LMFDB - Embedded newform 15.9.d.c.14.4

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			14.4
Root			$8.79222 + 30.8359i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.9.d.c.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.5844 q^{2} +(74.7380 + 31.2287i) q^{3} +53.2123 q^{4} +(-31.8709 - 624.187i) q^{5} +(-1314.22 - 549.140i) q^{6} +3426.92i q^{7} +3565.91 q^{8} +(4610.53 + 4667.95i) q^{9} +O(q^{10})$	\(q-17.5844 q^{2} +(74.7380 + 31.2287i) q^{3} +53.2123 q^{4} +(-31.8709 - 624.187i) q^{5} +(-1314.22 - 549.140i) q^{6} +3426.92i q^{7} +3565.91 q^{8} +(4610.53 + 4667.95i) q^{9} +(560.432 + 10976.0i) q^{10} +15724.8i q^{11} +(3976.98 + 1661.75i) q^{12} +27065.2i q^{13} -60260.4i q^{14} +(17110.6 - 47645.8i) q^{15} -76326.8 q^{16} -14218.4 q^{17} +(-81073.6 - 82083.2i) q^{18} +210073. q^{19} +(-1695.92 - 33214.4i) q^{20} +(-107018. + 256121. i) q^{21} -276511. i q^{22} -60230.4 q^{23} +(266509. + 111359. i) q^{24} +(-388593. + 39786.8i) q^{25} -475926. i q^{26} +(198808. + 492854. i) q^{27} +182354. i q^{28} -758209. i q^{29} +(-300880. + 837824. i) q^{30} +333379. q^{31} +429291. q^{32} +(-491064. + 1.17524e6i) q^{33} +250023. q^{34} +(2.13904e6 - 109219. i) q^{35} +(245337. + 248392. i) q^{36} +683328. i q^{37} -3.69401e6 q^{38} +(-845213. + 2.02280e6i) q^{39} +(-113649. - 2.22579e6i) q^{40} -1.23950e6i q^{41} +(1.88186e6 - 4.50374e6i) q^{42} +1.15567e6i q^{43} +836750. i q^{44} +(2.76673e6 - 3.02660e6i) q^{45} +1.05912e6 q^{46} -1.52165e6 q^{47} +(-5.70451e6 - 2.38359e6i) q^{48} -5.97898e6 q^{49} +(6.83320e6 - 699629. i) q^{50} +(-1.06266e6 - 444024. i) q^{51} +1.44020e6i q^{52} -4.73392e6 q^{53} +(-3.49592e6 - 8.66656e6i) q^{54} +(9.81519e6 - 501162. i) q^{55} +1.22201e7i q^{56} +(1.57004e7 + 6.56030e6i) q^{57} +1.33327e7i q^{58} +1.30629e7i q^{59} +(910494. - 2.53534e6i) q^{60} -6.62861e6 q^{61} -5.86228e6 q^{62} +(-1.59967e7 + 1.57999e7i) q^{63} +1.19908e7 q^{64} +(1.68938e7 - 862593. i) q^{65} +(8.63509e6 - 2.06659e7i) q^{66} -2.47970e7i q^{67} -756595. q^{68} +(-4.50150e6 - 1.88092e6i) q^{69} +(-3.76138e7 + 1.92056e6i) q^{70} -1.07106e7i q^{71} +(1.64407e7 + 1.66455e7i) q^{72} -3.48665e7i q^{73} -1.20159e7i q^{74} +(-3.02852e7 - 9.16170e6i) q^{75} +1.11784e7 q^{76} -5.38875e7 q^{77} +(1.48626e7 - 3.55698e7i) q^{78} +5.01757e7 q^{79} +(2.43260e6 + 4.76422e7i) q^{80} +(-532723. + 4.30434e7i) q^{81} +2.17960e7i q^{82} +4.50568e7 q^{83} +(-5.69469e6 + 1.36288e7i) q^{84} +(453154. + 8.87496e6i) q^{85} -2.03217e7i q^{86} +(2.36779e7 - 5.66670e7i) q^{87} +5.60730e7i q^{88} -7.30781e7i q^{89} +(-4.86514e7 + 5.32211e7i) q^{90} -9.27503e7 q^{91} -3.20500e6 q^{92} +(2.49161e7 + 1.04110e7i) q^{93} +2.67573e7 q^{94} +(-6.69521e6 - 1.31125e8i) q^{95} +(3.20843e7 + 1.34062e7i) q^{96} +1.45948e8i q^{97} +1.05137e8 q^{98} +(-7.34023e7 + 7.24995e7i) 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 $

$2$	−17.5844			−1.09903			−0.549514	−	0.835485i	$-0.685187\pi$
$2$	−17.5844			−1.09903			−0.549514	+	0.835485i	$0.685187\pi$
$3$	74.7380	+	31.2287i	0.922691	+	0.385540i
$3$	74.7380	+	31.2287i	0.922691	+	0.385540i
$4$	53.2123			0.207860
$5$	−31.8709	−	624.187i	−0.0509935	−	0.998699i
$5$	−31.8709	−	624.187i	−0.0509935	−	0.998699i
$6$	−1314.22	−	549.140i	−1.01406	−	0.423719i
$7$			3426.92i			1.42729i	0.700508	+	0.713644i	$0.252957\pi$
$7$			3426.92i			1.42729i	−0.700508	+	0.713644i	$0.747043\pi$
$8$	3565.91			0.870583
$9$	4610.53	+	4667.95i	0.702718	+	0.711469i
$10$	560.432	+	10976.0i	0.0560432	+	1.09760i
$11$			15724.8i			1.07402i	0.843575	+	0.537011i	$0.180447\pi$
$11$			15724.8i			1.07402i	−0.843575	+	0.537011i	$0.819553\pi$
$12$	3976.98	+	1661.75i	0.191791	+	0.0801385i
$13$			27065.2i			0.947628i	0.880625	+	0.473814i	$0.157123\pi$
$13$			27065.2i			0.947628i	−0.880625	+	0.473814i	$0.842877\pi$
$14$		−	60260.4i		−	1.56863i
$15$	17110.6	−	47645.8i	0.337987	−	0.941151i
$16$	−76326.8			−1.16465
$17$	−14218.4			−0.170238			−0.0851189	−	0.996371i	$-0.527127\pi$
$17$	−14218.4			−0.170238			−0.0851189	+	0.996371i	$0.527127\pi$
$18$	−81073.6	−	82083.2i	−0.772306	−	0.781923i
$19$	210073.			1.61196			0.805981	−	0.591941i	$-0.201638\pi$
$19$	210073.			1.61196			0.805981	+	0.591941i	$0.201638\pi$
$20$	−1695.92	−	33214.4i	−0.0105995	−	0.207590i
$21$	−107018.	+	256121.i	−0.550277	+	1.31695i
$22$		−	276511.i		−	1.18038i
$23$	−60230.4			−0.215231			−0.107615	−	0.994193i	$-0.534322\pi$
$23$	−60230.4			−0.215231			−0.107615	+	0.994193i	$0.534322\pi$
$24$	266509.	+	111359.i	0.803279	+	0.335645i
$25$	−388593.	+	39786.8i	−0.994799	+	0.101854i
$26$		−	475926.i		−	1.04147i
$27$	198808.	+	492854.i	0.374092	+	0.927392i
$28$			182354.i			0.296677i
$29$		−	758209.i		−	1.07201i	−0.844216	−	0.536003i	$-0.819934\pi$
$29$		−	758209.i		−	1.07201i	0.844216	−	0.536003i	$-0.180066\pi$
$30$	−300880.	+	837824.i	−0.371457	+	1.03435i
$31$	333379.			0.360987			0.180493	−	0.983576i	$-0.442231\pi$
$31$	333379.			0.360987			0.180493	+	0.983576i	$0.442231\pi$
$32$	429291.			0.409404
$33$	−491064.	+	1.17524e6i	−0.414078	+	0.990990i
$34$	250023.			0.187096
$35$	2.13904e6	−	109219.i	1.42543	−	0.0727824i
$36$	245337.	+	248392.i	0.146067	+	0.147886i
$37$			683328.i			0.364605i	0.983243	+	0.182302i	$0.0583550\pi$
$37$			683328.i			0.364605i	−0.983243	+	0.182302i	$0.941645\pi$
$38$	−3.69401e6			−1.77159
$39$	−845213.	+	2.02280e6i	−0.365349	+	0.874368i
$40$	−113649.	−	2.22579e6i	−0.0443940	−	0.869450i
$41$		−	1.23950e6i		−	0.438644i	−0.975653	−	0.219322i	$-0.929615\pi$
$41$		−	1.23950e6i		−	0.438644i	0.975653	−	0.219322i	$-0.0703846\pi$
$42$	1.88186e6	−	4.50374e6i	0.604769	−	1.44736i
$43$			1.15567e6i			0.338033i	0.985613	+	0.169016i	$0.0540591\pi$
$43$			1.15567e6i			0.338033i	−0.985613	+	0.169016i	$0.945941\pi$
$44$			836750.i			0.223247i
$45$	2.76673e6	−	3.02660e6i	0.674709	−	0.738084i
$46$	1.05912e6			0.236545
$47$	−1.52165e6			−0.311833			−0.155917	−	0.987770i	$-0.549833\pi$
$47$	−1.52165e6			−0.311833			−0.155917	+	0.987770i	$0.549833\pi$
$48$	−5.70451e6	−	2.38359e6i	−1.07462	−	0.449021i
$49$	−5.97898e6			−1.03715
$50$	6.83320e6	−	699629.i	1.09331	−	0.111941i
$51$	−1.06266e6	−	444024.i	−0.157077	−	0.0656335i
$52$			1.44020e6i			0.196974i
$53$	−4.73392e6			−0.599954			−0.299977	−	0.953947i	$-0.596979\pi$
$53$	−4.73392e6			−0.599954			−0.299977	+	0.953947i	$0.596979\pi$
$54$	−3.49592e6	−	8.66656e6i	−0.411137	−	1.01923i
$55$	9.81519e6	−	501162.i	1.07262	−	0.0547681i
$56$			1.22201e7i			1.24257i
$57$	1.57004e7	+	6.56030e6i	1.48734	+	0.621476i
$58$			1.33327e7i			1.17816i
$59$			1.30629e7i			1.07803i	0.842296	+	0.539016i	$0.181204\pi$
$59$			1.30629e7i			1.07803i	−0.842296	+	0.539016i	$0.818796\pi$
$60$	910494.	−	2.53534e6i	0.0702542	−	0.195628i
$61$	−6.62861e6			−0.478744			−0.239372	−	0.970928i	$-0.576941\pi$
$61$	−6.62861e6			−0.478744			−0.239372	+	0.970928i	$0.576941\pi$
$62$	−5.86228e6			−0.396734
$63$	−1.59967e7	+	1.57999e7i	−1.01547	+	1.00298i
$64$	1.19908e7			0.714709
$65$	1.68938e7	−	862593.i	0.946396	−	0.0483229i
$66$	8.63509e6	−	2.06659e7i	0.455083	−	1.08913i
$67$		−	2.47970e7i		−	1.23055i	−0.788312	−	0.615276i	$-0.789045\pi$
$67$		−	2.47970e7i		−	1.23055i	0.788312	−	0.615276i	$-0.210955\pi$
$68$	−756595.			−0.0353857
$69$	−4.50150e6	−	1.88092e6i	−0.198592	−	0.0829801i
$70$	−3.76138e7	+	1.92056e6i	−1.56659	+	0.0799898i
$71$		−	1.07106e7i		−	0.421485i	−0.977542	−	0.210742i	$-0.932412\pi$
$71$		−	1.07106e7i		−	0.421485i	0.977542	−	0.210742i	$-0.0675881\pi$
$72$	1.64407e7	+	1.66455e7i	0.611774	+	0.619392i
$73$		−	3.48665e7i		−	1.22777i	−0.789395	−	0.613885i	$-0.789606\pi$
$73$		−	3.48665e7i		−	1.22777i	0.789395	−	0.613885i	$-0.210394\pi$
$74$		−	1.20159e7i		−	0.400711i
$75$	−3.02852e7	−	9.16170e6i	−0.957161	−	0.289555i
$76$	1.11784e7			0.335063
$77$	−5.38875e7			−1.53294
$78$	1.48626e7	−	3.55698e7i	0.401528	−	0.960954i
$79$	5.01757e7			1.28820			0.644102	−	0.764939i	$-0.277231\pi$
$79$	5.01757e7			1.28820			0.644102	+	0.764939i	$0.277231\pi$
$80$	2.43260e6	+	4.76422e7i	0.0593898	+	1.16314i
$81$	−532723.	+	4.30434e7i	−0.0123754	+	0.999923i
$82$			2.17960e7i			0.482082i
$83$	4.50568e7			0.949398			0.474699	−	0.880148i	$-0.342557\pi$
