LMFDB - Embedded newform 15.9.d.c.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,9,Mod(14,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("15.14");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	15.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.11067915092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2096 x^{10} + 1966565 x^{8} + 942732880 x^{6} + 407378811520 x^{4} + 58185108489824 x^{2} + 32\!\cdots\!64 $ x^12 + 2096x^10 + 1966565x^8 + 942732880x^6 + 407378811520x^4 + 58185108489824*x^2 + 3250133486843364
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{18}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.6
Root			$2.83292 + 10.0603i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.9.d.c.14.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.66585 q^{2} +(-35.3550 + 72.8768i) q^{3} -223.898 q^{4} +(531.836 - 328.291i) q^{5} +(200.316 - 412.909i) q^{6} -1674.62i q^{7} +2719.03 q^{8} +(-4061.05 - 5153.12i) q^{9} +O(q^{10})$	\(q-5.66585 q^{2} +(-35.3550 + 72.8768i) q^{3} -223.898 q^{4} +(531.836 - 328.291i) q^{5} +(200.316 - 412.909i) q^{6} -1674.62i q^{7} +2719.03 q^{8} +(-4061.05 - 5153.12i) q^{9} +(-3013.30 + 1860.05i) q^{10} -21417.9i q^{11} +(7915.92 - 16317.0i) q^{12} +5980.82i q^{13} +9488.16i q^{14} +(5121.72 + 50365.3i) q^{15} +41912.3 q^{16} -69210.3 q^{17} +(23009.3 + 29196.8i) q^{18} -18044.8 q^{19} +(-119077. + 73503.8i) q^{20} +(122041. + 59206.3i) q^{21} +121351. i q^{22} -91800.0 q^{23} +(-96131.3 + 198154. i) q^{24} +(175075. - 349194. i) q^{25} -33886.4i q^{26} +(519121. - 113768. i) q^{27} +374945. i q^{28} -1.12754e6i q^{29} +(-29018.9 - 285362. i) q^{30} -1.27927e6 q^{31} -933541. q^{32} +(1.56087e6 + 757230. i) q^{33} +392135. q^{34} +(-549764. - 890626. i) q^{35} +(909261. + 1.15377e6i) q^{36} -2.19804e6i q^{37} +102239. q^{38} +(-435863. - 211452. i) q^{39} +(1.44608e6 - 892633. i) q^{40} +29007.4i q^{41} +(-691466. - 335454. i) q^{42} +6.78169e6i q^{43} +4.79543e6i q^{44} +(-3.85154e6 - 1.40741e6i) q^{45} +520125. q^{46} -1.96089e6 q^{47} +(-1.48181e6 + 3.05443e6i) q^{48} +2.96044e6 q^{49} +(-991948. + 1.97848e6i) q^{50} +(2.44693e6 - 5.04382e6i) q^{51} -1.33909e6i q^{52} +1.23039e7 q^{53} +(-2.94126e6 + 644591. i) q^{54} +(-7.03131e6 - 1.13908e7i) q^{55} -4.55335e6i q^{56} +(637973. - 1.31504e6i) q^{57} +6.38847e6i q^{58} -5.58621e6i q^{59} +(-1.14674e6 - 1.12767e7i) q^{60} +312034. q^{61} +7.24817e6 q^{62} +(-8.62953e6 + 6.80073e6i) q^{63} -5.44025e6 q^{64} +(1.96345e6 + 3.18082e6i) q^{65} +(-8.84365e6 - 4.29035e6i) q^{66} -853503. i q^{67} +1.54961e7 q^{68} +(3.24559e6 - 6.69009e6i) q^{69} +(3.11488e6 + 5.04615e6i) q^{70} +3.18282e7i q^{71} +(-1.10421e7 - 1.40115e7i) q^{72} +2.36800e6i q^{73} +1.24537e7i q^{74} +(1.92584e7 + 2.51047e7i) q^{75} +4.04019e6 q^{76} -3.58669e7 q^{77} +(2.46953e6 + 1.19805e6i) q^{78} +2.92328e7 q^{79} +(2.22905e7 - 1.37594e7i) q^{80} +(-1.00625e7 + 4.18541e7i) q^{81} -164351. i q^{82} -6.73076e7 q^{83} +(-2.73248e7 - 1.32562e7i) q^{84} +(-3.68086e7 + 2.27211e7i) q^{85} -3.84240e7i q^{86} +(8.21715e7 + 3.98642e7i) q^{87} -5.82360e7i q^{88} -4.90240e7i q^{89} +(2.18222e7 + 7.97416e6i) q^{90} +1.00156e7 q^{91} +2.05539e7 q^{92} +(4.52287e7 - 9.32293e7i) q^{93} +1.11101e7 q^{94} +(-9.59686e6 + 5.92394e6i) q^{95} +(3.30053e7 - 6.80334e7i) q^{96} +7.18400e7i q^{97} -1.67734e7 q^{98} +(-1.10369e8 + 8.69792e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9}+O(q^{10}) $ 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9	$ 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9} - 35280 q^{10} - 95520 q^{15} + 413328 q^{16} + 276192 q^{19} - 604044 q^{21} + 1173336 q^{24} - 2036220 q^{25} + 3563460 q^{30} - 279216 q^{31} - 1225344 q^{34} - 10311840 q^{36} + 3780864 q^{39} - 3347040 q^{40} + 9523980 q^{45} + 37414536 q^{46} - 6222300 q^{49} + 3931248 q^{51} - 53281692 q^{54} - 16903440 q^{55} + 9900720 q^{60} - 91958256 q^{61} + 57497760 q^{64} + 111065040 q^{66} + 8138748 q^{69} + 3903480 q^{70} + 15031440 q^{75} - 232646880 q^{76} + 420402672 q^{79} + 98480772 q^{81} - 528357816 q^{84} - 117091440 q^{85} + 218602080 q^{90} - 100211328 q^{91} + 543022776 q^{94} + 333306864 q^{96} - 640360080 q^{99}+O(q^{100}) $ 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9 - 35280 * q^10 - 95520 * q^15 + 413328 * q^16 + 276192 * q^19 - 604044 * q^21 + 1173336 * q^24 - 2036220 * q^25 + 3563460 * q^30 - 279216 * q^31 - 1225344 * q^34 - 10311840 * q^36 + 3780864 * q^39 - 3347040 * q^40 + 9523980 * q^45 + 37414536 * q^46 - 6222300 * q^49 + 3931248 * q^51 - 53281692 * q^54 - 16903440 * q^55 + 9900720 * q^60 - 91958256 * q^61 + 57497760 * q^64 + 111065040 * q^66 + 8138748 * q^69 + 3903480 * q^70 + 15031440 * q^75 - 232646880 * q^76 + 420402672 * q^79 + 98480772 * q^81 - 528357816 * q^84 - 117091440 * q^85 + 218602080 * q^90 - 100211328 * q^91 + 543022776 * q^94 + 333306864 * q^96 - 640360080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.66585			−0.354116			−0.177058	−	0.984200i	$-0.556658\pi$
$2$	−5.66585			−0.354116			−0.177058	+	0.984200i	$0.556658\pi$
$3$	−35.3550	+	72.8768i	−0.436481	+	0.899713i
$3$	−35.3550	+	72.8768i	−0.436481	+	0.899713i
$4$	−223.898			−0.874602
$5$	531.836	−	328.291i	0.850938	−	0.525266i
$5$	531.836	−	328.291i	0.850938	−	0.525266i
$6$	200.316	−	412.909i	0.154565	−	0.318602i
$7$		−	1674.62i		−	0.697469i	−0.937222	−	0.348734i	$-0.886612\pi$
$7$		−	1674.62i		−	0.697469i	0.937222	−	0.348734i	$-0.113388\pi$
$8$	2719.03			0.663826
$9$	−4061.05	−	5153.12i	−0.618968	−	0.785416i
$10$	−3013.30	+	1860.05i	−0.301330	+	0.186005i
$11$		−	21417.9i		−	1.46287i	−0.681910	−	0.731436i	$-0.738850\pi$
$11$		−	21417.9i		−	1.46287i	0.681910	−	0.731436i	$-0.261150\pi$
$12$	7915.92	−	16317.0i	0.381748	−	0.786891i
$13$			5980.82i			0.209405i	0.994504	+	0.104703i	$0.0333890\pi$
$13$			5980.82i			0.209405i	−0.994504	+	0.104703i	$0.966611\pi$
$14$			9488.16i			0.246985i
$15$	5121.72	+	50365.3i	0.101170	+	0.994869i
$16$	41912.3			0.639531
$17$	−69210.3			−0.828657			−0.414329	−	0.910127i	$-0.635984\pi$
$17$	−69210.3			−0.828657			−0.414329	+	0.910127i	$0.635984\pi$
$18$	23009.3	+	29196.8i	0.219186	+	0.278128i
$19$	−18044.8			−0.138464			−0.0692320	−	0.997601i	$-0.522055\pi$
$19$	−18044.8			−0.138464			−0.0692320	+	0.997601i	$0.522055\pi$
$20$	−119077.	+	73503.8i	−0.744233	+	0.459399i
$21$	122041.	+	59206.3i	0.627522	+	0.304432i
$22$			121351.i			0.518026i
$23$	−91800.0			−0.328043			−0.164022	−	0.986457i	$-0.552447\pi$
$23$	−91800.0			−0.328043			−0.164022	+	0.986457i	$0.552447\pi$
$24$	−96131.3	+	198154.i	−0.289748	+	0.597253i
$25$	175075.	−	349194.i	0.448192	−	0.893937i
$26$		−	33886.4i		−	0.0741536i
$27$	519121.	−	113768.i	0.976817	−	0.214074i
$28$			374945.i			0.610008i
$29$		−	1.12754e6i		−	1.59419i	−0.603854	−	0.797095i	$-0.706369\pi$
$29$		−	1.12754e6i		−	1.59419i	0.603854	−	0.797095i	$-0.293631\pi$
$30$	−29018.9	−	285362.i	−0.0358258	−	0.352299i
$31$	−1.27927e6			−1.38521			−0.692607	−	0.721316i	$-0.743538\pi$
$31$	−1.27927e6			−1.38521			−0.692607	+	0.721316i	$0.743538\pi$
$32$	−933541.			−0.890294
$33$	1.56087e6	+	757230.i	1.31617	+	0.638517i
$34$	392135.			0.293440
$35$	−549764.	−	890626.i	−0.366356	−	0.593503i
$36$	909261.	+	1.15377e6i	0.541351	+	0.686927i
$37$		−	2.19804e6i		−	1.17281i	−0.810018	−	0.586405i	$-0.800543\pi$
$37$		−	2.19804e6i		−	1.17281i	0.810018	−	0.586405i	$-0.199457\pi$
$38$	102239.			0.0490322
$39$	−435863.	−	211452.i	−0.188404	−	0.0914014i
$40$	1.44608e6	−	892633.i	0.564875	−	0.348685i
$41$			29007.4i			0.0102653i	0.999987	+	0.00513267i	$0.00163379\pi$
$41$			29007.4i			0.0102653i	−0.999987	+	0.00513267i	$0.998366\pi$
$42$	−691466.	−	335454.i	−0.222215	−	0.107804i
$43$			6.78169e6i			1.98365i	0.127625	+	0.991823i	$0.459265\pi$
$43$			6.78169e6i			1.98365i	−0.127625	+	0.991823i	$0.540735\pi$
$44$			4.79543e6i			1.27943i
$45$	−3.85154e6	−	1.40741e6i	−0.939256	−	0.343218i
$46$	520125.			0.116165
$47$	−1.96089e6			−0.401847			−0.200924	−	0.979607i	$-0.564394\pi$
$47$	−1.96089e6			−0.401847			−0.200924	+	0.979607i	$0.564394\pi$
$48$	−1.48181e6	+	3.05443e6i	−0.279143	+	0.575395i
$49$	2.96044e6			0.513537
$50$	−991948.	+	1.97848e6i	−0.158712	+	0.316557i
$51$	2.44693e6	−	5.04382e6i	0.361694	−	0.745554i
$52$		−	1.33909e6i		−	0.183146i
$53$	1.23039e7			1.55933			0.779664	−	0.626198i	$-0.215390\pi$
$53$	1.23039e7			1.55933			0.779664	+	0.626198i	$0.215390\pi$
$54$	−2.94126e6	+	644591.i	−0.345906	+	0.0758070i
$55$	−7.03131e6	−	1.13908e7i	−0.768397	−	1.24481i
$56$		−	4.55335e6i		−	0.462998i
