LMFDB - Embedded newform 19.8.a.b.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:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 540x^{4} + 610x^{3} + 80412x^{2} + 7680x - 2267712 $ x^6 - 3x^5 - 540x^4 + 610x^3 + 80412x^2 + 7680*x - 2267712
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			$-6.37480$ 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)

$f(q)$	$=$	$q-4.37480 q^{2} -63.9788 q^{3} -108.861 q^{4} +301.974 q^{5} +279.894 q^{6} +615.044 q^{7} +1036.22 q^{8} +1906.28 q^{9} +O(q^{10})$	\(q-4.37480 q^{2} -63.9788 q^{3} -108.861 q^{4} +301.974 q^{5} +279.894 q^{6} +615.044 q^{7} +1036.22 q^{8} +1906.28 q^{9} -1321.08 q^{10} -3516.90 q^{11} +6964.80 q^{12} +13653.1 q^{13} -2690.69 q^{14} -19319.9 q^{15} +9400.98 q^{16} +1625.53 q^{17} -8339.59 q^{18} -6859.00 q^{19} -32873.3 q^{20} -39349.8 q^{21} +15385.7 q^{22} +39958.3 q^{23} -66296.0 q^{24} +13063.5 q^{25} -59729.7 q^{26} +17960.0 q^{27} -66954.4 q^{28} +186991. q^{29} +84520.8 q^{30} +150652. q^{31} -173763. q^{32} +225007. q^{33} -7111.37 q^{34} +185727. q^{35} -207520. q^{36} -18057.4 q^{37} +30006.7 q^{38} -873511. q^{39} +312911. q^{40} +785775. q^{41} +172147. q^{42} -811509. q^{43} +382854. q^{44} +575648. q^{45} -174809. q^{46} +531124. q^{47} -601463. q^{48} -445264. q^{49} -57149.9 q^{50} -103999. q^{51} -1.48630e6 q^{52} -1.23725e6 q^{53} -78571.3 q^{54} -1.06201e6 q^{55} +637320. q^{56} +438830. q^{57} -818049. q^{58} -889223. q^{59} +2.10319e6 q^{60} +3.29342e6 q^{61} -659071. q^{62} +1.17245e6 q^{63} -443147. q^{64} +4.12290e6 q^{65} -984358. q^{66} +3.19028e6 q^{67} -176957. q^{68} -2.55648e6 q^{69} -812519. q^{70} -807613. q^{71} +1.97533e6 q^{72} -1.93161e6 q^{73} +78997.3 q^{74} -835783. q^{75} +746679. q^{76} -2.16305e6 q^{77} +3.82143e6 q^{78} -4.99581e6 q^{79} +2.83885e6 q^{80} -5.31810e6 q^{81} -3.43761e6 q^{82} +2.25877e6 q^{83} +4.28366e6 q^{84} +490869. q^{85} +3.55018e6 q^{86} -1.19635e7 q^{87} -3.64428e6 q^{88} +7.83465e6 q^{89} -2.51834e6 q^{90} +8.39728e6 q^{91} -4.34990e6 q^{92} -9.63851e6 q^{93} -2.32356e6 q^{94} -2.07124e6 q^{95} +1.11172e7 q^{96} -8.08479e6 q^{97} +1.94794e6 q^{98} -6.70420e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 15 q^{2} + 40 q^{3} + 357 q^{4} + 219 q^{5} + 925 q^{6} + 2105 q^{7} + 5835 q^{8} + 5916 q^{9}+O(q^{10}) $ 6 * q + 15 * q^2 + 40 * q^3 + 357 * q^4 + 219 * q^5 + 925 * q^6 + 2105 * q^7 + 5835 * q^8 + 5916 * q^9	\( 6 q + 15 q^{2} + 40 q^{3} + 357 q^{4} + 219 q^{5} + 925 q^{6} + 2105 q^{7} + 5835 q^{8} + 5916 q^{9} + 8212 q^{10} + 7257 q^{11} + 7025 q^{12} + 6850 q^{13} + 8859 q^{14} + 3650 q^{15} - 9159 q^{16} + 5415 q^{17} - 58980 q^{18} - 41154 q^{19} - 67620 q^{20} - 83290 q^{21} - 223870 q^{22} - 720 q^{23} - 151113 q^{24} - 53567 q^{25} - 106527 q^{26} + 199450 q^{27} + 91615 q^{28} + 381624 q^{29} - 137776 q^{30} + 264080 q^{31} + 259155 q^{32} + 496430 q^{33} + 297463 q^{34} + 739767 q^{35} - 147282 q^{36} + 1082300 q^{37} - 102885 q^{38} + 1129528 q^{39} - 524232 q^{40} + 485232 q^{41} - 1753105 q^{42} + 198705 q^{43} - 1729290 q^{44} - 478705 q^{45} - 1565713 q^{46} - 247125 q^{47} - 2937955 q^{48} - 538861 q^{49} - 2396859 q^{50} - 72176 q^{51} - 2647795 q^{52} + 3226770 q^{53} - 1217249 q^{54} - 1490553 q^{55} + 3718965 q^{56} - 274360 q^{57} + 1048405 q^{58} + 2305380 q^{59} + 647440 q^{60} + 585731 q^{61} + 2583780 q^{62} - 3209015 q^{63} + 2380137 q^{64} + 4809420 q^{65} + 2420402 q^{66} - 3264030 q^{67} + 8276595 q^{68} - 1867056 q^{69} + 5936880 q^{70} + 6833682 q^{71} + 3040530 q^{72} - 4160625 q^{73} + 20750550 q^{74} - 11237814 q^{75} - 2448663 q^{76} + 1659195 q^{77} - 1839095 q^{78} - 8680576 q^{79} + 14904048 q^{80} - 16541142 q^{81} - 9240140 q^{82} - 3785040 q^{83} - 18290321 q^{84} - 16108227 q^{85} + 11192544 q^{86} - 25742220 q^{87} - 24666570 q^{88} + 12473466 q^{89} - 4688908 q^{90} - 14289854 q^{91} + 9179655 q^{92} + 5742820 q^{93} - 10757712 q^{94} - 1502121 q^{95} - 8195689 q^{96} + 882830 q^{97} + 47239200 q^{98} + 10726225 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 + 40 * q^3 + 357 * q^4 + 219 * q^5 + 925 * q^6 + 2105 * q^7 + 5835 * q^8 + 5916 * q^9 + 8212 * q^10 + 7257 * q^11 + 7025 * q^12 + 6850 * q^13 + 8859 * q^14 + 3650 * q^15 - 9159 * q^16 + 5415 * q^17 - 58980 * q^18 - 41154 * q^19 - 67620 * q^20 - 83290 * q^21 - 223870 * q^22 - 720 * q^23 - 151113 * q^24 - 53567 * q^25 - 106527 * q^26 + 199450 * q^27 + 91615 * q^28 + 381624 * q^29 - 137776 * q^30 + 264080 * q^31 + 259155 * q^32 + 496430 * q^33 + 297463 * q^34 + 739767 * q^35 - 147282 * q^36 + 1082300 * q^37 - 102885 * q^38 + 1129528 * q^39 - 524232 * q^40 + 485232 * q^41 - 1753105 * q^42 + 198705 * q^43 - 1729290 * q^44 - 478705 * q^45 - 1565713 * q^46 - 247125 * q^47 - 2937955 * q^48 - 538861 * q^49 - 2396859 * q^50 - 72176 * q^51 - 2647795 * q^52 + 3226770 * q^53 - 1217249 * q^54 - 1490553 * q^55 + 3718965 * q^56 - 274360 * q^57 + 1048405 * q^58 + 2305380 * q^59 + 647440 * q^60 + 585731 * q^61 + 2583780 * q^62 - 3209015 * q^63 + 2380137 * q^64 + 4809420 * q^65 + 2420402 * q^66 - 3264030 * q^67 + 8276595 * q^68 - 1867056 * q^69 + 5936880 * q^70 + 6833682 * q^71 + 3040530 * q^72 - 4160625 * q^73 + 20750550 * q^74 - 11237814 * q^75 - 2448663 * q^76 + 1659195 * q^77 - 1839095 * q^78 - 8680576 * q^79 + 14904048 * q^80 - 16541142 * q^81 - 9240140 * q^82 - 3785040 * q^83 - 18290321 * q^84 - 16108227 * q^85 + 11192544 * q^86 - 25742220 * q^87 - 24666570 * q^88 + 12473466 * q^89 - 4688908 * q^90 - 14289854 * q^91 + 9179655 * q^92 + 5742820 * q^93 - 10757712 * q^94 - 1502121 * q^95 - 8195689 * q^96 + 882830 * q^97 + 47239200 * q^98 + 10726225 * 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 $

$2$	−4.37480	−0.386681	−0.193340	−	0.981132i	$-0.561932\pi$
$2$	−4.37480	−0.386681	−0.193340	+	0.981132i	$0.561932\pi$
$3$	−63.9788	−1.36808	−0.684040	−	0.729445i	$-0.739779\pi$
$3$	−63.9788	−1.36808	−0.684040	+	0.729445i	$0.739779\pi$
$4$	−108.861	−0.850478
$5$	301.974	1.08038	0.540188	−	0.841544i	$-0.318353\pi$
$5$	301.974	1.08038	0.540188	+	0.841544i	$0.318353\pi$
$6$	279.894	0.529010
$7$	615.044	0.677740	0.338870	−	0.940833i	$-0.389955\pi$
$7$	615.044	0.677740	0.338870	+	0.940833i	$0.389955\pi$
$8$	1036.22	0.715544
$9$	1906.28	0.871642
$10$	−1321.08	−0.417761
$11$	−3516.90	−0.796683	−0.398341	−	0.917237i	$-0.630414\pi$
$11$	−3516.90	−0.796683	−0.398341	+	0.917237i	$0.630414\pi$
$12$	6964.80	1.16352
$13$	13653.1	1.72358	0.861789	−	0.507267i	$-0.169344\pi$
$13$	13653.1	1.72358	0.861789	+	0.507267i	$0.169344\pi$
$14$	−2690.69	−0.262069
$15$	−19319.9	−1.47804
$16$	9400.98	0.573790
$17$	1625.53	0.0802461	0.0401231	−	0.999195i	$-0.487225\pi$
$17$	1625.53	0.0802461	0.0401231	+	0.999195i	$0.487225\pi$
$18$	−8339.59	−0.337047
