LMFDB - Embedded newform 19.8.a.b.1.5

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			1.5
Root			$14.6629$ 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)

$f(q)$	$=$	$q+16.6629 q^{2} +67.6316 q^{3} +149.652 q^{4} -74.3884 q^{5} +1126.94 q^{6} -1123.58 q^{7} +360.790 q^{8} +2387.04 q^{9} +O(q^{10})$	\(q+16.6629 q^{2} +67.6316 q^{3} +149.652 q^{4} -74.3884 q^{5} +1126.94 q^{6} -1123.58 q^{7} +360.790 q^{8} +2387.04 q^{9} -1239.53 q^{10} -1925.08 q^{11} +10121.2 q^{12} +8706.23 q^{13} -18722.2 q^{14} -5031.01 q^{15} -13143.7 q^{16} +28975.2 q^{17} +39775.0 q^{18} -6859.00 q^{19} -11132.4 q^{20} -75989.9 q^{21} -32077.4 q^{22} -66480.6 q^{23} +24400.8 q^{24} -72591.4 q^{25} +145071. q^{26} +13529.0 q^{27} -168147. q^{28} +133226. q^{29} -83831.2 q^{30} +261576. q^{31} -265193. q^{32} -130196. q^{33} +482810. q^{34} +83581.7 q^{35} +357226. q^{36} +516147. q^{37} -114291. q^{38} +588817. q^{39} -26838.6 q^{40} -631509. q^{41} -1.26621e6 q^{42} -127914. q^{43} -288092. q^{44} -177568. q^{45} -1.10776e6 q^{46} +739199. q^{47} -888929. q^{48} +438899. q^{49} -1.20958e6 q^{50} +1.95964e6 q^{51} +1.30291e6 q^{52} -639668. q^{53} +225432. q^{54} +143203. q^{55} -405378. q^{56} -463885. q^{57} +2.21993e6 q^{58} -3127.11 q^{59} -752902. q^{60} +241926. q^{61} +4.35862e6 q^{62} -2.68204e6 q^{63} -2.73649e6 q^{64} -647643. q^{65} -2.16944e6 q^{66} -2.61257e6 q^{67} +4.33620e6 q^{68} -4.49619e6 q^{69} +1.39271e6 q^{70} +1.62641e6 q^{71} +861220. q^{72} +4.48073e6 q^{73} +8.60051e6 q^{74} -4.90947e6 q^{75} -1.02647e6 q^{76} +2.16299e6 q^{77} +9.81139e6 q^{78} -1.45140e6 q^{79} +977738. q^{80} -4.30547e6 q^{81} -1.05228e7 q^{82} +437590. q^{83} -1.13721e7 q^{84} -2.15542e6 q^{85} -2.13141e6 q^{86} +9.01029e6 q^{87} -694548. q^{88} +28921.7 q^{89} -2.95880e6 q^{90} -9.78218e6 q^{91} -9.94898e6 q^{92} +1.76908e7 q^{93} +1.23172e7 q^{94} +510230. q^{95} -1.79354e7 q^{96} -9.35507e6 q^{97} +7.31333e6 q^{98} -4.59523e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	16.6629	1.47281	0.736403	−	0.676543i	$-0.236523\pi$
$2$	16.6629	1.47281	0.736403	+	0.676543i	$0.236523\pi$
$3$	67.6316	1.44619	0.723095	−	0.690748i	$-0.242719\pi$
$3$	67.6316	1.44619	0.723095	+	0.690748i	$0.242719\pi$
$4$	149.652	1.16916
$5$	−74.3884	−0.266140	−0.133070	−	0.991107i	$-0.542484\pi$
$5$	−74.3884	−0.266140	−0.133070	+	0.991107i	$0.542484\pi$
$6$	1126.94	2.12996
$7$	−1123.58	−1.23812	−0.619060	−	0.785344i	$-0.712486\pi$
$7$	−1123.58	−1.23812	−0.619060	+	0.785344i	$0.712486\pi$
$8$	360.790	0.249138
$9$	2387.04	1.09147
$10$	−1239.53	−0.391973
$11$	−1925.08	−0.436087	−0.218044	−	0.975939i	$-0.569968\pi$
$11$	−1925.08	−0.436087	−0.218044	+	0.975939i	$0.569968\pi$
$12$	10121.2	1.69083
$13$	8706.23	1.09908	0.549539	−	0.835468i	$-0.314803\pi$
$13$	8706.23	1.09908	0.549539	+	0.835468i	$0.314803\pi$
$14$	−18722.2	−1.82351
$15$	−5031.01	−0.384889
$16$	−13143.7	−0.802227
$17$	28975.2	1.43039	0.715195	−	0.698925i	$-0.246338\pi$
$17$	28975.2	1.43039	0.715195	+	0.698925i	$0.246338\pi$
$18$	39775.0	1.60752
$19$	−6859.00	−0.229416
$19$	−6859.00	−0.229416
$20$	−11132.4	−0.311160
$21$	−75989.9	−1.79056
$22$	−32077.4	−0.642272
$23$	−66480.6	−1.13932	−0.569662	−	0.821879i	$-0.692926\pi$
$23$	−66480.6	−1.13932	−0.569662	+	0.821879i	$0.692926\pi$
$24$	24400.8	0.360301
$25$	−72591.4	−0.929169
$26$	145071.	1.61873
$27$	13529.0	0.132279
$28$	−168147.	−1.44756
$29$	133226.	1.01437	0.507185	−	0.861837i	$-0.330686\pi$
$29$	133226.	1.01437	0.507185	+	0.861837i	$0.330686\pi$
$30$	−83831.2	−0.566867
$31$	261576.	1.57700	0.788501	−	0.615034i	$-0.210858\pi$
$31$	261576.	1.57700	0.788501	+	0.615034i	$0.210858\pi$
$32$	−265193.	−1.43066
$33$	−130196.	−0.630666
$34$	482810.	2.10669
$35$	83581.7	0.329513
$36$	357226.	1.27610
$37$	516147.	1.67520	0.837601	−	0.546282i	$-0.183957\pi$
$37$	516147.	1.67520	0.837601	+	0.546282i	$0.183957\pi$
$38$	−114291.	−0.337885
$39$	588817.	1.58948
$40$	−26838.6	−0.0663055
$41$	−631509.	−1.43099	−0.715494	−	0.698619i	$-0.753798\pi$
$41$	−631509.	−1.43099	−0.715494	+	0.698619i	$0.753798\pi$
$42$	−1.26621e6	−2.63714
$43$	−127914.	−0.245345	−0.122672	−	0.992447i	$-0.539146\pi$
$43$	−127914.	−0.245345	−0.122672	+	0.992447i	$0.539146\pi$
$44$	−288092.	−0.509855
$45$	−177568.	−0.290483
$46$	−1.10776e6	−1.67800
$47$	739199.	1.03853	0.519265	−	0.854614i	$-0.326206\pi$
$47$	739199.	1.03853	0.519265	+	0.854614i	$0.326206\pi$
$48$	−888929.	−1.16017
$49$	438899.	0.532940
$50$	−1.20958e6	−1.36849
$51$	1.95964e6	2.06862
$52$	1.30291e6	1.28500
$53$	−639668.	−0.590186	−0.295093	−	0.955469i	$-0.595351\pi$
$53$	−639668.	−0.590186	−0.295093	+	0.955469i	$0.595351\pi$
$54$	225432.	0.194822
$55$	143203.	0.116060
$56$	−405378.	−0.308462
$57$	−463885.	−0.331779
$58$	2.21993e6	1.49397
$59$	−3127.11	−0.00198226	−0.000991131	−	1.00000i	$-0.500315\pi$
$59$	−3127.11	−0.00198226	−0.000991131		1.00000i	$0.500315\pi$
$60$	−752902.	−0.449997
$61$	241926.	0.136467	0.0682335	−	0.997669i	$-0.478264\pi$
$61$	241926.	0.136467	0.0682335	+	0.997669i	$0.478264\pi$
$62$	4.35862e6	2.32262
$63$	−2.68204e6	−1.35137
$64$	−2.73649e6	−1.30486
$65$	−647643.	−0.292509
$66$	−2.16944e6	−0.928848
$67$	−2.61257e6	−1.06122	−0.530611	−	0.847615i	$-0.678038\pi$
$67$	−2.61257e6	−1.06122	−0.530611	+	0.847615i	$0.678038\pi$
$68$	4.33620e6	1.67235
$69$	−4.49619e6	−1.64768
$70$	1.39271e6	0.485309
$71$	1.62641e6	0.539295	0.269648	−	0.962959i	$-0.413093\pi$
$71$	1.62641e6	0.539295	0.269648	+	0.962959i	$0.413093\pi$
$72$	861220.	0.271926
$73$	4.48073e6	1.34809	0.674045	−	0.738691i	$-0.264556\pi$
$73$	4.48073e6	1.34809	0.674045	+	0.738691i	$0.264556\pi$
$74$	8.60051e6	2.46725
$75$	−4.90947e6	−1.34376
$76$	−1.02647e6	−0.268223
$77$	2.16299e6	0.539928
$78$	9.81139e6	2.34099
$79$	−1.45140e6	−0.331201	−0.165600	−	0.986193i	$-0.552956\pi$
$79$	−1.45140e6	−0.331201	−0.165600	+	0.986193i	$0.552956\pi$
