LMFDB - Embedded newform 19.8.a.a.1.2

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			1.2
Root			$-0.751230$ 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)

$f(q)$	$=$	$q-4.43255 q^{2} +22.5580 q^{3} -108.352 q^{4} +160.438 q^{5} -99.9896 q^{6} -1314.43 q^{7} +1047.64 q^{8} -1678.14 q^{9} +O(q^{10})$	\(q-4.43255 q^{2} +22.5580 q^{3} -108.352 q^{4} +160.438 q^{5} -99.9896 q^{6} -1314.43 q^{7} +1047.64 q^{8} -1678.14 q^{9} -711.151 q^{10} -3325.19 q^{11} -2444.22 q^{12} -14382.9 q^{13} +5826.26 q^{14} +3619.17 q^{15} +9225.38 q^{16} +32561.5 q^{17} +7438.42 q^{18} +6859.00 q^{19} -17383.9 q^{20} -29650.9 q^{21} +14739.1 q^{22} +56133.3 q^{23} +23632.8 q^{24} -52384.5 q^{25} +63752.8 q^{26} -87189.8 q^{27} +142421. q^{28} -150416. q^{29} -16042.2 q^{30} +188043. q^{31} -174990. q^{32} -75009.8 q^{33} -144330. q^{34} -210884. q^{35} +181830. q^{36} -240618. q^{37} -30402.9 q^{38} -324449. q^{39} +168082. q^{40} +513193. q^{41} +131429. q^{42} +231164. q^{43} +360293. q^{44} -269237. q^{45} -248814. q^{46} -1.27733e6 q^{47} +208106. q^{48} +904173. q^{49} +232197. q^{50} +734522. q^{51} +1.55842e6 q^{52} +327428. q^{53} +386473. q^{54} -533489. q^{55} -1.37705e6 q^{56} +154725. q^{57} +666725. q^{58} -898832. q^{59} -392146. q^{60} -724758. q^{61} -833510. q^{62} +2.20579e6 q^{63} -405194. q^{64} -2.30757e6 q^{65} +332485. q^{66} -385494. q^{67} -3.52811e6 q^{68} +1.26626e6 q^{69} +934756. q^{70} -662450. q^{71} -1.75809e6 q^{72} -2.78083e6 q^{73} +1.06655e6 q^{74} -1.18169e6 q^{75} -743190. q^{76} +4.37072e6 q^{77} +1.43814e6 q^{78} +731355. q^{79} +1.48010e6 q^{80} +1.70325e6 q^{81} -2.27475e6 q^{82} +3.58367e6 q^{83} +3.21274e6 q^{84} +5.22411e6 q^{85} -1.02465e6 q^{86} -3.39308e6 q^{87} -3.48362e6 q^{88} -4.54504e6 q^{89} +1.19341e6 q^{90} +1.89052e7 q^{91} -6.08218e6 q^{92} +4.24188e6 q^{93} +5.66184e6 q^{94} +1.10045e6 q^{95} -3.94744e6 q^{96} -1.57090e7 q^{97} -4.00779e6 q^{98} +5.58013e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.43255	−0.391786	−0.195893	−	0.980625i	$-0.562761\pi$
$2$	−4.43255	−0.391786	−0.195893	+	0.980625i	$0.562761\pi$
$3$	22.5580	0.482366	0.241183	−	0.970480i	$-0.422465\pi$
$3$	22.5580	0.482366	0.241183	+	0.970480i	$0.422465\pi$
$4$	−108.352	−0.846504
$5$	160.438	0.574002	0.287001	−	0.957930i	$-0.407342\pi$
$5$	160.438	0.574002	0.287001	+	0.957930i	$0.407342\pi$
$6$	−99.9896	−0.188984
$7$	−1314.43	−1.44842	−0.724208	−	0.689582i	$-0.757794\pi$
$7$	−1314.43	−1.44842	−0.724208	+	0.689582i	$0.757794\pi$
$8$	1047.64	0.723434
$9$	−1678.14	−0.767323
$10$	−711.151	−0.224886
$11$	−3325.19	−0.753256	−0.376628	−	0.926365i	$-0.622916\pi$
$11$	−3325.19	−0.753256	−0.376628	+	0.926365i	$0.622916\pi$
$12$	−2444.22	−0.408325
$13$	−14382.9	−1.81570	−0.907850	−	0.419295i	$-0.862277\pi$
$13$	−14382.9	−1.81570	−0.907850	+	0.419295i	$0.862277\pi$
$14$	5826.26	0.567469
$15$	3619.17	0.276879
$16$	9225.38	0.563073
$17$	32561.5	1.60743	0.803716	−	0.595013i	$-0.202853\pi$
$17$	32561.5	1.60743	0.803716	+	0.595013i	$0.202853\pi$
$18$	7438.42	0.300626
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	−17383.9	−0.485895
$21$	−29650.9	−0.698666
$22$	14739.1	0.295115
$23$	56133.3	0.961995	0.480997	−	0.876722i	$-0.340275\pi$
$23$	56133.3	0.961995	0.480997	+	0.876722i	$0.340275\pi$
$24$	23632.8	0.348960
$25$	−52384.5	−0.670522
$26$	63752.8	0.711366
$27$	−87189.8	−0.852496
$28$	142421.	1.22609
$29$	−150416.	−1.14525	−0.572625	−	0.819818i	$-0.694075\pi$
$29$	−150416.	−1.14525	−0.572625	+	0.819818i	$0.694075\pi$
$30$	−16042.2	−0.108477
$31$	188043.	1.13368	0.566841	−	0.823827i	$-0.308165\pi$
$31$	188043.	1.13368	0.566841	+	0.823827i	$0.308165\pi$
$32$	−174990.	−0.944038
$33$	−75009.8	−0.363345
$34$	−144330.	−0.629769
$35$	−210884.	−0.831393
$36$	181830.	0.649542
$37$	−240618.	−0.780948	−0.390474	−	0.920614i	$-0.627689\pi$
$37$	−240618.	−0.780948	−0.390474	+	0.920614i	$0.627689\pi$
$38$	−30402.9	−0.0898818
$39$	−324449.	−0.875832
$40$	168082.	0.415252
$41$	513193.	1.16289	0.581443	−	0.813587i	$-0.302488\pi$
$41$	513193.	1.16289	0.581443	+	0.813587i	$0.302488\pi$
$42$	131429.	0.273728
$43$	231164.	0.443385	0.221693	−	0.975117i	$-0.428842\pi$
$43$	231164.	0.443385	0.221693	+	0.975117i	$0.428842\pi$
$44$	360293.	0.637634
$45$	−269237.	−0.440445
$46$	−248814.	−0.376896
$47$	−1.27733e6	−1.79457	−0.897286	−	0.441449i	$-0.854465\pi$
$47$	−1.27733e6	−1.79457	−0.897286	+	0.441449i	$0.854465\pi$
$48$	208106.	0.271607
$49$	904173.	1.09791
$50$	232197.	0.262701
$51$	734522.	0.775370
$52$	1.55842e6	1.53700
$53$	327428.	0.302100	0.151050	−	0.988526i	$-0.451735\pi$
$53$	327428.	0.302100	0.151050	+	0.988526i	$0.451735\pi$
$54$	386473.	0.333996
$55$	−533489.	−0.432370
$56$	−1.37705e6	−1.04783
$57$	154725.	0.110662
$58$	666725.	0.448692
$59$	−898832.	−0.569766	−0.284883	−	0.958562i	$-0.591955\pi$
$59$	−898832.	−0.569766	−0.284883	+	0.958562i	$0.591955\pi$
$60$	−392146.	−0.234379
$61$	−724758.	−0.408826	−0.204413	−	0.978885i	$-0.565529\pi$
$61$	−724758.	−0.408826	−0.204413	+	0.978885i	$0.565529\pi$
$62$	−833510.	−0.444161
$63$	2.20579e6	1.11140
$64$	−405194.	−0.193212
$65$	−2.30757e6	−1.04221
$66$	332485.	0.142353
$67$	−385494.	−0.156587	−0.0782935	−	0.996930i	$-0.524947\pi$
$67$	−385494.	−0.156587	−0.0782935	+	0.996930i	$0.524947\pi$
$68$	−3.52811e6	−1.36070
$69$	1.26626e6	0.464034
$70$	934756.	0.325728
$71$	−662450.	−0.219659	−0.109830	−	0.993950i	$-0.535030\pi$
$71$	−662450.	−0.219659	−0.109830	+	0.993950i	$0.535030\pi$
$72$	−1.75809e6	−0.555108
$73$	−2.78083e6	−0.836651	−0.418325	−	0.908297i	$-0.637383\pi$
$73$	−2.78083e6	−0.836651	−0.418325	+	0.908297i	$0.637383\pi$
$74$	1.06655e6	0.305964
$75$	−1.18169e6	−0.323437
$76$	−743190.	−0.194201
$77$	4.37072e6	1.09103
$78$	1.43814e6	0.343139
$79$	731355.	0.166891	0.0834455	−	0.996512i	$-0.473408\pi$
$79$	731355.	0.166891	0.0834455	+	0.996512i	$0.473408\pi$
