LMFDB - Embedded newform 19.10.a.b.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,10,Mod(1,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	19.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.78568088711$
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} - 3356 x^{6} - 1330 x^{5} + 3186388 x^{4} - 1801192 x^{3} - 758043152 x^{2} + \cdots - 16080668672 $ x^8 - x^7 - 3356x^6 - 1330x^5 + 3186388x^4 - 1801192x^3 - 758043152x^2 + 6645763712x - 16080668672
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-28.7538$ of defining polynomial
Character	$\chi$	$=$	19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+30.7538 q^{2} +175.481 q^{3} +433.799 q^{4} +18.5839 q^{5} +5396.70 q^{6} +6967.83 q^{7} -2404.99 q^{8} +11110.5 q^{9} +571.527 q^{10} -18915.9 q^{11} +76123.3 q^{12} -9825.75 q^{13} +214288. q^{14} +3261.12 q^{15} -296068. q^{16} +36634.0 q^{17} +341689. q^{18} +130321. q^{19} +8061.68 q^{20} +1.22272e6 q^{21} -581737. q^{22} +1.08339e6 q^{23} -422030. q^{24} -1.95278e6 q^{25} -302179. q^{26} -1.50432e6 q^{27} +3.02264e6 q^{28} -3.36211e6 q^{29} +100292. q^{30} -4.13449e6 q^{31} -7.87386e6 q^{32} -3.31938e6 q^{33} +1.12664e6 q^{34} +129490. q^{35} +4.81970e6 q^{36} -1.42504e7 q^{37} +4.00787e6 q^{38} -1.72423e6 q^{39} -44694.2 q^{40} +2.20985e7 q^{41} +3.76033e7 q^{42} +3.72717e7 q^{43} -8.20569e6 q^{44} +206476. q^{45} +3.33184e7 q^{46} +3.22254e7 q^{47} -5.19541e7 q^{48} +8.19708e6 q^{49} -6.00555e7 q^{50} +6.42855e6 q^{51} -4.26240e6 q^{52} -7.25462e7 q^{53} -4.62635e7 q^{54} -351532. q^{55} -1.67576e7 q^{56} +2.28688e7 q^{57} -1.03398e8 q^{58} +9.76827e7 q^{59} +1.41467e6 q^{60} +1.68853e8 q^{61} -1.27151e8 q^{62} +7.74158e7 q^{63} -9.05648e7 q^{64} -182601. q^{65} -1.02084e8 q^{66} +1.35888e8 q^{67} +1.58918e7 q^{68} +1.90114e8 q^{69} +3.98231e6 q^{70} -7.63489e7 q^{71} -2.67206e7 q^{72} -1.04296e7 q^{73} -4.38254e8 q^{74} -3.42675e8 q^{75} +5.65331e7 q^{76} -1.31803e8 q^{77} -5.30267e7 q^{78} +4.35016e8 q^{79} -5.50210e6 q^{80} -4.82665e8 q^{81} +6.79612e8 q^{82} +5.43977e8 q^{83} +5.30414e8 q^{84} +680803. q^{85} +1.14625e9 q^{86} -5.89986e8 q^{87} +4.54926e7 q^{88} -3.73265e8 q^{89} +6.34993e6 q^{90} -6.84642e7 q^{91} +4.69974e8 q^{92} -7.25522e8 q^{93} +9.91054e8 q^{94} +2.42188e6 q^{95} -1.38171e9 q^{96} -9.35566e8 q^{97} +2.52092e8 q^{98} -2.10164e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 15 q^{2} + 7 q^{3} + 2645 q^{4} + 3894 q^{5} - 9723 q^{6} - 7133 q^{7} + 10911 q^{8} + 102715 q^{9} + 113172 q^{10} + 172818 q^{11} + 349117 q^{12} + 109291 q^{13} + 250959 q^{14} + 457332 q^{15}+ \cdots - 1682553420 q^{99}+O(q^{100}) $ 8 * q + 15 * q^2 + 7 * q^3 + 2645 * q^4 + 3894 * q^5 - 9723 * q^6 - 7133 * q^7 + 10911 * q^8 + 102715 * q^9 + 113172 * q^10 + 172818 * q^11 + 349117 * q^12 + 109291 * q^13 + 250959 * q^14 + 457332 * q^15 + 1590377 * q^16 + 583575 * q^17 + 308688 * q^18 + 1042568 * q^19 + 3191676 * q^20 + 372767 * q^21 + 57234 * q^22 - 2292405 * q^23 - 7378809 * q^24 + 205328 * q^25 - 821247 * q^26 - 15261551 * q^27 - 10217945 * q^28 + 4546335 * q^29 - 30417480 * q^30 - 8277416 * q^31 - 15773553 * q^32 + 13959234 * q^33 - 22393029 * q^34 + 15633768 * q^35 - 1486010 * q^36 + 24485536 * q^37 + 1954815 * q^38 + 16641725 * q^39 + 2543472 * q^40 + 35051946 * q^41 - 55902561 * q^42 + 36624268 * q^43 + 215210070 * q^44 + 138146370 * q^45 - 66065277 * q^46 + 9865524 * q^47 + 205312561 * q^48 + 111765087 * q^49 + 50599293 * q^50 + 109712553 * q^51 - 258827351 * q^52 + 13963683 * q^53 - 345545985 * q^54 + 261540660 * q^55 - 517172871 * q^56 + 912247 * q^57 - 399459963 * q^58 + 21215463 * q^59 - 275519064 * q^60 + 180552112 * q^61 - 451241340 * q^62 + 303758726 * q^63 + 180711569 * q^64 - 21864624 * q^65 - 1155635334 * q^66 + 1767355 * q^67 - 41475117 * q^68 + 504738939 * q^69 - 516193752 * q^70 + 273631578 * q^71 - 1360350726 * q^72 - 263711543 * q^73 + 677785566 * q^74 - 340714091 * q^75 + 344699045 * q^76 + 441243702 * q^77 + 1315717365 * q^78 + 744472174 * q^79 + 1904949528 * q^80 + 1867545184 * q^81 + 1284295572 * q^82 + 832139910 * q^83 - 917264533 * q^84 + 1013793492 * q^85 + 956757432 * q^86 - 231595575 * q^87 - 585082794 * q^88 - 291457734 * q^89 + 675674604 * q^90 - 1351077415 * q^91 + 2042025591 * q^92 + 537395144 * q^93 - 2759974128 * q^94 + 507469974 * q^95 - 1782885825 * q^96 - 3483837140 * q^97 + 4178510532 * q^98 - 1682553420 * 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 $

$2$	30.7538	1.35914	0.679570	−	0.733610i	$-0.262166\pi$
$2$	30.7538	1.35914	0.679570	+	0.733610i	$0.262166\pi$
$3$	175.481	1.25079	0.625394	−	0.780309i	$-0.284938\pi$
$3$	175.481	1.25079	0.625394	+	0.780309i	$0.284938\pi$
$4$	433.799	0.847263
$5$	18.5839	0.0132976	0.00664879	−	0.999978i	$-0.497884\pi$
$5$	18.5839	0.0132976	0.00664879	+	0.999978i	$0.497884\pi$
$6$	5396.70	1.70000
$7$	6967.83	1.09687	0.548437	−	0.836192i	$-0.315223\pi$
$7$	6967.83	1.09687	0.548437	+	0.836192i	$0.315223\pi$
$8$	−2404.99	−0.207591
$9$	11110.5	0.564470
$10$	571.527	0.0180733
$11$	−18915.9	−0.389547	−0.194774	−	0.980848i	$-0.562397\pi$
$11$	−18915.9	−0.389547	−0.194774	+	0.980848i	$0.562397\pi$
$12$	76123.3	1.05975
$13$	−9825.75	−0.0954159	−0.0477079	−	0.998861i	$-0.515192\pi$
$13$	−9825.75	−0.0954159	−0.0477079	+	0.998861i	$0.515192\pi$
$14$	214288.	1.49081
$15$	3261.12	0.0166324
$16$	−296068.	−1.12941
$17$	36634.0	0.106381	0.0531905	−	0.998584i	$-0.483061\pi$
$17$	36634.0	0.106381	0.0531905	+	0.998584i	$0.483061\pi$
$18$	341689.	0.767194
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	8061.68	0.0112665
$21$	1.22272e6	1.37196
$22$	−581737.	−0.529449
$23$	1.08339e6	0.807254	0.403627	−	0.914924i	$-0.367749\pi$
$23$	1.08339e6	0.807254	0.403627	+	0.914924i	$0.367749\pi$
$24$	−422030.	−0.259652
$25$	−1.95278e6	−0.999823
$26$	−302179.	−0.129684
$27$	−1.50432e6	−0.544756
$28$	3.02264e6	0.929340
$29$	−3.36211e6	−0.882717	−0.441359	−	0.897331i	$-0.645503\pi$
$29$	−3.36211e6	−0.882717	−0.441359	+	0.897331i	$0.645503\pi$
$30$	100292.	0.0226058
$31$	−4.13449e6	−0.804070	−0.402035	−	0.915624i	$-0.631697\pi$
$31$	−4.13449e6	−0.804070	−0.402035	+	0.915624i	$0.631697\pi$
$32$	−7.87386e6	−1.32743
$33$	−3.31938e6	−0.487241
$34$	1.12664e6	0.144587
$35$	129490.	0.0145858
$36$	4.81970e6	0.478254
$37$	−1.42504e7	−1.25002	−0.625012	−	0.780615i	$-0.714906\pi$
$37$	−1.42504e7	−1.25002	−0.625012	+	0.780615i	$0.714906\pi$
$38$	4.00787e6	0.311808
$39$	−1.72423e6	−0.119345
$40$	−44694.2	−0.00276046
$41$	2.20985e7	1.22133	0.610667	−	0.791887i	$-0.290901\pi$
