LMFDB - Embedded newform 29.9.c.a.12.13

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			12.13
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.30345 + 8.30345i) q^{2} +(-37.9600 - 37.9600i) q^{3} -118.106i q^{4} +774.671i q^{5} -630.398i q^{6} -18.6293 q^{7} +(3106.37 - 3106.37i) q^{8} -3679.07i q^{9} +O(q^{10})$	\(q+(8.30345 + 8.30345i) q^{2} +(-37.9600 - 37.9600i) q^{3} -118.106i q^{4} +774.671i q^{5} -630.398i q^{6} -18.6293 q^{7} +(3106.37 - 3106.37i) q^{8} -3679.07i q^{9} +(-6432.44 + 6432.44i) q^{10} +(-15329.7 - 15329.7i) q^{11} +(-4483.29 + 4483.29i) q^{12} -48555.2i q^{13} +(-154.687 - 154.687i) q^{14} +(29406.5 - 29406.5i) q^{15} +21352.0 q^{16} +(16678.0 + 16678.0i) q^{17} +(30549.0 - 30549.0i) q^{18} +(774.812 + 774.812i) q^{19} +91492.9 q^{20} +(707.168 + 707.168i) q^{21} -254578. i q^{22} -5088.20 q^{23} -235836. q^{24} -209490. q^{25} +(403176. - 403176. i) q^{26} +(-388713. + 388713. i) q^{27} +2200.22i q^{28} +(73799.3 - 703420. i) q^{29} +488351. q^{30} +(316754. + 316754. i) q^{31} +(-617934. - 617934. i) q^{32} +1.16383e6i q^{33} +276970. i q^{34} -14431.5i q^{35} -434519. q^{36} +(-2.03585e6 + 2.03585e6i) q^{37} +12867.2i q^{38} +(-1.84316e6 + 1.84316e6i) q^{39} +(2.40641e6 + 2.40641e6i) q^{40} +(2.10468e6 - 2.10468e6i) q^{41} +11743.9i q^{42} +(3.98368e6 + 3.98368e6i) q^{43} +(-1.81052e6 + 1.81052e6i) q^{44} +2.85007e6 q^{45} +(-42249.6 - 42249.6i) q^{46} +(3.40604e6 - 3.40604e6i) q^{47} +(-810525. - 810525. i) q^{48} -5.76445e6 q^{49} +(-1.73949e6 - 1.73949e6i) q^{50} -1.26620e6i q^{51} -5.73464e6 q^{52} -6.96399e6 q^{53} -6.45532e6 q^{54} +(1.18755e7 - 1.18755e7i) q^{55} +(-57869.3 + 57869.3i) q^{56} -58823.8i q^{57} +(6.45360e6 - 5.22802e6i) q^{58} +7.75970e6 q^{59} +(-3.47308e6 - 3.47308e6i) q^{60} +(-1.23316e7 - 1.23316e7i) q^{61} +5.26029e6i q^{62} +68538.4i q^{63} -1.57281e7i q^{64} +3.76143e7 q^{65} +(-9.66380e6 + 9.66380e6i) q^{66} +1.63852e7i q^{67} +(1.96977e6 - 1.96977e6i) q^{68} +(193148. + 193148. i) q^{69} +(119832. - 119832. i) q^{70} -1.55539e7i q^{71} +(-1.14285e7 - 1.14285e7i) q^{72} +(-1.15863e7 + 1.15863e7i) q^{73} -3.38092e7 q^{74} +(7.95225e6 + 7.95225e6i) q^{75} +(91509.6 - 91509.6i) q^{76} +(285581. + 285581. i) q^{77} -3.06091e7 q^{78} +(4.27708e7 + 4.27708e7i) q^{79} +1.65408e7i q^{80} +5.37278e6 q^{81} +3.49522e7 q^{82} +7.14717e7 q^{83} +(83520.4 - 83520.4i) q^{84} +(-1.29200e7 + 1.29200e7i) q^{85} +6.61565e7i q^{86} +(-2.95033e7 + 2.39004e7i) q^{87} -9.52392e7 q^{88} +(-5.02819e7 - 5.02819e7i) q^{89} +(2.36654e7 + 2.36654e7i) q^{90} +904548. i q^{91} +600945. i q^{92} -2.40480e7i q^{93} +5.65637e7 q^{94} +(-600224. + 600224. i) q^{95} +4.69136e7i q^{96} +(6.30071e7 - 6.30071e7i) q^{97} +(-4.78648e7 - 4.78648e7i) q^{98} +(-5.63990e7 + 5.63990e7i) 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 $

$2$	8.30345	+	8.30345i	0.518965	+	0.518965i	0.917258	−	0.398293i	$-0.130397\pi$
$2$	8.30345	+	8.30345i	0.518965	+	0.518965i	−0.398293	+	0.917258i	$0.630397\pi$
$3$	−37.9600	−	37.9600i	−0.468642	−	0.468642i	0.432832	−	0.901475i	$-0.357514\pi$
$3$	−37.9600	−	37.9600i	−0.468642	−	0.468642i	−0.901475	+	0.432832i	$0.857514\pi$
$4$		−	118.106i		−	0.461350i
$5$			774.671i			1.23947i	0.784810	+	0.619737i	$0.212761\pi$
$5$			774.671i			1.23947i	−0.784810	+	0.619737i	$0.787239\pi$
$6$		−	630.398i		−	0.486418i
$7$	−18.6293			−0.00775896			−0.00387948	−	0.999992i	$-0.501235\pi$
$7$	−18.6293			−0.00775896			−0.00387948	+	0.999992i	$0.501235\pi$
$8$	3106.37	−	3106.37i	0.758390	−	0.758390i
$9$		−	3679.07i		−	0.560748i
$10$	−6432.44	+	6432.44i	−0.643244	+	0.643244i
$11$	−15329.7	−	15329.7i	−1.04704	−	1.04704i	−0.998838	−	0.0482000i	$-0.984652\pi$
$11$	−15329.7	−	15329.7i	−1.04704	−	1.04704i	−0.0482000	−	0.998838i	$-0.515348\pi$
$12$	−4483.29	+	4483.29i	−0.216208	+	0.216208i
$13$		−	48555.2i		−	1.70005i	−0.526740	−	0.850027i	$-0.676586\pi$
$13$		−	48555.2i		−	1.70005i	0.526740	−	0.850027i	$-0.323414\pi$
$14$	−154.687	−	154.687i	−0.00402663	−	0.00402663i
$15$	29406.5	−	29406.5i	0.580870	−	0.580870i
$16$	21352.0			0.325806
$17$	16678.0	+	16678.0i	0.199686	+	0.199686i	0.799866	−	0.600179i	$-0.204904\pi$
$17$	16678.0	+	16678.0i	0.199686	+	0.199686i	−0.600179	+	0.799866i	$0.704904\pi$
$18$	30549.0	−	30549.0i	0.291009	−	0.291009i
$19$	774.812	+	774.812i	0.00594541	+	0.00594541i	0.710073	−	0.704128i	$-0.248662\pi$
$19$	774.812	+	774.812i	0.00594541	+	0.00594541i	−0.704128	+	0.710073i	$0.748662\pi$
$20$	91492.9			0.571831
$21$	707.168	+	707.168i	0.00363618	+	0.00363618i
$22$		−	254578.i		−	1.08675i
$23$	−5088.20			−0.0181825			−0.00909123	−	0.999959i	$-0.502894\pi$
$23$	−5088.20			−0.0181825			−0.00909123	+	0.999959i	$0.502894\pi$
$24$	−235836.			−0.710828
$25$	−209490.			−0.536294
$26$	403176.	−	403176.i	0.882269	−	0.882269i
$27$	−388713.	+	388713.i	−0.731433	+	0.731433i
$28$			2200.22i			0.00357960i
$29$	73799.3	−	703420.i	0.104342	−	0.994541i
$29$	73799.3	−	703420.i	0.104342	−	0.994541i
$30$	488351.			0.602903
$31$	316754.	+	316754.i	0.342985	+	0.342985i	0.857488	−	0.514504i	$-0.172024\pi$
$31$	316754.	+	316754.i	0.342985	+	0.342985i	−0.514504	+	0.857488i	$0.672024\pi$
$32$	−617934.	−	617934.i	−0.589308	−	0.589308i
$33$			1.16383e6i			0.981373i
$34$			276970.i			0.207261i
$35$		−	14431.5i		−	0.00961702i
$36$	−434519.			−0.258701
$37$	−2.03585e6	+	2.03585e6i	−1.08627	+	1.08627i	−0.0903649	+	0.995909i	$0.528803\pi$
$37$	−2.03585e6	+	2.03585e6i	−1.08627	+	1.08627i	−0.995909	+	0.0903649i	$0.971197\pi$
$38$			12867.2i			0.00617093i
$39$	−1.84316e6	+	1.84316e6i	−0.796717	+	0.796717i
$40$	2.40641e6	+	2.40641e6i	0.940004	+	0.940004i
$41$	2.10468e6	−	2.10468e6i	0.744818	−	0.744818i	−0.228683	−	0.973501i	$-0.573442\pi$
$41$	2.10468e6	−	2.10468e6i	0.744818	−	0.744818i	0.973501	+	0.228683i	$0.0734418\pi$
$42$			11743.9i			0.00377410i
$43$	3.98368e6	+	3.98368e6i	1.16523	+	1.16523i	0.983315	+	0.181912i	$0.0582285\pi$
$43$	3.98368e6	+	3.98368e6i	1.16523	+	1.16523i	0.181912	+	0.983315i	$0.441771\pi$
$44$	−1.81052e6	+	1.81052e6i	−0.483051	+	0.483051i
$45$	2.85007e6			0.695033
$46$	−42249.6	−	42249.6i	−0.00943607	−	0.00943607i
$47$	3.40604e6	−	3.40604e6i	0.698004	−	0.698004i	−0.265976	−	0.963980i	$-0.585694\pi$
$47$	3.40604e6	−	3.40604e6i	0.698004	−	0.698004i	0.963980	+	0.265976i	$0.0856940\pi$
$48$	−810525.	−	810525.i	−0.152687	−	0.152687i
$49$	−5.76445e6			−0.999940
$50$	−1.73949e6	−	1.73949e6i	−0.278318	−	0.278318i
$51$		−	1.26620e6i		−	0.187163i
$52$	−5.73464e6			−0.784319
$53$	−6.96399e6			−0.882581			−0.441290	−	0.897364i	$-0.645479\pi$
$53$	−6.96399e6			−0.882581			−0.441290	+	0.897364i	$0.645479\pi$
$54$	−6.45532e6			−0.759177
$55$	1.18755e7	−	1.18755e7i	1.29778	−	1.29778i
$56$	−57869.3	+	57869.3i	−0.00588432	+	0.00588432i
$57$		−	58823.8i		−	0.00557255i
$58$	6.45360e6	−	5.22802e6i	0.570283	−	0.461983i
$59$	7.75970e6			0.640379			0.320189	−	0.947354i	$-0.396253\pi$
$59$	7.75970e6			0.640379			0.320189	+	0.947354i	$0.396253\pi$
$60$	−3.47308e6	−	3.47308e6i	−0.267984	−	0.267984i
$61$	−1.23316e7	−	1.23316e7i	−0.890635	−	0.890635i	0.103948	−	0.994583i	$-0.466853\pi$
$61$	−1.23316e7	−	1.23316e7i	−0.890635	−	0.890635i	−0.994583	+	0.103948i	$0.966853\pi$
$62$			5.26029e6i			0.355994i
$63$			68538.4i			0.00435082i
$64$		−	1.57281e7i		−	0.937467i
$65$	3.76143e7			2.10717
$66$	−9.66380e6	+	9.66380e6i	−0.509298	+	0.509298i
$67$			1.63852e7i			0.813114i	0.913625	+	0.406557i	$0.133271\pi$
$67$			1.63852e7i			0.813114i	−0.913625	+	0.406557i	$0.866729\pi$
$68$	1.96977e6	−	1.96977e6i	0.0921253	−	0.0921253i
$69$	193148.	+	193148.i	0.00852107	+	0.00852107i
$70$	119832.	−	119832.i	0.00499090	−	0.00499090i
$71$		−	1.55539e7i		−	0.612078i	−0.952019	−	0.306039i	$-0.900996\pi$
$71$		−	1.55539e7i		−	0.612078i	0.952019	−	0.306039i	$-0.0990037\pi$
$72$	−1.14285e7	−	1.14285e7i	−0.425266	−	0.425266i
$73$	−1.15863e7	+	1.15863e7i	−0.407992	+	0.407992i	−0.881038	−	0.473046i	$-0.843155\pi$
$73$	−1.15863e7	+	1.15863e7i	−0.407992	+	0.407992i	0.473046	+	0.881038i	$0.343155\pi$
$74$	−3.38092e7			−1.12748
$75$	7.95225e6	+	7.95225e6i	0.251330	+	0.251330i
$76$	91509.6	−	91509.6i	0.00274292	−	0.00274292i
$77$	285581.	+	285581.i	0.00812392	+	0.00812392i
$78$	−3.06091e7			−0.826937
$79$	4.27708e7	+	4.27708e7i	1.09809	+	1.09809i	0.994634	+	0.103458i	$0.0329907\pi$
$79$	4.27708e7	+	4.27708e7i	1.09809	+	1.09809i	0.103458	+	0.994634i	$0.467009\pi$
$80$			1.65408e7i			0.403828i
$81$	5.37278e6			0.124813