$19$	−6859.00	−0.229416
$19$	−6859.00	−0.229416
$20$	−32873.3	−0.918836
$21$	−39349.8	−0.927202
$22$	15385.7	0.308062
$23$	39958.3	0.684793	0.342396	−	0.939556i	$-0.388761\pi$
$23$	39958.3	0.684793	0.342396	+	0.939556i	$0.388761\pi$
$24$	−66296.0	−0.978922
$25$	13063.5	0.167212
$26$	−59729.7	−0.666475
$27$	17960.0	0.175603
$28$	−66954.4	−0.576403
$29$	186991.	1.42373	0.711867	−	0.702315i	$-0.247850\pi$
$29$	186991.	1.42373	0.711867	+	0.702315i	$0.247850\pi$
$30$	84520.8	0.571530
$31$	150652.	0.908256	0.454128	−	0.890936i	$-0.349951\pi$
$31$	150652.	0.908256	0.454128	+	0.890936i	$0.349951\pi$
$32$	−173763.	−0.937418
$33$	225007.	1.08993
$34$	−7111.37	−0.0310297
$35$	185727.	0.732214
$36$	−207520.	−0.741313
$37$	−18057.4	−0.0586069	−0.0293034	−	0.999571i	$-0.509329\pi$
$37$	−18057.4	−0.0586069	−0.0293034	+	0.999571i	$0.509329\pi$
$38$	30006.7	0.0887107
$39$	−873511.	−2.35799
$40$	312911.	0.773057
$41$	785775.	1.78055	0.890276	−	0.455421i	$-0.150511\pi$
$41$	785775.	1.78055	0.890276	+	0.455421i	$0.150511\pi$
$42$	172147.	0.358531
$43$	−811509.	−1.55652	−0.778258	−	0.627945i	$-0.783896\pi$
$43$	−811509.	−1.55652	−0.778258	+	0.627945i	$0.783896\pi$
$44$	382854.	0.677561
$45$	575648.	0.941702
$46$	−174809.	−0.264796
$47$	531124.	0.746197	0.373098	−	0.927792i	$-0.378295\pi$
$47$	531124.	0.746197	0.373098	+	0.927792i	$0.378295\pi$
$48$	−601463.	−0.784991
$49$	−445264.	−0.540669
$50$	−57149.9	−0.0646578
$51$	−103999.	−0.109783
$52$	−1.48630e6	−1.46586
$53$	−1.23725e6	−1.14154	−0.570772	−	0.821109i	$-0.693356\pi$
$53$	−1.23725e6	−1.14154	−0.570772	+	0.821109i	$0.693356\pi$
$54$	−78571.3	−0.0679025
$55$	−1.06201e6	−0.860717
$56$	637320.	0.484953
$57$	438830.	0.313859
$58$	−818049.	−0.550530
$59$	−889223.	−0.563675	−0.281837	−	0.959462i	$-0.590944\pi$
$59$	−889223.	−0.563675	−0.281837	+	0.959462i	$0.590944\pi$
$60$	2.10319e6	1.25704
$61$	3.29342e6	1.85778	0.928888	−	0.370362i	$-0.120766\pi$
$61$	3.29342e6	1.85778	0.928888	+	0.370362i	$0.120766\pi$
$62$	−659071.	−0.351205
$63$	1.17245e6	0.590747
$64$	−443147.	−0.211309
$65$	4.12290e6	1.86211
$66$	−984358.	−0.421453
$67$	3.19028e6	1.29588	0.647942	−	0.761689i	$-0.275630\pi$
$67$	3.19028e6	1.29588	0.647942	+	0.761689i	$0.275630\pi$
$68$	−176957.	−0.0682476
$69$	−2.55648e6	−0.936851
$70$	−812519.	−0.283133
$71$	−807613.	−0.267793	−0.133896	−	0.990995i	$-0.542749\pi$
$71$	−807613.	−0.267793	−0.133896	+	0.990995i	$0.542749\pi$
$72$	1.97533e6	0.623699
$73$	−1.93161e6	−0.581150	−0.290575	−	0.956852i	$-0.593847\pi$
$73$	−1.93161e6	−0.581150	−0.290575	+	0.956852i	$0.593847\pi$
$74$	78997.3	0.0226622
$75$	−835783.	−0.228760
$76$	746679.	0.195113
$77$	−2.16305e6	−0.539944
$78$	3.82143e6	0.911791
$79$	−4.99581e6	−1.14002	−0.570008	−	0.821639i	$-0.693060\pi$
$79$	−4.99581e6	−1.14002	−0.570008	+	0.821639i	$0.693060\pi$
$80$	2.83885e6	0.619909
$81$	−5.31810e6	−1.11188
$82$	−3.43761e6	−0.688506
$83$	2.25877e6	0.433609	0.216805	−	0.976215i	$-0.430437\pi$
$83$	2.25877e6	0.433609	0.216805	+	0.976215i	$0.430437\pi$
$84$	4.28366e6	0.788565
$85$	490869.	0.0866960
$86$	3.55018e6	0.601875
$87$	−1.19635e7	−1.94778
$88$	−3.64428e6	−0.570062
$89$	7.83465e6	1.17803	0.589013	−	0.808124i	$-0.299517\pi$
$89$	7.83465e6	1.17803	0.589013	+	0.808124i	$0.299517\pi$
$90$	−2.51834e6	−0.364138
$91$	8.39728e6	1.16814
$92$	−4.34990e6	−0.582401
$93$	−9.63851e6	−1.24257
$94$	−2.32356e6	−0.288540
$95$	−2.07124e6	−0.247855
$96$	1.11172e7	1.28246
$97$	−8.08479e6	−0.899431	−0.449715	−	0.893172i	$-0.648475\pi$
$97$	−8.08479e6	−0.899431	−0.449715	+	0.893172i	$0.648475\pi$
$98$	1.94794e6	0.209066
$99$	−6.70420e6	−0.694422
$100$	−1.42210e6	−0.142210
$101$	1.17628e7	1.13602	0.568008	−	0.823023i	$-0.307714\pi$
$101$	1.17628e7	1.13602	0.568008	+	0.823023i	$0.307714\pi$
$102$	454976.	0.0424510
$103$	−5.86737e6	−0.529070	−0.264535	−	0.964376i	$-0.585218\pi$
$103$	−5.86737e6	−0.529070	−0.264535	+	0.964376i	$0.585218\pi$
$104$	1.41476e7	1.23330
$105$	−1.18826e7	−1.00173
$106$	5.41273e6	0.441413
$107$	7.05282e6	0.556570	0.278285	−	0.960499i	$-0.410234\pi$
$107$	7.05282e6	0.556570	0.278285	+	0.960499i	$0.410234\pi$
$108$	−1.95515e6	−0.149347
$109$	1.18752e7	0.878312	0.439156	−	0.898411i	$-0.355277\pi$
$109$	1.18752e7	0.878312	0.439156	+	0.898411i	$0.355277\pi$
$110$	4.64609e6	0.332823
$111$	1.15529e6	0.0801789
$112$	5.78202e6	0.388881
$113$	1.76426e7	1.15024	0.575121	−	0.818069i	$-0.304955\pi$
$113$	1.76426e7	1.15024	0.575121	+	0.818069i	$0.304955\pi$
$114$	−1.91979e6	−0.121363
$115$	1.20664e7	0.739834
$116$	−2.03561e7	−1.21085
$117$	2.60267e7	1.50234
$118$	3.89017e6	0.217962
$119$	999773.	0.0543860
$120$	−2.00197e7	−1.05760
$121$	−7.11860e6	−0.365297
$122$	−1.44081e7	−0.718366
$123$	−5.02729e7	−2.43594
$124$	−1.64001e7	−0.772452
$125$	−1.96469e7	−0.899724
$126$	−5.12922e6	−0.228431
$127$	1.54075e7	0.667450	0.333725	−	0.942670i	$-0.391694\pi$
$127$	1.54075e7	0.667450	0.333725	+	0.942670i	$0.391694\pi$
$128$	2.41804e7	1.01913
$129$	5.19193e7	2.12944
$130$	−1.80368e7	−0.720043
$131$	4.27367e7	1.66093	0.830465	−	0.557071i	$-0.188075\pi$
$131$	4.27367e7	1.66093	0.830465	+	0.557071i	$0.188075\pi$
$132$	−2.44945e7	−0.926957
$133$	−4.21859e6	−0.155484
$134$	−1.39568e7	−0.501094
$135$	5.42345e6	0.189718
$136$	1.68441e6	0.0574197
$137$	−6.09460e6	−0.202499	−0.101250	−	0.994861i	$-0.532284\pi$
$137$	−6.09460e6	−0.202499	−0.101250	+	0.994861i	$0.532284\pi$
$138$	1.11841e7	0.362262
$139$	−3.50602e7	−1.10729	−0.553647	−	0.832752i	$-0.686764\pi$
$139$	−3.50602e7	−1.10729	−0.553647	+	0.832752i	$0.686764\pi$
$140$	−2.02185e7	−0.622732
$141$	−3.39807e7	−1.02086
$142$	3.53314e6	0.103550
$143$	−4.80167e7	−1.37314
$144$	1.79209e7	0.500140
$145$	5.64666e7	1.53817
$146$	8.45038e6	0.224720
$147$	2.84874e7	0.739678
$148$	1.96575e6	0.0498439
$149$	−3.41058e7	−0.844650	−0.422325	−	0.906444i	$-0.638786\pi$
$149$	−3.41058e7	−0.844650	−0.422325	+	0.906444i	$0.638786\pi$
$150$	3.65638e6	0.0884570
$151$	−6.17264e7	−1.45899	−0.729494	−	0.683987i	$-0.760244\pi$
$151$	−6.17264e7	−1.45899	−0.729494	+	0.683987i	$0.760244\pi$
$152$	−7.10743e6	−0.164157
$153$	3.09872e6	0.0699459
$154$	9.46289e6	0.208786
$155$	4.54930e7	0.981258
$156$	9.50915e7	2.00542
$157$	−4.96686e7	−1.02431	−0.512157	−	0.858892i	$-0.671153\pi$
$157$	−4.96686e7	−1.02431	−0.512157	+	0.858892i	$0.671153\pi$
$158$	2.18556e7	0.440822
$159$	7.91579e7	1.56172
$160$	−5.24721e7	−1.01276
$161$	2.45761e7	0.464111
$162$	2.32656e7	0.429944
$163$	−2.68600e7	−0.485790	−0.242895	−	0.970053i	$-0.578097\pi$
$163$	−2.68600e7	−0.485790	−0.242895	+	0.970053i	$0.578097\pi$
$164$	−8.55404e7	−1.51432
$165$	6.79462e7	1.17753
$166$	−9.88166e6	−0.167669
$167$	−5.41378e6	−0.0899483	−0.0449742	−	0.998988i	$-0.514321\pi$
$167$	−5.41378e6	−0.0899483	−0.0449742	+	0.998988i	$0.514321\pi$
