LMFDB - Embedded newform 177.10.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

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:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.8477 q^{2} +81.0000 q^{3} -346.936 q^{4} -288.160 q^{5} -1040.66 q^{6} -11158.8 q^{7} +11035.4 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-12.8477 q^{2} +81.0000 q^{3} -346.936 q^{4} -288.160 q^{5} -1040.66 q^{6} -11158.8 q^{7} +11035.4 q^{8} +6561.00 q^{9} +3702.19 q^{10} -5354.27 q^{11} -28101.8 q^{12} -11968.9 q^{13} +143365. q^{14} -23340.9 q^{15} +35852.3 q^{16} -253224. q^{17} -84293.8 q^{18} -368392. q^{19} +99973.1 q^{20} -903863. q^{21} +68790.1 q^{22} -1.43580e6 q^{23} +893865. q^{24} -1.87009e6 q^{25} +153773. q^{26} +531441. q^{27} +3.87139e6 q^{28} -4.56562e6 q^{29} +299878. q^{30} -552087. q^{31} -6.11073e6 q^{32} -433696. q^{33} +3.25335e6 q^{34} +3.21552e6 q^{35} -2.27625e6 q^{36} +5.14812e6 q^{37} +4.73300e6 q^{38} -969482. q^{39} -3.17995e6 q^{40} -1.80732e7 q^{41} +1.16126e7 q^{42} -1.18322e7 q^{43} +1.85759e6 q^{44} -1.89062e6 q^{45} +1.84468e7 q^{46} +3.30018e7 q^{47} +2.90403e6 q^{48} +8.41652e7 q^{49} +2.40264e7 q^{50} -2.05111e7 q^{51} +4.15245e6 q^{52} -4.28341e7 q^{53} -6.82780e6 q^{54} +1.54289e6 q^{55} -1.23141e8 q^{56} -2.98398e7 q^{57} +5.86577e7 q^{58} -1.21174e7 q^{59} +8.09782e6 q^{60} +9.99497e7 q^{61} +7.09306e6 q^{62} -7.32129e7 q^{63} +6.01525e7 q^{64} +3.44896e6 q^{65} +5.57200e6 q^{66} -1.80984e8 q^{67} +8.78526e7 q^{68} -1.16300e8 q^{69} -4.13120e7 q^{70} -2.83834e8 q^{71} +7.24030e7 q^{72} -1.11541e8 q^{73} -6.61415e7 q^{74} -1.51477e8 q^{75} +1.27809e8 q^{76} +5.97473e7 q^{77} +1.24556e7 q^{78} +4.87439e8 q^{79} -1.03312e7 q^{80} +4.30467e7 q^{81} +2.32199e8 q^{82} +7.30631e7 q^{83} +3.13583e8 q^{84} +7.29690e7 q^{85} +1.52017e8 q^{86} -3.69815e8 q^{87} -5.90864e7 q^{88} +6.25788e8 q^{89} +2.42901e7 q^{90} +1.33559e8 q^{91} +4.98132e8 q^{92} -4.47191e7 q^{93} -4.23997e8 q^{94} +1.06156e8 q^{95} -4.94969e8 q^{96} +1.65134e8 q^{97} -1.08133e9 q^{98} -3.51294e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−12.8477	−0.567794	−0.283897	−	0.958855i	$-0.591627\pi$
$2$	−12.8477	−0.567794	−0.283897	+	0.958855i	$0.591627\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−346.936	−0.677610
$5$	−288.160	−0.206190	−0.103095	−	0.994671i	$-0.532875\pi$
$5$	−288.160	−0.206190	−0.103095	+	0.994671i	$0.532875\pi$
$6$	−1040.66	−0.327816
$7$	−11158.8	−1.75661	−0.878307	−	0.478098i	$-0.841327\pi$
$7$	−11158.8	−1.75661	−0.878307	+	0.478098i	$0.841327\pi$
$8$	11035.4	0.952537
$9$	6561.00	0.333333
$10$	3702.19	0.117074
$11$	−5354.27	−0.110264	−0.0551320	−	0.998479i	$-0.517558\pi$
$11$	−5354.27	−0.110264	−0.0551320	+	0.998479i	$0.517558\pi$
$12$	−28101.8	−0.391218
$13$	−11968.9	−0.116228	−0.0581139	−	0.998310i	$-0.518509\pi$
$13$	−11968.9	−0.116228	−0.0581139	+	0.998310i	$0.518509\pi$
$14$	143365.	0.997394
$15$	−23340.9	−0.119044
$16$	35852.3	0.136766
$17$	−253224.	−0.735334	−0.367667	−	0.929957i	$-0.619843\pi$
$17$	−253224.	−0.735334	−0.367667	+	0.929957i	$0.619843\pi$
$18$	−84293.8	−0.189265
$19$	−368392.	−0.648514	−0.324257	−	0.945969i	$-0.605114\pi$
$19$	−368392.	−0.648514	−0.324257	+	0.945969i	$0.605114\pi$
$20$	99973.1	0.139717
$21$	−903863.	−1.01418
$22$	68790.1	0.0626072
$23$	−1.43580e6	−1.06984	−0.534920	−	0.844902i	$-0.679658\pi$
$23$	−1.43580e6	−1.06984	−0.534920	+	0.844902i	$0.679658\pi$
$24$	893865.	0.549947
$25$	−1.87009e6	−0.957486
$26$	153773.	0.0659934
$27$	531441.	0.192450
$28$	3.87139e6	1.19030
$29$	−4.56562e6	−1.19869	−0.599347	−	0.800489i	$-0.704573\pi$
$29$	−4.56562e6	−1.19869	−0.599347	+	0.800489i	$0.704573\pi$
$30$	299878.	0.0675925
$31$	−552087.	−0.107369	−0.0536847	−	0.998558i	$-0.517097\pi$
$31$	−552087.	−0.107369	−0.0536847	+	0.998558i	$0.517097\pi$
$32$	−6.11073e6	−1.03019
$33$	−433696.	−0.0636609
$34$	3.25335e6	0.417518
$35$	3.21552e6	0.362197
$36$	−2.27625e6	−0.225870
$37$	5.14812e6	0.451586	0.225793	−	0.974175i	$-0.427503\pi$
$37$	5.14812e6	0.451586	0.225793	+	0.974175i	$0.427503\pi$
$38$	4.73300e6	0.368222
$39$	−969482.	−0.0671041
$40$	−3.17995e6	−0.196404
$41$	−1.80732e7	−0.998865	−0.499432	−	0.866353i	$-0.666458\pi$
$41$	−1.80732e7	−0.998865	−0.499432	+	0.866353i	$0.666458\pi$
$42$	1.16126e7	0.575846
$43$	−1.18322e7	−0.527787	−0.263893	−	0.964552i	$-0.585007\pi$
$43$	−1.18322e7	−0.527787	−0.263893	+	0.964552i	$0.585007\pi$
$44$	1.85759e6	0.0747159
$45$	−1.89062e6	−0.0687301
$46$	1.84468e7	0.607449
$47$	3.30018e7	0.986500	0.493250	−	0.869888i	$-0.335809\pi$
$47$	3.30018e7	0.986500	0.493250	+	0.869888i	$0.335809\pi$
$48$	2.90403e6	0.0789617
$49$	8.41652e7	2.08569
$50$	2.40264e7	0.543654
$51$	−2.05111e7	−0.424545
$52$	4.15245e6	0.0787571
$53$	−4.28341e7	−0.745673	−0.372836	−	0.927897i	$-0.621615\pi$
$53$	−4.28341e7	−0.745673	−0.372836	+	0.927897i	$0.621615\pi$
$54$	−6.82780e6	−0.109272
$55$	1.54289e6	0.0227354
$56$	−1.23141e8	−1.67324
$57$	−2.98398e7	−0.374420
$58$	5.86577e7	0.680612
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	8.09782e6	0.0806655
$61$	9.99497e7	0.924266	0.462133	−	0.886811i	$-0.347084\pi$
$61$	9.99497e7	0.924266	0.462133	+	0.886811i	$0.347084\pi$
$62$	7.09306e6	0.0609636
$63$	−7.32129e7	−0.585538
$64$	6.01525e7	0.448171
$65$	3.44896e6	0.0239650
$66$	5.57200e6	0.0361463
$67$	−1.80984e8	−1.09724	−0.548622	−	0.836070i	$-0.684848\pi$
$67$	−1.80984e8	−1.09724	−0.548622	+	0.836070i	$0.684848\pi$
$68$	8.78526e7	0.498270
$69$	−1.16300e8	−0.617673
$70$	−4.13120e7	−0.205653
$71$	−2.83834e8	−1.32557	−0.662784	−	0.748811i	$-0.730625\pi$
$71$	−2.83834e8	−1.32557	−0.662784	+	0.748811i	$0.730625\pi$
$72$	7.24030e7	0.317512
$73$	−1.11541e8	−0.459706	−0.229853	−	0.973225i	$-0.573825\pi$
$73$	−1.11541e8	−0.459706	−0.229853	+	0.973225i	$0.573825\pi$
$74$	−6.61415e7	−0.256408
$75$	−1.51477e8	−0.552805
$76$	1.27809e8	0.439440
$77$	5.97473e7	0.193691
$78$	1.24556e7	0.0381013
$79$	4.87439e8	1.40799	0.703993	−	0.710206i	$-0.251398\pi$