$82$	3.49522e7			0.773070
$83$	7.14717e7			1.50599			0.752994	−	0.658027i	$-0.228609\pi$
$83$	7.14717e7			1.50599			0.752994	+	0.658027i	$0.228609\pi$
$84$	83520.4	−	83520.4i	0.00167755	−	0.00167755i
$85$	−1.29200e7	+	1.29200e7i	−0.247506	+	0.247506i
$86$			6.61565e7i			1.20942i
$87$	−2.95033e7	+	2.39004e7i	−0.514984	+	0.417185i
$88$	−9.52392e7			−1.58813
$89$	−5.02819e7	−	5.02819e7i	−0.801404	−	0.801404i	0.181911	−	0.983315i	$-0.441772\pi$
$89$	−5.02819e7	−	5.02819e7i	−0.801404	−	0.801404i	−0.983315	+	0.181911i	$0.941772\pi$
$90$	2.36654e7	+	2.36654e7i	0.360698	+	0.360698i
$91$			904548.i			0.0131906i
$92$			600945.i			0.00838848i
$93$		−	2.40480e7i		−	0.321474i
$94$	5.65637e7			0.724480
$95$	−600224.	+	600224.i	−0.00736918	+	0.00736918i
$96$			4.69136e7i			0.552349i
$97$	6.30071e7	−	6.30071e7i	0.711709	−	0.711709i	−0.255184	−	0.966893i	$-0.582136\pi$
$97$	6.30071e7	−	6.30071e7i	0.711709	−	0.711709i	0.966893	+	0.255184i	$0.0821359\pi$
$98$	−4.78648e7	−	4.78648e7i	−0.518934	−	0.518934i
$99$	−5.63990e7	+	5.63990e7i	−0.587125	+	0.587125i
$100$			2.47419e7i			0.247419i
$101$	2.62258e7	+	2.62258e7i	0.252025	+	0.252025i	0.821800	−	0.569775i	$-0.192970\pi$
$101$	2.62258e7	+	2.62258e7i	0.252025	+	0.252025i	−0.569775	+	0.821800i	$0.692970\pi$
$102$	1.05138e7	−	1.05138e7i	0.0971312	−	0.0971312i
$103$	5.64121e7			0.501214			0.250607	−	0.968089i	$-0.419370\pi$
$103$	5.64121e7			0.501214			0.250607	+	0.968089i	$0.419370\pi$
$104$	−1.50830e8	−	1.50830e8i	−1.28930	−	1.28930i
$105$	−547822.	+	547822.i	−0.00450695	+	0.00450695i
$106$	−5.78251e7	−	5.78251e7i	−0.458029	−	0.458029i
$107$	−7.86344e7			−0.599898			−0.299949	−	0.953955i	$-0.596970\pi$
$107$	−7.86344e7			−0.599898			−0.299949	+	0.953955i	$0.596970\pi$
$108$	4.59092e7	+	4.59092e7i	0.337447	+	0.337447i
$109$			6.84581e6i			0.0484974i	0.999706	+	0.0242487i	$0.00771937\pi$
$109$			6.84581e6i			0.0484974i	−0.999706	+	0.0242487i	$0.992281\pi$
$110$	1.97214e8			1.34700
$111$	1.54562e8			1.01815
$112$	−397773.			−0.00252792
$113$	1.70627e8	−	1.70627e8i	1.04649	−	1.04649i	0.0476239	−	0.998865i	$-0.484835\pi$
$113$	1.70627e8	−	1.70627e8i	1.04649	−	1.04649i	0.998865	−	0.0476239i	$-0.0151649\pi$
$114$	488440.	−	488440.i	0.00289196	−	0.00289196i
$115$		−	3.94168e6i		−	0.0225367i
$116$	−8.30779e7	−	8.71611e6i	−0.458832	−	0.0481383i
$117$	−1.78638e8			−0.953302
$118$	6.44322e7	+	6.44322e7i	0.332334	+	0.332334i
$119$	−310699.	−	310699.i	−0.00154936	−	0.00154936i
$120$		−	1.82695e8i		−	0.881052i
$121$			2.55639e8i			1.19258i
$122$		−	2.04789e8i		−	0.924418i
$123$	−1.59787e8			−0.698107
$124$	3.74104e7	−	3.74104e7i	0.158236	−	0.158236i
$125$			1.40320e8i			0.574751i
$126$	−569105.	+	569105.i	−0.00225793	+	0.00225793i
$127$	−1.22684e8	−	1.22684e8i	−0.471599	−	0.471599i	0.430833	−	0.902432i	$-0.358220\pi$
$127$	−1.22684e8	−	1.22684e8i	−0.471599	−	0.471599i	−0.902432	+	0.430833i	$0.858220\pi$
$128$	−2.75938e7	+	2.75938e7i	−0.102795	+	0.102795i
$129$		−	3.02441e8i		−	1.09215i
$130$	3.12328e8	+	3.12328e8i	1.09355	+	1.09355i
$131$	4.76927e7	−	4.76927e7i	0.161945	−	0.161945i	−0.621483	−	0.783428i	$-0.713469\pi$
$131$	4.76927e7	−	4.76927e7i	0.161945	−	0.161945i	0.783428	+	0.621483i	$0.213469\pi$
$132$	1.37455e8			0.452756
$133$	−14434.2	−	14434.2i	−4.61302e−5	−	4.61302e-5i
$134$	−1.36053e8	+	1.36053e8i	−0.421978	+	0.421978i
$135$	−3.01125e8	−	3.01125e8i	−0.906592	−	0.906592i
$136$	1.03616e8			0.302880
$137$	−3.20999e6	−	3.20999e6i	−0.00911215	−	0.00911215i	0.702536	−	0.711648i	$-0.252051\pi$
$137$	−3.20999e6	−	3.20999e6i	−0.00911215	−	0.00911215i	−0.711648	+	0.702536i	$0.752051\pi$
$138$			3.20759e6i			0.00884428i
$139$	−1.29941e8			−0.348086			−0.174043	−	0.984738i	$-0.555683\pi$
$139$	−1.29941e8			−0.348086			−0.174043	+	0.984738i	$0.555683\pi$
$140$	−1.70445e6			−0.00443681
$141$	−2.58587e8			−0.654229
$142$	1.29151e8	−	1.29151e8i	0.317647	−	0.317647i
$143$	−7.44336e8	+	7.44336e8i	−1.78002	+	1.78002i
$144$		−	7.85557e7i		−	0.182695i
$145$	5.44919e8	+	5.71702e7i	1.23271	+	0.129329i
$146$	−1.92412e8			−0.423468
$147$	2.18819e8	+	2.18819e8i	0.468614	+	0.468614i
$148$	2.40445e8	+	2.40445e8i	0.501152	+	0.501152i
$149$			1.13495e8i			0.230266i	0.993350	+	0.115133i	$0.0367294\pi$
$149$			1.13495e8i			0.230266i	−0.993350	+	0.115133i	$0.963271\pi$
$150$			1.32062e8i			0.260863i
$151$			2.46664e8i			0.474459i	0.971454	+	0.237230i	$0.0762394\pi$
$151$			2.46664e8i			0.474459i	−0.971454	+	0.237230i	$0.923761\pi$
$152$	4.81370e6			0.00901788
$153$	6.13596e7	−	6.13596e7i	0.111974	−	0.111974i
$154$			4.74261e6i			0.00843207i
$155$	−2.45380e8	+	2.45380e8i	−0.425120	+	0.425120i
$156$	2.17687e8	+	2.17687e8i	0.367565	+	0.367565i
$157$	2.06375e8	−	2.06375e8i	0.339671	−	0.339671i	−0.516572	−	0.856243i	$-0.672792\pi$
$157$	2.06375e8	−	2.06375e8i	0.339671	−	0.339671i	0.856243	+	0.516572i	$0.172792\pi$
$158$			7.10289e8i			1.13974i
$159$	2.64353e8	+	2.64353e8i	0.413615	+	0.413615i
$160$	4.78695e8	−	4.78695e8i	0.730431	−	0.730431i
$161$	94789.4			0.000141077
$162$	4.46126e7	+	4.46126e7i	0.0647735	+	0.0647735i
$163$	9.86424e8	−	9.86424e8i	1.39738	−	1.39738i	0.589900	−	0.807476i	$-0.299167\pi$
$163$	9.86424e8	−	9.86424e8i	1.39738	−	1.39738i	0.807476	−	0.589900i	$-0.200833\pi$
$164$	−2.48574e8	−	2.48574e8i	−0.343622	−	0.343622i
$165$	−9.01586e8			−1.21639
$166$	5.93461e8	+	5.93461e8i	0.781556	+	0.781556i
$167$			9.60549e8i			1.23496i	0.786586	+	0.617481i	$0.211847\pi$
$167$			9.60549e8i			1.23496i	−0.786586	+	0.617481i	$0.788153\pi$
$168$	4.39344e6			0.00551528
$169$	−1.54188e9			−1.89018
$170$	−2.14561e8			−0.256894
$171$	2.85059e6	−	2.85059e6i	0.00333388	−	0.00333388i
$172$	4.70495e8	−	4.70495e8i	0.537577	−	0.537577i
$173$		−	1.01115e9i		−	1.12883i	−0.825490	−	0.564416i	$-0.809101\pi$
$173$		−	1.01115e9i		−	1.12883i	0.825490	−	0.564416i	$-0.190899\pi$
$174$	−4.43435e8	−	4.65230e7i	−0.483763	−	0.0507540i
$175$	3.90264e6			0.00416109
$176$	−3.27320e8	−	3.27320e8i	−0.341132	−	0.341132i
$177$	−2.94559e8	−	2.94559e8i	−0.300109	−	0.300109i
$178$		−	8.35026e8i		−	0.831802i
$179$		−	1.74052e9i		−	1.69538i	−0.530490	−	0.847691i	$-0.677992\pi$
$179$		−	1.74052e9i		−	1.69538i	0.530490	−	0.847691i	$-0.322008\pi$
$180$		−	3.36609e8i		−	0.320653i
$181$	1.38608e9			1.29144			0.645719	−	0.763575i	$-0.276558\pi$
$181$	1.38608e9			1.29144			0.645719	+	0.763575i	$0.276558\pi$
$182$	−7.51087e6	+	7.51087e6i	−0.00684549	+	0.00684549i
$183$			9.36216e8i			0.834779i
$184$	−1.58058e7	+	1.58058e7i	−0.0137894	+	0.0137894i
$185$	−1.57711e9	−	1.57711e9i	−1.34641	−	1.34641i
$186$	1.99681e8	−	1.99681e8i	0.166834	−	0.166834i
$187$		−	5.11337e8i		−	0.418159i
$188$	−4.02272e8	−	4.02272e8i	−0.322024	−	0.322024i
$189$	7.24145e6	−	7.24145e6i	0.00567516	−	0.00567516i
$190$	−9.96786e6			−0.00764870
$191$	1.19991e9	+	1.19991e9i	0.901601	+	0.901601i	0.995575	−	0.0939740i	$-0.0299571\pi$
$191$	1.19991e9	+	1.19991e9i	0.901601	+	0.901601i	−0.0939740	+	0.995575i	$0.529957\pi$
$192$	−5.97039e8	+	5.97039e8i	−0.439337	+	0.439337i
$193$	9.31743e8	+	9.31743e8i	0.671532	+	0.671532i	0.958069	−	0.286537i	$-0.0925041\pi$
$193$	9.31743e8	+	9.31743e8i	0.671532	+	0.671532i	−0.286537	+	0.958069i	$0.592504\pi$
$194$	1.04635e9			0.738705
$195$	−1.42784e9	−	1.42784e9i	−0.987510	−	0.987510i
$196$			6.80814e8i			0.461322i
$197$	−1.36959e7			−0.00909338			−0.00454669	−	0.999990i	$-0.501447\pi$
$197$	−1.36959e7			−0.00909338			−0.00454669	+	0.999990i	$0.501447\pi$
$198$	−9.36612e8			−0.609395
$199$	2.03103e9			1.29510			0.647552	−	0.762021i	$-0.275793\pi$
$199$	2.03103e9			1.29510			0.647552	+	0.762021i	$0.275793\pi$
$200$	−6.50752e8	+	6.50752e8i	−0.406720	+	0.406720i
$201$	6.21981e8	−	6.21981e8i	0.381060	−	0.381060i
$202$			4.35529e8i			0.261584i
$203$	−1.37483e6	+	1.31042e7i	−0.000809588	+	0.00771661i
$204$	−1.49545e8			−0.0863477
$205$	1.63043e9	+	1.63043e9i	0.923183	+	0.923183i
$206$	4.68414e8	+	4.68414e8i	0.260113	+	0.260113i
$207$			1.87198e7i			0.0101958i
$208$		−	1.03675e9i		−	0.553888i
$209$		−	2.37552e7i		−	0.0124501i
$210$	−9.09762e6			−0.00467790
$211$	7.80343e7	−	7.80343e7i	0.0393691	−	0.0393691i	−0.687148	−	0.726517i	$-0.741138\pi$
$211$	7.80343e7	−	7.80343e7i	0.0393691	−	0.0393691i	0.726517	+	0.687148i	$0.241138\pi$
$212$			8.22486e8i			0.407178i
$213$	−5.90427e8	+	5.90427e8i	−0.286846	+	0.286846i
$214$	−6.52937e8	−	6.52937e8i	−0.311326	−	0.311326i
$215$	−3.08604e9	+	3.08604e9i	−1.44427	+	1.44427i
$216$			2.41497e9i			1.10942i