$80$	977738.	0.213505
$81$	−4.30547e6	−0.900166
$82$	−1.05228e7	−2.10757
$83$	437590.	0.0840030	0.0420015	−	0.999118i	$-0.486627\pi$
$83$	437590.	0.0840030	0.0420015	+	0.999118i	$0.486627\pi$
$84$	−1.13721e7	−2.09344
$85$	−2.15542e6	−0.380684
$86$	−2.13141e6	−0.361345
$87$	9.01029e6	1.46697
$88$	−694548.	−0.108646
$89$	28921.7	0.00434869	0.00217435	−	0.999998i	$-0.499308\pi$
$89$	28921.7	0.00434869	0.00217435	+	0.999998i	$0.499308\pi$
$90$	−2.95880e6	−0.427826
$91$	−9.78218e6	−1.36079
$92$	−9.94898e6	−1.33205
$93$	1.76908e7	2.28064
$94$	1.23172e7	1.52955
$95$	510230.	0.0610567
$96$	−1.79354e7	−2.06901
$97$	−9.35507e6	−1.04075	−0.520375	−	0.853938i	$-0.674208\pi$
$97$	−9.35507e6	−1.04075	−0.520375	+	0.853938i	$0.674208\pi$
$98$	7.31333e6	0.784918
$99$	−4.59523e6	−0.475975
$100$	−1.08635e7	−1.08635
$101$	1.73362e7	1.67428	0.837142	−	0.546985i	$-0.184225\pi$
$101$	1.73362e7	1.67428	0.837142	+	0.546985i	$0.184225\pi$
$102$	3.26532e7	3.04667
$103$	−1.54020e7	−1.38882	−0.694410	−	0.719580i	$-0.744334\pi$
$103$	−1.54020e7	−1.38882	−0.694410	+	0.719580i	$0.744334\pi$
$104$	3.14112e6	0.273822
$105$	5.65277e6	0.476539
$106$	−1.06587e7	−0.869230
$107$	−1.17135e7	−0.924364	−0.462182	−	0.886785i	$-0.652933\pi$
$107$	−1.17135e7	−0.924364	−0.462182	+	0.886785i	$0.652933\pi$
$108$	2.02464e6	0.154655
$109$	−1.60749e7	−1.18893	−0.594464	−	0.804122i	$-0.702636\pi$
$109$	−1.60749e7	−1.18893	−0.594464	+	0.804122i	$0.702636\pi$
$110$	2.38618e6	0.170934
$111$	3.49079e7	2.42266
$112$	1.47680e7	0.993253
$113$	1.64878e7	1.07495	0.537475	−	0.843280i	$-0.319378\pi$
$113$	1.64878e7	1.07495	0.537475	+	0.843280i	$0.319378\pi$
$114$	−7.72968e6	−0.488646
$115$	4.94539e6	0.303220
$116$	1.99376e7	1.18596
$117$	2.07821e7	1.19961
$118$	−52106.7	−0.00291949
$119$	−3.25560e7	−1.77099
$120$	−1.81514e6	−0.0958904
$121$	−1.57813e7	−0.809828
$122$	4.03119e6	0.200990
$123$	−4.27100e7	−2.06948
$124$	3.91455e7	1.84376
$125$	1.12116e7	0.513429
$126$	−4.46906e7	−1.99030
$127$	1.47272e7	0.637980	0.318990	−	0.947758i	$-0.396656\pi$
$127$	1.47272e7	0.637980	0.318990	+	0.947758i	$0.396656\pi$
$128$	−1.16532e7	−0.491146
$129$	−8.65100e6	−0.354815
$130$	−1.07916e7	−0.430809
$131$	544321.	0.0211546	0.0105773	−	0.999944i	$-0.496633\pi$
$131$	544321.	0.0211546	0.0105773	+	0.999944i	$0.496633\pi$
$132$	−1.94841e7	−0.737348
$133$	7.70667e6	0.284044
$134$	−4.35330e7	−1.56298
$135$	−1.00640e6	−0.0352048
$136$	1.04539e7	0.356364
$137$	3.98992e7	1.32569	0.662845	−	0.748757i	$-0.269349\pi$
$137$	3.98992e7	1.32569	0.662845	+	0.748757i	$0.269349\pi$
$138$	−7.49196e7	−2.42671
$139$	−4.51787e7	−1.42686	−0.713431	−	0.700726i	$-0.752860\pi$
$139$	−4.51787e7	−1.42686	−0.713431	+	0.700726i	$0.752860\pi$
$140$	1.25082e7	0.385253
$141$	4.99932e7	1.50191
$142$	2.71008e7	0.794277
$143$	−1.67602e7	−0.479294
$144$	−3.13745e7	−0.875604
$145$	−9.91047e6	−0.269964
$146$	7.46619e7	1.98547
$147$	2.96835e7	0.770733
$148$	7.72426e7	1.95858
$149$	−4.72486e7	−1.17014	−0.585068	−	0.810984i	$-0.698932\pi$
$149$	−4.72486e7	−1.17014	−0.585068	+	0.810984i	$0.698932\pi$
$150$	−8.18061e7	−1.97909
$151$	3.39453e7	0.802344	0.401172	−	0.916003i	$-0.368603\pi$
$151$	3.39453e7	0.802344	0.401172	+	0.916003i	$0.368603\pi$
$152$	−2.47466e6	−0.0571561
$153$	6.91648e7	1.56122
$154$	3.60416e7	0.795210
$155$	−1.94582e7	−0.419703
$156$	8.81178e7	1.85835
$157$	1.61625e7	0.333319	0.166659	−	0.986015i	$-0.446702\pi$
$157$	1.61625e7	0.333319	0.166659	+	0.986015i	$0.446702\pi$
$158$	−2.41845e7	−0.487795
$159$	−4.32618e7	−0.853521
$160$	1.97273e7	0.380757
$161$	7.46966e7	1.41062
$162$	−7.17416e7	−1.32577
$163$	−2.59556e7	−0.469433	−0.234717	−	0.972064i	$-0.575416\pi$
$163$	−2.59556e7	−0.469433	−0.234717	+	0.972064i	$0.575416\pi$
$164$	−9.45068e7	−1.67305
$165$	9.68508e6	0.167845
$166$	7.29153e6	0.123720
$167$	1.05136e7	0.174681	0.0873405	−	0.996179i	$-0.472163\pi$
$167$	1.05136e7	0.174681	0.0873405	+	0.996179i	$0.472163\pi$
$168$	−2.74164e7	−0.446095
$169$	1.30499e7	0.207972
$170$	−3.59155e7	−0.560674
$171$	−1.63727e7	−0.250400
$172$	−1.91425e7	−0.286847
$173$	−9.80062e7	−1.43910	−0.719552	−	0.694439i	$-0.755653\pi$
$173$	−9.80062e7	−1.43910	−0.719552	+	0.694439i	$0.755653\pi$
$174$	1.50138e8	2.16056
$175$	8.15625e7	1.15042
$176$	2.53026e7	0.349841
$177$	−211492.	−0.00286673
$178$	481919.	0.00640478
$179$	3.24577e7	0.422992	0.211496	−	0.977379i	$-0.432166\pi$
$179$	3.24577e7	0.422992	0.211496	+	0.977379i	$0.432166\pi$
$180$	−2.65735e7	−0.339621
$181$	−1.09670e8	−1.37471	−0.687355	−	0.726322i	$-0.741228\pi$
$181$	−1.09670e8	−1.37471	−0.687355	+	0.726322i	$0.741228\pi$
$182$	−1.63000e8	−2.00418
$183$	1.63618e7	0.197357
$184$	−2.39855e7	−0.283849
$185$	−3.83954e7	−0.445839
$186$	2.94780e8	3.35895
$187$	−5.57794e7	−0.623775
$188$	1.10623e8	1.21421
$189$	−1.52009e7	−0.163778
$190$	8.50191e6	0.0899247
$191$	9.18322e7	0.953626	0.476813	−	0.879005i	$-0.341792\pi$
$191$	9.18322e7	0.953626	0.476813	+	0.879005i	$0.341792\pi$
$192$	−1.85074e8	−1.88708
$193$	1.17546e8	1.17695	0.588476	−	0.808515i	$-0.299728\pi$
$193$	1.17546e8	1.17695	0.588476	+	0.808515i	$0.299728\pi$
$194$	−1.55883e8	−1.53282
$195$	−4.38011e7	−0.423023
$196$	6.56823e7	0.623091
$197$	8.61642e7	0.802962	0.401481	−	0.915867i	$-0.368496\pi$
$197$	8.61642e7	0.802962	0.401481	+	0.915867i	$0.368496\pi$
$198$	−7.65699e7	−0.701019
$199$	−1.07839e8	−0.970037	−0.485019	−	0.874504i	$-0.661187\pi$
$199$	−1.07839e8	−0.970037	−0.485019	+	0.874504i	$0.661187\pi$
$200$	−2.61902e7	−0.231491
$201$	−1.76693e8	−1.53473
$202$	2.88871e8	2.46590
$203$	−1.49691e8	−1.25591
$204$	2.93264e8	2.41854
$205$	4.69769e7	0.380843
$206$	−2.56641e8	−2.04546
$207$	−1.58692e8	−1.24354
$208$	−1.14432e8	−0.881710
$209$	1.32041e7	0.100045
$210$	9.41915e7	0.701850
$211$	−1.18645e8	−0.869485	−0.434743	−	0.900555i	$-0.643161\pi$
$211$	−1.18645e8	−0.869485	−0.434743	+	0.900555i	$0.643161\pi$