$57$	637973.	−	1.31504e6i	0.0604370	−	0.124578i
$58$			6.38847e6i			0.564527i
$59$		−	5.58621e6i		−	0.461009i	−0.973071	−	0.230504i	$-0.925962\pi$
$59$		−	5.58621e6i		−	0.461009i	0.973071	−	0.230504i	$-0.0740376\pi$
$60$	−1.14674e6	−	1.12767e7i	−0.0884833	−	0.870115i
$61$	312034.			0.0225363			0.0112681	−	0.999937i	$-0.496413\pi$
$61$	312034.			0.0225363			0.0112681	+	0.999937i	$0.496413\pi$
$62$	7.24817e6			0.490525
$63$	−8.62953e6	+	6.80073e6i	−0.547803	+	0.431711i
$64$	−5.44025e6			−0.324264
$65$	1.96345e6	+	3.18082e6i	0.109993	+	0.178191i
$66$	−8.84365e6	−	4.29035e6i	−0.466075	−	0.226109i
$67$		−	853503.i		−	0.0423551i	−0.999776	−	0.0211775i	$-0.993258\pi$
$67$		−	853503.i		−	0.0423551i	0.999776	−	0.0211775i	$-0.00674153\pi$
$68$	1.54961e7			0.724746
$69$	3.24559e6	−	6.69009e6i	0.143185	−	0.295145i
$70$	3.11488e6	+	5.04615e6i	0.129733	+	0.210169i
$71$			3.18282e7i			1.25250i	0.779621	+	0.626252i	$0.215412\pi$
$71$			3.18282e7i			1.25250i	−0.779621	+	0.626252i	$0.784588\pi$
$72$	−1.10421e7	−	1.40115e7i	−0.410887	−	0.521379i
$73$			2.36800e6i			0.0833855i	0.999130	+	0.0416927i	$0.0132751\pi$
$73$			2.36800e6i			0.0833855i	−0.999130	+	0.0416927i	$0.986725\pi$
$74$			1.24537e7i			0.415310i
$75$	1.92584e7	+	2.51047e7i	0.608660	+	0.793431i
$76$	4.04019e6			0.121101
$77$	−3.58669e7			−1.02031
$78$	2.46953e6	+	1.19805e6i	0.0667170	+	0.0323667i
$79$	2.92328e7			0.750520			0.375260	−	0.926920i	$-0.377553\pi$
$79$	2.92328e7			0.750520			0.375260	+	0.926920i	$0.377553\pi$
$80$	2.22905e7	−	1.37594e7i	0.544202	−	0.335924i
$81$	−1.00625e7	+	4.18541e7i	−0.233757	+	0.972295i
$82$		−	164351.i		−	0.00363512i
$83$	−6.73076e7			−1.41825			−0.709124	−	0.705084i	$-0.750909\pi$
$83$	−6.73076e7			−1.41825			−0.709124	+	0.705084i	$0.750909\pi$
$84$	−2.73248e7	−	1.32562e7i	−0.548832	−	0.266257i
$85$	−3.68086e7	+	2.27211e7i	−0.705136	+	0.435265i
$86$		−	3.84240e7i		−	0.702439i
$87$	8.21715e7	+	3.98642e7i	1.43431	+	0.695834i
$88$		−	5.82360e7i		−	0.971093i
$89$		−	4.90240e7i		−	0.781355i	−0.920528	−	0.390678i	$-0.872241\pi$
$89$		−	4.90240e7i		−	0.781355i	0.920528	−	0.390678i	$-0.127759\pi$
$90$	2.18222e7	+	7.97416e6i	0.332605	+	0.121539i
$91$	1.00156e7			0.146054
$92$	2.05539e7			0.286908
$93$	4.52287e7	−	9.32293e7i	0.604620	−	1.24629i
$94$	1.11101e7			0.142300
$95$	−9.59686e6	+	5.92394e6i	−0.117824	+	0.0727304i
$96$	3.30053e7	−	6.80334e7i	0.388597	−	0.801009i
$97$			7.18400e7i			0.811483i	0.913988	+	0.405741i	$0.132987\pi$
$97$			7.18400e7i			0.811483i	−0.913988	+	0.405741i	$0.867013\pi$
$98$	−1.67734e7			−0.181851
$99$	−1.10369e8	+	8.69792e7i	−1.14896	+	0.905471i
$100$	−3.91990e7	+	7.81840e7i	−0.391990	+	0.781840i
$101$		−	1.12197e8i		−	1.07819i	−0.842244	−	0.539097i	$-0.818766\pi$
$101$		−	1.12197e8i		−	1.07819i	0.842244	−	0.539097i	$-0.181234\pi$
$102$	−1.38639e7	+	2.85775e7i	−0.128081	+	0.264012i
$103$		−	1.33889e8i		−	1.18959i	−0.803877	−	0.594795i	$-0.797233\pi$
$103$		−	1.33889e8i		−	1.18959i	0.803877	−	0.594795i	$-0.202767\pi$
$104$			1.62620e7i			0.139008i
$105$	8.43428e7	−	8.57695e6i	0.693890	−	0.0705628i
$106$	−6.97118e7			−0.552183
$107$	−3.67153e7			−0.280100			−0.140050	−	0.990144i	$-0.544726\pi$
$107$	−3.67153e7			−0.280100			−0.140050	+	0.990144i	$0.544726\pi$
$108$	−1.16230e8	+	2.54724e7i	−0.854327	+	0.187230i
$109$	1.68006e8			1.19020			0.595099	−	0.803652i	$-0.297113\pi$
$109$	1.68006e8			1.19020			0.595099	+	0.803652i	$0.297113\pi$
$110$	3.98383e7	+	6.45387e7i	0.272101	+	0.440808i
$111$	1.60186e8	+	7.77115e7i	1.05519	+	0.511910i
$112$		−	7.01873e7i		−	0.446053i
$113$	−9.78362e7			−0.600048			−0.300024	−	0.953932i	$-0.596995\pi$
$113$	−9.78362e7			−0.600048			−0.300024	+	0.953932i	$0.596995\pi$
$114$	−3.61466e6	+	7.45084e6i	−0.0214017	+	0.0441150i
$115$	−4.88226e7	+	3.01371e7i	−0.279145	+	0.172310i
$116$			2.52454e8i			1.39428i
$117$	3.08198e7	−	2.42884e7i	0.164470	−	0.129615i
$118$			3.16506e7i			0.163250i
$119$			1.15901e8i			0.577963i
$120$	1.39261e7	+	1.36945e8i	0.0671591	+	0.660420i
$121$	−2.44368e8			−1.14000
$122$	−1.76793e6			−0.00798044
$123$	−2.11397e6	−	1.02556e6i	−0.00923586	−	0.00448063i
$124$	2.86427e8			1.21151
$125$	−2.15261e7	−	2.43190e8i	−0.0881709	−	0.996105i
$126$	4.88936e7	−	3.85319e7i	0.193986	−	0.152876i
$127$			1.37799e8i			0.529701i	0.964289	+	0.264851i	$0.0853227\pi$
$127$			1.37799e8i			0.529701i	−0.964289	+	0.264851i	$0.914677\pi$
$128$	2.69810e8			1.00512
$129$	−4.94228e8	−	2.39767e8i	−1.78471	−	0.865824i
$130$	−1.11246e7	−	1.80220e7i	−0.0389503	−	0.0631001i
$131$		−	7.11572e7i		−	0.241620i	−0.992676	−	0.120810i	$-0.961451\pi$
$131$		−	7.11572e7i		−	0.241620i	0.992676	−	0.120810i	$-0.0385492\pi$
$132$	−3.49476e8	−	1.69543e8i	−1.15112	−	0.558448i
$133$			3.02182e7i			0.0965743i
$134$			4.83582e6i			0.0149986i
$135$	2.38738e8	−	2.30929e8i	0.718766	−	0.695253i
$136$	−1.88185e8			−0.550084
$137$	5.04740e8			1.43280			0.716400	−	0.697689i	$-0.245788\pi$
$137$	5.04740e8			1.43280			0.716400	+	0.697689i	$0.245788\pi$
$138$	−1.83890e7	+	3.79050e7i	−0.0507040	+	0.104515i
$139$	2.09113e8			0.560171			0.280086	−	0.959975i	$-0.409637\pi$
$139$	2.09113e8			0.560171			0.280086	+	0.959975i	$0.409637\pi$
$140$	1.23091e8	+	1.99409e8i	0.320416	+	0.519079i
$141$	6.93271e7	−	1.42903e8i	0.175399	−	0.361547i
$142$		−	1.80334e8i		−	0.443531i
$143$	1.28097e8			0.306333
$144$	−1.70208e8	−	2.15979e8i	−0.395849	−	0.502298i
$145$	−3.70161e8	−	5.99667e8i	−0.837373	−	1.35656i
$146$		−	1.34167e7i		−	0.0295281i
$147$	−1.04666e8	+	2.15747e8i	−0.224149	+	0.462036i
$148$			4.92136e8i			1.02574i
$149$		−	2.19726e8i		−	0.445796i	−0.974842	−	0.222898i	$-0.928448\pi$
$149$		−	2.19726e8i		−	0.445796i	0.974842	−	0.222898i	$-0.0715517\pi$
$150$	−1.09115e8	−	1.42239e8i	−0.215536	−	0.280966i
$151$	3.50620e8			0.674418			0.337209	−	0.941430i	$-0.390517\pi$
$151$	3.50620e8			0.674418			0.337209	+	0.941430i	$0.390517\pi$
$152$	−4.90643e7			−0.0919160
$153$	2.81066e8	+	3.56649e8i	0.512912	+	0.650841i
$154$	2.03217e8			0.361307
$155$	−6.80364e8	+	4.19974e8i	−1.17873	+	0.727605i
$156$	9.75889e7	+	4.73437e7i	0.164779	+	0.0799399i
$157$			7.08761e7i			0.116654i	0.998298	+	0.0583272i	$0.0185767\pi$
$157$			7.08761e7i			0.116654i	−0.998298	+	0.0583272i	$0.981423\pi$
$158$	−1.65629e8			−0.265771
$159$	−4.35003e8	+	8.96665e8i	−0.680618	+	1.40295i
$160$	−4.96491e8	+	3.06473e8i	−0.757585	+	0.467641i
$161$			1.53730e8i			0.228800i
$162$	5.70125e7	−	2.37139e8i	0.0827771	−	0.344305i
$163$			7.30934e8i			1.03545i	0.855548	+	0.517724i	$0.173220\pi$
$163$			7.30934e8i			1.03545i	−0.855548	+	0.517724i	$0.826780\pi$
$164$		−	6.49470e6i		−	0.00897809i
$165$	1.07872e9	−	1.09697e8i	1.45537	−	0.147998i
$166$	3.81355e8			0.502223
$167$	−1.02725e9			−1.32072			−0.660361	−	0.750948i	$-0.729597\pi$
$167$	−1.02725e9			−1.32072			−0.660361	+	0.750948i	$0.729597\pi$
$168$	3.31833e8	+	1.60984e8i	0.416565	+	0.202090i
$169$	7.79961e8			0.956150
$170$	2.08552e8	−	1.28734e8i	0.249700	−	0.154134i
$171$	7.32807e7	+	9.29868e7i	0.0857048	+	0.108752i
$172$		−	1.51841e9i		−	1.73490i
$173$	1.07140e8			0.119610			0.0598050	−	0.998210i	$-0.480952\pi$
$173$	1.07140e8			0.119610			0.0598050	+	0.998210i	$0.480952\pi$
$174$	−4.65571e8	−	2.25864e8i	−0.507913	−	0.246406i
$175$	−5.84769e8	−	2.93185e8i	−0.623494	−	0.312600i
$176$		−	8.97675e8i		−	0.935553i
$177$	4.07105e8	+	1.97500e8i	0.414776	+	0.201222i
$178$			2.77763e8i			0.276690i
$179$			1.76590e8i			0.172010i	0.996295	+	0.0860051i	$0.0274101\pi$
$179$			1.76590e8i			0.172010i	−0.996295	+	0.0860051i	$0.972590\pi$
$180$	8.62352e8	+	3.15116e8i	0.821475	+	0.300179i
$181$	−1.03775e9			−0.966896			−0.483448	−	0.875373i	$-0.660616\pi$
$181$	−1.03775e9			−0.966896			−0.483448	+	0.875373i	$0.660616\pi$
$182$	−5.67469e7			−0.0517198
$183$	−1.10319e7	+	2.27400e7i	−0.00983666	+	0.0202762i
$184$	−2.49607e8			−0.217764
$185$	−7.21595e8	−	1.16900e9i	−0.616037	−	0.997989i
$186$	−2.56259e8	+	5.28223e8i	−0.214105	+	0.441332i
$187$			1.48234e9i			1.21222i
$188$	4.39039e8			0.351456
$189$	−1.90518e8	−	8.69332e8i	−0.149310	−	0.681300i
$190$	5.43744e7	−	3.35641e7i	0.0417234	−	0.0257550i
$191$			4.41653e8i			0.331854i	0.986138	+	0.165927i	$0.0530617\pi$
$191$			4.41653e8i			0.331854i	−0.986138	+	0.165927i	$0.946938\pi$
$192$	1.92340e8	−	3.96468e8i	0.141535	−	0.291745i
$193$		−	1.80470e9i		−	1.30070i	−0.759635	−	0.650349i	$-0.774623\pi$
$193$		−	1.80470e9i		−	1.30070i	0.759635	−	0.650349i	$-0.225377\pi$
$194$		−	4.07034e8i		−	0.287359i
$195$	−3.01225e8	+	3.06321e7i	−0.208331	+	0.0211855i
$196$	−6.62837e8			−0.449141
$197$	1.84458e9			1.22471			0.612355	−	0.790583i	$-0.290222\pi$
