LMFDB - Embedded newform 7.9.b.b.6.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,9,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7.6");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	7.b (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:	$2.85165027043$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1016x^{2} + 51570 $ x^4 + 1016*x^2 + 51570
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.4
Root			$-7.32010i$ of defining polynomial
Character	$\chi$	$=$	7.6
Dual form			7.9.b.b.6.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+21.5647 q^{2} +119.877i q^{3} +209.035 q^{4} -786.953i q^{5} +2585.11i q^{6} +(1971.19 - 1370.84i) q^{7} -1012.79 q^{8} -7809.55 q^{9} +O(q^{10})$	\(q+21.5647 q^{2} +119.877i q^{3} +209.035 q^{4} -786.953i q^{5} +2585.11i q^{6} +(1971.19 - 1370.84i) q^{7} -1012.79 q^{8} -7809.55 q^{9} -16970.4i q^{10} -6464.40 q^{11} +25058.5i q^{12} +23304.2i q^{13} +(42508.1 - 29561.6i) q^{14} +94337.7 q^{15} -75353.4 q^{16} +85372.2i q^{17} -168410. q^{18} -171975. i q^{19} -164500. i q^{20} +(164332. + 236301. i) q^{21} -139403. q^{22} +145847. q^{23} -121411. i q^{24} -228670. q^{25} +502548. i q^{26} -149672. i q^{27} +(412048. - 286552. i) q^{28} -684636. q^{29} +2.03436e6 q^{30} +597349. i q^{31} -1.36570e6 q^{32} -774934. i q^{33} +1.84102e6i q^{34} +(-1.07878e6 - 1.55124e6i) q^{35} -1.63246e6 q^{36} +2.08191e6 q^{37} -3.70859e6i q^{38} -2.79365e6 q^{39} +797021. i q^{40} -226141. i q^{41} +(3.54377e6 + 5.09576e6i) q^{42} +3.79260e6 q^{43} -1.35128e6 q^{44} +6.14575e6i q^{45} +3.14514e6 q^{46} +105710. i q^{47} -9.03316e6i q^{48} +(2.00641e6 - 5.40437e6i) q^{49} -4.93120e6 q^{50} -1.02342e7 q^{51} +4.87139e6i q^{52} -3.46490e6 q^{53} -3.22763e6i q^{54} +5.08718e6i q^{55} +(-1.99641e6 + 1.38837e6i) q^{56} +2.06159e7 q^{57} -1.47639e7 q^{58} -1.35101e7i q^{59} +1.97198e7 q^{60} +842042. i q^{61} +1.28816e7i q^{62} +(-1.53941e7 + 1.07056e7i) q^{63} -1.01603e7 q^{64} +1.83393e7 q^{65} -1.67112e7i q^{66} +9.62973e6 q^{67} +1.78457e7i q^{68} +1.74837e7i q^{69} +(-2.32636e7 - 3.34519e7i) q^{70} -4.99364e6 q^{71} +7.90946e6 q^{72} +2.22669e7i q^{73} +4.48956e7 q^{74} -2.74123e7i q^{75} -3.59488e7i q^{76} +(-1.27426e7 + 8.86163e6i) q^{77} -6.02440e7 q^{78} -3.48440e7 q^{79} +5.92996e7i q^{80} -3.32962e7 q^{81} -4.87665e6i q^{82} -8.16858e7i q^{83} +(3.43511e7 + 4.93951e7i) q^{84} +6.71839e7 q^{85} +8.17862e7 q^{86} -8.20723e7i q^{87} +6.54710e6 q^{88} +7.05328e7i q^{89} +1.32531e8i q^{90} +(3.19463e7 + 4.59372e7i) q^{91} +3.04871e7 q^{92} -7.16086e7 q^{93} +2.27960e6i q^{94} -1.35336e8 q^{95} -1.63716e8i q^{96} -3.15476e7i q^{97} +(4.32677e7 - 1.16543e8i) q^{98} +5.04840e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 32 q^{4} + 1428 q^{7} + 3328 q^{8} - 8124 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 - 32 * q^4 + 1428 * q^7 + 3328 * q^8 - 8124 * q^9	$ 4 q + 32 q^{2} - 32 q^{4} + 1428 q^{7} + 3328 q^{8} - 8124 q^{9} - 22168 q^{11} + 99008 q^{14} + 72960 q^{15} - 65280 q^{16} - 378528 q^{18} + 545664 q^{21} - 227392 q^{22} + 908072 q^{23} - 2055740 q^{25} + 1389920 q^{28} - 1473016 q^{29} + 4712640 q^{30} - 4577280 q^{32} + 2304960 q^{35} - 4951584 q^{36} + 6715272 q^{37} - 9276288 q^{39} + 5880000 q^{42} + 5748072 q^{43} - 623424 q^{44} + 2860352 q^{46} - 1194620 q^{49} - 967840 q^{50} - 21727872 q^{51} + 6749576 q^{53} - 10723328 q^{56} + 33733440 q^{57} - 28950592 q^{58} + 65479680 q^{60} - 40211052 q^{63} - 31918080 q^{64} - 39184320 q^{65} + 70027112 q^{67} - 71359680 q^{70} + 49900712 q^{71} + 35881728 q^{72} + 75593152 q^{74} - 13869688 q^{77} - 99960000 q^{78} - 82167256 q^{79} - 75422268 q^{81} + 19869696 q^{84} + 108466560 q^{85} + 173795392 q^{86} - 11637248 q^{88} + 206157504 q^{91} - 77732160 q^{92} - 90960000 q^{93} - 424874880 q^{95} + 115512992 q^{98} + 66343656 q^{99}+O(q^{100}) $ 4 * q + 32 * q^2 - 32 * q^4 + 1428 * q^7 + 3328 * q^8 - 8124 * q^9 - 22168 * q^11 + 99008 * q^14 + 72960 * q^15 - 65280 * q^16 - 378528 * q^18 + 545664 * q^21 - 227392 * q^22 + 908072 * q^23 - 2055740 * q^25 + 1389920 * q^28 - 1473016 * q^29 + 4712640 * q^30 - 4577280 * q^32 + 2304960 * q^35 - 4951584 * q^36 + 6715272 * q^37 - 9276288 * q^39 + 5880000 * q^42 + 5748072 * q^43 - 623424 * q^44 + 2860352 * q^46 - 1194620 * q^49 - 967840 * q^50 - 21727872 * q^51 + 6749576 * q^53 - 10723328 * q^56 + 33733440 * q^57 - 28950592 * q^58 + 65479680 * q^60 - 40211052 * q^63 - 31918080 * q^64 - 39184320 * q^65 + 70027112 * q^67 - 71359680 * q^70 + 49900712 * q^71 + 35881728 * q^72 + 75593152 * q^74 - 13869688 * q^77 - 99960000 * q^78 - 82167256 * q^79 - 75422268 * q^81 + 19869696 * q^84 + 108466560 * q^85 + 173795392 * q^86 - 11637248 * q^88 + 206157504 * q^91 - 77732160 * q^92 - 90960000 * q^93 - 424874880 * q^95 + 115512992 * q^98 + 66343656 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	21.5647			1.34779			0.673896	−	0.738827i	$-0.264620\pi$
$2$	21.5647			1.34779			0.673896	+	0.738827i	$0.264620\pi$
$3$			119.877i			1.47997i	0.672626	+	0.739983i	$0.265166\pi$
$3$			119.877i			1.47997i	−0.672626	+	0.739983i	$0.734834\pi$
$4$	209.035			0.816541
$5$		−	786.953i		−	1.25912i	−0.776950	−	0.629562i	$-0.783234\pi$
$5$		−	786.953i		−	1.25912i	0.776950	−	0.629562i	$-0.216766\pi$
$6$			2585.11i			1.99468i
$7$	1971.19	−	1370.84i	0.820989	−	0.570944i
$7$	1971.19	−	1370.84i	0.820989	−	0.570944i
$8$	−1012.79			−0.247264
$9$	−7809.55			−1.19030
$10$		−	16970.4i		−	1.69704i
$11$	−6464.40			−0.441527			−0.220764	−	0.975327i	$-0.570855\pi$
$11$	−6464.40			−0.441527			−0.220764	+	0.975327i	$0.570855\pi$
$12$			25058.5i			1.20845i
$13$			23304.2i			0.815946i	0.912994	+	0.407973i	$0.133764\pi$
$13$			23304.2i			0.815946i	−0.912994	+	0.407973i	$0.866236\pi$
$14$	42508.1	−	29561.6i	1.10652	−	0.769513i
$15$	94337.7			1.86346
$16$	−75353.4			−1.14980
$17$			85372.2i			1.02216i	0.859532	+	0.511082i	$0.170755\pi$
$17$			85372.2i			1.02216i	−0.859532	+	0.511082i	$0.829245\pi$
$18$	−168410.			−1.60427
$19$		−	171975.i		−	1.31963i	−0.751429	−	0.659814i	$-0.770635\pi$
$19$		−	171975.i		−	1.31963i	0.751429	−	0.659814i	$-0.229365\pi$
$20$		−	164500.i		−	1.02813i
$21$	164332.	+	236301.i	0.844978	+	1.21504i
$22$	−139403.			−0.595086
$23$	145847.			0.521178			0.260589	−	0.965450i	$-0.416083\pi$
$23$	145847.			0.521178			0.260589	+	0.965450i	$0.416083\pi$
$24$		−	121411.i		−	0.365942i
$25$	−228670.			−0.585396
$26$			502548.i			1.09972i
$27$		−	149672.i		−	0.281634i
$28$	412048.	−	286552.i	0.670371	−	0.466199i
$29$	−684636.			−0.967983			−0.483992	−	0.875073i	$-0.660813\pi$
$29$	−684636.			−0.967983			−0.483992	+	0.875073i	$0.660813\pi$
$30$	2.03436e6			2.51156
$31$			597349.i			0.646817i	0.946259	+	0.323409i	$0.104829\pi$
$31$			597349.i			0.646817i	−0.946259	+	0.323409i	$0.895171\pi$
$32$	−1.36570e6			−1.30243
$33$		−	774934.i		−	0.653445i
$34$			1.84102e6i			1.37766i
$35$	−1.07878e6	−	1.55124e6i	−0.718890	−	1.03373i
$36$	−1.63246e6			−0.971927
$37$	2.08191e6			1.11085			0.555423	−	0.831568i	$-0.312556\pi$
$37$	2.08191e6			1.11085			0.555423	+	0.831568i	$0.312556\pi$
$38$		−	3.70859e6i		−	1.77858i
$39$	−2.79365e6			−1.20757
$40$			797021.i			0.311336i
$41$		−	226141.i		−	0.0800282i	−0.999199	−	0.0400141i	$-0.987260\pi$
$41$		−	226141.i		−	0.0800282i	0.999199	−	0.0400141i	$-0.0127403\pi$
$42$	3.54377e6	+	5.09576e6i	1.13885	+	1.63761i
$43$	3.79260e6			1.10934			0.554669	−	0.832071i	$-0.312845\pi$
$43$	3.79260e6			1.10934			0.554669	+	0.832071i	$0.312845\pi$
$44$	−1.35128e6			−0.360525
$45$			6.14575e6i			1.49873i
$46$	3.14514e6			0.702440
$47$			105710.i			0.0216633i	0.999941	+	0.0108317i	$0.00344789\pi$
$47$			105710.i			0.0216633i	−0.999941	+	0.0108317i	$0.996552\pi$
