LMFDB - Embedded newform 19.8.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,8,Mod(1,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("19.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	19.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:	$5.93531548420$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 255x^{2} + 475x + 500 $ x^4 - x^3 - 255x^2 + 475x + 500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-16.3077$ 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)

$f(q)$	$=$	$q+3.18411 q^{2} +20.6576 q^{3} -117.861 q^{4} -477.630 q^{5} +65.7761 q^{6} +883.696 q^{7} -782.850 q^{8} -1760.26 q^{9} +O(q^{10})$	\(q+3.18411 q^{2} +20.6576 q^{3} -117.861 q^{4} -477.630 q^{5} +65.7761 q^{6} +883.696 q^{7} -782.850 q^{8} -1760.26 q^{9} -1520.83 q^{10} -5160.04 q^{11} -2434.74 q^{12} +5645.42 q^{13} +2813.79 q^{14} -9866.70 q^{15} +12593.6 q^{16} -5865.48 q^{17} -5604.87 q^{18} +6859.00 q^{19} +56294.2 q^{20} +18255.1 q^{21} -16430.1 q^{22} -37133.4 q^{23} -16171.8 q^{24} +150005. q^{25} +17975.6 q^{26} -81541.1 q^{27} -104154. q^{28} +187685. q^{29} -31416.7 q^{30} -242165. q^{31} +140304. q^{32} -106594. q^{33} -18676.3 q^{34} -422080. q^{35} +207467. q^{36} -467834. q^{37} +21839.8 q^{38} +116621. q^{39} +373913. q^{40} -557213. q^{41} +58126.1 q^{42} +408555. q^{43} +608170. q^{44} +840754. q^{45} -118237. q^{46} -439207. q^{47} +260153. q^{48} -42624.4 q^{49} +477634. q^{50} -121167. q^{51} -665377. q^{52} -830248. q^{53} -259636. q^{54} +2.46459e6 q^{55} -691801. q^{56} +141691. q^{57} +597609. q^{58} -880709. q^{59} +1.16290e6 q^{60} +1.59095e6 q^{61} -771081. q^{62} -1.55554e6 q^{63} -1.16523e6 q^{64} -2.69642e6 q^{65} -339408. q^{66} -3.48201e6 q^{67} +691314. q^{68} -767088. q^{69} -1.34395e6 q^{70} +4.06081e6 q^{71} +1.37802e6 q^{72} +2.04518e6 q^{73} -1.48963e6 q^{74} +3.09875e6 q^{75} -808412. q^{76} -4.55991e6 q^{77} +371334. q^{78} +5.18855e6 q^{79} -6.01507e6 q^{80} +2.16525e6 q^{81} -1.77423e6 q^{82} -2.10622e6 q^{83} -2.15157e6 q^{84} +2.80153e6 q^{85} +1.30088e6 q^{86} +3.87712e6 q^{87} +4.03954e6 q^{88} +6.75005e6 q^{89} +2.67705e6 q^{90} +4.98884e6 q^{91} +4.37660e6 q^{92} -5.00256e6 q^{93} -1.39848e6 q^{94} -3.27606e6 q^{95} +2.89835e6 q^{96} +3.64028e6 q^{97} -135721. q^{98} +9.08303e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 9 q^{2} - 14 q^{3} + 37 q^{4} - 222 q^{5} - 603 q^{6} - 1246 q^{7} - 3555 q^{8} - 4898 q^{9}+O(q^{10}) $ 4 * q - 9 * q^2 - 14 * q^3 + 37 * q^4 - 222 * q^5 - 603 * q^6 - 1246 * q^7 - 3555 * q^8 - 4898 * q^9	\( 4 q - 9 q^{2} - 14 q^{3} + 37 q^{4} - 222 q^{5} - 603 q^{6} - 1246 q^{7} - 3555 q^{8} - 4898 q^{9} - 6444 q^{10} - 8718 q^{11} - 6281 q^{12} - 4480 q^{13} - 1935 q^{14} - 2760 q^{15} + 19393 q^{16} - 4440 q^{17} + 52722 q^{18} + 27436 q^{19} + 81228 q^{20} + 34124 q^{21} + 115182 q^{22} - 30528 q^{23} + 90135 q^{24} - 23906 q^{25} + 28521 q^{26} - 74942 q^{27} + 37439 q^{28} - 254244 q^{29} + 11340 q^{30} - 303460 q^{31} - 49059 q^{32} - 362364 q^{33} + 240309 q^{34} - 563862 q^{35} - 153410 q^{36} - 270460 q^{37} - 61731 q^{38} - 270304 q^{39} + 230868 q^{40} - 828564 q^{41} + 728307 q^{42} + 37454 q^{43} + 38874 q^{44} + 146694 q^{45} + 1909269 q^{46} + 335670 q^{47} + 1366243 q^{48} - 67560 q^{49} + 815013 q^{50} + 1047318 q^{51} + 1737887 q^{52} + 76728 q^{53} + 775215 q^{54} + 1008918 q^{55} - 973953 q^{56} - 96026 q^{57} + 1613565 q^{58} - 3191334 q^{59} + 669180 q^{60} + 346550 q^{61} - 4678848 q^{62} - 24766 q^{63} - 1917383 q^{64} - 4512972 q^{65} - 2532006 q^{66} - 270322 q^{67} - 9125409 q^{68} - 1452456 q^{69} + 235836 q^{70} - 2066124 q^{71} + 3929670 q^{72} - 416044 q^{73} - 8358894 q^{74} + 5984890 q^{75} + 253783 q^{76} - 3350514 q^{77} + 1418859 q^{78} + 16025864 q^{79} - 622428 q^{80} + 2742268 q^{81} + 7006752 q^{82} + 8524128 q^{83} + 1508165 q^{84} + 4323186 q^{85} - 9139572 q^{86} + 10085136 q^{87} + 4902930 q^{88} + 2899092 q^{89} + 10474488 q^{90} + 23189218 q^{91} - 24380829 q^{92} + 12902348 q^{93} - 9682776 q^{94} - 1522698 q^{95} + 514647 q^{96} - 4766908 q^{97} + 10655118 q^{98} + 25556322 q^{99}+O(q^{100}) \) 4 * q - 9 * q^2 - 14 * q^3 + 37 * q^4 - 222 * q^5 - 603 * q^6 - 1246 * q^7 - 3555 * q^8 - 4898 * q^9 - 6444 * q^10 - 8718 * q^11 - 6281 * q^12 - 4480 * q^13 - 1935 * q^14 - 2760 * q^15 + 19393 * q^16 - 4440 * q^17 + 52722 * q^18 + 27436 * q^19 + 81228 * q^20 + 34124 * q^21 + 115182 * q^22 - 30528 * q^23 + 90135 * q^24 - 23906 * q^25 + 28521 * q^26 - 74942 * q^27 + 37439 * q^28 - 254244 * q^29 + 11340 * q^30 - 303460 * q^31 - 49059 * q^32 - 362364 * q^33 + 240309 * q^34 - 563862 * q^35 - 153410 * q^36 - 270460 * q^37 - 61731 * q^38 - 270304 * q^39 + 230868 * q^40 - 828564 * q^41 + 728307 * q^42 + 37454 * q^43 + 38874 * q^44 + 146694 * q^45 + 1909269 * q^46 + 335670 * q^47 + 1366243 * q^48 - 67560 * q^49 + 815013 * q^50 + 1047318 * q^51 + 1737887 * q^52 + 76728 * q^53 + 775215 * q^54 + 1008918 * q^55 - 973953 * q^56 - 96026 * q^57 + 1613565 * q^58 - 3191334 * q^59 + 669180 * q^60 + 346550 * q^61 - 4678848 * q^62 - 24766 * q^63 - 1917383 * q^64 - 4512972 * q^65 - 2532006 * q^66 - 270322 * q^67 - 9125409 * q^68 - 1452456 * q^69 + 235836 * q^70 - 2066124 * q^71 + 3929670 * q^72 - 416044 * q^73 - 8358894 * q^74 + 5984890 * q^75 + 253783 * q^76 - 3350514 * q^77 + 1418859 * q^78 + 16025864 * q^79 - 622428 * q^80 + 2742268 * q^81 + 7006752 * q^82 + 8524128 * q^83 + 1508165 * q^84 + 4323186 * q^85 - 9139572 * q^86 + 10085136 * q^87 + 4902930 * q^88 + 2899092 * q^89 + 10474488 * q^90 + 23189218 * q^91 - 24380829 * q^92 + 12902348 * q^93 - 9682776 * q^94 - 1522698 * q^95 + 514647 * q^96 - 4766908 * q^97 + 10655118 * q^98 + 25556322 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.18411	0.281438	0.140719	−	0.990050i	$-0.455059\pi$
$2$	3.18411	0.281438	0.140719	+	0.990050i	$0.455059\pi$
$3$	20.6576	0.441729	0.220864	−	0.975305i	$-0.429112\pi$
$3$	20.6576	0.441729	0.220864	+	0.975305i	$0.429112\pi$
$4$	−117.861	−0.920792
$5$	−477.630	−1.70882	−0.854410	−	0.519599i	$-0.826081\pi$
$5$	−477.630	−1.70882	−0.854410	+	0.519599i	$0.826081\pi$
$6$	65.7761	0.124319
$7$	883.696	0.973777	0.486889	−	0.873464i	$-0.338132\pi$
$7$	883.696	0.973777	0.486889	+	0.873464i	$0.338132\pi$
$8$	−782.850	−0.540585
$9$	−1760.26	−0.804876
$10$	−1520.83	−0.480928
$11$	−5160.04	−1.16890	−0.584452	−	0.811428i	$-0.698690\pi$
$11$	−5160.04	−1.16890	−0.584452	+	0.811428i	$0.698690\pi$
$12$	−2434.74	−0.406741
$13$	5645.42	0.712680	0.356340	−	0.934356i	$-0.384024\pi$
$13$	5645.42	0.712680	0.356340	+	0.934356i	$0.384024\pi$
$14$	2813.79	0.274058
$15$	−9866.70	−0.754836
$16$	12593.6	0.768651
$17$	−5865.48	−0.289556	−0.144778	−	0.989464i	$-0.546247\pi$
$17$	−5865.48	−0.289556	−0.144778	+	0.989464i	$0.546247\pi$