$168$	−4.07750e7	−0.663454
$169$	1.23660e8	1.97072
$170$	−2.14745e6	−0.0335237
$171$	−1.30752e7	−0.199968
$172$	8.83418e7	1.32378
$173$	−3.40100e7	−0.499397	−0.249698	−	0.968324i	$-0.580331\pi$
$173$	−3.40100e7	−0.499397	−0.249698	+	0.968324i	$0.580331\pi$
$174$	5.23378e7	0.753170
$175$	8.03460e6	0.113326
$176$	−3.30623e7	−0.457129
$177$	5.68914e7	0.771152
$178$	−3.42750e7	−0.455520
$179$	−8.92929e6	−0.116367	−0.0581837	−	0.998306i	$-0.518531\pi$
$179$	−8.92929e6	−0.116367	−0.0581837	+	0.998306i	$0.518531\pi$
$180$	−6.26657e7	−0.800896
$181$	1.07773e7	0.135094	0.0675468	−	0.997716i	$-0.478483\pi$
$181$	1.07773e7	0.135094	0.0675468	+	0.997716i	$0.478483\pi$
$182$	−3.67364e7	−0.451696
$183$	−2.10709e8	−2.54158
$184$	4.14055e7	0.490000
$185$	−5.45286e6	−0.0633175
$186$	4.21665e7	0.480477
$187$	−5.71683e6	−0.0639307
$188$	−5.78188e7	−0.634624
$189$	1.10462e7	0.119013
$190$	9.06126e6	0.0958409
$191$	−1.27503e8	−1.32404	−0.662022	−	0.749484i	$-0.730302\pi$
$191$	−1.27503e8	−1.32404	−0.662022	+	0.749484i	$0.730302\pi$
$192$	2.83520e7	0.289087
$193$	4.53355e6	0.0453929	0.0226965	−	0.999742i	$-0.492775\pi$
$193$	4.53355e6	0.0453929	0.0226965	+	0.999742i	$0.492775\pi$
$194$	3.53693e7	0.347793
$195$	−2.63778e8	−2.54752
$196$	4.84720e7	0.459827
$197$	9.29329e7	0.866039	0.433020	−	0.901384i	$-0.357448\pi$
$197$	9.29329e7	0.866039	0.433020	+	0.901384i	$0.357448\pi$
$198$	2.93295e7	0.268520
$199$	−1.08475e8	−0.975763	−0.487882	−	0.872910i	$-0.662230\pi$
$199$	−1.08475e8	−0.975763	−0.487882	+	0.872910i	$0.662230\pi$
$200$	1.35366e7	0.119648
$201$	−2.04110e8	−1.77287
$202$	−5.14597e7	−0.439276
$203$	1.15008e8	0.964921
$204$	1.13215e7	0.0933681
$205$	2.37284e8	1.92367
$206$	2.56685e7	0.204581
$207$	7.61717e7	0.596894
$208$	1.28353e8	0.988973
$209$	2.41224e7	0.182772
$210$	5.19840e7	0.387349
$211$	1.03233e8	0.756534	0.378267	−	0.925696i	$-0.376520\pi$
$211$	1.03233e8	0.756534	0.378267	+	0.925696i	$0.376520\pi$
$212$	1.34689e8	0.970858
$213$	5.16701e7	0.366362
$214$	−3.08547e7	−0.215215
$215$	−2.45055e8	−1.68162
$216$	1.86105e7	0.125652
$217$	9.26575e7	0.615561
$218$	−5.19517e7	−0.339627
$219$	1.23582e8	0.795060
$220$	1.15612e8	0.732021
$221$	2.21936e7	0.138310
$222$	−5.05415e6	−0.0310037
$223$	−3.14660e8	−1.90009	−0.950047	−	0.312106i	$-0.898965\pi$
$223$	−3.14660e8	−1.90009	−0.950047	+	0.312106i	$0.898965\pi$
$224$	−1.06872e8	−0.635326
$225$	2.49026e7	0.145749
$226$	−7.71829e7	−0.444776
$227$	1.34511e8	0.763252	0.381626	−	0.924317i	$-0.375364\pi$
$227$	1.34511e8	0.763252	0.381626	+	0.924317i	$0.375364\pi$
$228$	−4.77716e7	−0.266930
$229$	−1.53036e8	−0.842109	−0.421054	−	0.907035i	$-0.638340\pi$
$229$	−1.53036e8	−0.842109	−0.421054	+	0.907035i	$0.638340\pi$
$230$	−5.27879e7	−0.286080
$231$	1.38389e8	0.738686
$232$	1.93764e8	1.01874
$233$	−3.42602e8	−1.77437	−0.887184	−	0.461415i	$-0.847342\pi$
$233$	−3.42602e8	−1.77437	−0.887184	+	0.461415i	$0.847342\pi$
$234$	−1.13862e8	−0.580928
$235$	1.60386e8	0.806173
$236$	9.68018e7	0.479393
$237$	3.19626e8	1.55963
$238$	−4.37380e6	−0.0210300
$239$	4.46983e6	0.0211787	0.0105893	−	0.999944i	$-0.496629\pi$
$239$	4.46983e6	0.0211787	0.0105893	+	0.999944i	$0.496629\pi$
$240$	−1.81626e8	−0.848086
$241$	2.82032e8	1.29789	0.648947	−	0.760834i	$-0.275210\pi$
$241$	2.82032e8	1.29789	0.648947	+	0.760834i	$0.275210\pi$
$242$	3.11424e7	0.141253
$243$	3.00967e8	1.34554
$244$	−3.58526e8	−1.58000
$245$	−1.34458e8	−0.584125
$246$	2.19934e8	0.941931
$247$	−9.36469e7	−0.395416
$248$	1.56108e8	0.649898
$249$	−1.44513e8	−0.593212
$250$	8.59512e7	0.347906
$251$	1.54677e8	0.617402	0.308701	−	0.951159i	$-0.400106\pi$
$251$	1.54677e8	0.617402	0.308701	+	0.951159i	$0.400106\pi$
$252$	−1.27634e8	−0.502417
$253$	−1.40529e8	−0.545562
$254$	−6.74046e7	−0.258090
$255$	−3.14052e7	−0.118607
$256$	−4.90615e7	−0.182768
$257$	−5.32092e8	−1.95533	−0.977666	−	0.210163i	$-0.932600\pi$
$257$	−5.32092e8	−1.95533	−0.977666	+	0.210163i	$0.932600\pi$
$258$	−2.27136e8	−0.823413
$259$	−1.11061e7	−0.0397202
$260$	−4.48824e8	−1.58369
$261$	3.56458e8	1.24099
$262$	−1.86964e8	−0.642250
$263$	4.71018e8	1.59659	0.798294	−	0.602268i	$-0.205736\pi$
$263$	4.71018e8	1.59659	0.798294	+	0.602268i	$0.205736\pi$
$264$	2.33156e8	0.779890
$265$	−3.73618e8	−1.23330
$266$	1.84555e7	0.0601228
$267$	−5.01251e8	−1.61163
$268$	−3.47297e8	−1.10212
$269$	1.80412e8	0.565111	0.282555	−	0.959251i	$-0.408818\pi$
$269$	1.80412e8	0.565111	0.282555	+	0.959251i	$0.408818\pi$
$270$	−2.37265e7	−0.0733602
$271$	5.29413e8	1.61585	0.807926	−	0.589284i	$-0.200590\pi$
$271$	5.29413e8	1.61585	0.807926	+	0.589284i	$0.200590\pi$
$272$	1.52816e7	0.0460445
$273$	−5.37248e8	−1.59811
$274$	2.66626e7	0.0783025
$275$	−4.59428e7	−0.133215
$276$	2.78301e8	0.796771
$277$	7.47583e7	0.211339	0.105670	−	0.994401i	$-0.466301\pi$
$277$	7.47583e7	0.211339	0.105670	+	0.994401i	$0.466301\pi$
$278$	1.53381e8	0.428169
$279$	2.87185e8	0.791675
$280$	1.92454e8	0.523932
$281$	3.03094e8	0.814900	0.407450	−	0.913227i	$-0.366418\pi$
$281$	3.03094e8	0.814900	0.407450	+	0.913227i	$0.366418\pi$
$282$	1.48658e8	0.394746
$283$	5.14440e7	0.134922	0.0674610	−	0.997722i	$-0.478510\pi$
$283$	5.14440e7	0.134922	0.0674610	+	0.997722i	$0.478510\pi$
$284$	8.79177e7	0.227752
$285$	1.32515e8	0.339086
$286$	2.10063e8	0.530969
$287$	4.83286e8	1.20675
$288$	−3.31242e8	−0.817094
$289$	−4.07696e8	−0.993561
$290$	−2.47030e8	−0.594780
$291$	5.17255e8	1.23049
$292$	2.10277e8	0.494255
$293$	−2.88300e8	−0.669588	−0.334794	−	0.942291i	$-0.608667\pi$
$293$	−2.88300e8	−0.669588	−0.334794	+	0.942291i	$0.608667\pi$
$294$	−1.24627e8	−0.286019
$295$	−2.68522e8	−0.608980
$296$	−1.87114e7	−0.0419358
$297$	−6.31634e7	−0.139900
$298$	1.49206e8	0.326610
$299$	5.45556e8	1.18029
$300$	9.09844e7	0.194555
$301$	−4.99113e8	−1.05491
$302$	2.70040e8	0.564163
$303$	−7.52567e8	−1.55416
$304$	−6.44813e7	−0.131637
$305$	9.94529e8	2.00710
$306$	−1.35563e7	−0.0270468
$307$	−1.36085e8	−0.268427	−0.134213	−	0.990952i	$-0.542851\pi$
$307$	−1.36085e8	−0.268427	−0.134213	+	0.990952i	$0.542851\pi$
$308$	2.35472e8	0.459210
$309$	3.75387e8	0.723810
$310$	−1.99022e8	−0.379434
$311$	2.78585e8	0.525166	0.262583	−	0.964909i	$-0.415426\pi$
$311$	2.78585e8	0.525166	0.262583	+	0.964909i	$0.415426\pi$
$312$	−9.05149e8	−1.68725
$313$	−3.48966e8	−0.643246	−0.321623	−	0.946868i	$-0.604228\pi$
$313$	−3.48966e8	−0.643246	−0.321623	+	0.946868i	$0.604228\pi$
$314$	2.17290e8	0.396083
$315$	3.54049e8	0.638229
$316$	5.43850e8	0.969558
$317$	−2.03519e8	−0.358837	−0.179418	−	0.983773i	$-0.557422\pi$
$317$	−2.03519e8	−0.358837	−0.179418	+	0.983773i	$0.557422\pi$
$318$	−3.46299e8	−0.603889
$319$	−6.57630e8	−1.13426
$320$	−1.33819e8	−0.228293
$321$	−4.51231e8	−0.761432
$322$	−1.07515e8	−0.179463
$323$	−1.11495e7	−0.0184097