$80$	1.48010e6	0.323205
$81$	1.70325e6	0.356108
$82$	−2.27475e6	−0.455602
$83$	3.58367e6	0.687947	0.343973	−	0.938979i	$-0.388227\pi$
$83$	3.58367e6	0.687947	0.343973	+	0.938979i	$0.388227\pi$
$84$	3.21274e6	0.591424
$85$	5.22411e6	0.922669
$86$	−1.02465e6	−0.173712
$87$	−3.39308e6	−0.552429
$88$	−3.48362e6	−0.544931
$89$	−4.54504e6	−0.683396	−0.341698	−	0.939810i	$-0.611002\pi$
$89$	−4.54504e6	−0.683396	−0.341698	+	0.939810i	$0.611002\pi$
$90$	1.19341e6	0.172560
$91$	1.89052e7	2.62989
$92$	−6.08218e6	−0.814332
$93$	4.24188e6	0.546850
$94$	5.66184e6	0.703088
$95$	1.10045e6	0.131685
$96$	−3.94744e6	−0.455372
$97$	−1.57090e7	−1.74762	−0.873810	−	0.486267i	$-0.838358\pi$
$97$	−1.57090e7	−1.74762	−0.873810	+	0.486267i	$0.838358\pi$
$98$	−4.00779e6	−0.430144
$99$	5.58013e6	0.577991
$100$	5.67600e6	0.567600
$101$	−1.03125e7	−0.995957	−0.497978	−	0.867190i	$-0.665924\pi$
$101$	−1.03125e7	−0.995957	−0.497978	+	0.867190i	$0.665924\pi$
$102$	−3.25581e6	−0.303779
$103$	7.86463e6	0.709166	0.354583	−	0.935025i	$-0.384623\pi$
$103$	7.86463e6	0.709166	0.354583	+	0.935025i	$0.384623\pi$
$104$	−1.50681e7	−1.31354
$105$	−4.75713e6	−0.401036
$106$	−1.45134e6	−0.118358
$107$	2.82081e6	0.222603	0.111302	−	0.993787i	$-0.464498\pi$
$107$	2.82081e6	0.222603	0.111302	+	0.993787i	$0.464498\pi$
$108$	9.44723e6	0.721642
$109$	−8.10723e6	−0.599625	−0.299812	−	0.953998i	$-0.596924\pi$
$109$	−8.10723e6	−0.599625	−0.299812	+	0.953998i	$0.596924\pi$
$110$	2.36472e6	0.169397
$111$	−5.42787e6	−0.376703
$112$	−1.21261e7	−0.815563
$113$	−875387.	−0.0570723	−0.0285361	−	0.999593i	$-0.509085\pi$
$113$	−875387.	−0.0570723	−0.0285361	+	0.999593i	$0.509085\pi$
$114$	−685829.	−0.0433559
$115$	9.00593e6	0.552187
$116$	1.62979e7	0.969458
$117$	2.41364e7	1.39323
$118$	3.98412e6	0.223226
$119$	−4.27996e7	−2.32823
$120$	3.79161e6	0.200304
$121$	−8.43025e6	−0.432605
$122$	3.21253e6	0.160172
$123$	1.15766e7	0.560936
$124$	−2.03749e7	−0.959666
$125$	−2.09387e7	−0.958882
$126$	−9.77726e6	−0.435432
$127$	2.94546e7	1.27597	0.637985	−	0.770049i	$-0.279768\pi$
$127$	2.94546e7	1.27597	0.637985	+	0.770049i	$0.279768\pi$
$128$	2.41948e7	1.01974
$129$	5.21461e6	0.213874
$130$	1.02284e7	0.408325
$131$	−1.33696e7	−0.519599	−0.259799	−	0.965663i	$-0.583656\pi$
$131$	−1.33696e7	−0.519599	−0.259799	+	0.965663i	$0.583656\pi$
$132$	8.12750e6	0.307573
$133$	−9.01565e6	−0.332289
$134$	1.70872e6	0.0613486
$135$	−1.39886e7	−0.489334
$136$	3.41128e7	1.16287
$137$	2.38509e7	0.792469	0.396235	−	0.918149i	$-0.370317\pi$
$137$	2.38509e7	0.792469	0.396235	+	0.918149i	$0.370317\pi$
$138$	−5.61274e6	−0.181802
$139$	1.54074e7	0.486606	0.243303	−	0.969950i	$-0.421769\pi$
$139$	1.54074e7	0.486606	0.243303	+	0.969950i	$0.421769\pi$
$140$	2.28498e7	0.703777
$141$	−2.88141e7	−0.865641
$142$	2.93634e6	0.0860593
$143$	4.78259e7	1.36769
$144$	−1.54814e7	−0.432059
$145$	−2.41324e7	−0.657375
$146$	1.23262e7	0.327788
$147$	2.03964e7	0.529593
$148$	2.60716e7	0.661075
$149$	−2.11681e7	−0.524241	−0.262120	−	0.965035i	$-0.584422\pi$
$149$	−2.11681e7	−0.524241	−0.262120	+	0.965035i	$0.584422\pi$
$150$	5.23791e6	0.126718
$151$	−4.38265e7	−1.03590	−0.517949	−	0.855411i	$-0.673304\pi$
$151$	−4.38265e7	−1.03590	−0.517949	+	0.855411i	$0.673304\pi$
$152$	7.18579e6	0.165967
$153$	−5.46425e7	−1.23342
$154$	−1.93734e7	−0.427449
$155$	3.01693e7	0.650736
$156$	3.51549e7	0.741395
$157$	−8.01743e7	−1.65343	−0.826716	−	0.562619i	$-0.809794\pi$
$157$	−8.01743e7	−1.65343	−0.826716	+	0.562619i	$0.809794\pi$
$158$	−3.24177e6	−0.0653856
$159$	7.38613e6	0.145723
$160$	−2.80752e7	−0.541879
$161$	−7.37830e7	−1.39337
$162$	−7.54975e6	−0.139518
$163$	3.44193e6	0.0622509	0.0311255	−	0.999515i	$-0.490091\pi$
$163$	3.44193e6	0.0622509	0.0311255	+	0.999515i	$0.490091\pi$
$164$	−5.56057e7	−0.984387
$165$	−1.20344e7	−0.208561
$166$	−1.58848e7	−0.269528
$167$	7.25618e7	1.20559	0.602796	−	0.797896i	$-0.294053\pi$
$167$	7.25618e7	1.20559	0.602796	+	0.797896i	$0.294053\pi$
$168$	−3.10636e7	−0.505439
$169$	1.44119e8	2.29677
$170$	−2.31561e7	−0.361489
$171$	−1.15103e7	−0.176036
$172$	−2.50472e7	−0.375327
$173$	3.51728e7	0.516470	0.258235	−	0.966082i	$-0.416859\pi$
$173$	3.51728e7	0.516470	0.258235	+	0.966082i	$0.416859\pi$
$174$	1.50400e7	0.216434
$175$	6.88556e7	0.971194
$176$	−3.06762e7	−0.424138
$177$	−2.02759e7	−0.274836
$178$	2.01461e7	0.267745
$179$	4.81285e6	0.0627215	0.0313608	−	0.999508i	$-0.490016\pi$
$179$	4.81285e6	0.0627215	0.0313608	+	0.999508i	$0.490016\pi$
$180$	2.91725e7	0.372838
$181$	−8.61630e7	−1.08005	−0.540027	−	0.841647i	$-0.681586\pi$
$181$	−8.61630e7	−1.08005	−0.540027	+	0.841647i	$0.681586\pi$
$182$	−8.37984e7	−1.03035
$183$	−1.63491e7	−0.197204
$184$	5.88077e7	0.695940
$185$	−3.86043e7	−0.448265
$186$	−1.88023e7	−0.214248
$187$	−1.08273e8	−1.21081
$188$	1.38402e8	1.51911
$189$	1.14605e8	1.23477
$190$	−4.87779e6	−0.0515923
$191$	1.58132e8	1.64211	0.821055	−	0.570849i	$-0.193386\pi$
$191$	1.58132e8	1.64211	0.821055	+	0.570849i	$0.193386\pi$
$192$	−9.14039e6	−0.0931988
$193$	1.32687e8	1.32855	0.664274	−	0.747489i	$-0.268741\pi$
$193$	1.32687e8	1.32855	0.664274	+	0.747489i	$0.268741\pi$
$194$	6.96309e7	0.684693
$195$	−5.20541e7	−0.502729
$196$	−9.79694e7	−0.929382
$197$	1.74932e8	1.63019	0.815094	−	0.579329i	$-0.196685\pi$
$197$	1.74932e8	1.63019	0.815094	+	0.579329i	$0.196685\pi$
$198$	−2.47342e7	−0.226449
$199$	−1.37161e8	−1.23380	−0.616898	−	0.787043i	$-0.711611\pi$
$199$	−1.37161e8	−1.23380	−0.616898	+	0.787043i	$0.711611\pi$
$200$	−5.48804e7	−0.485079
$201$	−8.69598e6	−0.0755323
$202$	4.57108e7	0.390202
$203$	1.97710e8	1.65880
$204$	−7.95873e7	−0.656354
$205$	8.23358e7	0.667498
$206$	−3.48604e7	−0.277841
$207$	−9.41992e7	−0.738161
$208$	−1.32688e8	−1.02237
$209$	−2.28075e7	−0.172809
$210$	2.10862e7	0.157120
$211$	−3.87683e7	−0.284111	−0.142056	−	0.989859i	$-0.545371\pi$
