LMFDB - Embedded newform 57.10.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,10,Mod(1,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, 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("57.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	57.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:	$29.3570426613$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 3446 x^{6} + 2146 x^{5} + 3632756 x^{4} + 1877896 x^{3} - 1128074928 x^{2} + \cdots - 684004608 $ x^8 - x^7 - 3446x^6 + 2146x^5 + 3632756x^4 + 1877896x^3 - 1128074928x^2 - 2326290816x - 684004608
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-22.5401$ of defining polynomial
Character	$\chi$	$=$	57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-20.5401 q^{2} +81.0000 q^{3} -90.1033 q^{4} +849.287 q^{5} -1663.75 q^{6} -10981.2 q^{7} +12367.3 q^{8} +6561.00 q^{9} -17444.5 q^{10} +34068.5 q^{11} -7298.37 q^{12} -70090.6 q^{13} +225555. q^{14} +68792.2 q^{15} -207892. q^{16} +51130.2 q^{17} -134764. q^{18} -130321. q^{19} -76523.6 q^{20} -889477. q^{21} -699771. q^{22} -512837. q^{23} +1.00175e6 q^{24} -1.23184e6 q^{25} +1.43967e6 q^{26} +531441. q^{27} +989443. q^{28} +3.83836e6 q^{29} -1.41300e6 q^{30} +2.93336e6 q^{31} -2.06191e6 q^{32} +2.75955e6 q^{33} -1.05022e6 q^{34} -9.32619e6 q^{35} -591168. q^{36} +1.23767e7 q^{37} +2.67681e6 q^{38} -5.67734e6 q^{39} +1.05034e7 q^{40} +7.42222e6 q^{41} +1.82700e7 q^{42} +3.06693e7 q^{43} -3.06968e6 q^{44} +5.57217e6 q^{45} +1.05337e7 q^{46} +5.92639e7 q^{47} -1.68393e7 q^{48} +8.02332e7 q^{49} +2.53021e7 q^{50} +4.14154e6 q^{51} +6.31540e6 q^{52} +7.73856e7 q^{53} -1.09159e7 q^{54} +2.89339e7 q^{55} -1.35808e8 q^{56} -1.05560e7 q^{57} -7.88404e7 q^{58} -1.89946e7 q^{59} -6.19841e6 q^{60} -1.21386e8 q^{61} -6.02516e7 q^{62} -7.20477e7 q^{63} +1.48793e8 q^{64} -5.95270e7 q^{65} -5.66814e7 q^{66} +2.07044e8 q^{67} -4.60700e6 q^{68} -4.15398e7 q^{69} +1.91561e8 q^{70} -4.75295e7 q^{71} +8.11417e7 q^{72} -1.79415e8 q^{73} -2.54220e8 q^{74} -9.97788e7 q^{75} +1.17424e7 q^{76} -3.74113e8 q^{77} +1.16613e8 q^{78} -1.96664e7 q^{79} -1.76560e8 q^{80} +4.30467e7 q^{81} -1.52453e8 q^{82} -1.31374e8 q^{83} +8.01449e7 q^{84} +4.34242e7 q^{85} -6.29951e8 q^{86} +3.10907e8 q^{87} +4.21334e8 q^{88} +7.24401e8 q^{89} -1.14453e8 q^{90} +7.69679e8 q^{91} +4.62083e7 q^{92} +2.37602e8 q^{93} -1.21729e9 q^{94} -1.10680e8 q^{95} -1.67015e8 q^{96} -2.74292e8 q^{97} -1.64800e9 q^{98} +2.23523e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 17 q^{2} + 648 q^{3} + 2833 q^{4} + 3902 q^{5} + 1377 q^{6} + 9488 q^{7} + 27927 q^{8} + 52488 q^{9} + 111324 q^{10} + 38328 q^{11} + 229473 q^{12} + 238594 q^{13} + 255570 q^{14} + 316062 q^{15}+ \cdots + 251470008 q^{99}+O(q^{100}) $ 8 * q + 17 * q^2 + 648 * q^3 + 2833 * q^4 + 3902 * q^5 + 1377 * q^6 + 9488 * q^7 + 27927 * q^8 + 52488 * q^9 + 111324 * q^10 + 38328 * q^11 + 229473 * q^12 + 238594 * q^13 + 255570 * q^14 + 316062 * q^15 + 875017 * q^16 + 340248 * q^17 + 111537 * q^18 - 1042568 * q^19 - 70298 * q^20 + 768528 * q^21 - 2034178 * q^22 + 36062 * q^23 + 2262087 * q^24 + 3100952 * q^25 - 3108174 * q^26 + 4251528 * q^27 + 7077616 * q^28 - 350456 * q^29 + 9017244 * q^30 + 15030666 * q^31 + 8323411 * q^32 + 3104568 * q^33 + 21887248 * q^34 + 32386908 * q^35 + 18587313 * q^36 + 29518626 * q^37 - 2215457 * q^38 + 19326114 * q^39 + 66983070 * q^40 + 20347628 * q^41 + 20701170 * q^42 + 107568604 * q^43 + 39497904 * q^44 + 25601022 * q^45 + 84573760 * q^46 + 77478390 * q^47 + 70876377 * q^48 + 66668124 * q^49 + 85335229 * q^50 + 27560088 * q^51 + 117837518 * q^52 + 99085464 * q^53 + 9034497 * q^54 + 49033668 * q^55 + 174919116 * q^56 - 84448008 * q^57 + 85663178 * q^58 + 194104536 * q^59 - 5694138 * q^60 + 268423708 * q^61 + 144870904 * q^62 + 62250768 * q^63 - 300291319 * q^64 + 5447796 * q^65 - 164768418 * q^66 - 151197308 * q^67 - 605814870 * q^68 + 2921022 * q^69 - 240578502 * q^70 - 121292496 * q^71 + 183229047 * q^72 - 102019552 * q^73 - 688853258 * q^74 + 251177112 * q^75 - 369199393 * q^76 - 117614964 * q^77 - 251762094 * q^78 - 138557962 * q^79 - 1299265658 * q^80 + 344373768 * q^81 - 1339779918 * q^82 - 464489416 * q^83 + 573286896 * q^84 - 1230030528 * q^85 - 2465913098 * q^86 - 28386936 * q^87 - 485295564 * q^88 - 1232352760 * q^89 + 730396764 * q^90 - 152984744 * q^91 - 4368234020 * q^92 + 1217483946 * q^93 - 752351790 * q^94 - 508512542 * q^95 + 674196291 * q^96 - 523291172 * q^97 - 5080621865 * q^98 + 251470008 * q^99

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 $

$2$	−20.5401	−0.907754	−0.453877	−	0.891064i	$-0.649959\pi$
$2$	−20.5401	−0.907754	−0.453877	+	0.891064i	$0.649959\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−90.1033	−0.175983
$5$	849.287	0.607700	0.303850	−	0.952720i	$-0.401728\pi$
$5$	849.287	0.607700	0.303850	+	0.952720i	$0.401728\pi$
$6$	−1663.75	−0.524092
$7$	−10981.2	−1.72866	−0.864328	−	0.502928i	$-0.832256\pi$
$7$	−10981.2	−1.72866	−0.864328	+	0.502928i	$0.832256\pi$
$8$	12367.3	1.06750
$9$	6561.00	0.333333
$10$	−17444.5	−0.551642
$11$	34068.5	0.701594	0.350797	−	0.936452i	$-0.385911\pi$
$11$	34068.5	0.701594	0.350797	+	0.936452i	$0.385911\pi$
$12$	−7298.37	−0.101604
$13$	−70090.6	−0.680635	−0.340318	−	0.940311i	$-0.610535\pi$
$13$	−70090.6	−0.680635	−0.340318	+	0.940311i	$0.610535\pi$
$14$	225555.	1.56919
$15$	68792.2	0.350856
$16$	−207892.	−0.793047
$17$	51130.2	0.148476	0.0742381	−	0.997241i	$-0.476348\pi$
$17$	51130.2	0.148476	0.0742381	+	0.997241i	$0.476348\pi$
$18$	−134764.	−0.302585
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−76523.6	−0.106945
$21$	−889477.	−0.998040
$22$	−699771.	−0.636874
$23$	−512837.	−0.382124	−0.191062	−	0.981578i	$-0.561193\pi$
$23$	−512837.	−0.382124	−0.191062	+	0.981578i	$0.561193\pi$
$24$	1.00175e6	0.616323
$25$	−1.23184e6	−0.630700
$26$	1.43967e6	0.617849
$27$	531441.	0.192450
$28$	989443.	0.304214
$29$	3.83836e6	1.00775	0.503877	−	0.863775i	$-0.331906\pi$
$29$	3.83836e6	1.00775	0.503877	+	0.863775i	$0.331906\pi$
$30$	−1.41300e6	−0.318491
$31$	2.93336e6	0.570476	0.285238	−	0.958457i	$-0.407927\pi$
$31$	2.93336e6	0.570476	0.285238	+	0.958457i	$0.407927\pi$
$32$	−2.06191e6	−0.347612
$33$	2.75955e6	0.405065
$34$	−1.05022e6	−0.134780
$35$	−9.32619e6	−1.05050
$36$	−591168.	−0.0586610
$37$	1.23767e7	1.08567	0.542835	−	0.839839i	$-0.317351\pi$
$37$	1.23767e7	1.08567	0.542835	+	0.839839i	$0.317351\pi$
$38$	2.67681e6	0.208253
$39$	−5.67734e6	−0.392965
$40$	1.05034e7	0.648722
