LMFDB - Embedded newform 177.9.c.a.58.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	177.c (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:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.20
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.61

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-19.2811i q^{2} -46.7654 q^{3} -115.759 q^{4} +525.267 q^{5} +901.686i q^{6} +658.593 q^{7} -2703.99i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q-19.2811i q^{2} -46.7654 q^{3} -115.759 q^{4} +525.267 q^{5} +901.686i q^{6} +658.593 q^{7} -2703.99i q^{8} +2187.00 q^{9} -10127.7i q^{10} +14544.7i q^{11} +5413.53 q^{12} +49404.0i q^{13} -12698.4i q^{14} -24564.3 q^{15} -81770.2 q^{16} -70791.4 q^{17} -42167.7i q^{18} +94835.6 q^{19} -60804.6 q^{20} -30799.4 q^{21} +280436. q^{22} -232818. i q^{23} +126453. i q^{24} -114720. q^{25} +952561. q^{26} -102276. q^{27} -76238.4 q^{28} -742936. q^{29} +473626. i q^{30} -644602. i q^{31} +884395. i q^{32} -680186. i q^{33} +1.36493e6i q^{34} +345937. q^{35} -253166. q^{36} -2.71240e6i q^{37} -1.82853e6i q^{38} -2.31040e6i q^{39} -1.42032e6i q^{40} -5.07256e6 q^{41} +593845. i q^{42} -4.10695e6i q^{43} -1.68368e6i q^{44} +1.14876e6 q^{45} -4.48899e6 q^{46} -1.20234e6i q^{47} +3.82401e6 q^{48} -5.33106e6 q^{49} +2.21191e6i q^{50} +3.31059e6 q^{51} -5.71898e6i q^{52} -1.48565e6 q^{53} +1.97199e6i q^{54} +7.63983e6i q^{55} -1.78083e6i q^{56} -4.43502e6 q^{57} +1.43246e7i q^{58} +(-7.46187e6 - 9.54730e6i) q^{59} +2.84355e6 q^{60} +3.27863e6i q^{61} -1.24286e7 q^{62} +1.44034e6 q^{63} -3.88108e6 q^{64} +2.59503e7i q^{65} -1.31147e7 q^{66} -1.38873e7i q^{67} +8.19477e6 q^{68} +1.08878e7i q^{69} -6.67004e6i q^{70} -1.94846e7 q^{71} -5.91362e6i q^{72} -3.54200e7i q^{73} -5.22980e7 q^{74} +5.36490e6 q^{75} -1.09781e7 q^{76} +9.57902e6i q^{77} -4.45469e7 q^{78} +4.27188e7 q^{79} -4.29512e7 q^{80} +4.78297e6 q^{81} +9.78044e7i q^{82} +4.18077e7i q^{83} +3.56532e6 q^{84} -3.71844e7 q^{85} -7.91865e7 q^{86} +3.47437e7 q^{87} +3.93286e7 q^{88} +1.03706e7i q^{89} -2.21493e7i q^{90} +3.25371e7i q^{91} +2.69509e7i q^{92} +3.01451e7i q^{93} -2.31823e7 q^{94} +4.98140e7 q^{95} -4.13591e7i q^{96} -9.94679e7i q^{97} +1.02788e8i q^{98} +3.18092e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	19.2811i		−	1.20507i	−0.798094	−	0.602533i	$-0.794158\pi$
$2$		−	19.2811i		−	1.20507i	0.798094	−	0.602533i	$-0.205842\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−115.759			−0.452185
$5$	525.267			0.840427			0.420214	−	0.907425i	$-0.361955\pi$
$5$	525.267			0.840427			0.420214	+	0.907425i	$0.361955\pi$
$6$			901.686i			0.695745i
$7$	658.593			0.274300			0.137150	−	0.990550i	$-0.456206\pi$
$7$	658.593			0.274300			0.137150	+	0.990550i	$0.456206\pi$
$8$		−	2703.99i		−	0.660153i
$9$	2187.00			0.333333
$10$		−	10127.7i		−	1.01277i
$11$			14544.7i			0.993420i	0.867917	+	0.496710i	$0.165459\pi$
$11$			14544.7i			0.993420i	−0.867917	+	0.496710i	$0.834541\pi$
$12$	5413.53			0.261069
$13$			49404.0i			1.72977i	0.501969	+	0.864885i	$0.332609\pi$
$13$			49404.0i			1.72977i	−0.501969	+	0.864885i	$0.667391\pi$
$14$		−	12698.4i		−	0.330549i
$15$	−24564.3			−0.485221
$16$	−81770.2			−1.24771
$17$	−70791.4			−0.847588			−0.423794	−	0.905759i	$-0.639302\pi$
$17$	−70791.4			−0.847588			−0.423794	+	0.905759i	$0.639302\pi$
$18$		−	42167.7i		−	0.401689i
$19$	94835.6			0.727708			0.363854	−	0.931456i	$-0.381461\pi$
$19$	94835.6			0.727708			0.363854	+	0.931456i	$0.381461\pi$
$20$	−60804.6			−0.380029
$21$	−30799.4			−0.158367
$22$	280436.			1.19714
$23$		−	232818.i		−	0.831967i	−0.909372	−	0.415983i	$-0.863437\pi$
$23$		−	232818.i		−	0.831967i	0.909372	−	0.415983i	$-0.136563\pi$
$24$			126453.i			0.381140i
$25$	−114720.			−0.293682
$26$	952561.			2.08449
$27$	−102276.			−0.192450
$28$	−76238.4			−0.124034
$29$	−742936.			−1.05041			−0.525206	−	0.850975i	$-0.676012\pi$
$29$	−742936.			−1.05041			−0.525206	+	0.850975i	$0.676012\pi$
$30$			473626.i			0.584723i
$31$		−	644602.i		−	0.697983i	−0.937126	−	0.348992i	$-0.886524\pi$
$31$		−	644602.i		−	0.697983i	0.937126	−	0.348992i	$-0.113476\pi$
$32$			884395.i			0.843425i
$33$		−	680186.i		−	0.573551i
$34$			1.36493e6i			1.02140i
$35$	345937.			0.230529
$36$	−253166.			−0.150728
$37$		−	2.71240e6i		−	1.44726i	−0.690187	−	0.723631i	$-0.742472\pi$
$37$		−	2.71240e6i		−	1.44726i	0.690187	−	0.723631i	$-0.257528\pi$
$38$		−	1.82853e6i		−	0.876936i
$39$		−	2.31040e6i		−	0.998684i
$40$		−	1.42032e6i		−	0.554811i
$41$	−5.07256e6			−1.79511			−0.897557	−	0.440899i	$-0.854660\pi$
$41$	−5.07256e6			−1.79511			−0.897557	+	0.440899i	$0.854660\pi$
$42$			593845.i			0.190843i
$43$		−	4.10695e6i		−	1.20129i	−0.799518	−	0.600643i	$-0.794912\pi$
$43$		−	4.10695e6i		−	1.20129i	0.799518	−	0.600643i	$-0.205088\pi$
$44$		−	1.68368e6i		−	0.449210i
$45$	1.14876e6			0.280142
$46$	−4.48899e6			−1.00258
$47$		−	1.20234e6i		−	0.246397i	−0.992382	−	0.123198i	$-0.960685\pi$
$47$		−	1.20234e6i		−	0.246397i	0.992382	−	0.123198i	$-0.0393151\pi$
$48$	3.82401e6			0.720368
$49$	−5.33106e6			−0.924760
$50$			2.21191e6i			0.353906i
$51$	3.31059e6			0.489355
$52$		−	5.71898e6i		−	0.782177i
$53$	−1.48565e6			−0.188283			−0.0941416	−	0.995559i	$-0.530011\pi$
$53$	−1.48565e6			−0.188283			−0.0941416	+	0.995559i	$0.530011\pi$
$54$			1.97199e6i			0.231915i
$55$			7.63983e6i			0.834897i
$56$		−	1.78083e6i		−	0.181080i
$57$	−4.43502e6			−0.420142
$58$			1.43246e7i			1.26582i
$59$	−7.46187e6	−	9.54730e6i	−0.615800	−	0.787902i
$59$	−7.46187e6	−	9.54730e6i	−0.615800	−	0.787902i
$60$	2.84355e6			0.219410
$61$			3.27863e6i			0.236796i	0.992966	+	0.118398i	$0.0377758\pi$
$61$			3.27863e6i			0.236796i	−0.992966	+	0.118398i	$0.962224\pi$
$62$	−1.24286e7			−0.841116
$63$	1.44034e6			0.0914332
$64$	−3.88108e6			−0.231331
$65$			2.59503e7i			1.45375i
$66$	−1.31147e7			−0.691167
$67$		−	1.38873e7i		−	0.689160i	−0.938757	−	0.344580i	$-0.888021\pi$
$67$		−	1.38873e7i		−	0.689160i	0.938757	−	0.344580i	$-0.111979\pi$
$68$	8.19477e6			0.383267
$69$			1.08878e7i			0.480336i
$70$		−	6.67004e6i		−	0.277803i
$71$	−1.94846e7			−0.766757			−0.383379	−	0.923591i	$-0.625240\pi$
$71$	−1.94846e7			−0.766757			−0.383379	+	0.923591i	$0.625240\pi$
$72$		−	5.91362e6i		−	0.220051i
$73$		−	3.54200e7i		−	1.24726i	−0.781719	−	0.623631i	$-0.785657\pi$
$73$		−	3.54200e7i		−	1.24726i	0.781719	−	0.623631i	$-0.214343\pi$
$74$	−5.22980e7			−1.74405
$75$	5.36490e6			0.169557
$76$	−1.09781e7			−0.329059
$77$			9.57902e6i			0.272495i
$78$	−4.45469e7			−1.20348
$79$	4.27188e7			1.09676			0.548379	−	0.836230i	$-0.315245\pi$
$79$	4.27188e7			1.09676			0.548379	+	0.836230i	$0.315245\pi$