$211$	−3.87683e7	−0.284111	−0.142056	+	0.989859i	$0.545371\pi$
$212$	−3.54777e7	−0.255729
$213$	−1.49436e7	−0.105956
$214$	−1.25034e7	−0.0872127
$215$	3.70876e7	0.254504
$216$	−9.13439e7	−0.616725
$217$	−2.47169e8	−1.64204
$218$	3.59357e7	0.234925
$219$	−6.27300e7	−0.403572
$220$	5.78048e7	0.366003
$221$	−4.68327e8	−2.91861
$222$	2.40593e7	0.147587
$223$	2.87380e8	1.73536	0.867679	−	0.497125i	$-0.165611\pi$
$223$	2.87380e8	1.73536	0.867679	+	0.497125i	$0.165611\pi$
$224$	2.30012e8	1.36736
$225$	8.79084e7	0.514507
$226$	3.88020e6	0.0223601
$227$	1.12245e8	0.636906	0.318453	−	0.947939i	$-0.396837\pi$
$227$	1.12245e8	0.636906	0.318453	+	0.947939i	$0.396837\pi$
$228$	−1.67649e7	−0.0936761
$229$	−5.79306e7	−0.318775	−0.159387	−	0.987216i	$-0.550952\pi$
$229$	−5.79306e7	−0.318775	−0.159387	+	0.987216i	$0.550952\pi$
$230$	−3.99192e7	−0.216339
$231$	9.85948e7	0.526274
$232$	−1.57582e8	−0.828512
$233$	−1.36315e8	−0.705988	−0.352994	−	0.935626i	$-0.614836\pi$
$233$	−1.36315e8	−0.705988	−0.352994	+	0.935626i	$0.614836\pi$
$234$	−1.06986e8	−0.545847
$235$	−2.04933e8	−1.03009
$236$	9.73907e7	0.482309
$237$	1.64979e7	0.0805026
$238$	1.89712e8	0.912167
$239$	−1.85736e8	−0.880043	−0.440022	−	0.897987i	$-0.645029\pi$
$239$	−1.85736e8	−0.880043	−0.440022	+	0.897987i	$0.645029\pi$
$240$	3.33882e7	0.155903
$241$	5.88352e7	0.270756	0.135378	−	0.990794i	$-0.456775\pi$
$241$	5.88352e7	0.270756	0.135378	+	0.990794i	$0.456775\pi$
$242$	3.73675e7	0.169489
$243$	2.29106e8	1.02427
$244$	7.85293e7	0.346073
$245$	1.45064e8	0.630200
$246$	−5.13139e7	−0.219767
$247$	−9.86522e7	−0.416550
$248$	1.97002e8	0.820144
$249$	8.08405e7	0.331842
$250$	9.28120e7	0.375677
$251$	1.23781e8	0.494080	0.247040	−	0.969005i	$-0.420542\pi$
$251$	1.23781e8	0.494080	0.247040	+	0.969005i	$0.420542\pi$
$252$	−2.39002e8	−0.940806
$253$	−1.86654e8	−0.724628
$254$	−1.30559e8	−0.499907
$255$	1.17845e8	0.445064
$256$	−5.53799e7	−0.206306
$257$	−1.53079e8	−0.562537	−0.281268	−	0.959629i	$-0.590755\pi$
$257$	−1.53079e8	−0.562537	−0.281268	+	0.959629i	$0.590755\pi$
$258$	−2.31140e7	−0.0837928
$259$	3.16275e8	1.13114
$260$	2.50030e8	0.882239
$261$	2.52418e8	0.878776
$262$	5.92614e7	0.203572
$263$	−2.05070e8	−0.695116	−0.347558	−	0.937658i	$-0.612989\pi$
$263$	−2.05070e8	−0.695116	−0.347558	+	0.937658i	$0.612989\pi$
$264$	−7.85836e7	−0.262856
$265$	5.25320e7	0.173406
$266$	3.99623e7	0.130186
$267$	−1.02527e8	−0.329647
$268$	4.17692e7	0.132552
$269$	−1.99707e8	−0.625546	−0.312773	−	0.949828i	$-0.601258\pi$
$269$	−1.99707e8	−0.625546	−0.312773	+	0.949828i	$0.601258\pi$
$270$	6.20051e7	0.191714
$271$	−4.24704e6	−0.0129626	−0.00648132	−	0.999979i	$-0.502063\pi$
$271$	−4.24704e6	−0.0129626	−0.00648132	+	0.999979i	$0.502063\pi$
$272$	3.00392e8	0.905101
$273$	4.26465e8	1.26857
$274$	−1.05720e8	−0.310478
$275$	1.74189e8	0.505075
$276$	−1.37202e8	−0.392806
$277$	6.55663e7	0.185354	0.0926769	−	0.995696i	$-0.470458\pi$
$277$	6.55663e7	0.185354	0.0926769	+	0.995696i	$0.470458\pi$
$278$	−6.82941e7	−0.190646
$279$	−3.15562e8	−0.869901
$280$	−2.20932e8	−0.601458
$281$	−5.92977e8	−1.59428	−0.797142	−	0.603792i	$-0.793656\pi$
$281$	−5.92977e8	−1.59428	−0.797142	+	0.603792i	$0.793656\pi$
$282$	1.27720e8	0.339146
$283$	−1.03930e8	−0.272576	−0.136288	−	0.990669i	$-0.543517\pi$
$283$	−1.03930e8	−0.272576	−0.136288	+	0.990669i	$0.543517\pi$
$284$	7.17781e7	0.185942
$285$	2.48239e7	0.0635204
$286$	−2.11991e8	−0.535840
$287$	−6.74554e8	−1.68434
$288$	2.93658e8	0.724382
$289$	6.49910e8	1.58384
$290$	1.06968e8	0.257550
$291$	−3.54364e8	−0.842993
$292$	3.01310e8	0.708228
$293$	2.59446e8	0.602573	0.301287	−	0.953534i	$-0.402584\pi$
$293$	2.59446e8	0.602573	0.301287	+	0.953534i	$0.402584\pi$
$294$	−9.04079e7	−0.207487
$295$	−1.44207e8	−0.327047
$296$	−2.52082e8	−0.564964
$297$	2.89923e8	0.642148
$298$	9.38288e7	0.205390
$299$	−8.07358e8	−1.74669
$300$	1.28039e8	0.273791
$301$	−3.03848e8	−0.642206
$302$	1.94263e8	0.405851
$303$	−2.32630e8	−0.480416
$304$	6.32769e7	0.129178
$305$	−1.16279e8	−0.234667
$306$	2.42206e8	0.483236
$307$	1.19410e8	0.235536	0.117768	−	0.993041i	$-0.462426\pi$
$307$	1.19410e8	0.235536	0.117768	+	0.993041i	$0.462426\pi$
$308$	−4.73579e8	−0.923559
$309$	1.77410e8	0.342078
$310$	−1.33727e8	−0.254949
$311$	−3.77913e8	−0.712411	−0.356206	−	0.934408i	$-0.615930\pi$
$311$	−3.77913e8	−0.712411	−0.356206	+	0.934408i	$0.615930\pi$
$312$	−3.39908e8	−0.633607
$313$	−1.94359e8	−0.358262	−0.179131	−	0.983825i	$-0.557329\pi$
$313$	−1.94359e8	−0.358262	−0.179131	+	0.983825i	$0.557329\pi$
$314$	3.55377e8	0.647792
$315$	3.53893e8	0.637947
$316$	−7.92441e7	−0.141274
$317$	−6.93663e8	−1.22304	−0.611520	−	0.791229i	$-0.709442\pi$
$317$	−6.93663e8	−1.22304	−0.611520	+	0.791229i	$0.709442\pi$
$318$	−3.27394e7	−0.0570921
$319$	5.00161e8	0.862666
$320$	−6.50087e7	−0.110904
$321$	6.36320e7	0.107376
$322$	3.27047e8	0.545902
$323$	2.23339e8	0.368770
$324$	−1.84552e8	−0.301447
$325$	7.53440e8	1.21747
$326$	−1.52565e7	−0.0243890
$327$	−1.82883e8	−0.289239
$328$	5.37644e8	0.841271
$329$	1.67896e9	2.59929
$330$	5.33433e7	0.0817111
$331$	9.04756e8	1.37130	0.685651	−	0.727930i	$-0.259517\pi$
$331$	9.04756e8	1.37130	0.685651	+	0.727930i	$0.259517\pi$
$332$	−3.88300e8	−0.582349
$333$	4.03790e8	0.599239
$334$	−3.21634e8	−0.472334
$335$	−6.18480e7	−0.0898812
$336$	−2.73540e8	−0.393400
$337$	6.08238e8	0.865703	0.432851	−	0.901465i	$-0.357508\pi$
$337$	6.08238e8	0.865703	0.432851	+	0.901465i	$0.357508\pi$
$338$	−6.38813e8	−0.899841
$339$	−1.97470e7	−0.0275297
$340$	−5.66045e8	−0.781042
$341$	−6.25280e8	−0.853953
$342$	5.10201e7	0.0689684
$343$	−1.05982e8	−0.141809
$344$	2.42178e8	0.320760
$345$	2.03156e8	0.266356
$346$	−1.55905e8	−0.202346
$347$	−8.60691e7	−0.110585	−0.0552923	−	0.998470i	$-0.517609\pi$
$347$	−8.60691e7	−0.110585	−0.0552923	+	0.998470i	$0.517609\pi$