$79$	4.87439e8	1.40799	0.703993	+	0.710206i	$0.251398\pi$
$80$	−1.03312e7	−0.0281997
$81$	4.30467e7	0.111111
$82$	2.32199e8	0.567149
$83$	7.30631e7	0.168984	0.0844922	−	0.996424i	$-0.473073\pi$
$83$	7.30631e7	0.168984	0.0844922	+	0.996424i	$0.473073\pi$
$84$	3.13583e8	0.687220
$85$	7.29690e7	0.151619
$86$	1.52017e8	0.299674
$87$	−3.69815e8	−0.692067
$88$	−5.90864e7	−0.105030
$89$	6.25788e8	1.05724	0.528619	−	0.848859i	$-0.322710\pi$
$89$	6.25788e8	1.05724	0.528619	+	0.848859i	$0.322710\pi$
$90$	2.42901e7	0.0390245
$91$	1.33559e8	0.204167
$92$	4.98132e8	0.724935
$93$	−4.47191e7	−0.0619897
$94$	−4.23997e8	−0.560129
$95$	1.06156e8	0.133717
$96$	−4.94969e8	−0.594781
$97$	1.65134e8	0.189393	0.0946965	−	0.995506i	$-0.469812\pi$
$97$	1.65134e8	0.189393	0.0946965	+	0.995506i	$0.469812\pi$
$98$	−1.08133e9	−1.18424
$99$	−3.51294e7	−0.0367546
$100$	6.48802e8	0.648802
$101$	8.61651e7	0.0823920	0.0411960	−	0.999151i	$-0.486883\pi$
$101$	8.61651e7	0.0823920	0.0411960	+	0.999151i	$0.486883\pi$
$102$	2.63521e8	0.241054
$103$	−4.41594e8	−0.386595	−0.193297	−	0.981140i	$-0.561918\pi$
$103$	−4.41594e8	−0.386595	−0.193297	+	0.981140i	$0.561918\pi$
$104$	−1.32081e8	−0.110711
$105$	2.60457e8	0.209114
$106$	5.50320e8	0.423388
$107$	−1.38847e9	−1.02402	−0.512012	−	0.858978i	$-0.671100\pi$
$107$	−1.38847e9	−1.02402	−0.512012	+	0.858978i	$0.671100\pi$
$108$	−1.84376e8	−0.130406
$109$	−2.18603e9	−1.48333	−0.741664	−	0.670771i	$-0.765963\pi$
$109$	−2.18603e9	−1.48333	−0.741664	+	0.670771i	$0.765963\pi$
$110$	−1.98226e7	−0.0129090
$111$	4.16998e8	0.260724
$112$	−4.00068e8	−0.240244
$113$	2.86843e9	1.65498	0.827488	−	0.561483i	$-0.189769\pi$
$113$	2.86843e9	1.65498	0.827488	+	0.561483i	$0.189769\pi$
$114$	3.83373e8	0.212593
$115$	4.13740e8	0.220591
$116$	1.58398e9	0.812248
$117$	−7.85281e7	−0.0387426
$118$	1.55680e8	0.0739205
$119$	2.82568e9	1.29170
$120$	−2.57576e8	−0.113394
$121$	−2.32928e9	−0.987842
$122$	−1.28412e9	−0.524793
$123$	−1.46393e9	−0.576695
$124$	1.91539e8	0.0727545
$125$	1.10170e9	0.403615
$126$	9.40618e8	0.332465
$127$	4.81144e9	1.64119	0.820595	−	0.571510i	$-0.193642\pi$
$127$	4.81144e9	1.64119	0.820595	+	0.571510i	$0.193642\pi$
$128$	2.35587e9	0.775723
$129$	−9.58410e8	−0.304718
$130$	−4.43112e7	−0.0136072
$131$	3.84589e9	1.14098	0.570488	−	0.821306i	$-0.306754\pi$
$131$	3.84589e9	1.14098	0.570488	+	0.821306i	$0.306754\pi$
$132$	1.50465e8	0.0431373
$133$	4.11082e9	1.13919
$134$	2.32523e9	0.623009
$135$	−1.53140e8	−0.0396814
$136$	−2.79442e9	−0.700433
$137$	4.88795e9	1.18545	0.592727	−	0.805404i	$-0.298051\pi$
$137$	4.88795e9	1.18545	0.592727	+	0.805404i	$0.298051\pi$
$138$	1.49419e9	0.350711
$139$	4.04703e9	0.919539	0.459769	−	0.888038i	$-0.347932\pi$
$139$	4.04703e9	0.919539	0.459769	+	0.888038i	$0.347932\pi$
$140$	−1.11558e9	−0.245428
$141$	2.67314e9	0.569556
$142$	3.64662e9	0.752649
$143$	6.40848e7	0.0128157
$144$	2.35227e8	0.0455885
$145$	1.31563e9	0.247159
$146$	1.43304e9	0.261018
$147$	6.81738e9	1.20417
$148$	−1.78607e9	−0.305999
$149$	4.92185e9	0.818070	0.409035	−	0.912519i	$-0.365865\pi$
$149$	4.92185e9	0.818070	0.409035	+	0.912519i	$0.365865\pi$
$150$	1.94613e9	0.313879
$151$	7.11467e9	1.11367	0.556837	−	0.830621i	$-0.312015\pi$
$151$	7.11467e9	1.11367	0.556837	+	0.830621i	$0.312015\pi$
$152$	−4.06534e9	−0.617733
$153$	−1.66140e9	−0.245111
$154$	−7.67615e8	−0.109977
$155$	1.59089e8	0.0221385
$156$	3.36349e8	0.0454704
$157$	7.84897e9	1.03101	0.515507	−	0.856886i	$-0.327604\pi$
$157$	7.84897e9	1.03101	0.515507	+	0.856886i	$0.327604\pi$
$158$	−6.26248e9	−0.799446
$159$	−3.46956e9	−0.430514
$160$	1.76087e9	0.212416
$161$	1.60218e10	1.87930
$162$	−5.53052e8	−0.0630882
$163$	1.00224e10	1.11206	0.556029	−	0.831163i	$-0.312324\pi$
$163$	1.00224e10	1.11206	0.556029	+	0.831163i	$0.312324\pi$
$164$	6.27023e9	0.676841
$165$	1.24974e8	0.0131263
$166$	−9.38693e8	−0.0959483
$167$	−5.55108e9	−0.552273	−0.276136	−	0.961118i	$-0.589054\pi$
$167$	−5.55108e9	−0.552273	−0.276136	+	0.961118i	$0.589054\pi$
$168$	−9.97445e9	−0.966045
$169$	−1.04612e10	−0.986491
$170$	−9.37484e8	−0.0860882
$171$	−2.41702e9	−0.216171
$172$	4.10503e9	0.357634
$173$	−5.37563e9	−0.456270	−0.228135	−	0.973629i	$-0.573263\pi$
$173$	−5.37563e9	−0.456270	−0.228135	+	0.973629i	$0.573263\pi$
$174$	4.75128e9	0.392951
$175$	2.08679e10	1.68193
$176$	−1.91963e8	−0.0150803
$177$	−9.81506e8	−0.0751646
$178$	−8.03995e9	−0.600293
$179$	−1.07723e10	−0.784275	−0.392137	−	0.919907i	$-0.628264\pi$
$179$	−1.07723e10	−0.784275	−0.392137	+	0.919907i	$0.628264\pi$
$180$	6.55924e8	0.0465722
$181$	−2.27451e10	−1.57520	−0.787598	−	0.616189i	$-0.788676\pi$
$181$	−2.27451e10	−1.57520	−0.787598	+	0.616189i	$0.788676\pi$
$182$	−1.71592e9	−0.115925
$183$	8.09592e9	0.533625
$184$	−1.58446e10	−1.01906
$185$	−1.48348e9	−0.0931128
$186$	5.74538e8	0.0351974
$187$	1.35583e9	0.0810808
$188$	−1.14495e10	−0.668462
$189$	−5.93024e9	−0.338060
$190$	−1.36386e9	−0.0759239
$191$	−4.63754e9	−0.252138	−0.126069	−	0.992021i	$-0.540236\pi$
$191$	−4.63754e9	−0.252138	−0.126069	+	0.992021i	$0.540236\pi$
$192$	4.87235e9	0.258752
$193$	1.78697e10	0.927066	0.463533	−	0.886080i	$-0.346582\pi$
$193$	1.78697e10	0.927066	0.463533	+	0.886080i	$0.346582\pi$
$194$	−2.12159e9	−0.107536
$195$	2.79366e8	0.0138362
$196$	−2.92000e10	−1.41329
$197$	5.80897e9	0.274790	0.137395	−	0.990516i	$-0.456127\pi$
$197$	5.80897e9	0.274790	0.137395	+	0.990516i	$0.456127\pi$
$198$	4.51332e8	0.0208691
$199$	2.52274e9	0.114034	0.0570168	−	0.998373i	$-0.481841\pi$
$199$	2.52274e9	0.114034	0.0570168	+	0.998373i	$0.481841\pi$
$200$	−2.06371e10	−0.912040
$201$	−1.46597e10	−0.633495
$202$	−1.10702e9	−0.0467817
$203$	5.09468e10	2.10564
$204$	7.11606e9	0.287676
$205$	5.20796e9	0.205956
$206$	5.67347e9	0.219506
$207$	−9.42029e9	−0.356614
$208$	−4.29113e8	−0.0158960
$209$	1.97247e9	0.0715077
$210$	−3.34627e9	−0.118734
$211$	−2.26437e10	−0.786459	−0.393230	−	0.919440i	$-0.628642\pi$
$211$	−2.26437e10	−0.786459	−0.393230	+	0.919440i	$0.628642\pi$