$324$	5.78934e8	0.945631
$325$	1.78357e8	0.288203
$326$	1.17507e8	0.187846
$327$	−7.59762e8	−1.20160
$328$	8.14235e8	1.27406
$329$	3.26665e8	0.505727
$330$	−2.97251e8	−0.455328
$331$	1.63772e8	0.248222	0.124111	−	0.992268i	$-0.460392\pi$
$331$	1.63772e8	0.248222	0.124111	+	0.992268i	$0.460392\pi$
$332$	−2.45892e8	−0.368775
$333$	−3.44225e7	−0.0510843
$334$	2.36842e7	0.0347813
$335$	9.63381e8	1.40004
$336$	−3.69926e8	−0.532020
$337$	−4.68363e8	−0.666619	−0.333309	−	0.942818i	$-0.608165\pi$
$337$	−4.68363e8	−0.666619	−0.333309	+	0.942818i	$0.608165\pi$
$338$	−5.40986e8	−0.762040
$339$	−1.12875e9	−1.57362
$340$	−5.34365e7	−0.0737330
$341$	−5.29827e8	−0.723592
$342$	5.72013e7	0.0773240
$343$	−7.80372e8	−1.04417
$344$	−8.40901e8	−1.11376
$345$	−7.71991e8	−1.01215
$346$	1.48787e8	0.193107
$347$	9.65822e8	1.24092	0.620460	−	0.784238i	$-0.286946\pi$
$347$	9.65822e8	1.24092	0.620460	+	0.784238i	$0.286946\pi$
$348$	1.30236e9	1.65654
$349$	3.92397e8	0.494124	0.247062	−	0.969000i	$-0.420535\pi$
$349$	3.92397e8	0.494124	0.247062	+	0.969000i	$0.420535\pi$
$350$	−3.51497e7	−0.0438211
$351$	2.45210e8	0.302666
$352$	6.11108e8	0.746825
$353$	−3.41774e8	−0.413549	−0.206775	−	0.978389i	$-0.566297\pi$
$353$	−3.41774e8	−0.413549	−0.206775	+	0.978389i	$0.566297\pi$
$354$	−2.48888e8	−0.298190
$355$	−2.43878e8	−0.289317
$356$	−8.52889e8	−1.00188
$357$	−6.39643e7	−0.0744044
$358$	3.90638e7	0.0449971
$359$	6.54681e8	0.746791	0.373395	−	0.927672i	$-0.378193\pi$
$359$	6.54681e8	0.746791	0.373395	+	0.927672i	$0.378193\pi$
$360$	5.96498e8	0.673829
$361$	4.70459e7	0.0526316
$362$	−4.71485e7	−0.0522381
$363$	4.55439e8	0.499755
$364$	−9.14138e8	−0.993475
$365$	−5.83295e8	−0.627861
$366$	9.21809e8	0.982782
$367$	−4.96988e8	−0.524826	−0.262413	−	0.964956i	$-0.584518\pi$
$367$	−4.96988e8	−0.524826	−0.262413	+	0.964956i	$0.584518\pi$
$368$	3.75647e8	0.392928
$369$	1.49791e9	1.55201
$370$	2.38552e7	0.0244837
$371$	−7.60965e8	−0.773670
$372$	1.04926e9	1.05678
$373$	6.77617e8	0.676088	0.338044	−	0.941130i	$-0.390235\pi$
$373$	6.77617e8	0.676088	0.338044	+	0.941130i	$0.390235\pi$
$374$	2.50100e7	0.0247208
$375$	1.25699e9	1.23089
$376$	5.50361e8	0.533937
$377$	2.55302e9	2.45392
$378$	−4.83248e7	−0.0460202
$379$	3.67931e8	0.347160	0.173580	−	0.984820i	$-0.444467\pi$
$379$	3.67931e8	0.347160	0.173580	+	0.984820i	$0.444467\pi$
$380$	2.25478e8	0.210795
$381$	−9.85752e8	−0.913125
$382$	5.57798e8	0.511983
$383$	−9.67606e8	−0.880041	−0.440021	−	0.897988i	$-0.645029\pi$
$383$	−9.67606e8	−0.880041	−0.440021	+	0.897988i	$0.645029\pi$
$384$	−1.54703e9	−1.39425
$385$	−6.53184e8	−0.583342
$386$	−1.98334e7	−0.0175526
$387$	−1.54696e9	−1.35673
$388$	8.80120e8	0.764946
$389$	1.79006e9	1.54186	0.770929	−	0.636921i	$-0.219792\pi$
$389$	1.79006e9	1.54186	0.770929	+	0.636921i	$0.219792\pi$
$390$	1.15397e9	0.985077
$391$	6.49534e7	0.0549520
$392$	−4.61391e8	−0.386873
$393$	−2.73424e9	−2.27228
$394$	−4.06562e8	−0.334881
$395$	−1.50861e9	−1.23165
$396$	7.29827e8	0.590591
$397$	−1.26653e9	−1.01589	−0.507946	−	0.861389i	$-0.669595\pi$
$397$	−1.26653e9	−1.01589	−0.507946	+	0.861389i	$0.669595\pi$
$398$	4.74556e8	0.377309
$399$	2.69900e8	0.212715
$400$	1.22809e8	0.0959448
$401$	−1.55938e9	−1.20766	−0.603831	−	0.797112i	$-0.706360\pi$
$401$	−1.55938e9	−1.20766	−0.603831	+	0.797112i	$0.706360\pi$
$402$	8.92939e8	0.685536
$403$	2.05687e9	1.56545
$404$	−1.28051e9	−0.966157
$405$	−1.60593e9	−1.20125
$406$	−5.03136e8	−0.373116
$407$	6.35060e7	0.0466911
$408$	−1.07766e8	−0.0785547
$409$	1.57141e8	0.113569	0.0567843	−	0.998386i	$-0.481915\pi$
$409$	1.57141e8	0.113569	0.0567843	+	0.998386i	$0.481915\pi$
$410$	−1.03807e9	−0.743845
$411$	3.89925e8	0.277035
$412$	6.38728e8	0.449962
$413$	−5.46911e8	−0.382025
$414$	−3.33236e8	−0.230808
$415$	6.82091e8	0.468461
$416$	−2.37242e9	−1.61571
$417$	2.24311e9	1.51487
$418$	−1.05531e8	−0.0706743
$419$	−1.73732e8	−0.115380	−0.0576900	−	0.998335i	$-0.518373\pi$
$419$	−1.73732e8	−0.115380	−0.0576900	+	0.998335i	$0.518373\pi$
$420$	1.29355e9	0.851947
$421$	−8.21203e6	−0.00536368	−0.00268184	−	0.999996i	$-0.500854\pi$
$421$	−8.21203e6	−0.00536368	−0.00268184	+	0.999996i	$0.500854\pi$
$422$	−4.51622e8	−0.292537
$423$	1.01247e9	0.650417
$424$	−1.28206e9	−0.816826
$425$	2.12351e7	0.0134181
$426$	−2.26046e8	−0.141665
$427$	2.02560e9	1.25909
$428$	−7.67779e8	−0.473350
$429$	3.07205e9	1.87857
$430$	1.07206e9	0.650251
$431$	−1.08880e9	−0.655053	−0.327526	−	0.944842i	$-0.606215\pi$
$431$	−1.08880e9	−0.655053	−0.327526	+	0.944842i	$0.606215\pi$
$432$	1.68842e8	0.100760
$433$	−2.95472e9	−1.74908	−0.874538	−	0.484957i	$-0.838835\pi$
$433$	−2.95472e9	−1.74908	−0.874538	+	0.484957i	$0.838835\pi$
$434$	−4.05357e8	−0.238026
$435$	−3.61266e9	−2.10434
$436$	−1.29275e9	−0.746985
$437$	−2.74074e8	−0.157102
$438$	−5.40645e8	−0.307434
$439$	2.56977e9	1.44967	0.724834	−	0.688924i	$-0.241917\pi$
$439$	2.56977e9	1.44967	0.724834	+	0.688924i	$0.241917\pi$
$440$	−1.10048e9	−0.615881
$441$	−8.48799e8	−0.471270
$442$	−9.70925e7	−0.0534820
$443$	2.43887e9	1.33283	0.666416	−	0.745580i	$-0.267827\pi$
$443$	2.43887e9	1.33283	0.666416	+	0.745580i	$0.267827\pi$
$444$	−1.25766e8	−0.0681904
$445$	2.36586e9	1.27271
$446$	1.37658e9	0.734730
$447$	2.18205e9	1.15555
$448$	−2.72555e8	−0.143212
$449$	−1.08002e9	−0.563082	−0.281541	−	0.959549i	$-0.590845\pi$
$449$	−1.08002e9	−0.563082	−0.281541	+	0.959549i	$0.590845\pi$
$450$	−1.08944e8	−0.0563584
$451$	−2.76349e9	−1.41854
$452$	−1.92060e9	−0.978255
$453$	3.94918e9	1.99601
$454$	−5.88459e8	−0.295135
$455$	2.53576e9	1.26203
$456$	4.54724e8	0.224580
$457$	−2.00991e9	−0.985075	−0.492537	−	0.870291i	$-0.663931\pi$
$457$	−2.00991e9	−0.985075	−0.492537	+	0.870291i	$0.663931\pi$
$458$	6.69499e8	0.325627
$459$	2.91945e7	0.0140915
$460$	−1.31356e9	−0.629212
$461$	5.71059e8	0.271474	0.135737	−	0.990745i	$-0.456660\pi$
$461$	5.71059e8	0.271474	0.135737	+	0.990745i	$0.456660\pi$
$462$	−6.05424e8	−0.285636
$463$	5.64782e8	0.264452	0.132226	−	0.991220i	$-0.457787\pi$
$463$	5.64782e8	0.264452	0.132226	+	0.991220i	$0.457787\pi$
$464$	1.75790e9	0.816924
$465$	−2.91058e9	−1.34244
$466$	1.49881e9	0.686114
$467$	1.79309e9	0.814692	0.407346	−	0.913274i	$-0.366454\pi$
$467$	1.79309e9	0.814692	0.407346	+	0.913274i	$0.366454\pi$
$468$	−2.83330e9	−1.27771
$469$	1.96216e9	0.878273
$470$	−7.01655e8	−0.311732
$471$	3.17774e9	1.40134
$472$	−9.21429e8	−0.403334
$473$	2.85399e9	1.24005
$474$	−1.39830e9	−0.603080
$475$	−8.96022e7	−0.0383611
$476$	−1.08836e8	−0.0462541
$477$	−2.35855e9	−0.995018
$478$	−1.95546e7	−0.00818938
$479$	−6.54408e8	−0.272066	−0.136033	−	0.990704i	$-0.543435\pi$
$479$	−6.54408e8	−0.272066	−0.136033	+	0.990704i	$0.543435\pi$
$480$	3.35710e9	1.38554
$481$	−2.46540e8	−0.101014
$482$	−1.23383e9	−0.501871
$483$	−1.57235e9	−0.634941