$348$	3.67649e8	0.467633
$349$	−5.57284e8	−0.701759	−0.350879	−	0.936421i	$-0.614117\pi$
$349$	−5.57284e8	−0.701759	−0.350879	+	0.936421i	$0.614117\pi$
$350$	−3.05206e8	−0.380500
$351$	1.25404e9	1.54788
$352$	5.81877e8	0.711102
$353$	5.48342e8	0.663498	0.331749	−	0.943368i	$-0.392361\pi$
$353$	5.48342e8	0.663498	0.331749	+	0.943368i	$0.392361\pi$
$354$	8.98738e7	0.107677
$355$	−1.06282e8	−0.126085
$356$	4.92466e8	0.578498
$357$	−9.65475e8	−1.12306
$358$	−2.13332e7	−0.0245734
$359$	−1.18781e9	−1.35493	−0.677466	−	0.735554i	$-0.736922\pi$
$359$	−1.18781e9	−1.35493	−0.677466	+	0.735554i	$0.736922\pi$
$360$	−2.82065e8	−0.318633
$361$	4.70459e7	0.0526316
$362$	3.81922e8	0.423150
$363$	−1.90170e8	−0.208674
$364$	−2.04843e9	−2.22621
$365$	−4.46152e8	−0.480239
$366$	7.24682e7	0.0772616
$367$	−6.08220e8	−0.642287	−0.321144	−	0.947030i	$-0.604067\pi$
$367$	−6.08220e8	−0.642287	−0.321144	+	0.947030i	$0.604067\pi$
$368$	5.17851e8	0.541673
$369$	−8.61207e8	−0.892309
$370$	1.71116e8	0.175624
$371$	−4.30380e8	−0.437566
$372$	−4.59618e8	−0.462910
$373$	8.53172e8	0.851247	0.425624	−	0.904900i	$-0.360055\pi$
$373$	8.53172e8	0.851247	0.425624	+	0.904900i	$0.360055\pi$
$374$	4.79926e8	0.474377
$375$	−4.72336e8	−0.462532
$376$	−1.33819e9	−1.29826
$377$	2.16341e9	2.07943
$378$	−5.07991e8	−0.483765
$379$	−4.73381e7	−0.0446656	−0.0223328	−	0.999751i	$-0.507109\pi$
$379$	−4.73381e7	−0.0446656	−0.0223328	+	0.999751i	$0.507109\pi$
$380$	−1.19236e8	−0.111472
$381$	6.64438e8	0.615484
$382$	−7.00927e8	−0.643356
$383$	−1.03286e9	−0.939393	−0.469697	−	0.882828i	$-0.655637\pi$
$383$	−1.03286e9	−0.939393	−0.469697	+	0.882828i	$0.655637\pi$
$384$	5.45787e8	0.491886
$385$	7.01231e8	0.626252
$386$	−5.88141e8	−0.520506
$387$	−3.87925e8	−0.340220
$388$	1.70211e9	1.47937
$389$	−3.58685e8	−0.308951	−0.154475	−	0.987997i	$-0.549369\pi$
$389$	−3.58685e8	−0.308951	−0.154475	+	0.987997i	$0.549369\pi$
$390$	2.30733e8	0.196962
$391$	1.82778e9	1.54634
$392$	9.47252e8	0.794263
$393$	−3.01591e8	−0.250637
$394$	−7.75396e8	−0.638685
$395$	1.17337e8	0.0957958
$396$	−6.04621e8	−0.489271
$397$	−8.16836e8	−0.655192	−0.327596	−	0.944818i	$-0.606238\pi$
$397$	−8.16836e8	−0.655192	−0.327596	+	0.944818i	$0.606238\pi$
$398$	6.07972e8	0.483384
$399$	−2.03375e8	−0.160285
$400$	−4.83267e8	−0.377553
$401$	−3.22104e8	−0.249454	−0.124727	−	0.992191i	$-0.539806\pi$
$401$	−3.22104e8	−0.249454	−0.124727	+	0.992191i	$0.539806\pi$
$402$	3.85454e7	0.0295925
$403$	−2.70460e9	−2.05843
$404$	1.11739e9	0.843081
$405$	2.73267e8	0.204406
$406$	−8.76361e8	−0.649893
$407$	8.00101e8	0.588254
$408$	7.69518e8	0.560929
$409$	8.01022e6	0.00578912	0.00289456	−	0.999996i	$-0.499079\pi$
$409$	8.01022e6	0.00578912	0.00289456	+	0.999996i	$0.499079\pi$
$410$	−3.64958e8	−0.261516
$411$	5.38029e8	0.382260
$412$	−8.52152e8	−0.600312
$413$	1.18145e9	0.825258
$414$	4.17543e8	0.289201
$415$	5.74958e8	0.394882
$416$	2.51687e9	1.71409
$417$	3.47561e8	0.234722
$418$	1.01095e8	0.0677040
$419$	−3.51229e7	−0.0233261	−0.0116630	−	0.999932i	$-0.503713\pi$
$419$	−3.51229e7	−0.0233261	−0.0116630	+	0.999932i	$0.503713\pi$
$420$	5.15447e8	0.339478
$421$	1.24169e8	0.0811009	0.0405504	−	0.999177i	$-0.487089\pi$
$421$	1.24169e8	0.0811009	0.0405504	+	0.999177i	$0.487089\pi$
$422$	1.71843e8	0.111311
$423$	2.14354e9	1.37702
$424$	3.43028e8	0.218549
$425$	−1.70572e9	−1.07782
$426$	6.62381e7	0.0415121
$427$	9.52640e8	0.592149
$428$	−3.05642e8	−0.188434
$429$	1.07886e9	0.659726
$430$	−1.64393e8	−0.0997110
$431$	−2.71792e9	−1.63518	−0.817592	−	0.575798i	$-0.804691\pi$
$431$	−2.71792e9	−1.63518	−0.817592	+	0.575798i	$0.804691\pi$
$432$	−8.04359e8	−0.480017
$433$	−5.25437e8	−0.311038	−0.155519	−	0.987833i	$-0.549705\pi$
$433$	−5.25437e8	−0.311038	−0.155519	+	0.987833i	$0.549705\pi$
$434$	1.09559e9	0.643329
$435$	−5.44380e8	−0.317095
$436$	8.78438e8	0.507585
$437$	3.85018e8	0.220697
$438$	2.78054e8	0.158114
$439$	9.29601e8	0.524410	0.262205	−	0.965012i	$-0.415550\pi$
$439$	9.29601e8	0.524410	0.262205	+	0.965012i	$0.415550\pi$
$440$	−5.58906e8	−0.312791
$441$	−1.51732e9	−0.842449
$442$	2.07589e9	1.14347
$443$	−3.39858e9	−1.85731	−0.928654	−	0.370946i	$-0.879034\pi$
$443$	−3.39858e9	−1.85731	−0.928654	+	0.370946i	$0.879034\pi$
$444$	5.88123e8	0.318880
$445$	−7.29199e8	−0.392271
$446$	−1.27383e9	−0.679889
$447$	−4.77511e8	−0.252876
$448$	5.32598e8	0.279851
$449$	2.55833e9	1.33381	0.666905	−	0.745143i	$-0.267619\pi$
$449$	2.55833e9	1.33381	0.666905	+	0.745143i	$0.267619\pi$
$450$	−3.89658e8	−0.201577
$451$	−1.70647e9	−0.875951
$452$	9.48503e7	0.0483119
$453$	−9.88639e8	−0.499682
$454$	−4.97531e8	−0.249531
$455$	3.03312e9	1.50956
$456$	1.62097e8	0.0800569
$457$	−3.58106e9	−1.75511	−0.877556	−	0.479474i	$-0.840828\pi$
$457$	−3.58106e9	−1.75511	−0.877556	+	0.479474i	$0.840828\pi$
$458$	2.56781e8	0.124892
$459$	−2.83903e9	−1.37033
$460$	−9.75814e8	−0.467428
$461$	−6.23890e8	−0.296589	−0.148294	−	0.988943i	$-0.547378\pi$
$461$	−6.23890e8	−0.296589	−0.148294	+	0.988943i	$0.547378\pi$
$462$	−4.37027e8	−0.206187
$463$	2.40707e9	1.12708	0.563541	−	0.826088i	$-0.309439\pi$
$463$	2.40707e9	1.12708	0.563541	+	0.826088i	$0.309439\pi$
$464$	−1.38764e9	−0.644858
$465$	6.80560e8	0.313893
$466$	6.04222e8	0.276596
$467$	2.56800e9	1.16677	0.583386	−	0.812195i	$-0.301727\pi$
$467$	2.56800e9	1.16677	0.583386	+	0.812195i	$0.301727\pi$
$468$	−2.61524e9	−1.17937
$469$	5.06703e8	0.226803
$470$	9.08376e8	0.403574
$471$	−1.80857e9	−0.797560
$472$	−9.41656e8	−0.412188
$473$	−7.68666e8	−0.333982
$474$	−7.31278e7	−0.0315398
$475$	−3.59306e8	−0.153828
$476$	4.63745e9	1.97085
$477$	−5.49469e8	−0.231808
$478$	8.23285e8	0.344788
$479$	−1.02122e7	−0.00424567	−0.00212283	−	0.999998i	$-0.500676\pi$
$479$	−1.02122e7	−0.00424567	−0.00212283	+	0.999998i	$0.500676\pi$
$480$	−6.33321e8	−0.261384
$481$	3.46078e9	1.41797
$482$	−2.60790e8	−0.106078