$41$	7.42222e6	0.410210	0.205105	−	0.978740i	$-0.434246\pi$
$41$	7.42222e6	0.410210	0.205105	+	0.978740i	$0.434246\pi$
$42$	1.82700e7	0.905975
$43$	3.06693e7	1.36803	0.684016	−	0.729467i	$-0.260232\pi$
$43$	3.06693e7	1.36803	0.684016	+	0.729467i	$0.260232\pi$
$44$	−3.06968e6	−0.123469
$45$	5.57217e6	0.202567
$46$	1.05337e7	0.346874
$47$	5.92639e7	1.77154	0.885768	−	0.464127i	$-0.153632\pi$
$47$	5.92639e7	1.77154	0.885768	+	0.464127i	$0.153632\pi$
$48$	−1.68393e7	−0.457866
$49$	8.02332e7	1.98825
$50$	2.53021e7	0.572521
$51$	4.14154e6	0.0857228
$52$	6.31540e6	0.119780
$53$	7.73856e7	1.34716	0.673579	−	0.739115i	$-0.264756\pi$
$53$	7.73856e7	1.34716	0.673579	+	0.739115i	$0.264756\pi$
$54$	−1.09159e7	−0.174697
$55$	2.89339e7	0.426359
$56$	−1.35808e8	−1.84535
$57$	−1.05560e7	−0.132453
$58$	−7.88404e7	−0.914793
$59$	−1.89946e7	−0.204078	−0.102039	−	0.994780i	$-0.532537\pi$
$59$	−1.89946e7	−0.204078	−0.102039	+	0.994780i	$0.532537\pi$
$60$	−6.19841e6	−0.0617447
$61$	−1.21386e8	−1.12249	−0.561247	−	0.827649i	$-0.689678\pi$
$61$	−1.21386e8	−1.12249	−0.561247	+	0.827649i	$0.689678\pi$
$62$	−6.02516e7	−0.517852
$63$	−7.20477e7	−0.576219
$64$	1.48793e8	1.10859
$65$	−5.95270e7	−0.413622
$66$	−5.66814e7	−0.367700
$67$	2.07044e8	1.25524	0.627620	−	0.778520i	$-0.284029\pi$
$67$	2.07044e8	1.25524	0.627620	+	0.778520i	$0.284029\pi$
$68$	−4.60700e6	−0.0261293
$69$	−4.15398e7	−0.220619
$70$	1.91561e8	0.953600
$71$	−4.75295e7	−0.221973	−0.110987	−	0.993822i	$-0.535401\pi$
$71$	−4.75295e7	−0.221973	−0.110987	+	0.993822i	$0.535401\pi$
$72$	8.11417e7	0.355834
$73$	−1.79415e8	−0.739444	−0.369722	−	0.929142i	$-0.620547\pi$
$73$	−1.79415e8	−0.739444	−0.369722	+	0.929142i	$0.620547\pi$
$74$	−2.54220e8	−0.985522
$75$	−9.97788e7	−0.364135
$76$	1.17424e7	0.0403733
$77$	−3.74113e8	−1.21281
$78$	1.16613e8	0.356715
$79$	−1.96664e7	−0.0568071	−0.0284035	−	0.999597i	$-0.509042\pi$
$79$	−1.96664e7	−0.0568071	−0.0284035	+	0.999597i	$0.509042\pi$
$80$	−1.76560e8	−0.481935
$81$	4.30467e7	0.111111
$82$	−1.52453e8	−0.372370
$83$	−1.31374e8	−0.303850	−0.151925	−	0.988392i	$-0.548547\pi$
$83$	−1.31374e8	−0.303850	−0.151925	+	0.988392i	$0.548547\pi$
$84$	8.01449e7	0.175638
$85$	4.34242e7	0.0902291
$86$	−6.29951e8	−1.24184
$87$	3.10907e8	0.581828
$88$	4.21334e8	0.748954
$89$	7.24401e8	1.22384	0.611919	−	0.790920i	$-0.290398\pi$
$89$	7.24401e8	1.22384	0.611919	+	0.790920i	$0.290398\pi$
$90$	−1.14453e8	−0.183881
$91$	7.69679e8	1.17658
$92$	4.62083e7	0.0672473
$93$	2.37602e8	0.329365
$94$	−1.21729e9	−1.60812
$95$	−1.10680e8	−0.139416
$96$	−1.67015e8	−0.200694
$97$	−2.74292e8	−0.314587	−0.157293	−	0.987552i	$-0.550277\pi$
$97$	−2.74292e8	−0.314587	−0.157293	+	0.987552i	$0.550277\pi$
$98$	−1.64800e9	−1.80484
$99$	2.23523e8	0.233865
$100$	1.10993e8	0.110993
$101$	1.85454e8	0.177333	0.0886664	−	0.996061i	$-0.471739\pi$
$101$	1.85454e8	0.177333	0.0886664	+	0.996061i	$0.471739\pi$
$102$	−8.50678e7	−0.0778152
$103$	1.17142e9	1.02552	0.512760	−	0.858532i	$-0.328623\pi$
$103$	1.17142e9	1.02552	0.512760	+	0.858532i	$0.328623\pi$
$104$	−8.66829e8	−0.726580
$105$	−7.55421e8	−0.606509
$106$	−1.58951e9	−1.22289
$107$	2.35004e9	1.73320	0.866600	−	0.499003i	$-0.166300\pi$
$107$	2.35004e9	1.73320	0.866600	+	0.499003i	$0.166300\pi$
$108$	−4.78846e7	−0.0338680
$109$	−8.61624e8	−0.584654	−0.292327	−	0.956318i	$-0.594429\pi$
$109$	−8.61624e8	−0.584654	−0.292327	+	0.956318i	$0.594429\pi$
$110$	−5.94306e8	−0.387029
$111$	1.00252e9	0.626812
$112$	2.28291e9	1.37091
$113$	−1.60777e9	−0.927623	−0.463811	−	0.885934i	$-0.653518\pi$
$113$	−1.60777e9	−0.927623	−0.463811	+	0.885934i	$0.653518\pi$
$114$	2.16822e8	0.120235
$115$	−4.35546e8	−0.232217
$116$	−3.45849e8	−0.177348
$117$	−4.59864e8	−0.226878
$118$	3.90151e8	0.185252
$119$	−5.61471e8	−0.256665
$120$	8.50773e8	0.374540
$121$	−1.19729e9	−0.507766
$122$	2.49328e9	1.01895
$123$	6.01200e8	0.236835
$124$	−2.64306e8	−0.100394
$125$	−2.70495e9	−0.990977
$126$	1.47987e9	0.523065
$127$	4.79972e9	1.63719	0.818595	−	0.574371i	$-0.194753\pi$
$127$	4.79972e9	1.63719	0.818595	+	0.574371i	$0.194753\pi$
$128$	−2.00053e9	−0.658717
$129$	2.48421e9	0.789833
$130$	1.22269e9	0.375467
$131$	2.34855e9	0.696753	0.348376	−	0.937355i	$-0.386733\pi$
$131$	2.34855e9	0.696753	0.348376	+	0.937355i	$0.386733\pi$
$132$	−2.48644e8	−0.0712847
$133$	1.43108e9	0.396581
$134$	−4.25271e9	−1.13945
$135$	4.51346e8	0.116952
$136$	6.32341e8	0.158499
$137$	−3.53989e9	−0.858515	−0.429257	−	0.903182i	$-0.641225\pi$
$137$	−3.53989e9	−0.858515	−0.429257	+	0.903182i	$0.641225\pi$
$138$	8.53233e8	0.200268
$139$	−5.73253e9	−1.30251	−0.651253	−	0.758861i	$-0.725756\pi$
$139$	−5.73253e9	−1.30251	−0.651253	+	0.758861i	$0.725756\pi$
$140$	8.40321e8	0.184871
$141$	4.80038e9	1.02280
$142$	9.76262e8	0.201497
$143$	−2.38788e9	−0.477530
$144$	−1.36398e9	−0.264349
$145$	3.25987e9	0.612413
$146$	3.68520e9	0.671233
$147$	6.49889e9	1.14792
$148$	−1.11518e9	−0.191060
$149$	9.46531e8	0.157325	0.0786623	−	0.996901i	$-0.474935\pi$
$149$	9.46531e8	0.157325	0.0786623	+	0.996901i	$0.474935\pi$
$150$	2.04947e9	0.330545
$151$	−2.23980e9	−0.350601	−0.175300	−	0.984515i	$-0.556090\pi$
$151$	−2.23980e9	−0.350601	−0.175300	+	0.984515i	$0.556090\pi$
$152$	−1.61172e9	−0.244902
$153$	3.35465e8	0.0494921
$154$	7.68433e9	1.10094
$155$	2.49126e9	0.346679
$156$	5.11547e8	0.0691552
$157$	5.26627e9	0.691759	0.345879	−	0.938279i	$-0.387581\pi$
$157$	5.26627e9	0.691759	0.345879	+	0.938279i	$0.387581\pi$
$158$	4.03950e8	0.0515668
$159$	6.26823e9	0.777782
$160$	−1.75115e9	−0.211244
$161$	5.63157e9	0.660561
$162$	−8.84185e8	−0.100862
$163$	−1.32402e10	−1.46910	−0.734549	−	0.678555i	$-0.762606\pi$
$163$	−1.32402e10	−1.46910	−0.734549	+	0.678555i	$0.762606\pi$
$164$	−6.68767e8	−0.0721901
$165$	2.34365e9	0.246158
$166$	2.69845e9	0.275821
$167$	7.00707e9	0.697128	0.348564	−	0.937285i	$-0.386669\pi$
$167$	7.00707e9	0.697128	0.348564	+	0.937285i	$0.386669\pi$
$168$	−1.10004e10	−1.06541
$169$	−5.69181e9	−0.536736
$170$	−8.91938e8	−0.0819058
$171$	−8.55036e8	−0.0764719
$172$	−2.76341e9	−0.240750
$173$	−1.50089e10	−1.27392	−0.636959	−	0.770898i	$-0.719808\pi$
$173$	−1.50089e10	−1.27392	−0.636959	+	0.770898i	$0.719808\pi$
$174$	−6.38607e9	−0.528156
$175$	1.35270e10	1.09026
$176$	−7.08258e9	−0.556397
$177$	−1.53856e9	−0.117824
$178$	−1.48793e10	−1.11094
$179$	−1.33981e10	−0.975451	−0.487726	−	0.872997i	$-0.662173\pi$
$179$	−1.33981e10	−0.975451	−0.487726	+	0.872997i	$0.662173\pi$
$180$	−5.02071e8	−0.0356483
$181$	2.66668e10	1.84679	0.923395	−	0.383852i	$-0.125403\pi$
