	9.35422e14i	0.715778	−	1.18377i
$955$			6.10007e14i			0.767923i
$956$	−9.39584e14	+	4.92885e14i	−1.17665	+	0.617243i
$957$	−4.82975e13			−0.0601679
$958$	1.03509e14	+	6.25877e13i	0.128277	+	0.0775642i
$959$		−	9.00195e13i		−	0.110980i
$960$	−3.11447e12	+	2.55180e13i	−0.00381969	+	0.0312961i
$961$	4.00577e14			0.488730
$962$	1.07115e14	−	1.77148e14i	0.130009	−	0.215012i
$963$		−	3.42718e14i		−	0.413814i
$964$	1.46089e14	+	2.78490e14i	0.175482	+	0.334522i
$965$	1.94806e14			0.232791
$966$	4.74555e12	+	2.86945e12i	0.00564158	+	0.00341125i
$967$		−	6.51171e14i		−	0.770127i	−0.922890	−	0.385064i	$-0.874179\pi$
$967$		−	6.51171e14i		−	0.770127i	0.922890	−	0.385064i	$-0.125821\pi$
$968$	4.88325e14	+	2.96898e13i	0.574556	+	0.0349326i
$969$	9.05251e13			0.105962
$970$	−1.09309e14	+	1.80777e14i	−0.127291	+	0.210516i
$971$		−	4.19590e14i		−	0.486104i	−0.970013	−	0.243052i	$-0.921851\pi$
$971$		−	4.19590e14i		−	0.486104i	0.970013	−	0.243052i	$-0.0781485\pi$
$972$	1.61424e14	−	8.46796e13i	0.186053	−	0.0975995i
$973$	1.81637e14			0.208277
$974$	1.23859e15	+	7.48927e14i	1.41297	+	0.854368i
$975$		−	4.86228e12i		−	0.00551844i
$976$	1.64179e14	−	2.37645e14i	0.185383	−	0.268337i
$977$	−1.70809e15			−1.91884			−0.959420	−	0.281982i	$-0.909008\pi$
$977$	−1.70809e15			−1.91884			−0.959420	+	0.281982i	$0.909008\pi$
$978$	−5.85224e13	+	9.67854e13i	−0.0654076	+	0.108172i
$979$		−	9.44312e14i		−	1.05003i
$980$	−1.82262e14	−	3.47445e14i	−0.201635	−	0.384375i
$981$	1.12662e15			1.24003
$982$	2.88899e14	+	1.74686e14i	0.316366	+	0.191294i
$983$			9.48625e13i			0.103354i	0.998664	+	0.0516770i	$0.0164566\pi$
$983$			9.48625e13i			0.103354i	−0.998664	+	0.0516770i	$0.983543\pi$
$984$	−1.00165e12	+	1.64747e13i	−0.00108578	+	0.0178584i
$985$	−3.88468e14			−0.418961
$986$	5.19603e14	−	8.59328e14i	0.557554	−	0.922092i
$987$		−	9.30367e12i		−	0.00993273i
$988$	−5.96243e14	+	3.12776e14i	−0.633343	+	0.332237i
$989$	−5.27045e14			−0.557014
$990$	−2.35908e14	−	1.42644e14i	−0.248065	−	0.149996i
$991$			3.49590e13i			0.0365756i	0.999833	+	0.0182878i	$0.00582151\pi$
$991$			3.49590e13i			0.0365756i	−0.999833	+	0.0182878i	$0.994178\pi$
$992$	6.26515e14	−	2.81583e14i	0.652188	−	0.293122i
$993$	3.66871e13			0.0379986
$994$	−1.19716e14	+	1.97988e14i	−0.123373	+	0.204036i
$995$		−	1.29897e14i		−	0.133194i
$996$	2.86013e13	+	5.45226e13i	0.0291803	+	0.0556263i
$997$	1.13389e15			1.15105			0.575524	−	0.817785i	$-0.304798\pi$
$997$	1.13389e15			1.15105			0.575524	+	0.817785i	$0.304798\pi$
$998$	1.42472e15	+	8.61473e14i	1.43905	+	0.870140i
$999$			8.98441e13i			0.0902946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.b.a.11.6	yes	20
3.2	odd	2		180.11.c.a.91.15		20
4.3	odd	2	inner	20.11.b.a.11.5	✓	20
5.2	odd	4		100.11.d.c.99.9		40
5.3	odd	4		100.11.d.c.99.32		40
5.4	even	2		100.11.b.e.51.15		20
8.3	odd	2		320.11.b.d.191.11		20
8.5	even	2		320.11.b.d.191.10		20
12.11	even	2		180.11.c.a.91.16		20
20.3	even	4		100.11.d.c.99.10		40
20.7	even	4		100.11.d.c.99.31		40
20.19	odd	2		100.11.b.e.51.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.5	✓	20	4.3	odd	2	inner
20.11.b.a.11.6	yes	20	1.1	even	1	trivial
100.11.b.e.51.15		20	5.4	even	2