$41$	2.20985e7	1.22133	0.610667	+	0.791887i	$0.290901\pi$
$42$	3.76033e7	1.86468
$43$	3.72717e7	1.66254	0.831269	−	0.555871i	$-0.187615\pi$
$43$	3.72717e7	1.66254	0.831269	+	0.555871i	$0.187615\pi$
$44$	−8.20569e6	−0.330049
$45$	206476.	0.00750608
$46$	3.33184e7	1.09717
$47$	3.22254e7	0.963291	0.481646	−	0.876366i	$-0.340039\pi$
$47$	3.22254e7	0.963291	0.481646	+	0.876366i	$0.340039\pi$
$48$	−5.19541e7	−1.41265
$49$	8.19708e6	0.203131
$50$	−6.00555e7	−1.35890
$51$	6.42855e6	0.133060
$52$	−4.26240e6	−0.0808423
$53$	−7.25462e7	−1.26291	−0.631456	−	0.775412i	$-0.717542\pi$
$53$	−7.25462e7	−1.26291	−0.631456	+	0.775412i	$0.717542\pi$
$54$	−4.62635e7	−0.740400
$55$	−351532.	−0.00518003
$56$	−1.67576e7	−0.227701
$57$	2.28688e7	0.286950
$58$	−1.03398e8	−1.19974
$59$	9.76827e7	1.04950	0.524751	−	0.851256i	$-0.324158\pi$
$59$	9.76827e7	1.04950	0.524751	+	0.851256i	$0.324158\pi$
$60$	1.41467e6	0.0140921
$61$	1.68853e8	1.56143	0.780717	−	0.624885i	$-0.214854\pi$
$61$	1.68853e8	1.56143	0.780717	+	0.624885i	$0.214854\pi$
$62$	−1.27151e8	−1.09284
$63$	7.74158e7	0.619152
$64$	−9.05648e7	−0.674760
$65$	−182601.	−0.00126880
$66$	−1.02084e8	−0.662229
$67$	1.35888e8	0.823840	0.411920	−	0.911220i	$-0.364858\pi$
$67$	1.35888e8	0.823840	0.411920	+	0.911220i	$0.364858\pi$
$68$	1.58918e7	0.0901326
$69$	1.90114e8	1.00970
$70$	3.98231e6	0.0198241
$71$	−7.63489e7	−0.356566	−0.178283	−	0.983979i	$-0.557054\pi$
$71$	−7.63489e7	−0.356566	−0.178283	+	0.983979i	$0.557054\pi$
$72$	−2.67206e7	−0.117179
$73$	−1.04296e7	−0.0429849	−0.0214925	−	0.999769i	$-0.506842\pi$
$73$	−1.04296e7	−0.0429849	−0.0214925	+	0.999769i	$0.506842\pi$
$74$	−4.38254e8	−1.69896
$75$	−3.42675e8	−1.25057
$76$	5.65331e7	0.194375
$77$	−1.31803e8	−0.427284
$78$	−5.30267e7	−0.162207
$79$	4.35016e8	1.25656	0.628280	−	0.777987i	$-0.283759\pi$
$79$	4.35016e8	1.25656	0.628280	+	0.777987i	$0.283759\pi$
$80$	−5.50210e6	−0.0150184
$81$	−4.82665e8	−1.24584
$82$	6.79612e8	1.65997
$83$	5.43977e8	1.25814	0.629071	−	0.777348i	$-0.283436\pi$
$83$	5.43977e8	1.25814	0.629071	+	0.777348i	$0.283436\pi$
$84$	5.30414e8	1.16241
$85$	680803.	0.00141461
$86$	1.14625e9	2.25962
$87$	−5.89986e8	−1.10409
$88$	4.54926e7	0.0808665
$89$	−3.73265e8	−0.630612	−0.315306	−	0.948990i	$-0.602107\pi$
$89$	−3.73265e8	−0.630612	−0.315306	+	0.948990i	$0.602107\pi$
$90$	6.34993e6	0.0102018
$91$	−6.84642e7	−0.104659
$92$	4.69974e8	0.683956
$93$	−7.25522e8	−1.00572
$94$	9.91054e8	1.30925
$95$	2.42188e6	0.00305067
$96$	−1.38171e9	−1.66034
$97$	−9.35566e8	−1.07300	−0.536502	−	0.843899i	$-0.680255\pi$
$97$	−9.35566e8	−1.07300	−0.536502	+	0.843899i	$0.680255\pi$
$98$	2.52092e8	0.276084
$99$	−2.10164e8	−0.219888
$100$	−8.47113e8	−0.847113
$101$	1.37471e9	1.31451	0.657257	−	0.753667i	$-0.271717\pi$
$101$	1.37471e9	1.31451	0.657257	+	0.753667i	$0.271717\pi$
$102$	1.97703e8	0.180847
$103$	5.76818e8	0.504977	0.252488	−	0.967600i	$-0.418751\pi$
$103$	5.76818e8	0.504977	0.252488	+	0.967600i	$0.418751\pi$
$104$	2.36308e7	0.0198075
$105$	2.27229e7	0.0182437
$106$	−2.23107e9	−1.71647
$107$	1.93168e9	1.42465	0.712325	−	0.701850i	$-0.247642\pi$
$107$	1.93168e9	1.42465	0.712325	+	0.701850i	$0.247642\pi$
$108$	−6.52570e8	−0.461552
$109$	−1.56006e9	−1.05858	−0.529289	−	0.848441i	$-0.677541\pi$
$109$	−1.56006e9	−1.05858	−0.529289	+	0.848441i	$0.677541\pi$
$110$	−1.08110e7	−0.00704039
$111$	−2.50066e9	−1.56351
$112$	−2.06295e9	−1.23882
$113$	3.24522e8	0.187237	0.0936183	−	0.995608i	$-0.470157\pi$
$113$	3.24522e8	0.187237	0.0936183	+	0.995608i	$0.470157\pi$
$114$	7.03304e8	0.390006
$115$	2.01337e7	0.0107345
$116$	−1.45848e9	−0.747893
$117$	−1.09169e8	−0.0538594
$118$	3.00412e9	1.42642
$119$	2.55259e8	0.116686
$120$	−7.84297e6	−0.00345275
$121$	−2.00014e9	−0.848253
$122$	5.19287e9	2.12221
$123$	3.87785e9	1.52763
$124$	−1.79353e9	−0.681259
$125$	−7.25870e7	−0.0265928
$126$	2.38083e9	0.841514
$127$	−2.50936e9	−0.855946	−0.427973	−	0.903792i	$-0.640772\pi$
$127$	−2.50936e9	−0.855946	−0.427973	+	0.903792i	$0.640772\pi$
$128$	1.24620e9	0.410339
$129$	6.54047e9	2.07948
$130$	−5.61568e6	−0.00172448
$131$	−4.96195e9	−1.47208	−0.736041	−	0.676937i	$-0.763307\pi$
$131$	−4.96195e9	−1.47208	−0.736041	+	0.676937i	$0.763307\pi$
$132$	−1.43994e9	−0.412821
$133$	9.08055e8	0.251640
$134$	4.17906e9	1.11972
$135$	−2.79561e7	−0.00724393
$136$	−8.81044e7	−0.0220837
$137$	1.27017e9	0.308048	0.154024	−	0.988067i	$-0.450777\pi$
$137$	1.27017e9	0.308048	0.154024	+	0.988067i	$0.450777\pi$
$138$	5.84674e9	1.37233
$139$	−6.65931e9	−1.51308	−0.756541	−	0.653946i	$-0.773112\pi$
$139$	−6.65931e9	−1.51308	−0.756541	+	0.653946i	$0.773112\pi$
$140$	5.61725e7	0.0123580
$141$	5.65493e9	1.20487
$142$	−2.34802e9	−0.484624
$143$	1.85863e8	0.0371690
$144$	−3.28945e9	−0.637517
$145$	−6.24813e7	−0.0117380
$146$	−3.20751e8	−0.0584226
$147$	1.43843e9	0.254074
$148$	−6.18179e9	−1.05910
$149$	−5.88858e9	−0.978752	−0.489376	−	0.872073i	$-0.662775\pi$
$149$	−5.88858e9	−0.978752	−0.489376	+	0.872073i	$0.662775\pi$
$150$	−1.05386e10	−1.69970
$151$	−9.02631e9	−1.41291	−0.706454	−	0.707759i	$-0.749706\pi$
$151$	−9.02631e9	−1.41291	−0.706454	+	0.707759i	$0.749706\pi$
$152$	−3.13421e8	−0.0476247
$153$	4.07020e8	0.0600488
$154$	−4.05344e9	−0.580739
$155$	−7.68350e7	−0.0106922
$156$	−7.47968e8	−0.101117
$157$	1.41058e10	1.85288	0.926442	−	0.376437i	$-0.122851\pi$
$157$	1.41058e10	1.85288	0.926442	+	0.376437i	$0.122851\pi$
$158$	1.33784e10	1.70784
$159$	−1.27304e10	−1.57963
$160$	−1.46327e8	−0.0176517
$161$	7.54889e9	0.885455
$162$	−1.48438e10	−1.69328
$163$	−5.08618e9	−0.564349	−0.282174	−	0.959363i	$-0.591056\pi$
$163$	−5.08618e9	−0.564349	−0.282174	+	0.959363i	$0.591056\pi$
$164$	9.58628e9	1.03479
$165$	−6.16870e7	−0.00647912
$166$	1.67294e10	1.70999
$167$	1.58605e10	1.57795	0.788973	−	0.614428i	$-0.210613\pi$
$167$	1.58605e10	1.57795	0.788973	+	0.614428i	$0.210613\pi$
$168$	−2.94063e9	−0.284806
$169$	−1.05080e10	−0.990896
$170$	2.09373e7	0.00192265
$171$	1.44793e9	0.129498
$172$	1.61684e10	1.40861
$173$	−8.55171e9	−0.725848	−0.362924	−	0.931819i	$-0.618221\pi$
$173$	−8.55171e9	−0.725848	−0.362924	+	0.931819i	$0.618221\pi$
$174$	−1.81443e10	−1.50062
$175$	−1.36066e10	−1.09668
$176$	5.60039e9	0.439958
$177$	1.71414e10	1.31270
$178$	−1.14793e10	−0.857090
$179$	−1.14032e10	−0.830207	−0.415103	−	0.909774i	$-0.636255\pi$
$179$	−1.14032e10	−0.830207	−0.415103	+	0.909774i	$0.636255\pi$
$180$	8.95690e7	0.00635962
$181$	2.11191e10	1.46258	0.731292	−	0.682064i	$-0.238918\pi$
$181$	2.11191e10	1.46258	0.731292	+	0.682064i	$0.238918\pi$