$18$	−5604.87	−0.226523
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	56294.2	1.57347
$21$	18255.1	0.430146
$22$	−16430.1	−0.328974
$23$	−37133.4	−0.636382	−0.318191	−	0.948027i	$-0.603075\pi$
$23$	−37133.4	−0.636382	−0.318191	+	0.948027i	$0.603075\pi$
$24$	−16171.8	−0.238792
$25$	150005.	1.92007
$26$	17975.6	0.200575
$27$	−81541.1	−0.797266
$28$	−104154.	−0.896647
$29$	187685.	1.42901	0.714507	−	0.699629i	$-0.246651\pi$
$29$	187685.	1.42901	0.714507	+	0.699629i	$0.246651\pi$
$30$	−31416.7	−0.212440
$31$	−242165.	−1.45998	−0.729988	−	0.683460i	$-0.760474\pi$
$31$	−242165.	−1.45998	−0.729988	+	0.683460i	$0.760474\pi$
$32$	140304.	0.756912
$33$	−106594.	−0.516339
$34$	−18676.3	−0.0814921
$35$	−422080.	−1.66401
$36$	207467.	0.741123
$37$	−467834.	−1.51840	−0.759199	−	0.650859i	$-0.774409\pi$
$37$	−467834.	−1.51840	−0.759199	+	0.650859i	$0.774409\pi$
$38$	21839.8	0.0645664
$39$	116621.	0.314811
$40$	373913.	0.923762
$41$	−557213.	−1.26264	−0.631318	−	0.775524i	$-0.717486\pi$
$41$	−557213.	−1.26264	−0.631318	+	0.775524i	$0.717486\pi$
$42$	58126.1	0.121059
$43$	408555.	0.783630	0.391815	−	0.920044i	$-0.371847\pi$
$43$	408555.	0.783630	0.391815	+	0.920044i	$0.371847\pi$
$44$	608170.	1.07632
$45$	840754.	1.37539
$46$	−118237.	−0.179102
$47$	−439207.	−0.617059	−0.308529	−	0.951215i	$-0.599837\pi$
$47$	−439207.	−0.617059	−0.308529	+	0.951215i	$0.599837\pi$
$48$	260153.	0.339536
$49$	−42624.4	−0.0517574
$50$	477634.	0.540381
$51$	−121167.	−0.127905
$52$	−665377.	−0.656230
$53$	−830248.	−0.766024	−0.383012	−	0.923743i	$-0.625113\pi$
$53$	−830248.	−0.766024	−0.383012	+	0.923743i	$0.625113\pi$
$54$	−259636.	−0.224381
$55$	2.46459e6	1.99745
$56$	−691801.	−0.526409
$57$	141691.	0.101340
$58$	597609.	0.402179
$59$	−880709.	−0.558278	−0.279139	−	0.960251i	$-0.590049\pi$
$59$	−880709.	−0.558278	−0.279139	+	0.960251i	$0.590049\pi$
$60$	1.16290e6	0.695047
$61$	1.59095e6	0.897434	0.448717	−	0.893674i	$-0.351881\pi$
$61$	1.59095e6	0.897434	0.448717	+	0.893674i	$0.351881\pi$
$62$	−771081.	−0.410893
$63$	−1.55554e6	−0.783770
$64$	−1.16523e6	−0.555627
$65$	−2.69642e6	−1.21784
$66$	−339408.	−0.145317
$67$	−3.48201e6	−1.41438	−0.707192	−	0.707021i	$-0.750039\pi$
$67$	−3.48201e6	−1.41438	−0.707192	+	0.707021i	$0.750039\pi$
$68$	691314.	0.266621
$69$	−767088.	−0.281108
$70$	−1.34395e6	−0.468316
$71$	4.06081e6	1.34651	0.673253	−	0.739412i	$-0.264897\pi$
$71$	4.06081e6	1.34651	0.673253	+	0.739412i	$0.264897\pi$
$72$	1.37802e6	0.435103
$73$	2.04518e6	0.615320	0.307660	−	0.951496i	$-0.400454\pi$
$73$	2.04518e6	0.615320	0.307660	+	0.951496i	$0.400454\pi$
$74$	−1.48963e6	−0.427335
$75$	3.09875e6	0.848150
$76$	−808412.	−0.211244
$77$	−4.55991e6	−1.13825
$78$	371334.	0.0886000
$79$	5.18855e6	1.18400	0.592000	−	0.805938i	$-0.298339\pi$
$79$	5.18855e6	1.18400	0.592000	+	0.805938i	$0.298339\pi$
$80$	−6.01507e6	−1.31349
$81$	2.16525e6	0.452700
$82$	−1.77423e6	−0.355354
$83$	−2.10622e6	−0.404325	−0.202162	−	0.979352i	$-0.564797\pi$
$83$	−2.10622e6	−0.404325	−0.202162	+	0.979352i	$0.564797\pi$
$84$	−2.15157e6	−0.396075
$85$	2.80153e6	0.494799
$86$	1.30088e6	0.220544
$87$	3.87712e6	0.631237
$88$	4.03954e6	0.631891
$89$	6.75005e6	1.01494	0.507472	−	0.861668i	$-0.330580\pi$
$89$	6.75005e6	1.01494	0.507472	+	0.861668i	$0.330580\pi$
$90$	2.67705e6	0.387087
$91$	4.98884e6	0.693992
$92$	4.37660e6	0.585975
$93$	−5.00256e6	−0.644914
$94$	−1.39848e6	−0.173664
$95$	−3.27606e6	−0.392030
$96$	2.89835e6	0.334350
$97$	3.64028e6	0.404980	0.202490	−	0.979284i	$-0.435097\pi$
$97$	3.64028e6	0.404980	0.202490	+	0.979284i	$0.435097\pi$
$98$	−135721.	−0.0145665
$99$	9.08303e6	0.940822
$100$	−1.76798e7	−1.76798
$101$	−1.30510e7	−1.26043	−0.630217	−	0.776419i	$-0.717034\pi$
$101$	−1.30510e7	−1.26043	−0.630217	+	0.776419i	$0.717034\pi$
$102$	−385809.	−0.0359974
$103$	7.15505e6	0.645182	0.322591	−	0.946538i	$-0.395446\pi$
$103$	7.15505e6	0.645182	0.322591	+	0.946538i	$0.395446\pi$
$104$	−4.41952e6	−0.385264
$105$	−8.71916e6	−0.735042
$106$	−2.64360e6	−0.215589
$107$	−2.09693e7	−1.65478	−0.827389	−	0.561629i	$-0.810175\pi$
$107$	−2.09693e7	−1.65478	−0.827389	+	0.561629i	$0.810175\pi$
$108$	9.61055e6	0.734116
$109$	−4.21802e6	−0.311972	−0.155986	−	0.987759i	$-0.549856\pi$
$109$	−4.21802e6	−0.311972	−0.155986	+	0.987759i	$0.549856\pi$
$110$	7.84753e6	0.562158
$111$	−9.66433e6	−0.670720
$112$	1.11289e7	0.748495
$113$	9.39297e6	0.612390	0.306195	−	0.951969i	$-0.400944\pi$
$113$	9.39297e6	0.612390	0.306195	+	0.951969i	$0.400944\pi$
$114$	451159.	0.0285208
$115$	1.77360e7	1.08746
$116$	−2.21208e7	−1.31582
$117$	−9.93742e6	−0.573619
$118$	−2.80428e6	−0.157121
$119$	−5.18330e6	−0.281963
$120$	7.72414e6	0.408052
$121$	7.13885e6	0.366336
$122$	5.06577e6	0.252572
$123$	−1.15107e7	−0.557743
$124$	2.85419e7	1.34434
$125$	−3.43322e7	−1.57223
$126$	−4.95300e6	−0.220583
$127$	8.91679e6	0.386274	0.193137	−	0.981172i	$-0.438134\pi$
$127$	8.91679e6	0.386274	0.193137	+	0.981172i	$0.438134\pi$
$128$	−2.16692e7	−0.913287
$129$	8.43978e6	0.346152
$130$	−8.58571e6	−0.342748
$131$	3.40018e7	1.32145	0.660727	−	0.750626i	$-0.270248\pi$
$131$	3.40018e7	1.32145	0.660727	+	0.750626i	$0.270248\pi$
$132$	1.25633e7	0.475441
$133$	6.06127e6	0.223400
$134$	−1.10871e7	−0.398062
$135$	3.89464e7	1.36238
$136$	4.59179e6	0.156529
$137$	4.86287e7	1.61574	0.807868	−	0.589364i	$-0.200622\pi$
$137$	4.86287e7	1.61574	0.807868	+	0.589364i	$0.200622\pi$
$138$	−2.44249e6	−0.0791146
$139$	4.43502e6	0.140070	0.0700348	−	0.997545i	$-0.477689\pi$
$139$	4.43502e6	0.140070	0.0700348	+	0.997545i	$0.477689\pi$
$140$	4.97469e7	1.53221
$141$	−9.07297e6	−0.272573
$142$	1.29301e7	0.378958
$143$	−2.91306e7	−0.833054
$144$	−2.21680e7	−0.618669
$145$	−8.96439e7	−2.44193
$146$	6.51207e6	0.173175
$147$	−880520.	−0.0228627
$148$	5.51396e7	1.39813
$149$	−5.80902e7	−1.43864	−0.719318	−	0.694681i	$-0.755546\pi$
$149$	−5.80902e7	−1.43864	−0.719318	+	0.694681i	$0.755546\pi$
$150$	9.86677e6	0.238702
$151$	−5.62611e7	−1.32981	−0.664904	−	0.746929i	$-0.731528\pi$
$151$	−5.62611e7	−1.32981	−0.664904	+	0.746929i	$0.731528\pi$
$152$	−5.36957e6	−0.124019
$153$	1.03248e7	0.233056
$154$	−1.45192e7	−0.320348
$155$	1.15665e8	2.49484
$156$	−1.37451e7	−0.289876
$157$	−8.71409e7	−1.79710	−0.898552	−	0.438866i	$-0.855380\pi$
$157$	−8.71409e7	−1.79710	−0.898552	+	0.438866i	$0.855380\pi$
$158$	1.65209e7	0.333223
$159$	−1.71510e7	−0.338375
$160$	−6.70135e7	−1.29343
$161$	−3.28147e7	−0.619694
$162$	6.89440e6	0.127407
$163$	576392.	0.0104247	0.00521233	−	0.999986i	$-0.498341\pi$
$163$	576392.	0.0104247	0.00521233	+	0.999986i	$0.498341\pi$
$164$	6.56739e7	1.16262
$165$	5.09126e7	0.882330
$166$	−6.70643e6	−0.113792
$167$	8.04266e6	0.133626	0.0668132	−	0.997766i	$-0.478717\pi$