$212$	1.48607e10	0.505275
$213$	−2.29906e10	−0.765317
$214$	1.78387e10	0.581435
$215$	3.40957e9	0.108825
$216$	5.86465e9	0.183316
$217$	6.16063e9	0.188606
$218$	2.80855e10	0.842225
$219$	−9.03479e9	−0.265412
$220$	−5.35283e8	−0.0154057
$221$	3.03082e9	0.0854662
$222$	−5.35746e9	−0.148037
$223$	−5.70112e10	−1.54379	−0.771895	−	0.635750i	$-0.780691\pi$
$223$	−5.70112e10	−1.54379	−0.771895	+	0.635750i	$0.780691\pi$
$224$	6.81884e10	1.80965
$225$	−1.22697e10	−0.319162
$226$	−3.68528e10	−0.939685
$227$	4.70965e9	0.117726	0.0588629	−	0.998266i	$-0.481253\pi$
$227$	4.70965e9	0.117726	0.0588629	+	0.998266i	$0.481253\pi$
$228$	1.03525e10	0.253711
$229$	−9.30975e9	−0.223706	−0.111853	−	0.993725i	$-0.535679\pi$
$229$	−9.30975e9	−0.223706	−0.111853	+	0.993725i	$0.535679\pi$
$230$	−5.31561e9	−0.125250
$231$	4.83953e9	0.111828
$232$	−5.03833e10	−1.14180
$233$	−2.22868e10	−0.495388	−0.247694	−	0.968838i	$-0.579673\pi$
$233$	−2.22868e10	−0.495388	−0.247694	+	0.968838i	$0.579673\pi$
$234$	1.00891e9	0.0219978
$235$	−9.50979e9	−0.203407
$236$	4.20395e9	0.0882173
$237$	3.94826e10	0.812902
$238$	−3.63035e10	−0.733418
$239$	6.22197e10	1.23349	0.616747	−	0.787161i	$-0.288450\pi$
$239$	6.22197e10	1.23349	0.616747	+	0.787161i	$0.288450\pi$
$240$	−8.36826e8	−0.0162811
$241$	−7.82772e10	−1.49471	−0.747357	−	0.664422i	$-0.768678\pi$
$241$	−7.82772e10	−1.49471	−0.747357	+	0.664422i	$0.768678\pi$
$242$	2.99259e10	0.560891
$243$	3.48678e9	0.0641500
$244$	−3.46762e10	−0.626292
$245$	−2.42530e10	−0.430049
$246$	1.88081e10	0.327444
$247$	4.40926e9	0.0753753
$248$	−6.09248e9	−0.102273
$249$	5.91811e9	0.0975632
$250$	−1.41543e10	−0.229170
$251$	−4.20358e10	−0.668479	−0.334239	−	0.942488i	$-0.608479\pi$
$251$	−4.20358e10	−0.668479	−0.334239	+	0.942488i	$0.608479\pi$
$252$	2.54002e10	0.396766
$253$	7.68767e9	0.117965
$254$	−6.18160e10	−0.931857
$255$	5.91049e9	0.0875372
$256$	−6.10656e10	−0.888621
$257$	3.72649e10	0.532845	0.266423	−	0.963856i	$-0.414158\pi$
$257$	3.72649e10	0.532845	0.266423	+	0.963856i	$0.414158\pi$
$258$	1.23134e10	0.173017
$259$	−5.74468e10	−0.793263
$260$	−1.19657e9	−0.0162390
$261$	−2.99550e10	−0.399565
$262$	−4.94109e10	−0.647839
$263$	−3.73389e9	−0.0481239	−0.0240619	−	0.999710i	$-0.507660\pi$
$263$	−3.73389e9	−0.0481239	−0.0240619	+	0.999710i	$0.507660\pi$
$264$	−4.78599e9	−0.0606394
$265$	1.23431e10	0.153751
$266$	−5.28146e10	−0.646824
$267$	5.06889e10	0.610396
$268$	6.27899e10	0.743504
$269$	−9.73102e10	−1.13311	−0.566556	−	0.824023i	$-0.691725\pi$
$269$	−9.73102e10	−1.13311	−0.566556	+	0.824023i	$0.691725\pi$
$270$	1.96750e9	0.0225308
$271$	1.33771e11	1.50661	0.753305	−	0.657671i	$-0.228458\pi$
$271$	1.33771e11	1.50661	0.753305	+	0.657671i	$0.228458\pi$
$272$	−9.07866e9	−0.100568
$273$	1.08183e10	0.117876
$274$	−6.27990e10	−0.673093
$275$	1.00130e10	0.105576
$276$	4.03487e10	0.418541
$277$	2.30470e10	0.235210	0.117605	−	0.993060i	$-0.462478\pi$
$277$	2.30470e10	0.235210	0.117605	+	0.993060i	$0.462478\pi$
$278$	−5.19951e10	−0.522109
$279$	−3.62225e9	−0.0357898
$280$	3.54844e10	0.345006
$281$	6.46954e10	0.619006	0.309503	−	0.950899i	$-0.399837\pi$
$281$	6.46954e10	0.619006	0.309503	+	0.950899i	$0.399837\pi$
$282$	−3.43438e10	−0.323390
$283$	−2.08643e10	−0.193359	−0.0966796	−	0.995316i	$-0.530822\pi$
$283$	−2.08643e10	−0.193359	−0.0966796	+	0.995316i	$0.530822\pi$
$284$	9.84723e10	0.898218
$285$	8.59862e9	0.0772017
$286$	−8.23343e8	−0.00727669
$287$	2.01675e11	1.75462
$288$	−4.00925e10	−0.343397
$289$	−5.44655e10	−0.459284
$290$	−1.69028e10	−0.140336
$291$	1.33759e10	0.109346
$292$	3.86975e10	0.311502
$293$	−1.83552e11	−1.45497	−0.727486	−	0.686123i	$-0.759311\pi$
$293$	−1.83552e11	−1.45497	−0.727486	+	0.686123i	$0.759311\pi$
$294$	−8.75877e10	−0.683723
$295$	3.49174e9	0.0268437
$296$	5.68114e10	0.430153
$297$	−2.84548e9	−0.0212203
$298$	−6.32345e10	−0.464495
$299$	1.71850e10	0.124345
$300$	5.25530e10	0.374586
$301$	1.32033e11	0.927117
$302$	−9.14072e10	−0.632338
$303$	6.97937e9	0.0475690
$304$	−1.32077e10	−0.0886944
$305$	−2.88015e10	−0.190575
$306$	2.13452e10	0.139173
$307$	1.37976e10	0.0886503	0.0443251	−	0.999017i	$-0.485886\pi$
$307$	1.37976e10	0.0886503	0.0443251	+	0.999017i	$0.485886\pi$
$308$	−2.07285e10	−0.131247
$309$	−3.57691e10	−0.223201
$310$	−2.04393e9	−0.0125701
$311$	−1.38946e10	−0.0842217	−0.0421109	−	0.999113i	$-0.513408\pi$
$311$	−1.38946e10	−0.0842217	−0.0421109	+	0.999113i	$0.513408\pi$
$312$	−1.06986e10	−0.0639191
$313$	−2.49015e11	−1.46648	−0.733238	−	0.679972i	$-0.761992\pi$
$313$	−2.49015e11	−1.46648	−0.733238	+	0.679972i	$0.761992\pi$
$314$	−1.00841e11	−0.585403
$315$	2.10970e10	0.120732
$316$	−1.69110e11	−0.954066
$317$	2.53996e11	1.41273	0.706365	−	0.707847i	$-0.250334\pi$
$317$	2.53996e11	1.41273	0.706365	+	0.707847i	$0.250334\pi$
$318$	4.45759e10	0.244443
$319$	2.44456e10	0.132173
$320$	−1.73335e10	−0.0924085
$321$	−1.12466e11	−0.591221
$322$	−2.05844e11	−1.06705
$323$	9.32858e10	0.476874
$324$	−1.49345e10	−0.0752900
$325$	2.23829e10	0.111286
$326$	−1.28765e11	−0.631419
$327$	−1.77069e11	−0.856400
$328$	−1.99444e11	−0.951455
$329$	−3.68260e11	−1.73290
$330$	−1.60563e9	−0.00745301
$331$	1.69491e11	0.776106	0.388053	−	0.921637i	$-0.373148\pi$
$331$	1.69491e11	0.776106	0.388053	+	0.921637i	$0.373148\pi$
$332$	−2.53482e10	−0.114506
$333$	3.37768e10	0.150529
$334$	7.13187e10	0.313577
$335$	5.21523e10	0.226241
$336$	−3.24055e10	−0.138705
$337$	2.08297e11	0.879728	0.439864	−	0.898064i	$-0.355027\pi$
$337$	2.08297e11	0.879728	0.439864	+	0.898064i	$0.355027\pi$
$338$	1.34403e11	0.560124
$339$	2.32343e11	0.955501
$340$	−2.53156e10	−0.102738
$341$	2.95603e9	0.0118390
$342$	3.10532e10	0.122741
$343$	−4.88884e11	−1.90714
$344$	−1.30573e11	−0.502736
$345$	3.35130e10	0.127358
$346$	6.90645e10	0.259067
$347$	3.01426e11	1.11609	0.558043	−	0.829812i	$-0.311552\pi$
$347$	3.01426e11	1.11609	0.558043	+	0.829812i	$0.311552\pi$
$348$	1.28302e11	0.468951