$48$		−	9.03316e6i		−	1.70167i
$49$	2.00641e6	−	5.40437e6i	0.348046	−	0.937478i
$50$	−4.93120e6			−0.788991
$51$	−1.02342e7			−1.51277
$52$			4.87139e6i			0.666253i
$53$	−3.46490e6			−0.439124			−0.219562	−	0.975599i	$-0.570463\pi$
$53$	−3.46490e6			−0.439124			−0.219562	+	0.975599i	$0.570463\pi$
$54$		−	3.22763e6i		−	0.379584i
$55$			5.08718e6i			0.555938i
$56$	−1.99641e6	+	1.38837e6i	−0.203001	+	0.141174i
$57$	2.06159e7			1.95300
$58$	−1.47639e7			−1.30464
$59$		−	1.35101e7i		−	1.11494i	−0.830198	−	0.557468i	$-0.811773\pi$
$59$		−	1.35101e7i		−	1.11494i	0.830198	−	0.557468i	$-0.188227\pi$
$60$	1.97198e7			1.52159
$61$			842042.i			0.0608156i	0.999538	+	0.0304078i	$0.00968059\pi$
$61$			842042.i			0.0608156i	−0.999538	+	0.0304078i	$0.990319\pi$
$62$			1.28816e7i			0.871775i
$63$	−1.53941e7	+	1.07056e7i	−0.977222	+	0.679594i
$64$	−1.01603e7			−0.605600
$65$	1.83393e7			1.02738
$66$		−	1.67112e7i		−	0.880707i
$67$	9.62973e6			0.477875			0.238938	−	0.971035i	$-0.423201\pi$
$67$	9.62973e6			0.477875			0.238938	+	0.971035i	$0.423201\pi$
$68$			1.78457e7i			0.834640i
$69$			1.74837e7i			0.771326i
$70$	−2.32636e7	−	3.34519e7i	−0.968914	−	1.39325i
$71$	−4.99364e6			−0.196509			−0.0982547	−	0.995161i	$-0.531326\pi$
$71$	−4.99364e6			−0.196509			−0.0982547	+	0.995161i	$0.531326\pi$
$72$	7.90946e6			0.294318
$73$			2.22669e7i			0.784095i	0.919945	+	0.392048i	$0.128233\pi$
$73$			2.22669e7i			0.784095i	−0.919945	+	0.392048i	$0.871767\pi$
$74$	4.48956e7			1.49719
$75$		−	2.74123e7i		−	0.866365i
$76$		−	3.59488e7i		−	1.07753i
$77$	−1.27426e7	+	8.86163e6i	−0.362489	+	0.252087i
$78$	−6.02440e7			−1.62755
$79$	−3.48440e7			−0.894582			−0.447291	−	0.894389i	$-0.647611\pi$
$79$	−3.48440e7			−0.894582			−0.447291	+	0.894389i	$0.647611\pi$
$80$			5.92996e7i			1.44774i
$81$	−3.32962e7			−0.773489
$82$		−	4.87665e6i		−	0.107861i
$83$		−	8.16858e7i		−	1.72121i	−0.509271	−	0.860606i	$-0.670085\pi$
$83$		−	8.16858e7i		−	1.72121i	0.509271	−	0.860606i	$-0.329915\pi$
$84$	3.43511e7	+	4.93951e7i	0.689959	+	0.992127i
$85$	6.71839e7			1.28703
$86$	8.17862e7			1.49515
$87$		−	8.20723e7i		−	1.43258i
$88$	6.54710e6			0.109174
$89$			7.05328e7i			1.12417i	0.827080	+	0.562084i	$0.190000\pi$
$89$			7.05328e7i			1.12417i	−0.827080	+	0.562084i	$0.810000\pi$
$90$			1.32531e8i			2.01998i
$91$	3.19463e7	+	4.59372e7i	0.465859	+	0.669882i
$92$	3.04871e7			0.425564
$93$	−7.16086e7			−0.957267
$94$			2.27960e6i			0.0291977i
$95$	−1.35336e8			−1.66158
$96$		−	1.63716e8i		−	1.92755i
$97$		−	3.15476e7i		−	0.356352i	−0.983999	−	0.178176i	$-0.942980\pi$
$97$		−	3.15476e7i		−	0.356352i	0.983999	−	0.178176i	$-0.0570197\pi$
$98$	4.32677e7	−	1.16543e8i	0.469093	−	1.26352i
$99$	5.04840e7			0.525549
$100$	−4.78000e7			−0.478000
$101$			4.13782e7i			0.397636i	0.980036	+	0.198818i	$0.0637103\pi$
$101$			4.13782e7i			0.397636i	−0.980036	+	0.198818i	$0.936290\pi$
$102$	−2.20697e8			−2.03890
$103$			1.44223e8i			1.28140i	0.767790	+	0.640701i	$0.221356\pi$
$103$			1.44223e8i			1.28140i	−0.767790	+	0.640701i	$0.778644\pi$
$104$		−	2.36024e7i		−	0.201754i
$105$	1.85958e8	−	1.29322e8i	1.52988	−	1.06393i
$106$	−7.47193e7			−0.591847
$107$	−1.97515e6			−0.0150683			−0.00753416	−	0.999972i	$-0.502398\pi$
$107$	−1.97515e6			−0.0150683			−0.00753416	+	0.999972i	$0.502398\pi$
$108$		−	3.12866e7i		−	0.229966i
$109$	2.26352e8			1.60353			0.801767	−	0.597636i	$-0.203893\pi$
$109$	2.26352e8			1.60353			0.801767	+	0.597636i	$0.203893\pi$
$110$			1.09703e8i			0.749288i
$111$			2.49573e8i			1.64401i
$112$	−1.48536e8	+	1.03297e8i	−0.943974	+	0.656472i
$113$	−1.03426e8			−0.634329			−0.317164	−	0.948371i	$-0.602731\pi$
$113$	−1.03426e8			−0.634329			−0.317164	+	0.948371i	$0.602731\pi$
$114$	4.44575e8			2.63224
$115$		−	1.14775e8i		−	0.656229i
$116$	−1.43113e8			−0.790398
$117$		−	1.81995e8i		−	0.971218i
$118$		−	2.91340e8i		−	1.50270i
$119$	1.17031e8	+	1.68285e8i	0.583599	+	0.839186i
$120$	−9.55447e7			−0.460767
$121$	−1.72570e8			−0.805054
$122$			1.81584e7i			0.0819667i
$123$	2.71091e7			0.118439
$124$			1.24867e8i			0.528153i
$125$		−	1.27451e8i		−	0.522039i
$126$	−3.31969e8	+	2.30863e8i	−1.31709	+	0.915950i
$127$	−7.49190e7			−0.287990			−0.143995	−	0.989578i	$-0.545995\pi$
$127$	−7.49190e7			−0.287990			−0.143995	+	0.989578i	$0.545995\pi$
$128$	1.30515e8			0.486206
$129$			4.54647e8i			1.64178i
$130$	3.95481e8			1.38469
$131$		−	5.60831e8i		−	1.90435i	−0.305553	−	0.952175i	$-0.598841\pi$
$131$		−	5.60831e8i		−	1.90435i	0.305553	−	0.952175i	$-0.401159\pi$
$132$		−	1.61988e8i		−	0.533565i
$133$	−2.35750e8	−	3.38997e8i	−0.753434	−	1.08340i
$134$	2.07662e8			0.644076
$135$	−1.17785e8			−0.354613
$136$		−	8.64644e7i		−	0.252745i
$137$	−2.79251e8			−0.792706			−0.396353	−	0.918098i	$-0.629724\pi$
$137$	−2.79251e8			−0.792706			−0.396353	+	0.918098i	$0.629724\pi$
$138$			3.77031e8i			1.03959i
$139$			3.08039e8i			0.825175i	0.910918	+	0.412588i	$0.135375\pi$
$139$			3.08039e8i			0.825175i	−0.910918	+	0.412588i	$0.864625\pi$
$140$	−2.25503e8	−	3.24262e8i	−0.587003	−	0.844081i
$141$	−1.26722e7			−0.0320610
$142$	−1.07686e8			−0.264854
$143$		−	1.50648e8i		−	0.360262i
$144$	5.88476e8			1.36861
$145$			5.38777e8i			1.21881i
$146$			4.80179e8i			1.05680i
$147$	6.47861e8	+	2.40523e8i	1.38743	+	0.515096i
$148$	4.35190e8			0.907052
$149$	−9.31424e8			−1.88974			−0.944870	−	0.327445i	$-0.893812\pi$
$149$	−9.31424e8			−1.88974			−0.944870	+	0.327445i	$0.893812\pi$
$150$		−	5.91138e8i		−	1.16768i
$151$	9.56551e8			1.83993			0.919963	−	0.392006i	$-0.128219\pi$
$151$	9.56551e8			1.83993			0.919963	+	0.392006i	$0.128219\pi$
$152$			1.74175e8i			0.326297i
$153$		−	6.66718e8i		−	1.21668i
$154$	−2.74789e8	+	1.91098e8i	−0.488559	+	0.339761i
$155$	4.70086e8			0.814424
$156$	−5.83968e8			−0.986032
$157$		−	1.79019e8i		−	0.294647i	−0.989088	−	0.147323i	$-0.952934\pi$
$157$		−	1.79019e8i		−	0.294647i	0.989088	−	0.147323i	$-0.0470658\pi$
$158$	−7.51400e8			−1.20571
$159$		−	4.15362e8i		−	0.649888i
$160$			1.07474e9i			1.63992i
$161$	2.87493e8	−	1.99933e8i	0.427882	−	0.297564i
$162$	−7.18020e8			−1.04250
$163$	−8.94662e8			−1.26739			−0.633693	−	0.773585i	$-0.718462\pi$
$163$	−8.94662e8			−1.26739			−0.633693	+	0.773585i	$0.718462\pi$
$164$		−	4.72712e7i		−	0.0653464i
$165$	−6.09837e8			−0.822769
$166$		−	1.76153e9i		−	2.31983i
$167$			7.60480e7i			0.0977736i	0.998804	+	0.0488868i	$0.0155674\pi$
$167$			7.60480e7i			0.0977736i	−0.998804	+	0.0488868i	$0.984433\pi$
$168$	−1.66434e8	−	2.39324e8i	−0.208933	−	0.300435i
$169$	2.72644e8			0.334233
$170$	1.44880e9			1.73465
$171$			1.34305e9i			1.57075i
$172$	7.92785e8			0.905819
$173$			1.27621e9i			1.42474i	0.701802	+	0.712372i	$0.252379\pi$
$173$			1.27621e9i			1.42474i	−0.701802	+	0.712372i	$0.747621\pi$
$174$		−	1.76986e9i		−	1.93082i
$175$	−4.50753e8	+	3.13469e8i	−0.480603	+	0.334228i
$176$	4.87114e8			0.507668
$177$	1.61955e9			1.65007
$178$			1.52102e9i			1.51514i
$179$	−6.63361e8			−0.646157			−0.323078	−	0.946372i	$-0.604718\pi$
$179$	−6.63361e8			−0.646157			−0.323078	+	0.946372i	$0.604718\pi$
$180$			1.28467e9i			1.22378i
$181$		−	9.11648e8i		−	0.849401i	−0.905334	−	0.424701i	$-0.860379\pi$
$181$		−	9.11648e8i		−	0.849401i	0.905334	−	0.424701i	$-0.139621\pi$
$182$	6.88911e8	+	9.90619e8i	0.627881	+	0.902862i
$183$	−1.00942e8			−0.0900049
$184$	−1.47713e8			−0.128869
$185$		−	1.63836e9i		−	1.39869i
$186$	−1.54421e9			−1.29020
$187$		−	5.51880e8i		−	0.451313i
$188$			2.20971e7i			0.0176890i
$189$	−2.05176e8	−	2.95033e8i	−0.160798	−	0.231219i
$190$	−2.91849e9			−2.23946
$191$	1.97881e9			1.48686			0.743431	−	0.668813i	$-0.233197\pi$
$191$	1.97881e9			1.48686			0.743431	+	0.668813i	$0.233197\pi$