$484$	7.74939e8	0.310677
$485$	−2.44140e9	−0.971723
$486$	−1.31667e9	−0.520295
$487$	2.66860e9	1.04696	0.523482	−	0.852037i	$-0.324633\pi$
$487$	2.66860e9	1.04696	0.523482	+	0.852037i	$0.324633\pi$
$488$	3.41271e9	1.32932
$489$	1.71847e9	0.664600
$490$	5.88227e8	0.225870
$491$	−2.72815e9	−1.04012	−0.520059	−	0.854131i	$-0.674090\pi$
$491$	−2.72815e9	−1.04012	−0.520059	+	0.854131i	$0.674090\pi$
$492$	5.47277e9	2.07171
$493$	3.03960e8	0.114249
$494$	4.09686e8	0.152900
$495$	−2.02450e9	−0.750237
$496$	1.41627e9	0.521149
$497$	−4.96717e8	−0.181494
$498$	6.32216e8	0.229384
$499$	−3.21086e9	−1.15683	−0.578416	−	0.815742i	$-0.696329\pi$
$499$	−3.21086e9	−1.15683	−0.578416	+	0.815742i	$0.696329\pi$
$500$	2.13879e9	0.765195
$501$	3.46367e8	0.123057
$502$	−6.76681e8	−0.238738
$503$	−2.99941e9	−1.05087	−0.525434	−	0.850834i	$-0.676097\pi$
$503$	−2.99941e9	−1.05087	−0.525434	+	0.850834i	$0.676097\pi$
$504$	1.21491e9	0.422706
$505$	3.55205e9	1.22732
$506$	6.14786e8	0.210959
$507$	−7.91160e9	−2.69610
$508$	−1.67728e9	−0.567651
$509$	−5.29454e9	−1.77957	−0.889787	−	0.456377i	$-0.849147\pi$
$509$	−5.29454e9	−1.77957	−0.889787	+	0.456377i	$0.849147\pi$
$510$	1.37391e8	0.0458631
$511$	−1.18802e9	−0.393869
$512$	−2.88046e9	−0.948454
$513$	−1.23188e8	−0.0402862
$514$	2.32779e9	0.756090
$515$	−1.77179e9	−0.571594
$516$	−5.65200e9	−1.81104
$517$	−1.86791e9	−0.594482
$518$	4.85868e7	0.0153591
$519$	2.17592e9	0.683215
$520$	4.27223e9	1.33242
$521$	−3.71685e9	−1.15144	−0.575722	−	0.817646i	$-0.695279\pi$
$521$	−3.71685e9	−1.15144	−0.575722	+	0.817646i	$0.695279\pi$
$522$	−1.55943e9	−0.479866
$523$	1.17959e9	0.360559	0.180280	−	0.983615i	$-0.442300\pi$
$523$	1.17959e9	0.360559	0.180280	+	0.983615i	$0.442300\pi$
$524$	−4.65237e9	−1.41258
$525$	−5.14044e8	−0.155040
$526$	−2.06061e9	−0.617370
$527$	2.44889e8	0.0728840
$528$	2.11528e9	0.625389
$529$	−1.80816e9	−0.531059
$530$	1.63450e9	0.476892
$531$	−1.69511e9	−0.491323
$532$	4.59240e8	0.132236
$533$	1.07283e10	3.06892
$534$	2.19287e9	0.623188
$535$	2.12977e9	0.601305
$536$	3.30582e9	0.927263
$537$	5.71285e8	0.159200
$538$	−7.89267e8	−0.218517
$539$	1.56595e9	0.430741
$540$	−5.90404e8	−0.161351
$541$	1.71433e9	0.465484	0.232742	−	0.972538i	$-0.425230\pi$
$541$	1.71433e9	0.465484	0.232742	+	0.972538i	$0.425230\pi$
$542$	−2.31607e9	−0.624819
$543$	−6.89518e8	−0.184819
$544$	−2.82458e8	−0.0752242
$545$	3.58601e9	0.948908
$546$	2.35035e9	0.617957
$547$	3.64234e8	0.0951534	0.0475767	−	0.998868i	$-0.484850\pi$
$547$	3.64234e8	0.0951534	0.0475767	+	0.998868i	$0.484850\pi$
$548$	6.63465e8	0.172221
$549$	6.27819e9	1.61932
$550$	2.00990e8	0.0515117
$551$	−1.28257e9	−0.326627
$552$	−2.64907e9	−0.670359
$553$	−3.07264e9	−0.772634
$554$	−3.27052e8	−0.0817208
$555$	3.48867e8	0.0866234
$556$	3.81669e9	0.941728
$557$	−2.75002e9	−0.674284	−0.337142	−	0.941454i	$-0.609460\pi$
$557$	−2.75002e9	−0.674284	−0.337142	+	0.941454i	$0.609460\pi$
$558$	−1.25637e9	−0.306125
$559$	−1.10796e10	−2.68278
$560$	1.74602e9	0.420137
$561$	3.65756e8	0.0874623
$562$	−1.32597e9	−0.315106
$563$	3.26803e9	0.771803	0.385902	−	0.922540i	$-0.373890\pi$
$563$	3.26803e9	0.771803	0.385902	+	0.922540i	$0.373890\pi$
$564$	3.69917e9	0.868216
$565$	5.32762e9	1.24269
$566$	−2.25057e8	−0.0521717
$567$	−3.27086e9	−0.753567
$568$	−8.36864e8	−0.191618
$569$	−6.75361e7	−0.0153689	−0.00768446	−	0.999970i	$-0.502446\pi$
$569$	−6.75361e7	−0.0153689	−0.00768446	+	0.999970i	$0.502446\pi$
$570$	−5.79728e8	−0.131118
$571$	−2.41036e9	−0.541820	−0.270910	−	0.962605i	$-0.587325\pi$
$571$	−2.41036e9	−0.541820	−0.270910	+	0.962605i	$0.587325\pi$
$572$	5.22716e9	1.16783
$573$	8.15747e9	1.81140
$574$	−2.11428e9	−0.466628
$575$	5.21993e8	0.114506
$576$	−8.44762e8	−0.184186
$577$	−2.85382e9	−0.618460	−0.309230	−	0.950987i	$-0.600071\pi$
$577$	−2.85382e9	−0.618460	−0.309230	+	0.950987i	$0.600071\pi$
$578$	1.78359e9	0.384191
$579$	−2.90051e8	−0.0621011
$580$	−6.14702e9	−1.30818
$581$	1.38924e9	0.293874
$582$	−2.26288e9	−0.475808
$583$	4.35129e9	0.909448
$584$	−2.00157e9	−0.415839
$585$	7.85941e9	1.62310
$586$	1.26125e9	0.258917
$587$	−3.59469e9	−0.733547	−0.366773	−	0.930310i	$-0.619538\pi$
$587$	−3.59469e9	−0.733547	−0.366773	+	0.930310i	$0.619538\pi$
$588$	−3.10118e9	−0.629080
$589$	−1.03332e9	−0.208368
$590$	1.17473e9	0.235481
$591$	−5.94573e9	−1.18481
$592$	−1.69757e8	−0.0336281
$593$	−6.70963e8	−0.132132	−0.0660658	−	0.997815i	$-0.521045\pi$
$593$	−6.70963e8	−0.132132	−0.0660658	+	0.997815i	$0.521045\pi$
$594$	2.76327e8	0.0540967
$595$	3.01906e8	0.0587573
$596$	3.71280e9	0.718356
$597$	6.94010e9	1.33492
$598$	−2.38670e9	−0.456397
$599$	−1.05696e9	−0.200938	−0.100469	−	0.994940i	$-0.532034\pi$
$599$	−1.05696e9	−0.200938	−0.100469	+	0.994940i	$0.532034\pi$
$600$	−8.66055e8	−0.163688
$601$	3.95642e8	0.0743433	0.0371716	−	0.999309i	$-0.488165\pi$
$601$	3.95642e8	0.0743433	0.0371716	+	0.999309i	$0.488165\pi$
$602$	2.18352e9	0.407915
$603$	6.08157e9	1.12955
$604$	6.71961e9	1.24084
$605$	−2.14963e9	−0.394658
$606$	3.29233e9	0.600965
$607$	−5.10797e9	−0.927018	−0.463509	−	0.886092i	$-0.653410\pi$
$607$	−5.10797e9	−0.927018	−0.463509	+	0.886092i	$0.653410\pi$
$608$	1.19184e9	0.215059
$609$	−7.35806e9	−1.32009
$610$	−4.35086e9	−0.776106
$611$	7.25151e9	1.28613
$612$	−3.37330e8	−0.0594875
$613$	−6.65712e9	−1.16728	−0.583640	−	0.812013i	$-0.698372\pi$
$613$	−6.65712e9	−1.16728	−0.583640	+	0.812013i	$0.698372\pi$
$614$	5.95344e8	0.103796
$615$	−1.51811e10	−2.63173
$616$	−2.24139e9	−0.386354
$617$	−3.97306e9	−0.680968	−0.340484	−	0.940250i	$-0.610591\pi$
$617$	−3.97306e9	−0.680968	−0.340484	+	0.940250i	$0.610591\pi$
$618$	−1.64224e9	−0.279883
$619$	−1.75656e9	−0.297677	−0.148838	−	0.988862i	$-0.547553\pi$
$619$	−1.75656e9	−0.297677	−0.148838	+	0.988862i	$0.547553\pi$
$620$	−4.95242e9	−0.834538
$621$	7.17650e8	0.120252
$622$	−1.21875e9	−0.203072
$623$	4.81865e9	0.798395
$624$	−8.21187e9	−1.35299
$625$	−6.95344e9	−1.13925
$626$	1.52665e9	0.248731
$627$	−1.54332e9	−0.250046
$628$	5.40698e9	0.871156
$629$	−2.93528e7	−0.00470298
$630$	−1.54889e9	−0.246791
$631$	8.91541e9	1.41266	0.706331	−	0.707881i	$-0.250349\pi$
$631$	8.91541e9	1.41266	0.706331	+	0.707881i	$0.250349\pi$
$632$	−5.17675e9	−0.815732
$633$	−6.60470e9	−1.03500
$634$	8.90352e8	0.138755
$635$	4.65266e9	0.721097
$636$	−8.61722e9	−1.32821
$637$	−6.07925e9	−0.931885
$638$	2.87699e9	0.438598
$639$	−1.53954e9	−0.233420
$640$	7.30186e9	1.10104
$641$	6.47465e9	0.970987	0.485493	−	0.874240i	$-0.338640\pi$
$641$	6.47465e9	0.970987	0.485493	+	0.874240i	$0.338640\pi$
$642$	1.97404e9	0.294431
$643$	9.86523e9	1.46342	0.731710	−	0.681616i	$-0.238723\pi$
$643$	9.86523e9	1.46342	0.731710	+	0.681616i	$0.238723\pi$
$644$	−2.67538e9	−0.394716
$645$	1.56783e10	2.30059