$80$	−4.29512e7			−1.04861
$81$	4.78297e6			0.111111
$82$			9.78044e7i			2.16323i
$83$			4.18077e7i			0.880935i	0.897769	+	0.440468i	$0.145187\pi$
$83$			4.18077e7i			0.880935i	−0.897769	+	0.440468i	$0.854813\pi$
$84$	3.56532e6			0.0716112
$85$	−3.71844e7			−0.712336
$86$	−7.91865e7			−1.44763
$87$	3.47437e7			0.606456
$88$	3.93286e7			0.655809
$89$			1.03706e7i			0.165290i	0.996579	+	0.0826448i	$0.0263367\pi$
$89$			1.03706e7i			0.165290i	−0.996579	+	0.0826448i	$0.973663\pi$
$90$		−	2.21493e7i		−	0.337590i
$91$			3.25371e7i			0.474476i
$92$			2.69509e7i			0.376203i
$93$			3.01451e7i			0.402981i
$94$	−2.31823e7			−0.296924
$95$	4.98140e7			0.611586
$96$		−	4.13591e7i		−	0.486952i
$97$		−	9.94679e7i		−	1.12356i	−0.827287	−	0.561780i	$-0.810117\pi$
$97$		−	9.94679e7i		−	1.12356i	0.827287	−	0.561780i	$-0.189883\pi$
$98$			1.02788e8i			1.11440i
$99$			3.18092e7i			0.331140i
$100$	1.32799e7			0.132799
$101$		−	7.18300e7i		−	0.690272i	−0.938553	−	0.345136i	$-0.887833\pi$
$101$		−	7.18300e7i		−	0.690272i	0.938553	−	0.345136i	$-0.112167\pi$
$102$		−	6.38316e7i		−	0.589706i
$103$			6.61524e7i			0.587755i	0.955843	+	0.293878i	$0.0949458\pi$
$103$			6.61524e7i			0.587755i	−0.955843	+	0.293878i	$0.905054\pi$
$104$	1.33588e8			1.14191
$105$	−1.61779e7			−0.133096
$106$			2.86448e7i			0.226894i
$107$	−7.05875e7			−0.538509			−0.269254	−	0.963069i	$-0.586777\pi$
$107$	−7.05875e7			−0.538509			−0.269254	+	0.963069i	$0.586777\pi$
$108$	1.18394e7			0.0870231
$109$			1.69697e8i			1.20218i	0.799182	+	0.601089i	$0.205266\pi$
$109$			1.69697e8i			1.20218i	−0.799182	+	0.601089i	$0.794734\pi$
$110$	1.47304e8			1.00611
$111$			1.26847e8i			0.835577i
$112$	−5.38533e7			−0.342247
$113$			5.74155e7i			0.352140i	0.984378	+	0.176070i	$0.0563385\pi$
$113$			5.74155e7i			0.352140i	−0.984378	+	0.176070i	$0.943661\pi$
$114$			8.55120e7i			0.506299i
$115$		−	1.22292e8i		−	0.699208i
$116$	8.60019e7			0.474981
$117$			1.08047e8i			0.576590i
$118$	−1.84082e8	+	1.43873e8i	−0.949475	+	0.742080i
$119$	−4.66228e7			−0.232493
$120$			6.64216e7i			0.320320i
$121$	2.81185e6			0.0131175
$122$	6.32156e7			0.285354
$123$	2.37220e8			1.03641
$124$			7.46188e7i			0.315618i
$125$	−2.65441e8			−1.08725
$126$		−	2.77714e7i		−	0.110183i
$127$	−1.66958e8			−0.641790			−0.320895	−	0.947115i	$-0.603984\pi$
$127$	−1.66958e8			−0.641790			−0.320895	+	0.947115i	$0.603984\pi$
$128$			3.01237e8i			1.12219i
$129$			1.92063e8i			0.693562i
$130$	5.00349e8			1.75186
$131$		−	1.16246e7i		−	0.0394724i	−0.999805	−	0.0197362i	$-0.993717\pi$
$131$		−	1.16246e7i		−	0.0394724i	0.999805	−	0.0197362i	$-0.00628264\pi$
$132$			7.87380e7i			0.259351i
$133$	6.24581e7			0.199610
$134$	−2.67763e8			−0.830483
$135$	−5.37221e7			−0.161740
$136$			1.91419e8i			0.559538i
$137$	5.56986e7			0.158111			0.0790555	−	0.996870i	$-0.474810\pi$
$137$	5.56986e7			0.158111			0.0790555	+	0.996870i	$0.474810\pi$
$138$	2.09929e8			0.578837
$139$	3.54284e8			0.949057			0.474528	−	0.880240i	$-0.342619\pi$
$139$	3.54284e8			0.949057			0.474528	+	0.880240i	$0.342619\pi$
$140$	−4.00455e7			−0.104242
$141$			5.62278e7i			0.142257i
$142$			3.75684e8i			0.923993i
$143$	−7.18564e8			−1.71839
$144$	−1.78831e8			−0.415905
$145$	−3.90240e8			−0.882795
$146$	−6.82936e8			−1.50303
$147$	2.49309e8			0.533910
$148$			3.13986e8i			0.654431i
$149$		−	8.93096e8i		−	1.81198i	−0.423301	−	0.905989i	$-0.639129\pi$
$149$		−	8.93096e8i		−	1.81198i	0.423301	−	0.905989i	$-0.360871\pi$
$150$		−	1.03441e8i		−	0.204328i
$151$			5.44878e8i			1.04807i	0.851696	+	0.524037i	$0.175575\pi$
$151$			5.44878e8i			1.04807i	−0.851696	+	0.524037i	$0.824425\pi$
$152$		−	2.56434e8i		−	0.480399i
$153$	−1.54821e8			−0.282529
$154$	1.84694e8			0.328374
$155$		−	3.38588e8i		−	0.586604i
$156$			2.67450e8i			0.451590i
$157$			7.55451e8i			1.24339i	0.783259	+	0.621695i	$0.213556\pi$
$157$			7.55451e8i			1.24339i	−0.783259	+	0.621695i	$0.786444\pi$
$158$		−	8.23664e8i		−	1.32167i
$159$	6.94768e7			0.108705
$160$			4.64544e8i			0.708837i
$161$		−	1.53333e8i		−	0.228208i
$162$		−	9.22207e7i		−	0.133896i
$163$	−1.03534e9			−1.46667			−0.733333	−	0.679870i	$-0.762036\pi$
$163$	−1.03534e9			−1.46667			−0.733333	+	0.679870i	$0.762036\pi$
$164$	5.87197e8			0.811724
$165$		−	3.57279e8i		−	0.482028i
$166$	8.06097e8			1.06159
$167$	−9.88619e8			−1.27105			−0.635526	−	0.772080i	$-0.719217\pi$
$167$	−9.88619e8			−1.27105			−0.635526	+	0.772080i	$0.719217\pi$
$168$			8.32811e7i			0.104546i
$169$	−1.62502e9			−1.99211
$170$			7.16955e8i			0.858413i
$171$	2.07405e8			0.242569
$172$			4.75419e8i			0.543203i
$173$		−	9.39023e8i		−	1.04831i	−0.851621	−	0.524157i	$-0.824380\pi$
$173$		−	9.39023e8i		−	1.04831i	0.851621	−	0.524157i	$-0.175620\pi$
$174$		−	6.69895e8i		−	0.730819i
$175$	−7.55535e7			−0.0805569
$176$		−	1.18932e9i		−	1.23950i
$177$	3.48957e8	+	4.46483e8i	0.355532	+	0.454896i
$178$	1.99957e8			0.199185
$179$			1.29444e9i			1.26087i	0.776241	+	0.630436i	$0.217124\pi$
$179$			1.29444e9i			1.26087i	−0.776241	+	0.630436i	$0.782876\pi$
$180$	−1.32980e8			−0.126676
$181$	2.02213e9			1.88406			0.942029	−	0.335531i	$-0.108916\pi$
$181$	2.02213e9			1.88406			0.942029	+	0.335531i	$0.108916\pi$
$182$	6.27351e8			0.571775
$183$		−	1.53327e8i		−	0.136714i
$184$	−6.29538e8			−0.549226
$185$		−	1.42474e9i		−	1.21632i
$186$	5.81229e8			0.485619
$187$		−	1.02964e9i		−	0.842011i
$188$			1.39182e8i			0.111417i
$189$	−6.73582e7			−0.0527890
$190$		−	9.60467e8i		−	0.737001i
$191$			2.35687e8i			0.177093i	0.996072	+	0.0885467i	$0.0282223\pi$
$191$			2.35687e8i			0.177093i	−0.996072	+	0.0885467i	$0.971778\pi$
$192$	1.81500e8			0.133559
$193$	1.43890e9			1.03705			0.518526	−	0.855062i	$-0.326481\pi$
$193$	1.43890e9			1.03705			0.518526	+	0.855062i	$0.326481\pi$
$194$	−1.91785e9			−1.35396
$195$		−	1.21357e9i		−	0.839321i
$196$	6.17120e8			0.418163
$197$	−4.37660e8			−0.290584			−0.145292	−	0.989389i	$-0.546412\pi$
$197$	−4.37660e8			−0.290584			−0.145292	+	0.989389i	$0.546412\pi$
$198$	6.13315e8			0.399046
$199$	−1.99159e9			−1.26996			−0.634978	−	0.772530i	$-0.718991\pi$
$199$	−1.99159e9			−1.26996			−0.634978	+	0.772530i	$0.718991\pi$
$200$			3.10200e8i			0.193875i
$201$			6.49447e8i			0.397887i
$202$	−1.38496e9			−0.831823
$203$	−4.89293e8			−0.288128
$204$	−3.83232e8			−0.221279
$205$	−2.66445e9			−1.50866
$206$	1.27549e9			0.708284
$207$		−	5.09174e8i		−	0.277322i
$208$		−	4.03977e9i		−	2.15826i
$209$			1.37935e9i			0.722919i
$210$			3.11927e8i			0.160389i
$211$			1.62074e9i			0.817680i	0.912606	+	0.408840i	$0.134067\pi$
$211$			1.62074e9i			0.817680i	−0.912606	+	0.408840i	$0.865933\pi$
$212$	1.71978e8			0.0851389