$181$	2.66668e10	1.84679	0.923395	+	0.383852i	$0.125403\pi$
$182$	−1.58093e10	−1.06805
$183$	−9.83225e9	−0.648072
$184$	−6.34240e9	−0.407918
$185$	1.05114e10	0.659762
$186$	−4.88038e9	−0.298982
$187$	1.74193e9	0.104170
$188$	−5.33988e9	−0.311761
$189$	−5.83586e9	−0.332680
$190$	2.27338e9	0.126555
$191$	−2.27990e10	−1.23956	−0.619778	−	0.784777i	$-0.712778\pi$
$191$	−2.27990e10	−1.23956	−0.619778	+	0.784777i	$0.712778\pi$
$192$	1.20522e10	0.640046
$193$	1.04482e10	0.542042	0.271021	−	0.962573i	$-0.412639\pi$
$193$	1.04482e10	0.542042	0.271021	+	0.962573i	$0.412639\pi$
$194$	5.63399e9	0.285567
$195$	−4.82169e9	−0.238805
$196$	−7.22928e9	−0.349899
$197$	1.56378e10	0.739736	0.369868	−	0.929084i	$-0.379403\pi$
$197$	1.56378e10	0.739736	0.369868	+	0.929084i	$0.379403\pi$
$198$	−4.59120e9	−0.212291
$199$	2.43388e10	1.10017	0.550086	−	0.835108i	$-0.314595\pi$
$199$	2.43388e10	1.10017	0.550086	+	0.835108i	$0.314595\pi$
$200$	−1.52345e10	−0.673275
$201$	1.67706e10	0.724713
$202$	−3.80924e9	−0.160975
$203$	−4.21498e10	−1.74206
$204$	−3.73167e8	−0.0150858
$205$	6.30360e9	0.249285
$206$	−2.40611e10	−0.930920
$207$	−3.36472e9	−0.127375
$208$	1.45713e10	0.539776
$209$	−4.43984e9	−0.160957
$210$	1.55165e10	0.550561
$211$	−4.12068e10	−1.43119	−0.715595	−	0.698515i	$-0.753845\pi$
$211$	−4.12068e10	−1.43119	−0.715595	+	0.698515i	$0.753845\pi$
$212$	−6.97270e9	−0.237077
$213$	−3.84989e9	−0.128156
$214$	−4.82702e10	−1.57332
$215$	2.60470e10	0.831353
$216$	6.57248e9	0.205441
$217$	−3.22118e10	−0.986158
$218$	1.76979e10	0.530721
$219$	−1.45326e10	−0.426918
$220$	−2.60704e9	−0.0750319
$221$	−3.58374e9	−0.101058
$222$	−2.05918e10	−0.568991
$223$	−3.39769e10	−0.920050	−0.460025	−	0.887906i	$-0.652160\pi$
$223$	−3.39769e10	−0.920050	−0.460025	+	0.887906i	$0.652160\pi$
$224$	2.26422e10	0.600901
$225$	−8.08208e9	−0.210233
$226$	3.30238e10	0.842053
$227$	6.07084e10	1.51751	0.758757	−	0.651374i	$-0.225807\pi$
$227$	6.07084e10	1.51751	0.758757	+	0.651374i	$0.225807\pi$
$228$	9.51131e8	0.0233095
$229$	5.90425e10	1.41875	0.709373	−	0.704833i	$-0.248978\pi$
$229$	5.90425e10	1.41875	0.709373	+	0.704833i	$0.248978\pi$
$230$	8.94617e9	0.210796
$231$	−3.03031e10	−0.700219
$232$	4.74701e10	1.07578
$233$	3.71808e10	0.826452	0.413226	−	0.910629i	$-0.364402\pi$
$233$	3.71808e10	0.826452	0.413226	+	0.910629i	$0.364402\pi$
$234$	9.44567e9	0.205950
$235$	5.03321e10	1.07656
$236$	1.71148e9	0.0359142
$237$	−1.59298e9	−0.0327976
$238$	1.15327e10	0.232988
$239$	6.58294e10	1.30506	0.652529	−	0.757764i	$-0.273708\pi$
$239$	6.58294e10	1.30506	0.652529	+	0.757764i	$0.273708\pi$
$240$	−1.43014e10	−0.278245
$241$	−1.54299e10	−0.294637	−0.147319	−	0.989089i	$-0.547064\pi$
$241$	−1.54299e10	−0.294637	−0.147319	+	0.989089i	$0.547064\pi$
$242$	2.45924e10	0.460927
$243$	3.48678e9	0.0641500
$244$	1.09373e10	0.197540
$245$	6.81410e10	1.20826
$246$	−1.23487e10	−0.214988
$247$	9.13427e9	0.156148
$248$	3.62777e10	0.608985
$249$	−1.06413e10	−0.175428
$250$	5.55599e10	0.899563
$251$	1.16470e11	1.85217	0.926087	−	0.377311i	$-0.123151\pi$
$251$	1.16470e11	1.85217	0.926087	+	0.377311i	$0.123151\pi$
$252$	6.49174e9	0.101405
$253$	−1.74716e10	−0.268096
$254$	−9.85868e10	−1.48617
$255$	3.51736e9	0.0520938
$256$	−3.50909e10	−0.510640
$257$	−8.76554e10	−1.25337	−0.626685	−	0.779272i	$-0.715589\pi$
$257$	−8.76554e10	−1.25337	−0.626685	+	0.779272i	$0.715589\pi$
$258$	−5.10261e10	−0.716974
$259$	−1.35911e11	−1.87675
$260$	5.36358e9	0.0727905
$261$	2.51835e10	0.335918
$262$	−4.82395e10	−0.632480
$263$	5.59843e10	0.721548	0.360774	−	0.932653i	$-0.382513\pi$
$263$	5.59843e10	0.721548	0.360774	+	0.932653i	$0.382513\pi$
$264$	3.41281e10	0.432409
$265$	6.57226e10	0.818668
$266$	−2.93946e10	−0.359998
$267$	5.86765e10	0.706583
$268$	−1.86554e10	−0.220901
$269$	1.34921e11	1.57107	0.785533	−	0.618820i	$-0.212389\pi$
$269$	1.34921e11	1.57107	0.785533	+	0.618820i	$0.212389\pi$
$270$	−9.27070e9	−0.106164
$271$	−1.25689e11	−1.41559	−0.707793	−	0.706420i	$-0.750309\pi$
$271$	−1.25689e11	−1.41559	−0.707793	+	0.706420i	$0.750309\pi$
$272$	−1.06296e10	−0.117749
$273$	6.23440e10	0.679301
$274$	7.27099e10	0.779320
$275$	−4.19668e10	−0.442496
$276$	3.74288e9	0.0388253
$277$	1.41815e10	0.144732	0.0723660	−	0.997378i	$-0.476945\pi$
$277$	1.41815e10	0.144732	0.0723660	+	0.997378i	$0.476945\pi$
$278$	1.17747e11	1.18235
$279$	1.92458e10	0.190159
$280$	−1.15340e11	−1.12142
$281$	−3.28603e9	−0.0314408	−0.0157204	−	0.999876i	$-0.505004\pi$
$281$	−3.28603e9	−0.0314408	−0.0157204	+	0.999876i	$0.505004\pi$
$282$	−9.86004e10	−0.928448
$283$	3.87463e9	0.0359080	0.0179540	−	0.999839i	$-0.494285\pi$
$283$	3.87463e9	0.0359080	0.0179540	+	0.999839i	$0.494285\pi$
$284$	4.28257e9	0.0390635
$285$	−8.96507e9	−0.0804919
$286$	4.90473e10	0.433479
$287$	−8.15049e10	−0.709113
$288$	−1.35282e10	−0.115871
$289$	−1.15974e11	−0.977955
$290$	−6.69581e10	−0.555920
$291$	−2.22176e10	−0.181627
$292$	1.61659e10	0.130130
$293$	−1.07217e11	−0.849885	−0.424943	−	0.905220i	$-0.639706\pi$
$293$	−1.07217e11	−0.849885	−0.424943	+	0.905220i	$0.639706\pi$
$294$	−1.33488e11	−1.04203
$295$	−1.61319e10	−0.124018
$296$	1.53066e11	1.15896
$297$	1.81054e10	0.135022
$298$	−1.94419e10	−0.142812
$299$	3.59450e10	0.260087
$300$	8.99040e9	0.0640816
$301$	−3.36786e11	−2.36486
$302$	4.60057e10	0.318259
$303$	1.50217e10	0.102383
$304$	2.70928e10	0.181937
$305$	−1.03091e11	−0.682139
$306$	−6.89049e9	−0.0449266
$307$	−6.88951e10	−0.442655	−0.221327	−	0.975200i	$-0.571039\pi$
$307$	−6.88951e10	−0.442655	−0.221327	+	0.975200i	$0.571039\pi$
$308$	3.37088e10	0.213435
$309$	9.48848e10	0.592084
$310$	−5.11709e10	−0.314699
$311$	1.72287e10	0.104431	0.0522157	−	0.998636i	$-0.483372\pi$
$311$	1.72287e10	0.104431	0.0522157	+	0.998636i	$0.483372\pi$
$312$	−7.02132e10	−0.419491
$313$	1.38189e11	0.813810	0.406905	−	0.913470i	$-0.366608\pi$
$313$	1.38189e11	0.813810	0.406905	+	0.913470i	$0.366608\pi$
$314$	−1.08170e11	−0.627946
$315$	−6.11891e10	−0.350168
$316$	1.77201e9	0.00999708
$317$	1.08730e11	0.604758	0.302379	−	0.953188i	$-0.402219\pi$
$317$	1.08730e11	0.604758	0.302379	+	0.953188i	$0.402219\pi$
$318$	−1.28750e11	−0.706035
$319$	1.30767e11	0.707035
$320$	1.26368e11	0.673692
$321$	1.90353e11	1.00066
$322$	−1.15673e11	−0.599627
$323$	−6.66334e9	−0.0340628
$324$	−3.87865e9	−0.0195537
$325$	8.63401e10	0.429277
$326$	2.71956e11	1.33358
$327$	−6.97915e10	−0.337550
$328$	9.17927e10	0.437901
$329$	−6.50789e11	−3.06238
$330$	−4.81388e10	−0.223451
