LMFDB - Embedded newform 24.8.d.a.13.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,8,Mod(13,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("24.13");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	24.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:	$7.49724061162$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 52 x^{12} + 300 x^{11} - 1005 x^{10} - 23250 x^{9} + 349930 x^{8} + \cdots + 3813237677250 $ x^14 - 6x^13 - 52x^12 + 300x^11 - 1005x^10 - 23250x^9 + 349930x^8 + 2867784x^7 - 20463993x^6 - 78987210x^5 + 94608296x^4 - 6477861300x^3 - 21982316987x^2 + 613270661346*x + 3813237677250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{37}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.14
Root			$8.85262 - 1.52851i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.8.d.a.13.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.38113 + 6.32411i) q^{2} -27.0000i q^{3} +(48.0111 + 118.655i) q^{4} -425.308i q^{5} +(170.751 - 253.290i) q^{6} +1664.03 q^{7} +(-299.987 + 1416.74i) q^{8} -729.000 q^{9} +O(q^{10})$	\(q+(9.38113 + 6.32411i) q^{2} -27.0000i q^{3} +(48.0111 + 118.655i) q^{4} -425.308i q^{5} +(170.751 - 253.290i) q^{6} +1664.03 q^{7} +(-299.987 + 1416.74i) q^{8} -729.000 q^{9} +(2689.70 - 3989.87i) q^{10} -2467.01i q^{11} +(3203.68 - 1296.30i) q^{12} +3767.59i q^{13} +(15610.5 + 10523.5i) q^{14} -11483.3 q^{15} +(-11773.9 + 11393.5i) q^{16} +16241.0 q^{17} +(-6838.84 - 4610.28i) q^{18} -4869.30i q^{19} +(50464.8 - 20419.5i) q^{20} -44928.9i q^{21} +(15601.7 - 23143.3i) q^{22} -108549. q^{23} +(38252.1 + 8099.65i) q^{24} -102762. q^{25} +(-23826.7 + 35344.2i) q^{26} +19683.0i q^{27} +(79892.1 + 197445. i) q^{28} +89066.4i q^{29} +(-107727. - 72621.9i) q^{30} -69483.3 q^{31} +(-182506. + 32424.6i) q^{32} -66609.3 q^{33} +(152359. + 102710. i) q^{34} -707727. i q^{35} +(-35000.1 - 86499.3i) q^{36} +418478. i q^{37} +(30794.0 - 45679.6i) q^{38} +101725. q^{39} +(602553. + 127587. i) q^{40} +274307. q^{41} +(284135. - 421483. i) q^{42} +462897. i q^{43} +(292722. - 118444. i) q^{44} +310050. i q^{45} +(-1.01831e6 - 686474. i) q^{46} +153501. q^{47} +(307624. + 317894. i) q^{48} +1.94546e6 q^{49} +(-964026. - 649880. i) q^{50} -438507. i q^{51} +(-447042. + 180886. i) q^{52} -181473. i q^{53} +(-124478. + 184649. i) q^{54} -1.04924e6 q^{55} +(-499188. + 2.35750e6i) q^{56} -131471. q^{57} +(-563266. + 835543. i) q^{58} -647716. i q^{59} +(-551328. - 1.36255e6i) q^{60} +2.26966e6i q^{61} +(-651832. - 439420. i) q^{62} -1.21308e6 q^{63} +(-1.91717e6 - 850009. i) q^{64} +1.60239e6 q^{65} +(-624870. - 421245. i) q^{66} -2.31785e6i q^{67} +(779748. + 1.92707e6i) q^{68} +2.93081e6i q^{69} +(4.47575e6 - 6.63928e6i) q^{70} +2.77599e6 q^{71} +(218691. - 1.03281e6i) q^{72} -4.45276e6 q^{73} +(-2.64650e6 + 3.92579e6i) q^{74} +2.77458e6i q^{75} +(577766. - 233781. i) q^{76} -4.10518e6i q^{77} +(954294. + 643320. i) q^{78} -3.14911e6 q^{79} +(4.84575e6 + 5.00752e6i) q^{80} +531441. q^{81} +(2.57331e6 + 1.73475e6i) q^{82} -3.33510e6i q^{83} +(5.33102e6 - 2.15709e6i) q^{84} -6.90743e6i q^{85} +(-2.92741e6 + 4.34250e6i) q^{86} +2.40479e6 q^{87} +(3.49512e6 + 740071. i) q^{88} -5.00420e6 q^{89} +(-1.96079e6 + 2.90862e6i) q^{90} +6.26939e6i q^{91} +(-5.21155e6 - 1.28798e7i) q^{92} +1.87605e6i q^{93} +(1.44001e6 + 970759. i) q^{94} -2.07096e6 q^{95} +(875463. + 4.92766e6i) q^{96} +8.06376e6 q^{97} +(1.82506e7 + 1.23033e7i) q^{98} +1.79845e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	9.38113	+	6.32411i	0.829182	+	0.558978i
$2$	9.38113	+	6.32411i	0.829182	+	0.558978i
$3$		−	27.0000i		−	0.577350i
$3$		−	27.0000i		−	0.577350i
$4$	48.0111	+	118.655i	0.375087	+	0.926990i
$5$		−	425.308i		−	1.52163i	−0.648969	−	0.760815i	$-0.724800\pi$
$5$		−	425.308i		−	1.52163i	0.648969	−	0.760815i	$-0.275200\pi$
$6$	170.751	−	253.290i	0.322726	−	0.478729i
$7$	1664.03			1.83366			0.916829	−	0.399279i	$-0.130740\pi$
$7$	1664.03			1.83366			0.916829	+	0.399279i	$0.130740\pi$
$8$	−299.987	+	1416.74i	−0.207151	+	0.978309i
$9$	−729.000			−0.333333
$10$	2689.70	−	3989.87i	0.850558	−	1.26171i
$11$		−	2467.01i		−	0.558852i	−0.960167	−	0.279426i	$-0.909856\pi$
$11$		−	2467.01i		−	0.558852i	0.960167	−	0.279426i	$-0.0901441\pi$
$12$	3203.68	−	1296.30i	0.535198	−	0.216557i
$13$			3767.59i			0.475622i	0.971311	+	0.237811i	$0.0764298\pi$
$13$			3767.59i			0.475622i	−0.971311	+	0.237811i	$0.923570\pi$
$14$	15610.5	+	10523.5i	1.52044	+	1.02497i
$15$	−11483.3			−0.878513
$16$	−11773.9	+	11393.5i	−0.718619	+	0.695404i
$17$	16241.0			0.801754			0.400877	−	0.916132i	$-0.368705\pi$
$17$	16241.0			0.801754			0.400877	+	0.916132i	$0.368705\pi$
$18$	−6838.84	−	4610.28i	−0.276394	−	0.186326i
$19$		−	4869.30i		−	0.162866i	−0.996679	−	0.0814328i	$-0.974050\pi$
$19$		−	4869.30i		−	0.162866i	0.996679	−	0.0814328i	$-0.0259496\pi$
$20$	50464.8	−	20419.5i	1.41053	−	0.570744i
$21$		−	44928.9i		−	1.05866i
$22$	15601.7	−	23143.3i	0.312386	−	0.463390i
$23$	−108549.			−1.86027			−0.930137	−	0.367212i	$-0.880313\pi$
$23$	−108549.			−1.86027			−0.930137	+	0.367212i	$0.880313\pi$
$24$	38252.1	+	8099.65i	0.564827	+	0.119599i
$25$	−102762.			−1.31536
$26$	−23826.7	+	35344.2i	−0.265862	+	0.394377i
$27$			19683.0i			0.192450i
$28$	79892.1	+	197445.i	0.687782	+	1.69978i
$29$			89066.4i			0.678142i	0.940761	+	0.339071i	$0.110113\pi$
$29$			89066.4i			0.678142i	−0.940761	+	0.339071i	$0.889887\pi$
$30$	−107727.	−	72621.9i	−0.728448	−	0.491070i
$31$	−69483.3			−0.418904			−0.209452	−	0.977819i	$-0.567168\pi$
$31$	−69483.3			−0.418904			−0.209452	+	0.977819i	$0.567168\pi$
$32$	−182506.	+	32424.6i	−0.984582	+	0.174924i
$33$	−66609.3			−0.322653
$34$	152359.	+	102710.i	0.664800	+	0.448163i
$35$		−	707727.i		−	2.79015i
$36$	−35000.1	−	86499.3i	−0.125029	−	0.308997i
$37$			418478.i			1.35821i	0.734042	+	0.679104i	$0.237631\pi$
$37$			418478.i			1.35821i	−0.734042	+	0.679104i	$0.762369\pi$
$38$	30794.0	−	45679.6i	0.0910383	−	0.135045i
$39$	101725.			0.274600
$40$	602553.	+	127587.i	1.48862	+	0.315207i
$41$	274307.			0.621574			0.310787	−	0.950480i	$-0.399407\pi$
$41$	274307.			0.621574			0.310787	+	0.950480i	$0.399407\pi$
$42$	284135.	−	421483.i	0.591770	−	0.877825i
$43$			462897.i			0.887861i	0.896061	+	0.443930i	$0.146416\pi$
$43$			462897.i			0.887861i	−0.896061	+	0.443930i	$0.853584\pi$
$44$	292722.	−	118444.i	0.518050	−	0.209618i
$45$			310050.i			0.507210i
$46$	−1.01831e6	−	686474.i	−1.54251	−	1.03985i
$47$	153501.			0.215660			0.107830	−	0.994169i	$-0.465610\pi$
$47$	153501.			0.215660			0.107830	+	0.994169i	$0.465610\pi$
$48$	307624.	+	317894.i	0.401491	+	0.414895i
$49$	1.94546e6			2.36230
$50$	−964026.	−	649880.i	−1.09067	−	0.735256i
$51$		−	438507.i		−	0.462893i
$52$	−447042.	+	180886.i	−0.440896	+	0.178400i
$53$		−	181473.i		−	0.167435i	−0.996490	−	0.0837176i	$-0.973321\pi$
$53$		−	181473.i		−	0.167435i	0.996490	−	0.0837176i	$-0.0266794\pi$
$54$	−124478.	+	184649.i	−0.107575	+	0.159576i
$55$	−1.04924e6			−0.850365
$56$	−499188.	+	2.35750e6i	−0.379845	+	1.79388i
$57$	−131471.			−0.0940305
$58$	−563266.	+	835543.i	−0.379067	+	0.562304i
$59$		−	647716.i		−	0.410584i	−0.978701	−	0.205292i	$-0.934186\pi$
$59$		−	647716.i		−	0.410584i	0.978701	−	0.205292i	$-0.0658145\pi$
$60$	−551328.	−	1.36255e6i	−0.329519	−	0.814373i
$61$			2.26966e6i			1.28028i	0.768257	+	0.640141i	$0.221124\pi$
$61$			2.26966e6i			1.28028i	−0.768257	+	0.640141i	$0.778876\pi$
$62$	−651832.	−	439420.i	−0.347348	−	0.234158i
$63$	−1.21308e6			−0.611220
$64$	−1.91717e6	−	850009.i	−0.914177	−	0.405316i
$65$	1.60239e6			0.723720
$66$	−624870.	−	421245.i	−0.267538	−	0.180356i
$67$		−	2.31785e6i		−	0.941506i	−0.882265	−	0.470753i	$-0.843982\pi$
$67$		−	2.31785e6i		−	0.941506i	0.882265	−	0.470753i	$-0.156018\pi$
$68$	779748.	+	1.92707e6i	0.300728	+	0.743218i
$69$			2.93081e6i			1.07403i
$70$	4.47575e6	−	6.63928e6i	1.55963	−	2.31354i
$71$	2.77599e6			0.920480			0.460240	−	0.887795i	$-0.347763\pi$
$71$	2.77599e6			0.920480			0.460240	+	0.887795i	$0.347763\pi$
$72$	218691.	−	1.03281e6i	0.0690504	−	0.326103i
$73$	−4.45276e6			−1.33967			−0.669837	−	0.742508i	$-0.733636\pi$
$73$	−4.45276e6			−1.33967			−0.669837	+	0.742508i	$0.733636\pi$
$74$	−2.64650e6	+	3.92579e6i	−0.759208	+	1.12620i
$75$			2.77458e6i			0.759422i
$76$	577766.	−	233781.i	0.150975	−	0.0610888i
$77$		−	4.10518e6i		−	1.02474i
$78$	954294.	+	643320.i	0.227694	+	0.153496i
$79$	−3.14911e6			−0.718610			−0.359305	−	0.933220i	$-0.616986\pi$