$213$	9.11204e8			0.442687
$214$			1.36100e9i			0.648939i
$215$		−	2.15725e9i		−	1.00959i
$216$			2.76553e8i			0.127047i
$217$		−	4.24531e8i		−	0.191457i
$218$	3.27194e9			1.44870
$219$			1.65643e9i			0.720107i
$220$		−	8.84382e8i		−	0.377528i
$221$		−	3.49738e9i		−	1.46613i
$222$	2.44574e9			1.00693
$223$	9.20977e8			0.372417			0.186208	−	0.982510i	$-0.440380\pi$
$223$	9.20977e8			0.372417			0.186208	+	0.982510i	$0.440380\pi$
$224$			5.82457e8i			0.231351i
$225$	−2.50892e8			−0.0978940
$226$	1.10703e9			0.424352
$227$		−	3.74299e9i		−	1.40966i	−0.709376	−	0.704831i	$-0.751023\pi$
$227$		−	3.74299e9i		−	1.40966i	0.709376	−	0.704831i	$-0.248977\pi$
$228$	5.13396e8			0.189982
$229$		−	1.40653e9i		−	0.511453i	−0.966749	−	0.255727i	$-0.917685\pi$
$229$		−	1.40653e9i		−	0.511453i	0.966749	−	0.255727i	$-0.0823147\pi$
$230$	−2.35792e9			−0.842592
$231$		−	4.47966e8i		−	0.157325i
$232$			2.00889e9i			0.693433i
$233$			4.23543e8i			0.143706i	0.997415	+	0.0718528i	$0.0228912\pi$
$233$			4.23543e8i			0.143706i	−0.997415	+	0.0718528i	$0.977109\pi$
$234$	2.08325e9			0.694830
$235$		−	6.31548e8i		−	0.207079i
$236$	8.63782e8	+	1.10519e9i	0.278456	+	0.356278i
$237$	−1.99776e9			−0.633214
$238$			8.98937e8i			0.280170i
$239$	−2.73773e9			−0.839070			−0.419535	−	0.907739i	$-0.637807\pi$
$239$	−2.73773e9			−0.839070			−0.419535	+	0.907739i	$0.637807\pi$
$240$	2.00863e9			0.605417
$241$	4.73208e9			1.40276			0.701381	−	0.712786i	$-0.252567\pi$
$241$	4.73208e9			1.40276			0.701381	+	0.712786i	$0.252567\pi$
$242$		−	5.42155e7i		−	0.0158075i
$243$	−2.23677e8			−0.0641500
$244$		−	3.79533e8i		−	0.107076i
$245$	−2.80023e9			−0.777193
$246$		−	4.57386e9i		−	1.24894i
$247$			4.68526e9i			1.25877i
$248$	−1.74300e9			−0.460776
$249$		−	1.95515e9i		−	0.508608i
$250$			5.11798e9i			1.31020i
$251$	−2.00699e9			−0.505651			−0.252826	−	0.967512i	$-0.581360\pi$
$251$	−2.00699e9			−0.505651			−0.252826	+	0.967512i	$0.581360\pi$
$252$	−1.66733e8			−0.0413448
$253$	3.38626e9			0.826492
$254$			3.21913e9i			0.773399i
$255$	1.73894e9			0.411268
$256$	4.81460e9			1.12099
$257$	6.66006e9			1.52667			0.763336	−	0.646002i	$-0.223560\pi$
$257$	6.66006e9			1.52667			0.763336	+	0.646002i	$0.223560\pi$
$258$	3.70318e9			0.835789
$259$		−	1.78637e9i		−	0.396984i
$260$		−	3.00399e9i		−	0.657363i
$261$	−1.62480e9			−0.350137
$262$	−2.24135e8			−0.0475669
$263$	8.23322e9			1.72087			0.860433	−	0.509564i	$-0.170193\pi$
$263$	8.23322e9			1.72087			0.860433	+	0.509564i	$0.170193\pi$
$264$	−1.83922e9			−0.378632
$265$	−7.80361e8			−0.158238
$266$		−	1.20426e9i		−	0.240543i
$267$		−	4.84987e8i		−	0.0954300i
$268$			1.60759e9i			0.311628i
$269$		−	4.98586e9i		−	0.952206i	−0.879390	−	0.476103i	$-0.842049\pi$
$269$		−	4.98586e9i		−	0.952206i	0.879390	−	0.476103i	$-0.157951\pi$
$270$			1.03582e9i			0.194908i
$271$	5.48294e9			1.01657			0.508284	−	0.861189i	$-0.330280\pi$
$271$	5.48294e9			1.01657			0.508284	+	0.861189i	$0.330280\pi$
$272$	5.78863e9			1.05755
$273$		−	1.52161e9i		−	0.273939i
$274$		−	1.07393e9i		−	0.190534i
$275$		−	1.66856e9i		−	0.291749i
$276$		−	1.26037e9i		−	0.217201i
$277$	3.95689e9			0.672101			0.336050	−	0.941844i	$-0.390909\pi$
$277$	3.95689e9			0.672101			0.336050	+	0.941844i	$0.390909\pi$
$278$		−	6.83097e9i		−	1.14368i
$279$		−	1.40974e9i		−	0.232661i
$280$		−	9.35411e8i		−	0.152184i
$281$	7.39388e9			1.18590			0.592949	−	0.805240i	$-0.297964\pi$
$281$	7.39388e9			1.18590			0.592949	+	0.805240i	$0.297964\pi$
$282$	1.08413e9			0.171429
$283$		−	2.48452e9i		−	0.387343i	−0.981066	−	0.193672i	$-0.937960\pi$
$283$		−	2.48452e9i		−	0.387343i	0.981066	−	0.193672i	$-0.0620397\pi$
$284$	2.25553e9			0.346716
$285$	−2.32957e9			−0.353099
$286$			1.38547e10i			2.07077i
$287$	−3.34076e9			−0.492399
$288$			1.93417e9i			0.281142i
$289$	−1.96433e9			−0.281594
$290$			7.52424e9i			1.06383i
$291$			4.65165e9i			0.648687i
$292$			4.10020e9i			0.563993i
$293$	−8.92655e9			−1.21119			−0.605596	−	0.795772i	$-0.707065\pi$
$293$	−8.92655e9			−1.21119			−0.605596	+	0.795772i	$0.707065\pi$
$294$		−	4.80694e9i		−	0.643397i
$295$	−3.91948e9	−	5.01488e9i	−0.517535	−	0.662175i
$296$	−7.33430e9			−0.955415
$297$		−	1.48757e9i		−	0.191184i
$298$	−1.72198e10			−2.18355
$299$	1.15022e10			1.43911
$300$	−6.21038e8			−0.0766713
$301$		−	2.70481e9i		−	0.329512i
$302$	1.05058e10			1.26300
$303$			3.35915e9i			0.398529i
$304$	−7.75472e9			−0.907971
$305$			1.72216e9i			0.199010i
$306$			2.98511e9i			0.340467i
$307$	−1.02239e10			−1.15097			−0.575486	−	0.817812i	$-0.695187\pi$
$307$	−1.02239e10			−1.15097			−0.575486	+	0.817812i	$0.695187\pi$
$308$		−	1.10886e9i		−	0.123218i
$309$		−	3.09364e9i		−	0.339341i
$310$	−6.52834e9			−0.706897
$311$	−2.42846e9			−0.259591			−0.129796	−	0.991541i	$-0.541432\pi$
$311$	−2.42846e9			−0.259591			−0.129796	+	0.991541i	$0.541432\pi$
$312$	−6.24728e9			−0.659284
$313$			5.66977e9i			0.590729i	0.955385	+	0.295364i	$0.0954410\pi$
$313$			5.66977e9i			0.590729i	−0.955385	+	0.295364i	$0.904559\pi$
$314$	1.45659e10			1.49837
$315$	7.56565e8			0.0768430
$316$	−4.94511e9			−0.495938
$317$	5.22965e9			0.517888			0.258944	−	0.965892i	$-0.416626\pi$
$317$	5.22965e9			0.517888			0.258944	+	0.965892i	$0.416626\pi$
$318$		−	1.33959e9i		−	0.130997i
$319$		−	1.08058e10i		−	1.04350i
$320$	−2.03861e9			−0.194417
$321$	3.30105e9			0.310908
$322$	−2.95642e9			−0.275006
$323$	−6.71355e9			−0.616797
$324$	−5.53674e8			−0.0502428
$325$		−	5.66760e9i		−	0.508002i
$326$			1.99624e10i			1.76743i
$327$		−	7.93595e9i		−	0.694078i
$328$			1.37161e10i			1.18505i
$329$		−	7.91852e8i		−	0.0675865i
$330$	−6.88873e9			−0.580876
$331$	−2.09706e10			−1.74702			−0.873512	−	0.486803i	$-0.838163\pi$
$331$	−2.09706e10			−1.74702			−0.873512	+	0.486803i	$0.838163\pi$
$332$		−	4.83964e9i		−	0.398346i
$333$		−	5.93202e9i		−	0.482421i
$334$			1.90616e10i			1.53170i
$335$		−	7.29456e9i		−	0.579189i
$336$	2.51847e9			0.197597
$337$			1.22375e10i			0.948797i	0.880310	+	0.474398i	$0.157334\pi$
$337$			1.22375e10i			0.948797i	−0.880310	+	0.474398i	$0.842666\pi$
$338$			3.13322e10i			2.40062i
$339$		−	2.68506e9i		−	0.203308i
$340$	4.30444e9			0.322108
$341$	9.37552e9			0.693390
$342$		−	3.99900e9i		−	0.292312i
$343$	−7.30766e9			−0.527961
$344$	−1.11052e10			−0.793032
$345$			5.71902e9i			0.403688i
$346$	−1.81054e10			−1.26329
$347$		−	1.91444e9i		−	0.132046i	−0.997818	−	0.0660229i	$-0.978969\pi$
$347$		−	1.91444e9i		−	0.132046i	0.997818	−	0.0660229i	$-0.0210310\pi$
$348$	−4.02191e9			−0.274230
$349$		−	1.67521e10i		−	1.12919i	−0.825367	−	0.564597i	$-0.809032\pi$
$349$		−	1.67521e10i		−	1.12919i	0.825367	−	0.564597i	$-0.190968\pi$