$182$	−2.10554e9	−0.142246
$183$	2.96304e10	1.95302
$184$	−2.60555e9	−0.167579
$185$	−2.64828e8	−0.0166223
$186$	−2.23126e10	−1.36692
$187$	−6.92965e8	−0.0414404
$188$	1.39793e10	0.816161
$189$	−1.04818e10	−0.597528
$190$	7.44820e7	0.00414629
$191$	−5.43960e8	−0.0295744	−0.0147872	−	0.999891i	$-0.504707\pi$
$191$	−5.43960e8	−0.0295744	−0.0147872	+	0.999891i	$0.504707\pi$
$192$	−1.58924e10	−0.843982
$193$	6.38397e9	0.331194	0.165597	−	0.986193i	$-0.447045\pi$
$193$	6.38397e9	0.331194	0.165597	+	0.986193i	$0.447045\pi$
$194$	−2.87722e10	−1.45836
$195$	−3.20429e7	−0.00158700
$196$	3.55588e9	0.172106
$197$	3.17781e10	1.50325	0.751624	−	0.659592i	$-0.229271\pi$
$197$	3.17781e10	1.50325	0.751624	+	0.659592i	$0.229271\pi$
$198$	−6.46336e9	−0.298858
$199$	−1.21029e10	−0.547082	−0.273541	−	0.961860i	$-0.588195\pi$
$199$	−1.21029e10	−0.547082	−0.273541	+	0.961860i	$0.588195\pi$
$200$	4.69642e9	0.207554
$201$	2.38456e10	1.03045
$202$	4.22776e10	1.78661
$203$	−2.34267e10	−0.968229
$204$	2.78870e9	0.112737
$205$	4.10676e8	0.0162408
$206$	1.77394e10	0.686335
$207$	1.20370e10	0.455670
$208$	2.90909e9	0.107763
$209$	−2.46514e9	−0.0893683
$210$	6.98817e8	0.0247957
$211$	2.05788e10	0.714743	0.357372	−	0.933962i	$-0.383673\pi$
$211$	2.05788e10	0.714743	0.357372	+	0.933962i	$0.383673\pi$
$212$	−3.14704e10	−1.07002
$213$	−1.33978e10	−0.445989
$214$	5.94066e10	1.93630
$215$	6.92655e8	0.0221077
$216$	3.61787e9	0.113086
$217$	−2.88084e10	−0.881963
$218$	−4.79780e10	−1.43876
$219$	−1.83020e9	−0.0537650
$220$	−1.52494e8	−0.00438885
$221$	−3.59956e8	−0.0101504
$222$	−7.69050e10	−2.12504
$223$	−1.86530e10	−0.505100	−0.252550	−	0.967584i	$-0.581269\pi$
$223$	−1.86530e10	−0.505100	−0.252550	+	0.967584i	$0.581269\pi$
$224$	−5.48637e10	−1.45603
$225$	−2.16963e10	−0.564370
$226$	9.98029e9	0.254481
$227$	−3.96935e10	−0.992208	−0.496104	−	0.868263i	$-0.665237\pi$
$227$	−3.96935e10	−0.992208	−0.496104	+	0.868263i	$0.665237\pi$
$228$	9.92046e9	0.243122
$229$	−5.29833e10	−1.27315	−0.636575	−	0.771215i	$-0.719649\pi$
$229$	−5.29833e10	−1.27315	−0.636575	+	0.771215i	$0.719649\pi$
$230$	6.19188e8	0.0145897
$231$	−2.31289e10	−0.534441
$232$	8.08586e9	0.183244
$233$	2.54211e10	0.565058	0.282529	−	0.959259i	$-0.408827\pi$
$233$	2.54211e10	0.565058	0.282529	+	0.959259i	$0.408827\pi$
$234$	−3.35735e9	−0.0732024
$235$	5.98874e8	0.0128094
$236$	4.23746e10	0.889204
$237$	7.63368e10	1.57169
$238$	7.85021e9	0.158593
$239$	4.24244e10	0.841056	0.420528	−	0.907280i	$-0.361845\pi$
$239$	4.24244e10	0.841056	0.420528	+	0.907280i	$0.361845\pi$
$240$	−9.65512e8	−0.0187848
$241$	4.99900e10	0.954568	0.477284	−	0.878749i	$-0.341621\pi$
$241$	4.99900e10	0.954568	0.477284	+	0.878749i	$0.341621\pi$
$242$	−6.15119e10	−1.15289
$243$	−5.50890e10	−1.01353
$244$	7.32480e10	1.32295
$245$	1.52334e8	0.00270115
$246$	1.19259e11	2.07626
$247$	−1.28050e9	−0.0218899
$248$	9.94341e9	0.166918
$249$	9.54575e10	1.57367
$250$	−2.23233e9	−0.0361434
$251$	−3.26128e10	−0.518628	−0.259314	−	0.965793i	$-0.583496\pi$
$251$	−3.26128e10	−0.518628	−0.259314	+	0.965793i	$0.583496\pi$
$252$	3.35829e10	0.524584
$253$	−2.04933e10	−0.314463
$254$	−7.71725e10	−1.16335
$255$	1.19468e8	0.00176938
$256$	8.46946e10	1.23247
$257$	−1.30374e10	−0.186420	−0.0932100	−	0.995646i	$-0.529713\pi$
$257$	−1.30374e10	−0.186420	−0.0932100	+	0.995646i	$0.529713\pi$
$258$	2.01144e11	2.82631
$259$	−9.92942e10	−1.37112
$260$	−7.92121e7	−0.00107501
$261$	−3.73546e10	−0.498267
$262$	−1.52599e11	−2.00077
$263$	8.97581e10	1.15684	0.578419	−	0.815740i	$-0.303670\pi$
$263$	8.97581e10	1.15684	0.578419	+	0.815740i	$0.303670\pi$
$264$	7.98307e9	0.101147
$265$	−1.34819e9	−0.0167937
$266$	2.79262e10	0.342014
$267$	−6.55007e10	−0.788761
$268$	5.89478e10	0.698010
$269$	−1.08597e11	−1.26454	−0.632271	−	0.774748i	$-0.717877\pi$
$269$	−1.08597e11	−1.26454	−0.632271	+	0.774748i	$0.717877\pi$
$270$	−8.59757e8	−0.00984553
$271$	−4.42538e10	−0.498412	−0.249206	−	0.968450i	$-0.580170\pi$
$271$	−4.42538e10	−0.498412	−0.249206	+	0.968450i	$0.580170\pi$
$272$	−1.08461e10	−0.120148
$273$	−1.20141e10	−0.130906
$274$	3.90625e10	0.418681
$275$	3.69386e10	0.389478
$276$	8.24713e10	0.855484
$277$	1.54037e10	0.157205	0.0786025	−	0.996906i	$-0.474954\pi$
$277$	1.54037e10	0.157205	0.0786025	+	0.996906i	$0.474954\pi$
$278$	−2.04799e11	−2.05649
$279$	−4.59360e10	−0.453873
$280$	−3.11422e8	−0.00302787
$281$	−1.11836e11	−1.07005	−0.535025	−	0.844836i	$-0.679698\pi$
$281$	−1.11836e11	−1.07005	−0.535025	+	0.844836i	$0.679698\pi$
$282$	1.73911e11	1.63759
$283$	−1.19515e11	−1.10760	−0.553802	−	0.832649i	$-0.686823\pi$
$283$	−1.19515e11	−1.10760	−0.553802	+	0.832649i	$0.686823\pi$
$284$	−3.31201e10	−0.302105
$285$	4.24992e8	0.00381574
$286$	5.71600e9	0.0505179
$287$	1.53978e11	1.33965
$288$	−8.74822e10	−0.749296
$289$	−1.17246e11	−0.988683
$290$	−1.92154e9	−0.0159536
$291$	−1.64174e11	−1.34210
$292$	−4.52436e9	−0.0364195
$293$	1.57483e11	1.24833	0.624164	−	0.781293i	$-0.285440\pi$
$293$	1.57483e11	1.24833	0.624164	+	0.781293i	$0.285440\pi$
$294$	4.42372e10	0.345322
$295$	1.81533e9	0.0139558
$296$	3.42720e10	0.259494
$297$	2.84555e10	0.212208
$298$	−1.81097e11	−1.33026
$299$	−1.06451e10	−0.0770248
$300$	−1.48652e11	−1.05956
$301$	2.59703e11	1.82359
$302$	−2.77594e11	−1.92034
$303$	2.41235e11	1.64418
$304$	−3.85838e10	−0.259104
$305$	3.13795e9	0.0207633
$306$	1.25174e10	0.0816148
$307$	−1.69212e11	−1.08720	−0.543599	−	0.839345i	$-0.682939\pi$
$307$	−1.69212e11	−1.08720	−0.543599	+	0.839345i	$0.682939\pi$
$308$	−5.71759e10	−0.362022
$309$	1.01220e11	0.631619
$310$	−2.36297e9	−0.0145322
$311$	8.35259e10	0.506290	0.253145	−	0.967428i	$-0.418535\pi$
$311$	8.35259e10	0.506290	0.253145	+	0.967428i	$0.418535\pi$
$312$	4.14676e9	0.0247750
$313$	−1.18434e11	−0.697474	−0.348737	−	0.937221i	$-0.613389\pi$
$313$	−1.18434e11	−0.697474	−0.348737	+	0.937221i	$0.613389\pi$
$314$	4.33806e11	2.51833
$315$	1.43869e9	0.00823322
$316$	1.88709e11	1.06464
$317$	1.69530e11	0.942933	0.471466	−	0.881884i	$-0.343725\pi$
$317$	1.69530e11	0.942933	0.471466	+	0.881884i	$0.343725\pi$
$318$	−3.91510e11	−2.14695
$319$	6.35974e10	0.343860
$320$	−1.68305e9	−0.00897268
$321$	3.38972e11	1.78193
$322$	2.32157e11	1.20346
$323$	4.77418e9	0.0244055
$324$	−2.09380e11	−1.05556
$325$	1.91875e10	0.0953990
$326$	−1.56420e11	−0.767029
$327$	−2.73761e11	−1.32406
$328$	−5.31466e10	−0.253538
$329$	2.24541e11	1.05661
$330$	−1.89711e9	−0.00880604
$331$	1.47461e11	0.675231	0.337616	−	0.941284i	$-0.390380\pi$
$331$	1.47461e11	0.675231	0.337616	+	0.941284i	$0.390380\pi$