$83$	4.50568e7			0.949398			0.474699	+	0.880148i	$0.342557\pi$
$84$	−5.69469e6	+	1.36288e7i	−0.114381	+	0.273741i
$85$	453154.	+	8.87496e6i	0.00868101	+	0.170016i
$86$		−	2.03217e7i		−	0.371507i
$87$	2.36779e7	−	5.66670e7i	0.413301	−	0.989130i
$88$			5.60730e7i			0.935025i
$89$		−	7.30781e7i		−	1.16473i	−0.812926	−	0.582367i	$-0.802127\pi$
$89$		−	7.30781e7i		−	1.16473i	0.812926	−	0.582367i	$-0.197873\pi$
$90$	−4.86514e7	+	5.32211e7i	−0.741523	+	0.811174i
$91$	−9.27503e7			−1.35254
$92$	−3.20500e6			−0.0447380
$93$	2.49161e7	+	1.04110e7i	0.333079	+	0.139175i
$94$	2.67573e7			0.342713
$95$	−6.69521e6	−	1.31125e8i	−0.0821996	−	1.60987i
$96$	3.20843e7	+	1.34062e7i	0.377753	+	0.157842i
$97$			1.45948e8i			1.64858i	0.566165	+	0.824292i	$0.308426\pi$
$97$			1.45948e8i			1.64858i	−0.566165	+	0.824292i	$0.691574\pi$
$98$	1.05137e8			1.13986
$99$	−7.34023e7	+	7.24995e7i	−0.764133	+	0.754734i
$100$	−2.06779e7	+	2.11715e6i	−0.206779	+	0.0211715i
$101$			1.21312e7i			0.116579i	0.998300	+	0.0582893i	$0.0185646\pi$
$101$			1.21312e7i			0.116579i	−0.998300	+	0.0582893i	$0.981435\pi$
$102$	1.86862e7	+	7.80790e6i	0.172632	+	0.0721330i
$103$		−	1.23716e8i		−	1.09920i	−0.835427	−	0.549602i	$-0.814780\pi$
$103$		−	1.23716e8i		−	1.09920i	0.835427	−	0.549602i	$-0.185220\pi$
$104$			9.65120e7i			0.824989i
$105$	1.63278e8	+	5.86367e7i	1.34329	+	0.482405i
$106$	8.32433e7			0.659365
$107$	−1.35805e8			−1.03605			−0.518024	−	0.855366i	$-0.673332\pi$
$107$	−1.35805e8			−1.03605			−0.518024	+	0.855366i	$0.673332\pi$
$108$	1.05790e7	+	2.62259e7i	0.0777589	+	0.192768i
$109$	2.65155e7			0.187843			0.0939214	−	0.995580i	$-0.470060\pi$
$109$	2.65155e7			0.187843			0.0939214	+	0.995580i	$0.470060\pi$
$110$	−1.72594e8	+	8.81265e6i	−1.17884	+	0.0601916i
$111$	−2.13395e7	+	5.10706e7i	−0.140570	+	0.336418i
$112$		−	2.61566e8i		−	1.66230i
$113$	1.84493e8			1.13153			0.565764	−	0.824567i	$-0.308581\pi$
$113$	1.84493e8			1.13153			0.565764	+	0.824567i	$0.308581\pi$
$114$	−2.76083e8	−	1.15359e8i	−1.63463	−	0.683019i
$115$	1.91960e6	+	3.75950e7i	0.0109754	+	0.214951i
$116$		−	4.03460e7i		−	0.222827i
$117$	−1.26339e8	+	1.24785e8i	−0.674208	+	0.665915i
$118$		−	2.29704e8i		−	1.18479i
$119$		−	4.87254e7i		−	0.242978i
$120$	6.10148e7	−	1.69900e8i	0.294246	−	0.819350i
$121$	−3.29090e7			−0.153523
$122$	1.16560e8			0.526152
$123$	3.87081e7	−	9.26380e7i	0.169115	−	0.404733i
$124$	1.77398e7			0.0750348
$125$	3.72192e7	+	2.41287e8i	0.152450	+	0.988311i
$126$	2.81293e8	−	2.77833e8i	1.11603	−	1.10230i
$127$			3.35553e7i			0.128987i	0.997918	+	0.0644936i	$0.0205432\pi$
$127$			3.35553e7i			0.128987i	−0.997918	+	0.0644936i	$0.979457\pi$
$128$	−3.20750e8			−1.19489
$129$	−3.60900e7	+	8.63722e7i	−0.130325	+	0.311900i
$130$	−2.97067e8	+	1.51682e7i	−1.04011	+	0.0531081i
$131$		−	2.26563e7i		−	0.0769315i	−0.999260	−	0.0384658i	$-0.987753\pi$
$131$		−	2.26563e7i		−	0.0769315i	0.999260	−	0.0384658i	$-0.0122471\pi$
$132$	−2.61306e7	+	6.25370e7i	−0.0860705	+	0.205988i
$133$			7.19902e8i			2.30074i
$134$			4.36041e8i			1.35241i
$135$	3.01297e8	−	1.39801e8i	0.907109	−	0.420896i
$136$	−5.07016e7			−0.148206
$137$	4.06245e8			1.15320			0.576602	−	0.817025i	$-0.304378\pi$
$137$	4.06245e8			1.15320			0.576602	+	0.817025i	$0.304378\pi$
$138$	7.91563e7	+	3.30749e7i	0.218258	+	0.0911974i
$139$	7.13135e8			1.91035			0.955174	−	0.296046i	$-0.0956683\pi$
$139$	7.13135e8			1.91035			0.955174	+	0.296046i	$0.0956683\pi$
$140$	1.13823e8	−	5.81179e6i	0.296291	−	0.0151286i
$141$	−1.13725e8	−	4.75191e7i	−0.287726	−	0.120224i
$142$			1.88340e8i			0.463223i
$143$	−4.25594e8			−1.01777
$144$	−3.51907e8	−	3.56289e8i	−0.818423	−	0.828615i
$145$	−4.73264e8	+	2.41648e7i	−1.07061	+	0.0546653i
$146$			6.13108e8i			1.34935i
$147$	−4.46857e8	−	1.86716e8i	−0.956972	−	0.399864i
$148$			3.63614e7i			0.0757869i
$149$		−	6.69006e8i		−	1.35733i	−0.734448	−	0.678665i	$-0.762559\pi$
$149$		−	6.69006e8i		−	1.35733i	0.734448	−	0.678665i	$-0.237441\pi$
$150$	5.32548e8	+	1.61103e8i	1.05195	+	0.318229i
$151$	−5.63219e8			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$151$	−5.63219e8			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$152$	7.49100e8			1.40335
$153$	−6.55545e7	−	6.63709e7i	−0.119629	−	0.121119i
$154$	9.47581e8			1.68474
$155$	−1.06251e7	−	2.08091e8i	−0.0184080	−	0.360517i
$156$	−4.49757e7	+	1.07638e8i	−0.0759415	+	0.181747i
$157$		−	1.50502e8i		−	0.247710i	−0.992300	−	0.123855i	$-0.960474\pi$
$157$		−	1.50502e8i		−	0.247710i	0.992300	−	0.123855i	$-0.0395258\pi$
$158$	−8.82311e8			−1.41577
$159$	−3.53804e8	−	1.47834e8i	−0.553572	−	0.231306i
$160$	−1.36819e7	−	2.67958e8i	−0.0208769	−	0.408871i
$161$		−	2.06405e8i		−	0.307197i
$162$	9.36762e6	−	7.56894e8i	0.0136010	−	1.09894i
$163$		−	1.13070e9i		−	1.60175i	−0.598830	−	0.800876i	$-0.704367\pi$
$163$		−	1.13070e9i		−	1.60175i	0.598830	−	0.800876i	$-0.295633\pi$
$164$		−	6.59568e7i		−	0.0911768i
$165$	7.49218e8	+	2.69060e8i	1.01082	+	0.363006i
$166$	−7.92299e8			−1.04341
$167$	−5.40340e8			−0.694707			−0.347353	−	0.937734i	$-0.612920\pi$
$167$	−5.40340e8			−0.694707			−0.347353	+	0.937734i	$0.612920\pi$
$168$	−3.81618e8	+	9.13304e8i	−0.479062	+	1.14651i
$169$	8.32048e7			0.102000
$170$	−7.96846e6	−	1.56061e8i	−0.00954067	−	0.186852i
$171$	9.68546e8	+	9.80608e8i	1.13276	+	1.14686i
$172$			6.14956e7i			0.0702636i
$173$	2.02228e8			0.225765			0.112883	−	0.993608i	$-0.463992\pi$
$173$	2.02228e8			0.225765			0.112883	+	0.993608i	$0.463992\pi$
$174$	−4.16363e8	+	9.96457e8i	−0.454229	+	1.08708i
$175$	−1.36346e8	−	1.33168e9i	−0.145375	−	1.41987i
$176$		−	1.20022e9i		−	1.25086i
$177$	−4.07938e8	+	9.76295e8i	−0.415624	+	0.994690i
$178$			1.28504e9i			1.28008i
$179$			8.47838e8i			0.825850i	0.910765	+	0.412925i	$0.135493\pi$
$179$			8.47838e8i			0.825850i	−0.910765	+	0.412925i	$0.864507\pi$
$180$	1.47224e8	−	1.61052e8i	0.140245	−	0.153418i
$181$	1.41633e9			1.31962			0.659810	−	0.751432i	$-0.270637\pi$
$181$	1.41633e9			1.31962			0.659810	+	0.751432i	$0.270637\pi$
$182$	1.63096e9			1.48648
$183$	−4.95409e8	−	2.07003e8i	−0.441733	−	0.184575i
$184$	−2.14776e8			−0.187376
$185$	4.26524e8	−	2.17783e7i	0.364130	−	0.0185925i
$186$	−4.38135e8	−	1.83072e8i	−0.366063	−	0.152957i
$187$		−	2.23581e8i		−	0.182839i
$188$	−8.09702e7			−0.0648177
$189$	−1.68897e9	+	6.81298e8i	−1.32366	+	0.533937i
$190$	1.17731e8	+	2.30575e9i	0.0903396	+	1.76929i
$191$		−	6.78044e8i		−	0.509476i	−0.967010	−	0.254738i	$-0.918011\pi$
$191$		−	6.78044e8i		−	0.509476i	0.967010	−	0.254738i	$-0.0819893\pi$
$192$	8.96170e8	+	3.74458e8i	0.659455	+	0.275549i
$193$			7.99869e8i			0.576487i	0.957557	+	0.288244i	$0.0930713\pi$
$193$			7.99869e8i			0.576487i	−0.957557	+	0.288244i	$0.906929\pi$
$194$		−	2.56641e9i		−	1.81184i
$195$	1.28954e9	+	4.63102e8i	0.891861	+	0.320286i
$196$	−3.18155e8			−0.215583
$197$	−2.31570e9			−1.53751			−0.768753	−	0.639546i	$-0.779122\pi$
$197$	−2.31570e9			−1.53751			−0.768753	+	0.639546i	$0.779122\pi$
$198$	1.29074e9	−	1.27486e9i	0.839803	−	0.829473i
$199$	−1.43493e9			−0.914997			−0.457498	−	0.889210i	$-0.651254\pi$
$199$	−1.43493e9			−0.914997			−0.457498	+	0.889210i	$0.651254\pi$
$200$	−1.38569e9	+	1.41876e8i	−0.866055	+	0.0886726i
$201$	7.74379e8	−	1.85328e9i	0.474427	−	1.13542i
$202$		−	2.13320e8i		−	0.128123i
$203$	2.59832e9			1.53006
$204$	−5.65464e7	−	2.36275e7i	−0.0326501	−	0.0136426i
$205$	−7.73682e8	+	3.95041e7i	−0.438074	+	0.0223680i
$206$			2.17548e9i			1.20805i
$207$	−2.77694e8	−	2.81152e8i	−0.151247	−	0.153130i
$208$		−	2.06580e9i		−	1.10366i
$209$			3.30334e9i			1.73128i
$210$	−2.87115e9	−	1.03109e9i	−1.47632	−	0.530176i
$211$	7.19293e8			0.362891			0.181445	−	0.983401i	$-0.441922\pi$
$211$	7.19293e8			0.362891			0.181445	+	0.983401i	$0.441922\pi$
$212$	−2.51903e8			−0.124707
$213$	3.34480e8	−	8.00491e8i	0.162499	−	0.388900i
$214$	2.38805e9			1.13865
$215$	7.21352e8	−	3.68321e7i	0.337593	−	0.0172375i
$216$	7.08930e8	+	1.75747e9i	0.325678	+	0.807371i
$217$			1.14246e9i			0.515232i
$218$	−4.66261e8			−0.206444
$219$	1.08884e9	−	2.60585e9i	0.473355	−	1.13285i
$220$	5.22288e8	−	2.66680e7i	0.222956	−	0.0113841i