$483$	−1.66440e9	−0.672113
$484$	9.13439e8	0.366202
$485$	−2.52032e9	−1.00314
$486$	−1.01552e9	−0.401295
$487$	−1.22192e9	−0.479394	−0.239697	−	0.970848i	$-0.577048\pi$
$487$	−1.22192e9	−0.479394	−0.239697	+	0.970848i	$0.577048\pi$
$488$	−7.59288e8	−0.295759
$489$	7.76432e7	0.0300277
$490$	−6.43004e8	−0.246903
$491$	4.50647e9	1.71811	0.859056	−	0.511882i	$-0.171051\pi$
$491$	4.50647e9	1.71811	0.859056	+	0.511882i	$0.171051\pi$
$492$	−1.25435e9	−0.474835
$493$	−4.89775e9	−1.84091
$494$	4.37281e8	0.163198
$495$	8.95266e8	0.331768
$496$	1.73477e9	0.638345
$497$	8.70742e8	0.318157
$498$	−3.58330e8	−0.130011
$499$	−1.07949e9	−0.388925	−0.194463	−	0.980910i	$-0.562296\pi$
$499$	−1.07949e9	−0.388925	−0.194463	+	0.980910i	$0.562296\pi$
$500$	2.26876e9	0.811698
$501$	1.63685e9	0.581536
$502$	−5.48667e8	−0.193574
$503$	5.73702e8	0.201001	0.100500	−	0.994937i	$-0.467956\pi$
$503$	5.73702e8	0.201001	0.100500	+	0.994937i	$0.467956\pi$
$504$	2.31088e9	0.804026
$505$	−1.65453e9	−0.571681
$506$	8.27353e8	0.283899
$507$	3.25103e9	1.10788
$508$	−3.19148e9	−1.08011
$509$	−4.59487e9	−1.54441	−0.772203	−	0.635376i	$-0.780845\pi$
$509$	−4.59487e9	−1.54441	−0.772203	+	0.635376i	$0.780845\pi$
$510$	−5.22356e8	−0.174370
$511$	3.65519e9	1.21182
$512$	−2.85146e9	−0.938908
$513$	−5.98035e8	−0.195576
$514$	6.78532e8	0.220394
$515$	1.26179e9	0.407062
$516$	−5.65016e8	−0.181045
$517$	4.24737e9	1.35177
$518$	−1.40190e9	−0.443163
$519$	7.93429e8	0.249128
$520$	−2.41751e9	−0.753974
$521$	5.15260e9	1.59623	0.798113	−	0.602507i	$-0.205832\pi$
$521$	5.15260e9	1.59623	0.798113	+	0.602507i	$0.205832\pi$
$522$	−1.11886e9	−0.344292
$523$	5.72233e9	1.74911	0.874555	−	0.484927i	$-0.161154\pi$
$523$	5.72233e9	1.74911	0.874555	+	0.484927i	$0.161154\pi$
$524$	1.44863e9	0.439843
$525$	1.55325e9	0.468471
$526$	9.08985e8	0.272337
$527$	6.12296e9	1.82232
$528$	−6.91994e8	−0.204590
$529$	−2.53884e8	−0.0745658
$530$	−2.32851e8	−0.0679379
$531$	1.50836e9	0.437195
$532$	9.76868e8	0.281284
$533$	−7.38119e9	−2.11145
$534$	4.54457e8	0.129151
$535$	4.52567e8	0.127775
$536$	−4.03861e8	−0.113280
$537$	1.08568e8	0.0302547
$538$	8.85209e8	0.245080
$539$	−3.00655e9	−0.827004
$540$	1.51570e9	0.414223
$541$	−3.96979e9	−1.07790	−0.538948	−	0.842339i	$-0.681178\pi$
$541$	−3.96979e9	−1.07790	−0.538948	+	0.842339i	$0.681178\pi$
$542$	1.88252e7	0.00507858
$543$	−1.94367e9	−0.520982
$544$	−5.69794e9	−1.51748
$545$	−1.30071e9	−0.344186
$546$	−1.89033e9	−0.497007
$547$	5.20229e9	1.35906	0.679530	−	0.733648i	$-0.262184\pi$
$547$	5.20229e9	1.35906	0.679530	+	0.733648i	$0.262184\pi$
$548$	−2.58430e9	−0.670828
$549$	1.21624e9	0.313701
$550$	−7.72101e8	−0.197881
$551$	−1.03170e9	−0.262738
$552$	1.32659e9	0.335698
$553$	−9.61311e8	−0.241728
$554$	−2.90626e8	−0.0726190
$555$	−8.70838e8	−0.216228
$556$	−1.66943e9	−0.411914
$557$	−2.14776e9	−0.526614	−0.263307	−	0.964712i	$-0.584813\pi$
$557$	−2.14776e9	−0.526614	−0.263307	+	0.964712i	$0.584813\pi$
$558$	1.39874e9	0.340815
$559$	−3.32481e9	−0.805054
$560$	−1.94549e9	−0.468134
$561$	−2.44243e9	−0.584052
$562$	2.62840e9	0.624618
$563$	−2.12264e9	−0.501300	−0.250650	−	0.968078i	$-0.580644\pi$
$563$	−2.12264e9	−0.501300	−0.250650	+	0.968078i	$0.580644\pi$
$564$	3.12208e9	0.732768
$565$	−1.40446e8	−0.0327596
$566$	4.60675e8	0.106792
$567$	−2.23880e9	−0.515792
$568$	−6.94012e8	−0.158909
$569$	3.97928e9	0.905547	0.452774	−	0.891625i	$-0.350435\pi$
$569$	3.97928e9	0.905547	0.452774	+	0.891625i	$0.350435\pi$
$570$	−1.10033e8	−0.0248864
$571$	−2.99237e9	−0.672650	−0.336325	−	0.941746i	$-0.609184\pi$
$571$	−2.99237e9	−0.672650	−0.336325	+	0.941746i	$0.609184\pi$
$572$	−5.18205e9	−1.15775
$573$	3.56714e9	0.792098
$574$	2.98999e9	0.659901
$575$	−2.94051e9	−0.645039
$576$	6.79971e8	0.148256
$577$	3.77263e9	0.817578	0.408789	−	0.912629i	$-0.365951\pi$
$577$	3.77263e9	0.817578	0.408789	+	0.912629i	$0.365951\pi$
$578$	−2.88076e9	−0.620525
$579$	2.99315e9	0.640846
$580$	2.61481e9	0.556470
$581$	−4.71047e9	−0.996432
$582$	1.57074e9	0.330273
$583$	−1.08876e9	−0.227559
$584$	−2.91332e9	−0.605262
$585$	3.87241e9	0.799715
$586$	−1.15001e9	−0.236080
$587$	−2.63654e9	−0.538023	−0.269011	−	0.963137i	$-0.586697\pi$
$587$	−2.63654e9	−0.538023	−0.269011	+	0.963137i	$0.586697\pi$
$588$	−2.21000e9	−0.448302
$589$	1.28979e9	0.260085
$590$	6.39205e8	0.128132
$591$	3.94612e9	0.786347
$592$	−2.21979e9	−0.439730
$593$	4.82120e9	0.949431	0.474716	−	0.880139i	$-0.342551\pi$
$593$	4.82120e9	0.949431	0.474716	+	0.880139i	$0.342551\pi$
$594$	−1.28510e9	−0.251585
$595$	−6.86670e9	−1.33641
$596$	2.29362e9	0.443772
$597$	−3.09407e9	−0.595142
$598$	3.57865e9	0.684330
$599$	−8.65639e9	−1.64567	−0.822835	−	0.568280i	$-0.807609\pi$
$599$	−8.65639e9	−1.64567	−0.822835	+	0.568280i	$0.807609\pi$
$600$	−1.23799e9	−0.233985
$601$	6.78656e9	1.27523	0.637616	−	0.770354i	$-0.279921\pi$
$601$	6.78656e9	1.27523	0.637616	+	0.770354i	$0.279921\pi$
$602$	1.34682e9	0.251607
$603$	6.46911e8	0.120153
$604$	4.74871e9	0.876892
$605$	−1.35254e9	−0.248316
$606$	1.03115e9	0.188220
$607$	4.48572e9	0.814089	0.407044	−	0.913408i	$-0.366559\pi$
$607$	4.48572e9	0.814089	0.407044	+	0.913408i	$0.366559\pi$
$608$	−1.20026e9	−0.216577
$609$	4.45995e9	0.800147
$610$	5.15412e8	0.0919391
$611$	1.83717e10	3.25841
$612$	5.92065e9	1.04409
$613$	−3.90637e9	−0.684955	−0.342477	−	0.939526i	$-0.611266\pi$
$613$	−3.90637e9	−0.684955	−0.342477	+	0.939526i	$0.611266\pi$
$614$	−5.29291e8	−0.0922795
$615$	1.85733e9	0.321978
$616$	4.57896e9	0.789286
$617$	−7.14720e8	−0.122501	−0.0612503	−	0.998122i	$-0.519509\pi$
$617$	−7.14720e8	−0.122501	−0.0612503	+	0.998122i	$0.519509\pi$
$618$	−7.86381e8	−0.134021
$619$	−6.53803e9	−1.10797	−0.553987	−	0.832525i	$-0.686894\pi$
$619$	−6.53803e9	−1.10797	−0.553987	+	0.832525i	$0.686894\pi$
$620$	−3.26892e9	−0.550850
$621$	−4.89425e9	−0.820097
$622$	1.67512e9	0.279113