$349$	2.59548e10	0.0936489	0.0468244	−	0.998903i	$-0.485090\pi$
$349$	2.59548e10	0.0936489	0.0468244	+	0.998903i	$0.485090\pi$
$350$	−2.68105e11	−0.954991
$351$	−6.36077e9	−0.0223680
$352$	3.27185e10	0.113593
$353$	−1.72509e11	−0.591325	−0.295662	−	0.955293i	$-0.595540\pi$
$353$	−1.72509e11	−0.591325	−0.295662	+	0.955293i	$0.595540\pi$
$354$	1.26101e10	0.0426780
$355$	8.17895e10	0.273319
$356$	−2.17109e11	−0.716395
$357$	2.28880e11	0.745762
$358$	1.38399e11	0.445306
$359$	−2.87460e11	−0.913383	−0.456692	−	0.889625i	$-0.650966\pi$
$359$	−2.87460e11	−0.913383	−0.456692	+	0.889625i	$0.650966\pi$
$360$	−2.08636e10	−0.0654680
$361$	−1.86975e11	−0.579430
$362$	2.92223e11	0.894387
$363$	−1.88672e11	−0.570331
$364$	−4.63364e10	−0.138346
$365$	3.21415e10	0.0947870
$366$	−1.04014e11	−0.302989
$367$	6.06272e11	1.74450	0.872249	−	0.489062i	$-0.162661\pi$
$367$	6.06272e11	1.74450	0.872249	+	0.489062i	$0.162661\pi$
$368$	−5.14768e10	−0.146317
$369$	−1.18578e11	−0.332955
$370$	1.90593e10	0.0528688
$371$	4.77977e11	1.30986
$372$	1.55147e10	0.0420048
$373$	−1.10006e11	−0.294256	−0.147128	−	0.989117i	$-0.547003\pi$
$373$	−1.10006e11	−0.294256	−0.147128	+	0.989117i	$0.547003\pi$
$374$	−1.74193e10	−0.0460372
$375$	8.92374e10	0.233027
$376$	3.64187e11	0.939677
$377$	5.46455e10	0.139322
$378$	7.61900e10	0.191949
$379$	−1.53320e11	−0.381701	−0.190850	−	0.981619i	$-0.561125\pi$
$379$	−1.53320e11	−0.381701	−0.190850	+	0.981619i	$0.561125\pi$
$380$	−3.68293e10	−0.0906082
$381$	3.89727e11	0.947541
$382$	5.95818e10	0.143162
$383$	−8.02971e8	−0.00190680	−0.000953400	−	1.00000i	$-0.500303\pi$
$383$	−8.02971e8	−0.00190680	−0.000953400		1.00000i	$0.500303\pi$
$384$	1.90826e11	0.447864
$385$	−1.72168e10	−0.0399372
$386$	−2.29585e11	−0.526382
$387$	−7.76312e10	−0.175929
$388$	−5.72910e10	−0.128335
$389$	7.71042e11	1.70728	0.853640	−	0.520864i	$-0.174390\pi$
$389$	7.71042e11	1.70728	0.853640	+	0.520864i	$0.174390\pi$
$390$	−3.58921e9	−0.00785612
$391$	3.63579e11	0.786691
$392$	9.28793e11	1.98670
$393$	3.11517e11	0.658743
$394$	−7.46319e10	−0.156024
$395$	−1.40460e11	−0.290313
$396$	1.21877e10	0.0249053
$397$	−8.59617e11	−1.73679	−0.868396	−	0.495872i	$-0.834849\pi$
$397$	−8.59617e11	−1.73679	−0.868396	+	0.495872i	$0.834849\pi$
$398$	−3.24114e10	−0.0647476
$399$	3.32976e11	0.657711
$400$	−6.70470e10	−0.130951
$401$	5.09559e11	0.984113	0.492056	−	0.870563i	$-0.336245\pi$
$401$	5.09559e11	0.984113	0.492056	+	0.870563i	$0.336245\pi$
$402$	1.88344e11	0.359694
$403$	6.60789e9	0.0124793
$404$	−2.98938e10	−0.0558297
$405$	−1.24043e10	−0.0229100
$406$	−6.54550e11	−1.19557
$407$	−2.75644e10	−0.0497937
$408$	−2.26348e11	−0.404395
$409$	−2.01097e11	−0.355346	−0.177673	−	0.984090i	$-0.556857\pi$
$409$	−2.01097e11	−0.355346	−0.177673	+	0.984090i	$0.556857\pi$
$410$	−6.69103e10	−0.116941
$411$	3.95924e11	0.684422
$412$	1.53205e11	0.261961
$413$	1.35215e11	0.228692
$414$	1.21029e11	0.202483
$415$	−2.10538e10	−0.0348430
$416$	7.31388e10	0.119737
$417$	3.27810e11	0.530896
$418$	−2.53418e10	−0.0406016
$419$	5.57874e11	0.884247	0.442123	−	0.896954i	$-0.354225\pi$
$419$	5.57874e11	0.884247	0.442123	+	0.896954i	$0.354225\pi$
$420$	−9.03620e10	−0.141698
$421$	−1.23812e12	−1.92085	−0.960424	−	0.278542i	$-0.910149\pi$
$421$	−1.23812e12	−1.92085	−0.960424	+	0.278542i	$0.910149\pi$
$422$	2.90920e11	0.446547
$423$	2.16525e11	0.328833
$424$	−4.72690e11	−0.710281
$425$	4.73551e11	0.704072
$426$	2.95376e11	0.434542
$427$	−1.11532e12	−1.62358
$428$	4.81712e11	0.693889
$429$	5.19087e9	0.00739916
$430$	−4.38052e10	−0.0617899
$431$	−6.13759e11	−0.856743	−0.428371	−	0.903603i	$-0.640913\pi$
$431$	−6.13759e11	−0.856743	−0.428371	+	0.903603i	$0.640913\pi$
$432$	1.90534e10	0.0263206
$433$	−3.09324e11	−0.422881	−0.211440	−	0.977391i	$-0.567815\pi$
$433$	−3.09324e11	−0.422881	−0.211440	+	0.977391i	$0.567815\pi$
$434$	−7.91500e10	−0.107090
$435$	1.06566e11	0.142698
$436$	7.58414e11	1.00512
$437$	5.28938e11	0.693807
$438$	1.16076e11	0.150699
$439$	2.58853e11	0.332632	0.166316	−	0.986073i	$-0.446813\pi$
$439$	2.58853e11	0.332632	0.166316	+	0.986073i	$0.446813\pi$
$440$	1.70263e10	0.0216563
$441$	5.52208e11	0.695230
$442$	−3.89391e10	−0.0485272
$443$	−6.08274e11	−0.750382	−0.375191	−	0.926948i	$-0.622423\pi$
$443$	−6.08274e11	−0.750382	−0.375191	+	0.926948i	$0.622423\pi$
$444$	−1.44672e11	−0.176669
$445$	−1.80327e11	−0.217992
$446$	7.32463e11	0.876554
$447$	3.98670e11	0.472313
$448$	−6.71229e11	−0.787263
$449$	−9.88861e11	−1.14822	−0.574112	−	0.818777i	$-0.694653\pi$
$449$	−9.88861e11	−1.14822	−0.574112	+	0.818777i	$0.694653\pi$
$450$	1.57637e11	0.181218
$451$	9.67686e10	0.110139
$452$	−9.95164e11	−1.12143
$453$	5.76288e11	0.642981
$454$	−6.05082e10	−0.0668440
$455$	−3.84863e10	−0.0420973
$456$	−3.29293e11	−0.356649
$457$	3.06396e11	0.328595	0.164297	−	0.986411i	$-0.447464\pi$
$457$	3.06396e11	0.328595	0.164297	+	0.986411i	$0.447464\pi$
$458$	1.19609e11	0.127019
$459$	−1.34574e11	−0.141515
$460$	−1.43542e11	−0.149475
$461$	4.36858e11	0.450491	0.225245	−	0.974302i	$-0.427682\pi$
$461$	4.36858e11	0.450491	0.225245	+	0.974302i	$0.427682\pi$
$462$	−6.21768e10	−0.0634950
$463$	−1.25176e12	−1.26592	−0.632960	−	0.774185i	$-0.718160\pi$
$463$	−1.25176e12	−1.26592	−0.632960	+	0.774185i	$0.718160\pi$
$464$	−1.63688e11	−0.163940
$465$	1.28862e10	0.0127817
$466$	2.86334e11	0.281278
$467$	−7.55685e11	−0.735216	−0.367608	−	0.929981i	$-0.619823\pi$
$467$	−7.55685e11	−0.735216	−0.367608	+	0.929981i	$0.619823\pi$
$468$	2.72442e10	0.0262524
$469$	2.01956e12	1.92744
$470$	1.22179e11	0.115493
$471$	6.35767e11	0.595256
$472$	−1.33719e11	−0.124010
$473$	6.33530e10	0.0581958
$474$	−5.07261e11	−0.461561
$475$	6.88926e11	0.620943
$476$	−9.80330e11	−0.875268
$477$	−2.81035e11	−0.248558
$478$	−7.99380e11	−0.700371
$479$	1.35024e12	1.17193	0.585963	−	0.810338i	$-0.300716\pi$
$479$	1.35024e12	1.17193	0.585963	+	0.810338i	$0.300716\pi$
$480$	1.42630e11	0.122638
$481$	−6.16174e10	−0.0524869
$482$	1.00568e12	0.848690
$483$	1.29777e12	1.08501