$221$		−	3.84825e8i		−	0.161322i
$222$	3.75243e8	−	8.98047e8i	0.154490	−	0.369732i
$223$		−	1.26189e9i		−	0.510274i	−0.966905	−	0.255137i	$-0.917879\pi$
$223$		−	1.26189e9i		−	0.510274i	0.966905	−	0.255137i	$-0.0821206\pi$
$224$			1.47115e9i			0.584338i
$225$	−1.97735e9	−	1.63050e9i	−0.771529	−	0.636194i
$226$	−3.24420e9			−1.24358
$227$	−4.20903e9			−1.58518			−0.792590	−	0.609755i	$-0.791268\pi$
$227$	−4.20903e9			−1.58518			−0.792590	+	0.609755i	$0.791268\pi$
$228$	8.35454e8	+	3.49089e8i	0.309160	+	0.129180i
$229$	7.15398e8			0.260139			0.130070	−	0.991505i	$-0.458480\pi$
$229$	7.15398e8			0.260139			0.130070	+	0.991505i	$0.458480\pi$
$230$	−3.37551e7	−	6.61087e8i	−0.0120622	−	0.236237i
$231$	−4.02744e9	−	1.68284e9i	−1.41443	−	0.591009i
$232$		−	2.70370e9i		−	0.933269i
$233$	3.80229e9			1.29009			0.645047	−	0.764143i	$-0.276838\pi$
$233$	3.80229e9			1.29009			0.645047	+	0.764143i	$0.276838\pi$
$234$	2.22160e9	−	2.19427e9i	0.740973	−	0.731859i
$235$	4.84962e7	+	9.49791e8i	0.0159014	+	0.311427i
$236$			6.95106e8i			0.224080i
$237$	3.75003e9	+	1.56692e9i	1.18861	+	0.496654i
$238$			8.56809e8i			0.267040i
$239$		−	3.64896e9i		−	1.11835i	−0.829050	−	0.559175i	$-0.811118\pi$
$239$		−	3.64896e9i		−	1.11835i	0.829050	−	0.559175i	$-0.188882\pi$
$240$	−1.30600e9	+	3.63665e9i	−0.393638	+	1.09612i
$241$	1.36444e9			0.404471			0.202235	−	0.979337i	$-0.435179\pi$
$241$	1.36444e9			0.404471			0.202235	+	0.979337i	$0.435179\pi$
$242$	5.78686e8			0.168726
$243$	−1.38401e9	+	3.20034e9i	−0.396929	+	0.917849i
$244$	−3.52723e8			−0.0995119
$245$	1.90556e8	+	3.73200e9i	0.0528880	+	1.03580i
$246$	−6.80661e8	+	1.62899e9i	−0.185862	+	0.444813i
$247$			5.68566e9i			1.52754i
$248$	1.18880e9			0.314269
$249$	3.36746e9	+	1.40707e9i	0.876001	+	0.366031i
$250$	−6.54479e8	−	4.24289e9i	−0.167547	−	1.08618i
$251$			7.18506e9i			1.81024i	0.425160	+	0.905118i	$0.360218\pi$
$251$			7.18506e9i			1.81024i	−0.425160	+	0.905118i	$0.639782\pi$
$252$	−8.51219e8	+	8.40750e8i	−0.211076	+	0.208480i
$253$		−	9.47109e8i		−	0.231163i
$254$		−	5.90051e8i		−	0.141760i
$255$	−2.43286e8	+	6.77448e8i	−0.0575382	+	0.160219i
$256$	2.57056e9			0.598506
$257$	−3.06178e9			−0.701846			−0.350923	−	0.936404i	$-0.614132\pi$
$257$	−3.06178e9			−0.701846			−0.350923	+	0.936404i	$0.614132\pi$
$258$	6.34622e8	−	1.51881e9i	0.143231	−	0.342786i
$259$	−2.34171e9			−0.520396
$260$	8.98955e8	−	4.59005e7i	0.196718	−	0.0100444i
$261$	3.53928e9	−	3.49575e9i	0.762698	−	0.753317i
$262$			3.98399e8i			0.0845498i
$263$	3.51144e9			0.733943			0.366971	−	0.930232i	$-0.380395\pi$
$263$	3.51144e9			0.733943			0.366971	+	0.930232i	$0.380395\pi$
$264$	−1.75109e9	+	4.19078e9i	−0.360490	+	0.862739i
$265$	1.50874e8	+	2.95485e9i	0.0305937	+	0.599173i
$266$		−	1.26591e10i		−	2.52857i
$267$	2.28214e9	−	5.46171e9i	0.449052	−	1.07469i
$268$		−	1.31950e9i		−	0.255783i
$269$			1.89915e9i			0.362703i	0.983418	+	0.181352i	$0.0580472\pi$
$269$			1.89915e9i			0.362703i	−0.983418	+	0.181352i	$0.941953\pi$
$270$	−5.29813e9	+	2.45832e9i	−0.996937	+	0.462576i
$271$	6.54442e7			0.0121337			0.00606686	−	0.999982i	$-0.498069\pi$
$271$	6.54442e7			0.0121337			0.00606686	+	0.999982i	$0.498069\pi$
$272$	1.08525e9			0.198268
$273$	−6.93197e9	−	2.89648e9i	−1.24798	−	0.521458i
$274$	−7.14359e9			−1.26740
$275$	−6.25638e8	−	6.11054e9i	−0.109394	−	1.06844i
$276$	−2.39535e8	−	1.00088e8i	−0.0412793	−	0.0172483i
$277$		−	6.90961e9i		−	1.17364i	−0.809718	−	0.586820i	$-0.800380\pi$
$277$		−	6.90961e9i		−	1.17364i	0.809718	−	0.586820i	$-0.199620\pi$
$278$	−1.25401e10			−2.09952
$279$	1.53705e9	+	1.55619e9i	0.253672	+	0.256831i
$280$	7.62761e9	−	3.89465e8i	1.24096	−	0.0633631i
$281$		−	1.73863e9i		−	0.278857i	−0.990232	−	0.139428i	$-0.955474\pi$
$281$		−	1.73863e9i		−	0.278857i	0.990232	−	0.139428i	$-0.0445265\pi$
$282$	1.99978e9	+	8.35596e8i	0.316218	+	0.132130i
$283$			4.14006e9i			0.645448i	0.946493	+	0.322724i	$0.104599\pi$
$283$			4.14006e9i			0.645448i	−0.946493	+	0.322724i	$0.895401\pi$
$284$		−	5.69937e8i		−	0.0876100i
$285$	3.59447e9	−	1.00091e10i	0.544823	−	1.51710i
$286$	7.48383e9			1.11856
$287$	4.24768e9			0.626072
$288$	1.97926e9	+	2.00391e9i	0.287695	+	0.291278i
$289$	−6.77359e9			−0.971019
$290$	8.32208e9	−	4.24925e8i	1.17663	−	0.0600786i
$291$	−4.55777e9	+	1.09079e10i	−0.635595	+	1.52113i
$292$		−	1.85533e9i		−	0.255205i
$293$	−6.87312e9			−0.932575			−0.466287	−	0.884633i	$-0.654409\pi$
$293$	−6.87312e9			−0.932575			−0.466287	+	0.884633i	$0.654409\pi$
$294$	7.85772e9	+	3.28330e9i	1.05174	+	0.439461i
$295$	8.15369e9	−	4.16327e8i	1.07663	−	0.0549726i
$296$			2.43668e9i			0.317419i
$297$	−7.75001e9	+	3.12620e9i	−0.996039	+	0.401783i
$298$			1.17641e10i			1.49174i
$299$		−	1.63015e9i		−	0.203959i
$300$	−1.61154e9	−	4.87515e8i	−0.198956	−	0.0601870i
$301$	−3.96038e9			−0.482470
$302$	9.90389e9			1.19063
$303$	−3.78842e8	+	9.06662e8i	−0.0449457	+	0.107566i
$304$	−1.60342e10			−1.87738
$305$	2.11260e8	+	4.13749e9i	0.0244128	+	0.478121i
$306$	1.15274e9	+	1.16709e9i	0.131476	+	0.133113i
$307$			2.34414e9i			0.263894i	0.991257	+	0.131947i	$0.0421229\pi$
$307$			2.34414e9i			0.263894i	−0.991257	+	0.131947i	$0.957877\pi$
$308$	−2.86747e9			−0.318637
$309$	3.86350e9	−	9.24630e9i	0.423787	−	1.01422i
$310$	1.86836e8	+	3.65916e9i	0.0202309	+	0.396218i
$311$		−	6.18587e9i		−	0.661240i	−0.943764	−	0.330620i	$-0.892742\pi$
$311$		−	6.18587e9i		−	0.661240i	0.943764	−	0.330620i	$-0.107258\pi$
$312$	−3.01395e9	+	7.21312e9i	−0.318066	+	0.761210i
$313$		−	6.33696e9i		−	0.660243i	−0.943939	−	0.330121i	$-0.892910\pi$
$313$		−	6.33696e9i		−	0.660243i	0.943939	−	0.330121i	$-0.107090\pi$
$314$			2.64649e9i			0.272240i
$315$	1.03719e10	+	9.48136e9i	1.05346	+	0.963005i
$316$	2.66996e9			0.267767
$317$	2.63659e9			0.261099			0.130550	−	0.991442i	$-0.458326\pi$
$317$	2.63659e9			0.261099			0.130550	+	0.991442i	$0.458326\pi$
$318$	6.22144e9	+	2.59958e9i	0.608390	+	0.254212i
$319$	1.19226e10			1.15136
$320$	−3.82158e8	−	7.48451e9i	−0.0364455	−	0.713779i
$321$	−1.01498e10	−	4.24101e9i	−0.955953	−	0.399438i
$322$			3.62951e9i			0.337617i
$323$	−2.98690e9			−0.274417
$324$	−2.83474e7	+	2.29044e9i	−0.00257237	+	0.207844i
$325$	−1.07684e9	−	1.05174e10i	−0.0965200	−	0.942700i
$326$			1.98826e10i			1.76037i
$327$	1.98172e9	+	8.28047e8i	0.173321	+	0.0724209i
$328$		−	4.41996e9i		−	0.381876i
$329$		−	5.21456e9i		−	0.445076i
$330$	−1.31746e10	−	4.73127e9i	−1.11091	−	0.398953i
$331$	−6.06785e9			−0.505502			−0.252751	−	0.967531i	$-0.581335\pi$
$331$	−6.06785e9			−0.505502			−0.252751	+	0.967531i	$0.581335\pi$
$332$	2.39758e9			0.197342
$333$	−3.18974e9	+	3.15051e9i	−0.259405	+	0.256214i
$334$	9.50158e9			0.763501
$335$	−1.54780e10	+	7.90303e8i	−1.22895	+	0.0627501i
$336$	8.16837e9	−	1.95489e10i	0.640882	−	1.53379i
$337$		−	1.29810e10i		−	1.00644i	−0.864158	−	0.503220i	$-0.832149\pi$
$337$		−	1.29810e10i		−	1.00644i	0.864158	−	0.503220i	$-0.167851\pi$
$338$	−1.46311e9			−0.112101
$339$	1.37886e10	+	5.76148e9i	1.04405	+	0.436249i
$340$	2.41134e7	+	4.72256e8i	0.00180444	+	0.0353397i
$341$			5.24230e9i			0.387708i
$342$	−1.70313e10	−	1.72434e10i	−1.24493	−	1.26043i
$343$		−	7.33974e8i		−	0.0530279i
$344$			4.12100e9i			0.294285i
$345$	−1.03058e9	+	2.86972e9i	−0.0727453	+	0.202565i
$346$	−3.55607e9			−0.248122
$347$	1.27979e10			0.882718			0.441359	−	0.897331i	$-0.354496\pi$
$347$	1.27979e10			0.882718			0.441359	+	0.897331i	$0.354496\pi$
$348$	1.25996e9	−	3.01538e9i	0.0859089	−	0.205601i
$349$	−7.93032e9			−0.534551			−0.267275	−	0.963620i	$-0.586123\pi$
$349$	−7.93032e9			−0.534551			−0.267275	+	0.963620i	$0.586123\pi$
$350$	2.39757e9	+	2.34168e10i	0.159771	+	1.56047i
$351$	−1.33392e10	+	5.38077e9i	−0.878823	+	0.354500i
$352$			6.75050e9i			0.439709i
$353$	1.11540e10			0.718342			0.359171	−	0.933272i	$-0.383059\pi$
$353$	1.11540e10			0.718342			0.359171	+	0.933272i	$0.383059\pi$
$354$	7.17336e9	−	1.71676e10i	0.456782	−	1.09319i
$355$	−6.68544e9	+	3.41358e8i	−0.420936	+	0.0214930i
$356$		−	3.88865e9i		−	0.242102i
$357$	1.52163e9	−	3.64164e9i	0.0936779	−	0.224194i
$358$		−	1.49088e10i		−	0.907631i