$192$		−	1.21799e9i		−	0.896267i
$193$	−2.76067e8			−0.198969			−0.0994846	−	0.995039i	$-0.531719\pi$
$193$	−2.76067e8			−0.198969			−0.0994846	+	0.995039i	$0.531719\pi$
$194$		−	6.80313e8i		−	0.480288i
$195$			2.19847e9i			1.52048i
$196$	4.19410e8	−	1.12970e9i	0.284194	−	0.765489i
$197$	4.93962e8			0.327966			0.163983	−	0.986463i	$-0.447566\pi$
$197$	4.93962e8			0.327966			0.163983	+	0.986463i	$0.447566\pi$
$198$	1.08867e9			0.708330
$199$		−	1.93233e9i		−	1.23216i	−0.787682	−	0.616082i	$-0.788719\pi$
$199$		−	1.93233e9i		−	1.23216i	0.787682	−	0.616082i	$-0.211281\pi$
$200$	2.31596e8			0.144747
$201$			1.15438e9i			0.707239i
$202$			8.92307e8i			0.535931i
$203$	−1.34955e9	+	9.38524e8i	−0.794704	+	0.552664i
$204$	−2.13930e9			−1.23524
$205$	−1.77962e8			−0.100766
$206$			3.11012e9i			1.72706i
$207$	−1.13900e9			−0.620358
$208$		−	1.75605e9i		−	0.938176i
$209$			1.11172e9i			0.582652i
$210$	4.01012e9	−	2.78878e9i	2.06196	−	1.43396i
$211$	8.33410e8			0.420464			0.210232	−	0.977652i	$-0.432578\pi$
$211$	8.33410e8			0.420464			0.210232	+	0.977652i	$0.432578\pi$
$212$	−7.24283e8			−0.358563
$213$		−	5.98623e8i		−	0.290827i
$214$	−4.25934e7			−0.0203089
$215$		−	2.98460e9i		−	1.39679i
$216$			1.51587e8i			0.0696381i
$217$	8.18869e8	+	1.17749e9i	0.369297	+	0.531030i
$218$	4.88120e9			2.16123
$219$	−2.66930e9			−1.16043
$220$			1.06340e9i			0.453946i
$221$	−1.98953e9			−0.834031
$222$			5.38196e9i			2.21579i
$223$		−	1.71586e9i		−	0.693843i	−0.937894	−	0.346921i	$-0.887227\pi$
$223$		−	1.71586e9i		−	0.693843i	0.937894	−	0.346921i	$-0.112773\pi$
$224$	−2.69205e9	+	1.87215e9i	−1.06928	+	0.743614i
$225$	1.78581e9			0.696795
$226$	−2.23034e9			−0.854942
$227$		−	7.60049e8i		−	0.286245i	−0.989705	−	0.143123i	$-0.954286\pi$
$227$		−	7.60049e8i		−	0.286245i	0.989705	−	0.143123i	$-0.0457143\pi$
$228$	4.30944e9			1.59471
$229$			3.48407e9i			1.26691i	0.773781	+	0.633453i	$0.218363\pi$
$229$			3.48407e9i			1.26691i	−0.773781	+	0.633453i	$0.781637\pi$
$230$		−	2.47508e9i		−	0.884459i
$231$	−1.06231e9	−	1.52755e9i	−0.373080	−	0.536471i
$232$	6.93395e8			0.239347
$233$	8.66821e8			0.294107			0.147054	−	0.989129i	$-0.453021\pi$
$233$	8.66821e8			0.294107			0.147054	+	0.989129i	$0.453021\pi$
$234$		−	3.92467e9i		−	1.30900i
$235$	8.31890e7			0.0272768
$236$		−	2.82407e9i		−	0.910391i
$237$		−	4.17701e9i		−	1.32395i
$238$	2.52374e9	+	3.62901e9i	0.786569	+	1.13105i
$239$	−3.59978e9			−1.10328			−0.551638	−	0.834084i	$-0.685997\pi$
$239$	−3.59978e9			−1.10328			−0.551638	+	0.834084i	$0.685997\pi$
$240$	−7.10867e9			−2.14261
$241$			6.07605e9i			1.80116i	0.434686	+	0.900582i	$0.356859\pi$
$241$			6.07605e9i			1.80116i	−0.434686	+	0.900582i	$0.643141\pi$
$242$	−3.72142e9			−1.08504
$243$		−	4.97345e9i		−	1.42637i
$244$			1.76016e8i			0.0496584i
$245$	−4.25299e9	−	1.57895e9i	−1.18040	−	0.438233i
$246$	5.84599e8			0.159631
$247$	4.00775e9			1.07674
$248$		−	6.04992e8i		−	0.159935i
$249$	9.79227e9			2.54733
$250$		−	2.74843e9i		−	0.703599i
$251$			2.42395e9i			0.610701i	0.952240	+	0.305350i	$0.0987736\pi$
$251$			2.42395e9i			0.610701i	−0.952240	+	0.305350i	$0.901226\pi$
$252$	−3.21791e9	+	2.23784e9i	−0.797942	+	0.554916i
$253$	−9.42813e8			−0.230114
$254$	−1.61560e9			−0.388150
$255$			8.05382e9i			1.90476i
$256$	5.41554e9			1.26090
$257$			2.33555e9i			0.535373i	0.963506	+	0.267686i	$0.0862591\pi$
$257$			2.33555e9i			0.535373i	−0.963506	+	0.267686i	$0.913741\pi$
$258$			9.80430e9i			2.21278i
$259$	4.10384e9	−	2.85395e9i	0.911993	−	0.634231i
$260$	3.83355e9			0.838896
$261$	5.34670e9			1.15219
$262$		−	1.20941e10i		−	2.56667i
$263$	2.69681e9			0.563673			0.281837	−	0.959462i	$-0.409056\pi$
$263$	2.69681e9			0.563673			0.281837	+	0.959462i	$0.409056\pi$
$264$			7.84848e8i			0.161573i
$265$			2.72671e9i			0.552912i
$266$	−5.08387e9	−	7.31035e9i	−1.01547	−	1.46020i
$267$	−8.45527e9			−1.66373
$268$	2.01295e9			0.390205
$269$		−	4.85295e9i		−	0.926823i	−0.886143	−	0.463412i	$-0.846625\pi$
$269$		−	4.85295e9i		−	0.926823i	0.886143	−	0.463412i	$-0.153375\pi$
$270$	−2.53999e9			−0.477944
$271$			8.17058e9i			1.51487i	0.652909	+	0.757436i	$0.273548\pi$
$271$			8.17058e9i			1.51487i	−0.652909	+	0.757436i	$0.726452\pi$
$272$		−	6.43309e9i		−	1.17529i
$273$	−5.50682e9	+	3.82963e9i	−0.991403	+	0.689456i
$274$	−6.02195e9			−1.06840
$275$	1.47821e9			0.258468
$276$			3.65471e9i			0.629820i
$277$	−7.55633e9			−1.28349			−0.641744	−	0.766919i	$-0.721789\pi$
$277$	−7.55633e9			−1.28349			−0.641744	+	0.766919i	$0.721789\pi$
$278$			6.64275e9i			1.11216i
$279$		−	4.66503e9i		−	0.769905i
$280$	1.09259e9	+	1.57108e9i	0.177756	+	0.255604i
$281$	6.19336e9			0.993347			0.496673	−	0.867938i	$-0.334555\pi$
$281$	6.19336e9			0.993347			0.496673	+	0.867938i	$0.334555\pi$
$282$	−2.73273e8			−0.0432115
$283$		−	7.64290e9i		−	1.19155i	−0.803151	−	0.595775i	$-0.796845\pi$
$283$		−	7.64290e9i		−	1.19155i	0.803151	−	0.595775i	$-0.203155\pi$
$284$	−1.04384e9			−0.160458
$285$		−	1.62238e10i		−	2.45908i
$286$		−	3.24867e9i		−	0.485558i
$287$	−3.10002e8	−	4.45767e8i	−0.0456916	−	0.0657023i
$288$	1.06655e10			1.55028
$289$	−3.12658e8			−0.0448207
$290$			1.16185e10i			1.64270i
$291$	3.78184e9			0.527389
$292$			4.65456e9i			0.640246i
$293$			9.50343e9i			1.28947i	0.764408	+	0.644733i	$0.223031\pi$
$293$			9.50343e9i			1.28947i	−0.764408	+	0.644733i	$0.776969\pi$
$294$	1.39709e10	+	5.18681e9i	1.86997	+	0.694242i
$295$	−1.06318e10			−1.40384
$296$	−2.10854e9			−0.274672
$297$			9.67540e8i			0.124349i
$298$	−2.00858e10			−2.54698
$299$			3.39885e9i			0.425253i
$300$		−	5.73013e9i		−	0.707423i
$301$	7.47596e9	−	5.19904e9i	0.910753	−	0.633369i
$302$	2.06277e10			2.47984
$303$	−4.96030e9			−0.588488
$304$			1.29589e10i			1.51731i
$305$	6.62648e8			0.0765744
$306$		−	1.43776e10i		−	1.63983i
$307$		−	1.40766e9i		−	0.158469i	−0.996856	−	0.0792343i	$-0.974752\pi$
$307$		−	1.40766e9i		−	0.158469i	0.996856	−	0.0792343i	$-0.0252475\pi$
$308$	−2.66364e9	+	1.85239e9i	−0.295987	+	0.205840i
$309$	−1.72890e10			−1.89643
$310$	1.01372e10			1.09767
$311$			2.56247e8i			0.0273916i	0.999906	+	0.0136958i	$0.00435964\pi$
$311$			2.56247e8i			0.0273916i	−0.999906	+	0.0136958i	$0.995640\pi$
$312$	2.82939e9			0.298589
$313$		−	8.27127e9i		−	0.861777i	−0.902405	−	0.430889i	$-0.858200\pi$
$313$		−	8.27127e9i		−	0.861777i	0.902405	−	0.430889i	$-0.141800\pi$
$314$		−	3.86049e9i		−	0.397122i
$315$	8.42481e9	+	1.21145e10i	0.855693	+	1.23044i
$316$	−7.28361e9			−0.730463
$317$	−4.96438e9			−0.491618			−0.245809	−	0.969318i	$-0.579054\pi$
$317$	−4.96438e9			−0.491618			−0.245809	+	0.969318i	$0.579054\pi$
$318$		−	8.95715e9i		−	0.875913i
$319$	4.42576e9			0.427391
$320$			7.99567e9i			0.762526i
$321$		−	2.36775e8i		−	0.0223006i
$322$	6.19969e9	−	4.31148e9i	0.576695	−	0.401054i
$323$	1.46819e10			1.34888
$324$	−6.96005e9			−0.631585
$325$		−	5.32898e9i		−	0.477651i
$326$	−1.92931e10			−1.70817
$327$			2.71344e10i			2.37318i
$328$			2.29034e8i			0.0197881i
$329$	1.44911e8	+	2.08375e8i	0.0123686	+	0.0177854i
$330$	−1.31509e10			−1.10892
$331$	5.89699e9			0.491268			0.245634	−	0.969363i	$-0.421004\pi$
$331$	5.89699e9			0.491268			0.245634	+	0.969363i	$0.421004\pi$
$332$		−	1.70752e10i		−	1.40544i
$333$	−1.62587e10			−1.32224
$334$			1.63995e9i			0.131778i
$335$		−	7.57814e9i		−	0.601705i
$336$	−1.23830e10	−	1.78061e10i	−0.971557	−	1.39705i
$337$	6.30457e9			0.488806			0.244403	−	0.969674i	$-0.421408\pi$
$337$	6.30457e9			0.488806			0.244403	+	0.969674i	$0.421408\pi$
$338$	5.87947e9			0.450476
$339$		−	1.23984e10i		−	0.938784i
$340$	1.40438e10			1.05092
$341$		−	3.86150e9i		−	0.285587i
$342$			2.89624e10i			2.11704i
$343$	−3.45348e9	−	1.34035e10i	−0.249505	−	0.968373i