$167$	8.04266e6	0.133626	0.0668132	+	0.997766i	$0.478717\pi$
$168$	−1.42910e7	−0.232530
$169$	−3.08777e7	−0.492087
$170$	8.92037e6	0.139255
$171$	−1.20736e7	−0.184651
$172$	−4.81529e7	−0.721561
$173$	−3.06395e7	−0.449904	−0.224952	−	0.974370i	$-0.572223\pi$
$173$	−3.06395e7	−0.449904	−0.224952	+	0.974370i	$0.572223\pi$
$174$	1.23452e7	0.177654
$175$	1.32559e8	1.86972
$176$	−6.49834e7	−0.898479
$177$	−1.81934e7	−0.246608
$178$	2.14929e7	0.285644
$179$	1.51315e7	0.197195	0.0985976	−	0.995127i	$-0.468564\pi$
$179$	1.51315e7	0.197195	0.0985976	+	0.995127i	$0.468564\pi$
$180$	−9.90925e7	−1.26645
$181$	−5.03260e7	−0.630838	−0.315419	−	0.948953i	$-0.602145\pi$
$181$	−5.03260e7	−0.630838	−0.315419	+	0.948953i	$0.602145\pi$
$182$	1.58850e7	0.195316
$183$	3.28653e7	0.396423
$184$	2.90699e7	0.344018
$185$	2.23451e8	2.59467
$186$	−1.59287e7	−0.181503
$187$	3.02661e7	0.338463
$188$	5.17655e7	0.568183
$189$	−7.20575e7	−0.776359
$190$	−1.04313e7	−0.110332
$191$	−3.11058e7	−0.323017	−0.161508	−	0.986871i	$-0.551636\pi$
$191$	−3.11058e7	−0.323017	−0.161508	+	0.986871i	$0.551636\pi$
$192$	−2.40710e7	−0.245437
$193$	1.63277e8	1.63484	0.817421	−	0.576041i	$-0.195403\pi$
$193$	1.63277e8	1.63484	0.817421	+	0.576041i	$0.195403\pi$
$194$	1.15911e7	0.113977
$195$	−5.57017e7	−0.537956
$196$	5.02378e6	0.0476578
$197$	−1.38947e8	−1.29485	−0.647424	−	0.762130i	$-0.724153\pi$
$197$	−1.38947e8	−1.29485	−0.647424	+	0.762130i	$0.724153\pi$
$198$	2.89214e7	0.264783
$199$	3.58585e7	0.322557	0.161279	−	0.986909i	$-0.448438\pi$
$199$	3.58585e7	0.322557	0.161279	+	0.986909i	$0.448438\pi$
$200$	−1.17432e8	−1.03796
$201$	−7.19299e7	−0.624775
$202$	−4.15559e7	−0.354734
$203$	1.65856e8	1.39154
$204$	1.42809e7	0.117774
$205$	2.66142e8	2.15762
$206$	2.27825e7	0.181579
$207$	6.53646e7	0.512208
$208$	7.10961e7	0.547802
$209$	−3.53927e7	−0.268165
$210$	−2.77628e7	−0.206869
$211$	−1.74126e8	−1.27607	−0.638035	−	0.770007i	$-0.720253\pi$
$211$	−1.74126e8	−1.27607	−0.638035	+	0.770007i	$0.720253\pi$
$212$	9.78543e7	0.705349
$213$	8.38866e7	0.594791
$214$	−6.67684e7	−0.465718
$215$	−1.95138e8	−1.33908
$216$	6.38344e7	0.430990
$217$	−2.14000e8	−1.42169
$218$	−1.34306e7	−0.0878009
$219$	4.22485e7	0.271805
$220$	−2.90480e8	−1.83923
$221$	−3.31131e7	−0.206361
$222$	−3.07723e7	−0.188766
$223$	−1.07026e8	−0.646281	−0.323140	−	0.946351i	$-0.604739\pi$
$223$	−1.07026e8	−0.646281	−0.323140	+	0.946351i	$0.604739\pi$
$224$	1.23986e8	0.737064
$225$	−2.64049e8	−1.54542
$226$	2.99083e7	0.172350
$227$	−4.45328e6	−0.0252691	−0.0126345	−	0.999920i	$-0.504022\pi$
$227$	−4.45328e6	−0.0252691	−0.0126345	+	0.999920i	$0.504022\pi$
$228$	−1.66999e7	−0.0933127
$229$	2.84234e8	1.56405	0.782026	−	0.623246i	$-0.214186\pi$
$229$	2.84234e8	1.56405	0.782026	+	0.623246i	$0.214186\pi$
$230$	5.64735e7	0.306053
$231$	−9.41968e7	−0.502799
$232$	−1.46929e8	−0.772503
$233$	−3.29147e7	−0.170468	−0.0852342	−	0.996361i	$-0.527164\pi$
$233$	−3.29147e7	−0.170468	−0.0852342	+	0.996361i	$0.527164\pi$
$234$	−3.16419e7	−0.161438
$235$	2.09778e8	1.05444
$236$	1.03802e8	0.514058
$237$	1.07183e8	0.523007
$238$	−1.65042e7	−0.0793551
$239$	6.94751e7	0.329183	0.164591	−	0.986362i	$-0.447369\pi$
$239$	6.94751e7	0.329183	0.164591	+	0.986362i	$0.447369\pi$
$240$	−1.24257e8	−0.580205
$241$	−1.38907e8	−0.639240	−0.319620	−	0.947546i	$-0.603555\pi$
$241$	−1.38907e8	−0.639240	−0.319620	+	0.947546i	$0.603555\pi$
$242$	2.27309e7	0.103101
$243$	2.23059e8	0.997237
$244$	−1.87512e8	−0.826350
$245$	2.03587e7	0.0884441
$246$	−3.66513e7	−0.156970
$247$	3.87219e7	0.163500
$248$	1.89579e8	0.789241
$249$	−4.35095e7	−0.178602
$250$	−1.09318e8	−0.442486
$251$	1.62375e8	0.648129	0.324064	−	0.946035i	$-0.394951\pi$
$251$	1.62375e8	0.648129	0.324064	+	0.946035i	$0.394951\pi$
$252$	1.83338e8	0.721689
$253$	1.91610e8	0.743869
$254$	2.83920e7	0.108712
$255$	5.78729e7	0.218567
$256$	8.01530e7	0.298593
$257$	−1.43008e8	−0.525528	−0.262764	−	0.964860i	$-0.584634\pi$
$257$	−1.43008e8	−0.525528	−0.262764	+	0.964860i	$0.584634\pi$
$258$	2.68732e7	0.0974205
$259$	−4.13423e8	−1.47858
$260$	3.17804e8	1.12138
$261$	−3.30375e8	−1.15018
$262$	1.08265e8	0.371908
$263$	2.14368e6	0.00726634	0.00363317	−	0.999993i	$-0.498844\pi$
$263$	2.14368e6	0.00726634	0.00363317	+	0.999993i	$0.498844\pi$
$264$	8.34472e7	0.279125
$265$	3.96552e8	1.30900
$266$	1.92998e7	0.0628733
$267$	1.39440e8	0.448330
$268$	4.10394e8	1.30235
$269$	−1.64191e7	−0.0514300	−0.0257150	−	0.999669i	$-0.508186\pi$
$269$	−1.64191e7	−0.0514300	−0.0257150	+	0.999669i	$0.508186\pi$
$270$	1.24010e8	0.383427
$271$	−2.74363e8	−0.837401	−0.418701	−	0.908124i	$-0.637514\pi$
$271$	−2.74363e8	−0.837401	−0.418701	+	0.908124i	$0.637514\pi$
$272$	−7.38674e7	−0.222567
$273$	1.03057e8	0.306556
$274$	1.54839e8	0.454730
$275$	−7.74034e8	−2.24438
$276$	9.04101e7	0.258842
$277$	−4.36876e8	−1.23503	−0.617517	−	0.786558i	$-0.711861\pi$
$277$	−4.36876e8	−1.23503	−0.617517	+	0.786558i	$0.711861\pi$
$278$	1.41216e7	0.0394209
$279$	4.26274e8	1.17510
$280$	3.30425e8	0.899539
$281$	−1.29544e8	−0.348294	−0.174147	−	0.984720i	$-0.555717\pi$
$281$	−1.29544e8	−0.348294	−0.174147	+	0.984720i	$0.555717\pi$
$282$	−2.88893e7	−0.0767124
$283$	1.76483e8	0.462861	0.231430	−	0.972851i	$-0.425659\pi$
$283$	1.76483e8	0.462861	0.231430	+	0.972851i	$0.425659\pi$
$284$	−4.78613e8	−1.23985
$285$	−6.76757e7	−0.173171
$286$	−9.27551e7	−0.234453
$287$	−4.92407e8	−1.22953
$288$	−2.46972e8	−0.609220
$289$	−3.75935e8	−0.916157
$290$	−2.85436e8	−0.687252
$291$	7.51996e7	0.178892
$292$	−2.41048e8	−0.566582
$293$	3.89477e7	0.0904577	0.0452289	−	0.998977i	$-0.485598\pi$
$293$	3.89477e7	0.0904577	0.0452289	+	0.998977i	$0.485598\pi$
$294$	−2.80367e6	−0.00643445
$295$	4.20653e8	0.953997
$296$	3.66244e8	0.820822
$297$	4.20755e8	0.931927
$298$	−1.84966e8	−0.404887
$299$	−2.09634e8	−0.453536
$300$	−3.65224e8	−0.780970
$301$	3.61039e8	0.763081
$302$	−1.79142e8	−0.374259
$303$	−2.69603e8	−0.556770
$304$	8.63794e7	0.176341
$305$	−7.59886e8	−1.53355
$306$	3.28752e7	0.0655910
$307$	7.00879e8	1.38248	0.691240	−	0.722625i	$-0.257065\pi$
$307$	7.00879e8	1.38248	0.691240	+	0.722625i	$0.257065\pi$
$308$	5.37437e8	1.04809
$309$	1.47806e8	0.284996
$310$	3.68291e8	0.702143
$311$	−3.22435e8	−0.607829	−0.303914	−	0.952699i	$-0.598294\pi$
$311$	−3.22435e8	−0.607829	−0.303914	+	0.952699i	$0.598294\pi$
$312$	−9.12967e7	−0.170182
$313$	9.90248e8	1.82532	0.912659	−	0.408721i	$-0.134025\pi$
$313$	9.90248e8	1.82532	0.912659	+	0.408721i	$0.134025\pi$
$314$	−2.77466e8	−0.505774
$315$	7.42971e8	1.33932
$316$	−6.11530e8	−1.09022
$317$	−7.18123e8	−1.26617	−0.633084	−	0.774083i	$-0.718211\pi$
$317$	−7.18123e8	−1.26617	−0.633084	+	0.774083i	$0.718211\pi$
$318$	−5.46105e7	−0.0952317
$319$	−9.68462e8	−1.67038
$320$	5.56551e8	0.949467
$321$	−4.33175e8	−0.730964
