LMFDB - Embedded newform 29.9.c.a.12.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.17
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.9289 + 17.9289i) q^{2} +(-42.9110 - 42.9110i) q^{3} +386.891i q^{4} -832.826i q^{5} -1538.69i q^{6} -3297.00 q^{7} +(-2346.74 + 2346.74i) q^{8} -2878.30i q^{9} +O(q^{10})$	\(q+(17.9289 + 17.9289i) q^{2} +(-42.9110 - 42.9110i) q^{3} +386.891i q^{4} -832.826i q^{5} -1538.69i q^{6} -3297.00 q^{7} +(-2346.74 + 2346.74i) q^{8} -2878.30i q^{9} +(14931.7 - 14931.7i) q^{10} +(-6087.35 - 6087.35i) q^{11} +(16601.9 - 16601.9i) q^{12} -7431.87i q^{13} +(-59111.6 - 59111.6i) q^{14} +(-35737.3 + 35737.3i) q^{15} +14895.4 q^{16} +(-2692.02 - 2692.02i) q^{17} +(51604.8 - 51604.8i) q^{18} +(84773.7 + 84773.7i) q^{19} +322213. q^{20} +(141477. + 141477. i) q^{21} -218279. i q^{22} -212553. q^{23} +201401. q^{24} -302974. q^{25} +(133245. - 133245. i) q^{26} +(-405049. + 405049. i) q^{27} -1.27558e6i q^{28} +(-57647.9 - 704928. i) q^{29} -1.28146e6 q^{30} +(-913977. - 913977. i) q^{31} +(867822. + 867822. i) q^{32} +522428. i q^{33} -96530.0i q^{34} +2.74583e6i q^{35} +1.11359e6 q^{36} +(2.00621e6 - 2.00621e6i) q^{37} +3.03980e6i q^{38} +(-318909. + 318909. i) q^{39} +(1.95442e6 + 1.95442e6i) q^{40} +(-3.00390e6 + 3.00390e6i) q^{41} +5.07307e6i q^{42} +(54970.1 + 54970.1i) q^{43} +(2.35514e6 - 2.35514e6i) q^{44} -2.39712e6 q^{45} +(-3.81084e6 - 3.81084e6i) q^{46} +(-1.43308e6 + 1.43308e6i) q^{47} +(-639174. - 639174. i) q^{48} +5.10541e6 q^{49} +(-5.43198e6 - 5.43198e6i) q^{50} +231034. i q^{51} +2.87533e6 q^{52} +1.53526e7 q^{53} -1.45242e7 q^{54} +(-5.06970e6 + 5.06970e6i) q^{55} +(7.73719e6 - 7.73719e6i) q^{56} -7.27544e6i q^{57} +(1.16050e7 - 1.36721e7i) q^{58} +3.82715e6 q^{59} +(-1.38265e7 - 1.38265e7i) q^{60} +(3.27145e6 + 3.27145e6i) q^{61} -3.27732e7i q^{62} +9.48976e6i q^{63} +2.73050e7i q^{64} -6.18945e6 q^{65} +(-9.36656e6 + 9.36656e6i) q^{66} -2.66245e7i q^{67} +(1.04152e6 - 1.04152e6i) q^{68} +(9.12085e6 + 9.12085e6i) q^{69} +(-4.92297e7 + 4.92297e7i) q^{70} -2.23678e7i q^{71} +(6.75461e6 + 6.75461e6i) q^{72} +(3.48965e7 - 3.48965e7i) q^{73} +7.19383e7 q^{74} +(1.30009e7 + 1.30009e7i) q^{75} +(-3.27982e7 + 3.27982e7i) q^{76} +(2.00700e7 + 2.00700e7i) q^{77} -1.14354e7 q^{78} +(3.30216e7 + 3.30216e7i) q^{79} -1.24052e7i q^{80} +1.58776e7 q^{81} -1.07713e8 q^{82} +4.41200e7 q^{83} +(-5.47364e7 + 5.47364e7i) q^{84} +(-2.24198e6 + 2.24198e6i) q^{85} +1.97111e6i q^{86} +(-2.77754e7 + 3.27228e7i) q^{87} +2.85708e7 q^{88} +(-5.35318e7 - 5.35318e7i) q^{89} +(-4.29778e7 - 4.29778e7i) q^{90} +2.45029e7i q^{91} -8.22349e7i q^{92} +7.84393e7i q^{93} -5.13873e7 q^{94} +(7.06017e7 - 7.06017e7i) q^{95} -7.44781e7i q^{96} +(-9.05760e7 + 9.05760e7i) q^{97} +(9.15344e7 + 9.15344e7i) q^{98} +(-1.75212e7 + 1.75212e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	17.9289	+	17.9289i	1.12056	+	1.12056i	0.991658	+	0.128899i	$0.0411442\pi$
$2$	17.9289	+	17.9289i	1.12056	+	1.12056i	0.128899	+	0.991658i	$0.458856\pi$
$3$	−42.9110	−	42.9110i	−0.529765	−	0.529765i	0.390737	−	0.920502i	$-0.372220\pi$
$3$	−42.9110	−	42.9110i	−0.529765	−	0.529765i	−0.920502	+	0.390737i	$0.872220\pi$
$4$			386.891i			1.51129i
$5$		−	832.826i		−	1.33252i	−0.745719	−	0.666260i	$-0.767894\pi$
$5$		−	832.826i		−	1.33252i	0.745719	−	0.666260i	$-0.232106\pi$
$6$		−	1538.69i		−	1.18726i
$7$	−3297.00			−1.37318			−0.686589	−	0.727046i	$-0.740893\pi$
$7$	−3297.00			−1.37318			−0.686589	+	0.727046i	$0.740893\pi$
$8$	−2346.74	+	2346.74i	−0.572933	+	0.572933i
$9$		−	2878.30i		−	0.438698i
$10$	14931.7	−	14931.7i	1.49317	−	1.49317i
$11$	−6087.35	−	6087.35i	−0.415774	−	0.415774i	0.467970	−	0.883744i	$-0.344986\pi$
$11$	−6087.35	−	6087.35i	−0.415774	−	0.415774i	−0.883744	+	0.467970i	$0.844986\pi$
$12$	16601.9	−	16601.9i	0.800630	−	0.800630i
$13$		−	7431.87i		−	0.260210i	−0.991500	−	0.130105i	$-0.958468\pi$
$13$		−	7431.87i		−	0.260210i	0.991500	−	0.130105i	$-0.0415315\pi$
$14$	−59111.6	−	59111.6i	−1.53872	−	1.53872i
$15$	−35737.3	+	35737.3i	−0.705923	+	0.705923i
$16$	14895.4			0.227285
$17$	−2692.02	−	2692.02i	−0.0322317	−	0.0322317i	0.690807	−	0.723039i	$-0.257255\pi$
$17$	−2692.02	−	2692.02i	−0.0322317	−	0.0322317i	−0.723039	+	0.690807i	$0.757255\pi$
$18$	51604.8	−	51604.8i	0.491586	−	0.491586i
$19$	84773.7	+	84773.7i	0.650499	+	0.650499i	0.953113	−	0.302614i	$-0.0978593\pi$
$19$	84773.7	+	84773.7i	0.650499	+	0.650499i	−0.302614	+	0.953113i	$0.597859\pi$
$20$	322213.			2.01383
$21$	141477.	+	141477.i	0.727461	+	0.727461i
$22$		−	218279.i		−	0.931797i
$23$	−212553.			−0.759549			−0.379775	−	0.925079i	$-0.623998\pi$
$23$	−212553.			−0.759549			−0.379775	+	0.925079i	$0.623998\pi$
$24$	201401.			0.607040
$25$	−302974.			−0.775612
$26$	133245.	−	133245.i	0.291580	−	0.291580i
$27$	−405049.	+	405049.i	−0.762172	+	0.762172i
$28$		−	1.27558e6i		−	2.07528i
$29$	−57647.9	−	704928.i	−0.0815064	−	0.996673i
$29$	−57647.9	−	704928.i	−0.0815064	−	0.996673i
$30$	−1.28146e6			−1.58205
$31$	−913977.	−	913977.i	−0.989666	−	0.989666i	0.0102812	−	0.999947i	$-0.496727\pi$
$31$	−913977.	−	913977.i	−0.989666	−	0.989666i	−0.999947	+	0.0102812i	$0.996727\pi$
$32$	867822.	+	867822.i	0.827619	+	0.827619i
$33$			522428.i			0.440525i
$34$		−	96530.0i		−	0.0722348i
$35$			2.74583e6i			1.82979i
$36$	1.11359e6			0.663002
$37$	2.00621e6	−	2.00621e6i	1.07046	−	1.07046i	0.0731364	−	0.997322i	$-0.476699\pi$
$37$	2.00621e6	−	2.00621e6i	1.07046	−	1.07046i	0.997322	−	0.0731364i	$-0.0233008\pi$
$38$			3.03980e6i			1.45784i
$39$	−318909.	+	318909.i	−0.137850	+	0.137850i
$40$	1.95442e6	+	1.95442e6i	0.763446	+	0.763446i
$41$	−3.00390e6	+	3.00390e6i	−1.06304	+	1.06304i	−0.0651678	+	0.997874i	$0.520758\pi$
$41$	−3.00390e6	+	3.00390e6i	−1.06304	+	1.06304i	−0.997874	+	0.0651678i	$0.979242\pi$
$42$			5.07307e6i			1.63032i
$43$	54970.1	+	54970.1i	0.0160788	+	0.0160788i	0.715100	−	0.699022i	$-0.246381\pi$
$43$	54970.1	+	54970.1i	0.0160788	+	0.0160788i	−0.699022	+	0.715100i	$0.746381\pi$
$44$	2.35514e6	−	2.35514e6i	0.628357	−	0.628357i
$45$	−2.39712e6			−0.584575
$46$	−3.81084e6	−	3.81084e6i	−0.851118	−	0.851118i
$47$	−1.43308e6	+	1.43308e6i	−0.293684	+	0.293684i	−0.838534	−	0.544850i	$-0.816587\pi$
$47$	−1.43308e6	+	1.43308e6i	−0.293684	+	0.293684i	0.544850	+	0.838534i	$0.316587\pi$
$48$	−639174.	−	639174.i	−0.120408	−	0.120408i
$49$	5.10541e6			0.885618
$50$	−5.43198e6	−	5.43198e6i	−0.869117	−	0.869117i
$51$			231034.i			0.0341504i
$52$	2.87533e6			0.393254
$53$	1.53526e7			1.94572			0.972858	−	0.231404i	$-0.0743319\pi$
$53$	1.53526e7			1.94572			0.972858	+	0.231404i	$0.0743319\pi$
$54$	−1.45242e7			−1.70811
$55$	−5.06970e6	+	5.06970e6i	−0.554028	+	0.554028i
$56$	7.73719e6	−	7.73719e6i	0.786740	−	0.786740i
$57$		−	7.27544e6i		−	0.689223i
$58$	1.16050e7	−	1.36721e7i	1.02550	−	1.20816i
$59$	3.82715e6			0.315840			0.157920	−	0.987452i	$-0.449521\pi$
$59$	3.82715e6			0.315840			0.157920	+	0.987452i	$0.449521\pi$
$60$	−1.38265e7	−	1.38265e7i	−1.06686	−	1.06686i
$61$	3.27145e6	+	3.27145e6i	0.236276	+	0.236276i	0.815306	−	0.579030i	$-0.196569\pi$
$61$	3.27145e6	+	3.27145e6i	0.236276	+	0.236276i	−0.579030	+	0.815306i	$0.696569\pi$
$62$		−	3.27732e7i		−	2.21795i
$63$			9.48976e6i			0.602411i
$64$			2.73050e7i			1.62750i
$65$	−6.18945e6			−0.346736
$66$	−9.36656e6	+	9.36656e6i	−0.493633	+	0.493633i
$67$		−	2.66245e7i		−	1.32124i	−0.750719	−	0.660622i	$-0.770293\pi$
$67$		−	2.66245e7i		−	1.32124i	0.750719	−	0.660622i	$-0.229707\pi$
$68$	1.04152e6	−	1.04152e6i	0.0487115	−	0.0487115i
$69$	9.12085e6	+	9.12085e6i	0.402382	+	0.402382i
$70$	−4.92297e7	+	4.92297e7i	−2.05038	+	2.05038i
$71$		−	2.23678e7i		−	0.880218i	−0.897944	−	0.440109i	$-0.854940\pi$
$71$		−	2.23678e7i		−	0.880218i	0.897944	−	0.440109i	$-0.145060\pi$
$72$	6.75461e6	+	6.75461e6i	0.251345	+	0.251345i
$73$	3.48965e7	−	3.48965e7i	1.22882	−	1.22882i	0.264416	−	0.964409i	$-0.414821\pi$
$73$	3.48965e7	−	3.48965e7i	1.22882	−	1.22882i	0.964409	−	0.264416i	$-0.0851792\pi$
$74$	7.19383e7			2.39902
$75$	1.30009e7	+	1.30009e7i	0.410892	+	0.410892i
$76$	−3.27982e7	+	3.27982e7i	−0.983096	+	0.983096i
$77$	2.00700e7	+	2.00700e7i	0.570932	+	0.570932i
$78$	−1.14354e7			−0.308938
$79$	3.30216e7	+	3.30216e7i	0.847793	+	0.847793i	0.989857	−	0.142064i	$-0.0453739\pi$
$79$	3.30216e7	+	3.30216e7i	0.847793	+	0.847793i	−0.142064	+	0.989857i	$0.545374\pi$
$80$		−	1.24052e7i		−	0.302862i