$646$	4.87769e7	0.00711869
$647$	3.47871e9	0.504955	0.252478	−	0.967603i	$-0.418755\pi$
$647$	3.47871e9	0.504955	0.252478	+	0.967603i	$0.418755\pi$
$648$	−5.51071e9	−0.795601
$649$	3.12730e9	0.449070
$650$	−7.80276e8	−0.111443
$651$	−5.92811e9	−0.842137
$652$	2.92401e9	0.413154
$653$	5.44770e9	0.765627	0.382813	−	0.923826i	$-0.374955\pi$
$653$	5.44770e9	0.765627	0.382813	+	0.923826i	$0.374955\pi$
$654$	3.32380e9	0.464636
$655$	1.29054e10	1.79443
$656$	7.38706e9	1.02166
$657$	−3.68218e9	−0.506555
$658$	−1.42909e9	−0.195555
$659$	−8.87341e9	−1.20779	−0.603895	−	0.797064i	$-0.706385\pi$
$659$	−8.87341e9	−1.20779	−0.603895	+	0.797064i	$0.706385\pi$
$660$	−7.39671e9	−1.00146
$661$	−3.87038e9	−0.521253	−0.260627	−	0.965440i	$-0.583929\pi$
$661$	−3.87038e9	−0.521253	−0.260627	+	0.965440i	$0.583929\pi$
$662$	−7.16467e8	−0.0959828
$663$	−1.41992e9	−0.189220
$664$	2.34058e9	0.310267
$665$	−1.27390e9	−0.167981
$666$	1.50591e8	0.0197533
$667$	7.47185e9	0.974962
$668$	5.89351e8	0.0764991
$669$	2.01316e10	2.59948
$670$	−4.21459e9	−0.541370
$671$	−1.15826e10	−1.48006
$672$	6.83755e9	0.869176
$673$	3.33996e9	0.422366	0.211183	−	0.977447i	$-0.432268\pi$
$673$	3.33996e9	0.422366	0.211183	+	0.977447i	$0.432268\pi$
$674$	2.04899e9	0.257769
$675$	2.34619e8	0.0293630
$676$	−1.34618e10	−1.67605
$677$	8.90861e9	1.10344	0.551721	−	0.834029i	$-0.313971\pi$
$677$	8.90861e9	1.10344	0.551721	+	0.834029i	$0.313971\pi$
$678$	4.93807e9	0.608490
$679$	−4.97250e9	−0.609580
$680$	5.08647e8	0.0620348
$681$	−8.60586e9	−1.04419
$682$	2.31788e9	0.279799
$683$	−5.28936e9	−0.635229	−0.317614	−	0.948220i	$-0.602882\pi$
$683$	−5.28936e9	−0.635229	−0.317614	+	0.948220i	$0.602882\pi$
$684$	1.42338e9	0.170069
$685$	−1.84041e9	−0.218775
$686$	3.41397e9	0.403762
$687$	9.79102e9	1.15207
$688$	−7.62898e9	−0.893114
$689$	−1.68924e10	−1.96754
$690$	3.37730e9	0.391380
$691$	1.57891e10	1.82047	0.910236	−	0.414089i	$-0.135900\pi$
$691$	1.57891e10	1.82047	0.910236	+	0.414089i	$0.135900\pi$
$692$	3.70237e9	0.424726
$693$	−4.12338e9	−0.470638
$694$	−4.22527e9	−0.479840
$695$	−1.05873e10	−1.19629
$696$	−1.23968e10	−1.39372
$697$	1.27730e9	0.142882
$698$	−1.71665e9	−0.191068
$699$	2.19192e10	2.42748
$700$	−8.74656e8	−0.0963816
$701$	6.02255e8	0.0660340	0.0330170	−	0.999455i	$-0.489488\pi$
$701$	6.02255e8	0.0660340	0.0330170	+	0.999455i	$0.489488\pi$
$702$	−1.07274e9	−0.117035
$703$	1.23856e8	0.0134453
$704$	1.55850e9	0.168346
$705$	−1.02613e10	−1.10291
$706$	1.49519e9	0.159912
$707$	7.23462e9	0.769924
$708$	−6.19326e9	−0.655848
$709$	6.37556e9	0.671826	0.335913	−	0.941893i	$-0.390955\pi$
$709$	6.37556e9	0.671826	0.335913	+	0.941893i	$0.390955\pi$
$710$	1.06692e9	0.111873
$711$	−9.52342e9	−0.993686
$712$	8.11841e9	0.842929
$713$	6.01978e9	0.621967
$714$	2.79831e8	0.0287708
$715$	−1.44998e10	−1.48351
$716$	9.72053e8	0.0989679
$717$	−2.85974e8	−0.0289741
$718$	−2.86409e9	−0.288770
$719$	9.49677e8	0.0952850	0.0476425	−	0.998864i	$-0.484829\pi$
$719$	9.49677e8	0.0952850	0.0476425	+	0.998864i	$0.484829\pi$
$720$	5.41166e9	0.540339
$721$	−3.60869e9	−0.358572
$722$	−2.05816e8	−0.0203516
$723$	−1.80441e10	−1.77562
$724$	−1.17323e9	−0.114894
$725$	2.44275e9	0.238066
$726$	−1.99245e9	−0.193246
$727$	1.11788e10	1.07901	0.539505	−	0.841982i	$-0.318611\pi$
$727$	1.11788e10	1.07901	0.539505	+	0.841982i	$0.318611\pi$
$728$	8.70143e9	0.835854
$729$	−7.62480e9	−0.728924
$730$	2.55180e9	0.242782
$731$	−1.31913e9	−0.124904
$732$	2.29380e10	2.16156
$733$	−1.72844e10	−1.62103	−0.810513	−	0.585721i	$-0.800812\pi$
$733$	−1.72844e10	−1.62103	−0.810513	+	0.585721i	$0.800812\pi$
$734$	2.17422e9	0.202940
$735$	8.60247e9	0.799130
$736$	−6.94328e9	−0.641937
$737$	−1.12199e10	−1.03241
$738$	−6.55304e9	−0.600131
$739$	6.03830e9	0.550376	0.275188	−	0.961390i	$-0.411260\pi$
$739$	6.03830e9	0.550376	0.275188	+	0.961390i	$0.411260\pi$
$740$	5.93605e8	0.0538501
$741$	5.99141e9	0.540961
$742$	3.32906e9	0.299163
$743$	5.42146e9	0.484904	0.242452	−	0.970163i	$-0.422048\pi$
$743$	5.42146e9	0.484904	0.242452	+	0.970163i	$0.422048\pi$
$744$	−9.98761e9	−0.889112
$745$	−1.02991e10	−0.912539
$746$	−2.96443e9	−0.261430
$747$	4.30585e9	0.377952
$748$	6.22341e8	0.0543717
$749$	4.33780e9	0.377210
$750$	−5.49905e9	−0.475963
$751$	−4.75889e9	−0.409983	−0.204991	−	0.978764i	$-0.565717\pi$
$751$	−4.75889e9	−0.409983	−0.204991	+	0.978764i	$0.565717\pi$
$752$	4.99309e9	0.428161
$753$	−9.89605e9	−0.844655
$754$	−1.11689e10	−0.948882
$755$	−1.86398e10	−1.57626
$756$	−1.20250e9	−0.101218
$757$	−3.85587e9	−0.323063	−0.161532	−	0.986868i	$-0.551643\pi$
$757$	−3.85587e9	−0.323063	−0.161532	+	0.986868i	$0.551643\pi$
$758$	−1.60962e9	−0.134240
$759$	8.99088e9	0.746373
$760$	−2.14626e9	−0.177351
$761$	−1.48111e10	−1.21826	−0.609131	−	0.793069i	$-0.708482\pi$
$761$	−1.48111e10	−1.21826	−0.609131	+	0.793069i	$0.708482\pi$
$762$	4.31246e9	0.353088
$763$	7.30378e9	0.595267
$764$	1.38801e10	1.12607
$765$	9.35734e8	0.0755679
$766$	4.23308e9	0.340295
$767$	−1.21407e10	−0.971537
$768$	3.13889e9	0.250042
$769$	−1.08487e10	−0.860268	−0.430134	−	0.902765i	$-0.641534\pi$
$769$	−1.08487e10	−0.860268	−0.430134	+	0.902765i	$0.641534\pi$
$770$	2.85755e9	0.225567
$771$	3.40426e10	2.67505
$772$	−4.93528e8	−0.0386057
$773$	8.43591e9	0.656907	0.328453	−	0.944520i	$-0.393473\pi$
$773$	8.43591e9	0.656907	0.328453	+	0.944520i	$0.393473\pi$
$774$	6.76765e9	0.524620
$775$	1.96803e9	0.151871
$776$	−8.37761e9	−0.643583
$777$	7.10553e8	0.0543404
$778$	−7.83115e9	−0.596207
$779$	−5.38963e9	−0.408487
$780$	2.87152e10	2.16661
$781$	2.84029e9	0.213346
$782$	−2.84158e8	−0.0212489
$783$	3.35836e9	0.250012
$784$	−4.18592e9	−0.310231
$785$	−1.49986e10	−1.10664
$786$	1.19617e10	0.878649
$787$	−1.44561e10	−1.05716	−0.528579	−	0.848884i	$-0.677275\pi$
$787$	−1.44561e10	−1.05716	−0.528579	+	0.848884i	$0.677275\pi$
$788$	−1.01168e10	−0.736547
$789$	−3.01352e10	−2.18426
$790$	6.59984e9	0.476254
$791$	1.08510e10	0.779565
$792$	−6.94702e9	−0.496890
$793$	4.49656e10	3.20202
$794$	5.54080e9	0.392826
$795$	2.39036e10	1.68725
$796$	1.18087e10	0.829865
$797$	−1.19231e10	−0.834232	−0.417116	−	0.908853i	$-0.636959\pi$
$797$	−1.19231e10	−0.834232	−0.417116	+	0.908853i	$0.636959\pi$
$798$	−1.18076e9	−0.0822527
$799$	8.63359e8	0.0598794
$800$	−2.26995e9	−0.156748
$801$	1.49351e10	1.02682
$802$	6.82195e9	0.466980
$803$	6.79326e9	0.462992
$804$	2.22196e10	1.50779
$805$	7.42135e9	0.501415
$806$	−8.99839e9	−0.605330
$807$	−1.15426e10	−0.773116
$808$	1.21888e10	0.812870
$809$	7.58714e9	0.503800	0.251900	−	0.967753i	$-0.418945\pi$
$809$	7.58714e9	0.503800	0.251900	+	0.967753i	$0.418945\pi$
$810$	7.02561e9	0.464501
$811$	1.57853e10	1.03915	0.519577	−	0.854424i	$-0.326090\pi$
$811$	1.57853e10	1.03915	0.519577	+	0.854424i	$0.326090\pi$
$812$	−1.25199e10	−0.820644