$79$	−3.14911e6			−0.718610			−0.359305	+	0.933220i	$0.616986\pi$
$80$	4.84575e6	+	5.00752e6i	1.05815	+	1.09347i
$81$	531441.			0.111111
$82$	2.57331e6	+	1.73475e6i	0.515398	+	0.347446i
$83$		−	3.33510e6i		−	0.640230i	−0.947379	−	0.320115i	$-0.896279\pi$
$83$		−	3.33510e6i		−	0.640230i	0.947379	−	0.320115i	$-0.103721\pi$
$84$	5.33102e6	−	2.15709e6i	0.981370	−	0.397091i
$85$		−	6.90743e6i		−	1.21997i
$86$	−2.92741e6	+	4.34250e6i	−0.496295	+	0.736198i
$87$	2.40479e6			0.391526
$88$	3.49512e6	+	740071.i	0.546729	+	0.115767i
$89$	−5.00420e6			−0.752435			−0.376218	−	0.926531i	$-0.622776\pi$
$89$	−5.00420e6			−0.752435			−0.376218	+	0.926531i	$0.622776\pi$
$90$	−1.96079e6	+	2.90862e6i	−0.283519	+	0.420570i
$91$			6.26939e6i			0.872128i
$92$	−5.21155e6	−	1.28798e7i	−0.697765	−	1.72446i
$93$			1.87605e6i			0.241854i
$94$	1.44001e6	+	970759.i	0.178821	+	0.120549i
$95$	−2.07096e6			−0.247821
$96$	875463.	+	4.92766e6i	0.100992	+	0.568449i
$97$	8.06376e6			0.897091			0.448545	−	0.893760i	$-0.351942\pi$
$97$	8.06376e6			0.897091			0.448545	+	0.893760i	$0.351942\pi$
$98$	1.82506e7	+	1.23033e7i	1.95878	+	1.32048i
$99$			1.79845e6i			0.186284i
$100$	−4.93373e6	−	1.21932e7i	−0.493373	−	1.21932i
$101$		−	1.31452e6i		−	0.126953i	−0.997983	−	0.0634764i	$-0.979781\pi$
$101$		−	1.31452e6i		−	0.126953i	0.997983	−	0.0634764i	$-0.0202187\pi$
$102$	2.77317e6	−	4.11369e6i	0.258747	−	0.383823i
$103$	−3.14528e6			−0.283615			−0.141807	−	0.989894i	$-0.545291\pi$
$103$	−3.14528e6			−0.283615			−0.141807	+	0.989894i	$0.545291\pi$
$104$	−5.33770e6	−	1.13023e6i	−0.465305	−	0.0985256i
$105$	−1.91086e7			−1.61089
$106$	1.14766e6	−	1.70242e6i	0.0935926	−	0.138834i
$107$		−	1.01610e7i		−	0.801850i	−0.916111	−	0.400925i	$-0.868689\pi$
$107$		−	1.01610e7i		−	0.801850i	0.916111	−	0.400925i	$-0.131311\pi$
$108$	−2.33548e6	+	945003.i	−0.178399	+	0.0721855i
$109$		−	1.48744e7i		−	1.10014i	−0.835119	−	0.550070i	$-0.814601\pi$
$109$		−	1.48744e7i		−	1.10014i	0.835119	−	0.550070i	$-0.185399\pi$
$110$	−9.84305e6	−	6.63551e6i	−0.705108	−	0.475335i
$111$	1.12989e7			0.784162
$112$	−1.95921e7	+	1.89591e7i	−1.31770	+	1.27513i
$113$	−1.17317e7			−0.764866			−0.382433	−	0.923983i	$-0.624914\pi$
$113$	−1.17317e7			−0.764866			−0.382433	+	0.923983i	$0.624914\pi$
$114$	−1.23335e6	−	831439.i	−0.0779684	−	0.0525610i
$115$			4.61667e7i			2.83065i
$116$	−1.05681e7	+	4.27618e6i	−0.628631	+	0.254362i
$117$		−	2.74657e6i		−	0.158541i
$118$	4.09623e6	−	6.07631e6i	0.229508	−	0.340449i
$119$	2.70255e7			1.47014
$120$	3.44485e6	−	1.62689e7i	0.181985	−	0.859457i
$121$	1.34010e7			0.687685
$122$	−1.43536e7	+	2.12919e7i	−0.715650	+	1.06159i
$123$		−	7.40628e6i		−	0.358866i
$124$	−3.33597e6	−	8.24452e6i	−0.157125	−	0.388320i
$125$			1.04784e7i			0.479856i
$126$	−1.13801e7	−	7.67165e6i	−0.506813	−	0.341658i
$127$	−1.58694e7			−0.687460			−0.343730	−	0.939068i	$-0.611691\pi$
$127$	−1.58694e7			−0.687460			−0.343730	+	0.939068i	$0.611691\pi$
$128$	−1.26096e7	−	2.00984e7i	−0.531457	−	0.847086i
$129$	1.24982e7			0.512607
$130$	1.50322e7	+	1.01337e7i	0.600096	+	0.404544i
$131$			2.35876e7i			0.916717i	0.888768	+	0.458358i	$0.151562\pi$
$131$			2.35876e7i			0.916717i	−0.888768	+	0.458358i	$0.848438\pi$
$132$	−3.19799e6	−	7.90350e6i	−0.121023	−	0.299096i
$133$		−	8.10268e6i		−	0.298640i
$134$	1.46583e7	−	2.17440e7i	0.526281	−	0.780680i
$135$	8.37135e6			0.292838
$136$	−4.87209e6	+	2.30093e7i	−0.166084	+	0.784363i
$137$	3.16838e7			1.05272			0.526362	−	0.850260i	$-0.323556\pi$
$137$	3.16838e7			1.05272			0.526362	+	0.850260i	$0.323556\pi$
$138$	−1.85348e7	+	2.74943e7i	−0.600359	+	0.890567i
$139$		−	3.89914e7i		−	1.23145i	−0.787961	−	0.615726i	$-0.788863\pi$
$139$		−	3.89914e7i		−	1.23145i	0.787961	−	0.615726i	$-0.211137\pi$
$140$	8.39751e7	−	3.39788e7i	2.58644	−	1.04655i
$141$		−	4.14453e6i		−	0.124511i
$142$	2.60420e7	+	1.75557e7i	0.763246	+	0.514528i
$143$	9.29468e6			0.265802
$144$	8.58314e6	−	8.30586e6i	0.239540	−	0.231801i
$145$	3.78807e7			1.03188
$146$	−4.17719e7	−	2.81598e7i	−1.11083	−	0.748848i
$147$		−	5.25274e7i		−	1.36388i
$148$	−4.96543e7	+	2.00916e7i	−1.25904	+	0.509446i
$149$			6.87705e6i			0.170314i	0.996368	+	0.0851570i	$0.0271392\pi$
$149$			6.87705e6i			0.170314i	−0.996368	+	0.0851570i	$0.972861\pi$
$150$	−1.75468e7	+	2.60287e7i	−0.424500	+	0.629699i
$151$	5.09509e6			0.120429			0.0602147	−	0.998185i	$-0.480821\pi$
$151$	5.09509e6			0.120429			0.0602147	+	0.998185i	$0.480821\pi$
$152$	6.89855e6	+	1.46073e6i	0.159333	+	0.0337378i
$153$	−1.18397e7			−0.267251
$154$	2.59616e7	−	3.85112e7i	0.572809	−	0.849699i
$155$			2.95518e7i			0.637417i
$156$	4.88393e6	+	1.20701e7i	0.102999	+	0.254552i
$157$			3.94930e7i			0.814463i	0.913325	+	0.407232i	$0.133506\pi$
$157$			3.94930e7i			0.814463i	−0.913325	+	0.407232i	$0.866494\pi$
$158$	−2.95422e7	−	1.99154e7i	−0.595859	−	0.401687i
$159$	−4.89977e6			−0.0966687
$160$	1.37904e7	+	7.76213e7i	0.266169	+	1.49817i
$161$	−1.80628e8			−3.41111
$162$	4.98552e6	+	3.36089e6i	0.0921314	+	0.0621087i
$163$		−	4.90817e6i		−	0.0887693i	−0.999015	−	0.0443847i	$-0.985867\pi$
$163$		−	4.90817e6i		−	0.0887693i	0.999015	−	0.0443847i	$-0.0141327\pi$
$164$	1.31698e7	+	3.25478e7i	0.233144	+	0.576193i
$165$			2.83295e7i			0.490958i
$166$	2.10916e7	−	3.12870e7i	0.357874	−	0.530867i
$167$	−6.43526e7			−1.06920			−0.534600	−	0.845105i	$-0.679538\pi$
$167$	−6.43526e7			−1.06920			−0.534600	+	0.845105i	$0.679538\pi$
$168$	6.36526e7	+	1.34781e7i	1.03570	+	0.219303i
$169$	4.85538e7			0.773784
$170$	4.36834e7	−	6.47995e7i	0.681938	−	1.01158i
$171$			3.54972e6i			0.0542885i
$172$	−5.49249e7	+	2.22242e7i	−0.823037	+	0.333025i
$173$			9.25082e7i			1.35837i	0.733966	+	0.679186i	$0.237667\pi$
$173$			9.25082e7i			1.35837i	−0.733966	+	0.679186i	$0.762333\pi$
$174$	2.25597e7	+	1.52082e7i	0.324646	+	0.218854i
$175$	−1.71000e8			−2.41192
$176$	2.81079e7	+	2.90462e7i	0.388627	+	0.401602i
$177$	−1.74883e7			−0.237051
$178$	−4.69450e7	−	3.16471e7i	−0.623906	−	0.420595i
$179$		−	1.35773e8i		−	1.76941i	−0.466150	−	0.884706i	$-0.654359\pi$
$179$		−	1.35773e8i		−	1.76941i	0.466150	−	0.884706i	$-0.345641\pi$
$180$	−3.67889e7	+	1.48858e7i	−0.470178	+	0.190248i
$181$		−	1.52234e8i		−	1.90826i	−0.299400	−	0.954128i	$-0.596787\pi$
$181$		−	1.52234e8i		−	1.90826i	0.299400	−	0.954128i	$-0.403213\pi$
$182$	−3.96483e7	+	5.88139e7i	−0.487500	+	0.723153i
$183$	6.12807e7			0.739171
$184$	3.25632e7	−	1.53786e8i	0.385358	−	1.81992i
$185$	1.77982e8			2.06669
$186$	−1.18644e7	+	1.75995e7i	−0.135191	+	0.200541i
$187$		−	4.00667e7i		−	0.448061i
$188$	7.36977e6	+	1.82136e7i	0.0808912	+	0.199914i
$189$			3.27531e7i			0.352888i
$190$	−1.94279e7	−	1.30970e7i	−0.205489	−	0.138527i
$191$	−1.14883e7			−0.119299			−0.0596497	−	0.998219i	$-0.518998\pi$
$191$	−1.14883e7			−0.119299			−0.0596497	+	0.998219i	$0.518998\pi$
$192$	−2.29502e7	+	5.17635e7i	−0.234009	+	0.527800i
$193$	1.30726e8			1.30892			0.654458	−	0.756098i	$-0.272897\pi$
$193$	1.30726e8			1.30892			0.654458	+	0.756098i	$0.272897\pi$
$194$	7.56471e7	+	5.09961e7i	0.743852	+	0.501454i
$195$		−	4.32644e7i		−	0.417840i
$196$	9.34037e7	+	2.30838e8i	0.886070	+	2.18983i
$197$			1.47421e8i			1.37381i	0.726745	+	0.686907i	$0.241032\pi$
$197$			1.47421e8i			1.37381i	−0.726745	+	0.686907i	$0.758968\pi$
$198$	−1.13736e7	+	1.68715e7i	−0.104129	+	0.154463i
$199$	−7.23843e7			−0.651116			−0.325558	−	0.945522i	$-0.605552\pi$
$199$	−7.23843e7			−0.651116			−0.325558	+	0.945522i	$0.605552\pi$
$200$	3.08273e7	−	1.45588e8i	0.272478	−	1.28683i
$201$	−6.25819e7			−0.543579
$202$	8.31317e6	−	1.23317e7i	0.0709638	−	0.105267i
$203$			1.48209e8i			1.24348i
$204$	5.20309e7	−	2.10532e7i	0.429097	−	0.173625i
$205$		−	1.16665e8i		−	0.945805i
$206$	−2.95063e7	−	1.98911e7i	−0.235169	−	0.158535i
$207$	7.91320e7			0.620092
$208$	−4.29260e7	−	4.43591e7i	−0.330749	−	0.341791i
$209$	−1.20126e7			−0.0910177
$210$	−1.79260e8	−	1.20845e8i	−1.33572	−	0.900454i
$211$			1.13987e8i			0.835349i	0.908597	+	0.417675i	$0.137155\pi$
$211$			1.13987e8i			0.835349i	−0.908597	+	0.417675i	$0.862845\pi$
$212$	2.15326e7	−	8.71273e6i	0.155211	−	0.0628028i
$213$		−	7.49519e7i		−	0.531439i
$214$	6.42593e7	−	9.53216e7i	0.448217	−	0.664880i
$215$	1.96874e8			1.35099
$216$	−2.78857e7	−	5.90465e6i	−0.188276	−	0.0398663i
$217$	−1.15622e8			−0.768127
$218$	9.40676e7	−	1.39539e8i	0.614954	−	0.912216i
$219$			1.20224e8i			0.773461i
$220$	−5.03752e7	−	1.24497e8i	−0.318961	−	0.788280i