$212$	−9.57277e7	−0.690021
$213$	1.09997e8	0.779924
$214$	−1.95181e8	−1.36141
$215$	9.51528e6	0.0652961
$216$	4.88112e6	0.0329558
$217$	−2.93903e8	−1.95252
$218$	−2.67855e8	−1.75106
$219$	3.03039e8	1.94959
$220$	2.14307e7	0.135693
$221$	2.52264e8	1.57211
$222$	5.81666e8	3.56811
$223$	1.58829e8	0.959099	0.479549	−	0.877515i	$-0.340800\pi$
$223$	1.58829e8	0.959099	0.479549	+	0.877515i	$0.340800\pi$
$224$	2.97967e8	1.77133
$225$	−1.73278e8	−1.01416
$226$	2.74735e8	1.58319
$227$	5.79209e7	0.328658	0.164329	−	0.986406i	$-0.447454\pi$
$227$	5.79209e7	0.328658	0.164329	+	0.986406i	$0.447454\pi$
$228$	−6.94215e7	−0.387902
$229$	−3.09194e7	−0.170140	−0.0850701	−	0.996375i	$-0.527111\pi$
$229$	−3.09194e7	−0.170140	−0.0850701	+	0.996375i	$0.527111\pi$
$230$	8.24045e7	0.446584
$231$	1.46286e8	0.780839
$232$	4.80666e7	0.252718
$233$	2.58070e8	1.33657	0.668286	−	0.743904i	$-0.267028\pi$
$233$	2.58070e8	1.33657	0.668286	+	0.743904i	$0.267028\pi$
$234$	3.46290e8	1.76679
$235$	−5.49878e7	−0.276394
$236$	−467979.	−0.00231758
$237$	−9.81604e7	−0.478980
$238$	−5.42478e8	−2.60833
$239$	−9.77046e7	−0.462937	−0.231469	−	0.972842i	$-0.574353\pi$
$239$	−9.77046e7	−0.462937	−0.231469	+	0.972842i	$0.574353\pi$
$240$	6.61260e7	0.308769
$241$	−2.25353e8	−1.03706	−0.518531	−	0.855059i	$-0.673521\pi$
$241$	−2.25353e8	−1.03706	−0.518531	+	0.855059i	$0.673521\pi$
$242$	−2.62961e8	−1.19272
$243$	−3.20774e8	−1.43409
$244$	3.62048e7	0.159552
$245$	−3.26490e7	−0.141837
$246$	−7.11672e8	−3.04795
$247$	−5.97160e7	−0.252146
$248$	9.43740e7	0.392891
$249$	2.95950e7	0.121484
$250$	1.86817e8	0.756182
$251$	1.92187e8	0.767124	0.383562	−	0.923515i	$-0.374697\pi$
$251$	1.92187e8	0.767124	0.383562	+	0.923515i	$0.374697\pi$
$252$	−4.01373e8	−1.57996
$253$	1.27980e8	0.496845
$254$	2.45398e8	0.939621
$255$	−1.45774e8	−0.550542
$256$	1.56095e8	0.581498
$257$	5.24050e8	1.92578	0.962890	−	0.269895i	$-0.0869890\pi$
$257$	5.24050e8	1.92578	0.962890	+	0.269895i	$0.0869890\pi$
$258$	−1.44151e8	−0.522574
$259$	−5.79935e8	−2.07410
$260$	−9.69212e7	−0.341989
$261$	3.18016e8	1.10715
$262$	9.06997e6	0.0311567
$263$	−3.77613e8	−1.27998	−0.639988	−	0.768385i	$-0.721061\pi$
$263$	−3.77613e8	−1.27998	−0.639988	+	0.768385i	$0.721061\pi$
$264$	−4.69734e7	−0.157123
$265$	4.75839e7	0.157072
$266$	1.28415e8	0.418342
$267$	1.95602e6	0.00628904
$268$	−3.90978e8	−1.24074
$269$	3.02542e8	0.947660	0.473830	−	0.880616i	$-0.342871\pi$
$269$	3.02542e8	0.947660	0.473830	+	0.880616i	$0.342871\pi$
$270$	−1.67695e7	−0.0518499
$271$	5.06348e8	1.54546	0.772728	−	0.634737i	$-0.218892\pi$
$271$	5.06348e8	1.54546	0.772728	+	0.634737i	$0.218892\pi$
$272$	−3.80840e8	−1.14750
$273$	−6.61585e8	−1.96796
$274$	6.64836e8	1.95248
$275$	1.39744e8	0.405199
$276$	−6.72866e8	−1.92640
$277$	3.72015e8	1.05167	0.525836	−	0.850586i	$-0.323752\pi$
$277$	3.72015e8	1.05167	0.525836	+	0.850586i	$0.323752\pi$
$278$	−7.52808e8	−2.10149
$279$	6.24392e8	1.72125
$280$	3.01554e7	0.0820942
$281$	4.05683e8	1.09072	0.545362	−	0.838200i	$-0.316392\pi$
$281$	4.05683e8	1.09072	0.545362	+	0.838200i	$0.316392\pi$
$282$	8.33032e8	2.21202
$283$	1.06526e8	0.279386	0.139693	−	0.990195i	$-0.455388\pi$
$283$	1.06526e8	0.279386	0.139693	+	0.990195i	$0.455388\pi$
$284$	2.43396e8	0.630522
$285$	3.45077e7	0.0882997
$286$	−2.79273e8	−0.705907
$287$	7.09554e8	1.77173
$288$	−6.33026e8	−1.56152
$289$	4.29221e8	1.04602
$290$	−1.65137e8	−0.397605
$291$	−6.32699e8	−1.50512
$292$	6.70551e8	1.57613
$293$	−5.25623e8	−1.22078	−0.610391	−	0.792100i	$-0.708988\pi$
$293$	−5.25623e8	−1.22078	−0.610391	+	0.792100i	$0.708988\pi$
$294$	4.94613e8	1.13514
$295$	232621.	0.000527559 0
$296$	1.86221e8	0.417356
$297$	−2.60443e7	−0.0576853
$298$	−7.87298e8	−1.72338
$299$	−5.78795e8	−1.25221
$300$	−7.34714e8	−1.57106
$301$	1.43722e8	0.303766
$302$	5.65627e8	1.18170
$303$	1.17248e9	2.42133
$304$	9.01525e7	0.184043
$305$	−1.79965e7	−0.0363194
$306$	1.15249e9	2.29938
$307$	8.25815e7	0.162892	0.0814458	−	0.996678i	$-0.474046\pi$
$307$	8.25815e7	0.162892	0.0814458	+	0.996678i	$0.474046\pi$
$308$	3.23696e8	0.631262
$309$	−1.04166e9	−2.00850
$310$	−3.24231e8	−0.618142
$311$	−1.05903e8	−0.199639	−0.0998197	−	0.995006i	$-0.531827\pi$
$311$	−1.05903e8	−0.199639	−0.0998197	+	0.995006i	$0.531827\pi$
$312$	2.12439e8	0.395998
$313$	−1.73063e8	−0.319006	−0.159503	−	0.987197i	$-0.550989\pi$
$313$	−1.73063e8	−0.319006	−0.159503	+	0.987197i	$0.550989\pi$
$314$	2.69314e8	0.490914
$315$	1.99513e8	0.359653
$316$	−2.17205e8	−0.387226
$317$	−3.97871e8	−0.701511	−0.350756	−	0.936467i	$-0.614075\pi$
$317$	−3.97871e8	−0.701511	−0.350756	+	0.936467i	$0.614075\pi$
$318$	−7.20867e8	−1.25707
$319$	−2.56470e8	−0.442354
$320$	2.03563e8	0.347276
$321$	−7.92202e8	−1.33681
$322$	1.24466e9	2.07757
$323$	−1.98741e8	−0.328154
$324$	−6.44323e8	−1.05244
$325$	−6.31997e8	−1.02123
$326$	−4.32495e8	−0.691385
$327$	−1.08717e9	−1.71942
$328$	−2.27842e8	−0.356513
$329$	−8.30552e8	−1.28582
$330$	1.61382e8	0.247204
$331$	5.08393e8	0.770552	0.385276	−	0.922801i	$-0.374106\pi$
$331$	5.08393e8	0.770552	0.385276	+	0.922801i	$0.374106\pi$
$332$	6.54864e7	0.0982128
$333$	1.23206e9	1.82843
$334$	1.75188e8	0.257271
$335$	1.94345e8	0.282434
$336$	9.98787e8	1.43643
$337$	−1.01905e9	−1.45041	−0.725206	−	0.688532i	$-0.758256\pi$
$337$	−1.01905e9	−1.45041	−0.725206	+	0.688532i	$0.758256\pi$
$338$	2.17450e8	0.306302
$339$	1.11510e9	1.55458
$340$	−3.22563e8	−0.445080
$341$	−5.03554e8	−0.687710
$342$	−2.72817e8	−0.368790
$343$	4.32180e8	0.578276
$344$	−4.61499e7	−0.0611246
$345$	3.34465e8	0.438514
$346$	−1.63307e9	−2.11952
$347$	6.90144e8	0.886720	0.443360	−	0.896344i	$-0.353786\pi$
$347$	6.90144e8	0.886720	0.443360	+	0.896344i	$0.353786\pi$
$348$	1.34841e9	1.71512
$349$	−8.60264e7	−0.108328	−0.0541642	−	0.998532i	$-0.517249\pi$
$349$	−8.60264e7	−0.108328	−0.0541642	+	0.998532i	$0.517249\pi$
$350$	1.35907e9	1.69435