$217$	−5.90088e6	−	5.90088e6i	−0.00266120	−	0.00266120i
$218$	−5.68438e7	+	5.68438e7i	−0.0251685	+	0.0251685i
$219$	8.79630e8			0.382405
$220$	−1.40256e9	−	1.40256e9i	−0.598729	−	0.598729i
$221$	8.09805e8	−	8.09805e8i	0.339478	−	0.339478i
$222$	1.28340e9	+	1.28340e9i	0.528384	+	0.528384i
$223$	−5.70916e8			−0.230862			−0.115431	−	0.993315i	$-0.536825\pi$
$223$	−5.70916e8			−0.230862			−0.115431	+	0.993315i	$0.536825\pi$
$224$	1.15117e7	+	1.15117e7i	0.00457242	+	0.00457242i
$225$			7.70728e8i			0.300726i
$226$	2.83359e9			1.08618
$227$	−3.53511e9			−1.33137			−0.665685	−	0.746233i	$-0.731861\pi$
$227$	−3.53511e9			−1.33137			−0.665685	+	0.746233i	$0.731861\pi$
$228$	−6.94742e6			−0.00257089
$229$	−9.71398e8	+	9.71398e8i	−0.353228	+	0.353228i	−0.861309	−	0.508081i	$-0.830355\pi$
$229$	−9.71398e8	+	9.71398e8i	−0.353228	+	0.353228i	0.508081	+	0.861309i	$0.330355\pi$
$230$	3.27295e7	−	3.27295e7i	0.0116958	−	0.0116958i
$231$		−	2.16813e7i		−	0.00761443i
$232$	−1.95583e9	−	2.41433e9i	−0.675118	−	0.833382i
$233$	5.70368e9			1.93523			0.967613	−	0.252438i	$-0.0812324\pi$
$233$	5.70368e9			1.93523			0.967613	+	0.252438i	$0.0812324\pi$
$234$	−1.48331e9	−	1.48331e9i	−0.494731	−	0.494731i
$235$	2.63856e9	+	2.63856e9i	0.865158	+	0.865158i
$236$		−	9.16464e8i		−	0.295439i
$237$		−	3.24716e9i		−	1.02922i
$238$		−	5.15975e6i		−	0.00160813i
$239$	−2.60777e9			−0.799241			−0.399620	−	0.916681i	$-0.630858\pi$
$239$	−2.60777e9			−0.799241			−0.399620	+	0.916681i	$0.630858\pi$
$240$	6.27890e8	−	6.27890e8i	0.189251	−	0.189251i
$241$			4.67745e9i			1.38657i	0.720664	+	0.693284i	$0.243837\pi$
$241$			4.67745e9i			1.38657i	−0.720664	+	0.693284i	$0.756163\pi$
$242$	−2.12269e9	+	2.12269e9i	−0.618906	+	0.618906i
$243$	2.34640e9	+	2.34640e9i	0.672940	+	0.672940i
$244$	−1.45643e9	+	1.45643e9i	−0.410894	+	0.410894i
$245$		−	4.46555e9i		−	1.23940i
$246$	−1.32679e9	−	1.32679e9i	−0.362293	−	0.362293i
$247$	3.76212e7	−	3.76212e7i	0.0101075	−	0.0101075i
$248$	1.96790e9			0.520232
$249$	−2.71307e9	−	2.71307e9i	−0.705770	−	0.705770i
$250$	−1.16514e9	+	1.16514e9i	−0.298276	+	0.298276i
$251$	−7.79982e8	−	7.79982e8i	−0.196512	−	0.196512i	0.601991	−	0.798503i	$-0.294374\pi$
$251$	−7.79982e8	−	7.79982e8i	−0.196512	−	0.196512i	−0.798503	+	0.601991i	$0.794374\pi$
$252$	8.09476e6			0.00200725
$253$	7.80004e7	+	7.80004e7i	0.0190377	+	0.0190377i
$254$		−	2.03740e9i		−	0.489487i
$255$	9.80885e8			0.231984
$256$	−4.48464e9			−1.04416
$257$	1.38426e9			0.317312			0.158656	−	0.987334i	$-0.449284\pi$
$257$	1.38426e9			0.317312			0.158656	+	0.987334i	$0.449284\pi$
$258$	2.51130e9	−	2.51130e9i	0.566788	−	0.566788i
$259$	3.79264e7	−	3.79264e7i	0.00842835	−	0.00842835i
$260$		−	4.44246e9i		−	0.972143i
$261$	−2.58793e9	−	2.71513e8i	−0.557688	−	0.0585098i
$262$	7.92028e8			0.168088
$263$	4.16987e9	+	4.16987e9i	0.871564	+	0.871564i	0.992643	−	0.121079i	$-0.0386355\pi$
$263$	4.16987e9	+	4.16987e9i	0.871564	+	0.871564i	−0.121079	+	0.992643i	$0.538635\pi$
$264$	3.61528e9	+	3.61528e9i	0.744263	+	0.744263i
$265$		−	5.39480e9i		−	1.09394i
$266$		−	239707.i		−	4.78800e-5i
$267$			3.81740e9i			0.751144i
$268$	1.93518e9			0.375130
$269$	4.64291e9	−	4.64291e9i	0.886710	−	0.886710i	−0.107496	−	0.994206i	$-0.534283\pi$
$269$	4.64291e9	−	4.64291e9i	0.886710	−	0.886710i	0.994206	+	0.107496i	$0.0342832\pi$
$270$		−	5.00075e9i		−	0.940979i
$271$	−4.24264e7	+	4.24264e7i	−0.00786608	+	0.00786608i	−0.711029	−	0.703163i	$-0.751770\pi$
$271$	−4.24264e7	+	4.24264e7i	−0.00786608	+	0.00786608i	0.703163	+	0.711029i	$0.251770\pi$
$272$	3.56110e8	+	3.56110e8i	0.0650591	+	0.0650591i
$273$	3.43367e7	−	3.43367e7i	0.00618170	−	0.00618170i
$274$		−	5.33079e7i		−	0.00945778i
$275$	3.21141e9	+	3.21141e9i	0.561520	+	0.561520i
$276$	2.28119e7	−	2.28119e7i	0.00393120	−	0.00393120i
$277$	2.52127e9			0.428253			0.214126	−	0.976806i	$-0.431310\pi$
$277$	2.52127e9			0.428253			0.214126	+	0.976806i	$0.431310\pi$
$278$	−1.07896e9	−	1.07896e9i	−0.180645	−	0.180645i
$279$	1.16536e9	−	1.16536e9i	0.192328	−	0.192328i
$280$	−4.48297e7	−	4.48297e7i	−0.00729346	−	0.00729346i
$281$	−5.59380e9			−0.897183			−0.448592	−	0.893737i	$-0.648074\pi$
$281$	−5.59380e9			−0.897183			−0.448592	+	0.893737i	$0.648074\pi$
$282$	−2.14716e9	−	2.14716e9i	−0.339522	−	0.339522i
$283$		−	3.83973e9i		−	0.598625i	−0.954155	−	0.299313i	$-0.903243\pi$
$283$		−	3.83973e9i		−	0.598625i	0.954155	−	0.299313i	$-0.0967574\pi$
$284$	−1.83700e9			−0.282382
$285$	4.55691e7			0.00690702
$286$	−1.23611e10			−1.84754
$287$	−3.92086e7	+	3.92086e7i	−0.00577902	+	0.00577902i
$288$	−2.27342e9	+	2.27342e9i	−0.330453	+	0.330453i
$289$		−	6.41945e9i		−	0.920251i
$290$	4.05000e9	+	4.99942e9i	0.572615	+	0.706850i
$291$	−4.78350e9			−0.667074
$292$	1.36840e9	+	1.36840e9i	0.188227	+	0.188227i
$293$	−5.37188e9	−	5.37188e9i	−0.728880	−	0.728880i	0.241517	−	0.970397i	$-0.422355\pi$
$293$	−5.37188e9	−	5.37188e9i	−0.728880	−	0.728880i	−0.970397	+	0.241517i	$0.922355\pi$
$294$			3.63390e9i			0.486389i
$295$			6.01121e9i			0.793732i
$296$			1.26482e10i			1.64764i
$297$	1.19177e10			1.53168
$298$	−9.42396e8	+	9.42396e8i	−0.119500	+	0.119500i
$299$			2.47059e8i			0.0309111i
$300$	9.39205e8	−	9.39205e8i	0.115951	−	0.115951i
$301$	−7.42130e7	−	7.42130e7i	−0.00904095	−	0.00904095i
$302$	−2.04817e9	+	2.04817e9i	−0.246228	+	0.246228i
$303$		−	1.99107e9i		−	0.236219i
$304$	1.65438e7	+	1.65438e7i	0.00193705	+	0.00193705i
$305$	9.55293e9	−	9.55293e9i	1.10392	−	1.10392i
$306$	1.01899e9			0.116221
$307$	1.30036e9	+	1.30036e9i	0.146390	+	0.146390i	0.776503	−	0.630113i	$-0.216992\pi$
$307$	1.30036e9	+	1.30036e9i	0.146390	+	0.146390i	−0.630113	+	0.776503i	$0.716992\pi$
$308$	3.37287e7	−	3.37287e7i	0.00374797	−	0.00374797i
$309$	−2.14140e9	−	2.14140e9i	−0.234890	−	0.234890i
$310$	−4.07499e9			−0.441245
$311$	3.21108e9	+	3.21108e9i	0.343250	+	0.343250i	0.857588	−	0.514338i	$-0.171962\pi$
$311$	3.21108e9	+	3.21108e9i	0.343250	+	0.343250i	−0.514338	+	0.857588i	$0.671962\pi$
$312$			1.14510e10i			1.20844i
$313$	−1.00746e10			−1.04966			−0.524832	−	0.851206i	$-0.675872\pi$
$313$	−1.00746e10			−1.04966			−0.524832	+	0.851206i	$0.675872\pi$
$314$	3.42725e9			0.352555
$315$	−5.30947e7			−0.00539273
$316$	5.05146e9	−	5.05146e9i	0.506604	−	0.506604i
$317$	−6.59648e9	+	6.59648e9i	−0.653244	+	0.653244i	−0.953773	−	0.300529i	$-0.902837\pi$
$317$	−6.59648e9	+	6.59648e9i	−0.653244	+	0.653244i	0.300529	+	0.953773i	$0.402837\pi$
$318$			4.39009e9i			0.429304i
$319$	−1.19145e10	+	9.65189e9i	−1.15057	+	0.932072i
$320$	1.21841e10			1.16197
$321$	2.98497e9	+	2.98497e9i	0.281138	+	0.281138i
$322$	787078.	+	787078.i	7.32141e−5	+	7.32141e-5i
$323$			2.58447e7i			0.00237444i
$324$		−	6.34555e8i		−	0.0575823i
$325$			1.01718e10i			0.911729i
$326$	1.63814e10			1.45038
$327$	2.59867e8	−	2.59867e8i	0.0227280	−	0.0227280i
$328$		−	1.30758e10i		−	1.12973i
$329$	−6.34520e7	+	6.34520e7i	−0.00541579	+	0.00541579i
$330$	−7.48627e9	−	7.48627e9i	−0.631262	−	0.631262i
$331$	−1.05091e10	+	1.05091e10i	−0.875497	+	0.875497i	−0.993065	−	0.117568i	$-0.962490\pi$
$331$	−1.05091e10	+	1.05091e10i	−0.875497	+	0.875497i	0.117568	+	0.993065i	$0.462490\pi$
$332$		−	8.44120e9i		−	0.694788i
$333$	7.49004e9	+	7.49004e9i	0.609126	+	0.609126i
$334$	−7.97587e9	+	7.97587e9i	−0.640903	+	0.640903i
$335$	−1.26931e10			−1.00783
$336$	1.50995e7	+	1.50995e7i	0.00118469	+	0.00118469i
$337$	8.94130e9	−	8.94130e9i	0.693236	−	0.693236i	−0.269707	−	0.962942i	$-0.586927\pi$
$337$	8.94130e9	−	8.94130e9i	0.693236	−	0.693236i	0.962942	+	0.269707i	$0.0869268\pi$
$338$	−1.28029e10	−	1.28029e10i	−0.980938	−	0.980938i
$339$	−1.29540e10			−0.980859
$340$	1.52592e9	+	1.52592e9i	0.114187	+	0.114187i
$341$		−	9.71146e9i		−	0.718236i
$342$	4.73394e7			0.00346034
$343$	2.14782e8			0.0155175
$344$	2.47495e10			1.76739
$345$	−1.49626e8	+	1.49626e8i	−0.0105616	+	0.0105616i
$346$	8.39600e9	−	8.39600e9i	0.585825	−	0.585825i
$347$			1.46174e10i			1.00822i	0.863641	+	0.504108i	$0.168179\pi$
$347$			1.46174e10i			1.00822i	−0.863641	+	0.504108i	$0.831821\pi$
$348$	2.82277e9	+	3.48450e9i	0.192468	+	0.237588i
$349$	−2.03613e10			−1.37248			−0.686238	−	0.727377i	$-0.740739\pi$
$349$	−2.03613e10			−1.37248			−0.686238	+	0.727377i	$0.740739\pi$
$350$	3.24054e7	+	3.24054e7i	0.00215946	+	0.00215946i
$351$	1.88741e10	+	1.88741e10i	1.24348	+	1.24348i
$352$			1.89455e10i			1.23405i
$353$		−	2.70317e10i		−	1.74091i	−0.492252	−	0.870453i	$-0.663826\pi$