$322$	−1.04486e8	−0.174406
$323$	−4.02313e7	−0.0664286
$324$	−2.55200e8	−0.416843
$325$	8.46843e8	1.36839
$326$	1.83530e6	0.00293390
$327$	−8.71343e7	−0.137807
$328$	4.36214e8	0.682561
$329$	−3.88125e8	−0.600878
$330$	1.62111e8	0.248321
$331$	−9.96038e8	−1.50966	−0.754828	−	0.655923i	$-0.772280\pi$
$331$	−9.96038e8	−1.50966	−0.754828	+	0.655923i	$0.772280\pi$
$332$	2.48242e8	0.372299
$333$	8.23510e8	1.22212
$334$	2.56087e7	0.0376076
$335$	1.66311e9	2.41693
$336$	2.29897e8	0.330632
$337$	1.06827e9	1.52047	0.760234	−	0.649649i	$-0.225084\pi$
$337$	1.06827e9	1.52047	0.760234	+	0.649649i	$0.225084\pi$
$338$	−9.83181e7	−0.138492
$339$	1.94036e8	0.270511
$340$	−3.30192e8	−0.455607
$341$	1.24958e9	1.70657
$342$	−3.84438e7	−0.0519679
$343$	−7.65429e8	−1.02418
$344$	−3.19837e8	−0.423618
$345$	3.66384e8	0.480364
$346$	−9.75595e7	−0.126620
$347$	−3.44438e8	−0.442546	−0.221273	−	0.975212i	$-0.571021\pi$
$347$	−3.44438e8	−0.442546	−0.221273	+	0.975212i	$0.571021\pi$
$348$	−4.56963e8	−0.581238
$349$	5.01694e8	0.631757	0.315879	−	0.948800i	$-0.397701\pi$
$349$	5.01694e8	0.631757	0.315879	+	0.948800i	$0.397701\pi$
$350$	4.22083e8	0.526211
$351$	−4.60334e8	−0.568195
$352$	−7.23975e8	−0.884758
$353$	1.93020e8	0.233556	0.116778	−	0.993158i	$-0.462743\pi$
$353$	1.93020e8	0.233556	0.116778	+	0.993158i	$0.462743\pi$
$354$	−5.79296e7	−0.0694048
$355$	−1.93956e9	−2.30094
$356$	−7.95571e8	−0.934553
$357$	−1.07075e8	−0.124551
$358$	4.81804e7	0.0554983
$359$	9.51518e8	1.08539	0.542696	−	0.839929i	$-0.317404\pi$
$359$	9.51518e8	1.08539	0.542696	+	0.839929i	$0.317404\pi$
$360$	−6.58184e8	−0.743514
$361$	4.70459e7	0.0526316
$362$	−1.60244e8	−0.177542
$363$	1.47472e8	0.161821
$364$	−5.87991e8	−0.639022
$365$	−9.76838e8	−1.05147
$366$	1.04647e8	0.111568
$367$	5.86467e8	0.619317	0.309658	−	0.950848i	$-0.399785\pi$
$367$	5.86467e8	0.619317	0.309658	+	0.950848i	$0.399785\pi$
$368$	−4.67643e8	−0.489156
$369$	9.80842e8	1.01626
$370$	7.11494e8	0.730239
$371$	−7.33687e8	−0.745937
$372$	5.89609e8	0.593832
$373$	−2.28831e8	−0.228314	−0.114157	−	0.993463i	$-0.536417\pi$
$373$	−2.28831e8	−0.228314	−0.114157	+	0.993463i	$0.536417\pi$
$374$	9.63706e7	0.0952564
$375$	−7.09222e8	−0.694500
$376$	3.43833e8	0.333572
$377$	1.05956e9	1.01843
$378$	−2.29439e8	−0.218497
$379$	4.66801e8	0.440448	0.220224	−	0.975449i	$-0.429321\pi$
$379$	4.66801e8	0.440448	0.220224	+	0.975449i	$0.429321\pi$
$380$	3.86122e8	0.360979
$381$	1.84200e8	0.170628
$382$	−9.90444e7	−0.0909093
$383$	−2.06999e9	−1.88267	−0.941333	−	0.337480i	$-0.890425\pi$
$383$	−2.06999e9	−1.88267	−0.941333	+	0.337480i	$0.890425\pi$
$384$	−4.47633e8	−0.403425
$385$	2.17795e9	1.94507
$386$	5.19894e8	0.460107
$387$	−7.19164e8	−0.630725
$388$	−4.29049e8	−0.372903
$389$	−7.92880e8	−0.682942	−0.341471	−	0.939892i	$-0.610925\pi$
$389$	−7.92880e8	−0.682942	−0.341471	+	0.939892i	$0.610925\pi$
$390$	−1.77360e8	−0.151401
$391$	2.17805e8	0.184268
$392$	3.33685e7	0.0279792
$393$	7.02396e8	0.583725
$394$	−4.42424e8	−0.364420
$395$	−2.47821e9	−2.02324
$396$	−1.07054e9	−0.866302
$397$	−1.60372e9	−1.28636	−0.643180	−	0.765715i	$-0.722385\pi$
$397$	−1.60372e9	−1.28636	−0.643180	+	0.765715i	$0.722385\pi$
$398$	1.14178e8	0.0907800
$399$	1.25211e8	0.0986822
$400$	1.88910e9	1.47586
$401$	−3.31722e8	−0.256903	−0.128452	−	0.991716i	$-0.541001\pi$
$401$	−3.31722e8	−0.256903	−0.128452	+	0.991716i	$0.541001\pi$
$402$	−2.29033e8	−0.175836
$403$	−1.36712e9	−1.04050
$404$	1.53821e9	1.16060
$405$	−1.03419e9	−0.773583
$406$	5.28105e8	0.391633
$407$	2.41404e9	1.77486
$408$	9.48554e7	0.0691435
$409$	1.78655e9	1.29117	0.645586	−	0.763688i	$-0.276613\pi$
$409$	1.78655e9	1.29117	0.645586	+	0.763688i	$0.276613\pi$
$410$	8.47425e8	0.607236
$411$	1.00455e9	0.713717
$412$	−8.43305e8	−0.594079
$413$	−7.78279e8	−0.543638
$414$	2.08128e8	0.144155
$415$	1.00599e9	0.690918
$416$	7.92076e8	0.539436
$417$	9.16169e7	0.0618728
$418$	−1.12694e8	−0.0754719
$419$	2.27084e9	1.50813	0.754063	−	0.656802i	$-0.228091\pi$
$419$	2.27084e9	1.50813	0.754063	+	0.656802i	$0.228091\pi$
$420$	1.02765e9	0.676821
$421$	−2.83287e9	−1.85029	−0.925145	−	0.379613i	$-0.876057\pi$
$421$	−2.83287e9	−1.85029	−0.925145	+	0.379613i	$0.876057\pi$
$422$	−5.54436e8	−0.359135
$423$	7.73119e8	0.496656
$424$	6.49960e8	0.414101
$425$	−8.79853e8	−0.555967
$426$	2.67104e8	0.167397
$427$	1.40592e9	0.873901
$428$	2.47147e9	1.52371
$429$	−6.01769e8	−0.367984
$430$	−6.21342e8	−0.376869
$431$	1.63164e9	0.981642	0.490821	−	0.871261i	$-0.336697\pi$
$431$	1.63164e9	0.981642	0.490821	+	0.871261i	$0.336697\pi$
$432$	−1.02689e9	−0.612819
$433$	1.37141e9	0.811818	0.405909	−	0.913913i	$-0.366955\pi$
$433$	1.37141e9	0.811818	0.405909	+	0.913913i	$0.366955\pi$
$434$	−6.81401e8	−0.400119
$435$	−1.85183e9	−1.07867
$436$	4.97142e8	0.287262
$437$	−2.54698e8	−0.145996
$438$	1.34524e8	0.0764962
$439$	−5.56895e8	−0.314158	−0.157079	−	0.987586i	$-0.550208\pi$
$439$	−5.56895e8	−0.314158	−0.157079	+	0.987586i	$0.550208\pi$
$440$	−1.92940e9	−1.07979
$441$	7.50302e7	0.0416583
$442$	−1.05436e8	−0.0580778
$443$	1.90508e9	1.04112	0.520559	−	0.853826i	$-0.325724\pi$
$443$	1.90508e9	1.04112	0.520559	+	0.853826i	$0.325724\pi$
$444$	1.13905e9	0.617594
$445$	−3.22403e9	−1.73436
$446$	−3.40782e8	−0.181888
$447$	−1.20001e9	−0.635487
$448$	−1.02971e9	−0.541057
$449$	−5.83593e8	−0.304262	−0.152131	−	0.988360i	$-0.548614\pi$
$449$	−5.83593e8	−0.304262	−0.152131	+	0.988360i	$0.548614\pi$
$450$	−8.40761e8	−0.434939
$451$	2.87524e9	1.47590
$452$	−1.10707e9	−0.563884
$453$	−1.16222e9	−0.587415
$454$	−1.41797e7	−0.00711169
$455$	−2.38282e9	−1.18591
$456$	−1.10922e8	−0.0547826
$457$	−1.57581e9	−0.772320	−0.386160	−	0.922432i	$-0.626199\pi$
$457$	−1.57581e9	−0.772320	−0.386160	+	0.922432i	$0.626199\pi$
$458$	9.05031e8	0.440184
$459$	4.78277e8	0.230853
$460$	−2.09039e9	−1.00133
$461$	2.51765e9	1.19686	0.598428	−	0.801176i	$-0.295792\pi$
$461$	2.51765e9	1.19686	0.598428	+	0.801176i	$0.295792\pi$
$462$	−2.99933e8	−0.141507
$463$	−2.27928e9	−1.06725	−0.533623	−	0.845722i	$-0.679170\pi$
$463$	−2.27928e9	−1.06725	−0.533623	+	0.845722i	$0.679170\pi$
$464$	2.36363e9	1.09841
$465$	2.38937e9	1.10204
$466$	−1.04804e8	−0.0479763
$467$	−9.84386e7	−0.0447256	−0.0223628	−	0.999750i	$-0.507119\pi$
$467$	−9.84386e7	−0.0447256	−0.0223628	+	0.999750i	$0.507119\pi$
$468$	1.17124e9	0.528184
$469$	−3.07703e9	−1.37730
$470$	6.67957e8	0.296761
$471$	−1.80012e9	−0.793833
$472$	6.89463e8	0.301796
$473$	−2.10816e9	−0.915988
$474$	3.41283e8	0.147194
$475$	1.02889e9	0.440494
$476$	6.10911e8	0.259629
$477$	1.46146e9	0.616554
$478$	2.21217e8	0.0926446
$479$	6.16209e8	0.256185	0.128093	−	0.991762i	$-0.459115\pi$
$479$	6.16209e8	0.256185	0.128093	+	0.991762i	$0.459115\pi$
$480$	−1.38434e9	−0.571344