$484$	8.08112e11	0.669372
$485$	−4.75850e10	−0.0390510
$486$	−4.47972e10	−0.0364240
$487$	1.13263e12	0.912447	0.456224	−	0.889865i	$-0.349202\pi$
$487$	1.13263e12	0.912447	0.456224	+	0.889865i	$0.349202\pi$
$488$	1.10298e12	0.880398
$489$	8.11814e11	0.642047
$490$	3.11596e11	0.244179
$491$	9.25546e11	0.718673	0.359337	−	0.933208i	$-0.383003\pi$
$491$	9.25546e11	0.718673	0.359337	+	0.933208i	$0.383003\pi$
$492$	5.07889e11	0.390774
$493$	1.15612e12	0.881441
$494$	−5.66488e10	−0.0427976
$495$	1.01229e10	0.00757845
$496$	−1.97936e10	−0.0146844
$497$	3.16725e12	2.32851
$498$	−7.60342e10	−0.0553958
$499$	−2.72332e12	−1.96628	−0.983141	−	0.182847i	$-0.941469\pi$
$499$	−2.72332e12	−1.96628	−0.983141	+	0.182847i	$0.941469\pi$
$500$	−3.82219e11	−0.273493
$501$	−4.49638e11	−0.318855
$502$	5.40064e11	0.379558
$503$	−2.02205e12	−1.40843	−0.704216	−	0.709985i	$-0.748701\pi$
$503$	−2.02205e12	−1.40843	−0.704216	+	0.709985i	$0.748701\pi$
$504$	−8.07931e11	−0.557746
$505$	−2.48293e10	−0.0169884
$506$	−9.87690e10	−0.0669797
$507$	−8.47361e11	−0.569551
$508$	−1.66927e12	−1.11209
$509$	3.50255e10	0.0231289	0.0115644	−	0.999933i	$-0.496319\pi$
$509$	3.50255e10	0.0231289	0.0115644	+	0.999933i	$0.496319\pi$
$510$	−7.59362e10	−0.0497031
$511$	1.24466e12	0.807526
$512$	−4.21653e11	−0.271169
$513$	−1.95779e11	−0.124807
$514$	−4.78769e11	−0.302546
$515$	1.27250e11	0.0797121
$516$	3.32507e11	0.206480
$517$	−1.76701e11	−0.108775
$518$	7.38060e11	0.450410
$519$	−4.35426e11	−0.263428
$520$	3.80605e10	0.0228276
$521$	6.72889e9	0.00400105	0.00200052	−	0.999998i	$-0.499363\pi$
$521$	6.72889e9	0.00400105	0.00200052	+	0.999998i	$0.499363\pi$
$522$	3.84853e11	0.226871
$523$	−1.94157e12	−1.13474	−0.567370	−	0.823463i	$-0.692039\pi$
$523$	−1.94157e12	−1.13474	−0.567370	+	0.823463i	$0.692039\pi$
$524$	−1.33428e12	−0.773137
$525$	1.69030e12	0.971064
$526$	4.79719e10	0.0273244
$527$	1.39802e11	0.0789523
$528$	−1.55490e10	−0.00870662
$529$	2.60374e11	0.144560
$530$	−1.58580e11	−0.0872986
$531$	−7.95020e10	−0.0433963
$532$	−1.42619e12	−0.771926
$533$	2.16316e11	0.116096
$534$	−6.51236e11	−0.346579
$535$	4.00102e11	0.211144
$536$	−1.99722e12	−1.04517
$537$	−8.72553e11	−0.452801
$538$	1.25021e12	0.643374
$539$	−4.50643e11	−0.229976
$540$	5.31298e10	0.0268885
$541$	−4.30477e11	−0.216054	−0.108027	−	0.994148i	$-0.534453\pi$
$541$	−4.30477e11	−0.216054	−0.108027	+	0.994148i	$0.534453\pi$
$542$	−1.71865e12	−0.855444
$543$	−1.84236e12	−0.909440
$544$	1.54738e12	0.757535
$545$	6.29927e11	0.305848
$546$	−1.38990e11	−0.0669293
$547$	3.69233e12	1.76343	0.881714	−	0.471784i	$-0.156390\pi$
$547$	3.69233e12	1.76343	0.881714	+	0.471784i	$0.156390\pi$
$548$	−1.69581e12	−0.803275
$549$	6.55770e11	0.308089
$550$	−1.28644e11	−0.0599455
$551$	1.68194e12	0.777370
$552$	−1.28341e12	−0.588356
$553$	−5.43924e12	−2.47329
$554$	−2.96101e11	−0.133551
$555$	−1.20162e11	−0.0537587
$556$	−1.40406e12	−0.623089
$557$	1.24067e12	0.546147	0.273073	−	0.961993i	$-0.411960\pi$
$557$	1.24067e12	0.546147	0.273073	+	0.961993i	$0.411960\pi$
$558$	4.65375e10	0.0203212
$559$	1.41619e11	0.0613434
$560$	1.15284e11	0.0495361
$561$	1.09822e11	0.0468120
$562$	−8.31187e11	−0.351468
$563$	1.17319e12	0.492132	0.246066	−	0.969253i	$-0.420862\pi$
$563$	1.17319e12	0.492132	0.246066	+	0.969253i	$0.420862\pi$
$564$	−9.27411e11	−0.385937
$565$	−8.26567e11	−0.341240
$566$	2.68059e11	0.109788
$567$	−4.80350e11	−0.195179
$568$	−3.13221e12	−1.26265
$569$	−2.91701e12	−1.16663	−0.583314	−	0.812247i	$-0.698244\pi$
$569$	−2.91701e12	−1.16663	−0.583314	+	0.812247i	$0.698244\pi$
$570$	−1.10473e11	−0.0438347
$571$	2.19394e11	0.0863699	0.0431850	−	0.999067i	$-0.486250\pi$
$571$	2.19394e11	0.0863699	0.0431850	+	0.999067i	$0.486250\pi$
$572$	−2.22334e10	−0.00868406
$573$	−3.75641e11	−0.145572
$574$	−2.59106e12	−0.996262
$575$	2.68508e12	1.02436
$576$	3.94660e11	0.149390
$577$	3.01436e12	1.13215	0.566075	−	0.824353i	$-0.308461\pi$
$577$	3.01436e12	1.13215	0.566075	+	0.824353i	$0.308461\pi$
$578$	6.99757e11	0.260778
$579$	1.44745e12	0.535242
$580$	−4.56439e11	−0.167478
$581$	−8.15296e11	−0.296840
$582$	−1.71849e11	−0.0620860
$583$	2.29346e11	0.0822208
$584$	−1.23089e12	−0.437887
$585$	2.26286e10	0.00798835
$586$	2.35822e12	0.826124
$587$	−3.73815e12	−1.29953	−0.649764	−	0.760136i	$-0.725132\pi$
$587$	−3.73815e12	−1.29953	−0.649764	+	0.760136i	$0.725132\pi$
$588$	−2.36520e12	−0.815961
$589$	2.03385e11	0.0696305
$590$	−4.48608e10	−0.0152417
$591$	4.70526e11	0.158650
$592$	1.84572e11	0.0617615
$593$	5.21655e12	1.73236	0.866179	−	0.499734i	$-0.166569\pi$
$593$	5.21655e12	1.73236	0.866179	+	0.499734i	$0.166569\pi$
$594$	3.65579e10	0.0120488
$595$	−8.14246e11	−0.266336
$596$	−1.70757e12	−0.554332
$597$	2.04342e11	0.0658373
$598$	−2.20788e11	−0.0706024
$599$	−3.22617e11	−0.102392	−0.0511960	−	0.998689i	$-0.516303\pi$
$599$	−3.22617e11	−0.102392	−0.0511960	+	0.998689i	$0.516303\pi$
$600$	−1.67161e12	−0.526567
$601$	5.74234e11	0.179537	0.0897685	−	0.995963i	$-0.471387\pi$
$601$	5.74234e11	0.179537	0.0897685	+	0.995963i	$0.471387\pi$
$602$	−1.69633e12	−0.526411
$603$	−1.18744e12	−0.365748
$604$	−2.46834e12	−0.754637
$605$	6.71205e11	0.203683
$606$	−8.96689e10	−0.0270094
$607$	−4.53684e11	−0.135645	−0.0678226	−	0.997697i	$-0.521605\pi$
$607$	−4.53684e11	−0.135645	−0.0678226	+	0.997697i	$0.521605\pi$
$608$	2.25114e12	0.668094
$609$	4.12669e12	1.21569
$610$	3.70033e11	0.108207
$611$	−3.94996e11	−0.114659
$612$	5.76401e11	0.166090
$613$	−3.50305e12	−1.00201	−0.501007	−	0.865443i	$-0.667037\pi$
$613$	−3.50305e12	−1.00201	−0.501007	+	0.865443i	$0.667037\pi$
$614$	−1.77267e11	−0.0503351
$615$	4.21844e11	0.118909
$616$	6.59333e11	0.184498
$617$	3.03553e12	0.843239	0.421620	−	0.906773i	$-0.361462\pi$
$617$	3.03553e12	0.843239	0.421620	+	0.906773i	$0.361462\pi$
$618$	4.59551e11	0.126732
$619$	−3.99709e12	−1.09430	−0.547149	−	0.837035i	$-0.684287\pi$
$619$	−3.99709e12	−1.09430	−0.547149	+	0.837035i	$0.684287\pi$