$332$	2.35977e11	1.06598
$333$	−1.58328e11	−0.705601
$334$	4.87771e11	2.14465
$335$	2.52532e9	0.0109551
$336$	−3.62008e11	−1.54950
$337$	1.06655e11	0.450449	0.225224	−	0.974307i	$-0.427688\pi$
$337$	1.06655e11	0.450449	0.225224	+	0.974307i	$0.427688\pi$
$338$	−3.23160e11	−1.34677
$339$	5.69473e10	0.234193
$340$	2.95331e8	0.00119855
$341$	7.82076e10	0.313223
$342$	4.45293e10	0.176006
$343$	−2.24061e11	−0.874064
$344$	−8.96382e10	−0.345128
$345$	3.53307e9	0.0134266
$346$	−2.62998e11	−0.986529
$347$	−1.42482e10	−0.0527566	−0.0263783	−	0.999652i	$-0.508397\pi$
$347$	−1.42482e10	−0.0527566	−0.0263783	+	0.999652i	$0.508397\pi$
$348$	−2.55935e11	−0.935456
$349$	9.88298e10	0.356594	0.178297	−	0.983977i	$-0.442941\pi$
$349$	9.88298e10	0.356594	0.178297	+	0.983977i	$0.442941\pi$
$350$	−4.18456e11	−1.49054
$351$	1.47810e10	0.0519784
$352$	1.48941e11	0.517098
$353$	−1.59794e11	−0.547739	−0.273870	−	0.961767i	$-0.588304\pi$
$353$	−1.59794e11	−0.547739	−0.273870	+	0.961767i	$0.588304\pi$
$354$	5.27164e11	1.78415
$355$	−1.41886e9	−0.00474147
$356$	−1.61922e11	−0.534294
$357$	4.47931e10	0.145950
$358$	−3.50691e11	−1.12837
$359$	2.23598e11	0.710466	0.355233	−	0.934778i	$-0.384401\pi$
$359$	2.23598e11	0.710466	0.355233	+	0.934778i	$0.384401\pi$
$360$	−4.96573e8	−0.00155819
$361$	1.69836e10	0.0526316
$362$	6.49492e11	1.98786
$363$	−3.50985e11	−1.06098
$364$	−2.96997e10	−0.0886738
$365$	−1.93824e8	−0.000571595 0
$366$	9.11248e11	2.65443
$367$	4.54458e11	1.30767	0.653833	−	0.756639i	$-0.273160\pi$
$367$	4.54458e11	1.30767	0.653833	+	0.756639i	$0.273160\pi$
$368$	−3.20757e11	−0.911719
$369$	2.45524e11	0.689406
$370$	−8.14447e9	−0.0225920
$371$	−5.05490e11	−1.38525
$372$	−3.14731e11	−0.852110
$373$	2.97149e11	0.794849	0.397424	−	0.917635i	$-0.369904\pi$
$373$	2.97149e11	0.794849	0.397424	+	0.917635i	$0.369904\pi$
$374$	−2.13113e10	−0.0563233
$375$	−1.27376e10	−0.0332619
$376$	−7.75018e10	−0.199971
$377$	3.30353e10	0.0842252
$378$	−3.22356e11	−0.812125
$379$	−7.10294e11	−1.76832	−0.884161	−	0.467182i	$-0.845269\pi$
$379$	−7.10294e11	−1.76832	−0.884161	+	0.467182i	$0.845269\pi$
$380$	1.05061e9	0.00258472
$381$	−4.40344e11	−1.07061
$382$	−1.67288e10	−0.0401958
$383$	−3.65667e11	−0.868342	−0.434171	−	0.900830i	$-0.642959\pi$
$383$	−3.65667e11	−0.868342	−0.434171	+	0.900830i	$0.642959\pi$
$384$	2.18684e11	0.513247
$385$	−2.44941e9	−0.00568184
$386$	1.96332e11	0.450140
$387$	4.14106e11	0.938452
$388$	−4.05847e11	−0.909117
$389$	−5.61998e11	−1.24440	−0.622202	−	0.782856i	$-0.713762\pi$
$389$	−5.61998e11	−1.24440	−0.622202	+	0.782856i	$0.713762\pi$
$390$	−9.85443e8	−0.00215695
$391$	3.96889e10	0.0858764
$392$	−1.97139e10	−0.0421682
$393$	−8.70727e11	−1.84126
$394$	9.77300e11	2.04312
$395$	8.08430e9	0.0167092
$396$	−9.11690e10	−0.186303
$397$	−4.61380e11	−0.932183	−0.466092	−	0.884736i	$-0.654338\pi$
$397$	−4.61380e11	−0.932183	−0.466092	+	0.884736i	$0.654338\pi$
$398$	−3.72212e11	−0.743561
$399$	1.59346e11	0.314748
$400$	5.78155e11	1.12921
$401$	4.85965e11	0.938545	0.469273	−	0.883053i	$-0.344516\pi$
$401$	4.85965e11	0.938545	0.469273	+	0.883053i	$0.344516\pi$
$402$	7.33345e11	1.40053
$403$	4.06244e10	0.0767210
$404$	5.96348e11	1.11374
$405$	−8.96982e9	−0.0165667
$406$	−7.20459e11	−1.31596
$407$	2.69559e11	0.486943
$408$	−1.54606e10	−0.0276221
$409$	−7.75782e11	−1.37083	−0.685417	−	0.728151i	$-0.740380\pi$
$409$	−7.75782e11	−1.37083	−0.685417	+	0.728151i	$0.740380\pi$
$410$	1.26299e10	0.0220735
$411$	2.22890e11	0.385303
$412$	2.50223e11	0.427848
$413$	6.80636e11	1.15117
$414$	3.70183e11	0.619320
$415$	1.01092e10	0.0167302
$416$	7.73666e10	0.126658
$417$	−1.16858e12	−1.89254
$418$	−7.58125e10	−0.121464
$419$	8.05113e11	1.27613	0.638063	−	0.769984i	$-0.279736\pi$
$419$	8.05113e11	1.27613	0.638063	+	0.769984i	$0.279736\pi$
$420$	9.85718e9	0.0154572
$421$	−2.23332e11	−0.346482	−0.173241	−	0.984879i	$-0.555424\pi$
$421$	−2.23332e11	−0.346482	−0.173241	+	0.984879i	$0.555424\pi$
$422$	6.32879e11	0.971436
$423$	3.58039e11	0.543749
$424$	1.74473e11	0.262169
$425$	−7.15381e10	−0.106362
$426$	−4.12032e11	−0.606161
$427$	1.17654e12	1.71270
$428$	8.37960e11	1.20705
$429$	3.26153e10	0.0464905
$430$	2.13018e10	0.0300475
$431$	1.41887e12	1.98059	0.990294	−	0.138985i	$-0.0443840\pi$
$431$	1.41887e12	1.98059	0.990294	+	0.138985i	$0.0443840\pi$
$432$	4.45379e11	0.615252
$433$	2.54646e10	0.0348131	0.0174065	−	0.999848i	$-0.494459\pi$
$433$	2.54646e10	0.0348131	0.0174065	+	0.999848i	$0.494459\pi$
$434$	−8.85969e11	−1.19871
$435$	−1.09643e10	−0.0146817
$436$	−6.76754e11	−0.896895
$437$	1.41189e11	0.185197
$438$	−5.62856e10	−0.0730742
$439$	−5.13529e11	−0.659895	−0.329947	−	0.943999i	$-0.607031\pi$
$439$	−5.13529e11	−0.659895	−0.329947	+	0.943999i	$0.607031\pi$
$440$	8.45431e8	0.00107533
$441$	9.10733e10	0.114661
$442$	−1.10700e10	−0.0137959
$443$	1.09746e12	1.35386	0.676929	−	0.736048i	$-0.263310\pi$
$443$	1.09746e12	1.35386	0.676929	+	0.736048i	$0.263310\pi$
$444$	−1.08478e12	−1.32471
$445$	−6.93672e9	−0.00838561
$446$	−5.73652e11	−0.686502
$447$	−1.03333e12	−1.22421
$448$	−6.31040e11	−0.740127
$449$	9.63066e11	1.11827	0.559136	−	0.829076i	$-0.311133\pi$
$449$	9.63066e11	1.11827	0.559136	+	0.829076i	$0.311133\pi$
$450$	−6.67244e11	−0.767058
$451$	−4.18012e11	−0.475767
$452$	1.40777e11	0.158639
$453$	−1.58394e12	−1.76725
$454$	−1.22073e12	−1.34855
$455$	−1.27233e9	−0.00139171
$456$	−5.49993e10	−0.0595683
$457$	−6.89529e11	−0.739486	−0.369743	−	0.929134i	$-0.620554\pi$
$457$	−6.89529e11	−0.739486	−0.369743	+	0.929134i	$0.620554\pi$
$458$	−1.62944e12	−1.73039
$459$	−5.51091e10	−0.0579517
$460$	8.73396e9	0.00909496
$461$	−1.22997e12	−1.26835	−0.634177	−	0.773188i	$-0.718661\pi$
$461$	−1.22997e12	−1.26835	−0.634177	+	0.773188i	$0.718661\pi$
$462$	−7.11301e11	−0.726381
$463$	−2.76406e11	−0.279533	−0.139767	−	0.990184i	$-0.544635\pi$
$463$	−2.76406e11	−0.279533	−0.139767	+	0.990184i	$0.544635\pi$
$464$	9.95413e11	0.996948
$465$	−1.34831e10	−0.0133737
$466$	7.81797e11	0.767993
$467$	−9.83451e11	−0.956812	−0.478406	−	0.878139i	$-0.658785\pi$
$467$	−9.83451e11	−0.956812	−0.478406	+	0.878139i	$0.658785\pi$
$468$	−4.73572e10	−0.0456330
$469$	9.46842e11	0.903649
$470$	1.84177e10	0.0174098
$471$	2.47529e12	2.31756
$472$	−2.34926e11	−0.217867
$473$	−7.05029e11	−0.647637
$474$	2.34765e12	2.13615
$475$	−2.54488e11	−0.229375
$476$	1.10731e11	0.0988641
$477$	−8.06021e11	−0.712875
$478$	1.30471e12	1.14311
$479$	−1.06153e12	−0.921343	−0.460672	−	0.887571i	$-0.652391\pi$
$479$	−1.06153e12	−0.921343	−0.460672	+	0.887571i	$0.652391\pi$