$81$	1.58776e7			0.368845
$82$	−1.07713e8			−2.38240
$83$	4.41200e7			0.929658			0.464829	−	0.885401i	$-0.346116\pi$
$83$	4.41200e7			0.929658			0.464829	+	0.885401i	$0.346116\pi$
$84$	−5.47364e7	+	5.47364e7i	−1.09941	+	1.09941i
$85$	−2.24198e6	+	2.24198e6i	−0.0429494	+	0.0429494i
$86$			1.97111e6i			0.0360344i
$87$	−2.77754e7	+	3.27228e7i	−0.484823	+	0.571181i
$88$	2.85708e7			0.476422
$89$	−5.35318e7	−	5.35318e7i	−0.853203	−	0.853203i	0.137324	−	0.990526i	$-0.456150\pi$
$89$	−5.35318e7	−	5.35318e7i	−0.853203	−	0.853203i	−0.990526	+	0.137324i	$0.956150\pi$
$90$	−4.29778e7	−	4.29778e7i	−0.655049	−	0.655049i
$91$			2.45029e7i			0.357315i
$92$		−	8.22349e7i		−	1.14790i
$93$			7.84393e7i			1.04858i
$94$	−5.13873e7			−0.658179
$95$	7.06017e7	−	7.06017e7i	0.866804	−	0.866804i
$96$		−	7.44781e7i		−	0.876887i
$97$	−9.05760e7	+	9.05760e7i	−1.02312	+	1.02312i	−0.0233926	+	0.999726i	$0.507447\pi$
$97$	−9.05760e7	+	9.05760e7i	−1.02312	+	1.02312i	−0.999726	+	0.0233926i	$0.992553\pi$
$98$	9.15344e7	+	9.15344e7i	0.992385	+	0.992385i
$99$	−1.75212e7	+	1.75212e7i	−0.182400	+	0.182400i
$100$		−	1.17218e8i		−	1.17218i
$101$	−2.87713e7	−	2.87713e7i	−0.276486	−	0.276486i	0.555218	−	0.831705i	$-0.312635\pi$
$101$	−2.87713e7	−	2.87713e7i	−0.276486	−	0.276486i	−0.831705	+	0.555218i	$0.812635\pi$
$102$	−4.14219e6	+	4.14219e6i	−0.0382675	+	0.0382675i
$103$	1.71473e8			1.52352			0.761759	−	0.647860i	$-0.224336\pi$
$103$	1.71473e8			1.52352			0.761759	+	0.647860i	$0.224336\pi$
$104$	1.74406e7	+	1.74406e7i	0.149083	+	0.149083i
$105$	1.17826e8	−	1.17826e8i	0.969358	−	0.969358i
$106$	2.75256e8	+	2.75256e8i	2.18028	+	2.18028i
$107$	−8.40438e7			−0.641166			−0.320583	−	0.947220i	$-0.603879\pi$
$107$	−8.40438e7			−0.641166			−0.320583	+	0.947220i	$0.603879\pi$
$108$	−1.56710e8	−	1.56710e8i	−1.15187	−	1.15187i
$109$		−	7.23702e7i		−	0.512689i	−0.966586	−	0.256344i	$-0.917482\pi$
$109$		−	7.23702e7i		−	0.512689i	0.966586	−	0.256344i	$-0.0825181\pi$
$110$	−1.81788e8			−1.24164
$111$	−1.72177e8			−1.13418
$112$	−4.91100e7			−0.312103
$113$	−7.85851e7	+	7.85851e7i	−0.481977	+	0.481977i	−0.905763	−	0.423785i	$-0.860701\pi$
$113$	−7.85851e7	+	7.85851e7i	−0.481977	+	0.481977i	0.423785	+	0.905763i	$0.360701\pi$
$114$	1.30441e8	−	1.30441e8i	0.772314	−	0.772314i
$115$			1.77020e8i			1.01212i
$116$	2.72730e8	−	2.23035e7i	1.50627	−	0.123180i
$117$	−2.13912e7			−0.114154
$118$	6.86165e7	+	6.86165e7i	0.353916	+	0.353916i
$119$	8.87559e6	+	8.87559e6i	0.0442598	+	0.0442598i
$120$		−	1.67732e8i		−	0.808894i
$121$		−	1.40247e8i		−	0.654263i
$122$			1.17307e8i			0.529522i
$123$	2.57801e8			1.12632
$124$	3.53610e8	−	3.53610e8i	1.49568	−	1.49568i
$125$		−	7.29984e7i		−	0.299001i
$126$	−1.70141e8	+	1.70141e8i	−0.675036	+	0.675036i
$127$	−1.35812e8	−	1.35812e8i	−0.522064	−	0.522064i	0.396131	−	0.918194i	$-0.370353\pi$
$127$	−1.35812e8	−	1.35812e8i	−0.522064	−	0.522064i	−0.918194	+	0.396131i	$0.870353\pi$
$128$	−2.67386e8	+	2.67386e8i	−0.996090	+	0.996090i
$129$		−	4.71764e6i		−	0.0170359i
$130$	−1.10970e8	−	1.10970e8i	−0.388537	−	0.388537i
$131$	−3.08174e8	+	3.08174e8i	−1.04643	+	1.04643i	−0.0475645	+	0.998868i	$0.515146\pi$
$131$	−3.08174e8	+	3.08174e8i	−1.04643	+	1.04643i	−0.998868	+	0.0475645i	$0.984854\pi$
$132$	−2.02123e8			−0.665763
$133$	−2.79499e8	−	2.79499e8i	−0.893251	−	0.893251i
$134$	4.77349e8	−	4.77349e8i	1.48053	−	1.48053i
$135$	3.37335e8	+	3.37335e8i	1.01561	+	1.01561i
$136$	1.26349e7			0.0369332
$137$	−3.50744e8	−	3.50744e8i	−0.995654	−	0.995654i	0.00433707	−	0.999991i	$-0.498619\pi$
$137$	−3.50744e8	−	3.50744e8i	−0.995654	−	0.995654i	−0.999991	+	0.00433707i	$0.998619\pi$
$138$			3.27054e8i			0.901785i
$139$	1.50432e8			0.402978			0.201489	−	0.979491i	$-0.435422\pi$
$139$	1.50432e8			0.402978			0.201489	+	0.979491i	$0.435422\pi$
$140$	−1.06234e9			−2.76535
$141$	1.22990e8			0.311167
$142$	4.01031e8	−	4.01031e8i	0.986334	−	0.986334i
$143$	−4.52404e7	+	4.52404e7i	−0.108189	+	0.108189i
$144$		−	4.28733e7i		−	0.0997096i
$145$	−5.87082e8	+	4.80107e7i	−1.32809	+	0.108609i
$146$	1.25131e9			2.75393
$147$	−2.19078e8	−	2.19078e8i	−0.469169	−	0.469169i
$148$	7.76185e8	+	7.76185e8i	1.61778	+	1.61778i
$149$			2.13759e8i			0.433689i	0.976206	+	0.216845i	$0.0695765\pi$
$149$			2.13759e8i			0.433689i	−0.976206	+	0.216845i	$0.930423\pi$
$150$			4.66183e8i			0.920856i
$151$			7.04970e8i			1.35601i	0.735057	+	0.678005i	$0.237155\pi$
$151$			7.04970e8i			1.35601i	−0.735057	+	0.678005i	$0.762845\pi$
$152$	−3.97883e8			−0.745386
$153$	−7.74844e6	+	7.74844e6i	−0.0141400	+	0.0141400i
$154$			7.19666e8i			1.27952i
$155$	−7.61184e8	+	7.61184e8i	−1.31875	+	1.31875i
$156$	−1.23383e8	−	1.23383e8i	−0.208332	−	0.208332i
$157$	−1.16281e8	+	1.16281e8i	−0.191386	+	0.191386i	−0.796295	−	0.604909i	$-0.793210\pi$
$157$	−1.16281e8	+	1.16281e8i	−0.191386	+	0.191386i	0.604909	+	0.796295i	$0.293210\pi$
$158$			1.18408e9i			1.90000i
$159$	−6.58796e8	−	6.58796e8i	−1.03077	−	1.03077i
$160$	7.22744e8	−	7.22744e8i	1.10282	−	1.10282i
$161$	7.00787e8			1.04300
$162$	2.84668e8	+	2.84668e8i	0.413312	+	0.413312i
$163$	5.78655e8	−	5.78655e8i	0.819728	−	0.819728i	−0.166341	−	0.986068i	$-0.553195\pi$
$163$	5.78655e8	−	5.78655e8i	0.819728	−	0.819728i	0.986068	+	0.166341i	$0.0531952\pi$
$164$	−1.16218e9	−	1.16218e9i	−1.60657	−	1.60657i
$165$	4.35092e8			0.587009
$166$	7.91023e8	+	7.91023e8i	1.04173	+	1.04173i
$167$		−	4.65087e8i		−	0.597954i	−0.954260	−	0.298977i	$-0.903355\pi$
$167$		−	4.65087e8i		−	0.597954i	0.954260	−	0.298977i	$-0.0966455\pi$
$168$	−6.64020e8			−0.833574
$169$	7.60498e8			0.932291
$170$	−8.03926e7			−0.0962544
$171$	2.44004e8	−	2.44004e8i	0.285373	−	0.285373i
$172$	−2.12675e7	+	2.12675e7i	−0.0242998	+	0.0242998i
$173$		−	1.02859e8i		−	0.114831i	−0.998350	−	0.0574153i	$-0.981714\pi$
$173$		−	1.02859e8i		−	0.114831i	0.998350	−	0.0574153i	$-0.0182859\pi$
$174$	−1.08467e9	+	8.87025e7i	−1.18331	+	0.0967696i
$175$	9.98904e8			1.06505
$176$	−9.06732e7	−	9.06732e7i	−0.0944993	−	0.0944993i
$177$	−1.64226e8	−	1.64226e8i	−0.167321	−	0.167321i
$178$		−	1.91953e9i		−	1.91212i
$179$		−	3.08971e8i		−	0.300957i	−0.988613	−	0.150479i	$-0.951919\pi$
$179$		−	3.08971e8i		−	0.300957i	0.988613	−	0.150479i	$-0.0480815\pi$
$180$		−	9.27425e8i		−	0.883464i
$181$	−4.42124e8			−0.411936			−0.205968	−	0.978559i	$-0.566034\pi$
$181$	−4.42124e8			−0.411936			−0.205968	+	0.978559i	$0.566034\pi$
$182$	−4.39310e8	+	4.39310e8i	−0.400392	+	0.400392i
$183$		−	2.80762e8i		−	0.250342i
$184$	4.98806e8	−	4.98806e8i	0.435171	−	0.435171i
$185$	−1.67082e9	−	1.67082e9i	−1.42641	−	1.42641i
$186$	−1.40633e9	+	1.40633e9i	−1.17499	+	1.17499i
$187$			3.27746e7i			0.0268022i
$188$	−5.54448e8	−	5.54448e8i	−0.443843	−	0.443843i
$189$	1.33545e9	−	1.33545e9i	1.04660	−	1.04660i
$190$	2.53162e9			1.94261
$191$	−1.41573e9	−	1.41573e9i	−1.06377	−	1.06377i	−0.997823	−	0.0659481i	$-0.978993\pi$
$191$	−1.41573e9	−	1.41573e9i	−1.06377	−	1.06377i	−0.0659481	−	0.997823i	$-0.521007\pi$
$192$	1.17168e9	−	1.17168e9i	0.862194	−	0.862194i
$193$	6.27749e8	+	6.27749e8i	0.452436	+	0.452436i	0.896162	−	0.443726i	$-0.146344\pi$
$193$	6.27749e8	+	6.27749e8i	0.452436	+	0.452436i	−0.443726	+	0.896162i	$0.646344\pi$
$194$	−3.24786e9			−2.29293
$195$	2.65595e8	+	2.65595e8i	0.183688	+	0.183688i
$196$			1.97524e9i			1.33843i
$197$	2.54785e9			1.69164			0.845822	−	0.533466i	$-0.179111\pi$
$197$	2.54785e9			1.69164			0.845822	+	0.533466i	$0.179111\pi$
$198$	−6.28273e8			−0.408778
$199$	−2.11759e9			−1.35030			−0.675150	−	0.737680i	$-0.735921\pi$
$199$	−2.11759e9			−1.35030			−0.675150	+	0.737680i	$0.735921\pi$
$200$	7.10999e8	−	7.10999e8i	0.444374	−	0.444374i
$201$	−1.14248e9	+	1.14248e9i	−0.699948	+	0.699948i
$202$		−	1.03167e9i		−	0.619637i
$203$	1.90065e8	+	2.32415e9i	0.111923	+	1.36861i
$204$	−8.93852e7			−0.0516113
$205$	2.50173e9	+	2.50173e9i	1.41653	+	1.41653i
$206$	3.07433e9	+	3.07433e9i	1.70719	+	1.70719i
$207$			6.11791e8i			0.333213i
$208$		−	1.10700e8i		−	0.0591419i
$209$		−	1.03210e9i		−	0.540922i
$210$	4.22498e9			2.17244
$211$	−1.88393e8	+	1.88393e8i	−0.0950461	+	0.0950461i	−0.753031	−	0.657985i	$-0.771409\pi$
$211$	−1.88393e8	+	1.88393e8i	−0.0950461	+	0.0950461i	0.657985	+	0.753031i	$0.271409\pi$
$212$			5.93980e9i			2.94055i
$213$	−9.59825e8	+	9.59825e8i	−0.466309	+	0.466309i
$214$	−1.50681e9	−	1.50681e9i	−0.718462	−	0.718462i
$215$	4.57805e7	−	4.57805e7i	0.0214253	−	0.0214253i