$623$	5.97412e9	0.989842
$624$	−2.99317e9	−0.493157
$625$	7.33166e8	0.120122
$626$	8.61508e8	0.140362
$627$	−5.14492e8	−0.0833571
$628$	8.68709e9	1.39964
$629$	−7.83487e9	−1.25532
$630$	−1.56865e9	−0.249939
$631$	−8.30168e9	−1.31542	−0.657708	−	0.753273i	$-0.728474\pi$
$631$	−8.30168e9	−1.31542	−0.657708	+	0.753273i	$0.728474\pi$
$632$	7.66200e8	0.120735
$633$	−8.74537e8	−0.137046
$634$	3.07470e9	0.479170
$635$	4.72565e9	0.732409
$636$	−8.00306e8	−0.123355
$637$	−1.30046e10	−1.99347
$638$	−2.21699e9	−0.337980
$639$	1.11168e9	0.168549
$640$	3.88178e9	0.585330
$641$	−2.74283e9	−0.411335	−0.205668	−	0.978622i	$-0.565937\pi$
$641$	−2.74283e9	−0.411335	−0.205668	+	0.978622i	$0.565937\pi$
$642$	−2.82052e8	−0.0420685
$643$	2.54891e9	0.378108	0.189054	−	0.981967i	$-0.439458\pi$
$643$	2.54891e9	0.378108	0.189054	+	0.981967i	$0.439458\pi$
$644$	7.99457e9	1.17949
$645$	8.36623e8	0.122764
$646$	−9.89962e8	−0.144479
$647$	−4.87618e9	−0.707807	−0.353904	−	0.935282i	$-0.615146\pi$
$647$	−4.87618e9	−0.707807	−0.353904	+	0.935282i	$0.615146\pi$
$648$	1.78440e9	0.257621
$649$	2.98879e9	0.429180
$650$	−3.33966e9	−0.476986
$651$	−5.57564e9	−0.792065
$652$	−3.72942e8	−0.0526957
$653$	−1.09977e10	−1.54563	−0.772814	−	0.634633i	$-0.781151\pi$
$653$	−1.09977e10	−1.54563	−0.772814	+	0.634633i	$0.781151\pi$
$654$	8.10639e8	0.113320
$655$	−2.14499e9	−0.298251
$656$	4.73440e9	0.654789
$657$	4.66661e9	0.641981
$658$	−7.44207e9	−1.01836
$659$	8.93273e9	1.21586	0.607932	−	0.793989i	$-0.291999\pi$
$659$	8.93273e9	1.21586	0.607932	+	0.793989i	$0.291999\pi$
$660$	1.30396e9	0.176547
$661$	1.14134e10	1.53712	0.768562	−	0.639776i	$-0.220973\pi$
$661$	1.14134e10	1.53712	0.768562	+	0.639776i	$0.220973\pi$
$662$	−4.01038e9	−0.537257
$663$	−1.05645e10	−1.40784
$664$	3.75441e9	0.497684
$665$	−1.44646e9	−0.190735
$666$	−1.78982e9	−0.234773
$667$	−8.44332e9	−1.10172
$668$	−7.86225e9	−1.02054
$669$	6.48272e9	0.837078
$670$	2.74145e8	0.0352142
$671$	2.40996e9	0.307951
$672$	5.18862e9	0.659567
$673$	−7.22285e9	−0.913389	−0.456694	−	0.889624i	$-0.650967\pi$
$673$	−7.22285e9	−0.913389	−0.456694	+	0.889624i	$0.650967\pi$
$674$	−2.69605e9	−0.339170
$675$	4.56740e9	0.571618
$676$	−1.56156e10	−1.94422
$677$	−7.14671e9	−0.885209	−0.442604	−	0.896717i	$-0.645945\pi$
$677$	−7.14671e9	−0.885209	−0.442604	+	0.896717i	$0.645945\pi$
$678$	8.75295e7	0.0107858
$679$	2.06483e10	2.53128
$680$	5.47301e9	0.667490
$681$	2.53202e9	0.307222
$682$	2.77158e9	0.334567
$683$	−1.01802e10	−1.22260	−0.611299	−	0.791400i	$-0.709353\pi$
$683$	−1.01802e10	−1.22260	−0.611299	+	0.791400i	$0.709353\pi$
$684$	1.24717e9	0.149015
$685$	3.82660e9	0.454879
$686$	4.69771e8	0.0555587
$687$	−1.30680e9	−0.153766
$688$	2.13258e9	0.249658
$689$	−4.70936e9	−0.548523
$690$	−9.00499e8	−0.104355
$691$	−9.17728e9	−1.05813	−0.529067	−	0.848580i	$-0.677458\pi$
$691$	−9.17728e9	−1.05813	−0.529067	+	0.848580i	$0.677458\pi$
$692$	−3.81106e9	−0.437194
$693$	−7.33466e9	−0.837170
$694$	3.81506e8	0.0433255
$695$	2.47194e9	0.279313
$696$	−3.55474e9	−0.399646
$697$	1.67103e10	1.86926
$698$	2.47019e9	0.274939
$699$	−3.07499e9	−0.340544
$700$	−7.46068e9	−0.822120
$701$	1.00080e10	1.09732	0.548662	−	0.836044i	$-0.315137\pi$
$701$	1.00080e10	1.09732	0.548662	+	0.836044i	$0.315137\pi$
$702$	−5.55860e9	−0.606437
$703$	−1.65040e9	−0.179162
$704$	1.34735e9	0.145538
$705$	−4.62288e9	−0.496879
$706$	−2.43055e9	−0.259949
$707$	1.35551e10	1.44256
$708$	2.19694e9	0.232649
$709$	−8.77235e9	−0.924387	−0.462194	−	0.886779i	$-0.652938\pi$
$709$	−8.77235e9	−0.924387	−0.462194	+	0.886779i	$0.652938\pi$
$710$	4.71102e8	0.0493982
$711$	−1.22731e9	−0.128059
$712$	−4.76159e9	−0.494392
$713$	1.05555e10	1.09060
$714$	4.27952e9	0.439998
$715$	7.67310e9	0.785055
$716$	−5.21484e8	−0.0530940
$717$	−4.18984e9	−0.424503
$718$	5.26504e9	0.530843
$719$	−1.65797e10	−1.66351	−0.831755	−	0.555143i	$-0.812664\pi$
$719$	−1.65797e10	−1.66351	−0.831755	+	0.555143i	$0.812664\pi$
$720$	−2.48382e9	−0.248002
$721$	−1.03375e10	−1.02717
$722$	−2.08533e8	−0.0206203
$723$	1.32721e9	0.130603
$724$	9.33598e9	0.914271
$725$	7.87945e9	0.767915
$726$	8.42938e8	0.0817556
$727$	−1.77157e9	−0.170997	−0.0854983	−	0.996338i	$-0.527248\pi$
$727$	−1.77157e9	−0.170997	−0.0854983	+	0.996338i	$0.527248\pi$
$728$	1.98060e10	1.90255
$729$	1.44317e9	0.137966
$730$	1.97759e9	0.188151
$731$	7.52704e9	0.712711
$732$	1.77147e9	0.166934
$733$	6.86124e9	0.643485	0.321743	−	0.946827i	$-0.395731\pi$
$733$	6.86124e9	0.643485	0.321743	+	0.946827i	$0.395731\pi$
$734$	2.69597e9	0.251639
$735$	3.27236e9	0.303987
$736$	−9.82278e9	−0.908160
$737$	1.28184e9	0.117950
$738$	3.81734e9	0.349594
$739$	1.14322e9	0.104201	0.0521007	−	0.998642i	$-0.483408\pi$
$739$	1.14322e9	0.104201	0.0521007	+	0.998642i	$0.483408\pi$
$740$	4.18288e9	0.379458
$741$	−2.22540e9	−0.200930
$742$	1.90768e9	0.171432
$743$	1.00401e10	0.897998	0.448999	−	0.893532i	$-0.351781\pi$
$743$	1.00401e10	0.897998	0.448999	+	0.893532i	$0.351781\pi$
$744$	4.44398e9	0.395610
$745$	−3.39618e9	−0.300915
$746$	−3.78173e9	−0.333507
$747$	−6.01388e9	−0.527877
$748$	1.17317e10	1.02495
$749$	−3.70775e9	−0.322422
$750$	2.09366e9	0.181214
$751$	−1.22278e10	−1.05343	−0.526717	−	0.850041i	$-0.676577\pi$
$751$	−1.22278e10	−1.05343	−0.526717	+	0.850041i	$0.676577\pi$
$752$	−1.17839e10	−1.01047
$753$	2.79226e9	0.238327
$754$	−9.58943e9	−0.814691
$755$	−7.03145e9	−0.594608
$756$	−1.24177e10	−1.04524
$757$	2.08572e10	1.74751	0.873757	−	0.486363i	$-0.161677\pi$
$757$	2.08572e10	1.74751	0.873757	+	0.486363i	$0.161677\pi$
$758$	2.09829e8	0.0174994
$759$	−4.21054e9	−0.349536
$760$	1.15288e9	0.0952654
$761$	1.14115e10	0.938638	0.469319	−	0.883029i	$-0.344499\pi$
$761$	1.14115e10	0.938638	0.469319	+	0.883029i	$0.344499\pi$
$762$	−2.94515e9	−0.241138
$763$	1.06564e10	0.868506
$764$	−1.71340e10	−1.39005
$765$	−8.76676e9	−0.707985
