LMFDB - Embedded newform 4.25.b.b.3.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,25,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 25, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 25);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	4.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:	$14.5986860903$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3 x^{9} + 1157886 x^{8} - 1182314620 x^{7} + 1715110302918 x^{6} + \cdots + 10\!\cdots\!86 $ x^10 - 3x^9 + 1157886x^8 - 1182314620x^7 + 1715110302918x^6 - 2255628699630474x^5 + 1518357032488149568x^4 - 1731829168106243136300x^3 + 1460524813513291203716721x^2 - 1269695210566625624700394443*x + 1028204700608421275722350402186
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{8}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.10
Root			$-734.642 + 844.151i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.25.b.b.3.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2318.57 + 3376.61i) q^{2} -962787. i q^{3} +(-6.02571e6 + 1.56578e7i) q^{4} +1.24317e8 q^{5} +(3.25095e9 - 2.23229e9i) q^{6} -3.87327e9i q^{7} +(-6.68411e10 + 1.59571e10i) q^{8} -6.44529e11 q^{9} +O(q^{10})$	\(q+(2318.57 + 3376.61i) q^{2} -962787. i q^{3} +(-6.02571e6 + 1.56578e7i) q^{4} +1.24317e8 q^{5} +(3.25095e9 - 2.23229e9i) q^{6} -3.87327e9i q^{7} +(-6.68411e10 + 1.59571e10i) q^{8} -6.44529e11 q^{9} +(2.88236e11 + 4.19768e11i) q^{10} -5.11020e12i q^{11} +(1.50751e13 + 5.80148e12i) q^{12} -2.88990e13 q^{13} +(1.30785e13 - 8.98044e12i) q^{14} -1.19690e14i q^{15} +(-2.08856e14 - 1.88699e14i) q^{16} +2.36831e14 q^{17} +(-1.49438e15 - 2.17632e15i) q^{18} -1.11159e15i q^{19} +(-7.49096e14 + 1.94652e15i) q^{20} -3.72914e15 q^{21} +(1.72551e16 - 1.18483e16i) q^{22} -9.54223e15i q^{23} +(1.53633e16 + 6.43538e16i) q^{24} -4.41501e16 q^{25} +(-6.70043e16 - 9.75806e16i) q^{26} +3.48625e17i q^{27} +(6.06468e16 + 2.33392e16i) q^{28} +4.61406e17 q^{29} +(4.04147e17 - 2.77510e17i) q^{30} +3.35661e17i q^{31} +(1.52913e17 - 1.14274e18i) q^{32} -4.92004e18 q^{33} +(5.49109e17 + 7.99685e17i) q^{34} -4.81512e17i q^{35} +(3.88375e18 - 1.00919e19i) q^{36} +7.73143e17 q^{37} +(3.75341e18 - 2.57730e18i) q^{38} +2.78236e19i q^{39} +(-8.30946e18 + 1.98373e18i) q^{40} +5.81991e18 q^{41} +(-8.64625e18 - 1.25918e19i) q^{42} +2.40400e19i q^{43} +(8.00144e19 + 3.07926e19i) q^{44} -8.01256e19 q^{45} +(3.22204e19 - 2.21243e19i) q^{46} -1.39171e20i q^{47} +(-1.81676e20 + 2.01084e20i) q^{48} +1.76579e20 q^{49} +(-1.02365e20 - 1.49077e20i) q^{50} -2.28018e20i q^{51} +(1.74137e20 - 4.52494e20i) q^{52} +6.00270e20 q^{53} +(-1.17717e21 + 8.08309e20i) q^{54} -6.35283e20i q^{55} +(6.18063e19 + 2.58894e20i) q^{56} -1.07023e21 q^{57} +(1.06980e21 + 1.55799e21i) q^{58} +1.87760e20i q^{59} +(1.87408e21 + 7.21220e20i) q^{60} +2.52930e21 q^{61} +(-1.13340e21 + 7.78253e20i) q^{62} +2.49644e21i q^{63} +(4.21311e21 - 2.13318e21i) q^{64} -3.59263e21 q^{65} +(-1.14074e22 - 1.66130e22i) q^{66} +7.53023e21i q^{67} +(-1.42708e21 + 3.70825e21i) q^{68} -9.18714e21 q^{69} +(1.62588e21 - 1.11642e21i) q^{70} -1.51186e22i q^{71} +(4.30810e22 - 1.02848e22i) q^{72} -4.83088e21 q^{73} +(1.79258e21 + 2.61060e21i) q^{74} +4.25071e22i q^{75} +(1.74050e22 + 6.69813e21i) q^{76} -1.97932e22 q^{77} +(-9.39493e22 + 6.45109e22i) q^{78} -2.60322e22i q^{79} +(-2.59643e22 - 2.34583e22i) q^{80} +1.53617e23 q^{81} +(1.34938e22 + 1.96515e22i) q^{82} +1.50802e22i q^{83} +(2.24707e22 - 5.83900e22i) q^{84} +2.94420e22 q^{85} +(-8.11738e22 + 5.57384e22i) q^{86} -4.44236e23i q^{87} +(8.15441e22 + 3.41572e23i) q^{88} -3.62220e23 q^{89} +(-1.85777e23 - 2.70553e23i) q^{90} +1.11934e23i q^{91} +(1.49410e23 + 5.74988e22i) q^{92} +3.23170e23 q^{93} +(4.69926e23 - 3.22678e23i) q^{94} -1.38189e23i q^{95} +(-1.10021e24 - 1.47222e23i) q^{96} +2.71719e23 q^{97} +(4.09410e23 + 5.96238e23i) q^{98} +3.29368e24i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9}+O(q^{10}) $ 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9	$ 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9} - 279847745800 q^{10} + 12433669328640 q^{12} - 24798065342764 q^{13} - 3829480368768 q^{14} - 588864378801920 q^{16} - 16\!\cdots\!64 q^{17}+ \cdots + 25\!\cdots\!08 q^{98}+O(q^{100}) $ 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9 - 279847745800 * q^10 + 12433669328640 * q^12 - 24798065342764 * q^13 - 3829480368768 * q^14 - 588864378801920 * q^16 - 1625038130621164 * q^17 - 3063761223370692 * q^18 - 3121315867314400 * q^20 - 2850064322141184 * q^21 + 13916632990560960 * q^22 + 10666682388698112 * q^24 + 71169859613334750 * q^25 - 74430147208248328 * q^26 + 57921192425034240 * q^28 + 1565608550658446804 * q^29 + 168458533397673600 * q^30 - 2011315973261284352 * q^32 - 3113879011632238080 * q^33 - 7482312029820836488 * q^34 - 4814867106633363312 * q^36 + 18108949413006125396 * q^37 - 3611284956625913280 * q^38 - 3297305262340163200 * q^40 + 75081428813585343380 * q^41 - 36295172789431572480 * q^42 + 120819410323173239040 * q^44 - 81006988268625062700 * q^45 - 106055608197057981312 * q^46 + 168479244993419243520 * q^48 - 275007343618256059766 * q^49 - 299814709349559655500 * q^50 + 1421183854718604927776 * q^52 - 1107525951871034057644 * q^53 - 3208227550047955403136 * q^54 + 4524093845691909838848 * q^56 - 1196103002381444528640 * q^57 - 1979853653083682157064 * q^58 + 14021053781344411123200 * q^60 + 7517404483697744564180 * q^61 - 21697281489429749629440 * q^62 + 27630501101980402880512 * q^64 - 2258152381762360458200 * q^65 - 60089835931903418403840 * q^66 + 44229260314628142476576 * q^68 - 3522613303126336828416 * q^69 - 111574643945445039187200 * q^70 + 150836748983093603875008 * q^72 + 51509134469807151432596 * q^73 - 140974046625084701216008 * q^74 + 274189896308379651183360 * q^76 - 19744531096531028198400 * q^77 - 388532048156284380666240 * q^78 + 337741777000410839974400 * q^80 - 21177053453795724717174 * q^81 - 127986376736882271652744 * q^82 + 466232221405535207153664 * q^84 - 156954763950404735571800 * q^85 - 425659539471164537308992 * q^86 + 273874512491499757685760 * q^88 - 817895256767034869026156 * q^89 - 170393126837835789371400 * q^90 - 461144040688182763215360 * q^92 + 251375897269064448430080 * q^93 + 1709617022527703840285952 * q^94 - 3254103234068698697613312 * q^96 + 2233072706882417490518036 * q^97 + 2593191981481623434770108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	2318.57	+	3376.61i	0.566056	+	0.824367i
$2$	2318.57	+	3376.61i	0.566056	+	0.824367i
$3$		−	962787.i		−	1.81165i	−0.423649	−	0.905827i	$-0.639251\pi$
$3$		−	962787.i		−	1.81165i	0.423649	−	0.905827i	$-0.360749\pi$
$4$	−6.02571e6	+	1.56578e7i	−0.359161	+	0.933276i
$5$	1.24317e8			0.509200			0.254600	−	0.967046i	$-0.418056\pi$
$5$	1.24317e8			0.509200			0.254600	+	0.967046i	$0.418056\pi$
$6$	3.25095e9	−	2.23229e9i	1.49347	−	1.02550i
$7$		−	3.87327e9i		−	0.279835i	−0.990163	−	0.139917i	$-0.955316\pi$
$7$		−	3.87327e9i		−	0.279835i	0.990163	−	0.139917i	$-0.0446837\pi$
$8$	−6.68411e10	+	1.59571e10i	−0.972666	+	0.232207i
$9$	−6.44529e11			−2.28209
$10$	2.88236e11	+	4.19768e11i	0.288236	+	0.419768i
$11$		−	5.11020e12i		−	1.62827i	−0.580677	−	0.814134i	$-0.697212\pi$
$11$		−	5.11020e12i		−	1.62827i	0.580677	−	0.814134i	$-0.302788\pi$
$12$	1.50751e13	+	5.80148e12i	1.69077	+	0.650674i
$13$	−2.88990e13			−1.24040			−0.620202	−	0.784442i	$-0.712949\pi$
$13$	−2.88990e13			−1.24040			−0.620202	+	0.784442i	$0.712949\pi$
$14$	1.30785e13	−	8.98044e12i	0.230686	−	0.158402i
$15$		−	1.19690e14i		−	0.922495i
$16$	−2.08856e14	−	1.88699e14i	−0.742007	−	0.670392i
$17$	2.36831e14			0.406492			0.203246	−	0.979128i	$-0.434851\pi$
$17$	2.36831e14			0.406492			0.203246	+	0.979128i	$0.434851\pi$
$18$	−1.49438e15	−	2.17632e15i	−1.29179	−	1.88128i
$19$		−	1.11159e15i		−	0.502229i	−0.967957	−	0.251115i	$-0.919203\pi$
$19$		−	1.11159e15i		−	0.502229i	0.967957	−	0.251115i	$-0.0807971\pi$
$20$	−7.49096e14	+	1.94652e15i	−0.182885	+	0.475224i
$21$	−3.72914e15			−0.506964
$22$	1.72551e16	−	1.18483e16i	1.34229	−	0.921692i
$23$		−	9.54223e15i		−	0.435428i	−0.976013	−	0.217714i	$-0.930140\pi$
$23$		−	9.54223e15i		−	0.435428i	0.976013	−	0.217714i	$-0.0698599\pi$
$24$	1.53633e16	+	6.43538e16i	0.420678	+	1.76213i
$25$	−4.41501e16			−0.740715
$26$	−6.70043e16	−	9.75806e16i	−0.702138	−	1.02255i
$27$			3.48625e17i			2.32270i
$28$	6.06468e16	+	2.33392e16i	0.261163	+	0.100506i
$29$	4.61406e17			1.30409			0.652044	−	0.758181i	$-0.273912\pi$
$29$	4.61406e17			1.30409			0.652044	+	0.758181i	$0.273912\pi$
$30$	4.04147e17	−	2.77510e17i	0.760474	−	0.522184i
$31$			3.35661e17i			0.426148i	0.977036	+	0.213074i	$0.0683476\pi$
$31$			3.35661e17i			0.426148i	−0.977036	+	0.213074i	$0.931652\pi$
$32$	1.52913e17	−	1.14274e18i	0.132631	−	0.991166i
$33$	−4.92004e18			−2.94986
$34$	5.49109e17	+	7.99685e17i	0.230097	+	0.335098i
$35$		−	4.81512e17i		−	0.142492i
$36$	3.88375e18	−	1.00919e19i	0.819636	−	2.12982i
$37$	7.73143e17			0.117446			0.0587232	−	0.998274i	$-0.481297\pi$