$216$		−	1.90109e9i		−	0.873348i
$217$	3.01338e9	+	3.01338e9i	1.35899	+	1.35899i
$218$	1.29752e9	−	1.29752e9i	0.574497	−	0.574497i
$219$	−2.99488e9			−1.30198
$220$	−1.96142e9	−	1.96142e9i	−0.837299	−	0.837299i
$221$	−2.00068e7	+	2.00068e7i	−0.00838702	+	0.00838702i
$222$	−3.08694e9	−	3.08694e9i	−1.27092	−	1.27092i
$223$	5.75374e8			0.232665			0.116332	−	0.993210i	$-0.462886\pi$
$223$	5.75374e8			0.232665			0.116332	+	0.993210i	$0.462886\pi$
$224$	−2.86121e9	−	2.86121e9i	−1.13647	−	1.13647i
$225$			8.72049e8i			0.340260i
$226$	−2.81789e9			−1.08017
$227$	−3.43865e9			−1.29504			−0.647522	−	0.762047i	$-0.724194\pi$
$227$	−3.43865e9			−1.29504			−0.647522	+	0.762047i	$0.724194\pi$
$228$	2.81480e9			1.04162
$229$	1.71421e7	−	1.71421e7i	0.00623336	−	0.00623336i	−0.703983	−	0.710217i	$-0.748597\pi$
$229$	1.71421e7	−	1.71421e7i	0.00623336	−	0.00623336i	0.710217	+	0.703983i	$0.248597\pi$
$230$	−3.17377e9	+	3.17377e9i	−1.13413	+	1.13413i
$231$		−	1.72245e9i		−	0.604920i
$232$	1.78956e9	+	1.51899e9i	0.617725	+	0.524329i
$233$	−5.51664e9			−1.87176			−0.935881	−	0.352316i	$-0.885394\pi$
$233$	−5.51664e9			−1.87176			−0.935881	+	0.352316i	$0.885394\pi$
$234$	−3.83520e8	−	3.83520e8i	−0.127916	−	0.127916i
$235$	1.19351e9	+	1.19351e9i	0.391340	+	0.391340i
$236$			1.48069e9i			0.477327i
$237$		−	2.83398e9i		−	0.898262i
$238$			3.18259e8i			0.0991912i
$239$	5.33030e9			1.63365			0.816827	−	0.576883i	$-0.195731\pi$
$239$	5.33030e9			1.63365			0.816827	+	0.576883i	$0.195731\pi$
$240$	−5.32320e8	+	5.32320e8i	−0.160446	+	0.160446i
$241$		−	2.17219e9i		−	0.643918i	−0.946754	−	0.321959i	$-0.895659\pi$
$241$		−	2.17219e9i		−	0.643918i	0.946754	−	0.321959i	$-0.104341\pi$
$242$	2.51448e9	−	2.51448e9i	0.733139	−	0.733139i
$243$	1.97621e9	+	1.97621e9i	0.566771	+	0.566771i
$244$	−1.26569e9	+	1.26569e9i	−0.357083	+	0.357083i
$245$		−	4.25192e9i		−	1.18010i
$246$	4.62208e9	+	4.62208e9i	1.26211	+	1.26211i
$247$	6.30027e8	−	6.30027e8i	0.169267	−	0.169267i
$248$	4.28973e9			1.13403
$249$	−1.89323e9	−	1.89323e9i	−0.492500	−	0.492500i
$250$	1.30878e9	−	1.30878e9i	0.335048	−	0.335048i
$251$	1.76581e9	+	1.76581e9i	0.444887	+	0.444887i	0.893651	−	0.448764i	$-0.148135\pi$
$251$	1.76581e9	+	1.76581e9i	0.444887	+	0.444887i	−0.448764	+	0.893651i	$0.648135\pi$
$252$	−3.67150e9			−0.910420
$253$	1.29389e9	+	1.29389e9i	0.315801	+	0.315801i
$254$		−	4.86992e9i		−	1.17000i
$255$	1.92411e8			0.0455061
$256$	−2.59780e9			−0.604847
$257$	7.68907e9			1.76255			0.881275	−	0.472604i	$-0.156686\pi$
$257$	7.68907e9			1.76255			0.881275	+	0.472604i	$0.156686\pi$
$258$	8.45821e7	−	8.45821e7i	0.0190897	−	0.0190897i
$259$	−6.61448e9	+	6.61448e9i	−1.46993	+	1.46993i
$260$		−	2.39464e9i		−	0.524020i
$261$	−2.02899e9	+	1.65928e8i	−0.437239	+	0.0357567i
$262$	−1.10505e10			−2.34517
$263$	3.88633e9	+	3.88633e9i	0.812300	+	0.812300i	0.984978	−	0.172678i	$-0.0552421\pi$
$263$	3.88633e9	+	3.88633e9i	0.812300	+	0.812300i	−0.172678	+	0.984978i	$0.555242\pi$
$264$	−1.22600e9	−	1.22600e9i	−0.252392	−	0.252392i
$265$		−	1.27861e10i		−	2.59271i
$266$		−	1.00222e10i		−	2.00188i
$267$			4.59420e9i			0.903994i
$268$	1.03008e10			1.99679
$269$	−1.90630e9	+	1.90630e9i	−0.364067	+	0.364067i	−0.865308	−	0.501241i	$-0.832877\pi$
$269$	−1.90630e9	+	1.90630e9i	−0.364067	+	0.364067i	0.501241	+	0.865308i	$0.332877\pi$
$270$			1.20961e10i			2.27610i
$271$	−2.08427e9	+	2.08427e9i	−0.386435	+	0.386435i	−0.873414	−	0.486979i	$-0.838099\pi$
$271$	−2.08427e9	+	2.08427e9i	−0.386435	+	0.386435i	0.486979	+	0.873414i	$0.338099\pi$
$272$	−4.00986e7	−	4.00986e7i	−0.00732578	−	0.00732578i
$273$	1.05144e9	−	1.05144e9i	0.189293	−	0.189293i
$274$		−	1.25769e10i		−	2.23137i
$275$	1.84431e9	+	1.84431e9i	0.322480	+	0.322480i
$276$	−3.52878e9	+	3.52878e9i	−0.608118	+	0.608118i
$277$	2.18409e9			0.370981			0.185490	−	0.982646i	$-0.440613\pi$
$277$	2.18409e9			0.370981			0.185490	+	0.982646i	$0.440613\pi$
$278$	2.69708e9	+	2.69708e9i	0.451560	+	0.451560i
$279$	−2.63070e9	+	2.63070e9i	−0.434165	+	0.434165i
$280$	−6.44373e9	−	6.44373e9i	−1.04835	−	1.04835i
$281$	2.50243e9			0.401363			0.200681	−	0.979657i	$-0.435684\pi$
$281$	2.50243e9			0.401363			0.200681	+	0.979657i	$0.435684\pi$
$282$	2.20508e9	+	2.20508e9i	0.348680	+	0.348680i
$283$			1.12559e10i			1.75482i	0.479738	+	0.877412i	$0.340732\pi$
$283$			1.12559e10i			1.75482i	−0.479738	+	0.877412i	$0.659268\pi$
$284$	8.65391e9			1.33027
$285$	−6.05917e9			−0.918405
$286$	−1.62222e9			−0.242463
$287$	9.90387e9	−	9.90387e9i	1.45975	−	1.45975i
$288$	2.49785e9	−	2.49785e9i	0.363075	−	0.363075i
$289$		−	6.96126e9i		−	0.997922i
$290$	−1.13865e10	−	9.66496e9i	−1.60990	−	1.36649i
$291$	7.77340e9			1.08402
$292$	1.35011e10	+	1.35011e10i	1.85711	+	1.85711i
$293$	−5.03066e9	−	5.03066e9i	−0.682581	−	0.682581i	0.278000	−	0.960581i	$-0.410328\pi$
$293$	−5.03066e9	−	5.03066e9i	−0.682581	−	0.682581i	−0.960581	+	0.278000i	$0.910328\pi$
$294$		−	7.85566e9i		−	1.05146i
$295$		−	3.18735e9i		−	0.420863i
$296$			9.41609e9i			1.22660i
$297$	4.93136e9			0.633783
$298$	−3.83246e9	+	3.83246e9i	−0.485973	+	0.485973i
$299$			1.57967e9i			0.197643i
$300$	−5.02993e9	+	5.02993e9i	−0.620979	+	0.620979i
$301$	−1.81237e8	−	1.81237e8i	−0.0220790	−	0.0220790i
$302$	−1.26393e10	+	1.26393e10i	−1.51949	+	1.51949i
$303$			2.46921e9i			0.292945i
$304$	1.26273e9	+	1.26273e9i	0.147849	+	0.147849i
$305$	2.72454e9	−	2.72454e9i	0.314843	−	0.314843i
$306$	−2.77842e8			−0.0316893
$307$	−3.13713e9	−	3.13713e9i	−0.353166	−	0.353166i	0.508120	−	0.861286i	$-0.330341\pi$
$307$	−3.13713e9	−	3.13713e9i	−0.353166	−	0.353166i	−0.861286	+	0.508120i	$0.830341\pi$
$308$	−7.76491e9	+	7.76491e9i	−0.862846	+	0.862846i
$309$	−7.35808e9	−	7.35808e9i	−0.807107	−	0.807107i
$310$	−2.72944e10			−2.95547
$311$	−4.90378e9	−	4.90378e9i	−0.524191	−	0.524191i	0.394643	−	0.918834i	$-0.370868\pi$
$311$	−4.90378e9	−	4.90378e9i	−0.524191	−	0.524191i	−0.918834	+	0.394643i	$0.870868\pi$
$312$		−	1.49679e9i		−	0.157958i
$313$	9.47876e9			0.987584			0.493792	−	0.869580i	$-0.335610\pi$
$313$	9.47876e9			0.987584			0.493792	+	0.869580i	$0.335610\pi$
$314$	−4.16958e9			−0.428917
$315$	7.90331e9			0.802725
$316$	−1.27758e10	+	1.27758e10i	−1.28126	+	1.28126i
$317$	1.58805e9	−	1.58805e9i	0.157263	−	0.157263i	−0.624090	−	0.781353i	$-0.714530\pi$
$317$	1.58805e9	−	1.58805e9i	0.157263	−	0.157263i	0.781353	+	0.624090i	$0.214530\pi$
$318$		−	2.36230e10i		−	2.31008i
$319$	−3.94022e9	+	4.64207e9i	−0.380503	+	0.448279i
$320$	2.27403e10			2.16868
$321$	3.60640e9	+	3.60640e9i	0.339667	+	0.339667i
$322$	1.25643e10	+	1.25643e10i	1.16874	+	1.16874i
$323$		−	4.56425e8i		−	0.0419334i
$324$			6.14290e9i			0.557434i
$325$			2.25166e9i			0.201822i
$326$	2.07493e10			1.83710
$327$	−3.10547e9	+	3.10547e9i	−0.271604	+	0.271604i
$328$		−	1.40987e10i		−	1.21810i
$329$	4.72488e9	−	4.72488e9i	0.403281	−	0.403281i
$330$	7.80071e9	+	7.80071e9i	0.657777	+	0.657777i
$331$	−9.97099e9	+	9.97099e9i	−0.830666	+	0.830666i	−0.987608	−	0.156942i	$-0.949836\pi$
$331$	−9.97099e9	+	9.97099e9i	−0.830666	+	0.830666i	0.156942	+	0.987608i	$0.449836\pi$
$332$			1.70696e10i			1.40499i
$333$	−5.77448e9	−	5.77448e9i	−0.469608	−	0.469608i
$334$	8.33850e9	−	8.33850e9i	0.670042	−	0.670042i
$335$	−2.21736e10			−1.76058
$336$	2.10736e9	+	2.10736e9i	0.165341	+	0.165341i
$337$	−1.37757e10	+	1.37757e10i	−1.06806	+	1.06806i	−0.0705489	+	0.997508i	$0.522475\pi$
$337$	−1.37757e10	+	1.37757e10i	−1.06806	+	1.06806i	−0.997508	+	0.0705489i	$0.977525\pi$
$338$	1.36349e10	+	1.36349e10i	1.04468	+	1.04468i
$339$	6.74433e9			0.510669
$340$	−8.67404e8	−	8.67404e8i	−0.0649091	−	0.0649091i
$341$			1.11274e10i			0.822955i
$342$	8.74946e9			0.639553
$343$	2.17401e9			0.157067
$344$	−2.58001e8			−0.0184241
$345$	7.59608e9	−	7.59608e9i	0.536183	−	0.536183i
$346$	1.84415e9	−	1.84415e9i	0.128674	−	0.128674i
$347$		−	1.05247e10i		−	0.725927i	−0.931803	−	0.362963i	$-0.881765\pi$
$347$		−	1.05247e10i		−	0.725927i	0.931803	−	0.362963i	$-0.118235\pi$
$348$	−1.26602e10	−	1.07461e10i	−0.863223	−	0.732710i
$349$	−5.06317e9			−0.341288			−0.170644	−	0.985333i	$-0.554585\pi$
$349$	−5.06317e9			−0.341288			−0.170644	+	0.985333i	$0.554585\pi$
$350$	1.79092e10	+	1.79092e10i	1.19345	+	1.19345i
$351$	3.01027e9	+	3.01027e9i	0.198325	+	0.198325i
$352$		−	1.05655e10i		−	0.688206i
$353$		−	1.28794e10i		−	0.829463i	−0.909944	−	0.414732i	$-0.863875\pi$