$197$	1.84458e9			1.22471			0.612355	+	0.790583i	$0.290222\pi$
$198$	6.25334e8	−	4.92811e8i	0.406866	−	0.320641i
$199$	1.80610e9			1.15167			0.575837	−	0.817564i	$-0.304676\pi$
$199$	1.80610e9			1.15167			0.575837	+	0.817564i	$0.304676\pi$
$200$	4.76034e8	−	9.49470e8i	0.297521	−	0.593419i
$201$	6.22005e7	+	3.01756e7i	0.0381074	+	0.0184872i
$202$			6.35693e8i			0.381805i
$203$	−1.88820e9			−1.11190
$204$	−5.47863e8	+	1.12930e9i	−0.316338	+	0.652063i
$205$	9.52287e6	+	1.54272e7i	0.00539203	+	0.00873517i
$206$			7.58597e8i			0.421253i
$207$	3.72804e8	+	4.73056e8i	0.203048	+	0.257651i
$208$			2.50670e8i			0.133921i
$209$			3.86481e8i			0.202555i
$210$	−4.77874e8	+	4.85957e7i	−0.245717	+	0.0249874i
$211$	2.94285e8			0.148470			0.0742350	−	0.997241i	$-0.476349\pi$
$211$	2.94285e8			0.148470			0.0742350	+	0.997241i	$0.476349\pi$
$212$	−2.75481e9			−1.36379
$213$	−2.31954e9	−	1.12529e9i	−1.12689	−	0.546695i
$214$	2.08024e8			0.0991876
$215$	2.22637e9	+	3.60675e9i	1.04194	+	1.68796i
$216$	1.41151e9	−	3.09338e8i	0.648437	−	0.142108i
$217$			2.14230e9i			0.966143i
$218$	−9.51897e8			−0.421468
$219$	−1.72572e8	−	8.37207e7i	−0.0750230	−	0.0363962i
$220$	1.57430e9	+	2.55039e9i	0.672042	+	1.08872i
$221$		−	4.13934e8i		−	0.173525i
$222$	−9.07588e8	−	4.40302e8i	−0.373660	−	0.181275i
$223$		−	3.54930e9i		−	1.43523i	−0.696438	−	0.717617i	$-0.745233\pi$
$223$		−	3.54930e9i		−	1.43523i	0.696438	−	0.717617i	$-0.254767\pi$
$224$			1.56333e9i			0.620952i
$225$	−2.51043e9	+	5.15913e8i	−0.979529	+	0.201301i
$226$	5.54325e8			0.212486
$227$	3.07376e9			1.15762			0.578811	−	0.815461i	$-0.303517\pi$
$227$	3.07376e9			1.15762			0.578811	+	0.815461i	$0.303517\pi$
$228$	−1.42841e8	+	2.94436e8i	−0.0528583	+	0.108956i
$229$	−2.58716e9			−0.940767			−0.470383	−	0.882462i	$-0.655884\pi$
$229$	−2.58716e9			−0.940767			−0.470383	+	0.882462i	$0.655884\pi$
$230$	2.76621e8	−	1.70752e8i	0.0988495	−	0.0610176i
$231$	1.26808e9	−	2.61387e9i	0.445346	−	0.917985i
$232$		−	3.06582e9i		−	1.05826i
$233$	4.46492e9			1.51492			0.757460	−	0.652882i	$-0.226440\pi$
$233$	4.46492e9			1.51492			0.757460	+	0.652882i	$0.226440\pi$
$234$	−1.74621e8	+	1.37614e8i	−0.0582414	+	0.0458987i
$235$	−1.04287e9	+	6.43741e8i	−0.341947	+	0.211077i
$236$			1.25074e9i			0.403199i
$237$	−1.03353e9	+	2.13039e9i	−0.327588	+	0.675253i
$238$		−	6.56678e8i		−	0.204666i
$239$		−	2.49405e9i		−	0.764388i	−0.924082	−	0.382194i	$-0.875169\pi$
$239$		−	2.49405e9i		−	0.764388i	0.924082	−	0.382194i	$-0.124831\pi$
$240$	2.14663e8	+	2.11092e9i	0.0647012	+	0.636250i
$241$	−1.06935e9			−0.316993			−0.158497	−	0.987360i	$-0.550665\pi$
$241$	−1.06935e9			−0.316993			−0.158497	+	0.987360i	$0.550665\pi$
$242$	1.38455e9			0.403691
$243$	−2.69443e9	−	2.21307e9i	−0.772756	−	0.634703i
$244$	−6.98637e7			−0.0197103
$245$	1.57447e9	−	9.71886e8i	0.436988	−	0.269743i
$246$	1.19774e7	+	5.81065e6i	0.00327056	+	0.00158666i
$247$		−	1.07922e8i		−	0.0289951i
$248$	−3.47838e9			−0.919540
$249$	2.37966e9	−	4.90516e9i	0.619039	−	1.27602i
$250$	1.21964e8	+	1.37788e9i	0.0312227	+	0.352736i
$251$		−	2.58790e9i		−	0.652007i	−0.945369	−	0.326003i	$-0.894298\pi$
$251$		−	2.58790e9i		−	0.652007i	0.945369	−	0.326003i	$-0.105702\pi$
$252$	1.93214e9	−	1.52267e9i	0.479110	−	0.377575i
$253$			1.96617e9i			0.479886i
$254$		−	7.80748e8i		−	0.187575i
$255$	−3.54476e8	−	3.48579e9i	−0.0838351	−	0.824406i
$256$	−1.35998e8			−0.0316644
$257$	−3.99995e9			−0.916900			−0.458450	−	0.888720i	$-0.651595\pi$
$257$	−3.99995e9			−0.916900			−0.458450	+	0.888720i	$0.651595\pi$
$258$	2.80022e9	+	1.35848e9i	0.631994	+	0.306602i
$259$	−3.68088e9			−0.817999
$260$	−4.39613e8	−	7.12179e8i	−0.0962004	−	0.155846i
$261$	−5.81035e9	+	4.57900e9i	−1.25210	+	0.986753i
$262$			4.03166e8i			0.0855615i
$263$	2.61772e9			0.547142			0.273571	−	0.961852i	$-0.411795\pi$
$263$	2.61772e9			0.547142			0.273571	+	0.961852i	$0.411795\pi$
$264$	4.24405e9	+	2.05893e9i	0.873705	+	0.423864i
$265$	6.54364e9	−	4.03925e9i	1.32689	−	0.819062i
$266$		−	1.71212e8i		−	0.0341985i
$267$	3.57271e9	+	1.73324e9i	0.702996	+	0.341047i
$268$			1.91098e8i			0.0370439i
$269$			6.21608e9i			1.18715i	0.804777	+	0.593577i	$0.202285\pi$
$269$			6.21608e9i			1.18715i	−0.804777	+	0.593577i	$0.797715\pi$
$270$	−1.35266e9	+	1.30841e9i	−0.254526	+	0.246200i
$271$	5.31021e9			0.984543			0.492271	−	0.870442i	$-0.336167\pi$
$271$	5.31021e9			0.984543			0.492271	+	0.870442i	$0.336167\pi$
$272$	−2.90076e9			−0.529952
$273$	−3.54102e8	+	7.29906e8i	−0.0637496	+	0.131406i
$274$	−2.85978e9			−0.507377
$275$	−7.47902e9	−	3.74974e9i	−1.30772	−	0.655648i
$276$	−7.26681e8	+	1.49790e9i	−0.125230	+	0.258135i
$277$			2.24918e9i			0.382037i	0.981586	+	0.191018i	$0.0611790\pi$
$277$			2.24918e9i			0.382037i	−0.981586	+	0.191018i	$0.938821\pi$
$278$	−1.18480e9			−0.198365
$279$	5.19519e9	+	6.59224e9i	0.857403	+	1.08797i
$280$	−1.49482e9	−	2.42164e9i	−0.243197	−	0.393983i
$281$			7.68684e9i			1.23289i	0.787400	+	0.616443i	$0.211427\pi$
$281$			7.68684e9i			1.23289i	−0.787400	+	0.616443i	$0.788573\pi$
$282$	−3.92797e8	+	8.09667e8i	−0.0621114	+	0.128029i
$283$			7.20498e9i			1.12328i	0.827382	+	0.561639i	$0.189829\pi$
$283$			7.20498e9i			1.12328i	−0.827382	+	0.561639i	$0.810171\pi$
$284$		−	7.12628e9i		−	1.09544i
$285$	−9.24202e7	−	9.08829e8i	−0.0140084	−	0.137754i
$286$	−7.25776e8			−0.108477
$287$	4.85765e7			0.00715976
$288$	3.79115e9	+	4.81064e9i	0.551063	+	0.699251i
$289$	−2.18569e9			−0.313327
$290$	2.09728e9	+	3.39762e9i	0.296527	+	0.480378i
$291$	−5.23547e9	−	2.53990e9i	−0.730102	−	0.354197i
$292$		−	5.30191e8i		−	0.0729291i
$293$	−3.98677e9			−0.540942			−0.270471	−	0.962728i	$-0.587179\pi$
$293$	−3.98677e9			−0.540942			−0.270471	+	0.962728i	$0.587179\pi$
$294$	5.93023e8	−	1.22239e9i	0.0793748	−	0.163614i
$295$	−1.83390e9	−	2.97095e9i	−0.242152	−	0.392290i
$296$		−	5.97653e9i		−	0.778542i
$297$	−2.43667e9	−	1.11185e10i	−0.313163	−	1.42896i
$298$			1.24493e9i			0.157863i
$299$		−	5.49039e8i		−	0.0686940i
$300$	−4.31192e9	−	5.62089e9i	−0.532335	−	0.693937i
$301$	1.13568e10			1.38353
$302$	−1.98656e9			−0.238822
$303$	8.17658e9	+	3.96674e9i	0.970066	+	0.470612i
$304$	−7.56298e8			−0.0885520
$305$	1.65951e8	−	1.02438e8i	0.0191770	−	0.0118375i
$306$	−1.59248e9	−	2.02072e9i	−0.181630	−	0.230473i
$307$		−	9.29130e9i		−	1.04598i	−0.852339	−	0.522990i	$-0.824817\pi$
$307$		−	9.29130e9i		−	1.04598i	0.852339	−	0.522990i	$-0.175183\pi$
$308$	8.03054e9			0.892364
$309$	9.75743e9	+	4.73366e9i	1.07029	+	0.519234i
$310$	3.85484e9	−	2.37951e9i	0.417407	−	0.257656i
$311$		−	1.12048e10i		−	1.19774i	−0.800847	−	0.598869i	$-0.795617\pi$
$311$		−	1.12048e10i		−	1.19774i	0.800847	−	0.598869i	$-0.204383\pi$
$312$	−1.18512e9	−	5.74944e8i	−0.125068	−	0.0606746i
$313$			9.45147e9i			0.984741i	0.870386	+	0.492371i	$0.163870\pi$
$313$			9.45147e9i			0.984741i	−0.870386	+	0.492371i	$0.836130\pi$
$314$		−	4.01573e8i		−	0.0413092i
$315$	−2.35688e9	+	6.44987e9i	−0.239384	+	0.655102i
$316$	−6.54518e9			−0.656407
$317$	8.48385e8			0.0840148			0.0420074	−	0.999117i	$-0.486625\pi$
$317$	8.48385e8			0.0840148			0.0420074	+	0.999117i	$0.486625\pi$
$318$	2.46466e9	−	5.08037e9i	0.241017	−	0.496806i
$319$	−2.41496e10			−2.33210
$320$	−2.89333e9	+	1.78599e9i	−0.275929	+	0.170325i
$321$	1.29807e9	−	2.67570e9i	0.122258	−	0.252009i
$322$		−	8.71013e8i		−	0.0810217i
$323$	1.24888e9			0.114739
$324$	2.25297e9	−	9.37106e9i	0.204445	−	0.850371i
$325$	2.08847e9	+	1.04709e9i	0.187195	+	0.0938537i
$326$		−	4.14136e9i		−	0.366668i
$327$	−5.93986e9	+	1.22437e10i	−0.519499	+	1.07084i
$328$			7.88720e7i			0.00681440i
$329$			3.28374e9i			0.280276i
$330$	−6.11186e9	+	6.21524e8i	−0.515368	+	0.0524086i
$331$	4.71539e9			0.392831			0.196415	−	0.980521i	$-0.437070\pi$
$331$	4.71539e9			0.392831			0.196415	+	0.980521i	$0.437070\pi$
$332$	1.50701e10			1.24040
$333$	−1.13267e10	+	8.92633e9i	−0.921144	+	0.725932i
$334$	5.82026e9			0.467688
$335$	−2.80197e8	−	4.53924e8i	−0.0222477	−	0.0360416i
$336$	5.11503e9	+	2.48147e9i	0.401320	+	0.194694i
$337$		−	3.45801e8i		−	0.0268106i	−0.999910	−	0.0134053i	$-0.995733\pi$
$337$		−	3.45801e8i		−	0.0268106i	0.999910	−	0.0134053i	$-0.00426716\pi$
$338$	−4.41914e9			−0.338587
$339$	3.45900e9	−	7.12999e9i	0.261910	−	0.539871i
$340$	8.24137e9	−	5.08722e9i	0.616714	−	0.380684i
$341$			2.73994e10i			2.02639i
$342$	−4.15197e8	−	5.26849e8i	−0.0303494	−	0.0385107i
$343$		−	1.46115e10i		−	1.05565i
$344$			1.84396e10i			1.31679i
$345$	−4.70174e8	−	4.62353e9i	−0.0331881	−	0.326360i
$346$	−6.07040e8			−0.0423558
$347$	−3.52962e9			−0.243450			−0.121725	−	0.992564i	$-0.538843\pi$