$37$	7.73143e17			0.117446			0.0587232	+	0.998274i	$0.481297\pi$
$38$	3.75341e18	−	2.57730e18i	0.414021	−	0.284290i
$39$			2.78236e19i			2.24718i
$40$	−8.30946e18	+	1.98373e18i	−0.495282	+	0.118240i
$41$	5.81991e18			0.257935			0.128967	−	0.991649i	$-0.458834\pi$
$41$	5.81991e18			0.257935			0.128967	+	0.991649i	$0.458834\pi$
$42$	−8.64625e18	−	1.25918e19i	−0.286970	−	0.417924i
$43$			2.40400e19i			0.601608i	0.953686	+	0.300804i	$0.0972550\pi$
$43$			2.40400e19i			0.601608i	−0.953686	+	0.300804i	$0.902745\pi$
$44$	8.00144e19	+	3.07926e19i	1.51962	+	0.584810i
$45$	−8.01256e19			−1.16204
$46$	3.22204e19	−	2.21243e19i	0.358952	−	0.246477i
$47$		−	1.39171e20i		−	1.19777i	−0.800834	−	0.598887i	$-0.795610\pi$
$47$		−	1.39171e20i		−	1.19777i	0.800834	−	0.598887i	$-0.204390\pi$
$48$	−1.81676e20	+	2.01084e20i	−1.21452	+	1.34426i
$49$	1.76579e20			0.921692
$50$	−1.02365e20	−	1.49077e20i	−0.419286	−	0.610621i
$51$		−	2.28018e20i		−	0.736422i
$52$	1.74137e20	−	4.52494e20i	0.445504	−	1.15764i
$53$	6.00270e20			1.22190			0.610951	−	0.791669i	$-0.290787\pi$
$53$	6.00270e20			1.22190			0.610951	+	0.791669i	$0.290787\pi$
$54$	−1.17717e21	+	8.08309e20i	−1.91476	+	1.31478i
$55$		−	6.35283e20i		−	0.829115i
$56$	6.18063e19	+	2.58894e20i	0.0649795	+	0.272186i
$57$	−1.07023e21			−0.909865
$58$	1.06980e21	+	1.55799e21i	0.738188	+	1.07505i
$59$			1.87760e20i			0.105531i	0.998607	+	0.0527653i	$0.0168035\pi$
$59$			1.87760e20i			0.105531i	−0.998607	+	0.0527653i	$0.983196\pi$
$60$	1.87408e21	+	7.21220e20i	0.860942	+	0.331324i
$61$	2.52930e21			0.952887			0.476444	−	0.879205i	$-0.341926\pi$
$61$	2.52930e21			0.952887			0.476444	+	0.879205i	$0.341926\pi$
$62$	−1.13340e21	+	7.78253e20i	−0.351303	+	0.241224i
$63$			2.49644e21i			0.638608i
$64$	4.21311e21	−	2.13318e21i	0.892160	−	0.451719i
$65$	−3.59263e21			−0.631614
$66$	−1.14074e22	−	1.66130e22i	−1.66979	−	2.43176i
$67$			7.53023e21i			0.920261i	0.887851	+	0.460130i	$0.152197\pi$
$67$			7.53023e21i			0.920261i	−0.887851	+	0.460130i	$0.847803\pi$
$68$	−1.42708e21	+	3.70825e21i	−0.145996	+	0.379369i
$69$	−9.18714e21			−0.788844
$70$	1.62588e21	−	1.11642e21i	0.117466	−	0.0806585i
$71$		−	1.51186e22i		−	0.921323i	−0.887576	−	0.460662i	$-0.847612\pi$
$71$		−	1.51186e22i		−	0.921323i	0.887576	−	0.460662i	$-0.152388\pi$
$72$	4.30810e22	−	1.02848e22i	2.21971	−	0.529916i
$73$	−4.83088e21			−0.210936			−0.105468	−	0.994423i	$-0.533634\pi$
$73$	−4.83088e21			−0.210936			−0.105468	+	0.994423i	$0.533634\pi$
$74$	1.79258e21	+	2.61060e21i	0.0664812	+	0.0968188i
$75$			4.25071e22i			1.34192i
$76$	1.74050e22	+	6.69813e21i	0.468718	+	0.180381i
$77$	−1.97932e22			−0.455646
$78$	−9.39493e22	+	6.45109e22i	−1.85250	+	1.27203i
$79$		−	2.60322e22i		−	0.440541i	−0.975439	−	0.220270i	$-0.929306\pi$
$79$		−	2.60322e22i		−	0.440541i	0.975439	−	0.220270i	$-0.0706939\pi$
$80$	−2.59643e22	−	2.34583e22i	−0.377830	−	0.341364i
$81$	1.53617e23			1.92584
$82$	1.34938e22	+	1.96515e22i	0.146006	+	0.212633i
$83$			1.50802e22i			0.141082i	0.997509	+	0.0705408i	$0.0224725\pi$
$83$			1.50802e22i			0.141082i	−0.997509	+	0.0705408i	$0.977528\pi$
$84$	2.24707e22	−	5.83900e22i	0.182081	−	0.473137i
$85$	2.94420e22			0.206986
$86$	−8.11738e22	+	5.57384e22i	−0.495946	+	0.340544i
$87$		−	4.44236e23i		−	2.36256i
$88$	8.15441e22	+	3.41572e23i	0.378095	+	1.58376i
$89$	−3.62220e23			−1.46654			−0.733268	−	0.679940i	$-0.762006\pi$
$89$	−3.62220e23			−1.46654			−0.733268	+	0.679940i	$0.762006\pi$
$90$	−1.85777e23	−	2.70553e23i	−0.657780	−	0.957947i
$91$			1.11934e23i			0.347108i
$92$	1.49410e23	+	5.74988e22i	0.406374	+	0.156388i
$93$	3.23170e23			0.772033
$94$	4.69926e23	−	3.22678e23i	0.987405	−	0.678007i
$95$		−	1.38189e23i		−	0.255735i
$96$	−1.10021e24	−	1.47222e23i	−1.79565	−	0.240281i
$97$	2.71719e23			0.391616			0.195808	−	0.980642i	$-0.437267\pi$
$97$	2.71719e23			0.391616			0.195808	+	0.980642i	$0.437267\pi$
$98$	4.09410e23	+	5.96238e23i	0.521730	+	0.759812i
$99$			3.29368e24i			3.71585i
$100$	2.66036e23	−	6.91291e23i	0.266036	−	0.691291i
$101$	−7.67668e23			−0.681266			−0.340633	−	0.940196i	$-0.610641\pi$
$101$	−7.67668e23			−0.681266			−0.340633	+	0.940196i	$0.610641\pi$
$102$	7.69927e23	−	5.28675e23i	0.607082	−	0.416856i
$103$		−	2.32424e24i		−	1.63018i	−0.579337	−	0.815088i	$-0.696688\pi$
$103$		−	2.32424e24i		−	1.63018i	0.579337	−	0.815088i	$-0.303312\pi$
$104$	1.93164e24	−	4.61145e23i	1.20650	−	0.288030i
$105$	−4.63593e23			−0.258146
$106$	1.39177e24	+	2.02688e24i	0.691665	+	1.00729i
$107$		−	4.75756e23i		−	0.211241i	−0.994406	−	0.105621i	$-0.966317\pi$
$107$		−	4.75756e23i		−	0.211241i	0.994406	−	0.105621i	$-0.0336829\pi$
$108$	−5.45868e24	−	2.10071e24i	−2.16772	−	0.834222i
$109$	−3.99874e24			−1.42169			−0.710846	−	0.703348i	$-0.751688\pi$
$109$	−3.99874e24			−1.42169			−0.710846	+	0.703348i	$0.751688\pi$
$110$	2.14510e24	−	1.47295e24i	0.683495	−	0.469326i
$111$		−	7.44372e23i		−	0.212772i
$112$	−7.30881e23	+	8.08958e23i	−0.187599	+	0.207639i
$113$	3.82244e24			0.881859			0.440929	−	0.897542i	$-0.354649\pi$
$113$	3.82244e24			0.881859			0.440929	+	0.897542i	$0.354649\pi$
$114$	−2.48139e24	−	3.61373e24i	−0.515035	−	0.750062i
$115$		−	1.18626e24i		−	0.221720i
$116$	−2.78030e24	+	7.22459e24i	−0.468377	+	1.21707i
$117$	1.86263e25			2.83071
$118$	−6.33991e23	+	4.35334e23i	−0.0869960	+	0.0597363i
$119$		−	9.17312e23i		−	0.113751i
$120$	1.90991e24	+	8.00023e24i	0.214209	+	0.897280i
$121$	−1.62645e25			−1.65126
$122$	5.86434e24	+	8.54043e24i	0.539388	+	0.785529i
$123$		−	5.60333e24i		−	0.467288i
$124$	−5.25571e24	−	2.02260e24i	−0.397714	−	0.153056i
$125$	−1.28984e25			−0.886373
$126$	−8.42948e24	+	5.78816e24i	−0.526447	+	0.361488i
$127$		−	2.56794e24i		−	0.145861i	−0.997337	−	0.0729307i	$-0.976765\pi$
$127$		−	2.56794e24i		−	0.145861i	0.997337	−	0.0729307i	$-0.0232352\pi$
$128$	1.69713e25	+	9.28007e24i	0.877395	+	0.479769i
$129$	2.31454e25			1.08991
$130$	−8.32974e24	−	1.21309e25i	−0.357529	−	0.520681i
$131$			5.23204e24i			0.204840i	0.994741	+	0.102420i	$0.0326586\pi$
$131$			5.23204e24i			0.204840i	−0.994741	+	0.102420i	$0.967341\pi$
$132$	2.96467e25	−	7.70368e25i	1.05947	−	2.75303i
$133$	−4.30550e24			−0.140541
$134$	−2.54266e25	+	1.74594e25i	−0.758632	+	0.520919i
$135$			4.33398e25i			1.18272i
$136$	−1.58301e25	+	3.77914e24i	−0.395381	+	0.0943901i
$137$	−5.42602e22			−0.00124118			−0.000620590	−	1.00000i	$-0.500198\pi$
$137$	−5.42602e22			−0.00124118			−0.000620590		1.00000i	$0.500198\pi$
$138$	−2.13010e25	−	3.10213e25i	−0.446530	−	0.650297i
$139$		−	4.57454e25i		−	0.879367i	−0.898153	−	0.439684i	$-0.855091\pi$
$139$		−	4.57454e25i		−	0.879367i	0.898153	−	0.439684i	$-0.144909\pi$
$140$	7.53940e24	+	2.90145e24i	0.132984	+	0.0511775i
$141$	−1.33992e26			−2.16995
$142$	5.10496e25	−	3.50535e25i	0.759508	−	0.521521i
$143$			1.47680e26i			2.01971i
$144$	1.34614e26	+	1.21622e26i	1.69333	+	1.52989i
$145$	5.73604e25			0.664043
$146$	−1.12007e25	−	1.63120e25i	−0.119402	−	0.173889i
$147$		−	1.70008e26i		−	1.66979i
$148$	−4.65874e24	+	1.21057e25i	−0.0421821	+	0.109610i
$149$	2.08894e26			1.74458			0.872292	−	0.488986i	$-0.162633\pi$
$149$	2.08894e26			1.74458			0.872292	+	0.488986i	$0.162633\pi$
$150$	−1.43530e26	+	9.85555e25i	−1.10623	+	0.759602i
$151$			7.23999e25i			0.515246i	0.966246	+	0.257623i	$0.0829392\pi$
$151$			7.23999e25i			0.515246i	−0.966246	+	0.257623i	$0.917061\pi$
$152$	1.77378e25	+	7.43000e25i	0.116621	+	0.488502i
$153$	−1.52645e26			−0.927650
$154$	−4.58919e25	−	6.68339e25i	−0.257921	−	0.375620i
$155$			4.17282e25i			0.216995i
$156$	−4.35656e26	−	1.67657e26i	−2.09724	−	0.807099i
$157$	2.81592e26			1.25552			0.627761	−	0.778406i	$-0.283971\pi$
$157$	2.81592e26			1.25552			0.627761	+	0.778406i	$0.283971\pi$
$158$	8.79005e25	−	6.03574e25i	0.363167	−	0.249371i
$159$		−	5.77932e26i		−	2.21366i
$160$	1.90096e25	−	1.42061e26i	0.0675356	−	0.504702i
$161$	−3.69597e25			−0.121848
$162$	3.56172e26	+	5.18704e26i	1.09013	+	1.58760i
$163$		−	2.35454e26i		−	0.669351i	−0.942333	−	0.334676i	$-0.891373\pi$
$163$		−	2.35454e26i		−	0.669351i	0.942333	−	0.334676i	$-0.108627\pi$
$164$	−3.50691e25	+	9.11268e25i	−0.0926400	+	0.240724i
$165$	−6.11642e26			−1.50207
$166$	−5.09199e25	+	3.49645e25i	−0.116303	+	0.0798601i
$167$			5.58258e26i			1.18642i	0.805049	+	0.593209i	$0.202139\pi$
$167$			5.58258e26i			1.18642i	−0.805049	+	0.593209i	$0.797861\pi$
$168$	2.49260e26	−	5.95063e25i	0.493107	−	0.117720i
$169$	2.92353e26			0.538601
$170$	6.82633e25	+	9.94141e25i	0.117166	+	0.170632i
$171$			7.16453e26i			1.14613i
$172$	−3.76413e26	−	1.44858e26i	−0.561466	−	0.216074i
$173$	4.14315e26			0.576470			0.288235	−	0.957560i	$-0.406931\pi$
$173$	4.14315e26			0.576470			0.288235	+	0.957560i	$0.406931\pi$
$174$	1.50001e27	−	1.02999e27i	1.94761	−	1.33734i
$175$			1.71005e26i			0.207278i
$176$	−9.64288e26	+	1.06730e27i	−1.09158	+	1.20819i
$177$	1.80773e26			0.191185
$178$	−8.39832e26	−	1.22308e27i	−0.830142	−	1.20896i
$179$			2.07966e27i			1.92201i	0.276530	+	0.961005i	$0.410815\pi$
$179$			2.07966e27i			1.92201i	−0.276530	+	0.961005i	$0.589185\pi$