$359$			3.89548e9i			0.234522i	0.993101	+	0.117261i	$0.0374114\pi$
$359$			3.89548e9i			0.234522i	−0.993101	+	0.117261i	$0.962589\pi$
$360$	9.86590e9	−	1.07926e10i	0.587390	−	0.642563i
$361$	2.71469e10			1.59842
$362$	−2.49053e10			−1.45030
$363$	−2.45955e9	−	1.02771e9i	−0.141654	−	0.0591893i
$364$	−4.93545e9			−0.281139
$365$	−2.17632e10	+	1.11123e9i	−1.22617	+	0.0626083i
$366$	8.71148e9	+	3.64003e9i	0.485476	+	0.202853i
$367$			2.72657e10i			1.50298i	0.659747	+	0.751488i	$0.270663\pi$
$367$			2.72657e10i			1.50298i	−0.659747	+	0.751488i	$0.729337\pi$
$368$	4.59720e9			0.250670
$369$	5.78594e9	−	5.71477e9i	0.312082	−	0.308243i
$370$	−7.50019e9	+	3.82959e8i	−0.400189	+	0.0204336i
$371$		−	1.62228e10i		−	0.856307i
$372$	1.32584e9	+	5.53993e8i	0.0692340	+	0.0289289i
$373$			8.68516e9i			0.448686i	0.974510	+	0.224343i	$0.0720236\pi$
$373$			8.68516e9i			0.448686i	−0.974510	+	0.224343i	$0.927976\pi$
$374$			3.93155e9i			0.200945i
$375$	−4.75340e9	+	1.91956e10i	−0.240369	+	0.970682i
$376$	−5.42605e9			−0.271476
$377$	2.05211e10			1.01586
$378$	2.96996e10	−	1.19802e10i	1.45473	−	0.586811i
$379$	−2.18982e10			−1.06133			−0.530666	−	0.847581i	$-0.678058\pi$
$379$	−2.18982e10			−1.06133			−0.530666	+	0.847581i	$0.678058\pi$
$380$	−3.56267e8	−	6.97744e9i	−0.0170860	−	0.334627i
$381$	−1.04789e9	+	2.50786e9i	−0.0497297	+	0.119015i
$382$			1.19230e10i			0.559928i
$383$	3.16884e10			1.47267			0.736334	−	0.676618i	$-0.236555\pi$
$383$	3.16884e10			1.47267			0.736334	+	0.676618i	$0.236555\pi$
$384$	−2.39722e10	−	1.00166e10i	−1.10251	−	0.460677i
$385$	1.71744e9	+	3.36359e10i	0.0781699	+	1.53094i
$386$		−	1.40652e10i		−	0.633575i
$387$	−5.39459e9	+	5.32824e9i	−0.240500	+	0.237542i
$388$			7.76622e9i			0.342675i
$389$			9.57908e9i			0.418336i	0.977880	+	0.209168i	$0.0670756\pi$
$389$			9.57908e9i			0.418336i	−0.977880	+	0.209168i	$0.932924\pi$
$390$	−2.26759e10	−	8.14339e9i	−0.980180	−	0.352003i
$391$	8.56382e8			0.0366404
$392$	−2.13205e10			−0.902928
$393$	7.07528e8	−	1.69329e9i	0.0296602	−	0.0709840i
$394$	4.07202e10			1.68976
$395$	−1.59914e9	−	3.13190e10i	−0.0656900	−	1.28653i
$396$	−3.90590e9	+	3.85786e9i	−0.158833	+	0.156879i
$397$		−	4.45553e10i		−	1.79365i	−0.442388	−	0.896824i	$-0.645868\pi$
$397$		−	4.45553e10i		−	1.79365i	0.442388	−	0.896824i	$-0.354132\pi$
$398$	2.52325e10			1.00561
$399$	−2.24816e10	+	5.38040e10i	−0.887026	+	2.12287i
$400$	2.96601e10	−	3.03680e9i	1.15860	−	0.118625i
$401$			2.51147e10i			0.971293i	0.874155	+	0.485647i	$0.161416\pi$
$401$			2.51147e10i			0.971293i	−0.874155	+	0.485647i	$0.838584\pi$
$402$	−1.36170e10	+	3.25888e10i	−0.521408	+	1.24786i
$403$			9.02297e9i			0.342081i
$404$			6.45529e8i			0.0242321i
$405$	2.68841e10	−	1.03931e9i	0.999254	−	0.0386302i
$406$	−4.56900e10			−1.68158
$407$	−1.07452e10			−0.391594
$408$	−3.78933e9	−	1.58335e9i	−0.136748	−	0.0571394i
$409$	−1.11563e10			−0.398683			−0.199341	−	0.979930i	$-0.563880\pi$
$409$	−1.11563e10			−0.398683			−0.199341	+	0.979930i	$0.563880\pi$
$410$	1.36048e10	−	6.94658e8i	0.481455	−	0.0245830i
$411$	3.03620e10	+	1.26865e10i	1.06405	+	0.444606i
$412$		−	6.58322e9i		−	0.228481i
$413$	−4.47655e10			−1.53866
$414$	4.88310e9	+	4.94391e9i	0.166224	+	0.168294i
$415$	−1.43600e9	−	2.81239e10i	−0.0484131	−	0.948163i
$416$			1.16189e10i			0.387963i
$417$	5.32982e10	+	2.22703e10i	1.76266	+	0.736515i
$418$		−	5.80874e10i		−	1.90273i
$419$		−	5.51814e10i		−	1.79034i	−0.445720	−	0.895172i	$-0.647052\pi$
$419$		−	5.51814e10i		−	1.79034i	0.445720	−	0.895172i	$-0.352948\pi$
$420$	8.68840e9	+	3.12019e9i	0.279218	+	0.100273i
$421$	2.21829e10			0.706139			0.353070	−	0.935597i	$-0.385138\pi$
$421$	2.21829e10			0.706139			0.353070	+	0.935597i	$0.385138\pi$
$422$	−1.26484e10			−0.398827
$423$	−7.01559e9	−	7.10296e9i	−0.219131	−	0.221859i
$424$	−1.68807e10			−0.522309
$425$	5.52519e9	−	5.65706e8i	0.169352	−	0.0173394i
$426$	−5.88163e9	+	1.40762e10i	−0.178591	+	0.427412i
$427$		−	2.27157e10i		−	0.683305i
$428$	−7.22648e9			−0.215354
$429$	−3.18080e10	−	1.32908e10i	−0.939091	−	0.392392i
$430$	−1.26846e10	+	6.47672e8i	−0.371024	+	0.0189444i
$431$		−	4.91950e10i		−	1.42565i	−0.701343	−	0.712824i	$-0.747416\pi$
$431$		−	4.91950e10i		−	1.42565i	0.701343	−	0.712824i	$-0.252584\pi$
$432$	−1.51744e10	−	3.76180e10i	−0.435688	−	1.08009i
$433$			1.97041e10i			0.560537i	0.959922	+	0.280268i	$0.0904235\pi$
$433$			1.97041e10i			0.560537i	−0.959922	+	0.280268i	$0.909577\pi$
$434$		−	2.00896e10i		−	0.566254i
$435$	−3.61254e10	−	1.29734e10i	−1.00892	−	0.362324i
$436$	1.41095e9			0.0390451
$437$	−1.26528e10			−0.346944
$438$	−1.91466e10	+	4.58224e10i	−0.520230	+	1.24504i
$439$	1.74433e10			0.469647			0.234824	−	0.972038i	$-0.424549\pi$
$439$	1.74433e10			0.469647			0.234824	+	0.972038i	$0.424549\pi$
$440$	3.50000e10	−	1.78710e9i	0.933809	−	0.0476802i
$441$	−2.75663e10	−	2.79096e10i	−0.728826	−	0.737902i
$442$			6.76693e9i			0.177297i
$443$	2.46881e10			0.641022			0.320511	−	0.947245i	$-0.396145\pi$
$443$	2.46881e10			0.641022			0.320511	+	0.947245i	$0.396145\pi$
$444$	−1.13552e9	+	2.71758e9i	−0.0292189	+	0.0699279i
$445$	−4.56144e10	+	2.32907e9i	−1.16322	+	0.0593939i
$446$			2.21897e10i			0.560805i
$447$	2.08922e10	−	5.00002e10i	0.523305	−	1.25240i
$448$			4.10916e10i			1.02010i
$449$			4.94885e10i			1.21764i	0.793308	+	0.608820i	$0.208357\pi$
$449$			4.94885e10i			1.21764i	−0.793308	+	0.608820i	$0.791643\pi$
$450$	3.47705e10	+	2.86713e10i	0.847932	+	0.699194i
$451$	1.94909e10			0.471114
$452$	9.81727e9			0.235200
$453$	−4.20939e10	−	1.75886e10i	−0.999599	−	0.417676i
$454$	7.40134e10			1.74216
$455$	2.95604e9	+	5.78935e10i	0.0689707	+	1.35078i
$456$	5.59862e10	+	2.33934e10i	1.29486	+	0.541047i
$457$			7.51747e10i			1.72348i	0.507349	+	0.861741i	$0.330626\pi$
$457$			7.51747e10i			1.72348i	−0.507349	+	0.861741i	$0.669374\pi$
$458$	−1.25799e10			−0.285900
$459$	−2.82673e9	−	7.00761e9i	−0.0636845	−	0.157877i
$460$	1.02146e8	+	2.00052e9i	0.00228134	+	0.0446798i
$461$		−	1.73856e10i		−	0.384933i	−0.981304	−	0.192466i	$-0.938351\pi$
$461$		−	1.73856e10i		−	0.384933i	0.981304	−	0.192466i	$-0.0616487\pi$
$462$	7.08203e10	+	2.95918e10i	1.55450	+	0.649535i
$463$		−	2.11164e10i		−	0.459511i	−0.973248	−	0.229755i	$-0.926207\pi$
$463$		−	2.11164e10i		−	0.459511i	0.973248	−	0.229755i	$-0.0737926\pi$
$464$			5.78717e10i			1.24852i
$465$	5.70431e9	−	1.58841e10i	0.122009	−	0.339743i
$466$	−6.68610e10			−1.41785
$467$	−1.49113e10			−0.313508			−0.156754	−	0.987638i	$-0.550103\pi$
$467$	−1.49113e10			−0.313508			−0.156754	+	0.987638i	$0.550103\pi$
$468$	−6.72278e9	+	6.64009e9i	−0.140141	+	0.138417i
$469$	8.49774e10			1.75635
$470$	−8.52779e8	−	1.67015e10i	−0.0174761	−	0.342267i
$471$	4.69999e9	−	1.12482e10i	0.0955022	−	0.228560i
$472$			4.65811e10i			0.938516i
$473$	−1.81726e10			−0.363054
$474$	−6.59421e10	−	2.75535e10i	−1.30632	−	0.545837i
$475$	−8.16329e10	+	8.35812e9i	−1.60358	+	0.164185i
$476$		−	2.59279e9i		−	0.0505056i
$477$	−2.18259e10	−	2.20977e10i	−0.421598	−	0.426848i
$478$			6.41649e10i			1.22910i
$479$		−	5.15755e9i		−	0.0979718i	−0.998799	−	0.0489859i	$-0.984401\pi$
$479$		−	5.15755e9i		−	0.0979718i	0.998799	−	0.0489859i	$-0.0155989\pi$
$480$	7.34543e9	−	2.04539e10i	0.138373	−	0.385311i
$481$	−1.84944e10			−0.345510
$482$	−2.39929e10			−0.444524
$483$	6.44576e9	−	1.54263e10i	0.118437	−	0.283448i
$484$	−1.75116e9			−0.0319114
$485$	9.10988e10	−	4.65149e9i	1.64644	−	0.0840670i
$486$	2.43370e10	−	5.62762e10i	0.436236	−	1.00874i
$487$		−	3.79969e10i		−	0.675510i	−0.941234	−	0.337755i	$-0.890332\pi$
$487$		−	3.79969e10i		−	0.675510i	0.941234	−	0.337755i	$-0.109668\pi$
$488$	−2.36370e10			−0.416786
$489$	3.53102e10	−	8.45059e10i	0.617540	−	1.47792i
$490$	−3.35081e9	−	6.56251e10i	−0.0581254	−	1.13838i
$491$			7.21946e10i			1.24216i	0.783746	+	0.621081i	$0.213306\pi$
$491$			7.21946e10i			1.24216i	−0.783746	+	0.621081i	$0.786694\pi$
$492$	2.05975e9	−	4.92948e9i	0.0351523	−	0.0841280i
$493$			1.07805e10i			0.182496i
$494$		−	9.99791e10i		−	1.67881i
$495$	4.75926e10	+	4.35061e10i	0.792718	+	0.724652i
$496$	−2.54457e10			−0.420425
$497$	3.67045e10			0.601580