$353$		−	2.70317e10i		−	1.74091i	0.492252	−	0.870453i	$-0.336174\pi$
$354$		−	4.89170e9i		−	0.311492i
$355$	1.20492e10			0.758654
$356$	−5.93857e9	+	5.93857e9i	−0.369728	+	0.369728i
$357$			2.35883e7i			0.00145219i
$358$	1.44523e10	−	1.44523e10i	0.879845	−	0.879845i
$359$	2.59081e9	+	2.59081e9i	0.155976	+	0.155976i	0.780781	−	0.624805i	$-0.214821\pi$
$359$	2.59081e9	+	2.59081e9i	0.155976	+	0.155976i	−0.624805	+	0.780781i	$0.714821\pi$
$360$	8.85335e9	−	8.85335e9i	0.527106	−	0.527106i
$361$		−	1.69824e10i		−	0.999929i
$362$	1.15092e10	+	1.15092e10i	0.670212	+	0.670212i
$363$	9.70408e9	−	9.70408e9i	0.558892	−	0.558892i
$364$	1.06832e8			0.00608550
$365$	−8.97554e9	−	8.97554e9i	−0.505696	−	0.505696i
$366$	−7.77382e9	+	7.77382e9i	−0.433221	+	0.433221i
$367$	−1.19982e10	−	1.19982e10i	−0.661382	−	0.661382i	0.294324	−	0.955706i	$-0.404906\pi$
$367$	−1.19982e10	−	1.19982e10i	−0.661382	−	0.661382i	−0.955706	+	0.294324i	$0.904906\pi$
$368$	−1.08643e8			−0.00592396
$369$	−7.74326e9	−	7.74326e9i	−0.417656	−	0.417656i
$370$		−	2.61910e10i		−	1.39748i
$371$	1.29734e8			0.00684791
$372$	−2.84020e9			−0.148312
$373$	−3.46876e10			−1.79200			−0.896001	−	0.444052i	$-0.853541\pi$
$373$	−3.46876e10			−1.79200			−0.896001	+	0.444052i	$0.853541\pi$
$374$	4.24586e9	−	4.24586e9i	0.217010	−	0.217010i
$375$	5.32656e9	−	5.32656e9i	0.269353	−	0.269353i
$376$		−	2.11608e10i		−	1.05872i
$377$	−3.41547e10	−	3.58334e9i	−1.69077	−	0.177387i
$378$	1.20258e8			0.00589042
$379$	1.34790e10	+	1.34790e10i	0.653284	+	0.653284i	0.953782	−	0.300498i	$-0.0971529\pi$
$379$	1.34790e10	+	1.34790e10i	0.653284	+	0.653284i	−0.300498	+	0.953782i	$0.597153\pi$
$380$	7.08898e7	+	7.08898e7i	0.00339977	+	0.00339977i
$381$			9.31418e9i			0.442023i
$382$			1.99267e10i			0.935799i
$383$		−	4.79376e9i		−	0.222783i	−0.993777	−	0.111391i	$-0.964469\pi$
$383$		−	4.79376e9i		−	0.222783i	0.993777	−	0.111391i	$-0.0355307\pi$
$384$	2.09492e9			0.0963480
$385$	−2.21231e8	+	2.21231e8i	−0.0100694	+	0.0100694i
$386$			1.54734e10i			0.697004i
$387$	1.46562e10	−	1.46562e10i	0.653399	−	0.653399i
$388$	−7.44149e9	−	7.44149e9i	−0.328347	−	0.328347i
$389$	−6.24027e8	+	6.24027e8i	−0.0272524	+	0.0272524i	−0.720602	−	0.693349i	$-0.756134\pi$
$389$	−6.24027e8	+	6.24027e8i	−0.0272524	+	0.0272524i	0.693349	+	0.720602i	$0.256134\pi$
$390$		−	2.37120e10i		−	1.02497i
$391$	−8.48610e7	−	8.48610e7i	−0.00363079	−	0.00363079i
$392$	−1.79065e10	+	1.79065e10i	−0.758344	+	0.758344i
$393$	−3.62084e9			−0.151788
$394$	−1.13723e8	−	1.13723e8i	−0.00471915	−	0.00471915i
$395$	−3.31333e10	+	3.31333e10i	−1.36106	+	1.36106i
$396$	6.66103e9	+	6.66103e9i	0.270870	+	0.270870i
$397$	1.04941e9			0.0422458			0.0211229	−	0.999777i	$-0.493276\pi$
$397$	1.04941e9			0.0422458			0.0211229	+	0.999777i	$0.493276\pi$
$398$	1.68646e10	+	1.68646e10i	0.672114	+	0.672114i
$399$			1.09584e6i			4.32372e-5i
$400$	−4.47304e9			−0.174728
$401$	3.32174e10			1.28466			0.642331	−	0.766428i	$-0.277968\pi$
$401$	3.32174e10			1.28466			0.642331	+	0.766428i	$0.277968\pi$
$402$	1.03292e10			0.395514
$403$	1.53800e10	−	1.53800e10i	0.583092	−	0.583092i
$404$	3.09741e9	−	3.09741e9i	0.116272	−	0.116272i
$405$			4.16214e9i			0.154702i
$406$	−1.20226e8	+	9.73942e7i	−0.00442480	+	0.00358450i
$407$	6.24179e10			2.27474
$408$	−3.93327e9	−	3.93327e9i	−0.141943	−	0.141943i
$409$	1.13704e10	+	1.13704e10i	0.406335	+	0.406335i	0.880458	−	0.474124i	$-0.157235\pi$
$409$	1.13704e10	+	1.13704e10i	0.406335	+	0.406335i	−0.474124	+	0.880458i	$0.657235\pi$
$410$			2.70764e10i			0.958200i
$411$			2.43702e8i			0.00854068i
$412$		−	6.66258e9i		−	0.231235i
$413$	−1.44557e8			−0.00496867
$414$	−1.55439e8	+	1.55439e8i	−0.00529126	+	0.00529126i
$415$			5.53670e10i			1.86663i
$416$	−3.00039e10	+	3.00039e10i	−1.00185	+	1.00185i
$417$	4.93256e9	+	4.93256e9i	0.163128	+	0.163128i
$418$	1.97250e8	−	1.97250e8i	0.00646119	−	0.00646119i
$419$			1.06596e10i			0.345848i	0.984935	+	0.172924i	$0.0553215\pi$
$419$			1.06596e10i			0.345848i	−0.984935	+	0.172924i	$0.944678\pi$
$420$	6.47008e7	+	6.47008e7i	0.00207928	+	0.00207928i
$421$	−1.72064e10	+	1.72064e10i	−0.547724	+	0.547724i	−0.925782	−	0.378058i	$-0.876592\pi$
$421$	−1.72064e10	+	1.72064e10i	−0.547724	+	0.547724i	0.378058	+	0.925782i	$0.376592\pi$
$422$	1.29591e9			0.0408624
$423$	−1.25311e10	−	1.25311e10i	−0.391405	−	0.391405i
$424$	−2.16327e10	+	2.16327e10i	−0.669340	+	0.669340i
$425$	−3.49388e9	−	3.49388e9i	−0.107091	−	0.107091i
$426$	−9.80516e9			−0.297726
$427$	2.29729e8	+	2.29729e8i	0.00691040	+	0.00691040i
$428$			9.28716e9i			0.276763i
$429$	5.65100e10			1.66839
$430$	−5.12495e10			−1.49905
$431$	−5.61334e10			−1.62672			−0.813360	−	0.581761i	$-0.802364\pi$
$431$	−5.61334e10			−1.62672			−0.813360	+	0.581761i	$0.802364\pi$
$432$	−8.29983e9	+	8.29983e9i	−0.238306	+	0.238306i
$433$	2.85435e10	−	2.85435e10i	0.811999	−	0.811999i	−0.172935	−	0.984933i	$-0.555325\pi$
$433$	2.85435e10	−	2.85435e10i	0.811999	−	0.811999i	0.984933	+	0.172935i	$0.0553249\pi$
$434$		−	9.79954e7i		−	0.00276215i
$435$	−1.85150e10	−	2.28553e10i	−0.517090	−	0.638308i
$436$	8.08528e8			0.0223743
$437$	−3.94240e6	−	3.94240e6i	−0.000108102	−	0.000108102i
$438$	7.30396e9	+	7.30396e9i	0.198455	+	0.198455i
$439$			4.02900e10i			1.08477i	0.840129	+	0.542387i	$0.182479\pi$
$439$			4.02900e10i			1.08477i	−0.840129	+	0.542387i	$0.817521\pi$
$440$		−	7.37790e10i		−	1.96844i
$441$			2.12078e10i			0.560715i
$442$	1.34483e10			0.352354
$443$	3.82183e10	−	3.82183e10i	0.992331	−	0.992331i	−0.00764026	−	0.999971i	$-0.502432\pi$
$443$	3.82183e10	−	3.82183e10i	0.992331	−	0.992331i	0.999971	+	0.00764026i	$0.00243199\pi$
$444$		−	1.82546e10i		−	0.469722i
$445$	3.89519e10	−	3.89519e10i	0.993319	−	0.993319i
$446$	−4.74057e9	−	4.74057e9i	−0.119810	−	0.119810i
$447$	4.30826e9	−	4.30826e9i	0.107912	−	0.107912i
$448$			2.93003e8i			0.00727377i
$449$	4.82295e10	+	4.82295e10i	1.18666	+	1.18666i	0.977984	+	0.208680i	$0.0669168\pi$
$449$	4.82295e10	+	4.82295e10i	1.18666	+	1.18666i	0.208680	+	0.977984i	$0.433083\pi$
$450$	−6.39970e9	+	6.39970e9i	−0.156066	+	0.156066i
$451$	−6.45281e10			−1.55971
$452$	−2.01520e10	−	2.01520e10i	−0.482798	−	0.482798i
$453$	9.36339e9	−	9.36339e9i	0.222352	−	0.222352i
$454$	−2.93536e10	−	2.93536e10i	−0.690935	−	0.690935i
$455$	−7.00727e8			−0.0163495
$456$	−1.82728e8	−	1.82728e8i	−0.00422616	−	0.00422616i
$457$			9.74438e9i			0.223403i	0.993742	+	0.111702i	$0.0356301\pi$
$457$			9.74438e9i			0.223403i	−0.993742	+	0.111702i	$0.964370\pi$
$458$	−1.61319e10			−0.366626
$459$	−1.29659e10			−0.292115
$460$	−4.65534e8			−0.0103973
$461$	−2.47639e10	+	2.47639e10i	−0.548296	+	0.548296i	−0.925948	−	0.377652i	$-0.876732\pi$
$461$	−2.47639e10	+	2.47639e10i	−0.548296	+	0.548296i	0.377652	+	0.925948i	$0.376732\pi$
$462$	1.80030e8	−	1.80030e8i	0.00395163	−	0.00395163i
$463$		−	7.03439e10i		−	1.53074i	−0.643589	−	0.765371i	$-0.722555\pi$
$463$		−	7.03439e10i		−	1.53074i	0.643589	−	0.765371i	$-0.277445\pi$
$464$	1.57577e9	−	1.50195e10i	0.0339954	−	0.324028i
$465$	1.86292e10			0.398459
$466$	4.73602e10	+	4.73602e10i	1.00432	+	1.00432i
$467$	−4.75135e10	−	4.75135e10i	−0.998964	−	0.998964i	0.00103554	−	0.999999i	$-0.499670\pi$
$467$	−4.75135e10	−	4.75135e10i	−0.998964	−	0.998964i	−0.999999	+	0.00103554i	$0.999670\pi$
$468$			2.10982e10i			0.439806i
$469$		−	3.05243e8i		−	0.00630892i
$470$			4.38183e10i			0.897974i
$471$	−1.56680e10			−0.318369
$472$	2.41045e10	−	2.41045e10i	0.485657	−	0.485657i
$473$		−	1.22137e11i		−	2.44007i
$474$	2.69626e10	−	2.69626e10i	0.534132	−	0.534132i
$475$	−1.62315e8	−	1.62315e8i	−0.00318849	−	0.00318849i
$476$	−3.66953e7	+	3.66953e7i	−0.000714797	+	0.000714797i
$477$			2.56210e10i			0.494906i
$478$	−2.16535e10	−	2.16535e10i	−0.414778	−	0.414778i
$479$	5.53417e10	−	5.53417e10i	1.05126	−	1.05126i	0.0526480	−	0.998613i	$-0.483234\pi$
$479$	5.53417e10	−	5.53417e10i	1.05126	−	1.05126i	0.998613	−	0.0526480i	$-0.0167661\pi$
$480$	−3.63426e10			−0.684622
$481$	9.88512e10	+	9.88512e10i	1.84672	+	1.84672i
$482$	−3.88390e10	+	3.88390e10i	−0.719581	+	0.719581i
$483$	−3.59821e6	−	3.59821e6i	−6.61147e−5	−	6.61147e-5i
$484$	3.01924e10			0.550195
$485$	4.88097e10	+	4.88097e10i	0.882144	+	0.882144i
$486$			3.89664e10i			0.698466i
$487$	1.89214e10			0.336385			0.168193	−	0.985754i	$-0.446207\pi$
$487$	1.89214e10			0.336385			0.168193	+	0.985754i	$0.446207\pi$
$488$	−7.66129e10			−1.35090
$489$	−7.48894e10			−1.30974