$353$		−	1.28794e10i		−	0.829463i	0.909944	−	0.414732i	$-0.136125\pi$
$354$		−	5.88880e9i		−	0.374985i
$355$	−1.86285e10			−1.17291
$356$	2.07110e10	−	2.07110e10i	1.28944	−	1.28944i
$357$		−	7.61720e8i		−	0.0468946i
$358$	5.53950e9	−	5.53950e9i	0.337240	−	0.337240i
$359$	9.20681e9	+	9.20681e9i	0.554283	+	0.554283i	0.927674	−	0.373391i	$-0.121805\pi$
$359$	9.20681e9	+	9.20681e9i	0.554283	+	0.554283i	−0.373391	+	0.927674i	$0.621805\pi$
$360$	5.62541e9	−	5.62541e9i	0.334923	−	0.334923i
$361$		−	2.61039e9i		−	0.153701i
$362$	−7.92681e9	−	7.92681e9i	−0.461598	−	0.461598i
$363$	−6.01814e9	+	6.01814e9i	−0.346606	+	0.346606i
$364$	−9.47995e9			−0.540008
$365$	−2.90627e10	−	2.90627e10i	−1.63743	−	1.63743i
$366$	5.03375e9	−	5.03375e9i	0.280522	−	0.280522i
$367$	4.35251e9	+	4.35251e9i	0.239925	+	0.239925i	0.816819	−	0.576894i	$-0.195735\pi$
$367$	4.35251e9	+	4.35251e9i	0.239925	+	0.239925i	−0.576894	+	0.816819i	$0.695735\pi$
$368$	−3.16605e9			−0.172634
$369$	8.64613e9	+	8.64613e9i	0.466355	+	0.466355i
$370$		−	5.99121e10i		−	3.19674i
$371$	−5.06176e10			−2.67181
$372$	−3.03475e10			−1.58471
$373$	−1.21381e10			−0.627070			−0.313535	−	0.949577i	$-0.601513\pi$
$373$	−1.21381e10			−0.627070			−0.313535	+	0.949577i	$0.601513\pi$
$374$	−5.87612e8	+	5.87612e8i	−0.0300334	+	0.0300334i
$375$	−3.13243e9	+	3.13243e9i	−0.158400	+	0.158400i
$376$		−	6.72614e9i		−	0.336523i
$377$	−5.23893e9	+	4.28432e8i	−0.259345	+	0.0212088i
$378$	4.78862e10			2.34554
$379$	1.61022e10	+	1.61022e10i	0.780421	+	0.780421i	0.979902	−	0.199481i	$-0.0639256\pi$
$379$	1.61022e10	+	1.61022e10i	0.780421	+	0.780421i	−0.199481	+	0.979902i	$0.563926\pi$
$380$	2.73152e10	+	2.73152e10i	1.31000	+	1.31000i
$381$			1.16556e10i			0.553142i
$382$		−	5.07651e10i		−	2.38403i
$383$			2.41153e10i			1.12072i	0.828249	+	0.560360i	$0.189337\pi$
$383$			2.41153e10i			1.12072i	−0.828249	+	0.560360i	$0.810663\pi$
$384$	2.29476e10			1.05539
$385$	1.67148e10	−	1.67148e10i	0.760779	−	0.760779i
$386$			2.25097e10i			1.01396i
$387$	1.58221e8	−	1.58221e8i	0.00705373	−	0.00705373i
$388$	−3.50431e10	−	3.50431e10i	−1.54623	−	1.54623i
$389$	−8.18165e9	+	8.18165e9i	−0.357308	+	0.357308i	−0.862820	−	0.505512i	$-0.831304\pi$
$389$	−8.18165e9	+	8.18165e9i	−0.357308	+	0.357308i	0.505512	+	0.862820i	$0.331304\pi$
$390$			9.52366e9i			0.411667i
$391$	5.72197e8	+	5.72197e8i	0.0244815	+	0.0244815i
$392$	−1.19810e10	+	1.19810e10i	−0.507400	+	0.507400i
$393$	2.64481e10			1.10873
$394$	4.56801e10	+	4.56801e10i	1.89558	+	1.89558i
$395$	2.75012e10	−	2.75012e10i	1.12970	−	1.12970i
$396$	−6.77881e9	−	6.77881e9i	−0.275659	−	0.275659i
$397$	2.44118e10			0.982739			0.491370	−	0.870951i	$-0.336496\pi$
$397$	2.44118e10			0.982739			0.491370	+	0.870951i	$0.336496\pi$
$398$	−3.79661e10	−	3.79661e10i	−1.51309	−	1.51309i
$399$			2.39871e10i			0.946426i
$400$	−4.51290e9			−0.176285
$401$	−4.47334e9			−0.173003			−0.0865016	−	0.996252i	$-0.527569\pi$
$401$	−4.47334e9			−0.173003			−0.0865016	+	0.996252i	$0.527569\pi$
$402$	−4.09670e10			−1.56866
$403$	−6.79256e9	+	6.79256e9i	−0.257521	+	0.257521i
$404$	1.11314e10	−	1.11314e10i	0.417852	−	0.417852i
$405$		−	1.32233e10i		−	0.491494i
$406$	−3.82617e10	+	4.50771e10i	−1.40819	+	1.65902i
$407$	−2.44250e10			−0.890138
$408$	−5.42177e8	−	5.42177e8i	−0.0195659	−	0.0195659i
$409$	2.88388e10	+	2.88388e10i	1.03059	+	1.03059i	0.999517	+	0.0310678i	$0.00989077\pi$
$409$	2.88388e10	+	2.88388e10i	1.03059	+	1.03059i	0.0310678	+	0.999517i	$0.490109\pi$
$410$			8.97065e10i			3.17459i
$411$			3.01015e10i			1.05492i
$412$			6.63415e10i			2.30248i
$413$	−1.26181e10			−0.433704
$414$	−1.09687e10	+	1.09687e10i	−0.373384	+	0.373384i
$415$		−	3.67443e10i		−	1.23879i
$416$	6.44954e9	−	6.44954e9i	0.215355	−	0.215355i
$417$	−6.45519e9	−	6.45519e9i	−0.213484	−	0.213484i
$418$	1.85043e10	−	1.85043e10i	0.606134	−	0.606134i
$419$		−	4.49948e10i		−	1.45984i	−0.683531	−	0.729921i	$-0.739557\pi$
$419$		−	4.49948e10i		−	1.45984i	0.683531	−	0.729921i	$-0.260443\pi$
$420$	4.55859e10	+	4.55859e10i	1.46498	+	1.46498i
$421$	2.47349e10	−	2.47349e10i	0.787376	−	0.787376i	−0.193688	−	0.981063i	$-0.562045\pi$
$421$	2.47349e10	−	2.47349e10i	0.787376	−	0.787376i	0.981063	+	0.193688i	$0.0620449\pi$
$422$	−6.75535e9			−0.213009
$423$	4.12485e9	+	4.12485e9i	0.128839	+	0.128839i
$424$	−3.60286e10	+	3.60286e10i	−1.11477	+	1.11477i
$425$	8.15611e8	+	8.15611e8i	0.0249993	+	0.0249993i
$426$	−3.44172e10			−1.04505
$427$	−1.07860e10	−	1.07860e10i	−0.324450	−	0.324450i
$428$		−	3.25158e10i		−	0.968990i
$429$	3.88262e9			0.114629
$430$	1.64159e9			0.0480165
$431$	1.27301e10			0.368911			0.184455	−	0.982841i	$-0.440948\pi$
$431$	1.27301e10			0.368911			0.184455	+	0.982841i	$0.440948\pi$
$432$	−6.03335e9	+	6.03335e9i	−0.173230	+	0.173230i
$433$	4.30961e10	−	4.30961e10i	1.22599	−	1.22599i	0.260521	−	0.965468i	$-0.416106\pi$
$433$	4.30961e10	−	4.30961e10i	1.22599	−	1.22599i	0.965468	−	0.260521i	$-0.0838942\pi$
$434$			1.08053e11i			3.04564i
$435$	2.72524e10	+	2.31321e10i	0.761111	+	0.646037i
$436$	2.79994e10			0.774823
$437$	−1.80189e10	−	1.80189e10i	−0.494086	−	0.494086i
$438$	−5.36949e10	−	5.36949e10i	−1.45894	−	1.45894i
$439$			5.52115e10i			1.48652i	0.669001	+	0.743261i	$0.266722\pi$
$439$			5.52115e10i			1.48652i	−0.669001	+	0.743261i	$0.733278\pi$
$440$		−	2.37945e10i		−	0.634842i
$441$		−	1.46949e10i		−	0.388519i
$442$	−7.17398e8			−0.0187963
$443$	2.96679e10	−	2.96679e10i	0.770321	−	0.770321i	−0.207842	−	0.978163i	$-0.566644\pi$
$443$	2.96679e10	−	2.96679e10i	0.770321	−	0.770321i	0.978163	+	0.207842i	$0.0666438\pi$
$444$		−	6.66137e10i		−	1.71408i
$445$	−4.45827e10	+	4.45827e10i	−1.13691	+	1.13691i
$446$	1.03158e10	+	1.03158e10i	0.260714	+	0.260714i
$447$	9.17259e9	−	9.17259e9i	0.229753	−	0.229753i
$448$		−	9.00245e10i		−	2.23485i
$449$	−2.33875e10	−	2.33875e10i	−0.575438	−	0.575438i	0.358205	−	0.933643i	$-0.383389\pi$
$449$	−2.33875e10	−	2.33875e10i	−0.575438	−	0.575438i	−0.933643	+	0.358205i	$0.883389\pi$
$450$	−1.56349e10	+	1.56349e10i	−0.381280	+	0.381280i
$451$	3.65716e10			0.883971
$452$	−3.04039e10	−	3.04039e10i	−0.728409	−	0.728409i
$453$	3.02509e10	−	3.02509e10i	0.718366	−	0.718366i
$454$	−6.16512e10	−	6.16512e10i	−1.45117	−	1.45117i
$455$	2.04066e10			0.476130
$456$	1.70735e10	+	1.70735e10i	0.394879	+	0.394879i
$457$			3.59672e10i			0.824597i	0.911049	+	0.412299i	$0.135274\pi$
$457$			3.59672e10i			0.824597i	−0.911049	+	0.412299i	$0.864726\pi$
$458$	6.14678e8			0.0139697
$459$	2.18080e9			0.0491321
$460$	−6.84873e10			−1.52960
$461$	−2.88822e10	+	2.88822e10i	−0.639480	+	0.639480i	−0.950427	−	0.310947i	$-0.899354\pi$
$461$	−2.88822e10	+	2.88822e10i	−0.639480	+	0.639480i	0.310947	+	0.950427i	$0.399354\pi$
$462$	3.08816e10	−	3.08816e10i	0.677847	−	0.677847i
$463$		−	2.06046e10i		−	0.448373i	−0.974546	−	0.224186i	$-0.928028\pi$
$463$		−	2.06046e10i		−	0.448373i	0.974546	−	0.224186i	$-0.0719725\pi$
$464$	−8.58686e8	−	1.05001e10i	−0.0185252	−	0.226529i
$465$	6.53262e10			1.39726
$466$	−9.89073e10	−	9.89073e10i	−2.09742	−	2.09742i
$467$	1.87210e10	+	1.87210e10i	0.393605	+	0.393605i	0.875970	−	0.482365i	$-0.160222\pi$
$467$	1.87210e10	+	1.87210e10i	0.393605	+	0.393605i	−0.482365	+	0.875970i	$0.660222\pi$
$468$		−	8.27605e9i		−	0.172520i
$469$			8.77811e10i			1.81430i
$470$			4.27966e10i			0.877038i
$471$	9.97944e9			0.202779
$472$	−8.98130e9	+	8.98130e9i	−0.180955	+	0.180955i
$473$		−	6.69245e8i		−	0.0133703i
$474$	5.08101e10	−	5.08101e10i	1.00655	−	1.00655i
$475$	−2.56842e10	−	2.56842e10i	−0.504535	−	0.504535i
$476$	−3.43389e9	+	3.43389e9i	−0.0668896	+	0.0668896i
$477$		−	4.41895e10i		−	0.853582i
$478$	9.55664e10	+	9.55664e10i	1.83060	+	1.83060i
$479$	−1.60635e10	+	1.60635e10i	−0.305139	+	0.305139i	−0.843020	−	0.537881i	$-0.819225\pi$
$479$	−1.60635e10	+	1.60635e10i	−0.305139	+	0.305139i	0.537881	+	0.843020i	$0.319225\pi$
$480$	−6.20273e10			−1.16847
$481$	−1.49099e10	−	1.49099e10i	−0.278544	−	0.278544i
$482$	3.89451e10	−	3.89451e10i	0.721547	−	0.721547i
$483$	−3.00715e10	−	3.00715e10i	−0.552543	−	0.552543i
$484$	5.42604e10			0.988784
$485$	7.54340e10	+	7.54340e10i	1.36333	+	1.36333i
$486$			7.08624e10i			1.27020i
$487$	2.76114e10			0.490876			0.245438	−	0.969412i	$-0.421068\pi$
$487$	2.76114e10			0.490876			0.245438	+	0.969412i	$0.421068\pi$
$488$	−1.53544e10			−0.270741
$489$	−4.96613e10			−0.868526
$490$	7.62322e10	−	7.62322e10i	1.32237	−	1.32237i