$344$	−3.84112e9			−0.274299
$345$	1.37589e10			0.971196
$346$			2.75210e10i			1.92026i
$347$	1.53411e10			1.05813			0.529063	−	0.848582i	$-0.322543\pi$
$347$	1.53411e10			1.05813			0.529063	+	0.848582i	$0.322543\pi$
$348$		−	1.71559e10i		−	1.16976i
$349$			7.69217e9i			0.518498i	0.965810	+	0.259249i	$0.0834751\pi$
$349$			7.69217e9i			0.518498i	−0.965810	+	0.259249i	$0.916525\pi$
$350$	−9.72034e9	+	6.75986e9i	−0.647753	+	0.450470i
$351$	3.48799e9			0.229798
$352$	8.82840e9			0.575057
$353$			1.38763e10i			0.893663i	0.894618	+	0.446832i	$0.147448\pi$
$353$			1.38763e10i			0.893663i	−0.894618	+	0.446832i	$0.852552\pi$
$354$	3.49251e10			2.22395
$355$			3.92976e9i			0.247430i
$356$			1.47438e10i			0.917929i
$357$	−2.01736e10	+	1.40294e10i	−1.24197	+	0.863706i
$358$	−1.43052e10			−0.870885
$359$	7.39469e9			0.445186			0.222593	−	0.974911i	$-0.428548\pi$
$359$	7.39469e9			0.445186			0.222593	+	0.974911i	$0.428548\pi$
$360$		−	6.22437e9i		−	0.370583i
$361$	−1.25919e10			−0.741419
$362$		−	1.96594e10i		−	1.14482i
$363$		−	2.06873e10i		−	1.19145i
$364$	6.67788e9	+	9.60245e9i	0.380393	+	0.546987i
$365$	1.75230e10			0.987274
$366$	−2.17677e9			−0.121308
$367$			4.89461e9i			0.269807i	0.990859	+	0.134904i	$0.0430725\pi$
$367$			4.89461e9i			0.269807i	−0.990859	+	0.134904i	$0.956928\pi$
$368$	−1.09901e10			−0.599252
$369$			1.76606e9i			0.0952574i
$370$		−	3.53307e10i		−	1.88515i
$371$	−6.82999e9	+	4.74981e9i	−0.360516	+	0.250715i
$372$	−1.49687e10			−0.781648
$373$	−3.07017e10			−1.58609			−0.793043	−	0.609165i	$-0.791505\pi$
$373$	−3.07017e10			−1.58609			−0.793043	+	0.609165i	$0.791505\pi$
$374$		−	1.19011e10i		−	0.608276i
$375$	1.52785e10			0.772599
$376$		−	1.07063e8i		−	0.00535657i
$377$		−	1.59549e10i		−	0.789822i
$378$	−4.42455e9	−	6.36228e9i	−0.216721	−	0.311635i
$379$	−1.58224e10			−0.766859			−0.383430	−	0.923570i	$-0.625257\pi$
$379$	−1.58224e10			−0.766859			−0.383430	+	0.923570i	$0.625257\pi$
$380$	−2.82900e10			−1.35675
$381$		−	8.98108e9i		−	0.426215i
$382$	4.26723e10			2.00398
$383$			1.55165e10i			0.721104i	0.932739	+	0.360552i	$0.117412\pi$
$383$			1.55165e10i			0.721104i	−0.932739	+	0.360552i	$0.882588\pi$
$384$			1.56458e10i			0.719568i
$385$	6.97369e9	+	1.00278e10i	0.317409	+	0.456419i
$386$	−5.95330e9			−0.268169
$387$	−2.96185e10			−1.32044
$388$		−	6.59454e9i		−	0.290976i
$389$	−1.17629e10			−0.513710			−0.256855	−	0.966450i	$-0.582686\pi$
$389$	−1.17629e10			−0.513710			−0.256855	+	0.966450i	$0.582686\pi$
$390$			4.74092e10i			2.04929i
$391$			1.24513e10i			0.532730i
$392$	−2.03208e9	+	5.47351e9i	−0.0860592	+	0.231805i
$393$	6.72309e10			2.81837
$394$	1.06521e10			0.442030
$395$			2.74206e10i			1.12639i
$396$	1.05529e10			0.429132
$397$		−	4.43659e10i		−	1.78602i	−0.450033	−	0.893012i	$-0.648588\pi$
$397$		−	4.43659e10i		−	1.78602i	0.450033	−	0.893012i	$-0.351412\pi$
$398$		−	4.16700e10i		−	1.66070i
$399$	4.06380e10	−	2.82611e10i	1.60340	−	1.11506i
$400$	1.72311e10			0.673089
$401$	1.00671e10			0.389337			0.194668	−	0.980869i	$-0.437637\pi$
$401$	1.00671e10			0.389337			0.194668	+	0.980869i	$0.437637\pi$
$402$			2.48939e10i			0.953211i
$403$	−1.39208e10			−0.527768
$404$			8.64947e9i			0.324686i
$405$			2.62025e10i			0.973919i
$406$	−2.91026e10	+	2.02390e10i	−1.07109	+	0.744876i
$407$	−1.34583e10			−0.490469
$408$	1.03651e10			0.374053
$409$		−	3.34366e8i		−	0.0119489i	−0.999982	−	0.00597447i	$-0.998098\pi$
$409$		−	3.34366e8i		−	0.0119489i	0.999982	−	0.00597447i	$-0.00190174\pi$
$410$	−3.83769e9			−0.135811
$411$		−	3.34758e10i		−	1.17318i
$412$			3.01476e10i			1.04632i
$413$	−1.85201e10	−	2.66310e10i	−0.636566	−	0.915350i
$414$	−2.45621e10			−0.836112
$415$	−6.42829e10			−2.16722
$416$		−	3.18265e10i		−	1.06271i
$417$	−3.69268e10			−1.22123
$418$			2.39738e10i			0.785293i
$419$			5.14322e10i			1.66870i	0.551232	+	0.834352i	$0.314158\pi$
$419$			5.14322e10i			1.66870i	−0.551232	+	0.834352i	$0.685842\pi$
$420$	3.88717e10	−	2.70327e10i	1.24921	−	0.868745i
$421$	5.97070e10			1.90063			0.950313	−	0.311297i	$-0.100763\pi$
$421$	5.97070e10			1.90063			0.950313	+	0.311297i	$0.100763\pi$
$422$	1.79722e10			0.566698
$423$		−	8.25548e8i		−	0.0257858i
$424$	3.50923e9			0.108580
$425$		−	1.95221e10i		−	0.598371i
$426$		−	1.29091e10i		−	0.391974i
$427$	1.15430e9	+	1.65983e9i	0.0347223	+	0.0499289i
$428$	−4.12874e8			−0.0123039
$429$	1.80592e10			0.533175
$430$		−	6.43619e10i		−	1.88259i
$431$	−2.34704e10			−0.680160			−0.340080	−	0.940396i	$-0.610454\pi$
$431$	−2.34704e10			−0.680160			−0.340080	+	0.940396i	$0.610454\pi$
$432$			1.12783e10i			0.323824i
$433$			2.35962e10i			0.671260i	0.941994	+	0.335630i	$0.108949\pi$
$433$			2.35962e10i			0.671260i	−0.941994	+	0.335630i	$0.891051\pi$
$434$	1.76586e10	+	2.53922e10i	0.497735	+	0.715718i
$435$	−6.45870e10			−1.80380
$436$	4.73154e10			1.30935
$437$		−	2.50821e10i		−	0.687762i
$438$	−5.75625e10			−1.56402
$439$			9.78599e9i			0.263479i	0.991284	+	0.131740i	$0.0420563\pi$
$439$			9.78599e9i			0.263479i	−0.991284	+	0.131740i	$0.957944\pi$
$440$		−	5.15226e9i		−	0.137463i
$441$	−1.56692e10	+	4.22057e10i	−0.414278	+	1.11588i
$442$	−4.29036e10			−1.12410
$443$	5.27088e10			1.36857			0.684287	−	0.729213i	$-0.260113\pi$
$443$	5.27088e10			1.36857			0.684287	+	0.729213i	$0.260113\pi$
$444$			5.21694e10i			1.34241i
$445$	5.55060e10			1.41547
$446$		−	3.70018e10i		−	0.935155i
$447$		−	1.11656e11i		−	2.79675i
$448$	−2.00279e10	+	1.39281e10i	−0.497191	+	0.345764i
$449$	−4.29146e10			−1.05589			−0.527946	−	0.849278i	$-0.677038\pi$
$449$	−4.29146e10			−1.05589			−0.527946	+	0.849278i	$0.677038\pi$
$450$	3.85104e10			0.939135
$451$			1.46186e9i			0.0353346i
$452$	−2.16195e10			−0.517955
$453$			1.14669e11i			2.72303i
$454$		−	1.63902e10i		−	0.385799i
$455$	3.61504e10	−	2.51402e10i	0.843466	−	0.586575i
$456$	−2.08797e10			−0.482908
$457$	1.49031e10			0.341675			0.170837	−	0.985299i	$-0.445353\pi$
$457$	1.49031e10			0.341675			0.170837	+	0.985299i	$0.445353\pi$
$458$			7.51327e10i			1.70752i
$459$	1.27778e10			0.287877
$460$		−	2.39919e10i		−	0.535838i
$461$			1.30027e10i			0.287891i	0.989586	+	0.143946i	$0.0459791\pi$
$461$			1.30027e10i			0.287891i	−0.989586	+	0.143946i	$0.954021\pi$
$462$	−2.29083e10	−	3.29410e10i	−0.502834	−	0.723051i
$463$	4.41828e10			0.961455			0.480728	−	0.876870i	$-0.340373\pi$
$463$	4.41828e10			0.961455			0.480728	+	0.876870i	$0.340373\pi$
$464$	5.15897e10			1.11299
$465$			5.63526e10i			1.20532i
$466$	1.86927e10			0.396395
$467$		−	4.47136e10i		−	0.940097i	−0.882641	−	0.470048i	$-0.844236\pi$
$467$		−	4.47136e10i		−	0.940097i	0.882641	−	0.470048i	$-0.155764\pi$
$468$		−	3.80433e10i		−	0.793040i
$469$	1.89821e10	−	1.32008e10i	0.392330	−	0.272840i
$470$	1.79394e9			0.0367635
$471$	2.14603e10			0.436067
$472$			1.36829e10i			0.275684i
$473$	−2.45169e10			−0.489802
$474$		−	9.00757e10i		−	1.78441i
$475$			3.93256e10i			0.772505i
$476$	2.44636e10	+	3.51774e10i	0.476533	+	0.685230i
$477$	2.70593e10			0.522688
$478$	−7.76280e10			−1.48699
$479$		−	1.63389e10i		−	0.310371i	−0.987885	−	0.155185i	$-0.950402\pi$
$479$		−	1.63389e10i		−	0.310371i	0.987885	−	0.155185i	$-0.0495975\pi$
$480$	−1.28837e11			−2.42703
$481$			4.85172e10i			0.906390i
$482$			1.31028e11i			2.42759i
$483$	2.39674e10	+	3.44639e10i	0.440384	+	0.633250i
$484$	−3.60732e10			−0.657360
$485$	−2.48265e10			−0.448692
$486$		−	1.07251e11i		−	1.92245i
$487$	2.29878e10			0.408678			0.204339	−	0.978900i	$-0.434496\pi$
$487$	2.29878e10			0.408678			0.204339	+	0.978900i	$0.434496\pi$
$488$		−	8.52815e8i		−	0.0150375i
$489$		−	1.07250e11i		−	1.87569i
$490$	−9.17142e10	−	3.40496e10i	−1.59093	−	0.590647i
$491$	−8.49647e10			−1.46188			−0.730942	−	0.682440i	$-0.760919\pi$