$221$			6.11893e7i			0.381332i
$222$	1.05996e8	+	7.14555e7i	0.650213	+	0.438329i
$223$	3.25338e8			1.96457			0.982285	−	0.187395i	$-0.0600045\pi$
$223$	3.25338e8			1.96457			0.982285	+	0.187395i	$0.0600045\pi$
$224$	−3.03696e8	+	5.39555e7i	−1.80539	+	0.320751i
$225$	7.49137e7			0.438452
$226$	−1.10056e8	−	7.41925e7i	−0.634214	−	0.427544i
$227$		−	1.77241e8i		−	1.00571i	−0.864370	−	0.502857i	$-0.832282\pi$
$227$		−	1.77241e8i		−	1.00571i	0.864370	−	0.502857i	$-0.167718\pi$
$228$	−6.31208e6	−	1.55997e7i	−0.0352696	−	0.0871653i
$229$			2.59923e8i			1.43028i	0.698983	+	0.715139i	$0.253636\pi$
$229$			2.59923e8i			1.43028i	−0.698983	+	0.715139i	$0.746364\pi$
$230$	−2.91963e8	+	4.33095e8i	−1.58227	+	2.34712i
$231$	−1.10840e8			−0.591636
$232$	−1.26184e8	−	2.67188e7i	−0.663433	−	0.140478i
$233$	−4.27541e7			−0.221428			−0.110714	−	0.993852i	$-0.535314\pi$
$233$	−4.27541e7			−0.221428			−0.110714	+	0.993852i	$0.535314\pi$
$234$	1.73696e7	−	2.57659e7i	0.0886207	−	0.131459i
$235$		−	6.52854e7i		−	0.328154i
$236$	7.68545e7	−	3.10976e7i	0.380608	−	0.154005i
$237$			8.50260e7i			0.414890i
$238$	2.53530e8	+	1.70912e8i	1.21902	+	0.821778i
$239$	−4.31118e6			−0.0204269			−0.0102135	−	0.999948i	$-0.503251\pi$
$239$	−4.31118e6			−0.0204269			−0.0102135	+	0.999948i	$0.503251\pi$
$240$	1.35203e8	−	1.30835e8i	0.631317	−	0.610921i
$241$	−1.51908e8			−0.699069			−0.349534	−	0.936924i	$-0.613660\pi$
$241$	−1.51908e8			−0.699069			−0.349534	+	0.936924i	$0.613660\pi$
$242$	1.25717e8	+	8.47497e7i	0.570216	+	0.384401i
$243$		−	1.43489e7i		−	0.0641500i
$244$	−2.69305e8	+	1.08969e8i	−1.18681	+	0.480217i
$245$		−	8.27420e8i		−	3.59455i
$246$	4.68382e7	−	6.94792e7i	0.200598	−	0.297565i
$247$	1.83455e7			0.0774624
$248$	2.08441e7	−	9.84400e7i	0.0867765	−	0.409818i
$249$	−9.00477e7			−0.369637
$250$	−6.62668e7	+	9.82995e7i	−0.268229	+	0.397888i
$251$			4.71376e7i			0.188152i	0.995565	+	0.0940761i	$0.0299897\pi$
$251$			4.71376e7i			0.188152i	−0.995565	+	0.0940761i	$0.970010\pi$
$252$	−5.82413e7	−	1.43938e8i	−0.229261	−	0.566594i
$253$			2.67791e8i			1.03962i
$254$	−1.48873e8	−	1.00360e8i	−0.570030	−	0.384275i
$255$	−1.86501e8			−0.704352
$256$	8.81212e6	−	2.68291e8i	0.0328277	−	0.999461i
$257$	3.54383e7			0.130229			0.0651143	−	0.997878i	$-0.479259\pi$
$257$	3.54383e7			0.130229			0.0651143	+	0.997878i	$0.479259\pi$
$258$	1.17247e8	+	7.90402e7i	0.425044	+	0.286536i
$259$			6.96360e8i			2.49049i
$260$	7.69324e7	+	1.90131e8i	0.271458	+	0.670881i
$261$		−	6.49294e7i		−	0.226047i
$262$	−1.49171e8	+	2.21279e8i	−0.512424	+	0.760125i
$263$	−2.32493e8			−0.788069			−0.394035	−	0.919096i	$-0.628921\pi$
$263$	−2.32493e8			−0.788069			−0.394035	+	0.919096i	$0.628921\pi$
$264$	1.99819e7	−	9.43682e7i	0.0668380	−	0.315654i
$265$	−7.71820e7			−0.254774
$266$	5.12422e7	−	7.60122e7i	0.166933	−	0.247627i
$267$			1.35113e8i			0.434419i
$268$	2.75023e8	−	1.11282e8i	0.872766	−	0.353147i
$269$		−	2.41676e8i		−	0.757008i	−0.925600	−	0.378504i	$-0.876439\pi$
$269$		−	2.41676e8i		−	0.757008i	0.925600	−	0.378504i	$-0.123561\pi$
$270$	7.85327e7	+	5.29413e7i	0.242816	+	0.163690i
$271$	3.99206e7			0.121844			0.0609220	−	0.998143i	$-0.480596\pi$
$271$	3.99206e7			0.121844			0.0609220	+	0.998143i	$0.480596\pi$
$272$	−1.91219e8	+	1.85042e8i	−0.576156	+	0.557543i
$273$	1.69273e8			0.503523
$274$	2.97229e8	+	2.00372e8i	0.872901	+	0.588450i
$275$			2.53515e8i			0.735089i
$276$	−3.47755e8	+	1.40712e8i	−0.995615	+	0.402855i
$277$		−	4.59198e8i		−	1.29814i	−0.760730	−	0.649069i	$-0.775159\pi$
$277$		−	4.59198e8i		−	1.29814i	0.760730	−	0.649069i	$-0.224841\pi$
$278$	2.46586e8	−	3.65784e8i	0.688354	−	1.02110i
$279$	5.06533e7			0.139635
$280$	1.00267e9	+	2.12309e8i	2.72963	+	0.577983i
$281$	−4.66896e8			−1.25530			−0.627651	−	0.778495i	$-0.715983\pi$
$281$	−4.66896e8			−1.25530			−0.627651	+	0.778495i	$0.715983\pi$
$282$	2.62105e7	−	3.88804e7i	0.0695991	−	0.103243i
$283$		−	7.16866e8i		−	1.88012i	−0.341011	−	0.940059i	$-0.610769\pi$
$283$		−	7.16866e8i		−	1.88012i	0.341011	−	0.940059i	$-0.389231\pi$
$284$	1.33279e8	+	3.29385e8i	0.345260	+	0.853275i
$285$			5.59158e7i			0.143080i
$286$	8.71946e7	+	5.87806e7i	0.220398	+	0.148577i
$287$	4.56455e8			1.13975
$288$	1.33047e8	−	2.36375e7i	0.328194	−	0.0583080i
$289$	−1.46569e8			−0.357190
$290$	3.55363e8	+	2.39562e8i	0.855618	+	0.576799i
$291$		−	2.17721e8i		−	0.517936i
$292$	−2.13782e8	−	5.28341e8i	−0.502494	−	1.24186i
$293$			5.97911e7i			0.138867i	0.997587	+	0.0694336i	$0.0221192\pi$
$293$			5.97911e7i			0.138867i	−0.997587	+	0.0694336i	$0.977881\pi$
$294$	3.32189e8	−	4.92766e8i	0.762377	−	1.13090i
$295$	−2.75479e8			−0.624757
$296$	−5.92875e8	−	1.25538e8i	−1.32875	−	0.281354i
$297$	4.85582e7			0.107551
$298$	−4.34912e7	+	6.45145e7i	−0.0952017	+	0.141221i
$299$		−	4.08967e8i		−	0.884787i
$300$	−3.29217e8	+	1.33211e8i	−0.703976	+	0.284849i
$301$			7.70275e8i			1.62803i
$302$	4.77977e7	+	3.22219e7i	0.0998579	+	0.0673174i
$303$	−3.54920e7			−0.0732962
$304$	5.54784e7	+	5.73305e7i	0.113257	+	0.117038i
$305$	9.65304e8			1.94812
$306$	−1.11070e8	−	7.48755e7i	−0.221600	−	0.149388i
$307$		−	1.89764e8i		−	0.374308i	−0.982331	−	0.187154i	$-0.940074\pi$
$307$		−	1.89764e8i		−	0.374308i	0.982331	−	0.187154i	$-0.0599263\pi$
$308$	4.87099e8	−	1.97095e8i	0.949926	−	0.384368i
$309$			8.49226e7i			0.163745i
$310$	−1.86889e8	+	2.77230e8i	−0.356302	+	0.528535i
$311$	−2.09202e8			−0.394371			−0.197185	−	0.980366i	$-0.563180\pi$
$311$	−2.09202e8			−0.394371			−0.197185	+	0.980366i	$0.563180\pi$
$312$	−3.05161e7	+	1.44118e8i	−0.0568838	+	0.268644i
$313$	−6.33548e8			−1.16782			−0.583908	−	0.811820i	$-0.698477\pi$
$313$	−6.33548e8			−1.16782			−0.583908	+	0.811820i	$0.698477\pi$
$314$	−2.49758e8	+	3.70489e8i	−0.455267	+	0.675339i
$315$			5.15933e8i			0.930050i
$316$	−1.51193e8	−	3.73657e8i	−0.269541	−	0.666144i
$317$			7.69116e8i			1.35608i	0.735027	+	0.678038i	$0.237170\pi$
$317$			7.69116e8i			1.35608i	−0.735027	+	0.678038i	$0.762830\pi$
$318$	−4.59654e7	−	3.09867e7i	−0.0801560	−	0.0540357i
$319$	2.19728e8			0.378981
$320$	−3.61516e8	+	8.15387e8i	−0.616741	+	1.39104i
$321$	−2.74347e8			−0.462948
$322$	−1.69450e9	−	1.14232e9i	−2.82843	−	1.90674i
$323$		−	7.90823e7i		−	0.130578i
$324$	2.55151e7	+	6.30580e7i	0.0416763	+	0.102999i
$325$		−	3.87166e8i		−	0.625612i
$326$	3.10398e7	−	4.60442e7i	0.0496201	−	0.0736060i
$327$	−4.01610e8			−0.635166
$328$	−8.22884e7	+	3.88622e8i	−0.128760	+	0.608091i
$329$	2.55431e8			0.395447
$330$	−1.79159e8	+	2.65762e8i	−0.274435	+	0.407094i
$331$		−	4.85538e8i		−	0.735911i	−0.929843	−	0.367955i	$-0.880058\pi$
$331$		−	4.85538e8i		−	0.735911i	0.929843	−	0.367955i	$-0.119942\pi$
$332$	3.95725e8	−	1.60122e8i	0.593486	−	0.240142i
$333$		−	3.05070e8i		−	0.452736i
$334$	−6.03700e8	−	4.06973e8i	−0.886561	−	0.597659i
$335$	−9.85800e8			−1.43262
$336$	5.11897e8	+	5.28986e8i	0.736198	+	0.760776i
$337$	−2.04774e7			−0.0291454			−0.0145727	−	0.999894i	$-0.504639\pi$
$337$	−2.04774e7			−0.0291454			−0.0145727	+	0.999894i	$0.504639\pi$
$338$	4.55489e8	+	3.07060e8i	0.641608	+	0.432528i
$339$			3.16755e8i			0.441596i
$340$	8.19599e8	−	3.31634e8i	1.13090	−	0.457596i
$341$			1.71416e8i			0.234105i
$342$	−2.24488e7	+	3.33004e7i	−0.0303461	+	0.0450151i
$343$	1.86690e9			2.49800
$344$	−6.55806e8	−	1.38863e8i	−0.868602	−	0.183921i
$345$	1.24650e9			1.63428
$346$	−5.85032e8	+	8.67831e8i	−0.759300	+	1.12634i
$347$			6.82874e8i			0.877379i	0.898639	+	0.438690i	$0.144557\pi$
$347$			6.82874e8i			0.877379i	−0.898639	+	0.438690i	$0.855443\pi$
$348$	1.15457e8	+	2.85340e8i	0.146856	+	0.362940i
$349$			9.14155e8i			1.15115i	0.817750	+	0.575573i	$0.195221\pi$
$349$			9.14155e8i			1.15115i	−0.817750	+	0.575573i	$0.804779\pi$
$350$	−1.60417e9	−	1.08142e9i	−1.99992	−	1.34821i
$351$	−7.41574e7			−0.0915334
$352$	7.99917e7	+	4.50244e8i	0.0977565	+	0.550235i
$353$	8.60893e8			1.04169			0.520844	−	0.853652i	$-0.325617\pi$
$353$	8.60893e8			1.04169			0.520844	+	0.853652i	$0.325617\pi$
$354$	−1.64060e8	−	1.10598e8i	−0.196559	−	0.132506i
$355$		−	1.18065e9i		−	1.40063i
$356$	−2.40257e8	−	5.93771e8i	−0.282229	−	0.697500i
$357$		−	7.29689e8i		−	0.848788i
$358$	8.58646e8	−	1.27371e9i	0.989062	−	1.46717i
$359$	−1.38426e9			−1.57902			−0.789512	−	0.613736i	$-0.789666\pi$
$359$	−1.38426e9			−1.57902			−0.789512	+	0.613736i	$0.789666\pi$
$360$	−4.39261e8	−	9.30109e7i	−0.496208	−	0.105069i
$361$	8.70162e8			0.973475