$490$	3.70795e10	−	3.70795e10i	0.643205	−	0.643205i
$491$	3.06483e10	−	3.06483e10i	0.527328	−	0.527328i	−0.392447	−	0.919775i	$-0.628371\pi$
$491$	3.06483e10	−	3.06483e10i	0.527328	−	0.527328i	0.919775	+	0.392447i	$0.128371\pi$
$492$			1.88718e10i			0.322072i
$493$	1.29625e10	−	1.05008e10i	0.219432	−	0.177761i
$494$	6.24771e8			0.0104909
$495$	−4.36906e10	−	4.36906e10i	−0.727726	−	0.727726i
$496$	6.76334e9	+	6.76334e9i	0.111747	+	0.111747i
$497$			2.89758e8i			0.00474909i
$498$		−	4.50556e10i		−	0.732541i
$499$			9.03516e10i			1.45725i	0.684914	+	0.728624i	$0.259840\pi$
$499$			9.03516e10i			1.45725i	−0.684914	+	0.728624i	$0.740160\pi$
$500$	1.65726e10			0.265161
$501$	3.64625e10	−	3.64625e10i	0.578756	−	0.578756i
$502$		−	1.29531e10i		−	0.203966i
$503$	2.19112e10	−	2.19112e10i	0.342289	−	0.342289i	−0.514938	−	0.857227i	$-0.672185\pi$
$503$	2.19112e10	−	2.19112e10i	0.342289	−	0.342289i	0.857227	+	0.514938i	$0.172185\pi$
$504$	2.12905e8	+	2.12905e8i	0.00329962	+	0.00329962i
$505$	−2.03164e10	+	2.03164e10i	−0.312378	+	0.312378i
$506$			1.29534e9i			0.0197598i
$507$	5.85298e10	+	5.85298e10i	0.885819	+	0.885819i
$508$	−1.44897e10	+	1.44897e10i	−0.217572	+	0.217572i
$509$	−2.04969e10			−0.305364			−0.152682	−	0.988275i	$-0.548791\pi$
$509$	−2.04969e10			−0.305364			−0.152682	+	0.988275i	$0.548791\pi$
$510$	8.14473e9	+	8.14473e9i	0.120392	+	0.120392i
$511$	2.15844e8	−	2.15844e8i	0.00316560	−	0.00316560i
$512$	−3.01739e10	−	3.01739e10i	−0.439089	−	0.439089i
$513$	−6.02360e8			−0.00869734
$514$	1.14941e10	+	1.14941e10i	0.164674	+	0.164674i
$515$			4.37008e10i			0.621241i
$516$	−3.57200e10			−0.503863
$517$	−1.04427e11			−1.46167
$518$	6.29840e8			0.00874805
$519$	−3.83831e10	+	3.83831e10i	−0.529019	+	0.529019i
$520$	1.16844e11	−	1.16844e11i	1.59806	−	1.59806i
$521$			6.11083e10i			0.829371i	0.909965	+	0.414686i	$0.136108\pi$
$521$			6.11083e10i			0.829371i	−0.909965	+	0.414686i	$0.863892\pi$
$522$	−1.92343e10	−	2.37433e10i	−0.259056	−	0.319785i
$523$	−3.39119e10			−0.453258			−0.226629	−	0.973981i	$-0.572770\pi$
$523$	−3.39119e10			−0.453258			−0.226629	+	0.973981i	$0.572770\pi$
$524$	−5.63278e9	−	5.63278e9i	−0.0747132	−	0.0747132i
$525$	−1.48144e8	−	1.48144e8i	−0.00195006	−	0.00195006i
$526$			6.92485e10i			0.904623i
$527$			1.05656e10i			0.136979i
$528$			2.48502e10i			0.319738i
$529$	−7.82851e10			−0.999669
$530$	4.47954e10	−	4.47954e10i	0.567715	−	0.567715i
$531$		−	2.85485e10i		−	0.359091i
$532$	−1.70476e6	+	1.70476e6i	−2.12822e−5	+	2.12822e-5i
$533$	−1.02193e11	−	1.02193e11i	−1.26623	−	1.26623i
$534$	−3.16976e10	+	3.16976e10i	−0.389818	+	0.389818i
$535$		−	6.09158e10i		−	0.743558i
$536$	5.08983e10	+	5.08983e10i	0.616657	+	0.616657i
$537$	−6.60703e10	+	6.60703e10i	−0.794528	+	0.794528i
$538$	7.71044e10			0.920343
$539$	8.83672e10	+	8.83672e10i	1.04697	+	1.04697i
$540$	−3.55645e10	+	3.55645e10i	−0.418256	+	0.418256i
$541$	6.45780e10	+	6.45780e10i	0.753869	+	0.753869i	0.975199	−	0.221330i	$-0.0710398\pi$
$541$	6.45780e10	+	6.45780e10i	0.753869	+	0.753869i	−0.221330	+	0.975199i	$0.571040\pi$
$542$	−7.04570e8			−0.00816445
$543$	−5.26156e10	−	5.26156e10i	−0.605223	−	0.605223i
$544$		−	2.06118e10i		−	0.235354i
$545$	−5.30325e9			−0.0601113
$546$	5.70226e8			0.00641617
$547$	−6.36173e9			−0.0710601			−0.0355301	−	0.999369i	$-0.511312\pi$
$547$	−6.36173e9			−0.0710601			−0.0355301	+	0.999369i	$0.511312\pi$
$548$	−3.79117e8	+	3.79117e8i	−0.00420389	+	0.00420389i
$549$	−4.53688e10	+	4.53688e10i	−0.499422	+	0.499422i
$550$			5.33316e10i			0.582819i
$551$	6.02199e8	−	4.87838e8i	0.00653332	−	0.00529260i
$552$	1.19998e9			0.0129246
$553$	−7.96788e8	−	7.96788e8i	−0.00852005	−	0.00852005i
$554$	2.09352e10	+	2.09352e10i	0.222248	+	0.222248i
$555$			1.19735e11i			1.26197i
$556$			1.53467e10i			0.160590i
$557$			4.61523e10i			0.479483i	0.970837	+	0.239741i	$0.0770627\pi$
$557$			4.61523e10i			0.479483i	−0.970837	+	0.239741i	$0.922937\pi$
$558$	1.93530e10			0.199623
$559$	1.93428e11	−	1.93428e11i	1.98095	−	1.98095i
$560$		−	3.08143e8i		−	0.00313329i
$561$	−1.94104e10	+	1.94104e10i	−0.195967	+	0.195967i
$562$	−4.64478e10	−	4.64478e10i	−0.465607	−	0.465607i
$563$	1.52872e10	−	1.52872e10i	0.152158	−	0.152158i	−0.626923	−	0.779081i	$-0.715686\pi$
$563$	1.52872e10	−	1.52872e10i	0.152158	−	0.152158i	0.779081	+	0.626923i	$0.215686\pi$
$564$			3.05405e10i			0.301828i
$565$	1.32180e11	+	1.32180e11i	1.29710	+	1.29710i
$566$	3.18830e10	−	3.18830e10i	0.310666	−	0.310666i
$567$	−1.00091e8			−0.000968417
$568$	−4.83162e10	−	4.83162e10i	−0.464193	−	0.464193i
$569$	−6.84851e10	+	6.84851e10i	−0.653351	+	0.653351i	−0.953798	−	0.300447i	$-0.902864\pi$
$569$	−6.84851e10	+	6.84851e10i	−0.653351	+	0.653351i	0.300447	+	0.953798i	$0.402864\pi$
$570$	3.78380e8	+	3.78380e8i	0.00358450	+	0.00358450i
$571$	−1.78255e11			−1.67686			−0.838431	−	0.545008i	$-0.816527\pi$
$571$	−1.78255e11			−1.67686			−0.838431	+	0.545008i	$0.816527\pi$
$572$	8.79102e10	+	8.79102e10i	0.821212	+	0.821212i
$573$		−	9.10971e10i		−	0.845057i
$574$	−6.51133e8			−0.00599822
$575$	1.06593e9			0.00975115
$576$	−5.78647e10			−0.525683
$577$	2.39444e10	−	2.39444e10i	0.216023	−	0.216023i	−0.590797	−	0.806820i	$-0.701187\pi$
$577$	2.39444e10	−	2.39444e10i	0.216023	−	0.216023i	0.806820	+	0.590797i	$0.201187\pi$
$578$	5.33035e10	−	5.33035e10i	0.477578	−	0.477578i
$579$		−	7.07380e10i		−	0.629417i
$580$	6.75212e9	−	6.43580e10i	0.0596661	−	0.568710i
$581$	−1.33146e9			−0.0116849
$582$	−3.97196e10	−	3.97196e10i	−0.346188	−	0.346188i
$583$	1.06756e11	+	1.06756e11i	0.924095	+	0.924095i
$584$			7.19824e10i			0.618835i
$585$		−	1.38386e11i		−	1.18159i
$586$		−	8.92102e10i		−	0.756526i
$587$	−1.35762e11			−1.14347			−0.571737	−	0.820437i	$-0.693730\pi$
$587$	−1.35762e11			−1.14347			−0.571737	+	0.820437i	$0.693730\pi$
$588$	2.58437e10	−	2.58437e10i	0.216195	−	0.216195i
$589$			4.90849e8i			0.00407837i
$590$	−4.99138e10	+	4.99138e10i	−0.411920	+	0.411920i
$591$	5.19896e8	+	5.19896e8i	0.00426154	+	0.00426154i
$592$	−4.34696e10	+	4.34696e10i	−0.353915	+	0.353915i
$593$		−	2.15735e11i		−	1.74462i	−0.488950	−	0.872312i	$-0.662620\pi$
$593$		−	2.15735e11i		−	1.74462i	0.488950	−	0.872312i	$-0.337380\pi$
$594$	9.89580e10	+	9.89580e10i	0.794887	+	0.794887i
$595$	2.40690e8	−	2.40690e8i	0.00192039	−	0.00192039i
$596$	1.34043e10			0.106233
$597$	−7.70981e10	−	7.70981e10i	−0.606941	−	0.606941i
$598$	−2.05144e9	+	2.05144e9i	−0.0160418	+	0.0160418i
$599$	−1.05461e11	−	1.05461e11i	−0.819187	−	0.819187i	0.166803	−	0.985990i	$-0.446656\pi$
$599$	−1.05461e11	−	1.05461e11i	−0.819187	−	0.819187i	−0.985990	+	0.166803i	$0.946656\pi$
$600$	4.94052e10			0.381213
$601$	1.47776e11	+	1.47776e11i	1.13267	+	1.13267i	0.989731	+	0.142943i	$0.0456565\pi$
$601$	1.47776e11	+	1.47776e11i	1.13267	+	1.13267i	0.142943	+	0.989731i	$0.454343\pi$
$602$		−	1.23245e9i		−	0.00938388i
$603$	6.02821e10			0.455952
$604$	2.91324e10			0.218892
$605$	−1.98036e11			−1.47817
$606$	1.65327e10	−	1.65327e10i	0.122590	−	0.122590i
$607$	1.46502e11	−	1.46502e11i	1.07917	−	1.07917i	0.0825864	−	0.996584i	$-0.473682\pi$
$607$	1.46502e11	−	1.46502e11i	1.07917	−	1.07917i	0.996584	−	0.0825864i	$-0.0263180\pi$
$608$		−	9.57565e8i		−	0.00700735i
$609$	5.49625e8	−	4.45248e8i	0.00399574	−	0.00323692i
$610$	1.58644e11			1.14579
$611$	−1.65381e11	−	1.65381e11i	−1.18664	−	1.18664i
$612$	−7.24691e9	−	7.24691e9i	−0.0516591	−	0.0516591i
$613$			1.55422e11i			1.10070i	0.834933	+	0.550352i	$0.185506\pi$
$613$			1.55422e11i			1.10070i	−0.834933	+	0.550352i	$0.814494\pi$
$614$			2.15950e10i			0.151943i
$615$		−	1.23783e11i		−	0.865285i
$616$	1.77424e9			0.0123222
$617$	1.03449e10	−	1.03449e10i	0.0713815	−	0.0713815i	−0.670515	−	0.741896i	$-0.733927\pi$
$617$	1.03449e10	−	1.03449e10i	0.0713815	−	0.0713815i	0.741896	+	0.670515i	$0.233927\pi$
$618$		−	3.55621e10i		−	0.243800i
$619$	9.52149e10	−	9.52149e10i	0.648548	−	0.648548i	−0.304094	−	0.952642i	$-0.598354\pi$
$619$	9.52149e10	−	9.52149e10i	0.648548	−	0.648548i	0.952642	+	0.304094i	$0.0983537\pi$
$620$	2.89807e10	+	2.89807e10i	0.196129	+	0.196129i
$621$	1.97785e9	−	1.97785e9i	0.0132993	−	0.0132993i
$622$			5.33261e10i			0.356269i
$623$	9.36714e8	+	9.36714e8i	0.00621806	+	0.00621806i
$624$	−3.93552e10	+	3.93552e10i	−0.259576	+	0.259576i
$625$	−1.90534e11			−1.24868
$626$	−8.36538e10	−	8.36538e10i	−0.544739	−	0.544739i
$627$	−9.01750e8	+	9.01750e8i	−0.00583467	+	0.00583467i
$628$	−2.43740e10	−	2.43740e10i	−0.156707	−	0.156707i