$813$	−3.38712e10	−2.21062
$814$	−2.77826e8	−0.0180546
$815$	−8.11102e9	−0.524836
$816$	−9.77697e8	−0.0629925
$817$	5.56614e9	0.357089
$818$	−6.87460e8	−0.0439148
$819$	1.60076e10	1.01820
$820$	−2.58310e10	−1.63604
$821$	−1.74887e10	−1.10295	−0.551477	−	0.834190i	$-0.685936\pi$
$821$	−1.74887e10	−1.10295	−0.551477	+	0.834190i	$0.685936\pi$
$822$	−1.70584e9	−0.107124
$823$	−2.00259e10	−1.25226	−0.626128	−	0.779721i	$-0.715361\pi$
$823$	−2.00259e10	−1.25226	−0.626128	+	0.779721i	$0.715361\pi$
$824$	−6.07988e9	−0.378573
$825$	2.93937e9	0.182249
$826$	2.39262e9	0.147722
$827$	−1.57975e10	−0.971225	−0.485612	−	0.874174i	$-0.661403\pi$
$827$	−1.57975e10	−0.971225	−0.485612	+	0.874174i	$0.661403\pi$
$828$	−8.29214e9	−0.507645
$829$	2.24934e10	1.37124	0.685622	−	0.727957i	$-0.259530\pi$
$829$	2.24934e10	1.37124	0.685622	+	0.727957i	$0.259530\pi$
$830$	−2.98401e9	−0.181145
$831$	−4.78294e9	−0.289129
$832$	−6.05034e9	−0.364207
$833$	−7.23791e8	−0.0433866
$834$	−9.81314e9	−0.585770
$835$	−1.63482e9	−0.0971780
$836$	−2.62599e9	−0.155443
$837$	2.70570e9	0.159493
$838$	7.60041e8	0.0446152
$839$	3.49882e9	0.204529	0.102264	−	0.994757i	$-0.467391\pi$
$839$	3.49882e9	0.204529	0.102264	+	0.994757i	$0.467391\pi$
$840$	−1.23130e10	−0.716780
$841$	1.77159e10	1.02702
$842$	3.59260e7	0.00207403
$843$	−1.93915e10	−1.11485
$844$	−1.12380e10	−0.643416
$845$	3.73421e10	2.12912
$846$	−4.42936e9	−0.251504
$847$	−4.37825e9	−0.247576
$848$	−1.16314e10	−0.655007
$849$	−3.29133e9	−0.184584
$850$	−9.28990e7	−0.00518854
$851$	−7.21541e8	−0.0401336
$852$	−5.62486e9	−0.311583
$853$	2.39951e9	0.132373	0.0661866	−	0.997807i	$-0.478917\pi$
$853$	2.39951e9	0.132373	0.0661866	+	0.997807i	$0.478917\pi$
$854$	−8.86159e9	−0.486865
$855$	−3.94837e9	−0.216041
$856$	7.30827e9	0.398251
$857$	−9.21713e9	−0.500222	−0.250111	−	0.968217i	$-0.580467\pi$
$857$	−9.21713e9	−0.500222	−0.250111	+	0.968217i	$0.580467\pi$
$858$	−1.34396e10	−0.726408
$859$	−1.89827e10	−1.02184	−0.510918	−	0.859629i	$-0.670695\pi$
$859$	−1.89827e10	−1.02184	−0.510918	+	0.859629i	$0.670695\pi$
$860$	2.66769e10	1.43018
$861$	−3.09201e10	−1.65093
$862$	4.76326e9	0.253296
$863$	−1.54984e10	−0.820823	−0.410412	−	0.911900i	$-0.634615\pi$
$863$	−1.54984e10	−0.820823	−0.410412	+	0.911900i	$0.634615\pi$
$864$	−3.12079e9	−0.164614
$865$	−1.02702e10	−0.539536
$866$	1.29263e10	0.676334
$867$	2.60839e10	1.35927
$868$	−1.00868e10	−0.523521
$869$	1.75697e10	0.908231
$870$	1.58047e10	0.813706
$871$	4.35573e10	2.23356
$872$	1.23053e10	0.628472
$873$	−1.54119e10	−0.783982
$874$	1.19902e9	0.0607484
$875$	−1.20837e10	−0.609779
$876$	−1.34532e10	−0.676181
$877$	−7.94415e9	−0.397694	−0.198847	−	0.980031i	$-0.563720\pi$
$877$	−7.94415e9	−0.397694	−0.198847	+	0.980031i	$0.563720\pi$
$878$	−1.12422e10	−0.560559
$879$	1.84451e10	0.916050
$880$	−9.98396e9	−0.493871
$881$	−1.75833e10	−0.866335	−0.433168	−	0.901313i	$-0.642604\pi$
$881$	−1.75833e10	−0.866335	−0.433168	+	0.901313i	$0.642604\pi$
$882$	3.71332e9	0.182231
$883$	9.57302e9	0.467936	0.233968	−	0.972244i	$-0.424829\pi$
$883$	9.57302e9	0.467936	0.233968	+	0.972244i	$0.424829\pi$
$884$	−2.41602e9	−0.117630
$885$	1.71797e10	0.833134
$886$	−1.06696e10	−0.515381
$887$	−3.02190e10	−1.45394	−0.726972	−	0.686667i	$-0.759073\pi$
$887$	−3.02190e10	−1.45394	−0.726972	+	0.686667i	$0.759073\pi$
$888$	1.19713e9	0.0573716
$889$	9.47628e9	0.452357
$890$	−1.03502e10	−0.492133
$891$	1.87032e10	0.885817
$892$	3.42543e10	1.61599
$893$	−3.64298e9	−0.171189
$894$	−9.54602e9	−0.446829
$895$	−2.69642e9	−0.125721
$896$	1.48720e10	0.690703
$897$	−3.49040e10	−1.61474
$898$	4.72489e9	0.217733
$899$	2.81706e10	1.29311
$900$	−2.71093e9	−0.123957
$901$	−2.01119e9	−0.0916045
$902$	1.20897e10	0.548520
$903$	3.19327e10	1.44320
$904$	1.82816e10	0.823049
$905$	3.25447e9	0.145952
$906$	−1.72769e10	−0.771820
$907$	−1.06315e10	−0.473115	−0.236558	−	0.971617i	$-0.576019\pi$
$907$	−1.06315e10	−0.473115	−0.236558	+	0.971617i	$0.576019\pi$
$908$	−1.46430e10	−0.649129
$909$	2.24232e10	0.990200
$910$	−1.10934e10	−0.488002
$911$	4.12786e10	1.80888	0.904441	−	0.426598i	$-0.140288\pi$
$911$	4.12786e10	1.80888	0.904441	+	0.426598i	$0.140288\pi$
$912$	4.12544e9	0.180089
$913$	−7.94386e9	−0.345449
$914$	8.79293e9	0.380910
$915$	−6.36287e10	−2.74587
$916$	1.66596e10	0.716195
$917$	2.62849e10	1.12568
$918$	−1.27720e8	−0.00544891
$919$	−1.21394e10	−0.515931	−0.257966	−	0.966154i	$-0.583052\pi$
$919$	−1.21394e10	−0.515931	−0.257966	+	0.966154i	$0.583052\pi$
$920$	1.25034e10	0.529384
$921$	8.70655e9	0.367229
$922$	−2.49827e9	−0.104974
$923$	−1.10265e10	−0.461562
$924$	−1.50652e10	−0.628236
$925$	−2.35892e8	−0.00979979
$926$	−2.47081e9	−0.102259
$927$	−1.11849e10	−0.461160
$928$	−3.24923e10	−1.33463
$929$	1.09547e10	0.448276	0.224138	−	0.974557i	$-0.428043\pi$
$929$	1.09547e10	0.448276	0.224138	+	0.974557i	$0.428043\pi$
$930$	1.27332e10	0.519096
$931$	3.05407e9	0.124038
$932$	3.72960e10	1.50906
$933$	−1.78235e10	−0.718469
$934$	−7.84441e9	−0.315026
$935$	−1.72633e9	−0.0690692
$936$	2.69694e10	1.07499
$937$	1.80268e10	0.715862	0.357931	−	0.933748i	$-0.383482\pi$
$937$	1.80268e10	0.715862	0.357931	+	0.933748i	$0.383482\pi$
$938$	−8.58405e9	−0.339611
$939$	2.23264e10	0.880013
$940$	−1.74598e10	−0.685632
$941$	2.26489e10	0.886101	0.443050	−	0.896497i	$-0.353896\pi$
$941$	2.26489e10	0.886101	0.443050	+	0.896497i	$0.353896\pi$
$942$	−1.39019e10	−0.541873
$943$	3.13982e10	1.21931
$944$	−8.35957e9	−0.323431
$945$	3.33566e9	0.128579
$946$	−1.24856e10	−0.479503
$947$	−4.97074e9	−0.190194	−0.0950968	−	0.995468i	$-0.530316\pi$
$947$	−4.97074e9	−0.190194	−0.0950968	+	0.995468i	$0.530316\pi$
$948$	−3.47948e10	−1.32643
$949$	−2.63725e10	−1.00166
$950$	3.91991e8	0.0148335
$951$	1.30209e10	0.490917
$952$	1.03598e9	0.0389156
$953$	3.02943e10	1.13380	0.566898	−	0.823788i	$-0.308143\pi$
$953$	3.02943e10	1.13380	0.566898	+	0.823788i	$0.308143\pi$
$954$	1.03182e10	0.384755
$955$	−3.85025e10	−1.43047
$956$	−4.86591e8	−0.0180120
$957$	4.20743e10	1.55176
$958$	2.86290e9	0.105203
$959$	−3.74845e9	−0.137242
$960$	8.56156e9	0.312323
$961$	−4.81666e9	−0.175071
$962$	1.07856e9	0.0390600
$963$	1.34447e10	0.485130
$964$	−3.07023e10	−1.10383
$965$	1.36902e9	0.0490414
$966$	6.87870e9	0.245520
$967$	−3.75959e10	−1.33705	−0.668526	−	0.743689i	$-0.733074\pi$
$967$	−3.75959e10	−1.33705	−0.668526	+	0.743689i	$0.733074\pi$
$968$	−7.37643e9	−0.261386
$969$	7.13333e8	0.0251860
$970$	1.06806e10	0.375747
$971$	3.55539e10	1.24629	0.623147	−	0.782105i	$-0.285854\pi$
$971$	3.55539e10	1.24629	0.623147	+	0.782105i	$0.285854\pi$
$972$	−3.27636e10	−1.14435
$973$	−2.15636e10	−0.750457
$974$	−1.16746e10	−0.404841
$975$	−1.14111e10	−0.394285
$976$	3.09614e10	1.06597
$977$	4.22370e10	1.44898	0.724489	−	0.689287i	$-0.242076\pi$