$347$	−3.52962e9			−0.243450			−0.121725	+	0.992564i	$0.538843\pi$
$348$	−1.83980e10	−	8.92552e9i	−1.25445	−	0.608578i
$349$	8.25013e9			0.556108			0.278054	−	0.960565i	$-0.410311\pi$
$349$	8.25013e9			0.556108			0.278054	+	0.960565i	$0.410311\pi$
$350$	3.31321e9	+	1.66114e9i	0.220789	+	0.110697i
$351$	6.80424e8	+	3.10477e9i	0.0448282	+	0.204550i
$352$			1.99945e10i			1.30239i
$353$	1.08036e10			0.695776			0.347888	−	0.937536i	$-0.386899\pi$
$353$	1.08036e10			0.695776			0.347888	+	0.937536i	$0.386899\pi$
$354$	−2.30659e9	−	1.11901e9i	−0.146878	−	0.0712557i
$355$	1.04489e10	+	1.69274e10i	0.657897	+	1.06580i
$356$			1.09764e10i			0.683375i
$357$	−8.44650e9	−	4.09768e9i	−0.520001	−	0.252270i
$358$		−	1.00053e9i		−	0.0609115i
$359$		−	1.78116e10i		−	1.07232i	−0.844115	−	0.536162i	$-0.819874\pi$
$359$		−	1.78116e10i		−	1.07232i	0.844115	−	0.536162i	$-0.180126\pi$
$360$	−1.04724e10	−	3.82679e9i	−0.623502	−	0.227837i
$361$	−1.66579e10			−0.980828
$362$	5.87975e9			0.342393
$363$	8.63965e9	−	1.78088e10i	0.497587	−	1.02567i
$364$	−2.24248e9			−0.127739
$365$	7.77394e8	+	1.25939e9i	0.0437995	+	0.0709559i
$366$	6.25053e7	−	1.28841e8i	0.00348331	−	0.00718011i
$367$		−	7.25059e9i		−	0.399677i	−0.979829	−	0.199839i	$-0.935958\pi$
$367$		−	7.25059e9i		−	0.399677i	0.979829	−	0.199839i	$-0.0640418\pi$
$368$	−3.84755e9			−0.209794
$369$	1.49478e8	−	1.17800e8i	0.00806256	−	0.00635392i
$370$	4.08845e9	+	6.62335e9i	0.218148	+	0.353404i
$371$		−	2.06043e10i		−	1.08758i
$372$	−1.01266e10	+	2.08739e10i	−0.528802	+	1.09001i
$373$		−	1.40594e10i		−	0.726325i	−0.931726	−	0.363163i	$-0.881697\pi$
$373$		−	1.40594e10i		−	0.726325i	0.931726	−	0.363163i	$-0.118303\pi$
$374$		−	8.39872e9i		−	0.429266i
$375$	1.84839e10	+	7.02922e9i	0.934694	+	0.355453i
$376$	−5.33171e9			−0.266757
$377$	6.74361e9			0.333831
$378$	1.07945e9	+	4.92550e9i	0.0528730	+	0.241259i
$379$	9.41156e9			0.456147			0.228073	−	0.973644i	$-0.426757\pi$
$379$	9.41156e9			0.456147			0.228073	+	0.973644i	$0.426757\pi$
$380$	2.14872e9	−	1.32636e9i	0.103049	−	0.0636102i
$381$	−1.00423e10	−	4.87188e9i	−0.476579	−	0.231205i
$382$		−	2.50234e9i		−	0.117515i
$383$	−2.22515e10			−1.03410			−0.517052	−	0.855954i	$-0.672971\pi$
$383$	−2.22515e10			−1.03410			−0.517052	+	0.855954i	$0.672971\pi$
$384$	−9.53913e9	+	1.96629e10i	−0.438716	+	0.904320i
$385$	−1.90753e10	+	1.17748e10i	−0.868219	+	0.535933i
$386$			1.02252e10i			0.460598i
$387$	3.49468e10	−	2.75408e10i	1.55799	−	1.22781i
$388$		−	1.60848e10i		−	0.709725i
$389$		−	1.67518e10i		−	0.731582i	−0.930697	−	0.365791i	$-0.880798\pi$
$389$		−	1.67518e10i		−	0.731582i	0.930697	−	0.365791i	$-0.119202\pi$
$390$	1.70670e9	−	1.73557e8i	0.0737731	−	0.00750210i
$391$	6.35351e9			0.271836
$392$	8.04952e9			0.340899
$393$	5.18570e9	+	2.51576e9i	0.217389	+	0.105463i
$394$	−1.04511e10			−0.433689
$395$	1.55471e10	−	9.59687e9i	0.638646	−	0.394223i
$396$	2.47114e10	−	1.94745e10i	1.00489	−	0.791927i
$397$		−	3.88428e9i		−	0.156368i	−0.996939	−	0.0781840i	$-0.975088\pi$
$397$		−	3.88428e9i		−	0.156368i	0.996939	−	0.0781840i	$-0.0249122\pi$
$398$	−1.02331e10			−0.407826
$399$	−2.20220e9	−	1.06836e9i	−0.0868892	−	0.0421529i
$400$	7.33780e9	−	1.46355e10i	0.286633	−	0.571701i
$401$		−	3.28950e10i		−	1.27219i	−0.771610	−	0.636096i	$-0.780548\pi$
$401$		−	3.28950e10i		−	1.27219i	0.771610	−	0.636096i	$-0.219452\pi$
$402$	−3.52419e8	−	1.70970e8i	−0.0134944	−	0.00654661i
$403$		−	7.65110e9i		−	0.290071i
$404$			2.51208e10i			0.942991i
$405$	8.38873e9	+	2.55630e10i	0.311800	+	0.950148i
$406$	1.06983e10			0.393740
$407$	−4.70774e10			−1.71567
$408$	6.65327e9	−	1.37143e10i	0.240101	−	0.494918i
$409$	−1.08495e9			−0.0387718			−0.0193859	−	0.999812i	$-0.506171\pi$
$409$	−1.08495e9			−0.0387718			−0.0193859	+	0.999812i	$0.506171\pi$
$410$	−5.39551e7	−	8.74081e7i	−0.00190940	−	0.00309326i
$411$	−1.78451e10	+	3.67838e10i	−0.625391	+	1.28911i
$412$			2.99776e10i			1.04042i
$413$	−9.35479e9			−0.321539
$414$	−2.11225e9	−	2.68026e9i	−0.0719026	−	0.0912381i
$415$	−3.57967e10	+	2.20965e10i	−1.20684	+	0.744957i
$416$		−	5.58334e9i		−	0.186432i
$417$	−7.39317e9	+	1.52395e10i	−0.244504	+	0.503994i
$418$		−	2.18974e9i		−	0.0717279i
$419$			3.39202e10i			1.10053i	0.834990	+	0.550266i	$0.185474\pi$
$419$			3.39202e10i			1.10053i	−0.834990	+	0.550266i	$0.814526\pi$
$420$	−1.88842e10	+	1.92036e9i	−0.606878	+	0.0617143i
$421$	2.88554e10			0.918542			0.459271	−	0.888296i	$-0.348111\pi$
$421$	2.88554e10			0.918542			0.459271	+	0.888296i	$0.348111\pi$
$422$	−1.66738e9			−0.0525755
$423$	7.96325e9	+	1.01047e10i	0.248731	+	0.315617i
$424$	3.34546e10			1.03512
$425$	−1.21170e10	+	2.41678e10i	−0.371398	+	0.740768i
$426$	1.31422e10	+	6.37570e9i	0.399051	+	0.193593i
$427$		−	5.22539e8i		−	0.0157183i
$428$	8.22050e9			0.244976
$429$	−4.52886e9	+	9.33527e9i	−0.133709	+	0.275612i
$430$	−1.26143e10	−	2.04353e10i	−0.368967	−	0.597733i
$431$			7.99799e8i			0.0231778i	0.999933	+	0.0115889i	$0.00368894\pi$
$431$			7.99799e8i			0.0231778i	−0.999933	+	0.0115889i	$0.996311\pi$
$432$	2.17576e10	−	4.76827e9i	0.624705	−	0.136907i
$433$			2.02420e10i			0.575839i	0.957655	+	0.287920i	$0.0929636\pi$
$433$			2.02420e10i			0.575839i	−0.957655	+	0.287920i	$0.907036\pi$
$434$		−	1.21380e10i		−	0.342126i
$435$	5.67889e10	−	5.77494e9i	1.58601	−	0.161284i
$436$	−3.76163e10			−1.04095
$437$	1.65651e9			0.0454222
$438$	9.77768e8	+	4.74349e8i	0.0265668	+	0.0128885i
$439$	4.16160e10			1.12048			0.560238	−	0.828332i	$-0.310710\pi$
$439$	4.16160e10			1.12048			0.560238	+	0.828332i	$0.310710\pi$
$440$	−1.91183e10	−	3.09720e10i	−0.510082	−	0.826340i
$441$	−1.20225e10	−	1.52555e10i	−0.317863	−	0.403340i
$442$			2.34529e9i			0.0614479i
$443$	−1.00330e10			−0.260504			−0.130252	−	0.991481i	$-0.541579\pi$
$443$	−1.00330e10			−0.260504			−0.130252	+	0.991481i	$0.541579\pi$
$444$	−3.58653e10	−	1.73995e10i	−0.922874	−	0.447718i
$445$	−1.60941e10	−	2.60727e10i	−0.410419	−	0.664885i
$446$			2.01098e10i			0.508239i
$447$	1.60129e10	+	7.76841e9i	0.401088	+	0.194582i
$448$			9.11037e9i			0.226164i
$449$		−	2.59211e10i		−	0.637775i	−0.947793	−	0.318888i	$-0.896691\pi$
$449$		−	2.59211e10i		−	0.637775i	0.947793	−	0.318888i	$-0.103309\pi$
$450$	1.42237e10	−	2.92309e9i	0.346867	−	0.0712839i
$451$	6.21278e8			0.0150169
$452$	2.19054e10			0.524803
$453$	−1.23962e10	+	2.55521e10i	−0.294371	+	0.606783i
$454$	−1.74155e10			−0.409932
$455$	5.32667e9	−	3.28804e9i	0.124283	−	0.0767169i
$456$	1.73467e9	−	3.57565e9i	0.0401196	−	0.0826980i
$457$		−	5.83258e10i		−	1.33720i	−0.743623	−	0.668599i	$-0.766894\pi$
$457$		−	5.83258e10i		−	1.33720i	0.743623	−	0.668599i	$-0.233106\pi$
$458$	1.46585e10			0.333140
$459$	−3.59285e10	+	7.87390e9i	−0.809447	+	0.177394i
$460$	1.09313e10	−	6.74765e9i	0.244141	−	0.150703i
$461$			2.73170e10i			0.604825i	0.953177	+	0.302412i	$0.0977920\pi$
$461$			2.73170e10i			0.604825i	−0.953177	+	0.302412i	$0.902208\pi$
$462$	−7.18472e9	+	1.48098e10i	−0.157704	+	0.325073i
$463$			5.50831e10i			1.19866i	0.800504	+	0.599328i	$0.204565\pi$
$463$			5.50831e10i			1.19866i	−0.800504	+	0.599328i	$0.795435\pi$
$464$		−	4.72578e10i		−	1.01953i
$465$	−6.55208e9	−	6.44309e10i	−0.140142	−	1.37811i
$466$	−2.52975e10			−0.536456
$467$	−4.06476e10			−0.854610			−0.427305	−	0.904108i	$-0.640537\pi$
$467$	−4.06476e10			−0.854610			−0.427305	+	0.904108i	$0.640537\pi$
$468$	−6.90051e9	+	5.43813e9i	−0.143846	+	0.113362i
$469$	−1.42929e9			−0.0295414
$470$	5.90875e9	−	3.64734e9i	0.121089	−	0.0747455i
$471$	−5.16522e9	−	2.50582e9i	−0.104956	−	0.0509175i
$472$		−	1.51891e10i		−	0.306029i
$473$	1.45250e11			2.90182
$474$	5.85580e9	−	1.20705e10i	0.116004	−	0.239118i
$475$	−3.15919e9	+	6.30113e9i	−0.0620585	+	0.123778i
$476$		−	2.59501e10i		−	0.505488i
$477$	−4.99666e10	−	6.34032e10i	−0.965175	−	1.22472i
$478$			1.41309e10i			0.270682i
$479$			1.08547e10i			0.206194i	0.994671	+	0.103097i	$0.0328752\pi$
$479$			1.08547e10i			0.206194i	−0.994671	+	0.103097i	$0.967125\pi$
$480$	−4.78133e9	−	4.70180e10i	−0.0900708	−	0.885726i
$481$	1.31460e10			0.245592
$482$	6.05876e9			0.112252
$483$	−1.12034e10	−	5.43514e9i	−0.205855	−	0.0998670i
$484$	5.47137e10			0.997044
$485$	2.35844e10	+	3.82071e10i	0.426244	+	0.690522i
$486$	1.52663e10	+	1.25389e10i	0.273645	+	0.224758i
$487$		−	1.77991e10i		−	0.316433i	−0.987404	−	0.158216i	$-0.949426\pi$
$487$		−	1.77991e10i		−	0.316433i	0.987404	−	0.158216i	$-0.0505743\pi$
$488$	8.48429e8			0.0149602
$489$	−5.32681e10	−	2.58422e10i	−0.931606	−	0.451953i
$490$	−8.92070e9	+	5.50656e9i	−0.154744	+	0.0955203i