$491$	3.85662e10	−	3.85662e10i	0.663560	−	0.663560i	−0.292657	−	0.956217i	$-0.594539\pi$
$491$	3.85662e10	−	3.85662e10i	0.663560	−	0.663560i	0.956217	+	0.292657i	$0.0945395\pi$
$492$			9.97408e10i			1.70221i
$493$	−1.74249e9	+	2.05287e9i	−0.0294973	+	0.0347515i
$494$	2.25914e10			0.379346
$495$	1.45921e10	+	1.45921e10i	0.243051	+	0.243051i
$496$	−1.36140e10	−	1.36140e10i	−0.224936	−	0.224936i
$497$			7.37467e10i			1.20870i
$498$		−	6.78871e10i		−	1.10375i
$499$		−	1.96988e9i		−	0.0317715i	−0.999874	−	0.0158857i	$-0.994943\pi$
$499$		−	1.96988e9i		−	0.0317715i	0.999874	−	0.0158857i	$-0.00505680\pi$
$500$	2.82424e10			0.451879
$501$	−1.99573e10	+	1.99573e10i	−0.316775	+	0.316775i
$502$			6.33182e10i			0.997042i
$503$	6.94966e10	−	6.94966e10i	1.08565	−	1.08565i	0.0896838	−	0.995970i	$-0.471414\pi$
$503$	6.94966e10	−	6.94966e10i	1.08565	−	1.08565i	0.995970	−	0.0896838i	$-0.0285856\pi$
$504$	−2.22700e10	−	2.22700e10i	−0.345141	−	0.345141i
$505$	−2.39615e10	+	2.39615e10i	−0.368424	+	0.368424i
$506$			4.63959e10i			0.707746i
$507$	−3.26337e10	−	3.26337e10i	−0.493895	−	0.493895i
$508$	5.25445e10	−	5.25445e10i	0.788991	−	0.788991i
$509$	−3.05866e9			−0.0455680			−0.0227840	−	0.999740i	$-0.507253\pi$
$509$	−3.05866e9			−0.0455680			−0.0227840	+	0.999740i	$0.507253\pi$
$510$	3.44972e9	+	3.44972e9i	0.0509922	+	0.0509922i
$511$	−1.15054e11	+	1.15054e11i	−1.68739	+	1.68739i
$512$	2.18751e10	+	2.18751e10i	0.318325	+	0.318325i
$513$	−6.86751e10			−0.991585
$514$	1.37857e11	+	1.37857e11i	1.97504	+	1.97504i
$515$		−	1.42807e11i		−	2.03012i
$516$	1.82521e9			0.0257463
$517$	1.74474e10			0.244213
$518$	−2.37181e11			−3.29428
$519$	−4.41378e9	+	4.41378e9i	−0.0608332	+	0.0608332i
$520$	1.45250e10	−	1.45250e10i	0.198657	−	0.198657i
$521$		−	2.98204e10i		−	0.404728i	−0.979310	−	0.202364i	$-0.935138\pi$
$521$		−	2.98204e10i		−	0.404728i	0.979310	−	0.202364i	$-0.0648624\pi$
$522$	−3.93525e10	−	3.34027e10i	−0.530018	−	0.449883i
$523$	−8.05283e10			−1.07632			−0.538161	−	0.842842i	$-0.680881\pi$
$523$	−8.05283e10			−1.07632			−0.538161	+	0.842842i	$0.680881\pi$
$524$	−1.19230e11	−	1.19230e11i	−1.58147	−	1.58147i
$525$	−4.28639e10	−	4.28639e10i	−0.564228	−	0.564228i
$526$			1.39355e11i			1.82046i
$527$			4.92089e9i			0.0637972i
$528$			7.78175e9i			0.100125i
$529$	−3.31322e10			−0.423085
$530$	2.29240e11	−	2.29240e11i	2.90527	−	2.90527i
$531$		−	1.10157e10i		−	0.138558i
$532$	1.08136e11	−	1.08136e11i	1.34997	−	1.34997i
$533$	2.23246e10	+	2.23246e10i	0.276615	+	0.276615i
$534$	−8.23691e10	+	8.23691e10i	−1.01298	+	1.01298i
$535$			6.99938e10i			0.854367i
$536$	6.24808e10	+	6.24808e10i	0.756985	+	0.756985i
$537$	−1.32582e10	+	1.32582e10i	−0.159437	+	0.159437i
$538$	−6.83556e10			−0.815915
$539$	−3.10784e10	−	3.10784e10i	−0.368217	−	0.368217i
$540$	−1.30512e11	+	1.30512e11i	−1.53488	+	1.53488i
$541$	8.08226e10	+	8.08226e10i	0.943504	+	0.943504i	0.998487	−	0.0549833i	$-0.0175106\pi$
$541$	8.08226e10	+	8.08226e10i	0.943504	+	0.943504i	−0.0549833	+	0.998487i	$0.517511\pi$
$542$	−7.47373e10			−0.866045
$543$	1.89720e10	+	1.89720e10i	0.218229	+	0.218229i
$544$		−	4.67239e9i		−	0.0533511i
$545$	−6.02717e10			−0.683168
$546$	3.77024e10			0.424227
$547$	7.45981e10			0.833256			0.416628	−	0.909077i	$-0.363212\pi$
$547$	7.45981e10			0.833256			0.416628	+	0.909077i	$0.363212\pi$
$548$	1.35700e11	−	1.35700e11i	1.50472	−	1.50472i
$549$	9.41620e9	−	9.41620e9i	0.103654	−	0.103654i
$550$			6.61328e10i			0.722713i
$551$	5.48723e10	−	6.46464e10i	0.595315	−	0.701355i
$552$	−4.28085e10			−0.461077
$553$	−1.08872e11	−	1.08872e11i	−1.16417	−	1.16417i
$554$	3.91583e10	+	3.91583e10i	0.415705	+	0.415705i
$555$			1.43393e11i			1.51132i
$556$			5.82009e10i			0.609018i
$557$			1.23923e10i			0.128745i	0.997926	+	0.0643724i	$0.0205045\pi$
$557$			1.23923e10i			0.128745i	−0.997926	+	0.0643724i	$0.979495\pi$
$558$	−9.43312e10			−0.973013
$559$	4.08531e8	−	4.08531e8i	0.00418387	−	0.00418387i
$560$			4.09000e10i			0.415884i
$561$	1.40639e9	−	1.40639e9i	0.0141989	−	0.0141989i
$562$	4.48659e10	+	4.48659e10i	0.449749	+	0.449749i
$563$	5.63939e10	−	5.63939e10i	0.561304	−	0.561304i	−0.368374	−	0.929678i	$-0.620085\pi$
$563$	5.63939e10	−	5.63939e10i	0.561304	−	0.561304i	0.929678	+	0.368374i	$0.120085\pi$
$564$			4.75838e10i			0.470265i
$565$	6.54477e10	+	6.54477e10i	0.642245	+	0.642245i
$566$	−2.01805e11	+	2.01805e11i	−1.96638	+	1.96638i
$567$	−5.23484e10			−0.506490
$568$	5.24914e10	+	5.24914e10i	0.504306	+	0.504306i
$569$	−1.22252e10	+	1.22252e10i	−0.116629	+	0.116629i	−0.763013	−	0.646384i	$-0.776281\pi$
$569$	−1.22252e10	+	1.22252e10i	−0.116629	+	0.116629i	0.646384	+	0.763013i	$0.276281\pi$
$570$	−1.08634e11	−	1.08634e11i	−1.02912	−	1.02912i
$571$	−1.39672e10			−0.131390			−0.0656952	−	0.997840i	$-0.520926\pi$
$571$	−1.39672e10			−0.131390			−0.0656952	+	0.997840i	$0.520926\pi$
$572$	−1.75031e10	−	1.75031e10i	−0.163505	−	0.163505i
$573$			1.21501e11i			1.12710i
$574$	3.55131e11			3.27146
$575$	6.43979e10			0.589116
$576$	7.85919e10			0.713983
$577$	3.21429e10	−	3.21429e10i	0.289990	−	0.289990i	−0.547087	−	0.837076i	$-0.684263\pi$
$577$	3.21429e10	−	3.21429e10i	0.289990	−	0.289990i	0.837076	+	0.547087i	$0.184263\pi$
$578$	1.24808e11	−	1.24808e11i	1.11823	−	1.11823i
$579$		−	5.38746e10i		−	0.479369i
$580$	−1.85749e10	−	2.27137e11i	−0.164140	−	2.00713i
$581$	−1.45464e11			−1.27659
$582$	1.39369e11	+	1.39369e11i	1.21471	+	1.21471i
$583$	−9.34569e10	−	9.34569e10i	−0.808979	−	0.808979i
$584$			1.63786e11i			1.40807i
$585$			1.78151e10i			0.152112i
$586$		−	1.80388e11i		−	1.52974i
$587$	−1.75840e10			−0.148103			−0.0740516	−	0.997254i	$-0.523593\pi$
$587$	−1.75840e10			−0.148103			−0.0740516	+	0.997254i	$0.523593\pi$
$588$	8.47594e10	−	8.47594e10i	0.709052	−	0.709052i
$589$		−	1.54963e11i		−	1.28755i
$590$	5.71456e10	−	5.71456e10i	0.471601	−	0.471601i
$591$	−1.09331e11	−	1.09331e11i	−0.896173	−	0.896173i
$592$	2.98832e10	−	2.98832e10i	0.243299	−	0.243299i
$593$			1.75539e11i			1.41956i	0.704422	+	0.709782i	$0.251206\pi$
$593$			1.75539e11i			1.41956i	−0.704422	+	0.709782i	$0.748794\pi$
$594$	8.84138e10	+	8.84138e10i	0.710190	+	0.710190i
$595$	7.39182e9	−	7.39182e9i	0.0589771	−	0.0589771i
$596$	−8.27014e10			−0.655432
$597$	9.08680e10	+	9.08680e10i	0.715342	+	0.715342i
$598$	−2.83217e10	+	2.83217e10i	−0.221470	+	0.221470i
$599$	−1.82857e10	−	1.82857e10i	−0.142038	−	0.142038i	0.632512	−	0.774550i	$-0.282024\pi$
$599$	−1.82857e10	−	1.82857e10i	−0.142038	−	0.142038i	−0.774550	+	0.632512i	$0.782024\pi$
$600$	−6.10193e10			−0.470828
$601$	7.68140e10	+	7.68140e10i	0.588766	+	0.588766i	0.937297	−	0.348531i	$-0.113320\pi$
$601$	7.68140e10	+	7.68140e10i	0.588766	+	0.588766i	−0.348531	+	0.937297i	$0.613320\pi$
$602$		−	6.49875e9i		−	0.0494816i
$603$	−7.66334e10			−0.579627
$604$	−2.72747e11			−2.04933
$605$	−1.16801e11			−0.871820
$606$	−4.42701e10	+	4.42701e10i	−0.328262	+	0.328262i
$607$	5.61992e10	−	5.61992e10i	0.413976	−	0.413976i	−0.469145	−	0.883121i	$-0.655438\pi$
$607$	5.61992e10	−	5.61992e10i	0.413976	−	0.413976i	0.883121	+	0.469145i	$0.155438\pi$
$608$			1.47137e11i			1.07673i
$609$	9.15755e10	−	1.07887e11i	0.665748	−	0.784334i
$610$	9.76962e10			0.705599
$611$	1.06505e10	+	1.06505e10i	0.0764197	+	0.0764197i
$612$	−2.99781e9	−	2.99781e9i	−0.0213697	−	0.0213697i
$613$		−	1.56743e11i		−	1.11006i	−0.831830	−	0.555031i	$-0.812706\pi$
$613$		−	1.56743e11i		−	1.11006i	0.831830	−	0.555031i	$-0.187294\pi$
$614$		−	1.12491e11i		−	0.791485i
$615$		−	2.14703e11i		−	1.50085i
$616$	−9.41980e10			−0.654212
$617$	9.08499e10	−	9.08499e10i	0.626879	−	0.626879i	−0.320402	−	0.947282i	$-0.603818\pi$
$617$	9.08499e10	−	9.08499e10i	0.626879	−	0.626879i	0.947282	+	0.320402i	$0.103818\pi$
$618$		−	2.63845e11i		−	1.80882i
$619$	−1.12007e11	+	1.12007e11i	−0.762928	+	0.762928i	−0.976851	−	0.213922i	$-0.931376\pi$
$619$	−1.12007e11	+	1.12007e11i	−0.762928	+	0.762928i	0.213922	+	0.976851i	$0.431376\pi$
$620$	−2.94495e11	−	2.94495e11i	−1.99302	−	1.99302i
$621$	8.60945e10	−	8.60945e10i	0.578907	−	0.578907i
$622$		−	1.75839e11i		−	1.17477i
$623$	1.76495e11	+	1.76495e11i	1.17160	+	1.17160i
$624$	−4.75026e9	+	4.75026e9i	−0.0313313	+	0.0313313i
$625$	−1.79144e11			−1.17404
$626$	1.69944e11	+	1.69944e11i	1.10664	+	1.10664i
$627$	−4.42882e10	+	4.42882e10i	−0.286561	+	0.286561i
$628$	−4.49880e10	−	4.49880e10i	−0.289240	−	0.289240i