$480$	−2.56776e10	−0.0220785
$481$	1.40021e11	0.119272
$482$	1.53739e12	1.29739
$483$	1.32468e12	1.10752
$484$	−8.67656e11	−0.718693
$485$	−1.73865e10	−0.0142684
$486$	−1.69420e12	−1.37753
$487$	1.77513e11	0.143005	0.0715024	−	0.997440i	$-0.477221\pi$
$487$	1.77513e11	0.143005	0.0715024	+	0.997440i	$0.477221\pi$
$488$	−4.06089e11	−0.324140
$489$	−8.92526e11	−0.705880
$490$	4.68485e9	0.00367125
$491$	1.81491e12	1.40925	0.704625	−	0.709580i	$-0.251115\pi$
$491$	1.81491e12	1.40925	0.704625	+	0.709580i	$0.251115\pi$
$492$	1.68221e12	1.29430
$493$	−1.23168e11	−0.0939043
$494$	−3.93803e10	−0.0297514
$495$	−3.90568e9	−0.00292397
$496$	1.22409e12	0.908124
$497$	−5.31986e11	−0.391108
$498$	2.93568e12	2.13884
$499$	−1.01252e12	−0.731060	−0.365530	−	0.930800i	$-0.619112\pi$
$499$	−1.01252e12	−0.731060	−0.365530	+	0.930800i	$0.619112\pi$
$500$	−3.14882e10	−0.0225311
$501$	2.78321e12	1.97368
$502$	−1.00297e12	−0.704888
$503$	1.30672e11	0.0910176	0.0455088	−	0.998964i	$-0.485509\pi$
$503$	1.30672e11	0.0910176	0.0455088	+	0.998964i	$0.485509\pi$
$504$	−1.86184e11	−0.128530
$505$	2.55475e10	0.0174798
$506$	−6.30249e11	−0.427400
$507$	−1.84394e12	−1.23940
$508$	−1.08856e12	−0.725211
$509$	4.82132e11	0.318373	0.159186	−	0.987249i	$-0.449113\pi$
$509$	4.82132e11	0.318373	0.159186	+	0.987249i	$0.449113\pi$
$510$	3.67409e9	0.00240483
$511$	−7.26719e10	−0.0471490
$512$	1.96663e12	1.26476
$513$	−1.96044e11	−0.124976
$514$	−4.00951e11	−0.253371
$515$	1.07195e10	0.00671497
$516$	2.83725e12	1.76187
$517$	−6.09572e11	−0.375248
$518$	−3.05368e12	−1.86354
$519$	−1.50066e12	−0.907881
$520$	4.39154e8	0.000263391 0
$521$	9.94202e11	0.591160	0.295580	−	0.955318i	$-0.404487\pi$
$521$	9.94202e11	0.591160	0.295580	+	0.955318i	$0.404487\pi$
$522$	−1.14880e12	−0.677215
$523$	1.89994e12	1.11041	0.555203	−	0.831715i	$-0.312640\pi$
$523$	1.89994e12	1.11041	0.555203	+	0.831715i	$0.312640\pi$
$524$	−2.15249e12	−1.24724
$525$	−2.38770e12	−1.37171
$526$	2.76041e12	1.57231
$527$	−1.51463e11	−0.0855378
$528$	9.82760e11	0.550294
$529$	−6.27416e11	−0.348341
$530$	−4.14621e10	−0.0228250
$531$	1.08530e12	0.592412
$532$	3.93913e11	0.213205
$533$	−2.17134e11	−0.116535
$534$	−2.01440e12	−1.07204
$535$	3.58982e10	0.0189444
$536$	−3.26809e11	−0.171022
$537$	−2.00103e12	−1.03841
$538$	−3.33978e12	−1.71869
$539$	−1.55055e11	−0.0791292
$540$	−1.21273e10	−0.00613752
$541$	1.36007e12	0.682610	0.341305	−	0.939953i	$-0.389131\pi$
$541$	1.36007e12	0.682610	0.341305	+	0.939953i	$0.389131\pi$
$542$	−1.36097e12	−0.677412
$543$	3.70599e12	1.82938
$544$	−2.88451e11	−0.141214
$545$	−2.89921e10	−0.0140765
$546$	−3.69481e11	−0.177920
$547$	3.58318e12	1.71130	0.855649	−	0.517557i	$-0.173158\pi$
$547$	3.58318e12	1.71130	0.855649	+	0.517557i	$0.173158\pi$
$548$	5.50997e11	0.260998
$549$	1.87603e12	0.881382
$550$	1.13600e12	0.529356
$551$	−4.38154e11	−0.202509
$552$	−4.57223e11	−0.209605
$553$	3.03112e12	1.37829
$554$	4.73723e11	0.213664
$555$	−4.64722e10	−0.0207910
$556$	−2.88880e12	−1.28198
$557$	2.74318e12	1.20755	0.603775	−	0.797154i	$-0.293662\pi$
$557$	2.74318e12	1.20755	0.603775	+	0.797154i	$0.293662\pi$
$558$	−1.41271e12	−0.616877
$559$	−3.66223e11	−0.158632
$560$	−3.83377e10	−0.0164733
$561$	−1.21602e11	−0.0518331
$562$	−3.43939e12	−1.45435
$563$	−3.94195e12	−1.65357	−0.826785	−	0.562517i	$-0.809833\pi$
$563$	−3.94195e12	−1.65357	−0.826785	+	0.562517i	$0.809833\pi$
$564$	2.45310e12	1.02084
$565$	6.03089e9	0.00248979
$566$	−3.67555e12	−1.50539
$567$	−3.36313e12	−1.36653
$568$	1.83619e11	0.0740200
$569$	−2.71080e12	−1.08416	−0.542078	−	0.840328i	$-0.682362\pi$
$569$	−2.71080e12	−1.08416	−0.542078	+	0.840328i	$0.682362\pi$
$570$	1.30701e10	0.00518613
$571$	−1.39653e12	−0.549777	−0.274889	−	0.961476i	$-0.588641\pi$
$571$	−1.39653e12	−0.549777	−0.274889	+	0.961476i	$0.588641\pi$
$572$	8.06271e10	0.0314919
$573$	−9.54544e10	−0.0369913
$574$	4.73543e12	1.82077
$575$	−2.11562e12	−0.807111
$576$	−1.00622e12	−0.380882
$577$	1.22532e12	0.460213	0.230106	−	0.973165i	$-0.426093\pi$
$577$	1.22532e12	0.460213	0.230106	+	0.973165i	$0.426093\pi$
$578$	−3.60576e12	−1.34376
$579$	1.12026e12	0.414254
$580$	−2.71043e10	−0.00994517
$581$	3.79034e12	1.38002
$582$	−5.04897e12	−1.82410
$583$	1.37228e12	0.491964
$584$	2.50832e10	0.00892329
$585$	−2.02878e9	−0.000716199 0
$586$	4.84320e12	1.69665
$587$	−1.64735e11	−0.0572683	−0.0286341	−	0.999590i	$-0.509116\pi$
$587$	−1.64735e11	−0.0572683	−0.0286341	+	0.999590i	$0.509116\pi$
$588$	6.23988e11	0.215268
$589$	−5.38810e11	−0.184466
$590$	5.58283e10	0.0189679
$591$	5.57645e12	1.88024
$592$	4.21907e12	1.41179
$593$	3.61210e12	1.19954	0.599768	−	0.800174i	$-0.295259\pi$
$593$	3.61210e12	1.19954	0.599768	+	0.800174i	$0.295259\pi$
$594$	8.75116e11	0.288421
$595$	4.74372e9	0.00155165
$596$	−2.55446e12	−0.829260
$597$	−2.12383e12	−0.684283
$598$	−3.27379e11	−0.104688
$599$	−3.73918e12	−1.18674	−0.593369	−	0.804930i	$-0.702203\pi$
$599$	−3.73918e12	−1.18674	−0.593369	+	0.804930i	$0.702203\pi$
$600$	8.24131e11	0.259606
$601$	−5.13623e12	−1.60587	−0.802934	−	0.596068i	$-0.796729\pi$
$601$	−5.13623e12	−1.60587	−0.802934	+	0.596068i	$0.796729\pi$
$602$	7.98687e12	2.47852
$603$	1.50977e12	0.465033
$604$	−3.91560e12	−1.19710
$605$	−3.71704e10	−0.0112797
$606$	7.41890e12	2.23467
$607$	−2.95357e12	−0.883075	−0.441537	−	0.897243i	$-0.645567\pi$
$607$	−2.95357e12	−0.883075	−0.441537	+	0.897243i	$0.645567\pi$
$608$	−1.02613e12	−0.304534
$609$	−4.11092e12	−1.21105
$610$	9.65039e10	0.0282202
$611$	−3.16639e11	−0.0919133
$612$	1.76565e11	0.0508771
$613$	3.52319e12	1.00778	0.503888	−	0.863769i	$-0.331902\pi$
$613$	3.52319e12	1.00778	0.503888	+	0.863769i	$0.331902\pi$
$614$	−5.20392e12	−1.47765
$615$	7.20657e10	0.0203138
$616$	3.16985e11	0.0887003
$617$	−4.38912e12	−1.21926	−0.609628	−	0.792688i	$-0.708681\pi$
$617$	−4.38912e12	−1.21926	−0.609628	+	0.792688i	$0.708681\pi$
$618$	3.11292e12	0.858459
$619$	1.94384e12	0.532174	0.266087	−	0.963949i	$-0.414269\pi$
$619$	1.94384e12	0.532174	0.266087	+	0.963949i	$0.414269\pi$
$620$	−3.33309e10	−0.00905909
$621$	−1.62976e12	−0.439756
$622$	2.56874e12	0.688120
$623$	−2.60085e12	−0.691701
$624$	5.10488e11	0.134789
$625$	3.81267e12	0.999470
$626$	−3.64231e12	−0.947965
$627$	−4.32584e11	−0.111781
$628$	6.11906e12	1.56988
$629$	−5.22048e11	−0.132979
$630$	4.42452e10	0.0111901
$631$	−3.30231e12	−0.829250	−0.414625	−	0.909992i	$-0.636087\pi$
$631$	−3.30231e12	−0.829250	−0.414625	+	0.909992i	$0.636087\pi$
$632$	−1.04621e12	−0.260851
$633$	3.61119e12	0.893992