$491$			7.93615e10i			1.36547i	0.730664	+	0.682737i	$0.239211\pi$
$491$			7.93615e10i			1.36547i	−0.730664	+	0.682737i	$0.760789\pi$
$492$	4.73313e8	+	2.29620e8i	0.00807771	+	0.00391877i
$493$			7.80374e10i			1.32104i
$494$			6.11472e8i			0.0102676i
$495$	−3.01438e10	+	8.24919e10i	−0.502084	+	1.37401i
$496$	−5.36173e10			−0.885887
$497$	5.33003e10			0.873582
$498$	−1.34828e10	+	2.77919e10i	−0.219211	+	0.451857i
$499$	6.54034e10			1.05487			0.527434	−	0.849596i	$-0.323154\pi$
$499$	6.54034e10			1.05487			0.527434	+	0.849596i	$0.323154\pi$
$500$	4.81965e9	+	5.44497e10i	0.0771144	+	0.871196i
$501$	3.63185e10	−	7.48629e10i	0.576471	−	1.18827i
$502$			1.46626e10i			0.230886i
$503$	−1.01074e11			−1.57894			−0.789471	−	0.613788i	$-0.789645\pi$
$503$	−1.01074e11			−1.57894			−0.789471	+	0.613788i	$0.789645\pi$
$504$	−2.34639e10	+	1.84914e10i	−0.363646	+	0.286581i
$505$	−3.68334e10	−	5.96706e10i	−0.566339	−	0.917477i
$506$		−	1.11400e10i		−	0.169935i
$507$	−2.75755e10	+	5.68410e10i	−0.417341	+	0.860260i
$508$		−	3.08529e10i		−	0.463278i
$509$			1.19907e11i			1.78638i	0.449681	+	0.893189i	$0.351538\pi$
$509$			1.19907e11i			1.78638i	−0.449681	+	0.893189i	$0.648462\pi$
$510$	2.00841e9	+	1.97500e10i	0.0296873	+	0.291935i
$511$	3.96551e9			0.0581588
$512$	−6.83008e10			−0.993908
$513$	−9.36741e9	+	2.05291e9i	−0.135254	+	0.0296416i
$514$	2.26631e10			0.324689
$515$	−4.39547e10	−	7.12073e10i	−0.624851	−	1.01227i
$516$	1.10657e11	+	5.36833e10i	1.56091	+	0.757252i
$517$			4.19981e10i			0.587851i
$518$	2.08553e10			0.289666
$519$	−3.78794e9	+	7.80802e9i	−0.0522076	+	0.107615i
$520$	5.33868e9	+	8.64874e9i	0.0730164	+	0.118288i
$521$		−	1.21461e11i		−	1.64849i	−0.566230	−	0.824247i	$-0.691599\pi$
$521$		−	1.21461e11i		−	1.64849i	0.566230	−	0.824247i	$-0.308401\pi$
$522$	3.29205e10	−	2.59439e10i	0.443389	−	0.349424i
$523$		−	8.02894e10i		−	1.07313i	−0.843860	−	0.536564i	$-0.819722\pi$
$523$		−	8.02894e10i		−	1.07313i	0.843860	−	0.536564i	$-0.180278\pi$
$524$			1.59320e10i			0.211322i
$525$	4.20408e10	−	3.22505e10i	0.553394	−	0.424521i
$526$	−1.48316e10			−0.193751
$527$	8.85389e10			1.14787
$528$	6.54196e10	+	3.17373e10i	0.841729	+	0.408351i
$529$	−6.98837e10			−0.892387
$530$	−3.70753e10	+	2.28858e10i	−0.469873	+	0.290043i
$531$	−2.87864e10	+	2.26859e10i	−0.362084	+	0.285350i
$532$		−	6.76580e9i		−	0.0844641i
$533$	−1.73488e8			−0.00214961
$534$	−2.02424e10	−	9.82029e9i	−0.248942	−	0.120770i
$535$	−1.95266e10	+	1.20533e10i	−0.238347	+	0.147127i
$536$		−	2.32070e9i		−	0.0281164i
$537$	−1.28693e10	−	6.24334e9i	−0.154760	−	0.0750793i
$538$		−	3.52193e10i		−	0.420390i
$539$		−	6.34064e10i		−	0.751239i
$540$	−5.34531e10	+	5.17045e10i	−0.628634	+	0.608069i
$541$	2.31499e10			0.270246			0.135123	−	0.990829i	$-0.456857\pi$
$541$	2.31499e10			0.270246			0.135123	+	0.990829i	$0.456857\pi$
$542$	−3.00868e10			−0.348642
$543$	3.66897e10	−	7.56281e10i	0.422032	−	0.869929i
$544$	6.46106e10			0.737748
$545$	8.93518e10	−	5.51549e10i	1.01279	−	0.625170i
$546$	2.00629e9	−	4.13553e9i	0.0225747	−	0.0465330i
$547$			1.06905e11i			1.19412i	0.802196	+	0.597061i	$0.203665\pi$
$547$			1.06905e11i			1.19412i	−0.802196	+	0.597061i	$0.796335\pi$
$548$	−1.13010e11			−1.25313
$549$	−1.26718e9	−	1.60794e9i	−0.0139492	−	0.0177003i
$550$	4.23750e10	+	2.12455e10i	0.463083	+	0.232175i
$551$			2.03462e10i			0.220738i
$552$	8.82485e9	−	1.81906e10i	0.0950498	−	0.195925i
$553$		−	4.89540e10i		−	0.523465i
$554$		−	1.27435e10i		−	0.135285i
$555$	1.10705e11	−	1.12577e10i	1.16679	−	0.118653i
$556$	−4.68199e10			−0.489927
$557$	3.49063e10			0.362646			0.181323	−	0.983424i	$-0.441962\pi$
$557$	3.49063e10			0.362646			0.181323	+	0.983424i	$0.441962\pi$
$558$	−2.94352e10	−	3.73507e10i	−0.303620	−	0.385267i
$559$	−4.05600e10			−0.415385
$560$	−2.30419e10	−	3.73282e10i	−0.234296	−	0.379564i
$561$	−1.08028e11	−	5.24081e10i	−1.09065	−	0.529112i
$562$		−	4.35525e10i		−	0.436584i
$563$	−1.11294e10			−0.110775			−0.0553873	−	0.998465i	$-0.517639\pi$
$563$	−1.11294e10			−0.110775			−0.0553873	+	0.998465i	$0.517639\pi$
$564$	−1.55222e10	+	3.19957e10i	−0.153404	+	0.316210i
$565$	−5.20329e10	+	3.21188e10i	−0.510604	+	0.315185i
$566$		−	4.08223e10i		−	0.397770i
$567$	7.00899e10	+	1.68509e10i	0.678146	+	0.163038i
$568$			8.65419e10i			0.831444i
$569$		−	1.10613e11i		−	1.05526i	−0.849475	−	0.527629i	$-0.823081\pi$
$569$		−	1.10613e11i		−	1.05526i	0.849475	−	0.527629i	$-0.176919\pi$
$570$	5.23639e8	+	5.14929e9i	0.00496058	+	0.0487807i
$571$	−3.15777e10			−0.297055			−0.148527	−	0.988908i	$-0.547453\pi$
$571$	−3.15777e10			−0.297055			−0.148527	+	0.988908i	$0.547453\pi$
$572$	−2.86806e10			−0.267919
$573$	−3.21862e10	−	1.56146e10i	−0.298574	−	0.144848i
$574$	−2.75227e8			−0.00253538
$575$	−1.60719e10	+	3.20560e10i	−0.147026	+	0.293250i
$576$	2.20931e10	+	2.80343e10i	0.200709	+	0.254683i
$577$		−	3.66049e10i		−	0.330245i	−0.986273	−	0.165123i	$-0.947198\pi$
$577$		−	3.66049e10i		−	0.330245i	0.986273	−	0.165123i	$-0.0528020\pi$
$578$	1.23838e10			0.110954
$579$	1.31521e11	+	6.38053e10i	1.17026	+	0.567731i
$580$	8.28785e10	+	1.34264e11i	0.732368	+	1.18645i
$581$			1.12715e11i			0.989184i
$582$	2.96634e10	+	1.43907e10i	0.258540	+	0.125427i
$583$		−	2.63523e11i		−	2.28110i
$584$			6.43867e9i			0.0553534i
$585$	8.41745e9	−	2.30353e10i	0.0718716	−	0.196685i
$586$	2.25884e10			0.191556
$587$	−5.45783e10			−0.459693			−0.229846	−	0.973227i	$-0.573822\pi$
$587$	−5.45783e10			−0.459693			−0.229846	+	0.973227i	$0.573822\pi$
$588$	2.34346e10	−	4.83054e10i	0.196042	−	0.404098i
$589$	2.30842e10			0.191802
$590$	1.03906e10	+	1.68329e10i	0.0857498	+	0.138916i
$591$	−6.52152e10	+	1.34427e11i	−0.534563	+	1.10189i
$592$		−	9.21248e10i		−	0.750049i
$593$	−8.35997e10			−0.676061			−0.338031	−	0.941135i	$-0.609761\pi$
$593$	−8.35997e10			−0.676061			−0.338031	+	0.941135i	$0.609761\pi$
$594$	1.38058e10	+	6.29957e10i	0.110896	+	0.506017i
$595$	3.80493e10	+	6.16405e10i	0.303584	+	0.491811i
$596$			4.91962e10i			0.389894i
$597$	−6.38547e10	+	1.31623e11i	−0.502684	+	1.03618i
$598$			3.11077e9i			0.0243256i
$599$		−	1.39529e10i		−	0.108382i	−0.998531	−	0.0541909i	$-0.982742\pi$
$599$		−	1.39529e10i		−	0.108382i	0.998531	−	0.0541909i	$-0.0172579\pi$
$600$	5.23641e10	+	6.82603e10i	0.404044	+	0.526700i
$601$	2.42138e11			1.85595			0.927974	−	0.372645i	$-0.121549\pi$
$601$	2.42138e11			1.85595			0.927974	+	0.372645i	$0.121549\pi$
$602$	−6.43457e10			−0.489930
$603$	−4.39820e9	+	3.46612e9i	−0.0332664	+	0.0262164i
$604$	−7.85032e10			−0.589847
$605$	−1.29964e11	+	8.02240e10i	−0.970067	+	0.598801i
$606$	−4.63273e10	−	2.24749e10i	−0.343515	−	0.166651i
$607$			1.24176e11i			0.914712i	0.889284	+	0.457356i	$0.151203\pi$
$607$			1.24176e11i			0.914712i	−0.889284	+	0.457356i	$0.848797\pi$
$608$	1.68455e10			0.123274
$609$	6.67575e10	−	1.37606e11i	0.485323	−	1.00039i
$610$	−9.40252e8	+	5.80397e8i	−0.00679086	+	0.00419185i
$611$		−	1.17277e10i		−	0.0841488i
$612$	−6.29302e10	−	7.98530e10i	−0.448594	−	0.569227i
$613$			1.73317e11i			1.22743i	0.789526	+	0.613717i	$0.210327\pi$
$613$			1.73317e11i			1.22743i	−0.789526	+	0.613717i	$0.789673\pi$
$614$			5.26431e10i			0.370397i
$615$	−1.46096e9	+	1.48568e8i	−0.0102127	+	0.00103854i
$616$	−9.75233e10			−0.677307
$617$	1.52659e11			1.05337			0.526687	−	0.850060i	$-0.323434\pi$
$617$	1.52659e11			1.05337			0.526687	+	0.850060i	$0.323434\pi$
$618$	−5.52841e10	−	2.68202e10i	−0.379006	−	0.183869i
$619$	−2.41342e11			−1.64388			−0.821942	−	0.569571i	$-0.807109\pi$
$619$	−2.41342e11			−1.64388			−0.821942	+	0.569571i	$0.807109\pi$
$620$	1.52332e11	−	9.40314e10i	1.03092	−	0.636365i
$621$	−4.76553e10	+	1.04439e10i	−0.320439	+	0.0702256i
$622$			6.34846e10i			0.424137i
$623$	−8.20967e10			−0.544971
$624$	−1.82680e10	−	8.86243e9i	−0.120491	−	0.0584541i
$625$	−9.12854e10	−	1.22270e11i	−0.598248	−	0.801311i
$626$		−	5.35506e10i		−	0.348712i
$627$	−2.81655e10	−	1.36640e10i	−0.182242	−	0.0884116i
$628$		−	1.58690e10i		−	0.102026i
$629$			1.52127e11i			0.971858i
$630$	1.33537e10	−	3.65440e10i	0.0847696	−	0.231982i
$631$	1.68033e11			1.05993			0.529966	−	0.848019i	$-0.322205\pi$
$631$	1.68033e11			1.05993			0.529966	+	0.848019i	$0.322205\pi$
$632$	7.94849e10			0.498215
$633$	−1.04045e10	+	2.14466e10i	−0.0648044	+	0.133580i
$634$	−4.80682e9			−0.0297510
$635$	4.52382e10	+	7.32865e10i	0.278234	+	0.450743i
$636$	9.73963e10	−	2.00762e11i	0.595270	−	1.22702i
$637$			1.77058e10i			0.107537i
$638$	1.36828e11			0.825832
$639$	1.64015e11	−	1.29256e11i	0.983737	−	0.775260i
$640$	1.43495e11	−	8.85762e10i	0.855296	−	0.527955i