$620$	−5.51939e10	−0.0150013
$621$	−7.63044e11	−0.205891
$622$	1.78514e11	0.0478206
$623$	−6.98305e12	−1.85716
$624$	−3.47581e10	−0.00917753
$625$	3.33505e12	0.874264
$626$	3.19927e12	0.832657
$627$	1.59770e11	0.0412850
$628$	−2.72309e12	−0.698625
$629$	−1.30363e12	−0.332067
$630$	−2.71048e11	−0.0685510
$631$	−3.92587e12	−0.985834	−0.492917	−	0.870076i	$-0.664069\pi$
$631$	−3.92587e12	−0.985834	−0.492917	+	0.870076i	$0.664069\pi$
$632$	5.37907e12	1.34116
$633$	−1.83414e12	−0.454063
$634$	−3.26326e12	−0.802140
$635$	−1.38646e12	−0.338397
$636$	1.20372e12	0.291721
$637$	−1.00737e12	−0.242415
$638$	−3.14070e11	−0.0750469
$639$	−1.86223e12	−0.441856
$640$	−6.78867e11	−0.159947
$641$	1.53691e12	0.359573	0.179787	−	0.983706i	$-0.442459\pi$
$641$	1.53691e12	0.359573	0.179787	+	0.983706i	$0.442459\pi$
$642$	1.44493e12	0.335691
$643$	9.66855e11	0.223055	0.111528	−	0.993761i	$-0.464426\pi$
$643$	9.66855e11	0.223055	0.111528	+	0.993761i	$0.464426\pi$
$644$	−5.55855e12	−1.27343
$645$	2.76175e11	0.0628299
$646$	−1.19851e12	−0.270766
$647$	−5.92400e12	−1.32906	−0.664532	−	0.747260i	$-0.731369\pi$
$647$	−5.92400e12	−1.32906	−0.664532	+	0.747260i	$0.731369\pi$
$648$	4.75036e11	0.105837
$649$	6.48797e10	0.0143551
$650$	−2.87569e11	−0.0631877
$651$	4.99011e11	0.108892
$652$	−3.47713e12	−0.753541
$653$	1.50571e12	0.324065	0.162033	−	0.986785i	$-0.448195\pi$
$653$	1.50571e12	0.324065	0.162033	+	0.986785i	$0.448195\pi$
$654$	2.27493e12	0.486259
$655$	−1.10823e12	−0.235258
$656$	−6.47964e11	−0.136610
$657$	−7.31818e11	−0.153235
$658$	4.73130e12	0.983929
$659$	1.30444e12	0.269426	0.134713	−	0.990885i	$-0.456989\pi$
$659$	1.30444e12	0.269426	0.134713	+	0.990885i	$0.456989\pi$
$660$	−4.33580e10	−0.00889449
$661$	1.94983e12	0.397273	0.198637	−	0.980073i	$-0.436349\pi$
$661$	1.94983e12	0.397273	0.198637	+	0.980073i	$0.436349\pi$
$662$	−2.17757e12	−0.440668
$663$	2.45496e11	0.0493439
$664$	8.06278e11	0.160964
$665$	−1.18457e12	−0.234890
$666$	−4.33955e11	−0.0854693
$667$	6.55532e12	1.28241
$668$	1.92587e12	0.374225
$669$	−4.61790e12	−0.891307
$670$	−6.70038e11	−0.128458
$671$	−5.35158e11	−0.101913
$672$	5.52326e12	1.04480
$673$	1.57403e12	0.295765	0.147882	−	0.989005i	$-0.452754\pi$
$673$	1.57403e12	0.295765	0.147882	+	0.989005i	$0.452754\pi$
$674$	−2.67614e12	−0.499504
$675$	−9.93842e11	−0.184268
$676$	3.62939e12	0.668456
$677$	−9.48856e11	−0.173601	−0.0868003	−	0.996226i	$-0.527664\pi$
$677$	−9.48856e11	−0.173601	−0.0868003	+	0.996226i	$0.527664\pi$
$678$	−2.98508e12	−0.542527
$679$	−1.84270e12	−0.332690
$680$	8.05239e11	0.144422
$681$	3.81481e11	0.0679691
$682$	−3.79782e10	−0.00672209
$683$	−6.32726e12	−1.11256	−0.556279	−	0.830996i	$-0.687771\pi$
$683$	−6.32726e12	−1.11256	−0.556279	+	0.830996i	$0.687771\pi$
$684$	8.38553e11	0.146480
$685$	−1.40851e12	−0.244429
$686$	6.28104e12	1.08286
$687$	−7.54090e11	−0.129157
$688$	−4.24212e11	−0.0721830
$689$	5.12678e11	0.0866679
$690$	−4.30565e11	−0.0723132
$691$	1.32805e12	0.221597	0.110798	−	0.993843i	$-0.464659\pi$
$691$	1.32805e12	0.221597	0.110798	+	0.993843i	$0.464659\pi$
$692$	1.86500e12	0.309173
$693$	3.92002e11	0.0645637
$694$	−3.87263e12	−0.633707
$695$	−1.16619e12	−0.189600
$696$	−4.08104e12	−0.659219
$697$	4.57656e12	0.734499
$698$	−3.33459e11	−0.0531732
$699$	−1.80523e12	−0.286012
$700$	−7.23985e12	−1.13969
$701$	2.84917e12	0.445643	0.222822	−	0.974859i	$-0.428473\pi$
$701$	2.84917e12	0.445643	0.222822	+	0.974859i	$0.428473\pi$
$702$	8.17214e10	0.0127004
$703$	−1.89653e12	−0.292860
$704$	−3.22073e11	−0.0494171
$705$	−7.70293e11	−0.117437
$706$	2.21635e12	0.335750
$707$	−9.61499e11	−0.144731
$708$	3.40520e11	0.0509323
$709$	1.69917e12	0.252540	0.126270	−	0.991996i	$-0.459700\pi$
$709$	1.69917e12	0.252540	0.126270	+	0.991996i	$0.459700\pi$
$710$	−1.05081e12	−0.155189
$711$	3.19809e12	0.469329
$712$	6.90580e12	1.00706
$713$	7.92688e11	0.114868
$714$	−2.94058e12	−0.423439
$715$	−1.84667e10	−0.00264248
$716$	3.73729e12	0.531432
$717$	5.03979e12	0.712158
$718$	3.69321e12	0.518613
$719$	8.44614e12	1.17863	0.589316	−	0.807902i	$-0.299397\pi$
$719$	8.44614e12	1.17863	0.589316	+	0.807902i	$0.299397\pi$
$720$	−6.77829e10	−0.00939992
$721$	4.92766e12	0.679098
$722$	2.40220e12	0.328997
$723$	−6.34045e12	−0.862974
$724$	7.89111e12	1.06737
$725$	8.53811e12	1.14773
$726$	2.42400e12	0.323830
$727$	−4.74564e12	−0.630071	−0.315036	−	0.949080i	$-0.602016\pi$
$727$	−4.74564e12	−0.630071	−0.315036	+	0.949080i	$0.602016\pi$
$728$	1.47387e12	0.194477
$729$	2.82430e11	0.0370370
$730$	−4.12945e11	−0.0538195
$731$	2.99620e12	0.388100
$732$	−2.80877e12	−0.361590
$733$	1.07965e13	1.38138	0.690692	−	0.723149i	$-0.257306\pi$
$733$	1.07965e13	1.38138	0.690692	+	0.723149i	$0.257306\pi$
$734$	−7.78921e12	−0.990515
$735$	−1.96449e12	−0.248289
$736$	8.77379e12	1.10214
$737$	9.69038e11	0.120987
$738$	1.52346e12	0.189050
$739$	−2.90351e12	−0.358116	−0.179058	−	0.983839i	$-0.557305\pi$
$739$	−2.90351e12	−0.358116	−0.179058	+	0.983839i	$0.557305\pi$
$740$	5.14673e11	0.0630941
$741$	3.57150e11	0.0435180
$742$	−6.14091e12	−0.743730
$743$	1.37305e13	1.65286	0.826429	−	0.563041i	$-0.190369\pi$
$743$	1.37305e13	1.65286	0.826429	+	0.563041i	$0.190369\pi$
$744$	−4.93491e11	−0.0590475
$745$	−1.41828e12	−0.168678
$746$	1.41332e12	0.167077
$747$	4.79367e11	0.0563281
$748$	−4.70387e11	−0.0549412
$749$	1.54937e13	1.79881
$750$	−1.14650e12	−0.132311
$751$	1.33843e13	1.53538	0.767691	−	0.640821i	$-0.221406\pi$
$751$	1.33843e13	1.53538	0.767691	+	0.640821i	$0.221406\pi$
$752$	1.18319e12	0.134919
$753$	−3.40490e12	−0.385946
$754$	−7.02070e11	−0.0791059
$755$	−2.05016e12	−0.229629
$756$	2.05742e12	0.229073
$757$	6.94181e12	0.768319	0.384159	−	0.923267i	$-0.374491\pi$
$757$	6.94181e12	0.768319	0.384159	+	0.923267i	$0.374491\pi$
$758$	1.96981e12	0.216727
$759$	6.22702e11	0.0681070
$760$	1.17147e12	0.127371
$761$	−1.81658e13	−1.96346	−0.981732	−	0.190269i	$-0.939064\pi$
$761$	−1.81658e13	−1.96346	−0.981732	+	0.190269i	$0.939064\pi$