$766$	4.57822e9	0.368041
$767$	1.29278e10	1.03452
$768$	−1.24926e9	−0.0995151
$769$	7.61292e9	0.603683	0.301842	−	0.953358i	$-0.402399\pi$
$769$	7.61292e9	0.603683	0.301842	+	0.953358i	$0.402399\pi$
$770$	−3.10824e9	−0.245357
$771$	−3.45317e9	−0.271348
$772$	−1.43769e10	−1.12462
$773$	−5.38833e9	−0.419591	−0.209795	−	0.977745i	$-0.567280\pi$
$773$	−5.38833e9	−0.419591	−0.209795	+	0.977745i	$0.567280\pi$
$774$	1.71950e9	0.133293
$775$	−9.85055e9	−0.760159
$776$	−1.64574e10	−1.26429
$777$	7.13453e9	0.545622
$778$	1.58989e9	0.121043
$779$	3.51999e9	0.266784
$780$	5.64019e9	0.425562
$781$	2.20278e9	0.165459
$782$	−8.10173e9	−0.605835
$783$	1.31147e10	0.976321
$784$	8.34134e9	0.618201
$785$	−1.28630e10	−0.949073
$786$	1.33682e9	0.0981960
$787$	−1.99352e10	−1.45784	−0.728918	−	0.684601i	$-0.759976\pi$
$787$	−1.99352e10	−1.45784	−0.728918	+	0.684601i	$0.759976\pi$
$788$	−1.89543e10	−1.37996
$789$	−4.62598e9	−0.335301
$790$	−5.20104e8	−0.0375314
$791$	1.15063e9	0.0826644
$792$	5.84599e9	0.418138
$793$	1.04241e10	0.742305
$794$	3.62067e9	0.256695
$795$	1.18502e9	0.0836451
$796$	1.48617e10	1.04441
$797$	1.30384e10	0.912267	0.456133	−	0.889911i	$-0.349234\pi$
$797$	1.30384e10	0.912267	0.456133	+	0.889911i	$0.349234\pi$
$798$	9.01471e8	0.0627974
$799$	−4.15918e10	−2.88465
$800$	9.16680e9	0.632998
$801$	7.62719e9	0.524386
$802$	1.42774e9	0.0977327
$803$	9.24679e9	0.630212
$804$	9.42231e8	0.0639384
$805$	−1.18376e10	−0.799796
$806$	1.19883e10	0.806463
$807$	−4.50498e9	−0.301742
$808$	−1.08039e10	−0.720509
$809$	1.58704e10	1.05382	0.526911	−	0.849920i	$-0.323350\pi$
$809$	1.58704e10	1.05382	0.526911	+	0.849920i	$0.323350\pi$
$810$	−1.21127e9	−0.0800836
$811$	−2.52643e10	−1.66316	−0.831580	−	0.555404i	$-0.812563\pi$
$811$	−2.52643e10	−1.66316	−0.831580	+	0.555404i	$0.812563\pi$
$812$	−2.14224e10	−1.40418
$813$	−9.58048e7	−0.00625274
$814$	−3.54649e9	−0.230469
$815$	5.52218e8	0.0357321
$816$	6.77625e9	0.436590
$817$	1.58556e9	0.101720
$818$	−3.55057e7	−0.00226810
$819$	−3.17255e10	−2.01797
$820$	−8.92129e9	−0.565040
$821$	5.58873e9	0.352462	0.176231	−	0.984349i	$-0.443609\pi$
$821$	5.58873e9	0.352462	0.176231	+	0.984349i	$0.443609\pi$
$822$	−2.38484e9	−0.149764
$823$	1.65947e10	1.03770	0.518849	−	0.854866i	$-0.326361\pi$
$823$	1.65947e10	1.03770	0.518849	+	0.854866i	$0.326361\pi$
$824$	8.23933e9	0.513035
$825$	3.92935e9	0.243631
$826$	−5.23683e9	−0.323324
$827$	1.93796e10	1.19145	0.595725	−	0.803189i	$-0.296865\pi$
$827$	1.93796e10	1.19145	0.595725	+	0.803189i	$0.296865\pi$
$828$	1.02067e10	0.624856
$829$	1.34677e9	0.0821019	0.0410510	−	0.999157i	$-0.486929\pi$
$829$	1.34677e9	0.0821019	0.0410510	+	0.999157i	$0.486929\pi$
$830$	−2.54853e9	−0.154709
$831$	1.47905e9	0.0894083
$832$	5.82786e9	0.350815
$833$	2.94412e10	1.76481
$834$	−1.54058e9	−0.0919609
$835$	1.16417e10	0.692011
$836$	2.47125e9	0.146283
$837$	−1.63954e10	−0.966460
$838$	1.55684e8	0.00913882
$839$	3.70776e9	0.216743	0.108371	−	0.994110i	$-0.465436\pi$
$839$	3.70776e9	0.216743	0.108371	+	0.994110i	$0.465436\pi$
$840$	−4.98379e9	−0.290123
$841$	5.37499e9	0.311596
$842$	−5.50385e8	−0.0317742
$843$	−1.33764e10	−0.769029
$844$	4.20064e9	0.240501
$845$	2.31222e10	1.31835
$846$	−9.50133e9	−0.539496
$847$	1.10809e10	0.626592
$848$	3.02065e9	0.170104
$849$	−2.34445e9	−0.131482
$850$	7.56068e9	0.422274
$851$	−1.35067e10	−0.751268
$852$	1.61917e9	0.0896922
$853$	−2.15592e10	−1.18935	−0.594677	−	0.803965i	$-0.702720\pi$
$853$	−2.15592e10	−1.18935	−0.594677	+	0.803965i	$0.702720\pi$
$854$	−4.22263e9	−0.231996
$855$	−1.84670e9	−0.101045
$856$	2.95521e9	0.161039
$857$	3.01352e10	1.63547	0.817733	−	0.575598i	$-0.195231\pi$
$857$	3.01352e10	1.63547	0.817733	+	0.575598i	$0.195231\pi$
$858$	−4.78209e9	−0.258471
$859$	−1.61177e10	−0.867615	−0.433808	−	0.901005i	$-0.642830\pi$
$859$	−1.61177e10	−0.867615	−0.433808	+	0.901005i	$0.642830\pi$
$860$	−4.01853e9	−0.215438
$861$	−1.52166e10	−0.812469
$862$	1.20473e10	0.640642
$863$	1.31758e10	0.697815	0.348908	−	0.937157i	$-0.386553\pi$
$863$	1.31758e10	0.697815	0.348908	+	0.937157i	$0.386553\pi$
$864$	1.52574e10	0.804789
$865$	5.64306e9	0.296455
$866$	2.32903e9	0.121860
$867$	1.46607e10	0.763989
$868$	2.67813e10	1.39000
$869$	−2.43190e9	−0.125712
$870$	2.41299e9	0.124233
$871$	5.54451e9	0.284315
$872$	−8.49349e9	−0.433789
$873$	2.63618e10	1.34099
$874$	−1.70661e9	−0.0864659
$875$	2.75224e10	1.38886
$876$	6.79695e9	0.341625
$877$	−1.36323e10	−0.682451	−0.341226	−	0.939981i	$-0.610842\pi$
$877$	−1.36323e10	−0.682451	−0.341226	+	0.939981i	$0.610842\pi$
$878$	−4.12050e9	−0.205456
$879$	5.85258e9	0.290661
$880$	−4.92164e9	−0.243456
$881$	−3.62854e10	−1.78779	−0.893894	−	0.448278i	$-0.852037\pi$
$881$	−3.62854e10	−1.78779	−0.893894	+	0.448278i	$0.852037\pi$
$882$	6.72562e9	0.330060
$883$	1.98699e9	0.0971257	0.0485628	−	0.998820i	$-0.484536\pi$
$883$	1.98699e9	0.0971257	0.0485628	+	0.998820i	$0.484536\pi$
$884$	5.07444e10	2.47062
$885$	−3.25303e9	−0.157756
$886$	1.50644e10	0.727667
$887$	−3.00798e10	−1.44724	−0.723622	−	0.690196i	$-0.757524\pi$
$887$	−3.00798e10	−1.44724	−0.723622	+	0.690196i	$0.757524\pi$
$888$	−5.68647e9	−0.272520
$889$	−3.87159e10	−1.84813
$890$	3.23221e9	0.153686
$891$	−5.66365e9	−0.268240
$892$	−3.11383e10	−1.46899
$893$	−8.76122e9	−0.411703
$894$	2.11659e9	0.0990732
$895$	7.72166e8	0.0360023
$896$	−3.18023e10	−1.47700
$897$	−1.82124e10	−0.842546
$898$	−1.13399e10	−0.522568
$899$	−2.82846e10	−1.29835
$900$	−9.52509e9	−0.435532
$901$	1.06615e10	0.485605
$902$	7.56400e9	0.343185
$903$	−6.85422e9	−0.309778
$904$	−9.17094e8	−0.0412880
$905$	−1.38238e10	−0.619953
$906$	4.38219e9	0.195768
$907$	−2.74545e9	−0.122177	−0.0610884	−	0.998132i	$-0.519457\pi$
$907$	−2.74545e9	−0.122177	−0.0610884	+	0.998132i	$0.519457\pi$
$908$	−1.21620e10	−0.539144
$909$	1.73058e10	0.764220
$910$	−1.34445e10	−0.591424