$362$	9.62745e8	−	1.42813e9i	1.06667	−	1.58229i
$363$		−	3.61828e8i		−	0.397035i
$364$	−7.43892e8	+	3.01000e8i	−0.808453	+	0.327124i
$365$			1.89380e9i			2.03849i
$366$	5.74882e8	+	3.87546e8i	0.612908	+	0.413180i
$367$	3.12309e8			0.329802			0.164901	−	0.986310i	$-0.447269\pi$
$367$	3.12309e8			0.329802			0.164901	+	0.986310i	$0.447269\pi$
$368$	1.27804e9	−	1.23675e9i	1.33683	−	1.29364i
$369$	−1.99970e8			−0.207191
$370$	1.66967e9	+	1.12558e9i	1.71366	+	1.15523i
$371$		−	3.01977e8i		−	0.307019i
$372$	−2.22602e8	+	9.00713e7i	−0.224196	+	0.0907164i
$373$		−	1.03487e8i		−	0.103253i	−0.998666	−	0.0516266i	$-0.983559\pi$
$373$		−	1.03487e8i		−	0.103253i	0.998666	−	0.0516266i	$-0.0164406\pi$
$374$	2.53386e8	−	3.75871e8i	0.250457	−	0.371525i
$375$	2.82918e8			0.277045
$376$	−4.60484e7	+	2.17472e8i	−0.0446742	+	0.210982i
$377$	−3.35565e8			−0.322539
$378$	−2.07135e8	+	3.07261e8i	−0.197257	+	0.292608i
$379$		−	1.96626e8i		−	0.185525i	−0.995688	−	0.0927626i	$-0.970430\pi$
$379$		−	1.96626e8i		−	0.185525i	0.995688	−	0.0927626i	$-0.0295697\pi$
$380$	−9.94289e7	−	2.45729e8i	−0.0929545	−	0.229728i
$381$			4.28474e8i			0.396905i
$382$	−1.07773e8	−	7.26532e7i	−0.0989209	−	0.0666857i
$383$	1.32285e9			1.20313			0.601567	−	0.798822i	$-0.294543\pi$
$383$	1.32285e9			1.20313			0.601567	+	0.798822i	$0.294543\pi$
$384$	−5.42658e8	+	3.40460e8i	−0.489065	+	0.306837i
$385$	−1.74597e9			−1.55928
$386$	1.22636e9	+	8.26728e8i	1.08533	+	0.731656i
$387$		−	3.37452e8i		−	0.295954i
$388$	3.87150e8	+	9.56802e8i	0.336487	+	0.831594i
$389$		−	2.23494e9i		−	1.92505i	−0.271189	−	0.962526i	$-0.587417\pi$
$389$		−	2.23494e9i		−	1.92505i	0.271189	−	0.962526i	$-0.412583\pi$
$390$	2.73609e8	−	4.05869e8i	0.233563	−	0.346466i
$391$	−1.76294e9			−1.49148
$392$	−5.83613e8	+	2.75621e9i	−0.489354	+	2.31106i
$393$	6.36866e8			0.529267
$394$	−9.32308e8	+	1.38298e9i	−0.767932	+	1.13914i
$395$			1.33934e9i			1.09346i
$396$	−2.13394e8	+	8.63456e7i	−0.172683	+	0.0698727i
$397$			1.06152e8i			0.0851456i	0.999093	+	0.0425728i	$0.0135554\pi$
$397$			1.06152e8i			0.0851456i	−0.999093	+	0.0425728i	$0.986445\pi$
$398$	−6.79046e8	−	4.57766e8i	−0.539894	−	0.363960i
$399$	−2.18772e8			−0.172420
$400$	1.20991e9	−	1.17082e9i	0.945241	−	0.914704i
$401$	−1.69252e9			−1.31078			−0.655388	−	0.755292i	$-0.727495\pi$
$401$	−1.69252e9			−1.31078			−0.655388	+	0.755292i	$0.727495\pi$
$402$	−5.87089e8	−	3.95775e8i	−0.450726	−	0.303849i
$403$		−	2.61784e8i		−	0.199240i
$404$	1.55974e8	−	6.31115e7i	0.117684	−	0.0476183i
$405$		−	2.26026e8i		−	0.169070i
$406$	−9.37292e8	+	1.39037e9i	−0.695079	+	1.03107i
$407$	1.03239e9			0.759037
$408$	6.21251e8	+	1.31546e8i	0.452852	+	0.0958888i
$409$	8.80345e8			0.636240			0.318120	−	0.948050i	$-0.396948\pi$
$409$	8.80345e8			0.636240			0.318120	+	0.948050i	$0.396948\pi$
$410$	7.37802e8	−	1.09445e9i	0.528684	−	0.784245i
$411$		−	8.55462e8i		−	0.607791i
$412$	−1.51009e8	−	3.73202e8i	−0.106380	−	0.262908i
$413$		−	1.07782e9i		−	0.752872i
$414$	7.42347e8	+	5.00440e8i	0.514169	+	0.346618i
$415$	−1.41845e9			−0.974192
$416$	−1.22162e8	−	6.87607e8i	−0.0831976	−	0.468289i
$417$	−1.05277e9			−0.710979
$418$	−1.12692e8	−	7.59692e7i	−0.0754702	−	0.0508769i
$419$			1.24808e9i			0.828886i	0.910075	+	0.414443i	$0.136024\pi$
$419$			1.24808e9i			0.828886i	−0.910075	+	0.414443i	$0.863976\pi$
$420$	−9.17427e8	−	2.26733e9i	−0.604225	−	1.49328i
$421$		−	1.98536e9i		−	1.29674i	−0.761326	−	0.648370i	$-0.775451\pi$
$421$		−	1.98536e9i		−	1.29674i	0.761326	−	0.648370i	$-0.224549\pi$
$422$	−7.20869e8	+	1.06933e9i	−0.466942	+	0.692657i
$423$	−1.11902e8			−0.0718866
$424$	2.57101e8	+	5.44396e7i	0.163803	+	0.0346844i
$425$	−1.66896e9			−1.05459
$426$	4.74004e8	−	7.03133e8i	0.297063	−	0.440660i
$427$			3.77678e9i			2.34760i
$428$	1.20565e9	−	4.87841e8i	0.743307	−	0.300764i
$429$		−	2.50956e8i		−	0.153461i
$430$	1.84690e9	+	1.24505e9i	1.12022	+	0.755176i
$431$	−1.92811e9			−1.16001			−0.580005	−	0.814613i	$-0.696949\pi$
$431$	−1.92811e9			−1.16001			−0.580005	+	0.814613i	$0.696949\pi$
$432$	−2.24258e8	−	2.31745e8i	−0.133830	−	0.138298i
$433$	7.31630e6			0.00433096			0.00216548	−	0.999998i	$-0.499311\pi$
$433$	7.31630e6			0.00433096			0.00216548	+	0.999998i	$0.499311\pi$
$434$	−1.08467e9	−	7.31210e8i	−0.636917	−	0.429366i
$435$		−	1.02278e9i		−	0.595757i
$436$	1.76492e9	−	7.14139e8i	1.01982	−	0.412648i
$437$			5.28556e8i			0.302975i
$438$	−7.60314e8	+	1.12784e9i	−0.432348	+	0.641340i
$439$	1.45798e9			0.822481			0.411241	−	0.911527i	$-0.365096\pi$
$439$	1.45798e9			0.822481			0.411241	+	0.911527i	$0.365096\pi$
$440$	3.14758e8	−	1.48650e9i	0.176154	−	0.831920i
$441$	−1.41824e9			−0.787435
$442$	−3.86968e8	+	5.74025e8i	−0.213156	+	0.316194i
$443$		−	7.48722e8i		−	0.409173i	−0.978848	−	0.204587i	$-0.934415\pi$
$443$		−	7.48722e8i		−	0.409173i	0.978848	−	0.204587i	$-0.0655850\pi$
$444$	5.42473e8	+	1.34067e9i	0.294129	+	0.726910i
$445$			2.12833e9i			1.14493i
$446$	3.05203e9	+	2.05747e9i	1.62899	+	1.09815i
$447$	1.85680e8			0.0983308
$448$	−3.19023e9	−	1.41444e9i	−1.67629	−	0.743211i
$449$	−1.02570e8			−0.0534760			−0.0267380	−	0.999642i	$-0.508512\pi$
$449$	−1.02570e8			−0.0534760			−0.0267380	+	0.999642i	$0.508512\pi$
$450$	7.02775e8	+	4.73763e8i	0.363557	+	0.245085i
$451$		−	6.76717e8i		−	0.347368i
$452$	−5.63251e8	−	1.39202e9i	−0.286891	−	0.709023i
$453$		−	1.37567e8i		−	0.0695299i
$454$	1.12089e9	−	1.66272e9i	0.562172	−	0.833920i
$455$	2.66642e9			1.32706
$456$	3.94397e7	−	1.86261e8i	0.0194785	−	0.0919908i
$457$	1.79099e9			0.877784			0.438892	−	0.898540i	$-0.355371\pi$
$457$	1.79099e9			0.877784			0.438892	+	0.898540i	$0.355371\pi$
$458$	−1.64378e9	+	2.43837e9i	−0.799494	+	1.18596i
$459$			3.19671e8i			0.154298i
$460$	−5.47789e9	+	2.21651e9i	−2.62398	+	1.06174i
$461$			1.38726e9i			0.659482i	0.944071	+	0.329741i	$0.106961\pi$
$461$			1.38726e9i			0.659482i	−0.944071	+	0.329741i	$0.893039\pi$
$462$	−1.03980e9	−	7.00964e8i	−0.490574	−	0.330711i
$463$	2.51864e9			1.17932			0.589662	−	0.807650i	$-0.299261\pi$
$463$	2.51864e9			1.17932			0.589662	+	0.807650i	$0.299261\pi$
$464$	−1.01478e9	−	1.04865e9i	−0.471582	−	0.487326i
$465$	7.97899e8			0.368013
$466$	−4.01082e8	−	2.70382e8i	−0.183604	−	0.123773i
$467$		−	4.98627e8i		−	0.226551i	−0.993564	−	0.113276i	$-0.963866\pi$
$467$		−	4.98627e8i		−	0.226551i	0.993564	−	0.113276i	$-0.0361343\pi$
$468$	3.25894e8	−	1.31866e8i	0.146965	−	0.0594665i
$469$		−	3.85697e9i		−	1.72640i
$470$	4.12872e8	−	6.12450e8i	0.183431	−	0.272100i
$471$	1.06631e9			0.470231
$472$	9.17647e8	+	1.94306e8i	0.401678	+	0.0850531i
$473$	1.14197e9			0.496182
$474$	−5.37714e8	+	7.97640e8i	−0.231914	+	0.344019i
$475$			5.00380e8i			0.214226i
$476$	1.29753e9	+	3.20670e9i	0.551432	+	1.36281i
$477$			1.32294e8i			0.0558117i
$478$	−4.04437e7	−	2.72644e7i	−0.0169377	−	0.0114182i
$479$	2.38769e9			0.992667			0.496334	−	0.868132i	$-0.334679\pi$
$479$	2.38769e9			0.992667			0.496334	+	0.868132i	$0.334679\pi$
$480$	2.09577e9	−	3.72342e8i	0.864968	−	0.153673i
$481$	−1.57665e9			−0.645993
$482$	−1.42506e9	−	9.60681e8i	−0.579655	−	0.390764i
$483$			4.87697e9i			1.96940i
$484$	6.43399e8	+	1.59010e9i	0.257942	+	0.637477i
$485$		−	3.42958e9i		−	1.36504i
$486$	9.07441e7	−	1.34609e8i	0.0358585	−	0.0531921i
$487$	3.95272e8			0.155076			0.0775380	−	0.996989i	$-0.475294\pi$
$487$	3.95272e8			0.155076			0.0775380	+	0.996989i	$0.475294\pi$
$488$	−3.21552e9	−	6.80867e8i	−1.25251	−	0.265212i
$489$	−1.32521e8			−0.0512510
$490$	5.23270e9	−	7.76213e9i	2.00928	−	2.98054i
$491$		−	4.21639e9i		−	1.60752i	−0.594956	−	0.803759i	$-0.702830\pi$
$491$		−	4.21639e9i		−	1.60752i	0.594956	−	0.803759i	$-0.297170\pi$
$492$	8.78789e8	−	3.55584e8i	0.332665	−	0.134606i
$493$			1.44653e9i			0.543703i
$494$	1.72102e8	+	1.16019e8i	0.0642305	+	0.0432998i
$495$	7.64896e8			0.283455
$496$	8.18087e8	−	7.91657e8i	0.301033	−	0.291307i
$497$	4.61934e9			1.68785
$498$	−8.44749e8	−	5.69472e8i	−0.306496	−	0.206619i
$499$			3.48633e9i			1.25608i	0.778181	+	0.628039i	$0.216142\pi$
$499$			3.48633e9i			1.25608i	−0.778181	+	0.628039i	$0.783858\pi$
$500$	−1.24331e9	+	5.03081e8i	−0.444822	+	0.179988i
$501$			1.73752e9i			0.617303i
$502$	−2.98104e8	+	4.42204e8i	−0.105173	+	0.156013i
$503$	−1.97546e9			−0.692117			−0.346058	−	0.938213i	$-0.612480\pi$
$503$	−1.97546e9			−0.692117			−0.346058	+	0.938213i	$0.612480\pi$
$504$	3.63908e8	−	1.71862e9i	0.126615	−	0.597962i
$505$	−5.59076e8			−0.193175
$506$	−1.69354e9	+	2.51218e9i	−0.581123	+	0.862033i