$481$	−2.64112e9	−1.08213
$482$	−4.42295e8	−0.179907
$483$	−6.77873e8	−0.273737
$484$	−8.41395e8	−0.337319
$485$	−1.73871e9	−0.692039
$486$	7.10245e8	0.280661
$487$	3.58545e9	1.40667	0.703335	−	0.710859i	$-0.251693\pi$
$487$	3.58545e9	1.40667	0.703335	+	0.710859i	$0.251693\pi$
$488$	−1.24548e9	−0.485139
$489$	1.19069e7	0.00460487
$490$	6.48244e7	0.0248916
$491$	4.87673e9	1.85928	0.929638	−	0.368475i	$-0.120120\pi$
$491$	4.87673e9	1.85928	0.929638	+	0.368475i	$0.120120\pi$
$492$	1.35667e9	0.513565
$493$	−1.10086e9	−0.413779
$494$	1.23295e8	0.0460152
$495$	−4.33833e9	−1.60770
$496$	−3.04973e9	−1.12221
$497$	3.58852e9	1.31120
$498$	−1.38539e8	−0.0502654
$499$	−6.34565e8	−0.228625	−0.114313	−	0.993445i	$-0.536467\pi$
$499$	−6.34565e8	−0.228625	−0.114313	+	0.993445i	$0.536467\pi$
$500$	4.04644e9	1.44770
$501$	1.66142e8	0.0590266
$502$	5.17020e8	0.182408
$503$	−1.06931e9	−0.374641	−0.187320	−	0.982299i	$-0.559980\pi$
$503$	−1.06931e9	−0.374641	−0.187320	+	0.982299i	$0.559980\pi$
$504$	1.21775e9	0.423694
$505$	6.23357e9	2.15386
$506$	6.10107e8	0.209353
$507$	−6.37861e8	−0.217369
$508$	−1.05095e9	−0.355678
$509$	6.81658e8	0.229115	0.114558	−	0.993417i	$-0.463455\pi$
$509$	6.81658e8	0.229115	0.114558	+	0.993417i	$0.463455\pi$
$510$	1.84274e8	0.0615131
$511$	1.80732e9	0.599185
$512$	3.02887e9	0.997323
$513$	−5.59290e8	−0.182905
$514$	−4.55355e8	−0.147904
$515$	−3.41747e9	−1.10250
$516$	−9.94724e8	−0.318734
$517$	2.26632e9	0.721282
$518$	−1.31638e9	−0.416129
$519$	−6.32939e8	−0.198736
$520$	2.11089e9	0.658347
$521$	1.08040e9	0.334698	0.167349	−	0.985898i	$-0.446479\pi$
$521$	1.08040e9	0.334698	0.167349	+	0.985898i	$0.446479\pi$
$522$	−1.05195e9	−0.323704
$523$	−4.49217e9	−1.37309	−0.686547	−	0.727085i	$-0.740874\pi$
$523$	−4.49217e9	−1.37309	−0.686547	+	0.727085i	$0.740874\pi$
$524$	−4.00750e9	−1.21679
$525$	2.73836e9	0.825909
$526$	6.82573e6	0.00204503
$527$	1.42041e9	0.422745
$528$	−1.34240e9	−0.396884
$529$	−2.02593e9	−0.595018
$530$	1.26266e9	0.368402
$531$	1.55028e9	0.449344
$532$	−7.14390e8	−0.205705
$533$	−3.14570e9	−0.899855
$534$	4.43993e8	0.126177
$535$	1.00155e10	2.82772
$536$	2.72589e9	0.764595
$537$	3.12581e8	0.0871069
$538$	−5.22803e7	−0.0144744
$539$	2.19944e8	0.0604994
$540$	−4.59028e9	−1.25447
$541$	1.42748e9	0.387596	0.193798	−	0.981041i	$-0.437919\pi$
$541$	1.42748e9	0.387596	0.193798	+	0.981041i	$0.437919\pi$
$542$	−8.73604e8	−0.235677
$543$	−1.03962e9	−0.278659
$544$	−8.22951e8	−0.219168
$545$	2.01465e9	0.533105
$546$	3.28146e8	0.0862767
$547$	−1.67939e9	−0.438728	−0.219364	−	0.975643i	$-0.570398\pi$
$547$	−1.67939e9	−0.438728	−0.219364	+	0.975643i	$0.570398\pi$
$548$	−5.73144e9	−1.48776
$549$	−2.80049e9	−0.722323
$550$	−2.46461e9	−0.631653
$551$	1.28733e9	0.327838
$552$	6.00515e8	0.151963
$553$	4.58510e9	1.15295
$554$	−1.39106e9	−0.347586
$555$	4.61597e9	1.14614
$556$	−5.22718e8	−0.128975
$557$	−5.27790e9	−1.29410	−0.647051	−	0.762447i	$-0.723998\pi$
$557$	−5.27790e9	−1.29410	−0.647051	+	0.762447i	$0.723998\pi$
$558$	1.35731e9	0.330718
$559$	2.30647e9	0.558478
$560$	−5.31549e9	−1.27904
$561$	6.25226e8	0.149509
$562$	−4.12483e8	−0.0980232
$563$	−4.93458e9	−1.16539	−0.582695	−	0.812691i	$-0.698002\pi$
$563$	−4.93458e9	−1.16539	−0.582695	+	0.812691i	$0.698002\pi$
$564$	1.06935e9	0.250983
$565$	−4.48636e9	−1.04647
$566$	5.61942e8	0.130267
$567$	1.91342e9	0.440829
$568$	−3.17900e9	−0.727900
$569$	−2.98930e9	−0.680263	−0.340131	−	0.940378i	$-0.610472\pi$
$569$	−2.98930e9	−0.680263	−0.340131	+	0.940378i	$0.610472\pi$
$570$	−2.15487e8	−0.0487370
$571$	−1.69611e8	−0.0381266	−0.0190633	−	0.999818i	$-0.506068\pi$
$571$	−1.69611e8	−0.0381266	−0.0190633	+	0.999818i	$0.506068\pi$
$572$	3.43337e9	0.767070
$573$	−6.42572e8	−0.142686
$574$	−1.56788e9	−0.346036
$575$	−5.57021e9	−1.22190
$576$	2.05112e9	0.447211
$577$	−6.38388e9	−1.38347	−0.691735	−	0.722152i	$-0.743153\pi$
$577$	−6.38388e9	−1.38347	−0.691735	+	0.722152i	$0.743153\pi$
$578$	−1.19702e9	−0.257842
$579$	3.37292e9	0.722157
$580$	1.05656e10	2.24851
$581$	−1.86126e9	−0.393722
$582$	2.39444e8	0.0503469
$583$	4.28412e9	0.895409
$584$	−1.60107e9	−0.332633
$585$	4.74641e9	0.980212
$586$	1.24014e8	0.0254583
$587$	6.98427e9	1.42524	0.712619	−	0.701551i	$-0.247509\pi$
$587$	6.98427e9	1.42524	0.712619	+	0.701551i	$0.247509\pi$
$588$	1.03779e8	0.0210518
$589$	−1.66101e9	−0.334942
$590$	1.33941e9	0.268491
$591$	−2.87032e9	−0.571971
$592$	−5.89170e9	−1.16712
$593$	−4.67620e9	−0.920878	−0.460439	−	0.887691i	$-0.652308\pi$
$593$	−4.67620e9	−0.920878	−0.460439	+	0.887691i	$0.652308\pi$
$594$	1.33973e9	0.262280
$595$	2.47570e9	0.481824
$596$	6.84659e9	1.32469
$597$	7.40752e8	0.142483
$598$	−6.67497e8	−0.127643
$599$	−2.57715e9	−0.489944	−0.244972	−	0.969530i	$-0.578779\pi$
$599$	−2.57715e9	−0.489944	−0.244972	+	0.969530i	$0.578779\pi$
$600$	−2.42586e9	−0.458497
$601$	−4.85436e9	−0.912161	−0.456081	−	0.889938i	$-0.650747\pi$
$601$	−4.85436e9	−0.912161	−0.456081	+	0.889938i	$0.650747\pi$
$602$	1.14959e9	0.214760
$603$	6.12924e9	1.13840
$604$	6.63102e9	1.22448
$605$	−3.40973e9	−0.626002
$606$	−8.58447e8	−0.156696
$607$	1.47535e9	0.267753	0.133876	−	0.990998i	$-0.457258\pi$
$607$	1.47535e9	0.267753	0.133876	+	0.990998i	$0.457258\pi$
$608$	9.62346e8	0.173648
$609$	3.42620e9	0.614684
$610$	−2.41956e9	−0.431601
$611$	−2.47951e9	−0.439765
$612$	−1.21689e9	−0.214597
$613$	−6.38630e9	−1.11979	−0.559896	−	0.828563i	$-0.689159\pi$
$613$	−6.38630e9	−1.11979	−0.559896	+	0.828563i	$0.689159\pi$
$614$	2.23168e9	0.389083
$615$	5.49785e9	0.953082
$616$	3.56972e9	0.615321
$617$	2.20653e9	0.378192	0.189096	−	0.981959i	$-0.439444\pi$
$617$	2.20653e9	0.378192	0.189096	+	0.981959i	$0.439444\pi$
$618$	4.70632e8	0.0802087
$619$	−4.28124e9	−0.725525	−0.362763	−	0.931882i	$-0.618166\pi$
$619$	−4.28124e9	−0.725525	−0.362763	+	0.931882i	$0.618166\pi$
$620$	−1.36325e10	−2.29723
$621$	3.02790e9	0.507365
$622$	−1.02667e9	−0.171066
$623$	5.96500e9	0.988330
$624$	1.46868e9	0.241980
$625$	4.67892e9	0.766594
$626$	3.15306e9	0.513715
$627$	−7.31129e8	−0.118456
$628$	1.02706e10	1.65476
$629$	2.74407e9	0.439661
$630$	2.36570e9	0.376936
$631$	9.01652e9	1.42868	0.714342	−	0.699797i	$-0.246726\pi$
$631$	9.01652e9	1.42868	0.714342	+	0.699797i	$0.246726\pi$
$632$	−4.06186e9	−0.640052
$633$	−3.59703e9	−0.563677
$634$	−2.28658e9	−0.356348
$635$	−4.25892e9	−0.660073
$636$	2.02144e9	0.311573
$637$	−2.40633e8	−0.0368865
$638$	−3.08369e9	−0.470109
$639$	−7.14809e9	−1.08377
$640$	1.03498e10	1.56064
$641$	2.46577e9	0.369786	0.184893	−	0.982759i	$-0.440806\pi$
$641$	2.46577e9	0.369786	0.184893	+	0.982759i	$0.440806\pi$
$642$	−1.37928e9	−0.205721
$643$	−1.24494e9	−0.184676	−0.0923379	−	0.995728i	$-0.529434\pi$
$643$	−1.24494e9	−0.184676	−0.0923379	+	0.995728i	$0.529434\pi$
$644$	3.86758e9	0.570610