$629$	−1.08015e10			−0.0690053
$630$	1.41698e11	+	1.41698e11i	0.899499	+	0.899499i
$631$			9.34182e10i			0.589270i	0.955610	+	0.294635i	$0.0951980\pi$
$631$			9.34182e10i			0.589270i	−0.955610	+	0.294635i	$0.904802\pi$
$632$	−1.54986e11			−0.971458
$633$	1.61682e10			0.100704
$634$	5.69438e10			0.352444
$635$	−1.13108e11	+	1.13108e11i	−0.695661	+	0.695661i
$636$	2.54882e11	−	2.54882e11i	1.55780	−	1.55780i
$637$		−	3.79427e10i		−	0.230447i
$638$	−1.53871e11	+	1.25833e10i	−0.928697	+	0.0759475i
$639$	−6.43813e10			−0.386150
$640$	2.22686e11	+	2.22686e11i	1.32731	+	1.32731i
$641$	2.13370e11	+	2.13370e11i	1.26386	+	1.26386i	0.949204	+	0.314661i	$0.101891\pi$
$641$	2.13370e11	+	2.13370e11i	1.26386	+	1.26386i	0.314661	+	0.949204i	$0.398109\pi$
$642$			1.29318e11i			0.761232i
$643$		−	2.95959e11i		−	1.73136i	−0.500597	−	0.865680i	$-0.666886\pi$
$643$		−	2.95959e11i		−	1.73136i	0.500597	−	0.865680i	$-0.333114\pi$
$644$			2.71128e11i			1.57627i
$645$	−3.92897e9			−0.0227007
$646$	8.18321e9	−	8.18321e9i	0.0469887	−	0.0469887i
$647$		−	2.61615e10i		−	0.149295i	−0.997210	−	0.0746475i	$-0.976217\pi$
$647$		−	2.61615e10i		−	0.149295i	0.997210	−	0.0746475i	$-0.0237832\pi$
$648$	−3.72605e10	+	3.72605e10i	−0.211324	+	0.211324i
$649$	−2.32972e10	−	2.32972e10i	−0.131318	−	0.131318i
$650$	−4.03698e10	+	4.03698e10i	−0.226153	+	0.226153i
$651$		−	2.58614e11i		−	1.43989i
$652$	2.23877e11	+	2.23877e11i	1.23885	+	1.23885i
$653$	5.46445e10	−	5.46445e10i	0.300534	−	0.300534i	−0.540689	−	0.841223i	$-0.681836\pi$
$653$	5.46445e10	−	5.46445e10i	0.300534	−	0.300534i	0.841223	+	0.540689i	$0.181836\pi$
$654$	−1.11355e11			−0.608696
$655$	2.56655e11	+	2.56655e11i	1.39439	+	1.39439i
$656$	−4.47442e10	+	4.47442e10i	−0.241614	+	0.241614i
$657$	−1.00442e11	−	1.00442e11i	−0.539083	−	0.539083i
$658$	1.69424e11			0.903797
$659$	3.11701e10	+	3.11701e10i	0.165271	+	0.165271i	0.784897	−	0.619626i	$-0.212716\pi$
$659$	3.11701e10	+	3.11701e10i	0.165271	+	0.165271i	−0.619626	+	0.784897i	$0.712716\pi$
$660$			1.68333e11i			0.887143i
$661$	−4.26733e10			−0.223538			−0.111769	−	0.993734i	$-0.535652\pi$
$661$	−4.26733e10			−0.223538			−0.111769	+	0.993734i	$0.535652\pi$
$662$	−3.57538e11			−1.86162
$663$	1.71702e9			0.00888629
$664$	−1.03538e11	+	1.03538e11i	−0.532632	+	0.532632i
$665$	−2.32774e11	+	2.32774e11i	−1.19028	+	1.19028i
$666$		−	2.07060e11i		−	1.05245i
$667$	1.22532e10	+	1.49835e11i	0.0619081	+	0.757022i
$668$	1.79938e11			0.903685
$669$	−2.46898e10	−	2.46898e10i	−0.123258	−	0.123258i
$670$	−3.97548e11	−	3.97548e11i	−1.97283	−	1.97283i
$671$		−	3.98289e10i		−	0.196475i
$672$			2.45554e11i			1.20412i
$673$			1.52391e11i			0.742845i	0.928464	+	0.371422i	$0.121130\pi$
$673$			1.52391e11i			0.742845i	−0.928464	+	0.371422i	$0.878870\pi$
$674$	−4.93967e11			−2.39364
$675$	1.22719e11	−	1.22719e11i	0.591150	−	0.591150i
$676$			2.94230e11i			1.40896i
$677$	2.79362e10	−	2.79362e10i	0.132988	−	0.132988i	−0.637479	−	0.770467i	$-0.720023\pi$
$677$	2.79362e10	−	2.79362e10i	0.132988	−	0.132988i	0.770467	+	0.637479i	$0.220023\pi$
$678$	1.20918e11	+	1.20918e11i	0.572234	+	0.572234i
$679$	2.98629e11	−	2.98629e11i	1.40492	−	1.40492i
$680$		−	1.05227e10i		−	0.0492143i
$681$	1.47556e11	+	1.47556e11i	0.686068	+	0.686068i
$682$	−1.99502e11	+	1.99502e11i	−0.922168	+	0.922168i
$683$	−1.55906e11			−0.716438			−0.358219	−	0.933638i	$-0.616616\pi$
$683$	−1.55906e11			−0.716438			−0.358219	+	0.933638i	$0.616616\pi$
$684$	9.44031e10	+	9.44031e10i	0.431282	+	0.431282i
$685$	−2.92109e11	+	2.92109e11i	−1.32673	+	1.32673i
$686$	3.89776e10	+	3.89776e10i	0.176003	+	0.176003i
$687$	−1.47117e9			−0.00660443
$688$	8.18800e8	+	8.18800e8i	0.00365447	+	0.00365447i
$689$		−	1.14099e11i		−	0.506295i
$690$	2.72379e11			1.20165
$691$	−5.78327e10			−0.253665			−0.126833	−	0.991924i	$-0.540481\pi$
$691$	−5.78327e10			−0.253665			−0.126833	+	0.991924i	$0.540481\pi$
$692$	3.97952e10			0.173543
$693$	5.77675e10	−	5.77675e10i	0.250467	−	0.250467i
$694$	1.88697e11	−	1.88697e11i	0.813442	−	0.813442i
$695$		−	1.25284e11i		−	0.536977i
$696$	−1.16104e10	−	1.41973e11i	−0.0494777	−	0.605020i
$697$	1.61731e10			0.0685272
$698$	−9.07772e10	−	9.07772e10i	−0.382433	−	0.382433i
$699$	2.36724e11	+	2.36724e11i	0.991594	+	0.991594i
$700$			3.86467e11i			1.60961i
$701$			2.42808e10i			0.100552i	0.998735	+	0.0502760i	$0.0160101\pi$
$701$			2.42808e10i			0.100552i	−0.998735	+	0.0502760i	$0.983990\pi$
$702$			1.07942e11i			0.444469i
$703$	3.40148e11			1.39266
$704$	1.66215e11	−	1.66215e11i	0.676674	−	0.676674i
$705$		−	1.02429e11i		−	0.414637i
$706$	2.30914e11	−	2.30914e11i	0.929460	−	0.929460i
$707$	9.48589e10	+	9.48589e10i	0.379665	+	0.379665i
$708$	6.35378e10	−	6.35378e10i	0.252871	−	0.252871i
$709$			2.07220e11i			0.820060i	0.912072	+	0.410030i	$0.134482\pi$
$709$			2.07220e11i			0.820060i	−0.912072	+	0.410030i	$0.865518\pi$
$710$	−3.33988e11	−	3.33988e11i	−1.31431	−	1.31431i
$711$	9.50461e10	−	9.50461e10i	0.371926	−	0.371926i
$712$	2.51250e11			0.977657
$713$	1.94269e11	+	1.94269e11i	0.751700	+	0.751700i
$714$	1.36568e10	−	1.36568e10i	0.0525480	−	0.0525480i
$715$	3.76774e10	+	3.76774e10i	0.144164	+	0.144164i
$716$	1.19538e11			0.454835
$717$	−2.28728e11	−	2.28728e11i	−0.865452	−	0.865452i
$718$			3.30136e11i			1.24221i
$719$	−1.66543e11			−0.623176			−0.311588	−	0.950217i	$-0.600861\pi$
$719$	−1.66543e11			−0.623176			−0.311588	+	0.950217i	$0.600861\pi$
$720$	−3.57060e10			−0.132865
$721$	−5.65348e11			−2.09206
$722$	4.68015e10	−	4.68015e10i	0.172231	−	0.172231i
$723$	−9.32110e10	+	9.32110e10i	−0.341125	+	0.341125i
$724$		−	1.71054e11i		−	0.622557i
$725$	1.74658e10	+	2.13574e11i	0.0632174	+	0.773032i
$726$	−2.15797e11			−0.776783
$727$	−2.17522e11	−	2.17522e11i	−0.778691	−	0.778691i	0.200918	−	0.979608i	$-0.435608\pi$
$727$	−2.17522e11	−	2.17522e11i	−0.778691	−	0.778691i	−0.979608	+	0.200918i	$0.935608\pi$
$728$	−5.75018e10	−	5.75018e10i	−0.204718	−	0.204718i
$729$		−	2.73775e11i		−	0.969356i
$730$		−	1.04212e12i		−	3.66968i
$731$		−	2.95962e8i		−	0.00103649i
$732$	1.08624e11			0.378340
$733$	−1.60430e11	+	1.60430e11i	−0.555736	+	0.555736i	−0.928091	−	0.372355i	$-0.878551\pi$
$733$	−1.60430e11	+	1.60430e11i	−0.555736	+	0.555736i	0.372355	+	0.928091i	$0.378551\pi$
$734$			1.56072e11i			0.537699i
$735$	−1.82454e11	+	1.82454e11i	−0.625178	+	0.625178i
$736$	−1.84458e11	−	1.84458e11i	−0.628618	−	0.628618i
$737$	−1.62073e11	+	1.62073e11i	−0.549339	+	0.549339i
$738$			3.10031e11i			1.04515i
$739$	−2.09029e11	−	2.09029e11i	−0.700855	−	0.700855i	0.263739	−	0.964594i	$-0.415044\pi$
$739$	−2.09029e11	−	2.09029e11i	−0.700855	−	0.700855i	−0.964594	+	0.263739i	$0.915044\pi$
$740$	6.46427e11	−	6.46427e11i	2.15572	−	2.15572i
$741$	−5.40701e10			−0.179343
$742$	−9.07519e11	−	9.07519e11i	−2.99392	−	2.99392i
$743$	3.99492e11	−	3.99492e11i	1.31085	−	1.31085i	0.390061	−	0.920789i	$-0.372454\pi$
$743$	3.99492e11	−	3.99492e11i	1.31085	−	1.31085i	0.920789	−	0.390061i	$-0.127546\pi$
$744$	−1.84076e11	−	1.84076e11i	−0.600767	−	0.600767i
$745$	1.78024e11			0.577900
$746$	−2.17623e11	−	2.17623e11i	−0.702667	−	0.702667i
$747$		−	1.26991e11i		−	0.407839i
$748$	−1.26802e10			−0.0405060
$749$	2.77092e11			0.880435
$750$	−1.12322e11			−0.354993
$751$	−1.95434e11	+	1.95434e11i	−0.614385	+	0.614385i	−0.944086	−	0.329700i	$-0.893052\pi$
$751$	−1.95434e11	+	1.95434e11i	−0.614385	+	0.614385i	0.329700	+	0.944086i	$0.393052\pi$
$752$	−2.13463e10	+	2.13463e10i	−0.0667500	+	0.0667500i
$753$		−	1.51545e11i		−	0.471371i
$754$	−1.01610e11	−	8.62470e10i	−0.314376	−	0.266845i
$755$	5.87117e11			1.80691
$756$	5.16673e11	+	5.16673e11i	1.58172	+	1.58172i
$757$	3.72844e11	+	3.72844e11i	1.13539	+	1.13539i	0.989267	+	0.146118i	$0.0466779\pi$
$757$	3.72844e11	+	3.72844e11i	1.13539	+	1.13539i	0.146118	+	0.989267i	$0.453322\pi$
$758$			5.77390e11i			1.74901i
$759$		−	1.11044e11i		−	0.334601i
$760$			3.31367e11i			0.993242i
$761$	1.70982e11			0.509813			0.254907	−	0.966966i	$-0.417955\pi$
$761$	1.70982e11			0.509813			0.254907	+	0.966966i	$0.417955\pi$
$762$	−2.08973e11	+	2.08973e11i	−0.619827	+	0.619827i
$763$			2.38605e11i			0.704013i
$764$	5.47735e11	−	5.47735e11i	1.60767	−	1.60767i
$765$	6.45310e9	+	6.45310e9i	0.0188418	+	0.0188418i
$766$	−4.32360e11	+	4.32360e11i	−1.25583	+	1.25583i
$767$		−	2.84429e10i		−	0.0821848i
$768$	1.11474e11	+	1.11474e11i	0.320427	+	0.320427i