$350$			1.45675e9i			0.0970764i
$351$		−	5.05284e9i		−	0.332895i
$352$	−1.28632e10			−0.837875
$353$			1.32816e10i			0.855364i	0.903929	+	0.427682i	$0.140670\pi$
$353$			1.32816e10i			0.855364i	−0.903929	+	0.427682i	$0.859330\pi$
$354$	8.60867e9	−	6.72827e9i	0.548180	−	0.428440i
$355$	−1.02346e10			−0.644404
$356$		−	1.20050e9i		−	0.0747415i
$357$	2.18033e9			0.134230
$358$	2.49583e10			1.51944
$359$	1.98321e10			1.19396			0.596982	−	0.802255i	$-0.296366\pi$
$359$	1.98321e10			1.19396			0.596982	+	0.802255i	$0.296366\pi$
$360$		−	3.10623e9i		−	0.184937i
$361$	−7.98977e9			−0.470441
$362$		−	3.89888e10i		−	2.27042i
$363$	−1.31497e8			−0.00757339
$364$		−	3.76648e9i		−	0.214551i
$365$		−	1.86050e10i		−	1.04823i
$366$	−2.95630e9			−0.164749
$367$			2.73377e10i			1.50694i	0.657480	+	0.753472i	$0.271622\pi$
$367$			2.73377e10i			1.50694i	−0.657480	+	0.753472i	$0.728378\pi$
$368$			1.90376e10i			1.03806i
$369$	−1.10937e10			−0.598371
$370$	−2.74704e10			−1.46575
$371$	−9.78437e8			−0.0516460
$372$		−	3.48958e9i		−	0.182222i
$373$	2.49022e9			0.128648			0.0643240	−	0.997929i	$-0.479511\pi$
$373$	2.49022e9			0.128648			0.0643240	+	0.997929i	$0.479511\pi$
$374$	−1.98525e10			−1.01468
$375$	1.24134e10			0.627722
$376$	−3.25111e9			−0.162660
$377$		−	3.67040e10i		−	1.81697i
$378$			1.29874e9i			0.0636142i
$379$	−2.25638e10			−1.09359			−0.546796	−	0.837266i	$-0.684153\pi$
$379$	−2.25638e10			−1.09359			−0.546796	+	0.837266i	$0.684153\pi$
$380$	−5.76644e9			−0.276550
$381$	7.80786e9			0.370538
$382$	4.54430e9			0.213409
$383$	1.56501e9			0.0727316			0.0363658	−	0.999339i	$-0.488422\pi$
$383$	1.56501e9			0.0727316			0.0363658	+	0.999339i	$0.488422\pi$
$384$		−	1.40874e10i		−	0.647899i
$385$			5.03154e9i			0.229012i
$386$		−	2.77435e10i		−	1.24972i
$387$		−	8.98191e9i		−	0.400428i
$388$			1.15143e10i			0.508057i
$389$	−7.34970e9			−0.320975			−0.160487	−	0.987038i	$-0.551307\pi$
$389$	−7.34970e9			−0.320975			−0.160487	+	0.987038i	$0.551307\pi$
$390$	−2.33990e10			−1.01144
$391$			1.64815e10i			0.705165i
$392$			1.44151e10i			0.610483i
$393$			5.43630e8i			0.0227894i
$394$			8.43856e9i			0.350173i
$395$	2.24388e10			0.921746
$396$		−	3.68221e9i		−	0.149737i
$397$			3.21142e10i			1.29281i	0.762994	+	0.646405i	$0.223728\pi$
$397$			3.21142e10i			1.29281i	−0.762994	+	0.646405i	$0.776272\pi$
$398$			3.84001e10i			1.53038i
$399$	−2.92088e9			−0.115245
$400$	9.38063e9			0.366431
$401$		−	3.08504e10i		−	1.19312i	−0.802569	−	0.596559i	$-0.796534\pi$
$401$		−	3.08504e10i		−	1.19312i	0.802569	−	0.596559i	$-0.203466\pi$
$402$	1.25220e10			0.479480
$403$	3.18459e10			1.20735
$404$			8.31500e9i			0.312131i
$405$	2.51234e9			0.0933808
$406$			9.43409e9i			0.347213i
$407$	3.94510e10			1.43774
$408$		−	8.95178e9i		−	0.323049i
$409$		−	2.38353e10i		−	0.851781i	−0.904775	−	0.425890i	$-0.859961\pi$
$409$		−	2.38353e10i		−	0.851781i	0.904775	−	0.425890i	$-0.140039\pi$
$410$			5.13734e10i			1.81804i
$411$	−2.60476e9			−0.0912854
$412$		−	7.65776e9i		−	0.265774i
$413$	−4.91434e9	−	6.28779e9i	−0.168914	−	0.216121i
$414$	−9.81741e9			−0.334192
$415$			2.19602e10i			0.740362i
$416$	−4.36926e10			−1.45893
$417$	−1.65682e10			−0.547938
$418$	2.65954e10			0.871166
$419$			4.71036e10i			1.52826i	0.645061	+	0.764131i	$0.276832\pi$
$419$			4.71036e10i			1.52826i	−0.645061	+	0.764131i	$0.723168\pi$
$420$	1.87274e9			0.0601840
$421$			7.15646e9i			0.227808i	0.993492	+	0.113904i	$0.0363357\pi$
$421$			7.15646e9i			0.227808i	−0.993492	+	0.113904i	$0.963664\pi$
$422$	3.12496e10			0.985359
$423$		−	2.62951e9i		−	0.0821322i
$424$			4.01717e9i			0.124296i
$425$	8.12116e9			0.248921
$426$		−	1.75690e10i		−	0.533468i
$427$			2.15929e9i			0.0649530i
$428$	8.17117e9			0.243506
$429$	3.36039e10			0.992112
$430$	−4.15940e10			−1.21663
$431$			6.27989e10i			1.81988i	0.414738	+	0.909941i	$0.363873\pi$
$431$			6.27989e10i			1.81988i	−0.414738	+	0.909941i	$0.636127\pi$
$432$	8.36311e9			0.240123
$433$	4.22007e10			1.20052			0.600258	−	0.799806i	$-0.295065\pi$
$433$	4.22007e10			1.20052			0.600258	+	0.799806i	$0.295065\pi$
$434$	−8.18541e9			−0.230718
$435$	1.82497e10			0.509682
$436$		−	1.96441e10i		−	0.543607i
$437$		−	2.20795e10i		−	0.605429i
$438$	3.19377e10			0.867776
$439$	−2.45400e10			−0.660718			−0.330359	−	0.943855i	$-0.607170\pi$
$439$	−2.45400e10			−0.660718			−0.330359	+	0.943855i	$0.607170\pi$
$440$	2.06580e10			0.551160
$441$	−1.16590e10			−0.308253
$442$	−6.74332e10			−1.76679
$443$			1.75287e10i			0.455129i	0.973763	+	0.227564i	$0.0730762\pi$
$443$			1.75287e10i			0.455129i	−0.973763	+	0.227564i	$0.926924\pi$
$444$		−	1.46837e10i		−	0.377836i
$445$			5.44735e9i			0.138914i
$446$		−	1.77574e10i		−	0.448787i
$447$			4.17660e10i			1.04615i
$448$	−2.55606e9			−0.0634539
$449$	−6.68959e10			−1.64594			−0.822971	−	0.568084i	$-0.807685\pi$
$449$	−6.68959e10			−1.64594			−0.822971	+	0.568084i	$0.807685\pi$
$450$			4.83746e9i			0.117969i
$451$		−	7.37787e10i		−	1.78330i
$452$		−	6.64639e9i		−	0.159233i
$453$		−	2.54814e10i		−	0.605105i
$454$	−7.21688e10			−1.69874
$455$			1.70907e10i			0.398762i
$456$			1.19922e10i			0.277358i
$457$			3.38572e10i			0.776223i	0.921612	+	0.388112i	$0.126873\pi$
$457$			3.38572e10i			0.776223i	−0.921612	+	0.388112i	$0.873127\pi$
$458$	−2.71193e10			−0.616335
$459$	7.24025e9			0.163118
$460$			1.41564e10i			0.316171i
$461$	2.71005e10			0.600030			0.300015	−	0.953934i	$-0.403008\pi$
$461$	2.71005e10			0.600030			0.300015	+	0.953934i	$0.403008\pi$
$462$	−8.63727e9			−0.189587
$463$			4.49647e10i			0.978471i	0.872152	+	0.489235i	$0.162724\pi$
$463$			4.49647e10i			0.978471i	−0.872152	+	0.489235i	$0.837276\pi$
$464$	6.07500e10			1.31061
$465$			1.58342e10i			0.338676i
$466$	8.16636e9			0.173175
$467$		−	3.77697e10i		−	0.794101i	−0.917797	−	0.397051i	$-0.870034\pi$
$467$		−	3.77697e10i		−	0.794101i	0.917797	−	0.397051i	$-0.129966\pi$
$468$		−	1.25074e10i		−	0.260726i
$469$		−	9.14611e9i		−	0.189036i
$470$	−1.21769e10			−0.249543
$471$		−	3.53289e10i		−	0.717872i
$472$	−2.58158e10	+	2.01768e10i	−0.520136	+	0.406522i
$473$	5.97342e10			1.19338
$474$			3.85190e10i			0.763065i
$475$	−1.08795e10			−0.213715
$476$	5.39703e9			0.105130
$477$	−3.24911e9			−0.0627611
$478$			5.27863e10i			1.01114i
$479$	−1.97679e10			−0.375507			−0.187753	−	0.982216i	$-0.560121\pi$
$479$	−1.97679e10			−0.375507			−0.187753	+	0.982216i	$0.560121\pi$
$480$		−	2.17246e10i		−	0.409247i
$481$	1.34003e11			2.50343
$482$		−	9.12396e10i		−	1.69042i
$483$			7.17066e9i			0.131756i
$484$	−3.25499e8			−0.00593154
$485$		−	5.22472e10i		−	0.944270i
$486$			4.31274e9i			0.0773051i
$487$	7.20058e10			1.28012			0.640061	−	0.768324i	$-0.278909\pi$