$498$	−5.92148e10	−	2.47425e10i	−0.962749	−	0.402278i
$499$	−2.25403e10			−0.363544			−0.181772	−	0.983341i	$-0.558183\pi$
$499$	−2.25403e10			−0.363544			−0.181772	+	0.983341i	$0.558183\pi$
$500$	1.98052e9	+	1.28394e10i	0.0316883	+	0.205431i
$501$	−4.03839e10	−	1.68741e10i	−0.641000	−	0.267837i
$502$		−	1.26345e11i		−	1.98950i
$503$	−1.10303e11			−1.72312			−0.861559	−	0.507657i	$-0.830512\pi$
$503$	−1.10303e11			−1.72312			−0.861559	+	0.507657i	$0.830512\pi$
$504$	−5.70427e10	+	5.63411e10i	−0.884052	+	0.873178i
$505$	7.57214e9	−	3.86633e8i	0.116427	−	0.00594474i
$506$			1.66544e10i			0.254054i
$507$	6.21856e9	+	2.59838e9i	0.0941148	+	0.0393252i
$508$			1.78555e9i			0.0268113i
$509$			9.85205e10i			1.46776i	0.679278	+	0.733881i	$0.262293\pi$
$509$			9.85205e10i			1.46776i	−0.679278	+	0.733881i	$0.737707\pi$
$510$	4.27804e9	−	1.19125e10i	0.0632360	−	0.176085i
$511$	1.19485e11			1.75238
$512$	3.69102e10			0.537114
$513$	4.17641e10	+	1.03535e11i	0.603022	+	1.49492i
$514$	5.38397e10			0.771348
$515$	−7.72221e10	+	3.94295e9i	−1.09777	+	0.0560522i
$516$	−1.92043e9	+	4.59606e9i	−0.0270894	+	0.0648316i
$517$		−	2.39275e10i		−	0.334915i
$518$	4.11777e10			0.571930
$519$	1.51141e10	+	6.31533e9i	0.208312	+	0.0870416i
$520$	6.02416e10	−	3.07593e9i	0.823916	−	0.0420690i
$521$			7.84071e10i			1.06415i	0.846696	+	0.532077i	$0.178588\pi$
$521$			7.84071e10i			1.06415i	−0.846696	+	0.532077i	$0.821412\pi$
$522$	−6.22362e10	+	6.14707e10i	−0.838226	+	0.827916i
$523$		−	1.26646e11i		−	1.69272i	−0.532613	−	0.846359i	$-0.678790\pi$
$523$		−	1.26646e11i		−	1.69272i	0.532613	−	0.846359i	$-0.321210\pi$
$524$		−	1.20559e9i		−	0.0159910i
$525$	3.13964e10	−	1.03785e11i	0.413279	−	1.36615i
$526$	−6.17467e10			−0.806623
$527$	−4.74012e9			−0.0614536
$528$	3.74814e10	−	8.97020e10i	0.482258	−	1.15416i
$529$	−7.46833e10			−0.953676
$530$	−2.65304e9	−	5.19594e10i	−0.0336233	−	0.658507i
$531$	−6.09769e10	+	6.02269e10i	−0.766986	+	0.757552i
$532$			3.83076e10i			0.478232i
$533$	3.35474e10			0.415672
$534$	−4.01301e10	+	9.60410e10i	−0.493520	+	1.18111i
$535$	4.32823e9	+	8.47676e10i	0.0528317	+	1.03470i
$536$		−	8.84238e10i		−	1.07130i
$537$	−2.64769e10	+	6.33657e10i	−0.318398	+	0.762004i
$538$		−	3.33956e10i		−	0.398620i
$539$		−	9.40180e10i		−	1.11392i
$540$	1.60327e10	−	7.43912e9i	0.188552	−	0.0874876i
$541$	−8.35314e10			−0.975126			−0.487563	−	0.873088i	$-0.662114\pi$
$541$	−8.35314e10			−0.975126			−0.487563	+	0.873088i	$0.662114\pi$
$542$	−1.15080e9			−0.0133353
$543$	1.05853e11	+	4.42301e10i	1.21760	+	0.508767i
$544$	−6.10384e9			−0.0696960
$545$	−8.45075e8	−	1.65507e10i	−0.00957876	−	0.187598i
$546$	1.21895e11	+	5.09329e10i	1.37156	+	0.573096i
$547$			2.75997e10i			0.308287i	0.988048	+	0.154144i	$0.0492618\pi$
$547$			2.75997e10i			0.308287i	−0.988048	+	0.154144i	$0.950738\pi$
$548$	2.16172e10			0.239705
$549$	−3.05614e10	−	3.09420e10i	−0.336422	−	0.340611i
$550$	1.10015e10	+	1.07450e11i	0.120227	+	1.17424i
$551$		−	1.59279e11i		−	1.72803i
$552$	−1.60519e10	−	6.70719e9i	−0.172890	−	0.0722411i
$553$			1.71948e11i			1.83864i
$554$			1.21502e11i			1.28986i
$555$	3.25577e10	+	1.16922e10i	0.343148	+	0.123232i
$556$	3.79475e10			0.397086
$557$	1.06328e11			1.10465			0.552326	−	0.833628i	$-0.313740\pi$
$557$	1.06328e11			1.10465			0.552326	+	0.833628i	$0.313740\pi$
$558$	−2.70282e10	−	2.73648e10i	−0.278792	−	0.282264i
$559$	−3.12784e10			−0.320329
$560$	−1.63266e11	+	8.33634e9i	−1.66014	+	0.0847663i
$561$	6.98216e9	−	1.67100e10i	0.0704918	−	0.168704i
$562$			3.05728e10i			0.306471i
$563$	1.35823e11			1.35188			0.675941	−	0.736956i	$-0.263737\pi$
$563$	1.35823e11			1.35188			0.675941	+	0.736956i	$0.263737\pi$
$564$	−6.05155e9	−	2.52860e9i	−0.0598067	−	0.0249898i
$565$	−5.87995e9	−	1.15158e11i	−0.0577005	−	1.13006i
$566$		−	7.28006e10i		−	0.709364i
$567$	−1.47506e11	−	1.82560e9i	−1.42718	−	0.0176633i
$568$		−	3.81931e10i		−	0.366937i
$569$		−	6.61732e10i		−	0.631296i	−0.948876	−	0.315648i	$-0.897778\pi$
$569$		−	6.61732e10i		−	0.631296i	0.948876	−	0.315648i	$-0.102222\pi$
$570$	−6.32067e10	+	1.76004e11i	−0.598775	+	1.66733i
$571$	9.17754e10			0.863340			0.431670	−	0.902032i	$-0.357925\pi$
$571$	9.17754e10			0.863340			0.431670	+	0.902032i	$0.357925\pi$
$572$	−2.26468e10			−0.211555
$573$	2.11744e10	−	5.06756e10i	0.196424	−	0.470089i
$574$	−7.46931e10			−0.688070
$575$	2.34052e10	−	2.39638e9i	0.214112	−	0.0219222i
$576$	5.52840e10	+	5.59725e10i	0.502238	+	0.508493i
$577$			1.35583e11i			1.22321i	0.791162	+	0.611607i	$0.209476\pi$
$577$			1.35583e11i			1.22321i	−0.791162	+	0.611607i	$0.790524\pi$
$578$	1.19110e11			1.06718
$579$	−2.49789e10	+	5.97806e10i	−0.222259	+	0.531920i
$580$	−2.51835e10	+	1.28586e9i	−0.222538	+	0.0113627i
$581$			1.54406e11i			1.35506i
$582$	8.01458e10	−	1.91808e11i	0.698536	−	1.67177i
$583$		−	7.44398e10i		−	0.644363i
$584$		−	1.24331e11i		−	1.06888i
$585$	8.19157e10	+	7.48821e10i	0.699429	+	0.639373i
$586$	1.20860e11			1.02492
$587$	−6.90011e10			−0.581171			−0.290585	−	0.956849i	$-0.593850\pi$
$587$	−6.90011e10			−0.581171			−0.290585	+	0.956849i	$0.593850\pi$
$588$	−2.37783e10	−	9.93558e9i	−0.198917	−	0.0831159i
$589$	7.00338e10			0.581897
$590$	−1.43378e11	+	7.32087e9i	−1.18324	+	0.0604163i
$591$	−1.73071e11	−	7.23163e10i	−1.41864	−	0.592770i
$592$		−	5.21562e10i		−	0.424639i
$593$	−2.17447e11			−1.75847			−0.879234	−	0.476391i	$-0.841945\pi$
$593$	−2.17447e11			−1.75847			−0.879234	+	0.476391i	$0.841945\pi$
$594$	1.36279e11	−	5.49725e10i	1.09467	−	0.441570i
$595$	−3.04138e10	+	1.55292e9i	−0.242662	+	0.0123903i
$596$		−	3.55993e10i		−	0.282135i
$597$	−1.07244e11	−	4.48112e10i	−0.844260	−	0.352768i
$598$			2.86653e10i			0.224156i
$599$			1.17194e11i			0.910327i	0.890408	+	0.455163i	$0.150419\pi$
$599$			1.17194e11i			0.910327i	−0.890408	+	0.455163i	$0.849581\pi$
$600$	−1.07994e11	−	3.26698e10i	−0.833288	−	0.252082i
$601$	−4.03470e10			−0.309253			−0.154626	−	0.987973i	$-0.549417\pi$
$601$	−4.03470e10			−0.309253			−0.154626	+	0.987973i	$0.549417\pi$
$602$	6.96410e10			0.530248
$603$	1.15751e11	−	1.14327e11i	0.875499	−	0.864731i
$604$	−2.99702e10			−0.225186
$605$	1.04884e9	+	2.05414e10i	0.00782867	+	0.153323i
$606$	6.66173e9	−	1.59431e10i	0.0493965	−	0.118218i
$607$		−	4.42279e10i		−	0.325793i	−0.986643	−	0.162896i	$-0.947916\pi$
$607$		−	4.42279e10i		−	0.325793i	0.986643	−	0.162896i	$-0.0520836\pi$
$608$	9.01823e10			0.659944
$609$	1.94193e11	+	8.11423e10i	1.41177	+	0.589900i
$610$	−3.71488e9	−	7.27554e10i	−0.0268303	−	0.525468i
$611$		−	4.11837e10i		−	0.295502i
$612$	−3.48830e9	−	3.53174e9i	−0.0248662	−	0.0251758i
$613$		−	2.22935e11i		−	1.57883i	−0.613858	−	0.789416i	$-0.710383\pi$
$613$		−	2.22935e11i		−	1.57883i	0.613858	−	0.789416i	$-0.289617\pi$
$614$		−	4.12204e10i		−	0.290027i
$615$	−5.90571e10	−	2.12087e10i	−0.412830	−	0.148256i
$616$	−1.92158e11			−1.33455
$617$	−1.00709e11			−0.694906			−0.347453	−	0.937697i	$-0.612953\pi$
$617$	−1.00709e11			−0.694906			−0.347453	+	0.937697i	$0.612953\pi$
$618$	−6.79375e10	+	1.62591e11i	−0.465753	+	1.11466i
$619$	9.16635e10			0.624358			0.312179	−	0.950023i	$-0.398941\pi$
$619$	9.16635e10			0.624358			0.312179	+	0.950023i	$0.398941\pi$
$620$	−5.65385e8	−	1.10730e10i	−0.00382629	−	0.0749372i
$621$	−1.19743e10	−	2.96848e10i	−0.0805161	−	0.199603i
$622$			1.08775e11i			0.726721i
$623$	2.50433e11			1.66241
$624$	6.45124e10	−	1.54394e11i	0.425505	−	1.01834i
$625$	1.49422e11	−	3.09218e10i	0.979251	−	0.202649i
$626$			1.11432e11i			0.725624i
$627$	−1.03159e11	+	2.46885e11i	−0.667479	+	1.59744i
$628$		−	8.00855e9i		−	0.0514891i
$629$		−	9.71585e9i		−	0.0620695i
$630$	−1.82385e11	−	1.66724e11i	−1.15778	−	1.05837i
$631$	−8.69834e10			−0.548680			−0.274340	−	0.961633i	$-0.588459\pi$
$631$	−8.69834e10			−0.548680			−0.274340	+	0.961633i	$0.588459\pi$
$632$	1.78922e11			1.12149
$633$	5.37585e10	+	2.24626e10i	0.334836	+	0.139909i
$634$	−4.63629e10			−0.286955
$635$	2.09448e10	−	1.06944e9i	0.128819	−	0.00657750i
$636$	−1.88267e10	−	7.86660e9i	−0.115066	−	0.0480794i
$637$		−	1.61822e11i		−	0.982836i
$638$	−2.09653e11			−1.26537
$639$	4.99967e10	−	4.93817e10i	0.299873	−	0.296185i