$911$	−2.05384e10	−0.900021	−0.450011	−	0.893023i	$-0.648580\pi$
$911$	−2.05384e10	−0.900021	−0.450011	+	0.893023i	$0.648580\pi$
$912$	1.42740e9	0.0623109
$913$	−1.19164e10	−0.518200
$914$	1.58732e10	0.687628
$915$	−2.62302e9	−0.113195
$916$	6.27693e9	0.269844
$917$	1.75733e10	0.752595
$918$	1.25841e10	0.536876
$919$	1.78785e10	0.759850	0.379925	−	0.925017i	$-0.375950\pi$
$919$	1.78785e10	0.759850	0.379925	+	0.925017i	$0.375950\pi$
$920$	9.43501e9	0.399471
$921$	2.69365e9	0.113614
$922$	2.76542e9	0.116199
$923$	9.52794e9	0.398835
$924$	−1.06830e10	−0.445493
$925$	1.26047e10	0.523643
$926$	−1.06695e10	−0.441575
$927$	−1.31979e10	−0.544159
$928$	2.63213e10	1.08116
$929$	−4.07379e10	−1.66703	−0.833515	−	0.552498i	$-0.813675\pi$
$929$	−4.07379e10	−1.66703	−0.833515	+	0.552498i	$0.813675\pi$
$930$	−3.01662e9	−0.122979
$931$	6.20172e9	0.251877
$932$	1.47700e10	0.597621
$933$	−8.52498e9	−0.343643
$934$	−1.13828e10	−0.457125
$935$	−1.73712e10	−0.695006
$936$	2.52864e10	1.00791
$937$	1.59909e10	0.635017	0.317508	−	0.948256i	$-0.397154\pi$
$937$	1.59909e10	0.635017	0.317508	+	0.948256i	$0.397154\pi$
$938$	−2.24599e9	−0.0888582
$939$	−4.38436e9	−0.172813
$940$	2.22050e10	0.871973
$941$	−3.18651e10	−1.24667	−0.623336	−	0.781954i	$-0.714223\pi$
$941$	−3.18651e10	−1.24667	−0.623336	+	0.781954i	$0.714223\pi$
$942$	8.01660e9	0.312473
$943$	2.88072e10	1.11869
$944$	−8.29207e9	−0.320820
$945$	1.83870e10	0.708759
$946$	3.40715e9	0.130850
$947$	−3.53401e10	−1.35221	−0.676103	−	0.736807i	$-0.736332\pi$
$947$	−3.53401e10	−1.35221	−0.676103	+	0.736807i	$0.736332\pi$
$948$	−1.78759e9	−0.0681457
$949$	3.99963e10	1.51911
$950$	1.59264e9	0.0602678
$951$	−1.56477e10	−0.589953
$952$	−4.48388e10	−1.68432
$953$	−2.13192e10	−0.797895	−0.398948	−	0.916974i	$-0.630625\pi$
$953$	−2.13192e10	−0.797895	−0.398948	+	0.916974i	$0.630625\pi$
$954$	2.43555e9	0.0908192
$955$	2.53704e10	0.942574
$956$	2.01250e10	0.744960
$957$	1.12826e10	0.416121
$958$	4.52662e7	0.00166339
$959$	−3.13502e10	−1.14782
$960$	−1.46647e9	−0.0534963
$961$	7.84757e9	0.285235
$962$	−1.53401e10	−0.555539
$963$	−4.73371e9	−0.170808
$964$	−6.37494e9	−0.229196
$965$	2.12880e10	0.762589
$966$	7.37753e9	0.263324
$967$	1.12438e10	0.399870	0.199935	−	0.979809i	$-0.435927\pi$
$967$	1.12438e10	0.399870	0.199935	+	0.979809i	$0.435927\pi$
$968$	−8.83191e9	−0.312961
$969$	5.03809e9	0.177882
$970$	1.11715e10	0.393015
$971$	3.46845e10	1.21582	0.607908	−	0.794008i	$-0.292009\pi$
$971$	3.46845e10	1.21582	0.607908	+	0.794008i	$0.292009\pi$
$972$	−2.48242e10	−0.867049
$973$	−2.02519e10	−0.704808
$974$	5.41624e9	0.187820
$975$	1.69961e10	0.587265
$976$	−6.68616e9	−0.230199
$977$	−5.08454e8	−0.0174430	−0.00872150	−	0.999962i	$-0.502776\pi$
$977$	−5.08454e8	−0.0174430	−0.00872150	+	0.999962i	$0.502776\pi$
$978$	−3.44158e8	−0.0117644
$979$	1.51131e10	0.514772
$980$	−1.57180e10	−0.533467
$981$	1.36050e10	0.460106
$982$	−1.99752e10	−0.673132
$983$	1.80355e10	0.605608	0.302804	−	0.953053i	$-0.402077\pi$
$983$	1.80355e10	0.605608	0.302804	+	0.953053i	$0.402077\pi$
$984$	1.21282e10	0.405801
$985$	2.80658e10	0.935731
$986$	2.17095e10	0.721243
$987$	3.78740e10	1.25381
$988$	1.06892e10	0.352611
$989$	1.29760e10	0.426534
$990$	−3.96831e9	−0.129982
$991$	1.39065e10	0.453901	0.226951	−	0.973906i	$-0.427124\pi$
$991$	1.39065e10	0.453901	0.226951	+	0.973906i	$0.427124\pi$
$992$	−3.29057e10	−1.07024
$993$	2.04095e10	0.661470
$994$	−3.85961e9	−0.124650
$995$	−2.20058e10	−0.708202
$996$	−8.75927e9	−0.280906
$997$	8.68078e8	0.0277412	0.0138706	−	0.999904i	$-0.495585\pi$
$997$	8.68078e8	0.0277412	0.0138706	+	0.999904i	$0.495585\pi$
$998$	4.78489e9	0.152375
$999$	2.09794e10	0.665755

Twists

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

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

\(f(q)\)	\(=\)	\(q-4.43255 q^{2} +22.5580 q^{3} -108.352 q^{4} +160.438 q^{5} -99.9896 q^{6} -1314.43 q^{7} +1047.64 q^{8} -1678.14 q^{9} +O(q^{10})\)	\(q-4.43255 q^{2} +22.5580 q^{3} -108.352 q^{4} +160.438 q^{5} -99.9896 q^{6} -1314.43 q^{7} +1047.64 q^{8} -1678.14 q^{9} -711.151 q^{10} -3325.19 q^{11} -2444.22 q^{12} -14382.9 q^{13} +5826.26 q^{14} +3619.17 q^{15} +9225.38 q^{16} +32561.5 q^{17} +7438.42 q^{18} +6859.00 q^{19} -17383.9 q^{20} -29650.9 q^{21} +14739.1 q^{22} +56133.3 q^{23} +23632.8 q^{24} -52384.5 q^{25} +63752.8 q^{26} -87189.8 q^{27} +142421. q^{28} -150416. q^{29} -16042.2 q^{30} +188043. q^{31} -174990. q^{32} -75009.8 q^{33} -144330. q^{34} -210884. q^{35} +181830. q^{36} -240618. q^{37} -30402.9 q^{38} -324449. q^{39} +168082. q^{40} +513193. q^{41} +131429. q^{42} +231164. q^{43} +360293. q^{44} -269237. q^{45} -248814. q^{46} -1.27733e6 q^{47} +208106. q^{48} +904173. q^{49} +232197. q^{50} +734522. q^{51} +1.55842e6 q^{52} +327428. q^{53} +386473. q^{54} -533489. q^{55} -1.37705e6 q^{56} +154725. q^{57} +666725. q^{58} -898832. q^{59} -392146. q^{60} -724758. q^{61} -833510. q^{62} +2.20579e6 q^{63} -405194. q^{64} -2.30757e6 q^{65} +332485. q^{66} -385494. q^{67} -3.52811e6 q^{68} +1.26626e6 q^{69} +934756. q^{70} -662450. q^{71} -1.75809e6 q^{72} -2.78083e6 q^{73} +1.06655e6 q^{74} -1.18169e6 q^{75} -743190. q^{76} +4.37072e6 q^{77} +1.43814e6 q^{78} +731355. q^{79} +1.48010e6 q^{80} +1.70325e6 q^{81} -2.27475e6 q^{82} +3.58367e6 q^{83} +3.21274e6 q^{84} +5.22411e6 q^{85} -1.02465e6 q^{86} -3.39308e6 q^{87} -3.48362e6 q^{88} -4.54504e6 q^{89} +1.19341e6 q^{90} +1.89052e7 q^{91} -6.08218e6 q^{92} +4.24188e6 q^{93} +5.66184e6 q^{94} +1.10045e6 q^{95} -3.94744e6 q^{96} -1.57090e7 q^{97} -4.00779e6 q^{98} +5.58013e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 9 q^{2} - 14 q^{3} + 37 q^{4} - 222 q^{5} - 603 q^{6} - 1246 q^{7} - 3555 q^{8} - 4898 q^{9}+O(q^{10}) \) 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

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