$487$	7.20058e10			1.28012			0.640061	+	0.768324i	$0.278909\pi$
$488$	8.86539e9			0.156321
$489$	4.84179e10			0.846780
$490$			5.39914e10i			0.936570i
$491$	−3.57453e10			−0.615026			−0.307513	−	0.951544i	$-0.599497\pi$
$491$	−3.57453e10			−0.615026			−0.307513	+	0.951544i	$0.599497\pi$
$492$	−2.74605e10			−0.468649
$493$	5.25935e10			0.890317
$494$	9.03367e10			1.51690
$495$			1.67083e10i			0.278299i
$496$			5.27092e10i			0.870883i
$497$	−1.28324e10			−0.210321
$498$	−3.76974e10			−0.612907
$499$	−6.71121e10			−1.08243			−0.541213	−	0.840885i	$-0.682035\pi$
$499$	−6.71121e10			−1.08243			−0.541213	+	0.840885i	$0.682035\pi$
$500$	3.07273e10			0.491636
$501$	4.62331e10			0.733842
$502$			3.86970e10i			0.609343i
$503$		−	2.60027e10i		−	0.406206i	−0.979157	−	0.203103i	$-0.934897\pi$
$503$		−	2.60027e10i		−	0.406206i	0.979157	−	0.203103i	$-0.0651026\pi$
$504$		−	3.89467e9i		−	0.0603599i
$505$		−	3.77299e10i		−	0.580123i
$506$		−	6.52908e10i		−	0.995978i
$507$	7.59948e10			1.15014
$508$	1.93270e10			0.290208
$509$			8.39364e10i			1.25049i	0.780430	+	0.625243i	$0.215000\pi$
$509$			8.39364e10i			1.25049i	−0.780430	+	0.625243i	$0.785000\pi$
$510$		−	3.35287e10i		−	0.495605i
$511$		−	2.33274e10i		−	0.342123i
$512$		−	1.57141e10i		−	0.228671i
$513$	−9.69939e9			−0.140047
$514$		−	1.28413e11i		−	1.83974i
$515$			3.47477e10i			0.493966i
$516$		−	2.22331e10i		−	0.313619i
$517$	1.74876e10			0.244775
$518$	−3.44431e10			−0.478392
$519$			4.39137e10i			0.605245i
$520$	7.01692e10			0.959695
$521$	−8.32616e10			−1.13004			−0.565020	−	0.825077i	$-0.691132\pi$
$521$	−8.32616e10			−1.13004			−0.565020	+	0.825077i	$0.691132\pi$
$522$			3.13279e10i			0.421939i
$523$	1.25002e11			1.67075			0.835374	−	0.549682i	$-0.185251\pi$
$523$	1.25002e11			1.67075			0.835374	+	0.549682i	$0.185251\pi$
$524$			1.34566e9i			0.0178489i
$525$	3.53329e9			0.0465095
$526$		−	1.58745e11i		−	2.07376i
$527$			4.56323e10i			0.591602i
$528$			5.56189e10i			0.715628i
$529$	2.41066e10			0.307831
$530$			1.50462e10i			0.190688i
$531$	−1.63191e10	−	2.08799e10i	−0.205267	−	0.262634i
$532$	−7.23012e9			−0.0902607
$533$		−	2.50605e11i		−	3.10514i
$534$	−9.35106e9			−0.114999
$535$	−3.70773e10			−0.452577
$536$	−3.75512e10			−0.454951
$537$		−	6.05352e10i		−	0.727965i
$538$	−9.61327e10			−1.14747
$539$		−	7.75384e10i		−	0.918674i
$540$	6.21885e9			0.0731366
$541$		−	9.03667e10i		−	1.05492i	−0.849580	−	0.527460i	$-0.823145\pi$
$541$		−	9.03667e10i		−	1.05492i	0.849580	−	0.527460i	$-0.176855\pi$
$542$		−	1.05717e11i		−	1.22503i
$543$	−9.45656e10			−1.08776
$544$		−	6.26076e10i		−	0.714877i
$545$			8.91363e10i			1.01034i
$546$	−2.93383e10			−0.330114
$547$	−1.07991e11			−1.20625			−0.603126	−	0.797646i	$-0.706078\pi$
$547$	−1.07991e11			−1.20625			−0.603126	+	0.797646i	$0.706078\pi$
$548$	−6.44764e9			−0.0714954
$549$			7.17037e9i			0.0789319i
$550$	−3.21715e10			−0.351577
$551$	−7.04568e10			−0.764393
$552$	2.94406e10			0.317096
$553$	2.81343e10			0.300840
$554$		−	7.62930e10i		−	0.809926i
$555$			6.66283e10i			0.702242i
$556$	−4.10117e10			−0.429150
$557$	−8.96481e10			−0.931366			−0.465683	−	0.884952i	$-0.654191\pi$
$557$	−8.96481e10			−0.931366			−0.465683	+	0.884952i	$0.654191\pi$
$558$	−2.71814e10			−0.280372
$559$	2.02900e11			2.07795
$560$	−2.82874e10			−0.287634
$561$			4.81513e10i			0.486135i
$562$		−	1.42562e11i		−	1.42908i
$563$		−	1.59253e11i		−	1.58509i	−0.609813	−	0.792545i	$-0.708756\pi$
$563$		−	1.59253e11i		−	1.58509i	0.609813	−	0.792545i	$-0.291244\pi$
$564$		−	6.50889e9i		−	0.0643266i
$565$			3.01585e10i			0.295948i
$566$	−4.79041e10			−0.466775
$567$	3.15003e9			0.0304777
$568$			5.26861e10i			0.506177i
$569$		−	1.92778e11i		−	1.83912i	−0.392955	−	0.919558i	$-0.628547\pi$
$569$		−	1.92778e11i		−	1.83912i	0.392955	−	0.919558i	$-0.371453\pi$
$570$			4.49166e10i			0.425508i
$571$		−	1.41928e11i		−	1.33513i	−0.744551	−	0.667566i	$-0.767336\pi$
$571$		−	1.41928e11i		−	1.33513i	0.744551	−	0.667566i	$-0.232664\pi$
$572$	8.31806e10			0.777030
$573$		−	1.10220e10i		−	0.102245i
$574$			6.44133e10i			0.593374i
$575$			2.67088e10i			0.244334i
$576$	−8.48793e9			−0.0771102
$577$	1.17501e11			1.06008			0.530040	−	0.847972i	$-0.322177\pi$
$577$	1.17501e11			1.06008			0.530040	+	0.847972i	$0.322177\pi$
$578$			3.78744e10i			0.339340i
$579$	−6.72905e10			−0.598742
$580$	4.51740e10			0.399187
$581$			2.75343e10i			0.241640i
$582$	8.96888e10			0.781711
$583$		−	2.16082e10i		−	0.187044i
$584$	−9.57753e10			−0.823383
$585$			5.67533e10i			0.484582i
$586$			1.72113e11i			1.45957i
$587$		−	6.44382e9i		−	0.0542739i	−0.999632	−	0.0271369i	$-0.991361\pi$
$587$		−	6.44382e9i		−	0.0542739i	0.999632	−	0.0271369i	$-0.00863901\pi$
$588$	−2.88598e10			−0.241426
$589$		−	6.11312e10i		−	0.507928i
$590$	−9.66922e10	+	7.55717e10i	−0.797965	+	0.623664i
$591$	2.04673e10			0.167769
$592$			2.21794e11i			1.80577i
$593$	1.22849e11			0.993466			0.496733	−	0.867903i	$-0.334533\pi$
$593$	1.22849e11			0.993466			0.496733	+	0.867903i	$0.334533\pi$
$594$	−2.86819e10			−0.230389
$595$	−2.44894e10			−0.195394
$596$			1.03384e11i			0.819350i
$597$	9.31376e10			0.733209
$598$		−	2.21774e11i		−	1.73423i
$599$	4.42262e10			0.343536			0.171768	−	0.985137i	$-0.445052\pi$
$599$	4.42262e10			0.343536			0.171768	+	0.985137i	$0.445052\pi$
$600$		−	1.45066e10i		−	0.111934i
$601$			2.24116e11i			1.71781i	0.512137	+	0.858904i	$0.328854\pi$
$601$			2.24116e11i			1.71781i	−0.512137	+	0.858904i	$0.671146\pi$
$602$	−5.21517e10			−0.397084
$603$		−	3.03716e10i		−	0.229720i
$604$		−	6.30748e10i		−	0.473923i
$605$	1.47697e9			0.0110243
$606$	6.47681e10			0.480253
$607$	2.43376e10			0.179276			0.0896380	−	0.995974i	$-0.471429\pi$
$607$	2.43376e10			0.179276			0.0896380	+	0.995974i	$0.471429\pi$
$608$			8.38722e10i			0.613767i
$609$	2.28820e10			0.166351
$610$	3.32051e10			0.239820
$611$	5.94003e10			0.426210
$612$	1.79220e10			0.127756
$613$			3.23496e10i			0.229101i	0.993417	+	0.114550i	$0.0365428\pi$
$613$			3.23496e10i			0.229101i	−0.993417	+	0.114550i	$0.963457\pi$
$614$			1.97128e11i			1.38700i
$615$	1.24604e11			0.871027
$616$	2.59015e10			0.179888
$617$	−1.44980e11			−1.00038			−0.500192	−	0.865915i	$-0.666737\pi$
$617$	−1.44980e11			−1.00038			−0.500192	+	0.865915i	$0.666737\pi$
$618$	−5.96487e10			−0.408928
$619$	−7.94802e10			−0.541373			−0.270686	−	0.962668i	$-0.587251\pi$
$619$	−7.94802e10			−0.541373			−0.270686	+	0.962668i	$0.587251\pi$
$620$			3.91948e10i			0.265254i
$621$			2.38117e10i			0.160112i
$622$			4.68233e10i			0.312824i
$623$			6.83003e9i			0.0453389i
$624$			1.88921e11i			1.24607i
$625$	−9.46150e10			−0.620069