$634$	5.21371e12	1.28158
$635$	−4.66338e10	−0.0113820
$636$	−5.52245e12	−1.33837
$637$	−8.05424e10	−0.0193819
$638$	1.95587e12	0.467354
$639$	−8.48271e11	−0.201271
$640$	2.31593e10	0.00545652
$641$	1.30981e12	0.306441	0.153220	−	0.988192i	$-0.451036\pi$
$641$	1.30981e12	0.306441	0.153220	+	0.988192i	$0.451036\pi$
$642$	1.04247e13	2.42190
$643$	−2.85583e12	−0.658845	−0.329422	−	0.944183i	$-0.606854\pi$
$643$	−2.85583e12	−0.658845	−0.329422	+	0.944183i	$0.606854\pi$
$644$	3.27470e12	0.750213
$645$	1.21548e11	0.0276521
$646$	1.46824e11	0.0331705
$647$	5.71955e12	1.28319	0.641597	−	0.767042i	$-0.278272\pi$
$647$	5.71955e12	1.28319	0.641597	+	0.767042i	$0.278272\pi$
$648$	1.16081e12	0.258626
$649$	−1.84776e12	−0.408831
$650$	5.90090e11	0.129661
$651$	−5.05532e12	−1.10315
$652$	−2.20638e12	−0.478152
$653$	5.16405e12	1.11143	0.555714	−	0.831373i	$-0.312445\pi$
$653$	5.16405e12	1.11143	0.555714	+	0.831373i	$0.312445\pi$
$654$	−8.41920e12	−1.79958
$655$	−9.22126e10	−0.0195751
$656$	−6.54264e12	−1.37939
$657$	−1.15878e11	−0.0242637
$658$	6.90550e12	1.43608
$659$	−5.94875e12	−1.22869	−0.614343	−	0.789039i	$-0.710579\pi$
$659$	−5.94875e12	−1.22869	−0.614343	+	0.789039i	$0.710579\pi$
$660$	−2.67598e10	−0.00548952
$661$	−3.54759e12	−0.722815	−0.361407	−	0.932408i	$-0.617704\pi$
$661$	−3.54759e12	−0.722815	−0.361407	+	0.932408i	$0.617704\pi$
$662$	4.53501e12	0.917734
$663$	−6.31653e10	−0.0126960
$664$	−1.30826e12	−0.261179
$665$	1.68752e10	0.00334620
$666$	−4.86920e12	−0.959010
$667$	−3.64249e12	−0.712577
$668$	6.88025e12	1.33694
$669$	−3.27325e12	−0.631773
$670$	7.76634e10	0.0148895
$671$	−3.19400e12	−0.608252
$672$	−9.62752e12	−1.82118
$673$	−4.90748e12	−0.922127	−0.461064	−	0.887367i	$-0.652532\pi$
$673$	−4.90748e12	−0.922127	−0.461064	+	0.887367i	$0.652532\pi$
$674$	3.28004e12	0.612223
$675$	2.93760e12	0.544660
$676$	−4.55834e12	−0.839549
$677$	4.39260e12	0.803661	0.401830	−	0.915714i	$-0.368374\pi$
$677$	4.39260e12	0.803661	0.401830	+	0.915714i	$0.368374\pi$
$678$	1.75135e12	0.318302
$679$	−6.51886e12	−1.17695
$680$	−1.63733e9	−0.000293660 0
$681$	−6.96544e12	−1.24104
$682$	2.40518e12	0.425714
$683$	9.86928e12	1.73537	0.867685	−	0.497114i	$-0.165607\pi$
$683$	9.86928e12	1.73537	0.867685	+	0.497114i	$0.165607\pi$
$684$	6.28108e11	0.109719
$685$	2.36047e10	0.00409629
$686$	−6.89075e12	−1.18798
$687$	−9.29755e12	−1.59244
$688$	−1.10350e13	−1.87768
$689$	7.12820e11	0.120502
$690$	1.08655e11	0.0182486
$691$	6.23342e12	1.04010	0.520050	−	0.854136i	$-0.325913\pi$
$691$	6.23342e12	1.04010	0.520050	+	0.854136i	$0.325913\pi$
$692$	−3.70972e12	−0.614984
$693$	−1.46439e12	−0.241189
$694$	−4.38187e11	−0.0717037
$695$	−1.23756e11	−0.0201203
$696$	1.41891e12	0.229200
$697$	8.09554e11	0.129927
$698$	3.03940e12	0.484661
$699$	4.46091e12	0.706767
$700$	−5.90254e12	−0.929176
$701$	7.27475e12	1.13786	0.568928	−	0.822388i	$-0.307358\pi$
$701$	7.27475e12	1.13786	0.568928	+	0.822388i	$0.307358\pi$
$702$	4.54573e11	0.0706459
$703$	−1.85712e12	−0.286775
$704$	1.71312e12	0.262851
$705$	1.05091e11	0.0160219
$706$	−4.91427e12	−0.744455
$707$	9.57875e12	1.44185
$708$	7.43592e12	1.11221
$709$	8.89732e12	1.32237	0.661183	−	0.750225i	$-0.270055\pi$
$709$	8.89732e12	1.32237	0.661183	+	0.750225i	$0.270055\pi$
$710$	−4.36355e10	−0.00644432
$711$	4.83322e12	0.709290
$712$	8.97699e11	0.130909
$713$	−4.47927e12	−0.649089
$714$	1.37756e12	0.198366
$715$	3.45406e9	0.000494257 0
$716$	−4.94667e12	−0.703404
$717$	7.44466e12	1.05198
$718$	6.87651e12	0.965624
$719$	3.34256e12	0.466444	0.233222	−	0.972424i	$-0.425073\pi$
$719$	3.34256e12	0.466444	0.233222	+	0.972424i	$0.425073\pi$
$720$	−6.11308e10	−0.00847743
$721$	4.01917e12	0.553896
$722$	5.22310e11	0.0715337
$723$	8.77228e12	1.19396
$724$	9.16142e12	1.23919
$725$	6.56547e12	0.882561
$726$	−1.07941e13	−1.44203
$727$	4.10387e12	0.544865	0.272433	−	0.962175i	$-0.412172\pi$
$727$	4.10387e12	0.544865	0.272433	+	0.962175i	$0.412172\pi$
$728$	1.64656e11	0.0217263
$729$	−1.66748e11	−0.0218668
$730$	−5.96082e9	−0.000776878 0
$731$	1.36541e12	0.176862
$732$	1.28536e13	1.65472
$733$	−2.80544e12	−0.358949	−0.179474	−	0.983763i	$-0.557440\pi$
$733$	−2.80544e12	−0.358949	−0.179474	+	0.983763i	$0.557440\pi$
$734$	1.39763e13	1.77730
$735$	2.67317e10	0.00337857
$736$	−8.53047e12	−1.07158
$737$	−2.57044e12	−0.320925
$738$	7.55080e12	0.937000
$739$	−1.41237e13	−1.74201	−0.871003	−	0.491277i	$-0.836530\pi$
$739$	−1.41237e13	−1.74201	−0.871003	+	0.491277i	$0.836530\pi$
$740$	−1.14882e11	−0.0140835
$741$	−2.24703e11	−0.0273796
$742$	−1.55457e13	−1.88276
$743$	−1.18845e13	−1.43064	−0.715319	−	0.698798i	$-0.753719\pi$
$743$	−1.18845e13	−1.43064	−0.715319	+	0.698798i	$0.753719\pi$
$744$	1.74488e12	0.208779
$745$	−1.09433e11	−0.0130150
$746$	9.13847e12	1.08031
$747$	6.04384e12	0.710183
$748$	−3.00607e11	−0.0351109
$749$	1.34596e13	1.56266
$750$	−3.91731e11	−0.0452077
$751$	−1.11983e13	−1.28461	−0.642307	−	0.766447i	$-0.722023\pi$
$751$	−1.11983e13	−1.28461	−0.642307	+	0.766447i	$0.722023\pi$
$752$	−9.54089e12	−1.08795
$753$	−5.72291e12	−0.648693
$754$	1.01596e12	0.114474
$755$	−1.67744e11	−0.0187882
$756$	−4.54700e12	−0.506264
$757$	−9.01390e12	−0.997657	−0.498829	−	0.866701i	$-0.666236\pi$
$757$	−9.01390e12	−0.997657	−0.498829	+	0.866701i	$0.666236\pi$
$758$	−2.18443e13	−2.40340
$759$	−3.59618e12	−0.393327
$760$	−5.82459e9	−0.000633293 0
$761$	1.74817e13	1.88952	0.944760	−	0.327762i	$-0.106294\pi$
$761$	1.74817e13	1.88952	0.944760	+	0.327762i	$0.106294\pi$
$762$	−1.35423e13	−1.45510
$763$	−1.08703e13	−1.16113
$764$	−2.35969e11	−0.0250573
$765$	7.56403e9	0.000798504 0
$766$	−1.12457e13	−1.18020
$767$	−9.59805e11	−0.100139
$768$	1.48623e13	1.54156
$769$	9.66287e12	0.996409	0.498204	−	0.867060i	$-0.333993\pi$
$769$	9.66287e12	0.996409	0.498204	+	0.867060i	$0.333993\pi$
$770$	−7.53289e10	−0.00772242
$771$	−2.28781e12	−0.233172
$772$	2.76936e12	0.280609
$773$	−7.02830e12	−0.708016	−0.354008	−	0.935242i	$-0.615181\pi$
$773$	−7.02830e12	−0.708016	−0.354008	+	0.935242i	$0.615181\pi$
$774$	1.27353e13	1.27549
$775$	8.07374e12	0.803928
$776$	2.25003e12	0.222746
$777$	−1.74242e13	−1.71498
$778$	−1.72836e13	−1.69132
$779$	2.87989e12	0.280193
$780$	−1.39002e10	−0.00134461
$781$	1.44421e12	0.138899
$782$	1.22059e12	0.116718
$783$	5.05768e12	0.480865
$784$	−2.42689e12	−0.229418
$785$	2.62141e11	0.0246389
$786$	−2.67782e13	−2.50253
$787$	1.54625e13	1.43679	0.718396	−	0.695635i	$-0.244877\pi$
$787$	1.54625e13	1.43679	0.718396	+	0.695635i	$0.244877\pi$
$788$	1.37853e13	1.27365
$789$	1.57508e13	1.44696