$351$	1.17786e8	0.145385
$352$	5.10517e8	0.623894
$353$	4.56090e8	0.551873	0.275936	−	0.961176i	$-0.411012\pi$
$353$	4.56090e8	0.551873	0.275936	+	0.961176i	$0.411012\pi$
$354$	−3.52406e6	−0.00422214
$355$	−1.20986e8	−0.143528
$356$	4.32820e6	0.00508431
$357$	−2.20182e9	−2.56120
$358$	5.40840e8	0.622986
$359$	6.52814e8	0.744661	0.372331	−	0.928100i	$-0.378559\pi$
$359$	6.52814e8	0.744661	0.372331	+	0.928100i	$0.378559\pi$
$360$	−6.40648e7	−0.0723703
$361$	4.70459e7	0.0526316
$362$	−1.82741e9	−2.02468
$363$	−1.06731e9	−1.17117
$364$	−1.46393e9	−1.59098
$365$	−3.33314e8	−0.358781
$366$	2.72636e8	0.290669
$367$	−7.09360e8	−0.749092	−0.374546	−	0.927208i	$-0.622201\pi$
$367$	−7.09360e8	−0.749092	−0.374546	+	0.927208i	$0.622201\pi$
$368$	8.73800e8	0.913997
$369$	−1.50744e9	−1.56188
$370$	−6.39778e8	−0.656634
$371$	7.18721e8	0.730721
$372$	2.64747e9	2.66643
$373$	1.02906e8	0.102674	0.0513370	−	0.998681i	$-0.483652\pi$
$373$	1.02906e8	0.102674	0.0513370	+	0.998681i	$0.483652\pi$
$374$	−9.29446e8	−0.918700
$375$	7.58256e8	0.742517
$376$	2.66695e8	0.258737
$377$	1.15990e9	1.11487
$378$	−2.53292e8	−0.241213
$379$	1.41344e9	1.33364	0.666822	−	0.745217i	$-0.267654\pi$
$379$	1.41344e9	1.33364	0.666822	+	0.745217i	$0.267654\pi$
$380$	7.63571e7	0.0713850
$381$	9.96024e8	0.922641
$382$	1.53019e9	1.40451
$383$	−6.08756e7	−0.0553665	−0.0276833	−	0.999617i	$-0.508813\pi$
$383$	−6.08756e7	−0.0553665	−0.0276833	+	0.999617i	$0.508813\pi$
$384$	−7.88126e8	−0.710291
$385$	−1.60901e8	−0.143697
$386$	1.95866e9	1.73342
$387$	−3.05335e8	−0.267786
$388$	−1.40001e9	−1.21680
$389$	3.32338e8	0.286257	0.143129	−	0.989704i	$-0.454284\pi$
$389$	3.32338e8	0.286257	0.143129	+	0.989704i	$0.454284\pi$
$390$	−7.29854e8	−0.623031
$391$	−1.92629e9	−1.62968
$392$	1.58350e8	0.132775
$393$	3.68133e7	0.0305937
$394$	1.43575e9	1.18261
$395$	1.07967e8	0.0881458
$396$	−6.87687e8	−0.556490
$397$	1.70808e9	1.37006	0.685032	−	0.728513i	$-0.259788\pi$
$397$	1.70808e9	1.37006	0.685032	+	0.728513i	$0.259788\pi$
$398$	−1.79690e9	−1.42868
$399$	5.21214e8	0.410782
$400$	9.54118e8	0.745405
$401$	1.51681e9	1.17470	0.587350	−	0.809333i	$-0.300171\pi$
$401$	1.51681e9	1.17470	0.587350	+	0.809333i	$0.300171\pi$
$402$	−2.94421e9	−2.26036
$403$	2.27734e9	1.73325
$404$	2.59440e9	1.95750
$405$	3.20277e8	0.239570
$406$	−2.49428e9	−1.84971
$407$	−9.93622e8	−0.730535
$408$	7.07017e8	0.515370
$409$	−8.15485e8	−0.589365	−0.294682	−	0.955595i	$-0.595214\pi$
$409$	−8.15485e8	−0.589365	−0.294682	+	0.955595i	$0.595214\pi$
$410$	7.82772e8	0.560908
$411$	2.69845e9	1.91720
$412$	−2.30494e9	−1.62375
$413$	3.51357e6	0.00245428
$414$	−2.64427e9	−1.83149
$415$	−3.25517e7	−0.0223566
$416$	−2.30883e9	−1.57241
$417$	−3.05551e9	−2.06351
$418$	2.20019e8	0.147347
$419$	−3.87675e8	−0.257465	−0.128733	−	0.991679i	$-0.541091\pi$
$419$	−3.87675e8	−0.257465	−0.128733	+	0.991679i	$0.541091\pi$
$420$	8.45949e8	0.557150
$421$	2.08525e9	1.36198	0.680989	−	0.732294i	$-0.261550\pi$
$421$	2.08525e9	1.36198	0.680989	+	0.732294i	$0.261550\pi$
$422$	−1.97698e9	−1.28058
$423$	1.76450e9	1.13352
$424$	−2.30786e8	−0.147038
$425$	−2.10335e9	−1.32907
$426$	1.83287e9	1.14868
$427$	−2.71824e8	−0.168963
$428$	−1.75295e9	−1.08073
$429$	−1.13352e9	−0.693150
$430$	1.58552e8	0.0961685
$431$	−3.37278e8	−0.202917	−0.101458	−	0.994840i	$-0.532351\pi$
$431$	−3.37278e8	−0.202917	−0.101458	+	0.994840i	$0.532351\pi$
$432$	−1.77821e8	−0.106118
$433$	−1.26209e9	−0.747108	−0.373554	−	0.927608i	$-0.621861\pi$
$433$	−1.26209e9	−0.747108	−0.373554	+	0.927608i	$0.621861\pi$
$434$	−4.89727e9	−2.87568
$435$	−6.70262e8	−0.390420
$436$	−2.40565e9	−1.39005
$437$	4.55990e8	0.261379
$438$	5.04951e9	2.87137
$439$	−3.16271e9	−1.78416	−0.892079	−	0.451879i	$-0.850754\pi$
$439$	−3.16271e9	−1.78416	−0.892079	+	0.451879i	$0.850754\pi$
$440$	5.16663e7	0.0289150
$441$	1.04767e9	0.581687
$442$	4.20346e9	2.31541
$443$	−2.05851e9	−1.12497	−0.562485	−	0.826808i	$-0.690154\pi$
$443$	−2.05851e9	−1.12497	−0.562485	+	0.826808i	$0.690154\pi$
$444$	5.22404e9	2.83248
$445$	−2.15144e6	−0.00115736
$446$	2.64656e9	1.41257
$447$	−3.19550e9	−1.69224
$448$	3.07468e9	1.61558
$449$	1.00726e9	0.525146	0.262573	−	0.964912i	$-0.415429\pi$
$449$	1.00726e9	0.525146	0.262573	+	0.964912i	$0.415429\pi$
$450$	−2.88732e9	−1.49366
$451$	1.21570e9	0.624036
$452$	2.46744e9	1.25679
$453$	2.29578e9	1.16034
$454$	9.65130e8	0.484050
$455$	7.27681e8	0.362161
$456$	−1.67365e8	−0.0826586
$457$	−2.12203e9	−1.04003	−0.520014	−	0.854158i	$-0.674073\pi$
$457$	−2.12203e9	−1.04003	−0.520014	+	0.854158i	$0.674073\pi$
$458$	−5.15207e8	−0.250583
$459$	3.92004e8	0.189211
$460$	7.40088e8	0.354512
$461$	3.07672e9	1.46263	0.731316	−	0.682039i	$-0.238907\pi$
$461$	3.07672e9	1.46263	0.731316	+	0.682039i	$0.238907\pi$
$462$	2.43755e9	1.15003
$463$	−1.99320e9	−0.933290	−0.466645	−	0.884445i	$-0.654537\pi$
$463$	−1.99320e9	−0.933290	−0.466645	+	0.884445i	$0.654537\pi$
$464$	−1.75108e9	−0.813754
$465$	−1.31599e9	−0.606971
$466$	4.30020e9	1.96851
$467$	1.14782e8	0.0521512	0.0260756	−	0.999660i	$-0.491699\pi$
$467$	1.14782e8	0.0521512	0.0260756	+	0.999660i	$0.491699\pi$
$468$	3.11009e9	1.40253
$469$	2.93545e9	1.31392
$470$	−9.16257e8	−0.407075
$471$	1.09310e9	0.482043
$472$	−1.12823e6	−0.000493856 0
$473$	2.46243e8	0.106992
$474$	−1.63564e9	−0.705444
$475$	4.97904e8	0.213166
$476$	−4.87208e9	−2.07057
$477$	−1.52691e9	−0.644169
$478$	−1.62804e9	−0.681817
$479$	−3.16751e9	−1.31687	−0.658437	−	0.752636i	$-0.728782\pi$
$479$	−3.16751e9	−1.31687	−0.658437	+	0.752636i	$0.728782\pi$
$480$	1.33419e9	0.550647
$481$	4.49369e9	1.84118
$482$	−3.75504e9	−1.52739
$483$	5.05185e9	2.04003
$484$	−2.36170e9	−0.946817
$485$	6.95909e8	0.276985
$486$	−5.34502e9	−2.11214
$487$	1.56380e9	0.613520	0.306760	−	0.951787i	$-0.400755\pi$
$487$	1.56380e9	0.613520	0.306760	+	0.951787i	$0.400755\pi$
$488$	8.72844e7	0.0339991