$180$	4.82814e26	−	1.25459e27i	0.417359	−	1.08450i
$181$	−2.08748e27			−1.68842			−0.844208	−	0.536016i	$-0.819929\pi$
$181$	−2.08748e27			−1.68842			−0.844208	+	0.536016i	$0.819929\pi$
$182$	−3.77956e26	+	2.59526e26i	−0.286144	+	0.196483i
$183$		−	2.43517e27i		−	1.72630i
$184$	1.52267e26	+	6.37814e26i	0.101109	+	0.423526i
$185$	9.61145e25			0.0598037
$186$	7.49292e26	+	1.09122e27i	0.437014	+	0.636438i
$187$		−	1.21026e27i		−	0.661878i
$188$	2.17911e27	+	8.38606e26i	1.11785	+	0.430193i
$189$	1.35032e27			0.649972
$190$	4.66610e26	−	3.20401e26i	0.210820	−	0.144761i
$191$		−	2.58911e27i		−	1.09837i	−0.835700	−	0.549187i	$-0.814938\pi$
$191$		−	2.58911e27i		−	1.09837i	0.835700	−	0.549187i	$-0.185062\pi$
$192$	−2.05380e27	−	4.05632e27i	−0.818359	−	1.61628i
$193$	−8.32940e26			−0.311836			−0.155918	−	0.987770i	$-0.549834\pi$
$193$	−8.32940e26			−0.311836			−0.155918	+	0.987770i	$0.549834\pi$
$194$	6.30000e26	+	9.17489e26i	0.221676	+	0.322835i
$195$			3.45893e27i			1.14427i
$196$	−1.06401e27	+	2.76483e27i	−0.331036	+	0.860193i
$197$	1.38903e27			0.406553			0.203277	−	0.979121i	$-0.434841\pi$
$197$	1.38903e27			0.406553			0.203277	+	0.979121i	$0.434841\pi$
$198$	−1.11214e28	+	7.63660e27i	−3.06322	+	2.10338i
$199$		−	9.36243e26i		−	0.242746i	−0.992607	−	0.121373i	$-0.961270\pi$
$199$		−	9.36243e26i		−	0.242746i	0.992607	−	0.121373i	$-0.0387297\pi$
$200$	2.95104e27	−	7.04508e26i	0.720469	−	0.171999i
$201$	7.25001e27			1.66719
$202$	−1.77989e27	−	2.59211e27i	−0.385635	−	0.561613i
$203$		−	1.78715e27i		−	0.364929i
$204$	3.57025e27	+	1.37397e27i	0.687285	+	0.264494i
$205$	7.23511e26			0.131341
$206$	7.84805e27	−	5.38891e27i	1.34386	−	0.922771i
$207$			6.15025e27i			0.993684i
$208$	6.03575e27	+	5.45320e27i	0.920388	+	0.831556i
$209$	−5.68046e27			−0.817764
$210$	−1.07487e27	−	1.56537e27i	−0.146125	−	0.212807i
$211$		−	1.15719e28i		−	1.48598i	−0.669301	−	0.742991i	$-0.733406\pi$
$211$		−	1.15719e28i		−	1.48598i	0.669301	−	0.742991i	$-0.266594\pi$
$212$	−3.61706e27	+	9.39889e27i	−0.438859	+	1.14037i
$213$	−1.45560e28			−1.66912
$214$	1.60644e27	−	1.10307e27i	0.174140	−	0.119575i
$215$			2.98857e27i			0.306339i
$216$	−5.56304e27	−	2.33025e28i	−0.539346	−	2.25921i
$217$	1.30011e27			0.119251
$218$	−9.27135e27	−	1.35022e28i	−0.804758	−	1.17200i
$219$			4.65110e27i			0.382144i
$220$	9.94711e27	+	3.82803e27i	0.773793	+	0.297785i
$221$	−6.84419e27			−0.504214
$222$	2.51345e27	−	1.72588e27i	0.175402	−	0.120441i
$223$			2.21317e28i			1.46338i	0.681640	+	0.731688i	$0.261267\pi$
$223$			2.21317e28i			1.46338i	−0.681640	+	0.731688i	$0.738733\pi$
$224$	−4.42613e27	−	5.92273e26i	−0.277363	−	0.0371147i
$225$	2.84560e28			1.69038
$226$	8.86257e27	+	1.29069e28i	0.499182	+	0.726975i
$227$		−	4.58106e27i		−	0.244712i	−0.992486	−	0.122356i	$-0.960955\pi$
$227$		−	4.58106e27i		−	0.244712i	0.992486	−	0.122356i	$-0.0390450\pi$
$228$	6.44887e27	−	1.67573e28i	0.326788	−	0.849155i
$229$	8.31603e27			0.399843			0.199922	−	0.979812i	$-0.435931\pi$
$229$	8.31603e27			0.399843			0.199922	+	0.979812i	$0.435931\pi$
$230$	4.00552e27	−	2.75042e27i	0.182778	−	0.125506i
$231$			1.90567e28i			0.825473i
$232$	−3.08409e28	+	7.36271e27i	−1.26844	+	0.302818i
$233$	−3.75017e28			−1.46481			−0.732403	−	0.680871i	$-0.761601\pi$
$233$	−3.75017e28			−1.46481			−0.732403	+	0.680871i	$0.761601\pi$
$234$	4.31862e28	+	6.28935e28i	1.60234	+	2.33354i
$235$		−	1.73013e28i		−	0.609907i
$236$	−2.93990e27	−	1.13139e27i	−0.0984892	−	0.0379025i
$237$	−2.50635e28			−0.798107
$238$	3.09740e27	−	2.12685e27i	0.0937722	−	0.0643892i
$239$		−	5.01152e28i		−	1.44276i	−0.692539	−	0.721381i	$-0.743508\pi$
$239$		−	5.01152e28i		−	1.44276i	0.692539	−	0.721381i	$-0.256492\pi$
$240$	−2.25854e28	+	2.49981e28i	−0.618433	+	0.684498i
$241$	6.57072e28			1.71162			0.855812	−	0.517286i	$-0.173058\pi$
$241$	6.57072e28			1.71162			0.855812	+	0.517286i	$0.173058\pi$
$242$	−3.77102e28	−	5.49187e28i	−0.934706	−	1.36124i
$243$		−	4.94387e28i		−	1.16625i
$244$	−1.52408e28	+	3.96031e28i	−0.342240	+	0.889307i
$245$	2.19517e28			0.469326
$246$	1.89202e28	−	1.29917e28i	0.385217	−	0.264512i
$247$			3.21239e28i			0.622967i
$248$	−5.35619e27	−	2.24360e28i	−0.0989545	−	0.414500i
$249$	1.45190e28			0.255591
$250$	−2.99058e28	−	4.35529e28i	−0.501737	−	0.730696i
$251$			2.99690e28i			0.479279i	0.970862	+	0.239639i	$0.0770292\pi$
$251$			2.99690e28i			0.479279i	−0.970862	+	0.239639i	$0.922971\pi$
$252$	−3.90886e28	−	1.50428e28i	−0.595997	−	0.229363i
$253$	−4.87628e28			−0.708993
$254$	8.67092e27	−	5.95394e27i	0.120243	−	0.0825657i
$255$		−	2.83464e28i		−	0.374986i
$256$	8.01391e27	+	7.88218e28i	0.101150	+	0.994871i
$257$	1.30915e29			1.57686			0.788429	−	0.615125i	$-0.210895\pi$
$257$	1.30915e29			1.57686			0.788429	+	0.615125i	$0.210895\pi$
$258$	5.36642e28	+	7.81530e28i	0.616948	+	0.898482i
$259$		−	2.99460e27i		−	0.0328656i
$260$	2.16481e28	−	5.62525e28i	0.226851	−	0.589470i
$261$	−2.97389e29			−2.97605
$262$	−1.76665e28	+	1.21308e28i	−0.168863	+	0.115951i
$263$			1.48764e28i			0.135840i	0.997691	+	0.0679200i	$0.0216363\pi$
$263$			1.48764e28i			0.135840i	−0.997691	+	0.0679200i	$0.978364\pi$
$264$	3.28861e29	−	7.85096e28i	2.86923	−	0.684977i
$265$	7.46235e28			0.622193
$266$	−9.98258e27	−	1.45380e28i	−0.0795542	−	0.115857i
$267$			3.48741e29i			2.65686i
$268$	−1.17907e29	−	4.53750e28i	−0.858857	−	0.330521i
$269$	−1.08951e29			−0.758933			−0.379467	−	0.925205i	$-0.623892\pi$
$269$	−1.08951e29			−0.758933			−0.379467	+	0.925205i	$0.623892\pi$
$270$	−1.46341e29	+	1.00486e29i	−0.974994	+	0.669485i
$271$		−	1.86801e29i		−	1.19055i	−0.803522	−	0.595275i	$-0.797043\pi$
$271$		−	1.86801e29i		−	1.19055i	0.803522	−	0.595275i	$-0.202957\pi$
$272$	−4.94637e28	−	4.46897e28i	−0.301620	−	0.272509i
$273$	1.07768e29			0.628839
$274$	−1.25806e26	−	1.83215e26i	−0.000702578	−	0.00102319i
$275$			2.25616e29i			1.20608i
$276$	5.53591e28	−	1.43850e29i	0.283322	−	0.736209i
$277$	2.79674e29			1.37055			0.685276	−	0.728283i	$-0.259682\pi$
$277$	2.79674e29			1.37055			0.685276	+	0.728283i	$0.259682\pi$
$278$	1.54464e29	−	1.06064e29i	0.724921	−	0.497771i
$279$		−	2.16343e29i		−	0.972508i
$280$	7.68354e27	+	3.21848e28i	0.0330876	+	0.138597i
$281$	−8.94583e28			−0.369101			−0.184550	−	0.982823i	$-0.559083\pi$
$281$	−8.94583e28			−0.369101			−0.184550	+	0.982823i	$0.559083\pi$
$282$	−3.10670e29	−	4.52439e29i	−1.22831	−	1.78884i
$283$		−	3.78939e29i		−	1.43593i	−0.696081	−	0.717964i	$-0.745074\pi$
$283$		−	3.78939e29i		−	1.43593i	0.696081	−	0.717964i	$-0.254926\pi$
$284$	2.36724e29	+	9.11005e28i	0.859848	+	0.330903i
$285$	−1.33047e29			−0.463304
$286$	−4.98657e29	+	3.42406e29i	−1.66498	+	1.14327i
$287$		−	2.25421e28i		−	0.0721791i
$288$	−9.85567e28	+	7.36526e29i	−0.302675	+	2.26193i
$289$	−2.83360e29			−0.834764
$290$	1.32994e29	+	1.93683e29i	0.375885	+	0.547415i
$291$		−	2.61608e29i		−	0.709472i
$292$	2.91095e28	−	7.56407e28i	0.0757600	−	0.196862i
$293$	−4.69282e29			−1.17226			−0.586128	−	0.810218i	$-0.699348\pi$
$293$	−4.69282e29			−1.17226			−0.586128	+	0.810218i	$0.699348\pi$
$294$	5.74050e29	−	3.94175e29i	1.37652	−	0.945194i
$295$			2.33417e28i			0.0537363i
$296$	−5.16778e28	+	1.23371e28i	−0.114236	+	0.0272718i
$297$	1.78154e30			3.78198
$298$	4.84336e29	+	7.05354e29i	0.987532	+	1.43818i
$299$			2.75761e29i			0.540106i
$300$	−6.65566e29	−	2.56136e29i	−1.25238	−	0.481964i
$301$	9.31137e28			0.168351
$302$	−2.44466e29	+	1.67864e29i	−0.424751	+	0.291658i
$303$			7.39101e29i			1.23422i
$304$	−2.09756e29	+	2.32163e29i	−0.336690	+	0.372658i
$305$	3.14433e29			0.485211
$306$	−3.53917e29	−	5.15420e29i	−0.525102	−	0.764724i
$307$		−	1.01489e30i		−	1.44797i	−0.689815	−	0.723986i	$-0.742308\pi$
$307$		−	1.01489e30i		−	1.44797i	0.689815	−	0.723986i	$-0.257692\pi$
$308$	1.19268e29	−	3.09918e29i	0.163650	−	0.425244i
$309$	−2.23775e30			−2.95331
$310$	−1.40900e29	+	9.67497e28i	−0.178883	+	0.122831i
$311$			1.29786e30i			1.58527i	0.609695	+	0.792636i	$0.291292\pi$
$311$			1.29786e30i			1.58527i	−0.609695	+	0.792636i	$0.708708\pi$
$312$	−4.43984e29	−	1.85976e30i	−0.521810	−	2.18576i
$313$	3.82848e29			0.433007			0.216503	−	0.976282i	$-0.430535\pi$
$313$	3.82848e29			0.433007			0.216503	+	0.976282i	$0.430535\pi$
$314$	6.52890e29	+	9.50825e29i	0.710697	+	1.03501i
$315$			3.10348e29i			0.325179i
$316$	4.07606e29	+	1.56863e29i	0.411146	+	0.158225i
$317$	−7.74868e29			−0.752518			−0.376259	−	0.926515i	$-0.622790\pi$
$317$	−7.74868e29			−0.752518			−0.376259	+	0.926515i	$0.622790\pi$
$318$	1.95145e30	−	1.33997e30i	1.82487	−	1.25306i
$319$		−	2.35788e30i		−	2.12341i
$320$	5.23759e29	−	2.65190e29i	0.454288	−	0.230016i
$321$	−4.58052e29			−0.382696
$322$	−8.56935e28	−	1.24798e29i	−0.0689727	−	0.100447i
$323$		−	2.63259e29i		−	0.204152i
$324$	−9.25653e29	+	2.40530e30i	−0.691685	+	1.79734i
$325$	1.27589e30			0.918785
$326$	7.95034e29	−	5.45915e29i	0.551791	−	0.378891i
$327$			3.84994e30i			2.57561i
$328$	−3.89009e29	+	9.28690e28i	−0.250885	+	0.0598942i
$329$	−5.39048e29			−0.335179
$330$	−1.41813e30	−	2.06527e30i	−0.850256	−	1.23826i