$629$	−6.79079e10			−0.433828
$630$	−4.40869e8	−	4.40869e8i	−0.00279864	−	0.00279864i
$631$		−	8.51929e10i		−	0.537385i	−0.963226	−	0.268693i	$-0.913408\pi$
$631$		−	8.51929e10i		−	0.537385i	0.963226	−	0.268693i	$-0.0865916\pi$
$632$	2.65723e11			1.66556
$633$	−5.92437e9			−0.0369001
$634$	−1.09547e11			−0.678022
$635$	9.50397e10	−	9.50397e10i	0.584535	−	0.584535i
$636$	3.12216e10	−	3.12216e10i	0.190821	−	0.190821i
$637$			2.79894e11i			1.69995i
$638$	−1.79076e11	−	1.87877e10i	−1.08082	−	0.113394i
$639$	−5.72240e10			−0.343222
$640$	−2.13761e10	−	2.13761e10i	−0.127411	−	0.127411i
$641$	1.04421e11	+	1.04421e11i	0.618525	+	0.618525i	0.945153	−	0.326628i	$-0.105912\pi$
$641$	1.04421e11	+	1.04421e11i	0.618525	+	0.618525i	−0.326628	+	0.945153i	$0.605912\pi$
$642$			4.95710e10i			0.291802i
$643$			2.10177e11i			1.22954i	0.788707	+	0.614769i	$0.210751\pi$
$643$			2.10177e11i			1.22954i	−0.788707	+	0.614769i	$0.789249\pi$
$644$		−	1.11952e7i		−	6.50859e-5i
$645$	2.34292e11			1.35369
$646$	−2.14600e8	+	2.14600e8i	−0.00123225	+	0.00123225i
$647$			1.65166e11i			0.942549i	0.881986	+	0.471275i	$0.156206\pi$
$647$			1.65166e11i			0.942549i	−0.881986	+	0.471275i	$0.843794\pi$
$648$	1.66898e10	−	1.66898e10i	0.0946567	−	0.0946567i
$649$	−1.18954e11	−	1.18954e11i	−0.670501	−	0.670501i
$650$	−8.44612e10	+	8.44612e10i	−0.473156	+	0.473156i
$651$			4.47996e8i			0.00249431i
$652$	−1.16502e11	−	1.16502e11i	−0.644679	−	0.644679i
$653$	−5.14541e10	+	5.14541e10i	−0.282987	+	0.282987i	−0.834299	−	0.551312i	$-0.814127\pi$
$653$	−5.14541e10	+	5.14541e10i	−0.282987	+	0.282987i	0.551312	+	0.834299i	$0.314127\pi$
$654$	4.31559e9			0.0235901
$655$	3.69462e10	+	3.69462e10i	0.200726	+	0.200726i
$656$	4.49392e10	−	4.49392e10i	0.242667	−	0.242667i
$657$	4.26267e10	+	4.26267e10i	0.228781	+	0.228781i
$658$	−1.05374e9			−0.00562121
$659$	8.18798e10	+	8.18798e10i	0.434145	+	0.434145i	0.890036	−	0.455890i	$-0.150679\pi$
$659$	8.18798e10	+	8.18798e10i	0.434145	+	0.434145i	−0.455890	+	0.890036i	$0.650679\pi$
$660$			1.06482e11i			0.561179i
$661$	−2.85475e11			−1.49542			−0.747708	−	0.664028i	$-0.768846\pi$
$661$	−2.85475e11			−1.49542			−0.747708	+	0.664028i	$0.768846\pi$
$662$	−1.74524e11			−0.908705
$663$	−6.14804e10			−0.318187
$664$	2.22017e11	−	2.22017e11i	1.14213	−	1.14213i
$665$	1.11817e7	−	1.11817e7i	5.71772e−5	−	5.71772e-5i
$666$			1.24386e11i			0.632231i
$667$	−3.75506e8	+	3.57914e9i	−0.00189720	+	0.0180832i
$668$	1.13446e11			0.569750
$669$	2.16720e10	+	2.16720e10i	0.108192	+	0.108192i
$670$	−1.05396e11	−	1.05396e11i	−0.523030	−	0.523030i
$671$			3.78079e11i			1.86506i
$672$		−	8.73966e8i		−	0.00428566i
$673$			1.58705e11i			0.773626i	0.922158	+	0.386813i	$0.126424\pi$
$673$			1.58705e11i			0.773626i	−0.922158	+	0.386813i	$0.873576\pi$
$674$	1.48487e11			0.719531
$675$	8.14316e10	−	8.14316e10i	0.392263	−	0.392263i
$676$			1.82104e11i			0.872035i
$677$	1.84787e11	−	1.84787e11i	0.879663	−	0.879663i	−0.113836	−	0.993500i	$-0.536314\pi$
$677$	1.84787e11	−	1.84787e11i	0.879663	−	0.879663i	0.993500	+	0.113836i	$0.0363140\pi$
$678$	−1.07563e11	−	1.07563e11i	−0.509032	−	0.509032i
$679$	−1.17378e9	+	1.17378e9i	−0.00552212	+	0.00552212i
$680$			8.02683e10i			0.375412i
$681$	1.34193e11	+	1.34193e11i	0.623937	+	0.623937i
$682$	8.06386e10	−	8.06386e10i	0.372739	−	0.372739i
$683$	1.55995e11			0.716850			0.358425	−	0.933559i	$-0.383314\pi$
$683$	1.55995e11			0.716850			0.358425	+	0.933559i	$0.383314\pi$
$684$	−3.36670e8	−	3.36670e8i	−0.00153809	−	0.00153809i
$685$	2.48668e9	−	2.48668e9i	0.0112943	−	0.0112943i
$686$	1.78343e9	+	1.78343e9i	0.00805302	+	0.00805302i
$687$	7.37486e10			0.331075
$688$	8.50597e10	+	8.50597e10i	0.379638	+	0.379638i
$689$			3.38138e11i			1.50043i
$690$	−2.48483e9			−0.0109623
$691$	−3.37360e10			−0.147972			−0.0739862	−	0.997259i	$-0.523572\pi$
$691$	−3.37360e10			−0.147972			−0.0739862	+	0.997259i	$0.523572\pi$
$692$	−1.19422e11			−0.520787
$693$	1.05067e9	−	1.05067e9i	0.00455548	−	0.00455548i
$694$	−1.21375e11	+	1.21375e11i	−0.523229	+	0.523229i
$695$		−	1.00661e11i		−	0.431444i
$696$	−1.74045e10	+	1.65891e11i	−0.0741694	+	0.706947i
$697$	7.02037e10			0.297460
$698$	−1.69069e11	−	1.69069e11i	−0.712267	−	0.712267i
$699$	−2.16512e11	−	2.16512e11i	−0.906929	−	0.906929i
$700$		−	4.60924e8i		−	0.00191972i
$701$		−	2.35269e11i		−	0.974298i	−0.873319	−	0.487149i	$-0.838037\pi$
$701$		−	2.35269e11i		−	0.974298i	0.873319	−	0.487149i	$-0.161963\pi$
$702$			3.13440e11i			1.29064i
$703$	−3.15480e9			−0.0129167
$704$	−2.41107e11	+	2.41107e11i	−0.981563	+	0.981563i
$705$		−	2.00320e11i		−	0.810899i
$706$	2.24457e11	−	2.24457e11i	0.903470	−	0.903470i
$707$	−4.88568e8	−	4.88568e8i	−0.00195545	−	0.00195545i
$708$	−3.47890e10	+	3.47890e10i	−0.138455	+	0.138455i
$709$			1.10179e11i			0.436028i	0.975946	+	0.218014i	$0.0699578\pi$
$709$			1.10179e11i			0.436028i	−0.975946	+	0.218014i	$0.930042\pi$
$710$	1.00050e11	+	1.00050e11i	0.393715	+	0.393715i
$711$	1.57357e11	−	1.57357e11i	0.615753	−	0.615753i
$712$	−3.12388e11			−1.21555
$713$	−1.61170e9	−	1.61170e9i	−0.00623630	−	0.00623630i
$714$	−1.95864e8	+	1.95864e8i	−0.000753637	+	0.000753637i
$715$	−5.76615e11	−	5.76615e11i	−2.20629	−	2.20629i
$716$	−2.05565e11			−0.782164
$717$	9.89910e10	+	9.89910e10i	0.374558	+	0.374558i
$718$			4.30253e10i			0.161892i
$719$	9.48907e10			0.355065			0.177533	−	0.984115i	$-0.443188\pi$
$719$	9.48907e10			0.355065			0.177533	+	0.984115i	$0.443188\pi$
$720$	6.08548e10			0.226446
$721$	−1.05092e9			−0.00388890
$722$	1.41012e11	−	1.41012e11i	0.518929	−	0.518929i
$723$	1.77556e11	−	1.77556e11i	0.649805	−	0.649805i
$724$		−	1.63704e11i		−	0.595805i
$725$	−1.54602e10	+	1.47359e11i	−0.0559582	+	0.533367i
$726$	1.61155e11			0.580091
$727$	3.46238e11	+	3.46238e11i	1.23947	+	1.23947i	0.960217	+	0.279256i	$0.0900877\pi$
$727$	3.46238e11	+	3.46238e11i	1.23947	+	1.23947i	0.279256	+	0.960217i	$0.409912\pi$
$728$	2.80986e9	+	2.80986e9i	0.0100037	+	0.0100037i
$729$		−	2.13390e11i		−	0.755550i
$730$		−	1.49056e11i		−	0.524877i
$731$			1.32880e11i			0.465360i
$732$	1.10572e11			0.385125
$733$	2.70396e11	−	2.70396e11i	0.936666	−	0.936666i	−0.0614443	−	0.998111i	$-0.519571\pi$
$733$	2.70396e11	−	2.70396e11i	0.936666	−	0.936666i	0.998111	+	0.0614443i	$0.0195707\pi$
$734$		−	1.99253e11i		−	0.686468i
$735$	−1.69513e11	+	1.69513e11i	−0.580835	+	0.580835i
$736$	3.14417e9	+	3.14417e9i	0.0107151	+	0.0107151i
$737$	2.51179e11	−	2.51179e11i	0.851361	−	0.851361i
$738$		−	1.28592e11i		−	0.433498i
$739$	−1.26188e11	−	1.26188e11i	−0.423098	−	0.423098i	0.463171	−	0.886269i	$-0.346712\pi$
$739$	−1.26188e11	−	1.26188e11i	−0.423098	−	0.423098i	−0.886269	+	0.463171i	$0.846712\pi$
$740$	−1.86266e11	+	1.86266e11i	−0.621165	+	0.621165i
$741$	−2.85620e9			−0.00947362
$742$	1.07724e9	+	1.07724e9i	0.00355383	+	0.00355383i
$743$	−1.74849e10	+	1.74849e10i	−0.0573731	+	0.0573731i	−0.735211	−	0.677838i	$-0.762917\pi$
$743$	−1.74849e10	+	1.74849e10i	−0.0573731	+	0.0573731i	0.677838	+	0.735211i	$0.262917\pi$
$744$	−7.47017e10	−	7.47017e10i	−0.243803	−	0.243803i
$745$	−8.79209e10			−0.285409
$746$	−2.88026e11	−	2.88026e11i	−0.929987	−	0.929987i
$747$		−	2.62949e11i		−	0.844481i
$748$	−6.03918e10			−0.192917
$749$	1.46490e9			0.00465459
$750$	8.84575e10			0.279569
$751$	−2.18801e11	+	2.18801e11i	−0.687845	+	0.687845i	−0.961755	−	0.273910i	$-0.911683\pi$
$751$	−2.18801e11	+	2.18801e11i	−0.687845	+	0.687845i	0.273910	+	0.961755i	$0.411683\pi$
$752$	7.27259e10	−	7.27259e10i	0.227414	−	0.227414i
$753$			5.92163e10i			0.184188i
$754$	−2.53848e11	−	3.13356e11i	−0.785395	−	0.969511i
$755$	−1.91084e11			−0.588079
$756$	−8.55255e8	−	8.55255e8i	−0.00261823	−	0.00261823i
$757$	2.08753e11	+	2.08753e11i	0.635694	+	0.635694i	0.949490	−	0.313796i	$-0.101601\pi$
$757$	2.08753e11	+	2.08753e11i	0.635694	+	0.635694i	−0.313796	+	0.949490i	$0.601601\pi$
$758$			2.23845e11i			0.678064i
$759$		−	5.92180e9i		−	0.0178438i
$760$			3.72903e9i			0.0111774i
$761$	4.09826e11			1.22197			0.610986	−	0.791642i	$-0.290773\pi$
$761$	4.09826e11			1.22197			0.610986	+	0.791642i	$0.290773\pi$
$762$	−7.73398e10	+	7.73398e10i	−0.229395	+	0.229395i
$763$		−	1.27532e8i		−	0.000376290i
$764$	1.41716e11	−	1.41716e11i	0.415953	−	0.415953i
$765$	4.75335e10	+	4.75335e10i	0.138789	+	0.138789i
$766$	3.98047e10	−	3.98047e10i	0.115616	−	0.115616i
$767$		−	3.76774e11i		−	1.08868i
$768$	1.70237e11	+	1.70237e11i	0.489338	+	0.489338i