$331$	2.09296e11	0.958373	0.479187	−	0.877713i	$-0.340932\pi$
$331$	2.09296e11	0.958373	0.479187	+	0.877713i	$0.340932\pi$
$332$	1.18373e10	0.0534725
$333$	8.12037e10	0.361890
$334$	−1.43926e11	−0.632821
$335$	1.75840e11	0.762809
$336$	1.84916e11	0.791493
$337$	−3.45160e11	−1.45776	−0.728880	−	0.684641i	$-0.759959\pi$
$337$	−3.45160e11	−1.45776	−0.728880	+	0.684641i	$0.759959\pi$
$338$	1.16911e11	0.487224
$339$	−1.30230e11	−0.535563
$340$	−3.91266e9	−0.0158788
$341$	9.99351e10	0.400243
$342$	1.75625e10	0.0694177
$343$	−4.37926e11	−1.70835
$344$	3.79296e11	1.46038
$345$	−3.52792e10	−0.134070
$346$	3.08285e11	1.15640
$347$	3.49438e11	1.29386	0.646930	−	0.762549i	$-0.276053\pi$
$347$	3.49438e11	1.29386	0.646930	+	0.762549i	$0.276053\pi$
$348$	−2.80138e10	−0.102392
$349$	5.41554e11	1.95401	0.977006	−	0.213212i	$-0.0683924\pi$
$349$	5.41554e11	1.95401	0.977006	+	0.213212i	$0.0683924\pi$
$350$	−2.77847e11	−0.989692
$351$	−3.72490e10	−0.130988
$352$	−7.02461e10	−0.243882
$353$	−3.61705e11	−1.23985	−0.619923	−	0.784662i	$-0.712836\pi$
$353$	−3.61705e11	−1.23985	−0.619923	+	0.784662i	$0.712836\pi$
$354$	3.16022e10	0.106956
$355$	−4.03662e10	−0.134893
$356$	−6.52710e10	−0.215375
$357$	−4.54791e10	−0.148185
$358$	2.75199e11	0.885469
$359$	−2.03771e11	−0.647467	−0.323733	−	0.946148i	$-0.604938\pi$
$359$	−2.03771e11	−0.647467	−0.323733	+	0.946148i	$0.604938\pi$
$360$	6.89126e10	0.216241
$361$	1.69836e10	0.0526316
$362$	−5.47739e11	−1.67643
$363$	−9.69802e10	−0.293159
$364$	−6.93506e10	−0.207059
$365$	−1.52375e11	−0.449360
$366$	2.01956e11	0.588290
$367$	2.55387e11	0.734856	0.367428	−	0.930052i	$-0.380238\pi$
$367$	2.55387e11	0.734856	0.367428	+	0.930052i	$0.380238\pi$
$368$	1.06615e11	0.303042
$369$	4.86972e10	0.136737
$370$	−2.15905e11	−0.598902
$371$	−8.49787e11	−2.32877
$372$	−2.14087e10	−0.0579626
$373$	−2.45551e11	−0.656830	−0.328415	−	0.944534i	$-0.606514\pi$
$373$	−2.45551e11	−0.656830	−0.328415	+	0.944534i	$0.606514\pi$
$374$	−3.57794e10	−0.0945608
$375$	−2.19101e11	−0.572141
$376$	7.32934e11	1.89112
$377$	−2.69033e11	−0.685914
$378$	1.19869e11	0.301992
$379$	5.69966e11	1.41897	0.709484	−	0.704722i	$-0.248928\pi$
$379$	5.69966e11	1.41897	0.709484	+	0.704722i	$0.248928\pi$
$380$	9.97263e9	0.0245349
$381$	3.88777e11	0.945232
$382$	4.68295e11	1.12521
$383$	3.15156e11	0.748395	0.374197	−	0.927349i	$-0.377918\pi$
$383$	3.15156e11	0.748395	0.374197	+	0.927349i	$0.377918\pi$
$384$	−1.62043e11	−0.380311
$385$	−3.17729e11	−0.737028
$386$	−2.14607e11	−0.492041
$387$	2.01221e11	0.456010
$388$	2.47146e10	0.0553619
$389$	−1.45206e11	−0.321522	−0.160761	−	0.986993i	$-0.551395\pi$
$389$	−1.45206e11	−0.321522	−0.160761	+	0.986993i	$0.551395\pi$
$390$	9.90381e10	0.216776
$391$	−2.62215e10	−0.0567363
$392$	9.92266e11	2.12247
$393$	1.90232e11	0.402270
$394$	−3.21202e11	−0.671498
$395$	−1.67024e10	−0.0345217
$396$	−2.01402e10	−0.0411562
$397$	6.01437e11	1.21516	0.607579	−	0.794259i	$-0.292141\pi$
$397$	6.01437e11	1.21516	0.607579	+	0.794259i	$0.292141\pi$
$398$	−4.99922e11	−0.998685
$399$	1.15918e11	0.228966
$400$	2.56090e11	0.500175
$401$	−6.07613e11	−1.17348	−0.586742	−	0.809774i	$-0.699590\pi$
$401$	−6.07613e11	−1.17348	−0.586742	+	0.809774i	$0.699590\pi$
$402$	−3.44470e11	−0.657861
$403$	−2.05601e11	−0.388286
$404$	−1.67100e10	−0.0312076
$405$	3.65590e10	0.0675223
$406$	8.65763e11	1.58136
$407$	4.21656e11	0.761700
$408$	5.12196e10	0.0915094
$409$	−6.88220e11	−1.21611	−0.608055	−	0.793895i	$-0.708050\pi$
$409$	−6.88220e11	−1.21611	−0.608055	+	0.793895i	$0.708050\pi$
$410$	−1.29477e11	−0.226289
$411$	−2.86731e11	−0.495664
$412$	−1.05549e11	−0.180474
$413$	2.08583e11	0.352780
$414$	6.91118e10	0.115625
$415$	−1.11575e11	−0.184650
$416$	1.44520e11	0.236597
$417$	−4.64335e11	−0.752002
$418$	9.11948e10	0.146109
$419$	−3.71568e10	−0.0588946	−0.0294473	−	0.999566i	$-0.509375\pi$
$419$	−3.71568e10	−0.0588946	−0.0294473	+	0.999566i	$0.509375\pi$
$420$	6.80660e10	0.106735
$421$	5.58155e11	0.865935	0.432968	−	0.901410i	$-0.357466\pi$
$421$	5.58155e11	0.865935	0.432968	+	0.901410i	$0.357466\pi$
$422$	8.46392e11	1.29917
$423$	3.88831e11	0.590512
$424$	9.57049e11	1.43810
$425$	−6.29840e10	−0.0936441
$426$	7.90772e10	0.116334
$427$	1.33296e12	1.94041
$428$	−2.11747e11	−0.305014
$429$	−1.93418e11	−0.275702
$430$	−5.35010e11	−0.754664
$431$	−9.86246e11	−1.37669	−0.688347	−	0.725381i	$-0.741663\pi$
$431$	−9.86246e11	−1.37669	−0.688347	+	0.725381i	$0.741663\pi$
$432$	−1.10483e11	−0.152622
$433$	−1.02917e12	−1.40699	−0.703497	−	0.710698i	$-0.748379\pi$
$433$	−1.02917e12	−1.40699	−0.703497	+	0.710698i	$0.748379\pi$
$434$	6.61635e11	0.895188
$435$	2.64050e11	0.353577
$436$	7.76352e10	0.102889
$437$	6.68334e10	0.0876652
$438$	2.98501e11	0.387537
$439$	−4.94349e11	−0.635248	−0.317624	−	0.948217i	$-0.602885\pi$
$439$	−4.94349e11	−0.635248	−0.317624	+	0.948217i	$0.602885\pi$
$440$	3.57834e11	0.455139
$441$	5.26410e11	0.662751
$442$	7.36105e10	0.0917360
$443$	−1.37930e12	−1.70153	−0.850767	−	0.525544i	$-0.823862\pi$
$443$	−1.37930e12	−1.70153	−0.850767	+	0.525544i	$0.823862\pi$
$444$	−9.03300e10	−0.110308
$445$	6.15224e11	0.743727
$446$	6.97889e11	0.835179
$447$	7.66690e10	0.0908314
$448$	−1.63392e12	−1.91638
$449$	5.05483e11	0.586945	0.293473	−	0.955967i	$-0.405189\pi$
$449$	5.05483e11	0.586945	0.293473	+	0.955967i	$0.405189\pi$
$450$	1.66007e11	0.190840
$451$	2.52864e11	0.287801
$452$	1.44866e11	0.163246
$453$	−1.81424e11	−0.202419
$454$	−1.24696e12	−1.37753
$455$	6.53678e11	0.715011
$456$	−1.30549e11	−0.141394
$457$	6.35644e11	0.681696	0.340848	−	0.940118i	$-0.389286\pi$
$457$	6.35644e11	0.681696	0.340848	+	0.940118i	$0.389286\pi$
$458$	−1.21274e12	−1.28787
$459$	2.71727e10	0.0285743
$460$	3.92441e10	0.0408662
$461$	−1.63724e12	−1.68834	−0.844168	−	0.536078i	$-0.819905\pi$
$461$	−1.63724e12	−1.68834	−0.844168	+	0.536078i	$0.819905\pi$
$462$	6.22430e11	0.635626
$463$	2.10608e11	0.212990	0.106495	−	0.994313i	$-0.466037\pi$
$463$	2.10608e11	0.212990	0.106495	+	0.994313i	$0.466037\pi$
$464$	−7.97966e11	−0.799197
$465$	2.01792e11	0.200155
$466$	−7.63699e11	−0.750215
$467$	1.74185e12	1.69467	0.847333	−	0.531062i	$-0.178207\pi$
$467$	1.74185e12	1.69467	0.847333	+	0.531062i	$0.178207\pi$
$468$	4.14353e10	0.0399268
$469$	−2.27359e12	−2.16988
$470$	−1.03383e12	−0.977255
$471$	4.26568e11	0.399387
$472$	−2.34911e11	−0.217854
$473$	1.04486e12	0.959802
$474$	3.27199e10	0.0297721
$475$	1.60534e11	0.144693
$476$	5.05904e10	0.0451686
$477$	5.07727e11	0.449053
$478$	−1.35214e12	−1.18467