$640$	1.02226e10	+	2.00208e11i	0.0609315	+	1.19333i
$641$			1.68189e11i			0.996243i	0.867107	+	0.498122i	$0.165977\pi$
$641$			1.68189e11i			0.996243i	−0.867107	+	0.498122i	$0.834023\pi$
$642$	1.78478e11	+	7.45758e10i	1.05062	+	0.438993i
$643$			1.47717e11i			0.864144i	0.901839	+	0.432072i	$0.142217\pi$
$643$			1.47717e11i			0.864144i	−0.901839	+	0.432072i	$0.857783\pi$
$644$		−	1.09833e10i		−	0.0638540i
$645$	5.50626e10	+	1.97741e10i	0.318140	+	0.114251i
$646$	5.25230e10			0.301592
$647$	−5.56399e10			−0.317518			−0.158759	−	0.987317i	$-0.550749\pi$
$647$	−5.56399e10			−0.317518			−0.158759	+	0.987317i	$0.550749\pi$
$648$	−1.89964e9	+	1.53489e11i	−0.0107739	+	0.870516i
$649$	−2.05411e11			−1.15783
$650$	1.89356e10	+	1.84942e11i	0.106078	+	1.03605i
$651$	−3.56777e10	+	8.53853e10i	−0.198643	+	0.475400i
$652$		−	6.01669e10i		−	0.332941i
$653$	−3.03168e11			−1.66737			−0.833683	−	0.552243i	$-0.813772\pi$
$653$	−3.03168e11			−1.66737			−0.833683	+	0.552243i	$0.813772\pi$
$654$	−3.48474e10	−	1.45607e10i	−0.190484	−	0.0795925i
$655$	−1.41418e10	+	7.22078e8i	−0.0768314	+	0.00392300i
$656$			9.46074e10i			0.510869i
$657$	1.62755e11	−	1.60753e11i	0.873520	−	0.862776i
$658$			9.16950e10i			0.489150i
$659$			4.09785e10i			0.217278i	0.994081	+	0.108639i	$0.0346492\pi$
$659$			4.09785e10i			0.217278i	−0.994081	+	0.108639i	$0.965351\pi$
$660$	3.98676e10	+	1.43173e10i	0.210109	+	0.0754545i
$661$	2.42879e11			1.27229			0.636143	−	0.771571i	$-0.280529\pi$
$661$	2.42879e11			1.27229			0.636143	+	0.771571i	$0.280529\pi$
$662$	1.06700e11			0.555560
$663$	1.20176e10	−	2.87610e10i	0.0621961	−	0.148851i
$664$	1.60668e11			0.826530
$665$	4.49353e11	−	2.29439e10i	2.29774	−	0.117323i
$666$	5.60898e10	−	5.53999e10i	0.285093	−	0.281586i
$667$			4.56673e10i			0.230729i
$668$	−2.87527e10			−0.144402
$669$	3.94074e10	−	9.43114e10i	0.196731	−	0.470825i
$670$	2.72171e11	−	1.38970e10i	1.35065	−	0.0689641i
$671$		−	1.04233e11i		−	0.514181i
$672$	−4.59420e10	+	1.09950e11i	−0.225286	+	0.539163i
$673$			2.34992e11i			1.14549i	0.819732	+	0.572747i	$0.194122\pi$
$673$			2.34992e11i			1.14549i	−0.819732	+	0.572747i	$0.805878\pi$
$674$			2.28263e11i			1.10610i
$675$	−9.68645e10	−	1.83610e11i	−0.466605	−	0.884466i
$676$	4.42752e9			0.0212018
$677$	−2.35523e11			−1.12119			−0.560595	−	0.828090i	$-0.689427\pi$
$677$	−2.35523e11			−1.12119			−0.560595	+	0.828090i	$0.689427\pi$
$678$	−2.42465e11	−	1.01312e11i	−1.14744	−	0.479450i
$679$	−5.00152e11			−2.35300
$680$	1.61591e9	+	3.16473e10i	0.00755754	+	0.148013i
$681$	−3.14574e11	−	1.31443e11i	−1.46263	−	0.611150i
$682$		−	9.21829e10i		−	0.426101i
$683$	−1.13979e11			−0.523772			−0.261886	−	0.965099i	$-0.584344\pi$
$683$	−1.13979e11			−0.523772			−0.261886	+	0.965099i	$0.584344\pi$
$684$	5.15385e10	+	5.21804e10i	0.235455	+	0.238387i
$685$	−1.29474e10	−	2.53573e11i	−0.0588059	−	1.15170i
$686$			1.29065e10i			0.0582791i
$687$	5.34674e10	+	2.23410e10i	0.240028	+	0.100294i
$688$		−	8.82083e10i		−	0.393691i
$689$		−	1.28125e11i		−	0.568533i
$690$	1.81221e10	−	5.04625e10i	0.0799490	−	0.222624i
$691$	2.47931e11			1.08747			0.543737	−	0.839256i	$-0.317009\pi$
$691$	2.47931e11			1.08747			0.543737	+	0.839256i	$0.317009\pi$
$692$	1.07610e10			0.0469277
$693$	−2.48450e11	−	2.51544e11i	−1.07722	−	1.09064i
$694$	−2.25044e11			−0.970131
$695$	−2.27283e10	−	4.45129e11i	−0.0974152	−	1.90786i
$696$	8.44332e10	−	2.02069e11i	0.359813	−	0.861119i
$697$			1.76238e10i			0.0746738i
$698$	1.39450e11			0.587485
$699$	2.84175e11	+	1.18741e11i	1.19036	+	0.497383i
$700$	−7.25529e9	−	7.08616e10i	−0.0302178	−	0.295134i
$701$		−	3.48469e11i		−	1.44308i	−0.692370	−	0.721542i	$-0.743434\pi$
$701$		−	3.48469e11i		−	1.44308i	0.692370	−	0.721542i	$-0.256566\pi$
$702$	2.34562e11	−	9.46178e10i	0.965850	−	0.389605i
$703$			1.43549e11i			0.587730i
$704$			1.88553e11i			0.767613i
$705$	−2.60363e10	+	7.25000e10i	−0.105396	+	0.293482i
$706$	−1.96137e11			−0.789477
$707$	−4.15727e10			−0.166391
$708$	−2.17073e10	+	5.19508e10i	−0.0863918	+	0.206757i
$709$	−3.19932e11			−1.26611			−0.633057	−	0.774105i	$-0.718200\pi$
$709$	−3.19932e11			−1.26611			−0.633057	+	0.774105i	$0.718200\pi$
$710$	1.17560e11	−	6.00258e9i	0.462620	−	0.0236213i
$711$	2.31337e11	+	2.34217e11i	0.905244	+	0.916517i
$712$		−	2.60590e11i		−	1.01400i
$713$	−2.00795e10			−0.0776955
$714$	−2.67571e10	+	6.40362e10i	−0.102955	+	0.246395i
$715$	1.35641e10	+	2.65650e11i	0.0518998	+	1.01645i
$716$			4.51154e10i			0.171661i
$717$	1.13952e11	−	2.72716e11i	0.431169	−	1.03189i
$718$		−	6.84998e10i		−	0.257746i
$719$			2.06854e11i			0.774014i	0.922077	+	0.387007i	$0.126491\pi$
$719$			2.06854e11i			0.774014i	−0.922077	+	0.387007i	$0.873509\pi$
$720$	−2.11176e11	+	2.31011e11i	−0.785803	+	0.859613i
$721$	4.23966e11			1.56888
$722$	−4.77364e11			−1.75671
$723$	1.01976e11	+	4.26098e10i	0.373201	+	0.155940i
$724$	7.53659e10			0.274297
$725$	3.01667e10	+	2.94635e11i	0.109188	+	1.06643i
$726$	4.32499e10	+	1.80716e10i	0.155682	+	0.0650506i
$727$			3.61835e11i			1.29531i	0.761934	+	0.647654i	$0.224250\pi$
$727$			3.61835e11i			1.29531i	−0.761934	+	0.647654i	$0.775750\pi$
$728$	−3.30739e11			−1.17750
$729$	−2.03381e11	+	1.95966e11i	−0.720111	+	0.693859i
$730$	3.82694e11	−	1.95403e10i	1.34760	−	0.0688082i
$731$		−	1.64318e10i		−	0.0575459i
$732$	−2.63618e10	−	1.10151e10i	−0.0918187	−	0.0383658i
$733$		−	2.04728e11i		−	0.709188i	−0.935020	−	0.354594i	$-0.884619\pi$
$733$		−	2.04728e11i		−	0.709188i	0.935020	−	0.354594i	$-0.115381\pi$
$734$		−	4.79451e11i		−	1.65181i
$735$	−1.02304e11	+	2.84873e11i	−0.350544	+	0.976117i
$736$	−2.58564e10			−0.0881164
$737$	3.89927e11			1.32164
$738$	−1.01742e11	+	1.00491e11i	−0.342986	+	0.338768i
$739$	4.92586e11			1.65160			0.825798	−	0.563966i	$-0.190725\pi$
$739$	4.92586e11			1.65160			0.825798	+	0.563966i	$0.190725\pi$
$740$	2.26963e10	−	1.15887e9i	0.0756883	−	0.00386464i
$741$	−1.77556e11	+	4.24935e11i	−0.588929	+	1.40945i
$742$			2.85268e11i			0.941104i
$743$	5.52619e11			1.81330			0.906652	−	0.421880i	$-0.138630\pi$
$743$	5.52619e11			1.81330			0.906652	+	0.421880i	$0.138630\pi$
$744$	8.88484e10	+	3.71247e10i	0.289973	+	0.121163i
$745$	−4.17585e11	+	2.13218e10i	−1.35556	+	0.0692149i
$746$		−	1.52724e11i		−	0.493118i
$747$	2.07736e11	+	2.10323e11i	0.667159	+	0.675467i
$748$		−	1.18973e10i		−	0.0380050i
$749$		−	4.65392e11i		−	1.47874i
$750$	8.35858e10	−	3.37544e11i	0.264172	−	1.06681i
$751$	−2.05834e11			−0.647079			−0.323540	−	0.946215i	$-0.604873\pi$
$751$	−2.05834e11			−0.647079			−0.323540	+	0.946215i	$0.604873\pi$
$752$	1.16142e11			0.363178
$753$	−2.24380e11	+	5.36997e11i	−0.697919	+	1.67029i
$754$	−3.60852e11			−1.11646
$755$	1.79503e10	+	3.51554e11i	0.0552439	+	1.08194i
$756$	−8.98740e10	+	3.62534e10i	−0.275136	+	0.110984i
$757$			1.27946e10i			0.0389622i	0.999810	+	0.0194811i	$0.00620142\pi$
$757$			1.27946e10i			0.0389622i	−0.999810	+	0.0194811i	$0.993799\pi$
$758$	3.85067e11			1.16643
$759$	2.95770e10	−	7.07850e10i	0.0891225	−	0.213292i
$760$	−2.38745e10	−	4.67578e11i	−0.0715615	−	1.40152i
$761$		−	2.92493e11i		−	0.872120i	−0.899918	−	0.436060i	$-0.856373\pi$
$761$		−	2.92493e11i		−	0.872120i	0.899918	−	0.436060i	$-0.143627\pi$
$762$	1.84266e10	−	4.40992e10i	0.0546543	−	0.130801i
$763$			9.08667e10i			0.268106i
$764$		−	3.60802e10i		−	0.105900i
$765$	−3.93385e10	+	4.30336e10i	−0.114861	+	0.125650i
$766$	−5.57222e11			−1.61850
$767$	−3.53550e11			−1.02157
$768$	1.92119e11	+	8.02754e10i	0.552236	+	0.230748i
$769$	4.81512e11			1.37690			0.688449	−	0.725285i	$-0.258292\pi$
$769$	4.81512e11			1.37690			0.688449	+	0.725285i	$0.258292\pi$
$770$	−3.02003e10	−	5.91467e11i	−0.0859108	−	1.68255i
$771$	−2.28831e11	−	9.56156e10i	−0.647587	−	0.270590i
$772$			4.25628e10i			0.119829i
$773$	−4.38699e11			−1.22871			−0.614354	−	0.789030i	$-0.710583\pi$
$773$	−4.38699e11			−1.22871			−0.614354	+	0.789030i	$0.710583\pi$
$774$	9.48608e10	−	9.36940e10i	0.264316	−	0.261065i
$775$	−1.29549e11	+	1.32641e10i	−0.359109	+	0.0367680i
$776$			5.20437e11i			1.43523i
$777$	−1.75015e11	−	7.31287e10i	−0.480165	−	0.200634i
$778$		−	1.68443e11i		−	0.459763i