$491$	−8.49647e10			−1.46188			−0.730942	+	0.682440i	$0.760919\pi$
$492$	5.66674e9			0.0967104
$493$		−	5.84489e10i		−	0.989438i
$494$	8.64258e10			1.45123
$495$		−	3.97285e10i		−	0.661732i
$496$		−	4.50123e10i		−	0.743712i
$497$	−9.84343e9	+	6.84546e9i	−0.161332	+	0.112196i
$498$	2.11167e11			3.43328
$499$	−1.03838e11			−1.67477			−0.837384	−	0.546615i	$-0.815916\pi$
$499$	−1.03838e11			−1.67477			−0.837384	+	0.546615i	$0.815916\pi$
$500$		−	2.66416e10i		−	0.426266i
$501$	−9.11642e9			−0.144702
$502$			5.22716e10i			0.823097i
$503$			4.42486e10i			0.691238i	0.938375	+	0.345619i	$0.112331\pi$
$503$			4.42486e10i			0.691238i	−0.938375	+	0.345619i	$0.887669\pi$
$504$	1.55911e10	−	1.08426e10i	0.241632	−	0.168039i
$505$	3.25627e10			0.500674
$506$	−2.03314e10			−0.310146
$507$			3.26838e10i			0.494653i
$508$	−1.56607e10			−0.235156
$509$			6.37566e10i			0.949847i	0.880027	+	0.474924i	$0.157524\pi$
$509$			6.37566e10i			0.949847i	−0.880027	+	0.474924i	$0.842476\pi$
$510$			1.73678e11i			2.56723i
$511$	3.05243e10	+	4.38925e10i	0.447675	+	0.643734i
$512$	8.33725e10			1.21323
$513$	−2.57399e10			−0.371653
$514$			5.03653e10i			0.721571i
$515$	1.13497e11			1.61345
$516$			9.50369e10i			1.34058i
$517$		−	6.83353e8i		−	0.00956495i
$518$	8.84979e10	−	6.15445e10i	1.22918	−	0.854811i
$519$	−1.52988e11			−2.10857
$520$	−1.85740e10			−0.254034
$521$		−	8.73971e10i		−	1.18617i	−0.805141	−	0.593084i	$-0.797910\pi$
$521$		−	8.73971e10i		−	1.18617i	0.805141	−	0.593084i	$-0.202090\pi$
$522$	1.15300e11			1.55291
$523$		−	1.17667e11i		−	1.57271i	−0.617777	−	0.786353i	$-0.711967\pi$
$523$		−	1.17667e11i		−	1.57271i	0.617777	−	0.786353i	$-0.288033\pi$
$524$		−	1.17233e11i		−	1.55498i
$525$	−3.75778e10	−	5.40351e10i	−0.494646	−	0.711277i
$526$	5.81558e10			0.759714
$527$	−5.09970e10			−0.661154
$528$			5.83939e10i			0.751332i
$529$	−5.70396e10			−0.728373
$530$			5.88006e10i			0.745210i
$531$			1.05508e11i			1.32711i
$532$	−4.92799e10	−	7.08620e10i	−0.615210	−	0.884641i
$533$	5.27003e9			0.0652987
$534$	−1.82335e11			−2.24236
$535$			1.55435e9i			0.0189729i
$536$	−9.75293e9			−0.118161
$537$		−	7.95219e10i		−	0.956290i
$538$		−	1.04652e11i		−	1.24916i
$539$	−1.29703e10	+	3.49360e10i	−0.153672	+	0.413922i
$540$	−2.46211e10			−0.289556
$541$	1.17278e11			1.36907			0.684536	−	0.728979i	$-0.260005\pi$
$541$	1.17278e11			1.36907			0.684536	+	0.728979i	$0.260005\pi$
$542$			1.76196e11i			2.04173i
$543$	1.09286e11			1.25708
$544$		−	1.16592e11i		−	1.33130i
$545$		−	1.78128e11i		−	2.01905i
$546$	−1.18753e11	+	8.25847e10i	−1.33620	+	0.929242i
$547$	1.38303e8			0.00154484			0.000772421	−	1.00000i	$-0.499754\pi$
$547$	1.38303e8			0.00154484			0.000772421		1.00000i	$0.499754\pi$
$548$	−5.83731e10			−0.647278
$549$		−	6.57597e9i		−	0.0723886i
$550$	3.18772e10			0.348361
$551$			1.17740e11i			1.27738i
$552$		−	1.77074e10i		−	0.190721i
$553$	−6.86844e10	+	4.77655e10i	−0.734442	+	0.510756i
$554$	−1.62950e11			−1.72987
$555$	1.96402e11			2.07002
$556$			6.43908e10i			0.673790i
$557$	−8.27119e10			−0.859304			−0.429652	−	0.902994i	$-0.641364\pi$
$557$	−8.27119e10			−0.859304			−0.429652	+	0.902994i	$0.641364\pi$
$558$		−	1.00600e11i		−	1.03767i
$559$			8.83837e10i			0.905159i
$560$	8.12901e10	+	1.16891e11i	0.826581	+	1.18858i
$561$	6.61578e10			0.667928
$562$	1.33558e11			1.33882
$563$		−	9.86261e10i		−	0.981653i	−0.871257	−	0.490827i	$-0.836695\pi$
$563$		−	9.86261e10i		−	0.981653i	0.871257	−	0.490827i	$-0.163305\pi$
$564$	−2.64894e9			−0.0261791
$565$			8.13911e10i			0.798699i
$566$		−	1.64816e11i		−	1.60596i
$567$	−6.56332e10	+	4.56436e10i	−0.635026	+	0.441619i
$568$	5.05752e9			0.0485897
$569$	−9.45296e9			−0.0901818			−0.0450909	−	0.998983i	$-0.514358\pi$
$569$	−9.45296e9			−0.0901818			−0.0450909	+	0.998983i	$0.514358\pi$
$570$		−	3.49860e11i		−	3.31432i
$571$	9.06450e10			0.852706			0.426353	−	0.904557i	$-0.359798\pi$
$571$	9.06450e10			0.852706			0.426353	+	0.904557i	$0.359798\pi$
$572$		−	3.14906e10i		−	0.294169i
$573$			2.37214e11i			2.20050i
$574$	−6.68509e9	−	9.61282e9i	−0.0615828	−	0.0885530i
$575$	−3.33509e10			−0.305096
$576$	7.93472e10			0.720845
$577$			2.11680e11i			1.90975i	0.297011	+	0.954874i	$0.404010\pi$
$577$			2.11680e11i			1.90975i	−0.297011	+	0.954874i	$0.595990\pi$
$578$	−6.74237e9			−0.0604089
$579$		−	3.30942e10i		−	0.294468i
$580$			1.12623e11i			0.995210i
$581$	−1.11978e11	−	1.61019e11i	−0.982716	−	1.41310i
$582$	8.15541e10			0.710810
$583$	2.23985e10			0.193885
$584$		−	2.25518e10i		−	0.193879i
$585$	−1.43222e11			−1.22289
$586$			2.04938e11i			1.73793i
$587$		−	3.78420e10i		−	0.318729i	−0.987220	−	0.159365i	$-0.949055\pi$
$587$		−	3.78420e10i		−	0.318729i	0.987220	−	0.159365i	$-0.0509445\pi$
$588$	1.35425e11	+	5.02777e10i	1.13290	+	0.420597i
$589$	1.02729e11			0.853559
$590$	−2.29271e11			−1.89209
$591$			5.92148e10i			0.485378i
$592$	−1.56879e11			−1.27725
$593$		−	9.79198e10i		−	0.791866i	−0.918279	−	0.395933i	$-0.870421\pi$
$593$		−	9.79198e10i		−	0.791866i	0.918279	−	0.395933i	$-0.129579\pi$
$594$			2.08647e10i			0.167597i
$595$	1.32433e11	−	9.20982e10i	1.05664	−	0.734824i
$596$	−1.94700e11			−1.54305
$597$	2.31642e11			1.82356
$598$			7.32951e10i			0.573153i
$599$	1.26460e11			0.982305			0.491152	−	0.871074i	$-0.336576\pi$
$599$	1.26460e11			0.982305			0.491152	+	0.871074i	$0.336576\pi$
$600$			2.77631e10i			0.214221i
$601$		−	2.23530e11i		−	1.71332i	−0.515883	−	0.856659i	$-0.672536\pi$
$601$		−	2.23530e11i		−	1.71332i	0.515883	−	0.856659i	$-0.327464\pi$
$602$	1.61216e11	−	1.12115e11i	1.22751	−	0.853650i
$603$	−7.52038e10			−0.568814
$604$	1.99952e11			1.50237
$605$			1.35805e11i			1.01366i
$606$	−1.06967e11			−0.793159
$607$		−	4.50465e9i		−	0.0331823i	−0.999862	−	0.0165911i	$-0.994719\pi$
$607$		−	4.50465e9i		−	0.0331823i	0.999862	−	0.0165911i	$-0.00528136\pi$
$608$			2.34866e11i			1.71872i
$609$	−1.12508e11	−	1.61780e11i	−0.817924	−	1.17613i
$610$	1.42898e10			0.103206
$611$	−2.46349e9			−0.0176761
$612$		−	1.39367e11i		−	0.993470i
$613$	−2.46267e11			−1.74407			−0.872037	−	0.489440i	$-0.837201\pi$
$613$	−2.46267e11			−1.74407			−0.872037	+	0.489440i	$0.837201\pi$
$614$		−	3.03556e10i		−	0.213583i
$615$		−	2.13336e10i		−	0.149130i
$616$	1.29056e10	−	8.97501e9i	0.0896305	−	0.0623321i
$617$	−1.54701e11			−1.06746			−0.533730	−	0.845655i	$-0.679210\pi$
$617$	−1.54701e11			−1.06746			−0.533730	+	0.845655i	$0.679210\pi$
$618$	−3.72832e11			−2.55599
$619$		−	1.53782e11i		−	1.04748i	−0.851879	−	0.523738i	$-0.824537\pi$
$619$		−	1.53782e11i		−	1.04748i	0.851879	−	0.523738i	$-0.175463\pi$
$620$	9.82642e10			0.665011
$621$		−	2.18292e10i		−	0.146782i
$622$			5.52588e9i			0.0369181i
$623$	9.66889e10	+	1.39034e11i	0.641837	+	0.922929i
$624$	2.10511e11			1.38847
$625$	−1.89622e11			−1.24271
$626$		−	1.78367e11i		−	1.16150i
$627$	−1.33269e11			−0.862304
$628$		−	3.74212e10i		−	0.240591i
$629$			1.77737e11i			1.13547i
$630$	1.81678e11	+	2.61244e11i	1.15330	+	1.65838i
$631$	1.06917e10			0.0674419			0.0337210	−	0.999431i	$-0.489264\pi$
$631$	1.06917e10			0.0674419			0.0337210	+	0.999431i	$0.489264\pi$
$632$	3.52898e10			0.221198
$633$			9.99068e10i			0.622272i
$634$	−1.07055e11			−0.662599
$635$			5.89578e10i			0.362615i
$636$		−	8.68251e10i		−	0.530660i
$637$	1.25945e11	+	4.67579e10i	0.764931	+	0.283986i
$638$	9.54400e10			0.576033
$639$	3.89980e10			0.233905
$640$		−	1.02709e11i		−	0.612194i
$641$	2.37351e11			1.40592			0.702958	−	0.711232i	$-0.251862\pi$
$641$	2.37351e11			1.40592			0.702958	+	0.711232i	$0.251862\pi$
$642$		−	5.10598e9i		−	0.0300565i
$643$		−	1.62640e11i		−	0.951444i	−0.879596	−	0.475722i	$-0.842187\pi$
$643$		−	1.62640e11i		−	0.951444i	0.879596	−	0.475722i	$-0.157813\pi$