$331$			1.24672e29i			0.0720833i	0.999350	+	0.0360417i	$0.0114749\pi$
$331$			1.24672e29i			0.0720833i	−0.999350	+	0.0360417i	$0.988525\pi$
$332$	−2.36122e29	−	9.08691e28i	−0.131668	−	0.0506709i
$333$	−4.98313e29			−0.268023
$334$	−1.88502e30	+	1.29436e30i	−0.978043	+	0.671579i
$335$			9.36132e29i			0.468597i
$336$	7.78855e29	+	7.03683e29i	0.376171	+	0.339864i
$337$	3.50619e30			1.63409			0.817046	−	0.576572i	$-0.195610\pi$
$337$	3.50619e30			1.63409			0.817046	+	0.576572i	$0.195610\pi$
$338$	6.77839e29	+	9.87160e29i	0.304878	+	0.444004i
$339$		−	3.68019e30i		−	1.59762i
$340$	−1.77409e29	+	4.60996e29i	−0.0743411	+	0.193175i
$341$	1.71530e30			0.693884
$342$	−2.41918e30	+	1.66114e30i	−0.944832	+	0.648775i
$343$		−	1.42599e30i		−	0.537756i
$344$	−3.83610e29	−	1.60686e30i	−0.139697	−	0.585164i
$345$	−1.14211e30			−0.401680
$346$	9.60616e29	+	1.39898e30i	0.326315	+	0.475223i
$347$			3.14730e30i			1.03272i	0.856370	+	0.516362i	$0.172714\pi$
$347$			3.14730e30i			1.03272i	−0.856370	+	0.516362i	$0.827286\pi$
$348$	6.95574e30	+	2.67684e30i	2.20492	+	0.848537i
$349$	−4.01019e30			−1.22817			−0.614086	−	0.789239i	$-0.710475\pi$
$349$	−4.01019e30			−1.22817			−0.614086	+	0.789239i	$0.710475\pi$
$350$	−5.77417e29	+	3.96487e29i	−0.170873	+	0.117331i
$351$		−	1.00749e31i		−	2.88108i
$352$	−5.83962e30	−	7.81416e29i	−1.61388	−	0.215958i
$353$	1.21894e30			0.325600			0.162800	−	0.986659i	$-0.447947\pi$
$353$	1.21894e30			0.325600			0.162800	+	0.986659i	$0.447947\pi$
$354$	4.19134e29	+	6.10398e29i	0.108221	+	0.157607i
$355$		−	1.87949e30i		−	0.469138i
$356$	2.18264e30	−	5.67156e30i	0.526722	−	1.36868i
$357$	−8.83176e29			−0.206077
$358$	−7.02219e30	+	4.82183e30i	−1.58444	+	1.08797i
$359$			2.23836e30i			0.488424i	0.969722	+	0.244212i	$0.0785293\pi$
$359$			2.23836e30i			0.488424i	−0.969722	+	0.244212i	$0.921471\pi$
$360$	5.35568e30	−	1.27857e30i	1.13028	−	0.269833i
$361$	3.66313e30			0.747766
$362$	−4.83996e30	−	7.04860e30i	−0.955738	−	1.39187i
$363$			1.56592e31i			2.99151i
$364$	−1.75263e30	−	6.74481e29i	−0.323948	−	0.124668i
$365$	−6.00558e29			−0.107409
$366$	8.22262e30	−	5.64611e30i	1.42311	−	0.977184i
$367$		−	3.94925e30i		−	0.661488i	−0.943721	−	0.330744i	$-0.892700\pi$
$367$		−	3.94925e30i		−	0.661488i	0.943721	−	0.330744i	$-0.107300\pi$
$368$	−1.80061e30	+	1.99296e30i	−0.291907	+	0.323090i
$369$	−3.75110e30			−0.588630
$370$	2.22848e29	+	3.24541e29i	0.0338523	+	0.0493002i
$371$		−	2.32501e30i		−	0.341931i
$372$	−1.94733e30	+	5.06013e30i	−0.277284	+	0.720520i
$373$	7.86026e30			1.08375			0.541877	−	0.840458i	$-0.317714\pi$
$373$	7.86026e30			1.08375			0.541877	+	0.840458i	$0.317714\pi$
$374$	4.08656e30	−	2.80606e30i	0.545630	−	0.374660i
$375$			1.24184e31i			1.60580i
$376$	2.22077e30	+	9.30236e30i	0.278131	+	1.16503i
$377$	−1.33342e31			−1.61760
$378$	3.13080e30	+	4.55949e30i	0.367921	+	0.535815i
$379$			8.21624e30i			0.935411i	0.883884	+	0.467706i	$0.154919\pi$
$379$			8.21624e30i			0.935411i	−0.883884	+	0.467706i	$0.845081\pi$
$380$	2.16373e30	+	8.32688e29i	0.238672	+	0.0918500i
$381$	−2.47238e30			−0.264250
$382$	8.74240e30	−	6.00302e30i	0.905462	−	0.621741i
$383$		−	1.06084e31i		−	1.06479i	−0.846495	−	0.532397i	$-0.821292\pi$
$383$		−	1.06084e31i		−	1.06479i	0.846495	−	0.532397i	$-0.178708\pi$
$384$	8.93473e30	−	1.63397e31i	0.869174	−	1.58954i
$385$	−2.46062e30			−0.232015
$386$	−1.93123e30	−	2.81251e30i	−0.176517	−	0.257067i
$387$		−	1.54945e31i		−	1.37292i
$388$	−1.63730e30	+	4.25452e30i	−0.140653	+	0.365485i
$389$	2.95604e30			0.246215			0.123108	−	0.992393i	$-0.460714\pi$
$389$	2.95604e30			0.246215			0.123108	+	0.992393i	$0.460714\pi$
$390$	−1.16795e31	+	8.01977e30i	−0.943294	+	0.647719i
$391$		−	2.25990e30i		−	0.176998i
$392$	−1.18027e31	+	2.81769e30i	−0.896499	+	0.214023i
$393$	5.03733e30			0.371099
$394$	3.22056e30	+	4.69021e30i	0.230132	+	0.335149i
$395$		−	3.23623e30i		−	0.224323i
$396$	−5.15716e31	−	1.98467e31i	−3.46791	−	1.33459i
$397$	1.32878e31			0.866898			0.433449	−	0.901178i	$-0.357296\pi$
$397$	1.32878e31			0.866898			0.433449	+	0.901178i	$0.357296\pi$
$398$	3.16132e30	−	2.17074e30i	0.200111	−	0.137408i
$399$			4.14528e30i			0.254612i
$400$	9.22103e30	+	8.33105e30i	0.549616	+	0.496569i
$401$	−3.17241e30			−0.183509			−0.0917545	−	0.995782i	$-0.529247\pi$
$401$	−3.17241e30			−0.183509			−0.0917545	+	0.995782i	$0.529247\pi$
$402$	1.68096e31	+	2.44804e31i	0.943725	+	1.37438i
$403$		−	9.70028e30i		−	0.528596i
$404$	4.62575e30	−	1.20200e31i	0.244684	−	0.635809i
$405$	1.90971e31			0.980637
$406$	6.03451e30	−	4.14363e30i	0.300836	−	0.206571i
$407$		−	3.95092e30i		−	0.191234i
$408$	3.63851e30	+	1.52410e31i	0.171002	+	0.716293i
$409$	8.62464e30			0.393605			0.196803	−	0.980443i	$-0.436944\pi$
$409$	8.62464e30			0.393605			0.196803	+	0.980443i	$0.436944\pi$
$410$	1.67751e30	+	2.44301e30i	0.0743461	+	0.108273i
$411$			5.22410e28i			0.00224859i
$412$	3.63924e31	+	1.40052e31i	1.52140	+	0.585495i
$413$	7.27245e29			0.0295312
$414$	−2.07670e31	+	1.42598e31i	−0.819160	+	0.562481i
$415$			1.87472e30i			0.0718388i
$416$	−4.41903e30	+	3.30240e31i	−0.164516	+	1.22945i
$417$	−4.40431e31			−1.59311
$418$	−1.31705e31	−	1.91807e31i	−0.462901	−	0.674137i
$419$		−	2.43356e31i		−	0.831140i	−0.909561	−	0.415570i	$-0.863582\pi$
$419$		−	2.43356e31i		−	0.831140i	0.909561	−	0.415570i	$-0.136418\pi$
$420$	2.79348e30	−	7.25884e30i	0.0927159	−	0.240922i
$421$	−4.51778e31			−1.45727			−0.728634	−	0.684903i	$-0.759845\pi$
$421$	−4.51778e31			−1.45727			−0.728634	+	0.684903i	$0.759845\pi$
$422$	3.90736e31	−	2.68301e31i	1.22499	−	0.841150i
$423$			8.96998e31i			2.73343i
$424$	−4.01227e31	+	9.57858e30i	−1.18850	+	0.283734i
$425$	−1.04561e31			−0.301095
$426$	−3.37491e31	−	4.91499e31i	−0.944815	−	1.37597i
$427$		−	9.79666e30i		−	0.266651i
$428$	7.44928e30	+	2.86677e30i	0.197146	+	0.0758696i
$429$	1.42184e32			3.65901
$430$	−1.00912e31	+	6.92921e30i	−0.252536	+	0.173405i
$431$		−	4.25086e30i		−	0.103455i	−0.998661	−	0.0517273i	$-0.983527\pi$
$431$		−	4.25086e30i		−	0.103455i	0.998661	−	0.0517273i	$-0.0164727\pi$
$432$	6.57849e31	−	7.28125e31i	1.55712	−	1.72346i
$433$	−3.87312e31			−0.891675			−0.445838	−	0.895114i	$-0.647094\pi$
$433$	−3.87312e31			−0.891675			−0.445838	+	0.895114i	$0.647094\pi$
$434$	3.01439e30	+	4.38995e30i	0.0675029	+	0.0983067i
$435$		−	5.52258e31i		−	1.20301i
$436$	2.40953e31	−	6.26114e31i	0.510616	−	1.32683i
$437$	−1.06071e31			−0.218684
$438$	−1.57049e31	+	1.07839e31i	−0.315026	+	0.216315i
$439$			6.49407e31i			1.26748i	0.773545	+	0.633742i	$0.218482\pi$
$439$			6.49407e31i			1.26748i	−0.773545	+	0.633742i	$0.781518\pi$
$440$	1.01373e31	+	4.24630e31i	0.192526	+	0.806452i
$441$	−1.13810e32			−2.10338
$442$	−1.58687e31	−	2.31101e31i	−0.285413	−	0.415657i
$443$			1.12412e32i			1.96773i	0.178899	+	0.983867i	$0.442746\pi$
$443$			1.12412e32i			1.96773i	−0.178899	+	0.983867i	$0.557254\pi$
$444$	1.16552e31	+	4.48538e30i	0.198575	+	0.0764193i
$445$	−4.50300e31			−0.746761
$446$	−7.47299e31	+	5.13137e31i	−1.20636	+	0.828353i
$447$		−	2.01121e32i		−	3.16058i
$448$	−8.26240e30	−	1.63185e31i	−0.126407	−	0.249657i
$449$	4.59583e31			0.684554			0.342277	−	0.939599i	$-0.388802\pi$
$449$	4.59583e31			0.684554			0.342277	+	0.939599i	$0.388802\pi$
$450$	6.59771e31	+	9.60846e31i	0.956848	+	1.39349i
$451$		−	2.97409e31i		−	0.419987i
$452$	−2.30329e31	+	5.98508e31i	−0.316729	+	0.823017i
$453$	6.97057e31			0.933447
$454$	1.54684e31	−	1.06215e31i	0.201732	−	0.138521i
$455$			1.39152e31i			0.176748i
$456$	7.15351e31	−	1.70777e31i	0.884995	−	0.211277i
$457$	2.18743e30			0.0263597			0.0131798	−	0.999913i	$-0.495805\pi$
$457$	2.18743e30			0.0263597			0.0131798	+	0.999913i	$0.495805\pi$
$458$	1.92813e31	+	2.80799e31i	0.226334	+	0.329618i
$459$			8.25652e31i			0.944158i
$460$	1.85741e31	+	7.14805e30i	0.206926	+	0.0796331i
$461$	1.25906e32			1.36658			0.683292	−	0.730145i	$-0.260548\pi$
$461$	1.25906e32			1.36658			0.683292	+	0.730145i	$0.260548\pi$
$462$	−6.43468e31	+	4.41841e31i	−0.680492	+	0.467264i
$463$			5.98500e31i			0.616726i	0.951269	+	0.308363i	$0.0997811\pi$
$463$			5.98500e31i			0.616726i	−0.951269	+	0.308363i	$0.900219\pi$
$464$	−9.63676e31	−	8.70666e31i	−0.967643	−	0.874250i
$465$	4.01754e31			0.393120
$466$	−8.69502e31	−	1.26628e32i	−0.829163	−	1.20754i
$467$			1.77676e31i			0.165130i	0.996586	+	0.0825649i	$0.0263112\pi$
$467$			1.77676e31i			0.165130i	−0.996586	+	0.0825649i	$0.973689\pi$
$468$	−1.12237e32	+	2.91646e32i	−1.01668	+	2.64183i
$469$	2.91667e31			0.257521
$470$	5.84196e31	−	4.01141e31i	0.502787	−	0.345242i
$471$		−	2.71113e32i		−	2.27457i
$472$	−2.99611e30	−	1.25501e31i	−0.0245049	−	0.102646i
$473$	1.22850e32			0.979580
$474$	−5.81113e31	−	8.46294e31i	−0.451773	−	0.657933i
$475$			4.90768e31i			0.372009i
$476$	1.43631e31	+	5.52746e30i	0.106161	+	0.0408547i
$477$	−3.86891e32			−2.78849
$478$	1.69219e32	−	1.16195e32i	1.18936	−	0.816684i
$479$		−	1.48154e32i		−	1.01552i	−0.861499	−	0.507759i	$-0.830474\pi$
$479$		−	1.48154e32i		−	1.01552i	0.861499	−	0.507759i	$-0.169526\pi$