$626$	1.09319e11			0.711867
$627$		−	6.45059e10i		−	0.417378i
$628$		−	8.74506e10i		−	0.562243i
$629$			1.92015e11i			1.22668i
$630$		−	1.45874e10i		−	0.0926009i
$631$	−2.09094e11			−1.31894			−0.659470	−	0.751731i	$-0.729219\pi$
$631$	−2.09094e11			−1.31894			−0.659470	+	0.751731i	$0.729219\pi$
$632$		−	1.15511e11i		−	0.724029i
$633$		−	7.57945e10i		−	0.472088i
$634$		−	1.00833e11i		−	0.624089i
$635$	−8.76976e10			−0.539378
$636$	−8.04259e9			−0.0491550
$637$		−	2.63375e11i		−	1.59962i
$638$	−2.08346e11			−1.25749
$639$	−4.26128e10			−0.255586
$640$			1.58230e11i			0.943122i
$641$	−1.17100e11			−0.693622			−0.346811	−	0.937935i	$-0.612736\pi$
$641$	−1.17100e11			−0.693622			−0.346811	+	0.937935i	$0.612736\pi$
$642$		−	6.36478e10i		−	0.374665i
$643$	5.14729e10			0.301116			0.150558	−	0.988601i	$-0.451893\pi$
$643$	5.14729e10			0.301116			0.150558	+	0.988601i	$0.451893\pi$
$644$			1.77497e10i			0.103192i
$645$			1.00885e11i			0.582889i
$646$			1.29444e11i			0.743281i
$647$	−2.12044e11			−1.21006			−0.605032	−	0.796201i	$-0.706840\pi$
$647$	−2.12044e11			−1.21006			−0.605032	+	0.796201i	$0.706840\pi$
$648$		−	1.29331e10i		−	0.0733503i
$649$	1.38862e11	−	1.08530e11i	0.782718	−	0.611748i
$650$	−1.09277e11			−0.612177
$651$			1.98533e10i			0.110538i
$652$	1.19850e11			0.663205
$653$	−1.00559e11			−0.553056			−0.276528	−	0.961006i	$-0.589184\pi$
$653$	−1.00559e11			−0.553056			−0.276528	+	0.961006i	$0.589184\pi$
$654$	−1.53014e11			−0.836410
$655$		−	6.10604e9i		−	0.0331737i
$656$	4.14784e11			2.23979
$657$		−	7.74636e10i		−	0.415754i
$658$	−1.52677e10			−0.0814463
$659$		−	2.49578e11i		−	1.32332i	−0.749804	−	0.661660i	$-0.769852\pi$
$659$		−	2.49578e11i		−	1.32332i	0.749804	−	0.661660i	$-0.230148\pi$
$660$			4.13585e10i			0.217966i
$661$	1.91052e11			1.00080			0.500399	−	0.865795i	$-0.333187\pi$
$661$	1.91052e11			1.00080			0.500399	+	0.865795i	$0.333187\pi$
$662$			4.04335e11i			2.10528i
$663$			1.63556e11i			0.846472i
$664$	1.13048e11			0.581552
$665$	3.28072e10			0.167758
$666$	−1.14376e11			−0.581349
$667$			1.72969e11i			0.873908i
$668$	1.14442e11			0.574751
$669$	−4.30698e10			−0.215015
$670$	−1.40647e11			−0.697961
$671$	−4.76866e10			−0.235237
$672$		−	2.72388e10i		−	0.133571i
$673$			1.66582e11i			0.812021i	0.913868	+	0.406011i	$0.133080\pi$
$673$			1.66582e11i			0.812021i	−0.913868	+	0.406011i	$0.866920\pi$
$674$	2.35952e11			1.14336
$675$	1.17330e10			0.0565191
$676$	1.88112e11			0.900801
$677$	−1.88891e11			−0.899201			−0.449600	−	0.893230i	$-0.648434\pi$
$677$	−1.88891e11			−0.899201			−0.449600	+	0.893230i	$0.648434\pi$
$678$	−5.17708e10			−0.245000
$679$		−	6.55089e10i		−	0.308192i
$680$			1.00546e11i			0.470251i
$681$			1.75042e11i			0.813868i
$682$		−	1.80770e11i		−	0.835581i
$683$			9.51587e10i			0.437286i	0.975805	+	0.218643i	$0.0701631\pi$
$683$			9.51587e10i			0.437286i	−0.975805	+	0.218643i	$0.929837\pi$
$684$	−2.40091e10			−0.109686
$685$	2.92566e10			0.132881
$686$			1.40899e11i			0.636228i
$687$			6.57768e10i			0.295288i
$688$			3.35826e11i			1.49886i
$689$		−	7.33968e10i		−	0.325687i
$690$	1.10269e11			0.486471
$691$		−	4.93618e9i		−	0.0216511i	−0.999941	−	0.0108255i	$-0.996554\pi$
$691$		−	4.93618e9i		−	0.0216511i	0.999941	−	0.0108255i	$-0.00344594\pi$
$692$			1.08701e11i			0.474032i
$693$			2.09493e10i			0.0908316i
$694$	−3.69125e10			−0.159124
$695$	1.86094e11			0.797613
$696$		−	9.39465e10i		−	0.400354i
$697$	3.59094e11			1.52152
$698$	−3.22999e11			−1.36075
$699$		−	1.98071e10i		−	0.0829685i
$700$	8.74603e9			0.0364266
$701$			4.07228e11i			1.68642i	0.537585	+	0.843210i	$0.319337\pi$
$701$			4.07228e11i			1.68642i	−0.537585	+	0.843210i	$0.680663\pi$
$702$	−9.74240e10			−0.401160
$703$		−	2.57232e11i		−	1.05318i
$704$		−	5.64490e10i		−	0.229808i
$705$			2.95346e10i			0.119557i
$706$	2.56083e11			1.03077
$707$		−	4.73067e10i		−	0.189341i
$708$	−4.03951e10	−	5.16846e10i	−0.160767	−	0.205697i
$709$	−1.16346e11			−0.460432			−0.230216	−	0.973140i	$-0.573943\pi$
$709$	−1.16346e11			−0.460432			−0.230216	+	0.973140i	$0.573943\pi$
$710$			1.97334e11i			0.776549i
$711$	9.34261e10			0.365586
$712$	2.80421e10			0.109116
$713$	−1.50075e11			−0.580699
$714$		−	4.20391e10i		−	0.161756i
$715$	−3.77438e11			−1.44418
$716$		−	1.49844e11i		−	0.570148i
$717$	1.28031e11			0.484438
$718$		−	3.82384e11i		−	1.43881i
$719$		−	1.41372e10i		−	0.0528992i	−0.999650	−	0.0264496i	$-0.991580\pi$
$719$		−	1.41372e10i		−	0.0528992i	0.999650	−	0.0264496i	$-0.00842015\pi$
$720$	−9.39342e10			−0.349538
$721$			4.35675e10i			0.161221i
$722$			1.54051e11i			0.566913i
$723$	−2.21298e11			−0.809885
$724$	−2.34080e11			−0.851943
$725$	8.52293e10			0.308487
$726$			2.53541e9i			0.00912644i
$727$	3.23346e11			1.15752			0.578761	−	0.815497i	$-0.303536\pi$
$727$	3.23346e11			1.15752			0.578761	+	0.815497i	$0.303536\pi$
$728$	8.79800e10			0.313227
$729$	1.04604e10			0.0370370
$730$	−3.58724e11			−1.26319
$731$			2.90737e11i			1.01820i
$732$			1.77490e10i			0.0618201i
$733$	−4.27347e11			−1.48035			−0.740175	−	0.672414i	$-0.765258\pi$
$733$	−4.27347e11			−1.48035			−0.740175	+	0.672414i	$0.765258\pi$
$734$	5.27099e11			1.81597
$735$	1.30954e11			0.448713
$736$	2.05903e11			0.701702
$737$	2.01987e11			0.684625
$738$			2.13898e11i			0.721077i
$739$			7.27228e9i			0.0243833i	0.999926	+	0.0121917i	$0.00388082\pi$
$739$			7.27228e9i			0.0243833i	−0.999926	+	0.0121917i	$0.996119\pi$
$740$			1.64927e11i			0.550001i
$741$		−	2.19108e11i		−	0.726750i
$742$			1.88653e10i			0.0622369i
$743$	−3.32988e11			−1.09263			−0.546316	−	0.837579i	$-0.683970\pi$
$743$	−3.32988e11			−1.09263			−0.546316	+	0.837579i	$0.683970\pi$
$744$	8.15119e10			0.266029
$745$		−	4.69114e11i		−	1.52284i
$746$		−	4.80141e10i		−	0.155029i
$747$			9.14335e10i			0.293645i
$748$			1.19190e11i			0.380745i
$749$	−4.64885e10			−0.147713
$750$		−	2.39344e11i		−	0.756446i
$751$			3.90325e11i			1.22706i	0.789670	+	0.613531i	$0.210252\pi$
$751$			3.90325e11i			1.22706i	−0.789670	+	0.613531i	$0.789748\pi$
$752$			9.83153e10i			0.307433i
$753$	9.38578e10			0.291938
$754$	−7.07692e11			−2.18957
$755$			2.86207e11i			0.880829i
$756$	7.79735e9			0.0238704
$757$	5.46555e11			1.66437			0.832186	−	0.554497i	$-0.187089\pi$
$757$	5.46555e11			1.66437			0.832186	+	0.554497i	$0.187089\pi$
$758$			4.35054e11i			1.31785i
$759$	−1.58360e11			−0.477175
$760$		−	1.34696e11i		−	0.403740i
$761$	−3.47259e11			−1.03542			−0.517708	−	0.855557i	$-0.673215\pi$
$761$	−3.47259e11			−1.03542			−0.517708	+	0.855557i	$0.673215\pi$
$762$		−	1.50544e11i		−	0.446522i
$763$			1.11761e11i			0.329757i
$764$		−	2.72830e10i		−	0.0800791i