$479$	−1.89986e12	−1.64897	−0.824484	−	0.565886i	$-0.808534\pi$
$479$	−1.89986e12	−1.64897	−0.824484	+	0.565886i	$0.808534\pi$
$480$	−1.41843e11	−0.121962
$481$	−8.67492e11	−0.738946
$482$	3.16933e11	0.267458
$483$	4.56157e11	0.381375
$484$	1.07879e11	0.0893583
$485$	−2.32953e11	−0.191174
$486$	−7.16190e10	−0.0582324
$487$	8.58404e11	0.691530	0.345765	−	0.938321i	$-0.387619\pi$
$487$	8.58404e11	0.691530	0.345765	+	0.938321i	$0.387619\pi$
$488$	−1.50121e12	−1.19826
$489$	−1.07246e12	−0.848184
$490$	−1.39962e12	−1.09680
$491$	−1.56518e12	−1.21534	−0.607671	−	0.794189i	$-0.707896\pi$
$491$	−1.56518e12	−1.21534	−0.607671	+	0.794189i	$0.707896\pi$
$492$	−5.41701e10	−0.0416790
$493$	1.96256e11	0.149628
$494$	−1.87619e11	−0.141744
$495$	1.89835e11	0.142120
$496$	−6.09823e11	−0.452415
$497$	5.21931e11	0.383716
$498$	2.18574e11	0.159245
$499$	2.19579e12	1.58540	0.792699	−	0.609613i	$-0.208675\pi$
$499$	2.19579e12	1.58540	0.792699	+	0.609613i	$0.208675\pi$
$500$	2.43725e11	0.174395
$501$	5.67573e11	0.402487
$502$	−2.39230e12	−1.68132
$503$	1.32838e12	0.925264	0.462632	−	0.886550i	$-0.346905\pi$
$503$	1.32838e12	0.925264	0.462632	+	0.886550i	$0.346905\pi$
$504$	−8.91033e11	−0.615115
$505$	1.57503e11	0.107765
$506$	3.58868e11	0.243365
$507$	−4.61037e11	−0.309884
$508$	−4.32471e11	−0.288118
$509$	−1.22144e12	−0.806568	−0.403284	−	0.915075i	$-0.632131\pi$
$509$	−1.22144e12	−0.806568	−0.403284	+	0.915075i	$0.632131\pi$
$510$	−7.22470e10	−0.0472883
$511$	1.97019e12	1.27824
$512$	1.74504e12	1.12225
$513$	−6.92579e10	−0.0441511
$514$	1.80045e12	1.13775
$515$	9.94870e11	0.623209
$516$	−2.23836e11	−0.138997
$517$	2.01903e12	1.24290
$518$	2.79164e12	1.70363
$519$	−1.21572e12	−0.735497
$520$	−7.36187e11	−0.441543
$521$	3.75797e11	0.223451	0.111726	−	0.993739i	$-0.464362\pi$
$521$	3.75797e11	0.223451	0.111726	+	0.993739i	$0.464362\pi$
$522$	−5.17272e11	−0.304931
$523$	1.79674e12	1.05009	0.525047	−	0.851073i	$-0.324048\pi$
$523$	1.79674e12	1.05009	0.525047	+	0.851073i	$0.324048\pi$
$524$	−2.11612e11	−0.122617
$525$	1.09569e12	0.629464
$526$	−1.14992e12	−0.654988
$527$	1.49983e11	0.0847022
$528$	−5.73689e11	−0.321236
$529$	−1.53815e12	−0.853981
$530$	−1.34995e12	−0.743149
$531$	−1.24623e11	−0.0680259
$532$	−1.28945e11	−0.0697916
$533$	−5.20228e11	−0.279204
$534$	−1.20522e12	−0.641404
$535$	1.99586e12	1.05327
$536$	2.56057e12	1.33997
$537$	−1.08525e12	−0.563177
$538$	−2.77129e12	−1.42614
$539$	2.73342e12	1.39495
$540$	−4.06678e10	−0.0205816
$541$	1.40714e12	0.706235	0.353118	−	0.935579i	$-0.385122\pi$
$541$	1.40714e12	0.706235	0.353118	+	0.935579i	$0.385122\pi$
$542$	2.58167e12	1.28500
$543$	2.16001e12	1.06624
$544$	−1.05426e11	−0.0516121
$545$	−7.31766e11	−0.355294
$546$	−1.28055e12	−0.616638
$547$	−1.35959e12	−0.649330	−0.324665	−	0.945829i	$-0.605252\pi$
$547$	−1.35959e12	−0.649330	−0.324665	+	0.945829i	$0.605252\pi$
$548$	3.18956e11	0.151084
$549$	−7.96412e11	−0.374164
$550$	8.62003e11	0.401677
$551$	−5.00219e11	−0.231195
$552$	−5.13734e11	−0.235512
$553$	2.15960e11	0.0981999
$554$	−2.91291e11	−0.131381
$555$	8.51423e11	0.380914
$556$	5.16520e11	0.229219
$557$	4.99582e11	0.219917	0.109958	−	0.993936i	$-0.464928\pi$
$557$	4.99582e11	0.219917	0.109958	+	0.993936i	$0.464928\pi$
$558$	−3.95311e11	−0.172617
$559$	−2.14963e12	−0.931130
$560$	1.93884e12	0.833100
$561$	1.41096e11	0.0601426
$562$	6.74955e10	0.0285405
$563$	2.30144e12	0.965412	0.482706	−	0.875782i	$-0.339654\pi$
$563$	2.30144e12	0.965412	0.482706	+	0.875782i	$0.339654\pi$
$564$	−4.32530e11	−0.179995
$565$	−1.36546e12	−0.563717
$566$	−7.95854e10	−0.0325957
$567$	−4.72705e11	−0.192073
$568$	−5.87810e11	−0.236957
$569$	−1.47757e12	−0.590938	−0.295469	−	0.955352i	$-0.595476\pi$
$569$	−1.47757e12	−0.590938	−0.295469	+	0.955352i	$0.595476\pi$
$570$	1.84144e11	0.0730668
$571$	3.51997e12	1.38572	0.692861	−	0.721071i	$-0.256350\pi$
$571$	3.51997e12	1.38572	0.692861	+	0.721071i	$0.256350\pi$
$572$	2.15156e11	0.0840371
$573$	−1.84672e12	−0.715659
$574$	1.67412e12	0.643700
$575$	6.31732e11	0.241006
$576$	9.76230e11	0.369531
$577$	1.93159e12	0.725476	0.362738	−	0.931891i	$-0.381842\pi$
$577$	1.93159e12	0.725476	0.362738	+	0.931891i	$0.381842\pi$
$578$	2.38211e12	0.887742
$579$	8.46303e11	0.312948
$580$	−2.93725e11	−0.107774
$581$	1.44265e12	0.525252
$582$	4.56353e11	0.164872
$583$	2.63641e12	0.945158
$584$	−2.21887e12	−0.789359
$585$	−3.90557e11	−0.137874
$586$	2.20225e12	0.771486
$587$	−2.05383e11	−0.0713990	−0.0356995	−	0.999363i	$-0.511366\pi$
$587$	−2.05383e11	−0.0713990	−0.0356995	+	0.999363i	$0.511366\pi$
$588$	−5.85572e11	−0.202014
$589$	−3.82278e11	−0.130876
$590$	3.31350e11	0.112578
$591$	1.26666e12	0.427087
$592$	−2.57303e12	−0.860988
$593$	6.35391e11	0.211006	0.105503	−	0.994419i	$-0.466355\pi$
$593$	6.35391e11	0.211006	0.105503	+	0.994419i	$0.466355\pi$
$594$	−3.71887e11	−0.122567
$595$	−4.76850e11	−0.155975
$596$	−8.52856e10	−0.0276865
$597$	1.97144e12	0.635185
$598$	−7.38316e11	−0.236095
$599$	−2.77298e12	−0.880089	−0.440044	−	0.897976i	$-0.645037\pi$
$599$	−2.77298e12	−0.880089	−0.440044	+	0.897976i	$0.645037\pi$
$600$	−1.23399e12	−0.388715
$601$	6.08041e11	0.190107	0.0950534	−	0.995472i	$-0.469698\pi$
$601$	6.08041e11	0.190107	0.0950534	+	0.995472i	$0.469698\pi$
$602$	6.91762e12	2.14671
$603$	1.35842e12	0.418413
$604$	2.01813e11	0.0616998
$605$	−1.01684e12	−0.308570
$606$	−3.08549e11	−0.0929387
$607$	2.15450e12	0.644164	0.322082	−	0.946712i	$-0.395617\pi$
$607$	2.15450e12	0.644164	0.322082	+	0.946712i	$0.395617\pi$
$608$	2.68710e11	0.0797476
$609$	−3.41414e12	−1.00578
$610$	2.11751e12	0.619215
$611$	−4.15384e12	−1.20577
$612$	−3.02265e10	−0.00870977
$613$	7.03883e11	0.201339	0.100670	−	0.994920i	$-0.467901\pi$
$613$	7.03883e11	0.201339	0.100670	+	0.994920i	$0.467901\pi$
$614$	1.41511e12	0.401822
$615$	5.10591e11	0.143925
$616$	−4.62676e12	−1.29468
$617$	−1.79432e12	−0.498445	−0.249222	−	0.968446i	$-0.580175\pi$
$617$	−1.79432e12	−0.498445	−0.249222	+	0.968446i	$0.580175\pi$
$618$	−1.94895e12	−0.537467
$619$	−1.11310e12	−0.304737	−0.152369	−	0.988324i	$-0.548690\pi$
$619$	−1.11310e12	−0.304737	−0.152369	+	0.988324i	$0.548690\pi$
$620$	−2.24471e11	−0.0610096
$621$	−2.72543e11	−0.0735398
$622$	−3.53880e11	−0.0947980
$623$	−7.95479e12	−2.11560
$624$	1.18028e12	0.311640
$625$	1.08655e11	0.0284834
$626$	−2.83841e12	−0.738739
$627$	−3.59627e11	−0.0929284
$628$	−4.74508e11	−0.121738
$629$	6.32824e11	0.161196
$630$	1.25683e12	0.317867
$631$	−5.70160e12	−1.43174	−0.715870	−	0.698233i	$-0.753970\pi$