$641$		−	1.07087e11i		−	0.634313i	−0.948373	−	0.317156i	$-0.897272\pi$
$641$		−	1.07087e11i		−	0.634313i	0.948373	−	0.317156i	$-0.102728\pi$
$642$	−7.35467e9	+	1.51601e10i	−0.0432935	+	0.0892404i
$643$		−	1.21734e11i		−	0.712142i	−0.934459	−	0.356071i	$-0.884116\pi$
$643$		−	1.21734e11i		−	0.712142i	0.934459	−	0.356071i	$-0.115884\pi$
$644$		−	3.44200e10i		−	0.200109i
$645$	−3.41561e11	+	3.47339e10i	−1.97347	+	0.200685i
$646$	−7.07598e9			−0.0406309
$647$	1.91646e11			1.09366			0.546829	−	0.837244i	$-0.315835\pi$
$647$	1.91646e11			1.09366			0.546829	+	0.837244i	$0.315835\pi$
$648$	−2.73602e10	+	1.13803e11i	−0.155174	+	0.645434i
$649$	−1.19645e11			−0.674397
$650$	−1.18329e10	−	5.93266e9i	−0.0662886	−	0.0332350i
$651$	−1.56124e11	−	7.57410e10i	−0.869252	−	0.421704i
$652$		−	1.63655e11i		−	0.905604i
$653$	1.71426e11			0.942811			0.471406	−	0.881917i	$-0.343747\pi$
$653$	1.71426e11			0.942811			0.471406	+	0.881917i	$0.343747\pi$
$654$	3.36543e10	−	6.93712e10i	0.183963	−	0.379200i
$655$	−2.33603e10	−	3.78440e10i	−0.126915	−	0.205604i
$656$			1.21577e9i			0.00656500i
$657$	1.22026e10	−	9.61657e9i	0.0654923	−	0.0516129i
$658$		−	1.86052e10i		−	0.0992501i
$659$		−	6.16692e10i		−	0.326984i	−0.986545	−	0.163492i	$-0.947724\pi$
$659$		−	6.16692e10i		−	0.326984i	0.986545	−	0.163492i	$-0.0522758\pi$
$660$	−2.41523e11	+	2.45609e10i	−1.27287	+	0.129440i
$661$	2.25974e10			0.118373			0.0591864	−	0.998247i	$-0.481149\pi$
$661$	2.25974e10			0.118373			0.0591864	+	0.998247i	$0.481149\pi$
$662$	−2.67167e10			−0.139107
$663$	3.01662e10	+	1.46346e10i	0.156123	+	0.0757404i
$664$	−1.83012e11			−0.941469
$665$	9.92036e9	+	1.60711e10i	0.0507272	+	0.0821788i
$666$	6.41755e10	−	5.05752e10i	0.326192	−	0.257064i
$667$			1.03508e11i			0.522964i
$668$	2.30000e11			1.15511
$669$	2.58661e11	+	1.25485e11i	1.29130	+	0.626453i
$670$	1.58756e9	+	2.57186e9i	0.00787825	+	0.0127629i
$671$		−	6.68311e9i		−	0.0329677i
$672$	−1.13930e11	−	5.52715e10i	−0.558679	−	0.271034i
$673$			3.18816e11i			1.55410i	0.629437	+	0.777051i	$0.283285\pi$
$673$			3.18816e11i			1.55410i	−0.629437	+	0.777051i	$0.716715\pi$
$674$			1.95925e9i			0.00949404i
$675$	5.11580e10	−	2.01192e11i	0.246433	−	0.969160i
$676$	−1.74632e11			−0.836250
$677$	−3.75454e11			−1.78732			−0.893660	−	0.448745i	$-0.851871\pi$
$677$	−3.75454e11			−1.78732			−0.893660	+	0.448745i	$0.851871\pi$
$678$	−1.95982e10	+	4.03974e10i	−0.0927463	+	0.191177i
$679$	1.20305e11			0.565984
$680$	−1.00084e11	+	6.17794e10i	−0.468088	+	0.288940i
$681$	−1.08673e11	+	2.24006e11i	−0.505281	+	1.04153i
$682$		−	1.55241e11i		−	0.717576i
$683$	−1.83700e11			−0.844162			−0.422081	−	0.906558i	$-0.638700\pi$
$683$	−1.83700e11			−0.844162			−0.422081	+	0.906558i	$0.638700\pi$
$684$	−1.64074e10	−	2.08196e10i	−0.0749576	−	0.0951146i
$685$	2.68439e11	−	1.65702e11i	1.21922	−	0.752601i
$686$			8.27865e10i			0.373820i
$687$	9.14692e10	−	1.88544e11i	0.410627	−	0.846420i
$688$			2.84236e11i			1.26860i
$689$			7.35871e10i			0.326531i
$690$	2.66393e9	+	2.61962e10i	0.0117524	+	0.115569i
$691$	1.46577e11			0.642916			0.321458	−	0.946924i	$-0.395827\pi$
$691$	1.46577e11			0.642916			0.321458	+	0.946924i	$0.395827\pi$
$692$	−2.39885e10			−0.104611
$693$	1.45657e11	+	1.84827e11i	0.631538	+	0.801367i
$694$	1.99983e10			0.0862095
$695$	1.11214e11	−	6.86498e10i	0.476671	−	0.294239i
$696$	2.23427e11	+	1.08392e11i	0.952134	+	0.461913i
$697$		−	2.00761e9i		−	0.00850645i
$698$	−4.67440e10			−0.196926
$699$	−1.57857e11	+	3.25389e11i	−0.661234	+	1.36299i
$700$	1.30929e11	+	6.56435e10i	0.545309	+	0.273401i
$701$			3.90726e11i			1.61808i	0.587753	+	0.809041i	$0.300013\pi$
$701$			3.90726e11i			1.61808i	−0.587753	+	0.809041i	$0.699987\pi$
$702$	−3.85518e9	−	1.75911e10i	−0.0158744	−	0.0724345i
$703$			3.96630e10i			0.162392i
$704$			1.16519e11i			0.474358i
$705$	−1.00431e10	−	9.87605e10i	−0.0406548	−	0.399785i
$706$	−6.12115e10			−0.246385
$707$	−1.87888e11			−0.752007
$708$	−9.11500e10	−	4.42200e10i	−0.362764	−	0.175989i
$709$	−3.36760e10			−0.133271			−0.0666354	−	0.997777i	$-0.521226\pi$
$709$	−3.36760e10			−0.133271			−0.0666354	+	0.997777i	$0.521226\pi$
$710$	−5.92020e10	−	9.59081e10i	−0.232972	−	0.377417i
$711$	−1.18716e11	−	1.50640e11i	−0.464548	−	0.589471i
$712$		−	1.33298e11i		−	0.518684i
$713$	1.17437e11			0.454410
$714$	4.78566e10	+	2.32169e10i	0.184140	+	0.0893327i
$715$	6.81265e10	−	4.20530e10i	0.260670	−	0.160906i
$716$		−	3.95382e10i		−	0.150441i
$717$	1.81758e11	+	8.81772e10i	0.687730	+	0.333641i
$718$			1.00918e11i			0.379726i
$719$		−	3.34576e11i		−	1.25193i	−0.779852	−	0.625964i	$-0.784706\pi$
$719$		−	3.34576e11i		−	1.25193i	0.779852	−	0.625964i	$-0.215294\pi$
$720$	−1.61427e11	−	5.89878e10i	−0.600683	−	0.219499i
$721$	−2.24214e11			−0.829703
$722$	9.43814e10			0.347326
$723$	3.78067e10	−	7.79305e10i	0.138362	−	0.285203i
$724$	2.32351e11			0.845649
$725$	−3.93731e11	−	1.97404e11i	−1.42511	−	0.714503i
$726$	−4.89509e10	+	1.00902e11i	−0.176203	+	0.363206i
$727$			7.75537e10i			0.277629i	0.990318	+	0.138815i	$0.0443292\pi$
$727$			7.75537e10i			0.277629i	−0.990318	+	0.138815i	$0.955671\pi$
$728$	2.72328e10			0.0969541
$729$	2.56543e11	−	1.18118e11i	0.908345	−	0.418223i
$730$	−4.40459e9	−	7.13551e9i	−0.0155101	−	0.0251266i
$731$		−	4.69363e11i		−	1.64376i
$732$	2.47003e9	−	5.09144e9i	0.00860316	−	0.0177336i
$733$		−	1.83371e10i		−	0.0635205i	−0.999496	−	0.0317603i	$-0.989889\pi$
$733$		−	1.83371e10i		−	0.0635205i	0.999496	−	0.0317603i	$-0.0101113\pi$
$734$			4.10808e10i			0.141532i
$735$	1.51625e10	+	1.49103e11i	0.0519544	+	0.510902i
$736$	8.56990e10			0.292055
$737$	−1.82803e10			−0.0619601
$738$	−8.46922e8	+	6.67439e8i	−0.00285508	+	0.00225002i
$739$	−4.44324e11			−1.48978			−0.744890	−	0.667187i	$-0.767498\pi$
$739$	−4.44324e11			−1.48978			−0.744890	+	0.667187i	$0.767498\pi$
$740$	1.61564e11	+	2.61736e11i	0.538787	+	0.872844i
$741$	7.86504e9	+	3.81560e9i	0.0260872	+	0.0126558i
$742$			1.16741e11i			0.385130i
$743$	−5.92783e10			−0.194509			−0.0972547	−	0.995260i	$-0.531006\pi$
$743$	−5.92783e10			−0.194509			−0.0972547	+	0.995260i	$0.531006\pi$
$744$	1.22978e11	−	2.53493e11i	0.401362	−	0.827323i
$745$	−7.21340e10	−	1.16858e11i	−0.234161	−	0.379345i
$746$			7.96584e10i			0.257203i
$747$	2.73340e11	+	3.46844e11i	0.877850	+	1.11391i
$748$		−	3.31893e11i		−	1.06021i
$749$			6.14843e10i			0.195361i
$750$	−1.04727e11	−	3.98265e10i	−0.330990	−	0.125871i
$751$	−1.35059e11			−0.424585			−0.212292	−	0.977206i	$-0.568093\pi$
$751$	−1.35059e11			−0.424585			−0.212292	+	0.977206i	$0.568093\pi$
$752$	−8.21853e10			−0.256994
$753$	1.88598e11	+	9.14950e10i	0.586619	+	0.284589i
$754$	−3.82083e10			−0.118215
$755$	1.86473e11	−	1.15105e11i	0.573888	−	0.354249i
$756$	4.26567e10	+	1.94642e11i	0.130587	+	0.595866i
$757$		−	3.52798e11i		−	1.07434i	−0.843473	−	0.537171i	$-0.819493\pi$
$757$		−	3.52798e11i		−	1.07434i	0.843473	−	0.537171i	$-0.180507\pi$
$758$	−5.33245e10			−0.161529
$759$	−1.43288e11	−	6.95138e10i	−0.431760	−	0.209461i
$760$	−2.60942e10	+	1.61074e10i	−0.0782148	+	0.0482803i
$761$		−	4.67185e11i		−	1.39300i	−0.717558	−	0.696499i	$-0.754740\pi$
$761$		−	4.67185e11i		−	1.39300i	0.717558	−	0.696499i	$-0.245260\pi$
$762$	5.68984e10	+	2.76033e10i	0.168764	+	0.0818732i
$763$		−	2.81347e11i		−	0.830126i
$764$		−	9.88853e10i		−	0.290241i
$765$	2.66566e11	+	9.74072e10i	0.778321	+	0.284410i
$766$	1.26074e11			0.366193
$767$	3.34101e10			0.0965375
$768$	4.80819e9	−	9.91106e9i	0.0138209	−	0.0284889i
$769$	−1.44792e11			−0.414038			−0.207019	−	0.978337i	$-0.566376\pi$
$769$	−1.44792e11			−0.414038			−0.207019	+	0.978337i	$0.566376\pi$
$770$	1.08078e11	−	6.67142e10i	0.307450	−	0.189782i
$771$	1.41418e11	−	2.91503e11i	0.400210	−	0.824947i
$772$			4.04070e11i			1.13759i
$773$	−1.13132e11			−0.316860			−0.158430	−	0.987370i	$-0.550643\pi$
$773$	−1.13132e11			−0.316860			−0.158430	+	0.987370i	$0.550643\pi$
$774$	−1.98003e11	+	1.56042e11i	−0.551707	+	0.434788i
$775$	−2.23969e11	+	4.46715e11i	−0.620841	+	1.23829i
$776$			1.95335e11i			0.538683i
$777$	1.30138e11	−	2.68251e11i	0.357041	−	0.735964i
$778$			9.49132e10i			0.259065i
$779$		−	5.23432e8i		−	0.00142138i
$780$	6.74438e10	−	6.85846e9i	0.182206	−	0.0185288i
$781$	6.81694e11			1.83225
$782$	−3.59980e10			−0.0962612
$783$	−1.28278e11	−	5.85330e11i	−0.341275	−	1.55723i
$784$	1.24079e11			0.328423
$785$	2.32680e10	+	3.76945e10i	0.0612746	+	0.0992657i
$786$	−2.93814e10	−	1.42539e10i	−0.0769808	−	0.0373460i
$787$			4.10788e10i			0.107083i	0.998566	+	0.0535413i	$0.0170509\pi$
$787$			4.10788e10i			0.107083i	−0.998566	+	0.0535413i	$0.982949\pi$