$489$	−1.75542e9	−0.678890
$490$	−5.44027e8	−0.208898
$491$	−5.78418e8	−0.220524	−0.110262	−	0.993903i	$-0.535169\pi$
$491$	−5.78418e8	−0.220524	−0.110262	+	0.993903i	$0.535169\pi$
$492$	−6.39165e9	−2.41955
$493$	3.86024e9	1.45094
$494$	−9.95042e8	−0.371362
$495$	3.41832e8	0.126676
$496$	−3.43807e9	−1.26511
$497$	−1.82741e9	−0.667712
$498$	4.93138e8	0.178923
$499$	−4.95429e9	−1.78496	−0.892482	−	0.451082i	$-0.851038\pi$
$499$	−4.95429e9	−1.78496	−0.892482	+	0.451082i	$0.851038\pi$
$500$	1.67783e9	0.600280
$501$	7.11055e8	0.252622
$502$	3.20239e9	1.12983
$503$	−1.06789e9	−0.374143	−0.187072	−	0.982346i	$-0.559900\pi$
$503$	−1.06789e9	−0.374143	−0.187072	+	0.982346i	$0.559900\pi$
$504$	−9.67653e8	−0.336677
$505$	−1.28961e9	−0.445594
$506$	2.13252e9	0.731757
$507$	8.82588e8	0.300767
$508$	2.20396e9	0.745900
$509$	4.23433e9	1.42322	0.711611	−	0.702574i	$-0.247966\pi$
$509$	4.23433e9	1.42322	0.711611	+	0.702574i	$0.247966\pi$
$510$	−2.42902e9	−0.810842
$511$	−5.03448e9	−1.66910
$512$	4.09260e9	1.34758
$513$	−9.27953e7	−0.0303469
$514$	8.73219e9	2.83630
$515$	1.14573e9	0.369620
$516$	−1.29464e9	−0.414835
$517$	−1.42301e9	−0.452889
$518$	−9.66339e9	−3.05475
$519$	−6.62832e9	−2.08122
$520$	−2.33663e8	−0.0728749
$521$	−4.83816e8	−0.149882	−0.0749408	−	0.997188i	$-0.523877\pi$
$521$	−4.83816e8	−0.149882	−0.0749408	+	0.997188i	$0.523877\pi$
$522$	5.29906e9	1.63062
$523$	1.52412e9	0.465868	0.232934	−	0.972493i	$-0.425167\pi$
$523$	1.52412e9	0.465868	0.232934	+	0.972493i	$0.425167\pi$
$524$	8.14589e7	0.0247331
$525$	5.51621e9	1.66373
$526$	−6.29213e9	−1.88516
$527$	7.57921e9	2.25573
$528$	1.71126e9	0.505937
$529$	1.01485e9	0.298061
$530$	7.92885e8	0.231337
$531$	−7.46453e6	−0.00216357
$532$	1.15332e9	0.332093
$533$	−5.49806e9	−1.57277
$534$	3.25930e7	0.00926254
$535$	8.71348e8	0.246010
$536$	−9.42590e8	−0.264391
$537$	2.19517e9	0.611728
$538$	5.04123e9	1.39572
$539$	−8.44914e8	−0.232408
$540$	−1.50610e8	−0.0411600
$541$	−5.89039e8	−0.159939	−0.0799694	−	0.996797i	$-0.525482\pi$
$541$	−5.89039e8	−0.159939	−0.0799694	+	0.996797i	$0.525482\pi$
$542$	8.43723e9	2.27616
$543$	−7.41713e9	−1.98809
$544$	−7.68401e9	−2.04641
$545$	1.19579e9	0.316421
$546$	−1.10239e10	−2.89843
$547$	−3.59633e9	−0.939516	−0.469758	−	0.882795i	$-0.655659\pi$
$547$	−3.59633e9	−0.939516	−0.469758	+	0.882795i	$0.655659\pi$
$548$	5.97100e9	1.54994
$549$	5.77487e8	0.148949
$550$	2.32854e9	0.596780
$551$	−9.13797e8	−0.232712
$552$	−1.62218e9	−0.410499
$553$	1.63077e9	0.410066
$554$	6.19884e9	1.54891
$555$	−2.59674e9	−0.644768
$556$	−6.76110e9	−1.66823
$557$	−3.55590e9	−0.871880	−0.435940	−	0.899976i	$-0.643584\pi$
$557$	−3.55590e9	−0.871880	−0.435940	+	0.899976i	$0.643584\pi$
$558$	1.04042e10	2.53506
$559$	−1.11364e9	−0.269653
$560$	−1.09857e9	−0.264344
$561$	−3.77245e9	−0.902098
$562$	6.75986e9	1.60643
$563$	−4.50291e9	−1.06344	−0.531721	−	0.846919i	$-0.678455\pi$
$563$	−4.50291e9	−1.06344	−0.531721	+	0.846919i	$0.678455\pi$
$564$	7.48160e9	1.75597
$565$	−1.22650e9	−0.286087
$566$	1.77504e9	0.411481
$567$	4.83756e9	1.11451
$568$	5.86793e8	0.134359
$569$	−3.88064e9	−0.883100	−0.441550	−	0.897237i	$-0.645571\pi$
$569$	−3.88064e9	−0.883100	−0.441550	+	0.897237i	$0.645571\pi$
$570$	5.74998e8	0.130048
$571$	−7.99481e8	−0.179714	−0.0898570	−	0.995955i	$-0.528641\pi$
$571$	−7.99481e8	−0.179714	−0.0898570	+	0.995955i	$0.528641\pi$
$572$	−2.50820e9	−0.560371
$573$	6.21076e9	1.37913
$574$	1.18232e10	2.60942
$575$	4.82592e9	1.05863
$576$	−6.53212e9	−1.42421
$577$	−1.06133e9	−0.230003	−0.115002	−	0.993365i	$-0.536687\pi$
$577$	−1.06133e9	−0.230003	−0.115002	+	0.993365i	$0.536687\pi$
$578$	7.15206e9	1.54058
$579$	7.94986e9	1.70210
$580$	−1.48312e9	−0.315631
$581$	−4.91670e8	−0.104006
$582$	−1.05426e10	−2.21675
$583$	1.23141e9	0.257373
$584$	1.61660e9	0.335860
$585$	−1.54595e9	−0.319264
$586$	−8.75841e9	−1.79797
$587$	−5.75442e9	−1.17427	−0.587135	−	0.809489i	$-0.699744\pi$
$587$	−5.75442e9	−1.17427	−0.587135	+	0.809489i	$0.699744\pi$
$588$	4.44220e9	0.901109
$589$	−1.79415e9	−0.361789
$590$	3.87614e6	0.000776993 0
$591$	5.82742e9	1.16124
$592$	−6.78407e9	−1.34389
$593$	5.26506e9	1.03684	0.518420	−	0.855126i	$-0.326520\pi$
$593$	5.26506e9	1.03684	0.518420	+	0.855126i	$0.326520\pi$
$594$	−4.33974e8	−0.0849593
$595$	2.42179e9	0.471333
$596$	−7.07086e9	−1.36808
$597$	−7.29330e9	−1.40286
$598$	−9.64441e9	−1.84426
$599$	−1.30192e9	−0.247508	−0.123754	−	0.992313i	$-0.539493\pi$
$599$	−1.30192e9	−0.247508	−0.123754	+	0.992313i	$0.539493\pi$
$600$	−1.77129e9	−0.334780
$601$	−7.22139e9	−1.35694	−0.678469	−	0.734629i	$-0.737356\pi$
$601$	−7.22139e9	−1.35694	−0.678469	+	0.734629i	$0.737356\pi$
$602$	2.39482e9	0.447389
$603$	−6.23631e9	−1.15829
$604$	5.07999e9	0.938067
$605$	1.17394e9	0.215528
$606$	1.95369e10	3.56616
$607$	−2.83463e9	−0.514442	−0.257221	−	0.966353i	$-0.582807\pi$
$607$	−2.83463e9	−0.514442	−0.257221	+	0.966353i	$0.582807\pi$
$608$	1.81896e9	0.328217
$609$	−1.01238e10	−1.81629
$610$	−2.99874e8	−0.0534914
$611$	6.43563e9	1.14142
$612$	1.03507e10	1.82532
$613$	8.97533e6	0.00157376	0.000786880	−	1.00000i	$-0.499750\pi$
$613$	8.97533e6	0.00157376	0.000786880		1.00000i	$0.499750\pi$
$614$	1.37605e9	0.239908
$615$	3.17713e9	0.550772
$616$	7.80384e8	0.134517
$617$	2.05751e9	0.352650	0.176325	−	0.984332i	$-0.443579\pi$
$617$	2.05751e9	0.352650	0.176325	+	0.984332i	$0.443579\pi$
$618$	−1.73571e10	−2.95813
$619$	9.78787e9	1.65871	0.829356	−	0.558721i	$-0.188708\pi$
$619$	9.78787e9	1.65871	0.829356	+	0.558721i	$0.188708\pi$
$620$	−2.91197e9	−0.490700
$621$	−8.99415e8	−0.150709
$622$	−1.76465e9	−0.294030
$623$	−3.24960e7	−0.00538420
$624$	−7.73922e9	−1.27512
$625$	4.83719e9	0.792525
$626$	−2.88373e9	−0.469834
$627$	8.93015e8	0.144685
$628$	2.41876e9	0.389703
$629$	1.49554e10	2.39619
$630$	3.32446e9	0.529699
$631$	−4.84496e9	−0.767693	−0.383846	−	0.923397i	$-0.625401\pi$