$762$	−5.00710e12	−0.538008
$763$	2.43935e13	2.60563
$764$	1.60893e12	0.170851
$765$	4.78749e11	0.0505396
$766$	1.03163e10	0.00108267
$767$	1.45032e11	0.0151316
$768$	−4.94631e12	−0.513046
$769$	6.48177e12	0.668382	0.334191	−	0.942505i	$-0.391537\pi$
$769$	6.48177e12	0.668382	0.334191	+	0.942505i	$0.391537\pi$
$770$	2.21196e11	0.0226761
$771$	3.01846e12	0.307638
$772$	−6.19966e12	−0.628189
$773$	−3.31272e12	−0.333716	−0.166858	−	0.985981i	$-0.553362\pi$
$773$	−3.31272e12	−0.333716	−0.166858	+	0.985981i	$0.553362\pi$
$774$	9.97383e11	0.0998913
$775$	1.03245e12	0.102805
$776$	1.82231e12	0.180404
$777$	−4.65319e12	−0.457990
$778$	−9.90612e12	−0.969383
$779$	6.65801e12	0.647778
$780$	−9.69222e10	−0.00937556
$781$	1.51972e12	0.146162
$782$	−4.67116e12	−0.446678
$783$	−2.42636e12	−0.230689
$784$	3.01751e12	0.285251
$785$	−2.26176e12	−0.212585
$786$	−4.00229e12	−0.374030
$787$	1.37042e13	1.27341	0.636704	−	0.771108i	$-0.280297\pi$
$787$	1.37042e13	1.27341	0.636704	+	0.771108i	$0.280297\pi$
$788$	−2.01534e12	−0.186200
$789$	−3.02445e11	−0.0277843
$790$	1.80459e12	0.164838
$791$	−3.20083e13	−2.90715
$792$	−3.87666e11	−0.0350101
$793$	−1.19629e12	−0.107425
$794$	1.10441e13	0.986140
$795$	9.99789e11	0.0887679
$796$	−8.75229e11	−0.0772703
$797$	−1.12390e13	−0.986659	−0.493329	−	0.869843i	$-0.664220\pi$
$797$	−1.12390e13	−0.986659	−0.493329	+	0.869843i	$0.664220\pi$
$798$	−4.27798e12	−0.373444
$799$	−8.35684e12	−0.725407
$800$	1.14276e13	0.986393
$801$	4.10580e12	0.352412
$802$	−6.54667e12	−0.558773
$803$	5.97219e11	0.0506890
$804$	5.08598e12	0.429262
$805$	−4.61684e12	−0.387493
$806$	−8.48962e10	−0.00708566
$807$	−7.88212e12	−0.654203
$808$	9.50863e11	0.0784814
$809$	6.71071e12	0.550808	0.275404	−	0.961329i	$-0.411188\pi$
$809$	6.71071e12	0.550808	0.275404	+	0.961329i	$0.411188\pi$
$810$	1.59367e11	0.0130082
$811$	3.22992e12	0.262179	0.131090	−	0.991371i	$-0.458152\pi$
$811$	3.22992e12	0.262179	0.131090	+	0.991371i	$0.458152\pi$
$812$	−1.76753e13	−1.42681
$813$	1.08355e13	0.869842
$814$	3.54140e11	0.0282725
$815$	−2.88805e12	−0.229295
$816$	−7.35371e11	−0.0580632
$817$	4.35890e12	0.342277
$818$	2.58364e12	0.201763
$819$	8.76279e11	0.0680557
$820$	−1.80683e12	−0.139558
$821$	−5.85236e12	−0.449559	−0.224780	−	0.974410i	$-0.572166\pi$
$821$	−5.85236e12	−0.449559	−0.224780	+	0.974410i	$0.572166\pi$
$822$	−5.08672e12	−0.388611
$823$	1.73378e13	1.31733	0.658665	−	0.752437i	$-0.271122\pi$
$823$	1.73378e13	1.31733	0.658665	+	0.752437i	$0.271122\pi$
$824$	−4.87315e12	−0.368246
$825$	8.11050e11	0.0609544
$826$	−1.73721e12	−0.129850
$827$	−1.21426e12	−0.0902683	−0.0451341	−	0.998981i	$-0.514372\pi$
$827$	−1.21426e12	−0.0902683	−0.0451341	+	0.998981i	$0.514372\pi$
$828$	3.26824e12	0.241645
$829$	1.64938e13	1.21290	0.606449	−	0.795122i	$-0.292593\pi$
$829$	1.64938e13	1.21290	0.606449	+	0.795122i	$0.292593\pi$
$830$	2.70494e11	0.0197836
$831$	1.86681e12	0.135799
$832$	−7.19960e11	−0.0520899
$833$	−2.13126e13	−1.53368
$834$	−4.21160e12	−0.301440
$835$	1.59960e12	0.113873
$836$	−6.84323e11	−0.0484543
$837$	−2.93402e11	−0.0206632
$838$	−7.16741e12	−0.502070
$839$	2.54317e13	1.77193	0.885964	−	0.463754i	$-0.153498\pi$
$839$	2.54317e13	1.77193	0.885964	+	0.463754i	$0.153498\pi$
$840$	2.87424e12	0.199189
$841$	6.33773e12	0.436869
$842$	1.59070e13	1.09065
$843$	5.24032e12	0.357383
$844$	7.85592e12	0.532913
$845$	3.01451e12	0.203405
$846$	−2.78185e12	−0.186710
$847$	2.59920e13	1.73526
$848$	−1.53570e12	−0.101982
$849$	−1.69001e12	−0.111636
$850$	−6.08405e12	−0.399768
$851$	−7.39168e12	−0.483126
$852$	7.97626e12	0.518586
$853$	−2.00195e12	−0.129474	−0.0647370	−	0.997902i	$-0.520621\pi$
$853$	−2.00195e12	−0.129474	−0.0647370	+	0.997902i	$0.520621\pi$
$854$	1.43293e13	0.921858
$855$	6.96488e11	0.0445724
$856$	−1.53223e13	−0.975421
$857$	1.17946e13	0.746913	0.373457	−	0.927648i	$-0.378172\pi$
$857$	1.17946e13	0.746913	0.373457	+	0.927648i	$0.378172\pi$
$858$	−6.66908e10	−0.00420120
$859$	−2.87741e12	−0.180315	−0.0901577	−	0.995927i	$-0.528737\pi$
$859$	−2.87741e12	−0.180315	−0.0901577	+	0.995927i	$0.528737\pi$
$860$	−1.18290e12	−0.0737406
$861$	1.63356e13	1.01303
$862$	7.88540e12	0.486453
$863$	9.28264e12	0.569669	0.284835	−	0.958577i	$-0.408061\pi$
$863$	9.28264e12	0.569669	0.284835	+	0.958577i	$0.408061\pi$
$864$	−3.24749e12	−0.198260
$865$	1.54904e12	0.0940785
$866$	3.97410e12	0.240109
$867$	−4.41170e12	−0.265168
$868$	−2.13735e12	−0.127802
$869$	−2.60988e12	−0.155250
$870$	−1.36913e12	−0.0810228
$871$	2.16618e12	0.127530
$872$	−2.41237e13	−1.41292
$873$	1.08344e12	0.0631310
$874$	−6.79564e12	−0.393939
$875$	−1.22936e13	−0.708995
$876$	3.13450e12	0.179846
$877$	4.93768e12	0.281854	0.140927	−	0.990020i	$-0.454992\pi$
$877$	4.93768e12	0.281854	0.140927	+	0.990020i	$0.454992\pi$
$878$	−3.32567e12	−0.188866
$879$	−1.48677e13	−0.840028
$880$	5.53160e10	0.00310941
$881$	−6.10283e11	−0.0341303	−0.0170651	−	0.999854i	$-0.505432\pi$
$881$	−6.10283e11	−0.0341303	−0.0170651	+	0.999854i	$0.505432\pi$
$882$	−7.09460e12	−0.394748
$883$	−7.15626e11	−0.0396153	−0.0198076	−	0.999804i	$-0.506305\pi$
$883$	−7.15626e11	−0.0396153	−0.0198076	+	0.999804i	$0.506305\pi$
$884$	−1.05150e12	−0.0579128
$885$	2.82831e11	0.0154982
$886$	7.81493e12	0.426062
$887$	−2.10952e13	−1.14427	−0.572134	−	0.820160i	$-0.693884\pi$
$887$	−2.10952e13	−1.14427	−0.572134	+	0.820160i	$0.693884\pi$
$888$	4.60172e12	0.248349
$889$	−5.36899e13	−2.88294
$890$	2.31679e12	0.123775
$891$	−2.30484e11	−0.0122515
$892$	1.97792e13	1.04609
$893$	−1.21576e13	−0.639759
$894$	−5.12199e12	−0.268176
$895$	3.10413e12	0.161710
$896$	−2.62887e13	−1.36265
$897$	1.39198e12	0.0717907
$898$	1.27046e13	0.651955
$899$	2.52062e12	0.128703
$900$	4.25679e12	0.216267
$901$	1.08466e13	0.548319
$902$	−1.24325e12	−0.0625361
$903$	1.06947e13	0.535271
$904$	3.16542e13	1.57643
$905$	6.55423e12	0.324790
$906$	−7.40398e12	−0.365080
$907$	−7.69464e12	−0.377533	−0.188767	−	0.982022i	$-0.560449\pi$