$507$		−	1.31095e9i		−	0.446744i
$508$	−7.61908e8	−	1.88298e9i	−0.257857	−	0.637268i
$509$			2.00763e9i			0.674796i	0.941362	+	0.337398i	$0.109547\pi$
$509$			2.00763e9i			0.674796i	−0.941362	+	0.337398i	$0.890453\pi$
$510$	−1.74959e9	−	1.17945e9i	−0.584036	−	0.393717i
$511$	−7.40953e9			−2.45651
$512$	1.77937e9	−	2.46114e9i	0.585897	−	0.810386i
$513$	9.58425e7			0.0313435
$514$	3.32451e8	+	2.24116e8i	0.107983	+	0.0727950i
$515$			1.33771e9i			0.431557i
$516$	6.00054e8	+	1.48297e9i	0.192272	+	0.475181i
$517$		−	3.78689e8i		−	0.120522i
$518$	−4.40386e9	+	6.53264e9i	−1.39213	+	2.06507i
$519$	2.49772e9			0.784257
$520$	−4.80695e8	+	2.27017e9i	−0.149920	+	0.708022i
$521$	−4.23829e8			−0.131298			−0.0656491	−	0.997843i	$-0.520912\pi$
$521$	−4.23829e8			−0.131298			−0.0656491	+	0.997843i	$0.520912\pi$
$522$	4.10621e8	−	6.09111e8i	0.126356	−	0.187435i
$523$		−	2.04172e9i		−	0.624081i	−0.950069	−	0.312040i	$-0.898988\pi$
$523$		−	2.04172e9i		−	0.624081i	0.950069	−	0.312040i	$-0.101012\pi$
$524$	−2.79878e9	+	1.13247e9i	−0.849787	+	0.343849i
$525$			4.61699e9i			1.39252i
$526$	−2.18105e9	−	1.47031e9i	−0.653453	−	0.440513i
$527$	−1.12848e9			−0.335858
$528$	7.84248e8	−	7.58912e8i	0.231865	−	0.224374i
$529$	8.37799e9			2.46062
$530$	−7.24055e8	−	4.88108e8i	−0.211254	−	0.142413i
$531$			4.72185e8i			0.136861i
$532$	9.61420e8	−	3.89019e8i	0.276836	−	0.112016i
$533$			1.03347e9i			0.295634i
$534$	−8.54472e8	+	1.26751e9i	−0.242831	+	0.360212i
$535$	−4.32156e9			−1.22012
$536$	3.28379e9	+	6.95324e8i	0.921084	+	0.195034i
$537$	−3.66588e9			−1.02157
$538$	1.52839e9	−	2.26719e9i	0.423151	−	0.627697i
$539$		−	4.79947e9i		−	1.32018i
$540$	4.01918e8	+	9.93299e8i	0.109840	+	0.271458i
$541$		−	4.11067e9i		−	1.11615i	−0.829791	−	0.558075i	$-0.811540\pi$
$541$		−	4.11067e9i		−	1.11615i	0.829791	−	0.558075i	$-0.188460\pi$
$542$	3.74500e8	+	2.52462e8i	0.101031	+	0.0681082i
$543$	−4.11032e9			−1.10173
$544$	−2.96408e9	+	5.26607e8i	−0.789393	+	0.140246i
$545$	−6.32622e9			−1.67400
$546$	1.58798e9	+	1.07050e9i	0.417513	+	0.281458i
$547$		−	3.47958e9i		−	0.909016i	−0.890743	−	0.454508i	$-0.849815\pi$
$547$		−	3.47958e9i		−	0.909016i	0.890743	−	0.454508i	$-0.150185\pi$
$548$	1.52117e9	+	3.75943e9i	0.394863	+	0.975865i
$549$		−	1.65458e9i		−	0.426761i
$550$	−1.60326e9	+	2.37826e9i	−0.410899	+	0.609523i
$551$	4.33691e8			0.110446
$552$	−4.15221e9	−	8.79206e8i	−1.05073	−	0.222487i
$553$	−5.24022e9			−1.31769
$554$	2.90402e9	−	4.30779e9i	0.725630	−	1.07639i
$555$		−	4.80552e9i		−	1.19320i
$556$	4.62651e9	−	1.87202e9i	1.14154	−	0.461902i
$557$			6.06054e9i			1.48600i	0.669293	+	0.742998i	$0.266597\pi$
$557$			6.06054e9i			1.48600i	−0.669293	+	0.742998i	$0.733403\pi$
$558$	4.75185e8	+	3.20337e8i	0.115783	+	0.0780527i
$559$	−1.74401e9			−0.422286
$560$	8.06348e9	+	8.33268e9i	1.94028	+	2.00506i
$561$	−1.08180e9			−0.258688
$562$	−4.38001e9	−	2.95270e9i	−1.04087	−	0.701686i
$563$		−	1.86742e9i		−	0.441024i	−0.975384	−	0.220512i	$-0.929227\pi$
$563$		−	1.86742e9i		−	0.441024i	0.975384	−	0.220512i	$-0.0707728\pi$
$564$	4.91768e8	−	1.98984e8i	0.115421	−	0.0467026i
$565$			4.98958e9i			1.16384i
$566$	4.53354e9	−	6.72501e9i	1.05094	−	1.55896i
$567$	8.84335e8			0.203740
$568$	−8.32762e8	+	3.93287e9i	−0.190679	+	0.900514i
$569$	−4.20147e8			−0.0956111			−0.0478056	−	0.998857i	$-0.515223\pi$
$569$	−4.20147e8			−0.0956111			−0.0478056	+	0.998857i	$0.515223\pi$
$570$	−3.53618e8	+	5.24553e8i	−0.0799783	+	0.118639i
$571$			7.99582e9i			1.79737i	0.438599	+	0.898683i	$0.355475\pi$
$571$			7.99582e9i			1.79737i	−0.438599	+	0.898683i	$0.644525\pi$
$572$	4.46248e8	+	1.10286e9i	0.0996989	+	0.246396i
$573$			3.10183e8i			0.0688775i
$574$	4.28206e9	+	2.88667e9i	0.945064	+	0.637098i
$575$	1.11547e10			2.44693
$576$	1.39762e9	+	6.19656e8i	0.304726	+	0.135105i
$577$	9.06331e9			1.96414			0.982068	−	0.188527i	$-0.0603712\pi$
$577$	9.06331e9			1.96414			0.982068	+	0.188527i	$0.0603712\pi$
$578$	−1.37498e9	−	9.26919e8i	−0.296176	−	0.199662i
$579$		−	3.52961e9i		−	0.755704i
$580$	1.81869e9	+	4.49472e9i	0.387045	+	0.956543i
$581$		−	5.54971e9i		−	1.17396i
$582$	1.37690e9	−	2.04247e9i	0.289515	−	0.429463i
$583$	−4.47696e8			−0.0935714
$584$	1.33577e9	−	6.30841e9i	0.277515	−	1.31062i
$585$	−1.16814e9			−0.241240
$586$	−3.78126e8	+	5.60908e8i	−0.0776237	+	0.115146i
$587$			1.24696e9i			0.254460i	0.991873	+	0.127230i	$0.0406086\pi$
$587$			1.24696e9i			0.254460i	−0.991873	+	0.127230i	$0.959391\pi$
$588$	6.23262e9	−	2.52190e9i	1.26430	−	0.511573i
$589$			3.38335e8i			0.0682250i
$590$	−2.58430e9	−	1.74216e9i	−0.518038	−	0.349226i
$591$	3.98037e9			0.793172
$592$	−4.76792e9	−	4.92710e9i	−0.944503	−	0.976035i
$593$	−4.61574e9			−0.908970			−0.454485	−	0.890754i	$-0.650177\pi$
$593$	−4.61574e9			−0.908970			−0.454485	+	0.890754i	$0.650177\pi$
$594$	4.55530e8	+	3.07087e8i	0.0891794	+	0.0601187i
$595$		−	1.14942e10i		−	2.23701i
$596$	−8.15994e8	+	3.30175e8i	−0.157879	+	0.0638825i
$597$			1.95437e9i			0.375922i
$598$	2.58635e9	−	3.83657e9i	0.494577	−	0.733650i
$599$	−9.32636e9			−1.77304			−0.886520	−	0.462690i	$-0.846884\pi$
$599$	−9.32636e9			−1.77304			−0.886520	+	0.462690i	$0.846884\pi$
$600$	−3.93087e9	−	8.32338e8i	−0.742949	−	0.157315i
$601$	2.37970e8			0.0447159			0.0223580	−	0.999750i	$-0.492883\pi$
$601$	2.37970e8			0.0447159			0.0223580	+	0.999750i	$0.492883\pi$
$602$	−4.87131e9	+	7.22605e9i	−0.910035	+	1.34994i
$603$			1.68971e9i			0.313835i
$604$	2.44621e8	+	6.04556e8i	0.0451715	+	0.111637i
$605$		−	5.69957e9i		−	1.04640i
$606$	−3.32955e8	−	2.24456e8i	−0.0607759	−	0.0409710i
$607$	−7.73975e8			−0.140464			−0.0702322	−	0.997531i	$-0.522374\pi$
$607$	−7.73975e8			−0.140464			−0.0702322	+	0.997531i	$0.522374\pi$
$608$	1.57885e8	+	8.88676e8i	0.0284891	+	0.160354i
$609$	4.00165e9			0.717924
$610$	9.05564e9	+	6.10469e9i	1.61534	+	1.08895i
$611$			5.78329e8i			0.102573i
$612$	−5.68437e8	−	1.40483e9i	−0.100243	−	0.247739i
$613$			1.51299e9i			0.265291i	0.991164	+	0.132646i	$0.0423472\pi$
$613$			1.51299e9i			0.265291i	−0.991164	+	0.132646i	$0.957653\pi$
$614$	1.20009e9	−	1.78020e9i	0.209230	−	0.310370i
$615$	−3.14995e9			−0.546061
$616$	5.81599e9	+	1.23150e9i	1.00252	+	0.212277i
$617$	1.14910e10			1.96952			0.984760	−	0.173917i	$-0.0556426\pi$
$617$	1.14910e10			1.96952			0.984760	+	0.173917i	$0.0556426\pi$
$618$	−5.37060e8	+	7.96670e8i	−0.0915300	+	0.135775i
$619$			8.37828e9i			1.41983i	0.704285	+	0.709917i	$0.251268\pi$
$619$			8.37828e9i			1.41983i	−0.704285	+	0.709917i	$0.748732\pi$
$620$	−3.50646e9	+	1.41882e9i	−0.590879	+	0.239087i
$621$		−	2.13656e9i		−	0.358010i
$622$	−1.96255e9	−	1.32302e9i	−0.327005	−	0.220444i
$623$	−8.32714e9			−1.37971
$624$	−1.19769e9	+	1.15900e9i	−0.197333	+	0.190958i
$625$	−3.57174e9			−0.585193
$626$	−5.94339e9	−	4.00663e9i	−0.968332	−	0.652783i
$627$			3.24341e8i			0.0525491i
$628$	−4.68603e9	+	1.89611e9i	−0.754999	+	0.305495i
$629$			6.79649e9i			1.08895i
$630$	−3.26282e9	+	4.84003e9i	−0.519877	+	0.771181i
$631$	3.05024e9			0.483316			0.241658	−	0.970362i	$-0.422309\pi$
$631$	3.05024e9			0.483316			0.241658	+	0.970362i	$0.422309\pi$
$632$	9.44693e8	−	4.46148e9i	0.148861	−	0.703023i
$633$	3.07766e9			0.482289
$634$	−4.86398e9	+	7.21517e9i	−0.758017	+	1.12444i
$635$			6.74939e9i			1.04606i
$636$	−2.35244e8	−	5.81381e8i	−0.0362592	−	0.0896109i
$637$			7.32969e9i			1.12356i
$638$	2.06129e9	+	1.38958e9i	0.314244	+	0.211842i
$639$	−2.02370e9			−0.306827
$640$	−8.54803e9	+	5.36299e9i	−1.28895	+	0.808680i
$641$	−4.51079e9			−0.676471			−0.338236	−	0.941061i	$-0.609830\pi$
$641$	−4.51079e9			−0.676471			−0.338236	+	0.941061i	$0.609830\pi$
$642$	−2.57368e9	−	1.73500e9i	−0.383869	−	0.258778i
$643$			7.40844e9i			1.09898i	0.835502	+	0.549488i	$0.185177\pi$
$643$			7.40844e9i			1.09898i	−0.835502	+	0.549488i	$0.814823\pi$
$644$	−8.67218e9	−	2.14324e10i	−1.27946	−	3.16206i
$645$		−	5.31560e9i		−	0.779997i
$646$	5.00125e8	−	7.41881e8i	0.0729903	−	0.108273i
$647$	7.43537e9			1.07929			0.539644	−	0.841893i	$-0.318559\pi$
$647$	7.43537e9			1.07929			0.539644	+	0.841893i	$0.318559\pi$
$648$	−1.59425e8	+	7.52915e8i	−0.0230168	+	0.108701i
$649$	−1.59792e9			−0.229456
$650$	2.44848e9	−	3.63205e9i	0.349704	−	0.518747i
$651$			3.12181e9i			0.443478i
$652$	5.82377e8	−	2.35647e8i	0.0822882	−	0.0332962i
$653$		−	4.56618e9i		−	0.641737i	−0.947124	−	0.320868i	$-0.896025\pi$
$653$		−	4.56618e9i		−	0.641737i	0.947124	−	0.320868i	$-0.103975\pi$