$631$	−4.84496e9	−0.767693	−0.383846	+	0.923397i	$0.625401\pi$
$632$	−5.23649e8	−0.0825146
$633$	−8.02418e9	−1.25744
$634$	−6.62968e9	−1.03319
$635$	−1.09553e9	−0.169792
$636$	−6.47422e9	−0.997902
$637$	3.82116e9	0.585743
$638$	−4.27354e9	−0.651501
$639$	3.88231e9	0.588623
$640$	8.66864e8	0.130714
$641$	7.60389e9	1.14034	0.570168	−	0.821528i	$-0.306878\pi$
$641$	7.60389e9	1.14034	0.570168	+	0.821528i	$0.306878\pi$
$642$	−1.32004e10	−1.96886
$643$	−4.44441e9	−0.659288	−0.329644	−	0.944105i	$-0.606929\pi$
$643$	−4.44441e9	−0.659288	−0.329644	+	0.944105i	$0.606929\pi$
$644$	1.11785e10	1.64924
$645$	6.43534e8	0.0944306
$646$	−3.31159e9	−0.483307
$647$	−2.50045e9	−0.362956	−0.181478	−	0.983395i	$-0.558088\pi$
$647$	−2.50045e9	−0.362956	−0.181478	+	0.983395i	$0.558088\pi$
$648$	−1.55337e9	−0.224265
$649$	6.01992e6	0.000864439 0
$650$	−1.05309e10	−1.50407
$651$	−1.98771e10	−2.82371
$652$	−3.88431e9	−0.548842
$653$	6.29436e9	0.884618	0.442309	−	0.896863i	$-0.354160\pi$
$653$	6.29436e9	0.884618	0.442309	+	0.896863i	$0.354160\pi$
$654$	−1.81154e10	−2.53237
$655$	−4.04912e7	−0.00563010
$656$	8.30035e9	1.14798
$657$	1.06957e10	1.47140
$658$	−1.38394e10	−1.89377
$659$	8.17191e9	1.11231	0.556153	−	0.831080i	$-0.312277\pi$
$659$	8.17191e9	1.11231	0.556153	+	0.831080i	$0.312277\pi$
$660$	1.44939e9	0.196238
$661$	4.31986e9	0.581787	0.290894	−	0.956755i	$-0.406047\pi$
$661$	4.31986e9	0.581787	0.290894	+	0.956755i	$0.406047\pi$
$662$	8.47131e9	1.13487
$663$	1.70611e10	2.27357
$664$	1.57878e8	0.0209283
$665$	−5.73287e8	−0.0755955
$666$	2.05297e10	2.69292
$667$	−8.85695e9	−1.15570
$668$	1.57339e9	0.204230
$669$	1.07419e10	1.38704
$670$	3.23835e9	0.415971
$671$	−4.65726e8	−0.0595116
$672$	2.01520e10	2.56168
$673$	−5.62721e9	−0.711608	−0.355804	−	0.934561i	$-0.615793\pi$
$673$	−5.62721e9	−0.711608	−0.355804	+	0.934561i	$0.615793\pi$
$674$	−1.69804e10	−2.13618
$675$	−9.82087e8	−0.122910
$676$	1.95295e9	0.243152
$677$	9.43437e9	1.16856	0.584282	−	0.811551i	$-0.301376\pi$
$677$	9.43437e9	1.16856	0.584282	+	0.811551i	$0.301376\pi$
$678$	1.85808e10	2.28960
$679$	1.05112e10	1.28857
$680$	−7.77652e8	−0.0948428
$681$	3.91728e9	0.475302
$682$	−8.39067e9	−1.01286
$683$	−1.22562e10	−1.47192	−0.735960	−	0.677025i	$-0.763269\pi$
$683$	−1.22562e10	−1.47192	−0.735960	+	0.677025i	$0.763269\pi$
$684$	−2.45021e9	−0.292757
$685$	−2.96803e9	−0.352819
$686$	7.20137e9	0.851689
$687$	−2.09113e9	−0.246055
$688$	1.68125e9	0.196822
$689$	−5.56909e9	−0.648660
$690$	5.57315e9	0.645846
$691$	−1.75134e8	−0.0201929	−0.0100964	−	0.999949i	$-0.503214\pi$
$691$	−1.75134e8	−0.0201929	−0.0100964	+	0.999949i	$0.503214\pi$
$692$	−1.46668e10	−1.68254
$693$	5.16313e9	0.589314
$694$	1.14998e10	1.30597
$695$	3.36077e9	0.379745
$696$	3.25082e9	0.365478
$697$	−1.82981e10	−2.04687
$698$	−1.43345e9	−0.159547
$699$	1.74537e10	1.93294
$700$	1.22060e10	1.34503
$701$	−3.40935e9	−0.373817	−0.186908	−	0.982377i	$-0.559847\pi$
$701$	−3.40935e9	−0.373817	−0.186908	+	0.982377i	$0.559847\pi$
$702$	1.96266e9	0.214124
$703$	−3.54025e9	−0.384318
$704$	5.26796e9	0.569034
$705$	−3.71892e9	−0.399719
$706$	7.59978e9	0.812801
$707$	−1.94787e10	−2.07296
$708$	−3.16502e7	−0.00335166
$709$	4.98216e9	0.524995	0.262498	−	0.964933i	$-0.415454\pi$
$709$	4.98216e9	0.524995	0.262498	+	0.964933i	$0.415454\pi$
$710$	−2.01598e9	−0.211389
$711$	−3.46454e9	−0.361495
$712$	1.04347e7	0.00108342
$713$	−1.73897e10	−1.79672
$714$	−3.66887e10	−3.77214
$715$	1.24676e9	0.127559
$716$	4.85737e9	0.494545
$717$	−6.60792e9	−0.669496
$718$	1.08778e10	1.09674
$719$	1.31535e9	0.131974	0.0659871	−	0.997820i	$-0.478980\pi$
$719$	1.31535e9	0.131974	0.0659871	+	0.997820i	$0.478980\pi$
$720$	2.33390e9	0.233033
$721$	1.73054e10	1.71952
$722$	7.83921e8	0.0775161
$723$	−1.52410e10	−1.49979
$724$	−1.64123e10	−1.60725
$725$	−9.67106e9	−0.942521
$726$	−1.77845e10	−1.72490
$727$	1.30775e10	1.26227	0.631137	−	0.775671i	$-0.282588\pi$
$727$	1.30775e10	1.26227	0.631137	+	0.775671i	$0.282588\pi$
$728$	−3.52931e9	−0.339024
$729$	−1.22784e10	−1.17380
$730$	−5.55398e9	−0.528414
$731$	−3.70631e9	−0.350939
$732$	2.44859e9	0.230742
$733$	3.87704e9	0.363610	0.181805	−	0.983335i	$-0.441806\pi$
$733$	3.87704e9	0.363610	0.181805	+	0.983335i	$0.441806\pi$
$734$	−1.18200e10	−1.10327
$735$	−2.20811e9	−0.205123
$736$	1.76302e10	1.62999
$737$	5.02940e9	0.462786
$738$	−2.51183e10	−2.30034
$739$	3.12958e9	0.285253	0.142627	−	0.989777i	$-0.454445\pi$
$739$	3.12958e9	0.285253	0.142627	+	0.989777i	$0.454445\pi$
$740$	−5.74595e9	−0.521256
$741$	−4.03869e9	−0.364651
$742$	1.19760e10	1.07621
$743$	−1.76182e10	−1.57580	−0.787898	−	0.615806i	$-0.788830\pi$
$743$	−1.76182e10	−1.57580	−0.787898	+	0.615806i	$0.788830\pi$
$744$	6.38267e9	0.568195
$745$	3.51475e9	0.311420
$746$	1.71472e9	0.151219
$747$	1.04455e9	0.0916865
$748$	−8.34751e9	−0.729292
$749$	1.31611e10	1.14447
$750$	1.26347e10	1.09358
$751$	7.38500e9	0.636225	0.318112	−	0.948053i	$-0.396951\pi$
$751$	7.38500e9	0.636225	0.318112	+	0.948053i	$0.396951\pi$
$752$	−9.71579e9	−0.833136
$753$	1.29979e10	1.10941
$754$	1.93272e10	1.64199
$755$	−2.52514e9	−0.213536
$756$	−2.27486e9	−0.191482
$757$	−7.08140e9	−0.593313	−0.296656	−	0.954984i	$-0.595872\pi$
$757$	−7.08140e9	−0.593313	−0.296656	+	0.954984i	$0.595872\pi$
$758$	2.35520e10	1.96420
$759$	8.65551e9	0.718533
$760$	1.84086e8	0.0152115
$761$	4.42247e9	0.363763	0.181882	−	0.983320i	$-0.441781\pi$
$761$	4.42247e9	0.363763	0.181882	+	0.983320i	$0.441781\pi$
$762$	1.65967e10	1.35887
$763$	1.80615e10	1.47204
$764$	1.37429e10	1.11494
$765$	−5.14506e9	−0.415504
$766$	−1.01436e9	−0.0815442
$767$	−2.72253e7	−0.00217866
$768$	1.05569e10	0.840958
$769$	−1.46886e10	−1.16476	−0.582381	−	0.812916i	$-0.697879\pi$
$769$	−1.46886e10	−1.16476	−0.582381	+	0.812916i	$0.697879\pi$
$770$	−2.68108e9	−0.211637
$771$	3.54423e10	2.78504