$480$	−1.36774e32	−	1.83022e31i	−0.914345	−	0.122351i
$481$	−2.23431e31			−0.145681
$482$	1.52347e32	+	2.21867e32i	0.968876	+	1.41101i
$483$			3.55843e31i			0.220746i
$484$	9.80050e31	−	2.54665e32i	0.593067	−	1.54108i
$485$	3.37792e31			0.199411
$486$	1.66935e32	−	1.14627e32i	0.961417	−	0.660163i
$487$			1.48153e32i			0.832459i	0.909260	+	0.416230i	$0.136649\pi$
$487$			1.48153e32i			0.832459i	−0.909260	+	0.416230i	$0.863351\pi$
$488$	−1.69061e32	+	4.03603e31i	−0.926842	+	0.221267i
$489$	−2.26692e32			−1.21263
$490$	5.08964e31	+	7.41222e31i	0.265665	+	0.386897i
$491$		−	1.16969e32i		−	0.595791i	−0.954599	−	0.297895i	$-0.903715\pi$
$491$		−	1.16969e32i		−	0.595791i	0.954599	−	0.297895i	$-0.0962846\pi$
$492$	8.77357e31	+	3.37641e31i	0.436109	+	0.167832i
$493$	1.09275e32			0.530101
$494$	−1.08470e32	+	7.44814e31i	−0.513553	+	0.352634i
$495$			4.09458e32i			1.89211i
$496$	6.33388e31	−	7.01050e31i	0.285686	−	0.316205i
$497$	−5.85586e31			−0.257818
$498$	3.36633e31	+	4.90250e31i	0.144679	+	0.210701i
$499$			4.34392e32i			1.82253i	0.411816	+	0.911267i	$0.364895\pi$
$499$			4.34392e32i			1.82253i	−0.411816	+	0.911267i	$0.635105\pi$
$500$	7.77222e31	−	2.01960e32i	0.318350	−	0.827230i
$501$	5.37484e32			2.14938
$502$	−1.01194e32	+	6.94852e31i	−0.395101	+	0.271299i
$503$			7.31542e31i			0.278884i	0.990230	+	0.139442i	$0.0445309\pi$
$503$			7.31542e31i			0.278884i	−0.990230	+	0.139442i	$0.955469\pi$
$504$	−3.98359e31	−	1.66865e32i	−0.148289	−	0.621152i
$505$	−9.54338e31			−0.346901
$506$	−1.13060e32	−	1.64653e32i	−0.401330	−	0.584470i
$507$		−	2.81473e32i		−	0.975758i
$508$	4.02082e31	+	1.54737e31i	0.136129	+	0.0523877i
$509$	−2.96345e32			−0.979906			−0.489953	−	0.871749i	$-0.662986\pi$
$509$	−2.96345e32			−0.979906			−0.489953	+	0.871749i	$0.662986\pi$
$510$	9.57146e31	−	6.57230e31i	0.309126	−	0.212263i
$511$			1.87113e31i			0.0590274i
$512$	−2.47569e32	+	2.09813e32i	−0.762882	+	0.646538i
$513$	3.87528e32			1.16653
$514$	3.03536e32	+	4.42049e32i	0.892591	+	1.29991i
$515$		−	2.88942e32i		−	0.830086i
$516$	−1.39468e32	+	3.62406e32i	−0.391451	+	1.01718i
$517$	−7.11193e32			−1.95030
$518$	1.01116e31	−	6.94317e30i	0.0270933	−	0.0186038i
$519$		−	3.98897e32i		−	1.04436i
$520$	2.40135e32	−	5.73279e31i	0.614350	−	0.146665i
$521$	−9.49615e31			−0.237408			−0.118704	−	0.992930i	$-0.537874\pi$
$521$	−9.49615e31			−0.237408			−0.118704	+	0.992930i	$0.537874\pi$
$522$	−6.89517e32	−	1.00417e33i	−1.68461	−	2.45335i
$523$		−	4.81915e32i		−	1.15067i	−0.817919	−	0.575334i	$-0.804872\pi$
$523$		−	4.81915e32i		−	1.15067i	0.817919	−	0.575334i	$-0.195128\pi$
$524$	−8.19220e31	−	3.15268e31i	−0.191172	−	0.0735705i
$525$	1.64642e32			0.375516
$526$	−5.02316e31	+	3.44918e31i	−0.111982	+	0.0768931i
$527$			7.94950e31i			0.173226i
$528$	1.02758e33	+	9.28404e32i	2.18882	+	1.97756i
$529$	3.89197e32			0.810403
$530$	1.73019e32	+	2.51974e32i	0.352196	+	0.512915i
$531$		−	1.21017e32i		−	0.240830i
$532$	2.59437e31	−	6.74145e31i	0.0504769	−	0.131164i
$533$	−1.68190e32			−0.319943
$534$	−1.17756e33	+	8.08579e32i	−2.19022	+	1.50393i
$535$		−	5.91443e31i		−	0.107564i
$536$	−1.20161e32	−	5.03329e32i	−0.213691	−	0.895107i
$537$	2.00227e33			3.48202
$538$	−2.52610e32	−	3.67884e32i	−0.429599	−	0.625639i
$539$		−	9.02355e32i		−	1.50076i
$540$	−6.78604e32	−	2.61153e32i	−1.10380	−	0.424786i
$541$	−5.75239e32			−0.915127			−0.457563	−	0.889177i	$-0.651278\pi$
$541$	−5.75239e32			−0.915127			−0.457563	+	0.889177i	$0.651278\pi$
$542$	6.30753e32	−	4.33110e32i	0.981449	−	0.673918i
$543$			2.00980e33i			3.05882i
$544$	3.62145e31	−	2.70636e32i	0.0539133	−	0.402901i
$545$	−4.97110e32			−0.723926
$546$	2.49868e32	+	3.63892e32i	0.355959	+	0.518394i
$547$			1.00541e33i			1.40118i	0.713562	+	0.700592i	$0.247081\pi$
$547$			1.00541e33i			1.40118i	−0.713562	+	0.700592i	$0.752919\pi$
$548$	3.26957e29	−	8.49594e29i	0.000445783	−	0.00115836i
$549$	−1.63020e33			−2.17457
$550$	−7.61816e32	+	5.23105e32i	−0.994255	+	0.682711i
$551$		−	5.12895e32i		−	0.654951i
$552$	6.14079e32	−	1.46600e32i	0.767282	−	0.183175i
$553$	−1.00830e32			−0.123279
$554$	6.48444e32	+	9.44350e32i	0.775810	+	1.12984i
$555$		−	9.25378e31i		−	0.108344i
$556$	7.16272e32	+	2.75649e32i	0.820692	+	0.315834i
$557$	1.46940e33			1.64770			0.823850	−	0.566808i	$-0.191822\pi$
$557$	1.46940e33			1.64770			0.823850	+	0.566808i	$0.191822\pi$
$558$	7.30506e32	−	5.01607e32i	0.801703	−	0.550494i
$559$		−	6.94734e32i		−	0.746237i
$560$	−9.08606e31	+	1.00567e32i	−0.0955255	+	0.105730i
$561$	−1.16522e33			−1.19909
$562$	−2.07415e32	−	3.02066e32i	−0.208932	−	0.304274i
$563$			4.66874e32i			0.460361i	0.973148	+	0.230181i	$0.0739317\pi$
$563$			4.66874e32i			0.460361i	−0.973148	+	0.230181i	$0.926068\pi$
$564$	8.07398e32	−	2.09802e33i	0.779361	−	2.02516i
$565$	4.75192e32			0.449043
$566$	1.27953e33	−	8.78596e32i	1.18373	−	0.812816i
$567$		−	5.95001e32i		−	0.538916i
$568$	2.41250e32	+	1.01055e33i	0.213937	+	0.896140i
$569$	−4.67895e32			−0.406257			−0.203129	−	0.979152i	$-0.565111\pi$
$569$	−4.67895e32			−0.406257			−0.203129	+	0.979152i	$0.565111\pi$
$570$	−3.08478e32	−	4.49246e32i	−0.262256	−	0.381932i
$571$			9.11507e32i			0.758799i	0.925233	+	0.379399i	$0.123869\pi$
$571$			9.11507e32i			0.758799i	−0.925233	+	0.379399i	$0.876131\pi$
$572$	−2.31234e33	−	8.89877e32i	−1.88495	−	0.725400i
$573$	−2.49276e33			−1.98987
$574$	7.61158e31	−	5.22654e31i	0.0595021	−	0.0408575i
$575$			4.21290e32i			0.322528i
$576$	−2.71547e33	+	1.37490e33i	−2.03599	+	1.03086i
$577$	1.87411e33			1.37621			0.688107	−	0.725609i	$-0.258442\pi$
$577$	1.87411e33			1.37621			0.688107	+	0.725609i	$0.258442\pi$
$578$	−6.56988e32	−	9.56794e32i	−0.472524	−	0.688152i
$579$			8.01944e32i			0.564938i
$580$	−3.45637e32	+	8.98135e32i	−0.238498	+	0.619735i
$581$	5.84098e31			0.0394795
$582$	8.83347e32	−	6.06555e32i	0.584865	−	0.401601i
$583$		−	3.06750e33i		−	1.98958i
$584$	3.22901e32	−	7.70868e31i	0.205171	−	0.0489808i
$585$	2.31555e33			1.44140
$586$	−1.08806e33	−	1.58458e33i	−0.663563	−	0.966369i
$587$			1.92708e33i			1.15144i	0.817647	+	0.575721i	$0.195278\pi$
$587$			1.92708e33i			1.15144i	−0.817647	+	0.575721i	$0.804722\pi$
$588$	2.66194e33	+	1.02442e33i	1.55837	+	0.599722i
$589$	3.73118e32			0.214024
$590$	−7.88155e31	+	5.41192e31i	−0.0442984	+	0.0304177i
$591$		−	1.33734e33i		−	0.736534i
$592$	−1.61476e32	−	1.45891e32i	−0.0871460	−	0.0787350i
$593$	9.60280e32			0.507857			0.253929	−	0.967223i	$-0.418277\pi$
$593$	9.60280e32			0.507857			0.253929	+	0.967223i	$0.418277\pi$
$594$	4.13063e33	+	6.01557e33i	2.14081	+	3.11774i
$595$		−	1.14037e32i		−	0.0579218i
$596$	−1.25874e33	+	3.27082e33i	−0.626586	+	1.62818i
$597$	−9.01402e32			−0.439771
$598$	−9.31137e32	+	6.39371e32i	−0.445245	+	0.305730i
$599$			8.37129e32i			0.392347i	0.980569	+	0.196174i	$0.0628516\pi$
$599$			8.37129e32i			0.392347i	−0.980569	+	0.196174i	$0.937148\pi$
$600$	−6.78291e32	−	2.84122e33i	−0.311602	−	1.30524i
$601$	1.63827e32			0.0737722			0.0368861	−	0.999319i	$-0.488256\pi$
$601$	1.63827e32			0.0737722			0.0368861	+	0.999319i	$0.488256\pi$
$602$	2.15890e32	+	3.14408e32i	0.0952961	+	0.138783i
$603$		−	4.85345e33i		−	2.10012i
$604$	−1.13362e33	−	4.36261e32i	−0.480866	−	0.185056i
$605$	−2.02194e33			−0.840822
$606$	−2.49565e33	+	1.71365e33i	−1.01745	+	0.698637i
$607$			9.64348e32i			0.385451i	0.981253	+	0.192726i	$0.0617327\pi$
$607$			9.64348e32i			0.385451i	−0.981253	+	0.192726i	$0.938267\pi$
$608$	−1.27026e33	−	1.69977e32i	−0.497792	−	0.0666110i
$609$	−1.72065e33			−0.661126
$610$	7.29034e32	+	1.06172e33i	0.274657	+	0.399991i
$611$			4.02191e33i			1.48572i
$612$	9.19793e32	−	2.39007e33i	0.333175	−	0.865753i
$613$	4.10235e33			1.45716			0.728580	−	0.684961i	$-0.240181\pi$
$613$	4.10235e33			1.45716			0.728580	+	0.684961i	$0.240181\pi$
$614$	3.42690e33	−	2.35310e33i	1.19366	−	0.819634i
$615$		−	6.96587e32i		−	0.237943i
$616$	1.32300e33	−	3.15843e32i	0.443192	−	0.105804i
$617$	−2.03076e33			−0.667171			−0.333585	−	0.942720i	$-0.608259\pi$
$617$	−2.03076e33			−0.667171			−0.333585	+	0.942720i	$0.608259\pi$
$618$	−5.18837e33	−	7.55600e33i	−1.67174	−	2.43461i
$619$		−	3.79372e33i		−	1.19888i	−0.800418	−	0.599442i	$-0.795389\pi$
$619$		−	3.79372e33i		−	1.19888i	0.800418	−	0.599442i	$-0.204611\pi$
$620$	−6.53371e32	−	2.51442e32i	−0.202516	−	0.0779360i
$621$	3.32666e33			1.01137
$622$	−4.38237e33	+	3.00918e33i	−1.30685	+	0.897353i
$623$			1.40298e33i			0.410388i
$624$	5.25027e33	−	5.81114e33i	1.50649	−	1.66742i
$625$	1.02806e33			0.289374
$626$	8.87659e32	+	1.29273e33i	0.245106	+	0.356956i
$627$			5.46907e33i			1.48151i
$628$	−1.69679e33	+	4.40910e33i	−0.450934	+	1.17175i
$629$	1.83104e32			0.0477410
$630$	−1.04792e33	+	7.19563e32i	−0.268067	+	0.184070i
$631$		−	2.11322e33i		−	0.530386i	−0.964195	−	0.265193i	$-0.914564\pi$
$631$		−	2.11322e33i		−	0.530386i	0.964195	−	0.265193i	$-0.0854357\pi$
$632$	4.15399e32	+	1.74002e33i	0.102296	+	0.428499i
$633$	−1.11412e34			−2.69209
$634$	−1.79658e33	−	2.61642e33i	−0.425967	−	0.620350i
$635$		−	3.19237e32i		−	0.0742727i
$636$	9.04913e33	+	3.48245e33i	2.06596	+	0.795060i