$779$		−	2.60386e11i		−	0.707078i
$780$	6.86195e10	+	2.46427e10i	0.185383	+	0.0665748i
$781$	1.68422e11			0.452684
$782$	−1.50590e10			−0.0402688
$783$	3.73686e11	−	1.50738e11i	0.994169	−	0.401028i
$784$	4.56356e11			1.20792
$785$	−9.39414e10	+	4.79664e9i	−0.247388	+	0.0126316i
$786$	−1.24415e10	+	2.97755e10i	−0.0325973	+	0.0780134i
$787$		−	3.97244e11i		−	1.03552i	−0.855526	−	0.517760i	$-0.826766\pi$
$787$		−	3.97244e11i		−	1.03552i	0.855526	−	0.517760i	$-0.173234\pi$
$788$	−1.23223e11			−0.319587
$789$	2.62438e11	+	1.09658e11i	0.677202	+	0.282964i
$790$	2.81201e10	+	5.50727e11i	0.0721951	+	1.41393i
$791$			6.32242e11i			1.61502i
$792$	−2.61746e11	+	2.58526e11i	−0.665241	+	0.657059i
$793$		−	1.79405e11i		−	0.453671i
$794$			7.83479e11i			1.97127i
$795$	−8.10003e10	+	2.25551e11i	−0.202777	+	0.564647i
$796$	−7.63561e10			−0.190192
$797$	−5.24995e10			−0.130113			−0.0650567	−	0.997882i	$-0.520723\pi$
$797$	−5.24995e10			−0.130113			−0.0650567	+	0.997882i	$0.520723\pi$
$798$	3.95327e11	−	9.46113e11i	0.974866	−	2.33309i
$799$	2.16354e10			0.0530858
$800$	−1.66820e11	+	1.70801e10i	−0.407275	+	0.0416995i
$801$	3.41125e11	−	3.36929e11i	0.828672	−	0.818480i
$802$		−	4.41628e11i		−	1.06748i
$803$	5.48267e11			1.31865
$804$	4.12065e10	−	9.86171e10i	0.0986146	−	0.236009i
$805$	−1.28835e11	+	6.57831e9i	−0.306797	+	0.0156650i
$806$		−	1.58664e11i		−	0.375957i
$807$	−5.93082e10	+	1.41939e11i	−0.139837	+	0.334663i
$808$			4.32588e10i			0.101491i
$809$			3.82829e11i			0.893739i	0.894599	+	0.446870i	$0.147461\pi$
$809$			3.82829e11i			0.893739i	−0.894599	+	0.446870i	$0.852539\pi$
$810$	−4.72742e11	+	1.82758e10i	−1.09821	+	0.0424556i
$811$	−4.50313e11			−1.04095			−0.520477	−	0.853876i	$-0.674246\pi$
$811$	−4.50313e11			−1.04095			−0.520477	+	0.853876i	$0.674246\pi$
$812$	1.38263e11			0.318039
$813$	4.89117e9	+	2.04374e9i	0.0111957	+	0.00467803i
$814$	1.88948e11			0.430372
$815$	−7.05765e11	+	3.60363e10i	−1.59967	+	0.0816789i
$816$	8.11092e10	+	3.38909e10i	0.182940	+	0.0764403i
$817$			2.42774e11i			0.544896i
$818$	1.96178e11			0.438163
$819$	−4.27628e11	−	4.32954e11i	−0.950453	−	0.962289i
$820$	−4.11694e10	+	2.10210e9i	−0.0910581	+	0.00464942i
$821$		−	4.00560e11i		−	0.881648i	−0.897593	−	0.440824i	$-0.854686\pi$
$821$		−	4.00560e11i		−	0.881648i	0.897593	−	0.440824i	$-0.145314\pi$
$822$	−5.33898e11	−	2.23085e11i	−1.16942	−	0.488634i
$823$		−	5.98531e11i		−	1.30463i	−0.757948	−	0.652315i	$-0.773798\pi$
$823$		−	5.98531e11i		−	1.30463i	0.757948	−	0.652315i	$-0.226202\pi$
$824$		−	4.41161e11i		−	0.956947i
$825$	1.44065e11	−	4.76227e11i	0.310988	−	1.02801i
$826$	7.87176e11			1.69103
$827$	1.33008e11			0.284352			0.142176	−	0.989841i	$-0.454590\pi$
$827$	1.33008e11			0.284352			0.142176	+	0.989841i	$0.454590\pi$
$828$	−1.47767e10	−	1.49608e10i	−0.0314382	−	0.0318297i
$829$	−3.30572e11			−0.699920			−0.349960	−	0.936765i	$-0.613805\pi$
$829$	−3.30572e11			−0.699920			−0.349960	+	0.936765i	$0.613805\pi$
$830$	2.52513e10	+	4.94543e11i	0.0532073	+	1.04206i
$831$	2.15779e11	−	5.16411e11i	0.452485	−	1.08291i
$832$			3.24534e11i			0.677278i
$833$	8.50117e10			0.176563
$834$	−9.37219e11	−	3.91611e11i	−1.93721	−	0.809450i
$835$	1.72211e10	+	3.37273e11i	0.0354255	+	0.693803i
$836$			1.75778e11i			0.359865i
$837$	6.62783e10	+	1.64307e11i	0.135042	+	0.334776i
$838$			9.70334e11i			1.96764i
$839$		−	6.49466e10i		−	0.131072i	−0.997850	−	0.0655358i	$-0.979124\pi$
$839$		−	6.49466e10i		−	0.131072i	0.997850	−	0.0655358i	$-0.0208757\pi$
$840$	5.82235e11	+	2.09093e11i	1.16945	+	0.419974i
$841$	−7.46344e10			−0.149195
$842$	−3.90074e11			−0.776066
$843$	5.42951e10	−	1.29941e11i	0.107510	−	0.257299i
$844$	3.82752e10			0.0754306
$845$	−2.65181e9	−	5.19354e10i	−0.00520135	−	0.101868i
$846$	1.23365e11	+	1.24902e11i	0.240830	+	0.243830i
$847$		−	1.12777e11i		−	0.219122i
$848$	3.61325e11			0.698739
$849$	−1.29289e11	+	3.09420e11i	−0.248846	+	0.595549i
$850$	−9.71573e10	+	9.94762e9i	−0.186123	+	0.0190565i
$851$		−	4.11571e10i		−	0.0784742i
$852$	1.77984e10	−	4.25959e10i	0.0337772	−	0.0808369i
$853$			4.77389e10i			0.0901730i	0.998983	+	0.0450865i	$0.0143563\pi$
$853$			4.77389e10i			0.0901730i	−0.998983	+	0.0450865i	$0.985644\pi$
$854$			3.99443e11i			0.750971i
$855$	5.81214e11	−	6.35807e11i	1.08761	−	1.18976i
$856$	−4.84268e11			−0.901966
$857$	8.80902e11			1.63307			0.816534	−	0.577297i	$-0.195892\pi$
$857$	8.80902e11			1.63307			0.816534	+	0.577297i	$0.195892\pi$
$858$	5.59326e11	+	2.33710e11i	1.03209	+	0.431250i
$859$	−7.72690e9			−0.0141916			−0.00709582	−	0.999975i	$-0.502259\pi$
$859$	−7.72690e9			−0.0141916			−0.00709582	+	0.999975i	$0.502259\pi$
$860$	3.83848e10	−	1.95992e9i	0.0701722	−	0.00358298i
$861$	3.17463e11	+	1.32650e11i	0.577671	+	0.241376i
$862$			8.65067e11i			1.56683i
$863$	−4.51506e11			−0.813993			−0.406996	−	0.913430i	$-0.633424\pi$
$863$	−4.51506e11			−0.813993			−0.406996	+	0.913430i	$0.633424\pi$
$864$	8.53464e10	+	2.11578e11i	0.153155	+	0.379678i
$865$	−6.44520e9	−	1.26228e11i	−0.0115126	−	0.225472i
$866$		−	3.46485e11i		−	0.616045i
$867$	−5.06245e11	−	2.11531e11i	−0.895951	−	0.374367i
$868$			6.07930e10i			0.107096i
$869$			7.89000e11i			1.38356i
$870$	6.35245e11	+	2.28130e11i	1.10883	+	0.398204i
$871$	6.71136e11			1.16611
$872$	9.45520e10			0.163533
$873$	−6.81277e11	+	6.72897e11i	−1.17292	+	1.15849i
$874$	2.22492e11			0.381301
$875$	−8.26871e11	+	1.27547e11i	−1.41061	+	0.217590i
$876$	5.79395e10	−	1.38663e11i	0.0983917	−	0.235475i
$877$		−	6.13569e11i		−	1.03721i	−0.855015	−	0.518603i	$-0.826452\pi$
$877$		−	6.13569e11i		−	1.03721i	0.855015	−	0.518603i	$-0.173548\pi$
$878$	−3.06731e11			−0.516155
$879$	−5.13683e11	−	2.14639e11i	−0.860478	−	0.359545i
$880$	−7.49162e11	+	3.82521e10i	−1.24924	+	0.0637859i
$881$			5.49493e11i			0.912134i	0.889945	+	0.456067i	$0.150742\pi$
$881$			5.49493e11i			0.912134i	−0.889945	+	0.456067i	$0.849258\pi$
$882$	4.84737e11	+	4.90774e11i	0.800999	+	0.810974i
$883$		−	2.86999e11i		−	0.472104i	−0.971740	−	0.236052i	$-0.924146\pi$
$883$		−	2.86999e11i		−	0.472104i	0.971740	−	0.236052i	$-0.0758536\pi$
$884$		−	2.04774e10i		−	0.0335325i
$885$	6.22392e11	+	2.23514e11i	1.01459	+	0.364361i
$886$	−4.34127e11			−0.704501
$887$	6.67473e11			1.07830			0.539150	−	0.842210i	$-0.318746\pi$
$887$	6.67473e11			1.07830			0.539150	+	0.842210i	$0.318746\pi$
$888$	−7.60946e10	+	1.82113e11i	−0.122378	+	0.292879i
$889$	−1.14991e11			−0.184102
$890$	8.02103e11	−	4.09553e10i	1.27841	−	0.0652755i
$891$	−6.76847e11	−	8.37693e9i	−1.07394	−	0.0132915i
$892$		−	6.71482e10i		−	0.106066i
$893$	−3.19656e11			−0.502663
$894$	−3.67378e11	+	8.79225e11i	−0.575126	+	1.37642i
$895$	5.29210e11	−	2.70214e10i	0.824775	−	0.0421129i
$896$		−	1.09919e12i		−	1.70545i
$897$	5.09075e10	−	1.21834e11i	0.0786343	−	0.188191i
$898$		−	8.70228e11i		−	1.33822i
$899$		−	2.52771e11i		−	0.386980i
$900$	−1.05219e11	−	8.67623e10i	−0.160370	−	0.132239i
$901$	6.73089e10			0.102135
$902$	−3.42736e11			−0.517767
$903$	−2.95991e11	−	1.23678e11i	−0.445171	−	0.186012i
$904$	6.57884e11			0.985089
$905$	−4.51396e10	−	8.84052e11i	−0.0672920	−	1.31790i
$906$	7.40197e11	+	3.09286e11i	1.09859	+	0.459037i
$907$		−	8.49166e11i		−	1.25477i	−0.778710	−	0.627384i	$-0.784126\pi$
$907$		−	8.49166e11i		−	1.25477i	0.778710	−	0.627384i	$-0.215874\pi$
$908$	−2.23972e11			−0.329496
$909$	−5.66278e10	+	5.59313e10i	−0.0829420	+	0.0819218i
$910$	−5.19802e10	−	1.01803e12i	−0.0758006	−	1.48454i
$911$			1.01144e12i			1.46847i	0.678895	+	0.734235i	$0.262459\pi$
$911$			1.01144e12i			1.46847i	−0.678895	+	0.734235i	$0.737541\pi$
$912$	−1.19836e12	−	5.00727e11i	−1.73224	−	0.723805i
$913$			7.08508e11i			1.01967i
$914$		−	1.32190e12i		−	1.89415i
$915$	−1.13419e11	+	3.15825e11i	−0.161809	+	0.450570i
$916$	3.80679e10			0.0540726
$917$	7.76414e10			0.109803
$918$	4.97065e10	+	1.23225e11i	0.0699910	+	0.173511i
$919$	2.59912e11			0.364389			0.182194	−	0.983263i	$-0.441680\pi$
$919$	2.59912e11			0.364389			0.182194	+	0.983263i	$0.441680\pi$
$920$	6.84511e9	+	1.34060e11i	0.00955497	+	0.187133i
$921$	−7.32046e10	+	1.75196e11i	−0.101742	+	0.243493i
$922$			3.05715e11i			0.423052i