$631$	−5.70160e12	−1.43174	−0.715870	+	0.698233i	$0.753970\pi$
$632$	−2.43219e11	−0.0606417
$633$	−3.33775e12	−0.826298
$634$	−2.23332e12	−0.548971
$635$	4.07634e12	0.994921
$636$	−5.64789e11	−0.136877
$637$	−5.62359e12	−1.35328
$638$	−2.68597e12	−0.641813
$639$	−3.11841e11	−0.0739911
$640$	−1.69902e12	−0.400303
$641$	−4.47302e12	−1.04650	−0.523251	−	0.852179i	$-0.675281\pi$
$641$	−4.47302e12	−1.04650	−0.523251	+	0.852179i	$0.675281\pi$
$642$	−3.90988e12	−0.908356
$643$	3.99810e12	0.922369	0.461184	−	0.887304i	$-0.347425\pi$
$643$	3.99810e12	0.922369	0.461184	+	0.887304i	$0.347425\pi$
$644$	−5.07423e11	−0.116248
$645$	2.10981e12	0.479982
$646$	1.36866e11	0.0309206
$647$	2.07881e12	0.466385	0.233193	−	0.972431i	$-0.425083\pi$
$647$	2.07881e12	0.466385	0.233193	+	0.972431i	$0.425083\pi$
$648$	5.32371e11	0.118611
$649$	−6.47117e11	−0.143180
$650$	−1.77344e12	−0.389678
$651$	−2.60916e12	−0.569358
$652$	1.19299e12	0.258537
$653$	9.14519e12	1.96826	0.984132	−	0.177436i	$-0.0567802\pi$
$653$	9.14519e12	1.96826	0.984132	+	0.177436i	$0.0567802\pi$
$654$	1.43353e12	0.306412
$655$	1.99459e12	0.423417
$656$	−1.54302e12	−0.325316
$657$	−1.17714e12	−0.246481
$658$	1.33673e13	2.77989
$659$	6.16598e12	1.27355	0.636777	−	0.771048i	$-0.280267\pi$
$659$	6.16598e12	1.27355	0.636777	+	0.771048i	$0.280267\pi$
$660$	−2.11170e11	−0.0433197
$661$	−7.12362e12	−1.45142	−0.725712	−	0.687999i	$-0.758489\pi$
$661$	−7.12362e12	−1.45142	−0.725712	+	0.687999i	$0.758489\pi$
$662$	−4.29896e12	−0.869967
$663$	−2.90283e11	−0.0583460
$664$	−1.62474e12	−0.324361
$665$	1.21540e12	0.241002
$666$	−1.66793e12	−0.328507
$667$	−1.96845e12	−0.385087
$668$	−6.31361e11	−0.122683
$669$	−2.75213e12	−0.531191
$670$	−3.61177e12	−0.692443
$671$	−4.13543e12	−0.787534
$672$	1.83402e12	0.346931
$673$	−5.12635e11	−0.0963253	−0.0481627	−	0.998840i	$-0.515337\pi$
$673$	−5.12635e11	−0.0963253	−0.0481627	+	0.998840i	$0.515337\pi$
$674$	7.08963e12	1.32329
$675$	−6.54649e11	−0.121378
$676$	5.12851e11	0.0944564
$677$	−5.87594e12	−1.07505	−0.537525	−	0.843248i	$-0.680641\pi$
$677$	−5.87594e12	−1.07505	−0.537525	+	0.843248i	$0.680641\pi$
$678$	2.67493e12	0.486160
$679$	3.01206e12	0.543812
$680$	5.37039e11	0.0963198
$681$	4.91738e12	0.876137
$682$	−2.05268e12	−0.363322
$683$	−2.56410e12	−0.450859	−0.225430	−	0.974259i	$-0.572379\pi$
$683$	−2.56410e12	−0.450859	−0.225430	+	0.974259i	$0.572379\pi$
$684$	7.70416e10	0.0134578
$685$	−3.00639e12	−0.521720
$686$	8.99505e12	1.55076
$687$	4.78244e12	0.819114
$688$	−6.37592e12	−1.08491
$689$	−5.42400e12	−0.916924
$690$	7.24639e11	0.121703
$691$	5.81266e12	0.969892	0.484946	−	0.874544i	$-0.338839\pi$
$691$	5.81266e12	0.969892	0.484946	+	0.874544i	$0.338839\pi$
$692$	1.35235e12	0.224188
$693$	−2.45455e12	−0.404272
$694$	−7.17750e12	−1.17451
$695$	−4.86856e12	−0.791533
$696$	3.84508e12	0.621103
$697$	3.79499e11	0.0609065
$698$	−1.11236e13	−1.77376
$699$	3.01165e12	0.477152
$700$	−1.21883e12	−0.191868
$701$	−3.02109e12	−0.472534	−0.236267	−	0.971688i	$-0.575924\pi$
$701$	−3.02109e12	−0.472534	−0.236267	+	0.971688i	$0.575924\pi$
$702$	7.65099e11	0.118905
$703$	−1.61295e12	−0.249070
$704$	5.06915e12	0.777782
$705$	4.07690e12	0.621554
$706$	7.42946e12	1.12548
$707$	−2.03650e12	−0.306548
$708$	1.38630e11	0.0207351
$709$	3.97322e12	0.590521	0.295260	−	0.955417i	$-0.404594\pi$
$709$	3.97322e12	0.590521	0.295260	+	0.955417i	$0.404594\pi$
$710$	8.29126e11	0.122450
$711$	−1.29031e11	−0.0189357
$712$	8.95887e12	1.30645
$713$	−1.50434e12	−0.217993
$714$	9.34147e11	0.134516
$715$	−2.02800e12	−0.290195
$716$	1.20722e12	0.171663
$717$	5.33218e12	0.753475
$718$	4.18548e12	0.587740
$719$	2.05393e12	0.286619	0.143309	−	0.989678i	$-0.454226\pi$
$719$	2.05393e12	0.286619	0.143309	+	0.989678i	$0.454226\pi$
$720$	−1.15841e12	−0.160645
$721$	−1.28636e13	−1.77277
$722$	−3.48844e11	−0.0477765
$723$	−1.24983e12	−0.170109
$724$	−2.40277e12	−0.325004
$725$	−4.72823e12	−0.635591
$726$	1.99198e12	0.266116
$727$	−4.17857e12	−0.554782	−0.277391	−	0.960757i	$-0.589470\pi$
$727$	−4.17857e12	−0.554782	−0.277391	+	0.960757i	$0.589470\pi$
$728$	9.51883e12	1.25601
$729$	2.82430e11	0.0370370
$730$	3.12979e12	0.407909
$731$	1.56813e12	0.203120
$732$	8.85919e11	0.114050
$733$	1.19821e13	1.53308	0.766541	−	0.642195i	$-0.221976\pi$
$733$	1.19821e13	1.53308	0.766541	+	0.642195i	$0.221976\pi$
$734$	−5.24569e12	−0.667068
$735$	5.51942e12	0.697590
$736$	1.05742e12	0.132831
$737$	7.05368e12	0.880668
$738$	−1.00025e12	−0.124123
$739$	−1.39659e13	−1.72254	−0.861271	−	0.508145i	$-0.830331\pi$
$739$	−1.39659e13	−1.72254	−0.861271	+	0.508145i	$0.830331\pi$
$740$	−9.47112e11	−0.116107
$741$	7.39876e11	0.0901524
$742$	1.74547e13	2.11395
$743$	1.20423e13	1.44964	0.724818	−	0.688940i	$-0.241924\pi$
$743$	1.20423e13	1.44964	0.724818	+	0.688940i	$0.241924\pi$
$744$	2.93849e12	0.351598
$745$	8.03877e11	0.0956062
$746$	5.04366e12	0.596240
$747$	−8.61947e11	−0.101283
$748$	−1.56954e11	−0.0183322
$749$	−2.58063e13	−2.99611
$750$	4.50035e12	0.519363
$751$	2.32972e11	0.0267254	0.0133627	−	0.999911i	$-0.495746\pi$
$751$	2.32972e11	0.0267254	0.0133627	+	0.999911i	$0.495746\pi$
$752$	−1.23205e13	−1.40491
$753$	9.43405e12	1.06935
$754$	5.52597e12	0.622641
$755$	−1.90223e12	−0.213060
$756$	5.25831e11	0.0585461
$757$	1.72848e12	0.191307	0.0956537	−	0.995415i	$-0.469506\pi$
$757$	1.72848e12	0.191307	0.0956537	+	0.995415i	$0.469506\pi$
$758$	−1.17072e13	−1.28807
$759$	−1.41520e12	−0.154785
$760$	−1.36881e12	−0.148827
$761$	5.62773e12	0.608278	0.304139	−	0.952628i	$-0.401631\pi$
$761$	5.62773e12	0.608278	0.304139	+	0.952628i	$0.401631\pi$
$762$	−7.98553e12	−0.858038
$763$	9.46167e12	1.01067
$764$	2.05427e12	0.218141
$765$	2.84906e11	0.0300764
$766$	−6.47334e12	−0.679358
$767$	1.33134e12	0.138903
$768$	−2.84236e12	−0.294818
$769$	1.05077e13	1.08353	0.541765	−	0.840530i	$-0.317756\pi$
$769$	1.05077e13	1.08353	0.541765	+	0.840530i	$0.317756\pi$
$770$	6.52620e12	0.669040
$771$	−7.10008e12	−0.723634
$772$	−9.41416e11	−0.0953902
$773$	8.46560e12	0.852805	0.426403	−	0.904533i	$-0.359781\pi$
$773$	8.46560e12	0.852805	0.426403	+	0.904533i	$0.359781\pi$
$774$	−4.13311e12	−0.413945
$775$	−3.61342e12	−0.359800
$776$	−3.39224e12	−0.335822
$777$	−1.10088e13	−1.08354
$778$	2.98255e12	0.291863
$779$	−9.67271e11	−0.0941087
$780$	4.34450e11	0.0420256
$781$	−1.61926e12	−0.155735
$782$	5.38592e11	0.0515026
$783$	2.03986e12	0.193943
$784$	−1.66799e13	−1.57678
$785$	4.47257e12	0.420382
$786$	−3.90740e12	−0.365162
$787$	−1.21018e13	−1.12451	−0.562255	−	0.826964i	$-0.690066\pi$