$637$	−5.10296e33			−1.14327
$638$	7.96163e33	−	5.46690e33i	1.75047	−	1.20197i
$639$			9.74439e33i			2.10254i
$640$	2.10981e33	+	1.15367e33i	0.446770	+	0.244298i
$641$	5.13499e33			1.06719			0.533597	−	0.845739i	$-0.320840\pi$
$641$	5.13499e33			1.06719			0.533597	+	0.845739i	$0.320840\pi$
$642$	−1.06202e33	−	1.54666e33i	−0.216628	−	0.315482i
$643$		−	7.37013e33i		−	1.47551i	−0.675066	−	0.737757i	$-0.735885\pi$
$643$		−	7.37013e33i		−	1.47551i	0.675066	−	0.737757i	$-0.264115\pi$
$644$	2.22709e32	−	5.78706e32i	0.0437629	−	0.113718i
$645$	2.87736e33			0.554980
$646$	8.88923e32	−	6.10385e32i	0.168296	−	0.115562i
$647$			3.52753e33i			0.655570i	0.944752	+	0.327785i	$0.106302\pi$
$647$			3.52753e33i			0.655570i	−0.944752	+	0.327785i	$0.893698\pi$
$648$	−1.02679e34	+	2.45129e33i	−1.87320	+	0.447192i
$649$	9.59491e32			0.171832
$650$	2.95824e33	+	4.30819e33i	0.520084	+	0.757416i
$651$		−	1.25173e33i		−	0.216042i
$652$	3.68668e33	+	1.41878e33i	0.624689	+	0.240405i
$653$	−4.94232e32			−0.0822190			−0.0411095	−	0.999155i	$-0.513089\pi$
$653$	−4.94232e32			−0.0822190			−0.0411095	+	0.999155i	$0.513089\pi$
$654$	−1.29997e34	+	8.92633e33i	−2.12325	+	1.45794i
$655$			6.50428e32i			0.104305i
$656$	−1.21553e33	−	1.09821e33i	−0.191390	−	0.172917i
$657$	3.11364e33			0.481375
$658$	−1.24982e33	−	1.82015e33i	−0.189730	−	0.276310i
$659$		−	3.55271e33i		−	0.529584i	−0.964306	−	0.264792i	$-0.914697\pi$
$659$		−	3.55271e33i		−	0.529584i	0.964306	−	0.264792i	$-0.0853033\pi$
$660$	3.68558e33	−	9.57695e33i	0.539484	−	1.40184i
$661$	2.03249e33			0.292154			0.146077	−	0.989273i	$-0.453335\pi$
$661$	2.03249e33			0.292154			0.146077	+	0.989273i	$0.453335\pi$
$662$	−4.20970e32	+	2.89061e32i	−0.0594231	+	0.0408032i
$663$			6.58950e33i			0.913461i
$664$	−2.40637e32	−	1.00798e33i	−0.0327601	−	0.137225i
$665$	−5.35244e32			−0.0715636
$666$	−1.15537e33	−	1.68261e33i	−0.151716	−	0.220949i
$667$		−	4.40284e33i		−	0.567836i
$668$	−8.74108e33	−	3.36391e33i	−1.10725	−	0.426114i
$669$	2.13081e34			2.65113
$670$	−3.16095e33	+	2.17049e33i	−0.386296	+	0.265252i
$671$		−	1.29252e34i		−	1.55156i
$672$	−5.70233e32	+	4.26142e33i	−0.0672389	+	0.502485i
$673$	−8.04217e33			−0.931520			−0.465760	−	0.884911i	$-0.654219\pi$
$673$	−8.04217e33			−0.931520			−0.465760	+	0.884911i	$0.654219\pi$
$674$	8.12933e33	+	1.18390e34i	0.924988	+	1.34709i
$675$		−	1.53918e34i		−	1.72046i
$676$	−1.76163e33	+	4.57759e33i	−0.193444	+	0.502663i
$677$	−1.24005e34			−1.33775			−0.668874	−	0.743376i	$-0.733224\pi$
$677$	−1.24005e34			−1.33775			−0.668874	+	0.743376i	$0.733224\pi$
$678$	1.24266e34	−	8.53277e33i	1.31703	−	0.904344i
$679$		−	1.05244e33i		−	0.109588i
$680$	−1.96794e33	+	4.69810e32i	−0.201328	+	0.0480635i
$681$	−4.41058e33			−0.443333
$682$	3.97703e33	+	5.79188e33i	0.392777	+	0.572015i
$683$			8.65513e33i			0.839895i	0.907548	+	0.419947i	$0.137952\pi$
$683$			8.65513e33i			0.839895i	−0.907548	+	0.419947i	$0.862048\pi$
$684$	−1.12181e34	−	4.31714e33i	−1.06966	−	0.411645i
$685$	−6.74544e30			−0.000632009
$686$	4.81499e33	−	3.30624e33i	0.443308	−	0.304400i
$687$		−	8.00656e33i		−	0.724378i
$688$	4.53632e33	−	5.02092e33i	0.403313	−	0.446398i
$689$	−1.73472e34			−1.51565
$690$	−2.64806e33	−	3.85646e33i	−0.227373	−	0.331131i
$691$			1.71448e34i			1.44676i	0.690452	+	0.723378i	$0.257411\pi$
$691$			1.71448e34i			1.44676i	−0.690452	+	0.723378i	$0.742589\pi$
$692$	−2.49654e33	+	6.48724e33i	−0.207045	+	0.538006i
$693$	1.27573e34			1.03982
$694$	−1.06272e34	+	7.29722e33i	−0.851343	+	0.584580i
$695$		−	5.68691e33i		−	0.447774i
$696$	7.08872e33	+	2.96932e34i	0.548601	+	2.29798i
$697$	1.37834e33			0.104848
$698$	−9.29788e33	−	1.35408e34i	−0.695215	−	1.01246i
$699$			3.61062e34i			2.65372i
$700$	−2.67756e33	−	1.03043e33i	−0.193447	−	0.0744460i
$701$	2.79316e34			1.98372			0.991859	−	0.127339i	$-0.0406436\pi$
$701$	2.79316e34			1.98372			0.991859	+	0.127339i	$0.0406436\pi$
$702$	3.40190e34	−	2.33593e34i	2.37507	−	1.63086i
$703$		−	8.59420e32i		−	0.0589850i
$704$	−1.09010e34	−	2.15298e34i	−0.735520	−	1.45268i
$705$	−1.66574e34			−1.10494
$706$	2.82618e33	+	4.11586e33i	0.184308	+	0.268414i
$707$			2.97339e33i			0.190642i
$708$	−1.08928e33	+	2.83050e33i	−0.0686661	+	0.178428i
$709$	1.69545e34			1.05083			0.525414	−	0.850847i	$-0.323911\pi$
$709$	1.69545e34			1.05083			0.525414	+	0.850847i	$0.323911\pi$
$710$	6.34631e33	−	4.35773e33i	0.386742	−	0.265559i
$711$			1.67785e34i			1.00535i
$712$	2.42112e34	−	5.77999e33i	1.42645	−	0.340539i
$713$	3.20296e33			0.185557
$714$	−2.04770e33	−	2.98214e33i	−0.116651	−	0.169883i
$715$			1.83591e34i			1.02844i
$716$	−3.25628e34	−	1.25314e34i	−1.79377	−	0.690310i
$717$	−4.82502e34			−2.61378
$718$	−7.55807e33	+	5.18979e33i	−0.402641	+	0.276476i
$719$		−	3.26667e34i		−	1.71143i	−0.517449	−	0.855714i	$-0.673118\pi$
$719$		−	3.26667e34i		−	1.71143i	0.517449	−	0.855714i	$-0.326882\pi$
$720$	1.67347e34	+	1.51196e34i	0.862242	+	0.779022i
$721$	−9.00242e33			−0.456180
$722$	8.49320e33	+	1.23689e34i	0.423278	+	0.616433i
$723$		−	6.32620e34i		−	3.10087i
$724$	1.25786e34	−	3.26853e34i	0.606412	−	1.57576i
$725$	−2.03711e34			−0.965958
$726$	−5.28750e34	+	3.63069e34i	−2.46610	+	1.69336i
$727$			1.73000e34i			0.793657i	0.917893	+	0.396828i	$0.129889\pi$
$727$			1.73000e34i			0.793657i	−0.917893	+	0.396828i	$0.870111\pi$
$728$	−1.78614e33	−	7.48178e33i	−0.0806008	−	0.337620i
$729$	−4.21290e33			−0.187004
$730$	−1.39243e33	−	2.02785e33i	−0.0607995	−	0.0885443i
$731$			5.69343e33i			0.244549i
$732$	3.81294e34	+	1.46737e34i	1.61112	+	0.620020i
$733$	1.32452e34			0.550566			0.275283	−	0.961363i	$-0.411228\pi$
$733$	1.32452e34			0.550566			0.275283	+	0.961363i	$0.411228\pi$
$734$	1.33351e34	−	9.15660e33i	0.545308	−	0.374439i
$735$		−	2.11348e34i		−	0.850256i
$736$	−1.09043e34	−	1.45913e33i	−0.431581	−	0.0577511i
$737$	3.84810e34			1.49843
$738$	−8.69718e33	−	1.26660e34i	−0.333198	−	0.485247i
$739$			2.67052e34i			1.00661i	0.864108	+	0.503307i	$0.167883\pi$
$739$			2.67052e34i			1.00661i	−0.864108	+	0.503307i	$0.832117\pi$
$740$	−5.79159e32	+	1.50494e33i	−0.0214791	+	0.0558134i
$741$	3.09285e34			1.12860
$742$	7.85064e33	−	5.39069e33i	0.281876	−	0.193552i
$743$			8.69824e33i			0.307302i	0.988125	+	0.153651i	$0.0491032\pi$
$743$			8.69824e33i			0.307302i	−0.988125	+	0.153651i	$0.950897\pi$
$744$	−2.16011e34	+	5.15687e33i	−0.750931	+	0.179271i
$745$	2.59690e34			0.888343
$746$	1.82245e34	+	2.65410e34i	0.613466	+	0.893411i
$747$		−	9.71963e33i		−	0.321961i
$748$	1.89499e34	+	7.29266e33i	0.617715	+	0.237720i
$749$	−1.84273e33			−0.0591127
$750$	−4.19321e34	+	2.87930e34i	−1.32377	+	0.908973i
$751$		−	2.66751e34i		−	0.828755i	−0.910105	−	0.414378i	$-0.863999\pi$
$751$		−	2.66751e34i		−	0.828755i	0.910105	−	0.414378i	$-0.136001\pi$
$752$	−2.62614e34	+	2.90668e34i	−0.802978	+	0.888757i
$753$	2.88538e34			0.868287
$754$	−3.09162e34	−	4.50243e34i	−0.915651	−	1.33349i
$755$			9.00050e33i			0.262363i
$756$	−8.13663e33	+	2.11430e34i	−0.233444	+	0.606603i
$757$	−3.60323e34			−1.01752			−0.508759	−	0.860909i	$-0.669895\pi$
$757$	−3.60323e34			−1.01752			−0.508759	+	0.860909i	$0.669895\pi$
$758$	−2.77430e34	+	1.90499e34i	−0.771122	+	0.529495i
$759$			4.69481e34i			1.28445i
$760$	2.20510e33	+	9.23672e33i	0.0593834	+	0.248745i
$761$	−1.38142e34			−0.366192			−0.183096	−	0.983095i	$-0.558612\pi$
$761$	−1.38142e34			−0.366192			−0.183096	+	0.983095i	$0.558612\pi$
$762$	−5.73237e33	−	8.34825e33i	−0.149580	−	0.217839i
$763$			1.54882e34i			0.397839i
$764$	4.05397e34	+	1.56012e34i	1.02509	+	0.394492i
$765$	−1.89762e34			−0.472360
$766$	3.58204e34	−	2.45963e34i	0.877780	−	0.602733i
$767$		−	5.42608e33i		−	0.130901i
$768$	7.58886e34	−	7.71569e33i	1.80236	−	0.183248i
$769$	−5.59413e34			−1.30803			−0.654013	−	0.756483i	$-0.726916\pi$
$769$	−5.59413e34			−1.30803			−0.654013	+	0.756483i	$0.726916\pi$
$770$	−5.70512e33	−	8.30856e33i	−0.131334	−	0.191266i
$771$		−	1.26043e35i		−	2.85672i
$772$	5.01906e33	−	1.30420e34i	0.111999	−	0.291029i
$773$	5.23030e34			1.14914			0.574570	−	0.818456i	$-0.305169\pi$
$773$	5.23030e34			1.14914			0.574570	+	0.818456i	$0.305169\pi$
$774$	5.23188e34	−	3.59250e34i	1.13179	−	0.777152i
$775$		−	1.48195e34i		−	0.315655i
$776$	−1.81620e34	+	4.33586e33i	−0.380911	+	0.0909357i
$777$	−2.88316e33			−0.0595410
$778$	6.85377e33	+	9.98138e33i	0.139372	+	0.202972i
$779$		−	6.46936e33i		−	0.129542i
$780$	−5.41592e34	−	2.08425e34i	−1.06792	−	0.410975i
$781$	−7.72592e34			−1.50016
$782$	7.63078e33	−	5.23972e33i	0.145911	−	0.100191i
$783$			1.60857e35i			3.02901i
$784$	−3.68797e34	−	3.33202e34i	−0.683903	−	0.617895i
$785$	3.50065e34			0.639313
$786$	1.16794e34	+	1.70091e34i	0.210063	+	0.305922i
$787$			8.18930e34i			1.45061i	0.688429	+	0.725304i	$0.258301\pi$
$787$			8.18930e34i			1.45061i	−0.688429	+	0.725304i	$0.741699\pi$
$788$	−8.36991e33	+	2.17491e34i	−0.146018	+	0.379426i
$789$	1.43228e34			0.246095
$790$	1.09275e34	−	7.50342e33i	0.184925	−	0.126980i
$791$		−	1.48053e34i		−	0.246775i
$792$	−5.25576e34	−	2.20153e35i	−0.862845	−	3.61428i