$907$	−7.69464e12	−0.377533	−0.188767	+	0.982022i	$0.560449\pi$
$908$	−1.63395e12	−0.0797723
$909$	5.65329e11	0.0274640
$910$	4.94460e11	0.0239026
$911$	−1.62851e13	−0.783353	−0.391676	−	0.920103i	$-0.628105\pi$
$911$	−1.62851e13	−0.783353	−0.391676	+	0.920103i	$0.628105\pi$
$912$	−1.06982e12	−0.0512077
$913$	−3.91200e11	−0.0186329
$914$	−3.93649e12	−0.186574
$915$	−2.33292e12	−0.110028
$916$	3.22989e12	0.151586
$917$	−4.29156e13	−2.00425
$918$	1.72896e12	0.0803514
$919$	6.17320e12	0.285490	0.142745	−	0.989759i	$-0.454407\pi$
$919$	6.17320e12	0.285490	0.142745	+	0.989759i	$0.454407\pi$
$920$	4.56577e12	0.210121
$921$	1.11760e12	0.0511823
$922$	−5.61262e12	−0.255786
$923$	3.39719e12	0.154068
$924$	−1.67901e12	−0.0757755
$925$	−9.62744e12	−0.432387
$926$	1.60822e13	0.718781
$927$	−2.89730e12	−0.128865
$928$	2.78992e13	1.23489
$929$	−2.36498e13	−1.04173	−0.520867	−	0.853638i	$-0.674391\pi$
$929$	−2.36498e13	−1.04173	−0.520867	+	0.853638i	$0.674391\pi$
$930$	−1.65559e11	−0.00725736
$931$	−3.10058e13	−1.35260
$932$	7.73209e12	0.335680
$933$	−1.12546e12	−0.0486254
$934$	9.70882e12	0.417451
$935$	−3.90696e11	−0.0167181
$936$	−8.66586e11	−0.0369037
$937$	−4.58998e13	−1.94528	−0.972642	−	0.232309i	$-0.925372\pi$
$937$	−4.58998e13	−1.94528	−0.972642	+	0.232309i	$0.925372\pi$
$938$	−2.59468e13	−1.09439
$939$	−2.01702e13	−0.846671
$940$	3.29929e12	0.137830
$941$	3.09088e13	1.28507	0.642537	−	0.766254i	$-0.277882\pi$
$941$	3.09088e13	1.28507	0.642537	+	0.766254i	$0.277882\pi$
$942$	−8.16814e12	−0.337983
$943$	2.59495e13	1.06863
$944$	−4.34435e11	−0.0178054
$945$	1.70886e12	0.0697048
$946$	−8.13940e11	−0.0330432
$947$	−3.03772e12	−0.122736	−0.0613682	−	0.998115i	$-0.519546\pi$
$947$	−3.03772e12	−0.122736	−0.0613682	+	0.998115i	$0.519546\pi$
$948$	−1.36979e13	−0.550830
$949$	1.33502e12	0.0534306
$950$	−8.85113e12	−0.352567
$951$	2.05736e13	0.815641
$952$	3.11824e13	1.23039
$953$	2.25232e13	0.884528	0.442264	−	0.896885i	$-0.354175\pi$
$953$	2.25232e13	0.884528	0.442264	+	0.896885i	$0.354175\pi$
$954$	3.61065e12	0.141129
$955$	1.33635e12	0.0519884
$956$	−2.15863e13	−0.835828
$957$	1.98009e12	0.0763100
$958$	−1.73474e13	−0.665412
$959$	−5.45437e13	−2.08238
$960$	−1.40402e12	−0.0533521
$961$	−2.61348e13	−0.988472
$962$	7.91642e11	0.0298017
$963$	−9.10977e12	−0.341341
$964$	2.71572e13	1.01283
$965$	−5.14934e12	−0.191152
$966$	−1.66733e13	−0.616064
$967$	−2.80300e13	−1.03087	−0.515434	−	0.856929i	$-0.672369\pi$
$967$	−2.80300e13	−1.03087	−0.515434	+	0.856929i	$0.672369\pi$
$968$	−2.57044e13	−0.940956
$969$	7.55615e12	0.275324
$970$	6.11358e11	0.0221729
$971$	−1.48038e13	−0.534424	−0.267212	−	0.963638i	$-0.586102\pi$
$971$	−1.48038e13	−0.534424	−0.267212	+	0.963638i	$0.586102\pi$
$972$	−1.20969e12	−0.0434687
$973$	−4.51600e13	−1.61527
$974$	−1.45517e13	−0.518082
$975$	1.81302e12	0.0642512
$976$	3.58342e12	0.126408
$977$	−4.58267e13	−1.60914	−0.804569	−	0.593859i	$-0.797604\pi$
$977$	−4.58267e13	−1.60914	−0.804569	+	0.593859i	$0.797604\pi$
$978$	−1.04299e13	−0.364550
$979$	−3.35064e12	−0.116575
$980$	8.41425e12	0.291406
$981$	−1.43426e13	−0.494443
$982$	−1.18911e13	−0.408058
$983$	4.73679e13	1.61806	0.809028	−	0.587770i	$-0.199994\pi$
$983$	4.73679e13	1.61806	0.809028	+	0.587770i	$0.199994\pi$
$984$	−1.61550e13	−0.549323
$985$	−1.67391e12	−0.0566590
$986$	−1.48535e13	−0.500477
$987$	−2.98291e13	−1.00049
$988$	−1.52973e12	−0.0510751
$989$	1.69887e13	0.564648
$990$	−1.30056e11	−0.00430300
$991$	3.56521e13	1.17423	0.587116	−	0.809503i	$-0.300263\pi$
$991$	3.56521e13	1.17423	0.587116	+	0.809503i	$0.300263\pi$
$992$	3.37365e12	0.110611
$993$	1.37288e13	0.448085
$994$	−4.06919e13	−1.32211
$995$	−7.26951e11	−0.0235126
$996$	−2.05321e12	−0.0661098
$997$	8.44601e11	0.0270722	0.0135361	−	0.999908i	$-0.495691\pi$
$997$	8.44601e11	0.0270722	0.0135361	+	0.999908i	$0.495691\pi$
$998$	3.49884e13	1.11644
$999$	2.73592e12	0.0869078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.8	✓	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-12.8477 q^{2} +81.0000 q^{3} -346.936 q^{4} -288.160 q^{5} -1040.66 q^{6} -11158.8 q^{7} +11035.4 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-12.8477 q^{2} +81.0000 q^{3} -346.936 q^{4} -288.160 q^{5} -1040.66 q^{6} -11158.8 q^{7} +11035.4 q^{8} +6561.00 q^{9} +3702.19 q^{10} -5354.27 q^{11} -28101.8 q^{12} -11968.9 q^{13} +143365. q^{14} -23340.9 q^{15} +35852.3 q^{16} -253224. q^{17} -84293.8 q^{18} -368392. q^{19} +99973.1 q^{20} -903863. q^{21} +68790.1 q^{22} -1.43580e6 q^{23} +893865. q^{24} -1.87009e6 q^{25} +153773. q^{26} +531441. q^{27} +3.87139e6 q^{28} -4.56562e6 q^{29} +299878. q^{30} -552087. q^{31} -6.11073e6 q^{32} -433696. q^{33} +3.25335e6 q^{34} +3.21552e6 q^{35} -2.27625e6 q^{36} +5.14812e6 q^{37} +4.73300e6 q^{38} -969482. q^{39} -3.17995e6 q^{40} -1.80732e7 q^{41} +1.16126e7 q^{42} -1.18322e7 q^{43} +1.85759e6 q^{44} -1.89062e6 q^{45} +1.84468e7 q^{46} +3.30018e7 q^{47} +2.90403e6 q^{48} +8.41652e7 q^{49} +2.40264e7 q^{50} -2.05111e7 q^{51} +4.15245e6 q^{52} -4.28341e7 q^{53} -6.82780e6 q^{54} +1.54289e6 q^{55} -1.23141e8 q^{56} -2.98398e7 q^{57} +5.86577e7 q^{58} -1.21174e7 q^{59} +8.09782e6 q^{60} +9.99497e7 q^{61} +7.09306e6 q^{62} -7.32129e7 q^{63} +6.01525e7 q^{64} +3.44896e6 q^{65} +5.57200e6 q^{66} -1.80984e8 q^{67} +8.78526e7 q^{68} -1.16300e8 q^{69} -4.13120e7 q^{70} -2.83834e8 q^{71} +7.24030e7 q^{72} -1.11541e8 q^{73} -6.61415e7 q^{74} -1.51477e8 q^{75} +1.27809e8 q^{76} +5.97473e7 q^{77} +1.24556e7 q^{78} +4.87439e8 q^{79} -1.03312e7 q^{80} +4.30467e7 q^{81} +2.32199e8 q^{82} +7.30631e7 q^{83} +3.13583e8 q^{84} +7.29690e7 q^{85} +1.52017e8 q^{86} -3.69815e8 q^{87} -5.90864e7 q^{88} +6.25788e8 q^{89} +2.42901e7 q^{90} +1.33559e8 q^{91} +4.98132e8 q^{92} -4.47191e7 q^{93} -4.23997e8 q^{94} +1.06156e8 q^{95} -4.94969e8 q^{96} +1.65134e8 q^{97} -1.08133e9 q^{98} -3.51294e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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