$769$	−2.10511e11	+	2.10511e11i	−0.601962	+	0.601962i	−0.940833	−	0.338871i	$-0.889955\pi$
$769$	−2.10511e11	+	2.10511e11i	−0.601962	+	0.601962i	0.338871	+	0.940833i	$0.389955\pi$
$770$	5.99357e11			1.70499
$771$	−3.29945e11	−	3.29945e11i	−0.933737	−	0.933737i
$772$	−2.42871e11	+	2.42871e11i	−0.683764	+	0.683764i
$773$	1.44200e11	+	1.44200e11i	0.403875	+	0.403875i	0.879596	−	0.475721i	$-0.157813\pi$
$773$	1.44200e11	+	1.44200e11i	0.403875	+	0.403875i	−0.475721	+	0.879596i	$0.657813\pi$
$774$	5.67344e9			0.0158082
$775$	2.76911e11	+	2.76911e11i	0.767597	+	0.767597i
$776$		−	4.25116e11i		−	1.17236i
$777$	5.67667e11			1.55743
$778$	−2.93376e11			−0.800767
$779$	−5.09304e11			−1.38302
$780$	−1.02756e11	+	1.02756e11i	−0.277607	+	0.277607i
$781$	−1.36161e11	+	1.36161e11i	−0.365972	+	0.365972i
$782$			2.05177e10i			0.0548659i
$783$	3.08881e11	+	2.62180e11i	0.821758	+	0.697514i
$784$	7.60469e10			0.201288
$785$	9.68417e10	+	9.68417e10i	0.255026	+	0.255026i
$786$	4.74186e11	+	4.74186e11i	1.24239	+	1.24239i
$787$		−	2.94107e11i		−	0.766665i	−0.923610	−	0.383333i	$-0.874776\pi$
$787$		−	2.94107e11i		−	0.766665i	0.923610	−	0.383333i	$-0.125224\pi$
$788$			9.85740e11i			2.55657i
$789$		−	3.33532e11i		−	0.860656i
$790$	9.86134e11			2.53179
$791$	2.59095e11	−	2.59095e11i	0.661841	−	0.661841i
$792$		−	8.22354e10i		−	0.209006i
$793$	2.43130e10	−	2.43130e10i	0.0614816	−	0.0614816i
$794$	4.37677e11	+	4.37677e11i	1.10121	+	1.10121i
$795$	−5.48662e11	+	5.48662e11i	−1.37352	+	1.37352i
$796$		−	8.19278e11i		−	2.04070i
$797$	−1.73917e10	−	1.73917e10i	−0.0431032	−	0.0431032i	0.685227	−	0.728330i	$-0.259703\pi$
$797$	−1.73917e10	−	1.73917e10i	−0.0431032	−	0.0431032i	−0.728330	+	0.685227i	$0.759703\pi$
$798$	−4.30063e11	+	4.30063e11i	−1.06052	+	1.06052i
$799$	7.71579e9			0.0189319
$800$	−2.62927e11	−	2.62927e11i	−0.641912	−	0.641912i
$801$	−1.54081e11	+	1.54081e11i	−0.374299	+	0.374299i
$802$	−8.02020e10	−	8.02020e10i	−0.193860	−	0.193860i
$803$	−4.24854e11			−1.02183
$804$	−4.42017e11	−	4.42017e11i	−1.05783	−	1.05783i
$805$		−	5.83634e11i		−	1.38981i
$806$	−2.43566e11			−0.577135
$807$	1.63602e11			0.385740
$808$	1.35037e11			0.316816
$809$	4.16558e10	−	4.16558e10i	0.0972481	−	0.0972481i	−0.656809	−	0.754057i	$-0.728094\pi$
$809$	4.16558e10	−	4.16558e10i	0.0972481	−	0.0972481i	0.754057	+	0.656809i	$0.228094\pi$
$810$	2.37078e11	−	2.37078e11i	0.550747	−	0.550747i
$811$			5.00008e11i			1.15583i	0.816097	+	0.577915i	$0.196133\pi$
$811$			5.00008e11i			1.15583i	−0.816097	+	0.577915i	$0.803867\pi$
$812$	−8.99192e11	+	7.35346e10i	−2.06837	+	0.169148i
$813$	1.78876e11			0.409440
$814$	−4.37914e11	−	4.37914e11i	−0.997450	−	0.997450i
$815$	−4.81919e11	−	4.81919e11i	−1.09230	−	1.09230i
$816$			3.44134e9i			0.00776188i
$817$			9.32005e9i			0.0209185i
$818$			1.03410e12i			2.30966i
$819$	7.05266e10			0.156754
$820$	−9.67896e11	+	9.67896e11i	−2.14079	+	2.14079i
$821$			2.05600e11i			0.452532i	0.974066	+	0.226266i	$0.0726519\pi$
$821$			2.05600e11i			0.452532i	−0.974066	+	0.226266i	$0.927348\pi$
$822$	−5.39688e11	+	5.39688e11i	−1.18210	+	1.18210i
$823$	2.44815e11	+	2.44815e11i	0.533628	+	0.533628i	0.921650	−	0.388022i	$-0.126842\pi$
$823$	2.44815e11	+	2.44815e11i	0.533628	+	0.533628i	−0.388022	+	0.921650i	$0.626842\pi$
$824$	−4.02403e11	+	4.02403e11i	−0.872875	+	0.872875i
$825$		−	1.58282e11i		−	0.341677i
$826$	−2.26229e11	−	2.26229e11i	−0.485990	−	0.485990i
$827$	4.82606e11	−	4.82606e11i	1.03174	−	1.03174i	0.0322612	−	0.999479i	$-0.489729\pi$
$827$	4.82606e11	−	4.82606e11i	1.03174	−	1.03174i	0.999479	−	0.0322612i	$-0.0102709\pi$
$828$	−2.36697e11			−0.503583
$829$	−1.66228e11	−	1.66228e11i	−0.351955	−	0.351955i	0.508882	−	0.860836i	$-0.330059\pi$
$829$	−1.66228e11	−	1.66228e11i	−0.351955	−	0.351955i	−0.860836	+	0.508882i	$0.830059\pi$
$830$	6.58784e11	−	6.58784e11i	1.38813	−	1.38813i
$831$	−9.37213e10	−	9.37213e10i	−0.196532	−	0.196532i
$832$	2.02927e11			0.423493
$833$	−1.37439e10	−	1.37439e10i	−0.0285449	−	0.0285449i
$834$		−	2.31469e11i		−	0.478441i
$835$	−3.87336e11			−0.796787
$836$	3.99308e11			0.817492
$837$	7.40412e11			1.50859
$838$	8.06707e11	−	8.06707e11i	1.63584	−	1.63584i
$839$	1.10689e11	−	1.10689e11i	0.223387	−	0.223387i	−0.586536	−	0.809923i	$-0.699509\pi$
$839$	1.10689e11	−	1.10689e11i	0.223387	−	0.223387i	0.809923	+	0.586536i	$0.199509\pi$
$840$			5.53013e11i			1.11075i
$841$	−4.93600e11	+	8.12753e10i	−0.986713	+	0.162470i
$842$	8.86940e11			1.76460
$843$	−1.07382e11	−	1.07382e11i	−0.212628	−	0.212628i
$844$	−7.28875e10	−	7.28875e10i	−0.143643	−	0.143643i
$845$		−	6.33362e11i		−	1.24230i
$846$			1.47908e11i			0.288742i
$847$			4.62395e11i			0.898420i
$848$	2.28683e11			0.442232
$849$	4.83000e11	−	4.83000e11i	0.929644	−	0.929644i
$850$			2.92460e10i			0.0560262i
$851$	−4.26426e11	+	4.26426e11i	−0.813066	+	0.813066i
$852$	−3.71348e11	−	3.71348e11i	−0.704729	−	0.704729i
$853$	4.55418e11	−	4.55418e11i	0.860228	−	0.860228i	−0.131136	−	0.991364i	$-0.541862\pi$
$853$	4.55418e11	−	4.55418e11i	0.860228	−	0.860228i	0.991364	+	0.131136i	$0.0418624\pi$
$854$		−	3.86761e11i		−	0.727128i
$855$	−2.03213e11	−	2.03213e11i	−0.380266	−	0.380266i
$856$	1.97228e11	−	1.97228e11i	0.367345	−	0.367345i
$857$	2.04176e11			0.378513			0.189257	−	0.981928i	$-0.439392\pi$
$857$	2.04176e11			0.378513			0.189257	+	0.981928i	$0.439392\pi$
$858$	6.96111e10	+	6.96111e10i	0.128449	+	0.128449i
$859$	2.01582e10	−	2.01582e10i	0.0370236	−	0.0370236i	−0.688353	−	0.725376i	$-0.741666\pi$
$859$	2.01582e10	−	2.01582e10i	0.0370236	−	0.0370236i	0.725376	+	0.688353i	$0.241666\pi$
$860$	1.77121e10	+	1.77121e10i	0.0323799	+	0.0323799i
$861$	−8.49969e11			−1.54664
$862$	2.28236e11	+	2.28236e11i	0.413385	+	0.413385i
$863$			4.75534e10i			0.0857311i	0.999081	+	0.0428656i	$0.0136487\pi$
$863$			4.75534e10i			0.0857311i	−0.999081	+	0.0428656i	$0.986351\pi$
$864$	−7.03021e11			−1.26158
$865$	−8.56636e10			−0.153014
$866$	1.54533e12			2.74758
$867$	−2.98714e11	+	2.98714e11i	−0.528664	+	0.528664i
$868$	−1.16585e12	+	1.16585e12i	−2.05383	+	2.05383i
$869$		−	4.02028e11i		−	0.704981i
$870$	7.38737e10	+	9.03339e11i	0.128947	+	1.57679i
$871$	−1.97870e11			−0.343801
$872$	1.69834e11	+	1.69834e11i	0.293736	+	0.293736i
$873$	2.60705e11	+	2.60705e11i	0.448841	+	0.448841i
$874$		−	6.46119e11i		−	1.10730i
$875$			2.40676e11i			0.410582i
$876$		−	1.15869e12i		−	1.96767i
$877$	2.55636e11			0.432140			0.216070	−	0.976378i	$-0.430676\pi$
$877$	2.55636e11			0.432140			0.216070	+	0.976378i	$0.430676\pi$
$878$	−9.89882e11	+	9.89882e11i	−1.66573	+	1.66573i
$879$			4.31741e11i			0.723215i
$880$	−7.55150e10	+	7.55150e10i	−0.125922	+	0.125922i
$881$	1.14103e11	+	1.14103e11i	0.189406	+	0.189406i	0.795439	−	0.606033i	$-0.207240\pi$
$881$	1.14103e11	+	1.14103e11i	0.189406	+	0.189406i	−0.606033	+	0.795439i	$0.707240\pi$
$882$	2.63464e11	−	2.63464e11i	0.435358	−	0.435358i
$883$		−	5.75600e11i		−	0.946844i	−0.880836	−	0.473422i	$-0.843019\pi$
$883$		−	5.75600e11i		−	0.946844i	0.880836	−	0.473422i	$-0.156981\pi$
$884$	−7.74044e9	−	7.74044e9i	−0.0126752	−	0.0126752i
$885$	−1.36772e11	+	1.36772e11i	−0.222959	+	0.222959i
$886$	1.06383e12			1.72638
$887$	5.44997e11	+	5.44997e11i	0.880440	+	0.880440i	0.993579	−	0.113139i	$-0.0360904\pi$
$887$	5.44997e11	+	5.44997e11i	0.880440	+	0.880440i	−0.113139	+	0.993579i	$0.536090\pi$
$888$	4.04054e11	−	4.04054e11i	0.649811	−	0.649811i
$889$	4.47772e11	+	4.47772e11i	0.716886	+	0.716886i
$890$	−1.59864e12			−2.54794
$891$	−9.66524e10	−	9.66524e10i	−0.153356	−	0.153356i
$892$			2.22607e11i			0.351625i
$893$	−2.42976e11			−0.382083
$894$	3.28909e11			0.514903
$895$	−2.57319e11			−0.401032
$896$	8.81571e11	−	8.81571e11i	1.36781	−	1.36781i
$897$	6.77850e10	−	6.77850e10i	0.104704	−	0.104704i
$898$		−	8.38625e11i		−	1.28962i
$899$	−5.91599e11	+	6.96977e11i	−0.905709	+	1.06704i
$900$	−3.37388e11			−0.514233
$901$	−4.13296e10	−	4.13296e10i	−0.0627137	−	0.0627137i
$902$	6.55689e11	+	6.55689e11i	0.990540	+	0.990540i
$903$			1.55541e10i			0.0233934i
$904$		−	3.68837e11i		−	0.552282i
$905$			3.68213e11i			0.548914i
$906$	1.08473e12			1.60994
$907$	6.82407e11	−	6.82407e11i	1.00836	−	1.00836i	0.00839272	−	0.999965i	$-0.497328\pi$
$907$	6.82407e11	−	6.82407e11i	1.00836	−	1.00836i	0.999965	−	0.00839272i	$-0.00267152\pi$
$908$		−	1.33038e12i		−	1.95719i
$909$	−8.28124e10	+	8.28124e10i	−0.121294	+	0.121294i
$910$	3.65868e11	+	3.65868e11i	0.533531	+	0.533531i