$793$	−7.30942e34			−1.18196
$794$	3.08087e34	+	4.48678e34i	0.490713	+	0.714642i
$795$		−	7.18465e34i		−	1.12720i
$796$	1.46595e34	+	5.64153e33i	0.226549	+	0.0871847i
$797$	−2.14047e34			−0.325843			−0.162922	−	0.986639i	$-0.552092\pi$
$797$	−2.14047e34			−0.325843			−0.162922	+	0.986639i	$0.552092\pi$
$798$	−1.39970e34	+	9.61110e33i	−0.209894	+	0.144125i
$799$		−	3.29601e34i		−	0.486885i
$800$	−6.75111e33	+	5.04519e34i	−0.0982415	+	0.734171i
$801$	2.33462e35			3.34676
$802$	−7.35545e33	−	1.07120e34i	−0.103876	−	0.151279i
$803$			2.46868e34i			0.343461i
$804$	−4.36865e34	+	1.13519e35i	−0.598790	+	1.55595i
$805$	−4.59470e33			−0.0620450
$806$	3.27540e34	−	2.24908e34i	0.435757	−	0.299215i
$807$			1.04897e35i			1.37492i
$808$	5.13118e34	−	1.22498e34i	0.662645	−	0.158195i
$809$	−7.61415e34			−0.968811			−0.484405	−	0.874844i	$-0.660964\pi$
$809$	−7.61415e34			−0.968811			−0.484405	+	0.874844i	$0.660964\pi$
$810$	4.42780e34	+	6.44835e34i	0.555096	+	0.808404i
$811$			7.07104e32i			0.00873440i	0.999990	+	0.00436720i	$0.00139013\pi$
$811$			7.07104e32i			0.00873440i	−0.999990	+	0.00436720i	$0.998610\pi$
$812$	2.79828e34	+	1.07689e34i	0.340580	+	0.131068i
$813$	−1.79849e35			−2.15686
$814$	1.33407e34	−	9.16047e33i	0.157647	−	0.108249i
$815$		−	2.92708e34i		−	0.340834i
$816$	−4.30266e34	+	4.76230e34i	−0.493691	+	0.546431i
$817$	2.67227e34			0.302145
$818$	1.99968e34	+	2.91220e34i	0.222803	+	0.324475i
$819$		−	7.21446e34i		−	0.792131i
$820$	−4.35967e33	+	1.13286e34i	−0.0471723	+	0.122577i
$821$	−4.88782e34			−0.521191			−0.260596	−	0.965448i	$-0.583919\pi$
$821$	−4.88782e34			−0.521191			−0.260596	+	0.965448i	$0.583919\pi$
$822$	−1.76397e32	+	1.21124e32i	−0.00185366	+	0.00127283i
$823$		−	1.35108e35i		−	1.39921i	−0.714531	−	0.699603i	$-0.753360\pi$
$823$		−	1.35108e35i		−	1.39921i	0.714531	−	0.699603i	$-0.246640\pi$
$824$	3.70882e34	+	1.55355e35i	0.378538	+	1.58562i
$825$	2.17220e35			2.18500
$826$	1.68617e33	+	2.45562e33i	0.0167163	+	0.0243445i
$827$			9.85430e34i			0.962852i	0.876487	+	0.481426i	$0.159881\pi$
$827$			9.85430e34i			0.962852i	−0.876487	+	0.481426i	$0.840119\pi$
$828$	−9.62991e34	−	3.70596e34i	−0.927381	−	0.356892i
$829$	1.18109e35			1.12106			0.560528	−	0.828136i	$-0.310598\pi$
$829$	1.18109e35			1.12106			0.560528	+	0.828136i	$0.310598\pi$
$830$	−6.33019e33	+	4.34666e33i	−0.0592215	+	0.0406648i
$831$		−	2.69267e35i		−	2.48297i
$832$	−1.21755e35	+	6.16469e34i	−1.10664	+	0.560314i
$833$	4.18194e34			0.374660
$834$	−1.02117e35	−	1.48716e35i	−0.901789	−	1.31331i
$835$			6.94007e34i			0.604124i
$836$	3.42288e34	−	8.89433e34i	0.293709	−	0.763199i
$837$	−1.17020e35			−0.989814
$838$	8.21718e34	−	5.64237e34i	0.685164	−	0.470472i
$839$		−	4.24492e34i		−	0.348920i	−0.984664	−	0.174460i	$-0.944182\pi$
$839$		−	4.24492e34i		−	0.348920i	0.984664	−	0.174460i	$-0.0558180\pi$
$840$	3.09871e34	−	7.39761e33i	0.251090	−	0.0599432i
$841$	8.77105e34			0.700648
$842$	−1.04748e35	−	1.52548e35i	−0.824896	−	1.20132i
$843$			8.61293e34i			0.668683i
$844$	1.81190e35	+	6.97287e34i	1.38683	+	0.533706i
$845$	3.63443e34			0.274256
$846$	−3.02881e35	+	2.07975e35i	−2.25334	+	1.54727i
$847$			6.29967e34i			0.462080i
$848$	−1.25370e35	−	1.13270e35i	−0.906660	−	0.819153i
$849$	−3.64838e35			−2.60140
$850$	−2.42432e34	−	3.53062e34i	−0.170436	−	0.248212i
$851$		−	7.37751e33i		−	0.0511394i
$852$	8.77103e34	−	2.27915e35i	0.599481	−	1.55775i
$853$	1.05546e35			0.711300			0.355650	−	0.934619i	$-0.384259\pi$
$853$	1.05546e35			0.711300			0.355650	+	0.934619i	$0.384259\pi$
$854$	3.30794e34	−	2.27142e34i	0.219818	−	0.150940i
$855$			8.90669e34i			0.583610i
$856$	7.59170e33	+	3.18001e34i	0.0490517	+	0.205467i
$857$	6.07447e34			0.387025			0.193512	−	0.981098i	$-0.438012\pi$
$857$	6.07447e34			0.387025			0.193512	+	0.981098i	$0.438012\pi$
$858$	3.29664e35	+	4.80100e35i	2.07121	+	3.01637i
$859$		−	4.06590e33i		−	0.0251906i	−0.999921	−	0.0125953i	$-0.995991\pi$
$859$		−	4.06590e33i		−	0.0251906i	0.999921	−	0.0125953i	$-0.00400932\pi$
$860$	−4.67944e34	−	1.80083e34i	−0.285899	−	0.110025i
$861$	−2.17032e34			−0.130764
$862$	1.43535e34	−	9.85590e33i	0.0852845	−	0.0585611i
$863$		−	8.38835e33i		−	0.0491527i	−0.999698	−	0.0245763i	$-0.992176\pi$
$863$		−	8.38835e33i		−	0.0491527i	0.999698	−	0.0245763i	$-0.00782368\pi$
$864$	3.98386e35	+	5.33091e34i	2.30218	+	0.308061i
$865$	5.15061e34			0.293539
$866$	−8.98010e34	−	1.30780e35i	−0.504738	−	0.735067i
$867$			2.72815e35i			1.51230i
$868$	−7.83408e33	+	2.03568e34i	−0.0428303	+	0.111294i
$869$	−1.33030e35			−0.717318
$870$	1.86476e35	−	1.28045e35i	0.991725	−	0.680974i
$871$		−	2.17616e35i		−	1.14149i
$872$	2.67280e35	−	6.38084e34i	1.38283	−	0.330126i
$873$	−1.75131e35			−0.893701
$874$	−2.45932e34	−	3.58159e34i	−0.123788	−	0.180276i
$875$			4.99591e34i			0.248038i
$876$	−7.28259e34	−	2.80262e34i	−0.356645	−	0.137251i
$877$	−5.97152e34			−0.288463			−0.144231	−	0.989544i	$-0.546071\pi$
$877$	−5.97152e34			−0.288463			−0.144231	+	0.989544i	$0.546071\pi$
$878$	−2.19279e35	+	1.50569e35i	−1.04487	+	0.717467i
$879$			4.51819e35i			2.12372i
$880$	−1.19877e35	+	1.32683e35i	−0.555832	+	0.615209i
$881$	2.17322e35			0.994014			0.497007	−	0.867747i	$-0.334432\pi$
$881$	2.17322e35			0.994014			0.497007	+	0.867747i	$0.334432\pi$
$882$	−2.63877e35	−	3.84292e35i	−1.19063	−	1.73396i
$883$			2.13919e35i			0.952184i	0.879395	+	0.476092i	$0.157947\pi$
$883$			2.13919e35i			0.952184i	−0.879395	+	0.476092i	$0.842053\pi$
$884$	4.12411e34	−	1.07165e35i	0.181094	−	0.470571i
$885$	2.24730e34			0.0973515
$886$	−3.79570e35	+	2.60634e35i	−1.62213	+	1.11385i
$887$		−	1.70478e35i		−	0.718760i	−0.933191	−	0.359380i	$-0.882988\pi$
$887$		−	1.70478e35i		−	0.718760i	0.933191	−	0.359380i	$-0.117012\pi$
$888$	1.18780e34	+	4.97547e34i	0.0494071	+	0.206956i
$889$	−9.94634e33			−0.0408171
$890$	−1.04405e35	−	1.52048e35i	−0.422709	−	0.615605i
$891$		−	7.85015e35i		−	3.13578i
$892$	−3.46533e35	−	1.33359e35i	−1.36573	−	0.525587i
$893$	−1.54701e35			−0.601557
$894$	6.79106e35	−	4.66312e35i	2.60548	−	1.78907i
$895$			2.58536e35i			0.978688i
$896$	3.59443e34	−	6.57345e34i	0.134256	−	0.245526i
$897$	2.65499e35			0.978485
$898$	1.06557e35	+	1.55183e35i	0.387496	+	0.564323i
$899$			1.54876e35i			0.555735i
$900$	−1.71468e35	+	4.45557e35i	−0.607117	+	1.57759i
$901$	1.42163e35			0.496693
$902$	1.00423e35	−	6.89563e34i	0.346223	−	0.237736i
$903$		−	8.96486e34i		−	0.304994i
$904$	−2.55496e35	+	6.09951e34i	−0.857754	+	0.204773i
$905$	−2.59508e35			−0.859742
$906$	1.61617e35	+	2.35369e35i	0.528383	+	0.769502i
$907$		−	4.35658e35i		−	1.40559i	−0.711393	−	0.702794i	$-0.751935\pi$
$907$		−	4.35658e35i		−	1.40559i	0.711393	−	0.702794i	$-0.248065\pi$
$908$	7.17291e34	+	2.76041e34i	0.228384	+	0.0878909i
$909$	4.94784e35			1.55471
$910$	−4.69862e34	+	3.22634e34i	−0.145705	+	0.100049i
$911$		−	3.10771e35i		−	0.951086i	−0.879692	−	0.475543i	$-0.842252\pi$
$911$		−	3.10771e35i		−	0.951086i	0.879692	−	0.475543i	$-0.157748\pi$
$912$	2.23524e35	+	2.01950e35i	0.675127	+	0.609966i
$913$	7.70630e34			0.229719
$914$	5.07171e33	+	7.38610e33i	0.0149211	+	0.0217300i
$915$		−	3.02732e35i		−	0.879033i
$916$	−5.01100e34	+	1.30210e35i	−0.143608	+	0.373164i
$917$	2.02651e34			0.0573214
$918$	−2.78790e35	+	1.91433e35i	−0.778332	+	0.534446i
$919$		−	3.98640e35i		−	1.09849i	−0.835662	−	0.549244i	$-0.814916\pi$
$919$		−	3.98640e35i		−	1.09849i	0.835662	−	0.549244i	$-0.185084\pi$
$920$	1.89292e34	+	7.92908e34i	0.0514848	+	0.215660i
$921$	−9.77127e35			−2.62322
$922$	2.91922e35	+	4.25136e35i	0.773563	+	1.12657i
$923$			4.36913e35i			1.14281i
$924$	−2.98385e35	−	1.14830e35i	−0.770394	−	0.296477i
$925$	−3.41343e34			−0.0869942
$926$	−2.02090e35	+	1.38766e35i	−0.508408	+	0.349102i
$927$			1.49804e36i			3.72020i
$928$	7.05549e34	−	5.27265e35i	0.172962	−	1.29257i
$929$	−1.11329e35			−0.269413			−0.134706	−	0.990886i	$-0.543009\pi$
$929$	−1.11329e35			−0.269413			−0.134706	+	0.990886i	$0.543009\pi$
$930$	9.31493e34	+	1.35656e35i	0.222528	+	0.324075i
$931$		−	1.96284e35i		−	0.462901i
$932$	2.25975e35	−	5.87193e35i	0.526101	−	1.36707i
$933$	1.24956e36			2.87196
$934$	−5.99941e34	+	4.11953e34i	−0.136128	+	0.0934728i
$935$		−	1.50455e35i		−	0.337028i
$936$	−1.24500e36	+	2.97221e35i	−2.75334	+	0.657309i
$937$	−3.92996e34			−0.0858051			−0.0429026	−	0.999079i	$-0.513661\pi$
$937$	−3.92996e34			−0.0858051			−0.0429026	+	0.999079i	$0.513661\pi$
$938$	6.76249e34	+	9.84843e34i	0.145771	+	0.212292i
$939$		−	3.68601e35i		−	0.784458i
$940$	2.70899e35	+	1.04253e35i	0.569211	+	0.219055i
$941$	3.89110e35			0.807230			0.403615	−	0.914929i	$-0.367754\pi$
$941$	3.89110e35			0.807230			0.403615	+	0.914929i	$0.367754\pi$
$942$	9.15442e35	−	6.28594e35i	1.87508	−	1.28754i
$943$		−	5.55349e34i		−	0.112312i
$944$	3.54300e34	−	3.92149e34i	0.0707469	−	0.0783045i
$945$	1.67867e35			0.330966
$946$	2.84835e35	+	4.14815e35i	0.554497	+	0.807533i
$947$			2.97834e35i			0.572498i	0.958155	+	0.286249i	$0.0924085\pi$
$947$			2.97834e35i			0.572498i	−0.958155	+	0.286249i	$0.907591\pi$