$772$	1.75911e10	1.37604
$773$	−6.65202e9	−0.517995	−0.258997	−	0.965878i	$-0.583392\pi$
$773$	−6.65202e9	−0.517995	−0.258997	+	0.965878i	$0.583392\pi$
$774$	−5.08776e9	−0.394397
$775$	−1.89882e10	−1.46530
$776$	−3.37522e9	−0.259290
$777$	−3.92219e10	−2.99955
$778$	5.53771e9	0.421601
$779$	4.33152e9	0.328291
$780$	−6.55494e9	−0.494581
$781$	−3.13097e9	−0.235180
$782$	−3.20975e10	−2.40020
$783$	1.80241e9	0.134180
$784$	−5.76875e9	−0.427539
$785$	−1.20230e9	−0.0887095
$786$	6.13417e8	0.0450585
$787$	1.51970e10	1.11134	0.555670	−	0.831403i	$-0.312462\pi$
$787$	1.51970e10	1.11134	0.555670	+	0.831403i	$0.312462\pi$
$788$	1.28947e10	0.938790
$789$	−2.55386e10	−1.85109
$790$	1.79905e9	0.129822
$791$	−1.85254e10	−1.33092
$792$	−1.65791e9	−0.118583
$793$	2.10626e9	0.149988
$794$	2.84615e10	2.01784
$795$	3.21817e9	0.227156
$796$	−1.61383e10	−1.13413
$797$	−3.15905e9	−0.221031	−0.110515	−	0.993874i	$-0.535250\pi$
$797$	−3.15905e9	−0.221031	−0.110515	+	0.993874i	$0.535250\pi$
$798$	8.68495e9	0.605002
$799$	2.14184e10	1.48550
$800$	1.92507e10	1.32933
$801$	6.90372e7	0.00474646
$802$	2.52745e10	1.73011
$803$	−8.62575e9	−0.587885
$804$	−2.64425e10	−1.79434
$805$	−5.55656e9	−0.375423
$806$	3.79471e10	2.55274
$807$	2.04614e10	1.37050
$808$	6.25473e9	0.417127
$809$	−2.96959e10	−1.97186	−0.985932	−	0.167145i	$-0.946545\pi$
$809$	−2.96959e10	−1.97186	−0.985932	+	0.167145i	$0.946545\pi$
$810$	5.33674e9	0.352841
$811$	−2.53055e10	−1.66587	−0.832936	−	0.553369i	$-0.813342\pi$
$811$	−2.53055e10	−1.66587	−0.832936	+	0.553369i	$0.813342\pi$
$812$	−2.24016e10	−1.46836
$813$	3.42452e10	2.23502
$814$	−1.65566e10	−1.07594
$815$	1.93079e9	0.124935
$816$	−2.57569e10	−1.65950
$817$	8.77359e8	0.0562860
$818$	−1.35883e10	−0.868020
$819$	−2.33505e10	−1.48526
$820$	7.03021e9	0.445266
$821$	2.04778e10	1.29146	0.645731	−	0.763565i	$-0.276553\pi$
$821$	2.04778e10	1.29146	0.645731	+	0.763565i	$0.276553\pi$
$822$	4.49639e10	2.82366
$823$	−1.78777e10	−1.11792	−0.558961	−	0.829194i	$-0.688800\pi$
$823$	−1.78777e10	−1.11792	−0.558961	+	0.829194i	$0.688800\pi$
$824$	−5.55687e9	−0.346007
$825$	9.45111e9	0.585995
$826$	5.85463e7	0.00361467
$827$	−2.82118e10	−1.73445	−0.867224	−	0.497918i	$-0.834098\pi$
$827$	−2.82118e10	−1.73445	−0.867224	+	0.497918i	$0.834098\pi$
$828$	−2.37486e10	−1.45389
$829$	2.31096e9	0.140881	0.0704404	−	0.997516i	$-0.477560\pi$
$829$	2.31096e9	0.140881	0.0704404	+	0.997516i	$0.477560\pi$
$830$	−5.42405e8	−0.0329269
$831$	2.51600e10	1.52092
$832$	−2.38245e10	−1.43414
$833$	1.27172e10	0.762312
$834$	−5.09137e10	−3.03916
$835$	−7.82093e8	−0.0464896
$836$	1.97602e9	0.116969
$837$	3.53886e9	0.208605
$838$	−6.45979e9	−0.379197
$839$	2.74572e10	1.60505	0.802526	−	0.596617i	$-0.203489\pi$
$839$	2.74572e10	1.60505	0.802526	+	0.596617i	$0.203489\pi$
$840$	2.03946e9	0.118724
$841$	4.99297e8	0.0289449
$842$	3.47462e10	2.00593
$843$	2.74370e10	1.57740
$844$	−1.77556e10	−1.01657
$845$	−9.70763e8	−0.0553496
$846$	2.94016e10	1.66946
$847$	1.77316e10	1.00266
$848$	8.40759e9	0.473463
$849$	7.20455e9	0.404045
$850$	−3.50478e10	−1.95747
$851$	−3.43138e10	−1.90860
$852$	1.64613e10	0.911854
$853$	−1.50719e10	−0.831467	−0.415734	−	0.909486i	$-0.636475\pi$
$853$	−1.50719e10	−0.831467	−0.415734	+	0.909486i	$0.636475\pi$
$854$	−4.52938e9	−0.248849
$855$	1.21794e9	0.0666414
$856$	−4.22611e9	−0.230294
$857$	−8.09011e9	−0.439058	−0.219529	−	0.975606i	$-0.570452\pi$
$857$	−8.09011e9	−0.439058	−0.219529	+	0.975606i	$0.570452\pi$
$858$	−1.88877e10	−1.02088
$859$	3.31553e10	1.78475	0.892375	−	0.451294i	$-0.149038\pi$
$859$	3.31553e10	1.78475	0.892375	+	0.451294i	$0.149038\pi$
$860$	1.42398e9	0.0763415
$861$	4.79883e10	2.56227
$862$	−5.62003e9	−0.298857
$863$	1.78586e10	0.945821	0.472911	−	0.881110i	$-0.343203\pi$
$863$	1.78586e10	0.945821	0.472911	+	0.881110i	$0.343203\pi$
$864$	−3.58779e9	−0.189247
$865$	7.29052e9	0.383003
$866$	−2.10301e10	−1.10035
$867$	2.90289e10	1.51274
$868$	−4.39832e10	−2.28280
$869$	2.79405e9	0.144433
$870$	−1.11685e10	−0.575013
$871$	−2.27457e10	−1.16637
$872$	−5.79966e9	−0.296207
$873$	−2.23309e10	−1.13594
$874$	7.59812e9	0.384961
$875$	−1.25971e10	−0.635687
$876$	4.53505e10	2.27938
$877$	−1.20316e10	−0.602317	−0.301159	−	0.953574i	$-0.597373\pi$
$877$	−1.20316e10	−0.602317	−0.301159	+	0.953574i	$0.597373\pi$
$878$	−5.26999e10	−2.62772
$879$	−3.55488e10	−1.76548
$880$	−1.88222e9	−0.0931067
$881$	−2.88664e10	−1.42225	−0.711126	−	0.703065i	$-0.751814\pi$
$881$	−2.88664e10	−1.42225	−0.711126	+	0.703065i	$0.751814\pi$
$882$	1.74572e10	0.856712
$883$	7.28484e9	0.356088	0.178044	−	0.984023i	$-0.443023\pi$
$883$	7.28484e9	0.356088	0.178044	+	0.984023i	$0.443023\pi$
$884$	3.77519e10	1.83805
$885$	1.57325e7	0.000762951 0
$886$	−3.43008e10	−1.65686
$887$	1.77616e9	0.0854575	0.0427287	−	0.999087i	$-0.486395\pi$
$887$	1.77616e9	0.0854575	0.0427287	+	0.999087i	$0.486395\pi$
$888$	1.25944e10	0.603577
$889$	−1.65472e10	−0.789895
$890$	−3.58492e7	−0.00170457
$891$	8.28835e9	0.392551
$892$	2.37692e10	1.12134
$893$	−5.07016e9	−0.238255
$894$	−5.32463e10	−2.49234
$895$	−2.41448e9	−0.112575
$896$	1.30934e10	0.608098
$897$	−3.91449e10	−1.81093
$898$	1.67839e10	0.773438
$899$	3.48487e10	1.59966
$900$	−2.59315e10	−1.18571
$901$	−1.85345e10	−0.844196
$902$	2.02571e10	0.919084
$903$	9.72013e9	0.439304
$904$	5.94863e9	0.267811
$905$	8.15814e9	0.365865
$906$	3.82543e10	1.70896
$907$	3.57814e10	1.59233	0.796163	−	0.605082i	$-0.206860\pi$
$907$	3.57814e10	1.59233	0.796163	+	0.605082i	$0.206860\pi$
$908$	8.66799e9	0.384254
$909$	4.13822e10	1.82743
$910$	1.21253e10	0.533393
$911$	2.49469e10	1.09321	0.546603	−	0.837392i	$-0.315921\pi$
$911$	2.49469e10	1.09321	0.546603	+	0.837392i	$0.315921\pi$
$912$	6.09716e9	0.266162
$913$	−8.42395e8	−0.0366326
$914$	−3.53592e10	−1.53176
$915$	−1.21713e9	−0.0525247
$916$	−4.62716e9	−0.198921
$917$	−6.11591e8	−0.0261920