$654$	−3.76755e9	−	2.53983e9i	−0.526668	−	0.355044i
$655$	1.00320e10			1.39490
$656$	−3.22965e9	+	3.12531e9i	−0.446675	+	0.432245i
$657$	3.24606e9			0.446558
$658$	2.39623e9	+	1.61537e9i	0.327897	+	0.221046i
$659$			6.99163e9i			0.951655i	0.879539	+	0.475828i	$0.157851\pi$
$659$			6.99163e9i			0.951655i	−0.879539	+	0.475828i	$0.842149\pi$
$660$	−3.36142e9	+	1.36013e9i	−0.455113	+	0.184152i
$661$		−	1.28732e10i		−	1.73374i	−0.498537	−	0.866868i	$-0.666129\pi$
$661$		−	1.28732e10i		−	1.73374i	0.498537	−	0.866868i	$-0.333871\pi$
$662$	3.07060e9	−	4.55489e9i	0.411358	−	0.610204i
$663$	1.65211e9			0.220162
$664$	4.72498e9	+	1.00049e9i	0.626342	+	0.132624i
$665$	−3.44614e9			−0.454419
$666$	1.92930e9	−	2.86190e9i	0.253069	−	0.375401i
$667$		−	9.66804e9i		−	1.26153i
$668$	−3.08964e9	−	7.63574e9i	−0.401043	−	0.991137i
$669$		−	8.78412e9i		−	1.13424i
$670$	−9.24792e9	−	6.23431e9i	−1.18791	−	0.800805i
$671$	5.59926e9			0.715488
$672$	1.45680e9	+	8.19978e9i	0.185186	+	1.04234i
$673$	−1.25348e10			−1.58513			−0.792563	−	0.609790i	$-0.791254\pi$
$673$	−1.25348e10			−1.58513			−0.792563	+	0.609790i	$0.791254\pi$
$674$	−1.92101e8	−	1.29502e8i	−0.0241669	−	0.0162917i
$675$		−	2.02267e9i		−	0.253141i
$676$	2.33112e9	+	5.76113e9i	0.290236	+	0.717290i
$677$			1.18534e10i			1.46819i	0.679049	+	0.734093i	$0.262392\pi$
$677$			1.18534e10i			1.46819i	−0.679049	+	0.734093i	$0.737608\pi$
$678$	−2.00320e9	+	2.97152e9i	−0.246842	+	0.366163i
$679$	1.34183e10			1.64496
$680$	9.78605e9	+	2.07214e9i	1.19351	+	0.252719i
$681$	−4.78551e9			−0.580649
$682$	−1.08405e9	+	1.60808e9i	−0.130860	+	0.194116i
$683$			2.84949e9i			0.342211i	0.985253	+	0.171106i	$0.0547339\pi$
$683$			2.84949e9i			0.342211i	−0.985253	+	0.171106i	$0.945266\pi$
$684$	−4.21191e8	+	1.70426e8i	−0.0503249	+	0.0203629i
$685$		−	1.34754e10i		−	1.60186i
$686$	1.75137e10	+	1.18065e10i	2.07130	+	1.39633i
$687$	7.01792e9			0.825771
$688$	−5.27401e9	−	5.45008e9i	−0.617421	−	0.638034i
$689$	6.83716e8			0.0796358
$690$	1.16936e10	+	7.88301e9i	1.35511	+	0.913525i
$691$		−	1.25711e9i		−	0.144944i	−0.997370	−	0.0724720i	$-0.976911\pi$
$691$		−	1.25711e9i		−	0.144944i	0.997370	−	0.0724720i	$-0.0230888\pi$
$692$	−1.09765e10	+	4.44142e9i	−1.25920	+	0.509508i
$693$			2.99268e9i			0.341581i
$694$	−4.31857e9	+	6.40613e9i	−0.490436	+	0.727508i
$695$	−1.65834e10			−1.87381
$696$	−7.21406e8	+	3.40697e9i	−0.0811050	+	0.383033i
$697$	4.45501e9			0.498349
$698$	−5.78122e9	+	8.57580e9i	−0.643466	+	0.954511i
$699$			1.15436e9i			0.127841i
$700$	−8.20989e9	−	2.02899e10i	−0.904678	−	2.23582i
$701$			8.39464e9i			0.920426i	0.887808	+	0.460213i	$0.152227\pi$
$701$			8.39464e9i			0.920426i	−0.887808	+	0.460213i	$0.847773\pi$
$702$	−6.95680e8	−	4.68980e8i	−0.0758979	−	0.0511652i
$703$	2.03769e9			0.221205
$704$	−2.09698e9	+	4.72967e9i	−0.226511	+	0.510889i
$705$	−1.76270e9			−0.189460
$706$	8.07614e9	+	5.44438e9i	0.863749	+	0.582281i
$707$		−	2.18740e9i		−	0.232788i
$708$	−8.39635e8	−	2.07507e9i	−0.0889148	−	0.219744i
$709$			9.69833e9i			1.02196i	0.859592	+	0.510982i	$0.170718\pi$
$709$			9.69833e9i			1.02196i	−0.859592	+	0.510982i	$0.829282\pi$
$710$	7.46659e9	−	1.10759e10i	0.782921	−	1.16138i
$711$	2.29570e9			0.239537
$712$	1.50119e9	−	7.08966e9i	0.155868	−	0.736114i
$713$	7.54232e9			0.779277
$714$	4.61464e9	−	6.84531e9i	0.474454	−	0.703800i
$715$		−	3.95310e9i		−	0.404452i
$716$	1.61101e10	−	6.51863e9i	1.64023	−	0.663683i
$717$			1.16402e8i			0.0117935i
$718$	−1.29860e10	−	8.75425e9i	−1.30930	−	0.882639i
$719$	1.10435e10			1.10804			0.554021	−	0.832503i	$-0.313093\pi$
$719$	1.10435e10			1.10804			0.554021	+	0.832503i	$0.313093\pi$
$720$	−3.53255e9	−	3.65048e9i	−0.352716	−	0.364491i
$721$	−5.23385e9			−0.520053
$722$	8.16310e9	+	5.50300e9i	0.807188	+	0.544151i
$723$			4.10150e9i			0.403607i
$724$	1.80633e10	−	7.30893e9i	1.76893	−	0.715762i
$725$		−	9.15266e9i		−	0.891999i
$726$	2.28824e9	−	3.39435e9i	0.221934	−	0.329215i
$727$	−8.43847e9			−0.814504			−0.407252	−	0.913316i	$-0.633513\pi$
$727$	−8.43847e9			−0.814504			−0.407252	+	0.913316i	$0.633513\pi$
$728$	−8.88211e9	−	1.88073e9i	−0.853211	−	0.180662i
$729$	−3.87420e8			−0.0370370
$730$	−1.19766e10	+	1.77659e10i	−1.13947	+	1.69028i
$731$			7.51790e9i			0.711846i
$732$	2.94216e9	+	7.27124e9i	0.277254	+	0.685204i
$733$			2.39430e9i			0.224551i	0.993677	+	0.112275i	$0.0358139\pi$
$733$			2.39430e9i			0.224551i	−0.993677	+	0.112275i	$0.964186\pi$
$734$	2.92981e9	+	1.97508e9i	0.273466	+	0.184352i
$735$	−2.23403e10			−2.07532
$736$	1.98108e10	−	3.51964e9i	1.83159	−	0.325407i
$737$	−5.71815e9			−0.526162
$738$	−1.87594e9	−	1.26463e9i	−0.171799	−	0.115815i
$739$			6.87252e9i			0.626412i	0.949685	+	0.313206i	$0.101403\pi$
$739$			6.87252e9i			0.626412i	−0.949685	+	0.313206i	$0.898597\pi$
$740$	8.54512e9	+	2.11184e10i	0.775188	+	1.91580i
$741$		−	4.95329e8i		−	0.0447229i
$742$	1.90974e9	−	2.83289e9i	0.171617	−	0.254575i
$743$	−4.79987e9			−0.429307			−0.214654	−	0.976690i	$-0.568862\pi$
$743$	−4.79987e9			−0.429307			−0.214654	+	0.976690i	$0.568862\pi$
$744$	−2.65788e9	−	5.62790e8i	−0.236608	−	0.0501004i
$745$	2.92487e9			0.259155
$746$	6.54462e8	−	9.70823e8i	0.0577163	−	0.0856158i
$747$			2.43129e9i			0.213410i
$748$	4.75410e9	−	1.92365e9i	0.415348	−	0.168062i
$749$		−	1.69082e10i		−	1.47032i
$750$	2.65409e9	+	1.78920e9i	0.229721	+	0.154862i
$751$	−1.02345e10			−0.881711			−0.440855	−	0.897578i	$-0.645325\pi$
$751$	−1.02345e10			−0.881711			−0.440855	+	0.897578i	$0.645325\pi$
$752$	−1.80730e9	+	1.74892e9i	−0.154977	+	0.149971i
$753$	1.27272e9			0.108630
$754$	−3.14798e9	−	2.12215e9i	−0.267444	−	0.180292i
$755$		−	2.16698e9i		−	0.183249i
$756$	−3.88631e9	+	1.57252e9i	−0.327123	+	0.132364i
$757$		−	8.82502e9i		−	0.739401i	−0.929151	−	0.369701i	$-0.879460\pi$
$757$		−	8.82502e9i		−	0.739401i	0.929151	−	0.369701i	$-0.120540\pi$
$758$	1.24348e9	−	1.84457e9i	0.103704	−	0.153834i
$759$	7.23035e9			0.600223
$760$	6.21260e8	−	2.93401e9i	0.0513364	−	0.242446i
$761$	−8.02572e9			−0.660143			−0.330071	−	0.943956i	$-0.607073\pi$
$761$	−8.02572e9			−0.660143			−0.330071	+	0.943956i	$0.607073\pi$
$762$	−2.70972e9	+	4.01957e9i	−0.221861	+	0.329107i
$763$		−	2.47515e10i		−	2.01728i
$764$	−5.51565e8	−	1.36314e9i	−0.0447476	−	0.110589i
$765$			5.03552e9i			0.406658i
$766$	1.24098e10	+	8.36584e9i	0.997618	+	0.672526i
$767$	2.44033e9			0.195283
$768$	−7.24385e9	−	2.37927e8i	−0.577039	−	0.0189531i
$769$	−1.84781e10			−1.46526			−0.732631	−	0.680626i	$-0.761708\pi$
$769$	−1.84781e10			−1.46526			−0.732631	+	0.680626i	$0.761708\pi$
$770$	−1.63792e10	−	1.10417e10i	−1.29293	−	0.871603i
$771$		−	9.56833e8i		−	0.0751876i
$772$	6.27631e9	+	1.55113e10i	0.490958	+	1.21335i
$773$			1.79885e9i			0.140077i	0.997544	+	0.0700387i	$0.0223123\pi$
$773$			1.79885e9i			0.140077i	−0.997544	+	0.0700387i	$0.977688\pi$
$774$	2.13408e9	−	3.16568e9i	0.165432	−	0.245399i
$775$	7.14026e9			0.551008
$776$	−2.41902e9	+	1.14243e10i	−0.185833	+	0.877632i
$777$	1.88017e10			1.43788
$778$	1.41340e10	−	2.09663e10i	1.07606	−	1.59622i
$779$		−	1.33568e9i		−	0.101233i
$780$	5.13353e9	−	2.07718e9i	0.387333	−	0.156726i
$781$		−	6.84841e9i		−	0.514412i
$782$	−1.65383e10	−	1.11490e10i	−1.23671	−	0.833706i
$783$	−1.75309e9			−0.130509
$784$	−2.29056e10	+	2.21656e10i	−1.69760	+	1.64275i
$785$	1.67967e10			1.23931
$786$	5.97453e9	+	4.02762e9i	0.438859	+	0.295848i
$787$		−	1.00314e9i		−	0.0733584i	−0.999327	−	0.0366792i	$-0.988322\pi$
$787$		−	1.00314e9i		−	0.0733584i	0.999327	−	0.0366792i	$-0.0116780\pi$
$788$	−1.74922e10	+	7.07786e9i	−1.27351	+	0.515300i
$789$			6.27731e9i			0.454992i
$790$	−8.47017e9	+	1.25646e10i	−0.611219	+	0.906677i
$791$	−1.95219e10			−1.40250
$792$	−2.54794e9	−	5.39512e8i	−0.182243	−	0.0385889i
$793$	−8.55113e9			−0.608930
$794$	−6.71319e8	+	9.95828e8i	−0.0475945	+	0.0706013i
$795$			2.08391e9i			0.147094i
$796$	−3.47525e9	−	8.58873e9i	−0.244225	−	0.603578i
$797$		−	1.35708e10i		−	0.949511i	−0.880118	−	0.474756i	$-0.842536\pi$
$797$		−	1.35708e10i		−	0.949511i	0.880118	−	0.474756i	$-0.157464\pi$
$798$	−2.05233e9	−	1.38354e9i	−0.142967	−	0.0963789i
$799$	2.49301e9			0.172906
$800$	1.87547e10	−	3.33202e9i	1.29508	−	0.230087i
$801$	3.64806e9			0.250812
$802$	−1.58778e10	−	1.07037e10i	−1.08687	−	0.732696i
$803$			1.09850e10i			0.748679i
$804$	−3.00463e9	−	7.42563e9i	−0.203889	−	0.503892i
$805$			7.68228e10i			5.19044i
$806$	1.65556e9	−	2.45583e9i	0.111371	−	0.165206i