$977$	4.22370e10	1.44898	0.724489	+	0.689287i	$0.242076\pi$
$978$	−7.51794e9	−0.256988
$979$	−2.75537e10	−0.938512
$980$	1.46373e10	0.496786
$981$	2.26375e10	0.765574
$982$	1.19351e10	0.402194
$983$	−4.61996e10	−1.55132	−0.775659	−	0.631152i	$-0.782582\pi$
$983$	−4.61996e10	−1.55132	−0.775659	+	0.631152i	$0.782582\pi$
$984$	−5.20938e10	−1.74302
$985$	2.80633e10	0.935648
$986$	−1.32976e9	−0.0441779
$987$	−2.08996e10	−0.691875
$988$	1.01945e10	0.336292
$989$	−3.24265e10	−1.06589
$990$	8.85675e9	0.290102
$991$	−4.74766e10	−1.54961	−0.774805	−	0.632201i	$-0.782152\pi$
$991$	−4.74766e10	−1.54961	−0.774805	+	0.632201i	$0.782152\pi$
$992$	−2.61778e10	−0.851416
$993$	−1.04779e10	−0.339588
$994$	2.17304e9	0.0701802
$995$	−3.27567e10	−1.05419
$996$	1.57319e10	0.504514
$997$	−3.72764e9	−0.119124	−0.0595622	−	0.998225i	$-0.518970\pi$
$997$	−3.72764e9	−0.119124	−0.0595622	+	0.998225i	$0.518970\pi$
$998$	1.40469e10	0.447324
$999$	−3.24310e8	−0.0102916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.8.a.b.1.3	✓	6
3.2	odd	2		171.8.a.f.1.4		6
4.3	odd	2		304.8.a.h.1.6		6
5.4	even	2		475.8.a.b.1.4		6
19.18	odd	2		361.8.a.c.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.8.a.b.1.3	✓	6	1.1	even	1	trivial
171.8.a.f.1.4		6	3.2	odd	2
304.8.a.h.1.6		6	4.3	odd	2
361.8.a.c.1.4		6	19.18	odd	2
475.8.a.b.1.4		6	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)

\(f(q)\)	\(=\)	\(q-4.37480 q^{2} -63.9788 q^{3} -108.861 q^{4} +301.974 q^{5} +279.894 q^{6} +615.044 q^{7} +1036.22 q^{8} +1906.28 q^{9} +O(q^{10})\)	\(q-4.37480 q^{2} -63.9788 q^{3} -108.861 q^{4} +301.974 q^{5} +279.894 q^{6} +615.044 q^{7} +1036.22 q^{8} +1906.28 q^{9} -1321.08 q^{10} -3516.90 q^{11} +6964.80 q^{12} +13653.1 q^{13} -2690.69 q^{14} -19319.9 q^{15} +9400.98 q^{16} +1625.53 q^{17} -8339.59 q^{18} -6859.00 q^{19} -32873.3 q^{20} -39349.8 q^{21} +15385.7 q^{22} +39958.3 q^{23} -66296.0 q^{24} +13063.5 q^{25} -59729.7 q^{26} +17960.0 q^{27} -66954.4 q^{28} +186991. q^{29} +84520.8 q^{30} +150652. q^{31} -173763. q^{32} +225007. q^{33} -7111.37 q^{34} +185727. q^{35} -207520. q^{36} -18057.4 q^{37} +30006.7 q^{38} -873511. q^{39} +312911. q^{40} +785775. q^{41} +172147. q^{42} -811509. q^{43} +382854. q^{44} +575648. q^{45} -174809. q^{46} +531124. q^{47} -601463. q^{48} -445264. q^{49} -57149.9 q^{50} -103999. q^{51} -1.48630e6 q^{52} -1.23725e6 q^{53} -78571.3 q^{54} -1.06201e6 q^{55} +637320. q^{56} +438830. q^{57} -818049. q^{58} -889223. q^{59} +2.10319e6 q^{60} +3.29342e6 q^{61} -659071. q^{62} +1.17245e6 q^{63} -443147. q^{64} +4.12290e6 q^{65} -984358. q^{66} +3.19028e6 q^{67} -176957. q^{68} -2.55648e6 q^{69} -812519. q^{70} -807613. q^{71} +1.97533e6 q^{72} -1.93161e6 q^{73} +78997.3 q^{74} -835783. q^{75} +746679. q^{76} -2.16305e6 q^{77} +3.82143e6 q^{78} -4.99581e6 q^{79} +2.83885e6 q^{80} -5.31810e6 q^{81} -3.43761e6 q^{82} +2.25877e6 q^{83} +4.28366e6 q^{84} +490869. q^{85} +3.55018e6 q^{86} -1.19635e7 q^{87} -3.64428e6 q^{88} +7.83465e6 q^{89} -2.51834e6 q^{90} +8.39728e6 q^{91} -4.34990e6 q^{92} -9.63851e6 q^{93} -2.32356e6 q^{94} -2.07124e6 q^{95} +1.11172e7 q^{96} -8.08479e6 q^{97} +1.94794e6 q^{98} -6.70420e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{2} + 40 q^{3} + 357 q^{4} + 219 q^{5} + 925 q^{6} + 2105 q^{7} + 5835 q^{8} + 5916 q^{9}+O(q^{10}) \) 6 * q + 15 * q^2 + 40 * q^3 + 357 * q^4 + 219 * q^5 + 925 * q^6 + 2105 * q^7 + 5835 * q^8 + 5916 * q^9	\( 6 q + 15 q^{2} + 40 q^{3} + 357 q^{4} + 219 q^{5} + 925 q^{6} + 2105 q^{7} + 5835 q^{8} + 5916 q^{9} + 8212 q^{10} + 7257 q^{11} + 7025 q^{12} + 6850 q^{13} + 8859 q^{14} + 3650 q^{15} - 9159 q^{16} + 5415 q^{17} - 58980 q^{18} - 41154 q^{19} - 67620 q^{20} - 83290 q^{21} - 223870 q^{22} - 720 q^{23} - 151113 q^{24} - 53567 q^{25} - 106527 q^{26} + 199450 q^{27} + 91615 q^{28} + 381624 q^{29} - 137776 q^{30} + 264080 q^{31} + 259155 q^{32} + 496430 q^{33} + 297463 q^{34} + 739767 q^{35} - 147282 q^{36} + 1082300 q^{37} - 102885 q^{38} + 1129528 q^{39} - 524232 q^{40} + 485232 q^{41} - 1753105 q^{42} + 198705 q^{43} - 1729290 q^{44} - 478705 q^{45} - 1565713 q^{46} - 247125 q^{47} - 2937955 q^{48} - 538861 q^{49} - 2396859 q^{50} - 72176 q^{51} - 2647795 q^{52} + 3226770 q^{53} - 1217249 q^{54} - 1490553 q^{55} + 3718965 q^{56} - 274360 q^{57} + 1048405 q^{58} + 2305380 q^{59} + 647440 q^{60} + 585731 q^{61} + 2583780 q^{62} - 3209015 q^{63} + 2380137 q^{64} + 4809420 q^{65} + 2420402 q^{66} - 3264030 q^{67} + 8276595 q^{68} - 1867056 q^{69} + 5936880 q^{70} + 6833682 q^{71} + 3040530 q^{72} - 4160625 q^{73} + 20750550 q^{74} - 11237814 q^{75} - 2448663 q^{76} + 1659195 q^{77} - 1839095 q^{78} - 8680576 q^{79} + 14904048 q^{80} - 16541142 q^{81} - 9240140 q^{82} - 3785040 q^{83} - 18290321 q^{84} - 16108227 q^{85} + 11192544 q^{86} - 25742220 q^{87} - 24666570 q^{88} + 12473466 q^{89} - 4688908 q^{90} - 14289854 q^{91} + 9179655 q^{92} + 5742820 q^{93} - 10757712 q^{94} - 1502121 q^{95} - 8195689 q^{96} + 882830 q^{97} + 47239200 q^{98} + 10726225 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 + 40 * q^3 + 357 * q^4 + 219 * q^5 + 925 * q^6 + 2105 * q^7 + 5835 * q^8 + 5916 * q^9 + 8212 * q^10 + 7257 * q^11 + 7025 * q^12 + 6850 * q^13 + 8859 * q^14 + 3650 * q^15 - 9159 * q^16 + 5415 * q^17 - 58980 * q^18 - 41154 * q^19 - 67620 * q^20 - 83290 * q^21 - 223870 * q^22 - 720 * q^23 - 151113 * q^24 - 53567 * q^25 - 106527 * q^26 + 199450 * q^27 + 91615 * q^28 + 381624 * q^29 - 137776 * q^30 + 264080 * q^31 + 259155 * q^32 + 496430 * q^33 + 297463 * q^34 + 739767 * q^35 - 147282 * q^36 + 1082300 * q^37 - 102885 * q^38 + 1129528 * q^39 - 524232 * q^40 + 485232 * q^41 - 1753105 * q^42 + 198705 * q^43 - 1729290 * q^44 - 478705 * q^45 - 1565713 * q^46 - 247125 * q^47 - 2937955 * q^48 - 538861 * q^49 - 2396859 * q^50 - 72176 * q^51 - 2647795 * q^52 + 3226770 * q^53 - 1217249 * q^54 - 1490553 * q^55 + 3718965 * q^56 - 274360 * q^57 + 1048405 * q^58 + 2305380 * q^59 + 647440 * q^60 + 585731 * q^61 + 2583780 * q^62 - 3209015 * q^63 + 2380137 * q^64 + 4809420 * q^65 + 2420402 * q^66 - 3264030 * q^67 + 8276595 * q^68 - 1867056 * q^69 + 5936880 * q^70 + 6833682 * q^71 + 3040530 * q^72 - 4160625 * q^73 + 20750550 * q^74 - 11237814 * q^75 - 2448663 * q^76 + 1659195 * q^77 - 1839095 * q^78 - 8680576 * q^79 + 14904048 * q^80 - 16541142 * q^81 - 9240140 * q^82 - 3785040 * q^83 - 18290321 * q^84 - 16108227 * q^85 + 11192544 * q^86 - 25742220 * q^87 - 24666570 * q^88 + 12473466 * q^89 - 4688908 * q^90 - 14289854 * q^91 + 9179655 * q^92 + 5742820 * q^93 - 10757712 * q^94 - 1502121 * q^95 - 8195689 * q^96 + 882830 * q^97 + 47239200 * q^98 + 10726225 * q^99

Introduction

L-functions

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