$918$	6.53193e9	0.278671
$919$	2.17274e10	0.923429	0.461715	−	0.887029i	$-0.347234\pi$
$919$	2.17274e10	0.923429	0.461715	+	0.887029i	$0.347234\pi$
$920$	1.78425e9	0.0755435
$921$	5.58512e9	0.235572
$922$	5.12671e10	2.15417
$923$	1.41599e10	0.592727
$924$	2.18921e10	0.912925
$925$	−3.74678e10	−1.55655
$926$	−3.32124e10	−1.37456
$927$	−3.67651e10	−1.51585
$928$	−3.53306e10	−1.45122
$929$	9.35900e9	0.382978	0.191489	−	0.981495i	$-0.438668\pi$
$929$	9.35900e9	0.382978	0.191489	+	0.981495i	$0.438668\pi$
$930$	−2.19282e10	−0.893951
$931$	−3.01041e9	−0.122265
$932$	3.86208e10	1.56267
$933$	−7.16238e9	−0.288717
$934$	1.91260e9	0.0768086
$935$	4.14934e9	0.166012
$936$	7.49798e9	0.298867
$937$	3.39356e10	1.34762	0.673810	−	0.738904i	$-0.264657\pi$
$937$	3.39356e10	1.34762	0.673810	+	0.738904i	$0.264657\pi$
$938$	4.89131e10	1.93515
$939$	−1.17045e10	−0.461344
$940$	−8.22905e9	−0.323149
$941$	−3.46625e10	−1.35611	−0.678056	−	0.735010i	$-0.737177\pi$
$941$	−3.46625e10	−1.35611	−0.678056	+	0.735010i	$0.737177\pi$
$942$	1.82142e10	0.709956
$943$	4.19831e10	1.63036
$944$	4.11017e7	0.00159022
$945$	1.13077e9	0.0435878
$946$	4.10313e9	0.157578
$947$	−6.61122e9	−0.252963	−0.126481	−	0.991969i	$-0.540368\pi$
$947$	−6.61122e9	−0.252963	−0.126481	+	0.991969i	$0.540368\pi$
$948$	−1.46899e10	−0.560003
$949$	3.90103e10	1.48165
$950$	8.29653e9	0.313952
$951$	−2.69087e10	−1.01452
$952$	−1.17459e10	−0.441221
$953$	−3.60306e10	−1.34849	−0.674244	−	0.738509i	$-0.735530\pi$
$953$	−3.60306e10	−1.34849	−0.674244	+	0.738509i	$0.735530\pi$
$954$	−2.54428e10	−0.948736
$955$	−6.83125e9	−0.253798
$956$	−1.46217e10	−0.541247
$957$	−1.73455e10	−0.639728
$958$	−5.27800e10	−1.93950
$959$	−4.48301e10	−1.64136
$960$	1.37673e10	0.502227
$961$	4.09094e10	1.48693
$962$	7.48780e10	2.71170
$963$	−2.79606e10	−1.00891
$964$	−3.37247e10	−1.21249
$965$	−8.74409e9	−0.313234
$966$	8.41785e10	3.00456
$967$	−3.45253e10	−1.22785	−0.613924	−	0.789365i	$-0.710410\pi$
$967$	−3.45253e10	−1.22785	−0.613924	+	0.789365i	$0.710410\pi$
$968$	−5.69372e9	−0.201759
$969$	−1.34412e10	−0.474573
$970$	1.15959e10	0.407945
$971$	3.36181e10	1.17843	0.589217	−	0.807975i	$-0.299436\pi$
$971$	3.36181e10	1.17843	0.589217	+	0.807975i	$0.299436\pi$
$972$	−4.80045e10	−1.67668
$973$	5.07621e10	1.76663
$974$	2.60574e10	0.903596
$975$	−4.27430e10	−1.47689
$976$	−3.17980e9	−0.109478
$977$	2.14703e10	0.736558	0.368279	−	0.929715i	$-0.379947\pi$
$977$	2.14703e10	0.736558	0.368279	+	0.929715i	$0.379947\pi$
$978$	−2.92504e10	−0.999874
$979$	−5.56765e7	−0.00189641
$980$	−4.88600e9	−0.165830
$981$	−3.83714e10	−1.29768
$982$	−9.63812e9	−0.324790
$983$	−3.37506e8	−0.0113330	−0.00566649	−	0.999984i	$-0.501804\pi$
$983$	−3.37506e8	−0.0113330	−0.00566649	+	0.999984i	$0.501804\pi$
$984$	−1.54093e10	−0.515586
$985$	−6.40962e9	−0.213700
$986$	6.43229e10	2.13696
$987$	−5.61716e10	−1.85955
$988$	−8.93664e9	−0.294798
$989$	8.50377e9	0.279527
$990$	5.69591e9	0.186569
$991$	−1.06802e10	−0.348596	−0.174298	−	0.984693i	$-0.555766\pi$
$991$	−1.06802e10	−0.348596	−0.174298	+	0.984693i	$0.555766\pi$
$992$	−6.93682e10	−2.25616
$993$	3.43835e10	1.11436
$994$	−3.04500e10	−0.983410
$995$	8.02194e9	0.258166
$996$	4.42895e9	0.142034
$997$	4.09772e9	0.130951	0.0654756	−	0.997854i	$-0.479144\pi$
$997$	4.09772e9	0.130951	0.0654756	+	0.997854i	$0.479144\pi$
$998$	−8.25529e10	−2.62891
$999$	6.98294e9	0.221595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.8.a.b.1.5	✓	6
3.2	odd	2		171.8.a.f.1.2		6
4.3	odd	2		304.8.a.h.1.2		6
5.4	even	2		475.8.a.b.1.2		6
19.18	odd	2		361.8.a.c.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.8.a.b.1.5	✓	6	1.1	even	1	trivial
171.8.a.f.1.2		6	3.2	odd	2
304.8.a.h.1.2		6	4.3	odd	2
361.8.a.c.1.2		6	19.18	odd	2
475.8.a.b.1.2		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)

\(f(q)\)	\(=\)	\(q+16.6629 q^{2} +67.6316 q^{3} +149.652 q^{4} -74.3884 q^{5} +1126.94 q^{6} -1123.58 q^{7} +360.790 q^{8} +2387.04 q^{9} +O(q^{10})\)	\(q+16.6629 q^{2} +67.6316 q^{3} +149.652 q^{4} -74.3884 q^{5} +1126.94 q^{6} -1123.58 q^{7} +360.790 q^{8} +2387.04 q^{9} -1239.53 q^{10} -1925.08 q^{11} +10121.2 q^{12} +8706.23 q^{13} -18722.2 q^{14} -5031.01 q^{15} -13143.7 q^{16} +28975.2 q^{17} +39775.0 q^{18} -6859.00 q^{19} -11132.4 q^{20} -75989.9 q^{21} -32077.4 q^{22} -66480.6 q^{23} +24400.8 q^{24} -72591.4 q^{25} +145071. q^{26} +13529.0 q^{27} -168147. q^{28} +133226. q^{29} -83831.2 q^{30} +261576. q^{31} -265193. q^{32} -130196. q^{33} +482810. q^{34} +83581.7 q^{35} +357226. q^{36} +516147. q^{37} -114291. q^{38} +588817. q^{39} -26838.6 q^{40} -631509. q^{41} -1.26621e6 q^{42} -127914. q^{43} -288092. q^{44} -177568. q^{45} -1.10776e6 q^{46} +739199. q^{47} -888929. q^{48} +438899. q^{49} -1.20958e6 q^{50} +1.95964e6 q^{51} +1.30291e6 q^{52} -639668. q^{53} +225432. q^{54} +143203. q^{55} -405378. q^{56} -463885. q^{57} +2.21993e6 q^{58} -3127.11 q^{59} -752902. q^{60} +241926. q^{61} +4.35862e6 q^{62} -2.68204e6 q^{63} -2.73649e6 q^{64} -647643. q^{65} -2.16944e6 q^{66} -2.61257e6 q^{67} +4.33620e6 q^{68} -4.49619e6 q^{69} +1.39271e6 q^{70} +1.62641e6 q^{71} +861220. q^{72} +4.48073e6 q^{73} +8.60051e6 q^{74} -4.90947e6 q^{75} -1.02647e6 q^{76} +2.16299e6 q^{77} +9.81139e6 q^{78} -1.45140e6 q^{79} +977738. q^{80} -4.30547e6 q^{81} -1.05228e7 q^{82} +437590. q^{83} -1.13721e7 q^{84} -2.15542e6 q^{85} -2.13141e6 q^{86} +9.01029e6 q^{87} -694548. q^{88} +28921.7 q^{89} -2.95880e6 q^{90} -9.78218e6 q^{91} -9.94898e6 q^{92} +1.76908e7 q^{93} +1.23172e7 q^{94} +510230. q^{95} -1.79354e7 q^{96} -9.35507e6 q^{97} +7.31333e6 q^{98} -4.59523e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{2} + 40 q^{3} + 357 q^{4} + 219 q^{5} + 925 q^{6} + 2105 q^{7} + 5835 q^{8} + 5916 q^{9}+O(q^{10}) \) 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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