$769$	−1.40869e11	+	1.40869e11i	−0.402820	+	0.402820i	−0.879226	−	0.476405i	$-0.841939\pi$
$769$	−1.40869e11	+	1.40869e11i	−0.402820	+	0.402820i	0.476405	+	0.879226i	$0.341939\pi$
$770$	−3.67396e9			−0.0104513
$771$	−5.25467e10	−	5.25467e10i	−0.148706	−	0.148706i
$772$	1.10044e11	−	1.10044e11i	0.309811	−	0.309811i
$773$	3.53317e11	+	3.53317e11i	0.989570	+	0.989570i	0.999946	−	0.0103757i	$-0.00330275\pi$
$773$	3.53317e11	+	3.53317e11i	0.989570	+	0.989570i	−0.0103757	+	0.999946i	$0.503303\pi$
$774$	2.43394e11			0.678183
$775$	−6.63567e10	−	6.63567e10i	−0.183941	−	0.183941i
$776$		−	3.91446e11i		−	1.07951i
$777$	−2.87938e9			−0.00789977
$778$	−1.03631e10			−0.0282861
$779$	3.26146e9			0.00885650
$780$	−1.68636e11	+	1.68636e11i	−0.455587	+	0.455587i
$781$	−2.38437e11	+	2.38437e11i	−0.640868	+	0.640868i
$782$		−	1.40928e9i		−	0.00376851i
$783$	2.44742e11	+	3.02116e11i	0.651121	+	0.803760i
$784$	−1.23083e11			−0.325787
$785$	1.59873e11	+	1.59873e11i	0.421013	+	0.421013i
$786$	−3.00654e10	−	3.00654e10i	−0.0787730	−	0.0787730i
$787$		−	1.47166e10i		−	0.0383628i	−0.999816	−	0.0191814i	$-0.993894\pi$
$787$		−	1.47166e10i		−	0.0383628i	0.999816	−	0.0191814i	$-0.00610600\pi$
$788$			1.61756e9i			0.00419523i
$789$		−	3.16577e11i		−	0.816904i
$790$	−5.50240e11			−1.41268
$791$	−3.17866e9	+	3.17866e9i	−0.00811967	+	0.00811967i
$792$			3.50392e11i			0.890539i
$793$	−5.98763e11	+	5.98763e11i	−1.51413	+	1.51413i
$794$	8.71373e9	+	8.71373e9i	0.0219241	+	0.0219241i
$795$	−2.04787e11	+	2.04787e11i	−0.512665	+	0.512665i
$796$		−	2.39876e11i		−	0.597496i
$797$	1.44759e11	+	1.44759e11i	0.358767	+	0.358767i	0.863358	−	0.504592i	$-0.168357\pi$
$797$	1.44759e11	+	1.44759e11i	0.358767	+	0.358767i	−0.504592	+	0.863358i	$0.668357\pi$
$798$	−9.09928e6	+	9.09928e6i	−2.24386e−5	+	2.24386e-5i
$799$	1.13612e11			0.278764
$800$	1.29451e11	+	1.29451e11i	0.316042	+	0.316042i
$801$	−1.84991e11	+	1.84991e11i	−0.449386	+	0.449386i
$802$	2.75819e11	+	2.75819e11i	0.666695	+	0.666695i
$803$	3.55228e11			0.854367
$804$	−7.34594e10	−	7.34594e10i	−0.175802	−	0.175802i
$805$			7.34306e7i			0.000174861i
$806$	2.55415e11			0.605209
$807$	−3.52490e11			−0.831100
$808$	1.62934e11			0.382266
$809$	−2.48858e11	+	2.48858e11i	−0.580976	+	0.580976i	−0.935171	−	0.354195i	$-0.884755\pi$
$809$	−2.48858e11	+	2.48858e11i	−0.580976	+	0.580976i	0.354195	+	0.935171i	$0.384755\pi$
$810$	−3.45601e10	+	3.45601e10i	−0.0802850	+	0.0802850i
$811$		−	7.26707e11i		−	1.67987i	−0.542687	−	0.839935i	$-0.682593\pi$
$811$		−	7.26707e11i		−	1.67987i	0.542687	−	0.839935i	$-0.317407\pi$
$812$	1.54768e9	+	1.62375e8i	0.00356006	+	0.000373503i
$813$	3.22101e9			0.00737276
$814$	5.18284e11	+	5.18284e11i	1.18051	+	1.18051i
$815$	7.64154e11	+	7.64154e11i	1.73201	+	1.73201i
$816$		−	2.70359e10i		−	0.0609789i
$817$			6.17320e9i			0.0138555i
$818$			1.88828e11i			0.421747i
$819$	3.32790e9			0.00739663
$820$	1.92563e11	−	1.92563e11i	0.425910	−	0.425910i
$821$		−	5.58567e11i		−	1.22943i	−0.788750	−	0.614714i	$-0.789272\pi$
$821$		−	5.58567e11i		−	1.22943i	0.788750	−	0.614714i	$-0.210728\pi$
$822$	−2.02357e9	+	2.02357e9i	−0.00443232	+	0.00443232i
$823$	2.75565e11	+	2.75565e11i	0.600654	+	0.600654i	0.940486	−	0.339832i	$-0.110370\pi$
$823$	2.75565e11	+	2.75565e11i	0.600654	+	0.600654i	−0.339832	+	0.940486i	$0.610370\pi$
$824$	1.75236e11	−	1.75236e11i	0.380116	−	0.380116i
$825$		−	2.43811e11i		−	0.526304i
$826$	−1.20033e9	−	1.20033e9i	−0.00257857	−	0.00257857i
$827$	4.28226e11	−	4.28226e11i	0.915485	−	0.915485i	−0.0812120	−	0.996697i	$-0.525879\pi$
$827$	4.28226e11	−	4.28226e11i	0.915485	−	0.915485i	0.996697	+	0.0812120i	$0.0258791\pi$
$828$	2.21092e9			0.00470382
$829$	−4.53403e10	−	4.53403e10i	−0.0959989	−	0.0959989i	0.657476	−	0.753475i	$-0.271624\pi$
$829$	−4.53403e10	−	4.53403e10i	−0.0959989	−	0.0959989i	−0.753475	+	0.657476i	$0.771624\pi$
$830$	−4.59737e11	+	4.59737e11i	−0.968718	+	0.968718i
$831$	−9.57074e10	−	9.57074e10i	−0.200697	−	0.200697i
$832$	−7.63681e11			−1.59374
$833$	−9.61396e10	−	9.61396e10i	−0.199674	−	0.199674i
$834$			8.19146e10i			0.169316i
$835$	−7.44110e11			−1.53070
$836$	−2.80563e9			−0.00574387
$837$	−2.46253e11			−0.501741
$838$	−8.85115e10	+	8.85115e10i	−0.179483	+	0.179483i
$839$	−1.91652e11	+	1.91652e11i	−0.386782	+	0.386782i	−0.873538	−	0.486756i	$-0.838180\pi$
$839$	−1.91652e11	+	1.91652e11i	−0.386782	+	0.386782i	0.486756	+	0.873538i	$0.338180\pi$
$840$			3.40347e9i			0.00683605i
$841$	−4.89354e11	−	1.03824e11i	−0.978225	−	0.207545i
$842$	−2.85745e11			−0.568500
$843$	2.12341e11	+	2.12341e11i	0.420458	+	0.420458i
$844$	−9.21628e9	−	9.21628e9i	−0.0181629	−	0.0181629i
$845$		−	1.19445e12i		−	2.34283i
$846$		−	2.08102e11i		−	0.406251i
$847$		−	4.76237e9i		−	0.00925315i
$848$	−1.48695e11			−0.287550
$849$	−1.45756e11	+	1.45756e11i	−0.280541	+	0.280541i
$850$		−	5.80224e10i		−	0.111153i
$851$	1.03588e10	−	1.03588e10i	0.0197511	−	0.0197511i
$852$	6.97328e10	+	6.97328e10i	0.132336	+	0.132336i
$853$	−3.38553e11	+	3.38553e11i	−0.639486	+	0.639486i	−0.950429	−	0.310943i	$-0.899355\pi$
$853$	−3.38553e11	+	3.38553e11i	−0.639486	+	0.639486i	0.310943	+	0.950429i	$0.399355\pi$
$854$			3.81508e9i			0.00717252i
$855$	2.20827e9	+	2.20827e9i	0.00413226	+	0.00413226i
$856$	−2.44267e11	+	2.44267e11i	−0.454957	+	0.454957i
$857$	−1.83014e10			−0.0339282			−0.0169641	−	0.999856i	$-0.505400\pi$
$857$	−1.83014e10			−0.0339282			−0.0169641	+	0.999856i	$0.505400\pi$
$858$	4.69228e11	+	4.69228e11i	0.865834	+	0.865834i
$859$	−5.51754e11	+	5.51754e11i	−1.01338	+	1.01338i	−0.0134712	+	0.999909i	$0.504288\pi$
$859$	−5.51754e11	+	5.51754e11i	−1.01338	+	1.01338i	−0.999909	+	0.0134712i	$0.995712\pi$
$860$	3.64478e11	+	3.64478e11i	0.666313	+	0.666313i
$861$	2.97672e9			0.00541659
$862$	−4.66101e11	−	4.66101e11i	−0.844211	−	0.844211i
$863$		−	2.75969e11i		−	0.497528i	−0.968564	−	0.248764i	$-0.919976\pi$
$863$		−	2.75969e11i		−	0.497528i	0.968564	−	0.248764i	$-0.0800244\pi$
$864$	4.80399e11			0.862078
$865$	7.83305e11			1.39916
$866$	4.74018e11			0.842798
$867$	−2.43682e11	+	2.43682e11i	−0.431269	+	0.431269i
$868$	−6.96927e8	+	6.96927e8i	−0.00122775	+	0.00122775i
$869$		−	1.31132e12i		−	2.29949i
$870$	3.60400e10	−	3.43516e11i	0.0629082	−	0.599612i
$871$	7.95585e11			1.38234
$872$	2.12656e10	+	2.12656e10i	0.0367800	+	0.0367800i
$873$	−2.31807e11	−	2.31807e11i	−0.399090	−	0.399090i
$874$		−	6.54710e7i		−	0.000112203i
$875$		−	2.61406e9i		−	0.00445947i
$876$		−	1.03889e11i		−	0.176423i
$877$	3.18641e11			0.538646			0.269323	−	0.963050i	$-0.413200\pi$
$877$	3.18641e11			0.538646			0.269323	+	0.963050i	$0.413200\pi$
$878$	−3.34546e11	+	3.34546e11i	−0.562960	+	0.562960i
$879$			4.07833e11i			0.683168i
$880$	2.53565e11	−	2.53565e11i	0.422824	−	0.422824i
$881$	1.21262e11	+	1.21262e11i	0.201289	+	0.201289i	0.800552	−	0.599263i	$-0.204540\pi$
$881$	1.21262e11	+	1.21262e11i	0.201289	+	0.201289i	−0.599263	+	0.800552i	$0.704540\pi$
$882$	−1.76098e11	+	1.76098e11i	−0.290992	+	0.290992i
$883$			8.10089e11i			1.33257i	0.745697	+	0.666285i	$0.232116\pi$
$883$			8.10089e11i			1.33257i	−0.745697	+	0.666285i	$0.767884\pi$
$884$	−9.56424e10	−	9.56424e10i	−0.156618	−	0.156618i
$885$	2.28186e11	−	2.28186e11i	0.371977	−	0.371977i
$886$	6.34687e11			1.02997
$887$	−6.93281e11	−	6.93281e11i	−1.11999	−	1.11999i	−0.991742	−	0.128249i	$-0.959064\pi$
$887$	−6.93281e11	−	6.93281e11i	−1.11999	−	1.11999i	−0.128249	−	0.991742i	$-0.540936\pi$
$888$	4.80126e11	−	4.80126e11i	0.772153	−	0.772153i
$889$	2.28551e9	+	2.28551e9i	0.00365912	+	0.00365912i
$890$	6.46870e11			1.03100
$891$	−8.23630e10	−	8.23630e10i	−0.130684	−	0.130684i
$892$			6.74284e10i			0.106508i
$893$	5.27808e9			0.00829985
$894$	7.15468e10			0.112006
$895$	1.34833e12			2.10138
$896$	5.14052e8	−	5.14052e8i	0.000797581	−	0.000797581i
$897$	9.37835e9	−	9.37835e9i	0.0144863	−	0.0144863i
$898$			8.00943e11i			1.23168i
$899$	2.46187e11	−	1.99435e11i	0.376900	−	0.305325i
$900$	9.10273e10			0.138740
$901$	−1.16145e11	−	1.16145e11i	−0.176239	−	0.176239i
$902$	−5.35806e11	−	5.35806e11i	−0.809433	−	0.809433i
$903$			5.63426e9i			0.00847394i
$904$		−	1.06006e12i		−	1.58729i
$905$			1.07376e12i			1.60070i
$906$	1.55497e11			0.230786
$907$	−3.57733e10	+	3.57733e10i	−0.0528603	+	0.0528603i	−0.733043	−	0.680183i	$-0.761901\pi$
$907$	−3.57733e10	+	3.57733e10i	−0.0528603	+	0.0528603i	0.680183	+	0.733043i	$0.261901\pi$
$908$			4.17516e11i			0.614228i
$909$	9.64866e10	−	9.64866e10i	0.141323	−	0.141323i