$765$	−8.13223e10			−0.237445
$766$		−	3.01751e10i		−	0.0876464i
$767$	4.71675e11	−	3.68646e11i	1.36289	−	1.06519i
$768$	−2.25157e11			−0.647202
$769$		−	3.50765e11i		−	1.00302i	−0.865151	−	0.501512i	$-0.832777\pi$
$769$		−	3.50765e11i		−	1.00302i	0.865151	−	0.501512i	$-0.167223\pi$
$770$	9.70135e10			0.275975
$771$	−3.11460e11			−0.881425
$772$	−1.66566e11			−0.468939
$773$		−	2.03514e11i		−	0.570001i	−0.958527	−	0.285001i	$-0.908006\pi$
$773$		−	2.03514e11i		−	0.570001i	0.958527	−	0.285001i	$-0.0919938\pi$
$774$	−1.73181e11			−0.482543
$775$			7.39485e10i			0.204985i
$776$	−2.68960e11			−0.741721
$777$			8.35403e10i			0.229199i
$778$			1.41710e11i			0.386796i
$779$	−4.81060e11			−1.30632
$780$			1.40483e11i			0.379529i
$781$		−	2.83397e11i		−	0.761712i
$782$	3.17782e11			0.849771
$783$	7.59845e10			0.202152
$784$	4.35921e11			1.15384
$785$			3.96813e11i			1.04498i
$786$	1.04818e10			0.0274628
$787$	5.65976e11			1.47536			0.737681	−	0.675149i	$-0.235921\pi$
$787$	5.65976e11			1.47536			0.737681	+	0.675149i	$0.235921\pi$
$788$	5.06633e10			0.131398
$789$	−3.85030e11			−0.993542
$790$		−	4.32644e11i		−	1.11076i
$791$			3.78135e10i			0.0965919i
$792$	8.60116e10			0.218603
$793$	−1.61978e11			−0.409602
$794$	6.19196e11			1.55792
$795$	3.64939e10			0.0913590
$796$	2.30546e11			0.574255
$797$		−	2.20498e11i		−	0.546476i	−0.961946	−	0.273238i	$-0.911905\pi$
$797$		−	2.20498e11i		−	0.546476i	0.961946	−	0.273238i	$-0.0880946\pi$
$798$			5.63176e10i			0.138878i
$799$			8.51152e10i			0.208843i
$800$		−	1.01457e11i		−	0.247699i
$801$			2.26806e10i			0.0550965i
$802$	−5.94829e11			−1.43779
$803$	5.15172e11			1.23905
$804$		−	7.51796e10i		−	0.179918i
$805$		−	8.05406e10i		−	0.191792i
$806$		−	6.14023e11i		−	1.45494i
$807$			2.33166e11i			0.549756i
$808$	−1.94227e11			−0.455685
$809$		−	1.22279e11i		−	0.285468i	−0.989761	−	0.142734i	$-0.954411\pi$
$809$		−	1.22279e11i		−	0.285468i	0.989761	−	0.142734i	$-0.0455893\pi$
$810$		−	4.84405e10i		−	0.112530i
$811$			4.22466e11i			0.976582i	0.872681	+	0.488291i	$0.162380\pi$
$811$			4.22466e11i			0.976582i	−0.872681	+	0.488291i	$0.837620\pi$
$812$	5.66403e10			0.130287
$813$	−2.56412e11			−0.586916
$814$		−	7.60657e11i		−	1.73257i
$815$	−5.43828e11			−1.23263
$816$	−2.70707e11			−0.610575
$817$		−	3.89486e11i		−	0.874185i
$818$	−4.59570e11			−1.02645
$819$			7.11587e10i			0.158159i
$820$	3.08435e11			0.682195
$821$		−	1.82564e11i		−	0.401829i	−0.979609	−	0.200915i	$-0.935609\pi$
$821$		−	1.82564e11i		−	0.401829i	0.979609	−	0.200915i	$-0.0643914\pi$
$822$			5.02226e10i			0.110005i
$823$		−	2.96986e11i		−	0.647346i	−0.946169	−	0.323673i	$-0.895082\pi$
$823$		−	2.96986e11i		−	0.647346i	0.946169	−	0.323673i	$-0.104918\pi$
$824$	1.78875e11			0.388009
$825$			7.80306e10i			0.168442i
$826$	−1.21235e11	+	9.47537e10i	−0.260441	+	0.203552i
$827$	−1.55763e11			−0.332998			−0.166499	−	0.986042i	$-0.553246\pi$
$827$	−1.55763e11			−0.332998			−0.166499	+	0.986042i	$0.553246\pi$
$828$			5.89417e10i			0.125401i
$829$	−7.93566e11			−1.68022			−0.840108	−	0.542420i	$-0.817508\pi$
$829$	−7.93566e11			−1.68022			−0.840108	+	0.542420i	$0.817508\pi$
$830$	4.23416e11			0.892185
$831$	−1.85045e11			−0.388038
$832$		−	1.91741e11i		−	0.400149i
$833$	3.77393e11			0.783815
$834$			3.19453e11i			0.660302i
$835$	−5.19289e11			−1.06823
$836$		−	1.59673e11i		−	0.326893i
$837$			6.59272e10i			0.134327i
$838$	9.08207e11			1.84166
$839$			1.41748e11i			0.286069i	0.989718	+	0.143034i	$0.0456859\pi$
$839$			1.41748e11i			0.286069i	−0.989718	+	0.143034i	$0.954314\pi$
$840$			4.37448e10i			0.0878637i
$841$	5.17080e10			0.103365
$842$	1.37984e11			0.274524
$843$	−3.45777e11			−0.684678
$844$		−	1.87616e11i		−	0.369743i
$845$	−8.53571e11			−1.67422
$846$	−5.06998e10			−0.0989748
$847$	1.85187e9			0.00359813
$848$	1.21481e11			0.234924
$849$			1.16189e11i			0.223633i
$850$		−	1.56585e11i		−	0.299967i
$851$	−6.31497e11			−1.20407
$852$	−1.05480e11			−0.200177
$853$	−9.08800e11			−1.71661			−0.858306	−	0.513138i	$-0.828483\pi$
$853$	−9.08800e11			−1.71661			−0.858306	+	0.513138i	$0.828483\pi$
$854$	4.16334e10			0.0782726
$855$	1.08943e11			0.203862
$856$			1.90868e11i			0.355498i
$857$			6.19242e11i			1.14799i	0.818859	+	0.573994i	$0.194607\pi$
$857$			6.19242e11i			1.14799i	−0.818859	+	0.573994i	$0.805393\pi$
$858$		−	6.47919e11i		−	1.19556i
$859$		−	1.19338e11i		−	0.219183i	−0.993977	−	0.109591i	$-0.965046\pi$
$859$		−	1.19338e11i		−	0.219183i	0.993977	−	0.109591i	$-0.0349543\pi$
$860$			2.49722e11i			0.456523i
$861$	1.56232e11			0.284287
$862$	1.21083e12			2.19308
$863$		−	6.34950e11i		−	1.14471i	−0.820005	−	0.572356i	$-0.806030\pi$
$863$		−	6.34950e11i		−	1.14471i	0.820005	−	0.572356i	$-0.193970\pi$
$864$		−	9.04523e10i		−	0.162317i
$865$		−	4.93238e11i		−	0.881032i
$866$		−	8.13674e11i		−	1.44670i
$867$	9.18628e10			0.162579
$868$			4.91434e10i			0.0865738i
$869$			6.21331e11i			1.08954i
$870$		−	3.51874e11i		−	0.614201i
$871$	6.86090e11			1.19209
$872$	4.58859e11			0.793621
$873$		−	2.17536e11i		−	0.374520i
$874$	−4.25716e11			−0.729582
$875$	−1.74818e11			−0.298231
$876$		−	1.91747e11i		−	0.325622i
$877$	−3.45266e11			−0.583654			−0.291827	−	0.956471i	$-0.594263\pi$
$877$	−3.45266e11			−0.583654			−0.291827	+	0.956471i	$0.594263\pi$
$878$			4.73157e11i			0.796209i
$879$	4.17453e11			0.699282
$880$		−	6.24710e11i		−	1.04171i
$881$		−	6.82105e11i		−	1.13226i	−0.824314	−	0.566132i	$-0.808439\pi$
$881$		−	6.82105e11i		−	1.13226i	0.824314	−	0.566132i	$-0.191561\pi$
$882$			2.24798e11i			0.371466i
$883$	1.02045e12			1.67860			0.839301	−	0.543667i	$-0.182965\pi$
$883$	1.02045e12			1.67860			0.839301	+	0.543667i	$0.182965\pi$
$884$			4.04854e11i			0.662964i
$885$	1.83296e11	+	2.34523e11i	0.298799	+	0.382307i
$886$	3.37972e11			0.548461
$887$		−	3.28243e11i		−	0.530275i	−0.964211	−	0.265138i	$-0.914583\pi$
$887$		−	3.28243e11i		−	0.530275i	0.964211	−	0.265138i	$-0.0854174\pi$
$888$	3.42991e11			0.551609
$889$	−1.09958e11			−0.176043
$890$	1.05031e11			0.167400
$891$			6.95666e10i			0.110380i
$892$	−1.06612e11			−0.168401
$893$		−	1.14024e11i		−	0.179305i
$894$	8.05292e11			1.26068
$895$			6.79929e11i			1.05967i
$896$			1.98392e11i			0.307817i
$897$	−5.37903e11			−0.830872
$898$			1.28982e12i			1.98347i
$899$			4.78898e11i			0.733170i
$900$	2.90431e10			0.0442662
$901$	1.05171e11			0.159587
$902$	−1.42253e12			−2.14900
$903$			1.26492e11i			0.190244i
$904$	1.55251e11			0.232466
$905$	1.06216e12			1.58341
$906$	−4.91309e11			−0.729192
$907$	2.06808e11			0.305590			0.152795	−	0.988258i	$-0.451173\pi$
$907$	2.06808e11			0.305590			0.152795	+	0.988258i	$0.451173\pi$
$908$			4.33286e11i			0.637428i