$788$	−4.12999e11			−1.07113
$789$	−9.25494e10	+	1.90771e11i	−0.238817	+	0.492271i
$790$	−8.80874e10	+	5.43744e10i	−0.226155	+	0.139600i
$791$			1.63839e11i			0.418515i
$792$	−3.00097e11	+	2.36499e11i	−0.762712	+	0.601075i
$793$			1.86622e9i			0.00471921i
$794$			2.20077e10i			0.0553723i
$795$	6.30169e10	+	6.19687e11i	0.157757	+	1.55133i
$796$	−4.04383e11			−1.00726
$797$	−1.01477e11			−0.251498			−0.125749	−	0.992062i	$-0.540133\pi$
$797$	−1.01477e11			−0.251498			−0.125749	+	0.992062i	$0.540133\pi$
$798$	1.24774e10	+	6.05319e9i	0.0307688	+	0.0149270i
$799$	1.35713e11			0.332994
$800$	−1.63440e11	+	3.25987e11i	−0.399022	+	0.795867i
$801$	−2.52626e11	+	1.99089e11i	−0.613689	+	0.483634i
$802$			1.86378e11i			0.450503i
$803$	5.07177e10			0.121982
$804$	−1.39266e10	−	6.75626e9i	−0.0333288	−	0.0161690i
$805$	5.04683e10	+	8.17594e10i	0.120181	+	0.194695i
$806$			4.33500e10i			0.102719i
$807$	−4.53008e11	−	2.19769e11i	−1.06810	−	0.518171i
$808$		−	3.05068e11i		−	0.715733i
$809$			2.81290e11i			0.656689i	0.944558	+	0.328344i	$0.106491\pi$
$809$			2.81290e11i			0.656689i	−0.944558	+	0.328344i	$0.893509\pi$
$810$	−4.75293e10	−	1.44836e11i	−0.110413	−	0.336462i
$811$	3.06605e11			0.708754			0.354377	−	0.935103i	$-0.384693\pi$
$811$	3.06605e11			0.708754			0.354377	+	0.935103i	$0.384693\pi$
$812$	4.22766e11			0.972468
$813$	−1.87742e11	+	3.86991e11i	−0.429735	+	0.885806i
$814$	2.66733e11			0.607546
$815$	2.39959e11	+	3.88738e11i	0.543885	+	0.881102i
$816$	1.02556e11	−	2.11398e11i	0.231314	−	0.476805i
$817$		−	1.22374e11i		−	0.274663i
$818$	6.14716e9			0.0137297
$819$	−4.06739e10	−	5.16116e10i	−0.0904024	−	0.114713i
$820$	−2.13215e9	−	3.45412e9i	−0.00471588	−	0.00763980i
$821$			5.33533e11i			1.17433i	0.809469	+	0.587163i	$0.199755\pi$
$821$			5.33533e11i			1.17433i	−0.809469	+	0.587163i	$0.800245\pi$
$822$	1.01108e11	−	2.08412e11i	0.221461	−	0.456494i
$823$		−	5.45096e11i		−	1.18816i	−0.804407	−	0.594078i	$-0.797517\pi$
$823$		−	5.45096e11i		−	1.18816i	0.804407	−	0.594078i	$-0.202483\pi$
$824$		−	3.64050e11i		−	0.789681i
$825$	5.37690e11	−	4.12474e11i	1.16069	−	0.890392i
$826$	5.30028e10			0.113862
$827$	7.10494e11			1.51893			0.759466	−	0.650547i	$-0.225460\pi$
$827$	7.10494e11			1.51893			0.759466	+	0.650547i	$0.225460\pi$
$828$	−8.34702e10	−	1.05916e11i	−0.177587	−	0.225342i
$829$	3.64341e11			0.771419			0.385710	−	0.922620i	$-0.373957\pi$
$829$	3.64341e11			0.771419			0.385710	+	0.922620i	$0.373957\pi$
$830$	2.02818e11	−	1.25195e11i	0.427361	−	0.263801i
$831$	−1.63913e11	−	7.95198e10i	−0.343724	−	0.166752i
$832$		−	3.25372e10i		−	0.0679026i
$833$	−2.04893e11			−0.425546
$834$	4.18886e10	−	8.63444e10i	0.0865828	−	0.178472i
$835$	−5.46331e11	+	3.37238e11i	−1.12385	+	0.693730i
$836$		−	8.65325e10i		−	0.177155i
$837$	−6.64098e11	+	1.45540e11i	−1.35310	+	0.296538i
$838$		−	1.92187e11i		−	0.389715i
$839$			3.80877e11i			0.768665i	0.923195	+	0.384333i	$0.125568\pi$
$839$			3.80877e11i			0.768665i	−0.923195	+	0.384333i	$0.874432\pi$
$840$	2.29331e11	−	2.33210e10i	0.460622	−	0.0468414i
$841$	−7.71101e11			−1.54144
$842$	−1.63490e11			−0.325270
$843$	−5.60192e11	−	2.71768e11i	−1.10924	−	0.538132i
$844$	−6.58899e10			−0.129852
$845$	4.14811e11	−	2.56054e11i	0.813624	−	0.502233i
$846$	−4.51186e10	−	5.72515e10i	−0.0880793	−	0.111765i
$847$			4.09225e11i			0.795112i
$848$	5.15683e11			0.997240
$849$	−5.25076e11	−	2.54732e11i	−1.01063	−	0.490290i
$850$	6.86530e10	−	1.36931e11i	0.131518	−	0.262317i
$851$			2.01780e11i			0.384733i
$852$	5.19340e11	+	2.51950e11i	0.985584	+	0.478140i
$853$			8.33398e11i			1.57419i	0.616834	+	0.787093i	$0.288415\pi$
$853$			8.33398e11i			1.57419i	−0.616834	+	0.787093i	$0.711585\pi$
$854$			2.96062e9i			0.00556611i
$855$	6.95001e10	+	2.53964e10i	0.130053	+	0.0475234i
$856$	−9.98301e10			−0.185937
$857$	−2.81549e11			−0.521952			−0.260976	−	0.965345i	$-0.584044\pi$
$857$	−2.81549e11			−0.521952			−0.260976	+	0.965345i	$0.584044\pi$
$858$	2.56598e10	−	5.28922e10i	0.0473483	−	0.0975984i
$859$	6.11769e11			1.12361			0.561804	−	0.827271i	$-0.310108\pi$
$859$	6.11769e11			1.12361			0.561804	+	0.827271i	$0.310108\pi$
$860$	−4.98480e11	−	8.07544e11i	−0.911284	−	1.47629i
$861$	−1.71742e9	+	3.54010e9i	−0.00312510	+	0.00644173i
$862$		−	4.53154e9i		−	0.00820761i
$863$	4.91320e11			0.885771			0.442886	−	0.896578i	$-0.353955\pi$
$863$	4.91320e11			0.885771			0.442886	+	0.896578i	$0.353955\pi$
$864$	−4.84620e11	+	1.06207e11i	−0.869654	+	0.190589i
$865$	5.69810e10	−	3.51731e10i	0.101781	−	0.0628270i
$866$		−	1.14688e11i		−	0.203914i
$867$	7.72752e10	−	1.59286e11i	0.136761	−	0.281904i
$868$		−	4.79657e11i		−	0.844991i
$869$		−	6.26106e11i		−	1.09792i
$870$	−3.21757e11	+	3.27200e10i	−0.561631	+	0.0571131i
$871$	5.10464e9			0.00886937
$872$	4.56814e11			0.790084
$873$	3.70200e11	−	2.91746e11i	0.637352	−	0.502282i
$874$	−9.38553e9			−0.0160847
$875$	−4.07251e11	+	3.60481e10i	−0.694753	+	0.0614964i
$876$	3.86386e10	+	1.87449e10i	0.0656153	+	0.0318322i
$877$		−	2.91940e11i		−	0.493509i	−0.969078	−	0.246755i	$-0.920636\pi$
$877$		−	2.91940e11i		−	0.493509i	0.969078	−	0.246755i	$-0.0793641\pi$
$878$	−2.35790e11			−0.396778
$879$	1.40952e11	−	2.90543e11i	0.236111	−	0.486693i
$880$	−2.94699e11	−	4.77416e11i	−0.491414	−	0.796098i
$881$		−	3.04364e11i		−	0.505230i	−0.967567	−	0.252615i	$-0.918709\pi$
$881$		−	3.04364e11i		−	0.505230i	0.967567	−	0.252615i	$-0.0812906\pi$
$882$	6.81176e10	+	8.64353e10i	0.112560	+	0.142829i
$883$		−	4.35514e11i		−	0.716407i	−0.933644	−	0.358203i	$-0.883389\pi$
$883$		−	4.35514e11i		−	0.716407i	0.933644	−	0.358203i	$-0.116611\pi$
$884$			9.26791e10i			0.151765i
$885$	2.81351e11	−	2.86110e10i	0.458643	−	0.0466401i
$886$	5.68453e10			0.0922486
$887$	−1.80753e11			−0.292006			−0.146003	−	0.989284i	$-0.546641\pi$
$887$	−1.80753e11			−0.292006			−0.146003	+	0.989284i	$0.546641\pi$
$888$	4.35550e11	+	2.11300e11i	0.700464	+	0.339819i
$889$	2.30761e11			0.369450
$890$	9.11869e10	+	1.47724e11i	0.145336	+	0.235446i
$891$	8.96428e11	+	2.15518e11i	1.42234	+	0.341957i
$892$			7.94681e11i			1.25526i
$893$	3.53837e10			0.0556414
$894$	−9.07267e10	−	4.40146e10i	−0.142032	−	0.0689044i
$895$	5.79730e10	+	9.39171e10i	0.0903511	+	0.146370i
$896$		−	4.51830e11i		−	0.701040i
$897$	4.00122e10	+	1.94113e10i	0.0618049	+	0.0299836i
$898$			1.46865e11i			0.225846i
$899$			1.44243e12i			2.20829i
$900$	5.62080e11	−	1.15512e11i	0.856699	−	0.176059i
$901$	−8.51553e11			−1.29215
$902$	−3.52007e9			−0.00531771
$903$	−4.01519e11	+	8.27645e11i	−0.603885	+	1.24478i
$904$	−2.66020e11			−0.398327
$905$	−5.51915e11	+	3.40685e11i	−0.822769	+	0.507877i
$906$	7.02348e10	−	1.44774e11i	0.104241	−	0.214871i
$907$		−	1.24264e12i		−	1.83618i	−0.396374	−	0.918089i	$-0.629732\pi$
$907$		−	1.24264e12i		−	1.83618i	0.396374	−	0.918089i	$-0.370268\pi$
$908$	−6.88210e11			−1.01246
$909$	−5.78166e11	+	4.55639e11i	−0.846832	+	0.667368i
$910$	−3.01801e10	+	1.86295e10i	−0.0440104	+	0.0271666i
$911$			3.34146e10i			0.0485135i	0.999706	+	0.0242568i	$0.00772193\pi$
$911$			3.34146e10i			0.0485135i	−0.999706	+	0.0242568i	$0.992278\pi$
$912$	2.67389e10	−	5.51166e10i	0.0386513	−	0.0796715i
$913$			1.44159e12i			2.07472i
$914$			3.30465e11i			0.473523i
$915$	1.59815e9	+	1.57156e10i	0.00227999	+	0.0224206i
$916$	5.79261e11			0.822797
$917$	−1.19161e11			−0.168523
$918$	2.03565e11	−	4.46123e10i	0.286638	−	0.0628180i
$919$	1.22601e12			1.71882			0.859412	−	0.511283i	$-0.170830\pi$
$919$	1.22601e12			1.71882			0.859412	+	0.511283i	$0.170830\pi$
$920$	−1.32750e11	+	8.19437e10i	−0.185303	+	0.114384i
$921$	6.77120e11	+	3.28494e11i	0.941081	+	0.456550i
$922$		−	1.54774e11i		−	0.214178i
$923$	−1.90359e11			−0.262281
$924$	−2.83920e11	+	5.85240e11i	−0.389500	+	0.802872i
$925$	−7.67541e11	−	3.84821e11i	−1.04842	−	0.525644i
$926$		−	3.12093e11i		−	0.424463i
$927$	−6.89948e11	+	5.43732e11i	−0.934324	+	0.736319i
$928$			1.05260e12i			1.41930i
$929$		−	1.46087e12i		−	1.96133i	−0.195701	−	0.980664i	$-0.562698\pi$
$929$		−	1.46087e12i		−	1.96133i	0.195701	−	0.980664i	$-0.437302\pi$
$930$	3.71231e10	+	3.65056e11i	0.0496263	+	0.488009i
$931$	−5.34204e10			−0.0711064
$932$	−9.99686e11			−1.32495
$933$	8.16568e11	+	3.96145e11i	1.07762	+	0.522790i
$934$	2.30303e11			0.302631
$935$	4.86639e11	+	7.88363e11i	0.636738	+	1.03152i
$936$	8.38001e10	−	6.60409e10i	0.109179	−	0.0860418i
$937$		−	1.02495e12i		−	1.32968i	−0.746987	−	0.664838i	$-0.768500\pi$
$937$		−	1.02495e12i		−	1.32968i	0.746987	−	0.664838i	$-0.231500\pi$
$938$	8.09817e9			0.0104611
$939$	−6.88793e11	−	3.34157e11i	−0.885985	−	0.429821i