$807$	−6.52525e9			−0.437058
$808$	1.86233e9	+	3.94339e8i	0.124199	+	0.0262984i
$809$	−8.33727e9			−0.553610			−0.276805	−	0.960926i	$-0.589276\pi$
$809$	−8.33727e9			−0.553610			−0.276805	+	0.960926i	$0.589276\pi$
$810$	1.42942e9	−	2.12038e9i	0.0945064	−	0.140190i
$811$		−	2.27829e10i		−	1.49981i	−0.661545	−	0.749906i	$-0.730099\pi$
$811$		−	2.27829e10i		−	1.49981i	0.661545	−	0.749906i	$-0.269901\pi$
$812$	−1.75857e10	+	7.11570e9i	−1.15269	+	0.466414i
$813$		−	1.07786e9i		−	0.0703467i
$814$	9.68497e9	+	6.52894e9i	0.629380	+	0.424285i
$815$	−2.08749e9			−0.135074
$816$	4.99612e9	+	5.16292e9i	0.321897	+	0.332644i
$817$	2.25399e9			0.144602
$818$	8.25863e9	+	5.56740e9i	0.527559	+	0.355644i
$819$		−	4.57038e9i		−	0.290709i
$820$	1.38428e10	−	5.60122e9i	0.876752	−	0.354759i
$821$			1.35551e10i			0.854871i	0.904046	+	0.427436i	$0.140583\pi$
$821$			1.35551e10i			0.854871i	−0.904046	+	0.427436i	$0.859417\pi$
$822$	5.41004e9	−	8.02520e9i	0.339742	−	0.503970i
$823$	1.12181e10			0.701487			0.350743	−	0.936472i	$-0.385929\pi$
$823$	1.12181e10			0.701487			0.350743	+	0.936472i	$0.385929\pi$
$824$	9.43544e8	−	4.45605e9i	0.0587512	−	0.277463i
$825$	6.84492e9			0.424404
$826$	6.81626e9	−	1.01112e10i	0.420839	−	0.624268i
$827$		−	2.37157e10i		−	1.45803i	−0.684496	−	0.729016i	$-0.739978\pi$
$827$		−	2.37157e10i		−	1.45803i	0.684496	−	0.729016i	$-0.260022\pi$
$828$	3.79922e9	+	9.38938e9i	0.232588	+	0.574818i
$829$			1.17633e10i			0.717113i	0.933508	+	0.358557i	$0.116731\pi$
$829$			1.17633e10i			0.717113i	−0.933508	+	0.358557i	$0.883269\pi$
$830$	−1.33066e10	−	8.97042e9i	−0.807783	−	0.544552i
$831$	−1.23983e10			−0.749480
$832$	3.20248e9	−	7.22310e9i	0.192777	−	0.434802i
$833$	3.15962e10			1.89399
$834$	−9.87616e9	−	6.65783e9i	−0.589531	−	0.397422i
$835$			2.73697e10i			1.62693i
$836$	−5.76739e8	−	1.42535e9i	−0.0341395	−	0.0843724i
$837$		−	1.36764e9i		−	0.0806181i
$838$	−7.89303e9	+	1.17084e10i	−0.463329	+	0.687298i
$839$	6.79741e9			0.397353			0.198677	−	0.980065i	$-0.436336\pi$
$839$	6.79741e9			0.397353			0.198677	+	0.980065i	$0.436336\pi$
$840$	5.73234e9	−	2.70720e10i	0.333699	−	1.57595i
$841$	9.31706e9			0.540123
$842$	1.25557e10	−	1.86249e10i	0.724849	−	1.07523i
$843$			1.26062e10i			0.724749i
$844$	−1.35251e10	+	5.47266e9i	−0.774360	+	0.313329i
$845$		−	2.06503e10i		−	1.17741i
$846$	−1.04977e9	−	7.07684e8i	−0.0596071	−	0.0401830i
$847$	2.22997e10			1.26098
$848$	2.06761e9	+	2.13664e9i	0.116435	+	0.120322i
$849$	−1.93554e10			−1.08549
$850$	−1.56567e10	−	1.05547e10i	−0.874450	−	0.589494i
$851$		−	4.54252e10i		−	2.52664i
$852$	8.89339e9	−	3.59852e9i	0.492639	−	0.199336i
$853$		−	2.68751e10i		−	1.48262i	−0.671165	−	0.741308i	$-0.734206\pi$
$853$		−	2.68751e10i		−	1.48262i	0.671165	−	0.741308i	$-0.265794\pi$
$854$	−2.38848e10	+	3.54305e10i	−1.31226	+	1.94659i
$855$	1.50973e9			0.0826070
$856$	1.43955e10	+	3.04817e9i	0.784457	+	0.166104i
$857$	2.07409e10			1.12563			0.562814	−	0.826584i	$-0.309719\pi$
$857$	2.07409e10			1.12563			0.562814	+	0.826584i	$0.309719\pi$
$858$	1.58708e9	−	2.35425e9i	0.0857812	−	0.127247i
$859$			1.85518e10i			0.998642i	0.866417	+	0.499321i	$0.166417\pi$
$859$			1.85518e10i			0.998642i	−0.866417	+	0.499321i	$0.833583\pi$
$860$	9.45214e9	+	2.33600e10i	0.506741	+	1.25236i
$861$		−	1.23243e10i		−	0.658037i
$862$	−1.80878e10	−	1.21936e10i	−0.961859	−	0.648420i
$863$	2.60997e10			1.38229			0.691144	−	0.722717i	$-0.257107\pi$
$863$	2.60997e10			1.38229			0.691144	+	0.722717i	$0.257107\pi$
$864$	−6.38213e8	−	3.59226e9i	−0.0336641	−	0.189483i
$865$	3.93445e10			2.06694
$866$	6.86351e7	+	4.62691e7i	0.00359115	+	0.00242091i
$867$			3.95736e9i			0.206224i
$868$	−5.55116e9	−	1.37191e10i	−0.288114	−	0.712046i
$869$			7.76889e9i			0.401596i
$870$	6.46817e9	−	9.59481e9i	0.333015	−	0.493991i
$871$	8.73269e9			0.447801
$872$	2.10732e10	+	4.46214e9i	1.07628	+	0.227895i
$873$	−5.87848e9			−0.299030
$874$	−3.34265e9	+	4.95846e9i	−0.169356	+	0.251221i
$875$			1.74364e10i			0.879892i
$876$	−1.42652e10	+	5.77212e9i	−0.716991	+	0.290115i
$877$			2.82084e9i			0.141215i	0.997504	+	0.0706074i	$0.0224937\pi$
$877$			2.82084e9i			0.141215i	−0.997504	+	0.0706074i	$0.977506\pi$
$878$	1.36775e10	+	9.22044e9i	0.681987	+	0.459749i
$879$	1.61436e9			0.0801750
$880$	1.23536e10	−	1.19545e10i	0.611089	−	0.591347i
$881$	9.92677e9			0.489094			0.244547	−	0.969637i	$-0.421361\pi$
$881$	9.92677e9			0.489094			0.244547	+	0.969637i	$0.421361\pi$
$882$	−1.33047e10	−	8.96911e9i	−0.652927	−	0.440159i
$883$			8.85510e9i			0.432844i	0.976300	+	0.216422i	$0.0694387\pi$
$883$			8.85510e9i			0.432844i	−0.976300	+	0.216422i	$0.930561\pi$
$884$	−7.26040e9	+	2.93777e9i	−0.353490	+	0.143033i
$885$			7.43793e9i			0.360704i
$886$	4.73500e9	−	7.02386e9i	0.228719	−	0.339279i
$887$	−6.69747e9			−0.322239			−0.161120	−	0.986935i	$-0.551510\pi$
$887$	−6.69747e9			−0.322239			−0.161120	+	0.986935i	$0.551510\pi$
$888$	−3.38952e9	+	1.60076e10i	−0.162440	+	0.767152i
$889$	−2.64072e10			−1.26057
$890$	−1.34598e10	+	1.99661e10i	−0.639990	+	0.949354i
$891$		−	1.31107e9i		−	0.0620946i
$892$	1.56198e10	+	3.86028e10i	0.736884	+	1.82114i
$893$		−	7.47444e8i		−	0.0351236i
$894$	1.74189e9	+	1.17426e9i	0.0815342	+	0.0549647i
$895$	−5.77455e10			−2.69239
$896$	−2.09828e10	−	3.34444e10i	−0.974510	−	1.55327i
$897$	−1.10421e10			−0.510832
$898$	−9.62224e8	−	6.48666e8i	−0.0443414	−	0.0298919i
$899$		−	6.18863e9i		−	0.284076i
$900$	3.59669e9	+	8.88886e9i	0.164458	+	0.406441i
$901$		−	2.94730e9i		−	0.134242i
$902$	4.27964e9	−	6.34837e9i	0.194171	−	0.288031i
$903$	2.07974e10			0.939945
$904$	3.51935e9	−	1.66208e10i	0.158443	−	0.748276i
$905$	−6.47464e10			−2.90366
$906$	8.69992e8	−	1.29054e9i	0.0388657	−	0.0576530i
$907$			4.12904e9i			0.183749i	0.995771	+	0.0918743i	$0.0292858\pi$
$907$			4.12904e9i			0.183749i	−0.995771	+	0.0918743i	$0.970714\pi$
$908$	2.10305e10	−	8.50955e9i	0.932286	−	0.377230i
$909$			9.58284e8i			0.0423176i
$910$	2.50141e10	+	1.68628e10i	1.10037	+	0.741795i
$911$	−1.66278e10			−0.728653			−0.364326	−	0.931271i	$-0.618701\pi$
$911$	−1.66278e10			−0.728653			−0.364326	+	0.931271i	$0.618701\pi$
$912$	1.54792e9	−	1.49792e9i	0.0675721	−	0.0653891i
$913$	−8.22773e9			−0.357793
$914$	1.68015e10	+	1.13265e10i	0.727843	+	0.490662i
$915$		−	2.60632e10i		−	1.12474i
$916$	−3.08411e10	+	1.24792e10i	−1.32585	+	0.536478i
$917$			3.92506e10i			1.68095i
$918$	−2.02164e9	+	2.99888e9i	−0.0862490	+	0.127941i
$919$	1.15132e10			0.489317			0.244658	−	0.969609i	$-0.421324\pi$
$919$	1.15132e10			0.489317			0.244658	+	0.969609i	$0.421324\pi$
$920$	−6.54063e10	−	1.38494e10i	−2.76925	−	0.586373i
$921$	−5.12362e9			−0.216107
$922$	−8.77316e9	+	1.30140e10i	−0.368636	+	0.546831i
$923$			1.04588e10i			0.437800i
$924$	−5.32155e9	−	1.31517e10i	−0.221915	−	0.548440i
$925$		−	4.30037e10i		−	1.78653i
$926$	2.36277e10	+	1.59282e10i	0.977876	+	0.659217i
$927$	2.29291e9			0.0945383
$928$	−2.88794e9	−	1.62551e10i	−0.118623	−	0.667687i
$929$	1.46627e10			0.600010			0.300005	−	0.953938i	$-0.403012\pi$
$929$	1.46627e10			0.600010			0.300005	+	0.953938i	$0.403012\pi$
$930$	7.48520e9	+	5.04601e9i	0.305150	+	0.205711i
$931$		−	9.47303e9i		−	0.384738i
$932$	−2.05267e9	−	5.07298e9i	−0.0830548	−	0.205261i
$933$			5.64845e9i			0.227690i
$934$	3.15337e9	−	4.67768e9i	0.126637	−	0.187852i
$935$	−1.70407e10			−0.681784
$936$	3.89119e9	+	8.23936e8i	0.155102	+	0.0328419i
$937$	−9.78575e9			−0.388602			−0.194301	−	0.980942i	$-0.562244\pi$
$937$	−9.78575e9			−0.388602			−0.194301	+	0.980942i	$0.562244\pi$
$938$	2.43919e10	−	3.61827e10i	0.965020	−	1.43150i
$939$			1.71058e10i			0.674238i
$940$	7.74641e9	−	3.13443e9i	0.304196	−	0.123086i
$941$			1.76197e10i			0.689341i	0.938724	+	0.344670i	$0.112009\pi$
$941$			1.76197e10i			0.689341i	−0.938724	+	0.344670i	$0.887991\pi$
$942$	1.00032e10	+	6.74348e9i	0.389907	+	0.262849i
$943$	−2.97756e10			−1.15630
$944$	7.37975e9	+	7.62612e9i	0.285522	+	0.295054i
$945$	1.39302e10			0.536964
$946$	1.07130e10	+	7.22196e9i	0.411426	+	0.277355i
$947$		−	1.90489e9i		−	0.0728862i	−0.999336	−	0.0364431i	$-0.988397\pi$
$947$		−	1.90489e9i		−	0.0728862i	0.999336	−	0.0364431i	$-0.0116028\pi$
$948$	−1.00887e10	+	4.08220e9i	−0.384599	+	0.155620i
$949$		−	1.67762e10i		−	0.637178i
$950$	−3.16446e9	+	4.69413e9i	−0.119748	+	0.177633i
$951$	2.07661e10			0.782931
$952$	−8.10731e9	+	3.82882e10i	−0.304542	+	1.43825i
$953$	−2.36695e10			−0.885857			−0.442928	−	0.896557i	$-0.646060\pi$