$923$	2.89886e11			0.399411
$924$	−2.14309e11	−	8.95476e10i	−0.294004	−	0.122847i
$925$	−2.71875e10	−	2.65537e11i	−0.0371366	−	0.362709i
$926$			3.71320e11i			0.505015i
$927$	5.77501e11	−	5.70398e11i	0.782049	−	0.772430i
$928$		−	3.25492e11i		−	0.438883i
$929$		−	4.58599e11i		−	0.615701i	−0.951435	−	0.307851i	$-0.900390\pi$
$929$		−	4.58599e11i		−	0.615701i	0.951435	−	0.307851i	$-0.0996097\pi$
$930$	−1.00307e11	+	2.79313e11i	−0.134091	+	0.373387i
$931$	−1.25602e12			−1.67185
$932$	2.02328e11			0.268159
$933$	1.93177e11	−	4.62319e11i	0.254935	−	0.610120i
$934$	2.62207e11			0.344554
$935$	−1.39557e11	+	7.12574e9i	−0.182601	+	0.00932360i
$936$	−4.50513e11	+	4.44972e11i	−0.586954	+	0.579734i
$937$			7.74108e11i			1.00425i	0.864794	+	0.502126i	$0.167449\pi$
$937$			7.74108e11i			1.00425i	−0.864794	+	0.502126i	$0.832551\pi$
$938$	−1.49428e12			−1.93028
$939$	1.97895e11	−	4.73612e11i	0.254550	−	0.609200i
$940$	2.58059e9	+	5.05405e10i	0.00330528	+	0.0647334i
$941$		−	6.66336e11i		−	0.849836i	−0.905232	−	0.424918i	$-0.860303\pi$
$941$		−	6.66336e11i		−	0.849836i	0.905232	−	0.424918i	$-0.139697\pi$
$942$	−8.26466e10	+	1.97794e11i	−0.104959	+	0.251194i
$943$			7.46558e10i			0.0944098i
$944$		−	9.97049e11i		−	1.25553i
$945$	4.79086e11	+	1.03252e12i	0.600740	+	1.29471i
$946$	3.19554e11			0.399007
$947$	−2.31471e11			−0.287804			−0.143902	−	0.989592i	$-0.545965\pi$
$947$	−2.31471e11			−0.287804			−0.143902	+	0.989592i	$0.545965\pi$
$948$	1.99547e11	+	8.33795e10i	0.247066	+	0.103235i
$949$	9.43670e11			1.16347
$950$	1.43547e12	−	1.46973e11i	1.76238	−	0.180444i
$951$	1.97053e11	+	8.23374e10i	0.240914	+	0.100664i
$952$		−	1.73750e11i		−	0.211533i
$953$	−7.87320e11			−0.954509			−0.477254	−	0.878765i	$-0.658368\pi$
$953$	−7.87320e11			−0.954509			−0.477254	+	0.878765i	$0.658368\pi$
$954$	3.83796e11	+	3.88575e11i	0.463348	+	0.469118i
$955$	−4.23226e11	+	2.16099e10i	−0.508814	+	0.0259800i
$956$		−	1.94169e11i		−	0.232461i
$957$	8.91075e11	+	3.72329e11i	1.06235	+	0.443894i
$958$			9.06926e10i			0.107674i
$959$			1.39217e12i			1.64595i
$960$	2.05170e11	−	5.71312e11i	0.241562	−	0.672648i
$961$	−7.41750e11			−0.869689
$962$	3.25214e11			0.379725
$963$	−6.26133e11	−	6.33930e11i	−0.728050	−	0.737116i
$964$	7.26050e10			0.0840734
$965$	4.99268e11	−	2.54926e10i	0.575737	−	0.0293971i
$966$	−1.13345e11	+	2.71262e11i	−0.130165	+	0.311517i
$967$			6.73055e11i			0.769741i	0.922971	+	0.384871i	$0.125754\pi$
$967$			6.73055e11i			0.769741i	−0.922971	+	0.384871i	$0.874246\pi$
$968$	−1.17351e11			−0.133654
$969$	−2.23235e11	−	9.32772e10i	−0.253202	−	0.105799i
$970$	−1.60192e12	+	8.17939e10i	−1.80948	+	0.0923919i
$971$			9.86603e10i			0.110985i	0.998459	+	0.0554927i	$0.0176729\pi$
$971$			9.86603e10i			0.110985i	−0.998459	+	0.0554927i	$0.982327\pi$
$972$	−7.36461e10	+	1.70297e11i	−0.0825059	+	0.190785i
$973$			2.44386e12i			2.72662i
$974$			6.68153e11i			0.742404i
$975$	2.47963e11	−	8.19675e11i	0.274391	−	0.907033i
$976$	5.05940e11			0.557571
$977$	2.61518e11			0.287028			0.143514	−	0.989648i	$-0.454160\pi$
$977$	2.61518e11			0.287028			0.143514	+	0.989648i	$0.454160\pi$
$978$	−6.20910e11	+	1.48599e12i	−0.678693	+	1.62428i
$979$	1.14913e12			1.25095
$980$	1.01399e10	+	1.98588e11i	0.0109933	+	0.215303i
$981$	1.22251e11	+	1.23773e11i	0.132000	+	0.133644i
$982$		−	1.26950e12i		−	1.36517i
$983$	9.90776e11			1.06111			0.530556	−	0.847650i	$-0.321983\pi$
$983$	9.90776e11			1.06111			0.530556	+	0.847650i	$0.321983\pi$
$984$	1.38030e11	−	3.30339e11i	0.147229	−	0.352354i
$985$	7.38034e10	+	1.44543e12i	0.0784028	+	1.53551i
$986$		−	1.89570e11i		−	0.200568i
$987$	1.62844e11	−	3.89726e11i	0.171595	−	0.410667i
$988$			3.02547e11i			0.317515i
$989$		−	6.96063e10i		−	0.0727551i
$990$	−8.36889e11	−	7.65031e11i	−0.871219	−	0.796412i
$991$	3.03368e11			0.314540			0.157270	−	0.987556i	$-0.449731\pi$
$991$	3.03368e11			0.314540			0.157270	+	0.987556i	$0.449731\pi$
$992$	1.43117e11			0.147789
$993$	−4.53499e11	−	1.89491e11i	−0.466422	−	0.194891i
$994$	−6.45428e11			−0.661153
$995$	4.57327e10	+	8.95667e11i	0.0466589	+	0.913806i
$996$	1.79190e11	+	7.48733e10i	0.182086	+	0.0760833i
$997$		−	2.24125e11i		−	0.226835i	−0.993547	−	0.113417i	$-0.963820\pi$
$997$		−	2.24125e11i		−	0.226835i	0.993547	−	0.113417i	$-0.0361797\pi$
$998$	3.96358e11			0.399545
$999$	−3.36781e11	+	1.35851e11i	−0.338132	+	0.136396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.9.d.c.14.4	yes	12
3.2	odd	2	inner	15.9.d.c.14.10	yes	12
4.3	odd	2		240.9.c.c.209.1		12
5.2	odd	4		75.9.c.h.26.4		12
5.3	odd	4		75.9.c.h.26.9		12
5.4	even	2	inner	15.9.d.c.14.9	yes	12
12.11	even	2		240.9.c.c.209.11		12
15.2	even	4		75.9.c.h.26.10		12
15.8	even	4		75.9.c.h.26.3		12
15.14	odd	2	inner	15.9.d.c.14.3	✓	12
20.19	odd	2		240.9.c.c.209.12		12
60.59	even	2		240.9.c.c.209.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.d.c.14.3	✓	12	15.14	odd	2	inner
15.9.d.c.14.4	yes	12	1.1	even	1	trivial
15.9.d.c.14.9	yes	12	5.4	even	2	inner
15.9.d.c.14.10	yes	12	3.2	odd	2	inner
75.9.c.h.26.3		12	15.8	even	4
75.9.c.h.26.4		12	5.2	odd	4
75.9.c.h.26.9		12	5.3	odd	4
75.9.c.h.26.10		12	15.2	even	4
240.9.c.c.209.1		12	4.3	odd	2
240.9.c.c.209.2		12	60.59	even	2
240.9.c.c.209.11		12	12.11	even	2
240.9.c.c.209.12		12	20.19	odd	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)

\(f(q)\)	\(=\)	\(q-17.5844 q^{2} +(74.7380 + 31.2287i) q^{3} +53.2123 q^{4} +(-31.8709 - 624.187i) q^{5} +(-1314.22 - 549.140i) q^{6} +3426.92i q^{7} +3565.91 q^{8} +(4610.53 + 4667.95i) q^{9} +O(q^{10})\)	\(q-17.5844 q^{2} +(74.7380 + 31.2287i) q^{3} +53.2123 q^{4} +(-31.8709 - 624.187i) q^{5} +(-1314.22 - 549.140i) q^{6} +3426.92i q^{7} +3565.91 q^{8} +(4610.53 + 4667.95i) q^{9} +(560.432 + 10976.0i) q^{10} +15724.8i q^{11} +(3976.98 + 1661.75i) q^{12} +27065.2i q^{13} -60260.4i q^{14} +(17110.6 - 47645.8i) q^{15} -76326.8 q^{16} -14218.4 q^{17} +(-81073.6 - 82083.2i) q^{18} +210073. q^{19} +(-1695.92 - 33214.4i) q^{20} +(-107018. + 256121. i) q^{21} -276511. i q^{22} -60230.4 q^{23} +(266509. + 111359. i) q^{24} +(-388593. + 39786.8i) q^{25} -475926. i q^{26} +(198808. + 492854. i) q^{27} +182354. i q^{28} -758209. i q^{29} +(-300880. + 837824. i) q^{30} +333379. q^{31} +429291. q^{32} +(-491064. + 1.17524e6i) q^{33} +250023. q^{34} +(2.13904e6 - 109219. i) q^{35} +(245337. + 248392. i) q^{36} +683328. i q^{37} -3.69401e6 q^{38} +(-845213. + 2.02280e6i) q^{39} +(-113649. - 2.22579e6i) q^{40} -1.23950e6i q^{41} +(1.88186e6 - 4.50374e6i) q^{42} +1.15567e6i q^{43} +836750. i q^{44} +(2.76673e6 - 3.02660e6i) q^{45} +1.05912e6 q^{46} -1.52165e6 q^{47} +(-5.70451e6 - 2.38359e6i) q^{48} -5.97898e6 q^{49} +(6.83320e6 - 699629. i) q^{50} +(-1.06266e6 - 444024. i) q^{51} +1.44020e6i q^{52} -4.73392e6 q^{53} +(-3.49592e6 - 8.66656e6i) q^{54} +(9.81519e6 - 501162. i) q^{55} +1.22201e7i q^{56} +(1.57004e7 + 6.56030e6i) q^{57} +1.33327e7i q^{58} +1.30629e7i q^{59} +(910494. - 2.53534e6i) q^{60} -6.62861e6 q^{61} -5.86228e6 q^{62} +(-1.59967e7 + 1.57999e7i) q^{63} +1.19908e7 q^{64} +(1.68938e7 - 862593. i) q^{65} +(8.63509e6 - 2.06659e7i) q^{66} -2.47970e7i q^{67} -756595. q^{68} +(-4.50150e6 - 1.88092e6i) q^{69} +(-3.76138e7 + 1.92056e6i) q^{70} -1.07106e7i q^{71} +(1.64407e7 + 1.66455e7i) q^{72} -3.48665e7i q^{73} -1.20159e7i q^{74} +(-3.02852e7 - 9.16170e6i) q^{75} +1.11784e7 q^{76} -5.38875e7 q^{77} +(1.48626e7 - 3.55698e7i) q^{78} +5.01757e7 q^{79} +(2.43260e6 + 4.76422e7i) q^{80} +(-532723. + 4.30434e7i) q^{81} +2.17960e7i q^{82} +4.50568e7 q^{83} +(-5.69469e6 + 1.36288e7i) q^{84} +(453154. + 8.87496e6i) q^{85} -2.03217e7i q^{86} +(2.36779e7 - 5.66670e7i) q^{87} +5.60730e7i q^{88} -7.30781e7i q^{89} +(-4.86514e7 + 5.32211e7i) q^{90} -9.27503e7 q^{91} -3.20500e6 q^{92} +(2.49161e7 + 1.04110e7i) q^{93} +2.67573e7 q^{94} +(-6.69521e6 - 1.31125e8i) q^{95} +(3.20843e7 + 1.34062e7i) q^{96} +1.45948e8i q^{97} +1.05137e8 q^{98} +(-7.34023e7 + 7.24995e7i) 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

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Groups

Database

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