$790$	2.48623e11	0.0227101
$791$	2.26121e12	0.205375
$792$	5.05444e11	0.0456467
$793$	−1.65910e12	−0.148986
$794$	−1.41892e13	−1.26697
$795$	−2.36582e11	−0.0210053
$796$	−5.25024e12	−0.463522
$797$	−5.78851e12	−0.508164	−0.254082	−	0.967183i	$-0.581773\pi$
$797$	−5.78851e12	−0.508164	−0.254082	+	0.967183i	$0.581773\pi$
$798$	4.90050e12	0.427787
$799$	1.18054e12	0.102476
$800$	1.53759e13	1.32720
$801$	−4.14714e12	−0.355961
$802$	1.49453e13	1.27561
$803$	1.97286e11	0.0167447
$804$	1.03442e13	0.873062
$805$	1.40288e11	0.0117744
$806$	1.24936e12	0.104275
$807$	−1.90567e13	−1.58167
$808$	−3.30617e12	−0.272881
$809$	1.36385e13	1.11943	0.559716	−	0.828684i	$-0.310910\pi$
$809$	1.36385e13	1.11943	0.559716	+	0.828684i	$0.310910\pi$
$810$	−2.75856e11	−0.0225165
$811$	−3.27696e12	−0.265997	−0.132999	−	0.991116i	$-0.542461\pi$
$811$	−3.27696e12	−0.265997	−0.132999	+	0.991116i	$0.542461\pi$
$812$	−1.01624e13	−0.820344
$813$	−7.76568e12	−0.623408
$814$	8.28996e12	0.661825
$815$	−9.45212e10	−0.00750447
$816$	−1.90329e12	−0.150279
$817$	4.85729e12	0.381412
$818$	−2.38583e13	−1.86315
$819$	−7.60668e11	−0.0590769
$820$	1.78151e11	0.0137602
$821$	9.44287e12	0.725370	0.362685	−	0.931912i	$-0.381860\pi$
$821$	9.44287e12	0.725370	0.362685	+	0.931912i	$0.381860\pi$
$822$	6.85472e12	0.523681
$823$	9.97478e12	0.757886	0.378943	−	0.925420i	$-0.376288\pi$
$823$	9.97478e12	0.757886	0.378943	+	0.925420i	$0.376288\pi$
$824$	−1.38724e12	−0.104829
$825$	6.48201e12	0.487155
$826$	2.09322e13	1.56460
$827$	−7.36925e12	−0.547834	−0.273917	−	0.961753i	$-0.588319\pi$
$827$	−7.36925e12	−0.547834	−0.273917	+	0.961753i	$0.588319\pi$
$828$	5.22162e12	0.386072
$829$	6.88866e12	0.506570	0.253285	−	0.967392i	$-0.418489\pi$
$829$	6.88866e12	0.506570	0.253285	+	0.967392i	$0.418489\pi$
$830$	3.10898e11	0.0227387
$831$	2.70305e12	0.196630
$832$	8.89867e11	0.0643828
$833$	3.00292e11	0.0216093
$834$	−3.59383e13	−2.57223
$835$	2.94750e11	0.0209829
$836$	−1.06937e12	−0.0757184
$837$	6.21957e12	0.438022
$838$	2.47603e13	1.73443
$839$	−1.64491e13	−1.14608	−0.573038	−	0.819529i	$-0.694235\pi$
$839$	−1.64491e13	−1.14608	−0.573038	+	0.819529i	$0.694235\pi$
$840$	−5.46485e10	−0.00378723
$841$	−3.20333e12	−0.220811
$842$	−6.86831e12	−0.470918
$843$	−1.96251e13	−1.33840
$844$	8.92708e12	0.605575
$845$	−1.95279e11	−0.0131765
$846$	1.10111e13	0.739031
$847$	−1.39366e13	−0.930426
$848$	2.14786e13	1.42634
$849$	−2.09726e13	−1.38538
$850$	−2.20007e12	−0.144561
$851$	−1.54387e13	−1.00909
$852$	−5.81193e12	−0.377870
$853$	1.01785e13	0.658282	0.329141	−	0.944281i	$-0.393241\pi$
$853$	1.01785e13	0.658282	0.329141	+	0.944281i	$0.393241\pi$
$854$	3.61830e13	2.32779
$855$	2.69081e10	0.00172201
$856$	−4.64567e12	−0.295745
$857$	−2.17224e13	−1.37561	−0.687804	−	0.725897i	$-0.741425\pi$
$857$	−2.17224e13	−1.37561	−0.687804	+	0.725897i	$0.741425\pi$
$858$	1.00305e12	0.0631871
$859$	−1.32470e13	−0.830132	−0.415066	−	0.909791i	$-0.636241\pi$
$859$	−1.32470e13	−0.830132	−0.415066	+	0.909791i	$0.636241\pi$
$860$	3.00473e11	0.0187311
$861$	2.70202e13	1.67562
$862$	4.36356e13	2.69190
$863$	−7.58119e12	−0.465252	−0.232626	−	0.972566i	$-0.574732\pi$
$863$	−7.58119e12	−0.465252	−0.232626	+	0.972566i	$0.574732\pi$
$864$	1.18448e13	0.723127
$865$	−1.58924e11	−0.00965202
$866$	7.83136e11	0.0473158
$867$	−2.05744e13	−1.23663
$868$	−1.24970e13	−0.747255
$869$	−8.22872e12	−0.489489
$870$	−3.37193e11	−0.0199546
$871$	−1.33520e12	−0.0786074
$872$	3.75194e12	0.219752
$873$	−1.03946e13	−0.605678
$874$	4.34209e12	0.251708
$875$	−5.05774e11	−0.0291689
$876$	−7.93938e11	−0.0455531
$877$	1.52429e13	0.870100	0.435050	−	0.900406i	$-0.356731\pi$
$877$	1.52429e13	0.870100	0.435050	+	0.900406i	$0.356731\pi$
$878$	−1.57930e13	−0.896889
$879$	2.76352e13	1.56139
$880$	1.04077e11	0.00585037
$881$	3.65973e12	0.204671	0.102336	−	0.994750i	$-0.467368\pi$
$881$	3.65973e12	0.204671	0.102336	+	0.994750i	$0.467368\pi$
$882$	2.80085e12	0.155841
$883$	9.65287e12	0.534359	0.267179	−	0.963647i	$-0.413908\pi$
$883$	9.65287e12	0.534359	0.267179	+	0.963647i	$0.413908\pi$
$884$	−1.56149e11	−0.00860008
$885$	3.18555e11	0.0174558
$886$	3.37512e13	1.84008
$887$	2.99592e12	0.162508	0.0812538	−	0.996693i	$-0.474108\pi$
$887$	2.99592e12	0.162508	0.0812538	+	0.996693i	$0.474108\pi$
$888$	6.01408e12	0.324572
$889$	−1.74848e13	−0.938864
$890$	−2.13331e11	−0.0113972
$891$	9.13005e12	0.485315
$892$	−8.09166e12	−0.427953
$893$	4.19964e12	0.220994
$894$	−3.17789e13	−1.66387
$895$	−2.11915e11	−0.0110397
$896$	8.68332e12	0.450090
$897$	−1.86801e12	−0.0963417
$898$	2.96180e13	1.51989
$899$	1.39006e13	0.709766
$900$	−9.41181e12	−0.478170
$901$	−2.65765e12	−0.134350
$902$	−1.28555e13	−0.646635
$903$	4.55729e13	2.28093
$904$	−7.80472e11	−0.0388687
$905$	3.92475e11	0.0194488
$906$	−4.87123e13	−2.40194
$907$	−3.69924e13	−1.81501	−0.907507	−	0.420037i	$-0.862017\pi$
$907$	−3.69924e13	−1.81501	−0.907507	+	0.420037i	$0.862017\pi$
$908$	−1.72190e13	−0.840661
$909$	1.52737e13	0.742003
$910$	−3.91291e10	−0.00189153
$911$	1.99144e12	0.0957930	0.0478965	−	0.998852i	$-0.484748\pi$
$911$	1.99144e12	0.0957930	0.0478965	+	0.998852i	$0.484748\pi$
$912$	−6.77072e12	−0.324084
$913$	−1.02898e13	−0.490105
$914$	−2.12057e13	−1.00507
$915$	5.50649e11	0.0259705
$916$	−2.29841e13	−1.07869
$917$	−3.45740e13	−1.61469
$918$	−1.69482e12	−0.0787645
$919$	3.16685e12	0.146456	0.0732282	−	0.997315i	$-0.476670\pi$
$919$	3.16685e12	0.146456	0.0732282	+	0.997315i	$0.476670\pi$
$920$	−4.84213e10	−0.00222839
$921$	−2.96934e13	−1.35985
$922$	−3.78263e13	−1.72387
$923$	7.50185e11	0.0340221
$924$	−1.00333e13	−0.452812
$925$	2.78278e13	1.24980
$926$	−8.50055e12	−0.379925
$927$	6.40871e12	0.285044
$928$	2.64728e13	1.17175
$929$	8.22120e12	0.362130	0.181065	−	0.983471i	$-0.442046\pi$
$929$	8.22120e12	0.362130	0.181065	+	0.983471i	$0.442046\pi$
$930$	−4.14656e11	−0.0181767
$931$	1.06825e12	0.0466015
$932$	1.10276e13	0.478752
$933$	1.46572e13	0.633262
$934$	−3.02449e13	−1.30044
$935$	−1.28780e10	−0.000551057 0
$936$	2.62549e11	0.0111807
$937$	−4.01692e13	−1.70241	−0.851207	−	0.524830i	$-0.824129\pi$
$937$	−4.01692e13	−1.70241	−0.851207	+	0.524830i	$0.824129\pi$
$938$	2.91190e13	1.22819
$939$	−2.07829e13	−0.872392
$940$	2.59791e11	0.0108530
$941$	2.17605e13	0.904724	0.452362	−	0.891834i	$-0.350582\pi$
$941$	2.17605e13	0.904724	0.452362	+	0.891834i	$0.350582\pi$
$942$	7.61246e13	3.14990
$943$	2.39413e13	0.985927
$944$	−2.89207e13	−1.18532
$945$	−1.94793e11	−0.00794568
$946$	−2.16823e13	−0.880229
$947$	−1.63289e13	−0.659752	−0.329876	−	0.944024i	$-0.607007\pi$