$645$	−4.03109e9	−0.591512
$646$	−1.28101e8	−0.0186956
$647$	7.76478e9	1.12710	0.563552	−	0.826081i	$-0.309434\pi$
$647$	7.76478e9	1.12710	0.563552	+	0.826081i	$0.309434\pi$
$648$	−1.69507e9	−0.244723
$649$	4.54449e9	0.652573
$650$	2.69644e9	0.385119
$651$	−4.42074e9	−0.628003
$652$	−6.79344e7	−0.00959894
$653$	−3.82832e9	−0.538036	−0.269018	−	0.963135i	$-0.586699\pi$
$653$	−3.82832e9	−0.538036	−0.269018	+	0.963135i	$0.586699\pi$
$654$	−2.77445e8	−0.0387842
$655$	−1.62403e10	−2.25813
$656$	−7.01731e9	−0.970526
$657$	−3.60005e9	−0.495256
$658$	−1.23583e9	−0.169110
$659$	−2.55523e9	−0.347802	−0.173901	−	0.984763i	$-0.555637\pi$
$659$	−2.55523e9	−0.347802	−0.173901	+	0.984763i	$0.555637\pi$
$660$	−6.00063e9	−0.812443
$661$	8.28276e9	1.11550	0.557751	−	0.830009i	$-0.311665\pi$
$661$	8.28276e9	1.11550	0.557751	+	0.830009i	$0.311665\pi$
$662$	−3.17149e9	−0.424875
$663$	−6.84038e8	−0.0911555
$664$	1.64885e9	0.218572
$665$	−2.89504e9	−0.381750
$666$	2.62215e9	0.343952
$667$	−6.96938e9	−0.909398
$668$	−9.47920e8	−0.123042
$669$	−2.21090e9	−0.285481
$670$	5.29553e9	0.680217
$671$	−8.20937e9	−1.04901
$672$	2.56126e9	0.325583
$673$	−2.78422e9	−0.352087	−0.176044	−	0.984382i	$-0.556330\pi$
$673$	−2.78422e9	−0.352087	−0.176044	+	0.984382i	$0.556330\pi$
$674$	3.40150e9	0.427918
$675$	−1.22316e10	−1.53080
$676$	3.63929e9	0.453110
$677$	1.16231e10	1.43967	0.719834	−	0.694147i	$-0.244218\pi$
$677$	1.16231e10	1.43967	0.719834	+	0.694147i	$0.244218\pi$
$678$	6.17833e8	0.0761320
$679$	3.21690e9	0.394361
$680$	−2.19318e9	−0.267481
$681$	−9.19942e7	−0.0111621
$682$	3.97881e9	0.480295
$683$	9.58761e9	1.15143	0.575715	−	0.817650i	$-0.304724\pi$
$683$	9.58761e9	1.15143	0.575715	+	0.817650i	$0.304724\pi$
$684$	1.42302e9	0.170025
$685$	−2.32265e10	−2.76100
$686$	−2.43721e9	−0.288243
$687$	5.87159e9	0.690887
$688$	5.14517e9	0.602338
$689$	−4.68710e9	−0.545930
$690$	1.16661e9	0.135193
$691$	6.94740e9	0.801031	0.400516	−	0.916290i	$-0.368831\pi$
$691$	6.94740e9	0.801031	0.400516	+	0.916290i	$0.368831\pi$
$692$	3.61121e9	0.414268
$693$	8.02663e9	0.916151
$694$	−1.09673e9	−0.124549
$695$	−2.11830e9	−0.239354
$696$	−3.03521e9	−0.341237
$697$	3.26832e9	0.365603
$698$	1.59745e9	0.177801
$699$	−6.79939e8	−0.0753008
$700$	−1.56236e10	−1.72162
$701$	−2.54494e9	−0.279039	−0.139519	−	0.990219i	$-0.544556\pi$
$701$	−2.54494e9	−0.279039	−0.139519	+	0.990219i	$0.544556\pi$
$702$	−1.46575e9	−0.159912
$703$	−3.20887e9	−0.348344
$704$	6.01266e9	0.649475
$705$	4.33352e9	0.465778
$706$	6.14596e8	0.0657315
$707$	−1.15331e10	−1.22738
$708$	2.14429e9	0.227074
$709$	−1.27039e10	−1.33868	−0.669340	−	0.742957i	$-0.733423\pi$
$709$	−1.27039e10	−1.33868	−0.669340	+	0.742957i	$0.733423\pi$
$710$	−6.17578e9	−0.647572
$711$	−9.13322e9	−0.952972
$712$	−5.28428e9	−0.548663
$713$	8.99243e9	0.929102
$714$	−3.40937e8	−0.0350535
$715$	1.39136e10	1.42354
$716$	−1.78342e9	−0.181576
$717$	1.43519e9	0.145409
$718$	3.02974e9	0.305471
$719$	1.58982e10	1.59514	0.797569	−	0.603228i	$-0.206119\pi$
$719$	1.58982e10	1.59514	0.797569	+	0.603228i	$0.206119\pi$
$720$	1.05881e10	1.05719
$721$	6.32289e9	0.628264
$722$	1.49799e8	0.0148125
$723$	−2.86948e9	−0.282371
$724$	5.93150e9	0.580871
$725$	2.81537e10	2.74380
$726$	4.69566e8	0.0455427
$727$	−4.04052e9	−0.390002	−0.195001	−	0.980803i	$-0.562471\pi$
$727$	−4.04052e9	−0.390002	−0.195001	+	0.980803i	$0.562471\pi$
$728$	−3.90551e9	−0.375161
$729$	−1.27531e8	−0.0121919
$730$	−3.11036e9	−0.295924
$731$	−2.39637e9	−0.226905
$732$	−3.87355e9	−0.365023
$733$	1.57745e10	1.47942	0.739711	−	0.672925i	$-0.234962\pi$
$733$	1.57745e10	1.47942	0.739711	+	0.672925i	$0.234962\pi$
$734$	1.86738e9	0.174299
$735$	4.20562e8	0.0390683
$736$	−5.20997e9	−0.481685
$737$	1.79673e10	1.65328
$738$	3.12311e9	0.286016
$739$	−4.64206e8	−0.0423111	−0.0211556	−	0.999776i	$-0.506735\pi$
$739$	−4.64206e8	−0.0423111	−0.0211556	+	0.999776i	$0.506735\pi$
$740$	−2.63363e10	−2.38915
$741$	7.99903e8	0.0722227
$742$	−2.33614e9	−0.209935
$743$	−4.26981e9	−0.381898	−0.190949	−	0.981600i	$-0.561157\pi$
$743$	−4.26981e9	−0.381898	−0.190949	+	0.981600i	$0.561157\pi$
$744$	3.91625e9	0.348630
$745$	2.77456e10	2.45837
$746$	−7.28622e8	−0.0642564
$747$	3.70750e9	0.325431
$748$	−3.56721e9	−0.311654
$749$	−1.85305e10	−1.61139
$750$	−2.25824e9	−0.195459
$751$	−1.01267e10	−0.872429	−0.436214	−	0.899843i	$-0.643681\pi$
$751$	−1.01267e10	−0.872429	−0.436214	+	0.899843i	$0.643681\pi$
$752$	−5.53119e9	−0.474303
$753$	3.35428e9	0.286297
$754$	3.37376e9	0.286625
$755$	2.68720e10	2.27240
$756$	8.49280e9	0.714866
$757$	−8.78839e9	−0.736332	−0.368166	−	0.929760i	$-0.620014\pi$
$757$	−8.78839e9	−0.736332	−0.368166	+	0.929760i	$0.620014\pi$
$758$	1.48635e9	0.123959
$759$	3.95821e9	0.328588
$760$	2.56467e9	0.211926
$761$	−1.58918e10	−1.30715	−0.653577	−	0.756860i	$-0.726732\pi$
$761$	−1.58918e10	−1.30715	−0.653577	+	0.756860i	$0.726732\pi$
$762$	5.86512e8	0.0480214
$763$	−3.72745e9	−0.303792
$764$	3.66618e9	0.297431
$765$	−4.93142e9	−0.398251
$766$	−6.59109e9	−0.529854
$767$	−4.97197e9	−0.397874
$768$	1.65577e9	0.131897
$769$	−1.10113e10	−0.873165	−0.436582	−	0.899664i	$-0.643811\pi$
$769$	−1.10113e10	−0.873165	−0.436582	+	0.899664i	$0.643811\pi$
$770$	6.93483e9	0.547417
$771$	−2.95421e9	−0.232141
$772$	−1.92441e10	−1.50535
$773$	−7.65650e9	−0.596214	−0.298107	−	0.954533i	$-0.596355\pi$
$773$	−7.65650e9	−0.596214	−0.298107	+	0.954533i	$0.596355\pi$
$774$	−2.28990e9	−0.177510
$775$	−3.63261e10	−2.80325
$776$	−2.84980e9	−0.218926
$777$	−8.54033e9	−0.653132
$778$	−2.52462e9	−0.192206
$779$	−3.82193e9	−0.289668
$780$	6.56508e9	0.495346
$781$	−2.09539e10	−1.57394
$782$	6.93516e8	0.0518601
$783$	−1.53040e10	−1.13930
$784$	−5.36794e8	−0.0397834
$785$	4.16211e10	3.07093
$786$	2.23651e9	0.164282
$787$	2.65923e10	1.94466	0.972332	−	0.233604i	$-0.0750520\pi$
$787$	2.65923e10	1.94466	0.972332	+	0.233604i	$0.0750520\pi$
$788$	1.63765e10	1.19229
$789$	4.42834e7	0.00320975
$790$	−7.89089e9	−0.569418
$791$	8.30053e9	0.596332
$792$	−7.11065e9	−0.508594
$793$	8.98159e9	0.639583
$794$	−5.10643e9	−0.362031
$795$	8.19181e9	0.578222
$796$	−4.22634e9	−0.297008
$797$	−1.24156e7	−0.000868689 0	−0.000434345	−	1.00000i	$-0.500138\pi$
$797$	−1.24156e7	−0.000868689 0	−0.000434345		1.00000i	$0.500138\pi$
$798$	3.98687e8	0.0277729
$799$	2.57616e9	0.178673
$800$	2.10464e10	1.45332
$801$	−1.18819e10	−0.816904
$802$	−1.05624e9	−0.0723024
$803$	−1.05532e10	−0.719250
$804$	8.47777e9	0.575288
$805$	1.56733e10	1.05895
$806$	−4.35308e9	−0.292835
$807$	−3.39180e8	−0.0227181
$808$	1.02170e10	0.681371
$809$	−3.05744e9	−0.203020	−0.101510	−	0.994835i	$-0.532367\pi$
$809$	−3.05744e9	−0.203020	−0.101510	+	0.994835i	$0.532367\pi$
$810$	−3.29297e9	−0.217716
$811$	6.30731e8	0.0415213	0.0207607	−	0.999784i	$-0.493391\pi$