$910$	−5.81845e9	−	5.81845e9i	−0.00848480	−	0.00848480i
$911$	−3.92311e11	+	3.92311e11i	−0.569583	+	0.569583i	−0.932011	−	0.362429i	$-0.881948\pi$
$911$	−3.92311e11	+	3.92311e11i	−0.569583	+	0.569583i	0.362429	+	0.932011i	$0.381948\pi$
$912$		−	1.25601e9i		−	0.00181557i
$913$	−1.09564e12	−	1.09564e12i	−1.57683	−	1.57683i
$914$	−8.09119e10	+	8.09119e10i	−0.115938	+	0.115938i
$915$	−7.25259e11			−1.03469
$916$	1.14728e11	+	1.14728e11i	0.162962	+	0.162962i
$917$	−8.88481e8	+	8.88481e8i	−0.00125652	+	0.00125652i
$918$	−1.07662e11	−	1.07662e11i	−0.151597	−	0.151597i
$919$	−4.58765e11			−0.643174			−0.321587	−	0.946880i	$-0.604216\pi$
$919$	−4.58765e11			−0.643174			−0.321587	+	0.946880i	$0.604216\pi$
$920$	−1.22443e10	−	1.22443e10i	−0.0170916	−	0.0170916i
$921$		−	9.87238e10i		−	0.137209i
$922$	−4.11251e11			−0.569093
$923$	−7.55224e11			−1.04056
$924$	−2.56068e9			−0.00351292
$925$	4.26490e11	−	4.26490e11i	0.582562	−	0.582562i
$926$	5.84096e11	−	5.84096e11i	0.794402	−	0.794402i
$927$		−	2.07544e11i		−	0.281055i
$928$	−4.80270e11	+	3.89064e11i	−0.647581	+	0.524601i
$929$	−9.90555e11			−1.32989			−0.664945	−	0.746893i	$-0.731545\pi$
$929$	−9.90555e11			−1.32989			−0.664945	+	0.746893i	$0.731545\pi$
$930$	1.54687e11	+	1.54687e11i	0.206786	+	0.206786i
$931$	−4.46637e9	−	4.46637e9i	−0.00594505	−	0.00594505i
$932$		−	6.73637e11i		−	0.892816i
$933$		−	2.43786e11i		−	0.321723i
$934$		−	7.89052e11i		−	1.03686i
$935$	3.96118e11			0.518296
$936$	−5.54915e11	+	5.54915e11i	−0.722975	+	0.722975i
$937$		−	8.98786e11i		−	1.16600i	−0.812473	−	0.582999i	$-0.801879\pi$
$937$		−	8.98786e11i		−	1.16600i	0.812473	−	0.582999i	$-0.198121\pi$
$938$	2.53457e9	−	2.53457e9i	0.00327411	−	0.00327411i
$939$	3.82432e11	+	3.82432e11i	0.491917	+	0.491917i
$940$	3.11628e11	−	3.11628e11i	0.399140	−	0.399140i
$941$			9.62446e11i			1.22749i	0.789504	+	0.613745i	$0.210338\pi$
$941$			9.62446e11i			1.22749i	−0.789504	+	0.613745i	$0.789662\pi$
$942$	−1.30098e11	−	1.30098e11i	−0.165222	−	0.165222i
$943$	−1.07090e10	+	1.07090e10i	−0.0135426	+	0.0135426i
$944$	1.65685e11			0.208639
$945$	5.60974e9	+	5.60974e9i	0.00703421	+	0.00703421i
$946$	1.01416e12	−	1.01416e12i	1.26631	−	1.26631i
$947$	1.67004e11	+	1.67004e11i	0.207648	+	0.207648i	0.803267	−	0.595619i	$-0.203093\pi$
$947$	1.67004e11	+	1.67004e11i	0.207648	+	0.207648i	−0.595619	+	0.803267i	$0.703093\pi$
$948$	−3.83508e11			−0.474833
$949$	5.62574e11	+	5.62574e11i	0.693609	+	0.693609i
$950$		−	2.69555e9i		−	0.00330943i
$951$	5.00806e11			0.612276
$952$	−1.93029e9			−0.00235004
$953$	−7.41867e11			−0.899403			−0.449702	−	0.893179i	$-0.648470\pi$
$953$	−7.41867e11			−0.899403			−0.449702	+	0.893179i	$0.648470\pi$
$954$	−2.12743e11	+	2.12743e11i	−0.256839	+	0.256839i
$955$	−9.29533e11	+	9.29533e11i	−1.11751	+	1.11751i
$956$			3.07992e11i			0.368730i
$957$	8.18662e11	+	8.58899e10i	0.976016	+	0.102399i
$958$	9.19054e11			1.09114
$959$	5.97997e7	+	5.97997e7i	7.07008e−5	+	7.07008e-5i
$960$	−4.62509e11	−	4.62509e11i	−0.544546	−	0.544546i
$961$		−	6.52225e11i		−	0.764723i
$962$			1.64161e12i			1.91677i
$963$			2.89302e11i			0.336392i
$964$	5.52433e11			0.639693
$965$	−7.21794e11	+	7.21794e11i	−0.832346	+	0.832346i
$966$		−	5.97551e7i		−	6.86224e-5i
$967$	−4.61156e11	+	4.61156e11i	−0.527403	+	0.527403i	−0.919797	−	0.392394i	$-0.871647\pi$
$967$	−4.61156e11	+	4.61156e11i	−0.527403	+	0.527403i	0.392394	+	0.919797i	$0.371647\pi$
$968$	7.94109e11	+	7.94109e11i	0.904438	+	0.904438i
$969$	9.81064e8	−	9.81064e8i	0.00111276	−	0.00111276i
$970$			8.10578e11i			0.915605i
$971$	−9.06355e11	−	9.06355e11i	−1.01958	−	1.01958i	−0.999804	−	0.0197763i	$-0.993705\pi$
$971$	−9.06355e11	−	9.06355e11i	−1.01958	−	1.01958i	−0.0197763	−	0.999804i	$-0.506295\pi$
$972$	2.77123e11	−	2.77123e11i	0.310461	−	0.310461i
$973$	2.42070e9			0.00270079
$974$	1.57113e11	+	1.57113e11i	0.174572	+	0.174572i
$975$	3.86123e11	−	3.86123e11i	0.427275	−	0.427275i
$976$	−2.63305e11	−	2.63305e11i	−0.290175	−	0.290175i
$977$	7.91809e11			0.869045			0.434523	−	0.900661i	$-0.356917\pi$
$977$	7.91809e11			0.869045			0.434523	+	0.900661i	$0.356917\pi$
$978$	−6.21840e11	−	6.21840e11i	−0.679710	−	0.679710i
$979$			1.54161e12i			1.67820i
$980$	−5.27407e11			−0.571796
$981$	2.51862e10			0.0271949
$982$	5.08973e11			0.547329
$983$	1.94511e11	−	1.94511e11i	0.208320	−	0.208320i	−0.595233	−	0.803553i	$-0.702940\pi$
$983$	1.94511e11	−	1.94511e11i	0.208320	−	0.208320i	0.803553	+	0.595233i	$0.202940\pi$
$984$	−4.96358e11	+	4.96358e11i	−0.529437	+	0.529437i
$985$		−	1.06098e10i		−	0.0112710i
$986$	1.94826e11	+	2.04402e10i	0.206129	+	0.0216261i
$987$	4.81728e9			0.00507614
$988$	−4.44327e9	−	4.44327e9i	−0.00466310	−	0.00466310i
$989$	−2.02697e10	−	2.02697e10i	−0.0211867	−	0.0211867i
$990$		−	7.25566e11i		−	0.755329i
$991$			1.70074e12i			1.76337i	0.471835	+	0.881687i	$0.343592\pi$
$991$			1.70074e12i			1.76337i	−0.471835	+	0.881687i	$0.656408\pi$
$992$		−	3.91466e11i		−	0.404247i
$993$	7.97853e11			0.820590
$994$	−2.40599e9	+	2.40599e9i	−0.00246461	+	0.00246461i
$995$			1.57338e12i			1.60525i
$996$	−3.20428e11	+	3.20428e11i	−0.325607	+	0.325607i
$997$	−8.20440e11	−	8.20440e11i	−0.830359	−	0.830359i	0.157207	−	0.987566i	$-0.449751\pi$
$997$	−8.20440e11	−	8.20440e11i	−0.830359	−	0.830359i	−0.987566	+	0.157207i	$0.949751\pi$
$998$	−7.50229e11	+	7.50229e11i	−0.756261	+	0.756261i
$999$		−	1.58273e12i		−	1.58907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.13	✓	38
29.17	odd	4	inner	29.9.c.a.17.13	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.13	✓	38	1.1	even	1	trivial
29.9.c.a.17.13	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)

\(f(q)\)	\(=\)	\(q+(8.30345 + 8.30345i) q^{2} +(-37.9600 - 37.9600i) q^{3} -118.106i q^{4} +774.671i q^{5} -630.398i q^{6} -18.6293 q^{7} +(3106.37 - 3106.37i) q^{8} -3679.07i q^{9} +O(q^{10})\)	\(q+(8.30345 + 8.30345i) q^{2} +(-37.9600 - 37.9600i) q^{3} -118.106i q^{4} +774.671i q^{5} -630.398i q^{6} -18.6293 q^{7} +(3106.37 - 3106.37i) q^{8} -3679.07i q^{9} +(-6432.44 + 6432.44i) q^{10} +(-15329.7 - 15329.7i) q^{11} +(-4483.29 + 4483.29i) q^{12} -48555.2i q^{13} +(-154.687 - 154.687i) q^{14} +(29406.5 - 29406.5i) q^{15} +21352.0 q^{16} +(16678.0 + 16678.0i) q^{17} +(30549.0 - 30549.0i) q^{18} +(774.812 + 774.812i) q^{19} +91492.9 q^{20} +(707.168 + 707.168i) q^{21} -254578. i q^{22} -5088.20 q^{23} -235836. q^{24} -209490. q^{25} +(403176. - 403176. i) q^{26} +(-388713. + 388713. i) q^{27} +2200.22i q^{28} +(73799.3 - 703420. i) q^{29} +488351. q^{30} +(316754. + 316754. i) q^{31} +(-617934. - 617934. i) q^{32} +1.16383e6i q^{33} +276970. i q^{34} -14431.5i q^{35} -434519. q^{36} +(-2.03585e6 + 2.03585e6i) q^{37} +12867.2i q^{38} +(-1.84316e6 + 1.84316e6i) q^{39} +(2.40641e6 + 2.40641e6i) q^{40} +(2.10468e6 - 2.10468e6i) q^{41} +11743.9i q^{42} +(3.98368e6 + 3.98368e6i) q^{43} +(-1.81052e6 + 1.81052e6i) q^{44} +2.85007e6 q^{45} +(-42249.6 - 42249.6i) q^{46} +(3.40604e6 - 3.40604e6i) q^{47} +(-810525. - 810525. i) q^{48} -5.76445e6 q^{49} +(-1.73949e6 - 1.73949e6i) q^{50} -1.26620e6i q^{51} -5.73464e6 q^{52} -6.96399e6 q^{53} -6.45532e6 q^{54} +(1.18755e7 - 1.18755e7i) q^{55} +(-57869.3 + 57869.3i) q^{56} -58823.8i q^{57} +(6.45360e6 - 5.22802e6i) q^{58} +7.75970e6 q^{59} +(-3.47308e6 - 3.47308e6i) q^{60} +(-1.23316e7 - 1.23316e7i) q^{61} +5.26029e6i q^{62} +68538.4i q^{63} -1.57281e7i q^{64} +3.76143e7 q^{65} +(-9.66380e6 + 9.66380e6i) q^{66} +1.63852e7i q^{67} +(1.96977e6 - 1.96977e6i) q^{68} +(193148. + 193148. i) q^{69} +(119832. - 119832. i) q^{70} -1.55539e7i q^{71} +(-1.14285e7 - 1.14285e7i) q^{72} +(-1.15863e7 + 1.15863e7i) q^{73} -3.38092e7 q^{74} +(7.95225e6 + 7.95225e6i) q^{75} +(91509.6 - 91509.6i) q^{76} +(285581. + 285581. i) q^{77} -3.06091e7 q^{78} +(4.27708e7 + 4.27708e7i) q^{79} +1.65408e7i q^{80} +5.37278e6 q^{81} +3.49522e7 q^{82} +7.14717e7 q^{83} +(83520.4 - 83520.4i) q^{84} +(-1.29200e7 + 1.29200e7i) q^{85} +6.61565e7i q^{86} +(-2.95033e7 + 2.39004e7i) q^{87} -9.52392e7 q^{88} +(-5.02819e7 - 5.02819e7i) q^{89} +(2.36654e7 + 2.36654e7i) q^{90} +904548. i q^{91} +600945. i q^{92} -2.40480e7i q^{93} +5.65637e7 q^{94} +(-600224. + 600224. i) q^{95} +4.69136e7i q^{96} +(6.30071e7 - 6.30071e7i) q^{97} +(-4.78648e7 - 4.78648e7i) q^{98} +(-5.63990e7 + 5.63990e7i) 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

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