$909$		−	1.57092e11i		−	0.230091i
$910$	3.29527e11			0.480535
$911$	1.08380e12			1.57353			0.786764	−	0.617253i	$-0.211755\pi$
$911$	1.08380e12			1.57353			0.786764	+	0.617253i	$0.211755\pi$
$912$	3.62653e11			0.524217
$913$	−6.08079e11			−0.875138
$914$	6.52804e11			0.935401
$915$		−	8.05374e10i		−	0.114898i
$916$			1.62819e11i			0.231272i
$917$		−	7.65591e9i		−	0.0108273i
$918$		−	1.39600e11i		−	0.196569i
$919$		−	7.29528e11i		−	1.02278i	−0.859350	−	0.511388i	$-0.829132\pi$
$919$		−	7.29528e11i		−	1.02278i	0.859350	−	0.511388i	$-0.170868\pi$
$920$	−3.30676e11			−0.461584
$921$	4.78126e11			0.664514
$922$		−	5.22526e11i		−	0.723077i
$923$		−	9.62616e11i		−	1.32631i
$924$			5.18563e10i			0.0711400i
$925$			3.11166e11i			0.425035i
$926$	8.66967e11			1.17912
$927$			1.44675e11i			0.195918i
$928$		−	6.57049e11i		−	0.885944i
$929$		−	3.80833e11i		−	0.511295i	−0.966770	−	0.255647i	$-0.917711\pi$
$929$		−	3.80833e11i		−	0.511295i	0.966770	−	0.255647i	$-0.0822886\pi$
$930$	3.05300e11			0.408127
$931$	−5.05574e11			−0.672955
$932$		−	4.90291e10i		−	0.0649816i
$933$	1.13568e11			0.149875
$934$	−7.28240e11			−0.956945
$935$		−	5.40834e11i		−	0.707649i
$936$	2.92156e11			0.380638
$937$			3.23834e11i			0.420112i	0.977689	+	0.210056i	$0.0673646\pi$
$937$			3.23834e11i			0.420112i	−0.977689	+	0.210056i	$0.932635\pi$
$938$	−1.76347e11			−0.227801
$939$		−	2.65149e11i		−	0.341057i
$940$			7.31077e10i			0.0936379i
$941$			8.82980e11i			1.12614i	0.826409	+	0.563070i	$0.190380\pi$
$941$			8.82980e11i			1.12614i	−0.826409	+	0.563070i	$0.809620\pi$
$942$	−6.81179e11			−0.865083
$943$			1.18099e12i			1.49348i
$944$	6.10159e11	+	7.80684e11i	0.768342	+	0.983077i
$945$	−3.53811e10			−0.0443653
$946$		−	1.15174e12i		−	1.43810i
$947$	1.08259e12			1.34606			0.673028	−	0.739617i	$-0.264993\pi$
$947$	1.08259e12			1.34606			0.673028	+	0.739617i	$0.264993\pi$
$948$	2.31260e11			0.286330
$949$	1.74989e12			2.15748
$950$			2.09768e11i			0.257540i
$951$	−2.44567e11			−0.299003
$952$			1.26067e11i			0.153481i
$953$	−6.32283e11			−0.766549			−0.383274	−	0.923634i	$-0.625204\pi$
$953$	−6.32283e11			−0.766549			−0.383274	+	0.923634i	$0.625204\pi$
$954$			6.26462e10i			0.0756313i
$955$			1.23799e11i			0.148834i
$956$	3.16918e11			0.379415
$957$			5.05335e11i			0.602465i
$958$			3.81145e11i			0.452510i
$959$	3.66827e10			0.0433698
$960$	9.53361e10			0.112246
$961$	4.37379e11			0.512819
$962$		−	2.58373e12i		−	3.01680i
$963$	−1.54375e11			−0.179503
$964$	−5.47783e11			−0.634309
$965$	7.55805e11			0.871566
$966$	1.38258e11			0.158775
$967$		−	3.63089e11i		−	0.415247i	−0.978209	−	0.207624i	$-0.933427\pi$
$967$		−	3.63089e11i		−	0.415247i	0.978209	−	0.207624i	$-0.0665730\pi$
$968$		−	7.60322e9i		−	0.00865956i
$969$	3.13962e11			0.356108
$970$	−1.00738e12			−1.13791
$971$	−2.34683e11			−0.264000			−0.132000	−	0.991250i	$-0.542140\pi$
$971$	−2.34683e11			−0.264000			−0.132000	+	0.991250i	$0.542140\pi$
$972$	2.58928e10			0.0290077
$973$	2.33329e11			0.260326
$974$		−	1.38835e12i		−	1.54263i
$975$			2.65047e11i			0.293295i
$976$		−	2.68095e11i		−	0.295453i
$977$			1.72154e12i			1.88946i	0.327847	+	0.944731i	$0.393677\pi$
$977$			1.72154e12i			1.88946i	−0.327847	+	0.944731i	$0.606323\pi$
$978$		−	9.33549e11i		−	1.02043i
$979$	−1.50837e11			−0.164202
$980$	3.24153e11			0.351435
$981$			3.71128e11i			0.400726i
$982$			6.89208e11i			0.741147i
$983$			6.79908e10i			0.0728176i	0.999337	+	0.0364088i	$0.0115918\pi$
$983$			6.79908e10i			0.0728176i	−0.999337	+	0.0364088i	$0.988408\pi$
$984$		−	6.41441e11i		−	0.684189i
$985$	−2.29889e11			−0.244215
$986$		−	1.01406e12i		−	1.07289i
$987$			3.70312e10i			0.0390211i
$988$		−	5.42363e11i		−	0.569196i
$989$	−9.56175e11			−0.999429
$990$	3.22154e11			0.335369
$991$			7.99837e11i			0.829291i	0.909983	+	0.414646i	$0.136094\pi$
$991$			7.99837e11i			0.829291i	−0.909983	+	0.414646i	$0.863906\pi$
$992$	5.70083e11			0.588696
$993$	9.80697e11			1.00864
$994$			2.47423e11i			0.253451i
$995$	−1.04612e12			−1.06731
$996$			2.26327e11i			0.229985i
$997$	1.26219e12			1.27745			0.638724	−	0.769436i	$-0.279462\pi$
$997$	1.26219e12			1.27745			0.638724	+	0.769436i	$0.279462\pi$
$998$			1.29399e12i			1.30440i
$999$			2.77413e11i			0.278526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.20	✓	80
59.58	odd	2	inner	177.9.c.a.58.61	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.20	✓	80	1.1	even	1	trivial
177.9.c.a.58.61	yes	80	59.58	odd	2	inner

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-19.2811i q^{2} -46.7654 q^{3} -115.759 q^{4} +525.267 q^{5} +901.686i q^{6} +658.593 q^{7} -2703.99i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q-19.2811i q^{2} -46.7654 q^{3} -115.759 q^{4} +525.267 q^{5} +901.686i q^{6} +658.593 q^{7} -2703.99i q^{8} +2187.00 q^{9} -10127.7i q^{10} +14544.7i q^{11} +5413.53 q^{12} +49404.0i q^{13} -12698.4i q^{14} -24564.3 q^{15} -81770.2 q^{16} -70791.4 q^{17} -42167.7i q^{18} +94835.6 q^{19} -60804.6 q^{20} -30799.4 q^{21} +280436. q^{22} -232818. i q^{23} +126453. i q^{24} -114720. q^{25} +952561. q^{26} -102276. q^{27} -76238.4 q^{28} -742936. q^{29} +473626. i q^{30} -644602. i q^{31} +884395. i q^{32} -680186. i q^{33} +1.36493e6i q^{34} +345937. q^{35} -253166. q^{36} -2.71240e6i q^{37} -1.82853e6i q^{38} -2.31040e6i q^{39} -1.42032e6i q^{40} -5.07256e6 q^{41} +593845. i q^{42} -4.10695e6i q^{43} -1.68368e6i q^{44} +1.14876e6 q^{45} -4.48899e6 q^{46} -1.20234e6i q^{47} +3.82401e6 q^{48} -5.33106e6 q^{49} +2.21191e6i q^{50} +3.31059e6 q^{51} -5.71898e6i q^{52} -1.48565e6 q^{53} +1.97199e6i q^{54} +7.63983e6i q^{55} -1.78083e6i q^{56} -4.43502e6 q^{57} +1.43246e7i q^{58} +(-7.46187e6 - 9.54730e6i) q^{59} +2.84355e6 q^{60} +3.27863e6i q^{61} -1.24286e7 q^{62} +1.44034e6 q^{63} -3.88108e6 q^{64} +2.59503e7i q^{65} -1.31147e7 q^{66} -1.38873e7i q^{67} +8.19477e6 q^{68} +1.08878e7i q^{69} -6.67004e6i q^{70} -1.94846e7 q^{71} -5.91362e6i q^{72} -3.54200e7i q^{73} -5.22980e7 q^{74} +5.36490e6 q^{75} -1.09781e7 q^{76} +9.57902e6i q^{77} -4.45469e7 q^{78} +4.27188e7 q^{79} -4.29512e7 q^{80} +4.78297e6 q^{81} +9.78044e7i q^{82} +4.18077e7i q^{83} +3.56532e6 q^{84} -3.71844e7 q^{85} -7.91865e7 q^{86} +3.47437e7 q^{87} +3.93286e7 q^{88} +1.03706e7i q^{89} -2.21493e7i q^{90} +3.25371e7i q^{91} +2.69509e7i q^{92} +3.01451e7i q^{93} -2.31823e7 q^{94} +4.98140e7 q^{95} -4.13591e7i q^{96} -9.94679e7i q^{97} +1.02788e8i q^{98} +3.18092e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

L-functions

Modular forms

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Database

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