$644$	6.00960e10	−	4.17928e10i	0.349383	−	0.242973i
$645$	3.57786e11			2.06721
$646$	3.16610e11			1.81801
$647$			8.80528e10i			0.502488i	0.967924	+	0.251244i	$0.0808397\pi$
$647$			8.80528e10i			0.502488i	−0.967924	+	0.251244i	$0.919160\pi$
$648$	3.37221e10			0.191256
$649$			8.73345e10i			0.492274i
$650$		−	1.14918e11i		−	0.643774i
$651$	−1.41154e11	+	9.81637e10i	−0.785906	+	0.546546i
$652$	−1.87015e11			−1.03487
$653$	−6.57014e9			−0.0361345			−0.0180673	−	0.999837i	$-0.505751\pi$
$653$	−6.57014e9			−0.0361345			−0.0180673	+	0.999837i	$0.505751\pi$
$654$			5.85145e11i			3.19855i
$655$	−4.41348e11			−2.39782
$656$			1.70405e10i			0.0920166i
$657$		−	1.73895e11i		−	0.933307i
$658$	3.12496e9	+	4.49354e9i	0.0166702	+	0.0239710i
$659$	1.71539e11			0.909537			0.454769	−	0.890610i	$-0.349722\pi$
$659$	1.71539e11			0.909537			0.454769	+	0.890610i	$0.349722\pi$
$660$	−1.27477e11			−0.671825
$661$		−	1.92585e11i		−	1.00883i	−0.863462	−	0.504415i	$-0.831708\pi$
$661$		−	1.92585e11i		−	1.00883i	0.863462	−	0.504415i	$-0.168292\pi$
$662$	1.27167e11			0.662127
$663$		−	2.38500e11i		−	1.23434i
$664$			8.27309e10i			0.425594i
$665$	−2.66775e11	+	1.85524e11i	−1.36414	+	0.948667i
$666$	−3.50614e11			−1.78210
$667$	−9.98522e10			−0.504492
$668$			1.58967e10i			0.0798362i
$669$	2.05692e11			1.02686
$670$		−	1.63420e11i		−	0.810973i
$671$		−	5.44330e9i		−	0.0268517i
$672$	−2.24428e11	−	3.22716e11i	−1.10052	−	1.58250i
$673$	−1.00806e9			−0.00491391			−0.00245695	−	0.999997i	$-0.500782\pi$
$673$	−1.00806e9			−0.00491391			−0.00245695	+	0.999997i	$0.500782\pi$
$674$	1.35956e11			0.658808
$675$			3.42256e10i			0.164868i
$676$	5.69920e10			0.272915
$677$		−	9.47240e10i		−	0.450926i	−0.974252	−	0.225463i	$-0.927610\pi$
$677$		−	9.47240e10i		−	0.450926i	0.974252	−	0.225463i	$-0.0723895\pi$
$678$		−	2.67367e11i		−	1.26529i
$679$	−4.32466e10	−	6.21865e10i	−0.203457	−	0.292561i
$680$	−6.80435e10			−0.318237
$681$	9.11125e10			0.423633
$682$		−	8.32720e10i		−	0.384912i
$683$	2.01827e11			0.927462			0.463731	−	0.885976i	$-0.346510\pi$
$683$	2.01827e11			0.927462			0.463731	+	0.885976i	$0.346510\pi$
$684$			2.80744e11i			1.28258i
$685$			2.19757e11i			0.998117i
$686$	−7.44730e10	−	2.89043e11i	−0.336281	−	1.30517i
$687$	−4.17660e11			−1.87498
$688$	−2.85786e11			−1.27552
$689$		−	8.07468e10i		−	0.358301i
$690$	2.96706e11			1.30897
$691$			2.13281e11i			0.935490i	0.883863	+	0.467745i	$0.154933\pi$
$691$			2.13281e11i			0.935490i	−0.883863	+	0.467745i	$0.845067\pi$
$692$			2.66771e11i			1.16336i
$693$	9.95138e10	−	6.92053e10i	0.431470	−	0.300059i
$694$	3.30825e11			1.42613
$695$	2.42412e11			1.03900
$696$			8.31223e10i			0.354226i
$697$	1.93061e10			0.0818020
$698$			1.65879e11i			0.698827i
$699$			1.03912e11i			0.435269i
$700$	−9.42230e10	+	6.55260e10i	−0.392433	+	0.272911i
$701$	−1.79932e11			−0.745136			−0.372568	−	0.928005i	$-0.621523\pi$
$701$	−1.79932e11			−0.745136			−0.372568	+	0.928005i	$0.621523\pi$
$702$	7.52174e10			0.309720
$703$		−	3.58036e11i		−	1.46590i
$704$	6.56801e10			0.267389
$705$			9.97246e9i			0.0403688i
$706$			2.99237e11i			1.20447i
$707$	5.67228e10	+	8.15645e10i	0.227028	+	0.326455i
$708$	3.38542e11			1.34735
$709$	1.40192e11			0.554802			0.277401	−	0.960754i	$-0.410527\pi$
$709$	1.40192e11			0.554802			0.277401	+	0.960754i	$0.410527\pi$
$710$			8.47439e10i			0.333484i
$711$	2.72116e11			1.06482
$712$		−	7.14352e10i		−	0.277966i
$713$			8.71217e10i			0.337107i
$714$	−4.35036e11	+	3.02539e11i	−1.67391	+	1.16410i
$715$	−1.18553e11			−0.453615
$716$	−1.38665e11			−0.527614
$717$		−	4.31531e11i		−	1.63281i
$718$	1.59464e11			0.600018
$719$			1.02803e11i			0.384670i	0.981329	+	0.192335i	$0.0616061\pi$
$719$			1.02803e11i			0.384670i	−0.981329	+	0.192335i	$0.938394\pi$
$720$		−	4.63103e11i		−	1.72325i
$721$	1.97706e11	+	2.84292e11i	0.731609	+	1.05202i
$722$	−2.71541e11			−0.999278
$723$	−7.28380e11			−2.66566
$724$		−	1.90566e11i		−	0.693571i
$725$	1.56556e11			0.566653
$726$		−	4.46114e11i		−	1.60583i
$727$			3.57100e10i			0.127836i	0.997955	+	0.0639179i	$0.0203596\pi$
$727$			3.57100e10i			0.127836i	−0.997955	+	0.0639179i	$0.979640\pi$
$728$	−3.23550e10	−	4.65249e10i	−0.115190	−	0.165638i
$729$	3.77747e11			1.33749
$730$	3.77878e11			1.33064
$731$			3.23783e11i			1.13393i
$732$	−2.11003e10			−0.0734927
$733$			1.48153e10i			0.0513209i	0.999671	+	0.0256604i	$0.00816886\pi$
$733$			1.48153e10i			0.0513209i	−0.999671	+	0.0256604i	$0.991831\pi$
$734$			1.05551e11i			0.363644i
$735$	1.89281e11	−	5.09836e11i	0.648570	−	1.74695i
$736$	−1.99183e11			−0.678798
$737$	−6.22504e10			−0.210995
$738$			3.80844e10i			0.128387i
$739$	−5.42526e10			−0.181904			−0.0909522	−	0.995855i	$-0.528991\pi$
$739$	−5.42526e10			−0.181904			−0.0909522	+	0.995855i	$0.528991\pi$
$740$		−	3.42474e11i		−	1.14209i
$741$			4.80438e11i			1.59355i
$742$	−1.47286e11	+	1.02428e11i	−0.485900	+	0.337912i
$743$	1.08455e11			0.355872			0.177936	−	0.984042i	$-0.443058\pi$
$743$	1.08455e11			0.355872			0.177936	+	0.984042i	$0.443058\pi$
$744$	7.25247e10			0.236698
$745$			7.32987e11i			2.37942i
$746$	−6.62071e11			−2.13771
$747$			6.37929e11i			2.04876i
$748$		−	1.15362e11i		−	0.368516i
$749$	−3.89340e9	+	2.70761e9i	−0.0123709	+	0.00860316i
$750$	3.29475e11			1.04130
$751$	−2.03007e11			−0.638191			−0.319095	−	0.947723i	$-0.603379\pi$
$751$	−2.03007e11			−0.638191			−0.319095	+	0.947723i	$0.603379\pi$
$752$		−	7.96562e9i		−	0.0249085i
$753$	−2.90576e11			−0.903816
$754$		−	3.44062e11i		−	1.06451i
$755$		−	7.52761e11i		−	2.31670i
$756$	−4.28889e10	−	6.16721e10i	−0.131298	−	0.188800i
$757$	3.33771e11			1.01640			0.508201	−	0.861239i	$-0.330311\pi$
$757$	3.33771e11			1.01640			0.508201	+	0.861239i	$0.330311\pi$
$758$	−3.41205e11			−1.03357
$759$		−	1.13022e11i		−	0.340561i
$760$	1.37068e11			0.410848
$761$		−	4.17513e11i		−	1.24489i	−0.782663	−	0.622445i	$-0.786139\pi$
$761$		−	4.17513e11i		−	1.24489i	0.782663	−	0.622445i	$-0.213861\pi$
$762$		−	1.93674e11i		−	0.574449i
$763$	4.46184e11	−	3.10292e11i	1.31648	−	0.915529i
$764$	4.13639e11			1.21408
$765$	−5.24676e11			−1.53195
$766$			3.34607e11i			0.971897i
$767$	3.14842e11			0.909727
$768$			6.49200e11i			1.86609i
$769$		−	6.52921e11i		−	1.86705i	−0.358514	−	0.933524i	$-0.616717\pi$
$769$		−	6.52921e11i		−	1.86705i	0.358514	−	0.933524i	$-0.383283\pi$
$770$	1.50385e11	+	2.16246e11i	0.427801	+	0.615157i
$771$	−2.79979e11			−0.792333
$772$	−5.77076e10			−0.162467
$773$		−	3.46148e11i		−	0.969492i	−0.874655	−	0.484746i	$-0.838912\pi$
$773$		−	3.46148e11i		−	0.969492i	0.874655	−	0.484746i	$-0.161088\pi$
$774$	−6.38713e11			−1.77968
$775$		−	1.36596e11i		−	0.378644i
$776$			3.19512e10i			0.0881131i
$777$	3.42124e11	+	4.91957e11i	0.938640	+	1.34972i
$778$	−2.53664e11			−0.692374
$779$	−3.88906e10			−0.105608
$780$			4.59556e11i			1.24154i
$781$	3.22808e10			0.0867642
$782$			2.68508e11i			0.718009i
$783$			1.02471e11i			0.272617i
$784$	−1.51190e11	+	4.07238e11i	−0.400184	+	1.07791i
$785$	−1.40880e11			−0.370997
$786$	1.44981e12			3.79858
$787$			7.39780e10i			0.192843i	0.995341	+	0.0964214i	$0.0307396\pi$
$787$			7.39780e10i			0.192843i	−0.995341	+	0.0964214i	$0.969260\pi$
$788$	1.03255e11			0.267798
$789$			3.23286e11i			0.834217i
$790$			5.91316e11i			1.51814i
$791$	−2.03872e11	+	1.41780e11i	−0.520777	+	0.362166i
$792$	−5.11299e10			−0.129949
$793$	−1.96231e10			−0.0496222
$794$		−	9.56736e11i		−	2.40719i
$795$	−3.26871e11			−0.818290
$796$		−	4.03923e11i		−	1.00611i
$797$			4.59000e11i			1.13757i	0.822485	+	0.568786i	$0.192587\pi$
$797$			4.59000e11i			1.13757i	−0.822485	+	0.568786i	$0.807413\pi$
$798$	8.76344e11	−	6.09440e11i	2.16104	−	1.50286i