$787$	−1.21018e13	−1.12451	−0.562255	+	0.826964i	$0.690066\pi$
$788$	−1.40901e12	−0.130181
$789$	4.53473e12	0.416586
$790$	3.43069e11	0.0313372
$791$	1.76553e13	1.60354
$792$	2.76438e12	0.249651
$793$	8.50800e12	0.764009
$794$	−1.23536e13	−1.10306
$795$	5.32353e12	0.472658
$796$	−2.19301e12	−0.193612
$797$	−6.33723e11	−0.0556336	−0.0278168	−	0.999613i	$-0.508856\pi$
$797$	−6.33723e11	−0.0556336	−0.0278168	+	0.999613i	$0.508856\pi$
$798$	−2.38096e12	−0.207845
$799$	3.03018e12	0.263031
$800$	2.53993e12	0.219239
$801$	4.75279e12	0.407946
$802$	1.24804e13	1.06524
$803$	−6.11239e12	−0.518789
$804$	−1.51109e12	−0.127537
$805$	4.78282e12	0.401423
$806$	4.22307e12	0.352468
$807$	1.09286e13	0.907055
$808$	2.29356e12	0.189303
$809$	−2.06139e13	−1.69197	−0.845983	−	0.533209i	$-0.820986\pi$
$809$	−2.06139e13	−1.69197	−0.845983	+	0.533209i	$0.820986\pi$
$810$	−7.50927e11	−0.0612936
$811$	8.21265e12	0.666637	0.333319	−	0.942814i	$-0.391832\pi$
$811$	8.21265e12	0.666637	0.333319	+	0.942814i	$0.391832\pi$
$812$	3.79784e12	0.306573
$813$	−1.01808e13	−0.817289
$814$	−8.66088e12	−0.691436
$815$	−1.12447e13	−0.892772
$816$	−8.60996e11	−0.0679822
$817$	−3.99686e12	−0.313848
$818$	1.41361e13	1.10393
$819$	5.04986e12	0.392195
$820$	−5.67975e11	−0.0438699
$821$	−5.92048e11	−0.0454792	−0.0227396	−	0.999741i	$-0.507239\pi$
$821$	−5.92048e11	−0.0454792	−0.0227396	+	0.999741i	$0.507239\pi$
$822$	5.88950e12	0.449941
$823$	2.20763e13	1.67737	0.838683	−	0.544620i	$-0.183326\pi$
$823$	2.20763e13	1.67737	0.838683	+	0.544620i	$0.183326\pi$
$824$	1.44872e13	1.09475
$825$	−3.39931e12	−0.255475
$826$	−4.28433e12	−0.320238
$827$	8.40134e12	0.624559	0.312280	−	0.949990i	$-0.398907\pi$
$827$	8.40134e12	0.624559	0.312280	+	0.949990i	$0.398907\pi$
$828$	3.03173e11	0.0224158
$829$	−1.32215e13	−0.972266	−0.486133	−	0.873885i	$-0.661593\pi$
$829$	−1.32215e13	−0.972266	−0.486133	+	0.873885i	$0.661593\pi$
$830$	2.29175e12	0.167616
$831$	1.14870e12	0.0835610
$832$	−1.04290e13	−0.754547
$833$	4.10234e12	0.295208
$834$	9.53749e12	0.682632
$835$	5.95102e12	0.423645
$836$	4.00044e11	0.0283257
$837$	1.55891e12	0.109788
$838$	7.63206e11	0.0534618
$839$	−2.02530e13	−1.41111	−0.705554	−	0.708657i	$-0.749302\pi$
$839$	−2.02530e13	−1.41111	−0.705554	+	0.708657i	$0.749302\pi$
$840$	−9.34251e12	−0.647451
$841$	2.25874e11	0.0155698
$842$	−1.14646e13	−0.786056
$843$	−2.66169e11	−0.0181524
$844$	3.71287e12	0.251865
$845$	−4.83398e12	−0.326174
$846$	−7.98663e12	−0.536040
$847$	1.31476e13	0.877753
$848$	−1.60879e13	−1.06836
$849$	3.13845e11	0.0207315
$850$	1.29370e12	0.0850057
$851$	−6.34725e12	−0.414861
$852$	3.46888e11	0.0225533
$853$	−2.08420e13	−1.34794	−0.673968	−	0.738761i	$-0.735411\pi$
$853$	−2.08420e13	−1.34794	−0.673968	+	0.738761i	$0.735411\pi$
$854$	−2.73792e13	−1.76141
$855$	−7.26171e11	−0.0464720
$856$	2.90636e13	1.85020
$857$	−2.03554e13	−1.28904	−0.644521	−	0.764587i	$-0.722943\pi$
$857$	−2.03554e13	−1.28904	−0.644521	+	0.764587i	$0.722943\pi$
$858$	3.97283e12	0.250269
$859$	3.16587e13	1.98392	0.991958	−	0.126569i	$-0.0403964\pi$
$859$	3.16587e13	1.98392	0.991958	+	0.126569i	$0.0403964\pi$
$860$	−2.34693e12	−0.146304
$861$	−6.60190e12	−0.409406
$862$	2.02576e13	1.24970
$863$	−5.17762e12	−0.317747	−0.158874	−	0.987299i	$-0.550786\pi$
$863$	−5.17762e12	−0.317747	−0.158874	+	0.987299i	$0.550786\pi$
$864$	−1.09578e12	−0.0668979
$865$	−1.27469e13	−0.774160
$866$	2.11393e13	1.27720
$867$	−9.39386e12	−0.564622
$868$	2.90239e12	0.173547
$869$	−6.70003e11	−0.0398555
$870$	−5.42361e12	−0.320961
$871$	−1.45118e13	−0.854360
$872$	−1.06559e13	−0.624119
$873$	−1.79963e12	−0.104862
$874$	−1.37277e12	−0.0795784
$875$	2.97036e13	1.71306
$876$	1.30944e12	0.0751304
$877$	1.52428e13	0.870093	0.435047	−	0.900408i	$-0.356732\pi$
$877$	1.52428e13	0.870093	0.435047	+	0.900408i	$0.356732\pi$
$878$	1.01540e13	0.576649
$879$	−8.68459e12	−0.490681
$880$	−6.01514e12	−0.338122
$881$	−1.32512e13	−0.741079	−0.370539	−	0.928817i	$-0.620827\pi$
$881$	−1.32512e13	−0.741079	−0.370539	+	0.928817i	$0.620827\pi$
$882$	−1.08125e13	−0.601615
$883$	−4.17400e12	−0.231062	−0.115531	−	0.993304i	$-0.536857\pi$
$883$	−4.17400e12	−0.231062	−0.115531	+	0.993304i	$0.536857\pi$
$884$	3.22907e11	0.0177845
$885$	−1.30668e12	−0.0716019
$886$	2.83309e13	1.54457
$887$	2.81553e13	1.52723	0.763613	−	0.645674i	$-0.223423\pi$
$887$	2.81553e13	1.52723	0.763613	+	0.645674i	$0.223423\pi$
$888$	1.23984e13	0.669124
$889$	−5.27067e13	−2.83014
$890$	−1.26368e13	−0.675121
$891$	1.46654e12	0.0779549
$892$	3.06143e12	0.161913
$893$	−7.72334e12	−0.406418
$894$	−1.57479e12	−0.0824526
$895$	−1.13789e13	−0.592782
$896$	2.19682e13	1.13870
$897$	2.91155e12	0.150161
$898$	−1.03827e13	−0.532802
$899$	1.12593e13	0.574900
$900$	7.28223e11	0.0369975
$901$	3.95674e12	0.200021
$902$	−5.19385e12	−0.261252
$903$	−2.72797e13	−1.36535
$904$	−1.98838e13	−0.990240
$905$	2.26478e13	1.12229
$906$	3.72646e12	0.183747
$907$	−2.79368e13	−1.37070	−0.685352	−	0.728212i	$-0.740352\pi$
$907$	−2.79368e13	−1.37070	−0.685352	+	0.728212i	$0.740352\pi$
$908$	−5.47003e12	−0.267057
$909$	1.21676e12	0.0591110
$910$	−1.34266e13	−0.649054
$911$	9.90365e12	0.476390	0.238195	−	0.971217i	$-0.423444\pi$
$911$	9.90365e12	0.476390	0.238195	+	0.971217i	$0.423444\pi$
$912$	2.19451e12	0.105042
$913$	−4.47573e12	−0.213179
$914$	−1.30562e13	−0.618813
$915$	−8.35040e12	−0.393833
$916$	−5.31992e12	−0.249675
$917$	−2.57899e13	−1.20445
$918$	−5.58130e11	−0.0259384
$919$	−2.42733e13	−1.12256	−0.561280	−	0.827626i	$-0.689691\pi$
$919$	−2.42733e13	−1.12256	−0.561280	+	0.827626i	$0.689691\pi$
$920$	−5.38652e12	−0.247892
$921$	−5.58050e12	−0.255567
$922$	3.36292e13	1.53259
$923$	3.33137e12	0.151083
$924$	2.73042e12	0.123227
$925$	−1.52461e13	−0.684733
$926$	−4.32591e12	−0.193343
$927$	7.68567e12	0.341840
$928$	−7.91435e12	−0.350308
$929$	1.19293e13	0.525463	0.262732	−	0.964869i	$-0.415377\pi$
$929$	1.19293e13	0.525463	0.262732	+	0.964869i	$0.415377\pi$
$930$	−4.14484e12	−0.181691
$931$	−1.04561e13	−0.456137
$932$	−3.35012e12	−0.145442
$933$	1.39553e12	0.0602935
$934$	−3.57778e13	−1.53834
$935$	1.47940e12	0.0633042
$936$	−5.68727e12	−0.242193
$937$	−1.17659e13	−0.498653	−0.249327	−	0.968419i	$-0.580209\pi$
$937$	−1.17659e13	−0.498653	−0.249327	+	0.968419i	$0.580209\pi$
$938$	4.66999e13	1.96971
$939$	1.11933e13	0.469854
$940$	−4.53509e12	−0.189457
$941$	−4.56502e12	−0.189797	−0.0948986	−	0.995487i	$-0.530253\pi$
$941$	−4.56502e12	−0.189797	−0.0948986	+	0.995487i	$0.530253\pi$