$940$	2.33497e11	−	1.44133e11i	0.299068	−	0.184608i
$941$			1.83735e11i			0.234333i	0.993112	+	0.117166i	$0.0373811\pi$
$941$			1.83735e11i			0.234333i	−0.993112	+	0.117166i	$0.962619\pi$
$942$	2.92654e10	+	1.41976e10i	0.0371664	+	0.0180307i
$943$		−	2.66288e9i		−	0.00336748i
$944$		−	2.34131e11i		−	0.294829i
$945$	−3.86718e11	−	3.99797e11i	−0.484917	−	0.501317i
$946$	−8.22962e11			−1.02758
$947$	−2.26053e11			−0.281067			−0.140533	−	0.990076i	$-0.544882\pi$
$947$	−2.26053e11			−0.281067			−0.140533	+	0.990076i	$0.544882\pi$
$948$	2.31405e11	−	4.76991e11i	0.286509	−	0.590578i
$949$	−1.41626e10			−0.0174613
$950$	1.78995e10	−	3.57012e10i	0.0219759	−	0.0438318i
$951$	−2.99946e10	+	6.18276e10i	−0.0366709	+	0.0755893i
$952$			3.15139e11i			0.383667i
$953$	1.49255e12			1.80949			0.904745	−	0.425953i	$-0.140061\pi$
$953$	1.49255e12			1.80949			0.904745	+	0.425953i	$0.140061\pi$
$954$	2.83103e11	+	3.59233e11i	0.341783	+	0.433693i
$955$	1.44991e11	+	2.34887e11i	0.174312	+	0.282388i
$956$			5.58414e11i			0.668535i
$957$	8.53808e11	−	1.75994e12i	1.01792	−	2.09822i
$958$		−	6.15012e10i		−	0.0730166i
$959$		−	8.45250e11i		−	0.999334i
$960$	−2.78635e10	−	2.74000e11i	−0.0328058	−	0.322601i
$961$	7.83650e11			0.918816
$962$	−7.44835e10			−0.0869681
$963$	1.49103e11	+	1.89198e11i	0.173373	+	0.219995i
$964$	2.39425e11			0.277243
$965$	−5.92468e11	−	9.59807e11i	−0.683212	−	1.10681i
$966$	6.34766e10	+	3.07947e10i	0.0728963	+	0.0353645i
$967$			7.94256e11i			0.908352i	0.890912	+	0.454176i	$0.150066\pi$
$967$			7.94256e11i			0.908352i	−0.890912	+	0.454176i	$0.849934\pi$
$968$	−6.64445e11			−0.756759
$969$	−4.41543e10	+	9.10146e10i	−0.0500815	+	0.103232i
$970$	−1.33626e11	−	2.16476e11i	−0.150940	−	0.244524i
$971$		−	7.55855e10i		−	0.0850279i	−0.999096	−	0.0425139i	$-0.986463\pi$
$971$		−	7.55855e10i		−	0.0850279i	0.999096	−	0.0425139i	$-0.0135367\pi$
$972$	6.03279e11	+	4.95503e11i	0.675854	+	0.555113i
$973$		−	3.50185e11i		−	0.390702i
$974$			1.00847e11i			0.112054i
$975$	−1.50146e11	+	1.15181e11i	−0.166149	+	0.127456i
$976$	1.30780e10			0.0144126
$977$	−1.31247e11			−0.144049			−0.0720244	−	0.997403i	$-0.522946\pi$
$977$	−1.31247e11			−0.144049			−0.0720244	+	0.997403i	$0.522946\pi$
$978$	3.01809e11	+	1.46418e11i	0.329896	+	0.160044i
$979$	−1.04999e12			−1.14302
$980$	−3.52521e11	+	2.17603e11i	−0.382191	+	0.235918i
$981$	−6.82281e11	−	8.65755e11i	−0.736694	−	0.934801i
$982$		−	4.49650e11i		−	0.483536i
$983$	−2.55150e11			−0.273264			−0.136632	−	0.990622i	$-0.543628\pi$
$983$	−2.55150e11			−0.273264			−0.136632	+	0.990622i	$0.543628\pi$
$984$	−5.74794e9	−	2.78852e9i	−0.00613100	−	0.00297436i
$985$	9.81017e11	−	6.05560e11i	1.04215	−	0.643298i
$986$		−	4.42148e11i		−	0.467800i
$987$	−2.39309e11	−	1.16097e11i	−0.252168	−	0.122335i
$988$			2.41636e10i			0.0253591i
$989$		−	6.22559e11i		−	0.650722i
$990$	1.70790e11	−	4.67386e11i	0.177796	−	0.486559i
$991$	−1.00441e12			−1.04139			−0.520697	−	0.853742i	$-0.674328\pi$
$991$	−1.00441e12			−1.04139			−0.520697	+	0.853742i	$0.674328\pi$
$992$	1.19425e12			1.23325
$993$	−1.66713e11	+	3.43642e11i	−0.171463	+	0.353435i
$994$	−3.01991e11			−0.309349
$995$	9.60550e11	−	5.92927e11i	0.980004	−	0.604935i
$996$	−5.32802e11	+	1.09826e12i	−0.541413	+	1.11601i
$997$			1.22258e12i			1.23737i	0.785641	+	0.618683i	$0.212333\pi$
$997$			1.22258e12i			1.23737i	−0.785641	+	0.618683i	$0.787667\pi$
$998$	−3.70566e11			−0.373545
$999$	−2.50066e11	−	1.14105e12i	−0.251068	−	1.14562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.9.d.c.14.6	yes	12
3.2	odd	2	inner	15.9.d.c.14.8	yes	12
4.3	odd	2		240.9.c.c.209.9		12
5.2	odd	4		75.9.c.h.26.6		12
5.3	odd	4		75.9.c.h.26.7		12
5.4	even	2	inner	15.9.d.c.14.7	yes	12
12.11	even	2		240.9.c.c.209.3		12
15.2	even	4		75.9.c.h.26.8		12
15.8	even	4		75.9.c.h.26.5		12
15.14	odd	2	inner	15.9.d.c.14.5	✓	12
20.19	odd	2		240.9.c.c.209.4		12
60.59	even	2		240.9.c.c.209.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.d.c.14.5	✓	12	15.14	odd	2	inner
15.9.d.c.14.6	yes	12	1.1	even	1	trivial
15.9.d.c.14.7	yes	12	5.4	even	2	inner
15.9.d.c.14.8	yes	12	3.2	odd	2	inner
75.9.c.h.26.5		12	15.8	even	4
75.9.c.h.26.6		12	5.2	odd	4
75.9.c.h.26.7		12	5.3	odd	4
75.9.c.h.26.8		12	15.2	even	4
240.9.c.c.209.3		12	12.11	even	2
240.9.c.c.209.4		12	20.19	odd	2
240.9.c.c.209.9		12	4.3	odd	2
240.9.c.c.209.10		12	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.66585 q^{2} +(-35.3550 + 72.8768i) q^{3} -223.898 q^{4} +(531.836 - 328.291i) q^{5} +(200.316 - 412.909i) q^{6} -1674.62i q^{7} +2719.03 q^{8} +(-4061.05 - 5153.12i) q^{9} +O(q^{10})\)	\(q-5.66585 q^{2} +(-35.3550 + 72.8768i) q^{3} -223.898 q^{4} +(531.836 - 328.291i) q^{5} +(200.316 - 412.909i) q^{6} -1674.62i q^{7} +2719.03 q^{8} +(-4061.05 - 5153.12i) q^{9} +(-3013.30 + 1860.05i) q^{10} -21417.9i q^{11} +(7915.92 - 16317.0i) q^{12} +5980.82i q^{13} +9488.16i q^{14} +(5121.72 + 50365.3i) q^{15} +41912.3 q^{16} -69210.3 q^{17} +(23009.3 + 29196.8i) q^{18} -18044.8 q^{19} +(-119077. + 73503.8i) q^{20} +(122041. + 59206.3i) q^{21} +121351. i q^{22} -91800.0 q^{23} +(-96131.3 + 198154. i) q^{24} +(175075. - 349194. i) q^{25} -33886.4i q^{26} +(519121. - 113768. i) q^{27} +374945. i q^{28} -1.12754e6i q^{29} +(-29018.9 - 285362. i) q^{30} -1.27927e6 q^{31} -933541. q^{32} +(1.56087e6 + 757230. i) q^{33} +392135. q^{34} +(-549764. - 890626. i) q^{35} +(909261. + 1.15377e6i) q^{36} -2.19804e6i q^{37} +102239. q^{38} +(-435863. - 211452. i) q^{39} +(1.44608e6 - 892633. i) q^{40} +29007.4i q^{41} +(-691466. - 335454. i) q^{42} +6.78169e6i q^{43} +4.79543e6i q^{44} +(-3.85154e6 - 1.40741e6i) q^{45} +520125. q^{46} -1.96089e6 q^{47} +(-1.48181e6 + 3.05443e6i) q^{48} +2.96044e6 q^{49} +(-991948. + 1.97848e6i) q^{50} +(2.44693e6 - 5.04382e6i) q^{51} -1.33909e6i q^{52} +1.23039e7 q^{53} +(-2.94126e6 + 644591. i) q^{54} +(-7.03131e6 - 1.13908e7i) q^{55} -4.55335e6i q^{56} +(637973. - 1.31504e6i) q^{57} +6.38847e6i q^{58} -5.58621e6i q^{59} +(-1.14674e6 - 1.12767e7i) q^{60} +312034. q^{61} +7.24817e6 q^{62} +(-8.62953e6 + 6.80073e6i) q^{63} -5.44025e6 q^{64} +(1.96345e6 + 3.18082e6i) q^{65} +(-8.84365e6 - 4.29035e6i) q^{66} -853503. i q^{67} +1.54961e7 q^{68} +(3.24559e6 - 6.69009e6i) q^{69} +(3.11488e6 + 5.04615e6i) q^{70} +3.18282e7i q^{71} +(-1.10421e7 - 1.40115e7i) q^{72} +2.36800e6i q^{73} +1.24537e7i q^{74} +(1.92584e7 + 2.51047e7i) q^{75} +4.04019e6 q^{76} -3.58669e7 q^{77} +(2.46953e6 + 1.19805e6i) q^{78} +2.92328e7 q^{79} +(2.22905e7 - 1.37594e7i) q^{80} +(-1.00625e7 + 4.18541e7i) q^{81} -164351. i q^{82} -6.73076e7 q^{83} +(-2.73248e7 - 1.32562e7i) q^{84} +(-3.68086e7 + 2.27211e7i) q^{85} -3.84240e7i q^{86} +(8.21715e7 + 3.98642e7i) q^{87} -5.82360e7i q^{88} -4.90240e7i q^{89} +(2.18222e7 + 7.97416e6i) q^{90} +1.00156e7 q^{91} +2.05539e7 q^{92} +(4.52287e7 - 9.32293e7i) q^{93} +1.11101e7 q^{94} +(-9.59686e6 + 5.92394e6i) q^{95} +(3.30053e7 - 6.80334e7i) q^{96} +7.18400e7i q^{97} -1.67734e7 q^{98} +(-1.10369e8 + 8.69792e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9}+O(q^{10}) \) 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9	\( 12 q + 1704 q^{4} - 3012 q^{6} - 22824 q^{9} - 35280 q^{10} - 95520 q^{15} + 413328 q^{16} + 276192 q^{19} - 604044 q^{21} + 1173336 q^{24} - 2036220 q^{25} + 3563460 q^{30} - 279216 q^{31} - 1225344 q^{34} - 10311840 q^{36} + 3780864 q^{39} - 3347040 q^{40} + 9523980 q^{45} + 37414536 q^{46} - 6222300 q^{49} + 3931248 q^{51} - 53281692 q^{54} - 16903440 q^{55} + 9900720 q^{60} - 91958256 q^{61} + 57497760 q^{64} + 111065040 q^{66} + 8138748 q^{69} + 3903480 q^{70} + 15031440 q^{75} - 232646880 q^{76} + 420402672 q^{79} + 98480772 q^{81} - 528357816 q^{84} - 117091440 q^{85} + 218602080 q^{90} - 100211328 q^{91} + 543022776 q^{94} + 333306864 q^{96} - 640360080 q^{99}+O(q^{100}) \) 12 * q + 1704 * q^4 - 3012 * q^6 - 22824 * q^9 - 35280 * q^10 - 95520 * q^15 + 413328 * q^16 + 276192 * q^19 - 604044 * q^21 + 1173336 * q^24 - 2036220 * q^25 + 3563460 * q^30 - 279216 * q^31 - 1225344 * q^34 - 10311840 * q^36 + 3780864 * q^39 - 3347040 * q^40 + 9523980 * q^45 + 37414536 * q^46 - 6222300 * q^49 + 3931248 * q^51 - 53281692 * q^54 - 16903440 * q^55 + 9900720 * q^60 - 91958256 * q^61 + 57497760 * q^64 + 111065040 * q^66 + 8138748 * q^69 + 3903480 * q^70 + 15031440 * q^75 - 232646880 * q^76 + 420402672 * q^79 + 98480772 * q^81 - 528357816 * q^84 - 117091440 * q^85 + 218602080 * q^90 - 100211328 * q^91 + 543022776 * q^94 + 333306864 * q^96 - 640360080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more