$947$	−1.63289e13	−0.659752	−0.329876	+	0.944024i	$0.607007\pi$
$948$	3.31148e13	1.33163
$949$	1.02479e11	0.00410144
$950$	−7.82649e12	−0.311753
$951$	2.97493e13	1.17941
$952$	−6.13897e11	−0.0242231
$953$	−3.27105e13	−1.28460	−0.642302	−	0.766452i	$-0.722021\pi$
$953$	−3.27105e13	−1.28460	−0.642302	+	0.766452i	$0.722021\pi$
$954$	−2.47882e13	−0.968898
$955$	−1.01089e10	−0.000393268 0
$956$	1.84036e13	0.712596
$957$	1.11601e13	0.430096
$958$	−3.26461e13	−1.25224
$959$	8.85032e12	0.337890
$960$	−2.95343e11	−0.0112229
$961$	−9.34564e12	−0.353471
$962$	4.30617e12	0.162108
$963$	2.14618e13	0.804171
$964$	2.16856e13	0.808770
$965$	1.18639e11	0.00440408
$966$	4.07391e13	1.50527
$967$	3.85406e13	1.41742	0.708712	−	0.705498i	$-0.249277\pi$
$967$	3.85406e13	1.41742	0.708712	+	0.705498i	$0.249277\pi$
$968$	4.81031e12	0.176090
$969$	8.37775e11	0.0305261
$970$	−5.34701e11	−0.0193927
$971$	4.84114e13	1.74768	0.873839	−	0.486216i	$-0.161623\pi$
$971$	4.84114e13	1.74768	0.873839	+	0.486216i	$0.161623\pi$
$972$	−2.38975e13	−0.858726
$973$	−4.64009e13	−1.65966
$974$	5.45922e12	0.194364
$975$	3.36704e12	0.119324
$976$	−4.99918e13	−1.76350
$977$	−4.12824e13	−1.44957	−0.724785	−	0.688975i	$-0.758061\pi$
$977$	−4.12824e13	−1.44957	−0.724785	+	0.688975i	$0.758061\pi$
$978$	−2.74486e13	−0.959390
$979$	7.06064e12	0.245653
$980$	6.60822e10	0.00228859
$981$	−1.73330e13	−0.597536
$982$	5.58154e13	1.91537
$983$	−1.19116e13	−0.406891	−0.203446	−	0.979086i	$-0.565214\pi$
$983$	−1.19116e13	−0.406891	−0.203446	+	0.979086i	$0.565214\pi$
$984$	−9.32620e12	−0.317122
$985$	5.90563e11	0.0199895
$986$	−3.78788e12	−0.127629
$987$	3.94026e13	1.32159
$988$	−5.55480e11	−0.0185465
$989$	4.03799e13	1.34209
$990$	−1.20115e11	−0.00397409
$991$	2.52732e12	0.0832394	0.0416197	−	0.999134i	$-0.486748\pi$
$991$	2.52732e12	0.0832394	0.0416197	+	0.999134i	$0.486748\pi$
$992$	3.25544e13	1.06735
$993$	2.58766e13	0.844571
$994$	−1.63606e13	−0.531571
$995$	−2.24920e11	−0.00727486
$996$	4.14093e13	1.33331
$997$	2.47258e13	0.792540	0.396270	−	0.918134i	$-0.370304\pi$
$997$	2.47258e13	0.792540	0.396270	+	0.918134i	$0.370304\pi$
$998$	−3.11390e13	−0.993613
$999$	2.14371e13	0.680958

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.a.b.1.7	✓	8
3.2	odd	2		171.10.a.f.1.2		8
4.3	odd	2		304.10.a.i.1.3		8
19.18	odd	2		361.10.a.c.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.a.b.1.7	✓	8	1.1	even	1	trivial
171.10.a.f.1.2		8	3.2	odd	2
304.10.a.i.1.3		8	4.3	odd	2
361.10.a.c.1.2		8	19.18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.a (trivial)

\(f(q)\)	\(=\)	\(q+30.7538 q^{2} +175.481 q^{3} +433.799 q^{4} +18.5839 q^{5} +5396.70 q^{6} +6967.83 q^{7} -2404.99 q^{8} +11110.5 q^{9} +571.527 q^{10} -18915.9 q^{11} +76123.3 q^{12} -9825.75 q^{13} +214288. q^{14} +3261.12 q^{15} -296068. q^{16} +36634.0 q^{17} +341689. q^{18} +130321. q^{19} +8061.68 q^{20} +1.22272e6 q^{21} -581737. q^{22} +1.08339e6 q^{23} -422030. q^{24} -1.95278e6 q^{25} -302179. q^{26} -1.50432e6 q^{27} +3.02264e6 q^{28} -3.36211e6 q^{29} +100292. q^{30} -4.13449e6 q^{31} -7.87386e6 q^{32} -3.31938e6 q^{33} +1.12664e6 q^{34} +129490. q^{35} +4.81970e6 q^{36} -1.42504e7 q^{37} +4.00787e6 q^{38} -1.72423e6 q^{39} -44694.2 q^{40} +2.20985e7 q^{41} +3.76033e7 q^{42} +3.72717e7 q^{43} -8.20569e6 q^{44} +206476. q^{45} +3.33184e7 q^{46} +3.22254e7 q^{47} -5.19541e7 q^{48} +8.19708e6 q^{49} -6.00555e7 q^{50} +6.42855e6 q^{51} -4.26240e6 q^{52} -7.25462e7 q^{53} -4.62635e7 q^{54} -351532. q^{55} -1.67576e7 q^{56} +2.28688e7 q^{57} -1.03398e8 q^{58} +9.76827e7 q^{59} +1.41467e6 q^{60} +1.68853e8 q^{61} -1.27151e8 q^{62} +7.74158e7 q^{63} -9.05648e7 q^{64} -182601. q^{65} -1.02084e8 q^{66} +1.35888e8 q^{67} +1.58918e7 q^{68} +1.90114e8 q^{69} +3.98231e6 q^{70} -7.63489e7 q^{71} -2.67206e7 q^{72} -1.04296e7 q^{73} -4.38254e8 q^{74} -3.42675e8 q^{75} +5.65331e7 q^{76} -1.31803e8 q^{77} -5.30267e7 q^{78} +4.35016e8 q^{79} -5.50210e6 q^{80} -4.82665e8 q^{81} +6.79612e8 q^{82} +5.43977e8 q^{83} +5.30414e8 q^{84} +680803. q^{85} +1.14625e9 q^{86} -5.89986e8 q^{87} +4.54926e7 q^{88} -3.73265e8 q^{89} +6.34993e6 q^{90} -6.84642e7 q^{91} +4.69974e8 q^{92} -7.25522e8 q^{93} +9.91054e8 q^{94} +2.42188e6 q^{95} -1.38171e9 q^{96} -9.35566e8 q^{97} +2.52092e8 q^{98} -2.10164e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 15 q^{2} + 7 q^{3} + 2645 q^{4} + 3894 q^{5} - 9723 q^{6} - 7133 q^{7} + 10911 q^{8} + 102715 q^{9} + 113172 q^{10} + 172818 q^{11} + 349117 q^{12} + 109291 q^{13} + 250959 q^{14} + 457332 q^{15}+ \cdots - 1682553420 q^{99}+O(q^{100}) \) 8 * q + 15 * q^2 + 7 * q^3 + 2645 * q^4 + 3894 * q^5 - 9723 * q^6 - 7133 * q^7 + 10911 * q^8 + 102715 * q^9 + 113172 * q^10 + 172818 * q^11 + 349117 * q^12 + 109291 * q^13 + 250959 * q^14 + 457332 * q^15 + 1590377 * q^16 + 583575 * q^17 + 308688 * q^18 + 1042568 * q^19 + 3191676 * q^20 + 372767 * q^21 + 57234 * q^22 - 2292405 * q^23 - 7378809 * q^24 + 205328 * q^25 - 821247 * q^26 - 15261551 * q^27 - 10217945 * q^28 + 4546335 * q^29 - 30417480 * q^30 - 8277416 * q^31 - 15773553 * q^32 + 13959234 * q^33 - 22393029 * q^34 + 15633768 * q^35 - 1486010 * q^36 + 24485536 * q^37 + 1954815 * q^38 + 16641725 * q^39 + 2543472 * q^40 + 35051946 * q^41 - 55902561 * q^42 + 36624268 * q^43 + 215210070 * q^44 + 138146370 * q^45 - 66065277 * q^46 + 9865524 * q^47 + 205312561 * q^48 + 111765087 * q^49 + 50599293 * q^50 + 109712553 * q^51 - 258827351 * q^52 + 13963683 * q^53 - 345545985 * q^54 + 261540660 * q^55 - 517172871 * q^56 + 912247 * q^57 - 399459963 * q^58 + 21215463 * q^59 - 275519064 * q^60 + 180552112 * q^61 - 451241340 * q^62 + 303758726 * q^63 + 180711569 * q^64 - 21864624 * q^65 - 1155635334 * q^66 + 1767355 * q^67 - 41475117 * q^68 + 504738939 * q^69 - 516193752 * q^70 + 273631578 * q^71 - 1360350726 * q^72 - 263711543 * q^73 + 677785566 * q^74 - 340714091 * q^75 + 344699045 * q^76 + 441243702 * q^77 + 1315717365 * q^78 + 744472174 * q^79 + 1904949528 * q^80 + 1867545184 * q^81 + 1284295572 * q^82 + 832139910 * q^83 - 917264533 * q^84 + 1013793492 * q^85 + 956757432 * q^86 - 231595575 * q^87 - 585082794 * q^88 - 291457734 * q^89 + 675674604 * q^90 - 1351077415 * q^91 + 2042025591 * q^92 + 537395144 * q^93 - 2759974128 * q^94 + 507469974 * q^95 - 1782885825 * q^96 - 3483837140 * q^97 + 4178510532 * q^98 - 1682553420 * q^99

Introduction

L-functions

Modular forms

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Database

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