$811$	6.30731e8	0.0415213	0.0207607	+	0.999784i	$0.493391\pi$
$812$	−1.95481e10	−1.28132
$813$	−5.66770e9	−0.369904
$814$	7.68657e9	0.499514
$815$	−2.75302e8	−0.0178139
$816$	−1.52592e9	−0.0983145
$817$	2.80228e9	0.179777
$818$	5.68858e9	0.363385
$819$	−8.78166e9	−0.558577
$820$	−3.13678e10	−1.98672
$821$	−8.90169e9	−0.561399	−0.280699	−	0.959796i	$-0.590566\pi$
$821$	−8.90169e9	−0.561399	−0.280699	+	0.959796i	$0.590566\pi$
$822$	3.19861e9	0.200867
$823$	7.49120e8	0.0468438	0.0234219	−	0.999726i	$-0.492544\pi$
$823$	7.49120e8	0.0468438	0.0234219	+	0.999726i	$0.492544\pi$
$824$	−5.60133e9	−0.348776
$825$	−1.59897e10	−0.991405
$826$	−2.47813e9	−0.153001
$827$	4.34431e9	0.267086	0.133543	−	0.991043i	$-0.457365\pi$
$827$	4.34431e9	0.267086	0.133543	+	0.991043i	$0.457365\pi$
$828$	−7.70397e9	−0.471637
$829$	7.11969e9	0.434030	0.217015	−	0.976168i	$-0.430368\pi$
$829$	7.11969e9	0.434030	0.217015	+	0.976168i	$0.430368\pi$
$830$	3.20319e9	0.194451
$831$	−9.02482e9	−0.545550
$832$	−6.57824e9	−0.395984
$833$	2.50013e8	0.0149867
$834$	2.91718e8	0.0174134
$835$	−3.84142e9	−0.228344
$836$	4.17144e9	0.246924
$837$	1.97464e10	1.16399
$838$	7.23061e9	0.424445
$839$	6.97857e9	0.407943	0.203971	−	0.978977i	$-0.434615\pi$
$839$	6.97857e9	0.407943	0.203971	+	0.978977i	$0.434615\pi$
$840$	6.82580e9	0.397352
$841$	1.79757e10	1.04208
$842$	−9.02018e9	−0.520743
$843$	−2.67608e9	−0.153852
$844$	2.05227e10	1.17500
$845$	1.47481e10	0.840889
$846$	2.46170e9	0.139778
$847$	6.30857e9	0.356729
$848$	−1.04558e10	−0.588806
$849$	3.64572e9	0.204459
$850$	−2.80155e9	−0.156470
$851$	1.73723e10	0.966280
$852$	−9.88700e9	−0.547679
$853$	−1.44048e10	−0.794668	−0.397334	−	0.917674i	$-0.630064\pi$
$853$	−1.44048e10	−0.794668	−0.397334	+	0.917674i	$0.630064\pi$
$854$	4.47660e9	0.245949
$855$	5.76673e9	0.315536
$856$	1.64158e10	0.894548
$857$	2.19667e10	1.19215	0.596077	−	0.802927i	$-0.296725\pi$
$857$	2.19667e10	1.19215	0.596077	+	0.802927i	$0.296725\pi$
$858$	−1.91610e9	−0.103565
$859$	−4.36190e9	−0.234801	−0.117400	−	0.993085i	$-0.537456\pi$
$859$	−4.36190e9	−0.234801	−0.117400	+	0.993085i	$0.537456\pi$
$860$	2.29993e10	1.23302
$861$	−1.01720e10	−0.543117
$862$	5.19531e9	0.276272
$863$	2.98255e10	1.57961	0.789805	−	0.613357i	$-0.210181\pi$
$863$	2.98255e10	1.57961	0.789805	+	0.613357i	$0.210181\pi$
$864$	−1.14405e10	−0.603460
$865$	1.46343e10	0.768806
$866$	4.36671e9	0.228477
$867$	−7.76592e9	−0.404693
$868$	2.52224e10	1.30908
$869$	−2.67731e10	−1.38398
$870$	−5.89643e9	−0.303579
$871$	−1.96574e10	−1.00800
$872$	3.30208e9	0.168647
$873$	−6.40785e9	−0.325959
$874$	−8.10987e8	−0.0410889
$875$	−3.03392e10	−1.53100
$876$	−4.97947e9	−0.250276
$877$	−9.18618e9	−0.459871	−0.229936	−	0.973206i	$-0.573852\pi$
$877$	−9.18618e9	−0.459871	−0.229936	+	0.973206i	$0.573852\pi$
$878$	−1.77322e9	−0.0884160
$879$	8.04568e8	0.0399578
$880$	3.10380e10	1.53534
$881$	−1.43084e10	−0.704979	−0.352490	−	0.935816i	$-0.614665\pi$
$881$	−1.43084e10	−0.704979	−0.352490	+	0.935816i	$0.614665\pi$
$882$	2.38905e8	0.0117242
$883$	4.83883e8	0.0236526	0.0118263	−	0.999930i	$-0.496235\pi$
$883$	4.83883e8	0.0236526	0.0118263	+	0.999930i	$0.496235\pi$
$884$	3.90276e9	0.190015
$885$	8.68969e9	0.421408
$886$	6.06598e9	0.293010
$887$	−3.22220e10	−1.55031	−0.775157	−	0.631768i	$-0.782329\pi$
$887$	−3.22220e10	−1.55031	−0.775157	+	0.631768i	$0.782329\pi$
$888$	7.56572e9	0.362581
$889$	7.87973e9	0.376145
$890$	−1.02657e10	−0.488115
$891$	−1.11728e10	−0.529163
$892$	1.26142e10	0.595090
$893$	−3.01252e9	−0.141563
$894$	−3.82095e9	−0.178850
$895$	−7.22726e9	−0.336971
$896$	−1.91490e10	−0.889339
$897$	−4.33054e9	−0.200340
$898$	−1.85822e9	−0.0856310
$899$	−4.54508e10	−2.08633
$900$	3.11212e10	1.42301
$901$	4.86980e9	0.221807
$902$	9.15509e9	0.415374
$903$	7.45820e9	0.337075
$904$	−7.35329e9	−0.331049
$905$	2.40372e10	1.07799
$906$	−3.70064e9	−0.165321
$907$	−3.03457e10	−1.35043	−0.675215	−	0.737621i	$-0.735949\pi$
$907$	−3.03457e10	−1.35043	−0.675215	+	0.737621i	$0.735949\pi$
$908$	5.24870e8	0.0232676
$909$	2.29733e10	1.01449
$910$	−7.58715e9	−0.333760
$911$	3.19647e10	1.40074	0.700368	−	0.713782i	$-0.253019\pi$
$911$	3.19647e10	1.40074	0.700368	+	0.713782i	$0.253019\pi$
$912$	1.78439e9	0.0778948
$913$	1.08682e10	0.472617
$914$	−5.01756e9	−0.217361
$915$	−1.56974e10	−0.677415
$916$	−3.35002e10	−1.44017
$917$	3.00472e10	1.28680
$918$	1.52289e9	0.0649708
$919$	−3.36055e10	−1.42826	−0.714128	−	0.700015i	$-0.753177\pi$
$919$	−3.36055e10	−1.42826	−0.714128	+	0.700015i	$0.753177\pi$
$920$	−1.38847e10	−0.587865
$921$	1.44785e10	0.610682
$922$	8.01647e9	0.336841
$923$	2.29250e10	0.959628
$924$	1.11022e10	0.462973
$925$	−7.01776e10	−2.91543
$926$	−7.25748e9	−0.300364
$927$	−1.25948e10	−0.519292
$928$	2.63330e10	1.08164
$929$	−2.00721e10	−0.821367	−0.410683	−	0.911778i	$-0.634710\pi$
$929$	−2.00721e10	−0.821367	−0.410683	+	0.911778i	$0.634710\pi$
$930$	7.60802e9	0.310157
$931$	−2.92361e8	−0.0118740
$932$	3.87937e9	0.156966
$933$	−6.66074e9	−0.268496
$934$	−3.13439e8	−0.0125875
$935$	−1.44560e10	−0.578372
$936$	7.77951e9	0.310089
$937$	−8.33854e9	−0.331132	−0.165566	−	0.986199i	$-0.552945\pi$
$937$	−8.33854e9	−0.331132	−0.165566	+	0.986199i	$0.552945\pi$
$938$	−9.79762e9	−0.387624
$939$	2.04562e10	0.806296
$940$	−2.47248e10	−0.970923
$941$	−3.90815e10	−1.52900	−0.764499	−	0.644624i	$-0.777014\pi$
$941$	−3.90815e10	−1.52900	−0.764499	+	0.644624i	$0.777014\pi$
$942$	−5.73179e9	−0.223415
$943$	2.06912e10	0.803518
$944$	−1.10913e10	−0.429121
$945$	3.44168e10	1.32666
$946$	−6.71262e9	−0.257794
$947$	1.89087e10	0.723497	0.361749	−	0.932276i	$-0.382180\pi$
$947$	1.89087e10	0.723497	0.361749	+	0.932276i	$0.382180\pi$
$948$	−1.26328e10	−0.481581
$949$	1.15459e10	0.438526
$950$	3.27609e9	0.123972
$951$	−1.48347e10	−0.559303
$952$	4.05775e9	0.152425
$953$	1.03422e10	0.387067	0.193533	−	0.981094i	$-0.438005\pi$
$953$	1.03422e10	0.387067	0.193533	+	0.981094i	$0.438005\pi$
$954$	4.65344e9	0.173522
$955$	1.48571e10	0.551978
$956$	−8.18844e9	−0.303109
$957$	−2.00061e10	−0.737855
$958$	1.96208e9	0.0721003
$959$	4.29729e10	1.57337
$960$	1.14970e10	0.419407
$961$	3.11314e10	1.13153
$962$	−8.40961e9	−0.304553
$963$	3.69114e10	1.33189
$964$	1.63718e10	0.588607
$965$	−7.79862e10	−2.79365
$966$	−2.15842e9	−0.0770400
$967$	7.17563e9	0.255192	0.127596	−	0.991826i	$-0.459274\pi$
$967$	7.17563e9	0.255192	0.127596	+	0.991826i	$0.459274\pi$
$968$	−5.58865e9	−0.198035
$969$	−8.31083e8	−0.0293435
$970$	−5.53624e9	−0.194766
$971$	1.03896e10	0.364192	0.182096	−	0.983281i	$-0.441712\pi$
$971$	1.03896e10	0.364192	0.182096	+	0.983281i	$0.441712\pi$
$972$	−2.62901e10	−0.918248
$973$	3.91921e9	0.136397
$974$	1.14165e10	0.395891
$975$	1.74938e10	0.604459
$976$	2.00358e10	0.689814