$953$	−2.36695e10			−0.885857			−0.442928	+	0.896557i	$0.646060\pi$
$954$	−8.36642e8	+	1.24107e9i	−0.0311975	+	0.0462781i
$955$			4.88606e9i			0.181529i
$956$	−2.06985e8	−	5.11542e8i	−0.00766188	−	0.0189356i
$957$		−	5.93264e9i		−	0.218805i
$958$	2.23992e10	+	1.51000e10i	0.823102	+	0.554879i
$959$	5.27228e10			1.93034
$960$	2.20155e10	+	9.76093e9i	0.803116	+	0.356075i
$961$	−2.26847e10			−0.824519
$962$	−1.47908e10	−	9.97093e9i	−0.535646	−	0.361096i
$963$			7.40737e9i			0.267283i
$964$	−7.29326e9	−	1.80245e10i	−0.262212	−	0.648029i
$965$		−	5.55990e10i		−	1.99169i
$966$	−3.08425e10	+	4.57515e10i	−1.10085	+	1.63300i
$967$	−1.02607e10			−0.364907			−0.182454	−	0.983214i	$-0.558404\pi$
$967$	−1.02607e10			−0.364907			−0.182454	+	0.983214i	$0.558404\pi$
$968$	−4.02014e9	+	1.89858e10i	−0.142455	+	0.672768i
$969$	−2.13522e9			−0.0753893
$970$	2.16891e10	−	3.21734e10i	0.763027	−	1.13187i
$971$			4.79387e10i			1.68042i	0.542258	+	0.840212i	$0.317570\pi$
$971$			4.79387e10i			1.68042i	−0.542258	+	0.840212i	$0.682430\pi$
$972$	1.70256e9	−	6.88907e8i	0.0594664	−	0.0240618i
$973$		−	6.48830e10i		−	2.25806i
$974$	3.70810e9	+	2.49974e9i	0.128586	+	0.0866841i
$975$	−1.04535e10			−0.361197
$976$	−2.58593e10	−	2.67226e10i	−0.890313	−	0.920036i
$977$	−2.78771e10			−0.956349			−0.478174	−	0.878265i	$-0.658701\pi$
$977$	−2.78771e10			−0.956349			−0.478174	+	0.878265i	$0.658701\pi$
$978$	−1.24319e9	−	8.38075e8i	−0.0424964	−	0.0286482i
$979$			1.23454e10i			0.420500i
$980$	9.81773e10	−	3.97254e10i	3.33211	−	1.34827i
$981$			1.08435e10i			0.366713i
$982$	2.66649e10	−	3.95545e10i	0.898567	−	1.33292i
$983$	−8.77775e9			−0.294745			−0.147372	−	0.989081i	$-0.547082\pi$
$983$	−8.77775e9			−0.294745			−0.147372	+	0.989081i	$0.547082\pi$
$984$	1.04928e10	+	2.22179e9i	0.351082	+	0.0743395i
$985$	6.26995e10			2.09044
$986$	−9.14799e9	+	1.35700e10i	−0.303918	+	0.450829i
$987$		−	6.89664e9i		−	0.228311i
$988$	8.80790e8	+	2.17678e9i	0.0290551	+	0.0718068i
$989$		−	5.02469e10i		−	1.65166i
$990$	7.17559e9	+	4.83729e9i	0.235036	+	0.158445i
$991$	4.78690e8			0.0156242			0.00781208	−	0.999969i	$-0.497513\pi$
$991$	4.78690e8			0.0156242			0.00781208	+	0.999969i	$0.497513\pi$
$992$	1.26811e10	−	2.25297e9i	0.412445	−	0.0732764i
$993$	−1.31095e10			−0.424878
$994$	4.33347e10	+	2.92133e10i	1.39953	+	0.943469i
$995$			3.07856e10i			0.990757i
$996$	−4.32329e9	−	1.06846e10i	−0.138646	−	0.342649i
$997$			4.09532e10i			1.30874i	0.756173	+	0.654371i	$0.227067\pi$
$997$			4.09532e10i			1.30874i	−0.756173	+	0.654371i	$0.772933\pi$
$998$	−2.20480e10	+	3.27057e10i	−0.702121	+	1.04152i
$999$	−8.23690e9			−0.261387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.8.d.a.13.14	yes	14
3.2	odd	2		72.8.d.d.37.1		14
4.3	odd	2		96.8.d.a.49.9		14
8.3	odd	2		96.8.d.a.49.6		14
8.5	even	2	inner	24.8.d.a.13.13	✓	14
12.11	even	2		288.8.d.d.145.12		14
24.5	odd	2		72.8.d.d.37.2		14
24.11	even	2		288.8.d.d.145.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.8.d.a.13.13	✓	14	8.5	even	2	inner
24.8.d.a.13.14	yes	14	1.1	even	1	trivial
72.8.d.d.37.1		14	3.2	odd	2
72.8.d.d.37.2		14	24.5	odd	2
96.8.d.a.49.6		14	8.3	odd	2
96.8.d.a.49.9		14	4.3	odd	2
288.8.d.d.145.3		14	24.11	even	2
288.8.d.d.145.12		14	12.11	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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(9.38113 + 6.32411i) q^{2} -27.0000i q^{3} +(48.0111 + 118.655i) q^{4} -425.308i q^{5} +(170.751 - 253.290i) q^{6} +1664.03 q^{7} +(-299.987 + 1416.74i) q^{8} -729.000 q^{9} +O(q^{10})\)	\(q+(9.38113 + 6.32411i) q^{2} -27.0000i q^{3} +(48.0111 + 118.655i) q^{4} -425.308i q^{5} +(170.751 - 253.290i) q^{6} +1664.03 q^{7} +(-299.987 + 1416.74i) q^{8} -729.000 q^{9} +(2689.70 - 3989.87i) q^{10} -2467.01i q^{11} +(3203.68 - 1296.30i) q^{12} +3767.59i q^{13} +(15610.5 + 10523.5i) q^{14} -11483.3 q^{15} +(-11773.9 + 11393.5i) q^{16} +16241.0 q^{17} +(-6838.84 - 4610.28i) q^{18} -4869.30i q^{19} +(50464.8 - 20419.5i) q^{20} -44928.9i q^{21} +(15601.7 - 23143.3i) q^{22} -108549. q^{23} +(38252.1 + 8099.65i) q^{24} -102762. q^{25} +(-23826.7 + 35344.2i) q^{26} +19683.0i q^{27} +(79892.1 + 197445. i) q^{28} +89066.4i q^{29} +(-107727. - 72621.9i) q^{30} -69483.3 q^{31} +(-182506. + 32424.6i) q^{32} -66609.3 q^{33} +(152359. + 102710. i) q^{34} -707727. i q^{35} +(-35000.1 - 86499.3i) q^{36} +418478. i q^{37} +(30794.0 - 45679.6i) q^{38} +101725. q^{39} +(602553. + 127587. i) q^{40} +274307. q^{41} +(284135. - 421483. i) q^{42} +462897. i q^{43} +(292722. - 118444. i) q^{44} +310050. i q^{45} +(-1.01831e6 - 686474. i) q^{46} +153501. q^{47} +(307624. + 317894. i) q^{48} +1.94546e6 q^{49} +(-964026. - 649880. i) q^{50} -438507. i q^{51} +(-447042. + 180886. i) q^{52} -181473. i q^{53} +(-124478. + 184649. i) q^{54} -1.04924e6 q^{55} +(-499188. + 2.35750e6i) q^{56} -131471. q^{57} +(-563266. + 835543. i) q^{58} -647716. i q^{59} +(-551328. - 1.36255e6i) q^{60} +2.26966e6i q^{61} +(-651832. - 439420. i) q^{62} -1.21308e6 q^{63} +(-1.91717e6 - 850009. i) q^{64} +1.60239e6 q^{65} +(-624870. - 421245. i) q^{66} -2.31785e6i q^{67} +(779748. + 1.92707e6i) q^{68} +2.93081e6i q^{69} +(4.47575e6 - 6.63928e6i) q^{70} +2.77599e6 q^{71} +(218691. - 1.03281e6i) q^{72} -4.45276e6 q^{73} +(-2.64650e6 + 3.92579e6i) q^{74} +2.77458e6i q^{75} +(577766. - 233781. i) q^{76} -4.10518e6i q^{77} +(954294. + 643320. i) q^{78} -3.14911e6 q^{79} +(4.84575e6 + 5.00752e6i) q^{80} +531441. q^{81} +(2.57331e6 + 1.73475e6i) q^{82} -3.33510e6i q^{83} +(5.33102e6 - 2.15709e6i) q^{84} -6.90743e6i q^{85} +(-2.92741e6 + 4.34250e6i) q^{86} +2.40479e6 q^{87} +(3.49512e6 + 740071. i) q^{88} -5.00420e6 q^{89} +(-1.96079e6 + 2.90862e6i) q^{90} +6.26939e6i q^{91} +(-5.21155e6 - 1.28798e7i) q^{92} +1.87605e6i q^{93} +(1.44001e6 + 970759. i) q^{94} -2.07096e6 q^{95} +(875463. + 4.92766e6i) q^{96} +8.06376e6 q^{97} +(1.82506e7 + 1.23033e7i) q^{98} +1.79845e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9	\( 14 q - 14 q^{2} - 208 q^{4} - 54 q^{6} + 1372 q^{7} - 428 q^{8} - 10206 q^{9} + 5020 q^{10} + 7668 q^{12} + 4636 q^{14} - 13500 q^{15} - 43336 q^{16} - 2908 q^{17} + 10206 q^{18} + 175096 q^{20} - 128480 q^{22} - 143416 q^{23} - 29268 q^{24} - 202626 q^{25} + 424984 q^{26} + 567520 q^{28} - 250668 q^{30} - 89468 q^{31} - 893944 q^{32} + 1109820 q^{34} + 151632 q^{36} - 823816 q^{38} + 474552 q^{39} - 860888 q^{40} - 441284 q^{41} + 427788 q^{42} + 1275264 q^{44} - 2167992 q^{46} - 1056408 q^{47} - 233280 q^{48} + 2158134 q^{49} + 324610 q^{50} - 2059248 q^{52} + 39366 q^{54} + 4757504 q^{55} + 1643704 q^{56} + 1551096 q^{57} - 5494676 q^{58} - 3203712 q^{60} + 5767172 q^{62} - 1000188 q^{63} + 3852224 q^{64} - 2520464 q^{65} - 3615840 q^{66} - 3735840 q^{68} + 12890312 q^{70} + 5172696 q^{71} + 312012 q^{72} - 5446196 q^{73} - 6468800 q^{74} - 9084624 q^{76} + 3542184 q^{78} - 14373548 q^{79} + 14369088 q^{80} + 7440174 q^{81} - 7935708 q^{82} - 2775816 q^{84} + 4738312 q^{86} + 7902036 q^{87} + 12598720 q^{88} - 11952620 q^{89} - 3659580 q^{90} + 11004480 q^{92} - 15440088 q^{94} - 69327376 q^{95} + 1341576 q^{96} + 133732 q^{97} + 53030538 q^{98}+O(q^{100}) \) 14 * q - 14 * q^2 - 208 * q^4 - 54 * q^6 + 1372 * q^7 - 428 * q^8 - 10206 * q^9 + 5020 * q^10 + 7668 * q^12 + 4636 * q^14 - 13500 * q^15 - 43336 * q^16 - 2908 * q^17 + 10206 * q^18 + 175096 * q^20 - 128480 * q^22 - 143416 * q^23 - 29268 * q^24 - 202626 * q^25 + 424984 * q^26 + 567520 * q^28 - 250668 * q^30 - 89468 * q^31 - 893944 * q^32 + 1109820 * q^34 + 151632 * q^36 - 823816 * q^38 + 474552 * q^39 - 860888 * q^40 - 441284 * q^41 + 427788 * q^42 + 1275264 * q^44 - 2167992 * q^46 - 1056408 * q^47 - 233280 * q^48 + 2158134 * q^49 + 324610 * q^50 - 2059248 * q^52 + 39366 * q^54 + 4757504 * q^55 + 1643704 * q^56 + 1551096 * q^57 - 5494676 * q^58 - 3203712 * q^60 + 5767172 * q^62 - 1000188 * q^63 + 3852224 * q^64 - 2520464 * q^65 - 3615840 * q^66 - 3735840 * q^68 + 12890312 * q^70 + 5172696 * q^71 + 312012 * q^72 - 5446196 * q^73 - 6468800 * q^74 - 9084624 * q^76 + 3542184 * q^78 - 14373548 * q^79 + 14369088 * q^80 + 7440174 * q^81 - 7935708 * q^82 - 2775816 * q^84 + 4738312 * q^86 + 7902036 * q^87 + 12598720 * q^88 - 11952620 * q^89 - 3659580 * q^90 + 11004480 * q^92 - 15440088 * q^94 - 69327376 * q^95 + 1341576 * q^96 + 133732 * q^97 + 53030538 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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