$799$	−9.02471e9			−0.0221435
$800$	3.12294e11			0.762436
$801$		−	5.50829e11i		−	1.33809i
$802$	2.17093e11			0.524744
$803$		−	1.43942e11i		−	0.346199i
$804$			2.41306e11i			0.577490i
$805$	−1.57338e11	−	2.26243e11i	−0.374670	−	0.538757i
$806$	−3.00197e11			−0.711321
$807$	5.81758e11			1.37167
$808$		−	4.19076e10i		−	0.0983212i
$809$	−7.57430e11			−1.76827			−0.884135	−	0.467232i	$-0.845251\pi$
$809$	−7.57430e11			−1.76827			−0.884135	+	0.467232i	$0.845251\pi$
$810$			5.65048e11i			1.31264i
$811$			2.03985e11i			0.471535i	0.971809	+	0.235768i	$0.0757605\pi$
$811$			2.03985e11i			0.471535i	−0.971809	+	0.235768i	$0.924240\pi$
$812$	−2.82103e11	+	1.96184e11i	−0.648908	+	0.451273i
$813$	−9.79467e11			−2.24196
$814$	−2.90223e11			−0.661050
$815$			7.04057e11i			1.59580i
$816$	7.71181e11			1.73938
$817$		−	6.52234e11i		−	1.46391i
$818$		−	7.21050e9i		−	0.0161047i
$819$	−2.49486e11	−	3.58748e11i	−0.554511	−	0.797360i
$820$	−3.72002e10			−0.0822792
$821$	−2.87113e11			−0.631947			−0.315974	−	0.948768i	$-0.602331\pi$
$821$	−2.87113e11			−0.631947			−0.315974	+	0.948768i	$0.602331\pi$
$822$		−	7.21895e11i		−	1.58120i
$823$	6.04082e10			0.131673			0.0658365	−	0.997830i	$-0.479028\pi$
$823$	6.04082e10			0.131673			0.0658365	+	0.997830i	$0.479028\pi$
$824$		−	1.46068e11i		−	0.316845i
$825$			1.77204e11i			0.382524i
$826$	−3.99380e11	−	5.74289e11i	−0.857958	−	1.23370i
$827$	7.83324e11			1.67463			0.837316	−	0.546720i	$-0.184124\pi$
$827$	7.83324e11			1.67463			0.837316	+	0.546720i	$0.184124\pi$
$828$	−2.38090e11			−0.506548
$829$			3.39080e11i			0.717934i	0.933350	+	0.358967i	$0.116871\pi$
$829$			3.39080e11i			0.717934i	−0.933350	+	0.358967i	$0.883129\pi$
$830$	−1.38624e12			−2.92096
$831$		−	9.05832e11i		−	1.89952i
$832$		−	2.36778e11i		−	0.494137i
$833$	4.61383e11	+	1.71292e11i	0.958256	+	0.355760i
$834$	−7.96315e11			−1.64596
$835$	5.98462e10			0.123109
$836$			2.32387e11i			0.475759i
$837$	8.94066e10			0.182166
$838$			1.10912e12i			2.24906i
$839$			1.06306e11i			0.214541i	0.994230	+	0.107271i	$0.0342111\pi$
$839$			1.06306e11i			0.214541i	−0.994230	+	0.107271i	$0.965789\pi$
$840$	−1.88337e11	+	1.30976e11i	−0.378285	+	0.263072i
$841$	−3.15198e10			−0.0630085
$842$	1.28756e12			2.56165
$843$			7.42442e11i			1.47012i
$844$	1.74211e11			0.343326
$845$		−	2.14558e11i		−	0.420841i
$846$		−	1.78027e10i		−	0.0347539i
$847$	−3.40170e11	+	2.36566e11i	−0.660940	+	0.459641i
$848$	2.61092e11			0.504905
$849$	9.16209e11			1.76345
$850$		−	4.20987e11i		−	0.806479i
$851$	3.03640e11			0.578949
$852$		−	1.25133e11i		−	0.237472i
$853$		−	2.60548e11i		−	0.492142i	−0.969252	−	0.246071i	$-0.920860\pi$
$853$		−	2.60548e11i		−	0.492142i	0.969252	−	0.246071i	$-0.0791397\pi$
$854$	2.48921e10	+	3.57937e10i	0.0467984	+	0.0672937i
$855$	1.05692e12			1.97777
$856$	2.00042e9			0.00372585
$857$		−	3.51886e10i		−	0.0652347i	−0.999468	−	0.0326174i	$-0.989616\pi$
$857$		−	3.51886e10i		−	0.0652347i	0.999468	−	0.0326174i	$-0.0103843\pi$
$858$	3.89441e11			0.718609
$859$			7.91386e11i			1.45350i	0.686901	+	0.726751i	$0.258971\pi$
$859$			7.91386e11i			1.45350i	−0.686901	+	0.726751i	$0.741029\pi$
$860$		−	6.23885e11i		−	1.14054i
$861$	5.34373e10	−	3.71622e10i	0.0972371	−	0.0676221i
$862$	−5.06131e11			−0.916714
$863$	−3.72768e11			−0.672041			−0.336020	−	0.941855i	$-0.609081\pi$
$863$	−3.72768e11			−0.672041			−0.336020	+	0.941855i	$0.609081\pi$
$864$			2.04406e11i			0.366809i
$865$	1.00432e12			1.79393
$866$			5.08844e11i			0.904718i
$867$		−	3.74806e10i		−	0.0663331i
$868$	1.71172e11	+	2.46137e11i	0.301546	+	0.433608i
$869$	2.25246e11			0.394982
$870$	−1.39280e12			−2.43115
$871$			2.24413e11i			0.389920i
$872$	−2.29248e11			−0.396497
$873$			2.46372e11i			0.424165i
$874$		−	5.40887e11i		−	0.926959i
$875$	−1.74714e11	−	2.51230e11i	−0.298055	−	0.428588i
$876$	−5.57975e11			−0.947542
$877$	−5.73691e11			−0.969795			−0.484897	−	0.874571i	$-0.661143\pi$
$877$	−5.73691e11			−0.969795			−0.484897	+	0.874571i	$0.661143\pi$
$878$			2.11031e11i			0.355115i
$879$	−1.13924e12			−1.90837
$880$		−	3.83336e11i		−	0.639218i
$881$			3.87231e10i			0.0642786i	0.999483	+	0.0321393i	$0.0102320\pi$
$881$			3.87231e10i			0.0642786i	−0.999483	+	0.0321393i	$0.989768\pi$
$882$	−3.37901e11	+	9.10151e11i	−0.558361	+	1.50397i
$883$	2.98959e11			0.491778			0.245889	−	0.969298i	$-0.420920\pi$
$883$	2.98959e11			0.491778			0.245889	+	0.969298i	$0.420920\pi$
$884$	−4.15881e11			−0.681021
$885$		−	1.27451e12i		−	2.07764i
$886$	1.13665e12			1.84455
$887$			6.35990e11i			1.02744i	0.857958	+	0.513719i	$0.171733\pi$
$887$			6.35990e11i			1.02744i	−0.857958	+	0.513719i	$0.828267\pi$
$888$		−	2.52766e11i		−	0.406506i
$889$	−1.47680e11	+	1.02702e11i	−0.236437	+	0.164426i
$890$	1.19697e12			1.90775
$891$	2.15240e11			0.341516
$892$		−	3.58673e11i		−	0.566551i
$893$	1.81795e10			0.0285876
$894$		−	2.40783e12i		−	3.76944i
$895$			5.22034e11i			0.813592i
$896$	2.57270e11	−	1.78915e11i	0.399170	−	0.277596i
$897$	−4.07445e11			−0.629360
$898$	−9.25438e11			−1.42312
$899$		−	4.08967e11i		−	0.626108i
$900$	3.73296e11			0.568962
$901$		−	2.95806e11i		−	0.448857i
$902$			3.15246e10i			0.0476237i
$903$	6.23246e11	+	8.96197e11i	0.937365	+	1.34788i
$904$	1.04749e11			0.156847
$905$	−7.17424e11			−1.06950
$906$			2.47279e12i			3.67007i
$907$	1.36448e11			0.201622			0.100811	−	0.994906i	$-0.467856\pi$
$907$	1.36448e11			0.201622			0.100811	+	0.994906i	$0.467856\pi$
$908$		−	1.58876e11i		−	0.233731i
$909$		−	3.23145e11i		−	0.473306i
$910$	7.79571e11	−	5.42140e11i	1.13682	−	0.790581i
$911$	−6.11198e10			−0.0887378			−0.0443689	−	0.999015i	$-0.514128\pi$
$911$	−6.11198e10			−0.0887378			−0.0443689	+	0.999015i	$0.514128\pi$
$912$	−1.55348e12			−2.24557
$913$			5.28050e11i			0.759962i
$914$	3.21381e11			0.460506
$915$			7.94364e10i			0.113327i
$916$			7.28290e11i			1.03448i
$917$	−7.68808e11	−	1.10551e12i	−1.08728	−	1.56345i
$918$	2.75550e11			0.387998
$919$	6.87678e10			0.0964102			0.0482051	−	0.998837i	$-0.484650\pi$
$919$	6.87678e10			0.0964102			0.0482051	+	0.998837i	$0.484650\pi$
$920$			1.16243e11i			0.162262i
$921$	1.68746e11			0.234528
$922$			2.80398e11i			0.388018i
$923$		−	1.16373e11i		−	0.160341i
$924$	−2.22059e11	−	3.19310e11i	−0.304636	−	0.438051i
$925$	−4.76070e11			−0.650285
$926$	9.52787e11			1.29584
$927$		−	1.12632e12i		−	1.52525i
$928$	9.35004e11			1.26073
$929$			1.07921e12i			1.44891i	0.689322	+	0.724455i	$0.257908\pi$
$929$			1.07921e12i			1.44891i	−0.689322	+	0.724455i	$0.742092\pi$
$930$			1.21522e12i			1.62452i
$931$	−9.29418e11	−	3.45054e11i	−1.23712	−	0.459291i
$932$	1.81196e11			0.240151
$933$	−3.07182e10			−0.0405386
$934$		−	9.64234e11i		−	1.26705i
$935$	−4.34304e11			−0.568260
$936$			1.84324e11i			0.240147i
$937$		−	1.93591e11i		−	0.251146i	−0.992084	−	0.125573i	$-0.959923\pi$
$937$		−	1.93591e11i		−	0.251146i	0.992084	−	0.125573i	$-0.0400769\pi$
$938$	4.09342e11	−	2.84670e11i	0.528780	−	0.367732i
$939$	9.91537e11			1.27540
$940$	1.73894e10			0.0222727
$941$			7.55658e10i			0.0963755i	0.998838	+	0.0481878i	$0.0153446\pi$
$941$			7.55658e10i			0.0963755i	−0.998838	+	0.0481878i	$0.984655\pi$
$942$	4.62785e11			0.587727
$943$		−	3.29820e10i		−	0.0417090i
$944$			1.01803e12i			1.28196i
$945$	−2.32177e11	+	1.61464e11i	−0.291133	+	0.202464i
$946$	−5.28698e11			−0.660151
$947$	1.06768e12			1.32752			0.663760	−	0.747945i	$-0.268960\pi$
$947$	1.06768e12			1.32752			0.663760	+	0.747945i	$0.268960\pi$
$948$		−	8.73139e11i		−	1.08106i
$949$	−5.18914e11			−0.639779
$950$			8.48044e11i			1.04118i
$951$		−	5.95116e11i		−	0.727578i
$952$	−1.18529e11	−	1.70438e11i	−0.144303	−	0.207501i
$953$	1.13047e12			1.37052			0.685261	−	0.728298i	$-0.259688\pi$