100.11.b.e.51.16		20	20.19	odd	2
100.11.d.c.99.9		40	5.2	odd	4
100.11.d.c.99.10		40	20.3	even	4
100.11.d.c.99.31		40	20.7	even	4
100.11.d.c.99.32		40	5.3	odd	4
180.11.c.a.91.15		20	3.2	odd	2
180.11.c.a.91.16		20	12.11	even	2
320.11.b.d.191.10		20	8.5	even	2
320.11.b.d.191.11		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)

\(f(q)\)	\(=\)	\(q+(-16.5576 + 27.3833i) q^{2} +17.1314i q^{3} +(-475.690 - 906.805i) q^{4} +1397.54 q^{5} +(-469.114 - 283.655i) q^{6} +2883.30i q^{7} +(32707.6 + 1988.60i) q^{8} +58755.5 q^{9} +O(q^{10})\)	\(q+(-16.5576 + 27.3833i) q^{2} +17.1314i q^{3} +(-475.690 - 906.805i) q^{4} +1397.54 q^{5} +(-469.114 - 283.655i) q^{6} +2883.30i q^{7} +(32707.6 + 1988.60i) q^{8} +58755.5 q^{9} +(-23140.0 + 38269.3i) q^{10} +104916. i q^{11} +(15534.8 - 8149.23i) q^{12} -145317. q^{13} +(-78954.1 - 47740.6i) q^{14} +23941.9i q^{15} +(-596015. + 862715. i) q^{16} -1.16784e6 q^{17} +(-972852. + 1.60892e6i) q^{18} +4.52473e6i q^{19} +(-664796. - 1.26730e6i) q^{20} -49394.9 q^{21} +(-2.87295e6 - 1.73716e6i) q^{22} +3.50848e6i q^{23} +(-34067.5 + 560327. i) q^{24} +1.95312e6 q^{25} +(2.40611e6 - 3.97926e6i) q^{26} +2.01816e6i q^{27} +(2.61459e6 - 1.37155e6i) q^{28} +2.68714e7 q^{29} +(-655607. - 396420. i) q^{30} +2.04707e7i q^{31} +(-1.37554e7 - 3.06054e7i) q^{32} -1.79736e6 q^{33} +(1.93367e7 - 3.19793e7i) q^{34} +4.02953e6i q^{35} +(-2.79494e7 - 5.32798e7i) q^{36} +4.45179e7 q^{37} +(-1.23902e8 - 7.49188e7i) q^{38} -2.48949e6i q^{39} +(4.57103e7 + 2.77915e6i) q^{40} +2.94019e7 q^{41} +(817862. - 1.35259e6i) q^{42} +1.50220e8i q^{43} +(9.51385e7 - 4.99075e7i) q^{44} +8.21133e7 q^{45} +(-9.60736e7 - 5.80921e7i) q^{46} +1.88353e8i q^{47} +(-1.47795e7 - 1.02106e7i) q^{48} +2.74162e8 q^{49} +(-3.23391e7 + 5.34830e7i) q^{50} -2.00067e7i q^{51} +(6.91259e7 + 1.31774e8i) q^{52} -5.81398e8 q^{53} +(-5.52638e7 - 3.34159e7i) q^{54} +1.46625e8i q^{55} +(-5.73372e6 + 9.43057e7i) q^{56} -7.75150e7 q^{57} +(-4.44926e8 + 7.35826e8i) q^{58} +1.80702e8i q^{59} +(2.17106e7 - 1.13889e7i) q^{60} -2.75462e8 q^{61} +(-5.60556e8 - 3.38947e8i) q^{62} +1.69410e8i q^{63} +(1.06583e9 + 1.30085e8i) q^{64} -2.03087e8 q^{65} +(2.97600e7 - 4.92177e7i) q^{66} -2.41173e9i q^{67} +(5.55529e8 + 1.05900e9i) q^{68} -6.01051e7 q^{69} +(-1.10342e8 - 6.67195e7i) q^{70} -2.50764e9i q^{71} +(1.92175e9 + 1.16841e8i) q^{72} -2.32959e8 q^{73} +(-7.37111e8 + 1.21905e9i) q^{74} +3.34598e7i q^{75} +(4.10305e9 - 2.15237e9i) q^{76} -3.02504e8 q^{77} +(6.81703e7 + 4.12200e7i) q^{78} -3.56415e9i q^{79} +(-8.32956e8 + 1.20568e9i) q^{80} +3.43488e9 q^{81} +(-4.86827e8 + 8.05122e8i) q^{82} +3.50970e9i q^{83} +(2.34966e7 + 4.47915e7i) q^{84} -1.63211e9 q^{85} +(-4.11353e9 - 2.48730e9i) q^{86} +4.60344e8i q^{87} +(-2.08636e8 + 3.43156e9i) q^{88} -9.00063e9 q^{89} +(-1.35960e9 + 2.24853e9i) q^{90} -4.18992e8i q^{91} +(3.18150e9 - 1.66895e9i) q^{92} -3.50692e8 q^{93} +(-5.15772e9 - 3.11868e9i) q^{94} +6.32350e9i q^{95} +(5.24313e8 - 2.35649e8i) q^{96} +4.72381e9 q^{97} +(-4.53947e9 + 7.50745e9i) q^{98} +6.16440e9i 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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