$911$	−5.48509e10	+	5.48509e10i	−0.0796361	+	0.0796361i	−0.745803	−	0.666167i	$-0.767934\pi$
$911$	−5.48509e10	+	5.48509e10i	−0.0796361	+	0.0796361i	0.666167	+	0.745803i	$0.267934\pi$
$912$		−	1.08370e11i		−	0.156650i
$913$	−2.68574e11	−	2.68574e11i	−0.386528	−	0.386528i
$914$	−6.44852e11	+	6.44852e11i	−0.924008	+	0.924008i
$915$	−2.33826e11			−0.333586
$916$	6.63213e9	+	6.63213e9i	0.00942044	+	0.00942044i
$917$	1.01605e12	−	1.01605e12i	1.43694	−	1.43694i
$918$	3.90994e10	+	3.90994e10i	0.0550553	+	0.0550553i
$919$	−1.37010e11			−0.192083			−0.0960417	−	0.995377i	$-0.530618\pi$
$919$	−1.37010e11			−0.192083			−0.0960417	+	0.995377i	$0.530618\pi$
$920$	−4.15418e11	−	4.15418e11i	−0.579875	−	0.579875i
$921$			2.69234e11i			0.374190i
$922$	−1.03565e12			−1.43315
$923$	−1.66235e11			−0.229042
$924$	6.66399e11			0.914211
$925$	−6.07829e11	+	6.07829e11i	−0.830261	+	0.830261i
$926$	3.69417e11	−	3.69417e11i	0.502427	−	0.502427i
$927$		−	4.93552e11i		−	0.668365i
$928$	5.61723e11	−	6.61780e11i	0.757409	−	0.892322i
$929$	−8.55265e11			−1.14825			−0.574127	−	0.818766i	$-0.694658\pi$
$929$	−8.55265e11			−1.14825			−0.574127	+	0.818766i	$0.694658\pi$
$930$	1.17123e12	+	1.17123e12i	1.56570	+	1.56570i
$931$	4.32805e11	+	4.32805e11i	0.576094	+	0.576094i
$932$		−	2.13434e12i		−	2.82878i
$933$			4.20852e11i			0.555396i
$934$			6.71292e11i			0.882113i
$935$	2.72955e10			0.0357145
$936$	5.01994e10	−	5.01994e10i	0.0654026	−	0.0654026i
$937$			1.79966e11i			0.233470i	0.993163	+	0.116735i	$0.0372428\pi$
$937$			1.79966e11i			0.233470i	−0.993163	+	0.116735i	$0.962757\pi$
$938$	−1.57382e12	+	1.57382e12i	−2.03303	+	2.03303i
$939$	−4.06742e11	−	4.06742e11i	−0.523187	−	0.523187i
$940$	−4.61758e11	+	4.61758e11i	−0.591430	+	0.591430i
$941$		−	1.41277e12i		−	1.80182i	−0.434002	−	0.900912i	$-0.642899\pi$
$941$		−	1.41277e12i		−	1.80182i	0.434002	−	0.900912i	$-0.357101\pi$
$942$	1.78920e11	+	1.78920e11i	0.227225	+	0.227225i
$943$	6.38489e11	−	6.38489e11i	0.807433	−	0.807433i
$944$	5.70067e10			0.0717857
$945$	−1.11220e12	−	1.11220e12i	−1.39461	−	1.39461i
$946$	1.19988e10	−	1.19988e10i	0.0149822	−	0.0149822i
$947$	−3.39805e11	−	3.39805e11i	−0.422503	−	0.422503i	0.463562	−	0.886065i	$-0.346571\pi$
$947$	−3.39805e11	−	3.39805e11i	−0.422503	−	0.422503i	−0.886065	+	0.463562i	$0.846571\pi$
$948$	1.09644e12			1.35754
$949$	−2.59346e11	−	2.59346e11i	−0.319753	−	0.319753i
$950$		−	9.20979e11i		−	1.13072i
$951$	−1.36289e11			−0.166625
$952$	−4.16573e10			−0.0507159
$953$	−1.43941e12			−1.74507			−0.872533	−	0.488556i	$-0.837524\pi$
$953$	−1.43941e12			−1.74507			−0.872533	+	0.488556i	$0.837524\pi$
$954$	7.92269e11	−	7.92269e11i	0.956487	−	0.956487i
$955$	−1.17906e12	+	1.17906e12i	−1.41750	+	1.41750i
$956$			2.06225e12i			2.46893i
$957$	3.68274e11	−	3.01169e10i	0.439060	−	0.0359056i
$958$	−5.76001e11			−0.683851
$959$	1.15640e12	+	1.15640e12i	1.36721	+	1.36721i
$960$	−9.75807e11	−	9.75807e11i	−1.14889	−	1.14889i
$961$			8.17818e11i			0.958877i
$962$		−	5.34636e11i		−	0.624250i
$963$			2.41903e11i			0.281278i
$964$	8.40403e11			0.973149
$965$	5.22806e11	−	5.22806e11i	0.602880	−	0.602880i
$966$		−	1.07830e12i		−	1.23831i
$967$	4.48892e11	−	4.48892e11i	0.513376	−	0.513376i	−0.402183	−	0.915559i	$-0.631749\pi$
$967$	4.48892e11	−	4.48892e11i	0.513376	−	0.513376i	0.915559	+	0.402183i	$0.131749\pi$
$968$	3.29123e11	+	3.29123e11i	0.374849	+	0.374849i
$969$	−1.95856e10	+	1.95856e10i	−0.0222148	+	0.0222148i
$970$			2.70490e12i			3.05537i
$971$	−8.16402e11	−	8.16402e11i	−0.918390	−	0.918390i	0.0785227	−	0.996912i	$-0.474980\pi$
$971$	−8.16402e11	−	8.16402e11i	−0.918390	−	0.918390i	−0.996912	+	0.0785227i	$0.974980\pi$
$972$	−7.64577e11	+	7.64577e11i	−0.856557	+	0.856557i
$973$	−4.95975e11			−0.553361
$974$	4.95042e11	+	4.95042e11i	0.550055	+	0.550055i
$975$	9.66209e10	−	9.66209e10i	0.106918	−	0.106918i
$976$	4.87293e10	+	4.87293e10i	0.0537021	+	0.0537021i
$977$	−1.39688e12			−1.53314			−0.766569	−	0.642162i	$-0.778037\pi$
$977$	−1.39688e12			−1.53314			−0.766569	+	0.642162i	$0.778037\pi$
$978$	−8.90373e11	−	8.90373e11i	−0.973232	−	0.973232i
$979$			6.51734e11i			0.709480i
$980$	1.64503e12			1.78348
$981$	−2.08303e11			−0.224916
$982$	1.38290e12			1.48711
$983$	−9.65413e11	+	9.65413e11i	−1.03395	+	1.03395i	−0.0345455	+	0.999403i	$0.510998\pi$
$983$	−9.65413e11	+	9.65413e11i	−1.03395	+	1.03395i	−0.999403	+	0.0345455i	$0.989002\pi$
$984$	−6.04990e11	+	6.04990e11i	−0.645309	+	0.645309i
$985$		−	2.12191e12i		−	2.25415i
$986$	−6.80467e10	+	5.56476e9i	−0.0719945	+	0.00588760i
$987$	−4.05498e11			−0.427288
$988$	2.43752e11	+	2.43752e11i	0.255812	+	0.255812i
$989$	−1.16841e10	−	1.16841e10i	−0.0122126	−	0.0122126i
$990$			5.23242e11i			0.544705i
$991$			1.07315e12i			1.11267i	0.830957	+	0.556336i	$0.187793\pi$
$991$			1.07315e12i			1.11267i	−0.830957	+	0.556336i	$0.812207\pi$
$992$		−	1.58634e12i		−	1.63813i
$993$	8.55729e11			0.880115
$994$	−1.32220e12	+	1.32220e12i	−1.35441	+	1.35441i
$995$			1.76359e12i			1.79930i
$996$	7.32474e11	−	7.32474e11i	0.744312	−	0.744312i
$997$	9.94267e11	+	9.94267e11i	1.00629	+	1.00629i	0.999980	+	0.00630787i	$0.00200787\pi$
$997$	9.94267e11	+	9.94267e11i	1.00629	+	1.00629i	0.00630787	+	0.999980i	$0.497992\pi$
$998$	3.53178e10	−	3.53178e10i	0.0356017	−	0.0356017i
$999$			1.62523e12i			1.63175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.17	✓	38
29.17	odd	4	inner	29.9.c.a.17.17	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.17	✓	38	1.1	even	1	trivial
29.9.c.a.17.17	yes	38	29.17	odd	4	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(17.9289 + 17.9289i) q^{2} +(-42.9110 - 42.9110i) q^{3} +386.891i q^{4} -832.826i q^{5} -1538.69i q^{6} -3297.00 q^{7} +(-2346.74 + 2346.74i) q^{8} -2878.30i q^{9} +O(q^{10})\)	\(q+(17.9289 + 17.9289i) q^{2} +(-42.9110 - 42.9110i) q^{3} +386.891i q^{4} -832.826i q^{5} -1538.69i q^{6} -3297.00 q^{7} +(-2346.74 + 2346.74i) q^{8} -2878.30i q^{9} +(14931.7 - 14931.7i) q^{10} +(-6087.35 - 6087.35i) q^{11} +(16601.9 - 16601.9i) q^{12} -7431.87i q^{13} +(-59111.6 - 59111.6i) q^{14} +(-35737.3 + 35737.3i) q^{15} +14895.4 q^{16} +(-2692.02 - 2692.02i) q^{17} +(51604.8 - 51604.8i) q^{18} +(84773.7 + 84773.7i) q^{19} +322213. q^{20} +(141477. + 141477. i) q^{21} -218279. i q^{22} -212553. q^{23} +201401. q^{24} -302974. q^{25} +(133245. - 133245. i) q^{26} +(-405049. + 405049. i) q^{27} -1.27558e6i q^{28} +(-57647.9 - 704928. i) q^{29} -1.28146e6 q^{30} +(-913977. - 913977. i) q^{31} +(867822. + 867822. i) q^{32} +522428. i q^{33} -96530.0i q^{34} +2.74583e6i q^{35} +1.11359e6 q^{36} +(2.00621e6 - 2.00621e6i) q^{37} +3.03980e6i q^{38} +(-318909. + 318909. i) q^{39} +(1.95442e6 + 1.95442e6i) q^{40} +(-3.00390e6 + 3.00390e6i) q^{41} +5.07307e6i q^{42} +(54970.1 + 54970.1i) q^{43} +(2.35514e6 - 2.35514e6i) q^{44} -2.39712e6 q^{45} +(-3.81084e6 - 3.81084e6i) q^{46} +(-1.43308e6 + 1.43308e6i) q^{47} +(-639174. - 639174. i) q^{48} +5.10541e6 q^{49} +(-5.43198e6 - 5.43198e6i) q^{50} +231034. i q^{51} +2.87533e6 q^{52} +1.53526e7 q^{53} -1.45242e7 q^{54} +(-5.06970e6 + 5.06970e6i) q^{55} +(7.73719e6 - 7.73719e6i) q^{56} -7.27544e6i q^{57} +(1.16050e7 - 1.36721e7i) q^{58} +3.82715e6 q^{59} +(-1.38265e7 - 1.38265e7i) q^{60} +(3.27145e6 + 3.27145e6i) q^{61} -3.27732e7i q^{62} +9.48976e6i q^{63} +2.73050e7i q^{64} -6.18945e6 q^{65} +(-9.36656e6 + 9.36656e6i) q^{66} -2.66245e7i q^{67} +(1.04152e6 - 1.04152e6i) q^{68} +(9.12085e6 + 9.12085e6i) q^{69} +(-4.92297e7 + 4.92297e7i) q^{70} -2.23678e7i q^{71} +(6.75461e6 + 6.75461e6i) q^{72} +(3.48965e7 - 3.48965e7i) q^{73} +7.19383e7 q^{74} +(1.30009e7 + 1.30009e7i) q^{75} +(-3.27982e7 + 3.27982e7i) q^{76} +(2.00700e7 + 2.00700e7i) q^{77} -1.14354e7 q^{78} +(3.30216e7 + 3.30216e7i) q^{79} -1.24052e7i q^{80} +1.58776e7 q^{81} -1.07713e8 q^{82} +4.41200e7 q^{83} +(-5.47364e7 + 5.47364e7i) q^{84} +(-2.24198e6 + 2.24198e6i) q^{85} +1.97111e6i q^{86} +(-2.77754e7 + 3.27228e7i) q^{87} +2.85708e7 q^{88} +(-5.35318e7 - 5.35318e7i) q^{89} +(-4.29778e7 - 4.29778e7i) q^{90} +2.45029e7i q^{91} -8.22349e7i q^{92} +7.84393e7i q^{93} -5.13873e7 q^{94} +(7.06017e7 - 7.06017e7i) q^{95} -7.44781e7i q^{96} +(-9.05760e7 + 9.05760e7i) q^{97} +(9.15344e7 + 9.15344e7i) q^{98} +(-1.75212e7 + 1.75212e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Introduction

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