$977$	4.68046e9	0.160567	0.0802837	−	0.996772i	$-0.474417\pi$
$977$	4.68046e9	0.160567	0.0802837	+	0.996772i	$0.474417\pi$
$978$	3.79129e7	0.00129599
$979$	−3.48306e10	−1.18637
$980$	−2.39951e9	−0.0814387
$981$	7.42482e9	0.251099
$982$	1.55281e10	0.523271
$983$	3.51296e10	1.17960	0.589801	−	0.807548i	$-0.299206\pi$
$983$	3.51296e10	1.17960	0.589801	+	0.807548i	$0.299206\pi$
$984$	9.01115e9	0.301507
$985$	6.63654e10	2.21266
$986$	−3.50526e9	−0.116453
$987$	−8.01774e9	−0.265425
$988$	−4.56382e9	−0.150550
$989$	−1.51711e10	−0.498688
$990$	−1.38137e10	−0.452467
$991$	1.82040e10	0.594168	0.297084	−	0.954851i	$-0.403986\pi$
$991$	1.82040e10	0.594168	0.297084	+	0.954851i	$0.403986\pi$
$992$	−3.39768e10	−1.10507
$993$	−2.05758e10	−0.666859
$994$	1.14262e10	0.369021
$995$	−1.71271e10	−0.551193
$996$	5.12809e9	0.164455
$997$	4.26461e10	1.36285	0.681423	−	0.731890i	$-0.261362\pi$
$997$	4.26461e10	1.36285	0.681423	+	0.731890i	$0.261362\pi$
$998$	−2.02053e9	−0.0643439
$999$	3.81477e10	1.21057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.8.a.a.1.3	✓	4
3.2	odd	2		171.8.a.d.1.2		4
4.3	odd	2		304.8.a.f.1.2		4
5.4	even	2		475.8.a.a.1.2		4
19.18	odd	2		361.8.a.b.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.8.a.a.1.3	✓	4	1.1	even	1	trivial
171.8.a.d.1.2		4	3.2	odd	2
304.8.a.f.1.2		4	4.3	odd	2
361.8.a.b.1.2		4	19.18	odd	2
475.8.a.a.1.2		4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	19.a (trivial)

\(f(q)\)	\(=\)	\(q+3.18411 q^{2} +20.6576 q^{3} -117.861 q^{4} -477.630 q^{5} +65.7761 q^{6} +883.696 q^{7} -782.850 q^{8} -1760.26 q^{9} +O(q^{10})\)	\(q+3.18411 q^{2} +20.6576 q^{3} -117.861 q^{4} -477.630 q^{5} +65.7761 q^{6} +883.696 q^{7} -782.850 q^{8} -1760.26 q^{9} -1520.83 q^{10} -5160.04 q^{11} -2434.74 q^{12} +5645.42 q^{13} +2813.79 q^{14} -9866.70 q^{15} +12593.6 q^{16} -5865.48 q^{17} -5604.87 q^{18} +6859.00 q^{19} +56294.2 q^{20} +18255.1 q^{21} -16430.1 q^{22} -37133.4 q^{23} -16171.8 q^{24} +150005. q^{25} +17975.6 q^{26} -81541.1 q^{27} -104154. q^{28} +187685. q^{29} -31416.7 q^{30} -242165. q^{31} +140304. q^{32} -106594. q^{33} -18676.3 q^{34} -422080. q^{35} +207467. q^{36} -467834. q^{37} +21839.8 q^{38} +116621. q^{39} +373913. q^{40} -557213. q^{41} +58126.1 q^{42} +408555. q^{43} +608170. q^{44} +840754. q^{45} -118237. q^{46} -439207. q^{47} +260153. q^{48} -42624.4 q^{49} +477634. q^{50} -121167. q^{51} -665377. q^{52} -830248. q^{53} -259636. q^{54} +2.46459e6 q^{55} -691801. q^{56} +141691. q^{57} +597609. q^{58} -880709. q^{59} +1.16290e6 q^{60} +1.59095e6 q^{61} -771081. q^{62} -1.55554e6 q^{63} -1.16523e6 q^{64} -2.69642e6 q^{65} -339408. q^{66} -3.48201e6 q^{67} +691314. q^{68} -767088. q^{69} -1.34395e6 q^{70} +4.06081e6 q^{71} +1.37802e6 q^{72} +2.04518e6 q^{73} -1.48963e6 q^{74} +3.09875e6 q^{75} -808412. q^{76} -4.55991e6 q^{77} +371334. q^{78} +5.18855e6 q^{79} -6.01507e6 q^{80} +2.16525e6 q^{81} -1.77423e6 q^{82} -2.10622e6 q^{83} -2.15157e6 q^{84} +2.80153e6 q^{85} +1.30088e6 q^{86} +3.87712e6 q^{87} +4.03954e6 q^{88} +6.75005e6 q^{89} +2.67705e6 q^{90} +4.98884e6 q^{91} +4.37660e6 q^{92} -5.00256e6 q^{93} -1.39848e6 q^{94} -3.27606e6 q^{95} +2.89835e6 q^{96} +3.64028e6 q^{97} -135721. q^{98} +9.08303e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 9 q^{2} - 14 q^{3} + 37 q^{4} - 222 q^{5} - 603 q^{6} - 1246 q^{7} - 3555 q^{8} - 4898 q^{9}+O(q^{10}) \) 4 * q - 9 * q^2 - 14 * q^3 + 37 * q^4 - 222 * q^5 - 603 * q^6 - 1246 * q^7 - 3555 * q^8 - 4898 * q^9	\( 4 q - 9 q^{2} - 14 q^{3} + 37 q^{4} - 222 q^{5} - 603 q^{6} - 1246 q^{7} - 3555 q^{8} - 4898 q^{9} - 6444 q^{10} - 8718 q^{11} - 6281 q^{12} - 4480 q^{13} - 1935 q^{14} - 2760 q^{15} + 19393 q^{16} - 4440 q^{17} + 52722 q^{18} + 27436 q^{19} + 81228 q^{20} + 34124 q^{21} + 115182 q^{22} - 30528 q^{23} + 90135 q^{24} - 23906 q^{25} + 28521 q^{26} - 74942 q^{27} + 37439 q^{28} - 254244 q^{29} + 11340 q^{30} - 303460 q^{31} - 49059 q^{32} - 362364 q^{33} + 240309 q^{34} - 563862 q^{35} - 153410 q^{36} - 270460 q^{37} - 61731 q^{38} - 270304 q^{39} + 230868 q^{40} - 828564 q^{41} + 728307 q^{42} + 37454 q^{43} + 38874 q^{44} + 146694 q^{45} + 1909269 q^{46} + 335670 q^{47} + 1366243 q^{48} - 67560 q^{49} + 815013 q^{50} + 1047318 q^{51} + 1737887 q^{52} + 76728 q^{53} + 775215 q^{54} + 1008918 q^{55} - 973953 q^{56} - 96026 q^{57} + 1613565 q^{58} - 3191334 q^{59} + 669180 q^{60} + 346550 q^{61} - 4678848 q^{62} - 24766 q^{63} - 1917383 q^{64} - 4512972 q^{65} - 2532006 q^{66} - 270322 q^{67} - 9125409 q^{68} - 1452456 q^{69} + 235836 q^{70} - 2066124 q^{71} + 3929670 q^{72} - 416044 q^{73} - 8358894 q^{74} + 5984890 q^{75} + 253783 q^{76} - 3350514 q^{77} + 1418859 q^{78} + 16025864 q^{79} - 622428 q^{80} + 2742268 q^{81} + 7006752 q^{82} + 8524128 q^{83} + 1508165 q^{84} + 4323186 q^{85} - 9139572 q^{86} + 10085136 q^{87} + 4902930 q^{88} + 2899092 q^{89} + 10474488 q^{90} + 23189218 q^{91} - 24380829 q^{92} + 12902348 q^{93} - 9682776 q^{94} - 1522698 q^{95} + 514647 q^{96} - 4766908 q^{97} + 10655118 q^{98} + 25556322 q^{99}+O(q^{100}) \) 4 * q - 9 * q^2 - 14 * q^3 + 37 * q^4 - 222 * q^5 - 603 * q^6 - 1246 * q^7 - 3555 * q^8 - 4898 * q^9 - 6444 * q^10 - 8718 * q^11 - 6281 * q^12 - 4480 * q^13 - 1935 * q^14 - 2760 * q^15 + 19393 * q^16 - 4440 * q^17 + 52722 * q^18 + 27436 * q^19 + 81228 * q^20 + 34124 * q^21 + 115182 * q^22 - 30528 * q^23 + 90135 * q^24 - 23906 * q^25 + 28521 * q^26 - 74942 * q^27 + 37439 * q^28 - 254244 * q^29 + 11340 * q^30 - 303460 * q^31 - 49059 * q^32 - 362364 * q^33 + 240309 * q^34 - 563862 * q^35 - 153410 * q^36 - 270460 * q^37 - 61731 * q^38 - 270304 * q^39 + 230868 * q^40 - 828564 * q^41 + 728307 * q^42 + 37454 * q^43 + 38874 * q^44 + 146694 * q^45 + 1909269 * q^46 + 335670 * q^47 + 1366243 * q^48 - 67560 * q^49 + 815013 * q^50 + 1047318 * q^51 + 1737887 * q^52 + 76728 * q^53 + 775215 * q^54 + 1008918 * q^55 - 973953 * q^56 - 96026 * q^57 + 1613565 * q^58 - 3191334 * q^59 + 669180 * q^60 + 346550 * q^61 - 4678848 * q^62 - 24766 * q^63 - 1917383 * q^64 - 4512972 * q^65 - 2532006 * q^66 - 270322 * q^67 - 9125409 * q^68 - 1452456 * q^69 + 235836 * q^70 - 2066124 * q^71 + 3929670 * q^72 - 416044 * q^73 - 8358894 * q^74 + 5984890 * q^75 + 253783 * q^76 - 3350514 * q^77 + 1418859 * q^78 + 16025864 * q^79 - 622428 * q^80 + 2742268 * q^81 + 7006752 * q^82 + 8524128 * q^83 + 1508165 * q^84 + 4323186 * q^85 - 9139572 * q^86 + 10085136 * q^87 + 4902930 * q^88 + 2899092 * q^89 + 10474488 * q^90 + 23189218 * q^91 - 24380829 * q^92 + 12902348 * q^93 - 9682776 * q^94 - 1522698 * q^95 + 514647 * q^96 - 4766908 * q^97 + 10655118 * q^98 + 25556322 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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