$953$	1.13047e12			1.37052			0.685261	+	0.728298i	$0.259688\pi$
$954$	5.83524e11			0.704475
$955$		−	1.55723e12i		−	1.87214i
$956$	−7.52478e11			−0.900870
$957$			5.30548e11i			0.632524i
$958$		−	3.52343e11i		−	0.418315i
$959$	−5.50458e11	+	3.82807e11i	−0.650803	+	0.452591i
$960$	−9.58498e11			−1.12851
$961$	4.96065e11			0.581627
$962$			1.04626e12i			1.22163i
$963$	1.54250e10			0.0179358
$964$			1.27010e12i			1.47072i
$965$			2.17252e11i			0.250527i
$966$	5.16848e11	+	7.43201e11i	0.593546	+	0.853489i
$967$	−8.33084e11			−0.952758			−0.476379	−	0.879240i	$-0.658051\pi$
$967$	−8.33084e11			−0.952758			−0.476379	+	0.879240i	$0.658051\pi$
$968$	1.74778e11			0.199061
$969$			1.76003e12i			1.99629i
$970$	−5.35375e11			−0.604743
$971$		−	6.95976e11i		−	0.782920i	−0.920195	−	0.391460i	$-0.871970\pi$
$971$		−	6.95976e11i		−	0.782920i	0.920195	−	0.391460i	$-0.128030\pi$
$972$		−	1.03962e12i		−	1.16469i
$973$	4.22271e11	+	6.07204e11i	0.471129	+	0.677460i
$974$	4.95724e11			0.550813
$975$	6.38823e11			0.706907
$976$		−	6.34508e10i		−	0.0699258i
$977$	1.06229e12			1.16591			0.582955	−	0.812504i	$-0.301896\pi$
$977$	1.06229e12			1.16591			0.582955	+	0.812504i	$0.301896\pi$
$978$		−	2.31280e12i		−	2.52803i
$979$		−	4.55952e11i		−	0.496350i
$980$	−8.89021e11	−	3.30056e11i	−0.963846	−	0.357835i
$981$	−1.76771e12			−1.90868
$982$	−1.83224e12			−1.97031
$983$		−	2.85163e11i		−	0.305407i	−0.988272	−	0.152704i	$-0.951202\pi$
$983$		−	2.85163e11i		−	0.305407i	0.988272	−	0.152704i	$-0.0487980\pi$
$984$	−2.74559e10			−0.0292857
$985$		−	3.88725e11i		−	0.412950i
$986$		−	1.26043e12i		−	1.33356i
$987$	−2.49795e10	+	1.73716e10i	−0.0263217	+	0.0183050i
$988$	8.37758e11			0.879207
$989$	5.53140e11			0.578162
$990$		−	8.56732e11i		−	0.891876i
$991$	−8.83520e11			−0.916056			−0.458028	−	0.888938i	$-0.651444\pi$
$991$	−8.83520e11			−0.916056			−0.458028	+	0.888938i	$0.651444\pi$
$992$		−	8.15797e11i		−	0.842433i
$993$			7.06915e11i			0.727060i
$994$	−2.12270e11	+	1.47620e11i	−0.217442	+	0.151217i
$995$	−1.52065e12			−1.55145
$996$	2.04692e12			2.08000
$997$			1.05207e12i			1.06479i	0.846495	+	0.532396i	$0.178708\pi$
$997$			1.05207e12i			1.06479i	−0.846495	+	0.532396i	$0.821292\pi$
$998$	−2.23923e12			−2.25724
$999$		−	3.11603e11i		−	0.312853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.9.b.b.6.4	yes	4
3.2	odd	2		63.9.d.c.55.2		4
4.3	odd	2		112.9.c.b.97.1		4
5.2	odd	4		175.9.c.c.174.8		8
5.3	odd	4		175.9.c.c.174.1		8
5.4	even	2		175.9.d.e.76.1		4
7.2	even	3		49.9.d.b.31.1		8
7.3	odd	6		49.9.d.b.19.1		8
7.4	even	3		49.9.d.b.19.2		8
7.5	odd	6		49.9.d.b.31.2		8
7.6	odd	2	inner	7.9.b.b.6.3	✓	4
21.20	even	2		63.9.d.c.55.1		4
28.27	even	2		112.9.c.b.97.4		4
35.13	even	4		175.9.c.c.174.2		8
35.27	even	4		175.9.c.c.174.7		8
35.34	odd	2		175.9.d.e.76.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.9.b.b.6.3	✓	4	7.6	odd	2	inner
7.9.b.b.6.4	yes	4	1.1	even	1	trivial
49.9.d.b.19.1		8	7.3	odd	6
49.9.d.b.19.2		8	7.4	even	3
49.9.d.b.31.1		8	7.2	even	3
49.9.d.b.31.2		8	7.5	odd	6
63.9.d.c.55.1		4	21.20	even	2
63.9.d.c.55.2		4	3.2	odd	2
112.9.c.b.97.1		4	4.3	odd	2
112.9.c.b.97.4		4	28.27	even	2
175.9.c.c.174.1		8	5.3	odd	4
175.9.c.c.174.2		8	35.13	even	4
175.9.c.c.174.7		8	35.27	even	4
175.9.c.c.174.8		8	5.2	odd	4
175.9.d.e.76.1		4	5.4	even	2
175.9.d.e.76.2		4	35.34	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+21.5647 q^{2} +119.877i q^{3} +209.035 q^{4} -786.953i q^{5} +2585.11i q^{6} +(1971.19 - 1370.84i) q^{7} -1012.79 q^{8} -7809.55 q^{9} +O(q^{10})\)	\(q+21.5647 q^{2} +119.877i q^{3} +209.035 q^{4} -786.953i q^{5} +2585.11i q^{6} +(1971.19 - 1370.84i) q^{7} -1012.79 q^{8} -7809.55 q^{9} -16970.4i q^{10} -6464.40 q^{11} +25058.5i q^{12} +23304.2i q^{13} +(42508.1 - 29561.6i) q^{14} +94337.7 q^{15} -75353.4 q^{16} +85372.2i q^{17} -168410. q^{18} -171975. i q^{19} -164500. i q^{20} +(164332. + 236301. i) q^{21} -139403. q^{22} +145847. q^{23} -121411. i q^{24} -228670. q^{25} +502548. i q^{26} -149672. i q^{27} +(412048. - 286552. i) q^{28} -684636. q^{29} +2.03436e6 q^{30} +597349. i q^{31} -1.36570e6 q^{32} -774934. i q^{33} +1.84102e6i q^{34} +(-1.07878e6 - 1.55124e6i) q^{35} -1.63246e6 q^{36} +2.08191e6 q^{37} -3.70859e6i q^{38} -2.79365e6 q^{39} +797021. i q^{40} -226141. i q^{41} +(3.54377e6 + 5.09576e6i) q^{42} +3.79260e6 q^{43} -1.35128e6 q^{44} +6.14575e6i q^{45} +3.14514e6 q^{46} +105710. i q^{47} -9.03316e6i q^{48} +(2.00641e6 - 5.40437e6i) q^{49} -4.93120e6 q^{50} -1.02342e7 q^{51} +4.87139e6i q^{52} -3.46490e6 q^{53} -3.22763e6i q^{54} +5.08718e6i q^{55} +(-1.99641e6 + 1.38837e6i) q^{56} +2.06159e7 q^{57} -1.47639e7 q^{58} -1.35101e7i q^{59} +1.97198e7 q^{60} +842042. i q^{61} +1.28816e7i q^{62} +(-1.53941e7 + 1.07056e7i) q^{63} -1.01603e7 q^{64} +1.83393e7 q^{65} -1.67112e7i q^{66} +9.62973e6 q^{67} +1.78457e7i q^{68} +1.74837e7i q^{69} +(-2.32636e7 - 3.34519e7i) q^{70} -4.99364e6 q^{71} +7.90946e6 q^{72} +2.22669e7i q^{73} +4.48956e7 q^{74} -2.74123e7i q^{75} -3.59488e7i q^{76} +(-1.27426e7 + 8.86163e6i) q^{77} -6.02440e7 q^{78} -3.48440e7 q^{79} +5.92996e7i q^{80} -3.32962e7 q^{81} -4.87665e6i q^{82} -8.16858e7i q^{83} +(3.43511e7 + 4.93951e7i) q^{84} +6.71839e7 q^{85} +8.17862e7 q^{86} -8.20723e7i q^{87} +6.54710e6 q^{88} +7.05328e7i q^{89} +1.32531e8i q^{90} +(3.19463e7 + 4.59372e7i) q^{91} +3.04871e7 q^{92} -7.16086e7 q^{93} +2.27960e6i q^{94} -1.35336e8 q^{95} -1.63716e8i q^{96} -3.15476e7i q^{97} +(4.32677e7 - 1.16543e8i) q^{98} +5.04840e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 32 q^{4} + 1428 q^{7} + 3328 q^{8} - 8124 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 - 32 * q^4 + 1428 * q^7 + 3328 * q^8 - 8124 * q^9	\( 4 q + 32 q^{2} - 32 q^{4} + 1428 q^{7} + 3328 q^{8} - 8124 q^{9} - 22168 q^{11} + 99008 q^{14} + 72960 q^{15} - 65280 q^{16} - 378528 q^{18} + 545664 q^{21} - 227392 q^{22} + 908072 q^{23} - 2055740 q^{25} + 1389920 q^{28} - 1473016 q^{29} + 4712640 q^{30} - 4577280 q^{32} + 2304960 q^{35} - 4951584 q^{36} + 6715272 q^{37} - 9276288 q^{39} + 5880000 q^{42} + 5748072 q^{43} - 623424 q^{44} + 2860352 q^{46} - 1194620 q^{49} - 967840 q^{50} - 21727872 q^{51} + 6749576 q^{53} - 10723328 q^{56} + 33733440 q^{57} - 28950592 q^{58} + 65479680 q^{60} - 40211052 q^{63} - 31918080 q^{64} - 39184320 q^{65} + 70027112 q^{67} - 71359680 q^{70} + 49900712 q^{71} + 35881728 q^{72} + 75593152 q^{74} - 13869688 q^{77} - 99960000 q^{78} - 82167256 q^{79} - 75422268 q^{81} + 19869696 q^{84} + 108466560 q^{85} + 173795392 q^{86} - 11637248 q^{88} + 206157504 q^{91} - 77732160 q^{92} - 90960000 q^{93} - 424874880 q^{95} + 115512992 q^{98} + 66343656 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 32 * q^4 + 1428 * q^7 + 3328 * q^8 - 8124 * q^9 - 22168 * q^11 + 99008 * q^14 + 72960 * q^15 - 65280 * q^16 - 378528 * q^18 + 545664 * q^21 - 227392 * q^22 + 908072 * q^23 - 2055740 * q^25 + 1389920 * q^28 - 1473016 * q^29 + 4712640 * q^30 - 4577280 * q^32 + 2304960 * q^35 - 4951584 * q^36 + 6715272 * q^37 - 9276288 * q^39 + 5880000 * q^42 + 5748072 * q^43 - 623424 * q^44 + 2860352 * q^46 - 1194620 * q^49 - 967840 * q^50 - 21727872 * q^51 + 6749576 * q^53 - 10723328 * q^56 + 33733440 * q^57 - 28950592 * q^58 + 65479680 * q^60 - 40211052 * q^63 - 31918080 * q^64 - 39184320 * q^65 + 70027112 * q^67 - 71359680 * q^70 + 49900712 * q^71 + 35881728 * q^72 + 75593152 * q^74 - 13869688 * q^77 - 99960000 * q^78 - 82167256 * q^79 - 75422268 * q^81 + 19869696 * q^84 + 108466560 * q^85 + 173795392 * q^86 - 11637248 * q^88 + 206157504 * q^91 - 77732160 * q^92 - 90960000 * q^93 - 424874880 * q^95 + 115512992 * q^98 + 66343656 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more