$942$	−8.76175e12	−0.362545
$943$	−3.80639e12	−0.156751
$944$	3.94883e12	0.161843
$945$	−4.95632e12	−0.202170
$946$	−2.14615e13	−0.871264
$947$	3.95574e13	1.59828	0.799140	−	0.601145i	$-0.205289\pi$
$947$	3.95574e13	1.59828	0.799140	+	0.601145i	$0.205289\pi$
$948$	1.43532e11	0.00577182
$949$	1.25753e13	0.503292
$950$	−3.29739e12	−0.131345
$951$	8.80711e12	0.349157
$952$	−6.94386e12	−0.273990
$953$	1.39350e13	0.547252	0.273626	−	0.961836i	$-0.411777\pi$
$953$	1.39350e13	0.547252	0.273626	+	0.961836i	$0.411777\pi$
$954$	−1.04288e13	−0.407629
$955$	−1.93629e13	−0.753279
$956$	−5.93145e12	−0.229668
$957$	1.05921e13	0.408207
$958$	3.90234e13	1.49686
$959$	3.88723e13	1.48408
$960$	1.02358e13	0.388956
$961$	−1.78350e13	−0.674557
$962$	1.78184e13	0.670781
$963$	1.54186e13	0.577733
$964$	1.39029e12	0.0518512
$965$	8.87350e12	0.329399
$966$	−9.36952e12	−0.346195
$967$	−9.51961e12	−0.350106	−0.175053	−	0.984559i	$-0.556010\pi$
$967$	−9.51961e12	−0.350106	−0.175053	+	0.984559i	$0.556010\pi$
$968$	−1.48072e13	−0.542042
$969$	−5.39730e11	−0.0196662
$970$	4.78487e12	0.173539
$971$	5.37528e13	1.94050	0.970252	−	0.242098i	$-0.0778356\pi$
$971$	5.37528e13	1.94050	0.970252	+	0.242098i	$0.0778356\pi$
$972$	−3.14171e11	−0.0112893
$973$	6.29500e13	2.25158
$974$	−1.76317e13	−0.627739
$975$	6.99355e12	0.247843
$976$	2.52352e13	0.890190
$977$	1.76883e13	0.621099	0.310549	−	0.950557i	$-0.399487\pi$
$977$	1.76883e13	0.621099	0.310549	+	0.950557i	$0.399487\pi$
$978$	2.20284e13	0.769943
$979$	2.46792e13	0.858637
$980$	−6.13973e12	−0.212634
$981$	−5.65312e12	−0.194885
$982$	3.21490e13	1.10323
$983$	4.71272e13	1.60983	0.804917	−	0.593388i	$-0.202210\pi$
$983$	4.71272e13	1.60983	0.804917	+	0.593388i	$0.202210\pi$
$984$	7.43521e12	0.252822
$985$	1.32809e13	0.449538
$986$	−4.03112e12	−0.135825
$987$	−5.27139e13	−1.76807
$988$	−8.23029e11	−0.0274795
$989$	−1.57284e13	−0.522757
$990$	−3.89924e12	−0.129010
$991$	1.41503e13	0.466052	0.233026	−	0.972470i	$-0.425137\pi$
$991$	1.41503e13	0.466052	0.233026	+	0.972470i	$0.425137\pi$
$992$	−6.04832e12	−0.198304
$993$	1.69530e13	0.553317
$994$	−1.07205e13	−0.348319
$995$	2.06706e13	0.668575
$996$	9.58819e11	0.0308723
$997$	1.07830e13	0.345631	0.172815	−	0.984954i	$-0.444714\pi$
$997$	1.07830e13	0.345631	0.172815	+	0.984954i	$0.444714\pi$
$998$	−4.51018e13	−1.43915
$999$	6.57750e12	0.208937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.10.a.d.1.3	✓	8
3.2	odd	2		171.10.a.e.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.10.a.d.1.3	✓	8	1.1	even	1	trivial
171.10.a.e.1.6		8	3.2	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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	57.a (trivial)

\(f(q)\)	\(=\)	\(q-20.5401 q^{2} +81.0000 q^{3} -90.1033 q^{4} +849.287 q^{5} -1663.75 q^{6} -10981.2 q^{7} +12367.3 q^{8} +6561.00 q^{9} -17444.5 q^{10} +34068.5 q^{11} -7298.37 q^{12} -70090.6 q^{13} +225555. q^{14} +68792.2 q^{15} -207892. q^{16} +51130.2 q^{17} -134764. q^{18} -130321. q^{19} -76523.6 q^{20} -889477. q^{21} -699771. q^{22} -512837. q^{23} +1.00175e6 q^{24} -1.23184e6 q^{25} +1.43967e6 q^{26} +531441. q^{27} +989443. q^{28} +3.83836e6 q^{29} -1.41300e6 q^{30} +2.93336e6 q^{31} -2.06191e6 q^{32} +2.75955e6 q^{33} -1.05022e6 q^{34} -9.32619e6 q^{35} -591168. q^{36} +1.23767e7 q^{37} +2.67681e6 q^{38} -5.67734e6 q^{39} +1.05034e7 q^{40} +7.42222e6 q^{41} +1.82700e7 q^{42} +3.06693e7 q^{43} -3.06968e6 q^{44} +5.57217e6 q^{45} +1.05337e7 q^{46} +5.92639e7 q^{47} -1.68393e7 q^{48} +8.02332e7 q^{49} +2.53021e7 q^{50} +4.14154e6 q^{51} +6.31540e6 q^{52} +7.73856e7 q^{53} -1.09159e7 q^{54} +2.89339e7 q^{55} -1.35808e8 q^{56} -1.05560e7 q^{57} -7.88404e7 q^{58} -1.89946e7 q^{59} -6.19841e6 q^{60} -1.21386e8 q^{61} -6.02516e7 q^{62} -7.20477e7 q^{63} +1.48793e8 q^{64} -5.95270e7 q^{65} -5.66814e7 q^{66} +2.07044e8 q^{67} -4.60700e6 q^{68} -4.15398e7 q^{69} +1.91561e8 q^{70} -4.75295e7 q^{71} +8.11417e7 q^{72} -1.79415e8 q^{73} -2.54220e8 q^{74} -9.97788e7 q^{75} +1.17424e7 q^{76} -3.74113e8 q^{77} +1.16613e8 q^{78} -1.96664e7 q^{79} -1.76560e8 q^{80} +4.30467e7 q^{81} -1.52453e8 q^{82} -1.31374e8 q^{83} +8.01449e7 q^{84} +4.34242e7 q^{85} -6.29951e8 q^{86} +3.10907e8 q^{87} +4.21334e8 q^{88} +7.24401e8 q^{89} -1.14453e8 q^{90} +7.69679e8 q^{91} +4.62083e7 q^{92} +2.37602e8 q^{93} -1.21729e9 q^{94} -1.10680e8 q^{95} -1.67015e8 q^{96} -2.74292e8 q^{97} -1.64800e9 q^{98} +2.23523e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 17 q^{2} + 648 q^{3} + 2833 q^{4} + 3902 q^{5} + 1377 q^{6} + 9488 q^{7} + 27927 q^{8} + 52488 q^{9} + 111324 q^{10} + 38328 q^{11} + 229473 q^{12} + 238594 q^{13} + 255570 q^{14} + 316062 q^{15}+ \cdots + 251470008 q^{99}+O(q^{100}) \) 8 * q + 17 * q^2 + 648 * q^3 + 2833 * q^4 + 3902 * q^5 + 1377 * q^6 + 9488 * q^7 + 27927 * q^8 + 52488 * q^9 + 111324 * q^10 + 38328 * q^11 + 229473 * q^12 + 238594 * q^13 + 255570 * q^14 + 316062 * q^15 + 875017 * q^16 + 340248 * q^17 + 111537 * q^18 - 1042568 * q^19 - 70298 * q^20 + 768528 * q^21 - 2034178 * q^22 + 36062 * q^23 + 2262087 * q^24 + 3100952 * q^25 - 3108174 * q^26 + 4251528 * q^27 + 7077616 * q^28 - 350456 * q^29 + 9017244 * q^30 + 15030666 * q^31 + 8323411 * q^32 + 3104568 * q^33 + 21887248 * q^34 + 32386908 * q^35 + 18587313 * q^36 + 29518626 * q^37 - 2215457 * q^38 + 19326114 * q^39 + 66983070 * q^40 + 20347628 * q^41 + 20701170 * q^42 + 107568604 * q^43 + 39497904 * q^44 + 25601022 * q^45 + 84573760 * q^46 + 77478390 * q^47 + 70876377 * q^48 + 66668124 * q^49 + 85335229 * q^50 + 27560088 * q^51 + 117837518 * q^52 + 99085464 * q^53 + 9034497 * q^54 + 49033668 * q^55 + 174919116 * q^56 - 84448008 * q^57 + 85663178 * q^58 + 194104536 * q^59 - 5694138 * q^60 + 268423708 * q^61 + 144870904 * q^62 + 62250768 * q^63 - 300291319 * q^64 + 5447796 * q^65 - 164768418 * q^66 - 151197308 * q^67 - 605814870 * q^68 + 2921022 * q^69 - 240578502 * q^70 - 121292496 * q^71 + 183229047 * q^72 - 102019552 * q^73 - 688853258 * q^74 + 251177112 * q^75 - 369199393 * q^76 - 117614964 * q^77 - 251762094 * q^78 - 138557962 * q^79 - 1299265658 * q^80 + 344373768 * q^81 - 1339779918 * q^82 - 464489416 * q^83 + 573286896 * q^84 - 1230030528 * q^85 - 2465913098 * q^86 - 28386936 * q^87 - 485295564 * q^88 - 1232352760 * q^89 + 730396764 * q^90 - 152984744 * q^91 - 4368234020 * q^92 + 1217483946 * q^93 - 752351790 * q^94 - 508512542 * q^95 + 674196291 * q^96 - 523291172 * q^97 - 5080621865 * q^98 + 251470008 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more