$948$	1.51025e35	−	3.92438e35i	0.286648	−	0.744854i
$949$	1.39608e35			0.261646
$950$	−1.65713e35	+	1.13788e35i	−0.306672	+	0.210578i
$951$			7.46033e35i			1.36330i
$952$	1.46377e34	+	6.13142e34i	0.0264136	+	0.110641i
$953$	−7.80591e35			−1.39094			−0.695470	−	0.718555i	$-0.744804\pi$
$953$	−7.80591e35			−1.39094			−0.695470	+	0.718555i	$0.744804\pi$
$954$	−8.97034e35	−	1.30638e36i	−1.57844	−	2.29874i
$955$		−	3.21869e35i		−	0.559292i
$956$	7.84692e35	+	3.01980e35i	1.34649	+	0.518183i
$957$	−2.27013e36			−3.84688
$958$	5.00258e35	−	3.43505e35i	0.837159	−	0.574840i
$959$			2.10165e32i			0.000347325i
$960$	−2.55321e35	−	5.04268e35i	−0.416708	−	0.823013i
$961$	5.07744e35			0.818398
$962$	−5.18039e34	−	7.54438e34i	−0.0824635	−	0.120094i
$963$			3.06639e35i			0.482071i
$964$	−3.95933e35	+	1.02883e36i	−0.614748	+	1.59742i
$965$	−1.03548e35			−0.158787
$966$	−1.20154e35	+	8.25046e34i	−0.181976	+	0.124955i
$967$		−	1.26019e36i		−	1.88502i	−0.334172	−	0.942512i	$-0.608457\pi$
$967$		−	1.26019e36i		−	1.88502i	0.334172	−	0.942512i	$-0.391543\pi$
$968$	1.08714e36	−	2.59534e35i	1.60612	−	0.383433i
$969$	−2.53463e35			−0.369853
$970$	7.83193e34	+	1.14059e35i	0.112878	+	0.164388i
$971$			1.47862e35i			0.210487i	0.994446	+	0.105243i	$0.0335622\pi$
$971$			1.47862e35i			0.210487i	−0.994446	+	0.105243i	$0.966438\pi$
$972$	7.74099e35	+	2.97903e35i	1.08843	+	0.418871i
$973$	−1.77185e35			−0.246078
$974$	−5.00254e35	+	3.43503e35i	−0.686252	+	0.471219i
$975$		−	1.22841e36i		−	1.66452i
$976$	−5.28260e35	−	4.77274e35i	−0.707049	−	0.638808i
$977$	−1.19198e35			−0.157592			−0.0787962	−	0.996891i	$-0.525108\pi$
$977$	−1.19198e35			−0.157592			−0.0787962	+	0.996891i	$0.525108\pi$
$978$	−5.25600e35	−	7.65448e35i	−0.686418	−	0.999654i
$979$			1.85102e36i			2.38792i
$980$	−1.32275e35	+	3.43714e35i	−0.168563	+	0.438011i
$981$	2.57731e36			3.24443
$982$	3.94959e35	−	2.71201e35i	0.491150	−	0.337251i
$983$			5.07185e35i			0.623052i	0.950238	+	0.311526i	$0.100840\pi$
$983$			5.07185e35i			0.623052i	−0.950238	+	0.311526i	$0.899160\pi$
$984$	8.94130e34	+	3.74533e35i	0.108507	+	0.454516i
$985$	1.72680e35			0.207017
$986$	2.53362e35	+	3.68980e35i	0.300067	+	0.436998i
$987$			5.18988e35i			0.607228i
$988$	−5.02989e35	−	1.93570e35i	−0.581400	−	0.223745i
$989$	2.29396e35			0.261957
$990$	−1.38258e36	+	9.49356e35i	−1.55980	+	1.07104i
$991$		−	5.74736e35i		−	0.640596i	−0.947317	−	0.320298i	$-0.896217\pi$
$991$		−	5.74736e35i		−	0.640596i	0.947317	−	0.320298i	$-0.103783\pi$
$992$	3.83572e35	+	5.13269e34i	0.422384	+	0.0565204i
$993$	1.20033e35			0.130590
$994$	−1.35772e35	−	1.97729e35i	−0.145940	−	0.212537i
$995$		−	1.16390e35i		−	0.123606i
$996$	−8.74875e34	+	2.27336e35i	−0.0917982	+	0.238537i
$997$	−5.09295e35			−0.527993			−0.263996	−	0.964524i	$-0.585041\pi$
$997$	−5.09295e35			−0.527993			−0.263996	+	0.964524i	$0.585041\pi$
$998$	−1.46677e36	+	1.00717e36i	−1.50244	+	1.03166i
$999$			2.69537e35i			0.272792i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.25.b.b.3.10	yes	10
3.2	odd	2		36.25.d.b.19.1		10
4.3	odd	2	inner	4.25.b.b.3.9	✓	10
8.3	odd	2		64.25.c.d.63.1		10
8.5	even	2		64.25.c.d.63.10		10
12.11	even	2		36.25.d.b.19.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.25.b.b.3.9	✓	10	4.3	odd	2	inner
4.25.b.b.3.10	yes	10	1.1	even	1	trivial
36.25.d.b.19.1		10	3.2	odd	2
36.25.d.b.19.2		10	12.11	even	2
64.25.c.d.63.1		10	8.3	odd	2
64.25.c.d.63.10		10	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2318.57 + 3376.61i) q^{2} -962787. i q^{3} +(-6.02571e6 + 1.56578e7i) q^{4} +1.24317e8 q^{5} +(3.25095e9 - 2.23229e9i) q^{6} -3.87327e9i q^{7} +(-6.68411e10 + 1.59571e10i) q^{8} -6.44529e11 q^{9} +O(q^{10})\)	\(q+(2318.57 + 3376.61i) q^{2} -962787. i q^{3} +(-6.02571e6 + 1.56578e7i) q^{4} +1.24317e8 q^{5} +(3.25095e9 - 2.23229e9i) q^{6} -3.87327e9i q^{7} +(-6.68411e10 + 1.59571e10i) q^{8} -6.44529e11 q^{9} +(2.88236e11 + 4.19768e11i) q^{10} -5.11020e12i q^{11} +(1.50751e13 + 5.80148e12i) q^{12} -2.88990e13 q^{13} +(1.30785e13 - 8.98044e12i) q^{14} -1.19690e14i q^{15} +(-2.08856e14 - 1.88699e14i) q^{16} +2.36831e14 q^{17} +(-1.49438e15 - 2.17632e15i) q^{18} -1.11159e15i q^{19} +(-7.49096e14 + 1.94652e15i) q^{20} -3.72914e15 q^{21} +(1.72551e16 - 1.18483e16i) q^{22} -9.54223e15i q^{23} +(1.53633e16 + 6.43538e16i) q^{24} -4.41501e16 q^{25} +(-6.70043e16 - 9.75806e16i) q^{26} +3.48625e17i q^{27} +(6.06468e16 + 2.33392e16i) q^{28} +4.61406e17 q^{29} +(4.04147e17 - 2.77510e17i) q^{30} +3.35661e17i q^{31} +(1.52913e17 - 1.14274e18i) q^{32} -4.92004e18 q^{33} +(5.49109e17 + 7.99685e17i) q^{34} -4.81512e17i q^{35} +(3.88375e18 - 1.00919e19i) q^{36} +7.73143e17 q^{37} +(3.75341e18 - 2.57730e18i) q^{38} +2.78236e19i q^{39} +(-8.30946e18 + 1.98373e18i) q^{40} +5.81991e18 q^{41} +(-8.64625e18 - 1.25918e19i) q^{42} +2.40400e19i q^{43} +(8.00144e19 + 3.07926e19i) q^{44} -8.01256e19 q^{45} +(3.22204e19 - 2.21243e19i) q^{46} -1.39171e20i q^{47} +(-1.81676e20 + 2.01084e20i) q^{48} +1.76579e20 q^{49} +(-1.02365e20 - 1.49077e20i) q^{50} -2.28018e20i q^{51} +(1.74137e20 - 4.52494e20i) q^{52} +6.00270e20 q^{53} +(-1.17717e21 + 8.08309e20i) q^{54} -6.35283e20i q^{55} +(6.18063e19 + 2.58894e20i) q^{56} -1.07023e21 q^{57} +(1.06980e21 + 1.55799e21i) q^{58} +1.87760e20i q^{59} +(1.87408e21 + 7.21220e20i) q^{60} +2.52930e21 q^{61} +(-1.13340e21 + 7.78253e20i) q^{62} +2.49644e21i q^{63} +(4.21311e21 - 2.13318e21i) q^{64} -3.59263e21 q^{65} +(-1.14074e22 - 1.66130e22i) q^{66} +7.53023e21i q^{67} +(-1.42708e21 + 3.70825e21i) q^{68} -9.18714e21 q^{69} +(1.62588e21 - 1.11642e21i) q^{70} -1.51186e22i q^{71} +(4.30810e22 - 1.02848e22i) q^{72} -4.83088e21 q^{73} +(1.79258e21 + 2.61060e21i) q^{74} +4.25071e22i q^{75} +(1.74050e22 + 6.69813e21i) q^{76} -1.97932e22 q^{77} +(-9.39493e22 + 6.45109e22i) q^{78} -2.60322e22i q^{79} +(-2.59643e22 - 2.34583e22i) q^{80} +1.53617e23 q^{81} +(1.34938e22 + 1.96515e22i) q^{82} +1.50802e22i q^{83} +(2.24707e22 - 5.83900e22i) q^{84} +2.94420e22 q^{85} +(-8.11738e22 + 5.57384e22i) q^{86} -4.44236e23i q^{87} +(8.15441e22 + 3.41572e23i) q^{88} -3.62220e23 q^{89} +(-1.85777e23 - 2.70553e23i) q^{90} +1.11934e23i q^{91} +(1.49410e23 + 5.74988e22i) q^{92} +3.23170e23 q^{93} +(4.69926e23 - 3.22678e23i) q^{94} -1.38189e23i q^{95} +(-1.10021e24 - 1.47222e23i) q^{96} +2.71719e23 q^{97} +(4.09410e23 + 5.96238e23i) q^{98} +3.29368e24i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9}+O(q^{10}) \) 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9	\( 10 q - 6212 q^{2} - 33193328 q^{4} + 56758100 q^{5} + 2428200768 q^{6} - 159817477952 q^{8} - 939054565686 q^{9} - 279847745800 q^{10} + 12433669328640 q^{12} - 24798065342764 q^{13} - 3829480368768 q^{14} - 588864378801920 q^{16} - 16\!\cdots\!64 q^{17}+ \cdots + 25\!\cdots\!08 q^{98}+O(q^{100}) \) 10 * q - 6212 * q^2 - 33193328 * q^4 + 56758100 * q^5 + 2428200768 * q^6 - 159817477952 * q^8 - 939054565686 * q^9 - 279847745800 * q^10 + 12433669328640 * q^12 - 24798065342764 * q^13 - 3829480368768 * q^14 - 588864378801920 * q^16 - 1625038130621164 * q^17 - 3063761223370692 * q^18 - 3121315867314400 * q^20 - 2850064322141184 * q^21 + 13916632990560960 * q^22 + 10666682388698112 * q^24 + 71169859613334750 * q^25 - 74430147208248328 * q^26 + 57921192425034240 * q^28 + 1565608550658446804 * q^29 + 168458533397673600 * q^30 - 2011315973261284352 * q^32 - 3113879011632238080 * q^33 - 7482312029820836488 * q^34 - 4814867106633363312 * q^36 + 18108949413006125396 * q^37 - 3611284956625913280 * q^38 - 3297305262340163200 * q^40 + 75081428813585343380 * q^41 - 36295172789431572480 * q^42 + 120819410323173239040 * q^44 - 81006988268625062700 * q^45 - 106055608197057981312 * q^46 + 168479244993419243520 * q^48 - 275007343618256059766 * q^49 - 299814709349559655500 * q^50 + 1421183854718604927776 * q^52 - 1107525951871034057644 * q^53 - 3208227550047955403136 * q^54 + 4524093845691909838848 * q^56 - 1196103002381444528640 * q^57 - 1979853653083682157064 * q^58 + 14021053781344411123200 * q^60 + 7517404483697744564180 * q^61 - 21697281489429749629440 * q^62 + 27630501101980402880512 * q^64 - 2258152381762360458200 * q^65 - 60089835931903418403840 * q^66 + 44229260314628142476576 * q^68 - 3522613303126336828416 * q^69 - 111574643945445039187200 * q^70 + 150836748983093603875008 * q^72 + 51509134469807151432596 * q^73 - 140974046625084701216008 * q^74 + 274189896308379651183360 * q^76 - 19744531096531028198400 * q^77 - 388532048156284380666240 * q^78 + 337741777000410839974400 * q^80 - 21177053453795724717174 * q^81 - 127986376736882271652744 * q^82 + 466232221405535207153664 * q^84 - 156954763950404735571800 * q^85 - 425659539471164537308992 * q^86 + 273874512491499757685760 * q^88 - 817895256767034869026156 * q^89 - 170393126837835789371400 * q^90 - 461144040688182763215360 * q^92 + 251375897269064448430080 * q^93 + 1709617022527703840285952 * q^94 - 3254103234068698697613312 * q^96 + 2233072706882417490518036 * q^97 + 2593191981481623434770108 * q^98

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